LMFDB - Embedded newform 69.7.f.a.7.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(7,69)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("69.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.f (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			7.17
Character	$\chi$	$=$	69.7
Dual form			69.7.f.a.10.17

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.04842 - 4.67213i) q^{2} +(-13.1138 + 8.42776i) q^{3} +(3.66909 + 25.5191i) q^{4} +(-6.23883 + 2.84918i) q^{5} +(-13.7148 + 95.3887i) q^{6} +(-83.3001 - 283.694i) q^{7} +(466.929 + 300.077i) q^{8} +(100.946 - 221.041i) q^{9} +O(q^{10})$	\(q+(4.04842 - 4.67213i) q^{2} +(-13.1138 + 8.42776i) q^{3} +(3.66909 + 25.5191i) q^{4} +(-6.23883 + 2.84918i) q^{5} +(-13.7148 + 95.3887i) q^{6} +(-83.3001 - 283.694i) q^{7} +(466.929 + 300.077i) q^{8} +(100.946 - 221.041i) q^{9} +(-11.9457 + 40.6833i) q^{10} +(-931.286 + 806.964i) q^{11} +(-263.185 - 303.731i) q^{12} +(-2357.37 - 692.187i) q^{13} +(-1662.69 - 759.325i) q^{14} +(57.8029 - 89.9430i) q^{15} +(1709.14 - 501.850i) q^{16} +(-4434.74 - 637.620i) q^{17} +(-624.058 - 1366.50i) q^{18} +(-5385.82 + 774.365i) q^{19} +(-95.5993 - 148.755i) q^{20} +(3483.29 + 3018.29i) q^{21} +7618.02i q^{22} +(-10720.4 - 5753.97i) q^{23} -8652.21 q^{24} +(-10201.4 + 11773.0i) q^{25} +(-12777.6 + 8211.68i) q^{26} +(539.088 + 3749.44i) q^{27} +(6933.98 - 3166.64i) q^{28} +(1597.10 - 11108.1i) q^{29} +(-186.215 - 634.190i) q^{30} +(23160.0 + 14884.0i) q^{31} +(-10182.0 + 22295.4i) q^{32} +(5411.84 - 18431.1i) q^{33} +(-20932.8 + 18138.3i) q^{34} +(1327.99 + 1532.58i) q^{35} +(6011.13 + 1765.03i) q^{36} +(-431.176 - 196.912i) q^{37} +(-18186.2 + 28298.2i) q^{38} +(36747.8 - 10790.1i) q^{39} +(-3768.06 - 541.765i) q^{40} +(-1055.50 - 2311.21i) q^{41} +(28203.7 - 4055.07i) q^{42} +(-16620.5 - 25862.0i) q^{43} +(-24010.0 - 20804.7i) q^{44} +1666.65i q^{45} +(-70284.1 + 26792.7i) q^{46} -75894.9 q^{47} +(-18184.0 + 20985.4i) q^{48} +(25429.2 - 16342.3i) q^{49} +(13705.6 + 95324.4i) q^{50} +(63530.3 - 29013.3i) q^{51} +(9014.56 - 62697.7i) q^{52} +(-46722.9 - 159124. i) q^{53} +(19700.3 + 12660.6i) q^{54} +(3510.95 - 7687.91i) q^{55} +(46234.8 - 157461. i) q^{56} +(64102.7 - 55545.3i) q^{57} +(-45432.5 - 52431.9i) q^{58} +(105793. + 31063.6i) q^{59} +(2507.35 + 1145.07i) q^{60} +(-118486. + 184368. i) q^{61} +(163302. - 47949.7i) q^{62} +(-71116.7 - 10225.0i) q^{63} +(110305. + 241533. i) q^{64} +(16679.4 - 2398.14i) q^{65} +(-64202.8 - 99901.5i) q^{66} +(174751. + 151423. i) q^{67} -115510. i q^{68} +(189079. - 14892.5i) q^{69} +12536.7 q^{70} +(370832. - 427963. i) q^{71} +(113464. - 72918.7i) q^{72} +(85740.2 + 596336. i) q^{73} +(-2665.58 + 1217.33i) q^{74} +(34559.2 - 240365. i) q^{75} +(-39522.2 - 134600. i) q^{76} +(306507. + 196980. i) q^{77} +(98357.7 - 215373. i) q^{78} +(123469. - 420497. i) q^{79} +(-9233.19 + 8000.61i) q^{80} +(-38668.9 - 44626.3i) q^{81} +(-15071.4 - 4425.35i) q^{82} +(-72747.6 - 33222.7i) q^{83} +(-64243.4 + 99964.7i) q^{84} +(29484.3 - 8657.38i) q^{85} +(-188117. - 27047.2i) q^{86} +(72671.9 + 159129. i) q^{87} +(-676995. + 97337.2i) q^{88} +(677036. + 1.05349e6i) q^{89} +(7786.79 + 6747.29i) q^{90} +726432. i q^{91} +(107502. - 294688. i) q^{92} -429156. q^{93} +(-307255. + 354591. i) q^{94} +(31394.9 - 20176.3i) q^{95} +(-54375.4 - 378189. i) q^{96} +(-1.24493e6 + 568542. i) q^{97} +(26594.5 - 184969. i) q^{98} +(84362.3 + 287312. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) $ 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{19}{22}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	4.04842	−	4.67213i	0.506053	−	0.584016i	−0.444031	−	0.896011i	$-0.646452\pi$
$2$	4.04842	−	4.67213i	0.506053	−	0.584016i	0.950084	+	0.311996i	$0.100997\pi$
$3$	−13.1138	+	8.42776i	−0.485698	+	0.312139i
$3$	−13.1138	+	8.42776i	−0.485698	+	0.312139i
$4$	3.66909	+	25.5191i	0.0573295	+	0.398736i
$5$	−6.23883	+	2.84918i	−0.0499106	+	0.0227934i	−0.440214	−	0.897893i	$-0.645097\pi$
$5$	−6.23883	+	2.84918i	−0.0499106	+	0.0227934i	0.390303	+	0.920686i	$0.372370\pi$
$6$	−13.7148	+	95.3887i	−0.0634945	+	0.441614i
$7$	−83.3001	−	283.694i	−0.242857	−	0.827097i	−0.987226	−	0.159327i	$-0.949067\pi$
$7$	−83.3001	−	283.694i	−0.242857	−	0.827097i	0.744368	−	0.667769i	$-0.232751\pi$
$8$	466.929	+	300.077i	0.911970	+	0.586088i
$9$	100.946	−	221.041i	0.138472	−	0.303211i
$10$	−11.9457	+	40.6833i	−0.0119457	+	0.0406833i
$11$	−931.286	+	806.964i	−0.699689	+	0.606284i	−0.930316	−	0.366758i	$-0.880468\pi$
$11$	−931.286	+	806.964i	−0.699689	+	0.606284i	0.230627	+	0.973042i	$0.425922\pi$
$12$	−263.185	−	303.731i	−0.152306	−	0.175770i
$13$	−2357.37	−	692.187i	−1.07300	−	0.315060i	−0.302922	−	0.953015i	$-0.597962\pi$
$13$	−2357.37	−	692.187i	−1.07300	−	0.315060i	−0.770073	+	0.637955i	$0.779780\pi$
$14$	−1662.69	−	759.325i	−0.605936	−	0.276722i
$15$	57.8029	−	89.9430i	0.0171268	−	0.0266498i
$16$	1709.14	−	501.850i	0.417271	−	0.122522i
$17$	−4434.74	−	637.620i	−0.902655	−	0.129782i	−0.324668	−	0.945828i	$-0.605253\pi$
$17$	−4434.74	−	637.620i	−0.902655	−	0.129782i	−0.577987	+	0.816046i	$0.696162\pi$
$18$	−624.058	−	1366.50i	−0.107006	−	0.234310i
$19$	−5385.82	+	774.365i	−0.785220	+	0.112898i	−0.523251	−	0.852179i	$-0.675281\pi$
$19$	−5385.82	+	774.365i	−0.785220	+	0.112898i	−0.261969	+	0.965076i	$0.584372\pi$
$20$	−95.5993	−	148.755i	−0.0119499	−	0.0185944i
$21$	3483.29	+	3018.29i	0.376125	+	0.325914i
$22$			7618.02i			0.715441i
$23$	−10720.4	−	5753.97i	−0.881107	−	0.472916i
$23$	−10720.4	−	5753.97i	−0.881107	−	0.472916i
$24$	−8652.21			−0.625883
$25$	−10201.4	+	11773.0i	−0.652889	+	0.753474i
$26$	−12777.6	+	8211.68i	−0.726992	+	0.467210i
$27$	539.088	+	3749.44i	0.0273885	+	0.190491i
$28$	6933.98	−	3166.64i	0.315870	−	0.144253i
$29$	1597.10	−	11108.1i	0.0654843	−	0.455453i	−0.930527	−	0.366224i	$-0.880650\pi$
$29$	1597.10	−	11108.1i	0.0654843	−	0.455453i	0.996011	−	0.0892296i	$-0.0284405\pi$
$30$	−186.215	−	634.190i	−0.00689685	−	0.0234885i
$31$	23160.0	+	14884.0i	0.777416	+	0.499615i	0.868175	−	0.496258i	$-0.165293\pi$
$31$	23160.0	+	14884.0i	0.777416	+	0.499615i	−0.0907590	+	0.995873i	$0.528929\pi$
$32$	−10182.0	+	22295.4i	−0.310729	+	0.680401i
$33$	5411.84	−	18431.1i	0.150593	−	0.512871i
$34$	−20932.8	+	18138.3i	−0.532586	+	0.461488i
$35$	1327.99	+	1532.58i	0.0309735	+	0.0357454i
$36$	6011.13	+	1765.03i	0.128839	+	0.0378307i
$37$	−431.176	−	196.912i	−0.00851236	−	0.00388746i	0.411154	−	0.911566i	$-0.365126\pi$
$37$	−431.176	−	196.912i	−0.00851236	−	0.00388746i	−0.419667	+	0.907678i	$0.637853\pi$
$38$	−18186.2	+	28298.2i	−0.331429	+	0.515713i
$39$	36747.8	−	10790.1i	0.619494	−	0.181900i
$40$	−3768.06	−	541.765i	−0.0588760	−	0.00846508i
$41$	−1055.50	−	2311.21i	−0.0153146	−	0.0335342i	0.901820	−	0.432112i	$-0.142231\pi$
$41$	−1055.50	−	2311.21i	−0.0153146	−	0.0335342i	−0.917135	+	0.398577i	$0.869504\pi$
$42$	28203.7	−	4055.07i	0.380678	−	0.0547332i
$43$	−16620.5	−	25862.0i	−0.209044	−	0.325279i	0.720860	−	0.693081i	$-0.243747\pi$
$43$	−16620.5	−	25862.0i	−0.209044	−	0.325279i	−0.929904	+	0.367801i	$0.880111\pi$
$44$	−24010.0	−	20804.7i	−0.281860	−	0.244233i
$45$			1666.65i			0.0182897i
$46$	−70284.1	+	26792.7i	−0.722077	+	0.275260i
$47$	−75894.9			−0.731003			−0.365502	−	0.930811i	$-0.619103\pi$
$47$	−75894.9			−0.731003			−0.365502	+	0.930811i	$0.619103\pi$
$48$	−18184.0	+	20985.4i	−0.164424	+	0.189755i
$49$	25429.2	−	16342.3i	0.216145	−	0.138908i
$50$	13705.6	+	95324.4i	0.109645	+	0.762595i
$51$	63530.3	−	29013.3i	0.478928	−	0.218719i
$52$	9014.56	−	62697.7i	0.0641113	−	0.445904i
$53$	−46722.9	−	159124.i	−0.313836	−	1.06883i	−0.953805	−	0.300426i	$-0.902871\pi$
$53$	−46722.9	−	159124.i	−0.313836	−	1.06883i	0.639970	−	0.768400i	$-0.278947\pi$
$54$	19700.3	+	12660.6i	0.125110	+	0.0804033i
$55$	3510.95	−	7687.91i	0.0211026	−	0.0462083i
$56$	46234.8	−	157461.i	0.263272	−	0.896623i
$57$	64102.7	−	55545.3i	0.346140	−	0.299932i
$58$	−45432.5	−	52431.9i	−0.232854	−	0.268727i
$59$	105793.	+	31063.6i	0.515111	+	0.151250i	0.528948	−	0.848654i	$-0.322586\pi$
$59$	105793.	+	31063.6i	0.515111	+	0.151250i	−0.0138373	+	0.999904i	$0.504405\pi$
$60$	2507.35	+	1145.07i	0.0116081	+	0.00530124i
$61$	−118486.	+	184368.i	−0.522010	+	0.812263i	−0.997731	−	0.0673330i	$-0.978551\pi$
$61$	−118486.	+	184368.i	−0.522010	+	0.812263i	0.475721	+	0.879596i	$0.342187\pi$
$62$	163302.	−	47949.7i	0.685197	−	0.201192i
$63$	−71116.7	−	10225.0i	−0.284413	−	0.0408925i
$64$	110305.	+	241533.i	0.420779	+	0.921377i
$65$	16679.4	−	2398.14i	0.0607352	−	0.00873240i
$66$	−64202.8	−	99901.5i	−0.223317	−	0.347488i
$67$	174751.	+	151423.i	0.581025	+	0.503461i	0.895057	−	0.445951i	$-0.147134\pi$
$67$	174751.	+	151423.i	0.581025	+	0.503461i	−0.314032	+	0.949412i	$0.601680\pi$
$68$		−	115510.i		−	0.367361i
$69$	189079.	−	14892.5i	0.575568	−	0.0453337i
$70$	12536.7			0.0365501
$71$	370832.	−	427963.i	1.03610	−	1.19572i	0.0557545	−	0.998445i	$-0.482244\pi$
$71$	370832.	−	427963.i	1.03610	−	1.19572i	0.980347	−	0.197280i	$-0.0632110\pi$
$72$	113464.	−	72918.7i	0.303990	−	0.195363i
$73$	85740.2	+	596336.i	0.220402	+	1.53293i	0.736522	+	0.676414i	$0.236467\pi$
$73$	85740.2	+	596336.i	0.220402	+	1.53293i	−0.516120	+	0.856516i	$0.672624\pi$
$74$	−2665.58	+	1217.33i	−0.00657804	+	0.00300409i
$75$	34559.2	−	240365.i	0.0819181	−	0.569753i
$76$	−39522.2	−	134600.i	−0.0900326	−	0.306623i
$77$	306507.	+	196980.i	0.671380	+	0.431470i
$78$	98357.7	−	215373.i	0.207264	−	0.453846i
$79$	123469.	−	420497.i	0.250425	−	0.852868i	−0.734311	−	0.678813i	$-0.762495\pi$
