LMFDB - Embedded newform 231.2.w.a.13.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(13,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("231.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.w (of order $10$, degree $4$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.9
Character	$\chi$	$=$	231.13
Dual form			231.2.w.a.160.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.332589 + 0.108065i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.51910 - 1.10369i) q^{4} +(3.96320 - 1.28772i) q^{5} +(-0.108065 - 0.332589i) q^{6} +(-2.37010 + 1.17584i) q^{7} +(-0.797068 - 1.09707i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.332589 + 0.108065i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.51910 - 1.10369i) q^{4} +(3.96320 - 1.28772i) q^{5} +(-0.108065 - 0.332589i) q^{6} +(-2.37010 + 1.17584i) q^{7} +(-0.797068 - 1.09707i) q^{8} +(-0.309017 + 0.951057i) q^{9} +1.45728 q^{10} +(-1.10010 - 3.12886i) q^{11} +1.87771i q^{12} +(1.97734 - 6.08561i) q^{13} +(-0.915338 + 0.134949i) q^{14} +(-3.37130 - 2.44939i) q^{15} +(1.01395 + 3.12060i) q^{16} +(0.623587 + 1.91920i) q^{17} +(-0.205551 + 0.282917i) q^{18} +(-1.36846 + 0.994244i) q^{19} +(-7.44173 - 2.41797i) q^{20} +(2.34439 + 1.22631i) q^{21} +(-0.0277621 - 1.15951i) q^{22} +1.56284 q^{23} +(-0.419043 + 1.28968i) q^{24} +(10.0037 - 7.26809i) q^{25} +(1.31528 - 1.81033i) q^{26} +(0.951057 - 0.309017i) q^{27} +(4.89818 + 0.829633i) q^{28} +(-2.42963 + 3.34409i) q^{29} +(-0.856565 - 1.17896i) q^{30} +(4.27791 + 1.38998i) q^{31} +3.85955i q^{32} +(-1.88468 + 2.72910i) q^{33} +0.705694i q^{34} +(-7.87904 + 7.71215i) q^{35} +(1.51910 - 1.10369i) q^{36} +(3.73861 + 2.71626i) q^{37} +(-0.562577 + 0.182792i) q^{38} +(-6.08561 + 1.97734i) q^{39} +(-4.57166 - 3.32151i) q^{40} +(-1.12819 + 0.819676i) q^{41} +(0.647198 + 0.661203i) q^{42} +7.48193i q^{43} +(-1.78213 + 5.96721i) q^{44} +4.16716i q^{45} +(0.519784 + 0.168888i) q^{46} +(1.86184 + 2.56260i) q^{47} +(1.92864 - 2.65454i) q^{48} +(4.23478 - 5.57375i) q^{49} +(4.11253 - 1.33624i) q^{50} +(1.18613 - 1.63257i) q^{51} +(-9.72038 + 7.06227i) q^{52} +(-3.46267 + 10.6570i) q^{53} +0.349705 q^{54} +(-8.38903 - 10.9837i) q^{55} +(3.17912 + 1.66294i) q^{56} +(1.60872 + 0.522705i) q^{57} +(-1.16945 + 0.849652i) q^{58} +(2.76071 - 3.79979i) q^{59} +(2.41797 + 7.44173i) q^{60} +(1.68748 + 5.19353i) q^{61} +(1.27258 + 0.924582i) q^{62} +(-0.385893 - 2.61746i) q^{63} +(1.61081 - 4.95756i) q^{64} -26.6648i q^{65} +(-0.921743 + 0.704001i) q^{66} +0.632056 q^{67} +(1.17091 - 3.60370i) q^{68} +(-0.918616 - 1.26437i) q^{69} +(-3.45389 + 1.71353i) q^{70} +(-1.44049 - 4.43338i) q^{71} +(1.28968 - 0.419043i) q^{72} +(-3.03577 - 2.20562i) q^{73} +(0.949888 + 1.30741i) q^{74} +(-11.7600 - 3.82106i) q^{75} +3.17616 q^{76} +(6.28641 + 6.12218i) q^{77} -2.23769 q^{78} +(5.24560 + 1.70440i) q^{79} +(8.03694 + 11.0619i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.463801 + 0.150698i) q^{82} +(-0.906968 - 2.79136i) q^{83} +(-2.20789 - 4.45036i) q^{84} +(4.94280 + 6.80319i) q^{85} +(-0.808533 + 2.48841i) q^{86} +4.13353 q^{87} +(-2.55572 + 3.70080i) q^{88} -8.75676i q^{89} +(-0.450323 + 1.38595i) q^{90} +(2.46925 + 16.7486i) q^{91} +(-2.37411 - 1.72489i) q^{92} +(-1.38998 - 4.27791i) q^{93} +(0.342300 + 1.05349i) q^{94} +(-4.14317 + 5.70259i) q^{95} +(3.12245 - 2.26859i) q^{96} +(4.60529 + 1.49635i) q^{97} +(2.01077 - 1.39614i) q^{98} +(3.31567 - 0.0793871i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9}+O(q^{10}) $ 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9	$ 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9} - 16 q^{11} + 12 q^{14} - 12 q^{15} - 16 q^{16} + 10 q^{18} - 40 q^{22} - 24 q^{23} + 44 q^{25} - 30 q^{28} - 40 q^{29} - 40 q^{35} - 12 q^{36} + 32 q^{37} - 2 q^{42} + 22 q^{44} - 70 q^{46} - 50 q^{49} - 40 q^{51} - 64 q^{53} + 80 q^{56} + 2 q^{58} - 36 q^{60} + 10 q^{63} + 72 q^{64} - 8 q^{67} - 26 q^{70} + 68 q^{71} - 10 q^{72} + 80 q^{74} + 90 q^{77} - 72 q^{78} + 40 q^{79} - 16 q^{81} + 60 q^{84} - 40 q^{85} - 62 q^{86} + 140 q^{88} + 54 q^{91} + 18 q^{92} - 20 q^{93} + 20 q^{95} - 4 q^{99}+O(q^{100}) $ 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9 - 16 * q^11 + 12 * q^14 - 12 * q^15 - 16 * q^16 + 10 * q^18 - 40 * q^22 - 24 * q^23 + 44 * q^25 - 30 * q^28 - 40 * q^29 - 40 * q^35 - 12 * q^36 + 32 * q^37 - 2 * q^42 + 22 * q^44 - 70 * q^46 - 50 * q^49 - 40 * q^51 - 64 * q^53 + 80 * q^56 + 2 * q^58 - 36 * q^60 + 10 * q^63 + 72 * q^64 - 8 * q^67 - 26 * q^70 + 68 * q^71 - 10 * q^72 + 80 * q^74 + 90 * q^77 - 72 * q^78 + 40 * q^79 - 16 * q^81 + 60 * q^84 - 40 * q^85 - 62 * q^86 + 140 * q^88 + 54 * q^91 + 18 * q^92 - 20 * q^93 + 20 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.332589	+	0.108065i	0.235176	+	0.0764133i	0.424234	−	0.905553i	$-0.360543\pi$
$2$	0.332589	+	0.108065i	0.235176	+	0.0764133i	−0.189058	+	0.981966i	$0.560543\pi$
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$4$	−1.51910	−	1.10369i	−0.759548	−	0.551844i
$5$	3.96320	−	1.28772i	1.77240	−	0.575887i	0.774039	−	0.633138i	$-0.218234\pi$
$5$	3.96320	−	1.28772i	1.77240	−	0.575887i	0.998360	+	0.0572509i	$0.0182335\pi$
$6$	−0.108065	−	0.332589i	−0.0441172	−	0.135779i
$7$	−2.37010	+	1.17584i	−0.895815	+	0.444428i
$7$	−2.37010	+	1.17584i	−0.895815	+	0.444428i
$8$	−0.797068	−	1.09707i	−0.281806	−	0.387873i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	1.45728			0.460831
$11$	−1.10010	−	3.12886i	−0.331693	−	0.943387i
$11$	−1.10010	−	3.12886i	−0.331693	−	0.943387i
$12$			1.87771i			0.542047i
$13$	1.97734	−	6.08561i	0.548414	−	1.68785i	−0.164317	−	0.986408i	$-0.552542\pi$
$13$	1.97734	−	6.08561i	0.548414	−	1.68785i	0.712731	−	0.701438i	$-0.247458\pi$
$14$	−0.915338	+	0.134949i	−0.244634	+	0.0360665i
$15$	−3.37130	−	2.44939i	−0.870467	−	0.632431i
$16$	1.01395	+	3.12060i	0.253486	+	0.780150i
$17$	0.623587	+	1.91920i	0.151242	+	0.465475i	0.997761	−	0.0668838i	$-0.0213057\pi$
$17$	0.623587	+	1.91920i	0.151242	+	0.465475i	−0.846519	+	0.532359i	$0.821306\pi$
$18$	−0.205551	+	0.282917i	−0.0484489	+	0.0666842i
$19$	−1.36846	+	0.994244i	−0.313946	+	0.228095i	−0.733588	−	0.679595i	$-0.762156\pi$
$19$	−1.36846	+	0.994244i	−0.313946	+	0.228095i	0.419642	+	0.907690i	$0.362156\pi$
$20$	−7.44173	−	2.41797i	−1.66402	−	0.540674i
$21$	2.34439	+	1.22631i	0.511588	+	0.267603i
$22$	−0.0277621	−	1.15951i	−0.00591889	−	0.247208i
$23$	1.56284			0.325875			0.162938	−	0.986636i	$-0.447903\pi$
$23$	1.56284			0.325875			0.162938	+	0.986636i	$0.447903\pi$
$24$	−0.419043	+	1.28968i	−0.0855369	+	0.263255i
$25$	10.0037	−	7.26809i	2.00073	−	1.45362i
$26$	1.31528	−	1.81033i	0.257948	−	0.355034i
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	4.89818	+	0.829633i	0.925669	+	0.156786i
$29$	−2.42963	+	3.34409i	−0.451170	+	0.620982i	−0.972648	−	0.232282i	$-0.925381\pi$
$29$	−2.42963	+	3.34409i	−0.451170	+	0.620982i	0.521478	+	0.853265i	$0.325381\pi$
$30$	−0.856565	−	1.17896i	−0.156387	−	0.215248i
$31$	4.27791	+	1.38998i	0.768335	+	0.249647i	0.666852	−	0.745190i	$-0.267641\pi$
$31$	4.27791	+	1.38998i	0.768335	+	0.249647i	0.101483	+	0.994837i	$0.467641\pi$
$32$			3.85955i			0.682279i
$33$	−1.88468	+	2.72910i	−0.328081	+	0.475075i
$34$			0.705694i			0.121025i
$35$	−7.87904	+	7.71215i	−1.33180	+	1.30359i
$36$	1.51910	−	1.10369i	0.253183	−	0.183948i
$37$	3.73861	+	2.71626i	0.614623	+	0.446550i	0.851039	−	0.525102i	$-0.175973\pi$
$37$	3.73861	+	2.71626i	0.614623	+	0.446550i	−0.236416	+	0.971652i	$0.575973\pi$
$38$	−0.562577	+	0.182792i	−0.0912621	+	0.0296529i
$39$	−6.08561	+	1.97734i	−0.974478	+	0.316627i
$40$	−4.57166	−	3.32151i	−0.722843	−	0.525177i
$41$	−1.12819	+	0.819676i	−0.176193	+	0.128012i	−0.672387	−	0.740200i	$-0.734731\pi$
$41$	−1.12819	+	0.819676i	−0.176193	+	0.128012i	0.496193	+	0.868212i	$0.334731\pi$
$42$	0.647198	+	0.661203i	0.0998648	+	0.102026i
$43$			7.48193i			1.14098i	0.821303	+	0.570492i	$0.193248\pi$
$43$			7.48193i			1.14098i	−0.821303	+	0.570492i	$0.806752\pi$
$44$	−1.78213	+	5.96721i	−0.268666	+	0.899591i
$45$			4.16716i			0.621203i
$46$	0.519784	+	0.168888i	0.0766380	+	0.0249012i
$47$	1.86184	+	2.56260i	0.271577	+	0.373794i	0.922921	−	0.384989i	$-0.125795\pi$
$47$	1.86184	+	2.56260i	0.271577	+	0.373794i	−0.651344	+	0.758782i	$0.725795\pi$
$48$	1.92864	−	2.65454i	0.278375	−	0.383150i
$49$	4.23478	−	5.57375i	0.604968	−	0.796250i
$50$	4.11253	−	1.33624i	0.581600	−	0.188973i
$51$	1.18613	−	1.63257i	0.166092	−	0.228606i
$52$	−9.72038	+	7.06227i	−1.34797	+	0.979361i
$53$	−3.46267	+	10.6570i	−0.475635	+	1.46385i	0.369465	+	0.929244i	$0.379541\pi$
$53$	−3.46267	+	10.6570i	−0.475635	+	1.46385i	−0.845100	+	0.534608i	$0.820459\pi$
$54$	0.349705			0.0475888
$55$	−8.38903	−	10.9837i	−1.13118	−	1.48104i
$56$	3.17912	+	1.66294i	0.424827	+	0.222220i
$57$	1.60872	+	0.522705i	0.213080	+	0.0692340i
$58$	−1.16945	+	0.849652i	−0.153556	+	0.111565i
$59$	2.76071	−	3.79979i	0.359414	−	0.494691i	−0.590572	−	0.806985i	$-0.701098\pi$
$59$	2.76071	−	3.79979i	0.359414	−	0.494691i	0.949985	+	0.312295i	$0.101098\pi$
$60$	2.41797	+	7.44173i	0.312158	+	0.960724i
$61$	1.68748	+	5.19353i	0.216060	+	0.664963i	0.999077	+	0.0429627i	$0.0136797\pi$
$61$	1.68748	+	5.19353i	0.216060	+	0.664963i	−0.783017	+	0.622000i	$0.786320\pi$
