LMFDB - Embedded newform 69.7.f.a.10.15

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			10.15
Character	$\chi$	$=$	69.10
Dual form			69.7.f.a.7.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.991787 + 1.14458i) q^{2} +(13.1138 + 8.42776i) q^{3} +(8.78172 - 61.0782i) q^{4} +(-45.4301 - 20.7472i) q^{5} +(3.35987 + 23.3684i) q^{6} +(28.4560 - 96.9124i) q^{7} +(160.160 - 102.928i) q^{8} +(100.946 + 221.041i) q^{9} +O(q^{10})$	\(q+(0.991787 + 1.14458i) q^{2} +(13.1138 + 8.42776i) q^{3} +(8.78172 - 61.0782i) q^{4} +(-45.4301 - 20.7472i) q^{5} +(3.35987 + 23.3684i) q^{6} +(28.4560 - 96.9124i) q^{7} +(160.160 - 102.928i) q^{8} +(100.946 + 221.041i) q^{9} +(-21.3100 - 72.5754i) q^{10} +(-1340.90 - 1161.90i) q^{11} +(629.914 - 726.960i) q^{12} +(-2565.35 + 753.254i) q^{13} +(139.147 - 63.5461i) q^{14} +(-420.911 - 654.950i) q^{15} +(-3512.58 - 1031.39i) q^{16} +(2498.34 - 359.207i) q^{17} +(-152.882 + 334.766i) q^{18} +(-187.909 - 27.0172i) q^{19} +(-1666.16 + 2592.59i) q^{20} +(1189.92 - 1031.07i) q^{21} -2687.13i q^{22} +(4831.81 - 11166.4i) q^{23} +2967.76 q^{24} +(-8598.75 - 9923.49i) q^{25} +(-3406.44 - 2189.19i) q^{26} +(-539.088 + 3749.44i) q^{27} +(-5669.34 - 2589.10i) q^{28} +(-3403.00 - 23668.4i) q^{29} +(332.191 - 1131.34i) q^{30} +(15560.3 - 10000.0i) q^{31} +(-7364.83 - 16126.7i) q^{32} +(-7792.18 - 26537.7i) q^{33} +(2888.96 + 2503.30i) q^{34} +(-3303.42 + 3812.36i) q^{35} +(14387.2 - 4224.47i) q^{36} +(-76017.9 + 34716.2i) q^{37} +(-155.442 - 241.873i) q^{38} +(-39989.8 - 11742.1i) q^{39} +(-9411.55 + 1353.18i) q^{40} +(-11665.4 + 25543.7i) q^{41} +(2360.30 + 339.359i) q^{42} +(48113.3 - 74865.8i) q^{43} +(-82742.0 + 71696.4i) q^{44} -12136.2i q^{45} +(17573.0 - 5544.32i) q^{46} +145455. q^{47} +(-37371.1 - 43128.6i) q^{48} +(90390.4 + 58090.4i) q^{49} +(2830.13 - 19684.0i) q^{50} +(35790.1 + 16344.8i) q^{51} +(23479.2 + 163302. i) q^{52} +(38408.7 - 130808. i) q^{53} +(-4826.20 + 3101.61i) q^{54} +(36811.1 + 80605.1i) q^{55} +(-5417.52 - 18450.4i) q^{56} +(-2236.52 - 1937.95i) q^{57} +(23715.4 - 27369.0i) q^{58} +(-129785. + 38108.4i) q^{59} +(-43699.5 + 19956.9i) q^{60} +(134134. + 208717. i) q^{61} +(26878.3 + 7892.19i) q^{62} +(24294.1 - 3492.96i) q^{63} +(-86175.9 + 188699. i) q^{64} +(132172. + 19003.5i) q^{65} +(22646.5 - 35238.6i) q^{66} +(-141458. + 122574. i) q^{67} -155748. i q^{68} +(157472. - 105714. i) q^{69} -7639.85 q^{70} +(148295. + 171141. i) q^{71} +(38918.8 + 25011.6i) q^{72} +(-87892.3 + 611304. i) q^{73} +(-115129. - 52577.7i) q^{74} +(-29130.0 - 202603. i) q^{75} +(-3300.33 + 11239.9i) q^{76} +(-150759. + 96886.9i) q^{77} +(-26221.6 - 57417.3i) q^{78} +(19836.7 + 67557.5i) q^{79} +(138178. + 119732. i) q^{80} +(-38668.9 + 44626.3i) q^{81} +(-40806.6 + 11981.9i) q^{82} +(257027. - 117380. i) q^{83} +(-52526.5 - 81732.9i) q^{84} +(-120952. - 35514.8i) q^{85} +(133408. - 19181.2i) q^{86} +(154845. - 339063. i) q^{87} +(-334351. - 48072.4i) q^{88} +(502314. - 781615. i) q^{89} +(13890.9 - 12036.6i) q^{90} +270049. i q^{91} +(-639595. - 393179. i) q^{92} +288333. q^{93} +(144261. + 166486. i) q^{94} +(7976.20 + 5125.99i) q^{95} +(39330.9 - 273552. i) q^{96} +(795766. + 363414. i) q^{97} +(23158.7 + 161073. i) q^{98} +(121468. - 413682. 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 $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{3}{22}\right)$	$1$

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 $

$2$	0.991787	+	1.14458i	0.123973	+	0.143073i	0.814343	−	0.580384i	$-0.197098\pi$
$2$	0.991787	+	1.14458i	0.123973	+	0.143073i	−0.690370	+	0.723457i	$0.742552\pi$
$3$	13.1138	+	8.42776i	0.485698	+	0.312139i
$3$	13.1138	+	8.42776i	0.485698	+	0.312139i
$4$	8.78172	−	61.0782i	0.137214	−	0.954347i
$5$	−45.4301	−	20.7472i	−0.363441	−	0.165978i	0.225321	−	0.974285i	$-0.427657\pi$
$5$	−45.4301	−	20.7472i	−0.363441	−	0.165978i	−0.588762	+	0.808307i	$0.700384\pi$
$6$	3.35987	+	23.3684i	0.0155550	+	0.108187i
$7$	28.4560	−	96.9124i	0.0829622	−	0.282543i	−0.907555	−	0.419934i	$-0.862053\pi$
$7$	28.4560	−	96.9124i	0.0829622	−	0.282543i	0.990517	+	0.137390i	$0.0438715\pi$
$8$	160.160	−	102.928i	0.312812	−	0.201032i
$9$	100.946	+	221.041i	0.138472	+	0.303211i
$10$	−21.3100	−	72.5754i	−0.0213100	−	0.0725754i
$11$	−1340.90	−	1161.90i	−1.00744	−	0.872951i	−0.0155272	−	0.999879i	$-0.504943\pi$
$11$	−1340.90	−	1161.90i	−1.00744	−	0.872951i	−0.991912	+	0.126929i	$0.959488\pi$
$12$	629.914	−	726.960i	0.364534	−	0.420694i
$13$	−2565.35	+	753.254i	−1.16766	+	0.342856i	−0.807405	−	0.589998i	$-0.799128\pi$
$13$	−2565.35	+	753.254i	−1.16766	+	0.342856i	−0.360255	+	0.932854i	$0.617310\pi$
$14$	139.147	−	63.5461i	0.0507094	−	0.0231582i
$15$	−420.911	−	654.950i	−0.124714	−	0.194059i
$16$	−3512.58	−	1031.39i	−0.857563	−	0.251803i
$17$	2498.34	−	359.207i	0.508516	−	0.0731135i	0.116718	−	0.993165i	$-0.462763\pi$
$17$	2498.34	−	359.207i	0.508516	−	0.0731135i	0.391797	+	0.920052i	$0.371853\pi$
$18$	−152.882	+	334.766i	−0.0262144	+	0.0574016i
$19$	−187.909	−	27.0172i	−0.0273960	−	0.00393895i	0.128603	−	0.991696i	$-0.458951\pi$
$19$	−187.909	−	27.0172i	−0.0273960	−	0.00393895i	−0.155999	+	0.987757i	$0.549860\pi$
$20$	−1666.16	+	2592.59i	−0.208270	+	0.324074i
$21$	1189.92	−	1031.07i	0.128487	−	0.111335i
$22$		−	2687.13i		−	0.252360i
$23$	4831.81	−	11166.4i	0.397124	−	0.917765i
$23$	4831.81	−	11166.4i	0.397124	−	0.917765i
$24$	2967.76			0.214682
$25$	−8598.75	−	9923.49i	−0.550320	−	0.635103i
$26$	−3406.44	−	2189.19i	−0.193812	−	0.124555i
$27$	−539.088	+	3749.44i	−0.0273885	+	0.190491i
$28$	−5669.34	−	2589.10i	−0.258261	−	0.117944i
$29$	−3403.00	−	23668.4i	−0.139530	−	0.970453i	−0.932494	−	0.361185i	$-0.882372\pi$
$29$	−3403.00	−	23668.4i	−0.139530	−	0.970453i	0.792964	−	0.609268i	$-0.208537\pi$
$30$	332.191	−	1131.34i	0.0123034	−	0.0419014i
$31$	15560.3	−	10000.0i	0.522316	−	0.335672i	−0.252772	−	0.967526i	$-0.581342\pi$
$31$	15560.3	−	10000.0i	0.522316	−	0.335672i	0.775087	+	0.631854i	$0.217706\pi$
$32$	−7364.83	−	16126.7i	−0.224757	−	0.492149i
$33$	−7792.18	−	26537.7i	−0.216829	−	0.738452i
$34$	2888.96	+	2503.30i	0.0735029	+	0.0636906i
$35$	−3303.42	+	3812.36i	−0.0770478	+	0.0889179i
$36$	14387.2	−	4224.47i	0.308368	−	0.0905452i
$37$	−76017.9	+	34716.2i	−1.50076	+	0.685373i	−0.985189	−	0.171474i	$-0.945147\pi$
$37$	−76017.9	+	34716.2i	−1.50076	+	0.685373i	−0.515570	+	0.856848i	$0.672420\pi$
$38$	−155.442	−	241.873i	−0.00283282	−	0.00440795i
$39$	−39989.8	−	11742.1i	−0.674149	−	0.197948i
$40$	−9411.55	+	1353.18i	−0.147055	+	0.0211434i
$41$	−11665.4	+	25543.7i	−0.169258	+	0.370624i	−0.975185	−	0.221392i	$-0.928940\pi$
$41$	−11665.4	+	25543.7i	−0.169258	+	0.370624i	0.805927	+	0.592015i	$0.201667\pi$
$42$	2360.30	+	339.359i	0.0318580	+	0.00458049i
$43$	48113.3	−	74865.8i	0.605146	−	0.941625i	−0.394595	−	0.918855i	$-0.629115\pi$
$43$	48113.3	−	74865.8i	0.605146	−	0.941625i	0.999741	−	0.0227701i	$-0.00724859\pi$
$44$	−82742.0	+	71696.4i	−0.971333	+	0.841665i
$45$		−	12136.2i		−	0.133182i
$46$	17573.0	−	5544.32i	0.180540	−	0.0569607i
$47$	145455.			1.40099			0.700496	−	0.713656i	$-0.252962\pi$
$47$	145455.			1.40099			0.700496	+	0.713656i	$0.252962\pi$
$48$	−37371.1	−	43128.6i	−0.337919	−	0.389979i
$49$	90390.4	+	58090.4i	0.768306	+	0.493760i
$50$	2830.13	−	19684.0i	0.0226410	−	0.157472i
$51$	35790.1	+	16344.8i	0.269807	+	0.123217i
$52$	23479.2	+	163302.i	0.166984	+	1.16140i
$53$	38408.7	−	130808.i	0.257989	−	0.878631i	−0.724017	−	0.689782i	$-0.757706\pi$
$53$	38408.7	−	130808.i	0.257989	−	0.878631i	0.982006	−	0.188849i	$-0.0604757\pi$
$54$	−4826.20	+	3101.61i	−0.0306496	+	0.0196973i
$55$	36811.1	+	80605.1i	0.221254	+	0.484479i
$56$	−5417.52	−	18450.4i	−0.0308487	−	0.105061i
$57$	−2236.52	−	1937.95i	−0.0120767	−	0.0104645i
$58$	23715.4	−	27369.0i	0.121547	−	0.140273i
$59$	−129785.	+	38108.4i	−0.631930	+	0.185551i	−0.581984	−	0.813201i	$-0.697723\pi$
$59$	−129785.	+	38108.4i	−0.631930	+	0.185551i	−0.0499464	+	0.998752i	$0.515905\pi$
$60$	−43699.5	+	19956.9i	−0.202312	+	0.0923930i
$61$	134134.	+	208717.i	0.590949	+	0.919534i	0.999975	+	0.00701171i	$0.00223191\pi$
$61$	134134.	+	208717.i	0.590949	+	0.919534i	−0.409027	+	0.912522i	$0.634132\pi$
$62$	26878.3	+	7892.19i	0.112779	+	0.0331148i
$63$	24294.1	−	3492.96i	0.0971581	−	0.0139692i
$64$	−86175.9	+	188699.i	−0.328735	+	0.719829i
$65$	132172.	+	19003.5i	0.481282	+	0.0691979i
$66$	22646.5	−	35238.6i	0.0787714	−	0.122571i
$67$	−141458.	+	122574.i	−0.470331	+	0.407544i	−0.857515	−	0.514458i	$-0.827993\pi$
$67$	−141458.	+	122574.i	−0.470331	+	0.407544i	0.387185	+	0.922002i	$0.373448\pi$
$68$		−	155748.i		−	0.495333i
$69$	157472.	−	105714.i	0.479353	−	0.321799i
$70$	−7639.85			−0.0222736
$71$	148295.	+	171141.i	0.414335	+	0.478168i	0.924103	−	0.382144i	$-0.124814\pi$
$71$	148295.	+	171141.i	0.414335	+	0.478168i	−0.509768	+	0.860312i	$0.670269\pi$
$72$	38918.8	+	25011.6i	0.104271	+	0.0670107i
$73$	−87892.3	+	611304.i	−0.225934	+	1.57141i	0.489043	+	0.872260i	$0.337346\pi$
$73$	−87892.3	+	611304.i	−0.225934	+	1.57141i	−0.714977	+	0.699148i	$0.753563\pi$
$74$	−115129.	−	52577.7i	−0.284112	−	0.129750i
$75$	−29130.0	−	202603.i	−0.0690488	−	0.480245i
$76$	−3300.33	+	11239.9i	−0.00751825	+	0.0256048i
$77$	−150759.	+	96886.9i	−0.330226	+	0.212223i
$78$	−26221.6	−	57417.3i	−0.0552555	−	0.120993i
$79$	19836.7	+	67557.5i	0.0402335	+	0.137023i	0.977161	−	0.212502i	$-0.0681612\pi$
$79$	19836.7	+	67557.5i	0.0402335	+	0.137023i	−0.936927	+	0.349525i	$0.886343\pi$
$80$	138178.	+	119732.i	0.269880	+	0.233852i
$81$	−38668.9	+	44626.3i	−0.0727623	+	0.0839722i
