LMFDB - Embedded newform 285.2.i.e.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(106,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("285.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.i (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:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$-0.309017 - 0.535233i$ of defining polynomial
Character	$\chi$	$=$	285.121
Dual form			285.2.i.e.106.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 - 0.535233i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.809017 - 1.40126i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.309017 + 0.535233i) q^{6} +5.23607 q^{7} -2.23607 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.309017 - 0.535233i) q^{10} +2.00000 q^{11} -1.61803 q^{12} +(-1.61803 + 2.80252i) q^{13} +(-1.61803 - 2.80252i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.927051 - 1.60570i) q^{16} +(-2.73607 - 4.73901i) q^{17} +0.618034 q^{18} +(2.35410 - 3.66854i) q^{19} +1.61803 q^{20} +(-2.61803 - 4.53457i) q^{21} +(-0.618034 - 1.07047i) q^{22} +(-3.23607 + 5.60503i) q^{23} +(1.11803 + 1.93649i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.00000 q^{26} +1.00000 q^{27} +(4.23607 - 7.33708i) q^{28} +(2.61803 - 4.53457i) q^{29} -0.618034 q^{30} -3.76393 q^{31} +(-2.80902 + 4.86536i) q^{32} +(-1.00000 - 1.73205i) q^{33} +(-1.69098 + 2.92887i) q^{34} +(2.61803 + 4.53457i) q^{35} +(0.809017 + 1.40126i) q^{36} -6.47214 q^{37} +(-2.69098 - 0.126351i) q^{38} +3.23607 q^{39} +(-1.11803 - 1.93649i) q^{40} +(2.85410 + 4.94345i) q^{41} +(-1.61803 + 2.80252i) q^{42} +(0.854102 + 1.47935i) q^{43} +(1.61803 - 2.80252i) q^{44} -1.00000 q^{45} +4.00000 q^{46} +(-3.11803 + 5.40059i) q^{47} +(-0.927051 + 1.60570i) q^{48} +20.4164 q^{49} +0.618034 q^{50} +(-2.73607 + 4.73901i) q^{51} +(2.61803 + 4.53457i) q^{52} +(0.500000 - 0.866025i) q^{53} +(-0.309017 - 0.535233i) q^{54} +(1.00000 + 1.73205i) q^{55} -11.7082 q^{56} +(-4.35410 - 0.204441i) q^{57} -3.23607 q^{58} +(1.00000 + 1.73205i) q^{59} +(-0.809017 - 1.40126i) q^{60} +(-1.76393 + 3.05522i) q^{61} +(1.16312 + 2.01458i) q^{62} +(-2.61803 + 4.53457i) q^{63} -0.236068 q^{64} -3.23607 q^{65} +(-0.618034 + 1.07047i) q^{66} +(-0.618034 + 1.07047i) q^{67} -8.85410 q^{68} +6.47214 q^{69} +(1.61803 - 2.80252i) q^{70} +(-2.38197 - 4.12569i) q^{71} +(1.11803 - 1.93649i) q^{72} +(6.23607 + 10.8012i) q^{73} +(2.00000 + 3.46410i) q^{74} +1.00000 q^{75} +(-3.23607 - 6.26662i) q^{76} +10.4721 q^{77} +(-1.00000 - 1.73205i) q^{78} +(0.927051 - 1.60570i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.76393 - 3.05522i) q^{82} -7.18034 q^{83} -8.47214 q^{84} +(2.73607 - 4.73901i) q^{85} +(0.527864 - 0.914287i) q^{86} -5.23607 q^{87} -4.47214 q^{88} +(-6.23607 + 10.8012i) q^{89} +(0.309017 + 0.535233i) q^{90} +(-8.47214 + 14.6742i) q^{91} +(5.23607 + 9.06914i) q^{92} +(1.88197 + 3.25966i) q^{93} +3.85410 q^{94} +(4.35410 + 0.204441i) q^{95} +5.61803 q^{96} +(1.00000 + 1.73205i) q^{97} +(-6.30902 - 10.9275i) q^{98} +(-1.00000 + 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 2 q^{3} + q^{4} + 2 q^{5} + q^{6} + 12 q^{7} - 2 q^{9} - q^{10} + 8 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{14} + 2 q^{15} + 3 q^{16} - 2 q^{17} - 2 q^{18} - 4 q^{19} + 2 q^{20} - 6 q^{21}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q + q^2 - 2 * q^3 + q^4 + 2 * q^5 + q^6 + 12 * q^7 - 2 * q^9 - q^10 + 8 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^14 + 2 * q^15 + 3 * q^16 - 2 * q^17 - 2 * q^18 - 4 * q^19 + 2 * q^20 - 6 * q^21 + 2 * q^22 - 4 * q^23 - 2 * q^25 + 8 * q^26 + 4 * q^27 + 8 * q^28 + 6 * q^29 + 2 * q^30 - 24 * q^31 - 9 * q^32 - 4 * q^33 - 9 * q^34 + 6 * q^35 + q^36 - 8 * q^37 - 13 * q^38 + 4 * q^39 - 2 * q^41 - 2 * q^42 - 10 * q^43 + 2 * q^44 - 4 * q^45 + 16 * q^46 - 8 * q^47 + 3 * q^48 + 28 * q^49 - 2 * q^50 - 2 * q^51 + 6 * q^52 + 2 * q^53 + q^54 + 4 * q^55 - 20 * q^56 - 4 * q^57 - 4 * q^58 + 4 * q^59 - q^60 - 16 * q^61 - 11 * q^62 - 6 * q^63 + 8 * q^64 - 4 * q^65 + 2 * q^66 + 2 * q^67 - 22 * q^68 + 8 * q^69 + 2 * q^70 - 14 * q^71 + 16 * q^73 + 8 * q^74 + 4 * q^75 - 4 * q^76 + 24 * q^77 - 4 * q^78 - 3 * q^80 - 2 * q^81 + 16 * q^82 + 16 * q^83 - 16 * q^84 + 2 * q^85 + 20 * q^86 - 12 * q^87 - 16 * q^89 - q^90 - 16 * q^91 + 12 * q^92 + 12 * q^93 + 2 * q^94 + 4 * q^95 + 18 * q^96 + 4 * q^97 - 23 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.309017	−	0.535233i	−0.218508	−	0.378467i	0.735844	−	0.677151i	$-0.236786\pi$
$2$	−0.309017	−	0.535233i	−0.218508	−	0.378467i	−0.954352	+	0.298684i	$0.903452\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.809017	−	1.40126i	0.404508	−	0.700629i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.309017	+	0.535233i	−0.126156	+	0.218508i
$7$	5.23607			1.97905			0.989524	−	0.144370i	$-0.0461154\pi$
$7$	5.23607			1.97905			0.989524	+	0.144370i	$0.0461154\pi$
$8$	−2.23607			−0.790569
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.309017	−	0.535233i	0.0977198	−	0.169256i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$	−1.61803			−0.467086
$13$	−1.61803	+	2.80252i	−0.448762	+	0.777278i	−0.998306	−	0.0581865i	$-0.981468\pi$
$13$	−1.61803	+	2.80252i	−0.448762	+	0.777278i	0.549544	+	0.835465i	$0.314802\pi$
$14$	−1.61803	−	2.80252i	−0.432438	−	0.749004i
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	−0.927051	−	1.60570i	−0.231763	−	0.401425i
$17$	−2.73607	−	4.73901i	−0.663594	−	1.14938i	−0.979664	−	0.200643i	$-0.935697\pi$
$17$	−2.73607	−	4.73901i	−0.663594	−	1.14938i	0.316071	−	0.948736i	$-0.397636\pi$
$18$	0.618034			0.145672
$19$	2.35410	−	3.66854i	0.540068	−	0.841621i
$19$	2.35410	−	3.66854i	0.540068	−	0.841621i
$20$	1.61803			0.361803
$21$	−2.61803	−	4.53457i	−0.571302	−	0.989524i
$22$	−0.618034	−	1.07047i	−0.131765	−	0.228224i
$23$	−3.23607	+	5.60503i	−0.674767	+	1.16873i	0.301770	+	0.953381i	$0.402422\pi$
$23$	−3.23607	+	5.60503i	−0.674767	+	1.16873i	−0.976537	+	0.215350i	$0.930911\pi$
$24$	1.11803	+	1.93649i	0.228218	+	0.395285i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.00000			0.392232
$27$	1.00000			0.192450
$28$	4.23607	−	7.33708i	0.800542	−	1.38658i
$29$	2.61803	−	4.53457i	0.486157	−	0.842048i	−0.513717	−	0.857960i	$-0.671732\pi$
$29$	2.61803	−	4.53457i	0.486157	−	0.842048i	0.999873	+	0.0159118i	$0.00506509\pi$
$30$	−0.618034			−0.112837
$31$	−3.76393			−0.676022			−0.338011	−	0.941142i	$-0.609754\pi$
$31$	−3.76393			−0.676022			−0.338011	+	0.941142i	$0.609754\pi$
$32$	−2.80902	+	4.86536i	−0.496569	+	0.860082i
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$	−1.69098	+	2.92887i	−0.290001	+	0.502297i
$35$	2.61803	+	4.53457i	0.442529	+	0.766482i
$36$	0.809017	+	1.40126i	0.134836	+	0.233543i
$37$	−6.47214			−1.06401			−0.532006	−	0.846740i	$-0.678562\pi$
$37$	−6.47214			−1.06401			−0.532006	+	0.846740i	$0.678562\pi$
$38$	−2.69098	−	0.126351i	−0.436535	−	0.0204969i
$39$	3.23607			0.518186
$40$	−1.11803	−	1.93649i	−0.176777	−	0.306186i
$41$	2.85410	+	4.94345i	0.445736	+	0.772037i	0.998103	−	0.0615637i	$-0.0196087\pi$
$41$	2.85410	+	4.94345i	0.445736	+	0.772037i	−0.552367	+	0.833601i	$0.686275\pi$
$42$	−1.61803	+	2.80252i	−0.249668	+	0.432438i
$43$	0.854102	+	1.47935i	0.130249	+	0.225598i	0.923773	−	0.382941i	$-0.125089\pi$
$43$	0.854102	+	1.47935i	0.130249	+	0.225598i	−0.793523	+	0.608540i	$0.791756\pi$
$44$	1.61803	−	2.80252i	0.243928	−	0.422495i
$45$	−1.00000			−0.149071
$46$	4.00000			0.589768
$47$	−3.11803	+	5.40059i	−0.454812	+	0.787757i	−0.998677	−	0.0514150i	$-0.983627\pi$
$47$	−3.11803	+	5.40059i	−0.454812	+	0.787757i	0.543865	+	0.839172i	$0.316960\pi$
$48$	−0.927051	+	1.60570i	−0.133808	+	0.231763i
$49$	20.4164			2.91663
$50$	0.618034			0.0874032
$51$	−2.73607	+	4.73901i	−0.383126	+	0.663594i
$52$	2.61803	+	4.53457i	0.363056	+	0.628831i
$53$	0.500000	−	0.866025i	0.0686803	−	0.118958i	−0.829640	−	0.558298i	$-0.811454\pi$
$53$	0.500000	−	0.866025i	0.0686803	−	0.118958i	0.898321	+	0.439340i	$0.144788\pi$
$54$	−0.309017	−	0.535233i	−0.0420519	−	0.0728360i
$55$	1.00000	+	1.73205i	0.134840	+	0.233550i
$56$	−11.7082			−1.56457
$57$	−4.35410	−	0.204441i	−0.576715	−	0.0270789i
$58$	−3.23607			−0.424917
$59$	1.00000	+	1.73205i	0.130189	+	0.225494i	0.923749	−	0.382998i	$-0.125108\pi$
$59$	1.00000	+	1.73205i	0.130189	+	0.225494i	−0.793560	+	0.608492i	$0.791775\pi$
$60$	−0.809017	−	1.40126i	−0.104444	−	0.180902i
$61$	−1.76393	+	3.05522i	−0.225848	+	0.391181i	−0.956574	−	0.291491i	$-0.905849\pi$
$61$	−1.76393	+	3.05522i	−0.225848	+	0.391181i	0.730725	+	0.682672i	$0.239182\pi$
