LMFDB - Embedded newform 207.4.m.a.4.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,4,Mod(4,207)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([22, 12])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("207.4"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	207.m (of order $33$, degree $20$, 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:	$12.2133953712$
Analytic rank:	$0$
Dimension:	$1400$
Relative dimension:	$70$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			4.9
Character	$\chi$	$=$	207.4
Dual form			207.4.m.a.52.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.69115 + 3.77920i) q^{2} +(4.57480 - 2.46398i) q^{3} +(-4.42348 - 12.7808i) q^{4} +(-10.4806 + 5.40314i) q^{5} +(-2.99960 + 23.9200i) q^{6} +(4.10886 - 3.23125i) q^{7} +(24.5932 + 7.22121i) q^{8} +(14.8576 - 22.5445i) q^{9} +(7.78546 - 54.1490i) q^{10} +(-55.5691 + 5.30621i) q^{11} +(-51.7282 - 47.5702i) q^{12} +(53.0858 + 41.7472i) q^{13} +(1.15393 + 24.2240i) q^{14} +(-34.6335 + 50.5424i) q^{15} +(-8.42568 + 6.62603i) q^{16} +(-39.8585 - 45.9992i) q^{17} +(45.2160 + 116.820i) q^{18} +(78.4939 - 90.5868i) q^{19} +(115.417 + 110.050i) q^{20} +(10.8355 - 24.9065i) q^{21} +(129.492 - 224.287i) q^{22} +(66.9836 - 87.6367i) q^{23} +(130.302 - 27.5617i) q^{24} +(8.14250 - 11.4345i) q^{25} +(-300.633 + 88.2738i) q^{26} +(12.4211 - 139.745i) q^{27} +(-59.4734 - 38.2212i) q^{28} +(97.3973 - 281.411i) q^{29} +(-97.8055 - 266.904i) q^{30} +(107.120 - 102.138i) q^{31} +(7.39048 + 155.145i) q^{32} +(-241.143 + 161.196i) q^{33} +(281.105 - 26.8423i) q^{34} +(-25.6046 + 56.0663i) q^{35} +(-353.859 - 90.1665i) q^{36} +(-29.8116 + 19.1588i) q^{37} +(131.106 + 540.427i) q^{38} +(345.721 + 60.1821i) q^{39} +(-296.769 + 57.1976i) q^{40} +(274.154 - 141.336i) q^{41} +(64.9666 + 107.977i) q^{42} +(-232.004 - 221.215i) q^{43} +(313.627 + 686.746i) q^{44} +(-33.9056 + 316.558i) q^{45} +(150.933 + 488.988i) q^{46} +(172.805 + 299.307i) q^{47} +(-22.2194 + 51.0735i) q^{48} +(-74.4235 + 306.778i) q^{49} +(21.3007 + 61.5442i) q^{50} +(-295.686 - 112.226i) q^{51} +(298.738 - 863.147i) q^{52} +(14.9783 + 104.176i) q^{53} +(494.698 + 423.018i) q^{54} +(553.729 - 355.860i) q^{55} +(124.384 - 49.7957i) q^{56} +(135.889 - 607.824i) q^{57} +(801.397 + 1125.40i) q^{58} +(120.579 + 94.8244i) q^{59} +(799.173 + 219.071i) q^{60} +(-25.7000 - 105.937i) q^{61} +(97.7255 + 679.696i) q^{62} +(-11.7991 - 140.641i) q^{63} +(-678.352 - 435.951i) q^{64} +(-781.938 - 150.706i) q^{65} +(39.7606 - 1345.13i) q^{66} +(-675.145 - 64.4685i) q^{67} +(-411.593 + 712.900i) q^{68} +(90.5010 - 565.967i) q^{69} +(-142.980 - 247.648i) q^{70} +(-356.267 - 780.115i) q^{71} +(528.193 - 447.151i) q^{72} +(-101.175 + 116.762i) q^{73} +(7.82291 - 164.223i) q^{74} +(9.07575 - 72.3737i) q^{75} +(-1504.99 - 602.506i) q^{76} +(-211.180 + 201.360i) q^{77} +(-1157.83 + 1144.59i) q^{78} +(-28.2719 + 11.3184i) q^{79} +(52.5051 - 114.970i) q^{80} +(-287.506 - 669.911i) q^{81} +(-203.654 + 1416.44i) q^{82} +(112.184 + 57.8350i) q^{83} +(-366.255 - 28.3129i) q^{84} +(666.282 + 266.739i) q^{85} +(1460.37 - 281.464i) q^{86} +(-247.820 - 1527.38i) q^{87} +(-1404.94 - 270.780i) q^{88} +(1388.95 - 407.833i) q^{89} +(-1105.09 - 980.041i) q^{90} +353.018 q^{91} +(-1416.37 - 468.446i) q^{92} +(238.383 - 731.203i) q^{93} +(-1596.19 - 152.417i) q^{94} +(-333.212 + 1373.52i) q^{95} +(416.085 + 691.548i) q^{96} +(27.6461 - 580.363i) q^{97} +(-959.089 - 1106.85i) q^{98} +(-705.996 + 1331.61i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1400 q - 9 q^{2} - 14 q^{3} + 263 q^{4} + 19 q^{5} - 35 q^{6} - 9 q^{7} - 74 q^{8} - 78 q^{9} - 68 q^{10} + 79 q^{11} + 54 q^{12} - 9 q^{13} + 159 q^{14} - 868 q^{15} + 1031 q^{16} - 308 q^{17} - 87 q^{18}+ \cdots + 7484 q^{99}+O(q^{100}) $ 1400 * q - 9 * q^2 - 14 * q^3 + 263 * q^4 + 19 * q^5 - 35 * q^6 - 9 * q^7 - 74 * q^8 - 78 * q^9 - 68 * q^10 + 79 * q^11 + 54 * q^12 - 9 * q^13 + 159 * q^14 - 868 * q^15 + 1031 * q^16 - 308 * q^17 - 87 * q^18 - 36 * q^19 + 119 * q^20 - 660 * q^21 - 52 * q^22 - 116 * q^23 + 2420 * q^24 + 1397 * q^25 + 432 * q^26 + 274 * q^27 - 324 * q^28 - 45 * q^29 + 768 * q^30 - 45 * q^31 + 111 * q^32 - 1664 * q^33 + 403 * q^34 - 536 * q^35 - 121 * q^36 - 180 * q^37 - 117 * q^38 - 46 * q^39 - 473 * q^40 - 333 * q^41 - 332 * q^42 - 9 * q^43 - 1908 * q^44 + 1762 * q^45 + 484 * q^46 + 216 * q^47 + 1072 * q^48 + 4615 * q^49 - 105 * q^50 + 1298 * q^51 - 708 * q^52 - 1380 * q^53 + 4116 * q^54 - 1328 * q^55 - 3971 * q^56 + 2154 * q^57 - 338 * q^58 + 1917 * q^59 + 154 * q^60 + 27 * q^61 - 3854 * q^62 - 4850 * q^63 - 5854 * q^64 + 3363 * q^65 - 2017 * q^66 + 603 * q^67 - 18454 * q^68 - 4653 * q^69 + 542 * q^70 - 5296 * q^71 - 8044 * q^72 - 36 * q^73 + 3243 * q^74 + 5140 * q^75 - 1029 * q^76 - 1661 * q^77 + 14687 * q^78 - 9 * q^79 + 10312 * q^80 - 294 * q^81 - 770 * q^82 - 2735 * q^83 + 2298 * q^84 + 241 * q^85 + 10507 * q^86 - 10268 * q^87 + 2183 * q^88 - 2980 * q^89 + 33928 * q^90 - 1452 * q^91 - 1973 * q^92 - 11406 * q^93 + 2034 * q^94 - 3339 * q^95 - 4446 * q^96 - 5193 * q^97 + 14820 * q^98 + 7484 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.69115	+	3.77920i	−0.951467	+	1.33615i	−0.00967448	+	0.999953i	$0.503080\pi$
$2$	−2.69115	+	3.77920i	−0.951467	+	1.33615i	−0.941792	+	0.336195i	$0.890860\pi$
$3$	4.57480	−	2.46398i	0.880420	−	0.474194i
$3$	4.57480	−	2.46398i	0.880420	−	0.474194i
$4$	−4.42348	−	12.7808i	−0.552935	−	1.59760i
$5$	−10.4806	+	5.40314i	−0.937416	+	0.483271i	−0.858045	−	0.513574i	$-0.828321\pi$
$5$	−10.4806	+	5.40314i	−0.937416	+	0.483271i	−0.0793702	+	0.996845i	$0.525291\pi$
$6$	−2.99960	+	23.9200i	−0.204097	+	1.62755i
$7$	4.10886	−	3.23125i	0.221858	−	0.174471i	−0.501044	−	0.865422i	$-0.667050\pi$
$7$	4.10886	−	3.23125i	0.221858	−	0.174471i	0.722902	+	0.690951i	$0.242808\pi$
$8$	24.5932	+	7.22121i	1.08688	+	0.319135i
$9$	14.8576	−	22.5445i	0.550280	−	0.834980i
$10$	7.78546	−	54.1490i	0.246198	−	1.71234i
$11$	−55.5691	+	5.30621i	−1.52316	+	0.145444i	−0.822792	−	0.568342i	$-0.807585\pi$
$11$	−55.5691	+	5.30621i	−1.52316	+	0.145444i	−0.700364	+	0.713786i	$0.746979\pi$
$12$	−51.7282	−	47.5702i	−1.24439	−	1.14436i
$13$	53.0858	+	41.7472i	1.13257	+	0.890660i	0.995004	−	0.0998334i	$-0.0318310\pi$
$13$	53.0858	+	41.7472i	1.13257	+	0.890660i	0.137562	+	0.990493i	$0.456073\pi$
$14$	1.15393	+	24.2240i	0.0220287	+	0.462438i
$15$	−34.6335	+	50.5424i	−0.596155	+	0.869999i
$16$	−8.42568	+	6.62603i	−0.131651	+	0.103532i
$17$	−39.8585	−	45.9992i	−0.568653	−	0.656261i	0.396473	−	0.918047i	$-0.370234\pi$
$17$	−39.8585	−	45.9992i	−0.568653	−	0.656261i	−0.965126	+	0.261786i	$0.915689\pi$
$18$	45.2160	+	116.820i	0.592084	+	1.52971i
$19$	78.4939	−	90.5868i	0.947775	−	1.09379i	−0.0477087	−	0.998861i	$-0.515192\pi$
$19$	78.4939	−	90.5868i	0.947775	−	1.09379i	0.995484	−	0.0949297i	$-0.0302626\pi$
$20$	115.417	+	110.050i	1.29040	+	1.23040i
$21$	10.8355	−	24.9065i	0.112595	−	0.258811i
$22$	129.492	−	224.287i	1.25490	−	2.17355i
$23$	66.9836	−	87.6367i	0.607263	−	0.794501i
$23$	66.9836	−	87.6367i	0.607263	−	0.794501i
$24$	130.302	−	27.5617i	1.10824	−	0.234417i
$25$	8.14250	−	11.4345i	0.0651400	−	0.0914763i
$26$	−300.633	+	88.2738i	−2.26765	+	0.665843i
$27$	12.4211	−	139.745i	0.0885348	−	0.996073i
$28$	−59.4734	−	38.2212i	−0.401408	−	0.257969i
$29$	97.3973	−	281.411i	0.623663	−	1.80196i	0.0267603	−	0.999642i	$-0.491481\pi$
$29$	97.3973	−	281.411i	0.623663	−	1.80196i	0.596903	−	0.802314i	$-0.296398\pi$
$30$	−97.8055	−	266.904i	−0.595225	−	1.62433i
$31$	107.120	−	102.138i	0.620621	−	0.591761i	−0.313119	−	0.949714i	$-0.601374\pi$
$31$	107.120	−	102.138i	0.620621	−	0.591761i	0.933739	+	0.357953i	$0.116525\pi$
$32$	7.39048	+	155.145i	0.0408270	+	0.857064i
$33$	−241.143	+	161.196i	−1.27205	+	0.850323i
$34$	281.105	−	26.8423i	1.41792	−	0.135395i
$35$	−25.6046	+	56.0663i	−0.123656	+	0.270769i
$36$	−353.859	−	90.1665i	−1.63823	−	0.417438i
$37$	−29.8116	+	19.1588i	−0.132459	+	0.0851265i	−0.605192	−	0.796079i	$-0.706904\pi$
$37$	−29.8116	+	19.1588i	−0.132459	+	0.0851265i	0.472733	+	0.881206i	$0.343267\pi$
$38$	131.106	+	540.427i	0.559690	+	2.30707i
$39$	345.721	+	60.1821i	1.41948	+	0.247099i
$40$	−296.769	+	57.1976i	−1.17308	+	0.226093i
$41$	274.154	−	141.336i	1.04429	−	0.538367i	0.151317	−	0.988485i	$-0.451649\pi$
$41$	274.154	−	141.336i	1.04429	−	0.538367i	0.892969	+	0.450119i	$0.148618\pi$
$42$	64.9666	+	107.977i	0.238680	+	0.396694i
$43$	−232.004	−	221.215i	−0.822796	−	0.784535i	0.156348	−	0.987702i	$-0.450028\pi$
$43$	−232.004	−	221.215i	−0.822796	−	0.784535i	−0.979144	+	0.203167i	$0.934876\pi$
$44$	313.627	+	686.746i	1.07457	+	2.35297i
$45$	−33.9056	+	316.558i	−0.112319	+	1.04866i
$46$	150.933	+	488.988i	0.483780	+	1.56733i
$47$	172.805	+	299.307i	0.536303	+	0.928904i	0.999099	+	0.0424390i	$0.0135128\pi$
$47$	172.805	+	299.307i	0.536303	+	0.928904i	−0.462796	+	0.886465i	$0.653154\pi$
$48$	−22.2194	+	51.0735i	−0.0668143	+	0.153580i
$49$	−74.4235	+	306.778i	−0.216978	+	0.894396i
$50$	21.3007	+	61.5442i	0.0602474	+	0.174073i
$51$	−295.686	−	112.226i	−0.811849	−	0.308133i
$52$	298.738	−	863.147i	0.796683	−	2.30187i
$53$	14.9783	+	104.176i	0.0388193	+	0.269994i	0.999982	−	0.00598794i	$-0.00190603\pi$
$53$	14.9783	+	104.176i	0.0388193	+	0.269994i	−0.961163	+	0.275982i	$0.910997\pi$
$54$	494.698	+	423.018i	1.24666	+	1.06603i
$55$	553.729	−	355.860i	1.35754	−	0.872439i
$56$	124.384	−	49.7957i	0.296812	−	0.118825i
$57$	135.889	−	607.824i	0.315771	−	1.41243i
$58$	801.397	+	1125.40i	1.81429	+	2.54781i
$59$	120.579	+	94.8244i	0.266069	+	0.209239i	0.742276	−	0.670094i	$-0.233746\pi$
