LMFDB - Embedded newform 129.2.n.b.20.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [129,2,Mod(5,129)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(129, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("129.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 129 = 3 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	129.n (of order $42$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.03007018607$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$12$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			20.5
Character	$\chi$	$=$	129.20
Dual form			129.2.n.b.71.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.606050 - 0.759962i) q^{2} +(-0.431951 - 1.67732i) q^{3} +(0.234796 - 1.02871i) q^{4} +(0.0149759 - 0.199839i) q^{5} +(-1.01292 + 1.34481i) q^{6} +(0.0942007 - 0.0543868i) q^{7} +(-2.67561 + 1.28851i) q^{8} +(-2.62684 + 1.44905i) q^{9} +O(q^{10})$	\(q+(-0.606050 - 0.759962i) q^{2} +(-0.431951 - 1.67732i) q^{3} +(0.234796 - 1.02871i) q^{4} +(0.0149759 - 0.199839i) q^{5} +(-1.01292 + 1.34481i) q^{6} +(0.0942007 - 0.0543868i) q^{7} +(-2.67561 + 1.28851i) q^{8} +(-2.62684 + 1.44905i) q^{9} +(-0.160946 + 0.109731i) q^{10} +(3.04483 - 0.694963i) q^{11} +(-1.82690 + 0.0505229i) q^{12} +(-2.93205 - 1.99904i) q^{13} +(-0.0984222 - 0.0386279i) q^{14} +(-0.341664 + 0.0612014i) q^{15} +(0.699432 + 0.336829i) q^{16} +(2.15961 - 0.161841i) q^{17} +(2.69321 + 1.11810i) q^{18} +(2.91075 - 3.13704i) q^{19} +(-0.202060 - 0.0623271i) q^{20} +(-0.131914 - 0.134513i) q^{21} +(-2.37346 - 1.89277i) q^{22} +(-0.722374 + 2.34188i) q^{23} +(3.31698 + 3.93129i) q^{24} +(4.90444 + 0.739226i) q^{25} +(0.257775 + 3.43977i) q^{26} +(3.56519 + 3.78014i) q^{27} +(-0.0338302 - 0.109675i) q^{28} +(0.956739 - 2.43773i) q^{29} +(0.253576 + 0.222561i) q^{30} +(5.18616 - 0.781688i) q^{31} +(1.15373 + 5.05482i) q^{32} +(-2.48090 - 4.80698i) q^{33} +(-1.43183 - 1.54314i) q^{34} +(-0.00945788 - 0.0196395i) q^{35} +(0.873873 + 3.04247i) q^{36} +(-4.96678 - 2.86757i) q^{37} +(-4.14809 - 0.310856i) q^{38} +(-2.08653 + 5.78149i) q^{39} +(0.217424 + 0.553988i) q^{40} +(3.78089 - 3.01516i) q^{41} +(-0.0222779 + 0.181771i) q^{42} +(1.33352 + 6.42041i) q^{43} -3.29541i q^{44} +(0.250237 + 0.546646i) q^{45} +(2.21753 - 0.870318i) q^{46} +(7.44244 + 1.69869i) q^{47} +(0.262850 - 1.31867i) q^{48} +(-3.49408 + 6.05193i) q^{49} +(-2.41055 - 4.17520i) q^{50} +(-1.20431 - 3.55247i) q^{51} +(-2.74486 + 2.54686i) q^{52} +(-6.81584 - 9.99701i) q^{53} +(0.712084 - 5.00036i) q^{54} +(-0.0932818 - 0.618885i) q^{55} +(-0.181967 + 0.266896i) q^{56} +(-6.51914 - 3.52722i) q^{57} +(-2.43241 + 0.750301i) q^{58} +(-1.96294 + 4.07608i) q^{59} +(-0.0172629 + 0.365842i) q^{60} +(0.478733 - 3.17619i) q^{61} +(-3.73713 - 3.46755i) q^{62} +(-0.168641 + 0.279366i) q^{63} +(4.11029 - 5.15415i) q^{64} +(-0.443397 + 0.556002i) q^{65} +(-2.14958 + 4.79866i) q^{66} +(0.190505 + 0.176763i) q^{67} +(0.340581 - 2.25961i) q^{68} +(4.24012 + 0.200078i) q^{69} +(-0.00919332 + 0.0190901i) q^{70} +(-9.73840 + 3.00390i) q^{71} +(5.16128 - 7.26177i) q^{72} +(-7.61510 + 11.1693i) q^{73} +(0.830869 + 5.51246i) q^{74} +(-0.878559 - 8.54565i) q^{75} +(-2.54366 - 3.73087i) q^{76} +(0.249029 - 0.231065i) q^{77} +(5.65826 - 1.91818i) q^{78} +(6.71699 + 11.6342i) q^{79} +(0.0777862 - 0.134730i) q^{80} +(4.80053 - 7.61281i) q^{81} +(-4.58281 - 1.04600i) q^{82} +(-2.55672 + 1.00344i) q^{83} +(-0.169347 + 0.104118i) q^{84} -0.433999i q^{85} +(4.07109 - 4.90452i) q^{86} +(-4.50213 - 0.551781i) q^{87} +(-7.25132 + 5.78273i) q^{88} +(-1.97459 - 5.03117i) q^{89} +(0.263774 - 0.521465i) q^{90} +(-0.384923 - 0.0288460i) q^{91} +(2.23950 + 1.29297i) q^{92} +(-3.55132 - 8.36123i) q^{93} +(-3.21955 - 6.68546i) q^{94} +(-0.583313 - 0.628662i) q^{95} +(7.98021 - 4.11861i) q^{96} +(3.10236 + 13.5923i) q^{97} +(6.71683 - 1.01240i) q^{98} +(-6.99124 + 6.23765i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 14 q^{3} - 48 q^{4} - 4 q^{6} - 42 q^{7}+O(q^{10}) $ 144 * q - 14 * q^3 - 48 * q^4 - 4 * q^6 - 42 * q^7	$ 144 q - 14 q^{3} - 48 q^{4} - 4 q^{6} - 42 q^{7} - 26 q^{10} - 4 q^{12} - 48 q^{13} - 19 q^{15} - 8 q^{16} + 16 q^{18} - 10 q^{19} - 15 q^{21} + 14 q^{22} - 11 q^{24} - 16 q^{25} - 14 q^{27} - 42 q^{28} - 6 q^{30} - 36 q^{31} + 7 q^{33} + 80 q^{34} + 48 q^{36} - 6 q^{37} + 7 q^{39} + 118 q^{40} + 46 q^{43} + 78 q^{46} - 41 q^{48} - 54 q^{49} + 7 q^{51} - 4 q^{52} - 52 q^{54} - 22 q^{55} - 110 q^{57} + 18 q^{58} - 9 q^{60} - 58 q^{61} - 82 q^{63} + 72 q^{64} - 127 q^{66} + 10 q^{67} - 15 q^{69} - 196 q^{70} + 179 q^{72} + 42 q^{73} + 119 q^{75} + 4 q^{76} + 62 q^{78} - 30 q^{79} + 200 q^{81} - 28 q^{82} + 111 q^{84} - 18 q^{87} - 14 q^{88} + 131 q^{90} - 38 q^{91} + 156 q^{93} + 28 q^{94} + 304 q^{96} + 72 q^{97} + 121 q^{99}+O(q^{100}) $ 144 * q - 14 * q^3 - 48 * q^4 - 4 * q^6 - 42 * q^7 - 26 * q^10 - 4 * q^12 - 48 * q^13 - 19 * q^15 - 8 * q^16 + 16 * q^18 - 10 * q^19 - 15 * q^21 + 14 * q^22 - 11 * q^24 - 16 * q^25 - 14 * q^27 - 42 * q^28 - 6 * q^30 - 36 * q^31 + 7 * q^33 + 80 * q^34 + 48 * q^36 - 6 * q^37 + 7 * q^39 + 118 * q^40 + 46 * q^43 + 78 * q^46 - 41 * q^48 - 54 * q^49 + 7 * q^51 - 4 * q^52 - 52 * q^54 - 22 * q^55 - 110 * q^57 + 18 * q^58 - 9 * q^60 - 58 * q^61 - 82 * q^63 + 72 * q^64 - 127 * q^66 + 10 * q^67 - 15 * q^69 - 196 * q^70 + 179 * q^72 + 42 * q^73 + 119 * q^75 + 4 * q^76 + 62 * q^78 - 30 * q^79 + 200 * q^81 - 28 * q^82 + 111 * q^84 - 18 * q^87 - 14 * q^88 + 131 * q^90 - 38 * q^91 + 156 * q^93 + 28 * q^94 + 304 * q^96 + 72 * q^97 + 121 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/129\mathbb{Z}\right)^\times$.

$n$	$44$	$46$
$\chi(n)$	$-1$	$e\left(\frac{37}{42}\right)$

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 $

$2$	−0.606050	−	0.759962i	−0.428542	−	0.537374i	0.519941	−	0.854202i	$-0.325954\pi$
$2$	−0.606050	−	0.759962i	−0.428542	−	0.537374i	−0.948483	+	0.316828i	$0.897382\pi$
$3$	−0.431951	−	1.67732i	−0.249387	−	0.968404i
$3$	−0.431951	−	1.67732i	−0.249387	−	0.968404i
$4$	0.234796	−	1.02871i	0.117398	−	0.514353i
$5$	0.0149759	−	0.199839i	0.00669742	−	0.0893708i	−0.992853	−	0.119340i	$-0.961922\pi$
$5$	0.0149759	−	0.199839i	0.00669742	−	0.0893708i	0.999551	+	0.0299696i	$0.00954105\pi$
$6$	−1.01292	+	1.34481i	−0.413523	+	0.549016i
$7$	0.0942007	−	0.0543868i	0.0356045	−	0.0205563i	−0.482092	−	0.876121i	$-0.660123\pi$
$7$	0.0942007	−	0.0543868i	0.0356045	−	0.0205563i	0.517697	+	0.855564i	$0.326790\pi$
$8$	−2.67561	+	1.28851i	−0.945971	+	0.455556i
$9$	−2.62684	+	1.44905i	−0.875612	+	0.483015i
$10$	−0.160946	+	0.109731i	−0.0508957	+	0.0347001i
$11$	3.04483	−	0.694963i	0.918051	−	0.209539i	0.262712	−	0.964874i	$-0.415383\pi$
$11$	3.04483	−	0.694963i	0.918051	−	0.209539i	0.655339	+	0.755335i	$0.272526\pi$
$12$	−1.82690	+	0.0505229i	−0.527379	+	0.0145847i
$13$	−2.93205	−	1.99904i	−0.813205	−	0.554434i	0.0837853	−	0.996484i	$-0.473299\pi$
$13$	−2.93205	−	1.99904i	−0.813205	−	0.554434i	−0.896990	+	0.442050i	$0.854251\pi$
$14$	−0.0984222	−	0.0386279i	−0.0263044	−	0.0103237i
$15$	−0.341664	+	0.0612014i	−0.0882173	+	0.0158021i
$16$	0.699432	+	0.336829i	0.174858	+	0.0842071i
$17$	2.15961	−	0.161841i	0.523783	−	0.0392521i	0.189785	−	0.981826i	$-0.439221\pi$
$17$	2.15961	−	0.161841i	0.523783	−	0.0392521i	0.333999	+	0.942574i	$0.391602\pi$
$18$	2.69321	+	1.11810i	0.634796	+	0.263539i
$19$	2.91075	−	3.13704i	0.667772	−	0.719687i	−0.304767	−	0.952427i	$-0.598579\pi$
$19$	2.91075	−	3.13704i	0.667772	−	0.719687i	0.972539	+	0.232740i	$0.0747692\pi$
$20$	−0.202060	−	0.0623271i	−0.0451819	−	0.0139368i
$21$	−0.131914	−	0.134513i	−0.0287861	−	0.0293531i
$22$	−2.37346	−	1.89277i	−0.506024	−	0.403541i
$23$	−0.722374	+	2.34188i	−0.150625	+	0.488316i	−0.999167	−	0.0408134i	$-0.987005\pi$
$23$	−0.722374	+	2.34188i	−0.150625	+	0.488316i	0.848541	+	0.529129i	$0.177481\pi$
$24$	3.31698	+	3.93129i	0.677075	+	0.802472i
$25$	4.90444	+	0.739226i	0.980889	+	0.147845i
$26$	0.257775	+	3.43977i	0.0505538	+	0.674594i
$27$	3.56519	+	3.78014i	0.686120	+	0.727488i
$28$	−0.0338302	−	0.109675i	−0.00639330	−	0.0207266i
$29$	0.956739	−	2.43773i	0.177662	−	0.452675i	−0.814107	−	0.580715i	$-0.802773\pi$
$29$	0.956739	−	2.43773i	0.177662	−	0.452675i	0.991769	+	0.128039i	$0.0408684\pi$
$30$	0.253576	+	0.222561i	0.0462965	+	0.0406338i
$31$	5.18616	−	0.781688i	0.931463	−	0.140395i	0.334255	−	0.942483i	$-0.391515\pi$
$31$	5.18616	−	0.781688i	0.931463	−	0.140395i	0.597207	+	0.802087i	$0.296277\pi$
$32$	1.15373	+	5.05482i	0.203952	+	0.893574i
$33$	−2.48090	−	4.80698i	−0.431869	−	0.836788i
$34$	−1.43183	−	1.54314i	−0.245556	−	0.264647i
$35$	−0.00945788	−	0.0196395i	−0.00159867	−	0.00331968i
$36$	0.873873	+	3.04247i	0.145646	+	0.507079i
$37$	−4.96678	−	2.86757i	−0.816534	−	0.471426i	0.0326859	−	0.999466i	$-0.489594\pi$
$37$	−4.96678	−	2.86757i	−0.816534	−	0.471426i	−0.849220	+	0.528040i	$0.822927\pi$
$38$	−4.14809	−	0.310856i	−0.672909	−	0.0504276i
$39$	−2.08653	+	5.78149i	−0.334113	+	0.925780i
$40$	0.217424	+	0.553988i	0.0343778	+	0.0875932i
$41$	3.78089	−	3.01516i	0.590476	−	0.470889i	−0.282088	−	0.959388i	$-0.591027\pi$
$41$	3.78089	−	3.01516i	0.590476	−	0.470889i	0.872564	+	0.488500i	$0.162456\pi$
$42$	−0.0222779	+	0.181771i	−0.00343755	+	0.0280479i
$43$	1.33352	+	6.42041i	0.203360	+	0.979104i
$43$	1.33352	+	6.42041i	0.203360	+	0.979104i
$44$		−	3.29541i		−	0.496802i
$45$	0.250237	+	0.546646i	0.0373031	+	0.0814891i
$46$	2.21753	−	0.870318i	0.326958	−	0.128321i
$47$	7.44244	+	1.69869i	1.08559	+	0.247779i	0.727639	−	0.685960i	$-0.240618\pi$
$47$	7.44244	+	1.69869i	1.08559	+	0.247779i	0.357953	+	0.933740i	$0.383475\pi$
$48$	0.262850	−	1.31867i	0.0379392	−	0.190333i
$49$	−3.49408	+	6.05193i	−0.499155	+	0.864562i
$50$	−2.41055	−	4.17520i	−0.340903	−	0.590462i
$51$	−1.20431	−	3.55247i	−0.168637	−	0.497445i
$52$	−2.74486	+	2.54686i	−0.380643	+	0.353185i
$53$	−6.81584	−	9.99701i	−0.936228	−	1.37319i	−0.927739	−	0.373231i	$-0.878250\pi$
