LMFDB - Embedded newform 7.8.c.a.4.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7,8,Mod(2,7)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7.2"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	7.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.18669517839$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 103x^{6} - 378x^{5} + 9744x^{4} - 22680x^{3} + 149400x^{2} + 216000x + 810000 $ x^8 - x^7 + 103x^6 - 378x^5 + 9744x^4 - 22680x^3 + 149400x^2 + 216000x + 810000
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.3
Root			$2.57145 - 4.45388i$ of defining polynomial
Character	$\chi$	$=$	7.4
Dual form			7.8.c.a.2.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.69038 + 6.39193i) q^{2} +(-37.1217 + 64.2967i) q^{3} +(36.7621 - 63.6739i) q^{4} +(145.409 + 251.857i) q^{5} -547.974 q^{6} +(358.327 - 833.753i) q^{7} +1487.40 q^{8} +(-1662.54 - 2879.61i) q^{9} +(-1073.23 + 1858.89i) q^{10} +(-1596.44 + 2765.12i) q^{11} +(2729.35 + 4727.37i) q^{12} +5186.70 q^{13} +(6651.66 - 786.465i) q^{14} -21591.4 q^{15} +(783.535 + 1357.12i) q^{16} +(1224.56 - 2120.99i) q^{17} +(12270.9 - 21253.7i) q^{18} +(-16159.1 - 27988.4i) q^{19} +21382.2 q^{20} +(40305.9 + 53989.6i) q^{21} -23565.9 q^{22} +(-31470.7 - 54508.9i) q^{23} +(-55215.0 + 95635.2i) q^{24} +(-3225.30 + 5586.38i) q^{25} +(19140.9 + 33153.0i) q^{26} +84495.7 q^{27} +(-39915.4 - 53466.7i) q^{28} +141752. q^{29} +(-79680.5 - 138011. i) q^{30} +(-141188. + 244545. i) q^{31} +(89410.7 - 154864. i) q^{32} +(-118525. - 205292. i) q^{33} +18076.3 q^{34} +(262090. - 30988.5i) q^{35} -244475. q^{36} +(65683.8 + 113768. i) q^{37} +(119267. - 206576. i) q^{38} +(-192539. + 333488. i) q^{39} +(216283. + 374612. i) q^{40} -65254.0 q^{41} +(-196354. + 456875. i) q^{42} -257876. q^{43} +(117377. + 203303. i) q^{44} +(483499. - 837445. i) q^{45} +(232278. - 402317. i) q^{46} +(-63728.7 - 110381. i) q^{47} -116345. q^{48} +(-566746. - 597513. i) q^{49} -47610.4 q^{50} +(90915.2 + 157470. i) q^{51} +(190674. - 330257. i) q^{52} +(-395323. + 684719. i) q^{53} +(311821. + 540090. i) q^{54} -928551. q^{55} +(532978. - 1.24013e6i) q^{56} +2.39942e6 q^{57} +(523119. + 906068. i) q^{58} +(-607173. + 1.05165e6i) q^{59} +(-793746. + 1.37481e6i) q^{60} +(-381042. - 659985. i) q^{61} -2.08415e6 q^{62} +(-2.99662e6 + 354308. i) q^{63} +1.52042e6 q^{64} +(754195. + 1.30630e6i) q^{65} +(874808. - 1.51521e6i) q^{66} +(1.72143e6 - 2.98160e6i) q^{67} +(-90034.6 - 155944. i) q^{68} +4.67299e6 q^{69} +(1.16529e6 + 1.56090e6i) q^{70} -3.99576e6 q^{71} +(-2.47287e6 - 4.28315e6i) q^{72} +(384669. - 666266. i) q^{73} +(-484797. + 839693. i) q^{74} +(-239457. - 414752. i) q^{75} -2.37617e6 q^{76} +(1.73338e6 + 2.32186e6i) q^{77} -2.84217e6 q^{78} +(2.91690e6 + 5.05222e6i) q^{79} +(-227867. + 394677. i) q^{80} +(499361. - 864918. i) q^{81} +(-240812. - 417099. i) q^{82} +1.39747e6 q^{83} +(4.91946e6 - 581657. i) q^{84} +712248. q^{85} +(-951662. - 1.64833e6i) q^{86} +(-5.26207e6 + 9.11418e6i) q^{87} +(-2.37455e6 + 4.11285e6i) q^{88} +(-808509. - 1.40038e6i) q^{89} +7.13719e6 q^{90} +(1.85854e6 - 4.32443e6i) q^{91} -4.62772e6 q^{92} +(-1.04823e7 - 1.81558e7i) q^{93} +(470367. - 814699. i) q^{94} +(4.69937e6 - 8.13955e6i) q^{95} +(6.63816e6 + 1.14976e7i) q^{96} -5.68544e6 q^{97} +(1.72775e6 - 5.82765e6i) q^{98} +1.06166e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{2} - 28 q^{3} - 348 q^{4} - 252 q^{5} + 2044 q^{6} + 672 q^{7} - 1968 q^{8} - 2008 q^{9} - 4774 q^{10} + 3972 q^{11} + 5404 q^{12} - 2352 q^{13} + 47502 q^{14} - 33112 q^{15} - 57264 q^{16} - 56364 q^{17}+ \cdots + 30427952 q^{99}+O(q^{100}) $ 8 * q + 6 * q^2 - 28 * q^3 - 348 * q^4 - 252 * q^5 + 2044 * q^6 + 672 * q^7 - 1968 * q^8 - 2008 * q^9 - 4774 * q^10 + 3972 * q^11 + 5404 * q^12 - 2352 * q^13 + 47502 * q^14 - 33112 * q^15 - 57264 * q^16 - 56364 * q^17 + 35908 * q^18 - 41748 * q^19 + 324744 * q^20 + 188524 * q^21 - 305908 * q^22 - 131748 * q^23 - 389592 * q^24 + 68016 * q^25 - 113652 * q^26 + 378056 * q^27 + 681548 * q^28 + 68112 * q^29 - 605378 * q^30 - 401212 * q^31 + 453408 * q^32 - 24052 * q^33 + 164220 * q^34 + 40404 * q^35 - 720176 * q^36 + 5396 * q^37 - 31794 * q^38 - 364840 * q^39 + 443688 * q^40 + 820848 * q^41 - 240856 * q^42 + 93088 * q^43 + 1465836 * q^44 + 1209656 * q^45 - 1379202 * q^46 - 1470084 * q^47 - 4037600 * q^48 - 2793784 * q^49 + 2791056 * q^50 + 1724796 * q^51 + 5269768 * q^52 + 642372 * q^53 + 4567318 * q^54 - 6126680 * q^55 - 6195168 * q^56 + 6718136 * q^57 + 1972220 * q^58 - 752220 * q^59 - 2123324 * q^60 - 1325772 * q^61 - 6032628 * q^62 - 6412616 * q^63 - 1731712 * q^64 + 4868808 * q^65 + 6013294 * q^66 + 290916 * q^67 - 2453556 * q^68 + 9830520 * q^69 + 11665990 * q^70 + 6755520 * q^71 - 4557744 * q^72 - 6706588 * q^73 - 3616878 * q^74 - 7223888 * q^75 + 5846008 * q^76 - 5310564 * q^77 - 32576264 * q^78 - 3946244 * q^79 - 10695888 * q^80 + 11731292 * q^81 + 17563252 * q^82 + 19084128 * q^83 + 38088092 * q^84 + 14012136 * q^85 - 23237832 * q^86 - 17836840 * q^87 + 8043336 * q^88 - 16165212 * q^89 + 6831496 * q^90 - 2414720 * q^91 - 38885256 * q^92 - 12552852 * q^93 - 5720442 * q^94 + 3268452 * q^95 + 8448608 * q^96 + 3066224 * q^97 + 60255006 * q^98 + 30427952 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	3.69038	+	6.39193i	0.326187	+	0.564972i	0.981752	−	0.190167i	$-0.0609028\pi$
$2$	3.69038	+	6.39193i	0.326187	+	0.564972i	−0.655565	+	0.755139i	$0.727569\pi$
$3$	−37.1217	+	64.2967i	−0.793787	+	1.37488i	0.129820	+	0.991538i	$0.458560\pi$
$3$	−37.1217	+	64.2967i	−0.793787	+	1.37488i	−0.923607	+	0.383341i	$0.874773\pi$
$4$	36.7621	−	63.6739i	0.287204	−	0.497452i
$5$	145.409	+	251.857i	0.520233	+	0.901069i	0.999723	+	0.0235223i	$0.00748807\pi$
$5$	145.409	+	251.857i	0.520233	+	0.901069i	−0.479491	+	0.877547i	$0.659179\pi$
$6$	−547.974			−1.03569
$7$	358.327	−	833.753i	0.394854	−	0.918744i
$7$	358.327	−	833.753i	0.394854	−	0.918744i
$8$	1487.40			1.02710
$9$	−1662.54	−	2879.61i	−0.760194	−	1.31669i
$10$	−1073.23	+	1858.89i	−0.339386	+	0.587834i
$11$	−1596.44	+	2765.12i	−0.361642	+	0.626382i	−0.988231	−	0.152967i	$-0.951117\pi$
$11$	−1596.44	+	2765.12i	−0.361642	+	0.626382i	0.626589	+	0.779350i	$0.284450\pi$
$12$	2729.35	+	4727.37i	0.455958	+	0.789742i
$13$	5186.70			0.654771			0.327385	−	0.944891i	$-0.393832\pi$
$13$	5186.70			0.654771			0.327385	+	0.944891i	$0.393832\pi$
$14$	6651.66	−	786.465i	0.647861	−	0.0766004i
$15$	−21591.4			−1.65181
$16$	783.535	+	1357.12i	0.0478232	+	0.0828322i
$17$	1224.56	−	2120.99i	0.0604515	−	0.104705i	−0.834216	−	0.551438i	$-0.814079\pi$
$17$	1224.56	−	2120.99i	0.0604515	−	0.104705i	0.894667	+	0.446733i	$0.147413\pi$
$18$	12270.9	−	21253.7i	0.495931	−	0.858977i
$19$	−16159.1	−	27988.4i	−0.540480	−	0.936139i	−0.998876	−	0.0473912i	$-0.984909\pi$
$19$	−16159.1	−	27988.4i	−0.540480	−	0.936139i	0.458396	−	0.888748i	$-0.348424\pi$
$20$	21382.2			0.597652
$21$	40305.9	+	53989.6i	0.949731	+	1.27216i
$22$	−23565.9			−0.471851
$23$	−31470.7	−	54508.9i	−0.539335	−	0.934156i	−0.998940	−	0.0460327i	$-0.985342\pi$
$23$	−31470.7	−	54508.9i	−0.539335	−	0.934156i	0.459604	−	0.888124i	$-0.347991\pi$
$24$	−55215.0	+	95635.2i	−0.815300	+	1.41214i
$25$	−3225.30	+	5586.38i	−0.0412838	+	0.0715057i
$26$	19140.9	+	33153.0i	0.213578	+	0.369927i
$27$	84495.7			0.826154
$28$	−39915.4	−	53466.7i	−0.343627	−	0.460288i
$29$	141752.			1.07928			0.539642	−	0.841895i	$-0.318560\pi$
$29$	141752.			1.07928			0.539642	+	0.841895i	$0.318560\pi$
$30$	−79680.5	−	138011.i	−0.538800	−	0.933229i
$31$	−141188.	+	244545.i	−0.851200	+	1.47432i	0.0289267	+	0.999582i	$0.490791\pi$
$31$	−141188.	+	244545.i	−0.851200	+	1.47432i	−0.880126	+	0.474739i	$0.842542\pi$
$32$	89410.7	−	154864.i	0.482353	−	0.835460i
$33$	−118525.	−	205292.i	−0.574133	−	0.994427i
$34$	18076.3			0.0788740
$35$	262090.	−	30988.5i	1.03327	−	0.122169i
$36$	−244475.			−0.873324
$37$	65683.8	+	113768.i	0.213183	+	0.369244i	0.952709	−	0.303884i	$-0.0982836\pi$
$37$	65683.8	+	113768.i	0.213183	+	0.369244i	−0.739526	+	0.673128i	$0.764950\pi$
$38$	119267.	−	206576.i	0.352595	−	0.610713i
$39$	−192539.	+	333488.i	−0.519748	+	0.900230i
$40$	216283.	+	374612.i	0.534332	+	0.925491i
$41$	−65254.0			−0.147864			−0.0739322	−	0.997263i	$-0.523555\pi$
$41$	−65254.0			−0.147864			−0.0739322	+	0.997263i	$0.523555\pi$
$42$	−196354.	+	456875.i	−0.408947	+	0.951535i
$43$	−257876.			−0.494620			−0.247310	−	0.968936i	$-0.579547\pi$
$43$	−257876.			−0.494620			−0.247310	+	0.968936i	$0.579547\pi$
$44$	117377.	+	203303.i	0.207730	+	0.359799i
$45$	483499.	−	837445.i	0.790955	−	1.36998i
$46$	232278.	−	402317.i	0.351848	−	0.609419i
$47$	−63728.7	−	110381.i	−0.0895349	−	0.155079i	0.817780	−	0.575531i	$-0.195205\pi$
$47$	−63728.7	−	110381.i	−0.0895349	−	0.155079i	−0.907315	+	0.420452i	$0.861871\pi$
$48$	−116345.			−0.151846
$49$	−566746.	−	597513.i	−0.688180	−	0.725540i
$50$	−47610.4			−0.0538650
$51$	90915.2	+	157470.i	0.0959712	+	0.166227i
$52$	190674.	−	330257.i	0.188053	−	0.325717i
$53$	−395323.	+	684719.i	−0.364743	+	0.631753i	−0.988735	−	0.149678i	$-0.952176\pi$
$53$	−395323.	+	684719.i	−0.364743	+	0.631753i	0.623992	+	0.781431i	$0.285510\pi$
$54$	311821.	+	540090.i	0.269481	+	0.466754i
$55$	−928551.			−0.752552
$56$	532978.	−	1.24013e6i	0.405556	−	0.943644i
$57$	2.39942e6			1.71610
$58$	523119.	+	906068.i	0.352048	+	0.609765i
$59$	−607173.	+	1.05165e6i	−0.384884	+	0.666639i	−0.991753	−	0.128163i	$-0.959092\pi$