$62$	1.16312	+	2.01458i	0.147716	+	0.255852i
$63$	−2.61803	+	4.53457i	−0.329841	+	0.571302i
$64$	−0.236068			−0.0295085
$65$	−3.23607			−0.401385
$66$	−0.618034	+	1.07047i	−0.0760747	+	0.131765i
$67$	−0.618034	+	1.07047i	−0.0755049	+	0.130778i	−0.901306	−	0.433184i	$-0.857390\pi$
$67$	−0.618034	+	1.07047i	−0.0755049	+	0.130778i	0.825801	+	0.563962i	$0.190724\pi$
$68$	−8.85410			−1.07372
$69$	6.47214			0.779154
$70$	1.61803	−	2.80252i	0.193392	−	0.334965i
$71$	−2.38197	−	4.12569i	−0.282687	−	0.489629i	0.689358	−	0.724420i	$-0.257893\pi$
$71$	−2.38197	−	4.12569i	−0.282687	−	0.489629i	−0.972046	+	0.234792i	$0.924559\pi$
$72$	1.11803	−	1.93649i	0.131762	−	0.228218i
$73$	6.23607	+	10.8012i	0.729877	+	1.26418i	0.956935	+	0.290302i	$0.0937558\pi$
$73$	6.23607	+	10.8012i	0.729877	+	1.26418i	−0.227058	+	0.973881i	$0.572911\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$	1.00000			0.115470
$76$	−3.23607	−	6.26662i	−0.371202	−	0.718830i
$77$	10.4721			1.19341
$78$	−1.00000	−	1.73205i	−0.113228	−	0.196116i
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	0.927051	−	1.60570i	0.103647	−	0.179523i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.76393	−	3.05522i	0.194794	−	0.337393i
$83$	−7.18034			−0.788145			−0.394072	−	0.919079i	$-0.628934\pi$
$83$	−7.18034			−0.788145			−0.394072	+	0.919079i	$0.628934\pi$
$84$	−8.47214			−0.924386
$85$	2.73607	−	4.73901i	0.296768	−	0.514018i
$86$	0.527864	−	0.914287i	0.0569210	−	0.0985901i
$87$	−5.23607			−0.561365
$88$	−4.47214			−0.476731
$89$	−6.23607	+	10.8012i	−0.661022	+	1.14492i	0.319326	+	0.947645i	$0.396544\pi$
$89$	−6.23607	+	10.8012i	−0.661022	+	1.14492i	−0.980347	+	0.197278i	$0.936790\pi$
$90$	0.309017	+	0.535233i	0.0325733	+	0.0564185i
$91$	−8.47214	+	14.6742i	−0.888121	+	1.53827i
$92$	5.23607	+	9.06914i	0.545898	+	0.945523i
$93$	1.88197	+	3.25966i	0.195151	+	0.338011i
$94$	3.85410			0.397520
$95$	4.35410	+	0.204441i	0.446721	+	0.0209752i
$96$	5.61803			0.573388
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	0.912317	−	0.409484i	$-0.134291\pi$
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	−0.810782	+	0.585348i	$0.800958\pi$
$98$	−6.30902	−	10.9275i	−0.637307	−	1.10385i
$99$	−1.00000	+	1.73205i	−0.100504	+	0.174078i
$100$	0.809017	+	1.40126i	0.0809017	+	0.140126i
$101$	7.09017	−	12.2805i	0.705498	−	1.22196i	−0.261013	−	0.965335i	$-0.584057\pi$
$101$	7.09017	−	12.2805i	0.705498	−	1.22196i	0.966511	−	0.256624i	$-0.0826101\pi$
$102$	3.38197			0.334865
$103$	−16.9443			−1.66957			−0.834784	−	0.550577i	$-0.814408\pi$
$103$	−16.9443			−1.66957			−0.834784	+	0.550577i	$0.814408\pi$
$104$	3.61803	−	6.26662i	0.354777	−	0.614493i
$105$	2.61803	−	4.53457i	0.255494	−	0.442529i
$106$	−0.618034			−0.0600288
$107$	17.6525			1.70653			0.853265	−	0.521478i	$-0.174619\pi$
$107$	17.6525			1.70653			0.853265	+	0.521478i	$0.174619\pi$
$108$	0.809017	−	1.40126i	0.0778477	−	0.134836i
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	0.983531	−	0.180741i	$-0.0578495\pi$
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	−0.648292	+	0.761392i	$0.724516\pi$
$110$	0.618034	−	1.07047i	0.0589272	−	0.102065i
$111$	3.23607	+	5.60503i	0.307154	+	0.532006i
$112$	−4.85410	−	8.40755i	−0.458670	−	0.794439i
$113$	15.4721			1.45550			0.727748	−	0.685845i	$-0.240567\pi$
$113$	15.4721			1.45550			0.727748	+	0.685845i	$0.240567\pi$
$114$	1.23607	+	2.39364i	0.115768	+	0.224184i
$115$	−6.47214			−0.603530
$116$	−4.23607	−	7.33708i	−0.393309	−	0.681231i
$117$	−1.61803	−	2.80252i	−0.149587	−	0.259093i
$118$	0.618034	−	1.07047i	0.0568946	−	0.0985444i
$119$	−14.3262	−	24.8138i	−1.31328	−	2.27467i
$120$	−1.11803	+	1.93649i	−0.102062	+	0.176777i
$121$	−7.00000			−0.636364
$122$	2.18034			0.197399
$123$	2.85410	−	4.94345i	0.257346	−	0.445736i
$124$	−3.04508	+	5.27424i	−0.273457	+	0.473641i
$125$	−1.00000			−0.0894427
$126$	3.23607			0.288292
$127$	5.38197	−	9.32184i	0.477572	−	0.827179i	−0.522097	−	0.852886i	$-0.674850\pi$
$127$	5.38197	−	9.32184i	0.477572	−	0.827179i	0.999670	+	0.0257065i	$0.00818354\pi$
$128$	5.69098	+	9.85707i	0.503017	+	0.871250i
$129$	0.854102	−	1.47935i	0.0751995	−	0.130249i
$130$	1.00000	+	1.73205i	0.0877058	+	0.151911i
$131$	−3.23607	−	5.60503i	−0.282737	−	0.489714i	0.689321	−	0.724456i	$-0.257909\pi$
$131$	−3.23607	−	5.60503i	−0.282737	−	0.489714i	−0.972058	+	0.234742i	$0.924576\pi$
$132$	−3.23607			−0.281664
$133$	12.3262	−	19.2087i	1.06882	−	1.66561i
$134$	0.763932			0.0659937
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	6.11803	+	10.5967i	0.524617	+	0.908663i
$137$	3.20820	−	5.55677i	0.274095	−	0.474747i	−0.695811	−	0.718225i	$-0.744955\pi$
$137$	3.20820	−	5.55677i	0.274095	−	0.474747i	0.969906	+	0.243478i	$0.0782883\pi$
$138$	−2.00000	−	3.46410i	−0.170251	−	0.294884i
$139$	−4.11803	+	7.13264i	−0.349287	+	0.604983i	−0.986123	−	0.166016i	$-0.946910\pi$
$139$	−4.11803	+	7.13264i	−0.349287	+	0.604983i	0.636836	+	0.770999i	$0.280243\pi$
$140$	8.47214			0.716026
$141$	6.23607			0.525172
$142$	−1.47214	+	2.54981i	−0.123539	+	0.213976i
$143$	−3.23607	+	5.60503i	−0.270614	+	0.468717i
$144$	1.85410			0.154508
$145$	5.23607			0.434832
$146$	3.85410	−	6.67550i	0.318968	−	0.552468i
$147$	−10.2082	−	17.6811i	−0.841958	−	1.45831i
$148$	−5.23607	+	9.06914i	−0.430402	+	0.745478i
$149$	−1.85410	−	3.21140i	−0.151894	−	0.263088i	0.780030	−	0.625742i	$-0.215204\pi$
$149$	−1.85410	−	3.21140i	−0.151894	−	0.263088i	−0.931924	+	0.362654i	$0.881871\pi$
$150$	−0.309017	−	0.535233i	−0.0252311	−	0.0437016i
$151$	−3.29180			−0.267883			−0.133941	−	0.990989i	$-0.542763\pi$
$151$	−3.29180			−0.267883			−0.133941	+	0.990989i	$0.542763\pi$
$152$	−5.26393	+	8.20311i	−0.426961	+	0.665360i
$153$	5.47214			0.442396
$154$	−3.23607	−	5.60503i	−0.260770	−	0.451667i
$155$	−1.88197	−	3.25966i	−0.151163	−	0.261822i
$156$	2.61803	−	4.53457i	0.209610	−	0.363056i
$157$	−10.0000	−	17.3205i	−0.798087	−	1.38233i	−0.920860	−	0.389892i	$-0.872512\pi$
$157$	−10.0000	−	17.3205i	−0.798087	−	1.38233i	0.122774	−	0.992435i	$-0.460821\pi$
$158$		0			0
$159$	−1.00000			−0.0793052
$160$	−5.61803			−0.444145
$161$	−16.9443	+	29.3483i	−1.33540	+	2.31297i
$162$	−0.309017	+	0.535233i	−0.0242787	+	0.0420519i
$163$	−8.94427			−0.700569			−0.350285	−	0.936643i	$-0.613915\pi$
$163$	−8.94427			−0.700569			−0.350285	+	0.936643i	$0.613915\pi$
$164$	9.23607			0.721216
$165$	1.00000	−	1.73205i	0.0778499	−	0.134840i
$166$	2.21885	+	3.84316i	0.172216	+	0.298287i
$167$	−11.5902	+	20.0748i	−0.896874	+	1.55343i	−0.0654066	+	0.997859i	$0.520834\pi$
$167$	−11.5902	+	20.0748i	−0.896874	+	1.55343i	−0.831468	+	0.555573i	$0.812499\pi$
$168$	5.85410	+	10.1396i	0.451654	+	0.782287i
$169$	1.26393	+	2.18919i	0.0972255	+	0.168400i
$170$	−3.38197			−0.259385
$171$	2.00000	+	3.87298i	0.152944	+	0.296174i
$172$	2.76393			0.210748
$173$	−11.9443	−	20.6881i	−0.908106	−	1.57289i	−0.816693	−	0.577073i	$-0.804195\pi$
$173$	−11.9443	−	20.6881i	−0.908106	−	1.57289i	−0.0914136	−	0.995813i	$-0.529139\pi$
$174$	1.61803	+	2.80252i	0.122663	+	0.212458i
$175$	−2.61803	+	4.53457i	−0.197905	+	0.342781i
$176$	−1.85410	−	3.21140i	−0.139758	−	0.242068i
$177$	1.00000	−	1.73205i	0.0751646	−	0.130189i
$178$	7.70820			0.577754
$179$	4.29180			0.320784			0.160392	−	0.987053i	$-0.448724\pi$
$179$	4.29180			0.320784			0.160392	+	0.987053i	$0.448724\pi$
$180$	−0.809017	+	1.40126i	−0.0603006	+	0.104444i
$181$	2.26393	−	3.92125i	0.168277	−	0.291464i	−0.769537	−	0.638602i	$-0.779513\pi$
$181$	2.26393	−	3.92125i	0.168277	−	0.291464i	0.937814	+	0.347138i	$0.112846\pi$
$182$	10.4721			0.776246
$183$	3.52786			0.260787
$184$	7.23607	−	12.5332i	0.533450	−	0.923963i
$185$	−3.23607	−	5.60503i	−0.237920	−	0.412090i
$186$	1.16312	−	2.01458i	0.0852840	−	0.147716i
$187$	−5.47214	−	9.47802i	−0.400162	−	0.693101i
$188$	5.04508	+	8.73834i	0.367951	+	0.637309i
$189$	5.23607			0.380868
$190$	−1.23607	−	2.39364i	−0.0896738	−	0.173653i
$191$	8.29180			0.599973			0.299987	−	0.953943i	$-0.403018\pi$
$191$	8.29180			0.599973			0.299987	+	0.953943i	$0.403018\pi$
$192$	0.118034	+	0.204441i	0.00851837	+	0.0147542i
$193$	−4.61803	−	7.99867i	−0.332413	−	0.575757i	0.650571	−	0.759445i	$-0.274530\pi$
$193$	−4.61803	−	7.99867i	−0.332413	−	0.575757i	−0.982985	+	0.183688i	$0.941196\pi$
$194$	0.618034	−	1.07047i	0.0443723	−	0.0768550i
$195$	1.61803	+	2.80252i	0.115870	+	0.200692i
$196$	16.5172	−	28.6087i	1.17980	−	2.04348i
$197$	2.52786			0.180103			0.0900514	−	0.995937i	$-0.471297\pi$
$197$	2.52786			0.180103			0.0900514	+	0.995937i	$0.471297\pi$
$198$	1.23607			0.0878435