$53$	−6.81584	−	9.99701i	−0.936228	−	1.37319i	−0.00848964	−	0.999964i	$-0.502702\pi$
$54$	0.712084	−	5.00036i	0.0969023	−	0.680462i
$55$	−0.0932818	−	0.618885i	−0.0125781	−	0.0834504i
$56$	−0.181967	+	0.266896i	−0.0243163	+	0.0356655i
$57$	−6.51914	−	3.52722i	−0.863481	−	0.467192i
$58$	−2.43241	+	0.750301i	−0.319392	+	0.0985193i
$59$	−1.96294	+	4.07608i	−0.255553	+	0.530660i	−0.988790	−	0.149312i	$-0.952294\pi$
$59$	−1.96294	+	4.07608i	−0.255553	+	0.530660i	0.733238	+	0.679973i	$0.238008\pi$
$60$	−0.0172629	+	0.365842i	−0.00222863	+	0.0472300i
$61$	0.478733	−	3.17619i	0.0612955	−	0.406669i	−0.937051	−	0.349192i	$-0.886456\pi$
$61$	0.478733	−	3.17619i	0.0612955	−	0.406669i	0.998347	−	0.0574775i	$-0.0183057\pi$
$62$	−3.73713	−	3.46755i	−0.474615	−	0.440379i
$63$	−0.168641	+	0.279366i	−0.0212468	+	0.0351969i
$64$	4.11029	−	5.15415i	0.513787	−	0.644268i
$65$	−0.443397	+	0.556002i	−0.0549966	+	0.0689635i
$66$	−2.14958	+	4.79866i	−0.264595	+	0.590674i
$67$	0.190505	+	0.176763i	0.0232739	+	0.0215950i	0.691724	−	0.722162i	$-0.256851\pi$
$67$	0.190505	+	0.176763i	0.0232739	+	0.0215950i	−0.668450	+	0.743757i	$0.733042\pi$
$68$	0.340581	−	2.25961i	0.0413015	−	0.274018i
$69$	4.24012	+	0.200078i	0.510451	+	0.0240865i
$70$	−0.00919332	+	0.0190901i	−0.00109881	+	0.00228171i
$71$	−9.73840	+	3.00390i	−1.15574	+	0.356497i	−0.812619	−	0.582795i	$-0.801959\pi$
$71$	−9.73840	+	3.00390i	−1.15574	+	0.356497i	−0.343117	+	0.939293i	$0.611483\pi$
$72$	5.16128	−	7.26177i	0.608263	−	0.855808i
$73$	−7.61510	+	11.1693i	−0.891279	+	1.30727i	0.0597648	+	0.998212i	$0.480965\pi$
$73$	−7.61510	+	11.1693i	−0.891279	+	1.30727i	−0.951044	+	0.309054i	$0.899987\pi$
$74$	0.830869	+	5.51246i	0.0965866	+	0.640810i
$75$	−0.878559	−	8.54565i	−0.101447	−	0.986767i
$76$	−2.54366	−	3.73087i	−0.291778	−	0.427960i
$77$	0.249029	−	0.231065i	0.0283794	−	0.0263323i
$78$	5.65826	−	1.91818i	0.640672	−	0.217192i
$79$	6.71699	+	11.6342i	0.755720	+	1.30895i	0.945016	+	0.327025i	$0.106046\pi$
$79$	6.71699	+	11.6342i	0.755720	+	1.30895i	−0.189296	+	0.981920i	$0.560620\pi$
$80$	0.0777862	−	0.134730i	0.00869676	−	0.0150632i
$81$	4.80053	−	7.61281i	0.533393	−	0.845868i
$82$	−4.58281	−	1.04600i	−0.506087	−	0.115511i
$83$	−2.55672	+	1.00344i	−0.280636	+	0.110142i	−0.501485	−	0.865167i	$-0.667213\pi$
$83$	−2.55672	+	1.00344i	−0.280636	+	0.110142i	0.220848	+	0.975308i	$0.429117\pi$
$84$	−0.169347	+	0.104118i	−0.0184773	+	0.0113602i
$85$		−	0.433999i		−	0.0470738i
$86$	4.07109	−	4.90452i	0.438997	−	0.528867i
$87$	−4.50213	−	0.551781i	−0.482679	−	0.0591571i
$88$	−7.25132	+	5.78273i	−0.772993	+	0.616441i
$89$	−1.97459	−	5.03117i	−0.209306	−	0.533303i	0.787212	−	0.616683i	$-0.211524\pi$
$89$	−1.97459	−	5.03117i	−0.209306	−	0.533303i	−0.996518	+	0.0833794i	$0.973429\pi$
$90$	0.263774	−	0.521465i	0.0278042	−	0.0549672i
$91$	−0.384923	−	0.0288460i	−0.0403509	−	0.00302388i
$92$	2.23950	+	1.29297i	0.233484	+	0.134802i
$93$	−3.55132	−	8.36123i	−0.368254	−	0.867019i
$94$	−3.21955	−	6.68546i	−0.332071	−	0.689553i
$95$	−0.583313	−	0.628662i	−0.0598466	−	0.0644993i
$96$	7.98021	−	4.11861i	0.814477	−	0.420354i
$97$	3.10236	+	13.5923i	0.314997	+	1.38009i	0.846209	+	0.532852i	$0.178880\pi$
$97$	3.10236	+	13.5923i	0.314997	+	1.38009i	−0.531212	+	0.847239i	$0.678263\pi$
$98$	6.71683	−	1.01240i	0.678502	−	0.102268i
$99$	−6.99124	+	6.23765i	−0.702646	+	0.626908i
$100$	1.91199	−	4.87167i	0.191199	−	0.487167i
$101$	4.71290	+	15.2789i	0.468951	+	1.52030i	0.813517	+	0.581541i	$0.197550\pi$
$101$	4.71290	+	15.2789i	0.468951	+	1.52030i	−0.344566	+	0.938762i	$0.611974\pi$
$102$	−1.96987	+	3.06820i	−0.195046	+	0.303797i
$103$	−1.03674	−	13.8344i	−0.102153	−	1.36314i	−0.779002	−	0.627021i	$-0.784274\pi$
$103$	−1.03674	−	13.8344i	−0.102153	−	1.36314i	0.676849	−	0.736122i	$-0.263345\pi$
$104$	10.4208	+	1.57068i	1.02184	+	0.154018i
$105$	−0.0288565	+	0.0243472i	−0.00281610	+	0.00237605i
$106$	−3.46661	+	11.2385i	−0.336707	+	1.09158i
$107$	11.5641	+	9.22203i	1.11794	+	0.891527i	0.994899	−	0.100874i	$-0.0321640\pi$
$107$	11.5641	+	9.22203i	1.11794	+	0.891527i	0.123041	+	0.992402i	$0.460735\pi$
$108$	4.72574	−	2.77997i	0.454735	−	0.267503i
$109$	8.42820	+	2.59976i	0.807275	+	0.249011i	0.670806	−	0.741633i	$-0.265948\pi$
$109$	8.42820	+	2.59976i	0.807275	+	0.249011i	0.136469	+	0.990644i	$0.456425\pi$
$110$	−0.413795	+	0.445965i	−0.0394538	+	0.0425211i
$111$	−2.66444	+	9.56956i	−0.252898	+	0.908302i
$112$	0.0842060	−	0.00631037i	0.00795672	−	0.000596274i
$113$	−9.56882	−	4.60810i	−0.900159	−	0.433494i	−0.0742125	−	0.997242i	$-0.523644\pi$
$113$	−9.56882	−	4.60810i	−0.900159	−	0.433494i	−0.825946	+	0.563749i	$0.809359\pi$
$114$	1.27037	+	7.09197i	0.118981	+	0.664224i
$115$	0.457181	+	0.179430i	0.0426324	+	0.0167320i
$116$	−2.28307	−	1.55657i	−0.211978	−	0.144524i
$117$	10.5987	+	1.00247i	0.979852	+	0.0926785i
$118$	4.28730	−	0.978549i	0.394678	−	0.0900827i
$119$	0.194635	−	0.132700i	0.0178422	−	0.0121646i
$120$	0.835301	−	0.603987i	0.0762522	−	0.0551362i
$121$	−1.12263	+	0.540630i	−0.102057	+	0.0491482i
$122$	−2.70392	+	1.56111i	−0.244801	+	0.141336i
$123$	−6.69056	−	5.03938i	−0.603268	−	0.454385i
$124$	0.413560	−	5.51858i	0.0371388	−	0.495583i
$125$	0.444140	−	1.94591i	0.0397251	−	0.174047i
$126$	0.314513	−	0.0411492i	0.0280190	−	0.00366586i
$127$	−4.57077	−	5.73157i	−0.405591	−	0.508595i	0.536524	−	0.843885i	$-0.319737\pi$
$127$	−4.57077	−	5.73157i	−0.405591	−	0.508595i	−0.942115	+	0.335290i	$0.891166\pi$
$128$	3.96162			0.350161
$129$	10.1931	−	5.01006i	0.897453	−	0.441111i
$130$	0.691261			0.0606276
$131$	13.7862	+	17.2874i	1.20451	+	1.51041i	0.804563	+	0.593867i	$0.202400\pi$
$131$	13.7862	+	17.2874i	1.20451	+	1.51041i	0.399946	+	0.916539i	$0.369029\pi$
$132$	−5.52748	+	1.42346i	−0.481105	+	0.123896i
$133$	0.103581	−	0.453818i	0.00898161	−	0.0393510i
$134$	0.0188776	−	0.251904i	0.00163077	−	0.0217612i
$135$	0.808812	−	0.655853i	0.0696114	−	0.0564468i
$136$	−5.56975	+	3.21570i	−0.477602	+	0.275744i
$137$	−10.0851	+	4.85674i	−0.861630	+	0.414939i	−0.811881	−	0.583823i	$-0.801556\pi$
$137$	−10.0851	+	4.85674i	−0.861630	+	0.414939i	−0.0497488	+	0.998762i	$0.515842\pi$
$138$	−2.41767	−	3.34359i	−0.205806	−	0.284625i
$139$	6.19418	−	4.22312i	0.525383	−	0.358200i	−0.271399	−	0.962467i	$-0.587486\pi$
$139$	6.19418	−	4.22312i	0.525383	−	0.358200i	0.796782	+	0.604267i	$0.206534\pi$
$140$	−0.0224239	+	0.00511812i	−0.00189517	+	0.000432560i
$141$	−0.365521	−	13.2171i	−0.0307824	−	1.11308i
$142$	8.18481	+	5.58031i	0.686854	+	0.468289i
$143$	−10.3169	−	4.04907i	−0.862740	−	0.338600i
$144$	−2.32537	+	0.128715i	−0.193781	+	0.0107262i
$145$	−0.472826	−	0.227701i	−0.0392661	−	0.0189096i
$146$	13.1034	−	0.981961i	1.08444	−	0.0812677i
$147$	11.6603	+	3.24657i	0.961728	+	0.267773i
$148$	−4.11607	+	4.43607i	−0.338339	+	0.364642i
$149$	−10.1582	−	3.13339i	−0.832191	−	0.256697i	−0.150752	−	0.988572i	$-0.548169\pi$
$149$	−10.1582	−	3.13339i	−0.832191	−	0.256697i	−0.681439	+	0.731875i	$0.738646\pi$
$150$	−5.96192	+	5.84676i	−0.486789	+	0.477386i
$151$	4.14212	+	3.30323i	0.337081	+	0.268813i	0.777371	−	0.629042i	$-0.216553\pi$
$151$	4.14212	+	3.30323i	0.337081	+	0.268813i	−0.440290	+	0.897856i	$0.645124\pi$
$152$	−3.74593	+	12.1440i	−0.303835	+	0.985010i
$153$	−5.43844	+	3.55451i	−0.439672	+	0.287365i
$154$	−0.326524	−	0.0492156i	−0.0263121	−	0.00396590i
$155$	−0.0785446	−	1.04811i	−0.00630886	−	0.0841859i
$156$	5.45755	+	3.50390i	0.436954	+	0.280537i
$157$	−2.70333	−	8.76397i	−0.215749	−	0.699441i	−0.997152	−	0.0754148i	$-0.975972\pi$
$157$	−2.70333	−	8.76397i	−0.215749	−	0.699441i	0.781403	−	0.624027i	$-0.214504\pi$
$158$	4.77069	−	12.1555i	0.379536	−	0.967042i
$159$	−13.8241	+	15.7506i	−1.09632	+	1.24910i
$160$	1.02743	−	0.154860i	0.0812254	−	0.0122428i
$161$	0.0593192	+	0.259894i	0.00467501	+	0.0204825i
$162$	−8.69481	+	0.965516i	−0.683129	+	0.0758581i
$163$	−11.8876	−	12.8118i	−0.931111	−	1.00350i	−0.999983	−	0.00587298i	$-0.998131\pi$
$163$	−11.8876	−	12.8118i	−0.931111	−	1.00350i	0.0688722	−	0.997625i	$-0.478060\pi$
$164$	−2.21398	−	4.59737i	−0.172883	−	0.358995i
$165$	−0.997777	+	0.423792i	−0.0776768	+	0.0329922i
$166$	2.31207	+	1.33487i	0.179452	+	0.103606i
$167$	−4.78760	−	0.358781i	−0.370476	−	0.0277633i	−0.111808	−	0.993730i	$-0.535664\pi$
$167$	−4.78760	−	0.358781i	−0.370476	−	0.0277633i	−0.258667	+	0.965966i	$0.583283\pi$
$168$	0.526272	+	0.189931i	0.0406028	+	0.0146535i
$169$	−0.148659	−	0.378778i	−0.0114353	−	0.0291368i
$170$	−0.329823	+	0.263025i	−0.0252963	+	0.0201731i
$171$	−3.10034	+	12.4583i	−0.237089	+	0.952710i
$172$	6.91783	+	0.135681i	0.527479	+	0.0103456i
$173$		−	25.4343i		−	1.93373i	−0.255287	−	0.966865i	$-0.582170\pi$
$173$		−	25.4343i		−	1.93373i	0.255287	−	0.966865i	$-0.417830\pi$
$174$	2.30918	+	3.75586i	0.175059	+	0.284731i
$175$	0.502206	−	0.197101i	0.0379632	−	0.0148995i
$176$	2.36374	+	0.539507i	0.178173	+	0.0406669i
$177$	7.68480	+	1.53181i	0.577625	+	0.115138i
$178$	−2.62680	+	4.54975i	−0.196887	+	0.341019i
$179$	−3.98263	−	6.89812i	−0.297676	−	0.515589i	0.677928	−	0.735128i	$-0.262878\pi$
$179$	−3.98263	−	6.89812i	−0.297676	−	0.515589i	−0.975604	+	0.219539i	$0.929545\pi$
$180$	0.621092	−	0.129070i	0.0462935	−	0.00962034i
$181$	−2.26008	+	2.09705i	−0.167991	+	0.155872i	−0.759688	−	0.650288i	$-0.774648\pi$
$181$	−2.26008	+	2.09705i	−0.167991	+	0.155872i	0.591698	+	0.806160i	$0.298458\pi$
$182$	0.211360	+	0.310009i	0.0156671	+	0.0229794i
$183$	−5.53429	+	0.568968i	−0.409106	+	0.0420593i
$184$	−1.08473	−	7.19674i	−0.0799676	−	0.530551i
$185$	−0.647435	+	0.949613i	−0.0476004	+	0.0698170i
$186$	−4.20194	+	7.76618i	−0.308101	+	0.569444i
$187$	6.46319	−	1.99363i	0.472635	−	0.145789i
$188$	3.49491	−	7.25725i	0.254892	−	0.529289i
$189$	0.541433	+	0.162193i	0.0393834	+	0.0117978i
$190$	−0.124243	+	0.824296i	−0.00901351	+	0.0598007i
$191$	−10.4775	−	9.72166i	−0.758123	−	0.703435i	0.203115	−	0.979155i	$-0.434893\pi$
$191$	−10.4775	−	9.72166i	−0.758123	−	0.703435i	−0.961238	+	0.275720i	$0.911084\pi$
