LMFDB - Embedded newform 390.2.bd.c.223.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(7,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 11]))

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

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

chi := DirichletCharacter("390.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bd (of order $12$, degree $4$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			223.5
Character	$\chi$	$=$	390.223
Dual form			390.2.bd.c.7.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.86235 - 1.23760i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-1.84360 + 3.19321i) q^{7} +1.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.86235 - 1.23760i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-1.84360 + 3.19321i) q^{7} +1.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +(2.23164 + 0.140614i) q^{10} +(0.762517 - 2.84575i) q^{11} +(-0.707107 - 0.707107i) q^{12} +(-0.692322 + 3.53846i) q^{13} -3.68720i q^{14} +(-1.67744 + 1.47858i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.79957 + 1.01809i) q^{17} +1.00000 q^{18} +(-7.83553 + 2.09952i) q^{19} +(-2.00297 + 0.994046i) q^{20} +(2.60724 + 2.60724i) q^{21} +(0.762517 + 2.84575i) q^{22} +(7.08152 + 1.89749i) q^{23} +(0.965926 + 0.258819i) q^{24} +(1.93671 + 4.60968i) q^{25} +(-1.16966 - 3.41056i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.84360 + 3.19321i) q^{28} +(-4.63913 + 2.67840i) q^{29} +(0.713415 - 2.11921i) q^{30} +(-2.94395 + 2.94395i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.55143 - 1.47307i) q^{33} +(2.78148 - 2.78148i) q^{34} +(7.38534 - 3.66525i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(1.13265 + 1.96180i) q^{37} +(5.73600 - 5.73600i) q^{38} +(3.23870 + 1.58455i) q^{39} +(1.23760 - 1.86235i) q^{40} +(-2.80230 - 0.750873i) q^{41} +(-3.56156 - 0.954318i) q^{42} +(-0.980250 - 3.65834i) q^{43} +(-2.08323 - 2.08323i) q^{44} +(0.994046 + 2.00297i) q^{45} +(-7.08152 + 1.89749i) q^{46} -12.3470 q^{47} +(-0.965926 + 0.258819i) q^{48} +(-3.29773 - 5.71183i) q^{49} +(-3.98208 - 3.02375i) q^{50} +3.93360i q^{51} +(2.71823 + 2.36880i) q^{52} +(-0.952075 - 0.952075i) q^{53} +(0.258819 - 0.965926i) q^{54} +(-4.94197 + 4.35610i) q^{55} +(-3.19321 - 1.84360i) q^{56} +8.11193i q^{57} +(2.67840 - 4.63913i) q^{58} +(-1.76659 - 6.59302i) q^{59} +(0.441768 + 2.19199i) q^{60} +(4.93418 - 8.54626i) q^{61} +(1.07756 - 4.02151i) q^{62} +(3.19321 - 1.84360i) q^{63} -1.00000 q^{64} +(5.66853 - 5.73304i) q^{65} +2.94614 q^{66} +(11.3773 - 6.56871i) q^{67} +(-1.01809 + 3.79957i) q^{68} +(3.66566 - 6.34911i) q^{69} +(-4.56327 + 6.86687i) q^{70} +(0.620887 + 2.31718i) q^{71} +(0.500000 - 0.866025i) q^{72} +8.67586i q^{73} +(-1.96180 - 1.13265i) q^{74} +(4.95387 - 0.677643i) q^{75} +(-2.09952 + 7.83553i) q^{76} +(7.68130 + 7.68130i) q^{77} +(-3.59707 + 0.247089i) q^{78} -10.8193i q^{79} +(-0.140614 + 2.23164i) q^{80} +(0.500000 + 0.866025i) q^{81} +(2.80230 - 0.750873i) q^{82} -10.4646 q^{83} +(3.56156 - 0.954318i) q^{84} +(8.33612 + 2.80629i) q^{85} +(2.67809 + 2.67809i) q^{86} +(1.38644 + 5.17428i) q^{87} +(2.84575 + 0.762517i) q^{88} +(9.57642 + 2.56600i) q^{89} +(-1.86235 - 1.23760i) q^{90} +(-10.0227 - 8.73423i) q^{91} +(5.18403 - 5.18403i) q^{92} +(2.08169 + 3.60559i) q^{93} +(10.6928 - 6.17348i) q^{94} +(17.1909 + 5.78717i) q^{95} +(0.707107 - 0.707107i) q^{96} +(2.77769 + 1.60370i) q^{97} +(5.71183 + 3.29773i) q^{98} +(-2.08323 + 2.08323i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4}+O(q^{10}) $ 32 * q + 16 * q^4	$ 32 q + 16 q^{4} - 4 q^{11} + 20 q^{13} + 4 q^{15} - 16 q^{16} - 20 q^{17} + 32 q^{18} - 20 q^{19} + 8 q^{21} - 4 q^{22} + 4 q^{23} + 8 q^{25} - 4 q^{26} - 24 q^{29} + 4 q^{30} + 12 q^{31} - 12 q^{33} + 16 q^{34} + 12 q^{35} + 20 q^{37} + 4 q^{38} + 20 q^{39} - 28 q^{41} + 8 q^{42} - 4 q^{43} + 4 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} + 28 q^{50} + 16 q^{52} - 4 q^{53} - 40 q^{55} - 12 q^{56} - 36 q^{59} - 4 q^{60} - 28 q^{61} - 36 q^{62} + 12 q^{63} - 32 q^{64} - 32 q^{65} - 36 q^{67} - 4 q^{68} + 20 q^{69} - 24 q^{70} - 4 q^{71} + 16 q^{72} - 24 q^{74} - 16 q^{76} - 20 q^{77} - 16 q^{78} + 16 q^{81} + 28 q^{82} - 40 q^{83} - 8 q^{84} + 88 q^{85} - 8 q^{86} - 16 q^{87} - 8 q^{88} + 16 q^{89} - 40 q^{91} + 20 q^{92} + 24 q^{94} - 8 q^{95} + 72 q^{97} + 72 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q + 16 * q^4 - 4 * q^11 + 20 * q^13 + 4 * q^15 - 16 * q^16 - 20 * q^17 + 32 * q^18 - 20 * q^19 + 8 * q^21 - 4 * q^22 + 4 * q^23 + 8 * q^25 - 4 * q^26 - 24 * q^29 + 4 * q^30 + 12 * q^31 - 12 * q^33 + 16 * q^34 + 12 * q^35 + 20 * q^37 + 4 * q^38 + 20 * q^39 - 28 * q^41 + 8 * q^42 - 4 * q^43 + 4 * q^44 - 4 * q^46 - 16 * q^47 - 20 * q^49 + 28 * q^50 + 16 * q^52 - 4 * q^53 - 40 * q^55 - 12 * q^56 - 36 * q^59 - 4 * q^60 - 28 * q^61 - 36 * q^62 + 12 * q^63 - 32 * q^64 - 32 * q^65 - 36 * q^67 - 4 * q^68 + 20 * q^69 - 24 * q^70 - 4 * q^71 + 16 * q^72 - 24 * q^74 - 16 * q^76 - 20 * q^77 - 16 * q^78 + 16 * q^81 + 28 * q^82 - 40 * q^83 - 8 * q^84 + 88 * q^85 - 8 * q^86 - 16 * q^87 - 8 * q^88 + 16 * q^89 - 40 * q^91 + 20 * q^92 + 24 * q^94 - 8 * q^95 + 72 * q^97 + 72 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.86235	−	1.23760i	−0.832869	−	0.553470i
$5$	−1.86235	−	1.23760i	−0.832869	−	0.553470i
$6$	0.258819	+	0.965926i	0.105662	+	0.394338i
$7$	−1.84360	+	3.19321i	−0.696816	+	1.20692i	0.272749	+	0.962085i	$0.412067\pi$
$7$	−1.84360	+	3.19321i	−0.696816	+	1.20692i	−0.969565	+	0.244835i	$0.921266\pi$
$8$			1.00000i			0.353553i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	2.23164	+	0.140614i	0.705707	+	0.0444662i
$11$	0.762517	−	2.84575i	0.229907	−	0.858026i	−0.750471	−	0.660903i	$-0.770173\pi$
$11$	0.762517	−	2.84575i	0.229907	−	0.858026i	0.980379	−	0.197123i	$-0.0631599\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	−0.692322	+	3.53846i	−0.192016	+	0.981392i
$13$	−0.692322	+	3.53846i	−0.192016	+	0.981392i
$14$		−	3.68720i		−	0.985446i
$15$	−1.67744	+	1.47858i	−0.433113	+	0.381768i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.79957	+	1.01809i	−0.921531	+	0.246923i	−0.688239	−	0.725484i	$-0.741616\pi$
$17$	−3.79957	+	1.01809i	−0.921531	+	0.246923i	−0.233291	+	0.972407i	$0.574949\pi$
$18$	1.00000			0.235702
$19$	−7.83553	+	2.09952i	−1.79759	+	0.481664i	−0.993598	−	0.112972i	$-0.963963\pi$
$19$	−7.83553	+	2.09952i	−1.79759	+	0.481664i	−0.803995	+	0.594636i	$0.797296\pi$
$20$	−2.00297	+	0.994046i	−0.447877	+	0.222275i
$21$	2.60724	+	2.60724i	0.568947	+	0.568947i
$22$	0.762517	+	2.84575i	0.162569	+	0.606716i
$23$	7.08152	+	1.89749i	1.47660	+	0.395653i	0.905188	−	0.425011i	$-0.139730\pi$
$23$	7.08152	+	1.89749i	1.47660	+	0.395653i	0.571410	+	0.820665i	$0.306397\pi$
$24$	0.965926	+	0.258819i	0.197169	+	0.0528312i
$25$	1.93671	+	4.60968i	0.387342	+	0.921936i
$26$	−1.16966	−	3.41056i	−0.229389	−	0.668865i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	1.84360	+	3.19321i	0.348408	+	0.603460i
$29$	−4.63913	+	2.67840i	−0.861464	+	0.497367i	−0.864502	−	0.502629i	$-0.832366\pi$
$29$	−4.63913	+	2.67840i	−0.861464	+	0.497367i	0.00303797	+	0.999995i	$0.499033\pi$
$30$	0.713415	−	2.11921i	0.130251	−	0.386913i
$31$	−2.94395	+	2.94395i	−0.528749	+	0.528749i	−0.920199	−	0.391450i	$-0.871974\pi$
$31$	−2.94395	+	2.94395i	−0.528749	+	0.528749i	0.391450	+	0.920199i	$0.371974\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−2.55143	−	1.47307i	−0.444147	−	0.256428i
$34$	2.78148	−	2.78148i	0.477019	−	0.477019i
$35$	7.38534	−	3.66525i	1.24835	−	0.619540i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	1.13265	+	1.96180i	0.186206	+	0.322519i	0.943982	−	0.329996i	$-0.107047\pi$
$37$	1.13265	+	1.96180i	0.186206	+	0.322519i	−0.757776	+	0.652515i	$0.773714\pi$
$38$	5.73600	−	5.73600i	0.930503	−	0.930503i
$39$	3.23870	+	1.58455i	0.518607	+	0.253731i
$40$	1.23760	−	1.86235i	0.195681	−	0.294464i
$41$	−2.80230	−	0.750873i	−0.437645	−	0.117267i	0.0332674	−	0.999446i	$-0.489409\pi$
$41$	−2.80230	−	0.750873i	−0.437645	−	0.117267i	−0.470913	+	0.882180i	$0.656075\pi$
$42$	−3.56156	−	0.954318i	−0.549561	−	0.147254i
$43$	−0.980250	−	3.65834i	−0.149487	−	0.557892i	−0.999515	−	0.0311543i	$-0.990082\pi$
$43$	−0.980250	−	3.65834i	−0.149487	−	0.557892i	0.850028	−	0.526738i	$-0.176585\pi$
$44$	−2.08323	−	2.08323i	−0.314059	−	0.314059i
$45$	0.994046	+	2.00297i	0.148184	+	0.298585i
$46$	−7.08152	+	1.89749i	−1.04411	+	0.279769i
$47$	−12.3470			−1.80099			−0.900494	−	0.434868i	$-0.856795\pi$
$47$	−12.3470			−1.80099			−0.900494	+	0.434868i	$0.856795\pi$
$48$	−0.965926	+	0.258819i	−0.139419	+	0.0373573i
$49$	−3.29773	−	5.71183i	−0.471104	−	0.815976i
$50$	−3.98208	−	3.02375i	−0.563151	−	0.427622i
$51$			3.93360i			0.550814i
$52$	2.71823	+	2.36880i	0.376951	+	0.328493i
$53$	−0.952075	−	0.952075i	−0.130778	−	0.130778i	0.638688	−	0.769466i	$-0.279477\pi$
$53$	−0.952075	−	0.952075i	−0.130778	−	0.130778i	−0.769466	+	0.638688i	$0.779477\pi$
$54$	0.258819	−	0.965926i	0.0352208	−	0.131446i
$55$	−4.94197	+	4.35610i	−0.666375	+	0.587377i
$56$	−3.19321	−	1.84360i	−0.426711	−	0.246361i
$57$			8.11193i			1.07445i
$58$	2.67840	−	4.63913i	0.351691	−	0.609147i
$59$	−1.76659	−	6.59302i	−0.229991	−	0.858338i	−0.980343	−	0.197300i	$-0.936783\pi$
$59$	−1.76659	−	6.59302i	−0.229991	−	0.858338i	0.750352	−	0.661038i	$-0.229884\pi$
$60$	0.441768	+	2.19199i	0.0570321	+	0.282985i
