LMFDB - Embedded newform 390.2.bn.c.67.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(67,390)]

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, 1]))

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

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

chi := DirichletCharacter("390.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bn (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			67.4
Character	$\chi$	$=$	390.67
Dual form			390.2.bn.c.163.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.23760 + 1.86235i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-3.19321 - 1.84360i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.23760 + 1.86235i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-3.19321 - 1.84360i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +(0.994046 - 2.00297i) q^{10} +(0.762517 - 2.84575i) q^{11} +(0.707107 - 0.707107i) q^{12} +(3.53846 + 0.692322i) q^{13} +3.68720i q^{14} +(-0.713415 - 2.11921i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.01809 - 3.79957i) q^{17} -1.00000i q^{18} +(7.83553 - 2.09952i) q^{19} +(-2.23164 + 0.140614i) q^{20} +(2.60724 + 2.60724i) q^{21} +(-2.84575 + 0.762517i) q^{22} +(1.89749 - 7.08152i) 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} +(3.19321 - 1.84360i) q^{28} +(4.63913 - 2.67840i) q^{29} +(-1.47858 + 1.67744i) q^{30} +(-2.94395 + 2.94395i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.47307 + 2.55143i) q^{33} +(-2.78148 + 2.78148i) q^{34} +(-0.518473 - 8.22851i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-1.96180 + 1.13265i) 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} +(0.954318 - 3.56156i) q^{42} +(-3.65834 + 0.980250i) q^{43} +(2.08323 + 2.08323i) q^{44} +(0.140614 + 2.23164i) q^{45} +(-7.08152 + 1.89749i) q^{46} -12.3470i q^{47} +(0.258819 + 0.965926i) q^{48} +(3.29773 + 5.71183i) q^{49} +(4.96046 - 0.627602i) q^{50} +3.93360i q^{51} +(-2.36880 + 2.71823i) q^{52} +(-0.952075 + 0.952075i) q^{53} +(-0.258819 + 0.965926i) q^{54} +(6.24348 - 2.10182i) q^{55} +(-3.19321 - 1.84360i) q^{56} -8.11193 q^{57} +(-4.63913 - 2.67840i) q^{58} +(1.76659 + 6.59302i) q^{59} +(2.19199 + 0.441768i) q^{60} +(4.93418 - 8.54626i) q^{61} +(4.02151 + 1.07756i) q^{62} +(-1.84360 - 3.19321i) q^{63} +1.00000 q^{64} +(3.08984 + 7.44667i) q^{65} +2.94614 q^{66} +(6.56871 + 11.3773i) q^{67} +(3.79957 + 1.01809i) q^{68} +(-3.66566 + 6.34911i) q^{69} +(-6.86687 + 4.56327i) q^{70} +(0.620887 + 2.31718i) q^{71} +(0.866025 + 0.500000i) q^{72} +8.67586 q^{73} +(1.96180 + 1.13265i) q^{74} +(3.06379 - 3.95135i) q^{75} +(-2.09952 + 7.83553i) q^{76} +(-7.68130 + 7.68130i) q^{77} +(0.247089 + 3.59707i) q^{78} +10.8193i q^{79} +(0.994046 - 2.00297i) q^{80} +(0.500000 + 0.866025i) q^{81} +(0.750873 + 2.80230i) q^{82} +10.4646i q^{83} +(-3.56156 + 0.954318i) q^{84} +(5.81615 - 6.59838i) q^{85} +(2.67809 + 2.67809i) q^{86} +(-5.17428 + 1.38644i) q^{87} +(0.762517 - 2.84575i) 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} +(3.60559 - 