LMFDB - Embedded newform 504.2.cs.b.85.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(85,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("504.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cs (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:	$4.02446026187$
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			85.5
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.b.421.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30114 - 0.554117i) q^{2} +(-1.71503 - 0.242257i) q^{3} +(1.38591 + 1.44196i) q^{4} +(3.59330 + 2.07459i) q^{5} +(2.09724 + 1.26553i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(-1.00424 - 2.64415i) q^{8} +(2.88262 + 0.830955i) q^{9} +O(q^{10})$	\(q+(-1.30114 - 0.554117i) q^{2} +(-1.71503 - 0.242257i) q^{3} +(1.38591 + 1.44196i) q^{4} +(3.59330 + 2.07459i) q^{5} +(2.09724 + 1.26553i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(-1.00424 - 2.64415i) q^{8} +(2.88262 + 0.830955i) q^{9} +(-3.52580 - 4.69043i) q^{10} +(2.37702 - 1.37237i) q^{11} +(-2.02754 - 2.80875i) q^{12} +(1.81463 + 1.04768i) q^{13} +(0.170688 + 1.40388i) q^{14} +(-5.66001 - 4.42848i) q^{15} +(-0.158517 + 3.99686i) q^{16} -5.99230 q^{17} +(-3.29024 - 2.67850i) q^{18} +5.32839i q^{19} +(1.98850 + 8.05660i) q^{20} +(0.647712 + 1.60638i) q^{21} +(-3.85328 + 0.468495i) q^{22} +(1.33625 - 2.31446i) q^{23} +(1.08173 + 4.77806i) q^{24} +(6.10786 + 10.5791i) q^{25} +(-1.78054 - 2.36869i) q^{26} +(-4.74247 - 2.12344i) q^{27} +(0.555823 - 1.92121i) q^{28} +(5.71158 - 3.29758i) q^{29} +(4.91055 + 8.89836i) q^{30} +(0.753745 - 1.30552i) q^{31} +(2.42098 - 5.11262i) q^{32} +(-4.40911 + 1.77780i) q^{33} +(7.79679 + 3.32044i) q^{34} -4.14918i q^{35} +(2.79684 + 5.30826i) q^{36} +6.50057i q^{37} +(2.95255 - 6.93296i) q^{38} +(-2.85833 - 2.23640i) q^{39} +(1.87700 - 11.5846i) q^{40} +(4.19000 - 7.25729i) q^{41} +(0.0473644 - 2.44903i) q^{42} +(-1.87479 + 1.08241i) q^{43} +(5.27324 + 1.52559i) q^{44} +(8.63423 + 8.96613i) q^{45} +(-3.02113 + 2.27098i) q^{46} +(1.47815 + 2.56022i) q^{47} +(1.24013 - 6.81631i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-2.08508 - 17.1493i) q^{50} +(10.2769 + 1.45168i) q^{51} +(1.00420 + 4.06861i) q^{52} +1.23720i q^{53} +(4.99395 + 5.39077i) q^{54} +11.3884 q^{55} +(-1.78778 + 2.19177i) q^{56} +(1.29084 - 9.13832i) q^{57} +(-9.25878 + 1.12572i) q^{58} +(10.4952 + 6.05943i) q^{59} +(-1.45855 - 14.2990i) q^{60} +(-2.57733 + 1.48802i) q^{61} +(-1.70414 + 1.28100i) q^{62} +(-0.721684 - 2.91190i) q^{63} +(-5.98301 + 5.31070i) q^{64} +(4.34700 + 7.52923i) q^{65} +(6.72196 + 0.130003i) q^{66} +(9.43042 + 5.44466i) q^{67} +(-8.30478 - 8.64068i) q^{68} +(-2.85240 + 3.64564i) q^{69} +(-2.29913 + 5.39865i) q^{70} -0.615579 q^{71} +(-0.697673 - 8.45655i) q^{72} +10.8436 q^{73} +(3.60208 - 8.45813i) q^{74} +(-7.91226 - 19.6231i) q^{75} +(-7.68335 + 7.38466i) q^{76} +(-2.37702 - 1.37237i) q^{77} +(2.47984 + 4.49371i) q^{78} +(-1.19028 - 2.06163i) q^{79} +(-8.86145 + 14.0330i) q^{80} +(7.61903 + 4.79066i) q^{81} +(-9.47314 + 7.12096i) q^{82} +(-10.2344 + 5.90884i) q^{83} +(-1.41868 + 3.16028i) q^{84} +(-21.5321 - 12.4316i) q^{85} +(3.03913 - 0.369509i) q^{86} +(-10.5944 + 4.27176i) q^{87} +(-6.01584 - 4.90699i) q^{88} -5.48402 q^{89} +(-6.26602 - 16.4505i) q^{90} -2.09535i q^{91} +(5.18929 - 1.28080i) q^{92} +(-1.60896 + 2.05641i) q^{93} +(-0.504604 - 4.15027i) q^{94} +(-11.0542 + 19.1465i) q^{95} +(-5.39061 + 8.18177i) q^{96} +(-0.192611 - 0.333611i) q^{97} +(1.13045 - 0.849758i) q^{98} +(7.99242 - 1.98084i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.30114	−	0.554117i	−0.920042	−	0.391820i
$2$	−1.30114	−	0.554117i	−0.920042	−	0.391820i
$3$	−1.71503	−	0.242257i	−0.990170	−	0.139867i
$3$	−1.71503	−	0.242257i	−0.990170	−	0.139867i
$4$	1.38591	+	1.44196i	0.692954	+	0.720982i
$5$	3.59330	+	2.07459i	1.60697	+	0.927785i	0.990043	+	0.140766i	$0.0449566\pi$
$5$	3.59330	+	2.07459i	1.60697	+	0.927785i	0.616928	+	0.787019i	$0.288377\pi$
$6$	2.09724	+	1.26553i	0.856195	+	0.516652i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	−1.00424	−	2.64415i	−0.355052	−	0.934847i
$9$	2.88262	+	0.830955i	0.960874	+	0.276985i
$10$	−3.52580	−	4.69043i	−1.11496	−	1.48325i
$11$	2.37702	−	1.37237i	0.716698	−	0.413786i	−0.0968383	−	0.995300i	$-0.530873\pi$
$11$	2.37702	−	1.37237i	0.716698	−	0.413786i	0.813536	+	0.581515i	$0.197540\pi$
$12$	−2.02754	−	2.80875i	−0.585301	−	0.810816i
$13$	1.81463	+	1.04768i	0.503288	+	0.290573i	0.730070	−	0.683372i	$-0.239487\pi$
$13$	1.81463	+	1.04768i	0.503288	+	0.290573i	−0.226783	+	0.973945i	$0.572821\pi$
$14$	0.170688	+	1.40388i	0.0456183	+	0.375201i
$15$	−5.66001	−	4.42848i	−1.46141	−	1.14343i
$16$	−0.158517	+	3.99686i	−0.0396294	+	0.999214i
$17$	−5.99230			−1.45335			−0.726673	−	0.686983i	$-0.758934\pi$
$17$	−5.99230			−1.45335			−0.726673	+	0.686983i	$0.758934\pi$
$18$	−3.29024	−	2.67850i	−0.775516	−	0.631328i
$19$			5.32839i			1.22242i	0.791470	+	0.611208i	$0.209316\pi$
$19$			5.32839i			1.22242i	−0.791470	+	0.611208i	$0.790684\pi$
$20$	1.98850	+	8.05660i	0.444641	+	1.80151i
$21$	0.647712	+	1.60638i	0.141342	+	0.350542i
$22$	−3.85328	+	0.468495i	−0.821521	+	0.0998835i
$23$	1.33625	−	2.31446i	0.278628	−	0.482598i	−0.692416	−	0.721499i	$-0.743454\pi$
$23$	1.33625	−	2.31446i	0.278628	−	0.482598i	0.971044	+	0.238900i	$0.0767869\pi$
$24$	1.08173	+	4.77806i	0.220807	+	0.975318i
$25$	6.10786	+	10.5791i	1.22157	+	2.11582i
$26$	−1.78054	−	2.36869i	−0.349193	−	0.464538i
$27$	−4.74247	−	2.12344i	−0.912688	−	0.408657i
$28$	0.555823	−	1.92121i	0.105041	−	0.363075i
$29$	5.71158	−	3.29758i	1.06061	−	0.612345i	0.135011	−	0.990844i	$-0.456893\pi$
$29$	5.71158	−	3.29758i	1.06061	−	0.612345i	0.925602	+	0.378499i	$0.123560\pi$
$30$	4.91055	+	8.89836i	0.896539	+	1.62461i
$31$	0.753745	−	1.30552i	0.135377	−	0.234479i	−0.790365	−	0.612637i	$-0.790109\pi$
$31$	0.753745	−	1.30552i	0.135377	−	0.234479i	0.925741	+	0.378158i	$0.123442\pi$
$32$	2.42098	−	5.11262i	0.427973	−	0.903792i
$33$	−4.40911	+	1.77780i	−0.767528	+	0.309476i
$34$	7.79679	+	3.32044i	1.33714	+	0.569450i
$35$		−	4.14918i		−	0.701340i
$36$	2.79684	+	5.30826i	0.466141	+	0.884711i
$37$			6.50057i			1.06869i	0.845267	+	0.534344i	$0.179441\pi$
$37$			6.50057i			1.06869i	−0.845267	+	0.534344i	$0.820559\pi$
$38$	2.95255	−	6.93296i	0.478967	−	1.12467i
$39$	−2.85833	−	2.23640i	−0.457699	−	0.358110i
$40$	1.87700	−	11.5846i	0.296779	−	1.83168i
$41$	4.19000	−	7.25729i	0.654367	−	1.13340i	−0.327685	−	0.944787i	$-0.606268\pi$
$41$	4.19000	−	7.25729i	0.654367	−	1.13340i	0.982052	−	0.188610i	$-0.0603983\pi$
$42$	0.0473644	−	2.44903i	0.00730848	−	0.377894i
$43$	−1.87479	+	1.08241i	−0.285902	+	0.165066i	−0.636092	−	0.771613i	$-0.719450\pi$
$43$	−1.87479	+	1.08241i	−0.285902	+	0.165066i	0.350190	+	0.936679i	$0.386117\pi$
$44$	5.27324	+	1.52559i	0.794970	+	0.229992i
$45$	8.63423	+	8.96613i	1.28711	+	1.33659i
$46$	−3.02113	+	2.27098i	−0.445441	+	0.334838i
$47$	1.47815	+	2.56022i	0.215610	+	0.373447i	0.953461	−	0.301516i	$-0.0974927\pi$
$47$	1.47815	+	2.56022i	0.215610	+	0.373447i	−0.737851	+	0.674963i	$0.764159\pi$
$48$	1.24013	−	6.81631i	0.178997	−	0.983850i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−2.08508	−	17.1493i	−0.294875	−	2.42528i
$51$	10.2769	+	1.45168i	1.43906	+	0.203276i
$52$	1.00420	+	4.06861i	0.139257	+	0.564215i
$53$			1.23720i			0.169942i	0.996383	+	0.0849711i	$0.0270798\pi$
$53$			1.23720i			0.169942i	−0.996383	+	0.0849711i	$0.972920\pi$
$54$	4.99395	+	5.39077i	0.679591	+	0.733591i
$55$	11.3884			1.53562
$56$	−1.78778	+	2.19177i	−0.238902	+	0.292887i
$57$	1.29084	−	9.13832i	0.170976	−	1.21040i
$58$	−9.25878	+	1.12572i	−1.21574	+	0.147814i
$59$	10.4952	+	6.05943i	1.36637	+	0.788871i	0.990462	−	0.137788i	$-0.0439992\pi$
$59$	10.4952	+	6.05943i	1.36637	+	0.788871i	0.375903	+	0.926659i	$0.377333\pi$
$60$	−1.45855	−	14.2990i	−0.188298	−	1.84599i
$61$	−2.57733	+	1.48802i	−0.329993	+	0.190522i	−0.655838	−	0.754902i	$-0.727685\pi$
$61$	−2.57733	+	1.48802i	−0.329993	+	0.190522i	0.325845	+	0.945423i	$0.394351\pi$
$62$	−1.70414	+	1.28100i	−0.216426	+	0.162687i
$63$	−0.721684	−	2.91190i	−0.0909236	−	0.366865i
$64$	−5.98301	+	5.31070i	−0.747877	+	0.663838i
$65$	4.34700	+	7.52923i	0.539179	+	0.933886i
$66$	6.72196	+	0.130003i	0.827416	+	0.0160023i
$67$	9.43042	+	5.44466i	1.15211	+	0.665171i	0.949400	−	0.314068i	$-0.101692\pi$
$67$	9.43042	+	5.44466i	1.15211	+	0.665171i	0.202709	+	0.979239i	$0.435025\pi$
$68$	−8.30478	−	8.64068i	−1.00710	−	1.04784i
$69$	−2.85240	+	3.64564i	−0.343389	+	0.438883i
$70$	−2.29913	+	5.39865i	−0.274799	+	0.645262i
$71$	−0.615579			−0.0730558			−0.0365279	−	0.999333i	$-0.511630\pi$
$71$	−0.615579			−0.0730558			−0.0365279	+	0.999333i	$0.511630\pi$
$72$	−0.697673	−	8.45655i	−0.0822216	−	0.996614i
$73$	10.8436			1.26915			0.634573	−	0.772863i	$-0.281176\pi$
$73$	10.8436			1.26915			0.634573	+	0.772863i	$0.281176\pi$
$74$	3.60208	−	8.45813i	0.418733	−	0.983237i