$192$	−10.4206	−	4.66796i	−0.752044	−	0.336881i
$193$	4.83393	−	6.06155i	0.347954	−	0.436320i	−0.576801	−	0.816885i	$-0.695699\pi$
$193$	4.83393	−	6.06155i	0.347954	−	0.436320i	0.924754	+	0.380565i	$0.124270\pi$
$194$	8.44946	−	10.5953i	0.606636	−	0.760698i
$195$	1.12412	+	0.503554i	0.0805000	+	0.0360603i
$196$	5.40527	+	5.01535i	0.386090	+	0.358240i
$197$	−1.82361	+	12.0989i	−0.129927	+	0.862010i	0.824992	+	0.565144i	$0.191179\pi$
$197$	−1.82361	+	12.0989i	−0.129927	+	0.862010i	−0.954919	+	0.296866i	$0.904059\pi$
$198$	8.97742	+	1.53275i	0.637997	+	0.108928i
$199$	3.81894	−	7.93011i	0.270717	−	0.562150i	−0.720645	−	0.693305i	$-0.756154\pi$
$199$	3.81894	−	7.93011i	0.270717	−	0.562150i	0.991362	+	0.131154i	$0.0418683\pi$
$200$	−14.0749	+	4.34152i	−0.995244	+	0.306992i
$201$	0.214200	−	0.395892i	0.0151085	−	0.0279241i
$202$	8.75510	−	12.8414i	0.616007	−	0.903516i
$203$	−0.0424549	−	0.281670i	−0.00297975	−	0.0197694i
$204$	−3.93721	+	0.404776i	−0.275660	+	0.0283400i
$205$	−0.545925	−	0.800725i	−0.0381291	−	0.0559251i
$206$	−9.88529	+	9.17221i	−0.688741	+	0.639058i
$207$	−1.49593	−	7.19849i	−0.103974	−	0.500329i
$208$	−1.37744	−	2.38579i	−0.0955081	−	0.165425i
$209$	6.68261	−	11.5746i	0.462246	−	0.800634i
$210$	0.0359914	+	0.00717418i	0.00248364	+	0.000495065i
$211$	1.14166	+	0.260577i	0.0785952	+	0.0179388i	0.261638	−	0.965166i	$-0.415737\pi$
$211$	1.14166	+	0.260577i	0.0785952	+	0.0179388i	−0.183043	+	0.983105i	$0.558595\pi$
$212$	−11.8843	+	4.66425i	−0.816218	+	0.320342i
$213$	9.24503	+	15.0369i	0.633459	+	1.03031i
$214$		−	14.3773i		−	0.982809i
$215$	1.30302	−	0.170339i	0.0888653	−	0.0116170i
$216$	−14.4098	−	5.52042i	−0.980461	−	0.375617i
$217$	0.446027	−	0.355695i	0.0302783	−	0.0241461i
$218$	−3.13219	−	7.98069i	−0.212139	−	0.540521i
$219$	22.0239	+	7.94840i	1.48824	+	0.537103i
$220$	−0.658553	−	0.0493517i	−0.0443996	−	0.00332729i
$221$	−6.65563	−	3.84263i	−0.447706	−	0.258483i
$222$	8.88728	−	3.77475i	0.596475	−	0.253345i
$223$	6.84381	+	14.2113i	0.458295	+	0.951660i	0.994217	+	0.107392i	$0.0342499\pi$
$223$	6.84381	+	14.2113i	0.458295	+	0.951660i	−0.535922	+	0.844268i	$0.680036\pi$
$224$	0.383597	+	0.413420i	0.0256302	+	0.0276228i
$225$	−13.9543	+	5.16494i	−0.930289	+	0.344329i
$226$	2.29720	+	10.0647i	0.152807	+	0.669492i
$227$	11.8369	−	1.78412i	0.785640	−	0.118416i	0.256043	−	0.966665i	$-0.417581\pi$
$227$	11.8369	−	1.78412i	0.785640	−	0.118416i	0.529597	+	0.848249i	$0.322343\pi$
$228$	−5.15914	+	5.87810i	−0.341672	+	0.389287i
$229$	4.84951	−	12.3564i	0.320465	−	0.816531i	−0.676335	−	0.736594i	$-0.736433\pi$
$229$	4.84951	−	12.3564i	0.320465	−	0.816531i	0.996800	−	0.0799367i	$-0.0254718\pi$
$230$	−0.140714	−	0.456184i	−0.00927842	−	0.0300799i
$231$	−0.495139	−	0.317893i	−0.0325777	−	0.0209158i
$232$	0.581171	+	7.75518i	0.0381557	+	0.509153i
$233$	18.3333	+	2.76330i	1.20105	+	0.181030i	0.718935	−	0.695077i	$-0.244630\pi$
$233$	18.3333	+	2.76330i	1.20105	+	0.181030i	0.482117	+	0.876107i	$0.339868\pi$
$234$	−5.66151	−	8.66217i	−0.370104	−	0.566264i
$235$	0.450922	−	1.46185i	0.0294149	−	0.0953608i
$236$	3.73220	+	2.97633i	0.242946	+	0.193743i
$237$	16.6129	−	16.2920i	1.07912	−	1.05828i
$238$	−0.218806	−	0.0674926i	−0.0141831	−	0.00437489i
$239$	−16.9664	+	18.2855i	−1.09747	+	1.18279i	−0.115584	+	0.993298i	$0.536874\pi$
$239$	−16.9664	+	18.2855i	−1.09747	+	1.18279i	−0.981883	+	0.189491i	$0.939316\pi$
$240$	−0.259585	−	0.0722760i	−0.0167561	−	0.00466540i
$241$	−17.2565	+	1.29320i	−1.11159	+	0.0833023i	−0.617842	−	0.786302i	$-0.711993\pi$
$241$	−17.2565	+	1.29320i	−1.11159	+	0.0833023i	−0.493749	+	0.869604i	$0.664374\pi$
$242$	1.09123	+	0.525508i	0.0701468	+	0.0337809i
$243$	−14.8428	−	4.76369i	−0.952163	−	0.305591i
$244$	−3.15496	−	1.23823i	−0.201976	−	0.0792696i
$245$	1.15709	+	0.788888i	0.0739235	+	0.0504002i
$246$	0.225076	+	8.13869i	0.0143503	+	0.518904i
$247$	−14.8055	+	3.37927i	−0.942054	+	0.215018i
$248$	−12.8689	+	8.77389i	−0.817178	+	0.557143i
$249$	2.78747	+	3.85501i	0.176649	+	0.244301i
$250$	−1.74799	+	0.841785i	−0.110552	+	0.0532392i
$251$	12.3361	−	7.12226i	0.778648	−	0.449553i	−0.0573027	−	0.998357i	$-0.518250\pi$
$251$	12.3361	−	7.12226i	0.778648	−	0.449553i	0.835951	+	0.548804i	$0.184917\pi$
$252$	0.247790	+	0.239076i	0.0156093	+	0.0150604i
$253$	−0.571988	+	7.63265i	−0.0359606	+	0.479861i
$254$	−1.58566	+	6.94723i	−0.0994932	+	0.435908i
$255$	−0.727958	+	0.187467i	−0.0455865	+	0.0117396i
$256$	−10.6215	−	13.3190i	−0.663845	−	0.832436i
$257$	29.3458			1.83054			0.915270	−	0.402840i	$-0.131977\pi$
$257$	29.3458			1.83054			0.915270	+	0.402840i	$0.131977\pi$
$258$	−9.98498	−	4.71003i	−0.621638	−	0.293234i
$259$	−0.623832			−0.0387631
$260$	0.467855	+	0.586672i	0.0290151	+	0.0363838i
$261$	1.01919	+	7.78988i	0.0630861	+	0.482181i
$262$	4.78262	−	20.9540i	0.295471	−	1.29454i
$263$	−0.320197	+	4.27273i	−0.0197442	+	0.263468i	0.978592	+	0.205809i	$0.0659826\pi$
$263$	−0.320197	+	4.27273i	−0.0197442	+	0.263468i	−0.998336	+	0.0576587i	$0.981636\pi$
$264$	12.8317	+	9.66495i	0.789739	+	0.594837i
$265$	−2.09987	+	1.21236i	−0.128994	+	0.0744746i
$266$	−0.407660	+	0.196319i	−0.0249952	+	0.0120371i
$267$	−7.58599	+	5.48525i	−0.464255	+	0.335692i
$268$	0.226567	−	0.154471i	0.0138398	−	0.00943580i
$269$	1.20213	−	0.274377i	0.0732949	−	0.0167291i	−0.185716	−	0.982603i	$-0.559461\pi$
$269$	1.20213	−	0.274377i	0.0732949	−	0.0167291i	0.259011	+	0.965874i	$0.416603\pi$
$270$	−0.988603	−	0.217187i	−0.0601645	−	0.0132176i
$271$	−8.49140	−	5.78934i	−0.515816	−	0.351677i	0.277265	−	0.960793i	$-0.410572\pi$
$271$	−8.49140	−	5.78934i	−0.515816	−	0.351677i	−0.793081	+	0.609116i	$0.791524\pi$
$272$	1.56502	+	0.614223i	0.0948930	+	0.0372428i
$273$	0.117884	+	0.658101i	0.00713466	+	0.0398301i
$274$	9.80302	+	4.72089i	0.592222	+	0.285199i
$275$	15.4469	−	1.15759i	0.931485	−	0.0698052i
$276$	1.20138	−	4.31487i	0.0723148	−	0.259724i
$277$	−4.96806	+	5.35430i	−0.298502	+	0.321708i	−0.864437	−	0.502741i	$-0.832325\pi$
$277$	−4.96806	+	5.35430i	−0.298502	+	0.321708i	0.565935	+	0.824450i	$0.308515\pi$
$278$	−6.96339	−	2.14792i	−0.417636	−	0.128824i
$279$	−12.4905	+	9.56835i	−0.747787	+	0.572842i
$280$	0.0506112	+	0.0403611i	0.00302460	+	0.00241204i
$281$	−8.64814	+	28.0366i	−0.515904	+	1.67252i	0.204419	+	0.978883i	$0.434469\pi$
$281$	−8.64814	+	28.0366i	−0.515904	+	1.67252i	−0.720324	+	0.693638i	$0.756007\pi$
$282$	−9.82300	+	8.28803i	−0.584951	+	0.493545i
$283$	24.4727	+	3.68866i	1.45475	+	0.219268i	0.828339	−	0.560227i	$-0.189286\pi$
$283$	24.4727	+	3.68866i	1.45475	+	0.219268i	0.626409	+	0.779495i	$0.284524\pi$
$284$	0.803597	+	10.7233i	0.0476847	+	0.636309i
$285$	−0.802507	+	1.24996i	−0.0475364	+	0.0740410i
$286$	3.17539	+	10.2944i	0.187765	+	0.608719i
$287$	0.192178	−	0.489661i	0.0113439	−	0.0289038i
$288$	−10.3553	−	11.6064i	−0.610193	−	0.683912i
$289$	−12.1724	+	1.83469i	−0.716022	+	0.107923i
$290$	0.113512	+	0.497328i	0.00666565	+	0.0292041i
$291$	21.4587	−	11.0749i	1.25793	−	0.649221i
$292$	9.70193	+	10.4562i	0.567763	+	0.611903i
$293$	8.73568	+	18.1398i	0.510344	+	1.05974i	0.983857	+	0.178954i	$0.0572713\pi$
$293$	8.73568	+	18.1398i	0.510344	+	1.05974i	−0.473513	+	0.880787i	$0.657014\pi$
$294$	−4.59946	−	10.8290i	−0.268246	−	0.631560i
$295$	0.785164	+	0.453315i	0.0457140	+	0.0263930i
$296$	16.9841	+	1.27278i	0.987178	+	0.0739788i
$297$	13.4824	+	9.03222i	0.782331	+	0.524102i
$298$	3.77511	+	9.61882i	0.218686	+	0.557203i
$299$	6.79955	−	5.42246i	0.393228	−	0.313589i
$300$	−8.99725	−	1.10270i	−0.519456	−	0.0636645i
$301$	0.474805	+	0.532282i	0.0273673	+	0.0306802i
$302$		−	5.14978i		−	0.296337i
$303$	23.5919	−	14.5048i	1.35532	−	0.833279i
$304$	3.09251	−	1.21372i	0.177368	−	0.0696118i
$305$	−0.627558	−	0.143236i	−0.0359338	−	0.00820167i
$306$	5.99725	+	1.97880i	0.342840	+	0.113120i
$307$	1.37748	−	2.38586i	0.0786168	−	0.136168i	−0.824037	−	0.566537i	$-0.808283\pi$
$307$	1.37748	−	2.38586i	0.0786168	−	0.136168i	0.902653	+	0.430368i	$0.141616\pi$
$308$	−0.179227	−	0.310430i	−0.0102124	−	0.0176884i
$309$	−22.7569	+	7.71474i	−1.29460	+	0.438876i
$310$	−0.748918	+	0.694895i	−0.0425357	+	0.0394674i
$311$	−12.7187	−	18.6549i	−0.721212	−	1.05782i	−0.995368	−	0.0961384i	$-0.969351\pi$
$311$	−12.7187	−	18.6549i	−0.721212	−	1.05782i	0.274156	−	0.961685i	$-0.411602\pi$
$312$	−1.86673	−	18.1575i	−0.105683	−	1.02797i
$313$	3.31511	+	21.9943i	0.187381	+	1.24319i	0.862719	+	0.505684i	$0.168760\pi$
$313$	3.31511	+	21.9943i	0.187381	+	1.24319i	−0.675337	+	0.737509i	$0.736002\pi$
$314$	−5.02194	+	7.36583i	−0.283404	+	0.415678i
$315$	0.0533028	+	0.0378848i	0.00300327	+	0.00213457i
$316$	13.5453	−	4.17816i	0.761980	−	0.235040i
$317$	−1.73495	+	3.60266i	−0.0974444	+	0.202345i	−0.943993	−	0.329967i	$-0.892962\pi$
$317$	−1.73495	+	3.60266i	−0.0974444	+	0.202345i	0.846548	+	0.532312i	$0.178677\pi$
$318$	20.3480	+	0.960155i	1.14106	+	0.0538428i
$319$	1.21898	−	8.08738i	0.0682496	−	0.452806i
$320$	−0.968445	−	0.898586i	−0.0541377	−	0.0502325i
$321$	10.4732	−	23.3802i	0.584558	−	1.30495i
$322$	0.161560	−	0.202589i	0.00900336	−	0.0112899i
$323$	5.77839	−	7.24588i	0.321518	−	0.403171i
$324$	−6.70420	−	6.72579i	−0.372456	−	0.373655i
$325$	−12.9023	−	11.9716i	−0.715693	−	0.664066i
$326$	−2.53200	+	16.7987i	−0.140235	+	0.930396i
$327$	0.720061	−	15.2598i	0.0398195	−	0.843869i
$328$	−6.23114	+	12.9391i	−0.344057	+	0.714442i
$329$	0.793470	−	0.244753i	0.0437454	−	0.0134937i
$330$	0.926768	+	0.501434i	0.0510169	+	0.0276030i
$331$	16.1073	−	23.6251i	0.885340	−	1.29855i	−0.0683188	−	0.997664i	$-0.521763\pi$
$331$	16.1073	−	23.6251i	0.885340	−	1.29855i	0.953658	−	0.300891i	$-0.0972841\pi$
$332$	0.431937	+	2.86571i	0.0237056	+	0.157276i
$333$	17.2022	+	0.335551i	0.942673	+	0.0183881i
$334$	2.62886	+	3.85583i	0.143845	+	0.210982i
$335$	0.0381771	−	0.0354232i	0.00208584	−	0.00193538i
$336$	−0.0469574	−	0.138515i	−0.00256174	−	0.00755661i
