LMFDB - Embedded newform 430.2.l.a.7.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(7,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("430.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.l (of order $12$, degree $4$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.5
Character	$\chi$	$=$	430.7
Dual form			430.2.l.a.123.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.348214 + 1.29955i) q^{3} -1.00000i q^{4} +(1.37552 + 1.76294i) q^{5} +(-0.672697 - 1.16515i) q^{6} +(0.277286 + 1.03484i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.03050 + 0.594958i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.348214 + 1.29955i) q^{3} -1.00000i q^{4} +(1.37552 + 1.76294i) q^{5} +(-0.672697 - 1.16515i) q^{6} +(0.277286 + 1.03484i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.03050 + 0.594958i) q^{9} +(-2.21922 - 0.273949i) q^{10} -4.21818 q^{11} +(1.29955 + 0.348214i) q^{12} +(0.603646 + 2.25284i) q^{13} +(-0.927816 - 0.535675i) q^{14} +(-2.77000 + 1.17367i) q^{15} -1.00000 q^{16} +(6.83222 - 1.83069i) q^{17} +(-1.14937 + 0.307973i) q^{18} +(-0.209764 - 0.363322i) q^{19} +(1.76294 - 1.37552i) q^{20} -1.44139 q^{21} +(2.98271 - 2.98271i) q^{22} +(0.261112 + 0.0699647i) q^{23} +(-1.16515 + 0.672697i) q^{24} +(-1.21591 + 4.84990i) q^{25} +(-2.01984 - 1.16616i) q^{26} +(-3.98602 + 3.98602i) q^{27} +(1.03484 - 0.277286i) q^{28} +(-4.97188 + 8.61154i) q^{29} +(1.12877 - 2.78860i) q^{30} +(-4.26369 - 7.38494i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.46883 - 5.48174i) q^{33} +(-3.53661 + 6.12560i) q^{34} +(-1.44296 + 1.91228i) q^{35} +(0.594958 - 1.03050i) q^{36} +(-8.21511 - 2.20123i) q^{37} +(0.405233 + 0.108582i) q^{38} -3.13788 q^{39} +(-0.273949 + 2.21922i) q^{40} -4.53157 q^{41} +(1.01921 - 1.01921i) q^{42} +(0.591424 - 6.53071i) q^{43} +4.21818i q^{44} +(0.368592 + 2.63508i) q^{45} +(-0.234106 + 0.135161i) q^{46} +(8.25998 + 8.25998i) q^{47} +(0.348214 - 1.29955i) q^{48} +(5.06816 - 2.92610i) q^{49} +(-2.56962 - 4.28918i) q^{50} +9.51628i q^{51} +(2.25284 - 0.603646i) q^{52} +(6.40204 + 1.71542i) q^{53} -5.63709i q^{54} +(-5.80218 - 7.43640i) q^{55} +(-0.535675 + 0.927816i) q^{56} +(0.545198 - 0.146085i) q^{57} +(-2.57363 - 9.60493i) q^{58} -8.33228i q^{59} +(1.17367 + 2.77000i) q^{60} +(-4.31917 - 2.49367i) q^{61} +(8.23683 + 2.20705i) q^{62} +(-0.329947 + 1.23138i) q^{63} +1.00000i q^{64} +(-3.14129 + 4.16301i) q^{65} +(2.83756 + 4.91480i) q^{66} +(-1.47439 + 5.50251i) q^{67} +(-1.83069 - 6.83222i) q^{68} +(-0.181845 + 0.314965i) q^{69} +(-0.331864 - 2.37251i) q^{70} +(4.65774 + 2.68915i) q^{71} +(0.307973 + 1.14937i) q^{72} +(0.898397 - 0.240725i) q^{73} +(7.36546 - 4.25245i) q^{74} +(-5.87930 - 3.26894i) q^{75} +(-0.363322 + 0.209764i) q^{76} +(-1.16964 - 4.36517i) q^{77} +(2.21881 - 2.21881i) q^{78} +(8.96598 + 5.17651i) q^{79} +(-1.37552 - 1.76294i) q^{80} +(-2.00718 - 3.47653i) q^{81} +(3.20431 - 3.20431i) q^{82} +(15.4795 + 4.14771i) q^{83} +1.44139i q^{84} +(12.6252 + 9.52664i) q^{85} +(4.19971 + 5.03611i) q^{86} +(-9.45986 - 9.45986i) q^{87} +(-2.98271 - 2.98271i) q^{88} +(5.34249 + 9.25346i) q^{89} +(-2.12392 - 1.60265i) q^{90} +(-2.16396 + 1.24936i) q^{91} +(0.0699647 - 0.261112i) q^{92} +(11.0818 - 2.96935i) q^{93} -11.6814 q^{94} +(0.351981 - 0.869557i) q^{95} +(0.672697 + 1.16515i) q^{96} +(10.7256 + 10.7256i) q^{97} +(-1.51466 + 5.65280i) q^{98} +(-4.34683 - 2.50964i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{6} + 12 q^{7}+O(q^{10}) $ 88 * q + 4 * q^6 + 12 * q^7	$ 88 q + 4 q^{6} + 12 q^{7} + 16 q^{13} - 88 q^{16} + 4 q^{17} - 16 q^{21} + 12 q^{23} - 8 q^{25} + 12 q^{28} - 36 q^{30} - 40 q^{31} + 12 q^{33} - 40 q^{35} - 40 q^{36} + 16 q^{38} - 56 q^{41} - 56 q^{43} + 24 q^{46} + 72 q^{47} + 24 q^{50} - 16 q^{52} + 20 q^{53} + 24 q^{55} - 8 q^{56} + 20 q^{57} + 8 q^{60} + 72 q^{61} + 36 q^{62} - 40 q^{66} - 16 q^{67} + 4 q^{68} + 24 q^{71} + 60 q^{73} - 48 q^{76} - 48 q^{77} + 40 q^{78} + 28 q^{81} + 20 q^{86} - 64 q^{87} - 8 q^{90} + 48 q^{91} - 12 q^{92} - 108 q^{93} + 4 q^{95} - 4 q^{96} - 48 q^{97} - 96 q^{98}+O(q^{100}) $ 88 * q + 4 * q^6 + 12 * q^7 + 16 * q^13 - 88 * q^16 + 4 * q^17 - 16 * q^21 + 12 * q^23 - 8 * q^25 + 12 * q^28 - 36 * q^30 - 40 * q^31 + 12 * q^33 - 40 * q^35 - 40 * q^36 + 16 * q^38 - 56 * q^41 - 56 * q^43 + 24 * q^46 + 72 * q^47 + 24 * q^50 - 16 * q^52 + 20 * q^53 + 24 * q^55 - 8 * q^56 + 20 * q^57 + 8 * q^60 + 72 * q^61 + 36 * q^62 - 40 * q^66 - 16 * q^67 + 4 * q^68 + 24 * q^71 + 60 * q^73 - 48 * q^76 - 48 * q^77 + 40 * q^78 + 28 * q^81 + 20 * q^86 - 64 * q^87 - 8 * q^90 + 48 * q^91 - 12 * q^92 - 108 * q^93 + 4 * q^95 - 4 * q^96 - 48 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.348214	+	1.29955i	−0.201041	+	0.750296i	0.789579	+	0.613649i	$0.210299\pi$
$3$	−0.348214	+	1.29955i	−0.201041	+	0.750296i	−0.990620	+	0.136647i	$0.956368\pi$
$4$		−	1.00000i		−	0.500000i
$5$	1.37552	+	1.76294i	0.615150	+	0.788410i
$5$	1.37552	+	1.76294i	0.615150	+	0.788410i
$6$	−0.672697	−	1.16515i	−0.274627	−	0.475669i
$7$	0.277286	+	1.03484i	0.104804	+	0.391135i	0.998323	−	0.0578915i	$-0.0184377\pi$
$7$	0.277286	+	1.03484i	0.104804	+	0.391135i	−0.893519	+	0.449026i	$0.851771\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.03050	+	0.594958i	0.343499	+	0.198319i
$10$	−2.21922	−	0.273949i	−0.701780	−	0.0866303i
$11$	−4.21818			−1.27183			−0.635915	−	0.771759i	$-0.719377\pi$
$11$	−4.21818			−1.27183			−0.635915	+	0.771759i	$0.719377\pi$
$12$	1.29955	+	0.348214i	0.375148	+	0.100521i
$13$	0.603646	+	2.25284i	0.167421	+	0.624825i	0.997719	+	0.0675047i	$0.0215038\pi$
$13$	0.603646	+	2.25284i	0.167421	+	0.624825i	−0.830298	+	0.557320i	$0.811830\pi$
$14$	−0.927816	−	0.535675i	−0.247969	−	0.143165i
$15$	−2.77000	+	1.17367i	−0.715211	+	0.303041i
$16$	−1.00000			−0.250000
$17$	6.83222	−	1.83069i	1.65706	−	0.444007i	0.695480	−	0.718546i	$-0.255192\pi$
$17$	6.83222	−	1.83069i	1.65706	−	0.444007i	0.961576	+	0.274539i	$0.0885253\pi$
$18$	−1.14937	+	0.307973i	−0.270909	+	0.0725899i
$19$	−0.209764	−	0.363322i	−0.0481232	−	0.0833518i	0.840960	−	0.541097i	$-0.181991\pi$
$19$	−0.209764	−	0.363322i	−0.0481232	−	0.0833518i	−0.889084	+	0.457745i	$0.848657\pi$
$20$	1.76294	−	1.37552i	0.394205	−	0.307575i
$21$	−1.44139			−0.314537
$22$	2.98271	−	2.98271i	0.635915	−	0.635915i
$23$	0.261112	+	0.0699647i	0.0544456	+	0.0145886i	0.285939	−	0.958248i	$-0.407695\pi$
$23$	0.261112	+	0.0699647i	0.0544456	+	0.0145886i	−0.231493	+	0.972836i	$0.574361\pi$
$24$	−1.16515	+	0.672697i	−0.237834	+	0.137314i
$25$	−1.21591	+	4.84990i	−0.243182	+	0.969981i
$26$	−2.01984	−	1.16616i	−0.396123	−	0.228702i
$27$	−3.98602	+	3.98602i	−0.767110	+	0.767110i
$28$	1.03484	−	0.277286i	0.195567	−	0.0524021i
$29$	−4.97188	+	8.61154i	−0.923254	+	1.59912i	−0.128909	+	0.991656i	$0.541148\pi$
$29$	−4.97188	+	8.61154i	−0.923254	+	1.59912i	−0.794345	+	0.607467i	$0.792186\pi$
$30$	1.12877	−	2.78860i	0.206085	−	0.509126i
$31$	−4.26369	−	7.38494i	−0.765782	−	1.32637i	−0.939832	−	0.341637i	$-0.889019\pi$
$31$	−4.26369	−	7.38494i	−0.765782	−	1.32637i	0.174050	−	0.984737i	$-0.444315\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	1.46883	−	5.48174i	0.255690	−	0.954249i
$34$	−3.53661	+	6.12560i	−0.606524	+	1.05053i
$35$	−1.44296	+	1.91228i	−0.243904	+	0.323235i
$36$	0.594958	−	1.03050i	0.0991596	−	0.171750i
$37$	−8.21511	−	2.20123i	−1.35056	−	0.361880i	−0.490216	−	0.871601i	$-0.663082\pi$
$37$	−8.21511	−	2.20123i	−1.35056	−	0.361880i	−0.860340	+	0.509721i	$0.829749\pi$
$38$	0.405233	+	0.108582i	0.0657375	+	0.0176143i
$39$	−3.13788			−0.502462
$40$	−0.273949	+	2.21922i	−0.0433151	+	0.350890i
$41$	−4.53157			−0.707713			−0.353856	−	0.935300i	$-0.615130\pi$
$41$	−4.53157			−0.707713			−0.353856	+	0.935300i	$0.615130\pi$
$42$	1.01921	−	1.01921i	0.157268	−	0.157268i
$43$	0.591424	−	6.53071i	0.0901914	−	0.995924i
$43$	0.591424	−	6.53071i	0.0901914	−	0.995924i
$44$			4.21818i			0.635915i
$45$	0.368592	+	2.63508i	0.0549464	+	0.392814i
$46$	−0.234106	+	0.135161i	−0.0345171	+	0.0199285i
$47$	8.25998	+	8.25998i	1.20484	+	1.20484i	0.972676	+	0.232165i	$0.0745810\pi$
$47$	8.25998	+	8.25998i	1.20484	+	1.20484i	0.232165	+	0.972676i	$0.425419\pi$
$48$	0.348214	−	1.29955i	0.0502603	−	0.187574i
$49$	5.06816	−	2.92610i	0.724023	−	0.418015i
$50$	−2.56962	−	4.28918i	−0.363400	−	0.606581i
$51$			9.51628i			1.33255i
$52$	2.25284	−	0.603646i	0.312413	−	0.0837107i
$53$	6.40204	+	1.71542i	0.879388	+	0.235631i	0.670143	−	0.742232i	$-0.266233\pi$
$53$	6.40204	+	1.71542i	0.879388	+	0.235631i	0.209245	+	0.977863i	$0.432899\pi$
$54$		−	5.63709i		−	0.767110i
$55$	−5.80218	−	7.43640i	−0.782366	−	1.00272i
$56$	−0.535675	+	0.927816i	−0.0715826	+	0.123985i
$57$	0.545198	−	0.146085i	0.0722133	−	0.0193495i
$58$	−2.57363	−	9.60493i	−0.337934	−	1.26119i
$59$		−	8.33228i		−	1.08477i	−0.840130	−	0.542386i	$-0.817521\pi$
$59$		−	8.33228i		−	1.08477i	0.840130	−	0.542386i	$-0.182479\pi$
$60$	1.17367	+	2.77000i	0.151521	+	0.357606i
$61$	−4.31917	−	2.49367i	−0.553013	−	0.319282i	0.197323	−	0.980338i	$-0.436775\pi$
$61$	−4.31917	−	2.49367i	−0.553013	−	0.319282i	−0.750336	+	0.661056i	$0.770108\pi$
$62$	8.23683	+	2.20705i	1.04608	+	0.280296i
$63$	−0.329947	+	1.23138i	−0.0415694	+	0.155139i
$64$			1.00000i			0.125000i
$65$	−3.14129	+	4.16301i	−0.389629	+	0.516358i