$75$	−7.91226	−	19.6231i	−0.913629	−	2.26588i
$76$	−7.68335	+	7.38466i	−0.881340	+	0.847079i
$77$	−2.37702	−	1.37237i	−0.270886	−	0.156396i
$78$	2.47984	+	4.49371i	0.280787	+	0.508812i
$79$	−1.19028	−	2.06163i	−0.133917	−	0.231952i	0.791266	−	0.611472i	$-0.209422\pi$
$79$	−1.19028	−	2.06163i	−0.133917	−	0.231952i	−0.925183	+	0.379520i	$0.876089\pi$
$80$	−8.86145	+	14.0330i	−0.990740	+	1.56894i
$81$	7.61903	+	4.79066i	0.846559	+	0.532295i
$82$	−9.47314	+	7.12096i	−1.04613	+	0.786379i
$83$	−10.2344	+	5.90884i	−1.12337	+	0.648579i	−0.942260	−	0.334884i	$-0.891303\pi$
$83$	−10.2344	+	5.90884i	−1.12337	+	0.648579i	−0.181112	+	0.983462i	$0.557970\pi$
$84$	−1.41868	+	3.16028i	−0.154790	+	0.344815i
$85$	−21.5321	−	12.4316i	−2.33549	−	1.34839i
$86$	3.03913	−	0.369509i	0.327718	−	0.0398451i
$87$	−10.5944	+	4.27176i	−1.13583	+	0.457981i
$88$	−6.01584	−	4.90699i	−0.641291	−	0.523087i
$89$	−5.48402			−0.581305			−0.290653	−	0.956829i	$-0.593872\pi$
$89$	−5.48402			−0.581305			−0.290653	+	0.956829i	$0.593872\pi$
$90$	−6.26602	−	16.4505i	−0.660496	−	1.73404i
$91$		−	2.09535i		−	0.219653i
$92$	5.18929	−	1.28080i	0.541021	−	0.133533i
$93$	−1.60896	+	2.05641i	−0.166842	+	0.213239i
$94$	−0.504604	−	4.15027i	−0.0520460	−	0.428067i
$95$	−11.0542	+	19.1465i	−1.13414	+	1.96439i
$96$	−5.39061	+	8.18177i	−0.550177	+	0.835048i
$97$	−0.192611	−	0.333611i	−0.0195566	−	0.0338731i	0.856081	−	0.516841i	$-0.172892\pi$
$97$	−0.192611	−	0.333611i	−0.0195566	−	0.0338731i	−0.875638	+	0.482968i	$0.839559\pi$
$98$	1.13045	−	0.849758i	0.114192	−	0.0858385i
$99$	7.99242	−	1.98084i	0.803269	−	0.199082i
$100$	−6.78977	+	23.4690i	−0.678977	+	2.34690i
$101$	−16.4536	+	9.49950i	−1.63720	+	0.945236i	−0.655404	+	0.755279i	$0.727501\pi$
$101$	−16.4536	+	9.49950i	−1.63720	+	0.945236i	−0.981792	+	0.189957i	$0.939165\pi$
$102$	−12.5673	−	7.58346i	−1.24435	−	0.750875i
$103$	−2.64680	+	4.58440i	−0.260797	+	0.451714i	−0.966454	−	0.256840i	$-0.917319\pi$
$103$	−2.64680	+	4.58440i	−0.260797	+	0.451714i	0.705657	+	0.708554i	$0.250652\pi$
$104$	0.947891	−	5.85026i	0.0929484	−	0.573665i
$105$	−1.00517	+	7.11595i	−0.0980945	+	0.694446i
$106$	0.685553	−	1.60976i	0.0665868	−	0.156354i
$107$		−	11.8230i		−	1.14297i	−0.820612	−	0.571486i	$-0.806367\pi$
$107$		−	11.8230i		−	1.14297i	0.820612	−	0.571486i	$-0.193633\pi$
$108$	−3.51069	−	9.78136i	−0.337817	−	0.941212i
$109$		−	14.6442i		−	1.40266i	−0.712837	−	0.701330i	$-0.752590\pi$
$109$		−	14.6442i		−	1.40266i	0.712837	−	0.701330i	$-0.247410\pi$
$110$	−14.8179	−	6.31053i	−1.41283	−	0.601686i
$111$	1.57481	−	11.1486i	0.149474	−	1.05818i
$112$	3.54064	−	1.86115i	0.334559	−	0.175862i
$113$	9.83257	−	17.0305i	0.924971	−	1.60210i	0.133363	−	0.991067i	$-0.457422\pi$
$113$	9.83257	−	17.0305i	0.924971	−	1.60210i	0.791608	−	0.611029i	$-0.209244\pi$
$114$	−6.74326	+	11.1749i	−0.631564	+	1.04663i
$115$	9.60312	−	5.54436i	0.895495	−	0.517014i
$116$	12.6707	+	3.66574i	1.17645	+	0.340356i
$117$	4.36032	+	4.52793i	0.403112	+	0.418607i
$118$	−10.2981	−	13.6997i	−0.948017	−	1.26116i
$119$	2.99615	+	5.18948i	0.274657	+	0.475719i
$120$	−6.02555	+	19.4131i	−0.550055	+	1.77217i
$121$	−1.73319	+	3.00198i	−0.157563	+	0.272907i
$122$	4.17799	−	0.507975i	0.378258	−	0.0459899i
$123$	−8.94408	+	11.4314i	−0.806460	+	1.03073i
$124$	2.92714	−	0.722464i	0.262865	−	0.0648792i
$125$			29.9393i			2.67785i
$126$	−0.674527	+	4.18868i	−0.0600916	+	0.373157i
$127$	−8.05995			−0.715205			−0.357602	−	0.933874i	$-0.616406\pi$
$127$	−8.05995			−0.715205			−0.357602	+	0.933874i	$0.616406\pi$
$128$	10.7275	−	3.59465i	0.948183	−	0.317725i
$129$	3.47753	−	1.40218i	0.306179	−	0.123455i
$130$	−1.48396	−	12.2053i	−0.130152	−	1.07048i
$131$	10.9686	+	6.33271i	0.958329	+	0.553292i	0.895658	−	0.444743i	$-0.146705\pi$
$131$	10.9686	+	6.33271i	0.958329	+	0.553292i	0.0626709	+	0.998034i	$0.480038\pi$
$132$	−8.67415	−	3.89391i	−0.754988	−	0.338921i
$133$	4.61452	−	2.66420i	0.400130	−	0.231015i
$134$	−9.25328	−	12.3098i	−0.799362	−	1.06340i
$135$	−12.6358	−	17.4688i	−1.08752	−	1.50348i
$136$	6.01769	+	15.8445i	0.516013	+	1.35866i
$137$	−2.32701	−	4.03049i	−0.198810	−	0.344348i	0.749333	−	0.662193i	$-0.230374\pi$
$137$	−2.32701	−	4.03049i	−0.198810	−	0.344348i	−0.948143	+	0.317845i	$0.897041\pi$
$138$	5.73148	−	3.16291i	0.487896	−	0.269244i
$139$	−5.95274	−	3.43681i	−0.504904	−	0.291507i	0.225832	−	0.974166i	$-0.427490\pi$
$139$	−5.95274	−	3.43681i	−0.504904	−	0.291507i	−0.730737	+	0.682659i	$0.760823\pi$
$140$	5.98297	−	5.75039i	0.505653	−	0.485996i
$141$	−1.91483	−	4.74894i	−0.161257	−	0.399933i
$142$	0.800952	+	0.341103i	0.0672144	+	0.0286247i
$143$	5.75121			0.480940
$144$	−3.77815	+	11.3897i	−0.314846	+	0.949143i
$145$	27.3645			2.27250
$146$	−14.1090	−	6.00862i	−1.16767	−	0.497277i
$147$	1.06731	−	1.36413i	0.0880305	−	0.112511i
$148$	−9.37359	+	9.00920i	−0.770504	+	0.740552i
$149$	−11.6397	−	6.72019i	−0.953562	−	0.550539i	−0.0593765	−	0.998236i	$-0.518911\pi$
$149$	−11.6397	−	6.72019i	−0.953562	−	0.550539i	−0.894186	+	0.447696i	$0.852245\pi$
$150$	−0.578590	+	29.9167i	−0.0472417	+	2.44269i
$151$	2.47375	+	4.28465i	0.201311	+	0.348680i	0.948951	−	0.315424i	$-0.102147\pi$
$151$	2.47375	+	4.28465i	0.201311	+	0.348680i	−0.747640	+	0.664104i	$0.768813\pi$
$152$	14.0890	−	5.35097i	1.14277	−	0.434021i
$153$	−17.2735	−	4.97933i	−1.39648	−	0.402555i
$154$	2.33237	+	3.10279i	0.187948	+	0.250030i
$155$	5.41686	−	3.12742i	0.435092	−	0.251201i
$156$	−0.736574	−	7.22105i	−0.0589731	−	0.578147i
$157$	3.79004	+	2.18818i	0.302479	+	0.174636i	0.643556	−	0.765399i	$-0.277458\pi$
$157$	3.79004	+	2.18818i	0.302479	+	0.174636i	−0.341077	+	0.940035i	$0.610792\pi$
$158$	0.406334	+	3.34202i	0.0323262	+	0.265877i
$159$	0.299720	−	2.12183i	0.0237694	−	0.168272i
$160$	19.3059	−	13.3486i	1.52626	−	1.05530i
$161$	−2.67251			−0.210623
$162$	−7.25880	−	10.4551i	−0.570305	−	0.821433i
$163$		−	10.6763i		−	0.836229i	−0.908394	−	0.418114i	$-0.862691\pi$
$163$		−	10.6763i		−	0.836229i	0.908394	−	0.418114i	$-0.137309\pi$
$164$	16.2717	−	4.01611i	1.27061	−	0.313605i
$165$	−19.5315	−	2.75893i	−1.52052	−	0.214783i
$166$	16.5905	−	2.01714i	1.28768	−	0.156560i
$167$	−1.05290	+	1.82367i	−0.0814757	+	0.141120i	−0.903884	−	0.427778i	$-0.859297\pi$
$167$	−1.05290	+	1.82367i	−0.0814757	+	0.141120i	0.822408	+	0.568898i	$0.192630\pi$
$168$	3.59706	−	3.32584i	0.277519	−	0.256594i
$169$	−4.30475	−	7.45604i	−0.331134	−	0.573542i
$170$	21.1277	+	28.1065i	1.62042	+	2.15567i
$171$	−4.42765	+	15.3597i	−0.338591	+	1.17459i
$172$	−4.15907	−	1.20325i	−0.317126	−	0.0917473i
$173$	7.21480	−	4.16546i	0.548531	−	0.316694i	−0.199998	−	0.979796i	$-0.564094\pi$
$173$	7.21480	−	4.16546i	0.548531	−	0.316694i	0.748529	+	0.663102i	$0.230760\pi$
$174$	16.1518	+	0.312376i	1.22446	+	0.0236811i
$175$	6.10786	−	10.5791i	0.461711	−	0.799706i
$176$	5.10838	+	9.71815i	0.385058	+	0.732533i
$177$	−16.5317	−	12.9346i	−1.24260	−	0.972227i
$178$	7.13546	+	3.03879i	0.534825	+	0.227767i
$179$		−	0.495217i		−	0.0370143i	−0.999829	−	0.0185071i	$-0.994109\pi$
$179$		−	0.495217i		−	0.0370143i	0.999829	−	0.0185071i	$-0.00589134\pi$
$180$	−0.962585	+	24.8765i	−0.0717468	+	1.85418i
$181$		−	2.98696i		−	0.222019i	−0.993819	−	0.111009i	$-0.964592\pi$
$181$		−	2.98696i		−	0.222019i	0.993819	−	0.111009i	$-0.0354084\pi$
$182$	−1.16107	+	2.72634i	−0.0860644	+	0.202090i
$183$	4.78067	−	1.92762i	0.353397	−	0.142494i
$184$	−7.46169	−	1.20898i	−0.550083	−	0.0891274i
$185$	−13.4860	+	23.3585i	−0.991513	+	1.71735i
$186$	3.23297	−	1.78411i	0.237053	−	0.130817i
$187$	−14.2438	+	8.22366i	−1.04161	+	0.601374i
$188$	−1.64318	+	5.67967i	−0.119841	+	0.414232i
$189$	0.532276	+	5.16882i	0.0387174	+	0.375976i
$190$	24.9925	−	18.7868i	1.81314	−	1.36294i
$191$	−0.0113932	−	0.0197336i	−0.000824383	−	0.00142787i	0.865613	−	0.500714i	$-0.166929\pi$
$191$	−0.0113932	−	0.0197336i	−0.000824383	−	0.00142787i	−0.866437	+	0.499286i	$0.833596\pi$
$192$	11.5476	−	7.65856i	0.833374	−	0.552709i
$193$	5.20464	−	9.01470i	0.374638	−	0.648892i	−0.615635	−	0.788032i	$-0.711100\pi$
$193$	5.20464	−	9.01470i	0.374638	−	0.648892i	0.990273	+	0.139139i	$0.0444336\pi$
$194$	0.0657527	+	0.540802i	0.00472077	+	0.0388273i
$195$	−5.63121	−	13.9659i	−0.403259	−	1.00012i
$196$	−1.94173	+	0.479250i	−0.138695	+	0.0342321i
$197$		−	0.733611i		−	0.0522676i	−0.999658	−	0.0261338i	$-0.991680\pi$
$197$		−	0.733611i		−	0.0522676i	0.999658	−	0.0261338i	$-0.00831960\pi$
$198$	−11.4968	−	1.85140i	−0.817045	−	0.131573i
$199$	−27.0314			−1.91621			−0.958103	−	0.286423i	$-0.907534\pi$
$199$	−27.0314			−1.91621			−0.958103	+	0.286423i	$0.907534\pi$
$200$	21.8390	−	26.7740i	1.54425	−	1.89321i
$201$	−14.8544	−	11.6223i	−1.04775	−	0.819775i
$202$	26.6722	−	3.24291i	1.87665	−	0.228170i
$203$	−5.71158	−	3.29758i	−0.400874	−	0.231445i
$204$	12.1496	+	16.8309i	0.850644	+	1.17840i
$205$	30.1118	−	17.3851i	2.10310	−	1.21422i
$206$	5.98414	−	4.49828i	0.416935	−	0.313410i
$207$	5.77513	−	5.56135i	0.401399	−	0.386540i
