LMFDB - Embedded newform 912.2.y.a.379.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(379,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 2]))

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

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

chi := DirichletCharacter("912.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.y (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$80$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			379.9
Character	$\chi$	$=$	912.379
Dual form			912.2.y.a.835.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35115 + 0.417616i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.65119 - 1.12852i) q^{4} +(-1.93786 - 1.93786i) q^{5} +(0.660105 - 1.25070i) q^{6} -0.339330 q^{7} +(-1.75971 + 2.21436i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.35115 + 0.417616i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.65119 - 1.12852i) q^{4} +(-1.93786 - 1.93786i) q^{5} +(0.660105 - 1.25070i) q^{6} -0.339330 q^{7} +(-1.75971 + 2.21436i) q^{8} -1.00000i q^{9} +(3.42761 + 1.80905i) q^{10} +(-0.232961 + 0.232961i) q^{11} +(-0.369584 + 1.96556i) q^{12} +(3.65227 + 3.65227i) q^{13} +(0.458485 - 0.141710i) q^{14} +2.74055 q^{15} +(1.45288 - 3.72681i) q^{16} -3.05495 q^{17} +(0.417616 + 1.35115i) q^{18} +(3.21403 - 2.94449i) q^{19} +(-5.38669 - 1.01286i) q^{20} +(0.239943 - 0.239943i) q^{21} +(0.217476 - 0.412052i) q^{22} +6.23596 q^{23} +(-0.321486 - 2.81010i) q^{24} +2.51059i q^{25} +(-6.45999 - 3.40950i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.560300 + 0.382942i) q^{28} +(-2.90301 - 2.90301i) q^{29} +(-3.70288 + 1.14450i) q^{30} -9.24970 q^{31} +(-0.406670 + 5.64222i) q^{32} -0.329456i q^{33} +(4.12769 - 1.27580i) q^{34} +(0.657574 + 0.657574i) q^{35} +(-1.12852 - 1.65119i) q^{36} +(0.229049 - 0.229049i) q^{37} +(-3.11295 + 5.32067i) q^{38} -5.16509 q^{39} +(7.70120 - 0.881046i) q^{40} -9.93099 q^{41} +(-0.223994 + 0.424402i) q^{42} +(-2.69741 + 2.69741i) q^{43} +(-0.121762 + 0.647564i) q^{44} +(-1.93786 + 1.93786i) q^{45} +(-8.42570 + 2.60424i) q^{46} -12.6542i q^{47} +(1.60792 + 3.66259i) q^{48} -6.88486 q^{49} +(-1.04846 - 3.39217i) q^{50} +(2.16018 - 2.16018i) q^{51} +(10.1523 + 1.90893i) q^{52} +(-7.49028 + 7.49028i) q^{53} +(-1.25070 - 0.660105i) q^{54} +0.902890 q^{55} +(0.597124 - 0.751400i) q^{56} +(-0.190592 + 4.35473i) q^{57} +(5.13473 + 2.71004i) q^{58} +(-0.338828 - 0.338828i) q^{59} +(4.52517 - 3.09277i) q^{60} +(-4.31437 + 4.31437i) q^{61} +(12.4977 - 3.86282i) q^{62} +0.339330i q^{63} +(-1.80681 - 7.79329i) q^{64} -14.1551i q^{65} +(0.137586 + 0.445144i) q^{66} +(6.76430 - 6.76430i) q^{67} +(-5.04432 + 3.44758i) q^{68} +(-4.40949 + 4.40949i) q^{69} +(-1.16309 - 0.613865i) q^{70} +1.39591i q^{71} +(2.21436 + 1.75971i) q^{72} -7.95811i q^{73} +(-0.213824 + 0.405133i) q^{74} +(-1.77525 - 1.77525i) q^{75} +(1.98406 - 8.48902i) q^{76} +(0.0790506 - 0.0790506i) q^{77} +(6.97879 - 2.15702i) q^{78} -6.90569 q^{79} +(-10.0375 + 4.40657i) q^{80} -1.00000 q^{81} +(13.4182 - 4.14734i) q^{82} +(-3.31359 - 3.31359i) q^{83} +(0.125411 - 0.666972i) q^{84} +(5.92006 + 5.92006i) q^{85} +(2.51812 - 4.77108i) q^{86} +4.10547 q^{87} +(-0.105915 - 0.925804i) q^{88} -10.2721 q^{89} +(1.80905 - 3.42761i) q^{90} +(-1.23932 - 1.23932i) q^{91} +(10.2968 - 7.03742i) q^{92} +(6.54052 - 6.54052i) q^{93} +(5.28460 + 17.0977i) q^{94} +(-11.9343 - 0.522325i) q^{95} +(-3.70209 - 4.27721i) q^{96} -11.3309i q^{97} +(9.30245 - 2.87523i) q^{98} +(0.232961 + 0.232961i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q+O(q^{10}) $ 160 * q	$ 160 q - 8 q^{16} - 8 q^{19} - 8 q^{24} + 40 q^{26} - 40 q^{28} - 48 q^{35} - 8 q^{36} + 48 q^{38} + 56 q^{44} + 160 q^{49} - 8 q^{54} - 56 q^{58} - 32 q^{61} + 24 q^{62} + 72 q^{64} + 48 q^{66} - 40 q^{68} + 40 q^{74} + 32 q^{76} + 56 q^{80} - 160 q^{81} - 120 q^{82} - 80 q^{83} + 32 q^{85} - 24 q^{92} - 40 q^{96}+O(q^{100}) $ 160 * q - 8 * q^16 - 8 * q^19 - 8 * q^24 + 40 * q^26 - 40 * q^28 - 48 * q^35 - 8 * q^36 + 48 * q^38 + 56 * q^44 + 160 * q^49 - 8 * q^54 - 56 * q^58 - 32 * q^61 + 24 * q^62 + 72 * q^64 + 48 * q^66 - 40 * q^68 + 40 * q^74 + 32 * q^76 + 56 * q^80 - 160 * q^81 - 120 * q^82 - 80 * q^83 + 32 * q^85 - 24 * q^92 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	−1.35115	+	0.417616i	−0.955405	+	0.295299i
$2$	−1.35115	+	0.417616i	−0.955405	+	0.295299i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.65119	−	1.12852i	0.825596	−	0.564261i
$5$	−1.93786	−	1.93786i	−0.866636	−	0.866636i	0.125462	−	0.992098i	$-0.459959\pi$
$5$	−1.93786	−	1.93786i	−0.866636	−	0.866636i	−0.992098	+	0.125462i	$0.959959\pi$
$6$	0.660105	−	1.25070i	0.269487	−	0.510598i
$7$	−0.339330			−0.128255			−0.0641274	−	0.997942i	$-0.520426\pi$
$7$	−0.339330			−0.128255			−0.0641274	+	0.997942i	$0.520426\pi$
$8$	−1.75971	+	2.21436i	−0.622153	+	0.782896i
$9$		−	1.00000i		−	0.333333i
$10$	3.42761	+	1.80905i	1.08391	+	0.572071i
$11$	−0.232961	+	0.232961i	−0.0702403	+	0.0702403i	−0.741354	−	0.671114i	$-0.765816\pi$
$11$	−0.232961	+	0.232961i	−0.0702403	+	0.0702403i	0.671114	+	0.741354i	$0.265816\pi$
$12$	−0.369584	+	1.96556i	−0.106690	+	0.567407i
$13$	3.65227	+	3.65227i	1.01296	+	1.01296i	0.999915	+	0.0130416i	$0.00415139\pi$
$13$	3.65227	+	3.65227i	1.01296	+	1.01296i	0.0130416	+	0.999915i	$0.495849\pi$
$14$	0.458485	−	0.141710i	0.122535	−	0.0378736i
$15$	2.74055			0.707606
$16$	1.45288	−	3.72681i	0.363219	−	0.931704i
$17$	−3.05495			−0.740935			−0.370467	−	0.928845i	$-0.620802\pi$
$17$	−3.05495			−0.740935			−0.370467	+	0.928845i	$0.620802\pi$
$18$	0.417616	+	1.35115i	0.0984331	+	0.318468i
$19$	3.21403	−	2.94449i	0.737349	−	0.675512i
$19$	3.21403	−	2.94449i	0.737349	−	0.675512i
$20$	−5.38669	−	1.01286i	−1.20450	−	0.226483i
$21$	0.239943	−	0.239943i	0.0523598	−	0.0523598i
$22$	0.217476	−	0.412052i	0.0463660	−	0.0878498i
$23$	6.23596			1.30029			0.650144	−	0.759811i	$-0.274709\pi$
$23$	6.23596			1.30029			0.650144	+	0.759811i	$0.274709\pi$
$24$	−0.321486	−	2.81010i	−0.0656230	−	0.573609i
$25$			2.51059i			0.502117i
$26$	−6.45999	−	3.40950i	−1.26691	−	0.668658i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−0.560300	+	0.382942i	−0.105887	+	0.0723692i
$29$	−2.90301	−	2.90301i	−0.539075	−	0.539075i	0.384183	−	0.923257i	$-0.374483\pi$
$29$	−2.90301	−	2.90301i	−0.539075	−	0.539075i	−0.923257	+	0.384183i	$0.874483\pi$
$30$	−3.70288	+	1.14450i	−0.676050	+	0.208956i
$31$	−9.24970			−1.66129			−0.830647	−	0.556799i	$-0.812029\pi$
$31$	−9.24970			−1.66129			−0.830647	+	0.556799i	$0.812029\pi$
$32$	−0.406670	+	5.64222i	−0.0718897	+	0.997413i
$33$		−	0.329456i		−	0.0573510i
$34$	4.12769	−	1.27580i	0.707893	−	0.218798i
$35$	0.657574	+	0.657574i	0.111150	+	0.111150i
$36$	−1.12852	−	1.65119i	−0.188087	−	0.275199i
$37$	0.229049	−	0.229049i	0.0376554	−	0.0376554i	−0.688028	−	0.725684i	$-0.741524\pi$
$37$	0.229049	−	0.229049i	0.0376554	−	0.0376554i	0.725684	+	0.688028i	$0.241524\pi$
$38$	−3.11295	+	5.32067i	−0.504988	+	0.863126i
$39$	−5.16509			−0.827076
$40$	7.70120	−	0.881046i	1.21767	−	0.139306i
$41$	−9.93099			−1.55096			−0.775480	−	0.631372i	$-0.782492\pi$
$41$	−9.93099			−1.55096			−0.775480	+	0.631372i	$0.782492\pi$
$42$	−0.223994	+	0.424402i	−0.0345630	+	0.0654866i
$43$	−2.69741	+	2.69741i	−0.411352	+	0.411352i	−0.882209	−	0.470858i	$-0.843945\pi$
$43$	−2.69741	+	2.69741i	−0.411352	+	0.411352i	0.470858	+	0.882209i	$0.343945\pi$
$44$	−0.121762	+	0.647564i	−0.0183563	+	0.0976240i
$45$	−1.93786	+	1.93786i	−0.288879	+	0.288879i
$46$	−8.42570	+	2.60424i	−1.24230	+	0.383974i
$47$		−	12.6542i		−	1.84580i	−0.385035	−	0.922902i	$-0.625811\pi$
$47$		−	12.6542i		−	1.84580i	0.385035	−	0.922902i	$-0.374189\pi$
$48$	1.60792	+	3.66259i	0.232083	+	0.528650i
$49$	−6.88486			−0.983551
$50$	−1.04846	−	3.39217i	−0.148275	−	0.479725i
$51$	2.16018	−	2.16018i	0.302485	−	0.302485i
$52$	10.1523	+	1.90893i	1.40787	+	0.264722i
$53$	−7.49028	+	7.49028i	−1.02887	+	1.02887i	−0.0292977	+	0.999571i	$0.509327\pi$
$53$	−7.49028	+	7.49028i	−1.02887	+	1.02887i	−0.999571	+	0.0292977i	$0.990673\pi$
$54$	−1.25070	−	0.660105i	−0.170199	−	0.0898290i
$55$	0.902890			0.121746
$56$	0.597124	−	0.751400i	0.0797941	−	0.100410i
$57$	−0.190592	+	4.35473i	−0.0252445	+	0.576798i
$58$	5.13473	+	2.71004i	0.674223	+	0.355846i
$59$	−0.338828	−	0.338828i	−0.0441116	−	0.0441116i	0.684707	−	0.728819i	$-0.259930\pi$
$59$	−0.338828	−	0.338828i	−0.0441116	−	0.0441116i	−0.728819	+	0.684707i	$0.759930\pi$
$60$	4.52517	−	3.09277i	0.584197	−	0.399274i
$61$	−4.31437	+	4.31437i	−0.552398	+	0.552398i	−0.927132	−	0.374734i	$-0.877734\pi$
$61$	−4.31437	+	4.31437i	−0.552398	+	0.552398i	0.374734	+	0.927132i	$0.377734\pi$
$62$	12.4977	−	3.86282i	1.58721	−	0.490579i
$63$			0.339330i			0.0427516i
$64$	−1.80681	−	7.79329i	−0.225852	−	0.974162i
$65$		−	14.1551i		−	1.75573i
