LMFDB - Embedded newform 69.7.f.a.37.4

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			37.4
Character	$\chi$	$=$	69.37
Dual form			69.7.f.a.28.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.8838 + 3.48940i) q^{2} +(-10.2083 - 11.7810i) q^{3} +(75.2085 - 48.3336i) q^{4} +(-156.478 + 22.4981i) q^{5} +(162.421 + 104.382i) q^{6} +(224.352 + 102.458i) q^{7} +(-206.018 + 237.757i) q^{8} +(-34.5825 + 240.527i) q^{9} +O(q^{10})$	\(q+(-11.8838 + 3.48940i) q^{2} +(-10.2083 - 11.7810i) q^{3} +(75.2085 - 48.3336i) q^{4} +(-156.478 + 22.4981i) q^{5} +(162.421 + 104.382i) q^{6} +(224.352 + 102.458i) q^{7} +(-206.018 + 237.757i) q^{8} +(-34.5825 + 240.527i) q^{9} +(1781.04 - 813.375i) q^{10} +(-525.692 + 1790.34i) q^{11} +(-1337.16 - 392.627i) q^{12} +(330.825 + 724.406i) q^{13} +(-3023.67 - 434.738i) q^{14} +(1862.41 + 1613.79i) q^{15} +(-758.208 + 1660.24i) q^{16} +(-2057.51 + 3201.55i) q^{17} +(-428.321 - 2979.04i) q^{18} +(1028.64 + 1600.60i) q^{19} +(-10681.0 + 9255.16i) q^{20} +(-1083.19 - 3689.00i) q^{21} -23110.4i q^{22} +(8692.65 - 8513.15i) q^{23} +4904.10 q^{24} +(8986.98 - 2638.82i) q^{25} +(-6459.20 - 7454.32i) q^{26} +(3186.66 - 2047.94i) q^{27} +(21825.3 - 3138.01i) q^{28} +(-31656.3 - 20344.2i) q^{29} +(-27763.7 - 12679.3i) q^{30} +(33257.6 - 38381.3i) q^{31} +(6082.54 - 42305.0i) q^{32} +(26458.4 - 12083.1i) q^{33} +(13279.6 - 45226.1i) q^{34} +(-37411.1 - 10984.9i) q^{35} +(9024.61 + 19761.1i) q^{36} +(-22762.5 - 3272.76i) q^{37} +(-17809.3 - 15431.8i) q^{38} +(5157.05 - 11292.4i) q^{39} +(26888.1 - 41838.7i) q^{40} +(11492.2 + 79930.3i) q^{41} +(25744.8 + 40059.7i) q^{42} +(-50084.4 + 43398.3i) q^{43} +(46997.1 + 160057. i) q^{44} -38415.1i q^{45} +(-73596.0 + 131501. i) q^{46} -11371.2 q^{47} +(27299.3 - 8015.79i) q^{48} +(-37207.6 - 42939.9i) q^{49} +(-97591.6 + 62718.3i) q^{50} +(58721.1 - 8442.82i) q^{51} +(59894.0 + 38491.5i) q^{52} +(-72981.0 - 33329.3i) q^{53} +(-30723.6 + 35456.9i) q^{54} +(41979.7 - 291975. i) q^{55} +(-70580.6 + 32233.1i) q^{56} +(8355.94 - 28457.7i) q^{57} +(447186. + 131306. i) q^{58} +(-27713.9 - 60685.0i) q^{59} +(218070. + 31353.7i) q^{60} +(-323123. - 279987. i) q^{61} +(-261299. + 572165. i) q^{62} +(-32402.5 + 50419.3i) q^{63} +(58711.3 + 408346. i) q^{64} +(-68064.5 - 105910. i) q^{65} +(-272263. + 235917. i) q^{66} +(59271.2 + 201859. i) q^{67} +340231. i q^{68} +(-189030. - 15503.4i) q^{69} +482917. q^{70} +(52118.7 - 15303.4i) q^{71} +(-50062.3 - 57775.0i) q^{72} +(301708. - 193896. i) q^{73} +(281925. - 40534.7i) q^{74} +(-122829. - 78937.6i) q^{75} +(154725. + 70660.6i) q^{76} +(-301375. + 347805. i) q^{77} +(-21881.8 + 152191. i) q^{78} +(342913. - 156603. i) q^{79} +(81290.2 - 276849. i) q^{80} +(-56657.1 - 16636.0i) q^{81} +(-415480. - 909774. i) q^{82} +(-42461.0 - 6104.97i) q^{83} +(-259768. - 225090. i) q^{84} +(249926. - 547261. i) q^{85} +(443758. - 690501. i) q^{86} +(83480.7 + 580621. i) q^{87} +(-317365. - 493829. i) q^{88} +(293560. - 254371. i) q^{89} +(134045. + 456517. i) q^{90} +196418. i q^{91} +(242291. - 1.06041e6i) q^{92} -791671. q^{93} +(135133. - 39678.6i) q^{94} +(-196970. - 227315. i) q^{95} +(-560486. + 360203. i) q^{96} +(-806751. + 115993. i) q^{97} +(592002. + 380457. i) q^{98} +(-412445. - 188357. 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 $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{21}{22}\right)$	$1$

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 $

$2$	−11.8838	+	3.48940i	−1.48547	+	0.436175i	−0.921094	−	0.389340i	$-0.872703\pi$
$2$	−11.8838	+	3.48940i	−1.48547	+	0.436175i	−0.564380	+	0.825515i	$0.690885\pi$
$3$	−10.2083	−	11.7810i	−0.378084	−	0.436332i
$3$	−10.2083	−	11.7810i	−0.378084	−	0.436332i
$4$	75.2085	−	48.3336i	1.17513	−	0.755212i
$5$	−156.478	+	22.4981i	−1.25182	+	0.179985i	−0.736159	−	0.676808i	$-0.763363\pi$
$5$	−156.478	+	22.4981i	−1.25182	+	0.179985i	−0.515661	+	0.856793i	$0.672454\pi$
$6$	162.421	+	104.382i	0.751951	+	0.483250i
$7$	224.352	+	102.458i	0.654087	+	0.298712i	0.714681	−	0.699451i	$-0.246572\pi$
$7$	224.352	+	102.458i	0.654087	+	0.298712i	−0.0605935	+	0.998163i	$0.519299\pi$
$8$	−206.018	+	237.757i	−0.402379	+	0.464370i
$9$	−34.5825	+	240.527i	−0.0474383	+	0.329940i
$10$	1781.04	−	813.375i	1.78104	−	0.813375i
$11$	−525.692	+	1790.34i	−0.394960	+	1.34511i	0.486842	+	0.873490i	$0.338149\pi$
$11$	−525.692	+	1790.34i	−0.394960	+	1.34511i	−0.881802	+	0.471620i	$0.843670\pi$
$12$	−1337.16	−	392.627i	−0.773822	−	0.227215i
$13$	330.825	+	724.406i	0.150580	+	0.329725i	0.969858	−	0.243673i	$-0.0783522\pi$
$13$	330.825	+	724.406i	0.150580	+	0.329725i	−0.819277	+	0.573398i	$0.805625\pi$
$14$	−3023.67	−	434.738i	−1.10192	−	0.158432i
$15$	1862.41	+	1613.79i	0.551826	+	0.478160i
$16$	−758.208	+	1660.24i	−0.185109	+	0.405333i
$17$	−2057.51	+	3201.55i	−0.418790	+	0.651650i	−0.984989	−	0.172619i	$-0.944777\pi$
$17$	−2057.51	+	3201.55i	−0.418790	+	0.651650i	0.566199	+	0.824269i	$0.308413\pi$
$18$	−428.321	−	2979.04i	−0.0734433	−	0.510810i
$19$	1028.64	+	1600.60i	0.149970	+	0.233357i	0.908108	−	0.418737i	$-0.137527\pi$
$19$	1028.64	+	1600.60i	0.149970	+	0.233357i	−0.758138	+	0.652094i	$0.773891\pi$
$20$	−10681.0	+	9255.16i	−1.33513	+	1.15690i
$21$	−1083.19	−	3689.00i	−0.116962	−	0.398337i
$22$		−	23110.4i		−	2.17040i
$23$	8692.65	−	8513.15i	0.714445	−	0.699692i
$23$	8692.65	−	8513.15i	0.714445	−	0.699692i
$24$	4904.10			0.354752
$25$	8986.98	−	2638.82i	0.575167	−	0.168884i
$26$	−6459.20	−	7454.32i	−0.367501	−	0.424119i
$27$	3186.66	−	2047.94i	0.161899	−	0.104046i
$28$	21825.3	−	3138.01i	0.994230	−	0.142949i
$29$	−31656.3	−	20344.2i	−1.29797	−	0.834157i	−0.304983	−	0.952358i	$-0.598651\pi$
$29$	−31656.3	−	20344.2i	−1.29797	−	0.834157i	−0.992990	+	0.118201i	$0.962287\pi$
$30$	−27763.7	−	12679.3i	−1.02829	−	0.469602i
$31$	33257.6	−	38381.3i	1.11636	−	1.28835i	0.162967	−	0.986631i	$-0.447893\pi$
$31$	33257.6	−	38381.3i	1.11636	−	1.28835i	0.953396	−	0.301721i	$-0.0975611\pi$
$32$	6082.54	−	42305.0i	0.185624	−	1.29105i
$33$	26458.4	−	12083.1i	0.736243	−	0.336231i
$34$	13279.6	−	45226.1i	0.337868	−	1.15067i
$35$	−37411.1	−	10984.9i	−0.872563	−	0.256208i
$36$	9024.61	+	19761.1i	0.193429	+	0.423550i
$37$	−22762.5	−	3272.76i	−0.449382	−	0.0646113i	−0.0860911	−	0.996287i	$-0.527438\pi$
$37$	−22762.5	−	3272.76i	−0.449382	−	0.0646113i	−0.363290	+	0.931676i	$0.618347\pi$
$38$	−17809.3	−	15431.8i	−0.324561	−	0.281233i
$39$	5157.05	−	11292.4i	0.0869377	−	0.190367i
$40$	26888.1	−	41838.7i	0.420126	−	0.653729i
$41$	11492.2	+	79930.3i	0.166745	+	1.15974i	0.885556	+	0.464532i	$0.153778\pi$
$41$	11492.2	+	79930.3i	0.166745	+	1.15974i	−0.718811	+	0.695205i	$0.755313\pi$
$42$	25744.8	+	40059.7i	0.347489	+	0.540704i
$43$	−50084.4	+	43398.3i	−0.629936	+	0.545843i	−0.910247	−	0.414066i	$-0.864108\pi$
$43$	−50084.4	+	43398.3i	−0.629936	+	0.545843i	0.280310	+	0.959909i	$0.409563\pi$
$44$	46997.1	+	160057.i	0.551713	+	1.87896i
$45$		−	38415.1i		−	0.421564i
$46$	−73596.0	+	131501.i	−0.756102	+	1.35100i
$47$	−11371.2			−0.109525			−0.0547624	−	0.998499i	$-0.517440\pi$
$47$	−11371.2			−0.109525			−0.0547624	+	0.998499i	$0.517440\pi$
$48$	27299.3	−	8015.79i	0.246847	−	0.0724807i
$49$	−37207.6	−	42939.9i	−0.316259	−	0.364983i
$50$	−97591.6	+	62718.3i	−0.780733	+	0.501746i
$51$	58721.1	−	8442.82i	0.442673	−	0.0636468i
$52$	59894.0	+	38491.5i	0.425964	+	0.273751i
$53$	−72981.0	−	33329.3i	−0.490210	−	0.223871i	0.154945	−	0.987923i	$-0.450480\pi$
$53$	−72981.0	−	33329.3i	−0.490210	−	0.223871i	−0.645155	+	0.764052i	$0.723207\pi$
$54$	−30723.6	+	35456.9i	−0.195115	+	0.225175i
$55$	41979.7	−	291975.i	0.252320	−	1.75492i
$56$	−70580.6	+	32233.1i	−0.401903	+	0.183543i
$57$	8355.94	−	28457.7i	0.0451202	−	0.153665i
$58$	447186.	+	131306.i	2.29194	+	0.672975i
$59$	−27713.9	−	60685.0i	−0.134940	−	0.295478i	0.830084	−	0.557638i	$-0.188292\pi$
$59$	−27713.9	−	60685.0i	−0.134940	−	0.295478i	−0.965024	+	0.262160i	$0.915565\pi$
$60$	218070.	+	31353.7i	1.00958	+	0.145156i
$61$	−323123.	−	279987.i	−1.42357	−	1.23353i	−0.931885	−	0.362753i	$-0.881837\pi$
$61$	−323123.	−	279987.i	−1.42357	−	1.23353i	−0.491682	−	0.870775i	$-0.663618\pi$
$62$	−261299.	+	572165.i	−1.09638	+	2.40074i
$63$	−32402.5	+	50419.3i	−0.129586	+	0.201639i
$64$	58711.3	+	408346.i	0.223966	+	1.55772i
$65$	−68064.5	−	105910.i	−0.247845	−	0.385655i
$66$	−272263.	+	235917.i	−0.947014	+	0.820593i
$67$	59271.2	+	201859.i	0.197069	+	0.671157i	0.997431	+	0.0716386i	$0.0228228\pi$
$67$	59271.2	+	201859.i	0.197069	+	0.671157i	−0.800361	+	0.599518i	$0.795359\pi$
$68$			340231.i			1.08205i
$69$	−189030.	−	15503.4i	−0.575418	−	0.0471932i
$70$	482917.			1.40792
$71$	52118.7	−	15303.4i	0.145619	−	0.0427577i	−0.208111	−	0.978105i	$-0.566731\pi$
$71$	52118.7	−	15303.4i	0.145619	−	0.0427577i	0.353730	+	0.935348i	$0.384913\pi$
$72$	−50062.3	−	57775.0i	−0.134126	−	0.154790i
$73$	301708.	−	193896.i	0.775566	−	0.498426i	−0.0919936	−	0.995760i	$-0.529324\pi$
$73$	301708.	−	193896.i	0.775566	−	0.498426i	0.867559	+	0.497334i	$0.165688\pi$
$74$	281925.	−	40534.7i	0.695727	−	0.100030i
$75$	−122829.	−	78937.6i	−0.291151	−	0.187111i
$76$	154725.	+	70660.6i	0.352469	+	0.160967i
$77$	−301375.	+	347805.i	−0.660138	+	0.761840i
$78$	−21881.8	+	152191.i	−0.0461104	+	0.320705i
$79$	342913.	−	156603.i	0.695508	−	0.317628i	−0.0361050	−	0.999348i	$-0.511495\pi$
$79$	342913.	−	156603.i	0.695508	−	0.317628i	0.731613	+	0.681720i	$0.238768\pi$
$80$	81290.2	−	276849.i	0.158770	−	0.540721i
$81$	−56657.1	−	16636.0i	−0.106610	−	0.0313036i
