LMFDB - Embedded newform 490.2.p.a.239.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(29,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 6]))

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

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

chi := DirichletCharacter("490.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.p (of order $14$, degree $6$, 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:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			239.23
Character	$\chi$	$=$	490.239
Dual form			490.2.p.a.449.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.781831 + 0.623490i) q^{2} +(0.534200 - 1.10928i) q^{3} +(0.222521 + 0.974928i) q^{4} +(2.12573 - 0.693744i) q^{5} +(1.10928 - 0.534200i) q^{6} +(1.96551 + 1.77110i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(0.925341 + 1.16034i) q^{9} +O(q^{10})$	\(q+(0.781831 + 0.623490i) q^{2} +(0.534200 - 1.10928i) q^{3} +(0.222521 + 0.974928i) q^{4} +(2.12573 - 0.693744i) q^{5} +(1.10928 - 0.534200i) q^{6} +(1.96551 + 1.77110i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(0.925341 + 1.16034i) q^{9} +(2.09450 + 0.782979i) q^{10} +(-0.144313 + 0.180963i) q^{11} +(1.20034 + 0.273969i) q^{12} +(-2.82896 - 2.25602i) q^{13} +(0.432435 + 2.61017i) q^{14} +(0.366010 - 2.72862i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-4.28876 - 0.978881i) q^{17} +1.48413i q^{18} -5.37451 q^{19} +(1.14937 + 1.91806i) q^{20} +(3.01461 - 1.23418i) q^{21} +(-0.225657 + 0.0515047i) q^{22} +(6.14036 - 1.40150i) q^{23} +(0.767645 + 0.962596i) q^{24} +(4.03744 - 2.94942i) q^{25} +(-0.805163 - 3.52765i) q^{26} +(5.38247 - 1.22851i) q^{27} +(-1.28932 + 2.31033i) q^{28} +(-1.35047 + 5.91680i) q^{29} +(1.98743 - 1.90512i) q^{30} +2.69865 q^{31} +(-0.974928 - 0.222521i) q^{32} +(0.123646 + 0.256754i) q^{33} +(-2.74276 - 3.43932i) q^{34} +(5.40682 + 2.40131i) q^{35} +(-0.925341 + 1.16034i) q^{36} +(8.34903 + 1.90561i) q^{37} +(-4.20196 - 3.35095i) q^{38} +(-4.01378 + 1.93294i) q^{39} +(-0.297277 + 2.21622i) q^{40} +(-9.33546 - 4.49572i) q^{41} +(3.12642 + 0.914664i) q^{42} +(-3.98100 - 8.26664i) q^{43} +(-0.208538 - 0.100427i) q^{44} +(2.77200 + 1.82462i) q^{45} +(5.67454 + 2.73272i) q^{46} +(-7.27879 - 5.80465i) q^{47} +1.23121i q^{48} +(0.726439 + 6.96220i) q^{49} +(4.99553 + 0.211351i) q^{50} +(-3.37691 + 4.23451i) q^{51} +(1.56995 - 3.26004i) q^{52} +(-9.43144 + 2.15266i) q^{53} +(4.97415 + 2.39542i) q^{54} +(-0.181228 + 0.484794i) q^{55} +(-2.44850 + 1.00241i) q^{56} +(-2.87106 + 5.96183i) q^{57} +(-4.74490 + 3.78393i) q^{58} +(8.60489 - 4.14390i) q^{59} +(2.74166 - 0.250343i) q^{60} +(-1.02985 + 4.51207i) q^{61} +(2.10989 + 1.68258i) q^{62} +(-0.236310 + 3.91952i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-7.57869 - 2.83311i) q^{65} +(-0.0634129 + 0.277830i) q^{66} -3.08915i q^{67} -4.39905i q^{68} +(1.72553 - 7.56005i) q^{69} +(2.73003 + 5.24852i) q^{70} +(-0.708740 - 3.10519i) q^{71} +(-1.44692 + 0.330250i) q^{72} +(-3.09591 + 2.46891i) q^{73} +(5.33940 + 6.69540i) q^{74} +(-1.11493 - 6.05423i) q^{75} +(-1.19594 - 5.23976i) q^{76} +(-0.604151 + 0.100092i) q^{77} +(-4.34327 - 0.991322i) q^{78} -8.99800 q^{79} +(-1.61421 + 1.54736i) q^{80} +(0.521803 - 2.28617i) q^{81} +(-4.49572 - 9.33546i) q^{82} +(-7.40122 + 5.90228i) q^{83} +(1.87405 + 2.66440i) q^{84} +(-9.79583 + 0.894465i) q^{85} +(2.04169 - 8.94523i) q^{86} +(5.84195 + 4.65880i) q^{87} +(-0.100427 - 0.208538i) q^{88} +(-6.17010 - 7.73706i) q^{89} +(1.02961 + 3.15486i) q^{90} +(-1.56471 - 9.44457i) q^{91} +(2.73272 + 5.67454i) q^{92} +(1.44162 - 2.99355i) q^{93} +(-2.07165 - 9.07651i) q^{94} +(-11.4247 + 3.72853i) q^{95} +(-0.767645 + 0.962596i) q^{96} +8.76785i q^{97} +(-3.77291 + 5.89620i) q^{98} -0.343517 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9}+O(q^{10}) $ 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9	$ 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9} - 4 q^{10} - 24 q^{11} + 4 q^{14} - 2 q^{15} - 28 q^{16} + 44 q^{19} - 10 q^{20} + 22 q^{26} - 2 q^{29} - 12 q^{30} - 16 q^{31} - 8 q^{34} - 4 q^{35} - 18 q^{36} - 80 q^{39} - 10 q^{40} + 52 q^{41} - 18 q^{44} - 72 q^{45} + 26 q^{46} - 52 q^{49} - 8 q^{50} + 64 q^{51} - 42 q^{54} - 60 q^{55} + 10 q^{56} - 58 q^{59} + 2 q^{60} + 32 q^{61} + 28 q^{64} + 4 q^{65} + 48 q^{66} - 48 q^{69} + 18 q^{70} - 68 q^{71} - 10 q^{74} - 16 q^{76} - 4 q^{80} + 34 q^{81} + 84 q^{84} - 48 q^{85} - 64 q^{86} + 100 q^{89} + 54 q^{90} + 78 q^{91} - 86 q^{94} - 64 q^{95} - 212 q^{99}+O(q^{100}) $ 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9 - 4 * q^10 - 24 * q^11 + 4 * q^14 - 2 * q^15 - 28 * q^16 + 44 * q^19 - 10 * q^20 + 22 * q^26 - 2 * q^29 - 12 * q^30 - 16 * q^31 - 8 * q^34 - 4 * q^35 - 18 * q^36 - 80 * q^39 - 10 * q^40 + 52 * q^41 - 18 * q^44 - 72 * q^45 + 26 * q^46 - 52 * q^49 - 8 * q^50 + 64 * q^51 - 42 * q^54 - 60 * q^55 + 10 * q^56 - 58 * q^59 + 2 * q^60 + 32 * q^61 + 28 * q^64 + 4 * q^65 + 48 * q^66 - 48 * q^69 + 18 * q^70 - 68 * q^71 - 10 * q^74 - 16 * q^76 - 4 * q^80 + 34 * q^81 + 84 * q^84 - 48 * q^85 - 64 * q^86 + 100 * q^89 + 54 * q^90 + 78 * q^91 - 86 * q^94 - 64 * q^95 - 212 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$3$	0.534200	−	1.10928i	0.308421	−	0.640442i	−0.687932	−	0.725775i	$-0.741481\pi$
$3$	0.534200	−	1.10928i	0.308421	−	0.640442i	0.996352	+	0.0853331i	$0.0271955\pi$
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	2.12573	−	0.693744i	0.950654	−	0.310252i
$5$	2.12573	−	0.693744i	0.950654	−	0.310252i
$6$	1.10928	−	0.534200i	0.452861	−	0.218086i
$7$	1.96551	+	1.77110i	0.742892	+	0.669411i
$7$	1.96551	+	1.77110i	0.742892	+	0.669411i
$8$	−0.433884	+	0.900969i	−0.153401	+	0.318541i
$9$	0.925341	+	1.16034i	0.308447	+	0.386780i
$10$	2.09450	+	0.782979i	0.662340	+	0.247600i
$11$	−0.144313	+	0.180963i	−0.0435120	+	0.0545623i	−0.803111	−	0.595829i	$-0.796824\pi$
$11$	−0.144313	+	0.180963i	−0.0435120	+	0.0545623i	0.759599	+	0.650391i	$0.225395\pi$
$12$	1.20034	+	0.273969i	0.346508	+	0.0790881i
$13$	−2.82896	−	2.25602i	−0.784612	−	0.625707i	0.147011	−	0.989135i	$-0.453035\pi$
$13$	−2.82896	−	2.25602i	−0.784612	−	0.625707i	−0.931622	+	0.363428i	$0.881606\pi$
$14$	0.432435	+	2.61017i	0.115573	+	0.697598i
$15$	0.366010	−	2.72862i	0.0945033	−	0.704527i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	−4.28876	−	0.978881i	−1.04018	−	0.237414i	−0.331875	−	0.943323i	$-0.607681\pi$
$17$	−4.28876	−	0.978881i	−1.04018	−	0.237414i	−0.708302	+	0.705910i	$0.750538\pi$
$18$			1.48413i			0.349813i
$19$	−5.37451			−1.23300			−0.616498	−	0.787356i	$-0.711449\pi$
$19$	−5.37451			−1.23300			−0.616498	+	0.787356i	$0.711449\pi$
$20$	1.14937	+	1.91806i	0.257007	+	0.428891i
$21$	3.01461	−	1.23418i	0.657843	−	0.269319i
$22$	−0.225657	+	0.0515047i	−0.0481102	+	0.0109808i
$23$	6.14036	−	1.40150i	1.28035	−	0.292232i	0.472350	−	0.881411i	$-0.343406\pi$
$23$	6.14036	−	1.40150i	1.28035	−	0.292232i	0.808003	+	0.589179i	$0.200549\pi$
$24$	0.767645	+	0.962596i	0.156695	+	0.196489i
$25$	4.03744	−	2.94942i	0.807488	−	0.589884i
$26$	−0.805163	−	3.52765i	−0.157906	−	0.691829i
$27$	5.38247	−	1.22851i	1.03586	−	0.236428i
$28$	−1.28932	+	2.31033i	−0.243659	+	0.436612i
$29$	−1.35047	+	5.91680i	−0.250776	+	1.09872i	0.680023	+	0.733190i	$0.261970\pi$
$29$	−1.35047	+	5.91680i	−0.250776	+	1.09872i	−0.930799	+	0.365531i	$0.880887\pi$
$30$	1.98743	−	1.90512i	0.362853	−	0.347826i
$31$	2.69865			0.484691			0.242346	−	0.970190i	$-0.422083\pi$
$31$	2.69865			0.484691			0.242346	+	0.970190i	$0.422083\pi$
$32$	−0.974928	−	0.222521i	−0.172345	−	0.0393365i
$33$	0.123646	+	0.256754i	0.0215240	+	0.0446951i
$34$	−2.74276	−	3.43932i	−0.470380	−	0.589838i
$35$	5.40682	+	2.40131i	0.913920	+	0.405895i
$36$	−0.925341	+	1.16034i	−0.154223	+	0.193390i
$37$	8.34903	+	1.90561i	1.37257	+	0.313280i	0.844334	−	0.535816i	$-0.179996\pi$
$37$	8.34903	+	1.90561i	1.37257	+	0.313280i	0.528237	+	0.849097i	$0.322853\pi$
$38$	−4.20196	−	3.35095i	−0.681648	−	0.543596i
$39$	−4.01378	+	1.93294i	−0.642720	+	0.309517i
$40$	−0.297277	+	2.21622i	−0.0470037	+	0.350415i
$41$	−9.33546	−	4.49572i	−1.45795	−	0.702113i	−0.473998	−	0.880526i	$-0.657190\pi$
$41$	−9.33546	−	4.49572i	−1.45795	−	0.702113i	−0.983956	+	0.178413i	$0.942904\pi$
$42$	3.12642	+	0.914664i	0.482416	+	0.141136i
$43$	−3.98100	−	8.26664i	−0.607097	−	1.26065i	−0.947315	−	0.320304i	$-0.896215\pi$
$43$	−3.98100	−	8.26664i	−0.607097	−	1.26065i	0.340218	−	0.940347i	$-0.389499\pi$
$44$	−0.208538	−	0.100427i	−0.0314383	−	0.0151399i
$45$	2.77200	+	1.82462i	0.413226	+	0.271998i
$46$	5.67454	+	2.73272i	0.836666	+	0.402917i
$47$	−7.27879	−	5.80465i	−1.06172	−	0.846695i	−0.0731308	−	0.997322i	$-0.523299\pi$
$47$	−7.27879	−	5.80465i	−1.06172	−	0.846695i	−0.988591	+	0.150628i	$0.951870\pi$
$48$			1.23121i			0.177709i
$49$	0.726439	+	6.96220i	0.103777	+	0.994601i
$50$	4.99553	+	0.211351i	0.706475	+	0.0298896i
$51$	−3.37691	+	4.23451i	−0.472862	+	0.592950i
$52$	1.56995	−	3.26004i	0.217713	−	0.452086i
$53$	−9.43144	+	2.15266i	−1.29551	+	0.295691i	−0.814058	−	0.580783i	$-0.802746\pi$
$53$	−9.43144	+	2.15266i	−1.29551	+	0.295691i	−0.481449	+	0.876474i	$0.659889\pi$
$54$	4.97415	+	2.39542i	0.676896	+	0.325976i
$55$	−0.181228	+	0.484794i	−0.0244368	+	0.0653696i
$56$	−2.44850	+	1.00241i	−0.327195	+	0.133953i
$57$	−2.87106	+	5.96183i	−0.380282	+	0.789663i
$58$	−4.74490	+	3.78393i	−0.623036	+	0.496855i
$59$	8.60489	−	4.14390i	1.12026	−	0.539490i	0.220289	−	0.975435i	$-0.429300\pi$