$66$	0.137586	+	0.445144i	0.0169357	+	0.0547934i
$67$	6.76430	−	6.76430i	0.826391	−	0.826391i	−0.160625	−	0.987016i	$-0.551351\pi$
$67$	6.76430	−	6.76430i	0.826391	−	0.826391i	0.987016	+	0.160625i	$0.0513508\pi$
$68$	−5.04432	+	3.44758i	−0.611713	+	0.418081i
$69$	−4.40949	+	4.40949i	−0.530840	+	0.530840i
$70$	−1.16309	−	0.613865i	−0.139016	−	0.0733709i
$71$			1.39591i			0.165664i	0.996564	+	0.0828320i	$0.0263965\pi$
$71$			1.39591i			0.165664i	−0.996564	+	0.0828320i	$0.973604\pi$
$72$	2.21436	+	1.75971i	0.260965	+	0.207384i
$73$		−	7.95811i		−	0.931426i	−0.884936	−	0.465713i	$-0.845798\pi$
$73$		−	7.95811i		−	0.931426i	0.884936	−	0.465713i	$-0.154202\pi$
$74$	−0.213824	+	0.405133i	−0.0248565	+	0.0470958i
$75$	−1.77525	−	1.77525i	−0.204989	−	0.204989i
$76$	1.98406	−	8.48902i	0.227587	−	0.973758i
$77$	0.0790506	−	0.0790506i	0.00900865	−	0.00900865i
$78$	6.97879	−	2.15702i	0.790192	−	0.244235i
$79$	−6.90569			−0.776951			−0.388475	−	0.921459i	$-0.626998\pi$
$79$	−6.90569			−0.776951			−0.388475	+	0.921459i	$0.626998\pi$
$80$	−10.0375	+	4.40657i	−1.12223	+	0.492669i
$81$	−1.00000			−0.111111
$82$	13.4182	−	4.14734i	1.48179	−	0.457998i
$83$	−3.31359	−	3.31359i	−0.363713	−	0.363713i	0.501465	−	0.865178i	$-0.332795\pi$
$83$	−3.31359	−	3.31359i	−0.363713	−	0.363713i	−0.865178	+	0.501465i	$0.832795\pi$
$84$	0.125411	−	0.666972i	0.0136835	−	0.0727726i
$85$	5.92006	+	5.92006i	0.642121	+	0.642121i
$86$	2.51812	−	4.77108i	0.271535	−	0.514479i
$87$	4.10547			0.440153
$88$	−0.105915	−	0.925804i	−0.0112906	−	0.0986910i
$89$	−10.2721			−1.08884			−0.544419	−	0.838813i	$-0.683250\pi$
$89$	−10.2721			−1.08884			−0.544419	+	0.838813i	$0.683250\pi$
$90$	1.80905	−	3.42761i	0.190690	−	0.361302i
$91$	−1.23932	−	1.23932i	−0.129916	−	0.129916i
$92$	10.2968	−	7.03742i	1.07351	−	0.733702i
$93$	6.54052	−	6.54052i	0.678221	−	0.678221i
$94$	5.28460	+	17.0977i	0.545065	+	1.76349i
$95$	−11.9343	−	0.522325i	−1.22444	−	0.0535894i
$96$	−3.70209	−	4.27721i	−0.377843	−	0.436541i
$97$		−	11.3309i		−	1.15048i	−0.817985	−	0.575239i	$-0.804909\pi$
$97$		−	11.3309i		−	1.15048i	0.817985	−	0.575239i	$-0.195091\pi$
$98$	9.30245	−	2.87523i	0.939689	−	0.290442i
$99$	0.232961	+	0.232961i	0.0234134	+	0.0234134i
$100$	2.83325	+	4.14546i	0.283325	+	0.414546i
$101$	6.36684	+	6.36684i	0.633524	+	0.633524i	0.948950	−	0.315426i	$-0.102147\pi$
$101$	6.36684	+	6.36684i	0.633524	+	0.633524i	−0.315426	+	0.948950i	$0.602147\pi$
$102$	−2.01659	+	3.82084i	−0.199672	+	0.378320i
$103$			4.03970i			0.398043i	0.979995	+	0.199022i	$0.0637764\pi$
$103$			4.03970i			0.398043i	−0.979995	+	0.199022i	$0.936224\pi$
$104$	−14.5144	+	1.66050i	−1.42325	+	0.162826i
$105$	−0.929950			−0.0907538
$106$	6.99240	−	13.2485i	0.679162	−	1.28681i
$107$	−7.65160	−	7.65160i	−0.739709	−	0.739709i	0.232813	−	0.972522i	$-0.425207\pi$
$107$	−7.65160	−	7.65160i	−0.739709	−	0.739709i	−0.972522	+	0.232813i	$0.925207\pi$
$108$	1.96556	+	0.369584i	0.189136	+	0.0355633i
$109$	−0.528348	−	0.528348i	−0.0506065	−	0.0506065i	0.681351	−	0.731957i	$-0.261393\pi$
$109$	−0.528348	−	0.528348i	−0.0506065	−	0.0506065i	−0.731957	+	0.681351i	$0.761393\pi$
$110$	−1.21994	+	0.377062i	−0.116316	+	0.0359514i
$111$			0.323924i			0.0307455i
$112$	−0.493005	+	1.26462i	−0.0465846	+	0.119495i
$113$		−	7.06167i		−	0.664306i	−0.943225	−	0.332153i	$-0.892225\pi$
$113$		−	7.06167i		−	0.664306i	0.943225	−	0.332153i	$-0.107775\pi$
$114$	−1.56109	−	5.96347i	−0.146209	−	0.558530i
$115$	−12.0844	−	12.0844i	−1.12688	−	1.12688i
$116$	−8.06953	−	1.51732i	−0.749237	−	0.140879i
$117$	3.65227	−	3.65227i	0.337652	−	0.337652i
$118$	0.599306	+	0.316306i	0.0551706	+	0.0291183i
$119$	1.03664			0.0950284
$120$	−4.82258	+	6.06856i	−0.440239	+	0.553982i
$121$			10.8915i			0.990133i
$122$	4.02759	−	7.63110i	0.364641	−	0.690887i
$123$	7.02227	−	7.02227i	0.633177	−	0.633177i
$124$	−15.2730	+	10.4385i	−1.37156	+	0.937404i
$125$	−4.82413	+	4.82413i	−0.431483	+	0.431483i
$126$	−0.141710	−	0.458485i	−0.0126245	−	0.0408451i
$127$	−15.6817			−1.39152			−0.695762	−	0.718272i	$-0.744933\pi$
$127$	−15.6817			−1.39152			−0.695762	+	0.718272i	$0.744933\pi$
$128$	5.69588	+	9.77533i	0.503449	+	0.864025i
$129$		−	3.81472i		−	0.335867i
$130$	5.91142	+	19.1257i	0.518466	+	1.67743i
$131$	−3.74934	−	3.74934i	−0.327581	−	0.327581i	0.524085	−	0.851666i	$-0.324407\pi$
$131$	−3.74934	−	3.74934i	−0.327581	−	0.327581i	−0.851666	+	0.524085i	$0.824407\pi$
$132$	−0.371799	−	0.543996i	−0.0323609	−	0.0473488i
$133$	−1.09062	+	0.999155i	−0.0945685	+	0.0866377i
$134$	−6.31468	+	11.9644i	−0.545505	+	1.03357i
$135$		−	2.74055i		−	0.235869i
$136$	5.37584	−	6.76478i	0.460975	−	0.580075i
$137$		−	9.73916i		−	0.832073i	−0.909348	−	0.416036i	$-0.863419\pi$
$137$		−	9.73916i		−	0.832073i	0.909348	−	0.416036i	$-0.136581\pi$
$138$	4.11639	−	7.79934i	0.350411	−	0.663924i
$139$	14.8799	−	14.8799i	1.26210	−	1.26210i	0.312025	−	0.950074i	$-0.398993\pi$
$139$	14.8799	−	14.8799i	1.26210	−	1.26210i	0.950074	−	0.312025i	$-0.101007\pi$
$140$	1.82787	+	0.343695i	0.154483	+	0.0290475i
$141$	8.94786	+	8.94786i	0.753546	+	0.753546i
$142$	−0.582955	−	1.88608i	−0.0489205	−	0.158276i
$143$	−1.70167			−0.142301
$144$	−3.72681	−	1.45288i	−0.310568	−	0.121073i
$145$			11.2512i			0.934363i
$146$	3.32344	+	10.7526i	0.275050	+	0.889889i
$147$	4.86833	−	4.86833i	0.401533	−	0.401533i
$148$	0.119717	−	0.636691i	0.00984070	−	0.0523356i
$149$	13.2203	+	13.2203i	1.08305	+	1.08305i	0.996223	+	0.0868289i	$0.0276734\pi$
$149$	13.2203	+	13.2203i	1.08305	+	1.08305i	0.0868289	+	0.996223i	$0.472327\pi$
$150$	3.14000	+	1.65725i	0.256380	+	0.135314i
$151$		−	13.3547i		−	1.08679i	−0.839478	−	0.543394i	$-0.817139\pi$
$151$		−	13.3547i		−	1.08679i	0.839478	−	0.543394i	$-0.182861\pi$
$152$	0.864403	+	12.2985i	0.0701123	+	0.997539i
$153$			3.05495i			0.246978i
$154$	−0.0737961	+	0.139822i	−0.00594666	+	0.0112672i
$155$	17.9246	+	17.9246i	1.43974	+	1.43974i
$156$	−8.52855	+	5.82891i	−0.682831	+	0.466686i
$157$	−14.8513	+	14.8513i	−1.18526	+	1.18526i	−0.206899	+	0.978362i	$0.566337\pi$
$157$	−14.8513	+	14.8513i	−1.18526	+	1.18526i	−0.978362	+	0.206899i	$0.933663\pi$
$158$	9.33060	−	2.88393i	0.742302	−	0.229433i
$159$		−	10.5928i		−	0.840068i
$160$	11.7219	−	10.1457i	0.926696	−	0.802092i
$161$	−2.11605			−0.166768
$162$	1.35115	−	0.417616i	0.106156	−	0.0328110i
$163$	0.409785	+	0.409785i	0.0320968	+	0.0320968i	0.722973	−	0.690876i	$-0.242775\pi$
$163$	0.409785	+	0.409785i	0.0320968	+	0.0320968i	−0.690876	+	0.722973i	$0.742775\pi$
$164$	−16.3980	+	11.2073i	−1.28047	+	0.875146i
$165$	−0.638439	+	0.638439i	−0.0497024	+	0.0497024i
$166$	5.86095	+	3.09333i	0.454898	+	0.240089i
$167$			15.4359i			1.19446i	0.802069	+	0.597232i	$0.203733\pi$
$167$			15.4359i			1.19446i	−0.802069	+	0.597232i	$0.796267\pi$
$168$	0.109090	+	0.953551i	0.00841646	+	0.0735680i
$169$			13.6781i			1.05216i
$170$	−10.4712	−	5.52656i	−0.803104	−	0.423868i
$171$	−2.94449	−	3.21403i	−0.225171	−	0.245783i
$172$	−1.40986	+	7.49804i	−0.107501	+	0.571720i
$173$	6.59642	+	6.59642i	0.501517	+	0.501517i	0.911909	−	0.410392i	$-0.134608\pi$
$173$	6.59642	+	6.59642i	0.501517	+	0.501517i	−0.410392	+	0.911909i	$0.634608\pi$
$174$	−5.54709	+	1.71451i	−0.420524	+	0.129977i
$175$		−	0.851918i		−	0.0643989i
$176$	0.529738	+	1.20666i	0.0399305	+	0.0909558i
$177$	0.479175			0.0360170
$178$	13.8791	−	4.28979i	1.04028	−	0.321534i
$179$	14.9503	−	14.9503i	1.11744	−	1.11744i	0.125325	−	0.992116i	$-0.460003\pi$
$179$	14.9503	−	14.9503i	1.11744	−	1.11744i	0.992116	−	0.125325i	$-0.0399974\pi$
$180$	−1.01286	+	5.38669i	−0.0754943	+	0.401500i
$181$	1.30905	−	1.30905i	0.0973008	−	0.0973008i	−0.656781	−	0.754082i	$-0.728082\pi$
$181$	1.30905	−	1.30905i	0.0973008	−	0.0973008i	0.754082	+	0.656781i	$0.228082\pi$
$182$	2.19207	+	1.15695i	0.162487	+	0.0857586i
$183$		−	6.10144i		−	0.451031i
$184$	−10.9735	+	13.8087i	−0.808978	+	1.01799i
$185$	−0.887728			−0.0652671
$186$	−6.10577	+	11.5686i	−0.447697	+	0.848253i
$187$	0.711684	−	0.711684i	0.0520435	−	0.0520435i
$188$	−14.2805	−	20.8945i	−1.04151	−	1.52389i
$189$	−0.239943	−	0.239943i	−0.0174533	−	0.0174533i
$190$	16.3432	−	4.27824i	1.18566	−	0.310376i
$191$		−	8.11581i		−	0.587239i	−0.955922	−	0.293620i	$-0.905140\pi$
$191$		−	8.11581i		−	0.587239i	0.955922	−	0.293620i	$-0.0948599\pi$
$192$	6.78830	+	4.23308i	0.489903	+	0.305496i
$193$			0.494581i			0.0356007i	0.999842	+	0.0178004i	$0.00566633\pi$
$193$			0.494581i			0.0356007i	−0.999842	+	0.0178004i	$0.994334\pi$
$194$	4.73197	+	15.3097i	0.339736	+	1.09917i
$195$	10.0092	+	10.0092i	0.716774	+	0.716774i
$196$	−11.3682	+	7.76971i	−0.812016	+	0.554979i
$197$	4.44148	+	4.44148i	0.316442	+	0.316442i	0.847399	−	0.530957i	$-0.178167\pi$
$197$	4.44148	+	4.44148i	0.316442	+	0.316442i	−0.530957	+	0.847399i	$0.678167\pi$
$198$	−0.412052	−	0.217476i	−0.0292833	−	0.0154553i