$208$	−4.47507	+	7.08674i	−0.310290	+	0.491377i
$209$	7.31253	+	12.6657i	0.505818	+	0.876103i
$210$	5.25093	−	8.70184i	0.362349	−	0.600484i
$211$	−12.4950	−	7.21398i	−0.860189	−	0.496631i	0.00388631	−	0.999992i	$-0.498763\pi$
$211$	−12.4950	−	7.21398i	−0.860189	−	0.496631i	−0.864076	+	0.503362i	$0.832096\pi$
$212$	−1.78399	+	1.71464i	−0.122525	+	0.117762i
$213$	1.05573	+	0.149129i	0.0723377	+	0.0102181i
$214$	−6.55132	+	15.3833i	−0.447839	+	1.05158i
$215$	−8.98222			−0.612582
$216$	−0.852134	+	14.6722i	−0.0579804	+	0.998318i
$217$	−1.50749			−0.102335
$218$	−8.11460	+	19.0541i	−0.549590	+	1.29051i
$219$	−18.5970	−	2.62694i	−1.25667	−	0.177512i
$220$	15.7833	+	16.4217i	1.06411	+	1.10715i
$221$	−10.8738	−	6.27799i	−0.731451	−	0.422303i
$222$	−8.22670	+	13.6333i	−0.552140	+	0.915005i
$223$	−6.96868	−	12.0701i	−0.466657	−	0.808274i	0.532617	−	0.846356i	$-0.321209\pi$
$223$	−6.96868	−	12.0701i	−0.466657	−	0.808274i	−0.999275	+	0.0380819i	$0.987875\pi$
$224$	−5.63815	+	0.459678i	−0.376715	+	0.0307135i
$225$	8.81588	+	35.5710i	0.587725	+	2.37140i
$226$	−22.2304	+	16.7106i	−1.47875	+	1.11157i
$227$	8.37584	−	4.83579i	0.555924	−	0.320963i	−0.195584	−	0.980687i	$-0.562660\pi$
$227$	8.37584	−	4.83579i	0.555924	−	0.320963i	0.751508	+	0.659724i	$0.229327\pi$
$228$	14.9661	−	10.8035i	0.991155	−	0.715481i
$229$	7.40674	+	4.27628i	0.489451	+	0.282585i	0.724347	−	0.689436i	$-0.242142\pi$
$229$	7.40674	+	4.27628i	0.489451	+	0.282585i	−0.234896	+	0.972021i	$0.575475\pi$
$230$	−15.5672	+	1.89271i	−1.02647	+	0.124802i
$231$	3.74418	+	2.92950i	0.246349	+	0.192747i
$232$	−14.4551	−	11.7907i	−0.949021	−	0.774097i
$233$	−4.10374			−0.268845			−0.134422	−	0.990924i	$-0.542918\pi$
$233$	−4.10374			−0.268845			−0.134422	+	0.990924i	$0.542918\pi$
$234$	−3.16436	−	8.30758i	−0.206861	−	0.543084i
$235$			12.2662i			0.800159i
$236$	5.80797	+	23.5316i	0.378066	+	1.53178i
$237$	1.54192	+	3.82410i	0.100158	+	0.248402i
$238$	−1.02281	−	8.41244i	−0.0662992	−	0.545298i
$239$	−5.23197	+	9.06204i	−0.338428	+	0.586175i	−0.984137	−	0.177409i	$-0.943229\pi$
$239$	−5.23197	+	9.06204i	−0.338428	+	0.586175i	0.645709	+	0.763584i	$0.276562\pi$
$240$	18.5972	−	21.9203i	1.20044	−	1.41495i
$241$	2.89700	+	5.01775i	0.186612	+	0.323222i	0.944119	−	0.329606i	$-0.106916\pi$
$241$	2.89700	+	5.01775i	0.186612	+	0.323222i	−0.757506	+	0.652828i	$0.773583\pi$
$242$	3.91857	−	2.94559i	0.251895	−	0.189350i
$243$	−11.9063	−	10.0619i	−0.763787	−	0.645469i
$244$	−5.71761	−	1.65415i	−0.366033	−	0.105896i
$245$	−3.59330	+	2.07459i	−0.229567	+	0.132541i
$246$	17.9718	−	9.91770i	1.14584	−	0.632329i
$247$	−5.58243	+	9.66905i	−0.355202	+	0.615227i
$248$	−4.20893	−	0.681954i	−0.267268	−	0.0433041i
$249$	18.9837	−	7.65444i	1.20304	−	0.485081i
$250$	16.5899	−	38.9551i	1.04924	−	2.46374i
$251$		−	16.2773i		−	1.02741i	−0.857966	−	0.513707i	$-0.828272\pi$
$251$		−	16.2773i		−	1.02741i	0.857966	−	0.513707i	$-0.171728\pi$
$252$	3.19867	−	5.07627i	0.201497	−	0.319775i
$253$		−	7.33535i		−	0.461169i
$254$	10.4871	+	4.46616i	0.658018	+	0.280232i
$255$	33.9165	+	26.5368i	2.12393	+	1.66180i
$256$	−15.9497	−	1.26714i	−0.996859	−	0.0791964i
$257$	−5.81147	+	10.0658i	−0.362510	+	0.627885i	−0.988373	−	0.152047i	$-0.951413\pi$
$257$	−5.81147	+	10.0658i	−0.362510	+	0.627885i	0.625863	+	0.779933i	$0.284747\pi$
$258$	−5.30170	−	0.102535i	−0.330070	−	0.00638356i
$259$	5.62966	−	3.25029i	0.349810	−	0.201963i
$260$	−4.83233	+	16.7030i	−0.299688	+	1.03588i
$261$	19.2045	−	4.75962i	1.18873	−	0.294613i
$262$	−10.7625	−	14.3176i	−0.664912	−	0.884544i
$263$	−12.1420	−	21.0305i	−0.748707	−	1.29680i	−0.948443	−	0.316949i	$-0.897342\pi$
$263$	−12.1420	−	21.0305i	−0.748707	−	1.29680i	0.199736	−	0.979850i	$-0.435992\pi$
$264$	9.12856	+	9.87300i	0.561824	+	0.607641i
$265$	−2.56668	+	4.44562i	−0.157670	+	0.273092i
$266$	−7.48040	+	0.909494i	−0.458652	+	0.0557646i
$267$	9.40523	+	1.32854i	0.575591	+	0.0813056i
$268$	5.21870	+	21.1441i	0.318783	+	1.29158i
$269$		−	28.3648i		−	1.72943i	−0.502263	−	0.864715i	$-0.667499\pi$
$269$		−	28.3648i		−	1.72943i	0.502263	−	0.864715i	$-0.332501\pi$
$270$	6.76112	+	29.7311i	0.411468	+	1.80937i
$271$	−0.966395			−0.0587043			−0.0293522	−	0.999569i	$-0.509344\pi$
$271$	−0.966395			−0.0587043			−0.0293522	+	0.999569i	$0.509344\pi$
$272$	0.949884	−	23.9504i	0.0575952	−	1.45220i
$273$	−0.507615	+	3.59358i	−0.0307222	+	0.217494i
$274$	0.794385	+	6.53365i	0.0479906	+	0.394712i
$275$	29.0370	+	16.7645i	1.75099	+	1.01094i
$276$	−9.21005	+	0.939459i	−0.554380	+	0.0565488i
$277$	3.36301	−	1.94163i	0.202064	−	0.116662i	−0.395554	−	0.918443i	$-0.629447\pi$
$277$	3.36301	−	1.94163i	0.202064	−	0.116662i	0.597618	+	0.801781i	$0.296114\pi$
$278$	5.84092	+	7.77027i	0.350315	+	0.466030i
$279$	3.25759	−	3.13701i	0.195027	−	0.187808i
$280$	−10.9710	+	4.16676i	−0.655645	+	0.249012i
$281$	1.12890	+	1.95532i	0.0673447	+	0.116644i	0.897732	−	0.440543i	$-0.145214\pi$
$281$	1.12890	+	1.95532i	0.0673447	+	0.116644i	−0.830387	+	0.557187i	$0.811881\pi$
$282$	−0.140023	+	7.24006i	−0.00833825	+	0.431139i
$283$	1.94707	+	1.12414i	0.115741	+	0.0668234i	0.556753	−	0.830678i	$-0.312047\pi$
$283$	1.94707	+	1.12414i	0.115741	+	0.0668234i	−0.441012	+	0.897501i	$0.645380\pi$
$284$	−0.853137	−	0.887643i	−0.0506243	−	0.0526719i
$285$	23.5967	−	30.1587i	1.39775	−	1.78645i
$286$	−7.48310	−	3.18684i	−0.442485	−	0.188442i
$287$	−8.37999			−0.494655
$288$	11.2271	−	12.7260i	0.661565	−	0.749888i
$289$	18.9077			1.11221
$290$	−35.6050	−	15.1632i	−2.09080	−	0.890411i
$291$	0.249512	+	0.618813i	0.0146267	+	0.0362755i
$292$	15.0282	+	15.6360i	0.879459	+	0.915031i
$293$	−11.9855	−	6.91983i	−0.700200	−	0.404261i	0.107222	−	0.994235i	$-0.465805\pi$
$293$	−11.9855	−	6.91983i	−0.700200	−	0.404261i	−0.807422	+	0.589974i	$0.799138\pi$
$294$	−2.14461	+	1.18350i	−0.125076	+	0.0690230i
$295$	25.1417	+	43.5467i	1.46381	+	2.53539i
$296$	17.1885	−	6.52812i	0.999059	−	0.379439i
$297$	−14.1871	+	1.46096i	−0.823218	+	0.0847736i
$298$	11.4211	+	15.1936i	0.661605	+	0.880144i
$299$	4.84961	−	2.79992i	0.280460	−	0.161924i
$300$	17.3302	−	38.6050i	1.00056	−	2.22886i
$301$	1.87479	+	1.08241i	0.108061	+	0.0623890i
$302$	−0.844479	−	6.94566i	−0.0485943	−	0.399678i
$303$	30.5197	−	12.3059i	1.75331	−	0.706954i
$304$	−21.2968	−	0.844643i	−1.22146	−	0.0484436i
$305$	−12.3481			−0.707053
$306$	19.7161	+	16.0503i	1.12709	+	0.917537i
$307$			31.9427i			1.82307i	0.411228	+	0.911533i	$0.365100\pi$
$307$			31.9427i			1.82307i	−0.411228	+	0.911533i	$0.634900\pi$
$308$	−1.31542	−	5.32955i	−0.0749529	−	0.303679i
$309$	5.64994	−	7.22115i	0.321414	−	0.410797i
$310$	−8.78103	+	1.06763i	−0.498729	+	0.0606372i
$311$	12.6963	−	21.9907i	0.719942	−	1.24698i	−0.241080	−	0.970505i	$-0.577502\pi$
$311$	12.6963	−	21.9907i	0.719942	−	1.24698i	0.961022	−	0.276471i	$-0.0891650\pi$
$312$	−3.04293	+	9.80371i	−0.172272	+	0.555026i
$313$	−10.8948	−	18.8704i	−0.615811	−	1.06662i	−0.990242	−	0.139361i	$-0.955495\pi$
$313$	−10.8948	−	18.8704i	−0.615811	−	1.06662i	0.374431	−	0.927255i	$-0.377838\pi$
$314$	−3.71885	−	4.94725i	−0.209867	−	0.279190i
$315$	3.44778	−	11.9605i	0.194261	−	0.673899i
$316$	1.32317	−	4.57357i	0.0744343	−	0.257284i
$317$	−23.6096	+	13.6310i	−1.32605	+	0.765595i	−0.984686	−	0.174337i	$-0.944222\pi$
$317$	−23.6096	+	13.6310i	−1.32605	+	0.765595i	−0.341363	+	0.939931i	$0.610889\pi$
$318$	−1.56572	+	2.59470i	−0.0878011	+	0.145504i
$319$	9.05101	−	15.6768i	0.506759	−	0.877733i
$320$	−32.5163	+	6.67062i	−1.81772	+	0.372899i
$321$	−2.86421	+	20.2767i	−0.159864	+	1.13174i
$322$	3.47730	+	1.48088i	0.193782	+	0.0825264i
$323$		−	31.9293i		−	1.77659i
$324$	3.65132	+	17.6258i	0.202851	+	0.979210i
$325$			25.5962i			1.41982i
$326$	−5.91590	+	13.8913i	−0.327651	+	0.769366i
$327$	−3.54766	+	25.1152i	−0.196186	+	1.38887i
$328$	−23.3971	−	3.79092i	−1.29189	−	0.209319i
$329$	1.47815	−	2.56022i	0.0814929	−	0.141150i
$330$	23.8843	+	14.4125i	1.31479	+	0.793380i
$331$	0.0401560	−	0.0231841i	0.00220717	−	0.00127431i	−0.498896	−	0.866662i	$-0.666261\pi$
$331$	0.0401560	−	0.0231841i	0.00220717	−	0.00127431i	0.501103	+	0.865388i	$0.332928\pi$
$332$	−22.7043	−	6.56853i	−1.24606	−	0.360495i
$333$	−5.40168	+	18.7387i	−0.296010	+	1.02687i
$334$	2.38049	−	1.78942i	0.130255	−	0.0979125i
$335$	22.5909	+	39.1285i	1.23427	+	2.13782i
$336$	−6.52316	+	2.33417i	−0.355868	+	0.127339i
$337$	6.71951	−	11.6385i	0.366035	−	0.633992i	−0.622907	−	0.782296i	$-0.714048\pi$
$337$	6.71951	−	11.6385i	0.366035	−	0.633992i	0.988942	+	0.148305i	$0.0473816\pi$
$338$	1.46954	+	12.0867i	0.0799324	+	0.657427i
$339$	−20.9889	+	26.8258i	−1.13996	+	1.45698i
$340$	−11.9157	−	48.2775i	−0.646217	−	2.61822i
$341$		−	4.13767i		−	0.224067i
$342$	14.2721	−	17.5317i	0.771745	−	0.948004i
$343$	1.00000			0.0539949
$344$	4.74478	+	3.87021i	0.255821	+	0.208668i
$345$	−17.8127	+	7.18229i	−0.959006	+	0.386682i
$346$	−11.6956	+	1.42199i	−0.628759	+	0.0764467i
$347$	−5.05180	−	2.91666i	−0.271195	−	0.156574i	0.358236	−	0.933631i	$-0.383378\pi$