$66$	2.83756	+	4.91480i	0.349279	+	0.604970i
$67$	−1.47439	+	5.50251i	−0.180126	+	0.672239i	0.815496	+	0.578763i	$0.196464\pi$
$67$	−1.47439	+	5.50251i	−0.180126	+	0.672239i	−0.995622	+	0.0934757i	$0.970202\pi$
$68$	−1.83069	−	6.83222i	−0.222003	−	0.828528i
$69$	−0.181845	+	0.314965i	−0.0218916	+	0.0379174i
$70$	−0.331864	−	2.37251i	−0.0396654	−	0.283570i
$71$	4.65774	+	2.68915i	0.552772	+	0.319143i	0.750239	−	0.661167i	$-0.229938\pi$
$71$	4.65774	+	2.68915i	0.552772	+	0.319143i	−0.197468	+	0.980309i	$0.563272\pi$
$72$	0.307973	+	1.14937i	0.0362949	+	0.135455i
$73$	0.898397	−	0.240725i	0.105149	−	0.0281747i	−0.205861	−	0.978581i	$-0.565999\pi$
$73$	0.898397	−	0.240725i	0.105149	−	0.0281747i	0.311010	+	0.950407i	$0.399333\pi$
$74$	7.36546	−	4.25245i	0.856218	−	0.494338i
$75$	−5.87930	−	3.26894i	−0.678883	−	0.377464i
$76$	−0.363322	+	0.209764i	−0.0416759	+	0.0240616i
$77$	−1.16964	−	4.36517i	−0.133293	−	0.497457i
$78$	2.21881	−	2.21881i	0.251231	−	0.251231i
$79$	8.96598	+	5.17651i	1.00875	+	0.582403i	0.910826	−	0.412791i	$-0.135446\pi$
$79$	8.96598	+	5.17651i	1.00875	+	0.582403i	0.0979257	+	0.995194i	$0.468779\pi$
$80$	−1.37552	−	1.76294i	−0.153787	−	0.197103i
$81$	−2.00718	−	3.47653i	−0.223020	−	0.386281i
$82$	3.20431	−	3.20431i	0.353856	−	0.353856i
$83$	15.4795	+	4.14771i	1.69909	+	0.455270i	0.972711	−	0.232021i	$-0.0745339\pi$
$83$	15.4795	+	4.14771i	1.69909	+	0.455270i	0.726382	+	0.687292i	$0.241201\pi$
$84$			1.44139i			0.157268i
$85$	12.6252	+	9.52664i	1.36940	+	1.03331i
$86$	4.19971	+	5.03611i	0.452867	+	0.543058i
$87$	−9.45986	−	9.45986i	−1.01420	−	1.01420i
$88$	−2.98271	−	2.98271i	−0.317958	−	0.317958i
$89$	5.34249	+	9.25346i	0.566302	+	0.980864i	0.996927	+	0.0783334i	$0.0249599\pi$
$89$	5.34249	+	9.25346i	0.566302	+	0.980864i	−0.430625	+	0.902531i	$0.641707\pi$
$90$	−2.12392	−	1.60265i	−0.223880	−	0.168934i
$91$	−2.16396	+	1.24936i	−0.226844	+	0.130969i
$92$	0.0699647	−	0.261112i	0.00729432	−	0.0272228i
$93$	11.0818	−	2.96935i	1.14913	−	0.307908i
$94$	−11.6814			−1.20484
$95$	0.351981	−	0.869557i	0.0361125	−	0.0892147i
$96$	0.672697	+	1.16515i	0.0686568	+	0.118917i
$97$	10.7256	+	10.7256i	1.08902	+	1.08902i	0.995630	+	0.0933904i	$0.0297705\pi$
$97$	10.7256	+	10.7256i	1.08902	+	1.08902i	0.0933904	+	0.995630i	$0.470230\pi$
$98$	−1.51466	+	5.65280i	−0.153004	+	0.571019i
$99$	−4.34683	−	2.50964i	−0.436873	−	0.252229i
$100$	4.84990	+	1.21591i	0.484990	+	0.121591i
$101$	8.74242	−	15.1423i	0.869903	−	1.50672i	0.00780779	−	0.999970i	$-0.497515\pi$
$101$	8.74242	−	15.1423i	0.869903	−	1.50672i	0.862095	−	0.506747i	$-0.169152\pi$
$102$	−6.72903	−	6.72903i	−0.666273	−	0.666273i
$103$	−3.96011	−	14.7793i	−0.390202	−	1.45625i	−0.829802	−	0.558059i	$-0.811546\pi$
$103$	−3.96011	−	14.7793i	−0.390202	−	1.45625i	0.439600	−	0.898194i	$-0.355120\pi$
$104$	−1.16616	+	2.01984i	−0.114351	+	0.198062i
$105$	−1.98265	−	2.54108i	−0.193487	−	0.247984i
$106$	−5.73991	+	3.31394i	−0.557509	+	0.321878i
$107$	−1.04978	−	1.04978i	−0.101486	−	0.101486i	0.654541	−	0.756027i	$-0.272862\pi$
$107$	−1.04978	−	1.04978i	−0.101486	−	0.101486i	−0.756027	+	0.654541i	$0.772862\pi$
$108$	3.98602	+	3.98602i	0.383555	+	0.383555i
$109$	5.75414	−	3.32215i	0.551147	−	0.318205i	−0.198438	−	0.980113i	$-0.563587\pi$
$109$	5.75414	−	3.32215i	0.551147	−	0.318205i	0.749584	+	0.661909i	$0.230253\pi$
$110$	9.36109	+	1.15557i	0.892545	+	0.110179i
$111$	5.72122	−	9.90945i	0.543034	−	0.940563i
$112$	−0.277286	−	1.03484i	−0.0262010	−	0.0977836i
$113$	−0.627664	−	0.627664i	−0.0590457	−	0.0590457i	0.676967	−	0.736013i	$-0.263294\pi$
$113$	−0.627664	−	0.627664i	−0.0590457	−	0.0590457i	−0.736013	+	0.676967i	$0.763294\pi$
$114$	−0.282215	+	0.488811i	−0.0264319	+	0.0457814i
$115$	0.235820	+	0.556562i	0.0219903	+	0.0518996i
$116$	8.61154	+	4.97188i	0.799562	+	0.461627i
$117$	−0.718288	+	2.68069i	−0.0664058	+	0.247830i
$118$	5.89181	+	5.89181i	0.542386	+	0.542386i
$119$	3.78895	+	6.56266i	0.347333	+	0.601598i
$120$	−2.78860	−	1.12877i	−0.254563	−	0.103043i
$121$	6.79308			0.617553
$122$	4.81741	−	1.29082i	0.436147	−	0.116865i
$123$	1.57795	−	5.88901i	0.142279	−	0.530994i
$124$	−7.38494	+	4.26369i	−0.663187	+	0.382891i
$125$	−10.2226	+	4.52755i	−0.914336	+	0.404957i
$126$	−0.637408	−	1.10402i	−0.0567848	−	0.0983542i
$127$	−1.11094	−	1.11094i	−0.0985802	−	0.0985802i	0.656097	−	0.754677i	$-0.272206\pi$
$127$	−1.11094	−	1.11094i	−0.0985802	−	0.0985802i	−0.754677	+	0.656097i	$0.772206\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	8.28105	+	3.04267i	0.729106	+	0.267892i
$130$	−0.722463	−	5.16492i	−0.0633642	−	0.452993i
$131$		−	4.07827i		−	0.356320i	−0.984002	−	0.178160i	$-0.942985\pi$
$131$		−	4.07827i		−	0.356320i	0.984002	−	0.178160i	$-0.0570145\pi$
$132$	−5.48174	−	1.46883i	−0.477125	−	0.127845i
$133$	0.317817	−	0.317817i	0.0275583	−	0.0275583i
$134$	−2.84831	−	4.93342i	−0.246057	−	0.426182i
$135$	−12.5100	−	1.54427i	−1.07669	−	0.132910i
$136$	6.12560	+	3.53661i	0.525266	+	0.303262i
$137$	15.1507	−	15.1507i	1.29441	−	1.29441i	0.362386	−	0.932028i	$-0.381962\pi$
$137$	15.1507	−	15.1507i	1.29441	−	1.29441i	0.932028	−	0.362386i	$-0.118038\pi$
$138$	−0.0941300	−	0.351298i	−0.00801288	−	0.0299045i
$139$	−2.07899	+	1.20031i	−0.176338	+	0.101809i	−0.585571	−	0.810621i	$-0.699130\pi$
$139$	−2.07899	+	1.20031i	−0.176338	+	0.101809i	0.409233	+	0.912430i	$0.365796\pi$
$140$	1.91228	+	1.44296i	0.161617	+	0.121952i
$141$	−13.6105	+	7.85802i	−1.14621	+	0.661765i
$142$	−5.19503	+	1.39200i	−0.435957	+	0.116814i
$143$	−2.54629	−	9.50289i	−0.212932	−	0.794671i
$144$	−1.03050	−	0.594958i	−0.0858748	−	0.0495798i
$145$	−22.0205	+	3.08020i	−1.82870	+	0.255797i
$146$	−0.465044	+	0.805480i	−0.0384873	+	0.0666620i
$147$	2.03782	+	7.60524i	0.168076	+	0.627270i
$148$	−2.20123	+	8.21511i	−0.180940	+	0.675278i
$149$	1.41988	+	2.45931i	0.116321	+	0.201474i	0.918307	−	0.395869i	$-0.129556\pi$
$149$	1.41988	+	2.45931i	0.116321	+	0.201474i	−0.801986	+	0.597343i	$0.796223\pi$
$150$	6.46878	−	1.84581i	0.528174	−	0.150709i
$151$			2.62176i			0.213356i	0.994294	+	0.106678i	$0.0340213\pi$
$151$			2.62176i			0.213356i	−0.994294	+	0.106678i	$0.965979\pi$
$152$	0.108582	−	0.405233i	0.00880716	−	0.0328688i
$153$	8.12976	+	2.17836i	0.657252	+	0.176110i
$154$	3.91370	+	2.25958i	0.315375	+	0.182082i
$155$	7.15441	−	17.6747i	0.574656	−	1.41967i
$156$			3.13788i			0.251231i
$157$	−2.05362	−	7.66421i	−0.163897	−	0.611670i	−0.998178	−	0.0603321i	$-0.980784\pi$
$157$	−2.05362	−	7.66421i	−0.163897	−	0.611670i	0.834282	−	0.551338i	$-0.185883\pi$
$158$	−10.0003	+	2.67956i	−0.795577	+	0.213174i
$159$	−4.45855	+	7.72244i	−0.353586	+	0.612429i
$160$	2.21922	+	0.273949i	0.175445	+	0.0216576i
$161$			0.289610i			0.0228245i
$162$	3.87757	+	1.03899i	0.304650	+	0.0816308i
$163$	−13.7039	+	3.67196i	−1.07337	+	0.287610i	−0.751879	−	0.659301i	$-0.770852\pi$
$163$	−13.7039	+	3.67196i	−1.07337	+	0.287610i	−0.321496	+	0.946911i	$0.604186\pi$
$164$			4.53157i			0.353856i
$165$	11.6844	−	4.95077i	0.909628	−	0.385417i
$166$	−13.8785	+	8.01276i	−1.07718	+	0.621911i
$167$	−4.47801	+	16.7122i	−0.346519	+	1.29323i	0.544309	+	0.838885i	$0.316792\pi$
$167$	−4.47801	+	16.7122i	−0.346519	+	1.29323i	−0.890828	+	0.454341i	$0.849875\pi$
$168$	−1.01921	−	1.01921i	−0.0786341	−	0.0786341i
$169$	6.54744	−	3.78016i	0.503649	−	0.290782i
$170$	−15.6637	+	2.19102i	−1.20135	+	0.168044i
$171$		−	0.499203i		−	0.0381750i
$172$	−6.53071	−	0.591424i	−0.497962	−	0.0450957i
$173$	−0.164533	+	0.164533i	−0.0125092	+	0.0125092i	−0.713334	−	0.700824i	$-0.752816\pi$
$173$	−0.164533	+	0.164533i	−0.0125092	+	0.0125092i	0.700824	+	0.713334i	$0.252816\pi$
$174$	13.3783			1.01420
$175$	−5.35605	+	0.0865336i	−0.404879	+	0.00654133i
$176$	4.21818			0.317958
$177$	10.8282	+	2.90141i	0.813899	+	0.218084i
$178$	−10.3209	−	2.76547i	−0.773583	−	0.207281i
$179$	−5.03108	+	8.71409i	−0.376041	+	0.651322i	−0.990482	−	0.137641i	$-0.956048\pi$
$179$	−5.03108	+	8.71409i	−0.376041	+	0.651322i	0.614441	+	0.788962i	$0.289381\pi$
$180$	2.63508	−	0.368592i	0.196407	−	0.0274732i
$181$	1.48733	−	2.57613i	0.110552	−	0.191482i	−0.805441	−	0.592676i	$-0.798071\pi$
$181$	1.48733	−	2.57613i	0.110552	−	0.191482i	0.915993	+	0.401194i	$0.131405\pi$
$182$	0.646716	−	2.41358i	0.0479378	−	0.178906i
$183$	4.74465	−	4.74465i	0.350734	−	0.350734i
$184$	0.135161	+	0.234106i	0.00996423	+	0.0172585i
$185$	−7.41938	−	17.5106i	−0.545484	−	1.28740i
$186$	−5.73635	+	9.93565i	−0.420609	+	0.728517i
$187$	−28.8195	+	7.72217i	−2.10749	+	0.564701i
$188$	8.25998	−	8.25998i	0.602421	−	0.602421i
$189$	−5.23018	−	3.01965i	−0.380440	−	0.219647i
$190$	0.365982	+	0.863758i	0.0265511	+	0.0626636i
$191$	9.26971	−	5.35187i	0.670733	−	0.387248i	−0.125621	−	0.992078i	$-0.540092\pi$
$191$	9.26971	−	5.35187i	0.670733	−	0.387248i	0.796354	+	0.604831i	$0.206759\pi$
$192$	−1.29955	−	0.348214i	−0.0937870	−	0.0251301i
$193$	−2.74746	+	2.74746i	−0.197767	+	0.197767i	−0.799042	−	0.601275i	$-0.794660\pi$
$193$	−2.74746	+	2.74746i	−0.197767	+	0.197767i	0.601275	+	0.799042i	$0.294660\pi$
$194$	−15.1683			−1.08902
$195$	−4.31620	−	5.53188i	−0.309089	−	0.396146i
$196$	−2.92610	−	5.06816i	−0.209007	−	0.362012i
$197$	7.27787	−	1.95010i	0.518527	−	0.138939i	0.00994177	−	0.999951i	$-0.496835\pi$
$197$	7.27787	−	1.95010i	0.518527	−	0.138939i	0.508585	+	0.861012i	$0.330169\pi$