$199$	−24.8033			−1.75826			−0.879129	−	0.476584i	$-0.841875\pi$
$199$	−24.8033			−1.75826			−0.879129	+	0.476584i	$0.841875\pi$
$200$	−5.55935	−	4.41792i	−0.393106	−	0.312394i
$201$			9.56617i			0.674745i
$202$	−11.2614	−	5.94363i	−0.792351	−	0.418193i
$203$	0.985077	+	0.985077i	0.0691389	+	0.0691389i
$204$	1.12906	−	6.00468i	0.0790502	−	0.420412i
$205$	19.2448	+	19.2448i	1.34412	+	1.34412i
$206$	−1.68705	−	5.45823i	−0.117542	−	0.380293i
$207$		−	6.23596i		−	0.433429i
$208$	18.9176	−	8.30503i	1.31170	−	0.575850i
$209$	−0.0627916	+	1.43469i	−0.00434339	+	0.0992398i
$210$	1.25650	−	0.388362i	0.0867066	−	0.0267995i
$211$	−14.2137	+	14.2137i	−0.978514	+	0.978514i	−0.999774	−	0.0212602i	$-0.993232\pi$
$211$	−14.2137	+	14.2137i	−0.978514	+	0.978514i	0.0212602	+	0.999774i	$0.493232\pi$
$212$	−3.91495	+	20.8208i	−0.268880	+	1.42998i
$213$	−0.987057	−	0.987057i	−0.0676321	−	0.0676321i
$214$	13.5339	+	7.14300i	0.925157	+	0.488286i
$215$	10.4544			0.712984
$216$	−2.81010	+	0.321486i	−0.191203	+	0.0218743i
$217$	3.13870			0.213069
$218$	0.934522	+	0.493228i	0.0632938	+	0.0334056i
$219$	5.62723	+	5.62723i	0.380253	+	0.380253i
$220$	1.49084	−	1.01893i	0.100513	−	0.0686963i
$221$	−11.1575	−	11.1575i	−0.750535	−	0.750535i
$222$	−0.135276	−	0.437669i	−0.00907913	−	0.0293744i
$223$	17.3288			1.16042			0.580211	−	0.814466i	$-0.302970\pi$
$223$	17.3288			1.16042			0.580211	+	0.814466i	$0.302970\pi$
$224$	0.137995	−	1.91457i	0.00922020	−	0.127923i
$225$	2.51059			0.167372
$226$	2.94907	+	9.54135i	0.196169	+	0.634681i
$227$	−9.89236	+	9.89236i	−0.656579	+	0.656579i	−0.954569	−	0.297990i	$-0.903684\pi$
$227$	−9.89236	+	9.89236i	−0.656579	+	0.656579i	0.297990	+	0.954569i	$0.403684\pi$
$228$	4.59970	+	7.40559i	0.304623	+	0.490447i
$229$	−0.479502	−	0.479502i	−0.0316864	−	0.0316864i	0.691086	−	0.722772i	$-0.257133\pi$
$229$	−0.479502	−	0.479502i	−0.0316864	−	0.0316864i	−0.722772	+	0.691086i	$0.757133\pi$
$230$	21.3745	+	11.2812i	1.40939	+	0.743858i
$231$			0.111794i			0.00735553i
$232$	11.5368	−	1.31985i	0.757426	−	0.0866524i
$233$			24.6670i			1.61599i	0.589188	+	0.807996i	$0.299448\pi$
$233$			24.6670i			1.61599i	−0.589188	+	0.807996i	$0.700552\pi$
$234$	−3.40950	+	6.45999i	−0.222886	+	0.422303i
$235$	−24.5220	+	24.5220i	−1.59964	+	1.59964i
$236$	−0.941845	−	0.177095i	−0.0613089	−	0.0115279i
$237$	4.88306	−	4.88306i	0.317189	−	0.317189i
$238$	−1.40065	+	0.432917i	−0.0907906	+	0.0280618i
$239$			6.47221i			0.418652i	0.977846	+	0.209326i	$0.0671270\pi$
$239$			6.47221i			0.418652i	−0.977846	+	0.209326i	$0.932873\pi$
$240$	3.98167	−	10.2135i	0.257016	−	0.659279i
$241$		−	7.00779i		−	0.451411i	−0.974196	−	0.225706i	$-0.927531\pi$
$241$		−	7.00779i		−	0.451411i	0.974196	−	0.225706i	$-0.0724688\pi$
$242$	−4.54845	−	14.7160i	−0.292386	−	0.945977i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−2.25500	+	11.9927i	−0.144361	+	0.767755i
$245$	13.3419	+	13.3419i	0.852381	+	0.852381i
$246$	−6.55550	+	12.4207i	−0.417963	+	0.791917i
$247$	22.4926	+	0.984422i	1.43117	+	0.0626373i
$248$	16.2768	−	20.4822i	1.03358	−	1.30062i
$249$	4.68612			0.296971
$250$	4.50347	−	8.53274i	0.284824	−	0.539658i
$251$	3.59508	−	3.59508i	0.226919	−	0.226919i	−0.584485	−	0.811404i	$-0.698703\pi$
$251$	3.59508	−	3.59508i	0.226919	−	0.226919i	0.811404	+	0.584485i	$0.198703\pi$
$252$	0.382942	+	0.560300i	0.0241231	+	0.0352956i
$253$	−1.45273	+	1.45273i	−0.0913326	+	0.0913326i
$254$	21.1883	−	6.54893i	1.32947	−	0.410916i
$255$	−8.37224			−0.524290
$256$	−11.7783	−	10.8292i	−0.736144	−	0.676825i
$257$		−	19.6395i		−	1.22508i	−0.790441	−	0.612538i	$-0.790149\pi$
$257$		−	19.6395i		−	1.22508i	0.790441	−	0.612538i	$-0.209851\pi$
$258$	1.59309	+	5.15424i	0.0991814	+	0.320889i
$259$	−0.0777232	+	0.0777232i	−0.00482949	+	0.00482949i
$260$	−15.9744	−	23.3729i	−0.990690	−	1.44952i
$261$	−2.90301	+	2.90301i	−0.179692	+	0.179692i
$262$	6.63169	+	3.50012i	0.409707	+	0.216238i
$263$	23.6654			1.45927			0.729635	−	0.683837i	$-0.239690\pi$
$263$	23.6654			1.45927			0.729635	+	0.683837i	$0.239690\pi$
$264$	0.729536	+	0.579749i	0.0448998	+	0.0356811i
$265$	29.0302			1.78331
$266$	1.05632	−	1.80546i	0.0647671	−	0.110700i
$267$	7.26346	−	7.26346i	0.444517	−	0.444517i
$268$	3.53550	−	18.8028i	0.215965	−	1.14857i
$269$	−15.7282	−	15.7282i	−0.958967	−	0.958967i	0.0402242	−	0.999191i	$-0.487193\pi$
$269$	−15.7282	−	15.7282i	−0.958967	−	0.958967i	−0.999191	+	0.0402242i	$0.987193\pi$
$270$	1.14450	+	3.70288i	0.0696519	+	0.225350i
$271$		−	13.0296i		−	0.791494i	−0.918360	−	0.395747i	$-0.870486\pi$
$271$		−	13.0296i		−	0.791494i	0.918360	−	0.395747i	$-0.129514\pi$
$272$	−4.43847	+	11.3852i	−0.269122	+	0.690332i
$273$	1.75267			0.106076
$274$	4.06723	+	13.1590i	0.245711	+	0.794966i
$275$	−0.584868	−	0.584868i	−0.0352689	−	0.0352689i
$276$	−2.30471	+	12.2571i	−0.138727	+	0.737792i
$277$	−18.8460	−	18.8460i	−1.13235	−	1.13235i	−0.989786	−	0.142563i	$-0.954466\pi$
$277$	−18.8460	−	18.8460i	−1.13235	−	1.13235i	−0.142563	−	0.989786i	$-0.545534\pi$
$278$	−13.8909	+	26.3191i	−0.833118	+	1.57851i
$279$			9.24970i			0.553765i
$280$	−2.61325	+	0.298966i	−0.156171	+	0.0178666i
$281$	7.43834			0.443734			0.221867	−	0.975077i	$-0.428785\pi$
$281$	7.43834			0.443734			0.221867	+	0.975077i	$0.428785\pi$
$282$	−15.8267	−	8.35310i	−0.942463	−	0.497420i
$283$	6.13258	−	6.13258i	0.364544	−	0.364544i	−0.500939	−	0.865483i	$-0.667012\pi$
$283$	6.13258	−	6.13258i	0.364544	−	0.364544i	0.865483	+	0.500939i	$0.167012\pi$
$284$	1.57531	+	2.30492i	0.0934777	+	0.136772i
$285$	8.80819	−	8.06951i	0.521752	−	0.477996i
$286$	2.29920	−	0.710645i	0.135955	−	0.0420213i
$287$	3.36988			0.198918
$288$	5.64222	+	0.406670i	0.332471	+	0.0239632i
$289$	−7.66726			−0.451016
$290$	−4.69870	−	15.2021i	−0.275917	−	0.892695i
$291$	8.01216	+	8.01216i	0.469681	+	0.469681i
$292$	−8.98090	−	13.1404i	−0.525567	−	0.768982i
$293$	−2.70615	+	2.70615i	−0.158095	+	0.158095i	−0.781722	−	0.623627i	$-0.785658\pi$
$293$	−2.70615	+	2.70615i	−0.158095	+	0.158095i	0.623627	+	0.781722i	$0.285658\pi$
$294$	−4.54473	+	8.61092i	−0.265054	+	0.502199i
$295$			1.31320i			0.0764575i
$296$	0.104137	+	0.910258i	0.00605284	+	0.0529077i
$297$	−0.329456			−0.0191170
$298$	−23.3836	−	12.3416i	−1.35458	−	0.714929i
$299$	22.7754	+	22.7754i	1.31714	+	1.31714i
$300$	−4.93470	−	0.927873i	−0.284905	−	0.0535708i
$301$	0.915313	−	0.915313i	0.0527578	−	0.0527578i
$302$	5.57713	+	18.0441i	0.320928	+	1.03832i
$303$	−9.00407			−0.517270
$304$	−6.30399	−	16.2561i	−0.361558	−	0.932349i
$305$	16.7213			0.957457
$306$	−1.27580	−	4.12769i	−0.0729325	−	0.235964i
$307$	14.8788	−	14.8788i	0.849178	−	0.849178i	−0.140853	−	0.990031i	$-0.544984\pi$
$307$	14.8788	−	14.8788i	0.849178	−	0.849178i	0.990031	+	0.140853i	$0.0449844\pi$
$308$	0.0413175	−	0.219738i	0.00235428	−	0.0125207i
$309$	−2.85650	−	2.85650i	−0.162501	−	0.162501i
$310$	−31.7044	−	16.7331i	−1.80069	−	0.950379i
$311$	−3.88977			−0.220569			−0.110284	−	0.993900i	$-0.535176\pi$
$311$	−3.88977			−0.220569			−0.110284	+	0.993900i	$0.535176\pi$
$312$	9.08907	−	11.4374i	0.514567	−	0.647514i
$313$		−	1.25027i		−	0.0706697i	−0.999376	−	0.0353348i	$-0.988750\pi$
$313$		−	1.25027i		−	0.0706697i	0.999376	−	0.0353348i	$-0.0112498\pi$
$314$	13.8641	−	26.2684i	0.782397	−	1.48241i
$315$	0.657574	−	0.657574i	0.0370501	−	0.0370501i
$316$	−11.4026	+	7.79322i	−0.641448	+	0.438403i
$317$	18.0008	+	18.0008i	1.01103	+	1.01103i	0.999939	+	0.0110868i	$0.00352910\pi$
$317$	18.0008	+	18.0008i	1.01103	+	1.01103i	0.0110868	+	0.999939i	$0.496471\pi$
$318$	4.42375	+	14.3125i	0.248071	+	0.802605i
$319$	1.35257			0.0757295
$320$	−11.6009	+	18.6036i	−0.648513	+	1.03998i
$321$	10.8210			0.603969
$322$	2.85909	−	0.883697i	0.159331	−	0.0492465i
$323$	−9.81870	+	8.99528i	−0.546327	+	0.500511i
$324$	−1.65119	+	1.12852i	−0.0917329	+	0.0626957i
$325$	−9.16933	+	9.16933i	−0.508623	+	0.508623i
$326$	−0.724813	−	0.382547i	−0.0401437	−	0.0211873i
$327$	0.747197			0.0413201
$328$	17.4757	−	21.9908i	0.964934	−	1.21424i
$329$			4.29395i			0.236733i
$330$	0.596002	−	1.12925i	0.0328088	−	0.0621630i
$331$	2.96135	+	2.96135i	0.162771	+	0.162771i	0.783793	−	0.621022i	$-0.213282\pi$
$331$	2.96135	+	2.96135i	0.162771	+	0.162771i	−0.621022	+	0.783793i	$0.713282\pi$
$332$	−9.21082	−	1.73192i	−0.505510	−	0.0950512i
$333$	−0.229049	−	0.229049i	−0.0125518	−	0.0125518i
$334$	−6.44627	−	20.8561i	−0.352724	−	1.14120i
$335$	−26.2165			−1.43236
$336$	−0.545615	−	1.24283i	−0.0297657	−	0.0678019i
$337$		−	0.0425249i		−	0.00231648i	−0.999999	−	0.00115824i	$-0.999631\pi$
$337$		−	0.0425249i		−	0.00231648i	0.999999	−	0.00115824i	$-0.000368679\pi$
$338$	−5.71220	−	18.4811i	−0.310703	−	1.00524i
$339$	4.99336	+	4.99336i	0.271202	+	0.271202i
$340$	16.4561	+	3.09425i	0.892457	+	0.167809i
$341$	2.15482	−	2.15482i	0.116690	−	0.116690i
