LMFDB - Embedded newform 820.2.k.c.247.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(83,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.83"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [108] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			247.10
Character	$\chi$	$=$	820.247
Dual form			820.2.k.c.83.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20951 + 0.732860i) q^{2} +(0.993723 + 0.993723i) q^{3} +(0.925834 - 1.77280i) q^{4} +(-1.63476 + 1.52564i) q^{5} +(-1.93018 - 0.473660i) q^{6} +(2.18364 - 2.18364i) q^{7} +(0.179410 + 2.82273i) q^{8} -1.02503i q^{9} +(0.859183 - 3.04332i) q^{10} -2.71794i q^{11} +(2.68170 - 0.841653i) q^{12} +(2.18477 - 2.18477i) q^{13} +(-1.04084 + 4.24144i) q^{14} +(-3.14056 - 0.108439i) q^{15} +(-2.28566 - 3.28264i) q^{16} +(-2.30155 - 2.30155i) q^{17} +(0.751202 + 1.23978i) q^{18} -6.76528 q^{19} +(1.19114 + 4.31059i) q^{20} +4.33987 q^{21} +(1.99187 + 3.28738i) q^{22} +(-6.72631 - 6.72631i) q^{23} +(-2.62673 + 2.98330i) q^{24} +(0.344874 - 4.98809i) q^{25} +(-1.04138 + 4.24364i) q^{26} +(3.99976 - 3.99976i) q^{27} +(-1.84948 - 5.89286i) q^{28} +8.06080i q^{29} +(3.87801 - 2.17043i) q^{30} -6.13091i q^{31} +(5.17025 + 2.29532i) q^{32} +(2.70088 - 2.70088i) q^{33} +(4.47046 + 1.09704i) q^{34} +(-0.238287 + 6.90117i) q^{35} +(-1.81717 - 0.949006i) q^{36} +(-1.43673 - 1.43673i) q^{37} +(8.18268 - 4.95800i) q^{38} +4.34212 q^{39} +(-4.59975 - 4.34077i) q^{40} +1.00000 q^{41} +(-5.24913 + 3.18052i) q^{42} +(2.56768 + 2.56768i) q^{43} +(-4.81838 - 2.51636i) q^{44} +(1.56382 + 1.67567i) q^{45} +(13.0650 + 3.20611i) q^{46} +(4.33955 - 4.33955i) q^{47} +(0.990721 - 5.53335i) q^{48} -2.53660i q^{49} +(3.23844 + 6.28590i) q^{50} -4.57421i q^{51} +(-1.85044 - 5.89591i) q^{52} +(-2.53419 + 2.53419i) q^{53} +(-1.90649 + 7.76902i) q^{54} +(4.14659 + 4.44318i) q^{55} +(6.55561 + 5.77207i) q^{56} +(-6.72281 - 6.72281i) q^{57} +(-5.90744 - 9.74963i) q^{58} +0.274019 q^{59} +(-3.09987 + 5.46719i) q^{60} -2.40072 q^{61} +(4.49310 + 7.41540i) q^{62} +(-2.23830 - 2.23830i) q^{63} +(-7.93562 + 1.01285i) q^{64} +(-0.238411 + 6.90475i) q^{65} +(-1.28738 + 5.24611i) q^{66} +(4.52096 - 4.52096i) q^{67} +(-6.21105 + 1.94934i) q^{68} -13.3682i q^{69} +(-4.76938 - 8.52168i) q^{70} +3.75962i q^{71} +(2.89338 - 0.183900i) q^{72} +(-2.07602 + 2.07602i) q^{73} +(2.79066 + 0.684820i) q^{74} +(5.29949 - 4.61407i) q^{75} +(-6.26352 + 11.9935i) q^{76} +(-5.93502 - 5.93502i) q^{77} +(-5.25184 + 3.18216i) q^{78} +12.3570 q^{79} +(8.74462 + 1.87924i) q^{80} +4.87423 q^{81} +(-1.20951 + 0.732860i) q^{82} +(2.57786 + 2.57786i) q^{83} +(4.01800 - 7.69374i) q^{84} +(7.27380 + 0.251154i) q^{85} +(-4.98739 - 1.22389i) q^{86} +(-8.01021 + 8.01021i) q^{87} +(7.67202 - 0.487625i) q^{88} +12.7695i q^{89} +(-3.11949 - 0.880687i) q^{90} -9.54154i q^{91} +(-18.1519 + 5.69698i) q^{92} +(6.09243 - 6.09243i) q^{93} +(-2.06845 + 8.42901i) q^{94} +(11.0596 - 10.3213i) q^{95} +(2.85688 + 7.41871i) q^{96} +(2.97817 + 2.97817i) q^{97} +(1.85897 + 3.06804i) q^{98} -2.78597 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) $ 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.20951	+	0.732860i	−0.855253	+	0.518210i
$2$	−1.20951	+	0.732860i	−0.855253	+	0.518210i
$3$	0.993723	+	0.993723i	0.573726	+	0.573726i	0.933168	−	0.359441i	$-0.117033\pi$
$3$	0.993723	+	0.993723i	0.573726	+	0.573726i	−0.359441	+	0.933168i	$0.617033\pi$
$4$	0.925834	−	1.77280i	0.462917	−	0.886402i
$5$	−1.63476	+	1.52564i	−0.731086	+	0.682285i
$5$	−1.63476	+	1.52564i	−0.731086	+	0.682285i
$6$	−1.93018	−	0.473660i	−0.787992	−	0.193371i
$7$	2.18364	−	2.18364i	0.825340	−	0.825340i	−0.161528	−	0.986868i	$-0.551642\pi$
$7$	2.18364	−	2.18364i	0.825340	−	0.825340i	0.986868	+	0.161528i	$0.0516424\pi$
$8$	0.179410	+	2.82273i	0.0634309	+	0.997986i
$9$		−	1.02503i		−	0.341676i
$10$	0.859183	−	3.04332i	0.271697	−	0.962383i
$11$		−	2.71794i		−	0.819491i	−0.912200	−	0.409745i	$-0.865618\pi$
$11$		−	2.71794i		−	0.819491i	0.912200	−	0.409745i	$-0.134382\pi$
$12$	2.68170	−	0.841653i	0.774140	−	0.242964i
$13$	2.18477	−	2.18477i	0.605947	−	0.605947i	−0.335937	−	0.941884i	$-0.609053\pi$
$13$	2.18477	−	2.18477i	0.605947	−	0.605947i	0.941884	+	0.335937i	$0.109053\pi$
$14$	−1.04084	+	4.24144i	−0.278175	+	1.13357i
$15$	−3.14056	−	0.108439i	−0.810888	−	0.0279988i
$16$	−2.28566	−	3.28264i	−0.571416	−	0.820661i
$17$	−2.30155	−	2.30155i	−0.558208	−	0.558208i	0.370589	−	0.928797i	$-0.379156\pi$
$17$	−2.30155	−	2.30155i	−0.558208	−	0.558208i	−0.928797	+	0.370589i	$0.879156\pi$
$18$	0.751202	+	1.23978i	0.177060	+	0.292220i
$19$	−6.76528			−1.55206			−0.776030	−	0.630695i	$-0.782770\pi$
$19$	−6.76528			−1.55206			−0.776030	+	0.630695i	$0.782770\pi$
$20$	1.19114	+	4.31059i	0.266346	+	0.963877i
$21$	4.33987			0.947038
$22$	1.99187	+	3.28738i	0.424668	+	0.700872i
$23$	−6.72631	−	6.72631i	−1.40253	−	1.40253i	−0.791961	−	0.610571i	$-0.790940\pi$
$23$	−6.72631	−	6.72631i	−1.40253	−	1.40253i	−0.610571	−	0.791961i	$-0.709060\pi$
$24$	−2.62673	+	2.98330i	−0.536179	+	0.608963i
$25$	0.344874	−	4.98809i	0.0689748	−	0.997618i
$26$	−1.04138	+	4.24364i	−0.204231	+	0.832246i
$27$	3.99976	−	3.99976i	0.769755	−	0.769755i
$28$	−1.84948	−	5.89286i	−0.349519	−	1.11365i
$29$			8.06080i			1.49685i	0.663217	+	0.748427i	$0.269190\pi$
$29$			8.06080i			1.49685i	−0.663217	+	0.748427i	$0.730810\pi$
$30$	3.87801	−	2.17043i	0.708024	−	0.396264i
$31$		−	6.13091i		−	1.10114i	−0.834788	−	0.550572i	$-0.814410\pi$
$31$		−	6.13091i		−	1.10114i	0.834788	−	0.550572i	$-0.185590\pi$
$32$	5.17025	+	2.29532i	0.913980	+	0.405759i
$33$	2.70088	−	2.70088i	0.470163	−	0.470163i
$34$	4.47046	+	1.09704i	0.766678	+	0.188140i
$35$	−0.238287	+	6.90117i	−0.0402779	+	1.16651i
$36$	−1.81717	−	0.949006i	−0.302862	−	0.158168i
$37$	−1.43673	−	1.43673i	−0.236197	−	0.236197i	0.579076	−	0.815273i	$-0.303413\pi$
$37$	−1.43673	−	1.43673i	−0.236197	−	0.236197i	−0.815273	+	0.579076i	$0.803413\pi$
$38$	8.18268	−	4.95800i	1.32741	−	0.804293i
$39$	4.34212			0.695296
$40$	−4.59975	−	4.34077i	−0.727284	−	0.686336i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	−5.24913	+	3.18052i	−0.809958	+	0.490765i
$43$	2.56768	+	2.56768i	0.391567	+	0.391567i	0.875246	−	0.483678i	$-0.160700\pi$
$43$	2.56768	+	2.56768i	0.391567	+	0.391567i	−0.483678	+	0.875246i	$0.660700\pi$
$44$	−4.81838	−	2.51636i	−0.726398	−	0.379356i
$45$	1.56382	+	1.67567i	0.233121	+	0.249795i
$46$	13.0650	+	3.20611i	1.92633	+	0.472714i
$47$	4.33955	−	4.33955i	0.632988	−	0.632988i	−0.315828	−	0.948816i	$-0.602282\pi$
$47$	4.33955	−	4.33955i	0.632988	−	0.632988i	0.948816	+	0.315828i	$0.102282\pi$
$48$	0.990721	−	5.53335i	0.142998	−	0.798671i
$49$		−	2.53660i		−	0.362371i
$50$	3.23844	+	6.28590i	0.457985	+	0.888960i
$51$		−	4.57421i		−	0.640517i
$52$	−1.85044	−	5.89591i	−0.256609	−	0.817616i
$53$	−2.53419	+	2.53419i	−0.348097	+	0.348097i	−0.859400	−	0.511303i	$-0.829163\pi$
$53$	−2.53419	+	2.53419i	−0.348097	+	0.348097i	0.511303	+	0.859400i	$0.329163\pi$
$54$	−1.90649	+	7.76902i	−0.259441	+	1.05723i
$55$	4.14659	+	4.44318i	0.559126	+	0.599118i
$56$	6.55561	+	5.77207i	0.876030	+	0.771326i
$57$	−6.72281	−	6.72281i	−0.890458	−	0.890458i
$58$	−5.90744	−	9.74963i	−0.775684	−	1.28019i
$59$	0.274019			0.0356742			0.0178371	−	0.999841i	$-0.494322\pi$
$59$	0.274019			0.0356742			0.0178371	+	0.999841i	$0.494322\pi$
$60$	−3.09987	+	5.46719i	−0.400192	+	0.705812i
$61$	−2.40072			−0.307380			−0.153690	−	0.988119i	$-0.549116\pi$
$61$	−2.40072			−0.307380			−0.153690	+	0.988119i	$0.549116\pi$
$62$	4.49310	+	7.41540i	0.570624	+	0.941757i
$63$	−2.23830	−	2.23830i	−0.281999	−	0.281999i
$64$	−7.93562	+	1.01285i	−0.991953	+	0.126606i
$65$	−0.238411	+	6.90475i	−0.0295712	+	0.856429i
$66$	−1.28738	+	5.24611i	−0.158465	+	0.645752i
$67$	4.52096	−	4.52096i	0.552323	−	0.552323i	−0.374788	−	0.927111i	$-0.622284\pi$
$67$	4.52096	−	4.52096i	0.552323	−	0.552323i	0.927111	+	0.374788i	$0.122284\pi$
$68$	−6.21105	+	1.94934i	−0.753200	+	0.236393i
$69$		−	13.3682i		−	1.60934i
$70$	−4.76938	−	8.52168i	−0.570050	−	1.01854i
$71$			3.75962i			0.446185i	0.974797	+	0.223092i	$0.0716152\pi$
$71$			3.75962i			0.446185i	−0.974797	+	0.223092i	$0.928385\pi$
$72$	2.89338	−	0.183900i	0.340988	−	0.0216728i
$73$	−2.07602	+	2.07602i	−0.242980	+	0.242980i	−0.818082	−	0.575102i	$-0.804962\pi$
$73$	−2.07602	+	2.07602i	−0.242980	+	0.242980i	0.575102	+	0.818082i	$0.304962\pi$
$74$	2.79066	+	0.684820i	0.324408	+	0.0796087i
$75$	5.29949	−	4.61407i	0.611933	−	0.532787i
$76$	−6.26352	+	11.9935i	−0.718475	+	1.37575i
$77$	−5.93502	−	5.93502i	−0.676358	−	0.676358i
