LMFDB - Embedded newform 555.2.bb.a.454.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(454,555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("555.454");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.bb (of order $6$, 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:	$4.43169731218$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			454.13
Character	$\chi$	$=$	555.454
Dual form			555.2.bb.a.544.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.950972 - 0.549044i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.397102 - 0.687801i) q^{4} +(0.837757 + 2.07320i) q^{5} -1.09809 q^{6} +(-1.35262 + 0.780936i) q^{7} +3.06828i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.950972 - 0.549044i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.397102 - 0.687801i) q^{4} +(0.837757 + 2.07320i) q^{5} -1.09809 q^{6} +(-1.35262 + 0.780936i) q^{7} +3.06828i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.341594 - 2.43152i) q^{10} +2.37717 q^{11} +(-0.687801 - 0.397102i) q^{12} +(-0.862816 + 0.498147i) q^{13} +1.71507 q^{14} +(1.76212 + 1.37657i) q^{15} +(0.890417 - 1.54225i) q^{16} +(0.307311 + 0.177426i) q^{17} +(-0.950972 + 0.549044i) q^{18} +(3.55593 + 6.15906i) q^{19} +(1.09327 - 1.39948i) q^{20} +(-0.780936 + 1.35262i) q^{21} +(-2.26062 - 1.30517i) q^{22} +4.22010i q^{23} +(1.53414 + 2.65721i) q^{24} +(-3.59632 + 3.47368i) q^{25} +1.09402 q^{26} -1.00000i q^{27} +(1.07426 + 0.620223i) q^{28} +7.52314 q^{29} +(-0.919931 - 2.27656i) q^{30} +0.998902 q^{31} +(3.62090 - 2.09053i) q^{32} +(2.05869 - 1.18859i) q^{33} +(-0.194830 - 0.337455i) q^{34} +(-2.75221 - 2.15002i) q^{35} -0.794204 q^{36} +(-1.35801 - 5.92923i) q^{37} -7.80946i q^{38} +(-0.498147 + 0.862816i) q^{39} +(-6.36116 + 2.57047i) q^{40} +(-1.59578 - 2.76397i) q^{41} +(1.48530 - 0.857537i) q^{42} +6.18070i q^{43} +(-0.943979 - 1.63502i) q^{44} +(2.21432 + 0.311081i) q^{45} +(2.31702 - 4.01319i) q^{46} -7.02323i q^{47} -1.78083i q^{48} +(-2.28028 + 3.94955i) q^{49} +(5.32721 - 1.32883i) q^{50} +0.354853 q^{51} +(0.685252 + 0.395630i) q^{52} +(11.9801 + 6.91673i) q^{53} +(-0.549044 + 0.950972i) q^{54} +(1.99149 + 4.92835i) q^{55} +(-2.39613 - 4.15022i) q^{56} +(6.15906 + 3.55593i) q^{57} +(-7.15429 - 4.13053i) q^{58} +(5.72918 - 9.92323i) q^{59} +(0.247062 - 1.75862i) q^{60} +(0.880813 + 1.52561i) q^{61} +(-0.949927 - 0.548441i) q^{62} +1.56187i q^{63} -8.15283 q^{64} +(-1.75559 - 1.37146i) q^{65} -2.61034 q^{66} +(-1.47011 + 0.848767i) q^{67} -0.281825i q^{68} +(2.11005 + 3.65471i) q^{69} +(1.43682 + 3.55569i) q^{70} +(-2.23650 - 3.87372i) q^{71} +(2.65721 + 1.53414i) q^{72} +5.60903i q^{73} +(-1.96398 + 6.38414i) q^{74} +(-1.37767 + 4.80646i) q^{75} +(2.82414 - 4.89155i) q^{76} +(-3.21541 + 1.85642i) q^{77} +(0.947448 - 0.547009i) q^{78} +(-5.47109 - 9.47620i) q^{79} +(3.94334 + 0.553984i) q^{80} +(-0.500000 - 0.866025i) q^{81} +3.50461i q^{82} +(6.26017 + 3.61431i) q^{83} +1.24045 q^{84} +(-0.110388 + 0.785758i) q^{85} +(3.39348 - 5.87768i) q^{86} +(6.51523 - 3.76157i) q^{87} +7.29383i q^{88} +(-7.72572 + 13.3813i) q^{89} +(-1.93496 - 1.51159i) q^{90} +(0.778043 - 1.34761i) q^{91} +(2.90258 - 1.67581i) q^{92} +(0.865074 - 0.499451i) q^{93} +(-3.85606 + 6.67890i) q^{94} +(-9.78996 + 12.5320i) q^{95} +(2.09053 - 3.62090i) q^{96} +4.07687i q^{97} +(4.33696 - 2.50394i) q^{98} +(1.18859 - 2.05869i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9}+O(q^{10}) $ 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9	$ 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9} - 8 q^{11} - 16 q^{14} - 24 q^{16} + 4 q^{19} + 4 q^{20} + 12 q^{21} + 10 q^{25} + 24 q^{26} + 16 q^{29} + 12 q^{30} + 24 q^{31} - 44 q^{34} - 2 q^{35} + 64 q^{36} - 8 q^{39} + 46 q^{40} - 48 q^{41} - 8 q^{44} - 4 q^{45} - 64 q^{46} + 32 q^{49} - 46 q^{50} - 8 q^{51} - 12 q^{55} - 72 q^{56} + 32 q^{59} - 68 q^{60} - 8 q^{61} - 136 q^{64} - 42 q^{65} - 32 q^{66} - 4 q^{69} + 4 q^{70} + 12 q^{71} - 96 q^{74} - 8 q^{75} + 8 q^{76} - 8 q^{79} - 44 q^{80} - 36 q^{81} + 136 q^{84} + 4 q^{85} + 8 q^{86} + 8 q^{91} - 28 q^{94} + 18 q^{95} - 20 q^{96} - 4 q^{99}+O(q^{100}) $ 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9 - 8 * q^11 - 16 * q^14 - 24 * q^16 + 4 * q^19 + 4 * q^20 + 12 * q^21 + 10 * q^25 + 24 * q^26 + 16 * q^29 + 12 * q^30 + 24 * q^31 - 44 * q^34 - 2 * q^35 + 64 * q^36 - 8 * q^39 + 46 * q^40 - 48 * q^41 - 8 * q^44 - 4 * q^45 - 64 * q^46 + 32 * q^49 - 46 * q^50 - 8 * q^51 - 12 * q^55 - 72 * q^56 + 32 * q^59 - 68 * q^60 - 8 * q^61 - 136 * q^64 - 42 * q^65 - 32 * q^66 - 4 * q^69 + 4 * q^70 + 12 * q^71 - 96 * q^74 - 8 * q^75 + 8 * q^76 - 8 * q^79 - 44 * q^80 - 36 * q^81 + 136 * q^84 + 4 * q^85 + 8 * q^86 + 8 * q^91 - 28 * q^94 + 18 * q^95 - 20 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.950972	−	0.549044i	−0.672439	−	0.388233i	0.124561	−	0.992212i	$-0.460248\pi$
$2$	−0.950972	−	0.549044i	−0.672439	−	0.388233i	−0.797000	+	0.603979i	$0.793581\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.397102	−	0.687801i	−0.198551	−	0.343900i
$5$	0.837757	+	2.07320i	0.374657	+	0.927164i
$5$	0.837757	+	2.07320i	0.374657	+	0.927164i
$6$	−1.09809			−0.448292
$7$	−1.35262	+	0.780936i	−0.511243	+	0.295166i	−0.733344	−	0.679857i	$-0.762042\pi$
$7$	−1.35262	+	0.780936i	−0.511243	+	0.295166i	0.222101	+	0.975024i	$0.428708\pi$
$8$			3.06828i			1.08480i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.341594	−	2.43152i	0.108022	−	0.768914i
$11$	2.37717			0.716744			0.358372	−	0.933579i	$-0.383332\pi$
$11$	2.37717			0.716744			0.358372	+	0.933579i	$0.383332\pi$
$12$	−0.687801	−	0.397102i	−0.198551	−	0.114633i
$13$	−0.862816	+	0.498147i	−0.239302	+	0.138161i	−0.614856	−	0.788639i	$-0.710786\pi$
$13$	−0.862816	+	0.498147i	−0.239302	+	0.138161i	0.375554	+	0.926801i	$0.377453\pi$
$14$	1.71507			0.458373
$15$	1.76212	+	1.37657i	0.454977	+	0.355428i
$16$	0.890417	−	1.54225i	0.222604	−	0.385562i
$17$	0.307311	+	0.177426i	0.0745339	+	0.0430322i	0.536804	−	0.843707i	$-0.319632\pi$
$17$	0.307311	+	0.177426i	0.0745339	+	0.0430322i	−0.462270	+	0.886739i	$0.652965\pi$
$18$	−0.950972	+	0.549044i	−0.224146	+	0.129411i
$19$	3.55593	+	6.15906i	0.815787	+	1.41299i	0.908761	+	0.417317i	$0.137029\pi$
$19$	3.55593	+	6.15906i	0.815787	+	1.41299i	−0.0929737	+	0.995669i	$0.529637\pi$
$20$	1.09327	−	1.39948i	0.244463	−	0.312934i
$21$	−0.780936	+	1.35262i	−0.170414	+	0.295166i
$22$	−2.26062	−	1.30517i	−0.481966	−	0.278263i
$23$			4.22010i			0.879951i	0.898010	+	0.439975i	$0.145013\pi$
$23$			4.22010i			0.879951i	−0.898010	+	0.439975i	$0.854987\pi$
$24$	1.53414	+	2.65721i	0.313155	+	0.542400i
$25$	−3.59632	+	3.47368i	−0.719265	+	0.694736i
$26$	1.09402			0.214555
$27$		−	1.00000i		−	0.192450i
$28$	1.07426	+	0.620223i	0.203016	+	0.117211i
$29$	7.52314			1.39701			0.698506	−	0.715604i	$-0.253849\pi$
$29$	7.52314			1.39701			0.698506	+	0.715604i	$0.253849\pi$
$30$	−0.919931	−	2.27656i	−0.167956	−	0.415640i
$31$	0.998902			0.179408			0.0897040	−	0.995968i	$-0.471408\pi$
$31$	0.998902			0.179408			0.0897040	+	0.995968i	$0.471408\pi$
$32$	3.62090	−	2.09053i	0.640090	−	0.369556i
$33$	2.05869	−	1.18859i	0.358372	−	0.206906i
$34$	−0.194830	−	0.337455i	−0.0334130	−	0.0578730i
$35$	−2.75221	−	2.15002i	−0.465208	−	0.363420i
$36$	−0.794204			−0.132367
$37$	−1.35801	−	5.92923i	−0.223256	−	0.974760i
$37$	−1.35801	−	5.92923i	−0.223256	−	0.974760i
$38$		−	7.80946i		−	1.26686i
$39$	−0.498147	+	0.862816i	−0.0797674	+	0.138161i
$40$	−6.36116	+	2.57047i	−1.00579	+	0.406428i
$41$	−1.59578	−	2.76397i	−0.249219	−	0.431660i	0.714090	−	0.700053i	$-0.246841\pi$
$41$	−1.59578	−	2.76397i	−0.249219	−	0.431660i	−0.963309	+	0.268394i	$0.913507\pi$
$42$	1.48530	−	0.857537i	0.229186	−	0.132321i
$43$			6.18070i			0.942549i	0.881987	+	0.471274i	$0.156206\pi$
$43$			6.18070i			0.942549i	−0.881987	+	0.471274i	$0.843794\pi$
$44$	−0.943979	−	1.63502i	−0.142310	−	0.246488i
$45$	2.21432	+	0.311081i	0.330092	+	0.0463733i
$46$	2.31702	−	4.01319i	0.341626	−	0.591713i
$47$		−	7.02323i		−	1.02444i	−0.858853	−	0.512222i	$-0.828823\pi$
$47$		−	7.02323i		−	1.02444i	0.858853	−	0.512222i	$-0.171177\pi$
$48$		−	1.78083i		−	0.257041i
$49$	−2.28028	+	3.94955i	−0.325754	+	0.564222i
$50$	5.32721	−	1.32883i	0.753381	−	0.187925i
$51$	0.354853			0.0496893
$52$	0.685252	+	0.395630i	0.0950273	+	0.0548641i
$53$	11.9801	+	6.91673i	1.64560	+	0.950086i	0.978793	+	0.204853i	$0.0656716\pi$
$53$	11.9801	+	6.91673i	1.64560	+	0.950086i	0.666804	+	0.745233i	$0.267662\pi$
$54$	−0.549044	+	0.950972i	−0.0747154	+	0.129411i
$55$	1.99149	+	4.92835i	0.268533	+	0.664539i
$56$	−2.39613	−	4.15022i	−0.320197	−	0.554597i
$57$	6.15906	+	3.55593i	0.815787	+	0.470995i
$58$	−7.15429	−	4.13053i	−0.939404	−	0.542365i
$59$	5.72918	−	9.92323i	0.745876	−	1.29189i	−0.203909	−	0.978990i	$-0.565365\pi$
$59$	5.72918	−	9.92323i	0.745876	−	1.29189i	0.949785	−	0.312905i	$-0.101302\pi$
$60$	0.247062	−	1.75862i	0.0318955	−	0.227037i