$79$	123469.	−	420497.i	0.250425	−	0.852868i	0.984736	−	0.174055i	$-0.0556871\pi$
$80$	−9233.19	+	8000.61i	−0.0180336	+	0.0156262i
$81$	−38668.9	−	44626.3i	−0.0727623	−	0.0839722i
$82$	−15071.4	−	4425.35i	−0.0273345	−	0.00802613i
$83$	−72747.6	−	33222.7i	−0.127228	−	0.0581033i	0.350784	−	0.936457i	$-0.385915\pi$
$83$	−72747.6	−	33222.7i	−0.127228	−	0.0581033i	−0.478012	+	0.878353i	$0.658643\pi$
$84$	−64243.4	+	99964.7i	−0.108390	+	0.168659i
$85$	29484.3	−	8657.38i	0.0480103	−	0.0140971i
$86$	−188117.	−	27047.2i	−0.295756	−	0.0425233i
$87$	72671.9	+	159129.i	0.110359	+	0.241653i
$88$	−676995.	+	97337.2i	−0.993431	+	0.142834i
$89$	677036.	+	1.05349e6i	0.960376	+	1.49437i	0.866735	+	0.498769i	$0.166214\pi$
$89$	677036.	+	1.05349e6i	0.960376	+	1.49437i	0.0936415	+	0.995606i	$0.470149\pi$
$90$	7786.79	+	6747.29i	0.0106815	+	0.00925554i
$91$			726432.i			0.963986i
$92$	107502.	−	294688.i	0.138055	−	0.378441i
$93$	−429156.			−0.533539
$94$	−307255.	+	354591.i	−0.369926	+	0.426918i
$95$	31394.9	−	20176.3i	0.0366175	−	0.0235326i
$96$	−54375.4	−	378189.i	−0.0614595	−	0.427460i
$97$	−1.24493e6	+	568542.i	−1.36405	+	0.622942i	−0.956900	−	0.290418i	$-0.906206\pi$
$97$	−1.24493e6	+	568542.i	−1.36405	+	0.622942i	−0.407153	+	0.913360i	$0.633478\pi$
$98$	26594.5	−	184969.i	0.0282562	−	0.196526i
$99$	84362.3	+	287312.i	0.0869447	+	0.296106i
$100$	−337867.	−	217134.i	−0.337867	−	0.217134i
$101$	413781.	−	906055.i	0.401612	−	0.879408i	−0.595492	−	0.803361i	$-0.703043\pi$
$101$	413781.	−	906055.i	0.401612	−	0.879408i	0.997104	−	0.0760466i	$-0.0242298\pi$
$102$	121643.	−	414280.i	0.114627	−	0.390385i
$103$	−1.50800e6	+	1.30669e6i	−1.38003	+	1.19581i	−0.422893	+	0.906180i	$0.638985\pi$
$103$	−1.50800e6	+	1.30669e6i	−1.38003	+	1.19581i	−0.957140	+	0.289625i	$0.906469\pi$
$104$	−893015.	−	1.03059e6i	−0.793887	−	0.916195i
$105$	−30331.3	−	8906.07i	−0.0262013	−	0.00769340i
$106$	−932600.	−	425904.i	−0.783029	−	0.357597i
$107$	41004.9	−	63804.8i	0.0334722	−	0.0520837i	−0.824114	−	0.566424i	$-0.808327\pi$
$107$	41004.9	−	63804.8i	0.0334722	−	0.0520837i	0.857586	+	0.514340i	$0.171963\pi$
$108$	−93704.3	+	27514.1i	−0.0743855	+	0.0218416i
$109$	115685.	+	16633.0i	0.0893302	+	0.0128437i	0.186835	−	0.982391i	$-0.440177\pi$
$109$	115685.	+	16633.0i	0.0893302	+	0.0128437i	−0.0975048	+	0.995235i	$0.531086\pi$
$110$	−21705.1	−	47527.5i	−0.0163074	−	0.0357081i
$111$	7313.90	−	1051.58i	0.00534786	−	0.000768907i
$112$	−284744.	−	443070.i	−0.202675	−	0.315368i
$113$	−975265.	−	845072.i	−0.675908	−	0.585677i	0.247783	−	0.968815i	$-0.420298\pi$
$113$	−975265.	−	845072.i	−0.675908	−	0.585677i	−0.923691	+	0.383138i	$0.874843\pi$
$114$		−	524367.i		−	0.353933i
$115$	83277.1	+	5353.61i	0.0547560	+	0.00352009i
$116$	289327.			0.185360
$117$	−390968.	+	451201.i	−0.244109	+	0.281717i
$118$	573428.	−	368520.i	0.349006	−	0.224293i
$119$	188526.	+	1.31122e6i	0.111874	+	0.778102i
$120$	53979.6	−	24651.7i	0.0312382	−	0.0142660i
$121$	−36016.6	+	250501.i	−0.0203304	+	0.141401i
$122$	381710.	+	1.29998e6i	0.210210	+	0.715910i
$123$	33319.9	+	21413.4i	0.0179056	+	0.0115072i
$124$	−294851.	+	645633.i	−0.154645	+	0.338626i
$125$	60293.5	−	205341.i	0.0308703	−	0.105134i
$126$	−335683.	+	290871.i	−0.167810	+	0.145408i
$127$	1.12605e6	+	1.29953e6i	0.549726	+	0.634417i	0.960819	−	0.277176i	$-0.0893985\pi$
$127$	1.12605e6	+	1.29953e6i	0.549726	+	0.634417i	−0.411094	+	0.911593i	$0.634853\pi$
$128$	69914.6	+	20528.8i	0.0333379	+	0.00978888i
$129$	435917.	+	199077.i	0.203065	+	0.0927366i
$130$	56320.9	−	87637.0i	0.0256353	−	0.0398894i
$131$	−2.73849e6	+	804092.i	−1.21814	+	0.357678i	−0.826762	−	0.562552i	$-0.809819\pi$
$131$	−2.73849e6	+	804092.i	−1.21814	+	0.357678i	−0.391377	+	0.920230i	$0.628001\pi$
$132$	490200.	+	70480.1i	0.213133	+	0.0306440i
$133$	668322.	+	1.46342e6i	0.284074	+	0.622035i
$134$	1.41493e6	−	203436.i	0.588059	−	0.0845501i
$135$	−14046.1	−	21856.2i	−0.00570893	−	0.00888326i
$136$	−1.87937e6	−	1.62849e6i	−0.747131	−	0.647393i
$137$			7802.66i			0.00303446i	0.999999	+	0.00151723i	$0.000482949\pi$
$137$			7802.66i			0.00303446i	−0.999999	+	0.00151723i	$0.999517\pi$
$138$	695892.	−	943693.i	0.264792	−	0.359082i
$139$	3.49416e6			1.30106			0.650532	−	0.759479i	$-0.274546\pi$
$139$	3.49416e6			1.30106			0.650532	+	0.759479i	$0.274546\pi$
$140$	−34237.6	+	39512.3i	−0.0124773	+	0.0143995i
$141$	995274.	−	639624.i	0.355047	−	0.228175i
$142$	−498213.	−	3.46515e6i	−0.174000	−	1.21020i
$143$	2.75396e6	−	1.25769e6i	0.941779	−	0.430096i
$144$	61601.7	−	428449.i	0.0206303	−	0.143487i
$145$	21684.8	+	73851.7i	0.00711298	+	0.0242246i
$146$	3.13327e6	+	2.01363e6i	1.00679	+	0.647025i
$147$	−195745.	+	428622.i	−0.0616224	+	0.134934i
$148$	3442.98	−	11725.7i	0.00106206	−	0.00361705i
$149$	−225254.	+	195184.i	−0.0680948	+	0.0590045i	−0.688243	−	0.725480i	$-0.741618\pi$
$149$	−225254.	+	195184.i	−0.0680948	+	0.0590045i	0.620148	+	0.784484i	$0.287072\pi$
$150$	−983104.	−	1.13456e6i	−0.291290	−	0.336167i
$151$	2.08964e6	+	613574.i	0.606934	+	0.178212i	0.570737	−	0.821133i	$-0.306658\pi$
$151$	2.08964e6	+	613574.i	0.606934	+	0.178212i	0.0361966	+	0.999345i	$0.488476\pi$
$152$	−2.74716e6	−	1.25459e6i	−0.782265	−	0.357248i
$153$	−588609.	+	915893.i	−0.164344	+	0.255724i
$154$	2.16119e6	−	634582.i	0.591739	−	0.173750i
$155$	−186899.	−	26872.0i	−0.0501893	−	0.00721613i
$156$	410185.	+	898180.i	0.108045	+	0.236586i
$157$	−17479.5	+	2513.17i	−0.00451679	+	0.000649417i	−0.144573	−	0.989494i	$-0.546181\pi$
$157$	−17479.5	+	2513.17i	−0.00451679	+	0.000649417i	0.140056	+	0.990144i	$0.455272\pi$
$158$	−1.46476e6	−	2.27921e6i	−0.371361	−	0.577848i
$159$	1.95377e6	+	1.69295e6i	0.486052	+	0.421166i
$160$		−	168107.i		−	0.0410418i
$161$	−739354.	+	3.52063e6i	−0.177164	+	0.843612i
$162$	−365047.			−0.0858626
$163$	4.55725e6	−	5.25935e6i	1.05230	−	1.21442i	0.0762038	−	0.997092i	$-0.475720\pi$
$163$	4.55725e6	−	5.25935e6i	1.05230	−	1.21442i	0.976098	−	0.217329i	$-0.0697345\pi$
$164$	55107.3	−	35415.3i	0.0124933	−	0.00802897i
$165$	18749.8	+	130407.i	0.00417392	+	0.0290302i
$166$	−449734.	+	205386.i	−0.0983176	+	0.0449001i
$167$	−64954.8	+	451771.i	−0.0139464	+	0.0969993i	−0.995606	−	0.0936442i	$-0.970148\pi$
$167$	−64954.8	+	451771.i	−0.0139464	+	0.0969993i	0.981659	+	0.190644i	$0.0610575\pi$
$168$	720730.	+	2.45458e6i	0.152000	+	0.517666i
$169$	1.01751e6	+	653913.i	0.210804	+	0.135475i
$170$	78916.6	−	172803.i	0.0160628	−	0.0351726i
$171$	−372511.	+	1.26865e6i	−0.0744990	+	0.253720i
$172$	598992.	−	519030.i	0.117716	−	0.102002i
$173$	−4.76263e6	−	5.49637e6i	−0.919832	−	1.06154i	−0.997912	−	0.0645952i	$-0.979424\pi$
$173$	−4.76263e6	−	5.49637e6i	−0.919832	−	1.06154i	0.0780799	−	0.996947i	$-0.475121\pi$
$174$	1.03768e6	+	304690.i	0.196977	+	0.0578376i
$175$	4.18972e6	+	1.91338e6i	0.781755	+	0.357016i
$176$	−1.18673e6	+	1.84658e6i	−0.217677	+	0.338712i
$177$	−1.64915e6	+	484234.i	−0.297400	+	0.0873244i
$178$	7.66296e6	+	1.10177e6i	1.35874	+	0.195357i
$179$	−1.64924e6	−	3.61133e6i	−0.287557	−	0.629663i	0.709633	−	0.704571i	$-0.248861\pi$
$179$	−1.64924e6	−	3.61133e6i	−0.287557	−	0.629663i	−0.997190	+	0.0749087i	$0.976133\pi$
$180$	−42531.3	+	6115.08i	−0.00729275	+	0.00104854i
$181$	−4.66146e6	−	7.25337e6i	−0.786115	−	1.22322i	−0.970674	−	0.240398i	$-0.922722\pi$
$181$	−4.66146e6	−	7.25337e6i	−0.786115	−	1.22322i	0.184559	−	0.982821i	$-0.440914\pi$
$182$	3.39398e6	+	2.94090e6i	0.562983	+	0.487828i
$183$		−	3.41635e6i		−	0.557454i
$184$	−3.27905e6	−	5.90365e6i	−0.526373	−	0.947692i
$185$	3251.07			0.000513466
$186$	−1.73740e6	+	2.00507e6i	−0.269999	+	0.311595i
$187$	4.64455e6	−	2.98487e6i	0.710263	−	0.456458i
$188$	−278465.	−	1.93677e6i	−0.0419081	−	0.291477i
$189$	1.01879e6	−	465265.i	0.150903	−	0.0689152i
$190$	32833.7	−	228363.i	0.00478695	−	0.0332940i
$191$	1.19134e6	+	4.05732e6i	0.170976	+	0.582290i	0.999742	+	0.0226957i	$0.00722487\pi$
$191$	1.19134e6	+	4.05732e6i	0.170976	+	0.582290i	−0.828767	+	0.559594i	$0.810957\pi$
$192$	−3.48210e6	−	2.23781e6i	−0.491969	−	0.316169i
$193$	−4.78355e6	+	1.04745e7i	−0.665394	+	1.45701i	0.212016	+	0.977266i	$0.431997\pi$
$193$	−4.78355e6	+	1.04745e7i	−0.665394	+	1.45701i	−0.877409	+	0.479743i	$0.840730\pi$
$194$	−2.38371e6	+	8.11819e6i	−0.326474	+	1.11187i
$195$	−198520.	+	172019.i	−0.0267732	+	0.0231991i
$196$	510344.	+	588968.i	0.0677789	+	0.0782210i
$197$	−4.41487e6	−	1.29632e6i	−0.577457	−	0.169557i	−0.0200541	−	0.999799i	$-0.506384\pi$
$197$	−4.41487e6	−	1.29632e6i	−0.577457	−	0.169557i	−0.557403	+	0.830242i	$0.688202\pi$
$198$	1.68389e6	+	769007.i	0.216929	+	0.0990683i
$199$	2.16657e6	−	3.37125e6i	0.274924	−	0.427791i	−0.676145	−	0.736769i	$-0.736351\pi$
$199$	2.16657e6	−	3.37125e6i	0.274924	−	0.427791i	0.951069	+	0.308978i	$0.0999870\pi$
$200$	−8.29614e6	+	2.43597e6i	−1.03702	+	0.304496i
$201$	−3.56781e6	−	512973.i	−0.439353	−	0.0631694i
$202$	−2.55804e6	−	5.60133e6i	−0.310351	−	0.679574i
$203$	−3.28433e6	+	472215.i	−0.392607	+	0.0564484i
$204$	973491.	+	1.51478e6i	0.114668	+	0.178427i
$205$	13170.1	+	11412.0i	0.00152872	+	0.00132464i
$206$			1.23356e7i			1.41110i
$207$	−2.35404e6	+	1.78881e6i	−0.265402	+	0.201676i
$208$	−4.37646e6			−0.486332
$209$	4.39086e6	−	5.06732e6i	0.480962	−	0.555059i
$210$	−164404.	+	105656.i	−0.0177523	+	0.0114087i
$211$	700777.	+	4.87401e6i	0.0745989	+	0.518847i	0.992520	+	0.122083i	$0.0389575\pi$
$211$	700777.	+	4.87401e6i	0.0745989	+	0.518847i	−0.917921	+	0.396763i	$0.870133\pi$
$212$	3.88926e6	−	1.77616e6i	0.408187	−	0.186413i
$213$	−1.25627e6	+	8.73752e6i	−0.130000	+	0.904169i
$214$	−132099.	−	449889.i	−0.0134790	−	0.0459054i
$215$	177378.	+	113994.i	0.0178478	+	0.0114701i