$82$	−415480.	−	909774.i	−0.753544	−	1.65003i
$83$	−42461.0	−	6104.97i	−0.0742602	−	0.0106770i	0.105085	−	0.994463i	$-0.466489\pi$
$83$	−42461.0	−	6104.97i	−0.0742602	−	0.0106770i	−0.179345	+	0.983786i	$0.557398\pi$
$84$	−259768.	−	225090.i	−0.438275	−	0.379768i
$85$	249926.	−	547261.i	0.406963	−	0.891124i
$86$	443758.	−	690501.i	0.697672	−	1.08560i
$87$	83480.7	+	580621.i	0.126773	+	0.881729i
$88$	−317365.	−	493829.i	−0.465705	−	0.724651i
$89$	293560.	−	254371.i	0.416415	−	0.360826i	−0.421311	−	0.906916i	$-0.638430\pi$
$89$	293560.	−	254371.i	0.416415	−	0.360826i	0.837726	+	0.546090i	$0.183884\pi$
$90$	134045.	+	456517.i	0.183876	+	0.626223i
$91$			196418.i			0.260649i
$92$	242291.	−	1.06041e6i	0.311152	−	1.36179i
$93$	−791671.			−0.984229
$94$	135133.	−	39678.6i	0.162696	−	0.0477719i
$95$	−196970.	−	227315.i	−0.229736	−	0.265129i
$96$	−560486.	+	360203.i	−0.633507	+	0.407130i
$97$	−806751.	+	115993.i	−0.883943	+	0.127092i	−0.569312	−	0.822122i	$-0.692790\pi$
$97$	−806751.	+	115993.i	−0.883943	+	0.127092i	−0.314632	+	0.949214i	$0.601881\pi$
$98$	592002.	+	380457.i	0.628992	+	0.404228i
$99$	−412445.	−	188357.i	−0.425070	−	0.194123i
$100$	548354.	−	632834.i	0.548354	−	0.632834i
$101$	257256.	−	1.78925e6i	0.249690	−	1.73663i	−0.350313	−	0.936633i	$-0.613925\pi$
$101$	257256.	−	1.78925e6i	0.249690	−	1.73663i	0.600003	−	0.799998i	$-0.295166\pi$
$102$	−668369.	+	305234.i	−0.629819	+	0.287629i
$103$	26053.7	−	88730.9i	0.0238429	−	0.0812013i	−0.946712	−	0.322081i	$-0.895618\pi$
$103$	26053.7	−	88730.9i	0.0238429	−	0.0812013i	0.970555	+	0.240880i	$0.0774359\pi$
$104$	−240389.	−	70584.5i	−0.213705	−	0.0627494i
$105$	252490.	+	552876.i	0.218110	+	0.477595i
$106$	983590.	+	141419.i	0.825841	+	0.118738i
$107$	840543.	+	728335.i	0.686134	+	0.594538i	0.926568	−	0.376127i	$-0.122744\pi$
$107$	840543.	+	728335.i	0.686134	+	0.594538i	−0.240434	+	0.970665i	$0.577290\pi$
$108$	140680.	−	308046.i	0.111676	−	0.244537i
$109$	−651017.	+	1.01300e6i	−0.502705	+	0.782224i	−0.996160	−	0.0875473i	$-0.972097\pi$
$109$	−651017.	+	1.01300e6i	−0.502705	+	0.782224i	0.493456	+	0.869771i	$0.335733\pi$
$110$	519939.	+	3.61626e6i	0.390638	+	2.71695i
$111$	193810.	+	301574.i	0.141712	+	0.220508i
$112$	−340211.	+	294794.i	−0.242155	+	0.209829i
$113$	−356496.	−	1.21412e6i	−0.247070	−	0.841443i	−0.985869	−	0.167517i	$-0.946425\pi$
$113$	−356496.	−	1.21412e6i	−0.247070	−	0.841443i	0.738799	−	0.673925i	$-0.235393\pi$
$114$			367343.i			0.247946i
$115$	−1.16868e6	+	1.52768e6i	−0.768423	+	1.00448i
$116$	−3.36413e6			−2.15526
$117$	−185680.	+	54520.5i	−0.115933	+	0.0340410i
$118$	541101.	+	624464.i	0.329331	+	0.380068i
$119$	−789632.	+	507466.i	−0.468580	+	0.301138i
$120$	−767381.	+	110333.i	−0.444086	+	0.0638500i
$121$	−1.43864e6	−	924556.i	−0.812073	−	0.521888i
$122$	4.81691e6	+	2.19981e6i	2.65271	+	1.21145i
$123$	824340.	−	951340.i	0.442987	−	0.511235i
$124$	646148.	−	4.49406e6i	0.338896	−	2.35708i
$125$	899993.	−	411013.i	0.460796	−	0.210439i
$126$	209132.	−	712238.i	0.104546	−	0.356052i
$127$	−1.53131e6	−	449634.i	−0.747572	−	0.219507i	−0.114311	−	0.993445i	$-0.536466\pi$
$127$	−1.53131e6	−	449634.i	−0.747572	−	0.219507i	−0.633261	+	0.773938i	$0.718284\pi$
$128$	−986283.	−	2.15966e6i	−0.470297	−	1.02981i
$129$	1.02255e6	+	147020.i	0.476338	+	0.0684870i
$130$	1.17843e6	+	1.02111e6i	0.536380	+	0.464776i
$131$	1.83202e6	−	4.01157e6i	0.814923	−	1.78443i	0.230316	−	0.973116i	$-0.426024\pi$
$131$	1.83202e6	−	4.01157e6i	0.814923	−	1.78443i	0.584607	−	0.811317i	$-0.301249\pi$
$132$	1.40587e6	−	2.18758e6i	0.611257	−	0.951135i
$133$	66783.5	+	464490.i	0.0283867	+	0.197434i
$134$	−1.40873e6	−	2.19203e6i	−0.585483	−	0.911029i
$135$	−452567.	+	392151.i	−0.183942	+	0.159387i
$136$	−337308.	−	1.14877e6i	−0.134094	−	0.456683i
$137$			2.68880e6i			1.04567i	0.852433	+	0.522837i	$0.175126\pi$
$137$			2.68880e6i			1.04567i	−0.852433	+	0.522837i	$0.824874\pi$
$138$	2.30049e6	−	475362.i	0.875354	−	0.180879i
$139$	884880.			0.329488			0.164744	−	0.986336i	$-0.447320\pi$
$139$	884880.			0.329488			0.164744	+	0.986336i	$0.447320\pi$
$140$	−3.34457e6	+	982056.i	−1.21887	+	0.357892i
$141$	116080.	+	133964.i	0.0414095	+	0.0477892i
$142$	−565969.	+	363726.i	−0.197664	+	0.127031i
$143$	−1.47085e6	+	211476.i	−0.502990	+	0.0723190i
$144$	−373112.	−	239784.i	−0.124954	−	0.0803033i
$145$	5.41120e6	+	2.47121e6i	1.77496	+	0.810599i
$146$	−2.90886e6	+	3.35700e6i	−0.934682	+	1.07868i
$147$	−126048.	+	876684.i	−0.0396811	+	0.275988i
$148$	−1.87012e6	+	854055.i	−0.576878	+	0.263451i
$149$	1.37797e6	−	4.69293e6i	0.416563	−	1.41868i	−0.437831	−	0.899057i	$-0.644253\pi$
$149$	1.37797e6	−	4.69293e6i	0.416563	−	1.41868i	0.854394	−	0.519626i	$-0.173929\pi$
$150$	1.73512e6	+	509478.i	0.514111	+	0.150957i
$151$	−1.15836e6	−	2.53646e6i	−0.336445	−	0.736711i	0.663490	−	0.748186i	$-0.269075\pi$
$151$	−1.15836e6	−	2.53646e6i	−0.336445	−	0.736711i	−0.999934	+	0.0114746i	$0.996347\pi$
$152$	−592472.	−	85184.7i	−0.168709	−	0.0242566i
$153$	−698905.	−	605605.i	−0.195139	−	0.169089i
$154$	2.36785e6	−	5.18486e6i	0.648323	−	1.41963i
$155$	−4.34056e6	+	6.75404e6i	−1.16560	+	1.81371i
$156$	−157946.	−	1.09854e6i	−0.0416041	−	0.289363i
$157$	1.72930e6	+	2.69085e6i	0.446861	+	0.695329i	0.989483	−	0.144648i	$-0.0462050\pi$
$157$	1.72930e6	+	2.69085e6i	0.446861	+	0.695329i	−0.542623	+	0.839977i	$0.682569\pi$
$158$	−3.52865e6	+	3.05760e6i	−0.894618	+	0.775191i
$159$	352358.	+	1.20002e6i	0.0876583	+	0.298537i
$160$			6.75663e6i			1.64957i
$161$	2.82245e6	−	1.01931e6i	0.676315	−	0.244246i
$162$	731351.			0.172021
$163$	1.42168e6	−	417442.i	0.328275	−	0.0963903i	−0.113442	−	0.993545i	$-0.536188\pi$
$163$	1.42168e6	−	417442.i	0.328275	−	0.0963903i	0.441717	+	0.897154i	$0.354369\pi$
$164$	4.72763e6	+	5.45598e6i	1.07180	+	1.23692i
$165$	−3.86829e6	+	2.48600e6i	−0.861127	+	0.553413i
$166$	525901.	−	75613.1i	0.114969	−	0.0165300i
$167$	−6.42867e6	−	4.13145e6i	−1.38029	−	0.887061i	−0.380998	−	0.924576i	$-0.624420\pi$
$167$	−6.42867e6	−	4.13145e6i	−1.38029	−	0.887061i	−0.999296	+	0.0375146i	$0.988056\pi$
$168$	1.10024e6	+	502464.i	0.232039	+	0.105969i
$169$	2.74557e6	−	3.16856e6i	0.568817	−	0.656449i
$170$	−1.06046e6	+	7.37564e6i	−0.215847	+	1.50125i
$171$	−420559.	+	192063.i	−0.0841083	+	0.0384110i
$172$	−1.66917e6	+	5.68468e6i	−0.328032	+	1.11717i
$173$	8.76465e6	+	2.57353e6i	1.69276	+	0.497040i	0.979088	−	0.203436i	$-0.0652109\pi$
$173$	8.76465e6	+	2.57353e6i	1.69276	+	0.497040i	0.713676	+	0.700476i	$0.247029\pi$
$174$	−3.01808e6	−	6.60868e6i	−0.572906	−	1.25449i
$175$	2.28661e6	+	328765.i	0.426657	+	0.0613440i
$176$	−2.57382e6	−	2.23023e6i	−0.472106	−	0.409082i
$177$	−432017.	+	945986.i	−0.0779079	+	0.170594i
$178$	−2.60100e6	+	4.04724e6i	−0.461191	+	0.717628i
$179$	−839615.	−	5.83965e6i	−0.146393	−	1.01819i	−0.922061	−	0.387045i	$-0.873496\pi$
$179$	−839615.	−	5.83965e6i	−0.146393	−	1.01819i	0.775668	−	0.631142i	$-0.217413\pi$
$180$	−1.85674e6	−	2.88914e6i	−0.318370	−	0.495394i
$181$	−8.56684e6	+	7.42321e6i	−1.44472	+	1.25186i	−0.529869	+	0.848079i	$0.677759\pi$
$181$	−8.56684e6	+	7.42321e6i	−1.44472	+	1.25186i	−0.914855	+	0.403782i	$0.867695\pi$
$182$	−685379.	−	2.33419e6i	−0.113689	−	0.387188i
$183$			6.66489e6i			1.08753i
$184$	233221.	+	3.82060e6i	0.0374381	+	0.613308i
$185$	3.63545e6			0.574174
$186$	9.40806e6	−	2.76246e6i	1.46205	−	0.429296i
$187$	−4.65026e6	−	5.36668e6i	−0.711135	−	0.820694i
$188$	−855210.	+	549610.i	−0.128706	+	0.0827144i
$189$	924762.	−	132961.i	0.136976	−	0.0196942i
$190$	3.13394e6	+	2.01406e6i	0.456909	+	0.293638i
$191$	4.43239e6	+	2.02420e6i	0.636118	+	0.290505i	0.707252	−	0.706961i	$-0.249935\pi$
$191$	4.43239e6	+	2.02420e6i	0.636118	+	0.290505i	−0.0711341	+	0.997467i	$0.522662\pi$
$192$	4.21137e6	−	4.86018e6i	0.595004	−	0.686671i
$193$	−136156.	+	946985.i	−0.0189393	+	0.131726i	−0.997097	−	0.0761365i	$-0.975742\pi$
$193$	−136156.	+	946985.i	−0.0189393	+	0.131726i	0.978158	+	0.207862i	$0.0666506\pi$
$194$	9.18252e6	−	4.19352e6i	1.25764	−	0.574346i
$195$	−552907.	+	1.88303e6i	−0.0745672	+	0.253953i
$196$	−4.87377e6	−	1.43107e6i	−0.647286	−	0.190060i
$197$	−1.27150e6	−	2.78420e6i	−0.166310	−	0.364168i	0.808067	−	0.589091i	$-0.200514\pi$
$197$	−1.27150e6	−	2.78420e6i	−0.166310	−	0.364168i	−0.974376	+	0.224923i	$0.927787\pi$
$198$	5.55866e6	+	799215.i	0.716102	+	0.102960i
$199$	−3.29516e6	−	2.85527e6i	−0.418135	−	0.362316i	0.420237	−	0.907414i	$-0.361947\pi$
$199$	−3.29516e6	−	2.85527e6i	−0.418135	−	0.362316i	−0.838372	+	0.545098i	$0.816492\pi$
$200$	−1.22408e6	+	2.68036e6i	−0.153010	+	0.335045i
$201$	1.77304e6	−	2.75890e6i	0.218338	−	0.339741i
$202$	3.18624e6	+	2.21608e7i	0.386567	+	2.68863i
$203$	−5.01771e6	−	7.80771e6i	−0.599815	−	0.933330i
$204$	4.00825e6	−	3.47317e6i	0.472133	−	0.409106i
$205$	−3.59656e6	−	1.22487e7i	−0.417470	−	1.42177i
$206$			1.14537e6i			0.131022i
$207$	1.74702e6	+	2.38522e6i	0.196965	+	0.268917i
$208$	−1.45352e6			−0.161522
$209$	−3.40636e6	+	1.00020e6i	−0.373123	+	0.109559i
$210$	−4.92975e6	−	5.68923e6i	−0.532313	−	0.614321i
$211$	−1.26900e7	+	8.15539e6i	−1.35088	+	0.868156i	−0.997725	−	0.0674107i	$-0.978526\pi$
$211$	−1.26900e7	+	8.15539e6i	−1.35088	+	0.868156i	−0.353151	+	0.935566i	$0.614890\pi$
$212$	−7.09971e6	+	1.02078e6i	−0.745132	+	0.107134i
$213$	−712331.	−	457788.i	−0.0737129	−	0.0473724i
$214$	−1.25303e7	−	5.72239e6i	−1.27856	−	0.583897i
$215$	6.86070e6	−	7.91767e6i	0.690324	−	0.796676i
$216$	−169596.	+	1.17957e6i	−0.0168288	+	0.117047i
$217$	1.13939e7	−	5.20341e6i	1.11504	−	0.509224i