$198$	4.84826	−	1.29909i	0.344551	−	0.0923220i
$199$	6.34616			0.449868			0.224934	−	0.974374i	$-0.427783\pi$
$199$	6.34616			0.449868			0.224934	+	0.974374i	$0.427783\pi$
$200$	−4.28918	+	2.56962i	−0.303291	+	0.181700i
$201$	−6.63739	−	3.83210i	−0.468165	−	0.270295i
$202$	4.52541	+	16.8891i	0.318407	+	1.18831i
$203$	−10.2902	−	2.75726i	−0.722233	−	0.193522i
$204$	9.51628			0.666273
$205$	−6.23325	−	7.98889i	−0.435349	−	0.557968i
$206$	13.2508	+	7.65035i	0.923227	+	0.533025i
$207$	0.227449	+	0.227449i	0.0158088	+	0.0158088i
$208$	−0.603646	−	2.25284i	−0.0418553	−	0.156206i
$209$	0.884824	+	1.53256i	0.0612046	+	0.106009i
$210$	3.19876	+	0.394867i	0.220735	+	0.0272484i
$211$		−	15.7541i		−	1.08456i	−0.840198	−	0.542279i	$-0.817562\pi$
$211$		−	15.7541i		−	1.08456i	0.840198	−	0.542279i	$-0.182438\pi$
$212$	1.71542	−	6.40204i	0.117816	−	0.439694i
$213$	−5.11657	+	5.11657i	−0.350581	+	0.350581i
$214$	1.48461			0.101486
$215$	12.3268	−	7.94046i	0.840678	−	0.541535i
$216$	−5.63709			−0.383555
$217$	6.46000	−	6.46000i	0.438533	−	0.438533i
$218$	−1.71967	+	6.41791i	−0.116471	+	0.434676i
$219$			1.25134i			0.0845574i
$220$	−7.43640	+	5.80218i	−0.501362	+	0.391183i
$221$	8.24848	+	14.2868i	0.554853	+	0.961034i
$222$	2.96152	+	11.0526i	0.198764	+	0.741799i
$223$	7.45621	+	7.45621i	0.499305	+	0.499305i	0.911222	−	0.411917i	$-0.135141\pi$
$223$	7.45621	+	7.45621i	0.499305	+	0.499305i	−0.411917	+	0.911222i	$0.635141\pi$
$224$	0.927816	+	0.535675i	0.0619923	+	0.0357913i
$225$	−4.13848	+	4.27440i	−0.275899	+	0.284960i
$226$	0.887651			0.0590457
$227$	13.5866	+	3.64052i	0.901775	+	0.241630i	0.679778	−	0.733418i	$-0.262076\pi$
$227$	13.5866	+	3.64052i	0.901775	+	0.241630i	0.221997	+	0.975047i	$0.428743\pi$
$228$	−0.146085	−	0.545198i	−0.00967475	−	0.0361066i
$229$	−18.5833	−	10.7291i	−1.22802	−	0.708999i	−0.261406	−	0.965229i	$-0.584186\pi$
$229$	−18.5833	−	10.7291i	−1.22802	−	0.708999i	−0.966616	+	0.256230i	$0.917519\pi$
$230$	−0.560298	−	0.226798i	−0.0369450	−	0.0149546i
$231$	6.08004			0.400037
$232$	−9.60493	+	2.57363i	−0.630594	+	0.168967i
$233$	−5.53260	+	1.48246i	−0.362453	+	0.0971190i	−0.435449	−	0.900213i	$-0.643411\pi$
$233$	−5.53260	+	1.48246i	−0.362453	+	0.0971190i	0.0729964	+	0.997332i	$0.476744\pi$
$234$	−1.38763	−	2.40344i	−0.0907120	−	0.157118i
$235$	−3.20010	+	25.9236i	−0.208752	+	1.69107i
$236$	−8.33228			−0.542386
$237$	−9.84921	+	9.84921i	−0.639775	+	0.639775i
$238$	−7.31969	−	1.96131i	−0.474465	−	0.127133i
$239$	6.23454	−	3.59951i	0.403279	−	0.232833i	−0.284619	−	0.958641i	$-0.591867\pi$
$239$	6.23454	−	3.59951i	0.403279	−	0.232833i	0.687898	+	0.725808i	$0.258534\pi$
$240$	2.77000	−	1.17367i	0.178803	−	0.0757603i
$241$	−9.04079	−	5.21970i	−0.582368	−	0.336230i	0.179706	−	0.983720i	$-0.442485\pi$
$241$	−9.04079	−	5.21970i	−0.582368	−	0.336230i	−0.762074	+	0.647490i	$0.775819\pi$
$242$	−4.80343	+	4.80343i	−0.308776	+	0.308776i
$243$	−11.1182	+	2.97910i	−0.713231	+	0.191110i
$244$	−2.49367	+	4.31917i	−0.159641	+	0.276506i
$245$	12.1299	+	4.90995i	0.774950	+	0.313685i
$246$	3.04837	+	5.27994i	0.194357	+	0.336637i
$247$	0.691883	−	0.691883i	0.0440235	−	0.0440235i
$248$	2.20705	−	8.23683i	0.140148	−	0.523039i
$249$	−10.7803	+	18.6721i	−0.683175	+	1.18329i
$250$	4.02700	−	10.4299i	0.254690	−	0.659646i
$251$	5.42876	−	9.40288i	0.342660	−	0.593505i	−0.642266	−	0.766482i	$-0.722005\pi$
$251$	5.42876	−	9.40288i	0.342660	−	0.593505i	0.984926	+	0.172977i	$0.0553388\pi$
$252$	1.23138	+	0.329947i	0.0775695	+	0.0207847i
$253$	−1.10142	−	0.295124i	−0.0692455	−	0.0185543i
$254$	1.57111			0.0985802
$255$	−16.7766	+	13.0898i	−1.05059	+	0.819715i
$256$	1.00000			0.0625000
$257$	−6.00687	+	6.00687i	−0.374698	+	0.374698i	−0.869185	−	0.494487i	$-0.835356\pi$
$257$	−6.00687	+	6.00687i	−0.374698	+	0.374698i	0.494487	+	0.869185i	$0.335356\pi$
$258$	−8.00708	+	3.70410i	−0.498499	+	0.230607i
$259$		−	9.11173i		−	0.566175i
$260$	4.16301	+	3.14129i	0.258179	+	0.194815i
$261$	−10.2470	+	5.91611i	−0.634274	+	0.366198i
$262$	2.88377	+	2.88377i	0.178160	+	0.178160i
$263$	−7.51794	+	28.0573i	−0.463576	+	1.73009i	0.197991	+	0.980204i	$0.436558\pi$
$263$	−7.51794	+	28.0573i	−0.463576	+	1.73009i	−0.661567	+	0.749886i	$0.730108\pi$
$264$	4.91480	−	2.83756i	0.302485	−	0.174640i
$265$	5.78193	+	13.6460i	0.355181	+	0.838267i
$266$			0.449462i			0.0275583i
$267$	−13.8857	+	3.72065i	−0.849789	+	0.227700i
$268$	5.50251	+	1.47439i	0.336119	+	0.0900629i
$269$			7.40250i			0.451338i	0.974204	+	0.225669i	$0.0724568\pi$
$269$			7.40250i			0.451338i	−0.974204	+	0.225669i	$0.927543\pi$
$270$	9.93784	−	7.75391i	0.604798	−	0.471888i
$271$	−13.8280	+	23.9509i	−0.839993	+	1.45491i	0.0499058	+	0.998754i	$0.484108\pi$
$271$	−13.8280	+	23.9509i	−0.839993	+	1.45491i	−0.889899	+	0.456157i	$0.849225\pi$
$272$	−6.83222	+	1.83069i	−0.414264	+	0.111002i
$273$	−0.870088	−	3.24721i	−0.0526601	−	0.196530i
$274$			21.4264i			1.29441i
$275$	5.12892	−	20.4578i	0.309286	−	1.23365i
$276$	0.314965	+	0.181845i	0.0189587	+	0.0109458i
$277$	12.1426	+	3.25361i	0.729580	+	0.195490i	0.604442	−	0.796649i	$-0.293396\pi$
$277$	12.1426	+	3.25361i	0.729580	+	0.195490i	0.125138	+	0.992139i	$0.460063\pi$
$278$	0.621324	−	2.31881i	0.0372646	−	0.139073i
$279$		−	10.1469i		−	0.607478i
$280$	−2.37251	+	0.331864i	−0.141785	+	0.0198327i
$281$	−9.52754	−	16.5022i	−0.568366	−	0.984438i	−0.996728	−	0.0808310i	$-0.974243\pi$
$281$	−9.52754	−	16.5022i	−0.568366	−	0.984438i	0.428362	−	0.903607i	$-0.359091\pi$
$282$	4.06761	−	15.1805i	0.242223	−	0.903988i
$283$	−0.238347	−	0.889523i	−0.0141683	−	0.0528766i	0.958480	−	0.285160i	$-0.0920469\pi$
$283$	−0.238347	−	0.889523i	−0.0141683	−	0.0528766i	−0.972648	+	0.232284i	$0.925380\pi$
$284$	2.68915	−	4.65774i	0.159571	−	0.276386i
$285$	1.00747	+	0.760208i	0.0596773	+	0.0450309i
$286$	8.52006	+	4.91906i	0.503802	+	0.290870i
$287$	−1.25654	−	4.68947i	−0.0741712	−	0.276811i
$288$	1.14937	−	0.307973i	0.0677273	−	0.0181475i
$289$	28.6053	−	16.5153i	1.68267	−	0.971488i
$290$	13.3928	−	17.7489i	0.786454	−	1.04225i
$291$	−17.6733	+	10.2037i	−1.03603	+	0.598149i
$292$	−0.240725	−	0.898397i	−0.0140873	−	0.0525747i
$293$	−13.8386	+	13.8386i	−0.808458	+	0.808458i	−0.984400	−	0.175942i	$-0.943703\pi$
$293$	−13.8386	+	13.8386i	−0.808458	+	0.808458i	0.175942	+	0.984400i	$0.443703\pi$
$294$	−6.81867	−	3.93676i	−0.397673	−	0.229597i
$295$	14.6893	−	11.4612i	0.855245	−	0.667297i
$296$	−4.25245	−	7.36546i	−0.247169	−	0.428109i
$297$	16.8138	−	16.8138i	0.975634	−	0.975634i
$298$	−2.74300	−	0.734984i	−0.158898	−	0.0425765i
$299$			0.630476i			0.0364614i
$300$	−3.26894	+	5.87930i	−0.188732	+	0.339442i
$301$	6.92227	−	1.19884i	0.398993	−	0.0691001i
$302$	−1.85386	−	1.85386i	−0.106678	−	0.106678i
$303$	16.6340	+	16.6340i	0.955596	+	0.955596i
$304$	0.209764	+	0.363322i	0.0120308	+	0.0208380i
$305$	−1.54489	−	11.0445i	−0.0884604	−	0.632407i
$306$	−7.28894	+	4.20827i	−0.416681	+	0.240571i
$307$	2.64977	−	9.88908i	0.151230	−	0.564399i	−0.848168	−	0.529727i	$-0.822294\pi$
$307$	2.64977	−	9.88908i	0.151230	−	0.564399i	0.999399	−	0.0346727i	$-0.0110389\pi$
$308$	−4.36517	+	1.16964i	−0.248728	+	0.0666466i
$309$	20.5855			1.17107
$310$	7.43900	+	17.5569i	0.422507	+	0.997163i
$311$	−7.19918	−	12.4693i	−0.408228	−	0.707072i	0.586463	−	0.809976i	$-0.300520\pi$
$311$	−7.19918	−	12.4693i	−0.408228	−	0.707072i	−0.994691	+	0.102904i	$0.967187\pi$
$312$	−2.21881	−	2.21881i	−0.125616	−	0.125616i
$313$	4.59717	−	17.1569i	0.259847	−	0.969764i	−0.705482	−	0.708728i	$-0.749269\pi$
$313$	4.59717	−	17.1569i	0.259847	−	0.969764i	0.965329	−	0.261036i	$-0.0840641\pi$
$314$	6.87154	+	3.96729i	0.387784	+	0.223887i
$315$	−2.62469	+	1.11210i	−0.147885	+	0.0626600i
$316$	5.17651	−	8.96598i	0.291201	−	0.504376i
$317$	−4.95123	−	4.95123i	−0.278089	−	0.278089i	0.554257	−	0.832346i	$-0.313003\pi$
$317$	−4.95123	−	4.95123i	−0.278089	−	0.278089i	−0.832346	+	0.554257i	$0.813003\pi$
$318$	−2.30792	−	8.61326i	−0.129422	−	0.483008i
$319$	20.9723	−	36.3251i	1.17422	−	2.03381i
$320$	−1.76294	+	1.37552i	−0.0985513	+	0.0768937i
$321$	1.72979	−	0.998694i	0.0965474	−	0.0557417i
$322$	−0.204785	−	0.204785i	−0.0114122	−	0.0114122i
$323$	−2.09828	−	2.09828i	−0.116752	−	0.116752i
$324$	−3.47653	+	2.00718i	−0.193141	+	0.111510i
$325$	−11.6600	+	0.188382i	−0.646782	+	0.0104496i
$326$	7.09367	−	12.2866i	0.392882	−	0.680492i
$327$	2.31364	+	8.63461i	0.127944	+	0.477495i
$328$	−3.20431	−	3.20431i	−0.176928	−	0.176928i
$329$	−6.25742	+	10.8382i	−0.344983	+	0.597528i
$330$	−4.76138	+	11.7628i	−0.262105	+	0.647522i
$331$	7.58827	+	4.38109i	0.417089	+	0.240806i	0.693831	−	0.720138i	$-0.255921\pi$
$331$	7.58827	+	4.38109i	0.417089	+	0.240806i	−0.276742	+	0.960944i	$0.589255\pi$
$332$	4.14771	−	15.4795i	0.227635	−	0.849546i
$333$	−7.15601	−	7.15601i	−0.392147	−	0.392147i
$334$	−8.65085	−	14.9837i	−0.473353	−	0.819872i
$335$	−11.7286	+	4.96953i	−0.640804	+	0.271514i
$336$	1.44139			0.0786341
$337$	12.9352	−	3.46597i	0.704623	−	0.188803i	0.111323	−	0.993784i	$-0.464491\pi$
$337$	12.9352	−	3.46597i	0.704623	−	0.188803i	0.593300	+	0.804981i	$0.297825\pi$
$338$	−1.95676	+	7.30272i	−0.106434	+	0.397215i
$339$	1.03424	−	0.597120i	0.0561723	−	0.0324311i
$340$	9.52664	−	12.6252i	0.516655	−	0.684698i
$341$	17.9851	+	31.1510i	0.973945	+	1.68692i
$342$	0.352990	+	0.352990i	0.0190875	+	0.0190875i