$59$	120.579	+	94.8244i	0.266069	+	0.209239i	−0.476207	+	0.879333i	$0.657989\pi$
$60$	799.173	+	219.071i	1.71955	+	0.471365i
$61$	−25.7000	−	105.937i	−0.0539434	−	0.222358i	0.938459	−	0.345390i	$-0.112253\pi$
$61$	−25.7000	−	105.937i	−0.0539434	−	0.222358i	−0.992403	+	0.123032i	$0.960738\pi$
$62$	97.7255	+	679.696i	0.200180	+	1.39228i
$63$	−11.7991	−	140.641i	−0.0235959	−	0.281255i
$64$	−678.352	−	435.951i	−1.32491	−	0.851466i
$65$	−781.938	−	150.706i	−1.49212	−	0.287582i
$66$	39.7606	−	1345.13i	0.0741544	−	2.50870i
$67$	−675.145	−	64.4685i	−1.23108	−	0.117553i	−0.540832	−	0.841131i	$-0.681891\pi$
$67$	−675.145	−	64.4685i	−1.23108	−	0.117553i	−0.690244	+	0.723577i	$0.742497\pi$
$68$	−411.593	+	712.900i	−0.734015	+	1.27135i
$69$	90.5010	−	565.967i	0.157899	−	0.987455i
$70$	−142.980	−	247.648i	−0.244133	−	0.422851i
$71$	−356.267	−	780.115i	−0.595508	−	1.30398i	−0.932056	−	0.362315i	$-0.881987\pi$
$71$	−356.267	−	780.115i	−0.595508	−	1.30398i	0.336548	−	0.941666i	$-0.390741\pi$
$72$	528.193	−	447.151i	0.864557	−	0.731906i
$73$	−101.175	+	116.762i	−0.162214	+	0.187204i	−0.831037	−	0.556216i	$-0.812253\pi$
$73$	−101.175	+	116.762i	−0.162214	+	0.187204i	0.668824	+	0.743421i	$0.266798\pi$
$74$	7.82291	−	164.223i	0.0122891	−	0.257980i
$75$	9.07575	−	72.3737i	0.0139730	−	0.111427i
$76$	−1504.99	−	602.506i	−2.27150	−	0.909371i
$77$	−211.180	+	201.360i	−0.312548	+	0.298014i
$78$	−1157.83	+	1144.59i	−1.68075	+	1.66153i
$79$	−28.2719	+	11.3184i	−0.0402638	+	0.0161192i	−0.391707	−	0.920090i	$-0.628115\pi$
$79$	−28.2719	+	11.3184i	−0.0402638	+	0.0161192i	0.351443	+	0.936209i	$0.385691\pi$
$80$	52.5051	−	114.970i	0.0733780	−	0.160676i
$81$	−287.506	−	669.911i	−0.394384	−	0.918946i
$82$	−203.654	+	1416.44i	−0.274266	+	1.90756i
$83$	112.184	+	57.8350i	0.148359	+	0.0764845i	0.530808	−	0.847492i	$-0.321889\pi$
$83$	112.184	+	57.8350i	0.148359	+	0.0764845i	−0.382448	+	0.923977i	$0.624919\pi$
$84$	−366.255	−	28.3129i	−0.475735	−	0.0367760i
$85$	666.282	+	266.739i	0.850217	+	0.340375i
$86$	1460.37	−	281.464i	1.83112	−	0.352919i
$87$	−247.820	−	1527.38i	−0.305391	−	1.88222i
$88$	−1404.94	−	270.780i	−1.70190	−	0.328014i
$89$	1388.95	−	407.833i	1.65425	−	0.485733i	0.684337	−	0.729166i	$-0.260092\pi$
$89$	1388.95	−	407.833i	1.65425	−	0.485733i	0.969918	+	0.243433i	$0.0782735\pi$
$90$	−1105.09	−	980.041i	−1.29429	−	1.14784i
$91$	353.018			0.406663
$92$	−1416.37	−	468.446i	−1.60507	−	0.530857i
$93$	238.383	−	731.203i	0.265798	−	0.815293i
$94$	−1596.19	−	152.417i	−1.75143	−	0.167241i
$95$	−333.212	+	1373.52i	−0.359862	+	1.48337i
$96$	416.085	+	691.548i	0.442360	+	0.735217i
$97$	27.6461	−	580.363i	0.0289385	−	0.607494i	−0.937095	−	0.349076i	$-0.886496\pi$
$97$	27.6461	−	580.363i	0.0289385	−	0.607494i	0.966033	−	0.258418i	$-0.0832013\pi$
$98$	−959.089	−	1106.85i	−0.988598	−	1.14090i
$99$	−705.996	+	1331.61i	−0.716720	+	1.35184i
$100$	−182.161	−	53.4872i	−0.182161	−	0.0534872i
$101$	775.703	+	399.903i	0.764211	+	0.393978i	0.795829	−	0.605522i	$-0.207036\pi$
$101$	775.703	+	399.903i	0.764211	+	0.393978i	−0.0316177	+	0.999500i	$0.510066\pi$
$102$	1219.86	−	815.438i	1.18416	−	0.791572i
$103$	−880.539	−	1236.54i	−0.842350	−	1.18292i	−0.981275	−	0.192613i	$-0.938304\pi$
$103$	−880.539	−	1236.54i	−0.842350	−	1.18292i	0.138925	−	0.990303i	$-0.455635\pi$
$104$	1004.08	+	1410.04i	0.946717	+	1.32948i
$105$	21.0105	+	319.581i	0.0195278	+	0.297028i
$106$	−434.011	−	223.748i	−0.397688	−	0.205022i
$107$	−558.120	−	163.879i	−0.504257	−	0.148063i	0.0197035	−	0.999806i	$-0.493728\pi$
$107$	−558.120	−	163.879i	−0.504257	−	0.148063i	−0.523960	+	0.851743i	$0.675546\pi$
$108$	−1841.00	+	459.408i	−1.64028	+	0.409320i
$109$	−652.019	−	752.471i	−0.572955	−	0.661226i	0.393120	−	0.919487i	$-0.371396\pi$
$109$	−652.019	−	752.471i	−0.572955	−	0.661226i	−0.966075	+	0.258262i	$0.916850\pi$
$110$	−145.305	+	3050.33i	−0.125948	+	2.64397i
$111$	−89.1752	+	161.103i	−0.0762535	+	0.137759i
$112$	−13.2096	+	54.4509i	−0.0111446	+	0.0459386i
$113$	−275.661	−	26.3224i	−0.229487	−	0.0219133i	−0.0203210	−	0.999794i	$-0.506469\pi$
$113$	−275.661	−	26.3224i	−0.229487	−	0.0219133i	−0.209166	+	0.977880i	$0.567075\pi$
$114$	1931.39	+	2149.30i	1.58676	+	1.76579i
$115$	−228.517	+	1280.41i	−0.185298	+	1.03825i
$116$	−4027.49			−3.22365
$117$	1729.89	−	576.531i	1.36691	−	0.455558i
$118$	−682.857	+	200.505i	−0.532729	+	0.156423i
$119$	−312.408	−	60.2117i	−0.240659	−	0.0463832i
$120$	−1216.72	+	992.902i	−0.925594	+	0.755326i
$121$	1752.82	−	337.829i	1.31692	−	0.253816i
$122$	469.519	+	187.967i	0.348428	+	0.139490i
$123$	905.950	−	1322.10i	0.664120	−	0.969183i
$124$	−1779.25	−	917.267i	−1.28856	−	0.664299i
$125$	186.206	−	1295.09i	0.133238	−	0.926690i
$126$	563.262	+	333.895i	0.398249	+	0.236077i
$127$	−711.234	+	1557.39i	−0.496944	+	1.08816i	0.480507	+	0.876991i	$0.340453\pi$
$127$	−711.234	+	1557.39i	−0.496944	+	1.08816i	−0.977451	+	0.211164i	$0.932275\pi$
$128$	2319.53	−	928.601i	1.60172	−	0.641231i
$129$	−1606.44	−	440.361i	−1.09643	−	0.300555i
$130$	2673.87	−	2549.53i	1.80395	−	1.72006i
$131$	−1864.39	−	746.387i	−1.24345	−	0.497803i	−0.345716	−	0.938339i	$-0.612364\pi$
$131$	−1864.39	−	746.387i	−1.24345	−	0.497803i	−0.897735	+	0.440536i	$0.854788\pi$
$132$	3126.91	+	2368.95i	2.06184	+	1.56205i
$133$	29.8125	−	625.842i	0.0194366	−	0.408025i
$134$	2060.56	−	2378.01i	1.32840	−	1.53305i
$135$	624.882	+	1531.73i	0.398380	+	0.976521i
$136$	−648.078	−	1419.09i	−0.408619	−	0.894751i
$137$	676.415	+	1171.59i	0.421825	+	0.730623i	0.996118	−	0.0880273i	$-0.0280563\pi$
$137$	676.415	+	1171.59i	0.421825	+	0.730623i	−0.574293	+	0.818650i	$0.694723\pi$
$138$	1895.35	+	1865.13i	1.16915	+	1.15051i
$139$	403.219	−	698.396i	0.246047	−	0.426167i	−0.716378	−	0.697712i	$-0.754201\pi$
$139$	403.219	−	698.396i	0.246047	−	0.426167i	0.962426	+	0.271546i	$0.0875348\pi$
$140$	829.833	+	79.2395i	0.500955	+	0.0478354i
$141$	1528.04	+	943.482i	0.912653	+	0.563514i
$142$	3906.98	+	753.009i	2.30892	+	0.445008i
$143$	−3171.45	−	2038.17i	−1.85462	−	1.19189i
$144$	24.1953	+	288.399i	0.0140019	+	0.166898i
$145$	499.718	+	3475.61i	0.286202	+	1.99058i
$146$	−168.989	−	696.583i	−0.0957920	−	0.394860i
$147$	415.424	+	1586.83i	0.233085	+	0.890334i
$148$	376.735	+	296.268i	0.209240	+	0.164548i
$149$	832.675	+	1169.33i	0.457821	+	0.642920i	0.977374	−	0.211518i	$-0.0678408\pi$
$149$	832.675	+	1169.33i	0.457821	+	0.642920i	−0.519553	+	0.854438i	$0.673901\pi$
$150$	249.090	+	229.068i	0.135588	+	0.124689i
$151$	−2625.32	+	1051.02i	−1.41487	+	0.566429i	−0.948106	−	0.317953i	$-0.897004\pi$
$151$	−2625.32	+	1051.02i	−1.41487	+	0.566429i	−0.466764	+	0.884382i	$0.654580\pi$
$152$	2584.56	−	1661.00i	1.37918	−	0.886346i
$153$	−1629.23	+	215.154i	−0.860884	+	0.113687i
$154$	−192.661	−	1339.98i	−0.100812	−	0.701162i
$155$	−570.813	+	1649.25i	−0.295799	+	0.854654i
$156$	−760.115	−	4684.81i	−0.390115	−	2.40439i
$157$	7.12924	+	20.5986i	0.00362404	+	0.0104710i	0.946798	−	0.321827i	$-0.104297\pi$
$157$	7.12924	+	20.5986i	0.00362404	+	0.0104710i	−0.943174	+	0.332298i	$0.892176\pi$
$158$	33.3098	−	137.305i	0.0167720	−	0.0691353i
$159$	325.211	+	439.679i	0.162207	+	0.219300i
$160$	−915.728	−	1586.09i	−0.452467	−	0.783695i
$161$	−7.94919	−	576.528i	−0.00389121	−	0.282216i
$162$	3305.45	+	716.293i	1.60309	+	0.347391i
$163$	870.262	+	1905.61i	0.418185	+	0.915698i	0.995098	+	0.0988924i	$0.0315300\pi$
$163$	870.262	+	1905.61i	0.418185	+	0.915698i	−0.576913	+	0.816806i	$0.695743\pi$
$164$	−3019.11	−	2878.71i	−1.43752	−	1.37067i
$165$	1656.36	−	2992.37i	0.781502	−	1.41185i
$166$	−520.475	+	268.323i	−0.243354	+	0.125457i
$167$	1984.46	−	382.474i	0.919535	−	0.177226i	0.292544	−	0.956252i	$-0.405498\pi$
$167$	1984.46	−	382.474i	0.919535	−	0.177226i	0.626991	+	0.779026i	$0.284286\pi$
$168$	446.334	−	534.284i	0.204973	−	0.245363i
$169$	557.318	+	2297.29i	0.253672	+	1.04565i
$170$	−2801.13	+	1800.18i	−1.26375	+	0.812160i
$171$	−876.003	−	3115.50i	−0.391752	−	1.39326i
$172$	−1801.04	+	3943.74i	−0.798420	+	1.74830i
$173$	−937.975	+	89.5658i	−0.412214	+	0.0393616i	−0.299103	−	0.954221i	$-0.596687\pi$
$173$	−937.975	+	89.5658i	−0.412214	+	0.0393616i	−0.113110	+	0.993582i	$0.536081\pi$
$174$	6439.21	+	3173.87i	2.80549	+	1.38282i
$175$	−3.49139	−	73.2934i	−0.00150814	−	0.0316598i
$176$	433.049	−	412.911i	0.185467	−	0.176843i
$177$	785.270	+	136.698i	0.333472	+	0.0580498i
$178$	−2196.60	+	6346.67i	−0.924957	+	2.67249i
$179$	−371.235	−	238.578i	−0.155013	−	0.0996211i	0.460835	−	0.887486i	$-0.347550\pi$
$179$	−371.235	−	238.578i	−0.155013	−	0.0996211i	−0.615848	+	0.787865i	$0.711186\pi$
$180$	4195.84	−	966.945i	1.73744	−	0.400399i
$181$	701.287	−	205.916i	0.287990	−	0.0845616i	−0.134547	−	0.990907i	$-0.542958\pi$
$181$	701.287	−	205.916i	0.287990	−	0.0845616i	0.422537	+	0.906346i	$0.361140\pi$
$182$	−950.026	+	1334.12i	−0.386926	+	0.543362i
$183$	−378.599	−	421.315i	−0.152934	−	0.170189i
$184$	2280.18	−	1671.56i	0.913573	−	0.669724i
$185$	208.927	−	361.872i	0.0830303	−	0.143813i
$186$	2121.83	+	2868.68i	0.836454	+	1.13087i
$187$	2458.98	+	2344.64i	0.961597	+	0.916881i
$188$	3060.99	−	3532.57i	1.18748	−	1.37042i
$189$	−400.515	−	614.330i	−0.154144	−	0.236433i
$190$	−4294.08	−	4955.63i	−1.63961	−	1.89221i
$191$	−1998.02	+	1571.26i	−0.756919	+	0.595248i	−0.920253	−	0.391323i	$-0.872018\pi$
$191$	−1998.02	+	1571.26i	−0.756919	+	0.595248i	0.163334	+	0.986571i	$0.447775\pi$
$192$	−4177.50	−	322.936i	−1.57024	−	0.121385i
$193$	0.582416	+	12.2264i	0.000217219	+	0.00455998i	0.998973	−	0.0453018i	$-0.0144249\pi$
$193$	0.582416	+	12.2264i	0.000217219	+	0.00455998i	−0.998756	+	0.0498618i	$0.984122\pi$
$194$	2118.91	+	1666.33i	0.784168	+	0.616676i