$59$	−607173.	+	1.05165e6i	−0.384884	+	0.666639i	0.606869	+	0.794802i	$0.292425\pi$
$60$	−793746.	+	1.37481e6i	−0.474408	+	0.821699i
$61$	−381042.	−	659985.i	−0.214941	−	0.372288i	0.738314	−	0.674458i	$-0.235622\pi$
$61$	−381042.	−	659985.i	−0.214941	−	0.372288i	−0.953254	+	0.302169i	$0.902289\pi$
$62$	−2.08415e6			−1.11060
$63$	−2.99662e6	+	354308.i	−1.50987	+	0.178521i
$64$	1.52042e6			0.724995
$65$	754195.	+	1.30630e6i	0.340633	+	0.589994i
$66$	874808.	−	1.51521e6i	0.374549	−	0.648738i
$67$	1.72143e6	−	2.98160e6i	0.699241	−	1.21112i	−0.269488	−	0.963004i	$-0.586855\pi$
$67$	1.72143e6	−	2.98160e6i	0.699241	−	1.21112i	0.968730	−	0.248118i	$-0.0798121\pi$
$68$	−90034.6	−	155944.i	−0.0347239	−	0.0601435i
$69$	4.67299e6			1.71247
$70$	1.16529e6	+	1.56090e6i	0.406061	+	0.543918i
$71$	−3.99576e6			−1.32494			−0.662469	−	0.749089i	$-0.730491\pi$
$71$	−3.99576e6			−1.32494			−0.662469	+	0.749089i	$0.730491\pi$
$72$	−2.47287e6	−	4.28315e6i	−0.780797	−	1.35238i
$73$	384669.	−	666266.i	0.115733	−	0.200455i	−0.802340	−	0.596868i	$-0.796412\pi$
$73$	384669.	−	666266.i	0.115733	−	0.200455i	0.918073	+	0.396412i	$0.129745\pi$
$74$	−484797.	+	839693.i	−0.139075	+	0.240885i
$75$	−239457.	−	414752.i	−0.0655411	−	0.113520i
$76$	−2.37617e6			−0.620913
$77$	1.73338e6	+	2.32186e6i	0.432689	+	0.579586i
$78$	−2.84217e6			−0.678140
$79$	2.91690e6	+	5.05222e6i	0.665620	+	1.15289i	0.979117	+	0.203299i	$0.0651663\pi$
$79$	2.91690e6	+	5.05222e6i	0.665620	+	1.15289i	−0.313496	+	0.949589i	$0.601500\pi$
$80$	−227867.	+	394677.i	−0.0497584	+	0.0861840i
$81$	499361.	−	864918.i	0.104404	−	0.180833i
$82$	−240812.	−	417099.i	−0.0482314	−	0.0835393i
$83$	1.39747e6			0.268267			0.134134	−	0.990963i	$-0.457175\pi$
$83$	1.39747e6			0.268267			0.134134	+	0.990963i	$0.457175\pi$
$84$	4.91946e6	−	581657.i	0.905607	−	0.107075i
$85$	712248.			0.125795
$86$	−951662.	−	1.64833e6i	−0.161339	−	0.279447i
$87$	−5.26207e6	+	9.11418e6i	−0.856721	+	1.48388i
$88$	−2.37455e6	+	4.11285e6i	−0.371443	+	0.643359i
$89$	−808509.	−	1.40038e6i	−0.121568	−	0.210562i	0.798818	−	0.601573i	$-0.205459\pi$
$89$	−808509.	−	1.40038e6i	−0.121568	−	0.210562i	−0.920386	+	0.391010i	$0.872126\pi$
$90$	7.13719e6			1.03200
$91$	1.85854e6	−	4.32443e6i	0.258539	−	0.601567i
$92$	−4.62772e6			−0.619598
$93$	−1.04823e7	−	1.81558e7i	−1.35134	−	2.34059i
$94$	470367.	−	814699.i	0.0584102	−	0.101170i
$95$	4.69937e6	−	8.13955e6i	0.562351	−	0.974020i
$96$	6.63816e6	+	1.14976e7i	0.765770	+	1.32635i
$97$	−5.68544e6			−0.632504			−0.316252	−	0.948675i	$-0.602424\pi$
$97$	−5.68544e6			−0.632504			−0.316252	+	0.948675i	$0.602424\pi$
$98$	1.72775e6	−	5.82765e6i	0.185435	−	0.625464i
$99$	1.06166e7			1.09967
$100$	237138.	+	410735.i	0.0237138	+	0.0410735i
$101$	−5.04402e6	+	8.73650e6i	−0.487138	+	0.843748i	−0.999891	−	0.0147883i	$-0.995293\pi$
$101$	−5.04402e6	+	8.73650e6i	−0.487138	+	0.843748i	0.512752	+	0.858537i	$0.328626\pi$
$102$	−671024.	+	1.16225e6i	−0.0626091	+	0.108442i
$103$	−4.66877e6	−	8.08655e6i	−0.420991	−	0.729177i	0.575046	−	0.818121i	$-0.304984\pi$
$103$	−4.66877e6	−	8.08655e6i	−0.420991	−	0.729177i	−0.996037	+	0.0889438i	$0.971651\pi$
$104$	7.71471e6			0.672517
$105$	−7.73679e6	+	1.80019e7i	−0.652226	+	1.51759i
$106$	−5.83557e6			−0.475897
$107$	7.20247e6	+	1.24750e7i	0.568379	+	0.984462i	0.996726	+	0.0808474i	$0.0257626\pi$
$107$	7.20247e6	+	1.24750e7i	0.568379	+	0.984462i	−0.428347	+	0.903614i	$0.640904\pi$
$108$	3.10624e6	−	5.38017e6i	0.237275	−	0.410972i
$109$	−4.27999e6	+	7.41316e6i	−0.316556	+	0.548291i	−0.979767	−	0.200142i	$-0.935860\pi$
$109$	−4.27999e6	+	7.41316e6i	−0.316556	+	0.548291i	0.663211	+	0.748432i	$0.269193\pi$
$110$	−3.42671e6	−	5.93523e6i	−0.245472	−	0.425171i
$111$	−9.75319e6			−0.676887
$112$	1.41227e6	−	166981.i	0.0949848	−	0.0112306i
$113$	1.15607e7			0.753722			0.376861	−	0.926270i	$-0.377003\pi$
$113$	1.15607e7			0.753722			0.376861	+	0.926270i	$0.377003\pi$
$114$	8.85476e6	+	1.53369e7i	0.559770	+	0.969551i
$115$	9.15227e6	−	1.58522e7i	0.561160	−	0.971957i
$116$	5.21110e6	−	9.02589e6i	0.309975	−	0.536892i
$117$	−8.62312e6	−	1.49357e7i	−0.497753	−	0.862133i
$118$	−8.96280e6			−0.502177
$119$	−1.32959e6	−	1.78099e6i	−0.0723276	−	0.0968827i
$120$	−3.21151e7			−1.69658
$121$	4.64633e6	+	8.04768e6i	0.238430	+	0.412973i
$122$	2.81238e6	−	4.87119e6i	0.140222	−	0.242871i
$123$	2.42234e6	−	4.19562e6i	0.117373	−	0.203296i
$124$	1.03807e7	+	1.79800e7i	0.488936	+	0.846862i
$125$	2.08443e7			0.954556
$126$	−1.33234e7	−	1.78467e7i	−0.593359	−	0.794804i
$127$	2.65100e7			1.14841			0.574204	−	0.818712i	$-0.305312\pi$
$127$	2.65100e7			1.14841			0.574204	+	0.818712i	$0.305312\pi$
$128$	−5.83363e6	−	1.01041e7i	−0.245869	−	0.425857i
$129$	9.57281e6	−	1.65806e7i	0.392623	−	0.680042i
$130$	−5.56654e6	+	9.64152e6i	−0.222220	+	0.384896i
$131$	−2.27287e6	−	3.93672e6i	−0.0883333	−	0.152998i	0.818473	−	0.574544i	$-0.194821\pi$
$131$	−2.27287e6	−	3.93672e6i	−0.0883333	−	0.152998i	−0.906807	+	0.421547i	$0.861487\pi$
$132$	−1.74290e7			−0.659574
$133$	−2.91257e7	+	3.44370e6i	−1.07348	+	0.126924i
$134$	2.54109e7			0.912334
$135$	1.22865e7	+	2.12808e7i	0.429792	+	0.744422i
$136$	1.82141e6	−	3.15477e6i	0.0620899	−	0.107543i
$137$	−2.46771e7	+	4.27420e7i	−0.819922	+	1.42015i	0.0858166	+	0.996311i	$0.472650\pi$
$137$	−2.46771e7	+	4.27420e7i	−0.819922	+	1.42015i	−0.905739	+	0.423836i	$0.860683\pi$
$138$	1.72451e7	+	2.98694e7i	0.558585	+	0.967497i
$139$	−4.41231e7			−1.39352			−0.696761	−	0.717303i	$-0.745376\pi$
$139$	−4.41231e7			−1.39352			−0.696761	+	0.717303i	$0.745376\pi$
$140$	7.66185e6	−	1.78275e7i	0.235985	−	0.549089i
$141$	9.46288e6			0.284287
$142$	−1.47459e7	−	2.55406e7i	−0.432177	−	0.748553i
$143$	−8.28026e6	+	1.43418e7i	−0.236793	+	0.410137i
$144$	2.60533e6	−	4.51256e6i	0.0727098	−	0.125937i
$145$	2.06121e7	+	3.57011e7i	0.561479	+	0.972509i
$146$	5.67830e6			0.151002
$147$	5.94567e7	−	1.42592e7i	1.54380	−	0.370240i
$148$	9.65872e6			0.244908
$149$	−1.11368e7	−	1.92894e7i	−0.275808	−	0.477714i	0.694531	−	0.719463i	$-0.255612\pi$
$149$	−1.11368e7	−	1.92894e7i	−0.275808	−	0.477714i	−0.970339	+	0.241750i	$0.922279\pi$
$150$	1.76738e6	−	3.06119e6i	0.0427573	−	0.0740578i
$151$	3.47581e7	−	6.02027e7i	0.821554	−	1.42297i	−0.0829702	−	0.996552i	$-0.526441\pi$
$151$	3.47581e7	−	6.02027e7i	0.821554	−	1.42297i	0.904524	−	0.426422i	$-0.140226\pi$
$152$	−2.40351e7	−	4.16300e7i	−0.555129	−	0.961511i
$153$	−8.14351e6			−0.183820
$154$	−8.44432e6	+	1.96482e7i	−0.186313	+	0.433511i
$155$	−8.21202e7			−1.77129
$156$	1.41563e7	+	2.45194e7i	0.298548	+	0.517100i
$157$	6.14609e6	−	1.06453e7i	0.126751	−	0.219538i	−0.795665	−	0.605737i	$-0.792879\pi$
$157$	6.14609e6	−	1.06453e7i	0.126751	−	0.219538i	0.922416	+	0.386198i	$0.126212\pi$
$158$	−2.15289e7	+	3.72892e7i	−0.434233	+	0.752114i
$159$	−2.93501e7	−	5.08359e7i	−0.579055	−	1.00295i
$160$	5.20047e7			1.00374
$161$	−5.67237e7	+	6.70678e6i	−1.07121	+	0.126655i
$162$	7.37133e6			0.136221
$163$	8.80901e6	+	1.52577e7i	0.159320	+	0.275950i	0.934624	−	0.355638i	$-0.115736\pi$
$163$	8.80901e6	+	1.52577e7i	0.159320	+	0.275950i	−0.775304	+	0.631589i	$0.782403\pi$
$164$	−2.39888e6	+	4.15498e6i	−0.0424673	+	0.0735555i
$165$	3.44694e7	−	5.97028e7i	0.597365	−	1.03467i
$166$	5.15718e6	+	8.93250e6i	0.0875053	+	0.151564i
$167$	1.13558e8			1.88673			0.943367	−	0.331751i	$-0.107639\pi$
$167$	1.13558e8			1.88673			0.943367	+	0.331751i	$0.107639\pi$
$168$	5.99511e7	+	8.03044e7i	0.975471	+	1.30664i
$169$	−3.58467e7			−0.571275
$170$	2.62847e6	+	4.55264e6i	0.0410328	+	0.0710709i
$171$	−5.37305e7	+	9.30639e7i	−0.821740	+	1.42329i
$172$	−9.48008e6	+	1.64200e7i	−0.142057	+	0.246050i
$173$	1.08140e7	+	1.87304e7i	0.158791	+	0.275034i	0.934433	−	0.356139i	$-0.115907\pi$
$173$	1.08140e7	+	1.87304e7i	0.158791	+	0.275034i	−0.775642	+	0.631173i	$0.782574\pi$
$174$	−7.76763e7			−1.11780
$175$	3.50195e6	+	4.69086e6i	0.0493943	+	0.0661636i
$176$	−5.00348e6			−0.0691795
$177$	−4.50786e7	−	7.80784e7i	−0.611032	−	1.05834i
$178$	5.96742e6	−	1.03359e7i	0.0793079	−	0.137365i
$179$	−5.41432e7	+	9.37787e7i	−0.705599	+	1.22213i	0.260875	+	0.965372i	$0.415989\pi$
$179$	−5.41432e7	+	9.37787e7i	−0.705599	+	1.22213i	−0.966475	+	0.256761i	$0.917345\pi$
$180$	−3.55489e7	−	6.15726e7i	−0.454332	−	0.786925i
$181$	6.56731e7			0.823214			0.411607	−	0.911361i	$-0.364968\pi$
$181$	6.56731e7			0.823214			0.411607	+	0.911361i	$0.364968\pi$
$182$	3.45002e7	−	4.07915e6i	0.424200	−	0.0501557i
$183$	5.65798e7			0.682468
$184$	−4.68096e7	−	8.10767e7i	−0.553953	−	0.959475i
$185$	−1.91021e7	+	3.30858e7i	−0.221809	+	0.384185i
$186$	7.73672e7	−	1.34004e8i	0.881580	−	1.52694i
$187$	3.90986e6	+	6.77208e6i	0.0437236	+	0.0757315i
$188$	−9.37121e6			−0.102859
$189$	3.02771e7	−	7.04485e7i	0.326211	−	0.759024i
$190$	6.93699e7			0.733726
$191$	7.23000e6	+	1.25227e7i	0.0750795	+	0.130042i	0.901121	−	0.433568i	$-0.142746\pi$
$191$	7.23000e6	+	1.25227e7i	0.0750795	+	0.130042i	−0.826041	+	0.563610i	$0.809412\pi$
$192$	−5.64408e7	+	9.77583e7i	−0.575491	+	0.996780i
$193$	3.11856e7	−	5.40150e7i	0.312251	−	0.540834i	−0.666599	−	0.745417i	$-0.732250\pi$
$193$	3.11856e7	−	5.40150e7i	0.312251	−	0.540834i	0.978849	+	0.204583i	$0.0655838\pi$
$194$	−2.09815e7	−	3.63410e7i	−0.206314	−	0.357347i
$195$	−1.11988e8			−1.08156
$196$	−5.88808e7	+	1.41211e7i	−0.558570	+	0.133959i
$197$	−1.35525e7			−0.126296			−0.0631478	−	0.998004i	$-0.520114\pi$