$78$	−5.25184	+	3.18216i	−0.594654	+	0.360309i
$79$	12.3570			1.39027			0.695134	−	0.718880i	$-0.255345\pi$
$79$	12.3570			1.39027			0.695134	+	0.718880i	$0.255345\pi$
$80$	8.74462	+	1.87924i	0.977679	+	0.210105i
$81$	4.87423			0.541581
$82$	−1.20951	+	0.732860i	−0.133568	+	0.0809308i
$83$	2.57786	+	2.57786i	0.282956	+	0.282956i	0.834287	−	0.551330i	$-0.185880\pi$
$83$	2.57786	+	2.57786i	0.282956	+	0.282956i	−0.551330	+	0.834287i	$0.685880\pi$
$84$	4.01800	−	7.69374i	0.438400	−	0.839456i
$85$	7.27380	+	0.251154i	0.788955	+	0.0272414i
$86$	−4.98739	−	1.22389i	−0.537804	−	0.131975i
$87$	−8.01021	+	8.01021i	−0.858784	+	0.858784i
$88$	7.67202	−	0.487625i	0.817840	−	0.0519810i
$89$			12.7695i			1.35356i	0.736185	+	0.676780i	$0.236625\pi$
$89$			12.7695i			1.35356i	−0.736185	+	0.676780i	$0.763375\pi$
$90$	−3.11949	−	0.880687i	−0.328823	−	0.0928325i
$91$		−	9.54154i		−	1.00022i
$92$	−18.1519	+	5.69698i	−1.89246	+	0.593951i
$93$	6.09243	−	6.09243i	0.631755	−	0.631755i
$94$	−2.06845	+	8.42901i	−0.213345	+	0.869386i
$95$	11.0596	−	10.3213i	1.13469	−	1.05895i
$96$	2.85688	+	7.41871i	0.291579	+	0.757169i
$97$	2.97817	+	2.97817i	0.302387	+	0.302387i	0.841947	−	0.539560i	$-0.181409\pi$
$97$	2.97817	+	2.97817i	0.302387	+	0.302387i	−0.539560	+	0.841947i	$0.681409\pi$
$98$	1.85897	+	3.06804i	0.187784	+	0.309919i
$99$	−2.78597			−0.280000
$100$	−8.52361	−	5.22954i	−0.852361	−	0.522954i
$101$	17.0594			1.69747			0.848736	−	0.528817i	$-0.177364\pi$
$101$	17.0594			1.69747			0.848736	+	0.528817i	$0.177364\pi$
$102$	3.35225	+	5.53255i	0.331922	+	0.547804i
$103$	−1.40268	−	1.40268i	−0.138210	−	0.138210i	0.634617	−	0.772827i	$-0.281158\pi$
$103$	−1.40268	−	1.40268i	−0.138210	−	0.138210i	−0.772827	+	0.634617i	$0.781158\pi$
$104$	6.55900	+	5.77506i	0.643163	+	0.566291i
$105$	−7.09465	+	6.62106i	−0.692367	+	0.646150i
$106$	1.20792	−	4.92233i	0.117324	−	0.478099i
$107$	0.127603	−	0.127603i	0.0123359	−	0.0123359i	−0.700912	−	0.713248i	$-0.747223\pi$
$107$	0.127603	−	0.127603i	0.0123359	−	0.0123359i	0.713248	+	0.700912i	$0.247223\pi$
$108$	−3.38768	−	10.7939i	−0.325980	−	1.03864i
$109$		−	5.88698i		−	0.563871i	−0.959433	−	0.281935i	$-0.909024\pi$
$109$		−	5.88698i		−	0.563871i	0.959433	−	0.281935i	$-0.0909764\pi$
$110$	−8.27157	−	2.33521i	−0.788664	−	0.222653i
$111$		−	2.85543i		−	0.271025i
$112$	−12.1592	−	2.17705i	−1.14894	−	0.205712i
$113$	−1.37230	+	1.37230i	−0.129095	+	0.129095i	−0.768702	−	0.639607i	$-0.779097\pi$
$113$	−1.37230	+	1.37230i	−0.129095	+	0.129095i	0.639607	+	0.768702i	$0.279097\pi$
$114$	13.0582	+	3.20444i	1.22301	+	0.300123i
$115$	21.2578	+	0.734000i	1.98230	+	0.0684459i
$116$	14.2902	+	7.46296i	1.32681	+	0.692919i
$117$	−2.23946	−	2.23946i	−0.207038	−	0.207038i
$118$	−0.331429	+	0.200817i	−0.0305105	+	0.0184867i
$119$	−10.0515			−0.921422
$120$	−0.257353	−	8.88440i	−0.0234930	−	0.811031i
$121$	3.61279			0.328435
$122$	2.90369	−	1.75939i	0.262888	−	0.159287i
$123$	0.993723	+	0.993723i	0.0896010	+	0.0896010i
$124$	−10.8689	−	5.67620i	−0.976056	−	0.509738i
$125$	7.04622	+	8.68048i	0.630233	+	0.776406i
$126$	4.34760	+	1.06689i	0.387315	+	0.0950459i
$127$	9.75905	−	9.75905i	0.865976	−	0.865976i	−0.126048	−	0.992024i	$-0.540229\pi$
$127$	9.75905	−	9.75905i	0.865976	−	0.865976i	0.992024	+	0.126048i	$0.0402295\pi$
$128$	8.85595	−	7.04075i	0.782763	−	0.622320i
$129$			5.10313i			0.449305i
$130$	−4.77185	−	8.52609i	−0.418519	−	0.747788i
$131$		−	2.40436i		−	0.210070i	−0.994469	−	0.105035i	$-0.966504\pi$
$131$		−	2.40436i		−	0.210070i	0.994469	−	0.105035i	$-0.0334955\pi$
$132$	−2.28757	−	7.28870i	−0.199107	−	0.634400i
$133$	−14.7730	+	14.7730i	−1.28098	+	1.28098i
$134$	−2.15492	+	8.78137i	−0.186157	+	0.758595i
$135$	−0.436469	+	12.6408i	−0.0375653	+	1.08795i
$136$	6.08374	−	6.90958i	0.521676	−	0.592491i
$137$	−16.0160	−	16.0160i	−1.36834	−	1.36834i	−0.862812	−	0.505525i	$-0.831299\pi$
$137$	−16.0160	−	16.0160i	−1.36834	−	1.36834i	−0.505525	−	0.862812i	$-0.668701\pi$
$138$	9.79700	+	16.1690i	0.833976	+	1.37639i
$139$	−16.7314			−1.41914			−0.709569	−	0.704636i	$-0.751110\pi$
$139$	−16.7314			−1.41914			−0.709569	+	0.704636i	$0.751110\pi$
$140$	12.0138	+	6.81178i	1.01535	+	0.575700i
$141$	8.62462			0.726324
$142$	−2.75527	−	4.54730i	−0.231217	−	0.381601i
$143$	−5.93809	−	5.93809i	−0.496568	−	0.496568i
$144$	−3.36480	+	2.34287i	−0.280400	+	0.195239i
$145$	−12.2978	−	13.1775i	−1.02128	−	1.09433i
$146$	0.989540	−	4.03241i	0.0818949	−	0.333724i
$147$	2.52068	−	2.52068i	0.207902	−	0.207902i
$148$	−3.87721	+	1.21687i	−0.318705	+	0.100026i
$149$			20.9742i			1.71828i	0.511745	+	0.859138i	$0.328999\pi$
$149$			20.9742i			1.71828i	−0.511745	+	0.859138i	$0.671001\pi$
$150$	−3.02833	+	9.46456i	−0.247262	+	0.772778i
$151$			4.61334i			0.375428i	0.982224	+	0.187714i	$0.0601078\pi$
$151$			4.61334i			0.375428i	−0.982224	+	0.187714i	$0.939892\pi$
$152$	−1.21376	−	19.0966i	−0.0984487	−	1.54894i
$153$	−2.35915	+	2.35915i	−0.190726	+	0.190726i
$154$	11.5280	+	2.82893i	0.928953	+	0.227962i
$155$	9.35353	+	10.0226i	0.751294	+	0.805032i
$156$	4.02008	−	7.69773i	0.321864	−	0.616311i
$157$	3.61162	+	3.61162i	0.288239	+	0.288239i	0.836383	−	0.548145i	$-0.184666\pi$
$157$	3.61162	+	3.61162i	0.288239	+	0.288239i	−0.548145	+	0.836383i	$0.684666\pi$
$158$	−14.9459	+	9.05593i	−1.18903	+	0.720451i
$159$	−5.03656			−0.399425
$160$	−11.9539	+	4.13562i	−0.945042	+	0.326949i
$161$	−29.3757			−2.31513
$162$	−5.89543	+	3.57213i	−0.463189	+	0.280653i
$163$	0.567596	+	0.567596i	0.0444575	+	0.0444575i	0.728986	−	0.684529i	$-0.239992\pi$
$163$	0.567596	+	0.567596i	0.0444575	+	0.0444575i	−0.684529	+	0.728986i	$0.739992\pi$
$164$	0.925834	−	1.77280i	0.0722955	−	0.138433i
$165$	−0.294730	+	8.53585i	−0.0229447	+	0.664515i
$166$	−5.00715	−	1.22874i	−0.388630	−	0.0953686i
$167$	5.16449	−	5.16449i	0.399640	−	0.399640i	−0.478466	−	0.878106i	$-0.658807\pi$
$167$	5.16449	−	5.16449i	0.399640	−	0.399640i	0.878106	+	0.478466i	$0.158807\pi$
$168$	0.778616	+	12.2503i	0.0600715	+	0.945131i
$169$			3.45352i			0.265656i
$170$	−8.98181	+	5.02690i	−0.688873	+	0.385546i
$171$			6.93460i			0.530302i
$172$	6.92924	−	2.17475i	0.528349	−	0.165823i
$173$	17.0896	−	17.0896i	1.29930	−	1.29930i	0.370439	−	0.928857i	$-0.379207\pi$
$173$	17.0896	−	17.0896i	1.29930	−	1.29930i	0.928857	−	0.370439i	$-0.120793\pi$
$174$	3.81808	−	15.5588i	0.289448	−	1.17951i
$175$	−10.1391	−	11.6453i	−0.766446	−	0.880302i
$176$	−8.92203	+	6.21230i	−0.672524	+	0.468270i
$177$	0.272299	+	0.272299i	0.0204672	+	0.0204672i
$178$	−9.35822	−	15.4448i	−0.701428	−	1.15764i
$179$	−19.9159			−1.48858			−0.744292	−	0.667854i	$-0.767213\pi$
$179$	−19.9159			−1.48858			−0.744292	+	0.667854i	$0.767213\pi$
$180$	4.41848	−	1.22095i	0.329334	−	0.0910042i
$181$	13.8609			1.03027			0.515136	−	0.857109i	$-0.327742\pi$
$181$	13.8609			1.03027			0.515136	+	0.857109i	$0.327742\pi$
$182$	6.99261	+	11.5406i	0.518326	+	0.855446i
$183$	−2.38565	−	2.38565i	−0.176352	−	0.176352i
$184$	17.7798	−	20.1933i	1.31074	−	1.48867i
$185$	4.54064	+	0.156781i	0.333834	+	0.0115268i
$186$	−2.90396	+	11.8338i	−0.212929	+	0.867693i
$187$	−6.25548	+	6.25548i	−0.457446	+	0.457446i
$188$	−3.67547	−	11.7109i	−0.268061	−	0.854103i
$189$		−	17.4681i		−	1.27062i
$190$	−5.81261	+	20.5889i	−0.421691	+	1.49368i
$191$		−	19.2894i		−	1.39573i	−0.716228	−	0.697867i	$-0.754133\pi$
$191$		−	19.2894i		−	1.39573i	0.716228	−	0.697867i	$-0.245867\pi$
$192$	−8.89231	−	6.87932i	−0.641747	−	0.496472i
$193$	−15.8130	+	15.8130i	−1.13824	+	1.13824i	−0.149476	+	0.988765i	$0.547759\pi$
$193$	−15.8130	+	15.8130i	−1.13824	+	1.13824i	−0.988765	+	0.149476i	$0.952241\pi$
$194$	−5.78471	−	1.41955i	−0.415318	−	0.101918i
$195$	−7.09832	+	6.62449i	−0.508321	+	0.474390i
$196$	−4.49689	−	2.34847i	−0.321206	−	0.167748i
$197$	−11.9408	−	11.9408i	−0.850746	−	0.850746i	0.139479	−	0.990225i	$-0.455457\pi$
$197$	−11.9408	−	11.9408i	−0.850746	−	0.850746i	−0.990225	+	0.139479i	$0.955457\pi$
$198$	3.36966	−	2.04172i	0.239471	−	0.145099i
$199$	−4.66652			−0.330801			−0.165401	−	0.986226i	$-0.552892\pi$
$199$	−4.66652			−0.330801			−0.165401	+	0.986226i	$0.552892\pi$
$200$	14.1419	+	0.0785747i	0.999985	+	0.00555607i
$201$	8.98516			0.633764
$202$	−20.6335	+	12.5021i	−1.45177	+	0.879647i
$203$	17.6019	+	17.6019i	1.23541	+	1.23541i
$204$	−8.10917	−	4.23495i	−0.567755	−	0.296506i
$205$	−1.63476	+	1.52564i	−0.114177	+	0.106555i
$206$	2.72452	+	0.668588i	0.189826	+	0.0465827i
$207$	−6.89466	+	6.89466i	−0.479212	+	0.479212i
$208$	−12.1655	−	2.17817i	−0.843525	−	0.151029i
$209$			18.3876i			1.27190i
$210$	3.72874	−	13.2076i	0.257308	−	0.911413i
