LMFDB - Embedded newform 471.2.e.b.169.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(169,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("471.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.e (of order $3$, 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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			169.9
Character	$\chi$	$=$	471.169
Dual form			471.2.e.b.301.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.06264 q^{2} +(0.500000 + 0.866025i) q^{3} +2.25447 q^{4} +(1.20043 + 2.07920i) q^{5} +(1.03132 + 1.78630i) q^{6} +1.31301 q^{7} +0.524880 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+2.06264 q^{2} +(0.500000 + 0.866025i) q^{3} +2.25447 q^{4} +(1.20043 + 2.07920i) q^{5} +(1.03132 + 1.78630i) q^{6} +1.31301 q^{7} +0.524880 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.47604 + 4.28863i) q^{10} +(-1.50523 - 2.60714i) q^{11} +(1.12724 + 1.95243i) q^{12} +(-0.726515 + 1.25836i) q^{13} +2.70826 q^{14} +(-1.20043 + 2.07920i) q^{15} -3.42630 q^{16} +(-2.47324 - 4.28378i) q^{17} +(-1.03132 + 1.78630i) q^{18} +(-0.558826 - 0.967916i) q^{19} +(2.70633 + 4.68749i) q^{20} +(0.656504 + 1.13710i) q^{21} +(-3.10474 - 5.37757i) q^{22} +4.06211 q^{23} +(0.262440 + 0.454559i) q^{24} +(-0.382048 + 0.661727i) q^{25} +(-1.49854 + 2.59554i) q^{26} -1.00000 q^{27} +2.96014 q^{28} +9.91749 q^{29} +(-2.47604 + 4.28863i) q^{30} +(-0.895501 + 1.55105i) q^{31} -8.11698 q^{32} +(1.50523 - 2.60714i) q^{33} +(-5.10140 - 8.83589i) q^{34} +(1.57617 + 2.73001i) q^{35} +(-1.12724 + 1.95243i) q^{36} +(2.08935 - 3.61886i) q^{37} +(-1.15266 - 1.99646i) q^{38} -1.45303 q^{39} +(0.630080 + 1.09133i) q^{40} -1.59561 q^{41} +(1.35413 + 2.34542i) q^{42} +(-1.59152 + 2.75660i) q^{43} +(-3.39350 - 5.87771i) q^{44} -2.40085 q^{45} +8.37866 q^{46} +(-0.813858 + 1.40964i) q^{47} +(-1.71315 - 2.96727i) q^{48} -5.27601 q^{49} +(-0.788027 + 1.36490i) q^{50} +(2.47324 - 4.28378i) q^{51} +(-1.63791 + 2.83694i) q^{52} +(3.85707 - 6.68064i) q^{53} -2.06264 q^{54} +(3.61384 - 6.25935i) q^{55} +0.689171 q^{56} +(0.558826 - 0.967916i) q^{57} +20.4562 q^{58} -8.25664 q^{59} +(-2.70633 + 4.68749i) q^{60} +(3.20343 + 5.54851i) q^{61} +(-1.84709 + 3.19926i) q^{62} +(-0.656504 + 1.13710i) q^{63} -9.88977 q^{64} -3.48851 q^{65} +(3.10474 - 5.37757i) q^{66} -10.2951 q^{67} +(-5.57585 - 9.65766i) q^{68} +(2.03106 + 3.51789i) q^{69} +(3.25106 + 5.63101i) q^{70} +(2.03662 - 3.52754i) q^{71} +(-0.262440 + 0.454559i) q^{72} +(1.15252 + 1.99622i) q^{73} +(4.30957 - 7.46439i) q^{74} -0.764097 q^{75} +(-1.25986 - 2.18214i) q^{76} +(-1.97638 - 3.42319i) q^{77} -2.99707 q^{78} -3.95769 q^{79} +(-4.11303 - 7.12397i) q^{80} +(-0.500000 - 0.866025i) q^{81} -3.29116 q^{82} +(-1.00141 + 1.73449i) q^{83} +(1.48007 + 2.56355i) q^{84} +(5.93789 - 10.2847i) q^{85} +(-3.28273 + 5.68586i) q^{86} +(4.95874 + 8.58880i) q^{87} +(-0.790065 - 1.36843i) q^{88} +(-0.254698 - 0.441149i) q^{89} -4.95209 q^{90} +(-0.953919 + 1.65224i) q^{91} +9.15791 q^{92} -1.79100 q^{93} +(-1.67869 + 2.90758i) q^{94} +(1.34166 - 2.32382i) q^{95} +(-4.05849 - 7.02951i) q^{96} +(-7.07399 + 12.2525i) q^{97} -10.8825 q^{98} +3.01046 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9}+O(q^{10}) $ 22 * q + 2 * q^2 + 11 * q^3 + 30 * q^4 - 4 * q^5 + q^6 + 4 * q^7 - 11 * q^9	\( 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9} - 5 q^{10} + 15 q^{12} + 3 q^{13} - 14 q^{14} + 4 q^{15} + 54 q^{16} - q^{17} - q^{18} - 22 q^{19} - 7 q^{20} + 2 q^{21} - 22 q^{22} - 10 q^{23} - 15 q^{25} - 10 q^{26} - 22 q^{27} - 38 q^{28} + 22 q^{29} + 5 q^{30} - 6 q^{31} + 32 q^{32} + 17 q^{34} - 11 q^{35} - 15 q^{36} + 8 q^{37} + 14 q^{38} + 6 q^{39} + 32 q^{40} - 7 q^{42} + q^{43} - 12 q^{44} + 8 q^{45} + 24 q^{46} + 7 q^{47} + 27 q^{48} + 22 q^{49} + 13 q^{50} + q^{51} + 17 q^{52} + 30 q^{53} - 2 q^{54} + 31 q^{55} - 82 q^{56} + 22 q^{57} - 90 q^{58} - 16 q^{59} + 7 q^{60} + 8 q^{61} - 28 q^{62} - 2 q^{63} - 32 q^{64} - 68 q^{65} + 22 q^{66} - 38 q^{67} - 8 q^{68} - 5 q^{69} + 43 q^{70} + 45 q^{71} - 4 q^{73} + 3 q^{74} - 30 q^{75} - 33 q^{76} + 21 q^{77} - 20 q^{78} + 26 q^{79} - 12 q^{80} - 11 q^{81} + 16 q^{82} + 8 q^{83} - 19 q^{84} - 28 q^{85} - 16 q^{86} + 11 q^{87} - 65 q^{88} + 15 q^{89} + 10 q^{90} - 3 q^{91} - 18 q^{92} - 12 q^{93} - 28 q^{94} - 5 q^{95} + 16 q^{96} - 35 q^{97} + 90 q^{98}+O(q^{100}) \) 22 * q + 2 * q^2 + 11 * q^3 + 30 * q^4 - 4 * q^5 + q^6 + 4 * q^7 - 11 * q^9 - 5 * q^10 + 15 * q^12 + 3 * q^13 - 14 * q^14 + 4 * q^15 + 54 * q^16 - q^17 - q^18 - 22 * q^19 - 7 * q^20 + 2 * q^21 - 22 * q^22 - 10 * q^23 - 15 * q^25 - 10 * q^26 - 22 * q^27 - 38 * q^28 + 22 * q^29 + 5 * q^30 - 6 * q^31 + 32 * q^32 + 17 * q^34 - 11 * q^35 - 15 * q^36 + 8 * q^37 + 14 * q^38 + 6 * q^39 + 32 * q^40 - 7 * q^42 + q^43 - 12 * q^44 + 8 * q^45 + 24 * q^46 + 7 * q^47 + 27 * q^48 + 22 * q^49 + 13 * q^50 + q^51 + 17 * q^52 + 30 * q^53 - 2 * q^54 + 31 * q^55 - 82 * q^56 + 22 * q^57 - 90 * q^58 - 16 * q^59 + 7 * q^60 + 8 * q^61 - 28 * q^62 - 2 * q^63 - 32 * q^64 - 68 * q^65 + 22 * q^66 - 38 * q^67 - 8 * q^68 - 5 * q^69 + 43 * q^70 + 45 * q^71 - 4 * q^73 + 3 * q^74 - 30 * q^75 - 33 * q^76 + 21 * q^77 - 20 * q^78 + 26 * q^79 - 12 * q^80 - 11 * q^81 + 16 * q^82 + 8 * q^83 - 19 * q^84 - 28 * q^85 - 16 * q^86 + 11 * q^87 - 65 * q^88 + 15 * q^89 + 10 * q^90 - 3 * q^91 - 18 * q^92 - 12 * q^93 - 28 * q^94 - 5 * q^95 + 16 * q^96 - 35 * q^97 + 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	2.06264			1.45850			0.729252	−	0.684245i	$-0.239868\pi$
$2$	2.06264			1.45850			0.729252	+	0.684245i	$0.239868\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	2.25447			1.12724
$5$	1.20043	+	2.07920i	0.536847	+	0.929846i	0.999071	+	0.0430835i	$0.0137181\pi$
$5$	1.20043	+	2.07920i	0.536847	+	0.929846i	−0.462224	+	0.886763i	$0.652949\pi$
$6$	1.03132	+	1.78630i	0.421034	+	0.729252i
$7$	1.31301			0.496270			0.248135	−	0.968725i	$-0.420182\pi$
$7$	1.31301			0.496270			0.248135	+	0.968725i	$0.420182\pi$
$8$	0.524880			0.185573
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.47604	+	4.28863i	0.782994	+	1.35619i
$11$	−1.50523	−	2.60714i	−0.453844	−	0.786081i	0.544777	−	0.838581i	$-0.316614\pi$
$11$	−1.50523	−	2.60714i	−0.453844	−	0.786081i	−0.998621	+	0.0525001i	$0.983281\pi$
$12$	1.12724	+	1.95243i	0.325405	+	0.563618i
$13$	−0.726515	+	1.25836i	−0.201499	+	0.349006i	−0.949012	−	0.315241i	$-0.897915\pi$
$13$	−0.726515	+	1.25836i	−0.201499	+	0.349006i	0.747513	+	0.664248i	$0.231248\pi$
$14$	2.70826			0.723812
$15$	−1.20043	+	2.07920i	−0.309949	+	0.536847i
$16$	−3.42630			−0.856576
$17$	−2.47324	−	4.28378i	−0.599849	−	1.03897i	−0.992843	−	0.119428i	$-0.961894\pi$
$17$	−2.47324	−	4.28378i	−0.599849	−	1.03897i	0.392993	−	0.919541i	$-0.371440\pi$
$18$	−1.03132	+	1.78630i	−0.243084	+	0.421034i
$19$	−0.558826	−	0.967916i	−0.128204	−	0.222055i	0.794777	−	0.606901i	$-0.207588\pi$
$19$	−0.558826	−	0.967916i	−0.128204	−	0.222055i	−0.922981	+	0.384846i	$0.874254\pi$
$20$	2.70633	+	4.68749i	0.605153	+	1.04816i
$21$	0.656504	+	1.13710i	0.143261	+	0.248135i
$22$	−3.10474	−	5.37757i	−0.661934	−	1.14650i
$23$	4.06211			0.847009			0.423505	−	0.905894i	$-0.360800\pi$
$23$	4.06211			0.847009			0.423505	+	0.905894i	$0.360800\pi$
$24$	0.262440	+	0.454559i	0.0535703	+	0.0927865i
$25$	−0.382048	+	0.661727i	−0.0764097	+	0.132345i
$26$	−1.49854	+	2.59554i	−0.293887	+	0.509027i
$27$	−1.00000			−0.192450
$28$	2.96014			0.559413
$29$	9.91749			1.84163			0.920816	−	0.389998i	$-0.127524\pi$
$29$	9.91749			1.84163			0.920816	+	0.389998i	$0.127524\pi$
$30$	−2.47604	+	4.28863i	−0.452062	+	0.782994i
$31$	−0.895501	+	1.55105i	−0.160837	+	0.278577i	−0.935169	−	0.354202i	$-0.884753\pi$
$31$	−0.895501	+	1.55105i	−0.160837	+	0.278577i	0.774332	+	0.632779i	$0.218086\pi$
$32$	−8.11698			−1.43489
$33$	1.50523	−	2.60714i	0.262027	−	0.453844i
$34$	−5.10140	−	8.83589i	−0.874883	−	1.51534i
$35$	1.57617	+	2.73001i	0.266421	+	0.461455i
$36$	−1.12724	+	1.95243i	−0.187873	+	0.325405i
$37$	2.08935	−	3.61886i	0.343487	−	0.594937i	−0.641591	−	0.767047i	$-0.721725\pi$
$37$	2.08935	−	3.61886i	0.343487	−	0.594937i	0.985078	+	0.172110i	$0.0550586\pi$
$38$	−1.15266	−	1.99646i	−0.186985	−	0.323868i
$39$	−1.45303			−0.232671
$40$	0.630080	+	1.09133i	0.0996244	+	0.172554i
$41$	−1.59561			−0.249192			−0.124596	−	0.992208i	$-0.539763\pi$
$41$	−1.59561			−0.249192			−0.124596	+	0.992208i	$0.539763\pi$
$42$	1.35413	+	2.34542i	0.208947	+	0.361906i
$43$	−1.59152	+	2.75660i	−0.242705	+	0.420377i	−0.961484	−	0.274861i	$-0.911368\pi$
$43$	−1.59152	+	2.75660i	−0.242705	+	0.420377i	0.718779	+	0.695239i	$0.244701\pi$
$44$	−3.39350	−	5.87771i	−0.511589	−	0.886098i
$45$	−2.40085			−0.357898
$46$	8.37866			1.23537
$47$	−0.813858	+	1.40964i	−0.118713	+	0.205618i	−0.919258	−	0.393656i	$-0.871210\pi$
