LMFDB - Embedded newform 312.2.t.e.187.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,2,Mod(187,312)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("312.187"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.t (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,-24,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			187.6
Character	$\chi$	$=$	312.187
Dual form			312.2.t.e.307.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.140104 + 1.40726i) q^{2} -1.00000 q^{3} +(-1.96074 - 0.394325i) q^{4} +(3.08779 + 3.08779i) q^{5} +(0.140104 - 1.40726i) q^{6} +(2.85816 - 2.85816i) q^{7} +(0.829624 - 2.70402i) q^{8} +1.00000 q^{9} +(-4.77792 + 3.91270i) q^{10} +(2.57668 + 2.57668i) q^{11} +(1.96074 + 0.394325i) q^{12} +(-3.51077 + 0.821294i) q^{13} +(3.62173 + 4.42261i) q^{14} +(-3.08779 - 3.08779i) q^{15} +(3.68902 + 1.54634i) q^{16} +1.07196i q^{17} +(-0.140104 + 1.40726i) q^{18} +(1.46161 - 1.46161i) q^{19} +(-4.83676 - 7.27194i) q^{20} +(-2.85816 + 2.85816i) q^{21} +(-3.98706 + 3.26505i) q^{22} -5.52786 q^{23} +(-0.829624 + 2.70402i) q^{24} +14.0688i q^{25} +(-0.663899 - 5.05561i) q^{26} -1.00000 q^{27} +(-6.73116 + 4.47707i) q^{28} +0.512377i q^{29} +(4.77792 - 3.91270i) q^{30} +(-2.85816 - 2.85816i) q^{31} +(-2.69294 + 4.97474i) q^{32} +(-2.57668 - 2.57668i) q^{33} +(-1.50852 - 0.150186i) q^{34} +17.6508 q^{35} +(-1.96074 - 0.394325i) q^{36} +(1.97885 - 1.97885i) q^{37} +(1.85209 + 2.26164i) q^{38} +(3.51077 - 0.821294i) q^{39} +(10.9111 - 5.78773i) q^{40} +(-0.0336607 + 0.0336607i) q^{41} +(-3.62173 - 4.42261i) q^{42} +3.49466i q^{43} +(-4.03616 - 6.06826i) q^{44} +(3.08779 + 3.08779i) q^{45} +(0.774476 - 7.77911i) q^{46} +(6.45565 - 6.45565i) q^{47} +(-3.68902 - 1.54634i) q^{48} -9.33817i q^{49} +(-19.7985 - 1.97110i) q^{50} -1.07196i q^{51} +(7.20756 - 0.225963i) q^{52} -8.04121i q^{53} +(0.140104 - 1.40726i) q^{54} +15.9125i q^{55} +(-5.35733 - 10.0997i) q^{56} +(-1.46161 + 1.46161i) q^{57} +(-0.721046 - 0.0717861i) q^{58} +(1.23075 + 1.23075i) q^{59} +(4.83676 + 7.27194i) q^{60} +4.66832i q^{61} +(4.42261 - 3.62173i) q^{62} +(2.85816 - 2.85816i) q^{63} +(-6.62345 - 4.48664i) q^{64} +(-13.3765 - 8.30451i) q^{65} +(3.98706 - 3.26505i) q^{66} +(2.03305 - 2.03305i) q^{67} +(0.422701 - 2.10184i) q^{68} +5.52786 q^{69} +(-2.47295 + 24.8392i) q^{70} +(-5.60969 - 5.60969i) q^{71} +(0.829624 - 2.70402i) q^{72} +(-5.73067 - 5.73067i) q^{73} +(2.50750 + 3.06199i) q^{74} -14.0688i q^{75} +(-3.44220 + 2.28950i) q^{76} +14.7292 q^{77} +(0.663899 + 5.05561i) q^{78} -6.65963i q^{79} +(6.61613 + 16.1657i) q^{80} +1.00000 q^{81} +(-0.0426532 - 0.0520852i) q^{82} +(0.153984 - 0.153984i) q^{83} +(6.73116 - 4.47707i) q^{84} +(-3.30998 + 3.30998i) q^{85} +(-4.91788 - 0.489616i) q^{86} -0.512377i q^{87} +(9.10509 - 4.82973i) q^{88} +(11.3765 + 11.3765i) q^{89} +(-4.77792 + 3.91270i) q^{90} +(-7.68694 + 12.3817i) q^{91} +(10.8387 + 2.17977i) q^{92} +(2.85816 + 2.85816i) q^{93} +(8.18029 + 9.98921i) q^{94} +9.02631 q^{95} +(2.69294 - 4.97474i) q^{96} +(8.80263 - 8.80263i) q^{97} +(13.1412 + 1.30832i) q^{98} +(2.57668 + 2.57668i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{3} - 6 q^{8} + 24 q^{9} + 8 q^{11} + 36 q^{14} + 28 q^{16} + 20 q^{19} - 20 q^{20} + 20 q^{22} + 6 q^{24} + 12 q^{26} - 24 q^{27} - 16 q^{28} - 30 q^{32} - 8 q^{33} + 16 q^{34} + 16 q^{35}+ \cdots + 8 q^{99}+O(q^{100}) $ 24 * q - 24 * q^3 - 6 * q^8 + 24 * q^9 + 8 * q^11 + 36 * q^14 + 28 * q^16 + 20 * q^19 - 20 * q^20 + 20 * q^22 + 6 * q^24 + 12 * q^26 - 24 * q^27 - 16 * q^28 - 30 * q^32 - 8 * q^33 + 16 * q^34 + 16 * q^35 + 36 * q^40 - 12 * q^41 - 36 * q^42 - 32 * q^44 - 44 * q^46 - 28 * q^48 - 36 * q^50 + 4 * q^52 - 20 * q^57 + 32 * q^58 - 16 * q^59 + 20 * q^60 - 76 * q^65 - 20 * q^66 + 28 * q^67 + 32 * q^68 - 40 * q^70 - 6 * q^72 - 8 * q^73 - 32 * q^74 - 36 * q^76 - 12 * q^78 - 32 * q^80 + 24 * q^81 - 72 * q^83 + 16 * q^84 + 4 * q^86 + 28 * q^89 - 4 * q^91 + 32 * q^92 + 28 * q^94 + 30 * q^96 + 24 * q^97 + 68 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−0.140104	+	1.40726i	−0.0990686	+	0.995081i
$2$	−0.140104	+	1.40726i	−0.0990686	+	0.995081i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.96074	−	0.394325i	−0.980371	−	0.197162i
$5$	3.08779	+	3.08779i	1.38090	+	1.38090i	0.843024	+	0.537875i	$0.180773\pi$
$5$	3.08779	+	3.08779i	1.38090	+	1.38090i	0.537875	+	0.843024i	$0.319227\pi$
$6$	0.140104	−	1.40726i	0.0571973	−	0.574510i
$7$	2.85816	−	2.85816i	1.08028	−	1.08028i	0.0838010	−	0.996483i	$-0.473294\pi$
$7$	2.85816	−	2.85816i	1.08028	−	1.08028i	0.996483	−	0.0838010i	$-0.0267060\pi$
$8$	0.829624	−	2.70402i	0.293316	−	0.956015i
$9$	1.00000			0.333333
$10$	−4.77792	+	3.91270i	−1.51091	+	1.23730i
$11$	2.57668	+	2.57668i	0.776900	+	0.776900i	0.979302	−	0.202403i	$-0.0648750\pi$
$11$	2.57668	+	2.57668i	0.776900	+	0.776900i	−0.202403	+	0.979302i	$0.564875\pi$
$12$	1.96074	+	0.394325i	0.566017	+	0.113832i
$13$	−3.51077	+	0.821294i	−0.973711	+	0.227786i
$13$	−3.51077	+	0.821294i	−0.973711	+	0.227786i
$14$	3.62173	+	4.42261i	0.967947	+	1.18199i
$15$	−3.08779	−	3.08779i	−0.797263	−	0.797263i
$16$	3.68902	+	1.54634i	0.922254	+	0.386585i
$17$			1.07196i			0.259989i	0.991515	+	0.129994i	$0.0414959\pi$
$17$			1.07196i			0.259989i	−0.991515	+	0.129994i	$0.958504\pi$
$18$	−0.140104	+	1.40726i	−0.0330229	+	0.331694i
$19$	1.46161	−	1.46161i	0.335317	−	0.335317i	−0.519284	−	0.854602i	$-0.673801\pi$
$19$	1.46161	−	1.46161i	0.335317	−	0.335317i	0.854602	+	0.519284i	$0.173801\pi$
$20$	−4.83676	−	7.27194i	−1.08153	−	1.62606i
$21$	−2.85816	+	2.85816i	−0.623702	+	0.623702i
$22$	−3.98706	+	3.26505i	−0.850044	+	0.696111i
$23$	−5.52786			−1.15264			−0.576319	−	0.817225i	$-0.695511\pi$
$23$	−5.52786			−1.15264			−0.576319	+	0.817225i	$0.695511\pi$
$24$	−0.829624	+	2.70402i	−0.169346	+	0.551956i
$25$			14.0688i			2.81377i
$26$	−0.663899	−	5.05561i	−0.130201	−	0.991488i
$27$	−1.00000			−0.192450
$28$	−6.73116	+	4.47707i	−1.27207	+	0.846087i
$29$			0.512377i			0.0951460i	0.998868	+	0.0475730i	$0.0151487\pi$
$29$			0.512377i			0.0951460i	−0.998868	+	0.0475730i	$0.984851\pi$
$30$	4.77792	−	3.91270i	0.872325	−	0.714357i
$31$	−2.85816	−	2.85816i	−0.513341	−	0.513341i	0.402208	−	0.915549i	$-0.368243\pi$
$31$	−2.85816	−	2.85816i	−0.513341	−	0.513341i	−0.915549	+	0.402208i	$0.868243\pi$
$32$	−2.69294	+	4.97474i	−0.476049	+	0.879419i
$33$	−2.57668	−	2.57668i	−0.448543	−	0.448543i
$34$	−1.50852	−	0.150186i	−0.258710	−	0.0257567i
$35$	17.6508			2.98353
$36$	−1.96074	−	0.394325i	−0.326790	−	0.0657208i
$37$	1.97885	−	1.97885i	0.325321	−	0.325321i	−0.525483	−	0.850804i	$-0.676115\pi$
$37$	1.97885	−	1.97885i	0.325321	−	0.325321i	0.850804	+	0.525483i	$0.176115\pi$
$38$	1.85209	+	2.26164i	0.300448	+	0.366887i
$39$	3.51077	−	0.821294i	0.562172	−	0.131512i
$40$	10.9111	−	5.78773i	1.72520	−	0.915121i
$41$	−0.0336607	+	0.0336607i	−0.00525692	+	0.00525692i	−0.709730	−	0.704473i	$-0.751183\pi$
$41$	−0.0336607	+	0.0336607i	−0.00525692	+	0.00525692i	0.704473	+	0.709730i	$0.251183\pi$
$42$	−3.62173	−	4.42261i	−0.558844	−	0.682423i
$43$			3.49466i			0.532931i	0.963844	+	0.266465i	$0.0858558\pi$
$43$			3.49466i			0.532931i	−0.963844	+	0.266465i	$0.914144\pi$
$44$	−4.03616	−	6.06826i	−0.608474	−	0.914825i
$45$	3.08779	+	3.08779i	0.460300	+	0.460300i
$46$	0.774476	−	7.77911i	0.114190	−	1.14697i
$47$	6.45565	−	6.45565i	0.941653	−	0.941653i	−0.0567363	−	0.998389i	$-0.518069\pi$
$47$	6.45565	−	6.45565i	0.941653	−	0.941653i	0.998389	+	0.0567363i	$0.0180694\pi$
$48$	−3.68902	−	1.54634i	−0.532464	−	0.223195i
$49$		−	9.33817i		−	1.33402i
$50$	−19.7985	−	1.97110i	−2.79993	−	0.278756i
$51$		−	1.07196i		−	0.150104i
$52$	7.20756	−	0.225963i	0.999509	−	0.0313355i
$53$		−	8.04121i		−	1.10455i	−0.833663	−	0.552273i	$-0.813761\pi$
$53$		−	8.04121i		−	1.10455i	0.833663	−	0.552273i	$-0.186239\pi$
$54$	0.140104	−	1.40726i	0.0190658	−	0.191503i
$55$			15.9125i			2.14564i
$56$	−5.35733	−	10.0997i	−0.715903	−	1.34963i
$57$	−1.46161	+	1.46161i	−0.193596	+	0.193596i
$58$	−0.721046	−	0.0717861i	−0.0946779	−	0.00942598i
$59$	1.23075	+	1.23075i	0.160231	+	0.160231i	0.782669	−	0.622438i	$-0.213858\pi$
$59$	1.23075	+	1.23075i	0.160231	+	0.160231i	−0.622438	+	0.782669i	$0.713858\pi$
$60$	4.83676	+	7.27194i	0.624423	+	0.938804i
$61$			4.66832i			0.597717i	0.954297	+	0.298859i	$0.0966059\pi$
$61$			4.66832i			0.597717i	−0.954297	+	0.298859i	$0.903394\pi$
$62$	4.42261	−	3.62173i	0.561672	−	0.459960i
$63$	2.85816	−	2.85816i	0.360094	−	0.360094i
$64$	−6.62345	−	4.48664i	−0.827931	−	0.560830i
$65$	−13.3765	−	8.30451i	−1.65915	−	1.03005i
$66$	3.98706	−	3.26505i	0.490773	−	0.401900i
$67$	2.03305	−	2.03305i	0.248376	−	0.248376i	−0.571928	−	0.820304i	$-0.693804\pi$
$67$	2.03305	−	2.03305i	0.248376	−	0.248376i	0.820304	+	0.571928i	$0.193804\pi$