$218$	4.20179e6	−	1.43100e7i	0.405569	−	1.38124i
$219$	−5.36420e6	−	1.57507e6i	−0.510708	−	0.149957i
$220$	−1.09550e7	−	2.39880e7i	−1.02883	−	2.25282i
$221$	−2.99990e6	−	431321.i	−0.277927	−	0.0399598i
$222$	−3.35551e6	−	2.90756e6i	−0.306690	−	0.265748i
$223$	−2.13457e6	+	4.67405e6i	−0.192484	+	0.421482i	−0.981126	−	0.193372i	$-0.938058\pi$
$223$	−2.13457e6	+	4.67405e6i	−0.192484	+	0.421482i	0.788641	+	0.614854i	$0.210785\pi$
$224$	5.69912e6	−	8.86800e6i	0.507065	−	0.789009i
$225$	323913.	+	2.25287e6i	0.0284368	+	0.197782i
$226$	8.47306e6	+	1.31843e7i	0.734032	+	1.14218i
$227$	−7.78941e6	+	6.74956e6i	−0.665927	+	0.577029i	−0.920843	−	0.389934i	$-0.872498\pi$
$227$	−7.78941e6	+	6.74956e6i	−0.665927	+	0.577029i	0.254916	+	0.966963i	$0.417952\pi$
$228$	−747026.	−	2.54414e6i	−0.0630276	−	0.214652i
$229$		−	1.50450e7i		−	1.25281i	−0.779496	−	0.626407i	$-0.784525\pi$
$229$		−	1.50450e7i		−	1.25281i	0.779496	−	0.626407i	$-0.215475\pi$
$230$	8.55760e6	−	2.22327e7i	0.703345	−	1.82729i
$231$	7.17399e6			0.582003
$232$	1.13587e7	−	3.33523e6i	0.909634	−	0.267093i
$233$	1.12287e7	+	1.29587e7i	0.887695	+	1.02445i	0.999528	+	0.0307273i	$0.00978233\pi$
$233$	1.12287e7	+	1.29587e7i	0.887695	+	1.02445i	−0.111833	+	0.993727i	$0.535672\pi$
$234$	2.01634e6	−	1.29582e6i	0.157368	−	0.101134i
$235$	1.77934e6	−	255830.i	0.137105	−	0.0197128i
$236$	−5.01745e6	−	3.22452e6i	−0.381722	−	0.245318i
$237$	−5.34548e6	−	2.44120e6i	−0.401552	−	0.183383i
$238$	7.61308e6	−	8.78596e6i	0.564715	−	0.651716i
$239$	3.44348e6	−	2.39499e7i	0.252234	−	1.75433i	−0.332501	−	0.943103i	$-0.607892\pi$
$239$	3.44348e6	−	2.39499e7i	0.252234	−	1.75433i	0.584735	−	0.811225i	$-0.301199\pi$
$240$	−4.09138e6	+	1.86847e6i	−0.295962	+	0.135161i
$241$	2.76590e6	−	9.41980e6i	0.197600	−	0.672962i	−0.799759	−	0.600322i	$-0.795039\pi$
$241$	2.76590e6	−	9.41980e6i	0.197600	−	0.672962i	0.997358	−	0.0726406i	$-0.0231426\pi$
$242$	2.03226e7	+	5.96726e6i	1.43395	+	0.421045i
$243$	382382.	+	837301.i	0.0266489	+	0.0583529i
$244$	−3.78344e7	−	5.43976e6i	−2.60446	−	0.374464i
$245$	6.78822e6	+	5.88203e6i	0.461591	+	0.399971i
$246$	−6.47669e6	+	1.41820e7i	−0.435059	+	0.952646i
$247$	−819182.	+	1.27467e6i	−0.0543613	+	0.0845878i
$248$	2.27378e6	+	1.58145e7i	0.149071	+	1.03681i
$249$	361531.	+	562553.i	0.0234179	+	0.0364389i
$250$	−9.26114e6	+	8.02483e6i	−0.592713	+	0.513589i
$251$	1.32937e6	+	4.52741e6i	0.0840667	+	0.286305i	0.990787	−	0.135427i	$-0.0432406\pi$
$251$	1.32937e6	+	4.52741e6i	0.0840667	+	0.286305i	−0.906721	+	0.421732i	$0.861422\pi$
$252$			5.35809e6i			0.334818i
$253$	1.06718e7	+	2.00381e7i	0.658985	+	1.23736i
$254$	1.97668e7			1.20624
$255$	−8.99858e6	+	2.64222e6i	−0.542692	+	0.159349i
$256$	1.96649e6	+	2.26945e6i	0.117212	+	0.135270i
$257$	−2.65872e6	+	1.70866e6i	−0.156629	+	0.100660i	−0.616608	−	0.787271i	$-0.711494\pi$
$257$	−2.65872e6	+	1.70866e6i	−0.156629	+	0.100660i	0.459978	+	0.887930i	$0.347857\pi$
$258$	−1.26648e7	+	1.82092e6i	−0.737460	+	0.106031i
$259$	−4.77149e6	−	3.06645e6i	−0.274634	−	0.176497i
$260$	−1.02381e7	−	4.67556e6i	−0.582502	−	0.266020i
$261$	5.98808e6	−	6.91062e6i	0.336796	−	0.388683i
$262$	−7.77342e6	+	5.40653e7i	−0.432223	+	3.00618i
$263$	2.80258e7	−	1.27990e7i	1.54060	−	0.703570i	0.549357	−	0.835588i	$-0.314873\pi$
$263$	2.80258e7	−	1.27990e7i	1.54060	−	0.703570i	0.991247	+	0.132017i	$0.0421454\pi$
$264$	−2.57804e6	+	8.78001e6i	−0.140113	+	0.477181i
$265$	1.21697e7	+	3.57336e6i	0.653948	+	0.192017i
$266$	−2.41443e6	−	5.28687e6i	−0.128283	−	0.280901i
$267$	−5.99348e6	−	861732.i	−0.314880	−	0.0452729i
$268$	1.42143e7	+	1.23167e7i	0.738448	+	0.639869i
$269$	−1.15866e7	+	2.53712e7i	−0.595251	+	1.30342i	0.336966	+	0.941517i	$0.390599\pi$
$269$	−1.15866e7	+	2.53712e7i	−0.595251	+	1.30342i	−0.932217	+	0.361900i	$0.882128\pi$
$270$	4.00984e6	−	6.23943e6i	0.203721	−	0.316996i
$271$	3.17797e6	+	2.21033e7i	0.159677	+	1.11058i	0.899229	+	0.437478i	$0.144128\pi$
$271$	3.17797e6	+	2.21033e7i	0.159677	+	1.11058i	−0.739552	+	0.673099i	$0.764963\pi$
$272$	−3.75534e6	−	5.84342e6i	−0.186613	−	0.290376i
$273$	2.31399e6	−	2.00508e6i	0.113730	−	0.0985472i
$274$	−9.38229e6	−	3.19531e7i	−0.456097	−	1.55332i
$275$			1.74770e7i			0.840365i
$276$	−1.49660e7	+	7.97051e6i	−0.711834	+	0.379104i
$277$	3.45134e7			1.62386			0.811930	−	0.583755i	$-0.198417\pi$
$277$	3.45134e7			1.62386			0.811930	+	0.583755i	$0.198417\pi$
$278$	−1.05157e7	+	3.08770e6i	−0.489447	+	0.143715i
$279$	8.08159e6	+	9.32666e6i	0.372121	+	0.429451i
$280$	1.03191e7	−	6.63168e6i	0.470076	−	0.302099i
$281$	−3.62773e7	+	5.21589e6i	−1.63499	+	0.235077i	−0.897736	−	0.440535i	$-0.854789\pi$
$281$	−3.62773e7	+	5.21589e6i	−1.63499	+	0.235077i	−0.737258	+	0.675611i	$0.763880\pi$
$282$	−1.84692e6	−	1.18695e6i	−0.0823573	−	0.0529278i
$283$	−2.52546e7	−	1.15334e7i	−1.11425	−	0.508859i	−0.228740	−	0.973488i	$-0.573461\pi$
$283$	−2.52546e7	−	1.15334e7i	−1.11425	−	0.508859i	−0.885506	+	0.464629i	$0.846188\pi$
$284$	3.18010e6	−	3.67003e6i	0.138831	−	0.160219i
$285$	−667274.	+	4.64099e6i	−0.0288250	+	0.200482i
$286$	1.67413e7	−	7.64550e6i	0.715635	−	0.326819i
$287$	−5.61120e6	+	1.91100e7i	−0.237361	+	0.808378i
$288$	9.96513e6	+	2.92603e6i	0.417163	+	0.122490i
$289$	4.01052e6	+	8.78182e6i	0.166153	+	0.363824i
$290$	−7.29286e7	−	1.04856e7i	−2.99023	−	0.429930i
$291$	9.60205e6	+	8.32022e6i	0.389659	+	0.337642i
$292$	1.33193e7	−	2.91653e7i	0.534975	−	1.17143i
$293$	−1.76413e7	+	2.74504e7i	−0.701339	+	1.09130i	0.289621	+	0.957142i	$0.406471\pi$
$293$	−1.76413e7	+	2.74504e7i	−0.701339	+	1.09130i	−0.990959	+	0.134163i	$0.957165\pi$
$294$	−1.56117e6	−	1.08582e7i	−0.0614338	−	0.427282i
$295$	5.70190e6	+	8.87233e6i	0.222103	+	0.345598i
$296$	5.46761e6	−	4.73771e6i	0.210825	−	0.182681i
$297$	1.99132e6	+	6.78180e6i	0.0760101	+	0.258866i
$298$			6.05781e7i			2.28911i
$299$	9.04273e6	+	3.48065e6i	0.338287	+	0.130211i
$300$	−1.30531e7			−0.483450
$301$	−1.56830e7	+	4.60495e6i	−0.575083	+	0.168860i
$302$	2.26165e7	+	2.61008e7i	0.821115	+	0.947617i
$303$	−2.37053e7	+	1.52344e7i	−0.852152	+	0.547645i
$304$	−3.43731e6	+	494210.i	−0.122348	+	0.0175910i
$305$	5.68606e7	+	3.65421e7i	2.00407	+	1.28794i
$306$	1.04188e7	+	4.75813e6i	0.363626	+	0.166063i
$307$	2.08655e7	−	2.40800e7i	0.721129	−	0.832227i	−0.270314	−	0.962772i	$-0.587127\pi$
$307$	2.08655e7	−	2.40800e7i	0.721129	−	0.832227i	0.991442	+	0.130546i	$0.0416729\pi$
$308$	−5.85529e6	+	4.07244e7i	−0.200399	+	1.39381i
$309$	−1.31130e6	+	598851.i	−0.0444454	+	0.0202975i
$310$	2.80148e7	−	9.54096e7i	0.940378	−	3.20263i
$311$	7.14517e6	+	2.09801e6i	0.237537	+	0.0697472i	0.398334	−	0.917240i	$-0.369588\pi$
$311$	7.14517e6	+	2.09801e6i	0.237537	+	0.0697472i	−0.160797	+	0.986987i	$0.551407\pi$
$312$	1.62240e6	+	3.55256e6i	0.0534188	+	0.116971i
$313$	−546492.	−	78573.6i	−0.0178218	−	0.00256238i	0.133398	−	0.991063i	$-0.457411\pi$
$313$	−546492.	−	78573.6i	−0.0178218	−	0.00256238i	−0.151220	+	0.988500i	$0.548320\pi$
$314$	−2.99401e7	−	2.59433e7i	−0.967085	−	0.837984i
$315$	3.93593e6	−	8.61849e6i	0.125926	−	0.275740i
$316$	1.82208e7	−	2.83521e7i	0.577438	−	0.898511i
$317$	−4.34683e6	−	3.02328e7i	−0.136457	−	0.949076i	−0.936882	−	0.349645i	$-0.886302\pi$
$317$	−4.34683e6	−	3.02328e7i	−0.136457	−	0.949076i	0.800426	−	0.599432i	$-0.204607\pi$
$318$	−8.37470e6	−	1.30313e7i	−0.260428	−	0.405234i
$319$	5.30646e7	−	4.59807e7i	1.63468	−	1.41646i
$320$	−1.83740e7	−	6.25761e7i	−0.560730	−	1.90967i
$321$		−	1.73375e7i		−	0.524168i
$322$	−2.99847e7	+	2.19619e7i	−0.898115	+	0.657813i
$323$	−7.24085e6			−0.214873
$324$	−5.06517e6	+	1.48727e6i	−0.148922	+	0.0437275i
$325$	4.88469e6	+	5.63724e6i	0.142294	+	0.164216i
$326$	−1.54383e7	+	9.92159e6i	−0.445601	+	0.286371i
$327$	1.85799e7	−	2.67139e6i	0.531374	−	0.0764000i
$328$	−2.13716e7	−	1.37347e7i	−0.605642	−	0.389222i
$329$	−2.55115e6	−	1.16507e6i	−0.0716387	−	0.0327163i
$330$	3.72953e7	−	4.30411e7i	1.03780	−	1.19768i
$331$	−1.28776e6	+	8.95660e6i	−0.0355102	+	0.246979i	−0.999843	−	0.0177137i	$-0.994361\pi$
$331$	−1.28776e6	+	8.95660e6i	−0.0355102	+	0.246979i	0.964333	+	0.264692i	$0.0852704\pi$
$332$	−3.48850e6	+	1.59315e6i	−0.0953290	+	0.0435353i
$333$	1.57437e6	−	5.36181e6i	0.0426358	−	0.145204i
$334$	9.08133e7	+	2.66652e7i	2.43731	+	0.715658i
$335$	−1.38160e7	−	3.02529e7i	−0.367493	−	0.804698i
$336$	6.94592e6	+	998673.i	0.183110	+	0.0263272i
$337$	−4.92112e7	−	4.26418e7i	−1.28580	−	1.11415i	−0.987151	−	0.159793i	$-0.948917\pi$
$337$	−4.92112e7	−	4.26418e7i	−1.28580	−	1.11415i	−0.298653	−	0.954362i	$-0.596537\pi$
$338$	−2.15714e7	+	4.72348e7i	−0.558636	+	1.22324i
$339$	−1.06642e7	+	1.65939e7i	−0.273735	+	0.425941i
$340$	−7.65454e6	−	5.32385e7i	−0.194752	−	1.35453i
$341$	5.12324e7	+	7.97192e7i	1.29206	+	2.01048i
$342$	4.32766e6	−	3.74994e6i	0.108187	−	0.0937445i
$343$	−1.21231e7	−	4.12874e7i	−0.300421	−	1.02314i
$344$		−	2.08488e7i		−	0.512159i
$345$	2.99278e7	−	1.82688e6i	0.728814	−	0.0444890i
$346$	−1.13137e8			−2.73135
$347$	−6.09738e7	+	1.79035e7i	−1.45933	+	0.428499i	−0.912616	−	0.408818i	$-0.865941\pi$
$347$	−6.09738e7	+	1.79035e7i	−1.45933	+	0.428499i	−0.546718	+	0.837317i	$0.684123\pi$
$348$	3.43419e7	+	3.96327e7i	0.814868	+	0.940407i
$349$	2.38795e6	−	1.53464e6i	0.0561757	−	0.0361019i	−0.512252	−	0.858835i	$-0.671188\pi$
$349$	2.38795e6	−	1.53464e6i	0.0561757	−	0.0361019i	0.568427	+	0.822734i	$0.307552\pi$
$350$	−2.83208e7	+	4.07192e6i	−0.660545	+	0.0949720i
$351$	2.53777e6	+	1.63093e6i	0.0586856	+	0.0377149i
$352$	7.25429e7	+	3.31292e7i	1.66328	+	0.759597i