$47$	−0.813858	+	1.40964i	−0.118713	+	0.205618i	0.800545	+	0.599273i	$0.204544\pi$
$48$	−1.71315	−	2.96727i	−0.247272	−	0.428288i
$49$	−5.27601			−0.753716
$50$	−0.788027	+	1.36490i	−0.111444	+	0.193026i
$51$	2.47324	−	4.28378i	0.346323	−	0.599849i
$52$	−1.63791	+	2.83694i	−0.227137	+	0.393412i
$53$	3.85707	−	6.68064i	0.529810	−	0.917657i	−0.469586	−	0.882887i	$-0.655597\pi$
$53$	3.85707	−	6.68064i	0.529810	−	0.917657i	0.999395	−	0.0347702i	$-0.0110699\pi$
$54$	−2.06264			−0.280689
$55$	3.61384	−	6.25935i	0.487290	−	0.844011i
$56$	0.689171			0.0920944
$57$	0.558826	−	0.967916i	0.0740184	−	0.128204i
$58$	20.4562			2.68603
$59$	−8.25664			−1.07492			−0.537461	−	0.843288i	$-0.680617\pi$
$59$	−8.25664			−1.07492			−0.537461	+	0.843288i	$0.680617\pi$
$60$	−2.70633	+	4.68749i	−0.349385	+	0.605153i
$61$	3.20343	+	5.54851i	0.410158	+	0.710414i	0.994907	−	0.100800i	$-0.0321404\pi$
$61$	3.20343	+	5.54851i	0.410158	+	0.710414i	−0.584749	+	0.811214i	$0.698807\pi$
$62$	−1.84709	+	3.19926i	−0.234581	+	0.406306i
$63$	−0.656504	+	1.13710i	−0.0827117	+	0.143261i
$64$	−9.88977			−1.23622
$65$	−3.48851			−0.432696
$66$	3.10474	−	5.37757i	0.382168	−	0.661934i
$67$	−10.2951			−1.25774			−0.628872	−	0.777509i	$-0.716483\pi$
$67$	−10.2951			−1.25774			−0.628872	+	0.777509i	$0.716483\pi$
$68$	−5.57585	−	9.65766i	−0.676171	−	1.17116i
$69$	2.03106	+	3.51789i	0.244510	+	0.423505i
$70$	3.25106	+	5.63101i	0.388577	+	0.673034i
$71$	2.03662	−	3.52754i	0.241703	−	0.418641i	−0.719497	−	0.694496i	$-0.755627\pi$
$71$	2.03662	−	3.52754i	0.241703	−	0.418641i	0.961199	+	0.275854i	$0.0889608\pi$
$72$	−0.262440	+	0.454559i	−0.0309288	+	0.0535703i
$73$	1.15252	+	1.99622i	0.134892	+	0.233640i	0.925556	−	0.378610i	$-0.123598\pi$
$73$	1.15252	+	1.99622i	0.134892	+	0.233640i	−0.790664	+	0.612250i	$0.790265\pi$
$74$	4.30957	−	7.46439i	0.500977	−	0.867718i
$75$	−0.764097			−0.0882303
$76$	−1.25986	−	2.18214i	−0.144516	−	0.250308i
$77$	−1.97638	−	3.42319i	−0.225229	−	0.390109i
$78$	−2.99707			−0.339351
$79$	−3.95769			−0.445275			−0.222637	−	0.974901i	$-0.571467\pi$
$79$	−3.95769			−0.445275			−0.222637	+	0.974901i	$0.571467\pi$
$80$	−4.11303	−	7.12397i	−0.459850	−	0.796484i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.29116			−0.363447
$83$	−1.00141	+	1.73449i	−0.109919	+	0.190385i	−0.915737	−	0.401778i	$-0.868392\pi$
$83$	−1.00141	+	1.73449i	−0.109919	+	0.190385i	0.805818	+	0.592163i	$0.201726\pi$
$84$	1.48007	+	2.56355i	0.161489	+	0.279707i
$85$	5.93789	−	10.2847i	0.644055	−	1.11554i
$86$	−3.28273	+	5.68586i	−0.353986	+	0.613122i
$87$	4.95874	+	8.58880i	0.531633	+	0.920816i
$88$	−0.790065	−	1.36843i	−0.0842212	−	0.145875i
$89$	−0.254698	−	0.441149i	−0.0269979	−	0.0467617i	0.852211	−	0.523199i	$-0.175261\pi$
$89$	−0.254698	−	0.441149i	−0.0269979	−	0.0467617i	−0.879209	+	0.476437i	$0.841928\pi$
$90$	−4.95209			−0.521996
$91$	−0.953919	+	1.65224i	−0.0999979	+	0.173201i
$92$	9.15791			0.954779
$93$	−1.79100			−0.185718
$94$	−1.67869	+	2.90758i	−0.173144	+	0.299894i
$95$	1.34166	−	2.32382i	0.137651	−	0.238419i
$96$	−4.05849	−	7.02951i	−0.414218	−	0.717447i
$97$	−7.07399	+	12.2525i	−0.718255	+	1.24405i	0.243436	+	0.969917i	$0.421725\pi$
$97$	−7.07399	+	12.2525i	−0.718255	+	1.24405i	−0.961691	+	0.274137i	$0.911608\pi$
$98$	−10.8825			−1.09930
$99$	3.01046			0.302563
$100$	−0.861317	+	1.49184i	−0.0861317	+	0.149184i
$101$	−6.89948			−0.686523			−0.343262	−	0.939240i	$-0.611532\pi$
$101$	−6.89948			−0.686523			−0.343262	+	0.939240i	$0.611532\pi$
$102$	5.10140	−	8.83589i	0.505114	−	0.874883i
$103$	−14.6752			−1.44599			−0.722994	−	0.690854i	$-0.757235\pi$
$103$	−14.6752			−1.44599			−0.722994	+	0.690854i	$0.757235\pi$
$104$	−0.381333	+	0.660488i	−0.0373928	+	0.0647662i
$105$	−1.57617	+	2.73001i	−0.153818	+	0.266421i
$106$	7.95574	−	13.7797i	0.772730	−	1.33841i
$107$	1.09497	−	1.89654i	0.105855	−	0.183346i	−0.808232	−	0.588864i	$-0.799576\pi$
$107$	1.09497	−	1.89654i	0.105855	−	0.183346i	0.914087	+	0.405518i	$0.132909\pi$
$108$	−2.25447			−0.216937
$109$	7.06626	+	12.2391i	0.676825	+	1.17230i	0.975932	+	0.218076i	$0.0699781\pi$
$109$	7.06626	+	12.2391i	0.676825	+	1.17230i	−0.299107	+	0.954220i	$0.596689\pi$
$110$	7.45403	−	12.9108i	0.710714	−	1.23099i
$111$	4.17870			0.396625
$112$	−4.49876			−0.425093
$113$	7.85572	+	13.6065i	0.739004	+	1.27999i	0.952944	+	0.303146i	$0.0980369\pi$
$113$	7.85572	+	13.6065i	0.739004	+	1.27999i	−0.213940	+	0.976847i	$0.568630\pi$
$114$	1.15266	−	1.99646i	0.107956	−	0.186985i
$115$	4.87627	+	8.44595i	0.454714	+	0.787589i
$116$	22.3587			2.07595
$117$	−0.726515	−	1.25836i	−0.0671663	−	0.116335i
$118$	−17.0304			−1.56778
$119$	−3.24739	−	5.62464i	−0.297687	−	0.515610i
$120$	−0.630080	+	1.09133i	−0.0575181	+	0.0996244i
$121$	0.968563	−	1.67760i	0.0880511	−	0.152509i
$122$	6.60752	+	11.4446i	0.598217	+	1.03614i
$123$	−0.797803	−	1.38184i	−0.0719355	−	0.124596i
$124$	−2.01888	+	3.49680i	−0.181301	+	0.314022i
$125$	10.1698			0.909613
$126$	−1.35413	+	2.34542i	−0.120635	+	0.208947i
$127$	5.85302	−	10.1377i	0.519372	−	0.899579i	−0.480375	−	0.877063i	$-0.659499\pi$
$127$	5.85302	−	10.1377i	0.519372	−	0.899579i	0.999747	−	0.0225151i	$-0.00716740\pi$
$128$	−4.16505			−0.368142
$129$	−3.18305			−0.280252
$130$	−7.19553			−0.631090
$131$	10.3921	−	17.9996i	0.907960	−	1.57263i	0.0910671	−	0.995845i	$-0.470972\pi$
$131$	10.3921	−	17.9996i	0.907960	−	1.57263i	0.816893	−	0.576789i	$-0.195694\pi$
$132$	3.39350	−	5.87771i	0.295366	−	0.511589i
$133$	−0.733743	−	1.27088i	−0.0636236	−	0.110199i
$134$	−21.2350			−1.83443
$135$	−1.20043	−	2.07920i	−0.103316	−	0.178949i
$136$	−1.29816	−	2.24847i	−0.111316	−	0.192805i
$137$	−1.67618	−	2.90323i	−0.143206	−	0.248039i	0.785496	−	0.618866i	$-0.212408\pi$
$137$	−1.67618	−	2.90323i	−0.143206	−	0.248039i	−0.928702	+	0.370827i	$0.879074\pi$
$138$	4.18933	+	7.25614i	0.356620	+	0.617683i
$139$	−6.55336	+	11.3507i	−0.555848	+	0.962758i	0.441989	+	0.897021i	$0.354273\pi$
$139$	−6.55336	+	11.3507i	−0.555848	+	0.962758i	−0.997837	+	0.0657370i	$0.979060\pi$
$140$	3.55343	+	6.15472i	0.300319	+	0.520168i
$141$	−1.62772			−0.137078
$142$	4.20081	−	7.27602i	0.352525	−	0.610590i
$143$	4.37429			0.365796
$144$	1.71315	−	2.96727i	0.142763	−	0.247272i
$145$	11.9052	+	20.6204i	0.988674	+	1.71243i
$146$	2.37723	+	4.11748i	0.196741	+	0.340765i
$147$	−2.63801	−	4.56916i	−0.217579	−	0.376858i
$148$	4.71038	−	8.15861i	0.387191	−	0.670634i
$149$	−16.6116			−1.36087			−0.680437	−	0.732807i	$-0.738210\pi$
$149$	−16.6116			−1.36087			−0.680437	+	0.732807i	$0.738210\pi$
$150$	−1.57605			−0.128684
$151$	1.23368	+	2.13680i	0.100396	+	0.173890i	0.911848	−	0.410529i	$-0.134656\pi$
$151$	1.23368	+	2.13680i	0.100396	+	0.173890i	−0.811452	+	0.584419i	$0.801322\pi$
$152$	−0.293317	−	0.508039i	−0.0237911	−	0.0412074i
$153$	4.94649			0.399900
$154$	−4.07655	−	7.06080i	−0.328498	−	0.568975i
$155$	−4.29993			−0.345379
$156$	−3.27581			−0.262275
$157$	−0.855619	+	12.5007i	−0.0682858	+	0.997666i
$157$	−0.855619	+	12.5007i	−0.0682858	+	0.997666i
$158$	−8.16327			−0.649435
$159$	7.71414			0.611771
$160$	−9.74384	−	16.8768i	−0.770318	−	1.33423i
$161$	5.33359			0.420345
$162$	−1.03132	−	1.78630i	−0.0810280	−	0.140345i
$163$	6.09881	+	10.5634i	0.477696	+	0.827393i	0.999673	−	0.0255662i	$-0.00813886\pi$
$163$	6.09881	+	10.5634i	0.477696	+	0.827393i	−0.521978	+	0.852959i	$0.674806\pi$
$164$	−3.59725			−0.280898
$165$	7.22768			0.562674
$166$	−2.06555	+	3.57763i	−0.160317	+	0.277678i
$167$	5.53424	+	9.58558i	0.428252	+	0.741754i	0.996718	−	0.0809526i	$-0.0257962\pi$
$167$	5.53424	+	9.58558i	0.428252	+	0.741754i	−0.568466	+	0.822707i	$0.692463\pi$
$168$	0.344586	+	0.596840i	0.0265854	+	0.0460472i
$169$	5.44435	+	9.42990i	0.418796	+	0.725377i
$170$	12.2477	−	21.2137i	0.939357	−	1.62701i
$171$	1.11765			0.0854690
$172$	−3.58804	+	6.21467i	−0.273586	+	0.473864i
$173$	18.2382			1.38663			0.693313	−	0.720637i	$-0.256150\pi$
$173$	18.2382			1.38663			0.693313	+	0.720637i	$0.256150\pi$
$174$	10.2281	+	17.7156i	0.775389	+	1.34301i
$175$	−0.501632	+	0.868853i	−0.0379198	+	0.0656791i
$176$	5.15738	+	8.93284i	0.388752	+	0.673338i
$177$	−4.12832	−	7.15046i	−0.310304	−	0.537461i
$178$	−0.525349	−	0.909930i	−0.0393765	−	0.0682022i
$179$	−7.42124	−	12.8540i	−0.554690	−	0.960751i	−0.997928	−	0.0643468i	$-0.979504\pi$
$179$	−7.42124	−	12.8540i	−0.554690	−	0.960751i	0.443238	−	0.896404i	$-0.353830\pi$
$180$	−5.41265			−0.403435
$181$	4.67163	+	8.09151i	0.347240	+	0.601437i	0.985758	−	0.168170i	$-0.0537857\pi$
$181$	4.67163	+	8.09151i	0.347240	+	0.601437i	−0.638518	+	0.769607i	$0.720452\pi$
$182$	−1.96759	+	3.40796i	−0.145847	+	0.252615i
$183$	−3.20343	+	5.54851i	−0.236805	+	0.410158i
$184$	2.13212			0.157182
$185$	10.0324			0.737600
$186$	−3.69419			−0.270871
$187$	−7.44560	+	12.8962i	−0.544476	+	0.943060i
$188$	−1.83482	+	3.17800i	−0.133818	+	0.231779i