$61$	0.880813	+	1.52561i	0.112777	+	0.195335i	0.916889	−	0.399143i	$-0.130692\pi$
$61$	0.880813	+	1.52561i	0.112777	+	0.195335i	−0.804112	+	0.594478i	$0.797359\pi$
$62$	−0.949927	−	0.548441i	−0.120641	−	0.0696520i
$63$			1.56187i			0.196777i
$64$	−8.15283			−1.01910
$65$	−1.75559	−	1.37146i	−0.217754	−	0.170109i
$66$	−2.61034			−0.321311
$67$	−1.47011	+	0.848767i	−0.179602	+	0.103693i	−0.587106	−	0.809510i	$-0.699733\pi$
$67$	−1.47011	+	0.848767i	−0.179602	+	0.103693i	0.407504	+	0.913204i	$0.366399\pi$
$68$		−	0.281825i		−	0.0341763i
$69$	2.11005	+	3.65471i	0.254020	+	0.439975i
$70$	1.43682	+	3.55569i	0.171732	+	0.424986i
$71$	−2.23650	−	3.87372i	−0.265423	−	0.459727i	0.702251	−	0.711929i	$-0.252178\pi$
$71$	−2.23650	−	3.87372i	−0.265423	−	0.459727i	−0.967674	+	0.252203i	$0.918845\pi$
$72$	2.65721	+	1.53414i	0.313155	+	0.180800i
$73$			5.60903i			0.656488i	0.944593	+	0.328244i	$0.106457\pi$
$73$			5.60903i			0.656488i	−0.944593	+	0.328244i	$0.893543\pi$
$74$	−1.96398	+	6.38414i	−0.228308	+	0.742141i
$75$	−1.37767	+	4.80646i	−0.159080	+	0.555002i
$76$	2.82414	−	4.89155i	0.323951	−	0.561099i
$77$	−3.21541	+	1.85642i	−0.366430	+	0.211559i
$78$	0.947448	−	0.547009i	0.107277	−	0.0619366i
$79$	−5.47109	−	9.47620i	−0.615546	−	1.06616i	−0.990289	−	0.139028i	$-0.955602\pi$
$79$	−5.47109	−	9.47620i	−0.615546	−	1.06616i	0.374743	−	0.927129i	$-0.377731\pi$
$80$	3.94334	+	0.553984i	0.440879	+	0.0619373i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			3.50461i			0.387020i
$83$	6.26017	+	3.61431i	0.687143	+	0.396722i	0.802541	−	0.596597i	$-0.203481\pi$
$83$	6.26017	+	3.61431i	0.687143	+	0.396722i	−0.115398	+	0.993319i	$0.536814\pi$
$84$	1.24045			0.135344
$85$	−0.110388	+	0.785758i	−0.0119733	+	0.0852275i
$86$	3.39348	−	5.87768i	0.365928	−	0.633806i
$87$	6.51523	−	3.76157i	0.698506	−	0.403282i
$88$			7.29383i			0.777525i
$89$	−7.72572	+	13.3813i	−0.818925	+	1.41842i	0.0875504	+	0.996160i	$0.472096\pi$
$89$	−7.72572	+	13.3813i	−0.818925	+	1.41842i	−0.906475	+	0.422259i	$0.861237\pi$
$90$	−1.93496	−	1.51159i	−0.203963	−	0.159336i
$91$	0.778043	−	1.34761i	0.0815610	−	0.141268i
$92$	2.90258	−	1.67581i	0.302615	−	0.174715i
$93$	0.865074	−	0.499451i	0.0897040	−	0.0517906i
$94$	−3.85606	+	6.67890i	−0.397722	+	0.688875i
$95$	−9.78996	+	12.5320i	−1.00443	+	1.28575i
$96$	2.09053	−	3.62090i	0.213363	−	0.369556i
$97$			4.07687i			0.413943i	0.978347	+	0.206972i	$0.0663608\pi$
$97$			4.07687i			0.413943i	−0.978347	+	0.206972i	$0.933639\pi$
$98$	4.33696	−	2.50394i	0.438099	−	0.252936i
$99$	1.18859	−	2.05869i	0.119457	−	0.206906i
$100$	3.81731	+	1.09415i	0.381731	+	0.109415i
$101$	−10.7216			−1.06684			−0.533420	−	0.845851i	$-0.679093\pi$
$101$	−10.7216			−1.06684			−0.533420	+	0.845851i	$0.679093\pi$
$102$	−0.337455	−	0.194830i	−0.0334130	−	0.0192910i
$103$		−	14.0705i		−	1.38641i	−0.720740	−	0.693206i	$-0.756198\pi$
$103$		−	14.0705i		−	1.38641i	0.720740	−	0.693206i	$-0.243802\pi$
$104$	−1.52846	−	2.64736i	−0.149877	−	0.259595i
$105$	−3.45849	−	0.485869i	−0.337514	−	0.0474160i
$106$	−7.59517	−	13.1552i	−0.737709	−	1.27775i
$107$	−0.269600	+	0.155653i	−0.0260632	+	0.0150476i	−0.512975	−	0.858404i	$-0.671457\pi$
$107$	−0.269600	+	0.155653i	−0.0260632	+	0.0150476i	0.486912	+	0.873451i	$0.338123\pi$
$108$	−0.687801	+	0.397102i	−0.0661836	+	0.0382111i
$109$	−3.38352	+	5.86043i	−0.324082	+	0.561327i	−0.981326	−	0.192351i	$-0.938389\pi$
$109$	−3.38352	+	5.86043i	−0.324082	+	0.561327i	0.657244	+	0.753678i	$0.271722\pi$
$110$	0.812028	−	5.78014i	0.0774239	−	0.551115i
$111$	−4.14069	−	4.45586i	−0.393017	−	0.422931i
$112$			2.78143i			0.262821i
$113$	8.10392	+	4.67880i	0.762353	+	0.440145i	0.830140	−	0.557555i	$-0.188260\pi$
$113$	8.10392	+	4.67880i	0.762353	+	0.440145i	−0.0677869	+	0.997700i	$0.521594\pi$
$114$	−3.90473	−	6.76319i	−0.365711	−	0.633431i
$115$	−8.74911	+	3.53542i	−0.815859	+	0.329679i
$116$	−2.98745	−	5.17442i	−0.277378	−	0.480433i
$117$			0.996294i			0.0921075i
$118$	−10.8966	+	6.29114i	−1.00311	+	0.579146i
$119$	−0.554235			−0.0508066
$120$	−4.22369	+	5.40668i	−0.385568	+	0.493560i
$121$	−5.34906			−0.486278
$122$		−	1.93442i		−	0.175134i
$123$	−2.76397	−	1.59578i	−0.249219	−	0.143887i
$124$	−0.396666	−	0.687045i	−0.0356216	−	0.0616985i
$125$	−10.2145	−	4.54580i	−0.913611	−	0.406589i
$126$	0.857537	−	1.48530i	0.0763954	−	0.132321i
$127$	−2.09886	−	1.21178i	−0.186244	−	0.107528i	0.403979	−	0.914768i	$-0.367627\pi$
$127$	−2.09886	−	1.21178i	−0.186244	−	0.107528i	−0.590223	+	0.807240i	$0.700960\pi$
$128$	0.511315	+	0.295208i	0.0451943	+	0.0260929i
$129$	3.09035	+	5.35265i	0.272090	+	0.471274i
$130$	0.916522	+	2.26812i	0.0803843	+	0.198927i
$131$	−0.185783	+	0.321786i	−0.0162319	+	0.0281145i	−0.874027	−	0.485877i	$-0.838500\pi$
$131$	−0.185783	+	0.321786i	−0.0162319	+	0.0281145i	0.857795	+	0.513991i	$0.171834\pi$
$132$	−1.63502	−	0.943979i	−0.142310	−	0.0821628i
$133$	−9.61967	−	5.55392i	−0.834131	−	0.481586i
$134$	1.86404			0.161029
$135$	2.07320	−	0.837757i	0.178433	−	0.0721027i
$136$	−0.544394	+	0.942917i	−0.0466814	+	0.0808545i
$137$		−	1.97987i		−	0.169152i	−0.996417	−	0.0845758i	$-0.973046\pi$
$137$		−	1.97987i		−	0.169152i	0.996417	−	0.0845758i	$-0.0269535\pi$
$138$		−	4.63404i		−	0.394475i
$139$	8.36823	−	14.4942i	0.709784	−	1.22938i	−0.255153	−	0.966901i	$-0.582126\pi$
$139$	8.36823	−	14.4942i	0.709784	−	1.22938i	0.964937	−	0.262482i	$-0.0845410\pi$
$140$	−0.385879	+	2.74675i	−0.0326127	+	0.232143i
$141$	−3.51162	−	6.08230i	−0.295731	−	0.512222i
$142$			4.91174i			0.412184i
$143$	−2.05106	+	1.18418i	−0.171518	+	0.0990262i
$144$	−0.890417	−	1.54225i	−0.0742014	−	0.128521i
$145$	6.30256	+	15.5970i	0.523399	+	1.29526i
$146$	3.07960	−	5.33403i	0.254870	−	0.441448i
$147$			4.56055i			0.376148i
$148$	−3.53886	+	3.28855i	−0.290893	+	0.270317i
$149$	−8.50847			−0.697041			−0.348520	−	0.937301i	$-0.613316\pi$
$149$	−8.50847			−0.697041			−0.348520	+	0.937301i	$0.613316\pi$
$150$	3.94908	−	3.81440i	0.322441	−	0.311445i
$151$	−5.46489	−	9.46547i	−0.444727	−	0.770289i	0.553306	−	0.832978i	$-0.313366\pi$
$151$	−5.46489	−	9.46547i	−0.444727	−	0.770289i	−0.998033	+	0.0626886i	$0.980033\pi$
$152$	−18.8977	+	10.9106i	−1.53281	+	0.884967i
$153$	0.307311	−	0.177426i	0.0248446	−	0.0143441i
$154$	4.07702			0.328536
$155$	0.836837	+	2.07092i	0.0672164	+	0.166341i
$156$	0.791261			0.0633516
$157$	−13.2975	−	7.67732i	−1.06126	−	0.612717i	−0.135477	−	0.990781i	$-0.543257\pi$
$157$	−13.2975	−	7.67732i	−1.06126	−	0.612717i	−0.925780	+	0.378064i	$0.876590\pi$
$158$			12.0155i			0.955899i
$159$	13.8335			1.09706
$160$	7.36751	+	5.75549i	0.582453	+	0.455012i
$161$	−3.29563	−	5.70819i	−0.259732	−	0.449869i
$162$			1.09809i			0.0862739i
$163$	−5.99201	−	3.45949i	−0.469331	−	0.270968i	0.246629	−	0.969110i	$-0.420677\pi$
$163$	−5.99201	−	3.45949i	−0.469331	−	0.270968i	−0.715959	+	0.698142i	$0.754010\pi$
$164$	−1.26737	+	2.19516i	−0.0989653	+	0.171413i
$165$	4.18886	+	3.27233i	0.326102	+	0.254751i
$166$	−3.96883	−	6.87421i	−0.308041	−	0.533543i
$167$	−15.9593	+	9.21410i	−1.23497	+	0.713008i	−0.968061	−	0.250714i	$-0.919335\pi$
$167$	−15.9593	+	9.21410i	−1.23497	+	0.713008i	−0.266906	+	0.963723i	$0.586001\pi$
$168$	−4.15022	−	2.39613i	−0.320197	−	0.184866i
$169$	−6.00370	+	10.3987i	−0.461823	+	0.799901i
$170$	0.536392	−	0.686626i	0.0411394	−	0.0526618i
$171$	7.11187			0.543858
$172$	4.25109	−	2.45437i	0.324143	−	0.187144i
$173$	11.5775	+	6.68428i	0.880221	+	0.508196i	0.870731	−	0.491759i	$-0.163646\pi$
$173$	11.5775	+	6.68428i	0.880221	+	0.508196i	0.00948996	+	0.999955i	$0.496979\pi$
$174$	−8.26106			−0.626270
$175$	2.15174	−	7.50708i	0.162657	−	0.567482i
$176$	2.11667	−	3.66618i	0.159550	−	0.276349i
$177$		−	11.4584i		−	0.861263i
$178$	14.6939	−	8.48352i	1.10135	−	0.635867i
$179$	−0.0705406			−0.00527245			−0.00263623	−	0.999997i	$-0.500839\pi$
$179$	−0.0705406			−0.00527245			−0.00263623	+	0.999997i	$0.500839\pi$
$180$	−0.665350	−	1.64654i	−0.0495923	−	0.122726i
$181$	7.84795	+	13.5930i	0.583334	+	1.01036i	0.995081	+	0.0990653i	$0.0315853\pi$
$181$	7.84795	+	13.5930i	0.583334	+	1.01036i	−0.411747	+	0.911298i	$0.635081\pi$
$182$	−1.47979	+	0.854359i	−0.109690	+	0.0633293i
$183$	1.52561	+	0.880813i	0.112777	+	0.0651115i
$184$	−12.9484			−0.954572
$185$	11.1548	−	7.78269i	0.820118	−	0.572195i
$186$	−1.09688			−0.0804272
$187$	0.730532	+	0.421773i	0.0534218	+	0.0308431i
$188$	−4.83058	+	2.78894i	−0.352307	+	0.203404i
$189$	0.780936	+	1.35262i	0.0568048	+	0.0983887i
$190$	16.1906	−	6.54243i	1.17459	−	0.474638i
$191$	−3.45326			−0.249869			−0.124934	−	0.992165i	$-0.539872\pi$
$191$	−3.45326			−0.249869			−0.124934	+	0.992165i	$0.539872\pi$
$192$	−7.06055	+	4.07641i	−0.509552	+	0.294190i
$193$		−	9.62917i		−	0.693123i	−0.938027	−	0.346561i	$-0.887349\pi$
$193$		−	9.62917i		−	0.693123i	0.938027	−	0.346561i	$-0.112651\pi$
$194$	2.23838	−	3.87699i	0.160706	−	0.278351i
$195$	−2.20612	−	0.309928i	−0.157983	−	0.0221944i
$196$	3.62201			0.258715