$199$	−10.9443	+	18.9560i	−0.775819	+	1.34376i	0.158514	+	0.987357i	$0.449330\pi$
$199$	−10.9443	+	18.9560i	−0.775819	+	1.34376i	−0.934333	+	0.356401i	$0.884004\pi$
$200$	1.11803	−	1.93649i	0.0790569	−	0.136931i
$201$	1.23607			0.0871855
$202$	−8.76393			−0.616628
$203$	13.7082	−	23.7433i	0.962127	−	1.66645i
$204$	4.42705	+	7.66788i	0.309956	+	0.536859i
$205$	−2.85410	+	4.94345i	−0.199339	+	0.345265i
$206$	5.23607	+	9.06914i	0.364814	+	0.631877i
$207$	−3.23607	−	5.60503i	−0.224922	−	0.389577i
$208$	6.00000			0.416025
$209$	4.70820	−	7.33708i	0.325673	−	0.507517i
$210$	−3.23607			−0.223310
$211$	1.59017	+	2.75426i	0.109472	+	0.189611i	0.915556	−	0.402190i	$-0.131751\pi$
$211$	1.59017	+	2.75426i	0.109472	+	0.189611i	−0.806085	+	0.591800i	$0.798417\pi$
$212$	−0.809017	−	1.40126i	−0.0555635	−	0.0962388i
$213$	−2.38197	+	4.12569i	−0.163210	+	0.282687i
$214$	−5.45492	−	9.44819i	−0.372890	−	0.645865i
$215$	−0.854102	+	1.47935i	−0.0582493	+	0.100891i
$216$	−2.23607			−0.152145
$217$	−19.7082			−1.33788
$218$	2.16312	−	3.74663i	0.146505	−	0.253754i
$219$	6.23607	−	10.8012i	0.421394	−	0.729877i
$220$	3.23607			0.218176
$221$	17.7082			1.19118
$222$	2.00000	−	3.46410i	0.134231	−	0.232495i
$223$	11.3262	+	19.6176i	0.758461	+	1.31369i	0.943635	+	0.330987i	$0.107382\pi$
$223$	11.3262	+	19.6176i	0.758461	+	1.31369i	−0.185174	+	0.982706i	$0.559285\pi$
$224$	−14.7082	+	25.4754i	−0.982733	+	1.70214i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	−4.78115	−	8.28120i	−0.318038	−	0.550857i
$227$	4.00000			0.265489			0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000			0.265489			0.132745	+	0.991150i	$0.457621\pi$
$228$	−3.80902	+	5.93583i	−0.252258	+	0.393110i
$229$	4.52786			0.299210			0.149605	−	0.988746i	$-0.452200\pi$
$229$	4.52786			0.299210			0.149605	+	0.988746i	$0.452200\pi$
$230$	2.00000	+	3.46410i	0.131876	+	0.228416i
$231$	−5.23607	−	9.06914i	−0.344508	−	0.596705i
$232$	−5.85410	+	10.1396i	−0.384341	+	0.665697i
$233$	8.97214	+	15.5402i	0.587784	+	1.01807i	0.994522	+	0.104527i	$0.0333329\pi$
$233$	8.97214	+	15.5402i	0.587784	+	1.01807i	−0.406738	+	0.913545i	$0.633334\pi$
$234$	−1.00000	+	1.73205i	−0.0653720	+	0.113228i
$235$	−6.23607			−0.406796
$236$	3.23607			0.210650
$237$		0			0
$238$	−8.85410	+	15.3358i	−0.573926	+	0.994069i
$239$	−19.1246			−1.23707			−0.618534	−	0.785758i	$-0.712273\pi$
$239$	−19.1246			−1.23707			−0.618534	+	0.785758i	$0.712273\pi$
$240$	−1.85410			−0.119682
$241$	−11.6803	+	20.2309i	−0.752397	+	1.30319i	0.194261	+	0.980950i	$0.437769\pi$
$241$	−11.6803	+	20.2309i	−0.752397	+	1.30319i	−0.946658	+	0.322240i	$0.895564\pi$
$242$	2.16312	+	3.74663i	0.139051	+	0.240843i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	2.85410	+	4.94345i	0.182715	+	0.316472i
$245$	10.2082	+	17.6811i	0.652178	+	1.12961i
$246$	−3.52786			−0.224928
$247$	6.47214	+	12.5332i	0.411812	+	0.797471i
$248$	8.41641			0.534442
$249$	3.59017	+	6.21836i	0.227518	+	0.394072i
$250$	0.309017	+	0.535233i	0.0195440	+	0.0338511i
$251$	−2.29180	+	3.96951i	−0.144657	+	0.250553i	−0.929245	−	0.369464i	$-0.879541\pi$
$251$	−2.29180	+	3.96951i	−0.144657	+	0.250553i	0.784588	+	0.620017i	$0.212875\pi$
$252$	4.23607	+	7.33708i	0.266847	+	0.462193i
$253$	−6.47214	+	11.2101i	−0.406900	+	0.704771i
$254$	−6.65248			−0.417413
$255$	−5.47214			−0.342678
$256$	3.28115	−	5.68312i	0.205072	−	0.355195i
$257$	10.7082	−	18.5472i	0.667959	−	1.15694i	−0.310514	−	0.950569i	$-0.600501\pi$
$257$	10.7082	−	18.5472i	0.667959	−	1.15694i	0.978474	−	0.206371i	$-0.0661654\pi$
$258$	−1.05573			−0.0657268
$259$	−33.8885			−2.10573
$260$	−2.61803	+	4.53457i	−0.162364	+	0.281222i
$261$	2.61803	+	4.53457i	0.162052	+	0.280683i
$262$	−2.00000	+	3.46410i	−0.123560	+	0.214013i
$263$	−4.35410	−	7.54153i	−0.268485	−	0.465030i	0.699985	−	0.714157i	$-0.253190\pi$
$263$	−4.35410	−	7.54153i	−0.268485	−	0.465030i	−0.968471	+	0.249127i	$0.919856\pi$
$264$	2.23607	+	3.87298i	0.137620	+	0.238366i
$265$	1.00000			0.0614295
$266$	−14.0902	−	0.661585i	−0.863924	−	0.0405644i
$267$	12.4721			0.763282
$268$	1.00000	+	1.73205i	0.0610847	+	0.105802i
$269$	−3.52786	−	6.11044i	−0.215098	−	0.372560i	0.738205	−	0.674576i	$-0.235674\pi$
$269$	−3.52786	−	6.11044i	−0.215098	−	0.372560i	−0.953303	+	0.302016i	$0.902340\pi$
$270$	0.309017	−	0.535233i	0.0188062	−	0.0325733i
$271$	−3.88197	−	6.72376i	−0.235813	−	0.408439i	0.723696	−	0.690119i	$-0.242442\pi$
$271$	−3.88197	−	6.72376i	−0.235813	−	0.408439i	−0.959509	+	0.281680i	$0.909109\pi$
$272$	−5.07295	+	8.78661i	−0.307593	+	0.532766i
$273$	16.9443			1.02551
$274$	−3.96556			−0.239568
$275$	−1.00000	+	1.73205i	−0.0603023	+	0.104447i
$276$	5.23607	−	9.06914i	0.315174	−	0.545898i
$277$	4.29180			0.257869			0.128935	−	0.991653i	$-0.458844\pi$
$277$	4.29180			0.257869			0.128935	+	0.991653i	$0.458844\pi$
$278$	5.09017			0.305288
$279$	1.88197	−	3.25966i	0.112670	−	0.195151i
$280$	−5.85410	−	10.1396i	−0.349850	−	0.605957i
$281$	1.61803	−	2.80252i	0.0965238	−	0.167184i	−0.813720	−	0.581257i	$-0.802561\pi$
$281$	1.61803	−	2.80252i	0.0965238	−	0.167184i	0.910244	+	0.414073i	$0.135894\pi$
$282$	−1.92705	−	3.33775i	−0.114754	−	0.198760i
$283$	6.09017	+	10.5485i	0.362023	+	0.627042i	0.988294	−	0.152563i	$-0.0487528\pi$
$283$	6.09017	+	10.5485i	0.362023	+	0.627042i	−0.626271	+	0.779606i	$0.715420\pi$
$284$	−7.70820			−0.457398
$285$	−2.00000	−	3.87298i	−0.118470	−	0.229416i
$286$	4.00000			0.236525
$287$	14.9443	+	25.8842i	0.882132	+	1.52790i
$288$	−2.80902	−	4.86536i	−0.165523	−	0.286694i
$289$	−6.47214	+	11.2101i	−0.380714	+	0.659416i
$290$	−1.61803	−	2.80252i	−0.0950142	−	0.164569i
$291$	1.00000	−	1.73205i	0.0586210	−	0.101535i
$292$	20.1803			1.18097
$293$	−30.4164			−1.77695			−0.888473	−	0.458929i	$-0.848233\pi$
$293$	−30.4164			−1.77695			−0.888473	+	0.458929i	$0.848233\pi$
$294$	−6.30902	+	10.9275i	−0.367949	+	0.637307i
$295$	−1.00000	+	1.73205i	−0.0582223	+	0.100844i
$296$	14.4721			0.841176
$297$	2.00000			0.116052
$298$	−1.14590	+	1.98475i	−0.0663801	+	0.114974i
$299$	−10.4721	−	18.1383i	−0.605619	−	1.04896i
$300$	0.809017	−	1.40126i	0.0467086	−	0.0809017i
$301$	4.47214	+	7.74597i	0.257770	+	0.446470i
$302$	1.01722	+	1.76188i	0.0585345	+	0.101385i
$303$	−14.1803			−0.814639
$304$	−8.07295	−	0.379054i	−0.463015	−	0.0217402i
$305$	−3.52786			−0.202005
$306$	−1.69098	−	2.92887i	−0.0966671	−	0.167432i
$307$	−1.09017	−	1.88823i	−0.0622193	−	0.107767i	0.833238	−	0.552915i	$-0.186484\pi$
$307$	−1.09017	−	1.88823i	−0.0622193	−	0.107767i	−0.895457	+	0.445148i	$0.853151\pi$
$308$	8.47214	−	14.6742i	0.482745	−	0.836138i
$309$	8.47214	+	14.6742i	0.481963	+	0.834784i
$310$	−1.16312	+	2.01458i	−0.0660607	+	0.114421i
$311$	5.41641			0.307136			0.153568	−	0.988138i	$-0.450924\pi$
$311$	5.41641			0.307136			0.153568	+	0.988138i	$0.450924\pi$
$312$	−7.23607			−0.409662
$313$	8.79837	−	15.2392i	0.497313	−	0.861372i	−0.502682	−	0.864472i	$-0.667653\pi$
$313$	8.79837	−	15.2392i	0.497313	−	0.861372i	0.999995	+	0.00309934i	$0.000986551\pi$
$314$	−6.18034	+	10.7047i	−0.348777	+	0.604099i
$315$	−5.23607			−0.295019
$316$		0			0
$317$	15.4443	−	26.7503i	0.867437	−	1.50244i	0.00282959	−	0.999996i	$-0.499099\pi$
$317$	15.4443	−	26.7503i	0.867437	−	1.50244i	0.864607	−	0.502448i	$-0.167567\pi$
$318$	0.309017	+	0.535233i	0.0173288	+	0.0300144i
$319$	5.23607	−	9.06914i	0.293164	−	0.507774i
$320$	−0.118034	−	0.204441i	−0.00659830	−	0.0114286i
$321$	−8.82624	−	15.2875i	−0.492633	−	0.853265i
$322$	20.9443			1.16718
$323$	−23.8262	−	1.11873i	−1.32573	−	0.0622477i
$324$	−1.61803			−0.0898908
$325$	−1.61803	−	2.80252i	−0.0897524	−	0.155456i
$326$	2.76393	+	4.78727i	0.153080	+	0.265142i
$327$	3.50000	−	6.06218i	0.193550	−	0.335239i
$328$	−6.38197	−	11.0539i	−0.352385	−	0.610349i
$329$	−16.3262	+	28.2779i	−0.900095	+	1.55901i
$330$	−1.23607			−0.0680433
$331$	6.47214			0.355741			0.177870	−	0.984054i	$-0.443079\pi$
$331$	6.47214			0.355741			0.177870	+	0.984054i	$0.443079\pi$
$332$	−5.80902	+	10.0615i	−0.318811	+	0.552197i
$333$	3.23607	−	5.60503i	0.177335	−	0.307154i
$334$	14.3262			0.783897
$335$	−1.23607			−0.0675336
$336$	−4.85410	+	8.40755i	−0.264813	+	0.458670i
$337$	−1.23607	−	2.14093i	−0.0673329	−	0.116624i	0.830394	−	0.557177i	$-0.188116\pi$
$337$	−1.23607	−	2.14093i	−0.0673329	−	0.116624i	−0.897726	+	0.440553i	$0.854782\pi$
$338$	0.781153	−	1.35300i	0.0424891	−	0.0735933i
$339$	−7.73607	−	13.3993i	−0.420166	−	0.727748i
$340$	−4.42705	−	7.66788i	−0.240091	−	0.415849i
$341$	−7.52786			−0.407657
$342$	1.45492	−	2.26728i	0.0786728	−	0.122601i
$343$	70.2492			3.79310