$197$	−1.35525e7			−0.126296			−0.0631478	+	0.998004i	$0.520114\pi$
$198$	3.91794e7	+	6.78607e7i	0.358699	+	0.621284i
$199$	1.48623e7	−	2.57423e7i	0.133691	−	0.231559i	−0.791406	−	0.611291i	$-0.790650\pi$
$199$	1.48623e7	−	2.57423e7i	0.133691	−	0.231559i	0.925097	+	0.379732i	$0.123984\pi$
$200$	−4.79732e6	+	8.30920e6i	−0.0424027	+	0.0734437i
$201$	1.27805e8	+	2.21364e8i	1.11010	+	1.92274i
$202$	−7.44575e7			−0.635593
$203$	5.07936e7	−	1.18186e8i	0.426160	−	0.991585i
$204$	1.33690e7			0.110253
$205$	−9.48855e6	−	1.64346e7i	−0.0769239	−	0.133236i
$206$	3.44591e7	−	5.96850e7i	0.274643	−	0.475696i
$207$	−1.04643e8	+	1.81247e8i	−0.819999	+	1.42028i
$208$	4.06396e6	+	7.03899e6i	0.0313132	+	0.0542361i
$209$	1.03188e8			0.781841
$210$	−1.43619e8	+	1.69809e7i	−1.07015	+	0.126530i
$211$	−1.45624e8			−1.06719			−0.533597	−	0.845739i	$-0.679160\pi$
$211$	−1.45624e8			−1.06719			−0.533597	+	0.845739i	$0.679160\pi$
$212$	2.90658e7	+	5.03435e7i	0.209511	+	0.362884i
$213$	1.48330e8	−	2.56914e8i	1.05172	−	1.82163i
$214$	−5.31597e7	+	9.20754e7i	−0.370796	+	0.642237i
$215$	−3.74976e7	−	6.49478e7i	−0.257317	−	0.445687i
$216$	1.25679e8			0.848545
$217$	1.53298e8	+	2.05343e8i	1.01842	+	1.36418i
$218$	−6.31792e7			−0.413025
$219$	2.85591e7	+	4.94659e7i	0.183735	+	0.318238i
$220$	−3.41355e7	+	5.91245e7i	−0.216136	+	0.374359i
$221$	6.35140e6	−	1.10010e7i	0.0395819	−	0.0685579i
$222$	−3.59930e7	−	6.23417e7i	−0.220792	−	0.382422i
$223$	−2.01327e8			−1.21573			−0.607863	−	0.794042i	$-0.707973\pi$
$223$	−2.01327e8			−1.21573			−0.607863	+	0.794042i	$0.707973\pi$
$224$	−9.70800e7	−	1.30039e8i	−0.577114	−	0.773043i
$225$	2.14488e7			0.125535
$226$	4.26636e7	+	7.38955e7i	0.245854	+	0.425832i
$227$	1.53854e8	−	2.66483e8i	0.873010	−	1.51210i	0.0141421	−	0.999900i	$-0.495498\pi$
$227$	1.53854e8	−	2.66483e8i	0.873010	−	1.51210i	0.858868	−	0.512197i	$-0.171168\pi$
$228$	8.82077e7	−	1.52780e8i	0.492872	−	0.853680i
$229$	−9.26335e7	−	1.60446e8i	−0.509734	−	0.882886i	−0.999936	−	0.0112769i	$-0.996410\pi$
$229$	−9.26335e7	−	1.60446e8i	−0.509734	−	0.882886i	0.490202	−	0.871609i	$-0.336923\pi$
$230$	1.35102e8			0.732172
$231$	−2.13634e8	+	2.52592e7i	−1.14032	+	0.134827i
$232$	2.10842e8			1.10854
$233$	1.24551e8	+	2.15729e8i	0.645062	+	1.11728i	0.984287	+	0.176576i	$0.0565020\pi$
$233$	1.24551e8	+	2.15729e8i	0.645062	+	1.11728i	−0.339225	+	0.940705i	$0.610165\pi$
$234$	6.36452e7	−	1.10237e8i	0.324721	−	0.562433i
$235$	1.85335e7	−	3.21010e7i	0.0931580	−	0.161354i
$236$	4.46420e7	+	7.73221e7i	0.221081	+	0.382923i
$237$	−4.33121e8			−2.11344
$238$	6.47724e6	−	1.50712e7i	0.0311437	−	0.0724650i
$239$	3.36485e6			0.0159431			0.00797156	−	0.999968i	$-0.497463\pi$
$239$	3.36485e6			0.0159431			0.00797156	+	0.999968i	$0.497463\pi$
$240$	−1.69176e7	−	2.93022e7i	−0.0789951	−	0.136823i
$241$	−1.09274e8	+	1.89269e8i	−0.502873	+	0.871001i	0.497122	+	0.867681i	$0.334390\pi$
$241$	−1.09274e8	+	1.89269e8i	−0.502873	+	0.871001i	−0.999994	+	0.00332052i	$0.998943\pi$
$242$	−3.42935e7	+	5.93981e7i	−0.155546	+	0.269413i
$243$	1.29470e8	+	2.24249e8i	0.578826	+	1.00256i
$244$	−5.60317e7			−0.246928
$245$	6.80774e7	−	2.29623e8i	0.295748	−	0.997547i
$246$	3.57575e7			0.153142
$247$	−8.38124e7	−	1.45167e8i	−0.353891	−	0.612957i
$248$	−2.10003e8	+	3.63736e8i	−0.874270	+	1.51428i
$249$	−5.18763e7	+	8.98524e7i	−0.212947	+	0.368835i
$250$	7.69233e7	+	1.33235e8i	0.311364	+	0.539298i
$251$	3.10664e8			1.24003			0.620017	−	0.784588i	$-0.287126\pi$
$251$	3.10664e8			1.24003			0.620017	+	0.784588i	$0.287126\pi$
$252$	−8.76020e7	+	2.03832e8i	−0.344836	+	0.802361i
$253$	2.00965e8			0.780185
$254$	9.78319e7	+	1.69450e8i	0.374596	+	0.648818i
$255$	−2.64399e7	+	4.57952e7i	−0.0998547	+	0.172953i
$256$	1.40364e8	−	2.43117e8i	0.522896	−	0.905682i
$257$	−1.48074e8	−	2.56472e8i	−0.544144	−	0.942486i	−0.998660	−	0.0517471i	$-0.983521\pi$
$257$	−1.48074e8	−	2.56472e8i	−0.544144	−	0.942486i	0.454516	−	0.890739i	$-0.349812\pi$
$258$	1.41309e8			0.512273
$259$	1.18391e8	−	1.39980e7i	0.423417	−	0.0500630i
$260$	1.10903e8			0.391325
$261$	−2.35669e8	−	4.08190e8i	−0.820465	−	1.42109i
$262$	1.67755e7	−	2.90560e7i	0.0576263	−	0.0998118i
$263$	−1.29723e8	+	2.24687e8i	−0.439717	+	0.761612i	−0.997667	−	0.0682625i	$-0.978254\pi$
$263$	−1.29723e8	+	2.24687e8i	−0.439717	+	0.761612i	0.557951	+	0.829874i	$0.311588\pi$
$264$	−1.76295e8	−	3.05352e8i	−0.589694	−	1.02138i
$265$	−2.29935e8			−0.759004
$266$	−1.29497e8	−	1.73461e8i	−0.421865	−	0.565087i
$267$	1.20053e8			0.385997
$268$	−1.26567e8	−	2.19220e8i	−0.401650	−	0.695679i
$269$	−7.32285e7	+	1.26835e8i	−0.229376	+	0.397290i	−0.957623	−	0.288024i	$-0.907002\pi$
$269$	−7.32285e7	+	1.26835e8i	−0.229376	+	0.397290i	0.728248	+	0.685314i	$0.240335\pi$
$270$	−9.06835e7	+	1.57068e8i	−0.280385	+	0.485642i
$271$	1.25786e8	+	2.17867e8i	0.383918	+	0.664965i	0.991618	−	0.129201i	$-0.0412413\pi$
$271$	1.25786e8	+	2.17867e8i	0.383918	+	0.664965i	−0.607701	+	0.794166i	$0.707908\pi$
$272$	3.83793e6			0.0115639
$273$	2.09054e8	+	2.80028e8i	0.621856	+	0.832975i
$274$	−3.64272e8			−1.06979
$275$	−1.02980e7	−	1.78367e7i	−0.0298599	−	0.0517189i
$276$	1.71789e8	−	2.97547e8i	0.491828	−	0.851872i
$277$	2.32652e8	−	4.02966e8i	0.657701	−	1.13917i	−0.323508	−	0.946225i	$-0.604862\pi$
$277$	2.32652e8	−	4.02966e8i	0.657701	−	1.13917i	0.981209	−	0.192946i	$-0.0618043\pi$
$278$	−1.62831e8	−	2.82032e8i	−0.454549	−	0.787302i
$279$	9.38924e8			2.58831
$280$	3.89834e8	−	4.60924e7i	1.06127	−	0.125480i
$281$	−5.58490e8			−1.50156			−0.750781	−	0.660551i	$-0.770323\pi$
$281$	−5.58490e8			−1.50156			−0.750781	+	0.660551i	$0.770323\pi$
$282$	3.49216e7	+	6.04861e7i	0.0927305	+	0.160614i
$283$	−3.76398e7	+	6.51940e7i	−0.0987176	+	0.170984i	−0.911154	−	0.412066i	$-0.864807\pi$
$283$	−3.76398e7	+	6.51940e7i	−0.0987176	+	0.170984i	0.812437	+	0.583050i	$0.198141\pi$
$284$	−1.46893e8	+	2.54426e8i	−0.380528	+	0.659094i
$285$	3.48898e8	+	6.04308e8i	0.892773	+	1.54633i
$286$	−1.22229e8			−0.308955
$287$	−2.33823e7	+	5.44058e7i	−0.0583849	+	0.135850i
$288$	−5.94597e8			−1.46673
$289$	2.02170e8	+	3.50169e8i	0.492691	+	0.853366i
$290$	−1.52133e8	+	2.63502e8i	−0.366294	+	0.634440i
$291$	2.11053e8	−	3.65555e8i	0.502073	−	0.869616i
$292$	−2.82825e7	−	4.89867e7i	−0.0664780	−	0.115143i
$293$	−5.90696e8			−1.37192			−0.685958	−	0.727641i	$-0.740617\pi$
$293$	−5.90696e8			−1.37192			−0.685958	+	0.727641i	$0.740617\pi$
$294$	3.10562e8	+	3.27421e8i	0.712742	+	0.751435i
$295$	−3.53155e8			−0.800918
$296$	9.76984e7	+	1.69219e8i	0.218961	+	0.379251i
$297$	−1.34892e8	+	2.33641e8i	−0.298772	+	0.517488i
$298$	8.21978e7	−	1.42371e8i	0.179930	−	0.311648i
$299$	−1.63229e8	−	2.82721e8i	−0.353141	−	0.611658i
$300$	−3.52119e7			−0.0752947
$301$	−9.24041e7	+	2.15005e8i	−0.195303	+	0.454429i
$302$	5.13082e8			1.07192
$303$	−3.74486e8	−	6.48628e8i	−0.773368	−	1.33951i
$304$	2.53225e7	−	4.38598e7i	0.0516950	−	0.0895384i
$305$	1.10814e8	−	1.91936e8i	0.223638	−	0.387353i
$306$	−3.00527e7	−	5.20528e7i	−0.0599595	−	0.103853i
$307$	6.49771e8			1.28167			0.640835	−	0.767679i	$-0.278588\pi$
$307$	6.49771e8			1.28167			0.640835	+	0.767679i	$0.278588\pi$
$308$	2.11564e8	−	2.50145e7i	0.412586	−	0.0487825i
$309$	6.93252e8			1.33671
$310$	−3.03055e8	−	5.24907e8i	−0.577771	−	1.00073i
$311$	−2.24291e7	+	3.88483e7i	−0.0422815	+	0.0732336i	−0.886392	−	0.462936i	$-0.846796\pi$
$311$	−2.24291e7	+	3.88483e7i	−0.0422815	+	0.0732336i	0.844110	+	0.536170i	$0.180129\pi$
$312$	−2.86384e8	+	4.96031e8i	−0.533835	+	0.924629i
$313$	−2.86009e6	−	4.95383e6i	−0.00527200	−	0.00913137i	0.863377	−	0.504559i	$-0.168345\pi$
$313$	−2.86009e6	−	4.95383e6i	−0.00527200	−	0.00913137i	−0.868649	+	0.495427i	$0.835011\pi$
$314$	9.07257e7			0.165378
$315$	−5.24972e8	−	7.03199e8i	−0.946344	−	1.26763i
$316$	4.28926e8			0.764676
$317$	1.39838e8	+	2.42207e8i	0.246558	+	0.427050i	0.962568	−	0.271039i	$-0.0873672\pi$
$317$	1.39838e8	+	2.42207e8i	0.246558	+	0.427050i	−0.716011	+	0.698089i	$0.754034\pi$
$318$	2.16626e8	−	3.75208e8i	0.377761	−	0.654301i
$319$	−2.26299e8	+	3.91961e8i	−0.390314	+	0.676044i
$320$	2.21084e8	+	3.82929e8i	0.377166	+	0.653271i
$321$	−1.06947e9			−1.80469
$322$	−2.52202e8	−	3.37824e8i	−0.420971	−	0.563890i
$323$	−7.91509e7			−0.130691
$324$	−3.67151e7	−	6.35925e7i	−0.0599705	−	0.103872i
$325$	−1.67287e7	+	2.89749e7i	−0.0270314	+	0.0468198i
$326$	−6.50172e7	+	1.12613e8i	−0.103936	+	0.180023i
$327$	−3.17761e8	−	5.50379e8i	−0.502555	−	0.870451i
$328$	−9.70591e7			−0.151872
$329$	−1.14867e8	+	1.35813e7i	−0.177831	+	0.0210260i
$330$	5.08821e8			0.779411
$331$	4.38853e8	+	7.60115e8i	0.665152	+	1.15208i	0.979244	+	0.202684i	$0.0649666\pi$
$331$	4.38853e8	+	7.60115e8i	0.665152	+	1.15208i	−0.314092	+	0.949392i	$0.601700\pi$
$332$	5.13738e7	−	8.89821e7i	0.0770475	−	0.133450i
$333$	2.18405e8	−	3.78288e8i	0.324121	−	0.561394i
$334$	4.19073e8	+	7.25856e8i	0.615428	+	1.06595i
$335$	1.00125e9			1.45507
$336$	−4.16895e7	+	9.70028e7i	−0.0599569	+	0.139507i
$337$	1.05320e8			0.149902			0.0749508	−	0.997187i	$-0.476120\pi$
$337$	1.05320e8			0.149902			0.0749508	+	0.997187i	$0.476120\pi$
$338$	−1.32288e8	−	2.29129e8i	−0.186342	−	0.322755i
$339$	−4.29155e8	+	7.43318e8i	−0.598294	+	1.03628i
$340$	2.61838e7	−	4.53516e7i	0.0361290	−	0.0625772i
$341$	−4.50796e8	−	7.80802e8i	−0.615659	−	1.06635i
$342$	−7.93144e8			−1.07216
$343$	−7.01259e8	+	2.58421e8i	−0.938316	+	0.345779i
$344$	−3.83566e8			−0.508025
