LMFDB - Embedded newform 560.2.bc.a.251.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(251,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, 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("560.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bc (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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.16
Character	$\chi$	$=$	560.251
Dual form			560.2.bc.a.531.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04480 - 0.953102i) q^{2} +(1.26143 - 1.26143i) q^{3} +(0.183195 + 1.99159i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-2.52022 + 0.115666i) q^{6} +(-1.76061 + 1.97491i) q^{7} +(1.70679 - 2.25541i) q^{8} -0.182435i q^{9} +O(q^{10})$	\(q+(-1.04480 - 0.953102i) q^{2} +(1.26143 - 1.26143i) q^{3} +(0.183195 + 1.99159i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-2.52022 + 0.115666i) q^{6} +(-1.76061 + 1.97491i) q^{7} +(1.70679 - 2.25541i) q^{8} -0.182435i q^{9} +(1.41273 - 0.0648373i) q^{10} +(-2.41574 + 2.41574i) q^{11} +(2.74335 + 2.28118i) q^{12} +(-3.19208 - 3.19208i) q^{13} +(3.72176 - 0.385334i) q^{14} +1.78394i q^{15} +(-3.93288 + 0.729699i) q^{16} +3.36940i q^{17} +(-0.173879 + 0.190607i) q^{18} +(-2.25728 + 2.25728i) q^{19} +(-1.53781 - 1.27873i) q^{20} +(0.270322 + 4.71211i) q^{21} +(4.82641 - 0.221509i) q^{22} -4.14123 q^{23} +(-0.692050 - 4.99805i) q^{24} -1.00000i q^{25} +(0.292694 + 6.37745i) q^{26} +(3.55417 + 3.55417i) q^{27} +(-4.25574 - 3.14462i) q^{28} +(-7.31132 + 7.31132i) q^{29} +(1.70027 - 1.86385i) q^{30} +5.03608 q^{31} +(4.80453 + 2.98605i) q^{32} +6.09461i q^{33} +(3.21138 - 3.52034i) q^{34} +(-0.151531 - 2.64141i) q^{35} +(0.363336 - 0.0334211i) q^{36} +(-6.98368 - 6.98368i) q^{37} +(4.50981 - 0.206978i) q^{38} -8.05321 q^{39} +(0.387934 + 2.80170i) q^{40} -0.221187 q^{41} +(4.20869 - 5.18083i) q^{42} +(1.77332 - 1.77332i) q^{43} +(-5.25373 - 4.36862i) q^{44} +(0.129001 + 0.129001i) q^{45} +(4.32674 + 3.94702i) q^{46} +11.6416 q^{47} +(-4.04060 + 5.88154i) q^{48} +(-0.800510 - 6.95408i) q^{49} +(-0.953102 + 1.04480i) q^{50} +(4.25028 + 4.25028i) q^{51} +(5.77256 - 6.94210i) q^{52} +(-0.300789 - 0.300789i) q^{53} +(-0.325896 - 7.10087i) q^{54} -3.41638i q^{55} +(1.44924 + 7.34164i) q^{56} +5.69481i q^{57} +(14.6073 - 0.670403i) q^{58} +(3.95846 + 3.95846i) q^{59} +(-3.55288 + 0.326808i) q^{60} +(-0.736150 - 0.736150i) q^{61} +(-5.26167 - 4.79990i) q^{62} +(0.360292 + 0.321197i) q^{63} +(-2.17375 - 7.69901i) q^{64} +4.51429 q^{65} +(5.80878 - 6.36762i) q^{66} +(6.90649 + 6.90649i) q^{67} +(-6.71048 + 0.617257i) q^{68} +(-5.22390 + 5.22390i) q^{69} +(-2.35921 + 2.90416i) q^{70} -9.82868 q^{71} +(-0.411465 - 0.311378i) q^{72} +10.0001 q^{73} +(0.640360 + 13.9527i) q^{74} +(-1.26143 - 1.26143i) q^{75} +(-4.90910 - 4.08205i) q^{76} +(-0.517687 - 9.02405i) q^{77} +(8.41396 + 7.67553i) q^{78} +2.12789i q^{79} +(2.26499 - 3.29694i) q^{80} +9.51402 q^{81} +(0.231096 + 0.210814i) q^{82} +(-2.97147 + 2.97147i) q^{83} +(-9.33508 + 1.40160i) q^{84} +(-2.38253 - 2.38253i) q^{85} +(-3.54291 + 0.162602i) q^{86} +18.4455i q^{87} +(1.32533 + 9.57165i) q^{88} +0.946648 q^{89} +(-0.0118286 - 0.257731i) q^{90} +(11.9241 - 0.684054i) q^{91} +(-0.758653 - 8.24765i) q^{92} +(6.35269 - 6.35269i) q^{93} +(-12.1631 - 11.0957i) q^{94} -3.19227i q^{95} +(9.82731 - 2.29390i) q^{96} +0.702211i q^{97} +(-5.79157 + 8.02855i) q^{98} +(0.440716 + 0.440716i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 4 q^{4}+O(q^{10}) $ 128 * q - 4 * q^4	$ 128 q - 4 q^{4} + 8 q^{11} - 8 q^{14} + 20 q^{16} + 20 q^{18} - 52 q^{22} - 16 q^{23} + 44 q^{28} + 16 q^{29} + 40 q^{32} + 16 q^{37} + 60 q^{42} - 8 q^{43} - 108 q^{44} - 40 q^{46} - 4 q^{50} + 80 q^{51} + 16 q^{53} + 12 q^{56} - 76 q^{58} - 56 q^{60} - 52 q^{64} + 40 q^{67} - 8 q^{70} - 64 q^{71} - 36 q^{72} + 60 q^{74} - 48 q^{78} - 128 q^{81} - 32 q^{84} + 76 q^{86} + 20 q^{88} - 32 q^{91} + 64 q^{92} - 76 q^{98} - 40 q^{99}+O(q^{100}) $ 128 * q - 4 * q^4 + 8 * q^11 - 8 * q^14 + 20 * q^16 + 20 * q^18 - 52 * q^22 - 16 * q^23 + 44 * q^28 + 16 * q^29 + 40 * q^32 + 16 * q^37 + 60 * q^42 - 8 * q^43 - 108 * q^44 - 40 * q^46 - 4 * q^50 + 80 * q^51 + 16 * q^53 + 12 * q^56 - 76 * q^58 - 56 * q^60 - 52 * q^64 + 40 * q^67 - 8 * q^70 - 64 * q^71 - 36 * q^72 + 60 * q^74 - 48 * q^78 - 128 * q^81 - 32 * q^84 + 76 * q^86 + 20 * q^88 - 32 * q^91 + 64 * q^92 - 76 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.04480	−	0.953102i	−0.738782	−	0.673945i
$2$	−1.04480	−	0.953102i	−0.738782	−	0.673945i
$3$	1.26143	−	1.26143i	0.728290	−	0.728290i	−0.241989	−	0.970279i	$-0.577800\pi$
$3$	1.26143	−	1.26143i	0.728290	−	0.728290i	0.970279	+	0.241989i	$0.0777999\pi$
$4$	0.183195	+	1.99159i	0.0915974	+	0.995796i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−2.52022	+	0.115666i	−1.02887	+	0.0472204i
$7$	−1.76061	+	1.97491i	−0.665448	+	0.746444i
$7$	−1.76061	+	1.97491i	−0.665448	+	0.746444i
$8$	1.70679	−	2.25541i	0.603441	−	0.797408i
$9$		−	0.182435i		−	0.0608116i
$10$	1.41273	−	0.0648373i	0.446743	−	0.0205034i
$11$	−2.41574	+	2.41574i	−0.728374	+	0.728374i	−0.970296	−	0.241922i	$-0.922222\pi$
$11$	−2.41574	+	2.41574i	−0.728374	+	0.728374i	0.241922	+	0.970296i	$0.422222\pi$
$12$	2.74335	+	2.28118i	0.791937	+	0.658519i
$13$	−3.19208	−	3.19208i	−0.885325	−	0.885325i	0.108745	−	0.994070i	$-0.465317\pi$
$13$	−3.19208	−	3.19208i	−0.885325	−	0.885325i	−0.994070	+	0.108745i	$0.965317\pi$
$14$	3.72176	−	0.385334i	0.994683	−	0.102985i
$15$			1.78394i			0.460611i
$16$	−3.93288	+	0.729699i	−0.983220	+	0.182425i
$17$			3.36940i			0.817201i	0.912713	+	0.408600i	$0.133983\pi$
$17$			3.36940i			0.817201i	−0.912713	+	0.408600i	$0.866017\pi$
$18$	−0.173879	+	0.190607i	−0.0409837	+	0.0449265i
$19$	−2.25728	+	2.25728i	−0.517855	+	0.517855i	−0.916922	−	0.399067i	$-0.869334\pi$
$19$	−2.25728	+	2.25728i	−0.517855	+	0.517855i	0.399067	+	0.916922i	$0.369334\pi$
$20$	−1.53781	−	1.27873i	−0.343864	−	0.285933i
$21$	0.270322	+	4.71211i	0.0589890	+	1.02827i
$22$	4.82641	−	0.221509i	1.02899	−	0.0472258i
$23$	−4.14123			−0.863507			−0.431754	−	0.901992i	$-0.642105\pi$
$23$	−4.14123			−0.863507			−0.431754	+	0.901992i	$0.642105\pi$
$24$	−0.692050	−	4.99805i	−0.141264	−	1.02022i
$25$		−	1.00000i		−	0.200000i
$26$	0.292694	+	6.37745i	0.0574021	+	1.25072i
$27$	3.55417	+	3.55417i	0.684001	+	0.684001i
$28$	−4.25574	−	3.14462i	−0.804260	−	0.594278i
$29$	−7.31132	+	7.31132i	−1.35768	+	1.35768i	−0.480905	+	0.876773i	$0.659692\pi$
$29$	−7.31132	+	7.31132i	−1.35768	+	1.35768i	−0.876773	+	0.480905i	$0.840308\pi$
$30$	1.70027	−	1.86385i	0.310426	−	0.340291i
$31$	5.03608			0.904507			0.452253	−	0.891889i	$-0.350620\pi$
$31$	5.03608			0.904507			0.452253	+	0.891889i	$0.350620\pi$
$32$	4.80453	+	2.98605i	0.849329	+	0.527864i
$33$			6.09461i			1.06093i
$34$	3.21138	−	3.52034i	0.550748	−	0.603733i
$35$	−0.151531	−	2.64141i	−0.0256134	−	0.446480i
$36$	0.363336	−	0.0334211i	0.0605560	−	0.00557019i
$37$	−6.98368	−	6.98368i	−1.14811	−	1.14811i	−0.986924	−	0.161185i	$-0.948468\pi$
$37$	−6.98368	−	6.98368i	−1.14811	−	1.14811i	−0.161185	−	0.986924i	$-0.551532\pi$
$38$	4.50981	−	0.206978i	0.731587	−	0.0335763i
$39$	−8.05321			−1.28955
$40$	0.387934	+	2.80170i	0.0613377	+	0.442987i
$41$	−0.221187			−0.0345437			−0.0172718	−	0.999851i	$-0.505498\pi$
$41$	−0.221187			−0.0345437			−0.0172718	+	0.999851i	$0.505498\pi$
$42$	4.20869	−	5.18083i	0.649415	−	0.799420i
$43$	1.77332	−	1.77332i	0.270428	−	0.270428i	−0.558844	−	0.829273i	$-0.688755\pi$
$43$	1.77332	−	1.77332i	0.270428	−	0.270428i	0.829273	+	0.558844i	$0.188755\pi$
$44$	−5.25373	−	4.36862i	−0.792029	−	0.658595i
$45$	0.129001	+	0.129001i	0.0192303	+	0.0192303i
$46$	4.32674	+	3.94702i	0.637943	+	0.581956i
$47$	11.6416			1.69811			0.849054	−	0.528307i	$-0.177173\pi$
$47$	11.6416			1.69811			0.849054	+	0.528307i	$0.177173\pi$
$48$	−4.04060	+	5.88154i	−0.583211	+	0.848927i
$49$	−0.800510	−	6.95408i	−0.114359	−	0.993440i
$50$	−0.953102	+	1.04480i	−0.134789	+	0.147756i
$51$	4.25028	+	4.25028i	0.595159	+	0.595159i
$52$	5.77256	−	6.94210i	0.800510	−	0.962696i
$53$	−0.300789	−	0.300789i	−0.0413165	−	0.0413165i	0.686147	−	0.727463i	$-0.259301\pi$
$53$	−0.300789	−	0.300789i	−0.0413165	−	0.0413165i	−0.727463	+	0.686147i	$0.759301\pi$
$54$	−0.325896	−	7.10087i	−0.0443488	−	0.966307i
$55$		−	3.41638i		−	0.460664i
$56$	1.44924	+	7.34164i	0.193662	+	0.981068i
$57$			5.69481i			0.754297i
$58$	14.6073	−	0.670403i	1.91803	−	0.0880282i
$59$	3.95846	+	3.95846i	0.515348	+	0.515348i	0.916160	−	0.400812i	$-0.131272\pi$
$59$	3.95846	+	3.95846i	0.515348	+	0.515348i	−0.400812	+	0.916160i	$0.631272\pi$
$60$	−3.55288	+	0.326808i	−0.458674	+	0.0421908i
$61$	−0.736150	−	0.736150i	−0.0942543	−	0.0942543i	0.658407	−	0.752662i	$-0.271230\pi$
$61$	−0.736150	−	0.736150i	−0.0942543	−	0.0942543i	−0.752662	+	0.658407i	$0.771230\pi$
$62$	−5.26167	−	4.79990i	−0.668233	−	0.609588i