$343$	9.73630	+	9.73630i	0.525711	+	0.525711i
$344$	5.03611	−	4.19971i	0.271529	−	0.226433i
$345$	−0.805396	+	0.112658i	−0.0433610	+	0.00606529i
$346$		−	0.232685i		−	0.0125092i
$347$	−18.6775	−	5.00463i	−1.00266	−	0.268663i	−0.280102	−	0.959970i	$-0.590368\pi$
$347$	−18.6775	−	5.00463i	−1.00266	−	0.268663i	−0.722561	+	0.691308i	$0.757035\pi$
$348$	−9.45986	+	9.45986i	−0.507102	+	0.507102i
$349$	−0.0491117	−	0.0850640i	−0.00262889	−	0.00455337i	0.864708	−	0.502275i	$-0.167503\pi$
$349$	−0.0491117	−	0.0850640i	−0.00262889	−	0.00455337i	−0.867337	+	0.497722i	$0.834170\pi$
$350$	3.72611	−	3.84849i	0.199169	−	0.205710i
$351$	−11.3860	−	6.57372i	−0.607740	−	0.350879i
$352$	−2.98271	+	2.98271i	−0.158979	+	0.158979i
$353$	−0.970648	−	3.62251i	−0.0516624	−	0.192807i	0.935272	−	0.353930i	$-0.115155\pi$
$353$	−0.970648	−	3.62251i	−0.0516624	−	0.192807i	−0.986934	+	0.161123i	$0.948488\pi$
$354$	−9.70832	+	5.60510i	−0.515991	+	0.297908i
$355$	1.66599	+	11.9103i	0.0884218	+	0.632131i
$356$	9.25346	−	5.34249i	0.490432	−	0.283151i
$357$	−9.84787	+	2.63873i	−0.521205	+	0.139656i
$358$	−2.60428	−	9.71930i	−0.137640	−	0.513681i
$359$	−26.9360	−	15.5515i	−1.42163	−	0.820776i	−0.425187	−	0.905105i	$-0.639792\pi$
$359$	−26.9360	−	15.5515i	−1.42163	−	0.820776i	−0.996438	+	0.0843297i	$0.973125\pi$
$360$	−1.60265	+	2.12392i	−0.0844670	+	0.111940i
$361$	9.41200	−	16.3021i	0.495368	−	0.858003i
$362$	0.769898	+	2.87330i	0.0404650	+	0.151017i
$363$	−2.36544	+	8.82795i	−0.124154	+	0.463347i
$364$	1.24936	+	2.16396i	0.0654843	+	0.113422i
$365$	1.66014	+	1.25270i	0.0868958	+	0.0655692i
$366$			6.70994i			0.350734i
$367$	−4.30707	+	16.0742i	−0.224827	+	0.839066i	0.757647	+	0.652665i	$0.226349\pi$
$367$	−4.30707	+	16.0742i	−0.224827	+	0.839066i	−0.982474	+	0.186401i	$0.940318\pi$
$368$	−0.261112	−	0.0699647i	−0.0136114	−	0.00364716i
$369$	−4.66977	−	2.69609i	−0.243099	−	0.140353i
$370$	17.6281	+	7.13554i	0.916443	+	0.370959i
$371$			7.10078i			0.368654i
$372$	−2.96935	−	11.0818i	−0.153954	−	0.574563i
$373$	23.4966	−	6.29589i	1.21661	−	0.325989i	0.407256	−	0.913314i	$-0.366486\pi$
$373$	23.4966	−	6.29589i	1.21661	−	0.325989i	0.809351	+	0.587325i	$0.199819\pi$
$374$	14.9181	−	25.8389i	0.771396	−	1.33610i
$375$	−2.32414	−	14.8613i	−0.120018	−	0.767435i
$376$			11.6814i			0.602421i
$377$	−22.4017	−	6.00251i	−1.15374	−	0.309145i
$378$	5.83351	−	1.56308i	0.300043	−	0.0803964i
$379$		−	13.2555i		−	0.680887i	−0.940265	−	0.340444i	$-0.889423\pi$
$379$		−	13.2555i		−	0.680887i	0.940265	−	0.340444i	$-0.110577\pi$
$380$	−0.869557	−	0.351981i	−0.0446073	−	0.0180562i
$381$	1.83057	−	1.05688i	0.0937830	−	0.0541456i
$382$	−2.77033	+	10.3390i	−0.141743	+	0.528990i
$383$	14.1976	+	14.1976i	0.725464	+	0.725464i	0.969713	−	0.244249i	$-0.0785413\pi$
$383$	14.1976	+	14.1976i	0.725464	+	0.725464i	−0.244249	+	0.969713i	$0.578541\pi$
$384$	1.16515	−	0.672697i	0.0594586	−	0.0343284i
$385$	6.08666	−	8.06637i	0.310205	−	0.411100i
$386$		−	3.88550i		−	0.197767i
$387$	4.49496	−	6.37801i	0.228492	−	0.324212i
$388$	10.7256	−	10.7256i	0.544510	−	0.544510i
$389$	19.0425			0.965491			0.482746	−	0.875761i	$-0.339640\pi$
$389$	19.0425			0.965491			0.482746	+	0.875761i	$0.339640\pi$
$390$	6.96365	+	0.859618i	0.352618	+	0.0435284i
$391$	1.91205			0.0966968
$392$	5.65280	+	1.51466i	0.285510	+	0.0765020i
$393$	5.29992	+	1.42011i	0.267346	+	0.0716350i
$394$	−3.76730	+	6.52516i	−0.189794	+	0.328733i
$395$	3.20698	+	22.9269i	0.161361	+	1.15358i
$396$	−2.50964	+	4.34683i	−0.126114	+	0.218436i
$397$	0.542449	−	2.02445i	0.0272247	−	0.101604i	−0.950977	−	0.309263i	$-0.899918\pi$
$397$	0.542449	−	2.02445i	0.0272247	−	0.101604i	0.978201	+	0.207659i	$0.0665844\pi$
$398$	−4.48742	+	4.48742i	−0.224934	+	0.224934i
$399$	0.302352	+	0.523688i	0.0151365	+	0.0262172i
$400$	1.21591	−	4.84990i	0.0607954	−	0.242495i
$401$	9.89177	−	17.1330i	0.493971	−	0.855583i	−0.506005	−	0.862531i	$-0.668878\pi$
$401$	9.89177	−	17.1330i	0.493971	−	0.855583i	0.999976	+	0.00694735i	$0.00221143\pi$
$402$	7.40305	−	1.98364i	0.369230	−	0.0989350i
$403$	14.0633	−	14.0633i	0.700543	−	0.700543i
$404$	−15.1423	−	8.74242i	−0.753358	−	0.434951i
$405$	3.36801	−	8.32056i	0.167358	−	0.413452i
$406$	9.22598	−	5.32662i	0.457877	−	0.264356i
$407$	34.6528	+	9.28520i	1.71768	+	0.460250i
$408$	−6.72903	+	6.72903i	−0.333136	+	0.333136i
$409$	−25.4407			−1.25796			−0.628981	−	0.777421i	$-0.716528\pi$
$409$	−25.4407			−1.25796			−0.628981	+	0.777421i	$0.716528\pi$
$410$	10.0566	+	1.24142i	0.496659	+	0.0613093i
$411$	14.4135	+	24.9648i	0.710963	+	1.23142i
$412$	−14.7793	+	3.96011i	−0.728126	+	0.195101i
$413$	8.62262	−	2.31042i	0.424291	−	0.113689i
$414$	−0.321661			−0.0158088
$415$	13.9801	+	32.9946i	0.686256	+	1.61964i
$416$	2.01984	+	1.16616i	0.0990308	+	0.0571755i
$417$	−0.835926	−	3.11972i	−0.0409355	−	0.152773i
$418$	−1.70935	−	0.458019i	−0.0836070	−	0.0224024i
$419$	27.1947			1.32855			0.664274	−	0.747489i	$-0.268741\pi$
$419$	27.1947			1.32855			0.664274	+	0.747489i	$0.268741\pi$
$420$	−2.54108	+	1.98265i	−0.123992	+	0.0967435i
$421$	−11.7142	−	6.76322i	−0.570918	−	0.329619i	0.186598	−	0.982436i	$-0.440254\pi$
$421$	−11.7142	−	6.76322i	−0.570918	−	0.329619i	−0.757516	+	0.652817i	$0.773587\pi$
$422$	11.1398	+	11.1398i	0.542279	+	0.542279i
$423$	3.59755	+	13.4262i	0.174919	+	0.652805i
$424$	3.31394	+	5.73991i	0.160939	+	0.278755i
$425$	0.571309	+	35.3615i	0.0277126	+	1.71529i
$426$		−	7.23592i		−	0.350581i
$427$	1.38292	−	5.16113i	0.0669242	−	0.249765i
$428$	−1.04978	+	1.04978i	−0.0507430	+	0.0507430i
$429$	13.2361			0.639047
$430$	−3.10159	+	14.3311i	−0.149572	+	0.691107i
$431$	−25.7714			−1.24136			−0.620682	−	0.784063i	$-0.713144\pi$
$431$	−25.7714			−1.24136			−0.620682	+	0.784063i	$0.713144\pi$
$432$	3.98602	−	3.98602i	0.191778	−	0.191778i
$433$	7.73667	−	28.8736i	0.371801	−	1.38758i	−0.486163	−	0.873868i	$-0.661604\pi$
$433$	7.73667	−	28.8736i	0.371801	−	1.38758i	0.857964	−	0.513710i	$-0.171729\pi$
$434$			9.13582i			0.438533i
$435$	3.66496	−	29.6893i	0.175721	−	1.42350i
$436$	−3.32215	−	5.75414i	−0.159102	−	0.275573i
$437$	−0.0293522	−	0.109544i	−0.00140410	−	0.00524019i
$438$	−0.884828	−	0.884828i	−0.0422787	−	0.0422787i
$439$	1.07864	+	0.622754i	0.0514807	+	0.0297224i	0.525519	−	0.850782i	$-0.323871\pi$
$439$	1.07864	+	0.622754i	0.0514807	+	0.0297224i	−0.474039	+	0.880504i	$0.657204\pi$
$440$	1.15557	−	9.36109i	0.0550895	−	0.446273i
$441$	6.96364			0.331602
$442$	−15.9348	−	4.26973i	−0.757943	−	0.203090i
$443$	−1.88558	−	7.03709i	−0.0895867	−	0.334342i	0.906557	−	0.422084i	$-0.138701\pi$
$443$	−1.88558	−	7.03709i	−0.0895867	−	0.334342i	−0.996143	+	0.0877424i	$0.972035\pi$
$444$	−9.90945	−	5.72122i	−0.470282	−	0.271517i
$445$	−8.96460	+	22.1468i	−0.424963	+	1.04986i
$446$	−10.5447			−0.499305
$447$	−3.69041	+	0.988843i	−0.174551	+	0.0467707i
$448$	−1.03484	+	0.277286i	−0.0488918	+	0.0131005i
$449$	−16.1624	−	27.9940i	−0.762749	−	1.32112i	−0.941428	−	0.337213i	$-0.890516\pi$
$449$	−16.1624	−	27.9940i	−0.762749	−	1.32112i	0.178679	−	0.983907i	$-0.442818\pi$
$450$	−0.0961103	−	5.94880i	−0.00453068	−	0.280429i
$451$	19.1150			0.900091
$452$	−0.627664	+	0.627664i	−0.0295228	+	0.0295228i
$453$	−3.40711	−	0.912932i	−0.160080	−	0.0428933i
$454$	−12.1814	+	7.03295i	−0.571702	+	0.330073i
$455$	−5.17910	−	2.09641i	−0.242800	−	0.0982810i
$456$	0.488811	+	0.282215i	0.0228907	+	0.0132159i
$457$	−17.7068	+	17.7068i	−0.828288	+	0.828288i	−0.987280	−	0.158992i	$-0.949176\pi$
$457$	−17.7068	+	17.7068i	−0.828288	+	0.828288i	0.158992	+	0.987280i	$0.449176\pi$
$458$	20.7270	−	5.55379i	0.968510	−	0.259512i
$459$	−19.9362	+	34.5305i	−0.930542	+	1.61175i
$460$	0.556562	−	0.235820i	0.0259498	−	0.0109952i
$461$	8.79501	+	15.2334i	0.409624	+	0.709490i	0.994848	−	0.101382i	$-0.0323264\pi$
$461$	8.79501	+	15.2334i	0.409624	+	0.709490i	−0.585223	+	0.810872i	$0.698993\pi$
$462$	−4.29924	+	4.29924i	−0.200019	+	0.200019i
$463$	2.01366	−	7.51509i	0.0935829	−	0.349256i	−0.903218	−	0.429182i	$-0.858802\pi$
$463$	2.01366	−	7.51509i	0.0935829	−	0.349256i	0.996801	+	0.0799262i	$0.0254685\pi$
$464$	4.97188	−	8.61154i	0.230814	−	0.399781i
$465$	20.4780	+	15.4521i	0.949642	+	0.716574i
$466$	2.86389	−	4.96040i	0.132667	−	0.229786i
$467$	−16.7035	−	4.47568i	−0.772944	−	0.207110i	−0.149272	−	0.988796i	$-0.547693\pi$
$467$	−16.7035	−	4.47568i	−0.772944	−	0.207110i	−0.623672	+	0.781686i	$0.714360\pi$
$468$	2.68069	+	0.718288i	0.123915	+	0.0332029i
$469$	−6.10307			−0.281814
$470$	−16.0679	−	20.5935i	−0.741158	−	0.949909i
$471$	10.6751			0.491884
$472$	5.89181	−	5.89181i	0.271193	−	0.271193i
$473$	−2.49474	+	27.5478i	−0.114708	+	1.26665i
$474$		−	13.9289i		−	0.639775i
$475$	2.01713	−	0.575570i	0.0925524	−	0.0264090i
$476$	6.56266	−	3.78895i	0.300799	−	0.173666i
$477$	5.57668	+	5.57668i	0.255339	+	0.255339i
$478$	−1.86324	+	6.95372i	−0.0852228	+	0.318056i
$479$	−17.7639	+	10.2560i	−0.811652	+	0.468607i	−0.847529	−	0.530749i	$-0.821911\pi$
$479$	−17.7639	+	10.2560i	−0.811652	+	0.468607i	0.0358773	+	0.999356i	$0.488577\pi$
$480$	−1.12877	+	2.78860i	−0.0515213	+	0.127282i
$481$		−	19.8361i		−	0.904447i
$482$	10.0837	−	2.70192i	0.459299	−	0.123069i
$483$	−0.376363	−	0.100846i	−0.0171251	−	0.00458866i
$484$		−	6.79308i		−	0.308776i
$485$	−4.15534	+	33.6618i	−0.188684	+	1.52850i