$337$	−0.0825945	−	0.143058i	−0.00449921	−	0.00779286i	0.863767	−	0.503891i	$-0.168099\pi$
$337$	−0.0825945	−	0.143058i	−0.00449921	−	0.00779286i	−0.868266	+	0.496099i	$0.834765\pi$
$338$	−0.197762	+	0.342534i	−0.0107568	+	0.0186314i
$339$	−3.59602	+	18.0405i	−0.195309	+	0.979825i
$340$	−0.446458	−	0.101901i	−0.0242126	−	0.00552636i
$341$	15.2478	−	5.98430i	0.825712	−	0.324068i
$342$	11.3468	−	5.19420i	0.613565	−	0.280870i
$343$			1.52154i			0.0821556i
$344$	−11.8407	−	15.4603i	−0.638409	−	0.833562i
$345$	0.103483	−	0.844347i	0.00557134	−	0.0454581i
$346$	−19.3291	+	15.4144i	−1.03914	+	0.828684i
$347$	−8.80044	−	22.4232i	−0.472433	−	1.20374i	−0.946343	−	0.323165i	$-0.895253\pi$
$347$	−8.80044	−	22.4232i	−0.472433	−	1.20374i	0.473910	−	0.880573i	$-0.342842\pi$
$348$	−1.62470	+	4.50182i	−0.0870931	+	0.241323i
$349$	−9.45066	−	0.708229i	−0.505882	−	0.0379106i	−0.180655	−	0.983547i	$-0.557822\pi$
$349$	−9.45066	−	0.708229i	−0.505882	−	0.0379106i	−0.325227	+	0.945636i	$0.605441\pi$
$350$	−0.454151	−	0.262204i	−0.0242754	−	0.0140154i
$351$	−2.89666	−	18.2105i	−0.154612	−	0.972005i
$352$	7.02582	+	14.5893i	0.374477	+	0.777610i
$353$	−15.1603	−	16.3389i	−0.806900	−	0.869632i	0.186719	−	0.982413i	$-0.440214\pi$
$353$	−15.1603	−	16.3389i	−0.806900	−	0.869632i	−0.993620	+	0.112781i	$0.964024\pi$
$354$	−3.49325	−	6.76851i	−0.185664	−	0.359742i
$355$	0.454456	+	1.99110i	0.0241200	+	0.105677i
$356$	−5.63923	+	0.849977i	−0.298878	+	0.0450487i
$357$	−0.306654	−	0.269146i	−0.0162299	−	0.0142447i
$358$	−2.82864	+	7.20725i	−0.149498	+	0.380915i
$359$	0.322868	+	1.04671i	0.0170403	+	0.0552434i	0.963694	−	0.267010i	$-0.0860358\pi$
$359$	0.322868	+	1.04671i	0.0170403	+	0.0552434i	−0.946653	+	0.322254i	$0.895560\pi$
$360$	−1.37389	−	1.14018i	−0.0724105	−	0.0600927i
$361$	0.0513031	+	0.684592i	0.00270016	+	0.0360312i
$362$	2.96340	+	0.446661i	0.155753	+	0.0234760i
$363$	1.39173	+	1.64949i	0.0730471	+	0.0865757i
$364$	−0.120052	+	0.389200i	−0.00629245	+	0.0203996i
$365$	2.11802	+	1.68906i	0.110862	+	0.0884097i
$366$	3.78645	+	3.86103i	0.197921	+	0.201819i
$367$	8.02454	+	2.47524i	0.418877	+	0.129207i	0.497027	−	0.867735i	$-0.334425\pi$
$367$	8.02454	+	2.47524i	0.418877	+	0.129207i	−0.0781496	+	0.996942i	$0.524901\pi$
$368$	−1.29406	+	1.39467i	−0.0674577	+	0.0727021i
$369$	−5.56268	+	13.3990i	−0.289581	+	0.697525i
$370$	1.11405	−	0.0834864i	0.0579166	−	0.00434025i
$371$	−1.18576	−	0.571033i	−0.0615617	−	0.0296466i
$372$	−9.43508	+	1.69008i	−0.489186	+	0.0876267i
$373$	−33.4022	−	13.1094i	−1.72950	−	0.678779i	−0.729514	−	0.683966i	$-0.760254\pi$
$373$	−33.4022	−	13.1094i	−1.72950	−	0.678779i	−0.999987	+	0.00518684i	$0.998349\pi$
$374$	−5.43210	−	3.70354i	−0.280887	−	0.191506i
$375$	−3.45576	+	0.0955692i	−0.178455	+	0.00493517i
$376$	−22.1018	+	5.04460i	−1.13982	+	0.260155i
$377$	−7.67833	+	5.23500i	−0.395454	+	0.269616i
$378$	−0.204875	−	0.509765i	−0.0105376	−	0.0262195i
$379$	−20.7561	+	9.99560i	−1.06617	+	0.513439i	−0.882870	−	0.469618i	$-0.844392\pi$
$379$	−20.7561	+	9.99560i	−1.06617	+	0.513439i	−0.183298	+	0.983057i	$0.558677\pi$
$380$	−0.783668	+	0.452451i	−0.0402013	+	0.0232102i
$381$	−7.63935	+	10.1424i	−0.391376	+	0.519613i
$382$	−1.03824	+	13.8543i	−0.0531207	+	0.708847i
$383$	−4.06210	+	17.7972i	−0.207564	+	0.909396i	0.758618	+	0.651535i	$0.225875\pi$
$383$	−4.06210	+	17.7972i	−0.207564	+	0.909396i	−0.966182	+	0.257861i	$0.916982\pi$
$384$	−1.71123	−	6.64492i	−0.0873257	−	0.339097i
$385$	−0.0424464	−	0.0532261i	−0.00216327	−	0.00271265i
$386$	−7.53615			−0.383580
$387$	−12.8064	−	14.9330i	−0.650987	−	0.759089i
$388$	14.7109			0.746834
$389$	6.47727	+	8.12224i	0.328411	+	0.411814i	0.918435	−	0.395571i	$-0.129453\pi$
$389$	6.47727	+	8.12224i	0.328411	+	0.411814i	−0.590025	+	0.807385i	$0.700882\pi$
$390$	−0.298591	−	1.15947i	−0.0151197	−	0.0587120i
$391$	−1.18104	+	5.17447i	−0.0597277	+	0.261684i
$392$	1.55086	−	20.6948i	0.0783301	−	1.04524i
$393$	23.0416	−	30.5913i	1.16229	−	1.54313i
$394$	10.2999	−	5.94664i	0.518901	−	0.299588i
$395$	2.42555	−	1.16809i	0.122043	−	0.0587728i
$396$	4.77520	+	8.65651i	0.239963	+	0.435006i
$397$	−20.3027	+	13.8421i	−1.01896	+	0.694716i	−0.952958	−	0.303104i	$-0.901977\pi$
$397$	−20.3027	+	13.8421i	−1.01896	+	0.694716i	−0.0660033	+	0.997819i	$0.521025\pi$
$398$	−8.34105	+	1.90379i	−0.418099	+	0.0954283i
$399$	−0.805942	+	0.0222884i	−0.0403476	+	0.00111581i
$400$	3.18133	+	2.16899i	0.159067	+	0.108450i
$401$	−32.6873	−	12.8288i	−1.63232	−	0.640640i	−0.640467	−	0.767986i	$-0.721259\pi$
$401$	−32.6873	−	12.8288i	−1.63232	−	0.640640i	−0.991858	+	0.127346i	$0.959354\pi$
$402$	−0.430679	+	0.0771464i	−0.0214803	+	0.00384771i
$403$	−16.7687	−	8.07540i	−0.835310	−	0.402264i
$404$	16.8240	−	1.26079i	0.837027	−	0.0627265i
$405$	−1.44945	−	1.07334i	−0.0720235	−	0.0533349i
$406$	−0.188329	+	0.202970i	−0.00934660	+	0.0100732i
$407$	−17.1159	−	5.27955i	−0.848402	−	0.261697i
$408$	7.79963	+	7.95326i	0.386139	+	0.393745i
$409$	−7.99286	−	6.37410i	−0.395222	−	0.315179i	0.405635	−	0.914035i	$-0.367051\pi$
$409$	−7.99286	−	6.37410i	−0.395222	−	0.315179i	−0.800856	+	0.598857i	$0.795622\pi$
$410$	−0.277663	+	0.900161i	−0.0137128	+	0.0444558i
$411$	12.5026	+	14.8181i	0.616708	+	0.730925i
$412$	−14.4750	−	2.18175i	−0.713130	−	0.107487i
$413$	0.0367749	+	0.490727i	0.00180958	+	0.0241471i
$414$	−4.56397	+	5.49949i	−0.224307	+	0.270285i
$415$	0.162237	+	0.525960i	0.00796390	+	0.0258183i
$416$	6.72198	−	17.1273i	0.329572	−	0.839737i
$417$	−9.75912	−	8.56546i	−0.477906	−	0.419453i
$418$	−12.8463	+	1.93626i	−0.628332	+	0.0947058i
$419$	−1.39876	−	6.12837i	−0.0683340	−	0.299391i	0.929200	−	0.369578i	$-0.120498\pi$
$419$	−1.39876	−	6.12837i	−0.0683340	−	0.299391i	−0.997534	+	0.0701869i	$0.977640\pi$
$420$	0.0182708	+	0.0354014i	0.000891524	+	0.00172741i
$421$	14.2222	+	15.3279i	0.693150	+	0.747038i	0.977327	−	0.211734i	$-0.0679110\pi$
$421$	14.2222	+	15.3279i	0.693150	+	0.747038i	−0.284178	+	0.958772i	$0.591721\pi$
$422$	−0.493875	−	1.02554i	−0.0240414	−	0.0499226i
$423$	−22.0116	+	6.32226i	−1.07024	+	0.307399i
$424$	31.1177	+	17.9658i	1.51121	+	0.872498i
$425$	10.7113	+	0.802704i	0.519576	+	0.0389369i
$426$	5.82455	−	16.1390i	0.282200	−	0.781937i
$427$	−0.127646	−	0.325236i	−0.00617721	−	0.0157393i
$428$	12.2020	−	9.73073i	0.589804	−	0.470353i
$429$	−2.33522	+	19.0537i	−0.112746	+	0.919923i
$430$	−0.919146	−	0.887013i	−0.0443252	−	0.0427756i
$431$		−	16.6973i		−	0.804280i	−0.915578	−	0.402140i	$-0.868267\pi$
$431$		−	16.6973i		−	0.804280i	0.915578	−	0.402140i	$-0.131733\pi$
$432$	1.22034	+	3.84481i	0.0587139	+	0.184983i
$433$	5.97374	−	2.34452i	0.287080	−	0.112671i	−0.217432	−	0.976076i	$-0.569768\pi$
$433$	5.97374	−	2.34452i	0.287080	−	0.112671i	0.504511	+	0.863405i	$0.331673\pi$
$434$	−0.540629	−	0.123395i	−0.0259510	−	0.00592315i
$435$	−0.177691	+	0.891439i	−0.00851962	+	0.0427412i
$436$	4.65329	−	8.05973i	0.222852	−	0.385991i
$437$	5.24392	+	9.08274i	0.250851	+	0.434486i
$438$	−7.30708	−	21.5544i	−0.349146	−	1.02991i
$439$	18.2029	−	16.8898i	0.868775	−	0.806105i	−0.113503	−	0.993538i	$-0.536207\pi$
$439$	18.2029	−	16.8898i	0.868775	−	0.806105i	0.982278	+	0.187432i	$0.0600165\pi$
$440$	1.04702	+	1.53570i	0.0499148	+	0.0732116i
$441$	0.408862	−	20.9605i	0.0194696	−	0.998120i
$442$	1.11339	+	7.38685i	0.0529585	+	0.351357i
$443$	6.20125	−	9.09556i	0.294630	−	0.432143i	−0.650171	−	0.759788i	$-0.725303\pi$
$443$	6.20125	−	9.09556i	0.294630	−	0.432143i	0.944801	+	0.327645i	$0.106255\pi$
$444$	9.21867	+	4.98782i	0.437499	+	0.236711i
$445$	−1.03500	+	0.319254i	−0.0490636	+	0.0151341i
$446$	6.65237	−	13.8138i	0.314999	−	0.654102i
$447$	−0.867862	+	18.3920i	−0.0410485	+	0.869914i
$448$	0.106875	−	0.709070i	0.00504938	−	0.0335004i
$449$	6.46566	+	5.99925i	0.305133	+	0.283122i	0.817845	−	0.575438i	$-0.195169\pi$
$449$	6.46566	+	5.99925i	0.305133	+	0.283122i	−0.512712	+	0.858561i	$0.671359\pi$
$450$	12.3822	+	7.47456i	0.583701	+	0.352354i
$451$	9.41675	−	11.8082i	0.443418	−	0.556028i
$452$	−6.98710	+	8.76155i	−0.328646	+	0.412108i
$453$	3.75140	−	8.37452i	0.176256	−	0.393469i
$454$	−8.52959	−	7.91430i	−0.400314	−	0.371437i
$455$	−0.0115291	+	0.0764907i	−0.000540493	+	0.00358594i
$456$	21.9875	+	1.03752i	1.02966	+	0.0485863i
$457$	5.95671	−	12.3692i	0.278643	−	0.578609i	−0.713936	−	0.700211i	$-0.753089\pi$
$457$	5.95671	−	12.3692i	0.278643	−	0.578609i	0.992579	+	0.121603i	$0.0388034\pi$
$458$	−12.3294	+	3.80312i	−0.576115	+	0.177708i
$459$	8.31121	+	7.58665i	0.387934	+	0.354115i
$460$	0.291925	−	0.428176i	0.0136111	−	0.0199638i
$461$	4.43679	+	29.4362i	0.206642	+	1.37098i	0.815985	+	0.578073i	$0.196195\pi$
$461$	4.43679	+	29.4362i	0.206642	+	1.37098i	−0.609343	+	0.792907i	$0.708567\pi$
$462$	0.0584920	+	0.568946i	0.00272129	+	0.0264697i
$463$	19.7893	+	29.0255i	0.919685	+	1.34893i	0.937092	+	0.349082i	$0.113507\pi$
$463$	19.7893	+	29.0255i	0.919685	+	1.34893i	−0.0174070	+	0.999848i	$0.505541\pi$
$464$	1.49027	−	1.38277i	0.0691841	−	0.0641935i
$465$	−1.72409	+	0.584475i	−0.0799526	+	0.0271044i
$466$	−9.01087	−	15.6073i	−0.417421	−	0.722994i
$467$	3.51751	−	6.09251i	0.162771	−	0.281928i	−0.773090	−	0.634296i	$-0.781290\pi$
$467$	3.51751	−	6.09251i	0.162771	−	0.281928i	0.935861	+	0.352368i	$0.114623\pi$
$468$	3.51978	−	10.6676i	0.162702	−	0.493110i
$469$	0.0275593	+	0.00629023i	0.00127257	+	0.000290456i
$470$	−1.38423	+	0.543272i	−0.0638499	+	0.0250593i
$471$	−13.5323	+	8.31997i	−0.623537	+	0.383364i
$472$		−	13.4353i		−	0.618408i
$473$	8.52230	+	18.6223i	0.391856	+	0.856256i
$474$	−22.4495	−	2.75140i	−1.03114	−	0.126376i
$475$	16.5946	−	13.2337i	0.761412	−	0.607206i
$476$	−0.0908099	−	0.231380i	−0.00416227	−	0.0106053i
$477$	32.3902	+	16.3840i	1.48305	+	0.750173i
$478$	24.1788	+	1.81195i	1.10591	+	0.0828765i
$479$	−28.2067	−	16.2852i	−1.28880	−	0.744088i	−0.310358	−	0.950620i	$-0.600449\pi$
$479$	−28.2067	−	16.2852i	−1.28880	−	0.744088i	−0.978440	+	0.206532i	$0.933782\pi$
$480$	−0.703550	−	1.65644i	−0.0321125	−	0.0756058i