$189$	−1.31301			−0.0955073
$190$	2.76736	−	4.79320i	0.200765	−	0.347736i
$191$	−4.34024	−	7.51751i	−0.314048	−	0.543948i	0.665186	−	0.746677i	$-0.268352\pi$
$191$	−4.34024	−	7.51751i	−0.314048	−	0.543948i	−0.979235	+	0.202730i	$0.935019\pi$
$192$	−4.94489	−	8.56480i	−0.356866	−	0.618111i
$193$	−6.85366	+	11.8709i	−0.493337	+	0.854485i	−0.999971	−	0.00767682i	$-0.997556\pi$
$193$	−6.85366	+	11.8709i	−0.493337	+	0.854485i	0.506634	+	0.862161i	$0.330890\pi$
$194$	−14.5911	+	25.2725i	−1.04758	+	1.81446i
$195$	−1.74425	−	3.02114i	−0.124909	−	0.216348i
$196$	−11.8946			−0.849615
$197$	−7.16554	−	12.4111i	−0.510524	−	0.884253i	−0.999926	−	0.0121946i	$-0.996118\pi$
$197$	−7.16554	−	12.4111i	−0.510524	−	0.884253i	0.489402	−	0.872058i	$-0.337215\pi$
$198$	6.20949			0.441289
$199$	−3.69328	−	6.39695i	−0.261810	−	0.453468i	0.704913	−	0.709294i	$-0.250986\pi$
$199$	−3.69328	−	6.39695i	−0.261810	−	0.453468i	−0.966723	+	0.255826i	$0.917653\pi$
$200$	−0.200529	+	0.347327i	−0.0141796	+	0.0245597i
$201$	−5.14754	−	8.91580i	−0.363080	−	0.628872i
$202$	−14.2311			−1.00130
$203$	13.0217			0.913947
$204$	5.57585	−	9.65766i	0.390388	−	0.676171i
$205$	−1.91541	−	3.31758i	−0.133778	−	0.231710i
$206$	−30.2696			−2.10898
$207$	−2.03106	+	3.51789i	−0.141168	+	0.244510i
$208$	2.48926	−	4.31152i	0.172599	−	0.298950i
$209$	−1.68233	+	2.91387i	−0.116369	+	0.201557i
$210$	−3.25106	+	5.63101i	−0.224345	+	0.388577i
$211$	9.13122			0.628619			0.314310	−	0.949321i	$-0.398227\pi$
$211$	9.13122			0.628619			0.314310	+	0.949321i	$0.398227\pi$
$212$	8.69565	−	15.0613i	0.597220	−	1.03442i
$213$	4.07325			0.279094
$214$	2.25852	−	3.91187i	0.154389	−	0.267410i
$215$	−7.64203			−0.521182
$216$	−0.524880			−0.0357136
$217$	−1.17580	+	2.03654i	−0.0798185	+	0.138250i
$218$	14.5751	+	25.2449i	0.987153	+	1.70980i
$219$	−1.15252	+	1.99622i	−0.0778800	+	0.134892i
$220$	8.14729	−	14.1115i	0.549290	−	0.951398i
$221$	7.18739			0.483476
$222$	8.61914			0.578479
$223$	4.54023	−	7.86391i	0.304036	−	0.526606i	−0.673010	−	0.739633i	$-0.734999\pi$
$223$	4.54023	−	7.86391i	0.304036	−	0.526606i	0.977046	+	0.213027i	$0.0683322\pi$
$224$	−10.6577			−0.712095
$225$	−0.382048	−	0.661727i	−0.0254699	−	0.0441151i
$226$	16.2035	+	28.0653i	1.07784	+	1.86687i
$227$	−8.49317	−	14.7106i	−0.563711	−	0.976377i	−0.997168	−	0.0752025i	$-0.976040\pi$
$227$	−8.49317	−	14.7106i	−0.563711	−	0.976377i	0.433457	−	0.901174i	$-0.357294\pi$
$228$	1.25986	−	2.18214i	0.0834361	−	0.144516i
$229$	−4.34778	+	7.53058i	−0.287310	+	0.497635i	−0.973167	−	0.230102i	$-0.926094\pi$
$229$	−4.34778	+	7.53058i	−0.287310	+	0.497635i	0.685857	+	0.727736i	$0.259428\pi$
$230$	10.0580	+	17.4209i	0.663203	+	1.14870i
$231$	1.97638	−	3.42319i	0.130036	−	0.225229i
$232$	5.20549			0.341757
$233$	−8.09877	−	14.0275i	−0.530568	−	0.918971i	−0.999364	−	0.0356642i	$-0.988645\pi$
$233$	−8.09877	−	14.0275i	−0.530568	−	0.918971i	0.468796	−	0.883307i	$-0.344688\pi$
$234$	−1.49854	−	2.59554i	−0.0979623	−	0.169676i
$235$	−3.90791			−0.254924
$236$	−18.6143			−1.21169
$237$	−1.97884	−	3.42746i	−0.128540	−	0.222637i
$238$	−6.69818	−	11.6016i	−0.434178	−	0.752019i
$239$	27.1219			1.75437			0.877185	−	0.480152i	$-0.159418\pi$
$239$	27.1219			1.75437			0.877185	+	0.480152i	$0.159418\pi$
$240$	4.11303	−	7.12397i	0.265495	−	0.459850i
$241$	5.02743	+	8.70777i	0.323845	+	0.560916i	0.981278	−	0.192597i	$-0.0616909\pi$
$241$	5.02743	+	8.70777i	0.323845	+	0.560916i	−0.657433	+	0.753513i	$0.728358\pi$
$242$	1.99779	−	3.46028i	0.128423	−	0.222435i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	7.22205	+	12.5089i	0.462344	+	0.800803i
$245$	−6.33346	−	10.9699i	−0.404630	−	0.700840i
$246$	−1.64558	−	2.85022i	−0.104918	−	0.181724i
$247$	1.62398			0.103332
$248$	−0.470030	+	0.814116i	−0.0298470	+	0.0516964i
$249$	−2.00282			−0.126924
$250$	20.9766			1.32667
$251$	11.1405	−	19.2959i	0.703180	−	1.21794i	−0.264164	−	0.964478i	$-0.585096\pi$
$251$	11.1405	−	19.2959i	0.703180	−	1.21794i	0.967344	−	0.253466i	$-0.0815705\pi$
$252$	−1.48007	+	2.56355i	−0.0932355	+	0.161489i
$253$	−6.11442	−	10.5905i	−0.384410	−	0.665818i
$254$	12.0727	−	20.9105i	0.757506	−	1.31204i
$255$	11.8758			0.743691
$256$	11.1886			0.699285
$257$	−3.90353	+	6.76111i	−0.243496	+	0.421747i	−0.961708	−	0.274078i	$-0.911627\pi$
$257$	−3.90353	+	6.76111i	−0.243496	+	0.421747i	0.718212	+	0.695824i	$0.244961\pi$
$258$	−6.56547			−0.408748
$259$	2.74333	−	4.75159i	0.170462	−	0.295249i
$260$	−7.86474			−0.487751
$261$	−4.95874	+	8.58880i	−0.306939	+	0.531633i
$262$	21.4351	−	37.1267i	1.32426	−	2.29369i
$263$	−11.3660	+	19.6865i	−0.700859	+	1.21392i	0.267306	+	0.963612i	$0.413866\pi$
$263$	−11.3660	+	19.6865i	−0.700859	+	1.21392i	−0.968165	+	0.250312i	$0.919467\pi$
$264$	0.790065	−	1.36843i	0.0486251	−	0.0842212i
$265$	18.5205			1.13771
$266$	−1.51345	−	2.62137i	−0.0927953	−	0.160726i
$267$	0.254698	−	0.441149i	0.0155872	−	0.0269979i
$268$	−23.2100			−1.41777
$269$	−14.5260			−0.885665			−0.442833	−	0.896604i	$-0.646026\pi$
$269$	−14.5260			−0.885665			−0.442833	+	0.896604i	$0.646026\pi$
$270$	−2.47604	−	4.28863i	−0.150687	−	0.260998i
$271$	−5.21238	+	9.02810i	−0.316629	+	0.548418i	−0.979782	−	0.200066i	$-0.935884\pi$
$271$	−5.21238	+	9.02810i	−0.316629	+	0.548418i	0.663153	+	0.748484i	$0.269218\pi$
$272$	8.47408	+	14.6775i	0.513817	+	0.889957i
$273$	−1.90784			−0.115468
$274$	−3.45735	−	5.98830i	−0.208866	−	0.361766i
$275$	2.30028			0.138712
$276$	4.57896	+	7.93099i	0.275621	+	0.477389i
$277$	4.03810	−	6.99420i	0.242626	−	0.420241i	−0.718835	−	0.695180i	$-0.755325\pi$
$277$	4.03810	−	6.99420i	0.242626	−	0.420241i	0.961462	+	0.274940i	$0.0886578\pi$
$278$	−13.5172	+	23.4125i	−0.810707	+	1.40419i
$279$	−0.895501	−	1.55105i	−0.0536122	−	0.0928591i
$280$	0.827300	+	1.43292i	0.0494406	+	0.0856336i
$281$	−11.3514	+	19.6612i	−0.677169	+	1.17289i	0.298661	+	0.954359i	$0.403460\pi$
$281$	−11.3514	+	19.6612i	−0.677169	+	1.17289i	−0.975830	+	0.218532i	$0.929873\pi$
$282$	−3.35739			−0.199929
$283$	12.0243	−	20.8267i	0.714769	−	1.23802i	−0.248279	−	0.968689i	$-0.579865\pi$
$283$	12.0243	−	20.8267i	0.714769	−	1.23802i	0.963048	−	0.269328i	$-0.0868017\pi$
$284$	4.59151	−	7.95272i	0.272456	−	0.471907i
$285$	2.68332			0.158946
$286$	9.02257			0.533516
$287$	−2.09504			−0.123666
$288$	4.05849	−	7.02951i	0.239149	−	0.414218i
$289$	−3.73386	+	6.46723i	−0.219639	+	0.380425i
$290$	24.5561	+	42.5325i	1.44199	+	2.49759i
$291$	−14.1480			−0.829369
$292$	2.59832	+	4.50042i	0.152055	+	0.263367i
$293$	13.1335	+	22.7480i	0.767270	+	1.32895i	0.939038	+	0.343813i	$0.111719\pi$
$293$	13.1335	+	22.7480i	0.767270	+	1.32895i	−0.171768	+	0.985137i	$0.554948\pi$
$294$	−5.44125	−	9.42452i	−0.317340	−	0.549649i
$295$	−9.91149	−	17.1672i	−0.577069	−	0.999513i
$296$	1.09666	−	1.89947i	0.0637419	−	0.110404i
$297$	1.50523	+	2.60714i	0.0873423	+	0.151281i
$298$	−34.2637			−1.98484
$299$	−2.95118	+	5.11160i	−0.170671	+	0.295612i
$300$	−1.72263			−0.0994563
$301$	−2.08968	+	3.61943i	−0.120447	+	0.208621i
$302$	2.54464	+	4.40744i	0.146427	+	0.253620i
$303$	−3.44974	−	5.97512i	−0.198182	−	0.343262i
$304$	1.91471	+	3.31637i	0.109816	+	0.190207i
$305$	−7.69097	+	13.3212i	−0.440384	+	0.762767i
$306$	10.2028			0.583255
$307$	4.32013			0.246563			0.123281	−	0.992372i	$-0.460658\pi$
$307$	4.32013			0.246563			0.123281	+	0.992372i	$0.460658\pi$
$308$	−4.45569	−	7.71748i	−0.253886	−	0.439744i
$309$	−7.33759	−	12.7091i	−0.417421	−	0.722994i
$310$	−8.86920			−0.503737
$311$	13.0203	+	22.5519i	0.738316	+	1.27880i	0.953253	+	0.302172i	$0.0977118\pi$
$311$	13.0203	+	22.5519i	0.738316	+	1.27880i	−0.214938	+	0.976628i	$0.568955\pi$
$312$	−0.762666			−0.0431774
$313$	14.4906			0.819055			0.409527	−	0.912298i	$-0.365694\pi$
$313$	14.4906			0.819055			0.409527	+	0.912298i	$0.365694\pi$
$314$	−1.76483	+	25.7844i	−0.0995952	+	1.45510i
$315$	−3.15234			−0.177614
$316$	−8.92249			−0.501929
$317$	4.76032	+	8.24512i	0.267366	+	0.463092i	0.968181	−	0.250252i	$-0.0805133\pi$
$317$	4.76032	+	8.24512i	0.267366	+	0.463092i	−0.700815	+	0.713343i	$0.747180\pi$
$318$	15.9115			0.892271
$319$	−14.9281	−	25.8562i	−0.835813	−	1.44767i
$320$	−11.8719	−	20.5628i	−0.663662	−	1.14950i
$321$	2.18994			0.122230
$322$	11.0013			0.613076
$323$	−2.76423	+	4.78778i	−0.153806	+	0.266399i
$324$	−1.12724	−	1.95243i	−0.0626242	−	0.108468i
$325$	−0.555127	−	0.961509i	−0.0307929	−	0.0533349i
$326$	12.5796	+	21.7886i	0.696721	+	1.20676i
$327$	−7.06626	+	12.2391i	−0.390765	+	0.676825i
$328$	−0.837502			−0.0462433
$329$	−1.06860	+	1.85087i	−0.0589139	+	0.102042i
$330$	14.9081			0.820662
$331$	−8.72537	−	15.1128i	−0.479590	−	0.830674i	0.520136	−	0.854083i	$-0.325881\pi$
$331$	−8.72537	−	15.1128i	−0.479590	−	0.830674i	−0.999726	+	0.0234095i	$0.992548\pi$
$332$	−2.25765	+	3.91036i	−0.123905	+	0.214609i