$62$	1.27258	+	0.924582i	0.161617	+	0.117422i
$63$	−0.385893	−	2.61746i	−0.0486179	−	0.329769i
$64$	1.61081	−	4.95756i	0.201351	−	0.619695i
$65$		−	26.6648i		−	3.30736i
$66$	−0.921743	+	0.704001i	−0.113459	+	0.0866566i
$67$	0.632056			0.0772180			0.0386090	−	0.999254i	$-0.487707\pi$
$67$	0.632056			0.0772180			0.0386090	+	0.999254i	$0.487707\pi$
$68$	1.17091	−	3.60370i	0.141994	−	0.437013i
$69$	−0.918616	−	1.26437i	−0.110588	−	0.152212i
$70$	−3.45389	+	1.71353i	−0.412819	+	0.204806i
$71$	−1.44049	−	4.43338i	−0.170955	−	0.526146i	0.828471	−	0.560033i	$-0.189211\pi$
$71$	−1.44049	−	4.43338i	−0.170955	−	0.526146i	−0.999426	+	0.0338870i	$0.989211\pi$
$72$	1.28968	−	0.419043i	0.151991	−	0.0493847i
$73$	−3.03577	−	2.20562i	−0.355310	−	0.258148i	0.395783	−	0.918344i	$-0.370473\pi$
$73$	−3.03577	−	2.20562i	−0.355310	−	0.258148i	−0.751093	+	0.660196i	$0.770473\pi$
$74$	0.949888	+	1.30741i	0.110422	+	0.151983i
$75$	−11.7600	−	3.82106i	−1.35793	−	0.441218i
$76$	3.17616			0.364330
$77$	6.28641	+	6.12218i	0.716403	+	0.697687i
$78$	−2.23769			−0.253368
$79$	5.24560	+	1.70440i	0.590176	+	0.191760i	0.588854	−	0.808239i	$-0.299579\pi$
$79$	5.24560	+	1.70440i	0.590176	+	0.191760i	0.00132191	+	0.999999i	$0.499579\pi$
$80$	8.03694	+	11.0619i	0.898557	+	1.23676i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−0.463801	+	0.150698i	−0.0512182	+	0.0166418i
$83$	−0.906968	−	2.79136i	−0.0995527	−	0.306392i	0.888861	−	0.458177i	$-0.151498\pi$
$83$	−0.906968	−	2.79136i	−0.0995527	−	0.306392i	−0.988413	+	0.151786i	$0.951498\pi$
$84$	−2.20789	−	4.45036i	−0.240901	−	0.485574i
$85$	4.94280	+	6.80319i	0.536122	+	0.737909i
$86$	−0.808533	+	2.48841i	−0.0871864	+	0.268332i
$87$	4.13353			0.443161
$88$	−2.55572	+	3.70080i	−0.272441	+	0.394507i
$89$		−	8.75676i		−	0.928215i	−0.885779	−	0.464107i	$-0.846375\pi$
$89$		−	8.75676i		−	0.928215i	0.885779	−	0.464107i	$-0.153625\pi$
$90$	−0.450323	+	1.38595i	−0.0474682	+	0.146092i
$91$	2.46925	+	16.7486i	0.258847	+	1.75573i
$92$	−2.37411	−	1.72489i	−0.247518	−	0.179832i
$93$	−1.38998	−	4.27791i	−0.144134	−	0.443598i
$94$	0.342300	+	1.05349i	0.0353056	+	0.108659i
$95$	−4.14317	+	5.70259i	−0.425081	+	0.585073i
$96$	3.12245	−	2.26859i	0.318683	−	0.231537i
$97$	4.60529	+	1.49635i	0.467596	+	0.151931i	0.533332	−	0.845906i	$-0.320939\pi$
$97$	4.60529	+	1.49635i	0.467596	+	0.151931i	−0.0657359	+	0.997837i	$0.520939\pi$
$98$	2.01077	−	1.39614i	0.203118	−	0.141031i
$99$	3.31567	−	0.0793871i	0.333238	−	0.00797871i
$100$	−23.2182			−2.32182
$101$	−0.189088	+	0.581955i	−0.0188150	+	0.0579066i	−0.960023	−	0.279920i	$-0.909692\pi$
$101$	−0.189088	+	0.581955i	−0.0188150	+	0.0579066i	0.941208	+	0.337827i	$0.109692\pi$
$102$	0.570918	−	0.414796i	0.0565293	−	0.0410710i
$103$	5.91799	−	8.14541i	0.583117	−	0.802591i	−0.410916	−	0.911673i	$-0.634791\pi$
$103$	5.91799	−	8.14541i	0.583117	−	0.802591i	0.994033	+	0.109082i	$0.0347911\pi$
$104$	−8.25241	+	2.68137i	−0.809215	+	0.262930i
$105$	10.8704	+	1.84119i	1.06085	+	0.179682i
$106$	−2.30329	+	3.17021i	−0.223716	+	0.307918i
$107$	6.56524	+	9.03628i	0.634686	+	0.873570i	0.998318	−	0.0579726i	$-0.0184636\pi$
$107$	6.56524	+	9.03628i	0.634686	+	0.873570i	−0.363633	+	0.931542i	$0.618464\pi$
$108$	−1.78581	−	0.580243i	−0.171839	−	0.0558339i
$109$		−	11.3390i		−	1.08608i	−0.839708	−	0.543038i	$-0.817274\pi$
$109$		−	11.3390i		−	1.08608i	0.839708	−	0.543038i	$-0.182726\pi$
$110$	−1.60315	−	4.55961i	−0.152854	−	0.434742i
$111$		−	4.62117i		−	0.438622i
$112$	−6.07250	−	6.20391i	−0.573797	−	0.586214i
$113$	−11.9029	+	8.64798i	−1.11973	+	0.813533i	−0.984168	−	0.177235i	$-0.943285\pi$
$113$	−11.9029	+	8.64798i	−1.11973	+	0.813533i	−0.135564	+	0.990769i	$0.543285\pi$
$114$	0.478557	+	0.347692i	0.0448210	+	0.0325643i
$115$	6.19387	−	2.01251i	0.577581	−	0.187667i
$116$	7.38167	−	2.39845i	0.685371	−	0.222691i
$117$	5.17673	+	3.76112i	0.478589	+	0.347715i
$118$	1.32880	−	0.965433i	0.122326	−	0.0888753i
$119$	−3.73465	−	3.81547i	−0.342355	−	0.349763i
$120$			5.65089i			0.515853i
$121$	−8.57955	+	6.88413i	−0.779959	+	0.625830i
$122$			1.90967i			0.172893i
$123$	1.32626	+	0.430929i	0.119585	+	0.0388556i
$124$	−4.96445	−	6.83298i	−0.445821	−	0.613620i
$125$	18.0403	−	24.8304i	1.61358	−	2.22090i
$126$	0.154511	−	0.912239i	0.0137650	−	0.0812687i
$127$	9.26531	−	3.01048i	0.822163	−	0.267137i	0.132422	−	0.991193i	$-0.457724\pi$
$127$	9.26531	−	3.01048i	0.822163	−	0.267137i	0.689741	+	0.724056i	$0.257724\pi$
$128$	5.60865	−	7.71965i	0.495740	−	0.682327i
$129$	6.05301	−	4.39777i	0.532938	−	0.387202i
$130$	2.88152	−	8.86841i	0.252726	−	0.777811i
$131$	−11.0983			−0.969665			−0.484833	−	0.874607i	$-0.661119\pi$
$131$	−11.0983			−0.969665			−0.484833	+	0.874607i	$0.661119\pi$
$132$	5.87508	−	2.06567i	0.511360	−	0.179793i
$133$	2.07431	−	3.96556i	0.179866	−	0.343857i
$134$	0.210215	+	0.0683030i	0.0181598	+	0.00590048i
$135$	3.37130	−	2.44939i	0.290156	−	0.210810i
$136$	1.60846	−	2.21385i	0.137924	−	0.189836i
$137$	−4.20500	−	12.9417i	−0.359258	−	1.10568i	−0.953499	−	0.301395i	$-0.902548\pi$
$137$	−4.20500	−	12.9417i	−0.359258	−	1.10568i	0.594242	−	0.804287i	$-0.297452\pi$
$138$	−0.168888	−	0.519784i	−0.0143767	−	0.0442470i
$139$	−4.85367	−	3.52640i	−0.411683	−	0.299105i	0.362600	−	0.931945i	$-0.381889\pi$
$139$	−4.85367	−	3.52640i	−0.411683	−	0.299105i	−0.774283	+	0.632840i	$0.781889\pi$
$140$	20.4808	−	3.01950i	1.73095	−	0.255194i
$141$	0.978826	−	3.01252i	0.0824321	−	0.253700i
$142$		−	1.63016i		−	0.136800i
$143$	−21.2163	+	0.507982i	−1.77420	+	0.0424796i
$144$	−3.28120			−0.273433
$145$	−5.32284	+	16.3820i	−0.442038	+	1.36045i
$146$	−0.771315	−	1.06162i	−0.0638345	−	0.0878607i
$147$	−6.99840	−	0.149841i	−0.577218	−	0.0123587i
$148$	−2.68140	−	8.25251i	−0.220410	−	0.678352i
$149$	−14.7925	+	4.80637i	−1.21185	+	0.393753i	−0.844107	−	0.536175i	$-0.819869\pi$
$149$	−14.7925	+	4.80637i	−1.21185	+	0.393753i	−0.367741	+	0.929928i	$0.619869\pi$
$150$	−3.49833	−	2.54169i	−0.285638	−	0.207528i
$151$	−7.45214	−	10.2570i	−0.606447	−	0.834702i	0.389832	−	0.920886i	$-0.372533\pi$
$151$	−7.45214	−	10.2570i	−0.606447	−	0.834702i	−0.996279	+	0.0861833i	$0.972533\pi$
$152$	2.18151	+	0.708815i	0.176944	+	0.0574925i
$153$	−2.01797			−0.163143
$154$	1.42920	+	2.71551i	0.115168	+	0.218822i
$155$	18.7441			1.50556
$156$	11.4270	+	3.71286i	0.914892	+	0.297266i
$157$	9.66057	+	13.2966i	0.770998	+	1.06119i	0.996219	+	0.0868796i	$0.0276895\pi$
$157$	9.66057	+	13.2966i	0.770998	+	1.06119i	−0.225221	+	0.974308i	$0.572310\pi$
$158$	1.56044	+	1.13373i	0.124142	+	0.0901946i
$159$	10.6570	−	3.46267i	0.845156	−	0.274608i
$160$	4.97004	+	15.2962i	0.392916	+	1.20927i
$161$	−3.70410	+	1.83766i	−0.291924	+	0.144828i
$162$	−0.205551	−	0.282917i	−0.0161496	−	0.0222281i
$163$	−4.39800	+	13.5357i	−0.344478	+	1.06019i	0.617385	+	0.786661i	$0.288192\pi$
$163$	−4.39800	+	13.5357i	−0.344478	+	1.06019i	−0.961863	+	0.273533i	$0.911808\pi$
$164$	2.61849			0.204470
$165$	−3.95504	+	13.2429i	−0.307900	+	1.03096i
$166$		−	1.02639i		−	0.0796631i
$167$	−2.95044	+	9.08052i	−0.228312	+	0.702672i	0.769627	+	0.638494i	$0.220442\pi$
$167$	−2.95044	+	9.08052i	−0.228312	+	0.702672i	−0.997938	+	0.0641776i	$0.979558\pi$
$168$	−0.523291	−	3.54941i	−0.0403728	−	0.273843i
$169$	−22.6076	−	16.4254i	−1.73905	−	1.26349i
$170$	0.908738	+	2.79681i	0.0696970	+	0.214505i
$171$	−0.522705	−	1.60872i	−0.0399723	−	0.123022i
$172$	8.25772	−	11.3658i	0.629645	−	0.866633i
$173$	−10.3010	+	7.48411i	−0.783170	+	0.569007i	−0.905929	−	0.423430i	$-0.860826\pi$
$173$	−10.3010	+	7.48411i	−0.783170	+	0.569007i	0.122758	+	0.992437i	$0.460826\pi$
$174$	1.37477	+	0.446688i	0.104221	+	0.0338634i
$175$	−15.1636	+	28.9889i	−1.14626	+	2.19135i
$176$	8.64849	−	6.60547i	0.651904	−	0.497906i
$177$	−4.69680			−0.353033
$178$	0.946297	−	2.91240i	0.0709279	−	0.218294i
$179$	−3.96245	+	2.87889i	−0.296167	+	0.215178i	−0.725938	−	0.687760i	$-0.758594\pi$
$179$	−3.96245	+	2.87889i	−0.296167	+	0.215178i	0.429771	+	0.902938i	$0.358594\pi$
$180$	4.59924	−	6.33032i	0.342807	−	0.471834i
$181$	−13.3750	+	4.34580i	−0.994156	+	0.323021i	−0.760528	−	0.649305i	$-0.775060\pi$
$181$	−13.3750	+	4.34580i	−0.994156	+	0.323021i	−0.233628	+	0.972326i	$0.575060\pi$
$182$	−0.988685	+	5.83723i	−0.0732862	+	0.432684i
$183$	3.20978	−	4.41788i	0.237273	−	0.326579i
$184$	−1.24569	−	1.71455i	−0.0918336	−	0.126398i
$185$	18.3146	+	5.95079i	1.34652	+	0.437511i
$186$		−	1.57299i		−	0.115337i
$187$	5.31891	−	4.06244i	0.388957	−	0.297075i
$188$		−	5.94773i		−	0.433783i
$189$	−1.89075	+	1.85070i	−0.137532	+	0.134618i
$190$	−1.99422	+	1.44889i	−0.144676	+	0.105113i
$191$	12.0083	+	8.72456i	0.868892	+	0.631287i	0.930289	−	0.366827i	$-0.119556\pi$
$191$	12.0083	+	8.72456i	0.868892	+	0.631287i	−0.0613977	+	0.998113i	$0.519556\pi$
$192$	−4.95756	+	1.61081i	−0.357781	+	0.116250i
$193$	8.11329	−	2.63617i	0.584007	−	0.189755i	−0.00208775	−	0.999998i	$-0.500665\pi$
$193$	8.11329	−	2.63617i	0.584007	−	0.189755i	0.586095	+	0.810242i	$0.300665\pi$
$194$	1.36997	+	0.995339i	0.0983579	+	0.0714612i
$195$	−21.5723	+	15.6732i	−1.54482	+	1.12238i
$196$	−12.5847	+	3.79318i	−0.898908	+	0.270942i
$197$			4.78093i			0.340627i	0.985390	+	0.170314i	$0.0544781\pi$
$197$			4.78093i			0.340627i	−0.985390	+	0.170314i	$0.945522\pi$
$198$	1.11134	+	0.331904i	0.0789792	+	0.0235874i