$197$	0.188275	+	0.108701i	0.0134141	+	0.00774461i	0.506692	−	0.862127i	$-0.330868\pi$
$197$	0.188275	+	0.108701i	0.0134141	+	0.00774461i	−0.493278	+	0.869872i	$0.664201\pi$
$198$	−2.26062	+	1.30517i	−0.160655	+	0.0927545i
$199$	0.390719			0.0276974			0.0138487	−	0.999904i	$-0.495592\pi$
$199$	0.390719			0.0276974			0.0138487	+	0.999904i	$0.495592\pi$
$200$	−10.6582	−	11.0345i	−0.753650	−	0.780259i
$201$	−0.848767	+	1.47011i	−0.0598674	+	0.103693i
$202$	10.1959	+	5.88663i	0.717384	+	0.414182i
$203$	−10.1760	+	5.87509i	−0.714212	+	0.412351i
$204$	−0.140913	−	0.244068i	−0.00986586	−	0.0170882i
$205$	4.39339	−	5.62391i	0.306848	−	0.392791i
$206$	−7.72534	+	13.3807i	−0.538250	+	0.932277i
$207$	3.65471	+	2.11005i	0.254020	+	0.146658i
$208$			1.77423i			0.123021i
$209$	8.45307	+	14.6411i	0.584711	+	1.01275i
$210$	3.02216	+	2.36091i	0.208549	+	0.162918i
$211$	14.5685			1.00294			0.501468	−	0.865176i	$-0.332794\pi$
$211$	14.5685			1.00294			0.501468	+	0.865176i	$0.332794\pi$
$212$		−	10.9866i		−	0.754562i
$213$	−3.87372	−	2.23650i	−0.265423	−	0.153242i
$214$	0.341842			0.0233679
$215$	−12.8138	+	5.17793i	−0.873897	+	0.353132i
$216$	3.06828			0.208770
$217$	−1.35114	+	0.780079i	−0.0917211	+	0.0529552i
$218$	6.43526	−	3.71540i	0.435851	−	0.251639i
$219$	2.80452	+	4.85757i	0.189512	+	0.328244i
$220$	2.59890	−	3.32681i	0.175218	−	0.224293i
$221$	−0.353538			−0.0237815
$222$	1.49122	+	6.51082i	0.100084	+	0.436977i
$223$		−	28.9482i		−	1.93852i	−0.246047	−	0.969258i	$-0.579132\pi$
$223$		−	28.9482i		−	1.93852i	0.246047	−	0.969258i	$-0.420868\pi$
$224$	−3.26513	+	5.65538i	−0.218161	+	0.377866i
$225$	1.21013	+	4.85135i	0.0806755	+	0.323423i
$226$	−5.13773	−	8.89882i	−0.341757	−	0.591941i
$227$	24.8759	−	14.3621i	1.65107	−	0.953248i	0.674444	−	0.738326i	$-0.264384\pi$
$227$	24.8759	−	14.3621i	1.65107	−	0.953248i	0.976631	−	0.214922i	$-0.0689497\pi$
$228$		−	5.64827i		−	0.374066i
$229$	−13.1544	−	22.7840i	−0.869265	−	1.50561i	−0.862749	−	0.505633i	$-0.831259\pi$
$229$	−13.1544	−	22.7840i	−0.869265	−	1.50561i	−0.00651613	−	0.999979i	$-0.502074\pi$
$230$	10.2613	+	1.44156i	0.676607	+	0.0950537i
$231$	−1.85642	+	3.21541i	−0.122143	+	0.211559i
$232$			23.0831i			1.51548i
$233$			2.82955i			0.185370i	0.995695	+	0.0926849i	$0.0295449\pi$
$233$			2.82955i			0.185370i	−0.995695	+	0.0926849i	$0.970455\pi$
$234$	0.547009	−	0.947448i	0.0357591	−	0.0619366i
$235$	14.5606	−	5.88377i	0.949827	−	0.383815i
$236$	−9.10027			−0.592377
$237$	−9.47620	−	5.47109i	−0.615546	−	0.355385i
$238$	0.527061	+	0.304299i	0.0341643	+	0.0197248i
$239$	−1.65160	+	2.86065i	−0.106833	+	0.185040i	−0.914486	−	0.404619i	$-0.867404\pi$
$239$	−1.65160	+	2.86065i	−0.106833	+	0.185040i	0.807653	+	0.589658i	$0.200738\pi$
$240$	3.69202	−	1.49191i	0.238319	−	0.0963021i
$241$	3.52974	+	6.11369i	0.227370	+	0.393817i	0.957028	−	0.289996i	$-0.0936538\pi$
$241$	3.52974	+	6.11369i	0.227370	+	0.393817i	−0.729658	+	0.683813i	$0.760320\pi$
$242$	5.08680	+	2.93687i	0.326992	+	0.188789i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	0.699545	−	1.21165i	0.0447838	−	0.0775677i
$245$	−10.0985	−	1.41870i	−0.645172	−	0.0906376i
$246$	1.75231	+	3.03508i	0.111723	+	0.193510i
$247$	−6.13624	−	3.54276i	−0.390439	−	0.225420i
$248$			3.06491i			0.194622i
$249$	7.22862			0.458095
$250$	7.21784	+	9.93113i	0.456496	+	0.628100i
$251$	8.08478			0.510307			0.255153	−	0.966901i	$-0.417874\pi$
$251$	8.08478			0.510307			0.255153	+	0.966901i	$0.417874\pi$
$252$	1.07426	−	0.620223i	0.0676718	−	0.0390704i
$253$			10.0319i			0.630700i
$254$	1.33064	+	2.30473i	0.0834917	+	0.144612i
$255$	0.297280	+	0.735681i	0.0186164	+	0.0460701i
$256$	7.82866	+	13.5596i	0.489291	+	0.847477i
$257$	10.3437	+	5.97195i	0.645224	+	0.372520i	0.786624	−	0.617432i	$-0.211827\pi$
$257$	10.3437	+	5.97195i	0.645224	+	0.372520i	−0.141400	+	0.989953i	$0.545160\pi$
$258$		−	6.78695i		−	0.422537i
$259$	6.46723	+	6.95949i	0.401854	+	0.432441i
$260$	−0.246146	+	1.75211i	−0.0152653	+	0.108661i
$261$	3.76157	−	6.51523i	0.232835	−	0.403282i
$262$	0.353349	−	0.204006i	0.0218300	−	0.0126035i
$263$	−7.49520	+	4.32736i	−0.462174	+	0.266836i	−0.712958	−	0.701207i	$-0.752645\pi$
$263$	−7.49520	+	4.32736i	−0.462174	+	0.266836i	0.250784	+	0.968043i	$0.419312\pi$
$264$	3.64691	+	6.31664i	0.224452	+	0.388762i
$265$	−4.30333	+	30.6318i	−0.264351	+	1.88169i
$266$	6.09869	+	10.5632i	0.373935	+	0.647674i
$267$			15.4514i			0.945613i
$268$	1.16756	+	0.674094i	0.0713204	+	0.0411768i
$269$	19.9944			1.21908			0.609539	−	0.792756i	$-0.291355\pi$
$269$	19.9944			1.21908			0.609539	+	0.792756i	$0.291355\pi$
$270$	−2.43152	−	0.341594i	−0.147978	−	0.0207888i
$271$	−4.98231	+	8.62961i	−0.302654	+	0.524211i	−0.976736	−	0.214445i	$-0.931206\pi$
$271$	−4.98231	+	8.62961i	−0.302654	+	0.524211i	0.674083	+	0.738656i	$0.264539\pi$
$272$	0.547270	−	0.315967i	0.0331831	−	0.0191583i
$273$		−	1.55609i		−	0.0941786i
$274$	−1.08703	+	1.88280i	−0.0656702	+	0.113744i
$275$	−8.54908	+	8.25753i	−0.515529	+	0.497948i
$276$	1.67581	−	2.90258i	0.100872	−	0.174715i
$277$	27.2528	−	15.7344i	1.63746	−	0.945389i	0.655760	−	0.754969i	$-0.272348\pi$
$277$	27.2528	−	15.7344i	1.63746	−	0.945389i	0.981703	−	0.190420i	$-0.0609850\pi$
$278$	−15.9159	+	9.18905i	−0.954573	+	0.551123i
$279$	0.499451	−	0.865074i	0.0299013	−	0.0517906i
$280$	6.59687	−	8.44454i	0.394238	−	0.504658i
$281$	5.84909	−	10.1309i	0.348927	−	0.604360i	−0.637132	−	0.770755i	$-0.719879\pi$
$281$	5.84909	−	10.1309i	0.348927	−	0.604360i	0.986059	+	0.166395i	$0.0532127\pi$
$282$			7.71212i			0.459250i
$283$	5.18065	−	2.99105i	0.307958	−	0.177800i	−0.338054	−	0.941127i	$-0.609769\pi$
$283$	5.18065	−	2.99105i	0.307958	−	0.177800i	0.646012	+	0.763327i	$0.276435\pi$
$284$	−1.77623	+	3.07653i	−0.105400	+	0.182558i
$285$	−2.21237	+	15.7480i	−0.131049	+	0.932830i
$286$	2.60067			0.153781
$287$	4.31697	+	2.49240i	0.254823	+	0.147122i
$288$		−	4.18105i		−	0.246371i
$289$	−8.43704	−	14.6134i	−0.496296	−	0.859611i
$290$	2.56986	−	18.2927i	0.150907	−	1.07418i
$291$	2.03843	+	3.53067i	0.119495	+	0.206972i
$292$	3.85790	−	2.22736i	0.225766	−	0.130346i
$293$	27.4959	−	15.8748i	1.60633	−	0.927413i	0.616145	−	0.787633i	$-0.288694\pi$
$293$	27.4959	−	15.8748i	1.60633	−	0.927413i	0.990183	−	0.139780i	$-0.0446397\pi$
$294$	2.50394	−	4.33696i	0.146033	−	0.252936i
$295$	25.3725	+	3.56448i	1.47724	+	0.207532i
$296$	18.1925	−	4.16676i	1.05742	−	0.242188i
$297$		−	2.37717i		−	0.137937i
$298$	8.09131	+	4.67152i	0.468717	+	0.270614i
$299$	−2.10223	−	3.64117i	−0.121575	−	0.210574i
$300$	3.85296	−	0.961091i	0.222451	−	0.0554886i
$301$	−4.82674	−	8.36015i	−0.278209	−	0.481871i
$302$			12.0019i			0.690629i
$303$	−9.28518	+	5.36080i	−0.533420	+	0.307970i
$304$	12.6651			0.726391
$305$	−2.42499	+	3.10419i	−0.138855	+	0.177746i
$306$	−0.389659			−0.0222753
$307$			10.1363i			0.578510i	0.957252	+	0.289255i	$0.0934076\pi$
$307$			10.1363i			0.578510i	−0.957252	+	0.289255i	$0.906592\pi$
$308$	2.55369	+	1.47438i	0.145510	+	0.0840103i
$309$	−7.03527	−	12.1854i	−0.400223	−	0.693206i
$310$	0.341219	−	2.42885i	0.0193799	−	0.137949i
$311$	9.69121	−	16.7857i	0.549538	−	0.951828i	−0.448768	−	0.893648i	$-0.648137\pi$
$311$	9.69121	−	16.7857i	0.549538	−	0.951828i	0.998306	−	0.0581799i	$-0.0185297\pi$
$312$	−2.64736	−	1.52846i	−0.149877	−	0.0865317i
$313$	−12.3130	−	7.10890i	−0.695970	−	0.401819i	0.109874	−	0.993945i	$-0.464955\pi$
$313$	−12.3130	−	7.10890i	−0.695970	−	0.401819i	−0.805845	+	0.592127i	$0.798288\pi$
$314$	8.43037	+	14.6018i	0.475753	+	0.824029i
$315$	−3.23808	+	1.30847i	−0.182445	+	0.0737240i
$316$	−4.34516	+	7.52604i	−0.244434	+	0.423373i
$317$	−16.0720	−	9.27915i	−0.902691	−	0.521169i	−0.0246186	−	0.999697i	$-0.507837\pi$
$317$	−16.0720	−	9.27915i	−0.902691	−	0.521169i	−0.878072	+	0.478528i	$0.841170\pi$
$318$	−13.1552	−	7.59517i	−0.737709	−	0.425916i
$319$	17.8838			1.00130
$320$	−6.83009	−	16.9024i	−0.381814	−	0.944875i
$321$	−0.155653	+	0.269600i	−0.00868773	+	0.0150476i
$322$			7.23777i			0.403345i
$323$			2.52366i			0.140420i
$324$	−0.397102	+	0.687801i	−0.0220612	+	0.0382111i
$325$	1.37256	−	4.78865i	0.0761361	−	0.265626i
$326$	3.79882	+	6.57975i	0.210397	+	0.364419i
$327$			6.76704i			0.374218i
$328$	8.48064	−	4.89630i	0.468265	−	0.270353i
$329$	5.48470	+	9.49978i	0.302381	+	0.523740i
$330$	−2.18683	−	5.41176i	−0.120381	−	0.297908i
$331$	−2.04667	+	3.54493i	−0.112495	+	0.194847i	−0.916776	−	0.399403i	$-0.869218\pi$
$331$	−2.04667	+	3.54493i	−0.112495	+	0.194847i	0.804281	+	0.594250i	$0.202551\pi$
$332$		−	5.74100i		−	0.315078i
$333$	−5.81387	−	1.78854i	−0.318598	−	0.0980115i
$334$	20.2358			1.10725
$335$	−2.99126	−	2.33677i	−0.163430	−	0.127671i
$336$	1.39072	+	2.40879i	0.0758699	+	0.131410i
$337$	19.1488	−	11.0556i	1.04310	−	0.602236i	0.122392	−	0.992482i	$-0.460943\pi$
$337$	19.1488	−	11.0556i	1.04310	−	0.602236i	0.920711	+	0.390246i	$0.127610\pi$
$338$	11.4187	−	6.59259i	0.621095	−	0.358589i
$339$	9.35761			0.508235
$340$	0.584280	−	0.236101i	0.0316870	−	0.0128044i