$347$	−5.05180	−	2.91666i	−0.271195	−	0.156574i	−0.629430	+	0.777057i	$0.716712\pi$
$348$	−20.8425	−	9.35641i	−1.11728	−	0.501556i
$349$	−9.14313	+	5.27879i	−0.489421	+	0.282567i	−0.724334	−	0.689449i	$-0.757853\pi$
$349$	−9.14313	+	5.27879i	−0.489421	+	0.282567i	0.234913	+	0.972016i	$0.424519\pi$
$350$	−13.8092	+	10.3804i	−0.738134	+	0.554856i
$351$	−6.38113	−	8.82184i	−0.340600	−	0.470875i
$352$	−1.26170	−	15.4753i	−0.0672487	−	0.824834i
$353$	4.98862	+	8.64055i	0.265518	+	0.459890i	0.967699	−	0.252108i	$-0.0811238\pi$
$353$	4.98862	+	8.64055i	0.265518	+	0.459890i	−0.702181	+	0.711998i	$0.747790\pi$
$354$	14.3426	+	25.9902i	0.762303	+	1.38136i
$355$	−2.21196	−	1.27708i	−0.117399	−	0.0677801i
$356$	−7.60035	−	7.90776i	−0.402818	−	0.419110i
$357$	−3.88128	−	9.62593i	−0.205419	−	0.509458i
$358$	−0.274408	+	0.644345i	−0.0145029	+	0.0340547i
$359$	18.9768			1.00156			0.500780	−	0.865575i	$-0.333047\pi$
$359$	18.9768			1.00156			0.500780	+	0.865575i	$0.333047\pi$
$360$	15.0369	−	31.8343i	0.792516	−	1.67781i
$361$	−9.39175			−0.494303
$362$	−1.65513	+	3.88644i	−0.0869915	+	0.204267i
$363$	3.69972	−	4.72859i	0.194185	−	0.248187i
$364$	3.02142	−	2.90397i	0.158366	−	0.152209i
$365$	38.9642	+	22.4960i	2.03948	+	1.17749i
$366$	−7.28842	−	0.140958i	−0.380972	−	0.00736802i
$367$	−8.37709	−	14.5095i	−0.437281	−	0.757392i	0.560198	−	0.828359i	$-0.310725\pi$
$367$	−8.37709	−	14.5095i	−0.437281	−	0.757392i	−0.997479	+	0.0709665i	$0.977392\pi$
$368$	9.03875	+	5.70770i	0.471177	+	0.297534i
$369$	18.1087	−	17.4383i	0.942699	−	0.907803i
$370$	30.4905	−	22.9197i	1.58513	−	1.19154i
$371$	1.07145	−	0.618599i	0.0556267	−	0.0321161i
$372$	−5.19514	+	0.529923i	−0.269355	+	0.0274753i
$373$	−27.3994	−	15.8190i	−1.41869	−	0.819079i	−0.422502	−	0.906362i	$-0.638848\pi$
$373$	−27.3994	−	15.8190i	−1.41869	−	0.819079i	−0.996184	+	0.0872835i	$0.972181\pi$
$374$	23.0900	−	2.80736i	1.19395	−	0.145165i
$375$	7.25302	−	51.3467i	0.374544	−	2.65153i
$376$	5.28520	−	6.47951i	0.272563	−	0.334155i
$377$	13.8192			0.711725
$378$	2.17157	−	7.02028i	0.111693	−	0.361084i
$379$			17.8442i			0.916594i	0.888799	+	0.458297i	$0.151540\pi$
$379$			17.8442i			0.916594i	−0.888799	+	0.458297i	$0.848460\pi$
$380$	−42.9287	+	10.5955i	−2.20220	+	0.543537i
$381$	13.8230	+	1.95258i	0.708174	+	0.100034i
$382$	0.00388937	+	0.0319892i	0.000198997	+	0.00163671i
$383$	−9.34556	+	16.1870i	−0.477536	+	0.827116i	−0.999668	−	0.0257482i	$-0.991803\pi$
$383$	−9.34556	+	16.1870i	−0.477536	+	0.827116i	0.522133	+	0.852864i	$0.325137\pi$
$384$	−19.2687	+	3.56611i	−0.983302	+	0.181982i
$385$	−5.69422	−	9.86268i	−0.290204	−	0.502649i
$386$	−11.7671	+	8.84537i	−0.598932	+	0.450217i
$387$	−6.30373	+	1.56231i	−0.320437	+	0.0794168i
$388$	0.214115	−	0.740092i	0.0108700	−	0.0375725i
$389$	−17.9406	+	10.3580i	−0.909624	+	0.525171i	−0.880310	−	0.474399i	$-0.842665\pi$
$389$	−17.9406	+	10.3580i	−0.909624	+	0.525171i	−0.0293136	+	0.999570i	$0.509332\pi$
$390$	−0.411786	+	21.2919i	−0.0208516	+	1.07816i
$391$	−8.00723	+	13.8689i	−0.404943	+	0.701382i
$392$	2.79202	+	0.452378i	0.141018	+	0.0228485i
$393$	−17.2772	−	13.5180i	−0.871522	−	0.681892i
$394$	−0.406507	+	0.954528i	−0.0204795	+	0.0480884i
$395$		−	9.87740i		−	0.496986i
$396$	13.9331	+	8.77953i	0.700162	+	0.441188i
$397$			1.98395i			0.0995718i	0.998760	+	0.0497859i	$0.0158539\pi$
$397$			1.98395i			0.0995718i	−0.998760	+	0.0497859i	$0.984146\pi$
$398$	35.1715	+	14.9786i	1.76299	+	0.750808i
$399$	−8.55944	+	3.45126i	−0.428508	+	0.172779i
$400$	−43.2514	+	22.7353i	−2.16257	+	1.13676i
$401$	−1.64571	+	2.85045i	−0.0821828	+	0.142345i	−0.904187	−	0.427136i	$-0.859522\pi$
$401$	−1.64571	+	2.85045i	−0.0821828	+	0.142345i	0.822004	+	0.569481i	$0.192856\pi$
$402$	12.8875	+	23.3533i	0.642769	+	1.16476i
$403$	2.73553	−	1.57936i	0.136267	−	0.0786736i
$404$	−36.5011	−	10.5601i	−1.81600	−	0.525384i
$405$	17.4388	+	33.0206i	0.866540	+	1.64081i
$406$	5.60429	+	7.45548i	0.278136	+	0.370009i
$407$	8.92120	+	15.4520i	0.442208	+	0.765926i
$408$	−6.48205	−	28.6316i	−0.320909	−	1.41747i
$409$	13.9510	−	24.1638i	0.689831	−	1.19482i	−0.282061	−	0.959396i	$-0.591018\pi$
$409$	13.9510	−	24.1638i	0.689831	−	1.19482i	0.971892	−	0.235426i	$-0.0756486\pi$
$410$	−48.8129	+	5.93485i	−2.41070	+	0.293101i
$411$	3.01446	+	7.47613i	0.148692	+	0.368770i
$412$	−10.2788	+	2.53696i	−0.506398	+	0.124987i
$413$		−	12.1189i		−	0.596331i
$414$	−10.5959	+	4.03597i	−0.520758	+	0.198357i
$415$	−49.0337			−2.40697
$416$	9.74955	−	6.74110i	0.478011	−	0.330510i
$417$	9.37650	+	7.33632i	0.459169	+	0.359261i
$418$	−2.49633	−	20.5318i	−0.122099	−	1.00424i
$419$	26.8564	+	15.5056i	1.31202	+	0.757497i	0.982431	−	0.186626i	$-0.0597553\pi$
$419$	26.8564	+	15.5056i	1.31202	+	0.757497i	0.329592	+	0.944123i	$0.393089\pi$
$420$	−11.6540	+	8.41264i	−0.568658	+	0.410495i
$421$	26.6589	−	15.3915i	1.29928	−	0.750137i	0.318997	−	0.947756i	$-0.396654\pi$
$421$	26.6589	−	15.3915i	1.29928	−	0.750137i	0.980279	+	0.197619i	$0.0633208\pi$
$422$	12.2603	+	16.3100i	0.596820	+	0.793960i
$423$	2.13351	+	8.60844i	0.103735	+	0.418556i
$424$	3.27133	−	1.24244i	0.158870	−	0.0603383i
$425$	−36.6001	−	63.3932i	−1.77537	−	3.07502i
$426$	−1.29102	−	0.779037i	−0.0625501	−	0.0377445i
$427$	2.57733	+	1.48802i	0.124726	+	0.0720104i
$428$	17.0483	−	16.3856i	0.824062	−	0.792027i
$429$	−9.86347	−	1.39327i	−0.476213	−	0.0672678i
$430$	11.6871	+	4.97720i	0.563601	+	0.240022i
$431$	−28.7975			−1.38713			−0.693563	−	0.720396i	$-0.743960\pi$
$431$	−28.7975			−1.38713			−0.693563	+	0.720396i	$0.743960\pi$
$432$	9.23887	−	18.6184i	0.444505	−	0.895776i
$433$	−6.87546			−0.330413			−0.165207	−	0.986259i	$-0.552829\pi$
$433$	−6.87546			−0.330413			−0.165207	+	0.986259i	$0.552829\pi$
$434$	1.96145	+	0.835326i	0.0941525	+	0.0400969i
$435$	−46.9309	−	6.62926i	−2.25016	−	0.317848i
$436$	21.1164	−	20.2955i	1.01129	−	0.971978i
$437$	12.3323	+	7.12008i	0.589936	+	0.340600i
$438$	22.7416	+	13.7229i	1.08664	+	0.655707i
$439$	3.26034	+	5.64708i	0.155608	+	0.269521i	0.933280	−	0.359149i	$-0.116933\pi$
$439$	3.26034	+	5.64708i	0.155608	+	0.269521i	−0.777672	+	0.628670i	$0.783600\pi$
$440$	−11.4367	−	30.1127i	−0.545223	−	1.43557i
$441$	−2.16094	+	2.08095i	−0.102902	+	0.0990927i
$442$	10.6695	+	14.1939i	0.507499	+	0.675134i
$443$	−7.85211	+	4.53342i	−0.373065	+	0.215389i	−0.674797	−	0.738004i	$-0.735769\pi$
$443$	−7.85211	+	4.53342i	−0.373065	+	0.215389i	0.301732	+	0.953393i	$0.402435\pi$
$444$	18.2585	−	13.1802i	0.866509	−	0.625504i
$445$	−19.7057	−	11.3771i	−0.934141	−	0.539326i
$446$	2.37894	+	19.5663i	0.112646	+	0.926492i
$447$	18.3344	+	14.3451i	0.867186	+	0.678500i
$448$	7.59071	+	2.52609i	0.358627	+	0.119347i
$449$	−27.4755			−1.29665			−0.648324	−	0.761364i	$-0.724530\pi$
$449$	−27.4755			−1.29665			−0.648324	+	0.761364i	$0.724530\pi$
$450$	8.23983	−	51.1677i	0.388429	−	2.41207i
$451$		−	23.0009i		−	1.08307i
$452$	38.1844	−	9.42452i	1.79604	−	0.443292i
$453$	−3.20455	−	7.94757i	−0.150563	−	0.373410i
$454$	−13.5777	+	1.65083i	−0.637233	+	0.0774771i
$455$	4.34700	−	7.52923i	0.203791	−	0.352976i
$456$	−25.4594	+	5.76388i	−1.19224	+	0.269918i
$457$	13.5081	+	23.3967i	0.631883	+	1.09445i	0.987167	+	0.159694i	$0.0510509\pi$
$457$	13.5081	+	23.3967i	0.631883	+	1.09445i	−0.355284	+	0.934758i	$0.615616\pi$
$458$	−7.26761	−	9.66822i	−0.339593	−	0.451766i
$459$	28.4183	+	12.7243i	1.32645	+	0.593920i
$460$	21.3038	+	6.16337i	0.993295	+	0.287368i
$461$	−5.52250	+	3.18842i	−0.257208	+	0.148499i	−0.623060	−	0.782174i	$-0.714111\pi$
$461$	−5.52250	+	3.18842i	−0.257208	+	0.148499i	0.365852	+	0.930673i	$0.380778\pi$
$462$	−3.24840	−	5.88639i	−0.151129	−	0.273860i
$463$	11.6805	−	20.2313i	0.542840	−	0.940226i	−0.455899	−	0.890031i	$-0.650682\pi$
$463$	11.6805	−	20.2313i	0.542840	−	0.940226i	0.998739	−	0.0501951i	$-0.0159843\pi$
$464$	12.2746	+	23.3511i	0.569833	+	1.08405i
$465$	−10.0477	+	4.05134i	−0.465950	+	0.187876i
$466$	5.33952	+	2.27395i	0.247348	+	0.105339i
$467$			37.0267i			1.71339i	0.515823	+	0.856695i	$0.327486\pi$
$467$			37.0267i			1.71339i	−0.515823	+	0.856695i	$0.672514\pi$
$468$	−0.486109	+	12.5627i	−0.0224704	+	0.580712i
$469$		−	10.8893i		−	0.502822i
$470$	6.79691	−	15.9600i	0.313518	−	0.736179i
$471$	−5.96992	−	4.67096i	−0.275079	−	0.215226i
$472$	5.48230	−	33.8361i	0.252344	−	1.55743i
$473$	−2.97093	+	5.14581i	−0.136604	+	0.236604i
$474$	0.112754	−	5.83008i	0.00517896	−	0.267784i
$475$	−56.3697	+	32.5450i	−2.58642	+	1.49327i
$476$	−3.33066	+	11.5125i	−0.152660	+	0.527674i
$477$	−1.02806	+	3.56638i	−0.0470714	+	0.163293i
$478$	11.8289	−	8.89182i	0.541043	−	0.406702i
$479$	−14.0733	−	24.3756i	−0.643024	−	1.11375i	−0.984754	−	0.173952i	$-0.944346\pi$
$479$	−14.0733	−	24.3756i	−0.643024	−	1.11375i	0.341730	−	0.939798i	$-0.388987\pi$
$480$	−36.3439	+	18.2162i	−1.65886	+	0.831452i
$481$	−6.81050	+	11.7961i	−0.310532	+	0.537857i
$482$	−0.988967	−	8.13405i	−0.0450462	−	0.370496i
$483$	4.58342	+	0.647435i	0.208553	+	0.0294593i