$199$		−	12.5728i		−	0.891260i	−0.895217	−	0.445630i	$-0.852980\pi$
$199$		−	12.5728i		−	0.891260i	0.895217	−	0.445630i	$-0.147020\pi$
$200$	−15.9472	−	5.18156i	−1.12764	−	0.366392i
$201$	−0.371513	−	0.511344i	−0.0262045	−	0.0360675i
$202$	−0.125778	+	0.173118i	−0.00884967	+	0.0121805i
$203$	1.82633	−	10.7827i	0.128183	−	0.756798i
$204$	−3.60370	+	1.17091i	−0.252310	+	0.0819803i
$205$	−3.41572	+	4.70134i	−0.238564	+	0.328356i
$206$	2.84849	−	2.06955i	0.198464	−	0.144192i
$207$	−0.482945	+	1.48635i	−0.0335670	+	0.103309i
$208$	20.9957			1.45579
$209$	4.61630	+	3.18795i	0.319316	+	0.220515i
$210$	3.41642	+	1.78707i	0.235756	+	0.123320i
$211$	8.65047	+	2.81071i	0.595523	+	0.193497i	0.591243	−	0.806494i	$-0.298638\pi$
$211$	8.65047	+	2.81071i	0.595523	+	0.193497i	0.00428028	+	0.999991i	$0.498638\pi$
$212$	17.0221	−	12.3673i	1.16909	−	0.849391i
$213$	−2.73998	+	3.77126i	−0.187740	+	0.258402i
$214$	1.20702	+	3.71484i	0.0825104	+	0.253941i
$215$	9.63466	+	29.6524i	0.657078	+	2.02228i
$216$	−1.09707	−	0.797068i	−0.0746461	−	0.0542336i
$217$	−11.7735	+	1.73577i	−0.799236	+	0.117832i
$218$	1.22534	−	3.77122i	0.0829907	−	0.255419i
$219$			3.75242i			0.253565i
$220$	0.621181	+	25.9442i	0.0418800	+	1.74916i
$221$	12.9126			0.868593
$222$	0.499386	−	1.53695i	0.0335166	−	0.103153i
$223$	−7.19733	−	9.90627i	−0.481969	−	0.663373i	0.496913	−	0.867800i	$-0.334467\pi$
$223$	−7.19733	−	9.90627i	−0.481969	−	0.663373i	−0.978882	+	0.204427i	$0.934467\pi$
$224$	−4.53824	−	9.14754i	−0.303224	−	0.611196i
$225$	3.82106	+	11.7600i	0.254737	+	0.784001i
$226$	−4.89332	+	1.58994i	−0.325499	+	0.105761i
$227$	−17.6489	−	12.8227i	−1.17140	−	0.851070i	−0.180221	−	0.983626i	$-0.557681\pi$
$227$	−17.6489	−	12.8227i	−1.17140	−	0.851070i	−0.991175	+	0.132556i	$0.957681\pi$
$228$	−1.86690	−	2.56957i	−0.123638	−	0.170174i
$229$	−18.7171	−	6.08155i	−1.23686	−	0.401880i	−0.383665	−	0.923472i	$-0.625338\pi$
$229$	−18.7171	−	6.08155i	−1.23686	−	0.401880i	−0.853195	+	0.521592i	$0.825338\pi$
$230$	2.27749			0.150173
$231$	1.25789	−	8.68434i	0.0827628	−	0.571387i
$232$	5.60528			0.368005
$233$	15.3915	+	5.00099i	1.00833	+	0.327626i	0.766189	−	0.642616i	$-0.222151\pi$
$233$	15.3915	+	5.00099i	1.00833	+	0.327626i	0.242139	+	0.970241i	$0.422151\pi$
$234$	1.31528	+	1.81033i	0.0859825	+	0.118345i
$235$	10.6788	+	7.75858i	0.696606	+	0.506114i
$236$	−8.38757	+	2.72529i	−0.545984	+	0.177401i
$237$	−1.70440	−	5.24560i	−0.110713	−	0.340738i
$238$	−0.829786	−	1.67257i	−0.0537871	−	0.108416i
$239$	2.86380	+	3.94168i	0.185244	+	0.254966i	0.891531	−	0.452959i	$-0.149632\pi$
$239$	2.86380	+	3.94168i	0.185244	+	0.254966i	−0.706288	+	0.707925i	$0.749632\pi$
$240$	4.22527	−	13.0040i	0.272740	−	0.839407i
$241$	11.2293			0.723342			0.361671	−	0.932306i	$-0.382206\pi$
$241$	11.2293			0.723342			0.361671	+	0.932306i	$0.382206\pi$
$242$	−3.59740	+	1.36244i	−0.231249	+	0.0875809i
$243$			1.00000i			0.0641500i
$244$	3.16859	−	9.75192i	0.202848	−	0.624303i
$245$	9.60585	−	27.5431i	0.613695	−	1.75967i
$246$	0.394533	+	0.286645i	0.0251545	+	0.0182758i
$247$	3.34468	+	10.2939i	0.212817	+	0.654983i
$248$	−1.88488	−	5.80107i	−0.119690	−	0.368368i
$249$	−1.72516	+	2.37447i	−0.109327	+	0.150476i
$250$	8.68330	−	6.30879i	0.549180	−	0.399003i
$251$	0.0277976	+	0.00903198i	0.00175457	+	0.000570094i	0.309894	−	0.950771i	$-0.399706\pi$
$251$	0.0277976	+	0.00903198i	0.00175457	+	0.000570094i	−0.308140	+	0.951341i	$0.599706\pi$
$252$	−2.30265	+	4.40208i	−0.145053	+	0.277305i
$253$	−1.71929	−	4.88992i	−0.108091	−	0.307427i
$254$	3.40687			0.213766
$255$	2.59859	−	7.99763i	0.162730	−	0.500831i
$256$	−5.73470	+	4.16651i	−0.358419	+	0.260407i
$257$	−16.0366	+	22.0725i	−1.00034	+	1.37684i	−0.0752173	+	0.997167i	$0.523965\pi$
$257$	−16.0366	+	22.0725i	−1.00034	+	1.37684i	−0.925119	+	0.379677i	$0.876035\pi$
$258$	2.48841	−	0.808533i	0.154922	−	0.0503371i
$259$	−12.0548	−	2.04179i	−0.749047	−	0.126870i
$260$	−29.4296	+	40.5064i	−1.82515	+	2.51210i
$261$	−2.42963	−	3.34409i	−0.150390	−	0.206994i
$262$	−3.69118	−	1.19934i	−0.228042	−	0.0740953i
$263$			3.76299i			0.232036i	0.993247	+	0.116018i	$0.0370131\pi$
$263$			3.76299i			0.232036i	−0.993247	+	0.116018i	$0.962987\pi$
$264$	4.49623	−	0.107653i	0.276724	−	0.00662559i
$265$			46.6949i			2.86844i
$266$	1.11843	−	1.09474i	0.0685754	−	0.0671229i
$267$	−7.08437	+	5.14709i	−0.433556	+	0.314997i
$268$	−0.960155	−	0.697593i	−0.0586508	−	0.0426123i
$269$	2.96082	−	0.962030i	0.180525	−	0.0586560i	−0.217360	−	0.976092i	$-0.569744\pi$
$269$	2.96082	−	0.962030i	0.180525	−	0.0586560i	0.397884	+	0.917436i	$0.369744\pi$
$270$	1.38595	−	0.450323i	0.0843463	−	0.0274058i
$271$	7.02003	+	5.10035i	0.426437	+	0.309824i	0.780223	−	0.625502i	$-0.215106\pi$
$271$	7.02003	+	5.10035i	0.426437	+	0.309824i	−0.353786	+	0.935326i	$0.615106\pi$
$272$	−5.35679	+	3.89193i	−0.324803	+	0.235983i
$273$	12.0985	−	11.8422i	0.732234	−	0.716724i
$274$		−	4.75867i		−	0.287482i
$275$	−33.7459	−	23.3045i	−2.03495	−	1.40531i
$276$			2.93456i			0.176640i
$277$	17.1198	+	5.56255i	1.02863	+	0.334221i	0.774247	−	0.632883i	$-0.218129\pi$
$277$	17.1198	+	5.56255i	1.02863	+	0.334221i	0.254380	+	0.967104i	$0.418129\pi$
$278$	−1.23320	−	1.69735i	−0.0739624	−	0.101800i
$279$	−2.64389	+	3.63900i	−0.158286	+	0.217862i
$280$	14.7409	+	2.49675i	0.880937	+	0.149209i
$281$	−0.836596	+	0.271827i	−0.0499072	+	0.0162158i	−0.333864	−	0.942621i	$-0.608353\pi$
$281$	−0.836596	+	0.271827i	−0.0499072	+	0.0162158i	0.283957	+	0.958837i	$0.408353\pi$
$282$	0.651094	−	0.896154i	0.0387721	−	0.0533652i
$283$	−10.1671	+	7.38686i	−0.604374	+	0.439103i	−0.847429	−	0.530909i	$-0.821850\pi$
$283$	−10.1671	+	7.38686i	−0.604374	+	0.439103i	0.243055	+	0.970013i	$0.421850\pi$
$284$	−2.70482	+	8.32459i	−0.160502	+	0.493973i
$285$	7.04879			0.417534
$286$	−7.11121	−	2.12379i	−0.420494	−	0.125582i
$287$	1.71011	−	3.26929i	0.100945	−	0.192980i
$288$	−3.67065	−	1.19267i	−0.216295	−	0.0702786i
$289$	10.4588	−	7.59877i	0.615224	−	0.446986i
$290$	−3.54063	+	4.87326i	−0.207913	+	0.286168i
$291$	−1.49635	−	4.60529i	−0.0877176	−	0.269967i
$292$	2.17732	+	6.70109i	0.127418	+	0.392152i
$293$	25.3447	+	18.4140i	1.48065	+	1.07576i	0.977346	+	0.211647i	$0.0678827\pi$
$293$	25.3447	+	18.4140i	1.48065	+	1.07576i	0.503305	+	0.864109i	$0.332117\pi$
$294$	−2.31140	−	0.806115i	−0.134803	−	0.0470136i
$295$	6.04818	−	18.6144i	0.352138	−	1.08377i
$296$		−	6.26655i		−	0.364236i
$297$	−2.01313	−	2.63577i	−0.116814	−	0.152943i
$298$	−5.43922			−0.315086
$299$	3.09026	−	9.51086i	0.178715	−	0.550027i
$300$	13.6473	+	18.7840i	0.787930	+	1.08449i
$301$	−8.79759	−	17.7330i	−0.507085	−	1.02211i
$302$	−1.37008	−	4.21668i	−0.0788393	−	0.242643i
$303$	0.581955	−	0.189088i	0.0334324	−	0.0108628i
$304$	−4.49018	−	3.26231i	−0.257530	−	0.187106i
$305$	13.3756	+	18.4100i	0.765887	+	1.05415i
$306$	−0.671155	−	0.218071i	−0.0383674	−	0.0124663i
$307$	17.1050			0.976235			0.488118	−	0.872778i	$-0.337684\pi$
$307$	17.1050			0.976235			0.488118	+	0.872778i	$0.337684\pi$
$308$	−2.79269	−	16.2384i	−0.159128	−	0.925270i
$309$	−10.0683			−0.572765
$310$	6.23409	+	2.02558i	0.354072	+	0.115045i
$311$	−12.9763	−	17.8603i	−0.735818	−	1.01277i	−0.998848	−	0.0479787i	$-0.984722\pi$
$311$	−12.9763	−	17.8603i	−0.735818	−	1.01277i	0.263031	−	0.964787i	$-0.415278\pi$
$312$	7.01992	+	5.10027i	0.397425	+	0.288746i
$313$	11.6534	−	3.78641i	0.658688	−	0.214021i	0.0394471	−	0.999222i	$-0.487440\pi$
$313$	11.6534	−	3.78641i	0.658688	−	0.214021i	0.619241	+	0.785201i	$0.287440\pi$
$314$	1.77610	+	5.46628i	0.100231	+	0.308480i
$315$	−4.89993	−	9.87660i	−0.276080	−	0.556483i
$316$	−6.08745	−	8.37865i	−0.342446	−	0.471336i
$317$	−4.19675	+	12.9163i	−0.235713	+	0.725450i	0.761313	+	0.648384i	$0.224555\pi$
$317$	−4.19675	+	12.9163i	−0.235713	+	0.725450i	−0.997026	+	0.0770654i	$0.975445\pi$
$318$	3.91860			0.219744
$319$	13.1360	+	3.92312i	0.735477	+	0.219653i
$320$		−	21.7221i		−	1.21430i
$321$	3.45155	−	10.6228i	0.192647	−	0.592906i
$322$	−1.43053	+	0.210903i	−0.0797203	+	0.0117532i
$323$	−2.76151	−	2.00635i	−0.153655	−	0.111637i
$324$	0.580243	+	1.78581i	0.0322357	+	0.0992114i
$325$	−24.4502	−	75.2499i	−1.35625	−	4.17411i
$326$	−2.92545	+	4.02654i	−0.162026	+	0.223009i
$327$	−9.17342	+	6.66488i	−0.507292	+	0.368569i
$328$	1.79848	+	0.584363i	0.0993047	+	0.0322660i
$329$	−7.42597	−	3.88440i	−0.409407	−	0.214154i
$330$	−2.74650	+	3.97705i	−0.151190	+	0.218929i
$331$	3.89389			0.214027			0.107014	−	0.994258i	$-0.465871\pi$
$331$	3.89389			0.214027			0.107014	+	0.994258i	$0.465871\pi$
$332$	−1.70302	+	5.24135i	−0.0934653	+	0.287657i
$333$	−3.73861	+	2.71626i	−0.204874	+	0.148850i
$334$	−1.96257	+	2.70124i	−0.107387	+	0.147805i
$335$	2.50497	−	0.813914i	0.136861	−	0.0444689i
$336$	−1.44974	+	8.55932i	−0.0790899	+	0.466949i
$337$	15.7851	−	21.7264i	0.859871	−	1.18351i	−0.121729	−	0.992563i	$-0.538844\pi$
$337$	15.7851	−	21.7264i	0.859871	−	1.18351i	0.981600	−	0.190948i	$-0.0611562\pi$
$338$	−5.74403	−	7.90599i	−0.312434	−	0.430029i
$339$	13.9927	+	4.54651i	0.759980	+	0.246933i
$340$		−	15.7900i		−	0.856334i
$341$	−0.357088	−	14.9141i	−0.0193374	−	0.807643i
$342$		−	0.591529i		−	0.0319862i
$343$	−3.48300	+	18.1898i	−0.188064	+	0.982157i
$344$	8.20820	−	5.96361i	0.442557	−	0.321536i