$353$	−1.31344e7	+	1.51579e7i	−0.298597	+	0.344599i	−0.885145	−	0.465315i	$-0.845941\pi$
$353$	−1.31344e7	+	1.51579e7i	−0.298597	+	0.344599i	0.586548	+	0.809914i	$0.300486\pi$
$354$	1.83308e6	−	1.27494e7i	0.0413212	−	0.287395i
$355$	−7.81111e6	+	3.56722e6i	−0.174593	+	0.0797342i
$356$	9.78354e6	−	3.33197e7i	0.216843	−	0.738500i
$357$	1.40392e7	+	4.12229e6i	0.308559	+	0.0906011i
$358$	3.03547e7	+	6.64674e7i	0.661571	+	1.44864i
$359$	−6.27802e7	−	9.02644e6i	−1.35687	−	0.195089i	−0.574810	−	0.818287i	$-0.694924\pi$
$359$	−6.27802e7	−	9.02644e6i	−1.35687	−	0.195089i	−0.782064	+	0.623198i	$0.785833\pi$
$360$	9.13346e6	+	7.91419e6i	0.195762	+	0.169629i
$361$	1.80398e7	−	3.95016e7i	0.383450	−	0.839639i
$362$	7.59041e7	−	1.18109e8i	1.60007	−	2.48976i
$363$	3.79383e6	+	2.63867e7i	0.0793155	+	0.551651i
$364$	9.49356e6	+	1.47723e7i	0.196845	+	0.306297i
$365$	−4.28483e7	+	3.71282e7i	−0.881160	+	0.763529i
$366$	−2.32564e7	−	7.92042e7i	−0.474351	−	1.61549i
$367$			8.28071e6i			0.167521i	0.996486	+	0.0837605i	$0.0266931\pi$
$367$			8.28071e6i			0.167521i	−0.996486	+	0.0837605i	$0.973307\pi$
$368$	7.54306e6	+	2.08866e7i	0.151358	+	0.419107i
$369$	−1.96228e7			−0.390555
$370$	−4.32030e7	+	1.26855e7i	−0.852921	+	0.250440i
$371$	−1.29586e7	−	1.49550e7i	−0.253767	−	0.292863i
$372$	−5.95404e7	+	3.82643e7i	−1.15660	+	0.743302i
$373$	2.91739e7	−	4.19458e6i	0.562171	−	0.0808280i	0.144630	−	0.989486i	$-0.453801\pi$
$373$	2.91739e7	−	4.19458e6i	0.562171	−	0.0808280i	0.417541	+	0.908658i	$0.362892\pi$
$374$	7.39892e7	+	4.75500e7i	1.41434	+	0.908940i
$375$	−1.40295e7	−	6.40706e6i	−0.266041	−	0.121497i
$376$	2.34267e6	−	2.70358e6i	0.0440704	−	0.0508600i
$377$	4.26481e6	−	2.96624e7i	0.0795931	−	0.553582i
$378$	−1.05257e7	+	4.80694e6i	−0.194884	+	0.0890007i
$379$	3.19421e6	−	1.08785e7i	0.0586741	−	0.199826i	−0.924940	−	0.380114i	$-0.875885\pi$
$379$	3.19421e6	−	1.08785e7i	0.0586741	−	0.199826i	0.983614	+	0.180288i	$0.0577030\pi$
$380$	−2.58008e7	−	7.57578e6i	−0.470199	−	0.138063i
$381$	1.03349e7	+	2.26303e7i	0.186867	+	0.409182i
$382$	−5.97369e7	−	8.58886e6i	−1.07165	−	0.154080i
$383$	4.00100e7	+	3.46689e7i	0.712151	+	0.617082i	0.933696	−	0.358068i	$-0.116564\pi$
$383$	4.00100e7	+	3.46689e7i	0.712151	+	0.617082i	−0.221544	+	0.975150i	$0.571110\pi$
$384$	−1.53746e7	+	3.36658e7i	−0.271526	+	0.594559i
$385$	3.93334e7	−	6.12040e7i	0.689255	−	1.07250i
$386$	−1.68636e6	−	1.17289e7i	−0.0293216	−	0.203936i
$387$	−8.70641e6	−	1.35474e7i	−0.150213	−	0.233735i
$388$	−5.50682e7	+	4.77169e7i	−0.942770	+	0.816915i
$389$	−6.44128e6	−	2.19370e7i	−0.109427	−	0.372673i	0.886512	−	0.462705i	$-0.153121\pi$
$389$	−6.44128e6	−	2.19370e7i	−0.109427	−	0.372673i	−0.995939	+	0.0900322i	$0.971303\pi$
$390$		−	2.43068e7i		−	0.409764i
$391$	9.37005e6	+	4.53459e7i	0.156751	+	0.758591i
$392$	1.78747e7			0.296743
$393$	−6.59619e7	+	1.93682e7i	−1.08671	+	0.319088i
$394$	2.48255e7	+	2.86501e7i	0.405890	+	0.468422i
$395$	−5.01349e7	+	3.22197e7i	−0.813483	+	0.522794i
$396$	−4.01233e7	+	5.76887e6i	−0.646118	+	0.0928977i
$397$	−4.25457e7	−	2.73424e7i	−0.679961	−	0.436984i	0.154543	−	0.987986i	$-0.450609\pi$
$397$	−4.25457e7	−	2.73424e7i	−0.679961	−	0.436984i	−0.834504	+	0.551002i	$0.814246\pi$
$398$	4.91221e7	+	2.24333e7i	0.779163	+	0.355832i
$399$	4.79040e6	−	5.52841e6i	0.0754141	−	0.0870325i
$400$	−2.43292e6	+	1.69213e7i	−0.0380144	+	0.264396i
$401$	3.77588e7	−	1.72439e7i	0.585578	−	0.267425i	−0.100518	−	0.994935i	$-0.532050\pi$
$401$	3.77588e7	−	1.72439e7i	0.585578	−	0.267425i	0.686097	+	0.727511i	$0.259323\pi$
$402$	−1.14435e7	+	3.89731e7i	−0.176150	+	0.599911i
$403$	3.88061e7	+	1.13945e7i	0.592905	+	0.174093i
$404$	−6.71331e7	−	1.47001e8i	−1.01811	−	2.22934i
$405$	9.23984e6	+	1.32849e6i	0.139091	+	0.0199983i
$406$	8.68736e7	+	7.52764e7i	1.29811	+	1.12481i
$407$	1.78254e7	−	3.90322e7i	0.264397	−	0.578949i
$408$	−1.00902e7	+	1.57007e7i	−0.148567	+	0.231174i
$409$	−1.22435e7	−	8.51556e7i	−0.178952	−	1.24464i	−0.859194	−	0.511650i	$-0.829034\pi$
$409$	−1.22435e7	−	8.51556e7i	−0.178952	−	1.24464i	0.680242	−	0.732988i	$-0.261875\pi$
$410$	8.54815e7	+	1.33012e8i	1.24028	+	1.92992i
$411$	3.16767e7	−	2.74480e7i	0.456261	−	0.395353i
$412$	−2.32922e6	−	7.93259e6i	−0.0333057	−	0.113429i
$413$		−	1.64543e7i		−	0.233577i
$414$	−2.90843e7	−	2.22494e7i	−0.409880	−	0.313558i
$415$	6.78155e6			0.0948821
$416$	3.26583e7	−	9.58933e6i	0.453642	−	0.133201i
$417$	−9.03310e6	−	1.04247e7i	−0.124574	−	0.143766i
$418$	3.69905e7	−	2.37723e7i	0.506478	−	0.325494i
$419$	−9.93447e7	+	1.42836e7i	−1.35052	+	0.194176i	−0.779317	−	0.626629i	$-0.784434\pi$
$419$	−9.93447e7	+	1.42836e7i	−1.35052	+	0.194176i	−0.571208	+	0.820806i	$0.693525\pi$
$420$	4.57119e7	+	2.93772e7i	0.616994	+	0.396518i
$421$	−6.16266e7	−	2.81439e7i	−0.825890	−	0.377171i	−0.0428028	−	0.999084i	$-0.513629\pi$
$421$	−6.16266e7	−	2.81439e7i	−0.825890	−	0.377171i	−0.783087	+	0.621912i	$0.786356\pi$
$422$	1.22348e8	−	1.41198e8i	1.62803	−	1.87884i
$423$	393244.	−	2.73507e6i	0.00519566	−	0.0361366i
$424$	2.29597e7	−	1.04853e7i	0.301209	−	0.137558i
$425$	−1.00425e7	+	3.42017e7i	−0.130821	+	0.445534i
$426$	1.00626e7	+	2.95465e6i	0.130161	+	0.0382188i
$427$	−4.38062e7	−	9.59222e7i	−0.562668	−	1.23207i
$428$	9.84190e7	+	1.41505e7i	1.25530	+	0.180485i
$429$	1.75062e7	+	1.51692e7i	0.221727	+	0.192128i
$430$	−5.39032e7	+	1.18032e8i	−0.677969	+	1.48454i
$431$	7.00639e7	−	1.09022e8i	0.875110	−	1.36170i	−0.0565633	−	0.998399i	$-0.518014\pi$
$431$	7.00639e7	−	1.09022e8i	0.875110	−	1.36170i	0.931673	−	0.363298i	$-0.118349\pi$
$432$	983933.	+	6.84340e6i	0.0122043	+	0.0848830i
$433$	3.67819e7	+	5.72338e7i	0.453076	+	0.705000i	0.990378	−	0.138390i	$-0.0441927\pi$
$433$	3.67819e7	+	5.72338e7i	0.453076	+	0.705000i	−0.537302	+	0.843390i	$0.680556\pi$
$434$	−1.17246e8	+	1.01594e8i	−1.43426	+	1.24279i
$435$	−2.61257e7	−	8.89760e7i	−0.317395	−	1.08095i
$436$			1.07652e8i			1.29887i
$437$	2.25678e7	+	5.15646e6i	0.270423	+	0.0617885i
$438$	6.92431e7			0.824052
$439$	−8.94633e7	+	2.62688e7i	−1.05743	+	0.310489i	−0.763815	−	0.645435i	$-0.776676\pi$
$439$	−8.94633e7	+	2.62688e7i	−1.05743	+	0.310489i	−0.293614	+	0.955924i	$0.594858\pi$
$440$	6.07707e7	+	7.01331e7i	0.713405	+	0.823313i
$441$	1.16149e7	−	7.46445e6i	0.135425	−	0.0870326i
$442$	3.71553e7	−	5.34212e6i	0.430283	−	0.0618653i
$443$	1.58341e7	+	1.01759e7i	0.182130	+	0.117048i	0.628529	−	0.777786i	$-0.283657\pi$
$443$	1.58341e7	+	1.01759e7i	0.182130	+	0.117048i	−0.446399	+	0.894834i	$0.647294\pi$
$444$	2.91523e7	+	1.33134e7i	0.333061	+	0.152104i
$445$	−4.02127e7	+	4.64079e7i	−0.456334	+	0.526638i
$446$	9.05714e6	−	6.29938e7i	0.102091	−	0.710057i
$447$	−6.93540e7	+	3.16729e7i	−0.776513	+	0.354622i
$448$	−2.86663e7	+	9.76286e7i	−0.318815	+	1.08578i
$449$	3.61717e7	+	1.06210e7i	0.399604	+	0.117334i	0.475358	−	0.879792i	$-0.342318\pi$
$449$	3.61717e7	+	1.06210e7i	0.399604	+	0.117334i	−0.0757546	+	0.997126i	$0.524137\pi$
$450$	−1.17105e7	−	2.56423e7i	−0.128510	−	0.281397i
$451$	−1.49144e8	−	2.14436e7i	−1.62583	−	0.233759i
$452$	−8.54941e7	−	7.40810e7i	−0.925807	−	0.802217i
$453$	−1.80571e7	+	3.95395e7i	−0.194246	+	0.425340i
$454$	6.90158e7	−	1.07391e8i	0.737532	−	1.14762i
$455$	−4.41902e6	−	3.07349e7i	−0.0469128	−	0.326286i
$456$	5.04456e6	+	7.84949e6i	0.0532021	+	0.0827841i
$457$	6.38819e7	−	5.53540e7i	0.669313	−	0.579963i	−0.252500	−	0.967597i	$-0.581253\pi$
$457$	6.38819e7	−	5.53540e7i	0.669313	−	0.579963i	0.921813	+	0.387634i	$0.126707\pi$
$458$	5.24981e7	+	1.78792e8i	0.546446	+	1.86102i
$459$			1.44160e7i			0.149075i
$460$	−1.40559e7	+	1.71381e8i	−0.144406	+	1.76072i
$461$	1.02708e8			1.04834			0.524171	−	0.851613i	$-0.324375\pi$
$461$	1.02708e8			1.04834			0.524171	+	0.851613i	$0.324375\pi$
$462$	−8.52543e7	+	2.50329e7i	−0.864550	+	0.253855i
$463$	−6.05081e6	−	6.98300e6i	−0.0609636	−	0.0703557i	0.724449	−	0.689329i	$-0.242094\pi$
$463$	−6.05081e6	−	6.98300e6i	−0.0609636	−	0.0703557i	−0.785412	+	0.618973i	$0.787549\pi$
$464$	5.77784e7	−	3.71319e7i	0.578378	−	0.371701i
$465$	1.23879e8	−	1.78111e7i	1.23208	−	0.177146i
$466$	−1.78658e8	−	1.14817e8i	−1.76549	−	1.13461i
$467$	−1.34605e8	−	6.14719e7i	−1.32163	−	0.603568i	−0.375339	−	0.926888i	$-0.622474\pi$
$467$	−1.34605e8	−	6.14719e7i	−1.32163	−	0.603568i	−0.946290	+	0.323320i	$0.895201\pi$
$468$	−1.13295e7	+	1.30750e7i	−0.110528	+	0.127557i
$469$	−7.38449e6	+	5.13603e7i	−0.0715817	+	0.497862i
$470$	−2.02526e7	+	9.24904e6i	−0.195068	+	0.0890847i
$471$	1.40476e7	−	4.78418e7i	0.134443	−	0.457872i
$472$	2.01379e7	+	5.91301e6i	0.191508	+	0.0562319i
$473$	−5.13689e7	−	1.12482e8i	−0.485419	−	1.06292i
$474$	7.20429e7	+	1.03582e7i	0.676482	+	0.0972634i
$475$	1.34681e7	+	1.16701e7i	0.125668	+	0.108892i
$476$	−3.48594e7	+	7.63315e7i	−0.323221	+	0.707755i
$477$	1.05404e7	−	1.64013e7i	0.0971190	−	0.151120i
$478$	4.26492e7	+	2.96632e8i	0.390506	+	2.71603i
$479$	−1.51605e7	−	2.35902e7i	−0.137945	−	0.214647i	0.765407	−	0.643547i	$-0.222538\pi$
$479$	−1.51605e7	−	2.35902e7i	−0.137945	−	0.214647i	−0.903352	+	0.428900i	$0.858901\pi$
$480$	7.95997e7	−	6.89735e7i	0.719760	−	0.623675i
$481$	−5.15961e6	−	1.75720e7i	−0.0463641	−	0.157902i
$482$			1.21594e8i			1.08586i
$483$	−4.08208e7	−	2.28459e7i	−0.362276	−	0.202753i
$484$	−1.52885e8			−1.34843
$485$	1.23629e8	−	3.63007e7i	1.08366	−	0.318192i
$486$	−7.46583e6	−	8.61603e6i	−0.0650383	−	0.0750582i
$487$	−1.34801e7	+	8.66313e6i	−0.116710	+	0.0750046i	−0.597693	−	0.801725i	$-0.703916\pi$
$487$	−1.34801e7	+	8.66313e6i	−0.116710	+	0.0750046i	0.480984	+	0.876729i	$0.340280\pi$
$488$	1.33138e8	−	1.91424e7i	1.14563	−	0.164716i