$59$	8.60489	−	4.14390i	1.12026	−	0.539490i	0.899973	+	0.435945i	$0.143586\pi$
$60$	2.74166	−	0.250343i	0.353946	−	0.0323191i
$61$	−1.02985	+	4.51207i	−0.131859	+	0.577711i	0.865224	+	0.501385i	$0.167176\pi$
$61$	−1.02985	+	4.51207i	−0.131859	+	0.577711i	−0.997083	+	0.0763259i	$0.975681\pi$
$62$	2.10989	+	1.68258i	0.267956	+	0.213688i
$63$	−0.236310	+	3.91952i	−0.0297723	+	0.493814i
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	−7.57869	−	2.83311i	−0.940021	−	0.351404i
$66$	−0.0634129	+	0.277830i	−0.00780559	+	0.0341985i
$67$		−	3.08915i		−	0.377400i	−0.982035	−	0.188700i	$-0.939573\pi$
$67$		−	3.08915i		−	0.377400i	0.982035	−	0.188700i	$-0.0604273\pi$
$68$		−	4.39905i		−	0.533463i
$69$	1.72553	−	7.56005i	0.207730	−	0.910122i
$70$	2.73003	+	5.24852i	0.326301	+	0.627318i
$71$	−0.708740	−	3.10519i	−0.0841120	−	0.368519i	0.915301	−	0.402770i	$-0.131953\pi$
$71$	−0.708740	−	3.10519i	−0.0841120	−	0.368519i	−0.999413	+	0.0342512i	$0.989095\pi$
$72$	−1.44692	+	0.330250i	−0.170521	+	0.0389204i
$73$	−3.09591	+	2.46891i	−0.362349	+	0.288964i	−0.787693	−	0.616068i	$-0.788725\pi$
$73$	−3.09591	+	2.46891i	−0.362349	+	0.288964i	0.425344	+	0.905032i	$0.360153\pi$
$74$	5.33940	+	6.69540i	0.620693	+	0.778324i
$75$	−1.11493	−	6.05423i	−0.128741	−	0.699082i
$76$	−1.19594	−	5.23976i	−0.137184	−	0.601041i
$77$	−0.604151	+	0.100092i	−0.0688494	+	0.0114065i
$78$	−4.34327	−	0.991322i	−0.491778	−	0.112245i
$79$	−8.99800			−1.01235			−0.506177	−	0.862430i	$-0.668942\pi$
$79$	−8.99800			−1.01235			−0.506177	+	0.862430i	$0.668942\pi$
$80$	−1.61421	+	1.54736i	−0.180474	+	0.173000i
$81$	0.521803	−	2.28617i	0.0579781	−	0.254019i
$82$	−4.49572	−	9.33546i	−0.496469	−	1.03093i
$83$	−7.40122	+	5.90228i	−0.812389	+	0.647859i	−0.938932	−	0.344102i	$-0.888183\pi$
$83$	−7.40122	+	5.90228i	−0.812389	+	0.647859i	0.126543	+	0.991961i	$0.459612\pi$
$84$	1.87405	+	2.66440i	0.204475	+	0.290710i
$85$	−9.79583	+	0.894465i	−1.06251	+	0.0970183i
$86$	2.04169	−	8.94523i	0.220161	−	0.964589i
$87$	5.84195	+	4.65880i	0.626323	+	0.499476i
$88$	−0.100427	−	0.208538i	−0.0107055	−	0.0222303i
$89$	−6.17010	−	7.73706i	−0.654029	−	0.820127i	0.338649	−	0.940913i	$-0.390030\pi$
$89$	−6.17010	−	7.73706i	−0.654029	−	0.820127i	−0.992679	+	0.120786i	$0.961459\pi$
$90$	1.02961	+	3.15486i	0.108530	+	0.332551i
$91$	−1.56471	−	9.44457i	−0.164026	−	0.990060i
$92$	2.73272	+	5.67454i	0.284905	+	0.591612i
$93$	1.44162	−	2.99355i	0.149489	−	0.310417i
$94$	−2.07165	−	9.07651i	−0.213675	−	0.936170i
$95$	−11.4247	+	3.72853i	−1.17215	+	0.382539i
$96$	−0.767645	+	0.962596i	−0.0783474	+	0.0982445i
$97$			8.76785i			0.890240i	0.895471	+	0.445120i	$0.146839\pi$
$97$			8.76785i			0.890240i	−0.895471	+	0.445120i	$0.853161\pi$
$98$	−3.77291	+	5.89620i	−0.381121	+	0.595606i
$99$	−0.343517			−0.0345248
$100$	3.77389	+	3.27990i	0.377389	+	0.327990i
$101$	17.3152	+	8.33854i	1.72292	+	0.829716i	0.988536	+	0.150985i	$0.0482445\pi$
$101$	17.3152	+	8.33854i	1.72292	+	0.829716i	0.734387	+	0.678731i	$0.237470\pi$
$102$	−5.28035	+	1.20520i	−0.522832	+	0.119333i
$103$	0.304159	−	0.631594i	0.0299697	−	0.0622328i	−0.885447	−	0.464741i	$-0.846147\pi$
$103$	0.304159	−	0.631594i	0.0299697	−	0.0622328i	0.915416	+	0.402509i	$0.131862\pi$
$104$	3.26004	−	1.56995i	0.319673	−	0.153947i
$105$	5.55205	−	4.71489i	0.541824	−	0.460126i
$106$	−8.71596	−	4.19738i	−0.846569	−	0.407686i
$107$	5.81852	−	4.64011i	0.562497	−	0.448577i	−0.300502	−	0.953781i	$-0.597154\pi$
$107$	5.81852	−	4.64011i	0.562497	−	0.448577i	0.863000	+	0.505204i	$0.168583\pi$
$108$	2.39542	+	4.97415i	0.230500	+	0.478638i
$109$	−4.42599	+	5.55001i	−0.423933	+	0.531595i	−0.947230	−	0.320555i	$-0.896130\pi$
$109$	−4.42599	+	5.55001i	−0.423933	+	0.531595i	0.523297	+	0.852150i	$0.324702\pi$
$110$	−0.443954	+	0.266033i	−0.0423294	+	0.0253653i
$111$	6.57391	−	8.24342i	0.623968	−	0.782431i
$112$	−2.53931	−	0.742900i	−0.239942	−	0.0701975i
$113$	−7.52545	+	6.00135i	−0.707935	+	0.564559i	−0.909897	−	0.414834i	$-0.863840\pi$
$113$	−7.52545	+	6.00135i	−0.707935	+	0.564559i	0.201962	+	0.979393i	$0.435268\pi$
$114$	−5.96183	+	2.87106i	−0.558376	+	0.268900i
$115$	12.0804	−	7.23903i	1.12651	−	0.675043i
$116$	−6.06896			−0.563488
$117$		−	5.37014i		−	0.496469i
$118$	9.31126	+	2.12523i	0.857171	+	0.195644i
$119$	−6.69589	−	9.51980i	−0.613812	−	0.872679i
$120$	2.29960	+	1.51367i	0.209924	+	0.138178i
$121$	2.43581	+	10.6720i	0.221437	+	0.970180i
$122$	−3.61840	+	2.88558i	−0.327594	+	0.261248i
$123$	−9.97401	+	7.95401i	−0.899326	+	0.717189i
$124$	0.600505	+	2.63099i	0.0539270	+	0.236270i
$125$	6.53635	−	9.07062i	0.584629	−	0.811301i
$126$	−2.62854	+	2.91707i	−0.234169	+	0.259873i
$127$	−9.56131	−	2.18231i	−0.848429	−	0.193648i	−0.223863	−	0.974621i	$-0.571867\pi$
$127$	−9.56131	−	2.18231i	−0.848429	−	0.193648i	−0.624566	+	0.780972i	$0.714724\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−11.2967			−0.994615
$130$	−4.15885	−	6.94025i	−0.364755	−	0.608700i
$131$	9.92723	−	4.78070i	0.867346	−	0.417692i	0.0533593	−	0.998575i	$-0.483007\pi$
$131$	9.92723	−	4.78070i	0.867346	−	0.417692i	0.813987	+	0.580884i	$0.197293\pi$
$132$	−0.222802	+	0.177679i	−0.0193925	+	0.0154650i
$133$	−10.5636	−	9.51877i	−0.915983	−	0.825382i
$134$	1.92605	−	2.41519i	0.166386	−	0.208641i
$135$	10.5894	−	6.34554i	0.911390	−	0.546137i
$136$	2.74276	−	3.43932i	0.235190	−	0.294919i
$137$	5.13734	+	10.6678i	0.438913	+	0.911412i	0.996680	+	0.0814145i	$0.0259438\pi$
$137$	5.13734	+	10.6678i	0.438913	+	0.911412i	−0.557768	+	0.829997i	$0.688342\pi$
$138$	6.06269	−	4.83483i	0.516090	−	0.411568i
$139$	4.04104	+	1.94606i	0.342757	+	0.165063i	0.597340	−	0.801988i	$-0.296224\pi$
$139$	4.04104	+	1.94606i	0.342757	+	0.165063i	−0.254584	+	0.967051i	$0.581938\pi$
$140$	−1.13797	+	5.80560i	−0.0961762	+	0.490663i
$141$	−10.3273	+	4.97337i	−0.869716	+	0.418833i
$142$	1.38194	−	2.86963i	0.115970	−	0.240814i
$143$	0.816510	−	0.186363i	0.0682800	−	0.0155845i
$144$	−1.33716	−	0.643940i	−0.111430	−	0.0536617i
$145$	1.23401	+	13.5144i	0.102479	+	1.12231i
$146$	−3.95982			−0.327717
$147$	8.11109	+	2.91339i	0.668991	+	0.240292i
$148$			8.56374i			0.703935i
$149$	11.2141	−	14.0620i	0.918691	−	1.15200i	−0.0693158	−	0.997595i	$-0.522082\pi$
$149$	11.2141	−	14.0620i	0.918691	−	1.15200i	0.988007	−	0.154408i	$-0.0493470\pi$
$150$	2.90306	−	5.42853i	0.237034	−	0.443238i
$151$	3.93832	+	17.2549i	0.320496	+	1.40418i	0.836674	+	0.547702i	$0.184497\pi$
$151$	3.93832	+	17.2549i	0.320496	+	1.40418i	−0.516178	+	0.856481i	$0.672646\pi$
$152$	2.33191	−	4.84226i	0.189143	−	0.392759i
$153$	−2.83273	−	5.88222i	−0.229012	−	0.475549i
$154$	−0.534750	−	0.298427i	−0.0430914	−	0.0240479i
$155$	5.73659	−	1.87217i	0.460774	−	0.150376i
$156$	−2.77762	−	3.48303i	−0.222388	−	0.278866i
$157$	3.54106	+	7.35310i	0.282608	+	0.586841i	0.993154	−	0.116809i	$-0.0372666\pi$
$157$	3.54106	+	7.35310i	0.282608	+	0.586841i	−0.710547	+	0.703650i	$0.751552\pi$
$158$	−7.03492	−	5.61016i	−0.559668	−	0.446320i
$159$	−2.65037	+	11.6120i	−0.210188	+	0.920895i
$160$	−2.22680	+	0.203331i	−0.176044	+	0.0160747i
$161$	14.5511	+	8.12051i	1.14679	+	0.639986i
$162$	1.83336	−	1.46206i	0.144043	−	0.114870i
$163$	−4.79158	−	9.94983i	−0.375306	−	0.779331i	0.624693	−	0.780870i	$-0.285224\pi$
$163$	−4.79158	−	9.94983i	−0.375306	−	0.779331i	−0.999999	+	0.00153989i	$0.999510\pi$
$164$	2.30567	−	10.1018i	0.180042	−	0.788817i
$165$	0.440959	+	0.460010i	0.0343286	+	0.0358117i
$166$	−9.46651			−0.734744
$167$	−9.49683	−	2.16759i	−0.734887	−	0.167733i	−0.161332	−	0.986900i	$-0.551579\pi$
$167$	−9.49683	−	2.16759i	−0.734887	−	0.167733i	−0.573555	+	0.819167i	$0.694436\pi$
$168$	−0.196038	+	3.25156i	−0.0151247	+	0.250863i
$169$	0.0206088	+	0.0902930i	0.00158529	+	0.00694561i
$170$	−8.21638	−	5.40828i	−0.630167	−	0.414796i
$171$	−4.97325	−	6.23626i	−0.380314	−	0.476899i
$172$	7.17352	−	5.72069i	0.546976	−	0.436199i
$173$	−11.5279	+	2.63117i	−0.876451	+	0.200044i	−0.637000	−	0.770864i	$-0.719825\pi$
$173$	−11.5279	+	2.63117i	−0.876451	+	0.200044i	−0.239452	+	0.970908i	$0.576968\pi$
$174$	1.66271	+	7.28480i	0.126049	+	0.552259i
$175$	13.1593	+	1.35358i	0.994751	+	0.102321i
$176$	0.0515047	−	0.225657i	0.00388231	−	0.0170095i
$177$		−	11.7589i		−	0.883853i
$178$		−	9.89607i		−	0.741742i
$179$	2.24504	−	9.83618i	0.167802	−	0.735191i	−0.819071	−	0.573693i	$-0.805510\pi$
$179$	2.24504	−	9.83618i	0.167802	−	0.735191i	0.986873	−	0.161498i	$-0.0516325\pi$
$180$	−1.16204	+	3.10852i	−0.0866136	+	0.231695i
$181$	−3.27268	−	4.10381i	−0.243257	−	0.305034i	0.645183	−	0.764028i	$-0.276781\pi$
$181$	−3.27268	−	4.10381i	−0.243257	−	0.305034i	−0.888439	+	0.458994i	$0.848210\pi$
$182$	4.66525	−	8.35965i	0.345812	−	0.619658i
$183$	4.45499	+	3.55274i	0.329323	+	0.262626i
$184$	−1.40150	+	6.14036i	−0.103320	+	0.452673i
$185$	19.0698	−	1.74128i	1.40204	−	0.128021i
$186$	2.99355	−	1.44162i	0.219498	−	0.105705i
$187$	0.796065	−	0.634840i	0.0582140	−	0.0464241i
$188$	4.03943	−	8.38796i	0.294605	−	0.611755i
$189$	12.7551	+	7.11822i	0.927797	+	0.517774i
$190$	−11.2569	−	4.20813i	−0.816663	−	0.305290i
$191$	−3.04526	−	1.46652i	−0.220348	−	0.106114i	0.320454	−	0.947264i	$-0.396165\pi$
$191$	−3.04526	−	1.46652i	−0.220348	−	0.106114i	−0.540801	+	0.841150i	$0.681879\pi$
$192$	−1.20034	+	0.273969i	−0.0866269	+	0.0197720i
$193$	−6.28688	+	13.0548i	−0.452540	+	0.939708i	0.542484	+	0.840066i	$0.317484\pi$
$193$	−6.28688	+	13.0548i	−0.452540	+	0.939708i	−0.995023	+	0.0996420i	$0.968230\pi$
$194$	−5.46666	+	6.85498i	−0.392484	+	0.492159i
$195$	−7.19125	+	6.89343i	−0.514976	+	0.493649i