$345$	−5.26882	−	3.82802i	−0.283664	−	0.206094i
$346$	−4.23477	+	1.37596i	−0.227663	+	0.0739720i
$347$	−27.7902	+	9.02957i	−1.49185	+	0.484733i	−0.937630	−	0.347634i	$-0.886985\pi$
$347$	−27.7902	+	9.02957i	−1.49185	+	0.484733i	−0.554224	+	0.832367i	$0.686985\pi$
$348$	−6.27923	−	4.56212i	−0.336602	−	0.244556i
$349$	27.5276	−	20.0000i	1.47352	−	1.07058i	0.493946	−	0.869493i	$-0.335554\pi$
$349$	27.5276	−	20.0000i	1.47352	−	1.07058i	0.979574	−	0.201082i	$-0.0644459\pi$
$350$	−8.17592	+	8.00274i	−0.437021	+	0.427764i
$351$		−	6.39879i		−	0.341542i
$352$	12.0760	−	4.24590i	0.643654	−	0.226307i
$353$		−	1.61968i		−	0.0862068i	−0.999071	−	0.0431034i	$-0.986276\pi$
$353$		−	1.61968i		−	0.0862068i	0.999071	−	0.0431034i	$-0.0137245\pi$
$354$	−1.56210	−	0.507558i	−0.0830249	−	0.0269764i
$355$	−11.4179	−	15.7154i	−0.606001	−	0.834089i
$356$	−9.66473	+	13.3024i	−0.512230	+	0.705024i
$357$	−0.891606	+	5.26407i	−0.0471888	+	0.278604i
$358$	−1.62897	+	0.529286i	−0.0860940	+	0.0279736i
$359$	5.09573	−	7.01367i	0.268942	−	0.370168i	−0.653090	−	0.757280i	$-0.726528\pi$
$359$	5.09573	−	7.01367i	0.268942	−	0.370168i	0.922032	+	0.387113i	$0.126528\pi$
$360$	4.57166	−	3.32151i	0.240948	−	0.175059i
$361$	−4.98716	+	15.3489i	−0.262482	+	0.807837i
$362$	−4.91801			−0.258485
$363$	10.6123	+	2.89461i	0.557002	+	0.151928i
$364$	14.7342	−	28.1680i	0.772281	−	1.47640i
$365$	−14.8716	−	4.83208i	−0.778416	−	0.252923i
$366$	1.54495	−	1.12247i	0.0807560	−	0.0586726i
$367$	8.88655	−	12.2313i	0.463874	−	0.638468i	−0.511432	−	0.859324i	$-0.670885\pi$
$367$	8.88655	−	12.2313i	0.463874	−	0.638468i	0.975307	+	0.220855i	$0.0708849\pi$
$368$	1.58464	+	4.87701i	0.0826049	+	0.254232i
$369$	−0.430929	−	1.32626i	−0.0224333	−	0.0690426i
$370$	5.44818	+	3.95833i	0.283237	+	0.205784i
$371$	−4.32410	−	29.3298i	−0.224496	−	1.52273i
$372$	−2.60997	+	8.03265i	−0.135321	+	0.416474i
$373$			1.90216i			0.0984899i	0.998787	+	0.0492450i	$0.0156815\pi$
$373$			1.90216i			0.0984899i	−0.998787	+	0.0492450i	$0.984318\pi$
$374$	2.20802	−	0.776335i	0.114174	−	0.0401433i
$375$	−30.6920			−1.58493
$376$	1.32734	−	4.08513i	0.0684523	−	0.210675i
$377$	15.5467	+	21.3982i	0.800694	+	1.10206i
$378$	−0.828836	+	0.411199i	−0.0426307	+	0.0211498i
$379$	5.71818	+	17.5988i	0.293723	+	0.903988i	0.983647	+	0.180106i	$0.0576440\pi$
$379$	5.71818	+	17.5988i	0.293723	+	0.903988i	−0.689924	+	0.723882i	$0.742356\pi$
$380$	12.5878	−	4.09001i	0.645738	−	0.209813i
$381$	−7.88154	−	5.72628i	−0.403784	−	0.293366i
$382$	3.05102	+	4.19937i	0.156104	+	0.214858i
$383$	10.4024	+	3.37995i	0.531539	+	0.172708i	0.562476	−	0.826814i	$-0.309849\pi$
$383$	10.4024	+	3.37995i	0.531539	+	0.172708i	−0.0309365	+	0.999521i	$0.509849\pi$
$384$	−9.54201			−0.486939
$385$	32.7980	+	16.1683i	1.67154	+	0.824012i
$386$	2.98327			0.151844
$387$	−7.11574	−	2.31204i	−0.361714	−	0.117528i
$388$	−5.34438	−	7.35591i	−0.271320	−	0.373440i
$389$	−5.14922	−	3.74113i	−0.261076	−	0.189683i	0.449545	−	0.893258i	$-0.351586\pi$
$389$	−5.14922	−	3.74113i	−0.261076	−	0.189683i	−0.710621	+	0.703575i	$0.751586\pi$
$390$	−8.86841	+	2.88152i	−0.449070	+	0.145912i
$391$	0.974569	+	2.99941i	0.0492861	+	0.151687i
$392$	−9.49019	−	0.203193i	−0.479327	−	0.0102628i
$393$	6.52343	+	8.97873i	0.329064	+	0.452917i
$394$	−0.516650	+	1.59009i	−0.0260285	+	0.0801073i
$395$	22.9842			1.15646
$396$	−5.12445	−	3.53887i	−0.257513	−	0.177835i
$397$			29.2990i			1.47047i	0.677810	+	0.735237i	$0.262929\pi$
$397$			29.2990i			1.47047i	−0.677810	+	0.735237i	$0.737071\pi$
$398$	1.35867	−	4.18157i	0.0681041	−	0.209603i
$399$	−4.42745	+	0.652741i	−0.221650	+	0.0326779i
$400$	32.8240	+	23.8480i	1.64120	+	1.19240i
$401$	3.73187	+	11.4855i	0.186361	+	0.573560i	0.999969	−	0.00785370i	$-0.00249994\pi$
$401$	3.73187	+	11.4855i	0.186361	+	0.573560i	−0.813608	+	0.581413i	$0.802500\pi$
$402$	−0.0683030	−	0.210215i	−0.00340664	−	0.0104846i
$403$	16.9177	−	23.2852i	0.842731	−	1.15992i
$404$	0.929540	−	0.675350i	0.0462463	−	0.0335999i
$405$	−3.96320	−	1.28772i	−0.196933	−	0.0639875i
$406$	1.77265	−	3.38885i	0.0879750	−	0.168186i
$407$	4.38594	−	14.6857i	0.217403	−	0.727945i
$408$	−2.73647			−0.135476
$409$	−1.02449	+	3.15307i	−0.0506580	+	0.155909i	−0.973185	−	0.230023i	$-0.926120\pi$
$409$	−1.02449	+	3.15307i	−0.0506580	+	0.155909i	0.922527	+	0.385932i	$0.126120\pi$
$410$	−1.64408	+	1.19449i	−0.0811953	+	0.0589919i
$411$	−7.99839	+	11.0088i	−0.394532	+	0.543026i
$412$	−17.9800	+	5.84205i	−0.885810	+	0.287817i
$413$	−2.07520	+	12.2521i	−0.102114	+	0.602885i
$414$	−0.321244	+	0.442155i	−0.0157883	+	0.0217307i
$415$	−7.18900	−	9.89481i	−0.352894	−	0.485717i
$416$	23.4878	+	7.63163i	1.15158	+	0.374172i
$417$			5.99947i			0.293795i
$418$	1.19082	+	1.55914i	0.0582451	+	0.0762599i
$419$		−	4.06652i		−	0.198662i	−0.995054	−	0.0993312i	$-0.968330\pi$
$419$		−	4.06652i		−	0.198662i	0.995054	−	0.0993312i	$-0.0316703\pi$
$420$	−14.4812	−	14.7945i	−0.706608	−	0.721899i
$421$	−19.6732	+	14.2934i	−0.958814	+	0.696619i	−0.952875	−	0.303363i	$-0.901891\pi$
$421$	−19.6732	+	14.2934i	−0.958814	+	0.696619i	−0.00593918	+	0.999982i	$0.501891\pi$
$422$	2.57331	+	1.86962i	0.125267	+	0.0910117i
$423$	−3.01252	+	0.978826i	−0.146474	+	0.0475922i
$424$	14.4515	−	4.69557i	0.701825	−	0.228037i
$425$	20.1871	+	14.6668i	0.979218	+	0.711444i
$426$	−1.31883	+	0.958184i	−0.0638974	+	0.0464242i
$427$	−10.1063	−	10.3250i	−0.489077	−	0.499661i
$428$		−	20.9730i		−	1.01377i
$429$	12.8816	+	16.8658i	0.621929	+	0.814287i
$430$			10.9032i			0.525801i
$431$	−28.2820	−	9.18939i	−1.36230	−	0.442637i	−0.465488	−	0.885054i	$-0.654121\pi$
$431$	−28.2820	−	9.18939i	−1.36230	−	0.442637i	−0.896809	+	0.442417i	$0.854121\pi$
$432$	1.92864	+	2.65454i	0.0927916	+	0.127717i
$433$	−5.98862	+	8.24263i	−0.287795	+	0.396116i	−0.928296	−	0.371841i	$-0.878727\pi$
$433$	−5.98862	+	8.24263i	−0.287795	+	0.396116i	0.640502	+	0.767957i	$0.278727\pi$
$434$	−4.10330	−	0.695000i	−0.196965	−	0.0333611i
$435$	16.3820	−	5.32284i	0.785457	−	0.255210i
$436$	−12.5147	+	17.2250i	−0.599345	+	0.824928i
$437$	−2.13869	+	1.55385i	−0.102307	+	0.0743306i
$438$	−0.405504	+	1.24801i	−0.0193757	+	0.0596324i
$439$	−36.6861			−1.75093			−0.875465	−	0.483281i	$-0.839445\pi$
$439$	−36.6861			−1.75093			−0.875465	+	0.483281i	$0.839445\pi$
$440$	−5.36325	+	17.9581i	−0.255683	+	0.856119i
$441$	3.99233	+	5.74990i	0.190111	+	0.273805i
$442$	4.29458	+	1.39539i	0.204272	+	0.0663721i
$443$	−29.3233	+	21.3046i	−1.39319	+	1.01221i	−0.397686	+	0.917521i	$0.630187\pi$
$443$	−29.3233	+	21.3046i	−1.39319	+	1.01221i	−0.995507	+	0.0946924i	$0.969813\pi$
$444$	−5.10033	+	7.02000i	−0.242051	+	0.333155i
$445$	−11.2763	−	34.7048i	−0.534547	−	1.64517i
$446$	−1.32323	−	4.07249i	−0.0626569	−	0.192838i
$447$	12.5832	+	9.14227i	0.595167	+	0.432414i
$448$	2.01154	+	13.6440i	0.0950362	+	0.644618i
$449$	−1.50233	+	4.62370i	−0.0708994	+	0.218206i	−0.980227	−	0.197874i	$-0.936596\pi$
$449$	−1.50233	+	4.62370i	−0.0708994	+	0.218206i	0.909328	+	0.416080i	$0.136596\pi$
$450$			4.32417i			0.203844i
$451$	3.80578	+	2.62822i	0.179207	+	0.123758i
$452$	27.6264			1.29943
$453$	−3.91782	+	12.0578i	−0.184075	+	0.566526i
$454$	−4.48414	−	6.17190i	−0.210451	−	0.289661i
$455$	31.3536	+	63.1983i	1.46988	+	2.96278i
$456$	−0.708815	−	2.18151i	−0.0331933	−	0.102159i
$457$	9.41570	−	3.05935i	0.440448	−	0.143110i	−0.0803943	−	0.996763i	$-0.525618\pi$
$457$	9.41570	−	3.05935i	0.440448	−	0.143110i	0.520842	+	0.853653i	$0.325618\pi$
$458$	−5.56790	−	4.04531i	−0.260171	−	0.189025i
$459$	1.18613	+	1.63257i	0.0553639	+	0.0762019i
$460$	−11.6303	−	3.77890i	−0.542264	−	0.176192i
$461$	−32.4336			−1.51058			−0.755291	−	0.655390i	$-0.772504\pi$
$461$	−32.4336			−1.51058			−0.755291	+	0.655390i	$0.772504\pi$
$462$	1.35683	−	2.75238i	0.0631254	−	0.128052i
$463$	−35.1871			−1.63528			−0.817641	−	0.575728i	$-0.804719\pi$
$463$	−35.1871			−1.63528			−0.817641	+	0.575728i	$0.804719\pi$
$464$	−12.8991	−	4.19117i	−0.598825	−	0.194570i
$465$	−11.0175	−	15.1643i	−0.510925	−	0.703228i
$466$	4.57860	+	3.32655i	0.212100	+	0.154099i
$467$	31.2059	−	10.1394i	1.44404	−	0.469196i	0.520883	−	0.853628i	$-0.325603\pi$
$467$	31.2059	−	10.1394i	1.44404	−	0.469196i	0.923153	+	0.384432i	$0.125603\pi$
$468$	−3.71286	−	11.4270i	−0.171627	−	0.528213i
$469$	−1.49804	+	0.743200i	−0.0691730	+	0.0343178i
$470$	2.71321	+	3.73442i	0.125151	+	0.172256i
$471$	5.07886	−	15.6311i	0.234022	−	0.720245i
$472$	−6.36911			−0.293162
$473$	23.4099	−	8.23089i	1.07639	−	0.378457i
$474$		−	1.92881i		−	0.0885934i
$475$	−6.46336	+	19.8922i	−0.296559	+	0.912716i
$476$	1.46221	+	9.91796i	0.0670202	+	0.454589i
$477$	−9.06539	−	6.58639i	−0.415076	−	0.301570i
$478$	0.526511	+	1.62043i	0.0240821	+	0.0741169i
$479$	−8.92389	−	27.4649i	−0.407743	−	1.25490i	−0.918583	−	0.395228i	$-0.870666\pi$
$479$	−8.92389	−	27.4649i	−0.407743	−	1.25490i	0.510840	−	0.859676i	$-0.329334\pi$
$480$	9.45357	−	13.0117i	0.431495	−	0.593901i
$481$	23.9226	−	17.3808i	1.09077	−	0.792494i
$482$	3.73474	+	1.21349i	0.170113	+	0.0552730i
$483$	3.66391	+	1.91653i	0.166714	+	0.0872051i
$484$	20.6311	−	0.988507i	0.937777	−	0.0449321i
$485$	20.1786			0.916263
$486$	−0.108065	+	0.332589i	−0.00490192	+	0.0150865i
$487$	12.3253	−	8.95484i	0.558512	−	0.405783i	−0.272402	−	0.962184i	$-0.587818\pi$