$333$	2.08935	+	3.61886i	0.114496	+	0.198312i
$334$	11.4151	+	19.7716i	0.624607	+	1.08185i
$335$	−12.3585	−	21.4055i	−0.675216	−	1.16951i
$336$	−2.24938	−	3.89604i	−0.122714	−	0.212547i
$337$	13.5896			0.740273			0.370136	−	0.928977i	$-0.379311\pi$
$337$	13.5896			0.740273			0.370136	+	0.928977i	$0.379311\pi$
$338$	11.2297	+	19.4505i	0.610816	+	1.05797i
$339$	−7.85572	+	13.6065i	−0.426664	+	0.739004i
$340$	13.3868	−	23.1866i	0.726001	−	1.25747i
$341$	5.39174			0.291979
$342$	2.30531			0.124657
$343$	−16.1185			−0.870317
$344$	−0.835358	+	1.44688i	−0.0450395	+	0.0780107i
$345$	−4.87627	+	8.44595i	−0.262530	+	0.454714i
$346$	37.6188			2.02240
$347$	−3.43982	+	5.95794i	−0.184659	+	0.319839i	−0.943462	−	0.331482i	$-0.892451\pi$
$347$	−3.43982	+	5.95794i	−0.184659	+	0.319839i	0.758802	+	0.651321i	$0.225785\pi$
$348$	11.1793	+	19.3632i	0.599276	+	1.03798i
$349$	6.34205	+	10.9848i	0.339482	+	0.588000i	0.984335	−	0.176306i	$-0.0564148\pi$
$349$	6.34205	+	10.9848i	0.339482	+	0.588000i	−0.644853	+	0.764306i	$0.723082\pi$
$350$	−1.03469	+	1.79213i	−0.0553063	+	0.0957932i
$351$	0.726515	−	1.25836i	0.0387785	−	0.0671663i
$352$	12.2179	+	21.1621i	0.651218	+	1.12794i
$353$	33.8244			1.80029			0.900145	−	0.435590i	$-0.143460\pi$
$353$	33.8244			1.80029			0.900145	+	0.435590i	$0.143460\pi$
$354$	−8.51522	−	14.7488i	−0.452579	−	0.783890i
$355$	9.77927			0.519030
$356$	−0.574208	−	0.994558i	−0.0304330	−	0.0527114i
$357$	3.24739	−	5.62464i	0.171870	−	0.297687i
$358$	−15.3073	−	26.5131i	−0.809017	−	1.40126i
$359$	−5.54733			−0.292777			−0.146388	−	0.989227i	$-0.546765\pi$
$359$	−5.54733			−0.292777			−0.146388	+	0.989227i	$0.546765\pi$
$360$	−1.26016			−0.0664162
$361$	8.87543	−	15.3727i	0.467128	−	0.809089i
$362$	9.63588	+	16.6898i	0.506451	+	0.877199i
$363$	1.93713			0.101673
$364$	−2.15058	+	3.72492i	−0.112721	+	0.195239i
$365$	−2.76703	+	4.79263i	−0.144833	+	0.250858i
$366$	−6.60752	+	11.4446i	−0.345381	+	0.598217i
$367$	−11.0861	+	19.2016i	−0.578688	+	1.00232i	0.416942	+	0.908933i	$0.363102\pi$
$367$	−11.0861	+	19.2016i	−0.578688	+	1.00232i	−0.995630	+	0.0933846i	$0.970231\pi$
$368$	−13.9180			−0.725528
$369$	0.797803	−	1.38184i	0.0415320	−	0.0719355i
$370$	20.6933			1.07579
$371$	5.06436	−	8.77174i	0.262929	−	0.455406i
$372$	−4.03776			−0.209348
$373$	−13.5746			−0.702864			−0.351432	−	0.936213i	$-0.614305\pi$
$373$	−13.5746			−0.702864			−0.351432	+	0.936213i	$0.614305\pi$
$374$	−15.3576	+	26.6001i	−0.794121	+	1.37546i
$375$	5.08489	+	8.80729i	0.262583	+	0.454807i
$376$	−0.427178	+	0.739893i	−0.0220300	+	0.0381571i
$377$	−7.20520	+	12.4798i	−0.371087	+	0.642741i
$378$	−2.70826			−0.139298
$379$	6.36913			0.327160			0.163580	−	0.986530i	$-0.447696\pi$
$379$	6.36913			0.327160			0.163580	+	0.986530i	$0.447696\pi$
$380$	3.02473	−	5.23899i	0.155166	−	0.268755i
$381$	11.7060			0.599719
$382$	−8.95233	−	15.5059i	−0.458041	−	0.793350i
$383$	−1.41852	−	2.45694i	−0.0724828	−	0.125544i	0.827506	−	0.561457i	$-0.189759\pi$
$383$	−1.41852	−	2.45694i	−0.0724828	−	0.125544i	−0.899989	+	0.435913i	$0.856426\pi$
$384$	−2.08253	−	3.60704i	−0.106273	−	0.184071i
$385$	4.74500	−	8.21857i	0.241827	−	0.418857i
$386$	−14.1366	+	24.4853i	−0.719534	+	1.24627i
$387$	−1.59152	−	2.75660i	−0.0809016	−	0.140126i
$388$	−15.9481	+	27.6229i	−0.809642	+	1.40234i
$389$	−13.5357			−0.686285			−0.343143	−	0.939283i	$-0.611491\pi$
$389$	−13.5357			−0.686285			−0.343143	+	0.939283i	$0.611491\pi$
$390$	−3.59776	−	6.23151i	−0.182180	−	0.315545i
$391$	−10.0466	−	17.4012i	−0.508078	−	0.880017i
$392$	−2.76927			−0.139869
$393$	20.7842			1.04842
$394$	−14.7799	−	25.5996i	−0.744601	−	1.28969i
$395$	−4.75091	−	8.22882i	−0.239044	−	0.414037i
$396$	6.78699			0.341059
$397$	8.48780	−	14.7013i	0.425990	−	0.737837i	−0.570522	−	0.821282i	$-0.693259\pi$
$397$	8.48780	−	14.7013i	0.425990	−	0.737837i	0.996512	+	0.0834453i	$0.0265924\pi$
$398$	−7.61790	−	13.1946i	−0.381851	−	0.661385i
$399$	0.733743	−	1.27088i	0.0367331	−	0.0636236i
$400$	1.30901	−	2.26728i	0.0654507	−	0.113364i
$401$	−4.86035	−	8.41838i	−0.242715	−	0.420394i	0.718772	−	0.695246i	$-0.244704\pi$
$401$	−4.86035	−	8.41838i	−0.242715	−	0.420394i	−0.961487	+	0.274852i	$0.911371\pi$
$402$	−10.6175	−	18.3901i	−0.529553	−	0.917213i
$403$	−1.30119	−	2.25372i	−0.0648168	−	0.112266i
$404$	−15.5547			−0.773873
$405$	1.20043	−	2.07920i	0.0596497	−	0.103316i
$406$	26.8591			1.33300
$407$	−12.5798			−0.623558
$408$	1.29816	−	2.24847i	0.0642683	−	0.111316i
$409$	−0.0732384	+	0.126853i	−0.00362141	+	0.00627246i	−0.867830	−	0.496860i	$-0.834486\pi$
$409$	−0.0732384	+	0.126853i	−0.00362141	+	0.00627246i	0.864209	+	0.503133i	$0.167819\pi$
$410$	−3.95079	−	6.84297i	−0.195116	−	0.337950i
$411$	1.67618	−	2.90323i	0.0826798	−	0.143206i
$412$	−33.0847			−1.62997
$413$	−10.8410			−0.533452
$414$	−4.18933	+	7.25614i	−0.205894	+	0.356620i
$415$	−4.80848			−0.236039
$416$	5.89710	−	10.2141i	0.289129	−	0.500787i
$417$	−13.1067			−0.641838
$418$	−3.47003	+	6.01026i	−0.169724	+	0.293971i
$419$	18.2252	−	31.5669i	0.890358	−	1.54215i	0.0509120	−	0.998703i	$-0.483787\pi$
$419$	18.2252	−	31.5669i	0.890358	−	1.54215i	0.839446	−	0.543443i	$-0.182879\pi$
$420$	−3.55343	+	6.15472i	−0.173389	+	0.300319i
$421$	16.5365	−	28.6421i	0.805942	−	1.39593i	−0.109711	−	0.993963i	$-0.534993\pi$
$421$	16.5365	−	28.6421i	0.805942	−	1.39593i	0.915653	−	0.401969i	$-0.131674\pi$
$422$	18.8344			0.916844
$423$	−0.813858	−	1.40964i	−0.0395711	−	0.0685392i
$424$	2.02450	−	3.50654i	0.0983184	−	0.170292i
$425$	3.77959			0.183337
$426$	8.40163			0.407060
$427$	4.20613	+	7.28523i	0.203549	+	0.352557i
$428$	2.46857	−	4.27569i	0.119323	−	0.206673i
$429$	2.18714	+	3.78824i	0.105596	+	0.182898i
$430$	−15.7627			−0.760146
$431$	−14.9128	−	25.8297i	−0.718324	−	1.24417i	−0.961663	−	0.274233i	$-0.911576\pi$
$431$	−14.9128	−	25.8297i	−0.718324	−	1.24417i	0.243339	−	0.969941i	$-0.421757\pi$
$432$	3.42630			0.164848
$433$	−9.64164	−	16.6998i	−0.463348	−	0.802541i	0.535778	−	0.844359i	$-0.320018\pi$
$433$	−9.64164	−	16.6998i	−0.463348	−	0.802541i	−0.999125	+	0.0418176i	$0.986685\pi$
$434$	−2.42525	+	4.20065i	−0.116416	+	0.201638i
$435$	−11.9052	+	20.6204i	−0.570811	+	0.988674i
$436$	15.9307	+	27.5927i	0.762941	+	1.32145i
$437$	−2.27002	−	3.93178i	−0.108590	−	0.188083i
$438$	−2.37723	+	4.11748i	−0.113588	+	0.196741i
$439$	−2.04433			−0.0975703			−0.0487852	−	0.998809i	$-0.515535\pi$
$439$	−2.04433			−0.0975703			−0.0487852	+	0.998809i	$0.515535\pi$
$440$	1.89683	−	3.28541i	0.0904278	−	0.156626i
$441$	2.63801	−	4.56916i	0.125619	−	0.217579i
$442$	14.8250			0.705152
$443$	11.3127			0.537480			0.268740	−	0.963213i	$-0.413393\pi$
$443$	11.3127			0.537480			0.268740	+	0.963213i	$0.413393\pi$
$444$	9.42075			0.447089
$445$	0.611491	−	1.05913i	0.0289875	−	0.0502078i
$446$	9.36485	−	16.2204i	0.443438	−	0.768058i
$447$	−8.30579	−	14.3861i	−0.392850	−	0.680437i
$448$	−12.9853			−0.613500
$449$	−10.9205	−	18.9148i	−0.515370	−	0.892646i	−0.999841	−	0.0178391i	$-0.994321\pi$
$449$	−10.9205	−	18.9148i	−0.515370	−	0.892646i	0.484471	−	0.874807i	$-0.339012\pi$
$450$	−0.788027	−	1.36490i	−0.0371479	−	0.0643421i
$451$	2.40176	+	4.15996i	0.113094	+	0.195885i
$452$	17.7105	+	30.6755i	0.833031	+	1.44285i
$453$	−1.23368	+	2.13680i	−0.0579634	+	0.100396i
$454$	−17.5183	−	30.3426i	−0.822176	−	1.42405i
$455$	−4.58044			−0.214734
$456$	0.293317	−	0.508039i	0.0137358	−	0.0237911i
$457$	−14.5469			−0.680476			−0.340238	−	0.940339i	$-0.610508\pi$
$457$	−14.5469			−0.680476			−0.340238	+	0.940339i	$0.610508\pi$
$458$	−8.96790	+	15.5329i	−0.419042	+	0.725802i
$459$	2.47324	+	4.28378i	0.115441	+	0.199950i
$460$	10.9934	+	19.0411i	0.512570	+	0.887797i
$461$	8.90726	+	15.4278i	0.414852	+	0.718546i	0.995413	−	0.0956716i	$-0.0304999\pi$
$461$	8.90726	+	15.4278i	0.414852	+	0.718546i	−0.580560	+	0.814217i	$0.697167\pi$
$462$	4.07655	−	7.06080i	0.189658	−	0.328498i
$463$	−13.9092			−0.646413			−0.323207	−	0.946328i	$-0.604761\pi$
$463$	−13.9092			−0.646413			−0.323207	+	0.946328i	$0.604761\pi$
$464$	−33.9803			−1.57750
$465$	−2.14997	−	3.72385i	−0.0997023	−	0.172689i
$466$	−16.7048	−	28.9336i	−0.773836	−	1.34032i
$467$	9.49311			0.439289			0.219644	−	0.975580i	$-0.429510\pi$
$467$	9.49311			0.439289			0.219644	+	0.975580i	$0.429510\pi$
$468$	−1.63791	−	2.83694i	−0.0757122	−	0.131137i
$469$	−13.5175			−0.624181
$470$	−8.06059			−0.371807
$471$	−11.2537	+	5.50937i	−0.518545	+	0.253858i
$472$	−4.33374			−0.199477
$473$	9.58243			0.440601
$474$	−4.08164	−	7.06960i	−0.187476	−	0.324718i
$475$	0.853995			0.0391840
$476$	−7.32114	−	12.6806i	−0.335564	−	0.581213i
$477$	3.85707	+	6.68064i	0.176603	+	0.305886i
$478$	55.9427			2.55876
$479$	−41.3873			−1.89104			−0.945518	−	0.325570i	$-0.894444\pi$
$479$	−41.3873			−1.89104			−0.945518	+	0.325570i	$0.894444\pi$
$480$	9.74384	−	16.8768i	0.444743	−	0.770318i
