LMFDB - Embedded newform 315.2.t.b.101.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(101,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("315.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.t (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.14
Character	$\chi$	$=$	315.101
Dual form			315.2.t.b.131.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.34636i q^{2} +(0.822112 - 1.52451i) q^{3} -3.50542 q^{4} +(0.500000 - 0.866025i) q^{5} +(3.57705 + 1.92897i) q^{6} +(2.00080 - 1.73112i) q^{7} -3.53226i q^{8} +(-1.64826 - 2.50664i) q^{9} +O(q^{10})$	\(q+2.34636i q^{2} +(0.822112 - 1.52451i) q^{3} -3.50542 q^{4} +(0.500000 - 0.866025i) q^{5} +(3.57705 + 1.92897i) q^{6} +(2.00080 - 1.73112i) q^{7} -3.53226i q^{8} +(-1.64826 - 2.50664i) q^{9} +(2.03201 + 1.17318i) q^{10} +(4.81384 - 2.77927i) q^{11} +(-2.88185 + 5.34405i) q^{12} +(-0.0395039 + 0.0228076i) q^{13} +(4.06185 + 4.69461i) q^{14} +(-0.909209 - 1.47423i) q^{15} +1.27713 q^{16} +(-0.320160 + 0.554533i) q^{17} +(5.88148 - 3.86742i) q^{18} +(-5.73840 + 3.31307i) q^{19} +(-1.75271 + 3.03578i) q^{20} +(-0.994235 - 4.47342i) q^{21} +(6.52118 + 11.2950i) q^{22} +(5.23103 + 3.02014i) q^{23} +(-5.38497 - 2.90391i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.0535149 - 0.0926905i) q^{26} +(-5.17645 + 0.452058i) q^{27} +(-7.01365 + 6.06832i) q^{28} +(5.95930 + 3.44060i) q^{29} +(3.45907 - 2.13333i) q^{30} +6.48092i q^{31} -4.06792i q^{32} +(-0.279512 - 9.62362i) q^{33} +(-1.30114 - 0.751211i) q^{34} +(-0.498797 - 2.59831i) q^{35} +(5.77785 + 8.78681i) q^{36} +(-3.67259 - 6.36111i) q^{37} +(-7.77366 - 13.4644i) q^{38} +(0.00229377 + 0.0789745i) q^{39} +(-3.05903 - 1.76613i) q^{40} +(0.580801 + 1.00598i) q^{41} +(10.4963 - 2.33284i) q^{42} +(-2.08247 + 3.60695i) q^{43} +(-16.8745 + 9.74251i) q^{44} +(-2.99494 + 0.174120i) q^{45} +(-7.08634 + 12.2739i) q^{46} -5.58472 q^{47} +(1.04994 - 1.94699i) q^{48} +(1.00641 - 6.92727i) q^{49} +(2.03201 - 1.17318i) q^{50} +(0.582184 + 0.943975i) q^{51} +(0.138478 - 0.0799502i) q^{52} +(-5.08648 - 2.93668i) q^{53} +(-1.06069 - 12.1458i) q^{54} -5.55854i q^{55} +(-6.11478 - 7.06735i) q^{56} +(0.333196 + 11.4720i) q^{57} +(-8.07290 + 13.9827i) q^{58} -2.95820 q^{59} +(3.18716 + 5.16778i) q^{60} +6.68719i q^{61} -15.2066 q^{62} +(-7.63715 - 2.16193i) q^{63} +12.0991 q^{64} +0.0456152i q^{65} +(22.5805 - 0.655838i) q^{66} +3.50291 q^{67} +(1.12229 - 1.94387i) q^{68} +(8.90472 - 5.49187i) q^{69} +(6.09657 - 1.17036i) q^{70} -7.67660i q^{71} +(-8.85409 + 5.82210i) q^{72} +(-3.76739 - 2.17511i) q^{73} +(14.9255 - 8.61722i) q^{74} +(-1.73132 + 0.0502852i) q^{75} +(20.1155 - 11.6137i) q^{76} +(4.82027 - 13.8941i) q^{77} +(-0.185303 + 0.00538201i) q^{78} +8.56625 q^{79} +(0.638563 - 1.10602i) q^{80} +(-3.56646 + 8.26320i) q^{81} +(-2.36039 + 1.36277i) q^{82} +(-0.725553 + 1.25670i) q^{83} +(3.48521 + 15.6812i) q^{84} +(0.320160 + 0.554533i) q^{85} +(-8.46321 - 4.88624i) q^{86} +(10.1444 - 6.25645i) q^{87} +(-9.81711 - 17.0037i) q^{88} +(9.24246 + 16.0084i) q^{89} +(-0.408548 - 7.02722i) q^{90} +(-0.0395567 + 0.114020i) q^{91} +(-18.3370 - 10.5868i) q^{92} +(9.88022 + 5.32804i) q^{93} -13.1038i q^{94} +6.62613i q^{95} +(-6.20158 - 3.34429i) q^{96} +(-5.49921 - 3.17497i) q^{97} +(16.2539 + 2.36141i) q^{98} +(-14.9011 - 7.48557i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9}+O(q^{10}) $ 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9	$ 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9} + 3 q^{10} + 9 q^{11} + 15 q^{12} - 12 q^{13} - 27 q^{14} - q^{15} + 42 q^{16} - 3 q^{17} - 4 q^{18} - 15 q^{20} + 4 q^{21} + 15 q^{22} + q^{24} - 15 q^{25} + 24 q^{26} - 5 q^{27} + 27 q^{28} - 2 q^{30} - 25 q^{33} + 48 q^{34} - 6 q^{35} + 21 q^{36} - 3 q^{37} - 30 q^{38} - 3 q^{39} + 3 q^{40} - 18 q^{41} - 16 q^{42} + 12 q^{43} + 15 q^{44} - 7 q^{45} + 9 q^{46} - 60 q^{47} - 40 q^{48} - 15 q^{49} + 3 q^{50} - 48 q^{51} - 33 q^{52} - 30 q^{53} + 35 q^{54} + 42 q^{56} - 21 q^{57} + 30 q^{59} + 33 q^{60} + 12 q^{62} - 47 q^{63} - 138 q^{64} + 100 q^{66} + 12 q^{67} - 21 q^{68} + 32 q^{69} - 18 q^{70} + 85 q^{72} + 6 q^{73} + 54 q^{74} - 5 q^{75} - 54 q^{76} - 9 q^{77} - 18 q^{78} + 24 q^{79} + 21 q^{80} - 14 q^{81} + 6 q^{82} - 6 q^{83} - 9 q^{84} + 3 q^{85} - 60 q^{86} - 16 q^{87} - 48 q^{88} - 3 q^{89} + 22 q^{90} + 15 q^{91} - 3 q^{92} + 69 q^{93} - 48 q^{96} + 36 q^{97} + 24 q^{98} - q^{99}+O(q^{100}) $ 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9 + 3 * q^10 + 9 * q^11 + 15 * q^12 - 12 * q^13 - 27 * q^14 - q^15 + 42 * q^16 - 3 * q^17 - 4 * q^18 - 15 * q^20 + 4 * q^21 + 15 * q^22 + q^24 - 15 * q^25 + 24 * q^26 - 5 * q^27 + 27 * q^28 - 2 * q^30 - 25 * q^33 + 48 * q^34 - 6 * q^35 + 21 * q^36 - 3 * q^37 - 30 * q^38 - 3 * q^39 + 3 * q^40 - 18 * q^41 - 16 * q^42 + 12 * q^43 + 15 * q^44 - 7 * q^45 + 9 * q^46 - 60 * q^47 - 40 * q^48 - 15 * q^49 + 3 * q^50 - 48 * q^51 - 33 * q^52 - 30 * q^53 + 35 * q^54 + 42 * q^56 - 21 * q^57 + 30 * q^59 + 33 * q^60 + 12 * q^62 - 47 * q^63 - 138 * q^64 + 100 * q^66 + 12 * q^67 - 21 * q^68 + 32 * q^69 - 18 * q^70 + 85 * q^72 + 6 * q^73 + 54 * q^74 - 5 * q^75 - 54 * q^76 - 9 * q^77 - 18 * q^78 + 24 * q^79 + 21 * q^80 - 14 * q^81 + 6 * q^82 - 6 * q^83 - 9 * q^84 + 3 * q^85 - 60 * q^86 - 16 * q^87 - 48 * q^88 - 3 * q^89 + 22 * q^90 + 15 * q^91 - 3 * q^92 + 69 * q^93 - 48 * q^96 + 36 * q^97 + 24 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$			2.34636i			1.65913i	0.558411	+	0.829565i	$0.311411\pi$
$2$			2.34636i			1.65913i	−0.558411	+	0.829565i	$0.688589\pi$
$3$	0.822112	−	1.52451i	0.474647	−	0.880176i
$3$	0.822112	−	1.52451i	0.474647	−	0.880176i
$4$	−3.50542			−1.75271
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	3.57705	+	1.92897i	1.46033	+	0.787500i
$7$	2.00080	−	1.73112i	0.756232	−	0.654304i
$7$	2.00080	−	1.73112i	0.756232	−	0.654304i
$8$		−	3.53226i		−	1.24884i
$9$	−1.64826	−	2.50664i	−0.549421	−	0.835546i
$10$	2.03201	+	1.17318i	0.642578	+	0.370993i
$11$	4.81384	−	2.77927i	1.45143	−	0.837982i	0.452864	−	0.891580i	$-0.350402\pi$
$11$	4.81384	−	2.77927i	1.45143	−	0.837982i	0.998563	+	0.0535979i	$0.0170689\pi$
$12$	−2.88185	+	5.34405i	−0.831918	+	1.54269i
$13$	−0.0395039	+	0.0228076i	−0.0109564	+	0.00632569i	−0.505468	−	0.862845i	$-0.668680\pi$
$13$	−0.0395039	+	0.0228076i	−0.0109564	+	0.00632569i	0.494512	+	0.869171i	$0.335347\pi$
$14$	4.06185	+	4.69461i	1.08557	+	1.25469i
$15$	−0.909209	−	1.47423i	−0.234757	−	0.380643i
$16$	1.27713			0.319282
$17$	−0.320160	+	0.554533i	−0.0776501	+	0.134494i	−0.902236	−	0.431243i	$-0.858075\pi$
$17$	−0.320160	+	0.554533i	−0.0776501	+	0.134494i	0.824586	+	0.565737i	$0.191408\pi$
$18$	5.88148	−	3.86742i	1.38628	−	0.911561i
$19$	−5.73840	+	3.31307i	−1.31648	+	0.760069i	−0.983160	−	0.182745i	$-0.941502\pi$
$19$	−5.73840	+	3.31307i	−1.31648	+	0.760069i	−0.333319	+	0.942814i	$0.608168\pi$
$20$	−1.75271	+	3.03578i	−0.391918	+	0.678822i
$21$	−0.994235	−	4.47342i	−0.216960	−	0.976181i
$22$	6.52118	+	11.2950i	1.39032	+	2.40810i
$23$	5.23103	+	3.02014i	1.09075	+	0.629742i	0.933775	−	0.357861i	$-0.116494\pi$
$23$	5.23103	+	3.02014i	1.09075	+	0.629742i	0.156971	+	0.987603i	$0.449827\pi$
$24$	−5.38497	−	2.90391i	−1.09920	−	0.592759i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.0535149	−	0.0926905i	−0.0104951	−	0.0181781i
$27$	−5.17645	+	0.452058i	−0.996208	+	0.0869987i
$28$	−7.01365	+	6.06832i	−1.32545	+	1.14680i
$29$	5.95930	+	3.44060i	1.10661	+	0.638904i	0.937950	−	0.346770i	$-0.112722\pi$
$29$	5.95930	+	3.44060i	1.10661	+	0.638904i	0.168663	+	0.985674i	$0.446055\pi$
$30$	3.45907	−	2.13333i	0.631536	−	0.389492i
$31$			6.48092i			1.16401i	0.813186	+	0.582003i	$0.197731\pi$
$31$			6.48092i			1.16401i	−0.813186	+	0.582003i	$0.802269\pi$
$32$		−	4.06792i		−	0.719113i
$33$	−0.279512	−	9.62362i	−0.0486569	−	1.67526i
$34$	−1.30114	−	0.751211i	−0.223143	−	0.128832i
$35$	−0.498797	−	2.59831i	−0.0843121	−	0.439194i
$36$	5.77785	+	8.78681i	0.962976	+	1.46447i
$37$	−3.67259	−	6.36111i	−0.603770	−	1.04576i	−0.992245	−	0.124300i	$-0.960331\pi$
$37$	−3.67259	−	6.36111i	−0.603770	−	1.04576i	0.388475	−	0.921459i	$-0.373002\pi$
$38$	−7.77366	−	13.4644i	−1.26105	−	2.18421i
$39$	0.00229377	+	0.0789745i	0.000367297	+	0.0126460i
$40$	−3.05903	−	1.76613i	−0.483675	−	0.279250i
$41$	0.580801	+	1.00598i	0.0907059	+	0.157107i	0.907808	−	0.419385i	$-0.137754\pi$
$41$	0.580801	+	1.00598i	0.0907059	+	0.157107i	−0.817102	+	0.576493i	$0.804421\pi$
$42$	10.4963	−	2.33284i	1.61961	−	0.359964i
$43$	−2.08247	+	3.60695i	−0.317574	+	0.550055i	−0.979981	−	0.199089i	$-0.936202\pi$
$43$	−2.08247	+	3.60695i	−0.317574	+	0.550055i	0.662407	+	0.749144i	$0.269535\pi$
$44$	−16.8745	+	9.74251i	−2.54393	+	1.46874i
$45$	−2.99494	+	0.174120i	−0.446460	+	0.0259562i
$46$	−7.08634	+	12.2739i	−1.04482	+	1.80969i
$47$	−5.58472			−0.814615			−0.407308	−	0.913291i	$-0.633532\pi$
$47$	−5.58472			−0.814615			−0.407308	+	0.913291i	$0.633532\pi$
$48$	1.04994	−	1.94699i	0.151546	−	0.281024i
$49$	1.00641	−	6.92727i	0.143773	−	0.989611i
$50$	2.03201	−	1.17318i	0.287370	−	0.165913i
$51$	0.582184	+	0.943975i	0.0815220	+	0.132183i
$52$	0.138478	−	0.0799502i	0.0192034	−	0.0110871i
$53$	−5.08648	−	2.93668i	−0.698682	−	0.403384i	0.108174	−	0.994132i	$-0.465500\pi$