$341$	2.37456			0.128590
$342$	−6.76319	−	3.90473i	−0.365711	−	0.211144i
$343$		−	18.0561i		−	0.974939i
$344$	−18.9641			−1.02248
$345$	−5.80924	+	7.43632i	−0.312759	+	0.400358i
$346$	−7.33992	−	12.7131i	−0.394597	−	0.683461i
$347$		−	2.23642i		−	0.120057i	−0.998197	−	0.0600287i	$-0.980881\pi$
$347$		−	2.23642i		−	0.120057i	0.998197	−	0.0600287i	$-0.0191192\pi$
$348$	−5.17442	−	2.98745i	−0.277378	−	0.160144i
$349$	−0.00232608	+	0.00402889i	−0.000124512	+	0.000215662i	−0.866088	−	0.499892i	$-0.833373\pi$
$349$	−0.00232608	+	0.00402889i	−0.000124512	+	0.000215662i	0.865963	+	0.500108i	$0.166706\pi$
$350$	−6.16796	+	5.95761i	−0.329691	+	0.318448i
$351$	0.498147	+	0.862816i	0.0265891	+	0.0460537i
$352$	8.60749	−	4.96954i	0.458781	−	0.264877i
$353$	−13.4942	−	7.79091i	−0.718226	−	0.414668i	0.0958732	−	0.995394i	$-0.469436\pi$
$353$	−13.4942	−	7.79091i	−0.718226	−	0.414668i	−0.814099	+	0.580725i	$0.802769\pi$
$354$	−6.29114	+	10.8966i	−0.334370	+	0.579146i
$355$	6.15737	−	7.88195i	0.326799	−	0.418330i
$356$	12.2716			0.650393
$357$	−0.479981	+	0.277117i	−0.0254033	+	0.0146666i
$358$	0.0670821	+	0.0387299i	0.00354540	+	0.00204694i
$359$	36.9609			1.95072			0.975361	−	0.220614i	$-0.0708061\pi$
$359$	36.9609			1.95072			0.975361	+	0.220614i	$0.0708061\pi$
$360$	−0.954484	+	6.79417i	−0.0503057	+	0.358084i
$361$	−15.7893	+	27.3480i	−0.831018	+	1.43937i
$362$		−	17.2355i		−	0.905876i
$363$	−4.63242	+	2.67453i	−0.243139	+	0.140376i
$364$	−1.23585			−0.0647761
$365$	−11.6287	+	4.69901i	−0.608672	+	0.245957i
$366$	−0.967209	−	1.67526i	−0.0505568	−	0.0875670i
$367$	7.26060	−	4.19191i	0.379000	−	0.218816i	−0.298383	−	0.954446i	$-0.596447\pi$
$367$	7.26060	−	4.19191i	0.379000	−	0.218816i	0.677383	+	0.735630i	$0.263114\pi$
$368$	6.50843	+	3.75764i	0.339275	+	0.195881i
$369$	−3.19156			−0.166146
$370$	−14.8809	+	1.27664i	−0.773623	+	0.0663695i
$371$	−21.6061			−1.12173
$372$	−0.687045	−	0.396666i	−0.0356216	−	0.0205662i
$373$	−8.64413	+	4.99069i	−0.447576	+	0.258408i	−0.706806	−	0.707408i	$-0.749865\pi$
$373$	−8.64413	+	4.99069i	−0.447576	+	0.258408i	0.259230	+	0.965816i	$0.416531\pi$
$374$	−0.463143	−	0.802188i	−0.0239486	−	0.0414801i
$375$	−11.1189	+	1.17046i	−0.574178	+	0.0604423i
$376$	21.5492			1.11132
$377$	−6.49109	+	3.74763i	−0.334308	+	0.193013i
$378$		−	1.71507i		−	0.0882139i
$379$	−5.37792	+	9.31484i	−0.276245	+	0.478471i	−0.970449	−	0.241308i	$-0.922424\pi$
$379$	−5.37792	+	9.31484i	−0.276245	+	0.478471i	0.694203	+	0.719779i	$0.255757\pi$
$380$	12.5071	+	1.75707i	0.641601	+	0.0901359i
$381$	−2.42356			−0.124163
$382$	3.28395	+	1.89599i	0.168021	+	0.0970072i
$383$	−19.3305	+	11.1605i	−0.987741	+	0.570273i	−0.904598	−	0.426265i	$-0.859829\pi$
$383$	−19.3305	+	11.1605i	−0.987741	+	0.570273i	−0.0831429	+	0.996538i	$0.526496\pi$
$384$	0.590416			0.0301295
$385$	−6.54247	−	5.11097i	−0.333435	−	0.260479i
$386$	−5.28683	+	9.15707i	−0.269093	+	0.466082i
$387$	5.35265	+	3.09035i	0.272090	+	0.157091i
$388$	2.80407	−	1.61893i	0.142355	−	0.0821888i
$389$	−15.9211	−	27.5762i	−0.807232	−	1.39817i	−0.914774	−	0.403966i	$-0.867631\pi$
$389$	−15.9211	−	27.5762i	−0.807232	−	1.39817i	0.107542	−	0.994201i	$-0.465702\pi$
$390$	1.92779	+	1.50599i	0.0976175	+	0.0762587i
$391$	−0.748756	+	1.29688i	−0.0378662	+	0.0655862i
$392$	−12.1183	−	6.99653i	−0.612069	−	0.353378i
$393$			0.371566i			0.0187430i
$394$	−0.119363	−	0.206743i	−0.00601342	−	0.0104155i
$395$	15.0626	−	19.2814i	0.757883	−	0.970154i
$396$	−1.88796			−0.0948735
$397$			23.6991i			1.18942i	0.803939	+	0.594712i	$0.202734\pi$
$397$			23.6991i			1.18942i	−0.803939	+	0.594712i	$0.797266\pi$
$398$	−0.371563	−	0.214522i	−0.0186248	−	0.0107530i
$399$	−11.1078			−0.556087
$400$	2.15504	+	8.63944i	0.107752	+	0.431972i
$401$	3.61336			0.180443			0.0902214	−	0.995922i	$-0.471243\pi$
$401$	3.61336			0.180443			0.0902214	+	0.995922i	$0.471243\pi$
$402$	1.61431	−	0.932020i	0.0805143	−	0.0464849i
$403$	−0.861869	+	0.497600i	−0.0429327	+	0.0247872i
$404$	4.25757	+	7.37432i	0.211822	+	0.366886i
$405$	1.37657	−	1.76212i	0.0684021	−	0.0875604i
$406$	12.9027			0.640352
$407$	−3.22823	−	14.0948i	−0.160017	−	0.698653i
$408$			1.08879i			0.0539030i
$409$	2.75003	−	4.76320i	0.135980	−	0.235525i	−0.789991	−	0.613118i	$-0.789915\pi$
$409$	2.75003	−	4.76320i	0.135980	−	0.235525i	0.925972	+	0.377593i	$0.123248\pi$
$410$	−7.26576	+	2.93601i	−0.358830	+	0.144999i
$411$	−0.989934	−	1.71462i	−0.0488299	−	0.0845758i
$412$	−9.67773	+	5.58744i	−0.476787	+	0.275273i
$413$			17.8965i			0.880629i
$414$	−2.31702	−	4.01319i	−0.113875	−	0.197238i
$415$	−2.24869	+	16.0065i	−0.110384	+	0.785729i
$416$	−2.08278	+	3.60748i	−0.102117	+	0.176871i
$417$		−	16.7365i		−	0.819588i
$418$		−	18.5644i		−	0.908015i
$419$	−8.47528	+	14.6796i	−0.414044	+	0.717146i	−0.995328	−	0.0965554i	$-0.969218\pi$
$419$	−8.47528	+	14.6796i	−0.414044	+	0.717146i	0.581283	+	0.813701i	$0.302551\pi$
$420$	1.03919	+	2.57169i	0.0507074	+	0.125486i
$421$	−15.8150			−0.770778			−0.385389	−	0.922754i	$-0.625933\pi$
$421$	−15.8150			−0.770778			−0.385389	+	0.922754i	$0.625933\pi$
$422$	−13.8542	−	7.99874i	−0.674413	−	0.389372i
$423$	−6.08230	−	3.51162i	−0.295731	−	0.170741i
$424$	−21.2225	+	36.7584i	−1.03065	+	1.78515i
$425$	−1.72151	+	0.429418i	−0.0835057	+	0.0208299i
$426$	2.45587	+	4.25369i	0.118987	+	0.206092i
$427$	−2.38281	−	1.37572i	−0.115312	−	0.0665756i
$428$	0.214117	+	0.123621i	0.0103497	+	0.00597543i
$429$	−1.18418	+	2.05106i	−0.0571728	+	0.0990262i
$430$	15.0285	+	2.11129i	0.724739	+	0.101816i
$431$	−15.2481	−	26.4105i	−0.734474	−	1.27215i	−0.954954	−	0.296755i	$-0.904095\pi$
$431$	−15.2481	−	26.4105i	−0.734474	−	1.27215i	0.220479	−	0.975392i	$-0.429238\pi$
$432$	−1.54225	−	0.890417i	−0.0742014	−	0.0428402i
$433$			25.6277i			1.23159i	0.787908	+	0.615793i	$0.211164\pi$
$433$			25.6277i			1.23159i	−0.787908	+	0.615793i	$0.788836\pi$
$434$	1.71319			0.0822357
$435$	13.2567	+	10.3561i	0.635609	+	0.496537i
$436$	5.37441			0.257388
$437$	−25.9918	+	15.0064i	−1.24336	+	0.717853i
$438$		−	6.15921i		−	0.294298i
$439$	−7.38403	−	12.7895i	−0.352421	−	0.610410i	0.634252	−	0.773126i	$-0.281308\pi$
$439$	−7.38403	−	12.7895i	−0.352421	−	0.610410i	−0.986673	+	0.162716i	$0.947975\pi$
$440$	−15.1216	+	6.11046i	−0.720893	+	0.291305i
$441$	2.28028	+	3.94955i	0.108585	+	0.188074i
$442$	0.336204	+	0.194108i	0.0159916	+	0.00923276i
$443$		−	38.9581i		−	1.85095i	−0.378804	−	0.925477i	$-0.623664\pi$
$443$		−	38.9581i		−	1.85095i	0.378804	−	0.925477i	$-0.376336\pi$
$444$	−1.42047	+	4.61740i	−0.0674124	+	0.219132i
$445$	−34.2145	−	4.80665i	−1.62192	−	0.227857i
$446$	−15.8938	+	27.5289i	−0.752595	+	1.30353i
$447$	−7.36855	+	4.25423i	−0.348520	+	0.201218i
$448$	11.0277	−	6.36684i	0.521009	−	0.300805i
$449$	−14.1411	−	24.4931i	−0.667360	−	1.15590i	−0.978640	−	0.205583i	$-0.934091\pi$
$449$	−14.1411	−	24.4931i	−0.667360	−	1.15590i	0.311280	−	0.950318i	$-0.399242\pi$
$450$	1.51280	−	5.27791i	0.0713141	−	0.248803i
$451$	−3.79344	−	6.57043i	−0.178626	−	0.309390i
$452$		−	7.43184i		−	0.349565i
$453$	−9.46547	−	5.46489i	−0.444727	−	0.256763i
$454$	−31.5418			−1.48033
$455$	3.44568	+	0.484069i	0.161536	+	0.0226935i
$456$	−10.9106	+	18.8977i	−0.510936	+	0.884967i
$457$	−3.50734	+	2.02496i	−0.164066	+	0.0947237i	−0.579785	−	0.814770i	$-0.696863\pi$
$457$	−3.50734	+	2.02496i	−0.164066	+	0.0947237i	0.415719	+	0.909493i	$0.363530\pi$
$458$			28.8893i			1.34991i
$459$	0.177426	−	0.307311i	0.00828155	−	0.0143441i
$460$	5.90595	+	4.61372i	0.275366	+	0.215116i
$461$	−7.92444	+	13.7255i	−0.369078	+	0.639262i	−0.989422	−	0.145068i	$-0.953660\pi$
$461$	−7.92444	+	13.7255i	−0.369078	+	0.639262i	0.620344	+	0.784330i	$0.286993\pi$
$462$	3.53081	−	2.03851i	0.164268	−	0.0948401i
$463$	−11.5202	+	6.65120i	−0.535390	+	0.309108i	−0.743209	−	0.669060i	$-0.766697\pi$
$463$	−11.5202	+	6.65120i	−0.535390	+	0.309108i	0.207818	+	0.978167i	$0.433364\pi$
$464$	6.69873	−	11.6025i	0.310981	−	0.538634i
$465$	1.76018	+	1.37505i	0.0816266	+	0.0637666i
$466$	1.55354	−	2.69082i	0.0719666	−	0.124650i
$467$			35.0328i			1.62112i	0.585652	+	0.810562i	$0.300838\pi$
$467$			35.0328i			1.62112i	−0.585652	+	0.810562i	$0.699162\pi$
$468$	0.685252	−	0.395630i	0.0316758	−	0.0182880i
$469$	1.32567	−	2.29612i	0.0612136	−	0.106025i
$470$	−17.0771	−	2.39910i	−0.787710	−	0.110662i
$471$	−15.3546			−0.707504
$472$	30.4473	+	17.5787i	1.40145	+	0.809127i
$473$			14.6926i			0.675566i
$474$	6.00774	+	10.4057i	0.275944	+	0.477950i
$475$	−34.1829	−	9.79780i	−1.56842	−	0.449554i
$476$	0.220088	+	0.381203i	0.0100877	+	0.0174724i
$477$	11.9801	−	6.91673i	0.548532	−	0.316695i
$478$	3.14124	−	1.81360i	0.143677	−	0.0829520i
$479$	20.3553	−	35.2564i	0.930057	−	1.61091i	0.146836	−	0.989161i	$-0.453091\pi$
$479$	20.3553	−	35.2564i	0.930057	−	1.61091i	0.783220	−	0.621744i	$-0.213576\pi$
$480$	9.25820	+	1.30065i	0.422577	+	0.0593661i
$481$	4.12535	+	4.43935i	0.188100	+	0.202417i
$482$		−	7.75193i		−	0.353091i