2.08169i) q^{93} +(-10.6928 + 6.17348i) q^{94} +(13.6073 + 11.9941i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-1.60370 + 2.77769i) q^{97} +(3.29773 - 5.71183i) q^{98} +(2.08323 - 2.08323i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8	$ 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8} - 4 q^{11} + 8 q^{13} - 4 q^{15} - 16 q^{16} - 4 q^{17} + 20 q^{19} + 8 q^{21} + 8 q^{22} - 16 q^{23} - 8 q^{25} - 4 q^{26} + 12 q^{28} + 24 q^{29} + 8 q^{30} + 12 q^{31} - 16 q^{32} - 16 q^{34} + 12 q^{35} - 24 q^{37} - 4 q^{38} - 20 q^{39} - 28 q^{41} - 16 q^{42} + 4 q^{43} - 4 q^{44} - 4 q^{46} + 20 q^{49} - 8 q^{50} - 4 q^{52} - 4 q^{53} + 68 q^{55} - 12 q^{56} + 16 q^{57} - 24 q^{58} + 36 q^{59} - 4 q^{60} - 28 q^{61} - 48 q^{62} + 32 q^{64} - 28 q^{65} - 28 q^{67} + 20 q^{68} - 20 q^{69} - 24 q^{70} - 4 q^{71} - 48 q^{73} + 24 q^{74} + 24 q^{75} - 16 q^{76} + 20 q^{77} + 4 q^{78} + 16 q^{81} + 44 q^{82} + 8 q^{84} + 64 q^{85} - 8 q^{86} + 20 q^{87} - 4 q^{88} - 16 q^{89} - 40 q^{91} + 20 q^{92} - 24 q^{93} - 24 q^{94} + 68 q^{95} + 8 q^{97} + 20 q^{98} - 4 q^{99}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8 - 4 * q^11 + 8 * q^13 - 4 * q^15 - 16 * q^16 - 4 * q^17 + 20 * q^19 + 8 * q^21 + 8 * q^22 - 16 * q^23 - 8 * q^25 - 4 * q^26 + 12 * q^28 + 24 * q^29 + 8 * q^30 + 12 * q^31 - 16 * q^32 - 16 * q^34 + 12 * q^35 - 24 * q^37 - 4 * q^38 - 20 * q^39 - 28 * q^41 - 16 * q^42 + 4 * q^43 - 4 * q^44 - 4 * q^46 + 20 * q^49 - 8 * q^50 - 4 * q^52 - 4 * q^53 + 68 * q^55 - 12 * q^56 + 16 * q^57 - 24 * q^58 + 36 * q^59 - 4 * q^60 - 28 * q^61 - 48 * q^62 + 32 * q^64 - 28 * q^65 - 28 * q^67 + 20 * q^68 - 20 * q^69 - 24 * q^70 - 4 * q^71 - 48 * q^73 + 24 * q^74 + 24 * q^75 - 16 * q^76 + 20 * q^77 + 4 * q^78 + 16 * q^81 + 44 * q^82 + 8 * q^84 + 64 * q^85 - 8 * q^86 + 20 * q^87 - 4 * q^88 - 16 * q^89 - 40 * q^91 + 20 * q^92 - 24 * q^93 - 24 * q^94 + 68 * q^95 + 8 * q^97 + 20 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.23760	+	1.86235i	0.553470	+	0.832869i
$5$	1.23760	+	1.86235i	0.553470	+	0.832869i
$6$	0.258819	+	0.965926i	0.105662	+	0.394338i
$7$	−3.19321	−	1.84360i	−1.20692	−	0.696816i	−0.244835	−	0.969565i	$-0.578734\pi$
$7$	−3.19321	−	1.84360i	−1.20692	−	0.696816i	−0.962085	+	0.272749i	$0.912067\pi$
$8$	1.00000			0.353553
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	0.994046	−	2.00297i	0.314345	−	0.633394i
$11$	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
$13$	3.53846	+	0.692322i	0.981392	+	0.192016i
$13$	3.53846	+	0.692322i	0.981392	+	0.192016i
$14$			3.68720i			0.985446i
$15$	−0.713415	−	2.11921i	−0.184203	−	0.547177i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.01809	−	3.79957i	−0.246923	−	0.921531i	−0.972407	−	0.233291i	$-0.925051\pi$
$17$	−1.01809	−	3.79957i	−0.246923	−	0.921531i	0.725484	−	0.688239i	$-0.241616\pi$
$18$		−	1.00000i		−	0.235702i
$19$	7.83553	−	2.09952i	1.79759	−	0.481664i	0.803995	−	0.594636i	$-0.202704\pi$
$19$	7.83553	−	2.09952i	1.79759	−	0.481664i	0.993598	+	0.112972i	$0.0360372\pi$