$61$	4.93418	−	8.54626i	0.631758	−	1.09424i	−0.355435	−	0.934701i	$-0.615667\pi$
$61$	4.93418	−	8.54626i	0.631758	−	1.09424i	0.987192	−	0.159535i	$-0.0509995\pi$
$62$	1.07756	−	4.02151i	0.136850	−	0.510733i
$63$	3.19321	−	1.84360i	0.402307	−	0.232272i
$64$	−1.00000			−0.125000
$65$	5.66853	−	5.73304i	0.703095	−	0.711096i
$66$	2.94614			0.362645
$67$	11.3773	−	6.56871i	1.38996	−	0.802496i	0.396653	−	0.917969i	$-0.370172\pi$
$67$	11.3773	−	6.56871i	1.38996	−	0.802496i	0.993311	+	0.115473i	$0.0368384\pi$
$68$	−1.01809	+	3.79957i	−0.123462	+	0.460765i
$69$	3.66566	−	6.34911i	0.441294	−	0.764344i
$70$	−4.56327	+	6.86687i	−0.545415	+	0.820747i
$71$	0.620887	+	2.31718i	0.0736858	+	0.274999i	0.992932	−	0.118684i	$-0.0378675\pi$
$71$	0.620887	+	2.31718i	0.0736858	+	0.274999i	−0.919246	+	0.393683i	$0.871201\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$			8.67586i			1.01543i	0.861524	+	0.507716i	$0.169510\pi$
$73$			8.67586i			1.01543i	−0.861524	+	0.507716i	$0.830490\pi$
$74$	−1.96180	−	1.13265i	−0.228055	−	0.131668i
$75$	4.95387	−	0.677643i	0.572023	−	0.0782475i
$76$	−2.09952	+	7.83553i	−0.240832	+	0.898797i
$77$	7.68130	+	7.68130i	0.875366	+	0.875366i
$78$	−3.59707	+	0.247089i	−0.407289	+	0.0279773i
$79$		−	10.8193i		−	1.21727i	−0.793452	−	0.608633i	$-0.791718\pi$
$79$		−	10.8193i		−	1.21727i	0.793452	−	0.608633i	$-0.208282\pi$
$80$	−0.140614	+	2.23164i	−0.0157212	+	0.249505i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	2.80230	−	0.750873i	0.309462	−	0.0829201i
$83$	−10.4646			−1.14864			−0.574318	−	0.818632i	$-0.694733\pi$
$83$	−10.4646			−1.14864			−0.574318	+	0.818632i	$0.694733\pi$
$84$	3.56156	−	0.954318i	0.388598	−	0.104125i
$85$	8.33612	+	2.80629i	0.904179	+	0.304385i
$86$	2.67809	+	2.67809i	0.288786	+	0.288786i
$87$	1.38644	+	5.17428i	0.148642	+	0.554741i
$88$	2.84575	+	0.762517i	0.303358	+	0.0812846i
$89$	9.57642	+	2.56600i	1.01510	+	0.271995i	0.727758	−	0.685834i	$-0.240562\pi$
$89$	9.57642	+	2.56600i	1.01510	+	0.271995i	0.287341	+	0.957828i	$0.407229\pi$
$90$	−1.86235	−	1.23760i	−0.196309	−	0.130454i
$91$	−10.0227	−	8.73423i	−1.05066	−	0.915597i
$92$	5.18403	−	5.18403i	0.540473	−	0.540473i
$93$	2.08169	+	3.60559i	0.215861	+	0.373882i
$94$	10.6928	−	6.17348i	1.10288	−	0.636746i
$95$	17.1909	+	5.78717i	1.76375	+	0.593751i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	2.77769	+	1.60370i	0.282032	+	0.162831i	0.634343	−	0.773052i	$-0.281271\pi$
$97$	2.77769	+	1.60370i	0.282032	+	0.162831i	−0.352311	+	0.935883i	$0.614604\pi$
$98$	5.71183	+	3.29773i	0.576982	+	0.333121i
$99$	−2.08323	+	2.08323i	−0.209373	+	0.209373i
$100$	4.96046	+	0.627602i	0.496046	+	0.0627602i
$101$	6.82771	−	3.94198i	0.679382	−	0.392241i	−0.120240	−	0.992745i	$-0.538366\pi$
$101$	6.82771	−	3.94198i	0.679382	−	0.392241i	0.799622	+	0.600503i	$0.205033\pi$
$102$	−1.96680	−	3.40660i	−0.194742	−	0.337304i
$103$	2.29199	−	2.29199i	0.225837	−	0.225837i	−0.585114	−	0.810951i	$-0.698950\pi$
$103$	2.29199	−	2.29199i	0.225837	−	0.225837i	0.810951	+	0.585114i	$0.198950\pi$
$104$	−3.53846	−	0.692322i	−0.346974	−	0.0678878i
$105$	−1.62889	−	8.08233i	−0.158963	−	0.788754i
$106$	1.30056	+	0.348484i	0.126321	+	0.0338477i
$107$	−17.1331	−	4.59079i	−1.65632	−	0.443809i	−0.694946	−	0.719062i	$-0.744572\pi$
$107$	−17.1331	−	4.59079i	−1.65632	−	0.443809i	−0.961372	+	0.275253i	$0.911238\pi$
$108$	0.258819	+	0.965926i	0.0249049	+	0.0929463i
$109$	6.45231	+	6.45231i	0.618019	+	0.618019i	0.945023	−	0.327004i	$-0.106039\pi$
$109$	6.45231	+	6.45231i	0.618019	+	0.618019i	−0.327004	+	0.945023i	$0.606039\pi$
$110$	2.10182	−	6.24348i	0.200400	−	0.595292i
$111$	2.18811	−	0.586302i	0.207686	−	0.0556493i
$112$	3.68720			0.348408
$113$	−7.85641	+	2.10512i	−0.739069	+	0.198033i	−0.608664	−	0.793428i	$-0.708294\pi$
$113$	−7.85641	+	2.10512i	−0.739069	+	0.198033i	−0.130405	+	0.991461i	$0.541628\pi$
$114$	−4.05597	−	7.02514i	−0.379876	−	0.657965i
$115$	−10.8400	−	12.2979i	−1.01083	−	1.14678i
$116$			5.35680i			0.497367i
$117$	2.36880	−	2.71823i	0.218995	−	0.251301i
$118$	4.82642	+	4.82642i	0.444308	+	0.444308i
$119$	3.75391	−	14.0098i	0.344120	−	1.28427i
$120$	−1.47858	−	1.67744i	−0.134975	−	0.153129i
$121$	2.00941	+	1.16013i	0.182674	+	0.105467i
$122$			9.86837i			0.893440i
$123$	−1.45058	+	2.51247i	−0.130794	+	0.226542i
$124$	1.07756	+	4.02151i	0.0967678	+	0.361142i
$125$	2.09809	−	10.9817i	0.187659	−	0.982234i
$126$	−1.84360	+	3.19321i	−0.164241	+	0.284474i
$127$	−3.57670	+	13.3484i	−0.317381	+	1.18448i	0.604372	+	0.796703i	$0.293424\pi$
$127$	−3.57670	+	13.3484i	−0.317381	+	1.18448i	−0.921752	+	0.387779i	$0.873242\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−3.78739			−0.333461
$130$	−2.04257	+	7.79922i	−0.179146	+	0.684037i
$131$	−10.2728			−0.897543			−0.448771	−	0.893647i	$-0.648138\pi$
$131$	−10.2728			−0.897543			−0.448771	+	0.893647i	$0.648138\pi$
$132$	−2.55143	+	1.47307i	−0.222074	+	0.128214i
$133$	7.74136	−	28.8912i	0.671261	−	2.50518i
$134$	−6.56871	+	11.3773i	−0.567450	+	0.982852i
$135$	2.19199	−	0.441768i	0.188657	−	0.0380214i
$136$	−1.01809	−	3.79957i	−0.0873006	−	0.325810i
$137$	−1.88296	+	3.26137i	−0.160872	+	0.278638i	−0.935182	−	0.354169i	$-0.884764\pi$
$137$	−1.88296	+	3.26137i	−0.160872	+	0.278638i	0.774310	+	0.632807i	$0.218097\pi$
$138$			7.33133i			0.624084i
$139$	5.02846	+	2.90318i	0.426508	+	0.246245i	0.697858	−	0.716236i	$-0.254137\pi$
$139$	5.02846	+	2.90318i	0.426508	+	0.246245i	−0.271350	+	0.962481i	$0.587470\pi$
$140$	0.518473	−	8.22851i	0.0438190	−	0.695436i
$141$	−3.19563	+	11.9262i	−0.269120	+	1.00437i
$142$	−1.69630	−	1.69630i	−0.142350	−	0.142350i
$143$	9.54167	+	4.66831i	0.797914	+	0.390384i
$144$			1.00000i			0.0833333i
$145$	11.9545	+	0.753244i	0.992765	+	0.0625535i
$146$	−4.33793	−	7.51351i	−0.359009	−	0.621823i
$147$	−6.37072	+	1.70703i	−0.525448	+	0.140793i
$148$	2.26530			0.186206
$149$	7.14371	−	1.91415i	0.585235	−	0.156813i	0.0459607	−	0.998943i	$-0.485365\pi$
$149$	7.14371	−	1.91415i	0.585235	−	0.156813i	0.539275	+	0.842130i	$0.318698\pi$
$150$	−3.95135	+	3.06379i	−0.322627	+	0.250157i
$151$	4.50334	+	4.50334i	0.366477	+	0.366477i	0.866191	−	0.499714i	$-0.166561\pi$
$151$	4.50334	+	4.50334i	0.366477	+	0.366477i	−0.499714	+	0.866191i	$0.666561\pi$
$152$	−2.09952	−	7.83553i	−0.170294	−	0.635545i
$153$	3.79957	+	1.01809i	0.307177	+	0.0823078i
$154$	−10.4929	−	2.81155i	−0.845538	−	0.226561i
$155$	9.12610	−	1.83925i	0.733026	−	0.147732i
$156$	2.99161	−	2.01252i	0.239521	−	0.161131i
$157$	−1.82943	+	1.82943i	−0.146005	+	0.146005i	−0.776331	−	0.630326i	$-0.782921\pi$
$157$	−1.82943	+	1.82943i	−0.146005	+	0.146005i	0.630326	+	0.776331i	$0.282921\pi$
$158$	5.40965	+	9.36978i	0.430368	+	0.745420i
$159$	−1.16605	+	0.673219i	−0.0924737	+	0.0533897i
$160$	−0.994046	−	2.00297i	−0.0785862	−	0.158348i
$161$	−19.1146	+	19.1146i	−1.50644	+	1.50644i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−14.8159	−	8.55396i	−1.16047	−	0.669998i	−0.209054	−	0.977904i	$-0.567038\pi$
$163$	−14.8159	−	8.55396i	−1.16047	−	0.669998i	−0.951417	+	0.307906i	$0.900372\pi$
$164$	−2.05142	+	2.05142i	−0.160189	+	0.160189i
$165$	2.92860	+	5.90102i	0.227991	+	0.459393i
$166$	9.06259	−	5.23229i	0.703393	−	0.406104i
$167$	−1.14754	−	1.98761i	−0.0887997	−	0.153806i	0.818204	−	0.574928i	$-0.194970\pi$
$167$	−1.14754	−	1.98761i	−0.0887997	−	0.153806i	−0.907004	+	0.421122i	$0.861636\pi$
$168$	−2.60724	+	2.60724i	−0.201153	+	0.201153i
$169$	−12.0414	−	4.89951i	−0.926260	−	0.376885i
$170$	−8.62243	+	1.73774i	−0.661311	+	0.133279i
$171$	7.83553	+	2.09952i	0.599198	+	0.160555i
$172$	−3.65834	−	0.980250i	−0.278946	−	0.0747433i
$173$	5.52705	+	20.6272i	0.420214	+	1.56826i	0.774158	+	0.632992i	$0.218173\pi$
$173$	5.52705	+	20.6272i	0.420214	+	1.56826i	−0.353945	+	0.935266i	$0.615160\pi$
$174$	−3.78783	−	3.78783i	−0.287155	−	0.287155i
$175$	−18.2902	−	2.31409i	−1.38261	−	0.174929i
$176$	−2.84575	+	0.762517i	−0.214507	+	0.0574769i
$177$	−6.82559			−0.513043
$178$	−9.57642	+	2.56600i	−0.717783	+	0.192329i
$179$	−0.651952	−	1.12921i	−0.0487292	−	0.0844014i	0.840632	−	0.541607i	$-0.182184\pi$
$179$	−0.651952	−	1.12921i	−0.0487292	−	0.0844014i	−0.889361	+	0.457205i	$0.848850\pi$
$180$	2.23164	+	0.140614i	0.166337	+	0.0104808i
$181$			14.5495i			1.08145i	0.841198	+	0.540727i	$0.181851\pi$
$181$			14.5495i			1.08145i	−0.841198	+	0.540727i	$0.818149\pi$
$182$	13.0470	+	2.55273i	0.967109	+	0.189221i
$183$	−6.97799	−	6.97799i	−0.515828	−	0.515828i
$184$	−1.89749	+	7.08152i	−0.139885	+	0.522056i
$185$	0.318533	−	5.05533i	0.0234190	−	0.371675i
$186$	−3.60559	−	2.08169i	−0.264375	−	0.152637i
$187$			11.5889i			0.847467i
$188$	−6.17348	+	10.6928i	−0.450247	+	0.779851i
$189$	−0.954318	−	3.56156i	−0.0694164	−	0.259066i
$190$	−17.7813	+	3.58360i	−1.28999	+	0.259981i
$191$	5.91683	−	10.2482i	0.428127	−	0.741537i	−0.568580	−	0.822628i	$-0.692507\pi$
$191$	5.91683	−	10.2482i	0.428127	−	0.741537i	0.996707	+	0.0810909i	$0.0258404\pi$
$192$	−0.258819	+	0.965926i	−0.0186787	+	0.0697097i
$193$	−4.40954	+	2.54585i	−0.317406	+	0.183254i	−0.650236	−	0.759733i	$-0.725330\pi$
$193$	−4.40954	+	2.54585i	−0.317406	+	0.183254i	0.332830	+	0.942987i	$0.391997\pi$
$194$	−3.20740			−0.230278
$195$	−4.07057	−	6.95920i	−0.291499	−	0.498359i
$196$	−6.59545			−0.471104
$197$	3.04740	−	1.75942i	0.217118	−	0.125353i	−0.387497	−	0.921871i	$-0.626660\pi$