$481$	3.03589	+	5.25831i	0.138424	+	0.239758i
$482$	10.3698	+	17.9610i	0.472330	+	0.818099i
$483$	2.66679	+	4.61902i	0.121343	+	0.210173i
$484$	2.18360	−	3.78210i	0.0992543	−	0.171914i
$485$	−33.9672			−1.54237
$486$	1.03132	−	1.78630i	0.0467816	−	0.0810280i
$487$	−28.2994			−1.28237			−0.641183	−	0.767388i	$-0.721556\pi$
$487$	−28.2994			−1.28237			−0.641183	+	0.767388i	$0.721556\pi$
$488$	1.68142	+	2.91230i	0.0761142	+	0.131834i
$489$	−6.09881	+	10.5634i	−0.275798	+	0.477696i
$490$	−13.0636	−	22.6269i	−0.590155	−	1.02218i
$491$	−8.52111	−	14.7590i	−0.384552	−	0.666064i	0.607155	−	0.794584i	$-0.292311\pi$
$491$	−8.52111	−	14.7590i	−0.384552	−	0.666064i	−0.991707	+	0.128520i	$0.958977\pi$
$492$	−1.79862	−	3.11531i	−0.0810882	−	0.140449i
$493$	−24.5284	−	42.4844i	−1.10470	−	1.91340i
$494$	3.34969			0.150709
$495$	3.61384	+	6.25935i	0.162430	+	0.281337i
$496$	3.06826	−	5.31438i	0.137769	−	0.238623i
$497$	2.67410	−	4.63168i	0.119950	−	0.207759i
$498$	−4.13109			−0.185119
$499$	−17.1657			−0.768443			−0.384222	−	0.923241i	$-0.625530\pi$
$499$	−17.1657			−0.768443			−0.384222	+	0.923241i	$0.625530\pi$
$500$	22.9275			1.02535
$501$	−5.53424	+	9.58558i	−0.247251	+	0.428252i
$502$	22.9787	−	39.8003i	1.02559	−	1.77638i
$503$	6.11879			0.272823			0.136412	−	0.990652i	$-0.456443\pi$
$503$	6.11879			0.272823			0.136412	+	0.990652i	$0.456443\pi$
$504$	−0.344586	+	0.596840i	−0.0153491	+	0.0265854i
$505$	−8.28231	−	14.3454i	−0.368558	−	0.638361i
$506$	−12.6118	−	21.8443i	−0.560664	−	0.971098i
$507$	−5.44435	+	9.42990i	−0.241792	+	0.418796i
$508$	13.1955	−	22.8552i	0.585454	−	1.01404i
$509$	4.54384	+	7.87015i	0.201402	+	0.348838i	0.948980	−	0.315335i	$-0.102117\pi$
$509$	4.54384	+	7.87015i	0.201402	+	0.348838i	−0.747578	+	0.664174i	$0.768784\pi$
$510$	24.4954			1.08468
$511$	1.51327	+	2.62105i	0.0669429	+	0.115949i
$512$	31.4080			1.38805
$513$	0.558826	+	0.967916i	0.0246728	+	0.0427345i
$514$	−8.05157	+	13.9457i	−0.355139	+	0.615120i
$515$	−17.6165	−	30.5126i	−0.776275	−	1.34455i
$516$	−7.17608			−0.315909
$517$	4.90017			0.215509
$518$	5.65850	−	9.80080i	0.248620	−	0.430623i
$519$	9.11911	+	15.7948i	0.400284	+	0.693313i
$520$	−1.83105			−0.0802968
$521$	14.1883	−	24.5749i	0.621601	−	1.07664i	−0.367587	−	0.929989i	$-0.619816\pi$
$521$	14.1883	−	24.5749i	0.621601	−	1.07664i	0.989188	−	0.146655i	$-0.0468508\pi$
$522$	−10.2281	+	17.7156i	−0.447671	+	0.775389i
$523$	−3.89464	+	6.74572i	−0.170301	+	0.294970i	−0.938525	−	0.345211i	$-0.887807\pi$
$523$	−3.89464	+	6.74572i	−0.170301	+	0.294970i	0.768224	+	0.640181i	$0.221141\pi$
$524$	23.4286	−	40.5796i	1.02348	−	1.77273i
$525$	−1.00326			−0.0437861
$526$	−23.4440	+	40.6062i	−1.02221	+	1.77051i
$527$	8.85916			0.385911
$528$	−5.15738	+	8.93284i	−0.224446	+	0.388752i
$529$	−6.49923			−0.282575
$530$	38.2011			1.65935
$531$	4.12832	−	7.15046i	0.179154	−	0.310304i
$532$	−1.65420	−	2.86516i	−0.0717188	−	0.124221i
$533$	1.15923	−	2.00785i	0.0502119	−	0.0869695i
$534$	0.525349	−	0.909930i	0.0227341	−	0.0393765i
$535$	5.25772			0.227311
$536$	−5.40368			−0.233403
$537$	7.42124	−	12.8540i	0.320250	−	0.554690i
$538$	−29.9618			−1.29175
$539$	7.94161	+	13.7553i	0.342069	+	0.592482i
$540$	−2.70633	−	4.68749i	−0.116462	−	0.201718i
$541$	−8.89498	−	15.4066i	−0.382425	−	0.662379i	0.608983	−	0.793183i	$-0.291578\pi$
$541$	−8.89498	−	15.4066i	−0.382425	−	0.662379i	−0.991408	+	0.130804i	$0.958244\pi$
$542$	−10.7512	+	18.6217i	−0.461805	+	0.799870i
$543$	−4.67163	+	8.09151i	−0.200479	+	0.347240i
$544$	20.0753	+	34.7714i	0.860720	+	1.49081i
$545$	−16.9651	+	29.3843i	−0.726703	+	1.25869i
$546$	−3.93518			−0.168410
$547$	7.80599	+	13.5204i	0.333760	+	0.578089i	0.983246	−	0.182284i	$-0.0583491\pi$
$547$	7.80599	+	13.5204i	0.333760	+	0.578089i	−0.649486	+	0.760374i	$0.725016\pi$
$548$	−3.77889	−	6.54524i	−0.161426	−	0.279599i
$549$	−6.40687			−0.273438
$550$	4.74465			0.202312
$551$	−5.54215	−	9.59929i	−0.236104	−	0.408944i
$552$	1.06606	+	1.84647i	0.0453746	+	0.0785910i
$553$	−5.19647			−0.220977
$554$	8.32914	−	14.4265i	0.353871	−	0.612923i
$555$	5.01622	+	8.68835i	0.212927	+	0.368800i
$556$	−14.7743	+	25.5899i	−0.626572	+	1.08525i
$557$	21.5761	−	37.3709i	0.914209	−	1.58346i	0.106154	−	0.994350i	$-0.466146\pi$
$557$	21.5761	−	37.3709i	0.914209	−	1.58346i	0.808055	−	0.589107i	$-0.200520\pi$
$558$	−1.84709	−	3.19926i	−0.0781937	−	0.135435i
$559$	−2.31253	−	4.00542i	−0.0978096	−	0.169411i
$560$	−5.40044	−	9.35383i	−0.228210	−	0.395271i
$561$	−14.8912			−0.628707
$562$	−23.4139	+	40.5540i	−0.987654	+	1.71067i
$563$	−30.4621			−1.28382			−0.641912	−	0.766778i	$-0.721859\pi$
$563$	−30.4621			−1.28382			−0.641912	+	0.766778i	$0.721859\pi$
$564$	−3.66964			−0.154520
$565$	−18.8604	+	32.6672i	−0.793464	+	1.37432i
$566$	24.8017	−	42.9578i	1.04249	−	1.80565i
$567$	−0.656504	−	1.13710i	−0.0275706	−	0.0477536i
$568$	1.06898	−	1.85153i	0.0448535	−	0.0776886i
$569$	−13.1404			−0.550876			−0.275438	−	0.961319i	$-0.588823\pi$
$569$	−13.1404			−0.550876			−0.275438	+	0.961319i	$0.588823\pi$
$570$	5.53472			0.231824
$571$	5.07288	−	8.78649i	0.212293	−	0.367703i	−0.740138	−	0.672454i	$-0.765240\pi$
$571$	5.07288	−	8.78649i	0.212293	−	0.367703i	0.952432	+	0.304751i	$0.0985734\pi$
$572$	9.86170			0.412338
$573$	4.34024	−	7.51751i	0.181316	−	0.314048i
$574$	−4.32131			−0.180368
$575$	−1.55192	+	2.68801i	−0.0647197	+	0.112098i
$576$	4.94489	−	8.56480i	0.206037	−	0.356866i
$577$	16.9435	−	29.3471i	0.705369	−	1.22173i	−0.261189	−	0.965288i	$-0.584115\pi$
$577$	16.9435	−	29.3471i	0.705369	−	1.22173i	0.966558	−	0.256447i	$-0.0825519\pi$
$578$	−7.70159	+	13.3395i	−0.320344	+	0.554852i
$579$	−13.7073			−0.569656
$580$	26.8400	+	46.4882i	1.11447	+	1.93032i
$581$	−1.31486	+	2.27740i	−0.0545495	+	0.0944826i
$582$	−29.1821			−1.20964
$583$	−23.2231			−0.961804
$584$	0.604934	+	1.04778i	0.0250323	+	0.0433573i
$585$	1.74425	−	3.02114i	0.0721161	−	0.124909i
$586$	27.0897	+	46.9208i	1.11907	+	1.93828i
$587$	−40.0347			−1.65241			−0.826205	−	0.563369i	$-0.809505\pi$
$587$	−40.0347			−1.65241			−0.826205	+	0.563369i	$0.809505\pi$
$588$	−5.94731	−	10.3010i	−0.245263	−	0.424808i
$589$	2.00172			0.0824793
$590$	−20.4438	−	35.4097i	−0.841658	−	1.45779i
$591$	7.16554	−	12.4111i	0.294751	−	0.510524i
$592$	−7.15875	+	12.3993i	−0.294223	+	0.509609i
$593$	12.0307	+	20.8377i	0.494040	+	0.855702i	0.999976	−	0.00686836i	$-0.00218629\pi$
$593$	12.0307	+	20.8377i	0.494040	+	0.855702i	−0.505936	+	0.862571i	$0.668853\pi$
$594$	3.10474	+	5.37757i	0.127389	+	0.220645i
$595$	7.79650	−	13.5039i	0.319625	−	0.553607i
$596$	−37.4503			−1.53402
$597$	3.69328	−	6.39695i	0.151156	−	0.261810i
$598$	−6.08722	+	10.5434i	−0.248925	+	0.431151i
$599$	45.0926			1.84243			0.921217	−	0.389049i	$-0.127196\pi$
$599$	45.0926			1.84243			0.921217	+	0.389049i	$0.127196\pi$
$600$	−0.401059			−0.0163732
$601$	4.99236			0.203643			0.101821	−	0.994803i	$-0.467533\pi$
$601$	4.99236			0.203643			0.101821	+	0.994803i	$0.467533\pi$
$602$	−4.31025	+	7.46558i	−0.175673	+	0.304274i
$603$	5.14754	−	8.91580i	0.209624	−	0.363080i
$604$	2.78130	+	4.81735i	0.113169	+	0.196015i
$605$	4.65075			0.189080
$606$	−7.11556	−	12.3245i	−0.289050	−	0.500649i
$607$	7.82984	+	13.5617i	0.317803	+	0.550451i	0.980029	−	0.198853i	$-0.0637215\pi$
$607$	7.82984	+	13.5617i	0.317803	+	0.550451i	−0.662226	+	0.749304i	$0.730388\pi$
$608$	4.53598	+	7.85655i	0.183958	+	0.318625i
$609$	6.51087	+	11.2772i	0.263834	+	0.456973i
$610$	−15.8637	+	27.4767i	−0.642302	+	1.11250i
$611$	−1.18256	−	2.04825i	−0.0478412	−	0.0828634i
$612$	11.1517			0.450781
$613$	−0.635733	+	1.10112i	−0.0256770	+	0.0444739i	−0.878578	−	0.477598i	$-0.841507\pi$
$613$	−0.635733	+	1.10112i	−0.0256770	+	0.0444739i	0.852901	+	0.522072i	$0.174841\pi$
$614$	8.91086			0.359613
$615$	1.91541	−	3.31758i	0.0772367	−	0.133778i
$616$	−1.03736	−	1.79676i	−0.0417965	−	0.0723936i
$617$	22.9766	+	39.7967i	0.925003	+	1.60215i	0.791556	+	0.611097i	$0.209271\pi$
$617$	22.9766	+	39.7967i	0.925003	+	1.60215i	0.133448	+	0.991056i	$0.457395\pi$
$618$	−15.1348	−	26.2142i	−0.608810	−	1.05449i
$619$	11.0258	−	19.0973i	0.443164	−	0.767583i	−0.554758	−	0.832012i	$-0.687189\pi$
$619$	11.0258	−	19.0973i	0.443164	−	0.767583i	0.997922	+	0.0644285i	$0.0205225\pi$
$620$	−9.69407			−0.389323
$621$	−4.06211			−0.163007
$622$	26.8562	+	46.5163i	1.07684	+	1.86514i
$623$	−0.334420	−	0.579232i	−0.0133982	−	0.0232064i
$624$	4.97852			0.199300
$625$	14.1183	+	24.4536i	0.564733	+	0.978146i
$626$	29.8888			1.19460
$627$	−3.36465			−0.134371
$628$	−1.92897	+	28.1825i	−0.0769742	+	1.12460i
$629$	−20.6699			−0.824162
$630$	−6.50213			−0.259051
$631$	15.4249	+	26.7168i	0.614057	+	1.06358i	0.990549	+	0.137159i	$0.0437970\pi$
$631$	15.4249	+	26.7168i	0.614057	+	1.06358i	−0.376492	+	0.926420i	$0.622870\pi$
$632$	−2.07731			−0.0826310