$344$	−1.90983	−	3.30792i	−0.102971	−	0.178351i
$345$	3.23607	+	5.60503i	0.174224	+	0.301765i
$346$	−7.38197	+	12.7859i	−0.396857	+	0.687376i
$347$	−6.06231	−	10.5002i	−0.325442	−	0.563681i	0.656160	−	0.754622i	$-0.272180\pi$
$347$	−6.06231	−	10.5002i	−0.325442	−	0.563681i	−0.981602	+	0.190940i	$0.938846\pi$
$348$	−4.23607	+	7.33708i	−0.227077	+	0.393309i
$349$	−27.0000			−1.44528			−0.722638	−	0.691226i	$-0.757071\pi$
$349$	−27.0000			−1.44528			−0.722638	+	0.691226i	$0.757071\pi$
$350$	3.23607			0.172975
$351$	−1.61803	+	2.80252i	−0.0863643	+	0.149587i
$352$	−5.61803	+	9.73072i	−0.299442	+	0.518649i
$353$	13.0557			0.694886			0.347443	−	0.937701i	$-0.387050\pi$
$353$	13.0557			0.694886			0.347443	+	0.937701i	$0.387050\pi$
$354$	−1.23607			−0.0656963
$355$	2.38197	−	4.12569i	0.126422	−	0.218969i
$356$	10.0902	+	17.4767i	0.534778	+	0.926263i
$357$	−14.3262	+	24.8138i	−0.758225	+	1.31328i
$358$	−1.32624	−	2.29711i	−0.0700939	−	0.121406i
$359$	−16.2361	−	28.1217i	−0.856907	−	1.48421i	−0.874865	−	0.484368i	$-0.839050\pi$
$359$	−16.2361	−	28.1217i	−0.856907	−	1.48421i	0.0179577	−	0.999839i	$-0.494284\pi$
$360$	2.23607			0.117851
$361$	−7.91641	−	17.2722i	−0.416653	−	0.909066i
$362$	−2.79837			−0.147079
$363$	3.50000	+	6.06218i	0.183702	+	0.318182i
$364$	13.7082	+	23.7433i	0.718505	+	1.24449i
$365$	−6.23607	+	10.8012i	−0.326411	+	0.565360i
$366$	−1.09017	−	1.88823i	−0.0569841	−	0.0986993i
$367$	8.09017	−	14.0126i	0.422303	−	0.731451i	−0.573861	−	0.818953i	$-0.694555\pi$
$367$	8.09017	−	14.0126i	0.422303	−	0.731451i	0.996164	+	0.0875018i	$0.0278883\pi$
$368$	12.0000			0.625543
$369$	−5.70820			−0.297157
$370$	−2.00000	+	3.46410i	−0.103975	+	0.180090i
$371$	2.61803	−	4.53457i	0.135922	−	0.235423i
$372$	6.09017			0.315761
$373$	−13.5967			−0.704013			−0.352006	−	0.935998i	$-0.614500\pi$
$373$	−13.5967			−0.704013			−0.352006	+	0.935998i	$0.614500\pi$
$374$	−3.38197	+	5.85774i	−0.174877	+	0.302896i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	6.97214	−	12.0761i	0.359560	−	0.622777i
$377$	8.47214	+	14.6742i	0.436337	+	0.755758i
$378$	−1.61803	−	2.80252i	−0.0832227	−	0.144146i
$379$	34.4721			1.77071			0.885357	−	0.464911i	$-0.153914\pi$
$379$	34.4721			1.77071			0.885357	+	0.464911i	$0.153914\pi$
$380$	3.80902	−	5.93583i	0.195398	−	0.304501i
$381$	−10.7639			−0.551453
$382$	−2.56231	−	4.43804i	−0.131099	−	0.227070i
$383$	2.06231	+	3.57202i	0.105379	+	0.182522i	0.913893	−	0.405955i	$-0.133061\pi$
$383$	2.06231	+	3.57202i	0.105379	+	0.182522i	−0.808514	+	0.588477i	$0.799728\pi$
$384$	5.69098	−	9.85707i	0.290417	−	0.503017i
$385$	5.23607	+	9.06914i	0.266855	+	0.462206i
$386$	−2.85410	+	4.94345i	−0.145270	+	0.251615i
$387$	−1.70820			−0.0868329
$388$	3.23607			0.164286
$389$	16.5623	−	28.6868i	0.839742	−	1.45448i	−0.0503679	−	0.998731i	$-0.516039\pi$
$389$	16.5623	−	28.6868i	0.839742	−	1.45448i	0.890110	−	0.455745i	$-0.150627\pi$
$390$	1.00000	−	1.73205i	0.0506370	−	0.0877058i
$391$	35.4164			1.79108
$392$	−45.6525			−2.30580
$393$	−3.23607	+	5.60503i	−0.163238	+	0.282737i
$394$	−0.781153	−	1.35300i	−0.0393539	−	0.0681630i
$395$		0			0
$396$	1.61803	+	2.80252i	0.0813093	+	0.140832i
$397$	−4.09017	−	7.08438i	−0.205280	−	0.355555i	0.744942	−	0.667129i	$-0.232477\pi$
$397$	−4.09017	−	7.08438i	−0.205280	−	0.355555i	−0.950222	+	0.311574i	$0.899144\pi$
$398$	13.5279			0.678091
$399$	−22.7984	−	1.07047i	−1.14135	−	0.0535903i
$400$	1.85410			0.0927051
$401$	−10.1459	−	17.5732i	−0.506662	−	0.877564i	−0.999970	−	0.00770974i	$-0.997546\pi$
$401$	−10.1459	−	17.5732i	−0.506662	−	0.877564i	0.493308	−	0.869855i	$-0.335787\pi$
$402$	−0.381966	−	0.661585i	−0.0190507	−	0.0329968i
$403$	6.09017	−	10.5485i	0.303373	−	0.525457i
$404$	−11.4721	−	19.8703i	−0.570760	−	0.988585i
$405$	0.500000	−	0.866025i	0.0248452	−	0.0430331i
$406$	−16.9443			−0.840930
$407$	−12.9443			−0.641624
$408$	6.11803	−	10.5967i	0.302888	−	0.524617i
$409$	13.1803	−	22.8290i	0.651726	−	1.12882i	−0.330978	−	0.943638i	$-0.607379\pi$
$409$	13.1803	−	22.8290i	0.651726	−	1.12882i	0.982704	−	0.185184i	$-0.0592881\pi$
$410$	3.52786			0.174229
$411$	−6.41641			−0.316498
$412$	−13.7082	+	23.7433i	−0.675355	+	1.16975i
$413$	5.23607	+	9.06914i	0.257650	+	0.446263i
$414$	−2.00000	+	3.46410i	−0.0982946	+	0.170251i
$415$	−3.59017	−	6.21836i	−0.176235	−	0.305247i
$416$	−9.09017	−	15.7446i	−0.445682	−	0.771944i
$417$	8.23607			0.403322
$418$	−5.38197	−	0.252703i	−0.263241	−	0.0123601i
$419$	17.0557			0.833227			0.416613	−	0.909084i	$-0.363217\pi$
$419$	17.0557			0.833227			0.416613	+	0.909084i	$0.363217\pi$
$420$	−4.23607	−	7.33708i	−0.206699	−	0.358013i
$421$	−13.1803	−	22.8290i	−0.642370	−	1.11262i	−0.984902	−	0.173112i	$-0.944618\pi$
$421$	−13.1803	−	22.8290i	−0.642370	−	1.11262i	0.342532	−	0.939506i	$-0.388716\pi$
$422$	0.982779	−	1.70222i	0.0478409	−	0.0828629i
$423$	−3.11803	−	5.40059i	−0.151604	−	0.262586i
$424$	−1.11803	+	1.93649i	−0.0542965	+	0.0940443i
$425$	5.47214			0.265438
$426$	2.94427			0.142650
$427$	−9.23607	+	15.9973i	−0.446965	+	0.774165i
$428$	14.2812	−	24.7357i	0.690306	−	1.19564i
$429$	6.47214			0.312478
$430$	1.05573			0.0509117
$431$	5.23607	−	9.06914i	0.252213	−	0.436845i	−0.711922	−	0.702258i	$-0.752175\pi$
$431$	5.23607	−	9.06914i	0.252213	−	0.436845i	0.964135	+	0.265413i	$0.0855085\pi$
$432$	−0.927051	−	1.60570i	−0.0446028	−	0.0772542i
$433$	19.7984	−	34.2918i	0.951449	−	1.64796i	0.209157	−	0.977882i	$-0.432928\pi$
$433$	19.7984	−	34.2918i	0.951449	−	1.64796i	0.742292	−	0.670076i	$-0.233739\pi$
$434$	6.09017	+	10.5485i	0.292338	+	0.506343i
$435$	−2.61803	−	4.53457i	−0.125525	−	0.217416i
$436$	11.3262			0.542428
$437$	12.9443	+	25.0665i	0.619208	+	1.19909i
$438$	−7.70820			−0.368312
$439$	0.881966	+	1.52761i	0.0420939	+	0.0729088i	0.886305	−	0.463102i	$-0.153264\pi$
$439$	0.881966	+	1.52761i	0.0420939	+	0.0729088i	−0.844211	+	0.536011i	$0.819930\pi$
$440$	−2.23607	−	3.87298i	−0.106600	−	0.184637i
$441$	−10.2082	+	17.6811i	−0.486105	+	0.841958i
$442$	−5.47214	−	9.47802i	−0.260283	−	0.450823i
$443$	3.35410	−	5.80948i	0.159358	−	0.276016i	−0.775279	−	0.631619i	$-0.782391\pi$
$443$	3.35410	−	5.80948i	0.159358	−	0.276016i	0.934637	+	0.355602i	$0.115724\pi$
$444$	10.4721			0.496986
$445$	−12.4721			−0.591236
$446$	7.00000	−	12.1244i	0.331460	−	0.574105i
$447$	−1.85410	+	3.21140i	−0.0876960	+	0.151894i
$448$	−1.23607			−0.0583987
$449$	32.0689			1.51342			0.756712	−	0.653748i	$-0.226804\pi$
$449$	32.0689			1.51342			0.756712	+	0.653748i	$0.226804\pi$
$450$	−0.309017	+	0.535233i	−0.0145672	+	0.0252311i
$451$	5.70820	+	9.88690i	0.268789	+	0.465556i
$452$	12.5172	−	21.6805i	0.588761	−	1.01976i
$453$	1.64590	+	2.85078i	0.0773310	+	0.133941i
$454$	−1.23607	−	2.14093i	−0.0580115	−	0.100479i
$455$	−16.9443			−0.794360
$456$	9.73607	+	0.457144i	0.455933	+	0.0214077i
$457$	29.2361			1.36761			0.683803	−	0.729667i	$-0.260325\pi$
$457$	29.2361			1.36761			0.683803	+	0.729667i	$0.260325\pi$
$458$	−1.39919	−	2.42346i	−0.0653797	−	0.113241i
$459$	−2.73607	−	4.73901i	−0.127709	−	0.221198i
$460$	−5.23607	+	9.06914i	−0.244133	+	0.422851i
$461$	19.6180	+	33.9794i	0.913703	+	1.58258i	0.808789	+	0.588099i	$0.200123\pi$
$461$	19.6180	+	33.9794i	0.913703	+	1.58258i	0.104914	+	0.994481i	$0.466543\pi$
$462$	−3.23607	+	5.60503i	−0.150556	+	0.260770i
$463$	−24.2918			−1.12894			−0.564468	−	0.825455i	$-0.690919\pi$
$463$	−24.2918			−1.12894			−0.564468	+	0.825455i	$0.690919\pi$
$464$	−9.70820			−0.450692
$465$	−1.88197	+	3.25966i	−0.0872741	+	0.151163i
$466$	5.54508	−	9.60437i	0.256871	−	0.444914i
$467$	−20.2361			−0.936414			−0.468207	−	0.883619i	$-0.655100\pi$
$467$	−20.2361			−0.936414			−0.468207	+	0.883619i	$0.655100\pi$
$468$	−5.23607			−0.242037
$469$	−3.23607	+	5.60503i	−0.149428	+	0.258816i
$470$	1.92705	+	3.33775i	0.0888882	+	0.153959i
$471$	−10.0000	+	17.3205i	−0.460776	+	0.798087i
$472$	−2.23607	−	3.87298i	−0.102923	−	0.178269i
$473$	1.70820	+	2.95870i	0.0785433	+	0.136041i
$474$		0			0
$475$	2.00000	+	3.87298i	0.0917663	+	0.177705i
$476$	−46.3607			−2.12494
$477$	0.500000	+	0.866025i	0.0228934	+	0.0396526i
$478$	5.90983	+	10.2361i	0.270309	+	0.468190i
$479$	−12.0344	+	20.8443i	−0.549868	+	0.952399i	0.448415	+	0.893825i	$0.351989\pi$
$479$	−12.0344	+	20.8443i	−0.549868	+	0.952399i	−0.998283	+	0.0585735i	$0.981345\pi$
$480$	2.80902	+	4.86536i	0.128213	+	0.222072i
$481$	10.4721	−	18.1383i	0.477488	−	0.827034i
$482$	14.4377			0.657619
$483$	33.8885			1.54198
$484$	−5.66312	+	9.80881i	−0.257414	+	0.445855i
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$	0.618034			0.0280346