$483$	−5.70819	−	3.29563i	−0.259732	−	0.149956i
$484$	2.12412	+	3.67908i	0.0965509	+	0.167231i
$485$	−8.45217	+	3.41543i	−0.383793	+	0.155087i
$486$	0.549044	+	0.950972i	0.0249051	+	0.0431370i
$487$		−	30.8485i		−	1.39788i	−0.715182	−	0.698939i	$-0.753656\pi$
$487$		−	30.8485i		−	1.39788i	0.715182	−	0.698939i	$-0.246344\pi$
$488$	−4.68101	+	2.70258i	−0.211899	+	0.122340i
$489$	−6.91898			−0.312887
$490$	8.82450	+	6.89369i	0.398650	+	0.311425i
$491$	10.4475			0.471490			0.235745	−	0.971815i	$-0.424247\pi$
$491$	10.4475			0.471490			0.235745	+	0.971815i	$0.424247\pi$
$492$			2.53475i			0.114275i
$493$	2.31195	+	1.33480i	0.104125	+	0.0601165i
$494$	3.89026	+	6.73813i	0.175031	+	0.303163i
$495$	5.26383	+	0.739493i	0.236591	+	0.0332378i
$496$	0.889438	−	1.54055i	0.0399370	−	0.0691729i
$497$	6.05027	+	3.49312i	0.271392	+	0.156688i
$498$	−6.87421	−	3.96883i	−0.308041	−	0.177848i
$499$	−14.1327	−	24.4785i	−0.632665	−	1.09581i	−0.987005	−	0.160691i	$-0.948628\pi$
$499$	−14.1327	−	24.4785i	−0.632665	−	1.09581i	0.354340	−	0.935117i	$-0.384706\pi$
$500$	0.929584	+	8.83067i	0.0415723	+	0.394920i
$501$	−9.21410	+	15.9593i	−0.411656	+	0.713008i
$502$	−7.68840	−	4.43890i	−0.343150	−	0.198118i
$503$	23.9064	+	13.8024i	1.06594	+	0.615418i	0.927068	−	0.374893i	$-0.122321\pi$
$503$	23.9064	+	13.8024i	1.06594	+	0.615418i	0.138867	+	0.990311i	$0.455654\pi$
$504$	−4.79226			−0.213464
$505$	−8.98210	−	22.2280i	−0.399698	−	0.989135i
$506$	5.50795	−	9.54004i	0.244858	−	0.424107i
$507$			12.0074i			0.533267i
$508$			1.92480i			0.0853991i
$509$	9.21906	−	15.9679i	0.408628	−	0.707764i	−0.586109	−	0.810232i	$-0.699341\pi$
$509$	9.21906	−	15.9679i	0.408628	−	0.707764i	0.994736	+	0.102469i	$0.0326742\pi$
$510$	0.121216	−	0.862831i	0.00536752	−	0.0382068i
$511$	−4.38030	−	7.58690i	−0.193773	−	0.335625i
$512$		−	18.3739i		−	0.812021i
$513$	6.15906	−	3.55593i	0.271929	−	0.156998i
$514$	−6.55773	−	11.3583i	−0.289249	−	0.500994i
$515$	29.1711	−	11.7877i	1.28543	−	0.519428i
$516$	2.45437	−	4.25109i	0.108048	−	0.187144i
$517$		−	16.6954i		−	0.734264i
$518$	−2.32909	−	10.1691i	−0.102334	−	0.446803i
$519$	13.3686			0.586814
$520$	4.20804	−	5.38664i	0.184535	−	0.236220i
$521$	5.80884	+	10.0612i	0.254490	+	0.440789i	0.964757	−	0.263143i	$-0.0847592\pi$
$521$	5.80884	+	10.0612i	0.254490	+	0.440789i	−0.710267	+	0.703932i	$0.751426\pi$
$522$	−7.15429	+	4.13053i	−0.313135	+	0.180788i
$523$	8.93715	−	5.15987i	0.390794	−	0.225625i	−0.291710	−	0.956507i	$-0.594224\pi$
$523$	8.93715	−	5.15987i	0.390794	−	0.225625i	0.682504	+	0.730882i	$0.260891\pi$
$524$	0.295099			0.0128915
$525$	−1.89007	−	7.57719i	−0.0824895	−	0.330696i
$526$	9.50364			0.414378
$527$	0.306974	+	0.177231i	0.0133720	+	0.00772032i
$528$		−	4.23334i		−	0.184233i
$529$	5.19079			0.225686
$530$	20.9105	−	26.7672i	0.908295	−	1.16269i
$531$	−5.72918	−	9.92323i	−0.248625	−	0.430632i
$532$			8.82189i			0.382477i
$533$	2.75373	+	1.58987i	0.119277	+	0.0688647i
$534$	8.48352	−	14.6939i	0.367118	−	0.635867i
$535$	−0.548560	−	0.428535i	−0.0237163	−	0.0185272i
$536$	−2.60425	−	4.51070i	−0.112487	−	0.194833i
$537$	−0.0610900	+	0.0352703i	−0.00263623	+	0.00152203i
$538$	−19.0141	−	10.9778i	−0.819754	−	0.473285i
$539$	−5.42061	+	9.38877i	−0.233482	+	0.404403i
$540$	−1.39948	−	1.09327i	−0.0602241	−	0.0470470i
$541$	36.2054			1.55659			0.778297	−	0.627897i	$-0.216084\pi$
$541$	36.2054			1.55659			0.778297	+	0.627897i	$0.216084\pi$
$542$	9.47607	−	5.47101i	0.407032	−	0.235000i
$543$	13.5930	+	7.84795i	0.583334	+	0.336788i
$544$	1.48366			0.0636112
$545$	−14.9844	−	2.10510i	−0.641862	−	0.0901725i
$546$	−0.854359	+	1.47979i	−0.0365632	+	0.0633293i
$547$		−	33.0151i		−	1.41162i	−0.708399	−	0.705812i	$-0.750582\pi$
$547$		−	33.0151i		−	1.41162i	0.708399	−	0.705812i	$-0.249418\pi$
$548$	−1.36175	+	0.786209i	−0.0581713	+	0.0335852i
$549$	1.76163			0.0751843
$550$	12.6637	−	3.15886i	0.539981	−	0.134694i
$551$	26.7518	+	46.3355i	1.13966	+	1.97396i
$552$	−11.2137	+	6.47422i	−0.477286	+	0.275561i
$553$	14.8006	+	8.54515i	0.629387	+	0.363377i
$554$	−34.5555			−1.46812
$555$	5.76900	−	12.3174i	0.244880	−	0.522845i
$556$	−13.2922			−0.563713
$557$	18.3710	+	10.6065i	0.778404	+	0.449412i	0.835864	−	0.548936i	$-0.184967\pi$
$557$	18.3710	+	10.6065i	0.778404	+	0.449412i	−0.0574603	+	0.998348i	$0.518300\pi$
$558$	−0.949927	+	0.548441i	−0.0402136	+	0.0232173i
$559$	−3.07890	−	5.33281i	−0.130224	−	0.225554i
$560$	−5.76647	+	2.33017i	−0.243678	+	0.0984676i
$561$	0.843545			0.0356145
$562$	−11.1246	+	6.42281i	−0.469264	+	0.270930i
$563$			36.0071i			1.51752i	0.651372	+	0.758758i	$0.274194\pi$
$563$			36.0071i			1.51752i	−0.651372	+	0.758758i	$0.725806\pi$
$564$	−2.78894	+	4.83058i	−0.117436	+	0.203404i
$565$	−2.91098	+	20.7208i	−0.122466	+	0.871729i
$566$	−6.56887			−0.276110
$567$	1.35262	+	0.780936i	0.0568048	+	0.0327962i
$568$	11.8857	−	6.86220i	0.498712	−	0.287931i
$569$	9.42791			0.395239			0.197619	−	0.980279i	$-0.436679\pi$
$569$	9.42791			0.395239			0.197619	+	0.980279i	$0.436679\pi$
$570$	10.7502	−	13.7612i	0.450278	−	0.576393i
$571$	11.3964	−	19.7391i	0.476923	−	0.826055i	−0.522727	−	0.852500i	$-0.675085\pi$
$571$	11.3964	−	19.7391i	0.476923	−	0.826055i	0.999650	+	0.0264449i	$0.00841864\pi$
$572$	1.62896	+	0.940481i	0.0681103	+	0.0393235i
$573$	−2.99061	+	1.72663i	−0.124934	+	0.0721309i
$574$	−2.73688	−	4.74041i	−0.114235	−	0.197861i
$575$	−14.6593	−	15.1768i	−0.611333	−	0.632918i
$576$	−4.07641	+	7.06055i	−0.169851	+	0.294190i
$577$	−23.6606	−	13.6605i	−0.985005	−	0.568693i	−0.0812273	−	0.996696i	$-0.525884\pi$
$577$	−23.6606	−	13.6605i	−0.985005	−	0.568693i	−0.903777	+	0.428003i	$0.859217\pi$
$578$			18.5292i			0.770714i
$579$	−4.81458	−	8.33910i	−0.200087	−	0.346561i
$580$	8.22485	−	10.5285i	0.341518	−	0.437172i
$581$	−11.2902			−0.468396
$582$		−	4.47676i		−	0.185568i
$583$	28.4788	+	16.4422i	1.17947	+	0.680968i
$584$	−17.2101			−0.712158
$585$	−2.06552	+	0.834653i	−0.0853987	+	0.0345087i
$586$	−34.8638			−1.44021
$587$	2.42341	−	1.39916i	0.100025	−	0.0577493i	−0.449153	−	0.893455i	$-0.648274\pi$
$587$	2.42341	−	1.39916i	0.100025	−	0.0577493i	0.549178	+	0.835705i	$0.314941\pi$
$588$	3.13675	−	1.81100i	0.129357	−	0.0746845i
$589$	3.55203	+	6.15229i	0.146359	+	0.253501i
$590$	−22.1715	−	17.3203i	−0.912786	−	0.713067i
$591$	0.217401			0.00894270
$592$	−10.3535	−	3.18510i	−0.425528	−	0.130907i
$593$			23.7997i			0.977338i	0.872469	+	0.488669i	$0.162517\pi$
$593$			23.7997i			0.977338i	−0.872469	+	0.488669i	$0.837483\pi$
$594$	−1.30517	+	2.26062i	−0.0535518	+	0.0927545i
$595$	−0.464314	−	1.14904i	−0.0190350	−	0.0471060i
$596$	3.37873	+	5.85213i	0.138398	+	0.239713i
$597$	0.338373	−	0.195360i	0.0138487	−	0.00799554i
$598$			4.61686i			0.188798i
$599$	−7.61483	−	13.1893i	−0.311133	−	0.538899i	0.667475	−	0.744633i	$-0.267375\pi$
$599$	−7.61483	−	13.1893i	−0.311133	−	0.538899i	−0.978608	+	0.205734i	$0.934042\pi$
$600$	−14.7476	−	4.22707i	−0.602067	−	0.172570i
$601$	−16.8893	+	29.2530i	−0.688927	+	1.19326i	0.283258	+	0.959044i	$0.408585\pi$
$601$	−16.8893	+	29.2530i	−0.688927	+	1.19326i	−0.972185	+	0.234213i	$0.924749\pi$
$602$			10.6004i			0.432038i
$603$			1.69753i			0.0691289i
$604$	−4.34024	+	7.51751i	−0.176602	+	0.305883i
$605$	−4.48121	−	11.0897i	−0.182187	−	0.450859i
$606$	11.7733			0.478256
$607$	17.2951	+	9.98536i	0.701988	+	0.405293i	0.808088	−	0.589062i	$-0.200503\pi$
$607$	17.2951	+	9.98536i	0.701988	+	0.405293i	−0.106099	+	0.994356i	$0.533836\pi$
$608$	25.7513	+	14.8675i	1.04435	+	0.602958i
$609$	−5.87509	+	10.1760i	−0.238071	+	0.412351i
$610$	4.01044	−	1.62057i	0.162378	−	0.0656151i
$611$	3.49860	+	6.05976i	0.141538	+	0.245152i
$612$	−0.244068	−	0.140913i	−0.00986586	−	0.00569605i
$613$	−29.1728	−	16.8429i	−1.17828	−	0.680280i	−0.222663	−	0.974895i	$-0.571475\pi$
$613$	−29.1728	−	16.8429i	−1.17828	−	0.680280i	−0.955616	+	0.294616i	$0.904808\pi$
$614$	5.56528	−	9.63935i	0.224596	−	0.389012i
$615$	0.992834	−	7.06714i	0.0400349	−	0.284975i
$616$	−5.69602	−	9.86579i	−0.229499	−	0.397504i
$617$	−18.6738	−	10.7813i	−0.751780	−	0.434040i	0.0745570	−	0.997217i	$-0.476246\pi$
$617$	−18.6738	−	10.7813i	−0.751780	−	0.434040i	−0.826337	+	0.563177i	$0.809579\pi$
$618$			15.4507i			0.621518i
$619$	35.4957			1.42669			0.713346	−	0.700812i	$-0.247179\pi$
$619$	35.4957			1.42669			0.713346	+	0.700812i	$0.247179\pi$
$620$	1.09207	−	1.39794i	0.0438587	−	0.0561428i
$621$	4.22010			0.169347
$622$	−18.4321	+	10.6418i	−0.739062	+	0.426697i
$623$		−	24.1332i		−	0.966876i
$624$	0.887117	+	1.53653i	0.0355131	+	0.0615105i
$625$	0.867103	−	24.9850i	0.0346841	−	0.999398i
$626$	7.80619	+	13.5207i	0.311998	+	0.540397i
$627$	14.6411	+	8.45307i	0.584711	+	0.337583i
$628$			12.1947i			0.486622i
$629$	0.634669	−	2.06307i	0.0253059	−	0.0822599i
$630$	3.79773	+	0.533527i	0.151305	+	0.0212562i
$631$	−11.7813	+	20.4057i	−0.469005	+	0.812340i	−0.999372	−	0.0354280i	$-0.988721\pi$
$631$	−11.7813	+	20.4057i	−0.469005	+	0.812340i	0.530368	+	0.847768i	$0.322054\pi$