$63$	0.360292	+	0.321197i	0.0453925	+	0.0404670i
$64$	−2.17375	−	7.69901i	−0.271718	−	0.962377i
$65$	4.51429			0.559929
$66$	5.80878	−	6.36762i	0.715011	−	0.783799i
$67$	6.90649	+	6.90649i	0.843762	+	0.843762i	0.989346	−	0.145584i	$-0.0465060\pi$
$67$	6.90649	+	6.90649i	0.843762	+	0.843762i	−0.145584	+	0.989346i	$0.546506\pi$
$68$	−6.71048	+	0.617257i	−0.813765	+	0.0748535i
$69$	−5.22390	+	5.22390i	−0.628883	+	0.628883i
$70$	−2.35921	+	2.90416i	−0.281980	+	0.347113i
$71$	−9.82868			−1.16645			−0.583225	−	0.812311i	$-0.698209\pi$
$71$	−9.82868			−1.16645			−0.583225	+	0.812311i	$0.698209\pi$
$72$	−0.411465	−	0.311378i	−0.0484917	−	0.0366962i
$73$	10.0001			1.17043			0.585214	−	0.810879i	$-0.301011\pi$
$73$	10.0001			1.17043			0.585214	+	0.810879i	$0.301011\pi$
$74$	0.640360	+	13.9527i	0.0744403	+	1.62196i
$75$	−1.26143	−	1.26143i	−0.145658	−	0.145658i
$76$	−4.90910	−	4.08205i	−0.563112	−	0.468244i
$77$	−0.517687	−	9.02405i	−0.0589959	−	1.02839i
$78$	8.41396	+	7.67553i	0.952693	+	0.869082i
$79$			2.12789i			0.239407i	0.992810	+	0.119703i	$0.0381943\pi$
$79$			2.12789i			0.239407i	−0.992810	+	0.119703i	$0.961806\pi$
$80$	2.26499	−	3.29694i	0.253234	−	0.368609i
$81$	9.51402			1.05711
$82$	0.231096	+	0.210814i	0.0255202	+	0.0232805i
$83$	−2.97147	+	2.97147i	−0.326161	+	0.326161i	−0.851125	−	0.524963i	$-0.824079\pi$
$83$	−2.97147	+	2.97147i	−0.326161	+	0.326161i	0.524963	+	0.851125i	$0.324079\pi$
$84$	−9.33508	+	1.40160i	−1.01854	+	0.152928i
$85$	−2.38253	−	2.38253i	−0.258422	−	0.258422i
$86$	−3.54291	+	0.162602i	−0.382041	+	0.0175339i
$87$			18.4455i			1.97757i
$88$	1.32533	+	9.57165i	0.141280	+	1.02034i
$89$	0.946648			0.100344			0.0501722	−	0.998741i	$-0.484023\pi$
$89$	0.946648			0.100344			0.0501722	+	0.998741i	$0.484023\pi$
$90$	−0.0118286	−	0.257731i	−0.00124684	−	0.0271672i
$91$	11.9241	−	0.684054i	1.24998	−	0.0717084i
$92$	−0.758653	−	8.24765i	−0.0790950	−	0.859877i
$93$	6.35269	−	6.35269i	0.658743	−	0.658743i
$94$	−12.1631	−	11.0957i	−1.25453	−	1.14443i
$95$		−	3.19227i		−	0.327520i
$96$	9.82731	−	2.29390i	1.00300	−	0.234120i
$97$			0.702211i			0.0712987i	0.999364	+	0.0356494i	$0.0113500\pi$
$97$			0.702211i			0.0712987i	−0.999364	+	0.0356494i	$0.988650\pi$
$98$	−5.79157	+	8.02855i	−0.585037	+	0.811006i
$99$	0.440716	+	0.440716i	0.0442936	+	0.0442936i
$100$	1.99159	−	0.183195i	0.199159	−	0.0183195i
$101$	−5.87283	+	5.87283i	−0.584368	+	0.584368i	−0.936101	−	0.351732i	$-0.885593\pi$
$101$	−5.87283	+	5.87283i	−0.584368	+	0.584368i	0.351732	+	0.936101i	$0.385593\pi$
$102$	−0.389725	−	8.49163i	−0.0385885	−	0.840796i
$103$		−	5.33964i		−	0.526131i	−0.964778	−	0.263065i	$-0.915267\pi$
$103$		−	5.33964i		−	0.526131i	0.964778	−	0.263065i	$-0.0847335\pi$
$104$	−12.6477	+	1.75124i	−1.24021	+	0.171724i
$105$	−3.52311	−	3.14082i	−0.343820	−	0.306512i
$106$	0.0275805	+	0.600945i	0.00267885	+	0.0583690i
$107$	−3.71627	+	3.71627i	−0.359266	+	0.359266i	−0.863542	−	0.504277i	$-0.831759\pi$
$107$	−3.71627	+	3.71627i	−0.359266	+	0.359266i	0.504277	+	0.863542i	$0.331759\pi$
$108$	−6.42736	+	7.72957i	−0.618473	+	0.743778i
$109$	4.19466	−	4.19466i	0.401776	−	0.401776i	−0.477083	−	0.878858i	$-0.658306\pi$
$109$	4.19466	−	4.19466i	0.401776	−	0.401776i	0.878858	+	0.477083i	$0.158306\pi$
$110$	−3.25615	+	3.56942i	−0.310462	+	0.340330i
$111$	−17.6189			−1.67231
$112$	5.48318	−	9.05178i	0.518112	−	0.855313i
$113$	−7.59251			−0.714244			−0.357122	−	0.934058i	$-0.616242\pi$
$113$	−7.59251			−0.714244			−0.357122	+	0.934058i	$0.616242\pi$
$114$	5.42774	−	5.94992i	0.508354	−	0.557261i
$115$	2.92830	−	2.92830i	0.273065	−	0.273065i
$116$	−15.9006	−	13.2218i	−1.47633	−	1.22761i
$117$	−0.582348	+	0.582348i	−0.0538381	+	0.0538381i
$118$	−0.362966	−	7.90860i	−0.0334138	−	0.728045i
$119$	−6.65426	−	5.93220i	−0.609995	−	0.543804i
$120$	4.02351	+	3.04481i	0.367295	+	0.277951i
$121$		−	0.671633i		−	0.0610575i
$122$	0.0675004	+	1.47075i	0.00611120	+	0.133156i
$123$	−0.279013	+	0.279013i	−0.0251578	+	0.0251578i
$124$	0.922584	+	10.0298i	0.0828505	+	0.900704i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−0.0702983	−	0.678980i	−0.00626267	−	0.0604883i
$127$			15.9634i			1.41652i	0.705951	+	0.708261i	$0.250520\pi$
$127$			15.9634i			1.41652i	−0.705951	+	0.708261i	$0.749480\pi$
$128$	−5.06682	+	10.1157i	−0.447848	+	0.894110i
$129$		−	4.47385i		−	0.393900i
$130$	−4.71651	−	4.30258i	−0.413665	−	0.377361i
$131$	−1.90921	+	1.90921i	−0.166809	+	0.166809i	−0.785575	−	0.618766i	$-0.787633\pi$
$131$	−1.90921	+	1.90921i	−0.166809	+	0.166809i	0.618766	+	0.785575i	$0.287633\pi$
$132$	−12.1380	+	1.11650i	−1.05647	+	0.0971789i
$133$	−0.483728	−	8.43209i	−0.0419445	−	0.731155i
$134$	−0.633283	−	13.7985i	−0.0547073	−	1.19201i
$135$	−5.02636			−0.432600
$136$	7.59939	+	5.75086i	0.651642	+	0.493132i
$137$		−	20.5600i		−	1.75656i	−0.478150	−	0.878278i	$-0.658692\pi$
$137$		−	20.5600i		−	1.75656i	0.478150	−	0.878278i	$-0.341308\pi$
$138$	10.4368	−	0.478999i	0.888440	−	0.0407751i
$139$	−14.6788	−	14.6788i	−1.24504	−	1.24504i	−0.957884	−	0.287154i	$-0.907291\pi$
$139$	−14.6788	−	14.6788i	−1.24504	−	1.24504i	−0.287154	−	0.957884i	$-0.592709\pi$
$140$	5.23285	−	0.785680i	0.442256	−	0.0664021i
$141$	14.6852	−	14.6852i	1.23671	−	1.23671i
$142$	10.2690	+	9.36773i	0.861752	+	0.786122i
$143$	15.4225			1.28970
$144$	0.133123	+	0.717495i	0.0110935	+	0.0597912i
$145$		−	10.3398i		−	0.858671i
$146$	−10.4481	−	9.53115i	−0.864691	−	0.788803i
$147$	−9.78190	−	7.76232i	−0.806798	−	0.640226i
$148$	12.6293	−	15.1880i	1.03812	−	1.24845i
$149$	−12.0986	−	12.0986i	−0.991157	−	0.991157i	0.00880421	−	0.999961i	$-0.497197\pi$
$149$	−12.0986	−	12.0986i	−0.991157	−	0.991157i	−0.999961	+	0.00880421i	$0.997197\pi$
$150$	0.115666	+	2.52022i	0.00944407	+	0.205775i
$151$	17.6269			1.43446			0.717228	−	0.696839i	$-0.245411\pi$
$151$	17.6269			1.43446			0.717228	+	0.696839i	$0.245411\pi$
$152$	1.23839	+	8.94378i	0.100447	+	0.725436i
$153$	0.614697			0.0496953
$154$	−8.05996	+	9.92169i	−0.649490	+	0.799513i
$155$	−3.56105	+	3.56105i	−0.286030	+	0.286030i
$156$	−1.47531	−	16.0387i	−0.118119	−	1.28412i
$157$	−16.9527	−	16.9527i	−1.35297	−	1.35297i	−0.882321	−	0.470648i	$-0.844020\pi$
$157$	−16.9527	−	16.9527i	−1.35297	−	1.35297i	−0.470648	−	0.882321i	$-0.655980\pi$
$158$	2.02810	−	2.22321i	0.161347	−	0.176869i
$159$	−0.758851			−0.0601808
$160$	−5.50877	+	1.28586i	−0.435507	+	0.101656i
$161$	7.29110	−	8.17855i	0.574619	−	0.644560i
$162$	−9.94021	−	9.06783i	−0.780976	−	0.712436i
$163$	0.139889	+	0.139889i	0.0109570	+	0.0109570i	0.712564	−	0.701607i	$-0.247534\pi$
$163$	0.139889	+	0.139889i	0.0109570	+	0.0109570i	−0.701607	+	0.712564i	$0.747534\pi$
$164$	−0.0405204	−	0.440515i	−0.00316411	−	0.0343985i
$165$	−4.30954	−	4.30954i	−0.335497	−	0.335497i
$166$	5.93669	−	0.272466i	0.460777	−	0.0211474i
$167$			21.9903i			1.70166i	0.525439	+	0.850832i	$0.323901\pi$
$167$			21.9903i			1.70166i	−0.525439	+	0.850832i	$0.676099\pi$
$168$	11.0891	+	7.43289i	0.855544	+	0.573460i
$169$			7.37880i			0.567600i
$170$	0.218463	+	4.76005i	0.0167554	+	0.365079i
$171$	0.411806	+	0.411806i	0.0314916	+	0.0314916i
$172$	3.85659	+	3.20686i	0.294062	+	0.244521i
$173$	2.40549	+	2.40549i	0.182886	+	0.182886i	0.792612	−	0.609726i	$-0.208721\pi$
$173$	2.40549	+	2.40549i	0.182886	+	0.182886i	−0.609726	+	0.792612i	$0.708721\pi$
$174$	17.5804	−	19.2718i	1.33277	−	1.46099i
$175$	1.97491	+	1.76061i	0.149289	+	0.133090i
$176$	7.73806	−	11.2636i	0.583278	−	0.849025i
$177$	9.98668			0.750645
$178$	−0.989053	−	0.902251i	−0.0741327	−	0.0676266i
$179$	11.3642	+	11.3642i	0.849399	+	0.849399i	0.990058	−	0.140659i	$-0.0449220\pi$
$179$	11.3642	+	11.3642i	0.849399	+	0.849399i	−0.140659	+	0.990058i	$0.544922\pi$
$180$	−0.233285	+	0.280550i	−0.0173880	+	0.0209109i
$181$	−8.82475	+	8.82475i	−0.655938	+	0.655938i	−0.954416	−	0.298478i	$-0.903521\pi$
$181$	−8.82475	+	8.82475i	−0.655938	+	0.655938i	0.298478	+	0.954416i	$0.403521\pi$
$182$	−13.1102	−	10.6502i	−0.971792	−	0.789443i
$183$	−1.85721			−0.137289
$184$	−7.06821	+	9.34018i	−0.521076	+	0.688567i
$185$	9.87641			0.726128
$186$	−12.6920	+	0.582502i	−0.930624	+	0.0427111i
$187$	−8.13962	−	8.13962i	−0.595228	−	0.595228i
$188$	2.13269	+	23.1854i	0.155542	+	1.69097i
$189$	−13.2767	+	0.761649i	−0.965736	+	0.0554018i
$190$	−3.04256	+	3.33527i	−0.220730	+	0.241966i
$191$			22.9401i			1.65989i	0.557848	+	0.829943i	$0.311627\pi$
$191$			22.9401i			1.65989i	−0.557848	+	0.829943i	$0.688373\pi$
$192$	−12.4538	−	6.96977i	−0.898779	−	0.503000i
$193$	−18.8345			−1.35574			−0.677869	−	0.735182i	$-0.737097\pi$
$193$	−18.8345			−1.35574			−0.677869	+	0.735182i	$0.737097\pi$
$194$	0.669278	−	0.733667i	0.0480514	−	0.0526742i
$195$	5.69448	−	5.69448i	0.407790	−	0.407790i
$196$	13.7030	−	2.86824i	0.978788	−	0.204874i
$197$	12.7045	+	12.7045i	0.905159	+	0.905159i	0.995877	−	0.0907178i	$-0.0289161\pi$
$197$	12.7045	+	12.7045i	0.905159	+	0.905159i	−0.0907178	+	0.995877i	$0.528916\pi$