$216$	−873404.	+	1.91249e6i	−0.0866671	+	0.189774i
$217$	2.29328e6	−	7.81020e6i	0.224429	−	0.764334i
$218$	546054.	−	473159.i	0.0527067	−	0.0456707i
$219$	−6.15016e6	−	7.09766e6i	−0.585536	−	0.675745i
$220$	209070.	+	61388.6i	0.0196347	+	0.00576527i
$221$	1.00130e7	+	4.57278e6i	0.927656	+	0.423646i
$222$	24696.7	−	38428.7i	0.00225725	−	0.00351235i
$223$	−1.13981e7	+	3.34679e6i	−1.02782	+	0.301796i	−0.751825	−	0.659363i	$-0.770826\pi$
$223$	−1.13981e7	+	3.34679e6i	−1.02782	+	0.301796i	−0.275997	+	0.961158i	$0.589008\pi$
$224$	7.17323e6	+	1.03135e6i	0.638220	+	0.0917622i
$225$	1.57253e6	+	3.44336e6i	0.138055	+	0.302298i
$226$	−7.89657e6	+	1.13536e6i	−0.684090	+	0.0983573i
$227$	−7.12870e6	−	1.10925e7i	−0.609443	−	0.948311i	−0.999620	−	0.0275714i	$-0.991223\pi$
$227$	−7.12870e6	−	1.10925e7i	−0.609443	−	0.948311i	0.390177	−	0.920740i	$-0.372414\pi$
$228$	1.65266e6	+	1.43204e6i	0.139438	+	0.120823i
$229$		−	1.32226e7i		−	1.10106i	−0.834817	−	0.550528i	$-0.814427\pi$
$229$		−	1.32226e7i		−	1.10106i	0.834817	−	0.550528i	$-0.185573\pi$
$230$	362153.	−	367407.i	0.0297652	−	0.0301970i
$231$	−5.67959e6			−0.460766
$232$	4.07900e6	−	4.70742e6i	0.326655	−	0.376980i
$233$	−1.43569e7	+	9.22661e6i	−1.13499	+	0.729414i	−0.966596	−	0.256305i	$-0.917495\pi$
$233$	−1.43569e7	+	9.22661e6i	−1.13499	+	0.729414i	−0.168395	+	0.985720i	$0.553858\pi$
$234$	525266.	+	3.65331e6i	0.0409951	+	0.285127i
$235$	473496.	−	216238.i	0.0364848	−	0.0166621i
$236$	−404551.	+	2.81372e6i	−0.0307778	+	0.214064i
$237$	1.92469e6	+	6.55491e6i	0.144583	+	0.492404i
$238$	6.88944e6	+	4.42758e6i	0.511038	+	0.328424i
$239$	2.86664e6	−	6.27706e6i	0.209981	−	0.459793i	−0.775111	−	0.631825i	$-0.782306\pi$
$239$	2.86664e6	−	6.27706e6i	0.209981	−	0.459793i	0.985091	+	0.172032i	$0.0550333\pi$
$240$	53655.5	−	182734.i	0.00388133	−	0.0132186i
$241$	−8.57791e6	+	7.43280e6i	−0.612817	+	0.531009i	−0.905032	−	0.425344i	$-0.860153\pi$
$241$	−8.57791e6	+	7.43280e6i	−0.612817	+	0.531009i	0.292215	+	0.956353i	$0.405608\pi$
$242$	1.02456e6	+	1.18241e6i	0.0722923	+	0.0834297i
$243$	883197.	+	259330.i	0.0615515	+	0.0180732i
$244$	−5.13965e6	−	2.34720e6i	−0.353805	−	0.161577i
$245$	−112086.	+	174409.i	−0.00762173	+	0.0118596i
$246$	234939.	−	68984.4i	0.0157816	−	0.00463389i
$247$	1.32324e7	+	1.90253e6i	0.878107	+	0.126253i
$248$	6.34772e6	+	1.38996e7i	0.416162	+	0.911268i
$249$	1.23399e6	−	177421.i	0.0799309	−	0.0114923i
$250$	−715285.	−	1.11300e6i	−0.0457782	−	0.0712323i
$251$	3.06314e6	+	2.65422e6i	0.193707	+	0.167848i	0.746314	−	0.665594i	$-0.231822\pi$
$251$	3.06314e6	+	2.65422e6i	0.193707	+	0.167848i	−0.552607	+	0.833442i	$0.686367\pi$
$252$		−	1.85235e6i		−	0.115750i
$253$	1.46270e7	−	3.29241e6i	0.903223	−	0.203307i
$254$	1.06303e7			0.648700
$255$	−313690.	+	362018.i	−0.0189182	+	0.0218328i
$256$	−1.39172e7	+	8.94402e6i	−0.829528	+	0.533105i
$257$	−557361.	−	3.87653e6i	−0.0328350	−	0.228372i	0.966796	−	0.255551i	$-0.0822568\pi$
$257$	−557361.	−	3.87653e6i	−0.0328350	−	0.228372i	−0.999631	+	0.0271785i	$0.991348\pi$
$258$	2.69489e6	−	1.23071e6i	0.156921	−	0.0716635i
$259$	−19945.6	+	138725.i	−0.00114802	+	0.00798464i
$260$	122396.	+	416844.i	0.00696384	+	0.0237167i
$261$	−2.29411e6	−	1.47434e6i	−0.129031	−	0.0829229i
$262$	−7.32973e6	+	1.60499e7i	−0.407553	+	0.892416i
$263$	9.42923e6	−	3.21130e7i	0.518333	−	1.76528i	−0.117095	−	0.993121i	$-0.537358\pi$
$263$	9.42923e6	−	3.21130e7i	0.518333	−	1.76528i	0.635428	−	0.772160i	$-0.280824\pi$
$264$	8.05768e6	−	6.98202e6i	0.437923	−	0.379463i
$265$	744868.	+	859623.i	0.0400259	+	0.0461924i
$266$	9.54295e6	+	2.80206e6i	0.507035	+	0.148879i
$267$	−1.77571e7	−	8.10939e6i	−0.932906	−	0.426044i
$268$	−3.22299e6	+	5.01507e6i	−0.167438	+	0.260539i
$269$	−8.76212e6	+	2.57279e6i	−0.450145	+	0.132174i	−0.498944	−	0.866634i	$-0.666279\pi$
$269$	−8.76212e6	+	2.57279e6i	−0.450145	+	0.132174i	0.0487993	+	0.998809i	$0.484461\pi$
$270$	−158979.	−	22857.8i	−0.00807698	−	0.00116129i
$271$	−2.30960e6	−	5.05733e6i	−0.116046	−	0.254105i	0.842692	−	0.538395i	$-0.180969\pi$
$271$	−2.30960e6	−	5.05733e6i	−0.116046	−	0.254105i	−0.958738	+	0.284290i	$0.908242\pi$
$272$	−7.89960e6	+	1.13579e6i	−0.392553	+	0.0564406i
$273$	−6.12219e6	−	9.52631e6i	−0.300898	−	0.468206i
$274$	36455.0	+	31588.4i	0.00177217	+	0.00153559i
$275$		−	1.91962e7i		−	0.923034i
$276$	1.07379e6	+	4.77049e6i	0.0510732	+	0.226900i
$277$	2.48195e7			1.16776			0.583880	−	0.811840i	$-0.301534\pi$
$277$	2.48195e7			1.16776			0.583880	+	0.811840i	$0.301534\pi$
$278$	1.41458e7	−	1.63252e7i	0.658407	−	0.759842i
$279$	5.62788e6	−	3.61682e6i	0.259139	−	0.166538i
$280$	160184.	+	1.11411e6i	0.00729702	+	0.0507519i
$281$	−3.52579e6	+	1.61017e6i	−0.158905	+	0.0725695i	−0.493280	−	0.869871i	$-0.664202\pi$
$281$	−3.52579e6	+	1.61017e6i	−0.158905	+	0.0725695i	0.334375	+	0.942440i	$0.391475\pi$
$282$	1.04089e6	−	7.23952e6i	0.0464147	−	0.322821i
$283$	1.30713e6	+	4.45167e6i	0.0576711	+	0.196410i	0.983290	−	0.182048i	$-0.0582726\pi$
$283$	1.30713e6	+	4.45167e6i	0.0576711	+	0.196410i	−0.925618	+	0.378458i	$0.876454\pi$
$284$	1.22818e7	+	7.89306e6i	0.536178	+	0.344580i
$285$	−241667.	+	529178.i	−0.0104396	+	0.0228595i
$286$	5.27309e6	−	1.79585e7i	0.225407	−	0.767665i
$287$	−567754.	+	491962.i	−0.0240168	+	0.0208107i
$288$	3.90036e6	+	4.50125e6i	0.163278	+	0.188433i
$289$	−3.89943e6	−	1.14497e6i	−0.161550	−	0.0474354i
$290$	432834.	+	197669.i	0.0177471	+	0.00810482i
$291$	1.15343e7	−	1.79478e7i	0.468073	−	0.728336i
$292$	−1.49034e7	+	4.37602e6i	−0.598598	+	0.175764i
$293$	−3.22592e7	−	4.63817e6i	−1.28248	−	0.184393i	−0.532827	−	0.846224i	$-0.678870\pi$
$293$	−3.22592e7	−	4.63817e6i	−1.28248	−	0.184393i	−0.749653	+	0.661831i	$0.769780\pi$
$294$	1.21012e6	+	2.64979e6i	0.0476196	+	0.104272i
$295$	−748530.	+	107622.i	−0.0291570	+	0.00419215i
$296$	−142240.	−	221330.i	−0.00548462	−	0.00853424i
$297$	−3.52771e6	−	3.05678e6i	−0.134655	−	0.116679i
$298$			1.84260e6i			0.0696278i
$299$	2.12892e7	+	2.09848e7i	0.796428	+	0.785039i
$300$	6.26069e6			0.231877
$301$	−5.95240e6	+	6.86944e6i	−0.218269	+	0.251896i
$302$	1.13265e7	−	7.27907e6i	0.411219	−	0.264274i
$303$	2.20974e6	+	1.53691e7i	0.0794354	+	0.552485i
$304$	−8.81653e6	+	4.02637e6i	−0.313817	+	0.143316i
$305$	213918.	−	1.48783e6i	0.00753959	−	0.0524390i
$306$	1.89623e6	+	6.45798e6i	0.0661801	+	0.225389i
$307$	2.30356e7	+	1.48041e7i	0.796131	+	0.511642i	0.874351	−	0.485294i	$-0.161287\pi$
$307$	2.30356e7	+	1.48041e7i	0.796131	+	0.511642i	−0.0782204	+	0.996936i	$0.524924\pi$
$308$	−3.90215e6	+	8.54452e6i	−0.133552	+	0.292439i
$309$	8.76321e6	−	2.98448e7i	0.297022	−	1.01156i
$310$	−882194.	+	764425.i	−0.0296128	+	0.0256596i
$311$	−2.52574e7	−	2.91486e7i	−0.839669	−	0.969030i	0.160168	−	0.987090i	$-0.448796\pi$
$311$	−2.52574e7	−	2.91486e7i	−0.839669	−	0.969030i	−0.999837	+	0.0180601i	$0.994251\pi$
$312$	2.03965e7	+	5.98894e6i	0.671570	+	0.197191i
$313$	−2.08377e7	−	9.51627e6i	−0.679544	−	0.310337i	0.0455751	−	0.998961i	$-0.485488\pi$
$313$	−2.08377e7	−	9.51627e6i	−0.679544	−	0.310337i	−0.725119	+	0.688624i	$0.758215\pi$
$314$	−59022.6	+	91840.9i	−0.00190647	+	0.00296652i
$315$	472818.	−	138832.i	0.0151273	−	0.00444179i
$316$	1.11837e7	+	1.60798e6i	0.354426	+	0.0509587i
$317$	1.61195e7	+	3.52968e7i	0.506028	+	1.10805i	0.974463	+	0.224548i	$0.0720907\pi$
$317$	1.61195e7	+	3.52968e7i	0.506028	+	1.10805i	−0.468435	+	0.883498i	$0.655182\pi$
$318$	1.58194e7	−	2.27448e6i	0.491935	−	0.0707296i
$319$	7.47644e6	+	1.16336e7i	0.230315	+	0.358378i
$320$	−1.37634e6	−	1.19261e6i	−0.0420027	−	0.0363955i
$321$			1.18231e6i			0.0357449i
$322$	1.34556e7	+	1.77074e7i	0.403029	+	0.530379i
$323$	2.43785e7			0.723435
$324$	996942.	−	1.15053e6i	0.0293113	−	0.0338270i
$325$	3.21976e7	−	2.06922e7i	0.937937	−	0.602775i
$326$	−6.12268e6	−	4.25841e7i	−0.176721	−	1.22912i
$327$	−1.65726e6	+	756844.i	−0.0473965	+	0.0216453i
$328$	200700.	−	1.39590e6i	0.00568757	−	0.0395579i
$329$	6.32206e6	+	2.15309e7i	0.177530	+	0.604610i
$330$	685187.	+	440343.i	0.0190664	+	0.0122532i
$331$	−1.72175e7	+	3.77011e7i	−0.474774	+	1.03961i	0.509094	+	0.860711i	$0.329981\pi$
$331$	−1.72175e7	+	3.77011e7i	−0.474774	+	1.03961i	−0.983868	+	0.178899i	$0.942747\pi$
$332$	580896.	−	1.97835e6i	0.0158739	−	0.0540616i
$333$	−87050.9	+	75430.1i	−0.00235744	+	0.00204273i
$334$	1.84777e6	+	2.13244e6i	0.0495915	+	0.0572317i
$335$	−1.52167e6	−	446803.i	−0.0404750	−	0.0118845i
$336$	7.46816e6	+	3.41060e6i	0.196877	+	0.0899109i
$337$	−3.32954e7	+	5.18087e7i	−0.869951	+	1.35367i	0.0646259	+	0.997910i	$0.479415\pi$
$337$	−3.32954e7	+	5.18087e7i	−0.869951	+	1.35367i	−0.934577	+	0.355761i	$0.884222\pi$
$338$	7.17447e6	−	2.10661e6i	0.185797	−	0.0545550i
$339$	1.99115e7	+	2.86285e6i	0.511100	+	0.0734851i
$340$	329109.	+	720648.i	0.00837342	+	0.0183352i
$341$	−3.35795e7	+	4.82800e6i	−0.846858	+	0.121760i
$342$	4.41924e6	+	6.87647e6i	0.110476	+	0.171904i
$343$	−3.30435e7	−	2.86324e7i	−0.818849	−	0.709537i
$344$		−	1.70631e7i		−	0.419163i
$345$	−1.13720e6	+	631632.i	−0.0276936	+	0.0153818i
$346$	−4.49608e7			−1.08544
$347$	1.23123e7	−	1.42091e7i	0.294680	−	0.340079i	−0.589032	−	0.808110i	$-0.700491\pi$
$347$	1.23123e7	−	1.42091e7i	0.294680	−	0.340079i	0.883712	+	0.468031i	$0.155036\pi$
$348$	−3.79419e6	+	2.43838e6i	−0.0900289	+	0.0578580i
$349$	7.98403e6	+	5.55301e7i	0.187822	+	1.30633i	0.837633	+	0.546233i	$0.183939\pi$
$349$	7.98403e6	+	5.55301e7i	0.187822	+	1.30633i	−0.649811	+	0.760096i	$0.725152\pi$
$350$	2.59013e7	−	1.18287e7i	0.604112	−	0.275889i
$351$	1.32448e6	−	9.21197e6i	0.0306284	−	0.213025i
$352$	−8.50925e6	−	2.89798e7i	−0.195103	−	0.664459i