$633$	4.56561	+	7.90787i	0.181467	+	0.314310i
$634$	9.81881	+	17.0067i	0.389955	+	0.675422i
$635$	28.1045			1.11529
$636$	17.3913			0.689610
$637$	3.83310	−	6.63912i	0.151873	−	0.263052i
$638$	−30.7913	−	53.3320i	−1.21904	−	2.11144i
$639$	2.03662	+	3.52754i	0.0805676	+	0.139547i
$640$	−4.99984	−	8.65997i	−0.197636	−	0.342315i
$641$	−3.64891	+	6.32009i	−0.144123	+	0.249629i	−0.929045	−	0.369966i	$-0.879369\pi$
$641$	−3.64891	+	6.32009i	−0.144123	+	0.249629i	0.784922	+	0.619594i	$0.212703\pi$
$642$	4.51704			0.178273
$643$	−9.46309	+	16.3906i	−0.373188	+	0.646381i	−0.990054	−	0.140688i	$-0.955069\pi$
$643$	−9.46309	+	16.3906i	−0.373188	+	0.646381i	0.616866	+	0.787068i	$0.288402\pi$
$644$	12.0244			0.473828
$645$	−3.82101	−	6.61819i	−0.150452	−	0.260591i
$646$	−5.70159	+	9.87545i	−0.224326	+	0.388544i
$647$	−9.38182	−	16.2498i	−0.368837	−	0.638845i	0.620547	−	0.784169i	$-0.286911\pi$
$647$	−9.38182	−	16.2498i	−0.368837	−	0.638845i	−0.989384	+	0.145324i	$0.953577\pi$
$648$	−0.262440	−	0.454559i	−0.0103096	−	0.0178568i
$649$	12.4281	+	21.5262i	0.487847	+	0.844976i
$650$	−1.14503	−	1.98324i	−0.0449116	−	0.0777892i
$651$	−2.35160			−0.0921664
$652$	13.7496	+	23.8150i	0.538475	+	0.932666i
$653$	1.90696	−	3.30296i	0.0746253	−	0.129255i	−0.826298	−	0.563233i	$-0.809557\pi$
$653$	1.90696	−	3.30296i	0.0746253	−	0.129255i	0.900923	+	0.433978i	$0.142891\pi$
$654$	−14.5751	+	25.2449i	−0.569933	+	0.987153i
$655$	49.8997			1.94974
$656$	5.46703			0.213452
$657$	−2.30504			−0.0899280
$658$	−2.20414	+	3.81768i	−0.0859262	+	0.148829i
$659$	5.41693	−	9.38240i	0.211014	−	0.365487i	−0.741018	−	0.671485i	$-0.765657\pi$
$659$	5.41693	−	9.38240i	0.211014	−	0.365487i	0.952032	+	0.305998i	$0.0989902\pi$
$660$	16.2946			0.634266
$661$	−4.62557	+	8.01173i	−0.179914	+	0.311620i	−0.941851	−	0.336031i	$-0.890915\pi$
$661$	−4.62557	+	8.01173i	−0.179914	+	0.311620i	0.761937	+	0.647651i	$0.224249\pi$
$662$	−17.9973	−	31.1722i	−0.699484	−	1.21154i
$663$	3.59369	+	6.22446i	0.139567	+	0.241738i
$664$	−0.525620	+	0.910400i	−0.0203980	+	0.0353304i
$665$	1.76161	−	3.05120i	0.0683123	−	0.118320i
$666$	4.30957	+	7.46439i	0.166992	+	0.289239i
$667$	40.2860			1.55988
$668$	12.4768	+	21.6104i	0.482741	+	0.836131i
$669$	9.08046			0.351071
$670$	−25.4911	−	44.1518i	−0.984806	−	1.70573i
$671$	9.64381	−	16.7036i	0.372295	−	0.644834i
$672$	−5.32883	−	9.22980i	−0.205564	−	0.356047i
$673$	−22.7423			−0.876652			−0.438326	−	0.898816i	$-0.644428\pi$
$673$	−22.7423			−0.876652			−0.438326	+	0.898816i	$0.644428\pi$
$674$	28.0304			1.07969
$675$	0.382048	−	0.661727i	0.0147050	−	0.0254699i
$676$	12.2741	+	21.2594i	0.472082	+	0.817670i
$677$	32.4589			1.24750			0.623748	−	0.781626i	$-0.285609\pi$
$677$	32.4589			1.24750			0.623748	+	0.781626i	$0.285609\pi$
$678$	−16.2035	+	28.0653i	−0.622292	+	1.07784i
$679$	−9.28820	+	16.0876i	−0.356448	+	0.617387i
$680$	3.11668	−	5.39825i	0.119519	−	0.207013i
$681$	8.49317	−	14.7106i	0.325459	−	0.563711i
$682$	11.1212			0.425853
$683$	22.8012	−	39.4928i	0.872462	−	1.51115i	0.0130205	−	0.999915i	$-0.495855\pi$
$683$	22.8012	−	39.4928i	0.872462	−	1.51115i	0.859442	−	0.511234i	$-0.170811\pi$
$684$	2.51972			0.0963437
$685$	4.02426	−	6.97022i	0.153759	−	0.266318i
$686$	−33.2466			−1.26936
$687$	−8.69556			−0.331756
$688$	5.45304	−	9.44494i	0.207895	−	0.360085i
$689$	5.60444	+	9.70717i	0.213512	+	0.369814i
$690$	−10.0580	+	17.4209i	−0.382900	+	0.663203i
$691$	8.83751	−	15.3070i	0.336195	−	0.582307i	−0.647519	−	0.762050i	$-0.724193\pi$
$691$	8.83751	−	15.3070i	0.336195	−	0.582307i	0.983714	+	0.179743i	$0.0575266\pi$
$692$	41.1175			1.56305
$693$	3.95276			0.150153
$694$	−7.09510	+	12.2891i	−0.269326	+	0.466487i
$695$	−31.4673			−1.19362
$696$	2.60274	+	4.50809i	0.0986568	+	0.170879i
$697$	3.94632	+	6.83523i	0.149478	+	0.258903i
$698$	13.0813	+	22.6576i	0.495136	+	0.857601i
$699$	8.09877	−	14.0275i	0.306324	−	0.530568i
$700$	−1.13092	+	1.95880i	−0.0427446	+	0.0740358i
$701$	10.7185	+	18.5650i	0.404832	+	0.701190i	0.994302	−	0.106600i	$-0.0339966\pi$
$701$	10.7185	+	18.5650i	0.404832	+	0.701190i	−0.589470	+	0.807791i	$0.700663\pi$
$702$	1.49854	−	2.59554i	0.0565586	−	0.0979623i
$703$	−4.67033			−0.176145
$704$	14.8864	+	25.7840i	0.561052	+	0.971770i
$705$	−1.95395	−	3.38435i	−0.0735901	−	0.127462i
$706$	69.7674			2.62573
$707$	−9.05906			−0.340701
$708$	−9.30717	−	16.1205i	−0.349785	−	0.605845i
$709$	−12.4441	−	21.5539i	−0.467350	−	0.809473i	0.531954	−	0.846773i	$-0.321458\pi$
$709$	−12.4441	−	21.5539i	−0.467350	−	0.809473i	−0.999304	+	0.0372995i	$0.988124\pi$
$710$	20.1711			0.757007
$711$	1.97884	−	3.42746i	0.0742124	−	0.128540i
$712$	−0.133686	−	0.231550i	−0.00501008	−	0.00867771i
$713$	−3.63763	+	6.30055i	−0.136230	+	0.235958i
$714$	6.69818	−	11.6016i	0.250673	−	0.434178i
$715$	5.25101	+	9.09502i	0.196377	+	0.340134i
$716$	−16.7310	−	28.9789i	−0.625266	−	1.08299i
$717$	13.5610	+	23.4883i	0.506443	+	0.877185i
$718$	−11.4421			−0.427016
$719$	−21.4640	+	37.1768i	−0.800473	+	1.38646i	0.118832	+	0.992914i	$0.462085\pi$
$719$	−21.4640	+	37.1768i	−0.800473	+	1.38646i	−0.919305	+	0.393546i	$0.871248\pi$
$720$	8.22605			0.306567
$721$	−19.2686			−0.717601
$722$	18.3068	−	31.7083i	0.681308	−	1.18006i
$723$	−5.02743	+	8.70777i	−0.186972	+	0.323845i
$724$	10.5321	+	18.2421i	0.391421	+	0.677961i
$725$	−3.78896	+	6.56267i	−0.140718	+	0.243731i
$726$	3.99559			0.148290
$727$	−28.9577			−1.07398			−0.536992	−	0.843588i	$-0.680439\pi$
$727$	−28.9577			−1.07398			−0.536992	+	0.843588i	$0.680439\pi$
$728$	−0.500693	+	0.867226i	−0.0185569	+	0.0321415i
$729$	1.00000			0.0370370
$730$	−5.70737	+	9.88546i	−0.211239	+	0.365877i
$731$	15.7449			0.582346
$732$	−7.22205	+	12.5089i	−0.266934	+	0.462344i
$733$	9.78657	−	16.9508i	0.361475	−	0.626094i	−0.626729	−	0.779238i	$-0.715607\pi$
$733$	9.78657	−	16.9508i	0.361475	−	0.626094i	0.988204	+	0.153144i	$0.0489399\pi$
$734$	−22.8665	+	39.6060i	−0.844020	+	1.46188i
$735$	6.33346	−	10.9699i	0.233613	−	0.404630i
$736$	−32.9721			−1.21537
$737$	15.4965	+	26.8407i	0.570820	+	0.988689i
$738$	1.64558	−	2.85022i	0.0605746	−	0.104918i
$739$	−47.7308			−1.75581			−0.877903	−	0.478838i	$-0.841058\pi$
$739$	−47.7308			−1.75581			−0.877903	+	0.478838i	$0.841058\pi$
$740$	22.6178			0.831449
$741$	0.811991	+	1.40641i	0.0298292	+	0.0516658i
$742$	10.4459	−	18.0929i	0.383483	−	0.664211i
$743$	−6.15010	−	10.6523i	−0.225625	−	0.390795i	0.730881	−	0.682504i	$-0.239109\pi$
$743$	−6.15010	−	10.6523i	−0.225625	−	0.390795i	−0.956507	+	0.291710i	$0.905776\pi$
$744$	−0.940061			−0.0344643
$745$	−19.9410	−	34.5388i	−0.730581	−	1.26540i
$746$	−27.9994			−1.02513
$747$	−1.00141	−	1.73449i	−0.0366397	−	0.0634618i
$748$	−16.7859	+	29.0740i	−0.613753	+	1.06305i
$749$	1.43770	−	2.49017i	0.0525325	−	0.0909889i
$750$	10.4883	+	18.1662i	0.382978	+	0.663337i
$751$	15.7164	+	27.2215i	0.573498	+	0.993328i	0.996203	+	0.0870608i	$0.0277475\pi$
$751$	15.7164	+	27.2215i	0.573498	+	0.993328i	−0.422705	+	0.906268i	$0.638919\pi$
$752$	2.78852	−	4.82987i	0.101687	−	0.176127i
$753$	22.2809			0.811962
$754$	−14.8617	+	25.7412i	−0.541232	+	0.937441i
$755$	−2.96189	+	5.13014i	−0.107794	+	0.186705i
$756$	−2.96014			−0.107659
$757$	51.1834			1.86029			0.930146	−	0.367190i	$-0.119680\pi$
$757$	51.1834			1.86029			0.930146	+	0.367190i	$0.119680\pi$
$758$	13.1372			0.477165
$759$	6.11442	−	10.5905i	0.221939	−	0.384410i
$760$	0.704210	−	1.21973i	0.0255444	−	0.0442442i
$761$	14.2772	+	24.7289i	0.517549	+	0.896421i	0.999792	+	0.0203834i	$0.00648870\pi$
$761$	14.2772	+	24.7289i	0.517549	+	0.896421i	−0.482244	+	0.876037i	$0.660178\pi$
$762$	24.1453			0.874693
$763$	9.27806	+	16.0701i	0.335888	+	0.581775i
$764$	−9.78493	−	16.9480i	−0.354006	−	0.613157i
$765$	5.93789	+	10.2847i	0.214685	+	0.371845i
$766$	−2.92589	−	5.06778i	−0.105717	−	0.183106i
$767$	5.99857	−	10.3898i	0.216596	−	0.375155i
$768$	5.59428	+	9.68958i	0.201866	+	0.349643i
$769$	13.5648			0.489158			0.244579	−	0.969629i	$-0.421350\pi$
$769$	13.5648			0.489158			0.244579	+	0.969629i	$0.421350\pi$
$770$	9.78720	−	16.9519i	0.352706	−	0.610905i
$771$	−7.80706			−0.281165
$772$	−15.4514	+	26.7625i	−0.556107	+	0.963205i
$773$	27.0737	+	46.8931i	0.973774	+	1.68663i	0.683922	+	0.729555i	$0.260273\pi$
$773$	27.0737	+	46.8931i	0.973774	+	1.68663i	0.289852	+	0.957071i	$0.406394\pi$
$774$	−3.28273	−	5.68586i	−0.117995	−	0.204374i
$775$	−0.684249	−	1.18515i	−0.0245789	−	0.0425720i
$776$	−3.71299	+	6.43110i	−0.133289	+	0.230863i
$777$	5.48666			0.196833
$778$	−27.9192			−1.00095
$779$	0.891667	+	1.54441i	0.0319473	+	0.0553343i
$780$	−3.93237	−	6.81107i	−0.140801	−	0.243875i
$781$	−12.2624			−0.438781
$782$	−20.7225	−	35.8924i	−0.741034	−	1.28351i
$783$	−9.91749			−0.354422
$784$	18.0772			0.645615
$785$	−27.0186	+	13.2272i	−0.964335	+	0.472099i
$786$	42.8702			1.52913