$198$	−0.0404109	−	0.880505i	−0.00287188	−	0.0625748i
$199$			6.52407i			0.462479i	0.972897	+	0.231240i	$0.0742781\pi$
$199$			6.52407i			0.462479i	−0.972897	+	0.231240i	$0.925722\pi$
$200$	−2.25541	−	1.70679i	−0.159482	−	0.120688i
$201$	17.4242			1.22901
$202$	11.7333	−	0.538502i	0.825552	−	0.0378889i
$203$	−1.56679	−	27.3115i	−0.109967	−	1.91689i
$204$	−7.68620	+	9.24346i	−0.538142	+	0.647172i
$205$	0.156403	−	0.156403i	0.0109237	−	0.0109237i
$206$	−5.08922	+	5.57883i	−0.354583	+	0.388696i
$207$			0.755506i			0.0525113i
$208$	14.8833	+	10.2248i	1.03197	+	0.708964i
$209$		−	10.9060i		−	0.754384i
$210$	0.687411	+	6.63939i	0.0474359	+	0.458162i
$211$	−2.55743	−	2.55743i	−0.176061	−	0.176061i	0.613576	−	0.789636i	$-0.289731\pi$
$211$	−2.55743	−	2.55743i	−0.176061	−	0.176061i	−0.789636	+	0.613576i	$0.789731\pi$
$212$	0.543946	−	0.654152i	0.0373584	−	0.0449273i
$213$	−12.3982	+	12.3982i	−0.849513	+	0.849513i
$214$	7.42473	−	0.340759i	0.507544	−	0.0232938i
$215$			2.50785i			0.171034i
$216$	14.0823	−	1.94989i	0.958182	−	0.132674i
$217$	−8.86657	+	9.94579i	−0.601902	+	0.675164i
$218$	−8.38050	+	0.384625i	−0.567599	+	0.0260501i
$219$	12.6145	−	12.6145i	0.852410	−	0.852410i
$220$	6.80403	−	0.625863i	0.458728	−	0.0421956i
$221$	10.7554	−	10.7554i	0.723488	−	0.723488i
$222$	18.4082	+	16.7926i	1.23547	+	1.12705i
$223$	2.17136			0.145405			0.0727024	−	0.997354i	$-0.476838\pi$
$223$	2.17136			0.145405			0.0727024	+	0.997354i	$0.476838\pi$
$224$	−14.3561	+	4.23124i	−0.959205	+	0.282711i
$225$	−0.182435			−0.0121623
$226$	7.93262	+	7.23644i	0.527670	+	0.481361i
$227$	1.60426	−	1.60426i	0.106479	−	0.106479i	−0.651860	−	0.758339i	$-0.726011\pi$
$227$	1.60426	−	1.60426i	0.106479	−	0.106479i	0.758339	+	0.651860i	$0.226011\pi$
$228$	−11.3417	+	1.04326i	−0.751126	+	0.0690916i
$229$	11.4424	−	11.4424i	0.756135	−	0.756135i	−0.219482	−	0.975617i	$-0.570437\pi$
$229$	11.4424	−	11.4424i	0.756135	−	0.756135i	0.975617	+	0.219482i	$0.0704366\pi$
$230$	−5.85043	+	0.268507i	−0.385766	+	0.0177048i
$231$	−12.0363	−	10.7302i	−0.791929	−	0.705997i
$232$	4.01114	+	28.9689i	0.263344	+	1.90190i
$233$			14.8538i			0.973107i	0.873651	+	0.486553i	$0.161746\pi$
$233$			14.8538i			0.973107i	−0.873651	+	0.486553i	$0.838254\pi$
$234$	1.16347	−	0.0533977i	0.0760584	−	0.00349072i
$235$	−8.23188	+	8.23188i	−0.536989	+	0.536989i
$236$	−7.15847	+	8.60881i	−0.465977	+	0.560386i
$237$	2.68420	+	2.68420i	0.174357	+	0.174357i
$238$	1.29834	+	12.5401i	0.0841592	+	0.812855i
$239$		−	9.10839i		−	0.589173i	−0.955625	−	0.294586i	$-0.904818\pi$
$239$		−	9.10839i		−	0.589173i	0.955625	−	0.294586i	$-0.0951819\pi$
$240$	−1.30174	−	7.01601i	−0.0840268	−	0.452882i
$241$			25.1123i			1.61763i	0.588066	+	0.808813i	$0.299889\pi$
$241$			25.1123i			1.61763i	−0.588066	+	0.808813i	$0.700111\pi$
$242$	−0.640134	+	0.701719i	−0.0411494	+	0.0451082i
$243$	1.33879	−	1.33879i	0.0858837	−	0.0858837i
$244$	1.33125	−	1.60097i	0.0852246	−	0.102492i
$245$	5.48332	+	4.35123i	0.350317	+	0.277990i
$246$	0.557440	−	0.0255838i	0.0355411	−	0.00163116i
$247$	14.4108			0.916939
$248$	8.59553	−	11.3584i	0.545816	−	0.721261i
$249$			7.49663i			0.475080i
$250$	−0.0648373	−	1.41273i	−0.00410067	−	0.0893487i
$251$	−16.4683	−	16.4683i	−1.03947	−	1.03947i	−0.999188	−	0.0402794i	$-0.987175\pi$
$251$	−16.4683	−	16.4683i	−1.03947	−	1.03947i	−0.0402794	−	0.999188i	$-0.512825\pi$
$252$	−0.573689	+	0.776396i	−0.0361390	+	0.0489084i
$253$	10.0042	−	10.0042i	0.628956	−	0.628956i
$254$	15.2147	−	16.6785i	0.954657	−	1.04650i
$255$	−6.01081			−0.376411
$256$	14.9351	−	5.73963i	0.933442	−	0.358727i
$257$		−	8.79531i		−	0.548637i	−0.961639	−	0.274318i	$-0.911548\pi$
$257$		−	8.79531i		−	0.548637i	0.961639	−	0.274318i	$-0.0884522\pi$
$258$	−4.26403	+	4.67426i	−0.265467	+	0.291007i
$259$	26.0876	−	1.49658i	1.62101	−	0.0929931i
$260$	0.826994	+	8.99062i	0.0512880	+	0.557575i
$261$	1.33384	+	1.33384i	0.0825626	+	0.0825626i
$262$	3.81441	−	0.175063i	0.235655	−	0.0108154i
$263$	−18.5083			−1.14127			−0.570636	−	0.821203i	$-0.693303\pi$
$263$	−18.5083			−1.14127			−0.570636	+	0.821203i	$0.693303\pi$
$264$	13.7458	+	10.4022i	0.845997	+	0.640211i
$265$	0.425380			0.0261309
$266$	−7.53124	+	9.27085i	−0.461770	+	0.568433i
$267$	1.19413	−	1.19413i	0.0730798	−	0.0730798i
$268$	−12.4897	+	15.0201i	−0.762929	+	0.917502i
$269$	13.4121	+	13.4121i	0.817748	+	0.817748i	0.985781	−	0.168033i	$-0.0537417\pi$
$269$	13.4121	+	13.4121i	0.817748	+	0.817748i	−0.168033	+	0.985781i	$0.553742\pi$
$270$	5.25152	+	4.79063i	0.319597	+	0.291549i
$271$	6.89041			0.418563			0.209281	−	0.977855i	$-0.432888\pi$
$271$	6.89041			0.418563			0.209281	+	0.977855i	$0.432888\pi$
$272$	−2.45865	−	13.2515i	−0.149078	−	0.803488i
$273$	14.1786	−	15.9043i	0.858125	−	0.962574i
$274$	−19.5957	+	21.4810i	−1.18382	+	1.29771i
$275$	2.41574	+	2.41574i	0.145675	+	0.145675i
$276$	−11.3609	−	9.44688i	−0.683844	−	0.568635i
$277$	−2.88597	−	2.88597i	−0.173401	−	0.173401i	0.615071	−	0.788472i	$-0.289127\pi$
$277$	−2.88597	−	2.88597i	−0.173401	−	0.173401i	−0.788472	+	0.615071i	$0.789127\pi$
$278$	1.34595	+	29.3267i	0.0807250	+	1.75890i
$279$		−	0.918757i		−	0.0550046i
$280$	−6.21609	−	4.16656i	−0.371482	−	0.249000i
$281$			18.8373i			1.12374i	0.827226	+	0.561869i	$0.189918\pi$
$281$			18.8373i			1.12374i	−0.827226	+	0.561869i	$0.810082\pi$
$282$	−29.3394	+	1.34654i	−1.74714	+	0.0801852i
$283$	15.5617	+	15.5617i	0.925050	+	0.925050i	0.997381	−	0.0723307i	$-0.0230437\pi$
$283$	15.5617	+	15.5617i	0.925050	+	0.925050i	−0.0723307	+	0.997381i	$0.523044\pi$
$284$	−1.80056	−	19.5747i	−0.106844	−	1.16155i
$285$	−4.02684	−	4.02684i	−0.238530	−	0.238530i
$286$	−16.1134	−	14.6992i	−0.952803	−	0.869183i
$287$	0.389425	−	0.436824i	0.0229870	−	0.0257849i
$288$	0.544759	−	0.876514i	0.0321003	−	0.0516491i
$289$	5.64711			0.332183
$290$	−9.85485	+	10.8029i	−0.578697	+	0.634370i
$291$	0.885793	+	0.885793i	0.0519261	+	0.0519261i
$292$	1.83197	+	19.9162i	0.107208	+	1.16551i
$293$	20.1174	−	20.1174i	1.17527	−	1.17527i	0.194337	−	0.980935i	$-0.437744\pi$
$293$	20.1174	−	20.1174i	1.17527	−	1.17527i	0.980935	−	0.194337i	$-0.0622555\pi$
$294$	2.82181	+	17.4332i	0.164571	+	1.01672i
$295$	−5.59811			−0.325934
$296$	−27.6707	+	3.83139i	−1.60833	+	0.222695i
$297$	−17.1719			−0.996417
$298$	1.10937	+	24.1718i	0.0642640	+	1.40023i
$299$	13.2192	+	13.2192i	0.764484	+	0.764484i
$300$	2.28118	−	2.74335i	0.131704	−	0.158387i
$301$	0.380017	+	6.62426i	0.0219038	+	0.381816i
$302$	−18.4165	−	16.8002i	−1.05975	−	0.966744i
$303$			14.8164i			0.851178i
$304$	7.23047	−	10.5247i	0.414696	−	0.603635i
$305$	1.04107			0.0596117
$306$	−0.642233	−	0.585869i	−0.0367140	−	0.0334919i
$307$	9.06102	−	9.06102i	0.517140	−	0.517140i	−0.399565	−	0.916705i	$-0.630839\pi$
$307$	9.06102	−	9.06102i	0.517140	−	0.517140i	0.916705	+	0.399565i	$0.130839\pi$
$308$	17.8774	−	2.68418i	1.01866	−	0.152945i
$309$	−6.73561	−	6.73561i	−0.383175	−	0.383175i
$310$	7.11461	−	0.326526i	0.404082	−	0.0185454i
$311$			21.6643i			1.22847i	0.789124	+	0.614234i	$0.210535\pi$
$311$			21.6643i			1.22847i	−0.789124	+	0.614234i	$0.789465\pi$
$312$	−13.7451	+	18.1633i	−0.778165	+	1.02829i
$313$	0.638170			0.0360715			0.0180358	−	0.999837i	$-0.494259\pi$
$313$	0.638170			0.0360715			0.0180358	+	0.999837i	$0.494259\pi$
$314$	1.55445	+	33.8697i	0.0877229	+	1.91138i
$315$	−0.481885	+	0.0276445i	−0.0271512	+	0.00155759i
$316$	−4.23790	+	0.389819i	−0.238400	+	0.0219290i
$317$	−16.4665	+	16.4665i	−0.924853	+	0.924853i	−0.997367	−	0.0725140i	$-0.976898\pi$
$317$	−16.4665	+	16.4665i	−0.924853	+	0.924853i	0.0725140	+	0.997367i	$0.476898\pi$
$318$	0.792844	+	0.723262i	0.0444605	+	0.0405585i
$319$		−	35.3245i		−	1.97779i
$320$	6.98110	+	3.90696i	0.390255	+	0.218405i
$321$			9.37567i			0.523299i
$322$	−15.4127	+	1.59576i	−0.858916	+	0.0889281i
$323$	−7.60568	−	7.60568i	−0.423191	−	0.423191i
$324$	1.74292	+	18.9481i	0.0968289	+	1.05267i
$325$	−3.19208	+	3.19208i	−0.177065	+	0.177065i
$326$	−0.0128270	−	0.279484i	−0.000710420	−	0.0154792i
$327$		−	10.5826i		−	0.585218i
$328$	−0.377520	+	0.498868i	−0.0208451	+	0.0275454i
$329$	−20.4964	+	22.9911i	−1.13000	+	1.26754i
$330$	0.395158	+	8.61001i	0.0217527	+	0.473965i
$331$	−4.44059	+	4.44059i	−0.244077	+	0.244077i	−0.818534	−	0.574458i	$-0.805213\pi$
$331$	−4.44059	+	4.44059i	−0.244077	+	0.244077i	0.574458	+	0.818534i	$0.305213\pi$
$332$	−6.46232	−	5.37360i	−0.354666	−	0.294915i
$333$	−1.27407	+	1.27407i	−0.0698184	+	0.0698184i
$334$	20.9590	−	22.9754i	1.14683	−	1.25716i
$335$	−9.76725			−0.533642
$336$	−4.50156	−	18.3349i	−0.245580	−	1.00025i
$337$	5.01245			0.273045			0.136523	−	0.990637i	$-0.456407\pi$
$337$	5.01245			0.273045			0.136523	+	0.990637i	$0.456407\pi$
$338$	7.03275	−	7.70934i	0.382531	−	0.419333i
$339$	−9.57746	+	9.57746i	−0.520176	+	0.520176i
$340$	4.30856	−	5.18149i	0.233664	−	0.281006i
$341$	−12.1659	+	12.1659i	−0.658819	+	0.658819i