$68$	0.422701	−	2.10184i	0.0512600	−	0.254885i
$69$	5.52786			0.665476
$70$	−2.47295	+	24.8392i	−0.295574	+	2.96885i
$71$	−5.60969	−	5.60969i	−0.665747	−	0.665747i	0.290981	−	0.956729i	$-0.406018\pi$
$71$	−5.60969	−	5.60969i	−0.665747	−	0.665747i	−0.956729	+	0.290981i	$0.906018\pi$
$72$	0.829624	−	2.70402i	0.0977722	−	0.318672i
$73$	−5.73067	−	5.73067i	−0.670724	−	0.670724i	0.287159	−	0.957883i	$-0.407289\pi$
$73$	−5.73067	−	5.73067i	−0.670724	−	0.670724i	−0.957883	+	0.287159i	$0.907289\pi$
$74$	2.50750	+	3.06199i	0.291491	+	0.355949i
$75$		−	14.0688i		−	1.62453i
$76$	−3.44220	+	2.28950i	−0.394847	+	0.262623i
$77$	14.7292			1.67854
$78$	0.663899	+	5.05561i	0.0751717	+	0.572436i
$79$		−	6.65963i		−	0.749267i	−0.927173	−	0.374633i	$-0.877769\pi$
$79$		−	6.65963i		−	0.749267i	0.927173	−	0.374633i	$-0.122231\pi$
$80$	6.61613	+	16.1657i	0.739706	+	1.80737i
$81$	1.00000			0.111111
$82$	−0.0426532	−	0.0520852i	−0.00471026	−	0.00575185i
$83$	0.153984	−	0.153984i	0.0169020	−	0.0169020i	−0.698605	−	0.715507i	$-0.746196\pi$
$83$	0.153984	−	0.153984i	0.0169020	−	0.0169020i	0.715507	+	0.698605i	$0.246196\pi$
$84$	6.73116	−	4.47707i	0.734430	−	0.488489i
$85$	−3.30998	+	3.30998i	−0.359018	+	0.359018i
$86$	−4.91788	−	0.489616i	−0.530309	−	0.0527967i
$87$		−	0.512377i		−	0.0549326i
$88$	9.10509	−	4.82973i	0.970606	−	0.514851i
$89$	11.3765	+	11.3765i	1.20590	+	1.20590i	0.972342	+	0.233562i	$0.0750381\pi$
$89$	11.3765	+	11.3765i	1.20590	+	1.20590i	0.233562	+	0.972342i	$0.424962\pi$
$90$	−4.77792	+	3.91270i	−0.503637	+	0.412434i
$91$	−7.68694	+	12.3817i	−0.805811	+	1.29796i
$92$	10.8387	+	2.17977i	1.13001	+	0.227257i
$93$	2.85816	+	2.85816i	0.296378	+	0.296378i
$94$	8.18029	+	9.98921i	0.843732	+	1.03031i
$95$	9.02631			0.926079
$96$	2.69294	−	4.97474i	0.274847	−	0.507733i
$97$	8.80263	−	8.80263i	0.893772	−	0.893772i	−0.101104	−	0.994876i	$-0.532238\pi$
$97$	8.80263	−	8.80263i	0.893772	−	0.893772i	0.994876	+	0.101104i	$0.0322376\pi$
$98$	13.1412	+	1.30832i	1.32746	+	0.132160i
$99$	2.57668	+	2.57668i	0.258967	+	0.258967i
$100$	5.54769	−	27.5854i	0.554769	−	2.75854i
$101$	−2.89040			−0.287605			−0.143803	−	0.989606i	$-0.545933\pi$
$101$	−2.89040			−0.287605			−0.143803	+	0.989606i	$0.545933\pi$
$102$	1.50852	+	0.150186i	0.149366	+	0.0148706i
$103$	−7.15687			−0.705187			−0.352594	−	0.935777i	$-0.614700\pi$
$103$	−7.15687			−0.705187			−0.352594	+	0.935777i	$0.614700\pi$
$104$	−0.691821	+	10.1745i	−0.0678386	+	0.997696i
$105$	−17.6508			−1.72254
$106$	11.3160	+	1.12661i	1.09911	+	0.109426i
$107$	−10.6510			−1.02967			−0.514833	−	0.857290i	$-0.672146\pi$
$107$	−10.6510			−1.02967			−0.514833	+	0.857290i	$0.672146\pi$
$108$	1.96074	+	0.394325i	0.188672	+	0.0379439i
$109$	−1.78060	−	1.78060i	−0.170551	−	0.170551i	0.616671	−	0.787221i	$-0.288481\pi$
$109$	−1.78060	−	1.78060i	−0.170551	−	0.170551i	−0.787221	+	0.616671i	$0.788481\pi$
$110$	−22.3930	−	2.22941i	−2.13509	−	0.212566i
$111$	−1.97885	+	1.97885i	−0.187824	+	0.187824i
$112$	14.9635	−	6.12412i	1.41392	−	0.578675i
$113$	2.99536			0.281780			0.140890	−	0.990025i	$-0.455004\pi$
$113$	2.99536			0.281780			0.140890	+	0.990025i	$0.455004\pi$
$114$	−1.85209	−	2.26164i	−0.173464	−	0.211822i
$115$	−17.0688	−	17.0688i	−1.59168	−	1.59168i
$116$	0.202043	−	1.00464i	0.0187592	−	0.0932784i
$117$	−3.51077	+	0.821294i	−0.324570	+	0.0759287i
$118$	−1.90442	+	1.55955i	−0.175316	+	0.143569i
$119$	3.06383	+	3.06383i	0.280861	+	0.280861i
$120$	−10.9111	+	5.78773i	−0.996046	+	0.528345i
$121$			2.27861i			0.207146i
$122$	−6.56952	−	0.654051i	−0.594777	−	0.0592150i
$123$	0.0336607	−	0.0336607i	0.00303508	−	0.00303508i
$124$	4.47707	+	6.73116i	0.402053	+	0.604476i
$125$	−28.0026	+	28.0026i	−2.50463	+	2.50463i
$126$	3.62173	+	4.42261i	0.322649	+	0.393997i
$127$	−16.1639			−1.43431			−0.717156	−	0.696913i	$-0.754557\pi$
$127$	−16.1639			−1.43431			−0.717156	+	0.696913i	$0.754557\pi$
$128$	7.24183	−	8.69229i	0.640093	−	0.768297i
$129$		−	3.49466i		−	0.307688i
$130$	13.5607	−	17.6606i	1.18935	−	1.54894i
$131$	−0.118526			−0.0103557			−0.00517783	−	0.999987i	$-0.501648\pi$
$131$	−0.118526			−0.0103557			−0.00517783	+	0.999987i	$0.501648\pi$
$132$	4.03616	+	6.06826i	0.351303	+	0.528175i
$133$		−	8.35506i		−	0.724476i
$134$	2.57618	+	3.14586i	0.222548	+	0.271761i
$135$	−3.08779	−	3.08779i	−0.265754	−	0.265754i
$136$	2.89860	+	0.889324i	0.248553	+	0.0762589i
$137$	8.38715	+	8.38715i	0.716563	+	0.716563i	0.967900	−	0.251337i	$-0.0808702\pi$
$137$	8.38715	+	8.38715i	0.716563	+	0.716563i	−0.251337	+	0.967900i	$0.580870\pi$
$138$	−0.774476	+	7.77911i	−0.0659278	+	0.662202i
$139$	−9.73531			−0.825738			−0.412869	−	0.910790i	$-0.635473\pi$
$139$	−9.73531			−0.825738			−0.412869	+	0.910790i	$0.635473\pi$
$140$	−34.6086	−	6.96014i	−2.92496	−	0.588239i
$141$	−6.45565	+	6.45565i	−0.543664	+	0.543664i
$142$	8.68021	−	7.10833i	0.728427	−	0.596518i
$143$	−11.1624	−	6.92992i	−0.933443	−	0.579509i
$144$	3.68902	+	1.54634i	0.307418	+	0.128862i
$145$	−1.58211	+	1.58211i	−0.131387	+	0.131387i
$146$	8.86741	−	7.26163i	0.733872	−	0.600977i
$147$			9.33817i			0.770200i
$148$	−4.66032	+	3.09970i	−0.383076	+	0.254794i
$149$	6.39777	+	6.39777i	0.524126	+	0.524126i	0.918815	−	0.394689i	$-0.129148\pi$
$149$	6.39777	+	6.39777i	0.524126	+	0.524126i	−0.394689	+	0.918815i	$0.629148\pi$
$150$	19.7985	+	1.97110i	1.61654	+	0.160940i
$151$	6.23105	−	6.23105i	0.507076	−	0.507076i	−0.406552	−	0.913628i	$-0.633269\pi$
$151$	6.23105	−	6.23105i	0.507076	−	0.507076i	0.913628	+	0.406552i	$0.133269\pi$
$152$	−2.73964	−	5.16483i	−0.222214	−	0.418923i
$153$			1.07196i			0.0866628i
$154$	−2.06362	+	20.7277i	−0.166291	+	1.67029i
$155$		−	17.6508i		−	1.41774i
$156$	−7.20756	+	0.225963i	−0.577067	+	0.0180915i
$157$		−	23.8222i		−	1.90122i	−0.310393	−	0.950608i	$-0.600461\pi$
$157$		−	23.8222i		−	1.90122i	0.310393	−	0.950608i	$-0.399539\pi$
$158$	9.37180	+	0.933041i	0.745581	+	0.0742288i
$159$			8.04121i			0.637710i
$160$	−23.6762	+	7.04572i	−1.87177	+	0.557013i
$161$	−15.7995	+	15.7995i	−1.24518	+	1.24518i
$162$	−0.140104	+	1.40726i	−0.0110076	+	0.110565i
$163$	4.03428	+	4.03428i	0.315989	+	0.315989i	0.847224	−	0.531235i	$-0.178272\pi$
$163$	4.03428	+	4.03428i	0.315989	+	0.315989i	−0.531235	+	0.847224i	$0.678272\pi$
$164$	0.0792732	−	0.0527267i	0.00619020	−	0.00411726i
$165$		−	15.9125i		−	1.23879i
$166$	0.195121	+	0.238269i	0.0151444	+	0.0184933i
$167$	4.78853	−	4.78853i	0.370548	−	0.370548i	−0.497129	−	0.867677i	$-0.665612\pi$
$167$	4.78853	−	4.78853i	0.370548	−	0.370548i	0.867677	+	0.497129i	$0.165612\pi$
$168$	5.35733	+	10.0997i	0.413327	+	0.779211i
$169$	11.6510	−	5.76674i	0.896227	−	0.443596i
$170$	−4.19425	−	5.12174i	−0.321685	−	0.392819i
$171$	1.46161	−	1.46161i	0.111772	−	0.111772i
$172$	1.37803	−	6.85213i	0.105074	−	0.522470i
$173$	−1.81603			−0.138070			−0.0690350	−	0.997614i	$-0.521992\pi$
$173$	−1.81603			−0.138070			−0.0690350	+	0.997614i	$0.521992\pi$
$174$	0.721046	+	0.0717861i	0.0546623	+	0.00544209i
$175$	40.2110	+	40.2110i	3.03967	+	3.03967i
$176$	5.52100	+	13.4899i	0.416161	+	1.01684i
$177$	−1.23075	−	1.23075i	−0.0925092	−	0.0925092i
$178$	−17.6035	+	14.4157i	−1.31944	+	1.08050i
$179$			10.4962i			0.784521i	0.919854	+	0.392261i	$0.128307\pi$
$179$			10.4962i			0.784521i	−0.919854	+	0.392261i	$0.871693\pi$
$180$	−4.83676	−	7.27194i	−0.360511	−	0.542018i
$181$	14.0565			1.04481			0.522407	−	0.852696i	$-0.325034\pi$
$181$	14.0565			1.04481			0.522407	+	0.852696i	$0.325034\pi$
$182$	−16.3473	−	12.5522i	−1.21174	−	0.930433i
$183$		−	4.66832i		−	0.345092i
$184$	−4.58605	+	14.9474i	−0.338088	+	1.10194i
$185$	12.2205			0.898470
$186$	−4.42261	+	3.62173i	−0.324281	+	0.265558i
$187$	−2.76210	+	2.76210i	−0.201985	+	0.201985i
$188$	−15.2035	+	10.1122i	−1.10883	+	0.737510i
$189$	−2.85816	+	2.85816i	−0.207901	+	0.207901i
$190$	−1.26462	+	12.7023i	−0.0917454	+	0.921524i
$191$		−	15.1540i		−	1.09650i	−0.836313	−	0.548252i	$-0.815294\pi$
$191$		−	15.1540i		−	1.09650i	0.836313	−	0.548252i	$-0.184706\pi$
$192$	6.62345	+	4.48664i	0.478006	+	0.323795i
$193$	−16.5694	−	16.5694i	−1.19269	−	1.19269i	−0.976309	−	0.216380i	$-0.930575\pi$
$193$	−16.5694	−	16.5694i	−1.19269	−	1.19269i	−0.216380	−	0.976309i	$-0.569425\pi$
$194$	11.1543	+	13.6208i	0.800830	+	0.977919i
$195$	13.3765	+	8.30451i	0.957909	+	0.594698i
$196$	−3.68227	+	18.3097i	−0.263020	+	1.30784i
$197$	−6.24885	−	6.24885i	−0.445212	−	0.445212i	0.448547	−	0.893759i	$-0.351942\pi$
$197$	−6.24885	−	6.24885i	−0.445212	−	0.445212i	−0.893759	+	0.448547i	$0.851942\pi$
$198$	−3.98706	+	3.26505i	−0.283348	+	0.232037i
$199$	4.22848			0.299749			0.149875	−	0.988705i	$-0.452113\pi$
$199$	4.22848			0.299749			0.149875	+	0.988705i	$0.452113\pi$
$200$	38.0424	+	11.6719i	2.69001	+	0.825325i
$201$	−2.03305	+	2.03305i	−0.143400	+	0.143400i
$202$	0.404956	−	4.06753i	0.0284926	−	0.286190i