$196$	−6.62600	+	2.25746i	−0.473286	+	0.161247i
$197$		−	25.5439i		−	1.81993i	−0.414685	−	0.909965i	$-0.636108\pi$
$197$		−	25.5439i		−	1.81993i	0.414685	−	0.909965i	$-0.363892\pi$
$198$	−0.268572	−	0.214179i	−0.0190866	−	0.0152211i
$199$	−8.50815	−	4.09731i	−0.603127	−	0.290451i	0.107294	−	0.994227i	$-0.465781\pi$
$199$	−8.50815	−	4.09731i	−0.603127	−	0.290451i	−0.710421	+	0.703777i	$0.751496\pi$
$200$	0.905558	+	4.91731i	0.0640326	+	0.347707i
$201$	−3.42673	−	1.65023i	−0.241703	−	0.116398i
$202$	8.33854	+	17.3152i	0.586698	+	1.21829i
$203$	−13.1336	+	9.23769i	−0.921796	+	0.648359i
$204$	−4.87977	−	2.34998i	−0.341653	−	0.164531i
$205$	−22.9635	−	3.08026i	−1.60384	−	0.215135i
$206$	0.631594	−	0.304159i	0.0440052	−	0.0211918i
$207$	7.30813	+	5.82804i	0.507950	+	0.405077i
$208$	3.52765	+	0.805163i	0.244599	+	0.0558280i
$209$	0.775611	−	0.972586i	0.0536501	−	0.0672752i
$210$	7.28045	−	0.224605i	0.502399	−	0.0154992i
$211$	16.4768	+	20.6613i	1.13431	+	1.42238i	0.891914	+	0.452205i	$0.149363\pi$
$211$	16.4768	+	20.6613i	1.13431	+	1.42238i	0.242398	+	0.970177i	$0.422066\pi$
$212$	−4.19738	−	8.71596i	−0.288278	−	0.598614i
$213$	−3.82313	−	0.872606i	−0.261957	−	0.0597899i
$214$	7.44216			0.508736
$215$	−14.1975	−	14.8108i	−0.968259	−	1.01009i
$216$	−1.22851	+	5.38247i	−0.0835898	+	0.366231i
$217$	5.30421	+	4.77956i	0.360073	+	0.324458i
$218$	−6.92076	+	1.57962i	−0.468733	+	0.106985i
$219$	1.08487	+	4.75312i	0.0733087	+	0.321186i
$220$	−0.512966	−	0.0688078i	−0.0345842	−	0.00463902i
$221$	9.92434	+	12.4447i	0.667583	+	0.837123i
$222$	10.2794	−	2.34620i	0.689906	−	0.157467i
$223$	24.2100	−	5.52578i	1.62122	−	0.370034i	0.686983	−	0.726674i	$-0.258935\pi$
$223$	24.2100	−	5.52578i	1.62122	−	0.370034i	0.934242	+	0.356640i	$0.116078\pi$
$224$	−1.52212	−	2.16406i	−0.101701	−	0.144592i
$225$	7.15834	+	1.95558i	0.477223	+	0.130372i
$226$	−9.62541			−0.640273
$227$			4.41786i			0.293224i	0.989194	+	0.146612i	$0.0468369\pi$
$227$			4.41786i			0.293224i	−0.989194	+	0.146612i	$0.953163\pi$
$228$	−6.45122	−	1.47245i	−0.427243	−	0.0975153i
$229$	7.96982	−	3.83806i	0.526661	−	0.253626i	−0.151608	−	0.988441i	$-0.548445\pi$
$229$	7.96982	−	3.83806i	0.526661	−	0.253626i	0.678268	+	0.734814i	$0.262731\pi$
$230$	13.9583	+	1.87233i	0.920386	+	0.123458i
$231$	−0.211708	+	0.723640i	−0.0139294	+	0.0476120i
$232$	−4.74490	−	3.78393i	−0.311518	−	0.248427i
$233$	1.33987	+	0.305816i	0.0877777	+	0.0200347i	0.266184	−	0.963922i	$-0.414237\pi$
$233$	1.33987	+	0.305816i	0.0877777	+	0.0200347i	−0.178406	+	0.983957i	$0.557094\pi$
$234$	3.34823	−	4.19854i	0.218880	−	0.274467i
$235$	−19.4997	−	7.28948i	−1.27202	−	0.475513i
$236$	5.95477	+	7.46705i	0.387623	+	0.486063i
$237$	−4.80674	+	9.98129i	−0.312231	+	0.648354i
$238$	0.700437	−	11.6177i	0.0454026	−	0.753064i
$239$	19.9531	−	9.60889i	1.29066	−	0.621547i	0.342549	−	0.939500i	$-0.388710\pi$
$239$	19.9531	−	9.60889i	1.29066	−	0.621547i	0.948107	+	0.317953i	$0.102995\pi$
$240$	0.854142	+	2.61721i	0.0551346	+	0.168940i
$241$	5.45020	+	23.8789i	0.351078	+	1.53817i	0.774697	+	0.632333i	$0.217902\pi$
$241$	5.45020	+	23.8789i	0.351078	+	1.53817i	−0.423619	+	0.905840i	$0.639241\pi$
$242$	−4.74948	+	9.86239i	−0.305308	+	0.633978i
$243$	10.6920	+	8.52656i	0.685890	+	0.546979i
$244$	−4.62811			−0.296284
$245$	6.37420	+	14.2958i	0.407233	+	0.913324i
$246$	−12.7572			−0.813372
$247$	15.2042	+	12.1250i	0.967423	+	0.771494i
$248$	−1.17090	+	2.43140i	−0.0743522	+	0.154394i
$249$	2.59353	+	11.3630i	0.164358	+	0.720102i
$250$	10.7658	−	3.01634i	0.680887	−	0.190770i
$251$	18.4834	−	8.90114i	1.16666	−	0.561835i	0.252664	−	0.967554i	$-0.418693\pi$
$251$	18.4834	−	8.90114i	1.16666	−	0.561835i	0.913998	+	0.405719i	$0.132979\pi$
$252$	−3.87384	+	0.641791i	−0.244029	+	0.0404290i
$253$	−0.632514	+	1.31343i	−0.0397658	+	0.0825746i
$254$	−6.11469	−	7.66758i	−0.383670	−	0.481107i
$255$	−4.24072	+	11.3441i	−0.265564	+	0.710397i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	−8.39741	−	1.91665i	−0.523816	−	0.119558i	−0.0475670	−	0.998868i	$-0.515147\pi$
$257$	−8.39741	−	1.91665i	−0.523816	−	0.119558i	−0.476249	+	0.879310i	$0.658004\pi$
$258$	−8.83208	−	7.04335i	−0.549861	−	0.438500i
$259$	13.0351	+	18.5324i	0.809959	+	1.15155i
$260$	1.07566	−	8.01910i	0.0667096	−	0.497324i
$261$	−8.11514	+	3.90805i	−0.502315	+	0.241902i
$262$	10.7421	+	2.45182i	0.663651	+	0.151474i
$263$		−	4.85081i		−	0.299114i	−0.988753	−	0.149557i	$-0.952215\pi$
$263$		−	4.85081i		−	0.299114i	0.988753	−	0.149557i	$-0.0477847\pi$
$264$	−0.284975			−0.0175390
$265$	−18.5553	+	11.1190i	−1.13984	+	0.683033i
$266$	−2.32413	−	14.0284i	−0.142501	−	0.860136i
$267$	−11.8786	+	2.71122i	−0.726960	+	0.165924i
$268$	3.01170	−	0.687401i	0.183969	−	0.0419897i
$269$	0.797616	+	1.00018i	0.0486315	+	0.0609820i	0.805552	−	0.592524i	$-0.201869\pi$
$269$	0.797616	+	1.00018i	0.0486315	+	0.0609820i	−0.756921	+	0.653506i	$0.773297\pi$
$270$	12.2355	+	1.64123i	0.744629	+	0.0998824i
$271$	−0.0714708	−	0.313134i	−0.00434154	−	0.0190215i	0.972711	−	0.232021i	$-0.0745338\pi$
$271$	−0.0714708	−	0.313134i	−0.00434154	−	0.0190215i	−0.977052	+	0.213000i	$0.931677\pi$
$272$	4.28876	−	0.978881i	0.260044	−	0.0593534i
$273$	−11.3125	−	3.30959i	−0.684666	−	0.200306i
$274$	−2.63473	+	11.5435i	−0.159170	+	0.697368i
$275$	−0.0489194	+	1.15627i	−0.00294995	+	0.0697255i
$276$	7.75447			0.466764
$277$	1.44997	+	0.330946i	0.0871201	+	0.0198846i	0.265859	−	0.964012i	$-0.414345\pi$
$277$	1.44997	+	0.330946i	0.0871201	+	0.0198846i	−0.178739	+	0.983897i	$0.557202\pi$
$278$	1.94606	+	4.04104i	0.116717	+	0.242366i
$279$	2.49717	+	3.13135i	0.149501	+	0.187469i
$280$	−4.50944	+	3.82949i	−0.269490	+	0.228856i
$281$	−10.9815	+	13.7704i	−0.655101	+	0.821470i	−0.992800	−	0.119784i	$-0.961780\pi$
$281$	−10.9815	+	13.7704i	−0.655101	+	0.821470i	0.337699	+	0.941254i	$0.390351\pi$
$282$	−11.1751	−	2.55063i	−0.665465	−	0.151888i
$283$	15.9572	+	12.7254i	0.948558	+	0.756449i	0.969946	−	0.243322i	$-0.0782371\pi$
$283$	15.9572	+	12.7254i	0.948558	+	0.756449i	−0.0213881	+	0.999771i	$0.506809\pi$
$284$	2.86963	−	1.38194i	0.170281	−	0.0820031i
$285$	−1.96712	+	14.6650i	−0.116522	+	0.868680i
$286$	0.754569	+	0.363381i	0.0446186	+	0.0214872i
$287$	−10.3866	−	25.3704i	−0.613099	−	1.49757i
$288$	−0.643940	−	1.33716i	−0.0379445	−	0.0787927i
$289$	2.11877	+	1.02035i	0.124634	+	0.0600203i
$290$	−7.46129	+	11.3354i	−0.438142	+	0.665635i
$291$	9.72598	+	4.68379i	0.570147	+	0.274568i
$292$	−3.09591	−	2.46891i	−0.181175	−	0.144482i
$293$		−	29.1245i		−	1.70147i	−0.525593	−	0.850736i	$-0.676157\pi$
$293$		−	29.1245i		−	1.70147i	0.525593	−	0.850736i	$-0.323843\pi$
$294$	4.52504	+	7.33496i	0.263905	+	0.427784i
$295$	15.4169	−	14.7784i	0.897604	−	0.860431i
$296$	−5.33940	+	6.69540i	−0.310346	+	0.389162i
$297$	−0.554445	+	1.15132i	−0.0321722	+	0.0668062i
$298$	17.5350	−	4.00225i	1.01578	−	0.231844i
$299$	−20.5326	−	9.88798i	−1.18743	−	0.571837i
$300$	5.65434	−	2.43417i	0.326453	−	0.140537i
$301$	6.81632	−	23.2989i	0.392886	−	1.34292i
$302$	−7.67915	+	15.9459i	−0.441885	+	0.917584i
$303$	18.4995	−	14.7529i	1.06277	−	0.847531i
$304$	4.84226	−	2.33191i	0.277723	−	0.133744i
$305$	0.941038	+	10.3059i	0.0538837	+	0.590113i
$306$	1.45279	−	6.36508i	0.0830504	−	0.363867i
$307$	6.82346	+	5.44153i	0.389435	+	0.310564i	0.798561	−	0.601914i	$-0.205595\pi$
$307$	6.82346	+	5.44153i	0.389435	+	0.310564i	−0.409126	+	0.912478i	$0.634166\pi$
$308$	−0.232018	−	0.566731i	−0.0132205	−	0.0322925i
$309$	−0.538131	−	0.674795i	−0.0306132	−	0.0383877i
$310$	5.65232	+	2.11298i	0.321030	+	0.120009i
$311$	−2.43790	+	10.6811i	−0.138241	+	0.605672i	0.857581	+	0.514350i	$0.171967\pi$
$311$	−2.43790	+	10.6811i	−0.138241	+	0.605672i	−0.995821	+	0.0913226i	$0.970891\pi$
$312$		−	4.45496i		−	0.252213i
$313$			6.88990i			0.389440i	0.980859	+	0.194720i	$0.0623799\pi$
$313$			6.88990i			0.389440i	−0.980859	+	0.194720i	$0.937620\pi$
$314$	−1.81606	+	7.95670i	−0.102486	+	0.449023i
$315$	2.21681	+	8.49578i	0.124903	+	0.478683i
$316$	−2.00224	−	8.77240i	−0.112635	−	0.493486i
$317$	1.67670	−	0.382696i	0.0941728	−	0.0214943i	−0.175175	−	0.984537i	$-0.556049\pi$
$317$	1.67670	−	0.382696i	0.0941728	−	0.0214943i	0.269348	+	0.963043i	$0.413192\pi$
$318$	−9.31214	+	7.42618i	−0.522199	+	0.416440i
$319$	−0.875829	−	1.09826i	−0.0490370	−	0.0614905i
$320$	−1.86776	−	1.22942i	−0.104411	−	0.0687266i
$321$	−2.03892	−	8.93311i	−0.113802	−	0.498597i
$322$	6.31345	+	15.4213i	0.351835	+	0.859397i
$323$	23.0500	+	5.26100i	1.28253	+	0.292730i
$324$	2.34496			0.130276
$325$	−18.0757	−	0.764748i	−1.00266	−	0.0424206i
$326$	2.45740	−	10.7666i	0.136103	−	0.596306i
$327$	3.79215	+	7.87447i	0.209706	+	0.435459i
$328$	8.10101	−	6.46034i	0.447303	−	0.356712i
$329$	−4.02594	−	24.3005i	−0.221957	−	1.33973i
$330$	0.0579443	+	0.634584i	0.00318973	+	0.0349327i
$331$	2.29933	−	10.0740i	0.126383	−	0.553719i	−0.871599	−	0.490219i	$-0.836917\pi$
$331$	2.29933	−	10.0740i	0.126383	−	0.553719i	0.997982	−	0.0634996i	$-0.0202262\pi$
$332$	−7.40122	−	5.90228i	−0.406195	−	0.323929i
$333$	5.51454	+	11.4511i	0.302195	+	0.627514i
$334$	−6.07345	−	7.61587i	−0.332324	−	0.416722i
$335$	−2.14308	−	6.56669i	−0.117089	−	0.358777i
$336$	−2.18058	+	2.41995i	−0.118961	+	0.132019i
$337$	0.275766	+	0.572633i	0.0150219	+	0.0311933i	0.908345	−	0.418222i	$-0.137347\pi$
$337$	0.275766	+	0.572633i	0.0150219	+	0.0311933i	−0.893323	+	0.449415i	$0.851632\pi$
$338$	−0.0401841	+	0.0834432i	−0.00218573	+	0.00453871i
$339$	2.63707	+	11.5537i	0.143226	+	0.627513i