$632$	29.0757	−	16.7868i	1.15657	−	0.667744i
$633$	12.6167	−	7.28424i	0.501468	−	0.289523i
$634$	10.1893	+	17.6484i	0.404669	+	0.700908i
$635$	0.753923	−	5.36654i	0.0299185	−	0.212965i
$636$	−5.49329	−	9.51466i	−0.217823	−	0.377281i
$637$		−	4.54365i		−	0.180026i
$638$	−17.0070	−	9.81898i	−0.673313	−	0.388737i
$639$	−4.47299			−0.176949
$640$	−0.183667	+	1.30737i	−0.00726009	+	0.0516784i
$641$	−12.6932	+	21.9853i	−0.501351	+	0.868365i	0.498648	+	0.866805i	$0.333830\pi$
$641$	−12.6932	+	21.9853i	−0.501351	+	0.868365i	−0.999999	+	0.00156059i	$0.999503\pi$
$642$	0.296044	−	0.170921i	0.0116839	−	0.00674572i
$643$			27.5301i			1.08568i	0.839835	+	0.542841i	$0.182651\pi$
$643$			27.5301i			1.08568i	−0.839835	+	0.542841i	$0.817349\pi$
$644$	−2.61740	+	4.53347i	−0.103140	+	0.178644i
$645$	−8.50815	+	10.8911i	−0.335008	+	0.428838i
$646$	1.38560	−	2.39993i	0.0545158	−	0.0944241i
$647$	11.1478	−	6.43619i	0.438265	−	0.253033i	−0.264596	−	0.964359i	$-0.585239\pi$
$647$	11.1478	−	6.43619i	0.438265	−	0.253033i	0.702862	+	0.711327i	$0.251905\pi$
$648$	2.65721	−	1.53414i	0.104385	−	0.0602667i
$649$	13.6192	−	23.5892i	0.534602	−	0.925958i
$650$	−3.93445	+	3.80027i	−0.154322	+	0.149059i
$651$	−0.780079	+	1.35114i	−0.0305737	+	0.0529552i
$652$			5.49508i			0.215204i
$653$	33.9461	−	19.5988i	1.32841	−	0.766960i	0.343360	−	0.939204i	$-0.388435\pi$
$653$	33.9461	−	19.5988i	1.32841	−	0.766960i	0.985054	+	0.172244i	$0.0551016\pi$
$654$	3.71540	−	6.43526i	0.145284	−	0.251639i
$655$	−0.822767	−	0.115587i	−0.0321482	−	0.00451637i
$656$	−5.68363			−0.221909
$657$	4.85757	+	2.80452i	0.189512	+	0.109415i
$658$		−	12.0454i		−	0.469577i
$659$	−10.9239	−	18.9207i	−0.425535	−	0.737047i	0.570936	−	0.820995i	$-0.306581\pi$
$659$	−10.9239	−	18.9207i	−0.425535	−	0.737047i	−0.996470	+	0.0839474i	$0.973247\pi$
$660$	0.587308	−	4.18055i	0.0228609	−	0.162728i
$661$	9.27901	+	16.0717i	0.360912	+	0.625117i	0.988111	−	0.153741i	$-0.0491323\pi$
$661$	9.27901	+	16.0717i	0.360912	+	0.625117i	−0.627200	+	0.778859i	$0.715799\pi$
$662$	3.89264	−	2.24742i	0.151292	−	0.0873484i
$663$	−0.306173	+	0.176769i	−0.0118908	+	0.00686513i
$664$	−11.0897	+	19.2080i	−0.430365	+	0.745413i
$665$	3.45544	−	24.5963i	0.133996	−	0.953805i
$666$	4.54684	+	4.89292i	0.176186	+	0.189597i
$667$			31.7484i			1.22930i
$668$	12.6749	+	7.31787i	0.490408	+	0.283137i
$669$	−14.4741	−	25.0699i	−0.559601	−	0.969258i
$670$	1.56161	+	3.86453i	0.0603304	+	0.149300i
$671$	2.09384	+	3.62664i	0.0808319	+	0.140005i
$672$			6.53027i			0.251911i
$673$	−19.2083	+	11.0899i	−0.740425	+	0.427485i	−0.822224	−	0.569164i	$-0.807267\pi$
$673$	−19.2083	+	11.0899i	−0.740425	+	0.427485i	0.0817986	+	0.996649i	$0.473934\pi$
$674$	−24.2800			−0.935230
$675$	3.47368	+	3.59632i	0.133702	+	0.138423i
$676$	9.53632			0.366782
$677$			10.5037i			0.403691i	0.979417	+	0.201845i	$0.0646939\pi$
$677$			10.5037i			0.403691i	−0.979417	+	0.201845i	$0.935306\pi$
$678$	−8.89882	−	5.13773i	−0.341757	−	0.197314i
$679$	−3.18377	−	5.51446i	−0.122182	−	0.211626i
$680$	−2.41093	−	0.338701i	−0.0924548	−	0.0129886i
$681$	14.3621	−	24.8759i	0.550358	−	0.953248i
$682$	−2.25814	−	1.30374i	−0.0864686	−	0.0499227i
$683$	8.59111	+	4.96008i	0.328730	+	0.189792i	0.655277	−	0.755389i	$-0.272552\pi$
$683$	8.59111	+	4.96008i	0.328730	+	0.189792i	−0.326547	+	0.945181i	$0.605885\pi$
$684$	−2.82414	−	4.89155i	−0.107984	−	0.187033i
$685$	4.10467	−	1.65865i	0.156831	−	0.0633737i
$686$	−9.91360	+	17.1709i	−0.378503	+	0.655586i
$687$	−22.7840	−	13.1544i	−0.869265	−	0.501870i
$688$	9.53217	+	5.50340i	0.363411	+	0.209815i
$689$	−13.7822			−0.525060
$690$	9.60729	−	3.88220i	0.365743	−	0.147793i
$691$	−6.40771	+	11.0985i	−0.243761	+	0.422206i	−0.961782	−	0.273815i	$-0.911714\pi$
$691$	−6.40771	+	11.0985i	−0.243761	+	0.422206i	0.718022	+	0.696021i	$0.245048\pi$
$692$		−	10.6174i		−	0.403611i
$693$			3.71284i			0.141039i
$694$	−1.22789	+	2.12677i	−0.0466102	+	0.0807312i
$695$	37.0600	+	5.20640i	1.40576	+	0.197490i
$696$	11.5415	+	19.9905i	0.437481	+	0.757740i
$697$		−	1.13253i		−	0.0428977i
$698$	0.00442408	−	0.00255424i	0.000167454	−	9.66795e-5i
$699$	1.41477	+	2.45046i	0.0535116	+	0.0926849i
$700$	−6.01783	+	1.50110i	−0.227453	+	0.0567364i
$701$	−2.58378	+	4.47524i	−0.0975880	+	0.169027i	−0.910686	−	0.413100i	$-0.864446\pi$
$701$	−2.58378	+	4.47524i	−0.0975880	+	0.169027i	0.813098	+	0.582127i	$0.197779\pi$
$702$		−	1.09402i		−	0.0412911i
$703$	31.6895	−	29.4480i	1.19519	−	1.11065i
$704$	−19.3807			−0.730436
$705$	9.66794	−	12.3758i	0.364116	−	0.466099i
$706$	8.55510	+	14.8179i	0.321975	+	0.557678i
$707$	14.5023	−	8.37289i	0.545414	−	0.314895i
$708$	−7.88107	+	4.55014i	−0.296189	+	0.171005i
$709$	−10.2320			−0.384270			−0.192135	−	0.981368i	$-0.561541\pi$
$709$	−10.2320			−0.384270			−0.192135	+	0.981368i	$0.561541\pi$
$710$	−10.1830	+	4.11484i	−0.382162	+	0.154427i
$711$	−10.9422			−0.410364
$712$	−41.0577	−	23.7047i	−1.53870	−	0.888370i
$713$			4.21546i			0.157870i
$714$	0.608598			0.0227762
$715$	−4.17334	−	3.26021i	−0.156074	−	0.121925i
$716$	0.0280118	+	0.0485179i	0.00104685	+	0.00181320i
$717$			3.30319i			0.123360i
$718$	−35.1488	−	20.2932i	−1.31174	−	0.757334i
$719$	−13.9276	+	24.1234i	−0.519413	+	0.899650i	0.480332	+	0.877087i	$0.340516\pi$
$719$	−13.9276	+	24.1234i	−0.519413	+	0.899650i	−0.999745	+	0.0225632i	$0.992817\pi$
$720$	2.45143	−	3.13804i	0.0913596	−	0.116948i
$721$	10.9882	+	19.0321i	0.409222	+	0.708793i
$722$	30.0304	−	17.3381i	1.11762	−	0.645257i
$723$	6.11369	+	3.52974i	0.227370	+	0.131272i
$724$	6.23287	−	10.7956i	0.231643	−	0.401217i
$725$	−27.0556	+	26.1330i	−1.00482	+	0.970554i
$726$	5.87373			0.217995
$727$	17.7001	−	10.2192i	0.656462	−	0.379009i	−0.134466	−	0.990918i	$-0.542932\pi$
$727$	17.7001	−	10.2192i	0.656462	−	0.379009i	0.790928	+	0.611910i	$0.209598\pi$
$728$	4.13484	+	2.38725i	0.153247	+	0.0884775i
$729$	−1.00000			−0.0370370
$730$	13.6385	+	1.91601i	0.504783	+	0.0709149i
$731$	−1.09662	+	1.89940i	−0.0405599	+	0.0702519i
$732$		−	1.39909i		−	0.0517118i
$733$	−40.8810	+	23.6027i	−1.50997	+	0.871784i	−0.510042	+	0.860150i	$0.670370\pi$
$733$	−40.8810	+	23.6027i	−1.50997	+	0.871784i	−0.999932	+	0.0116343i	$0.996297\pi$
$734$	−9.20617			−0.339806
$735$	−9.45494	+	3.82064i	−0.348751	+	0.140926i
$736$	8.82222	+	15.2805i	0.325191	+	0.563248i
$737$	−3.49470	+	2.01766i	−0.128729	+	0.0743216i
$738$	3.03508	+	1.75231i	0.111723	+	0.0645033i
$739$	6.84162			0.251673			0.125837	−	0.992051i	$-0.459839\pi$
$739$	6.84162			0.251673			0.125837	+	0.992051i	$0.459839\pi$
$740$	−9.78253	−	4.58176i	−0.359613	−	0.168429i
$741$	−7.08552			−0.260293
$742$	20.5468	+	11.8627i	0.754297	+	0.435493i
$743$	−4.89977	+	2.82889i	−0.179755	+	0.103782i	−0.587178	−	0.809458i	$-0.699761\pi$
$743$	−4.89977	+	2.82889i	−0.179755	+	0.103782i	0.407422	+	0.913240i	$0.366428\pi$
$744$	1.53246	+	2.65429i	0.0561825	+	0.0973110i
$745$	−7.12803	−	17.6398i	−0.261151	−	0.646271i
$746$	10.9604			0.401290
$747$	6.26017	−	3.61431i	0.229048	−	0.132241i
$748$		−	0.669947i		−	0.0244957i
$749$	0.243111	−	0.421081i	0.00888308	−	0.0153859i
$750$	11.2164	+	4.99169i	0.409565	+	0.182271i
$751$	11.8415			0.432104			0.216052	−	0.976382i	$-0.430682\pi$
$751$	11.8415			0.432104			0.216052	+	0.976382i	$0.430682\pi$
$752$	−10.8316	−	6.25360i	−0.394986	−	0.228045i
$753$	7.00162	−	4.04239i	0.255153	−	0.147313i
$754$	8.23045			0.299735
$755$	15.0456	−	19.2596i	0.547564	−	0.700928i
$756$	0.620223	−	1.07426i	0.0225573	−	0.0390704i
$757$	1.77180	+	1.02295i	0.0643971	+	0.0371797i	0.531853	−	0.846837i	$-0.321496\pi$
$757$	1.77180	+	1.02295i	0.0643971	+	0.0371797i	−0.467456	+	0.884016i	$0.654829\pi$
$758$	10.2285	−	5.90543i	0.371516	−	0.214495i
$759$	5.01595	+	8.68787i	0.182067	+	0.315350i
$760$	−38.4516	−	30.0383i	−1.39479	−	1.08960i
$761$	7.66394	−	13.2743i	0.277818	−	0.481194i	−0.693025	−	0.720914i	$-0.743722\pi$
$761$	7.66394	−	13.2743i	0.277818	−	0.481194i	0.970842	+	0.239720i	$0.0770556\pi$
$762$	2.30473	+	1.33064i	0.0834917	+	0.0482040i
$763$		−	10.5693i		−	0.382633i
$764$	1.37129	+	2.37515i	0.0496117	+	0.0859300i
$765$	0.625293	+	0.488478i	0.0226075	+	0.0176610i
$766$	24.5103			0.885594
$767$			11.4159i			0.412204i
$768$	13.5596	+	7.82866i	0.489291	+	0.282492i
$769$	52.1217			1.87955			0.939777	−	0.341787i	$-0.111032\pi$
$769$	52.1217			1.87955			0.939777	+	0.341787i	$0.111032\pi$
$770$	3.41556	+	8.45249i	0.123088	+	0.304607i
$771$	11.9439			0.430149
$772$	−6.62295	+	3.82376i	−0.238365	+	0.137620i
$773$	−15.9090	+	9.18507i	−0.572207	+	0.330364i	−0.758030	−	0.652219i	$-0.773838\pi$
$773$	−15.9090	+	9.18507i	−0.572207	+	0.330364i	0.185823	+	0.982583i	$0.440505\pi$
$774$	−3.39348	−	5.87768i	−0.121976	−	0.211269i
$775$	−3.59237	+	3.46986i	−0.129042	+	0.124641i
$776$	−12.5090			−0.449046
$777$	9.08053	+	2.79348i	0.325762	+	0.100215i
$778$			34.9655i			1.25357i
$779$	11.3490	−	19.6570i	0.406619	−	0.704285i
$780$	0.662885	+	1.64044i	0.0237351	+	0.0587373i