$203$	1.46446	+	1.46446i	0.102785	+	0.102785i
$204$	−0.422701	+	2.10184i	−0.0295950	+	0.147158i
$205$	−0.207874			−0.0145186
$206$	1.00271	−	10.0715i	0.0698619	−	0.701718i
$207$	−5.52786			−0.384213
$208$	−14.2213	−	2.39907i	−0.986068	−	0.166345i
$209$	7.53224			0.521016
$210$	2.47295	−	24.8392i	0.170650	−	1.71407i
$211$	−24.8295			−1.70934			−0.854668	−	0.519175i	$-0.826239\pi$
$211$	−24.8295			−1.70934			−0.854668	+	0.519175i	$0.826239\pi$
$212$	−3.17085	+	15.7667i	−0.217775	+	1.08286i
$213$	5.60969	+	5.60969i	0.384369	+	0.384369i
$214$	1.49224	−	14.9886i	0.102008	−	1.02460i
$215$	−10.7908	+	10.7908i	−0.735924	+	0.735924i
$216$	−0.829624	+	2.70402i	−0.0564488	+	0.183985i
$217$	−16.3382			−1.10911
$218$	2.75523	−	2.25629i	0.186608	−	0.152815i
$219$	5.73067	+	5.73067i	0.387243	+	0.387243i
$220$	6.27469	−	31.2003i	0.423040	−	2.10352i
$221$	−0.880394	−	3.76340i	−0.0592217	−	0.253154i
$222$	−2.50750	−	3.06199i	−0.168293	−	0.205507i
$223$	−1.83341	−	1.83341i	−0.122774	−	0.122774i	0.643050	−	0.765824i	$-0.277669\pi$
$223$	−1.83341	−	1.83341i	−0.122774	−	0.122774i	−0.765824	+	0.643050i	$0.777669\pi$
$224$	6.52176	+	21.9155i	0.435753	+	1.46429i
$225$			14.0688i			0.937923i
$226$	−0.419662	+	4.21524i	−0.0279155	+	0.280394i
$227$	9.42020	−	9.42020i	0.625240	−	0.625240i	−0.321626	−	0.946867i	$-0.604229\pi$
$227$	9.42020	−	9.42020i	0.625240	−	0.625240i	0.946867	+	0.321626i	$0.104229\pi$
$228$	3.44220	−	2.28950i	0.227965	−	0.151626i
$229$	4.97977	−	4.97977i	0.329073	−	0.329073i	−0.523161	−	0.852234i	$-0.675247\pi$
$229$	4.97977	−	4.97977i	0.329073	−	0.329073i	0.852234	+	0.523161i	$0.175247\pi$
$230$	26.4117	−	21.6288i	1.74153	−	1.42616i
$231$	−14.7292			−0.969108
$232$	1.38548	+	0.425080i	0.0909610	+	0.0279079i
$233$		−	5.38474i		−	0.352766i	−0.984322	−	0.176383i	$-0.943560\pi$
$233$		−	5.38474i		−	0.352766i	0.984322	−	0.176383i	$-0.0564397\pi$
$234$	−0.663899	−	5.05561i	−0.0434004	−	0.330496i
$235$	39.8673			2.60066
$236$	−1.92788	−	2.89851i	−0.125494	−	0.188677i
$237$			6.65963i			0.432589i
$238$	−4.74086	+	3.88235i	−0.307304	+	0.251655i
$239$	−6.48045	−	6.48045i	−0.419186	−	0.419186i	0.465737	−	0.884923i	$-0.345789\pi$
$239$	−6.48045	−	6.48045i	−0.419186	−	0.419186i	−0.884923	+	0.465737i	$0.845789\pi$
$240$	−6.61613	−	16.1657i	−0.427069	−	1.04349i
$241$	16.2281	+	16.2281i	1.04534	+	1.04534i	0.998922	+	0.0464205i	$0.0147814\pi$
$241$	16.2281	+	16.2281i	1.04534	+	1.04534i	0.0464205	+	0.998922i	$0.485219\pi$
$242$	−3.20659	−	0.319242i	−0.206127	−	0.0205217i
$243$	−1.00000			−0.0641500
$244$	1.84083	−	9.15337i	0.117847	−	0.585984i
$245$	28.8343	−	28.8343i	1.84215	−	1.84215i
$246$	0.0426532	+	0.0520852i	0.00271947	+	0.00332083i
$247$	−3.93097	+	6.33180i	−0.250122	+	0.402883i
$248$	−10.0997	+	5.35733i	−0.641333	+	0.340191i
$249$	−0.153984	+	0.153984i	−0.00975835	+	0.00975835i
$250$	−35.4836	−	43.3302i	−2.24418	−	2.74044i
$251$		−	0.990551i		−	0.0625230i	−0.999511	−	0.0312615i	$-0.990048\pi$
$251$		−	0.990551i		−	0.0625230i	0.999511	−	0.0312615i	$-0.00995247\pi$
$252$	−6.73116	+	4.47707i	−0.424023	+	0.282029i
$253$	−14.2435	−	14.2435i	−0.895484	−	0.895484i
$254$	2.26463	−	22.7467i	0.142095	−	1.42726i
$255$	3.30998	−	3.30998i	0.207279	−	0.207279i
$256$	11.2177	+	11.4089i	0.701105	+	0.713058i
$257$		−	16.9182i		−	1.05533i	−0.849453	−	0.527665i	$-0.823068\pi$
$257$		−	16.9182i		−	1.05533i	0.849453	−	0.527665i	$-0.176932\pi$
$258$	4.91788	+	0.489616i	0.306174	+	0.0304822i
$259$		−	11.3117i		−	0.702877i
$260$	22.9531	+	21.5577i	1.42349	+	1.33695i
$261$			0.512377i			0.0317153i
$262$	0.0166060	−	0.166796i	0.00102592	−	0.0103047i
$263$			28.7035i			1.76993i	0.465655	+	0.884966i	$0.345819\pi$
$263$			28.7035i			1.76993i	−0.465655	+	0.884966i	$0.654181\pi$
$264$	−9.10509	+	4.82973i	−0.560379	+	0.297249i
$265$	24.8295	−	24.8295i	1.52527	−	1.52527i
$266$	11.7577	+	1.17058i	0.720912	+	0.0717728i
$267$	−11.3765	−	11.3765i	−0.696229	−	0.696229i
$268$	−4.78796	+	3.18460i	−0.292471	+	0.194530i
$269$			25.8818i			1.57804i	0.614366	+	0.789021i	$0.289412\pi$
$269$			25.8818i			1.57804i	−0.614366	+	0.789021i	$0.710588\pi$
$270$	4.77792	−	3.91270i	0.290775	−	0.238119i
$271$	−6.06113	+	6.06113i	−0.368187	+	0.368187i	−0.866816	−	0.498628i	$-0.833837\pi$
$271$	−6.06113	+	6.06113i	−0.368187	+	0.368187i	0.498628	+	0.866816i	$0.333837\pi$
$272$	−1.65761	+	3.95448i	−0.100508	+	0.239775i
$273$	7.68694	−	12.3817i	0.465235	−	0.749376i
$274$	−12.9779	+	10.6278i	−0.784026	+	0.642049i
$275$	−36.2510	+	36.2510i	−2.18602	+	2.18602i
$276$	−10.8387	−	2.17977i	−0.652413	−	0.131207i
$277$	−2.49785			−0.150081			−0.0750407	−	0.997180i	$-0.523909\pi$
$277$	−2.49785			−0.150081			−0.0750407	+	0.997180i	$0.523909\pi$
$278$	1.36396	−	13.7001i	0.0818047	−	0.821676i
$279$	−2.85816	−	2.85816i	−0.171114	−	0.171114i
$280$	14.6435	−	47.7281i	0.875117	−	2.85230i
$281$	−6.26380	−	6.26380i	−0.373667	−	0.373667i	0.495144	−	0.868811i	$-0.335115\pi$
$281$	−6.26380	−	6.26380i	−0.373667	−	0.373667i	−0.868811	+	0.495144i	$0.835115\pi$
$282$	−8.18029	−	9.98921i	−0.487129	−	0.594849i
$283$			11.9847i			0.712416i	0.934407	+	0.356208i	$0.115931\pi$
$283$			11.9847i			0.712416i	−0.934407	+	0.356208i	$0.884069\pi$
$284$	8.78711	+	13.2112i	0.521419	+	0.783940i
$285$	−9.02631			−0.534672
$286$	11.3161	−	14.7374i	0.669133	−	0.871440i
$287$			0.192415i			0.0113579i
$288$	−2.69294	+	4.97474i	−0.158683	+	0.293140i
$289$	15.8509			0.932406
$290$	−2.00477	−	2.44809i	−0.117724	−	0.143757i
$291$	−8.80263	+	8.80263i	−0.516019	+	0.516019i
$292$	8.97662	+	13.4961i	0.525317	+	0.789800i
$293$	−3.26151	+	3.26151i	−0.190539	+	0.190539i	−0.795929	−	0.605390i	$-0.793017\pi$
$293$	−3.26151	+	3.26151i	−0.190539	+	0.190539i	0.605390	+	0.795929i	$0.293017\pi$
$294$	−13.1412	−	1.30832i	−0.766411	−	0.0763026i
$295$			7.60061i			0.442525i
$296$	−3.70914	−	6.99255i	−0.215590	−	0.406433i
$297$	−2.57668	−	2.57668i	−0.149514	−	0.149514i
$298$	−9.89966	+	8.10695i	−0.573472	+	0.469623i
$299$	19.4070	−	4.54000i	1.12234	−	0.262555i
$300$	−5.54769	+	27.5854i	−0.320296	+	1.59264i
$301$	9.98830	+	9.98830i	0.575716	+	0.575716i
$302$	7.89570	+	9.64169i	0.454346	+	0.554817i
$303$	2.89040			0.166049
$304$	7.65207	−	3.13177i	0.438876	−	0.179619i
$305$	−14.4148	+	14.4148i	−0.825387	+	0.825387i
$306$	−1.50852	−	0.150186i	−0.0862365	−	0.00858556i
$307$	−7.00180	−	7.00180i	−0.399614	−	0.399614i	0.478483	−	0.878097i	$-0.341187\pi$
$307$	−7.00180	−	7.00180i	−0.399614	−	0.399614i	−0.878097	+	0.478483i	$0.841187\pi$
$308$	−28.8801	−	5.80807i	−1.64560	−	0.330946i
$309$	7.15687			0.407140
$310$	24.8392	+	2.47295i	1.41077	+	0.140454i
$311$	29.2550			1.65890			0.829450	−	0.558582i	$-0.188654\pi$
$311$	29.2550			1.65890			0.829450	+	0.558582i	$0.188654\pi$
$312$	0.691821	−	10.1745i	0.0391666	−	0.576020i
$313$	2.65852			0.150269			0.0751343	−	0.997173i	$-0.476061\pi$
$313$	2.65852			0.150269			0.0751343	+	0.997173i	$0.476061\pi$
$314$	33.5239	+	3.33758i	1.89186	+	0.188351i
$315$	17.6508			0.994509
$316$	−2.62606	+	13.0578i	−0.147727	+	0.734559i
$317$	5.19502	+	5.19502i	0.291781	+	0.291781i	0.837784	−	0.546002i	$-0.183851\pi$
$317$	5.19502	+	5.19502i	0.291781	+	0.291781i	−0.546002	+	0.837784i	$0.683851\pi$
$318$	−11.3160	−	1.12661i	−0.634573	−	0.0631770i
$319$	−1.32023	+	1.32023i	−0.0739189	+	0.0739189i
$320$	−6.59800	−	34.3056i	−0.368839	−	1.91774i
$321$	10.6510			0.594478
$322$	−20.0204	−	24.4475i	−1.11569	−	1.36241i
$323$	1.56679	+	1.56679i	0.0871787	+	0.0871787i
$324$	−1.96074	−	0.394325i	−0.108930	−	0.0219069i
$325$	−11.5547	−	49.3924i	−0.640937	−	2.73980i
$326$	−6.24248	+	5.11204i	−0.345739	+	0.283130i
$327$	1.78060	+	1.78060i	0.0984675	+	0.0984675i
$328$	0.0630935	+	0.118945i	0.00348375	+	0.00656764i
$329$		−	36.9026i		−	2.03450i
$330$	22.3930	+	2.22941i	1.23269	+	0.122725i
$331$	−14.6385	+	14.6385i	−0.804603	+	0.804603i	−0.983811	−	0.179208i	$-0.942647\pi$
$331$	−14.6385	+	14.6385i	−0.804603	+	0.804603i	0.179208	+	0.983811i	$0.442647\pi$
$332$	−0.362643	+	0.241203i	−0.0199026	+	0.0132378i
$333$	1.97885	−	1.97885i	0.108440	−	0.108440i
$334$	6.06780	+	7.40959i	0.332015	+	0.405435i
$335$	12.5552			0.685965
$336$	−14.9635	+	6.12412i	−0.816325	+	0.334098i
$337$			19.9550i			1.08702i	0.839404	+	0.543508i	$0.182904\pi$
$337$			19.9550i			1.08702i	−0.839404	+	0.543508i	$0.817096\pi$
$338$	6.48294	+	17.2038i	0.352625	+	0.935765i
$339$	−2.99536			−0.162686
$340$	7.79523	−	5.18481i	0.422756	−	0.281186i
$341$		−	14.7292i		−	0.797629i
$342$	1.85209	+	2.26164i	0.100149	+	0.122296i
$343$	−6.68288	−	6.68288i	−0.360841	−	0.360841i
$344$	9.44963	+	2.89926i	0.509490	+	0.156317i
$345$	17.0688	+	17.0688i	0.918956	+	0.918956i
$346$	0.254433	−	2.55562i	0.0136784	−	0.137391i
$347$	−13.2961			−0.713770			−0.356885	−	0.934148i	$-0.616161\pi$
$347$	−13.2961			−0.713770			−0.356885	+	0.934148i	$0.616161\pi$