$345$	6.79496e8	+	1.17692e9i	0.890882	+	1.54305i
$346$	−7.98157e7	+	1.38245e8i	−0.103591	+	0.179425i
$347$	−1.79512e8	+	3.10925e8i	−0.230644	+	0.399486i	−0.957998	−	0.286776i	$-0.907416\pi$
$347$	−1.79512e8	+	3.10925e8i	−0.230644	+	0.399486i	0.727354	+	0.686262i	$0.240750\pi$
$348$	3.86890e8	+	6.70113e8i	0.492108	+	0.852356i
$349$	−1.99439e8			−0.251142			−0.125571	−	0.992085i	$-0.540076\pi$
$349$	−1.99439e8			−0.251142			−0.125571	+	0.992085i	$0.540076\pi$
$350$	−1.70601e7	+	3.96953e7i	−0.0212688	+	0.0494881i
$351$	4.38254e8			0.540942
$352$	2.85478e8	+	4.94463e8i	0.348878	+	0.604274i
$353$	8.23100e8	−	1.42565e9i	0.995958	−	1.72505i	0.420191	−	0.907436i	$-0.361963\pi$
$353$	8.23100e8	−	1.42565e9i	0.995958	−	1.72505i	0.575767	−	0.817614i	$-0.304703\pi$
$354$	3.32715e8	−	5.76279e8i	0.398621	−	0.690432i
$355$	−5.81022e8	−	1.00636e9i	−0.689276	−	1.19386i
$356$	−1.18890e8			−0.139660
$357$	1.63868e8	−	1.93751e7i	0.190615	−	0.0225375i
$358$	−7.99236e8			−0.920629
$359$	−1.20711e7	−	2.09077e7i	−0.0137694	−	0.0238493i	0.859059	−	0.511877i	$-0.171050\pi$
$359$	−1.20711e7	−	2.09077e7i	−0.0137694	−	0.0238493i	−0.872828	+	0.488028i	$0.837716\pi$
$360$	7.19159e8	−	1.24562e9i	0.812393	−	1.40711i
$361$	−7.52977e7	+	1.30419e8i	−0.0842377	+	0.145904i
$362$	2.42359e8	+	4.19778e8i	0.268522	+	0.465093i
$363$	−6.89919e8			−0.757051
$364$	−2.07029e8	−	2.77315e8i	−0.224997	−	0.301383i
$365$	2.23738e8			0.240832
$366$	2.08801e8	+	3.61654e8i	0.222612	+	0.385576i
$367$	7.76929e8	−	1.34568e9i	0.820447	−	1.42106i	−0.0849034	−	0.996389i	$-0.527058\pi$
$367$	7.76929e8	−	1.34568e9i	0.820447	−	1.42106i	0.905350	−	0.424666i	$-0.139609\pi$
$368$	4.93168e7	−	8.54192e7i	0.0515855	−	0.0893487i
$369$	1.08488e8	+	1.87906e8i	0.112406	+	0.194692i
$370$	−2.81976e8			−0.289405
$371$	4.29232e8	+	5.74955e8i	0.436399	+	0.584555i
$372$	−1.54140e9			−1.55244
$373$	−7.61551e8	−	1.31905e9i	−0.759833	−	1.31607i	−0.942935	−	0.332976i	$-0.891947\pi$
$373$	−7.61551e8	−	1.31905e9i	−0.759833	−	1.31607i	0.183102	−	0.983094i	$-0.441386\pi$
$374$	−2.88578e7	+	4.99832e7i	−0.0285241	+	0.0494053i
$375$	−7.73775e8	+	1.34022e9i	−0.757714	+	1.31240i
$376$	−9.47903e7	−	1.64182e8i	−0.0919616	−	0.159282i
$377$	7.35224e8			0.706684
$378$	5.62036e8	−	6.64528e7i	0.535233	−	0.0632838i
$379$	9.32142e8			0.879518			0.439759	−	0.898116i	$-0.355064\pi$
$379$	9.32142e8			0.879518			0.439759	+	0.898116i	$0.355064\pi$
$380$	−3.45518e8	−	5.98455e8i	−0.323019	−	0.559485i
$381$	−9.84095e8	+	1.70450e9i	−0.911591	+	1.57892i
$382$	−5.33629e7	+	9.24273e7i	−0.0489799	+	0.0848357i
$383$	8.77369e8	+	1.51965e9i	0.797970	+	1.38213i	0.920936	+	0.389714i	$0.127426\pi$
$383$	8.77369e8	+	1.51965e9i	0.797970	+	1.38213i	−0.122965	+	0.992411i	$0.539240\pi$
$384$	8.66217e8			0.780670
$385$	−3.32725e8	+	7.74182e8i	−0.297148	+	0.691402i
$386$	4.60347e8			0.407408
$387$	4.28731e8	+	7.42583e8i	0.376007	+	0.651263i
$388$	−2.09009e8	+	3.62014e8i	−0.181658	+	0.314640i
$389$	4.60335e8	−	7.97323e8i	0.396506	−	0.686769i	−0.596786	−	0.802400i	$-0.703556\pi$
$389$	4.60335e8	−	7.97323e8i	0.396506	−	0.686769i	0.993292	+	0.115632i	$0.0368892\pi$
$390$	−4.13279e8	−	7.15820e8i	−0.352791	−	0.611051i
$391$	−1.54151e8			−0.130415
$392$	−8.42980e8	−	8.88744e8i	−0.706832	−	0.745204i
$393$	3.37491e8			0.280471
$394$	−5.00140e7	−	8.66268e7i	−0.0411960	−	0.0713535i
$395$	−8.48289e8	+	1.46928e9i	−0.692555	+	1.19954i
$396$	3.90290e8	−	6.76002e8i	0.315831	−	0.547035i
$397$	4.67778e8	+	8.10215e8i	0.375209	+	0.649881i	0.990358	−	0.138530i	$-0.0442377\pi$
$397$	4.67778e8	+	8.10215e8i	0.375209	+	0.649881i	−0.615149	+	0.788410i	$0.710904\pi$
$398$	2.19391e8			0.174433
$399$	8.59776e8	−	2.00052e9i	0.677611	−	1.57666i
$400$	−1.01085e7			−0.00789730
$401$	−9.74458e8	−	1.68781e9i	−0.754671	−	1.30713i	−0.945538	−	0.325513i	$-0.894463\pi$
$401$	−9.74458e8	−	1.68781e9i	−0.754671	−	1.30713i	0.190867	−	0.981616i	$-0.438870\pi$
$402$	−9.43297e8	+	1.63384e9i	−0.724198	+	1.25435i
$403$	−7.32299e8	+	1.26838e9i	−0.557341	+	0.965342i
$404$	3.70858e8	+	6.42345e8i	0.279816	+	0.484656i
$405$	2.90447e8			0.217257
$406$	9.42885e8	−	1.11483e8i	0.699226	−	0.0826736i
$407$	−4.19442e8			−0.308384
$408$	1.35228e8	+	2.34221e8i	0.0985723	+	0.170732i
$409$	1.50260e8	−	2.60258e8i	0.108596	−	0.188093i	−0.806606	−	0.591089i	$-0.798698\pi$
$409$	1.50260e8	−	2.60258e8i	0.108596	−	0.188093i	0.915202	+	0.402997i	$0.132031\pi$
$410$	7.00328e7	−	1.21300e8i	0.0501831	−	0.0869197i
$411$	−1.83212e9	−	3.17332e9i	−1.30169	−	2.25459i
$412$	−6.86536e8			−0.483641
$413$	6.59253e8	+	8.83069e8i	0.460497	+	0.616836i
$414$	−1.54469e9			−1.06989
$415$	2.03205e8	+	3.51961e8i	0.139561	+	0.241727i
$416$	4.63747e8	−	8.03233e8i	0.315831	−	0.547034i
$417$	1.63792e9	−	2.83697e9i	1.10616	−	1.91592i
$418$	3.80804e8	+	6.59573e8i	0.255026	+	0.441719i
$419$	−7.41204e8			−0.492253			−0.246127	−	0.969238i	$-0.579158\pi$
$419$	−7.41204e8			−0.492253			−0.246127	+	0.969238i	$0.579158\pi$
$420$	8.61830e8	+	1.15442e9i	0.567609	+	0.760311i
$421$	2.25657e9			1.47388			0.736940	−	0.675958i	$-0.236270\pi$
$421$	2.25657e9			1.47388			0.736940	+	0.675958i	$0.236270\pi$
$422$	−5.37407e8	−	9.30817e8i	−0.348105	−	0.602935i
$423$	−2.11904e8	+	3.67028e8i	−0.136128	+	0.235780i
$424$	−5.88005e8	+	1.01845e9i	−0.374628	+	0.648875i
$425$	7.89912e6	+	1.36817e7i	0.00499134	+	0.00864526i
$426$	2.18957e9			1.37223
$427$	−6.86802e8	+	8.12046e7i	−0.426908	+	0.0504758i
$428$	1.05911e9			0.652964
$429$	−6.14755e8	−	1.06479e9i	−0.375925	−	0.651122i
$430$	2.76761e8	−	4.79364e8i	0.167867	−	0.290754i
$431$	−1.09503e7	+	1.89664e7i	−0.00658802	+	0.0114108i	−0.869301	−	0.494284i	$-0.835430\pi$
$431$	−1.09503e7	+	1.89664e7i	−0.00658802	+	0.0114108i	0.862713	+	0.505695i	$0.168764\pi$
$432$	6.62053e7	+	1.14671e8i	0.0395094	+	0.0684322i
$433$	1.42535e9			0.843749			0.421875	−	0.906654i	$-0.361372\pi$
$433$	1.42535e9			0.843749			0.421875	+	0.906654i	$0.361372\pi$
$434$	−7.46808e8	+	1.73767e9i	−0.438525	+	1.02036i
$435$	−3.06062e9			−1.78278
$436$	3.14683e8	+	5.45047e8i	0.181832	+	0.314943i
$437$	−1.01708e9	+	1.76163e9i	−0.583000	+	1.00979i
$438$	−2.10788e8	+	3.65096e8i	−0.119864	+	0.207610i
$439$	−1.25618e9	−	2.17576e9i	−0.708640	−	1.22740i	−0.965362	−	0.260915i	$-0.915976\pi$
$439$	−1.25618e9	−	2.17576e9i	−0.708640	−	1.22740i	0.256722	−	0.966485i	$-0.417357\pi$
$440$	−1.38113e9			−0.772948
$441$	−7.78366e8	+	2.62540e9i	−0.432164	+	1.45767i
$442$	9.37564e7			0.0516444
$443$	7.35054e8	+	1.27315e9i	0.401704	+	0.695772i	0.993932	−	0.109999i	$-0.0350847\pi$
$443$	7.35054e8	+	1.27315e9i	0.401704	+	0.695772i	−0.592228	+	0.805771i	$0.701751\pi$
$444$	−3.58548e8	+	6.21024e8i	−0.194405	+	0.336719i
$445$	2.35130e8	−	4.07257e8i	0.126487	−	0.219083i
$446$	−7.42975e8	−	1.28687e9i	−0.396554	−	0.686852i
$447$	1.65366e9			0.875731
$448$	5.44810e8	−	1.26766e9i	0.286267	−	0.666085i
$449$	−2.83997e9			−1.48064			−0.740322	−	0.672252i	$-0.765327\pi$
$449$	−2.83997e9			−1.48064			−0.740322	+	0.672252i	$0.765327\pi$
$450$	7.91543e7	+	1.37099e8i	0.0409478	+	0.0709237i
$451$	1.04174e8	−	1.80435e8i	0.0534740	−	0.0926197i
$452$	4.24998e8	−	7.36117e8i	0.216472	−	0.374941i
$453$	2.58056e9	+	4.46966e9i	1.30428	+	2.25907i
$454$	2.27113e9			1.13906
$455$	1.35938e9	−	1.60728e8i	0.676554	−	0.0799929i
$456$	3.56890e9			1.76261
$457$	2.06011e8	+	3.56821e8i	0.100968	+	0.174882i	0.912084	−	0.410004i	$-0.134473\pi$
$457$	2.06011e8	+	3.56821e8i	0.100968	+	0.174882i	−0.811116	+	0.584886i	$0.801139\pi$
$458$	6.83706e8	−	1.18421e9i	0.332537	−	0.575971i
$459$	1.03470e8	−	1.79215e8i	0.0499423	−	0.0865026i
$460$	−6.72914e8	−	1.16552e9i	−0.322335	−	0.558300i
$461$	−4.14604e9			−1.97097			−0.985484	−	0.169766i	$-0.945699\pi$
$461$	−4.14604e9			−1.97097			−0.985484	+	0.169766i	$0.945699\pi$
$462$	−9.49845e8	−	1.27232e9i	−0.448132	−	0.600272i
$463$	−2.49603e9			−1.16873			−0.584367	−	0.811490i	$-0.698657\pi$
$463$	−2.49603e9			−1.16873			−0.584367	+	0.811490i	$0.698657\pi$
$464$	1.11068e8	+	1.92375e8i	0.0516148	+	0.0893995i
$465$	3.04844e9	−	5.28006e9i	1.40602	−	2.43530i
$466$	−9.19282e8	+	1.59224e9i	−0.420822	+	0.728885i
$467$	1.36711e9	+	2.36791e9i	0.621148	+	1.07586i	0.989272	+	0.146084i	$0.0466670\pi$
$467$	1.36711e9	+	2.36791e9i	0.621148	+	1.07586i	−0.368124	+	0.929777i	$0.620000\pi$
$468$	−1.26802e9			−0.571827
$469$	−1.86908e9	−	2.50364e9i	−0.836612	−	1.12064i
$470$	2.73583e8			0.121548
$471$	4.56307e8	+	7.90347e8i	0.201226	+	0.348533i
$472$	−9.03111e8	+	1.56423e9i	−0.395316	+	0.684707i
$473$	4.11684e8	−	7.13058e8i	0.178875	−	0.309821i
$474$	−1.59838e9	−	2.76848e9i	−0.689377	−	1.19404i
$475$	2.08472e8			0.0892524
$476$	−1.62281e8	+	1.91874e7i	−0.0689673	+	0.00815441i
$477$	2.62897e9			1.10910
$478$	1.24176e7	+	2.15079e7i	0.00520044	+	0.00900742i
$479$	−6.08065e8	+	1.05320e9i	−0.252799	+	0.437861i	−0.964295	−	0.264829i	$-0.914685\pi$
$479$	−6.08065e8	+	1.05320e9i	−0.252799	+	0.437861i	0.711496	+	0.702690i	$0.248018\pi$
$480$	−1.93050e9	+	3.34373e9i	−0.796757	+	1.38002i
$481$	3.40682e8	+	5.90079e8i	0.139586	+	0.241770i
$482$	−1.61306e9			−0.656122
$483$	1.67446e9	−	3.89612e9i	0.676176	−	1.57332i
$484$	6.83236e8			0.273913
$485$	−8.26717e8	−	1.43192e9i	−0.329049	−	0.569930i
$486$	−9.55590e8	+	1.65513e9i	−0.377611	+	0.654041i
$487$	1.19069e9	−	2.06233e9i	0.467140	−	0.809110i	−0.532155	−	0.846647i	$-0.678618\pi$
$487$	1.19069e9	−	2.06233e9i	0.467140	−	0.809110i	0.999295	+	0.0375368i	$0.0119511\pi$
$488$	−5.66764e8	−	9.81663e8i	−0.220766	−	0.382378i