$211$			14.6843i			1.01091i	0.862853	+	0.505455i	$0.168675\pi$
$211$			14.6843i			1.01091i	−0.862853	+	0.505455i	$0.831325\pi$
$212$	2.14638	+	6.83885i	0.147414	+	0.469694i
$213$	−3.73602	+	3.73602i	−0.255988	+	0.255988i
$214$	−0.0608223	+	0.247853i	−0.00415772	+	0.0169429i
$215$	−8.11488	−	0.280195i	−0.553430	−	0.0191091i
$216$	12.0079	+	10.5727i	0.817031	+	0.719379i
$217$	−13.3877	−	13.3877i	−0.908818	−	0.908818i
$218$	4.31433	+	7.12037i	0.292203	+	0.482252i
$219$	−4.12599			−0.278808
$220$	11.7159	−	3.23744i	0.789888	−	0.218268i
$221$	−10.0567			−0.676489
$222$	2.09263	+	3.45367i	0.140448	+	0.231795i
$223$	15.3997	+	15.3997i	1.03124	+	1.03124i	0.999496	+	0.0317462i	$0.0101068\pi$
$223$	15.3997	+	15.3997i	1.03124	+	1.03124i	0.0317462	+	0.999496i	$0.489893\pi$
$224$	16.3021	−	6.27782i	1.08923	−	0.419455i
$225$	−5.11294	−	0.353506i	−0.340862	−	0.0235671i
$226$	0.654109	−	2.66552i	0.0435107	−	0.177308i
$227$	−3.00885	+	3.00885i	−0.199705	+	0.199705i	−0.799873	−	0.600169i	$-0.795100\pi$
$227$	−3.00885	+	3.00885i	−0.199705	+	0.199705i	0.600169	+	0.799873i	$0.295100\pi$
$228$	−18.1424	+	5.69402i	−1.20151	+	0.377096i
$229$			6.86713i			0.453793i	0.973919	+	0.226896i	$0.0728578\pi$
$229$			6.86713i			0.453793i	−0.973919	+	0.226896i	$0.927142\pi$
$230$	−26.2495	+	14.6912i	−1.73084	+	0.968709i
$231$		−	11.7955i		−	0.776089i
$232$	−22.7535	+	1.44619i	−1.49384	+	0.0949468i
$233$	1.03444	−	1.03444i	0.0677686	−	0.0677686i	−0.672410	−	0.740179i	$-0.734741\pi$
$233$	1.03444	−	1.03444i	0.0677686	−	0.0677686i	0.740179	+	0.672410i	$0.234741\pi$
$234$	4.34985	+	1.06744i	0.284359	+	0.0697807i
$235$	−0.473548	+	13.7147i	−0.0308909	+	0.894648i
$236$	0.253696	−	0.485782i	0.0165142	−	0.0316217i
$237$	12.2794	+	12.2794i	0.797634	+	0.797634i
$238$	12.1574	−	7.36636i	0.788049	−	0.477490i
$239$	17.3251			1.12067			0.560335	−	0.828266i	$-0.310673\pi$
$239$	17.3251			1.12067			0.560335	+	0.828266i	$0.310673\pi$
$240$	6.82229	+	10.5572i	0.440377	+	0.681463i
$241$	−22.3773			−1.44145			−0.720724	−	0.693222i	$-0.756190\pi$
$241$	−22.3773			−1.44145			−0.720724	+	0.693222i	$0.756190\pi$
$242$	−4.36971	+	2.64767i	−0.280895	+	0.170198i
$243$	−7.15566	−	7.15566i	−0.459036	−	0.459036i
$244$	−2.22266	+	4.25600i	−0.142291	+	0.272462i
$245$	3.86992	+	4.14672i	0.247240	+	0.264925i
$246$	−1.93018	−	0.473660i	−0.123064	−	0.0301994i
$247$	−14.7806	+	14.7806i	−0.940467	+	0.940467i
$248$	17.3059	−	1.09994i	1.09893	−	0.0698466i
$249$			5.12335i			0.324679i
$250$	−14.8841	−	5.33524i	−0.941350	−	0.337431i
$251$		−	1.82781i		−	0.115371i	−0.998335	−	0.0576853i	$-0.981628\pi$
$251$		−	1.82781i		−	0.115371i	0.998335	−	0.0576853i	$-0.0183720\pi$
$252$	−6.04035	+	1.89577i	−0.380506	+	0.119422i
$253$	−18.2817	+	18.2817i	−1.14936	+	1.14936i
$254$	−4.65167	+	18.9557i	−0.291871	+	1.18939i
$255$	6.97857	+	7.47772i	0.437015	+	0.468273i
$256$	−5.55148	+	15.0060i	−0.346968	+	0.937877i
$257$	3.78147	+	3.78147i	0.235882	+	0.235882i	0.815142	−	0.579261i	$-0.196659\pi$
$257$	3.78147	+	3.78147i	0.235882	+	0.235882i	−0.579261	+	0.815142i	$0.696659\pi$
$258$	−3.73987	−	6.17229i	−0.232834	−	0.384270i
$259$	−6.27462			−0.389886
$260$	12.0200	+	6.81530i	0.745451	+	0.422667i
$261$	8.26255			0.511439
$262$	1.76206	+	2.90810i	0.108860	+	0.179663i
$263$	−12.4045	−	12.4045i	−0.764892	−	0.764892i	0.212310	−	0.977202i	$-0.431901\pi$
$263$	−12.4045	−	12.4045i	−0.764892	−	0.764892i	−0.977202	+	0.212310i	$0.931901\pi$
$264$	8.10843	+	7.13930i	0.499039	+	0.439394i
$265$	0.276540	−	8.00903i	0.0169877	−	0.491991i
$266$	7.04155	−	28.6945i	0.431745	−	1.75938i
$267$	−12.6893	+	12.6893i	−0.776573	+	0.776573i
$268$	−3.82911	−	12.2004i	−0.233900	−	0.745259i
$269$		−	8.88991i		−	0.542027i	−0.962575	−	0.271014i	$-0.912641\pi$
$269$		−	8.88991i		−	0.542027i	0.962575	−	0.271014i	$-0.0873589\pi$
$270$	−8.73604	−	15.6091i	−0.531658	−	0.949939i
$271$			12.0953i			0.734736i	0.930076	+	0.367368i	$0.119741\pi$
$271$			12.0953i			0.734736i	−0.930076	+	0.367368i	$0.880259\pi$
$272$	−2.29460	+	12.8157i	−0.139130	+	0.777068i
$273$	9.48164	−	9.48164i	0.573855	−	0.573855i
$274$	31.1090	+	7.63404i	1.87936	+	0.461189i
$275$	−13.5573	−	0.937348i	−0.817539	−	0.0565242i
$276$	−23.6992	−	12.3767i	−1.42652	−	0.744990i
$277$	−5.20193	−	5.20193i	−0.312554	−	0.312554i	0.533344	−	0.845898i	$-0.320935\pi$
$277$	−5.20193	−	5.20193i	−0.312554	−	0.312554i	−0.845898	+	0.533344i	$0.820935\pi$
$278$	20.2368	−	12.2618i	1.21372	−	0.735412i
$279$	−6.28436			−0.376235
$280$	−19.5229	+	0.565517i	−1.16672	+	0.0337961i
$281$	−15.4384			−0.920975			−0.460488	−	0.887666i	$-0.652325\pi$
$281$	−15.4384			−0.920975			−0.460488	+	0.887666i	$0.652325\pi$
$282$	−10.4316	+	6.32064i	−0.621191	+	0.376388i
$283$	−4.40585	−	4.40585i	−0.261900	−	0.261900i	0.563925	−	0.825826i	$-0.309291\pi$
$283$	−4.40585	−	4.40585i	−0.261900	−	0.261900i	−0.825826	+	0.563925i	$0.809291\pi$
$284$	6.66507	+	3.48078i	0.395499	+	0.206547i
$285$	21.2467	+	0.733619i	1.25855	+	0.0434558i
$286$	11.5340	+	2.83040i	0.682018	+	0.167365i
$287$	2.18364	−	2.18364i	0.128896	−	0.128896i
$288$	2.35277	−	5.29966i	0.138638	−	0.312285i
$289$		−	6.40574i		−	0.376808i
$290$	24.5316	+	6.92570i	1.44055	+	0.406691i
$291$			5.91895i			0.346975i
$292$	1.75833	+	5.60243i	0.102898	+	0.327858i
$293$	20.1427	−	20.1427i	1.17675	−	1.17675i	0.196184	−	0.980567i	$-0.437145\pi$
$293$	20.1427	−	20.1427i	1.17675	−	1.17675i	0.980567	−	0.196184i	$-0.0628549\pi$
$294$	−1.20148	+	4.89608i	−0.0700719	+	0.285545i
$295$	−0.447955	+	0.418053i	−0.0260810	+	0.0243400i
$296$	3.79774	−	4.31327i	0.220739	−	0.250704i
$297$	−10.8711	−	10.8711i	−0.630807	−	0.630807i
$298$	−15.3712	−	25.3686i	−0.890427	−	1.46956i
$299$	−29.3909			−1.69972
$300$	−3.27340	−	13.6668i	−0.188990	−	0.789054i
$301$	11.2138			0.646352
$302$	−3.38093	−	5.57988i	−0.194551	−	0.321086i
$303$	16.9523	+	16.9523i	0.973885	+	0.973885i
$304$	15.4631	+	22.2080i	0.886872	+	1.27372i
$305$	3.92459	−	3.66262i	0.224722	−	0.209721i
$306$	1.12449	−	4.58235i	0.0642831	−	0.261956i
$307$	15.0025	−	15.0025i	0.856236	−	0.856236i	−0.134656	−	0.990892i	$-0.542993\pi$
$307$	15.0025	−	15.0025i	0.856236	−	0.856236i	0.990892	+	0.134656i	$0.0429930\pi$
$308$	−16.0165	+	5.02678i	−0.912622	+	0.286427i
$309$		−	2.78774i		−	0.158589i
$310$	−18.6583	−	5.26757i	−1.05972	−	0.299178i
$311$		−	24.2214i		−	1.37347i	−0.726909	−	0.686734i	$-0.759044\pi$
$311$		−	24.2214i		−	1.37347i	0.726909	−	0.686734i	$-0.240956\pi$
$312$	0.779019	+	12.2566i	0.0441033	+	0.693896i
$313$	11.2618	−	11.2618i	0.636555	−	0.636555i	−0.313149	−	0.949704i	$-0.601384\pi$
$313$	11.2618	−	11.2618i	0.636555	−	0.636555i	0.949704	+	0.313149i	$0.101384\pi$
$314$	−7.01511	−	1.72148i	−0.395885	−	0.0971490i
$315$	7.07390	+	0.244251i	0.398569	+	0.0137620i
$316$	11.4405	−	21.9065i	0.643579	−	1.23234i
$317$	20.0917	+	20.0917i	1.12846	+	1.12846i	0.990428	+	0.138032i	$0.0440777\pi$
$317$	20.0917	+	20.0917i	1.12846	+	1.12846i	0.138032	+	0.990428i	$0.455922\pi$
$318$	6.09178	−	3.69109i	0.341610	−	0.206986i
$319$	21.9088			1.22666
$320$	11.4276	−	13.7626i	0.638822	−	0.769355i
$321$	0.253605			0.0141548
$322$	35.5303	−	21.5283i	1.98002	−	1.19972i
$323$	15.5706	+	15.5706i	0.866373	+	0.866373i
$324$	4.51273	−	8.64105i	0.250707	−	0.480058i
$325$	−10.1444	−	11.6513i	−0.562709	−	0.646299i
$326$	−1.10248	−	0.270545i	−0.0610608	−	0.0149841i
$327$	5.85003	−	5.85003i	0.323507	−	0.323507i
$328$	0.179410	+	2.82273i	0.00990624	+	0.155859i
$329$		−	18.9521i		−	1.04486i
$330$	−5.89910	−	10.5402i	−0.324735	−	0.580219i
$331$			7.80993i			0.429273i	0.976694	+	0.214636i	$0.0688566\pi$
$331$			7.80993i			0.429273i	−0.976694	+	0.214636i	$0.931143\pi$
$332$	6.95670	−	2.18337i	0.381798	−	0.119828i
$333$	−1.47269	+	1.47269i	−0.0807029	+	0.0807029i
$334$	−2.46166	+	10.0314i	−0.134696	+	0.548891i
$335$	−0.493344	+	14.2880i	−0.0269542	+	0.780637i
$336$	−9.91949	−	14.2463i	−0.541153	−	0.777197i
$337$	8.78775	+	8.78775i	0.478699	+	0.478699i	0.904715	−	0.426016i	$-0.140083\pi$
$337$	8.78775	+	8.78775i	0.478699	+	0.478699i	−0.426016	+	0.904715i	$0.640083\pi$
$338$	−2.53095	−	4.17708i	−0.137665	−	0.227203i
$339$	−2.72737			−0.148131
$340$	7.17958	−	12.6625i	0.389367	−	0.686720i
$341$	−16.6635			−0.902377
$342$	−5.08209	−	8.38748i	−0.274808	−	0.453543i
$343$	9.74648	+	9.74648i	0.526260	+	0.526260i
$344$	−6.78720	+	7.70854i	−0.365941	+	0.415616i
$345$	20.3950	+	21.8538i	1.09803	+	1.17657i
$346$	−8.14577	+	33.1943i	−0.437919	+	1.78454i
$347$	4.87857	−	4.87857i	0.261895	−	0.261895i	−0.563928	−	0.825824i	$-0.690711\pi$
$347$	4.87857	−	4.87857i	0.261895	−	0.261895i	0.825824	+	0.563928i	$0.190711\pi$