$348$	−0.202043	+	1.00464i	−0.0108306	+	0.0538543i
$349$	−20.5685	+	20.5685i	−1.10101	+	1.10101i	−0.106716	+	0.994290i	$0.534033\pi$
$349$	−20.5685	+	20.5685i	−1.10101	+	1.10101i	−0.994290	+	0.106716i	$0.965967\pi$
$350$	−62.2210	+	50.9535i	−3.32585	+	2.72358i
$351$	3.51077	−	0.821294i	0.187391	−	0.0438374i
$352$	−19.7572	+	5.87948i	−1.05306	+	0.313378i
$353$	3.37647	−	3.37647i	0.179712	−	0.179712i	−0.611519	−	0.791230i	$-0.709441\pi$
$353$	3.37647	−	3.37647i	0.179712	−	0.179712i	0.791230	+	0.611519i	$0.209441\pi$
$354$	1.90442	−	1.55955i	0.101219	−	0.0828894i
$355$		−	34.6430i		−	1.83866i
$356$	−17.8203	−	26.7924i	−0.944474	−	1.41999i
$357$	−3.06383	−	3.06383i	−0.162155	−	0.162155i
$358$	−14.7708	−	1.47056i	−0.780662	−	0.0777214i
$359$	−10.1733	+	10.1733i	−0.536927	+	0.536927i	−0.922625	−	0.385698i	$-0.873961\pi$
$359$	−10.1733	+	10.1733i	−0.536927	+	0.536927i	0.385698	+	0.922625i	$0.373961\pi$
$360$	10.9111	−	5.78773i	0.575067	−	0.305040i
$361$			14.7274i			0.775124i
$362$	−1.96938	+	19.7811i	−0.103508	+	1.03967i
$363$		−	2.27861i		−	0.119596i
$364$	19.9545	−	21.2462i	1.04590	−	1.11360i
$365$		−	35.3902i		−	1.85241i
$366$	6.56952	+	0.654051i	0.343394	+	0.0341878i
$367$		−	12.7553i		−	0.665820i	−0.942959	−	0.332910i	$-0.891970\pi$
$367$		−	12.7553i		−	0.665820i	0.942959	−	0.332910i	$-0.108030\pi$
$368$	−20.3924	−	8.54794i	−1.06303	−	0.445592i
$369$	−0.0336607	+	0.0336607i	−0.00175231	+	0.00175231i
$370$	−1.71215	+	17.1974i	−0.0890102	+	0.894050i
$371$	−22.9831	−	22.9831i	−1.19322	−	1.19322i
$372$	−4.47707	−	6.73116i	−0.232125	−	0.348994i
$373$		−	13.6959i		−	0.709147i	−0.935028	−	0.354573i	$-0.884626\pi$
$373$		−	13.6959i		−	0.709147i	0.935028	−	0.354573i	$-0.115374\pi$
$374$	−3.50001	−	4.27397i	−0.180981	−	0.221002i
$375$	28.0026	−	28.0026i	1.44605	−	1.44605i
$376$	−12.1004	−	22.8120i	−0.624032	−	1.17644i
$377$	−0.420812	−	1.79884i	−0.0216729	−	0.0926447i
$378$	−3.62173	−	4.42261i	−0.186281	−	0.227474i
$379$	−16.8734	+	16.8734i	−0.866730	+	0.866730i	−0.992109	−	0.125379i	$-0.959985\pi$
$379$	−16.8734	+	16.8734i	−0.866730	+	0.866730i	0.125379	+	0.992109i	$0.459985\pi$
$380$	−17.6983	−	3.55930i	−0.907901	−	0.182588i
$381$	16.1639			0.828100
$382$	21.3255	+	2.12313i	1.09111	+	0.108629i
$383$	2.81081	+	2.81081i	0.143625	+	0.143625i	0.775263	−	0.631638i	$-0.217617\pi$
$383$	2.81081	+	2.81081i	0.143625	+	0.143625i	−0.631638	+	0.775263i	$0.717617\pi$
$384$	−7.24183	+	8.69229i	−0.369558	+	0.443577i
$385$	45.4805	+	45.4805i	2.31790	+	2.31790i
$386$	25.6388	−	20.9959i	1.30498	−	1.06866i
$387$			3.49466i			0.177644i
$388$	−20.7308	+	13.7886i	−1.05245	+	0.700009i
$389$	−34.2597			−1.73703			−0.868517	−	0.495660i	$-0.834926\pi$
$389$	−34.2597			−1.73703			−0.868517	+	0.495660i	$0.834926\pi$
$390$	−13.5607	+	17.6606i	−0.686672	+	0.894281i
$391$		−	5.92564i		−	0.299673i
$392$	−25.2506	−	7.74717i	−1.27535	−	0.391291i
$393$	0.118526			0.00597884
$394$	9.66923	−	7.91825i	0.487129	−	0.398916i
$395$	20.5635	−	20.5635i	1.03466	−	1.03466i
$396$	−4.03616	−	6.06826i	−0.202825	−	0.304942i
$397$	−16.1956	+	16.1956i	−0.812836	+	0.812836i	−0.985058	−	0.172223i	$-0.944905\pi$
$397$	−16.1956	+	16.1956i	−0.812836	+	0.812836i	0.172223	+	0.985058i	$0.444905\pi$
$398$	−0.592428	+	5.95056i	−0.0296957	+	0.298274i
$399$			8.35506i			0.418276i
$400$	−21.7552	+	51.9002i	−1.08776	+	2.59501i
$401$	18.5045	+	18.5045i	0.924069	+	0.924069i	0.997314	−	0.0732452i	$-0.0233356\pi$
$401$	18.5045	+	18.5045i	0.924069	+	0.924069i	−0.0732452	+	0.997314i	$0.523336\pi$
$402$	−2.57618	−	3.14586i	−0.128488	−	0.156901i
$403$	12.3817	+	7.68694i	0.616778	+	0.382914i
$404$	5.66732	+	1.13975i	0.281960	+	0.0567049i
$405$	3.08779	+	3.08779i	0.153433	+	0.153433i
$406$	−2.26604	+	1.85569i	−0.112462	+	0.0920963i
$407$	10.1977			0.505483
$408$	−2.89860	−	0.889324i	−0.143502	−	0.0440281i
$409$	−19.3758	+	19.3758i	−0.958070	+	0.958070i	−0.999156	−	0.0410856i	$-0.986918\pi$
$409$	−19.3758	+	19.3758i	−0.958070	+	0.958070i	0.0410856	+	0.999156i	$0.486918\pi$
$410$	0.0291240	−	0.292532i	0.00143833	−	0.0144471i
$411$	−8.38715	−	8.38715i	−0.413708	−	0.413708i
$412$	14.0328	+	2.82213i	0.691345	+	0.139036i
$413$	7.03539			0.346189
$414$	0.774476	−	7.77911i	0.0380634	−	0.382323i
$415$	0.950941			0.0466798
$416$	5.36856	−	19.6769i	0.263215	−	0.964737i
$417$	9.73531			0.476740
$418$	−1.05530	+	10.5998i	−0.0516163	+	0.518453i
$419$	36.1631			1.76668			0.883341	−	0.468731i	$-0.155289\pi$
$419$	36.1631			1.76668			0.883341	+	0.468731i	$0.155289\pi$
$420$	34.6086	+	6.96014i	1.68873	+	0.339620i
$421$	0.701961	+	0.701961i	0.0342115	+	0.0342115i	0.724006	−	0.689794i	$-0.242299\pi$
$421$	0.701961	+	0.701961i	0.0342115	+	0.0342115i	−0.689794	+	0.724006i	$0.742299\pi$
$422$	3.47872	−	34.9415i	0.169342	−	1.70093i
$423$	6.45565	−	6.45565i	0.313884	−	0.313884i
$424$	−21.7436	−	6.67119i	−1.05596	−	0.323981i
$425$	−15.0812			−0.731547
$426$	−8.68021	+	7.10833i	−0.420557	+	0.344400i
$427$	13.3428	+	13.3428i	0.645704	+	0.645704i
$428$	20.8838	+	4.19994i	1.00945	+	0.203012i
$429$	11.1624	+	6.92992i	0.538923	+	0.334580i
$430$	−13.6735	−	16.6972i	−0.659397	−	0.805211i
$431$	2.65259	+	2.65259i	0.127771	+	0.127771i	0.768100	−	0.640330i	$-0.221202\pi$
$431$	2.65259	+	2.65259i	0.127771	+	0.127771i	−0.640330	+	0.768100i	$0.721202\pi$
$432$	−3.68902	−	1.54634i	−0.177488	−	0.0743982i
$433$		−	27.2434i		−	1.30923i	−0.755961	−	0.654617i	$-0.772830\pi$
$433$		−	27.2434i		−	1.30923i	0.755961	−	0.654617i	$-0.227170\pi$
$434$	2.28905	−	22.9920i	0.109878	−	1.10365i
$435$	1.58211	−	1.58211i	0.0758564	−	0.0758564i
$436$	2.78916	+	4.19344i	0.133577	+	0.200829i
$437$	−8.07960	+	8.07960i	−0.386500	+	0.386500i
$438$	−8.86741	+	7.26163i	−0.423701	+	0.346974i
$439$	28.4482			1.35776			0.678878	−	0.734251i	$-0.262466\pi$
$439$	28.4482			1.35776			0.678878	+	0.734251i	$0.262466\pi$
$440$	43.0277	+	13.2014i	2.05127	+	0.629352i
$441$		−	9.33817i		−	0.444675i
$442$	5.41942	−	0.711673i	0.257775	−	0.0338508i
$443$	−26.2562			−1.24747			−0.623735	−	0.781636i	$-0.714386\pi$
$443$	−26.2562			−1.24747			−0.623735	+	0.781636i	$0.714386\pi$
$444$	4.66032	−	3.09970i	0.221169	−	0.147105i
$445$			70.2562i			3.33046i
$446$	2.83694	−	2.32321i	0.134333	−	0.110007i
$447$	−6.39777	−	6.39777i	−0.302604	−	0.302604i
$448$	−31.7544	+	6.10734i	−1.50026	+	0.288545i
$449$	−10.3557	−	10.3557i	−0.488717	−	0.488717i	0.419185	−	0.907901i	$-0.362316\pi$
$449$	−10.3557	−	10.3557i	−0.488717	−	0.488717i	−0.907901	+	0.419185i	$0.862316\pi$
$450$	−19.7985	−	1.97110i	−0.933309	−	0.0929187i
$451$	−0.173466			−0.00816820
$452$	−5.87313	−	1.18115i	−0.276249	−	0.0555564i
$453$	−6.23105	+	6.23105i	−0.292760	+	0.292760i
$454$	11.9368	+	14.5764i	0.560223	+	0.684106i
$455$	−61.9678	+	14.4965i	−2.90509	+	0.679605i
$456$	2.73964	+	5.16483i	0.128296	+	0.241865i
$457$	20.3069	−	20.3069i	0.949918	−	0.949918i	−0.0488865	−	0.998804i	$-0.515567\pi$
$457$	20.3069	−	20.3069i	0.949918	−	0.949918i	0.998804	+	0.0488865i	$0.0155673\pi$
$458$	6.31013	+	7.70550i	0.294853	+	0.360055i
$459$		−	1.07196i		−	0.0500348i
$460$	26.7369	+	40.1983i	1.24662	+	1.87425i
$461$	13.3085	+	13.3085i	0.619838	+	0.619838i	0.945490	−	0.325652i	$-0.105584\pi$
$461$	13.3085	+	13.3085i	0.619838	+	0.619838i	−0.325652	+	0.945490i	$0.605584\pi$
$462$	2.06362	−	20.7277i	0.0960081	−	0.964340i
$463$	−3.24915	+	3.24915i	−0.151001	+	0.151001i	−0.778565	−	0.627564i	$-0.784052\pi$
$463$	−3.24915	+	3.24915i	−0.151001	+	0.151001i	0.627564	+	0.778565i	$0.284052\pi$
$464$	−0.792308	+	1.89017i	−0.0367820	+	0.0877488i
$465$			17.6508i			0.818535i
$466$	7.57771	+	0.754424i	0.351031	+	0.0349480i
$467$			40.2993i			1.86483i	0.361392	+	0.932414i	$0.382302\pi$
$467$			40.2993i			1.86483i	−0.361392	+	0.932414i	$0.617698\pi$
$468$	7.20756	−	0.225963i	0.333170	−	0.0104452i
$469$		−	11.6215i		−	0.536633i
$470$	−5.58557	+	56.1035i	−0.257643	+	2.58786i
$471$			23.8222i			1.09767i
$472$	4.34905	−	2.30692i	0.200181	−	0.106185i
$473$	−9.00464	+	9.00464i	−0.414034	+	0.414034i
$474$	−9.37180	−	0.933041i	−0.430461	−	0.0428560i
$475$	20.5632	+	20.5632i	0.943506	+	0.943506i
$476$	−4.79924	−	7.21554i	−0.219973	−	0.330724i
$477$		−	8.04121i		−	0.368182i
$478$	10.0276	−	8.21172i	0.458652	−	0.375595i
$479$	−19.0201	+	19.0201i	−0.869049	+	0.869049i	−0.992367	−	0.123318i	$-0.960646\pi$
$479$	−19.0201	+	19.0201i	−0.869049	+	0.869049i	0.123318	+	0.992367i	$0.460646\pi$
$480$	23.6762	−	7.04572i	1.08066	−	0.321591i
$481$	−5.32206	+	8.57249i	−0.242665	+	0.390872i
$482$	−25.1107	+	20.5634i	−1.14376	+	0.936639i
$483$	15.7995	−	15.7995i	0.718903	−	0.718903i
$484$	0.898512	−	4.46776i	0.0408415	−	0.203080i
$485$	54.3613			2.46842
$486$	0.140104	−	1.40726i	0.00635525	−	0.0638345i
$487$	8.43408	+	8.43408i	0.382184	+	0.382184i	0.871889	−	0.489704i	$-0.162895\pi$