$342$	−0.0377601	−	0.822746i	−0.00204183	−	0.0444890i
$343$	15.1430	+	10.6625i	0.817647	+	0.575720i
$344$	−0.972880	−	7.02624i	−0.0524541	−	0.378829i
$345$		−	7.38771i		−	0.397741i
$346$	−0.220568	−	4.80591i	−0.0118578	−	0.258367i
$347$	16.5236	−	16.5236i	0.887033	−	0.887033i	−0.107204	−	0.994237i	$-0.534190\pi$
$347$	16.5236	−	16.5236i	0.887033	−	0.887033i	0.994237	+	0.107204i	$0.0341899\pi$
$348$	−36.7359	+	3.37912i	−1.96925	+	0.181140i
$349$	25.3113	+	25.3113i	1.35489	+	1.35489i	0.880104	+	0.474782i	$0.157473\pi$
$349$	25.3113	+	25.3113i	1.35489	+	1.35489i	0.474782	+	0.880104i	$0.342527\pi$
$350$	−0.385334	−	3.72176i	−0.0205969	−	0.198937i
$351$		−	22.6904i		−	1.21113i
$352$	−18.8200	+	4.39299i	−1.00311	+	0.234147i
$353$		−	14.5067i		−	0.772113i	−0.922475	−	0.386057i	$-0.873837\pi$
$353$		−	14.5067i		−	0.772113i	0.922475	−	0.386057i	$-0.126163\pi$
$354$	−10.4340	−	9.51832i	−0.554563	−	0.505893i
$355$	6.94992	−	6.94992i	0.368864	−	0.368864i
$356$	0.173421	+	1.88534i	0.00919129	+	0.0999226i
$357$	−15.8770	+	0.910823i	−0.840300	+	0.0482059i
$358$	−1.04203	−	22.7045i	−0.0550728	−	1.19997i
$359$	1.58532			0.0836698			0.0418349	−	0.999125i	$-0.486680\pi$
$359$	1.58532			0.0836698			0.0418349	+	0.999125i	$0.486680\pi$
$360$	0.511127	−	0.0707727i	0.0269388	−	0.00373005i
$361$			8.80940i			0.463653i
$362$	17.6309	−	0.809175i	0.926662	−	0.0425293i
$363$	−0.847221	−	0.847221i	−0.0444676	−	0.0444676i
$364$	3.54679	+	23.6226i	0.185902	+	1.23816i
$365$	−7.07117	+	7.07117i	−0.370122	+	0.370122i
$366$	1.94040	+	1.77011i	0.101427	+	0.0925251i
$367$	13.4222			0.700636			0.350318	−	0.936631i	$-0.386074\pi$
$367$	13.4222			0.700636			0.350318	+	0.936631i	$0.386074\pi$
$368$	16.2870	−	3.02185i	0.849017	−	0.157525i
$369$			0.0403523i			0.00210066i
$370$	−10.3188	−	9.41322i	−0.536450	−	0.489370i
$371$	1.12360	−	0.0644582i	0.0583345	−	0.00334650i
$372$	13.8157	+	11.4882i	0.716313	+	0.595635i
$373$	−16.5051	−	16.5051i	−0.854602	−	0.854602i	0.136094	−	0.990696i	$-0.456545\pi$
$373$	−16.5051	−	16.5051i	−0.854602	−	0.854602i	−0.990696	+	0.136094i	$0.956545\pi$
$374$	0.746353	+	16.2621i	0.0385930	+	0.840894i
$375$	1.78394			0.0921222
$376$	19.8698	−	26.2567i	1.02471	−	1.35408i
$377$	46.6767			2.40397
$378$	14.5973	+	11.8583i	0.750806	+	0.609923i
$379$	8.09894	−	8.09894i	0.416015	−	0.416015i	−0.467813	−	0.883827i	$-0.654958\pi$
$379$	8.09894	−	8.09894i	0.416015	−	0.416015i	0.883827	+	0.467813i	$0.154958\pi$
$380$	6.35770	−	0.584808i	0.326143	−	0.0300000i
$381$	20.1368	+	20.1368i	1.03164	+	1.03164i
$382$	21.8642	−	23.9677i	1.11867	−	1.22629i
$383$	15.6724			0.800821			0.400411	−	0.916336i	$-0.368868\pi$
$383$	15.6724			0.800821			0.400411	+	0.916336i	$0.368868\pi$
$384$	6.36882	+	19.1518i	0.325008	+	0.977334i
$385$	6.74702	+	6.01491i	0.343860	+	0.306548i
$386$	19.6782	+	17.9512i	1.00160	+	0.913693i
$387$	−0.323515	−	0.323515i	−0.0164452	−	0.0164452i
$388$	−1.39852	+	0.128641i	−0.0709990	+	0.00653078i
$389$	10.7754	+	10.7754i	0.546333	+	0.546333i	0.925378	−	0.379045i	$-0.123748\pi$
$389$	10.7754	+	10.7754i	0.546333	+	0.546333i	−0.379045	+	0.925378i	$0.623748\pi$
$390$	−11.3770	+	0.522149i	−0.576096	+	0.0264400i
$391$		−	13.9535i		−	0.705659i
$392$	−17.0506	−	10.0637i	−0.861185	−	0.508292i
$393$			4.81670i			0.242970i
$394$	−1.16493	−	25.3823i	−0.0586881	−	1.27874i
$395$	−1.50465	−	1.50465i	−0.0757070	−	0.0757070i
$396$	−0.796990	+	0.958463i	−0.0400502	+	0.0481646i
$397$	−26.2346	−	26.2346i	−1.31668	−	1.31668i	−0.916389	−	0.400289i	$-0.868910\pi$
$397$	−26.2346	−	26.2346i	−1.31668	−	1.31668i	−0.400289	−	0.916389i	$-0.631090\pi$
$398$	6.21810	−	6.81632i	0.311685	−	0.341671i
$399$	−11.2467	−	10.0263i	−0.563041	−	0.501945i
$400$	0.729699	+	3.93288i	0.0364849	+	0.196644i
$401$	1.82770			0.0912709			0.0456355	−	0.998958i	$-0.485469\pi$
$401$	1.82770			0.0912709			0.0456355	+	0.998958i	$0.485469\pi$
$402$	−18.2047	−	16.6070i	−0.907968	−	0.828282i
$403$	−16.0756	−	16.0756i	−0.800782	−	0.800782i
$404$	−12.7721	−	10.6204i	−0.635438	−	0.528385i
$405$	−6.72743	+	6.72743i	−0.334289	+	0.334289i
$406$	−24.3937	+	30.0283i	−1.21064	+	1.49028i
$407$	33.7415			1.67251
$408$	16.8405	−	2.33180i	0.833727	−	0.115441i
$409$	−4.69842			−0.232322			−0.116161	−	0.993230i	$-0.537059\pi$
$409$	−4.69842			−0.232322			−0.116161	+	0.993230i	$0.537059\pi$
$410$	−0.312477	+	0.0143412i	−0.0154322	+	0.000708261i
$411$	−25.9351	−	25.9351i	−1.27928	−	1.27928i
$412$	10.6344	−	0.978195i	0.523919	−	0.0481922i
$413$	−14.7869	+	0.848286i	−0.727615	+	0.0417414i
$414$	0.720074	−	0.789349i	0.0353897	−	0.0387944i
$415$		−	4.20229i		−	0.206283i
$416$	−5.80475	−	24.8682i	−0.284601	−	1.21926i
$417$	−37.0327			−1.81350
$418$	−10.3945	+	11.3945i	−0.508413	+	0.557325i
$419$	2.80823	−	2.80823i	0.137191	−	0.137191i	−0.635176	−	0.772367i	$-0.719073\pi$
$419$	2.80823	−	2.80823i	0.137191	−	0.137191i	0.772367	+	0.635176i	$0.219073\pi$
$420$	5.60981	−	7.59198i	0.273731	−	0.370451i
$421$	−3.94040	−	3.94040i	−0.192043	−	0.192043i	0.604535	−	0.796578i	$-0.293359\pi$
$421$	−3.94040	−	3.94040i	−0.192043	−	0.192043i	−0.796578	+	0.604535i	$0.793359\pi$
$422$	0.234500	+	5.10947i	0.0114153	+	0.248725i
$423$		−	2.12384i		−	0.103265i
$424$	−1.19179	+	0.165019i	−0.0578782	+	0.00801404i
$425$	3.36940			0.163440
$426$	24.7704	−	1.13684i	1.20013	−	0.0550801i
$427$	2.74990	−	0.157755i	0.133077	−	0.00763429i
$428$	−8.08210	−	6.72050i	−0.390663	−	0.324847i
$429$	19.4545	−	19.4545i	0.939272	−	0.939272i
$430$	2.39024	−	2.62019i	0.115267	−	0.126357i
$431$			14.4076i			0.693987i	0.937867	+	0.346994i	$0.112797\pi$
$431$			14.4076i			0.693987i	−0.937867	+	0.346994i	$0.887203\pi$
$432$	−16.5716	−	11.3847i	−0.797302	−	0.547745i
$433$		−	4.29234i		−	0.206277i	−0.994667	−	0.103138i	$-0.967112\pi$
$433$		−	4.29234i		−	0.206277i	0.994667	−	0.103138i	$-0.0328884\pi$
$434$	18.7431	−	1.94057i	0.899698	−	0.0931504i
$435$	−13.0429	−	13.0429i	−0.625361	−	0.625361i
$436$	9.12250	+	7.58562i	0.436888	+	0.363285i
$437$	9.34791	−	9.34791i	0.447171	−	0.447171i
$438$	−25.2025	+	1.15667i	−1.20422	+	0.0552680i
$439$			22.1530i			1.05731i	0.848838	+	0.528653i	$0.177303\pi$
$439$			22.1530i			1.05731i	−0.848838	+	0.528653i	$0.822697\pi$
$440$	−7.70533	−	5.83103i	−0.367337	−	0.277984i
$441$	−1.26867	+	0.146041i	−0.0604127	+	0.00695433i
$442$	−21.4882	+	0.986206i	−1.02209	+	0.0469090i
$443$	6.67413	−	6.67413i	0.317098	−	0.317098i	−0.530554	−	0.847651i	$-0.678016\pi$
$443$	6.67413	−	6.67413i	0.317098	−	0.317098i	0.847651	+	0.530554i	$0.178016\pi$
$444$	−3.22769	−	35.0897i	−0.153179	−	1.66528i
$445$	−0.669381	+	0.669381i	−0.0317317	+	0.0317317i
$446$	−2.26862	−	2.06952i	−0.107422	−	0.0979948i
$447$	−30.5232			−1.44370
$448$	19.0319	+	9.26201i	0.899175	+	0.437589i
$449$	16.9705			0.800887			0.400444	−	0.916321i	$-0.368856\pi$
$449$	16.9705			0.800887			0.400444	+	0.916321i	$0.368856\pi$
$450$	0.190607	+	0.173879i	0.00898531	+	0.00819674i
$451$	0.534332	−	0.534332i	0.0251607	−	0.0251607i
$452$	−1.39091	−	15.1212i	−0.0654229	−	0.711241i
$453$	22.2352	−	22.2352i	1.04470	−	1.04470i
$454$	−3.20515	+	0.147101i	−0.150425	+	0.00690379i
$455$	−7.94790	+	8.91530i	−0.372603	+	0.417956i
$456$	12.8441	+	9.71984i	0.601482	+	0.455173i
$457$			6.13480i			0.286974i	0.989652	+	0.143487i	$0.0458315\pi$
$457$			6.13480i			0.286974i	−0.989652	+	0.143487i	$0.954169\pi$
$458$	−22.8607	+	1.04920i	−1.06821	+	0.0490258i
$459$	−11.9755	+	11.9755i	−0.558966	+	0.558966i
$460$	6.36842	+	5.29552i	0.296929	+	0.246905i
$461$	21.5315	+	21.5315i	1.00282	+	1.00282i	0.999996	+	0.00282660i	$0.000899735\pi$
$461$	21.5315	+	21.5315i	1.00282	+	1.00282i	0.00282660	+	0.999996i	$0.499100\pi$
$462$	2.34846	+	22.6827i	0.109260	+	1.05529i
$463$		−	29.9038i		−	1.38975i	−0.719131	−	0.694874i	$-0.755460\pi$
$463$		−	29.9038i		−	1.38975i	0.719131	−	0.694874i	$-0.244540\pi$
$464$	23.4195	−	34.0896i	1.08722	−	1.58257i
$465$			8.98406i			0.416626i
$466$	14.1572	−	15.5192i	0.655820	−	0.718914i
$467$	−2.16053	+	2.16053i	−0.0999776	+	0.0999776i	−0.755326	−	0.655349i	$-0.772522\pi$
$467$	−2.16053	+	2.16053i	−0.0999776	+	0.0999776i	0.655349	+	0.755326i	$0.272522\pi$
$468$	−1.26648	−	1.05312i	−0.0585432	−	0.0486803i
$469$	−25.7993	+	1.48004i	−1.19130	+	0.0683419i
$470$	16.4464	−	0.754813i	0.758618	−	0.0348169i
$471$	−42.7693			−1.97071
$472$	15.6842	−	2.17169i	0.721924	−	0.0999604i
$473$			8.56776i			0.393946i
$474$	−0.246124	−	5.36275i	−0.0113049	−	0.246319i
$475$	2.25728	+	2.25728i	0.103571	+	0.103571i
$476$	10.5955	−	14.3393i	0.485644	−	0.657242i
$477$	−0.0548744	+	0.0548744i	−0.00251253	+	0.00251253i
$478$	−8.68122	+	9.51641i	−0.397070	+	0.435270i
$479$	−14.4850			−0.661838			−0.330919	−	0.943659i	$-0.607359\pi$
$479$	−14.4850			−0.661838			−0.330919	+	0.943659i	$0.607359\pi$
$480$	−5.32692	+	8.57099i	−0.243140	+	0.391210i
$481$			44.5850i			2.03290i
$482$	23.9346	−	26.2372i	1.09019	−	1.19507i
$483$	−1.11947	−	19.5139i	−0.0509375	−	0.887915i