$348$	6.78440	+	21.6166i	0.363682	+	1.15877i
$349$		−	18.6081i		−	0.996066i	−0.867158	−	0.498033i	$-0.834056\pi$
$349$		−	18.6081i		−	0.996066i	0.867158	−	0.498033i	$-0.165944\pi$
$350$	20.7978	+	6.65455i	1.11169	+	0.355701i
$351$		−	17.4772i		−	0.932862i
$352$	6.23855	−	14.0524i	0.332516	−	0.748998i
$353$	−17.3807	+	17.3807i	−0.925082	+	0.925082i	−0.997383	−	0.0723013i	$-0.976966\pi$
$353$	−17.3807	+	17.3807i	−0.925082	+	0.925082i	0.0723013	+	0.997383i	$0.476966\pi$
$354$	−0.528906	−	0.129792i	−0.0281110	−	0.00689835i
$355$	−5.73581	−	6.14607i	−0.304425	−	0.326200i
$356$	22.6377	+	11.8224i	1.19980	+	0.626586i
$357$	−9.98844	−	9.98844i	−0.528644	−	0.528644i
$358$	24.0885	−	14.5956i	1.27312	−	0.771399i
$359$	23.4677			1.23858			0.619290	−	0.785162i	$-0.287420\pi$
$359$	23.4677			1.23858			0.619290	+	0.785162i	$0.287420\pi$
$360$	−4.44942	+	4.71488i	−0.234505	+	0.248496i
$361$	26.7690			1.40889
$362$	−16.7649	+	10.1581i	−0.881143	+	0.533897i
$363$	3.59011	+	3.59011i	0.188432	+	0.188432i
$364$	−16.9153	−	8.83388i	−0.886601	−	0.463021i
$365$	0.226544	−	6.56105i	0.0118578	−	0.343421i
$366$	4.63381	+	1.13712i	0.242213	+	0.0594383i
$367$	7.03324	−	7.03324i	0.367132	−	0.367132i	−0.499298	−	0.866430i	$-0.666409\pi$
$367$	7.03324	−	7.03324i	0.367132	−	0.367132i	0.866430	+	0.499298i	$0.166409\pi$
$368$	−6.70599	+	37.4542i	−0.349574	+	1.95243i
$369$		−	1.02503i		−	0.0533609i
$370$	−5.60685	+	3.13802i	−0.291486	+	0.163138i
$371$			11.0675i			0.574597i
$372$	−5.16010	−	16.4413i	−0.267539	−	0.852439i
$373$	21.1346	−	21.1346i	1.09431	−	1.09431i	0.0992429	−	0.995063i	$-0.468358\pi$
$373$	21.1346	−	21.1346i	1.09431	−	1.09431i	0.995063	−	0.0992429i	$-0.0316421\pi$
$374$	2.98168	−	12.1505i	0.154179	−	0.628285i
$375$	−1.62400	+	15.6280i	−0.0838630	+	0.807026i
$376$	13.0279	+	11.4708i	0.671865	+	0.591563i
$377$	17.6110	+	17.6110i	0.907014	+	0.907014i
$378$	12.8017	+	21.1279i	0.658447	+	1.08670i
$379$	38.6365			1.98462			0.992311	−	0.123772i	$-0.0394991\pi$
$379$	38.6365			1.98462			0.992311	+	0.123772i	$0.0394991\pi$
$380$	−8.05837	−	29.1623i	−0.413385	−	1.49600i
$381$	19.3956			0.993666
$382$	14.1364	+	23.3308i	0.723283	+	1.19371i
$383$	−7.17196	−	7.17196i	−0.366470	−	0.366470i	0.499718	−	0.866188i	$-0.333437\pi$
$383$	−7.17196	−	7.17196i	−0.366470	−	0.366470i	−0.866188	+	0.499718i	$0.833437\pi$
$384$	15.7969	+	1.80380i	0.806133	+	0.0920499i
$385$	18.7570	+	0.647651i	0.955945	+	0.0330074i
$386$	7.53727	−	30.7146i	0.383637	−	1.56333i
$387$	2.63195	−	2.63195i	0.133789	−	0.133789i
$388$	8.03700	−	2.52242i	0.408017	−	0.128056i
$389$			11.6806i			0.592228i	0.955153	+	0.296114i	$0.0956908\pi$
$389$			11.6806i			0.592228i	−0.955153	+	0.296114i	$0.904309\pi$
$390$	3.73068	−	13.2145i	0.188910	−	0.669141i
$391$			30.9619i			1.56581i
$392$	7.16013	−	0.455090i	0.361641	−	0.0229855i
$393$	2.38927	−	2.38927i	0.120523	−	0.120523i
$394$	23.1934	+	5.69159i	1.16847	+	0.286738i
$395$	−20.2007	+	18.8522i	−1.01641	+	0.948559i
$396$	−2.57934	+	4.93898i	−0.129617	+	0.248193i
$397$	3.43766	+	3.43766i	0.172531	+	0.172531i	0.788090	−	0.615559i	$-0.211070\pi$
$397$	3.43766	+	3.43766i	0.172531	+	0.172531i	−0.615559	+	0.788090i	$0.711070\pi$
$398$	5.64421	−	3.41991i	0.282919	−	0.171424i
$399$	−29.3604			−1.46986
$400$	−17.1624	+	10.2690i	−0.858119	+	0.513450i
$401$	22.6158			1.12938			0.564690	−	0.825303i	$-0.308996\pi$
$401$	22.6158			1.12938			0.564690	+	0.825303i	$0.308996\pi$
$402$	−10.8676	+	6.58486i	−0.542029	+	0.328423i
$403$	−13.3947	−	13.3947i	−0.667235	−	0.667235i
$404$	15.7942	−	30.2429i	0.785789	−	1.50464i
$405$	−7.96819	+	7.43630i	−0.395943	+	0.369513i
$406$	−34.1895	−	8.38998i	−1.69679	−	0.416388i
$407$	−3.90495	+	3.90495i	−0.193561	+	0.193561i
$408$	12.9118	−	0.820657i	0.639227	−	0.0406286i
$409$		−	33.7737i		−	1.67000i	−0.550250	−	0.835000i	$-0.685467\pi$
$409$		−	33.7737i		−	1.67000i	0.550250	−	0.835000i	$-0.314533\pi$
$410$	0.859183	−	3.04332i	0.0424320	−	0.150299i
$411$		−	31.8309i		−	1.57010i
$412$	−3.78531	+	1.18802i	−0.186489	+	0.0585298i
$413$	0.598360	−	0.598360i	0.0294434	−	0.0294434i
$414$	3.28635	−	13.3920i	0.161515	−	0.658180i
$415$	−8.14704	−	0.281305i	−0.399923	−	0.0138087i
$416$	16.3106	−	6.28107i	0.799693	−	0.307955i
$417$	−16.6264	−	16.6264i	−0.814197	−	0.814197i
$418$	−13.4756	−	22.2400i	−0.659111	−	1.08780i
$419$	−30.4530			−1.48773			−0.743863	−	0.668332i	$-0.767008\pi$
$419$	−30.4530			−1.48773			−0.743863	+	0.668332i	$0.767008\pi$
$420$	5.16938	+	18.7074i	0.252240	+	0.912829i
$421$	−38.9736			−1.89946			−0.949728	−	0.313075i	$-0.898641\pi$
$421$	−38.9736			−1.89946			−0.949728	+	0.313075i	$0.898641\pi$
$422$	−10.7615	−	17.7608i	−0.523863	−	0.864584i
$423$	−4.44816	−	4.44816i	−0.216277	−	0.216277i
$424$	−7.60799	−	6.69867i	−0.369477	−	0.325316i
$425$	−12.2741	+	10.6866i	−0.595381	+	0.518376i
$426$	1.78078	−	7.25674i	0.0862791	−	0.351590i
$427$	−5.24231	+	5.24231i	−0.253693	+	0.253693i
$428$	−0.108076	−	0.344355i	−0.00522405	−	0.0166450i
$429$		−	11.8016i		−	0.569788i
$430$	10.0204	−	5.60817i	0.483226	−	0.270450i
$431$		−	18.8141i		−	0.906242i	−0.891449	−	0.453121i	$-0.850311\pi$
$431$		−	18.8141i		−	0.906242i	0.891449	−	0.453121i	$-0.149689\pi$
$432$	−22.2719	−	3.98768i	−1.07156	−	0.191857i
$433$	13.2965	−	13.2965i	0.638988	−	0.638988i	−0.311318	−	0.950306i	$-0.600770\pi$
$433$	13.2965	−	13.2965i	0.638988	−	0.638988i	0.950306	+	0.311318i	$0.100770\pi$
$434$	26.0039	+	6.38128i	1.24823	+	0.306311i
$435$	0.874104	−	25.3154i	0.0419101	−	1.21378i
$436$	−10.4365	−	5.45037i	−0.499816	−	0.261025i
$437$	45.5053	+	45.5053i	2.17682	+	2.17682i
$438$	4.99042	−	3.02377i	0.238452	−	0.144481i
$439$	−26.4361			−1.26173			−0.630864	−	0.775894i	$-0.717299\pi$
$439$	−26.4361			−1.26173			−0.630864	+	0.775894i	$0.717299\pi$
$440$	−11.7980	+	12.5019i	−0.562446	+	0.596003i
$441$	−2.60008			−0.123814
$442$	12.1637	−	7.37017i	0.578570	−	0.350563i
$443$	12.4954	+	12.4954i	0.593676	+	0.593676i	0.938622	−	0.344946i	$-0.112103\pi$
$443$	12.4954	+	12.4954i	0.593676	+	0.593676i	−0.344946	+	0.938622i	$0.612103\pi$
$444$	−5.06211	−	2.64365i	−0.240237	−	0.125462i
$445$	−19.4815	−	20.8750i	−0.923513	−	0.989569i
$446$	−29.9120	−	7.34030i	−1.41637	−	0.347573i
$447$	−20.8426	+	20.8426i	−0.985820	+	0.985820i
$448$	−15.1169	+	19.5403i	−0.714205	+	0.923191i
$449$			32.1509i			1.51729i	0.651502	+	0.758647i	$0.274139\pi$
$449$			32.1509i			1.51729i	−0.651502	+	0.758647i	$0.725861\pi$
$450$	6.44322	−	3.31950i	0.303737	−	0.156483i
$451$		−	2.71794i		−	0.127983i
$452$	1.16230	+	3.70334i	0.0546698	+	0.174191i
$453$	−4.58438	+	4.58438i	−0.215393	+	0.215393i
$454$	1.43417	−	5.84431i	0.0673091	−	0.274287i
$455$	14.5569	+	15.5981i	0.682438	+	0.731251i
$456$	17.7706	−	20.1828i	0.832182	−	0.945148i
$457$	−0.136202	−	0.136202i	−0.00637126	−	0.00637126i	0.703914	−	0.710285i	$-0.251434\pi$
$457$	−0.136202	−	0.136202i	−0.00637126	−	0.00637126i	−0.710285	+	0.703914i	$0.751434\pi$
$458$	−5.03264	−	8.30587i	−0.235160	−	0.388108i
$459$	−18.4113			−0.859366
$460$	20.9824	−	37.0063i	0.978310	−	1.72543i
$461$	15.5834			0.725793			0.362897	−	0.931829i	$-0.381788\pi$
$461$	15.5834			0.725793			0.362897	+	0.931829i	$0.381788\pi$
$462$	8.64447	+	14.2668i	0.402177	+	0.663753i
$463$	5.03455	+	5.03455i	0.233975	+	0.233975i	0.814350	−	0.580374i	$-0.197094\pi$
$463$	5.03455	+	5.03455i	0.233975	+	0.233975i	−0.580374	+	0.814350i	$0.697094\pi$
$464$	26.4607	−	18.4243i	1.22841	−	0.855326i
$465$	−0.664829	+	19.2545i	−0.0308307	+	0.892905i
$466$	−0.493069	+	2.00927i	−0.0228410	+	0.0930777i
$467$	21.5717	−	21.5717i	0.998219	−	0.998219i	−0.00177974	−	0.999998i	$-0.500567\pi$
$467$	21.5717	−	21.5717i	0.998219	−	0.998219i	0.999998	+	0.00177974i	$0.000566508\pi$
$468$	−6.04348	+	1.89675i	−0.279360	+	0.0876774i
$469$		−	19.7443i		−	0.911708i
$470$	−9.47818	−	16.9351i	−0.437196	−	0.781158i
$471$			7.17790i			0.330740i
$472$	0.0491617	+	0.773482i	0.00226285	+	0.0356024i
$473$	6.97881	−	6.97881i	0.320886	−	0.320886i
$474$	−23.8512	−	5.85300i	−1.09552	−	0.268837i
$475$	−2.33317	+	33.7458i	−0.107053	+	1.54836i
$476$	−9.30604	+	17.8194i	−0.426542	+	0.816750i
$477$	2.59762	+	2.59762i	0.118937	+	0.118937i
$478$	−20.9549	+	12.6969i	−0.958456	+	0.580742i
$479$	−6.50061			−0.297020			−0.148510	−	0.988911i	$-0.547448\pi$
$479$	−6.50061			−0.297020			−0.148510	+	0.988911i	$0.547448\pi$
$480$	−15.9886	−	7.76924i	−0.729775	−	0.354616i
$481$	−6.27786			−0.286246
$482$	27.0656	−	16.3994i	1.23280	−	0.746973i
$483$	−29.1913	−	29.1913i	−1.32825	−	1.32825i
$484$	3.34484	−	6.40476i	0.152038	−	0.291126i
$485$	−9.41219	−	0.324989i	−0.427386	−	0.0147570i