$486$	5.75519	−	9.96828i	0.261061	−	0.452170i
$487$	9.35667	−	2.50711i	0.423991	−	0.113608i	−0.0405131	−	0.999179i	$-0.512899\pi$
$487$	9.35667	−	2.50711i	0.423991	−	0.113608i	0.464504	+	0.885571i	$0.346233\pi$
$488$	−1.29082	−	4.81741i	−0.0584327	−	0.218074i
$489$		−	19.0876i		−	0.863170i
$490$	−12.0490	+	5.10526i	−0.544318	+	0.230632i
$491$	3.94427	+	2.27722i	0.178002	+	0.102770i	0.586354	−	0.810055i	$-0.300563\pi$
$491$	3.94427	+	2.27722i	0.178002	+	0.102770i	−0.408351	+	0.912825i	$0.633896\pi$
$492$	−5.88901	−	1.57795i	−0.265497	−	0.0711397i
$493$	−18.2039	+	67.9379i	−0.819862	+	3.05977i
$494$			0.978470i			0.0440235i
$495$	−1.55479	−	11.1152i	−0.0698825	−	0.499593i
$496$	4.26369	+	7.38494i	0.191446	+	0.331593i
$497$	−1.49132	+	5.56569i	−0.0668950	+	0.249656i
$498$	−5.58030	−	20.8260i	−0.250059	−	0.933234i
$499$	10.0862	−	17.4698i	0.451521	−	0.782057i	−0.546960	−	0.837159i	$-0.684215\pi$
$499$	10.0862	−	17.4698i	0.451521	−	0.782057i	0.998481	+	0.0551015i	$0.0175482\pi$
$500$	4.52755	+	10.2226i	0.202478	+	0.457168i
$501$	−20.1590	−	11.6388i	−0.900637	−	0.519983i
$502$	2.81013	+	10.4876i	0.125422	+	0.468082i
$503$	−12.2863	+	3.29211i	−0.547820	+	0.146788i	−0.522105	−	0.852881i	$-0.674853\pi$
$503$	−12.2863	+	3.29211i	−0.547820	+	0.146788i	−0.0257153	+	0.999669i	$0.508186\pi$
$504$	−1.10402	+	0.637408i	−0.0491771	+	0.0283924i
$505$	38.7203	−	5.41615i	1.72303	−	0.241016i
$506$	0.987504	−	0.570136i	0.0438999	−	0.0253456i
$507$	2.63261	+	9.82503i	0.116918	+	0.436345i
$508$	−1.11094	+	1.11094i	−0.0492901	+	0.0492901i
$509$	0.576959	+	0.333107i	0.0255732	+	0.0147647i	0.512732	−	0.858549i	$-0.328633\pi$
$509$	0.576959	+	0.333107i	0.0255732	+	0.0147647i	−0.487159	+	0.873313i	$0.661967\pi$
$510$	2.60697	−	21.1187i	0.115439	−	0.935154i
$511$	0.498225	+	0.862951i	0.0220402	+	0.0381747i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	2.28434	+	0.612086i	0.100856	+	0.0270242i
$514$		−	8.49500i		−	0.374698i
$515$	20.6079	−	27.3107i	0.908092	−	1.20345i
$516$	3.04267	−	8.28105i	0.133946	−	0.364553i
$517$	−34.8421	−	34.8421i	−1.53235	−	1.53235i
$518$	6.44297	+	6.44297i	0.283088	+	0.283088i
$519$	−0.156527	−	0.271112i	−0.00687076	−	0.0119005i
$520$	−5.16492	+	0.722463i	−0.226497	+	0.0316821i
$521$	13.4904	−	7.78870i	0.591026	−	0.341229i	−0.174477	−	0.984661i	$-0.555823\pi$
$521$	13.4904	−	7.78870i	0.591026	−	0.341229i	0.765503	+	0.643432i	$0.222490\pi$
$522$	3.06241	−	11.4291i	0.134038	−	0.500236i
$523$	−1.17579	+	0.315051i	−0.0514136	+	0.0137762i	−0.284434	−	0.958696i	$-0.591806\pi$
$523$	−1.17579	+	0.315051i	−0.0514136	+	0.0137762i	0.233021	+	0.972472i	$0.425139\pi$
$524$	−4.07827			−0.178160
$525$	1.75259	−	6.99059i	0.0764895	−	0.305094i
$526$	−14.5236	−	25.1555i	−0.633257	−	1.09683i
$527$	−42.6500	−	42.6500i	−1.85786	−	1.85786i
$528$	−1.46883	+	5.48174i	−0.0639226	+	0.238562i
$529$	−19.8553	−	11.4635i	−0.863274	−	0.498411i
$530$	−13.7376	−	5.56073i	−0.596724	−	0.241543i
$531$	4.95736	−	8.58640i	0.215131	−	0.372618i
$532$	−0.317817	−	0.317817i	−0.0137791	−	0.0137791i
$533$	−2.73547	−	10.2089i	−0.118486	−	0.442197i
$534$	7.18775	−	12.4495i	0.311044	−	0.538744i
$535$	0.406708	−	3.29469i	0.0175835	−	0.142442i
$536$	−4.93342	+	2.84831i	−0.213091	+	0.123028i
$537$	−9.57251	−	9.57251i	−0.413084	−	0.413084i
$538$	−5.23436	−	5.23436i	−0.225669	−	0.225669i
$539$	−21.3784	+	12.3428i	−0.920835	+	0.531644i
$540$	−1.54427	+	12.5100i	−0.0664550	+	0.538343i
$541$	−17.8348	+	30.8908i	−0.766778	+	1.32810i	0.172523	+	0.985005i	$0.444808\pi$
$541$	−17.8348	+	30.8908i	−0.766778	+	1.32810i	−0.939301	+	0.343093i	$0.888525\pi$
$542$	−7.15792	−	26.7137i	−0.307459	−	1.14745i
$543$	2.82990	+	2.82990i	0.121443	+	0.121443i
$544$	3.53661	−	6.12560i	0.151631	−	0.262633i
$545$	13.7717	+	5.57452i	0.589913	+	0.238786i
$546$	2.91137	+	1.68088i	0.124595	+	0.0719351i
$547$	−4.70154	+	17.5464i	−0.201023	+	0.750230i	0.789602	+	0.613620i	$0.210287\pi$
$547$	−4.70154	+	17.5464i	−0.201023	+	0.750230i	−0.990625	+	0.136610i	$0.956379\pi$
$548$	−15.1507	−	15.1507i	−0.647207	−	0.647207i
$549$	−2.96726	−	5.13945i	−0.126640	−	0.219346i
$550$	10.8391	+	18.0925i	0.462183	+	0.771468i
$551$	4.17169			0.177720
$552$	−0.351298	+	0.0941300i	−0.0149522	+	0.00400644i
$553$	−2.87075	+	10.7138i	−0.122077	+	0.455596i
$554$	−10.8868	+	6.28549i	−0.462535	+	0.267045i
$555$	25.3394	−	3.54444i	1.07560	−	0.150453i
$556$	1.20031	+	2.07899i	0.0509043	+	0.0881689i
$557$	11.9019	+	11.9019i	0.504299	+	0.504299i	0.912771	−	0.408472i	$-0.133938\pi$
$557$	11.9019	+	11.9019i	0.504299	+	0.504299i	−0.408472	+	0.912771i	$0.633938\pi$
$558$	7.17492	+	7.17492i	0.303739	+	0.303739i
$559$	15.0697	−	2.60986i	0.637378	−	0.110385i
$560$	1.44296	−	1.91228i	0.0609761	−	0.0808087i
$561$		−	40.1414i		−	1.69477i
$562$	18.4058	+	4.93182i	0.776402	+	0.208036i
$563$	−2.02318	+	2.02318i	−0.0852670	+	0.0852670i	−0.748454	−	0.663187i	$-0.769203\pi$
$563$	−2.02318	+	2.02318i	−0.0852670	+	0.0852670i	0.663187	+	0.748454i	$0.269203\pi$
$564$	7.85802	+	13.6105i	0.330882	+	0.573105i
$565$	0.243171	−	1.96990i	0.0102303	−	0.0828741i
$566$	0.797524	+	0.460451i	0.0335224	+	0.0193542i
$567$	3.04111	−	3.04111i	0.127715	−	0.127715i
$568$	1.39200	+	5.19503i	0.0584072	+	0.217979i
$569$	−34.5980	+	19.9752i	−1.45042	+	0.837403i	−0.998505	−	0.0546557i	$-0.982594\pi$
$569$	−34.5980	+	19.9752i	−1.45042	+	0.837403i	−0.451919	+	0.892059i	$0.649261\pi$
$570$	−1.24994	+	0.174840i	−0.0523541	+	0.00732323i
$571$	9.35306	−	5.39999i	0.391413	−	0.225983i	−0.291359	−	0.956614i	$-0.594107\pi$
$571$	9.35306	−	5.39999i	0.391413	−	0.225983i	0.682772	+	0.730631i	$0.260774\pi$
$572$	−9.50289	+	2.54629i	−0.397336	+	0.106466i
$573$	3.72719	+	13.9101i	0.155705	+	0.581101i
$574$	4.20447	+	2.42745i	0.175491	+	0.101320i
$575$	−0.656810	+	1.18130i	−0.0273909	+	0.0492634i
$576$	−0.594958	+	1.03050i	−0.0247899	+	0.0429374i
$577$	−2.82316	−	10.5362i	−0.117530	−	0.438627i	0.881934	−	0.471373i	$-0.156241\pi$
$577$	−2.82316	−	10.5362i	−0.117530	−	0.438627i	−0.999464	+	0.0327462i	$0.989575\pi$
$578$	−8.54894	+	31.9051i	−0.355589	+	1.32708i
$579$	−2.61377	−	4.52717i	−0.108624	−	0.188143i
$580$	3.08020	+	22.0205i	0.127899	+	0.914352i
$581$			17.1689i			0.712288i
$582$	5.28180	−	19.7120i	0.218938	−	0.817087i
$583$	−27.0050	−	7.23596i	−1.11843	−	0.299683i
$584$	0.805480	+	0.465044i	0.0333310	+	0.0192437i
$585$	−5.71391	+	2.42103i	−0.236241	+	0.100097i
$586$		−	19.5707i		−	0.808458i
$587$	−3.97804	−	14.8462i	−0.164191	−	0.612770i	−0.998142	−	0.0609311i	$-0.980593\pi$
$587$	−3.97804	−	14.8462i	−0.164191	−	0.612770i	0.833951	−	0.551839i	$-0.186074\pi$
$588$	7.60524	−	2.03782i	0.313635	−	0.0840382i
$589$	−1.78874	+	3.09819i	−0.0737038	+	0.127659i
$590$	−2.28262	+	18.4912i	−0.0939740	+	0.761271i
$591$			10.1370i			0.416981i
$592$	8.21511	+	2.20123i	0.337639	+	0.0904701i
$593$	−30.4788	+	8.16677i	−1.25161	+	0.335369i	−0.822960	−	0.568099i	$-0.807679\pi$
$593$	−30.4788	+	8.16677i	−1.25161	+	0.335369i	−0.428654	+	0.903469i	$0.641012\pi$
$594$			23.7783i			0.975634i
$595$	−6.35780	+	15.7067i	−0.260644	+	0.643913i
$596$	2.45931	−	1.41988i	0.100737	−	0.0581606i
$597$	−2.20982	+	8.24716i	−0.0904419	+	0.337534i
$598$	−0.445814	−	0.445814i	−0.0182307	−	0.0182307i
$599$	16.1227	−	9.30845i	0.658756	−	0.380333i	−0.133047	−	0.991110i	$-0.542476\pi$
$599$	16.1227	−	9.30845i	0.658756	−	0.380333i	0.791803	+	0.610777i	$0.209143\pi$
$600$	−1.84581	−	6.46878i	−0.0753547	−	0.264087i
$601$		−	40.8342i		−	1.66566i	−0.553527	−	0.832831i	$-0.686719\pi$
$601$		−	40.8342i		−	1.66566i	0.553527	−	0.832831i	$-0.313281\pi$
$602$	−4.04707	+	5.74249i	−0.164946	+	0.234046i
$603$	−4.79312	+	4.79312i	−0.195191	+	0.195191i
$604$	2.62176			0.106678
$605$	9.34399	+	11.9758i	0.379887	+	0.486885i
$606$	−23.5240			−0.955596
$607$	6.56457	+	1.75897i	0.266448	+	0.0713945i	0.389569	−	0.920997i	$-0.372624\pi$
$607$	6.56457	+	1.75897i	0.266448	+	0.0713945i	−0.123122	+	0.992392i	$0.539291\pi$
$608$	−0.405233	−	0.108582i	−0.0164344	−	0.00440358i
$609$	7.16640	−	12.4126i	0.290397	−	0.502983i
$610$	8.90206	+	6.71725i	0.360434	+	0.271973i
$611$	−13.6223	+	23.5945i	−0.551099	+	0.954531i
$612$	2.17836	−	8.12976i	0.0880551	−	0.328626i
$613$	2.07330	−	2.07330i	0.0837398	−	0.0837398i	−0.663996	−	0.747736i	$-0.731141\pi$
$613$	2.07330	−	2.07330i	0.0837398	−	0.0837398i	0.747736	+	0.663996i	$0.231141\pi$
$614$	5.11896	+	8.86630i	0.206585	+	0.357815i
$615$	12.5525	−	5.31859i	0.506164	−	0.214466i
$616$	2.25958	−	3.91370i	0.0910409	−	0.157687i
$617$	12.4796	−	3.34389i	0.502408	−	0.134620i	0.00129093	−	0.999999i	$-0.499589\pi$
$617$	12.4796	−	3.34389i	0.502408	−	0.134620i	0.501118	+	0.865379i	$0.332922\pi$
$618$	−14.5561	+	14.5561i	−0.585533	+	0.585533i
$619$	7.13348	+	4.11852i	0.286719	+	0.165537i	0.636461	−	0.771309i	$-0.280398\pi$
$619$	7.13348	+	4.11852i	0.286719	+	0.165537i	−0.349742	+	0.936846i	$0.613731\pi$
$620$	−17.6747	−	7.15441i	−0.709835	−	0.287328i
$621$	−1.31968	+	0.761916i	−0.0529568	+	0.0305746i
$622$	13.9077	+	3.72657i	0.557650	+	0.149422i
$623$	−8.09449	+	8.09449i	−0.324299	+	0.324299i
$624$	3.13788			0.125616
$625$	−22.0431	−	11.7941i	−0.881725	−	0.471763i
$626$	8.88105	+	15.3824i	0.354958	+	0.614806i
$627$	−2.29975	+	0.616215i	−0.0918431	+	0.0246093i
$628$	−7.66421	+	2.05362i	−0.305835	+	0.0819483i
$629$	−60.1571			−2.39862
$630$	1.06956	−	2.64231i	0.0426123	−	0.105272i