$53$	−5.08648	−	2.93668i	−0.698682	−	0.403384i	−0.806856	+	0.590748i	$0.798833\pi$
$54$	−1.06069	−	12.1458i	−0.144342	−	1.65284i
$55$		−	5.55854i		−	0.749514i
$56$	−6.11478	−	7.06735i	−0.817122	−	0.944415i
$57$	0.333196	+	11.4720i	0.0441329	+	1.51950i
$58$	−8.07290	+	13.9827i	−1.06002	+	1.83601i
$59$	−2.95820			−0.385124			−0.192562	−	0.981285i	$-0.561680\pi$
$59$	−2.95820			−0.385124			−0.192562	+	0.981285i	$0.561680\pi$
$60$	3.18716	+	5.16778i	0.411460	+	0.667157i
$61$			6.68719i			0.856207i	0.903730	+	0.428103i	$0.140818\pi$
$61$			6.68719i			0.856207i	−0.903730	+	0.428103i	$0.859182\pi$
$62$	−15.2066			−1.93124
$63$	−7.63715	−	2.16193i	−0.962190	−	0.272378i
$64$	12.0991			1.51238
$65$			0.0456152i			0.00565787i
$66$	22.5805	−	0.655838i	2.77947	−	0.0807280i
$67$	3.50291			0.427949			0.213974	−	0.976839i	$-0.431359\pi$
$67$	3.50291			0.427949			0.213974	+	0.976839i	$0.431359\pi$
$68$	1.12229	−	1.94387i	0.136098	−	0.235729i
$69$	8.90472	−	5.49187i	1.07200	−	0.661143i
$70$	6.09657	−	1.17036i	0.728680	−	0.139885i
$71$		−	7.67660i		−	0.911045i	−0.890224	−	0.455523i	$-0.849452\pi$
$71$		−	7.67660i		−	0.911045i	0.890224	−	0.455523i	$-0.150548\pi$
$72$	−8.85409	+	5.82210i	−1.04346	+	0.686141i
$73$	−3.76739	−	2.17511i	−0.440940	−	0.254577i	0.263056	−	0.964781i	$-0.415270\pi$
$73$	−3.76739	−	2.17511i	−0.440940	−	0.254577i	−0.703996	+	0.710204i	$0.748603\pi$
$74$	14.9255	−	8.61722i	1.73505	−	1.00173i
$75$	−1.73132	+	0.0502852i	−0.199916	+	0.00580644i
$76$	20.1155	−	11.6137i	2.30741	−	1.33218i
$77$	4.82027	−	13.8941i	0.549321	−	1.58338i
$78$	−0.185303	+	0.00538201i	−0.0209814	+	0.000609393i
$79$	8.56625			0.963779			0.481889	−	0.876232i	$-0.339951\pi$
$79$	8.56625			0.963779			0.481889	+	0.876232i	$0.339951\pi$
$80$	0.638563	−	1.10602i	0.0713935	−	0.123657i
$81$	−3.56646	+	8.26320i	−0.396273	+	0.918133i
$82$	−2.36039	+	1.36277i	−0.260661	+	0.150493i
$83$	−0.725553	+	1.25670i	−0.0796398	+	0.137940i	−0.903095	−	0.429442i	$-0.858710\pi$
$83$	−0.725553	+	1.25670i	−0.0796398	+	0.137940i	0.823455	+	0.567382i	$0.192044\pi$
$84$	3.48521	+	15.6812i	0.380267	+	1.71096i
$85$	0.320160	+	0.554533i	0.0347262	+	0.0601475i
$86$	−8.46321	−	4.88624i	−0.912612	−	0.526897i
$87$	10.1444	−	6.25645i	1.08760	−	0.670762i
$88$	−9.81711	−	17.0037i	−1.04651	−	1.81260i
$89$	9.24246	+	16.0084i	0.979699	+	1.69689i	0.663467	+	0.748206i	$0.269084\pi$
$89$	9.24246	+	16.0084i	0.979699	+	1.69689i	0.316232	+	0.948682i	$0.397582\pi$
$90$	−0.408548	−	7.02722i	−0.0430647	−	0.740734i
$91$	−0.0395567	+	0.114020i	−0.00414667	+	0.0119525i
$92$	−18.3370	−	10.5868i	−1.91176	−	1.10376i
$93$	9.88022	+	5.32804i	1.02453	+	0.552492i
$94$		−	13.1038i		−	1.35155i
$95$			6.62613i			0.679827i
$96$	−6.20158	−	3.34429i	−0.632947	−	0.341325i
$97$	−5.49921	−	3.17497i	−0.558360	−	0.322369i	0.194127	−	0.980976i	$-0.437813\pi$
$97$	−5.49921	−	3.17497i	−0.558360	−	0.322369i	−0.752487	+	0.658607i	$0.771146\pi$
$98$	16.2539	+	2.36141i	1.64189	+	0.238539i
$99$	−14.9011	−	7.48557i	−1.49762	−	0.752328i
$100$	1.75271	+	3.03578i	0.175271	+	0.303578i
$101$	5.61259	+	9.72129i	0.558473	+	0.967304i	0.997624	+	0.0688908i	$0.0219460\pi$
$101$	5.61259	+	9.72129i	0.558473	+	0.967304i	−0.439151	+	0.898413i	$0.644721\pi$
$102$	−2.21491	+	1.36601i	−0.219309	+	0.135256i
$103$	−9.29958	−	5.36911i	−0.916315	−	0.529034i	−0.0338571	−	0.999427i	$-0.510779\pi$
$103$	−9.29958	−	5.36911i	−0.916315	−	0.529034i	−0.882457	+	0.470392i	$0.844112\pi$
$104$	0.0805623	+	0.139538i	0.00789979	+	0.0136828i
$105$	−4.37121	−	1.37568i	−0.426587	−	0.134252i
$106$	6.89052	−	11.9347i	0.669267	−	1.15920i
$107$	−1.55054	+	0.895206i	−0.149897	+	0.0865429i	−0.573072	−	0.819505i	$-0.694249\pi$
$107$	−1.55054	+	0.895206i	−0.149897	+	0.0865429i	0.423176	+	0.906048i	$0.360915\pi$
$108$	18.1456	−	1.58465i	1.74606	−	0.152483i
$109$	−9.14606	+	15.8414i	−0.876034	+	1.51733i	−0.0203763	+	0.999792i	$0.506486\pi$
$109$	−9.14606	+	15.8414i	−0.876034	+	1.51733i	−0.855657	+	0.517543i	$0.826847\pi$
$110$	13.0424			1.24354
$111$	−12.7169	+	0.369354i	−1.20703	+	0.0350575i
$112$	2.55528	−	2.21086i	0.241451	−	0.208907i
$113$	−5.20067	+	3.00261i	−0.489238	+	0.282461i	−0.724258	−	0.689529i	$-0.757818\pi$
$113$	−5.20067	+	3.00261i	−0.489238	+	0.282461i	0.235021	+	0.971990i	$0.424484\pi$
$114$	−26.9174	+	0.781800i	−2.52104	+	0.0732223i
$115$	5.23103	−	3.02014i	0.487796	−	0.281629i
$116$	−20.8898	−	12.0607i	−1.93957	−	1.11981i
$117$	0.122283	+	0.0614290i	0.0113051	+	0.00567911i
$118$		−	6.94100i		−	0.638971i
$119$	0.319390	+	1.66375i	0.0292784	+	0.152515i
$120$	−5.20735	+	3.21156i	−0.475364	+	0.293174i
$121$	9.94869	−	17.2316i	0.904426	−	1.56651i
$122$	−15.6906			−1.42056
$123$	2.01111	−	0.0584114i	0.181335	−	0.00526678i
$124$		−	22.7183i		−	2.04017i
$125$	−1.00000			−0.0894427
$126$	5.07268	−	17.9195i	0.451910	−	1.59640i
$127$	−15.6793			−1.39132			−0.695658	−	0.718373i	$-0.744887\pi$
$127$	−15.6793			−1.39132			−0.695658	+	0.718373i	$0.744887\pi$
$128$			20.2530i			1.79013i
$129$	3.78681	+	6.14007i	0.333410	+	0.540603i
$130$	−0.107030			−0.00938713
$131$	−7.94216	+	13.7562i	−0.693910	+	1.20189i	0.276637	+	0.960975i	$0.410780\pi$
$131$	−7.94216	+	13.7562i	−0.693910	+	1.20189i	−0.970547	+	0.240913i	$0.922553\pi$
$132$	0.979808	+	33.7348i	0.0852814	+	2.93624i
$133$	−5.74607	+	16.5627i	−0.498247	+	1.43617i
$134$			8.21911i			0.710023i
$135$	−2.19673	+	4.70897i	−0.189065	+	0.405283i
$136$	1.95875	+	1.13089i	0.167962	+	0.0969728i
$137$	9.31344	−	5.37712i	0.795701	−	0.459398i	−0.0462648	−	0.998929i	$-0.514732\pi$
$137$	9.31344	−	5.37712i	0.795701	−	0.459398i	0.841966	+	0.539531i	$0.181398\pi$
$138$	12.8859	+	20.8937i	1.09692	+	1.77859i
$139$	5.11830	−	2.95505i	0.434129	−	0.250644i	−0.266975	−	0.963703i	$-0.586024\pi$
$139$	5.11830	−	2.95505i	0.434129	−	0.250644i	0.701104	+	0.713059i	$0.252691\pi$
$140$	1.74849	+	9.10816i	0.147775	+	0.769780i
$141$	−4.59127	+	8.51397i	−0.386654	+	0.717005i
$142$	18.0121			1.51154
$143$	−0.126777	+	0.219584i	−0.0106016	+	0.0183625i
$144$	−2.10504	−	3.20129i	−0.175420	−	0.266774i
$145$	5.95930	−	3.44060i	0.494893	−	0.285726i
$146$	5.10359	−	8.83968i	0.422376	−	0.731577i
$147$	−9.73332	−	7.22928i	−0.802790	−	0.596261i
$148$	12.8740	+	22.2983i	1.05823	+	1.83291i
$149$	6.22180	+	3.59216i	0.509709	+	0.294281i	0.732714	−	0.680536i	$-0.238253\pi$
$149$	6.22180	+	3.59216i	0.509709	+	0.294281i	−0.223005	+	0.974817i	$0.571587\pi$
$150$	−0.117987	−	4.06231i	−0.00963363	−	0.331686i
$151$	−6.86549	−	11.8914i	−0.558706	−	0.967707i	−0.997605	−	0.0691704i	$-0.977965\pi$
$151$	−6.86549	−	11.8914i	−0.558706	−	0.967707i	0.438899	−	0.898536i	$-0.355369\pi$
$152$	11.7026	+	20.2695i	0.949207	+	1.64407i
$153$	1.91772	−	0.111492i	0.155038	−	0.00901361i
$154$	32.6007	+	11.3101i	2.62704	+	0.911394i
$155$	5.61264	+	3.24046i	0.450818	+	0.260280i
$156$	−0.00804062	−	0.276839i	−0.000643765	−	0.0221648i
$157$		−	2.01969i		−	0.161189i	−0.996747	−	0.0805945i	$-0.974318\pi$
$157$		−	2.01969i		−	0.161189i	0.996747	−	0.0805945i	$-0.0256819\pi$
$158$			20.0995i			1.59903i
$159$	−8.65866	+	5.34011i	−0.686676	+	0.423498i
$160$	−3.52292	−	2.03396i	−0.278511	−	0.160799i
$161$	15.6945	−	3.01287i	1.23690	−	0.237448i
$162$	−19.3885	−	8.36820i	−1.52330	−	0.657468i
$163$	4.14847	+	7.18537i	0.324934	+	0.562801i	0.981499	−	0.191468i	$-0.0613247\pi$
$163$	4.14847	+	7.18537i	0.324934	+	0.562801i	−0.656565	+	0.754269i	$0.727991\pi$
$164$	−2.03595	−	3.52637i	−0.158981	−	0.275363i
$165$	−8.47405	−	4.56974i	−0.659704	−	0.355754i
$166$	−2.94866	−	1.70241i	−0.228861	−	0.132133i
$167$	−1.67285	−	2.89747i	−0.129449	−	0.224213i	0.794014	−	0.607899i	$-0.207988\pi$
$167$	−1.67285	−	2.89747i	−0.129449	−	0.224213i	−0.923463	+	0.383687i	$0.874654\pi$
$168$	−15.8013	+	3.51190i	−1.21910	+	0.270949i
$169$	−6.49896	+	11.2565i	−0.499920	+	0.865887i
$170$	−1.30114	+	0.751211i	−0.0997925	+	0.0576152i
$171$	17.7630	+	8.92327i	1.35837	+	0.682380i
$172$	7.29994	−	12.6439i	0.556615	−	0.964086i
$173$	13.4794			1.02482			0.512411	−	0.858740i	$-0.328753\pi$
$173$	13.4794			1.02482			0.512411	+	0.858740i	$0.328753\pi$
$174$	14.6799	+	23.8025i	1.11288	+	1.80447i
$175$	−2.49960	−	0.867183i	−0.188952	−	0.0655528i
$176$	6.14788	−	3.54948i	0.463414	−	0.267552i
$177$	−2.43197	+	4.50980i	−0.182798	+	0.338977i
$178$	−37.5615	+	21.6862i	−2.81536	+	1.62545i
$179$	−17.5857	−	10.1531i	−1.31442	−	0.758881i	−0.331596	−	0.943422i	$-0.607587\pi$
$179$	−17.5857	−	10.1531i	−1.31442	−	0.758881i	−0.982825	+	0.184541i	$0.940920\pi$
$180$	10.4985	−	0.610362i	0.782514	−	0.0454937i
$181$		−	7.86227i		−	0.584398i	−0.956358	−	0.292199i	$-0.905613\pi$
$181$		−	7.86227i		−	0.584398i	0.956358	−	0.292199i	$-0.0943870\pi$
$182$	−0.267531	−	0.0928143i	−0.0198308	−	0.00687986i
$183$	10.1947	+	5.49762i	0.753613	+	0.406396i
$184$	10.6679	−	18.4774i	0.786449	−	1.36217i
$185$	−7.34517			−0.540028
$186$	−12.5015	+	23.1826i	−0.916655	+	1.69983i
$187$			3.55924i			0.260277i
$188$	19.5768			1.42778
$189$	−9.57448	+	9.86556i	−0.696441	+	0.717614i
$190$	−15.5473			−1.12792
$191$			1.66196i			0.120255i	0.998191	+	0.0601274i	$0.0191507\pi$
$191$			1.66196i			0.120255i	−0.998191	+	0.0601274i	$0.980849\pi$
$192$	9.94679	−	18.4452i	0.717848	−	1.33116i
$193$	11.1111			0.799795			0.399897	−	0.916560i	$-0.369046\pi$
$193$	11.1111			0.799795			0.399897	+	0.916560i	$0.369046\pi$