$197$	3.04740	−	1.75942i	0.217118	−	0.125353i	0.604615	+	0.796518i	$0.293327\pi$
$198$	0.762517	−	2.84575i	0.0541897	−	0.202239i
$199$	−6.19744	+	10.7343i	−0.439325	+	0.760933i	−0.997638	−	0.0686976i	$-0.978116\pi$
$199$	−6.19744	+	10.7343i	−0.439325	+	0.760933i	0.558313	+	0.829631i	$0.311449\pi$
$200$	−4.60968	+	1.93671i	−0.325954	+	0.136946i
$201$	−3.40021	−	12.6898i	−0.239833	−	0.895068i
$202$	−3.94198	+	6.82771i	−0.277357	+	0.480396i
$203$		−	19.7516i		−	1.38629i
$204$	3.40660	+	1.96680i	0.238510	+	0.137704i
$205$	4.28959	+	4.86650i	0.299598	+	0.339891i
$206$	−0.838927	+	3.13092i	−0.0584508	+	0.218141i
$207$	−5.18403	−	5.18403i	−0.360315	−	0.360315i
$208$	3.41056	−	1.16966i	0.236480	−	0.0811014i
$209$			23.8989i			1.65312i
$210$	5.45182	+	6.18505i	0.376211	+	0.426809i
$211$	−13.4158	−	23.2369i	−0.923583	−	1.59969i	−0.793824	−	0.608147i	$-0.791913\pi$
$211$	−13.4158	−	23.2369i	−0.923583	−	1.59969i	−0.129759	−	0.991546i	$-0.541420\pi$
$212$	−1.30056	+	0.348484i	−0.0893228	+	0.0239340i
$213$	2.39892			0.164372
$214$	17.1331	−	4.59079i	1.17119	−	0.313820i
$215$	−2.70198	+	8.02627i	−0.184274	+	0.547387i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−3.97318	−	14.8281i	−0.269717	−	1.00660i
$218$	−8.81402	−	2.36171i	−0.596961	−	0.159955i
$219$	8.38023	+	2.24548i	0.566284	+	0.151735i
$220$	1.30151	+	6.45792i	0.0877479	+	0.435393i
$221$	−0.971949	−	14.1495i	−0.0653804	−	0.951796i
$222$	−1.60181	+	1.60181i	−0.107506	+	0.107506i
$223$	−12.5595	−	21.7537i	−0.841046	−	1.45673i	−0.889012	−	0.457885i	$-0.848607\pi$
$223$	−12.5595	−	21.7537i	−0.841046	−	1.45673i	0.0479660	−	0.998849i	$-0.484726\pi$
$224$	−3.19321	+	1.84360i	−0.213355	+	0.123181i
$225$	0.627602	−	4.96046i	0.0418401	−	0.330697i
$226$	5.75129	−	5.75129i	0.382570	−	0.382570i
$227$	15.6557	+	9.03882i	1.03910	+	0.599928i	0.919580	−	0.392904i	$-0.128529\pi$
$227$	15.6557	+	9.03882i	1.03910	+	0.599928i	0.119525	+	0.992831i	$0.461863\pi$
$228$	7.02514	+	4.05597i	0.465251	+	0.268613i
$229$	−8.19344	+	8.19344i	−0.541437	+	0.541437i	−0.923950	−	0.382513i	$-0.875059\pi$
$229$	−8.19344	+	8.19344i	−0.541437	+	0.541437i	0.382513	+	0.923950i	$0.375059\pi$
$230$	15.5366	+	5.23028i	1.02445	+	0.344874i
$231$	9.40764	−	5.43150i	0.618977	−	0.357367i
$232$	−2.67840	−	4.63913i	−0.175846	−	0.304574i
$233$	−20.2207	+	20.2207i	−1.32470	+	1.32470i	−0.414785	+	0.909919i	$0.636143\pi$
$233$	−20.2207	+	20.2207i	−1.32470	+	1.32470i	−0.909919	+	0.414785i	$0.863857\pi$
$234$	−0.692322	+	3.53846i	−0.0452585	+	0.231316i
$235$	22.9944	+	15.2806i	1.49999	+	0.996793i
$236$	−6.59302	−	1.76659i	−0.429169	−	0.114995i
$237$	−10.4506	−	2.80024i	−0.678842	−	0.181895i
$238$	3.75391	+	14.0098i	0.243330	+	0.908119i
$239$	3.98481	+	3.98481i	0.257756	+	0.257756i	0.824141	−	0.566385i	$-0.191658\pi$
$239$	3.98481	+	3.98481i	0.257756	+	0.257756i	−0.566385	+	0.824141i	$0.691658\pi$
$240$	2.11921	+	0.713415i	0.136794	+	0.0460507i
$241$	−11.8387	+	3.17216i	−0.762595	+	0.204337i	−0.619098	−	0.785314i	$-0.712502\pi$
$241$	−11.8387	+	3.17216i	−0.762595	+	0.204337i	−0.143497	+	0.989651i	$0.545835\pi$
$242$	−2.32027			−0.149153
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	−4.93418	−	8.54626i	−0.315879	−	0.547118i
$245$	−0.927415	+	14.7187i	−0.0592504	+	0.940343i
$246$		−	2.90115i		−	0.184971i
$247$	−2.00437	−	29.1792i	−0.127535	−	1.85663i
$248$	−2.94395	−	2.94395i	−0.186941	−	0.186941i
$249$	−2.70843	+	10.1080i	−0.171640	+	0.640569i
$250$	3.67385	+	10.5595i	0.232355	+	0.667841i
$251$	−0.934747	−	0.539676i	−0.0590007	−	0.0340641i	0.470209	−	0.882555i	$-0.344178\pi$
$251$	−0.934747	−	0.539676i	−0.0590007	−	0.0340641i	−0.529210	+	0.848491i	$0.677512\pi$
$252$		−	3.68720i		−	0.232272i
$253$	10.7995	−	18.7054i	0.678962	−	1.17600i
$254$	−3.57670	−	13.3484i	−0.224422	−	0.837555i
$255$	4.86821	−	7.32575i	0.304859	−	0.458756i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.34662	+	5.02566i	−0.0840000	+	0.313492i	−0.995123	−	0.0986424i	$-0.968550\pi$
$257$	−1.34662	+	5.02566i	−0.0840000	+	0.313492i	0.911123	+	0.412135i	$0.135217\pi$
$258$	3.27998	−	1.89370i	0.204203	−	0.117896i
$259$	−8.35261			−0.519006
$260$	−2.13069	−	7.77561i	−0.132140	−	0.482223i
$261$	5.35680			0.331578
$262$	8.89655	−	5.13642i	0.549631	−	0.317329i
$263$	−2.70814	+	10.1069i	−0.166991	+	0.623220i	0.830787	+	0.556591i	$0.187891\pi$
$263$	−2.70814	+	10.1069i	−0.166991	+	0.623220i	−0.997778	+	0.0666287i	$0.978776\pi$
$264$	1.47307	−	2.55143i	0.0906611	−	0.157030i
$265$	0.594814	+	2.95138i	0.0365391	+	0.181302i
$266$	7.74136	+	28.8912i	0.474653	+	1.77143i
$267$	4.95712	−	8.58599i	0.303371	−	0.525454i
$268$		−	13.1374i		−	0.802496i
$269$	11.6065	+	6.70100i	0.707659	+	0.408567i	0.810194	−	0.586162i	$-0.199362\pi$
$269$	11.6065	+	6.70100i	0.707659	+	0.408567i	−0.102535	+	0.994729i	$0.532695\pi$
$270$	−1.67744	+	1.47858i	−0.102086	+	0.0899835i
$271$	−1.30945	+	4.88695i	−0.0795437	+	0.296861i	−0.994225	−	0.107314i	$-0.965775\pi$
$271$	−1.30945	+	4.88695i	−0.0795437	+	0.296861i	0.914681	+	0.404176i	$0.132442\pi$
$272$	2.78148	+	2.78148i	0.168652	+	0.168652i
$273$	−11.0307	+	7.42058i	−0.667607	+	0.449114i
$274$		−	3.76591i		−	0.227507i
$275$	14.5948	−	1.99643i	0.880098	−	0.120389i
$276$	−3.66566	−	6.34911i	−0.220647	−	0.382172i
$277$	5.55169	−	1.48757i	0.333569	−	0.0893794i	−0.0881474	−	0.996107i	$-0.528095\pi$
$277$	5.55169	−	1.48757i	0.333569	−	0.0893794i	0.421716	+	0.906728i	$0.361428\pi$
$278$	−5.80636			−0.348243
$279$	4.02151	−	1.07756i	0.240762	−	0.0645119i
$280$	3.66525	+	7.38534i	0.219040	+	0.441358i
$281$	17.9758	+	17.9758i	1.07235	+	1.07235i	0.997170	+	0.0751771i	$0.0239522\pi$
$281$	17.9758	+	17.9758i	1.07235	+	1.07235i	0.0751771	+	0.997170i	$0.476048\pi$
$282$	−3.19563	−	11.9262i	−0.190297	−	0.710197i
$283$	8.86275	+	2.37477i	0.526836	+	0.141165i	0.512427	−	0.858731i	$-0.328747\pi$
$283$	8.86275	+	2.37477i	0.526836	+	0.141165i	0.0144091	+	0.999896i	$0.495413\pi$
$284$	2.31718	+	0.620887i	0.137500	+	0.0368429i
$285$	10.0393	−	15.1073i	0.594677	−	0.894878i
$286$	−10.5975	+	0.727958i	−0.626642	+	0.0430450i
$287$	7.56401	−	7.56401i	0.446490	−	0.446490i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−1.32223	+	0.763387i	−0.0777780	+	0.0449051i
$290$	−10.7295	+	5.32491i	−0.630058	+	0.312689i
$291$	2.26797	−	2.26797i	0.132951	−	0.132951i
$292$	7.51351	+	4.33793i	0.439695	+	0.253858i
$293$	−9.64744	−	5.56995i	−0.563610	−	0.325400i	0.190983	−	0.981593i	$-0.438832\pi$
$293$	−9.64744	−	5.56995i	−0.563610	−	0.325400i	−0.754593	+	0.656193i	$0.772166\pi$
$294$	4.66369	−	4.66369i	0.271992	−	0.271992i
$295$	−4.86948	+	14.4648i	−0.283512	+	0.842176i
$296$	−1.96180	+	1.13265i	−0.114028	+	0.0658339i
$297$	1.47307	+	2.55143i	0.0854761	+	0.148049i
$298$	−5.22956	+	5.22956i	−0.302940	+	0.302940i
$299$	−11.6169	+	23.7440i	−0.671821	+	1.37315i
$300$	1.89008	−	4.62900i	0.109124	−	0.267255i
$301$	13.4890	+	3.61438i	0.777496	+	0.208329i
$302$	−6.15168	−	1.64834i	−0.353989	−	0.0948512i
$303$	−2.04052	−	7.61532i	−0.117225	−	0.437489i
$304$	5.73600	+	5.73600i	0.328982	+	0.328982i
$305$	−19.7660	+	9.80961i	−1.13180	+	0.561697i
$306$	−3.79957	+	1.01809i	−0.217207	+	0.0582004i
$307$	31.8543			1.81802			0.909010	−	0.416773i	$-0.136839\pi$
$307$	31.8543			1.81802			0.909010	+	0.416773i	$0.136839\pi$
$308$	10.4929	−	2.81155i	0.597886	−	0.160203i
$309$	−1.62068	−	2.80710i	−0.0921974	−	0.159691i
$310$	−6.98381	+	6.15588i	−0.396654	+	0.349631i
$311$		−	9.69424i		−	0.549710i	−0.961486	−	0.274855i	$-0.911370\pi$
$311$		−	9.69424i		−	0.549710i	0.961486	−	0.274855i	$-0.0886298\pi$
$312$	−1.58455	+	3.23870i	−0.0897076	+	0.183355i
$313$	12.1109	+	12.1109i	0.684549	+	0.684549i	0.961022	−	0.276472i	$-0.0891654\pi$
$313$	12.1109	+	12.1109i	0.684549	+	0.684549i	−0.276472	+	0.961022i	$0.589165\pi$
$314$	0.669620	−	2.49905i	0.0377888	−	0.141030i
$315$	−8.22851	−	0.518473i	−0.463624	−	0.0292127i
$316$	−9.36978	−	5.40965i	−0.527091	−	0.304316i
$317$		−	0.342702i		−	0.0192480i	−0.999954	−	0.00962402i	$-0.996937\pi$
$317$		−	0.342702i		−	0.0192480i	0.999954	−	0.00962402i	$-0.00306347\pi$
$318$	0.673219	−	1.16605i	0.0377522	−	0.0653888i
$319$	4.08465	+	15.2441i	0.228697	+	0.853507i
$320$	1.86235	+	1.23760i	0.104109	+	0.0691838i
$321$	−8.86873	+	15.3611i	−0.495004	+	0.857373i
$322$	6.99642	−	26.1110i	0.389895	−	1.45511i
$323$	27.6341	−	15.9546i	1.53760	−	0.887736i
$324$	1.00000			0.0555556
$325$	−17.6520	+	3.66158i	−0.979156	+	0.203108i
$326$	17.1079			0.947520
$327$	7.90243	−	4.56247i	0.437005	−	0.252305i
$328$	0.750873	−	2.80230i	0.0414600	−	0.154731i
$329$	22.7629	−	39.4264i	1.25496	−	2.17365i
$330$	−5.48675	−	3.64613i	−0.302035	−	0.200713i
$331$	6.97963	+	26.0483i	0.383635	+	1.43175i	0.840307	+	0.542110i	$0.182374\pi$
$331$	6.97963	+	26.0483i	0.383635	+	1.43175i	−0.456672	+	0.889635i	$0.650959\pi$
$332$	−5.23229	+	9.06259i	−0.287159	+	0.497374i
$333$		−	2.26530i		−	0.124138i
$334$	1.98761	+	1.14754i	0.108757	+	0.0627908i
$335$	−29.3180	−	1.84731i	−1.60181	−	0.100929i
$336$	0.954318	−	3.56156i	0.0520623	−	0.194299i
$337$	−1.69270	−	1.69270i	−0.0922074	−	0.0922074i	0.659498	−	0.751706i	$-0.270769\pi$
$337$	−1.69270	−	1.69270i	−0.0922074	−	0.0922074i	−0.751706	+	0.659498i	$0.770769\pi$
$338$	12.8779	−	1.77759i	0.700465	−	0.0966883i
$339$			8.13356i			0.441754i
$340$	6.59838	−	5.81615i	0.357847	−	0.315425i
$341$	6.13294	+	10.6226i	0.332117	+	0.575244i
$342$	−7.83553	+	2.09952i	−0.423697	+	0.113529i