$340$	−3.05182	−	9.35119i	−0.165508	−	0.507139i
$341$	−0.389450	+	0.488355i	−0.0210899	+	0.0264459i
$342$		−	7.97647i		−	0.431318i
$343$	−10.9029	+	14.9709i	−0.588702	+	0.808350i
$344$	9.17528			0.494698
$345$	−1.57673	−	17.2677i	−0.0848880	−	0.929660i
$346$	−10.6534	−	5.13041i	−0.572730	−	0.275812i
$347$	20.9457	−	4.78073i	1.12443	−	0.256643i	0.380419	−	0.924814i	$-0.375780\pi$
$347$	20.9457	−	4.78073i	1.12443	−	0.256643i	0.744007	+	0.668172i	$0.232923\pi$
$348$	−3.24204	+	6.73216i	−0.173792	+	0.360882i
$349$	24.3977	−	11.7493i	1.30598	−	0.628927i	0.354045	−	0.935228i	$-0.384806\pi$
$349$	24.3977	−	11.7493i	1.30598	−	0.628927i	0.951934	+	0.306302i	$0.0990917\pi$
$350$	9.44443	+	9.26298i	0.504826	+	0.495127i
$351$	−17.9983	−	8.66754i	−0.960680	−	0.462639i
$352$	0.180963	−	0.144313i	0.00964535	−	0.00769191i
$353$	−2.16660	−	4.49899i	−0.115316	−	0.239457i	0.835320	−	0.549764i	$-0.185282\pi$
$353$	−2.16660	−	4.49899i	−0.115316	−	0.239457i	−0.950636	+	0.310307i	$0.899568\pi$
$354$	7.33155	−	9.19348i	0.389668	−	0.488628i
$355$	−3.66080	−	6.10911i	−0.194295	−	0.324238i
$356$	6.17010	−	7.73706i	0.327015	−	0.410064i
$357$	−14.1371	+	2.34213i	−0.748213	+	0.123959i
$358$	7.88800	−	6.29047i	0.416894	−	0.332462i
$359$	−3.11550	+	1.50035i	−0.164430	+	0.0791853i	−0.514289	−	0.857617i	$-0.671944\pi$
$359$	−3.11550	+	1.50035i	−0.164430	+	0.0791853i	0.349858	+	0.936803i	$0.386230\pi$
$360$	−2.84665	+	1.70581i	−0.150032	+	0.0899043i
$361$	9.88533			0.520280
$362$		−	5.24897i		−	0.275880i
$363$	13.1394	+	2.99898i	0.689640	+	0.157406i
$364$	8.85960	−	3.62710i	0.464369	−	0.190112i
$365$	−4.86828	+	7.39600i	−0.254817	+	0.387124i
$366$	1.26796	+	5.55529i	0.0662772	+	0.290380i
$367$	1.00049	−	0.797868i	0.0522254	−	0.0416483i	−0.597029	−	0.802219i	$-0.703652\pi$
$367$	1.00049	−	0.797868i	0.0522254	−	0.0416483i	0.649255	+	0.760571i	$0.275081\pi$
$368$	−4.92418	+	3.92691i	−0.256691	+	0.204704i
$369$	−3.42191	−	14.9924i	−0.178138	−	0.780472i
$370$	15.9950	+	10.5284i	0.831541	+	0.547346i
$371$	−22.3501	−	12.4729i	−1.16036	−	0.647561i
$372$	3.23929	+	0.739346i	0.167949	+	0.0383333i
$373$			3.61072i			0.186956i	0.995621	+	0.0934781i	$0.0297985\pi$
$373$			3.61072i			0.186956i	−0.995621	+	0.0934781i	$0.970201\pi$
$374$	1.01820			0.0526501
$375$	−6.57012	−	12.0962i	−0.339279	−	0.624643i
$376$	8.38796	−	4.03943i	0.432576	−	0.208318i
$377$	17.1688	−	13.6917i	0.884239	−	0.705157i
$378$	5.53420	+	13.5179i	0.284649	+	0.695287i
$379$	13.3457	−	16.7350i	0.685522	−	0.859618i	−0.310327	−	0.950630i	$-0.600439\pi$
$379$	13.3457	−	16.7350i	0.685522	−	0.859618i	0.995850	+	0.0910119i	$0.0290101\pi$
$380$	−6.17729	−	10.3086i	−0.316888	−	0.528821i
$381$	−7.52844	+	9.44037i	−0.385694	+	0.483645i
$382$	−1.46652	−	3.04526i	−0.0750338	−	0.155809i
$383$	9.52352	−	7.59475i	0.486629	−	0.388074i	−0.349213	−	0.937043i	$-0.613551\pi$
$383$	9.52352	−	7.59475i	0.486629	−	0.388074i	0.835842	+	0.548970i	$0.184980\pi$
$384$	−1.10928	−	0.534200i	−0.0566076	−	0.0272608i
$385$	−1.21482	+	0.631893i	−0.0619131	+	0.0322043i
$386$	−13.0548	+	6.28688i	−0.664474	+	0.319994i
$387$	5.90833	−	12.2688i	0.300337	−	0.623657i
$388$	−8.54802	+	1.95103i	−0.433960	+	0.0990485i
$389$	−10.8246	−	5.21285i	−0.548828	−	0.264302i	0.138855	−	0.990313i	$-0.455658\pi$
$389$	−10.8246	−	5.21285i	−0.548828	−	0.264302i	−0.687683	+	0.726011i	$0.741372\pi$
$390$	−9.92033	+	0.905833i	−0.502335	+	0.0458686i
$391$	−27.7064			−1.40117
$392$	−6.58792	−	2.36629i	−0.332740	−	0.119516i
$393$		−	13.5659i		−	0.684310i
$394$	15.9264	−	19.9711i	0.802360	−	1.00613i
$395$	−19.1273	+	6.24231i	−0.962399	+	0.314085i
$396$	−0.0764397	−	0.334904i	−0.00384124	−	0.0168296i
$397$	−11.5652	+	24.0154i	−0.580440	+	1.20530i	0.379526	+	0.925181i	$0.376087\pi$
$397$	−11.5652	+	24.0154i	−0.580440	+	1.20530i	−0.959966	+	0.280116i	$0.909627\pi$
$398$	−4.09731	−	8.50815i	−0.205380	−	0.426475i
$399$	−16.2021	+	6.63308i	−0.811118	+	0.332070i
$400$	−2.35790	+	4.40912i	−0.117895	+	0.220456i
$401$	7.42633	+	9.31233i	0.370853	+	0.465036i	0.931882	−	0.362761i	$-0.118166\pi$
$401$	7.42633	+	9.31233i	0.370853	+	0.465036i	−0.561029	+	0.827796i	$0.689594\pi$
$402$	−1.65023	−	3.42673i	−0.0823057	−	0.170910i
$403$	−7.63436	−	6.08820i	−0.380294	−	0.303275i
$404$	−4.27649	+	18.7365i	−0.212763	+	0.932177i
$405$	−0.476804	−	5.22177i	−0.0236926	−	0.259472i
$406$	−16.0278	−	0.966327i	−0.795449	−	0.0479580i
$407$	−1.54972	+	1.23586i	−0.0768166	+	0.0612592i
$408$	−2.34998	−	4.87977i	−0.116341	−	0.241585i
$409$	2.89952	−	12.7036i	0.143372	−	0.628153i	−0.851266	−	0.524734i	$-0.824165\pi$
$409$	2.89952	−	12.7036i	0.143372	−	0.628153i	0.994638	−	0.103419i	$-0.0329782\pi$
$410$	−16.0331	−	16.7258i	−0.791818	−	0.826027i
$411$	14.5779			0.719076
$412$	0.683440	+	0.155991i	0.0336707	+	0.00768511i
$413$	24.2522	+	7.09523i	1.19337	+	0.349133i
$414$	2.08000	+	9.11309i	0.102227	+	0.447884i
$415$	−11.6383	+	17.6812i	−0.571302	+	0.867935i
$416$	2.25602	+	2.82896i	0.110610	+	0.138701i
$417$	4.31745	−	3.44305i	0.211427	−	0.168607i
$418$	1.21279	−	0.276812i	0.0593197	−	0.0135393i
$419$	3.32487	+	14.5672i	0.162431	+	0.711655i	0.988889	+	0.148657i	$0.0474950\pi$
$419$	3.32487	+	14.5672i	0.162431	+	0.711655i	−0.826458	+	0.562998i	$0.809648\pi$
$420$	5.83212	+	4.36368i	0.284579	+	0.212926i
$421$	0.0811884	−	0.355710i	0.00395688	−	0.0173362i	−0.972911	−	0.231180i	$-0.925741\pi$
$421$	0.0811884	−	0.355710i	0.00395688	−	0.0173362i	0.976868	+	0.213844i	$0.0685984\pi$
$422$			26.4268i			1.28644i
$423$		−	13.8172i		−	0.671813i
$424$	2.15266	−	9.43144i	0.104543	−	0.458031i
$425$	−20.2027	+	8.69718i	−0.979977	+	0.421875i
$426$	−2.44499	−	3.06592i	−0.118460	−	0.148544i
$427$	−10.0155	+	7.04454i	−0.484683	+	0.340909i
$428$	5.81852	+	4.64011i	0.281249	+	0.224288i
$429$	0.229452	−	1.00529i	0.0110780	−	0.0485360i
$430$	−1.86562	−	20.4315i	−0.0899682	−	0.985296i
$431$	14.4089	−	6.93895i	0.694051	−	0.334237i	−0.0533824	−	0.998574i	$-0.517000\pi$
$431$	14.4089	−	6.93895i	0.694051	−	0.334237i	0.747433	+	0.664337i	$0.231286\pi$
$432$	−4.31641	+	3.44222i	−0.207673	+	0.165614i
$433$	−13.0612	+	27.1219i	−0.627683	+	1.30340i	0.308279	+	0.951296i	$0.400247\pi$
$433$	−13.0612	+	27.1219i	−0.627683	+	1.30340i	−0.935962	+	0.352101i	$0.885467\pi$
$434$	1.16699	+	7.04393i	0.0560173	+	0.338120i
$435$	15.6504	+	5.85053i	0.750380	+	0.280511i
$436$	−6.39574	−	3.08003i	−0.306300	−	0.147506i
$437$	−33.0014	+	7.53235i	−1.57867	+	0.360321i
$438$	−2.11534	+	4.39255i	−0.101075	+	0.209884i
$439$	−2.96807	+	3.72185i	−0.141658	+	0.177634i	−0.847599	−	0.530637i	$-0.821953\pi$
$439$	−2.96807	+	3.72185i	−0.141658	+	0.177634i	0.705941	+	0.708271i	$0.250524\pi$
$440$	−0.358152	−	0.373625i	−0.0170742	−	0.0178119i
$441$	−7.40632	+	7.28533i	−0.352682	+	0.346920i
$442$			15.9174i			0.757114i
$443$	12.5500	+	10.0083i	0.596271	+	0.475510i	0.874514	−	0.485001i	$-0.161181\pi$
$443$	12.5500	+	10.0083i	0.596271	+	0.475510i	−0.278243	+	0.960511i	$0.589752\pi$
$444$	9.49957	+	4.57475i	0.450830	+	0.217108i
$445$	−18.4835	−	12.1664i	−0.876202	−	0.576744i
$446$	22.3734	+	10.7745i	1.05941	+	0.510187i
$447$	−9.60810	−	19.9514i	−0.454448	−	0.943670i
$448$	0.159225	−	2.64096i	0.00752266	−	0.124773i
$449$	−9.90698	−	4.77095i	−0.467539	−	0.225155i	0.185255	−	0.982691i	$-0.440689\pi$
$449$	−9.90698	−	4.77095i	−0.467539	−	0.225155i	−0.652794	+	0.757536i	$0.726403\pi$
$450$	4.37733	+	5.99209i	0.206349	+	0.282470i
$451$	2.16079	−	1.04058i	0.101747	−	0.0489990i
$452$	−7.52545	−	6.00135i	−0.353967	−	0.282280i
$453$	21.2443	+	4.84888i	0.998146	+	0.227820i
$454$	−2.75449	+	3.45402i	−0.129275	+	0.162105i
$455$	−9.87827	−	18.9911i	−0.463100	−	0.890316i
$456$	−4.12571	−	5.17348i	−0.193204	−	0.242270i
$457$	−0.492668	−	1.02304i	−0.0230460	−	0.0478556i	0.889128	−	0.457658i	$-0.151312\pi$
$457$	−0.492668	−	1.02304i	−0.0230460	−	0.0478556i	−0.912174	+	0.409803i	$0.865597\pi$
$458$	8.62405	+	1.96838i	0.402975	+	0.0919765i
$459$	−24.2867			−1.13361
$460$	9.74569	+	10.1667i	0.454395	+	0.474026i
$461$	7.10093	−	31.1112i	0.330723	−	1.44899i	−0.487010	−	0.873396i	$-0.661913\pi$
$461$	7.10093	−	31.1112i	0.330723	−	1.44899i	0.817733	−	0.575597i	$-0.195230\pi$
$462$	−0.616702	+	0.433767i	−0.0286916	+	0.0201807i
$463$	−1.29519	+	0.295618i	−0.0601925	+	0.0137385i	−0.252511	−	0.967594i	$-0.581256\pi$
$463$	−1.29519	+	0.295618i	−0.0601925	+	0.0137385i	0.192319	+	0.981333i	$0.438399\pi$
$464$	−1.35047	−	5.91680i	−0.0626940	−	0.274680i
$465$	0.987730	−	7.36359i	0.0458049	−	0.341478i
$466$	0.856878	+	1.07449i	0.0396941	+	0.0497749i
$467$	−33.7605	+	7.70561i	−1.56225	+	0.356573i	−0.914276	−	0.405091i	$-0.867240\pi$
$467$	−33.7605	+	7.70561i	−1.56225	+	0.356573i	−0.647972	+	0.761664i	$0.724383\pi$
$468$	5.23550	−	1.19497i	0.242011	−	0.0552374i
$469$	5.47118	−	6.07175i	0.252636	−	0.280367i
$470$	−10.7005	−	17.8570i	−0.493579	−	0.823682i
$471$	10.0483			0.463000
$472$			9.55071i			0.439607i
$473$	2.07046	+	0.472570i	0.0952000	+	0.0217288i
$474$	−9.98129	+	4.80674i	−0.458456	+	0.220781i
$475$	−21.6992	+	15.8517i	−0.995630	+	0.727325i
$476$	7.79114	−	8.64637i	0.357106	−	0.396306i
$477$	−11.2251	−	8.95173i	−0.513963	−	0.409872i
$478$	21.5910	+	4.92800i	0.987548	+	0.225401i
$479$	−11.5701	+	14.5084i	−0.528650	+	0.662906i	−0.972420	−	0.233235i	$-0.925069\pi$
$479$	−11.5701	+	14.5084i	−0.528650	+	0.662906i	0.443771	+	0.896140i	$0.353640\pi$
$480$	−0.964009	+	2.57877i	−0.0440008	+	0.117704i
$481$	−19.3199	−	24.2264i	−0.880914	−	1.10463i
$482$	−10.6271	+	22.0674i	−0.484051	+	1.00514i