$82$	−40806.6	+	11981.9i	−0.0740097	+	0.0217312i
$83$	257027.	−	117380.i	0.449516	−	0.205287i	−0.177776	−	0.984071i	$-0.556890\pi$
$83$	257027.	−	117380.i	0.449516	−	0.205287i	0.627292	+	0.778784i	$0.284163\pi$
$84$	−52526.5	−	81732.9i	−0.0886219	−	0.137898i
$85$	−120952.	−	35514.8i	−0.196951	−	0.0578299i
$86$	133408.	−	19181.2i	0.209743	−	0.0301565i
$87$	154845.	−	339063.i	0.235147	−	0.514900i
$88$	−334351.	−	48072.4i	−0.490630	−	0.0705419i
$89$	502314.	−	781615.i	0.712533	−	1.10872i	−0.276498	−	0.961014i	$-0.589174\pi$
$89$	502314.	−	781615.i	0.712533	−	1.10872i	0.989031	−	0.147708i	$-0.0471897\pi$
$90$	13890.9	−	12036.6i	0.0190548	−	0.0165111i
$91$			270049.i			0.358359i
$92$	−639595.	−	393179.i	−0.821375	−	0.504925i
$93$	288333.			0.358464
$94$	144261.	+	166486.i	0.173686	+	0.200444i
$95$	7976.20	+	5125.99i	0.00930304	+	0.00597870i
$96$	39330.9	−	273552.i	0.0444549	−	0.309191i
$97$	795766.	+	363414.i	0.871907	+	0.398187i	0.800551	−	0.599264i	$-0.204540\pi$
$97$	795766.	+	363414.i	0.871907	+	0.398187i	0.0713558	+	0.997451i	$0.477267\pi$
$98$	23158.7	+	161073.i	0.0246057	+	0.171137i
$99$	121468.	−	413682.i	0.125186	−	0.426345i
$100$	−681621.	+	438051.i	−0.681621	+	0.438051i
$101$	−341343.	−	747437.i	−0.331304	−	0.725455i	0.668530	−	0.743685i	$-0.266924\pi$
$101$	−341343.	−	747437.i	−0.331304	−	0.725455i	−0.999834	+	0.0182307i	$0.994197\pi$
$102$	16788.2	+	57175.3i	0.0158199	+	0.0538776i
$103$	−445535.	−	386058.i	−0.407728	−	0.353298i	0.426721	−	0.904383i	$-0.359668\pi$
$103$	−445535.	−	386058.i	−0.407728	−	0.353298i	−0.834449	+	0.551085i	$0.814214\pi$
$104$	−333334.	+	384688.i	−0.296333	+	0.341986i
$105$	−75450.2	+	22154.2i	−0.0651767	+	0.0191376i
$106$	187814.	−	85771.7i	0.157692	−	0.0720156i
$107$	−937777.	−	1.45921e6i	−0.765505	−	1.19115i	−0.976889	−	0.213746i	$-0.931433\pi$
$107$	−937777.	−	1.45921e6i	−0.765505	−	1.19115i	0.211384	−	0.977403i	$-0.432203\pi$
$108$	224275.	+	65853.0i	0.178037	+	0.0522763i
$109$	51867.5	−	7457.41i	0.0400512	−	0.00575849i	−0.122260	−	0.992498i	$-0.539014\pi$
$109$	51867.5	−	7457.41i	0.0400512	−	0.00575849i	0.162311	+	0.986740i	$0.448105\pi$
$110$	−55750.5	+	122076.i	−0.0418861	+	0.0917179i
$111$	−1.28947e6	−	185397.i	−0.942847	−	0.135561i
$112$	−199908.	+	311063.i	−0.142291	+	0.221409i
$113$	1.24785e6	−	1.08127e6i	0.864822	−	0.749372i	−0.104667	−	0.994507i	$-0.533378\pi$
$113$	1.24785e6	−	1.08127e6i	0.864822	−	0.749372i	0.969489	+	0.245135i	$0.0788323\pi$
$114$		−	4481.91i		−	0.00302516i
$115$	−451183.	+	407046.i	−0.296660	+	0.267639i
$116$	−1.47551e6			−0.945295
$117$	−425461.	−	491008.i	−0.265645	−	0.306571i
$118$	−172337.	−	110754.i	−0.104890	−	0.0674086i
$119$	36281.2	−	252341.i	0.0215298	−	0.149743i
$120$	−134826.	−	61572.9i	−0.0780242	−	0.0356325i
$121$	195891.	+	1.36245e6i	0.110575	+	0.769068i
$122$	−105861.	+	360530.i	−0.0582985	+	0.198546i
$123$	−368255.	+	236663.i	−0.197894	+	0.127179i
$124$	−474136.	−	1.03821e6i	−0.248678	−	0.544530i
$125$	404612.	+	1.37798e6i	0.207161	+	0.705526i
$126$	28092.5	+	24342.3i	0.0140436	+	0.0121689i
$127$	2.42199e6	−	2.79513e6i	1.18239	−	1.36455i	0.266147	−	0.963932i	$-0.414249\pi$
$127$	2.42199e6	−	2.79513e6i	1.18239	−	1.36455i	0.916244	−	0.400620i	$-0.131205\pi$
$128$	−1.39013e6	+	408180.i	−0.662868	+	0.194636i
$129$	1.26190e6	−	576291.i	0.587836	−	0.268456i
$130$	109335.	+	170129.i	0.0497658	+	0.0774370i
$131$	−698114.	−	204985.i	−0.310536	−	0.0911817i	0.122751	−	0.992437i	$-0.460828\pi$
$131$	−698114.	−	204985.i	−0.310536	−	0.0911817i	−0.433287	+	0.901256i	$0.642647\pi$
$132$	−1.68931e6	+	242886.i	−0.734491	+	0.105604i
$133$	−7965.45	+	17441.9i	−0.00338576	+	0.00741377i
$134$	−280593.	−	40343.1i	−0.116617	−	0.0167670i
$135$	102281.	−	159153.i	0.0415714	−	0.0646864i
$136$	363160.	−	314680.i	0.144372	−	0.125099i
$137$		−	2.87236e6i		−	1.11706i	−0.829484	−	0.558531i	$-0.811365\pi$
$137$		−	2.87236e6i		−	1.11706i	0.829484	−	0.558531i	$-0.188635\pi$
$138$	277176.	+	75393.9i	0.105468	+	0.0286879i
$139$	433274.			0.161331			0.0806655	−	0.996741i	$-0.474295\pi$
$139$	433274.			0.161331			0.0806655	+	0.996741i	$0.474295\pi$
$140$	203842.	+	235246.i	0.0742865	+	0.0857312i
$141$	1.90748e6	+	1.22586e6i	0.680459	+	0.437305i
$142$	−48808.7	+	339472.i	−0.0170464	+	0.118560i
$143$	4.31508e6	+	1.97063e6i	1.47564	+	0.673903i
$144$	−126602.	−	880536.i	−0.0423988	−	0.294890i
$145$	−336455.	+	1.14586e6i	−0.110363	+	0.375861i
$146$	−786859.	+	505683.i	−0.252836	+	0.162488i
$147$	695794.	+	1.52358e6i	0.219043	+	0.479636i
$148$	1.45284e6	+	4.94791e6i	0.448158	+	1.52629i
$149$	4.04235e6	+	3.50271e6i	1.22201	+	1.05888i	0.996410	+	0.0846576i	$0.0269796\pi$
$149$	4.04235e6	+	3.50271e6i	1.22201	+	1.05888i	0.225600	+	0.974220i	$0.427566\pi$
$150$	203006.	−	234281.i	0.0601498	−	0.0694166i
$151$	1.80198e6	−	529109.i	0.523382	−	0.153679i	−0.00936047	−	0.999956i	$-0.502980\pi$
$151$	1.80198e6	−	529109.i	0.523382	−	0.153679i	0.532743	+	0.846277i	$0.321161\pi$
$152$	−32876.3	+	15014.1i	−0.00936164	+	0.00427532i
$153$	331596.	+	515973.i	0.0925838	+	0.144063i
$154$	−260416.	−	76465.0i	−0.0713026	−	0.0209363i
$155$	−914379.	+	131468.i	−0.245545	+	0.0353041i
$156$	−1.06836e6	+	2.33939e6i	−0.281414	+	0.616210i
$157$	−5.18995e6	−	746203.i	−1.34111	−	0.192823i	−0.565873	−	0.824492i	$-0.691461\pi$
$157$	−5.18995e6	−	746203.i	−1.34111	−	0.192823i	−0.775238	+	0.631670i	$0.782370\pi$
$158$	−57651.4	+	89707.4i	−0.0146163	+	0.0227435i
$159$	1.60610e6	−	1.39170e6i	0.399560	−	0.346221i
$160$			885439.i			0.216172i
$161$	−944672.	−	786015.i	−0.226362	−	0.188345i
$162$	−89429.7			−0.0210347
$163$	−1.51987e6	−	1.75402e6i	−0.350948	−	0.405015i	0.552639	−	0.833421i	$-0.313621\pi$
$163$	−1.51987e6	−	1.75402e6i	−0.350948	−	0.405015i	−0.903587	+	0.428406i	$0.859075\pi$
$164$	1.45772e6	+	936822.i	0.330479	+	0.212386i
$165$	−196585.	+	1.36728e6i	−0.0437621	+	0.304372i
$166$	389268.	+	177773.i	0.0850990	+	0.0388634i
$167$	611067.	+	4.25007e6i	0.131202	+	0.912528i	0.943991	+	0.329971i	$0.107039\pi$
$167$	611067.	+	4.25007e6i	0.131202	+	0.912528i	−0.812789	+	0.582558i	$0.802052\pi$
$168$	84450.8	−	287613.i	0.0178105	−	0.0606570i
$169$	1.95305e6	−	1.25515e6i	0.404625	−	0.260037i
$170$	−79309.2	−	173663.i	−0.0161427	−	0.0353476i
$171$	−12996.7	−	44262.8i	−0.00259924	−	0.00885219i
$172$	−4.15015e6	−	3.59613e6i	−0.815603	−	0.706724i
$173$	−1.25200e6	+	1.44488e6i	−0.241805	+	0.279058i	−0.863660	−	0.504074i	$-0.831834\pi$
$173$	−1.25200e6	+	1.44488e6i	−0.241805	+	0.279058i	0.621855	+	0.783132i	$0.286379\pi$
$174$	541659.	−	159045.i	0.102820	−	0.0301907i
$175$	−1.20640e6	+	550942.i	−0.225100	+	0.102800i
$176$	3.51166e6	+	5.46424e6i	0.644131	+	1.00229i
$177$	−2.02315e6	−	594050.i	−0.364845	−	0.107128i
$178$	1.39281e6	−	200256.i	0.246963	−	0.0355080i
$179$	−3.25170e6	+	7.12022e6i	−0.566958	+	1.24147i	0.381443	+	0.924392i	$0.375427\pi$
$179$	−3.25170e6	+	7.12022e6i	−0.566958	+	1.24147i	−0.948401	+	0.317073i	$0.897300\pi$
$180$	−741260.	−	106577.i	−0.127102	−	0.0182745i
$181$	4.13921e6	−	6.44074e6i	0.698043	−	1.08618i	−0.293445	−	0.955976i	$-0.594802\pi$
$181$	4.13921e6	−	6.44074e6i	0.698043	−	1.08618i	0.991488	−	0.130200i	$-0.0415620\pi$
$182$	−309093.	+	267831.i	−0.0512714	+	0.0444269i
$183$			3.86753e6i			0.631074i
$184$	−375483.	−	2.28574e6i	−0.0602749	−	0.366922i
$185$	4.17377e6			0.659194
$186$	285965.	+	330021.i	0.0444400	+	0.0512865i
$187$	−3.76738e6	−	2.42115e6i	−0.576123	−	0.370252i
$188$	1.27735e6	−	8.88415e6i	0.192236	−	1.33703i
$189$	348027.	+	158938.i	0.0515498	+	0.0235420i
$190$	2043.56	+	14213.3i	0.000297939	+	0.00207221i
$191$	1.81306e6	−	6.17473e6i	0.260204	−	0.886172i	−0.720957	−	0.692979i	$-0.756298\pi$
$191$	1.81306e6	−	6.17473e6i	0.260204	−	0.886172i	0.981161	−	0.193192i	$-0.0618842\pi$
$192$	−2.72040e6	+	1.74830e6i	−0.384353	+	0.247008i
$193$	−3.37660e6	−	7.39371e6i	−0.469685	−	1.02847i	−0.985172	−	0.171570i	$-0.945116\pi$
$193$	−3.37660e6	−	7.39371e6i	−0.469685	−	1.02847i	0.515487	−	0.856898i	$-0.327611\pi$
$194$	373272.	+	1.27125e6i	0.0511235	+	0.174111i
$195$	1.57313e6	+	1.36312e6i	0.212158	+	0.183836i
$196$	4.34184e6	−	5.01075e6i	0.576641	−	0.665479i
$197$	−7.61195e6	+	2.23507e6i	−0.995629	+	0.292343i	−0.738661	−	0.674077i	$-0.764542\pi$
$197$	−7.61195e6	+	2.23507e6i	−0.995629	+	0.292343i	−0.256968	+	0.966420i	$0.582723\pi$
$198$	593964.	−	271254.i	0.0765182	−	0.0349447i
$199$	2.30962e6	+	3.59383e6i	0.293076	+	0.456036i	0.956301	−	0.292385i	$-0.0944489\pi$
$199$	2.30962e6	+	3.59383e6i	0.293076	+	0.456036i	−0.663224	+	0.748421i	$0.730813\pi$
$200$	−2.39858e6	−	704287.i	−0.299823	−	0.0880359i
$201$	−2.88809e6	+	415244.i	−0.355649	+	0.0511346i
$202$	516964.	−	1.13199e6i	0.0627200	−	0.137338i
$203$	−2.39059e6	−	343716.i	−0.285771	−	0.0410876i
$204$	1.31261e6	−	2.04246e6i	0.154613	−	0.240582i
$205$	1.05992e6	−	918430.i	0.123031	−	0.106607i
$206$		−	892839.i		−	0.102134i
$207$	2.95599e6	−	59180.1i	0.333267	−	0.00667213i
$208$	9.78788e6			1.08767
$209$	220576.	+	254559.i	0.0241613	+	0.0278836i
$210$	−100188.	−	64386.8i	−0.0108182	−	0.00695247i
$211$	−997902.	+	6.94056e6i	−0.106228	+	0.738835i	0.865187	+	0.501449i	$0.167200\pi$
$211$	−997902.	+	6.94056e6i	−0.106228	+	0.738835i	−0.971415	+	0.237386i	$0.923709\pi$
$212$	−7.65223e6	−	3.49465e6i	−0.803119	−	0.366772i
$213$	502378.	+	3.49412e6i	0.0519867	+	0.361575i
$214$	740111.	−	2.52059e6i	0.0755189	−	0.257194i
$215$	−3.73905e6	+	2.40294e6i	−0.376224	+	0.241784i
$216$	299584.	+	655996.i	0.0297274	+	0.0650939i
$217$	−526339.	−	1.79255e6i	−0.0515094	−	0.175425i
$218$	59977.1	+	51970.4i	0.00578916	+	0.00501634i