$195$	−3948.55	+	1237.23i	−1.45006	+	0.454360i
$196$	4250.08	−	405.833i	1.54886	−	0.147898i
$197$	226.043	−	1572.17i	0.0817509	−	0.568590i	−0.907240	−	0.420613i	$-0.861815\pi$
$197$	226.043	−	1572.17i	0.0817509	−	0.568590i	0.988991	−	0.147977i	$-0.0472760\pi$
$198$	−3132.49	−	6251.68i	−1.12432	−	2.24387i
$199$	1558.22	+	457.535i	0.555072	+	0.162984i	0.547225	−	0.836985i	$-0.315684\pi$
$199$	1558.22	+	457.535i	0.555072	+	0.162984i	0.00784668	+	0.999969i	$0.497502\pi$
$200$	282.821	−	222.413i	0.0999923	−	0.0786348i
$201$	−3247.50	+	1368.62i	−1.13961	+	0.480272i
$202$	−3598.85	+	1855.33i	−1.25353	+	0.646242i
$203$	−509.116	−	1470.99i	−0.176024	−	0.508589i
$204$	−126.380	+	4275.53i	−0.0433744	+	1.46739i
$205$	−2109.65	+	2962.59i	−0.718753	+	1.00935i
$206$	7042.81			2.38202
$207$	−980.510	−	2812.18i	−0.329228	−	0.944251i
$208$	−723.902			−0.241315
$209$	−3881.16	+	5450.33i	−1.28452	+	1.80386i
$210$	−1264.30	−	780.639i	−0.415453	−	0.256520i
$211$	−936.138	−	2704.79i	−0.305433	−	0.882491i	−0.988377	−	0.152020i	$-0.951422\pi$
$211$	−936.138	−	2704.79i	−0.305433	−	0.882491i	0.682944	−	0.730471i	$-0.260699\pi$
$212$	1265.20	−	652.255i	0.409878	−	0.211307i
$213$	−3552.04	−	2691.03i	−1.14264	−	0.865665i
$214$	2121.32	−	1668.22i	0.677618	−	0.532884i
$215$	3626.80	+	1064.92i	1.15045	+	0.337801i
$216$	1314.60	−	3347.08i	0.414108	−	1.05435i
$217$	110.106	−	765.802i	0.0344445	−	0.239567i
$218$	4598.42	−	439.096i	1.42864	−	0.136419i
$219$	−175.154	+	783.454i	−0.0540449	+	0.241739i
$220$	−6997.59	−	5502.96i	−2.14444	−	1.68641i
$221$	−195.587	−	4105.88i	−0.0595322	−	1.24974i
$222$	−368.855	−	770.563i	−0.111513	−	0.232959i
$223$	2470.74	−	1943.01i	0.741941	−	0.583469i	−0.174017	−	0.984743i	$-0.555675\pi$
$223$	2470.74	−	1943.01i	0.741941	−	0.583469i	0.915958	+	0.401274i	$0.131432\pi$
$224$	531.679	+	613.590i	0.158591	+	0.183023i
$225$	−136.808	−	353.458i	−0.0405357	−	0.104728i
$226$	841.324	−	970.940i	0.247629	−	0.285779i
$227$	2672.55	+	2548.27i	0.781423	+	0.745086i	0.971591	−	0.236666i	$-0.0760547\pi$
$227$	2672.55	+	2548.27i	0.781423	+	0.745086i	−0.190168	+	0.981752i	$0.560903\pi$
$228$	−8369.58	+	951.923i	−2.43109	+	0.276503i
$229$	538.241	−	932.261i	0.155319	−	0.269020i	−0.777856	−	0.628442i	$-0.783693\pi$
$229$	538.241	−	932.261i	0.155319	−	0.269020i	0.933175	+	0.359422i	$0.117026\pi$
$230$	−4223.95	−	4309.39i	−1.21095	−	1.23545i
$231$	−469.959	+	1441.53i	−0.133857	+	0.410587i
$232$	4427.44	−	6217.47i	1.25291	−	1.75947i
$233$	−3504.32	+	1028.96i	−0.985303	+	0.289311i	−0.734412	−	0.678704i	$-0.762542\pi$
$233$	−3504.32	+	1028.96i	−0.985303	+	0.289311i	−0.250891	+	0.968015i	$0.580724\pi$
$234$	−2476.58	+	8089.14i	−0.691878	+	2.25985i
$235$	−3428.31	−	2203.24i	−0.951651	−	0.611589i
$236$	678.553	−	1960.55i	0.187161	−	0.540767i
$237$	−101.450	+	121.441i	−0.0278055	+	0.0332845i
$238$	1068.29	−	1018.61i	0.290954	−	0.277424i
$239$	−166.521	−	3495.70i	−0.0450683	−	0.946101i	−0.902284	−	0.431143i	$-0.858111\pi$
$239$	−166.521	−	3495.70i	−0.0450683	−	0.946101i	0.857215	−	0.514958i	$-0.172193\pi$
$240$	−43.0844	−	655.336i	−0.0115879	−	0.176257i
$241$	3698.31	−	353.145i	0.988501	−	0.0943904i	0.411738	−	0.911302i	$-0.364922\pi$
$241$	3698.31	−	353.145i	0.988501	−	0.0943904i	0.576763	+	0.816912i	$0.304316\pi$
$242$	−3440.40	+	7533.42i	−0.913873	+	2.00110i
$243$	−2965.93	−	2356.30i	−0.782982	−	0.622044i
$244$	−1240.27	+	797.076i	−0.325411	+	0.209129i
$245$	−877.558	−	3617.34i	−0.228837	−	0.943280i
$246$	2558.42	+	6981.73i	0.663084	+	1.80951i
$247$	7948.65	−	1531.98i	2.04761	−	0.394645i
$248$	3371.97	−	1738.37i	0.863389	−	0.445108i
$249$	655.725	−	11.8368i	0.166887	−	0.00301257i
$250$	4393.29	+	4188.99i	1.11142	+	1.05974i
$251$	−2509.82	−	5495.73i	−0.631148	−	1.38202i	−0.907126	−	0.420858i	$-0.861729\pi$
$251$	−2509.82	−	5495.73i	−0.631148	−	1.38202i	0.275978	−	0.961164i	$-0.410998\pi$
$252$	−1745.31	+	772.922i	−0.436286	+	0.193212i
$253$	−3257.20	+	5225.32i	−0.809402	+	1.29847i
$254$	−3971.63	−	6879.06i	−0.981111	−	1.69933i
$255$	3705.35	−	421.431i	0.909952	−	0.103494i
$256$	−1212.01	+	4995.95i	−0.295900	+	1.21972i
$257$	2567.68	+	7418.84i	0.623221	+	1.80068i	0.598692	+	0.800979i	$0.295687\pi$
$257$	2567.68	+	7418.84i	0.623221	+	1.80068i	0.0245284	+	0.999699i	$0.492192\pi$
$258$	5987.39	−	4885.98i	1.44480	−	1.17902i
$259$	−60.5852	+	175.049i	−0.0145351	+	0.0419963i
$260$	1532.74	+	10660.4i	0.365602	+	2.54282i
$261$	−4897.18	−	6376.85i	−1.16141	−	1.51233i
$262$	7838.10	−	5037.24i	1.84824	−	1.18779i
$263$	3128.71	−	1252.55i	0.733553	−	0.293670i	0.0253494	−	0.999679i	$-0.491930\pi$
$263$	3128.71	−	1252.55i	0.733553	−	0.293670i	0.708203	+	0.706008i	$0.249506\pi$
$264$	−7094.51	+	2222.99i	−1.65393	+	0.518240i
$265$	−719.860	−	1010.90i	−0.166870	−	0.234337i
$266$	2284.95	+	1796.90i	0.526689	+	0.414193i
$267$	5349.28	−	5288.11i	1.22611	−	1.21209i
$268$	2162.53	+	8914.07i	0.492901	+	2.03177i
$269$	157.162	+	1093.08i	0.0356220	+	0.247756i	0.999850	−	0.0173178i	$-0.00551270\pi$
$269$	157.162	+	1093.08i	0.0356220	+	0.247756i	−0.964228	+	0.265074i	$0.914604\pi$
$270$	−7470.36	−	1760.57i	−1.68382	−	0.396833i
$271$	−1008.10	−	647.864i	−0.225969	−	0.145221i	0.422758	−	0.906242i	$-0.361062\pi$
$271$	−1008.10	−	647.864i	−0.225969	−	0.145221i	−0.648727	+	0.761021i	$0.724698\pi$
$272$	640.627	+	123.471i	0.142808	+	0.0275239i
$273$	1614.99	−	869.831i	0.358034	−	0.192837i
$274$	−6247.99	−	596.611i	−1.37757	−	0.131542i
$275$	−391.797	+	678.613i	−0.0859137	+	0.148807i
$276$	−7633.84	+	1346.87i	−1.66487	+	0.293739i
$277$	−85.7358	−	148.499i	−0.0185970	−	0.0322109i	0.856577	−	0.516019i	$-0.172587\pi$
$277$	−85.7358	−	148.499i	−0.0185970	−	0.0322109i	−0.875174	+	0.483808i	$0.839253\pi$
$278$	1554.25	+	3403.34i	0.335316	+	0.734239i
$279$	−711.118	−	3932.48i	−0.152593	−	0.843840i
$280$	−1034.56	+	1193.95i	−0.220811	+	0.254829i
$281$	−415.966	+	8732.19i	−0.0883075	+	1.85380i	0.328122	+	0.944635i	$0.393584\pi$
$281$	−415.966	+	8732.19i	−0.0883075	+	1.85380i	−0.416429	+	0.909168i	$0.636719\pi$
$282$	−7677.79	+	3235.70i	−1.62130	+	0.683274i
$283$	7508.39	+	3005.91i	1.57713	+	0.631387i	0.984703	−	0.174239i	$-0.0557464\pi$
$283$	7508.39	+	3005.91i	1.57713	+	0.631387i	0.592425	+	0.805626i	$0.298171\pi$
$284$	−8394.56	+	8004.20i	−1.75396	+	1.67240i
$285$	1859.95	+	7104.60i	0.386576	+	1.47663i
$286$	16237.5	−	6500.52i	3.35715	−	1.34400i
$287$	669.770	−	1466.59i	0.137754	−	0.301638i
$288$	3607.47	+	2138.46i	0.738098	+	0.437536i
$289$	171.970	−	1196.08i	0.0350030	−	0.243451i
$290$	−14479.9	−	7464.88i	−2.93202	−	1.51156i
$291$	−1303.53	−	2723.16i	−0.262592	−	0.548572i
$292$	1939.85	+	776.600i	0.388772	+	0.155641i
$293$	833.257	−	160.597i	0.166141	−	0.0320211i	−0.105502	−	0.994419i	$-0.533645\pi$
$293$	833.257	−	160.597i	0.166141	−	0.0320211i	0.271643	+	0.962398i	$0.412433\pi$
$294$	−7114.90	−	2700.42i	−1.41139	−	0.535687i
$295$	−1776.09	−	342.314i	−0.350536	−	0.0675603i
$296$	−871.512	+	255.899i	−0.171134	+	0.0502494i
$297$	51.2878	+	7831.43i	0.0100203	+	1.53005i
$298$	−6659.98			−1.29464
$299$	7214.46	−	1855.89i	1.39540	−	0.358960i
$300$	−965.140	+	204.148i	−0.185741	+	0.0392883i
$301$	−1668.07	−	159.282i	−0.319422	−	0.0305011i
$302$	3093.13	−	12750.1i	0.589370	−	2.42941i
$303$	4534.04	−	81.8464i	0.859649	−	0.0155180i
$304$	−61.1339	+	1283.36i	−0.0115338	+	0.242124i
$305$	841.743	+	971.423i	0.158026	+	0.182372i
$306$	3571.39	−	6736.18i	0.667199	−	1.25844i
$307$	7513.35	+	2206.12i	1.39677	+	0.410130i	0.891575	−	0.452873i	$-0.149601\pi$
$307$	7513.35	+	2206.12i	1.39677	+	0.410130i	0.505199	+	0.863003i	$0.331419\pi$
$308$	3507.70	+	1808.34i	0.648927	+	0.334545i
$309$	−7075.11	−	3487.30i	−1.30255	−	0.642025i
$310$	−4696.71	−	6595.61i	−0.860502	−	1.20841i
$311$	4769.80	+	6698.24i	0.869680	+	1.22129i	0.973954	+	0.226746i	$0.0728087\pi$
$311$	4769.80	+	6698.24i	0.869680	+	1.22129i	−0.104274	+	0.994549i	$0.533252\pi$
$312$	8067.80	+	3976.60i	1.46394	+	0.721572i
$313$	57.1125	+	29.4435i	0.0103137	+	0.00531708i	0.463376	−	0.886162i	$-0.346638\pi$
$313$	57.1125	+	29.4435i	0.0103137	+	0.00531708i	−0.453062	+	0.891479i	$0.649668\pi$
$314$	−97.0320	−	28.4912i	−0.0174390	−	0.00512054i
$315$	883.562	+	1410.25i	0.158042	+	0.252249i
$316$	269.718	+	311.272i	0.0480153	+	0.0554126i
$317$	79.4299	−	1667.44i	0.0140733	−	0.295435i	−0.980848	−	0.194776i	$-0.937602\pi$
$317$	79.4299	−	1667.44i	0.0140733	−	0.295435i	0.994921	−	0.100659i	$-0.0320950\pi$
$318$	−2536.83	+	45.7936i	−0.447352	+	0.00807541i
$319$	−3919.06	+	16154.6i	−0.687853	+	2.83537i
$320$	9465.06	+	903.804i	1.65348	+	0.157888i
$321$	−2957.08	+	625.486i	−0.514168	+	0.108758i
$322$	2200.21	+	1521.48i	0.380785	+	0.263320i
$323$	−7295.56			−1.25677
$324$	−7290.23	+	6637.90i	−1.25004	+	1.13819i
$325$	909.610	−	267.086i	0.155250	−	0.0455854i
$326$	−9543.68	−	1839.39i	−1.62140	−	0.312499i
$327$	−4836.93	−	1835.83i	−0.817991	−	0.310464i
$328$	7762.95	−	1496.19i	1.30682	−	0.251869i
$329$	1677.17	+	671.437i	0.281050	+	0.112515i
$330$	6851.22	+	14312.7i	1.14287	+	2.38753i
$331$	−4441.20	−	2289.60i	−0.737494	−	0.380205i	0.0481854	−	0.998838i	$-0.484656\pi$
$331$	−4441.20	−	2289.60i	−0.737494	−	0.380205i	−0.785679	+	0.618634i	$0.787686\pi$
$332$	242.933	−	1689.64i	0.0401587	−	0.279310i
$333$	−11.0037	+	956.739i	−0.00181080	+	0.157444i
$334$	−3895.05	+	8528.97i	−0.638107	+	1.39726i
$335$	7424.27	−	2972.23i	1.21084	−	0.484747i
$336$	73.7348	+	281.650i	0.0119719	+	0.0457300i
$337$	3464.64	−	3303.52i	0.560032	−	0.533989i	−0.356319	−	0.934364i	$-0.615969\pi$
$337$	3464.64	−	3303.52i	0.560032	−	0.533989i	0.916352	+	0.400375i	$0.131120\pi$
$338$	−10181.8	−	4076.16i	−1.63850	−	0.655958i
$339$	−1325.95	+	558.805i	−0.212436	+	0.0895284i