$484$	1.33762	−	0.123040i	0.0608009	−	0.00559271i
$485$	−0.496538	−	0.496538i	−0.0225466	−	0.0225466i
$486$	−2.67477	+	0.122759i	−0.121330	+	0.00556847i
$487$	23.9991			1.08750			0.543751	−	0.839247i	$-0.317004\pi$
$487$	23.9991			1.08750			0.543751	+	0.839247i	$0.317004\pi$
$488$	−2.91677	+	0.403867i	−0.132036	+	0.0182822i
$489$	0.352922			0.0159597
$490$	−1.58179	−	9.77231i	−0.0714578	−	0.441468i
$491$	−1.18454	+	1.18454i	−0.0534575	+	0.0534575i	−0.733330	−	0.679873i	$-0.762035\pi$
$491$	−1.18454	+	1.18454i	−0.0534575	+	0.0534575i	0.679873	+	0.733330i	$0.262035\pi$
$492$	−0.606795	−	0.504567i	−0.0273564	−	0.0227477i
$493$	−24.6348	−	24.6348i	−1.10950	−	1.10950i
$494$	−15.0564	−	13.7350i	−0.677418	−	0.617966i
$495$	−0.623267			−0.0280137
$496$	−19.8063	+	3.67482i	−0.889329	+	0.165004i
$497$	17.3045	−	19.4107i	0.776211	−	0.870690i
$498$	7.14505	−	7.83245i	0.320177	−	0.350980i
$499$	10.8685	+	10.8685i	0.486539	+	0.486539i	0.907212	−	0.420673i	$-0.138206\pi$
$499$	10.8685	+	10.8685i	0.486539	+	0.486539i	−0.420673	+	0.907212i	$0.638206\pi$
$500$	−1.27873	+	1.53781i	−0.0571865	+	0.0687728i
$501$	27.7394	+	27.7394i	1.23930	+	1.23930i
$502$	1.51004	+	32.9019i	0.0673963	+	1.46848i
$503$		−	30.0228i		−	1.33865i	−0.742970	−	0.669325i	$-0.766583\pi$
$503$		−	30.0228i		−	1.33865i	0.742970	−	0.669325i	$-0.233417\pi$
$504$	1.33937	−	0.264391i	0.0596604	−	0.0117769i
$505$		−	8.30543i		−	0.369587i
$506$	−19.9873	+	0.917320i	−0.888543	+	0.0407798i
$507$	9.30787	+	9.30787i	0.413377	+	0.413377i
$508$	−31.7925	+	2.92441i	−1.41057	+	0.129750i
$509$	−1.83317	−	1.83317i	−0.0812538	−	0.0812538i	0.665312	−	0.746566i	$-0.268299\pi$
$509$	−1.83317	−	1.83317i	−0.0812538	−	0.0812538i	−0.746566	+	0.665312i	$0.768299\pi$
$510$	6.28006	+	5.72891i	0.278086	+	0.253680i
$511$	−17.6063	+	19.7493i	−0.778858	+	0.873659i
$512$	−21.0746	−	8.23790i	−0.931373	−	0.364067i
$513$	−16.0455			−0.708427
$514$	−8.38283	+	9.18930i	−0.369751	+	0.405323i
$515$	3.77570	+	3.77570i	0.166377	+	0.166377i
$516$	8.91008	−	0.819586i	0.392245	−	0.0360803i
$517$	−28.1232	+	28.1232i	−1.23686	+	1.23686i
$518$	−28.6826	−	23.3005i	−1.26024	−	1.02377i
$519$	6.06873			0.266388
$520$	7.70494	−	10.1816i	0.337884	−	0.446491i
$521$	−32.1359			−1.40790			−0.703950	−	0.710249i	$-0.748582\pi$
$521$	−32.1359			−1.40790			−0.703950	+	0.710249i	$0.748582\pi$
$522$	−0.122305	−	2.66487i	−0.00535314	−	0.116638i
$523$	−30.1214	−	30.1214i	−1.31712	−	1.31712i	−0.916047	−	0.401071i	$-0.868638\pi$
$523$	−30.1214	−	30.1214i	−1.31712	−	1.31712i	−0.401071	−	0.916047i	$-0.631362\pi$
$524$	−4.15213	−	3.45262i	−0.181387	−	0.150828i
$525$	4.71211	−	0.270322i	0.205653	−	0.0117978i
$526$	19.3374	+	17.6403i	0.843151	+	0.769154i
$527$			16.9686i			0.739164i
$528$	−4.44723	−	23.9693i	−0.193541	−	1.04313i
$529$	−5.85018			−0.254355
$530$	−0.444435	−	0.405430i	−0.0193050	−	0.0176108i
$531$	0.722161	−	0.722161i	0.0313391	−	0.0313391i
$532$	16.7047	−	2.50810i	0.724239	−	0.108740i
$533$	0.706049	+	0.706049i	0.0305824	+	0.0305824i
$534$	−2.38576	+	0.109495i	−0.103242	+	0.00473830i
$535$		−	5.25560i		−	0.227220i
$536$	27.3649	−	3.78905i	1.18198	−	0.163662i
$537$	28.6704			1.23722
$538$	−1.22980	−	26.7959i	−0.0530206	−	1.15525i
$539$	18.7331	+	14.8654i	0.806891	+	0.640300i
$540$	−0.920803	−	10.0105i	−0.0396251	−	0.430782i
$541$	−7.40843	+	7.40843i	−0.318513	+	0.318513i	−0.848196	−	0.529683i	$-0.822311\pi$
$541$	−7.40843	+	7.40843i	−0.318513	+	0.318513i	0.529683	+	0.848196i	$0.322311\pi$
$542$	−7.19907	−	6.56727i	−0.309227	−	0.282088i
$543$			22.2637i			0.955426i
$544$	−10.0612	+	16.1884i	−0.431370	+	0.694072i
$545$			5.93215i			0.254105i
$546$	−29.9721	+	3.10317i	−1.28269	+	0.132804i
$547$	4.96207	+	4.96207i	0.212163	+	0.212163i	0.805186	−	0.593023i	$-0.202066\pi$
$547$	4.96207	+	4.96207i	0.212163	+	0.212163i	−0.593023	+	0.805186i	$0.702066\pi$
$548$	40.9471	−	3.76648i	1.74917	−	0.160896i
$549$	−0.134299	+	0.134299i	−0.00573176	+	0.00573176i
$550$	−0.221509	−	4.82641i	−0.00944517	−	0.205799i
$551$		−	33.0073i		−	1.40616i
$552$	2.86594	+	20.6981i	0.121983	+	0.880970i
$553$	−4.20239	−	3.74639i	−0.178704	−	0.159313i
$554$	0.264625	+	5.76586i	0.0112428	+	0.244968i
$555$	12.4584	−	12.4584i	0.528832	−	0.528832i
$556$	26.5451	−	31.9232i	1.12576	−	1.35385i
$557$	−25.8757	+	25.8757i	−1.09639	+	1.09639i	−0.101560	+	0.994829i	$0.532383\pi$
$557$	−25.8757	+	25.8757i	−1.09639	+	1.09639i	−0.994829	+	0.101560i	$0.967617\pi$
$558$	−0.875669	+	0.959913i	−0.0370700	+	0.0406364i
$559$	−11.3212			−0.478834
$560$	2.52339	+	10.2778i	0.106632	+	0.434315i
$561$	−20.5352			−0.866996
$562$	17.9538	−	19.6811i	0.757337	−	0.830197i
$563$	−24.5210	+	24.5210i	−1.03343	+	1.03343i	−0.0340136	+	0.999421i	$0.510829\pi$
$563$	−24.5210	+	24.5210i	−1.03343	+	1.03343i	−0.999421	+	0.0340136i	$0.989171\pi$
$564$	31.9371	+	26.5566i	1.34479	+	1.11824i
$565$	5.36872	−	5.36872i	0.225864	−	0.225864i
$566$	−1.42692	−	31.0908i	−0.0599778	−	1.30684i
$567$	−16.7505	+	18.7893i	−0.703454	+	0.789077i
$568$	−16.7755	+	22.1677i	−0.703883	+	0.930136i
$569$		−	10.3523i		−	0.433991i	−0.976173	−	0.216996i	$-0.930374\pi$
$569$		−	10.3523i		−	0.433991i	0.976173	−	0.216996i	$-0.0696257\pi$
$570$	0.369237	+	8.04522i	0.0154656	+	0.336977i
$571$	−8.27473	+	8.27473i	−0.346287	+	0.346287i	−0.858724	−	0.512438i	$-0.828743\pi$
$571$	−8.27473	+	8.27473i	−0.346287	+	0.346287i	0.512438	+	0.858724i	$0.328743\pi$
$572$	2.82532	+	30.7154i	0.118133	+	1.28427i
$573$	28.9374	+	28.9374i	1.20888	+	1.20888i
$574$	−0.823207	+	0.0852309i	−0.0343600	+	0.00355747i
$575$			4.14123i			0.172701i
$576$	−1.40457	+	0.396567i	−0.0585237	+	0.0165236i
$577$			13.0459i			0.543108i	0.962423	+	0.271554i	$0.0875376\pi$
$577$			13.0459i			0.543108i	−0.962423	+	0.271554i	$0.912462\pi$
$578$	−5.90008	−	5.38227i	−0.245411	−	0.223873i
$579$	−23.7585	+	23.7585i	−0.987371	+	0.987371i
$580$	20.5926	−	1.89419i	0.855061	−	0.0786520i
$581$	−0.636778	−	11.1000i	−0.0264180	−	0.460505i
$582$	−0.0812218	−	1.76972i	−0.00336675	−	0.0733574i
$583$	1.45326			0.0601878
$584$	17.0681	−	22.5544i	0.706284	−	0.933308i
$585$		−	0.823564i		−	0.0340502i
$586$	−40.1925	+	1.84464i	−1.66034	+	0.0762015i
$587$	6.36487	+	6.36487i	0.262706	+	0.262706i	0.826153	−	0.563446i	$-0.190525\pi$
$587$	6.36487	+	6.36487i	0.262706	+	0.262706i	−0.563446	+	0.826153i	$0.690525\pi$
$588$	13.6674	−	20.9036i	0.563634	−	0.862049i
$589$	−11.3678	+	11.3678i	−0.468403	+	0.468403i
$590$	5.84888	+	5.33557i	0.240794	+	0.219662i
$591$	32.0518			1.31844
$592$	32.5619	+	22.3700i	1.33829	+	0.919400i
$593$			30.7359i			1.26217i	0.775714	+	0.631085i	$0.217390\pi$
$593$			30.7359i			1.26217i	−0.775714	+	0.631085i	$0.782610\pi$
$594$	17.9412	+	16.3666i	0.736135	+	0.671530i
$595$	8.89997	−	0.510569i	0.364863	−	0.0209313i
$596$	21.8791	−	26.3119i	0.896203	−	1.07778i
$597$	8.22969	+	8.22969i	0.336819	+	0.336819i
$598$	−1.21212	−	26.4105i	−0.0495671	−	1.08001i
$599$	−2.56060			−0.104623			−0.0523116	−	0.998631i	$-0.516659\pi$
$599$	−2.56060			−0.104623			−0.0523116	+	0.998631i	$0.516659\pi$
$600$	−4.99805	+	0.692050i	−0.204045	+	0.0282528i
$601$	16.8009			0.685324			0.342662	−	0.939459i	$-0.388671\pi$
$601$	16.8009			0.685324			0.342662	+	0.939459i	$0.388671\pi$
$602$	5.91655	−	7.28319i	0.241141	−	0.296841i
$603$	1.25999	−	1.25999i	0.0513106	−	0.0513106i
$604$	3.22915	+	35.1056i	0.131392	+	1.42843i
$605$	0.474916	+	0.474916i	0.0193081	+	0.0193081i
$606$	14.1215	−	15.4801i	0.573647	−	0.628835i
$607$	−44.3444			−1.79988			−0.899941	−	0.436011i	$-0.856391\pi$
$607$	−44.3444			−1.79988			−0.899941	+	0.436011i	$0.856391\pi$
$608$	−17.5855	+	4.10482i	−0.713186	+	0.166472i
$609$	−36.4281	−	32.4753i	−1.47614	−	1.31597i
$610$	−1.08771	−	0.992248i	−0.0440400	−	0.0401750i
$611$	−37.1611	−	37.1611i	−1.50338	−	1.50338i
$612$	0.112609	+	1.22423i	0.00455196	+	0.0494864i
$613$	11.0348	+	11.0348i	0.445692	+	0.445692i	0.893920	−	0.448227i	$-0.147945\pi$
$613$	11.0348	+	11.0348i	0.445692	+	0.445692i	−0.448227	+	0.893920i	$0.647945\pi$
$614$	−18.1030	+	0.830840i	−0.730577	+	0.0335300i
$615$		−	0.394585i		−	0.0159112i
$616$	−21.2365	−	14.2345i	−0.855643	−	0.573526i
$617$		−	16.3068i		−	0.656486i	−0.944593	−	0.328243i	$-0.893543\pi$
$617$		−	16.3068i		−	0.656486i	0.944593	−	0.328243i	$-0.106457\pi$
$618$	0.617614	+	13.4571i	0.0248441	+	0.541322i
$619$	4.52819	+	4.52819i	0.182003	+	0.182003i	0.792228	−	0.610225i	$-0.208921\pi$
$619$	4.52819	+	4.52819i	0.182003	+	0.182003i	−0.610225	+	0.792228i	$0.708921\pi$
$620$	−7.74452	−	6.43979i	−0.311027	−	0.258628i
$621$	−14.7187	−	14.7187i	−0.590640	−	0.590640i
$622$	20.6483	−	22.6347i	0.827920	−	0.907570i
$623$	−1.66668	+	1.86954i	−0.0667740	+	0.0749016i
$624$	31.6723	−	5.87642i	1.26791	−	0.235245i
$625$	−1.00000			−0.0400000
$626$	−0.666758	−	0.608241i	−0.0266490	−	0.0243102i
$627$	−13.7572	−	13.7572i	−0.549410	−	0.549410i
$628$	30.6571	−	36.8684i	1.22335	−	1.47121i
$629$	23.5308	−	23.5308i	0.938236	−	0.938236i