$486$	13.8989	+	3.41075i	0.630469	+	0.154715i
$487$	−14.0175	+	14.0175i	−0.635193	+	0.635193i	−0.949366	−	0.314173i	$-0.898273\pi$
$487$	−14.0175	+	14.0175i	−0.635193	+	0.635193i	0.314173	+	0.949366i	$0.398273\pi$
$488$	−0.430712	−	6.77658i	−0.0194974	−	0.306761i
$489$			1.12807i			0.0510129i
$490$	−7.71968	−	2.17940i	−0.348740	−	0.0984553i
$491$			28.8171i			1.30050i	0.759721	+	0.650249i	$0.225335\pi$
$491$			28.8171i			1.30050i	−0.759721	+	0.650249i	$0.774665\pi$
$492$	2.68170	−	0.841653i	0.120900	−	0.0379447i
$493$	18.5523	−	18.5523i	0.835555	−	0.835555i
$494$	7.04520	−	28.7094i	0.316978	−	1.29170i
$495$	4.55439	−	4.25037i	0.204705	−	0.191040i
$496$	−20.1256	+	14.0132i	−0.903666	+	0.629211i
$497$	8.20967	+	8.20967i	0.368254	+	0.368254i
$498$	−3.75470	−	6.19675i	−0.168252	−	0.277683i
$499$	9.69310			0.433923			0.216961	−	0.976180i	$-0.430385\pi$
$499$	9.69310			0.433923			0.216961	+	0.976180i	$0.430385\pi$
$500$	21.9124	−	4.45489i	0.979953	−	0.199229i
$501$	10.2642			0.458568
$502$	1.33953	+	2.21076i	0.0597862	+	0.0986711i
$503$	−1.91779	−	1.91779i	−0.0855098	−	0.0855098i	0.663058	−	0.748568i	$-0.269258\pi$
$503$	−1.91779	−	1.91779i	−0.0855098	−	0.0855098i	−0.748568	+	0.663058i	$0.769258\pi$
$504$	5.91654	−	6.71968i	0.263544	−	0.299319i
$505$	−27.8880	+	26.0264i	−1.24100	+	1.15816i
$506$	8.71401	−	35.5099i	0.387385	−	1.57861i
$507$	−3.43185	+	3.43185i	−0.152414	+	0.152414i
$508$	−8.26562	−	26.3361i	−0.366728	−	1.16848i
$509$		−	16.5964i		−	0.735621i	−0.929901	−	0.367811i	$-0.880107\pi$
$509$		−	16.5964i		−	0.735621i	0.929901	−	0.367811i	$-0.119893\pi$
$510$	−13.9208	−	3.93008i	−0.616422	−	0.174027i
$511$			9.06659i			0.401082i
$512$	−4.28273	−	22.2184i	−0.189272	−	0.981925i
$513$	−27.0595	+	27.0595i	−1.19471	+	1.19471i
$514$	−7.34502	−	1.80244i	−0.323975	−	0.0795024i
$515$	4.43301	+	0.153065i	0.195342	+	0.00674486i
$516$	9.04684	+	4.72465i	0.398265	+	0.207991i
$517$	−11.7946	−	11.7946i	−0.518728	−	0.518728i
$518$	7.58922	−	4.59841i	0.333451	−	0.202043i
$519$	33.9646			1.49088
$520$	−19.5330	+	0.565809i	−0.856580	+	0.0248124i
$521$	−19.6006			−0.858719			−0.429359	−	0.903134i	$-0.641261\pi$
$521$	−19.6006			−0.858719			−0.429359	+	0.903134i	$0.641261\pi$
$522$	−9.99365	+	6.05529i	−0.437410	+	0.265033i
$523$	9.06625	+	9.06625i	0.396439	+	0.396439i	0.876975	−	0.480536i	$-0.159558\pi$
$523$	9.06625	+	9.06625i	0.396439	+	0.396439i	−0.480536	+	0.876975i	$0.659558\pi$
$524$	−4.26246	−	2.22604i	−0.186207	−	0.0972451i
$525$	1.49671	−	21.6477i	0.0653218	−	0.944783i
$526$	24.0941	+	5.91261i	1.05055	+	0.257802i
$527$	−14.1106	+	14.1106i	−0.614667	+	0.614667i
$528$	−15.0393	−	2.69272i	−0.654503	−	0.117186i
$529$			67.4865i			2.93420i
$530$	5.53502	+	9.88968i	0.240426	+	0.429580i
$531$		−	0.280877i		−	0.0121890i
$532$	12.5122	+	39.8668i	0.542474	+	1.72845i
$533$	2.18477	−	2.18477i	0.0946331	−	0.0946331i
$534$	6.04838	−	24.6473i	0.261739	−	1.06659i
$535$	−0.0139245	+	0.403277i	−0.000602011	+	0.0174352i
$536$	13.5725	+	11.9503i	0.586245	+	0.516176i
$537$	−19.7909	−	19.7909i	−0.854040	−	0.854040i
$538$	6.51506	+	10.7524i	0.280884	+	0.463571i
$539$	−6.89432			−0.296960
$540$	22.0056	+	12.4771i	0.946971	+	0.536928i
$541$	−14.4657			−0.621930			−0.310965	−	0.950421i	$-0.600652\pi$
$541$	−14.4657			−0.621930			−0.310965	+	0.950421i	$0.600652\pi$
$542$	−8.86414	−	14.6294i	−0.380748	−	0.628386i
$543$	13.7739	+	13.7739i	0.591094	+	0.591094i
$544$	−6.61679	−	17.1824i	−0.283693	−	0.736689i
$545$	8.98139	+	9.62380i	0.384720	+	0.412238i
$546$	−4.51944	+	18.4169i	−0.193414	+	0.788169i
$547$	14.0753	−	14.0753i	0.601817	−	0.601817i	−0.338977	−	0.940795i	$-0.610081\pi$
$547$	14.0753	−	14.0753i	0.601817	−	0.601817i	0.940795	+	0.338977i	$0.110081\pi$
$548$	−43.2213	+	13.5650i	−1.84632	+	0.579470i
$549$			2.46080i			0.105025i
$550$	17.0847	−	8.80190i	0.728494	−	0.375314i
$551$		−	54.5336i		−	2.32321i
$552$	37.7348	−	2.39838i	1.60610	−	0.102082i
$553$	26.9832	−	26.9832i	1.14744	−	1.14744i
$554$	10.1041	+	2.47951i	0.429281	+	0.105344i
$555$	4.35634	+	4.66793i	0.184916	+	0.198143i
$556$	−15.4905	+	29.6615i	−0.656943	+	1.25793i
$557$	25.7681	+	25.7681i	1.09183	+	1.09183i	0.995333	+	0.0964958i	$0.0307634\pi$
$557$	25.7681	+	25.7681i	1.09183	+	1.09183i	0.0964958	+	0.995333i	$0.469237\pi$
$558$	7.60100	−	4.60555i	0.321776	−	0.194969i
$559$	11.2196			0.474539
$560$	23.1987	−	14.9916i	0.980325	−	0.633509i
$561$	−12.4324			−0.524898
$562$	18.6729	−	11.3141i	0.787667	−	0.477258i
$563$	−19.3185	−	19.3185i	−0.814178	−	0.814178i	0.171080	−	0.985257i	$-0.445274\pi$
$563$	−19.3185	−	19.3185i	−0.814178	−	0.814178i	−0.985257	+	0.171080i	$0.945274\pi$
$564$	7.98497	−	15.2898i	0.336228	−	0.643815i
$565$	0.149751	−	4.33701i	0.00630006	−	0.182459i
$566$	8.55778	+	2.10005i	0.359711	+	0.0882718i
$567$	10.6436	−	10.6436i	0.446988	−	0.446988i
$568$	−10.6124	+	0.674513i	−0.445286	+	0.0283019i
$569$			17.6554i			0.740153i	0.929001	+	0.370077i	$0.120669\pi$
$569$			17.6554i			0.740153i	−0.929001	+	0.370077i	$0.879331\pi$
$570$	−26.2358	+	14.6836i	−1.09890	+	0.615026i
$571$		−	3.84224i		−	0.160793i	−0.996763	−	0.0803965i	$-0.974381\pi$
$571$		−	3.84224i		−	0.160793i	0.996763	−	0.0803965i	$-0.0256186\pi$
$572$	−16.0248	+	5.02938i	−0.670029	+	0.210289i
$573$	19.1683	−	19.1683i	0.800769	−	0.800769i
$574$	−1.04084	+	4.24144i	−0.0434437	+	0.177034i
$575$	−35.8712	+	31.2317i	−1.49593	+	1.30245i
$576$	1.03820	+	8.13424i	0.0432584	+	0.338927i
$577$	10.6921	+	10.6921i	0.445116	+	0.445116i	0.893727	−	0.448611i	$-0.148081\pi$
$577$	10.6921	+	10.6921i	0.445116	+	0.445116i	−0.448611	+	0.893727i	$0.648081\pi$
$578$	4.69451	+	7.74781i	0.195266	+	0.322266i
$579$	−31.4274			−1.30608
$580$	−34.7468	+	9.60151i	−1.44278	+	0.398681i
$581$	11.2582			0.467070
$582$	−4.33776	−	7.15904i	−0.179806	−	0.296752i
$583$	6.88778	+	6.88778i	0.285263	+	0.285263i
$584$	−6.23252	−	5.48760i	−0.257903	−	0.227078i
$585$	7.07756	+	0.244378i	0.292621	+	0.0101038i
$586$	−9.60106	+	39.1246i	−0.396616	+	1.61622i
$587$	−9.62931	+	9.62931i	−0.397444	+	0.397444i	−0.877331	−	0.479886i	$-0.840678\pi$
$587$	−9.62931	+	9.62931i	−0.397444	+	0.397444i	0.479886	+	0.877331i	$0.340678\pi$
$588$	−2.13494	−	6.80239i	−0.0880432	−	0.280526i
$589$			41.4773i			1.70904i
$590$	0.235432	−	0.833928i	0.00969260	−	0.0343323i
$591$		−	23.7317i		−	0.976190i
$592$	−1.43239	+	8.00016i	−0.0588709	+	0.328804i
$593$	19.6693	−	19.6693i	0.807722	−	0.807722i	−0.176567	−	0.984289i	$-0.556499\pi$
$593$	19.6693	−	19.6693i	0.807722	−	0.807722i	0.984289	+	0.176567i	$0.0564992\pi$
$594$	21.1158	+	5.18174i	0.866390	+	0.212609i
$595$	16.4318	−	15.3350i	0.673639	−	0.628672i
$596$	37.1832	+	19.4186i	1.52308	+	0.795419i
$597$	−4.63723	−	4.63723i	−0.189789	−	0.189789i
$598$	35.5487	−	21.5394i	1.45369	−	0.880813i
$599$	−18.5597			−0.758327			−0.379164	−	0.925330i	$-0.623788\pi$
$599$	−18.5597			−0.758327			−0.379164	+	0.925330i	$0.623788\pi$
$600$	13.9751	+	14.1312i	0.570530	+	0.576905i
$601$	9.90611			0.404079			0.202039	−	0.979377i	$-0.435243\pi$
$601$	9.90611			0.404079			0.202039	+	0.979377i	$0.435243\pi$
$602$	−13.5632	+	8.21814i	−0.552795	+	0.334946i
$603$	−4.63411	−	4.63411i	−0.188716	−	0.188716i
$604$	8.17854	+	4.27118i	0.332780	+	0.173792i
$605$	−5.90604	+	5.51180i	−0.240115	+	0.224086i
$606$	−32.9277	−	8.08034i	−1.33759	−	0.328241i
$607$	22.3106	−	22.3106i	0.905560	−	0.905560i	−0.0903500	−	0.995910i	$-0.528799\pi$
$607$	22.3106	−	22.3106i	0.905560	−	0.905560i	0.995910	+	0.0903500i	$0.0287986\pi$
$608$	−34.9782	−	15.5285i	−1.41855	−	0.629763i
$609$			34.9829i			1.41758i
$610$	−2.06265	+	7.30615i	−0.0835144	+	0.295817i
$611$		−	18.9619i		−	0.767115i
$612$	1.99813	+	6.36650i	0.0807697	+	0.257351i
$613$	−3.29602	+	3.29602i	−0.133125	+	0.133125i	−0.770529	−	0.637405i	$-0.780008\pi$
$613$	−3.29602	+	3.29602i	−0.133125	+	0.133125i	0.637405	+	0.770529i	$0.280008\pi$
$614$	−7.15095	+	29.1404i	−0.288589	+	1.17601i
$615$	−3.14056	−	0.108439i	−0.126639	−	0.00437267i
$616$	15.6882	−	17.8178i	0.632094	−	0.717898i
$617$	−12.5202	−	12.5202i	−0.504043	−	0.504043i	0.408648	−	0.912692i	$-0.366000\pi$
$617$	−12.5202	−	12.5202i	−0.504043	−	0.504043i	−0.912692	+	0.408648i	$0.866000\pi$
$618$	2.04302	+	3.37181i	0.0821825	+	0.135634i
$619$	−2.29628			−0.0922953			−0.0461476	−	0.998935i	$-0.514694\pi$
$619$	−2.29628			−0.0922953			−0.0461476	+	0.998935i	$0.514694\pi$
$620$	26.4278	−	7.30275i	1.06137	−	0.293285i
$621$	−53.8073			−2.15921
$622$	17.7509	+	29.2960i	0.711745	+	1.17466i
$623$	27.8839	+	27.8839i	1.11715	+	1.11715i
$624$	−9.92463	−	14.2536i	−0.397303	−	0.570602i
$625$	−24.7621	−	3.44053i	−0.990485	−	0.137621i