$194$	7.44963	−	12.9031i	0.534852	−	0.926392i
$195$	0.0695408	+	0.0375008i	0.00497992	+	0.00268549i
$196$	−3.52790	+	24.2830i	−0.251993	+	1.73450i
$197$		−	13.1636i		−	0.937866i	−0.883234	−	0.468933i	$-0.844639\pi$
$197$		−	13.1636i		−	0.937866i	0.883234	−	0.468933i	$-0.155361\pi$
$198$	17.5639	−	34.9634i	1.24821	−	2.48474i
$199$	−8.32489	−	4.80638i	−0.590136	−	0.340715i	0.175015	−	0.984566i	$-0.444003\pi$
$199$	−8.32489	−	4.80638i	−0.590136	−	0.340715i	−0.765151	+	0.643850i	$0.777336\pi$
$200$	−3.05903	+	1.76613i	−0.216306	+	0.124884i
$201$	2.87979	−	5.34023i	0.203125	−	0.376671i
$202$	−22.8097	+	13.1692i	−1.60488	+	0.926579i
$203$	17.8795	−	3.43233i	1.25489	−	0.240902i
$204$	−2.04080	−	3.30903i	−0.142884	−	0.231678i
$205$	1.16160			0.0811299
$206$	12.5979	−	21.8202i	0.877737	−	1.52028i
$207$	−1.05173	−	18.0903i	−0.0731003	−	1.25736i
$208$	−0.0504515	+	0.0291282i	−0.00349818	+	0.00201967i
$209$	−18.4158	+	31.8971i	−1.27385	+	2.20637i
$210$	3.22784	−	10.2565i	0.222742	−	0.707763i
$211$	5.40390	+	9.35982i	0.372020	+	0.644357i	0.989876	−	0.141934i	$-0.0453321\pi$
$211$	5.40390	+	9.35982i	0.372020	+	0.644357i	−0.617857	+	0.786291i	$0.711999\pi$
$212$	17.8303	+	10.2943i	1.22459	+	0.707015i
$213$	−11.7031	−	6.31103i	−0.801881	−	0.432425i
$214$	−2.10048	−	3.63814i	−0.143586	−	0.248698i
$215$	2.08247	+	3.60695i	0.142024	+	0.245992i
$216$	1.59679	+	18.2846i	0.108648	+	1.24411i
$217$	11.2193	+	12.9670i	0.761614	+	0.880259i
$218$	−37.1698	−	21.4600i	−2.51745	−	1.45345i
$219$	−6.41319	+	3.95525i	−0.433363	+	0.267271i
$220$			19.4850i			1.31368i
$221$		−	0.0292083i		−	0.00196476i
$222$	−0.866638	−	29.8384i	−0.0581649	−	2.00262i
$223$	−4.21977	−	2.43629i	−0.282577	−	0.163146i	0.352012	−	0.935995i	$-0.385497\pi$
$223$	−4.21977	−	2.43629i	−0.282577	−	0.163146i	−0.634589	+	0.772849i	$0.718831\pi$
$224$	−7.04208	−	8.13910i	−0.470518	−	0.543816i
$225$	−1.34668	+	2.68076i	−0.0897786	+	0.178717i
$226$	−7.04520	−	12.2027i	−0.468640	−	0.811708i
$227$	3.37952	+	5.85351i	0.224307	+	0.388511i	0.956111	−	0.293004i	$-0.0946549\pi$
$227$	3.37952	+	5.85351i	0.224307	+	0.388511i	−0.731804	+	0.681515i	$0.761322\pi$
$228$	−1.16799	−	40.2140i	−0.0773522	−	2.66324i
$229$	−6.42997	−	3.71235i	−0.424905	−	0.245319i	0.272269	−	0.962221i	$-0.412226\pi$
$229$	−6.42997	−	3.71235i	−0.424905	−	0.245319i	−0.697174	+	0.716902i	$0.745559\pi$
$230$	7.08634	+	12.2739i	0.467259	+	0.809317i
$231$	−17.2189	−	18.7711i	−1.13292	−	1.23505i
$232$	12.1531	−	21.0498i	0.797890	−	1.38199i
$233$	16.5989	−	9.58336i	1.08743	−	0.627827i	0.154538	−	0.987987i	$-0.450611\pi$
$233$	16.5989	−	9.58336i	1.08743	−	0.627827i	0.932891	+	0.360160i	$0.117278\pi$
$234$	−0.144135	+	0.286921i	−0.00942239	+	0.0187566i
$235$	−2.79236	+	4.83651i	−0.182154	+	0.315499i
$236$	10.3697			0.675011
$237$	7.04242	−	13.0593i	0.457454	−	0.848295i
$238$	−3.90375	+	0.749404i	−0.253043	+	0.0485766i
$239$	6.68576	−	3.86002i	0.432466	−	0.249684i	−0.267931	−	0.963438i	$-0.586340\pi$
$239$	6.68576	−	3.86002i	0.432466	−	0.249684i	0.700396	+	0.713754i	$0.253007\pi$
$240$	−1.16117	−	1.88277i	−0.0749535	−	0.121532i
$241$	16.5717	−	9.56767i	1.06748	−	0.616308i	0.139985	−	0.990154i	$-0.455294\pi$
$241$	16.5717	−	9.56767i	1.06748	−	0.616308i	0.927491	+	0.373846i	$0.121961\pi$
$242$	40.4317	+	23.3432i	2.59905	+	1.50056i
$243$	9.66530	+	12.2304i	0.620029	+	0.784579i
$244$		−	23.4414i		−	1.50068i
$245$	−5.49599	−	4.33522i	−0.351126	−	0.276967i
$246$	0.137054	+	4.71879i	0.00873827	+	0.300859i
$247$	0.151126	−	0.261758i	0.00961592	−	0.0166553i
$248$	22.8923			1.45366
$249$	1.31936	+	2.13926i	0.0836110	+	0.135570i
$250$		−	2.34636i		−	0.148397i
$251$	−10.1633			−0.641501			−0.320751	−	0.947164i	$-0.603935\pi$
$251$	−10.1633			−0.641501			−0.320751	+	0.947164i	$0.603935\pi$
$252$	26.7714	+	7.57848i	1.68644	+	0.477399i
$253$	33.5751			2.11085
$254$		−	36.7894i		−	2.30837i
$255$	1.10860	−	0.0321986i	0.0694231	−	0.00201635i
$256$	−23.3227			−1.45767
$257$	−1.49188	+	2.58401i	−0.0930610	+	0.161186i	−0.908798	−	0.417237i	$-0.862998\pi$
$257$	−1.49188	+	2.58401i	−0.0930610	+	0.161186i	0.815737	+	0.578423i	$0.196332\pi$
$258$	−14.4068	+	8.88522i	−0.896930	+	0.553170i
$259$	−18.3600	−	6.36961i	−1.14083	−	0.395788i
$260$		−	0.159900i		−	0.00991660i
$261$	−1.19815	−	20.6088i	−0.0741638	−	1.27565i
$262$	−32.2771	−	18.6352i	−1.99409	−	1.15129i
$263$	−7.18059	+	4.14572i	−0.442774	+	0.255636i	−0.704774	−	0.709432i	$-0.748951\pi$
$263$	−7.18059	+	4.14572i	−0.442774	+	0.255636i	0.262000	+	0.965068i	$0.415618\pi$
$264$	−33.9931	+	0.987311i	−2.09213	+	0.0607648i
$265$	−5.08648	+	2.93668i	−0.312460	+	0.180399i
$266$	−38.8620	−	13.4824i	−2.38278	−	0.826656i
$267$	32.0033	−	0.929518i	1.95857	−	0.0568856i
$268$	−12.2792			−0.750070
$269$	10.8332	−	18.7636i	0.660510	−	1.14404i	−0.319972	−	0.947427i	$-0.603674\pi$
$269$	10.8332	−	18.7636i	0.660510	−	1.14404i	0.980482	−	0.196609i	$-0.0629931\pi$
$270$	−11.0489	−	5.15433i	−0.672417	−	0.313682i
$271$	19.4905	−	11.2529i	1.18396	−	0.683562i	0.227036	−	0.973886i	$-0.427097\pi$
$271$	19.4905	−	11.2529i	1.18396	−	0.683562i	0.956928	+	0.290324i	$0.0937632\pi$
$272$	−0.408884	+	0.708208i	−0.0247922	+	0.0429414i
$273$	0.141304	+	0.154042i	0.00855211	+	0.00932302i
$274$	12.6167	+	21.8527i	0.762201	+	1.32017i
$275$	−4.81384	−	2.77927i	−0.290285	−	0.167596i
$276$	−31.2148	+	19.2513i	−1.87891	+	1.15879i
$277$	−2.95062	−	5.11062i	−0.177285	−	0.307067i	0.763664	−	0.645613i	$-0.223398\pi$
$277$	−2.95062	−	5.11062i	−0.177285	−	0.307067i	−0.940950	+	0.338546i	$0.890065\pi$
$278$	6.93363	+	12.0094i	0.415851	+	0.720276i
$279$	16.2453	−	10.6823i	0.972581	−	0.639530i
$280$	−9.17790	+	1.76188i	−0.548484	+	0.105293i
$281$	11.9850	+	6.91952i	0.714963	+	0.412784i	0.812896	−	0.582409i	$-0.197890\pi$
$281$	11.9850	+	6.91952i	0.714963	+	0.412784i	−0.0979331	+	0.995193i	$0.531223\pi$
$282$	−19.9769	−	10.7728i	−1.18960	−	0.641510i
$283$		−	19.4460i		−	1.15594i	−0.816056	−	0.577972i	$-0.803844\pi$
$283$		−	19.4460i		−	1.15594i	0.816056	−	0.577972i	$-0.196156\pi$
$284$			26.9097i			1.59680i
$285$	10.1016	+	5.44742i	0.598368	+	0.322677i
$286$	−0.515224	−	0.297465i	−0.0304658	−	0.0175895i
$287$	2.90354	+	1.00732i	0.171391	+	0.0594603i
$288$	−10.1968	+	6.70500i	−0.600852	+	0.395096i
$289$	8.29500	+	14.3674i	0.487941	+	0.845138i
$290$	8.07290	+	13.9827i	0.474057	+	0.821091i
$291$	−9.36124	+	5.77342i	−0.548766	+	0.338444i
$292$	13.2063	+	7.62466i	0.772840	+	0.446199i
$293$	−10.0926	−	17.4810i	−0.589619	−	1.02125i	−0.994282	−	0.106784i	$-0.965945\pi$
$293$	−10.0926	−	17.4810i	−0.589619	−	1.02125i	0.404664	−	0.914466i	$-0.367389\pi$
$294$	16.9625	−	22.8379i	0.989275	−	1.33193i
$295$	−1.47910	+	2.56187i	−0.0861164	+	0.149158i
$296$	−22.4691	+	12.9725i	−1.30599	+	0.754013i
$297$	−23.6622	+	16.5629i	−1.37302	+	0.961077i
$298$	−8.42850	+	14.5986i	−0.488250	+	0.845674i
$299$	−0.275528			−0.0159342
$300$	6.06901	−	0.176271i	0.350394	−	0.0101770i
$301$	2.07746	+	10.8218i	0.119743	+	0.623759i
$302$	27.9015	−	16.1089i	1.60555	−	0.926965i
$303$	19.4344	−	0.564460i	1.11648	−	0.0324274i
$304$	−7.32866	+	4.23120i	−0.420327	+	0.242676i
$305$	5.79128	+	3.34359i	0.331607	+	0.191454i
$306$	0.261601	+	4.49967i	0.0149547	+	0.257229i
$307$			14.7616i			0.842487i	0.906947	+	0.421244i	$0.138406\pi$
$307$			14.7616i			0.842487i	−0.906947	+	0.421244i	$0.861594\pi$
$308$	−16.8971	+	48.7047i	−0.962800	+	2.77521i
$309$	−15.8306	+	9.76329i	−0.900569	+	0.555414i
$310$	−7.60329	+	13.1693i	−0.431838	+	0.747965i
$311$	−8.60556			−0.487977			−0.243988	−	0.969778i	$-0.578456\pi$
$311$	−8.60556			−0.487977			−0.243988	+	0.969778i	$0.578456\pi$
$312$	0.278958	−	0.00810219i	0.0157929	−	0.000458696i
$313$		−	17.7685i		−	1.00433i	−0.864771	−	0.502167i	$-0.832536\pi$
$313$		−	17.7685i		−	1.00433i	0.864771	−	0.502167i	$-0.167464\pi$
$314$	4.73893			0.267434
$315$	−5.69086	+	5.53300i	−0.320644	+	0.311749i
$316$	−30.0283			−1.68922
$317$			24.7923i			1.39248i	0.717811	+	0.696238i	$0.245144\pi$
$317$			24.7923i			1.39248i	−0.717811	+	0.696238i	$0.754856\pi$
$318$	−12.5298	−	20.3164i	−0.702639	−	1.13928i
$319$	38.2494			2.14156
$320$	6.04953	−	10.4781i	0.338179	−	0.585744i
$321$	0.0900313	+	3.09978i	0.00502506	+	0.173013i
$322$	7.06929	+	36.8250i	0.393956	+	2.05218i
$323$		−	4.24284i		−	0.236078i
$324$	12.5019	−	28.9660i	0.694551	−	1.60922i
$325$	0.0395039	+	0.0228076i	0.00219128	+	0.00126514i
$326$	−16.8595	+	9.73383i	−0.933760	+	0.539107i
$327$	16.6314	+	26.9667i	0.919716	+	1.49126i
$328$	3.55337	−	2.05154i	0.196202	−	0.113277i
$329$	−11.1739	+	9.66785i	−0.616038	+	0.533006i
$330$	10.7223	−	19.8832i	0.590242	−	1.09453i
$331$	−8.56584			−0.470821			−0.235410	−	0.971896i	$-0.575643\pi$
$331$	−8.56584			−0.470821			−0.235410	+	0.971896i	$0.575643\pi$
$332$	2.54337	−	4.40524i	0.139586	−	0.241769i
$333$	−9.89159	+	19.6906i	−0.542056	+	1.07904i
$334$	6.79851	−	3.92512i	0.371998	−	0.214773i
$335$	1.75146	−	3.03361i	0.0956923	−	0.165744i
$336$	−1.26976	−	5.71312i	−0.0692712	−	0.311676i
$337$	−9.72589	−	16.8457i	−0.529803	−	0.917646i	−0.999396	−	0.0347626i	$-0.988932\pi$
$337$	−9.72589	−	16.8457i	−0.529803	−	0.917646i	0.469592	−	0.882883i	$-0.344401\pi$
$338$	−26.4119	−	15.2489i	−1.43662	−	0.829432i
$339$	0.301973	+	10.3969i	0.0164009	+	0.564685i
$340$	−1.12229	−	1.94387i	−0.0608649	−	0.105421i