$630$	0.529819	+	0.430403i	0.0211085	+	0.0171477i
$631$	3.43457			0.136728			0.0683641	−	0.997660i	$-0.478222\pi$
$631$	3.43457			0.136728			0.0683641	+	0.997660i	$0.478222\pi$
$632$	4.79927	+	3.63186i	0.190905	+	0.144468i
$633$	−6.45205			−0.256446
$634$	32.8985	−	1.50988i	1.30656	−	0.0599650i
$635$	−11.2878	−	11.2878i	−0.447943	−	0.447943i
$636$	−0.139018	−	1.51132i	−0.00551241	−	0.0599278i
$637$	−19.6427	+	24.7533i	−0.778272	+	0.980761i
$638$	−33.6679	+	36.9069i	−1.33292	+	1.46116i
$639$			1.79309i			0.0709337i
$640$	−3.57009	−	10.7357i	−0.141120	−	0.424364i
$641$	26.0969			1.03077			0.515384	−	0.856960i	$-0.327649\pi$
$641$	26.0969			1.03077			0.515384	+	0.856960i	$0.327649\pi$
$642$	8.93596	−	9.79566i	0.352674	−	0.386604i
$643$	−8.47461	+	8.47461i	−0.334206	+	0.334206i	−0.854181	−	0.519975i	$-0.825941\pi$
$643$	−8.47461	+	8.47461i	−0.334206	+	0.334206i	0.519975	+	0.854181i	$0.325941\pi$
$644$	17.6240	+	13.0226i	0.694484	+	0.513163i
$645$	3.16349	+	3.16349i	0.124562	+	0.124562i
$646$	0.697394	+	15.1954i	0.0274386	+	0.597854i
$647$			17.5756i			0.690967i	0.938425	+	0.345484i	$0.112285\pi$
$647$			17.5756i			0.690967i	−0.938425	+	0.345484i	$0.887715\pi$
$648$	16.2384	−	21.4580i	0.637906	−	0.842951i
$649$	−19.1252			−0.750732
$650$	6.37745	−	0.292694i	0.250144	−	0.0114804i
$651$	1.36136	+	23.7306i	0.0533560	+	0.930074i
$652$	−0.252975	+	0.304229i	−0.00990727	+	0.0119145i
$653$	7.89040	−	7.89040i	0.308775	−	0.308775i	−0.535659	−	0.844434i	$-0.679937\pi$
$653$	7.89040	−	7.89040i	0.308775	−	0.308775i	0.844434	+	0.535659i	$0.179937\pi$
$654$	−10.0863	+	11.0566i	−0.394405	+	0.432349i
$655$		−	2.70004i		−	0.105499i
$656$	0.869903	−	0.161400i	0.0339640	−	0.00630162i
$657$		−	1.82437i		−	0.0711756i
$658$	43.3274	−	4.48591i	1.68908	−	0.174879i
$659$	17.3048	+	17.3048i	0.674099	+	0.674099i	0.958658	−	0.284560i	$-0.0918474\pi$
$659$	17.3048	+	17.3048i	0.674099	+	0.674099i	−0.284560	+	0.958658i	$0.591847\pi$
$660$	7.79335	−	9.37232i	0.303356	−	0.364817i
$661$	20.6500	−	20.6500i	0.803191	−	0.803191i	−0.180402	−	0.983593i	$-0.557740\pi$
$661$	20.6500	−	20.6500i	0.803191	−	0.803191i	0.983593	+	0.180402i	$0.0577398\pi$
$662$	8.87183	−	0.407174i	0.344814	−	0.0158253i
$663$		−	27.1345i		−	1.05382i
$664$	1.63021	+	11.7736i	0.0632645	+	0.456903i
$665$	6.30444	+	5.62034i	0.244476	+	0.217948i
$666$	2.54545	−	0.116824i	0.0986343	−	0.00452684i
$667$	30.2779	−	30.2779i	1.17236	−	1.17236i
$668$	−43.7958	+	4.02851i	−1.69451	+	0.155868i
$669$	2.73903	−	2.73903i	0.105897	−	0.105897i
$670$	10.2048	+	9.30918i	0.394245	+	0.359645i
$671$	3.55670			0.137305
$672$	−12.7718	+	23.4467i	−0.492683	+	0.904475i
$673$	−34.8579			−1.34367			−0.671837	−	0.740699i	$-0.734495\pi$
$673$	−34.8579			−1.34367			−0.671837	+	0.740699i	$0.734495\pi$
$674$	−5.23698	−	4.77737i	−0.201721	−	0.184017i
$675$	3.55417	−	3.55417i	0.136800	−	0.136800i
$676$	−14.6956	+	1.35176i	−0.565214	+	0.0519907i
$677$	24.0457	−	24.0457i	0.924153	−	0.924153i	−0.0731668	−	0.997320i	$-0.523311\pi$
$677$	24.0457	−	24.0457i	0.924153	−	0.924153i	0.997320	+	0.0731668i	$0.0233106\pi$
$678$	19.1348	−	0.878194i	0.734867	−	0.0337268i
$679$	−1.38680	−	1.23632i	−0.0532205	−	0.0474456i
$680$	−9.44005	+	1.30711i	−0.362009	+	0.0501252i
$681$		−	4.04734i		−	0.155095i
$682$	24.3062	−	1.11554i	0.930732	−	0.0427161i
$683$	−20.0011	+	20.0011i	−0.765319	+	0.765319i	−0.977279	−	0.211959i	$-0.932016\pi$
$683$	−20.0011	+	20.0011i	−0.765319	+	0.765319i	0.211959	+	0.977279i	$0.432016\pi$
$684$	−0.744709	+	0.895591i	−0.0284747	+	0.0342438i
$685$	14.5381	+	14.5381i	0.555472	+	0.555472i
$686$	−5.65895	−	25.5730i	−0.216060	−	0.976380i
$687$		−	28.8677i		−	1.10137i
$688$	−5.68026	+	8.26823i	−0.216558	+	0.315223i
$689$			1.92029i			0.0731571i
$690$	−7.04123	+	7.71864i	−0.268055	+	0.293844i
$691$	−15.8719	+	15.8719i	−0.603794	+	0.603794i	−0.941317	−	0.337523i	$-0.890411\pi$
$691$	−15.8719	+	15.8719i	−0.603794	+	0.603794i	0.337523	+	0.941317i	$0.390411\pi$
$692$	−4.35007	+	5.23142i	−0.165365	+	0.198869i
$693$	−1.64630	+	0.0944441i	−0.0625378	+	0.00358764i
$694$	−33.0124	+	1.51511i	−1.25313	+	0.0575128i
$695$	20.7589			0.787431
$696$	41.6022	+	31.4826i	1.57693	+	1.19334i
$697$		−	0.745270i		−	0.0282291i
$698$	−2.32089	−	50.5695i	−0.0878471	−	1.91408i
$699$	18.7371	+	18.7371i	0.708703	+	0.708703i
$700$	−3.14462	+	4.25574i	−0.118856	+	0.160852i
$701$	−7.57115	+	7.57115i	−0.285958	+	0.285958i	−0.835480	−	0.549521i	$-0.814810\pi$
$701$	−7.57115	+	7.57115i	−0.285958	+	0.285958i	0.549521	+	0.835480i	$0.314810\pi$
$702$	−21.6263	+	23.7069i	−0.816232	+	0.894758i
$703$	31.5282			1.18911
$704$	23.8501	+	13.3476i	0.898883	+	0.503058i
$705$			20.7680i			0.782167i
$706$	−13.8263	+	15.1565i	−0.520361	+	0.570423i
$707$	−1.25853	−	21.9380i	−0.0473319	−	0.825065i
$708$	1.82951	+	19.8894i	0.0687571	+	0.747489i
$709$	13.0539	+	13.0539i	0.490249	+	0.490249i	0.908385	−	0.418135i	$-0.137316\pi$
$709$	13.0539	+	13.0539i	0.490249	+	0.490249i	−0.418135	+	0.908385i	$0.637316\pi$
$710$	−13.8852	+	0.637265i	−0.521103	+	0.0239161i
$711$	0.388202			0.0145587
$712$	1.61573	−	2.13508i	0.0605519	−	0.0800154i
$713$	−20.8556			−0.781048
$714$	17.4563	+	14.1808i	0.653286	+	0.530702i
$715$	−10.9054	+	10.9054i	−0.407837	+	0.407837i
$716$	−20.5510	+	24.7147i	−0.768026	+	0.923631i
$717$	−11.4896	−	11.4896i	−0.429089	−	0.429089i
$718$	−1.65633	−	1.51097i	−0.0618137	−	0.0563888i
$719$	50.5317			1.88451			0.942256	−	0.334892i	$-0.108700\pi$
$719$	50.5317			1.88451			0.942256	+	0.334892i	$0.108700\pi$
$720$	−0.601477	−	0.413213i	−0.0224157	−	0.0153996i
$721$	10.5453	+	9.40102i	0.392727	+	0.350112i
$722$	8.39625	−	9.20402i	0.312476	−	0.342538i
$723$	31.6775	+	31.6775i	1.17810	+	1.17810i
$724$	−19.1920	−	15.9587i	−0.713263	−	0.593099i
$725$	7.31132	+	7.31132i	0.271536	+	0.271536i
$726$	0.0776849	+	1.69266i	0.00288316	+	0.0628205i
$727$			35.6847i			1.32347i	0.749737	+	0.661736i	$0.230180\pi$
$727$			35.6847i			1.32347i	−0.749737	+	0.661736i	$0.769820\pi$
$728$	18.8091	−	28.0612i	0.697110	−	1.04002i
$729$			25.1645i			0.932017i
$730$	14.1275	−	0.648382i	0.522881	−	0.0239977i
$731$	5.97502	+	5.97502i	0.220994	+	0.220994i
$732$	−0.340231	−	3.69880i	−0.0125753	−	0.136712i
$733$	2.17858	+	2.17858i	0.0804676	+	0.0804676i	0.746195	−	0.665727i	$-0.231879\pi$
$733$	2.17858	+	2.17858i	0.0804676	+	0.0804676i	−0.665727	+	0.746195i	$0.731879\pi$
$734$	−14.0235	−	12.7928i	−0.517617	−	0.472190i
$735$	12.4056	−	1.42806i	0.457589	−	0.0526748i
$736$	−19.8967	−	12.3659i	−0.733402	−	0.455814i
$737$	−33.3686			−1.22915
$738$	0.0384599	−	0.0421599i	0.00141573	−	0.00155193i
$739$	15.6094	+	15.6094i	0.574200	+	0.574200i	0.933299	−	0.359099i	$-0.116916\pi$
$739$	15.6094	+	15.6094i	0.574200	+	0.574200i	−0.359099	+	0.933299i	$0.616916\pi$
$740$	1.80931	+	19.6698i	0.0665115	+	0.723076i
$741$	18.1783	−	18.1783i	0.667798	−	0.667798i
$742$	−1.23537	−	1.00356i	−0.0453518	−	0.0368419i
$743$	4.29450			0.157550			0.0787750	−	0.996892i	$-0.474899\pi$
$743$	4.29450			0.157550			0.0787750	+	0.996892i	$0.474899\pi$
$744$	−3.48522	−	25.1706i	−0.127774	−	0.922799i
$745$	17.1100			0.626863
$746$	1.51342	+	32.9755i	0.0554101	+	1.20732i
$747$	0.542100	+	0.542100i	0.0198344	+	0.0198344i
$748$	14.7197	−	17.7019i	0.538204	−	0.647247i
$749$	−0.796386	−	13.8822i	−0.0290993	−	0.507244i
$750$	−1.86385	−	1.70027i	−0.0680582	−	0.0620852i
$751$		−	24.1826i		−	0.882436i	−0.897400	−	0.441218i	$-0.854547\pi$
$751$		−	24.1826i		−	0.882436i	0.897400	−	0.441218i	$-0.145453\pi$
$752$	−45.7852	+	8.49489i	−1.66961	+	0.309777i
$753$	−41.5473			−1.51407
$754$	−48.7676	−	44.4876i	−1.77601	−	1.62014i
$755$	−12.4641	+	12.4641i	−0.453615	+	0.453615i
$756$	−3.94911	−	26.3022i	−0.143628	−	0.956601i
$757$	1.96239	+	1.96239i	0.0713241	+	0.0713241i	0.741869	−	0.670545i	$-0.233940\pi$
$757$	1.96239	+	1.96239i	0.0713241	+	0.0713241i	−0.670545	+	0.741869i	$0.733940\pi$
$758$	−16.1808	+	0.742623i	−0.587715	+	0.0269733i
$759$		−	25.2392i		−	0.916125i
$760$	−7.19988	−	5.44853i	−0.261167	−	0.197639i
$761$	16.9390			0.614037			0.307019	−	0.951704i	$-0.400669\pi$
$761$	16.9390			0.614037			0.307019	+	0.951704i	$0.400669\pi$
$762$	−1.84642	−	40.2312i	−0.0668886	−	1.45742i
$763$	0.898904	+	15.6692i	0.0325425	+	0.567264i
$764$	−45.6873	+	4.20251i	−1.65291	+	0.152041i
$765$	−0.434656	+	0.434656i	−0.0157150	+	0.0157150i
$766$	−16.3744	−	14.9374i	−0.591632	−	0.539709i
$767$		−	25.2715i		−	0.912500i
$768$	11.5995	−	26.0798i	0.418559	−	0.941074i
$769$		−	2.28616i		−	0.0824410i	−0.999150	−	0.0412205i	$-0.986875\pi$
$769$		−	2.28616i		−	0.0824410i	0.999150	−	0.0412205i	$-0.0131246\pi$
$770$	−1.31644	−	12.7149i	−0.0474414	−	0.458215i
$771$	−11.0947	−	11.0947i	−0.399566	−	0.399566i
$772$	−3.45039	−	37.5107i	−0.124182	−	1.35004i
$773$	−29.6974	+	29.6974i	−1.06814	+	1.06814i	−0.0706379	+	0.997502i	$0.522503\pi$
$773$	−29.6974	+	29.6974i	−1.06814	+	1.06814i	−0.997502	+	0.0706379i	$0.977497\pi$