$626$	−5.36795	+	21.8746i	−0.214547	+	0.874284i
$627$	−18.2722	+	18.2722i	−0.729722	+	0.729722i
$628$	9.74646	−	3.05893i	0.388926	−	0.122065i
$629$			6.61341i			0.263694i
$630$	−8.73496	+	4.88875i	−0.348009	+	0.194773i
$631$			28.5052i			1.13477i	0.823451	+	0.567387i	$0.192046\pi$
$631$			28.5052i			1.13477i	−0.823451	+	0.567387i	$0.807954\pi$
$632$	2.21696	+	34.8804i	0.0881860	+	1.38747i
$633$	−14.5921	+	14.5921i	−0.579985	+	0.579985i
$634$	−39.0254	−	9.57672i	−1.54990	−	0.380340i
$635$	−1.06494	+	30.8424i	−0.0422610	+	1.22395i
$636$	−4.66302	+	8.92883i	−0.184901	+	0.354051i
$637$	−5.54189	−	5.54189i	−0.219578	−	0.219578i
$638$	−26.4989	+	16.0561i	−1.04910	+	0.635666i
$639$	3.85372			0.152451
$640$	−3.73572	+	25.0209i	−0.147667	+	0.989037i
$641$	−3.50670			−0.138506			−0.0692531	−	0.997599i	$-0.522062\pi$
$641$	−3.50670			−0.138506			−0.0692531	+	0.997599i	$0.522062\pi$
$642$	−0.306738	+	0.185857i	−0.0121060	+	0.00733517i
$643$	7.27320	+	7.27320i	0.286827	+	0.286827i	0.835824	−	0.548997i	$-0.184990\pi$
$643$	7.27320	+	7.27320i	0.286827	+	0.286827i	−0.548997	+	0.835824i	$0.684990\pi$
$644$	−27.1970	+	52.0774i	−1.07171	+	2.05214i
$645$	−7.78551	−	8.34238i	−0.306554	−	0.328481i
$646$	−30.2439	−	7.42176i	−1.18993	−	0.292005i
$647$	24.8718	−	24.8718i	0.977811	−	0.977811i	−0.0219486	−	0.999759i	$-0.506987\pi$
$647$	24.8718	−	24.8718i	0.977811	−	0.977811i	0.999759	+	0.0219486i	$0.00698701\pi$
$648$	0.874484	+	13.7586i	0.0343530	+	0.540491i
$649$		−	0.744768i		−	0.0292347i
$650$	20.8085	+	6.65800i	0.816178	+	0.261148i
$651$		−	26.6074i		−	1.04283i
$652$	1.53174	−	0.480736i	0.0599874	−	0.0188271i
$653$	18.3243	−	18.3243i	0.717084	−	0.717084i	−0.250923	−	0.968007i	$-0.580734\pi$
$653$	18.3243	−	18.3243i	0.717084	−	0.717084i	0.968007	+	0.250923i	$0.0807342\pi$
$654$	−2.78843	+	11.3629i	−0.109036	+	0.444326i
$655$	3.66818	+	3.93056i	0.143328	+	0.153580i
$656$	−2.28566	−	3.28264i	−0.0892402	−	0.128166i
$657$	2.12798	+	2.12798i	0.0830206	+	0.0830206i
$658$	13.8892	+	22.9227i	0.541457	+	0.893621i
$659$	8.78138			0.342074			0.171037	−	0.985265i	$-0.445288\pi$
$659$	8.78138			0.342074			0.171037	+	0.985265i	$0.445288\pi$
$660$	14.8595	+	8.42528i	0.578406	+	0.327954i
$661$	42.1014			1.63756			0.818778	−	0.574110i	$-0.194652\pi$
$661$	42.1014			1.63756			0.818778	+	0.574110i	$0.194652\pi$
$662$	−5.72358	−	9.44620i	−0.222453	−	0.367137i
$663$	−9.99361	−	9.99361i	−0.388120	−	0.388120i
$664$	−6.81410	+	7.73909i	−0.264438	+	0.300335i
$665$	1.61208	−	46.6884i	0.0625138	−	1.81050i
$666$	0.701960	−	2.86051i	0.0272004	−	0.110843i
$667$	54.2195	−	54.2195i	2.09939	−	2.09939i
$668$	−4.37417	−	13.9371i	−0.169242	−	0.539242i
$669$			30.6061i			1.18330i
$670$	−9.87440	−	17.6430i	−0.381481	−	0.681610i
$671$			6.52501i			0.251895i
$672$	22.4382	+	9.96141i	0.865574	+	0.384270i
$673$	21.6779	−	21.6779i	0.835623	−	0.835623i	−0.152656	−	0.988279i	$-0.548783\pi$
$673$	21.6779	−	21.6779i	0.835623	−	0.835623i	0.988279	+	0.152656i	$0.0487828\pi$
$674$	−17.0691	−	4.18869i	−0.657476	−	0.161342i
$675$	−18.5718	−	21.3306i	−0.714828	−	0.821015i
$676$	6.12242	+	3.19739i	0.235478	+	0.122977i
$677$	−21.0156	−	21.0156i	−0.807696	−	0.807696i	0.176588	−	0.984285i	$-0.443494\pi$
$677$	−21.0156	−	21.0156i	−0.807696	−	0.807696i	−0.984285	+	0.176588i	$0.943494\pi$
$678$	3.29879	−	1.99878i	0.126689	−	0.0767628i
$679$	13.0065			0.499145
$680$	0.596052	+	20.5771i	0.0228575	+	0.789094i
$681$	−5.97993			−0.229152
$682$	20.1546	−	12.2120i	0.771761	−	0.467621i
$683$	10.1214	+	10.1214i	0.387285	+	0.387285i	0.873718	−	0.486433i	$-0.161702\pi$
$683$	10.1214	+	10.1214i	0.387285	+	0.387285i	−0.486433	+	0.873718i	$0.661702\pi$
$684$	12.2937	+	6.42029i	0.470061	+	0.245486i
$685$	50.6168	+	1.74772i	1.93397	+	0.0667771i
$686$	−18.9313	−	4.64567i	−0.722800	−	0.177373i
$687$	−6.82402	+	6.82402i	−0.260353	+	0.260353i
$688$	2.55992	−	14.2976i	0.0975961	−	0.545092i
$689$			11.0733i			0.421857i
$690$	−40.6837	−	11.4857i	−1.54880	−	0.437253i
$691$			48.2691i			1.83624i	0.396300	+	0.918121i	$0.370294\pi$
$691$			48.2691i			1.83624i	−0.396300	+	0.918121i	$0.629706\pi$
$692$	−14.4743	−	46.1185i	−0.550232	−	1.75316i
$693$	−6.08356	+	6.08356i	−0.231095	+	0.231095i
$694$	−2.32538	+	9.47599i	−0.0882701	+	0.359704i
$695$	27.3518	−	25.5260i	1.03751	−	0.968257i
$696$	−24.0478	−	21.1736i	−0.911528	−	0.802581i
$697$	−2.30155	−	2.30155i	−0.0871774	−	0.0871774i
$698$	13.6371	+	22.5066i	0.516171	+	0.851889i
$699$	2.05590			0.0777613
$700$	−30.0320	+	7.19308i	−1.13510	+	0.271873i
$701$	−25.0751			−0.947072			−0.473536	−	0.880774i	$-0.657023\pi$
$701$	−25.0751			−0.947072			−0.473536	+	0.880774i	$0.657023\pi$
$702$	12.8083	+	21.1388i	0.483418	+	0.797833i
$703$	9.71988	+	9.71988i	0.366592	+	0.366592i
$704$	2.75287	+	21.5686i	0.103753	+	0.812896i
$705$	−14.0992	+	13.1580i	−0.531006	+	0.495560i
$706$	8.28454	−	33.7598i	0.311793	−	1.27057i
$707$	37.2516	−	37.2516i	1.40099	−	1.40099i
$708$	0.734836	−	0.230629i	0.0276168	−	0.00866757i
$709$			15.2941i			0.574382i	0.957873	+	0.287191i	$0.0927215\pi$
$709$			15.2941i			0.574382i	−0.957873	+	0.287191i	$0.907278\pi$
$710$	11.4417	+	3.23020i	0.429401	+	0.121227i
$711$		−	12.6663i		−	0.475022i
$712$	−36.0447	+	2.29096i	−1.35083	+	0.0858575i
$713$	−41.2384	+	41.2384i	−1.54439	+	1.54439i
$714$	19.4012	+	4.76100i	0.726073	+	0.178176i
$715$	18.7667	+	0.647987i	0.701835	+	0.0242333i
$716$	−18.4388	+	35.3070i	−0.689091	+	1.31948i
$717$	17.2164	+	17.2164i	0.642957	+	0.642957i
$718$	−28.3845	+	17.1986i	−1.05930	+	0.641845i
$719$	0.416660			0.0155388			0.00776940	−	0.999970i	$-0.497527\pi$
$719$	0.416660			0.0155388			0.00776940	+	0.999970i	$0.497527\pi$
$720$	1.92628	−	8.96349i	0.0717880	−	0.334050i
$721$	−6.12589			−0.228140
$722$	−32.3774	+	19.6179i	−1.20496	+	0.730103i
$723$	−22.2368	−	22.2368i	−0.826997	−	0.826997i
$724$	12.8329	−	24.5726i	0.476930	−	0.913234i
$725$	40.2080	+	2.77996i	1.49329	+	0.103245i
$726$	−6.97333	−	1.71123i	−0.258804	−	0.0635098i
$727$	−33.5877	+	33.5877i	−1.24570	+	1.24570i	−0.288100	+	0.957600i	$0.593024\pi$
$727$	−33.5877	+	33.5877i	−1.24570	+	1.24570i	−0.957600	+	0.288100i	$0.906976\pi$
$728$	26.9332	−	1.71184i	0.998210	−	0.0634452i
$729$		−	28.8442i		−	1.06830i
$730$	4.53432	+	8.10169i	0.167823	+	0.299857i
$731$		−	11.8193i		−	0.437152i
$732$	−6.43800	+	2.02057i	−0.237955	+	0.0746824i
$733$	−19.6838	+	19.6838i	−0.727036	+	0.727036i	−0.970028	−	0.242992i	$-0.921871\pi$
$733$	−19.6838	+	19.6838i	−0.727036	+	0.727036i	0.242992	+	0.970028i	$0.421871\pi$
$734$	−3.35240	+	13.6612i	−0.123740	+	0.504243i
$735$	−0.275066	+	7.96633i	−0.0101459	+	0.293842i
$736$	−19.3377	−	50.2158i	−0.712796	−	1.85098i
$737$	−12.2877	−	12.2877i	−0.452623	−	0.452623i
$738$	0.751202	+	1.23978i	0.0276521	+	0.0456371i
$739$	−4.62503			−0.170134			−0.0850672	−	0.996375i	$-0.527111\pi$
$739$	−4.62503			−0.170134			−0.0850672	+	0.996375i	$0.527111\pi$
$740$	4.48182	−	7.90450i	0.164755	−	0.290575i
$741$	−29.3757			−1.07914
$742$	−8.11094	−	13.3863i	−0.297762	−	0.491426i
$743$	−0.265741	−	0.265741i	−0.00974911	−	0.00974911i	0.702215	−	0.711965i	$-0.252194\pi$
$743$	−0.265741	−	0.265741i	−0.00974911	−	0.00974911i	−0.711965	+	0.702215i	$0.752194\pi$
$744$	18.2903	+	16.1042i	0.670556	+	0.590410i
$745$	−31.9990	−	34.2878i	−1.17235	−	1.25621i
$746$	−10.0738	+	41.0512i	−0.368829	+	1.50299i
$747$	2.64238	−	2.64238i	0.0966795	−	0.0966795i
$748$	5.29820	+	16.8813i	0.193721	+	0.617240i
$749$		−	0.557280i		−	0.0203626i
$750$	−9.48888	−	20.0924i	−0.346485	−	0.733670i
$751$		−	37.3620i		−	1.36336i	−0.731650	−	0.681680i	$-0.761250\pi$
$751$		−	37.3620i		−	1.36336i	0.731650	−	0.681680i	$-0.238750\pi$
$752$	−24.1639	−	4.32644i	−0.881168	−	0.157769i
$753$	1.81634	−	1.81634i	0.0661912	−	0.0661912i
$754$	−34.2072	−	8.39433i	−1.24575	−	0.305703i
$755$	−7.03827	−	7.54170i	−0.256149	−	0.274470i
$756$	−30.9675	−	16.1726i	−1.12628	−	0.588191i
$757$	12.8124	+	12.8124i	0.465675	+	0.465675i	0.900510	−	0.434835i	$-0.143193\pi$
$757$	12.8124	+	12.8124i	0.465675	+	0.465675i	−0.434835	+	0.900510i	$0.643193\pi$
$758$	−46.7312	+	28.3151i	−1.69735	+	1.02845i
$759$	−36.3339			−1.31884
$760$	31.1186	+	29.3665i	1.12879	+	1.06524i
$761$	17.2334			0.624710			0.312355	−	0.949965i	$-0.398882\pi$
$761$	17.2334			0.624710			0.312355	+	0.949965i	$0.398882\pi$
$762$	−23.4592	+	14.2142i	−0.849836	+	0.514928i
$763$	−12.8551	−	12.8551i	−0.465385	−	0.465385i
$764$	−34.1964	−	17.8588i	−1.23718	−	0.646109i
$765$	0.257440	−	7.45586i	0.00930776	−	0.269567i
$766$	13.9306	+	3.41852i	0.503333	+	0.123516i
$767$	0.598670	−	0.598670i	0.0216167	−	0.0216167i