$481$	8.83047	+	18.3367i	0.402635	+	0.836080i
$482$	11.4411	+	12.3306i	0.521128	+	0.561642i
$483$	0.410304	−	0.211759i	0.0186695	−	0.00963538i
$484$	0.292561	+	1.28179i	0.0132982	+	0.0582634i
$485$	2.76274	−	0.416416i	0.125450	−	0.0189085i
$486$	5.37522	+	14.1670i	0.243825	+	0.642626i
$487$	1.82924	−	4.66084i	0.0828909	−	0.211203i	−0.883419	−	0.468584i	$-0.844764\pi$
$487$	1.82924	−	4.66084i	0.0828909	−	0.211203i	0.966310	+	0.257381i	$0.0828596\pi$
$488$	2.81163	+	9.11509i	0.127277	+	0.412621i
$489$	−16.3547	+	25.4735i	−0.739585	+	1.15195i
$490$	−0.101727	−	1.35745i	−0.00459554	−	0.0613232i
$491$	−8.42444	−	1.26978i	−0.380189	−	0.0573043i	−0.0438325	−	0.999039i	$-0.513957\pi$
$491$	−8.42444	−	1.26978i	−0.380189	−	0.0573043i	−0.336357	+	0.941735i	$0.609195\pi$
$492$	−6.75496	+	5.69940i	−0.304537	+	0.256949i
$493$	1.67166	−	5.41940i	0.0752879	−	0.244077i
$494$	11.5410	+	9.20365i	0.519254	+	0.414092i
$495$	1.14183	+	1.49054i	0.0513213	+	0.0669947i
$496$	3.89066	+	1.20011i	0.174696	+	0.0538865i
$497$	−0.753992	+	0.812610i	−0.0338212	+	0.0364506i
$498$	1.24032	−	4.45470i	0.0555799	−	0.199620i
$499$	−16.8791	+	1.26491i	−0.755610	+	0.0566252i	−0.446964	−	0.894552i	$-0.647495\pi$
$499$	−16.8791	+	1.26491i	−0.755610	+	0.0566252i	−0.308646	+	0.951177i	$0.599876\pi$
$500$	−1.89748	−	0.913780i	−0.0848580	−	0.0408655i
$501$	1.46622	+	8.18534i	0.0655058	+	0.365694i
$502$	−12.8889	−	5.05854i	−0.575261	−	0.225773i
$503$	31.0455	+	21.1665i	1.38425	+	0.943765i	0.999787	+	0.0206247i	$0.00656551\pi$
$503$	31.0455	+	21.1665i	1.38425	+	0.943765i	0.384462	+	0.923141i	$0.374387\pi$
$504$	0.0912520	−	0.964770i	0.00406469	−	0.0429743i
$505$	3.12390	−	0.713009i	0.139012	−	0.0317285i
$506$	6.14718	−	4.19108i	0.273275	−	0.186316i
$507$	−0.571120	+	0.412964i	−0.0253643	+	0.0183404i
$508$	−6.96930	+	3.35624i	−0.309213	+	0.148909i
$509$	−0.523811	+	0.302423i	−0.0232175	+	0.0134046i	−0.511564	−	0.859245i	$-0.670934\pi$
$509$	−0.523811	+	0.302423i	−0.0232175	+	0.0134046i	0.488346	+	0.872650i	$0.337600\pi$
$510$	0.583646	+	0.439606i	0.0258443	+	0.0194661i
$511$	−0.109885	+	1.46632i	−0.00486104	+	0.0648660i
$512$	−1.92166	+	8.41933i	−0.0849260	+	0.372085i
$513$	22.2358	−	0.181096i	0.981735	−	0.00799559i
$514$	−17.7850	−	22.3017i	−0.784463	−	0.983685i
$515$	−2.78018			−0.122509
$516$	−2.76058	−	11.6620i	−0.121528	−	0.513393i
$517$	23.8415			1.04855
$518$	0.378073	+	0.474089i	0.0166116	+	0.0208303i
$519$	−42.6615	+	10.9864i	−1.87263	+	0.482248i
$520$	0.469945	−	2.05896i	0.0206084	−	0.0902915i
$521$	−1.65903	+	22.1382i	−0.0726835	+	0.969894i	0.835003	+	0.550245i	$0.185466\pi$
$521$	−1.65903	+	22.1382i	−0.0726835	+	0.969894i	−0.907687	+	0.419649i	$0.862153\pi$
$522$	5.30234	−	5.49560i	0.232077	−	0.240536i
$523$	−22.2719	+	12.8587i	−0.973883	+	0.562272i	−0.900418	−	0.435026i	$-0.856739\pi$
$523$	−22.2719	+	12.8587i	−0.973883	+	0.562272i	−0.0734651	+	0.997298i	$0.523406\pi$
$524$	21.0206	−	10.1230i	0.918289	−	0.442225i
$525$	−0.547532	−	0.757225i	−0.0238962	−	0.0330480i
$526$	3.44117	−	2.34615i	0.150042	−	0.102297i
$527$	11.0736	−	2.52748i	0.482374	−	0.110099i
$528$	−0.116090	−	4.19779i	−0.00505217	−	0.182685i
$529$	14.0409	+	9.57293i	0.610475	+	0.416215i
$530$	2.19397	+	0.861070i	0.0953000	+	0.0374025i
$531$	−0.750113	−	13.5516i	−0.0325521	−	0.588088i
$532$	−0.442525	−	0.213109i	−0.0191859	−	0.00923944i
$533$	−17.1132	+	1.28246i	−0.741255	+	0.0555494i
$534$	8.76607	+	2.44073i	0.379345	+	0.105621i
$535$	2.01611	−	2.17284i	0.0871638	−	0.0939403i
$536$	−0.737477	−	0.227482i	−0.0318542	−	0.00982571i
$537$	−9.85008	+	9.65981i	−0.425062	+	0.416852i
$538$	−0.937064	−	0.747284i	−0.0403997	−	0.0322177i
$539$	−6.43303	+	20.8554i	−0.277090	+	0.898304i
$540$	−0.484775	−	0.986021i	−0.0208614	−	0.0424316i
$541$	−26.1961	−	3.94843i	−1.12626	−	0.169756i	−0.440617	−	0.897695i	$-0.645240\pi$
$541$	−26.1961	−	3.94843i	−1.12626	−	0.169756i	−0.685642	+	0.727939i	$0.740478\pi$
$542$	0.746531	+	9.96177i	0.0320663	+	0.427895i
$543$	4.49368	+	2.88507i	0.192842	+	0.123810i
$544$	3.30968	+	10.7297i	0.141902	+	0.460033i
$545$	0.645753	−	1.64535i	0.0276610	−	0.0704791i
$546$	0.428688	−	0.488429i	0.0183462	−	0.0209028i
$547$	−12.3756	+	1.86532i	−0.529141	+	0.0797551i	−0.408179	−	0.912902i	$-0.633836\pi$
$547$	−12.3756	+	1.86532i	−0.529141	+	0.0797551i	−0.120962	+	0.992657i	$0.538598\pi$
$548$	2.62822	+	11.5150i	0.112272	+	0.491895i
$549$	3.34489	+	9.03703i	0.142756	+	0.385691i
$550$	−10.2413	−	11.0375i	−0.436692	−	0.470642i
$551$	−4.86244	−	10.0970i	−0.207147	−	0.430145i
$552$	−11.6027	+	4.92809i	−0.493844	+	0.209754i
$553$	1.26549	+	0.730631i	0.0538141	+	0.0310696i
$554$	7.07995	+	0.530569i	0.300798	+	0.0225417i
$555$	1.87247	+	0.675773i	0.0794819	+	0.0286849i
$556$	−2.88998	−	7.36356i	−0.122563	−	0.312285i
$557$	−5.12765	+	4.08917i	−0.217266	+	0.173263i	−0.726075	−	0.687616i	$-0.758657\pi$
$557$	−5.12765	+	4.08917i	−0.217266	+	0.173263i	0.508809	+	0.860879i	$0.330086\pi$
$558$	14.8414	+	3.69341i	0.628289	+	0.156354i
$559$	8.92471	−	21.4908i	0.377475	−	0.908962i
$560$		−	0.0169222i		−	0.000715092i
$561$	−6.13575	−	9.97972i	−0.259051	−	0.421344i
$562$	26.5479	−	10.4193i	1.11986	−	0.439511i
$563$	3.34891	+	0.764368i	0.141140	+	0.0322143i	0.292507	−	0.956263i	$-0.405510\pi$
$563$	3.34891	+	0.764368i	0.141140	+	0.0322143i	−0.151367	+	0.988478i	$0.548368\pi$
$564$	−13.6824	−	2.72731i	−0.576132	−	0.114841i
$565$	−1.06418	+	1.84322i	−0.0447704	+	0.0775446i
$566$	−12.0284	−	20.8338i	−0.505591	−	0.875710i
$567$	0.0381774	−	0.978218i	0.00160330	−	0.0410813i
$568$	22.1856	−	20.5853i	0.930888	−	0.863738i
$569$	−0.328250	−	0.481455i	−0.0137610	−	0.0201836i	0.819297	−	0.573370i	$-0.194364\pi$
$569$	−0.328250	−	0.481455i	−0.0137610	−	0.0201836i	−0.833058	+	0.553186i	$0.813412\pi$
$570$	1.43628	−	0.147661i	0.0601591	−	0.00618482i
$571$	5.65401	+	37.5119i	0.236613	+	1.56983i	0.719720	+	0.694264i	$0.244270\pi$
$571$	5.65401	+	37.5119i	0.236613	+	1.56983i	−0.483107	+	0.875561i	$0.660492\pi$
$572$	−6.58766	+	9.66232i	−0.275444	+	0.404002i
$573$	−11.7806	+	21.7734i	−0.492143	+	0.909597i
$574$	−0.488593	+	0.150711i	−0.0203935	+	0.00629055i
$575$	−5.27402	+	10.9516i	−0.219942	+	0.456714i
$576$	−3.32848	+	19.4951i	−0.138687	+	0.812296i
$577$	−0.559481	+	3.71192i	−0.0232915	+	0.154529i	−0.997453	−	0.0713220i	$-0.977278\pi$
$577$	−0.559481	+	3.71192i	−0.0232915	+	0.154529i	0.974162	+	0.225851i	$0.0725163\pi$
$578$	8.77136	+	8.13863i	0.364841	+	0.338523i
$579$	−12.2552	−	5.48977i	−0.509309	−	0.228147i
$580$	−0.345255	+	0.432936i	−0.0143359	+	0.0179767i
$581$	−0.186271	+	0.233576i	−0.00772781	+	0.00969037i
$582$	−21.4215	−	9.59584i	−0.887950	−	0.397761i
$583$	−27.7007	−	25.7024i	−1.14724	−	1.06449i
$584$	5.98332	−	39.6968i	0.247592	−	1.64266i
$585$	0.359058	−	2.10303i	0.0148452	−	0.0869495i
$586$	8.49133	−	17.6324i	0.350774	−	0.728389i
$587$	35.3980	−	10.9188i	1.46103	−	0.450668i	0.540502	−	0.841343i	$-0.318234\pi$
$587$	35.3980	−	10.9188i	1.46103	−	0.450668i	0.920529	+	0.390674i	$0.127758\pi$
$588$	6.07756	−	11.2328i	0.250635	−	0.463232i
$589$	12.6434	−	18.5445i	0.520964	−	0.764113i
$590$	−0.131346	−	0.871426i	−0.00540744	−	0.0358760i
$591$	21.0815	−	2.16734i	0.867176	−	0.0891524i
$592$	−2.50804	−	3.67862i	−0.103080	−	0.151191i
$593$	6.56927	−	6.09539i	0.269768	−	0.250308i	−0.533675	−	0.845689i	$-0.679190\pi$
$593$	6.56927	−	6.09539i	0.269768	−	0.250308i	0.803443	+	0.595382i	$0.202999\pi$
$594$	−1.30689	−	15.7201i	−0.0536223	−	0.645004i
$595$	−0.0236038	−	0.0408831i	−0.000967663	−	0.00167604i
$596$	−5.60843	+	9.71409i	−0.229730	+	0.397905i
$597$	−14.9510	−	2.98018i	−0.611902	−	0.121971i
$598$	−8.24173	−	1.88112i	−0.337029	−	0.0769247i
$599$	−27.2456	+	10.6931i	−1.11323	+	0.436909i	−0.849447	−	0.527674i	$-0.823064\pi$
$599$	−27.2456	+	10.6931i	−1.11323	+	0.436909i	−0.263779	+	0.964583i	$0.584969\pi$
$600$	13.3618	+	21.7328i	0.545493	+	0.887238i
$601$		−	16.4779i		−	0.672148i	−0.941836	−	0.336074i	$-0.890901\pi$
$601$		−	16.4779i		−	0.672148i	0.941836	−	0.336074i	$-0.109099\pi$
$602$	0.116759	−	0.683423i	0.00475873	−	0.0278542i
$603$	−0.756563	−	0.188277i	−0.0308096	−	0.00766722i
$604$	4.37061	−	3.48545i	0.177838	−	0.141821i
$605$	0.0912268	+	0.232442i	0.00370890	+	0.00945011i
$606$	−25.3209	−	9.13830i	−1.02859	−	0.371218i
$607$	−31.3069	−	2.34613i	−1.27071	−	0.0952263i	−0.577755	−	0.816210i	$-0.696071\pi$
$607$	−31.3069	−	2.34613i	−1.27071	−	0.0952263i	−0.692952	+	0.720984i	$0.743690\pi$
$608$	19.2154	+	11.0940i	0.779287	+	0.449921i
$609$	−0.454114	+	0.192878i	−0.0184016	+	0.00781583i
$610$	0.271477	+	0.563728i	0.0109918	+	0.0228247i
$611$	−18.4259	−	19.8584i	−0.745432	−	0.803384i
$612$	2.37963	+	6.42914i	0.0961906	+	0.259883i
$613$	5.94710	+	26.0560i	0.240201	+	1.05239i	0.940834	+	0.338868i	$0.110044\pi$
$613$	5.94710	+	26.0560i	0.240201	+	1.05239i	−0.700632	+	0.713522i	$0.747099\pi$
$614$	−2.64798	+	0.399119i	−0.106864	+	0.0161071i
$615$	−1.10726	+	1.26157i	−0.0446491	+	0.0508713i
$616$	−0.368575	+	0.939114i	−0.0148503	+	0.0378380i
$617$	−4.28923	−	13.9053i	−0.172678	−	0.559808i	0.827320	−	0.561730i	$-0.189864\pi$
$617$	−4.28923	−	13.9053i	−0.172678	−	0.559808i	−0.999998	+	0.00192280i	$0.999388\pi$
$618$	19.6547	+	12.6189i	0.790630	+	0.507606i
$619$	−2.83801	−	37.8706i	−0.114069	−	1.52215i	−0.701381	−	0.712787i	$-0.747433\pi$
$619$	−2.83801	−	37.8706i	−0.114069	−	1.52215i	0.587311	−	0.809361i	$-0.300186\pi$
$620$	−1.09663	−	0.165291i	−0.0440419	−	0.00663825i
$621$	−11.4280	+	5.61856i	−0.458591	+	0.225465i
$622$	−6.46886	+	20.9715i	−0.259378	+	0.840882i
$623$	−0.459637	−	0.366549i	−0.0184150	−	0.0146855i
$624$	−3.40676	+	3.34095i	−0.136380	+	0.133745i
$625$	23.3152	+	7.19179i	0.932609	+	0.287672i
$626$	14.7057	−	15.8490i	0.587759	−	0.633454i
$627$	−22.3010	−	6.20924i	−0.890615	−	0.247973i
$628$	−9.65029	+	0.723189i	−0.385088	+	0.0288584i
$629$	−11.1904	−	5.38902i	−0.446191	−	0.214874i
$630$	−0.00351312	−	0.0634682i	−0.000139966	−	0.00252863i