$353$	−6.88227e6	−	4.42297e6i	−0.156462	−	0.100552i	0.460067	−	0.887884i	$-0.347825\pi$
$353$	−6.88227e6	−	4.42297e6i	−0.156462	−	0.100552i	−0.616529	+	0.787332i	$0.711462\pi$
$354$	−4.41405e6	+	9.66542e6i	−0.0995010	+	0.217877i
$355$	−1.09422e6	+	3.72656e6i	−0.0244578	+	0.0832957i
$356$	−2.43999e7	+	2.11427e7i	−0.540803	+	0.468608i
$357$	−1.35230e7	−	1.56064e7i	−0.297213	−	0.343002i
$358$	−2.35494e7	−	6.91473e6i	−0.513252	−	0.150704i
$359$	8.83696e6	+	4.03571e6i	0.190994	+	0.0872240i	0.508616	−	0.860993i	$-0.330157\pi$
$359$	8.83696e6	+	4.03571e6i	0.190994	+	0.0872240i	−0.317622	+	0.948217i	$0.602884\pi$
$360$	−500122.	+	778205.i	−0.0107194	+	0.0166796i
$361$	−1.67327e7	+	4.91317e6i	−0.355668	+	0.104434i
$362$	−5.27602e7	−	7.58578e6i	−1.11220	−	0.159910i
$363$	−1.63884e6	−	3.58857e6i	−0.0342624	−	0.0750242i
$364$	−1.85379e7	+	2.66534e6i	−0.384376	+	0.0552649i
$365$	−2.23399e6	−	3.47615e6i	−0.0459411	−	0.0714858i
$366$	−1.59616e7	−	1.38308e7i	−0.325562	−	0.282101i
$367$			1.12381e7i			0.227350i	0.993518	+	0.113675i	$0.0362623\pi$
$367$			1.12381e7i			0.227350i	−0.993518	+	0.113675i	$0.963738\pi$
$368$	−2.12104e7	−	4.45431e6i	−0.425603	−	0.0893793i
$369$	−617420.			−0.0122886
$370$	13161.7	−	15189.4i	0.000259841	−	0.000299872i
$371$	−4.12504e7	+	2.65100e7i	−0.807805	+	0.519145i
$372$	−1.57461e6	−	1.09517e7i	−0.0305875	−	0.212741i
$373$	−1.10510e7	+	5.04684e6i	−0.212950	+	0.0972508i	−0.519034	−	0.854754i	$-0.673708\pi$
$373$	−1.10510e7	+	5.04684e6i	−0.212950	+	0.0972508i	0.306085	+	0.952004i	$0.400981\pi$
$374$	4.85740e6	−	3.37840e7i	0.0928515	−	0.645797i
$375$	939882.	+	3.20094e6i	0.0178229	+	0.0606994i
$376$	−3.54375e7	−	2.27743e7i	−0.666653	−	0.428432i
$377$	−1.14538e7	+	2.50803e7i	−0.213760	+	0.468068i
$378$	1.95071e6	−	6.64349e6i	0.0361174	−	0.123005i
$379$	6.44453e7	−	5.58421e7i	1.18379	−	1.02576i	0.184710	−	0.982793i	$-0.440865\pi$
$379$	6.44453e7	−	5.58421e7i	1.18379	−	1.02576i	0.999077	−	0.0429636i	$-0.0136800\pi$
$380$	630072.	+	727141.i	0.0114826	+	0.0132516i
$381$	−2.57189e7	−	7.55176e6i	−0.465027	−	0.136544i
$382$	2.37794e7	+	1.08597e7i	0.426589	+	0.194817i
$383$	−3.53462e7	+	5.49998e7i	−0.629139	+	0.978959i	0.369622	+	0.929182i	$0.379487\pi$
$383$	−3.53462e7	+	5.49998e7i	−0.629139	+	0.978959i	−0.998760	+	0.0497767i	$0.984149\pi$
$384$	−1.08986e6	+	320012.i	−0.0192476	+	0.00565161i
$385$	−2.47348e6	−	355632.i	−0.0433437	−	0.00623188i
$386$	2.95725e7	+	6.47546e7i	0.514192	+	1.12592i
$387$	−7.39432e6	+	1.06314e6i	−0.127575	+	0.0183425i
$388$	−1.90765e7	−	2.96835e7i	−0.326590	−	0.508183i
$389$	−5.79756e7	−	5.02361e7i	−0.984910	−	0.853429i	0.00429201	−	0.999991i	$-0.498634\pi$
$389$	−5.79756e7	−	5.02361e7i	−0.984910	−	0.853429i	−0.989202	+	0.146562i	$0.953179\pi$
$390$			1.62392e6i			0.0273760i
$391$	4.38735e7	+	3.23530e7i	0.733960	+	0.541232i
$392$	1.67776e7			0.278529
$393$	2.91354e7	−	3.36240e7i	0.480002	−	0.553952i
$394$	−2.39299e7	+	1.53788e7i	−0.391247	+	0.251439i
$395$	427769.	+	2.97520e6i	0.00694093	+	0.0482752i
$396$	−7.02240e6	+	3.20702e6i	−0.113084	+	0.0516436i
$397$	−3.60283e6	+	2.50582e7i	−0.0575801	+	0.400478i	0.940566	+	0.339612i	$0.110296\pi$
$397$	−3.60283e6	+	2.50582e7i	−0.0575801	+	0.400478i	−0.998146	+	0.0608669i	$0.980613\pi$
$398$	−6.97971e6	−	2.37707e7i	−0.110710	−	0.377045i
$399$	−2.10976e7	−	1.35586e7i	−0.332135	−	0.213450i
$400$	−1.15273e7	+	2.52414e7i	−0.180115	+	0.394396i
$401$	−3.77773e6	+	1.28658e7i	−0.0585865	+	0.199527i	−0.983586	−	0.180442i	$-0.942247\pi$
$401$	−3.77773e6	+	1.28658e7i	−0.0585865	+	0.199527i	0.924999	+	0.379969i	$0.124065\pi$
$402$	−1.68407e7	+	1.45925e7i	−0.259228	+	0.224622i
$403$	−4.42942e7	−	5.11182e7i	−0.676756	−	0.781018i
$404$	2.46399e7	+	7.23492e6i	0.373675	+	0.109721i
$405$	368397.	+	168241.i	0.00554563	+	0.00253260i
$406$	−1.10901e7	+	1.72565e7i	−0.165713	+	0.257855i
$407$	560449.	−	164563.i	0.00831291	−	0.00244089i
$408$	3.83703e7	+	5.51682e6i	0.564956	+	0.0812285i
$409$	3.77323e7	+	8.26222e7i	0.551497	+	1.20761i	0.956079	+	0.293109i	$0.0946898\pi$
$409$	3.77323e7	+	8.26222e7i	0.551497	+	1.20761i	−0.404582	+	0.914502i	$0.632583\pi$
$410$	106636.	−	15332.0i	0.00154723	−	0.000222457i
$411$	−65758.9	−	102323.i	−0.000947172	−	0.00147383i
$412$	−3.88785e7	−	3.36884e7i	−0.555927	−	0.481713i
$413$		−	3.26005e7i		−	0.462779i
$414$	−1.17261e6	+	1.82403e7i	−0.0165254	+	0.257057i
$415$	548517.			0.00767443
$416$	3.94352e7	−	4.55107e7i	0.547778	−	0.632169i
$417$	−4.58219e7	+	2.94480e7i	−0.631924	+	0.406113i
$418$	−5.89912e6	−	4.10293e7i	−0.0807716	−	0.561779i
$419$	9.30962e7	−	4.25156e7i	1.26558	−	0.577972i	0.334367	−	0.942443i	$-0.391478\pi$
$419$	9.30962e7	−	4.25156e7i	1.26558	−	0.577972i	0.931215	+	0.364471i	$0.118750\pi$
$420$	115987.	−	806704.i	0.00156552	−	0.0108885i
$421$	2.29941e7	+	7.83106e7i	0.308155	+	1.04948i	0.957367	+	0.288873i	$0.0932805\pi$
$421$	2.29941e7	+	7.83106e7i	0.308155	+	1.04948i	−0.649212	+	0.760607i	$0.724901\pi$
$422$	2.56090e7	+	1.64579e7i	0.340766	+	0.218997i
$423$	−7.66128e6	+	1.67759e7i	−0.101223	+	0.221648i
$424$	2.59330e7	−	8.83198e7i	0.340217	−	1.15867i
$425$	5.27473e7	−	4.57058e7i	0.687121	−	0.595394i
$426$	3.57369e7	+	4.12426e7i	0.462262	+	0.533479i
$427$	6.21741e7	+	1.82560e7i	0.798594	+	0.234488i
$428$	1.77869e6	+	812301.i	0.0226866	+	0.0103606i
$429$	−2.55155e7	+	3.97028e7i	−0.323170	+	0.502863i
$430$	1.25069e6	−	367237.i	0.0157306	−	0.00461892i
$431$	1.08350e8	+	1.55784e7i	1.35331	+	0.194577i	0.780523	−	0.625127i	$-0.214953\pi$
$431$	1.08350e8	+	1.55784e7i	1.35331	+	0.194577i	0.572788	+	0.819704i	$0.305862\pi$
$432$	2.80303e6	+	6.13778e6i	0.0347678	+	0.0761308i
$433$	6.65423e7	−	9.56734e6i	0.819661	−	0.117849i	0.280287	−	0.959916i	$-0.409570\pi$
$433$	6.65423e7	−	9.56734e6i	0.819661	−	0.117849i	0.539373	+	0.842067i	$0.318661\pi$
$434$	−2.72061e7	−	4.23335e7i	−0.332810	−	0.517863i
$435$	−906775.	−	785725.i	−0.0110162	−	0.00954559i
$436$			3.01321e6i			0.0363555i
$437$	6.21940e7	+	2.26883e7i	0.745254	+	0.271868i
$438$	−5.80596e7			−0.690958
$439$	8.86062e7	−	1.02257e8i	1.04730	−	1.20865i	0.0698324	−	0.997559i	$-0.477754\pi$
$439$	8.86062e7	−	1.02257e8i	1.04730	−	1.20865i	0.977467	−	0.211089i	$-0.0677010\pi$
$440$	3.94633e6	−	2.53615e6i	0.0463271	−	0.0297726i
$441$	−1.04535e6	−	7.27057e6i	−0.0121884	−	0.0847721i
$442$	6.19014e7	−	2.82694e7i	0.716859	−	0.327379i
$443$	−7.15063e6	+	4.97337e7i	−0.0822495	+	0.572058i	0.906469	+	0.422272i	$0.138767\pi$
$443$	−7.15063e6	+	4.97337e7i	−0.0822495	+	0.572058i	−0.988719	+	0.149785i	$0.952142\pi$
$444$	53670.8	+	182786.i	0.000613181	+	0.00208830i
$445$	−7.22549e6	−	4.64354e6i	−0.0819949	−	0.0526949i
$446$	−3.05077e7	+	6.68026e7i	−0.343879	+	0.752989i
$447$	1.30899e6	−	4.45800e6i	0.0146559	−	0.0499134i
$448$	5.93332e7	−	5.14125e7i	0.659878	−	0.571788i
$449$	1.01907e8	+	1.17607e8i	1.12581	+	1.29926i	0.949093	+	0.314995i	$0.102003\pi$
$449$	1.01907e8	+	1.17607e8i	1.12581	+	1.29926i	0.176719	+	0.984261i	$0.443452\pi$
$450$	2.24541e7	+	6.59312e6i	0.246410	+	0.0723524i
$451$	2.84803e6	+	1.30065e6i	0.0310467	+	0.0141785i
$452$	1.79871e7	−	2.79885e7i	0.194781	−	0.303085i
$453$	−3.25743e7	+	9.56468e6i	−0.350413	+	0.102891i
$454$	−8.06854e7	−	1.16008e7i	−0.862239	−	0.123971i
$455$	−2.06973e6	−	4.53208e6i	−0.0219725	−	0.0481131i
$456$	4.65993e7	−	6.69996e6i	0.491456	−	0.0706607i
$457$	−7.46595e7	−	1.16172e8i	−0.782234	−	1.21718i	−0.971915	−	0.235333i	$-0.924382\pi$
$457$	−7.46595e7	−	1.16172e8i	−0.782234	−	1.21718i	0.189681	−	0.981846i	$-0.439255\pi$
$458$	−6.17775e7	−	5.35305e7i	−0.643034	−	0.557192i
$459$		−	1.69715e7i		−	0.175502i
$460$	168932.	+	2.14480e6i	0.00173555	+	0.0220350i
$461$	−4.52428e7			−0.461793			−0.230896	−	0.972978i	$-0.574166\pi$
$461$	−4.52428e7			−0.461793			−0.230896	+	0.972978i	$0.574166\pi$
$462$	−2.29934e7	+	2.65358e7i	−0.233172	+	0.269095i
$463$	8.29603e7	−	5.33154e7i	0.835848	−	0.537167i	−0.0512831	−	0.998684i	$-0.516331\pi$
$463$	8.29603e7	−	5.33154e7i	0.835848	−	0.537167i	0.887131	+	0.461517i	$0.152695\pi$
$464$	−2.84490e6	−	1.97867e7i	−0.0284783	−	0.198071i
$465$	2.67743e6	−	1.22274e6i	0.0266293	−	0.0121612i
$466$	−1.50148e7	+	1.04430e8i	−0.148376	+	1.03198i
$467$	1.50944e7	+	5.14069e7i	0.148206	+	0.504744i	0.999811	−	0.0194405i	$-0.00618850\pi$
$467$	1.50944e7	+	5.14069e7i	0.148206	+	0.504744i	−0.851605	+	0.524184i	$0.824370\pi$
$468$	−1.29487e7	−	8.32165e6i	−0.126325	−	0.0811843i
$469$	2.84009e7	−	6.21893e7i	0.275305	−	0.602833i
$470$	906617.	−	3.08766e6i	0.00873234	−	0.0297396i
$471$	208043.	−	180270.i	0.00199109	−	0.00172529i
$472$	4.00763e7	+	4.62505e7i	0.381120	+	0.439836i
$473$	3.63481e7	+	1.06728e7i	0.343478	+	0.100854i
$474$	3.84173e7	+	1.75446e7i	0.360738	+	0.164744i
$475$	4.58263e7	−	7.13071e7i	0.427596	−	0.665353i
$476$	−3.27695e7	+	9.62201e6i	−0.303843	+	0.0892164i
$477$	−3.98892e7	−	5.73521e6i	−0.367537	−	0.0528438i
$478$	−1.77219e7	−	3.88055e7i	−0.162265	−	0.355312i
$479$	−1.67008e7	+	2.40122e6i	−0.151961	+	0.0218487i	−0.217875	−	0.975977i	$-0.569913\pi$
$479$	−1.67008e7	+	2.40122e6i	−0.151961	+	0.0218487i	0.0659146	+	0.997825i	$0.479004\pi$
$480$	1.41677e6	+	2.20453e6i	0.0128108	+	0.0199339i
$481$	880143.	+	762649.i	0.00790894	+	0.00685313i
$482$			7.01682e7i			0.626613i
$483$	−1.99752e7	−	5.24001e7i	−0.177276	−	0.465040i
$484$	−6.52470e6			−0.0575472
$485$	6.14705e6	−	7.09408e6i	0.0538817	−	0.0621828i
$486$	4.78718e6	−	3.07653e6i	0.0417033	−	0.0268011i
$487$	−6.75043e6	−	4.69503e7i	−0.0584447	−	0.406491i	−0.997952	−	0.0639634i	$-0.979626\pi$
$487$	−6.75043e6	−	4.69503e7i	−0.0584447	−	0.406491i	0.939508	−	0.342528i	$-0.111283\pi$