$631$	18.6254	+	10.7534i	0.741465	+	0.428085i	0.822602	−	0.568618i	$-0.192522\pi$
$631$	18.6254	+	10.7534i	0.741465	+	0.428085i	−0.0811367	+	0.996703i	$0.525855\pi$
$632$	2.67956	+	10.0003i	0.106587	+	0.397789i
$633$	20.4733	+	5.48580i	0.813739	+	0.218041i
$634$	7.00210			0.278089
$635$	0.430404	−	3.48664i	0.0170801	−	0.138363i
$636$	7.72244	+	4.45855i	0.306215	+	0.176793i
$637$	9.65142	+	9.65142i	0.382403	+	0.382403i
$638$	10.8561	+	40.5154i	0.429795	+	1.60402i
$639$	3.19986	+	5.54231i	0.126584	+	0.219251i
$640$	0.273949	−	2.21922i	0.0108288	−	0.0877225i
$641$			27.3640i			1.08081i	0.841404	+	0.540407i	$0.181730\pi$
$641$			27.3640i			1.08081i	−0.841404	+	0.540407i	$0.818270\pi$
$642$	−0.516962	+	1.92933i	−0.0204029	+	0.0761445i
$643$	−9.68538	+	9.68538i	−0.381954	+	0.381954i	−0.871806	−	0.489852i	$-0.837051\pi$
$643$	−9.68538	+	9.68538i	−0.381954	+	0.381954i	0.489852	+	0.871806i	$0.337051\pi$
$644$	0.289610			0.0114122
$645$	6.02668	+	18.7842i	0.237300	+	0.739628i
$646$	2.96742			0.116752
$647$	23.6687	−	23.6687i	0.930514	−	0.930514i	−0.0672237	−	0.997738i	$-0.521414\pi$
$647$	23.6687	−	23.6687i	0.930514	−	0.930514i	0.997738	+	0.0672237i	$0.0214141\pi$
$648$	1.03899	−	3.87757i	0.0408154	−	0.152325i
$649$			35.1471i			1.37964i
$650$	8.11168	−	8.37809i	0.318166	−	0.328616i
$651$	6.14564	+	10.6446i	0.240867	+	0.417193i
$652$	3.67196	+	13.7039i	0.143805	+	0.536687i
$653$	−8.63401	−	8.63401i	−0.337875	−	0.337875i	0.517692	−	0.855567i	$-0.326791\pi$
$653$	−8.63401	−	8.63401i	−0.337875	−	0.337875i	−0.855567	+	0.517692i	$0.826791\pi$
$654$	−7.74158	−	4.46960i	−0.302720	−	0.174775i
$655$	7.18974	−	5.60973i	0.280927	−	0.219190i
$656$	4.53157			0.176928
$657$	1.06902	+	0.286442i	0.0417063	+	0.0111752i
$658$	−3.23908	−	12.0884i	−0.126272	−	0.471255i
$659$	18.4122	+	10.6303i	0.717237	+	0.414097i	0.813735	−	0.581236i	$-0.197431\pi$
$659$	18.4122	+	10.6303i	0.717237	+	0.414097i	−0.0964980	+	0.995333i	$0.530764\pi$
$660$	−4.95077	−	11.6844i	−0.192709	−	0.454814i
$661$	27.2110			1.05838			0.529192	−	0.848502i	$-0.322495\pi$
$661$	27.2110			1.05838			0.529192	+	0.848502i	$0.322495\pi$
$662$	−8.46361	+	2.26782i	−0.328948	+	0.0881413i
$663$	−21.4386	+	5.74447i	−0.832608	+	0.223097i
$664$	8.01276	+	13.8785i	0.310955	+	0.538591i
$665$	0.997456	+	0.123130i	0.0386797	+	0.00477476i
$666$	10.1201			0.392147
$667$	−1.90072	+	1.90072i	−0.0735961	+	0.0735961i
$668$	16.7122	+	4.47801i	0.646613	+	0.173259i
$669$	−12.2861	+	7.09337i	−0.475007	+	0.274246i
$670$	4.77942	−	11.8074i	0.184645	−	0.456159i
$671$	18.2190	+	10.5188i	0.703339	+	0.406073i
$672$	−1.01921	+	1.01921i	−0.0393171	+	0.0393171i
$673$	−14.1119	+	3.78128i	−0.543975	+	0.145758i	−0.520334	−	0.853963i	$-0.674192\pi$
$673$	−14.1119	+	3.78128i	−0.543975	+	0.145758i	−0.0236409	+	0.999721i	$0.507526\pi$
$674$	−6.69573	+	11.5973i	−0.257910	+	0.446713i
$675$	−14.4852	−	24.1785i	−0.557535	−	0.930629i
$676$	−3.78016	−	6.54744i	−0.145391	−	0.251825i
$677$	−11.0390	+	11.0390i	−0.424263	+	0.424263i	−0.886668	−	0.462406i	$-0.846986\pi$
$677$	−11.0390	+	11.0390i	−0.424263	+	0.424263i	0.462406	+	0.886668i	$0.346986\pi$
$678$	−0.309092	+	1.15355i	−0.0118706	+	0.0443017i
$679$	−8.12528	+	14.0734i	−0.311819	+	0.540087i
$680$	2.19102	+	15.6637i	0.0840219	+	0.600676i
$681$	−9.46208	+	16.3888i	−0.362588	+	0.628020i
$682$	−34.7445	−	9.30975i	−1.33043	−	0.356489i
$683$	−32.6052	−	8.73654i	−1.24760	−	0.334294i	−0.426193	−	0.904632i	$-0.640146\pi$
$683$	−32.6052	−	8.73654i	−1.24760	−	0.334294i	−0.821410	+	0.570338i	$0.806812\pi$
$684$	−0.499203			−0.0190875
$685$	47.5499	+	5.86973i	1.81679	+	0.224271i
$686$	−13.7692			−0.525711
$687$	20.4140	−	20.4140i	0.778842	−	0.778842i
$688$	−0.591424	+	6.53071i	−0.0225478	+	0.248981i
$689$			15.4583i			0.588913i
$690$	0.489840	−	0.649162i	0.0186479	−	0.0247132i
$691$	−1.84214	+	1.06356i	−0.0700784	+	0.0404598i	−0.534630	−	0.845086i	$-0.679549\pi$
$691$	−1.84214	+	1.06356i	−0.0700784	+	0.0404598i	0.464551	+	0.885546i	$0.346216\pi$
$692$	0.164533	+	0.164533i	0.00625462	+	0.00625462i
$693$	1.39178	−	5.19418i	0.0528692	−	0.197311i
$694$	16.7458	−	9.66820i	0.635663	−	0.367000i
$695$	−4.97575	−	2.01409i	−0.188741	−	0.0763989i
$696$		−	13.3783i		−	0.507102i
$697$	−30.9607	+	8.29589i	−1.17272	+	0.314229i
$698$	0.0948766	+	0.0254221i	0.00359113	+	0.000962241i
$699$		−	7.70611i		−	0.291472i
$700$	0.0865336	+	5.35605i	0.00327066	+	0.202440i
$701$	−17.3322	+	30.0202i	−0.654628	+	1.13385i	0.327359	+	0.944900i	$0.393841\pi$
$701$	−17.3322	+	30.0202i	−0.654628	+	1.13385i	−0.981987	+	0.188949i	$0.939492\pi$
$702$	12.6994	−	3.40281i	0.479310	−	0.128431i
$703$	0.923479	+	3.44647i	0.0348297	+	0.129986i
$704$		−	4.21818i		−	0.158979i
$705$	−32.5747	−	13.1856i	−1.22683	−	0.496600i
$706$	3.24785	+	1.87515i	0.122234	+	0.0705721i
$707$	18.0941	+	4.84830i	0.680498	+	0.182339i
$708$	2.90141	−	10.8282i	0.109042	−	0.406950i
$709$			52.1541i			1.95869i	0.202201	+	0.979344i	$0.435190\pi$
$709$			52.1541i			1.95869i	−0.202201	+	0.979344i	$0.564810\pi$
$710$	−9.59987	−	7.24380i	−0.360277	−	0.271855i
$711$	6.15961	+	10.6688i	0.231003	+	0.400110i
$712$	−2.76547	+	10.3209i	−0.103641	+	0.386792i
$713$	−0.596616	−	2.22660i	−0.0223434	−	0.0833869i
$714$	5.09763	−	8.82936i	0.190774	−	0.330430i
$715$	13.2505	−	17.5603i	0.495542	−	0.656719i
$716$	8.71409	+	5.03108i	0.325661	+	0.188020i
$717$	2.50680	+	9.35550i	0.0936181	+	0.349387i
$718$	30.0432	−	8.05004i	1.12120	−	0.300425i
$719$	31.1248	−	17.9699i	1.16076	−	0.670165i	0.209274	−	0.977857i	$-0.432890\pi$
$719$	31.1248	−	17.9699i	1.16076	−	0.670165i	0.951486	+	0.307691i	$0.0995565\pi$
$720$	−0.368592	−	2.63508i	−0.0137366	−	0.0982036i
$721$	14.1962	−	8.19621i	0.528696	−	0.305243i
$722$	4.87201	+	18.1826i	0.181317	+	0.676686i
$723$	9.93139	−	9.93139i	0.369352	−	0.369352i
$724$	−2.57613	−	1.48733i	−0.0957411	−	0.0552762i
$725$	−35.7198	−	34.5840i	−1.32660	−	1.28442i
$726$	−4.56968	−	7.91492i	−0.169597	−	0.293750i
$727$	−26.2504	+	26.2504i	−0.973572	+	0.973572i	−0.999660	−	0.0260875i	$-0.991695\pi$
$727$	−26.2504	+	26.2504i	−0.973572	+	0.973572i	0.0260875	+	0.999660i	$0.491695\pi$
$728$	−2.41358	−	0.646716i	−0.0894532	−	0.0239689i
$729$		−	27.5290i		−	1.01959i
$730$	−2.05969	+	0.288107i	−0.0762325	+	0.0106633i
$731$	−7.91495	−	45.7020i	−0.292745	−	1.69035i
$732$	−4.74465	−	4.74465i	−0.175367	−	0.175367i
$733$	−12.7683	−	12.7683i	−0.471607	−	0.471607i	0.430827	−	0.902434i	$-0.358222\pi$
$733$	−12.7683	−	12.7683i	−0.471607	−	0.471607i	−0.902434	+	0.430827i	$0.858222\pi$
$734$	−8.32061	−	14.4117i	−0.307119	−	0.531947i
$735$	−10.6045	+	14.0537i	−0.391154	+	0.518378i
$736$	0.234106	−	0.135161i	0.00862927	−	0.00498211i
$737$	6.21926	−	23.2106i	0.229090	−	0.854974i
$738$	5.20845	−	1.39560i	0.191726	−	0.0513728i
$739$	28.1544			1.03568			0.517838	−	0.855479i	$-0.326737\pi$
$739$	28.1544			1.03568			0.517838	+	0.855479i	$0.326737\pi$
$740$	−17.5106	+	7.41938i	−0.643701	+	0.272742i
$741$	0.658214	+	1.14006i	0.0241801	+	0.0418811i
$742$	−5.02101	−	5.02101i	−0.184327	−	0.184327i
$743$	10.4169	−	38.8764i	0.382159	−	1.42624i	−0.460437	−	0.887692i	$-0.652307\pi$
$743$	10.4169	−	38.8764i	0.382159	−	1.42624i	0.842596	−	0.538546i	$-0.181026\pi$
$744$	9.93565	+	5.73635i	0.364258	+	0.210305i
$745$	−2.38254	+	5.88598i	−0.0872894	+	0.215646i
$746$	−12.1627	+	21.0665i	−0.445309	+	0.771298i
$747$	13.4838	+	13.4838i	0.493348	+	0.493348i
$748$	7.72217	+	28.8195i	0.282351	+	1.05375i
$749$	0.795270	−	1.37745i	0.0290585	−	0.0503308i
$750$	12.1520	+	8.86513i	0.443727	+	0.323709i
$751$	27.0360	−	15.6092i	0.986558	−	0.569589i	0.0823140	−	0.996606i	$-0.473769\pi$
$751$	27.0360	−	15.6092i	0.986558	−	0.569589i	0.904244	+	0.427017i	$0.140436\pi$
$752$	−8.25998	−	8.25998i	−0.301210	−	0.301210i
$753$	10.3292	+	10.3292i	0.376415	+	0.376415i
$754$	20.0848	−	11.5960i	0.731445	−	0.422300i
$755$	−4.62200	+	3.60627i	−0.168212	+	0.131246i
$756$	−3.01965	+	5.23018i	−0.109823	+	0.190220i
$757$	−10.5556	−	39.3940i	−0.383650	−	1.43180i	−0.840284	−	0.542146i	$-0.817612\pi$
$757$	−10.5556	−	39.3940i	−0.383650	−	1.43180i	0.456634	−	0.889655i	$-0.349055\pi$
$758$	9.37303	+	9.37303i	0.340444	+	0.340444i
$759$	0.767057	−	1.32858i	0.0278424	−	0.0482244i
$760$	0.863758	−	0.365982i	0.0313318	−	0.0132756i
$761$	−37.4175	−	21.6030i	−1.35638	−	0.783108i	−0.367248	−	0.930123i	$-0.619700\pi$
$761$	−37.4175	−	21.6030i	−1.35638	−	0.783108i	−0.989134	+	0.147015i	$0.953033\pi$
$762$	−0.547082	+	2.04174i	−0.0198187	+	0.0739643i
$763$	5.03345	+	5.03345i	0.182223	+	0.182223i
$764$	−5.35187	−	9.26971i	−0.193624	−	0.335366i
$765$	7.34230	+	17.3286i	0.265461	+	0.626519i
$766$	−20.0784			−0.725464
$767$	18.7713	−	5.02975i	0.677792	−	0.181614i
$768$	−0.348214	+	1.29955i	−0.0125651	+	0.0468935i
$769$	−47.0075	+	27.1398i	−1.69513	+	0.978686i	−0.744886	+	0.667192i	$0.767496\pi$
$769$	−47.0075	+	27.1398i	−1.69513	+	0.978686i	−0.950248	+	0.311495i	$0.899170\pi$
$770$	1.39987	+	10.0077i	0.0504476	+	0.360652i
$771$	−5.71456	−	9.89790i	−0.205805	−	0.356464i
$772$	2.74746	+	2.74746i	0.0988834	+	0.0988834i
$773$	14.0608	+	14.0608i	0.505730	+	0.505730i	0.913213	−	0.407483i	$-0.133593\pi$
$773$	14.0608	+	14.0608i	0.505730	+	0.505730i	−0.407483	+	0.913213i	$0.633593\pi$
$774$	1.33152	+	7.68835i	0.0478604	+	0.276352i
$775$	41.0005	−	11.6991i	1.47278	−	0.420244i