$787$	38.6408			1.37740			0.688698	−	0.725048i	$-0.258183\pi$
$787$	38.6408			1.37740			0.688698	+	0.725048i	$0.258183\pi$
$788$	−16.1545	−	27.9804i	−0.575480	−	0.996761i
$789$	−22.7320			−0.809282
$790$	−9.79941	−	16.9731i	−0.348647	−	0.603875i
$791$	10.3146	+	17.8654i	0.366746	+	0.635222i
$792$	1.58013			0.0561475
$793$	−9.30936			−0.330585
$794$	17.5072	−	30.3234i	0.621309	−	1.07614i
$795$	9.26026	+	16.0392i	0.328428	+	0.568853i
$796$	−8.32639	−	14.4217i	−0.295121	−	0.511165i
$797$	−14.2433	−	24.6701i	−0.504524	−	0.873861i	−0.999986	−	0.00523176i	$-0.998335\pi$
$797$	−14.2433	−	24.6701i	−0.504524	−	0.873861i	0.495462	−	0.868629i	$-0.334999\pi$
$798$	1.51345	−	2.62137i	0.0535754	−	0.0927953i
$799$	8.05147			0.284841
$800$	3.10108	−	5.37123i	0.109640	−	0.189901i
$801$	0.509395			0.0179986
$802$	−10.0251	−	17.3641i	−0.354000	−	0.613146i
$803$	3.46961	−	6.00954i	0.122440	−	0.212072i
$804$	−11.6050	−	20.1004i	−0.409276	−	0.708887i
$805$	6.40258	+	11.0896i	0.225661	+	0.390857i
$806$	−2.68388	−	4.64862i	−0.0945356	−	0.163740i
$807$	−7.26299	−	12.5799i	−0.255669	−	0.442833i
$808$	−3.62140			−0.127400
$809$	−7.43872	−	12.8842i	−0.261531	−	0.452986i	0.705118	−	0.709090i	$-0.250894\pi$
$809$	−7.43872	−	12.8842i	−0.261531	−	0.452986i	−0.966649	+	0.256105i	$0.917561\pi$
$810$	2.47604	−	4.28863i	0.0869993	−	0.150687i
$811$	−17.8244	+	30.8728i	−0.625900	+	1.08409i	0.362467	+	0.931997i	$0.381935\pi$
$811$	−17.8244	+	30.8728i	−0.625900	+	1.08409i	−0.988366	+	0.152093i	$0.951399\pi$
$812$	29.3571			1.03023
$813$	−10.4248			−0.365612
$814$	−25.9476			−0.909462
$815$	−14.6423	+	25.3613i	−0.512899	+	0.888367i
$816$	−8.47408	+	14.6775i	−0.296652	+	0.513817i
$817$	3.55754			0.124463
$818$	−0.151064	+	0.261651i	−0.00528184	+	0.00914841i
$819$	−0.953919	−	1.65224i	−0.0333326	−	0.0577338i
$820$	−4.31823	−	7.47940i	−0.150799	−	0.261192i
$821$	5.13521	−	8.89445i	0.179220	−	0.310418i	−0.762393	−	0.647114i	$-0.775976\pi$
$821$	5.13521	−	8.89445i	0.179220	−	0.310418i	0.941614	+	0.336695i	$0.109309\pi$
$822$	3.45735	−	5.98830i	0.120589	−	0.208866i
$823$	−4.65119	−	8.05610i	−0.162130	−	0.280818i	0.773502	−	0.633794i	$-0.218503\pi$
$823$	−4.65119	−	8.05610i	−0.162130	−	0.280818i	−0.935632	+	0.352976i	$0.885170\pi$
$824$	−7.70270			−0.268336
$825$	1.15014	+	1.99210i	0.0400428	+	0.0693561i
$826$	−22.3611			−0.778042
$827$	19.8137	+	34.3183i	0.688989	+	1.19336i	0.972165	+	0.234296i	$0.0752786\pi$
$827$	19.8137	+	34.3183i	0.688989	+	1.19336i	−0.283176	+	0.959068i	$0.591388\pi$
$828$	−4.57896	+	7.93099i	−0.159130	+	0.275621i
$829$	−12.6419	−	21.8964i	−0.439071	−	0.760493i	0.558547	−	0.829473i	$-0.311359\pi$
$829$	−12.6419	−	21.8964i	−0.439071	−	0.760493i	−0.997618	+	0.0689798i	$0.978026\pi$
$830$	−9.91814			−0.344264
$831$	8.07621			0.280161
$832$	7.18506	−	12.4449i	0.249097	−	0.431449i
$833$	13.0489	+	22.6013i	0.452116	+	0.783088i
$834$	−27.0344			−0.936124
$835$	−13.2869	+	23.0136i	−0.459812	+	0.796417i
$836$	−3.79275	+	6.56924i	−0.131175	+	0.227202i
$837$	0.895501	−	1.55105i	0.0309530	−	0.0536122i
$838$	37.5919	−	65.1111i	1.29859	−	2.24923i
$839$	−9.61355			−0.331897			−0.165948	−	0.986134i	$-0.553068\pi$
$839$	−9.61355			−0.331897			−0.165948	+	0.986134i	$0.553068\pi$
$840$	−0.827300	+	1.43292i	−0.0285445	+	0.0494406i
$841$	69.3566			2.39161
$842$	34.1089	−	59.0783i	1.17547	−	2.03597i
$843$	−22.7028			−0.781927
$844$	20.5861			0.708602
$845$	−13.0711	+	22.6398i	−0.449659	+	0.778833i
$846$	−1.67869	−	2.90758i	−0.0577147	−	0.0999647i
$847$	1.27173	−	2.20270i	0.0436972	−	0.0756857i
$848$	−13.2155	+	22.8899i	−0.453822	+	0.786043i
$849$	24.0486			0.825345
$850$	7.79593			0.267398
$851$	8.48717	−	14.7002i	0.290937	−	0.503917i
$852$	9.18302			0.314605
$853$	−23.7013	−	41.0519i	−0.811518	−	1.40559i	−0.911801	−	0.410632i	$-0.865308\pi$
$853$	−23.7013	−	41.0519i	−0.811518	−	1.40559i	0.100283	−	0.994959i	$-0.468025\pi$
$854$	8.67572	+	15.0268i	0.296877	+	0.514206i
$855$	1.34166	+	2.32382i	0.0458838	+	0.0794731i
$856$	0.574727	−	0.995456i	0.0196438	−	0.0340240i
$857$	−16.1830	+	28.0299i	−0.552802	+	0.957482i	0.445269	+	0.895397i	$0.353108\pi$
$857$	−16.1830	+	28.0299i	−0.552802	+	0.957482i	−0.998071	+	0.0620846i	$0.980225\pi$
$858$	4.51128	+	7.81377i	0.154013	+	0.266758i
$859$	−20.5687	+	35.6260i	−0.701795	+	1.21554i	0.266041	+	0.963962i	$0.414284\pi$
$859$	−20.5687	+	35.6260i	−0.701795	+	1.21554i	−0.967836	+	0.251583i	$0.919049\pi$
$860$	−17.2287			−0.587494
$861$	−1.04752	−	1.81436i	−0.0356994	−	0.0618332i
$862$	−30.7597	−	53.2774i	−1.04768	−	1.81463i
$863$	45.7117			1.55604			0.778022	−	0.628237i	$-0.216223\pi$
$863$	45.7117			1.55604			0.778022	+	0.628237i	$0.216223\pi$
$864$	8.11698			0.276145
$865$	21.8936	+	37.9209i	0.744406	+	1.28935i
$866$	−19.8872	−	34.4456i	−0.675794	−	1.17051i
$867$	−7.46771			−0.253617
$868$	−2.65080	+	4.59133i	−0.0899742	+	0.155840i
$869$	5.95723	+	10.3182i	0.202085	+	0.350022i
$870$	−24.5561	+	42.5325i	−0.832531	+	1.44199i
$871$	7.47953	−	12.9549i	0.253434	−	0.438961i
$872$	3.70894	+	6.42407i	0.125601	+	0.217547i
$873$	−7.07399	−	12.2525i	−0.239418	−	0.414685i
$874$	−4.68222	−	8.10984i	−0.158378	−	0.274319i
$875$	13.3530			0.451414
$876$	−2.59832	+	4.50042i	−0.0877890	+	0.152055i
$877$	31.1218			1.05091			0.525454	−	0.850822i	$-0.323895\pi$
$877$	31.1218			1.05091			0.525454	+	0.850822i	$0.323895\pi$
$878$	−4.21670			−0.142307
$879$	−13.1335	+	22.7480i	−0.442984	+	0.767270i
$880$	−12.3821	+	21.4464i	−0.417401	+	0.722959i
$881$	3.99129	+	6.91311i	0.134470	+	0.232909i	0.925395	−	0.379005i	$-0.123734\pi$
$881$	3.99129	+	6.91311i	0.134470	+	0.232909i	−0.790925	+	0.611913i	$0.790400\pi$
$882$	5.44125	−	9.42452i	0.183216	−	0.317340i
$883$	9.22002			0.310278			0.155139	−	0.987893i	$-0.450417\pi$
$883$	9.22002			0.310278			0.155139	+	0.987893i	$0.450417\pi$
$884$	16.2038			0.544991
$885$	9.91149	−	17.1672i	0.333171	−	0.577069i
$886$	23.3339			0.783917
$887$	−0.862181	+	1.49334i	−0.0289492	+	0.0501415i	−0.880137	−	0.474720i	$-0.842549\pi$
$887$	−0.862181	+	1.49334i	−0.0289492	+	0.0501415i	0.851188	+	0.524861i	$0.175883\pi$
$888$	2.19331			0.0736028
$889$	7.68507	−	13.3109i	0.257749	−	0.446434i
$890$	1.26128	−	2.18461i	0.0422784	−	0.0732283i
$891$	−1.50523	+	2.60714i	−0.0504271	+	0.0873423i
$892$	10.2358	−	17.7290i	0.342720	−	0.593609i
$893$	1.81922			0.0608779
$894$	−17.1318	−	29.6732i	−0.572974	−	0.992420i
$895$	17.8173	−	30.8605i	0.595567	−	1.03155i
$896$	−5.46874			−0.182698
$897$	−5.90237			−0.197074
$898$	−22.5250	−	39.0144i	−0.751669	−	1.30193i
$899$	−8.88112	+	15.3825i	−0.296202	+	0.513037i
$900$	−0.861317	−	1.49184i	−0.0287106	−	0.0497281i
$901$	−38.1579			−1.27122
$902$	4.95395	+	8.58049i	0.164948	+	0.285699i
$903$	−4.17936			−0.139080
$904$	4.12331	+	7.14178i	0.137139	+	0.237532i
$905$	−11.2159	+	19.4265i	−0.372829	+	0.645759i
$906$	−2.54464	+	4.40744i	−0.0845399	+	0.146427i
$907$	−20.0293	−	34.6917i	−0.665061	−	1.15192i	−0.979269	−	0.202566i	$-0.935072\pi$
$907$	−20.0293	−	34.6917i	−0.665061	−	1.15192i	0.314207	−	0.949354i	$-0.398261\pi$
$908$	−19.1476	−	33.1646i	−0.635435	−	1.10061i
$909$	3.44974	−	5.97512i	0.114421	−	0.198182i
$910$	−9.44778			−0.313191
$911$	−3.35733	+	5.81506i	−0.111233	+	0.192661i	−0.916268	−	0.400566i	$-0.868813\pi$
$911$	−3.35733	+	5.81506i	−0.111233	+	0.192661i	0.805035	+	0.593228i	$0.202147\pi$
$912$	−1.91471	+	3.31637i	−0.0634024	+	0.109816i
$913$	6.02941			0.199544
$914$	−30.0050			−0.992478
$915$	−15.3819			−0.508511
$916$	−9.80195	+	16.9775i	−0.323865	+	0.560951i
$917$	13.6449	−	23.6336i	0.450594	−	0.780451i
$918$	5.10140	+	8.83589i	0.168371	+	0.291628i
$919$	−31.2910			−1.03219			−0.516097	−	0.856530i	$-0.672616\pi$
$919$	−31.2910			−1.03219			−0.516097	+	0.856530i	$0.672616\pi$
$920$	2.55946	+	4.43311i	0.0843827	+	0.146155i
$921$	2.16007	+	3.74134i	0.0711766	+	0.123281i
$922$	18.3724	+	31.8220i	0.605064	+	1.04800i
$923$	2.95927	+	5.12561i	0.0974057	+	0.168712i
$924$	4.45569	−	7.71748i	0.146581	−	0.253886i
$925$	1.59646	+	2.76516i	0.0524914	+	0.0909178i
$926$	−28.6895			−0.942796
$927$	7.33759	−	12.7091i	0.240998	−	0.417421i
$928$	−80.5001			−2.64254
$929$	0.263290	−	0.456032i	0.00863827	−	0.0149619i	−0.861674	−	0.507462i	$-0.830584\pi$
$929$	0.263290	−	0.456032i	0.00863827	−	0.0149619i	0.870312	+	0.492500i	$0.163917\pi$
$930$	−4.43460	−	7.68095i	−0.145416	−	0.251868i
$931$	2.94837	+	5.10673i	0.0966291	+	0.167366i
$932$	−18.2584	−	31.6245i	−0.598075	−	1.03590i
$933$	−13.0203	+	22.5519i	−0.426267	+	0.738316i
$934$	19.5808			0.640705
$935$	−35.7516			−1.16920
$936$	−0.381333	−	0.660488i	−0.0124643	−	0.0215887i
$937$	−12.3074	−	21.3171i	−0.402066	−	0.696398i	0.591909	−	0.806005i	$-0.298374\pi$
$937$	−12.3074	−	21.3171i	−0.402066	−	0.696398i	−0.993975	+	0.109606i	$0.965041\pi$
$938$	−27.8817			−0.910371