$487$	12.3253	−	8.95484i	0.558512	−	0.405783i	0.830914	+	0.556401i	$0.187818\pi$
$488$	4.35262	−	5.99087i	0.197034	−	0.271194i
$489$	13.5357	−	4.39800i	0.612103	−	0.198884i
$490$	6.17124	−	8.12248i	0.278788	−	0.366936i
$491$	13.7341	−	18.9034i	0.619811	−	0.853097i	−0.377528	−	0.925998i	$-0.623226\pi$
$491$	13.7341	−	18.9034i	0.619811	−	0.853097i	0.997339	+	0.0729013i	$0.0232258\pi$
$492$	−1.53911	−	2.11841i	−0.0693885	−	0.0955051i
$493$	−7.93308	−	2.57761i	−0.357288	−	0.116090i
$494$			3.78507i			0.170298i
$495$	13.0385	−	4.58430i	0.586035	−	0.206049i
$496$			14.7590i			0.662699i
$497$	8.62709	+	8.81378i	0.386978	+	0.395352i
$498$	−0.830364	+	0.603295i	−0.0372095	+	0.0270343i
$499$	−2.90613	−	2.11143i	−0.130096	−	0.0945204i	0.520834	−	0.853658i	$-0.325621\pi$
$499$	−2.90613	−	2.11143i	−0.130096	−	0.0945204i	−0.650930	+	0.759137i	$0.725621\pi$
$500$	−54.8100	+	17.8088i	−2.45118	+	0.796436i
$501$	9.08052	−	2.95044i	0.405688	−	0.131816i
$502$	0.00826913	+	0.00600788i	0.000369070	+	0.000268145i
$503$	−29.4940	+	21.4287i	−1.31507	+	0.955457i	−0.315094	+	0.949061i	$0.602036\pi$
$503$	−29.4940	+	21.4287i	−1.31507	+	0.955457i	−0.999980	+	0.00639620i	$0.997964\pi$
$504$	−2.56395	+	2.50964i	−0.114207	+	0.111788i
$505$			2.54990i			0.113469i
$506$	−0.0433877	−	1.81213i	−0.00192882	−	0.0805589i
$507$			27.9445i			1.24106i
$508$	−17.3975	−	5.65280i	−0.771891	−	0.250802i
$509$	−12.5767	−	17.3103i	−0.557451	−	0.767266i	0.433549	−	0.901130i	$-0.357261\pi$
$509$	−12.5767	−	17.3103i	−0.557451	−	0.767266i	−0.991000	+	0.133865i	$0.957261\pi$
$510$	1.72852	−	2.37911i	0.0765403	−	0.105349i
$511$	9.78856	+	1.65794i	0.433020	+	0.0733432i
$512$	−20.5075	+	6.66330i	−0.906314	+	0.294479i
$513$	−0.994244	+	1.36846i	−0.0438969	+	0.0604190i
$514$	−7.71886	+	5.60808i	−0.340464	+	0.247362i
$515$	12.9652	−	39.9027i	0.571313	−	1.75832i
$516$	−14.0489			−0.618467
$517$	5.96981	−	8.64456i	0.262552	−	0.380187i
$518$	−3.78864	−	1.98177i	−0.166463	−	0.0870741i
$519$	12.1096	+	3.93463i	0.531550	+	0.172711i
$520$	−29.2531	+	21.2536i	−1.28283	+	0.932034i
$521$	17.9903	−	24.7615i	0.788169	−	1.08482i	−0.206164	−	0.978517i	$-0.566098\pi$
$521$	17.9903	−	24.7615i	0.788169	−	1.08482i	0.994334	−	0.106304i	$-0.0339018\pi$
$522$	−0.446688	−	1.37477i	−0.0195510	−	0.0601718i
$523$	10.5730	+	32.5404i	0.462326	+	1.42289i	0.862315	+	0.506373i	$0.169014\pi$
$523$	10.5730	+	32.5404i	0.462326	+	1.42289i	−0.399989	+	0.916520i	$0.630986\pi$
$524$	16.8594	+	12.2491i	0.736508	+	0.535104i
$525$	32.3654	−	4.77165i	1.41254	−	0.208252i
$526$	−0.406647	+	1.25153i	−0.0177307	+	0.0545693i
$527$			9.07694i			0.395398i
$528$	−10.4274	−	3.11418i	−0.453794	−	0.135527i
$529$	−20.5575			−0.893805
$530$	−5.04607	+	15.5302i	−0.219187	+	0.674589i
$531$	2.76071	+	3.79979i	0.119805	+	0.164897i
$532$	−7.52782	+	3.73467i	−0.326372	+	0.161918i
$533$	2.75743	+	8.48649i	0.119437	+	0.367591i
$534$	−2.91240	+	0.946297i	−0.126032	+	0.0409503i
$535$	37.6556	+	27.3584i	1.62799	+	1.18281i
$536$	−0.503792	−	0.693410i	−0.0217605	−	0.0299507i
$537$	4.65814	+	1.51352i	0.201014	+	0.0653133i
$538$	1.08870			0.0469372
$539$	−22.0982	−	7.11835i	−0.951836	−	0.306609i
$540$	−7.82470			−0.336722
$541$	−24.7281	−	8.03463i	−1.06314	−	0.345436i	−0.275329	−	0.961350i	$-0.588787\pi$
$541$	−24.7281	−	8.03463i	−1.06314	−	0.345436i	−0.787813	+	0.615914i	$0.788787\pi$
$542$	1.78362	+	2.45494i	0.0766130	+	0.105449i
$543$	11.3775	+	8.26621i	0.488254	+	0.354737i
$544$	−7.40727	+	2.40677i	−0.317584	+	0.103189i
$545$	−14.6015	−	44.9387i	−0.625458	−	1.92496i
$546$	5.30355	−	2.63117i	0.226971	−	0.112604i
$547$	9.52877	+	13.1152i	0.407421	+	0.560766i	0.962587	−	0.270973i	$-0.0873454\pi$
$547$	9.52877	+	13.1152i	0.407421	+	0.560766i	−0.555166	+	0.831739i	$0.687345\pi$
$548$	−7.89576	+	24.3007i	−0.337290	+	1.03807i
$549$	−5.46080			−0.233061
$550$	−8.70513	−	11.3976i	−0.371188	−	0.485993i
$551$		−	6.99190i		−	0.297865i
$552$	−0.654899	+	2.01557i	−0.0278743	+	0.0857884i
$553$	−14.4367	+	2.12841i	−0.613912	+	0.0905092i
$554$	5.09273	+	3.70008i	0.216369	+	0.157202i
$555$	−5.95079	−	18.3146i	−0.252597	−	0.777413i
$556$	3.48115	+	10.7139i	0.147634	+	0.454370i
$557$	−14.1946	+	19.5371i	−0.601443	+	0.827815i	−0.995839	−	0.0911253i	$-0.970954\pi$
$557$	−14.1946	+	19.5371i	−0.601443	+	0.827815i	0.394397	+	0.918940i	$0.370954\pi$
$558$	−1.27258	+	0.924582i	−0.0538725	+	0.0391407i
$559$	45.5321	+	14.7943i	1.92580	+	0.625732i
$560$	−32.0555	−	16.7677i	−1.35459	−	0.708563i
$561$	−6.41296	−	1.91525i	−0.270755	−	0.0808620i
$562$	−0.307618			−0.0129761
$563$	12.9189	−	39.7602i	0.544465	−	1.67569i	−0.177792	−	0.984068i	$-0.556895\pi$
$563$	12.9189	−	39.7602i	0.544465	−	1.67569i	0.722258	−	0.691624i	$-0.243105\pi$
$564$	−4.81181	+	3.49599i	−0.202614	+	0.147208i
$565$	−36.0375	+	49.6014i	−1.51611	+	2.08674i
$566$	−4.17974	+	1.35808i	−0.175687	+	0.0570843i
$567$	2.60860	+	0.441833i	0.109551	+	0.0185553i
$568$	−3.71556	+	5.11403i	−0.155901	+	0.214580i
$569$	6.65514	+	9.16002i	0.278998	+	0.384008i	0.925402	−	0.378988i	$-0.123728\pi$
$569$	6.65514	+	9.16002i	0.278998	+	0.384008i	−0.646404	+	0.762996i	$0.723728\pi$
$570$	2.34435	+	0.761725i	0.0981940	+	0.0319052i
$571$			32.8774i			1.37588i	0.725769	+	0.687939i	$0.241484\pi$
$571$			32.8774i			1.37588i	−0.725769	+	0.687939i	$0.758516\pi$
$572$	32.7903	+	22.6445i	1.37103	+	0.946815i
$573$		−	14.8431i		−	0.620079i
$574$	0.922059	−	0.902528i	0.0384860	−	0.0376708i
$575$	15.6342	−	11.3589i	0.651990	−	0.473698i
$576$	4.21715	+	3.06394i	0.175715	+	0.127664i
$577$	−16.8833	+	5.48571i	−0.702860	+	0.228373i	−0.638576	−	0.769559i	$-0.720476\pi$
$577$	−16.8833	+	5.48571i	−0.702860	+	0.228373i	−0.0642839	+	0.997932i	$0.520476\pi$
$578$	4.29964	−	1.39704i	0.178842	−	0.0581092i
$579$	−6.90157	−	5.01429i	−0.286820	−	0.208387i
$580$	26.1665	−	19.0111i	1.08651	−	0.789393i
$581$	5.43181	+	5.54936i	0.225350	+	0.230226i
$582$		−	1.69337i		−	0.0701925i
$583$	37.1536	−	0.889568i	1.53874	−	0.0368421i
$584$			5.08848i			0.210563i
$585$	25.3597	+	8.23987i	1.04850	+	0.340677i
$586$	6.43946	+	8.86315i	0.266011	+	0.366133i
$587$	−4.82629	+	6.64281i	−0.199202	+	0.274178i	−0.896919	−	0.442196i	$-0.854200\pi$
$587$	−4.82629	+	6.64281i	−0.199202	+	0.274178i	0.697716	+	0.716374i	$0.254200\pi$
$588$	10.4659	+	7.95167i	0.431605	+	0.327921i
$589$	−7.23612	+	2.35116i	−0.298159	+	0.0968777i
$590$	4.02311	−	5.53734i	0.165629	−	0.227969i
$591$	3.86785	−	2.81016i	0.159102	−	0.115595i
$592$	−4.68561	+	14.4208i	−0.192578	+	0.592693i
$593$	−12.7967			−0.525496			−0.262748	−	0.964864i	$-0.584629\pi$
$593$	−12.7967			−0.525496			−0.262748	+	0.964864i	$0.584629\pi$
$594$	−0.384711	−	1.09418i	−0.0157849	−	0.0448947i
$595$	−19.7144	−	10.3123i	−0.808214	−	0.422762i
$596$	27.7760	+	9.02496i	1.13775	+	0.369677i
$597$	−10.1716	+	7.39009i	−0.416295	+	0.302456i
$598$	2.05558	−	2.82926i	0.0840588	−	0.115697i
$599$	5.28291	+	16.2591i	0.215854	+	0.664330i	0.999092	+	0.0426077i	$0.0135666\pi$
$599$	5.28291	+	16.2591i	0.215854	+	0.664330i	−0.783238	+	0.621722i	$0.786433\pi$
$600$	5.18156	+	15.9472i	0.211536	+	0.651042i
$601$	−28.9050	−	21.0007i	−1.17906	−	0.856636i	−0.186993	−	0.982361i	$-0.559874\pi$
$601$	−28.9050	−	21.0007i	−1.17906	−	0.856636i	−0.992065	+	0.125725i	$0.959874\pi$
$602$	−1.00968	−	6.84850i	−0.0411513	−	0.279124i
$603$	−0.195316	+	0.601121i	−0.00795389	+	0.0244796i
$604$			23.8062i			0.968661i
$605$	−25.1377	+	38.3313i	−1.02199	+	1.55839i
$606$	0.213985			0.00869257
$607$	12.6187	−	38.8363i	0.512176	−	1.57632i	−0.276185	−	0.961104i	$-0.589070\pi$
$607$	12.6187	−	38.8363i	0.512176	−	1.57632i	0.788362	−	0.615212i	$-0.210930\pi$
$608$	−3.83734	−	5.28164i	−0.155625	−	0.214199i
$609$	−9.79688	+	4.86039i	−0.396990	+	0.196953i
$610$	2.45912	+	7.56840i	0.0995669	+	0.306435i
$611$	19.2765	−	6.26331i	0.779843	−	0.253386i
$612$	3.06549	+	2.22721i	0.123915	+	0.0900296i
$613$	−14.0061	−	19.2778i	−0.565702	−	0.778622i	0.426336	−	0.904565i	$-0.359804\pi$
$613$	−14.0061	−	19.2778i	−0.565702	−	0.778622i	−0.992037	+	0.125943i	$0.959804\pi$
$614$	5.68894	+	1.84845i	0.229587	+	0.0745974i
$615$	5.81117			0.234329
$616$	1.70576	−	11.7764i	0.0687270	−	0.474485i
$617$	−4.46249			−0.179653			−0.0898265	−	0.995957i	$-0.528631\pi$
$617$	−4.46249			−0.179653			−0.0898265	+	0.995957i	$0.528631\pi$
$618$	−3.34860	−	1.08803i	−0.134700	−	0.0437668i
$619$	28.7769	+	39.6080i	1.15664	+	1.59198i	0.722921	+	0.690931i	$0.242799\pi$
$619$	28.7769	+	39.6080i	1.15664	+	1.59198i	0.433720	+	0.901048i	$0.357201\pi$
$620$	−28.4741	−	20.6877i	−1.14355	−	0.830837i
$621$	1.48635	−	0.482945i	0.0596453	−	0.0193799i
$622$	−2.38570	−	7.34243i	−0.0956578	−	0.294404i
$623$	10.2966	+	20.7544i	0.412524	+	0.831508i
$624$	−12.3410	−	16.9859i	−0.494033	−	0.679979i
$625$	20.4175	−	62.8387i	0.816701	−	2.51355i
$626$	4.28496			0.171262
$627$	−0.134284	−	5.60849i	−0.00536279	−	0.223982i
$628$		−	30.8611i		−	1.23149i
$629$	−2.88170	+	8.86897i	−0.114901	+	0.353629i
$630$	−0.562352	−	3.81436i	−0.0224046	−	0.151968i
$631$	−6.72921	−	4.88906i	−0.267886	−	0.194630i	0.445730	−	0.895167i	$-0.352944\pi$
$631$	−6.72921	−	4.88906i	−0.267886	−	0.194630i	−0.713616	+	0.700537i	$0.752944\pi$
$632$	−2.31125	−	7.11331i	−0.0919368	−	0.282952i
$633$	−2.81071	−	8.65047i	−0.111716	−	0.343825i