$488$	−1.10649e8	+	5.05319e7i	−0.952115	+	0.434816i
$489$	−1.54386e7	+	1.07378e8i	−0.132033	+	0.918307i
$490$	361091.	+	1.22976e6i	0.00306922	+	0.0104528i
$491$	−1.73888e7	−	1.11751e7i	−0.146901	−	0.0944074i	0.465126	−	0.885245i	$-0.346009\pi$
$491$	−1.73888e7	−	1.11751e7i	−0.146901	−	0.0944074i	−0.612027	+	0.790837i	$0.709645\pi$
$492$	−424197.	+	928862.i	−0.00356182	+	0.00779931i
$493$	−1.41654e7	+	4.82430e7i	−0.118220	+	0.402619i
$494$	6.24592e7	−	5.41212e7i	0.518102	−	0.448938i
$495$	−1.34492e6	−	1.55213e6i	−0.0110887	−	0.0127971i
$496$	4.70533e7	+	1.38161e7i	0.385607	+	0.113224i
$497$	−1.52301e8	−	6.95535e7i	−1.24061	−	0.566565i
$498$	4.16679e6	−	6.48365e6i	0.0337376	−	0.0524967i
$499$	−1.10537e8	+	3.24566e7i	−0.889625	+	0.261217i	−0.694441	−	0.719549i	$-0.744348\pi$
$499$	−1.10537e8	+	3.24566e7i	−0.889625	+	0.261217i	−0.195183	+	0.980767i	$0.562530\pi$
$500$	5.46133e6	+	785221.i	0.0436906	+	0.00628176i
$501$	−2.95561e6	−	6.47187e6i	−0.0235035	−	0.0514656i
$502$	2.48017e7	−	3.56595e6i	0.196052	−	0.0281880i
$503$	−2.74276e7	−	4.26782e7i	−0.215518	−	0.335353i	0.716615	−	0.697469i	$-0.245691\pi$
$503$	−2.74276e7	−	4.26782e7i	−0.215518	−	0.335353i	−0.932133	+	0.362116i	$0.882054\pi$
$504$	−3.01381e7	−	2.61148e7i	−0.235410	−	0.203984i
$505$			6.83166e6i			0.0530459i
$506$	4.38338e7	−	8.16685e7i	0.338344	−	0.630380i
$507$	−1.88545e7			−0.144674
$508$	−2.90312e7	+	3.35038e7i	−0.221449	+	0.255566i
$509$	−1.69946e8	+	1.09217e8i	−1.28871	+	0.828206i	−0.991936	−	0.126741i	$-0.959548\pi$
$509$	−1.69946e8	+	1.09217e8i	−1.28871	+	0.828206i	−0.296778	+	0.954947i	$0.595912\pi$
$510$	421443.	+	2.93120e6i	0.00317708	+	0.0220971i
$511$	1.62035e8	−	7.39988e7i	1.21435	−	0.554577i
$512$	−1.52186e7	+	1.05848e8i	−0.113388	+	0.788628i
$513$	−5.80687e6	−	1.97764e7i	−0.0430120	−	0.146485i
$514$	−2.03681e7	−	1.30898e7i	−0.149989	−	0.0963923i
$515$	5.68516e6	−	1.24488e7i	0.0416218	−	0.0911391i
$516$	−3.48083e6	+	1.18546e7i	−0.0253358	+	0.0862857i
$517$	7.06799e7	−	6.12445e7i	0.511475	−	0.443195i
$518$	567393.	+	654806.i	0.00408220	+	0.00471111i
$519$	1.08778e8	+	3.19402e7i	0.778109	+	0.228473i
$520$	8.50772e6	+	3.88534e6i	0.0605066	+	0.0276325i
$521$	−6.97214e7	+	1.08489e8i	−0.493007	+	0.767133i	−0.995225	−	0.0976076i	$-0.968881\pi$
$521$	−6.97214e7	+	1.08489e8i	−0.493007	+	0.767133i	0.502218	+	0.864741i	$0.332517\pi$
$522$	−1.61758e7	+	4.74965e6i	−0.113725	+	0.0333926i
$523$	−1.85424e8	−	2.66599e7i	−1.29616	−	0.186360i	−0.540513	−	0.841336i	$-0.681770\pi$
$523$	−1.85424e8	−	2.66599e7i	−1.29616	−	0.186360i	−0.755650	+	0.654975i	$0.772679\pi$
$524$	−3.05675e7	−	6.69334e7i	−0.212454	−	0.465210i
$525$	−7.10688e7	+	1.02182e7i	−0.491135	+	0.0706146i
$526$	−1.11863e8	−	1.74062e8i	−0.768648	−	1.19604i
$527$	−9.32184e7	−	8.07742e7i	−0.636898	−	0.551875i
$528$		−	3.42172e7i		−	0.232457i
$529$	8.18195e7	+	1.23370e8i	0.552701	+	0.833380i
$530$	7.03181e6			0.0472323
$531$	1.75457e7	−	2.02488e7i	0.117189	−	0.135243i
$532$	−3.48931e7	+	2.24244e7i	−0.231742	+	0.148931i
$533$	888404.	+	6.17899e6i	0.00586717	+	0.0408071i
$534$	−1.09776e8	+	5.01331e7i	−0.720916	+	0.329231i
$535$	−74031.1	+	514898.i	−0.000483451	+	0.00336248i
$536$	3.61578e7	+	1.23142e8i	0.234805	+	0.799673i
$537$	5.20633e7	+	3.34590e7i	0.336208	+	0.216068i
$538$	−2.34523e7	+	5.13535e7i	−0.150605	+	0.329779i
$539$	−1.04942e7	+	3.57398e7i	−0.0670165	+	0.228237i
$540$	506213.	−	438636.i	0.00321478	−	0.00278563i
$541$	−5.01338e6	−	5.78574e6i	−0.0316620	−	0.0365399i	0.739698	−	0.672939i	$-0.234968\pi$
$541$	−5.01338e6	−	5.78574e6i	−0.0316620	−	0.0365399i	−0.771360	+	0.636399i	$0.780423\pi$
$542$	−3.29787e7	−	9.68343e6i	−0.207127	−	0.0608179i
$543$	1.22259e8	+	5.58340e7i	0.763629	+	0.348738i
$544$	5.93704e7	−	9.23821e7i	0.368785	−	0.573840i
$545$	−769131.	+	225837.i	−0.00475128	+	0.00139510i
$546$	−6.92934e7	−	9.96288e6i	−0.425710	−	0.0612078i
$547$	6.04619e7	+	1.32393e8i	0.369419	+	0.808916i	0.999476	+	0.0323665i	$0.0103044\pi$
$547$	6.04619e7	+	1.32393e8i	0.369419	+	0.808916i	−0.630057	+	0.776549i	$0.716968\pi$
$548$	−199117.	+	28628.7i	−0.00120995	+	0.000173964i
$549$	2.87922e7	+	4.48015e7i	0.174003	+	0.270754i
$550$	−8.96872e7	−	7.77144e7i	−0.539066	−	0.467104i
$551$			6.10628e7i			0.365024i
$552$	9.27554e7	+	4.97845e7i	0.551470	+	0.295990i
$553$	−1.29578e8			−0.766222
$554$	1.00480e8	−	1.15960e8i	0.590948	−	0.681990i
$555$	−42634.1	+	27399.3i	−0.000249389	+	0.000160273i
$556$	1.28204e7	+	8.91678e7i	0.0745894	+	0.518781i
$557$	−2.60969e8	+	1.19181e8i	−1.51016	+	0.689669i	−0.986726	−	0.162395i	$-0.948078\pi$
$557$	−2.60969e8	+	1.19181e8i	−1.51016	+	0.689669i	−0.523438	+	0.852064i	$0.675351\pi$
$558$	5.88579e6	−	4.09366e7i	0.0338768	−	0.235618i
$559$	2.12793e7	+	7.24708e7i	0.121821	+	0.414885i
$560$	3.03885e6	+	1.95295e6i	0.0173039	+	0.0111206i
$561$	−3.57522e7	+	7.82863e7i	−0.202495	+	0.443402i
$562$	−6.75095e6	+	2.29916e7i	−0.0380326	+	0.129527i
$563$	2.35464e8	−	2.04031e8i	1.31947	−	1.14333i	0.340294	−	0.940319i	$-0.389473\pi$
$563$	2.35464e8	−	2.04031e8i	1.31947	−	1.14333i	0.979177	−	0.203009i	$-0.0650720\pi$
$564$	1.99744e7	+	2.30517e7i	0.111336	+	0.128489i
$565$	8.49227e6	+	2.49356e6i	0.0470846	+	0.0138253i
$566$	2.60906e7	+	1.19152e7i	0.143891	+	0.0657129i
$567$	−9.43909e6	+	1.46875e7i	−0.0517822	+	0.0805747i
$568$	3.01574e8	−	8.85501e7i	1.64569	−	0.483219i
$569$	−2.37406e8	−	3.41339e7i	−1.28871	−	0.185289i	−0.536325	−	0.844011i	$-0.680188\pi$
$569$	−2.37406e8	−	3.41339e7i	−1.28871	−	0.185289i	−0.752386	+	0.658723i	$0.771097\pi$
$570$	1.49401e6	+	3.27144e6i	0.00806734	+	0.0176650i
$571$	2.68787e7	−	3.86457e6i	0.144378	−	0.0207584i	−0.0697470	−	0.997565i	$-0.522219\pi$
$571$	2.68787e7	−	3.86457e6i	0.144378	−	0.0207584i	0.214125	+	0.976806i	$0.431310\pi$
$572$	4.21996e7	+	6.56639e7i	0.225486	+	0.350864i
$573$	−4.98171e7	−	4.31668e7i	−0.264798	−	0.229449i
$574$			4.64429e6i			0.0245575i
$575$	1.77105e8	−	6.75135e7i	0.931596	−	0.355130i
$576$	6.45235e7			0.337637
$577$	−1.24104e8	+	1.43223e8i	−0.646037	+	0.745567i	−0.980430	−	0.196867i	$-0.936923\pi$
$577$	−1.24104e8	+	1.43223e8i	−0.646037	+	0.745567i	0.334393	+	0.942434i	$0.391469\pi$
$578$	−2.11360e7	+	1.35833e7i	−0.109456	+	0.0703430i
$579$	−2.55459e7	−	1.77676e8i	−0.131609	−	0.915362i
$580$	−1.80506e6	+	824345.i	−0.00925142	+	0.00422498i
$581$	−3.36521e6	+	2.34055e7i	−0.0171587	+	0.119341i
$582$	−3.71584e7	−	1.26550e8i	−0.188490	−	0.641938i
$583$	1.71919e8	+	1.10486e8i	0.867599	+	0.557572i
$584$	−1.38912e8	+	3.04175e8i	−0.697431	+	1.52716i
$585$	1.15363e6	−	3.92891e6i	0.00576235	−	0.0196248i
$586$	−1.52269e8	+	1.31942e8i	−0.756691	+	0.655676i
$587$	−1.57654e8	−	1.81942e8i	−0.779453	−	0.899536i	0.217617	−	0.976034i	$-0.430172\pi$
$587$	−1.57654e8	−	1.81942e8i	−0.779453	−	0.899536i	−0.997070	+	0.0764979i	$0.975626\pi$
$588$	−1.16562e7	−	3.42258e6i	−0.0573359	−	0.0168353i
$589$	−1.36261e8	−	6.22285e7i	−0.666848	−	0.304539i
$590$	−2.52754e6	+	3.93293e6i	−0.0123067	+	0.0191496i
$591$	6.88211e7	−	2.02077e7i	0.333395	−	0.0978936i
$592$	−835762.	−	120164.i	−0.00402826	−	0.000579176i
$593$	2.42181e7	+	5.30303e7i	0.116139	+	0.254308i	0.958770	−	0.284182i	$-0.0917221\pi$
$593$	2.42181e7	+	5.30303e7i	0.116139	+	0.254308i	−0.842632	+	0.538490i	$0.818995\pi$
$594$	−2.85633e7	+	4.10678e6i	−0.136285	+	0.0195949i
$595$	−4.91209e6	−	7.64337e6i	−0.0233193	−	0.0362856i
$596$	−5.80739e6	−	5.03213e6i	−0.0274310	−	0.0237691i
$597$			6.24693e7i			0.293592i
$598$	1.84231e8	−	1.45107e7i	0.861509	−	0.0678555i
$599$	−2.96400e8			−1.37910			−0.689552	−	0.724236i	$-0.742193\pi$
$599$	−2.96400e8			−1.37910			−0.689552	+	0.724236i	$0.742193\pi$
$600$	8.82646e7	−	1.01863e8i	0.408632	−	0.471587i
$601$	−1.47834e8	+	9.50072e7i	−0.681007	+	0.437656i	−0.834878	−	0.550434i	$-0.814462\pi$
$601$	−1.47834e8	+	9.50072e7i	−0.681007	+	0.437656i	0.153872	+	0.988091i	$0.450826\pi$
$602$	7.99706e6	+	5.56208e7i	0.0366557	+	0.254946i
$603$	5.11109e7	−	2.33416e7i	0.233110	−	0.106458i
$604$	−7.99077e6	+	5.55770e7i	−0.0362642	+	0.252223i
$605$	−489020.	−	1.66545e6i	−0.00220831	−	0.00752082i
$606$	8.07524e7	+	5.18964e7i	0.362859	+	0.233195i
$607$	−1.12827e8	+	2.47057e8i	−0.504484	+	1.10467i	0.470502	+	0.882399i	$0.344073\pi$
$607$	−1.12827e8	+	2.47057e8i	−0.504484	+	1.10467i	−0.974986	+	0.222267i	$0.928654\pi$
$608$	3.75735e7	−	1.27964e8i	0.167175	−	0.569345i
$609$	3.90905e7	−	3.38721e7i	0.173069	−	0.149965i
$610$	−6.08531e6	−	7.02282e6i	−0.0268098	−	0.0309401i
$611$	1.78913e8	+	5.25335e7i	0.784363	+	0.230310i
$612$	−2.55324e7	−	1.16603e7i	−0.111388	−	0.0508691i
$613$	1.65578e8	−	2.57644e8i	0.718820	−	1.11851i	−0.269036	−	0.963130i	$-0.586705\pi$
$613$	1.65578e8	−	2.57644e8i	0.718820	−	1.11851i	0.987856	−	0.155375i	$-0.0496587\pi$
$614$	1.62424e8	−	4.76921e7i	0.701691	−	0.206035i
$615$	−268888.	−	38660.3i	−0.00115597	−	0.000166203i
$616$	8.40078e7	+	1.83951e8i	0.359399	+	0.786975i
$617$	3.89457e8	−	5.59955e7i	1.65808	−	0.238395i	0.751285	−	0.659977i	$-0.229434\pi$
$617$	3.89457e8	−	5.59955e7i	1.65808	−	0.238395i	0.906790	+	0.421582i	$0.138525\pi$
$618$	−1.03961e8	−	1.61767e8i	−0.440460	−	0.685369i
$619$	−1.49309e8	−	1.29377e8i	−0.629526	−	0.545488i	0.280597	−	0.959826i	$-0.409468\pi$
$619$	−1.49309e8	−	1.29377e8i	−0.629526	−	0.545488i	−0.910123	+	0.414338i	$0.864013\pi$
$620$		−	4.86808e6i		−	0.0204260i
$621$	1.57949e7	−	4.32975e7i	0.0659542	−	0.180796i
$622$	−2.38439e8			−0.990846
$623$	2.42471e8	−	2.79827e8i	1.00276	−	1.15724i
$624$	5.73922e7	−	3.68837e7i	0.236210	−	0.151803i
$625$	−3.44313e7	−	2.39475e8i	−0.141031	−	0.980891i
$626$	−1.28821e8	+	5.88307e7i	−0.525127	+	0.239817i
$627$	−1.48749e7	+	1.03457e8i	−0.0603464	+	0.419718i