$768$	−20.4285	+	9.39520i	−0.737149	+	0.339020i
$769$		−	44.4030i		−	1.60121i	−0.599189	−	0.800607i	$-0.704510\pi$
$769$		−	44.4030i		−	1.60121i	0.599189	−	0.800607i	$-0.295490\pi$
$770$	−23.1614	+	12.9629i	−0.834680	+	0.467151i
$771$			7.51547i			0.270663i
$772$	13.3931	+	42.6734i	0.482028	+	1.53585i
$773$	−18.7943	+	18.7943i	−0.675986	+	0.675986i	−0.959089	−	0.283104i	$-0.908636\pi$
$773$	−18.7943	+	18.7943i	−0.675986	+	0.675986i	0.283104	+	0.959089i	$0.408636\pi$
$774$	−1.25452	+	5.11221i	−0.0450928	+	0.183755i
$775$	−30.5815	−	2.11439i	−1.09852	−	0.0759512i
$776$	−7.87226	+	8.94089i	−0.282598	+	0.320959i
$777$	−6.23523	−	6.23523i	−0.223688	−	0.223688i
$778$	−8.56021	−	14.1278i	−0.306898	−	0.506505i
$779$	−6.76528			−0.242391
$780$	5.17206	+	18.7171i	0.185189	+	0.670180i
$781$	10.2184			0.365644
$782$	−22.6907	−	37.4487i	−0.811418	−	1.33916i
$783$	32.2413	+	32.2413i	1.15221	+	1.15221i
$784$	−8.32674	+	5.79781i	−0.297384	+	0.207065i
$785$	−11.4141	−	0.394114i	−0.407388	−	0.0140665i
$786$	−1.13885	+	4.64085i	−0.0406214	+	0.165534i
$787$	2.42768	−	2.42768i	0.0865374	−	0.0865374i	−0.662513	−	0.749050i	$-0.730510\pi$
$787$	2.42768	−	2.42768i	0.0865374	−	0.0865374i	0.749050	+	0.662513i	$0.230510\pi$
$788$	−32.2238	+	10.1135i	−1.14793	+	0.360278i
$789$		−	24.6532i		−	0.877678i
$790$	10.6169	−	37.6063i	0.377732	−	1.33797i
$791$			5.99323i			0.213095i
$792$	−0.499830	−	7.86404i	−0.0177607	−	0.279437i
$793$	−5.24502	+	5.24502i	−0.186256	+	0.186256i
$794$	−6.67720	−	1.63856i	−0.236965	−	0.0581504i
$795$	8.23357	−	7.68396i	0.292014	−	0.272522i
$796$	−4.32042	+	8.27283i	−0.153133	+	0.293223i
$797$	−34.8480	−	34.8480i	−1.23438	−	1.23438i	−0.962265	−	0.272115i	$-0.912277\pi$
$797$	−34.8480	−	34.8480i	−1.23438	−	1.23438i	−0.272115	−	0.962265i	$-0.587723\pi$
$798$	35.5118	−	21.5171i	1.25710	−	0.761697i
$799$	−19.9754			−0.706678
$800$	13.2324	−	24.9981i	0.467835	−	0.883816i
$801$	13.0891			0.462479
$802$	−27.3541	+	16.5742i	−0.965906	+	0.585256i
$803$	5.64251	+	5.64251i	0.199120	+	0.199120i
$804$	8.31876	−	15.9289i	0.293380	−	0.561770i
$805$	48.0222	−	44.8166i	1.69256	−	1.57958i
$806$	26.0174	+	6.38458i	0.916423	+	0.224887i
$807$	8.83411	−	8.83411i	0.310975	−	0.310975i
$808$	3.06062	+	48.1541i	0.107672	+	1.69405i
$809$			4.48291i			0.157611i	0.996890	+	0.0788053i	$0.0251105\pi$
$809$			4.48291i			0.157611i	−0.996890	+	0.0788053i	$0.974889\pi$
$810$	4.18785	−	14.8338i	0.147146	−	0.521208i
$811$			2.66675i			0.0936421i	0.998903	+	0.0468210i	$0.0149091\pi$
$811$			2.66675i			0.0936421i	−0.998903	+	0.0468210i	$0.985091\pi$
$812$	47.5012	−	14.9083i	1.66697	−	0.523178i
$813$	−12.0194	+	12.0194i	−0.421538	+	0.421538i
$814$	1.86130	−	7.58486i	0.0652386	−	0.265849i
$815$	−1.79383	−	0.0619382i	−0.0628350	−	0.00216960i
$816$	−15.0155	+	10.4551i	−0.525647	+	0.366002i
$817$	−17.3711	−	17.3711i	−0.607737	−	0.607737i
$818$	24.7514	+	40.8496i	0.865411	+	1.42827i
$819$	−9.78035			−0.341753
$820$	1.19114	+	4.31059i	0.0415963	+	0.150532i
$821$	−39.8688			−1.39143			−0.695715	−	0.718318i	$-0.744913\pi$
$821$	−39.8688			−1.39143			−0.695715	+	0.718318i	$0.744913\pi$
$822$	23.3276	+	38.4998i	0.813642	+	1.34283i
$823$	−11.0245	−	11.0245i	−0.384291	−	0.384291i	0.488355	−	0.872645i	$-0.337597\pi$
$823$	−11.0245	−	11.0245i	−0.384291	−	0.384291i	−0.872645	+	0.488355i	$0.837597\pi$
$824$	3.70772	−	4.21103i	0.129165	−	0.146698i
$825$	−12.5408	−	14.4037i	−0.436614	−	0.501473i
$826$	−0.285209	+	1.16224i	−0.00992369	+	0.0404394i
$827$	17.8984	−	17.8984i	0.622389	−	0.622389i	−0.323753	−	0.946142i	$-0.604945\pi$
$827$	17.8984	−	17.8984i	0.622389	−	0.622389i	0.946142	+	0.323753i	$0.104945\pi$
$828$	5.83957	+	18.6062i	0.202939	+	0.646610i
$829$		−	9.35550i		−	0.324930i	−0.986714	−	0.162465i	$-0.948056\pi$
$829$		−	9.35550i		−	0.324930i	0.986714	−	0.162465i	$-0.0519445\pi$
$830$	10.0601	−	5.63040i	0.349191	−	0.195434i
$831$		−	10.3386i		−	0.358641i
$832$	−15.1247	+	19.5504i	−0.524355	+	0.677788i
$833$	−5.83810	+	5.83810i	−0.202278	+	0.202278i
$834$	32.2946	+	7.92499i	1.11827	+	0.274420i
$835$	−0.563569	+	16.3218i	−0.0195031	+	0.564840i
$836$	32.5977	+	17.0239i	1.12741	+	0.588784i
$837$	−24.5222	−	24.5222i	−0.847611	−	0.847611i
$838$	36.8332	−	22.3178i	1.27238	−	0.770954i
$839$	30.7199			1.06057			0.530284	−	0.847820i	$-0.322085\pi$
$839$	30.7199			1.06057			0.530284	+	0.847820i	$0.322085\pi$
$840$	−19.9623	−	18.8384i	−0.688766	−	0.649987i
$841$	−35.9765			−1.24057
$842$	47.1390	−	28.5622i	1.62452	−	0.984317i
$843$	−15.3415	−	15.3415i	−0.528388	−	0.528388i
$844$	26.0324	+	13.5952i	0.896072	+	0.467967i
$845$	−5.26882	−	5.64568i	−0.181253	−	0.194217i
$846$	8.63998	+	2.12022i	0.297049	+	0.0728948i
$847$	7.88904	−	7.88904i	0.271071	−	0.271071i
$848$	14.1111	+	2.52653i	0.484578	+	0.0867615i
$849$		−	8.75638i		−	0.300518i
$850$	7.01387	−	21.9207i	0.240574	−	0.751875i
$851$			19.3278i			0.662548i
$852$	3.16430	+	10.0822i	0.108407	+	0.345409i
$853$	13.4478	−	13.4478i	0.460443	−	0.460443i	−0.438358	−	0.898801i	$-0.644440\pi$
$853$	13.4478	−	13.4478i	0.460443	−	0.460443i	0.898801	+	0.438358i	$0.144440\pi$
$854$	2.49875	−	10.1825i	0.0855056	−	0.348438i
$855$	−10.5797	−	11.3364i	−0.361817	−	0.387697i
$856$	0.383083	+	0.337296i	0.0130935	+	0.0115286i
$857$	−3.55613	−	3.55613i	−0.121475	−	0.121475i	0.643756	−	0.765231i	$-0.277375\pi$
$857$	−3.55613	−	3.55613i	−0.121475	−	0.121475i	−0.765231	+	0.643756i	$0.777375\pi$
$858$	8.64894	+	14.2742i	0.295270	+	0.487313i
$859$	17.7033			0.604029			0.302014	−	0.953303i	$-0.402341\pi$
$859$	17.7033			0.604029			0.302014	+	0.953303i	$0.402341\pi$
$860$	−8.00976	+	14.1267i	−0.273131	+	0.481716i
$861$	4.33987			0.147903
$862$	13.7881	+	22.7558i	0.469623	+	0.775066i
$863$	8.49802	+	8.49802i	0.289276	+	0.289276i	0.836794	−	0.547518i	$-0.184427\pi$
$863$	8.49802	+	8.49802i	0.289276	+	0.289276i	−0.547518	+	0.836794i	$0.684427\pi$
$864$	29.8605	−	11.4990i	1.01588	−	0.391205i
$865$	−1.86488	+	54.0098i	−0.0634078	+	1.83639i
$866$	−6.33778	+	25.8267i	−0.215367	+	0.877626i
$867$	6.36553	−	6.36553i	0.216185	−	0.216185i
$868$	−36.1286	+	11.3390i	−1.22628	+	0.384871i
$869$		−	33.5856i		−	1.13931i
$870$	17.4954	+	31.2599i	0.593150	+	1.05981i
$871$		−	19.7545i		−	0.669357i
$872$	16.6174	−	1.05618i	0.562735	−	0.0357668i
$873$	3.05271	−	3.05271i	0.103319	−	0.103319i
$874$	−88.3882	−	21.6902i	−2.98978	−	0.733682i
$875$	34.3415	+	3.56864i	1.16096	+	0.120642i
$876$	−3.81998	+	7.31456i	−0.129065	+	0.247136i
$877$	38.5282	+	38.5282i	1.30100	+	1.30100i	0.927715	+	0.373290i	$0.121770\pi$
$877$	38.5282	+	38.5282i	1.30100	+	1.30100i	0.373290	+	0.927715i	$0.378230\pi$
$878$	31.9748	−	19.3740i	1.07910	−	0.653840i
$879$	40.0326			1.35027
$880$	5.10767	−	23.7674i	0.172179	−	0.801198i
$881$	−47.0291			−1.58445			−0.792226	−	0.610228i	$-0.791078\pi$
$881$	−47.0291			−1.58445			−0.792226	+	0.610228i	$0.791078\pi$
$882$	3.14483	−	1.90550i	0.105892	−	0.0641614i
$883$	−0.326591	−	0.326591i	−0.0109907	−	0.0109907i	0.701590	−	0.712581i	$-0.252474\pi$
$883$	−0.326591	−	0.326591i	−0.0109907	−	0.0109907i	−0.712581	+	0.701590i	$0.752474\pi$
$884$	−9.31086	+	17.8286i	−0.313158	+	0.599641i
$885$	−0.860572	−	0.0297143i	−0.0289278	−	0.000998835i
$886$	−24.2708	−	5.95597i	−0.815392	−	0.200095i
$887$	12.1036	−	12.1036i	0.406399	−	0.406399i	−0.474082	−	0.880481i	$-0.657220\pi$
$887$	12.1036	−	12.1036i	0.406399	−	0.406399i	0.880481	+	0.474082i	$0.157220\pi$
$888$	8.06010	−	0.512291i	0.270479	−	0.0171914i
$889$		−	42.6206i		−	1.42945i
$890$	38.8616	+	10.9713i	1.30264	+	0.367759i
$891$		−	13.2479i		−	0.443821i
$892$	41.5583	−	13.0431i	1.39147	−	0.436715i
$893$	−29.3583	+	29.3583i	−0.982437	+	0.982437i
$894$	9.93464	−	40.4840i	0.332264	−	1.35399i
$895$	32.5577	−	30.3844i	1.08828	−	1.01564i
$896$	3.96374	−	34.7127i	0.132419	−	1.15967i
$897$	−29.2065	−	29.2065i	−0.975175	−	0.975175i
$898$	−23.5621	−	38.8868i	−0.786277	−	1.29767i
$899$	49.4201			1.64825
$900$	−5.36043	+	8.73695i	−0.178681	+	0.291232i
$901$	11.6651			0.388621
$902$	1.99187	+	3.28738i	0.0663220	+	0.109458i
$903$	11.1434	+	11.1434i	0.370829	+	0.370829i
$904$	−4.11984	−	3.62743i	−0.137024	−	0.120647i
$905$	−22.6592	+	21.1467i	−0.753217	+	0.702939i
$906$	2.18515	−	8.90457i	0.0725968	−	0.295834i
$907$	−11.1419	+	11.1419i	−0.369959	+	0.369959i	−0.867462	−	0.497503i	$-0.834250\pi$
$907$	−11.1419	+	11.1419i	−0.369959	+	0.369959i	0.497503	+	0.867462i	$0.334250\pi$
$908$	2.54841	+	8.11980i	0.0845718	+	0.269465i
$909$		−	17.4864i		−	0.579986i
$910$	−29.0380	−	8.19792i	−0.962599	−	0.271758i
$911$			47.0481i			1.55877i	0.626544	+	0.779386i	$0.284469\pi$