$489$	−1.30802e9			−0.505865
$490$	1.71896e9	−	4.12250e8i	0.660056	−	0.158297i
$491$	4.90402e9			1.86968			0.934839	−	0.355072i	$-0.115544\pi$
$491$	4.90402e9			1.86968			0.934839	+	0.355072i	$0.115544\pi$
$492$	−1.78101e8	−	3.08480e8i	−0.0674199	−	0.116775i
$493$	1.73583e8	−	3.00655e8i	0.0652444	−	0.113007i
$494$	6.18600e8	−	1.07145e9i	0.230869	−	0.399877i
$495$	1.54376e9	+	2.67387e9i	0.572085	+	0.990881i
$496$	−4.42503e8			−0.162828
$497$	−1.43179e9	+	3.33148e9i	−0.523158	+	1.21728i
$498$	−7.65774e8			−0.277842
$499$	1.45354e9	+	2.51760e9i	0.523690	+	0.907057i	0.999620	+	0.0275740i	$0.00877819\pi$
$499$	1.45354e9	+	2.51760e9i	0.523690	+	0.907057i	−0.475930	+	0.879483i	$0.657888\pi$
$500$	7.66280e8	−	1.32724e9i	0.274153	−	0.474846i
$501$	−4.21547e9	+	7.30142e9i	−1.49766	+	2.59403i
$502$	1.14647e9	+	1.98575e9i	0.404483	+	0.700585i
$503$	−7.90853e7			−0.0277082			−0.0138541	−	0.999904i	$-0.504410\pi$
$503$	−7.90853e7			−0.0277082			−0.0138541	+	0.999904i	$0.504410\pi$
$504$	−4.45718e9	+	5.26999e8i	−1.55079	+	0.183359i
$505$	−2.93379e9			−1.01370
$506$	7.41636e8	+	1.28455e9i	0.254486	+	0.440783i
$507$	1.33069e9	−	2.30482e9i	0.453471	−	0.785434i
$508$	9.74563e8	−	1.68799e9i	0.329828	−	0.571278i
$509$	1.69924e9	+	2.94316e9i	0.571138	+	0.989241i	0.996449	+	0.0841935i	$0.0268314\pi$
$509$	1.69924e9	+	2.94316e9i	0.571138	+	0.989241i	−0.425311	+	0.905047i	$0.639835\pi$
$510$	−3.90293e8			−0.130285
$511$	−4.17664e8	−	5.59460e8i	−0.138469	−	0.185480i
$512$	5.78577e8			0.190509
$513$	−1.36537e9	−	2.36490e9i	−0.446520	−	0.773395i
$514$	1.09290e9	−	1.89296e9i	0.354986	−	0.614853i
$515$	1.35777e9	−	2.35172e9i	0.438026	−	0.758684i
$516$	−7.03834e8	−	1.21908e9i	−0.225526	−	0.390622i
$517$	4.06957e8			0.129518
$518$	5.26381e8	+	7.05086e8i	0.166397	+	0.222889i
$519$	−1.60574e9			−0.504184
$520$	1.12179e9	+	1.94300e9i	0.349865	+	0.605984i
$521$	1.79657e9	−	3.11176e9i	0.556561	−	0.963992i	−0.441219	−	0.897399i	$-0.645454\pi$
$521$	1.79657e9	−	3.11176e9i	0.556561	−	0.963992i	0.997780	−	0.0665929i	$-0.0212129\pi$
$522$	1.73942e9	−	3.01276e9i	0.535250	−	0.927080i
$523$	−1.09639e9	−	1.89900e9i	−0.335126	−	0.580456i	0.648383	−	0.761315i	$-0.275446\pi$
$523$	−1.09639e9	−	1.89900e9i	−0.335126	−	0.580456i	−0.983509	+	0.180859i	$0.942112\pi$
$524$	−3.34222e8			−0.101479
$525$	−4.31605e8	+	5.10312e7i	−0.130175	+	0.0153914i
$526$	−1.91492e9			−0.573719
$527$	3.45785e8	+	5.98917e8i	0.102913	+	0.178250i
$528$	1.85738e8	−	3.21707e8i	0.0549138	−	0.0951134i
$529$	−2.78397e8	+	4.82198e8i	−0.0817655	+	0.141622i
$530$	−8.48547e8	−	1.46973e9i	−0.247577	−	0.428816i
$531$	4.03781e9			1.17035
$532$	−8.51448e8	+	1.98114e9i	−0.245170	+	0.570460i
$533$	−3.38453e8			−0.0968173
$534$	4.43042e8	+	7.67371e8i	0.125907	+	0.218077i
$535$	−2.09461e9	+	3.62798e9i	−0.591379	+	1.02430i
$536$	2.56046e9	−	4.43485e9i	0.718193	−	1.24395i
$537$	−4.01978e9	−	6.96246e9i	−1.12019	−	1.94023i
$538$	−1.08097e9			−0.299277
$539$	2.55697e9	−	6.13224e8i	0.703340	−	0.168678i
$540$	1.80671e9			0.493753
$541$	2.39445e8	+	4.14730e8i	0.0650152	+	0.112610i	0.896701	−	0.442637i	$-0.145957\pi$
$541$	2.39445e8	+	4.14730e8i	0.0650152	+	0.112610i	−0.831686	+	0.555247i	$0.812624\pi$
$542$	−9.28394e8	+	1.60803e9i	−0.250458	+	0.433806i
$543$	−2.43790e9	+	4.22257e9i	−0.653456	+	1.13182i
$544$	−2.18977e8	−	3.79279e8i	−0.0583179	−	0.101010i
$545$	−2.48940e9			−0.658730
$546$	−1.01843e9	+	2.36967e9i	−0.267767	+	0.623037i
$547$	−1.52985e9			−0.399664			−0.199832	−	0.979830i	$-0.564040\pi$
$547$	−1.52985e9			−0.399664			−0.199832	+	0.979830i	$0.564040\pi$
$548$	1.81437e9	+	3.14258e9i	0.470970	+	0.815744i
$549$	−1.26700e9	+	2.19451e9i	−0.326793	+	0.566023i
$550$	7.60072e7	−	1.31648e8i	0.0194798	−	0.0337401i
$551$	−2.29058e9	−	3.96741e9i	−0.583332	−	1.01036i
$552$	6.95062e9			1.75888
$553$	5.25751e9	−	6.21626e8i	1.32203	−	0.156312i
$554$	3.43431e9			0.858134
$555$	−1.41821e9	−	2.45640e9i	−0.352139	−	0.609922i
$556$	−1.62206e9	+	2.80949e9i	−0.400226	+	0.693211i
$557$	−2.45884e8	+	4.25884e8i	−0.0602889	+	0.104423i	−0.894595	−	0.446879i	$-0.852536\pi$
$557$	−2.45884e8	+	4.25884e8i	−0.0602889	+	0.104423i	0.834306	+	0.551302i	$0.185869\pi$
$558$	3.46499e9	+	6.00154e9i	0.844272	+	1.46232i
$559$	−1.33753e9			−0.323863
$560$	2.47412e8	+	3.31408e8i	0.0595337	+	0.0797453i
$561$	−5.80564e8			−0.138829
$562$	−2.06104e9	−	3.56983e9i	−0.489790	−	0.848341i
$563$	5.62247e8	−	9.73840e8i	0.132785	−	0.229990i	−0.791964	−	0.610567i	$-0.790942\pi$
$563$	5.62247e8	−	9.73840e8i	0.132785	−	0.229990i	0.924749	+	0.380578i	$0.124275\pi$
$564$	3.47876e8	−	6.02538e8i	0.0816483	−	0.141419i
$565$	1.68104e9	+	2.91165e9i	0.392111	+	0.679156i
$566$	−5.55621e8			−0.128801
$567$	−5.42194e8	−	7.26267e8i	−0.124915	−	0.167323i
$568$	−5.94331e9			−1.36085
$569$	−1.53913e9	−	2.66585e9i	−0.350253	−	0.606656i	0.636041	−	0.771656i	$-0.280571\pi$
$569$	−1.53913e9	−	2.66585e9i	−0.350253	−	0.606656i	−0.986294	+	0.164999i	$0.947238\pi$
$570$	−2.57513e9	+	4.46026e9i	−0.582422	+	1.00878i
$571$	−4.59821e8	+	7.96433e8i	−0.103362	+	0.179029i	−0.913068	−	0.407807i	$-0.866293\pi$
$571$	−4.59821e8	+	7.96433e8i	−0.103362	+	0.179029i	0.809706	+	0.586836i	$0.199627\pi$
$572$	6.08801e8	+	1.05447e9i	0.136016	+	0.235586i
$573$	−1.07356e9			−0.238388
$574$	−4.34047e8	+	5.13200e7i	−0.0957956	+	0.0113265i
$575$	4.06010e8			0.0890633
$576$	−2.52777e9	−	4.37823e9i	−0.551137	−	0.954597i
$577$	−2.43160e9	+	4.21166e9i	−0.526959	+	0.912720i	0.472547	+	0.881305i	$0.343335\pi$
$577$	−2.43160e9	+	4.21166e9i	−0.526959	+	0.912720i	−0.999506	+	0.0314146i	$0.989999\pi$
$578$	−1.49217e9	+	2.58452e9i	−0.321419	+	0.556714i
$579$	2.31533e9	+	4.01026e9i	0.495721	+	0.858614i
$580$	3.03097e9			0.645036
$581$	5.00750e8	−	1.16514e9i	0.105927	−	0.246469i
$582$	3.11547e9			0.655078
$583$	−1.26222e9	−	2.18623e9i	−0.263812	−	0.456936i
$584$	5.72158e8	−	9.91007e8i	0.118870	−	0.205888i
$585$	2.50777e9	−	4.34358e9i	0.517895	−	0.897020i
$586$	−2.17990e9	−	3.77569e9i	−0.447501	−	0.775095i
$587$	1.16578e9			0.237894			0.118947	−	0.992901i	$-0.462048\pi$
$587$	1.16578e9			0.237894			0.118947	+	0.992901i	$0.462048\pi$
$588$	1.27782e9	−	4.31004e9i	0.259208	−	0.874300i
$589$	9.12588e9			1.84023
$590$	−1.30328e9	−	2.25734e9i	−0.261249	−	0.452496i
$591$	5.03093e8	−	8.71382e8i	0.100252	−	0.173641i
$592$	−1.02931e8	+	1.78282e8i	−0.0203902	+	0.0353168i
$593$	1.67754e9	+	2.90559e9i	0.330356	+	0.572193i	0.982582	−	0.185832i	$-0.0594980\pi$
$593$	1.67754e9	+	2.90559e9i	0.330356	+	0.572193i	−0.652226	+	0.758025i	$0.726165\pi$
$594$	−1.99122e9			−0.389822
$595$	2.55218e8	−	5.93839e8i	0.0496709	−	0.115574i
$596$	−1.63765e9			−0.316853
$597$	1.10343e9	+	1.91120e9i	0.212244	+	0.367617i
$598$	1.20476e9	−	2.08670e9i	0.230380	−	0.399030i
$599$	1.16072e9	−	2.01043e9i	0.220666	−	0.382205i	−0.734344	−	0.678777i	$-0.762510\pi$
$599$	1.16072e9	−	2.01043e9i	0.220666	−	0.382205i	0.955010	+	0.296572i	$0.0958436\pi$
$600$	−3.56170e8	−	6.16904e8i	−0.0673174	−	0.116597i
$601$	4.38113e9			0.823238			0.411619	−	0.911356i	$-0.364964\pi$
$601$	4.38113e9			0.823238			0.411619	+	0.911356i	$0.364964\pi$
$602$	−1.71530e9	+	2.02810e8i	−0.320445	+	0.0378881i
$603$	−1.14478e10			−2.12624
$604$	−2.55556e9	−	4.42636e9i	−0.471908	−	0.817368i
$605$	−1.35124e9	+	2.34042e9i	−0.248078	+	0.429684i
$606$	2.76399e9	−	4.78737e9i	0.504525	−	0.873863i
$607$	−2.16431e9	−	3.74869e9i	−0.392788	−	0.680329i	0.600028	−	0.799979i	$-0.295156\pi$
$607$	−2.16431e9	−	3.74869e9i	−0.392788	−	0.680329i	−0.992816	+	0.119650i	$0.961823\pi$
$608$	−5.77919e9			−1.04281
$609$	5.71343e9	+	7.65313e9i	1.02503	+	1.37303i
$610$	1.63579e9			0.291792
$611$	−3.30542e8	−	5.72515e8i	−0.0586249	−	0.101541i
$612$	−2.99373e8	+	5.18529e8i	−0.0527938	+	0.0914415i
$613$	−9.51623e8	+	1.64826e9i	−0.166860	+	0.289011i	−0.937314	−	0.348485i	$-0.886696\pi$
$613$	−9.51623e8	+	1.64826e9i	−0.166860	+	0.289011i	0.770454	+	0.637496i	$0.220030\pi$
$614$	2.39791e9	+	4.15329e9i	0.418064	+	0.724108i
$615$	1.40893e9			0.244245
$616$	2.57823e9	+	3.45354e9i	0.444416	+	0.595294i
$617$	−8.11496e9			−1.39088			−0.695438	−	0.718586i	$-0.744790\pi$
$617$	−8.11496e9			−1.39088			−0.695438	+	0.718586i	$0.744790\pi$
$618$	2.55836e9	+	4.43122e9i	0.436016	+	0.755202i
$619$	2.30171e9	−	3.98668e9i	0.390062	−	0.675608i	−0.602395	−	0.798198i	$-0.705787\pi$
$619$	2.30171e9	−	3.98668e9i	0.390062	−	0.675608i	0.992457	+	0.122590i	$0.0391201\pi$
$620$	−3.01891e9	+	5.22891e9i	−0.508721	+	0.881131i
$621$	−2.65914e9	−	4.60576e9i	−0.445574	−	0.771757i
$622$	−3.31087e8			−0.0551666
$623$	−1.45728e9	+	1.72303e8i	−0.241455	+	0.0285486i
$624$	−6.03445e8			−0.0994241
$625$	3.28293e9	+	5.68620e9i	0.537875	+	0.931627i
$626$	2.11097e7	−	3.65631e7i	0.00343931	−	0.00595706i
$627$	−3.83053e9	+	6.63467e9i	−0.620615	+	1.07494i
$628$	−4.51887e8	−	7.82691e8i	−0.0728066	−	0.126105i
$629$	3.21734e8			0.0515490
$630$	2.55745e9	−	5.95066e9i	0.407489	−	0.948141i
$631$	3.73470e9			0.591770			0.295885	−	0.955224i	$-0.404385\pi$
$631$	3.73470e9			0.591770			0.295885	+	0.955224i	$0.404385\pi$
$632$	4.33861e9	+	7.51469e9i	0.683660	+	1.18413i
$633$	5.40580e9	−	9.36313e9i	0.847124	−	1.46726i
$634$	−1.03211e9	+	1.78767e9i	−0.160848	+	0.278596i
$635$	3.85480e9	+	6.67671e9i	0.597439	+	1.03479i
$636$	−4.31590e9			−0.665229
$637$	−2.93954e9	−	3.09912e9i	−0.450600	−	0.475062i
$638$	−3.34051e9			−0.509262
$639$	6.64313e9	+	1.15062e10i	1.00721	+	1.74454i