$341$	18.0122	+	31.1981i	0.975416	+	1.68947i
$342$	−20.9372	+	41.6786i	−1.13216	+	2.25372i
$343$	−9.97834	−	15.6023i	−0.538780	−	0.842447i
$344$	12.7407	+	7.35584i	0.686932	+	0.396600i
$345$	−0.303736	−	10.4577i	−0.0163526	−	0.563021i
$346$			31.6276i			1.70031i
$347$		−	9.66618i		−	0.518908i	−0.965756	−	0.259454i	$-0.916457\pi$
$347$		−	9.66618i		−	0.518908i	0.965756	−	0.259454i	$-0.0835426\pi$
$348$	−35.5605	+	21.9315i	−1.90624	+	1.17565i
$349$	−22.7845	−	13.1546i	−1.21962	−	0.704151i	−0.254787	−	0.966997i	$-0.582005\pi$
$349$	−22.7845	−	13.1546i	−1.21962	−	0.704151i	−0.964838	+	0.262847i	$0.915339\pi$
$350$	2.03473	−	5.86497i	0.108761	−	0.313496i
$351$	0.194180	−	0.135920i	0.0103645	−	0.00725490i
$352$	−11.3058	−	19.5823i	−0.602604	−	1.04374i
$353$	12.6668	+	21.9395i	0.674186	+	1.16772i	0.976706	+	0.214581i	$0.0688387\pi$
$353$	12.6668	+	21.9395i	0.674186	+	1.16772i	−0.302520	+	0.953143i	$0.597828\pi$
$354$	−10.5816	−	5.70628i	−0.562407	−	0.303285i
$355$	−6.64813	−	3.83830i	−0.352846	−	0.203716i
$356$	−32.3987	−	56.1162i	−1.71713	−	2.97415i
$357$	2.79897	+	0.880873i	0.148137	+	0.0466208i
$358$	23.8229	−	41.2625i	1.25908	−	2.18079i
$359$	3.18127	−	1.83671i	0.167901	−	0.0969378i	−0.413695	−	0.910416i	$-0.635762\pi$
$359$	3.18127	−	1.83671i	0.167901	−	0.0969378i	0.581596	+	0.813478i	$0.302429\pi$
$360$	0.615036	+	10.5789i	0.0324152	+	0.557558i
$361$	12.4528	−	21.5689i	0.655411	−	1.13521i
$362$	18.4477			0.969592
$363$	−18.0909	−	29.3332i	−0.949524	−	1.53959i
$364$	0.138663	−	0.399687i	0.00726790	−	0.0209493i
$365$	−3.76739	+	2.17511i	−0.197194	+	0.113850i
$366$	−12.8994	+	23.9204i	−0.674263	+	1.25034i
$367$	29.8207	−	17.2170i	1.55663	−	0.898720i	0.559052	−	0.829132i	$-0.311165\pi$
$367$	29.8207	−	17.2170i	1.55663	−	0.898720i	0.997576	−	0.0695875i	$-0.0221683\pi$
$368$	6.68069	+	3.85710i	0.348255	+	0.201065i
$369$	1.56431	−	3.11397i	0.0814345	−	0.162107i
$370$		−	17.2344i		−	0.895976i
$371$	−15.2608	+	2.92962i	−0.792301	+	0.152098i
$372$	−34.6343	−	18.6770i	−1.79571	−	0.968358i
$373$	−3.03069	+	5.24931i	−0.156923	+	0.271799i	−0.933758	−	0.357906i	$-0.883491\pi$
$373$	−3.03069	+	5.24931i	−0.156923	+	0.271799i	0.776834	+	0.629705i	$0.216824\pi$
$374$	−8.35127			−0.431834
$375$	−0.822112	+	1.52451i	−0.0424537	+	0.0787254i
$376$			19.7267i			1.01733i
$377$	−0.313887			−0.0161660
$378$	−23.1482	−	22.4652i	−1.19061	−	1.15549i
$379$	−23.3855			−1.20123			−0.600616	−	0.799537i	$-0.705078\pi$
$379$	−23.3855			−1.20123			−0.600616	+	0.799537i	$0.705078\pi$
$380$		−	23.2274i		−	1.19154i
$381$	−12.8902	+	23.9033i	−0.660384	+	1.22460i
$382$	−3.89955			−0.199518
$383$	3.81397	−	6.60599i	0.194885	−	0.337550i	−0.751978	−	0.659188i	$-0.770900\pi$
$383$	3.81397	−	6.60599i	0.194885	−	0.337550i	0.946863	+	0.321638i	$0.104233\pi$
$384$	30.8759	+	16.6502i	1.57563	+	0.849677i
$385$	−9.62253	−	11.1215i	−0.490409	−	0.566806i
$386$			26.0707i			1.32696i
$387$	12.4738	−	0.725199i	0.634078	−	0.0368639i
$388$	19.2770	+	11.1296i	0.978643	+	0.565020i
$389$	24.6463	−	14.2296i	1.24962	−	0.721467i	0.278584	−	0.960412i	$-0.410135\pi$
$389$	24.6463	−	14.2296i	1.24962	−	0.721467i	0.971033	+	0.238945i	$0.0768015\pi$
$390$	−0.0879905	+	0.163168i	−0.00445557	+	0.00826233i
$391$	−3.34953	+	1.93385i	−0.169393	+	0.0977991i
$392$	−24.4689	−	3.55491i	−1.23587	−	0.179550i
$393$	14.4422	+	23.4171i	0.728511	+	1.18124i
$394$	30.8865			1.55604
$395$	4.28313	−	7.41859i	0.215508	−	0.373270i
$396$	52.2346	+	26.2401i	2.62489	+	1.31861i
$397$	−4.05711	+	2.34237i	−0.203620	+	0.117560i	−0.598343	−	0.801240i	$-0.704174\pi$
$397$	−4.05711	+	2.34237i	−0.203620	+	0.117560i	0.394723	+	0.918800i	$0.370841\pi$
$398$	11.2775	−	19.5332i	0.565291	−	0.979112i
$399$	20.5261	+	22.3763i	1.02759	+	1.12022i
$400$	−0.638563	−	1.10602i	−0.0319282	−	0.0553012i
$401$	27.5136	+	15.8850i	1.37396	+	0.793258i	0.991425	−	0.130681i	$-0.0417163\pi$
$401$	27.5136	+	15.8850i	1.37396	+	0.793258i	0.382540	+	0.923939i	$0.375050\pi$
$402$	12.5301	+	6.75703i	0.624945	+	0.337010i
$403$	−0.147814	−	0.256021i	−0.00736314	−	0.0127533i
$404$	−19.6745	−	34.0772i	−0.978842	−	1.69540i
$405$	5.37291	+	7.22024i	0.266982	+	0.358777i
$406$	8.05348	+	41.9517i	0.399688	+	2.08203i
$407$	−35.3585	−	20.4142i	−1.75265	−	1.01190i
$408$	3.33436	−	2.05642i	0.165076	−	0.101808i
$409$		−	21.1774i		−	1.04715i	−0.851979	−	0.523577i	$-0.824597\pi$
$409$		−	21.1774i		−	1.04715i	0.851979	−	0.523577i	$-0.175403\pi$
$410$			2.72554i			0.134605i
$411$	−0.540779	−	18.6190i	−0.0266747	−	0.918409i
$412$	32.5989	+	18.8210i	1.60603	+	0.927244i
$413$	−5.91876	+	5.12101i	−0.291243	+	0.251988i
$414$	42.4464	−	2.46774i	2.08612	−	0.121283i
$415$	0.725553	+	1.25670i	0.0356160	+	0.0616888i
$416$	0.0927794	+	0.160699i	0.00454889	+	0.00787890i
$417$	−0.297191	−	10.2323i	−0.0145535	−	0.501077i
$418$	−74.8422	−	43.2102i	−3.66065	−	2.11348i
$419$	−4.78529	−	8.28837i	−0.233777	−	0.404913i	0.725140	−	0.688602i	$-0.241775\pi$
$419$	−4.78529	−	8.28837i	−0.233777	−	0.404913i	−0.958917	+	0.283688i	$0.908442\pi$
$420$	15.3229	+	4.82233i	0.747683	+	0.235306i
$421$	9.69705	−	16.7958i	0.472605	−	0.818576i	−0.526903	−	0.849925i	$-0.676647\pi$
$421$	9.69705	−	16.7958i	0.472605	−	0.818576i	0.999509	+	0.0313489i	$0.00998031\pi$
$422$	−21.9615	+	12.6795i	−1.06907	+	0.617228i
$423$	9.20509	+	13.9989i	0.447567	+	0.680648i
$424$	−10.3731	+	17.9668i	−0.503763	+	0.872544i
$425$	0.640319			0.0310600
$426$	14.8080	−	27.4596i	0.717448	−	1.33042i
$427$	11.5764	+	13.3797i	0.560219	+	0.647491i
$428$	5.43530	−	3.13807i	0.262725	−	0.151685i
$429$	0.230533	+	0.373795i	0.0111303	+	0.0180470i
$430$	−8.46321	+	4.88624i	−0.408132	+	0.235635i
$431$	−10.4849	−	6.05345i	−0.505039	−	0.291585i	0.225753	−	0.974185i	$-0.427516\pi$
$431$	−10.4849	−	6.05345i	−0.505039	−	0.291585i	−0.730792	+	0.682600i	$0.760849\pi$
$432$	−6.61098	+	0.577335i	−0.318071	+	0.0277771i
$433$			31.4855i			1.51310i	0.653937	+	0.756549i	$0.273116\pi$
$433$			31.4855i			1.51310i	−0.653937	+	0.756549i	$0.726884\pi$
$434$	−30.4253	+	26.3245i	−1.46046	+	1.26362i
$435$	−0.346023	−	11.9136i	−0.0165905	−	0.571212i
$436$	32.0608	−	55.5309i	1.53543	−	2.65945i
$437$	−40.0237			−1.91459
$438$	−9.28045	−	15.0477i	−0.443437	−	0.719006i
$439$			22.5850i			1.07792i	0.842330	+	0.538962i	$0.181183\pi$
$439$			22.5850i			1.07792i	−0.842330	+	0.538962i	$0.818817\pi$
$440$	−19.6342			−0.936024
$441$	−19.0230	+	8.89526i	−0.905857	+	0.423584i
$442$	0.0685332			0.00325979
$443$			8.52787i			0.405171i	0.979265	+	0.202586i	$0.0649344\pi$
$443$			8.52787i			0.405171i	−0.979265	+	0.202586i	$0.935066\pi$
$444$	44.5779	−	1.29474i	2.11557	−	0.0614456i
$445$	18.4849			0.876269
$446$	5.71642	−	9.90112i	0.270680	−	0.468832i
$447$	10.5913	−	6.53204i	0.500951	−	0.308955i
$448$	24.2078	−	20.9450i	1.14371	−	0.989558i
$449$			9.99820i			0.471844i	0.971772	+	0.235922i	$0.0758110\pi$
$449$			9.99820i			0.471844i	−0.971772	+	0.235922i	$0.924189\pi$
$450$	−6.29003	−	3.15980i	−0.296515	−	0.148954i
$451$	5.59177	+	3.22841i	0.263306	+	0.152020i
$452$	18.2305	−	10.5254i	0.857491	−	0.495073i
$453$	−23.7727	+	0.690465i	−1.11694	+	0.0324409i
$454$	−13.7345	+	7.92959i	−0.644590	+	0.372154i
$455$	0.0789656	+	0.0912669i	0.00370196	+	0.00427866i
$456$	40.5219	−	1.17694i	1.89761	−	0.0551151i
$457$	33.8690			1.58432			0.792162	−	0.610311i	$-0.208955\pi$
$457$	33.8690			1.58432			0.792162	+	0.610311i	$0.208955\pi$
$458$	8.71051	−	15.0871i	0.407016	−	0.704972i
$459$	1.40661	−	3.01524i	0.0656549	−	0.140739i
$460$	−18.3370	+	10.5868i	−0.854965	+	0.493614i
$461$	17.8667	−	30.9461i	0.832136	−	1.44130i	−0.0642045	−	0.997937i	$-0.520451\pi$
$461$	17.8667	−	30.9461i	0.832136	−	1.44130i	0.896341	−	0.443366i	$-0.146216\pi$
$462$	44.0438	−	40.4019i	2.04910	−	1.87966i
$463$	−2.36387	−	4.09435i	−0.109858	−	0.190280i	0.805854	−	0.592114i	$-0.201706\pi$
$463$	−2.36387	−	4.09435i	−0.109858	−	0.190280i	−0.915713	+	0.401833i	$0.868373\pi$
$464$	7.61077	+	4.39408i	0.353321	+	0.203990i
$465$	9.55433	−	5.89250i	0.443071	−	0.273258i
$466$	22.4860	+	38.9470i	1.04165	+	1.80418i
$467$	−14.7227	−	25.5005i	−0.681285	−	1.18002i	−0.974589	−	0.224001i	$-0.928088\pi$
$467$	−14.7227	−	25.5005i	−0.681285	−	1.18002i	0.293304	−	0.956019i	$-0.405245\pi$
$468$	−0.428654	−	0.215334i	−0.0198145	−	0.00995384i
$469$	7.00863	−	6.06398i	0.323629	−	0.280009i
$470$	−11.3482	−	6.55189i	−0.523454	−	0.302216i
$471$	−3.07904	−	1.66041i	−0.141875	−	0.0765079i
$472$			10.4491i			0.480960i
$473$			23.1510i			1.06449i
$474$	30.6420	+	16.5241i	1.40743	+	0.758976i
$475$	5.73840	+	3.31307i	0.263296	+	0.152014i
$476$	−1.11959	−	5.83213i	−0.0513165	−	0.267315i
$477$	1.02267	+	17.5904i	0.0468247	+	0.805408i
$478$	9.05702	+	15.6872i	0.414258	+	0.717516i
$479$	−17.8578	−	30.9306i	−0.815944	−	1.41326i	−0.908648	−	0.417562i	$-0.862885\pi$
$479$	−17.8578	−	30.9306i	−0.815944	−	1.41326i	0.0927045	−	0.995694i	$-0.470449\pi$
$480$	−5.99703	+	3.69859i	−0.273726	+	0.168817i
$481$	0.290163	+	0.167526i	0.0132303	+	0.00763852i
$482$	22.4492	+	38.8832i	1.02253	+	1.77108i
$483$	8.30947	−	26.4033i	0.378094	−	1.20139i
$484$	−34.8743	+	60.4041i	−1.58520	+	2.74564i
$485$	−5.49921	+	3.17497i	−0.249706	+	0.144168i
$486$	−28.6969	+	22.6783i	−1.30172	+	1.02871i
$487$	−5.47609	+	9.48486i	−0.248145	+	0.429800i	−0.963011	−	0.269461i	$-0.913154\pi$