$487$	−20.2918			−0.919509			−0.459755	−	0.888046i	$-0.652063\pi$
$487$	−20.2918			−0.919509			−0.459755	+	0.888046i	$0.652063\pi$
$488$	3.94427	−	6.83168i	0.178549	−	0.309256i
$489$	4.47214	+	7.74597i	0.202237	+	0.350285i
$490$	6.30902	−	10.9275i	0.285012	−	0.493656i
$491$	4.14590	+	7.18091i	0.187102	+	0.324070i	0.944283	−	0.329135i	$-0.106757\pi$
$491$	4.14590	+	7.18091i	0.187102	+	0.324070i	−0.757181	+	0.653205i	$0.773424\pi$
$492$	−4.61803	−	7.99867i	−0.208197	−	0.360608i
$493$	−28.6525			−1.29044
$494$	4.70820	−	7.33708i	0.211832	−	0.330111i
$495$	−2.00000			−0.0898933
$496$	3.48936	+	6.04374i	0.156677	+	0.271372i
$497$	−12.4721	−	21.6024i	−0.559452	−	0.968999i
$498$	2.21885	−	3.84316i	0.0994289	−	0.172216i
$499$	−3.82624	−	6.62724i	−0.171286	−	0.296676i	0.767584	−	0.640949i	$-0.221459\pi$
$499$	−3.82624	−	6.62724i	−0.171286	−	0.296676i	−0.938870	+	0.344273i	$0.888126\pi$
$500$	−0.809017	+	1.40126i	−0.0361803	+	0.0626662i
$501$	23.1803			1.03562
$502$	2.83282			0.126435
$503$	−14.1180	+	24.4532i	−0.629492	+	1.09031i	0.358162	+	0.933660i	$0.383404\pi$
$503$	−14.1180	+	24.4532i	−0.629492	+	1.09031i	−0.987654	+	0.156653i	$0.949930\pi$
$504$	5.85410	−	10.1396i	0.260762	−	0.451654i
$505$	14.1803			0.631017
$506$	8.00000			0.355643
$507$	1.26393	−	2.18919i	0.0561332	−	0.0972255i
$508$	−8.70820	−	15.0831i	−0.386364	−	0.669202i
$509$	−10.8541	+	18.7999i	−0.481100	+	0.833289i	−0.999765	−	0.0216885i	$-0.993096\pi$
$509$	−10.8541	+	18.7999i	−0.481100	+	0.833289i	0.518665	+	0.854977i	$0.326429\pi$
$510$	1.69098	+	2.92887i	0.0748780	+	0.129692i
$511$	32.6525	+	56.5557i	1.44446	+	2.50188i
$512$	18.7082			0.826794
$513$	2.35410	−	3.66854i	0.103936	−	0.161970i
$514$	−13.2361			−0.583818
$515$	−8.47214	−	14.6742i	−0.373327	−	0.646621i
$516$	−1.38197	−	2.39364i	−0.0608377	−	0.105374i
$517$	−6.23607	+	10.8012i	−0.274262	+	0.475036i
$518$	10.4721	+	18.1383i	0.460119	+	0.796950i
$519$	−11.9443	+	20.6881i	−0.524295	+	0.908106i
$520$	7.23607			0.317323
$521$	1.41641			0.0620540			0.0310270	−	0.999519i	$-0.490122\pi$
$521$	1.41641			0.0620540			0.0310270	+	0.999519i	$0.490122\pi$
$522$	1.61803	−	2.80252i	0.0708194	−	0.122663i
$523$	4.41641	−	7.64944i	0.193116	−	0.334487i	−0.753165	−	0.657831i	$-0.771474\pi$
$523$	4.41641	−	7.64944i	0.193116	−	0.334487i	0.946281	+	0.323345i	$0.104807\pi$
$524$	−10.4721			−0.457477
$525$	5.23607			0.228521
$526$	−2.69098	+	4.66092i	−0.117332	+	0.203226i
$527$	10.2984	+	17.8373i	0.448604	+	0.777005i
$528$	−1.85410	+	3.21140i	−0.0806894	+	0.139758i
$529$	−9.44427	−	16.3580i	−0.410621	−	0.711216i
$530$	−0.309017	−	0.535233i	−0.0134228	−	0.0232490i
$531$	−2.00000			−0.0867926
$532$	−16.9443	−	32.8124i	−0.734627	−	1.42260i
$533$	−18.4721			−0.800117
$534$	−3.85410	−	6.67550i	−0.166783	−	0.288877i
$535$	8.82624	+	15.2875i	0.381592	+	0.660936i
$536$	1.38197	−	2.39364i	0.0596918	−	0.103389i
$537$	−2.14590	−	3.71680i	−0.0926023	−	0.160392i
$538$	−2.18034	+	3.77646i	−0.0940011	+	0.162815i
$539$	40.8328			1.75879
$540$	1.61803			0.0696291
$541$	7.79180	−	13.4958i	0.334995	−	0.580229i	−0.648488	−	0.761224i	$-0.724599\pi$
$541$	7.79180	−	13.4958i	0.334995	−	0.580229i	0.983484	+	0.180995i	$0.0579319\pi$
$542$	−2.39919	+	4.15551i	−0.103054	+	0.178495i
$543$	−4.52786			−0.194309
$544$	30.7426			1.31808
$545$	−3.50000	+	6.06218i	−0.149924	+	0.259675i
$546$	−5.23607	−	9.06914i	−0.224083	−	0.388123i
$547$	14.4164	−	24.9700i	0.616401	−	1.06764i	−0.373736	−	0.927535i	$-0.621923\pi$
$547$	14.4164	−	24.9700i	0.616401	−	1.06764i	0.990137	−	0.140103i	$-0.0447433\pi$
$548$	−5.19098	−	8.99105i	−0.221748	−	0.384078i
$549$	−1.76393	−	3.05522i	−0.0752828	−	0.130394i
$550$	1.23607			0.0527061
$551$	−10.4721	−	20.2792i	−0.446128	−	0.863923i
$552$	−14.4721			−0.615975
$553$		0			0
$554$	−1.32624	−	2.29711i	−0.0563464	−	0.0975949i
$555$	−3.23607	+	5.60503i	−0.137363	+	0.237920i
$556$	6.66312	+	11.5409i	0.282579	+	0.489442i
$557$	15.1803	−	26.2931i	0.643212	−	1.11408i	−0.341500	−	0.939882i	$-0.610935\pi$
$557$	15.1803	−	26.2931i	0.643212	−	1.11408i	0.984711	−	0.174193i	$-0.0557318\pi$
$558$	−2.32624			−0.0984775
$559$	−5.52786			−0.233804
$560$	4.85410	−	8.40755i	0.205123	−	0.355284i
$561$	−5.47214	+	9.47802i	−0.231034	+	0.400162i
$562$	−2.00000			−0.0843649
$563$	−37.0689			−1.56227			−0.781134	−	0.624364i	$-0.785358\pi$
$563$	−37.0689			−1.56227			−0.781134	+	0.624364i	$0.785358\pi$
$564$	5.04508	−	8.73834i	0.212436	−	0.367951i
$565$	7.73607	+	13.3993i	0.325459	+	0.563711i
$566$	3.76393	−	6.51932i	0.158210	−	0.274028i
$567$	−2.61803	−	4.53457i	−0.109947	−	0.190434i
$568$	5.32624	+	9.22531i	0.223484	+	0.387086i
$569$	2.94427			0.123430			0.0617151	−	0.998094i	$-0.480343\pi$
$569$	2.94427			0.123430			0.0617151	+	0.998094i	$0.480343\pi$
$570$	−1.45492	+	2.26728i	−0.0609397	+	0.0949661i
$571$	−15.6525			−0.655036			−0.327518	−	0.944845i	$-0.606212\pi$
$571$	−15.6525			−0.655036			−0.327518	+	0.944845i	$0.606212\pi$
$572$	5.23607	+	9.06914i	0.218931	+	0.379200i
$573$	−4.14590	−	7.18091i	−0.173197	−	0.299987i
$574$	9.23607	−	15.9973i	0.385506	−	0.667716i
$575$	−3.23607	−	5.60503i	−0.134953	−	0.233746i
$576$	0.118034	−	0.204441i	0.00491808	−	0.00851837i
$577$	−18.0000			−0.749350			−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000			−0.749350			−0.374675	+	0.927156i	$0.622246\pi$
$578$	8.00000			0.332756
$579$	−4.61803	+	7.99867i	−0.191919	+	0.332413i
$580$	4.23607	−	7.33708i	0.175893	−	0.304656i
$581$	−37.5967			−1.55978
$582$	−1.23607			−0.0512367
$583$	1.00000	−	1.73205i	0.0414158	−	0.0717342i
$584$	−13.9443	−	24.1522i	−0.577018	−	0.999425i
$585$	1.61803	−	2.80252i	0.0668975	−	0.115870i
$586$	9.39919	+	16.2799i	0.388277	+	0.672515i
$587$	1.82624	+	3.16314i	0.0753769	+	0.130557i	0.901250	−	0.433299i	$-0.142651\pi$
$587$	1.82624	+	3.16314i	0.0753769	+	0.130557i	−0.825873	+	0.563856i	$0.809317\pi$
$588$	−33.0344			−1.36232
$589$	−8.86068	+	13.8081i	−0.365098	+	0.568955i
$590$	1.23607			0.0508881
$591$	−1.26393	−	2.18919i	−0.0519912	−	0.0900514i
$592$	6.00000	+	10.3923i	0.246598	+	0.427121i
$593$	−11.4443	+	19.8221i	−0.469960	+	0.813994i	−0.999410	−	0.0343466i	$-0.989065\pi$
$593$	−11.4443	+	19.8221i	−0.469960	+	0.813994i	0.529450	+	0.848341i	$0.322398\pi$
$594$	−0.618034	−	1.07047i	−0.0253582	−	0.0439218i
$595$	14.3262	−	24.8138i	0.587318	−	1.01727i
$596$	−6.00000			−0.245770
$597$	21.8885			0.895838
$598$	−6.47214	+	11.2101i	−0.264665	+	0.458414i
$599$	0.562306	−	0.973942i	0.0229752	−	0.0397942i	−0.854309	−	0.519765i	$-0.826019\pi$
$599$	0.562306	−	0.973942i	0.0229752	−	0.0397942i	0.877284	+	0.479971i	$0.159353\pi$
$600$	−2.23607			−0.0912871
$601$	23.8885			0.974434			0.487217	−	0.873281i	$-0.338012\pi$
$601$	23.8885			0.974434			0.487217	+	0.873281i	$0.338012\pi$
$602$	2.76393	−	4.78727i	0.112649	−	0.195115i
$603$	−0.618034	−	1.07047i	−0.0251683	−	0.0435928i
$604$	−2.66312	+	4.61266i	−0.108361	+	0.187686i
$605$	−3.50000	−	6.06218i	−0.142295	−	0.246463i
$606$	4.38197	+	7.58979i	0.178005	+	0.308314i
$607$	39.4164			1.59986			0.799931	−	0.600092i	$-0.204869\pi$
$607$	39.4164			1.59986			0.799931	+	0.600092i	$0.204869\pi$
$608$	11.2361	+	21.7586i	0.455683	+	0.882426i
$609$	−27.4164			−1.11097
$610$	1.09017	+	1.88823i	0.0441397	+	0.0764522i
$611$	−10.0902	−	17.4767i	−0.408205	−	0.707031i
$612$	4.42705	−	7.66788i	0.178953	−	0.309956i
$613$	−11.0000	−	19.0526i	−0.444286	−	0.769526i	0.553716	−	0.832705i	$-0.313209\pi$
$613$	−11.0000	−	19.0526i	−0.444286	−	0.769526i	−0.998002	+	0.0631797i	$0.979876\pi$
$614$	−0.673762	+	1.16699i	−0.0271908	+	0.0470959i
$615$	5.70820			0.230177
$616$	−23.4164			−0.943474
$617$	−3.20820	+	5.55677i	−0.129157	+	0.223707i	−0.923350	−	0.383958i	$-0.874561\pi$
$617$	−3.20820	+	5.55677i	−0.129157	+	0.223707i	0.794193	+	0.607666i	$0.207894\pi$
$618$	5.23607	−	9.06914i	0.210626	−	0.364814i
$619$	0.708204			0.0284651			0.0142326	−	0.999899i	$-0.495469\pi$
$619$	0.708204			0.0284651			0.0142326	+	0.999899i	$0.495469\pi$
$620$	−6.09017			−0.244587
$621$	−3.23607	+	5.60503i	−0.129859	+	0.224922i
$622$	−1.67376	−	2.89904i	−0.0671117	−	0.116241i
$623$	−32.6525	+	56.5557i	−1.30819	+	2.26586i
$624$	−3.00000	−	5.19615i	−0.120096	−	0.208013i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−10.8754			−0.434668
$627$	−8.70820	−	0.408882i	−0.347772	−	0.0163292i
$628$	−32.3607			−1.29133
$629$	17.7082	+	30.6715i	0.706072	+	1.22295i
$630$	1.61803	+	2.80252i	0.0644640	+	0.111655i
$631$	−15.3541	+	26.5941i	−0.611237	+	1.05869i	0.379795	+	0.925071i	$0.375995\pi$