$219$	−6.30453e6	+	7.27582e6i	−0.600234	+	0.692707i
$220$	5.24648e6	−	1.54051e6i	0.492720	−	0.144676i
$221$	−6.13853e6	+	2.80337e6i	−0.568706	+	0.259719i
$222$	−1.06667e6	−	1.65978e6i	−0.0974928	−	0.151702i
$223$	−1.31135e7	−	3.85046e6i	−1.18251	−	0.347215i	−0.369366	−	0.929284i	$-0.620425\pi$
$223$	−1.31135e7	−	3.85046e6i	−1.18251	−	0.347215i	−0.813140	+	0.582069i	$0.802243\pi$
$224$	−1.77245e6	+	254840.i	−0.157700	+	0.0226738i
$225$	1.32549e6	−	2.90241e6i	0.116366	−	0.254807i
$226$	2.47520e6	+	355880.i	0.214430	+	0.0308303i
$227$	8.30937e6	−	1.29296e7i	0.710380	−	1.10537i	−0.279038	−	0.960280i	$-0.590016\pi$
$227$	8.30937e6	−	1.29296e7i	0.710380	−	1.10537i	0.989418	−	0.145093i	$-0.0463481\pi$
$228$	−138007.	+	119584.i	−0.0116439	+	0.0100895i
$229$		−	1.76688e7i		−	1.47130i	−0.677361	−	0.735651i	$-0.736877\pi$
$229$		−	1.76688e7i		−	1.47130i	0.677361	−	0.735651i	$-0.263123\pi$
$230$	−913375.	−	112713.i	−0.0750698	−	0.00926382i
$231$	−2.79357e6			−0.226633
$232$	−2.98117e6	−	3.44046e6i	−0.238739	−	0.275519i
$233$	2.54617e6	+	1.63633e6i	0.201289	+	0.129361i	0.637402	−	0.770531i	$-0.280009\pi$
$233$	2.54617e6	+	1.63633e6i	0.201289	+	0.129361i	−0.436113	+	0.899892i	$0.643645\pi$
$234$	140033.	−	973951.i	0.0109291	−	0.0760133i
$235$	−6.60805e6	−	3.01780e6i	−0.509178	−	0.232534i
$236$	1.18785e6	+	8.26170e6i	0.0903705	+	0.628541i
$237$	−309223.	+	1.05312e6i	−0.0232288	+	0.0791101i
$238$	324809.	−	208742.i	0.0240933	−	0.0154838i
$239$	1.03443e6	+	2.26509e6i	0.0757718	+	0.165917i	0.943727	−	0.330725i	$-0.107293\pi$
$239$	1.03443e6	+	2.26509e6i	0.0757718	+	0.165917i	−0.867955	+	0.496642i	$0.834566\pi$
$240$	802976.	+	2.73468e6i	0.0580856	+	0.197821i
$241$	−997375.	−	864230.i	−0.0712537	−	0.0617416i	0.618506	−	0.785780i	$-0.287738\pi$
$241$	−997375.	−	864230.i	−0.0712537	−	0.0617416i	−0.689760	+	0.724039i	$0.742284\pi$
$242$	−1.36516e6	+	1.57547e6i	−0.0963244	+	0.111164i
$243$	−883197.	+	259330.i	−0.0615515	+	0.0180732i
$244$	1.39260e7	−	6.35978e6i	0.958641	−	0.437797i
$245$	−2.90123e6	−	4.51440e6i	−0.197280	−	0.306974i
$246$	−636111.	−	186779.i	−0.0427295	−	0.0125465i
$247$	502403.	−	72234.7i	0.0333397	−	0.00479352i
$248$	1.46285e6	−	3.20320e6i	0.0959058	−	0.210004i
$249$	4.35987e6	+	626855.i	0.282407	+	0.0406040i
$250$	−1.17592e6	+	1.82977e6i	−0.0752592	+	0.117106i
$251$	9.79622e6	−	8.48847e6i	0.619494	−	0.536795i	−0.287585	−	0.957755i	$-0.592852\pi$
$251$	9.79622e6	−	8.48847e6i	0.619494	−	0.536795i	0.907079	+	0.420960i	$0.138307\pi$
$252$		−	1.51451e6i		−	0.0946393i
$253$	−1.94532e7	+	9.35903e6i	−1.20124	+	0.577922i
$254$	5.60135e6			0.341815
$255$	−1.28684e6	−	1.48509e6i	−0.0776075	−	0.0895638i
$256$	9.32299e6	+	5.99152e6i	0.555693	+	0.357122i
$257$	−2.75930e6	+	1.91914e7i	−0.162555	+	1.13059i	0.731241	+	0.682119i	$0.238941\pi$
$257$	−2.75930e6	+	1.91914e7i	−0.162555	+	1.13059i	−0.893796	+	0.448474i	$0.851968\pi$
$258$	1.91115e6	+	872793.i	0.111285	+	0.0508220i
$259$	1.20126e6	+	8.35496e6i	0.0691414	+	0.480889i
$260$	2.32140e6	−	7.90595e6i	0.132078	−	0.449815i
$261$	4.88815e6	−	3.14143e6i	0.274931	−	0.176687i
$262$	−457758.	−	1.00235e6i	−0.0254526	−	0.0557334i
$263$	−4.66831e6	−	1.58988e7i	−0.256621	−	0.873971i	−0.982518	−	0.186167i	$-0.940393\pi$
$263$	−4.66831e6	−	1.58988e7i	−0.256621	−	0.873971i	0.725897	−	0.687803i	$-0.241425\pi$
$264$	−3.97948e6	−	3.44824e6i	−0.216279	−	0.187407i
$265$	−4.45882e6	+	5.14575e6i	−0.239597	+	0.276510i
$266$	−27863.7	+	8181.53i	−0.00148045	+	0.000434700i
$267$	1.31745e7	−	6.01660e6i	0.692152	−	0.316095i
$268$	6.24437e6	+	9.71642e6i	0.324402	+	0.504780i
$269$	−2.50937e6	−	736819.i	−0.128917	−	0.0378533i	0.216638	−	0.976252i	$-0.430491\pi$
$269$	−2.50937e6	−	736819.i	−0.128917	−	0.0378533i	−0.345554	+	0.938399i	$0.612309\pi$
$270$	283605.	−	40776.2i	0.0144086	−	0.00207165i
$271$	−9.90526e6	+	2.16895e7i	−0.497689	+	1.08979i	0.479524	+	0.877529i	$0.340809\pi$
$271$	−9.90526e6	+	2.16895e7i	−0.497689	+	1.08979i	−0.977214	+	0.212259i	$0.931918\pi$
$272$	−9.14608e6	−	1.31501e6i	−0.454494	−	0.0653464i
$273$	−2.27590e6	+	3.54138e6i	−0.111858	+	0.174054i
$274$	3.28765e6	−	2.84877e6i	0.159821	−	0.138486i
$275$			2.32973e7i			1.12023i
$276$	−5.07393e6	−	1.05464e7i	−0.241333	−	0.501624i
$277$	−6.17226e6			−0.290405			−0.145203	−	0.989402i	$-0.546383\pi$
$277$	−6.17226e6			−0.290405			−0.145203	+	0.989402i	$0.546383\pi$
$278$	429715.	+	495918.i	0.0200007	+	0.0230821i
$279$	3.78116e6	+	2.43000e6i	0.174105	+	0.111891i
$280$	−136676.	+	950602.i	−0.00622613	+	0.0433037i
$281$	1.00078e7	+	4.57042e6i	0.451046	+	0.205986i	0.627968	−	0.778239i	$-0.283887\pi$
$281$	1.00078e7	+	4.57042e6i	0.451046	+	0.205986i	−0.176922	+	0.984225i	$0.556614\pi$
$282$	488711.	+	3.39906e6i	0.0217924	+	0.151569i
$283$	−5.11164e6	+	1.74086e7i	−0.225528	+	0.768078i	0.766520	+	0.642220i	$0.221987\pi$
$283$	−5.11164e6	+	1.74086e7i	−0.225528	+	0.768078i	−0.992048	+	0.125858i	$0.959832\pi$
$284$	1.17553e7	−	7.55467e6i	0.513191	−	0.329808i
$285$	61398.0	+	134443.i	0.00265228	+	0.00580769i
$286$	2.02409e6	+	6.89342e6i	0.0865230	+	0.294670i
$287$	2.14355e6	+	1.85740e6i	0.0906752	+	0.0785705i
$288$	2.82121e6	−	3.25585e6i	0.118102	−	0.136297i
$289$	−1.70472e7	+	5.00550e6i	−0.706251	+	0.207374i
$290$	−1.64522e6	+	751348.i	−0.0674576	+	0.0308069i
$291$	7.37279e6	+	1.14723e7i	0.299194	+	0.465555i
$292$	3.65655e7	+	1.07366e7i	1.46867	+	0.431240i
$293$	1.64411e7	−	2.36388e6i	0.653626	−	0.0939772i	0.192479	−	0.981301i	$-0.438347\pi$
$293$	1.64411e7	−	2.36388e6i	0.653626	−	0.0939772i	0.461147	+	0.887324i	$0.347438\pi$
$294$	−1.05378e6	+	2.30746e6i	−0.0414675	+	0.0908012i
$295$	6.68680e6	+	961416.i	0.260467	+	0.0374494i
$296$	−8.60172e6	+	1.33845e7i	−0.331673	+	0.516093i
$297$	5.07933e6	−	4.40126e6i	0.193882	−	0.167999i
$298$			8.10074e6i			0.306109i
$299$	−3.98411e6	+	3.22854e7i	−0.149045	+	1.20779i
$300$	−1.26305e7			−0.467795
$301$	−5.88631e6	−	6.79316e6i	−0.215846	−	0.249099i
$302$	2.39279e6	+	1.53775e6i	0.0868727	+	0.0558297i
$303$	1.82290e6	−	1.26785e7i	0.0655291	−	0.455765i
$304$	632180.	+	288707.i	0.0225019	+	0.0102763i
$305$	−1.76343e6	−	1.22649e7i	−0.0621526	−	0.432281i
$306$	−261702.	+	891275.i	−0.00913361	+	0.0311062i
$307$	1.51836e7	−	9.75791e6i	0.524759	−	0.337242i	−0.251293	−	0.967911i	$-0.580856\pi$
$307$	1.51836e7	−	9.75791e6i	0.524759	−	0.337242i	0.776052	+	0.630669i	$0.217219\pi$
$308$	4.59376e6	+	1.00589e7i	0.157223	+	0.344270i
$309$	−2.58907e6	−	8.81757e6i	−0.0877543	−	0.298864i
$310$	−1.05735e6	−	916195.i	−0.0354921	−	0.0307541i
$311$	3.77493e6	−	4.35650e6i	0.125495	−	0.144829i	−0.689525	−	0.724262i	$-0.742180\pi$
$311$	3.77493e6	−	4.35650e6i	0.125495	−	0.144829i	0.815020	+	0.579433i	$0.196726\pi$
$312$	−7.61335e6	+	2.23548e6i	−0.250676	+	0.0736050i
$313$	−1.39796e7	+	6.38426e6i	−0.455891	+	0.208198i	−0.630106	−	0.776509i	$-0.716989\pi$
$313$	−1.39796e7	+	6.38426e6i	−0.455891	+	0.208198i	0.174215	+	0.984708i	$0.444261\pi$
$314$	−4.29324e6	−	6.68041e6i	−0.138674	−	0.215781i
$315$	−1.17615e6	−	345349.i	−0.0376298	−	0.0110491i
$316$	4.30049e6	−	618317.i	0.136288	−	0.0195952i
$317$	1.81275e7	−	3.96937e7i	0.569063	−	1.24607i	−0.378231	−	0.925711i	$-0.623468\pi$
$317$	1.81275e7	−	3.96937e7i	0.569063	−	1.24607i	0.947295	−	0.320364i	$-0.103805\pi$
$318$	3.18582e6	+	458052.i	0.0990696	+	0.0142441i
$319$	−2.29372e7	+	3.56909e7i	−0.706590	+	1.09948i
$320$	7.82996e6	−	6.78470e6i	0.238951	−	0.207053i
$321$		−	2.70392e7i		−	0.817483i
$322$	−37254.3	−	1.86081e6i	−0.00111586	−	0.0557360i
$323$	−479165.			−0.0142193
$324$	2.38611e6	+	2.75372e6i	0.0701546	+	0.0809627i
$325$	2.95337e7	+	1.89802e7i	0.860335	+	0.552904i
$326$	500237.	−	3.47922e6i	0.0144385	−	0.100422i
$327$	743031.	+	339331.i	0.0212502	+	0.00970466i
$328$	760843.	+	5.29178e6i	0.0215612	+	0.149962i
$329$	4.13908e6	−	1.40964e7i	0.116229	−	0.395841i
$330$	−1.75993e6	+	1.13104e6i	−0.0489728	+	0.0314729i
$331$	2.58252e7	+	5.65493e7i	0.712130	+	1.55935i	0.824615	+	0.565695i	$0.191392\pi$
$331$	2.58252e7	+	5.65493e7i	0.712130	+	1.55935i	−0.112484	+	0.993653i	$0.535881\pi$
$332$	−4.91225e6	−	1.67296e7i	−0.134235	−	0.457163i
$333$	−1.53474e7	−	1.32986e7i	−0.415625	−	0.360141i
$334$	−4.25851e6	+	4.91458e6i	−0.114293	+	0.131901i
$335$	8.96953e6	−	2.63369e6i	0.238581	−	0.0700536i
$336$	−5.24313e6	+	2.39446e6i	−0.138221	+	0.0631232i
$337$	−2.28891e7	−	3.56161e7i	−0.598052	−	0.930588i	−0.999889	−	0.0148764i	$-0.995265\pi$
$337$	−2.28891e7	−	3.56161e7i	−0.598052	−	0.930588i	0.401837	−	0.915711i	$-0.368372\pi$
$338$	3.37363e6	+	990587.i	0.0873670	+	0.0256533i
$339$	2.54768e7	−	3.66300e6i	0.653951	−	0.0940239i
$340$	−3.23135e6	+	7.07567e6i	−0.0822142	+	0.180024i
$341$	−3.24838e7	−	4.67047e6i	−0.819227	−	0.117787i
$342$	37772.5	−	58775.1i	0.000944272	−	0.00146932i
$343$	1.71824e7	−	1.48886e7i	0.425796	−	0.368954i
$344$		−	1.69427e7i		−	0.416205i
$345$	−9.34722e6	+	1.53548e6i	−0.227628	+	0.0373928i
$346$	−2.89551e6			−0.0699031
$347$	−3.06242e7	−	3.53422e7i	−0.732953	−	0.845872i	0.259848	−	0.965649i	$-0.416327\pi$
$347$	−3.06242e7	−	3.53422e7i	−0.732953	−	0.845872i	−0.992801	+	0.119777i	$0.961782\pi$
$348$	−1.93496e7	−	1.24352e7i	−0.459128	−	0.295063i
$349$	8.24963e6	−	5.73774e7i	0.194070	−	1.34979i	−0.627027	−	0.778997i	$-0.715729\pi$
$349$	8.24963e6	−	5.73774e7i	0.194070	−	1.34979i	0.821097	−	0.570788i	$-0.193362\pi$
$350$	−1.82709e6	−	834402.i	−0.0426142	−	0.0194613i
$351$	−1.44133e6	−	1.00247e7i	−0.0333306	−	0.231819i
$352$	−8.86210e6	+	3.01815e7i	−0.203193	+	0.692011i
$353$	−2.27039e7	+	1.45909e7i	−0.516150	+	0.331709i	−0.772647	−	0.634836i	$-0.781068\pi$