$487$	−5.47609	+	9.48486i	−0.248145	+	0.429800i	0.714866	+	0.699261i	$0.246488\pi$
$488$	23.6209			1.06927
$489$	14.3647	−	0.417214i	0.649593	−	0.0188671i
$490$	10.1720	−	12.8956i	0.459524	−	0.582563i
$491$	−2.96611	+	1.71249i	−0.133859	+	0.0772834i	−0.565434	−	0.824794i	$-0.691291\pi$
$491$	−2.96611	+	1.71249i	−0.133859	+	0.0772834i	0.431575	+	0.902077i	$0.357958\pi$
$492$	−7.04977	+	0.204757i	−0.317828	+	0.00923114i
$493$	−3.81585	+	2.20308i	−0.171857	+	0.0992219i
$494$	0.614179	+	0.354597i	0.0276332	+	0.0159541i
$495$	−13.9332	+	9.16194i	−0.626253	+	0.411799i
$496$			8.27695i			0.371646i
$497$	−13.2892	−	15.3594i	−0.596100	−	0.688962i
$498$	−5.01948	+	3.09570i	−0.224928	+	0.138721i
$499$	−19.9201	+	34.5026i	−0.891746	+	1.54455i	−0.0539652	+	0.998543i	$0.517186\pi$
$499$	−19.9201	+	34.5026i	−0.891746	+	1.54455i	−0.837781	+	0.546007i	$0.816147\pi$
$500$	3.50542			0.156767
$501$	−5.79249	+	0.168239i	−0.258789	+	0.00751639i
$502$		−	23.8468i		−	1.06433i
$503$	13.7558			0.613339			0.306669	−	0.951816i	$-0.400785\pi$
$503$	13.7558			0.613339			0.306669	+	0.951816i	$0.400785\pi$
$504$	−7.63651	+	26.9764i	−0.340157	+	1.20162i
$505$	11.2252			0.499514
$506$			78.7794i			3.50217i
$507$	11.8178	+	19.1619i	0.524848	+	0.851008i
$508$	54.9627			2.43857
$509$	−5.02626	+	8.70574i	−0.222785	+	0.385875i	−0.955653	−	0.294496i	$-0.904848\pi$
$509$	−5.02626	+	8.70574i	−0.222785	+	0.385875i	0.732868	+	0.680371i	$0.238181\pi$
$510$	0.0755496	+	2.60117i	0.00334539	+	0.115182i
$511$	−11.3032	+	2.16987i	−0.500024	+	0.0959896i
$512$		−	14.2175i		−	0.628332i
$513$	28.2068	−	19.7440i	1.24536	−	0.871719i
$514$	−6.06304	−	3.50050i	−0.267429	−	0.154400i
$515$	−9.29958	+	5.36911i	−0.409788	+	0.236591i
$516$	−13.2743	−	21.5235i	−0.584370	−	0.947520i
$517$	−26.8839	+	15.5215i	−1.18235	+	0.682633i
$518$	14.9454	−	43.0792i	0.656664	−	1.89279i
$519$	11.0816	−	20.5495i	0.486428	−	0.902024i
$520$	0.161125			0.00706578
$521$	−16.0928	+	27.8735i	−0.705038	+	1.22116i	0.261640	+	0.965166i	$0.415737\pi$
$521$	−16.0928	+	27.8735i	−0.705038	+	1.22116i	−0.966678	+	0.255996i	$0.917596\pi$
$522$	48.3557	−	2.81130i	2.11647	−	0.123047i
$523$	−13.2068	+	7.62493i	−0.577492	+	0.333415i	−0.760136	−	0.649764i	$-0.774868\pi$
$523$	−13.2068	+	7.62493i	−0.577492	+	0.333415i	0.182644	+	0.983179i	$0.441534\pi$
$524$	27.8406	−	48.2214i	1.21622	−	2.10656i
$525$	−3.37698	+	3.09774i	−0.147383	+	0.135197i
$526$	−9.72735	−	16.8483i	−0.424133	−	0.734619i
$527$	−3.59388	−	2.07493i	−0.156552	−	0.0903853i
$528$	−0.356973	−	12.2906i	−0.0155352	−	0.534879i
$529$	6.74246	+	11.6783i	0.293150	+	0.507751i
$530$	−6.89052	−	11.9347i	−0.299305	−	0.518412i
$531$	4.87589	+	7.41512i	0.211595	+	0.321789i
$532$	20.1424	−	58.0591i	0.873283	−	2.51718i
$533$	−0.0458878	−	0.0264934i	−0.00198762	−	0.00114755i
$534$	2.18099	+	75.0914i	0.0943805	+	3.24952i
$535$			1.79041i			0.0774063i
$536$		−	12.3732i		−	0.534441i
$537$	−29.9360	+	18.4626i	−1.29183	+	0.796722i
$538$	44.0262	+	25.4185i	1.89810	+	1.09587i
$539$	−14.4081	−	36.1439i	−0.620599	−	1.55683i
$540$	7.70046	−	16.5069i	0.331375	−	0.710344i
$541$	5.21897	+	9.03953i	0.224381	+	0.388640i	0.956134	−	0.292931i	$-0.0946306\pi$
$541$	5.21897	+	9.03953i	0.224381	+	0.388640i	−0.731752	+	0.681571i	$0.761297\pi$
$542$	26.4033	+	45.7318i	1.13412	+	1.96435i
$543$	−11.9861	−	6.46367i	−0.514374	−	0.277383i
$544$	2.25579	+	1.30238i	0.0967164	+	0.0558392i
$545$	9.14606	+	15.8414i	0.391774	+	0.678573i
$546$	−0.361437	+	0.331551i	−0.0154681	+	0.0141891i
$547$	0.223525	−	0.387157i	0.00955724	−	0.0165536i	−0.861207	−	0.508254i	$-0.830291\pi$
$547$	0.223525	−	0.387157i	0.00955724	−	0.0165536i	0.870764	+	0.491700i	$0.163624\pi$
$548$	−32.6475	+	18.8490i	−1.39463	+	0.805191i
$549$	16.7624	−	11.0222i	0.715400	−	0.470418i
$550$	6.52118	−	11.2950i	0.278064	−	0.481621i
$551$	−45.5958			−1.94244
$552$	−19.3987	−	31.4538i	−0.825664	−	1.33876i
$553$	17.1394	−	14.8293i	0.728840	−	0.630604i
$554$	11.9914	−	6.92322i	0.509465	−	0.294140i
$555$	−6.03856	+	11.1978i	−0.256322	+	0.475320i
$556$	−17.9418	+	10.3587i	−0.760902	+	0.439307i
$557$	−31.9305	−	18.4351i	−1.35294	−	0.781120i	−0.364280	−	0.931290i	$-0.618685\pi$
$557$	−31.9305	−	18.4351i	−1.35294	−	0.781120i	−0.988660	+	0.150169i	$0.952018\pi$
$558$	25.0644	+	38.1174i	1.06106	+	1.61364i
$559$		−	0.189985i		−	0.00803550i
$560$	−0.637027	−	3.31837i	−0.0269193	−	0.140227i
$561$	5.42610	+	2.92609i	0.229090	+	0.123540i
$562$	−16.2357	+	28.1211i	−0.684862	+	1.18622i
$563$	−32.6381			−1.37553			−0.687767	−	0.725932i	$-0.741409\pi$
$563$	−32.6381			−1.37553			−0.687767	+	0.725932i	$0.741409\pi$
$564$	16.0943	−	29.8450i	0.677693	−	1.25670i
$565$			6.00521i			0.252641i
$566$	45.6274			1.91786
$567$	7.16885	+	22.7070i	0.301064	+	0.953604i
$568$	−27.1158			−1.13775
$569$		−	4.57525i		−	0.191804i	−0.995391	−	0.0959022i	$-0.969426\pi$
$569$		−	4.57525i		−	0.191804i	0.995391	−	0.0959022i	$-0.0305736\pi$
$570$	−12.7816	+	23.7020i	−0.535364	+	0.992769i
$571$	−0.907832			−0.0379916			−0.0189958	−	0.999820i	$-0.506047\pi$
$571$	−0.907832			−0.0379916			−0.0189958	+	0.999820i	$0.506047\pi$
$572$	0.444406	−	0.769734i	0.0185816	−	0.0321842i
$573$	2.53367	+	1.36631i	0.105846	+	0.0570786i
$574$	−2.36354	+	6.81276i	−0.0986523	+	0.284359i
$575$		−	6.04027i		−	0.251897i
$576$	−19.9425	−	30.3280i	−0.830935	−	1.26367i
$577$	−1.41559	−	0.817294i	−0.0589319	−	0.0340244i	0.470245	−	0.882536i	$-0.344166\pi$
$577$	−1.41559	−	0.817294i	−0.0589319	−	0.0340244i	−0.529176	+	0.848512i	$0.677499\pi$
$578$	−33.7110	+	19.4631i	−1.40219	+	0.809557i
$579$	9.13457	−	16.9390i	0.379620	−	0.703961i
$580$	−20.8898	+	12.0607i	−0.867403	+	0.500795i
$581$	0.723808	+	3.77042i	0.0300286	+	0.156423i
$582$	−13.5465	−	21.9649i	−0.561522	−	0.910473i
$583$	−32.6473			−1.35211
$584$	−7.68304	+	13.3074i	−0.317927	+	0.550665i
$585$	0.114341	−	0.0751858i	0.00472741	−	0.00310855i
$586$	41.0167	−	23.6810i	1.69438	−	0.978254i
$587$	13.7267	−	23.7753i	0.566561	−	0.981312i	−0.430342	−	0.902666i	$-0.641607\pi$
$587$	13.7267	−	23.7753i	0.566561	−	0.981312i	0.996903	−	0.0786460i	$-0.0250597\pi$
$588$	34.1194	+	25.3417i	1.40706	+	1.04507i
$589$	−21.4717	−	37.1901i	−0.884726	−	1.53239i
$590$	−6.01108	−	3.47050i	−0.247472	−	0.142878i
$591$	−20.0680	−	10.8219i	−0.825487	−	0.445155i
$592$	−4.69036	−	8.12394i	−0.192772	−	0.333892i
$593$	−12.8076	−	22.1834i	−0.525944	−	0.910961i	−0.999543	−	0.0302209i	$-0.990379\pi$
$593$	−12.8076	−	22.1834i	−0.525944	−	0.910961i	0.473600	−	0.880740i	$-0.342954\pi$
$594$	−38.8626	−	55.5201i	−1.59455	−	2.27802i
$595$	1.60054	+	0.555274i	0.0656158	+	0.0227640i
$596$	−21.8100	−	12.5920i	−0.893373	−	0.515789i
$597$	−14.1714	+	8.74000i	−0.579996	+	0.357705i
$598$		−	0.646489i		−	0.0264369i
$599$		−	4.59140i		−	0.187600i	−0.995591	−	0.0937998i	$-0.970099\pi$
$599$		−	4.59140i		−	0.187600i	0.995591	−	0.0937998i	$-0.0299014\pi$
$600$	0.177620	+	6.11548i	0.00725132	+	0.249663i
$601$	−1.61392	−	0.931798i	−0.0658333	−	0.0380088i	0.466722	−	0.884404i	$-0.345435\pi$
$601$	−1.61392	−	0.931798i	−0.0658333	−	0.0380088i	−0.532555	+	0.846395i	$0.678768\pi$
$602$	−25.3919	+	4.87449i	−1.03490	+	0.198669i
$603$	−5.77372	−	8.78053i	−0.235124	−	0.357571i
$604$	24.0664	+	41.6843i	0.979249	+	1.69611i
$605$	−9.94869	−	17.2316i	−0.404472	−	0.700566i
$606$	1.32443	+	45.6001i	0.0538012	+	1.85238i
$607$	32.1319	+	18.5514i	1.30420	+	0.752977i	0.981121	−	0.193396i	$-0.0619503\pi$
$607$	32.1319	+	18.5514i	1.30420	+	0.752977i	0.323074	+	0.946374i	$0.395284\pi$
$608$	13.4773	+	23.3433i	0.546576	+	0.946698i
$609$	9.46632	−	30.0792i	0.383595	−	1.21887i
$610$	−7.84529	+	13.5884i	−0.317646	+	0.550180i
$611$	0.220618	−	0.127374i	0.00892526	−	0.00515300i
$612$	−6.72241	+	0.390827i	−0.271737	+	0.0157982i
$613$	21.2995	−	36.8918i	0.860278	−	1.49005i	−0.0113827	−	0.999935i	$-0.503623\pi$
$613$	21.2995	−	36.8918i	0.860278	−	1.49005i	0.871661	−	0.490110i	$-0.163043\pi$
$614$	−34.6360			−1.39780
$615$	0.954968	−	1.77088i	0.0385080	−	0.0714086i
$616$	−49.0777	−	17.0264i	−1.97740	−	0.686015i
$617$	−0.787957	+	0.454927i	−0.0317220	+	0.0183147i	−0.515777	−	0.856723i	$-0.672497\pi$
$617$	−0.787957	+	0.454927i	−0.0317220	+	0.0183147i	0.484055	+	0.875037i	$0.339163\pi$
$618$	−22.9082	−	37.1442i	−0.921504	−	1.49416i
$619$	−28.9686	+	16.7250i	−1.16435	+	0.672235i	−0.952342	−	0.305033i	$-0.901332\pi$
$619$	−28.9686	+	16.7250i	−1.16435	+	0.672235i	−0.212004	+	0.977269i	$0.567999\pi$
$620$	−19.6746	−	11.3592i	−0.790153	−	0.456195i
$621$	−28.4435	−	13.2689i	−1.14140	−	0.532461i
$622$		−	20.1918i		−	0.809616i
$623$	46.2049	+	16.0298i	1.85116	+	0.642220i
$624$	0.00292943	+	0.100860i	0.000117271	+	0.00403765i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	41.6913			1.66632
$627$	33.4876	+	54.2981i	1.33737	+	2.16846i
$628$			7.07987i			0.282518i
$629$	4.70326			0.187531
$630$	−12.9824	−	13.3528i	−0.517232	−	0.531990i
$631$	−25.0870			−0.998697			−0.499348	−	0.866401i	$-0.666427\pi$
$631$	−25.0870			−0.998697			−0.499348	+	0.866401i	$0.666427\pi$
$632$		−	30.2582i		−	1.20361i
$633$	18.7118	−	0.543472i	0.743725	−	0.0216011i
$634$	−58.1718			−2.31030
$635$	−7.83967	+	13.5787i	−0.311108	+	0.538855i
$636$	30.3522	−	18.7193i	1.20354	−	0.742270i
$637$	0.118237	+	0.296608i	0.00468473	+	0.0117520i