$631$	−15.3541	+	26.5941i	−0.611237	+	1.05869i	−0.991032	+	0.133623i	$0.957339\pi$
$632$		0			0
$633$	1.59017	−	2.75426i	0.0632036	−	0.109472i
$634$	−19.0902			−0.758168
$635$	10.7639			0.427154
$636$	−0.809017	+	1.40126i	−0.0320796	+	0.0555635i
$637$	−33.0344	+	57.2173i	−1.30887	+	2.26703i
$638$	−6.47214			−0.256234
$639$	4.76393			0.188458
$640$	−5.69098	+	9.85707i	−0.224956	+	0.389635i
$641$	8.52786	+	14.7707i	0.336830	+	0.583407i	0.983835	−	0.179079i	$-0.0573118\pi$
$641$	8.52786	+	14.7707i	0.336830	+	0.583407i	−0.647004	+	0.762486i	$0.723978\pi$
$642$	−5.45492	+	9.44819i	−0.215288	+	0.372890i
$643$	5.18034	+	8.97261i	0.204293	+	0.353845i	0.949907	−	0.312532i	$-0.101177\pi$
$643$	5.18034	+	8.97261i	0.204293	+	0.353845i	−0.745614	+	0.666378i	$0.767844\pi$
$644$	27.4164	+	47.4866i	1.08036	+	1.87123i
$645$	1.70820			0.0672605
$646$	6.76393	+	13.0983i	0.266123	+	0.515346i
$647$	−22.5967			−0.888370			−0.444185	−	0.895935i	$-0.646507\pi$
$647$	−22.5967			−0.888370			−0.444185	+	0.895935i	$0.646507\pi$
$648$	1.11803	+	1.93649i	0.0439205	+	0.0760726i
$649$	2.00000	+	3.46410i	0.0785069	+	0.135978i
$650$	−1.00000	+	1.73205i	−0.0392232	+	0.0679366i
$651$	9.85410	+	17.0678i	0.386213	+	0.668940i
$652$	−7.23607	+	12.5332i	−0.283386	+	0.490839i
$653$	−12.4721			−0.488072			−0.244036	−	0.969766i	$-0.578472\pi$
$653$	−12.4721			−0.488072			−0.244036	+	0.969766i	$0.578472\pi$
$654$	−4.32624			−0.169169
$655$	3.23607	−	5.60503i	0.126444	−	0.219007i
$656$	5.29180	−	9.16566i	0.206610	−	0.357859i
$657$	−12.4721			−0.486584
$658$	20.1803			0.786712
$659$	−2.76393	+	4.78727i	−0.107668	+	0.186486i	−0.914825	−	0.403851i	$-0.867672\pi$
$659$	−2.76393	+	4.78727i	−0.107668	+	0.186486i	0.807157	+	0.590336i	$0.201005\pi$
$660$	−1.61803	−	2.80252i	−0.0629819	−	0.109088i
$661$	23.2082	−	40.1978i	0.902695	−	1.56351i	0.0787121	−	0.996897i	$-0.474919\pi$
$661$	23.2082	−	40.1978i	0.902695	−	1.56351i	0.823982	−	0.566615i	$-0.191747\pi$
$662$	−2.00000	−	3.46410i	−0.0777322	−	0.134636i
$663$	−8.85410	−	15.3358i	−0.343865	−	0.595591i
$664$	16.0557			0.623083
$665$	22.7984	+	1.07047i	0.884083	+	0.0415109i
$666$	−4.00000			−0.154997
$667$	16.9443	+	29.3483i	0.656085	+	1.13637i
$668$	18.7533	+	32.4816i	0.725587	+	1.25675i
$669$	11.3262	−	19.6176i	0.437898	−	0.758461i
$670$	0.381966	+	0.661585i	0.0147566	+	0.0255592i
$671$	−3.52786	+	6.11044i	−0.136192	+	0.235891i
$672$	29.4164			1.13476
$673$	2.29180			0.0883422			0.0441711	−	0.999024i	$-0.485935\pi$
$673$	2.29180			0.0883422			0.0441711	+	0.999024i	$0.485935\pi$
$674$	−0.763932	+	1.32317i	−0.0294256	+	0.0509666i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	4.09017			0.157314
$677$	15.0000			0.576497			0.288248	−	0.957556i	$-0.406927\pi$
$677$	15.0000			0.576497			0.288248	+	0.957556i	$0.406927\pi$
$678$	−4.78115	+	8.28120i	−0.183619	+	0.318038i
$679$	5.23607	+	9.06914i	0.200942	+	0.348041i
$680$	−6.11803	+	10.5967i	−0.234616	+	0.406367i
$681$	−2.00000	−	3.46410i	−0.0766402	−	0.132745i
$682$	2.32624	+	4.02916i	0.0890763	+	0.154285i
$683$	12.8197			0.490531			0.245265	−	0.969456i	$-0.421125\pi$
$683$	12.8197			0.490531			0.245265	+	0.969456i	$0.421125\pi$
$684$	7.04508	+	0.330792i	0.269376	+	0.0126482i
$685$	6.41641			0.245158
$686$	−21.7082	−	37.5997i	−0.828823	−	1.43556i
$687$	−2.26393	−	3.92125i	−0.0863744	−	0.149605i
$688$	1.58359	−	2.74286i	0.0603739	−	0.104571i
$689$	1.61803	+	2.80252i	0.0616422	+	0.106767i
$690$	2.00000	−	3.46410i	0.0761387	−	0.131876i
$691$	−27.1803			−1.03399			−0.516994	−	0.855989i	$-0.672949\pi$
$691$	−27.1803			−1.03399			−0.516994	+	0.855989i	$0.672949\pi$
$692$	−38.6525			−1.46935
$693$	−5.23607	+	9.06914i	−0.198902	+	0.344508i
$694$	−3.74671	+	6.48949i	−0.142223	+	0.246338i
$695$	−8.23607			−0.312412
$696$	11.7082			0.443798
$697$	15.6180	−	27.0512i	0.591575	−	1.02464i
$698$	8.34346	+	14.4513i	0.315805	+	0.546990i
$699$	8.97214	−	15.5402i	0.339357	−	0.587784i
$700$	4.23607	+	7.33708i	0.160108	+	0.277316i
$701$	17.1803	+	29.7572i	0.648892	+	1.12391i	0.983388	+	0.181517i	$0.0581008\pi$
$701$	17.1803	+	29.7572i	0.648892	+	1.12391i	−0.334495	+	0.942397i	$0.608566\pi$
$702$	2.00000			0.0754851
$703$	−15.2361	+	23.7433i	−0.574639	+	0.895496i
$704$	−0.472136			−0.0177943
$705$	3.11803	+	5.40059i	0.117432	+	0.203398i
$706$	−4.03444	−	6.98786i	−0.151838	−	0.262992i
$707$	37.1246	−	64.3017i	1.39621	−	2.41831i
$708$	−1.61803	−	2.80252i	−0.0608094	−	0.105325i
$709$	5.91641	−	10.2475i	0.222195	−	0.384854i	−0.733279	−	0.679928i	$-0.762011\pi$
$709$	5.91641	−	10.2475i	0.222195	−	0.384854i	0.955474	+	0.295074i	$0.0953444\pi$
$710$	−2.94427			−0.110497
$711$		0			0
$712$	13.9443	−	24.1522i	0.522584	−	0.905141i
$713$	12.1803	−	21.0970i	0.456157	−	0.790088i
$714$	17.7082			0.662713
$715$	−6.47214			−0.242044
$716$	3.47214	−	6.01392i	0.129760	−	0.224751i
$717$	9.56231	+	16.5624i	0.357111	+	0.618534i
$718$	−10.0344	+	17.3802i	−0.374482	+	0.648622i
$719$	10.4721	+	18.1383i	0.390545	+	0.676443i	0.992521	−	0.122070i	$-0.0389533\pi$
$719$	10.4721	+	18.1383i	0.390545	+	0.676443i	−0.601977	+	0.798514i	$0.705620\pi$
$720$	0.927051	+	1.60570i	0.0345492	+	0.0598409i
$721$	−88.7214			−3.30416
$722$	−6.79837	+	9.57454i	−0.253009	+	0.356328i
$723$	23.3607			0.868793
$724$	−3.66312	−	6.34471i	−0.136139	−	0.235799i
$725$	2.61803	+	4.53457i	0.0972313	+	0.168410i
$726$	2.16312	−	3.74663i	0.0802809	−	0.139051i
$727$	−18.3820	−	31.8385i	−0.681749	−	1.18082i	−0.974447	−	0.224619i	$-0.927886\pi$
$727$	−18.3820	−	31.8385i	−0.681749	−	1.18082i	0.292697	−	0.956205i	$-0.405447\pi$
$728$	18.9443	−	32.8124i	0.702121	−	1.21611i
$729$	1.00000			0.0370370
$730$	7.70820			0.285293
$731$	4.67376	−	8.09519i	0.172865	−	0.299412i
$732$	2.85410	−	4.94345i	0.105491	−	0.182715i
$733$	8.87539			0.327820			0.163910	−	0.986475i	$-0.447589\pi$
$733$	8.87539			0.327820			0.163910	+	0.986475i	$0.447589\pi$
$734$	−10.0000			−0.369107
$735$	10.2082	−	17.6811i	0.376535	−	0.652178i
$736$	−18.1803	−	31.4893i	−0.670136	−	1.16071i
$737$	−1.23607	+	2.14093i	−0.0455311	+	0.0788623i
$738$	1.76393	+	3.05522i	0.0649312	+	0.112464i
$739$	−5.82624	−	10.0913i	−0.214322	−	0.371216i	0.738741	−	0.673990i	$-0.235421\pi$
$739$	−5.82624	−	10.0913i	−0.214322	−	0.371216i	−0.953063	+	0.302774i	$0.902087\pi$
$740$	−10.4721			−0.384963
$741$	7.61803	−	11.8717i	0.279855	−	0.436116i
$742$	−3.23607			−0.118800
$743$	3.06231	+	5.30407i	0.112345	+	0.194587i	0.916715	−	0.399541i	$-0.130830\pi$
$743$	3.06231	+	5.30407i	0.112345	+	0.194587i	−0.804370	+	0.594128i	$0.797497\pi$
$744$	−4.20820	−	7.28882i	−0.154280	−	0.267221i
$745$	1.85410	−	3.21140i	0.0679290	−	0.117657i
$746$	4.20163	+	7.27743i	0.153832	+	0.266446i
$747$	3.59017	−	6.21836i	0.131357	−	0.227518i
$748$	−17.7082			−0.647476
$749$	92.4296			3.37730
$750$	0.309017	−	0.535233i	0.0112837	−	0.0195440i
$751$	−14.8262	+	25.6798i	−0.541017	+	0.937069i	0.457829	+	0.889040i	$0.348627\pi$
$751$	−14.8262	+	25.6798i	−0.541017	+	0.937069i	−0.998846	+	0.0480288i	$0.984706\pi$
$752$	11.5623			0.421634
$753$	4.58359			0.167035
$754$	5.23607	−	9.06914i	0.190686	−	0.330278i
$755$	−1.64590	−	2.85078i	−0.0599004	−	0.103750i
$756$	4.23607	−	7.33708i	0.154064	−	0.266847i
$757$	9.56231	+	16.5624i	0.347548	+	0.601971i	0.985813	−	0.167846i	$-0.0536811\pi$
$757$	9.56231	+	16.5624i	0.347548	+	0.601971i	−0.638265	+	0.769816i	$0.720348\pi$
$758$	−10.6525	−	18.4506i	−0.386915	−	0.670157i
$759$	12.9443			0.469847
$760$	−9.73607	−	0.457144i	−0.353164	−	0.0165823i
$761$	10.0000			0.362500			0.181250	−	0.983437i	$-0.441986\pi$
$761$	10.0000			0.362500			0.181250	+	0.983437i	$0.441986\pi$
$762$	3.32624	+	5.76121i	0.120497	+	0.208707i
$763$	18.3262	+	31.7420i	0.663454	+	1.14914i
$764$	6.70820	−	11.6190i	0.242694	−	0.420359i
$765$	2.73607	+	4.73901i	0.0989227	+	0.171339i
$766$	1.27458	−	2.20763i	0.0460523	−	0.0797649i
$767$	−6.47214			−0.233695
$768$	−6.56231			−0.236797
$769$	−9.91641	+	17.1757i	−0.357595	+	0.619372i	−0.987558	−	0.157252i	$-0.949736\pi$
$769$	−9.91641	+	17.1757i	−0.357595	+	0.619372i	0.629964	+	0.776625i	$0.283070\pi$
$770$	3.23607	−	5.60503i	0.116620	−	0.201991i
$771$	−21.4164			−0.771293
$772$	−14.9443			−0.537856
$773$	−9.47214	+	16.4062i	−0.340689	+	0.590091i	−0.984561	−	0.175043i	$-0.943994\pi$
$773$	−9.47214	+	16.4062i	−0.340689	+	0.590091i	0.643872	+	0.765133i	$0.277327\pi$
$774$	0.527864	+	0.914287i	0.0189737	+	0.0328634i
$775$	1.88197	−	3.25966i	0.0676022	−	0.117090i
$776$	−2.23607	−	3.87298i	−0.0802702	−	0.139032i
$777$	16.9443	+	29.3483i	0.607872	+	1.05287i
$778$	−20.4721			−0.733962
$779$	24.8541	+	1.16699i	0.890491	+	0.0418118i