$776$			15.1683i			0.544510i
$777$	11.8412	+	3.17283i	0.424799	+	0.113825i
$778$	−13.4651	+	13.4651i	−0.482746	+	0.482746i
$779$	0.950562	+	1.64642i	0.0340574	+	0.0589892i
$780$	−5.53188	+	4.31620i	−0.198073	+	0.154545i
$781$	−19.6472	−	11.3433i	−0.703032	−	0.405896i
$782$	−1.35203	+	1.35203i	−0.0483484	+	0.0483484i
$783$	−14.5078	−	54.1438i	−0.518466	−	1.93494i
$784$	−5.06816	+	2.92610i	−0.181006	+	0.104504i
$785$	10.6867	−	14.1627i	0.381426	−	0.505487i
$786$	−4.75178	+	2.74344i	−0.169490	+	0.0978553i
$787$	30.6940	−	8.22442i	1.09412	−	0.293169i	0.333753	−	0.942661i	$-0.391685\pi$
$787$	30.6940	−	8.22442i	1.09412	−	0.293169i	0.760369	+	0.649492i	$0.225018\pi$
$788$	−1.95010	−	7.27787i	−0.0694694	−	0.259263i
$789$	−33.8441	−	19.5399i	−1.20488	−	0.695639i
$790$	−18.4794	−	13.9441i	−0.657468	−	0.496107i
$791$	0.475492	−	0.823577i	0.0169066	−	0.0292830i
$792$	−1.29909	−	4.84826i	−0.0461610	−	0.172275i
$793$	3.01059	−	11.2357i	0.106909	−	0.398991i
$794$	1.04793	+	1.81507i	0.0371897	+	0.0644144i
$795$	−19.7470	+	2.76219i	−0.700354	+	0.0979647i
$796$		−	6.34616i		−	0.224934i
$797$	9.74991	−	36.3872i	0.345359	−	1.28890i	−0.546832	−	0.837242i	$-0.684166\pi$
$797$	9.74991	−	36.3872i	0.345359	−	1.28890i	0.892192	−	0.451657i	$-0.149167\pi$
$798$	−0.584098	−	0.156509i	−0.0206769	−	0.00554035i
$799$	71.5554	+	41.3125i	2.53145	+	1.46153i
$800$	2.56962	+	4.28918i	0.0908499	+	0.151645i
$801$			12.7142i			0.449235i
$802$	5.12036	+	19.1094i	0.180806	+	0.674777i
$803$	−3.78960	+	1.01542i	−0.133732	+	0.0358334i
$804$	−3.83210	+	6.63739i	−0.135148	+	0.234083i
$805$	−0.510565	+	0.398364i	−0.0179951	+	0.0140405i
$806$			19.8885i			0.700543i
$807$	−9.61992	−	2.57765i	−0.338637	−	0.0907376i
$808$	16.8891	−	4.52541i	0.594155	−	0.159203i
$809$		−	39.6266i		−	1.39320i	−0.717461	−	0.696599i	$-0.754696\pi$
$809$		−	39.6266i		−	1.39320i	0.717461	−	0.696599i	$-0.245304\pi$
$810$	3.50198	+	8.26506i	0.123047	+	0.290405i
$811$	0.00538454	−	0.00310877i	0.000189077	−	0.000109164i	−0.499905	−	0.866080i	$-0.666632\pi$
$811$	0.00538454	−	0.00310877i	0.000189077	−	0.000109164i	0.500095	+	0.865971i	$0.333299\pi$
$812$	−2.75726	+	10.2902i	−0.0967609	+	0.361117i
$813$	−26.3102	−	26.3102i	−0.922741	−	0.922741i
$814$	−31.0689	+	17.9376i	−1.08896	+	0.628714i
$815$	−25.3234	−	19.1083i	−0.887040	−	0.669336i
$816$		−	9.51628i		−	0.333136i
$817$	−2.49681	+	1.15503i	−0.0873524	+	0.0404095i
$818$	17.9893	−	17.9893i	0.628981	−	0.628981i
$819$	−2.97327			−0.103894
$820$	−7.98889	+	6.23325i	−0.278984	+	0.217675i
$821$	−7.29753			−0.254685			−0.127343	−	0.991859i	$-0.540645\pi$
$821$	−7.29753			−0.254685			−0.127343	+	0.991859i	$0.540645\pi$
$822$	−27.8447	−	7.46095i	−0.971194	−	0.260231i
$823$	−2.21657	−	0.593929i	−0.0772649	−	0.0207031i	0.219979	−	0.975504i	$-0.429401\pi$
$823$	−2.21657	−	0.593929i	−0.0772649	−	0.0207031i	−0.297244	+	0.954801i	$0.596068\pi$
$824$	7.65035	−	13.2508i	0.266513	−	0.461613i
$825$	24.8000	+	13.7890i	0.863424	+	0.480070i
$826$	−4.46340	+	7.73083i	−0.155301	+	0.268990i
$827$	−10.0943	+	37.6726i	−0.351014	+	1.31000i	0.534412	+	0.845224i	$0.320533\pi$
$827$	−10.0943	+	37.6726i	−0.351014	+	1.31000i	−0.885427	+	0.464779i	$0.846134\pi$
$828$	0.227449	−	0.227449i	0.00790439	−	0.00790439i
$829$	10.4356	+	18.0749i	0.362442	+	0.627767i	0.988362	−	0.152119i	$-0.0486099\pi$
$829$	10.4356	+	18.0749i	0.362442	+	0.627767i	−0.625920	+	0.779887i	$0.715277\pi$
$830$	−33.2161	−	13.4453i	−1.15295	−	0.466693i
$831$	−8.45645	+	14.6470i	−0.293351	+	0.508099i
$832$	−2.25284	+	0.603646i	−0.0781031	+	0.0209277i
$833$	29.2700	−	29.2700i	1.01415	−	1.01415i
$834$	2.79706	+	1.61488i	0.0968543	+	0.0559189i
$835$	−35.6221	+	15.0934i	−1.23275	+	0.522328i
$836$	1.53256	−	0.884824i	0.0530047	−	0.0306023i
$837$	46.4317	+	12.4413i	1.60491	+	0.430036i
$838$	−19.2296	+	19.2296i	−0.664274	+	0.664274i
$839$	−45.2046			−1.56064			−0.780318	−	0.625383i	$-0.784943\pi$
$839$	−45.2046			−1.56064			−0.780318	+	0.625383i	$0.784943\pi$
$840$	0.394867	−	3.19876i	0.0136242	−	0.110368i
$841$	−34.9391	−	60.5163i	−1.20480	−	2.08677i
$842$	13.0655	−	3.50090i	0.450268	−	0.120649i
$843$	24.7630	−	6.63524i	0.852885	−	0.228530i
$844$	−15.7541			−0.542279
$845$	15.6703	+	6.34305i	0.539075	+	0.218208i
$846$	−12.0376	−	6.94992i	−0.413862	−	0.238943i
$847$	1.88362	+	7.02978i	0.0647221	+	0.241546i
$848$	−6.40204	−	1.71542i	−0.219847	−	0.0589078i
$849$	1.23898			0.0425215
$850$	−25.4084	−	24.6004i	−0.871499	−	0.843787i
$851$	−1.99105	−	1.14953i	−0.0682524	−	0.0394055i
$852$	5.11657	+	5.11657i	0.175291	+	0.175291i
$853$	−8.11701	−	30.2931i	−0.277921	−	1.03722i	−0.953858	−	0.300257i	$-0.902928\pi$
$853$	−8.11701	−	30.2931i	−0.277921	−	1.03722i	0.675937	−	0.736959i	$-0.263739\pi$
$854$	2.67160	+	4.62734i	0.0914202	+	0.158344i
$855$	0.880065	−	0.686663i	0.0300976	−	0.0234834i
$856$		−	1.48461i		−	0.0507430i
$857$	5.09830	−	19.0271i	0.174155	−	0.649954i	−0.822539	−	0.568708i	$-0.807443\pi$
$857$	5.09830	−	19.0271i	0.174155	−	0.649954i	0.996694	−	0.0812460i	$-0.0258899\pi$
$858$	−9.35936	+	9.35936i	−0.319523	+	0.319523i
$859$	17.7943			0.607134			0.303567	−	0.952810i	$-0.401822\pi$
$859$	17.7943			0.607134			0.303567	+	0.952810i	$0.401822\pi$
$860$	−7.94046	−	12.3268i	−0.270767	−	0.420339i
$861$	6.53175			0.222602
$862$	18.2231	−	18.2231i	0.620682	−	0.620682i
$863$	−4.69358	+	17.5167i	−0.159771	+	0.596275i	0.838878	+	0.544319i	$0.183212\pi$
$863$	−4.69358	+	17.5167i	−0.159771	+	0.596275i	−0.998649	+	0.0519554i	$0.983455\pi$
$864$			5.63709i			0.191778i
$865$	−0.516381	−	0.0637439i	−0.0175575	−	0.00216736i
$866$	14.9461	+	25.8874i	0.507889	+	0.879690i
$867$	11.5017	+	42.9249i	0.390618	+	1.45781i
$868$	−6.46000	−	6.46000i	−0.219267	−	0.219267i
$869$	−37.8202	−	21.8355i	−1.28296	−	0.740718i
$870$	18.4020	+	23.5851i	0.623887	+	0.799608i
$871$	−13.2863			−0.450189
$872$	6.41791	+	1.71967i	0.217338	+	0.0582355i
$873$	4.67142	+	17.4340i	0.158104	+	0.590051i
$874$	0.0982143	+	0.0567040i	0.00332215	+	0.00191804i
$875$	−7.51989	−	9.32336i	−0.254219	−	0.315187i
$876$	1.25134			0.0422787
$877$	−25.5515	+	6.84651i	−0.862813	+	0.231190i	−0.662978	−	0.748639i	$-0.730708\pi$
$877$	−25.5515	+	6.84651i	−0.862813	+	0.231190i	−0.199836	+	0.979829i	$0.564041\pi$
$878$	−1.20307	+	0.322361i	−0.0406016	+	0.0108792i
$879$	−13.1651	−	22.8027i	−0.444049	−	0.769116i
$880$	5.80218	+	7.43640i	0.195592	+	0.250681i
$881$	46.4662			1.56548			0.782742	−	0.622346i	$-0.213820\pi$
$881$	46.4662			1.56548			0.782742	+	0.622346i	$0.213820\pi$
$882$	−4.92403	+	4.92403i	−0.165801	+	0.165801i
$883$	37.9142	+	10.1591i	1.27592	+	0.341880i	0.832294	−	0.554334i	$-0.187027\pi$
$883$	37.9142	+	10.1591i	1.27592	+	0.341880i	0.443621	+	0.896215i	$0.353694\pi$
$884$	14.2868	−	8.24848i	0.480517	−	0.277427i
$885$	9.77939	+	23.0804i	0.328731	+	0.775841i
$886$	6.30928	+	3.64266i	0.211964	+	0.122378i
$887$	−24.7517	+	24.7517i	−0.831081	+	0.831081i	−0.987665	−	0.156583i	$-0.949952\pi$
$887$	−24.7517	+	24.7517i	−0.831081	+	0.831081i	0.156583	+	0.987665i	$0.449952\pi$
$888$	11.0526	−	2.96152i	0.370899	−	0.0993822i
$889$	0.841604	−	1.45770i	0.0282265	−	0.0488897i
$890$	−9.32119	−	21.9991i	−0.312447	−	0.737410i
$891$	8.46664	+	14.6647i	0.283643	+	0.491284i
$892$	7.45621	−	7.45621i	0.249652	−	0.249652i
$893$	1.26839	−	4.73368i	0.0424449	−	0.158407i
$894$	1.91030	−	3.30873i	0.0638900	−	0.110661i
$895$	−22.2827	+	3.11688i	−0.744830	+	0.104186i
$896$	0.535675	−	0.927816i	0.0178956	−	0.0309962i
$897$	−0.819336	−	0.219540i	−0.0273568	−	0.00733024i
$898$	31.2233	+	8.36625i	1.04193	+	0.279186i
$899$	84.7943			2.82805
$900$	4.27440	+	4.13848i	0.142480	+	0.137949i
$901$	46.8805			1.56182
$902$	−13.5164	+	13.5164i	−0.450045	+	0.450045i
$903$	−0.852472	+	9.41329i	−0.0283685	+	0.313255i
$904$		−	0.887651i		−	0.0295228i
$905$	6.58741	−	0.921439i	0.218973	−	0.0306297i
$906$	3.05473	−	1.76365i	0.101487	−	0.0585933i
$907$	−1.66156	−	1.66156i	−0.0551712	−	0.0551712i	0.678983	−	0.734154i	$-0.262421\pi$
$907$	−1.66156	−	1.66156i	−0.0551712	−	0.0551712i	−0.734154	+	0.678983i	$0.762421\pi$
$908$	3.64052	−	13.5866i	0.120815	−	0.450888i
$909$	18.0181	−	10.4027i	0.597622	−	0.345037i
$910$	5.14456	−	2.17980i	0.170541	−	0.0722595i
$911$			33.7608i			1.11854i	0.828984	+	0.559272i	$0.188919\pi$
$911$			33.7608i			1.11854i	−0.828984	+	0.559272i	$0.811081\pi$
$912$	−0.545198	+	0.146085i	−0.0180533	+	0.00483737i
$913$	−65.2953	−	17.4958i	−2.16096	−	0.579027i
$914$		−	25.0412i		−	0.828288i
$915$	14.8909	+	1.83818i	0.492277	+	0.0607684i
$916$	−10.7291	+	18.5833i	−0.354499	+	0.614011i
$917$	4.22038	−	1.13085i	0.139369	−	0.0373439i
$918$	−10.3197	−	38.5138i	−0.340602	−	1.27114i
$919$		−	51.1340i		−	1.68675i	−0.537322	−	0.843377i	$-0.680564\pi$
$919$		−	51.1340i		−	1.68675i	0.537322	−	0.843377i	$-0.319436\pi$
$920$	−0.226798	+	0.560298i	−0.00747732	+	0.0184725i
$921$	11.9287	+	6.88702i	0.393063	+	0.226935i
$922$	−16.9907	−	4.55263i	−0.559557	−	0.149933i
$923$	−3.24658	+	12.1164i	−0.106863	+	0.398817i
$924$		−	6.08004i		−	0.200019i
$925$	20.6646	−	37.1660i	0.679447	−	1.22201i
$926$	3.89010	+	6.73785i	0.127837	+	0.221419i
$927$	4.71220	−	17.5862i	0.154769	−	0.577606i
$928$	2.57363	+	9.60493i	0.0844836	+	0.315297i
$929$	−10.3788	+	17.9767i	−0.340519	+	0.589795i	−0.984529	−	0.175221i	$-0.943936\pi$