$638$			89.7471i			3.55312i
$639$	−19.2425	+	12.6531i	−0.761220	+	0.500548i
$640$	17.5396	+	10.1265i	0.693313	+	0.400284i
$641$	26.2582	−	15.1602i	1.03714	−	0.598792i	0.118116	−	0.993000i	$-0.462314\pi$
$641$	26.2582	−	15.1602i	1.03714	−	0.598792i	0.919021	+	0.394208i	$0.128981\pi$
$642$	−7.27321	+	0.211246i	−0.287051	+	0.00833722i
$643$	−3.01202	+	1.73899i	−0.118782	+	0.0685790i	−0.558214	−	0.829697i	$-0.688513\pi$
$643$	−3.01202	+	1.73899i	−0.118782	+	0.0685790i	0.439432	+	0.898276i	$0.355180\pi$
$644$	−55.0158	+	10.5614i	−2.16792	+	0.416177i
$645$	7.21086	−	0.209435i	0.283927	−	0.00824651i
$646$	9.95524			0.391684
$647$	14.6521	−	25.3782i	0.576035	−	0.997721i	−0.419894	−	0.907573i	$-0.637933\pi$
$647$	14.6521	−	25.3782i	0.576035	−	0.997721i	0.995928	−	0.0901479i	$-0.0287340\pi$
$648$	29.1878	+	12.5976i	1.14660	+	0.494882i
$649$	−14.2403	+	8.22163i	−0.558980	+	0.322727i
$650$	−0.0535149	+	0.0926905i	−0.00209903	+	0.00363562i
$651$	28.9919	−	6.44355i	1.13628	−	0.252543i
$652$	−14.5421	−	25.1877i	−0.569514	−	0.986427i
$653$	−25.1102	−	14.4974i	−0.982636	−	0.567325i	−0.0795713	−	0.996829i	$-0.525355\pi$
$653$	−25.1102	−	14.4974i	−0.982636	−	0.567325i	−0.903065	+	0.429504i	$0.858688\pi$
$654$	−63.2737	+	39.0232i	−2.47420	+	1.52593i
$655$	7.94216	+	13.7562i	0.310326	+	0.537500i
$656$	0.741757	+	1.28476i	0.0289607	+	0.0501615i
$657$	0.757458	+	13.0286i	0.0295512	+	0.508296i
$658$	−22.6843	−	26.2181i	−0.884326	−	1.02209i
$659$	23.0794	+	13.3249i	0.899047	+	0.519065i	0.876891	−	0.480689i	$-0.159614\pi$
$659$	23.0794	+	13.3249i	0.899047	+	0.519065i	0.0221563	+	0.999755i	$0.492947\pi$
$660$	29.7051	+	16.0189i	1.15627	+	0.623534i
$661$		−	11.8375i		−	0.460425i	−0.973140	−	0.230212i	$-0.926058\pi$
$661$		−	11.8375i		−	0.460425i	0.973140	−	0.230212i	$-0.0739421\pi$
$662$		−	20.0986i		−	0.781153i
$663$	−0.0445283	−	0.0240125i	−0.00172934	−	0.000932567i
$664$	4.43898	+	2.56284i	0.172266	+	0.0994576i
$665$	11.4707	+	13.2576i	0.444813	+	0.514107i
$666$	−46.2013	−	23.2093i	−1.79027	−	0.899341i
$667$	20.7822	+	35.9958i	0.804689	+	1.39376i
$668$	5.86405	+	10.1568i	0.226887	+	0.392980i
$669$	−7.18327	+	4.43019i	−0.277721	+	0.171281i
$670$	7.11795	+	4.10955i	0.274991	+	0.158766i
$671$	18.5855	+	32.1910i	0.717486	+	1.24272i
$672$	−18.1975	+	4.04447i	−0.701984	+	0.156019i
$673$	−2.82034	+	4.88498i	−0.108716	+	0.188302i	−0.915250	−	0.402885i	$-0.868007\pi$
$673$	−2.82034	+	4.88498i	−0.108716	+	0.188302i	0.806534	+	0.591187i	$0.201341\pi$
$674$	39.5262	−	22.8205i	1.52249	−	0.879012i
$675$	2.97972	+	4.25691i	0.114689	+	0.163848i
$676$	22.7816	−	39.4589i	0.876215	−	1.51765i
$677$	−18.8248			−0.723495			−0.361748	−	0.932276i	$-0.617820\pi$
$677$	−18.8248			−0.723495			−0.361748	+	0.932276i	$0.617820\pi$
$678$	−24.3950	+	0.708539i	−0.936885	+	0.0272113i
$679$	−16.4991	+	3.16733i	−0.633177	+	0.121551i
$680$	1.95875	−	1.13089i	0.0751148	−	0.0433675i
$681$	11.7021	−	0.339880i	0.448425	−	0.0130242i
$682$	−73.2020	+	42.2632i	−2.80305	+	1.61834i
$683$	24.2727	+	14.0138i	0.928769	+	0.536225i	0.886422	−	0.462878i	$-0.153183\pi$
$683$	24.2727	+	14.0138i	0.928769	+	0.536225i	0.0423467	+	0.999103i	$0.486517\pi$
$684$	−62.2669	−	31.2798i	−2.38084	−	1.19601i
$685$		−	10.7542i		−	0.410898i
$686$	36.6087	−	23.4128i	1.39773	−	0.893905i
$687$	−10.9457	+	6.75060i	−0.417603	+	0.257551i
$688$	−2.65958	+	4.60653i	−0.101396	+	0.175622i
$689$	0.267914			0.0102067
$690$	24.5374	−	0.712676i	0.934125	−	0.0271311i
$691$		−	33.6338i		−	1.27949i	−0.768587	−	0.639745i	$-0.779040\pi$
$691$		−	33.6338i		−	1.27949i	0.768587	−	0.639745i	$-0.220960\pi$
$692$	−47.2510			−1.79621
$693$	−42.7726	+	10.8185i	−1.62480	+	0.410961i
$694$	22.6804			0.860935
$695$		−	5.91011i		−	0.224183i
$696$	−22.0994	−	35.8328i	−0.837676	−	1.35824i
$697$	−0.743797			−0.0281733
$698$	30.8655	−	53.4606i	1.16828	−	2.02351i
$699$	−0.963803	−	33.1837i	−0.0364544	−	1.25512i
$700$	8.76214	+	3.03984i	0.331178	+	0.114895i
$701$			34.5173i			1.30370i	0.758348	+	0.651850i	$0.226007\pi$
$701$			34.5173i			1.30370i	−0.758348	+	0.651850i	$0.773993\pi$
$702$	0.318919	+	0.455616i	0.0120368	+	0.0171961i
$703$	42.1495	+	24.3350i	1.58970	+	0.917814i
$704$	58.2429	−	33.6266i	2.19511	−	1.26735i
$705$	5.07768	+	8.23314i	0.191236	+	0.310078i
$706$	−51.4781	+	29.7209i	−1.93741	+	1.11856i
$707$	28.0584	+	9.73428i	1.05525	+	0.366095i
$708$	8.52507	−	15.8087i	0.320392	−	0.594129i
$709$	−35.3379			−1.32714			−0.663571	−	0.748113i	$-0.730960\pi$
$709$	−35.3379			−1.32714			−0.663571	+	0.748113i	$0.730960\pi$
$710$	9.00605	−	15.5989i	0.337991	−	0.585418i
$711$	−14.1194	−	21.4725i	−0.529521	−	0.805281i
$712$	56.5459	−	32.6468i	2.11915	−	1.22349i
$713$	−19.5733	+	33.9019i	−0.733024	+	1.26963i
$714$	−2.06685	+	6.56740i	−0.0773499	+	0.245779i
$715$	0.126777	+	0.219584i	0.00474119	+	0.00821198i
$716$	61.6454	+	35.5910i	2.30380	+	1.33010i
$717$	−0.388204	−	13.3659i	−0.0144977	−	0.499158i
$718$	4.30959	+	7.46442i	0.160832	+	0.278570i
$719$	11.8838	+	20.5833i	0.443191	+	0.767629i	0.997924	−	0.0643994i	$-0.0205132\pi$
$719$	11.8838	+	20.5833i	0.443191	+	0.767629i	−0.554734	+	0.832028i	$0.687180\pi$
$720$	−3.82492	+	0.222373i	−0.142546	+	0.00828734i
$721$	−27.9012	+	5.35620i	−1.03910	+	0.199475i
$722$	50.6085	+	29.2188i	1.88345	+	1.08741i
$723$	−0.962224	−	33.1294i	−0.0357855	−	1.23210i
$724$			27.5606i			1.02428i
$725$		−	6.88120i		−	0.255561i
$726$	68.8264	−	42.4478i	2.55439	−	1.57538i
$727$	−13.3342	−	7.69848i	−0.494537	−	0.285521i	0.231918	−	0.972735i	$-0.425500\pi$
$727$	−13.3342	−	7.69848i	−0.494537	−	0.285521i	−0.726455	+	0.687214i	$0.758833\pi$
$728$	0.402747	+	0.139725i	0.0149268	+	0.00517853i
$729$	26.5913	−	4.68012i	0.984862	−	0.173338i
$730$	−5.10359	−	8.83968i	−0.188892	−	0.327171i
$731$	−1.33345	−	2.30960i	−0.0493194	−	0.0854236i
$732$	−35.7367	−	19.2715i	−1.32086	−	0.712294i
$733$	−11.3907	−	6.57644i	−0.420726	−	0.242906i	0.274662	−	0.961541i	$-0.411434\pi$
$733$	−11.3907	−	6.57644i	−0.420726	−	0.242906i	−0.695388	+	0.718635i	$0.744767\pi$
$734$	40.3973	+	69.9702i	1.49109	+	2.58265i
$735$	−11.1274	+	4.81466i	−0.410440	+	0.177591i
$736$	12.2857	−	21.2794i	0.452856	−	0.784370i
$737$	16.8625	−	9.73554i	0.621137	−	0.358613i
$738$	7.30651	+	3.67043i	0.268956	+	0.135110i
$739$	1.91303	−	3.31347i	0.0703721	−	0.121888i	−0.828692	−	0.559704i	$-0.810915\pi$
$739$	1.91303	−	3.31347i	0.0703721	−	0.121888i	0.899064	+	0.437816i	$0.144248\pi$
$740$	25.7479			0.946512
$741$	−0.274810	−	0.445588i	−0.0100954	−	0.0163691i
$742$	−6.87395	−	35.8074i	−0.252351	−	1.31453i
$743$	4.53102	−	2.61598i	0.166227	−	0.0959711i	−0.414579	−	0.910014i	$-0.636071\pi$
$743$	4.53102	−	2.61598i	0.166227	−	0.0959711i	0.580806	+	0.814042i	$0.302738\pi$
$744$	18.8200	−	34.8995i	0.689975	−	1.27948i
$745$	6.22180	−	3.59216i	0.227949	−	0.131606i
$746$	−12.3168	−	7.11110i	−0.450950	−	0.260356i
$747$	4.34598	−	0.252666i	0.159011	−	0.00924457i
$748$		−	12.4766i		−	0.456191i
$749$	−1.55261	+	4.47531i	−0.0567313	+	0.163524i
$750$	−3.57705	−	1.92897i	−0.130616	−	0.0704361i
$751$	14.4486	−	25.0258i	0.527238	−	0.913204i	−0.472258	−	0.881461i	$-0.656561\pi$
$751$	14.4486	−	25.0258i	0.527238	−	0.913204i	0.999496	−	0.0317433i	$-0.0101059\pi$
$752$	−7.13239			−0.260092
$753$	−8.35537	+	15.4940i	−0.304487	+	0.564634i
$754$		−	0.736493i		−	0.0268215i
$755$	−13.7310			−0.499722
$756$	33.5626	−	34.5829i	1.22066	−	1.25777i
$757$	−12.9857			−0.471973			−0.235987	−	0.971756i	$-0.575832\pi$
$757$	−12.9857			−0.471973			−0.235987	+	0.971756i	$0.575832\pi$
$758$		−	54.8709i		−	1.99300i
$759$	27.6025	−	51.1856i	1.00191	−	1.85792i
$760$	23.4052			0.848997
$761$	13.8402	−	23.9719i	0.501707	−	0.868982i	−0.498291	−	0.867010i	$-0.666039\pi$
$761$	13.8402	−	23.9719i	0.501707	−	0.868982i	0.999998	−	0.00197242i	$-0.000627842\pi$
$762$	−56.0859	−	30.2450i	−2.03178	−	1.09566i
$763$	9.12406	+	47.5286i	0.330313	+	1.72065i
$764$		−	5.82585i		−	0.210772i
$765$	0.862305	−	1.71654i	0.0311767	−	0.0620616i
$766$	15.5001	+	8.94896i	0.560040	+	0.323339i
$767$	0.116860	−	0.0674693i	0.00421958	−	0.00243618i
$768$	−19.1739	+	35.5557i	−0.691877	+	1.28300i
$769$	−7.98441	+	4.60980i	−0.287925	+	0.166234i	−0.637006	−	0.770859i	$-0.719827\pi$
$769$	−7.98441	+	4.60980i	−0.287925	+	0.166234i	0.349081	+	0.937093i	$0.386494\pi$
$770$	26.0952	−	22.5779i	0.940404	−	0.813653i
$771$	2.71286	+	4.39874i	0.0977014	+	0.158417i
$772$	−38.9491			−1.40181
$773$	−13.3446	+	23.1135i	−0.479971	+	0.831335i	−0.999736	−	0.0229749i	$-0.992686\pi$
$773$	−13.3446	+	23.1135i	−0.479971	+	0.831335i	0.519765	+	0.854309i	$0.326020\pi$
$774$	1.70158	+	29.2680i	0.0611621	+	1.05202i
$775$	5.61264	−	3.24046i	0.201612	−	0.116401i
$776$	−11.2148	+	19.4246i	−0.402589	+	0.697304i
$777$	−24.8045	+	22.7535i	−0.889856	+	0.816276i
$778$	33.3877	+	57.8292i	1.19701	+	2.07328i
$779$	−6.66574	−	3.84847i	−0.238825	−	0.137886i
$780$	−0.243770	−	0.131456i	−0.00872836	−	0.00470688i
$781$	−21.3354	−	36.9539i	−0.763439	−	1.32232i
$782$	−4.53752	−	7.85921i	−0.162261	−	0.281045i
$783$	−32.4034	−	15.1162i	−1.15800	−	0.540207i
$784$	1.28532	−	8.84700i	0.0459042	−	0.315964i
$785$	−1.74911	−	1.00985i	−0.0624283	−	0.0360430i
$786$	−54.9450	+	33.8866i	−1.95982	+	1.20869i
$787$			2.38323i			0.0849531i	0.999097	+	0.0424765i	$0.0135248\pi$
$787$			2.38323i			0.0849531i	−0.999097	+	0.0424765i	$0.986475\pi$