$640$	1.69653e9	−	2.93847e9i	0.255818	−	0.443090i
$641$	3.64484e9	−	6.31304e9i	0.546607	−	0.946750i	−0.451897	−	0.892070i	$-0.649253\pi$
$641$	3.64484e9	−	6.31304e9i	0.546607	−	0.946750i	0.998504	−	0.0546804i	$-0.0174140\pi$
$642$	−3.94676e9	−	6.83599e9i	−0.588665	−	1.01960i
$643$	4.01680e9			0.595856			0.297928	−	0.954588i	$-0.403704\pi$
$643$	4.01680e9			0.595856			0.297928	+	0.954588i	$0.403704\pi$
$644$	−1.65824e9	+	3.85838e9i	−0.244651	+	0.569252i
$645$	5.56791e9			0.817020
$646$	−2.92097e8	−	5.05927e8i	−0.0426298	−	0.0738370i
$647$	−1.77143e9	+	3.06820e9i	−0.257133	+	0.445368i	−0.965473	−	0.260504i	$-0.916111\pi$
$647$	−1.77143e9	+	3.06820e9i	−0.257133	+	0.445368i	0.708339	+	0.705872i	$0.249445\pi$
$648$	7.42751e8	−	1.28648e9i	0.107234	−	0.185734i
$649$	−1.93863e9	−	3.35781e9i	−0.278381	−	0.482169i
$650$	−2.46941e8			−0.0352692
$651$	−1.88936e10	+	2.23390e9i	−2.68399	+	0.317344i
$652$	1.29535e9			0.183030
$653$	−5.59905e9	−	9.69783e9i	−0.786897	−	1.36295i	−0.927859	−	0.372931i	$-0.878353\pi$
$653$	−5.59905e9	−	9.69783e9i	−0.786897	−	1.36295i	0.140962	−	0.990015i	$-0.454980\pi$
$654$	2.34532e9	−	4.06222e9i	0.327854	−	0.567860i
$655$	6.60993e8	−	1.14487e9i	0.0919078	−	0.159189i
$656$	−5.11288e7	−	8.85577e7i	−0.00707135	−	0.0122479i
$657$	−2.55812e9			−0.351918
$658$	−5.10713e8	−	6.84099e8i	−0.0698853	−	0.0936113i
$659$	8.68249e9			1.18180			0.590902	−	0.806743i	$-0.298772\pi$
$659$	8.68249e9			1.18180			0.590902	+	0.806743i	$0.298772\pi$
$660$	−2.53434e9	−	4.38960e9i	−0.343132	−	0.594322i
$661$	−5.17499e9	+	8.96335e9i	−0.696955	+	1.20716i	0.272562	+	0.962138i	$0.412129\pi$
$661$	−5.17499e9	+	8.96335e9i	−0.696955	+	1.20716i	−0.969517	+	0.245023i	$0.921204\pi$
$662$	−3.23907e9	+	5.61023e9i	−0.433928	+	0.751585i
$663$	4.71550e8	+	8.16748e8i	0.0628392	+	0.108841i
$664$	2.07860e9			0.275538
$665$	−5.10246e9	−	6.83474e9i	−0.672828	−	0.901252i
$666$	3.22399e9			0.422896
$667$	−4.46103e9	−	7.72673e9i	−0.582096	−	1.00822i
$668$	4.17464e9	−	7.23069e9i	0.541878	−	0.938560i
$669$	7.47362e9	−	1.29447e10i	0.965027	−	1.67148i
$670$	3.69499e9	+	6.39991e9i	0.474626	+	0.822076i
$671$	2.43325e9			0.310926
$672$	1.19648e10	−	1.41467e9i	1.52095	−	0.179830i
$673$	1.94227e9			0.245617			0.122808	−	0.992430i	$-0.460810\pi$
$673$	1.94227e9			0.245617			0.122808	+	0.992430i	$0.460810\pi$
$674$	3.88671e8	+	6.73198e8i	0.0488959	+	0.0846902i
$675$	−2.72524e8	+	4.72025e8i	−0.0341068	+	0.0590747i
$676$	−1.31780e9	+	2.28250e9i	−0.164073	+	0.284182i
$677$	−2.69675e9	−	4.67091e9i	−0.334027	−	0.578551i	0.649271	−	0.760557i	$-0.275074\pi$
$677$	−2.69675e9	−	4.67091e9i	−0.334027	−	0.578551i	−0.983297	+	0.182006i	$0.941741\pi$
$678$	−6.33498e9			−0.780623
$679$	−2.03725e9	+	4.74026e9i	−0.249747	+	0.581109i
$680$	1.05940e9			0.129205
$681$	1.14227e10	+	1.97847e10i	1.38597	+	2.40057i
$682$	3.32722e9	−	5.76292e9i	0.401640	−	0.695660i
$683$	−5.57579e9	+	9.65754e9i	−0.669628	+	1.15983i	0.308380	+	0.951263i	$0.400213\pi$
$683$	−5.57579e9	+	9.65754e9i	−0.669628	+	1.15983i	−0.978008	+	0.208567i	$0.933120\pi$
$684$	3.95049e9	+	6.84246e9i	0.472014	+	0.817553i
$685$	−1.43531e10			−1.70620
$686$	−4.23972e9	−	3.52873e9i	−0.501422	−	0.417334i
$687$	1.37549e10			1.61848
$688$	−2.02055e8	−	3.49970e8i	−0.0236543	−	0.0409705i
$689$	−2.05042e9	+	3.55143e9i	−0.238823	+	0.413653i
$690$	−5.01520e9	+	8.68659e9i	−0.581188	+	1.00665i
$691$	2.14163e9	+	3.70942e9i	0.246929	+	0.427693i	0.962672	−	0.270670i	$-0.0872453\pi$
$691$	2.14163e9	+	3.70942e9i	0.246929	+	0.427693i	−0.715743	+	0.698363i	$0.753912\pi$
$692$	1.59019e9			0.182422
$693$	3.80423e9	−	8.85164e9i	0.434210	−	1.01032i
$694$	−2.64988e9			−0.300932
$695$	−6.41591e9	−	1.11127e10i	−0.724956	−	1.25566i
$696$	−7.82683e9	+	1.35565e10i	−0.879941	+	1.52410i
$697$	−7.99072e7	+	1.38403e8i	−0.00893863	+	0.0154822i
$698$	−7.36005e8	−	1.27480e9i	−0.0819194	−	0.141888i
$699$	−1.84942e10			−2.04817
$700$	4.27424e8	−	5.05369e7i	0.0470995	−	0.00556885i
$701$	−9.26658e8			−0.101603			−0.0508015	−	0.998709i	$-0.516178\pi$
$701$	−9.26658e8			−0.101603			−0.0508015	+	0.998709i	$0.516178\pi$
$702$	1.61732e9	+	2.80129e9i	0.176448	+	0.305617i
$703$	2.12278e9	−	3.67677e9i	0.230442	−	0.399138i
$704$	−2.42727e9	+	4.20416e9i	−0.262189	+	0.454124i
$705$	1.37599e9	+	2.38329e9i	0.147895	+	0.256162i
$706$	1.21502e10			1.29947
$707$	5.47668e9	+	7.33600e9i	0.582840	+	0.780713i
$708$	−6.62874e9			−0.701964
$709$	2.79426e9	+	4.83980e9i	0.294446	+	0.509995i	0.974856	−	0.222837i	$-0.0715317\pi$
$709$	2.79426e9	+	4.83980e9i	0.294446	+	0.509995i	−0.680410	+	0.732831i	$0.738198\pi$
$710$	4.28839e9	−	7.42770e9i	0.449666	−	0.778843i
$711$	9.69895e9	−	1.67991e10i	1.01200	−	1.75284i
$712$	−1.20258e9	−	2.08293e9i	−0.124863	−	0.216269i
$713$	1.77731e10			1.83633
$714$	7.28582e8	+	9.75934e8i	0.0749091	+	0.100341i
$715$	−4.81611e9			−0.492749
$716$	3.98084e9	+	6.89501e9i	0.405302	+	0.702004i
$717$	−1.24909e8	+	2.16349e8i	−0.0126554	+	0.0219199i
$718$	8.90938e7	−	1.54315e8i	0.00898281	−	0.0155587i
$719$	−6.60046e9	−	1.14323e10i	−0.662252	−	1.14705i	−0.980023	−	0.198886i	$-0.936268\pi$
$719$	−6.60046e9	−	1.14323e10i	−0.662252	−	1.14705i	0.317771	−	0.948168i	$-0.397066\pi$
$720$	1.51536e9			0.151304
$721$	−8.41514e9	+	9.94971e8i	−0.836157	+	0.0988637i
$722$	−1.11151e9			−0.109909
$723$	−8.11290e9	−	1.40520e10i	−0.798347	−	1.38278i
$724$	2.41428e9	−	4.18166e9i	0.236431	−	0.409510i
$725$	−4.57192e8	+	7.91880e8i	−0.0445570	+	0.0771749i
$726$	−2.54607e9	−	4.40992e9i	−0.246940	−	0.427713i
$727$	−7.32749e9			−0.707269			−0.353635	−	0.935384i	$-0.615054\pi$
$727$	−7.32749e9			−0.707269			−0.353635	+	0.935384i	$0.615054\pi$
$728$	2.76439e9	−	6.43217e9i	0.265546	−	0.617871i
$729$	−1.70404e10			−1.62905
$730$	8.25679e8	+	1.43012e9i	0.0785563	+	0.136064i
$731$	−3.15784e8	+	5.46953e8i	−0.0299005	+	0.0517892i
$732$	2.07999e9	−	3.60265e9i	0.196008	−	0.339495i
$733$	6.96170e9	+	1.20580e10i	0.652907	+	1.13087i	0.982414	+	0.186715i	$0.0597841\pi$
$733$	6.96170e9	+	1.20580e10i	0.652907	+	1.13087i	−0.329507	+	0.944153i	$0.606883\pi$
$734$	1.14687e10			1.07048
$735$	1.22368e10	+	1.29011e10i	1.13675	+	1.19846i
$736$	−1.12553e10			−1.04060
$737$	5.49632e9	+	9.51991e9i	0.505750	+	0.875985i
$738$	−8.00723e8	+	1.38689e9i	−0.0733305	+	0.127012i
$739$	−1.47710e9	+	2.55841e9i	−0.134634	+	0.233193i	−0.925458	−	0.378851i	$-0.876319\pi$
$739$	−1.47710e9	+	2.55841e9i	−0.134634	+	0.233193i	0.790824	+	0.612044i	$0.209653\pi$
$740$	1.40447e9	+	2.43261e9i	0.127409	+	0.220679i
$741$	1.24450e10			1.12365
$742$	−2.09105e9	+	4.86543e9i	−0.187910	+	0.437227i
$743$	−5.39743e9			−0.482754			−0.241377	−	0.970431i	$-0.577599\pi$
$743$	−5.39743e9			−0.482754			−0.241377	+	0.970431i	$0.577599\pi$
$744$	−1.55914e10	−	2.70050e10i	−1.38797	−	2.40403i
$745$	3.23878e9	−	5.60973e9i	0.286969	−	0.497044i
$746$	5.62083e9	−	9.73557e9i	0.495695	−	0.858569i
$747$	−2.32335e9	−	4.02416e9i	−0.203935	−	0.353226i
$748$	5.74940e8			0.0502304
$749$	1.29819e10	−	1.53493e9i	1.12889	−	0.133476i
$750$	−1.14221e10			−0.988625
$751$	−5.61607e8	−	9.72733e8i	−0.0483830	−	0.0838019i	0.840820	−	0.541315i	$-0.182073\pi$
$751$	−5.61607e8	−	9.72733e8i	−0.0483830	−	0.0838019i	−0.889203	+	0.457513i	$0.848740\pi$
$752$	9.98674e7	−	1.72975e8i	0.00856370	−	0.0148328i
$753$	−1.15324e10	+	1.99747e10i	−0.984322	+	1.70490i
$754$	2.71326e9	+	4.69950e9i	0.230511	+	0.399257i
$755$	2.02166e10			1.70960
$756$	−3.37268e9	−	4.51770e9i	−0.283889	−	0.380269i
$757$	9.72000e9			0.814387			0.407193	−	0.913342i	$-0.366507\pi$
$757$	9.72000e9			0.814387			0.407193	+	0.913342i	$0.366507\pi$
$758$	3.43996e9	+	5.95819e9i	0.286887	+	0.496904i
$759$	−7.46015e9	+	1.29214e10i	−0.619301	+	1.07266i
$760$	6.98986e9	−	1.21068e10i	0.577592	−	1.00042i
$761$	−9.55634e9	−	1.65521e10i	−0.786041	−	1.36146i	−0.928375	−	0.371644i	$-0.878794\pi$
$761$	−9.55634e9	−	1.65521e10i	−0.786041	−	1.36146i	0.142334	−	0.989819i	$-0.454539\pi$
$762$	−1.45268e10			−1.18940
$763$	4.64711e9	+	6.22480e9i	0.378745	+	0.507328i
$764$	1.06316e9			0.0862526
$765$	−1.18414e9	−	2.05100e9i	−0.0956289	−	0.165634i
$766$	−6.47566e9	+	1.12162e10i	−0.520575	+	0.901662i
$767$	−3.14922e9	+	5.45461e9i	−0.252011	+	0.436496i
$768$	1.04211e10	+	1.80499e10i	0.830136	+	1.43784i
$769$	−1.69816e10			−1.34660			−0.673298	−	0.739371i	$-0.735123\pi$
$769$	−1.69816e10			−1.34660			−0.673298	+	0.739371i	$0.735123\pi$
$770$	−6.17640e9	+	7.30272e8i	−0.487549	+	0.0576458i
$771$	2.19871e10			1.72774
$772$	−2.29290e9	−	3.97142e9i	−0.179359	−	0.310660i
$773$	−8.18943e9	+	1.41845e10i	−0.637713	+	1.10455i	0.348220	+	0.937413i	$0.386786\pi$
$773$	−8.18943e9	+	1.41845e10i	−0.637713	+	1.10455i	−0.985933	+	0.167139i	$0.946547\pi$
$774$	−3.16436e9	+	5.48083e9i	−0.245297	+	0.424867i
$775$	−9.10746e8	−	1.57746e9i	−0.0702816	−	0.121731i
$776$	−8.45655e9			−0.649646
$777$	−3.49484e9	+	8.13175e9i	−0.267272	+	0.621886i
$778$	6.79524e9			0.517341
$779$	1.05445e9	+	1.82636e9i	0.0799178	+	0.138422i
$780$	−4.11692e9	+	7.13072e9i	−0.310629	+	0.538024i
$781$	6.37901e9	−	1.10488e10i	0.479153	−	0.829918i
$782$	−5.68874e8	−	9.85319e8i	−0.0425395	−	0.0736806i
$783$	1.19774e10			0.891655
$784$	3.66834e8	−	1.23732e9i	0.0271871	−	0.0917011i
$785$	3.57480e9			0.263759
$786$	1.24547e9	+	2.15722e9i	0.0914860	+	0.158458i
$787$	6.77582e9	−	1.17361e10i	0.495508	−	0.858245i	−0.504479	−	0.863424i	$-0.668315\pi$
$787$	6.77582e9	−	1.17361e10i	0.495508	−	0.858245i	0.999987	+	0.00517934i	$0.00164864\pi$