$342$	5.32067	+	3.11295i	0.287709	+	0.168329i
$343$	4.71155			0.254400
$344$	−1.22638	−	10.7197i	−0.0661218	−	0.577969i
$345$	17.0899			0.920091
$346$	−11.6675	−	6.15796i	−0.627249	−	0.331054i
$347$	−8.69502	+	8.69502i	−0.466773	+	0.466773i	−0.900868	−	0.434094i	$-0.857069\pi$
$347$	−8.69502	+	8.69502i	−0.466773	+	0.466773i	0.434094	+	0.900868i	$0.357069\pi$
$348$	6.77892	−	4.63311i	0.363388	−	0.248361i
$349$	−10.8700	+	10.8700i	−0.581858	+	0.581858i	−0.935414	−	0.353555i	$-0.884973\pi$
$349$	−10.8700	+	10.8700i	−0.581858	+	0.581858i	0.353555	+	0.935414i	$0.384973\pi$
$350$	0.355775	+	1.15107i	0.0190170	+	0.0615271i
$351$			5.16509i			0.275692i
$352$	−1.21968	−	1.40915i	−0.0650090	−	0.0751081i
$353$	−18.8516			−1.00337			−0.501686	−	0.865050i	$-0.667287\pi$
$353$	−18.8516			−1.00337			−0.501686	+	0.865050i	$0.667287\pi$
$354$	−0.647435	+	0.200111i	−0.0344108	+	0.0106358i
$355$	2.70508	−	2.70508i	0.143570	−	0.143570i
$356$	−16.9612	+	11.5923i	−0.898942	+	0.614389i
$357$	−0.733013	+	0.733013i	−0.0387952	+	0.0387952i
$358$	−13.9566	+	26.4436i	−0.737629	+	1.39759i
$359$	−14.7830			−0.780219			−0.390110	−	0.920768i	$-0.627563\pi$
$359$	−14.7830			−0.780219			−0.390110	+	0.920768i	$0.627563\pi$
$360$	−0.881046	−	7.70120i	−0.0464352	−	0.405889i
$361$	1.65995	−	18.9273i	0.0873658	−	0.996176i
$362$	−1.22204	+	2.31540i	−0.0642288	+	0.121694i
$363$	−7.70142	−	7.70142i	−0.404220	−	0.404220i
$364$	−3.44497	−	0.647759i	−0.180565	−	0.0339518i
$365$	−15.4217	+	15.4217i	−0.807208	+	0.807208i
$366$	2.54806	+	8.24394i	0.133189	+	0.430918i
$367$			14.7136i			0.768043i	0.923324	+	0.384021i	$0.125461\pi$
$367$			14.7136i			0.768043i	−0.923324	+	0.384021i	$0.874539\pi$
$368$	9.06008	−	23.2403i	0.472290	−	1.21148i
$369$			9.93099i			0.516987i
$370$	1.19945	−	0.370730i	0.0623565	−	0.0192733i
$371$	2.54168	−	2.54168i	0.131957	−	0.131957i
$372$	3.41854	−	18.1808i	0.177243	−	0.942630i
$373$	−16.5325	+	16.5325i	−0.856022	+	0.856022i	−0.990867	−	0.134845i	$-0.956946\pi$
$373$	−16.5325	+	16.5325i	−0.856022	+	0.856022i	0.134845	+	0.990867i	$0.456946\pi$
$374$	−0.664378	+	1.25880i	−0.0343542	+	0.0650910i
$375$		−	6.82235i		−	0.352305i
$376$	28.0210	+	22.2678i	1.44507	+	1.14837i
$377$		−	21.2051i		−	1.09212i
$378$	0.424402	+	0.223994i	0.0218289	+	0.0115210i
$379$	−2.24349	−	2.24349i	−0.115240	−	0.115240i	0.647135	−	0.762375i	$-0.275967\pi$
$379$	−2.24349	−	2.24349i	−0.115240	−	0.115240i	−0.762375	+	0.647135i	$0.775967\pi$
$380$	−20.2953	+	12.6057i	−1.04113	+	0.646659i
$381$	11.0886	−	11.0886i	0.568087	−	0.568087i
$382$	3.38930	+	10.9656i	0.173411	+	0.561051i
$383$	−0.101664			−0.00519477			−0.00259738	−	0.999997i	$-0.500827\pi$
$383$	−0.101664			−0.00519477			−0.00259738	+	0.999997i	$0.500827\pi$
$384$	−10.9398	−	2.88461i	−0.558269	−	0.147204i
$385$	−0.306378			−0.0156145
$386$	−0.206545	−	0.668252i	−0.0105129	−	0.0340131i
$387$	2.69741	+	2.69741i	0.137117	+	0.137117i
$388$	−12.7872	−	18.7095i	−0.649170	−	0.949831i
$389$	−24.2541	−	24.2541i	−1.22973	−	1.22973i	−0.964066	−	0.265664i	$-0.914409\pi$
$389$	−24.2541	−	24.2541i	−1.22973	−	1.22973i	−0.265664	−	0.964066i	$-0.585591\pi$
$390$	−17.7039	−	9.34389i	−0.896472	−	0.473146i
$391$	−19.0506			−0.963429
$392$	12.1154	−	15.2456i	0.611919	−	0.770018i
$393$	5.30236			0.267469
$394$	−7.85593	−	4.14626i	−0.395776	−	0.208885i
$395$	13.3822	+	13.3822i	0.673334	+	0.673334i
$396$	0.647564	+	0.121762i	0.0325413	+	0.00611876i
$397$	−10.3479	+	10.3479i	−0.519348	+	0.519348i	−0.917374	−	0.398026i	$-0.869695\pi$
$397$	−10.3479	+	10.3479i	−0.519348	+	0.519348i	0.398026	+	0.917374i	$0.369695\pi$
$398$	33.5129	−	10.3583i	1.67985	−	0.519213i
$399$	0.0646735	−	1.47769i	0.00323772	−	0.0739771i
$400$	9.35649	+	3.64757i	0.467825	+	0.182379i
$401$		−	12.7126i		−	0.634836i	−0.948286	−	0.317418i	$-0.897184\pi$
$401$		−	12.7126i		−	0.634836i	0.948286	−	0.317418i	$-0.102816\pi$
$402$	−3.99499	−	12.9253i	−0.199252	−	0.644655i
$403$	−33.7824	−	33.7824i	−1.68282	−	1.68282i
$404$	17.6980	+	3.32776i	0.880508	+	0.165562i
$405$	1.93786	+	1.93786i	0.0962929	+	0.0962929i
$406$	−1.74237	−	0.919599i	−0.0864723	−	0.0456389i
$407$			0.106719i			0.00528985i
$408$	0.982124	+	8.58471i	0.0486224	+	0.425007i
$409$	−30.4457			−1.50544			−0.752722	−	0.658338i	$-0.771260\pi$
$409$	−30.4457			−1.50544			−0.752722	+	0.658338i	$0.771260\pi$
$410$	−34.0396	−	17.9656i	−1.68109	−	0.887260i
$411$	6.88663	+	6.88663i	0.339692	+	0.339692i
$412$	4.55889	+	6.67032i	0.224600	+	0.328623i
$413$	0.114974	+	0.114974i	0.00565752	+	0.00565752i
$414$	2.60424	+	8.42570i	0.127991	+	0.414100i
$415$			12.8425i			0.630414i
$416$	−22.0921	+	19.1216i	−1.08316	+	0.937514i
$417$			21.0434i			1.03050i
$418$	−0.514311	−	1.96470i	−0.0251558	−	0.0960968i
$419$	15.3811	+	15.3811i	0.751416	+	0.751416i	0.974743	−	0.223328i	$-0.0716920\pi$
$419$	15.3811	+	15.3811i	0.751416	+	0.751416i	−0.223328	+	0.974743i	$0.571692\pi$
$420$	−1.53553	+	1.04947i	−0.0749260	+	0.0512088i
$421$	3.39338	−	3.39338i	0.165383	−	0.165383i	−0.619563	−	0.784947i	$-0.712690\pi$
$421$	3.39338	−	3.39338i	0.165383	−	0.165383i	0.784947	+	0.619563i	$0.212690\pi$
$422$	13.2689	−	25.1407i	0.645922	−	1.22383i
$423$	−12.6542			−0.615268
$424$	−3.40545	−	29.7669i	−0.165383	−	1.44561i
$425$		−	7.66972i		−	0.372036i
$426$	1.74587	+	0.921448i	0.0845877	+	0.0446443i
$427$	1.46400	−	1.46400i	0.0708477	−	0.0708477i
$428$	−21.2693	−	3.99927i	−1.02809	−	0.193312i
$429$	1.20326	−	1.20326i	0.0580940	−	0.0580940i
$430$	−14.1254	+	4.36593i	−0.681189	+	0.210544i
$431$	20.3316			0.979339			0.489669	−	0.871908i	$-0.337117\pi$
$431$	20.3316			0.979339			0.489669	+	0.871908i	$0.337117\pi$
$432$	3.66259	−	1.60792i	0.176217	−	0.0773610i
$433$		−	32.6746i		−	1.57024i	−0.619344	−	0.785120i	$-0.712601\pi$
$433$		−	32.6746i		−	1.57024i	0.619344	−	0.785120i	$-0.287399\pi$
$434$	−4.24084	+	1.31077i	−0.203567	+	0.0629191i
$435$	−7.95582	−	7.95582i	−0.381452	−	0.381452i
$436$	−1.46866	−	0.276152i	−0.0703359	−	0.0132253i
$437$	20.0426	−	18.3617i	0.958766	−	0.878361i
$438$	−9.95324	−	5.25319i	−0.475584	−	0.251007i
$439$		−	7.80679i		−	0.372598i	−0.982493	−	0.186299i	$-0.940351\pi$
$439$		−	7.80679i		−	0.372598i	0.982493	−	0.186299i	$-0.0596493\pi$
$440$	−1.58883	+	1.99933i	−0.0757444	+	0.0953141i
$441$			6.88486i			0.327850i
$442$	19.7350	+	10.4159i	0.938697	+	0.495432i
$443$	15.7445	−	15.7445i	0.748042	−	0.748042i	−0.226069	−	0.974111i	$-0.572588\pi$
$443$	15.7445	−	15.7445i	0.748042	−	0.748042i	0.974111	+	0.226069i	$0.0725875\pi$
$444$	0.365555	+	0.534861i	0.0173485	+	0.0253834i
$445$	19.9058	+	19.9058i	0.943628	+	0.943628i
$446$	−23.4137	+	7.23679i	−1.10867	+	0.342672i
$447$	−18.6964			−0.884308
$448$	0.613106	+	2.64450i	0.0289665	+	0.124941i
$449$		−	3.00383i		−	0.141760i	−0.997485	−	0.0708798i	$-0.977419\pi$
$449$		−	3.00383i		−	0.141760i	0.997485	−	0.0708798i	$-0.0225807\pi$
$450$	−3.39217	+	1.04846i	−0.159908	+	0.0494250i
$451$	2.31353	−	2.31353i	0.108940	−	0.108940i
$452$	−7.96925	−	11.6602i	−0.374842	−	0.548449i
$453$	9.44318	+	9.44318i	0.443679	+	0.443679i
$454$	9.23481	−	17.4972i	0.433411	−	0.821186i
$455$			4.80327i			0.225181i
$456$	−9.30757	−	8.08512i	−0.435867	−	0.378620i
$457$		−	3.88665i		−	0.181810i	−0.995860	−	0.0909049i	$-0.971024\pi$
$457$		−	3.88665i		−	0.181810i	0.995860	−	0.0909049i	$-0.0289759\pi$
$458$	0.848125	+	0.447629i	0.0396303	+	0.0209163i
$459$	−2.16018	−	2.16018i	−0.100828	−	0.100828i
$460$	−33.5912	−	6.31617i	−1.56620	−	0.294493i
$461$	22.2950	−	22.2950i	1.03838	−	1.03838i	0.0391493	−	0.999233i	$-0.487535\pi$
$461$	22.2950	−	22.2950i	1.03838	−	1.03838i	0.999233	−	0.0391493i	$-0.0124648\pi$
$462$	−0.0466872	−	0.151051i	−0.00217208	−	0.00702751i
$463$			32.5456i			1.51252i	0.654270	+	0.756261i	$0.272976\pi$
$463$			32.5456i			1.51252i	−0.654270	+	0.756261i	$0.727024\pi$
$464$	−15.0367	+	6.60126i	−0.698060	+	0.306456i
$465$	−25.3492			−1.17554
$466$	−10.3014	−	33.3288i	−0.477201	−	1.54393i
$467$	12.0990	+	12.0990i	0.559877	+	0.559877i	0.929272	−	0.369395i	$-0.120435\pi$
$467$	12.0990	+	12.0990i	0.559877	+	0.559877i	−0.369395	+	0.929272i	$0.620435\pi$
$468$	1.90893	−	10.1523i	0.0882405	−	0.469288i
$469$	−2.29533	+	2.29533i	−0.105989	+	0.105989i
$470$	22.8920	−	43.3736i	1.05593	−	2.00068i
$471$		−	21.0029i		−	0.967762i
$472$	1.34653	−	0.154048i	0.0619790	−	0.00709063i
$473$		−	1.25678i		−	0.0577869i
$474$	−4.55848	+	8.63697i	−0.209378	+	0.396709i
$475$	7.39240	+	8.06910i	0.339187	+	0.370236i
$476$	1.71169	−	1.16987i	0.0784551	−	0.0536208i
$477$	7.49028	+	7.49028i	0.342956	+	0.342956i
$478$	−2.70290	−	8.74490i	−0.123628	−	0.399982i
$479$		−	17.1319i		−	0.782778i	−0.920225	−	0.391389i	$-0.871995\pi$
$479$		−	17.1319i		−	0.782778i	0.920225	−	0.391389i	$-0.128005\pi$
$480$	−1.11450	+	15.4628i	−0.0508696	+	0.705775i
$481$	1.67310			0.0762866