$353$	−2.27039e7	+	1.45909e7i	−0.516150	+	0.331709i	0.256497	+	0.966545i	$0.417431\pi$
$354$	−1.32659e6	−	2.90483e6i	−0.0299039	−	0.0654804i
$355$	−3.18634e6	−	1.08517e7i	−0.0712209	−	0.242556i
$356$	−4.33285e7	−	3.75443e7i	−0.960337	−	0.832136i
$357$	2.60246e6	−	3.00340e6i	0.0571978	−	0.0660097i
$358$	−1.13747e7	+	3.33991e6i	−0.247908	+	0.0727922i
$359$	−1.05687e7	+	4.82654e6i	−0.228421	+	0.104316i	−0.526338	−	0.850275i	$-0.676435\pi$
$359$	−1.05687e7	+	4.82654e6i	−0.228421	+	0.104316i	0.297917	+	0.954592i	$0.403708\pi$
$360$	−1.24916e6	−	1.94374e6i	−0.0267739	−	0.0416610i
$361$	−4.51056e7	−	1.32442e7i	−0.958758	−	0.281517i
$362$	1.14772e7	−	1.65017e6i	0.241941	−	0.0347859i
$363$	−8.91352e6	+	1.95179e7i	−0.186350	+	0.408050i
$364$	1.64941e7	+	2.37149e6i	0.341998	+	0.0491719i
$365$	1.66758e7	−	2.59481e7i	0.342933	−	0.533614i
$366$	−4.42671e6	+	3.83576e6i	−0.0902896	+	0.0782363i
$367$			5.27269e7i			1.06668i	0.845901	+	0.533340i	$0.179063\pi$
$367$			5.27269e7i			1.06668i	−0.845901	+	0.533340i	$0.820937\pi$
$368$	−2.84890e7	+	3.42395e7i	−0.571655	+	0.687044i
$369$	−6.82378e6			−0.135814
$370$	4.13949e6	+	4.77722e6i	0.0817224	+	0.0943127i
$371$	−1.15840e7	−	7.44456e6i	−0.226848	−	0.145786i
$372$	2.53206e6	−	1.76109e7i	0.0491864	−	0.342099i
$373$	−2.29849e7	−	1.04969e7i	−0.442911	−	0.202271i	0.181460	−	0.983398i	$-0.441918\pi$
$373$	−2.29849e7	−	1.04969e7i	−0.442911	−	0.202271i	−0.624371	+	0.781128i	$0.714645\pi$
$374$	−965234.	−	6.71335e6i	−0.0184509	−	0.128329i
$375$	−6.30727e6	+	2.14806e7i	−0.119605	+	0.407336i
$376$	2.32961e7	−	1.49715e7i	0.438247	−	0.281644i
$377$	2.65582e7	+	5.81543e7i	0.495649	+	1.08532i
$378$	163250.	+	555978.i	0.00302258	+	0.0102940i
$379$	−3.43496e7	−	2.97641e7i	−0.630963	−	0.546732i	0.279593	−	0.960119i	$-0.409801\pi$
$379$	−3.43496e7	−	2.97641e7i	−0.630963	−	0.546732i	−0.910556	+	0.413386i	$0.864346\pi$
$380$	383131.	−	442157.i	0.00698227	−	0.00805797i
$381$	5.53182e7	−	1.62429e7i	1.00022	−	0.293690i
$382$	8.86566e6	−	4.04881e6i	0.159045	−	0.0726336i
$383$	3.41233e7	+	5.30970e7i	0.607373	+	0.945090i	0.999681	+	0.0252566i	$0.00804029\pi$
$383$	3.41233e7	+	5.30970e7i	0.607373	+	0.945090i	−0.392308	+	0.919834i	$0.628323\pi$
$384$	−2.16701e7	−	6.36290e6i	−0.382707	−	0.112373i
$385$	8.85913e6	−	1.27375e6i	0.155242	−	0.0223204i
$386$	5.11385e6	−	1.11978e7i	0.0889173	−	0.194702i
$387$	2.14052e7	+	3.07761e6i	0.369306	+	0.0530982i
$388$	2.91849e7	−	4.54126e7i	0.499646	−	0.777465i
$389$	3.10067e7	−	2.68674e7i	0.526752	−	0.456433i	−0.350432	−	0.936588i	$-0.613965\pi$
$389$	3.10067e7	−	2.68674e7i	0.526752	−	0.456433i	0.877184	+	0.480155i	$0.159420\pi$
$390$			3.15250e6i			0.0531449i
$391$	8.06043e6	−	2.96332e7i	0.134843	−	0.495733i
$392$	2.04560e7			0.339597
$393$	−7.42740e6	−	8.57167e6i	−0.122366	−	0.141217i
$394$	−1.01077e7	−	6.49580e6i	−0.165258	−	0.106205i
$395$	500449.	−	3.48070e6i	0.00812024	−	0.0564775i
$396$	−2.42003e7	−	1.10519e7i	−0.389704	−	0.177972i
$397$	−1.19663e7	−	8.32273e7i	−0.191244	−	1.33013i	−0.828721	−	0.559662i	$-0.810931\pi$
$397$	−1.19663e7	−	8.32273e7i	−0.191244	−	1.33013i	0.637477	−	0.770469i	$-0.279978\pi$
$398$	−1.82279e6	+	6.20786e6i	−0.0289127	+	0.0984675i
$399$	−251454.	+	161600.i	−0.00395858	+	0.00254403i
$400$	1.99688e7	+	4.37257e7i	0.312013	+	0.683213i
$401$	−3.16601e7	−	1.07824e8i	−0.490997	−	1.67218i	−0.716220	−	0.697875i	$-0.754129\pi$
$401$	−3.16601e7	−	1.07824e8i	−0.490997	−	1.67218i	0.225223	−	0.974307i	$-0.427689\pi$
$402$	−3.33965e6	−	2.89382e6i	−0.0514070	−	0.0445444i
$403$	−3.23851e7	+	3.73744e7i	−0.494800	+	0.571030i
$404$	−4.86497e7	+	1.42848e7i	−0.737795	+	0.216636i
$405$	2.68260e6	−	1.22510e6i	0.0403823	−	0.0184420i
$406$	−1.97755e6	−	3.07713e6i	−0.0295494	−	0.0459798i
$407$	1.42269e8	+	4.17740e7i	2.11022	+	0.619616i
$408$	7.41448e6	−	1.06604e6i	0.109169	−	0.0156962i
$409$	−5.05446e7	+	1.10677e8i	−0.738763	+	1.61766i	0.0468163	+	0.998904i	$0.485092\pi$
$409$	−5.05446e7	+	1.10677e8i	−0.738763	+	1.61766i	−0.785579	+	0.618761i	$0.787635\pi$
$410$	2.10244e6	+	302285.i	0.0305050	+	0.00438596i
$411$	2.42076e7	−	3.76677e7i	0.348679	−	0.542555i
$412$	−2.74923e7	+	2.38222e7i	−0.393115	+	0.340636i
$413$			1.36622e7i			0.193941i
$414$	2.99945e6	+	3.32468e6i	0.0422708	+	0.0468542i
$415$	−1.41121e7			−0.197446
$416$	3.10409e7	+	3.58231e7i	0.431175	+	0.497603i
$417$	5.68188e6	+	3.65152e6i	0.0783581	+	0.0503577i
$418$	−72598.8	+	504936.i	−0.000994032	+	0.00691365i
$419$	−2.93338e7	−	1.33963e7i	−0.398774	−	0.182114i	0.205926	−	0.978568i	$-0.433979\pi$
$419$	−2.93338e7	−	1.33963e7i	−0.398774	−	0.182114i	−0.604699	+	0.796454i	$0.706707\pi$
$420$	690555.	+	4.80291e6i	0.00932074	+	0.0648272i
$421$	7.46230e6	−	2.54143e7i	0.100006	−	0.340589i	−0.894257	−	0.447554i	$-0.852295\pi$
$421$	7.46230e6	−	2.54143e7i	0.100006	−	0.340589i	0.994263	+	0.106965i	$0.0341133\pi$
$422$	−8.93376e6	+	5.74138e6i	−0.118877	+	0.0763974i
$423$	1.46831e7	+	3.21515e7i	0.193998	+	0.424796i
$424$	−7.31233e6	−	2.49035e7i	−0.0959309	−	0.326711i
$425$	−2.50472e7	−	2.17035e7i	−0.326281	−	0.282724i
$426$	−3.50105e6	+	4.04043e6i	−0.0452866	+	0.0522636i
$427$	2.40442e7	−	7.06000e6i	0.308835	−	0.0906820i
$428$	−9.73612e7	+	4.44634e7i	−1.24181	+	0.567115i
$429$	3.99793e7	+	6.22090e7i	0.506365	+	0.787919i
$430$	−6.45871e6	−	1.89645e6i	−0.0812345	−	0.0238526i
$431$	2.39254e7	−	3.43995e6i	0.298832	−	0.0429656i	0.00873210	−	0.999962i	$-0.497220\pi$
$431$	2.39254e7	−	3.43995e6i	0.298832	−	0.0429656i	0.290100	+	0.956996i	$0.406311\pi$
$432$	5.76071e6	−	1.26142e7i	0.0714537	−	0.156462i
$433$	1.21272e8	+	1.74363e7i	1.49381	+	0.214778i	0.840294	−	0.542131i	$-0.182382\pi$
$433$	1.21272e8	+	1.74363e7i	1.49381	+	0.214778i	0.653520	+	0.756909i	$0.273291\pi$
$434$	1.52970e6	−	2.38026e6i	0.0187128	−	0.0291176i
$435$	−1.40692e7	+	1.21911e7i	−0.170924	+	0.148107i
$436$		−	3.23346e6i		−	0.0390129i
$437$	−1.20963e6	+	1.96773e6i	−0.0144946	+	0.0235788i
$438$	−1.45805e7			−0.173520
$439$	−7.53335e7	−	8.69395e7i	−0.890419	−	1.02760i	−0.999437	−	0.0335586i	$-0.989316\pi$
$439$	−7.53335e7	−	8.69395e7i	−0.890419	−	1.02760i	0.109018	−	0.994040i	$-0.465230\pi$
$440$	1.41922e7	+	9.12078e6i	0.166607	+	0.107072i
$441$	−3.71580e6	+	2.58439e7i	−0.0433247	+	0.301330i
$442$	−9.29680e6	−	4.24571e6i	−0.107663	−	0.0491681i
$443$	1.82214e7	+	1.26733e8i	0.209590	+	1.45773i	0.774498	+	0.632576i	$0.218002\pi$
$443$	1.82214e7	+	1.26733e8i	0.209590	+	1.45773i	−0.564909	+	0.825154i	$0.691089\pi$
$444$	−2.26475e7	+	7.71302e7i	−0.258744	+	0.881202i
$445$	−3.90365e7	+	2.50872e7i	−0.442987	+	0.284691i
$446$	−8.59860e6	−	1.88283e7i	−0.0969221	−	0.212230i
$447$	2.34907e7	+	8.00020e7i	0.263011	+	0.895732i
$448$	1.58350e7	+	1.37211e7i	0.176110	+	0.152600i
$449$	−1.29642e7	+	1.49615e7i	−0.143221	+	0.165286i	−0.822828	−	0.568290i	$-0.807605\pi$
$449$	−1.29642e7	+	1.49615e7i	−0.143221	+	0.165286i	0.679607	+	0.733577i	$0.262150\pi$
$450$	4.63664e6	−	1.36144e6i	0.0508822	−	0.0149404i
$451$	4.53214e7	−	2.06976e7i	0.494053	−	0.225627i
$452$	−5.50836e7	−	8.57118e7i	−0.596495	−	0.928165i
$453$	2.80901e7	+	8.24799e6i	0.302175	+	0.0887265i
$454$	2.30402e7	−	3.31268e6i	0.246217	−	0.0354007i
$455$	5.60276e6	−	1.22683e7i	0.0594796	−	0.130242i
$456$	−557670.	−	80180.8i	−0.00588143	−	0.000845621i
$457$	2.83113e7	−	4.40532e7i	0.296627	−	0.461561i	−0.660666	−	0.750680i	$-0.729726\pi$
$457$	2.83113e7	−	4.40532e7i	0.296627	−	0.461561i	0.957293	+	0.289119i	$0.0933624\pi$
$458$	2.02234e7	−	1.75237e7i	0.210503	−	0.182402i
$459$			9.56100e6i			0.0988702i
$460$	2.08995e7	+	3.11320e7i	0.214715	+	0.319840i
$461$	1.70758e8			1.74292			0.871461	−	0.490465i	$-0.163173\pi$
$461$	1.70758e8			1.74292			0.871461	+	0.490465i	$0.163173\pi$
$462$	−2.77062e6	−	3.19747e6i	−0.0280965	−	0.0324251i
$463$	3.04419e7	+	1.95638e7i	0.306711	+	0.197111i	0.684937	−	0.728602i	$-0.259830\pi$
$463$	3.04419e7	+	1.95638e7i	0.306711	+	0.197111i	−0.378227	+	0.925713i	$0.623466\pi$
$464$	−1.24579e7	+	8.66468e7i	−0.124707	+	0.867359i
$465$	−1.30990e7	−	5.98212e6i	−0.130281	−	0.0594971i
$466$	652349.	+	4.53719e6i	0.00644648	+	0.0448362i
$467$	−4.47429e7	+	1.52380e8i	−0.439312	+	1.49616i	0.381179	+	0.924501i	$0.375518\pi$
$467$	−4.47429e7	+	1.52380e8i	−0.439312	+	1.49616i	−0.820491	+	0.571659i	$0.806300\pi$
$468$	−3.37262e7	+	2.16745e7i	−0.329026	+	0.211452i
$469$	7.85362e6	+	1.71970e7i	0.0761292	+	0.166700i
$470$	−3.09966e6	−	1.05565e7i	−0.0298552	−	0.101678i
$471$	−6.17714e7	−	5.35253e7i	−0.591187	−	0.512267i
$472$	−1.68639e7	+	1.94620e7i	−0.160373	+	0.185081i
$473$	−1.51502e8	+	4.44849e7i	−1.43164	+	0.420368i
$474$	−1.51206e6	+	690536.i	−0.0141983	+	0.00648413i
$475$	1.34768e6	+	2.09703e6i	0.0125749	+	0.0195670i
$476$	−1.50939e7	−	4.43198e6i	−0.139953	−	0.0410939i
$477$	3.27911e7	−	4.71465e6i	0.302135	−	0.0434404i
$478$	−1.56665e6	+	3.43047e6i	−0.0143446	+	0.0314102i
$479$	1.64827e8	+	2.36985e7i	1.49976	+	0.215633i	0.842772	−	0.538270i	$-0.180922\pi$
$479$	1.64827e8	+	2.36985e7i	1.49976	+	0.215633i	0.656986	+	0.753903i	$0.271831\pi$
$480$	−7.46226e6	+	1.16115e7i	−0.0674756	+	0.104994i
$481$	1.68862e8	−	1.46320e8i	1.51739	−	1.31483i
$482$		−	1.99871e6i		−	0.0178488i
$483$	−5.76394e6	−	1.82691e7i	−0.0511539	−	0.162135i
$484$	8.49363e7			0.749130
$485$	−2.86119e7	−	3.30199e7i	−0.250796	−	0.289435i
$486$	−1.17277e6	−	753692.i	−0.0102165	−	0.00656576i
$487$	1.28660e7	−	8.94848e7i	0.111392	−	0.774752i	−0.855175	−	0.518339i	$-0.826550\pi$
$487$	1.28660e7	−	8.94848e7i	0.111392	−	0.774752i	0.966568	−	0.256412i	$-0.0825405\pi$
$488$	4.29658e7	+	1.96218e7i	0.369712	+	0.168842i
$489$	−5.14884e6	−	3.58110e7i	−0.0440335	−	0.306260i