$634$	−2.79159	+	3.84229i	−0.110868	+	0.152597i
$635$	32.8436	−	23.8623i	1.30336	−	0.946946i
$636$	−20.0107	−	6.50188i	−0.793477	−	0.257816i
$637$	−25.5461	−	36.7924i	−1.01217	−	1.45777i
$638$	3.94495	+	2.72433i	0.156182	+	0.107857i
$639$	4.66153			0.184407
$640$	12.2875	−	37.8169i	0.485705	−	1.49485i
$641$	−0.499651	+	0.363018i	−0.0197350	+	0.0143383i	−0.597609	−	0.801788i	$-0.703882\pi$
$641$	−0.499651	+	0.363018i	−0.0197350	+	0.0143383i	0.577874	+	0.816126i	$0.303882\pi$
$642$	2.29590	−	3.16003i	0.0906118	−	0.124716i
$643$	−23.8101	+	7.73638i	−0.938979	+	0.305093i	−0.738229	−	0.674550i	$-0.764338\pi$
$643$	−23.8101	+	7.73638i	−0.938979	+	0.305093i	−0.200750	+	0.979643i	$0.564338\pi$
$644$	7.65509	+	1.29659i	0.301653	+	0.0510927i
$645$	18.3262	−	25.2239i	0.721594	−	0.993189i
$646$	−0.701632	−	0.965713i	−0.0276053	−	0.0379955i
$647$	9.84152	+	3.19770i	0.386910	+	0.125715i	0.496012	−	0.868316i	$-0.334797\pi$
$647$	9.84152	+	3.19770i	0.386910	+	0.125715i	−0.109102	+	0.994031i	$0.534797\pi$
$648$			1.35605i			0.0532708i
$649$	−14.9261	−	4.45772i	−0.585900	−	0.174981i
$650$		−	27.6695i		−	1.08529i
$651$	8.32454	+	8.50468i	0.326264	+	0.333325i
$652$	21.6201	−	15.7079i	0.846709	−	0.615170i
$653$	−19.8206	−	14.4005i	−0.775642	−	0.563537i	0.128026	−	0.991771i	$-0.459136\pi$
$653$	−19.8206	−	14.4005i	−0.775642	−	0.563537i	−0.903668	+	0.428234i	$0.859136\pi$
$654$	−3.77122	+	1.22534i	−0.147466	+	0.0479147i
$655$	−43.9849	+	14.2916i	−1.71863	+	0.558418i
$656$	−3.70180	−	2.68952i	−0.144531	−	0.105008i
$657$	3.03577	−	2.20562i	0.118437	−	0.0860494i
$658$	−2.05003	−	2.09439i	−0.0799185	−	0.0816479i
$659$			3.33279i			0.129827i	0.997891	+	0.0649136i	$0.0206772\pi$
$659$			3.33279i			0.129827i	−0.997891	+	0.0649136i	$0.979323\pi$
$660$	20.6241	−	15.7521i	0.802794	−	0.613151i
$661$			0.988745i			0.0384577i	0.999815	+	0.0192289i	$0.00612111\pi$
$661$			0.988745i			0.0384577i	−0.999815	+	0.0192289i	$0.993879\pi$
$662$	1.29506	+	0.420792i	0.0503341	+	0.0163545i
$663$	−7.58982	−	10.4465i	−0.294764	−	0.405708i
$664$	−2.33940	+	3.21991i	−0.0907864	+	0.124957i
$665$	3.11439	−	18.3875i	0.120771	−	0.713035i
$666$	−1.53695	+	0.499386i	−0.0595556	+	0.0193508i
$667$	−3.79712	+	5.22629i	−0.147025	+	0.202363i
$668$	14.5041	−	10.5378i	0.561179	−	0.407721i
$669$	−3.78386	+	11.6455i	−0.146292	+	0.450242i
$670$	0.921080			0.0355844
$671$	14.3934	−	10.9933i	0.555652	−	0.424391i
$672$	−4.73301	+	9.04830i	−0.182580	+	0.349046i
$673$	−7.32075	−	2.37866i	−0.282194	−	0.0916905i	0.164500	−	0.986377i	$-0.447399\pi$
$673$	−7.32075	−	2.37866i	−0.282194	−	0.0916905i	−0.446694	+	0.894687i	$0.647399\pi$
$674$	7.59782	−	5.52014i	0.292657	−	0.212628i
$675$	7.26809	−	10.0037i	0.279749	−	0.385041i
$676$	16.2146	+	49.9035i	0.623639	+	1.91936i
$677$	−5.49225	−	16.9034i	−0.211084	−	0.649650i	−0.999408	−	0.0343903i	$-0.989051\pi$
$677$	−5.49225	−	16.9034i	−0.211084	−	0.649650i	0.788324	−	0.615260i	$-0.210949\pi$
$678$	4.16251	+	3.02424i	0.159860	+	0.116145i
$679$	−12.6745	+	1.86860i	−0.486402	+	0.0717104i
$680$	3.52382	−	10.8452i	0.135132	−	0.415894i
$681$			21.8152i			0.835961i
$682$	1.49292	−	4.99885i	0.0571670	−	0.191416i
$683$	48.1503			1.84242			0.921210	−	0.389067i	$-0.127202\pi$
$683$	48.1503			1.84242			0.921210	+	0.389067i	$0.127202\pi$
$684$	−0.981487	+	3.02071i	−0.0375281	+	0.115500i
$685$	−33.3306	−	45.8756i	−1.27350	−	1.75282i
$686$	−3.12408	+	5.67334i	−0.119278	+	0.216609i
$687$	6.08155	+	18.7171i	0.232026	+	0.714101i
$688$	−23.3481	+	7.58627i	−0.890139	+	0.289224i
$689$	58.0076	+	42.1450i	2.20991	+	1.60560i
$690$	−1.33868	−	1.84253i	−0.0509626	−	0.0701439i
$691$	25.7950	+	8.38130i	0.981288	+	0.318840i	0.755364	−	0.655305i	$-0.227460\pi$
$691$	25.7950	+	8.38130i	0.981288	+	0.318840i	0.225924	+	0.974145i	$0.427460\pi$
$692$	23.9083			0.908859
$693$	−7.76514	+	4.08687i	−0.294973	+	0.155248i
$694$	−10.2185			−0.387888
$695$	−23.7771	−	7.72565i	−0.901918	−	0.293051i
$696$	−3.29470	−	4.53477i	−0.124885	−	0.171890i
$697$	−2.27665	−	1.65408i	−0.0862342	−	0.0626528i
$698$	11.3167	−	3.67701i	0.428343	−	0.139177i
$699$	−5.00099	−	15.3915i	−0.189155	−	0.582158i
$700$	55.0296	−	27.3011i	2.07992	−	1.03188i
$701$	−16.8744	−	23.2256i	−0.637336	−	0.877218i	0.361134	−	0.932514i	$-0.382390\pi$
$701$	−16.8744	−	23.2256i	−0.637336	−	0.877218i	−0.998470	+	0.0552963i	$0.982390\pi$
$702$	0.691484	−	2.12817i	0.0260984	−	0.0803225i
$703$	−7.81675			−0.294814
$704$	−17.2836	+	0.413820i	−0.651399	+	0.0155964i
$705$		−	13.1997i		−	0.497129i
$706$	0.175030	−	0.538687i	0.00658735	−	0.0202738i
$707$	−0.236129	−	1.60163i	−0.00888054	−	0.0602355i
$708$	7.13489	+	5.18380i	0.268146	+	0.194819i
$709$	−10.0272	−	30.8604i	−0.376578	−	1.15899i	−0.942408	−	0.334465i	$-0.891444\pi$
$709$	−10.0272	−	30.8604i	−0.376578	−	1.15899i	0.565830	−	0.824522i	$-0.308556\pi$
$710$	−2.09920	−	6.46066i	−0.0787814	−	0.242464i
$711$	−3.24196	+	4.46217i	−0.121583	+	0.167345i
$712$	−9.60677	+	6.97973i	−0.360029	+	0.261576i
$713$	6.68570	+	2.17231i	0.250381	+	0.0813538i
$714$	−0.865399	+	1.65442i	−0.0323867	+	0.0619152i
$715$	−83.4304	+	29.3340i	−3.12012	+	1.09703i
$716$	9.19674			0.343698
$717$	1.50559	−	4.63372i	0.0562272	−	0.173049i
$718$	2.45272	−	1.78200i	0.0915345	−	0.0665037i
$719$	4.45078	−	6.12597i	0.165986	−	0.228460i	−0.717919	−	0.696127i	$-0.754905\pi$
$719$	4.45078	−	6.12597i	0.165986	−	0.228460i	0.883905	+	0.467667i	$0.154905\pi$
$720$	−13.0040	+	4.22527i	−0.484632	+	0.157467i
$721$	−4.44850	+	26.2641i	−0.165671	+	0.978126i
$722$	−3.31735	+	4.56594i	−0.123459	+	0.169927i
$723$	−6.60041	−	9.08469i	−0.245472	−	0.337863i
$724$	25.1143	+	8.16014i	0.933367	+	0.303269i
$725$			51.1119i			1.89825i
$726$	3.21673	+	2.10953i	0.119384	+	0.0782921i
$727$		−	10.9908i		−	0.407627i	−0.979010	−	0.203813i	$-0.934666\pi$
$727$		−	10.9908i		−	0.407627i	0.979010	−	0.203813i	$-0.0653336\pi$
$728$	16.4062	−	16.0587i	0.608054	−	0.595174i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	−4.42396	−	3.21419i	−0.163738	−	0.118963i
$731$	−14.3594	+	4.66564i	−0.531100	+	0.172565i
$732$	−9.75192	+	3.16859i	−0.360441	+	0.117114i
$733$	−2.00863	−	1.45935i	−0.0741903	−	0.0539024i	0.550072	−	0.835117i	$-0.314600\pi$
$733$	−2.00863	−	1.45935i	−0.0741903	−	0.0539024i	−0.624262	+	0.781215i	$0.714600\pi$
$734$	4.27734	−	3.10767i	0.157880	−	0.114706i
$735$	−27.9290	+	8.41814i	−1.03018	+	0.310508i
$736$			6.03188i			0.222338i
$737$	−0.695326	−	1.97762i	−0.0256127	−	0.0728465i
$738$		−	0.487669i		−	0.0179514i
$739$	18.8600	+	6.12798i	0.693776	+	0.225421i	0.634617	−	0.772827i	$-0.281158\pi$
$739$	18.8600	+	6.12798i	0.693776	+	0.225421i	0.0591592	+	0.998249i	$0.481158\pi$
$740$	−21.2539	−	29.2535i	−0.781309	−	1.07538i
$741$	6.36196	−	8.75649i	0.233712	−	0.321678i
$742$	1.73137	−	10.2220i	0.0635605	−	0.375263i
$743$	−31.9883	+	10.3936i	−1.17354	+	0.381305i	−0.829962	−	0.557821i	$-0.811638\pi$
$743$	−31.9883	+	10.3936i	−1.17354	+	0.381305i	−0.343574	+	0.939125i	$0.611638\pi$
$744$	−3.58526	+	4.93468i	−0.131442	+	0.180914i
$745$	−52.4364	+	38.0973i	−1.92112	+	1.39578i
$746$	−0.205556	+	0.632636i	−0.00752594	+	0.0231625i
$747$	2.93501			0.107386
$748$	−12.5636	+	0.300810i	−0.459371	+	0.0109987i
$749$	−26.1856	−	13.6972i	−0.956799	−	0.500485i
$750$	−10.2078	−	3.31673i	−0.372737	−	0.121110i
$751$	19.9838	−	14.5191i	0.729221	−	0.529810i	−0.160096	−	0.987101i	$-0.551180\pi$
$751$	19.9838	−	14.5191i	0.729221	−	0.529810i	0.889317	+	0.457292i	$0.151180\pi$
$752$	−6.10906	+	8.40839i	−0.222774	+	0.306623i
$753$	−0.00903198	−	0.0277976i	−0.000329144	−	0.00101300i
$754$	2.85827	+	8.79684i	0.104092	+	0.320362i
$755$	−42.7425	−	31.0543i	−1.55556	−	1.13018i
$756$	4.91482	−	0.724593i	0.178750	−	0.0263532i
$757$	−7.92578	+	24.3930i	−0.288067	+	0.886580i	0.697395	+	0.716687i	$0.254342\pi$
$757$	−7.92578	+	24.3930i	−0.288067	+	0.886580i	−0.985463	+	0.169893i	$0.945658\pi$
$758$			6.47109i			0.235041i
$759$	−2.94546	+	4.26515i	−0.106913	+	0.154815i
$760$	9.55853			0.346724
$761$	−15.6492	+	48.1634i	−0.567284	+	1.74592i	0.0937808	+	0.995593i	$0.470105\pi$
$761$	−15.6492	+	48.1634i	−0.567284	+	1.74592i	−0.661065	+	0.750329i	$0.729895\pi$
$762$	−2.00251	−	2.75621i	−0.0725431	−	0.0998471i
$763$	13.3329	+	26.8745i	0.482682	+	0.972924i
$764$	−8.61261	−	26.5069i	−0.311593	−	0.958985i
$765$	−7.99763	+	2.59859i	−0.289155	+	0.0939521i
$766$	3.09448	+	2.24827i	0.111808	+	0.0812333i
$767$	−17.6652	−	24.3141i	−0.637854	−	0.877930i
$768$	6.74155	+	2.19046i	0.243265	+	0.0790415i
$769$	34.6575			1.24978			0.624890	−	0.780713i	$-0.285144\pi$
$769$	34.6575			1.24978			0.624890	+	0.780713i	$0.285144\pi$
$770$	9.16103	+	8.92170i	0.330141	+	0.321516i
$771$	27.2831			0.982577
$772$	−15.2344	−	4.94995i	−0.548297	−	0.178153i
$773$	−4.28759	−	5.90136i	−0.154214	−	0.212257i	0.724919	−	0.688834i	$-0.241877\pi$
$773$	−4.28759	−	5.90136i	−0.154214	−	0.212257i	−0.879133	+	0.476577i	$0.841877\pi$
$774$	−2.11677	−	1.53792i	−0.0760856	−	0.0552794i
$775$	52.8972	−	17.1874i	1.90012	−	0.617388i
$776$	−2.02913	−	6.24502i	−0.0728415	−	0.224183i
$777$	5.43378	+	10.9527i	0.194936	+	0.392924i
$778$	−1.30829	−	1.80071i	−0.0469045	−	0.0645585i
$779$	0.728921	−	2.24339i	0.0261163	−	0.0803777i
$780$	50.0686			1.79274
$781$	−12.2867	+	9.38427i	−0.439654	+	0.335796i
$782$			1.10289i			0.0394392i