$482$	2.92657	+	9.46855i	0.133302	+	0.431281i
$483$	1.49627	−	1.49627i	0.0680828	−	0.0680828i
$484$	12.2912	+	17.9839i	0.558693	+	0.817450i
$485$	−21.9577	+	21.9577i	−0.997047	+	0.997047i
$486$	−0.660105	+	1.25070i	−0.0299430	+	0.0567331i
$487$		−	16.9325i		−	0.767285i	−0.923482	−	0.383643i	$-0.874669\pi$
$487$		−	16.9325i		−	0.767285i	0.923482	−	0.383643i	$-0.125331\pi$
$488$	−1.96153	−	17.1456i	−0.0887941	−	0.776147i
$489$	−0.579524			−0.0262070
$490$	−23.5986	−	12.4550i	−1.06608	−	0.562661i
$491$	4.15401	−	4.15401i	0.187468	−	0.187468i	−0.607133	−	0.794600i	$-0.707680\pi$
$491$	4.15401	−	4.15401i	0.187468	−	0.187468i	0.794600	+	0.607133i	$0.207680\pi$
$492$	3.67034	−	19.5199i	0.165472	−	0.880025i
$493$	8.86854	+	8.86854i	0.399419	+	0.399419i
$494$	−30.8018	+	8.06316i	−1.38584	+	0.362779i
$495$		−	0.902890i		−	0.0405819i
$496$	−13.4387	+	34.4719i	−0.603414	+	1.54783i
$497$		−	0.473674i		−	0.0212472i
$498$	−6.33163	+	1.95700i	−0.283727	+	0.0876953i
$499$	−1.39169	−	1.39169i	−0.0623006	−	0.0623006i	0.675270	−	0.737571i	$-0.264027\pi$
$499$	−1.39169	−	1.39169i	−0.0623006	−	0.0623006i	−0.737571	+	0.675270i	$0.764027\pi$
$500$	−2.52143	+	13.4097i	−0.112762	+	0.599700i
$501$	−10.9148	−	10.9148i	−0.487638	−	0.487638i
$502$	−3.35611	+	6.35884i	−0.149791	+	0.283809i
$503$	13.3363			0.594636			0.297318	−	0.954778i	$-0.403908\pi$
$503$	13.3363			0.594636			0.297318	+	0.954778i	$0.403908\pi$
$504$	−0.751400	−	0.597124i	−0.0334700	−	0.0265980i
$505$		−	24.6761i		−	1.09807i
$506$	1.35617	−	2.56954i	0.0602891	−	0.114230i
$507$	−9.67188	−	9.67188i	−0.429543	−	0.429543i
$508$	−25.8935	+	17.6971i	−1.14884	+	0.785183i
$509$	1.72191	+	1.72191i	0.0763223	+	0.0763223i	0.744237	−	0.667915i	$-0.232813\pi$
$509$	1.72191	+	1.72191i	0.0763223	+	0.0763223i	−0.667915	+	0.744237i	$0.732813\pi$
$510$	11.3121	−	3.49638i	0.500909	−	0.154822i
$511$			2.70043i			0.119460i
$512$	20.4367	+	9.71303i	0.903181	+	0.429259i
$513$	4.35473	+	0.190592i	0.192266	+	0.00841483i
$514$	8.20176	+	26.5358i	0.361764	+	1.17044i
$515$	7.82836	−	7.82836i	0.344959	−	0.344959i
$516$	−4.30499	−	6.29883i	−0.189517	−	0.277291i
$517$	2.94793	+	2.94793i	0.129650	+	0.129650i
$518$	0.0725569	−	0.137474i	0.00318797	−	0.00604026i
$519$	−9.32875			−0.409487
$520$	31.3446	+	24.9090i	1.37455	+	1.09233i
$521$	40.5684			1.77733			0.888666	−	0.458555i	$-0.151633\pi$
$521$	40.5684			1.77733			0.888666	+	0.458555i	$0.151633\pi$
$522$	2.71004	−	5.13473i	0.118615	−	0.224741i
$523$	23.1394	+	23.1394i	1.01181	+	1.01181i	0.999929	+	0.0118854i	$0.00378334\pi$
$523$	23.1394	+	23.1394i	1.01181	+	1.01181i	0.0118854	+	0.999929i	$0.496217\pi$
$524$	−10.4221	−	1.95967i	−0.455291	−	0.0856086i
$525$	0.602397	+	0.602397i	0.0262908	+	0.0262908i
$526$	−31.9754	+	9.88305i	−1.39419	+	0.430921i
$527$	28.2574			1.23091
$528$	−1.22782	−	0.478659i	−0.0534341	−	0.0208310i
$529$	15.8872			0.690749
$530$	−39.2240	+	12.1235i	−1.70378	+	0.526610i
$531$	−0.338828	+	0.338828i	−0.0147039	+	0.0147039i
$532$	−0.673251	+	2.88058i	−0.0291891	+	0.124889i
$533$	−36.2706	−	36.2706i	−1.57106	−	1.57106i
$534$	−6.78066	+	12.8473i	−0.293428	+	0.555959i
$535$			29.6554i			1.28212i
$536$	3.07539	+	26.8819i	0.132836	+	1.16112i
$537$			21.1430i			0.912387i
$538$	27.8195	+	14.6828i	1.19938	+	0.633019i
$539$	1.60390	−	1.60390i	0.0690849	−	0.0690849i
$540$	−3.09277	−	4.52517i	−0.133091	−	0.194732i
$541$	12.0422	−	12.0422i	0.517733	−	0.517733i	−0.399152	−	0.916885i	$-0.630695\pi$
$541$	12.0422	−	12.0422i	0.517733	−	0.517733i	0.916885	+	0.399152i	$0.130695\pi$
$542$	5.44139	+	17.6049i	0.233728	+	0.756197i
$543$			1.85127i			0.0794457i
$544$	1.24236	−	17.2367i	0.0532656	−	0.739018i
$545$			2.04773i			0.0877149i
$546$	−2.36811	+	0.731944i	−0.101346	+	0.0313243i
$547$	6.87638	−	6.87638i	0.294013	−	0.294013i	−0.544650	−	0.838663i	$-0.683338\pi$
$547$	6.87638	−	6.87638i	0.294013	−	0.294013i	0.838663	+	0.544650i	$0.183338\pi$
$548$	−10.9909	−	16.0812i	−0.469506	−	0.686956i
$549$	4.31437	+	4.31437i	0.184133	+	0.184133i
$550$	1.03449	+	0.545992i	0.0441109	+	0.0232812i
$551$	−17.8782	−	0.782468i	−0.761637	−	0.0333343i
$552$	−2.00477	−	17.5237i	−0.0853288	−	0.745857i
$553$	2.34331			0.0996476
$554$	33.3342	+	17.5933i	1.41623	+	0.747470i
$555$	0.627719	−	0.627719i	0.0266452	−	0.0266452i
$556$	7.77731	−	41.3620i	0.329831	−	1.75414i
$557$	19.2708	−	19.2708i	0.816529	−	0.816529i	−0.169074	−	0.985603i	$-0.554078\pi$
$557$	19.2708	−	19.2708i	0.816529	−	0.816529i	0.985603	+	0.169074i	$0.0540778\pi$
$558$	−3.86282	−	12.4977i	−0.163526	−	0.529069i
$559$	−19.7033			−0.833363
$560$	3.40603	−	1.49528i	0.143931	−	0.0631872i
$561$			1.00647i			0.0424933i
$562$	−10.0503	+	3.10637i	−0.423945	+	0.131034i
$563$	8.75849	−	8.75849i	0.369126	−	0.369126i	−0.498032	−	0.867158i	$-0.665944\pi$
$563$	8.75849	−	8.75849i	0.369126	−	0.369126i	0.867158	+	0.498032i	$0.165944\pi$
$564$	24.8725	+	4.67679i	1.04732	+	0.196928i
$565$	−13.6845	+	13.6845i	−0.575712	+	0.575712i
$566$	−5.72495	+	10.8471i	−0.240637	+	0.455937i
$567$	0.339330			0.0142505
$568$	−3.09105	−	2.45640i	−0.129698	−	0.103068i
$569$	−0.126784			−0.00531506			−0.00265753	−	0.999996i	$-0.500846\pi$
$569$	−0.126784			−0.00531506			−0.00265753	+	0.999996i	$0.500846\pi$
$570$	−8.53119	+	14.5815i	−0.357332	+	0.610753i
$571$	−4.82543	+	4.82543i	−0.201938	+	0.201938i	−0.800830	−	0.598892i	$-0.795608\pi$
$571$	−4.82543	+	4.82543i	−0.201938	+	0.201938i	0.598892	+	0.800830i	$0.295608\pi$
$572$	−2.80978	+	1.92037i	−0.117483	+	0.0802947i
$573$	5.73874	+	5.73874i	0.239739	+	0.239739i
$574$	−4.55321	+	1.40732i	−0.190047	+	0.0587404i
$575$			15.6559i			0.652897i
$576$	−7.79329	+	1.80681i	−0.324721	+	0.0752839i
$577$	−5.58586			−0.232542			−0.116271	−	0.993217i	$-0.537094\pi$
$577$	−5.58586			−0.232542			−0.116271	+	0.993217i	$0.537094\pi$
$578$	10.3596	−	3.20198i	0.430902	−	0.133185i
$579$	−0.349722	−	0.349722i	−0.0145339	−	0.0145339i
$580$	12.6973	+	18.5779i	0.527225	+	0.771407i
$581$	1.12440	+	1.12440i	0.0466480	+	0.0466480i
$582$	−14.1716	−	7.47959i	−0.587432	−	0.310039i
$583$		−	3.48988i		−	0.144536i
$584$	17.6221	+	14.0040i	0.729210	+	0.579490i
$585$	−14.1551			−0.585243
$586$	2.52628	−	4.78655i	0.104360	−	0.197730i
$587$	5.92169	−	5.92169i	0.244414	−	0.244414i	−0.574259	−	0.818674i	$-0.694710\pi$
$587$	5.92169	−	5.92169i	0.244414	−	0.244414i	0.818674	+	0.574259i	$0.194710\pi$
$588$	2.54453	−	13.5326i	0.104935	−	0.558073i
$589$	−29.7288	+	27.2356i	−1.22495	+	1.12223i
$590$	−0.548414	−	1.77433i	−0.0225778	−	0.0730478i
$591$	−6.28120			−0.258374
$592$	−0.520843	−	1.18640i	−0.0214065	−	0.0487608i
$593$	16.3832			0.672779			0.336389	−	0.941723i	$-0.390794\pi$
$593$	16.3832			0.672779			0.336389	+	0.941723i	$0.390794\pi$
$594$	0.445144	−	0.137586i	0.0182645	−	0.00564524i
$595$	−2.00886	−	2.00886i	−0.0823551	−	0.0823551i
$596$	36.7488	+	6.90989i	1.50529	+	0.283040i
$597$	17.5386	−	17.5386i	0.717806	−	0.717806i
$598$	−40.2843	−	21.2615i	−1.64735	−	0.869448i
$599$			38.0726i			1.55560i	0.628510	+	0.777802i	$0.283665\pi$
$599$			38.0726i			1.55560i	−0.628510	+	0.777802i	$0.716335\pi$
$600$	7.05499	−	0.807118i	0.288019	−	0.0329505i
$601$	−33.1595			−1.35260			−0.676301	−	0.736625i	$-0.736418\pi$
$601$	−33.1595			−1.35260			−0.676301	+	0.736625i	$0.736418\pi$
$602$	−0.854473	+	1.61897i	−0.0348257	+	0.0659844i
$603$	−6.76430	−	6.76430i	−0.275464	−	0.275464i
$604$	−15.0710	−	22.0511i	−0.613232	−	0.897248i
$605$	21.1061	−	21.1061i	0.858085	−	0.858085i
$606$	12.1658	−	3.76025i	0.494203	−	0.152750i
$607$	4.50158			0.182713			0.0913567	−	0.995818i	$-0.470880\pi$
$607$	4.50158			0.182713			0.0913567	+	0.995818i	$0.470880\pi$
$608$	15.3064	+	19.3317i	0.620757	+	0.784003i
$609$	−1.39311			−0.0564517
$610$	−22.5929	+	6.98308i	−0.914759	+	0.282737i
$611$	46.2165	−	46.2165i	1.86972	−	1.86972i
$612$	3.44758	+	5.04432i	0.139360	+	0.203904i
$613$	10.9137	+	10.9137i	0.440802	+	0.440802i	0.892282	−	0.451479i	$-0.149104\pi$
$613$	10.9137	+	10.9137i	0.440802	+	0.440802i	−0.451479	+	0.892282i	$0.649104\pi$
$614$	−13.8898	+	26.3171i	−0.560547	+	1.06207i
$615$	−27.2163			−1.09747
$616$	0.0359403	+	0.314153i	0.00144808	+	0.0126576i
$617$			8.25703i			0.332415i	0.986091	+	0.166208i	$0.0531522\pi$
$617$			8.25703i			0.332415i	−0.986091	+	0.166208i	$0.946848\pi$
$618$	5.05247	+	2.66663i	0.203240	+	0.107267i
$619$	5.33298	−	5.33298i	0.214351	−	0.214351i	−0.591762	−	0.806113i	$-0.701567\pi$
$619$	5.33298	−	5.33298i	0.214351	−	0.214351i	0.806113	+	0.591762i	$0.201567\pi$
$620$	49.8253	+	9.36867i	2.00103	+	0.376255i
$621$	4.40949	+	4.40949i	0.176947	+	0.176947i
$622$	5.25565	−	1.62443i	0.210733	−	0.0651339i
$623$	3.48563			0.139649
$624$	−7.50423	+	19.2493i	−0.300410	+	0.770589i
$625$	31.2499			1.25000
$626$	0.522135	+	1.68930i	0.0208687	+	0.0675182i
$627$	−0.970081	−	1.05888i	−0.0387413	−	0.0422876i