$628$	−128268.	−	436840.i	−0.000517892	−	0.00176378i
$629$	1.78660e6	+	1.14818e6i	0.00717920	+	0.00461379i
$630$	1.26553e6	−	2.77112e6i	0.00506115	−	0.0110824i
$631$	−2.80514e6	+	9.55341e6i	−0.0111652	+	0.0380251i	−0.964887	−	0.262665i	$-0.915399\pi$
$631$	−2.80514e6	+	9.55341e6i	−0.0111652	+	0.0380251i	0.953722	+	0.300690i	$0.0972169\pi$
$632$	1.83833e8	−	1.59292e8i	0.728235	−	0.631020i
$633$	−5.02668e7	−	5.80110e7i	−0.198185	−	0.228718i
$634$	2.30170e8	+	6.75840e7i	0.903193	+	0.265202i
$635$	−1.07278e7	−	4.89923e6i	−0.0418977	−	0.0191340i
$636$	−3.60340e7	+	5.60701e7i	−0.140069	+	0.217951i
$637$	−7.12580e7	+	2.09232e7i	−0.275686	+	0.0809488i
$638$	8.46213e7	+	1.21667e7i	0.325850	+	0.0468502i
$639$	−5.71632e7	−	1.25170e8i	−0.219086	−	0.479731i
$640$	−494675.	+	71123.6i	−0.00188704	+	0.000271315i
$641$	5.46945e7	+	8.51064e7i	0.207668	+	0.323138i	0.929427	−	0.369007i	$-0.120302\pi$
$641$	5.46945e7	+	8.51064e7i	0.207668	+	0.323138i	−0.721758	+	0.692145i	$0.756666\pi$
$642$	5.52388e6	+	4.78647e6i	0.0208756	+	0.0180888i
$643$			2.39143e8i			0.899549i	0.893142	+	0.449774i	$0.148496\pi$
$643$			2.39143e8i			0.899549i	−0.893142	+	0.449774i	$0.851504\pi$
$644$	−9.25560e7	−	5.95013e6i	−0.346535	−	0.0222776i
$645$	−3.28682e6			−0.0122489
$646$	9.86945e7	−	1.13899e8i	0.366096	−	0.422498i
$647$	1.24365e8	−	7.99245e7i	0.459182	−	0.295099i	−0.290526	−	0.956867i	$-0.593830\pi$
$647$	1.24365e8	−	7.99245e7i	0.459182	−	0.295099i	0.749708	+	0.661769i	$0.230194\pi$
$648$	−4.66430e6	−	3.24409e7i	−0.0171420	−	0.119225i
$649$	−1.23591e8	+	5.64420e7i	−0.452118	+	0.206475i
$650$	3.36732e7	−	2.34202e8i	0.122615	−	0.852806i
$651$	3.57487e7	+	1.21749e8i	0.129574	+	0.441288i
$652$	1.50935e8	+	9.69999e7i	0.544561	+	0.349968i
$653$	3.27317e7	−	7.16724e7i	0.117552	−	0.257402i	−0.841705	−	0.539937i	$-0.818448\pi$
$653$	3.27317e7	−	7.16724e7i	0.117552	−	0.257402i	0.959257	+	0.282535i	$0.0911753\pi$
$654$	−3.17320e6	+	1.08069e7i	−0.0113440	+	0.0386340i
$655$	1.47940e7	−	1.28190e7i	0.0526454	−	0.0456175i
$656$	−2.96387e6	−	3.42049e6i	−0.0104990	−	0.0121165i
$657$	1.40470e8	+	4.12456e7i	0.495320	+	0.145439i
$658$	1.26190e8	+	5.76289e7i	0.442941	+	0.202285i
$659$	9.42424e7	−	1.46644e8i	0.329299	−	0.512399i	−0.636643	−	0.771159i	$-0.719677\pi$
$659$	9.42424e7	−	1.46644e8i	0.329299	−	0.512399i	0.965942	+	0.258760i	$0.0833138\pi$
$660$	−3.25909e6	+	956954.i	−0.0113361	+	0.00332858i
$661$	−5.19643e8	−	7.47134e7i	−1.79929	−	0.258699i	−0.840295	−	0.542129i	$-0.817618\pi$
$661$	−5.19643e8	−	7.47134e7i	−1.79929	−	0.258699i	−0.958993	+	0.283431i	$0.908527\pi$
$662$	1.06441e8	+	2.33073e8i	0.366888	+	0.803373i
$663$	−1.69847e8	+	2.44203e7i	−0.582797	+	0.0837936i
$664$	−2.39986e7	−	3.73425e7i	−0.0819749	−	0.127556i
$665$	−8.33910e6	−	7.22587e6i	−0.0283566	−	0.0245711i
$666$			712086.i			0.00241051i
$667$	−8.10370e7	+	1.09894e8i	−0.273090	+	0.370335i
$668$	−1.17671e7			−0.0394766
$669$	1.21267e8	−	1.39950e8i	0.405009	−	0.467405i
$670$	−8.24789e6	+	5.30059e6i	−0.0274232	+	0.0176238i
$671$	−3.84339e7	−	2.67314e8i	−0.127218	−	0.884818i
$672$	−1.02761e8	+	4.69292e7i	−0.338625	+	0.154645i
$673$	5.42107e7	−	3.77044e8i	0.177844	−	1.23693i	−0.683894	−	0.729581i	$-0.739715\pi$
$673$	5.42107e7	−	3.77044e8i	0.177844	−	1.23693i	0.861738	−	0.507353i	$-0.169376\pi$
$674$	1.07263e8	+	3.65304e8i	0.350324	+	1.19309i
$675$	−4.96417e7	−	3.19028e7i	−0.161412	−	0.103733i
$676$	−1.29539e7	+	2.83651e7i	−0.0419335	+	0.0918216i
$677$	1.42453e8	−	4.85152e8i	0.459100	−	1.56355i	−0.326736	−	0.945116i	$-0.605949\pi$
$677$	1.42453e8	−	4.85152e8i	0.459100	−	1.56355i	0.785836	−	0.618435i	$-0.212233\pi$
$678$	9.39859e7	−	8.14392e7i	0.301560	−	0.261303i
$679$	2.64995e8	+	3.05821e8i	0.846503	+	0.976917i
$680$	1.63649e7	+	4.80518e6i	0.0520461	+	0.0152821i
$681$	1.86969e8	+	8.53860e7i	0.592010	+	0.270362i
$682$	−1.13387e8	+	1.76433e8i	−0.357445	+	0.556196i
$683$	5.19968e8	−	1.52676e8i	1.63198	−	0.479192i	0.667777	−	0.744361i	$-0.267246\pi$
$683$	5.19968e8	−	1.52676e8i	1.63198	−	0.479192i	0.964202	+	0.265169i	$0.0854278\pi$
$684$	−3.37417e7	−	4.85132e6i	−0.105438	−	0.0151597i
$685$	−22231.2	−	48679.5i	−6.91656e−5	−	0.000151452i
$686$	−2.67548e8	+	3.84676e7i	−0.828762	+	0.119158i
$687$	1.11437e8	+	1.73399e8i	0.343682	+	0.534780i
$688$	−4.13856e7	−	3.58608e7i	−0.127082	−	0.110117i
$689$			4.07454e8i			1.24572i
$690$	−1.65280e6	+	7.87026e6i	−0.00503123	+	0.0239575i
$691$	−6.12008e8			−1.85491			−0.927456	−	0.373932i	$-0.878009\pi$
$691$	−6.12008e8			−1.85491			−0.927456	+	0.373932i	$0.878009\pi$
$692$	1.22788e8	−	1.41705e8i	0.370541	−	0.427627i
$693$	7.44812e7	−	4.78662e7i	0.223793	−	0.143823i
$694$	−1.65416e7	−	1.15049e8i	−0.0494879	−	0.344196i
$695$	−2.17995e7	+	9.95549e6i	−0.0649369	+	0.0296557i
$696$	−1.38184e7	+	9.61092e7i	−0.0409855	+	0.285061i
$697$	3.20718e6	+	1.09226e7i	0.00947163	+	0.0322574i
$698$	2.91767e8	+	1.87507e8i	0.857965	+	0.551380i
$699$	1.10514e8	−	2.41993e8i	0.323584	−	0.708550i
$700$	−3.34553e7	+	1.13938e8i	−0.0975372	+	0.332181i
$701$	1.93118e8	−	1.67337e8i	0.560619	−	0.485779i	−0.327841	−	0.944733i	$-0.606321\pi$
$701$	1.93118e8	−	1.67337e8i	0.560619	−	0.485779i	0.888460	+	0.458953i	$0.151776\pi$
$702$	−3.76774e7	−	4.34821e7i	−0.108911	−	0.125690i
$703$	2.47472e6	+	726644.i	0.00712296	+	0.00209149i
$704$	−2.97634e8	−	1.35925e8i	−0.853030	−	0.389566i
$705$	−4.38695e6	+	6.82622e6i	−0.0125197	+	0.0194811i
$706$	−4.85270e7	+	1.42488e7i	−0.137902	+	0.0404916i
$707$	−2.91510e8	−	4.19129e7i	−0.824889	−	0.118601i
$708$	−1.84081e7	−	4.03081e7i	−0.0518691	−	0.113578i
$709$	−9.93964e7	+	1.42910e7i	−0.278889	+	0.0400982i	−0.280340	−	0.959901i	$-0.590447\pi$
$709$	−9.93964e7	+	1.42910e7i	−0.278889	+	0.0400982i	0.00145081	+	0.999999i	$0.499538\pi$
$710$	1.29811e7	+	2.01990e7i	0.0362691	+	0.0564358i
$711$	−8.04833e7	−	6.97392e7i	−0.223922	−	0.194030i
$712$			6.95067e8i			1.92569i
$713$	−1.62643e8	−	2.92825e8i	−0.448711	−	0.807867i
$714$	−1.27662e8			−0.350724
$715$	−1.35981e7	+	1.56930e7i	−0.0372014	+	0.0429327i
$716$	8.61066e7	−	5.53374e7i	0.234584	−	0.150758i
$717$	1.53089e7	+	1.06476e8i	0.0415323	+	0.288864i
$718$	5.46311e7	−	2.49492e7i	0.147593	−	0.0674036i
$719$	−7.38946e7	+	5.13948e8i	−0.198804	+	1.38271i	0.608956	+	0.793204i	$0.291589\pi$
$719$	−7.38946e7	+	5.13948e8i	−0.198804	+	1.38271i	−0.807760	+	0.589511i	$0.799321\pi$
$720$	836406.	+	2.84854e6i	0.00224089	+	0.00763176i
$721$	4.96316e8	+	3.18963e8i	1.32420	+	0.851010i
$722$	−4.47862e7	+	9.80681e7i	−0.118996	+	0.260565i
$723$	4.98476e7	−	1.69765e8i	0.131895	−	0.449194i
$724$	1.67996e8	−	1.45570e8i	0.442674	−	0.383579i
$725$	1.14483e8	+	1.32120e8i	0.300418	+	0.346701i
$726$	−2.34010e7	−	6.87115e6i	−0.0611539	−	0.0179564i
$727$	−5.15538e8	−	2.35438e8i	−1.34171	−	0.612737i	−0.390304	−	0.920686i	$-0.627630\pi$
$727$	−5.15538e8	−	2.35438e8i	−1.34171	−	0.612737i	−0.951403	+	0.307949i	$0.900357\pi$
$728$	−2.17985e8	+	3.39192e8i	−0.564980	+	0.879126i
$729$	−1.37677e7	+	4.04255e6i	−0.0355368	+	0.0104345i
$730$	−2.52851e7	−	3.63545e6i	−0.0649975	−	0.00934523i
$731$	5.72175e7	+	1.25289e8i	0.146479	+	0.320745i
$732$	8.71822e7	−	1.25349e7i	0.222277	−	0.0319586i
$733$	−1.82693e8	−	2.84276e8i	−0.463885	−	0.721820i	0.527960	−	0.849269i	$-0.322957\pi$
$733$	−1.82693e8	−	2.84276e8i	−0.463885	−	0.721820i	−0.991845	+	0.127450i	$0.959321\pi$
$734$	5.25060e7	+	4.54967e7i	0.132776	+	0.115051i
$735$		−	3.23181e6i		−	0.00813925i
$736$	2.37442e8	−	1.80429e8i	0.595558	−	0.452558i
$737$	−2.84936e8			−0.711778
$738$	−2.49957e6	+	2.88466e6i	−0.00621866	+	0.00717672i
$739$	2.54054e8	−	1.63271e8i	0.629496	−	0.404553i	−0.186627	−	0.982431i	$-0.559756\pi$
$739$	2.54054e8	−	1.63271e8i	0.629496	−	0.404553i	0.816123	+	0.577878i	$0.196119\pi$
$740$	11928.5	+	82964.4i	2.94368e−5	+	0.000204737i
$741$	−1.89562e8	+	8.65699e7i	−0.465903	+	0.212771i
$742$	−4.31408e7	+	3.00051e8i	−0.105603	+	0.734485i
$743$	4.47186e7	+	1.52298e8i	0.109024	+	0.371301i	0.995873	−	0.0907578i	$-0.0289289\pi$
$743$	4.47186e7	+	1.52298e8i	0.109024	+	0.371301i	−0.886849	+	0.462059i	$0.847111\pi$
$744$	−2.00385e8	−	1.28780e8i	−0.486572	−	0.312701i
$745$	849209.	−	1.85951e6i	0.00205374	−	0.00449707i
$746$	−2.11598e7	+	7.20636e7i	−0.0509677	+	0.173580i
$747$	−1.46871e7	+	1.27265e7i	−0.0352351	+	0.0305314i
$748$	9.32125e7	+	1.07573e8i	0.222725	+	0.257039i
$749$	−2.15168e7	−	6.31789e6i	−0.0512073	−	0.0150358i
$750$	1.87603e7	+	8.56752e6i	0.0444688	+	0.0203082i
$751$	1.65016e8	−	2.56771e8i	0.389590	−	0.606213i	−0.589956	−	0.807435i	$-0.700855\pi$
$751$	1.65016e8	−	2.56771e8i	0.389590	−	0.606213i	0.979546	+	0.201222i	$0.0644913\pi$
$752$	−1.29715e8	+	3.80878e7i	−0.305027	+	0.0895639i
$753$	−6.25387e7	−	8.99170e6i	−0.146475	−	0.0210599i
$754$	7.08087e7	+	1.55049e8i	0.165186	+	0.361706i
$755$	−1.47851e7	+	2.12578e6i	−0.0343545	+	0.00493943i
$756$	1.56112e7	+	2.42914e7i	0.0361301	+	0.0562196i
$757$	−4.24775e8	−	3.68069e8i	−0.979199	−	0.848481i	0.00926190	−	0.999957i	$-0.497052\pi$
$757$	−4.24775e8	−	3.68069e8i	−0.979199	−	0.848481i	−0.988461	+	0.151476i	$0.951597\pi$
$758$		−	5.27169e8i		−	1.21044i
$759$	−1.64069e8	+	1.66449e8i	−0.375233	+	0.380677i
$760$	2.07136e7			0.0471863
$761$	−1.15262e8	+	1.33019e8i	−0.261535	+	0.301828i	−0.871296	−	0.490758i	$-0.836720\pi$
$761$	−1.15262e8	+	1.33019e8i	−0.261535	+	0.301828i	0.609761	+	0.792586i	$0.291266\pi$
$762$	−1.39404e8	+	8.95894e7i	−0.315072	+	0.202485i
$763$	−4.91790e6	−	3.42047e7i	−0.0110715	−	0.0770039i
$764$	−9.91680e7	+	4.52885e7i	−0.222378	+	0.101557i
$765$	1.06269e6	−	7.39116e6i	0.00237368	−	0.0165093i
$766$	1.13870e8	+	3.87804e8i	0.253350	+	0.862832i