$343$	−1.49165			−0.0805415
$344$	3.65834	−	0.980250i	0.197245	−	0.0528515i
$345$	−14.6844	+	7.28767i	−0.790581	+	0.392355i
$346$	−15.1002	−	15.1002i	−0.811790	−	0.811790i
$347$	1.02305	+	3.81806i	0.0549201	+	0.204964i	0.987934	−	0.154876i	$-0.0494978\pi$
$347$	1.02305	+	3.81806i	0.0549201	+	0.204964i	−0.933014	+	0.359840i	$0.882831\pi$
$348$	5.17428	+	1.38644i	0.277370	+	0.0743211i
$349$	6.30915	+	1.69053i	0.337721	+	0.0904921i	0.423694	−	0.905805i	$-0.360733\pi$
$349$	6.30915	+	1.69053i	0.337721	+	0.0904921i	−0.0859729	+	0.996297i	$0.527400\pi$
$350$	16.9968	−	7.14103i	0.908518	−	0.381704i
$351$	−2.01252	−	2.99161i	−0.107421	−	0.159681i
$352$	2.08323	−	2.08323i	0.111037	−	0.111037i
$353$	−13.7281	−	23.7777i	−0.730671	−	1.26556i	−0.956597	−	0.291414i	$-0.905874\pi$
$353$	−13.7281	−	23.7777i	−0.730671	−	1.26556i	0.225926	−	0.974144i	$-0.427459\pi$
$354$	5.91114	−	3.41280i	0.314173	−	0.181388i
$355$	1.71143	−	5.08382i	0.0908331	−	0.269821i
$356$	7.01043	−	7.01043i	0.371552	−	0.371552i
$357$	−12.5608	−	7.25199i	−0.664789	−	0.383816i
$358$	1.12921	+	0.651952i	0.0596808	+	0.0344567i
$359$	−2.54684	+	2.54684i	−0.134417	+	0.134417i	−0.771114	−	0.636697i	$-0.780300\pi$
$359$	−2.54684	+	2.54684i	−0.134417	+	0.134417i	0.636697	+	0.771114i	$0.280300\pi$
$360$	−2.00297	+	0.994046i	−0.105566	+	0.0523908i
$361$	40.5330	−	23.4017i	2.13332	−	1.23167i
$362$	−7.27474	−	12.6002i	−0.382352	−	0.662253i
$363$	1.64068	−	1.64068i	0.0861133	−	0.0861133i
$364$	−12.5754	+	4.31277i	−0.659130	+	0.226051i
$365$	10.7372	−	16.1575i	0.562011	−	0.845722i
$366$	9.53211	+	2.55412i	0.498252	+	0.133506i
$367$	11.6185	+	3.11318i	0.606482	+	0.162506i	0.548975	−	0.835839i	$-0.315018\pi$
$367$	11.6185	+	3.11318i	0.606482	+	0.162506i	0.0575071	+	0.998345i	$0.481685\pi$
$368$	−1.89749	−	7.08152i	−0.0989133	−	0.369150i
$369$	2.05142	+	2.05142i	0.106793	+	0.106793i
$370$	2.25181	+	4.53731i	0.117066	+	0.235884i
$371$	4.79542	−	1.28493i	0.248966	−	0.0667102i
$372$	4.16338			0.215861
$373$	−29.5102	+	7.90723i	−1.52798	+	0.409421i	−0.922360	−	0.386332i	$-0.873742\pi$
$373$	−29.5102	+	7.90723i	−1.52798	+	0.409421i	−0.605621	+	0.795753i	$0.707075\pi$
$374$	−5.79447	−	10.0363i	−0.299625	−	0.518965i
$375$	−10.0645	−	4.86888i	−0.519728	−	0.251428i
$376$		−	12.3470i		−	0.636746i
$377$	−6.26564	−	18.2697i	−0.322697	−	0.940936i
$378$	2.60724	+	2.60724i	0.134102	+	0.134102i
$379$	−6.78244	+	25.3124i	−0.348391	+	1.30021i	0.540210	+	0.841530i	$0.318345\pi$
$379$	−6.78244	+	25.3124i	−0.348391	+	1.30021i	−0.888601	+	0.458682i	$0.848322\pi$
$380$	13.6073	−	11.9941i	0.698038	−	0.615287i
$381$	11.9679	+	6.90965i	0.613133	+	0.353992i
$382$			11.8337i			0.605462i
$383$	−10.4347	+	18.0734i	−0.533187	+	0.923507i	0.466062	+	0.884752i	$0.345672\pi$
$383$	−10.4347	+	18.0734i	−0.533187	+	0.923507i	−0.999249	+	0.0387549i	$0.987661\pi$
$384$	−0.258819	−	0.965926i	−0.0132078	−	0.0492922i
$385$	−4.79893	−	23.8116i	−0.244576	−	1.21355i
$386$	2.54585	−	4.40954i	0.129580	−	0.224440i
$387$	−0.980250	+	3.65834i	−0.0498289	+	0.185964i
$388$	2.77769	−	1.60370i	0.141016	−	0.0814155i
$389$	19.1719			0.972054			0.486027	−	0.873944i	$-0.338446\pi$
$389$	19.1719			0.972054			0.486027	+	0.873944i	$0.338446\pi$
$390$	7.00481	+	3.99156i	0.354703	+	0.202121i
$391$	−28.8385			−1.45843
$392$	5.71183	−	3.29773i	0.288491	−	0.166560i
$393$	−2.65881	+	9.92281i	−0.134119	+	0.500540i
$394$	−1.75942	+	3.04740i	−0.0886381	+	0.153526i
$395$	−13.3899	+	20.1493i	−0.673720	+	1.01382i
$396$	0.762517	+	2.84575i	0.0383179	+	0.143004i
$397$	−4.98999	+	8.64291i	−0.250440	+	0.433775i	−0.963647	−	0.267178i	$-0.913909\pi$
$397$	−4.98999	+	8.64291i	−0.250440	+	0.433775i	0.713207	+	0.700954i	$0.247242\pi$
$398$		−	12.3949i		−	0.621299i
$399$	−25.9031	−	14.9552i	−1.29678	−	0.748695i
$400$	3.02375	−	3.98208i	0.151187	−	0.199104i
$401$	2.77303	−	10.3491i	0.138479	−	0.516809i	−0.861481	−	0.507790i	$-0.830463\pi$
$401$	2.77303	−	10.3491i	0.138479	−	0.516809i	0.999959	−	0.00901876i	$-0.00287080\pi$
$402$	9.28956	+	9.28956i	0.463321	+	0.463321i
$403$	−8.37889	−	12.4552i	−0.417382	−	0.620438i
$404$		−	7.88396i		−	0.392241i
$405$	0.140614	−	2.23164i	0.00698718	−	0.110891i
$406$	9.87581	+	17.1054i	0.490128	+	0.848927i
$407$	6.44647	−	1.72733i	0.319540	−	0.0856204i
$408$	−3.93360			−0.194742
$409$	−5.77688	+	1.54791i	−0.285648	+	0.0765393i	−0.398798	−	0.917039i	$-0.630573\pi$
$409$	−5.77688	+	1.54791i	−0.285648	+	0.0765393i	0.113150	+	0.993578i	$0.463906\pi$
$410$	−6.14814	−	2.06972i	−0.303635	−	0.102216i
$411$	2.66290	+	2.66290i	0.131351	+	0.131351i
$412$	−0.838927	−	3.13092i	−0.0413310	−	0.154249i
$413$	24.3098	+	6.51379i	1.19621	+	0.320522i
$414$	7.08152	+	1.89749i	0.348038	+	0.0932564i
$415$	19.4887	+	12.9509i	0.956664	+	0.635736i
$416$	−2.36880	+	2.71823i	−0.116140	+	0.133272i
$417$	4.10572	−	4.10572i	0.201058	−	0.201058i
$418$	−11.9494	−	20.6970i	−0.584466	−	1.01233i
$419$	−4.96010	+	2.86371i	−0.242317	+	0.139902i	−0.616241	−	0.787558i	$-0.711345\pi$
$419$	−4.96010	+	2.86371i	−0.242317	+	0.139902i	0.373924	+	0.927459i	$0.378012\pi$
$420$	−7.81394	−	2.63050i	−0.381281	−	0.128355i
$421$	24.6539	−	24.6539i	1.20156	−	1.20156i	0.227867	−	0.973692i	$-0.426825\pi$
$421$	24.6539	−	24.6539i	1.20156	−	1.20156i	0.973692	−	0.227867i	$-0.0731751\pi$
$422$	23.2369	+	13.4158i	1.13115	+	0.653072i
$423$	10.6928	+	6.17348i	0.519901	+	0.300165i
$424$	0.952075	−	0.952075i	0.0462369	−	0.0462369i
$425$	−12.0517	−	15.5431i	−0.584595	−	0.753949i
$426$	−2.07753	+	1.19946i	−0.100657	+	0.0581141i
$427$	18.1933	+	31.5118i	0.880437	+	1.52496i
$428$	−12.5423	+	12.5423i	−0.606254	+	0.606254i
$429$	6.97881	−	8.00829i	0.336940	−	0.386644i
$430$	−1.67315	−	8.30195i	−0.0806865	−	0.400356i
$431$	4.72288	+	1.26549i	0.227493	+	0.0609566i	0.370765	−	0.928727i	$-0.379096\pi$
$431$	4.72288	+	1.26549i	0.227493	+	0.0609566i	−0.143272	+	0.989683i	$0.545762\pi$
$432$	0.965926	+	0.258819i	0.0464731	+	0.0124524i
$433$	1.06181	+	3.96274i	0.0510274	+	0.190437i	0.986735	−	0.162340i	$-0.0519041\pi$
$433$	1.06181	+	3.96274i	0.0510274	+	0.190437i	−0.935707	+	0.352777i	$0.885237\pi$
$434$	10.8549	+	10.8549i	0.521054	+	0.521054i
$435$	3.82162	−	11.3522i	0.183233	−	0.544295i
$436$	8.81402	−	2.36171i	0.422115	−	0.113105i
$437$	−59.4712			−2.84490
$438$	−8.38023	+	2.24548i	−0.400423	+	0.107293i
$439$	0.444561	+	0.770002i	0.0212177	+	0.0367502i	0.876439	−	0.481512i	$-0.159912\pi$
$439$	0.444561	+	0.770002i	0.0212177	+	0.0367502i	−0.855222	+	0.518263i	$0.826579\pi$
$440$	−4.35610	−	4.94197i	−0.207669	−	0.235599i
$441$			6.59545i			0.314069i
$442$	7.91646	+	11.7678i	0.376548	+	0.559738i
$443$	2.43706	+	2.43706i	0.115788	+	0.115788i	0.762627	−	0.646839i	$-0.223909\pi$
$443$	2.43706	+	2.43706i	0.115788	+	0.115788i	−0.646839	+	0.762627i	$0.723909\pi$
$444$	0.586302	−	2.18811i	0.0278247	−	0.103843i
$445$	−14.6590	−	16.6305i	−0.694903	−	0.788363i
$446$	21.7537	+	12.5595i	1.03007	+	0.594709i
$447$		−	7.39571i		−	0.349805i
$448$	1.84360	−	3.19321i	0.0871019	−	0.150865i
$449$	−3.19285	−	11.9159i	−0.150680	−	0.562344i	−0.999437	−	0.0335612i	$-0.989315\pi$
$449$	−3.19285	−	11.9159i	−0.150680	−	0.562344i	0.848757	−	0.528783i	$-0.177352\pi$
$450$	1.93671	+	4.60968i	0.0912973	+	0.217302i
$451$	−4.27360	+	7.40209i	−0.201236	+	0.348551i
$452$	−2.10512	+	7.85641i	−0.0990165	+	0.369535i
$453$	5.51545	−	3.18434i	0.259138	−	0.149614i
$454$	−18.0776			−0.848426
$455$	7.85629	+	28.6702i	0.368308	+	1.34408i
$456$	−8.11193			−0.379876
$457$	15.6657	−	9.04457i	0.732808	−	0.423087i	−0.0866404	−	0.996240i	$-0.527613\pi$
$457$	15.6657	−	9.04457i	0.732808	−	0.423087i	0.819449	+	0.573153i	$0.194280\pi$
$458$	2.99901	−	11.1924i	0.140134	−	0.522988i
$459$	1.96680	−	3.40660i	0.0918024	−	0.159006i
$460$	−16.0702	+	3.23875i	−0.749278	+	0.151007i
$461$	4.35995	+	16.2715i	0.203063	+	0.757841i	0.990031	+	0.140848i	$0.0449828\pi$
$461$	4.35995	+	16.2715i	0.203063	+	0.757841i	−0.786968	+	0.616993i	$0.788350\pi$
$462$	−5.43150	+	9.40764i	−0.252696	+	0.437683i
$463$			8.14963i			0.378745i	0.981905	+	0.189373i	$0.0606454\pi$
$463$			8.14963i			0.378745i	−0.981905	+	0.189373i	$0.939355\pi$
$464$	4.63913	+	2.67840i	0.215366	+	0.124342i
$465$	0.585431	−	9.29117i	0.0271487	−	0.430868i
$466$	7.40130	−	27.6220i	0.342859	−	1.27957i
$467$	−13.9799	−	13.9799i	−0.646912	−	0.646912i	0.305333	−	0.952246i	$-0.401232\pi$
$467$	−13.9799	−	13.9799i	−0.646912	−	0.646912i	−0.952246	+	0.305333i	$0.901232\pi$
$468$	−1.16966	−	3.41056i	−0.0540676	−	0.157653i
$469$			48.4403i			2.23677i
$470$	−27.5540	−	1.73616i	−1.27097	−	0.0800831i
$471$	1.29361	+	2.24059i	0.0596062	+	0.103241i
$472$	6.59302	−	1.76659i	0.303468	−	0.0813141i
$473$	−11.1582			−0.513054
$474$	10.4506	−	2.80024i	0.480014	−	0.128619i
$475$	−24.8533	−	32.0531i	−1.14035	−	1.47070i
$476$	−10.2559	−	10.2559i	−0.470077	−	0.470077i
$477$	0.348484	+	1.30056i	0.0159560	+	0.0595485i
$478$	−5.44335	−	1.45854i	−0.248973	−	0.0667122i
$479$	−2.72948	−	0.731362i	−0.124713	−	0.0334168i	0.195923	−	0.980619i	$-0.437230\pi$
$479$	−2.72948	−	0.731362i	−0.124713	−	0.0334168i	−0.320636	+	0.947203i	$0.603897\pi$
$480$	−2.19199	+	0.441768i	−0.100050	+	0.0201639i
$481$	−7.72592	+	2.64963i	−0.352272	+	0.120813i
$482$	8.66650	−	8.66650i	0.394748	−	0.394748i
$483$	13.5160	+	23.4105i	0.615001	+	1.06521i
$484$	2.00941	−	1.16013i	0.0913369	−	0.0527334i