$487$	8.43408	+	8.43408i	0.382184	+	0.382184i	−0.489704	+	0.871889i	$0.662895\pi$
$488$	12.6232	+	3.87295i	0.571427	+	0.175320i
$489$	−4.03428	−	4.03428i	−0.182436	−	0.182436i
$490$	36.5374	+	44.6170i	1.65059	+	2.01559i
$491$			23.3787i			1.05507i	0.849534	+	0.527533i	$0.176883\pi$
$491$			23.3787i			1.05507i	−0.849534	+	0.527533i	$0.823117\pi$
$492$	−0.0792732	+	0.0527267i	−0.00357391	+	0.00237710i
$493$	−0.549248			−0.0247369
$494$	−8.35972	−	6.41900i	−0.376122	−	0.288804i
$495$			15.9125i			0.715214i
$496$	−6.12412	−	14.9635i	−0.274981	−	0.671880i
$497$	−32.0668			−1.43839
$498$	−0.195121	−	0.238269i	−0.00874360	−	0.0106771i
$499$	−18.6272	+	18.6272i	−0.833867	+	0.833867i	−0.988043	−	0.154176i	$-0.950728\pi$
$499$	−18.6272	+	18.6272i	−0.833867	+	0.833867i	0.154176	+	0.988043i	$0.450728\pi$
$500$	65.9481	−	43.8638i	2.94929	−	1.96165i
$501$	−4.78853	+	4.78853i	−0.213936	+	0.213936i
$502$	1.39396	+	0.138780i	0.0622154	+	0.00619407i
$503$		−	12.2441i		−	0.545939i	−0.962023	−	0.272969i	$-0.911994\pi$
$503$		−	12.2441i		−	0.545939i	0.962023	−	0.272969i	$-0.0880058\pi$
$504$	−5.35733	−	10.0997i	−0.238634	−	0.449878i
$505$	−8.92492	−	8.92492i	−0.397154	−	0.397154i
$506$	22.0399	−	18.0487i	0.979793	−	0.802365i
$507$	−11.6510	+	5.76674i	−0.517437	+	0.256110i
$508$	31.6932	+	6.37382i	1.40616	+	0.282792i
$509$	−25.7075	−	25.7075i	−1.13947	−	1.13947i	−0.988546	−	0.150920i	$-0.951776\pi$
$509$	−25.7075	−	25.7075i	−1.13947	−	1.13947i	−0.150920	−	0.988546i	$-0.548224\pi$
$510$	4.19425	+	5.12174i	0.185725	+	0.226794i
$511$	−32.7584			−1.44914
$512$	−17.6269	+	14.1877i	−0.779008	+	0.627014i
$513$	−1.46161	+	1.46161i	−0.0645319	+	0.0645319i
$514$	23.8083	+	2.37031i	1.05014	+	0.104550i
$515$	−22.0989	−	22.0989i	−0.973793	−	0.973793i
$516$	−1.37803	+	6.85213i	−0.0606645	+	0.301648i
$517$	33.2683			1.46314
$518$	15.9185	+	1.58482i	0.699419	+	0.0696330i
$519$	1.81603			0.0797148
$520$	−33.5530	+	29.2806i	−1.47140	+	1.28404i
$521$	−41.6747			−1.82580			−0.912902	−	0.408179i	$-0.866164\pi$
$521$	−41.6747			−1.82580			−0.912902	+	0.408179i	$0.866164\pi$
$522$	−0.721046	−	0.0717861i	−0.0315593	−	0.00314199i
$523$	16.6394			0.727591			0.363796	−	0.931479i	$-0.381481\pi$
$523$	16.6394			0.727591			0.363796	+	0.931479i	$0.381481\pi$
$524$	0.232399	+	0.0467377i	0.0101524	+	0.00204175i
$525$	−40.2110	−	40.2110i	−1.75495	−	1.75495i
$526$	−40.3932	−	4.02148i	−1.76123	−	0.175345i
$527$	3.06383	−	3.06383i	0.133463	−	0.133463i
$528$	−5.52100	−	13.4899i	−0.240271	−	0.587071i
$529$	7.55722			0.328575
$530$	31.4628	+	38.4203i	1.36666	+	1.66887i
$531$	1.23075	+	1.23075i	0.0534102	+	0.0534102i
$532$	−3.29461	+	16.3821i	−0.142839	+	0.710255i
$533$	0.0905295	−	0.145820i	0.00392127	−	0.00631617i
$534$	17.6035	−	14.4157i	0.761778	−	0.623829i
$535$	−32.8879	−	32.8879i	−1.42187	−	1.42187i
$536$	−3.81073	−	7.18406i	−0.164599	−	0.310304i
$537$		−	10.4962i		−	0.452944i
$538$	−36.4224	−	3.62615i	−1.57028	−	0.156334i
$539$	24.0615	−	24.0615i	1.03640	−	1.03640i
$540$	4.83676	+	7.27194i	0.208141	+	0.312935i
$541$	23.7679	−	23.7679i	1.02186	−	1.02186i	0.0221074	−	0.999756i	$-0.492962\pi$
$541$	23.7679	−	23.7679i	1.02186	−	1.02186i	0.999756	−	0.0221074i	$-0.00703757\pi$
$542$	−7.68037	−	9.37875i	−0.329900	−	0.402852i
$543$	−14.0565			−0.603223
$544$	−5.33273	−	2.88673i	−0.228639	−	0.123767i
$545$		−	10.9962i		−	0.471027i
$546$	16.3473	+	12.5522i	0.699600	+	0.537186i
$547$	20.4838			0.875824			0.437912	−	0.899018i	$-0.355718\pi$
$547$	20.4838			0.875824			0.437912	+	0.899018i	$0.355718\pi$
$548$	−13.1378	−	19.7523i	−0.561218	−	0.843776i
$549$			4.66832i			0.199239i
$550$	−45.9355	−	56.0933i	−1.95870	−	2.39183i
$551$	0.748898	+	0.748898i	0.0319041	+	0.0319041i
$552$	4.58605	−	14.9474i	0.195195	−	0.636205i
$553$	−19.0343	−	19.0343i	−0.809420	−	0.809420i
$554$	0.349960	−	3.51512i	0.0148684	−	0.149343i
$555$	−12.2205			−0.518732
$556$	19.0884	+	3.83887i	0.809529	+	0.162805i
$557$	−30.8045	+	30.8045i	−1.30523	+	1.30523i	−0.380408	+	0.924819i	$0.624217\pi$
$557$	−30.8045	+	30.8045i	−1.30523	+	1.30523i	−0.924819	+	0.380408i	$0.875783\pi$
$558$	4.42261	−	3.62173i	0.187224	−	0.153320i
$559$	−2.87014	−	12.2689i	−0.121394	−	0.518921i
$560$	65.1140	+	27.2941i	2.75157	+	1.15339i
$561$	2.76210	−	2.76210i	0.116616	−	0.116616i
$562$	9.69236	−	7.93719i	0.408847	−	0.334810i
$563$		−	33.7226i		−	1.42124i	−0.703578	−	0.710618i	$-0.748415\pi$
$563$		−	33.7226i		−	1.42124i	0.703578	−	0.710618i	$-0.251585\pi$
$564$	15.2035	−	10.1122i	0.640182	−	0.425802i
$565$	9.24903	+	9.24903i	0.389110	+	0.389110i
$566$	−16.8655	−	1.67911i	−0.708912	−	0.0705781i
$567$	2.85816	−	2.85816i	0.120031	−	0.120031i
$568$	−19.8226	+	10.5148i	−0.831739	+	0.441190i
$569$		−	37.5317i		−	1.57341i	−0.617329	−	0.786705i	$-0.711785\pi$
$569$		−	37.5317i		−	1.57341i	0.617329	−	0.786705i	$-0.288215\pi$
$570$	1.26462	−	12.7023i	0.0529692	−	0.532042i
$571$		−	10.4261i		−	0.436318i	−0.975913	−	0.218159i	$-0.929995\pi$
$571$		−	10.4261i		−	0.436318i	0.975913	−	0.218159i	$-0.0700051\pi$
$572$	19.1538	+	17.9894i	0.800863	+	0.752174i
$573$			15.1540i			0.633066i
$574$	−0.270778	−	0.0269582i	−0.0113021	−	0.00112521i
$575$		−	77.7706i		−	3.24326i
$576$	−6.62345	−	4.48664i	−0.275977	−	0.186943i
$577$	−5.95723	+	5.95723i	−0.248003	+	0.248003i	−0.820150	−	0.572148i	$-0.806110\pi$
$577$	−5.95723	+	5.95723i	−0.248003	+	0.248003i	0.572148	+	0.820150i	$0.306110\pi$
$578$	−2.22078	+	22.3063i	−0.0923721	+	0.927819i
$579$	16.5694	+	16.5694i	0.688600	+	0.688600i
$580$	3.72597	−	2.47824i	0.154713	−	0.102903i
$581$		−	0.880223i		−	0.0365178i
$582$	−11.1543	−	13.6208i	−0.462359	−	0.564602i
$583$	20.7197	−	20.7197i	0.858121	−	0.858121i
$584$	−20.2501	+	10.7415i	−0.837957	+	0.444488i
$585$	−13.3765	−	8.30451i	−0.553049	−	0.343349i
$586$	−4.13283	−	5.04673i	−0.170726	−	0.208478i
$587$	1.72078	−	1.72078i	0.0710241	−	0.0710241i	−0.670702	−	0.741727i	$-0.734007\pi$
$587$	1.72078	−	1.72078i	0.0710241	−	0.0710241i	0.741727	+	0.670702i	$0.234007\pi$
$588$	3.68227	−	18.3097i	0.151854	−	0.755081i
$589$	−8.35506			−0.344264
$590$	−10.6960	−	1.06488i	−0.440348	−	0.0438403i
$591$	6.24885	+	6.24885i	0.257044	+	0.257044i
$592$	10.3600	−	4.24003i	0.425792	−	0.174264i
$593$	13.4905	+	13.4905i	0.553990	+	0.553990i	0.927590	−	0.373600i	$-0.121877\pi$
$593$	13.4905	+	13.4905i	0.553990	+	0.553990i	−0.373600	+	0.927590i	$0.621877\pi$
$594$	3.98706	−	3.26505i	0.163591	−	0.133967i
$595$			18.9209i			0.775683i
$596$	−10.0216	−	15.0672i	−0.410500	−	0.617175i
$597$	−4.22848			−0.173060
$598$	3.66994	+	27.9467i	0.150075	+	1.14283i
$599$			37.0916i			1.51552i	0.652533	+	0.757760i	$0.273706\pi$
$599$			37.0916i			1.51552i	−0.652533	+	0.757760i	$0.726294\pi$
$600$	−38.0424	−	11.6719i	−1.55308	−	0.476501i
$601$	−17.3441			−0.707483			−0.353741	−	0.935343i	$-0.615091\pi$
$601$	−17.3441			−0.707483			−0.353741	+	0.935343i	$0.615091\pi$
$602$	−15.4555	+	12.6567i	−0.629919	+	0.515849i
$603$	2.03305	−	2.03305i	0.0827920	−	0.0827920i
$604$	−14.6745	+	9.76043i	−0.597099	+	0.397146i
$605$	−7.03585	+	7.03585i	−0.286048	+	0.286048i
$606$	−0.404956	+	4.06753i	−0.0164502	+	0.165232i
$607$		−	0.0268909i		−	0.00109147i	−1.00000		0.000545735i	$-0.999826\pi$
$607$		−	0.0268909i		−	0.00109147i	1.00000		0.000545735i	$-0.000173713\pi$
$608$	3.33512	+	11.2072i	0.135257	+	0.454512i
$609$	−1.46446	−	1.46446i	−0.0593427	−	0.0593427i
$610$	−18.2657	−	22.3049i	−0.739557	−	0.903097i
$611$	−17.3623	+	27.9662i	−0.702403	+	1.13139i
$612$	0.422701	−	2.10184i	0.0170867	−	0.0849617i
$613$	21.4415	+	21.4415i	0.866013	+	0.866013i	0.992028	−	0.126015i	$-0.0402188\pi$
$613$	21.4415	+	21.4415i	0.866013	+	0.866013i	−0.126015	+	0.992028i	$0.540219\pi$
$614$	10.8343	−	8.87234i	0.437237	−	0.358059i
$615$	0.207874			0.00838229
$616$	12.2197	−	39.8279i	0.492345	−	1.60471i
$617$	−10.1510	+	10.1510i	−0.408663	+	0.408663i	−0.881272	−	0.472609i	$-0.843312\pi$
$617$	−10.1510	+	10.1510i	−0.408663	+	0.408663i	0.472609	+	0.881272i	$0.343312\pi$
$618$	−1.00271	+	10.0715i	−0.0403348	+	0.405137i
$619$	−10.4442	−	10.4442i	−0.419789	−	0.419789i	0.465342	−	0.885131i	$-0.345931\pi$
$619$	−10.4442	−	10.4442i	−0.419789	−	0.419789i	−0.885131	+	0.465342i	$0.845931\pi$
$620$	−6.96014	+	34.6086i	−0.279526	+	1.38992i
$621$	5.52786			0.221825
$622$	−4.09875	+	41.1693i	−0.164345	+	1.65074i
$623$	65.0316			2.60544
$624$	14.2213	+	2.39907i	0.569306	+	0.0960395i
$625$	−102.588			−4.10352
$626$	−0.372470	+	3.74122i	−0.0148869	+	0.149529i
$627$	−7.53224			−0.300809
$628$	−9.39368	+	46.7091i	−0.374848	+	1.86390i
$629$	2.12125	+	2.12125i	0.0845796	+	0.0845796i
$630$	−2.47295	+	24.8392i	−0.0985246	+	0.989616i
$631$	−21.3320	+	21.3320i	−0.849215	+	0.849215i	−0.990035	−	0.140820i	$-0.955026\pi$
$631$	−21.3320	+	21.3320i	−0.849215	+	0.849215i	0.140820	+	0.990035i	$0.455026\pi$
$632$	−18.0078	−	5.52499i	−0.716310	−	0.219772i