$490$	2.28971e6	−	7.79802e6i	0.0194622	−	0.0662821i
$491$	−5.06743e7	+	3.25664e7i	−0.428098	+	0.275122i	−0.736897	−	0.676005i	$-0.763710\pi$
$491$	−5.06743e7	+	3.25664e7i	−0.428098	+	0.275122i	0.308798	+	0.951128i	$0.400073\pi$
$492$	1.12211e7	+	2.45707e7i	0.0942190	+	0.206311i
$493$	−1.70037e7	−	5.79092e7i	−0.141906	−	0.483289i
$494$	580955.	+	503401.i	0.00481905	+	0.00417573i
$495$	−1.41011e7	+	1.62735e7i	−0.116262	+	0.134173i
$496$	−6.49707e7	+	1.90771e7i	−0.532442	+	0.156339i
$497$	2.08056e7	−	9.50161e6i	0.169477	−	0.0773977i
$498$	3.60658e6	+	5.61194e6i	0.0292016	+	0.0454386i
$499$	1.21097e8	+	3.55572e7i	0.974610	+	0.286171i	0.729998	−	0.683450i	$-0.239521\pi$
$499$	1.21097e8	+	3.55572e7i	0.974610	+	0.286171i	0.244613	+	0.969621i	$0.421339\pi$
$500$	8.77178e7	−	1.26119e7i	0.701742	−	0.100895i
$501$	−2.78051e7	+	6.08847e7i	−0.221111	+	0.484166i
$502$	1.94315e7	+	2.79383e6i	0.153602	+	0.0220846i
$503$	−1.25169e7	+	1.94767e7i	−0.0983544	+	0.153042i	−0.886943	−	0.461878i	$-0.847176\pi$
$503$	−1.25169e7	+	1.94767e7i	−0.0983544	+	0.153042i	0.788589	+	0.614921i	$0.210812\pi$
$504$	3.53141e6	−	3.05998e6i	0.0275839	−	0.0239016i
$505$			4.10381e7i			0.318649i
$506$	−3.00057e7	−	1.29837e7i	−0.231607	−	0.100218i
$507$	3.61901e7			0.277693
$508$	−1.49452e8	−	1.72477e8i	−1.14002	−	1.31565i
$509$	−1.38834e8	−	8.92234e7i	−1.05279	−	0.676589i	−0.104675	−	0.994506i	$-0.533380\pi$
$509$	−1.38834e8	−	8.92234e7i	−1.05279	−	0.676589i	−0.948119	+	0.317917i	$0.897017\pi$
$510$	423540.	−	2.94579e6i	0.00319289	−	0.0222071i
$511$	5.67419e7	+	2.59131e7i	0.425247	+	0.194204i
$512$	1.55847e7	+	1.08394e8i	0.116115	+	0.807599i
$513$	202599.	−	689989.i	0.00150067	−	0.00511081i
$514$	−2.47027e7	+	1.58755e7i	−0.181910	+	0.116906i
$515$	1.22311e7	+	2.67823e7i	0.0895452	+	0.196077i
$516$	−2.41172e7	−	8.21355e7i	−0.175540	−	0.597836i
$517$	−1.95041e8	−	1.69004e8i	−1.41141	−	1.22300i
$518$	−8.37155e6	+	9.66128e6i	−0.0602305	+	0.0695097i
$519$	−2.85957e7	+	8.39645e6i	−0.204549	+	0.0600611i
$520$	2.31246e7	−	1.05607e7i	0.164462	−	0.0751071i
$521$	−7.05799e7	−	1.09824e8i	−0.499077	−	0.776579i	0.496745	−	0.867897i	$-0.334529\pi$
$521$	−7.05799e7	−	1.09824e8i	−0.499077	−	0.776579i	−0.995822	+	0.0913175i	$0.970892\pi$
$522$	8.44363e6	+	2.47927e6i	0.0593632	+	0.0174306i
$523$	−1.61704e8	+	2.32495e7i	−1.13036	+	0.162521i	−0.682013	−	0.731340i	$-0.738895\pi$
$523$	−1.61704e8	+	2.32495e7i	−1.13036	+	0.162521i	−0.448344	+	0.893861i	$0.647986\pi$
$524$	−1.86507e7	+	4.08394e7i	−0.129629	+	0.283848i
$525$	−2.04637e7	−	2.94223e6i	−0.141418	−	0.0203329i
$526$	1.35675e7	−	2.11115e7i	0.0932273	−	0.145065i
$527$	3.52828e7	−	3.05728e7i	0.241064	−	0.208883i
$528$			1.01253e8i			0.687867i
$529$	−1.01343e8	−	1.07908e8i	−0.684585	−	0.728933i
$530$	−1.03119e7			−0.0692648
$531$	−2.15248e7	−	2.48409e7i	−0.143766	−	0.165914i
$532$	995370.	+	639686.i	0.00661073	+	0.00424846i
$533$	1.06850e7	−	7.43156e7i	0.0705654	−	0.490793i
$534$	1.99528e7	+	9.11215e6i	0.131033	+	0.0598407i
$535$	1.23287e7	+	8.57483e7i	0.0805114	+	0.559969i
$536$	−1.00395e7	+	3.41915e7i	−0.0651957	+	0.222036i
$537$	−1.02650e8	+	6.59690e7i	−0.662880	+	0.426007i
$538$	−1.64541e6	−	3.60295e6i	−0.0105664	−	0.0231373i
$539$	−5.37095e7	−	1.82918e8i	−0.342993	−	1.16813i
$540$	−8.82256e6	−	7.64480e6i	−0.0560291	−	0.0485495i
$541$	1.33717e8	−	1.54318e8i	0.844493	−	0.974596i	−0.155420	−	0.987849i	$-0.549673\pi$
$541$	1.33717e8	−	1.54318e8i	0.844493	−	0.974596i	0.999912	+	0.0132521i	$0.00421840\pi$
$542$	−3.46493e7	+	1.01740e7i	−0.217619	+	0.0638988i
$543$	1.08562e8	−	4.95786e7i	0.678076	−	0.309667i
$544$	−2.41926e7	−	3.76445e7i	−0.150275	−	0.233832i
$545$	−2.51106e6	−	737315.i	−0.0155120	−	0.00455474i
$546$	−6.31061e6	+	907328.i	−0.0387698	+	0.00557425i
$547$	1.15805e7	−	2.53578e7i	0.0707563	−	0.154935i	−0.870949	−	0.491373i	$-0.836495\pi$
$547$	1.15805e7	−	2.53578e7i	0.0707563	−	0.154935i	0.941705	+	0.336438i	$0.109222\pi$
$548$	−1.75439e8	−	2.52243e7i	−1.06606	−	0.153277i
$549$	−3.25946e7	+	5.07182e7i	−0.196983	+	0.306511i
$550$	−2.66657e7	+	2.31059e7i	−0.160275	+	0.138879i
$551$			4.53944e6i			0.0271361i
$552$	1.43397e7	−	3.31394e7i	0.0852554	−	0.197028i
$553$	7.11163e6			0.0420527
$554$	−6.12156e6	−	7.06466e6i	−0.0360025	−	0.0415491i
$555$	5.47341e7	+	3.51755e7i	0.320169	+	0.205760i
$556$	3.80489e6	−	2.64636e7i	0.0221369	−	0.153966i
$557$	1.36720e8	+	6.24380e7i	0.791165	+	0.361313i	0.769659	−	0.638456i	$-0.220426\pi$
$557$	1.36720e8	+	6.24380e7i	0.791165	+	0.361313i	0.0215065	+	0.999769i	$0.493154\pi$
$558$	968762.	+	6.73789e6i	0.00557590	+	0.0387812i
$559$	−6.70345e7	+	2.28298e8i	−0.383763	+	1.30698i
$560$	1.55355e7	−	9.98409e6i	0.0884632	−	0.0568518i
$561$	−2.90000e7	−	6.35012e7i	−0.164252	−	0.359661i
$562$	4.69440e6	+	1.59877e7i	0.0264467	+	0.0900691i
$563$	1.34876e8	+	1.16871e8i	0.755804	+	0.654908i	0.945014	−	0.327028i	$-0.106047\pi$
$563$	1.34876e8	+	1.16871e8i	0.755804	+	0.654908i	−0.189210	+	0.981937i	$0.560593\pi$
$564$	9.16244e7	−	1.05740e8i	0.510709	−	0.589390i
$565$	−7.91232e7	+	2.32327e7i	−0.438691	+	0.128811i
$566$	−2.49953e7	+	1.14150e7i	−0.137851	+	0.0629543i
$567$	3.22447e6	+	5.01738e6i	0.0176893	+	0.0275250i
$568$	4.13662e7	+	1.21462e7i	0.225736	+	0.0662820i
$569$	1.13566e8	−	1.63283e7i	0.616467	−	0.0886346i	0.172995	−	0.984923i	$-0.444656\pi$
$569$	1.13566e8	−	1.63283e7i	0.616467	−	0.0886346i	0.443472	+	0.896288i	$0.353747\pi$
$570$	−92987.3	+	203614.i	−0.000502110	+	0.00109947i
$571$	−1.72424e8	−	2.47908e7i	−0.926167	−	0.133163i	−0.337304	−	0.941396i	$-0.609515\pi$
$571$	−1.72424e8	−	2.47908e7i	−0.926167	−	0.133163i	−0.588863	+	0.808233i	$0.700424\pi$
$572$	1.58257e8	−	2.46252e8i	0.845617	−	1.31581i
$573$	7.58154e7	−	6.56944e7i	0.402989	−	0.349192i
$574$			4.29562e6i			0.0227138i
$575$	−1.52358e8	+	4.80691e7i	−0.801421	+	0.252850i
$576$	−5.04092e7			−0.263780
$577$	−1.18910e8	−	1.37229e8i	−0.619000	−	0.714364i	0.356517	−	0.934289i	$-0.383964\pi$
$577$	−1.18910e8	−	1.37229e8i	−0.619000	−	0.714364i	−0.975517	+	0.219925i	$0.929419\pi$
$578$	−2.26364e7	−	1.45475e7i	−0.117226	−	0.0753364i
$579$	1.80323e7	−	1.25417e8i	0.0928997	−	0.646132i
$580$	6.70324e7	+	3.06127e7i	0.343559	+	0.156898i
$581$	−4.06164e6	−	2.82493e7i	−0.0207097	−	0.144039i
$582$	−5.81874e6	+	1.98168e7i	−0.0295162	+	0.100523i
$583$	−2.03488e8	+	1.30774e8i	−1.02691	+	0.659955i
$584$	4.88438e7	+	1.06953e8i	0.245228	+	0.536975i
$585$	9.14168e6	+	3.11337e7i	0.0456624	+	0.155512i
$586$	1.90118e7	+	1.64738e7i	0.0944777	+	0.0818654i
$587$	2.84920e7	−	3.28815e7i	0.140867	−	0.162569i	−0.680932	−	0.732346i	$-0.738425\pi$
$587$	2.84920e7	−	3.28815e7i	0.140867	−	0.162569i	0.821799	+	0.569778i	$0.192971\pi$
$588$	9.91676e7	−	2.91182e7i	0.487795	−	0.143230i
$589$	−3.19410e6	+	1.45870e6i	−0.0156316	+	0.00713869i
$590$	5.53146e6	+	8.60711e6i	0.0269329	+	0.0419084i
$591$	−1.18659e8	−	3.48413e7i	−0.574826	−	0.168784i
$592$	3.02825e8	−	4.35396e7i	1.45957	−	0.209855i
$593$	−5.52140e7	+	1.20902e8i	−0.264780	+	0.579787i	−0.994592	−	0.103861i	$-0.966880\pi$
$593$	−5.52140e7	+	1.20902e8i	−0.264780	+	0.579787i	0.729812	+	0.683648i	$0.239608\pi$
$594$	1.00752e7	+	1.44860e6i	0.0480723	+	0.00691176i
$595$	−6.88364e6	+	1.07112e7i	−0.0326789	+	0.0508494i
$596$	2.49438e8	−	2.16139e8i	1.17821	−	1.02093i
$597$			6.65939e7i			0.312976i
$598$	−4.09047e7	+	2.74601e7i	−0.191280	+	0.128410i
$599$	2.93297e8			1.36467			0.682333	−	0.731041i	$-0.260965\pi$
$599$	2.93297e8			1.36467			0.682333	+	0.731041i	$0.260965\pi$
$600$	−2.55191e7	−	2.94506e7i	−0.118144	−	0.136345i
$601$	−4.66080e6	−	2.99531e6i	−0.0214702	−	0.0137981i	0.529862	−	0.848084i	$-0.322244\pi$
$601$	−4.66080e6	−	2.99531e6i	−0.0214702	−	0.0137981i	−0.551332	+	0.834286i	$0.685880\pi$
$602$	1.93737e6	−	1.34747e7i	0.00888023	−	0.0617633i
$603$	−4.13735e7	−	1.88946e7i	−0.188699	−	0.0861760i
$604$	−1.64925e7	−	1.14708e8i	−0.0748474	−	0.520575i
$605$	1.93677e7	−	6.59605e7i	0.0874607	−	0.297864i
$606$	1.63195e7	−	1.04879e7i	0.0733314	−	0.0471272i
$607$	1.30134e8	+	2.84955e8i	0.581870	+	1.27412i	0.940232	+	0.340535i	$0.110608\pi$
$607$	1.30134e8	+	2.84955e8i	0.581870	+	1.27412i	−0.358361	+	0.933583i	$0.616664\pi$
$608$	948218.	+	3.22934e6i	0.00421888	+	0.0143682i
$609$	−2.84531e7	−	2.46548e7i	−0.125973	−	0.109156i
$610$	1.22893e7	−	1.41826e7i	0.0541424	−	0.0624836i
$611$	−3.73143e8	+	1.09565e8i	−1.63588	+	0.480339i
$612$	3.44267e7	−	1.57222e7i	0.150190	−	0.0685895i
$613$	1.89505e8	+	2.94876e8i	0.822697	+	1.28014i	0.957258	+	0.289237i	$0.0934015\pi$
$613$	1.89505e8	+	2.94876e8i	0.822697	+	1.28014i	−0.134560	+	0.990905i	$0.542962\pi$
$614$	2.62276e7	+	7.70113e6i	0.113306	+	0.0332697i
$615$	2.16400e7	−	3.11136e6i	0.0930318	−	0.0133760i
$616$	−1.41731e7	+	3.10348e7i	−0.0606349	+	0.132772i
$617$	−1.05442e8	−	1.51603e7i	−0.448908	−	0.0645433i	−0.0858466	−	0.996308i	$-0.527359\pi$
$617$	−1.05442e8	−	1.51603e7i	−0.448908	−	0.0645433i	−0.363062	+	0.931765i	$0.618269\pi$
$618$	7.52463e6	−	1.17086e7i	0.0318801	−	0.0496064i
$619$	1.90786e8	−	1.65317e8i	0.804404	−	0.697020i	−0.152219	−	0.988347i	$-0.548642\pi$
$619$	1.90786e8	−	1.65317e8i	0.804404	−	0.697020i	0.956624	+	0.291326i	$0.0940966\pi$
$620$			5.70032e7i			0.239179i
$621$	3.92631e7	+	2.41363e7i	0.163950	+	0.100785i
$622$	8.73030e6			0.0362792
$623$	−6.14543e7	−	7.09221e7i	−0.254149	−	0.293304i
$624$	1.28357e8	+	8.24899e7i	0.528281	+	0.339506i
$625$	−1.89905e7	+	1.32082e8i	−0.0777851	+	0.541007i
$626$	−2.11721e7	−	9.66896e6i	−0.0863059	−	0.0394146i
$627$	747245.	+	5.19720e6i	0.00303152	+	0.0210847i
$628$	−9.11535e7	+	3.10440e8i	−0.368039	+	1.25343i