$340$	461.855	−	9695.53i	0.0736695	−	1.54651i
$341$	−5410.57	+	6244.13i	−0.859234	+	0.991609i
$342$	14131.6	+	5073.70i	2.23435	+	0.802206i
$343$	1430.29	+	3131.90i	0.225156	+	0.493022i
$344$	−4108.27	−	7115.73i	−0.643904	−	1.11527i
$345$	2109.49	+	6420.68i	0.329192	+	1.00196i
$346$	2185.75	−	3785.83i	0.339615	−	0.588230i
$347$	−4253.82	−	406.191i	−0.658090	−	0.0628400i	−0.239332	−	0.970938i	$-0.576928\pi$
$347$	−4253.82	−	406.191i	−0.658090	−	0.0628400i	−0.418758	+	0.908098i	$0.637534\pi$
$348$	−18425.0	+	9923.69i	−2.83817	+	1.52864i
$349$	−8458.14	−	1630.17i	−1.29729	−	0.250032i	−0.506564	−	0.862203i	$-0.669085\pi$
$349$	−8458.14	−	1630.17i	−1.29729	−	0.250032i	−0.790726	+	0.612170i	$0.790297\pi$
$350$	286.386	+	184.049i	0.0437371	+	0.0281081i
$351$	6493.35	−	6899.94i	0.987434	−	1.04926i
$352$	−1233.92	−	8582.07i	−0.186841	−	1.29951i
$353$	619.785	+	2554.79i	0.0934499	+	0.385206i	0.999259	−	0.0384794i	$-0.0122514\pi$
$353$	619.785	+	2554.79i	0.0934499	+	0.385206i	−0.905809	+	0.423685i	$0.860736\pi$
$354$	−2629.89	+	2599.82i	−0.394851	+	0.390335i
$355$	7948.97	+	6251.14i	1.18842	+	0.934580i
$356$	−11356.4	−	15947.9i	−1.69070	−	2.37426i
$357$	−1577.56	+	494.312i	−0.233875	+	0.0732823i
$358$	1900.68	−	760.919i	0.280599	−	0.112335i
$359$	−8965.62	+	5761.85i	−1.31807	+	0.847072i	−0.995055	−	0.0993214i	$-0.968333\pi$
$359$	−8965.62	+	5761.85i	−1.31807	+	0.847072i	−0.323015	+	0.946394i	$0.604696\pi$
$360$	−3119.78	+	7540.32i	−0.456741	+	1.10392i
$361$	−1068.54	−	7431.83i	−0.155786	−	1.08351i
$362$	−1109.07	+	3204.46i	−0.161026	+	0.465255i
$363$	7186.41	−	5864.43i	1.03909	−	0.847942i
$364$	−1561.57	−	4511.85i	−0.224858	−	0.649685i
$365$	429.493	−	1770.40i	0.0615910	−	0.253882i
$366$	2611.10	−	296.976i	0.372908	−	0.0424131i
$367$	−2898.23	−	5019.88i	−0.412224	−	0.713994i	0.582908	−	0.812538i	$-0.301915\pi$
$367$	−2898.23	−	5019.88i	−0.412224	−	0.713994i	−0.995133	+	0.0985443i	$0.968581\pi$
$368$	16.3007	+	1182.23i	0.00230906	+	0.167468i
$369$	886.910	−	8280.58i	0.125124	−	1.16821i
$370$	805.331	+	1763.43i	0.113155	+	0.247774i
$371$	398.162	+	379.647i	0.0557185	+	0.0531275i
$372$	−10399.8	+	187.733i	−1.44948	+	0.0261654i
$373$	844.902	−	435.577i	0.117285	−	0.0604647i	−0.398586	−	0.917131i	$-0.630499\pi$
$373$	844.902	−	435.577i	0.117285	−	0.0604647i	0.515871	+	0.856666i	$0.327468\pi$
$374$	−15478.3	+	2983.21i	−2.14002	+	0.412454i
$375$	−2339.22	−	6383.57i	−0.322125	−	0.879057i
$376$	2088.47	+	8608.78i	0.286448	+	1.18076i
$377$	16918.5	−	10872.9i	2.31127	−	1.48536i
$378$	3399.52	+	139.632i	0.462573	+	0.0189997i
$379$	−100.242	+	219.498i	−0.0135859	+	0.0297490i	−0.916303	−	0.400485i	$-0.868842\pi$
$379$	−100.242	+	219.498i	−0.0135859	+	0.0297490i	0.902717	+	0.430234i	$0.141569\pi$
$380$	19028.6	−	1817.01i	2.56881	−	0.245292i
$381$	583.622	+	8877.20i	0.0784773	+	1.19368i
$382$	−561.122	−	11779.4i	−0.0751558	−	1.57771i
$383$	−1291.35	+	1231.30i	−0.172284	+	0.164273i	−0.771316	−	0.636453i	$-0.780401\pi$
$383$	−1291.35	+	1231.30i	−0.172284	+	0.164273i	0.599031	+	0.800726i	$0.295552\pi$
$384$	8323.34	−	9963.46i	1.10612	−	1.32408i
$385$	1125.33	−	3251.42i	0.148966	−	0.430409i
$386$	−47.7734	−	30.7021i	−0.00629949	−	0.00404843i
$387$	−8434.19	+	1943.69i	−1.10784	+	0.255305i
$388$	−7539.80	+	2213.88i	−0.986534	+	0.289672i
$389$	6290.92	−	8834.37i	0.819955	−	1.15147i	−0.166274	−	0.986080i	$-0.553174\pi$
$389$	6290.92	−	8834.37i	0.819955	−	1.15147i	0.986229	−	0.165386i	$-0.0528870\pi$
$390$	5950.40	−	18251.9i	0.772591	−	2.36980i
$391$	−6701.08	+	411.877i	−0.866722	+	0.0532725i
$392$	−4045.62	+	7007.22i	−0.521262	+	0.902852i
$393$	−10368.3	+	1179.25i	−1.33081	+	0.151362i
$394$	5333.21	+	5085.21i	0.681937	+	0.650226i
$395$	235.153	−	271.381i	0.0299540	−	0.0345687i
$396$	20142.1	+	3132.83i	2.55600	+	0.397552i
$397$	2700.63	+	3116.69i	0.341412	+	0.394011i	0.900327	−	0.435214i	$-0.143327\pi$
$397$	2700.63	+	3116.69i	0.341412	+	0.394011i	−0.558915	+	0.829225i	$0.688782\pi$
$398$	−5922.53	+	4657.53i	−0.745903	+	0.586585i
$399$	−1405.68	−	2936.56i	−0.176371	−	0.368451i
$400$	7.15949	+	150.296i	0.000894936	+	0.0187870i
$401$	−3200.38	−	2516.80i	−0.398552	−	0.313424i	0.398689	−	0.917086i	$-0.369465\pi$
$401$	−3200.38	−	2516.80i	−0.398552	−	0.313424i	−0.797240	+	0.603662i	$0.793708\pi$
$402$	3567.26	−	15956.1i	0.442583	−	1.97965i
$403$	9950.51	−	950.159i	1.22995	−	0.117446i
$404$	1679.77	−	11683.1i	0.206861	−	1.43875i
$405$	6632.87	+	5467.66i	0.813802	+	0.670839i
$406$	6929.29	+	2034.62i	0.847032	+	0.248711i
$407$	1554.94	−	1222.82i	0.189375	−	0.148926i
$408$	−6461.45	−	4895.21i	−0.784042	−	0.593992i
$409$	−3811.36	+	1964.90i	−0.460782	+	0.237550i	−0.672956	−	0.739682i	$-0.734976\pi$
$409$	−3811.36	+	1964.90i	−0.460782	+	0.237550i	0.212174	+	0.977232i	$0.431946\pi$
$410$	−5518.81	−	15945.6i	−0.664768	−	1.92072i
$411$	5981.23	+	3693.09i	0.717840	+	0.443228i
$412$	−11909.0	+	16723.8i	−1.42406	+	1.99981i
$413$	801.844			0.0955355
$414$	13266.5	+	3862.46i	1.57491	+	0.458526i
$415$	−1488.25			−0.176037
$416$	−6084.54	+	8544.54i	−0.717113	+	1.00704i
$417$	123.809	−	4188.55i	0.0145394	−	0.491880i
$418$	−10153.1	−	29335.4i	−1.18805	−	3.43263i
$419$	14215.6	−	7328.67i	1.65747	−	0.854485i	0.663098	−	0.748533i	$-0.269241\pi$
$419$	14215.6	−	7328.67i	1.65747	−	0.854485i	0.994371	−	0.105952i	$-0.0337888\pi$
$420$	3991.56	−	1682.19i	0.463734	−	0.195435i
$421$	−4459.80	+	3507.23i	−0.516288	+	0.406014i	−0.842018	−	0.539449i	$-0.818632\pi$
$421$	−4459.80	+	3507.23i	−0.516288	+	0.406014i	0.325730	+	0.945463i	$0.394390\pi$
$422$	12741.2	+	3741.17i	1.46975	+	0.431557i
$423$	9315.19	+	551.175i	1.07073	+	0.0633547i
$424$	−383.914	+	2670.18i	−0.0439730	+	0.305839i
$425$	−850.527	+	81.2155i	−0.0970744	+	0.00926948i
$426$	19729.0	−	6181.88i	2.24384	−	0.703082i
$427$	−447.906	−	352.237i	−0.0507627	−	0.0399202i
$428$	374.329	+	7858.13i	0.0422754	+	0.887470i
$429$	−19530.8	−	1509.80i	−2.19803	−	0.169916i
$430$	−13784.8	+	10840.5i	−1.54596	+	1.21576i
$431$	785.203	+	906.172i	0.0877538	+	0.101273i	0.797928	−	0.602753i	$-0.205929\pi$
$431$	785.203	+	906.172i	0.0877538	+	0.101273i	−0.710174	+	0.704026i	$0.751384\pi$
$432$	821.299	+	1259.75i	0.0914694	+	0.140300i
$433$	−710.924	+	820.450i	−0.0789026	+	0.0910584i	−0.793828	−	0.608142i	$-0.791915\pi$
$433$	−710.924	+	820.450i	−0.0789026	+	0.0910584i	0.714926	+	0.699201i	$0.246461\pi$
$434$	2597.81	+	2477.00i	0.287324	+	0.273963i
$435$	10850.0	+	14668.9i	1.19590	+	1.61683i
$436$	−6732.98	+	11661.9i	−0.739568	+	1.28097i
$437$	−2680.92	−	12946.8i	−0.293469	−	1.41723i
$438$	−2489.46	−	2770.34i	−0.271578	−	0.302219i
$439$	−2608.94	+	3663.74i	−0.283639	+	0.398316i	−0.931674	−	0.363295i	$-0.881652\pi$
$439$	−2608.94	+	3663.74i	−0.283639	+	0.398316i	0.648035	+	0.761611i	$0.275591\pi$
$440$	16187.7	−	4753.14i	1.75390	−	0.514993i
$441$	5810.39	+	6235.81i	0.627404	+	0.673341i
$442$	16043.3	+	10310.4i	1.72648	+	1.10954i
$443$	4794.24	−	13852.1i	0.514179	−	1.48562i	−0.327083	−	0.944996i	$-0.606066\pi$
$443$	4794.24	−	13852.1i	0.514179	−	1.48562i	0.841262	−	0.540628i	$-0.181813\pi$
$444$	2453.49	+	427.096i	0.262246	+	0.0456511i
$445$	−12353.5	+	11779.0i	−1.31598	+	1.25479i
$446$	693.881	+	14566.3i	0.0736686	+	1.54649i
$447$	6690.53	+	3297.74i	0.707944	+	0.348944i
$448$	−4195.92	+	400.662i	−0.442497	+	0.0422534i
$449$	−151.977	+	332.783i	−0.0159738	+	0.0349777i	−0.917451	−	0.397849i	$-0.869757\pi$
$449$	−151.977	+	332.783i	−0.0159738	+	0.0349777i	0.901477	+	0.432827i	$0.142484\pi$
$450$	1703.96	+	434.185i	0.178501	+	0.0454837i
$451$	−14484.6	+	9308.66i	−1.51231	+	0.971902i
$452$	882.959	+	3639.61i	0.0918826	+	0.378745i
$453$	−9420.61	+	11276.9i	−0.977083	+	1.16962i
$454$	−16822.6	+	3242.30i	−1.73904	+	0.335173i
$455$	−3699.85	+	1907.40i	−0.381212	+	0.196529i
$456$	7731.17	−	13967.0i	0.793959	−	1.43436i
$457$	3371.46	+	3214.68i	0.345099	+	0.329051i	0.842729	−	0.538338i	$-0.180948\pi$
$457$	3371.46	+	3214.68i	0.345099	+	0.329051i	−0.497630	+	0.867389i	$0.665796\pi$
$458$	2074.71	+	4542.98i	0.211670	+	0.463492i
$459$	−6923.25	+	4998.67i	−0.704030	+	0.508318i
$460$	17375.5	−	2743.23i	1.76117	−	0.278052i
$461$	5096.14	+	8826.77i	0.514861	+	0.891765i	0.999851	+	0.0172454i	$0.00548966\pi$
$461$	5096.14	+	8826.77i	0.514861	+	0.891765i	−0.484991	+	0.874519i	$0.661177\pi$
$462$	−4183.08	−	5655.44i	−0.421244	−	0.569513i
$463$	−2472.07	+	10190.0i	−0.248136	+	1.02283i	0.702293	+	0.711888i	$0.252160\pi$
$463$	−2472.07	+	10190.0i	−0.248136	+	1.02283i	−0.950429	+	0.310943i	$0.899355\pi$
$464$	1044.00	+	3016.44i	0.104454	+	0.301799i
$465$	1452.39	+	8951.48i	0.144845	+	0.892720i
$466$	5542.02	−	16012.6i	0.550921	−	1.59178i
$467$	−1059.00	−	7365.51i	−0.104935	−	0.729839i	−0.972565	−	0.232630i	$-0.925267\pi$
$467$	−1059.00	−	7365.51i	−0.104935	−	0.729839i	0.867630	−	0.497210i	$-0.165642\pi$
$468$	−15020.7	−	19559.2i	−1.48361	−	1.93189i
$469$	−2982.39	+	1916.67i	−0.293633	+	0.188707i
$470$	17552.6	−	7026.99i	1.72264	−	0.689640i
$471$	83.3694	+	76.6680i	0.00815596	+	0.00750037i
$472$	2280.67	+	3202.76i	0.222408	+	0.312328i
$473$	14066.1	+	11061.7i	1.36735	+	1.07530i
$474$	−185.931	−	710.216i	−0.0180171	−	0.0688213i
$475$	−396.682	−	1635.14i	−0.0383179	−	0.157948i
$476$	612.376	+	4259.17i	0.0589668	+	0.410123i
$477$	2571.14	+	1210.13i	0.246801	+	0.116159i
$478$	13659.1	+	8778.16i	1.30701	+	0.839966i
$479$	6467.57	+	1246.52i	0.616933	+	0.118904i	0.488137	−	0.872767i	$-0.337677\pi$
$479$	6467.57	+	1246.52i	0.616933	+	0.118904i	0.128796	+	0.991671i	$0.458889\pi$
$480$	−8097.37	−	4999.69i	−0.769984	−	0.475424i
$481$	−2382.40	−	227.491i	−0.225838	−	0.0215649i
$482$	−8618.11	+	14927.0i	−0.814407	+	1.41059i