$485$	−3.18830	−	6.42431i	−0.144773	−	0.291713i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	−10.6025	−	6.12135i	−0.480445	−	0.277385i	0.240157	−	0.970734i	$-0.422801\pi$
$487$	−10.6025	−	6.12135i	−0.480445	−	0.277385i	−0.720602	+	0.693349i	$0.756134\pi$
$488$	8.54626	+	4.93418i	0.386871	+	0.223360i
$489$	−12.0971	+	12.0971i	−0.547051	+	0.547051i
$490$	−6.55618	−	13.2105i	−0.296178	−	0.596788i
$491$	−29.4491	+	17.0024i	−1.32902	+	0.767309i	−0.985148	−	0.171708i	$-0.945072\pi$
$491$	−29.4491	+	17.0024i	−1.32902	+	0.767309i	−0.343871	+	0.939017i	$0.611738\pi$
$492$	1.45058	+	2.51247i	0.0653970	+	0.113271i
$493$	14.8998	−	14.8998i	0.671054	−	0.671054i
$494$	16.3255	+	24.2678i	0.734517	+	1.09186i
$495$	6.45792	−	1.30151i	0.290262	−	0.0584986i
$496$	4.02151	+	1.07756i	0.180571	+	0.0483839i
$497$	−8.54392	−	2.28934i	−0.383247	−	0.102691i
$498$	−2.70843	−	10.1080i	−0.121368	−	0.452951i
$499$	−13.5016	−	13.5016i	−0.604414	−	0.604414i	0.337067	−	0.941481i	$-0.390565\pi$
$499$	−13.5016	−	13.5016i	−0.604414	−	0.604414i	−0.941481	+	0.337067i	$0.890565\pi$
$500$	−8.46139	−	7.30786i	−0.378405	−	0.326817i
$501$	−2.21689	+	0.594013i	−0.0990431	+	0.0265385i
$502$	1.07935			0.0481739
$503$	1.40288	−	0.375901i	0.0625515	−	0.0167606i	−0.227408	−	0.973800i	$-0.573025\pi$
$503$	1.40288	−	0.375901i	0.0625515	−	0.0167606i	0.289959	+	0.957039i	$0.406358\pi$
$504$	1.84360	+	3.19321i	0.0821205	+	0.142237i
$505$	−17.5942	−	1.10860i	−0.782930	−	0.0493319i
$506$			21.5991i			0.960197i
$507$	−7.84910	+	10.3630i	−0.348591	+	0.460237i
$508$	9.77173	+	9.77173i	0.433550	+	0.433550i
$509$	0.337646	−	1.26011i	0.0149659	−	0.0558534i	−0.958039	−	0.286638i	$-0.907462\pi$
$509$	0.337646	−	1.26011i	0.0149659	−	0.0558534i	0.973005	+	0.230784i	$0.0741291\pi$
$510$	−0.553121	+	8.77839i	−0.0244926	+	0.388714i
$511$	−27.7038	−	15.9948i	−1.22555	−	0.707569i
$512$		−	1.00000i		−	0.0441942i
$513$	4.05597	−	7.02514i	0.179075	−	0.310168i
$514$	−1.34662	−	5.02566i	−0.0593970	−	0.221672i
$515$	−7.10505	+	1.43193i	−0.313086	+	0.0630985i
$516$	−1.89370	+	3.27998i	−0.0833654	+	0.144393i
$517$	−9.41476	+	35.1364i	−0.414061	+	1.54530i
$518$	7.23357	−	4.17630i	0.317825	−	0.183496i
$519$	21.3549			0.937375
$520$	5.73304	+	5.66853i	0.251410	+	0.248582i
$521$	−5.16162			−0.226135			−0.113067	−	0.993587i	$-0.536068\pi$
$521$	−5.16162			−0.226135			−0.113067	+	0.993587i	$0.536068\pi$
$522$	−4.63913	+	2.67840i	−0.203049	+	0.117230i
$523$	−6.42597	+	23.9820i	−0.280988	+	1.04866i	0.670734	+	0.741698i	$0.265979\pi$
$523$	−6.42597	+	23.9820i	−0.280988	+	1.04866i	−0.951721	+	0.306963i	$0.900687\pi$
$524$	−5.13642	+	8.89655i	−0.224386	+	0.388647i
$525$	−6.96909	+	17.0680i	−0.304156	+	0.744910i
$526$	−2.70814	−	10.1069i	−0.118081	−	0.440683i
$527$	8.18853	−	14.1830i	0.356698	−	0.617819i
$528$			2.94614i			0.128214i
$529$	26.6288	+	15.3742i	1.15778	+	0.668442i
$530$	−1.99082	−	2.25857i	−0.0864755	−	0.0981059i
$531$	−1.76659	+	6.59302i	−0.0766636	+	0.286113i
$532$	−21.1498	−	21.1498i	−0.916960	−	0.916960i
$533$	4.59703	−	9.39597i	0.199119	−	0.406985i
$534$			9.91424i			0.429031i
$535$	26.2263	+	29.7535i	1.13386	+	1.28636i
$536$	6.56871	+	11.3773i	0.283725	+	0.491426i
$537$	−1.25947	+	0.337475i	−0.0543503	+	0.0145631i
$538$	−13.4020			−0.577801
$539$	−18.7690	+	5.02914i	−0.808439	+	0.216620i
$540$	0.713415	−	2.11921i	0.0307005	−	0.0911962i
$541$	−1.21403	−	1.21403i	−0.0521954	−	0.0521954i	0.680527	−	0.732723i	$-0.261751\pi$
$541$	−1.21403	−	1.21403i	−0.0521954	−	0.0521954i	−0.732723	+	0.680527i	$0.761751\pi$
$542$	−1.30945	−	4.88695i	−0.0562459	−	0.209913i
$543$	14.0537	+	3.76568i	0.603103	+	0.161601i
$544$	−3.79957	−	1.01809i	−0.162905	−	0.0436503i
$545$	−4.03111	−	20.0018i	−0.172674	−	0.856784i
$546$	5.84256	−	11.9417i	0.250039	−	0.511060i
$547$	30.4542	−	30.4542i	1.30213	−	1.30213i	0.375172	−	0.926955i	$-0.377584\pi$
$547$	30.4542	−	30.4542i	1.30213	−	1.30213i	0.926955	−	0.375172i	$-0.122416\pi$
$548$	1.88296	+	3.26137i	0.0804359	+	0.139319i
$549$	−8.54626	+	4.93418i	−0.364745	+	0.210586i
$550$	−11.6412	+	9.02635i	−0.496384	+	0.384885i
$551$	30.7266	−	30.7266i	1.30900	−	1.30900i
$552$	6.34911	+	3.66566i	0.270236	+	0.156021i
$553$	34.5483	+	19.9465i	1.46914	+	0.848210i
$554$	−4.06412	+	4.06412i	−0.172668	+	0.172668i
$555$	−4.80063	−	1.61610i	−0.203776	−	0.0685995i
$556$	5.02846	−	2.90318i	0.213254	−	0.123122i
$557$	13.8168	+	23.9313i	0.585435	+	1.01400i	0.994821	+	0.101641i	$0.0324094\pi$
$557$	13.8168	+	23.9313i	0.585435	+	1.01400i	−0.409387	+	0.912361i	$0.634257\pi$
$558$	−2.94395	+	2.94395i	−0.124627	+	0.124627i
$559$	13.6235	−	0.935823i	0.576214	−	0.0395811i
$560$	−6.86687	−	4.56327i	−0.290178	−	0.192833i
$561$	11.1941	+	2.99944i	0.472613	+	0.126636i
$562$	−24.5554	−	6.57961i	−1.03581	−	0.277544i
$563$	−1.84404	−	6.88207i	−0.0777172	−	0.290045i	0.916118	−	0.400908i	$-0.131305\pi$
$563$	−1.84404	−	6.88207i	−0.0777172	−	0.290045i	−0.993836	+	0.110863i	$0.964639\pi$
$564$	8.73061	+	8.73061i	0.367625	+	0.367625i
$565$	17.2367	+	5.80260i	0.725153	+	0.244117i
$566$	−8.86275	+	2.37477i	−0.372529	+	0.0998189i
$567$	−3.68720			−0.154848
$568$	−2.31718	+	0.620887i	−0.0972268	+	0.0260519i
$569$	−6.40701	−	11.0973i	−0.268596	−	0.465222i	0.699904	−	0.714237i	$-0.253226\pi$
$569$	−6.40701	−	11.0973i	−0.268596	−	0.465222i	−0.968499	+	0.249016i	$0.919893\pi$
$570$	−1.14065	+	18.1029i	−0.0477768	+	0.758249i
$571$			27.7231i			1.16018i	0.814554	+	0.580088i	$0.196982\pi$
$571$			27.7231i			1.16018i	−0.814554	+	0.580088i	$0.803018\pi$
$572$	8.81371	−	5.92917i	0.368520	−	0.247911i
$573$	−8.36766	−	8.36766i	−0.349564	−	0.349564i
$574$	−2.76862	+	10.3326i	−0.115560	+	0.431276i
$575$	4.96802	+	36.3184i	0.207181	+	1.51458i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$		−	13.4871i		−	0.561474i	−0.959785	−	0.280737i	$-0.909421\pi$
$577$		−	13.4871i		−	0.561474i	0.959785	−	0.280737i	$-0.0905788\pi$
$578$	0.763387	−	1.32223i	0.0317527	−	0.0549973i
$579$	1.31783	+	4.91821i	0.0547671	+	0.204394i
$580$	6.62956	−	9.97625i	0.275278	−	0.414241i
$581$	19.2925	−	33.4156i	0.800388	−	1.38631i
$582$	−0.830136	+	3.09811i	−0.0344102	+	0.128421i
$583$	−3.43534	+	1.98340i	−0.142277	+	0.0821439i
$584$	−8.67586			−0.359009
$585$	−7.77561	+	2.13069i	−0.321482	+	0.0880933i
$586$	11.1399			0.460185
$587$	8.81513	−	5.08942i	0.363839	−	0.210063i	−0.306924	−	0.951734i	$-0.599300\pi$
$587$	8.81513	−	5.08942i	0.363839	−	0.210063i	0.670764	+	0.741671i	$0.265966\pi$
$588$	−1.70703	+	6.37072i	−0.0703967	+	0.262724i
$589$	16.8865	−	29.2483i	0.695797	−	1.20516i
$590$	−3.01533	−	14.9617i	−0.124139	−	0.615962i
$591$	−0.910741	−	3.39893i	−0.0374629	−	0.139813i
$592$	1.13265	−	1.96180i	0.0465516	−	0.0806297i
$593$			2.71984i			0.111690i	0.998439	+	0.0558452i	$0.0177853\pi$
$593$			2.71984i			0.111690i	−0.998439	+	0.0558452i	$0.982215\pi$
$594$	−2.55143	−	1.47307i	−0.104686	−	0.0604408i
$595$	−24.3295	+	21.4453i	−0.997414	+	0.879172i
$596$	1.91415	−	7.14371i	0.0784067	−	0.292618i
$597$	8.76450	+	8.76450i	0.358707	+	0.358707i
$598$	−1.81149	−	26.3713i	−0.0740773	−	1.07840i
$599$			14.9558i			0.611079i	0.952179	+	0.305540i	$0.0988369\pi$
$599$			14.9558i			0.611079i	−0.952179	+	0.305540i	$0.901163\pi$
$600$	0.677643	+	4.95387i	0.0276647	+	0.202241i
$601$	−15.9466	−	27.6203i	−0.650476	−	1.12666i	−0.983008	−	0.183565i	$-0.941236\pi$
$601$	−15.9466	−	27.6203i	−0.650476	−	1.12666i	0.332532	−	0.943092i	$-0.392097\pi$
$602$	−13.4890	+	3.61438i	−0.549772	+	0.147311i
$603$	−13.1374			−0.534997
$604$	6.15168	−	1.64834i	0.250308	−	0.0670699i
$605$	−2.30645	−	4.64742i	−0.0937707	−	0.188945i
$606$	5.57480	+	5.57480i	0.226461	+	0.226461i
$607$	9.27282	+	34.6067i	0.376372	+	1.40464i	0.851329	+	0.524632i	$0.175797\pi$
$607$	9.27282	+	34.6067i	0.376372	+	1.40464i	−0.474957	+	0.880009i	$0.657536\pi$
$608$	−7.83553	−	2.09952i	−0.317773	−	0.0851469i
$609$	−19.0786	−	5.11209i	−0.773104	−	0.207152i
$610$	12.2131	−	18.3784i	0.494492	−	0.744119i
$611$	8.54807	−	43.6892i	0.345818	−	1.76748i
$612$	2.78148	−	2.78148i	0.112435	−	0.112435i
$613$	3.95933	+	6.85777i	0.159916	+	0.276983i	0.934838	−	0.355074i	$-0.115544\pi$
$613$	3.95933	+	6.85777i	0.159916	+	0.276983i	−0.774922	+	0.632057i	$0.782211\pi$
$614$	−27.5866	+	15.9272i	−1.11331	+	0.642767i
$615$	5.81091	−	2.88388i	0.234318	−	0.116289i
$616$	−7.68130	+	7.68130i	−0.309489	+	0.309489i
$617$	−36.1546	−	20.8739i	−1.45553	−	0.840350i	−0.456742	−	0.889599i	$-0.650984\pi$
$617$	−36.1546	−	20.8739i	−1.45553	−	0.840350i	−0.998787	+	0.0492496i	$0.984317\pi$
$618$	2.80710	+	1.62068i	0.112918	+	0.0651934i
$619$	14.0868	−	14.0868i	0.566197	−	0.566197i	−0.364864	−	0.931061i	$-0.618884\pi$
$619$	14.0868	−	14.0868i	0.566197	−	0.566197i	0.931061	+	0.364864i	$0.118884\pi$
$620$	2.97021	−	8.82306i	0.119287	−	0.354342i
$621$	−6.34911	+	3.66566i	−0.254781	+	0.147098i
$622$	4.84712	+	8.39546i	0.194352	+	0.336627i
$623$	−25.8489	+	25.8489i	−1.03561	+	1.03561i
$624$	−0.247089	−	3.59707i	−0.00989147	−	0.143998i
$625$	−17.4983	+	17.8552i	−0.699933	+	0.714209i
$626$	−16.5438	−	4.43290i	−0.661224	−	0.177174i
$627$	23.0845	+	6.18549i	0.921908	+	0.247024i
$628$	0.669620	+	2.49905i	0.0267207	+	0.0997231i
$629$	−6.30087	−	6.30087i	−0.251232	−	0.251232i
$630$	7.38534	−	3.66525i	0.294239	−	0.146027i
$631$	10.8721	−	2.91318i	0.432813	−	0.115972i	−0.0358331	−	0.999358i	$-0.511408\pi$
$631$	10.8721	−	2.91318i	0.432813	−	0.115972i	0.468647	+	0.883386i	$0.344742\pi$