$484$	−6.73079	+	1.66126i	−0.305945	+	0.0755120i
$485$		−	1.59835i		−	0.0725774i
$486$	9.91620	+	19.6893i	0.449808	+	0.893125i
$487$	15.2775			0.692291			0.346146	−	0.938181i	$-0.387490\pi$
$487$	15.2775			0.692291			0.346146	+	0.938181i	$0.387490\pi$
$488$	6.52280	+	5.32051i	0.295273	+	0.240848i
$489$	−2.58640	+	18.3100i	−0.116961	+	0.828009i
$490$	5.82493	−	0.708216i	0.263144	−	0.0319940i
$491$	−24.2006	−	13.9722i	−1.09216	−	0.630557i	−0.158007	−	0.987438i	$-0.550507\pi$
$491$	−24.2006	−	13.9722i	−1.09216	−	0.630557i	−0.934150	+	0.356881i	$0.883840\pi$
$492$	−28.8793	+	2.94579i	−1.30198	+	0.132807i
$493$	−34.2255	+	19.7601i	−1.54144	+	0.889950i
$494$	12.6213	−	9.48743i	0.567859	−	0.426860i
$495$	32.8286	+	9.46328i	1.47553	+	0.425343i
$496$	5.09851	+	3.21956i	0.228930	+	0.144562i
$497$	0.307790	+	0.533107i	0.0138063	+	0.0239131i
$498$	−28.9419	−	0.559737i	−1.29692	−	0.0250824i
$499$	26.5541	+	15.3310i	1.18873	+	0.686311i	0.958017	−	0.286712i	$-0.0925622\pi$
$499$	26.5541	+	15.3310i	1.18873	+	0.686311i	0.230709	+	0.973023i	$0.425896\pi$
$500$	−43.1714	+	41.4931i	−1.93068	+	1.85563i
$501$	2.24754	−	2.87257i	0.100413	−	0.128337i
$502$	−9.01952	+	21.1790i	−0.402561	+	0.945263i
$503$	33.9094			1.51195			0.755974	−	0.654602i	$-0.227164\pi$
$503$	33.9094			1.51195			0.755974	+	0.654602i	$0.227164\pi$
$504$	−6.97475	+	4.83248i	−0.310680	+	0.215256i
$505$	−78.8303			−3.50790
$506$	−4.06464	+	9.54428i	−0.180695	+	0.424295i
$507$	5.57647	+	13.8302i	0.247660	+	0.614219i
$508$	−11.1703	−	11.6222i	−0.495604	−	0.515650i
$509$	−11.3523	−	6.55427i	−0.503183	−	0.290513i	0.226844	−	0.973931i	$-0.427159\pi$
$509$	−11.3523	−	6.55427i	−0.503183	−	0.290513i	−0.730027	+	0.683418i	$0.760493\pi$
$510$	−29.4255	−	53.3216i	−1.30298	−	2.36112i
$511$	−5.42179	−	9.39082i	−0.239846	−	0.415425i
$512$	20.0506	+	10.4868i	0.886121	+	0.463453i
$513$	11.3145	−	25.2697i	0.499549	−	1.11569i
$514$	13.1391	−	9.87669i	0.579542	−	0.435642i
$515$	−19.0215	+	10.9821i	−0.838187	+	0.483928i
$516$	6.84142	+	3.07118i	0.301177	+	0.135201i
$517$	7.02716	+	4.05713i	0.309054	+	0.178432i
$518$	−9.12599	+	1.10957i	−0.400973	+	0.0487518i
$519$	−13.3827	+	5.39604i	−0.587434	+	0.236860i
$520$	15.5430	−	19.0552i	0.681604	−	0.835628i
$521$	−15.8422			−0.694058			−0.347029	−	0.937854i	$-0.612809\pi$
$521$	−15.8422			−0.694058			−0.347029	+	0.937854i	$0.612809\pi$
$522$	−27.6250	−	4.44861i	−1.20911	−	0.194711i
$523$		−	8.08582i		−	0.353568i	−0.984250	−	0.176784i	$-0.943431\pi$
$523$		−	8.08582i		−	0.353568i	0.984250	−	0.176784i	$-0.0565694\pi$
$524$	6.06990	+	24.5929i	0.265165	+	1.07434i
$525$	−13.0380	+	16.6638i	−0.569025	+	0.727267i
$526$	4.14499	+	34.0917i	0.180730	+	1.48647i
$527$	−4.51666	+	7.82309i	−0.196749	+	0.340779i
$528$	−6.40670	−	17.9044i	−0.278816	−	0.779189i
$529$	7.92885	+	13.7332i	0.344733	+	0.597094i
$530$	5.80300	−	4.36211i	0.252066	−	0.189478i
$531$	25.2187	+	26.1881i	1.09440	+	1.13647i
$532$	10.2370	+	2.96164i	0.443829	+	0.128403i
$533$	15.2066	−	8.77952i	0.658670	−	0.380283i
$534$	−11.5013	−	6.94022i	−0.497711	−	0.300333i
$535$	24.5279	−	42.4835i	1.06043	−	1.83672i
$536$	4.92608	−	30.4031i	0.212774	−	1.31322i
$537$	−0.119970	+	0.849310i	−0.00517709	+	0.0366504i
$538$	−15.7174	+	36.9064i	−0.677625	+	1.59115i
$539$			2.74474i			0.118224i
$540$	7.67736	−	42.4306i	0.330381	−	1.82592i
$541$		−	16.2217i		−	0.697425i	−0.937230	−	0.348712i	$-0.886619\pi$
$541$		−	16.2217i		−	0.697425i	0.937230	−	0.348712i	$-0.113381\pi$
$542$	1.25741	+	0.535496i	0.0540104	+	0.0230015i
$543$	−0.723613	+	5.12271i	−0.0310532	+	0.219837i
$544$	−14.5072	+	30.6363i	−0.621993	+	1.31352i
$545$	30.3807	−	52.6209i	1.30137	−	2.25403i
$546$	2.65174	−	4.39446i	0.113484	−	0.188066i
$547$	17.2995	−	9.98786i	0.739672	−	0.427050i	−0.0822780	−	0.996609i	$-0.526220\pi$
$547$	17.2995	−	9.98786i	0.739672	−	0.427050i	0.821950	+	0.569560i	$0.192886\pi$
$548$	2.58681	−	8.94135i	0.110503	−	0.381956i
$549$	−8.66594	+	2.14776i	−0.369853	+	0.0916642i
$550$	−28.4915	−	37.9028i	−1.21488	−	1.61618i
$551$	17.5708	+	30.4335i	0.748541	+	1.29651i
$552$	12.5041	+	3.88108i	0.532210	+	0.165190i
$553$	−1.19028	+	2.06163i	−0.0506160	+	0.0876694i
$554$	−5.45162	+	0.662828i	−0.231617	+	0.0281609i
$555$	28.7877	−	36.7933i	1.22197	−	1.56179i
$556$	−3.29419	−	13.3467i	−0.139705	−	0.566028i
$557$		−	5.39715i		−	0.228684i	−0.993441	−	0.114342i	$-0.963524\pi$
$557$		−	5.39715i		−	0.228684i	0.993441	−	0.114342i	$-0.0364760\pi$
$558$	−5.97684	+	2.27658i	−0.253020	+	0.0963754i
$559$	−4.53606			−0.191855
$560$	16.5837	+	0.657718i	0.700789	+	0.0277936i
$561$	26.4207	−	10.6531i	1.11548	−	0.449775i
$562$	−0.385381	−	3.16968i	−0.0162563	−	0.133705i
$563$	−13.0789	−	7.55112i	−0.551211	−	0.318242i	0.198399	−	0.980121i	$-0.436426\pi$
$563$	−13.0789	−	7.55112i	−0.551211	−	0.318242i	−0.749610	+	0.661879i	$0.769759\pi$
$564$	4.19403	−	9.34271i	0.176600	−	0.393399i
$565$	70.6627	−	40.7971i	2.97280	−	1.71635i
$566$	−1.91050	−	2.54157i	−0.0803043	−	0.106830i
$567$	0.339317	−	8.99360i	0.0142500	−	0.377696i
$568$	0.618188	+	1.62768i	0.0259386	+	0.0682960i
$569$	2.99165	+	5.18170i	0.125417	+	0.217228i	0.921896	−	0.387438i	$-0.126640\pi$
$569$	2.99165	+	5.18170i	0.125417	+	0.217228i	−0.796479	+	0.604666i	$0.793307\pi$
$570$	−47.4139	+	26.1653i	−1.98595	+	1.09594i
$571$	24.3881	+	14.0805i	1.02061	+	0.589249i	0.914280	−	0.405083i	$-0.132757\pi$
$571$	24.3881	+	14.0805i	1.02061	+	0.589249i	0.106328	+	0.994331i	$0.466091\pi$
$572$	7.97065	+	8.29303i	0.333269	+	0.346749i
$573$	0.0147590	+	0.0366037i	0.000616567	+	0.00152914i
$574$	10.9035	+	4.64350i	0.455104	+	0.193816i
$575$	32.6466			1.36146
$576$	−21.6597	+	10.3371i	−0.902488	+	0.430714i
$577$	23.7529			0.988847			0.494424	−	0.869221i	$-0.335379\pi$
$577$	23.7529			0.988847			0.494424	+	0.869221i	$0.335379\pi$
$578$	−24.6014	−	10.4771i	−1.02328	−	0.435788i
$579$	−11.1100	+	14.1996i	−0.461714	+	0.590114i
$580$	37.9247	+	39.4586i	1.57474	+	1.63843i
$581$	10.2344	+	5.90884i	0.424595	+	0.245140i
$582$	0.0182458	−	0.943419i	0.000756311	−	0.0391060i
$583$	1.69790	+	2.94084i	0.0703197	+	0.121797i
$584$	−10.8895	−	28.6720i	−0.450612	−	1.18646i
$585$	6.27432	+	25.3161i	0.259411	+	1.04669i
$586$	11.7604	+	15.6450i	0.485816	+	0.646289i
$587$	−16.6826	+	9.63170i	−0.688564	+	0.397543i	−0.803074	−	0.595879i	$-0.796804\pi$
$587$	−16.6826	+	9.63170i	−0.688564	+	0.397543i	0.114510	+	0.993422i	$0.463470\pi$
$588$	3.44622	−	0.351527i	0.142120	−	0.0144967i
$589$	6.95634	+	4.01625i	0.286631	+	0.165487i
$590$	−8.58278	−	70.5916i	−0.353348	−	2.90621i
$591$	−0.177723	+	1.25816i	−0.00731053	+	0.0517539i
$592$	−25.9819	−	1.03045i	−1.06785	−	0.0423514i
$593$	31.0134			1.27357			0.636784	−	0.771043i	$-0.280264\pi$
$593$	31.0134			1.27357			0.636784	+	0.771043i	$0.280264\pi$
$594$	19.2689	+	5.96040i	0.790611	+	0.244558i
$595$			24.8631i			1.01929i
$596$	−6.44130	−	26.0976i	−0.263846	−	1.06900i
$597$	46.3596	+	6.54856i	1.89737	+	0.268015i
$598$	−7.86149	+	0.955828i	−0.321480	+	0.0390867i
$599$	12.1145	−	20.9829i	0.494984	−	0.857338i	−0.504999	−	0.863120i	$-0.668507\pi$
$599$	12.1145	−	20.9829i	0.494984	−	0.857338i	0.999983	+	0.00578191i	$0.00184045\pi$
$600$	−43.9406	+	40.6274i	−1.79387	+	1.65861i
$601$	−18.0824	−	31.3196i	−0.737595	−	1.27755i	−0.953576	−	0.301154i	$-0.902628\pi$
$601$	−18.0824	−	31.3196i	−0.737595	−	1.27755i	0.215981	−	0.976398i	$-0.430705\pi$
$602$	−1.83957	−	2.44721i	−0.0749753	−	0.0997409i
$603$	22.6601	+	23.5311i	0.922790	+	0.958262i
$604$	−2.74993	+	9.50519i	−0.111893	+	0.386761i
$605$	−12.4558	+	7.19133i	−0.506398	+	0.292369i
$606$	−46.5292	−	0.899876i	−1.89012	−	0.0365550i
$607$	−4.05931	+	7.03093i	−0.164762	+	0.285377i	−0.936571	−	0.350478i	$-0.886019\pi$
$607$	−4.05931	+	7.03093i	−0.164762	+	0.285377i	0.771809	+	0.635855i	$0.219352\pi$
$608$	27.2420	+	12.8999i	1.10481	+	0.523161i
$609$	8.99664	+	7.03910i	0.364562	+	0.285239i
$610$	16.0666	+	6.84232i	0.650518	+	0.277037i
$611$			6.19448i			0.250602i
$612$	−16.7595	−	31.8087i	−0.677464	−	1.28579i
$613$			15.8055i			0.638380i	0.947691	+	0.319190i	$0.103411\pi$
$613$			15.8055i			0.638380i	−0.947691	+	0.319190i	$0.896589\pi$
$614$	17.7000	−	41.5618i	0.714314	−	1.67730i
$615$	−55.8541	+	22.5210i	−2.25226	+	0.908135i
$616$	−1.24166	+	7.66337i	−0.0500279	+	0.308766i
$617$	9.64767	−	16.7103i	0.388400	−	0.672729i	−0.603834	−	0.797110i	$-0.706361\pi$
$617$	9.64767	−	16.7103i	0.388400	−	0.672729i	0.992235	+	0.124381i	$0.0396944\pi$
$618$	−11.3527	+	6.26497i	−0.456672	+	0.252014i
$619$	−3.25223	+	1.87768i	−0.130718	+	0.0754701i	−0.563933	−	0.825820i	$-0.690712\pi$
$619$	−3.25223	+	1.87768i	−0.130718	+	0.0754701i	0.433215	+	0.901291i	$0.357379\pi$
$620$	12.0169	+	3.47659i	0.482610	+	0.139623i
$621$	−11.2518	+	8.13879i	−0.451518	+	0.326598i
$622$	−28.7050	+	21.5776i	−1.15097	+	0.865183i
$623$	2.74201	+	4.74930i	0.109856	+	0.190277i
$624$	9.39166	−	11.0698i	0.375967	−	0.443148i
$625$	−31.5725	+	54.6852i	−1.26290	+	2.18741i