$631$	17.4892	+	6.86402i	0.696236	+	0.273252i	0.686950	−	0.726704i	$-0.258949\pi$
$631$	17.4892	+	6.86402i	0.696236	+	0.273252i	0.00928560	+	0.999957i	$0.497044\pi$
$632$	−32.9627	−	22.4736i	−1.31119	−	0.893952i
$633$	−0.0560704	−	2.02749i	−0.00222860	−	0.0805856i
$634$	3.78935	−	0.864894i	0.150494	−	0.0343493i
$635$	−1.21384	+	0.827585i	−0.0481699	+	0.0328417i
$636$	12.9569	+	17.9191i	0.513775	+	0.710540i
$637$	22.3429	−	10.7598i	0.885258	−	0.426318i
$638$	−6.88486	+	3.97498i	−0.272574	+	0.157371i
$639$	21.2284	−	22.0021i	0.839783	−	0.870391i
$640$	0.0593288	−	0.791687i	0.00234518	−	0.0312942i
$641$	6.67325	−	29.2374i	0.263577	−	1.15481i	−0.653761	−	0.756701i	$-0.726810\pi$
$641$	6.67325	−	29.2374i	0.263577	−	1.15481i	0.917339	−	0.398107i	$-0.130333\pi$
$642$	−24.1153	+	6.21027i	−0.951756	+	0.245100i
$643$	15.9009	+	19.9391i	0.627070	+	0.786321i	0.989320	−	0.145760i	$-0.0465626\pi$
$643$	15.9009	+	19.9391i	0.627070	+	0.786321i	−0.362250	+	0.932081i	$0.617991\pi$
$644$	0.281283			0.0110841
$645$	−0.848555	−	2.11201i	−0.0334118	−	0.0831604i
$646$	−9.00858			−0.354438
$647$	3.43853	+	4.31177i	0.135182	+	0.169513i	0.844815	−	0.535059i	$-0.179710\pi$
$647$	3.43853	+	4.31177i	0.135182	+	0.169513i	−0.709633	+	0.704572i	$0.751139\pi$
$648$	−3.03521	+	26.5544i	−0.119234	+	1.04316i
$649$	−3.14409	+	13.7751i	−0.123416	+	0.540722i
$650$	−1.27852	+	17.0607i	−0.0501478	+	0.669175i
$651$	−0.789277	−	0.594489i	−0.0309342	−	0.0232999i
$652$	−15.9708	+	9.22072i	−0.625463	+	0.361111i
$653$	−22.2962	+	10.7373i	−0.872517	+	0.420182i	−0.815886	−	0.578213i	$-0.803750\pi$
$653$	−22.2962	+	10.7373i	−0.872517	+	0.420182i	−0.0566314	+	0.998395i	$0.518036\pi$
$654$	−12.0333	+	8.70097i	−0.470538	+	0.340235i
$655$	3.66116	−	2.49614i	0.143053	−	0.0975321i
$656$	3.66007	−	0.835386i	0.142902	−	0.0326164i
$657$	3.81879	−	40.3745i	0.148985	−	1.57516i
$658$	−0.666885	−	0.454674i	−0.0259979	−	0.0177251i
$659$	21.1606	+	8.30493i	0.824301	+	0.323514i	0.739730	−	0.672903i	$-0.234953\pi$
$659$	21.1606	+	8.30493i	0.824301	+	0.323514i	0.0845702	+	0.996418i	$0.473048\pi$
$660$	0.201684	+	1.12592i	0.00785054	+	0.0438265i
$661$	6.41177	+	3.08774i	0.249389	+	0.120099i	0.554403	−	0.832249i	$-0.312947\pi$
$661$	6.41177	+	3.08774i	0.249389	+	0.120099i	−0.305014	+	0.952348i	$0.598661\pi$
$662$	−27.7161	+	2.07703i	−1.07722	+	0.0807261i
$663$	−3.57043	+	12.8235i	−0.138664	+	0.498023i
$664$	5.54784	−	5.97915i	0.215298	−	0.232036i
$665$	−0.0891394	−	0.0274959i	−0.00345668	−	0.00106624i
$666$	−10.1704	−	13.2764i	−0.394093	−	0.514448i
$667$	5.01775	+	4.00152i	0.194288	+	0.154940i
$668$	−1.49319	+	4.84080i	−0.0577732	+	0.187296i
$669$	20.8808	−	17.6179i	0.807298	−	0.681147i
$670$	−0.0500575	−	0.00754496i	−0.00193389	−	0.000291487i
$671$	−0.749671	−	10.0037i	−0.0289407	−	0.386187i
$672$	0.527744	−	0.821995i	0.0203581	−	0.0317091i
$673$	−8.56425	−	27.7646i	−0.330128	−	1.07025i	−0.956747	−	0.290922i	$-0.906038\pi$
$673$	−8.56425	−	27.7646i	−0.330128	−	1.07025i	0.626619	−	0.779326i	$-0.284438\pi$
$674$	−0.0586622	+	0.149469i	−0.00225958	+	0.00575733i
$675$	14.6909	+	21.1750i	0.565452	+	0.815024i
$676$	−0.424556	+	0.0639915i	−0.0163291	+	0.00246121i
$677$	−0.896642	−	3.92844i	−0.0344607	−	0.150982i	0.954770	−	0.297344i	$-0.0961008\pi$
$677$	−0.896642	−	3.92844i	−0.0344607	−	0.150982i	−0.989231	+	0.146362i	$0.953244\pi$
$678$	15.8895	−	8.20060i	0.610231	−	0.314942i
$679$	1.03149	+	1.11168i	0.0395849	+	0.0426623i
$680$	0.559211	+	1.16121i	0.0214447	+	0.0445305i
$681$	−8.10550	−	19.0836i	−0.310603	−	0.731286i
$682$	−13.7887	−	7.96093i	−0.527998	−	0.304840i
$683$	−23.3899	−	1.75283i	−0.894991	−	0.0670703i	−0.380712	−	0.924694i	$-0.624321\pi$
$683$	−23.3899	−	1.75283i	−0.894991	−	0.0670703i	−0.514279	+	0.857623i	$0.671940\pi$
$684$	12.0880	+	6.11450i	0.462196	+	0.233794i
$685$	0.819533	+	2.08814i	0.0313128	+	0.0797836i
$686$	1.15632	−	0.922131i	0.0441483	−	0.0352071i
$687$	−22.8204	−	2.79686i	−0.870651	−	0.106707i
$688$	−1.22987	+	4.93981i	−0.0468884	+	0.188328i
$689$			42.9369i			1.63577i
$690$	−0.704387	+	0.433073i	−0.0268156	+	0.0164868i
$691$	12.2334	−	4.80127i	0.465382	−	0.182649i	−0.121052	−	0.992646i	$-0.538627\pi$
$691$	12.2334	−	4.80127i	0.465382	−	0.182649i	0.586434	+	0.809997i	$0.300531\pi$
$692$	−26.1644	−	5.97185i	−0.994621	−	0.227016i
$693$	−0.319334	+	0.967823i	−0.0121305	+	0.0367645i
$694$	−11.7072	+	20.2776i	−0.444401	+	0.769725i
$695$	−0.751182	−	1.30108i	−0.0284939	−	0.0493529i
$696$	12.7569	−	4.32467i	0.483550	−	0.163926i
$697$	7.67729	−	7.12348i	0.290798	−	0.269821i
$698$	5.18934	+	7.61137i	0.196420	+	0.288095i
$699$	−3.28414	−	31.9445i	−0.124218	−	1.20825i
$700$	−0.0848437	−	0.562901i	−0.00320679	−	0.0212757i
$701$	21.5803	−	31.6525i	0.815078	−	1.19550i	−0.162869	−	0.986648i	$-0.552075\pi$
$701$	21.5803	−	31.6525i	0.815078	−	1.19550i	0.977947	−	0.208852i	$-0.0669727\pi$
$702$	−12.0838	+	13.2378i	−0.456073	+	0.499630i
$703$	−23.4527	+	7.23421i	−0.884537	+	0.272844i
$704$	8.93322	−	18.5500i	0.336683	−	0.699130i
$705$	−2.64678	−	0.124893i	−0.0996834	−	0.00470374i
$706$	−3.22906	+	21.4234i	−0.121527	+	0.806281i
$707$	1.27493	+	1.18296i	0.0479486	+	0.0444898i
$708$	3.38014	−	7.54574i	0.127034	−	0.283586i
$709$	8.81622	−	11.0552i	0.331100	−	0.415186i	−0.588218	−	0.808703i	$-0.700170\pi$
$709$	8.81622	−	11.0552i	0.331100	−	0.415186i	0.919318	+	0.393517i	$0.128742\pi$
$710$	1.23774	−	1.55208i	0.0464515	−	0.0582483i
$711$	−34.5028	−	20.8278i	−1.29396	−	0.781104i
$712$	11.7659	+	10.9172i	0.440947	+	0.409139i
$713$	−1.91573	+	12.7100i	−0.0717447	+	0.475995i
$714$	−0.0186936	+	0.396162i	−0.000699590	+	0.0148260i
$715$	−0.963668	+	2.00108i	−0.0360391	+	0.0748360i
$716$	−8.03124	+	2.47731i	−0.300142	+	0.0925814i
$717$	37.9993	+	20.5598i	1.41911	+	0.767819i
$718$	0.599788	−	0.879728i	0.0223839	−	0.0328311i
$719$	−3.55288	−	23.5718i	−0.132500	−	0.879080i	−0.952021	−	0.306032i	$-0.900999\pi$
$719$	−3.55288	−	23.5718i	−0.132500	−	0.879080i	0.819521	−	0.573049i	$-0.194239\pi$
$720$	−0.00910219	+	0.466628i	−0.000339219	+	0.0173902i
$721$	−0.850070	−	1.24682i	−0.0316583	−	0.0464342i
$722$	0.489172	−	0.453885i	0.0182051	−	0.0168919i
$723$	9.62310	+	28.3862i	0.357887	+	1.05570i
$724$	1.62659	+	2.81734i	0.0604518	+	0.104706i
$725$	6.49431	−	11.2485i	0.241192	−	0.417758i
$726$	0.410090	−	2.05734i	0.0152199	−	0.0763550i
$727$	−4.78533	−	1.09222i	−0.177478	−	0.0405082i	0.132858	−	0.991135i	$-0.457585\pi$
$727$	−4.78533	−	1.09222i	−0.177478	−	0.0405082i	−0.310336	+	0.950627i	$0.600442\pi$
$728$	1.06707	−	0.418795i	0.0395483	−	0.0155216i
$729$	−1.57891	+	26.9538i	−0.0584781	+	0.998289i
$730$		−	2.63327i		−	0.0974618i
$731$	3.91898	+	13.6498i	0.144949	+	0.504856i
$732$	−0.714126	+	5.82675i	−0.0263948	+	0.215363i
$733$	22.9307	−	18.2867i	0.846966	−	0.675433i	−0.100623	−	0.994925i	$-0.532084\pi$
$733$	22.9307	−	18.2867i	0.846966	−	0.675433i	0.947589	+	0.319492i	$0.103512\pi$
$734$	−2.98218	−	7.59846i	−0.110074	−	0.280464i
$735$	0.823416	−	2.28157i	0.0303722	−	0.0841570i
$736$	−12.6712	−	0.949575i	−0.467066	−	0.0350018i
$737$	0.702900	+	0.405819i	0.0258916	+	0.0149485i
$738$	13.5540	−	3.89304i	0.498930	−	0.143305i
$739$	13.3243	+	27.6682i	0.490142	+	1.01779i	0.988556	+	0.150852i	$0.0482016\pi$
$739$	13.3243	+	27.6682i	0.490142	+	1.01779i	−0.498414	+	0.866939i	$0.666084\pi$
$740$	0.824858	+	0.888986i	0.0303224	+	0.0326798i
$741$	12.0634	+	23.3740i	0.443160	+	0.858666i
$742$	0.284667	+	1.24721i	0.0104505	+	0.0457865i
$743$	29.6460	−	4.46841i	1.08760	−	0.163930i	0.419322	−	0.907838i	$-0.362268\pi$
$743$	29.6460	−	4.46841i	1.08760	−	0.163930i	0.668282	+	0.743908i	$0.267030\pi$
$744$	20.2754	+	17.7955i	0.743333	+	0.652414i
$745$	−0.778301	+	1.98308i	−0.0285147	+	0.0726544i
$746$	10.2807	+	33.3294i	0.376405	+	1.22027i
$747$	5.26205	−	6.34066i	0.192528	−	0.231993i
$748$	−0.533332	−	7.11682i	−0.0195005	−	0.260217i
$749$	1.59090	+	0.239790i	0.0581302	+	0.00876172i
$750$	2.16699	+	2.56833i	0.0791274	+	0.0937821i
$751$	−3.70850	+	12.0227i	−0.135325	+	0.438713i	−0.997717	−	0.0675273i	$-0.978489\pi$
$751$	−3.70850	+	12.0227i	−0.135325	+	0.438713i	0.862392	+	0.506241i	$0.168965\pi$
$752$	4.63331	+	3.69494i	0.168960	+	0.134741i
$753$	−17.2749	−	17.6152i	−0.629534	−	0.641933i
$754$	8.63185	+	2.66257i	0.314353	+	0.0969652i
$755$	0.722148	−	0.778290i	0.0262816	−	0.0283249i
$756$	0.293975	−	0.518893i	0.0106918	−	0.0188720i
$757$	−36.3039	+	2.72060i	−1.31949	+	0.0988818i	−0.715780	−	0.698325i	$-0.753929\pi$
$757$	−36.3039	+	2.72060i	−1.31949	+	0.0988818i	−0.603706	+	0.797207i	$0.706310\pi$
$758$	20.1755	+	9.71600i	0.732806	+	0.352901i
$759$	13.0495	−	2.33753i	0.473667	−	0.0848468i
$760$	2.37075	+	0.930452i	0.0859962	+	0.0337510i
$761$	6.50105	+	4.43234i	0.235663	+	0.160672i	0.675394	−	0.737457i	$-0.263974\pi$
$761$	6.50105	+	4.43234i	0.235663	+	0.160672i	−0.439731	+	0.898130i	$0.644926\pi$
$762$	12.3377	−	0.341199i	0.446947	−	0.0123603i
$763$	0.935335	−	0.213484i	0.0338614	−	0.00772864i
$764$	−12.4608	+	8.49563i	−0.450816	+	0.307361i
$765$	0.628885	+	1.14005i	0.0227374	+	0.0412184i
$766$	15.9871	−	7.69896i	0.577636	−	0.278175i
$767$	13.9037	−	8.02729i	0.502033	−	0.289849i
$768$	−17.7523	+	23.5689i	−0.640580	+	0.850469i
$769$	0.457709	−	6.10770i	0.0165054	−	0.220249i	−0.982852	−	0.184398i	$-0.940967\pi$
$769$	0.457709	−	6.10770i	0.0165054	−	0.220249i	0.999357	−	0.0358517i	$-0.0114144\pi$
$770$	−0.0147252	+	0.0645153i	−0.000530659	+	0.00232497i
$771$	−12.6760	−	49.2224i	−0.456513	−	1.77270i
$772$	−5.10057	−	6.39592i	−0.183574	−	0.230194i
$773$	−2.01537			−0.0724878			−0.0362439	−	0.999343i	$-0.511539\pi$
$773$	−2.01537			−0.0724878			−0.0362439	+	0.999343i	$0.511539\pi$
$774$	−3.58722	+	18.7826i	−0.128940	+	0.675125i
$775$	26.0131			0.934418
$776$	−25.8145	−	32.3703i	−0.926686	−	1.16203i
$777$	0.269465	+	1.04637i	0.00966701	+	0.0375383i
$778$	2.24705	−	9.84496i	0.0805605	−	0.352959i
$779$	1.54654	−	20.6372i	0.0554107	−	0.739404i
$780$	0.781948	−	1.03816i	0.0279982	−	0.0371720i