$489$	−1.94307e7	−	1.24874e7i	−0.166174	−	0.106793i
$490$	−1.01195e8	−	4.62140e7i	−0.860140	−	0.392813i
$491$	−9.18661e7	+	1.06019e8i	−0.776088	+	0.895653i	−0.996820	−	0.0796812i	$-0.974610\pi$
$491$	−9.18661e7	+	1.06019e8i	−0.776088	+	0.895653i	0.220733	+	0.975334i	$0.429155\pi$
$492$	1.60158e7	−	1.11392e8i	0.134478	−	0.935318i
$493$	1.30266e8	−	5.94907e7i	1.08716	−	0.496487i
$494$	5.28716e6	−	1.80064e7i	0.0438573	−	0.149364i
$495$	6.87760e7	+	2.01945e7i	0.567050	+	0.166501i
$496$	3.85061e7	+	8.43167e7i	0.315562	+	0.690985i
$497$	1.32609e7	+	1.90663e6i	0.108020	+	0.0155309i
$498$	−6.25933e6	−	5.42374e6i	−0.0506804	−	0.0439148i
$499$	6.91226e7	−	1.51357e8i	0.556312	−	1.21815i	−0.397460	−	0.917620i	$-0.630108\pi$
$499$	6.91226e7	−	1.51357e8i	0.556312	−	1.21815i	0.953771	−	0.300533i	$-0.0971646\pi$
$500$	4.78214e7	−	7.44115e7i	0.382571	−	0.595292i
$501$	1.69530e7	+	1.17911e8i	0.134814	+	0.937651i
$502$	−3.15959e7	−	4.91642e7i	−0.249758	−	0.388631i
$503$	−1.36418e8	+	1.18206e8i	−1.07193	+	0.928832i	−0.997658	−	0.0684056i	$-0.978209\pi$
$503$	−1.36418e8	+	1.18206e8i	−1.07193	+	0.928832i	−0.0742722	+	0.997238i	$0.523663\pi$
$504$	−5.31206e6	−	1.80912e7i	−0.0414927	−	0.141311i
$505$			2.85766e8i			2.21889i
$506$	−1.96742e8	−	2.00891e8i	−1.51861	−	1.55063i
$507$	−6.53562e7			−0.501490
$508$	−1.36900e8	+	4.01975e7i	−1.04427	+	0.306625i
$509$	9.58318e7	+	1.10596e8i	0.726702	+	0.838658i	0.992096	−	0.125481i	$-0.0400476\pi$
$509$	9.58318e7	+	1.10596e8i	0.726702	+	0.838658i	−0.265394	+	0.964140i	$0.585502\pi$
$510$	9.77176e7	−	6.27993e7i	0.736652	−	0.473417i
$511$	8.75550e7	−	1.25885e7i	0.656173	−	0.0943434i
$512$	9.65397e7	+	6.20423e7i	0.719277	+	0.462251i
$513$	6.55587e6	+	2.99397e6i	0.0485600	+	0.0221766i
$514$	2.56335e7	−	2.95827e7i	0.188764	−	0.217845i
$515$	−2.08055e6	+	1.44706e7i	−0.0152320	+	0.105941i
$516$	8.40104e7	−	3.83663e7i	0.611482	−	0.279255i
$517$	5.97774e6	−	2.03583e7i	0.0432579	−	0.147323i
$518$	6.74035e7	+	1.97915e7i	0.484946	+	0.142393i
$519$	−5.91532e7	−	1.29527e8i	−0.423132	−	0.926530i
$520$	3.92035e7	+	5.63661e6i	0.278814	+	0.0400874i
$521$	7.56909e7	+	6.55866e7i	0.535218	+	0.463769i	0.880040	−	0.474899i	$-0.157515\pi$
$521$	7.56909e7	+	6.55866e7i	0.535218	+	0.463769i	−0.344822	+	0.938668i	$0.612061\pi$
$522$	−4.70473e7	+	1.03019e8i	−0.330768	+	0.724280i
$523$	−9.22432e6	+	1.43533e7i	−0.0644807	+	0.100334i	−0.871997	−	0.489512i	$-0.837175\pi$
$523$	−9.22432e6	+	1.43533e7i	−0.0644807	+	0.100334i	0.807516	+	0.589846i	$0.200811\pi$
$524$	−5.61098e7	−	3.90252e8i	−0.389982	−	2.71239i
$525$	−1.94692e7	−	3.02947e7i	−0.134546	−	0.209357i
$526$	−2.88393e8	+	2.49894e8i	−1.98165	+	1.71711i
$527$	5.44519e7	+	1.85446e8i	0.372033	+	1.26703i
$528$			5.30888e7i			0.360663i
$529$	3.08853e6	−	1.48004e8i	0.0208634	−	0.999782i
$530$	−1.57091e8			−1.05518
$531$	1.55548e7	−	4.56730e6i	0.103892	−	0.0305053i
$532$	2.74731e7	+	3.17057e7i	0.182462	+	0.210573i
$533$	−5.41001e7	+	3.47680e7i	−0.357286	+	0.229614i
$534$	7.42322e7	−	1.06730e7i	0.487493	−	0.0700909i
$535$	−1.47912e8	−	9.50575e7i	−0.965924	−	0.620762i
$536$	−6.02044e7	−	2.74944e7i	−0.390961	−	0.178546i
$537$	−6.02257e7	+	6.95042e7i	−0.388919	+	0.448836i
$538$	4.91630e7	−	3.41936e8i	0.315712	−	2.19583i
$539$	9.64367e7	−	4.40412e7i	0.615852	−	0.281250i
$540$	−1.50828e7	+	5.13673e7i	−0.0957856	+	0.326216i
$541$	−8.50952e7	−	2.49862e7i	−0.537420	−	0.157801i	0.00174903	−	0.999998i	$-0.499443\pi$
$541$	−8.50952e7	−	2.49862e7i	−0.537420	−	0.157801i	−0.539169	+	0.842198i	$0.681261\pi$
$542$	−1.14893e8	−	2.51582e8i	−0.721602	−	1.58009i
$543$	1.74905e8	+	2.51476e7i	1.09245	+	0.157071i
$544$	1.22927e8	+	1.06517e8i	0.763572	+	0.661639i
$545$	7.90789e7	−	1.73159e8i	0.488508	−	1.06968i
$546$	−2.05024e7	+	3.19024e7i	−0.125959	+	0.195995i
$547$	2.05349e7	+	1.42823e8i	0.125467	+	0.872645i	0.951198	+	0.308580i	$0.0998539\pi$
$547$	2.05349e7	+	1.42823e8i	0.125467	+	0.872645i	−0.825731	+	0.564064i	$0.809237\pi$
$548$	1.29959e8	+	2.02220e8i	0.789706	+	1.22881i
$549$	7.85188e7	−	6.80370e7i	0.474522	−	0.411176i
$550$	−6.09841e7	−	2.07693e8i	−0.366546	−	1.24834i
$551$		−	7.15959e7i		−	0.427990i
$552$	4.26296e7	−	4.17493e7i	0.253451	−	0.248217i
$553$	9.29783e7			0.549802
$554$	−4.10150e8	+	1.20431e8i	−2.41220	+	0.708286i
$555$	−3.71117e7	−	4.28292e7i	−0.217086	−	0.250531i
$556$	6.65505e7	−	4.27694e7i	0.387193	−	0.248834i
$557$	−1.65419e8	+	2.37836e7i	−0.957235	+	0.137630i	−0.603189	−	0.797598i	$-0.706103\pi$
$557$	−1.65419e8	+	2.37836e7i	−0.957235	+	0.137630i	−0.354046	+	0.935228i	$0.615194\pi$
$558$	−1.28584e8	−	8.26362e7i	−0.740092	−	0.475628i
$559$	−4.80072e7	−	2.19241e7i	−0.274834	−	0.125513i
$560$	4.66030e7	−	5.37827e7i	0.265369	−	0.306252i
$561$	−1.57537e7	+	1.09569e8i	−0.0892263	+	0.620582i
$562$	4.12912e8	−	1.88571e8i	2.32621	−	1.06234i
$563$	−4.57367e7	+	1.55765e8i	−0.256294	+	0.872859i	0.726344	+	0.687331i	$0.241218\pi$
$563$	−4.57367e7	+	1.55765e8i	−0.256294	+	0.872859i	−0.982639	+	0.185528i	$0.940600\pi$
$564$	1.52051e7	+	4.46463e6i	0.0847527	+	0.0248856i
$565$	8.30989e7	+	1.81961e8i	0.460734	+	1.00887i
$566$	3.40365e8	+	4.89371e7i	1.87713	+	0.269891i
$567$	−1.10066e7	−	9.53730e6i	−0.0603817	−	0.0523210i
$568$	−7.09889e6	+	1.55444e7i	−0.0387387	+	0.0848260i
$569$	−1.09171e8	+	1.69873e8i	−0.592612	+	0.922123i	0.407348	+	0.913273i	$0.366453\pi$
$569$	−1.09171e8	+	1.69873e8i	−0.592612	+	0.922123i	−0.999961	+	0.00885004i	$0.997183\pi$
$570$	−8.26451e6	−	5.74810e7i	−0.0446265	−	0.310384i
$571$	−8.01047e7	−	1.24645e8i	−0.430279	−	0.669527i	0.556639	−	0.830755i	$-0.312091\pi$
$571$	−8.01047e7	−	1.24645e8i	−0.430279	−	0.669527i	−0.986917	+	0.161228i	$0.948454\pi$
$572$	−1.00399e8	+	8.69960e7i	−0.536464	+	0.464848i
$573$	−2.13999e7	−	7.28815e7i	−0.113749	−	0.387394i
$574$		−	2.46679e8i		−	1.30436i
$575$	5.56561e7	−	9.94458e7i	0.292758	−	0.523098i
$576$	−1.00248e8			−0.524578
$577$	1.78265e8	−	5.23432e7i	0.927979	−	0.272479i	0.217388	−	0.976085i	$-0.430246\pi$
$577$	1.78265e8	−	5.23432e7i	0.927979	−	0.272479i	0.710590	+	0.703606i	$0.248428\pi$
$578$	−7.83035e7	−	9.03670e7i	−0.405506	−	0.467979i
$579$	1.25463e7	−	8.06303e6i	0.0646369	−	0.0415396i
$580$	5.26411e8	−	7.56864e7i	2.69799	−	0.387913i
$581$	−8.90070e6	−	5.72013e6i	−0.0453833	−	0.0291661i
$582$	−1.43141e8	−	6.53705e7i	−0.726100	−	0.331599i
$583$	9.80363e7	−	1.13140e8i	0.494745	−	0.570966i
$584$	−1.60571e7	+	1.11679e8i	−0.0806172	+	0.560705i
$585$	2.78281e7	−	1.27087e7i	0.139000	−	0.0634793i
$586$	1.13860e8	−	3.87773e8i	0.565821	−	1.92701i
$587$	−3.78578e8	−	1.11161e8i	−1.87172	−	0.549587i	−0.998004	−	0.0631575i	$-0.979883\pi$
$587$	−3.78578e8	−	1.11161e8i	−1.87172	−	0.549587i	−0.873720	−	0.486430i	$-0.838299\pi$
$588$	3.28934e7	+	7.20264e7i	0.161799	+	0.354291i
$589$	9.56432e7	+	1.37514e7i	0.468067	+	0.0672979i
$590$	−9.87193e7	−	8.55408e7i	−0.480669	−	0.416502i
$591$	−1.98208e7	+	4.34014e7i	−0.0960191	+	0.210253i
$592$	2.26923e7	−	3.53099e7i	0.109374	−	0.170189i
$593$	−5.64886e6	−	3.92887e7i	−0.0270892	−	0.188410i	0.971784	−	0.235874i	$-0.0757952\pi$
$593$	−5.64886e6	−	3.92887e7i	−0.0270892	−	0.188410i	−0.998873	+	0.0474639i	$0.984886\pi$
$594$	−4.73288e7	−	7.36451e7i	−0.225822	−	0.351386i
$595$	1.12143e8	−	9.71722e7i	0.532378	−	0.461308i
$596$	−1.23191e8	−	4.19550e8i	−0.581890	−	1.98173i
$597$			6.79675e7i			0.319432i
$598$	−1.19607e8	−	9.80964e6i	−0.559312	−	0.0458722i
$599$	−1.80431e8			−0.839520			−0.419760	−	0.907635i	$-0.637886\pi$
$599$	−1.80431e8			−0.839520			−0.419760	+	0.907635i	$0.637886\pi$
$600$	4.40730e7	−	1.29410e7i	0.204042	−	0.0599121i
$601$	2.21691e8	+	2.55845e8i	1.02123	+	1.17856i	0.983801	+	0.179264i	$0.0573715\pi$
$601$	2.21691e8	+	2.55845e8i	1.02123	+	1.17856i	0.0374295	+	0.999299i	$0.488083\pi$
$602$	1.70305e8	−	1.09449e8i	0.780619	−	0.501673i
$603$	−5.06022e7	+	7.27550e6i	−0.230790	+	0.0331826i
$604$	−2.09715e8	−	1.34776e8i	−0.951740	−	0.611646i
$605$	2.45915e8	+	1.12306e8i	1.11050	+	0.507149i
$606$	2.28549e8	−	2.63760e8i	1.02698	−	1.18520i
$607$	−1.92445e7	+	1.33848e8i	−0.0860479	+	0.598476i	0.900482	+	0.434894i	$0.143214\pi$
$607$	−1.92445e7	+	1.33848e8i	−0.0860479	+	0.598476i	−0.986530	+	0.163583i	$0.947695\pi$
$608$	7.39701e7	−	3.37810e7i	0.329113	−	0.150301i
$609$	−4.07602e7	+	1.38817e8i	−0.180462	+	0.614596i
$610$	−8.03230e8	−	2.35850e8i	−3.53875	−	1.03907i
$611$	−3.76187e6	−	8.23736e6i	−0.0164923	−	0.0361131i
$612$	−8.18346e7	−	1.17660e7i	−0.357012	−	0.0513306i
$613$	5.26815e7	+	4.56488e7i	0.228706	+	0.198174i	0.761674	−	0.647961i	$-0.224378\pi$
$613$	5.26815e7	+	4.56488e7i	0.228706	+	0.198174i	−0.532968	+	0.846135i	$0.678923\pi$
$614$	−1.63936e8	+	3.58970e8i	−0.708222	+	1.55079i
$615$	−1.07587e8	+	1.67409e8i	−0.462526	+	0.719705i
$616$	−2.06046e7	−	1.43308e8i	−0.0881499	−	0.613096i
$617$	4.48783e7	+	6.98320e7i	0.191065	+	0.297303i	0.923548	−	0.383482i	$-0.125275\pi$
$617$	4.48783e7	+	6.98320e7i	0.191065	+	0.297303i	−0.732483	+	0.680785i	$0.761639\pi$
$618$	1.34936e7	−	1.16923e7i	0.0571692	−	0.0495374i
$619$	6.89439e7	+	2.34801e8i	0.290686	+	0.989985i	0.967297	+	0.253645i	$0.0816294\pi$
$619$	6.89439e7	+	2.34801e8i	0.290686	+	0.989985i	−0.676612	+	0.736340i	$0.736552\pi$
$620$			7.17756e8i			3.01163i
$621$	1.02661e7	−	4.49306e7i	0.0428678	−	0.187615i
$622$	−9.22326e7			−0.383277
$623$	9.19231e7	−	2.69911e7i	0.380155	−	0.111624i
$624$	1.48380e7	+	1.71239e7i	0.0610690	+	0.0704774i
$625$	−2.54699e8	+	1.63685e8i	−1.04325	+	0.670454i
$626$	6.76857e6	−	973174.i	0.0275914	−	0.00396705i
$627$	4.65564e7	+	2.99200e7i	0.188876	+	0.121383i