$626$	3.71923	+	30.5899i	0.148650	+	1.22262i
$627$	−9.47282	−	23.4935i	−0.378308	−	0.938239i
$628$	2.09737	+	8.49773i	0.0836943	+	0.339096i
$629$		−	38.9534i		−	1.55317i
$630$	−11.1136	+	13.6518i	−0.442775	+	0.543900i
$631$	−17.4125			−0.693182			−0.346591	−	0.938016i	$-0.612661\pi$
$631$	−17.4125			−0.693182			−0.346591	+	0.938016i	$0.612661\pi$
$632$	−4.25592	+	5.21765i	−0.169292	+	0.207547i
$633$	19.6816	+	15.3991i	0.782272	+	0.612061i
$634$	38.2725	−	4.65331i	1.52000	−	0.184807i
$635$	−28.9618	−	16.7211i	−1.14931	−	0.663556i
$636$	3.47498	−	2.50847i	0.137792	−	0.0994673i
$637$	−1.81463	+	1.04768i	−0.0718982	+	0.0415105i
$638$	−20.4634	+	15.3823i	−0.810153	+	0.608993i
$639$	−1.77448	−	0.511519i	−0.0701975	−	0.0202354i
$640$	46.0044	+	9.33845i	1.81848	+	0.369135i
$641$	−9.05539	−	15.6844i	−0.357666	−	0.619496i	0.629904	−	0.776673i	$-0.283094\pi$
$641$	−9.05539	−	15.6844i	−0.357666	−	0.619496i	−0.987571	+	0.157177i	$0.949761\pi$
$642$	14.9624	−	24.7957i	0.590519	−	0.978607i
$643$	28.2517	+	16.3111i	1.11414	+	0.643248i	0.939898	−	0.341455i	$-0.110920\pi$
$643$	28.2517	+	16.3111i	1.11414	+	0.643248i	0.174240	+	0.984703i	$0.444253\pi$
$644$	−3.70385	−	3.85366i	−0.145952	−	0.151855i
$645$	15.4047	+	2.17601i	0.606561	+	0.0856802i
$646$	−17.6926	+	41.5444i	−0.696105	+	1.63454i
$647$	37.0535			1.45673			0.728363	−	0.685192i	$-0.240282\pi$
$647$	37.0535			1.45673			0.728363	+	0.685192i	$0.240282\pi$
$648$	5.01588	−	24.9568i	0.197042	−	0.980395i
$649$	33.2632			1.30569
$650$	14.1833	−	33.3042i	0.556315	−	1.30630i
$651$	2.58538	+	0.365200i	0.101329	+	0.0143133i
$652$	15.3948	−	14.7963i	0.602906	−	0.579468i
$653$	−11.7269	−	6.77052i	−0.458909	−	0.264951i	0.252677	−	0.967551i	$-0.418689\pi$
$653$	−11.7269	−	6.77052i	−0.458909	−	0.264951i	−0.711585	+	0.702600i	$0.752022\pi$
$654$	18.5327	−	30.7124i	0.724687	−	1.20095i
$655$	26.2756	+	45.5106i	1.02667	+	1.77825i
$656$	28.3421	+	17.8972i	1.10658	+	0.698769i
$657$	31.2580	+	9.01052i	1.21949	+	0.351534i
$658$	−3.34193	+	2.51213i	−0.130282	+	0.0979332i
$659$	−14.4240	+	8.32769i	−0.561878	+	0.324401i	−0.753899	−	0.656990i	$-0.771829\pi$
$659$	−14.4240	+	8.32769i	−0.561878	+	0.324401i	0.192021	+	0.981391i	$0.438496\pi$
$660$	−23.0905	−	31.9873i	−0.898798	−	1.24510i
$661$	−19.0259	−	10.9846i	−0.740021	−	0.427252i	0.0820557	−	0.996628i	$-0.473851\pi$
$661$	−19.0259	−	10.9846i	−0.740021	−	0.427252i	−0.822077	+	0.569376i	$0.807185\pi$
$662$	−0.0650951	+	0.00791450i	−0.00252999	+	0.000307606i
$663$	17.1280	+	13.4012i	0.665195	+	0.520458i
$664$	25.9016	+	21.1274i	1.00518	+	0.819901i
$665$	22.1085			0.857329
$666$	17.4118	−	21.3884i	0.674692	−	0.828785i
$667$		−	17.6256i		−	0.682467i
$668$	−4.08889	+	1.00920i	−0.158204	+	0.0390472i
$669$	9.02739	+	22.3888i	0.349019	+	0.865599i
$670$	−7.71199	−	63.4295i	−0.297940	−	2.45050i
$671$	−4.08424	+	7.07410i	−0.157670	+	0.273093i
$672$	9.78092	+	0.577523i	0.377307	+	0.0222784i
$673$	−5.38474	−	9.32664i	−0.207566	−	0.359516i	0.743381	−	0.668868i	$-0.233221\pi$
$673$	−5.38474	−	9.32664i	−0.207566	−	0.359516i	−0.950947	+	0.309353i	$0.899888\pi$
$674$	−15.1921	+	11.4199i	−0.585178	+	0.439879i
$675$	−6.50213	−	63.1408i	−0.250267	−	2.43029i
$676$	4.78535	−	16.5407i	0.184052	−	0.636180i
$677$	−32.5041	+	18.7663i	−1.24923	+	0.721246i	−0.970957	−	0.239255i	$-0.923097\pi$
$677$	−32.5041	+	18.7663i	−1.24923	+	0.721246i	−0.278278	+	0.960501i	$0.589764\pi$
$678$	42.1740	−	23.2736i	1.61968	−	0.893819i
$679$	−0.192611	+	0.333611i	−0.00739171	+	0.0128028i
$680$	−11.2475	+	69.4183i	−0.431323	+	2.66207i
$681$	−15.5363	+	6.26440i	−0.595352	+	0.240052i
$682$	−2.29276	+	5.38367i	−0.0877941	+	0.206151i
$683$		−	1.33335i		−	0.0510192i	−0.999675	−	0.0255096i	$-0.991879\pi$
$683$		−	1.33335i		−	0.0510192i	0.999675	−	0.0255096i	$-0.00812084\pi$
$684$	−28.2845	+	14.9027i	−1.08149	+	0.569818i
$685$		−	19.3103i		−	0.737810i
$686$	−1.30114	−	0.554117i	−0.0496776	−	0.0211563i
$687$	−11.6668	−	9.12827i	−0.445115	−	0.348265i
$688$	−4.02905	−	7.66483i	−0.153606	−	0.292219i
$689$	−1.29618	+	2.24506i	−0.0493807	+	0.0855298i
$690$	27.1566	+	0.525211i	1.03384	+	0.0199944i
$691$	1.72220	−	0.994311i	0.0655154	−	0.0378254i	−0.466884	−	0.884318i	$-0.654624\pi$
$691$	1.72220	−	0.994311i	0.0655154	−	0.0378254i	0.532400	+	0.846493i	$0.321290\pi$
$692$	16.0055	+	4.63052i	0.608438	+	0.176026i
$693$	−5.71167	−	5.93122i	−0.216968	−	0.225309i
$694$	4.95690	+	6.59425i	0.188162	+	0.250314i
$695$	−14.2600	−	24.6990i	−0.540911	−	0.936886i
$696$	21.9344	+	23.7232i	0.831422	+	0.899224i
$697$	−25.1077	+	43.4878i	−0.951022	+	1.64722i
$698$	14.8215	−	1.80205i	0.561003	−	0.0682088i
$699$	7.03801	+	0.994160i	0.266202	+	0.0376026i
$700$	23.7196	−	5.85438i	0.896518	−	0.221275i
$701$			25.7168i			0.971309i	0.874151	+	0.485654i	$0.161419\pi$
$701$			25.7168i			0.971309i	−0.874151	+	0.485654i	$0.838581\pi$
$702$	3.41439	+	15.0143i	0.128868	+	0.566678i
$703$	−34.6376			−1.30638
$704$	−6.93347	+	20.8345i	−0.261315	+	0.785232i
$705$	2.97158	−	21.0368i	0.111916	−	0.792293i
$706$	−1.70300	−	14.0068i	−0.0640932	−	0.527153i
$707$	16.4536	+	9.49950i	0.618802	+	0.357265i
$708$	−4.26011	−	41.7643i	−0.160105	−	1.56960i
$709$	−42.4379	+	24.5016i	−1.59379	+	0.920175i	−0.601142	+	0.799142i	$0.705287\pi$
$709$	−42.4379	+	24.5016i	−1.59379	+	0.920175i	−0.992648	+	0.121033i	$0.961379\pi$
$710$	2.17041	+	2.88733i	0.0814540	+	0.108360i
$711$	−1.71801	−	6.93197i	−0.0644306	−	0.259969i
$712$	5.50726	+	14.5006i	0.206393	+	0.543431i
$713$	−2.01439	−	3.48902i	−0.0754395	−	0.130665i
$714$	−0.283822	+	14.6753i	−0.0106218	+	0.549210i
$715$	20.6658	+	11.9314i	0.772857	+	0.446209i
$716$	0.714085	−	0.686325i	0.0266866	−	0.0256492i
$717$	11.1683	−	14.2741i	0.417088	−	0.533078i
$718$	−24.6914	−	10.5154i	−0.921477	−	0.392431i
$719$	−40.1381			−1.49690			−0.748449	−	0.663192i	$-0.769201\pi$
$719$	−40.1381			−1.49690			−0.748449	+	0.663192i	$0.769201\pi$
$720$	−37.2050	+	33.0885i	−1.38655	+	1.23314i
$721$	5.29360			0.197144
$722$	12.2199	+	5.20413i	0.454779	+	0.193678i
$723$	−3.75284	−	9.30739i	−0.139570	−	0.346145i
$724$	4.30709	−	4.13965i	0.160072	−	0.153849i
$725$	69.7710	+	40.2823i	2.59123	+	1.49605i
$726$	−7.43403	+	4.10246i	−0.275903	+	0.152256i
$727$	−9.19737	−	15.9303i	−0.341112	−	0.590823i	0.643528	−	0.765423i	$-0.277470\pi$
$727$	−9.19737	−	15.9303i	−0.341112	−	0.590823i	−0.984639	+	0.174600i	$0.944137\pi$
$728$	−5.54042	+	2.10423i	−0.205342	+	0.0779881i
$729$	17.9820	+	20.1407i	0.665999	+	0.745953i
$730$	−38.2323	−	50.8611i	−1.41504	−	1.88245i
$731$	11.2343	−	6.48611i	0.415515	−	0.239898i
$732$	9.40512	+	4.22205i	0.347623	+	0.156051i
$733$	0.865933	+	0.499947i	0.0319840	+	0.0184660i	0.515907	−	0.856645i	$-0.327455\pi$
$733$	0.865933	+	0.499947i	0.0319840	+	0.0184660i	−0.483923	+	0.875111i	$0.660788\pi$
$734$	2.85974	+	23.5208i	0.105555	+	0.868168i
$735$	6.66518	−	2.68747i	0.245849	−	0.0991290i
$736$	−8.59790	−	12.4350i	−0.316923	−	0.458361i
$737$	29.8884			1.10095
$738$	−33.2247	+	12.6553i	−1.22302	+	0.465848i
$739$		−	14.4632i		−	0.532036i	−0.963968	−	0.266018i	$-0.914292\pi$
$739$		−	14.4632i		−	0.532036i	0.963968	−	0.266018i	$-0.0857081\pi$
$740$	−52.3725	+	12.9264i	−1.92525	+	0.475182i
$741$	11.9164	−	15.2303i	0.437760	−	0.559499i
$742$	−1.73687	+	0.211175i	−0.0637626	+	0.00775249i
$743$	24.7126	−	42.8034i	0.906616	−	1.57031i	0.0878834	−	0.996131i	$-0.471990\pi$
$743$	24.7126	−	42.8034i	0.906616	−	1.57031i	0.818733	−	0.574175i	$-0.194677\pi$
$744$	7.05322	+	2.18921i	0.258584	+	0.0802605i
$745$	−27.8833	−	48.2953i	−1.02156	−	1.76940i
$746$	26.8847	+	35.7652i	0.984319	+	1.30946i
$747$	−34.4119	+	8.52862i	−1.25907	+	0.312046i
$748$	−31.5988	−	9.14180i	−1.15537	−	0.334257i
$749$	−10.2390	+	5.91149i	−0.374125	+	0.216001i
$750$	−37.8892	+	62.7900i	−1.38352	+	2.29277i
$751$	−2.34447	+	4.06073i	−0.0855508	+	0.148178i	−0.905626	−	0.424078i	$-0.860598\pi$
$751$	−2.34447	+	4.06073i	−0.0855508	+	0.148178i	0.820075	+	0.572256i	$0.193932\pi$
$752$	−10.4672	+	5.50210i	−0.381698	+	0.200641i
$753$	−3.94329	+	27.9160i	−0.143701	+	1.01731i
$754$	−17.9806	−	7.65745i	−0.654817	−	0.278868i
$755$			20.5280i			0.747092i
$756$	−6.71556	+	7.93103i	−0.244243	+	0.288449i
$757$			46.5413i			1.69157i	0.533523	+	0.845785i	$0.320868\pi$
$757$			46.5413i			1.69157i	−0.533523	+	0.845785i	$0.679132\pi$
$758$	9.88777	−	23.2177i	0.359140	−	0.843305i
$759$	−1.77704	+	12.5803i	−0.0645025	+	0.456636i
$760$	61.7272	+	10.0014i	2.23908	+	0.362788i
$761$	−0.879096	+	1.52264i	−0.0318672	+	0.0551956i	−0.881519	−	0.472148i	$-0.843479\pi$
$761$	−0.879096	+	1.52264i	−0.0318672	+	0.0551956i	0.849652	+	0.527344i	$0.176812\pi$
$762$	−16.9037	−	10.2001i	−0.612355	−	0.369512i
$763$	−12.6822	+	7.32210i	−0.459128	+	0.265078i
$764$	0.0126652	−	0.0437775i	0.000458211	−	0.00158382i
$765$	−51.7389	−	53.7277i	−1.87062	−	1.94253i
$766$	21.1293	−	15.8829i	0.763433	−	0.573873i
$767$	12.6967	+	21.9913i	0.458450	+	0.794058i
$768$	27.0472	+	6.03712i	0.975983	+	0.217846i