$781$	−5.31653	−	9.20851i	−0.190241	−	0.329506i
$782$	1.42409	−	0.822200i	0.0509254	−	0.0294018i
$783$		−	7.52314i		−	0.268855i
$784$	4.06079	+	7.03350i	0.145028	+	0.251196i
$785$	4.77654	−	34.0001i	0.170482	−	1.21352i
$786$	0.204006	−	0.353349i	0.00727665	−	0.0126035i
$787$		−	6.93422i		−	0.247178i	−0.992333	−	0.123589i	$-0.960559\pi$
$787$		−	6.93422i		−	0.247178i	0.992333	−	0.123589i	$-0.0394405\pi$
$788$		−	0.172661i		−	0.00615080i
$789$	−4.32736	+	7.49520i	−0.154058	+	0.266836i
$790$	−24.9105	+	10.0661i	−0.886275	+	0.358134i
$791$	−14.6154			−0.519663
$792$	6.31664	+	3.64691i	0.224452	+	0.129587i
$793$	−1.51996	−	0.877549i	−0.0539753	−	0.0311627i
$794$	13.0118	−	22.5372i	0.461773	−	0.799814i
$795$	11.5891	+	28.6795i	0.411022	+	1.01716i
$796$	−0.155155	−	0.268737i	−0.00549934	−	0.00952513i
$797$	−18.8684	−	10.8937i	−0.668352	−	0.385873i	0.127100	−	0.991890i	$-0.459433\pi$
$797$	−18.8684	−	10.8937i	−0.668352	−	0.385873i	−0.795452	+	0.606017i	$0.792766\pi$
$798$	10.5632	+	6.09869i	0.373935	+	0.215891i
$799$	1.24611	−	2.15832i	0.0440841	−	0.0763558i
$800$	−5.76010	+	20.0960i	−0.203650	+	0.710502i
$801$	7.72572	+	13.3813i	0.272975	+	0.472806i
$802$	−3.43621	−	1.98390i	−0.121337	−	0.0700538i
$803$			13.3336i			0.470534i
$804$	1.34819			0.0475469
$805$	9.07330	−	11.6146i	0.319792	−	0.409360i
$806$	1.09282			0.0384928
$807$	17.3156	−	9.99718i	0.609539	−	0.351917i
$808$		−	32.8969i		−	1.15731i
$809$	22.5543	+	39.0651i	0.792965	+	1.37346i	0.924123	+	0.382095i	$0.124797\pi$
$809$	22.5543	+	39.0651i	0.792965	+	1.37346i	−0.131158	+	0.991362i	$0.541869\pi$
$810$	−2.27656	+	0.919931i	−0.0799900	+	0.0323231i
$811$	−13.9896	−	24.2308i	−0.491243	−	0.850857i	0.508707	−	0.860940i	$-0.330124\pi$
$811$	−13.9896	−	24.2308i	−0.491243	−	0.850857i	−0.999949	+	0.0100828i	$0.996791\pi$
$812$	8.08178	+	4.66602i	0.283615	+	0.163745i
$813$			9.96461i			0.349474i
$814$	−4.66871	+	15.1762i	−0.163638	+	0.531925i
$815$	2.15236	−	15.3209i	0.0753940	−	0.536666i
$816$	0.315967	−	0.547270i	0.0110610	−	0.0191583i
$817$	−38.0673	+	21.9782i	−1.33181	+	0.768919i
$818$	−5.23041	+	3.01978i	−0.182877	+	0.105584i
$819$	−0.778043	−	1.34761i	−0.0271870	−	0.0470893i
$820$	−5.61275	−	0.788513i	−0.196006	−	0.0275361i
$821$	15.2529	+	26.4189i	0.532331	+	0.922025i	0.999287	+	0.0377446i	$0.0120173\pi$
$821$	15.2529	+	26.4189i	0.532331	+	0.922025i	−0.466956	+	0.884281i	$0.654649\pi$
$822$			2.17407i			0.0758294i
$823$	−36.1602	−	20.8771i	−1.26046	−	0.727729i	−0.287300	−	0.957841i	$-0.592758\pi$
$823$	−36.1602	−	20.8771i	−1.26046	−	0.727729i	−0.973164	+	0.230111i	$0.926091\pi$
$824$	43.1724			1.50398
$825$	−3.27495	+	11.4258i	−0.114019	+	0.397794i
$826$	9.82596	−	17.0191i	0.341889	−	0.592169i
$827$	−45.0941	+	26.0351i	−1.56808	+	0.905329i	−0.571682	+	0.820475i	$0.693709\pi$
$827$	−45.0941	+	26.0351i	−1.56808	+	0.905329i	−0.996393	+	0.0848540i	$0.972958\pi$
$828$		−	3.35162i		−	0.116477i
$829$	−16.8996	+	29.2710i	−0.586948	+	1.01662i	0.407681	+	0.913124i	$0.366337\pi$
$829$	−16.8996	+	29.2710i	−0.586948	+	1.01662i	−0.994629	+	0.103500i	$0.966996\pi$
$830$	10.9267	−	13.9871i	0.379272	−	0.485500i
$831$	15.7344	−	27.2528i	0.545821	−	0.945389i
$832$	7.03439	−	4.06131i	0.243874	−	0.140800i
$833$	−1.40151	+	0.809162i	−0.0485594	+	0.0280358i
$834$	−9.18905	+	15.9159i	−0.318191	+	0.551123i
$835$	−32.4727	−	25.3676i	−1.12376	−	0.877883i
$836$	6.71346	−	11.6280i	0.232190	−	0.402164i
$837$		−	0.998902i		−	0.0345271i
$838$	16.1195	−	9.30660i	0.556839	−	0.321491i
$839$	−5.12023	+	8.86849i	−0.176770	+	0.306174i	−0.940772	−	0.339039i	$-0.889898\pi$
$839$	−5.12023	+	8.86849i	−0.176770	+	0.306174i	0.764002	+	0.645213i	$0.223232\pi$
$840$	1.49078	−	10.6116i	0.0514369	−	0.366136i
$841$	27.5976			0.951641
$842$	15.0397	+	8.68315i	0.518301	+	0.299241i
$843$		−	11.6982i		−	0.402906i
$844$	−5.78517	−	10.0202i	−0.199134	−	0.344910i
$845$	−26.5883	−	3.73528i	−0.914664	−	0.128497i
$846$	3.85606	+	6.67890i	0.132574	+	0.229625i
$847$	7.23525	−	4.17727i	0.248606	−	0.143533i
$848$	21.3346	−	12.3175i	0.732633	−	0.422986i
$849$	2.99105	−	5.18065i	0.102653	−	0.177800i
$850$	1.87288	+	0.536821i	0.0642392	+	0.0184128i
$851$	25.0219	−	5.73094i	0.857741	−	0.196454i
$852$			3.55247i			0.121706i
$853$	−20.5566	−	11.8684i	−0.703846	−	0.406366i	0.104932	−	0.994479i	$-0.466537\pi$
$853$	−20.5566	−	11.8684i	−0.703846	−	0.406366i	−0.808778	+	0.588114i	$0.799871\pi$
$854$	1.51066	+	2.61654i	0.0516937	+	0.0895360i
$855$	5.95802	+	14.7443i	0.203760	+	0.504246i
$856$	−0.477589	−	0.827208i	−0.0163236	−	0.0282734i
$857$		−	11.0247i		−	0.376596i	−0.982112	−	0.188298i	$-0.939703\pi$
$857$		−	11.0247i		−	0.376596i	0.982112	−	0.188298i	$-0.0602971\pi$
$858$	2.25225	−	1.30033i	0.0768904	−	0.0443927i
$859$	28.7259			0.980116			0.490058	−	0.871690i	$-0.336976\pi$
$859$	28.7259			0.980116			0.490058	+	0.871690i	$0.336976\pi$
$860$	8.64978	+	6.75720i	0.294955	+	0.230419i
$861$	4.98481			0.169882
$862$			33.4875i			1.14059i
$863$	−5.76554	−	3.32874i	−0.196261	−	0.113312i	0.398649	−	0.917104i	$-0.369479\pi$
$863$	−5.76554	−	3.32874i	−0.196261	−	0.113312i	−0.594910	+	0.803792i	$0.702812\pi$
$864$	−2.09053	−	3.62090i	−0.0711211	−	0.123185i
$865$	−4.15870	+	29.6023i	−0.141400	+	1.00651i
$866$	14.0707	−	24.3712i	0.478142	−	0.828166i
$867$	−14.6134	−	8.43704i	−0.496296	−	0.286537i
$868$	1.07308	+	0.619541i	0.0364226	+	0.0210286i
$869$	−13.0057	−	22.5266i	−0.441189	−	0.764161i
$870$	−6.92077	−	17.1268i	−0.234636	−	0.580654i
$871$	0.845622	−	1.46466i	0.0286528	−	0.0496281i
$872$	−17.9814	−	10.3816i	−0.608928	−	0.351565i
$873$	3.53067	+	2.03843i	0.119495	+	0.0689905i
$874$	32.9567			1.11478
$875$	17.3663	−	1.82811i	0.587089	−	0.0618014i
$876$	2.22736	−	3.85790i	0.0752554	−	0.130346i
$877$			51.9779i			1.75517i	0.479421	+	0.877585i	$0.340847\pi$
$877$			51.9779i			1.75517i	−0.479421	+	0.877585i	$0.659153\pi$
$878$			16.2166i			0.547285i
$879$	15.8748	−	27.4959i	0.535442	−	0.927413i
$880$	9.37399	+	1.31691i	0.315997	+	0.0443932i
$881$	19.8779	+	34.4295i	0.669704	+	1.15996i	0.977987	+	0.208666i	$0.0669122\pi$
$881$	19.8779	+	34.4295i	0.669704	+	1.15996i	−0.308283	+	0.951295i	$0.599754\pi$
$882$		−	5.00789i		−	0.168624i
$883$	−21.0107	+	12.1305i	−0.707066	+	0.408224i	−0.809974	−	0.586466i	$-0.800519\pi$
$883$	−21.0107	+	12.1305i	−0.707066	+	0.408224i	0.102908	+	0.994691i	$0.467185\pi$
$884$	0.140390	+	0.243163i	0.00472184	+	0.00817847i
$885$	23.7555	−	9.59933i	0.798532	−	0.322678i
$886$	−21.3897	+	37.0480i	−0.718601	+	1.24465i
$887$		−	1.72554i		−	0.0579379i	−0.999580	−	0.0289689i	$-0.990778\pi$
$887$		−	1.72554i		−	0.0579379i	0.999580	−	0.0289689i	$-0.00922239\pi$
$888$	13.6718	−	12.7048i	0.458796	−	0.426345i
$889$	3.78529			0.126954
$890$	29.8979	+	23.3562i	1.00218	+	0.782903i
$891$	−1.18859	−	2.05869i	−0.0398191	−	0.0689687i
$892$	−19.9106	+	11.4954i	−0.666656	+	0.384894i
$893$	43.2565	−	24.9742i	1.44752	−	0.835728i
$894$	9.34304			0.312478
$895$	−0.0590959	−	0.146245i	−0.00197536	−	0.00488843i
$896$	−0.922154			−0.0308070
$897$	−3.64117	−	2.10223i	−0.121575	−	0.0701914i
$898$			31.0563i			1.03636i
$899$	7.51487			0.250635
$900$	2.85621	−	2.75881i	0.0952071	−	0.0919603i
$901$	2.45442	+	4.25118i	0.0817685	+	0.141627i
$902$			8.33106i			0.277394i
$903$	−8.36015	−	4.82674i	−0.278209	−	0.160624i
$904$	−14.3559	+	24.8651i	−0.477469	+	0.827001i
$905$	−21.6064	+	27.6581i	−0.718222	+	0.919385i
$906$	6.00093	+	10.3939i	0.199368	+	0.345315i
$907$	7.31783	−	4.22495i	0.242984	−	0.140287i	−0.373563	−	0.927605i	$-0.621864\pi$
$907$	7.31783	−	4.22495i	0.242984	−	0.140287i	0.616548	+	0.787318i	$0.288531\pi$
$908$	−19.7566	−	11.4065i	−0.655645	−	0.378537i
$909$	−5.36080	+	9.28518i	−0.177807	+	0.307970i
$910$	−3.01097	−	2.35216i	−0.0998125	−	0.0779734i
$911$	−37.7877			−1.25196			−0.625981	−	0.779838i	$-0.715301\pi$
$911$	−37.7877			−1.25196			−0.625981	+	0.779838i	$0.715301\pi$
$912$	10.9683	−	6.33253i	0.363195	−	0.209691i
$913$	14.8815	+	8.59184i	0.492506	+	0.284348i
$914$	4.44717			0.147099
$915$	−0.548009	+	3.90081i	−0.0181166	+	0.128957i
$916$	−10.4472	+	18.0952i	−0.345187	+	0.597881i
$917$		−	0.580339i		−	0.0191645i
$918$	−0.337455	+	0.194830i	−0.0111377	+	0.00643033i
$919$	51.8831			1.71147			0.855733	−	0.517418i	$-0.173107\pi$
$919$	51.8831			1.71147			0.855733	+	0.517418i	$0.173107\pi$
$920$	−10.8477	−	26.8447i	−0.357636	−	0.885044i
$921$	5.06816	+	8.77831i	0.167001	+	0.289255i
$922$	15.0718	−	8.70173i	0.496365	−	0.286576i
$923$	3.85937	+	2.22821i	0.127033	+	0.0733424i
$924$	2.94875			0.0970068
$925$	25.4801	+	16.6061i	0.837781	+	0.546007i
$926$	14.6072			0.480023
$927$	−12.1854	−	7.03527i	−0.400223	−	0.231069i
$928$	27.2405	−	15.7273i	0.894213	−	0.516274i
$929$	15.9492	+	27.6249i	0.523277	+	0.906343i	0.999633	+	0.0270903i	$0.00862416\pi$
$929$	15.9492	+	27.6249i	0.523277	+	0.906343i	−0.476356	+	0.879253i	$0.658043\pi$
$930$	−0.918921	−	2.27406i	−0.0301326	−	0.0745692i
$931$	−32.4341			−1.06298