$929$	−10.3788	+	17.9767i	−0.340519	+	0.589795i	0.644011	+	0.765017i	$0.277269\pi$
$930$	−25.4064	+	3.55382i	−0.833108	+	0.116534i
$931$	−2.12624	−	1.22758i	−0.0696846	−	0.0402324i
$932$	1.48246	+	5.53260i	0.0485595	+	0.181226i
$933$	18.7114	−	5.01370i	0.612584	−	0.164141i
$934$	14.9759	−	8.64635i	0.490027	−	0.282917i
$935$	−53.2555	−	40.1851i	−1.74164	−	1.31419i
$936$	−2.40344	+	1.38763i	−0.0785589	+	0.0453560i
$937$	1.83849	+	6.86134i	0.0600608	+	0.224150i	0.989432	−	0.144996i	$-0.0463169\pi$
$937$	1.83849	+	6.86134i	0.0600608	+	0.224150i	−0.929371	+	0.369146i	$0.879650\pi$
$938$	4.31553	−	4.31553i	0.140907	−	0.140907i
$939$	20.6954	+	11.9485i	0.675370	+	0.389925i
$940$	25.9236	+	3.20010i	0.845534	+	0.104376i
$941$	12.6080	+	21.8376i	0.411008	+	0.711886i	0.995000	−	0.0998729i	$-0.0318436\pi$
$941$	12.6080	+	21.8376i	0.411008	+	0.711886i	−0.583993	+	0.811759i	$0.698510\pi$
$942$	−7.54845	+	7.54845i	−0.245942	+	0.245942i
$943$	−1.18325	−	0.317050i	−0.0385318	−	0.0103246i
$944$			8.33228i			0.271193i
$945$	−1.87075	−	13.3741i	−0.0608555	−	0.435058i
$946$	−17.7152	−	21.2432i	−0.575969	−	0.690678i
$947$	14.0905	+	14.0905i	0.457880	+	0.457880i	0.897959	−	0.440079i	$-0.145050\pi$
$947$	14.0905	+	14.0905i	0.457880	+	0.457880i	−0.440079	+	0.897959i	$0.645050\pi$
$948$	9.84921	+	9.84921i	0.319888	+	0.319888i
$949$	1.08463	+	1.87863i	0.0352085	+	0.0609829i
$950$	−1.01934	+	1.83332i	−0.0330717	+	0.0594807i
$951$	8.15846	−	4.71029i	0.264556	−	0.152742i
$952$	−1.96131	+	7.31969i	−0.0635663	+	0.237233i
$953$	−14.1048	+	3.77936i	−0.456898	+	0.122425i	−0.479925	−	0.877309i	$-0.659336\pi$
$953$	−14.1048	+	3.77936i	−0.456898	+	0.122425i	0.0230273	+	0.999735i	$0.492670\pi$
$954$	−7.88662			−0.255339
$955$	22.1857	+	8.98035i	0.717911	+	0.290597i
$956$	−3.59951	−	6.23454i	−0.116417	−	0.201639i
$957$	39.9034	+	39.9034i	1.28989	+	1.28989i
$958$	5.30888	−	19.8130i	0.171522	−	0.640130i
$959$	19.8797	+	11.4776i	0.641950	+	0.370630i
$960$	−1.17367	−	2.77000i	−0.0378802	−	0.0894014i
$961$	−20.8582	+	36.1274i	−0.672845	+	1.16540i
$962$	14.0262	+	14.0262i	0.452224	+	0.452224i
$963$	−0.457220	−	1.70637i	−0.0147337	−	0.0549870i
$964$	−5.21970	+	9.04079i	−0.168115	+	0.291184i
$965$	−8.62280	−	1.06443i	−0.277578	−	0.0342652i
$966$	0.337438	−	0.194820i	0.0108569	−	0.00626823i
$967$	−7.34160	−	7.34160i	−0.236090	−	0.236090i	0.579139	−	0.815229i	$-0.303389\pi$
$967$	−7.34160	−	7.34160i	−0.236090	−	0.236090i	−0.815229	+	0.579139i	$0.803389\pi$
$968$	4.80343	+	4.80343i	0.154388	+	0.154388i
$969$	3.45748	−	1.99617i	0.111070	−	0.0641264i
$970$	−20.8642	−	26.7408i	−0.669910	−	0.858595i
$971$	−3.86350	+	6.69178i	−0.123986	+	0.214749i	−0.921336	−	0.388767i	$-0.872901\pi$
$971$	−3.86350	+	6.69178i	−0.123986	+	0.214749i	0.797350	+	0.603517i	$0.206234\pi$
$972$	2.97910	+	11.1182i	0.0955548	+	0.356615i
$973$	−1.81861	−	1.81861i	−0.0583018	−	0.0583018i
$974$	−4.84337	+	8.38896i	−0.155192	+	0.268800i
$975$	3.81537	−	15.2184i	0.122190	−	0.487379i
$976$	4.31917	+	2.49367i	0.138253	+	0.0798205i
$977$	−3.06460	+	11.4372i	−0.0980451	+	0.365909i	−0.997464	−	0.0711794i	$-0.977324\pi$
$977$	−3.06460	+	11.4372i	−0.0980451	+	0.365909i	0.899418	+	0.437089i	$0.143990\pi$
$978$	13.4969	+	13.4969i	0.431585	+	0.431585i
$979$	−22.5356	−	39.0328i	−0.720241	−	1.24749i
$980$	4.90995	−	12.1299i	0.156843	−	0.387475i
$981$	7.90617			0.252424
$982$	−4.39926	+	1.17878i	−0.140386	+	0.0376163i
$983$	7.49184	−	27.9599i	0.238953	−	0.891783i	−0.737375	−	0.675484i	$-0.763935\pi$
$983$	7.49184	−	27.9599i	0.238953	−	0.891783i	0.976327	−	0.216299i	$-0.0693986\pi$
$984$	5.27994	−	3.04837i	0.168318	−	0.0971786i
$985$	13.4487	+	10.1480i	0.428513	+	0.323344i
$986$	−35.1672	−	60.9114i	−1.11995	−	1.93981i
$987$	−11.9058	−	11.9058i	−0.378967	−	0.378967i
$988$	−0.691883	−	0.691883i	−0.0220117	−	0.0220117i
$989$	0.611347	−	1.66387i	0.0194397	−	0.0529079i
$990$	8.95907	+	6.76027i	0.284738	+	0.214855i
$991$		−	4.53419i		−	0.144033i	−0.997403	−	0.0720167i	$-0.977057\pi$
$991$		−	4.53419i		−	0.144033i	0.997403	−	0.0720167i	$-0.0229435\pi$
$992$	−8.23683	−	2.20705i	−0.261519	−	0.0700739i
$993$	−8.33578	+	8.33578i	−0.264528	+	0.264528i
$994$	−2.88102	−	4.99007i	−0.0913803	−	0.158275i
$995$	8.72926	+	11.1879i	0.276736	+	0.354680i
$996$	18.6721	+	10.7803i	0.591647	+	0.341588i
$997$	3.48376	−	3.48376i	0.110332	−	0.110332i	−0.649786	−	0.760117i	$-0.725141\pi$
$997$	3.48376	−	3.48376i	0.110332	−	0.110332i	0.760117	+	0.649786i	$0.225141\pi$
$998$	5.22101	+	19.4851i	0.165268	+	0.616789i
$999$	41.5198	−	23.9714i	1.31363	−	0.758423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.l.a.7.5	✓	88
5.3	odd	4	inner	430.2.l.a.93.16	yes	88
43.37	odd	6	inner	430.2.l.a.37.16	yes	88
215.123	even	12	inner	430.2.l.a.123.5	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.l.a.7.5	✓	88	1.1	even	1	trivial
430.2.l.a.37.16	yes	88	43.37	odd	6	inner
430.2.l.a.93.16	yes	88	5.3	odd	4	inner
430.2.l.a.123.5	yes	88	215.123	even	12	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.348214 + 1.29955i) q^{3} -1.00000i q^{4} +(1.37552 + 1.76294i) q^{5} +(-0.672697 - 1.16515i) q^{6} +(0.277286 + 1.03484i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.03050 + 0.594958i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.348214 + 1.29955i) q^{3} -1.00000i q^{4} +(1.37552 + 1.76294i) q^{5} +(-0.672697 - 1.16515i) q^{6} +(0.277286 + 1.03484i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.03050 + 0.594958i) q^{9} +(-2.21922 - 0.273949i) q^{10} -4.21818 q^{11} +(1.29955 + 0.348214i) q^{12} +(0.603646 + 2.25284i) q^{13} +(-0.927816 - 0.535675i) q^{14} +(-2.77000 + 1.17367i) q^{15} -1.00000 q^{16} +(6.83222 - 1.83069i) q^{17} +(-1.14937 + 0.307973i) q^{18} +(-0.209764 - 0.363322i) q^{19} +(1.76294 - 1.37552i) q^{20} -1.44139 q^{21} +(2.98271 - 2.98271i) q^{22} +(0.261112 + 0.0699647i) q^{23} +(-1.16515 + 0.672697i) q^{24} +(-1.21591 + 4.84990i) q^{25} +(-2.01984 - 1.16616i) q^{26} +(-3.98602 + 3.98602i) q^{27} +(1.03484 - 0.277286i) q^{28} +(-4.97188 + 8.61154i) q^{29} +(1.12877 - 2.78860i) q^{30} +(-4.26369 - 7.38494i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.46883 - 5.48174i) q^{33} +(-3.53661 + 6.12560i) q^{34} +(-1.44296 + 1.91228i) q^{35} +(0.594958 - 1.03050i) q^{36} +(-8.21511 - 2.20123i) q^{37} +(0.405233 + 0.108582i) q^{38} -3.13788 q^{39} +(-0.273949 + 2.21922i) q^{40} -4.53157 q^{41} +(1.01921 - 1.01921i) q^{42} +(0.591424 - 6.53071i) q^{43} +4.21818i q^{44} +(0.368592 + 2.63508i) q^{45} +(-0.234106 + 0.135161i) q^{46} +(8.25998 + 8.25998i) q^{47} +(0.348214 - 1.29955i) q^{48} +(5.06816 - 2.92610i) q^{49} +(-2.56962 - 4.28918i) q^{50} +9.51628i q^{51} +(2.25284 - 0.603646i) q^{52} +(6.40204 + 1.71542i) q^{53} -5.63709i q^{54} +(-5.80218 - 7.43640i) q^{55} +(-0.535675 + 0.927816i) q^{56} +(0.545198 - 0.146085i) q^{57} +(-2.57363 - 9.60493i) q^{58} -8.33228i q^{59} +(1.17367 + 2.77000i) q^{60} +(-4.31917 - 2.49367i) q^{61} +(8.23683 + 2.20705i) q^{62} +(-0.329947 + 1.23138i) q^{63} +1.00000i q^{64} +(-3.14129 + 4.16301i) q^{65} +(2.83756 + 4.91480i) q^{66} +(-1.47439 + 5.50251i) q^{67} +(-1.83069 - 6.83222i) q^{68} +(-0.181845 + 0.314965i) q^{69} +(-0.331864 - 2.37251i) q^{70} +(4.65774 + 2.68915i) q^{71} +(0.307973 + 1.14937i) q^{72} +(0.898397 - 0.240725i) q^{73} +(7.36546 - 4.25245i) q^{74} +(-5.87930 - 3.26894i) q^{75} +(-0.363322 + 0.209764i) q^{76} +(-1.16964 - 4.36517i) q^{77} +(2.21881 - 2.21881i) q^{78} +(8.96598 + 5.17651i) q^{79} +(-1.37552 - 1.76294i) q^{80} +(-2.00718 - 3.47653i) q^{81} +(3.20431 - 3.20431i) q^{82} +(15.4795 + 4.14771i) q^{83} +1.44139i q^{84} +(12.6252 + 9.52664i) q^{85} +(4.19971 + 5.03611i) q^{86} +(-9.45986 - 9.45986i) q^{87} +(-2.98271 - 2.98271i) q^{88} +(5.34249 + 9.25346i) q^{89} +(-2.12392 - 1.60265i) q^{90} +(-2.16396 + 1.24936i) q^{91} +(0.0699647 - 0.261112i) q^{92} +(11.0818 - 2.96935i) q^{93} -11.6814 q^{94} +(0.351981 - 0.869557i) q^{95} +(0.672697 + 1.16515i) q^{96} +(10.7256 + 10.7256i) q^{97} +(-1.51466 + 5.65280i) q^{98} +(-4.34683 - 2.50964i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{6} + 12 q^{7}+O(q^{10}) \) 88 * q + 4 * q^6 + 12 * q^7	\( 88 q + 4 q^{6} + 12 q^{7} + 16 q^{13} - 88 q^{16} + 4 q^{17} - 16 q^{21} + 12 q^{23} - 8 q^{25} + 12 q^{28} - 36 q^{30} - 40 q^{31} + 12 q^{33} - 40 q^{35} - 40 q^{36} + 16 q^{38} - 56 q^{41} - 56 q^{43} + 24 q^{46} + 72 q^{47} + 24 q^{50} - 16 q^{52} + 20 q^{53} + 24 q^{55} - 8 q^{56} + 20 q^{57} + 8 q^{60} + 72 q^{61} + 36 q^{62} - 40 q^{66} - 16 q^{67} + 4 q^{68} + 24 q^{71} + 60 q^{73} - 48 q^{76} - 48 q^{77} + 40 q^{78} + 28 q^{81} + 20 q^{86} - 64 q^{87} - 8 q^{90} + 48 q^{91} - 12 q^{92} - 108 q^{93} + 4 q^{95} - 4 q^{96} - 48 q^{97} - 96 q^{98}+O(q^{100}) \) 88 * q + 4 * q^6 + 12 * q^7 + 16 * q^13 - 88 * q^16 + 4 * q^17 - 16 * q^21 + 12 * q^23 - 8 * q^25 + 12 * q^28 - 36 * q^30 - 40 * q^31 + 12 * q^33 - 40 * q^35 - 40 * q^36 + 16 * q^38 - 56 * q^41 - 56 * q^43 + 24 * q^46 + 72 * q^47 + 24 * q^50 - 16 * q^52 + 20 * q^53 + 24 * q^55 - 8 * q^56 + 20 * q^57 + 8 * q^60 + 72 * q^61 + 36 * q^62 - 40 * q^66 - 16 * q^67 + 4 * q^68 + 24 * q^71 + 60 * q^73 - 48 * q^76 - 48 * q^77 + 40 * q^78 + 28 * q^81 + 20 * q^86 - 64 * q^87 - 8 * q^90 + 48 * q^91 - 12 * q^92 - 108 * q^93 + 4 * q^95 - 4 * q^96 - 48 * q^97 - 96 * q^98

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