$628$	−7.76234	+	41.2823i	−0.309751	+	1.64734i
$629$	−0.699734	+	0.699734i	−0.0279002	+	0.0279002i
$630$	−0.613865	+	1.16309i	−0.0244570	+	0.0463387i
$631$	40.9332			1.62952			0.814762	−	0.579795i	$-0.196867\pi$
$631$	40.9332			1.62952			0.814762	+	0.579795i	$0.196867\pi$
$632$	12.1520	−	15.2917i	0.483382	−	0.608271i
$633$		−	20.1013i		−	0.798953i
$634$	−31.8391	−	16.8043i	−1.26449	−	0.667383i
$635$	30.3889	+	30.3889i	1.20595	+	1.20595i
$636$	−11.9543	−	17.4908i	−0.474017	−	0.693557i
$637$	−25.1453	−	25.1453i	−0.996294	−	0.996294i
$638$	−1.82752	+	0.564857i	−0.0723523	+	0.0223629i
$639$	1.39591			0.0552213
$640$	7.90539	−	29.9810i	0.312488	−	1.18510i
$641$		−	33.6793i		−	1.33025i	−0.746731	−	0.665126i	$-0.768378\pi$
$641$		−	33.6793i		−	1.33025i	0.746731	−	0.665126i	$-0.231622\pi$
$642$	−14.6208	+	4.51903i	−0.577035	+	0.178352i
$643$	−5.89765	−	5.89765i	−0.232581	−	0.232581i	0.581188	−	0.813769i	$-0.302588\pi$
$643$	−5.89765	−	5.89765i	−0.232581	−	0.232581i	−0.813769	+	0.581188i	$0.802588\pi$
$644$	−3.49401	+	2.38801i	−0.137683	+	0.0941007i
$645$	−7.39238	+	7.39238i	−0.291075	+	0.291075i
$646$	9.50993	−	16.2544i	0.374163	−	0.639520i
$647$	−28.0568			−1.10303			−0.551513	−	0.834166i	$-0.685949\pi$
$647$	−28.0568			−1.10303			−0.551513	+	0.834166i	$0.685949\pi$
$648$	1.75971	−	2.21436i	0.0691281	−	0.0869884i
$649$	0.157867			0.00619683
$650$	8.55985	−	16.2184i	0.335745	−	0.636137i
$651$	−2.21940	+	2.21940i	−0.0869850	+	0.0869850i
$652$	1.13909	+	0.214183i	0.0446100	+	0.00838804i
$653$	8.88894	−	8.88894i	0.347851	−	0.347851i	−0.511458	−	0.859309i	$-0.670894\pi$
$653$	8.88894	−	8.88894i	0.347851	−	0.347851i	0.859309	+	0.511458i	$0.170894\pi$
$654$	−1.00957	+	0.312042i	−0.0394774	+	0.0122018i
$655$			14.5314i			0.567787i
$656$	−14.4285	+	37.0110i	−0.563338	+	1.44504i
$657$	−7.95811			−0.310475
$658$	−1.79322	−	5.80175i	−0.0699071	−	0.226176i
$659$	−12.1000	+	12.1000i	−0.471348	+	0.471348i	−0.902351	−	0.431002i	$-0.858160\pi$
$659$	−12.1000	+	12.1000i	−0.471348	+	0.471348i	0.431002	+	0.902351i	$0.358160\pi$
$660$	−0.333694	+	1.77468i	−0.0129890	+	0.0690793i
$661$	−10.7877	+	10.7877i	−0.419594	+	0.419594i	−0.885064	−	0.465470i	$-0.845885\pi$
$661$	−10.7877	+	10.7877i	−0.419594	+	0.419594i	0.465470	+	0.885064i	$0.345885\pi$
$662$	−5.23793	−	2.76451i	−0.203578	−	0.107446i
$663$	15.7791			0.612809
$664$	13.1684	−	1.50652i	0.511035	−	0.0584643i
$665$	4.04968	+	0.177241i	0.157040	+	0.00687310i
$666$	0.405133	+	0.213824i	0.0156986	+	0.00828551i
$667$	−18.1030	−	18.1030i	−0.700952	−	0.700952i
$668$	17.4197	+	25.4876i	0.673989	+	0.986145i
$669$	−12.2533	+	12.2533i	−0.473740	+	0.473740i
$670$	35.4223	−	10.9484i	1.36848	−	0.422975i
$671$		−	2.01016i		−	0.0776013i
$672$	1.25623	+	1.45139i	0.0484602	+	0.0559884i
$673$			29.5361i			1.13853i	0.822153	+	0.569267i	$0.192773\pi$
$673$			29.5361i			1.13853i	−0.822153	+	0.569267i	$0.807227\pi$
$674$	0.0177591	+	0.0574574i	0.000684055	+	0.00221318i
$675$	−1.77525	+	1.77525i	−0.0683295	+	0.0683295i
$676$	15.4360	+	22.5852i	0.593694	+	0.868661i
$677$	25.2746	−	25.2746i	0.971381	−	0.971381i	−0.0282202	−	0.999602i	$-0.508984\pi$
$677$	25.2746	−	25.2746i	0.971381	−	0.971381i	0.999602	+	0.0282202i	$0.00898397\pi$
$678$	−8.83206	−	4.66145i	−0.339193	−	0.179022i
$679$			3.84492i			0.147554i
$680$	−23.5268	+	2.69155i	−0.902211	+	0.103216i
$681$		−	13.9899i		−	0.536095i
$682$	−2.01158	+	3.81136i	−0.0770276	+	0.145944i
$683$	−7.57582	−	7.57582i	−0.289881	−	0.289881i	0.547152	−	0.837033i	$-0.315712\pi$
$683$	−7.57582	−	7.57582i	−0.289881	−	0.289881i	−0.837033	+	0.547152i	$0.815712\pi$
$684$	−8.48902	−	1.98406i	−0.324586	−	0.0758624i
$685$	−18.8731	+	18.8731i	−0.721105	+	0.721105i
$686$	−6.36599	+	1.96762i	−0.243055	+	0.0751241i
$687$	0.678118			0.0258718
$688$	6.13375	+	13.9718i	0.233847	+	0.532669i
$689$	−54.7130			−2.08440
$690$	−23.0910	+	7.13704i	−0.879060	+	0.271702i
$691$	−28.0451	−	28.0451i	−1.06689	−	1.06689i	−0.997597	−	0.0692887i	$-0.977927\pi$
$691$	−28.0451	−	28.0451i	−1.06689	−	1.06689i	−0.0692887	−	0.997597i	$-0.522073\pi$
$692$	18.3362	+	3.44776i	0.697037	+	0.131064i
$693$	−0.0790506	−	0.0790506i	−0.00300288	−	0.00300288i
$694$	8.11707	−	15.3794i	0.308120	−	0.583795i
$695$	−57.6704			−2.18756
$696$	−7.22445	+	9.09100i	−0.273842	+	0.344594i
$697$	30.3387			1.14916
$698$	10.1475	−	19.2265i	0.384088	−	0.727733i
$699$	−17.4422	−	17.4422i	−0.659726	−	0.659726i
$700$	−0.961408	−	1.40668i	−0.0363378	−	0.0531675i
$701$	−4.61647	+	4.61647i	−0.174362	+	0.174362i	−0.788893	−	0.614531i	$-0.789345\pi$
$701$	−4.61647	+	4.61647i	−0.174362	+	0.174362i	0.614531	+	0.788893i	$0.289345\pi$
$702$	−2.15702	−	6.97879i	−0.0814116	−	0.263397i
$703$	0.0617372	−	1.41060i	0.00232846	−	0.0532019i
$704$	2.23645	+	1.39461i	0.0842893	+	0.0525615i
$705$		−	34.6794i		−	1.30610i
$706$	25.4713	−	7.87275i	0.958626	−	0.296295i
$707$	−2.16046	−	2.16046i	−0.0812525	−	0.0812525i
$708$	0.791210	−	0.540759i	0.0297355	−	0.0203230i
$709$	−14.3706	−	14.3706i	−0.539698	−	0.539698i	0.383742	−	0.923440i	$-0.374635\pi$
$709$	−14.3706	−	14.3706i	−0.539698	−	0.539698i	−0.923440	+	0.383742i	$0.874635\pi$
$710$	−2.52527	+	4.78464i	−0.0947716	+	0.179564i
$711$			6.90569i			0.258984i
$712$	18.0759	−	22.7461i	0.677424	−	0.852447i
$713$	−57.6808			−2.16016
$714$	0.684290	−	1.29653i	0.0256089	−	0.0485213i
$715$	3.29759	+	3.29759i	0.123323	+	0.123323i
$716$	7.81411	−	41.5577i	0.292027	−	1.55308i
$717$	−4.57654	−	4.57654i	−0.170914	−	0.170914i
$718$	19.9741	−	6.17364i	0.745425	−	0.230398i
$719$		−	2.08235i		−	0.0776586i	−0.999246	−	0.0388293i	$-0.987637\pi$
$719$		−	2.08235i		−	0.0776586i	0.999246	−	0.0388293i	$-0.0123629\pi$
$720$	4.40657	+	10.0375i	0.164223	+	0.374076i
$721$		−	1.37079i		−	0.0510510i
$722$	5.66154	+	26.2668i	0.210701	+	0.977551i
$723$	4.95526	+	4.95526i	0.184288	+	0.184288i
$724$	0.684202	−	3.63878i	0.0254281	−	0.135234i
$725$	7.28825	−	7.28825i	0.270679	−	0.270679i
$726$	13.6220	+	7.18951i	0.505560	+	0.266828i
$727$	−5.76761			−0.213909			−0.106954	−	0.994264i	$-0.534110\pi$
$727$	−5.76761			−0.213909			−0.106954	+	0.994264i	$0.534110\pi$
$728$	4.92517	−	0.563458i	0.182539	−	0.0208832i
$729$			1.00000i			0.0370370i
$730$	14.3966	−	27.2773i	0.532842	−	1.00958i
$731$	8.24047	−	8.24047i	0.304785	−	0.304785i
$732$	−6.88561	−	10.0747i	−0.254499	−	0.372370i
$733$	27.2329	−	27.2329i	1.00587	−	1.00587i	0.00588582	−	0.999983i	$-0.498126\pi$
$733$	27.2329	−	27.2329i	1.00587	−	1.00587i	0.999983	−	0.00588582i	$-0.00187353\pi$
$734$	−6.14463	−	19.8802i	−0.226803	−	0.733792i
$735$	−18.8683			−0.695966
$736$	−2.53598	+	35.1847i	−0.0934773	+	1.29692i
$737$			3.15163i			0.116092i
$738$	−4.14734	−	13.4182i	−0.152666	−	0.493932i
$739$	33.8316	+	33.8316i	1.24452	+	1.24452i	0.958107	+	0.286409i	$0.0924617\pi$
$739$	33.8316	+	33.8316i	1.24452	+	1.24452i	0.286409	+	0.958107i	$0.407538\pi$
$740$	−1.46581	+	1.00182i	−0.0538843	+	0.0368277i
$741$	−16.6007	+	15.2085i	−0.609843	+	0.558700i
$742$	−2.37273	+	4.49562i	−0.0871057	+	0.165040i
$743$			49.5578i			1.81810i	0.416687	+	0.909050i	$0.363191\pi$
$743$			49.5578i			1.81810i	−0.416687	+	0.909050i	$0.636809\pi$
$744$	2.97365	+	25.9925i	0.109019	+	0.952933i
$745$		−	51.2383i		−	1.87722i
$746$	15.4336	−	29.2421i	0.565064	−	1.07063i
$747$	−3.31359	+	3.31359i	−0.121238	+	0.121238i
$748$	0.371977	−	1.97828i	0.0136008	−	0.0723330i
$749$	2.59642	+	2.59642i	0.0948711	+	0.0948711i
$750$	2.84912	+	9.21799i	0.104035	+	0.336593i
$751$	−13.9564			−0.509276			−0.254638	−	0.967036i	$-0.581956\pi$
$751$	−13.9564			−0.509276			−0.254638	+	0.967036i	$0.581956\pi$
$752$	−47.1598	−	18.3850i	−1.71974	−	0.670431i
$753$			5.08421i			0.185279i
$754$	8.85560	+	28.6512i	0.322502	+	1.04341i
$755$	−25.8795	+	25.8795i	−0.941850	+	0.941850i
$756$	−0.666972	−	0.125411i	−0.0242575	−	0.00456116i
$757$	9.63549	+	9.63549i	0.350208	+	0.350208i	0.860187	−	0.509979i	$-0.170347\pi$
$757$	9.63549	+	9.63549i	0.350208	+	0.350208i	−0.509979	+	0.860187i	$0.670347\pi$
$758$	3.96820	+	2.09437i	0.144132	+	0.0760708i
$759$		−	2.05448i		−	0.0745728i
$760$	22.1576	−	25.5078i	0.803742	−	0.925266i
$761$			32.7351i			1.18665i	0.804964	+	0.593323i	$0.202184\pi$
$761$			32.7351i			1.18665i	−0.804964	+	0.593323i	$0.797816\pi$
$762$	−10.3516	+	19.6131i	−0.374998	+	0.710509i
$763$	0.179284	+	0.179284i	0.00649053	+	0.00649053i
$764$	−9.15887	−	13.4008i	−0.331356	−	0.484823i
$765$	5.92006	−	5.92006i	0.214040	−	0.214040i
$766$	0.137362	−	0.0424564i	0.00496310	−	0.00153401i
$767$		−	2.47498i		−	0.0893663i
$768$	15.9859	−	0.671112i	0.576842	−	0.0242167i
$769$	52.1663			1.88117			0.940583	−	0.339564i	$-0.110280\pi$
$769$	52.1663			1.88117			0.940583	+	0.339564i	$0.110280\pi$
$770$	0.413961	−	0.127948i	0.0149181	−	0.00461094i
$771$	13.8872	+	13.8872i	0.500135	+	0.500135i
$772$	0.558146	+	0.816649i	0.0200881	+	0.0293919i