$788$			46.1438i			1.64381i
$789$	0.416936	+	14.3551i	0.0148433	+	0.511056i
$790$	17.4067	+	10.0498i	0.619303	+	0.357555i
$791$	−5.20762	+	15.0106i	−0.185161	+	0.533716i
$792$	−26.4410	+	52.6345i	−0.939540	+	1.87029i
$793$	−0.152519	−	0.264170i	−0.00541610	−	0.00938095i
$794$	−5.49605	−	9.51945i	−0.195048	−	0.337832i
$795$	0.295343	+	10.1687i	0.0104747	+	0.360646i
$796$	29.1822	+	16.8484i	1.03434	+	0.597175i
$797$	3.26653	+	5.65780i	0.115707	+	0.200410i	0.918062	−	0.396437i	$-0.129753\pi$
$797$	3.26653	+	5.65780i	0.115707	+	0.200410i	−0.802355	+	0.596847i	$0.796420\pi$
$798$	−52.5029	+	48.1616i	−1.85858	+	1.70490i
$799$	1.78800	−	3.09691i	0.0632550	−	0.109561i
$800$	−3.52292	+	2.03396i	−0.124554	+	0.0719113i
$801$	24.8933	−	49.5536i	0.879560	−	1.75089i
$802$	−37.2720	+	64.5569i	−1.31612	+	2.27958i
$803$	−24.1808			−0.853323
$804$	−10.0949	+	18.7197i	−0.356018	+	0.660194i
$805$	5.23802	−	15.0983i	0.184616	−	0.532144i
$806$	0.600719	−	0.346825i	0.0211594	−	0.0122164i
$807$	−19.6992	−	31.9410i	−0.693445	−	1.12438i
$808$	34.3381	−	19.8251i	1.20801	−	0.697445i
$809$	−41.1230	−	23.7424i	−1.44581	−	0.834737i	−0.447579	−	0.894244i	$-0.647714\pi$
$809$	−41.1230	−	23.7424i	−1.44581	−	0.834737i	−0.998228	+	0.0595072i	$0.981047\pi$
$810$	−16.9413	+	12.6068i	−0.595257	+	0.442958i
$811$			43.6693i			1.53344i	0.641985	+	0.766718i	$0.278111\pi$
$811$			43.6693i			1.53344i	−0.641985	+	0.766718i	$0.721889\pi$
$812$	−62.6751	+	12.0317i	−2.19946	+	0.422231i
$813$	−1.13170	−	38.9646i	−0.0396906	−	1.36655i
$814$	47.8992	−	82.9638i	1.67887	−	2.90788i
$815$	8.29695			0.290629
$816$	0.743522	+	1.20557i	0.0260285	+	0.0422036i
$817$		−	27.5975i		−	0.965514i
$818$	49.6898			1.73736
$819$	0.351006	−	0.0887802i	0.0122651	−	0.00310223i
$820$	−4.07190			−0.142197
$821$		−	35.4125i		−	1.23590i	−0.786216	−	0.617952i	$-0.787963\pi$
$821$		−	35.4125i		−	1.23590i	0.786216	−	0.617952i	$-0.212037\pi$
$822$	43.6870	−	1.26886i	1.52376	−	0.0442567i
$823$	−27.2533			−0.949991			−0.474996	−	0.879988i	$-0.657550\pi$
$823$	−27.2533			−0.949991			−0.474996	+	0.879988i	$0.657550\pi$
$824$	−18.9651	+	32.8485i	−0.660681	+	1.14433i
$825$	−8.19454	+	5.05387i	−0.285297	+	0.175953i
$826$	−12.0157	−	13.8876i	−0.418081	−	0.483210i
$827$		−	24.8957i		−	0.865708i	−0.901464	−	0.432854i	$-0.857507\pi$
$827$		−	24.8957i		−	0.865708i	0.901464	−	0.432854i	$-0.142493\pi$
$828$	3.68676	+	63.4140i	0.128124	+	2.20379i
$829$	24.5019	+	14.1462i	0.850987	+	0.491318i	0.860984	−	0.508632i	$-0.169849\pi$
$829$	24.5019	+	14.1462i	0.850987	+	0.491318i	−0.00999656	+	0.999950i	$0.503182\pi$
$830$	−2.94866	+	1.70241i	−0.102350	+	0.0590916i
$831$	−10.2169	+	0.296745i	−0.354421	+	0.0102940i
$832$	−0.477960	+	0.275951i	−0.0165703	+	0.00956686i
$833$	3.51919	+	2.77592i	0.121933	+	0.0961800i
$834$	24.0087	−	0.697318i	0.831352	−	0.0241461i
$835$	−3.34571			−0.115783
$836$	64.5551	−	111.813i	2.23269	−	3.86713i
$837$	−2.92975	−	33.5481i	−0.101267	−	1.15959i
$838$	19.4475	−	11.2280i	0.671804	−	0.387866i
$839$	3.89651	−	6.74895i	0.134522	−	0.233000i	−0.790892	−	0.611955i	$-0.790383\pi$
$839$	3.89651	−	6.74895i	0.134522	−	0.233000i	0.925415	+	0.378955i	$0.123717\pi$
$840$	−4.85925	+	15.4403i	−0.167660	+	0.532740i
$841$	9.17547	+	15.8924i	0.316396	+	0.548013i
$842$	39.4090	+	22.7528i	1.35812	+	0.784113i
$843$	20.4019	−	12.5826i	0.702677	−	0.433367i
$844$	−18.9429	−	32.8101i	−0.652042	−	1.12937i
$845$	6.49896	+	11.2565i	0.223571	+	0.387236i
$846$	−32.8464	+	21.5985i	−1.12928	+	0.742571i
$847$	−9.92476	−	51.6995i	−0.341019	−	1.77642i
$848$	−6.49608	−	3.75051i	−0.223076	−	0.128793i
$849$	−29.6456	−	15.9868i	−1.01744	−	0.548665i
$850$			1.50242i			0.0515326i
$851$		−	44.3669i		−	1.52088i
$852$	41.0241	+	22.1228i	1.40546	+	0.757915i
$853$	2.00649	+	1.15845i	0.0687008	+	0.0396644i	0.533957	−	0.845512i	$-0.320704\pi$
$853$	2.00649	+	1.15845i	0.0687008	+	0.0396644i	−0.465256	+	0.885176i	$0.654038\pi$
$854$	−31.3937	+	27.1623i	−1.07427	+	0.929476i
$855$	16.6093	−	10.9216i	0.568026	−	0.373511i
$856$	3.16210	+	5.47692i	0.108078	+	0.187197i
$857$	17.4804	+	30.2770i	0.597120	+	1.03424i	0.993244	+	0.116045i	$0.0370216\pi$
$857$	17.4804	+	30.2770i	0.597120	+	1.03424i	−0.396124	+	0.918197i	$0.629645\pi$
$858$	−0.877060	+	0.540915i	−0.0299423	+	0.0184665i
$859$	33.9938	+	19.6263i	1.15985	+	0.669641i	0.951269	−	0.308363i	$-0.0997813\pi$
$859$	33.9938	+	19.6263i	1.15985	+	0.669641i	0.208584	+	0.978004i	$0.433115\pi$
$860$	−7.29994	−	12.6439i	−0.248926	−	0.431153i
$861$	3.92271	−	3.59835i	0.133686	−	0.122631i
$862$	14.2036	−	24.6014i	0.483777	−	0.837926i
$863$	−9.76990	+	5.64065i	−0.332571	+	0.192010i	−0.656982	−	0.753906i	$-0.728167\pi$
$863$	−9.76990	+	5.64065i	−0.332571	+	0.192010i	0.324411	+	0.945916i	$0.394834\pi$
$864$	1.83894	+	21.0574i	0.0625619	+	0.716387i
$865$	6.73971	−	11.6735i	0.229157	−	0.396912i
$866$	−73.8765			−2.51042
$867$	28.7226	−	0.834231i	0.975470	−	0.0283320i
$868$	−39.3283	−	45.4549i	−1.33489	−	1.54284i
$869$	41.2366	−	23.8079i	1.39885	−	0.807629i
$870$	27.9536	−	0.811895i	0.947714	−	0.0275258i
$871$	−0.138379	+	0.0798930i	−0.00468879	+	0.00270707i
$872$	55.9561	+	32.3063i	1.89491	+	1.09403i
$873$	1.10565	+	19.0177i	0.0374206	+	0.643652i
$874$		−	93.9100i		−	3.17655i
$875$	−2.00080	+	1.73112i	−0.0676394	+	0.0585227i
$876$	22.4809	−	13.8648i	0.759560	−	0.468449i
$877$	8.50390	−	14.7292i	0.287156	−	0.497369i	−0.685974	−	0.727626i	$-0.740623\pi$
$877$	8.50390	−	14.7292i	0.287156	−	0.497369i	0.973130	+	0.230257i	$0.0739568\pi$
$878$	−52.9926			−1.78841
$879$	−34.9472	+	1.01502i	−1.17874	+	0.0342358i
$880$		−	7.09896i		−	0.239306i
$881$	−3.86189			−0.130110			−0.0650552	−	0.997882i	$-0.520722\pi$
$881$	−3.86189			−0.130110			−0.0650552	+	0.997882i	$0.520722\pi$
$882$	−20.8715	−	44.6349i	−0.702780	−	1.50293i
$883$	−45.6227			−1.53533			−0.767663	−	0.640854i	$-0.778580\pi$
$883$	−45.6227			−1.53533			−0.767663	+	0.640854i	$0.778580\pi$
$884$			0.102387i			0.00344366i
$885$	2.68962	+	4.36105i	0.0904105	+	0.146595i
$886$	−20.0095			−0.672231
$887$	−20.2318	+	35.0425i	−0.679316	+	1.17661i	0.295871	+	0.955228i	$0.404390\pi$
$887$	−20.2318	+	35.0425i	−0.679316	+	1.17661i	−0.975187	+	0.221382i	$0.928943\pi$
$888$	1.30465	+	44.9192i	0.0437813	+	1.50739i
$889$	−31.3713	+	27.1429i	−1.05216	+	0.910344i
$890$			43.3723i			1.45384i
$891$	5.79732	+	49.6898i	0.194217	+	1.66467i
$892$	14.7921	+	8.54021i	0.495275	+	0.285947i
$893$	32.0474	−	18.5026i	1.07242	−	0.619164i
$894$	15.3265	+	24.8510i	0.512596	+	0.831142i
$895$	−17.5857	+	10.1531i	−0.587827	+	0.339382i
$896$	35.0604	+	40.5222i	1.17129	+	1.35375i
$897$	−0.226515	+	0.420046i	−0.00756312	+	0.0140249i
$898$	−23.4594			−0.782850
$899$	−22.2982	+	38.6217i	−0.743688	+	1.28811i
$900$	4.72068	−	9.39718i	0.157356	−	0.313239i
$901$	3.25697	−	1.88041i	0.108505	−	0.0626457i
$902$	−7.57502	+	13.1203i	−0.252221	+	0.436859i
$903$	18.2059	+	5.72963i	0.605854	+	0.190670i
$904$	10.6060	+	18.3701i	0.352750	+	0.610981i
$905$	−6.80893	−	3.93114i	−0.226336	−	0.130675i
$906$	−1.62008	−	55.7795i	−0.0538236	−	1.85315i
$907$	21.0317	+	36.4280i	0.698346	+	1.20957i	0.969040	+	0.246905i	$0.0794137\pi$
$907$	21.0317	+	36.4280i	0.698346	+	1.20957i	−0.270693	+	0.962666i	$0.587253\pi$
$908$	−11.8467	−	20.5190i	−0.393145	−	0.680947i
$909$	15.1167	−	30.0920i	0.501390	−	0.998087i
$910$	−0.214145	+	0.185282i	−0.00709885	+	0.00614203i
$911$	−6.34565	−	3.66366i	−0.210241	−	0.121382i	0.391183	−	0.920313i	$-0.372066\pi$
$911$	−6.34565	−	3.66366i	−0.210241	−	0.121382i	−0.601423	+	0.798931i	$0.705399\pi$
$912$	0.425534	+	14.6511i	0.0140908	+	0.485148i
$913$			8.06604i			0.266947i
$914$			79.4689i			2.62860i
$915$	9.85842	−	6.08005i	0.325909	−	0.201000i
$916$	22.5398	+	13.0133i	0.744735	+	0.429973i
$917$	7.92306	+	41.2724i	0.261642	+	1.36293i
$918$	7.07485	+	3.30042i	0.233505	+	0.108930i
$919$	−23.8899	−	41.3785i	−0.788054	−	1.36495i	−0.927157	−	0.374672i	$-0.877755\pi$
$919$	−23.8899	−	41.3785i	−0.788054	−	1.36495i	0.139103	−	0.990278i	$-0.455578\pi$
$920$	−10.6679	−	18.4774i	−0.351711	−	0.609181i
$921$	22.5042	+	12.1357i	0.741538	+	0.399884i
$922$	72.6107	+	41.9218i	2.39131	+	1.38062i
$923$	0.175085	+	0.303256i	0.00576299	+	0.00998179i
$924$	60.3596	+	65.8005i	1.98568	+	2.16468i
$925$	−3.67259	+	6.36111i	−0.120754	+	0.209152i
$926$	9.60682	−	5.54650i	0.315700	−	0.182269i
$927$	1.86974	+	32.1604i	0.0614102	+	1.05629i
$928$	13.9961	−	24.2419i	0.459444	−	0.795780i
$929$	15.1698			0.497705			0.248853	−	0.968541i	$-0.419947\pi$
$929$	15.1698			0.497705			0.248853	+	0.968541i	$0.419947\pi$
$930$	13.8260	+	22.4179i	0.453371	+	0.735113i
$931$	17.1753	+	43.0858i	0.562898	+	1.41208i
$932$	−58.1860	+	33.5937i	−1.90595	+	1.10040i
$933$	−7.07474	+	13.1193i	−0.231616	+	0.429506i
$934$	59.8333	−	34.5448i	1.95781	−	1.13034i
$935$	3.08239	+	1.77962i	0.100805	+	0.0581998i
$936$	0.216983	−	0.431936i	0.00709232	−	0.0141183i
$937$			34.1681i			1.11622i	0.829765	+	0.558112i	$0.188474\pi$
$937$			34.1681i			1.11622i	−0.829765	+	0.558112i	$0.811526\pi$
$938$	14.2283	+	16.4448i	0.464570	+	0.536942i
$939$	−27.0882	−	14.6077i	−0.883991	−	0.476704i
$940$	9.78840	−	16.9540i	0.319262	−	0.552978i
$941$	−31.2636			−1.01916			−0.509582	−	0.860422i	$-0.670200\pi$
$941$	−31.2636			−1.01916			−0.509582	+	0.860422i	$0.670200\pi$