$629$	−1.77448e8	+	1.14039e8i	−0.713049	+	0.458249i
$630$	−771211.	−	1.68872e6i	−0.00308426	−	0.00675360i
$631$	3.92427e7	+	1.33648e8i	0.156196	+	0.531956i	0.999989	−	0.00471373i	$-0.00150043\pi$
$631$	3.92427e7	+	1.33648e8i	0.156196	+	0.531956i	−0.843793	+	0.536669i	$0.819682\pi$
$632$	1.01306e7	+	8.77823e6i	0.0401315	+	0.0347741i
$633$	−7.15797e7	+	8.26074e7i	−0.282214	+	0.325693i
$634$	6.34114e7	−	1.86193e7i	0.248828	−	0.0730625i
$635$	−1.68022e8	+	7.67333e7i	−0.656215	+	0.299683i
$636$	−7.08980e7	−	1.10319e8i	−0.275589	−	0.428826i
$637$	−2.75640e8	−	8.09351e7i	−1.06641	−	0.313126i
$638$	−6.36000e7	+	9.14429e6i	−0.244903	+	0.0352118i
$639$	−2.28595e7	+	5.00552e7i	−0.0876119	+	0.191843i
$640$	7.16226e7	+	1.02978e7i	0.273218	+	0.0392829i
$641$	2.20346e8	−	3.42865e8i	0.836624	−	1.30181i	−0.114631	−	0.993408i	$-0.536569\pi$
$641$	2.20346e8	−	3.42865e8i	0.836624	−	1.30181i	0.951255	−	0.308405i	$-0.0997951\pi$
$642$	3.09486e7	−	2.68171e7i	0.116960	−	0.101346i
$643$			4.27722e8i			1.60890i	0.594022	+	0.804449i	$0.297539\pi$
$643$			4.27722e8i			1.60890i	−0.594022	+	0.804449i	$0.702461\pi$
$644$	−5.63042e7	+	5.07963e7i	−0.210806	+	0.190184i
$645$	−6.92848e7			−0.258201
$646$	−475229.	−	548444.i	−0.00176281	−	0.00203439i
$647$	−2.92577e8	−	1.88028e8i	−1.08026	−	0.694238i	−0.125639	−	0.992076i	$-0.540098\pi$
$647$	−2.92577e8	−	1.88028e8i	−1.08026	−	0.694238i	−0.954617	+	0.297838i	$0.903735\pi$
$648$	−1.59989e6	+	1.11275e7i	−0.00587982	+	0.0408950i
$649$	2.18307e8	+	9.96975e7i	0.798608	+	0.364712i
$650$	7.56677e6	+	5.26280e7i	0.0275531	+	0.191636i
$651$	8.20482e6	−	2.79430e7i	0.0297390	−	0.101282i
$652$	−1.20479e8	+	7.74274e7i	−0.434680	+	0.279352i
$653$	2.24065e8	+	4.90633e8i	0.804700	+	1.76205i	0.628685	+	0.777660i	$0.283594\pi$
$653$	2.24065e8	+	4.90633e8i	0.804700	+	1.76205i	0.176015	+	0.984387i	$0.443679\pi$
$654$	348536.	+	1.18700e6i	0.00124599	+	0.00424345i
$655$	2.74625e7	+	2.37964e7i	0.0977275	+	0.0846813i
$656$	6.73212e7	−	7.76928e7i	0.238474	−	0.275213i
$657$	−1.43995e8	+	4.22809e7i	−0.507753	+	0.149090i
$658$	2.02396e7	−	9.24312e6i	0.0710435	−	0.0324445i
$659$	1.49413e7	+	2.32492e7i	0.0522075	+	0.0812364i	0.866376	−	0.499392i	$-0.166443\pi$
$659$	1.49413e7	+	2.32492e7i	0.0522075	+	0.0812364i	−0.814169	+	0.580628i	$0.802807\pi$
$660$	8.17846e7	+	2.40141e7i	0.284472	+	0.0835285i
$661$	4.32610e8	−	6.22000e7i	1.49793	−	0.215370i	0.655922	−	0.754829i	$-0.272280\pi$
$661$	4.32610e8	−	6.22000e7i	1.49793	−	0.215370i	0.842012	+	0.539459i	$0.181371\pi$
$662$	−3.91123e7	+	8.56439e7i	−0.134815	+	0.295204i
$663$	−1.04126e8	−	1.49710e7i	−0.357288	−	0.0513702i
$664$	2.90836e7	−	4.52550e7i	0.0993447	−	0.154583i
$665$	723743.	−	627127.i	0.00246104	−	0.00213251i
$666$		−	3.07557e7i		−	0.104113i
$667$	−2.80734e8	−	7.63617e7i	−0.946059	−	0.257335i
$668$	2.64953e8			0.888872
$669$	−1.39517e8	−	1.61012e8i	−0.465961	−	0.537748i
$670$	1.19103e7	+	7.65431e6i	0.0396004	+	0.0254497i
$671$	6.26469e7	−	4.35719e8i	0.207363	−	1.44224i
$672$	−2.53914e7	−	1.15959e7i	−0.0836718	−	0.0382116i
$673$	6.73188e7	+	4.68212e8i	0.220847	+	1.53602i	0.734847	+	0.678233i	$0.237254\pi$
$673$	6.73188e7	+	4.68212e8i	0.220847	+	1.53602i	−0.514000	+	0.857790i	$0.671837\pi$
$674$	1.80645e7	−	6.15221e7i	0.0589993	−	0.200933i
$675$	4.18430e7	−	2.68909e7i	0.136054	−	0.0874366i
$676$	−5.95111e7	−	1.30311e8i	−0.192645	−	0.421834i
$677$	−2.25996e7	−	7.69673e7i	−0.0728342	−	0.248051i	0.915026	−	0.403394i	$-0.132170\pi$
$677$	−2.25996e7	−	7.69673e7i	−0.0728342	−	0.248051i	−0.987860	+	0.155344i	$0.950352\pi$
$678$	2.94601e7	+	2.55273e7i	0.0945247	+	0.0819061i
$679$	5.78637e7	−	6.67782e7i	0.184840	−	0.213317i
$680$	−2.30272e7	+	6.76138e6i	−0.0732341	+	0.0215035i
$681$	2.17936e8	−	9.95279e7i	0.690060	−	0.315140i
$682$	−2.68713e7	−	4.18125e7i	−0.0847101	−	0.131812i
$683$	−6.81357e7	−	2.00065e7i	−0.213852	−	0.0627925i	0.173052	−	0.984913i	$-0.444637\pi$
$683$	−6.81357e7	−	2.00065e7i	−0.213852	−	0.0627925i	−0.386904	+	0.922120i	$0.626455\pi$
$684$	−2.81763e6	+	405114.i	−0.00880471	+	0.00126593i
$685$	−5.95936e7	+	1.30492e8i	−0.185408	+	0.405986i
$686$	3.40825e7	+	4.90033e6i	0.105575	+	0.0151793i
$687$	1.48909e8	−	2.31706e8i	0.459251	−	0.714608i
$688$	−2.46217e8	+	2.13349e8i	−0.756055	+	0.655125i
$689$			3.64500e8i			1.11440i
$690$	−1.10279e7	−	9.17580e6i	−0.0335697	−	0.0279317i
$691$	4.31088e8			1.30657			0.653283	−	0.757114i	$-0.273391\pi$
$691$	4.31088e8			1.30657			0.653283	+	0.757114i	$0.273391\pi$
$692$	7.72563e7	+	8.91585e7i	0.233139	+	0.269057i
$693$	−3.66344e7	−	2.35435e7i	−0.110075	−	0.0707411i
$694$	1.00794e7	−	7.01038e7i	0.0301548	−	0.209731i
$695$	−1.96837e7	−	8.98923e6i	−0.0586343	−	0.0267774i
$696$	−1.00993e7	−	7.02422e7i	−0.0299546	−	0.208339i
$697$	−1.99687e7	+	6.80072e7i	−0.0589728	+	0.200843i
$698$	7.38551e7	−	4.74638e7i	0.217177	−	0.139571i
$699$	1.95996e7	+	4.29170e7i	0.0573871	+	0.125660i
$700$	2.30563e7	+	7.85227e7i	0.0672196	+	0.228929i
$701$	−3.85859e8	−	3.34349e8i	−1.12015	−	0.970611i	−0.120390	−	0.992727i	$-0.538414\pi$
$701$	−3.85859e8	−	3.34349e8i	−1.12015	−	0.970611i	−0.999755	+	0.0221152i	$0.992960\pi$
$702$	1.00446e7	−	1.15921e7i	0.0290349	−	0.0335081i
$703$	1.52224e7	−	4.46970e6i	0.0438144	−	0.0128651i
$704$	3.34802e8	−	1.52899e8i	0.959556	−	0.438214i
$705$	−6.12237e7	−	9.52659e7i	−0.174724	−	0.271876i
$706$	−3.92179e7	−	1.15154e7i	−0.111447	−	0.0327239i
$707$	−8.21491e7	+	1.18113e7i	−0.232458	+	0.0334224i
$708$	−5.40503e7	+	1.18354e8i	−0.152299	+	0.333489i
$709$	1.03222e8	+	1.48411e7i	0.289624	+	0.0416416i	0.285595	−	0.958350i	$-0.407809\pi$
$709$	1.03222e8	+	1.48411e7i	0.289624	+	0.0416416i	0.00402829	+	0.999992i	$0.498718\pi$
$710$	9.26048e6	−	1.44096e7i	0.0258737	−	0.0402603i
$711$	−1.29305e7	+	1.12044e7i	−0.0359755	+	0.0311730i
$712$		−	1.76886e8i		−	0.490064i
$713$	−3.64800e7	−	2.22072e8i	−0.100644	−	0.612667i
$714$	6.01872e6			0.0165352
$715$	−1.55150e8	−	1.79052e8i	−0.424456	−	0.489848i
$716$	4.06335e8	+	2.61136e8i	1.10699	+	0.711422i
$717$	−5.52424e6	+	3.84219e7i	−0.0149870	+	0.104237i
$718$	−1.60062e7	−	7.30980e6i	−0.0432430	−	0.0197484i
$719$	2.42561e7	+	1.68705e8i	0.0652580	+	0.453879i	0.996084	+	0.0884157i	$0.0281804\pi$
$719$	2.42561e7	+	1.68705e8i	0.0652580	+	0.453879i	−0.930826	+	0.365463i	$0.880911\pi$
$720$	−1.25172e7	+	4.26295e7i	−0.0335358	+	0.114212i
$721$	−5.00920e7	+	3.21922e7i	−0.133648	+	0.0858903i
$722$	−2.95761e7	−	6.47625e7i	−0.0785830	−	0.172073i
$723$	−5.79590e6	−	1.97390e7i	−0.0153358	−	0.0522288i
$724$	−3.57040e8	−	3.09377e8i	−0.940807	−	0.815214i
$725$	−2.05611e8	+	2.37288e8i	−0.539552	+	0.622676i
$726$	−3.11802e7	+	9.15532e6i	−0.0814833	+	0.0239256i
$727$	−1.74375e8	+	7.96345e7i	−0.453818	+	0.207252i	−0.629191	−	0.777250i	$-0.716614\pi$
$727$	−1.74375e8	+	7.96345e7i	−0.453818	+	0.207252i	0.175374	+	0.984502i	$0.443887\pi$
$728$	2.77957e7	+	4.32509e7i	0.0720415	+	0.112099i
$729$	−1.37677e7	−	4.04255e6i	−0.0355368	−	0.0104345i
$730$	4.62386e7	−	6.64811e6i	0.118860	−	0.0170895i
$731$	9.33110e7	−	2.04323e8i	0.238881	−	0.523075i
$732$	2.36222e8	+	3.39636e7i	0.602264	+	0.0865924i
$733$	−1.71242e7	+	2.66457e7i	−0.0434808	+	0.0676575i	−0.862314	−	0.506375i	$-0.830985\pi$
$733$	−1.71242e7	+	2.66457e7i	−0.0434808	+	0.0676575i	0.818833	+	0.574032i	$0.194622\pi$
$734$	−6.03504e7	+	5.22939e7i	−0.152613	+	0.132240i
$735$		−	8.36520e7i		−	0.210676i
$736$	−2.15664e8	+	4.31767e6i	−0.540933	+	0.0108297i
$737$	3.32100e8			0.829596
$738$	−6.76774e6	−	7.81038e6i	−0.0168374	−	0.0194314i
$739$	2.08157e8	+	1.33775e8i	0.515773	+	0.331467i	0.772498	−	0.635017i	$-0.219007\pi$
$739$	2.08157e8	+	1.33775e8i	0.515773	+	0.331467i	−0.256725	+	0.966485i	$0.582643\pi$
$740$	3.66529e7	−	2.54926e8i	0.0904509	−	0.629100i
$741$	7.19721e6	+	3.28686e6i	0.0176893	+	0.00807841i
$742$	−2.96790e6	−	2.06422e7i	−0.00726504	−	0.0505294i
$743$	−6.71289e7	+	2.28620e8i	−0.163660	+	0.557375i	0.836298	+	0.548274i	$0.184715\pi$
$743$	−6.71289e7	+	2.28620e8i	−0.163660	+	0.557375i	−0.999959	+	0.00910074i	$0.997103\pi$
$744$	4.61793e7	−	2.96777e7i	0.112132	−	0.0720628i
$745$	−1.10973e8	−	2.42996e8i	−0.268378	−	0.587666i
$746$	−1.07816e7	−	3.67188e7i	−0.0259697	−	0.0884447i
$747$	5.18917e7	+	4.49644e7i	0.124490	+	0.107872i
$748$	−1.80964e8	+	2.08843e8i	−0.432401	+	0.499017i
$749$	−1.68101e8	+	4.93589e7i	−0.400059	+	0.117468i
$750$	−3.08418e7	+	1.40850e7i	−0.0731065	+	0.0333866i
$751$	1.55186e8	+	2.41475e8i	0.366382	+	0.570101i	0.974679	−	0.223608i	$-0.0717836\pi$
$751$	1.55186e8	+	2.41475e8i	0.366382	+	0.570101i	−0.608297	+	0.793709i	$0.708147\pi$
$752$	−5.10923e8	−	1.50021e8i	−1.20144	−	0.352775i
$753$	2.00005e8	−	2.87564e7i	0.468442	−	0.0673517i
$754$	−4.02224e7	+	8.80747e7i	−0.0938326	+	0.205465i
$755$	−9.28417e7	−	1.33486e7i	−0.215726	−	0.0310167i
$756$	1.27639e7	−	1.98611e7i	0.0295406	−	0.0459661i
$757$	5.23384e8	−	4.53515e8i	1.20651	−	1.04545i	0.208795	−	0.977960i	$-0.433046\pi$
$757$	5.23384e8	−	4.53515e8i	1.20651	−	1.04545i	0.997720	−	0.0674912i	$-0.0214995\pi$
$758$		−	6.88356e7i		−	0.158054i
$759$	−3.33983e8	−	4.12143e7i	−0.763833	−	0.0942590i
$760$	1.80508e6			0.00411201
$761$	−5.51887e8	−	6.36911e8i	−1.25226	−	1.44519i	−0.847523	−	0.530759i	$-0.821907\pi$
$761$	−5.51887e8	−	6.36911e8i	−1.25226	−	1.44519i	−0.404742	−	0.914431i	$-0.632639\pi$
$762$	7.34552e7	+	4.72068e7i	0.166019	+	0.106694i
$763$	753227.	−	5.23881e6i	0.00169571	−	0.0117939i
$764$	−3.61220e8	−	1.64963e8i	−0.810012	−	0.369920i
$765$	−4.35942e6	−	3.03204e7i	−0.00973743	−	0.0677253i
$766$	−2.69308e7	+	9.17179e7i	−0.0599188	+	0.204065i
$767$	3.04239e8	−	1.95522e8i	0.674262	−	0.433322i