$20$	−2.23164	+	0.140614i	−0.499010	+	0.0314423i
$21$	2.60724	+	2.60724i	0.568947	+	0.568947i
$22$	−2.84575	+	0.762517i	−0.606716	+	0.162569i
$23$	1.89749	−	7.08152i	0.395653	−	1.47660i	−0.425011	−	0.905188i	$-0.639730\pi$
$23$	1.89749	−	7.08152i	0.395653	−	1.47660i	0.820665	−	0.571410i	$-0.193603\pi$
$24$	−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
$28$	3.19321	−	1.84360i	0.603460	−	0.348408i
$29$	4.63913	−	2.67840i	0.861464	−	0.497367i	−0.00303797	−	0.999995i	$-0.500967\pi$
$29$	4.63913	−	2.67840i	0.861464	−	0.497367i	0.864502	+	0.502629i	$0.167634\pi$
$30$	−1.47858	+	1.67744i	−0.269951	+	0.306257i
$31$	−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	$0.371974\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.47307	+	2.55143i	−0.256428	+	0.444147i
$34$	−2.78148	+	2.78148i	−0.477019	+	0.477019i
$35$	−0.518473	−	8.22851i	−0.0876380	−	1.39087i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	−1.96180	+	1.13265i	−0.322519	+	0.186206i	−0.652515	−	0.757776i	$-0.726286\pi$
$37$	−1.96180	+	1.13265i	−0.322519	+	0.186206i	0.329996	+	0.943982i	$0.392953\pi$
$38$	−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	$0.656075\pi$
$42$	0.954318	−	3.56156i	0.147254	−	0.549561i
$43$	−3.65834	+	0.980250i	−0.557892	+	0.149487i	−0.526738	−	0.850028i	$-0.676585\pi$
$43$	−3.65834	+	0.980250i	−0.557892	+	0.149487i	−0.0311543	+	0.999515i	$0.509918\pi$
$44$	2.08323	+	2.08323i	0.314059	+	0.314059i
$45$	0.140614	+	2.23164i	0.0209616	+	0.332674i
$46$	−7.08152	+	1.89749i	−1.04411	+	0.279769i
$47$		−	12.3470i		−	1.80099i	−0.434868	−	0.900494i	$-0.643205\pi$
$47$		−	12.3470i		−	1.80099i	0.434868	−	0.900494i	$-0.356795\pi$
$48$	0.258819	+	0.965926i	0.0373573	+	0.139419i
$49$	3.29773	+	5.71183i	0.471104	+	0.815976i
$50$	4.96046	−	0.627602i	0.701514	−	0.0887563i
$51$			3.93360i			0.550814i
$52$	−2.36880	+	2.71823i	−0.328493	+	0.376951i
$53$	−0.952075	+	0.952075i	−0.130778	+	0.130778i	−0.769466	−	0.638688i	$-0.779477\pi$
$53$	−0.952075	+	0.952075i	−0.130778	+	0.130778i	0.638688	+	0.769466i	$0.279477\pi$
$54$	−0.258819	+	0.965926i	−0.0352208	+	0.131446i
$55$	6.24348	−	2.10182i	0.841870	−	0.283409i
$56$	−3.19321	−	1.84360i	−0.426711	−	0.246361i
$57$	−8.11193			−1.07445
$58$	−4.63913	−	2.67840i	−0.609147	−	0.351691i
$59$	1.76659	+	6.59302i	0.229991	+	0.858338i	0.980343	+	0.197300i	$0.0632172\pi$
$59$	1.76659	+	6.59302i	0.229991	+	0.858338i	−0.750352	+	0.661038i	$0.770116\pi$
$60$	2.19199	+	0.441768i	0.282985	+	0.0570321i
$61$	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	$-0.0509995\pi$
$62$	4.02151	+	1.07756i	0.510733	+	0.136850i
$63$	−1.84360	−	3.19321i	−0.232272	−	0.402307i
$64$	1.00000			0.125000
$65$	3.08984	+	7.44667i	0.383247	+	0.923646i
$66$	2.94614			0.362645
$67$	6.56871	+	11.3773i	0.802496	+	1.38996i	0.917969	+	0.396653i	$0.129828\pi$
$67$	6.56871	+	11.3773i	0.802496	+	1.38996i	−0.115473	+	0.993311i	$0.536838\pi$
$68$	3.79957	+	1.01809i	0.460765	+	0.123462i
$69$	−3.66566	+	6.34911i	−0.441294	+	0.764344i