$788$	−4.98220e8	+	8.62942e8i	−0.0362726	+	0.0628260i
$789$	−9.63111e9	−	1.66816e10i	−0.698082	−	1.20911i
$790$	−1.25220e10			−0.903609
$791$	4.14253e9	−	9.63880e9i	0.297610	−	0.692477i
$792$	1.57912e10			1.12948
$793$	−1.97635e9	−	3.42314e9i	−0.140737	−	0.243763i
$794$	−3.45256e9	+	5.98001e9i	−0.244776	+	0.423965i
$795$	8.53557e9	−	1.47840e10i	0.602487	−	1.04354i
$796$	−1.09274e9	−	1.89269e9i	−0.0767931	−	0.133010i
$797$	−5.21891e7			−0.00365153			−0.00182577	−	0.999998i	$-0.500581\pi$
$797$	−5.21891e7			−0.00365153			−0.00182577	+	0.999998i	$0.500581\pi$
$798$	1.59601e10	−	1.88706e9i	1.11180	−	0.131454i
$799$	−3.12157e8			−0.0216501
$800$	5.76753e8	+	9.98965e8i	0.0398267	+	0.0689819i
$801$	−2.68837e9	+	4.65639e9i	−0.184831	+	0.320136i
$802$	7.19225e9	−	1.24573e10i	0.492328	−	0.852736i
$803$	1.22820e9	+	2.12731e9i	0.0837078	+	0.144986i
$804$	1.87935e10			1.27530
$805$	−9.93731e9	−	1.33110e10i	−0.671403	−	0.899344i
$806$	−1.08099e10			−0.727189
$807$	−5.43674e9	−	9.41670e9i	−0.364151	−	0.630727i
$808$	−7.50250e9	+	1.29947e10i	−0.500341	+	0.866616i
$809$	−6.80229e9	+	1.17819e10i	−0.451685	+	0.782341i	−0.998491	−	0.0549185i	$-0.982510\pi$
$809$	−6.80229e9	+	1.17819e10i	−0.451685	+	0.782341i	0.546806	+	0.837259i	$0.315843\pi$
$810$	1.07186e9	+	1.85652e9i	0.0708665	+	0.122744i
$811$	−3.10614e9			−0.204479			−0.102239	−	0.994760i	$-0.532601\pi$
$811$	−3.10614e9			−0.204479			−0.102239	+	0.994760i	$0.532601\pi$
$812$	−5.65809e9	−	7.57900e9i	−0.370871	−	0.496782i
$813$	−1.86775e10			−1.21900
$814$	−1.54790e9	−	2.68104e9i	−0.100591	−	0.174228i
$815$	−2.56183e9	+	4.43721e9i	−0.165767	+	0.287117i
$816$	−1.42471e8	+	2.46766e8i	−0.00917930	+	0.0158990i
$817$	4.16705e9	+	7.21754e9i	0.267332	+	0.463033i
$818$	2.21807e9			0.141690
$819$	−1.55426e10	+	1.83769e9i	−0.988619	+	0.116890i
$820$	−1.39528e9			−0.0883715
$821$	−5.28866e9	−	9.16022e9i	−0.333537	−	0.577704i	0.649665	−	0.760220i	$-0.274909\pi$
$821$	−5.28866e9	−	9.16022e9i	−0.333537	−	0.577704i	−0.983203	+	0.182517i	$0.941576\pi$
$822$	1.35224e10	−	2.34215e10i	0.849186	−	1.47083i
$823$	−5.14054e9	+	8.90368e9i	−0.321447	+	0.556762i	−0.980787	−	0.195083i	$-0.937503\pi$
$823$	−5.14054e9	+	8.90368e9i	−0.321447	+	0.556762i	0.659340	+	0.751845i	$0.270836\pi$
$824$	−6.94435e9	−	1.20280e10i	−0.432401	−	0.748940i
$825$	1.52912e9			0.0948096
$826$	−3.21162e9	+	7.47277e9i	−0.198287	+	0.461372i
$827$	1.76194e9			0.108323			0.0541617	−	0.998532i	$-0.482751\pi$
$827$	1.76194e9			0.108323			0.0541617	+	0.998532i	$0.482751\pi$
$828$	7.69379e9	+	1.33260e10i	0.471015	+	0.815821i
$829$	9.25086e9	−	1.60230e10i	0.563951	−	0.976792i	−0.433196	−	0.901300i	$-0.642614\pi$
$829$	9.25086e9	−	1.60230e10i	0.563951	−	0.976792i	0.997146	−	0.0754917i	$-0.0240526\pi$
$830$	−1.49981e9	+	2.59774e9i	−0.0910462	+	0.157697i
$831$	1.72729e10	+	2.99176e10i	1.04415	+	1.80852i
$832$	7.88599e9			0.474706
$833$	−1.96133e9	+	4.70376e8i	−0.117569	+	0.0281960i
$834$	2.41783e10			1.44326
$835$	1.65124e10	+	2.86004e10i	0.981541	+	1.70008i
$836$	3.79342e9	−	6.57040e9i	0.224548	−	0.388929i
$837$	−1.19298e10	+	2.06630e10i	−0.703222	+	1.21802i
$838$	−2.73533e9	−	4.73772e9i	−0.160567	−	0.278109i
$839$	−1.91428e10			−1.11902			−0.559512	−	0.828822i	$-0.689012\pi$
$839$	−1.91428e10			−1.11902			−0.559512	+	0.828822i	$0.689012\pi$
$840$	−1.15077e10	+	2.67761e10i	−0.669903	+	1.55873i
$841$	2.84370e9			0.164854
$842$	8.32762e9	+	1.44239e10i	0.480760	+	0.832701i
$843$	2.07321e10	−	3.59091e10i	1.19192	−	2.06447i
$844$	−5.35344e9	+	9.27243e9i	−0.306503	+	0.530878i
$845$	−5.21244e9	−	9.02822e9i	−0.297196	−	0.514759i
$846$	−3.12802e9			−0.177613
$847$	8.37469e9	−	9.90188e8i	0.473562	−	0.0559920i
$848$	−1.23900e9			−0.0697726
$849$	−2.79451e9	−	4.84023e9i	−0.156721	−	0.271449i
$850$	−5.83015e7	+	1.00981e8i	−0.00325622	+	0.00563994i
$851$	4.13423e9	−	7.16070e9i	0.229954	−	0.398292i
$852$	−1.09058e10	−	1.88895e10i	−0.604116	−	1.04636i
$853$	7.28376e9			0.401822			0.200911	−	0.979609i	$-0.435610\pi$
$853$	7.28376e9			0.401822			0.200911	+	0.979609i	$0.435610\pi$
$854$	−3.05362e9	−	4.09032e9i	−0.167769	−	0.224726i
$855$	−3.12517e10			−1.70998
$856$	1.07130e10	+	1.85554e10i	0.583784	+	1.01114i
$857$	−1.38663e10	+	2.40172e10i	−0.752539	+	1.30344i	0.194049	+	0.980992i	$0.437838\pi$
$857$	−1.38663e10	+	2.40172e10i	−0.752539	+	1.30344i	−0.946588	+	0.322444i	$0.895496\pi$
$858$	4.53737e9	−	7.85895e9i	0.245244	−	0.424775i
$859$	−9.92987e8	−	1.71990e9i	−0.0534524	−	0.0925823i	0.838061	−	0.545576i	$-0.183689\pi$
$859$	−9.92987e8	−	1.71990e9i	−0.0534524	−	0.0925823i	−0.891514	+	0.452994i	$0.850356\pi$
$860$	−5.51397e9			−0.295611
$861$	−2.63012e9	−	3.52304e9i	−0.140431	−	0.188108i
$862$	−1.61643e8			−0.00859570
$863$	4.84554e9	+	8.39271e9i	0.256628	+	0.444493i	0.965336	−	0.261009i	$-0.0840552\pi$
$863$	4.84554e9	+	8.39271e9i	0.256628	+	0.444493i	−0.708708	+	0.705501i	$0.750722\pi$
$864$	7.55482e9	−	1.30853e10i	0.398498	−	0.690219i
$865$	−3.14492e9	+	5.44716e9i	−0.165216	+	0.286163i
$866$	5.26008e9	+	9.11073e9i	0.275220	+	0.476695i
$867$	−3.00196e10			−1.56437
$868$	1.87106e10	−	2.21226e9i	0.971108	−	0.114820i
$869$	−1.86266e10			−0.962865
$870$	−1.12949e10	−	1.95633e10i	−0.581518	−	1.00722i
$871$	8.92853e9	−	1.54647e10i	0.457843	−	0.793007i
$872$	−6.36608e9	+	1.10264e10i	−0.325135	+	0.563151i
$873$	9.45230e9	+	1.63719e10i	0.480826	+	0.832814i
$874$	−1.50136e10			−0.760668
$875$	7.46907e9	−	1.73790e10i	0.376911	−	0.876993i
$876$	4.19958e9			0.211077
$877$	−4.03240e9	−	6.98431e9i	−0.201867	−	0.349643i	0.747263	−	0.664528i	$-0.231367\pi$
$877$	−4.03240e9	−	6.98431e9i	−0.201867	−	0.349643i	−0.949130	+	0.314885i	$0.898034\pi$
$878$	9.27156e9	−	1.60588e10i	0.462298	−	0.800723i
$879$	2.19277e10	−	3.79798e10i	1.08901	−	1.88622i
$880$	−7.27553e8	−	1.26016e9i	−0.0359894	−	0.0623355i
$881$	3.72296e10			1.83431			0.917156	−	0.398529i	$-0.130479\pi$
$881$	3.72296e10			1.83431			0.917156	+	0.398529i	$0.130479\pi$
$882$	−1.96538e10	+	4.71347e9i	−0.964512	+	0.231313i
$883$	1.71532e10			0.838458			0.419229	−	0.907880i	$-0.362300\pi$
$883$	1.71532e10			0.838458			0.419229	+	0.907880i	$0.362300\pi$
$884$	−4.66982e8	−	8.08837e8i	−0.0227362	−	0.0393802i
$885$	1.31097e10	−	2.27067e10i	0.635758	−	1.10116i
$886$	−5.42526e9	+	9.39683e9i	−0.262061	+	0.453903i
$887$	1.09654e10	+	1.89927e10i	0.527586	+	0.913806i	0.999483	+	0.0321523i	$0.0102362\pi$
$887$	1.09654e10	+	1.89927e10i	0.527586	+	0.913806i	−0.471897	+	0.881654i	$0.656431\pi$
$888$	−1.45069e10			−0.695233
$889$	9.49925e9	−	2.21028e10i	0.453454	−	1.05509i
$890$	3.47088e9			0.165034
$891$	1.59440e9	+	2.76158e9i	0.0755137	+	0.130793i
$892$	−7.40122e9	+	1.28193e10i	−0.349162	+	0.604766i
$893$	−2.05960e9	+	3.56733e9i	−0.0967837	+	0.167634i
$894$	6.10265e9	+	1.05701e10i	0.285652	+	0.494764i
$895$	−3.14917e10			−1.46830
$896$	−1.05147e10	+	1.24321e9i	−0.488336	+	0.0577389i
$897$	2.42374e10			1.12127
$898$	−1.04806e10	−	1.81529e10i	−0.482967	−	0.836523i
$899$	−2.00136e10	+	3.46646e10i	−0.918686	+	1.59121i
$900$	7.88504e8	−	1.36573e9i	0.0360542	−	0.0624476i
$901$	9.68190e8	+	1.67695e9i	0.0440985	+	0.0763808i
$902$	1.53777e9			0.0697700
$903$	−1.03939e10	−	1.39226e10i	−0.469756	−	0.629237i
$904$	1.71955e10			0.774150
$905$	9.54949e9	+	1.65402e10i	0.428263	+	0.741773i
$906$	−1.90465e10	+	3.29895e10i	−0.850876	+	1.47376i
$907$	1.25298e9	−	2.17022e9i	0.0557593	−	0.0965779i	−0.836798	−	0.547511i	$-0.815575\pi$
$907$	1.25298e9	−	2.17022e9i	0.0557593	−	0.0965779i	0.892558	+	0.450933i	$0.148909\pi$
$908$	−1.13120e10	−	1.95930e10i	−0.501464	−	0.868562i
$909$	3.35437e10			1.48128
$910$	6.04401e9	+	8.09594e9i	0.265877	+	0.356141i
$911$	−8.68527e9			−0.380600			−0.190300	−	0.981726i	$-0.560946\pi$
$911$	−8.68527e9			−0.380600			−0.190300	+	0.981726i	$0.560946\pi$
$912$	1.88003e9	+	3.25630e9i	0.0820696	+	0.142149i
$913$	−2.23097e9	+	3.86416e9i	−0.0970167	+	0.168038i
$914$	−1.52052e9	+	2.63361e9i	−0.0658688	+	0.114088i
$915$	8.22723e9	+	1.42500e10i	0.355042	+	0.614951i
$916$	−1.36216e10			−0.585591
$917$	−4.09669e9	+	4.84375e8i	−0.175445	+	0.0207438i
$918$	1.52737e9			0.0651621
$919$	−3.34164e9	−	5.78789e9i	−0.142022	−	0.245989i	0.786236	−	0.617926i	$-0.212027\pi$
$919$	−3.34164e9	−	5.78789e9i	−0.142022	−	0.245989i	−0.928258	+	0.371937i	$0.878694\pi$
$920$	1.36131e10	−	2.35786e10i	0.576369	−	0.998300i
$921$	−2.41206e10	+	4.17782e10i	−1.01737	+	1.76214i
$922$	−1.53005e10	−	2.65012e10i	−0.642904	−	1.11354i
$923$	−2.07248e10			−0.867531
$924$	−6.24528e9	+	1.45315e10i	−0.260436	+	0.605979i
$925$	−8.47400e8			−0.0352040
$926$	−9.21129e9	−	1.59544e10i	−0.381226	−	0.660302i
$927$	−1.55241e10	+	2.68885e10i	−0.640069	+	1.10863i
$928$	1.26741e10	−	2.19522e10i	0.520596	−	0.901698i
$929$	6.08895e9	+	1.05464e10i	0.249165	+	0.431567i	0.963294	−	0.268447i	$-0.0865105\pi$
$929$	6.08895e9	+	1.05464e10i	0.249165	+	0.431567i	−0.714129	+	0.700014i	$0.753177\pi$
$930$	4.49997e10			1.83451
$931$	−7.56533e9	+	2.55176e10i	−0.307259	+	1.03637i
$932$	1.83151e10			0.741059
$933$	−1.66521e9	−	2.88423e9i	−0.0671249	−	0.116264i
$934$	−1.00903e10	+	1.74770e10i	−0.405221	+	0.701863i
$935$	−1.13706e9	+	1.96945e9i	−0.0454929	+	0.0787960i
$936$	−1.28261e10	−	2.22154e10i	−0.511243	−	0.885500i
$937$	4.28141e10			1.70019			0.850097	−	0.526626i	$-0.176543\pi$
$937$	4.28141e10			1.70019			0.850097	+	0.526626i	$0.176543\pi$
$938$	9.10543e9	−	2.11864e10i	0.360239	−	0.838201i
$939$	4.24687e8			0.0167394