$483$	−1456.92	−	2617.91i	−0.137251	−	0.246624i
$484$	−12071.3	−	20908.1i	−1.13367	−	1.96357i
$485$	2846.03	+	6231.94i	0.266457	+	0.583459i
$486$	16886.7	−	4867.69i	1.57612	−	0.454327i
$487$	9328.73	−	10765.9i	0.868018	−	1.00175i	−0.131927	−	0.991259i	$-0.542116\pi$
$487$	9328.73	−	10765.9i	0.868018	−	1.00175i	0.999945	−	0.0104870i	$-0.00333819\pi$
$488$	132.947	−	2790.91i	0.0123325	−	0.258890i
$489$	8676.67	+	6573.46i	0.802398	+	0.607898i
$490$	16032.3	+	6418.37i	1.47809	+	0.591739i
$491$	5949.09	−	5672.45i	0.546800	−	0.521373i	−0.365546	−	0.930793i	$-0.619118\pi$
$491$	5949.09	−	5672.45i	0.546800	−	0.521373i	0.912346	+	0.409421i	$0.134269\pi$
$492$	−20904.9	−	5730.50i	−1.91558	−	0.525103i
$493$	−16826.8	+	6736.43i	−1.53720	+	0.615403i
$494$	−15601.4	+	34162.3i	−1.42093	+	3.11141i
$495$	204.385	−	17770.7i	0.0185584	−	1.61361i
$496$	−225.784	+	1570.36i	−0.0204395	+	0.142160i
$497$	−3984.60	−	2054.20i	−0.359625	−	0.185400i
$498$	−1719.92	+	2509.97i	−0.154762	+	0.225852i
$499$	5005.96	+	2004.08i	0.449093	+	0.179790i	0.585174	−	0.810908i	$-0.301026\pi$
$499$	5005.96	+	2004.08i	0.449093	+	0.179790i	−0.136080	+	0.990698i	$0.543451\pi$
$500$	−17375.9	+	3348.94i	−1.55415	+	0.299538i
$501$	8136.11	−	6639.43i	0.725538	−	0.592071i
$502$	27523.8	+	5304.77i	2.44710	+	0.471641i
$503$	−11707.4	+	3437.61i	−1.03779	+	0.304722i	−0.755874	−	0.654717i	$-0.772788\pi$
$503$	−11707.4	+	3437.61i	−1.03779	+	0.304722i	−0.281915	+	0.959439i	$0.590970\pi$
$504$	725.419	−	3544.00i	0.0641126	−	0.313219i
$505$	−10290.6			−0.906782
$506$	−10981.9	−	26371.8i	−0.964832	−	2.31693i
$507$	8210.11	+	9136.43i	0.719179	+	0.800322i
$508$	23050.8	+	2201.08i	2.01321	+	0.192239i
$509$	2276.06	−	9382.07i	0.198202	−	0.817000i	−0.782684	−	0.622419i	$-0.786150\pi$
$509$	2276.06	−	9382.07i	0.198202	−	0.817000i	0.980886	−	0.194581i	$-0.0623347\pi$
$510$	−8378.99	+	15137.4i	−0.727506	+	1.31430i
$511$	−38.4268	+	806.678i	−0.00332662	+	0.0698343i
$512$	−2529.61	−	2919.33i	−0.218348	−	0.251987i
$513$	−11684.1	−	12094.3i	−1.00558	−	1.04089i
$514$	−34947.3	−	10261.4i	−2.99895	−	0.880570i
$515$	15909.8	+	8202.08i	1.36130	+	0.701800i
$516$	1477.89	+	22479.5i	0.126087	+	1.91784i
$517$	−11190.8	−	15715.3i	−0.951976	−	1.33686i
$518$	−498.502	−	700.048i	−0.0422836	−	0.0593791i
$519$	−4070.36	+	2720.90i	−0.344256	+	0.230124i
$520$	−18142.1	−	9352.89i	−1.52997	−	0.788752i
$521$	−197.989	−	58.1347i	−0.0166488	−	0.00488854i	0.273398	−	0.961901i	$-0.411853\pi$
$521$	−197.989	−	58.1347i	−0.0166488	−	0.00488854i	−0.290046	+	0.957013i	$0.593671\pi$
$522$	37278.4	−	1346.31i	3.12573	−	0.112885i
$523$	8583.73	+	9906.15i	0.717668	+	0.828233i	0.991025	−	0.133680i	$-0.0426794\pi$
$523$	8583.73	+	9906.15i	0.717668	+	0.828233i	−0.273357	+	0.961913i	$0.588134\pi$
$524$	−1292.36	+	27130.0i	−0.107742	+	2.26179i
$525$	−196.566	−	326.700i	−0.0163407	−	0.0271587i
$526$	−3686.22	+	15194.8i	−0.305564	+	1.25955i
$527$	−8967.90	−	856.331i	−0.741267	−	0.0707824i
$528$	963.703	−	2956.01i	0.0794315	−	0.243644i
$529$	−3193.39	−	11740.5i	−0.262463	−	0.964942i
$530$	5757.65			0.471880
$531$	3929.27	−	1309.53i	0.321122	−	0.107022i
$532$	−8130.64	+	2387.37i	−0.662609	+	0.194560i
$533$	20454.1	+	3942.20i	1.66222	+	0.320367i
$534$	5589.08	+	34447.1i	0.452927	+	2.79152i
$535$	6734.90	−	1298.05i	0.544253	−	0.104896i
$536$	−16138.4	−	6460.85i	−1.30051	−	0.520646i
$537$	−2286.18	−	176.730i	−0.183717	−	0.0142020i
$538$	−4553.92	−	2347.71i	−0.364932	−	0.188136i
$539$	2507.82	−	17442.3i	0.200407	−	1.39386i
$540$	16812.6	−	14762.1i	1.33981	−	1.17640i
$541$	−3667.16	+	8029.96i	−0.291430	+	0.638142i	−0.997551	−	0.0699491i	$-0.977716\pi$
$541$	−3667.16	+	8029.96i	−0.291430	+	0.638142i	0.706121	+	0.708091i	$0.250444\pi$
$542$	5161.35	−	2066.29i	0.409039	−	0.163754i
$543$	2700.87	−	2669.99i	0.213454	−	0.211013i
$544$	6841.98	−	6523.81i	0.539242	−	0.514166i
$545$	10899.3	+	4363.41i	0.856649	+	0.342950i
$546$	−1058.91	+	8444.20i	−0.0829987	+	0.661865i
$547$	1184.95	−	24875.2i	0.0926233	−	1.94440i	−0.182951	−	0.983122i	$-0.558565\pi$
$547$	1184.95	−	24875.2i	0.0926233	−	1.94440i	0.275574	−	0.961280i	$-0.411132\pi$
$548$	11981.7	−	13827.6i	0.934001	−	1.07790i
$549$	−2770.13	−	994.569i	−0.215348	−	0.0773173i
$550$	−1510.23	−	3306.93i	−0.117084	−	0.256378i
$551$	−17847.0	−	30911.9i	−1.37987	−	2.39001i
$552$	6312.67	−	13265.4i	0.486749	−	1.02285i
$553$	−79.5931	+	137.859i	−0.00612051	+	0.0106010i
$554$	791.935	+	75.6206i	0.0607330	+	0.00579930i
$555$	64.1512	−	2170.28i	0.00490643	−	0.165988i
$556$	−10709.7	−	2064.12i	−0.816892	−	0.157443i
$557$	−14639.2	−	9408.01i	−1.11361	−	0.715674i	−0.151533	−	0.988452i	$-0.548421\pi$
$557$	−14639.2	−	9408.01i	−1.11361	−	0.715674i	−0.962077	+	0.272779i	$0.912057\pi$
$558$	16775.3	+	7895.45i	1.27268	+	0.598998i
$559$	−3081.01	−	21428.9i	−0.233118	−	1.62137i
$560$	−155.760	−	642.053i	−0.0117537	−	0.0484495i
$561$	17026.5	+	4667.34i	1.28139	+	0.351257i
$562$	−31881.2	−	25071.7i	−2.39293	−	1.88182i
$563$	2976.71	+	4180.20i	0.222830	+	0.312921i	0.910824	−	0.412796i	$-0.135448\pi$
$563$	2976.71	+	4180.20i	0.222830	+	0.312921i	−0.687994	+	0.725717i	$0.741508\pi$
$564$	5299.21	−	23703.0i	0.395633	−	1.76964i
$565$	3031.32	−	1213.56i	0.225715	−	0.0903625i
$566$	−31566.1	+	20286.3i	−2.34421	+	1.50653i
$567$	−3345.97	−	1823.57i	−0.247827	−	0.135067i
$568$	−3128.36	−	21758.2i	−0.231097	−	1.60731i
$569$	−5950.07	+	17191.6i	−0.438383	+	1.26663i	0.482194	+	0.876065i	$0.339840\pi$
$569$	−5950.07	+	17191.6i	−0.438383	+	1.26663i	−0.920577	+	0.390561i	$0.872281\pi$
$570$	−31855.1	−	12090.5i	−2.34081	−	0.888445i
$571$	3266.70	+	9438.51i	0.239417	+	0.691750i	0.999138	+	0.0415015i	$0.0132141\pi$
$571$	3266.70	+	9438.51i	0.239417	+	0.691750i	−0.759721	+	0.650249i	$0.774665\pi$
$572$	−12020.6	+	49549.5i	−0.878681	+	3.62197i
$573$	−5268.97	+	12111.3i	−0.384144	+	0.882995i
$574$	3740.09	+	6478.02i	0.271966	+	0.471058i
$575$	−456.671	−	1479.51i	−0.0331209	−	0.107304i
$576$	−19906.9	+	8815.93i	−1.44003	+	0.637727i
$577$	8057.13	+	17642.6i	0.581322	+	1.27292i	0.940546	+	0.339666i	$0.110314\pi$
$577$	8057.13	+	17642.6i	0.581322	+	1.27292i	−0.359225	+	0.933251i	$0.616959\pi$
$578$	4057.41	+	3868.73i	0.291983	+	0.278405i
$579$	32.7901	+	54.4983i	0.00235356	+	0.00391170i
$580$	42210.7	−	21761.1i	3.02190	−	1.55790i
$581$	647.829	−	124.859i	0.0462590	−	0.00891569i
$582$	13799.4	+	2402.15i	0.982822	+	0.171087i
$583$	−1385.11	−	5709.50i	−0.0983968	−	0.405597i
$584$	−3331.37	+	2140.94i	−0.236049	+	0.151700i
$585$	−15015.3	+	15389.3i	−1.06121	+	1.08764i
$586$	−1635.49	+	3581.23i	−0.115293	+	0.252456i
$587$	−4740.96	+	452.707i	−0.333357	+	0.0318317i	−0.260392	−	0.965503i	$-0.583852\pi$
$587$	−4740.96	+	452.707i	−0.333357	+	0.0318317i	−0.0729642	+	0.997335i	$0.523246\pi$
$588$	18443.3	−	12328.7i	1.29352	−	0.864674i
$589$	−844.148	−	17720.8i	−0.0590535	−	1.23969i
$590$	6073.41	−	5790.98i	0.423794	−	0.404087i
$591$	−2839.69	−	7749.31i	−0.197647	−	0.539364i
$592$	124.237	−	358.958i	0.00862516	−	0.0249208i
$593$	7428.71	+	4774.14i	0.514436	+	0.330608i	0.771967	−	0.635662i	$-0.219273\pi$
$593$	7428.71	+	4774.14i	0.514436	+	0.330608i	−0.257532	+	0.966270i	$0.582909\pi$
$594$	−29734.5	−	20881.8i	−2.05391	−	1.44241i
$595$	3599.56	−	1056.93i	0.248013	−	0.0728232i
$596$	11261.6	−	15814.8i	0.773984	−	1.08691i
$597$	8255.90	−	1746.30i	0.565983	−	0.119718i
$598$	−12401.5	+	32259.4i	−0.848049	+	2.20599i
$599$	−2990.38	+	5179.48i	−0.203979	+	0.353302i	−0.949807	−	0.312837i	$-0.898721\pi$
$599$	−2990.38	+	5179.48i	−0.203979	+	0.353302i	0.745828	+	0.666139i	$0.232054\pi$
$600$	745.827	−	1714.36i	0.0507471	−	0.116647i
$601$	17888.5	+	17056.7i	1.21412	+	1.15766i	0.982778	+	0.184792i	$0.0591612\pi$
$601$	17888.5	+	17056.7i	1.21412	+	1.15766i	0.231345	+	0.972872i	$0.425687\pi$
$602$	5091.00	−	5875.33i	0.344674	−	0.397775i
$603$	−11484.4	+	14262.9i	−0.775591	+	0.963237i
$604$	25045.9	+	28904.5i	1.68726	+	1.94720i
$605$	−16545.4	+	13011.4i	−1.11184	+	0.874362i
$606$	−11892.5	+	17355.3i	−0.797193	+	1.16338i
$607$	−929.474	−	19512.1i	−0.0621519	−	1.30473i	−0.787486	−	0.616332i	$-0.788618\pi$
$607$	−929.474	−	19512.1i	−0.0621519	−	1.30473i	0.725335	−	0.688396i	$-0.241685\pi$
$608$	14634.2	+	11508.5i	0.976144	+	0.767648i
$609$	−5953.61	−	5475.05i	−0.396145	−	0.364302i
$610$	−5936.46	+	566.863i	−0.394033	+	0.0376256i
$611$	−3321.73	+	23103.1i	−0.219939	+	1.52971i
$612$	9956.69	+	19871.1i	0.657639	+	1.31249i
$613$	−7402.51	−	2173.57i	−0.487740	−	0.143213i	0.0286106	−	0.999591i	$-0.490892\pi$
$613$	−7402.51	−	2173.57i	−0.487740	−	0.143213i	−0.516351	+	0.856377i	$0.672710\pi$
$614$	−28556.9	+	22457.4i	−1.87698	+	1.47607i
$615$	−2351.45	+	18751.4i	−0.154178	+	1.22948i
$616$	−6647.66	+	3427.11i	−0.434808	+	0.224159i
$617$	3765.04	+	10878.4i	0.245664	+	0.709801i	0.998659	+	0.0517738i	$0.0164875\pi$
$617$	3765.04	+	10878.4i	0.245664	+	0.709801i	−0.752994	+	0.658027i	$0.771391\pi$
$618$	32219.4	−	17353.4i	2.09718	−	1.12954i
$619$	−15607.0	+	21916.9i	−1.01341	+	1.42313i	−0.110205	+	0.993909i	$0.535151\pi$
$619$	−15607.0	+	21916.9i	−1.01341	+	1.42313i	−0.903200	+	0.429219i	$0.858789\pi$
$620$	23603.8			1.52895
$621$	−11414.8	−	10449.2i	−0.737617	−	0.675219i
$622$	−38150.3			−2.45930
$623$	4389.21	−	6163.78i	0.282263	−	0.396383i
$624$	−3311.71	+	1783.68i	−0.212459	+	0.114430i
$625$	5619.89	+	16237.6i	0.359673	+	1.03921i
$626$	−264.971	+	136.602i	−0.0169175	+	0.00872160i
$627$	−4326.00	+	34497.3i	−0.275541	+	2.19727i
$628$	231.730	−	182.235i	0.0147246	−	0.0115796i
$629$	2069.53	+	607.670i	0.131189	+	0.0385205i
$630$	−7707.41	−	456.044i	−0.487414	−	0.0288400i
$631$	2853.63	−	19847.5i	0.180034	−	1.25216i	−0.676644	−	0.736311i	$-0.736566\pi$