$769$	−12.1946	+	21.1217i	−0.439749	+	0.761667i	−0.997670	−	0.0682267i	$-0.978266\pi$
$769$	−12.1946	+	21.1217i	−0.439749	+	0.761667i	0.557921	+	0.829894i	$0.311599\pi$
$770$	1.94387	+	15.9879i	0.0700523	+	0.576166i
$771$	12.4053	−	15.8552i	0.446767	−	0.571010i
$772$	20.2120	−	4.98864i	0.727446	−	0.179545i
$773$		−	20.8617i		−	0.750343i	−0.926955	−	0.375172i	$-0.877584\pi$
$773$		−	20.8617i		−	0.750343i	0.926955	−	0.375172i	$-0.122416\pi$
$774$	9.06772	+	1.46023i	0.325932	+	0.0524868i
$775$	18.4151			0.661488
$776$	−0.688690	+	0.844315i	−0.0247225	+	0.0303092i
$777$	−10.4424	+	4.21050i	−0.374620	+	0.151051i
$778$	29.0827	−	3.53598i	1.04266	−	0.126771i
$779$	38.6697	+	22.3259i	1.38548	+	0.799910i
$780$	12.3340	−	27.4755i	0.441628	−	0.983779i
$781$	−1.46324	+	0.844804i	−0.0523590	+	0.0302295i
$782$	18.1035	−	13.6084i	0.647380	−	0.486636i
$783$	−34.0892	+	3.51045i	−1.21825	+	0.125453i
$784$	−3.38212	−	2.13571i	−0.120790	−	0.0762753i
$785$	9.07917	+	15.7256i	0.324050	+	0.561270i
$786$	14.9895	+	27.1623i	0.534658	+	0.968849i
$787$	7.67049	+	4.42856i	0.273423	+	0.157861i	0.630442	−	0.776236i	$-0.282874\pi$
$787$	7.67049	+	4.42856i	0.273423	+	0.157861i	−0.357019	+	0.934097i	$0.616207\pi$
$788$	1.05784	−	1.01672i	0.0376840	−	0.0362191i
$789$	15.7290	+	39.0094i	0.559968	+	1.38877i
$790$	−5.47324	+	12.8518i	−0.194729	+	0.457248i
$791$	−19.6651			−0.699212
$792$	−13.2639	−	19.1439i	−0.471313	−	0.680249i
$793$	−6.23586			−0.221442
$794$	1.09934	−	2.58139i	0.0390142	−	0.0916102i
$795$	5.47891	−	7.00256i	0.194317	−	0.248355i
$796$	−37.4631	−	38.9783i	−1.32784	−	1.38155i
$797$	−9.18965	−	5.30565i	−0.325514	−	0.187936i	0.328334	−	0.944562i	$-0.393513\pi$
$797$	−9.18965	−	5.30565i	−0.325514	−	0.187936i	−0.653848	+	0.756626i	$0.726846\pi$
$798$	13.0494	+	0.252376i	0.461944	+	0.00893401i
$799$	−8.85750	−	15.3416i	−0.313356	−	0.542748i
$800$	68.8740	−	5.61529i	2.43506	−	0.198531i
$801$	−15.8084	−	4.55697i	−0.558561	−	0.161013i
$802$	3.72077	−	2.79691i	0.131385	−	0.0987622i
$803$	25.7754	−	14.8814i	0.909593	−	0.525154i
$804$	−3.82789	−	37.5270i	−0.134999	−	1.32347i
$805$	−9.60312	−	5.54436i	−0.338465	−	0.195413i
$806$	−4.43445	+	0.539157i	−0.156197	+	0.0189910i
$807$	−6.87157	+	48.6463i	−0.241891	+	1.71243i
$808$	41.6414	+	33.9660i	1.46494	+	1.19492i
$809$	−39.7523			−1.39762			−0.698808	−	0.715310i	$-0.746286\pi$
$809$	−39.7523			−1.39762			−0.698808	+	0.715310i	$0.746286\pi$
$810$	−4.39292	−	52.6274i	−0.154351	−	1.84914i
$811$		−	48.3117i		−	1.69645i	−0.529634	−	0.848226i	$-0.677671\pi$
$811$		−	48.3117i		−	1.69645i	0.529634	−	0.848226i	$-0.322329\pi$
$812$	−3.16073	−	12.8060i	−0.110920	−	0.449404i
$813$	1.65739	+	0.234116i	0.0581273	+	0.00821082i
$814$	−3.04549	−	25.0485i	−0.106744	−	0.877950i
$815$	22.1489	−	38.3630i	0.775841	−	1.34380i
$816$	−7.43123	+	40.8454i	−0.260145	+	1.42987i
$817$	−5.76749	−	9.98959i	−0.201779	−	0.349492i
$818$	−31.5417	+	23.7099i	−1.10283	+	0.828997i
$819$	1.74114	−	6.04011i	0.0608405	−	0.211059i
$820$	66.8008	+	19.3260i	2.33279	+	0.674894i
$821$	36.2337	−	20.9195i	1.26456	−	0.730096i	0.290610	−	0.956842i	$-0.406142\pi$
$821$	36.2337	−	20.9195i	1.26456	−	0.730096i	0.973954	+	0.226745i	$0.0728085\pi$
$822$	0.220434	−	11.3978i	0.00768853	−	0.397545i
$823$	−13.3910	+	23.1938i	−0.466780	+	0.808486i	−0.999280	−	0.0379436i	$-0.987919\pi$
$823$	−13.3910	+	23.1938i	−0.466780	+	0.808486i	0.532500	+	0.846430i	$0.321253\pi$
$824$	14.7798	+	2.39471i	0.514880	+	0.0834236i
$825$	−45.7378	−	35.7860i	−1.59239	−	1.24591i
$826$	−6.71527	+	15.7683i	−0.233654	+	0.548649i
$827$			28.5827i			0.993917i	0.867774	+	0.496958i	$0.165550\pi$
$827$			28.5827i			0.993917i	−0.867774	+	0.496958i	$0.834450\pi$
$828$	16.0231	+	0.620005i	0.556840	+	0.0215467i
$829$			12.7669i			0.443413i	0.975113	+	0.221707i	$0.0711627\pi$
$829$			12.7669i			0.443413i	−0.975113	+	0.221707i	$0.928837\pi$
$830$	63.7995	+	27.1704i	2.21451	+	0.943098i
$831$	−6.23802	+	2.51524i	−0.216395	+	0.0872527i
$832$	−16.4209	+	3.36869i	−0.569291	+	0.116788i
$833$	2.99615	−	5.18948i	0.103810	−	0.179805i
$834$	−8.13492	−	14.7412i	−0.281689	−	0.510447i
$835$	−7.56675	+	4.36866i	−0.261858	+	0.151184i
$836$	−8.12895	+	28.0979i	−0.281145	+	0.971785i
$837$	−6.34682	+	4.59087i	−0.219378	+	0.158684i
$838$	−26.3520	−	35.0565i	−0.910314	−	1.21101i
$839$	−22.1660	−	38.3926i	−0.765254	−	1.32546i	−0.940112	−	0.340866i	$-0.889280\pi$
$839$	−22.1660	−	38.3926i	−0.765254	−	1.32546i	0.174858	−	0.984594i	$-0.444053\pi$
$840$	19.8250	−	4.48829i	0.684029	−	0.154861i
$841$	7.24808	−	12.5540i	0.249934	−	0.432898i
$842$	−43.2156	+	5.25430i	−1.48931	+	0.181075i
$843$	−1.46241	−	3.62690i	−0.0503680	−	0.124917i
$844$	−6.91459	−	28.0152i	−0.238010	−	0.964323i
$845$		−	35.7224i		−	1.22889i
$846$	1.99410	−	12.3830i	0.0685585	−	0.425735i
$847$	3.46638			0.119106
$848$	−4.94491	−	0.196117i	−0.169809	−	0.00673470i
$849$	−3.06695	−	2.39963i	−0.105257	−	0.0823550i
$850$	12.4944	+	102.764i	0.428555	+	3.52477i
$851$	15.0453	+	8.68642i	0.515747	+	0.297767i
$852$	1.24811	+	1.72901i	0.0427596	+	0.0592349i
$853$	−4.84975	+	2.80001i	−0.166052	+	0.0958704i	−0.580723	−	0.814101i	$-0.697230\pi$
$853$	−4.84975	+	2.80001i	−0.166052	+	0.0958704i	0.414671	+	0.909972i	$0.363897\pi$
$854$	−2.52892	−	3.36426i	−0.0865377	−	0.115123i
$855$	−47.7750	+	46.0065i	−1.63387	+	1.57339i
$856$	−31.2617	+	11.8731i	−1.06850	+	0.405814i
$857$	−7.89265	−	13.6705i	−0.269608	−	0.466975i	0.699153	−	0.714972i	$-0.253561\pi$
$857$	−7.89265	−	13.6705i	−0.269608	−	0.466975i	−0.968761	+	0.247998i	$0.920227\pi$
$858$	12.0617	+	7.27835i	0.411779	+	0.248479i
$859$	−15.9353	−	9.20028i	−0.543707	−	0.313909i	0.202873	−	0.979205i	$-0.434972\pi$
$859$	−15.9353	−	9.20028i	−0.543707	−	0.313909i	−0.746580	+	0.665296i	$0.768305\pi$
$860$	−12.4485	−	12.9520i	−0.424491	−	0.441661i
$861$	14.3719	+	2.03011i	0.489793	+	0.0691861i
$862$	37.4694	+	15.9572i	1.27621	+	0.543504i
$863$	32.0354			1.09050			0.545248	−	0.838275i	$-0.316435\pi$
$863$	32.0354			1.09050			0.545248	+	0.838275i	$0.316435\pi$
$864$	−22.3378	+	19.1056i	−0.759947	+	0.649986i
$865$	34.5665			1.17530
$866$	8.94590	+	3.80981i	0.303994	+	0.129463i
$867$	−32.4271	−	4.58052i	−1.10128	−	0.155562i
$868$	−2.08924	−	2.17374i	−0.0709135	−	0.0737817i
$869$	−5.65865	−	3.26702i	−0.191956	−	0.110826i
$870$	57.3900	+	34.6308i	1.94570	+	1.17409i
$871$	11.4085	+	19.7601i	0.386562	+	0.669544i
$872$	−38.7214	+	14.7062i	−1.31127	+	0.498016i
$873$	−0.278008	−	1.12173i	−0.00940914	−	0.0379647i
$874$	−12.1007	−	16.0978i	−0.409312	−	0.544515i
$875$	25.9282	−	14.9697i	0.876533	−	0.506067i
$876$	−21.9858	−	30.4569i	−0.742832	−	1.02904i
$877$	11.9555	+	6.90253i	0.403709	+	0.233082i	0.688083	−	0.725632i	$-0.258452\pi$
$877$	11.9555	+	6.90253i	0.403709	+	0.233082i	−0.284374	+	0.958713i	$0.591786\pi$
$878$	−1.11300	−	9.15423i	−0.0375621	−	0.308940i
$879$	18.8791	+	14.7713i	0.636775	+	0.498222i
$880$	−1.80527	+	45.5180i	−0.0608555	+	1.53441i
$881$	12.0252			0.405140			0.202570	−	0.979268i	$-0.435071\pi$
$881$	12.0252			0.405140			0.202570	+	0.979268i	$0.435071\pi$
$882$	3.96476	−	1.51018i	0.133501	−	0.0508504i
$883$		−	42.7774i		−	1.43957i	−0.694195	−	0.719787i	$-0.744239\pi$
$883$		−	42.7774i		−	1.43957i	0.694195	−	0.719787i	$-0.255761\pi$
$884$	−6.01745	−	24.3803i	−0.202389	−	0.820000i
$885$	−32.5691	−	80.7744i	−1.09480	−	2.71520i
$886$	12.7287	−	1.54760i	0.427629	−	0.0519927i
$887$	−18.8428	+	32.6367i	−0.632679	+	1.09583i	0.354322	+	0.935123i	$0.384712\pi$
$887$	−18.8428	+	32.6367i	−0.632679	+	1.09583i	−0.987002	+	0.160710i	$0.948622\pi$
$888$	−31.0601	+	7.03186i	−1.04231	+	0.235974i
$889$	4.02997	+	6.98012i	0.135161	+	0.234106i
$890$	19.3356	+	25.7224i	0.648130	+	0.862218i
$891$	24.6851	+	0.931338i	0.826983	+	0.0312010i
$892$	7.74671	−	26.7766i	0.259379	−	0.896549i
$893$	−13.6419	+	7.87614i	−0.456508	+	0.263565i
$894$	−15.9067	−	28.8243i	−0.531998	−	0.964029i
$895$	1.02737	−	1.77946i	0.0343413	−	0.0594809i
$896$	−8.47679	−	7.49293i	−0.283190	−	0.250321i
$897$	−8.99551	+	3.62709i	−0.300351	+	0.121105i
$898$	35.7494	+	15.2246i	1.19297	+	0.508053i
$899$		−	9.94214i		−	0.331589i
$900$	−39.0740	+	62.0103i	−1.30247	+	2.06701i
$901$		−	7.41366i		−	0.246985i
$902$	−12.7452	+	29.9273i	−0.424369	+	0.996471i
$903$	−2.95308	−	2.31054i	−0.0982725	−	0.0768899i
$904$	−54.9054	−	8.89607i	−1.82613	−	0.295879i
$905$	6.19672	−	10.7330i	0.205986	−	0.356778i
$906$	−0.234335	+	12.1166i	−0.00778526	+	0.402546i
$907$	−2.55710	+	1.47634i	−0.0849072	+	0.0490212i	−0.541852	−	0.840474i	$-0.682277\pi$
$907$	−2.55710	+	1.47634i	−0.0849072	+	0.0490212i	0.456945	+	0.889495i	$0.348944\pi$
$908$	18.5812	+	5.37569i	0.616638	+	0.178399i
$909$	−55.3232	+	13.7113i	−1.83496	+	0.454774i
$910$	−9.82811	+	7.38780i	−0.325799	+	0.244903i
$911$	−2.02754	−	3.51181i	−0.0671755	−	0.116351i	0.830481	−	0.557046i	$-0.188065\pi$
$911$	−2.02754	−	3.51181i	−0.0671755	−	0.116351i	−0.897657	+	0.440695i	$0.854732\pi$
$912$	36.3200	+	6.60789i	1.20267	+	0.218809i