$911$			47.0481i			1.55877i	−0.626544	+	0.779386i	$0.715531\pi$
$912$	−6.70250	+	37.4347i	−0.221942	+	1.23959i
$913$	7.00647	−	7.00647i	0.231880	−	0.231880i
$914$	0.264555	+	0.0649208i	0.00875069	+	0.00214739i
$915$	7.53959	+	0.260331i	0.249251	+	0.00860627i
$916$	12.1741	+	6.35782i	0.402243	+	0.210068i
$917$	−5.25027	−	5.25027i	−0.173379	−	0.173379i
$918$	22.2687	−	13.4929i	0.734976	−	0.445332i
$919$	−9.03302			−0.297972			−0.148986	−	0.988839i	$-0.547601\pi$
$919$	−9.03302			−0.297972			−0.148986	+	0.988839i	$0.547601\pi$
$920$	1.74197	+	60.1367i	0.0574310	+	1.98265i
$921$	29.8166			0.982491
$922$	−18.8483	+	11.4205i	−0.620737	+	0.376113i
$923$	8.21392	+	8.21392i	0.270365	+	0.270365i
$924$	−20.9112	−	10.9207i	−0.687926	−	0.359265i
$925$	−7.66204	+	6.67105i	−0.251926	+	0.219343i
$926$	−9.77896	−	2.39973i	−0.321357	−	0.0788599i
$927$	−1.43778	+	1.43778i	−0.0472230	+	0.0472230i
$928$	−18.5021	+	41.6764i	−0.607362	+	1.36809i
$929$		−	2.95772i		−	0.0970396i	−0.998822	−	0.0485198i	$-0.984550\pi$
$929$		−	2.95772i		−	0.0970396i	0.998822	−	0.0485198i	$-0.0154504\pi$
$930$	−13.3067	−	23.7757i	−0.436344	−	0.779637i
$931$			17.1608i			0.562422i
$932$	−0.876142	−	2.79159i	−0.0286990	−	0.0914415i
$933$	24.0693	−	24.0693i	0.787995	−	0.787995i
$934$	−10.2822	+	41.9002i	−0.336443	+	1.37102i
$935$	0.682621	−	19.7698i	0.0223241	−	0.646541i
$936$	5.91960	−	6.72316i	0.193488	−	0.219753i
$937$	39.0596	+	39.0596i	1.27602	+	1.27602i	0.942875	+	0.333146i	$0.108110\pi$
$937$	39.0596	+	39.0596i	1.27602	+	1.27602i	0.333146	+	0.942875i	$0.391890\pi$
$938$	14.4698	+	23.8810i	0.472456	+	0.779741i
$939$	22.3822			0.730416
$940$	23.8750	+	13.5370i	0.778717	+	0.441529i
$941$	0.430959			0.0140488			0.00702442	−	0.999975i	$-0.497764\pi$
$941$	0.430959			0.0140488			0.00702442	+	0.999975i	$0.497764\pi$
$942$	−5.26040	−	8.68175i	−0.171393	−	0.282867i
$943$	−6.72631	−	6.72631i	−0.219039	−	0.219039i
$944$	−0.626315	−	0.899506i	−0.0203848	−	0.0292764i
$945$	26.6500	+	28.5562i	0.866924	+	0.928932i
$946$	−3.32646	+	13.5554i	−0.108152	+	0.440725i
$947$	−42.0097	+	42.0097i	−1.36513	+	1.36513i	−0.497897	+	0.867236i	$0.665894\pi$
$947$	−42.0097	+	42.0097i	−1.36513	+	1.36513i	−0.867236	+	0.497897i	$0.834106\pi$
$948$	33.1377	−	10.4003i	1.07626	−	0.337786i
$949$			9.07129i			0.294466i
$950$	−21.9090	−	42.5258i	−0.710820	−	1.37972i
$951$			39.9311i			1.29485i
$952$	−1.80334	−	28.3728i	−0.0584466	−	0.919566i
$953$	7.48736	−	7.48736i	0.242539	−	0.242539i	−0.575361	−	0.817900i	$-0.695138\pi$
$953$	7.48736	−	7.48736i	0.242539	−	0.242539i	0.817900	+	0.575361i	$0.195138\pi$
$954$	−5.04553	−	1.23816i	−0.163355	−	0.0400868i
$955$	29.4286	+	31.5336i	0.952288	+	1.02040i
$956$	16.0402	−	30.7140i	0.518777	−	0.993363i
$957$	21.7713	+	21.7713i	0.703766	+	0.703766i
$958$	7.86256	−	4.76403i	0.254028	−	0.153919i
$959$	−69.9463			−2.25869
$960$	25.0321	−	2.32039i	0.807908	−	0.0748901i
$961$	−6.58807			−0.212518
$962$	7.59315	−	4.60079i	0.244813	−	0.148336i
$963$	−0.130797	−	0.130797i	−0.00421487	−	0.00421487i
$964$	−20.7176	+	39.6705i	−0.667271	+	1.27770i
$965$	1.72557	−	49.9752i	0.0555480	−	1.60876i
$966$	56.7004	+	13.9141i	1.82431	+	0.447679i
$967$	−24.5885	+	24.5885i	−0.790712	+	0.790712i	−0.981610	−	0.190898i	$-0.938860\pi$
$967$	−24.5885	+	24.5885i	−0.790712	+	0.790712i	0.190898	+	0.981610i	$0.438860\pi$
$968$	0.648169	+	10.1979i	0.0208329	+	0.327774i
$969$			30.9458i			0.994121i
$970$	11.6223	−	6.50474i	0.373170	−	0.208855i
$971$		−	48.1163i		−	1.54412i	−0.635547	−	0.772062i	$-0.719225\pi$
$971$		−	48.1163i		−	1.54412i	0.635547	−	0.772062i	$-0.280775\pi$
$972$	−19.3105	+	6.06062i	−0.619385	+	0.194395i
$973$	−36.5354	+	36.5354i	−1.17127	+	1.17127i
$974$	6.68145	−	27.2271i	0.214088	−	0.872414i
$975$	1.49749	−	21.6589i	0.0479579	−	0.693640i
$976$	5.48723	+	7.88069i	0.175642	+	0.252255i
$977$	14.9950	+	14.9950i	0.479733	+	0.479733i	0.905046	−	0.425313i	$-0.139836\pi$
$977$	14.9950	+	14.9950i	0.479733	+	0.479733i	−0.425313	+	0.905046i	$0.639836\pi$
$978$	−0.826714	−	1.36441i	−0.0264354	−	0.0436290i
$979$	34.7067			1.10923
$980$	10.9342	−	3.02143i	0.349281	−	0.0965161i
$981$	−6.03433			−0.192661
$982$	−21.1189	−	34.8546i	−0.673931	−	1.11226i
$983$	−41.9049	−	41.9049i	−1.33656	−	1.33656i	−0.899368	−	0.437192i	$-0.855973\pi$
$983$	−41.9049	−	41.9049i	−1.33656	−	1.33656i	−0.437192	−	0.899368i	$-0.644027\pi$
$984$	−2.62673	+	2.98330i	−0.0837371	+	0.0951040i
$985$	37.7376	+	1.30302i	1.20242	+	0.0415178i
$986$	−8.84300	+	36.0355i	−0.281618	+	1.14760i
$987$	18.8331	−	18.8331i	0.599464	−	0.599464i
$988$	12.5187	+	39.8875i	0.398274	+	1.26899i
$989$		−	34.5420i		−	1.09837i
$990$	−2.39366	+	8.47860i	−0.0760754	+	0.269468i
$991$			30.8521i			0.980049i	0.871709	+	0.490024i	$0.163012\pi$
$991$			30.8521i			0.980049i	−0.871709	+	0.490024i	$0.836988\pi$
$992$	14.0724	−	31.6983i	0.446800	−	1.00642i
$993$	−7.76091	+	7.76091i	−0.246285	+	0.246285i
$994$	−15.9462	−	3.91315i	−0.505784	−	0.124118i
$995$	7.62864	−	7.11941i	0.241844	−	0.225701i
$996$	9.08269	+	4.74337i	0.287796	+	0.150299i
$997$	13.1331	+	13.1331i	0.415930	+	0.415930i	0.883798	−	0.467868i	$-0.154978\pi$
$997$	13.1331	+	13.1331i	0.415930	+	0.415930i	−0.467868	+	0.883798i	$0.654978\pi$
$998$	−11.7239	+	7.10368i	−0.371114	+	0.224863i
$999$	−11.4932			−0.363628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.k.c.247.10	yes	108
4.3	odd	2	inner	820.2.k.c.247.35	yes	108
5.3	odd	4	inner	820.2.k.c.83.35	yes	108
20.3	even	4	inner	820.2.k.c.83.10	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.10	✓	108	20.3	even	4	inner
820.2.k.c.83.35	yes	108	5.3	odd	4	inner
820.2.k.c.247.10	yes	108	1.1	even	1	trivial
820.2.k.c.247.35	yes	108	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20951 + 0.732860i) q^{2} +(0.993723 + 0.993723i) q^{3} +(0.925834 - 1.77280i) q^{4} +(-1.63476 + 1.52564i) q^{5} +(-1.93018 - 0.473660i) q^{6} +(2.18364 - 2.18364i) q^{7} +(0.179410 + 2.82273i) q^{8} -1.02503i q^{9} +(0.859183 - 3.04332i) q^{10} -2.71794i q^{11} +(2.68170 - 0.841653i) q^{12} +(2.18477 - 2.18477i) q^{13} +(-1.04084 + 4.24144i) q^{14} +(-3.14056 - 0.108439i) q^{15} +(-2.28566 - 3.28264i) q^{16} +(-2.30155 - 2.30155i) q^{17} +(0.751202 + 1.23978i) q^{18} -6.76528 q^{19} +(1.19114 + 4.31059i) q^{20} +4.33987 q^{21} +(1.99187 + 3.28738i) q^{22} +(-6.72631 - 6.72631i) q^{23} +(-2.62673 + 2.98330i) q^{24} +(0.344874 - 4.98809i) q^{25} +(-1.04138 + 4.24364i) q^{26} +(3.99976 - 3.99976i) q^{27} +(-1.84948 - 5.89286i) q^{28} +8.06080i q^{29} +(3.87801 - 2.17043i) q^{30} -6.13091i q^{31} +(5.17025 + 2.29532i) q^{32} +(2.70088 - 2.70088i) q^{33} +(4.47046 + 1.09704i) q^{34} +(-0.238287 + 6.90117i) q^{35} +(-1.81717 - 0.949006i) q^{36} +(-1.43673 - 1.43673i) q^{37} +(8.18268 - 4.95800i) q^{38} +4.34212 q^{39} +(-4.59975 - 4.34077i) q^{40} +1.00000 q^{41} +(-5.24913 + 3.18052i) q^{42} +(2.56768 + 2.56768i) q^{43} +(-4.81838 - 2.51636i) q^{44} +(1.56382 + 1.67567i) q^{45} +(13.0650 + 3.20611i) q^{46} +(4.33955 - 4.33955i) q^{47} +(0.990721 - 5.53335i) q^{48} -2.53660i q^{49} +(3.23844 + 6.28590i) q^{50} -4.57421i q^{51} +(-1.85044 - 5.89591i) q^{52} +(-2.53419 + 2.53419i) q^{53} +(-1.90649 + 7.76902i) q^{54} +(4.14659 + 4.44318i) q^{55} +(6.55561 + 5.77207i) q^{56} +(-6.72281 - 6.72281i) q^{57} +(-5.90744 - 9.74963i) q^{58} +0.274019 q^{59} +(-3.09987 + 5.46719i) q^{60} -2.40072 q^{61} +(4.49310 + 7.41540i) q^{62} +(-2.23830 - 2.23830i) q^{63} +(-7.93562 + 1.01285i) q^{64} +(-0.238411 + 6.90475i) q^{65} +(-1.28738 + 5.24611i) q^{66} +(4.52096 - 4.52096i) q^{67} +(-6.21105 + 1.94934i) q^{68} -13.3682i q^{69} +(-4.76938 - 8.52168i) q^{70} +3.75962i q^{71} +(2.89338 - 0.183900i) q^{72} +(-2.07602 + 2.07602i) q^{73} +(2.79066 + 0.684820i) q^{74} +(5.29949 - 4.61407i) q^{75} +(-6.26352 + 11.9935i) q^{76} +(-5.93502 - 5.93502i) q^{77} +(-5.25184 + 3.18216i) q^{78} +12.3570 q^{79} +(8.74462 + 1.87924i) q^{80} +4.87423 q^{81} +(-1.20951 + 0.732860i) q^{82} +(2.57786 + 2.57786i) q^{83} +(4.01800 - 7.69374i) q^{84} +(7.27380 + 0.251154i) q^{85} +(-4.98739 - 1.22389i) q^{86} +(-8.01021 + 8.01021i) q^{87} +(7.67202 - 0.487625i) q^{88} +12.7695i q^{89} +(-3.11949 - 0.880687i) q^{90} -9.54154i q^{91} +(-18.1519 + 5.69698i) q^{92} +(6.09243 - 6.09243i) q^{93} +(-2.06845 + 8.42901i) q^{94} +(11.0596 - 10.3213i) q^{95} +(2.85688 + 7.41871i) q^{96} +(2.97817 + 2.97817i) q^{97} +(1.85897 + 3.06804i) q^{98} -2.78597 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) \) 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Introduction

L-functions

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