$628$	2.60116e8	+	1.18791e8i	1.05024	+	0.479629i
$629$	5.73121e7	−	6.61417e7i	0.230300	−	0.265781i
$630$	−1.67005e7	+	1.16154e8i	−0.0667894	+	0.464530i
$631$	−2.55135e8	+	1.16516e8i	−1.01551	+	0.463766i	−0.852426	−	0.522847i	$-0.824870\pi$
$631$	−2.55135e8	+	1.16516e8i	−1.01551	+	0.463766i	−0.163079	+	0.986613i	$0.552142\pi$
$632$	−3.34126e7	+	1.13793e8i	−0.132361	+	0.450780i
$633$	2.25622e8	+	6.62485e7i	0.889549	+	0.261195i
$634$	1.57151e8	+	3.44113e8i	0.616666	+	1.35031i
$635$	2.49732e8	+	3.59060e7i	0.975333	+	0.140232i
$636$	8.45016e7	+	7.32211e7i	0.328469	+	0.284620i
$637$	1.87967e7	−	4.11590e7i	0.0727216	−	0.159238i
$638$	−4.70164e8	+	7.31589e8i	−1.81045	+	2.81712i
$639$	1.87849e6	+	1.30652e7i	0.00719956	+	0.0500740i
$640$	2.02919e8	+	3.15749e8i	0.774076	+	1.20449i
$641$	2.56107e8	−	2.21918e8i	0.972406	−	0.842594i	−0.0151465	−	0.999885i	$-0.504821\pi$
$641$	2.56107e8	−	2.21918e8i	0.972406	−	0.842594i	0.987552	+	0.157291i	$0.0502760\pi$
$642$	6.04973e7	+	2.06035e8i	0.228629	+	0.778638i
$643$			4.00716e8i			1.50731i	0.657268	+	0.753657i	$0.271712\pi$
$643$			4.00716e8i			1.50731i	−0.657268	+	0.753657i	$0.728288\pi$
$644$	1.63006e8	−	2.13080e8i	0.610302	−	0.797783i
$645$	−1.63314e8			−0.608616
$646$	8.60488e7	−	2.52662e7i	0.319188	−	0.0937222i
$647$	1.81126e8	+	2.09031e8i	0.668758	+	0.771788i	0.984181	−	0.177163i	$-0.0566921\pi$
$647$	1.81126e8	+	2.09031e8i	0.668758	+	0.771788i	−0.315424	+	0.948951i	$0.602147\pi$
$648$	1.56277e7	−	1.00433e7i	0.0574342	−	0.0369107i
$649$	1.23216e8	−	1.77158e7i	0.450747	−	0.0648076i
$650$	−7.77193e7	−	4.99472e7i	−0.283001	−	0.181874i
$651$	−1.77613e8	−	8.11131e7i	−0.643771	−	0.294001i
$652$	8.67457e7	−	1.00110e8i	0.312972	−	0.361189i
$653$	4.75124e7	−	3.30456e8i	0.170635	−	1.18679i	−0.706912	−	0.707301i	$-0.749913\pi$
$653$	4.75124e7	−	3.30456e8i	0.170635	−	1.18679i	0.877547	−	0.479490i	$-0.159178\pi$
$654$	−2.11478e8	+	9.65789e7i	−0.756019	+	0.345262i
$655$	−1.96418e8	+	6.68937e8i	−0.698967	+	2.38046i
$656$	−1.41417e8	−	4.15238e7i	−0.500946	−	0.147091i
$657$	3.62033e7	+	7.92743e7i	0.127659	+	0.279535i
$658$	3.43827e7	+	4.94349e6i	0.120687	+	0.0173522i
$659$	2.12693e8	+	1.84299e8i	0.743183	+	0.643972i	0.941826	−	0.336100i	$-0.109108\pi$
$659$	2.12693e8	+	1.84299e8i	0.743183	+	0.643972i	−0.198643	+	0.980072i	$0.563653\pi$
$660$	−1.70771e8	+	3.73937e8i	−0.593995	+	1.30067i
$661$	−1.16953e8	+	1.81982e8i	−0.404954	+	0.630120i	−0.982505	−	0.186234i	$-0.940372\pi$
$661$	−1.16953e8	+	1.81982e8i	−0.404954	+	0.630120i	0.577552	+	0.816354i	$0.304008\pi$
$662$	−1.59496e7	−	1.10932e8i	−0.0549764	−	0.382369i
$663$	2.55424e7	+	3.97448e7i	0.0876439	+	0.136377i
$664$	1.01992e7	−	8.83768e6i	0.0348388	−	0.0301880i
$665$	−2.09003e7	−	7.11797e7i	−0.0710700	−	0.242042i
$666$			6.92123e7i			0.234294i
$667$	−4.48370e8	+	9.26490e7i	−1.51098	+	0.312222i
$668$	−6.83179e8			−2.29195
$669$	7.68551e7	−	2.25667e7i	0.256681	−	0.0753684i
$670$	2.69752e8	+	3.11310e8i	0.896891	+	1.03507i
$671$	6.71136e8	−	4.31313e8i	2.22148	−	1.42766i
$672$	−1.62652e8	+	2.33858e7i	−0.535983	+	0.0770627i
$673$	−6.85489e7	−	4.40537e7i	−0.224882	−	0.144523i	0.423349	−	0.905967i	$-0.360855\pi$
$673$	−6.85489e7	−	4.40537e7i	−0.224882	−	0.144523i	−0.648231	+	0.761444i	$0.724491\pi$
$674$	7.33610e8	+	3.35029e8i	2.39599	+	1.09421i
$675$	2.32343e7	−	2.68139e7i	0.0755473	−	0.0871863i
$676$	5.33425e7	−	3.71005e8i	0.172677	−	1.20099i
$677$	1.62802e8	−	7.43491e7i	0.524678	−	0.239612i	−0.135425	−	0.990788i	$-0.543240\pi$
$677$	1.62802e8	−	7.43491e7i	0.524678	−	0.239612i	0.660103	+	0.751175i	$0.270513\pi$
$678$	6.88290e7	−	2.34410e8i	0.220842	−	0.752120i
$679$	−1.92881e8	−	5.66349e7i	−0.616140	−	0.180915i
$680$	7.86262e7	+	1.72167e8i	0.250058	+	0.547550i
$681$	1.59033e8	+	2.28655e7i	0.503553	+	0.0724000i
$682$	−8.87007e8	−	7.68596e8i	−2.79624	−	2.42295i
$683$	6.86155e7	−	1.50247e8i	0.215357	−	0.471567i	−0.770864	−	0.637000i	$-0.780175\pi$
$683$	6.86155e7	−	1.50247e8i	0.215357	−	0.471567i	0.986221	+	0.165433i	$0.0529023\pi$
$684$	−2.23466e7	+	3.47719e7i	−0.0698300	+	0.108658i
$685$	−6.04928e7	−	4.20737e8i	−0.188205	−	1.30900i
$686$	2.88137e8	+	4.48349e8i	0.892537	+	1.38881i
$687$	−1.77245e8	+	1.53584e8i	−0.546643	+	0.473669i
$688$	−3.40774e7	−	1.16057e8i	−0.104641	−	0.356374i
$689$		−	6.38941e7i		−	0.195345i
$690$	−3.49281e8	+	1.26140e8i	−1.06323	+	0.383978i
$691$	2.62931e8			0.796908			0.398454	−	0.917188i	$-0.369547\pi$
$691$	2.62931e8			0.796908			0.398454	+	0.917188i	$0.369547\pi$
$692$	7.83564e8	−	2.30075e8i	2.36459	−	0.694307i
$693$	−7.32341e7	−	8.45166e7i	−0.220046	−	0.253947i
$694$	6.62127e8	−	4.25523e8i	1.98090	−	1.27305i
$695$	−1.38464e8	+	1.99081e7i	−0.412460	+	0.0593028i
$696$	−1.55245e8	−	9.97702e7i	−0.460459	−	0.295919i
$697$	−2.79547e8	−	1.27665e8i	−0.825574	−	0.377027i
$698$	−2.30229e7	+	2.65699e7i	−0.0677008	+	0.0781309i
$699$	3.80396e7	−	2.64571e8i	0.111379	−	0.774660i
$700$	1.87863e8	−	8.57943e7i	0.547706	−	0.250129i
$701$	2.84510e7	−	9.68952e7i	0.0825930	−	0.281286i	−0.907833	−	0.419333i	$-0.862264\pi$
$701$	2.84510e7	−	9.68952e7i	0.0825930	−	0.281286i	0.990426	+	0.138046i	$0.0440823\pi$
$702$	−3.58493e7	−	1.05263e7i	−0.103626	−	0.0304274i
$703$	−1.81761e7	−	3.98001e7i	−0.0523161	−	0.114556i
$704$	−7.61942e8	−	1.09551e8i	−2.18376	−	0.313977i
$705$	−2.11779e7	−	1.83507e7i	−0.0604386	−	0.0523704i
$706$	1.03194e8	−	2.25964e8i	0.293253	−	0.642134i
$707$	2.41039e8	−	3.75064e8i	0.682071	−	1.06132i
$708$	1.32315e7	+	9.20271e7i	0.0372829	+	0.259308i
$709$	−2.62264e8	−	4.08092e8i	−0.735869	−	1.14504i	−0.984320	−	0.176391i	$-0.943558\pi$
$709$	−2.62264e8	−	4.08092e8i	−0.735869	−	1.14504i	0.248451	−	0.968645i	$-0.420079\pi$
$710$	8.03783e7	−	6.96482e7i	0.224576	−	0.194596i
$711$	2.58084e7	+	8.78953e7i	0.0718046	+	0.244544i
$712$			1.22201e8i			0.338559i
$713$	−3.76490e7	−	6.16762e8i	−0.103869	−	1.70157i
$714$	−1.81223e8			−0.497874
$715$	2.25397e8	−	6.61824e7i	0.616636	−	0.181061i
$716$	−3.45397e8	−	3.98610e8i	−0.940979	−	1.08595i
$717$	−3.17305e8	+	2.03920e8i	−0.860835	+	0.553225i
$718$	7.77565e8	−	1.11797e8i	2.10070	−	0.302034i
$719$	−1.89872e8	−	1.22023e8i	−0.510827	−	0.328288i	0.259707	−	0.965687i	$-0.416374\pi$
$719$	−1.89872e8	−	1.22023e8i	−0.510827	−	0.328288i	−0.770534	+	0.637399i	$0.780010\pi$
$720$	6.37783e7	+	2.91266e7i	0.170874	+	0.0780355i
$721$	1.49364e7	−	1.72375e7i	0.0398511	−	0.0459906i
$722$	−7.65442e7	+	5.32376e8i	−0.203376	+	1.41451i
$723$	−1.39210e8	+	6.35749e7i	−0.368344	+	0.168217i
$724$	−2.85509e8	+	9.72355e8i	−0.752323	+	2.56218i
$725$	−3.38179e8	−	9.92983e7i	−0.887427	−	0.260572i
$726$	−1.37159e8	−	3.00336e8i	−0.358437	−	0.784868i
$727$	5.11919e8	+	7.36028e7i	1.33229	+	0.191554i	0.771406	−	0.636343i	$-0.219554\pi$
$727$	5.11919e8	+	7.36028e7i	1.33229	+	0.191554i	0.560880	+	0.827897i	$0.310463\pi$
$728$	−4.66997e7	−	4.04655e7i	−0.121038	−	0.104880i
$729$	5.96075e6	−	1.30522e7i	0.0153857	−	0.0336901i
$730$	3.79645e8	−	5.90739e8i	0.975908	−	1.51854i
$731$	−3.58929e7	−	2.49640e8i	−0.0918874	−	0.639091i
$732$	3.22138e8	+	5.01256e8i	0.821312	+	1.27799i
$733$	2.73053e8	−	2.36602e8i	0.693323	−	0.600768i	−0.235242	−	0.971937i	$-0.575588\pi$
$733$	2.73053e8	−	2.36602e8i	0.693323	−	0.600768i	0.928565	+	0.371169i	$0.121043\pi$
$734$	−2.88947e7	−	9.84063e7i	−0.0730684	−	0.248848i
$735$		−	1.40017e8i		−	0.352630i
$736$	−3.07275e8	−	4.19524e8i	−0.770716	−	1.05226i
$737$	−3.92555e8			−0.980614
$738$	2.33193e8	−	6.84717e7i	0.580159	−	0.170350i
$739$	9.13219e7	+	1.05391e8i	0.226278	+	0.261138i	0.857524	−	0.514444i	$-0.172002\pi$
$739$	9.13219e7	+	1.05391e8i	0.226278	+	0.261138i	−0.631246	+	0.775583i	$0.717456\pi$
$740$	2.73417e8	−	1.75714e8i	0.674731	−	0.433623i
$741$	2.33793e7	−	3.36144e6i	0.0574615	−	0.00826172i
$742$	2.06181e8	+	1.32504e8i	0.504704	+	0.324353i
$743$	−2.09047e8	−	9.54686e7i	−0.509657	−	0.232752i	0.143953	−	0.989585i	$-0.454019\pi$
$743$	−2.09047e8	−	9.54686e7i	−0.509657	−	0.232752i	−0.653609	+	0.756832i	$0.726746\pi$
$744$	1.63098e8	−	1.88226e8i	0.396033	−	0.457046i
$745$	−1.10039e8	+	7.65340e8i	−0.266121	+	1.85091i
$746$	−3.32061e8	+	1.51647e8i	−0.799836	+	0.365273i
$747$	2.93682e6	−	1.00019e7i	0.00704555	−	0.0239949i
$748$	−6.09130e8	−	1.78857e8i	−1.45548	−	0.427366i
$749$	1.13954e8	+	2.49524e8i	0.271196	+	0.593836i
$750$	1.89080e8	+	2.71857e7i	0.448191	+	0.0644401i
$751$	−5.05698e8	−	4.38190e8i	−1.19391	−	1.03453i	−0.998552	−	0.0537975i	$-0.982867\pi$
$751$	−5.05698e8	−	4.38190e8i	−1.19391	−	1.03453i	−0.195359	−	0.980732i	$-0.562587\pi$
$752$	8.62172e6	−	1.88789e7i	0.0202740	−	0.0443940i
$753$	3.97668e7	−	6.18783e7i	0.0931398	−	0.144928i
$754$	5.28217e7	+	3.67383e8i	0.123225	+	0.857048i
$755$	2.38323e8	+	3.70838e8i	0.553765	+	0.861675i
$756$	6.31235e7	−	5.46968e7i	0.146092	−	0.126589i
$757$	1.44256e8	+	4.91292e8i	0.332543	+	1.13254i	0.940847	+	0.338833i	$0.110032\pi$
$757$	1.44256e8	+	4.91292e8i	0.332543	+	1.13254i	−0.608304	+	0.793704i	$0.708150\pi$
$758$			1.40424e8i			0.322428i
$759$	1.27128e8	−	3.30278e8i	0.290747	−	0.755361i
$760$	9.46251e7			0.215559
$761$	−5.56314e8	+	1.63349e8i	−1.26231	+	0.370648i	−0.843354	−	0.537359i	$-0.819422\pi$
$761$	−5.56314e8	+	1.63349e8i	−1.26231	+	0.370648i	−0.418956	+	0.908006i	$0.637604\pi$
$762$	−2.01784e8	−	2.32872e8i	−0.456061	−	0.526322i
$763$	−2.49847e8	+	1.60567e8i	−0.562472	+	0.361479i
$764$	4.31190e8	−	6.19958e7i	0.966916	−	0.139022i
$765$	1.22988e8	+	7.90395e7i	0.274712	+	0.176547i
$766$	−5.96444e8	−	2.72387e8i	−1.32704	−	0.606038i
$767$	3.47921e7	−	4.01523e7i	0.0771072	−	0.0889865i