$774$	0.0296643	+	0.646350i	0.00106626	+	0.0232326i
$775$		−	5.03608i		−	0.180901i
$776$	1.58377	+	1.19853i	0.0568542	+	0.0430246i
$777$	31.0200	−	34.7957i	1.11284	−	1.24829i
$778$	−0.988034	−	21.5281i	−0.0354228	−	0.771819i
$779$	0.499281	−	0.499281i	0.0178886	−	0.0178886i
$780$	12.3843	+	10.2979i	0.443428	+	0.368723i
$781$	23.7436	−	23.7436i	0.849611	−	0.849611i
$782$	−13.2991	+	14.5785i	−0.475575	+	0.521328i
$783$	−51.9714			−1.85731
$784$	8.22269	+	26.7654i	0.293668	+	0.955908i
$785$	23.9747			0.855693
$786$	4.59080	−	5.03246i	0.163749	−	0.179502i
$787$	7.61315	−	7.61315i	0.271380	−	0.271380i	−0.558276	−	0.829655i	$-0.688537\pi$
$787$	7.61315	−	7.61315i	0.271380	−	0.271380i	0.829655	+	0.558276i	$0.188537\pi$
$788$	−22.9748	+	27.6296i	−0.818443	+	0.984264i
$789$	−23.3470	+	23.3470i	−0.831177	+	0.831177i
$790$	0.137967	+	3.00613i	0.00490864	+	0.106953i
$791$	13.3674	−	14.9945i	0.475292	−	0.533143i
$792$	1.74620	−	0.241786i	0.0620487	−	0.00859149i
$793$			4.69970i			0.166891i
$794$	2.40555	+	52.4141i	0.0853699	+	1.86011i
$795$	0.536589	−	0.536589i	0.0190308	−	0.0190308i
$796$	−12.9933	+	1.19518i	−0.460535	+	0.0423619i
$797$	20.4113	+	20.4113i	0.723006	+	0.723006i	0.969216	−	0.246210i	$-0.0791854\pi$
$797$	20.4113	+	20.4113i	0.723006	+	0.723006i	−0.246210	+	0.969216i	$0.579185\pi$
$798$	2.19440	+	21.1947i	0.0776810	+	0.750286i
$799$			39.2254i			1.38769i
$800$	2.98605	−	4.80453i	0.105573	−	0.169866i
$801$		−	0.172702i		−	0.00610211i
$802$	−1.90957	−	1.74198i	−0.0674293	−	0.0615115i
$803$	−24.1578	+	24.1578i	−0.852509	+	0.852509i
$804$	3.19202	+	34.7019i	0.112574	+	1.22384i
$805$	0.627525	+	10.9387i	0.0221174	+	0.385538i
$806$	1.47403	+	32.1174i	0.0519206	+	1.13129i
$807$	33.8369			1.19111
$808$	3.22196	+	23.2693i	0.113348	+	0.818611i
$809$		−	13.4600i		−	0.473230i	−0.971603	−	0.236615i	$-0.923962\pi$
$809$		−	13.4600i		−	0.473230i	0.971603	−	0.236615i	$-0.0760380\pi$
$810$	13.4407	−	0.616864i	0.472258	−	0.0216744i
$811$	−18.4727	−	18.4727i	−0.648665	−	0.648665i	0.304005	−	0.952670i	$-0.401676\pi$
$811$	−18.4727	−	18.4727i	−0.648665	−	0.648665i	−0.952670	+	0.304005i	$0.901676\pi$
$812$	54.1064	−	8.12375i	1.89876	−	0.285088i
$813$	8.69181	−	8.69181i	0.304835	−	0.304835i
$814$	−35.2530	−	32.1591i	−1.23562	−	1.12718i
$815$	−0.197833			−0.00692979
$816$	−19.8173	−	13.6144i	−0.693743	−	0.476600i
$817$			8.00574i			0.280085i
$818$	4.90889	+	4.47807i	0.171635	+	0.156572i
$819$	−0.124795	−	2.17537i	−0.00436070	−	0.0760135i
$820$	0.340144	+	0.282839i	0.0118783	+	0.00987717i
$821$	−18.8284	−	18.8284i	−0.657115	−	0.657115i	0.297581	−	0.954696i	$-0.403820\pi$
$821$	−18.8284	−	18.8284i	−0.657115	−	0.657115i	−0.954696	+	0.297581i	$0.903820\pi$
$822$	2.37808	+	51.8156i	0.0829452	+	1.80728i
$823$	−35.2135			−1.22747			−0.613733	−	0.789514i	$-0.710333\pi$
$823$	−35.2135			−1.22747			−0.613733	+	0.789514i	$0.710333\pi$
$824$	−12.0431	−	9.11364i	−0.419541	−	0.317489i
$825$	6.09461			0.212187
$826$	16.2578	+	13.2071i	0.565680	+	0.459535i
$827$	−4.02494	+	4.02494i	−0.139961	+	0.139961i	−0.773616	−	0.633655i	$-0.781554\pi$
$827$	−4.02494	+	4.02494i	−0.139961	+	0.139961i	0.633655	+	0.773616i	$0.281554\pi$
$828$	−1.50466	+	0.138405i	−0.0522905	+	0.00480990i
$829$	31.3680	+	31.3680i	1.08945	+	1.08945i	0.995584	+	0.0938701i	$0.0299238\pi$
$829$	31.3680	+	31.3680i	1.08945	+	1.08945i	0.0938701	+	0.995584i	$0.470076\pi$
$830$	−4.00521	+	4.39054i	−0.139023	+	0.152398i
$831$	−7.28091			−0.252572
$832$	−17.6371	+	31.5147i	−0.611457	+	1.09257i
$833$	23.4311	−	2.69724i	0.811839	−	0.0934539i
$834$	38.6916	+	35.2959i	1.33978	+	1.22220i
$835$	−15.5495	−	15.5495i	−0.538113	−	0.538113i
$836$	21.7203	−	1.99792i	0.751213	−	0.0690996i
$837$	17.8991	+	17.8991i	0.618684	+	0.618684i
$838$	−5.61054	+	0.257497i	−0.193813	+	0.00889508i
$839$		−	31.1502i		−	1.07542i	−0.843129	−	0.537712i	$-0.819289\pi$
$839$		−	31.1502i		−	1.07542i	0.843129	−	0.537712i	$-0.180711\pi$
$840$	−13.0970	+	2.58535i	−0.451891	+	0.0892029i
$841$		−	77.9108i		−	2.68658i
$842$	0.361310	+	7.87251i	0.0124516	+	0.271305i
$843$	23.7620	+	23.7620i	0.818407	+	0.818407i
$844$	4.62484	−	5.56186i	0.159194	−	0.191447i
$845$	−5.21760	−	5.21760i	−0.179491	−	0.179491i
$846$	−2.02424	+	2.21898i	−0.0695947	+	0.0762901i
$847$	1.32641	+	1.18248i	0.0455761	+	0.0406306i
$848$	1.40245	+	0.963481i	0.0481604	+	0.0330861i
$849$	39.2603			1.34741
$850$	−3.52034	−	3.21138i	−0.120747	−	0.110150i
$851$	28.9210	+	28.9210i	0.991401	+	0.991401i
$852$	−26.9635	−	22.4209i	−0.923755	−	0.768128i
$853$	−6.59201	+	6.59201i	−0.225706	+	0.225706i	−0.810896	−	0.585190i	$-0.801020\pi$
$853$	−6.59201	+	6.59201i	−0.225706	+	0.225706i	0.585190	+	0.810896i	$0.301020\pi$
$854$	−3.02344	−	2.45611i	−0.103460	−	0.0840464i
$855$	−0.582382			−0.0199170
$856$	2.03883	+	14.7246i	0.0696856	+	0.503277i
$857$	20.8988			0.713890			0.356945	−	0.934125i	$-0.383818\pi$
$857$	20.8988			0.713890			0.356945	+	0.934125i	$0.383818\pi$
$858$	−38.8681	+	1.78386i	−1.32693	+	0.0608999i
$859$	7.97216	+	7.97216i	0.272007	+	0.272007i	0.829908	−	0.557901i	$-0.188393\pi$
$859$	7.97216	+	7.97216i	0.272007	+	0.272007i	−0.557901	+	0.829908i	$0.688393\pi$
$860$	−4.99461	+	0.459425i	−0.170315	+	0.0156663i
$861$	−0.0597918	−	1.04226i	−0.00203770	−	0.0355201i
$862$	13.7319	−	15.0529i	0.467709	−	0.512705i
$863$		−	17.5267i		−	0.596614i	−0.954470	−	0.298307i	$-0.903578\pi$
$863$		−	17.5267i		−	0.596614i	0.954470	−	0.298307i	$-0.0964220\pi$
$864$	6.46321	+	27.6891i	0.219883	+	0.942001i
$865$	−3.40187			−0.115667
$866$	−4.09104	+	4.48462i	−0.139019	+	0.152393i
$867$	7.12347	−	7.12347i	0.241926	−	0.241926i
$868$	−21.4323	−	15.8366i	−0.727459	−	0.537528i
$869$	−5.14044	−	5.14044i	−0.174378	−	0.174378i
$870$	1.19596	+	26.0584i	0.0405467	+	0.883464i
$871$		−	44.0922i		−	1.49401i
$872$	−2.30128	−	16.6201i	−0.0779312	−	0.562827i
$873$	0.128108			0.00433579
$874$	−18.6762	+	0.857146i	−0.631731	+	0.0289934i
$875$	−2.64141	+	0.151531i	−0.0892959	+	0.00512268i
$876$	27.4339	+	22.8121i	0.926905	+	0.770748i
$877$	−37.4670	+	37.4670i	−1.26517	+	1.26517i	−0.316615	+	0.948554i	$0.602546\pi$
$877$	−37.4670	+	37.4670i	−1.26517	+	1.26517i	−0.948554	+	0.316615i	$0.897454\pi$
$878$	21.1141	−	23.1454i	0.712566	−	0.781119i
$879$		−	50.7536i		−	1.71188i
$880$	2.49293	+	13.4362i	0.0840365	+	0.452934i
$881$		−	19.7619i		−	0.665797i	−0.942963	−	0.332898i	$-0.891973\pi$
$881$		−	19.7619i		−	0.665797i	0.942963	−	0.332898i	$-0.108027\pi$
$882$	1.46469	+	1.05659i	0.0493186	+	0.0355771i
$883$	27.9228	+	27.9228i	0.939676	+	0.939676i	0.998281	−	0.0586054i	$-0.0186654\pi$
$883$	27.9228	+	27.9228i	0.939676	+	0.939676i	−0.0586054	+	0.998281i	$0.518665\pi$
$884$	23.3908	+	19.4501i	0.786716	+	0.654177i
$885$	−7.06165	+	7.06165i	−0.237375	+	0.237375i
$886$	−13.3342	+	0.611977i	−0.447972	+	0.0205598i
$887$		−	20.4054i		−	0.685145i	−0.939491	−	0.342572i	$-0.888702\pi$
$887$		−	20.4054i		−	0.685145i	0.939491	−	0.342572i	$-0.111298\pi$
$888$	−30.0717	+	39.7378i	−1.00914	+	1.33351i
$889$	−31.5262	−	28.1053i	−1.05735	−	0.942621i
$890$	1.33735	−	0.0613781i	0.0448282	−	0.00205740i
$891$	−22.9834	+	22.9834i	−0.769974	+	0.769974i
$892$	0.397781	+	4.32446i	0.0133187	+	0.144794i
$893$	−26.2784	+	26.2784i	−0.879373	+	0.879373i
$894$	31.8905	+	29.0917i	1.06658	+	0.972973i
$895$	−16.0714			−0.537207
$896$	−11.0569	−	27.8163i	−0.369384	−	0.929277i
$897$	33.3502			1.11353
$898$	−17.7307	−	16.1746i	−0.591681	−	0.539754i
$899$	−36.8204	+	36.8204i	−1.22803	+	1.22803i
$900$	−0.0334211	−	0.363336i	−0.00111404	−	0.0121112i
$901$	1.01348	−	1.01348i	0.0337639	−	0.0337639i
$902$	−1.06754	+	0.0489950i	−0.0355452	+	0.00163135i
$903$	8.83543	+	7.87670i	0.294025	+	0.262120i
$904$	−12.9588	+	17.1242i	−0.431004	+	0.569543i
$905$		−	12.4801i		−	0.414852i
$906$	−44.4236	+	2.03883i	−1.47587	+	0.0677355i
$907$	−36.1169	+	36.1169i	−1.19924	+	1.19924i	−0.224850	+	0.974393i	$0.572189\pi$
$907$	−36.1169	+	36.1169i	−1.19924	+	1.19924i	−0.974393	+	0.224850i	$0.927811\pi$
$908$	3.48893	+	2.90114i	0.115784	+	0.0962778i
$909$	1.07141	+	1.07141i	0.0355364	+	0.0355364i
$910$	16.8011	−	1.73951i	0.556951	−	0.0576641i
$911$			13.3080i			0.440913i	0.975397	+	0.220457i	$0.0707547\pi$
$911$			13.3080i			0.440913i	−0.975397	+	0.220457i	$0.929245\pi$
$912$	−4.15550	−	22.3970i	−0.137602	−	0.741639i
$913$		−	14.3566i		−	0.475135i
$914$	5.84709	−	6.40961i	0.193404	−	0.212011i
$915$	1.31325	−	1.31325i	0.0434146	−	0.0434146i
$916$	24.8848	+	20.6924i	0.822216	+	0.683696i
$917$	−0.409139	−	7.13190i	−0.0135110	−	0.235516i
$918$	23.9257	−	1.09807i	0.789666	−	0.0362419i
$919$	−46.7818			−1.54319			−0.771594	−	0.636115i	$-0.780540\pi$
$919$	−46.7818			−1.54319			−0.771594	+	0.636115i	$0.780540\pi$
$920$	−1.60652	−	11.6025i	−0.0529655	−	0.382523i
$921$		−	22.8598i		−	0.753255i
$922$	−1.97431	−	43.0177i	−0.0650203	−	1.41671i
$923$	31.3740	+	31.3740i	1.03269	+	1.03269i
$924$	19.1652	−	25.9371i	0.630490	−	0.853267i