$633$	24.8295			0.986886
$634$	−8.03857	+	6.58288i	−0.319252	+	0.261440i
$635$	−49.9106	−	49.9106i	−1.98064	−	1.98064i
$636$	3.17085	−	15.7667i	0.125732	−	0.625192i
$637$	7.66939	+	32.7841i	0.303872	+	1.29895i
$638$	−1.67294	−	2.04288i	−0.0662322	−	0.0808783i
$639$	−5.60969	−	5.60969i	−0.221916	−	0.221916i
$640$	49.2011	−	4.47873i	1.94485	−	0.177037i
$641$			28.5426i			1.12736i	0.825992	+	0.563682i	$0.190616\pi$
$641$			28.5426i			1.12736i	−0.825992	+	0.563682i	$0.809384\pi$
$642$	−1.49224	+	14.9886i	−0.0588941	+	0.591554i
$643$	18.1283	−	18.1283i	0.714912	−	0.714912i	−0.252647	−	0.967559i	$-0.581301\pi$
$643$	18.1283	−	18.1283i	0.714912	−	0.714912i	0.967559	+	0.252647i	$0.0813010\pi$
$644$	37.2089	−	24.7486i	1.46624	−	0.975232i
$645$	10.7908	−	10.7908i	0.424886	−	0.424886i
$646$	−2.42439	+	1.98536i	−0.0953865	+	0.0781131i
$647$	23.0407			0.905824			0.452912	−	0.891555i	$-0.350385\pi$
$647$	23.0407			0.905824			0.452912	+	0.891555i	$0.350385\pi$
$648$	0.829624	−	2.70402i	0.0325907	−	0.106224i
$649$			6.34253i			0.248966i
$650$	71.1266	−	9.34028i	2.78982	−	0.366356i
$651$	16.3382			0.640343
$652$	−6.31936	−	9.50099i	−0.247485	−	0.372087i
$653$			14.8261i			0.580191i	0.956998	+	0.290095i	$0.0936870\pi$
$653$			14.8261i			0.580191i	−0.956998	+	0.290095i	$0.906313\pi$
$654$	−2.75523	+	2.25629i	−0.107738	+	0.0882281i
$655$	−0.365983	−	0.365983i	−0.0143001	−	0.0143001i
$656$	−0.176226	+	0.0721240i	−0.00688046	+	0.00281597i
$657$	−5.73067	−	5.73067i	−0.223575	−	0.223575i
$658$	51.9314	+	5.17020i	2.02450	+	0.201555i
$659$	14.8920			0.580112			0.290056	−	0.957010i	$-0.406326\pi$
$659$	14.8920			0.580112			0.290056	+	0.957010i	$0.406326\pi$
$660$	−6.27469	+	31.2003i	−0.244242	+	1.21447i
$661$	21.6359	−	21.6359i	0.841538	−	0.841538i	−0.147521	−	0.989059i	$-0.547129\pi$
$661$	21.6359	−	21.6359i	0.841538	−	0.841538i	0.989059	+	0.147521i	$0.0471293\pi$
$662$	−18.5492	−	22.6510i	−0.720934	−	0.880356i
$663$	0.880394	+	3.76340i	0.0341917	+	0.146158i
$664$	−0.288627	−	0.544125i	−0.0112009	−	0.0211162i
$665$	25.7986	−	25.7986i	1.00043	−	1.00043i
$666$	2.50750	+	3.06199i	0.0971637	+	0.118650i
$667$		−	2.83235i		−	0.109669i
$668$	−11.2773	+	7.50084i	−0.436332	+	0.290216i
$669$	1.83341	+	1.83341i	0.0708836	+	0.0708836i
$670$	−1.75904	+	17.6684i	−0.0679576	+	0.682590i
$671$	−12.0288	+	12.0288i	−0.464366	+	0.464366i
$672$	−6.52176	−	21.9155i	−0.251582	−	0.845408i
$673$		−	35.0331i		−	1.35043i	−0.737623	−	0.675213i	$-0.764052\pi$
$673$		−	35.0331i		−	1.35043i	0.737623	−	0.675213i	$-0.235948\pi$
$674$	−28.0817	−	2.79577i	−1.08167	−	0.107689i
$675$		−	14.0688i		−	0.541510i
$676$	−25.1185	+	6.71283i	−0.966095	+	0.258186i
$677$			7.24823i			0.278572i	0.990252	+	0.139286i	$0.0444807\pi$
$677$			7.24823i			0.278572i	−0.990252	+	0.139286i	$0.955519\pi$
$678$	0.419662	−	4.21524i	0.0161170	−	0.161885i
$679$		−	50.3187i		−	1.93105i
$680$	6.20422	+	11.6963i	0.237921	+	0.448533i
$681$	−9.42020	+	9.42020i	−0.360983	+	0.360983i
$682$	20.7277	+	2.06362i	0.793705	+	0.0790200i
$683$	−7.11346	−	7.11346i	−0.272189	−	0.272189i	0.557792	−	0.829981i	$-0.311649\pi$
$683$	−7.11346	−	7.11346i	−0.272189	−	0.272189i	−0.829981	+	0.557792i	$0.811649\pi$
$684$	−3.44220	+	2.28950i	−0.131616	+	0.0875411i
$685$			51.7955i			1.97900i
$686$	10.3408	−	8.46822i	0.394814	−	0.323318i
$687$	−4.97977	+	4.97977i	−0.189990	+	0.189990i
$688$	−5.40393	+	12.8919i	−0.206023	+	0.491497i
$689$	6.60420	+	28.2308i	0.251600	+	1.07551i
$690$	−26.4117	+	21.6288i	−1.00547	+	0.823395i
$691$	32.6940	−	32.6940i	1.24374	−	1.24374i	0.285298	−	0.958439i	$-0.407908\pi$
$691$	32.6940	−	32.6940i	1.24374	−	1.24374i	0.958439	−	0.285298i	$-0.0920924\pi$
$692$	3.56076	+	0.716105i	0.135360	+	0.0272222i
$693$	14.7292			0.559515
$694$	1.86283	−	18.7110i	0.0707122	−	0.710259i
$695$	−30.0605	−	30.0605i	−1.14026	−	1.14026i
$696$	−1.38548	−	0.425080i	−0.0525164	−	0.0161126i
$697$	−0.0360829	−	0.0360829i	−0.00136674	−	0.00136674i
$698$	−26.0634	−	31.8268i	−0.986514	−	1.20466i
$699$			5.38474i			0.203670i
$700$	−62.9872	−	94.6996i	−2.38069	−	3.57931i
$701$	29.6221			1.11881			0.559406	−	0.828894i	$-0.311029\pi$
$701$	29.6221			1.11881			0.559406	+	0.828894i	$0.311029\pi$
$702$	0.663899	+	5.05561i	0.0250572	+	0.190812i
$703$		−	5.78463i		−	0.218171i
$704$	−5.50588	−	28.6272i	−0.207511	−	1.07893i
$705$	−39.8673			−1.50149
$706$	4.27851	+	5.22462i	0.161024	+	0.196631i
$707$	−8.26122	+	8.26122i	−0.310695	+	0.310695i
$708$	1.92788	+	2.89851i	0.0724540	+	0.108933i
$709$	−25.8554	+	25.8554i	−0.971021	+	0.971021i	−0.999592	−	0.0285709i	$-0.990904\pi$
$709$	−25.8554	+	25.8554i	−0.971021	+	0.971021i	0.0285709	+	0.999592i	$0.490904\pi$
$710$	48.7516	+	4.85363i	1.82962	+	0.182154i
$711$		−	6.65963i		−	0.249756i
$712$	40.2004	−	21.3240i	1.50657	−	0.799151i
$713$	15.7995	+	15.7995i	0.591696	+	0.591696i
$714$	4.74086	−	3.88235i	0.177422	−	0.145293i
$715$	−13.0688	−	55.8651i	−0.488747	−	2.08923i
$716$	4.13891	−	20.5803i	0.154678	−	0.769122i
$717$	6.48045	+	6.48045i	0.242017	+	0.242017i
$718$	−12.8911	−	15.7418i	−0.481093	−	0.587478i
$719$	31.2277			1.16460			0.582299	−	0.812975i	$-0.302153\pi$
$719$	31.2277			1.16460			0.582299	+	0.812975i	$0.302153\pi$
$720$	6.61613	+	16.1657i	0.246569	+	0.602458i
$721$	−20.4555	+	20.4555i	−0.761802	+	0.761802i
$722$	−20.7252	−	2.06336i	−0.771311	−	0.0767905i
$723$	−16.2281	−	16.2281i	−0.603529	−	0.603529i
$724$	−27.5612	−	5.54284i	−1.02430	−	0.205998i
$725$	−7.20855			−0.267719
$726$	3.20659	+	0.319242i	0.119008	+	0.0118482i
$727$	21.2172			0.786902			0.393451	−	0.919346i	$-0.371281\pi$
$727$	21.2172			0.786902			0.393451	+	0.919346i	$0.371281\pi$
$728$	27.1032	+	31.0578i	1.00451	+	1.15108i
$729$	1.00000			0.0370370
$730$	49.8030	+	4.95831i	1.84329	+	0.183515i
$731$	−3.74614			−0.138556
$732$	−1.84083	+	9.15337i	−0.0680392	+	0.338318i
$733$	−23.8649	−	23.8649i	−0.881469	−	0.881469i	0.112215	−	0.993684i	$-0.464206\pi$
$733$	−23.8649	−	23.8649i	−0.881469	−	0.881469i	−0.993684	+	0.112215i	$0.964206\pi$
$734$	17.9499	+	1.78707i	0.662544	+	0.0659618i
$735$	−28.8343	+	28.8343i	−1.06357	+	1.06357i
$736$	14.8862	−	27.4997i	0.548712	−	1.01365i
$737$	10.4770			0.385927
$738$	−0.0426532	−	0.0520852i	−0.00157009	−	0.00191728i
$739$	28.5318	+	28.5318i	1.04956	+	1.04956i	0.998706	+	0.0508533i	$0.0161941\pi$
$739$	28.5318	+	28.5318i	1.04956	+	1.04956i	0.0508533	+	0.998706i	$0.483806\pi$
$740$	−23.9613	−	4.81885i	−0.880834	−	0.177145i
$741$	3.93097	−	6.33180i	0.144408	−	0.232605i
$742$	35.5631	−	29.1231i	1.30556	−	1.06914i
$743$	−14.7470	−	14.7470i	−0.541013	−	0.541013i	0.382813	−	0.923826i	$-0.374956\pi$
$743$	−14.7470	−	14.7470i	−0.541013	−	0.541013i	−0.923826	+	0.382813i	$0.874956\pi$
$744$	10.0997	−	5.35733i	0.370274	−	0.196409i
$745$			39.5099i			1.44753i
$746$	19.2736	+	1.91885i	0.705658	+	0.0702542i
$747$	0.153984	−	0.153984i	0.00563399	−	0.00563399i
$748$	6.50494	−	4.32660i	0.237844	−	0.158196i
$749$	−30.4421	+	30.4421i	−1.11233	+	1.11233i
$750$	35.4836	+	43.3302i	1.29568	+	1.58219i
$751$	−44.2644			−1.61523			−0.807615	−	0.589710i	$-0.799242\pi$
$751$	−44.2644			−1.61523			−0.807615	+	0.589710i	$0.799242\pi$
$752$	33.7976	−	13.8324i	1.23247	−	0.504415i
$753$			0.990551i			0.0360977i
$754$	2.59038	−	0.340166i	0.0943361	−	0.0123881i
$755$	38.4803			1.40044
$756$	6.73116	−	4.47707i	0.244810	−	0.162830i
$757$			15.4803i			0.562641i	0.959614	+	0.281320i	$0.0907724\pi$
$757$			15.4803i			0.562641i	−0.959614	+	0.281320i	$0.909228\pi$
$758$	−21.3812	−	26.1093i	−0.776601	−	0.948332i
$759$	14.2435	+	14.2435i	0.517008	+	0.517008i
$760$	7.48844	−	24.4073i	0.271634	−	0.885346i
$761$	15.3450	+	15.3450i	0.556257	+	0.556257i	0.928240	−	0.371983i	$-0.121322\pi$
$761$	15.3450	+	15.3450i	0.556257	+	0.556257i	−0.371983	+	0.928240i	$0.621322\pi$
$762$	−2.26463	+	22.7467i	−0.0820387	+	0.824027i
$763$	−10.1785			−0.368486
$764$	−5.97559	+	29.7130i	−0.216189	+	1.07498i
$765$	−3.30998	+	3.30998i	−0.119673	+	0.119673i
$766$	−4.34933	+	3.56172i	−0.157148	+	0.128690i
$767$	−5.33170	−	3.31008i	−0.192517	−	0.119520i
$768$	−11.2177	−	11.4089i	−0.404783	−	0.411684i
$769$	0.693724	−	0.693724i	0.0250163	−	0.0250163i	−0.694488	−	0.719504i	$-0.744369\pi$
$769$	0.693724	−	0.693724i	0.0250163	−	0.0250163i	0.719504	+	0.694488i	$0.244369\pi$
$770$	−70.3747	+	57.6307i	−2.53613	+	2.07687i
$771$			16.9182i			0.609295i
$772$	25.9545	+	39.0220i	0.934124	+	1.40443i
$773$	−2.77394	−	2.77394i	−0.0997716	−	0.0997716i	0.655459	−	0.755231i	$-0.272475\pi$
$773$	−2.77394	−	2.77394i	−0.0997716	−	0.0997716i	−0.755231	+	0.655459i	$0.772475\pi$
$774$	−4.91788	−	0.489616i	−0.176770	−	0.0175989i
$775$	40.2110	−	40.2110i	1.44442	−	1.44442i
$776$	−16.4996	−	31.1054i	−0.592301	−	1.11662i
$777$			11.3117i			0.405806i
$778$	4.79992	−	48.2121i	0.172085	−	1.72849i
$779$			0.0983980i			0.00352547i