$768$	7.17651e7	+	1.57144e8i	0.158427	+	0.346907i
$769$	−1.27892e8	−	4.35560e8i	−0.281232	−	0.957787i	−0.972053	−	0.234761i	$-0.924569\pi$
$769$	−1.27892e8	−	4.35560e8i	−0.281232	−	0.957787i	0.690821	−	0.723025i	$-0.257249\pi$
$770$	1.02443e7	+	8.87672e6i	0.0224393	+	0.0194438i
$771$	−1.97925e8	+	2.28418e8i	−0.431855	+	0.498387i
$772$	−4.81247e8	+	1.41307e8i	−1.04596	+	0.307122i
$773$	−2.21218e8	+	1.01027e8i	−0.478941	+	0.218725i	−0.640232	−	0.768182i	$-0.721162\pi$
$773$	−2.21218e8	+	1.01027e8i	−0.478941	+	0.218725i	0.161291	+	0.986907i	$0.448434\pi$
$774$	1.77068e7	+	2.75524e7i	0.0381872	+	0.0594205i
$775$	−2.33034e8	−	6.84250e7i	−0.500627	−	0.146997i
$776$	1.64855e8	−	2.37026e7i	0.352791	−	0.0507237i
$777$	−5.46604e7	+	1.19690e8i	−0.116523	+	0.255149i
$778$	6.15040e7	+	8.84294e6i	0.130606	+	0.0187784i
$779$	2.88216e6	−	4.48473e6i	0.00609686	−	0.00948690i
$780$	9.70718e7	−	8.41132e7i	0.204555	−	0.177248i
$781$		−	4.01787e8i		−	0.843419i
$782$	4.19118e7	−	2.01639e7i	0.0876428	−	0.0421653i
$783$	9.05777e7			0.188684
$784$	−2.57590e8	−	2.97274e8i	−0.534540	−	0.616892i
$785$	2.20299e8	+	1.41577e8i	0.455410	+	0.292674i
$786$	2.44460e6	−	1.70025e7i	0.00503431	−	0.0350144i
$787$	−2.61195e8	−	1.19284e8i	−0.535848	−	0.244713i	0.129063	−	0.991636i	$-0.458803\pi$
$787$	−2.61195e8	−	1.19284e8i	−0.535848	−	0.244713i	−0.664911	+	0.746923i	$0.731530\pi$
$788$	6.96681e7	+	4.84552e8i	0.142382	+	0.990289i
$789$	7.27717e7	−	2.47838e8i	0.148160	−	0.504587i
$790$	4.48029e6	−	2.87931e6i	0.00908709	−	0.00583992i
$791$	−6.92793e7	−	1.51701e8i	−0.139983	−	0.306519i
$792$	−2.31254e7	−	7.87577e7i	−0.0465493	−	0.158532i
$793$	−5.01318e8	−	4.34394e8i	−1.00529	−	0.871093i
$794$	8.33926e7	−	9.62402e7i	0.166596	−	0.192263i
$795$	−1.01839e8	+	2.99027e7i	−0.202682	+	0.0595127i
$796$	2.39787e8	−	1.09507e8i	0.475430	−	0.217122i
$797$	−1.62546e8	−	2.52926e8i	−0.321071	−	0.499595i	0.642776	−	0.766054i	$-0.277783\pi$
$797$	−1.62546e8	−	2.52926e8i	−0.321071	−	0.499595i	−0.963846	+	0.266459i	$0.914146\pi$
$798$	−434353.	−	127537.i	−0.000854740	−	0.000250974i
$799$	3.63396e8	−	5.22485e7i	0.712427	−	0.102431i
$800$	−9.67050e7	+	2.11755e8i	−0.188877	+	0.413583i
$801$	2.23475e8	+	3.21309e7i	0.434842	+	0.0625209i
$802$	9.20138e7	−	1.43176e8i	0.178373	−	0.277554i
$803$	8.28128e8	−	7.17577e8i	1.59938	−	1.38587i
$804$			1.80046e8i			0.346429i
$805$	2.66089e7	+	5.53081e7i	0.0510082	+	0.106023i
$806$	−7.48971e7			−0.143041
$807$	−2.66978e7	−	3.08109e7i	−0.0507990	−	0.0586252i
$808$	−1.31602e8	−	8.45753e7i	−0.249475	−	0.160328i
$809$	−1.17403e8	+	8.16556e8i	−0.221735	+	1.54220i	0.509739	+	0.860329i	$0.329742\pi$
$809$	−1.17403e8	+	8.16556e8i	−0.221735	+	1.54220i	−0.731473	+	0.681870i	$0.761167\pi$
$810$	4.06280e6	+	1.85542e6i	0.00764488	+	0.00349130i
$811$	9.97043e7	+	6.93459e8i	0.186918	+	1.30004i	0.839929	+	0.542696i	$0.182596\pi$
$811$	9.97043e7	+	6.93459e8i	0.186918	+	1.30004i	−0.653011	+	0.757348i	$0.726494\pi$
$812$	−4.19871e7	+	1.42995e8i	−0.0784237	+	0.267087i
$813$	−3.12690e8	+	2.00954e8i	−0.581892	+	0.373959i
$814$	9.32869e7	+	2.04270e8i	0.172961	+	0.378731i
$815$	3.26566e7	+	1.11218e8i	0.0603252	+	0.205449i
$816$	−1.08858e8	−	9.43258e7i	−0.200350	−	0.173604i
$817$	−1.10636e7	+	1.27681e7i	−0.0202876	+	0.0234131i
$818$	−1.76809e8	+	5.19157e7i	−0.323031	+	0.0948504i
$819$	−5.96917e7	+	2.72603e7i	−0.108658	+	0.0496225i
$820$	−4.67881e7	−	7.28037e7i	−0.0848582	−	0.132042i
$821$	9.79267e8	+	2.87539e8i	1.76959	+	0.519597i	0.993779	−	0.111373i	$-0.0355249\pi$
$821$	9.79267e8	+	2.87539e8i	1.76959	+	0.519597i	0.775807	+	0.630970i	$0.217343\pi$
$822$	6.71225e7	−	9.65076e6i	0.120852	−	0.0173759i
$823$	2.23915e8	−	4.90306e8i	0.401684	−	0.879564i	−0.595413	−	0.803420i	$-0.703012\pi$
$823$	2.23915e8	−	4.90306e8i	0.401684	−	0.879564i	0.997097	−	0.0761447i	$-0.0242611\pi$
$824$	−1.11093e8	−	1.59728e7i	−0.198566	−	0.0285495i
$825$	−1.96344e8	+	3.05517e8i	−0.349668	+	0.544094i
$826$	−1.56375e7	+	1.35500e7i	−0.0277477	+	0.0240436i
$827$			1.78273e8i			0.315187i	0.987504	+	0.157593i	$0.0503735\pi$
$827$			1.78273e8i			0.315187i	−0.987504	+	0.157593i	$0.949626\pi$
$828$	2.23441e7	−	1.81066e8i	0.0393614	−	0.318967i
$829$	−1.04666e8			−0.183714			−0.0918570	−	0.995772i	$-0.529280\pi$
$829$	−1.04666e8			−0.183714			−0.0918570	+	0.995772i	$0.529280\pi$
$830$	−1.39962e7	−	1.61525e7i	−0.0244780	−	0.0282491i
$831$	−8.09420e7	−	5.20183e7i	−0.141049	−	0.0906469i
$832$	7.89329e7	−	5.48991e8i	0.137053	−	0.953224i
$833$	2.46692e8	+	1.12660e8i	0.426796	+	0.194911i
$834$	1.45574e6	+	1.01249e7i	0.00250950	+	0.0174539i
$835$	6.04163e7	−	2.05759e8i	0.103775	−	0.353427i
$836$	1.74850e7	−	1.12369e7i	0.0299259	−	0.0192322i
$837$	2.91060e7	+	6.37333e7i	0.0496371	+	0.108690i
$838$	−1.37597e7	−	4.68612e7i	−0.0233817	−	0.0796309i
$839$	−3.89803e8	−	3.37766e8i	−0.660023	−	0.571913i	0.259116	−	0.965846i	$-0.416569\pi$
$839$	−3.89803e8	−	3.37766e8i	−0.660023	−	0.571913i	−0.919139	+	0.393933i	$0.871114\pi$
$840$	−9.80379e6	+	1.13142e7i	−0.0165408	+	0.0190891i
$841$	2.21168e7	−	6.49407e6i	0.0371821	−	0.0109177i
$842$	3.64897e7	−	1.66643e7i	0.0611272	−	0.0279159i
$843$	9.27226e7	+	1.44279e8i	0.154776	+	0.240836i
$844$	4.15154e8	+	1.21900e8i	0.690529	+	0.202758i
$845$	−1.14768e8	+	1.65012e7i	−0.190218	+	0.0273492i
$846$	−2.22376e7	+	4.86935e7i	−0.0367262	+	0.0804192i
$847$	1.37613e8	+	1.97857e7i	0.226469	+	0.0325613i
$848$	−2.69827e8	+	4.19859e8i	−0.442484	+	0.688519i
$849$	−2.13749e8	+	1.85215e8i	−0.349286	+	0.302658i
$850$		−	5.01938e7i		−	0.0817322i
$851$	2.03526e7	+	1.01659e9i	0.0330241	+	1.64952i
$852$	2.17826e8			0.352201
$853$	5.11933e8	+	5.90802e8i	0.824833	+	0.951908i	0.999464	−	0.0327259i	$-0.0104188\pi$
$853$	5.11933e8	+	5.90802e8i	0.824833	+	0.951908i	−0.174631	+	0.984634i	$0.555873\pi$
$854$	3.19274e7	+	2.05185e7i	0.0512614	+	0.0329437i
$855$	−327888.	+	2.28051e6i	−0.000524599	+	0.00364866i
$856$	−3.00388e8	−	1.37183e8i	−0.478918	−	0.218715i
$857$	−1.04721e7	−	7.28350e7i	−0.0166376	−	0.115717i	0.979810	−	0.199930i	$-0.0640715\pi$
$857$	−1.04721e7	−	7.28350e7i	−0.0166376	−	0.115717i	−0.996448	+	0.0842129i	$0.973162\pi$
$858$	−3.15524e7	+	1.07458e8i	−0.0499541	+	0.170128i
$859$	6.85910e8	−	4.40808e8i	1.08215	−	0.695456i	0.127097	−	0.991890i	$-0.459434\pi$
$859$	6.85910e8	−	4.40808e8i	1.08215	−	0.695456i	0.955053	+	0.296434i	$0.0957976\pi$
$860$	1.13932e8	+	2.49477e8i	0.179123	+	0.392224i
$861$	1.24565e7	+	4.24230e7i	0.0195158	+	0.0664648i
$862$	2.76662e7	+	2.39729e7i	0.0431944	+	0.0374282i
$863$	−7.33705e8	+	8.46740e8i	−1.14153	+	1.31740i	−0.200266	+	0.979742i	$0.564181\pi$
$863$	−7.33705e8	+	8.46740e8i	−1.14153	+	1.31740i	−0.941268	+	0.337659i	$0.890365\pi$
$864$	6.44365e7	−	1.89203e7i	0.0999057	−	0.0293350i
$865$	8.68559e7	−	3.96657e7i	0.134199	−	0.0612868i
$866$	1.00319e8	+	1.56099e8i	0.154464	+	0.240351i
$867$	−2.65739e8	−	7.80280e7i	−0.407754	−	0.119727i
$868$	−1.14108e8	+	1.64062e7i	−0.174484	+	0.0250870i
$869$	5.18959e7	−	1.13636e8i	0.0790813	−	0.173164i
$870$	−2.79074e7	−	4.01248e6i	−0.0423800	−	0.00609333i
$871$	2.70560e8	−	4.20999e8i	0.409458	−	0.637128i
$872$	7.53950e6	−	6.53301e6i	0.0113708	−	0.00985290i
$873$			2.12582e8i			0.319509i
$874$	−3.45193e6	+	567053.i	−0.00517044	+	0.000849356i
$875$	1.45057e8			0.216528
$876$	3.89029e8	+	4.48964e8i	0.578722	+	0.667881i
$877$	5.65645e8	+	3.63518e8i	0.838581	+	0.538923i	0.887994	−	0.459855i	$-0.152099\pi$
$877$	5.65645e8	+	3.63518e8i	0.838581	+	0.538923i	−0.0494127	+	0.998778i	$0.515735\pi$
$878$	2.47947e7	−	1.72451e8i	0.0366332	−	0.254790i
$879$	2.35529e8	+	1.07562e8i	0.346799	+	0.158378i
$880$	−4.61670e7	−	3.21098e8i	−0.0677459	−	0.471183i
$881$	−2.20265e8	+	7.50152e8i	−0.322119	+	1.09704i	0.626185	+	0.779675i	$0.284616\pi$
$881$	−2.20265e8	+	7.50152e8i	−0.322119	+	1.09704i	−0.948304	+	0.317363i	$0.897203\pi$
$882$	−3.32658e7	+	2.13786e7i	−0.0484833	+	0.0311583i
$883$	3.76958e8	+	8.25422e8i	0.547533	+	1.19893i	0.957924	+	0.287021i	$0.0926648\pi$
$883$	3.76958e8	+	8.25422e8i	0.547533	+	1.19893i	−0.410391	+	0.911910i	$0.634608\pi$
$884$	1.17318e8	+	3.99549e8i	0.169828	+	0.578380i
$885$	7.95870e7	+	6.89626e7i	0.114819	+	0.0994909i
$886$	−1.26984e8	+	1.46548e8i	−0.182578	+	0.210706i
$887$	1.20714e9	−	3.54448e8i	1.72976	−	0.507904i	0.742892	−	0.669411i	$-0.233454\pi$
$887$	1.20714e9	−	3.54448e8i	1.72976	−	0.507904i	0.986872	+	0.161507i	$0.0516354\pi$
$888$	−2.25603e8	+	1.03030e8i	−0.322186	+	0.147137i
$889$	−2.01962e8	−	3.14259e8i	−0.287451	−	0.447283i
$890$	−6.74303e7	−	1.97993e7i	−0.0956501	−	0.0280854i
$891$	1.03702e8	−	1.49101e7i	0.146607	−	0.0210789i
$892$	−3.50338e8	+	7.67134e8i	−0.493620	+	1.08088i
$893$	−2.73324e7	−	3.92980e6i	−0.0383816	−	0.00551844i
$894$	−6.82711e7	+	1.06232e8i	−0.0955486	+	0.148677i
$895$	2.95450e8	−	2.56009e8i	0.412112	−	0.357097i
$896$			1.46336e8i			0.203436i
$897$	−3.24340e8	+	3.89809e8i	−0.449390	+	0.540100i
$898$	−2.99824e7			−0.0414036
$899$	−2.89636e8	−	3.34257e8i	−0.398633	−	0.460047i
$900$	−1.65634e8	−	1.06446e8i	−0.227207	−	0.146017i
$901$	4.89708e7	−	3.40599e8i	0.0669518	−	0.465660i
$902$	6.86393e7	+	3.13465e7i	0.0935305	+	0.0427139i
$903$	−1.99410e7	−	1.38693e8i	−0.0270822	−	0.188361i
$904$	8.85620e7	−	3.01614e8i	0.119879	−	0.408269i
$905$	−3.21673e8	+	2.06726e8i	−0.433979	+	0.278901i
$906$	1.84189e7	+	4.03317e7i	0.0247673	+	0.0542327i
$907$	−3.41614e8	−	1.16343e9i	−0.457841	−	1.55926i	−0.788208	−	0.615409i	$-0.788991\pi$
$907$	−3.41614e8	−	1.16343e9i	−0.457841	−	1.55926i	0.330367	−	0.943853i	$-0.392827\pi$
$908$	−7.16749e8	−	6.21066e8i	−0.957435	−	0.829622i
$909$	1.30757e8	−	1.50901e8i	0.174089	−	0.200910i