$783$	−1.27733	+	3.93122i	−0.0456480	+	0.140490i
$784$	21.6873	+	7.56358i	0.774546	+	0.270128i
$785$	55.4092	+	40.2571i	1.97764	+	1.43684i
$786$	1.19934	+	3.69118i	0.0427790	+	0.131660i
$787$	−10.9233	−	33.6184i	−0.389373	−	1.19837i	−0.933258	−	0.359206i	$-0.883047\pi$
$787$	−10.9233	−	33.6184i	−0.389373	−	1.19837i	0.543886	−	0.839159i	$-0.316953\pi$
$788$	5.27666	−	7.26270i	0.187973	−	0.258723i
$789$	3.04433	−	2.21183i	0.108381	−	0.0787433i
$790$	7.64428	+	2.48378i	0.271971	+	0.0883689i
$791$	18.0425	−	34.4926i	0.641516	−	1.22642i
$792$	−2.72991	−	3.57425i	−0.0970031	−	0.127005i
$793$	34.9425			1.24084
$794$	−3.16619	+	9.74452i	−0.112364	+	0.345820i
$795$	37.7769	−	27.4466i	1.33981	−	0.973429i
$796$	−13.8764	+	19.0993i	−0.491837	+	0.676955i
$797$	11.8910	−	3.86361i	0.421200	−	0.136856i	−0.0907456	−	0.995874i	$-0.528925\pi$
$797$	11.8910	−	3.86361i	0.421200	−	0.136856i	0.511945	+	0.859018i	$0.328925\pi$
$798$	−1.54306	−	0.261357i	−0.0546238	−	0.00925194i
$799$	−3.75713	+	5.17125i	−0.132918	+	0.182946i
$800$	28.0516	+	38.6097i	0.991774	+	1.36506i
$801$	8.32817	+	2.70599i	0.294262	+	0.0956114i
$802$			4.22324i			0.149128i
$803$	−3.56142	+	11.9249i	−0.125680	+	0.420821i
$804$			1.18682i			0.0418558i
$805$	−12.3137	+	12.0529i	−0.434001	+	0.424808i
$806$	8.14296	−	5.91620i	0.286823	−	0.208389i
$807$	−2.51863	−	1.82989i	−0.0886599	−	0.0644152i
$808$	0.789161	−	0.256414i	0.0277626	−	0.00902061i
$809$	32.8771	−	10.6824i	1.15590	−	0.375573i	0.332535	−	0.943091i	$-0.392096\pi$
$809$	32.8771	−	10.6824i	1.15590	−	0.375573i	0.823361	+	0.567518i	$0.192096\pi$
$810$	−1.17896	−	0.856565i	−0.0414245	−	0.0300966i
$811$	5.26980	−	3.82874i	0.185048	−	0.134445i	−0.491405	−	0.870931i	$-0.663516\pi$
$811$	5.26980	−	3.82874i	0.185048	−	0.134445i	0.676453	+	0.736486i	$0.263516\pi$
$812$	−14.6751	+	14.3643i	−0.514996	+	0.504087i
$813$		−	8.67724i		−	0.304324i
$814$	3.04573	−	4.41035i	0.106753	−	0.154583i
$815$			59.3079i			2.07747i
$816$	6.29728	+	2.04611i	0.220449	+	0.0716282i
$817$	−7.43887	−	10.2387i	−0.260253	−	0.358208i
$818$	−0.681472	+	0.937965i	−0.0238271	+	0.0327952i
$819$	−16.6919	−	2.82720i	−0.583261	−	0.0987903i
$820$	10.3776	−	3.37189i	0.362402	−	0.117752i
$821$	19.4282	−	26.7406i	0.678048	−	0.933253i	−0.321861	−	0.946787i	$-0.604308\pi$
$821$	19.4282	−	26.7406i	0.678048	−	0.933253i	0.999908	+	0.0135345i	$0.00430829\pi$
$822$	−3.84985	+	2.79708i	−0.134279	+	0.0975593i
$823$	10.3896	−	31.9759i	0.362158	−	1.11461i	−0.589583	−	0.807708i	$-0.700708\pi$
$823$	10.3896	−	31.9759i	0.362158	−	1.11461i	0.951741	−	0.306901i	$-0.0992922\pi$
$824$	−13.6531			−0.475629
$825$	0.981639	+	40.9990i	0.0341763	+	1.42740i
$826$	−2.01421	+	3.85064i	−0.0700832	+	0.133981i
$827$	23.2553	+	7.55610i	0.808665	+	0.262751i	0.684032	−	0.729452i	$-0.260225\pi$
$827$	23.2553	+	7.55610i	0.808665	+	0.262751i	0.124633	+	0.992203i	$0.460225\pi$
$828$	2.37411	−	1.72489i	0.0825060	−	0.0599441i
$829$	−13.1925	+	18.1579i	−0.458195	+	0.630652i	−0.974133	−	0.225974i	$-0.927443\pi$
$829$	−13.1925	+	18.1579i	−0.458195	+	0.630652i	0.515938	+	0.856626i	$0.327443\pi$
$830$	−1.32170	−	4.06778i	−0.0458769	−	0.141195i
$831$	−5.56255	−	17.1198i	−0.192963	−	0.593878i
$832$	−26.9847	−	19.6055i	−0.935525	−	0.679699i
$833$	13.3379	+	4.65168i	0.462131	+	0.161171i
$834$	−0.648331	+	1.99536i	−0.0224499	+	0.0690936i
$835$			39.7873i			1.37690i
$836$	−3.49410	−	9.93776i	−0.120846	−	0.343705i
$837$	4.49806			0.155476
$838$	0.439447	−	1.35248i	0.0151804	−	0.0467206i
$839$	11.1916	+	15.4039i	0.386377	+	0.531802i	0.957260	−	0.289229i	$-0.0933990\pi$
$839$	11.1916	+	15.4039i	0.386377	+	0.531802i	−0.570883	+	0.821032i	$0.693399\pi$
$840$	−6.64457	−	13.3932i	−0.229259	−	0.462109i
$841$	3.68162	+	11.3308i	0.126952	+	0.390719i
$842$	−8.08771	+	2.62786i	−0.278721	+	0.0905620i
$843$	0.711651	+	0.517045i	0.0245106	+	0.0178080i
$844$	−10.0388	−	13.8172i	−0.345548	−	0.475606i
$845$	−110.750	−	35.9848i	−3.80991	−	1.23792i
$846$	−1.10771			−0.0380838
$847$	12.2398	−	26.4043i	0.420563	−	0.907263i
$848$	−36.7672			−1.26259
$849$	11.9522	+	3.88350i	0.410198	+	0.133281i
$850$	5.12905	+	7.05953i	0.175925	+	0.242140i
$851$	5.84285	+	4.24508i	0.200290	+	0.145520i
$852$	8.32459	−	2.70482i	0.285196	−	0.0926657i
$853$	−0.729862	−	2.24628i	−0.0249900	−	0.0769113i	0.937784	−	0.347220i	$-0.112874\pi$
$853$	−0.729862	−	2.24628i	−0.0249900	−	0.0769113i	−0.962774	+	0.270309i	$0.912874\pi$
$854$	−2.24547	−	4.52611i	−0.0768384	−	0.154880i
$855$	−4.14317	−	5.70259i	−0.141694	−	0.195024i
$856$	4.68048	−	14.4050i	0.159976	−	0.492354i
$857$	19.6527			0.671323			0.335662	−	0.941983i	$-0.391040\pi$
$857$	19.6527			0.671323			0.335662	+	0.941983i	$0.391040\pi$
$858$	2.46168	+	7.00142i	0.0840405	+	0.239024i
$859$		−	24.7271i		−	0.843676i	−0.906671	−	0.421838i	$-0.861385\pi$
$859$		−	24.7271i		−	0.843676i	0.906671	−	0.421838i	$-0.138615\pi$
$860$	18.0911	−	55.6786i	0.616900	−	1.89862i
$861$	−3.65009	+	0.538134i	−0.124395	+	0.0183396i
$862$	−8.41324	−	6.11258i	−0.286556	−	0.208195i
$863$	6.59104	+	20.2851i	0.224362	+	0.690514i	0.998356	+	0.0573212i	$0.0182559\pi$
$863$	6.59104	+	20.2851i	0.224362	+	0.690514i	−0.773994	+	0.633193i	$0.781744\pi$
$864$	1.19267	+	3.67065i	0.0405754	+	0.124878i
$865$	−31.1875	+	42.9259i	−1.06041	+	1.45952i
$866$	−2.88249	+	2.09425i	−0.0979509	+	0.0711655i
$867$	−12.2951	−	3.99491i	−0.417562	−	0.135674i
$868$	19.8008	+	10.3574i	0.672083	+	0.351555i
$869$	−0.437864	−	18.2878i	−0.0148535	−	0.620370i
$870$	6.02369			0.204222
$871$	1.24979	−	3.84645i	0.0423474	−	0.130332i
$872$	−12.4396	+	9.03793i	−0.421260	+	0.306063i
$873$	−2.84623	+	3.91749i	−0.0963302	+	0.132587i
$874$	−0.879220	+	0.285676i	−0.0297401	+	0.00966313i
$875$	−13.5608	+	80.0632i	−0.458437	+	2.70663i
$876$	4.14150	−	5.70029i	0.139928	−	0.192595i
$877$	14.7361	+	20.2825i	0.497602	+	0.684890i	0.981767	−	0.190087i	$-0.0608768\pi$
$877$	14.7361	+	20.2825i	0.497602	+	0.684890i	−0.484166	+	0.874976i	$0.660877\pi$
$878$	−12.2014	−	3.96447i	−0.411777	−	0.133794i
$879$		−	31.3277i		−	1.05666i
$880$	25.7697	−	37.3157i	0.868697	−	1.25791i
$881$		−	0.735946i		−	0.0247946i	−0.999923	−	0.0123973i	$-0.996054\pi$
$881$		−	0.735946i		−	0.0247946i	0.999923	−	0.0123973i	$-0.00394629\pi$
$882$	0.706444	+	2.34378i	0.0237872	+	0.0789193i
$883$	10.3909	−	7.54940i	0.349680	−	0.254057i	−0.399055	−	0.916927i	$-0.630662\pi$
$883$	10.3909	−	7.54940i	0.349680	−	0.254057i	0.748735	+	0.662870i	$0.230662\pi$
$884$	−19.6154	−	14.2514i	−0.659739	−	0.479328i
$885$	−18.6144	+	6.04818i	−0.625715	+	0.203307i
$886$	−12.0549	+	3.91687i	−0.404992	+	0.131590i
$887$	−16.6373	−	12.0877i	−0.558626	−	0.405866i	0.272330	−	0.962204i	$-0.412206\pi$
$887$	−16.6373	−	12.0877i	−0.558626	−	0.405866i	−0.830956	+	0.556338i	$0.812206\pi$
$888$	−5.06975	+	3.68339i	−0.170130	+	0.123606i
$889$	−18.4199	+	18.0297i	−0.617783	+	0.604697i
$890$		−	12.7610i		−	0.427750i
$891$	−0.949098	+	3.17793i	−0.0317960	+	0.106465i
$892$			22.9922i			0.769835i
$893$	−5.09570	−	1.65569i	−0.170521	−	0.0554057i
$894$	3.19709	+	4.40042i	0.106927	+	0.147172i
$895$	−11.9968	+	16.5122i	−0.401008	+	0.551941i
$896$	−4.21598	+	24.8913i	−0.140846	+	0.831559i
$897$	−9.51086	+	3.09026i	−0.317558	+	0.103181i
$898$	−0.999318	+	1.37544i	−0.0333477	+	0.0458991i
$899$	−15.0419	+	10.9286i	−0.501676	+	0.364489i
$900$	7.17483	−	22.0819i	0.239161	−	0.736062i
$901$	−22.6122			−0.753323
$902$	0.981742	+	1.28539i	0.0326884	+	0.0427987i
$903$	−9.17517	+	17.5406i	−0.305330	+	0.583714i
$904$	18.9749	+	6.16531i	0.631095	+	0.205055i
$905$	−47.4117	+	34.4466i	−1.57602	+	1.14504i
$906$	−2.60605	+	3.58692i	−0.0865802	+	0.119167i
$907$	4.68276	+	14.4120i	0.155488	+	0.478544i	0.998210	−	0.0598054i	$-0.0190480\pi$
$907$	4.68276	+	14.4120i	0.155488	+	0.478544i	−0.842722	+	0.538350i	$0.819048\pi$
$908$	12.6581	+	38.9577i	0.420075	+	1.29286i
$909$	−0.495040	−	0.359668i	−0.0164194	−	0.0119294i
$910$	3.59837	+	24.4073i	0.119285	+	0.809093i
$911$	−12.4520	+	38.3234i	−0.412554	+	1.26971i	0.501867	+	0.864945i	$0.332647\pi$
$911$	−12.4520	+	38.3234i	−0.412554	+	1.26971i	−0.914421	+	0.404765i	$0.867353\pi$
$912$			5.55017i			0.183785i
$913$	−7.73602	+	5.90856i	−0.256025	+	0.195545i
$914$	3.46217			0.114518
$915$	7.03199	−	21.6422i	0.232471	−	0.715471i
$916$	21.7209	+	29.8963i	0.717679	+	0.987801i
$917$	26.3042	−	13.0499i	0.868641	−	0.430946i
$918$	0.218071	+	0.671155i	0.00719743	+	0.0221514i
$919$	55.9948	−	18.1938i	1.84710	−	0.600158i	0.849766	−	0.527160i	$-0.176743\pi$
$919$	55.9948	−	18.1938i	1.84710	−	0.600158i	0.997332	−	0.0729982i	$-0.0232567\pi$
$920$	−7.14479	−	5.19100i	−0.235557	−	0.171142i
$921$	−10.0541	−	13.8383i	−0.331293	−	0.455986i
$922$	−10.7870	−	3.50492i	−0.355252	−	0.115429i
$923$	−29.8282			−0.981806
$924$	−11.4957	+	11.8040i	−0.378179	+	0.388324i
$925$	57.1418			1.87881
$926$	−11.7028	−	3.80248i	−0.384579	−	0.124957i
$927$	5.91799	+	8.14541i	0.194372	+	0.267530i
$928$	−12.9067	−	9.37727i	−0.423684	−	0.307824i
$929$	−37.3784	+	12.1450i	−1.22635	+	0.398464i	−0.849389	−	0.527767i	$-0.823030\pi$
$929$	−37.3784	+	12.1450i	−1.22635	+	0.398464i	−0.376957	+	0.926231i	$0.623030\pi$
$930$	−2.02558	−	6.23409i	−0.0664213	−	0.204424i
$931$	−0.253458	+	11.8379i	−0.00830675	+	0.387970i
$932$	−17.8616	−	24.5844i	−0.585075	−	0.805287i