$780$	−22.9531	−	21.5577i	−0.821854	−	0.771889i
$781$		−	28.9088i		−	1.03444i
$782$	8.33890	+	0.830207i	0.298198	+	0.0296881i
$783$		−	0.512377i		−	0.0183109i
$784$	14.4400	−	34.4487i	0.515713	−	1.23031i
$785$	73.5578	−	73.5578i	2.62539	−	2.62539i
$786$	−0.0166060	+	0.166796i	−0.000592316	+	0.00594943i
$787$	9.16585	+	9.16585i	0.326727	+	0.326727i	0.851341	−	0.524613i	$-0.175790\pi$
$787$	9.16585	+	9.16585i	0.326727	+	0.326727i	−0.524613	+	0.851341i	$0.675790\pi$
$788$	9.78831	+	14.7165i	0.348694	+	0.524252i
$789$		−	28.7035i		−	1.02187i
$790$	26.0571	+	31.8192i	0.927070	+	1.13207i
$791$	8.56123	−	8.56123i	0.304402	−	0.304402i
$792$	9.10509	−	4.82973i	0.323535	−	0.171617i
$793$	−3.83406	−	16.3894i	−0.136152	−	0.582004i
$794$	−20.5223	−	25.0605i	−0.728310	−	0.889363i
$795$	−24.8295	+	24.8295i	−0.880613	+	0.880613i
$796$	−8.29096	−	1.66740i	−0.293865	−	0.0590993i
$797$	−21.6299			−0.766172			−0.383086	−	0.923713i	$-0.625139\pi$
$797$	−21.6299			−0.766172			−0.383086	+	0.923713i	$0.625139\pi$
$798$	−11.7577	−	1.17058i	−0.416219	−	0.0414380i
$799$	6.92020	+	6.92020i	0.244819	+	0.244819i
$800$	−69.9889	−	37.8866i	−2.47448	−	1.33949i
$801$	11.3765	+	11.3765i	0.401968	+	0.401968i
$802$	−28.6331	+	23.4480i	−1.01107	+	0.827977i
$803$		−	29.5323i		−	1.04217i
$804$	4.78796	−	3.18460i	0.168858	−	0.112312i
$805$	−97.5710			−3.43893
$806$	−12.5522	+	16.3473i	−0.442134	+	0.575809i
$807$		−	25.8818i		−	0.911084i
$808$	−2.39794	+	7.81569i	−0.0843593	+	0.274955i
$809$	−12.8260			−0.450937			−0.225468	−	0.974250i	$-0.572391\pi$
$809$	−12.8260			−0.450937			−0.225468	+	0.974250i	$0.572391\pi$
$810$	−4.77792	+	3.91270i	−0.167879	+	0.137478i
$811$	5.35046	−	5.35046i	0.187880	−	0.187880i	−0.606899	−	0.794779i	$-0.707587\pi$
$811$	5.35046	−	5.35046i	0.187880	−	0.187880i	0.794779	+	0.606899i	$0.207587\pi$
$812$	−2.29395	−	3.44889i	−0.0805018	−	0.121032i
$813$	6.06113	−	6.06113i	0.212573	−	0.212573i
$814$	−1.42874	+	14.3508i	−0.0500775	+	0.502996i
$815$			24.9140i			0.872698i
$816$	1.65761	−	3.95448i	0.0580281	−	0.138434i
$817$	5.10785	+	5.10785i	0.178701	+	0.178701i
$818$	−24.5520	−	29.9813i	−0.858442	−	1.04827i
$819$	−7.68694	+	12.3817i	−0.268604	+	0.432653i
$820$	0.407587	+	0.0819699i	0.0142336	+	0.00286251i
$821$	11.7654	+	11.7654i	0.410614	+	0.410614i	0.881953	−	0.471338i	$-0.156229\pi$
$821$	11.7654	+	11.7654i	0.410614	+	0.410614i	−0.471338	+	0.881953i	$0.656229\pi$
$822$	12.9779	−	10.6278i	0.452658	−	0.370687i
$823$	−9.95031			−0.346846			−0.173423	−	0.984847i	$-0.555483\pi$
$823$	−9.95031			−0.346846			−0.173423	+	0.984847i	$0.555483\pi$
$824$	−5.93751	+	19.3523i	−0.206843	+	0.674170i
$825$	36.2510	−	36.2510i	1.26210	−	1.26210i
$826$	−0.985687	+	9.90060i	−0.0342965	+	0.344486i
$827$	−0.583398	−	0.583398i	−0.0202867	−	0.0202867i	0.696891	−	0.717177i	$-0.254566\pi$
$827$	−0.583398	−	0.583398i	−0.0202867	−	0.0202867i	−0.717177	+	0.696891i	$0.754566\pi$
$828$	10.8387	+	2.17977i	0.376671	+	0.0757523i
$829$	43.6976			1.51768			0.758840	−	0.651277i	$-0.225766\pi$
$829$	43.6976			1.51768			0.758840	+	0.651277i	$0.225766\pi$
$830$	−0.133231	+	1.33822i	−0.00462450	+	0.0464502i
$831$	2.49785			0.0866496
$832$	26.9382	+	10.3117i	0.933915	+	0.357496i
$833$	10.0101			0.346831
$834$	−1.36396	+	13.7001i	−0.0472300	+	0.474395i
$835$	29.5719			1.02338
$836$	−14.7688	−	2.97015i	−0.510789	−	0.102725i
$837$	2.85816	+	2.85816i	0.0987925	+	0.0987925i
$838$	−5.06660	+	50.8907i	−0.175023	+	1.75799i
$839$	25.4022	−	25.4022i	0.876982	−	0.876982i	−0.116239	−	0.993221i	$-0.537084\pi$
$839$	25.4022	−	25.4022i	0.876982	−	0.876982i	0.993221	+	0.116239i	$0.0370838\pi$
$840$	−14.6435	+	47.7281i	−0.505249	+	1.64677i
$841$	28.7375			0.990947
$842$	−1.08619	+	0.889491i	−0.0374325	+	0.0306539i
$843$	6.26380	+	6.26380i	0.215737	+	0.215737i
$844$	48.6843	+	9.79091i	1.67578	+	0.337017i
$845$	53.7821	+	18.1692i	1.85016	+	0.625039i
$846$	8.18029	+	9.98921i	0.281244	+	0.343436i
$847$	6.51263	+	6.51263i	0.223777	+	0.223777i
$848$	12.4344	−	29.6642i	0.427000	−	1.01867i
$849$		−	11.9847i		−	0.411314i
$850$	2.11294	−	21.2232i	0.0724734	−	0.727949i
$851$	−10.9388	+	10.9388i	−0.374977	+	0.374977i
$852$	−8.78711	−	13.2112i	−0.301041	−	0.452608i
$853$	15.3474	−	15.3474i	0.525486	−	0.525486i	−0.393737	−	0.919223i	$-0.628818\pi$
$853$	15.3474	−	15.3474i	0.525486	−	0.525486i	0.919223	+	0.393737i	$0.128818\pi$
$854$	−20.6461	+	16.9074i	−0.706496	+	0.578558i
$855$	9.02631			0.308693
$856$	−8.83629	+	28.8004i	−0.302018	+	0.984377i
$857$			45.0479i			1.53881i	0.638762	+	0.769404i	$0.279447\pi$
$857$			45.0479i			1.53881i	−0.638762	+	0.769404i	$0.720553\pi$
$858$	−11.3161	+	14.7374i	−0.386324	+	0.503126i
$859$	−24.0655			−0.821106			−0.410553	−	0.911837i	$-0.634664\pi$
$859$	−24.0655			−0.821106			−0.410553	+	0.911837i	$0.634664\pi$
$860$	25.4130	−	16.9028i	0.866575	−	0.576382i
$861$		−	0.192415i		−	0.00655750i
$862$	−4.10451	+	3.36123i	−0.139800	+	0.114484i
$863$	−7.38306	−	7.38306i	−0.251322	−	0.251322i	0.570190	−	0.821513i	$-0.306869\pi$
$863$	−7.38306	−	7.38306i	−0.251322	−	0.251322i	−0.821513	+	0.570190i	$0.806869\pi$
$864$	2.69294	−	4.97474i	0.0916157	−	0.169244i
$865$	−5.60750	−	5.60750i	−0.190661	−	0.190661i
$866$	38.3384	+	3.81691i	1.30279	+	0.129704i
$867$	−15.8509			−0.538325
$868$	32.0349	+	6.44255i	1.08734	+	0.218674i
$869$	17.1598	−	17.1598i	0.582105	−	0.582105i
$870$	2.00477	+	2.44809i	0.0679682	+	0.0829982i
$871$	−5.46782	+	8.80728i	−0.185270	+	0.298423i
$872$	−6.29201	+	3.33755i	−0.213074	+	0.113024i
$873$	8.80263	−	8.80263i	0.297924	−	0.297924i
$874$	−10.2381	−	12.5021i	−0.346308	−	0.422888i
$875$			160.072i			5.41143i
$876$	−8.97662	−	13.4961i	−0.303292	−	0.455991i
$877$	−0.141964	−	0.141964i	−0.00479380	−	0.00479380i	0.704706	−	0.709500i	$-0.251079\pi$
$877$	−0.141964	−	0.141964i	−0.00479380	−	0.00479380i	−0.709500	+	0.704706i	$0.751079\pi$
$878$	−3.98570	+	40.0339i	−0.134511	+	1.35108i
$879$	3.26151	−	3.26151i	0.110008	−	0.110008i
$880$	−24.6061	+	58.7015i	−0.829472	+	1.97883i
$881$			15.3692i			0.517802i	0.965904	+	0.258901i	$0.0833604\pi$
$881$			15.3692i			0.517802i	−0.965904	+	0.258901i	$0.916640\pi$
$882$	13.1412	+	1.30832i	0.442487	+	0.0440533i
$883$		−	47.6748i		−	1.60438i	−0.597066	−	0.802192i	$-0.703667\pi$
$883$		−	47.6748i		−	1.60438i	0.597066	−	0.802192i	$-0.296333\pi$
$884$	0.242224	+	7.72622i	0.00814686	+	0.259861i
$885$		−	7.60061i		−	0.255492i
$886$	3.67860	−	36.9492i	0.123585	−	1.24133i
$887$			50.4271i			1.69317i	0.532250	+	0.846587i	$0.321347\pi$
$887$			50.4271i			1.69317i	−0.532250	+	0.846587i	$0.678653\pi$
$888$	3.70914	+	6.99255i	0.124471	+	0.234654i
$889$	−46.1990	+	46.1990i	−1.54946	+	1.54946i
$890$	−98.8685	−	9.84319i	−3.31408	−	0.329944i
$891$	2.57668	+	2.57668i	0.0863222	+	0.0863222i
$892$	2.87188	+	4.31780i	0.0961577	+	0.144571i
$893$		−	18.8713i		−	0.631505i
$894$	9.89966	−	8.10695i	0.331094	−	0.271137i
$895$	−32.4100	+	32.4100i	−1.08335	+	1.08335i
$896$	−4.14567	−	45.5423i	−0.138497	−	1.52146i
$897$	−19.4070	+	4.54000i	−0.647981	+	0.151586i
$898$	16.0240	−	13.1223i	0.534729	−	0.437896i
$899$	1.46446	−	1.46446i	0.0488423	−	0.0488423i
$900$	5.54769	−	27.5854i	0.184923	−	0.919512i
$901$	8.61986			0.287169
$902$	0.0243033	−	0.244111i	0.000809212	−	0.00812801i
$903$	−9.98830	−	9.98830i	−0.332390	−	0.332390i
$904$	2.48502	−	8.09952i	0.0826507	−	0.269386i
$905$	43.4036	+	43.4036i	1.44278	+	1.44278i
$906$	−7.89570	−	9.64169i	−0.262317	−	0.320324i
$907$			31.3735i			1.04174i	0.853636	+	0.520870i	$0.174392\pi$
$907$			31.3735i			1.04174i	−0.853636	+	0.520870i	$0.825608\pi$
$908$	−22.1852	+	14.7560i	−0.736241	+	0.489694i
$909$	−2.89040			−0.0958684
$910$	−11.7183	−	89.2355i	−0.388459	−	2.95813i
$911$			37.5437i			1.24388i	0.783066	+	0.621939i	$0.213655\pi$
$911$			37.5437i			1.24388i	−0.783066	+	0.621939i	$0.786345\pi$
$912$	−7.65207	+	3.13177i	−0.253385	+	0.103703i
$913$	0.793538			0.0262623
$914$	25.7320	+	31.4221i	0.851138	+	1.03935i
$915$	14.4148	−	14.4148i	0.476538	−	0.476538i
$916$	−11.7277	+	7.80040i	−0.387494	+	0.257732i
$917$	−0.338766	+	0.338766i	−0.0111870	+	0.0111870i
$918$	1.50852	+	0.150186i	0.0497887	+	0.00495688i
$919$		−	30.2192i		−	0.996841i	−0.866935	−	0.498420i	$-0.833914\pi$
$919$		−	30.2192i		−	0.996841i	0.866935	−	0.498420i	$-0.166086\pi$
$920$	−60.3152	+	31.9938i	−1.98853	+	1.05480i
$921$	7.00180	+	7.00180i	0.230717	+	0.230717i
$922$	−20.5930	+	16.8639i	−0.678195	+	0.555382i
$923$	24.3015	+	15.0871i	0.799894	+	0.496598i
$924$	28.8801	+	5.80807i	0.950085	+	0.191072i
$925$	27.8401	+	27.8401i	0.915377	+	0.915377i
$926$	−4.11716	−	5.02760i	−0.135298	−	0.165217i
$927$	−7.15687			−0.235062
$928$	−2.54894	−	1.37980i	−0.0836732	−	0.0452942i
$929$	21.2995	−	21.2995i	0.698815	−	0.698815i	−0.265340	−	0.964155i	$-0.585484\pi$
$929$	21.2995	−	21.2995i	0.698815	−	0.698815i	0.964155	+	0.265340i	$0.0854842\pi$