$767$	−2.27892e8	−	1.46457e8i	−0.505059	−	0.324582i
$768$	1.07130e8	−	2.34581e8i	0.236497	−	0.517856i
$769$	2.61356e7	−	8.90095e7i	0.0574715	−	0.195730i	−0.925753	−	0.378128i	$-0.876568\pi$
$769$	2.61356e7	−	8.90095e7i	0.0574715	−	0.195730i	0.983225	+	0.182398i	$0.0583860\pi$
$770$	−1.16752e7	+	1.01167e7i	−0.0255737	+	0.0221597i
$771$	3.99796e7	+	4.61389e7i	0.0872318	+	0.100671i
$772$	−2.84852e8	−	8.36399e7i	−0.619108	−	0.181787i
$773$	7.87923e7	+	3.59833e7i	0.170587	+	0.0779044i	0.498878	−	0.866672i	$-0.333746\pi$
$773$	7.87923e7	+	3.59833e7i	0.170587	+	0.0779044i	−0.328291	+	0.944577i	$0.606473\pi$
$774$	−2.49682e7	+	3.88512e7i	−0.0538473	+	0.0837880i
$775$	−4.11495e8	+	1.20826e8i	−0.884014	+	0.259570i
$776$	−7.51902e8	−	1.08107e8i	−1.60907	−	0.231350i
$777$	−907576.	−	1.98732e6i	−0.00193473	−	0.00423647i
$778$	−4.69419e8	+	6.74923e7i	−0.996832	+	0.143323i
$779$	7.47443e6	+	1.16304e7i	0.0158112	+	0.0246028i
$780$	−5.11815e6	−	4.43490e6i	−0.0107852	−	0.00934545i
$781$			6.97804e8i			1.46481i
$782$	3.28776e8	−	7.40044e7i	0.687511	−	0.154752i
$783$	4.25099e7			0.0885534
$784$	3.52607e7	−	4.06930e7i	0.0731716	−	0.0844446i
$785$	101891.	−	65481.5i	0.000210634	−	0.000135366i
$786$	−3.91434e7	−	2.72249e8i	−0.0806105	−	0.560658i
$787$	6.24859e8	−	2.85364e8i	1.28191	−	0.585429i	0.346188	−	0.938165i	$-0.387476\pi$
$787$	6.24859e8	−	2.85364e8i	1.28191	−	0.585429i	0.935723	+	0.352736i	$0.114749\pi$
$788$	1.68824e7	−	1.17420e8i	0.0345029	−	0.239973i
$789$	1.46987e8	+	5.00592e8i	0.299260	+	1.01919i
$790$	1.56323e7	+	1.00463e7i	0.0317060	+	0.0203762i
$791$	−1.58502e8	+	3.47072e8i	−0.320263	+	0.701277i
$792$	−4.68244e7	+	1.59469e8i	−0.0942533	+	0.320997i
$793$	4.06934e8	−	3.52610e8i	0.816026	−	0.707091i
$794$	1.02490e8	+	1.18279e8i	0.204747	+	0.236291i
$795$	−1.70128e7	−	4.99540e6i	−0.0338590	−	0.00994189i
$796$	9.39805e7	+	4.29194e7i	0.186337	+	0.0850971i
$797$	1.36336e8	−	2.12142e8i	0.269299	−	0.419037i	−0.680096	−	0.733123i	$-0.738062\pi$
$797$	1.36336e8	−	2.12142e8i	0.269299	−	0.419037i	0.949394	+	0.314086i	$0.101698\pi$
$798$	−1.48760e8	+	4.36798e7i	−0.292737	+	0.0859552i
$799$	3.36575e8	+	4.83921e7i	0.659844	+	0.0948712i
$800$	−1.58614e8	−	3.47317e8i	−0.309793	−	0.678353i
$801$	3.01208e8	−	4.33071e7i	0.586095	−	0.0842678i
$802$	4.48167e7	+	6.97361e7i	0.0868793	+	0.135187i
$803$	−5.61070e8	−	4.86170e8i	−1.08360	−	0.938948i
$804$		−	9.29294e7i		−	0.178807i
$805$	−5.41820e6	−	2.40712e7i	−0.0103865	−	0.0461434i
$806$	−4.18153e8			−0.798601
$807$	9.32222e7	−	1.07584e8i	0.177378	−	0.204705i
$808$	4.65092e8	−	2.98897e8i	0.881668	−	0.566614i
$809$	6.69245e7	+	4.65470e8i	0.126398	+	0.879116i	0.950067	+	0.312045i	$0.101014\pi$
$809$	6.69245e7	+	4.65470e8i	0.126398	+	0.879116i	−0.823669	+	0.567070i	$0.808077\pi$
$810$	2.27747e6	−	1.04009e6i	0.00428546	−	0.00195710i
$811$	−5.72106e7	+	3.97908e8i	−0.107254	+	0.745968i	0.863231	+	0.504808i	$0.168437\pi$
$811$	−5.72106e7	+	3.97908e8i	−0.107254	+	0.745968i	−0.970485	+	0.241160i	$0.922472\pi$
$812$	−2.41010e7	−	8.20805e7i	−0.0450160	−	0.153310i
$813$	7.29097e7	+	4.68562e7i	0.135679	+	0.0871958i
$814$	1.50008e6	−	3.28471e6i	0.00278125	−	0.00609009i
$815$	−1.34471e7	+	4.57966e7i	−0.0248402	+	0.0845981i
$816$	9.40220e7	−	8.14705e7i	0.173045	−	0.149944i
$817$	1.09542e8	+	1.26418e8i	0.200869	+	0.231815i
$818$	5.38778e8	+	1.58199e8i	0.984351	+	0.289031i
$819$	1.60571e8	+	7.33303e7i	0.292291	+	0.133485i
$820$	−242901.	+	377961.i	−0.000440542	+	0.000685496i
$821$	−6.53750e7	+	1.91958e7i	−0.118136	+	0.0346879i	−0.340266	−	0.940329i	$-0.610517\pi$
$821$	−6.53750e7	+	1.91958e7i	−0.118136	+	0.0346879i	0.222130	+	0.975017i	$0.428699\pi$
$822$	−744285.	−	107012.i	−0.00134006	−	0.000192671i
$823$	−2.49403e8	−	5.46117e8i	−0.447407	−	0.979684i	−0.990179	−	0.139804i	$-0.955353\pi$
$823$	−2.49403e8	−	5.46117e8i	−0.447407	−	0.979684i	0.542773	−	0.839880i	$-0.317375\pi$
$824$	−1.09624e9	+	1.57615e8i	−1.95940	+	0.281719i
$825$	1.61781e8	+	2.51736e8i	0.288115	+	0.448316i
$826$	−1.52314e8	−	1.31980e8i	−0.270270	−	0.234191i
$827$			5.77814e8i			1.02158i	0.859706	+	0.510789i	$0.170647\pi$
$827$			5.77814e8i			1.02158i	−0.859706	+	0.510789i	$0.829353\pi$
$828$	−5.42860e7	−	5.35097e7i	−0.0956307	−	0.0942631i
$829$	−5.22247e8			−0.916668			−0.458334	−	0.888780i	$-0.651554\pi$
$829$	−5.22247e8			−0.916668			−0.458334	+	0.888780i	$0.651554\pi$
$830$	2.22063e6	−	2.56274e6i	0.00388366	−	0.00448199i
$831$	−3.25479e8	+	2.09173e8i	−0.567179	+	0.364504i
$832$	−9.28427e7	−	6.45735e8i	−0.161205	−	1.12120i
$833$	−1.23192e8	+	5.62600e7i	−0.213132	+	0.0973340i
$834$	−4.79218e7	+	3.33304e8i	−0.0826105	+	0.574568i
$835$	−881933.	−	3.00359e6i	−0.00151487	−	0.00515918i
$836$	1.45424e8	+	9.34582e7i	0.248895	+	0.159955i
$837$	−4.33215e7	+	9.48608e7i	−0.0738800	+	0.161775i
$838$	1.78254e8	−	6.07079e8i	0.302906	−	1.03160i
$839$	−2.74842e8	+	2.38152e8i	−0.465369	+	0.403244i	−0.855734	−	0.517416i	$-0.826894\pi$
$839$	−2.74842e8	+	2.38152e8i	−0.465369	+	0.403244i	0.390366	+	0.920660i	$0.372349\pi$
$840$	−1.14900e7	−	1.32602e7i	−0.0193858	−	0.0223724i
$841$	4.49891e8	+	1.32100e8i	0.756343	+	0.222082i
$842$	4.58967e8	+	2.09603e8i	0.768856	+	0.351125i
$843$	3.26665e7	−	5.08301e7i	0.0545281	−	0.0848473i
$844$	−1.21809e8	+	3.57664e7i	−0.202606	+	0.0594905i
$845$	−8.21118e6	−	1.18059e6i	−0.0136093	−	0.00195672i
$846$	4.73629e7	+	1.03710e8i	0.0782217	+	0.171282i
$847$	7.40658e7	−	1.06491e7i	0.121890	−	0.0175251i
$848$	−1.59712e8	−	2.48517e8i	−0.261909	−	0.407538i
$849$	−5.46590e7	−	4.73623e7i	−0.0893180	−	0.0773945i
$850$		−	4.31478e8i		−	0.702591i
$851$	3.48937e6	+	4.59196e6i	0.00566186	+	0.00745090i
$852$	−2.27583e8			−0.367977
$853$	6.64293e8	−	7.66635e8i	1.07032	−	1.23521i	0.0995891	−	0.995029i	$-0.468247\pi$
$853$	6.64293e8	−	7.66635e8i	1.07032	−	1.23521i	0.970728	−	0.240183i	$-0.0772074\pi$
$854$	3.37001e8	−	2.16578e8i	0.541076	−	0.347728i
$855$	−1.29059e6	−	8.97627e6i	−0.00206486	−	0.0143614i
$856$	3.82927e7	−	1.74877e7i	0.0610513	−	0.0278812i
$857$	4.76362e7	−	3.31317e8i	0.0756823	−	0.526382i	−0.916348	−	0.400383i	$-0.868877\pi$
$857$	4.76362e7	−	3.31317e8i	0.0756823	−	0.526382i	0.992030	−	0.125999i	$-0.0402137\pi$
$858$	8.21993e7	+	2.79945e8i	0.130139	+	0.443212i
$859$	−2.67994e8	−	1.72229e8i	−0.422810	−	0.271724i	0.311886	−	0.950119i	$-0.399039\pi$
$859$	−2.67994e8	−	1.72229e8i	−0.422810	−	0.271724i	−0.734697	+	0.678396i	$0.762676\pi$
$860$	−2.25820e6	+	4.94477e6i	−0.00355032	+	0.00777412i
$861$	3.29931e6	−	1.12364e7i	0.00516908	−	0.0176043i
$862$	5.11431e8	−	4.43158e8i	0.798483	−	0.691889i
$863$	9.87504e7	+	1.13964e8i	0.153641	+	0.177311i	0.827352	−	0.561684i	$-0.189846\pi$
$863$	9.87504e7	+	1.13964e8i	0.153641	+	0.177311i	−0.673711	+	0.738995i	$0.735301\pi$
$864$	−8.90841e7	−	2.61575e7i	−0.138121	−	0.0405559i
$865$	4.53734e7	+	2.07213e7i	0.0701056	+	0.0320161i
$866$	2.24692e8	−	3.49627e8i	0.345966	−	0.538333i
$867$	6.07860e7	−	1.78484e7i	0.0932710	−	0.0273868i
$868$	2.07723e8	+	2.98661e7i	0.317633	+	0.0456688i
$869$	2.24341e8	+	4.91238e8i	0.341861	+	0.748571i
$870$	−7.34202e6	+	1.05562e6i	−0.0111496	+	0.00160306i
$871$	−3.07140e8	−	4.77919e8i	−0.464817	−	0.723270i
$872$	4.90256e7	+	4.24809e7i	0.0739389	+	0.0640684i
$873$			3.32573e8i			0.499855i
$874$	3.57791e8	−	1.98727e8i	0.535913	−	0.297661i
$875$	−6.32764e7			−0.0944534
$876$	1.58560e8	−	1.82988e8i	0.235875	−	0.272214i
$877$	1.07204e9	−	6.88956e8i	1.58932	−	1.02139i	0.617228	−	0.786785i	$-0.288256\pi$
$877$	1.07204e9	−	6.88956e8i	1.58932	−	1.02139i	0.972090	−	0.234608i	$-0.0753806\pi$
$878$	−1.19043e8	−	8.27959e8i	−0.175881	−	1.22328i
$879$	4.62131e8	−	2.11048e8i	0.680454	−	0.310753i
$880$	2.14254e6	−	1.49017e7i	0.00314399	−	0.0218669i
$881$	3.56144e8	+	1.21291e9i	0.520832	+	1.77379i	0.626535	+	0.779393i	$0.284473\pi$
$881$	3.56144e8	+	1.21291e9i	0.520832	+	1.77379i	−0.105703	+	0.994398i	$0.533709\pi$
$882$	−3.82011e7	−	2.45503e7i	−0.0556762	−	0.0357809i
$883$	−4.21661e8	+	9.23309e8i	−0.612465	+	1.34111i	0.308409	+	0.951254i	$0.400203\pi$
$883$	−4.21661e8	+	9.23309e8i	−0.612465	+	1.34111i	−0.920875	+	0.389858i	$0.872524\pi$
$884$	−7.99546e7	+	2.72300e8i	−0.115741	+	0.394177i
$885$	8.90910e6	−	7.71978e6i	0.0128530	−	0.0111372i
$886$	2.03414e8	+	2.34752e8i	0.292468	+	0.337526i
$887$	1.00931e9	+	2.96359e8i	1.44628	+	0.424666i	0.908310	−	0.418297i	$-0.137373\pi$
$887$	1.00931e9	+	2.96359e8i	1.44628	+	0.424666i	0.537971	+	0.842963i	$0.319191\pi$
$888$	3.73063e6	+	1.70372e6i	0.00532774	+	0.00243310i
$889$	2.74869e8	−	4.27704e8i	0.391219	−	0.608749i
$890$	−5.09470e7	+	1.49594e7i	−0.0722684	+	0.0212199i
$891$	7.20236e7	+	1.03554e7i	0.101822	+	0.0146398i
$892$	−1.27228e8	−	2.78590e8i	−0.179261	−	0.392528i
$893$	4.08757e8	−	5.87704e7i	0.573998	−	0.0825285i
$894$	−1.55290e7	−	2.41636e7i	−0.0217336	−	0.0338181i
$895$	2.05786e7	+	1.78315e7i	0.0287043	+	0.0248725i
$896$		−	2.15444e7i		−	0.0299509i
$897$	−4.56038e8	−	9.57709e7i	−0.631865	−	0.132695i
$898$	9.62039e8			1.32851
$899$	2.02321e8	−	2.33491e8i	0.278460	−	0.321360i
$900$	−8.21017e7	+	5.27635e7i	−0.112622	+	0.0723780i
$901$	1.05744e8	+	7.35464e8i	0.144571	+	1.00551i
$902$	1.76069e7	−	8.04078e6i	0.0239918	−	0.0109567i
$903$	2.01649e7	−	1.40250e8i	0.0273863	−	0.190476i
$904$	−2.01793e8	−	6.87243e8i	−0.273149	−	0.930261i
$905$	4.97482e7	+	3.19712e7i	0.0671169	+	0.0431334i
$906$	−8.71871e7	+	1.90913e8i	−0.117238	+	0.256715i
$907$	−3.33352e8	+	1.13529e9i	−0.446767	+	1.52155i	0.361296	+	0.932451i	$0.382334\pi$
$907$	−3.33352e8	+	1.13529e9i	−0.446767	+	1.52155i	−0.808063	+	0.589096i	$0.799484\pi$
$908$	2.56914e8	−	2.22617e8i	0.343186	−	0.297373i