$483$	16.7811	−	11.8032i	0.763567	−	0.537066i
$484$	−9.86239	+	4.74948i	−0.448290	+	0.215885i
$485$	6.08264	+	18.6381i	0.276198	+	0.846311i
$486$	3.04309	+	13.3327i	0.138038	+	0.604782i
$487$	−3.81954	+	7.93136i	−0.173080	+	0.359404i	−0.969406	−	0.245464i	$-0.921060\pi$
$487$	−3.81954	+	7.93136i	−0.173080	+	0.359404i	0.796326	+	0.604868i	$0.206774\pi$
$488$	−3.61840	−	2.88558i	−0.163797	−	0.130624i
$489$	−13.5968			−0.614868
$490$	−3.92973	+	15.1511i	−0.177527	+	0.684459i
$491$	11.8352			0.534114			0.267057	−	0.963681i	$-0.413949\pi$
$491$	11.8352			0.534114			0.267057	+	0.963681i	$0.413949\pi$
$492$	−9.97401	−	7.95401i	−0.449663	−	0.358594i
$493$	11.5837	−	24.0538i	0.521703	−	1.08333i
$494$	4.32736	+	18.9594i	0.194697	+	0.853023i
$495$	−0.730224	+	0.238313i	−0.0328211	+	0.0107114i
$496$	−2.43140	+	1.17090i	−0.109173	+	0.0525749i
$497$	4.10656	−	7.35853i	0.184204	−	0.330075i
$498$	−5.05702	+	10.5010i	−0.226610	+	0.470561i
$499$	7.53965	+	9.45443i	0.337521	+	0.423238i	0.921408	−	0.388597i	$-0.127040\pi$
$499$	7.53965	+	9.45443i	0.337521	+	0.423238i	−0.583887	+	0.811835i	$0.698469\pi$
$500$	10.2977	+	4.35407i	0.460526	+	0.194720i
$501$	−7.47767	+	9.37670i	−0.334078	+	0.418920i
$502$	20.0007	+	4.56502i	0.892674	+	0.203747i
$503$	−15.9912	−	12.7526i	−0.713014	−	0.568609i	0.198390	−	0.980123i	$-0.436429\pi$
$503$	−15.9912	−	12.7526i	−0.713014	−	0.568609i	−0.911404	+	0.411514i	$0.865000\pi$
$504$	−3.42884	−	1.91353i	−0.152733	−	0.0852352i
$505$	42.5921	+	5.71319i	1.89533	+	0.254233i
$506$	−1.31343	+	0.632514i	−0.0583891	+	0.0281187i
$507$	0.111169	+	0.0253737i	0.00493720	+	0.00112688i
$508$		−	9.80720i		−	0.435124i
$509$	−13.1089			−0.581043			−0.290522	−	0.956868i	$-0.593829\pi$
$509$	−13.1089			−0.581043			−0.290522	+	0.956868i	$0.593829\pi$
$510$	−10.3885	+	6.22514i	−0.460009	+	0.275654i
$511$	−10.4577	−	0.630501i	−0.462622	−	0.0278917i
$512$	0.974928	−	0.222521i	0.0430861	−	0.00983413i
$513$	−28.9281	+	6.60266i	−1.27721	+	0.291514i
$514$	−5.37034	−	6.73420i	−0.236876	−	0.297033i
$515$	0.208396	−	1.55360i	0.00918303	−	0.0684600i
$516$	−2.51374	−	11.0134i	−0.110661	−	0.484839i
$517$	2.10085	−	0.479505i	0.0923952	−	0.0210886i
$518$	−1.36356	+	22.6165i	−0.0599113	+	0.993710i
$519$	−3.23952	+	14.1932i	−0.142199	+	0.623014i
$520$	5.84081	−	5.59893i	0.256137	−	0.245529i
$521$	6.36523			0.278866			0.139433	−	0.990232i	$-0.455472\pi$
$521$	6.36523			0.278866			0.139433	+	0.990232i	$0.455472\pi$
$522$	−8.78130	−	2.00427i	−0.384347	−	0.0877247i
$523$	2.30478	+	4.78592i	0.100781	+	0.209274i	0.945263	−	0.326311i	$-0.105806\pi$
$523$	2.30478	+	4.78592i	0.100781	+	0.209274i	−0.844482	+	0.535585i	$0.820091\pi$
$524$	6.86985	+	8.61453i	0.300111	+	0.376327i
$525$	8.53121	−	13.8743i	0.372333	−	0.605523i
$526$	3.02443	−	3.79251i	0.131871	−	0.165361i
$527$	−11.5738	−	2.64165i	−0.504165	−	0.115072i
$528$	−0.222802	−	0.177679i	−0.00969623	−	0.00773249i
$529$	15.0175	−	7.23205i	0.652935	−	0.314437i
$530$	−21.4397	−	2.87585i	−0.931280	−	0.124919i
$531$	12.7708	+	6.15009i	0.554205	+	0.266891i
$532$	6.92948	−	12.4169i	0.300431	−	0.538341i
$533$	16.2672	+	33.7792i	0.704610	+	1.46314i
$534$	−10.9775	−	5.28649i	−0.475043	−	0.228769i
$535$	9.14954	−	13.9002i	0.395569	−	0.600957i
$536$	2.78323	+	1.34033i	0.120217	+	0.0578935i
$537$	−9.71176	−	7.74487i	−0.419093	−	0.334216i
$538$			1.27928i			0.0551535i
$539$	−1.36473	−	0.873278i	−0.0587833	−	0.0376147i
$540$	8.54281	+	8.91188i	0.367624	+	0.383506i
$541$	−27.8708	+	34.9489i	−1.19826	+	1.50257i	−0.382721	+	0.923864i	$0.625013\pi$
$541$	−27.8708	+	34.9489i	−1.19826	+	1.50257i	−0.815537	+	0.578705i	$0.803558\pi$
$542$	0.139358	−	0.289379i	0.00598593	−	0.0124299i
$543$	−6.30054	+	1.43806i	−0.270382	+	0.0617129i
$544$	3.96341	+	1.90868i	0.169930	+	0.0818339i
$545$	−5.55816	+	14.8683i	−0.238085	+	0.636889i
$546$	−6.78100	−	9.64079i	−0.290200	−	0.412588i
$547$	8.22620	−	17.0819i	0.351727	−	0.730369i	−0.647778	−	0.761829i	$-0.724302\pi$
$547$	8.22620	−	17.0819i	0.351727	−	0.730369i	0.999505	+	0.0314606i	$0.0100159\pi$
$548$	−9.25717	+	7.38235i	−0.395447	+	0.315358i
$549$	−6.18850	+	2.98022i	−0.264119	+	0.127193i
$550$	−0.759167	+	0.873504i	−0.0323710	+	0.0372463i
$551$	7.25811	−	31.7999i	0.309206	−	1.35472i
$552$	6.06269	+	4.83483i	0.258045	+	0.205784i
$553$	−17.6856	−	15.9363i	−0.752070	−	0.677681i
$554$	0.927289	+	1.16278i	0.0393967	+	0.0494019i
$555$	8.25552	−	22.0839i	0.350427	−	0.937408i
$556$	−0.998055	+	4.37277i	−0.0423270	+	0.185447i
$557$		−	29.2014i		−	1.23730i	−0.785665	−	0.618652i	$-0.787679\pi$
$557$		−	29.2014i		−	1.23730i	0.785665	−	0.618652i	$-0.212321\pi$
$558$			4.00515i			0.169551i
$559$	−7.38760	+	32.3672i	−0.312462	+	1.36899i
$560$	−5.91327	+	0.182427i	−0.249881	+	0.00770894i
$561$	−0.278957	−	1.22219i	−0.0117776	−	0.0516009i
$562$	−17.1713	+	3.91925i	−0.724330	+	0.165324i
$563$	6.63164	−	5.28856i	0.279490	−	0.222886i	−0.473704	−	0.880684i	$-0.657083\pi$
$563$	6.63164	−	5.28856i	0.279490	−	0.222886i	0.753194	+	0.657798i	$0.228512\pi$
$564$	−7.14672	−	8.96170i	−0.300931	−	0.377356i
$565$	−11.8337	+	17.9780i	−0.497846	+	0.756339i
$566$	4.54166	+	19.8983i	0.190900	+	0.836388i
$567$	5.07463	−	3.56932i	0.213114	−	0.149897i
$568$	3.10519	+	0.708740i	0.130291	+	0.0297381i
$569$	12.9982			0.544912			0.272456	−	0.962168i	$-0.412164\pi$
$569$	12.9982			0.544912			0.272456	+	0.962168i	$0.412164\pi$
$570$	−10.6814	+	10.2391i	−0.447396	+	0.428868i
$571$	9.63013	−	42.1924i	0.403008	−	1.76570i	−0.212095	−	0.977249i	$-0.568029\pi$
$571$	9.63013	−	42.1924i	0.403008	−	1.76570i	0.615103	−	0.788446i	$-0.289114\pi$
$572$	0.363381	+	0.754569i	0.0151937	+	0.0315501i
$573$	−3.25356	+	2.59463i	−0.135920	+	0.108392i
$574$	7.69762	−	26.3113i	0.321292	−	1.09821i
$575$	20.6577	−	23.7690i	0.861486	−	0.991234i
$576$	0.330250	−	1.44692i	0.0137604	−	0.0602884i
$577$	5.61925	+	4.48120i	0.233932	+	0.186555i	0.733439	−	0.679755i	$-0.237914\pi$
$577$	5.61925	+	4.48120i	0.233932	+	0.186555i	−0.499507	+	0.866310i	$0.666485\pi$
$578$	1.02035	+	2.11877i	0.0424408	+	0.0881292i
$579$	11.1230	+	13.9478i	0.462256	+	0.579651i
$580$	−12.9010	+	4.21030i	−0.535683	+	0.174823i
$581$	−25.0006	−	1.50730i	−1.03720	−	0.0625334i
$582$	4.68379	+	9.72598i	0.194149	+	0.403155i
$583$	0.971527	−	2.01740i	0.0402365	−	0.0835520i
$584$	−0.881144	−	3.86054i	−0.0364620	−	0.159750i
$585$	−3.72550	−	11.4155i	−0.154030	−	0.471971i
$586$	18.1588	−	22.7705i	0.750135	−	0.940639i
$587$			13.5620i			0.559765i	0.960034	+	0.279882i	$0.0902954\pi$
$587$			13.5620i			0.559765i	−0.960034	+	0.279882i	$0.909705\pi$
$588$	−1.03546	+	8.55602i	−0.0427015	+	0.352844i
$589$	−14.5039			−0.597623
$590$	21.2676	−	1.94196i	0.875572	−	0.0799492i
$591$	−28.3353	−	13.6456i	−1.16556	−	0.561304i
$592$	−8.34903	+	1.90561i	−0.343143	+	0.0783201i
$593$	2.72036	−	5.64889i	0.111712	−	0.231972i	−0.837616	−	0.546259i	$-0.816051\pi$
$593$	2.72036	−	5.64889i	0.111712	−	0.231972i	0.949328	+	0.314287i	$0.101766\pi$
$594$	−1.15132	+	0.554445i	−0.0472391	+	0.0227492i
$595$	−20.8380	−	15.5913i	−0.854273	−	0.639180i
$596$	16.2048	+	7.80381i	0.663774	+	0.319657i
$597$	−9.09012	+	7.24913i	−0.372034	+	0.296687i
$598$	−9.88798	−	20.5326i	−0.404350	−	0.839641i
$599$	−30.0202	+	37.6442i	−1.22659	+	1.53810i	−0.472505	+	0.881328i	$0.656650\pi$
$599$	−30.0202	+	37.6442i	−1.22659	+	1.53810i	−0.754089	+	0.656772i	$0.771921\pi$
$600$	5.93842	+	1.62231i	0.242435	+	0.0662307i
$601$	16.1310	−	20.2276i	0.657996	−	0.825101i	−0.335127	−	0.942173i	$-0.608779\pi$
$601$	16.1310	−	20.2276i	0.657996	−	0.825101i	0.993123	+	0.117072i	$0.0373508\pi$
$602$	19.8558	−	13.9659i	0.809263	−	0.569207i
$603$	3.58447	−	2.85852i	0.145971	−	0.116408i
$604$	−15.9459	+	7.67915i	−0.648830	+	0.312460i
$605$	12.5815	+	20.9959i	0.511510	+	0.853604i
$606$	23.6618			0.961195
$607$		−	15.2713i		−	0.619842i	−0.950762	−	0.309921i	$-0.899697\pi$
$607$		−	15.2713i		−	0.619842i	0.950762	−	0.309921i	$-0.100303\pi$
$608$	5.23976	+	1.19594i	0.212500	+	0.0485018i
$609$	3.23122	+	19.5036i	0.130936	+	0.790324i
$610$	−5.68988	+	8.64419i	−0.230376	+	0.349993i
$611$	7.49601	+	32.8422i	0.303256	+	1.32865i
$612$	5.10440	−	4.07062i	0.206333	−	0.164545i
$613$	26.5074	−	21.1389i	1.07062	−	0.853792i	0.0808891	−	0.996723i	$-0.474224\pi$
$613$	26.5074	−	21.1389i	1.07062	−	0.853792i	0.989733	+	0.142931i	$0.0456526\pi$
$614$	1.94206	+	8.50871i	0.0783751	+	0.343384i
$615$	−15.6840	+	23.8275i	−0.632439	+	0.960816i
$616$	0.171952	−	0.587749i	0.00692813	−	0.0236811i
$617$	28.8063	+	6.57484i	1.15970	+	0.264693i	0.758733	−	0.651401i	$-0.225818\pi$
$617$	28.8063	+	6.57484i	1.15970	+	0.264693i	0.400963	+	0.916094i	$0.368676\pi$
$618$		−	0.863095i		−	0.0347188i
$619$	−23.6599			−0.950971			−0.475486	−	0.879724i	$-0.657728\pi$
$619$	−23.6599			−0.950971			−0.475486	+	0.879724i	$0.657728\pi$
$620$	3.10174	+	5.17616i	0.124569	+	0.207880i
$621$	31.3285	−	15.0870i	1.25717	−	0.605421i
$622$	−8.56561	+	6.83085i	−0.343450	+	0.273892i
$623$	1.57570	−	26.1351i	0.0631290	−	1.04708i
$624$	2.77762	−	3.48303i	0.111194	−	0.139433i
$625$	7.60183	−	23.8162i	0.304073	−	0.952649i
$626$	−4.29578	+	5.38674i	−0.171694	+	0.215298i
$627$	−0.664537	−	1.37992i	−0.0265390	−	0.0551089i
$628$	−6.38078	+	5.08850i	−0.254621	+	0.203053i
$629$	−33.9416	−	16.3454i	−1.35334	−	0.651734i
$630$	−3.56386	+	8.02443i	−0.141987	+	0.319701i
$631$	−35.8648	+	17.2716i	−1.42776	+	0.687572i	−0.978579	−	0.205871i	$-0.933997\pi$
$631$	−35.8648	+	17.2716i	−1.42776	+	0.687572i	−0.449178	+	0.893442i	$0.648283\pi$