$930$	−24.8392	−	2.47295i	−0.814509	−	0.0810911i
$931$	−13.6488	−	13.6488i	−0.447322	−	0.447322i
$932$	−2.12334	+	10.5581i	−0.0695522	+	0.345841i
$933$	−29.2550			−0.957766
$934$	−56.7114	−	5.64609i	−1.85565	−	0.184746i
$935$	−17.0576			−0.557842
$936$	−0.691821	+	10.1745i	−0.0226129	+	0.332565i
$937$	35.9894			1.17572			0.587861	−	0.808962i	$-0.299970\pi$
$937$	35.9894			1.17572			0.587861	+	0.808962i	$0.299970\pi$
$938$	16.3545	+	1.62823i	0.533993	+	0.0531635i
$939$	−2.65852			−0.0867576
$940$	−78.1695	−	15.7207i	−2.54961	−	0.512752i
$941$	−11.4948	−	11.4948i	−0.374720	−	0.374720i	0.494473	−	0.869193i	$-0.335361\pi$
$941$	−11.4948	−	11.4948i	−0.374720	−	0.374720i	−0.869193	+	0.494473i	$0.835361\pi$
$942$	−33.5239	−	3.33758i	−1.09227	−	0.108744i
$943$	0.186072	−	0.186072i	0.00605932	−	0.00605932i
$944$	2.63711	+	6.44344i	0.0858306	+	0.209716i
$945$	−17.6508			−0.574180
$946$	−11.4102	−	13.9334i	−0.370979	−	0.453015i
$947$	5.55235	+	5.55235i	0.180427	+	0.180427i	0.791542	−	0.611115i	$-0.209279\pi$
$947$	5.55235	+	5.55235i	0.180427	+	0.180427i	−0.611115	+	0.791542i	$0.709279\pi$
$948$	2.62606	−	13.0578i	0.0852904	−	0.424098i
$949$	24.8256	+	15.4125i	0.805873	+	0.500310i
$950$	−31.8187	+	26.0567i	−1.03234	+	0.845392i
$951$	−5.19502	−	5.19502i	−0.168460	−	0.168460i
$952$	10.8265	−	5.74284i	0.350889	−	0.186126i
$953$			10.6622i			0.345384i	0.984976	+	0.172692i	$0.0552465\pi$
$953$			10.6622i			0.345384i	−0.984976	+	0.172692i	$0.944753\pi$
$954$	11.3160	+	1.12661i	0.366371	+	0.0364753i
$955$	46.7922	−	46.7922i	1.51416	−	1.51416i
$956$	10.1511	+	15.2619i	0.328310	+	0.493605i
$957$	1.32023	−	1.32023i	0.0426771	−	0.0426771i
$958$	−24.1013	−	29.4309i	−0.778678	−	0.950869i
$959$	47.9437			1.54818
$960$	6.59800	+	34.3056i	0.212950	+	1.10721i
$961$		−	14.6618i		−	0.472962i
$962$	−11.3180	−	8.69054i	−0.364909	−	0.280194i
$963$	−10.6510			−0.343222
$964$	−25.4199	−	38.2182i	−0.818721	−	1.23093i
$965$		−	102.325i		−	3.29397i
$966$	20.0204	+	24.4475i	0.644145	+	0.786587i
$967$	0.807895	+	0.807895i	0.0259801	+	0.0259801i	0.719978	−	0.693997i	$-0.244152\pi$
$967$	0.807895	+	0.807895i	0.0259801	+	0.0259801i	−0.693997	+	0.719978i	$0.744152\pi$
$968$	6.16140	+	1.89039i	0.198035	+	0.0607594i
$969$	−1.56679	−	1.56679i	−0.0503326	−	0.0503326i
$970$	−7.61624	+	76.5002i	−0.244543	+	2.45627i
$971$	12.7850			0.410290			0.205145	−	0.978732i	$-0.434233\pi$
$971$	12.7850			0.410290			0.205145	+	0.978732i	$0.434233\pi$
$972$	1.96074	+	0.394325i	0.0628908	+	0.0126480i
$973$	−27.8251	+	27.8251i	−0.892031	+	0.892031i
$974$	−13.0506	+	10.6873i	−0.418167	+	0.342442i
$975$	11.5547	+	49.3924i	0.370045	+	1.58182i
$976$	−7.21880	+	17.2215i	−0.231068	+	0.551247i
$977$	10.2997	−	10.2997i	0.329517	−	0.329517i	−0.522886	−	0.852403i	$-0.675145\pi$
$977$	10.2997	−	10.2997i	0.329517	−	0.329517i	0.852403	+	0.522886i	$0.175145\pi$
$978$	6.24248	−	5.11204i	0.199612	−	0.163465i
$979$			58.6272i			1.87373i
$980$	−67.9066	+	45.1665i	−2.16920	+	1.44279i
$981$	−1.78060	−	1.78060i	−0.0568502	−	0.0568502i
$982$	−32.8998	−	3.27545i	−1.04988	−	0.104524i
$983$	−36.2990	+	36.2990i	−1.15776	+	1.15776i	−0.172800	+	0.984957i	$0.555282\pi$
$983$	−36.2990	+	36.2990i	−1.15776	+	1.15776i	−0.984957	+	0.172800i	$0.944718\pi$
$984$	−0.0630935	−	0.118945i	−0.00201135	−	0.00379183i
$985$		−	38.5902i		−	1.22959i
$986$	0.0769518	−	0.772932i	0.00245065	−	0.0246152i
$987$			36.9026i			1.17462i
$988$	10.2044	−	10.8649i	0.324645	−	0.345660i
$989$		−	19.3180i		−	0.614276i
$990$	−22.3930	−	2.22941i	−0.711695	−	0.0708552i
$991$			22.9756i			0.729843i	0.931038	+	0.364922i	$0.118904\pi$
$991$			22.9756i			0.729843i	−0.931038	+	0.364922i	$0.881096\pi$
$992$	21.9155	−	6.52176i	0.695817	−	0.207066i
$993$	14.6385	−	14.6385i	0.464538	−	0.464538i
$994$	4.49269	−	45.1262i	0.142499	−	1.43132i
$995$	13.0566	+	13.0566i	0.413923	+	0.413923i
$996$	0.362643	−	0.241203i	0.0114908	−	0.00764282i
$997$		−	38.3954i		−	1.21599i	−0.793940	−	0.607997i	$-0.791973\pi$
$997$		−	38.3954i		−	1.21599i	0.793940	−	0.607997i	$-0.208027\pi$
$998$	−23.6035	−	28.8230i	−0.747155	−	0.912375i
$999$	−1.97885	+	1.97885i	−0.0626080	+	0.0626080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.t.e.187.6	yes	24
3.2	odd	2		936.2.w.j.811.7		24
4.3	odd	2		1248.2.bb.f.655.12		24
8.3	odd	2	inner	312.2.t.e.187.1	✓	24
8.5	even	2		1248.2.bb.f.655.1		24
13.8	odd	4	inner	312.2.t.e.307.1	yes	24
24.11	even	2		936.2.w.j.811.12		24
39.8	even	4		936.2.w.j.307.12		24
52.47	even	4		1248.2.bb.f.463.1		24
104.21	odd	4		1248.2.bb.f.463.12		24
104.99	even	4	inner	312.2.t.e.307.6	yes	24
312.203	odd	4		936.2.w.j.307.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.t.e.187.1	✓	24	8.3	odd	2	inner
312.2.t.e.187.6	yes	24	1.1	even	1	trivial
312.2.t.e.307.1	yes	24	13.8	odd	4	inner
312.2.t.e.307.6	yes	24	104.99	even	4	inner
936.2.w.j.307.7		24	312.203	odd	4
936.2.w.j.307.12		24	39.8	even	4
936.2.w.j.811.7		24	3.2	odd	2
936.2.w.j.811.12		24	24.11	even	2
1248.2.bb.f.463.1		24	52.47	even	4
1248.2.bb.f.463.12		24	104.21	odd	4
1248.2.bb.f.655.1		24	8.5	even	2
1248.2.bb.f.655.12		24	4.3	odd	2

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.140104 + 1.40726i) q^{2} -1.00000 q^{3} +(-1.96074 - 0.394325i) q^{4} +(3.08779 + 3.08779i) q^{5} +(0.140104 - 1.40726i) q^{6} +(2.85816 - 2.85816i) q^{7} +(0.829624 - 2.70402i) q^{8} +1.00000 q^{9} +(-4.77792 + 3.91270i) q^{10} +(2.57668 + 2.57668i) q^{11} +(1.96074 + 0.394325i) q^{12} +(-3.51077 + 0.821294i) q^{13} +(3.62173 + 4.42261i) q^{14} +(-3.08779 - 3.08779i) q^{15} +(3.68902 + 1.54634i) q^{16} +1.07196i q^{17} +(-0.140104 + 1.40726i) q^{18} +(1.46161 - 1.46161i) q^{19} +(-4.83676 - 7.27194i) q^{20} +(-2.85816 + 2.85816i) q^{21} +(-3.98706 + 3.26505i) q^{22} -5.52786 q^{23} +(-0.829624 + 2.70402i) q^{24} +14.0688i q^{25} +(-0.663899 - 5.05561i) q^{26} -1.00000 q^{27} +(-6.73116 + 4.47707i) q^{28} +0.512377i q^{29} +(4.77792 - 3.91270i) q^{30} +(-2.85816 - 2.85816i) q^{31} +(-2.69294 + 4.97474i) q^{32} +(-2.57668 - 2.57668i) q^{33} +(-1.50852 - 0.150186i) q^{34} +17.6508 q^{35} +(-1.96074 - 0.394325i) q^{36} +(1.97885 - 1.97885i) q^{37} +(1.85209 + 2.26164i) q^{38} +(3.51077 - 0.821294i) q^{39} +(10.9111 - 5.78773i) q^{40} +(-0.0336607 + 0.0336607i) q^{41} +(-3.62173 - 4.42261i) q^{42} +3.49466i q^{43} +(-4.03616 - 6.06826i) q^{44} +(3.08779 + 3.08779i) q^{45} +(0.774476 - 7.77911i) q^{46} +(6.45565 - 6.45565i) q^{47} +(-3.68902 - 1.54634i) q^{48} -9.33817i q^{49} +(-19.7985 - 1.97110i) q^{50} -1.07196i q^{51} +(7.20756 - 0.225963i) q^{52} -8.04121i q^{53} +(0.140104 - 1.40726i) q^{54} +15.9125i q^{55} +(-5.35733 - 10.0997i) q^{56} +(-1.46161 + 1.46161i) q^{57} +(-0.721046 - 0.0717861i) q^{58} +(1.23075 + 1.23075i) q^{59} +(4.83676 + 7.27194i) q^{60} +4.66832i q^{61} +(4.42261 - 3.62173i) q^{62} +(2.85816 - 2.85816i) q^{63} +(-6.62345 - 4.48664i) q^{64} +(-13.3765 - 8.30451i) q^{65} +(3.98706 - 3.26505i) q^{66} +(2.03305 - 2.03305i) q^{67} +(0.422701 - 2.10184i) q^{68} +5.52786 q^{69} +(-2.47295 + 24.8392i) q^{70} +(-5.60969 - 5.60969i) q^{71} +(0.829624 - 2.70402i) q^{72} +(-5.73067 - 5.73067i) q^{73} +(2.50750 + 3.06199i) q^{74} -14.0688i q^{75} +(-3.44220 + 2.28950i) q^{76} +14.7292 q^{77} +(0.663899 + 5.05561i) q^{78} -6.65963i q^{79} +(6.61613 + 16.1657i) q^{80} +1.00000 q^{81} +(-0.0426532 - 0.0520852i) q^{82} +(0.153984 - 0.153984i) q^{83} +(6.73116 - 4.47707i) q^{84} +(-3.30998 + 3.30998i) q^{85} +(-4.91788 - 0.489616i) q^{86} -0.512377i q^{87} +(9.10509 - 4.82973i) q^{88} +(11.3765 + 11.3765i) q^{89} +(-4.77792 + 3.91270i) q^{90} +(-7.68694 + 12.3817i) q^{91} +(10.8387 + 2.17977i) q^{92} +(2.85816 + 2.85816i) q^{93} +(8.18029 + 9.98921i) q^{94} +9.02631 q^{95} +(2.69294 - 4.97474i) q^{96} +(8.80263 - 8.80263i) q^{97} +(13.1412 + 1.30832i) q^{98} +(2.57668 + 2.57668i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{3} - 6 q^{8} + 24 q^{9} + 8 q^{11} + 36 q^{14} + 28 q^{16} + 20 q^{19} - 20 q^{20} + 20 q^{22} + 6 q^{24} + 12 q^{26} - 24 q^{27} - 16 q^{28} - 30 q^{32} - 8 q^{33} + 16 q^{34} + 16 q^{35}+ \cdots + 8 q^{99}+O(q^{100}) \) 24 * q - 24 * q^3 - 6 * q^8 + 24 * q^9 + 8 * q^11 + 36 * q^14 + 28 * q^16 + 20 * q^19 - 20 * q^20 + 20 * q^22 + 6 * q^24 + 12 * q^26 - 24 * q^27 - 16 * q^28 - 30 * q^32 - 8 * q^33 + 16 * q^34 + 16 * q^35 + 36 * q^40 - 12 * q^41 - 36 * q^42 - 32 * q^44 - 44 * q^46 - 28 * q^48 - 36 * q^50 + 4 * q^52 - 20 * q^57 + 32 * q^58 - 16 * q^59 + 20 * q^60 - 76 * q^65 - 20 * q^66 + 28 * q^67 + 32 * q^68 - 40 * q^70 - 6 * q^72 - 8 * q^73 - 32 * q^74 - 36 * q^76 - 12 * q^78 - 32 * q^80 + 24 * q^81 - 72 * q^83 + 16 * q^84 + 4 * q^86 + 28 * q^89 - 4 * q^91 + 32 * q^92 + 28 * q^94 + 30 * q^96 + 24 * q^97 + 68 * q^98 + 8 * q^99

Introduction

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