$780$	5.23607			0.187481
$781$	−4.76393	−	8.25137i	−0.170467	−	0.295257i
$782$	−10.9443	−	18.9560i	−0.391366	−	0.677866i
$783$	2.61803	−	4.53457i	0.0935609	−	0.162052i
$784$	−18.9271	−	32.7826i	−0.675966	−	1.17081i
$785$	10.0000	−	17.3205i	0.356915	−	0.618195i
$786$	4.00000			0.142675
$787$	14.7639			0.526277			0.263139	−	0.964758i	$-0.415242\pi$
$787$	14.7639			0.526277			0.263139	+	0.964758i	$0.415242\pi$
$788$	2.04508	−	3.54219i	0.0728531	−	0.126185i
$789$	−4.35410	+	7.54153i	−0.155010	+	0.268485i
$790$		0			0
$791$	81.0132			2.88050
$792$	2.23607	−	3.87298i	0.0794552	−	0.137620i
$793$	−5.70820	−	9.88690i	−0.202704	−	0.351094i
$794$	−2.52786	+	4.37839i	−0.0897105	+	0.155383i
$795$	−0.500000	−	0.866025i	−0.0177332	−	0.0307148i
$796$	17.7082	+	30.6715i	0.627651	+	1.08712i
$797$	−52.3050			−1.85274			−0.926368	−	0.376619i	$-0.877087\pi$
$797$	−52.3050			−1.85274			−0.926368	+	0.376619i	$0.877087\pi$
$798$	6.47214	+	12.5332i	0.229111	+	0.443672i
$799$	34.1246			1.20724
$800$	−2.80902	−	4.86536i	−0.0993137	−	0.172016i
$801$	−6.23607	−	10.8012i	−0.220341	−	0.381641i
$802$	−6.27051	+	10.8608i	−0.221419	+	0.383510i
$803$	12.4721	+	21.6024i	0.440132	+	0.762331i
$804$	1.00000	−	1.73205i	0.0352673	−	0.0610847i
$805$	−33.8885			−1.19441
$806$	−7.52786			−0.265158
$807$	−3.52786	+	6.11044i	−0.124187	+	0.215098i
$808$	−15.8541	+	27.4601i	−0.557745	+	0.966043i
$809$	−23.7082			−0.833536			−0.416768	−	0.909013i	$-0.636837\pi$
$809$	−23.7082			−0.833536			−0.416768	+	0.909013i	$0.636837\pi$
$810$	−0.618034			−0.0217155
$811$	10.5344	−	18.2462i	0.369914	−	0.640710i	−0.619638	−	0.784888i	$-0.712720\pi$
$811$	10.5344	−	18.2462i	0.369914	−	0.640710i	0.989552	+	0.144178i	$0.0460537\pi$
$812$	−22.1803	−	38.4175i	−0.778377	−	1.34819i
$813$	−3.88197	+	6.72376i	−0.136146	+	0.235813i
$814$	4.00000	+	6.92820i	0.140200	+	0.242833i
$815$	−4.47214	−	7.74597i	−0.156652	−	0.271329i
$816$	10.1459			0.355177
$817$	7.43769	+	0.349227i	0.260212	+	0.0122179i
$818$	−16.2918			−0.569629
$819$	−8.47214	−	14.6742i	−0.296040	−	0.512757i
$820$	4.61803	+	7.99867i	0.161269	+	0.279326i
$821$	−17.5623	+	30.4188i	−0.612929	+	1.06162i	0.377815	+	0.925881i	$0.376675\pi$
$821$	−17.5623	+	30.4188i	−0.612929	+	1.06162i	−0.990744	+	0.135743i	$0.956658\pi$
$822$	1.98278	+	3.43427i	0.0691574	+	0.119784i
$823$	4.76393	−	8.25137i	0.166060	−	0.287625i	−0.770971	−	0.636870i	$-0.780229\pi$
$823$	4.76393	−	8.25137i	0.166060	−	0.287625i	0.937031	+	0.349245i	$0.113562\pi$
$824$	37.8885			1.31991
$825$	2.00000			0.0696311
$826$	3.23607	−	5.60503i	0.112597	−	0.195024i
$827$	−21.8262	+	37.8042i	−0.758973	+	1.31458i	0.184402	+	0.982851i	$0.440965\pi$
$827$	−21.8262	+	37.8042i	−0.758973	+	1.31458i	−0.943375	+	0.331728i	$0.892368\pi$
$828$	−10.4721			−0.363932
$829$	−14.4164			−0.500703			−0.250351	−	0.968155i	$-0.580546\pi$
$829$	−14.4164			−0.500703			−0.250351	+	0.968155i	$0.580546\pi$
$830$	−2.21885	+	3.84316i	−0.0770173	+	0.133398i
$831$	−2.14590	−	3.71680i	−0.0744404	−	0.128935i
$832$	0.381966	−	0.661585i	0.0132423	−	0.0229363i
$833$	−55.8607	−	96.7535i	−1.93546	−	3.35231i
$834$	−2.54508	−	4.40822i	−0.0881291	−	0.152644i
$835$	−23.1803			−0.802189
$836$	−6.47214	−	12.5332i	−0.223844	−	0.433471i
$837$	−3.76393			−0.130101
$838$	−5.27051	−	9.12879i	−0.182067	−	0.315349i
$839$	−10.0902	−	17.4767i	−0.348351	−	0.603362i	0.637605	−	0.770363i	$-0.279925\pi$
$839$	−10.0902	−	17.4767i	−0.348351	−	0.603362i	−0.985957	+	0.167001i	$0.946592\pi$
$840$	−5.85410	+	10.1396i	−0.201986	+	0.349850i
$841$	0.791796	+	1.37143i	0.0273033	+	0.0472907i
$842$	−8.14590	+	14.1091i	−0.280726	+	0.486232i
$843$	−3.23607			−0.111456
$844$	5.14590			0.177129
$845$	−1.26393	+	2.18919i	−0.0434806	+	0.0753106i
$846$	−1.92705	+	3.33775i	−0.0662534	+	0.114754i
$847$	−36.6525			−1.25939
$848$	−1.85410			−0.0636701
$849$	6.09017	−	10.5485i	0.209014	−	0.362023i
$850$	−1.69098	−	2.92887i	−0.0580002	−	0.100459i
$851$	20.9443	−	36.2765i	0.717960	−	1.24354i
$852$	3.85410	+	6.67550i	0.132039	+	0.228699i
$853$	−25.2361	−	43.7102i	−0.864067	−	1.49661i	−0.867971	−	0.496615i	$-0.834576\pi$
$853$	−25.2361	−	43.7102i	−0.864067	−	1.49661i	0.00390458	−	0.999992i	$-0.498757\pi$
$854$	11.4164			0.390661
$855$	−2.35410	+	3.66854i	−0.0805086	+	0.125462i
$856$	−39.4721			−1.34913
$857$	1.55573	+	2.69460i	0.0531427	+	0.0920458i	0.891373	−	0.453271i	$-0.149743\pi$
$857$	1.55573	+	2.69460i	0.0531427	+	0.0920458i	−0.838230	+	0.545316i	$0.816410\pi$
$858$	−2.00000	−	3.46410i	−0.0682789	−	0.118262i
$859$	15.0623	−	26.0887i	0.513919	−	0.890134i	−0.485950	−	0.873986i	$-0.661526\pi$
$859$	15.0623	−	26.0887i	0.513919	−	0.890134i	0.999870	−	0.0161478i	$-0.00514024\pi$
$860$	1.38197	+	2.39364i	0.0471246	+	0.0816223i
$861$	14.9443	−	25.8842i	0.509299	−	0.882132i
$862$	−6.47214			−0.220442
$863$	45.3050			1.54220			0.771099	−	0.636715i	$-0.219707\pi$
$863$	45.3050			1.54220			0.771099	+	0.636715i	$0.219707\pi$
$864$	−2.80902	+	4.86536i	−0.0955647	+	0.165523i
$865$	11.9443	−	20.6881i	0.406117	−	0.703416i
$866$	−24.4721			−0.831597
$867$	12.9443			0.439611
$868$	−15.9443	+	27.6163i	−0.541184	+	0.937358i
$869$		0			0
$870$	−1.61803	+	2.80252i	−0.0548565	+	0.0950142i
$871$	−2.00000	−	3.46410i	−0.0677674	−	0.117377i
$872$	−7.82624	−	13.5554i	−0.265030	−	0.459045i
$873$	−2.00000			−0.0676897
$874$	9.41641	−	14.6742i	0.318515	−	0.496361i
$875$	−5.23607			−0.177011
$876$	−10.0902	−	17.4767i	−0.340915	−	0.590483i
$877$	16.3607	+	28.3375i	0.552461	+	0.956890i	0.998096	+	0.0616758i	$0.0196445\pi$
$877$	16.3607	+	28.3375i	0.552461	+	0.956890i	−0.445635	+	0.895215i	$0.647022\pi$
$878$	0.545085	−	0.944115i	0.0183957	−	0.0318623i
$879$	15.2082	+	26.3414i	0.512960	+	0.888473i
$880$	1.85410	−	3.21140i	0.0625018	−	0.108256i
$881$	−36.0689			−1.21519			−0.607596	−	0.794246i	$-0.707866\pi$
$881$	−36.0689			−1.21519			−0.607596	+	0.794246i	$0.707866\pi$
$882$	12.6180			0.424871
$883$	17.8885	−	30.9839i	0.601997	−	1.04269i	−0.390521	−	0.920594i	$-0.627705\pi$
$883$	17.8885	−	30.9839i	0.601997	−	1.04269i	0.992518	−	0.122096i	$-0.0389616\pi$
$884$	14.3262	−	24.8138i	0.481844	−	0.834577i
$885$	2.00000			0.0672293
$886$	−4.14590			−0.139284
$887$	5.93769	−	10.2844i	0.199368	−	0.345316i	−0.748956	−	0.662620i	$-0.769444\pi$
$887$	5.93769	−	10.2844i	0.199368	−	0.345316i	0.948324	+	0.317304i	$0.102778\pi$
$888$	−7.23607	−	12.5332i	−0.242827	−	0.420588i
$889$	28.1803	−	48.8098i	0.945138	−	1.63703i
$890$	3.85410	+	6.67550i	0.129190	+	0.223763i
$891$	−1.00000	−	1.73205i	−0.0335013	−	0.0580259i
$892$	36.6525			1.22722
$893$	12.4721	+	24.1522i	0.417364	+	0.808222i
$894$	2.29180			0.0766491
$895$	2.14590	+	3.71680i	0.0717295	+	0.124239i
$896$	29.7984	+	51.6123i	0.995494	+	1.72425i
$897$	−10.4721	+	18.1383i	−0.349654	+	0.605619i
$898$	−9.90983	−	17.1643i	−0.330695	−	0.572781i
$899$	−9.85410	+	17.0678i	−0.328653	+	0.569243i
$900$	−1.61803			−0.0539345
$901$	−5.47214			−0.182303
$902$	3.52786	−	6.11044i	0.117465	−	0.203455i
$903$	4.47214	−	7.74597i	0.148823	−	0.257770i
$904$	−34.5967			−1.15067
$905$	4.52786			0.150511
$906$	1.01722	−	1.76188i	0.0337949	−	0.0585345i
$907$	−9.18034	−	15.9008i	−0.304828	−	0.527978i	0.672395	−	0.740193i	$-0.265266\pi$
$907$	−9.18034	−	15.9008i	−0.304828	−	0.527978i	−0.977223	+	0.212215i	$0.931932\pi$
$908$	3.23607	−	5.60503i	0.107393	−	0.186010i
$909$	7.09017	+	12.2805i	0.235166	+	0.407320i
$910$	5.23607	+	9.06914i	0.173574	+	0.300639i
$911$	−0.403252			−0.0133603			−0.00668017	−	0.999978i	$-0.502126\pi$
$911$	−0.403252			−0.0133603			−0.00668017	+	0.999978i	$0.502126\pi$
$912$	3.70820	+	7.18091i	0.122791	+	0.237784i
$913$	−14.3607			−0.475269
$914$	−9.03444	−	15.6481i	−0.298833	−	0.517594i
$915$	1.76393	+	3.05522i	0.0583138	+	0.101002i
$916$	3.66312	−	6.34471i	0.121033	−	0.209635i
$917$	−16.9443	−	29.3483i	−0.559549	−	0.969168i
$918$	−1.69098	+	2.92887i	−0.0558108	+	0.0966671i
$919$	6.70820			0.221283			0.110642	−	0.993860i	$-0.464709\pi$
$919$	6.70820			0.221283			0.110642	+	0.993860i	$0.464709\pi$
$920$	14.4721			0.477132
$921$	−1.09017	+	1.88823i	−0.0359223	+	0.0622193i
$922$	12.1246	−	21.0004i	0.399303	−	0.691613i
$923$	15.4164			0.507437
$924$	−16.9443			−0.557426
$925$	3.23607	−	5.60503i	0.106401	−	0.184292i
$926$	7.50658	+	13.0018i	0.246681	+	0.427265i
$927$	8.47214	−	14.6742i	0.278261	−	0.481963i
$928$	14.7082	+	25.4754i	0.482820	+	0.836270i
$929$	7.88854	+	13.6634i	0.258815	+	0.448280i	0.965925	−	0.258823i	$-0.0833348\pi$
$929$	7.88854	+	13.6634i	0.258815	+	0.448280i	−0.707110	+	0.707104i	$0.750001\pi$