$631$	2853.63	−	19847.5i	0.180034	−	1.25216i	0.856677	−	0.515852i	$-0.172525\pi$
$632$	−777.029	+	74.1973i	−0.0489060	+	0.00466995i
$633$	−10947.2	−	10067.3i	−0.687382	−	0.632128i
$634$	6087.83	+	4787.52i	0.381354	+	0.299900i
$635$	−960.591	−	20165.3i	−0.0600313	−	1.26021i
$636$	4180.88	−	6101.37i	0.260665	−	0.380401i
$637$	−16757.9	+	13178.6i	−1.04234	+	0.819709i
$638$	−50504.5	−	58285.3i	−3.13400	−	3.61683i
$639$	−22880.5	−	3558.76i	−1.41649	−	0.220317i
$640$	−19292.8	+	22265.1i	−1.19159	+	1.37516i
$641$	−18962.1	−	18080.3i	−1.16842	−	1.11409i	−0.991533	−	0.129856i	$-0.958549\pi$
$641$	−18962.1	−	18080.3i	−1.16842	−	1.11409i	−0.176888	−	0.984231i	$-0.556603\pi$
$642$	5594.12	−	12858.7i	0.343898	−	0.790485i
$643$	9079.66	−	15726.4i	0.556869	−	0.964525i	−0.440887	−	0.897563i	$-0.645336\pi$
$643$	9079.66	−	15726.4i	0.556869	−	0.964525i	0.997755	−	0.0669625i	$-0.0213308\pi$
$644$	−7333.33	+	2651.86i	−0.448717	+	0.162264i
$645$	19215.8	−	4064.57i	1.17306	−	0.248127i
$646$	19633.5	−	27571.4i	1.19577	−	1.67923i
$647$	14165.1	−	4159.24i	0.860720	−	0.252730i	0.178556	−	0.983930i	$-0.442857\pi$
$647$	14165.1	−	4159.24i	0.860720	−	0.252730i	0.682164	+	0.731199i	$0.261039\pi$
$648$	−2233.12	−	18551.4i	−0.135378	−	1.12464i
$649$	−7203.63	−	4629.49i	−0.435697	−	0.280005i
$650$	−1438.53	+	4156.37i	−0.0868060	+	0.250809i
$651$	−1383.21	−	3774.69i	−0.0832756	−	0.227253i
$652$	20505.6	−	19552.1i	1.23169	−	1.17441i
$653$	−274.234	−	5756.89i	−0.0164343	−	0.344999i	−0.992077	−	0.125633i	$-0.959904\pi$
$653$	−274.234	−	5756.89i	−0.0164343	−	0.344999i	0.975643	−	0.219367i	$-0.0703991\pi$
$654$	19954.9	−	13339.2i	1.19312	−	0.797560i
$655$	23572.8	−	2250.93i	1.40620	−	0.134276i
$656$	−1373.44	+	3007.41i	−0.0817435	+	0.178993i
$657$	1129.12	+	4015.72i	0.0670492	+	0.238460i
$658$	−7051.02	+	4531.41i	−0.417747	+	0.268469i
$659$	6884.98	+	28380.3i	0.406981	+	1.67760i	0.694238	+	0.719746i	$0.255742\pi$
$659$	6884.98	+	28380.3i	0.406981	+	1.67760i	−0.287256	+	0.957854i	$0.592743\pi$
$660$	−45571.8	−	7933.00i	−2.68769	−	0.467866i
$661$	12723.6	−	2452.27i	0.748700	−	0.144300i	0.199391	−	0.979920i	$-0.436103\pi$
$661$	12723.6	−	2452.27i	0.748700	−	0.144300i	0.549308	+	0.835620i	$0.314891\pi$
$662$	20604.8	−	10622.5i	1.20971	−	0.623649i
$663$	−11011.6	−	18301.7i	−0.645031	−	1.07206i
$664$	2341.33	+	2232.45i	0.136839	+	0.130476i
$665$	3069.06	+	6720.30i	0.178967	+	0.391883i
$666$	−3586.09	−	2616.32i	−0.208646	−	0.152223i
$667$	−18137.9	−	27385.5i	−1.05293	−	1.58976i
$668$	−13666.6	−	23671.2i	−0.791579	−	1.37106i
$669$	6515.58	−	14976.7i	0.376542	−	0.865522i
$670$	−8747.22	+	36056.5i	−0.504380	+	2.07908i
$671$	1990.25	+	5750.44i	0.114505	+	0.330840i
$672$	3944.20	+	1497.00i	0.226415	+	0.0859347i
$673$	−971.644	+	2807.38i	−0.0556525	+	0.160797i	−0.969401	−	0.245484i	$-0.921053\pi$
$673$	−971.644	+	2807.38i	−0.0556525	+	0.160797i	0.913748	+	0.406281i	$0.133174\pi$
$674$	3160.80	+	21983.8i	0.180637	+	1.25636i
$675$	−1496.78	−	1279.90i	−0.0853499	−	0.0729830i
$676$	26896.0	−	17285.0i	1.53027	−	0.983443i
$677$	−25944.6	+	10386.6i	−1.47287	+	0.589647i	−0.962734	−	0.270449i	$-0.912828\pi$
$677$	−25944.6	+	10386.6i	−1.47287	+	0.589647i	−0.510132	+	0.860096i	$0.670404\pi$
$678$	1456.51	−	6514.87i	0.0825027	−	0.369029i
$679$	−1761.70	−	2473.96i	−0.0995698	−	0.139826i
$680$	14459.8	+	11371.3i	0.815454	+	0.641280i
$681$	18505.2	+	5072.69i	1.04130	+	0.285442i
$682$	−9037.13	−	37251.5i	−0.507404	−	2.09155i
$683$	1373.60	+	9553.62i	0.0769538	+	0.535226i	0.991435	+	0.130598i	$0.0416898\pi$
$683$	1373.60	+	9553.62i	0.0769538	+	0.535226i	−0.914482	+	0.404628i	$0.867401\pi$
$684$	−35943.6	+	24977.4i	−2.00927	+	1.39625i
$685$	−13419.5	−	8624.18i	−0.748514	−	0.481041i
$686$	−15685.2	−	3023.07i	−0.872979	−	0.168253i
$687$	165.267	−	5591.12i	0.00917809	−	0.310502i
$688$	3420.57	+	326.625i	0.189546	+	0.0180995i
$689$	−3553.92	+	6155.58i	−0.196508	+	0.340361i
$690$	−29942.0	−	9306.85i	−1.65199	−	0.513487i
$691$	8518.18	+	14753.9i	0.468954	+	0.812252i	0.999370	−	0.0354855i	$-0.0112978\pi$
$691$	8518.18	+	14753.9i	0.468954	+	0.812252i	−0.530416	+	0.847737i	$0.677964\pi$
$692$	5293.84	+	11591.9i	0.290811	+	0.636788i
$693$	1401.93	+	7752.67i	0.0768470	+	0.424963i
$694$	12982.8	−	14982.9i	0.710114	−	0.819516i
$695$	−452.459	+	9498.27i	−0.0246946	+	0.518403i
$696$	4934.89	−	39352.8i	0.268759	−	2.14319i
$697$	−17428.7	−	6977.41i	−0.947146	−	0.379180i
$698$	28922.9	−	27578.0i	1.56841	−	1.49547i
$699$	−13496.2	+	13341.9i	−0.730291	+	0.721940i
$700$	−921.304	+	368.835i	−0.0497458	+	0.0199152i
$701$	−5135.55	+	11245.3i	−0.276701	+	0.605890i	−0.996053	−	0.0887551i	$-0.971711\pi$
$701$	−5135.55	+	11245.3i	−0.276701	+	0.605890i	0.719353	+	0.694645i	$0.244438\pi$
$702$	8601.65	+	43108.5i	0.462462	+	2.31770i
$703$	−604.499	+	4204.38i	−0.0324312	+	0.225564i
$704$	40008.7	+	20625.9i	2.14188	+	1.10422i
$705$	−21112.6	−	1632.08i	−1.12786	−	0.0871880i
$706$	−11323.0	−	4533.04i	−0.603607	−	0.241648i
$707$	4479.44	−	863.342i	0.238284	−	0.0459255i
$708$	−1726.52	−	10641.1i	−0.0916479	−	0.564853i
$709$	−1575.09	−	303.573i	−0.0834325	−	0.0160803i	0.147364	−	0.989082i	$-0.452921\pi$
$709$	−1575.09	−	303.573i	−0.0834325	−	0.0160803i	−0.230797	+	0.973002i	$0.574133\pi$
$710$	−45016.2	+	13217.9i	−2.37948	+	0.698677i
$711$	−164.885	+	805.539i	−0.00869715	+	0.0424896i
$712$	37103.8			1.95298
$713$	−1775.81	−	16229.2i	−0.0932742	−	0.852438i
$714$	2377.36	−	7292.20i	0.124609	−	0.382218i
$715$	44251.3	+	4225.49i	2.31455	+	0.221013i
$716$	−1407.07	+	5800.03i	−0.0734424	+	0.302734i
$717$	−9375.15	−	15581.8i	−0.488315	−	0.811595i
$718$	2352.68	−	49388.9i	0.122286	−	2.56710i
$719$	−18212.1	−	21017.9i	−0.944640	−	1.09017i	−0.995807	−	0.0914820i	$-0.970840\pi$
$719$	−18212.1	−	21017.9i	−0.944640	−	1.09017i	0.0511672	−	0.998690i	$-0.483706\pi$
$720$	−1811.84	−	2891.87i	−0.0937824	−	0.149686i
$721$	−7613.59	−	2235.55i	−0.393266	−	0.115473i
$722$	30961.9	+	15962.0i	1.59596	+	0.822775i
$723$	16048.9	−	10728.1i	0.825537	−	0.551845i
$724$	−5733.91	−	8052.15i	−0.294336	−	0.413336i
$725$	−2424.75	−	3405.08i	−0.124211	−	0.174430i
$726$	2823.11	+	42941.0i	0.144319	+	2.19516i
$727$	2693.46	+	1388.57i	0.137407	+	0.0708382i	0.525559	−	0.850757i	$-0.323856\pi$
$727$	2693.46	+	1388.57i	0.137407	+	0.0708382i	−0.388152	+	0.921595i	$0.626886\pi$
$728$	8681.83	+	2549.22i	0.441992	+	0.129781i
$729$	−19374.4	−	3471.58i	−0.984323	−	0.176374i
$730$	5534.84	+	6387.55i	0.280622	+	0.323855i
$731$	−928.389	+	19489.3i	−0.0469736	+	0.986098i
$732$	−3710.02	+	6702.48i	−0.187331	+	0.338430i
$733$	−7616.93	+	31397.4i	−0.383817	+	1.58211i	0.372580	+	0.928000i	$0.378473\pi$
$733$	−7616.93	+	31397.4i	−0.383817	+	1.58211i	−0.756397	+	0.654113i	$0.773042\pi$
$734$	26770.7	+	2556.29i	1.34622	+	0.128548i
$735$	−12927.7	−	14386.3i	−0.648771	−	0.721970i
$736$	14091.5	+	9744.51i	0.705731	+	0.488027i
$737$	37859.3			1.89222
$738$	28907.1	+	25636.1i	1.44185	+	1.27870i
$739$	−12558.9	+	3687.64i	−0.625153	+	0.183562i	−0.578940	−	0.815370i	$-0.696533\pi$
$739$	−12558.9	+	3687.64i	−0.625153	+	0.183562i	−0.0462131	+	0.998932i	$0.514715\pi$
$740$	−5549.20	−	1069.52i	−0.275666	−	0.0531302i
$741$	32588.7	−	26593.8i	1.61562	−	1.31842i
$742$	−2506.28	+	483.046i	−0.124001	+	0.0238991i
$743$	26405.9	+	10571.3i	1.30382	+	0.521972i	0.916523	−	0.399982i	$-0.130984\pi$
$743$	26405.9	+	10571.3i	1.30382	+	0.521972i	0.387300	+	0.921954i	$0.373408\pi$
$744$	11142.8	−	16261.2i	0.549078	−	0.801296i
$745$	−15045.0	−	7756.23i	−0.739874	−	0.381431i
$746$	−627.629	+	4365.26i	−0.0308031	+	0.214240i
$747$	2970.64	−	1669.85i	0.145502	−	0.0817892i
$748$	19089.1	−	41799.2i	0.933109	−	2.04322i
$749$	−2822.77	+	1130.07i	−0.137706	+	0.0551292i
$750$	30420.0	+	8338.79i	1.48104	+	0.405986i
$751$	−5428.18	+	5175.76i	−0.263751	+	0.251486i	−0.810402	−	0.585875i	$-0.800751\pi$
$751$	−5428.18	+	5175.76i	−0.263751	+	0.251486i	0.546651	+	0.837361i	$0.315903\pi$
$752$	−3439.22	−	1376.86i	−0.166776	−	0.0667670i
$753$	−25023.3	−	18957.7i	−1.21102	−	0.917474i
$754$	−4439.62	+	93199.0i	−0.214431	+	4.50147i
$755$	21836.2	−	25200.3i	1.05258	−	1.21475i
$756$	−6079.96	+	7836.37i	−0.292495	+	0.376992i
$757$	−7615.10	−	16674.7i	−0.365621	−	0.800599i	−0.999628	−	0.0272715i	$-0.991318\pi$
$757$	−7615.10	−	16674.7i	−0.365621	−	0.800599i	0.634007	−	0.773328i	$-0.281409\pi$
$758$	−559.762	−	969.537i	−0.0268225	−	0.0464580i
$759$	−2025.92	+	31930.5i	−0.0968859	+	1.52701i
$760$	−18113.2	+	31373.0i	−0.864520	+	1.49739i
$761$	10721.9	+	1023.82i	0.510733	+	0.0487691i	0.347242	−	0.937776i	$-0.387118\pi$
$761$	10721.9	+	1023.82i	0.510733	+	0.0487691i	0.163491	+	0.986545i	$0.447724\pi$
$762$	−35119.3	−	21684.3i	−1.66960	−	1.03089i
$763$	−5110.48	−	984.964i	−0.242479	−	0.0467341i
$764$	28920.2	+	18585.9i	1.36950	+	0.880121i
$765$	15912.8	−	11057.9i	0.752064	−	0.522612i
$766$	−1178.10	−	8193.88i	−0.0555699	−	0.386497i
$767$	2442.39	+	10067.7i	0.114980	+	0.473953i
$768$	6765.28	+	25841.8i	0.317866	+	1.21418i
$769$	16574.0	+	13033.9i	0.777207	+	0.611202i	0.925938	−	0.377675i	$-0.123276\pi$
$769$	16574.0	+	13033.9i	0.777207	+	0.611202i	−0.148731	+	0.988878i	$0.547519\pi$
$770$	9259.32	+	13002.9i	0.433354	+	0.608561i
$771$	30026.5	+	27612.9i	1.40257	+	1.28983i
$772$	153.687	−	61.5270i	0.00716492	−	0.00286840i
$773$	−9572.45	+	6151.84i	−0.445404	+	0.286243i	−0.744055	−	0.668119i	$-0.767100\pi$
$773$	−9572.45	+	6151.84i	−0.445404	+	0.286243i	0.298651	+	0.954362i	$0.403463\pi$
$774$	15352.1	−	37105.2i	0.712947	−	1.72315i
$775$	−295.683	−	2056.52i	−0.0137049	−	0.0953193i
$776$	4870.83	−	14073.3i	0.225325	−	0.651035i