$768$	6.66188e6	−	4.63344e7i	0.0147066	−	0.102287i
$769$	5.21420e8	−	2.38125e8i	1.14659	−	0.523631i	0.250771	−	0.968046i	$-0.419316\pi$
$769$	5.21420e8	−	2.38125e8i	1.14659	−	0.523631i	0.895821	+	0.444416i	$0.146589\pi$
$770$	−2.53865e8	+	8.64586e8i	−0.556072	+	1.89381i
$771$	4.72706e7	+	1.38799e7i	0.103140	+	0.0302847i
$772$	3.55311e7	+	7.78022e7i	0.0772247	+	0.169099i
$773$	−3.70443e8	−	5.32616e7i	−0.802016	−	0.115312i	−0.270895	−	0.962609i	$-0.587320\pi$
$773$	−3.70443e8	−	5.32616e7i	−0.802016	−	0.115312i	−0.531120	+	0.847296i	$0.678229\pi$
$774$	1.50738e8	+	1.30615e8i	0.325086	+	0.281689i
$775$	1.97604e8	−	4.32693e8i	0.424513	−	0.929554i
$776$	1.38627e8	−	2.15708e8i	0.296662	−	0.461616i
$777$	1.25829e7	+	8.75160e7i	0.0268236	+	0.186563i
$778$	1.53094e8	+	2.38218e8i	0.325101	+	0.505867i
$779$	−1.16115e8	+	1.00614e8i	−0.245627	+	0.212837i
$780$	4.94301e7	+	1.68344e8i	0.104162	+	0.354742i
$781$			1.01355e8i			0.212761i
$782$	−2.69582e8	−	5.06186e8i	−0.563729	−	1.05850i
$783$	−1.42542e8			−0.296932
$784$	9.95017e7	−	2.92163e7i	0.206482	−	0.0606286i
$785$	−3.31136e8	−	3.82151e8i	−0.684538	−	0.789998i
$786$	7.16295e8	−	4.60335e8i	1.47511	−	0.947995i
$787$	5.13206e8	−	7.37879e7i	1.05285	−	0.151377i	0.405908	−	0.913914i	$-0.366955\pi$
$787$	5.13206e8	−	7.37879e7i	1.05285	−	0.151377i	0.646945	+	0.762537i	$0.276046\pi$
$788$	−2.30198e8	−	1.47939e8i	−0.470460	−	0.302347i
$789$	−4.36879e8	−	1.99516e8i	−0.889468	−	0.406207i
$790$	4.83365e8	−	5.57833e8i	0.980379	−	1.13142i
$791$	4.44153e7	−	3.08915e8i	0.0897434	−	0.624179i
$792$	1.29754e8	−	5.92568e7i	0.261184	−	0.119279i
$793$	9.59275e7	−	3.26699e8i	0.192364	−	0.655131i
$794$	6.01013e8	+	1.76473e8i	1.20067	+	0.352547i
$795$	−8.21343e7	−	1.79849e8i	−0.163464	−	0.357937i
$796$	−3.85829e8	−	5.54739e7i	−0.764990	−	0.109989i
$797$	7.58110e8	+	6.56906e8i	1.49747	+	1.29756i	0.837759	+	0.546040i	$0.183865\pi$
$797$	7.58110e8	+	6.56906e8i	1.49747	+	1.29756i	0.659708	+	0.751522i	$0.270680\pi$
$798$	−3.76373e7	+	8.24141e7i	−0.0740644	+	0.162178i
$799$	2.33964e7	−	3.64055e7i	0.0458678	−	0.0713717i
$800$	−5.69714e7	−	3.96245e8i	−0.111272	−	0.773916i
$801$	5.10310e7	+	7.94058e7i	0.0992971	+	0.154509i
$802$	−3.88547e8	+	3.36678e8i	−0.753218	+	0.652667i
$803$	1.88535e8	+	6.42090e8i	0.364120	+	1.24008i
$804$		−	2.93190e8i		−	0.564133i
$805$	−4.18718e8	+	2.22999e8i	−0.802665	+	0.427479i
$806$	−5.00924e8			−0.956680
$807$	4.17176e8	−	1.22494e8i	0.793777	−	0.233074i
$808$	3.72409e8	+	4.29782e8i	0.705969	+	0.814732i
$809$	−2.49194e8	+	1.60147e8i	−0.470643	+	0.302464i	−0.754380	−	0.656438i	$-0.772062\pi$
$809$	−2.49194e8	+	1.60147e8i	−0.470643	+	0.302464i	0.283737	+	0.958902i	$0.408426\pi$
$810$	−1.14440e8	+	1.64540e7i	−0.215339	+	0.0309611i
$811$	1.19642e8	+	7.68890e7i	0.224295	+	0.144146i	0.647963	−	0.761672i	$-0.275621\pi$
$811$	1.19642e8	+	7.68890e7i	0.224295	+	0.144146i	−0.423668	+	0.905818i	$0.639258\pi$
$812$	−7.54749e8	−	3.44682e8i	−1.40972	−	0.643800i
$813$	2.27956e8	−	2.63076e8i	0.424209	−	0.489564i
$814$	−7.56347e7	+	5.26051e8i	−0.140232	+	0.975337i
$815$	−2.13069e8	+	9.73053e7i	−0.393593	+	0.179748i
$816$	−3.05056e7	+	1.03893e8i	−0.0561448	+	0.191212i
$817$	−1.20982e8	−	3.55236e7i	−0.221848	−	0.0651404i
$818$	4.42641e8	+	9.69249e8i	0.808708	+	1.77082i
$819$	−4.72437e7	−	6.79261e6i	−0.0859987	−	0.0123647i
$820$	−8.62517e8	−	7.47375e8i	−1.56432	−	1.35549i
$821$	−2.46411e8	+	5.39566e8i	−0.445278	+	0.975023i	0.545321	+	0.838227i	$0.316408\pi$
$821$	−2.46411e8	+	5.39566e8i	−0.445278	+	0.975023i	−0.990599	+	0.136796i	$0.956320\pi$
$822$	−2.80662e8	+	4.36719e8i	−0.505322	+	0.786296i
$823$	−4.60664e6	−	3.20399e7i	−0.00826390	−	0.0574767i	0.985272	−	0.170993i	$-0.0546976\pi$
$823$	−4.60664e6	−	3.20399e7i	−0.00826390	−	0.0574767i	−0.993536	+	0.113517i	$0.963789\pi$
$824$	1.57289e7	+	2.44746e7i	0.0281136	+	0.0437456i
$825$	2.05896e8	−	1.78410e8i	0.366678	−	0.317729i
$826$	5.74156e7	+	1.95540e8i	0.101880	+	0.346972i
$827$		−	1.00877e9i		−	1.78351i	−0.452519	−	0.891755i	$-0.649475\pi$
$827$		−	1.00877e9i		−	1.78351i	0.452519	−	0.891755i	$-0.350525\pi$
$828$	2.46677e8	+	9.49489e7i	0.434548	+	0.167263i
$829$	−3.57101e8			−0.626797			−0.313399	−	0.949622i	$-0.601468\pi$
$829$	−3.57101e8			−0.626797			−0.313399	+	0.949622i	$0.601468\pi$
$830$	−8.05905e7	+	2.36635e7i	−0.140945	+	0.0413852i
$831$	−3.52322e8	−	4.06601e8i	−0.613955	−	0.708542i
$832$	−2.76385e8	+	1.77622e8i	−0.479893	+	0.308409i
$833$	2.14030e8	−	3.07728e7i	0.370287	−	0.0532393i
$834$	1.43724e8	+	9.23655e7i	0.247759	+	0.159225i
$835$	1.09889e9	+	5.01847e8i	1.88754	+	0.862010i
$836$	−2.07844e8	+	2.39865e8i	−0.355729	+	0.410533i
$837$	2.73780e7	−	1.90418e8i	0.0466901	−	0.324737i
$838$	1.13075e9	−	5.16397e8i	1.92148	−	0.877509i
$839$	−4.52690e7	+	1.54172e8i	−0.0766505	+	0.261048i	−0.988899	−	0.148590i	$-0.952527\pi$
$839$	−4.52690e7	+	1.54172e8i	−0.0766505	+	0.261048i	0.912248	+	0.409637i	$0.134345\pi$
$840$	−1.83468e8	−	5.38710e7i	−0.309544	−	0.0908903i
$841$	3.41132e8	+	7.46975e8i	0.573502	+	1.25579i
$842$	8.30563e8	+	1.19417e8i	1.39135	+	0.200046i
$843$	4.31777e8	+	3.74137e8i	0.720736	+	0.624522i
$844$	−5.60220e8	+	1.22671e9i	−0.931818	+	2.04040i
$845$	−3.58333e8	+	5.57578e8i	−0.593905	+	0.924135i
$846$	4.87052e6	+	3.38752e7i	0.00804386	+	0.0559463i
$847$	−2.28033e8	−	3.54826e8i	−0.375273	−	0.583936i
$848$	1.10669e8	−	9.58956e7i	0.181485	−	0.157257i
$849$	1.21931e8	+	4.15259e8i	0.199247	+	0.678573i
$850$		−	4.41489e8i		−	0.718890i
$851$	−2.25728e8	+	1.65332e8i	−0.366266	+	0.268267i
$852$	−7.56999e7			−0.122399
$853$	−7.93839e8	+	2.33092e8i	−1.27904	+	0.375561i	−0.849550	−	0.527509i	$-0.823126\pi$
$853$	−7.93839e8	+	2.33092e8i	−1.27904	+	0.375561i	−0.429494	+	0.903070i	$0.641308\pi$
$854$	8.55295e8	+	9.87063e8i	1.37323	+	1.58479i
$855$	6.14871e7	−	3.95153e7i	0.0983751	−	0.0632219i
$856$	−3.46334e8	+	4.97953e7i	−0.552171	+	0.0793902i
$857$	−7.15706e8	−	4.59956e8i	−1.13708	−	0.730759i	−0.170056	−	0.985434i	$-0.554395\pi$
$857$	−7.15706e8	−	4.59956e8i	−1.13708	−	0.730759i	−0.967026	+	0.254676i	$0.918031\pi$
$858$	−2.60971e8	−	1.19182e8i	−0.413172	−	0.188689i
$859$	−4.31494e8	+	4.97971e8i	−0.680762	+	0.785641i	−0.986020	−	0.166629i	$-0.946712\pi$
$859$	−4.31494e8	+	4.97971e8i	−0.680762	+	0.785641i	0.305258	+	0.952270i	$0.401257\pi$
$860$	1.33294e8	−	9.27078e8i	0.209563	−	1.45754i
$861$	2.82415e8	−	1.28974e8i	0.442464	−	0.202066i
$862$	−4.52206e8	+	1.54007e9i	−0.706015	+	2.40447i
$863$	7.57680e8	+	2.22475e8i	1.17884	+	0.346138i	0.811725	−	0.584039i	$-0.198529\pi$
$863$	7.57680e8	+	2.22475e8i	1.17884	+	0.346138i	0.367111	+	0.930177i	$0.380347\pi$
$864$	−6.72553e7	−	1.47269e8i	−0.104276	−	0.228333i
$865$	−1.42937e9	−	2.05513e8i	−2.20850	−	0.317534i
$866$	−6.36821e8	−	5.51808e8i	−0.980536	−	0.849639i
$867$	6.25179e7	−	1.36895e8i	0.0959283	−	0.210054i
$868$	6.05417e8	−	9.42047e8i	0.925754	−	1.44050i
$869$	1.00106e8	+	6.96255e8i	0.152547	+	1.06099i
$870$	6.20945e8	+	9.66210e8i	0.942965	+	1.46728i
$871$	−1.26620e8	+	1.09716e8i	−0.191622	+	0.166042i
$872$	−1.06728e8	−	3.63481e8i	−0.160963	−	0.548191i
$873$		−	1.98057e8i		−	0.297678i
$874$	−2.86184e8	+	1.74695e7i	−0.428657	+	0.0261665i
$875$	2.44027e8			0.364261
$876$	−4.79562e8	+	1.40812e8i	−0.713400	+	0.209473i
$877$	−5.22260e8	−	6.02720e8i	−0.774262	−	0.893546i	0.222419	−	0.974951i	$-0.428605\pi$
$877$	−5.22260e8	−	6.02720e8i	−0.774262	−	0.893546i	−0.996681	+	0.0814053i	$0.974059\pi$
$878$	9.71501e8	−	6.24346e8i	1.43536	−	0.922448i
$879$	5.03480e8	−	7.23894e7i	0.741336	−	0.106588i
$880$	4.52920e8	+	2.91074e8i	0.664621	+	0.427126i
$881$	2.93002e8	+	1.33810e8i	0.428493	+	0.195686i	0.617974	−	0.786198i	$-0.287954\pi$
$881$	2.93002e8	+	1.33810e8i	0.428493	+	0.195686i	−0.189482	+	0.981884i	$0.560681\pi$
$882$	−1.11983e8	+	1.29235e8i	−0.163210	+	0.188354i
$883$	1.23921e7	−	8.61890e7i	0.0179996	−	0.125190i	−0.978840	−	0.204625i	$-0.934403\pi$
$883$	1.23921e7	−	8.61890e7i	0.0179996	−	0.125190i	0.996840	+	0.0794350i	$0.0253116\pi$
$884$	−2.46466e8	+	1.12557e8i	−0.356779	+	0.162936i
$885$	4.63181e7	−	1.57745e8i	0.0668223	−	0.227576i
$886$	−2.23677e8	−	6.56773e7i	−0.321602	−	0.0944310i
$887$	−4.62119e8	−	1.01190e9i	−0.662191	−	1.45000i	−0.880467	−	0.474108i	$-0.842771\pi$
$887$	−4.62119e8	−	1.01190e9i	−0.662191	−	1.45000i	0.218276	−	0.975887i	$-0.429957\pi$
$888$	−1.11630e8	−	1.60499e7i	−0.159419	−	0.0229210i
$889$	−2.97484e8	−	2.57772e8i	−0.423408	−	0.366885i
$890$	3.15944e8	−	6.91820e8i	0.448167	−	0.981348i
$891$	5.95683e7	−	9.26901e7i	0.0842136	−	0.131039i
$892$	6.53759e7	+	4.54699e8i	0.0921135	+	0.640663i
$893$	−1.16969e7	−	1.82007e7i	−0.0164254	−	0.0255584i
$894$	7.13669e8	−	6.18398e8i	0.998813	−	0.865477i
$895$	2.62762e8	+	8.94884e8i	0.366516	+	1.24824i
$896$		−	5.85576e8i		−	0.814066i
$897$	−5.13052e7	−	1.42063e8i	−0.0710859	−	0.196836i
$898$	−4.66918e8			−0.644780
$899$	−1.83365e9	+	5.38408e8i	−2.52370	+	0.741024i
$900$	1.33250e8	+	1.53779e8i	0.182785	+	0.210945i
$901$	2.56865e8	−	1.65077e8i	0.351181	−	0.225690i
$902$	1.84722e9	−	2.65590e8i	2.51709	−	0.361903i
$903$	2.14347e8	+	1.37753e8i	0.291108	+	0.187084i
$904$	3.62109e8	+	1.65370e8i	0.490156	+	0.223847i
$905$	1.17351e9	−	1.35430e9i	1.58322	−	1.82713i
$906$	7.66177e7	−	5.32888e8i	0.103025	−	0.716558i
$907$	7.38767e8	−	3.37383e8i	0.990115	−	0.452170i	0.146553	−	0.989203i	$-0.453182\pi$
$907$	7.38767e8	−	3.37383e8i	0.990115	−	0.452170i	0.843562	+	0.537033i	$0.180455\pi$
$908$	−2.59599e8	+	8.84114e8i	−0.346774	+	1.18100i
$909$	4.21466e8	+	1.23754e8i	0.561140	+	0.164766i