$70$	−6.86687	+	4.56327i	−0.820747	+	0.545415i
$71$	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	$0.871201\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	8.67586			1.01543			0.507716	−	0.861524i	$-0.330490\pi$
$73$	8.67586			1.01543			0.507716	+	0.861524i	$0.330490\pi$
$74$	1.96180	+	1.13265i	0.228055	+	0.131668i
$75$	3.06379	−	3.95135i	0.353776	−	0.456263i
$76$	−2.09952	+	7.83553i	−0.240832	+	0.898797i
$77$	−7.68130	+	7.68130i	−0.875366	+	0.875366i
$78$	0.247089	+	3.59707i	0.0279773	+	0.407289i
$79$			10.8193i			1.21727i	0.793452	+	0.608633i	$0.208282\pi$
$79$			10.8193i			1.21727i	−0.793452	+	0.608633i	$0.791718\pi$
$80$	0.994046	−	2.00297i	0.111138	−	0.223938i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	0.750873	+	2.80230i	0.0829201	+	0.309462i
$83$			10.4646i			1.14864i	0.818632	+	0.574318i	$0.194733\pi$
$83$			10.4646i			1.14864i	−0.818632	+	0.574318i	$0.805267\pi$
$84$	−3.56156	+	0.954318i	−0.388598	+	0.104125i
$85$	5.81615	−	6.59838i	0.630850	−	0.715694i
$86$	2.67809	+	2.67809i	0.288786	+	0.288786i
$87$	−5.17428	+	1.38644i	−0.554741	+	0.148642i
$88$	0.762517	−	2.84575i	0.0812846	−	0.303358i
$89$	−9.57642	−	2.56600i	−1.01510	−	0.271995i	−0.287341	−	0.957828i	$-0.592771\pi$
$89$	−9.57642	−	2.56600i	−1.01510	−	0.271995i	−0.727758	+	0.685834i	$0.759438\pi$
$90$	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
$93$	3.60559	−	2.08169i	0.373882	−	0.215861i
$94$	−10.6928	+	6.17348i	−1.10288	+	0.636746i
$95$	13.6073	+	11.9941i	1.39608	+	1.23057i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	−1.60370	+	2.77769i	−0.162831	+	0.282032i	−0.935883	−	0.352311i	$-0.885396\pi$
$97$	−1.60370	+	2.77769i	−0.162831	+	0.282032i	0.773052	+	0.634343i	$0.218729\pi$
$98$	3.29773	−	5.71183i	0.333121	−	0.576982i
$99$	2.08323	−	2.08323i	0.209373	−	0.209373i
$100$	−3.02375	−	3.98208i	−0.302375	−	0.398208i
$101$	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	$0.205033\pi$
$102$	3.40660	−	1.96680i	0.337304	−	0.194742i
$103$	−2.29199	−	2.29199i	−0.225837	−	0.225837i	0.585114	−	0.810951i	$-0.301050\pi$
$103$	−2.29199	−	2.29199i	−0.225837	−	0.225837i	−0.810951	+	0.585114i	$0.801050\pi$
$104$	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
$107$	4.59079	−	17.1331i	0.443809	−	1.65632i	−0.275253	−	0.961372i	$-0.588762\pi$
$107$	4.59079	−	17.1331i	0.443809	−	1.65632i	0.719062	−	0.694946i	$-0.244572\pi$
$108$	0.965926	−	0.258819i	0.0929463	−	0.0249049i
$109$	−6.45231	−	6.45231i	−0.618019	−	0.618019i	0.327004	−	0.945023i	$-0.393961\pi$
$109$	−6.45231	−	6.45231i	−0.618019	−	0.618019i	−0.945023	+	0.327004i	$0.893961\pi$
$110$	−4.94197	−	4.35610i	−0.471198	−	0.415338i
$111$	2.18811	−	0.586302i	0.207686	−	0.0556493i
$112$			3.68720i			0.348408i
$113$	2.10512	+	7.85641i	0.198033	+	0.739069i	0.991461	+	0.130405i	$0.0416277\pi$
$113$	2.10512	+	7.85641i	0.198033	+	0.739069i	−0.793428	+	0.608664i	$0.791706\pi$
$114$	4.05597	+	7.02514i	0.379876	+	0.657965i
$115$	15.5366	−	5.23028i	1.44880	−	0.487726i
$116$			5.35680i			0.497367i
$117$	2.71823	+	2.36880i	0.251301	+	0.218995i