$910$	1.95989e7	−	5.75475e6i	0.0260080	−	0.00763664i
$911$	3.06060e8	−	1.39773e8i	0.404810	−	0.184870i	−0.202596	−	0.979262i	$-0.564938\pi$
$911$	3.06060e8	−	1.39773e8i	0.404810	−	0.184870i	0.607405	+	0.794392i	$0.292210\pi$
$912$	5.85716e6	+	9.11392e6i	0.00772151	+	0.0120149i
$913$	−4.81033e8	−	1.41244e8i	−0.632066	−	0.185591i
$914$	7.85013e7	−	1.12868e7i	0.102811	−	0.0147819i
$915$	8.02405e7	−	1.75702e8i	0.104744	−	0.229358i
$916$	−1.07918e9	−	1.55163e8i	−1.40413	−	0.201884i
$917$	−3.97311e7	+	6.18228e7i	−0.0515256	+	0.0801754i
$918$	−1.09434e7	+	9.48248e6i	−0.0141456	+	0.0122573i
$919$			3.01808e8i			0.388852i	0.980917	+	0.194426i	$0.0622845\pi$
$919$			3.01808e8i			0.388852i	−0.980917	+	0.194426i	$0.937716\pi$
$920$	−3.03647e7	+	1.11632e8i	−0.0389946	+	0.143359i
$921$	2.81353e8			0.360141
$922$	1.69355e8	+	1.95446e8i	0.216076	+	0.249365i
$923$	−5.09341e8	−	3.27334e8i	−0.647744	−	0.416280i
$924$	−2.45323e7	+	1.70626e8i	−0.0310973	+	0.216287i
$925$	9.98165e8	+	4.55847e8i	1.26118	+	0.575962i
$926$	7.79946e6	+	5.42464e7i	0.00982271	+	0.0683185i
$927$	4.03596e7	−	1.37452e8i	0.0506650	−	0.172549i
$928$	−3.56631e8	+	2.29193e8i	−0.446247	+	0.286785i
$929$	1.41730e8	+	3.10346e8i	0.176773	+	0.387078i	0.977191	−	0.212364i	$-0.0681164\pi$
$929$	1.41730e8	+	3.10346e8i	0.176773	+	0.387078i	−0.800418	+	0.599442i	$0.795389\pi$
$930$	−6.14439e6	−	2.09259e7i	−0.00763889	−	0.0260157i
$931$	−1.54157e7	−	1.33578e7i	−0.0191036	−	0.0165534i
$932$	1.22304e8	−	1.41146e8i	0.151075	−	0.174349i
$933$	8.62194e7	−	2.53163e7i	0.106160	−	0.0311713i
$934$	−2.18787e8	+	9.99168e7i	−0.268523	+	0.122630i
$935$	1.20921e8	+	1.88156e8i	0.147933	+	0.230188i
$936$	−1.18680e8	−	3.48477e7i	−0.144728	−	0.0424959i
$937$	1.07870e9	−	1.55093e8i	1.31124	−	0.188527i	0.548997	−	0.835824i	$-0.315010\pi$
$937$	1.07870e9	−	1.55093e8i	1.31124	−	0.188527i	0.762238	+	0.647297i	$0.224101\pi$
$938$	−1.18943e7	+	2.60449e7i	−0.0144122	+	0.0315583i
$939$	−2.37131e8	−	3.40943e7i	−0.286412	−	0.0411799i
$940$	−2.42352e8	+	3.77106e8i	−0.291785	+	0.454026i
$941$	7.41979e8	−	6.42928e8i	0.890477	−	0.771602i	−0.0839119	−	0.996473i	$-0.526741\pi$
$941$	7.41979e8	−	6.42928e8i	0.890477	−	0.771602i	0.974389	+	0.224871i	$0.0721960\pi$
$942$		−	1.23788e8i		−	0.148090i
$943$	2.28868e8	+	2.53684e8i	0.272929	+	0.302523i
$944$	4.95185e8			0.588642
$945$	−1.25134e7	−	1.44412e7i	−0.0148279	−	0.0171123i
$946$	−2.01174e8	−	1.29287e8i	−0.237628	−	0.152714i
$947$	1.41482e8	−	9.84029e8i	0.166591	−	1.15867i	−0.719275	−	0.694725i	$-0.755526\pi$
$947$	1.41482e8	−	9.84029e8i	0.166591	−	1.15867i	0.885866	−	0.463941i	$-0.153565\pi$
$948$	6.16070e7	+	2.81350e7i	0.0723111	+	0.0330234i
$949$	−2.34993e8	−	1.63441e9i	−0.274952	−	1.91233i
$950$	−1.06361e6	+	3.62233e6i	−0.00124055	+	0.00422491i
$951$	5.72250e8	−	3.67763e8i	0.665342	−	0.427589i
$952$	−2.01623e7	−	4.41493e7i	−0.0233684	−	0.0511697i
$953$	3.24939e8	+	1.10664e9i	0.375425	+	1.27858i	0.903209	+	0.429201i	$0.141205\pi$
$953$	3.24939e8	+	1.10664e9i	0.375425	+	1.27858i	−0.527784	+	0.849379i	$0.676977\pi$
$954$	3.79181e7	+	3.28562e7i	0.0436718	+	0.0378418i
$955$	−2.10476e8	+	2.42903e8i	−0.241654	+	0.278883i
$956$	1.47432e8	−	4.32898e7i	0.168739	−	0.0495464i
$957$	−6.01589e8	+	2.74736e8i	−0.686379	+	0.313459i
$958$	1.36348e8	+	2.12162e8i	0.155079	+	0.241307i
$959$	−2.78367e8	−	8.17360e7i	−0.315618	−	0.0926739i
$960$	1.59861e8	−	2.29845e7i	0.180687	−	0.0259789i
$961$	−2.26559e8	+	4.96095e8i	−0.255277	+	0.558978i
$962$	3.34951e8	+	4.81586e7i	0.376232	+	0.0540940i
$963$	2.27880e8	−	3.54588e8i	0.255168	−	0.397050i
$964$	−6.15443e7	+	5.33284e7i	−0.0687000	+	0.0595289i
$965$			4.05952e8i			0.451745i
$966$	1.51939e7	−	2.47164e7i	0.0168554	−	0.0274191i
$967$	−2.00240e8			−0.221448			−0.110724	−	0.993851i	$-0.535317\pi$
$967$	−2.00240e8			−0.221448			−0.110724	+	0.993851i	$0.535317\pi$
$968$	1.71609e8	+	1.98047e8i	0.189197	+	0.218344i
$969$	−6.28369e6	−	4.03829e6i	−0.00690627	−	0.00443839i
$970$	9.41710e6	−	6.54974e7i	0.0103182	−	0.0717643i
$971$	−1.11894e9	−	5.11002e8i	−1.22222	−	0.558168i	−0.303404	−	0.952862i	$-0.598123\pi$
$971$	−1.11894e9	−	5.11002e8i	−1.22222	−	0.558168i	−0.918812	+	0.394694i	$0.870850\pi$
$972$	8.08342e6	+	5.62214e7i	0.00880231	+	0.0612214i
$973$	1.23292e7	−	4.19896e7i	0.0133844	−	0.0455830i
$974$	1.15183e8	−	7.40237e7i	0.124656	−	0.0801113i
$975$	2.27340e8	+	4.97806e8i	0.245280	+	0.537089i
$976$	−2.55889e8	−	8.71478e8i	−0.275234	−	0.937361i
$977$	−3.89086e8	−	3.37145e8i	−0.417217	−	0.361521i	0.420810	−	0.907149i	$-0.361746\pi$
$977$	−3.89086e8	−	3.37145e8i	−0.417217	−	0.361521i	−0.838028	+	0.545628i	$0.816291\pi$
$978$	3.58821e7	−	4.14101e7i	0.0383584	−	0.0442680i
$979$	−1.58171e9	+	4.64432e8i	−1.68569	+	0.494964i
$980$	−3.01209e8	+	1.37558e8i	−0.320030	+	0.146153i
$981$	6.88420e6	+	1.07120e7i	0.00729199	+	0.0113466i
$982$	−8.75331e7	−	2.57020e7i	−0.0924353	−	0.0271414i
$983$	−8.70935e7	+	1.25222e7i	−0.0916907	+	0.0131831i	−0.188007	−	0.982168i	$-0.560203\pi$
$983$	−8.70935e7	+	1.25222e7i	−0.0916907	+	0.0131831i	0.0963168	+	0.995351i	$0.469294\pi$
$984$	−3.46203e7	+	7.58078e7i	−0.0363367	+	0.0795662i
$985$	3.92183e8	+	5.63875e7i	0.410375	+	0.0590030i
$986$	4.94179e7	−	7.68957e7i	0.0515529	−	0.0802179i
$987$	1.73080e8	−	1.49975e8i	0.180010	−	0.155980i
$988$		−	3.13202e7i		−	0.0324754i
$989$	−6.03510e8	−	8.98992e8i	−0.623873	−	0.929324i
$990$	−3.26116e7			−0.0336099
$991$	−5.43987e8	−	6.27795e8i	−0.558943	−	0.645055i	0.404000	−	0.914759i	$-0.367620\pi$
$991$	−5.43987e8	−	6.27795e8i	−0.558943	−	0.645055i	−0.962943	+	0.269704i	$0.913074\pi$
$992$	−2.75866e8	−	1.77289e8i	−0.282595	−	0.181612i
$993$	−1.37916e8	+	9.59227e8i	−0.140853	+	0.979656i
$994$	3.15101e7	+	1.43902e7i	0.0320842	+	0.0146523i
$995$	−3.03640e7	−	2.11186e8i	−0.0308241	−	0.214386i
$996$	7.65744e7	−	2.60788e8i	0.0775006	−	0.263943i
$997$	−2.47462e8	+	1.59034e8i	−0.249703	+	0.160474i	−0.659505	−	0.751700i	$-0.729234\pi$
$997$	−2.47462e8	+	1.59034e8i	−0.249703	+	0.160474i	0.409802	+	0.912174i	$0.365598\pi$
$998$	7.94040e7	+	1.73870e8i	0.0798823	+	0.174918i
$999$	−8.91860e7	−	3.03740e8i	−0.0894541	−	0.304653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.f.a.10.15	yes	240
23.7	odd	22	inner	69.7.f.a.7.15	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.f.a.7.15	✓	240	23.7	odd	22	inner
69.7.f.a.10.15	yes	240	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.991787 + 1.14458i) q^{2} +(13.1138 + 8.42776i) q^{3} +(8.78172 - 61.0782i) q^{4} +(-45.4301 - 20.7472i) q^{5} +(3.35987 + 23.3684i) q^{6} +(28.4560 - 96.9124i) q^{7} +(160.160 - 102.928i) q^{8} +(100.946 + 221.041i) q^{9} +O(q^{10})\)	\(q+(0.991787 + 1.14458i) q^{2} +(13.1138 + 8.42776i) q^{3} +(8.78172 - 61.0782i) q^{4} +(-45.4301 - 20.7472i) q^{5} +(3.35987 + 23.3684i) q^{6} +(28.4560 - 96.9124i) q^{7} +(160.160 - 102.928i) q^{8} +(100.946 + 221.041i) q^{9} +(-21.3100 - 72.5754i) q^{10} +(-1340.90 - 1161.90i) q^{11} +(629.914 - 726.960i) q^{12} +(-2565.35 + 753.254i) q^{13} +(139.147 - 63.5461i) q^{14} +(-420.911 - 654.950i) q^{15} +(-3512.58 - 1031.39i) q^{16} +(2498.34 - 359.207i) q^{17} +(-152.882 + 334.766i) q^{18} +(-187.909 - 27.0172i) q^{19} +(-1666.16 + 2592.59i) q^{20} +(1189.92 - 1031.07i) q^{21} -2687.13i q^{22} +(4831.81 - 11166.4i) q^{23} +2967.76 q^{24} +(-8598.75 - 9923.49i) q^{25} +(-3406.44 - 2189.19i) q^{26} +(-539.088 + 3749.44i) q^{27} +(-5669.34 - 2589.10i) q^{28} +(-3403.00 - 23668.4i) q^{29} +(332.191 - 1131.34i) q^{30} +(15560.3 - 10000.0i) q^{31} +(-7364.83 - 16126.7i) q^{32} +(-7792.18 - 26537.7i) q^{33} +(2888.96 + 2503.30i) q^{34} +(-3303.42 + 3812.36i) q^{35} +(14387.2 - 4224.47i) q^{36} +(-76017.9 + 34716.2i) q^{37} +(-155.442 - 241.873i) q^{38} +(-39989.8 - 11742.1i) q^{39} +(-9411.55 + 1353.18i) q^{40} +(-11665.4 + 25543.7i) q^{41} +(2360.30 + 339.359i) q^{42} +(48113.3 - 74865.8i) q^{43} +(-82742.0 + 71696.4i) q^{44} -12136.2i q^{45} +(17573.0 - 5544.32i) q^{46} +145455. q^{47} +(-37371.1 - 43128.6i) q^{48} +(90390.4 + 58090.4i) q^{49} +(2830.13 - 19684.0i) q^{50} +(35790.1 + 16344.8i) q^{51} +(23479.2 + 163302. i) q^{52} +(38408.7 - 130808. i) q^{53} +(-4826.20 + 3101.61i) q^{54} +(36811.1 + 80605.1i) q^{55} +(-5417.52 - 18450.4i) q^{56} +(-2236.52 - 1937.95i) q^{57} +(23715.4 - 27369.0i) q^{58} +(-129785. + 38108.4i) q^{59} +(-43699.5 + 19956.9i) q^{60} +(134134. + 208717. i) q^{61} +(26878.3 + 7892.19i) q^{62} +(24294.1 - 3492.96i) q^{63} +(-86175.9 + 188699. i) q^{64} +(132172. + 19003.5i) q^{65} +(22646.5 - 35238.6i) q^{66} +(-141458. + 122574. i) q^{67} -155748. i q^{68} +(157472. - 105714. i) q^{69} -7639.85 q^{70} +(148295. + 171141. i) q^{71} +(38918.8 + 25011.6i) q^{72} +(-87892.3 + 611304. i) q^{73} +(-115129. - 52577.7i) q^{74} +(-29130.0 - 202603. i) q^{75} +(-3300.33 + 11239.9i) q^{76} +(-150759. + 96886.9i) q^{77} +(-26221.6 - 57417.3i) q^{78} +(19836.7 + 67557.5i) q^{79} +(138178. + 119732. i) q^{80} +(-38668.9 + 44626.3i) q^{81} +(-40806.6 + 11981.9i) q^{82} +(257027. - 117380. i) q^{83} +(-52526.5 - 81732.9i) q^{84} +(-120952. - 35514.8i) q^{85} +(133408. - 19181.2i) q^{86} +(154845. - 339063. i) q^{87} +(-334351. - 48072.4i) q^{88} +(502314. - 781615. i) q^{89} +(13890.9 - 12036.6i) q^{90} +270049. i q^{91} +(-639595. - 393179. i) q^{92} +288333. q^{93} +(144261. + 166486. i) q^{94} +(7976.20 + 5125.99i) q^{95} +(39330.9 - 273552. i) q^{96} +(795766. + 363414. i) q^{97} +(23158.7 + 161073. i) q^{98} +(121468. - 413682. 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

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