$777$	154.154	+	950.097i	0.00711744	+	0.0438668i
$778$	16457.0	+	47549.3i	0.758369	+	2.19116i
$779$	8716.23	−	35928.8i	0.400888	−	1.65248i
$780$	33279.2	+	44992.7i	1.52767	+	2.06538i
$781$	23936.9	+	41459.9i	1.09671	+	1.89955i
$782$	16477.1	−	26433.1i	0.753477	−	1.20876i
$783$	−38116.1	−	17106.2i	−1.73966	−	0.780750i
$784$	−1405.65	−	3077.94i	−0.0640329	−	0.140212i
$785$	−186.016	−	177.366i	−0.00845756	−	0.00806427i
$786$	23446.0	−	42357.3i	1.06398	−	1.92218i
$787$	−4583.21	+	2362.81i	−0.207591	+	0.107020i	−0.558887	−	0.829244i	$-0.688771\pi$
$787$	−4583.21	+	2362.81i	−0.207591	+	0.107020i	0.351296	+	0.936264i	$0.385741\pi$
$788$	−21093.5	+	4065.43i	−0.953583	+	0.183788i
$789$	11227.0	−	13439.2i	0.506578	−	0.606400i
$790$	392.769	+	1619.02i	0.0176887	+	0.0729140i
$791$	−1217.71	+	782.574i	−0.0547367	+	0.0351771i
$792$	−26978.5	+	27650.5i	−1.21040	+	1.24055i
$793$	3058.25	−	6696.64i	0.136951	−	0.299880i
$794$	−19046.4	+	1818.71i	−0.851299	+	0.0812892i
$795$	−5784.06	−	2850.95i	−0.258037	−	0.127186i
$796$	−1045.09	−	21939.2i	−0.0465356	−	0.976903i
$797$	−14146.2	+	13488.4i	−0.628712	+	0.599476i	−0.935940	−	0.352160i	$-0.885447\pi$
$797$	−14146.2	+	13488.4i	−0.628712	+	0.599476i	0.307227	+	0.951636i	$0.400599\pi$
$798$	14880.7	+	2590.39i	0.660116	+	0.114911i
$799$	6880.13	−	19878.8i	0.304633	−	0.880179i
$800$	1834.19	+	1178.76i	0.0810605	+	0.0520944i
$801$	11442.1	−	37372.6i	0.504726	−	1.64856i
$802$	18124.2	−	5321.75i	0.797990	−	0.234311i
$803$	5002.62	−	7025.20i	0.219849	−	0.308735i
$804$	31857.3	+	35451.6i	1.39741	+	1.55508i
$805$	3198.37	+	5999.42i	0.140035	+	0.262673i
$806$	−23187.5	+	40162.0i	−1.01333	+	1.75514i
$807$	3412.32	+	4613.39i	0.148847	+	0.201238i
$808$	16189.2	+	15436.4i	0.704870	+	0.672092i
$809$	−522.532	+	603.034i	−0.0227086	+	0.0262071i	−0.766990	−	0.641659i	$-0.778247\pi$
$809$	−522.532	+	603.034i	−0.0227086	+	0.0262071i	0.744282	+	0.667866i	$0.232792\pi$
$810$	−38513.4	+	10352.6i	−1.67065	+	0.449079i
$811$	−9345.05	−	10784.8i	−0.404623	−	0.466960i	0.516468	−	0.856306i	$-0.327246\pi$
$811$	−9345.05	−	10784.8i	−0.404623	−	0.466960i	−0.921091	+	0.389347i	$0.872701\pi$
$812$	−16548.4	+	13013.8i	−0.715192	+	0.562433i
$813$	−6208.16	−	479.914i	−0.267810	−	0.0207027i
$814$	436.690	+	9167.25i	0.0188034	+	0.394732i
$815$	−19417.2	−	15269.8i	−0.834544	−	0.656293i
$816$	3234.97	−	1013.64i	0.138783	−	0.0434860i
$817$	−38250.0	+	3652.44i	−1.63794	+	0.156405i
$818$	2831.24	−	19691.7i	0.121017	−	0.841694i
$819$	5244.98	−	7958.60i	0.223778	−	0.339556i
$820$	47196.2	+	13858.1i	2.00996	+	0.590176i
$821$	1890.22	−	1486.49i	0.0803523	−	0.0631898i	−0.577175	−	0.816621i	$-0.695845\pi$
$821$	1890.22	−	1486.49i	0.0803523	−	0.0631898i	0.657527	+	0.753431i	$0.271602\pi$
$822$	−30053.3	+	12665.6i	−1.27522	+	0.537424i
$823$	17940.4	−	9248.90i	0.759856	−	0.391733i	−0.0343276	−	0.999411i	$-0.510929\pi$
$823$	17940.4	−	9248.90i	0.759856	−	0.391733i	0.794184	+	0.607678i	$0.207899\pi$
$824$	−12725.9	−	36769.1i	−0.538020	−	1.55451i
$825$	−120.302	+	4069.90i	−0.00507681	+	0.171752i
$826$	−2157.89	+	3030.33i	−0.0908988	+	0.127650i
$827$	−15555.9			−0.654089			−0.327044	−	0.945009i	$-0.606053\pi$
$827$	−15555.9			−0.654089			−0.327044	+	0.945009i	$0.606053\pi$
$828$	−31604.6	+	24971.3i	−1.32649	+	1.04808i
$829$	34769.1			1.45667			0.728336	−	0.685220i	$-0.240294\pi$
$829$	34769.1			1.45667			0.728336	+	0.685220i	$0.240294\pi$
$830$	4005.11	−	5624.40i	0.167493	−	0.235212i
$831$	−758.123	−	468.100i	−0.0316474	−	0.0195406i
$832$	−17811.2	−	51462.1i	−0.742178	−	2.14438i
$833$	17077.9	−	8804.29i	0.710343	−	0.366207i
$834$	15496.2	+	11739.9i	0.643391	+	0.487434i
$835$	−18731.9	+	14730.9i	−0.776338	+	0.610519i
$836$	86827.9	+	25495.0i	3.59211	+	1.05474i
$837$	−12942.8	−	16238.1i	−0.534490	−	0.670575i
$838$	−10560.0	+	73446.3i	−0.435309	+	3.02764i
$839$	38869.3	−	3711.57i	1.59943	−	0.152727i	0.743106	−	0.669174i	$-0.233352\pi$
$839$	38869.3	−	3711.57i	1.59943	−	0.152727i	0.856319	+	0.516447i	$0.172746\pi$
$840$	−1791.05	+	8011.24i	−0.0735678	+	0.329064i
$841$	−50534.9	−	39741.1i	−2.07204	−	1.62947i
$842$	−1252.49	−	26293.0i	−0.0512632	−	1.07615i
$843$	19613.0	+	40972.9i	0.801315	+	1.67400i
$844$	−30428.4	+	23929.2i	−1.24098	+	0.975920i
$845$	−18253.6	−	21065.8i	−0.743129	−	0.857617i
$846$	−27151.6	+	33720.6i	−1.10342	+	1.37038i
$847$	6110.51	−	7051.90i	0.247886	−	0.286076i
$848$	−816.476	−	778.508i	−0.0330636	−	0.0315260i
$849$	41755.9	−	4749.15i	1.68794	−	0.191979i
$850$	1981.97	−	3432.87i	0.0799777	−	0.138525i
$851$	−317.879	+	3895.91i	−0.0128046	+	0.156933i
$852$	−18681.2	+	57301.7i	−0.751183	+	2.30414i
$853$	18597.4	−	26116.4i	0.746497	−	1.04831i	−0.250287	−	0.968172i	$-0.580525\pi$
$853$	18597.4	−	26116.4i	0.746497	−	1.04831i	0.996784	−	0.0801369i	$-0.0255357\pi$
$854$	2536.56	−	744.800i	0.101638	−	0.0298437i
$855$	26014.5	+	27919.2i	1.04056	+	1.11675i
$856$	−12542.5	−	8060.60i	−0.500812	−	0.321852i
$857$	1038.81	−	3001.43i	0.0414060	−	0.119635i	−0.922403	−	0.386229i	$-0.873777\pi$
$857$	1038.81	−	3001.43i	0.0414060	−	0.119635i	0.963809	+	0.266595i	$0.0858985\pi$
$858$	58266.1	−	69747.5i	2.31838	−	2.77522i
$859$	11167.8	−	10648.5i	0.443587	−	0.422959i	−0.435082	−	0.900391i	$-0.643281\pi$
$859$	11167.8	−	10648.5i	0.443587	−	0.422959i	0.878669	+	0.477432i	$0.158432\pi$
$860$	−2432.48	−	51064.1i	−0.0964500	−	2.02473i
$861$	−549.598	−	8359.67i	−0.0217541	−	0.330891i
$862$	−5537.71	+	528.787i	−0.218811	+	0.0208939i
$863$	−6721.60	+	14718.2i	−0.265128	+	0.580550i	−0.994638	−	0.103421i	$-0.967021\pi$
$863$	−6721.60	+	14718.2i	−0.265128	+	0.580550i	0.729509	+	0.683971i	$0.239748\pi$
$864$	21772.6	+	894.289i	0.857313	+	0.0352134i
$865$	9346.63	−	6006.72i	0.367393	−	0.236109i
$866$	−1187.44	−	4894.68i	−0.0465944	−	0.192065i
$867$	−2160.39	−	5895.54i	−0.0846258	−	0.230938i
$868$	−10274.6	+	1980.27i	−0.401778	+	0.0774364i
$869$	1510.99	−	778.969i	0.0589837	−	0.0304082i
$870$	−84635.8	+	1527.81i	−3.29819	+	0.0595374i
$871$	−33149.2	−	31607.7i	−1.28957	−	1.22961i
$872$	−10601.5	−	23214.0i	−0.411710	−	0.901520i
$873$	−12673.2	−	9246.04i	−0.491321	−	0.358455i
$874$	56143.2	+	24710.0i	2.17285	+	0.956327i
$875$	−3419.66	−	5923.02i	−0.132121	−	0.228839i
$876$	10788.0	−	1226.98i	0.416086	−	0.0473240i
$877$	−1860.34	+	7668.42i	−0.0716296	+	0.295261i	−0.996347	−	0.0853920i	$-0.972786\pi$
$877$	−1860.34	+	7668.42i	−0.0716296	+	0.295261i	0.924718	+	0.380653i	$0.124301\pi$
$878$	−6824.94	−	19719.4i	−0.262335	−	0.757969i
$879$	3416.27	−	2787.83i	0.131090	−	0.106975i
$880$	−2307.61	+	6667.39i	−0.0883970	+	0.255406i
$881$	7045.28	+	49001.0i	0.269423	+	1.87388i	0.453919	+	0.891043i	$0.350026\pi$
$881$	7045.28	+	49001.0i	0.269423	+	1.87388i	−0.184496	+	0.982833i	$0.559065\pi$
$882$	−39203.0	+	5177.10i	−1.49664	+	0.197644i
$883$	−33247.7	+	21367.0i	−1.26713	+	0.814334i	−0.989243	−	0.146280i	$-0.953270\pi$
$883$	−33247.7	+	21367.0i	−1.26713	+	0.814334i	−0.277885	+	0.960614i	$0.589634\pi$
$884$	−51611.3	+	20662.1i	−1.96366	+	0.786131i
$885$	−8968.72	+	2810.25i	−0.340656	+	0.106741i
$886$	39447.6	+	55396.4i	1.49579	+	2.10054i
$887$	3271.69	+	2572.89i	0.123847	+	0.0973947i	0.678162	−	0.734913i	$-0.262777\pi$
$887$	3271.69	+	2572.89i	0.123847	+	0.0973947i	−0.554314	+	0.832308i	$0.687019\pi$
$888$	−3356.46	+	3318.08i	−0.126842	+	0.125391i
$889$	2109.93	+	8697.26i	0.0796006	+	0.328118i
$890$	−11270.1	−	78385.6i	−0.424468	−	2.95224i
$891$	19531.1	+	35700.8i	0.734364	+	1.34234i
$892$	−35762.5	−	22983.2i	−1.34240	−	0.862705i
$893$	40677.4	+	7839.93i	1.52432	+	0.293789i
$894$	−30468.1	+	16410.1i	−1.13983	+	0.613910i
$895$	5179.84	+	494.615i	0.193456	+	0.0184728i
$896$	6530.11	−	11310.5i	0.243477	−	0.421715i
$897$	28431.8	−	26266.7i	1.05832	−	0.977724i
$898$	−848.659	−	1469.92i	−0.0315369	−	0.0546235i
$899$	−18309.7	−	40092.6i	−0.679268	−	1.48739i
$900$	−3912.30	+	3312.03i	−0.144900	+	0.122668i
$901$	4195.00	−	4841.29i	0.155112	−	0.179009i
$902$	3800.92	−	79791.0i	0.140307	−	2.94540i
$903$	−8023.57	+	3381.43i	−0.295689	+	0.124614i
$904$	−6589.30	−	2637.96i	−0.242430	−	0.0970544i
$905$	−6237.33	+	5947.28i	−0.229100	+	0.218447i
$906$	−17265.5	−	65950.3i	−0.633121	−	2.41838i
$907$	37291.7	−	14929.3i	1.36521	−	0.546549i	0.430707	−	0.902492i	$-0.358264\pi$
$907$	37291.7	−	14929.3i	1.36521	−	0.546549i	0.934508	+	0.355943i	$0.115840\pi$
$908$	20747.0	−	45429.5i	0.758273	−	1.66039i
$909$	20540.6	−	11546.2i	0.749494	−	0.421303i
$910$	2748.41	−	19115.6i	0.100119	−	0.696346i
$911$	−15107.6	−	7788.53i	−0.549438	−	0.283255i	0.161071	−	0.986943i	$-0.448505\pi$
$911$	−15107.6	−	7788.53i	−0.549438	−	0.283255i	−0.710509	+	0.703688i	$0.751535\pi$
$912$	2882.50	+	6021.74i	0.104659	+	0.218640i
$913$	−6540.86	−	2618.57i	−0.237099	−	0.0949199i
$914$	−21222.0	+	4090.21i	−0.768011	+	0.148022i
$915$	6244.38	+	2370.02i	0.225610	+	0.0856290i
$916$	−14295.9	−	2755.32i	−0.515667	−	0.0993867i
$917$	−10072.3	+	2957.49i	−0.362722	+	0.106505i
$918$	−259.448	−	39616.5i	−0.00932794	−	1.42434i
$919$	48409.2			1.73762			0.868809	−	0.495148i	$-0.164886\pi$
$919$	48409.2			1.73762			0.868809	+	0.495148i	$0.164886\pi$
$920$	−14866.1	+	29839.2i	−0.532739	+	1.06931i
$921$	39807.9	−	8420.23i	1.42423	−	0.301255i
$922$	−47072.6	−	4494.89i	−1.68140	−	0.160554i
$923$	13654.9	−	56286.2i	0.486951	−	2.00724i
$924$	20502.7	−	370.106i	0.729968	−	0.0131771i
$925$	−23.6694	+	496.882i	−0.000841346	+	0.0176620i
$926$	−31857.4	−	36765.4i	−1.13056	−	1.30474i
$927$	−40959.9	+	1479.26i	−1.45124	+	0.0524113i
$928$	44379.4	+	13031.0i	1.56985	+	0.460951i
$929$	−35405.1	−	18252.6i	−1.25038	−	0.644617i	−0.299478	−	0.954103i	$-0.596813\pi$
$929$	−35405.1	−	18252.6i	−1.25038	−	0.644617i	−0.950904	+	0.309486i	$0.899843\pi$