$632$	10.8193			0.430368
$633$	−25.9174	+	6.94454i	−1.03012	+	0.276021i
$634$	0.171351	+	0.296788i	0.00680521	+	0.0117870i
$635$	23.1810	−	20.4330i	0.919912	−	0.810857i
$636$			1.34644i			0.0533897i
$637$	22.4942	−	7.71444i	0.891251	−	0.305657i
$638$	−11.1595	−	11.1595i	−0.441808	−	0.441808i
$639$	0.620887	−	2.31718i	0.0245619	−	0.0916663i
$640$	−2.23164	−	0.140614i	−0.0882134	−	0.00555827i
$641$	33.7235	+	19.4703i	1.33200	+	0.769030i	0.985606	−	0.169059i	$-0.0540728\pi$
$641$	33.7235	+	19.4703i	1.33200	+	0.769030i	0.346394	+	0.938089i	$0.387406\pi$
$642$		−	17.7375i		−	0.700042i
$643$	14.1844	−	24.5681i	0.559379	−	0.968873i	−0.438170	−	0.898892i	$-0.644373\pi$
$643$	14.1844	−	24.5681i	0.559379	−	0.968873i	0.997548	−	0.0699802i	$-0.0222936\pi$
$644$	6.99642	+	26.1110i	0.275697	+	1.02892i
$645$	7.05346	+	4.68727i	0.277730	+	0.184561i
$646$	−15.9546	+	27.6341i	−0.627724	+	1.08725i
$647$	1.79277	−	6.69072i	0.0704812	−	0.263040i	−0.921690	−	0.387928i	$-0.873191\pi$
$647$	1.79277	−	6.69072i	0.0704812	−	0.263040i	0.992171	+	0.124889i	$0.0398574\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−20.1091			−0.789353
$650$	13.4563	−	11.9970i	0.527799	−	0.470562i
$651$	−15.3512			−0.601661
$652$	−14.8159	+	8.55396i	−0.580235	+	0.334999i
$653$	5.08406	−	18.9740i	0.198954	−	0.742508i	−0.792253	−	0.610193i	$-0.791092\pi$
$653$	5.08406	−	18.9740i	0.198954	−	0.742508i	0.991208	−	0.132316i	$-0.0422412\pi$
$654$	−4.56247	+	7.90243i	−0.178407	+	0.309009i
$655$	19.1317	+	12.7136i	0.747536	+	0.496763i
$656$	0.750873	+	2.80230i	0.0293167	+	0.109411i
$657$	4.33793	−	7.51351i	0.169239	−	0.293130i
$658$			45.5257i			1.77478i
$659$	0.440581	+	0.254370i	0.0171626	+	0.00990883i	0.508557	−	0.861028i	$-0.330179\pi$
$659$	0.440581	+	0.254370i	0.0171626	+	0.00990883i	−0.491394	+	0.870937i	$0.663513\pi$
$660$	6.57473	+	0.414269i	0.255921	+	0.0161254i
$661$	−3.09409	+	11.5473i	−0.120346	+	0.449137i	−0.999631	−	0.0271584i	$-0.991354\pi$
$661$	−3.09409	+	11.5473i	−0.120346	+	0.449137i	0.879285	+	0.476296i	$0.158021\pi$
$662$	−19.0687	−	19.0687i	−0.741126	−	0.741126i
$663$	−13.9189	−	2.72332i	−0.540565	−	0.105765i
$664$		−	10.4646i		−	0.406104i
$665$	−50.1728	+	44.2248i	−1.94562	+	1.71497i
$666$	1.13265	+	1.96180i	0.0438892	+	0.0760184i
$667$	−37.9343	+	10.1645i	−1.46882	+	0.393570i
$668$	−2.29509			−0.0887997
$669$	−24.2631	+	6.50127i	−0.938064	+	0.251354i
$670$	26.3138	−	13.0592i	1.01659	−	0.504521i
$671$	−20.5581	−	20.5581i	−0.793638	−	0.793638i
$672$	0.954318	+	3.56156i	0.0368136	+	0.137390i
$673$	−25.6562	−	6.87456i	−0.988974	−	0.264995i	−0.272154	−	0.962254i	$-0.587736\pi$
$673$	−25.6562	−	6.87456i	−0.988974	−	0.264995i	−0.716819	+	0.697259i	$0.754403\pi$
$674$	2.31228	+	0.619572i	0.0890655	+	0.0238650i
$675$	−4.62900	−	1.89008i	−0.178170	−	0.0727491i
$676$	−10.2638	+	7.97839i	−0.394761	+	0.306861i
$677$	−7.82287	+	7.82287i	−0.300657	+	0.300657i	−0.841271	−	0.540614i	$-0.818192\pi$
$677$	−7.82287	+	7.82287i	−0.300657	+	0.300657i	0.540614	+	0.841271i	$0.318192\pi$
$678$	−4.06678	−	7.04387i	−0.156184	−	0.270518i
$679$	−10.2419	+	5.91316i	−0.393048	+	0.226926i
$680$	−2.80629	+	8.33612i	−0.107616	+	0.319676i
$681$	12.7828	−	12.7828i	0.489839	−	0.489839i
$682$	−10.6226	−	6.13294i	−0.406759	−	0.234842i
$683$	17.4901	+	10.0979i	0.669241	+	0.386387i	0.795789	−	0.605574i	$-0.207056\pi$
$683$	17.4901	+	10.0979i	0.669241	+	0.386387i	−0.126548	+	0.991961i	$0.540390\pi$
$684$	5.73600	−	5.73600i	0.219322	−	0.219322i
$685$	7.54299	−	3.74349i	0.288203	−	0.143031i
$686$	1.29181	−	0.745825i	0.0493214	−	0.0284757i
$687$	5.79363	+	10.0349i	0.221041	+	0.382854i
$688$	−2.67809	+	2.67809i	−0.102101	+	0.102101i
$689$	4.02802	−	2.70974i	0.153455	−	0.103233i
$690$	9.07323	−	13.6535i	0.345412	−	0.519780i
$691$	−11.7139	−	3.13872i	−0.445616	−	0.119402i	0.0290313	−	0.999579i	$-0.490758\pi$
$691$	−11.7139	−	3.13872i	−0.445616	−	0.119402i	−0.474647	+	0.880176i	$0.657424\pi$
$692$	20.6272	+	5.52705i	0.784129	+	0.210107i
$693$	−2.81155	−	10.4929i	−0.106802	−	0.398591i
$694$	−2.79502	−	2.79502i	−0.106097	−	0.106097i
$695$	−5.77179	−	11.6300i	−0.218937	−	0.441149i
$696$	−5.17428	+	1.38644i	−0.196130	+	0.0525530i
$697$	11.4120			0.432259
$698$	−6.30915	+	1.69053i	−0.238805	+	0.0639876i
$699$	14.2982	+	24.7652i	0.540808	+	0.936708i
$700$	−11.1492	+	14.6827i	−0.421399	+	0.554955i
$701$			12.7429i			0.481293i	0.970613	+	0.240647i	$0.0773595\pi$
$701$			12.7429i			0.481293i	−0.970613	+	0.240647i	$0.922641\pi$
$702$	3.23870	+	1.58455i	0.122237	+	0.0598051i
$703$	−12.9938	−	12.9938i	−0.490069	−	0.490069i
$704$	−0.762517	+	2.84575i	−0.0287384	+	0.107253i
$705$	20.7113	−	18.2560i	0.780031	−	0.687559i
$706$	23.7777	+	13.7281i	0.894885	+	0.516662i
$707$			29.0697i			1.09328i
$708$	−3.41280	+	5.91114i	−0.128261	+	0.222154i
$709$	2.41602	+	9.01670i	0.0907355	+	0.338629i	0.996338	−	0.0854972i	$-0.0272479\pi$
$709$	2.41602	+	9.01670i	0.0907355	+	0.338629i	−0.905603	+	0.424126i	$0.860581\pi$
$710$	1.05977	+	5.25843i	0.0397724	+	0.197345i
$711$	−5.40965	+	9.36978i	−0.202878	+	0.351394i
$712$	−2.56600	+	9.57642i	−0.0961647	+	0.358892i
$713$	−26.4338	+	15.2615i	−0.989952	+	0.571549i
$714$	14.5040			0.542798
$715$	−11.9925	−	20.5028i	−0.448492	−	0.766760i
$716$	−1.30390			−0.0487292
$717$	4.88038	−	2.81769i	0.182261	−	0.105228i
$718$	0.932207	−	3.47904i	0.0347897	−	0.129837i
$719$	18.9523	−	32.8264i	0.706802	−	1.22422i	−0.259235	−	0.965814i	$-0.583470\pi$
$719$	18.9523	−	32.8264i	0.706802	−	1.22422i	0.966037	−	0.258403i	$-0.0831962\pi$
$720$	1.23760	−	1.86235i	0.0461225	−	0.0694058i
$721$	3.09329	+	11.5443i	0.115200	+	0.429933i
$722$	−23.4017	+	40.5330i	−0.870923	+	1.50848i
$723$			12.2563i			0.455816i
$724$	12.6002	+	7.27474i	0.468283	+	0.270363i
$725$	−21.3312	−	16.1976i	−0.792221	−	0.601564i
$726$	−0.600530	+	2.24121i	−0.0222878	+	0.0831790i
$727$	8.59009	+	8.59009i	0.318589	+	0.318589i	0.848225	−	0.529636i	$-0.177672\pi$
$727$	8.59009	+	8.59009i	0.318589	+	0.318589i	−0.529636	+	0.848225i	$0.677672\pi$
$728$	8.73423	−	10.0227i	0.323712	−	0.371465i
$729$		−	1.00000i		−	0.0370370i
$730$	−1.21995	+	19.3614i	−0.0451524	+	0.716598i
$731$	7.44905	+	12.9021i	0.275513	+	0.477203i
$732$	−9.53211	+	2.55412i	−0.352317	+	0.0944031i
$733$	50.9118			1.88047			0.940235	−	0.340526i	$-0.110605\pi$
$733$	50.9118			1.88047			0.940235	+	0.340526i	$0.110605\pi$
$734$	−11.6185	+	3.11318i	−0.428848	+	0.114909i
$735$	13.9771	+	4.70529i	0.515554	+	0.173557i
$736$	5.18403	+	5.18403i	0.191086	+	0.191086i
$737$	−10.0175	−	37.3858i	−0.368999	−	1.37712i
$738$	−2.80230	−	0.750873i	−0.103154	−	0.0276400i
$739$	−37.0613	−	9.93055i	−1.36332	−	0.365301i	−0.498287	−	0.867012i	$-0.666037\pi$
$739$	−37.0613	−	9.93055i	−1.36332	−	0.365301i	−0.865035	+	0.501711i	$0.832704\pi$
$740$	−4.21878	−	2.80352i	−0.155085	−	0.103060i
$741$	−28.7037	−	5.61607i	−1.05446	−	0.206312i
$742$	−3.51049	+	3.51049i	−0.128874	+	0.128874i
$743$	−21.0845	−	36.5195i	−0.773517	−	1.33977i	−0.935624	−	0.352997i	$-0.885162\pi$
$743$	−21.0845	−	36.5195i	−0.773517	−	1.33977i	0.162107	−	0.986773i	$-0.448171\pi$
$744$	−3.60559	+	2.08169i	−0.132187	+	0.0763184i
$745$	−15.6730	−	5.27621i	−0.574216	−	0.193305i
$746$	21.6030	−	21.6030i	0.790941	−	0.790941i
$747$	9.06259	+	5.23229i	0.331583	+	0.191439i
$748$	10.0363	+	5.79447i	0.366964	+	0.211867i
$749$	46.2459	−	46.2459i	1.68979	−	1.68979i
$750$	11.1505	−	0.815673i	0.407160	−	0.0297841i
$751$	−22.8142	+	13.1718i	−0.832501	+	0.480645i	−0.854708	−	0.519109i	$-0.826264\pi$
$751$	−22.8142	+	13.1718i	−0.832501	+	0.480645i	0.0222070	+	0.999753i	$0.492931\pi$
$752$	6.17348	+	10.6928i	0.225124	+	0.389925i
$753$	−0.763218	+	0.763218i	−0.0278132	+	0.0278132i
$754$	14.5610	+	12.6892i	0.530282	+	0.462113i
$755$	−2.81349	−	13.9601i	−0.102393	−	0.508061i
$756$	−3.56156	−	0.954318i	−0.129533	−	0.0347082i
$757$	−4.60716	−	1.23449i	−0.167450	−	0.0448681i	0.174120	−	0.984724i	$-0.444292\pi$
$757$	−4.60716	−	1.23449i	−0.167450	−	0.0448681i	−0.341570	+	0.939856i	$0.610959\pi$
$758$	−6.78244	−	25.3124i	−0.246349	−	0.919389i
$759$	−15.2729	−	15.2729i	−0.554370	−	0.554370i
$760$	−5.78717	+	17.1909i	−0.209923	+	0.623578i
$761$	11.8899	−	3.18590i	0.431010	−	0.115489i	−0.0367903	−	0.999323i	$-0.511713\pi$
$761$	11.8899	−	3.18590i	0.431010	−	0.115489i	0.467800	+	0.883834i	$0.345047\pi$
$762$	−13.8193			−0.500621
$763$	−32.4991	+	8.70809i	−1.17654	+	0.315254i
$764$	−5.91683	−	10.2482i	−0.214063	−	0.370768i
$765$	−5.81615	−	6.59838i	−0.210283	−	0.238565i
$766$		−	20.8694i		−	0.754040i
$767$	24.5522	−	1.68653i	0.886527	−	0.0608970i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	13.6011	−	50.7601i	0.490470	−	1.83046i	−0.0635845	−	0.997976i	$-0.520253\pi$
$769$	13.6011	−	50.7601i	0.490470	−	1.83046i	0.554054	−	0.832481i	$-0.313080\pi$
$770$	16.0618	+	18.2220i	0.578828	+	0.656676i
$771$	4.50589	+	2.60147i	0.162276	+	0.0936898i
$772$			5.09170i			0.183254i
$773$	−4.03663	+	6.99165i	−0.145188	+	0.251472i	−0.929443	−	0.368966i	$-0.879712\pi$
$773$	−4.03663	+	6.99165i	−0.145188	+	0.251472i	0.784255	+	0.620438i	$0.213045\pi$
$774$	−0.980250	−	3.65834i	−0.0352344	−	0.131496i
$775$	−19.2723	−	7.86910i	−0.692280	−	0.282666i
$776$	−1.60370	+	2.77769i	−0.0575694	+	0.0997132i
$777$	−2.16181	+	8.06800i	−0.0775546	+	0.289438i
$778$	−16.6034	+	9.58595i	−0.595259	+	0.343673i
$779$	23.5340			0.843191
$780$	−8.06213	+	0.0456133i	−0.288671	+	0.00163322i