$925$	−6.98368	+	6.98368i	−0.229622	+	0.229622i
$926$	−28.5014	+	31.2434i	−0.936613	+	1.02672i
$927$	−0.974137			−0.0319949
$928$	−56.9594	+	13.2955i	−1.86978	+	0.436447i
$929$		−	0.743558i		−	0.0243953i	−0.999926	−	0.0121977i	$-0.996117\pi$
$929$		−	0.743558i		−	0.0243953i	0.999926	−	0.0121977i	$-0.00388273\pi$
$930$	8.56272	−	9.38650i	0.280783	−	0.307796i
$931$	17.5042	+	13.8903i	0.573679	+	0.455236i
$932$	−29.5828	+	2.72114i	−0.969016	+	0.0891340i
$933$	27.3281	+	27.3281i	0.894681	+	0.894681i
$934$	4.31653	−	0.198108i	0.141241	−	0.00648228i
$935$	11.5112			0.376455
$936$	0.319488	+	2.30738i	0.0104428	+	0.0754190i
$937$	−14.8647			−0.485609			−0.242805	−	0.970075i	$-0.578067\pi$
$937$	−14.8647			−0.485609			−0.242805	+	0.970075i	$0.578067\pi$
$938$	28.3656	+	23.0430i	0.926171	+	0.752381i
$939$	0.805010	−	0.805010i	0.0262705	−	0.0262705i
$940$	−17.9026	−	14.8865i	−0.583918	−	0.485544i
$941$	−40.0517	−	40.0517i	−1.30565	−	1.30565i	−0.924523	−	0.381125i	$-0.875537\pi$
$941$	−40.0517	−	40.0517i	−1.30565	−	1.30565i	−0.381125	−	0.924523i	$-0.624463\pi$
$942$	44.6852	+	40.7635i	1.45592	+	1.32815i
$943$	0.915989			0.0298287
$944$	−18.4566	−	12.6797i	−0.600712	−	0.412688i
$945$	8.84946	−	9.92659i	0.287873	−	0.322912i
$946$	8.16595	−	8.95156i	0.265498	−	0.291040i
$947$	−24.7962	−	24.7962i	−0.805770	−	0.805770i	0.178221	−	0.983991i	$-0.442966\pi$
$947$	−24.7962	−	24.7962i	−0.805770	−	0.805770i	−0.983991	+	0.178221i	$0.942966\pi$
$948$	−4.85410	+	5.83756i	−0.157654	+	0.189595i
$949$	−31.9213	−	31.9213i	−1.03621	−	1.03621i
$950$	−0.206978	−	4.50981i	−0.00671526	−	0.146317i
$951$			41.5429i			1.34712i
$952$	−24.7370	+	4.88306i	−0.801730	+	0.158261i
$953$			5.62927i			0.182350i	0.995835	+	0.0911749i	$0.0290622\pi$
$953$			5.62927i			0.182350i	−0.995835	+	0.0911749i	$0.970938\pi$
$954$	0.109633	−	0.00503165i	0.00354951	−	0.000162906i
$955$	−16.2211	−	16.2211i	−0.524902	−	0.524902i
$956$	18.1402	−	1.66861i	0.586696	−	0.0539667i
$957$	−44.5596	−	44.5596i	−1.44041	−	1.44041i
$958$	15.1339	+	13.8057i	0.488954	+	0.446042i
$959$	40.6040	+	36.1981i	1.31117	+	1.16890i
$960$	13.7346	−	3.87783i	0.443281	−	0.125156i
$961$	−5.63788			−0.181867
$962$	42.4940	−	46.5822i	1.37006	−	1.50187i
$963$	0.677978	+	0.677978i	0.0218475	+	0.0218475i
$964$	−50.0135	+	4.60044i	−1.61083	+	0.148170i
$965$	13.3180	−	13.3180i	0.428722	−	0.428722i
$966$	−17.4292	+	21.4550i	−0.560774	+	0.690305i
$967$	−1.99352			−0.0641074			−0.0320537	−	0.999486i	$-0.510205\pi$
$967$	−1.99352			−0.0641074			−0.0320537	+	0.999486i	$0.510205\pi$
$968$	−1.51481	−	1.14634i	−0.0486878	−	0.0368446i
$969$	−19.1881			−0.616412
$970$	0.0455295	+	0.992032i	0.00146186	+	0.0318522i
$971$	−7.84875	−	7.84875i	−0.251878	−	0.251878i	0.569862	−	0.821740i	$-0.306997\pi$
$971$	−7.84875	−	7.84875i	−0.251878	−	0.251878i	−0.821740	+	0.569862i	$0.806997\pi$
$972$	2.91159	+	2.42107i	0.0933894	+	0.0776560i
$973$	54.8328	−	3.14562i	1.75786	−	0.100844i
$974$	−25.0741	−	22.8736i	−0.803427	−	0.732916i
$975$			8.05321i			0.257909i
$976$	3.43236	+	2.35802i	0.109867	+	0.0754784i
$977$	27.3167			0.873937			0.436969	−	0.899477i	$-0.356052\pi$
$977$	27.3167			0.873937			0.436969	+	0.899477i	$0.356052\pi$
$978$	−0.368731	−	0.336370i	−0.0117907	−	0.0107559i
$979$	−2.28686	+	2.28686i	−0.0730883	+	0.0730883i
$980$	−7.66136	+	11.7177i	−0.244733	+	0.374307i
$981$	−0.765253	−	0.765253i	−0.0244326	−	0.0244326i
$982$	2.36659	−	0.108615i	0.0755208	−	0.00346604i
$983$			13.6089i			0.434058i	0.976165	+	0.217029i	$0.0696366\pi$
$983$			13.6089i			0.434058i	−0.976165	+	0.217029i	$0.930363\pi$
$984$	0.153073	+	1.10551i	0.00487978	+	0.0352423i
$985$	−17.9669			−0.572473
$986$	2.25886	+	49.2178i	0.0719367	+	1.56741i
$987$	3.14699	+	54.8567i	0.100170	+	1.74611i
$988$	2.63999	+	28.7005i	0.0839893	+	0.913085i
$989$	−7.34373	+	7.34373i	−0.233517	+	0.233517i
$990$	0.651186	+	0.594036i	0.0206960	+	0.0188797i
$991$		−	27.5287i		−	0.874479i	−0.899345	−	0.437240i	$-0.855956\pi$
$991$		−	27.5287i		−	0.874479i	0.899345	−	0.437240i	$-0.144044\pi$
$992$	24.1960	+	15.0380i	0.768224	+	0.477456i
$993$			11.2030i			0.355517i
$994$	−36.5800	+	3.78732i	−1.16025	+	0.120126i
$995$	−4.61322	−	4.61322i	−0.146249	−	0.146249i
$996$	−14.9302	+	1.37334i	−0.473083	+	0.0435161i
$997$	8.31823	−	8.31823i	0.263441	−	0.263441i	−0.563009	−	0.826451i	$-0.690357\pi$
$997$	8.31823	−	8.31823i	0.263441	−	0.263441i	0.826451	+	0.563009i	$0.190357\pi$
$998$	−0.996571	−	21.7141i	−0.0315459	−	0.687347i
$999$		−	49.6424i		−	1.57062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bc.a.251.16	yes	128
7.6	odd	2	inner	560.2.bc.a.251.15	✓	128
16.3	odd	4	inner	560.2.bc.a.531.15	yes	128
112.83	even	4	inner	560.2.bc.a.531.16	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bc.a.251.15	✓	128	7.6	odd	2	inner
560.2.bc.a.251.16	yes	128	1.1	even	1	trivial
560.2.bc.a.531.15	yes	128	16.3	odd	4	inner
560.2.bc.a.531.16	yes	128	112.83	even	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04480 - 0.953102i) q^{2} +(1.26143 - 1.26143i) q^{3} +(0.183195 + 1.99159i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-2.52022 + 0.115666i) q^{6} +(-1.76061 + 1.97491i) q^{7} +(1.70679 - 2.25541i) q^{8} -0.182435i q^{9} +O(q^{10})\)	\(q+(-1.04480 - 0.953102i) q^{2} +(1.26143 - 1.26143i) q^{3} +(0.183195 + 1.99159i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-2.52022 + 0.115666i) q^{6} +(-1.76061 + 1.97491i) q^{7} +(1.70679 - 2.25541i) q^{8} -0.182435i q^{9} +(1.41273 - 0.0648373i) q^{10} +(-2.41574 + 2.41574i) q^{11} +(2.74335 + 2.28118i) q^{12} +(-3.19208 - 3.19208i) q^{13} +(3.72176 - 0.385334i) q^{14} +1.78394i q^{15} +(-3.93288 + 0.729699i) q^{16} +3.36940i q^{17} +(-0.173879 + 0.190607i) q^{18} +(-2.25728 + 2.25728i) q^{19} +(-1.53781 - 1.27873i) q^{20} +(0.270322 + 4.71211i) q^{21} +(4.82641 - 0.221509i) q^{22} -4.14123 q^{23} +(-0.692050 - 4.99805i) q^{24} -1.00000i q^{25} +(0.292694 + 6.37745i) q^{26} +(3.55417 + 3.55417i) q^{27} +(-4.25574 - 3.14462i) q^{28} +(-7.31132 + 7.31132i) q^{29} +(1.70027 - 1.86385i) q^{30} +5.03608 q^{31} +(4.80453 + 2.98605i) q^{32} +6.09461i q^{33} +(3.21138 - 3.52034i) q^{34} +(-0.151531 - 2.64141i) q^{35} +(0.363336 - 0.0334211i) q^{36} +(-6.98368 - 6.98368i) q^{37} +(4.50981 - 0.206978i) q^{38} -8.05321 q^{39} +(0.387934 + 2.80170i) q^{40} -0.221187 q^{41} +(4.20869 - 5.18083i) q^{42} +(1.77332 - 1.77332i) q^{43} +(-5.25373 - 4.36862i) q^{44} +(0.129001 + 0.129001i) q^{45} +(4.32674 + 3.94702i) q^{46} +11.6416 q^{47} +(-4.04060 + 5.88154i) q^{48} +(-0.800510 - 6.95408i) q^{49} +(-0.953102 + 1.04480i) q^{50} +(4.25028 + 4.25028i) q^{51} +(5.77256 - 6.94210i) q^{52} +(-0.300789 - 0.300789i) q^{53} +(-0.325896 - 7.10087i) q^{54} -3.41638i q^{55} +(1.44924 + 7.34164i) q^{56} +5.69481i q^{57} +(14.6073 - 0.670403i) q^{58} +(3.95846 + 3.95846i) q^{59} +(-3.55288 + 0.326808i) q^{60} +(-0.736150 - 0.736150i) q^{61} +(-5.26167 - 4.79990i) q^{62} +(0.360292 + 0.321197i) q^{63} +(-2.17375 - 7.69901i) q^{64} +4.51429 q^{65} +(5.80878 - 6.36762i) q^{66} +(6.90649 + 6.90649i) q^{67} +(-6.71048 + 0.617257i) q^{68} +(-5.22390 + 5.22390i) q^{69} +(-2.35921 + 2.90416i) q^{70} -9.82868 q^{71} +(-0.411465 - 0.311378i) q^{72} +10.0001 q^{73} +(0.640360 + 13.9527i) q^{74} +(-1.26143 - 1.26143i) q^{75} +(-4.90910 - 4.08205i) q^{76} +(-0.517687 - 9.02405i) q^{77} +(8.41396 + 7.67553i) q^{78} +2.12789i q^{79} +(2.26499 - 3.29694i) q^{80} +9.51402 q^{81} +(0.231096 + 0.210814i) q^{82} +(-2.97147 + 2.97147i) q^{83} +(-9.33508 + 1.40160i) q^{84} +(-2.38253 - 2.38253i) q^{85} +(-3.54291 + 0.162602i) q^{86} +18.4455i q^{87} +(1.32533 + 9.57165i) q^{88} +0.946648 q^{89} +(-0.0118286 - 0.257731i) q^{90} +(11.9241 - 0.684054i) q^{91} +(-0.758653 - 8.24765i) q^{92} +(6.35269 - 6.35269i) q^{93} +(-12.1631 - 11.0957i) q^{94} -3.19227i q^{95} +(9.82731 - 2.29390i) q^{96} +0.702211i q^{97} +(-5.79157 + 8.02855i) q^{98} +(0.440716 + 0.440716i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 4 q^{4}+O(q^{10}) \) 128 * q - 4 * q^4	\( 128 q - 4 q^{4} + 8 q^{11} - 8 q^{14} + 20 q^{16} + 20 q^{18} - 52 q^{22} - 16 q^{23} + 44 q^{28} + 16 q^{29} + 40 q^{32} + 16 q^{37} + 60 q^{42} - 8 q^{43} - 108 q^{44} - 40 q^{46} - 4 q^{50} + 80 q^{51} + 16 q^{53} + 12 q^{56} - 76 q^{58} - 56 q^{60} - 52 q^{64} + 40 q^{67} - 8 q^{70} - 64 q^{71} - 36 q^{72} + 60 q^{74} - 48 q^{78} - 128 q^{81} - 32 q^{84} + 76 q^{86} + 20 q^{88} - 32 q^{91} + 64 q^{92} - 76 q^{98} - 40 q^{99}+O(q^{100}) \) 128 * q - 4 * q^4 + 8 * q^11 - 8 * q^14 + 20 * q^16 + 20 * q^18 - 52 * q^22 - 16 * q^23 + 44 * q^28 + 16 * q^29 + 40 * q^32 + 16 * q^37 + 60 * q^42 - 8 * q^43 - 108 * q^44 - 40 * q^46 - 4 * q^50 + 80 * q^51 + 16 * q^53 + 12 * q^56 - 76 * q^58 - 56 * q^60 - 52 * q^64 + 40 * q^67 - 8 * q^70 - 64 * q^71 - 36 * q^72 + 60 * q^74 - 48 * q^78 - 128 * q^81 - 32 * q^84 + 76 * q^86 + 20 * q^88 - 32 * q^91 + 64 * q^92 - 76 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more