$118$	4.82642	−	4.82642i	0.444308	−	0.444308i
$119$	−3.75391	+	14.0098i	−0.344120	+	1.28427i
$120$	−0.713415	−	2.11921i	−0.0651255	−	0.193456i
$121$	2.00941	+	1.16013i	0.182674	+	0.105467i
$122$	−9.86837			−0.893440
$123$	2.51247	+	1.45058i	0.226542	+	0.130794i
$124$	−1.07756	−	4.02151i	−0.0967678	−	0.361142i
$125$	−10.9817	+	2.09809i	−0.982234	+	0.187659i
$126$	−1.84360	+	3.19321i	−0.164241	+	0.284474i
$127$	−13.3484	−	3.57670i	−1.18448	−	0.317381i	−0.387779	−	0.921752i	$-0.626758\pi$
$127$	−13.3484	−	3.57670i	−1.18448	−	0.317381i	−0.796703	+	0.604372i	$0.793424\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	3.78739			0.333461
$130$	4.90409	−	6.39921i	0.430117	−	0.561248i
$131$	−10.2728			−0.897543			−0.448771	−	0.893647i	$-0.648138\pi$
$131$	−10.2728			−0.897543			−0.448771	+	0.893647i	$0.648138\pi$
$132$	−1.47307	−	2.55143i	−0.128214	−	0.222074i
$133$	−28.8912	−	7.74136i	−2.50518	−	0.671261i
$134$	6.56871	−	11.3773i	0.567450	−	0.982852i
$135$	0.441768	−	2.19199i	0.0380214	−	0.188657i
$136$	−1.01809	−	3.79957i	−0.0873006	−	0.325810i
$137$	−3.26137	−	1.88296i	−0.278638	−	0.160872i	0.354169	−	0.935182i	$-0.384764\pi$
$137$	−3.26137	−	1.88296i	−0.278638	−	0.160872i	−0.632807	+	0.774310i	$0.718097\pi$
$138$	7.33133			0.624084
$139$	−5.02846	−	2.90318i	−0.426508	−	0.246245i	0.271350	−	0.962481i	$-0.412530\pi$
$139$	−5.02846	−	2.90318i	−0.426508	−	0.246245i	−0.697858	+	0.716236i	$0.745863\pi$
$140$	7.38534	+	3.66525i	0.624175	+	0.309770i
$141$	−3.19563	+	11.9262i	−0.269120	+	1.00437i
$142$	1.69630	−	1.69630i	0.142350	−	0.142350i
$143$	4.66831	−	9.54167i	0.390384	−	0.797914i
$144$		−	1.00000i		−	0.0833333i
$145$	10.7295	+	5.32491i	0.891036	+	0.442209i
$146$	−4.33793	−	7.51351i	−0.359009	−	0.621823i
$147$	−1.70703	−	6.37072i	−0.140793	−	0.525448i
$148$		−	2.26530i		−	0.186206i
$149$	−7.14371	+	1.91415i	−0.585235	+	0.156813i	−0.539275	−	0.842130i	$-0.681302\pi$
$149$	−7.14371	+	1.91415i	−0.585235	+	0.156813i	−0.0459607	+	0.998943i	$0.514635\pi$
$150$	−4.95387	−	0.677643i	−0.404482	−	0.0553293i
$151$	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	$0.666561\pi$
$152$	7.83553	−	2.09952i	0.635545	−	0.170294i
$153$	1.01809	−	3.79957i	0.0823078	−	0.307177i
$154$	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	0.630326	−	0.776331i	$-0.282921\pi$
$157$	−1.82943	−	1.82943i	−0.146005	−	0.146005i	−0.776331	+	0.630326i	$0.782921\pi$
$158$	9.36978	−	5.40965i	0.745420	−	0.430368i
$159$	1.16605	−	0.673219i	0.0924737	−	0.0533897i
$160$	−2.23164	+	0.140614i	−0.176427	+	0.0111165i
$161$	−19.1146	+	19.1146i	−1.50644	+	1.50644i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−8.55396	+	14.8159i	−0.669998	+	1.16047i	0.307906	+	0.951417i	$0.400372\pi$
$163$	−8.55396	+	14.8159i	−0.669998	+	1.16047i	−0.977904	+	0.209054i	$0.932962\pi$
$164$	2.05142	−	2.05142i	0.160189	−	0.160189i
$165$	−6.57473	+	0.414269i	−0.511842	+	0.0322508i
$166$	9.06259	−	5.23229i	0.703393	−	0.406104i
$167$	1.98761	−	1.14754i	0.153806	−	0.0887997i	−0.421122	−	0.907004i	$-0.638364\pi$