$940$	−1.36266e9	−	2.36020e9i	−0.0535107	−	0.0926833i
$941$	1.97417e10	−	3.41937e10i	0.772363	−	1.33777i	−0.163902	−	0.986477i	$-0.552408\pi$
$941$	1.97417e10	−	3.41937e10i	0.772363	−	1.33777i	0.936265	−	0.351295i	$-0.114259\pi$
$942$	−3.36789e9	+	5.83336e9i	−0.131274	+	0.227374i
$943$	2.05359e9	+	3.55692e9i	0.0797485	+	0.138129i
$944$	−1.90297e9			−0.0736256
$945$	2.21455e10	−	2.61839e9i	0.853639	−	0.100931i
$946$	6.07709e9			0.233387
$947$	−5.55513e9	−	9.62176e9i	−0.212554	−	0.368154i	0.739959	−	0.672652i	$-0.234845\pi$
$947$	−5.55513e9	−	9.62176e9i	−0.212554	−	0.368154i	−0.952513	+	0.304498i	$0.901511\pi$
$948$	−1.59225e10	+	2.75785e10i	−0.606989	+	1.05134i
$949$	1.99516e9	−	3.45572e9i	0.0757786	−	0.131252i
$950$	7.69341e8	+	1.33254e9i	0.0291129	+	0.0504251i
$951$	−2.07641e10			−0.782856
$952$	−1.97764e9	−	2.64905e9i	−0.0742879	−	0.0995085i
$953$	−3.33302e10			−1.24742			−0.623711	−	0.781655i	$-0.714376\pi$
$953$	−3.33302e10			−1.24742			−0.623711	+	0.781655i	$0.714376\pi$
$954$	9.70190e9	+	1.68042e10i	0.361774	+	0.626611i
$955$	−2.10262e9	+	3.64184e9i	−0.0781176	+	0.135304i
$956$	1.23699e8	−	2.14253e8i	0.00457893	−	0.00793095i
$957$	−1.68012e10	−	2.91005e10i	−0.619652	−	1.07327i
$958$	−8.97597e9			−0.329839
$959$	2.67938e10	+	3.58903e10i	0.981001	+	1.31405i
$960$	−3.28281e10			−1.19756
$961$	−2.61117e10	−	4.52268e10i	−0.949082	−	1.64386i
$962$	−2.51450e9	+	4.35524e9i	−0.0910622	+	0.157724i
$963$	2.39488e10	−	4.14806e10i	0.864157	−	1.49676i
$964$	8.03431e9	+	1.39158e10i	0.288854	+	0.500311i
$965$	1.81387e10			0.649772
$966$	3.10831e10	−	3.67514e9i	1.10944	−	0.131176i
$967$	−5.24781e10			−1.86632			−0.933158	−	0.359466i	$-0.882959\pi$
$967$	−5.24781e10			−1.86632			−0.933158	+	0.359466i	$0.882959\pi$
$968$	6.91097e9	+	1.19702e10i	0.244892	+	0.424166i
$969$	2.93822e9	−	5.08914e9i	0.103741	−	0.179685i
$970$	6.10180e9	−	1.05686e10i	0.214663	−	0.371807i
$971$	−1.74484e10	−	3.02216e10i	−0.611630	−	1.05937i	−0.990966	−	0.134115i	$-0.957181\pi$
$971$	−1.74484e10	−	3.02216e10i	−0.611630	−	1.05937i	0.379336	−	0.925259i	$-0.376153\pi$
$972$	1.90384e10			0.664965
$973$	−1.58105e10	+	3.67878e10i	−0.550238	+	1.28029i
$974$	1.75764e10			0.609499
$975$	−1.24199e9	−	2.15119e9i	−0.0429144	−	0.0743299i
$976$	5.97120e8	−	1.03424e9i	0.0205583	−	0.0356080i
$977$	2.82223e10	−	4.88824e10i	0.968191	−	1.67696i	0.267404	−	0.963585i	$-0.413834\pi$
$977$	2.82223e10	−	4.88824e10i	0.968191	−	1.67696i	0.700787	−	0.713371i	$-0.252832\pi$
$978$	−4.82710e9	−	8.36079e9i	−0.165006	−	0.285799i
$979$	5.16295e9			0.175857
$980$	−1.21183e10	−	1.27762e10i	−0.411292	−	0.433620i
$981$	2.84627e10			0.962575
$982$	1.80977e10	+	3.13461e10i	0.609864	+	1.05632i
$983$	4.20622e7	−	7.28538e7i	0.00141239	−	0.00244633i	−0.865318	−	0.501223i	$-0.832884\pi$
$983$	4.20622e7	−	7.28538e7i	0.00141239	−	0.00244633i	0.866731	+	0.498776i	$0.166217\pi$
$984$	3.60300e9	−	6.24058e9i	0.120554	−	0.208806i
$985$	−1.97066e9	−	3.41329e9i	−0.0657031	−	0.113801i
$986$	2.56235e9			0.0851274
$987$	3.39081e9	−	7.88970e9i	0.112252	−	0.261186i
$988$	−1.23245e10			−0.406556
$989$	8.11554e9	+	1.40565e10i	0.266766	+	0.462052i
$990$	−1.13941e10	+	1.97352e10i	−0.373213	+	0.646425i
$991$	−6.49617e9	+	1.12517e10i	−0.212031	+	0.367249i	−0.952350	−	0.305007i	$-0.901341\pi$
$991$	−6.49617e9	+	1.12517e10i	−0.212031	+	0.367249i	0.740319	+	0.672256i	$0.234674\pi$
$992$	2.52474e10	+	4.37298e10i	0.821157	+	1.42229i
$993$	−6.51639e10			−2.11195
$994$	−2.65785e10	+	3.14253e9i	−0.858376	+	0.101491i
$995$	8.64449e9			0.278201
$996$	3.81417e9	+	6.60634e9i	0.122319	+	0.211862i
$997$	1.11340e8	−	1.92846e8i	0.00355808	−	0.00616278i	−0.864241	−	0.503078i	$-0.832201\pi$
$997$	1.11340e8	−	1.92846e8i	0.00355808	−	0.00616278i	0.867799	+	0.496915i	$0.165534\pi$
$998$	−1.07282e10	+	1.85818e10i	−0.341641	+	0.591740i
$999$	5.55000e9	+	9.61288e9i	0.176122	+	0.305052i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.8.c.a.4.3	yes	8
3.2	odd	2		63.8.e.b.46.2		8
4.3	odd	2		112.8.i.c.81.4		8
7.2	even	3	inner	7.8.c.a.2.3	✓	8
7.3	odd	6		49.8.a.e.1.2		4
7.4	even	3		49.8.a.f.1.2		4
7.5	odd	6		49.8.c.g.30.3		8
7.6	odd	2		49.8.c.g.18.3		8
21.2	odd	6		63.8.e.b.37.2		8
21.11	odd	6		441.8.a.s.1.3		4
21.17	even	6		441.8.a.t.1.3		4
28.23	odd	6		112.8.i.c.65.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.8.c.a.2.3	✓	8	7.2	even	3	inner
7.8.c.a.4.3	yes	8	1.1	even	1	trivial
49.8.a.e.1.2		4	7.3	odd	6
49.8.a.f.1.2		4	7.4	even	3
49.8.c.g.18.3		8	7.6	odd	2
49.8.c.g.30.3		8	7.5	odd	6
63.8.e.b.37.2		8	21.2	odd	6
63.8.e.b.46.2		8	3.2	odd	2
112.8.i.c.65.4		8	28.23	odd	6
112.8.i.c.81.4		8	4.3	odd	2
441.8.a.s.1.3		4	21.11	odd	6
441.8.a.t.1.3		4	21.17	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	7.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.69038 + 6.39193i) q^{2} +(-37.1217 + 64.2967i) q^{3} +(36.7621 - 63.6739i) q^{4} +(145.409 + 251.857i) q^{5} -547.974 q^{6} +(358.327 - 833.753i) q^{7} +1487.40 q^{8} +(-1662.54 - 2879.61i) q^{9} +(-1073.23 + 1858.89i) q^{10} +(-1596.44 + 2765.12i) q^{11} +(2729.35 + 4727.37i) q^{12} +5186.70 q^{13} +(6651.66 - 786.465i) q^{14} -21591.4 q^{15} +(783.535 + 1357.12i) q^{16} +(1224.56 - 2120.99i) q^{17} +(12270.9 - 21253.7i) q^{18} +(-16159.1 - 27988.4i) q^{19} +21382.2 q^{20} +(40305.9 + 53989.6i) q^{21} -23565.9 q^{22} +(-31470.7 - 54508.9i) q^{23} +(-55215.0 + 95635.2i) q^{24} +(-3225.30 + 5586.38i) q^{25} +(19140.9 + 33153.0i) q^{26} +84495.7 q^{27} +(-39915.4 - 53466.7i) q^{28} +141752. q^{29} +(-79680.5 - 138011. i) q^{30} +(-141188. + 244545. i) q^{31} +(89410.7 - 154864. i) q^{32} +(-118525. - 205292. i) q^{33} +18076.3 q^{34} +(262090. - 30988.5i) q^{35} -244475. q^{36} +(65683.8 + 113768. i) q^{37} +(119267. - 206576. i) q^{38} +(-192539. + 333488. i) q^{39} +(216283. + 374612. i) q^{40} -65254.0 q^{41} +(-196354. + 456875. i) q^{42} -257876. q^{43} +(117377. + 203303. i) q^{44} +(483499. - 837445. i) q^{45} +(232278. - 402317. i) q^{46} +(-63728.7 - 110381. i) q^{47} -116345. q^{48} +(-566746. - 597513. i) q^{49} -47610.4 q^{50} +(90915.2 + 157470. i) q^{51} +(190674. - 330257. i) q^{52} +(-395323. + 684719. i) q^{53} +(311821. + 540090. i) q^{54} -928551. q^{55} +(532978. - 1.24013e6i) q^{56} +2.39942e6 q^{57} +(523119. + 906068. i) q^{58} +(-607173. + 1.05165e6i) q^{59} +(-793746. + 1.37481e6i) q^{60} +(-381042. - 659985. i) q^{61} -2.08415e6 q^{62} +(-2.99662e6 + 354308. i) q^{63} +1.52042e6 q^{64} +(754195. + 1.30630e6i) q^{65} +(874808. - 1.51521e6i) q^{66} +(1.72143e6 - 2.98160e6i) q^{67} +(-90034.6 - 155944. i) q^{68} +4.67299e6 q^{69} +(1.16529e6 + 1.56090e6i) q^{70} -3.99576e6 q^{71} +(-2.47287e6 - 4.28315e6i) q^{72} +(384669. - 666266. i) q^{73} +(-484797. + 839693. i) q^{74} +(-239457. - 414752. i) q^{75} -2.37617e6 q^{76} +(1.73338e6 + 2.32186e6i) q^{77} -2.84217e6 q^{78} +(2.91690e6 + 5.05222e6i) q^{79} +(-227867. + 394677. i) q^{80} +(499361. - 864918. i) q^{81} +(-240812. - 417099. i) q^{82} +1.39747e6 q^{83} +(4.91946e6 - 581657. i) q^{84} +712248. q^{85} +(-951662. - 1.64833e6i) q^{86} +(-5.26207e6 + 9.11418e6i) q^{87} +(-2.37455e6 + 4.11285e6i) q^{88} +(-808509. - 1.40038e6i) q^{89} +7.13719e6 q^{90} +(1.85854e6 - 4.32443e6i) q^{91} -4.62772e6 q^{92} +(-1.04823e7 - 1.81558e7i) q^{93} +(470367. - 814699. i) q^{94} +(4.69937e6 - 8.13955e6i) q^{95} +(6.63816e6 + 1.14976e7i) q^{96} -5.68544e6 q^{97} +(1.72775e6 - 5.82765e6i) q^{98} +1.06166e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{2} - 28 q^{3} - 348 q^{4} - 252 q^{5} + 2044 q^{6} + 672 q^{7} - 1968 q^{8} - 2008 q^{9} - 4774 q^{10} + 3972 q^{11} + 5404 q^{12} - 2352 q^{13} + 47502 q^{14} - 33112 q^{15} - 57264 q^{16} - 56364 q^{17}+ \cdots + 30427952 q^{99}+O(q^{100}) \) 8 * q + 6 * q^2 - 28 * q^3 - 348 * q^4 - 252 * q^5 + 2044 * q^6 + 672 * q^7 - 1968 * q^8 - 2008 * q^9 - 4774 * q^10 + 3972 * q^11 + 5404 * q^12 - 2352 * q^13 + 47502 * q^14 - 33112 * q^15 - 57264 * q^16 - 56364 * q^17 + 35908 * q^18 - 41748 * q^19 + 324744 * q^20 + 188524 * q^21 - 305908 * q^22 - 131748 * q^23 - 389592 * q^24 + 68016 * q^25 - 113652 * q^26 + 378056 * q^27 + 681548 * q^28 + 68112 * q^29 - 605378 * q^30 - 401212 * q^31 + 453408 * q^32 - 24052 * q^33 + 164220 * q^34 + 40404 * q^35 - 720176 * q^36 + 5396 * q^37 - 31794 * q^38 - 364840 * q^39 + 443688 * q^40 + 820848 * q^41 - 240856 * q^42 + 93088 * q^43 + 1465836 * q^44 + 1209656 * q^45 - 1379202 * q^46 - 1470084 * q^47 - 4037600 * q^48 - 2793784 * q^49 + 2791056 * q^50 + 1724796 * q^51 + 5269768 * q^52 + 642372 * q^53 + 4567318 * q^54 - 6126680 * q^55 - 6195168 * q^56 + 6718136 * q^57 + 1972220 * q^58 - 752220 * q^59 - 2123324 * q^60 - 1325772 * q^61 - 6032628 * q^62 - 6412616 * q^63 - 1731712 * q^64 + 4868808 * q^65 + 6013294 * q^66 + 290916 * q^67 - 2453556 * q^68 + 9830520 * q^69 + 11665990 * q^70 + 6755520 * q^71 - 4557744 * q^72 - 6706588 * q^73 - 3616878 * q^74 - 7223888 * q^75 + 5846008 * q^76 - 5310564 * q^77 - 32576264 * q^78 - 3946244 * q^79 - 10695888 * q^80 + 11731292 * q^81 + 17563252 * q^82 + 19084128 * q^83 + 38088092 * q^84 + 14012136 * q^85 - 23237832 * q^86 - 17836840 * q^87 + 8043336 * q^88 - 16165212 * q^89 + 6831496 * q^90 - 2414720 * q^91 - 38885256 * q^92 - 12552852 * q^93 - 5720442 * q^94 + 3268452 * q^95 + 8448608 * q^96 + 3066224 * q^97 + 60255006 * q^98 + 30427952 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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