$781$	−27.5642	+	15.9142i	−0.986325	+	0.569455i
$782$	4.64817	−	2.23844i	0.166218	−	0.0800464i
$783$	12.6259	−	5.07436i	0.451213	−	0.181343i
$784$	−4.48234	+	3.05601i	−0.160083	+	0.109143i
$785$	−1.79187	+	0.408983i	−0.0639546	+	0.0145972i
$786$	−37.2126	+	1.02912i	−1.32733	+	0.0367073i
$787$	−18.3499	−	12.5108i	−0.654105	−	0.445961i	0.190257	−	0.981734i	$-0.439068\pi$
$787$	−18.3499	−	12.5108i	−0.654105	−	0.445961i	−0.844362	+	0.535773i	$0.820020\pi$
$788$	12.0180	+	4.71673i	0.428124	+	0.168026i
$789$	7.30506	−	1.30854i	0.260067	−	0.0465852i
$790$	−2.35771	−	1.13541i	−0.0838834	−	0.0403961i
$791$	−1.15201	+	0.0863312i	−0.0409607	+	0.00306958i
$792$	10.6686	−	25.6978i	0.379091	−	0.913131i
$793$	−7.75300	+	8.35575i	−0.275317	+	0.296721i
$794$	22.8239	+	7.04024i	0.809990	+	0.249849i
$795$	2.94056	+	2.99848i	0.104291	+	0.106345i
$796$	−7.26108	−	5.79052i	−0.257362	−	0.205240i
$797$	13.4939	−	43.7460i	0.477977	−	1.54956i	−0.320326	−	0.947307i	$-0.603792\pi$
$797$	13.4939	−	43.7460i	0.477977	−	1.54956i	0.798303	−	0.602256i	$-0.205731\pi$
$798$	0.505379	+	0.598977i	0.0178902	+	0.0212036i
$799$	16.3477	+	2.46402i	0.578341	+	0.0871709i
$800$	1.92175	+	25.6439i	0.0679440	+	0.906649i
$801$	12.4773	+	10.3548i	0.440865	+	0.365869i
$802$	10.0607	+	32.6160i	0.355256	+	1.15171i
$803$	−15.4244	+	39.3008i	−0.544317	+	1.38690i
$804$	−0.356963	−	0.313302i	−0.0125891	−	0.0110493i
$805$	0.0528255	−	0.00796216i	0.00186185	−	0.000280629i
$806$	4.02569	+	17.6377i	0.141799	+	0.621261i
$807$	−0.979480	−	1.89784i	−0.0344793	−	0.0668070i
$808$	−32.2968	−	34.8077i	−1.13620	−	1.22453i
$809$	−7.27116	−	15.0987i	−0.255640	−	0.530843i	0.733165	−	0.680050i	$-0.238042\pi$
$809$	−7.27116	−	15.0987i	−0.255640	−	0.530843i	−0.988806	+	0.149207i	$0.952328\pi$
$810$	0.0627355	+	1.75202i	0.00220430	+	0.0615598i
$811$	2.02752	+	1.17059i	0.0711958	+	0.0411049i	0.535175	−	0.844741i	$-0.320246\pi$
$811$	2.02752	+	1.17059i	0.0711958	+	0.0411049i	−0.463980	+	0.885846i	$0.653579\pi$
$812$	−0.299724	−	0.0224612i	−0.0105183	−	0.000788234i
$813$	−6.04273	+	16.7435i	−0.211928	+	0.587222i
$814$	6.36081	+	16.2071i	0.222946	+	0.568058i
$815$	−2.73833	+	2.18375i	−0.0959195	+	0.0764933i
$816$	0.354241	−	2.89035i	0.0124009	−	0.101183i
$817$	24.0227	+	14.5049i	0.840446	+	0.507462i
$818$			9.93729i			0.347449i
$819$	1.05293	−	0.481997i	0.0367923	−	0.0168423i
$820$	−0.951892	+	0.373590i	−0.0332415	+	0.0130463i
$821$	6.47945	+	1.47889i	0.226134	+	0.0516137i	0.334087	−	0.942542i	$-0.391572\pi$
$821$	6.47945	+	1.47889i	0.226134	+	0.0516137i	−0.107952	+	0.994156i	$0.534429\pi$
$822$	3.68403	−	18.4820i	0.128495	−	0.644635i
$823$	−22.4461	+	38.8777i	−0.782421	+	1.35519i	0.148107	+	0.988971i	$0.452682\pi$
$823$	−22.4461	+	38.8777i	−0.782421	+	1.35519i	−0.930528	+	0.366222i	$0.880651\pi$
$824$	20.5996	+	35.6796i	0.717622	+	1.24296i
$825$	−8.61398	−	25.4095i	−0.299900	−	0.884646i
$826$	0.350647	−	0.325353i	0.0122006	−	0.0113205i
$827$	0.350471	+	0.514047i	0.0121871	+	0.0178752i	0.832284	−	0.554350i	$-0.187033\pi$
$827$	0.350471	+	0.514047i	0.0121871	+	0.0178752i	−0.820097	+	0.572225i	$0.806081\pi$
$828$	−7.75637	−	0.151298i	−0.269552	−	0.00525797i
$829$	0.668160	+	4.43295i	0.0232061	+	0.153963i	0.997433	−	0.0716086i	$-0.0228132\pi$
$829$	0.668160	+	4.43295i	0.0232061	+	0.153963i	−0.974227	+	0.225571i	$0.927575\pi$
$830$	0.301386	−	0.442052i	0.0104612	−	0.0153438i
$831$	11.1269	+	6.02025i	0.385986	+	0.208840i
$832$	−22.3549	+	6.89559i	−0.775018	+	0.239061i
$833$	−6.56643	+	13.6353i	−0.227513	+	0.472436i
$834$	−0.594915	+	12.6077i	−0.0206002	+	0.436568i
$835$	−0.143397	+	0.951377i	−0.00496246	+	0.0329238i
$836$	−10.3378	−	9.59212i	−0.357542	−	0.331750i
$837$	21.4445	+	16.8176i	0.741231	+	0.581300i
$838$	−3.80961	+	4.77710i	−0.131601	+	0.165022i
$839$	−32.9728	+	41.3466i	−1.13835	+	1.42744i	−0.250013	+	0.968242i	$0.580435\pi$
$839$	−32.9728	+	41.3466i	−1.13835	+	1.42744i	−0.888333	+	0.459199i	$0.848136\pi$
$840$	0.0458371	−	0.102325i	0.00158153	−	0.00353056i
$841$	16.2313	+	15.0605i	0.559701	+	0.519326i
$842$	3.02926	−	20.0979i	0.104395	−	0.692618i
$843$	50.7620	+	2.39530i	1.74834	+	0.0824984i
$844$	0.536114	−	1.11325i	0.0184538	−	0.0383197i
$845$	−0.0779210	+	0.0240354i	−0.00268056	+	0.000826844i
$846$	18.1448	+	12.8963i	0.623830	+	0.443385i
$847$	−0.0763494	+	0.111984i	−0.00262340	+	0.00384782i
$848$	−1.39994	−	9.28799i	−0.0480741	−	0.318951i
$849$	−4.38392	−	42.6419i	−0.150456	−	1.46347i
$850$	−5.88158	−	8.62669i	−0.201736	−	0.295893i
$851$	10.3034	−	9.56014i	0.353195	−	0.327717i
$852$	17.6393	−	5.97982i	0.604312	−	0.204865i
$853$	6.97924	+	12.0884i	0.238965	+	0.413899i	0.960417	−	0.278565i	$-0.0898587\pi$
$853$	6.97924	+	12.0884i	0.238965	+	0.413899i	−0.721453	+	0.692463i	$0.756525\pi$
$854$	−0.169807	+	0.294115i	−0.00581069	+	0.0100644i
$855$	2.44323	+	0.806144i	0.0835566	+	0.0275696i
$856$	−42.8235	−	9.77419i	−1.46368	−	0.334075i
$857$	30.7964	−	12.0867i	1.05198	−	0.412873i	0.224565	−	0.974459i	$-0.427904\pi$
$857$	30.7964	−	12.0867i	1.05198	−	0.412873i	0.827418	+	0.561586i	$0.189809\pi$
$858$	15.8954	−	9.77283i	0.542659	−	0.333639i
$859$			2.15856i			0.0736490i	0.999322	+	0.0368245i	$0.0117243\pi$
$859$			2.15856i			0.0736490i	−0.999322	+	0.0368245i	$0.988276\pi$
$860$	0.130715	−	1.38042i	0.00445735	−	0.0470720i
$861$	−0.904332	−	0.110835i	−0.0308195	−	0.00377724i
$862$	−12.6893	+	10.1194i	−0.432199	+	0.344667i
$863$	15.4832	+	39.4504i	0.527053	+	1.34291i	0.908255	+	0.418417i	$0.137415\pi$
$863$	15.4832	+	39.4504i	0.527053	+	1.34291i	−0.381202	+	0.924492i	$0.624490\pi$
$864$	−14.9947	+	22.3826i	−0.510128	+	0.761472i
$865$	−5.08276	−	0.380900i	−0.172819	−	0.0129510i
$866$	−5.40213	−	3.11892i	−0.183572	−	0.105985i
$867$	8.33525	+	19.6245i	0.283080	+	0.666484i
$868$	−0.261180	−	0.542346i	−0.00886503	−	0.0184084i
$869$	28.5374	+	30.7560i	0.968065	+	1.04333i
$870$	0.785149	−	0.405218i	0.0266191	−	0.0137382i
$871$	−0.205215	−	0.899106i	−0.00695344	−	0.0304650i
$872$	−25.9004	+	3.90385i	−0.877097	+	0.132201i
$873$	−27.8453	−	31.2093i	−0.942420	−	1.05628i
$874$	3.72446	−	9.48977i	0.125982	−	0.320996i
$875$	−0.0639933	−	0.207461i	−0.00216337	−	0.00701346i
$876$	13.3477	−	20.7899i	0.450976	−	0.702424i
$877$	1.66337	+	22.1961i	0.0561680	+	0.749510i	0.952191	+	0.305503i	$0.0988246\pi$
$877$	1.66337	+	22.1961i	0.0561680	+	0.749510i	−0.896023	+	0.444007i	$0.853556\pi$
$878$	−23.8674	−	3.59744i	−0.805487	−	0.121408i
$879$	26.6530	−	22.4881i	0.898983	−	0.758505i
$880$	0.143214	−	0.464287i	0.00482773	−	0.0156511i
$881$	−44.4264	−	35.4288i	−1.49676	−	1.19363i	−0.928804	−	0.370571i	$-0.879162\pi$
$881$	−44.4264	−	35.4288i	−1.49676	−	1.19363i	−0.567958	−	0.823057i	$-0.692266\pi$
$882$	−16.1770	+	12.3924i	−0.544708	+	0.417274i
$883$	−1.11807	−	0.344879i	−0.0376261	−	0.0116061i	0.275885	−	0.961191i	$-0.411029\pi$
$883$	−1.11807	−	0.344879i	−0.0376261	−	0.0116061i	−0.313511	+	0.949585i	$0.601505\pi$
$884$	−5.51565	+	5.94446i	−0.185511	+	0.199934i
$885$	0.421203	−	1.51278i	0.0141586	−	0.0508517i
$886$	−10.6705	+	0.799647i	−0.358484	+	0.0268647i
$887$	−26.5405	−	12.7812i	−0.891141	−	0.429151i	−0.0684601	−	0.997654i	$-0.521809\pi$
$887$	−26.5405	−	12.7812i	−0.891141	−	0.429151i	−0.822681	+	0.568503i	$0.807523\pi$
$888$	−5.20142	−	29.0375i	−0.174548	−	0.974436i
$889$	−0.742292	−	0.291328i	−0.0248957	−	0.00977083i
$890$	0.869881	+	0.593075i	0.0291585	+	0.0198799i
$891$	9.32620	−	26.5159i	0.312439	−	0.888317i
$892$	16.2262	−	3.70352i	0.543292	−	0.124003i
$893$	26.9919	−	18.4028i	0.903251	−	0.615826i
$894$	14.5032	−	10.4869i	0.485060	−	0.350736i
$895$	−1.43816	+	0.692580i	−0.0480723	+	0.0231504i
$896$	0.373188	−	0.215460i	0.0124673	−	0.00719801i
$897$	−12.0323	−	9.06281i	−0.401747	−	0.302599i
$898$	0.640697	−	8.54950i	0.0213803	−	0.285301i
$899$	3.05626	−	13.3903i	0.101932	−	0.446593i
$900$	2.03679	+	15.5676i	0.0678929	+	0.518921i
$901$	−16.3375	−	20.4866i	−0.544282	−	0.682508i
$902$	−14.6808			−0.488818
$903$	0.687717	−	1.02632i	0.0228858	−	0.0341538i
$904$	31.5400			1.04900
$905$	0.385226	+	0.483058i	0.0128053	+	0.0160574i
$906$	−8.63785	+	2.22445i	−0.286973	+	0.0739026i
$907$	−2.81752	+	12.3444i	−0.0935542	+	0.409888i	−0.999921	−	0.0126049i	$-0.995988\pi$
$907$	−2.81752	+	12.3444i	−0.0935542	+	0.409888i	0.906366	+	0.422493i	$0.138845\pi$
$908$	0.943907	−	12.5956i	0.0313247	−	0.417999i
$909$	−34.5198	−	33.3058i	−1.14495	−	1.10469i
$910$	0.0651172	−	0.0375955i	0.00215862	−	0.00124628i
$911$	14.1253	−	6.80240i	0.467993	−	0.225374i	−0.184998	−	0.982739i	$-0.559228\pi$
$911$	14.1253	−	6.80240i	0.467993	−	0.225374i	0.652992	+	0.757365i	$0.273514\pi$
$912$	−3.37162	−	4.66288i	−0.111646	−	0.154403i
$913$	−7.08742	+	4.83212i	−0.234559	+	0.159920i
$914$	−13.0102	+	2.96950i	−0.430340	+	0.0982222i
$915$	0.0308212	+	1.11449i	0.00101892	+	0.0368439i
$916$	−11.5724	−	7.88994i	−0.382363	−	0.260691i
$917$	2.23888	+	0.878695i	0.0739343	+	0.0290171i
$918$	0.728565	−	10.9141i	0.0240462	−	0.360219i
$919$	−8.96551	−	4.31756i	−0.295745	−	0.142423i	0.280128	−	0.959963i	$-0.409623\pi$
$919$	−8.96551	−	4.31756i	−0.295745	−	0.142423i	−0.575872	+	0.817540i	$0.695337\pi$
$920$	−1.45444	+	0.108995i	−0.0479513	+	0.00359345i
$921$	−4.59687	−	1.27990i	−0.151472	−	0.0421742i
$922$	19.6815	−	21.2116i	0.648175	−	0.698566i
$923$	34.5584	+	10.6599i	1.13750	+	0.350874i
$924$	−0.443275	+	0.434713i	−0.0145827	+	0.0143010i
$925$	−22.2395	−	17.7354i	−0.731231	−	0.583137i
$926$	10.0650	−	32.6300i	0.330757	−	1.07229i
$927$	22.7700	+	34.8384i	0.747866	+	1.14424i
$928$	13.4261	+	2.02366i	0.440733	+	0.0664299i
$929$	−1.28717	−	17.1761i	−0.0422308	−	0.563531i	−0.977684	−	0.210081i	$-0.932627\pi$
$929$	−1.28717	−	17.1761i	−0.0422308	−	0.563531i	0.935453	−	0.353450i	$-0.114992\pi$
$930$	1.48906	+	0.956019i	0.0488282	+	0.0313491i
$931$	8.81476	+	28.5767i	0.288892	+	0.936565i
$932$	7.14719	−	18.2107i	0.234114	−	0.596513i
$933$	−25.7965	+	29.3914i	−0.844539	+	0.962232i