$773$	−21.0728	+	21.0728i	−0.757935	+	0.757935i	−0.975946	−	0.218011i	$-0.930043\pi$
$773$	−21.0728	+	21.0728i	−0.757935	+	0.757935i	0.218011	+	0.975946i	$0.430043\pi$
$774$	−4.77108	−	2.51812i	−0.171493	−	0.0905118i
$775$		−	23.2222i		−	0.834165i
$776$	25.0907	+	19.9391i	0.900705	+	0.715774i
$777$		−	0.109917i		−	0.00394326i
$778$	42.8997	+	22.6419i	1.53803	+	0.811751i
$779$	−31.9185	+	29.2417i	−1.14360	+	1.04769i
$780$	27.8227	+	5.23152i	0.996213	+	0.187318i
$781$	−0.325192	−	0.325192i	−0.0116363	−	0.0116363i
$782$	25.7401	−	7.95583i	0.920464	−	0.284500i
$783$		−	4.10547i		−	0.146718i
$784$	−10.0028	+	25.6586i	−0.357244	+	0.916378i
$785$	57.5594			2.05438
$786$	−7.16427	+	2.21435i	−0.255541	+	0.0789834i
$787$	9.53297	−	9.53297i	0.339814	−	0.339814i	−0.516483	−	0.856297i	$-0.672759\pi$
$787$	9.53297	−	9.53297i	0.339814	−	0.339814i	0.856297	+	0.516483i	$0.172759\pi$
$788$	12.3461	+	2.32143i	0.439810	+	0.0826976i
$789$	−16.7339	+	16.7339i	−0.595744	+	0.595744i
$790$	−23.6700	−	12.4927i	−0.842141	−	0.444471i
$791$			2.39624i			0.0852004i
$792$	−0.925804	+	0.105915i	−0.0328970	+	0.00376354i
$793$	−31.5145			−1.11911
$794$	9.66011	−	18.3030i	0.342824	−	0.649551i
$795$	−20.5274	+	20.5274i	−0.728033	+	0.728033i
$796$	−40.9550	+	27.9910i	−1.45161	+	0.992116i
$797$	28.7568	+	28.7568i	1.01862	+	1.01862i	0.999823	+	0.0187955i	$0.00598315\pi$
$797$	28.7568	+	28.7568i	1.01862	+	1.01862i	0.0187955	+	0.999823i	$0.494017\pi$
$798$	0.529725	+	2.02359i	0.0187521	+	0.0716342i
$799$			38.6580i			1.36762i
$800$	−14.1653	−	1.02098i	−0.500818	−	0.0360971i
$801$			10.2721i			0.362946i
$802$	5.30898	+	17.1766i	0.187467	+	0.606526i
$803$	1.85393	+	1.85393i	0.0654237	+	0.0654237i
$804$	10.7956	+	15.7956i	0.380733	+	0.557067i
$805$	4.10060	+	4.10060i	0.144527	+	0.144527i
$806$	59.7530	+	31.5368i	2.10471	+	1.11084i
$807$	22.2431			0.782993
$808$	−25.3023	+	2.89468i	−0.890132	+	0.101835i
$809$			43.2407i			1.52026i	0.649771	+	0.760130i	$0.274865\pi$
$809$			43.2407i			1.52026i	−0.649771	+	0.760130i	$0.725135\pi$
$810$	−3.42761	−	1.80905i	−0.120434	−	0.0635635i
$811$	−35.0692	−	35.0692i	−1.23145	−	1.23145i	−0.963408	−	0.268038i	$-0.913625\pi$
$811$	−35.0692	−	35.0692i	−1.23145	−	1.23145i	−0.268038	−	0.963408i	$-0.586375\pi$
$812$	2.73823	+	0.514871i	0.0960932	+	0.0180684i
$813$	9.21334	+	9.21334i	0.323126	+	0.323126i
$814$	−0.0445675	−	0.144193i	−0.00156209	−	0.00505395i
$815$		−	1.58821i		−	0.0556326i
$816$	−4.91211	−	11.1891i	−0.171958	−	0.391695i
$817$	−0.727053	+	16.6121i	−0.0254364	+	0.581183i
$818$	41.1366	−	12.7146i	1.43831	−	0.444557i
$819$	−1.23932	+	1.23932i	−0.0433055	+	0.0433055i
$820$	53.4952	+	10.0587i	1.86813	+	0.351266i
$821$	21.9729	+	21.9729i	0.766859	+	0.766859i	0.977552	−	0.210693i	$-0.0675722\pi$
$821$	21.9729	+	21.9729i	0.766859	+	0.766859i	−0.210693	+	0.977552i	$0.567572\pi$
$822$	−12.1808	−	6.42887i	−0.424855	−	0.224233i
$823$	39.1080			1.36322			0.681609	−	0.731716i	$-0.261280\pi$
$823$	39.1080			1.36322			0.681609	+	0.731716i	$0.261280\pi$
$824$	−8.94536	−	7.10872i	−0.311627	−	0.247644i
$825$	0.827128			0.0287969
$826$	−0.203363	−	0.107332i	−0.00707589	−	0.00373456i
$827$	3.03787	+	3.03787i	0.105637	+	0.105637i	0.757950	−	0.652313i	$-0.226201\pi$
$827$	3.03787	+	3.03787i	0.105637	+	0.105637i	−0.652313	+	0.757950i	$0.726201\pi$
$828$	−7.03742	−	10.2968i	−0.244567	−	0.357838i
$829$	8.54970	+	8.54970i	0.296943	+	0.296943i	0.839815	−	0.542872i	$-0.182663\pi$
$829$	8.54970	+	8.54970i	0.296943	+	0.296943i	−0.542872	+	0.839815i	$0.682663\pi$
$830$	−5.36325	−	17.3521i	−0.186161	−	0.602301i
$831$	26.6523			0.924559
$832$	21.8642	−	35.0622i	0.758006	−	1.21556i
$833$	21.0329			0.728747
$834$	−8.78807	−	28.4327i	−0.304306	−	0.984544i
$835$	29.9125	−	29.9125i	1.03517	−	1.03517i
$836$	1.51540	+	2.43982i	0.0524112	+	0.0843828i
$837$	−6.54052	−	6.54052i	−0.226074	−	0.226074i
$838$	−27.2055	−	14.3587i	−0.939799	−	0.496013i
$839$		−	44.7463i		−	1.54481i	−0.635128	−	0.772407i	$-0.719053\pi$
$839$		−	44.7463i		−	1.54481i	0.635128	−	0.772407i	$-0.280947\pi$
$840$	1.63645	−	2.05925i	0.0564627	−	0.0710508i
$841$		−	12.1451i		−	0.418797i
$842$	−3.16782	+	6.00209i	−0.109170	+	0.206846i
$843$	−5.25970	+	5.25970i	−0.181154	+	0.181154i
$844$	−7.42911	+	39.5101i	−0.255720	+	1.35999i
$845$	26.5062	−	26.5062i	0.911842	−	0.911842i
$846$	17.0977	−	5.28460i	0.587830	−	0.181688i
$847$		−	3.69580i		−	0.126989i
$848$	17.0324	+	38.7973i	0.584896	+	1.33231i
$849$			8.67278i			0.297649i
$850$	3.20300	+	10.3629i	0.109862	+	0.355445i
$851$	1.42834	−	1.42834i	0.0489629	−	0.0489629i
$852$	−2.74374	−	0.515906i	−0.0939989	−	0.0176747i
$853$	5.24229	+	5.24229i	0.179493	+	0.179493i	0.791135	−	0.611642i	$-0.209491\pi$
$853$	5.24229	+	5.24229i	0.179493	+	0.179493i	−0.611642	+	0.791135i	$0.709491\pi$
$854$	−1.36668	+	2.58946i	−0.0467670	+	0.0886096i
$855$	−0.522325	+	11.9343i	−0.0178631	+	0.408146i
$856$	30.4081	−	3.47880i	1.03933	−	0.118903i
$857$	−48.0963			−1.64294			−0.821469	−	0.570253i	$-0.806845\pi$
$857$	−48.0963			−1.64294			−0.821469	+	0.570253i	$0.806845\pi$
$858$	−1.12328	+	2.12828i	−0.0383482	+	0.0726584i
$859$	−38.9257	+	38.9257i	−1.32813	+	1.32813i	−0.421124	+	0.907003i	$0.638364\pi$
$859$	−38.9257	+	38.9257i	−1.32813	+	1.32813i	−0.907003	+	0.421124i	$0.861636\pi$
$860$	17.2622	−	11.7980i	0.588638	−	0.402309i
$861$	−2.38287	+	2.38287i	−0.0812079	+	0.0812079i
$862$	−27.4710	+	8.49081i	−0.935665	+	0.289198i
$863$	−17.2633			−0.587650			−0.293825	−	0.955859i	$-0.594928\pi$
$863$	−17.2633			−0.587650			−0.293825	+	0.955859i	$0.594928\pi$
$864$	−4.27721	+	3.70209i	−0.145514	+	0.125948i
$865$		−	25.5659i		−	0.869266i
$866$	13.6454	+	44.1481i	0.463691	+	1.50021i
$867$	5.42157	−	5.42157i	0.184126	−	0.184126i
$868$	5.18260	−	3.54209i	0.175909	−	0.120226i
$869$	1.60875	−	1.60875i	0.0545732	−	0.0545732i
$870$	14.0720	+	7.42699i	0.477084	+	0.251799i
$871$	49.4101			1.67420
$872$	2.09970	−	0.240213i	0.0711046	−	0.00813464i
$873$	−11.3309			−0.383493
$874$	−19.4123	+	33.1795i	−0.656630	+	1.12231i
$875$	1.63697	−	1.63697i	0.0553398	−	0.0553398i
$876$	15.6421	+	2.94119i	0.528498	+	0.0993737i
$877$	25.9879	+	25.9879i	0.877549	+	0.877549i	0.993281	−	0.115731i	$-0.0369211\pi$
$877$	25.9879	+	25.9879i	0.877549	+	0.877549i	−0.115731	+	0.993281i	$0.536921\pi$
$878$	3.26025	+	10.5481i	0.110028	+	0.355982i
$879$		−	3.82708i		−	0.129084i
$880$	1.31179	−	3.36490i	0.0442203	−	0.113431i
$881$	−29.9415			−1.00875			−0.504377	−	0.863484i	$-0.668278\pi$
$881$	−29.9415			−1.00875			−0.504377	+	0.863484i	$0.668278\pi$
$882$	−2.87523	−	9.30245i	−0.0968140	−	0.313230i
$883$	6.83056	+	6.83056i	0.229867	+	0.229867i	0.812637	−	0.582770i	$-0.198031\pi$
$883$	6.83056	+	6.83056i	0.229867	+	0.229867i	−0.582770	+	0.812637i	$0.698031\pi$
$884$	−31.0147	−	5.83170i	−1.04314	−	0.196141i
$885$	−0.928573	−	0.928573i	−0.0312136	−	0.0312136i
$886$	−14.6979	+	27.8482i	−0.493787	+	0.935579i
$887$		−	21.7160i		−	0.729152i	−0.931174	−	0.364576i	$-0.881214\pi$
$887$		−	21.7160i		−	0.729152i	0.931174	−	0.364576i	$-0.118786\pi$
$888$	−0.717286	−	0.570014i	−0.0240705	−	0.0191284i
$889$	5.32127			0.178470
$890$	−35.2087	−	18.5827i	−1.18020	−	0.622894i
$891$	0.232961	−	0.232961i	0.00780448	−	0.00780448i
$892$	28.6132	−	19.5559i	0.958040	−	0.654781i
$893$	−37.2601	−	40.6709i	−1.24686	−	1.36100i
$894$	25.2615	−	7.80792i	0.844872	−	0.261136i
$895$	−57.9433			−1.93683
$896$	−1.93278	−	3.31706i	−0.0645697	−	0.110815i
$897$	−32.2093			−1.07544
$898$	1.25445	+	4.05862i	0.0418615	+	0.135438i
$899$	26.8519	+	26.8519i	0.895562	+	0.895562i
$900$	4.14546	−	2.83325i	0.138182	−	0.0944418i
$901$	22.8824	−	22.8824i	0.762324	−	0.762324i
$902$	−2.15975	+	4.09209i	−0.0719118	+	0.136252i
$903$			1.29445i			0.0430766i
$904$	15.6371	+	12.4265i	0.520083	+	0.413300i
$905$	−5.07350			−0.168649
$906$	−16.7027	−	8.81549i	−0.554912	−	0.292875i
$907$	−8.41931	−	8.41931i	−0.279558	−	0.279558i	0.553374	−	0.832933i	$-0.313340\pi$
$907$	−8.41931	−	8.41931i	−0.279558	−	0.279558i	−0.832933	+	0.553374i	$0.813340\pi$
$908$	−5.17045	+	27.4979i	−0.171587	+	0.912551i
$909$	6.36684	−	6.36684i	0.211175	−	0.211175i
$910$	−2.00592	−	6.48992i	−0.0664957	−	0.215139i
$911$	−18.1441			−0.601141			−0.300570	−	0.953760i	$-0.597177\pi$
$911$	−18.1441			−0.601141			−0.300570	+	0.953760i	$0.597177\pi$
$912$	15.9524	+	7.03719i	0.528236	+	0.233024i
$913$	1.54387			0.0510947
$914$	1.62313	+	5.25143i	0.0536883	+	0.173702i
$915$	−11.8237	+	11.8237i	−0.390880	+	0.390880i
$916$	−1.33288	−	0.250622i	−0.0440395	−	0.00828077i
$917$	1.27226	+	1.27226i	0.0420138	+	0.0420138i
$918$	3.82084	+	2.01659i	0.126107	+	0.0665574i
$919$	28.2975			0.933447			0.466723	−	0.884403i	$-0.345434\pi$
$919$	28.2975			0.933447			0.466723	+	0.884403i	$0.345434\pi$
$920$	48.0244	−	5.49417i	1.58332	−	0.181137i
$921$			21.0418i			0.693351i