$933$	−6.82204	+	20.9961i	−0.223343	+	0.687381i
$934$	11.4745			0.375456
$935$	15.8486	−	22.9495i	0.518306	−	0.750531i
$936$		−	8.67710i		−	0.283620i
$937$	3.59646	−	11.0688i	0.117491	−	0.361601i	−0.874967	−	0.484182i	$-0.839117\pi$
$937$	3.59646	−	11.0688i	0.117491	−	0.361601i	0.992459	+	0.122581i	$0.0391171\pi$
$938$	−0.578545	+	0.0852951i	−0.0188902	+	0.00278498i
$939$	−9.91296	−	7.20219i	−0.323497	−	0.235034i
$940$	−7.65903	−	23.5721i	−0.249810	−	0.768836i
$941$	−3.14739	−	9.68666i	−0.102602	−	0.315776i	0.886558	−	0.462617i	$-0.153089\pi$
$941$	−3.14739	−	9.68666i	−0.102602	−	0.315776i	−0.989160	+	0.146841i	$0.953089\pi$
$942$	3.37835	−	4.64990i	0.110073	−	0.151502i
$943$	−1.76318	+	1.28103i	−0.0574171	+	0.0417159i
$944$	14.6568	+	4.76230i	0.477040	+	0.155000i
$945$	−5.11023	+	9.76945i	−0.166236	+	0.317800i
$946$	8.67536	−	0.207714i	0.282060	−	0.00675336i
$947$	14.5095			0.471497			0.235748	−	0.971814i	$-0.424246\pi$
$947$	14.5095			0.471497			0.235748	+	0.971814i	$0.424246\pi$
$948$	−3.20036	+	9.84970i	−0.103943	+	0.319903i
$949$	−19.4253	+	14.1133i	−0.630571	+	0.458137i
$950$	−4.29929	+	5.91746i	−0.139487	+	0.191988i
$951$	12.9163	−	4.19675i	0.418839	−	0.136089i
$952$	−1.20907	+	7.13836i	−0.0391860	+	0.231356i
$953$	5.61786	−	7.73232i	0.181980	−	0.250474i	−0.708275	−	0.705937i	$-0.750526\pi$
$953$	5.61786	−	7.73232i	0.181980	−	0.250474i	0.890255	+	0.455463i	$0.150526\pi$
$954$	−2.30329	−	3.17021i	−0.0745719	−	0.102639i
$955$	58.8262	+	19.1138i	1.90357	+	0.618508i
$956$		−	9.14853i		−	0.295885i
$957$	−4.54730	−	12.9332i	−0.146993	−	0.418072i
$958$		−	10.0989i		−	0.326280i
$959$	25.1837	+	25.7287i	0.813224	+	0.830822i
$960$	−17.5735	+	12.7679i	−0.567184	+	0.412083i
$961$	−8.71108	−	6.32897i	−0.281002	−	0.204160i
$962$	9.83463	−	3.19546i	0.317081	−	0.103026i
$963$	−10.6228	+	3.45155i	−0.342314	+	0.111225i
$964$	−17.0584	−	12.3936i	−0.549413	−	0.399172i
$965$	28.7600	−	20.8953i	0.925816	−	0.672645i
$966$	1.01147	+	1.03336i	0.0325435	+	0.0332477i
$967$		−	54.1042i		−	1.73988i	−0.493162	−	0.869938i	$-0.664159\pi$
$967$		−	54.1042i		−	1.73988i	0.493162	−	0.869938i	$-0.335841\pi$
$968$	14.3909	+	3.92525i	0.462540	+	0.126162i
$969$			3.41341i			0.109655i
$970$	6.71118	+	2.18059i	0.215483	+	0.0700147i
$971$	24.5257	+	33.7568i	0.787068	+	1.08331i	0.994467	+	0.105050i	$0.0335004\pi$
$971$	24.5257	+	33.7568i	0.787068	+	1.08331i	−0.207398	+	0.978257i	$0.566500\pi$
$972$	1.10369	−	1.51910i	0.0354008	−	0.0487250i
$973$	15.6502	+	2.65077i	0.501722	+	0.0849796i
$974$	5.06696	−	1.64635i	0.162356	−	0.0527526i
$975$	−46.5070	+	64.0114i	−1.48942	+	2.05001i
$976$	−14.4959	+	10.5319i	−0.464003	+	0.337118i
$977$	0.412655	−	1.27002i	0.0132020	−	0.0406315i	−0.944239	−	0.329262i	$-0.893200\pi$
$977$	0.412655	−	1.27002i	0.0132020	−	0.0406315i	0.957441	+	0.288631i	$0.0932000\pi$
$978$	4.97708			0.159149
$979$	−27.3987	+	9.63332i	−0.875666	+	0.307882i
$980$	−44.9912	+	31.2388i	−1.43719	+	0.997887i
$981$	10.7840	+	3.50394i	0.344307	+	0.111872i
$982$	6.61060	−	4.80288i	0.210953	−	0.153266i
$983$	−4.82318	+	6.63854i	−0.153836	+	0.211737i	−0.878978	−	0.476862i	$-0.841774\pi$
$983$	−4.82318	+	6.63854i	−0.153836	+	0.211737i	0.725142	+	0.688599i	$0.241774\pi$
$984$	−0.584363	−	1.79848i	−0.0186288	−	0.0573336i
$985$	6.15652	+	18.9478i	0.196163	+	0.603727i
$986$	−2.35991	−	1.71457i	−0.0751547	−	0.0546031i
$987$	1.22233	+	8.29093i	0.0389073	+	0.263903i
$988$	6.28033	−	19.3289i	0.199804	−	0.614933i
$989$			11.6931i			0.371819i
$990$	4.83185	−	0.115689i	0.153566	−	0.00367683i
$991$	−17.1633			−0.545209			−0.272605	−	0.962126i	$-0.587885\pi$
$991$	−17.1633			−0.545209			−0.272605	+	0.962126i	$0.587885\pi$
$992$	−5.36469	+	16.5108i	−0.170329	+	0.524219i
$993$	−2.28877	−	3.15022i	−0.0726319	−	0.0999692i
$994$	1.91682	+	3.86365i	0.0607977	+	0.122547i
$995$	−16.1903	−	49.8285i	−0.513266	−	1.57967i
$996$	5.24135	−	1.70302i	0.166079	−	0.0539622i
$997$	−22.8490	−	16.6008i	−0.723635	−	0.525751i	0.163909	−	0.986476i	$-0.447590\pi$
$997$	−22.8490	−	16.6008i	−0.723635	−	0.525751i	−0.887543	+	0.460724i	$0.847590\pi$
$998$	−0.738376	−	1.01629i	−0.0233729	−	0.0321700i
$999$	4.39499	+	1.42802i	0.139051	+	0.0451806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.w.a.13.9	✓	64
3.2	odd	2		693.2.bu.f.244.7		64
7.6	odd	2	inner	231.2.w.a.13.10	yes	64
11.6	odd	10	inner	231.2.w.a.160.10	yes	64
21.20	even	2		693.2.bu.f.244.8		64
33.17	even	10		693.2.bu.f.622.8		64
77.6	even	10	inner	231.2.w.a.160.9	yes	64
231.83	odd	10		693.2.bu.f.622.7		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.w.a.13.9	✓	64	1.1	even	1	trivial
231.2.w.a.13.10	yes	64	7.6	odd	2	inner
231.2.w.a.160.9	yes	64	77.6	even	10	inner
231.2.w.a.160.10	yes	64	11.6	odd	10	inner
693.2.bu.f.244.7		64	3.2	odd	2
693.2.bu.f.244.8		64	21.20	even	2
693.2.bu.f.622.7		64	231.83	odd	10
693.2.bu.f.622.8		64	33.17	even	10

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.332589 + 0.108065i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.51910 - 1.10369i) q^{4} +(3.96320 - 1.28772i) q^{5} +(-0.108065 - 0.332589i) q^{6} +(-2.37010 + 1.17584i) q^{7} +(-0.797068 - 1.09707i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.332589 + 0.108065i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.51910 - 1.10369i) q^{4} +(3.96320 - 1.28772i) q^{5} +(-0.108065 - 0.332589i) q^{6} +(-2.37010 + 1.17584i) q^{7} +(-0.797068 - 1.09707i) q^{8} +(-0.309017 + 0.951057i) q^{9} +1.45728 q^{10} +(-1.10010 - 3.12886i) q^{11} +1.87771i q^{12} +(1.97734 - 6.08561i) q^{13} +(-0.915338 + 0.134949i) q^{14} +(-3.37130 - 2.44939i) q^{15} +(1.01395 + 3.12060i) q^{16} +(0.623587 + 1.91920i) q^{17} +(-0.205551 + 0.282917i) q^{18} +(-1.36846 + 0.994244i) q^{19} +(-7.44173 - 2.41797i) q^{20} +(2.34439 + 1.22631i) q^{21} +(-0.0277621 - 1.15951i) q^{22} +1.56284 q^{23} +(-0.419043 + 1.28968i) q^{24} +(10.0037 - 7.26809i) q^{25} +(1.31528 - 1.81033i) q^{26} +(0.951057 - 0.309017i) q^{27} +(4.89818 + 0.829633i) q^{28} +(-2.42963 + 3.34409i) q^{29} +(-0.856565 - 1.17896i) q^{30} +(4.27791 + 1.38998i) q^{31} +3.85955i q^{32} +(-1.88468 + 2.72910i) q^{33} +0.705694i q^{34} +(-7.87904 + 7.71215i) q^{35} +(1.51910 - 1.10369i) q^{36} +(3.73861 + 2.71626i) q^{37} +(-0.562577 + 0.182792i) q^{38} +(-6.08561 + 1.97734i) q^{39} +(-4.57166 - 3.32151i) q^{40} +(-1.12819 + 0.819676i) q^{41} +(0.647198 + 0.661203i) q^{42} +7.48193i q^{43} +(-1.78213 + 5.96721i) q^{44} +4.16716i q^{45} +(0.519784 + 0.168888i) q^{46} +(1.86184 + 2.56260i) q^{47} +(1.92864 - 2.65454i) q^{48} +(4.23478 - 5.57375i) q^{49} +(4.11253 - 1.33624i) q^{50} +(1.18613 - 1.63257i) q^{51} +(-9.72038 + 7.06227i) q^{52} +(-3.46267 + 10.6570i) q^{53} +0.349705 q^{54} +(-8.38903 - 10.9837i) q^{55} +(3.17912 + 1.66294i) q^{56} +(1.60872 + 0.522705i) q^{57} +(-1.16945 + 0.849652i) q^{58} +(2.76071 - 3.79979i) q^{59} +(2.41797 + 7.44173i) q^{60} +(1.68748 + 5.19353i) q^{61} +(1.27258 + 0.924582i) q^{62} +(-0.385893 - 2.61746i) q^{63} +(1.61081 - 4.95756i) q^{64} -26.6648i q^{65} +(-0.921743 + 0.704001i) q^{66} +0.632056 q^{67} +(1.17091 - 3.60370i) q^{68} +(-0.918616 - 1.26437i) q^{69} +(-3.45389 + 1.71353i) q^{70} +(-1.44049 - 4.43338i) q^{71} +(1.28968 - 0.419043i) q^{72} +(-3.03577 - 2.20562i) q^{73} +(0.949888 + 1.30741i) q^{74} +(-11.7600 - 3.82106i) q^{75} +3.17616 q^{76} +(6.28641 + 6.12218i) q^{77} -2.23769 q^{78} +(5.24560 + 1.70440i) q^{79} +(8.03694 + 11.0619i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.463801 + 0.150698i) q^{82} +(-0.906968 - 2.79136i) q^{83} +(-2.20789 - 4.45036i) q^{84} +(4.94280 + 6.80319i) q^{85} +(-0.808533 + 2.48841i) q^{86} +4.13353 q^{87} +(-2.55572 + 3.70080i) q^{88} -8.75676i q^{89} +(-0.450323 + 1.38595i) q^{90} +(2.46925 + 16.7486i) q^{91} +(-2.37411 - 1.72489i) q^{92} +(-1.38998 - 4.27791i) q^{93} +(0.342300 + 1.05349i) q^{94} +(-4.14317 + 5.70259i) q^{95} +(3.12245 - 2.26859i) q^{96} +(4.60529 + 1.49635i) q^{97} +(2.01077 - 1.39614i) q^{98} +(3.31567 - 0.0793871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9}+O(q^{10}) \) 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9	\( 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9} - 16 q^{11} + 12 q^{14} - 12 q^{15} - 16 q^{16} + 10 q^{18} - 40 q^{22} - 24 q^{23} + 44 q^{25} - 30 q^{28} - 40 q^{29} - 40 q^{35} - 12 q^{36} + 32 q^{37} - 2 q^{42} + 22 q^{44} - 70 q^{46} - 50 q^{49} - 40 q^{51} - 64 q^{53} + 80 q^{56} + 2 q^{58} - 36 q^{60} + 10 q^{63} + 72 q^{64} - 8 q^{67} - 26 q^{70} + 68 q^{71} - 10 q^{72} + 80 q^{74} + 90 q^{77} - 72 q^{78} + 40 q^{79} - 16 q^{81} + 60 q^{84} - 40 q^{85} - 62 q^{86} + 140 q^{88} + 54 q^{91} + 18 q^{92} - 20 q^{93} + 20 q^{95} - 4 q^{99}+O(q^{100}) \) 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9 - 16 * q^11 + 12 * q^14 - 12 * q^15 - 16 * q^16 + 10 * q^18 - 40 * q^22 - 24 * q^23 + 44 * q^25 - 30 * q^28 - 40 * q^29 - 40 * q^35 - 12 * q^36 + 32 * q^37 - 2 * q^42 + 22 * q^44 - 70 * q^46 - 50 * q^49 - 40 * q^51 - 64 * q^53 + 80 * q^56 + 2 * q^58 - 36 * q^60 + 10 * q^63 + 72 * q^64 - 8 * q^67 - 26 * q^70 + 68 * q^71 - 10 * q^72 + 80 * q^74 + 90 * q^77 - 72 * q^78 + 40 * q^79 - 16 * q^81 + 60 * q^84 - 40 * q^85 - 62 * q^86 + 140 * q^88 + 54 * q^91 + 18 * q^92 - 20 * q^93 + 20 * q^95 - 4 * q^99

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