$632$	3.90409	−	8.10692i	0.155296	−	0.322476i
$633$	31.7211	−	7.24013i	1.26080	−	0.287769i
$634$	1.54950	+	0.746201i	0.0615386	+	0.0296354i
$635$	−21.8387	+	1.99411i	−0.866643	+	0.0791338i
$636$	−11.9107			−0.472289
$637$	13.6518	−	21.3346i	0.540904	−	0.845309i
$638$		−	1.40472i		−	0.0556134i
$639$	2.94726	−	3.69574i	0.116592	−	0.146201i
$640$	−0.693744	−	2.12573i	−0.0274226	−	0.0840268i
$641$	2.80704	+	12.2984i	0.110871	+	0.485760i	0.999625	+	0.0273747i	$0.00871472\pi$
$641$	2.80704	+	12.2984i	0.110871	+	0.485760i	−0.888754	+	0.458385i	$0.848428\pi$
$642$	3.97561	−	8.25543i	0.156905	−	0.325816i
$643$	−6.00221	−	12.4637i	−0.236704	−	0.491521i	0.748451	−	0.663190i	$-0.230798\pi$
$643$	−6.00221	−	12.4637i	−0.236704	−	0.491521i	−0.985155	+	0.171670i	$0.945084\pi$
$644$	−4.67899	+	15.9933i	−0.184378	+	0.630223i
$645$	−24.0136	+	7.83699i	−0.945535	+	0.308581i
$646$	14.7410	+	18.4846i	0.579977	+	0.727268i
$647$	−10.6613	−	22.1383i	−0.419137	−	0.870348i	−0.998472	−	0.0552580i	$-0.982402\pi$
$647$	−10.6613	−	22.1383i	−0.419137	−	0.870348i	0.579335	−	0.815090i	$-0.303312\pi$
$648$	1.83336	+	1.46206i	0.0720214	+	0.0574351i
$649$	−0.491907	+	2.15518i	−0.0193090	+	0.0845984i
$650$	−13.6553	−	11.8679i	−0.535606	−	0.465498i
$651$	8.13538	−	3.33060i	0.318851	−	0.130537i
$652$	8.63414	−	6.88549i	0.338139	−	0.269657i
$653$	1.99798	+	4.14885i	0.0781871	+	0.162357i	0.936398	−	0.350940i	$-0.114138\pi$
$653$	1.99798	+	4.14885i	0.0781871	+	0.162357i	−0.858211	+	0.513298i	$0.828424\pi$
$654$	−1.94483	+	8.52088i	−0.0760491	+	0.333193i
$655$	17.7860	−	17.0494i	0.694957	−	0.666176i
$656$	10.3616			0.404552
$657$	−5.72955	−	1.30773i	−0.223531	−	0.0510195i
$658$	12.0035	−	21.5090i	0.467946	−	0.838510i
$659$	−9.88847	−	43.3242i	−0.385200	−	1.68767i	−0.680889	−	0.732387i	$-0.738406\pi$
$659$	−9.88847	−	43.3242i	−0.385200	−	1.68767i	0.295689	−	0.955284i	$-0.404451\pi$
$660$	−0.350354	+	0.532265i	−0.0136375	+	0.0207184i
$661$	24.6563	+	30.9180i	0.959019	+	1.20257i	0.979225	+	0.202776i	$0.0649962\pi$
$661$	24.6563	+	30.9180i	0.959019	+	1.20257i	−0.0202065	+	0.999796i	$0.506432\pi$
$662$	8.07875	−	6.44258i	0.313989	−	0.250398i
$663$	19.1063	−	4.36088i	0.742026	−	0.169362i
$664$	−2.10650	−	9.22917i	−0.0817480	−	0.358161i
$665$	−29.0590	−	12.9059i	−1.12686	−	0.500468i
$666$	−2.82818	+	12.3910i	−0.109590	+	0.480143i
$667$			38.2239i			1.48004i
$668$		−	9.74106i		−	0.376893i
$669$	6.80338	−	29.8076i	0.263034	−	1.15243i
$670$	2.41874	−	6.47023i	0.0934440	−	0.249967i
$671$	−0.667896	−	0.837515i	−0.0257838	−	0.0323319i
$672$	−3.21366	+	0.532417i	−0.123970	+	0.0205384i
$673$	23.5514	+	18.7816i	0.907839	+	0.723977i	0.961565	−	0.274578i	$-0.0885383\pi$
$673$	23.5514	+	18.7816i	0.907839	+	0.723977i	−0.0537260	+	0.998556i	$0.517110\pi$
$674$	−0.141429	+	0.619640i	−0.00544763	+	0.0238676i
$675$	18.1080	−	20.8352i	0.696977	−	0.801948i
$676$	−0.0834432	+	0.0401841i	−0.00320936	+	0.00154554i
$677$	16.9989	−	13.5562i	0.653321	−	0.521006i	−0.239800	−	0.970822i	$-0.577082\pi$
$677$	16.9989	−	13.5562i	0.653321	−	0.521006i	0.893121	+	0.449816i	$0.148510\pi$
$678$	−5.14190	+	10.6773i	−0.197473	+	0.410058i
$679$	−15.5287	+	17.2333i	−0.595937	+	0.661352i
$680$	3.44436	−	9.21383i	0.132085	−	0.353334i
$681$	4.90064	+	2.36002i	0.187793	+	0.0904363i
$682$	−0.608968	+	0.138993i	−0.0233186	+	0.00532232i
$683$	−21.6511	+	44.9590i	−0.828457	+	1.72031i	−0.146124	+	0.989266i	$0.546680\pi$
$683$	−21.6511	+	44.9590i	−0.828457	+	1.72031i	−0.682332	+	0.731042i	$0.739034\pi$
$684$	4.97325	−	6.23626i	0.190157	−	0.238449i
$685$	18.3213	+	19.1128i	0.700021	+	0.730264i
$686$	−17.8584	+	4.90683i	−0.681837	+	0.187344i
$687$		−	10.8910i		−	0.415519i
$688$	7.17352	+	5.72069i	0.273488	+	0.218099i
$689$	31.5376	+	15.1877i	1.20149	+	0.578605i
$690$	9.53349	−	14.4835i	0.362934	−	0.551377i
$691$	24.4060	+	11.7533i	0.928450	+	0.447118i	0.836080	−	0.548607i	$-0.184842\pi$
$691$	24.4060	+	11.7533i	0.928450	+	0.447118i	0.0923693	+	0.995725i	$0.470556\pi$
$692$	−5.13041	−	10.6534i	−0.195029	−	0.404981i
$693$	−0.675185	−	0.608402i	−0.0256482	−	0.0231113i
$694$	19.3568	+	9.32173i	0.734773	+	0.353848i
$695$	9.94023	+	1.33335i	0.377054	+	0.0505770i
$696$	−6.73216	+	3.24204i	−0.255182	+	0.122889i
$697$	35.6367	+	28.4194i	1.34984	+	1.07646i
$698$	26.4005	+	6.02574i	0.999273	+	0.228077i
$699$	1.05499	−	1.32292i	0.0399035	−	0.0500375i
$700$	1.60858	+	13.1306i	0.0607986	+	0.496290i
$701$	−20.5924	−	25.8221i	−0.777764	−	0.975285i	−1.00000		0.000292485i	$-0.999907\pi$
$701$	−20.5924	−	25.8221i	−0.777764	−	0.975285i	0.222236	−	0.974993i	$-0.428665\pi$
$702$	−8.66754	−	17.9983i	−0.327135	−	0.679303i
$703$	−44.8719	−	10.2417i	−1.69238	−	0.386274i
$704$	0.231460			0.00872348
$705$	−18.5028	+	17.7365i	−0.696856	+	0.667996i
$706$	1.11116	−	4.86830i	0.0418190	−	0.183221i
$707$	19.2647	+	47.0563i	0.724524	+	1.76973i
$708$	11.4641	−	2.61660i	0.430846	−	0.0983379i
$709$	1.24502	+	5.45481i	0.0467579	+	0.204860i	0.992911	−	0.118860i	$-0.0379238\pi$
$709$	1.24502	+	5.45481i	0.0467579	+	0.204860i	−0.946153	+	0.323719i	$0.895067\pi$
$710$	0.946843	−	7.05877i	0.0355344	−	0.264911i
$711$	−8.32621	−	10.4407i	−0.312257	−	0.391558i
$712$	9.64796	−	2.20208i	0.361573	−	0.0825266i
$713$	16.5707	−	3.78214i	0.620576	−	0.141642i
$714$	−12.5131	−	6.98316i	−0.468291	−	0.261338i
$715$	1.60639	−	0.962607i	0.0600756	−	0.0359994i
$716$	10.0891			0.377049
$717$		−	27.2666i		−	1.01829i
$718$	−3.37125	−	0.769466i	−0.125814	−	0.0287162i
$719$	24.6568	−	11.8741i	0.919545	−	0.442829i	0.0866361	−	0.996240i	$-0.472388\pi$
$719$	24.6568	−	11.8741i	0.919545	−	0.442829i	0.832909	+	0.553411i	$0.186674\pi$
$720$	−3.28916	−	0.441198i	−0.122580	−	0.0164425i
$721$	1.71644	−	0.702706i	0.0639236	−	0.0261702i
$722$	7.72866	+	6.16340i	0.287631	+	0.229378i
$723$	29.3998	+	6.71031i	1.09339	+	0.249559i
$724$	3.27268	−	4.10381i	0.121628	−	0.152517i
$725$	11.9987	+	27.8718i	0.445620	+	1.03513i
$726$	8.40296	+	10.5370i	0.311863	+	0.391064i
$727$	−11.4806	+	23.8397i	−0.425792	+	0.884166i	0.572157	+	0.820144i	$0.306107\pi$
$727$	−11.4806	+	23.8397i	−0.425792	+	0.884166i	−0.997949	+	0.0640216i	$0.979607\pi$
$728$	9.18817	+	2.68809i	0.340536	+	0.0996273i
$729$	21.5082	−	10.3578i	0.796600	−	0.383622i
$730$	−8.41751	+	2.74710i	−0.311546	+	0.101675i
$731$	8.98150	+	39.3505i	0.332193	+	1.45543i
$732$	−2.47234	+	5.13386i	−0.0913801	+	0.189753i
$733$	35.4934	+	28.3050i	1.31098	+	1.04547i	0.995324	+	0.0965968i	$0.0307957\pi$
$733$	35.4934	+	28.3050i	1.31098	+	1.04547i	0.315655	+	0.948874i	$0.397776\pi$
$734$	1.27968			0.0472339
$735$	19.2631	+	0.566055i	0.710531	+	0.0208793i
$736$	−6.29827			−0.232157
$737$	0.559021	+	0.445804i	0.0205918	+	0.0164214i
$738$	6.67224	−	13.8550i	0.245608	−	0.510011i
$739$	−4.68334	−	20.5191i	−0.172280	−	0.754806i	−0.985057	−	0.172231i	$-0.944902\pi$
$739$	−4.68334	−	20.5191i	−0.172280	−	0.754806i	0.812777	−	0.582575i	$-0.197955\pi$
$740$	5.94104	+	18.2042i	0.218397	+	0.669199i
$741$	21.5721	−	10.3886i	0.792471	−	0.381634i
$742$	−9.69731	−	23.6868i	−0.355999	−	0.869569i
$743$	−5.65367	+	11.7400i	−0.207413	+	0.430697i	−0.978561	−	0.205959i	$-0.933969\pi$
$743$	−5.65367	+	11.7400i	−0.207413	+	0.430697i	0.771148	+	0.636656i	$0.219683\pi$
$744$	2.07160	+	2.59771i	0.0759486	+	0.0952365i
$745$	14.0826	−	37.6716i	0.515947	−	1.38018i
$746$	−2.25125	+	2.82298i	−0.0824241	+	0.103357i
$747$	−13.6973	−	3.12632i	−0.501158	−	0.114386i
$748$	0.796065	+	0.634840i	0.0291070	+	0.0232121i
$749$	19.6544	+	1.18498i	0.718157	+	0.0432981i
$750$	2.40511	−	13.5536i	0.0878222	−	0.494906i
$751$	−41.8880	+	20.1722i	−1.52851	+	0.736094i	−0.994032	−	0.109086i	$-0.965207\pi$
$751$	−41.8880	+	20.1722i	−1.52851	+	0.736094i	−0.534482	+	0.845180i	$0.679493\pi$
$752$	9.07651	+	2.07165i	0.330986	+	0.0755454i
$753$		−	25.2582i		−	0.920461i
$754$	21.9597			0.799727
$755$	20.3423	+	33.9470i	0.740331	+	1.23546i
$756$	−4.10147	+	14.0193i	−0.149169	+	0.509875i
$757$	10.8430	−	2.47484i	0.394095	−	0.0899497i	−0.0208808	−	0.999782i	$-0.506647\pi$
$757$	10.8430	−	2.47484i	0.394095	−	0.0899497i	0.414976	+	0.909832i	$0.363790\pi$
$758$	20.8682	−	4.76302i	0.757966	−	0.173001i
$759$	1.11907	+	1.40327i	0.0406197	+	0.0509355i
$760$	1.59772	−	11.9111i	0.0579553	−	0.432060i
$761$	3.00804	+	13.1791i	0.109041	+	0.477742i	0.999732	+	0.0231325i	$0.00736395\pi$
$761$	3.00804	+	13.1791i	0.109041	+	0.477742i	−0.890691	+	0.454609i	$0.849779\pi$
$762$	−11.7719	+	2.68687i	−0.426453	+	0.0973350i
$763$	−18.5289	+	3.06974i	−0.670792	+	0.111132i
$764$	0.752118	−	3.29525i	0.0272107	−	0.119218i
$765$	−10.1024	−	10.5388i	−0.365252	−	0.381031i
$766$	12.1810			0.440119
$767$	−33.6916	−	7.68989i	−1.21653	−	0.277666i
$768$	−0.534200	−	1.10928i	−0.0192763	−	0.0400276i
$769$	29.6821	+	37.2202i	1.07036	+	1.34220i	0.936292	+	0.351224i	$0.114234\pi$
$769$	29.6821	+	37.2202i	1.07036	+	1.34220i	0.134073	+	0.990971i	$0.457194\pi$
$770$	−1.34376	−	0.263395i	−0.0484259	−	0.00949210i
$771$	−6.61200	+	8.29119i	−0.238125	+	0.298600i
$772$	−14.1265	−	3.22428i	−0.508424	−	0.116044i
$773$	−1.46847	−	1.17107i	−0.0528172	−	0.0421203i	0.596725	−	0.802446i	$-0.296468\pi$
$773$	−1.46847	−	1.17107i	−0.0528172	−	0.0421203i	−0.649543	+	0.760325i	$0.725040\pi$
$774$	12.2688	−	5.90833i	0.440992	−	0.212371i
$775$	10.8956	−	7.95945i	0.391382	−	0.285912i
$776$	−7.89956	−	3.80423i	−0.283578	−	0.136564i
$777$	27.5209	−	4.55948i	0.987308	−	0.163570i
$778$	−5.21285	−	10.8246i	−0.186890	−	0.388080i
$779$	50.1735	+	24.1623i	1.79765	+	0.865703i
$780$	−8.32080	−	5.47701i	−0.297933	−	0.196109i