$909$	−1.58505e8	−	1.82925e8i	−0.211034	−	0.243546i
$910$	−2.95536e7	−	8.67773e6i	−0.0392181	−	0.0115155i
$911$	3.93643e8	+	1.79771e8i	0.520652	+	0.237774i	0.658366	−	0.752698i	$-0.271248\pi$
$911$	3.93643e8	+	1.79771e8i	0.520652	+	0.237774i	−0.137713	+	0.990472i	$0.543975\pi$
$912$	8.16853e7	−	1.27105e8i	0.107686	−	0.167563i
$913$	9.45583e7	−	2.77648e7i	0.124247	−	0.0364823i
$914$	−8.45026e8	−	1.21496e8i	−1.10670	−	0.159120i
$915$	9.73380e6	+	2.13140e7i	0.0127063	+	0.0278229i
$916$	3.37428e8	−	4.85148e7i	0.439030	−	0.0631230i
$917$	4.56233e8	+	7.09912e8i	0.591668	+	0.920654i
$918$	−7.92932e7	−	6.87079e7i	−0.102496	−	0.0888135i
$919$			9.20831e8i			1.18641i	0.805053	+	0.593203i	$0.202137\pi$
$919$			9.20831e8i			1.18641i	−0.805053	+	0.593203i	$0.797863\pi$
$920$	3.72780e7	+	2.74893e7i	0.0478728	+	0.0353020i
$921$	−4.26850e8			−0.546383
$922$	−1.83162e8	+	2.11380e8i	−0.233691	+	0.269694i
$923$	−1.17042e9	+	7.52183e8i	−1.48846	+	0.956574i
$924$	−2.08389e7	−	1.44938e8i	−0.0264155	−	0.183724i
$925$	6.71685e6	−	3.06748e6i	0.00848673	−	0.00387576i
$926$	8.67622e7	−	6.03444e8i	0.109269	−	0.759984i
$927$	1.36605e8	+	4.65234e8i	0.171485	+	0.584026i
$928$	2.31397e8	+	1.48710e8i	0.289543	+	0.186078i
$929$	1.78995e8	−	3.91944e8i	0.223251	−	0.488851i	−0.764552	−	0.644562i	$-0.777040\pi$
$929$	1.78995e8	−	3.91944e8i	0.223251	−	0.488851i	0.987803	+	0.155711i	$0.0497669\pi$
$930$	5.12656e6	−	1.74595e7i	0.00637349	−	0.0217061i
$931$	−1.24302e8	+	1.07708e8i	−0.154039	+	0.133475i
$932$	−2.88131e8	−	3.32521e8i	−0.355912	−	0.410745i
$933$	5.76880e8	+	1.69387e8i	0.710298	+	0.208562i
$934$	3.01288e8	+	1.37594e8i	0.369778	+	0.168872i
$935$	−2.04721e7	+	3.18553e7i	−0.0250454	+	0.0389714i
$936$	−3.17949e8	+	9.33584e7i	−0.387731	+	0.113848i
$937$	−4.40211e8	−	6.32928e7i	−0.535109	−	0.0769371i	−0.130537	−	0.991443i	$-0.541670\pi$
$937$	−4.40211e8	−	6.32928e7i	−0.535109	−	0.0769371i	−0.404572	+	0.914506i	$0.632579\pi$
$938$	−1.75578e8	−	3.84461e8i	−0.212746	−	0.465848i
$939$	3.53464e8	−	5.08204e7i	0.426921	−	0.0613820i
$940$	7.25550e6	+	1.12898e7i	0.00873542	+	0.0135926i
$941$	8.99938e8	+	7.79801e8i	1.08005	+	0.935869i	0.998152	−	0.0607721i	$-0.0193563\pi$
$941$	8.99938e8	+	7.79801e8i	1.08005	+	0.935869i	0.0818983	+	0.996641i	$0.473902\pi$
$942$		−	1.70182e6i		−	0.00203592i
$943$	−1.98328e6	+	3.08505e7i	−0.00236510	+	0.0367898i
$944$	1.96405e8			0.233472
$945$	−5.03042e6	+	5.80542e6i	−0.00596086	+	0.00687920i
$946$	1.97017e8	−	1.26615e8i	0.232718	−	0.149559i
$947$	−8.84498e7	−	6.15182e8i	−0.104147	−	0.724359i	−0.973254	−	0.229734i	$-0.926214\pi$
$947$	−8.84498e7	−	6.15182e8i	−0.104147	−	0.724359i	0.869106	−	0.494625i	$-0.164695\pi$
$948$	−1.60213e8	+	7.31670e7i	−0.188050	+	0.0858796i
$949$	2.10654e8	−	1.46513e9i	0.246474	−	1.71427i
$950$	−1.47632e8	−	5.02787e8i	−0.172190	−	0.586427i
$951$	−5.08862e8	−	3.27026e8i	−0.591641	−	0.380225i
$952$	−3.05440e8	+	6.68821e8i	−0.354010	+	0.775173i
$953$	3.80105e8	−	1.29452e9i	0.439163	−	1.49565i	−0.381571	−	0.924339i	$-0.624617\pi$
$953$	3.80105e8	−	1.29452e9i	0.439163	−	1.49565i	0.820734	−	0.571311i	$-0.193565\pi$
$954$	−1.88284e8	+	1.63149e8i	−0.216855	+	0.187906i
$955$	−1.89926e7	−	2.19186e7i	−0.0218059	−	0.0251653i
$956$	1.70703e8	+	5.01229e7i	0.195374	+	0.0573670i
$957$	−1.96090e8	−	8.95512e7i	−0.223727	−	0.102173i
$958$	−5.63932e7	+	8.77495e7i	−0.0641402	+	0.0998041i
$959$	2.21357e6	−	649962.i	0.00250979	−	0.000736940i
$960$	2.81002e7	+	4.04019e6i	0.0317611	+	0.00456655i
$961$	−5.38309e7	−	1.17873e8i	−0.0606543	−	0.132814i
$962$	7.12638e6	−	1.02462e6i	0.00800468	−	0.00115090i
$963$	−9.96418e6	−	1.55046e7i	−0.0111574	−	0.0173612i
$964$	−2.21152e8	−	1.91629e8i	−0.246865	−	0.213909i
$965$		−	7.89779e7i		−	0.0878869i
$966$	−3.25688e8	−	1.18811e8i	−0.361302	−	0.131803i
$967$	1.31034e8			0.144912			0.0724561	−	0.997372i	$-0.476916\pi$
$967$	1.31034e8			0.144912			0.0724561	+	0.997372i	$0.476916\pi$
$968$	−9.19867e7	+	1.06158e8i	−0.101414	+	0.117038i
$969$	−3.19696e8	+	2.05456e8i	−0.351371	+	0.225812i
$970$	−8.25857e6	−	5.74396e7i	−0.00904877	−	0.0629356i
$971$	−7.51909e8	+	3.43385e8i	−0.821311	+	0.375080i	−0.781328	−	0.624120i	$-0.785458\pi$
$971$	−7.51909e8	+	3.43385e8i	−0.821311	+	0.375080i	−0.0399827	+	0.999200i	$0.512730\pi$
$972$	−3.37734e6	+	2.34899e7i	−0.00367769	+	0.0255789i
$973$	−2.91064e8	−	9.91273e8i	−0.315973	−	1.07611i
$974$	−2.46686e8	−	1.58536e8i	−0.266974	−	0.171574i
$975$	−2.47846e8	+	5.42707e8i	−0.267404	+	0.585534i
$976$	−1.09985e8	+	3.74574e8i	−0.118300	+	0.402892i
$977$	9.95517e7	−	8.62621e7i	0.106749	−	0.0924988i	−0.599851	−	0.800112i	$-0.704773\pi$
$977$	9.95517e7	−	8.62621e7i	0.106749	−	0.0924988i	0.706600	+	0.707613i	$0.250228\pi$
$978$	4.39181e8	+	5.06841e8i	0.469490	+	0.541821i
$979$	−1.48064e9	−	4.34755e8i	−1.57798	−	0.463337i
$980$	−4.86202e6	−	2.22041e6i	−0.00516581	−	0.00235915i
$981$	1.53545e7	−	2.38921e7i	0.0162641	−	0.0253074i
$982$	−1.22608e8	+	3.60011e7i	−0.129475	+	0.0380173i
$983$	−1.05852e9	−	1.52192e8i	−1.11439	−	0.160226i	−0.439573	−	0.898207i	$-0.644870\pi$
$983$	−1.05852e9	−	1.52192e8i	−1.11439	−	0.160226i	−0.674821	+	0.737981i	$0.735779\pi$
$984$	9.13236e6	+	1.99971e7i	0.00958513	+	0.0209885i
$985$	3.12371e7	−	4.49122e6i	0.0326860	−	0.00469954i
$986$	1.68050e8	+	2.61491e8i	0.175310	+	0.272788i
$987$	−2.64364e8	−	2.29073e8i	−0.274948	−	0.238244i
$988$			3.44659e8i			0.357371i
$989$	2.93698e7	+	3.72885e8i	0.0303607	+	0.385466i
$990$	−1.26965e7			−0.0130852
$991$	−1.18364e9	+	1.36599e9i	−1.21618	+	1.40355i	−0.327605	+	0.944815i	$0.606242\pi$
$991$	−1.18364e9	+	1.36599e9i	−1.21618	+	1.40355i	−0.888575	+	0.458732i	$0.848304\pi$
$992$	−5.67659e8	+	3.64813e8i	−0.581504	+	0.373710i
$993$	−9.19479e7	−	6.39512e8i	−0.0939062	−	0.653132i
$994$	−9.41542e8	+	4.29988e8i	−0.958695	+	0.437821i
$995$	−3.91157e6	+	2.72056e7i	−0.00397084	+	0.0276178i
$996$	9.05527e6	+	3.08394e7i	0.00916481	+	0.0312125i
$997$	2.97015e8	+	1.90880e8i	0.299704	+	0.192608i	0.681846	−	0.731495i	$-0.261177\pi$
$997$	2.97015e8	+	1.90880e8i	0.299704	+	0.192608i	−0.382142	+	0.924103i	$0.624814\pi$
$998$	−2.95860e8	+	6.47842e8i	−0.297642	+	0.651745i
$999$	505866.	−	1.72282e6i	0.000507387	−	0.00172800i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.f.a.7.17	✓	240
23.10	odd	22	inner	69.7.f.a.10.17	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.f.a.7.17	✓	240	1.1	even	1	trivial
69.7.f.a.10.17	yes	240	23.10	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(4.04842 - 4.67213i) q^{2} +(-13.1138 + 8.42776i) q^{3} +(3.66909 + 25.5191i) q^{4} +(-6.23883 + 2.84918i) q^{5} +(-13.7148 + 95.3887i) q^{6} +(-83.3001 - 283.694i) q^{7} +(466.929 + 300.077i) q^{8} +(100.946 - 221.041i) q^{9} +O(q^{10})\)	\(q+(4.04842 - 4.67213i) q^{2} +(-13.1138 + 8.42776i) q^{3} +(3.66909 + 25.5191i) q^{4} +(-6.23883 + 2.84918i) q^{5} +(-13.7148 + 95.3887i) q^{6} +(-83.3001 - 283.694i) q^{7} +(466.929 + 300.077i) q^{8} +(100.946 - 221.041i) q^{9} +(-11.9457 + 40.6833i) q^{10} +(-931.286 + 806.964i) q^{11} +(-263.185 - 303.731i) q^{12} +(-2357.37 - 692.187i) q^{13} +(-1662.69 - 759.325i) q^{14} +(57.8029 - 89.9430i) q^{15} +(1709.14 - 501.850i) q^{16} +(-4434.74 - 637.620i) q^{17} +(-624.058 - 1366.50i) q^{18} +(-5385.82 + 774.365i) q^{19} +(-95.5993 - 148.755i) q^{20} +(3483.29 + 3018.29i) q^{21} +7618.02i q^{22} +(-10720.4 - 5753.97i) q^{23} -8652.21 q^{24} +(-10201.4 + 11773.0i) q^{25} +(-12777.6 + 8211.68i) q^{26} +(539.088 + 3749.44i) q^{27} +(6933.98 - 3166.64i) q^{28} +(1597.10 - 11108.1i) q^{29} +(-186.215 - 634.190i) q^{30} +(23160.0 + 14884.0i) q^{31} +(-10182.0 + 22295.4i) q^{32} +(5411.84 - 18431.1i) q^{33} +(-20932.8 + 18138.3i) q^{34} +(1327.99 + 1532.58i) q^{35} +(6011.13 + 1765.03i) q^{36} +(-431.176 - 196.912i) q^{37} +(-18186.2 + 28298.2i) q^{38} +(36747.8 - 10790.1i) q^{39} +(-3768.06 - 541.765i) q^{40} +(-1055.50 - 2311.21i) q^{41} +(28203.7 - 4055.07i) q^{42} +(-16620.5 - 25862.0i) q^{43} +(-24010.0 - 20804.7i) q^{44} +1666.65i q^{45} +(-70284.1 + 26792.7i) q^{46} -75894.9 q^{47} +(-18184.0 + 20985.4i) q^{48} +(25429.2 - 16342.3i) q^{49} +(13705.6 + 95324.4i) q^{50} +(63530.3 - 29013.3i) q^{51} +(9014.56 - 62697.7i) q^{52} +(-46722.9 - 159124. i) q^{53} +(19700.3 + 12660.6i) q^{54} +(3510.95 - 7687.91i) q^{55} +(46234.8 - 157461. i) q^{56} +(64102.7 - 55545.3i) q^{57} +(-45432.5 - 52431.9i) q^{58} +(105793. + 31063.6i) q^{59} +(2507.35 + 1145.07i) q^{60} +(-118486. + 184368. i) q^{61} +(163302. - 47949.7i) q^{62} +(-71116.7 - 10225.0i) q^{63} +(110305. + 241533. i) q^{64} +(16679.4 - 2398.14i) q^{65} +(-64202.8 - 99901.5i) q^{66} +(174751. + 151423. i) q^{67} -115510. i q^{68} +(189079. - 14892.5i) q^{69} +12536.7 q^{70} +(370832. - 427963. i) q^{71} +(113464. - 72918.7i) q^{72} +(85740.2 + 596336. i) q^{73} +(-2665.58 + 1217.33i) q^{74} +(34559.2 - 240365. i) q^{75} +(-39522.2 - 134600. i) q^{76} +(306507. + 196980. i) q^{77} +(98357.7 - 215373. i) q^{78} +(123469. - 420497. i) q^{79} +(-9233.19 + 8000.61i) q^{80} +(-38668.9 - 44626.3i) q^{81} +(-15071.4 - 4425.35i) q^{82} +(-72747.6 - 33222.7i) q^{83} +(-64243.4 + 99964.7i) q^{84} +(29484.3 - 8657.38i) q^{85} +(-188117. - 27047.2i) q^{86} +(72671.9 + 159129. i) q^{87} +(-676995. + 97337.2i) q^{88} +(677036. + 1.05349e6i) q^{89} +(7786.79 + 6747.29i) q^{90} +726432. i q^{91} +(107502. - 294688. i) q^{92} -429156. q^{93} +(-307255. + 354591. i) q^{94} +(31394.9 - 20176.3i) q^{95} +(-54375.4 - 378189. i) q^{96} +(-1.24493e6 + 568542. i) q^{97} +(26594.5 - 184969. i) q^{98} +(84362.3 + 287312. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more