$930$	−37738.0	−	18601.0i	−1.33062	−	0.655860i
$931$	21948.2	+	30822.0i	0.772636	+	1.08502i
$932$	28652.2	+	40236.4i	1.00701	+	1.41415i
$933$	38325.2	+	18890.4i	1.34481	+	0.662855i
$934$	30685.6	+	15819.5i	1.07502	+	0.554209i
$935$	−38440.1	−	11287.0i	−1.34452	−	0.394786i
$936$	46706.8	−	1686.81i	1.63105	−	0.0589051i
$937$	26623.8	+	30725.5i	0.928242	+	1.07125i	0.997285	+	0.0736345i	$0.0234598\pi$
$937$	26623.8	+	30725.5i	0.928242	+	1.07125i	−0.0690435	+	0.997614i	$0.521995\pi$
$938$	782.615	−	16429.1i	0.0272423	−	0.571886i
$939$	333.826	−	6.02608i	0.0116017	−	0.000209429i
$940$	−12994.1	+	53562.5i	−0.450874	+	1.85853i
$941$	−56367.2	−	5382.41i	−1.95273	−	0.186463i	−0.957829	−	0.287338i	$-0.907230\pi$
$941$	−56367.2	−	5382.41i	−1.95273	−	0.186463i	−0.994899	+	0.100875i	$0.967836\pi$
$942$	−514.103	+	108.744i	−0.0177817	+	0.00376122i
$943$	5977.60	−	33493.2i	0.206423	−	1.15662i
$944$	−1644.27			−0.0566911
$945$	7516.95	+	4274.52i	0.258758	+	0.147143i
$946$	−79658.2	+	23389.8i	−2.73775	+	0.803876i
$947$	−23825.7	−	4592.03i	−0.817562	−	0.157572i	−0.236709	−	0.971581i	$-0.576069\pi$
$947$	−23825.7	−	4592.03i	−0.817562	−	0.157572i	−0.580853	+	0.814009i	$0.697281\pi$
$948$	2000.88	+	759.423i	0.0685500	+	0.0260178i
$949$	−10245.4	+	1974.64i	−0.350453	+	0.0675443i
$950$	7247.06	+	2901.29i	0.247501	+	0.0990844i
$951$	−3745.17	−	7823.91i	−0.127703	−	0.266780i
$952$	−7248.30	−	3736.76i	−0.246763	−	0.127215i
$953$	3143.90	−	21866.3i	0.106863	−	0.743251i	−0.863978	−	0.503529i	$-0.832035\pi$
$953$	3143.90	−	21866.3i	0.106863	−	0.743251i	0.970842	−	0.239722i	$-0.0770563\pi$
$954$	−11492.6	+	6460.20i	−0.390029	+	0.219242i
$955$	12450.8	−	27263.3i	0.421882	−	0.923792i
$956$	−43941.3	+	17591.4i	−1.48657	+	0.595134i
$957$	21875.7	+	83560.4i	0.738915	+	2.82249i
$958$	−22116.1	+	21087.7i	−0.745865	+	0.711181i
$959$	6564.98	+	2628.22i	0.221058	+	0.0884981i
$960$	45527.7	−	19187.0i	1.53062	−	0.645062i
$961$	−375.144	+	7875.25i	−0.0125925	+	0.264350i
$962$	7271.13	−	8391.34i	0.243691	−	0.281234i
$963$	−11986.9	+	10147.7i	−0.401112	+	0.339568i
$964$	−20872.9	−	45705.2i	−0.697375	−	1.52704i
$965$	−72.1651	−	124.994i	−0.00240733	−	0.00416962i
$966$	13814.4	+	1539.21i	0.460115	+	0.0512663i
$967$	9886.74	−	17124.3i	0.328786	−	0.569474i	−0.653485	−	0.756939i	$-0.726694\pi$
$967$	9886.74	−	17124.3i	0.328786	−	0.569474i	0.982271	+	0.187465i	$0.0600272\pi$
$968$	45547.1	+	4349.22i	1.51233	+	0.144410i
$969$	−33375.7	+	17976.2i	−1.10648	+	0.595952i
$970$	−31210.8	−	6015.40i	−1.03311	−	0.199116i
$971$	−40655.5	−	26127.7i	−1.34366	−	0.863520i	−0.346445	−	0.938070i	$-0.612611\pi$
$971$	−40655.5	−	26127.7i	−1.34366	−	0.863520i	−0.997217	+	0.0745506i	$0.976248\pi$
$972$	−16995.6	+	48330.1i	−0.560839	+	1.59484i
$973$	−599.917	−	4172.51i	−0.0197661	−	0.137477i
$974$	15581.5	+	64227.9i	0.512591	+	2.11293i
$975$	3503.19	−	3463.13i	0.115069	−	0.113753i
$976$	918.480	+	722.301i	0.0301228	+	0.0236888i
$977$	−8322.60	−	11687.5i	−0.272532	−	0.382717i	0.655514	−	0.755183i	$-0.272452\pi$
$977$	−8322.60	−	11687.5i	−0.272532	−	0.382717i	−0.928046	+	0.372465i	$0.878513\pi$
$978$	−48192.7	+	15100.6i	−1.57570	+	0.493727i
$979$	−75018.8	+	30033.0i	−2.44904	+	0.980448i
$980$	−42350.7	+	27217.2i	−1.38045	+	0.887163i
$981$	−26651.5	+	3519.56i	−0.867396	+	0.114547i
$982$	5427.38	+	37748.2i	0.176369	+	1.22668i
$983$	−6879.57	+	19877.2i	−0.223219	+	0.644949i	0.776668	+	0.629910i	$0.216908\pi$
$983$	−6879.57	+	19877.2i	−0.223219	+	0.644949i	−0.999887	+	0.0150387i	$0.995213\pi$
$984$	31827.3	−	25972.5i	1.03112	−	0.841437i
$985$	6125.56	+	17698.6i	0.198149	+	0.572513i
$986$	19825.2	−	81720.5i	0.640327	−	2.63946i
$987$	9327.12	−	1060.83i	0.300796	−	0.0342113i
$988$	−54740.6	−	94813.5i	−1.76268	−	3.05306i
$989$	−34927.0	+	5514.26i	−1.12297	+	0.177293i
$990$	66609.1	+	48596.2i	2.13836	+	1.56009i
$991$	18409.4	+	40310.9i	0.590103	+	1.29215i	0.935380	+	0.353645i	$0.115058\pi$
$991$	18409.4	+	40310.9i	0.590103	+	1.29215i	−0.345276	+	0.938501i	$0.612215\pi$
$992$	16637.9	+	15864.2i	0.532515	+	0.507752i
$993$	−25959.1	+	468.603i	−0.829596	+	0.0149755i
$994$	18486.4	−	9530.40i	0.589893	−	0.304111i
$995$	−18803.2	+	3624.03i	−0.599098	+	0.115467i
$996$	−3051.87	−	8328.33i	−0.0970906	−	0.264953i
$997$	−1916.36	−	7899.33i	−0.0608743	−	0.250927i	0.933242	−	0.359249i	$-0.116967\pi$
$997$	−1916.36	−	7899.33i	−0.0608743	−	0.250927i	−0.994116	+	0.108322i	$0.965452\pi$
$998$	−21045.6	+	13525.2i	−0.667523	+	0.428991i
$999$	2307.05	+	4404.00i	0.0730649	+	0.139476i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.m.a.4.9	✓	1400
9.7	even	3	inner	207.4.m.a.142.62	yes	1400
23.6	even	11	inner	207.4.m.a.121.62	yes	1400
207.52	even	33	inner	207.4.m.a.52.9	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.m.a.4.9	✓	1400	1.1	even	1	trivial
207.4.m.a.52.9	yes	1400	207.52	even	33	inner
207.4.m.a.121.62	yes	1400	23.6	even	11	inner
207.4.m.a.142.62	yes	1400	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	207.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.69115 + 3.77920i) q^{2} +(4.57480 - 2.46398i) q^{3} +(-4.42348 - 12.7808i) q^{4} +(-10.4806 + 5.40314i) q^{5} +(-2.99960 + 23.9200i) q^{6} +(4.10886 - 3.23125i) q^{7} +(24.5932 + 7.22121i) q^{8} +(14.8576 - 22.5445i) q^{9} +(7.78546 - 54.1490i) q^{10} +(-55.5691 + 5.30621i) q^{11} +(-51.7282 - 47.5702i) q^{12} +(53.0858 + 41.7472i) q^{13} +(1.15393 + 24.2240i) q^{14} +(-34.6335 + 50.5424i) q^{15} +(-8.42568 + 6.62603i) q^{16} +(-39.8585 - 45.9992i) q^{17} +(45.2160 + 116.820i) q^{18} +(78.4939 - 90.5868i) q^{19} +(115.417 + 110.050i) q^{20} +(10.8355 - 24.9065i) q^{21} +(129.492 - 224.287i) q^{22} +(66.9836 - 87.6367i) q^{23} +(130.302 - 27.5617i) q^{24} +(8.14250 - 11.4345i) q^{25} +(-300.633 + 88.2738i) q^{26} +(12.4211 - 139.745i) q^{27} +(-59.4734 - 38.2212i) q^{28} +(97.3973 - 281.411i) q^{29} +(-97.8055 - 266.904i) q^{30} +(107.120 - 102.138i) q^{31} +(7.39048 + 155.145i) q^{32} +(-241.143 + 161.196i) q^{33} +(281.105 - 26.8423i) q^{34} +(-25.6046 + 56.0663i) q^{35} +(-353.859 - 90.1665i) q^{36} +(-29.8116 + 19.1588i) q^{37} +(131.106 + 540.427i) q^{38} +(345.721 + 60.1821i) q^{39} +(-296.769 + 57.1976i) q^{40} +(274.154 - 141.336i) q^{41} +(64.9666 + 107.977i) q^{42} +(-232.004 - 221.215i) q^{43} +(313.627 + 686.746i) q^{44} +(-33.9056 + 316.558i) q^{45} +(150.933 + 488.988i) q^{46} +(172.805 + 299.307i) q^{47} +(-22.2194 + 51.0735i) q^{48} +(-74.4235 + 306.778i) q^{49} +(21.3007 + 61.5442i) q^{50} +(-295.686 - 112.226i) q^{51} +(298.738 - 863.147i) q^{52} +(14.9783 + 104.176i) q^{53} +(494.698 + 423.018i) q^{54} +(553.729 - 355.860i) q^{55} +(124.384 - 49.7957i) q^{56} +(135.889 - 607.824i) q^{57} +(801.397 + 1125.40i) q^{58} +(120.579 + 94.8244i) q^{59} +(799.173 + 219.071i) q^{60} +(-25.7000 - 105.937i) q^{61} +(97.7255 + 679.696i) q^{62} +(-11.7991 - 140.641i) q^{63} +(-678.352 - 435.951i) q^{64} +(-781.938 - 150.706i) q^{65} +(39.7606 - 1345.13i) q^{66} +(-675.145 - 64.4685i) q^{67} +(-411.593 + 712.900i) q^{68} +(90.5010 - 565.967i) q^{69} +(-142.980 - 247.648i) q^{70} +(-356.267 - 780.115i) q^{71} +(528.193 - 447.151i) q^{72} +(-101.175 + 116.762i) q^{73} +(7.82291 - 164.223i) q^{74} +(9.07575 - 72.3737i) q^{75} +(-1504.99 - 602.506i) q^{76} +(-211.180 + 201.360i) q^{77} +(-1157.83 + 1144.59i) q^{78} +(-28.2719 + 11.3184i) q^{79} +(52.5051 - 114.970i) q^{80} +(-287.506 - 669.911i) q^{81} +(-203.654 + 1416.44i) q^{82} +(112.184 + 57.8350i) q^{83} +(-366.255 - 28.3129i) q^{84} +(666.282 + 266.739i) q^{85} +(1460.37 - 281.464i) q^{86} +(-247.820 - 1527.38i) q^{87} +(-1404.94 - 270.780i) q^{88} +(1388.95 - 407.833i) q^{89} +(-1105.09 - 980.041i) q^{90} +353.018 q^{91} +(-1416.37 - 468.446i) q^{92} +(238.383 - 731.203i) q^{93} +(-1596.19 - 152.417i) q^{94} +(-333.212 + 1373.52i) q^{95} +(416.085 + 691.548i) q^{96} +(27.6461 - 580.363i) q^{97} +(-959.089 - 1106.85i) q^{98} +(-705.996 + 1331.61i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1400 q - 9 q^{2} - 14 q^{3} + 263 q^{4} + 19 q^{5} - 35 q^{6} - 9 q^{7} - 74 q^{8} - 78 q^{9} - 68 q^{10} + 79 q^{11} + 54 q^{12} - 9 q^{13} + 159 q^{14} - 868 q^{15} + 1031 q^{16} - 308 q^{17} - 87 q^{18}+ \cdots + 7484 q^{99}+O(q^{100}) \) 1400 * q - 9 * q^2 - 14 * q^3 + 263 * q^4 + 19 * q^5 - 35 * q^6 - 9 * q^7 - 74 * q^8 - 78 * q^9 - 68 * q^10 + 79 * q^11 + 54 * q^12 - 9 * q^13 + 159 * q^14 - 868 * q^15 + 1031 * q^16 - 308 * q^17 - 87 * q^18 - 36 * q^19 + 119 * q^20 - 660 * q^21 - 52 * q^22 - 116 * q^23 + 2420 * q^24 + 1397 * q^25 + 432 * q^26 + 274 * q^27 - 324 * q^28 - 45 * q^29 + 768 * q^30 - 45 * q^31 + 111 * q^32 - 1664 * q^33 + 403 * q^34 - 536 * q^35 - 121 * q^36 - 180 * q^37 - 117 * q^38 - 46 * q^39 - 473 * q^40 - 333 * q^41 - 332 * q^42 - 9 * q^43 - 1908 * q^44 + 1762 * q^45 + 484 * q^46 + 216 * q^47 + 1072 * q^48 + 4615 * q^49 - 105 * q^50 + 1298 * q^51 - 708 * q^52 - 1380 * q^53 + 4116 * q^54 - 1328 * q^55 - 3971 * q^56 + 2154 * q^57 - 338 * q^58 + 1917 * q^59 + 154 * q^60 + 27 * q^61 - 3854 * q^62 - 4850 * q^63 - 5854 * q^64 + 3363 * q^65 - 2017 * q^66 + 603 * q^67 - 18454 * q^68 - 4653 * q^69 + 542 * q^70 - 5296 * q^71 - 8044 * q^72 - 36 * q^73 + 3243 * q^74 + 5140 * q^75 - 1029 * q^76 - 1661 * q^77 + 14687 * q^78 - 9 * q^79 + 10312 * q^80 - 294 * q^81 - 770 * q^82 - 2735 * q^83 + 2298 * q^84 + 241 * q^85 + 10507 * q^86 - 10268 * q^87 + 2183 * q^88 - 2980 * q^89 + 33928 * q^90 - 1452 * q^91 - 1973 * q^92 - 11406 * q^93 + 2034 * q^94 - 3339 * q^95 - 4446 * q^96 - 5193 * q^97 + 14820 * q^98 + 7484 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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