$913$	−16.2182	+	28.0908i	−0.536745	+	0.929670i
$914$	−4.61135	−	37.9274i	−0.152530	−	1.25453i
$915$	21.1774	+	2.99143i	0.700102	+	0.0988935i
$916$	4.09882	+	16.6068i	0.135429	+	0.548703i
$917$		−	12.6654i		−	0.418249i
$918$	−29.9253	−	32.3031i	−0.987681	−	1.06616i
$919$	30.1468			0.994452			0.497226	−	0.867621i	$-0.334352\pi$
$919$	30.1468			0.994452			0.497226	+	0.867621i	$0.334352\pi$
$920$	−24.3039	−	19.8242i	−0.801276	−	0.653584i
$921$	7.73835	−	54.7825i	0.254987	−	1.80515i
$922$	8.95228	−	1.08845i	0.294828	−	0.0358462i
$923$	−1.11705	−	0.644928i	−0.0367681	−	0.0212281i
$924$	0.964852	+	9.45899i	0.0317413	+	0.311178i
$925$	−68.7703	+	39.7046i	−2.26115	+	1.30548i
$926$	−26.4084	+	19.8512i	−0.867835	+	0.652352i
$927$	−11.4392	+	11.0157i	−0.375711	+	0.361803i
$928$	−3.03165	−	37.1845i	−0.0995188	−	1.22064i
$929$	−6.09557	−	10.5578i	−0.199989	−	0.346391i	0.748535	−	0.663095i	$-0.230757\pi$
$929$	−6.09557	−	10.5578i	−0.199989	−	0.346391i	−0.948525	+	0.316703i	$0.897424\pi$
$930$	15.3183	+	0.296257i	0.502308	+	0.00971465i
$931$	−4.61452	−	2.66420i	−0.151235	−	0.0873155i
$932$	−5.68740	−	5.91744i	−0.186297	−	0.193832i
$933$	−27.1019	+	34.6388i	−0.887277	+	1.13402i
$934$	20.5171	−	48.1767i	0.671341	−	1.57639i
$935$	−68.2429			−2.23178
$936$	7.59371	−	16.0764i	0.248208	−	0.525475i
$937$	44.0708			1.43973			0.719864	−	0.694115i	$-0.244204\pi$
$937$	44.0708			1.43973			0.719864	+	0.694115i	$0.244204\pi$
$938$	−6.03396	+	14.1685i	−0.197016	+	0.462617i
$939$	14.1134	+	35.0025i	0.460573	+	1.14226i
$940$	−17.6874	+	16.9998i	−0.576900	+	0.554473i
$941$	9.13800	+	5.27583i	0.297890	+	0.171987i	0.641495	−	0.767127i	$-0.278315\pi$
$941$	9.13800	+	5.27583i	0.297890	+	0.171987i	−0.343605	+	0.939114i	$0.611648\pi$
$942$	5.17942	+	9.38558i	0.168755	+	0.305799i
$943$	−11.1978	−	19.3952i	−0.364650	−	0.631593i
$944$	−25.8824	+	40.9875i	−0.842400	+	1.33403i
$945$	−8.81056	+	19.6774i	−0.286607	+	0.640104i
$946$	6.71697	−	5.04915i	0.218387	−	0.164162i
$947$	−32.5147	+	18.7724i	−1.05659	+	0.610020i	−0.924486	−	0.381216i	$-0.875505\pi$
$947$	−32.5147	+	18.7724i	−1.05659	+	0.610020i	−0.132100	+	0.991236i	$0.542172\pi$
$948$	−3.37726	+	7.52325i	−0.109688	+	0.244344i
$949$	19.6771	+	11.3606i	0.638745	+	0.368780i
$950$	91.3784	−	11.1101i	2.96471	−	0.360460i
$951$	43.7933	−	17.6580i	1.42010	−	0.572598i
$952$	10.7129	−	13.1337i	0.347207	−	0.425667i
$953$	44.4383			1.43950			0.719749	−	0.694235i	$-0.244257\pi$
$953$	44.4383			1.43950			0.719749	+	0.694235i	$0.244257\pi$
$954$	3.31383	−	4.07068i	0.107289	−	0.131793i
$955$		−	0.0945449i		−	0.00305940i
$956$	−20.3182	+	5.01485i	−0.657137	+	0.162192i
$957$	−19.3205	+	24.6935i	−0.624544	+	0.798226i
$958$	4.80428	+	39.5142i	0.155219	+	1.27665i
$959$	−2.32701	+	4.03049i	−0.0751429	+	0.130151i
$960$	57.3822	−	3.56298i	1.85200	−	0.114995i
$961$	14.3637	+	24.8787i	0.463346	+	0.802539i
$962$	15.3978	−	11.5746i	0.496446	−	0.373179i
$963$	9.82437	−	34.0812i	0.316586	−	1.09825i
$964$	−3.22044	+	11.1315i	−0.103723	+	0.358522i
$965$	37.4036	−	21.5950i	1.20407	−	0.695167i
$966$	−5.60489	−	3.38215i	−0.180335	−	0.108819i
$967$	−1.95885	+	3.39283i	−0.0629924	+	0.109106i	−0.895802	−	0.444454i	$-0.853398\pi$
$967$	−1.95885	+	3.39283i	−0.0629924	+	0.109106i	0.832809	+	0.553560i	$0.186731\pi$
$968$	9.67820	+	1.56811i	0.311069	+	0.0504011i
$969$	−7.73511	+	54.7596i	−0.248487	+	1.75913i
$970$	−0.885675	+	2.07967i	−0.0284373	+	0.0667743i
$971$		−	37.3701i		−	1.19926i	−0.800276	−	0.599632i	$-0.795313\pi$
$971$		−	37.3701i		−	1.19926i	0.800276	−	0.599632i	$-0.204687\pi$
$972$	−1.99213	−	31.1132i	−0.0638977	−	0.997956i
$973$			6.87363i			0.220358i
$974$	−19.8782	−	8.46555i	−0.636937	−	0.271254i
$975$	6.20087	−	43.8982i	0.198587	−	1.40587i
$976$	−5.53886	−	10.5371i	−0.177295	−	0.337284i
$977$	−24.7556	+	42.8780i	−0.792003	+	1.37179i	0.132722	+	0.991153i	$0.457628\pi$
$977$	−24.7556	+	42.8780i	−0.792003	+	1.37179i	−0.924725	+	0.380636i	$0.875705\pi$
$978$	13.5112	−	22.3907i	0.432040	−	0.715975i
$979$	−13.0356	+	7.52611i	−0.416620	+	0.240536i
$980$	−7.97146	−	2.30621i	−0.254639	−	0.0736692i
$981$	12.1687	−	42.2137i	0.388515	−	1.34778i
$982$	23.7460	+	31.5897i	0.757765	+	1.00807i
$983$	9.52357	+	16.4953i	0.303755	+	0.526118i	0.976983	−	0.213316i	$-0.0684264\pi$
$983$	9.52357	+	16.4953i	0.303755	+	0.526118i	−0.673229	+	0.739434i	$0.735093\pi$
$984$	39.2082	+	12.1696i	1.24991	+	0.387954i
$985$	1.52194	−	2.63608i	0.0484931	−	0.0839926i
$986$	55.4814	−	6.74563i	1.76689	−	0.214825i
$987$	−3.15529	+	4.03276i	−0.100434	+	0.128364i
$988$	−21.6792	+	5.35076i	−0.689706	+	0.170230i
$989$			5.78549i			0.183968i
$990$	−37.4707	−	30.5039i	−1.19090	−	0.969477i
$991$	22.8814			0.726851			0.363426	−	0.931623i	$-0.381607\pi$
$991$	22.8814			0.726851			0.363426	+	0.931623i	$0.381607\pi$
$992$	−4.84984	−	7.01426i	−0.153983	−	0.222703i
$993$	−0.0744850	+	0.0300332i	−0.00236371	+	0.000953074i
$994$	−0.105072	−	0.864197i	−0.00333269	−	0.0274107i
$995$	−97.1319	−	56.0791i	−3.07929	−	1.77783i
$996$	37.3471	+	16.7655i	1.18339	+	0.531234i
$997$	27.0598	−	15.6230i	0.856993	−	0.494785i	−0.00601137	−	0.999982i	$-0.501913\pi$
$997$	27.0598	−	15.6230i	0.856993	−	0.494785i	0.863004	+	0.505197i	$0.168580\pi$
$998$	−26.0553	−	34.6618i	−0.824767	−	1.09720i
$999$	13.8036	−	30.8288i	0.436727	−	0.975379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.b.85.5	✓	72
8.5	even	2	inner	504.2.cs.b.85.21	yes	72
9.7	even	3	inner	504.2.cs.b.421.21	yes	72
72.61	even	6	inner	504.2.cs.b.421.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.b.85.5	✓	72	1.1	even	1	trivial
504.2.cs.b.85.21	yes	72	8.5	even	2	inner
504.2.cs.b.421.5	yes	72	72.61	even	6	inner
504.2.cs.b.421.21	yes	72	9.7	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30114 - 0.554117i) q^{2} +(-1.71503 - 0.242257i) q^{3} +(1.38591 + 1.44196i) q^{4} +(3.59330 + 2.07459i) q^{5} +(2.09724 + 1.26553i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(-1.00424 - 2.64415i) q^{8} +(2.88262 + 0.830955i) q^{9} +O(q^{10})\)	\(q+(-1.30114 - 0.554117i) q^{2} +(-1.71503 - 0.242257i) q^{3} +(1.38591 + 1.44196i) q^{4} +(3.59330 + 2.07459i) q^{5} +(2.09724 + 1.26553i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(-1.00424 - 2.64415i) q^{8} +(2.88262 + 0.830955i) q^{9} +(-3.52580 - 4.69043i) q^{10} +(2.37702 - 1.37237i) q^{11} +(-2.02754 - 2.80875i) q^{12} +(1.81463 + 1.04768i) q^{13} +(0.170688 + 1.40388i) q^{14} +(-5.66001 - 4.42848i) q^{15} +(-0.158517 + 3.99686i) q^{16} -5.99230 q^{17} +(-3.29024 - 2.67850i) q^{18} +5.32839i q^{19} +(1.98850 + 8.05660i) q^{20} +(0.647712 + 1.60638i) q^{21} +(-3.85328 + 0.468495i) q^{22} +(1.33625 - 2.31446i) q^{23} +(1.08173 + 4.77806i) q^{24} +(6.10786 + 10.5791i) q^{25} +(-1.78054 - 2.36869i) q^{26} +(-4.74247 - 2.12344i) q^{27} +(0.555823 - 1.92121i) q^{28} +(5.71158 - 3.29758i) q^{29} +(4.91055 + 8.89836i) q^{30} +(0.753745 - 1.30552i) q^{31} +(2.42098 - 5.11262i) q^{32} +(-4.40911 + 1.77780i) q^{33} +(7.79679 + 3.32044i) q^{34} -4.14918i q^{35} +(2.79684 + 5.30826i) q^{36} +6.50057i q^{37} +(2.95255 - 6.93296i) q^{38} +(-2.85833 - 2.23640i) q^{39} +(1.87700 - 11.5846i) q^{40} +(4.19000 - 7.25729i) q^{41} +(0.0473644 - 2.44903i) q^{42} +(-1.87479 + 1.08241i) q^{43} +(5.27324 + 1.52559i) q^{44} +(8.63423 + 8.96613i) q^{45} +(-3.02113 + 2.27098i) q^{46} +(1.47815 + 2.56022i) q^{47} +(1.24013 - 6.81631i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-2.08508 - 17.1493i) q^{50} +(10.2769 + 1.45168i) q^{51} +(1.00420 + 4.06861i) q^{52} +1.23720i q^{53} +(4.99395 + 5.39077i) q^{54} +11.3884 q^{55} +(-1.78778 + 2.19177i) q^{56} +(1.29084 - 9.13832i) q^{57} +(-9.25878 + 1.12572i) q^{58} +(10.4952 + 6.05943i) q^{59} +(-1.45855 - 14.2990i) q^{60} +(-2.57733 + 1.48802i) q^{61} +(-1.70414 + 1.28100i) q^{62} +(-0.721684 - 2.91190i) q^{63} +(-5.98301 + 5.31070i) q^{64} +(4.34700 + 7.52923i) q^{65} +(6.72196 + 0.130003i) q^{66} +(9.43042 + 5.44466i) q^{67} +(-8.30478 - 8.64068i) q^{68} +(-2.85240 + 3.64564i) q^{69} +(-2.29913 + 5.39865i) q^{70} -0.615579 q^{71} +(-0.697673 - 8.45655i) q^{72} +10.8436 q^{73} +(3.60208 - 8.45813i) q^{74} +(-7.91226 - 19.6231i) q^{75} +(-7.68335 + 7.38466i) q^{76} +(-2.37702 - 1.37237i) q^{77} +(2.47984 + 4.49371i) q^{78} +(-1.19028 - 2.06163i) q^{79} +(-8.86145 + 14.0330i) q^{80} +(7.61903 + 4.79066i) q^{81} +(-9.47314 + 7.12096i) q^{82} +(-10.2344 + 5.90884i) q^{83} +(-1.41868 + 3.16028i) q^{84} +(-21.5321 - 12.4316i) q^{85} +(3.03913 - 0.369509i) q^{86} +(-10.5944 + 4.27176i) q^{87} +(-6.01584 - 4.90699i) q^{88} -5.48402 q^{89} +(-6.26602 - 16.4505i) q^{90} -2.09535i q^{91} +(5.18929 - 1.28080i) q^{92} +(-1.60896 + 2.05641i) q^{93} +(-0.504604 - 4.15027i) q^{94} +(-11.0542 + 19.1465i) q^{95} +(-5.39061 + 8.18177i) q^{96} +(-0.192611 - 0.333611i) q^{97} +(1.13045 - 0.849758i) q^{98} +(7.99242 - 1.98084i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

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