$930$	2.32624			0.0762803
$931$	48.0623	−	74.8985i	1.57518	−	2.45470i
$932$	29.0344			0.951055
$933$	−2.70820	−	4.69075i	−0.0886626	−	0.153568i
$934$	6.25329	+	10.8310i	0.204614	+	0.354402i
$935$	5.47214	−	9.47802i	0.178958	−	0.309964i
$936$	3.61803	+	6.26662i	0.118259	+	0.204831i
$937$	−18.9443	+	32.8124i	−0.618882	+	1.07194i	0.370808	+	0.928710i	$0.379081\pi$
$937$	−18.9443	+	32.8124i	−0.618882	+	1.07194i	−0.989690	+	0.143226i	$0.954252\pi$
$938$	4.00000			0.130605
$939$	−17.5967			−0.574248
$940$	−5.04508	+	8.73834i	−0.164553	+	0.285013i
$941$	18.4721	−	31.9947i	0.602174	−	1.04300i	−0.390317	−	0.920681i	$-0.627635\pi$
$941$	18.4721	−	31.9947i	0.602174	−	1.04300i	0.992491	−	0.122316i	$-0.0390322\pi$
$942$	12.3607			0.402733
$943$	−36.9443			−1.20307
$944$	1.85410	−	3.21140i	0.0603459	−	0.104522i
$945$	2.61803	+	4.53457i	0.0851647	+	0.147510i
$946$	1.05573	−	1.82857i	0.0343247	−	0.0594521i
$947$	−12.4721	−	21.6024i	−0.405290	−	0.701983i	0.589065	−	0.808085i	$-0.299496\pi$
$947$	−12.4721	−	21.6024i	−0.405290	−	0.701983i	−0.994355	+	0.106103i	$0.966163\pi$
$948$		0			0
$949$	−40.3607			−1.31016
$950$	1.45492	−	2.26728i	0.0472037	−	0.0735604i
$951$	−30.8885			−1.00163
$952$	32.0344	+	55.4853i	1.03824	+	1.79829i
$953$	−1.08359	−	1.87684i	−0.0351010	−	0.0607967i	0.847941	−	0.530090i	$-0.177842\pi$
$953$	−1.08359	−	1.87684i	−0.0351010	−	0.0607967i	−0.883042	+	0.469294i	$0.844509\pi$
$954$	0.309017	−	0.535233i	0.0100048	−	0.0173288i
$955$	4.14590	+	7.18091i	0.134158	+	0.232369i
$956$	−15.4721	+	26.7985i	−0.500405	+	0.866726i
$957$	−10.4721			−0.338516
$958$	14.8754			0.480602
$959$	16.7984	−	29.0956i	0.542448	−	0.939547i
$960$	−0.118034	+	0.204441i	−0.00380953	+	0.00659830i
$961$	−16.8328			−0.542994
$962$	−12.9443			−0.417340
$963$	−8.82624	+	15.2875i	−0.284422	+	0.492633i
$964$	18.8992	+	32.7344i	0.608702	+	1.05430i
$965$	4.61803	−	7.99867i	0.148660	−	0.257486i
$966$	−10.4721	−	18.1383i	−0.336935	−	0.583589i
$967$	0.527864	+	0.914287i	0.0169750	+	0.0294015i	0.874388	−	0.485227i	$-0.161263\pi$
$967$	0.527864	+	0.914287i	0.0169750	+	0.0294015i	−0.857413	+	0.514629i	$0.827930\pi$
$968$	15.6525			0.503090
$969$	10.9443	+	21.1935i	0.351581	+	0.680833i
$970$	1.23607			0.0396878
$971$	14.0902	+	24.4049i	0.452175	+	0.783190i	0.998521	−	0.0543695i	$-0.0173149\pi$
$971$	14.0902	+	24.4049i	0.452175	+	0.783190i	−0.546346	+	0.837560i	$0.683982\pi$
$972$	0.809017	+	1.40126i	0.0259492	+	0.0449454i
$973$	−21.5623	+	37.3470i	−0.691256	+	1.19729i
$974$	6.27051	+	10.8608i	0.200920	+	0.348004i
$975$	−1.61803	+	2.80252i	−0.0518186	+	0.0897524i
$976$	6.54102			0.209373
$977$	−37.7214			−1.20681			−0.603407	−	0.797434i	$-0.706190\pi$
$977$	−37.7214			−1.20681			−0.603407	+	0.797434i	$0.706190\pi$
$978$	2.76393	−	4.78727i	0.0883808	−	0.153080i
$979$	−12.4721	+	21.6024i	−0.398611	+	0.690415i
$980$	33.0344			1.05525
$981$	−7.00000			−0.223493
$982$	2.56231	−	4.43804i	0.0817665	−	0.141624i
$983$	−0.826238	−	1.43109i	−0.0263529	−	0.0456446i	0.852548	−	0.522649i	$-0.175056\pi$
$983$	−0.826238	−	1.43109i	−0.0263529	−	0.0456446i	−0.878901	+	0.477004i	$0.841723\pi$
$984$	−6.38197	+	11.0539i	−0.203450	+	0.352385i
$985$	1.26393	+	2.18919i	0.0402722	+	0.0697535i
$986$	8.85410	+	15.3358i	0.281972	+	0.488390i
$987$	32.6525			1.03934
$988$	22.7984	+	1.07047i	0.725313	+	0.0340561i
$989$	−11.0557			−0.351552
$990$	0.618034	+	1.07047i	0.0196424	+	0.0340217i
$991$	−5.82624	−	10.0913i	−0.185077	−	0.320562i	0.758526	−	0.651643i	$-0.225920\pi$
$991$	−5.82624	−	10.0913i	−0.185077	−	0.320562i	−0.943602	+	0.331081i	$0.892587\pi$
$992$	10.5729	−	18.3129i	0.335691	−	0.581435i
$993$	−3.23607	−	5.60503i	−0.102694	−	0.177870i
$994$	−7.70820	+	13.3510i	−0.244489	+	0.423468i
$995$	−21.8885			−0.693913
$996$	11.6180			0.368131
$997$	20.5279	−	35.5553i	0.650124	−	1.12605i	−0.332968	−	0.942938i	$-0.608050\pi$
$997$	20.5279	−	35.5553i	0.650124	−	1.12605i	0.983092	−	0.183110i	$-0.0586164\pi$
$998$	−2.36475	+	4.09586i	−0.0748547	+	0.129652i
$999$	−6.47214			−0.204769

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.i.e.121.1	yes	4
3.2	odd	2		855.2.k.e.406.2		4
19.7	even	3		5415.2.a.q.1.2		2
19.11	even	3	inner	285.2.i.e.106.1	✓	4
19.12	odd	6		5415.2.a.t.1.1		2
57.11	odd	6		855.2.k.e.676.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.e.106.1	✓	4	19.11	even	3	inner
285.2.i.e.121.1	yes	4	1.1	even	1	trivial
855.2.k.e.406.2		4	3.2	odd	2
855.2.k.e.676.2		4	57.11	odd	6
5415.2.a.q.1.2		2	19.7	even	3
5415.2.a.t.1.1		2	19.12	odd	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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.535233i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.809017 - 1.40126i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.309017 + 0.535233i) q^{6} +5.23607 q^{7} -2.23607 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.309017 - 0.535233i) q^{10} +2.00000 q^{11} -1.61803 q^{12} +(-1.61803 + 2.80252i) q^{13} +(-1.61803 - 2.80252i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.927051 - 1.60570i) q^{16} +(-2.73607 - 4.73901i) q^{17} +0.618034 q^{18} +(2.35410 - 3.66854i) q^{19} +1.61803 q^{20} +(-2.61803 - 4.53457i) q^{21} +(-0.618034 - 1.07047i) q^{22} +(-3.23607 + 5.60503i) q^{23} +(1.11803 + 1.93649i) q^{24} +(-0.500000 + 0.866025i) q^{25} +2.00000 q^{26} +1.00000 q^{27} +(4.23607 - 7.33708i) q^{28} +(2.61803 - 4.53457i) q^{29} -0.618034 q^{30} -3.76393 q^{31} +(-2.80902 + 4.86536i) q^{32} +(-1.00000 - 1.73205i) q^{33} +(-1.69098 + 2.92887i) q^{34} +(2.61803 + 4.53457i) q^{35} +(0.809017 + 1.40126i) q^{36} -6.47214 q^{37} +(-2.69098 - 0.126351i) q^{38} +3.23607 q^{39} +(-1.11803 - 1.93649i) q^{40} +(2.85410 + 4.94345i) q^{41} +(-1.61803 + 2.80252i) q^{42} +(0.854102 + 1.47935i) q^{43} +(1.61803 - 2.80252i) q^{44} -1.00000 q^{45} +4.00000 q^{46} +(-3.11803 + 5.40059i) q^{47} +(-0.927051 + 1.60570i) q^{48} +20.4164 q^{49} +0.618034 q^{50} +(-2.73607 + 4.73901i) q^{51} +(2.61803 + 4.53457i) q^{52} +(0.500000 - 0.866025i) q^{53} +(-0.309017 - 0.535233i) q^{54} +(1.00000 + 1.73205i) q^{55} -11.7082 q^{56} +(-4.35410 - 0.204441i) q^{57} -3.23607 q^{58} +(1.00000 + 1.73205i) q^{59} +(-0.809017 - 1.40126i) q^{60} +(-1.76393 + 3.05522i) q^{61} +(1.16312 + 2.01458i) q^{62} +(-2.61803 + 4.53457i) q^{63} -0.236068 q^{64} -3.23607 q^{65} +(-0.618034 + 1.07047i) q^{66} +(-0.618034 + 1.07047i) q^{67} -8.85410 q^{68} +6.47214 q^{69} +(1.61803 - 2.80252i) q^{70} +(-2.38197 - 4.12569i) q^{71} +(1.11803 - 1.93649i) q^{72} +(6.23607 + 10.8012i) q^{73} +(2.00000 + 3.46410i) q^{74} +1.00000 q^{75} +(-3.23607 - 6.26662i) q^{76} +10.4721 q^{77} +(-1.00000 - 1.73205i) q^{78} +(0.927051 - 1.60570i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.76393 - 3.05522i) q^{82} -7.18034 q^{83} -8.47214 q^{84} +(2.73607 - 4.73901i) q^{85} +(0.527864 - 0.914287i) q^{86} -5.23607 q^{87} -4.47214 q^{88} +(-6.23607 + 10.8012i) q^{89} +(0.309017 + 0.535233i) q^{90} +(-8.47214 + 14.6742i) q^{91} +(5.23607 + 9.06914i) q^{92} +(1.88197 + 3.25966i) q^{93} +3.85410 q^{94} +(4.35410 + 0.204441i) q^{95} +5.61803 q^{96} +(1.00000 + 1.73205i) q^{97} +(-6.30902 - 10.9275i) q^{98} +(-1.00000 + 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 2 q^{3} + q^{4} + 2 q^{5} + q^{6} + 12 q^{7} - 2 q^{9} - q^{10} + 8 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{14} + 2 q^{15} + 3 q^{16} - 2 q^{17} - 2 q^{18} - 4 q^{19} + 2 q^{20} - 6 q^{21}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 + q^4 + 2 * q^5 + q^6 + 12 * q^7 - 2 * q^9 - q^10 + 8 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^14 + 2 * q^15 + 3 * q^16 - 2 * q^17 - 2 * q^18 - 4 * q^19 + 2 * q^20 - 6 * q^21 + 2 * q^22 - 4 * q^23 - 2 * q^25 + 8 * q^26 + 4 * q^27 + 8 * q^28 + 6 * q^29 + 2 * q^30 - 24 * q^31 - 9 * q^32 - 4 * q^33 - 9 * q^34 + 6 * q^35 + q^36 - 8 * q^37 - 13 * q^38 + 4 * q^39 - 2 * q^41 - 2 * q^42 - 10 * q^43 + 2 * q^44 - 4 * q^45 + 16 * q^46 - 8 * q^47 + 3 * q^48 + 28 * q^49 - 2 * q^50 - 2 * q^51 + 6 * q^52 + 2 * q^53 + q^54 + 4 * q^55 - 20 * q^56 - 4 * q^57 - 4 * q^58 + 4 * q^59 - q^60 - 16 * q^61 - 11 * q^62 - 6 * q^63 + 8 * q^64 - 4 * q^65 + 2 * q^66 + 2 * q^67 - 22 * q^68 + 8 * q^69 + 2 * q^70 - 14 * q^71 + 16 * q^73 + 8 * q^74 + 4 * q^75 - 4 * q^76 + 24 * q^77 - 4 * q^78 - 3 * q^80 - 2 * q^81 + 16 * q^82 + 16 * q^83 - 16 * q^84 + 2 * q^85 + 20 * q^86 - 12 * q^87 - 16 * q^89 - q^90 - 16 * q^91 + 12 * q^92 + 12 * q^93 + 2 * q^94 + 4 * q^95 + 18 * q^96 + 4 * q^97 - 23 * q^98 - 4 * q^99

Introduction

L-functions

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