$781$	0.664205	+	0.319864i	0.0237671	+	0.0114456i
$782$	−21.6617	−	17.2747i	−0.774622	−	0.617741i
$783$			33.5060i			1.19741i
$784$	−3.67529	−	5.95754i	−0.131260	−	0.212769i
$785$	12.6285	+	13.1741i	0.450731	+	0.470203i
$786$	8.45821	−	10.6063i	0.301694	−	0.378313i
$787$	−4.28731	+	8.90269i	−0.152826	+	0.317347i	−0.963300	−	0.268429i	$-0.913496\pi$
$787$	−4.28731	+	8.90269i	−0.152826	+	0.317347i	0.810473	+	0.585775i	$0.199210\pi$
$788$	24.9035	−	5.68406i	0.887150	−	0.202486i
$789$	−5.38090	−	2.59130i	−0.191565	−	0.0922528i
$790$	−18.8463	−	7.04524i	−0.670523	−	0.250659i
$791$	−25.4203	−	1.53260i	−0.903841	−	0.0544931i
$792$	0.149046	−	0.309498i	0.00529614	−	0.0109975i
$793$	13.0927	−	10.4411i	0.464936	−	0.370774i
$794$	−24.0154	+	11.5652i	−0.852274	+	0.410433i
$795$	2.42181	+	26.5227i	0.0858928	+	0.940664i
$796$	2.10134	−	9.20657i	0.0744800	−	0.326318i
$797$	−39.0797	−	31.1651i	−1.38428	−	1.10392i	−0.982100	−	0.188361i	$-0.939683\pi$
$797$	−39.0797	−	31.1651i	−1.38428	−	1.10392i	−0.402176	−	0.915562i	$-0.631746\pi$
$798$	−16.8029	−	4.91587i	−0.594818	−	0.174020i
$799$	25.5349	+	32.0198i	0.903361	+	1.13278i
$800$	−4.59252	+	1.97706i	−0.162370	+	0.0698996i
$801$	3.26818	−	14.3188i	0.115475	−	0.505931i
$802$			11.9109i			0.420589i
$803$		−	0.916541i		−	0.0323440i
$804$	0.846332	−	3.70802i	0.0298478	−	0.130772i
$805$	36.5652	+	7.16725i	1.28876	+	0.252613i
$806$	−2.17285	−	9.51989i	−0.0765354	−	0.335324i
$807$	1.53556	−	0.350482i	0.0540544	−	0.0123376i
$808$	−15.0255	+	11.9825i	−0.528596	+	0.421542i
$809$	−30.7263	−	38.5296i	−1.08028	−	1.35463i	−0.930660	−	0.365885i	$-0.880766\pi$
$809$	−30.7263	−	38.5296i	−1.08028	−	1.35463i	−0.149620	−	0.988744i	$-0.547805\pi$
$810$	2.88294	−	4.37983i	0.101296	−	0.153891i
$811$	3.97153	+	17.4004i	0.139459	+	0.611012i	0.995554	+	0.0941925i	$0.0300269\pi$
$811$	3.97153	+	17.4004i	0.139459	+	0.611012i	−0.856095	+	0.516819i	$0.827116\pi$
$812$	−11.9286	−	10.7487i	−0.418611	−	0.377206i
$813$	−0.385533	−	0.0879953i	−0.0135212	−	0.00308613i
$814$	−1.98216			−0.0694748
$815$	−17.0882	−	17.8265i	−0.598575	−	0.624435i
$816$	1.20520	−	5.28035i	0.0421906	−	0.184849i
$817$	21.3959	+	44.4291i	0.748549	+	1.55438i
$818$	10.1875	−	8.12426i	0.356198	−	0.284058i
$819$	9.51103	−	10.5550i	0.332342	−	0.368823i
$820$	−2.10683	−	23.0732i	−0.0735738	−	0.805751i
$821$	−4.63781	+	20.3196i	−0.161861	+	0.709159i	0.827231	+	0.561861i	$0.189915\pi$
$821$	−4.63781	+	20.3196i	−0.161861	+	0.709159i	−0.989092	+	0.147297i	$0.952943\pi$
$822$	11.3975	+	9.08919i	0.397533	+	0.317022i
$823$	−5.53947	−	11.5028i	−0.193094	−	0.400963i	0.781833	−	0.623487i	$-0.214285\pi$
$823$	−5.53947	−	11.5028i	−0.193094	−	0.400963i	−0.974927	+	0.222524i	$0.928570\pi$
$824$	0.437076	+	0.548076i	0.0152263	+	0.0190931i
$825$	1.25649	+	0.671943i	0.0437453	+	0.0233940i
$826$	14.5374	+	20.6683i	0.505819	+	0.719142i
$827$	15.5084	+	32.2036i	0.539281	+	1.11983i	0.975502	+	0.219989i	$0.0706020\pi$
$827$	15.5084	+	32.2036i	0.539281	+	1.11983i	−0.436222	+	0.899839i	$0.643684\pi$
$828$	−4.05571	+	8.42176i	−0.140946	+	0.292677i
$829$	−7.67666	−	33.6336i	−0.266621	−	1.16814i	−0.913916	−	0.405904i	$-0.866957\pi$
$829$	−7.67666	−	33.6336i	−0.266621	−	1.16814i	0.647294	−	0.762240i	$-0.275900\pi$
$830$	−20.1232	+	6.56734i	−0.698488	+	0.227956i
$831$	1.14168	−	1.43163i	0.0396046	−	0.0496626i
$832$			3.61837i			0.125444i
$833$	3.69965	−	30.5703i	0.128185	−	1.05920i
$834$	5.52223			0.191219
$835$	−21.6914	+	1.98066i	−0.750663	+	0.0685436i
$836$	1.12079	+	0.539744i	0.0387634	+	0.0186674i
$837$	14.5254	−	3.31532i	0.502071	−	0.114594i
$838$	−6.48302	+	13.4621i	−0.223952	+	0.465042i
$839$	−36.0855	+	17.3778i	−1.24581	+	0.599950i	−0.936385	−	0.350975i	$-0.885850\pi$
$839$	−36.0855	+	17.3778i	−1.24581	+	0.599950i	−0.309423	+	0.950924i	$0.600136\pi$
$840$	1.83903	+	7.04794i	0.0634524	+	0.243177i
$841$	−7.05660	−	3.39828i	−0.243331	−	0.117182i
$842$	0.285257	−	0.227485i	0.00983060	−	0.00783965i
$843$	9.40884	+	19.5377i	0.324058	+	0.672913i
$844$	−16.4768	+	20.6613i	−0.567156	+	0.711191i
$845$	0.106449	+	0.177641i	0.00366195	+	0.00611104i
$846$	8.61485	−	10.8027i	0.296185	−	0.371404i
$847$	−14.1135	+	25.2899i	−0.484945	+	0.868971i
$848$	7.56342	−	6.03163i	0.259729	−	0.207127i
$849$	22.6404	−	10.9030i	0.777017	−	0.374192i
$850$	−21.2177	−	5.79647i	−0.727762	−	0.198817i
$851$	53.9367			1.84893
$852$		−	3.92145i		−	0.134347i
$853$	−32.9546	−	7.52167i	−1.12834	−	0.257537i	−0.382694	−	0.923875i	$-0.625004\pi$
$853$	−32.9546	−	7.52167i	−1.12834	−	0.257537i	−0.745650	+	0.666338i	$0.767861\pi$
$854$	−12.2226	−	0.736908i	−0.418249	−	0.0252165i
$855$	−14.8981	−	9.80643i	−0.509506	−	0.335373i
$856$	1.65604	+	7.25557i	0.0566022	+	0.247990i
$857$	−16.2456	+	12.9554i	−0.554938	+	0.442549i	−0.860373	−	0.509664i	$-0.829770\pi$
$857$	−16.2456	+	12.9554i	−0.554938	+	0.442549i	0.305435	+	0.952213i	$0.401198\pi$
$858$	0.806182	−	0.642909i	0.0275226	−	0.0219485i
$859$	9.39720	+	41.1718i	0.320628	+	1.40476i	0.836438	+	0.548061i	$0.184634\pi$
$859$	9.39720	+	41.1718i	0.320628	+	1.40476i	−0.515810	+	0.856703i	$0.672509\pi$
$860$	11.2803	−	17.1372i	0.384654	−	0.584374i
$861$	−33.6913	−	2.03127i	−1.14820	−	0.0692254i
$862$	15.5917	+	3.55870i	0.531054	+	0.121210i
$863$		−	30.4458i		−	1.03639i	−0.855264	−	0.518193i	$-0.826605\pi$
$863$		−	30.4458i		−	1.03639i	0.855264	−	0.518193i	$-0.173395\pi$
$864$	−5.52089			−0.187825
$865$	−22.6799	+	13.5906i	−0.771138	+	0.462094i
$866$	−27.1219	+	13.0612i	−0.921641	+	0.443839i
$867$	2.26370	−	1.80524i	0.0768791	−	0.0613091i
$868$	−3.47943	+	6.23478i	−0.118100	+	0.211622i
$869$	1.29853	−	1.62830i	0.0440495	−	0.0552364i
$870$	8.58824	+	14.3320i	0.291169	+	0.485900i
$871$	−6.96918	+	8.73907i	−0.236142	+	0.296112i
$872$	−3.08003	−	6.39574i	−0.104303	−	0.216587i
$873$	−10.1737	+	8.11324i	−0.344327	+	0.274592i
$874$	−30.4979	−	14.6870i	−1.03161	−	0.496795i
$875$	28.9122	−	6.25185i	0.977410	−	0.211351i
$876$	−4.39255	+	2.11534i	−0.148410	+	0.0714707i
$877$	−9.42388	+	19.5689i	−0.318222	+	0.660795i	−0.997313	−	0.0732594i	$-0.976660\pi$
$877$	−9.42388	+	19.5689i	−0.318222	+	0.660795i	0.679091	+	0.734054i	$0.262374\pi$
$878$	−4.64107	+	1.05929i	−0.156628	+	0.0357494i
$879$	−32.3072	−	15.5583i	−1.08969	−	0.524769i
$880$	−0.0470631	−	0.515416i	−0.00158650	−	0.0173747i
$881$	−14.0186			−0.472298			−0.236149	−	0.971717i	$-0.575885\pi$
$881$	−14.0186			−0.472298			−0.236149	+	0.971717i	$0.575885\pi$
$882$	−10.3328	+	1.07813i	−0.347924	+	0.0363026i
$883$		−	17.9348i		−	0.603553i	−0.953379	−	0.301777i	$-0.902420\pi$
$883$		−	17.9348i		−	0.603553i	0.953379	−	0.301777i	$-0.0975797\pi$
$884$	−9.92434	+	12.4447i	−0.333792	+	0.418562i
$885$	−8.15766	−	24.9962i	−0.274217	−	0.840239i
$886$	3.57193	+	15.6496i	0.120001	+	0.525760i
$887$	−7.06238	+	14.6652i	−0.237131	+	0.492409i	−0.985242	−	0.171165i	$-0.945247\pi$
$887$	−7.06238	+	14.6652i	−0.237131	+	0.492409i	0.748111	+	0.663574i	$0.230961\pi$
$888$	4.57475	+	9.49957i	0.153519	+	0.318785i
$889$	−14.9278	−	21.2233i	−0.500661	−	0.711808i
$890$	−6.86534	−	21.0364i	−0.230127	−	0.705140i
$891$	0.338408	+	0.424351i	0.0113371	+	0.0142163i
$892$	10.7745	+	22.3734i	0.360756	+	0.749118i
$893$	39.1199	+	31.1971i	1.30910	+	1.04397i
$894$	4.92760	−	21.5892i	0.164803	−	0.722051i
$895$	−2.05144	−	22.4665i	−0.0685720	−	0.750973i
$896$	1.77110	−	1.96551i	0.0591682	−	0.0656630i
$897$	−21.9371	+	17.4942i	−0.732457	+	0.584115i
$898$	−4.77095	−	9.90698i	−0.159209	−	0.330600i
$899$	−3.64444	+	15.9673i	−0.121549	+	0.532541i
$900$	−0.313673	+	7.41402i	−0.0104558	+	0.247134i
$901$	42.5564			1.41776
$902$	2.33816	+	0.533670i	0.0778522	+	0.0177693i
$903$	−22.2037	−	20.0075i	−0.738892	−	0.665807i
$904$	−2.14186	−	9.38408i	−0.0712371	−	0.312110i
$905$	−9.80383	−	6.45319i	−0.325890	−	0.214511i
$906$	13.5863	+	17.0366i	0.451373	+	0.566004i
$907$	16.6741	−	13.2972i	0.553655	−	0.441525i	−0.306270	−	0.951945i	$-0.599081\pi$
$907$	16.6741	−	13.2972i	0.553655	−	0.441525i	0.859926	+	0.510419i	$0.170510\pi$
$908$	−4.30710	+	0.983067i	−0.142936	+	0.0326242i
$909$	6.34687	+	27.8075i	0.210513	+	0.922316i
$910$	4.11761	−	21.0068i	0.136497	−	0.696370i
$911$	7.10603	−	31.1336i	0.235433	−	1.03150i	−0.709620	−	0.704585i	$-0.751133\pi$
$911$	7.10603	−	31.1336i	0.235433	−	1.03150i	0.945053	−	0.326916i	$-0.106009\pi$
$912$		−	6.61713i		−	0.219115i
$913$		−	2.19112i		−	0.0725155i
$914$	0.252669	−	1.10701i	0.00835754	−	0.0366168i
$915$	11.9348	+	4.46153i	0.394552	+	0.147494i
$916$	5.51529	+	6.91595i	0.182230	+	0.228509i
$917$	27.9791	+	8.18557i	0.923952	+	0.270311i
$918$	−18.9881	−	15.1425i	−0.626700	−	0.499777i
$919$	−1.22744	+	5.37776i	−0.0404895	+	0.177396i	−0.991129	−	0.132900i	$-0.957571\pi$
$919$	−1.22744	+	5.37776i	−0.0404895	+	0.177396i	0.950640	+	0.310296i	$0.100428\pi$
$920$	1.28063	+	14.0250i	0.0422213	+	0.462391i
$921$	9.68126	−	4.66225i	0.319008	−	0.153626i
$922$	24.9493	−	19.8964i	0.821660	−	0.655252i
$923$	−5.00038	+	10.3834i	−0.164589	+	0.341773i
$924$	−0.752607	−	0.0453750i	−0.0247589	−	0.00149273i
$925$	39.3291	−	16.9310i	1.29313	−	0.556688i
$926$	−1.19693	−	0.576413i	−0.0393337	−	0.0189421i
$927$	1.01431	−	0.231511i	0.0333145	−	0.00760381i
$928$	2.63322	−	5.46794i	0.0864397	−	0.179494i
$929$	15.9230	−	19.9667i	0.522415	−	0.655088i	−0.448705	−	0.893680i	$-0.648115\pi$
$929$	15.9230	−	19.9667i	0.522415	−	0.655088i	0.971120	+	0.238592i	$0.0766859\pi$
$930$	5.36336	−	5.14125i	0.175872	−	0.168588i
$931$	−3.90425	−	37.4184i	−0.127957	−	1.22634i