$910$	1.59761e8	+	3.49828e8i	0.212005	+	0.464227i
$911$	−7.87456e8	−	1.13219e8i	−1.04153	−	0.149749i	−0.399738	−	0.916629i	$-0.630899\pi$
$911$	−7.87456e8	−	1.13219e8i	−1.04153	−	0.149749i	−0.641791	+	0.766880i	$0.721808\pi$
$912$	4.09112e7	+	3.54498e7i	0.0539334	+	0.0467336i
$913$	3.32514e7	−	7.28104e7i	0.0436915	−	0.0956711i
$914$	−5.66008e8	+	8.80725e8i	−0.741282	+	1.15346i
$915$	−1.49947e8	−	1.04291e9i	−0.195738	−	1.36139i
$916$	−7.27180e8	−	1.13151e9i	−0.946140	−	1.47222i
$917$	8.22035e8	−	7.12297e8i	1.06606	−	0.923747i
$918$	−5.03030e7	−	1.71316e8i	−0.0650228	−	0.221447i
$919$			4.40037e8i			0.566948i	0.958980	+	0.283474i	$0.0914869\pi$
$919$			4.40037e8i			0.566948i	−0.958980	+	0.283474i	$0.908513\pi$
$920$	−1.22450e8	−	5.92591e8i	−0.157252	−	0.761013i
$921$	−4.96686e8			−0.635774
$922$	−1.22057e9	+	3.58390e8i	−1.55729	+	0.457260i
$923$	2.83281e7	+	3.26924e7i	0.0360257	+	0.0415759i
$924$	5.39545e8	−	3.46745e8i	0.683931	−	0.439535i
$925$	−2.13203e8	+	3.06539e7i	−0.269381	+	0.0387312i
$926$	9.62730e7	+	6.18709e7i	0.121247	+	0.0779208i
$927$	2.04411e7	+	9.33516e6i	0.0256605	+	0.0117188i
$928$	−1.05321e9	+	1.21547e9i	−1.31787	+	1.52090i
$929$	−5.19695e7	+	3.61456e8i	−0.0648189	+	0.450825i	0.931404	+	0.363988i	$0.118585\pi$
$929$	−5.19695e7	+	3.61456e8i	−0.0648189	+	0.450825i	−0.996223	+	0.0868372i	$0.972324\pi$
$930$	−1.41000e9	+	6.43926e8i	−1.75295	+	0.800547i
$931$	3.04562e7	−	1.03724e8i	0.0377421	−	0.128538i
$932$	1.47084e9	+	4.31876e8i	1.81684	+	0.533472i
$933$	−4.82232e7	−	1.05594e8i	−0.0593761	−	0.130015i
$934$	1.81411e9	+	2.60830e8i	2.22651	+	0.320123i
$935$	8.48401e8	+	7.35143e8i	1.03793	+	0.899368i
$936$	2.52907e7	−	5.53789e7i	0.0308413	−	0.0675331i
$937$	7.73911e8	−	1.20423e9i	0.940746	−	1.46383i	0.0556345	−	0.998451i	$-0.482282\pi$
$937$	7.73911e8	−	1.20423e9i	0.940746	−	1.46383i	0.885112	−	0.465379i	$-0.154082\pi$
$938$	−9.14606e7	−	6.36122e8i	−0.110822	−	0.770783i
$939$	4.65306e6	+	7.24030e6i	0.00562007	+	0.00874500i
$940$	1.21456e8	−	1.05242e8i	0.146230	−	0.126709i
$941$	4.50355e8	+	1.53377e9i	0.540488	+	1.84073i	0.541448	+	0.840734i	$0.317876\pi$
$941$	4.50355e8	+	1.53377e9i	0.540488	+	1.84073i	−0.000959791		1.00000i	$0.500306\pi$
$942$			6.17559e8i			0.738798i
$943$	7.80356e8	+	5.96971e8i	0.930589	+	0.711899i
$944$	1.21765e8			0.144746
$945$	−1.41713e8	+	4.16108e7i	−0.167925	+	0.0493072i
$946$	1.00295e9	+	1.15747e9i	1.18470	+	1.36721i
$947$	7.71885e7	−	4.96061e7i	0.0908872	−	0.0584097i	−0.494408	−	0.869230i	$-0.664615\pi$
$947$	7.71885e7	−	4.96061e7i	0.0908872	−	0.0584097i	0.585295	+	0.810820i	$0.300979\pi$
$948$	−5.20017e8	+	7.47672e7i	−0.610369	+	0.0877579i
$949$	2.40272e8	+	1.54414e8i	0.281129	+	0.180670i
$950$	−2.00774e8	−	9.16902e7i	−0.234172	−	0.106943i
$951$	−3.11799e8	+	3.59835e8i	−0.362521	+	0.418371i
$952$	4.20246e7	−	2.92288e8i	0.0487072	−	0.338766i
$953$	−8.68554e8	+	3.96655e8i	−1.00350	+	0.458284i	−0.848253	−	0.529592i	$-0.822345\pi$
$953$	−8.68554e8	+	3.96655e8i	−1.00350	+	0.458284i	−0.155249	+	0.987875i	$0.549618\pi$
$954$	−6.80300e7	+	2.31689e8i	−0.0783530	+	0.266846i
$955$	−7.39110e8	−	2.17022e8i	−0.848592	−	0.249169i
$956$	−8.98607e8	−	1.96767e9i	−1.02848	−	2.25206i
$957$	−1.08339e9	−	1.55769e8i	−1.23609	−	0.177723i
$958$	2.62480e8	+	2.27440e8i	0.298538	+	0.258684i
$959$	−2.75489e8	+	6.03237e8i	−0.312355	+	0.683962i
$960$	−5.49640e8	+	8.55257e8i	−0.621248	+	0.966680i
$961$	−2.40752e8	−	1.67447e9i	−0.271269	−	1.88672i
$962$	1.22632e8	+	1.90818e8i	0.137745	+	0.214336i
$963$	−2.04252e8	+	1.76985e8i	−0.228711	+	0.198179i
$964$	−2.47273e8	−	8.42135e8i	−0.276023	−	0.940050i
$965$		−	1.51245e8i		−	0.168306i
$966$	5.64824e8	+	1.29056e8i	0.626588	+	0.143168i
$967$	−1.14068e9			−1.26149			−0.630747	−	0.775989i	$-0.717251\pi$
$967$	−1.14068e9			−1.26149			−0.630747	+	0.775989i	$0.717251\pi$
$968$	5.16205e8	−	1.51571e8i	0.569110	−	0.167106i
$969$	7.39165e7	+	8.53042e7i	0.0812400	+	0.0937560i
$970$	−1.34251e9	+	8.62780e8i	−1.47097	+	0.945334i
$971$	9.02197e8	−	1.29716e8i	0.985470	−	0.141689i	0.369307	−	0.929307i	$-0.379595\pi$
$971$	9.02197e8	−	1.29716e8i	0.985470	−	0.141689i	0.616164	+	0.787618i	$0.288686\pi$
$972$	6.92281e7	+	4.44902e7i	0.0753848	+	0.0484469i
$973$	1.98525e8	+	9.06631e7i	0.215514	+	0.0984220i
$974$	1.29966e8	−	1.49988e8i	0.140654	−	0.162323i
$975$	1.65479e7	−	1.15093e8i	0.0178537	−	0.124175i
$976$	7.09841e8	−	3.24174e8i	0.763505	−	0.348681i
$977$	1.87055e7	−	6.37050e7i	0.0200579	−	0.0683109i	−0.948856	−	0.315709i	$-0.897758\pi$
$977$	1.87055e7	−	6.37050e7i	0.0200579	−	0.0683109i	0.968914	+	0.247399i	$0.0795757\pi$
$978$	2.74484e8	+	8.05958e7i	0.293428	+	0.0861581i
$979$	3.01089e8	+	6.59293e8i	0.320883	+	0.702636i
$980$	7.94831e8	+	1.14279e8i	0.844494	+	0.121420i
$981$	−2.21140e8	−	1.91619e8i	−0.234240	−	0.202970i
$982$	7.21775e8	−	1.58047e9i	0.762198	−	1.66898i
$983$	−1.95421e8	+	3.04080e8i	−0.205736	+	0.320131i	−0.928753	−	0.370699i	$-0.879118\pi$
$983$	−1.95421e8	+	3.04080e8i	−0.205736	+	0.320131i	0.723017	+	0.690830i	$0.242755\pi$
$984$	5.63591e7	+	3.91986e8i	0.0591532	+	0.411420i
$985$	2.61601e8	+	4.07059e8i	0.273735	+	0.425940i
$986$	−1.34047e9	+	1.16153e9i	−1.39839	+	1.21171i
$987$	1.23171e7	+	4.19483e7i	0.0128103	+	0.0436278i
$988$			1.35460e8i			0.140456i
$989$	−6.59094e7	+	8.03622e8i	−0.0681332	+	0.830736i
$990$	−8.87787e8			−0.914962
$991$	6.27862e7	−	1.84357e7i	0.0645124	−	0.0189426i	−0.249317	−	0.968422i	$-0.580206\pi$
$991$	6.27862e7	−	1.84357e7i	0.0645124	−	0.0189426i	0.313830	+	0.949479i	$0.398388\pi$
$992$	−1.42143e9	−	1.64042e9i	−1.45610	−	1.68043i
$993$	1.18663e8	−	7.62603e7i	0.121191	−	0.0778844i
$994$	−1.64243e8	+	2.36145e7i	−0.167235	+	0.0240448i
$995$	5.79856e8	+	3.72651e8i	0.588642	+	0.378297i
$996$	5.43804e7	+	2.48347e7i	0.0550382	+	0.0251351i
$997$	−5.28504e8	+	6.09926e8i	−0.533289	+	0.615449i	−0.956908	−	0.290392i	$-0.906214\pi$
$997$	−5.28504e8	+	6.09926e8i	−0.533289	+	0.615449i	0.423618	+	0.905841i	$0.360760\pi$
$998$	−2.93293e8	+	2.03990e9i	−0.295060	+	2.05218i
$999$	−7.92389e7	+	3.61872e7i	−0.0794771	+	0.0362960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.f.a.37.4	yes	240
23.5	odd	22	inner	69.7.f.a.28.4	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.f.a.28.4	✓	240	23.5	odd	22	inner
69.7.f.a.37.4	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)

\(f(q)\)	\(=\)	\(q+(-11.8838 + 3.48940i) q^{2} +(-10.2083 - 11.7810i) q^{3} +(75.2085 - 48.3336i) q^{4} +(-156.478 + 22.4981i) q^{5} +(162.421 + 104.382i) q^{6} +(224.352 + 102.458i) q^{7} +(-206.018 + 237.757i) q^{8} +(-34.5825 + 240.527i) q^{9} +O(q^{10})\)	\(q+(-11.8838 + 3.48940i) q^{2} +(-10.2083 - 11.7810i) q^{3} +(75.2085 - 48.3336i) q^{4} +(-156.478 + 22.4981i) q^{5} +(162.421 + 104.382i) q^{6} +(224.352 + 102.458i) q^{7} +(-206.018 + 237.757i) q^{8} +(-34.5825 + 240.527i) q^{9} +(1781.04 - 813.375i) q^{10} +(-525.692 + 1790.34i) q^{11} +(-1337.16 - 392.627i) q^{12} +(330.825 + 724.406i) q^{13} +(-3023.67 - 434.738i) q^{14} +(1862.41 + 1613.79i) q^{15} +(-758.208 + 1660.24i) q^{16} +(-2057.51 + 3201.55i) q^{17} +(-428.321 - 2979.04i) q^{18} +(1028.64 + 1600.60i) q^{19} +(-10681.0 + 9255.16i) q^{20} +(-1083.19 - 3689.00i) q^{21} -23110.4i q^{22} +(8692.65 - 8513.15i) q^{23} +4904.10 q^{24} +(8986.98 - 2638.82i) q^{25} +(-6459.20 - 7454.32i) q^{26} +(3186.66 - 2047.94i) q^{27} +(21825.3 - 3138.01i) q^{28} +(-31656.3 - 20344.2i) q^{29} +(-27763.7 - 12679.3i) q^{30} +(33257.6 - 38381.3i) q^{31} +(6082.54 - 42305.0i) q^{32} +(26458.4 - 12083.1i) q^{33} +(13279.6 - 45226.1i) q^{34} +(-37411.1 - 10984.9i) q^{35} +(9024.61 + 19761.1i) q^{36} +(-22762.5 - 3272.76i) q^{37} +(-17809.3 - 15431.8i) q^{38} +(5157.05 - 11292.4i) q^{39} +(26888.1 - 41838.7i) q^{40} +(11492.2 + 79930.3i) q^{41} +(25744.8 + 40059.7i) q^{42} +(-50084.4 + 43398.3i) q^{43} +(46997.1 + 160057. i) q^{44} -38415.1i q^{45} +(-73596.0 + 131501. i) q^{46} -11371.2 q^{47} +(27299.3 - 8015.79i) q^{48} +(-37207.6 - 42939.9i) q^{49} +(-97591.6 + 62718.3i) q^{50} +(58721.1 - 8442.82i) q^{51} +(59894.0 + 38491.5i) q^{52} +(-72981.0 - 33329.3i) q^{53} +(-30723.6 + 35456.9i) q^{54} +(41979.7 - 291975. i) q^{55} +(-70580.6 + 32233.1i) q^{56} +(8355.94 - 28457.7i) q^{57} +(447186. + 131306. i) q^{58} +(-27713.9 - 60685.0i) q^{59} +(218070. + 31353.7i) q^{60} +(-323123. - 279987. i) q^{61} +(-261299. + 572165. i) q^{62} +(-32402.5 + 50419.3i) q^{63} +(58711.3 + 408346. i) q^{64} +(-68064.5 - 105910. i) q^{65} +(-272263. + 235917. i) q^{66} +(59271.2 + 201859. i) q^{67} +340231. i q^{68} +(-189030. - 15503.4i) q^{69} +482917. q^{70} +(52118.7 - 15303.4i) q^{71} +(-50062.3 - 57775.0i) q^{72} +(301708. - 193896. i) q^{73} +(281925. - 40534.7i) q^{74} +(-122829. - 78937.6i) q^{75} +(154725. + 70660.6i) q^{76} +(-301375. + 347805. i) q^{77} +(-21881.8 + 152191. i) q^{78} +(342913. - 156603. i) q^{79} +(81290.2 - 276849. i) q^{80} +(-56657.1 - 16636.0i) q^{81} +(-415480. - 909774. i) q^{82} +(-42461.0 - 6104.97i) q^{83} +(-259768. - 225090. i) q^{84} +(249926. - 547261. i) q^{85} +(443758. - 690501. i) q^{86} +(83480.7 + 580621. i) q^{87} +(-317365. - 493829. i) q^{88} +(293560. - 254371. i) q^{89} +(134045. + 456517. i) q^{90} +196418. i q^{91} +(242291. - 1.06041e6i) q^{92} -791671. q^{93} +(135133. - 39678.6i) q^{94} +(-196970. - 227315. i) q^{95} +(-560486. + 360203. i) q^{96} +(-806751. + 115993. i) q^{97} +(592002. + 380457. i) q^{98} +(-412445. - 188357. 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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