$781$	7.06756			0.252897
$782$	24.9749	−	14.4193i	0.893100	−	0.515632i
$783$	1.38644	−	5.17428i	0.0495474	−	0.184914i
$784$	−3.29773	+	5.71183i	−0.117776	+	0.203994i
$785$	5.67115	−	1.14295i	0.202412	−	0.0407936i
$786$	−2.65881	−	9.92281i	−0.0948366	−	0.353935i
$787$	26.1222	−	45.2450i	0.931157	−	1.61281i	0.149810	−	0.988715i	$-0.452134\pi$
$787$	26.1222	−	45.2450i	0.931157	−	1.61281i	0.781347	−	0.624096i	$-0.214533\pi$
$788$		−	3.51883i		−	0.125353i
$789$	9.06162	+	5.23173i	0.322602	+	0.186255i
$790$	1.52135	−	24.1448i	0.0541271	−	0.859033i
$791$	7.76200	−	28.9682i	0.275985	−	1.02999i
$792$	−2.08323	−	2.08323i	−0.0740245	−	0.0740245i
$793$	26.8245	+	23.3762i	0.952567	+	0.830112i
$794$		−	9.97998i		−	0.354176i
$795$	3.00477	+	0.189329i	0.106568	+	0.00671479i
$796$	6.19744	+	10.7343i	0.219662	+	0.380467i
$797$	−41.4597	+	11.1091i	−1.46858	+	0.393504i	−0.902443	−	0.430809i	$-0.858228\pi$
$797$	−41.4597	+	11.1091i	−1.46858	+	0.393504i	−0.566135	+	0.824313i	$0.691562\pi$
$798$	29.9103			1.05881
$799$	46.9131	−	12.5703i	1.65967	−	0.444706i
$800$	−0.627602	+	4.96046i	−0.0221891	+	0.175379i
$801$	−7.01043	−	7.01043i	−0.247701	−	0.247701i
$802$	2.77303	+	10.3491i	0.0979191	+	0.365439i
$803$	24.6893	+	6.61549i	0.871267	+	0.233455i
$804$	−12.6898	−	3.40021i	−0.447534	−	0.119916i
$805$	59.2542	−	11.9419i	2.08843	−	0.420897i
$806$	13.4839	+	6.59709i	0.474951	+	0.232372i
$807$	9.47665	−	9.47665i	0.333594	−	0.333594i
$808$	3.94198	+	6.82771i	0.138678	+	0.240198i
$809$	2.44761	−	1.41313i	0.0860534	−	0.0496829i	−0.456356	−	0.889797i	$-0.650846\pi$
$809$	2.44761	−	1.41313i	0.0860534	−	0.0496829i	0.542409	+	0.840114i	$0.317512\pi$
$810$	0.994046	+	2.00297i	0.0349272	+	0.0703771i
$811$	9.76865	−	9.76865i	0.343024	−	0.343024i	−0.514479	−	0.857503i	$-0.672015\pi$
$811$	9.76865	−	9.76865i	0.343024	−	0.343024i	0.857503	+	0.514479i	$0.172015\pi$
$812$	−17.1054	−	9.87581i	−0.600282	−	0.346573i
$813$	4.38152	+	2.52967i	0.153667	+	0.0887195i
$814$	−4.71914	+	4.71914i	−0.165406	+	0.165406i
$815$	17.0061	+	34.2666i	0.595696	+	1.20031i
$816$	3.40660	−	1.96680i	0.119255	−	0.0688518i
$817$	15.3615	+	26.6070i	0.537433	+	0.930860i
$818$	4.22897	−	4.22897i	0.147862	−	0.147862i
$819$	4.31277	+	12.5754i	0.150701	+	0.439420i
$820$	6.35931	−	1.28164i	0.222077	−	0.0447567i
$821$	−53.0802	−	14.2228i	−1.85251	−	0.496379i	−0.852844	−	0.522165i	$-0.825125\pi$
$821$	−53.0802	−	14.2228i	−1.85251	−	0.496379i	−0.999667	+	0.0257859i	$0.991791\pi$
$822$	−3.63759	−	0.974690i	−0.126876	−	0.0339962i
$823$	−1.43367	−	5.35052i	−0.0499745	−	0.186507i	0.936427	−	0.350864i	$-0.114112\pi$
$823$	−1.43367	−	5.35052i	−0.0499745	−	0.186507i	−0.986401	+	0.164356i	$0.947445\pi$
$824$	2.29199	+	2.29199i	0.0798453	+	0.0798453i
$825$	1.84900	−	14.6142i	0.0643740	−	0.508801i
$826$	−24.3098	+	6.51379i	−0.845845	+	0.226644i
$827$	31.8131			1.10625			0.553126	−	0.833098i	$-0.313435\pi$
$827$	31.8131			1.10625			0.553126	+	0.833098i	$0.313435\pi$
$828$	−7.08152	+	1.89749i	−0.246100	+	0.0659422i
$829$	5.52347	+	9.56694i	0.191838	+	0.332274i	0.945859	−	0.324577i	$-0.105222\pi$
$829$	5.52347	+	9.56694i	0.191838	+	0.332274i	−0.754021	+	0.656850i	$0.771888\pi$
$830$	−23.3532	−	1.47147i	−0.810601	−	0.0510755i
$831$		−	5.74753i		−	0.199380i
$832$	0.692322	−	3.53846i	0.0240019	−	0.122674i
$833$	18.3451	+	18.3451i	0.635620	+	0.635620i
$834$	−1.50280	+	5.60852i	−0.0520376	+	0.194207i
$835$	−0.322722	+	5.12182i	−0.0111683	+	0.177248i
$836$	20.6970	+	11.9494i	0.715822	+	0.413280i
$837$		−	4.16338i		−	0.143907i
$838$	2.86371	−	4.96010i	0.0989253	−	0.171344i
$839$	7.14130	+	26.6517i	0.246545	+	0.920118i	0.972601	+	0.232482i	$0.0746847\pi$
$839$	7.14130	+	26.6517i	0.246545	+	0.920118i	−0.726056	+	0.687636i	$0.758649\pi$
$840$	8.08233	−	1.62889i	0.278867	−	0.0562020i
$841$	−0.152327	+	0.263838i	−0.00525266	+	0.00909787i
$842$	−9.02397	+	33.6779i	−0.310986	+	1.16062i
$843$	22.0158	−	12.7108i	0.758264	−	0.437784i
$844$	−26.8316			−0.923583
$845$	16.3617	+	24.0270i	0.562859	+	0.826553i
$846$	−12.3470			−0.424497
$847$	−7.40911	+	4.27765i	−0.254580	+	0.146982i
$848$	−0.348484	+	1.30056i	−0.0119670	+	0.0446614i
$849$	4.58770	−	7.94612i	0.157449	−	0.272710i
$850$	18.2086	+	7.43481i	0.624551	+	0.255012i
$851$	4.29837	+	16.0417i	0.147346	+	0.549904i
$852$	1.19946	−	2.07753i	0.0410929	−	0.0711750i
$853$			4.04387i			0.138460i	0.997601	+	0.0692298i	$0.0220542\pi$
$853$			4.04387i			0.138460i	−0.997601	+	0.0692298i	$0.977946\pi$
$854$	−31.5118	−	18.1933i	−1.07831	−	0.622563i
$855$	−11.9941	−	13.6073i	−0.410191	−	0.465359i
$856$	4.59079	−	17.1331i	0.156910	−	0.585597i
$857$	−6.00540	−	6.00540i	−0.205141	−	0.205141i	0.597058	−	0.802198i	$-0.296336\pi$
$857$	−6.00540	−	6.00540i	−0.205141	−	0.205141i	−0.802198	+	0.597058i	$0.796336\pi$
$858$	−2.03968	+	10.4248i	−0.0696334	+	0.355896i
$859$		−	14.6934i		−	0.501332i	−0.968074	−	0.250666i	$-0.919350\pi$
$859$		−	14.6934i		−	0.501332i	0.968074	−	0.250666i	$-0.0806496\pi$
$860$	5.59997	+	6.35312i	0.190957	+	0.216640i
$861$	−5.34857	−	9.26399i	−0.182279	−	0.315716i
$862$	−4.72288	+	1.26549i	−0.160862	+	0.0431028i
$863$	−37.9938			−1.29332			−0.646662	−	0.762777i	$-0.723836\pi$
$863$	−37.9938			−1.29332			−0.646662	+	0.762777i	$0.723836\pi$
$864$	−0.965926	+	0.258819i	−0.0328615	+	0.00880520i
$865$	15.2349	−	45.2554i	0.518001	−	1.53873i
$866$	−2.90093	−	2.90093i	−0.0985774	−	0.0985774i
$867$	0.395158	+	1.47475i	0.0134203	+	0.0500852i
$868$	−14.8281	−	3.97318i	−0.503299	−	0.134859i
$869$	−30.7890	−	8.24989i	−1.04445	−	0.279858i
$870$	2.36647	+	11.7421i	0.0802307	+	0.398094i
$871$	15.3663	+	44.8059i	0.520668	+	1.51819i
$872$	−6.45231	+	6.45231i	−0.218503	+	0.218503i
$873$	−1.60370	−	2.77769i	−0.0542770	−	0.0940105i
$874$	51.5036	−	29.7356i	1.74214	−	1.00582i
$875$	31.1989	+	26.9455i	1.05471	+	0.910926i
$876$	6.13476	−	6.13476i	0.207274	−	0.207274i
$877$	−46.2858	−	26.7231i	−1.56296	−	0.902375i	−0.996956	−	0.0779723i	$-0.975155\pi$
$877$	−46.2858	−	26.7231i	−1.56296	−	0.902375i	−0.566004	−	0.824403i	$-0.691511\pi$
$878$	−0.770002	−	0.444561i	−0.0259863	−	0.0150032i
$879$	−7.87710	+	7.87710i	−0.265688	+	0.265688i
$880$	6.24348	+	2.10182i	0.210468	+	0.0708523i
$881$	−22.6466	+	13.0750i	−0.762982	+	0.440508i	−0.830365	−	0.557219i	$-0.811868\pi$
$881$	−22.6466	+	13.0750i	−0.762982	+	0.440508i	0.0673832	+	0.997727i	$0.478535\pi$
$882$	−3.29773	−	5.71183i	−0.111040	−	0.192327i
$883$	−2.17489	+	2.17489i	−0.0731907	+	0.0731907i	−0.742755	−	0.669564i	$-0.766481\pi$
$883$	−2.17489	+	2.17489i	−0.0731907	+	0.0731907i	0.669564	+	0.742755i	$0.266481\pi$
$884$	−12.7398	−	6.23300i	−0.428485	−	0.209638i
$885$	12.7117	+	8.44733i	0.427298	+	0.283954i
$886$	−3.32909	−	0.892027i	−0.111843	−	0.0299682i
$887$	35.0618	+	9.39478i	1.17726	+	0.315446i	0.793839	−	0.608128i	$-0.208079\pi$
$887$	35.0618	+	9.39478i	1.17726	+	0.315446i	0.383421	+	0.923574i	$0.374746\pi$
$888$	0.586302	+	2.18811i	0.0196750	+	0.0734281i
$889$	−36.0303	−	36.0303i	−1.20842	−	1.20842i
$890$	21.0103	+	7.07297i	0.704268	+	0.237086i
$891$	2.84575	−	0.762517i	0.0953362	−	0.0255453i
$892$	−25.1190			−0.841046
$893$	96.7449	−	25.9227i	3.23744	−	0.867471i
$894$	3.69786	+	6.40487i	0.123675	+	0.214211i
$895$	−0.183348	+	2.90985i	−0.00612863	+	0.0972654i
$896$			3.68720i			0.123181i
$897$	19.9283	+	17.3664i	0.665385	+	0.579848i
$898$	8.72302	+	8.72302i	0.291091	+	0.291091i
$899$	5.77228	−	21.5425i	0.192516	−	0.718481i
$900$	−3.98208	−	3.02375i	−0.132736	−	0.100792i
$901$	4.58677	+	2.64818i	0.152808	+	0.0882235i
$902$		−	8.54719i		−	0.284590i
$903$	6.98244	−	12.0939i	0.232361	−	0.402461i
$904$	−2.10512	−	7.85641i	−0.0700152	−	0.261300i
$905$	18.0064	−	27.0962i	0.598552	−	0.900710i
$906$	−3.18434	+	5.51545i	−0.105793	+	0.183238i
$907$	1.92283	−	7.17611i	0.0638466	−	0.238279i	−0.926627	−	0.375982i	$-0.877305\pi$
$907$	1.92283	−	7.17611i	0.0638466	−	0.238279i	0.990474	+	0.137703i	$0.0439721\pi$
$908$	15.6557	−	9.03882i	0.519552	−	0.299964i
$909$	−7.88396			−0.261494
$910$	−21.1389	−	20.9010i	−0.700747	−	0.692862i
$911$	−41.1547			−1.36352			−0.681759	−	0.731577i	$-0.738785\pi$
$911$	−41.1547			−1.36352			−0.681759	+	0.731577i	$0.738785\pi$
$912$	7.02514	−	4.05597i	0.232626	−	0.134306i
$913$	−7.97942	+	29.7796i	−0.264080	+	0.985560i
$914$	−9.04457	+	15.6657i	−0.299168	+	0.518174i
$915$	4.35953	+	21.6314i	0.144122	+	0.715112i
$916$	2.99901	+	11.1924i	0.0990899	+	0.369809i
$917$	18.9390	−	32.8034i	0.625422	−	1.08326i
$918$			3.93360i			0.129828i
$919$	2.96561	+	1.71220i	0.0978264	+	0.0564801i	0.548115	−	0.836403i	$-0.315346\pi$
$919$	2.96561	+	1.71220i	0.0978264	+	0.0564801i	−0.450289	+	0.892883i	$0.648679\pi$
$920$	12.2979	−	10.8400i	0.405448	−	0.357383i
$921$	8.24450	−	30.7689i	0.271665	−	1.01387i
$922$	−11.9116	−	11.9116i	−0.392288	−	0.392288i
$923$	−8.62911	+	0.592747i	−0.284031	+	0.0195105i
$924$		−	10.8630i		−	0.357367i
$925$	−6.84969	+	9.02059i	−0.225216	+	0.296595i
$926$	−4.07481	−	7.05778i	−0.133907	−	0.231933i
$927$	−3.13092	+	0.838927i	−0.102833	+	0.0275540i
$928$	−5.35680			−0.175846
$929$	−24.8807	+	6.66677i	−0.816310	+	0.218730i	−0.642733	−	0.766091i	$-0.722199\pi$
$929$	−24.8807	+	6.66677i	−0.816310	+	0.218730i	−0.173578	+	0.984820i	$0.555533\pi$
$930$	4.13859	+	8.33910i	0.135710	+	0.273450i
$931$	37.8315	+	37.8315i	1.23988	+	1.23988i
$932$	7.40130	+	27.6220i	0.242438	+	0.904790i