$932$			1.37433i			0.0450176i
$933$	10.5460	+	8.41018i	0.345262	+	0.275337i
$934$	−31.1994	−	15.0248i	−1.02087	−	0.491627i
$935$	1.25180	−	1.90176i	0.0409382	−	0.0621943i
$936$	4.83833	+	2.33002i	0.158146	+	0.0761589i
$937$	−23.8468	−	49.5184i	−0.779042	−	1.61770i	−0.786395	−	0.617724i	$-0.788055\pi$
$937$	−23.8468	−	49.5184i	−0.779042	−	1.61770i	0.00735368	−	0.999973i	$-0.497659\pi$
$938$	8.06321	−	1.33586i	0.263273	−	0.0436173i
$939$	7.64282	+	3.68059i	0.249414	+	0.120111i
$940$	2.76763	−	20.6328i	0.0902701	−	0.672969i
$941$	11.8332	−	5.69857i	0.385752	−	0.185768i	−0.230949	−	0.972966i	$-0.574183\pi$
$941$	11.8332	−	5.69857i	0.385752	−	0.185768i	0.616701	+	0.787198i	$0.288469\pi$
$942$	7.85605	+	6.26499i	0.255964	+	0.204125i
$943$	−63.6238	−	14.5217i	−2.07188	−	0.472892i
$944$	−5.95477	+	7.46705i	−0.193811	+	0.243032i
$945$	32.0521	+	6.28262i	1.04265	+	0.204374i
$946$	1.32411	+	1.66038i	0.0430506	+	0.0539837i
$947$	17.7763	+	36.9129i	0.577653	+	1.19951i	0.961165	+	0.275973i	$0.0890002\pi$
$947$	17.7763	+	36.9129i	0.577653	+	1.19951i	−0.383512	+	0.923536i	$0.625286\pi$
$948$	−10.8006	−	2.46517i	−0.350788	−	0.0800651i
$949$	14.3281			0.465110
$950$	−26.8485	−	1.13591i	−0.871081	−	0.0368538i
$951$	0.471177	−	2.06436i	0.0152790	−	0.0669416i
$952$	11.4823	−	1.90231i	0.372143	−	0.0616541i
$953$	−5.95396	+	1.35895i	−0.192868	+	0.0440208i	−0.317863	−	0.948136i	$-0.602965\pi$
$953$	−5.95396	+	1.35895i	−0.192868	+	0.0440208i	0.124996	+	0.992157i	$0.460108\pi$
$954$	−3.19484	−	13.9975i	−0.103437	−	0.453185i
$955$	−7.49079	−	1.00479i	−0.242396	−	0.0325144i
$956$	13.8079	+	17.3146i	0.446581	+	0.559995i
$957$	−1.68614	+	0.384850i	−0.0545051	+	0.0124404i
$958$	−18.0917	+	4.12931i	−0.584516	+	0.133412i
$959$	−8.79621	+	30.0664i	−0.284045	+	0.970894i
$960$	−2.36153	+	1.41511i	−0.0762179	+	0.0456725i
$961$	−23.7173			−0.765074
$962$		−	30.9868i		−	0.999054i
$963$	10.7682	+	2.45778i	0.347001	+	0.0792007i
$964$	−22.0674	+	10.6271i	−0.710743	+	0.342276i
$965$	−4.30748	+	32.1125i	−0.138663	+	1.03374i
$966$	20.4792	+	1.23470i	0.658908	+	0.0397259i
$967$	−41.2581	−	32.9023i	−1.32677	−	1.05807i	−0.993331	−	0.115294i	$-0.963219\pi$
$967$	−41.2581	−	32.9023i	−1.32677	−	1.05807i	−0.333440	−	0.942771i	$-0.608210\pi$
$968$	−10.6720	−	2.43581i	−0.343010	−	0.0782899i
$969$	18.1492	−	22.7584i	0.583037	−	0.731105i
$970$	−6.86504	+	18.3643i	−0.220423	+	0.589642i
$971$	12.4252	+	15.5807i	0.398743	+	0.500008i	0.940154	−	0.340750i	$-0.110681\pi$
$971$	12.4252	+	15.5807i	0.398743	+	0.500008i	−0.541411	+	0.840758i	$0.682110\pi$
$972$	−5.93359	+	12.3212i	−0.190320	+	0.395204i
$973$	4.49604	+	10.9821i	0.144136	+	0.352069i
$974$	−7.93136	+	3.81954i	−0.254137	+	0.122386i
$975$	−10.5044	+	19.6424i	−0.336409	+	0.629062i
$976$	−1.02985	−	4.51207i	−0.0329647	−	0.144428i
$977$	2.04585	−	4.24826i	0.0654526	−	0.135914i	−0.865676	−	0.500605i	$-0.833111\pi$
$977$	2.04585	−	4.24826i	0.0654526	−	0.135914i	0.931129	+	0.364691i	$0.118825\pi$
$978$	−10.6304	−	8.47746i	−0.339923	−	0.271079i
$979$	2.29055			0.0732062
$980$	−12.5190	+	9.39550i	−0.399904	+	0.300128i
$981$	−10.5355			−0.336371
$982$	9.25312	+	7.37912i	0.295279	+	0.235477i
$983$	−13.0559	+	27.1108i	−0.416417	+	0.864700i	0.582246	+	0.813013i	$0.302174\pi$
$983$	−13.0559	+	27.1108i	−0.416417	+	0.864700i	−0.998663	+	0.0516869i	$0.983540\pi$
$984$	−2.83875	−	12.4374i	−0.0904961	−	0.396489i
$985$	−17.7210	−	54.2995i	−0.564636	−	1.73012i
$986$	24.0538	−	11.5837i	0.766028	−	0.368899i
$987$	−29.1067	−	8.51545i	−0.926477	−	0.271050i
$988$	−8.43772	+	17.5211i	−0.268440	+	0.557421i
$989$	−36.0304	−	45.1807i	−1.14570	−	1.43666i
$990$	−0.719498	−	0.268967i	−0.0228671	−	0.00854832i
$991$	9.03606	−	11.3309i	0.287040	−	0.359937i	−0.617316	−	0.786715i	$-0.711780\pi$
$991$	9.03606	−	11.3309i	0.287040	−	0.359937i	0.904356	+	0.426778i	$0.140352\pi$
$992$	−2.63099	−	0.600505i	−0.0835339	−	0.0190661i
$993$	−9.94660	−	7.93215i	−0.315646	−	0.251719i
$994$	7.79861	−	3.19273i	0.247357	−	0.101267i
$995$	−20.9285	−	2.80729i	−0.663478	−	0.0889970i
$996$	−10.5010	+	5.05702i	−0.332737	+	0.160238i
$997$	−24.1586	−	5.51405i	−0.765111	−	0.174632i	−0.177881	−	0.984052i	$-0.556924\pi$
$997$	−24.1586	−	5.51405i	−0.765111	−	0.174632i	−0.587230	+	0.809420i	$0.699781\pi$
$998$			12.0927i			0.382787i
$999$	47.2795			1.49586

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.p.a.239.23	yes	168
5.4	even	2	inner	490.2.p.a.239.6	✓	168
49.8	even	7	inner	490.2.p.a.449.6	yes	168
245.204	even	14	inner	490.2.p.a.449.23	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.p.a.239.6	✓	168	5.4	even	2	inner
490.2.p.a.239.23	yes	168	1.1	even	1	trivial
490.2.p.a.449.6	yes	168	49.8	even	7	inner
490.2.p.a.449.23	yes	168	245.204	even	14	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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.p (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.781831 + 0.623490i) q^{2} +(0.534200 - 1.10928i) q^{3} +(0.222521 + 0.974928i) q^{4} +(2.12573 - 0.693744i) q^{5} +(1.10928 - 0.534200i) q^{6} +(1.96551 + 1.77110i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(0.925341 + 1.16034i) q^{9} +O(q^{10})\)	\(q+(0.781831 + 0.623490i) q^{2} +(0.534200 - 1.10928i) q^{3} +(0.222521 + 0.974928i) q^{4} +(2.12573 - 0.693744i) q^{5} +(1.10928 - 0.534200i) q^{6} +(1.96551 + 1.77110i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(0.925341 + 1.16034i) q^{9} +(2.09450 + 0.782979i) q^{10} +(-0.144313 + 0.180963i) q^{11} +(1.20034 + 0.273969i) q^{12} +(-2.82896 - 2.25602i) q^{13} +(0.432435 + 2.61017i) q^{14} +(0.366010 - 2.72862i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-4.28876 - 0.978881i) q^{17} +1.48413i q^{18} -5.37451 q^{19} +(1.14937 + 1.91806i) q^{20} +(3.01461 - 1.23418i) q^{21} +(-0.225657 + 0.0515047i) q^{22} +(6.14036 - 1.40150i) q^{23} +(0.767645 + 0.962596i) q^{24} +(4.03744 - 2.94942i) q^{25} +(-0.805163 - 3.52765i) q^{26} +(5.38247 - 1.22851i) q^{27} +(-1.28932 + 2.31033i) q^{28} +(-1.35047 + 5.91680i) q^{29} +(1.98743 - 1.90512i) q^{30} +2.69865 q^{31} +(-0.974928 - 0.222521i) q^{32} +(0.123646 + 0.256754i) q^{33} +(-2.74276 - 3.43932i) q^{34} +(5.40682 + 2.40131i) q^{35} +(-0.925341 + 1.16034i) q^{36} +(8.34903 + 1.90561i) q^{37} +(-4.20196 - 3.35095i) q^{38} +(-4.01378 + 1.93294i) q^{39} +(-0.297277 + 2.21622i) q^{40} +(-9.33546 - 4.49572i) q^{41} +(3.12642 + 0.914664i) q^{42} +(-3.98100 - 8.26664i) q^{43} +(-0.208538 - 0.100427i) q^{44} +(2.77200 + 1.82462i) q^{45} +(5.67454 + 2.73272i) q^{46} +(-7.27879 - 5.80465i) q^{47} +1.23121i q^{48} +(0.726439 + 6.96220i) q^{49} +(4.99553 + 0.211351i) q^{50} +(-3.37691 + 4.23451i) q^{51} +(1.56995 - 3.26004i) q^{52} +(-9.43144 + 2.15266i) q^{53} +(4.97415 + 2.39542i) q^{54} +(-0.181228 + 0.484794i) q^{55} +(-2.44850 + 1.00241i) q^{56} +(-2.87106 + 5.96183i) q^{57} +(-4.74490 + 3.78393i) q^{58} +(8.60489 - 4.14390i) q^{59} +(2.74166 - 0.250343i) q^{60} +(-1.02985 + 4.51207i) q^{61} +(2.10989 + 1.68258i) q^{62} +(-0.236310 + 3.91952i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-7.57869 - 2.83311i) q^{65} +(-0.0634129 + 0.277830i) q^{66} -3.08915i q^{67} -4.39905i q^{68} +(1.72553 - 7.56005i) q^{69} +(2.73003 + 5.24852i) q^{70} +(-0.708740 - 3.10519i) q^{71} +(-1.44692 + 0.330250i) q^{72} +(-3.09591 + 2.46891i) q^{73} +(5.33940 + 6.69540i) q^{74} +(-1.11493 - 6.05423i) q^{75} +(-1.19594 - 5.23976i) q^{76} +(-0.604151 + 0.100092i) q^{77} +(-4.34327 - 0.991322i) q^{78} -8.99800 q^{79} +(-1.61421 + 1.54736i) q^{80} +(0.521803 - 2.28617i) q^{81} +(-4.49572 - 9.33546i) q^{82} +(-7.40122 + 5.90228i) q^{83} +(1.87405 + 2.66440i) q^{84} +(-9.79583 + 0.894465i) q^{85} +(2.04169 - 8.94523i) q^{86} +(5.84195 + 4.65880i) q^{87} +(-0.100427 - 0.208538i) q^{88} +(-6.17010 - 7.73706i) q^{89} +(1.02961 + 3.15486i) q^{90} +(-1.56471 - 9.44457i) q^{91} +(2.73272 + 5.67454i) q^{92} +(1.44162 - 2.99355i) q^{93} +(-2.07165 - 9.07651i) q^{94} +(-11.4247 + 3.72853i) q^{95} +(-0.767645 + 0.962596i) q^{96} +8.76785i q^{97} +(-3.77291 + 5.89620i) q^{98} -0.343517 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9}+O(q^{10}) \) 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9	\( 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9} - 4 q^{10} - 24 q^{11} + 4 q^{14} - 2 q^{15} - 28 q^{16} + 44 q^{19} - 10 q^{20} + 22 q^{26} - 2 q^{29} - 12 q^{30} - 16 q^{31} - 8 q^{34} - 4 q^{35} - 18 q^{36} - 80 q^{39} - 10 q^{40} + 52 q^{41} - 18 q^{44} - 72 q^{45} + 26 q^{46} - 52 q^{49} - 8 q^{50} + 64 q^{51} - 42 q^{54} - 60 q^{55} + 10 q^{56} - 58 q^{59} + 2 q^{60} + 32 q^{61} + 28 q^{64} + 4 q^{65} + 48 q^{66} - 48 q^{69} + 18 q^{70} - 68 q^{71} - 10 q^{74} - 16 q^{76} - 4 q^{80} + 34 q^{81} + 84 q^{84} - 48 q^{85} - 64 q^{86} + 100 q^{89} + 54 q^{90} + 78 q^{91} - 86 q^{94} - 64 q^{95} - 212 q^{99}+O(q^{100}) \) 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9 - 4 * q^10 - 24 * q^11 + 4 * q^14 - 2 * q^15 - 28 * q^16 + 44 * q^19 - 10 * q^20 + 22 * q^26 - 2 * q^29 - 12 * q^30 - 16 * q^31 - 8 * q^34 - 4 * q^35 - 18 * q^36 - 80 * q^39 - 10 * q^40 + 52 * q^41 - 18 * q^44 - 72 * q^45 + 26 * q^46 - 52 * q^49 - 8 * q^50 + 64 * q^51 - 42 * q^54 - 60 * q^55 + 10 * q^56 - 58 * q^59 + 2 * q^60 + 32 * q^61 + 28 * q^64 + 4 * q^65 + 48 * q^66 - 48 * q^69 + 18 * q^70 - 68 * q^71 - 10 * q^74 - 16 * q^76 - 4 * q^80 + 34 * q^81 + 84 * q^84 - 48 * q^85 - 64 * q^86 + 100 * q^89 + 54 * q^90 + 78 * q^91 - 86 * q^94 - 64 * q^95 - 212 * q^99

Introduction

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