$932$	1.94616	−	1.12362i	0.0637487	−	0.0368053i
$933$		−	19.3824i		−	0.634552i
$934$	19.2345	−	33.3152i	0.629374	−	1.09011i
$935$	−0.262411	+	1.86788i	−0.00858176	+	0.0610863i
$936$	−3.05691			−0.0999182
$937$	−39.7749	−	22.9641i	−1.29939	−	0.750203i	−0.319091	−	0.947724i	$-0.603378\pi$
$937$	−39.7749	−	22.9641i	−1.29939	−	0.750203i	−0.980299	+	0.197521i	$0.936711\pi$
$938$	−2.52134	+	1.45570i	−0.0823247	+	0.0475302i
$939$	−14.2178			−0.463980
$940$	−9.82889	−	7.67832i	−0.320583	−	0.250439i
$941$	15.7614	−	27.2996i	0.513808	−	0.889941i	−0.486064	−	0.873923i	$-0.661568\pi$
$941$	15.7614	−	27.2996i	0.513808	−	0.889941i	0.999872	−	0.0160181i	$-0.00509893\pi$
$942$	14.6018	+	8.43037i	0.475753	+	0.274676i
$943$	11.6642	−	6.73434i	0.379839	−	0.219300i
$944$	−10.2027	−	17.6716i	−0.332070	−	0.575162i
$945$	−2.15002	+	2.75221i	−0.0699402	+	0.0895293i
$946$	8.06688	−	13.9722i	0.262277	−	0.454277i
$947$	−28.4351	−	16.4170i	−0.924015	−	0.533480i	−0.0391015	−	0.999235i	$-0.512450\pi$
$947$	−28.4351	−	16.4170i	−0.924015	−	0.533480i	−0.884914	+	0.465755i	$0.845783\pi$
$948$			8.69032i			0.282248i
$949$	−2.79412	−	4.83957i	−0.0907011	−	0.157099i
$950$	27.1275	+	28.0853i	0.880134	+	0.911209i
$951$	−18.5583			−0.601794
$952$		−	1.70055i		−	0.0551150i
$953$	9.60554	+	5.54576i	0.311154	+	0.179645i	0.647443	−	0.762114i	$-0.275838\pi$
$953$	9.60554	+	5.54576i	0.311154	+	0.179645i	−0.336289	+	0.941759i	$0.609172\pi$
$954$	−15.1903			−0.491806
$955$	−2.89299	−	7.15930i	−0.0936150	−	0.231669i
$956$	2.62341			0.0848471
$957$	15.4878	−	8.94189i	0.500650	−	0.289050i
$958$	−38.7146	+	22.3519i	−1.25081	+	0.722156i
$959$	1.54615	+	2.67801i	0.0499278	+	0.0864775i
$960$	−14.3663	−	11.2229i	−0.463669	−	0.362218i
$961$	−30.0022			−0.967813
$962$	−1.48569	−	6.48669i	−0.0479006	−	0.209139i
$963$			0.311307i			0.0100317i
$964$	2.80333	−	4.85551i	0.0902892	−	0.156386i
$965$	19.9632	−	8.06691i	0.642638	−	0.259683i
$966$	3.61889	+	6.26810i	0.116436	+	0.201673i
$967$	0.838606	−	0.484169i	0.0269677	−	0.0155698i	−0.486456	−	0.873705i	$-0.661710\pi$
$967$	0.838606	−	0.484169i	0.0269677	−	0.0155698i	0.513423	+	0.858136i	$0.328377\pi$
$968$		−	16.4124i		−	0.527515i
$969$	1.26183	+	2.18556i	0.0405359	+	0.0702102i
$970$	9.91299	+	1.39264i	0.318287	+	0.0447148i
$971$	0.512275	−	0.887286i	0.0164397	−	0.0284744i	−0.857689	−	0.514170i	$-0.828100\pi$
$971$	0.512275	−	0.887286i	0.0164397	−	0.0284744i	0.874128	+	0.485695i	$0.161434\pi$
$972$			0.794204i			0.0254741i
$973$			26.1402i			0.838018i
$974$	−16.9372	+	29.3360i	−0.542701	+	0.939986i
$975$	−1.20565	−	4.83337i	−0.0386116	−	0.154792i
$976$	3.13716			0.100418
$977$	0.801145	+	0.462541i	0.0256309	+	0.0147980i	0.512761	−	0.858532i	$-0.328623\pi$
$977$	0.801145	+	0.462541i	0.0256309	+	0.0147980i	−0.487130	+	0.873330i	$0.661956\pi$
$978$	6.57975	+	3.79882i	0.210397	+	0.121473i
$979$	−18.3654	+	31.8097i	−0.586959	+	1.01664i
$980$	3.03436	+	7.50915i	0.0969292	+	0.239871i
$981$	3.38352	+	5.86043i	0.108027	+	0.187109i
$982$	−9.93531	−	5.73615i	−0.317048	−	0.183048i
$983$	35.2235	+	20.3363i	1.12345	+	0.648627i	0.942281	−	0.334824i	$-0.108677\pi$
$983$	35.2235	+	20.3363i	1.12345	+	0.648627i	0.181174	+	0.983451i	$0.442010\pi$
$984$	4.89630	−	8.48064i	0.156088	−	0.270353i
$985$	−0.0676295	+	0.481397i	−0.00215486	+	0.0153386i
$986$	−1.46573	−	2.53872i	−0.0466783	−	0.0808493i
$987$	9.49978	+	5.48470i	0.302381	+	0.174580i
$988$			5.62734i			0.179030i
$989$	−26.0832			−0.829396
$990$	−4.59974	−	3.59331i	−0.146189	−	0.114203i
$991$	−31.2403			−0.992382			−0.496191	−	0.868213i	$-0.665268\pi$
$991$	−31.2403			−0.992382			−0.496191	+	0.868213i	$0.665268\pi$
$992$	3.61692	−	2.08823i	0.114837	−	0.0663013i
$993$			4.09333i			0.129898i
$994$	−3.83575	−	6.64372i	−0.121663	−	0.210726i
$995$	0.327328	+	0.810040i	0.0103770	+	0.0256800i
$996$	−2.87050	−	4.97185i	−0.0909552	−	0.157539i
$997$	10.7281	+	6.19389i	0.339763	+	0.196162i	0.660167	−	0.751119i	$-0.270485\pi$
$997$	10.7281	+	6.19389i	0.339763	+	0.196162i	−0.320404	+	0.947281i	$0.603819\pi$
$998$			31.0378i			0.982484i
$999$	−5.92923	+	1.35801i	−0.187593	+	0.0429656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.bb.a.454.13	✓	72
5.4	even	2	inner	555.2.bb.a.454.24	yes	72
37.26	even	3	inner	555.2.bb.a.544.24	yes	72
185.174	even	6	inner	555.2.bb.a.544.13	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.bb.a.454.13	✓	72	1.1	even	1	trivial
555.2.bb.a.454.24	yes	72	5.4	even	2	inner
555.2.bb.a.544.13	yes	72	185.174	even	6	inner
555.2.bb.a.544.24	yes	72	37.26	even	3	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:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.950972 - 0.549044i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.397102 - 0.687801i) q^{4} +(0.837757 + 2.07320i) q^{5} -1.09809 q^{6} +(-1.35262 + 0.780936i) q^{7} +3.06828i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.950972 - 0.549044i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.397102 - 0.687801i) q^{4} +(0.837757 + 2.07320i) q^{5} -1.09809 q^{6} +(-1.35262 + 0.780936i) q^{7} +3.06828i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.341594 - 2.43152i) q^{10} +2.37717 q^{11} +(-0.687801 - 0.397102i) q^{12} +(-0.862816 + 0.498147i) q^{13} +1.71507 q^{14} +(1.76212 + 1.37657i) q^{15} +(0.890417 - 1.54225i) q^{16} +(0.307311 + 0.177426i) q^{17} +(-0.950972 + 0.549044i) q^{18} +(3.55593 + 6.15906i) q^{19} +(1.09327 - 1.39948i) q^{20} +(-0.780936 + 1.35262i) q^{21} +(-2.26062 - 1.30517i) q^{22} +4.22010i q^{23} +(1.53414 + 2.65721i) q^{24} +(-3.59632 + 3.47368i) q^{25} +1.09402 q^{26} -1.00000i q^{27} +(1.07426 + 0.620223i) q^{28} +7.52314 q^{29} +(-0.919931 - 2.27656i) q^{30} +0.998902 q^{31} +(3.62090 - 2.09053i) q^{32} +(2.05869 - 1.18859i) q^{33} +(-0.194830 - 0.337455i) q^{34} +(-2.75221 - 2.15002i) q^{35} -0.794204 q^{36} +(-1.35801 - 5.92923i) q^{37} -7.80946i q^{38} +(-0.498147 + 0.862816i) q^{39} +(-6.36116 + 2.57047i) q^{40} +(-1.59578 - 2.76397i) q^{41} +(1.48530 - 0.857537i) q^{42} +6.18070i q^{43} +(-0.943979 - 1.63502i) q^{44} +(2.21432 + 0.311081i) q^{45} +(2.31702 - 4.01319i) q^{46} -7.02323i q^{47} -1.78083i q^{48} +(-2.28028 + 3.94955i) q^{49} +(5.32721 - 1.32883i) q^{50} +0.354853 q^{51} +(0.685252 + 0.395630i) q^{52} +(11.9801 + 6.91673i) q^{53} +(-0.549044 + 0.950972i) q^{54} +(1.99149 + 4.92835i) q^{55} +(-2.39613 - 4.15022i) q^{56} +(6.15906 + 3.55593i) q^{57} +(-7.15429 - 4.13053i) q^{58} +(5.72918 - 9.92323i) q^{59} +(0.247062 - 1.75862i) q^{60} +(0.880813 + 1.52561i) q^{61} +(-0.949927 - 0.548441i) q^{62} +1.56187i q^{63} -8.15283 q^{64} +(-1.75559 - 1.37146i) q^{65} -2.61034 q^{66} +(-1.47011 + 0.848767i) q^{67} -0.281825i q^{68} +(2.11005 + 3.65471i) q^{69} +(1.43682 + 3.55569i) q^{70} +(-2.23650 - 3.87372i) q^{71} +(2.65721 + 1.53414i) q^{72} +5.60903i q^{73} +(-1.96398 + 6.38414i) q^{74} +(-1.37767 + 4.80646i) q^{75} +(2.82414 - 4.89155i) q^{76} +(-3.21541 + 1.85642i) q^{77} +(0.947448 - 0.547009i) q^{78} +(-5.47109 - 9.47620i) q^{79} +(3.94334 + 0.553984i) q^{80} +(-0.500000 - 0.866025i) q^{81} +3.50461i q^{82} +(6.26017 + 3.61431i) q^{83} +1.24045 q^{84} +(-0.110388 + 0.785758i) q^{85} +(3.39348 - 5.87768i) q^{86} +(6.51523 - 3.76157i) q^{87} +7.29383i q^{88} +(-7.72572 + 13.3813i) q^{89} +(-1.93496 - 1.51159i) q^{90} +(0.778043 - 1.34761i) q^{91} +(2.90258 - 1.67581i) q^{92} +(0.865074 - 0.499451i) q^{93} +(-3.85606 + 6.67890i) q^{94} +(-9.78996 + 12.5320i) q^{95} +(2.09053 - 3.62090i) q^{96} +4.07687i q^{97} +(4.33696 - 2.50394i) q^{98} +(1.18859 - 2.05869i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9}+O(q^{10}) \) 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9	\( 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9} - 8 q^{11} - 16 q^{14} - 24 q^{16} + 4 q^{19} + 4 q^{20} + 12 q^{21} + 10 q^{25} + 24 q^{26} + 16 q^{29} + 12 q^{30} + 24 q^{31} - 44 q^{34} - 2 q^{35} + 64 q^{36} - 8 q^{39} + 46 q^{40} - 48 q^{41} - 8 q^{44} - 4 q^{45} - 64 q^{46} + 32 q^{49} - 46 q^{50} - 8 q^{51} - 12 q^{55} - 72 q^{56} + 32 q^{59} - 68 q^{60} - 8 q^{61} - 136 q^{64} - 42 q^{65} - 32 q^{66} - 4 q^{69} + 4 q^{70} + 12 q^{71} - 96 q^{74} - 8 q^{75} + 8 q^{76} - 8 q^{79} - 44 q^{80} - 36 q^{81} + 136 q^{84} + 4 q^{85} + 8 q^{86} + 8 q^{91} - 28 q^{94} + 18 q^{95} - 20 q^{96} - 4 q^{99}+O(q^{100}) \) 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9 - 8 * q^11 - 16 * q^14 - 24 * q^16 + 4 * q^19 + 4 * q^20 + 12 * q^21 + 10 * q^25 + 24 * q^26 + 16 * q^29 + 12 * q^30 + 24 * q^31 - 44 * q^34 - 2 * q^35 + 64 * q^36 - 8 * q^39 + 46 * q^40 - 48 * q^41 - 8 * q^44 - 4 * q^45 - 64 * q^46 + 32 * q^49 - 46 * q^50 - 8 * q^51 - 12 * q^55 - 72 * q^56 + 32 * q^59 - 68 * q^60 - 8 * q^61 - 136 * q^64 - 42 * q^65 - 32 * q^66 - 4 * q^69 + 4 * q^70 + 12 * q^71 - 96 * q^74 - 8 * q^75 + 8 * q^76 - 8 * q^79 - 44 * q^80 - 36 * q^81 + 136 * q^84 + 4 * q^85 + 8 * q^86 + 8 * q^91 - 28 * q^94 + 18 * q^95 - 20 * q^96 - 4 * q^99

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