$942$	3.89593	−	7.22455i	0.126936	−	0.235389i
$943$			7.01640i			0.228485i
$944$	−3.77799			−0.122963
$945$	3.75659	+	13.2245i	0.122202	+	0.430194i
$946$	−54.3207			−1.76612
$947$			2.28421i			0.0742269i	0.999311	+	0.0371134i	$0.0118163\pi$
$947$			2.28421i			0.0742269i	−0.999311	+	0.0371134i	$0.988184\pi$
$948$	−24.6866	+	45.7785i	−0.801785	+	1.48682i
$949$	0.198436			0.00644150
$950$	−7.77366	+	13.4644i	−0.252211	+	0.436842i
$951$	37.7962	+	20.3821i	1.22562	+	0.660934i
$952$	5.87678	−	1.12817i	0.190468	−	0.0365641i
$953$		−	32.2871i		−	1.04588i	−0.852369	−	0.522940i	$-0.824835\pi$
$953$		−	32.2871i		−	1.04588i	0.852369	−	0.522940i	$-0.175165\pi$
$954$	−41.2734	+	2.39955i	−1.33628	+	0.0776883i
$955$	1.43930	+	0.830978i	0.0465745	+	0.0268898i
$956$	−23.4364	+	13.5310i	−0.757987	+	0.437624i
$957$	31.4453	−	58.3117i	1.01648	−	1.88495i
$958$	72.5745	−	41.9009i	2.34477	−	1.35376i
$959$	9.32588	−	26.8813i	0.301148	−	0.868041i
$960$	−11.0006	−	17.8367i	−0.355042	−	0.575679i
$961$	−11.0023			−0.354912
$962$	−0.393076	+	0.680828i	−0.0126733	+	0.0219508i
$963$	4.79966	+	2.41111i	0.154667	+	0.0776970i
$964$	−58.0907	+	33.5387i	−1.87098	+	1.08021i
$965$	5.55555	−	9.62250i	0.178840	−	0.309759i
$966$	61.9518	+	19.4970i	1.99327	+	0.627307i
$967$	19.5539	+	33.8684i	0.628811	+	1.08913i	0.987791	+	0.155788i	$0.0497916\pi$
$967$	19.5539	+	33.8684i	0.628811	+	1.08913i	−0.358979	+	0.933346i	$0.616875\pi$
$968$	−60.8666	−	35.1414i	−1.95633	−	1.12949i
$969$	−6.46825	−	3.48809i	−0.207790	−	0.112054i
$970$	−7.44963	−	12.9031i	−0.239193	−	0.414295i
$971$	17.4132	+	30.1605i	0.558816	+	0.967898i	0.997596	+	0.0693032i	$0.0220776\pi$
$971$	17.4132	+	30.1605i	0.558816	+	0.967898i	−0.438779	+	0.898595i	$0.644589\pi$
$972$	−33.8809	−	42.8726i	−1.08673	−	1.37514i
$973$	5.12514	−	14.7729i	0.164304	−	0.473597i
$974$	−22.2549	−	12.8489i	−0.713094	−	0.411705i
$975$	0.0672470	−	0.0414737i	0.00215363	−	0.00132822i
$976$			8.54038i			0.273371i
$977$		−	25.2981i		−	0.809357i	−0.914459	−	0.404678i	$-0.867383\pi$
$977$		−	25.2981i		−	0.809357i	0.914459	−	0.404678i	$-0.132617\pi$
$978$	0.978935	+	33.7047i	0.0313029	+	1.07776i
$979$	88.9834	+	51.3746i	2.84392	+	1.64194i
$980$	19.2657	+	15.1968i	0.615422	+	0.485442i
$981$	54.7839	−	3.18502i	1.74911	−	0.101690i
$982$	−4.01811	−	6.95958i	−0.128223	−	0.222089i
$983$	−26.3270	−	45.5996i	−0.839699	−	1.45440i	−0.890146	−	0.455675i	$-0.849398\pi$
$983$	−26.3270	−	45.5996i	−0.839699	−	1.45440i	0.0504466	−	0.998727i	$-0.483936\pi$
$984$	−0.206324	−	7.10375i	−0.00657738	−	0.226459i
$985$	−11.4000	−	6.58179i	−0.363234	−	0.209713i
$986$	−5.16923	−	8.95337i	−0.164622	−	0.285134i
$987$	5.55252	+	24.9828i	0.176739	+	0.795212i
$988$	−0.529760	+	0.917572i	−0.0168539	+	0.0291918i
$989$	−21.7870	+	12.5787i	−0.692785	+	0.399980i
$990$	−21.4972	−	32.6924i	−0.683227	−	1.03903i
$991$	−18.6241	+	32.2578i	−0.591613	+	1.02470i	0.402403	+	0.915463i	$0.368175\pi$
$991$	−18.6241	+	32.2578i	−0.591613	+	1.02470i	−0.994015	+	0.109240i	$0.965158\pi$
$992$	26.3638			0.837053
$993$	−7.04208	+	13.0587i	−0.223474	+	0.414405i
$994$	36.0386	−	31.1812i	1.14308	−	0.989008i
$995$	−8.32489	+	4.80638i	−0.263917	+	0.152372i
$996$	−4.62491	−	7.49900i	−0.146546	−	0.237615i
$997$	−9.45155	+	5.45685i	−0.299333	+	0.172820i	−0.642143	−	0.766585i	$-0.721955\pi$
$997$	−9.45155	+	5.45685i	−0.299333	+	0.172820i	0.342810	+	0.939405i	$0.388621\pi$
$998$	−80.9557	−	46.7398i	−2.56261	−	1.47952i
$999$	21.8866	+	31.2677i	0.692460	+	0.989267i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.t.b.101.14	✓	30
3.2	odd	2		945.2.t.b.521.2		30
7.5	odd	6		315.2.be.b.236.14	yes	30
9.4	even	3		945.2.be.b.206.2		30
9.5	odd	6		315.2.be.b.311.14	yes	30
21.5	even	6		945.2.be.b.656.2		30
63.5	even	6	inner	315.2.t.b.131.2	yes	30
63.40	odd	6		945.2.t.b.341.14		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.14	✓	30	1.1	even	1	trivial
315.2.t.b.131.2	yes	30	63.5	even	6	inner
315.2.be.b.236.14	yes	30	7.5	odd	6
315.2.be.b.311.14	yes	30	9.5	odd	6
945.2.t.b.341.14		30	63.40	odd	6
945.2.t.b.521.2		30	3.2	odd	2
945.2.be.b.206.2		30	9.4	even	3
945.2.be.b.656.2		30	21.5	even	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.34636i q^{2} +(0.822112 - 1.52451i) q^{3} -3.50542 q^{4} +(0.500000 - 0.866025i) q^{5} +(3.57705 + 1.92897i) q^{6} +(2.00080 - 1.73112i) q^{7} -3.53226i q^{8} +(-1.64826 - 2.50664i) q^{9} +O(q^{10})\)	\(q+2.34636i q^{2} +(0.822112 - 1.52451i) q^{3} -3.50542 q^{4} +(0.500000 - 0.866025i) q^{5} +(3.57705 + 1.92897i) q^{6} +(2.00080 - 1.73112i) q^{7} -3.53226i q^{8} +(-1.64826 - 2.50664i) q^{9} +(2.03201 + 1.17318i) q^{10} +(4.81384 - 2.77927i) q^{11} +(-2.88185 + 5.34405i) q^{12} +(-0.0395039 + 0.0228076i) q^{13} +(4.06185 + 4.69461i) q^{14} +(-0.909209 - 1.47423i) q^{15} +1.27713 q^{16} +(-0.320160 + 0.554533i) q^{17} +(5.88148 - 3.86742i) q^{18} +(-5.73840 + 3.31307i) q^{19} +(-1.75271 + 3.03578i) q^{20} +(-0.994235 - 4.47342i) q^{21} +(6.52118 + 11.2950i) q^{22} +(5.23103 + 3.02014i) q^{23} +(-5.38497 - 2.90391i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.0535149 - 0.0926905i) q^{26} +(-5.17645 + 0.452058i) q^{27} +(-7.01365 + 6.06832i) q^{28} +(5.95930 + 3.44060i) q^{29} +(3.45907 - 2.13333i) q^{30} +6.48092i q^{31} -4.06792i q^{32} +(-0.279512 - 9.62362i) q^{33} +(-1.30114 - 0.751211i) q^{34} +(-0.498797 - 2.59831i) q^{35} +(5.77785 + 8.78681i) q^{36} +(-3.67259 - 6.36111i) q^{37} +(-7.77366 - 13.4644i) q^{38} +(0.00229377 + 0.0789745i) q^{39} +(-3.05903 - 1.76613i) q^{40} +(0.580801 + 1.00598i) q^{41} +(10.4963 - 2.33284i) q^{42} +(-2.08247 + 3.60695i) q^{43} +(-16.8745 + 9.74251i) q^{44} +(-2.99494 + 0.174120i) q^{45} +(-7.08634 + 12.2739i) q^{46} -5.58472 q^{47} +(1.04994 - 1.94699i) q^{48} +(1.00641 - 6.92727i) q^{49} +(2.03201 - 1.17318i) q^{50} +(0.582184 + 0.943975i) q^{51} +(0.138478 - 0.0799502i) q^{52} +(-5.08648 - 2.93668i) q^{53} +(-1.06069 - 12.1458i) q^{54} -5.55854i q^{55} +(-6.11478 - 7.06735i) q^{56} +(0.333196 + 11.4720i) q^{57} +(-8.07290 + 13.9827i) q^{58} -2.95820 q^{59} +(3.18716 + 5.16778i) q^{60} +6.68719i q^{61} -15.2066 q^{62} +(-7.63715 - 2.16193i) q^{63} +12.0991 q^{64} +0.0456152i q^{65} +(22.5805 - 0.655838i) q^{66} +3.50291 q^{67} +(1.12229 - 1.94387i) q^{68} +(8.90472 - 5.49187i) q^{69} +(6.09657 - 1.17036i) q^{70} -7.67660i q^{71} +(-8.85409 + 5.82210i) q^{72} +(-3.76739 - 2.17511i) q^{73} +(14.9255 - 8.61722i) q^{74} +(-1.73132 + 0.0502852i) q^{75} +(20.1155 - 11.6137i) q^{76} +(4.82027 - 13.8941i) q^{77} +(-0.185303 + 0.00538201i) q^{78} +8.56625 q^{79} +(0.638563 - 1.10602i) q^{80} +(-3.56646 + 8.26320i) q^{81} +(-2.36039 + 1.36277i) q^{82} +(-0.725553 + 1.25670i) q^{83} +(3.48521 + 15.6812i) q^{84} +(0.320160 + 0.554533i) q^{85} +(-8.46321 - 4.88624i) q^{86} +(10.1444 - 6.25645i) q^{87} +(-9.81711 - 17.0037i) q^{88} +(9.24246 + 16.0084i) q^{89} +(-0.408548 - 7.02722i) q^{90} +(-0.0395567 + 0.114020i) q^{91} +(-18.3370 - 10.5868i) q^{92} +(9.88022 + 5.32804i) q^{93} -13.1038i q^{94} +6.62613i q^{95} +(-6.20158 - 3.34429i) q^{96} +(-5.49921 - 3.17497i) q^{97} +(16.2539 + 2.36141i) q^{98} +(-14.9011 - 7.48557i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9}+O(q^{10}) \) 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9	\( 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9} + 3 q^{10} + 9 q^{11} + 15 q^{12} - 12 q^{13} - 27 q^{14} - q^{15} + 42 q^{16} - 3 q^{17} - 4 q^{18} - 15 q^{20} + 4 q^{21} + 15 q^{22} + q^{24} - 15 q^{25} + 24 q^{26} - 5 q^{27} + 27 q^{28} - 2 q^{30} - 25 q^{33} + 48 q^{34} - 6 q^{35} + 21 q^{36} - 3 q^{37} - 30 q^{38} - 3 q^{39} + 3 q^{40} - 18 q^{41} - 16 q^{42} + 12 q^{43} + 15 q^{44} - 7 q^{45} + 9 q^{46} - 60 q^{47} - 40 q^{48} - 15 q^{49} + 3 q^{50} - 48 q^{51} - 33 q^{52} - 30 q^{53} + 35 q^{54} + 42 q^{56} - 21 q^{57} + 30 q^{59} + 33 q^{60} + 12 q^{62} - 47 q^{63} - 138 q^{64} + 100 q^{66} + 12 q^{67} - 21 q^{68} + 32 q^{69} - 18 q^{70} + 85 q^{72} + 6 q^{73} + 54 q^{74} - 5 q^{75} - 54 q^{76} - 9 q^{77} - 18 q^{78} + 24 q^{79} + 21 q^{80} - 14 q^{81} + 6 q^{82} - 6 q^{83} - 9 q^{84} + 3 q^{85} - 60 q^{86} - 16 q^{87} - 48 q^{88} - 3 q^{89} + 22 q^{90} + 15 q^{91} - 3 q^{92} + 69 q^{93} - 48 q^{96} + 36 q^{97} + 24 q^{98} - q^{99}+O(q^{100}) \) 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9 + 3 * q^10 + 9 * q^11 + 15 * q^12 - 12 * q^13 - 27 * q^14 - q^15 + 42 * q^16 - 3 * q^17 - 4 * q^18 - 15 * q^20 + 4 * q^21 + 15 * q^22 + q^24 - 15 * q^25 + 24 * q^26 - 5 * q^27 + 27 * q^28 - 2 * q^30 - 25 * q^33 + 48 * q^34 - 6 * q^35 + 21 * q^36 - 3 * q^37 - 30 * q^38 - 3 * q^39 + 3 * q^40 - 18 * q^41 - 16 * q^42 + 12 * q^43 + 15 * q^44 - 7 * q^45 + 9 * q^46 - 60 * q^47 - 40 * q^48 - 15 * q^49 + 3 * q^50 - 48 * q^51 - 33 * q^52 - 30 * q^53 + 35 * q^54 + 42 * q^56 - 21 * q^57 + 30 * q^59 + 33 * q^60 + 12 * q^62 - 47 * q^63 - 138 * q^64 + 100 * q^66 + 12 * q^67 - 21 * q^68 + 32 * q^69 - 18 * q^70 + 85 * q^72 + 6 * q^73 + 54 * q^74 - 5 * q^75 - 54 * q^76 - 9 * q^77 - 18 * q^78 + 24 * q^79 + 21 * q^80 - 14 * q^81 + 6 * q^82 - 6 * q^83 - 9 * q^84 + 3 * q^85 - 60 * q^86 - 16 * q^87 - 48 * q^88 - 3 * q^89 + 22 * q^90 + 15 * q^91 - 3 * q^92 + 69 * q^93 - 48 * q^96 + 36 * q^97 + 24 * q^98 - q^99

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