$933$	−9.36392	−	2.50905i	−0.306561	−	0.0821427i
$934$	19.0969	+	5.11700i	0.624869	+	0.167433i
$935$	14.3424	−	21.5827i	0.469048	−	0.705829i
$936$	2.71823	+	2.36880i	0.0888483	+	0.0774266i
$937$	−21.9487	+	21.9487i	−0.717031	+	0.717031i	−0.967996	−	0.250965i	$-0.919252\pi$
$937$	−21.9487	+	21.9487i	−0.717031	+	0.717031i	0.250965	+	0.967996i	$0.419252\pi$
$938$	−24.2202	−	41.9505i	−0.790816	−	1.36973i
$939$	14.8328	−	8.56371i	0.484050	−	0.279466i
$940$	24.7305	−	12.2734i	0.806621	−	0.400315i
$941$	−11.5453	+	11.5453i	−0.376366	+	0.376366i	−0.869789	−	0.493423i	$-0.835745\pi$
$941$	−11.5453	+	11.5453i	−0.376366	+	0.376366i	0.493423	+	0.869789i	$0.335745\pi$
$942$	−2.24059	−	1.29361i	−0.0730024	−	0.0421480i
$943$	−18.4197	−	10.6346i	−0.599829	−	0.346312i
$944$	−4.82642	+	4.82642i	−0.157087	+	0.157087i
$945$	−2.63050	+	7.81394i	−0.0855703	+	0.254188i
$946$	9.66327	−	5.57909i	0.314180	−	0.181392i
$947$	−0.413175	−	0.715640i	−0.0134264	−	0.0232552i	0.859234	−	0.511583i	$-0.170941\pi$
$947$	−0.413175	−	0.715640i	−0.0134264	−	0.0232552i	−0.872661	+	0.488327i	$0.837607\pi$
$948$	−7.65040	+	7.65040i	−0.248473	+	0.248473i
$949$	−30.6992	−	6.00649i	−0.996537	−	0.194979i
$950$	37.5501	+	15.3322i	1.21829	+	0.497442i
$951$	−0.331024	−	0.0886977i	−0.0107342	−	0.00287622i
$952$	14.0098	+	3.75391i	0.454059	+	0.121665i
$953$	11.4991	+	42.9151i	0.372492	+	1.39016i	0.856975	+	0.515357i	$0.172341\pi$
$953$	11.4991	+	42.9151i	0.372492	+	1.39016i	−0.484484	+	0.874800i	$0.660993\pi$
$954$	−0.952075	−	0.952075i	−0.0308246	−	0.0308246i
$955$	−23.7024	+	11.7632i	−0.766992	+	0.380648i
$956$	5.44335	−	1.45854i	0.176051	−	0.0471726i
$957$	15.7819			0.510156
$958$	2.72948	−	0.731362i	0.0881855	−	0.0236292i
$959$	−6.94284	−	12.0253i	−0.224196	−	0.388319i
$960$	1.67744	−	1.47858i	0.0541391	−	0.0477210i
$961$			13.6663i			0.440848i
$962$	5.36603	−	6.15761i	0.173008	−	0.198529i
$963$	12.5423	+	12.5423i	0.404169	+	0.404169i
$964$	−3.17216	+	11.8387i	−0.102168	+	0.381298i
$965$	11.3629	+	0.715966i	0.365783	+	0.0230478i
$966$	−23.4105	−	13.5160i	−0.753219	−	0.434871i
$967$			16.8946i			0.543295i	0.962397	+	0.271647i	$0.0875684\pi$
$967$			16.8946i			0.543295i	−0.962397	+	0.271647i	$0.912432\pi$
$968$	−1.16013	+	2.00941i	−0.0372881	+	0.0645850i
$969$	−8.25869	−	30.8218i	−0.265307	−	0.990140i
$970$	5.97330	+	3.96947i	0.191791	+	0.127452i
$971$	−27.0453	+	46.8439i	−0.867925	+	1.50329i	−0.00381254	+	0.999993i	$0.501214\pi$
$971$	−27.0453	+	46.8439i	−0.867925	+	1.50329i	−0.864113	+	0.503298i	$0.832120\pi$
$972$	0.258819	−	0.965926i	0.00830162	−	0.0309821i
$973$	−18.5409	+	10.7046i	−0.594395	+	0.343174i
$974$	12.2427			0.392282
$975$	−1.03186	+	17.9982i	−0.0330459	+	0.576404i
$976$	−9.86837			−0.315879
$977$	12.9424	−	7.47231i	0.414065	−	0.239060i	−0.278470	−	0.960445i	$-0.589827\pi$
$977$	12.9424	−	7.47231i	0.414065	−	0.239060i	0.692535	+	0.721385i	$0.256494\pi$
$978$	4.42786	−	16.5250i	0.141587	−	0.528411i
$979$	14.6044	−	25.2955i	0.466758	−	0.808448i
$980$	12.2831	+	8.16251i	0.392368	+	0.260742i
$981$	−2.36171	−	8.81402i	−0.0754036	−	0.281410i
$982$	17.0024	−	29.4491i	0.542570	−	0.939758i
$983$		−	26.7656i		−	0.853689i	−0.904325	−	0.426844i	$-0.859625\pi$
$983$		−	26.7656i		−	0.853689i	0.904325	−	0.426844i	$-0.140375\pi$
$984$	−2.51247	−	1.45058i	−0.0800947	−	0.0462427i
$985$	−7.85277	−	0.494798i	−0.250210	−	0.0157656i
$986$	−5.45371	+	20.3535i	−0.173682	+	0.648189i
$987$	−32.1915	−	32.1915i	−1.02467	−	1.02467i
$988$	−26.2721	−	12.8538i	−0.835828	−	0.408933i
$989$		−	27.7666i		−	0.882927i
$990$	−4.94197	+	4.35610i	−0.157066	+	0.138446i
$991$	19.9714	+	34.5915i	0.634412	+	1.09883i	0.986639	+	0.162920i	$0.0520911\pi$
$991$	19.9714	+	34.5915i	0.634412	+	1.09883i	−0.352227	+	0.935915i	$0.614576\pi$
$992$	−4.02151	+	1.07756i	−0.127683	+	0.0342126i
$993$	26.9672			0.855778
$994$	8.54392	−	2.28934i	0.270997	−	0.0726133i
$995$	24.8265	−	12.3211i	0.787054	−	0.390604i
$996$	7.39957	+	7.39957i	0.234464	+	0.234464i
$997$	−14.9852	−	55.9256i	−0.474586	−	1.77118i	−0.622965	−	0.782250i	$-0.714072\pi$
$997$	−14.9852	−	55.9256i	−0.474586	−	1.77118i	0.148378	−	0.988931i	$-0.452595\pi$
$998$	18.4435	+	4.94192i	0.583819	+	0.156434i
$999$	−2.18811	−	0.586302i	−0.0692287	−	0.0185498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bd.c.223.5	yes	32
5.2	odd	4		390.2.bn.c.67.4	yes	32
13.7	odd	12		390.2.bn.c.163.4	yes	32
65.7	even	12	inner	390.2.bd.c.7.5	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.c.7.5	✓	32	65.7	even	12	inner
390.2.bd.c.223.5	yes	32	1.1	even	1	trivial
390.2.bn.c.67.4	yes	32	5.2	odd	4
390.2.bn.c.163.4	yes	32	13.7	odd	12

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.86235 - 1.23760i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-1.84360 + 3.19321i) q^{7} +1.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.86235 - 1.23760i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-1.84360 + 3.19321i) q^{7} +1.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +(2.23164 + 0.140614i) q^{10} +(0.762517 - 2.84575i) q^{11} +(-0.707107 - 0.707107i) q^{12} +(-0.692322 + 3.53846i) q^{13} -3.68720i q^{14} +(-1.67744 + 1.47858i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.79957 + 1.01809i) q^{17} +1.00000 q^{18} +(-7.83553 + 2.09952i) q^{19} +(-2.00297 + 0.994046i) q^{20} +(2.60724 + 2.60724i) q^{21} +(0.762517 + 2.84575i) q^{22} +(7.08152 + 1.89749i) q^{23} +(0.965926 + 0.258819i) q^{24} +(1.93671 + 4.60968i) q^{25} +(-1.16966 - 3.41056i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.84360 + 3.19321i) q^{28} +(-4.63913 + 2.67840i) q^{29} +(0.713415 - 2.11921i) q^{30} +(-2.94395 + 2.94395i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.55143 - 1.47307i) q^{33} +(2.78148 - 2.78148i) q^{34} +(7.38534 - 3.66525i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(1.13265 + 1.96180i) q^{37} +(5.73600 - 5.73600i) q^{38} +(3.23870 + 1.58455i) q^{39} +(1.23760 - 1.86235i) q^{40} +(-2.80230 - 0.750873i) q^{41} +(-3.56156 - 0.954318i) q^{42} +(-0.980250 - 3.65834i) q^{43} +(-2.08323 - 2.08323i) q^{44} +(0.994046 + 2.00297i) q^{45} +(-7.08152 + 1.89749i) q^{46} -12.3470 q^{47} +(-0.965926 + 0.258819i) q^{48} +(-3.29773 - 5.71183i) q^{49} +(-3.98208 - 3.02375i) q^{50} +3.93360i q^{51} +(2.71823 + 2.36880i) q^{52} +(-0.952075 - 0.952075i) q^{53} +(0.258819 - 0.965926i) q^{54} +(-4.94197 + 4.35610i) q^{55} +(-3.19321 - 1.84360i) q^{56} +8.11193i q^{57} +(2.67840 - 4.63913i) q^{58} +(-1.76659 - 6.59302i) q^{59} +(0.441768 + 2.19199i) q^{60} +(4.93418 - 8.54626i) q^{61} +(1.07756 - 4.02151i) q^{62} +(3.19321 - 1.84360i) q^{63} -1.00000 q^{64} +(5.66853 - 5.73304i) q^{65} +2.94614 q^{66} +(11.3773 - 6.56871i) q^{67} +(-1.01809 + 3.79957i) q^{68} +(3.66566 - 6.34911i) q^{69} +(-4.56327 + 6.86687i) q^{70} +(0.620887 + 2.31718i) q^{71} +(0.500000 - 0.866025i) q^{72} +8.67586i q^{73} +(-1.96180 - 1.13265i) q^{74} +(4.95387 - 0.677643i) q^{75} +(-2.09952 + 7.83553i) q^{76} +(7.68130 + 7.68130i) q^{77} +(-3.59707 + 0.247089i) q^{78} -10.8193i q^{79} +(-0.140614 + 2.23164i) q^{80} +(0.500000 + 0.866025i) q^{81} +(2.80230 - 0.750873i) q^{82} -10.4646 q^{83} +(3.56156 - 0.954318i) q^{84} +(8.33612 + 2.80629i) q^{85} +(2.67809 + 2.67809i) q^{86} +(1.38644 + 5.17428i) q^{87} +(2.84575 + 0.762517i) q^{88} +(9.57642 + 2.56600i) q^{89} +(-1.86235 - 1.23760i) q^{90} +(-10.0227 - 8.73423i) q^{91} +(5.18403 - 5.18403i) q^{92} +(2.08169 + 3.60559i) q^{93} +(10.6928 - 6.17348i) q^{94} +(17.1909 + 5.78717i) q^{95} +(0.707107 - 0.707107i) q^{96} +(2.77769 + 1.60370i) q^{97} +(5.71183 + 3.29773i) q^{98} +(-2.08323 + 2.08323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4}+O(q^{10}) \) 32 * q + 16 * q^4	\( 32 q + 16 q^{4} - 4 q^{11} + 20 q^{13} + 4 q^{15} - 16 q^{16} - 20 q^{17} + 32 q^{18} - 20 q^{19} + 8 q^{21} - 4 q^{22} + 4 q^{23} + 8 q^{25} - 4 q^{26} - 24 q^{29} + 4 q^{30} + 12 q^{31} - 12 q^{33} + 16 q^{34} + 12 q^{35} + 20 q^{37} + 4 q^{38} + 20 q^{39} - 28 q^{41} + 8 q^{42} - 4 q^{43} + 4 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} + 28 q^{50} + 16 q^{52} - 4 q^{53} - 40 q^{55} - 12 q^{56} - 36 q^{59} - 4 q^{60} - 28 q^{61} - 36 q^{62} + 12 q^{63} - 32 q^{64} - 32 q^{65} - 36 q^{67} - 4 q^{68} + 20 q^{69} - 24 q^{70} - 4 q^{71} + 16 q^{72} - 24 q^{74} - 16 q^{76} - 20 q^{77} - 16 q^{78} + 16 q^{81} + 28 q^{82} - 40 q^{83} - 8 q^{84} + 88 q^{85} - 8 q^{86} - 16 q^{87} - 8 q^{88} + 16 q^{89} - 40 q^{91} + 20 q^{92} + 24 q^{94} - 8 q^{95} + 72 q^{97} + 72 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q + 16 * q^4 - 4 * q^11 + 20 * q^13 + 4 * q^15 - 16 * q^16 - 20 * q^17 + 32 * q^18 - 20 * q^19 + 8 * q^21 - 4 * q^22 + 4 * q^23 + 8 * q^25 - 4 * q^26 - 24 * q^29 + 4 * q^30 + 12 * q^31 - 12 * q^33 + 16 * q^34 + 12 * q^35 + 20 * q^37 + 4 * q^38 + 20 * q^39 - 28 * q^41 + 8 * q^42 - 4 * q^43 + 4 * q^44 - 4 * q^46 - 16 * q^47 - 20 * q^49 + 28 * q^50 + 16 * q^52 - 4 * q^53 - 40 * q^55 - 12 * q^56 - 36 * q^59 - 4 * q^60 - 28 * q^61 - 36 * q^62 + 12 * q^63 - 32 * q^64 - 32 * q^65 - 36 * q^67 - 4 * q^68 + 20 * q^69 - 24 * q^70 - 4 * q^71 + 16 * q^72 - 24 * q^74 - 16 * q^76 - 20 * q^77 - 16 * q^78 + 16 * q^81 + 28 * q^82 - 40 * q^83 - 8 * q^84 + 88 * q^85 - 8 * q^86 - 16 * q^87 - 8 * q^88 + 16 * q^89 - 40 * q^91 + 20 * q^92 + 24 * q^94 - 8 * q^95 + 72 * q^97 + 72 * q^98 + 4 * q^99

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