$934$	−6.76186	+	1.01919i	−0.221255	+	0.0333488i
$935$	−0.301614	−	1.32146i	−0.00986382	−	0.0432162i
$936$	−29.6497	+	10.9743i	−0.969132	+	0.358706i
$937$	30.6334	+	33.0150i	1.00075	+	1.07855i	0.996909	+	0.0785588i	$0.0250318\pi$
$937$	30.6334	+	33.0150i	1.00075	+	1.07855i	0.00383999	+	0.999993i	$0.498778\pi$
$938$	−0.0119220	−	0.0247562i	−0.000389266	−	0.000808319i
$939$	35.4597	−	15.0610i	1.15718	−	0.491497i
$940$	−1.39794	−	0.807103i	−0.0455959	−	0.0263248i
$941$	−49.2293	−	3.68923i	−1.60483	−	0.120265i	−0.758045	−	0.652202i	$-0.773846\pi$
$941$	−49.2293	−	3.68923i	−1.60483	−	0.120265i	−0.846784	+	0.531936i	$0.821465\pi$
$942$	14.5241	+	5.24174i	0.473221	+	0.170785i
$943$	4.32992	+	11.0325i	0.141002	+	0.359266i
$944$	−2.74588	+	2.18977i	−0.0893708	+	0.0712708i
$945$	0.0405209	−	0.105771i	0.00131815	−	0.00344072i
$946$	8.98733	−	17.7627i	0.292203	−	0.577515i
$947$			24.1247i			0.783947i	0.919977	+	0.391973i	$0.128208\pi$
$947$			24.1247i			0.783947i	−0.919977	+	0.391973i	$0.871792\pi$
$948$	−12.8590	−	20.9150i	−0.417642	−	0.679289i
$949$	44.6557	−	17.5261i	1.44959	−	0.568921i
$950$	−20.1143	−	4.59095i	−0.652593	−	0.148950i
$951$	6.79224	+	1.35390i	0.220253	+	0.0439032i
$952$	−0.349783	+	0.605842i	−0.0113365	+	0.0196355i
$953$	7.04364	+	12.1999i	0.228166	+	0.395195i	0.957265	−	0.289214i	$-0.0933938\pi$
$953$	7.04364	+	12.1999i	0.228166	+	0.395195i	−0.729099	+	0.684409i	$0.760060\pi$
$954$	−7.17884	−	34.5449i	−0.232423	−	1.11843i
$955$	−2.09968	+	1.94822i	−0.0679440	+	0.0630428i
$956$	14.8267	+	21.7468i	0.479531	+	0.703342i
$957$	−14.0917	+	1.44874i	−0.455520	+	0.0468310i
$958$	4.71857	+	31.3056i	0.152450	+	1.01144i
$959$	−0.685883	+	1.00601i	−0.0221483	+	0.0324856i
$960$	−1.08890	+	2.01254i	−0.0351441	+	0.0649545i
$961$	−3.33750	+	1.02948i	−0.107661	+	0.0332091i
$962$	8.58347	−	17.8238i	0.276742	−	0.574661i
$963$	−43.7400	−	7.46791i	−1.40950	−	0.240650i
$964$	−2.72144	+	18.0556i	−0.0876516	+	0.581530i
$965$	−1.13894	−	1.05679i	−0.0366639	−	0.0340191i
$966$	−0.409594	−	0.183479i	−0.0131785	−	0.00590334i
$967$	22.0021	−	27.5897i	0.707539	−	0.887226i	−0.290023	−	0.957020i	$-0.593663\pi$
$967$	22.0021	−	27.5897i	0.707539	−	0.887226i	0.997561	+	0.0697942i	$0.0222342\pi$
$968$	2.30712	−	2.89303i	0.0741535	−	0.0929855i
$969$	−14.6497	−	6.56238i	−0.470615	−	0.210814i
$970$	−1.99082	−	1.84721i	−0.0639213	−	0.0593103i
$971$	−2.93447	+	19.4690i	−0.0941717	+	0.624789i	0.891102	+	0.453803i	$0.149933\pi$
$971$	−2.93447	+	19.4690i	−0.0941717	+	0.624789i	−0.985274	+	0.170985i	$0.945305\pi$
$972$	−8.38545	+	14.1503i	−0.268963	+	0.453872i
$973$	0.353814	−	0.734702i	0.0113428	−	0.0235535i
$974$	−4.65067	+	1.43454i	−0.149017	+	0.0459657i
$975$	−14.5071	+	26.8126i	−0.464600	+	0.858690i
$976$	1.40467	−	2.06028i	0.0449625	−	0.0659478i
$977$	−5.34751	−	35.4784i	−0.171082	−	1.13506i	−0.895293	−	0.445477i	$-0.853034\pi$
$977$	−5.34751	−	35.4784i	−0.171082	−	1.13506i	0.724211	−	0.689578i	$-0.242204\pi$
$978$	29.2706	−	3.00925i	0.935972	−	0.0962251i
$979$	−9.50878	−	13.9468i	−0.303902	−	0.445742i
$980$	1.08321	−	1.00507i	0.0346020	−	0.0321059i
$981$	−25.9067	+	5.38371i	−0.827136	+	0.171889i
$982$	4.14064	+	7.17180i	0.132133	+	0.228861i
$983$	−6.10805	+	10.5795i	−0.194817	+	0.337432i	−0.946840	−	0.321704i	$-0.895744\pi$
$983$	−6.10805	+	10.5795i	−0.194817	+	0.337432i	0.752024	+	0.659136i	$0.229078\pi$
$984$	24.3946	+	4.86258i	0.777671	+	0.155013i
$985$	2.39052	+	0.545621i	0.0761683	+	0.0173849i
$986$	−5.13165	+	2.01402i	−0.163425	+	0.0641396i
$987$	−0.753271	−	1.22519i	−0.0239769	−	0.0389981i
$988$			16.0240i			0.509791i
$989$	−15.9991	−	1.51499i	−0.508743	−	0.0481740i
$990$	0.440748	−	1.77109i	0.0140079	−	0.0562888i
$991$	−34.9437	+	27.8666i	−1.11002	+	0.885213i	−0.994145	−	0.108051i	$-0.965539\pi$
$991$	−34.9437	+	27.8666i	−1.11002	+	0.885213i	−0.115877	+	0.993264i	$0.536968\pi$
$992$	9.93472	+	25.3132i	0.315428	+	0.803696i
$993$	−46.5846	−	16.8123i	−1.47832	−	0.533523i
$994$	1.07451	+	0.0805234i	0.0340814	+	0.00255405i
$995$	−1.52755	−	0.881934i	−0.0484267	−	0.0279592i
$996$	4.62016	−	1.96235i	0.146395	−	0.0621794i
$997$	−13.1509	−	27.3081i	−0.416493	−	0.864856i	−0.998658	−	0.0517859i	$-0.983509\pi$
$997$	−13.1509	−	27.3081i	−0.416493	−	0.864856i	0.582165	−	0.813070i	$-0.302206\pi$
$998$	11.1908	+	12.0608i	0.354239	+	0.381779i
$999$	−6.86767	−	28.9986i	−0.217283	−	0.917474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	129.2.n.b.20.5	✓	144
3.2	odd	2	inner	129.2.n.b.20.8	yes	144
43.28	odd	42	inner	129.2.n.b.71.8	yes	144
129.71	even	42	inner	129.2.n.b.71.5	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
129.2.n.b.20.5	✓	144	1.1	even	1	trivial
129.2.n.b.20.8	yes	144	3.2	odd	2	inner
129.2.n.b.71.5	yes	144	129.71	even	42	inner
129.2.n.b.71.8	yes	144	43.28	odd	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 129 = 3 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	129.n (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.606050 - 0.759962i) q^{2} +(-0.431951 - 1.67732i) q^{3} +(0.234796 - 1.02871i) q^{4} +(0.0149759 - 0.199839i) q^{5} +(-1.01292 + 1.34481i) q^{6} +(0.0942007 - 0.0543868i) q^{7} +(-2.67561 + 1.28851i) q^{8} +(-2.62684 + 1.44905i) q^{9} +O(q^{10})\)	\(q+(-0.606050 - 0.759962i) q^{2} +(-0.431951 - 1.67732i) q^{3} +(0.234796 - 1.02871i) q^{4} +(0.0149759 - 0.199839i) q^{5} +(-1.01292 + 1.34481i) q^{6} +(0.0942007 - 0.0543868i) q^{7} +(-2.67561 + 1.28851i) q^{8} +(-2.62684 + 1.44905i) q^{9} +(-0.160946 + 0.109731i) q^{10} +(3.04483 - 0.694963i) q^{11} +(-1.82690 + 0.0505229i) q^{12} +(-2.93205 - 1.99904i) q^{13} +(-0.0984222 - 0.0386279i) q^{14} +(-0.341664 + 0.0612014i) q^{15} +(0.699432 + 0.336829i) q^{16} +(2.15961 - 0.161841i) q^{17} +(2.69321 + 1.11810i) q^{18} +(2.91075 - 3.13704i) q^{19} +(-0.202060 - 0.0623271i) q^{20} +(-0.131914 - 0.134513i) q^{21} +(-2.37346 - 1.89277i) q^{22} +(-0.722374 + 2.34188i) q^{23} +(3.31698 + 3.93129i) q^{24} +(4.90444 + 0.739226i) q^{25} +(0.257775 + 3.43977i) q^{26} +(3.56519 + 3.78014i) q^{27} +(-0.0338302 - 0.109675i) q^{28} +(0.956739 - 2.43773i) q^{29} +(0.253576 + 0.222561i) q^{30} +(5.18616 - 0.781688i) q^{31} +(1.15373 + 5.05482i) q^{32} +(-2.48090 - 4.80698i) q^{33} +(-1.43183 - 1.54314i) q^{34} +(-0.00945788 - 0.0196395i) q^{35} +(0.873873 + 3.04247i) q^{36} +(-4.96678 - 2.86757i) q^{37} +(-4.14809 - 0.310856i) q^{38} +(-2.08653 + 5.78149i) q^{39} +(0.217424 + 0.553988i) q^{40} +(3.78089 - 3.01516i) q^{41} +(-0.0222779 + 0.181771i) q^{42} +(1.33352 + 6.42041i) q^{43} -3.29541i q^{44} +(0.250237 + 0.546646i) q^{45} +(2.21753 - 0.870318i) q^{46} +(7.44244 + 1.69869i) q^{47} +(0.262850 - 1.31867i) q^{48} +(-3.49408 + 6.05193i) q^{49} +(-2.41055 - 4.17520i) q^{50} +(-1.20431 - 3.55247i) q^{51} +(-2.74486 + 2.54686i) q^{52} +(-6.81584 - 9.99701i) q^{53} +(0.712084 - 5.00036i) q^{54} +(-0.0932818 - 0.618885i) q^{55} +(-0.181967 + 0.266896i) q^{56} +(-6.51914 - 3.52722i) q^{57} +(-2.43241 + 0.750301i) q^{58} +(-1.96294 + 4.07608i) q^{59} +(-0.0172629 + 0.365842i) q^{60} +(0.478733 - 3.17619i) q^{61} +(-3.73713 - 3.46755i) q^{62} +(-0.168641 + 0.279366i) q^{63} +(4.11029 - 5.15415i) q^{64} +(-0.443397 + 0.556002i) q^{65} +(-2.14958 + 4.79866i) q^{66} +(0.190505 + 0.176763i) q^{67} +(0.340581 - 2.25961i) q^{68} +(4.24012 + 0.200078i) q^{69} +(-0.00919332 + 0.0190901i) q^{70} +(-9.73840 + 3.00390i) q^{71} +(5.16128 - 7.26177i) q^{72} +(-7.61510 + 11.1693i) q^{73} +(0.830869 + 5.51246i) q^{74} +(-0.878559 - 8.54565i) q^{75} +(-2.54366 - 3.73087i) q^{76} +(0.249029 - 0.231065i) q^{77} +(5.65826 - 1.91818i) q^{78} +(6.71699 + 11.6342i) q^{79} +(0.0777862 - 0.134730i) q^{80} +(4.80053 - 7.61281i) q^{81} +(-4.58281 - 1.04600i) q^{82} +(-2.55672 + 1.00344i) q^{83} +(-0.169347 + 0.104118i) q^{84} -0.433999i q^{85} +(4.07109 - 4.90452i) q^{86} +(-4.50213 - 0.551781i) q^{87} +(-7.25132 + 5.78273i) q^{88} +(-1.97459 - 5.03117i) q^{89} +(0.263774 - 0.521465i) q^{90} +(-0.384923 - 0.0288460i) q^{91} +(2.23950 + 1.29297i) q^{92} +(-3.55132 - 8.36123i) q^{93} +(-3.21955 - 6.68546i) q^{94} +(-0.583313 - 0.628662i) q^{95} +(7.98021 - 4.11861i) q^{96} +(3.10236 + 13.5923i) q^{97} +(6.71683 - 1.01240i) q^{98} +(-6.99124 + 6.23765i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 14 q^{3} - 48 q^{4} - 4 q^{6} - 42 q^{7}+O(q^{10}) \) 144 * q - 14 * q^3 - 48 * q^4 - 4 * q^6 - 42 * q^7	\( 144 q - 14 q^{3} - 48 q^{4} - 4 q^{6} - 42 q^{7} - 26 q^{10} - 4 q^{12} - 48 q^{13} - 19 q^{15} - 8 q^{16} + 16 q^{18} - 10 q^{19} - 15 q^{21} + 14 q^{22} - 11 q^{24} - 16 q^{25} - 14 q^{27} - 42 q^{28} - 6 q^{30} - 36 q^{31} + 7 q^{33} + 80 q^{34} + 48 q^{36} - 6 q^{37} + 7 q^{39} + 118 q^{40} + 46 q^{43} + 78 q^{46} - 41 q^{48} - 54 q^{49} + 7 q^{51} - 4 q^{52} - 52 q^{54} - 22 q^{55} - 110 q^{57} + 18 q^{58} - 9 q^{60} - 58 q^{61} - 82 q^{63} + 72 q^{64} - 127 q^{66} + 10 q^{67} - 15 q^{69} - 196 q^{70} + 179 q^{72} + 42 q^{73} + 119 q^{75} + 4 q^{76} + 62 q^{78} - 30 q^{79} + 200 q^{81} - 28 q^{82} + 111 q^{84} - 18 q^{87} - 14 q^{88} + 131 q^{90} - 38 q^{91} + 156 q^{93} + 28 q^{94} + 304 q^{96} + 72 q^{97} + 121 q^{99}+O(q^{100}) \) 144 * q - 14 * q^3 - 48 * q^4 - 4 * q^6 - 42 * q^7 - 26 * q^10 - 4 * q^12 - 48 * q^13 - 19 * q^15 - 8 * q^16 + 16 * q^18 - 10 * q^19 - 15 * q^21 + 14 * q^22 - 11 * q^24 - 16 * q^25 - 14 * q^27 - 42 * q^28 - 6 * q^30 - 36 * q^31 + 7 * q^33 + 80 * q^34 + 48 * q^36 - 6 * q^37 + 7 * q^39 + 118 * q^40 + 46 * q^43 + 78 * q^46 - 41 * q^48 - 54 * q^49 + 7 * q^51 - 4 * q^52 - 52 * q^54 - 22 * q^55 - 110 * q^57 + 18 * q^58 - 9 * q^60 - 58 * q^61 - 82 * q^63 + 72 * q^64 - 127 * q^66 + 10 * q^67 - 15 * q^69 - 196 * q^70 + 179 * q^72 + 42 * q^73 + 119 * q^75 + 4 * q^76 + 62 * q^78 - 30 * q^79 + 200 * q^81 - 28 * q^82 + 111 * q^84 - 18 * q^87 - 14 * q^88 + 131 * q^90 - 38 * q^91 + 156 * q^93 + 28 * q^94 + 304 * q^96 + 72 * q^97 + 121 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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