$939$	7.24528	+	12.5492i	0.236441	+	0.409527i
$940$	−8.81026			−0.287359
$941$	−13.5703			−0.442378			−0.221189	−	0.975231i	$-0.570994\pi$
$941$	−13.5703			−0.442378			−0.221189	+	0.975231i	$0.570994\pi$
$942$	−23.2124	+	11.3638i	−0.756301	+	0.370254i
$943$	−6.48153			−0.211068
$944$	28.2898			0.920753
$945$	−1.57617	−	2.73001i	−0.0512728	−	0.0888071i
$946$	19.7651			0.642618
$947$	−7.41437	−	12.8421i	−0.240935	−	0.417311i	0.720046	−	0.693926i	$-0.244121\pi$
$947$	−7.41437	−	12.8421i	−0.240935	−	0.417311i	−0.960981	+	0.276615i	$0.910787\pi$
$948$	−4.46124	−	7.72710i	−0.144894	−	0.250965i
$949$	−3.34929			−0.108722
$950$	1.76148			0.0571500
$951$	−4.76032	+	8.24512i	−0.154364	+	0.267366i
$952$	−1.70449	−	2.95226i	−0.0552428	−	0.0956833i
$953$	27.7105	+	47.9960i	0.897631	+	1.55474i	0.830514	+	0.556998i	$0.188047\pi$
$953$	27.7105	+	47.9960i	0.897631	+	1.55474i	0.0671178	+	0.997745i	$0.478620\pi$
$954$	7.95574	+	13.7797i	0.257577	+	0.446136i
$955$	10.4203	−	18.0484i	0.337192	−	0.584034i
$956$	61.1455			1.97759
$957$	14.9281	−	25.8562i	0.482557	−	0.835813i
$958$	−85.3670			−2.75808
$959$	−2.20083	−	3.81196i	−0.0710687	−	0.123095i
$960$	11.8719	−	20.5628i	0.383165	−	0.663662i
$961$	13.8962	+	24.0689i	0.448263	+	0.776415i
$962$	6.26193	+	10.8460i	0.201893	+	0.349688i
$963$	1.09497	+	1.89654i	0.0352849	+	0.0611152i
$964$	11.3342	+	19.6314i	0.365050	+	0.632285i
$965$	−32.9092			−1.05939
$966$	5.50063	+	9.52736i	0.176980	+	0.306538i
$967$	−7.49597	+	12.9834i	−0.241054	+	0.417518i	−0.961015	−	0.276497i	$-0.910826\pi$
$967$	−7.49597	+	12.9834i	−0.241054	+	0.417518i	0.719961	+	0.694015i	$0.244160\pi$
$968$	0.508379	−	0.880538i	0.0163399	−	0.0283016i
$969$	−5.52845			−0.177599
$970$	−70.0620			−2.24956
$971$	−15.3145			−0.491464			−0.245732	−	0.969338i	$-0.579028\pi$
$971$	−15.3145			−0.491464			−0.245732	+	0.969338i	$0.579028\pi$
$972$	1.12724	−	1.95243i	0.0361561	−	0.0626242i
$973$	−8.60461	+	14.9036i	−0.275851	+	0.477788i
$974$	−58.3713			−1.87034
$975$	0.555127	−	0.961509i	0.0177783	−	0.0307929i
$976$	−10.9759	−	19.0109i	−0.351331	−	0.608523i
$977$	−14.8647	−	25.7465i	−0.475565	−	0.823702i	0.524044	−	0.851691i	$-0.324423\pi$
$977$	−14.8647	−	25.7465i	−0.475565	−	0.823702i	−0.999608	+	0.0279894i	$0.991090\pi$
$978$	−12.5796	+	21.7886i	−0.402252	+	0.696721i
$979$	−0.766757	+	1.32806i	−0.0245057	+	0.0424451i
$980$	−14.2786	−	24.7313i	−0.456113	−	0.790012i
$981$	−14.1325			−0.451217
$982$	−17.5759	−	30.4424i	−0.560871	−	0.971457i
$983$	55.3815			1.76640			0.883198	−	0.469001i	$-0.155386\pi$
$983$	55.3815			1.76640			0.883198	+	0.469001i	$0.155386\pi$
$984$	−0.418751	−	0.725298i	−0.0133493	−	0.0231216i
$985$	17.2034	−	29.7972i	0.548146	−	0.949417i
$986$	−50.5931	−	87.6298i	−1.61121	−	2.79070i
$987$	−2.13720			−0.0680279
$988$	3.66122			0.116479
$989$	−6.46495	+	11.1976i	−0.205573	+	0.356063i
$990$	7.45403	+	12.9108i	0.236905	+	0.410331i
$991$	−35.4652			−1.12659			−0.563294	−	0.826256i	$-0.690466\pi$
$991$	−35.4652			−1.12659			−0.563294	+	0.826256i	$0.690466\pi$
$992$	7.26876	−	12.5899i	0.230783	−	0.399729i
$993$	8.72537	−	15.1128i	0.276891	−	0.479590i
$994$	5.51570	−	9.55348i	0.174947	−	0.303018i
$995$	8.86702	−	15.3581i	0.281104	−	0.486886i
$996$	−4.51530			−0.143073
$997$	9.15726	−	15.8608i	0.290013	−	0.502318i	−0.683799	−	0.729670i	$-0.739674\pi$
$997$	9.15726	−	15.8608i	0.290013	−	0.502318i	0.973813	+	0.227352i	$0.0730069\pi$
$998$	−35.4067			−1.12078
$999$	−2.08935	+	3.61886i	−0.0661041	+	0.114496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.e.b.169.9	✓	22
157.144	even	3	inner	471.2.e.b.301.9	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.e.b.169.9	✓	22	1.1	even	1	trivial
471.2.e.b.301.9	yes	22	157.144	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.06264 q^{2} +(0.500000 + 0.866025i) q^{3} +2.25447 q^{4} +(1.20043 + 2.07920i) q^{5} +(1.03132 + 1.78630i) q^{6} +1.31301 q^{7} +0.524880 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+2.06264 q^{2} +(0.500000 + 0.866025i) q^{3} +2.25447 q^{4} +(1.20043 + 2.07920i) q^{5} +(1.03132 + 1.78630i) q^{6} +1.31301 q^{7} +0.524880 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.47604 + 4.28863i) q^{10} +(-1.50523 - 2.60714i) q^{11} +(1.12724 + 1.95243i) q^{12} +(-0.726515 + 1.25836i) q^{13} +2.70826 q^{14} +(-1.20043 + 2.07920i) q^{15} -3.42630 q^{16} +(-2.47324 - 4.28378i) q^{17} +(-1.03132 + 1.78630i) q^{18} +(-0.558826 - 0.967916i) q^{19} +(2.70633 + 4.68749i) q^{20} +(0.656504 + 1.13710i) q^{21} +(-3.10474 - 5.37757i) q^{22} +4.06211 q^{23} +(0.262440 + 0.454559i) q^{24} +(-0.382048 + 0.661727i) q^{25} +(-1.49854 + 2.59554i) q^{26} -1.00000 q^{27} +2.96014 q^{28} +9.91749 q^{29} +(-2.47604 + 4.28863i) q^{30} +(-0.895501 + 1.55105i) q^{31} -8.11698 q^{32} +(1.50523 - 2.60714i) q^{33} +(-5.10140 - 8.83589i) q^{34} +(1.57617 + 2.73001i) q^{35} +(-1.12724 + 1.95243i) q^{36} +(2.08935 - 3.61886i) q^{37} +(-1.15266 - 1.99646i) q^{38} -1.45303 q^{39} +(0.630080 + 1.09133i) q^{40} -1.59561 q^{41} +(1.35413 + 2.34542i) q^{42} +(-1.59152 + 2.75660i) q^{43} +(-3.39350 - 5.87771i) q^{44} -2.40085 q^{45} +8.37866 q^{46} +(-0.813858 + 1.40964i) q^{47} +(-1.71315 - 2.96727i) q^{48} -5.27601 q^{49} +(-0.788027 + 1.36490i) q^{50} +(2.47324 - 4.28378i) q^{51} +(-1.63791 + 2.83694i) q^{52} +(3.85707 - 6.68064i) q^{53} -2.06264 q^{54} +(3.61384 - 6.25935i) q^{55} +0.689171 q^{56} +(0.558826 - 0.967916i) q^{57} +20.4562 q^{58} -8.25664 q^{59} +(-2.70633 + 4.68749i) q^{60} +(3.20343 + 5.54851i) q^{61} +(-1.84709 + 3.19926i) q^{62} +(-0.656504 + 1.13710i) q^{63} -9.88977 q^{64} -3.48851 q^{65} +(3.10474 - 5.37757i) q^{66} -10.2951 q^{67} +(-5.57585 - 9.65766i) q^{68} +(2.03106 + 3.51789i) q^{69} +(3.25106 + 5.63101i) q^{70} +(2.03662 - 3.52754i) q^{71} +(-0.262440 + 0.454559i) q^{72} +(1.15252 + 1.99622i) q^{73} +(4.30957 - 7.46439i) q^{74} -0.764097 q^{75} +(-1.25986 - 2.18214i) q^{76} +(-1.97638 - 3.42319i) q^{77} -2.99707 q^{78} -3.95769 q^{79} +(-4.11303 - 7.12397i) q^{80} +(-0.500000 - 0.866025i) q^{81} -3.29116 q^{82} +(-1.00141 + 1.73449i) q^{83} +(1.48007 + 2.56355i) q^{84} +(5.93789 - 10.2847i) q^{85} +(-3.28273 + 5.68586i) q^{86} +(4.95874 + 8.58880i) q^{87} +(-0.790065 - 1.36843i) q^{88} +(-0.254698 - 0.441149i) q^{89} -4.95209 q^{90} +(-0.953919 + 1.65224i) q^{91} +9.15791 q^{92} -1.79100 q^{93} +(-1.67869 + 2.90758i) q^{94} +(1.34166 - 2.32382i) q^{95} +(-4.05849 - 7.02951i) q^{96} +(-7.07399 + 12.2525i) q^{97} -10.8825 q^{98} +3.01046 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9}+O(q^{10}) \) 22 * q + 2 * q^2 + 11 * q^3 + 30 * q^4 - 4 * q^5 + q^6 + 4 * q^7 - 11 * q^9	\( 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9} - 5 q^{10} + 15 q^{12} + 3 q^{13} - 14 q^{14} + 4 q^{15} + 54 q^{16} - q^{17} - q^{18} - 22 q^{19} - 7 q^{20} + 2 q^{21} - 22 q^{22} - 10 q^{23} - 15 q^{25} - 10 q^{26} - 22 q^{27} - 38 q^{28} + 22 q^{29} + 5 q^{30} - 6 q^{31} + 32 q^{32} + 17 q^{34} - 11 q^{35} - 15 q^{36} + 8 q^{37} + 14 q^{38} + 6 q^{39} + 32 q^{40} - 7 q^{42} + q^{43} - 12 q^{44} + 8 q^{45} + 24 q^{46} + 7 q^{47} + 27 q^{48} + 22 q^{49} + 13 q^{50} + q^{51} + 17 q^{52} + 30 q^{53} - 2 q^{54} + 31 q^{55} - 82 q^{56} + 22 q^{57} - 90 q^{58} - 16 q^{59} + 7 q^{60} + 8 q^{61} - 28 q^{62} - 2 q^{63} - 32 q^{64} - 68 q^{65} + 22 q^{66} - 38 q^{67} - 8 q^{68} - 5 q^{69} + 43 q^{70} + 45 q^{71} - 4 q^{73} + 3 q^{74} - 30 q^{75} - 33 q^{76} + 21 q^{77} - 20 q^{78} + 26 q^{79} - 12 q^{80} - 11 q^{81} + 16 q^{82} + 8 q^{83} - 19 q^{84} - 28 q^{85} - 16 q^{86} + 11 q^{87} - 65 q^{88} + 15 q^{89} + 10 q^{90} - 3 q^{91} - 18 q^{92} - 12 q^{93} - 28 q^{94} - 5 q^{95} + 16 q^{96} - 35 q^{97} + 90 q^{98}+O(q^{100}) \) 22 * q + 2 * q^2 + 11 * q^3 + 30 * q^4 - 4 * q^5 + q^6 + 4 * q^7 - 11 * q^9 - 5 * q^10 + 15 * q^12 + 3 * q^13 - 14 * q^14 + 4 * q^15 + 54 * q^16 - q^17 - q^18 - 22 * q^19 - 7 * q^20 + 2 * q^21 - 22 * q^22 - 10 * q^23 - 15 * q^25 - 10 * q^26 - 22 * q^27 - 38 * q^28 + 22 * q^29 + 5 * q^30 - 6 * q^31 + 32 * q^32 + 17 * q^34 - 11 * q^35 - 15 * q^36 + 8 * q^37 + 14 * q^38 + 6 * q^39 + 32 * q^40 - 7 * q^42 + q^43 - 12 * q^44 + 8 * q^45 + 24 * q^46 + 7 * q^47 + 27 * q^48 + 22 * q^49 + 13 * q^50 + q^51 + 17 * q^52 + 30 * q^53 - 2 * q^54 + 31 * q^55 - 82 * q^56 + 22 * q^57 - 90 * q^58 - 16 * q^59 + 7 * q^60 + 8 * q^61 - 28 * q^62 - 2 * q^63 - 32 * q^64 - 68 * q^65 + 22 * q^66 - 38 * q^67 - 8 * q^68 - 5 * q^69 + 43 * q^70 + 45 * q^71 - 4 * q^73 + 3 * q^74 - 30 * q^75 - 33 * q^76 + 21 * q^77 - 20 * q^78 + 26 * q^79 - 12 * q^80 - 11 * q^81 + 16 * q^82 + 8 * q^83 - 19 * q^84 - 28 * q^85 - 16 * q^86 + 11 * q^87 - 65 * q^88 + 15 * q^89 + 10 * q^90 - 3 * q^91 - 18 * q^92 - 12 * q^93 - 28 * q^94 - 5 * q^95 + 16 * q^96 - 35 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

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