$922$	−20.8131	+	39.4346i	−0.685442	+	1.29871i
$923$	−5.09824	+	5.09824i	−0.167810	+	0.167810i
$924$	0.126162	+	0.184594i	0.00415044	+	0.00607270i
$925$	0.575047	+	0.575047i	0.0189074	+	0.0189074i
$926$	−13.5916	−	43.9739i	−0.446647	−	1.44507i
$927$	4.03970			0.132681
$928$	17.5600	−	15.1988i	0.576434	−	0.498926i
$929$	−44.8400			−1.47115			−0.735576	−	0.677442i	$-0.763088\pi$
$929$	−44.8400			−1.47115			−0.735576	+	0.677442i	$0.763088\pi$
$930$	34.2505	−	10.5862i	1.12312	−	0.347137i
$931$	−22.1281	+	20.2724i	−0.725220	+	0.664401i
$932$	27.8373	+	40.7300i	0.911841	+	1.33416i
$933$	2.75049	−	2.75049i	0.0900469	−	0.0900469i
$934$	−21.4003	−	11.2948i	−0.700240	−	0.369578i
$935$	−2.75828			−0.0902056
$936$	1.66050	+	14.5144i	0.0542752	+	0.474418i
$937$			44.1667i			1.44286i	0.692486	+	0.721432i	$0.256516\pi$
$937$			44.1667i			1.44286i	−0.692486	+	0.721432i	$0.743484\pi$
$938$	2.14276	−	4.05990i	0.0699636	−	0.132560i
$939$	0.884078	+	0.884078i	0.0288508	+	0.0288508i
$940$	−12.8170	+	68.1642i	−0.418043	+	2.22327i
$941$	−24.6664	−	24.6664i	−0.804103	−	0.804103i	0.179631	−	0.983734i	$-0.442510\pi$
$941$	−24.6664	−	24.6664i	−0.804103	−	0.804103i	−0.983734	+	0.179631i	$0.942510\pi$
$942$	8.77115	+	28.3780i	0.285780	+	0.924604i
$943$	−61.9293			−2.01669
$944$	−1.75502	+	0.770474i	−0.0571211	+	0.0250768i
$945$			0.929950i			0.0302513i
$946$	0.524853	+	1.69810i	0.0170644	+	0.0552099i
$947$	6.25980	+	6.25980i	0.203416	+	0.203416i	0.801462	−	0.598046i	$-0.204056\pi$
$947$	6.25980	+	6.25980i	0.203416	+	0.203416i	−0.598046	+	0.801462i	$0.704056\pi$
$948$	2.55223	−	13.5735i	0.0828927	−	0.440847i
$949$	29.0651	−	29.0651i	0.943494	−	0.943494i
$950$	−13.3580	−	7.81534i	−0.433391	−	0.253563i
$951$	−25.4570			−0.825499
$952$	−1.82419	+	2.29549i	−0.0591222	+	0.0743973i
$953$	9.47877			0.307047			0.153524	−	0.988145i	$-0.450938\pi$
$953$	9.47877			0.307047			0.153524	+	0.988145i	$0.450938\pi$
$954$	−13.2485	−	6.99240i	−0.428937	−	0.226387i
$955$	−15.7273	+	15.7273i	−0.508923	+	0.508923i
$956$	7.30403	+	10.6869i	0.236229	+	0.345638i
$957$	−0.956413	+	0.956413i	−0.0309164	+	0.0309164i
$958$	7.15457	+	23.1477i	0.231154	+	0.747870i
$959$			3.30479i			0.106717i
$960$	−4.95165	−	21.3579i	−0.159814	−	0.689322i
$961$	54.5569			1.75990
$962$	−2.26060	+	0.698712i	−0.0728846	+	0.0225274i
$963$	−7.65160	+	7.65160i	−0.246570	+	0.246570i
$964$	−7.90844	−	11.5712i	−0.254714	−	0.372684i
$965$	0.958429	−	0.958429i	0.0308529	−	0.0308529i
$966$	−1.39682	+	2.64655i	−0.0449418	+	0.0851514i
$967$	25.9960			0.835976			0.417988	−	0.908453i	$-0.362735\pi$
$967$	25.9960			0.835976			0.417988	+	0.908453i	$0.362735\pi$
$968$	−24.1177	−	19.1659i	−0.775171	−	0.616014i
$969$	0.582248	−	13.3035i	0.0187045	−	0.427370i
$970$	20.4981	−	38.8379i	0.658156	−	1.24701i
$971$	6.16596	+	6.16596i	0.197875	+	0.197875i	0.799089	−	0.601213i	$-0.205316\pi$
$971$	6.16596	+	6.16596i	0.197875	+	0.197875i	−0.601213	+	0.799089i	$0.705316\pi$
$972$	0.369584	−	1.96556i	0.0118544	−	0.0630452i
$973$	−5.04921	+	5.04921i	−0.161870	+	0.161870i
$974$	7.07129	+	22.8783i	0.226579	+	0.733068i
$975$		−	12.9674i		−	0.415289i
$976$	9.81061	+	22.3471i	0.314030	+	0.715313i
$977$		−	9.98977i		−	0.319601i	−0.987149	−	0.159801i	$-0.948915\pi$
$977$		−	9.98977i		−	0.319601i	0.987149	−	0.159801i	$-0.0510851\pi$
$978$	0.783021	−	0.242019i	0.0250383	−	0.00773890i
$979$	2.39299	−	2.39299i	0.0764804	−	0.0764804i
$980$	37.0866	+	6.97341i	1.18469	+	0.222757i
$981$	−0.528348	+	0.528348i	−0.0168688	+	0.0168688i
$982$	−3.87789	+	7.34745i	−0.123748	+	0.234467i
$983$			30.1319i			0.961058i	0.876979	+	0.480529i	$0.159555\pi$
$983$			30.1319i			0.961058i	−0.876979	+	0.480529i	$0.840445\pi$
$984$	3.19267	+	27.9070i	0.101779	+	0.889644i
$985$		−	17.2139i		−	0.548481i
$986$	−15.6864	−	8.27905i	−0.499555	−	0.263659i
$987$	−3.03628	−	3.03628i	−0.0966459	−	0.0966459i
$988$	38.2505	−	23.7579i	1.21691	−	0.755838i
$989$	−16.8210	+	16.8210i	−0.534876	+	0.534876i
$990$	0.377062	+	1.21994i	0.0119838	+	0.0387721i
$991$	62.0062			1.96969			0.984847	−	0.173427i	$-0.0554842\pi$
$991$	62.0062			1.96969			0.984847	+	0.173427i	$0.0554842\pi$
$992$	3.76157	−	52.1888i	0.119430	−	1.65700i
$993$	−4.18798			−0.132902
$994$	0.197814	+	0.640003i	0.00627429	+	0.0202997i
$995$	48.0652	+	48.0652i	1.52377	+	1.52377i
$996$	7.73768	−	5.28839i	0.245178	−	0.167569i
$997$	−7.92697	−	7.92697i	−0.251050	−	0.251050i	0.570351	−	0.821401i	$-0.306807\pi$
$997$	−7.92697	−	7.92697i	−0.251050	−	0.251050i	−0.821401	+	0.570351i	$0.806807\pi$
$998$	2.46157	+	1.29918i	0.0779196	+	0.0411250i
$999$	0.323924			0.0102485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.y.a.379.9	✓	160
16.3	odd	4	inner	912.2.y.a.835.72	yes	160
19.18	odd	2	inner	912.2.y.a.379.72	yes	160
304.227	even	4	inner	912.2.y.a.835.9	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.y.a.379.9	✓	160	1.1	even	1	trivial
912.2.y.a.379.72	yes	160	19.18	odd	2	inner
912.2.y.a.835.9	yes	160	304.227	even	4	inner
912.2.y.a.835.72	yes	160	16.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35115 + 0.417616i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.65119 - 1.12852i) q^{4} +(-1.93786 - 1.93786i) q^{5} +(0.660105 - 1.25070i) q^{6} -0.339330 q^{7} +(-1.75971 + 2.21436i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.35115 + 0.417616i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.65119 - 1.12852i) q^{4} +(-1.93786 - 1.93786i) q^{5} +(0.660105 - 1.25070i) q^{6} -0.339330 q^{7} +(-1.75971 + 2.21436i) q^{8} -1.00000i q^{9} +(3.42761 + 1.80905i) q^{10} +(-0.232961 + 0.232961i) q^{11} +(-0.369584 + 1.96556i) q^{12} +(3.65227 + 3.65227i) q^{13} +(0.458485 - 0.141710i) q^{14} +2.74055 q^{15} +(1.45288 - 3.72681i) q^{16} -3.05495 q^{17} +(0.417616 + 1.35115i) q^{18} +(3.21403 - 2.94449i) q^{19} +(-5.38669 - 1.01286i) q^{20} +(0.239943 - 0.239943i) q^{21} +(0.217476 - 0.412052i) q^{22} +6.23596 q^{23} +(-0.321486 - 2.81010i) q^{24} +2.51059i q^{25} +(-6.45999 - 3.40950i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.560300 + 0.382942i) q^{28} +(-2.90301 - 2.90301i) q^{29} +(-3.70288 + 1.14450i) q^{30} -9.24970 q^{31} +(-0.406670 + 5.64222i) q^{32} -0.329456i q^{33} +(4.12769 - 1.27580i) q^{34} +(0.657574 + 0.657574i) q^{35} +(-1.12852 - 1.65119i) q^{36} +(0.229049 - 0.229049i) q^{37} +(-3.11295 + 5.32067i) q^{38} -5.16509 q^{39} +(7.70120 - 0.881046i) q^{40} -9.93099 q^{41} +(-0.223994 + 0.424402i) q^{42} +(-2.69741 + 2.69741i) q^{43} +(-0.121762 + 0.647564i) q^{44} +(-1.93786 + 1.93786i) q^{45} +(-8.42570 + 2.60424i) q^{46} -12.6542i q^{47} +(1.60792 + 3.66259i) q^{48} -6.88486 q^{49} +(-1.04846 - 3.39217i) q^{50} +(2.16018 - 2.16018i) q^{51} +(10.1523 + 1.90893i) q^{52} +(-7.49028 + 7.49028i) q^{53} +(-1.25070 - 0.660105i) q^{54} +0.902890 q^{55} +(0.597124 - 0.751400i) q^{56} +(-0.190592 + 4.35473i) q^{57} +(5.13473 + 2.71004i) q^{58} +(-0.338828 - 0.338828i) q^{59} +(4.52517 - 3.09277i) q^{60} +(-4.31437 + 4.31437i) q^{61} +(12.4977 - 3.86282i) q^{62} +0.339330i q^{63} +(-1.80681 - 7.79329i) q^{64} -14.1551i q^{65} +(0.137586 + 0.445144i) q^{66} +(6.76430 - 6.76430i) q^{67} +(-5.04432 + 3.44758i) q^{68} +(-4.40949 + 4.40949i) q^{69} +(-1.16309 - 0.613865i) q^{70} +1.39591i q^{71} +(2.21436 + 1.75971i) q^{72} -7.95811i q^{73} +(-0.213824 + 0.405133i) q^{74} +(-1.77525 - 1.77525i) q^{75} +(1.98406 - 8.48902i) q^{76} +(0.0790506 - 0.0790506i) q^{77} +(6.97879 - 2.15702i) q^{78} -6.90569 q^{79} +(-10.0375 + 4.40657i) q^{80} -1.00000 q^{81} +(13.4182 - 4.14734i) q^{82} +(-3.31359 - 3.31359i) q^{83} +(0.125411 - 0.666972i) q^{84} +(5.92006 + 5.92006i) q^{85} +(2.51812 - 4.77108i) q^{86} +4.10547 q^{87} +(-0.105915 - 0.925804i) q^{88} -10.2721 q^{89} +(1.80905 - 3.42761i) q^{90} +(-1.23932 - 1.23932i) q^{91} +(10.2968 - 7.03742i) q^{92} +(6.54052 - 6.54052i) q^{93} +(5.28460 + 17.0977i) q^{94} +(-11.9343 - 0.522325i) q^{95} +(-3.70209 - 4.27721i) q^{96} -11.3309i q^{97} +(9.30245 - 2.87523i) q^{98} +(0.232961 + 0.232961i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q+O(q^{10}) \) 160 * q	\( 160 q - 8 q^{16} - 8 q^{19} - 8 q^{24} + 40 q^{26} - 40 q^{28} - 48 q^{35} - 8 q^{36} + 48 q^{38} + 56 q^{44} + 160 q^{49} - 8 q^{54} - 56 q^{58} - 32 q^{61} + 24 q^{62} + 72 q^{64} + 48 q^{66} - 40 q^{68} + 40 q^{74} + 32 q^{76} + 56 q^{80} - 160 q^{81} - 120 q^{82} - 80 q^{83} + 32 q^{85} - 24 q^{92} - 40 q^{96}+O(q^{100}) \) 160 * q - 8 * q^16 - 8 * q^19 - 8 * q^24 + 40 * q^26 - 40 * q^28 - 48 * q^35 - 8 * q^36 + 48 * q^38 + 56 * q^44 + 160 * q^49 - 8 * q^54 - 56 * q^58 - 32 * q^61 + 24 * q^62 + 72 * q^64 + 48 * q^66 - 40 * q^68 + 40 * q^74 + 32 * q^76 + 56 * q^80 - 160 * q^81 - 120 * q^82 - 80 * q^83 + 32 * q^85 - 24 * q^92 - 40 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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