$167$	1.98761	−	1.14754i	0.153806	−	0.0887997i	0.574928	+	0.818204i	$0.305030\pi$
$168$	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
$172$	0.980250	−	3.65834i	0.0747433	−	0.278946i
$173$	20.6272	−	5.52705i	1.56826	−	0.420214i	0.632992	−	0.774158i	$-0.281827\pi$
$173$	20.6272	−	5.52705i	1.56826	−	0.420214i	0.935266	+	0.353945i	$0.115160\pi$
$174$	3.78783	+	3.78783i	0.287155	+	0.287155i
$175$	14.6827	−	11.1492i	1.10991	−	0.842797i
$176$	−2.84575	+	0.762517i	−0.214507	+	0.0574769i
$177$		−	6.82559i		−	0.513043i
$178$	2.56600	+	9.57642i	0.192329	+	0.717783i
$179$	0.651952	+	1.12921i	0.0487292	+	0.0844014i	0.889361	−	0.457205i	$-0.151150\pi$
$179$	0.651952	+	1.12921i	0.0487292	+	0.0844014i	−0.840632	+	0.541607i	$0.817816\pi$
$180$	−2.00297	−	0.994046i	−0.149292	−	0.0740918i
$181$			14.5495i			1.08145i	0.841198	+	0.540727i	$0.181851\pi$
$181$			14.5495i			1.08145i	−0.841198	+	0.540727i	$0.818149\pi$
$182$	−2.55273	+	13.0470i	−0.189221	+	0.967109i
$183$	−6.97799	+	6.97799i	−0.515828	+	0.515828i
$184$	1.89749	−	7.08152i	0.139885	−	0.522056i
$185$	−4.53731	−	2.25181i	−0.333590	−	0.165556i
$186$	−3.60559	−	2.08169i	−0.264375	−	0.152637i
$187$	−11.5889			−0.847467
$188$	10.6928	+	6.17348i	0.779851	+	0.450247i
$189$	0.954318	+	3.56156i	0.0694164	+	0.259066i
$190$	3.58360	−	17.7813i	0.259981	−	1.28999i
$191$	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	$0.0258404\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	2.54585	+	4.40954i	0.183254	+	0.317406i	0.942987	−	0.332830i	$-0.108003\pi$
$193$	2.54585	+	4.40954i	0.183254	+	0.317406i	−0.759733	+	0.650236i	$0.774670\pi$
$194$	3.20740			0.230278
$195$	−1.05721	−	7.99264i	−0.0757087	−	0.572365i
$196$	−6.59545			−0.471104
$197$	1.75942	+	3.04740i	0.125353	+	0.217118i	0.921871	−	0.387497i	$-0.126660\pi$
$197$	1.75942	+	3.04740i	0.125353	+	0.217118i	−0.796518	+	0.604615i	$0.793327\pi$
$198$	−2.84575	−	0.762517i	−0.202239	−	0.0541897i
$199$	6.19744	−	10.7343i	0.439325	−	0.760933i	−0.558313	−	0.829631i	$-0.688551\pi$
$199$	6.19744	−	10.7343i	0.439325	−	0.760933i	0.997638	+	0.0686976i	$0.0218844\pi$
$200$	−1.93671	+	4.60968i	−0.136946	+	0.325954i
$201$	−3.40021	−	12.6898i	−0.239833	−	0.895068i
$202$	−6.82771	−	3.94198i	−0.480396	−	0.277357i
$203$	−19.7516			−1.38629
$204$	−3.40660	−	1.96680i	−0.238510	−	0.137704i
$205$	−2.06972	−	6.14814i	−0.144556	−	0.429405i
$206$	−0.838927	+	3.13092i	−0.0584508	+	0.218141i
$207$	5.18403	−	5.18403i	0.360315	−	0.360315i
$208$	−1.16966	−	3.41056i	−0.0811014	−	0.236480i
$209$		−	23.8989i		−	1.65312i
$210$	7.81394	−	2.63050i	0.539213	−	0.181522i
$211$	−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	$-0.541420\pi$
$212$	−0.348484	−	1.30056i	−0.0239340	−	0.0893228i
$213$		−	2.39892i		−	0.164372i
$214$	−17.1331	+	4.59079i	−1.17119	+	0.313820i
$215$	−6.35312	−	5.59997i	−0.433279	−	0.381915i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	14.8281	−	3.97318i	1.00660	−	0.269717i
$218$	−2.36171	+	8.81402i	−0.159955	+	0.596961i
$219$	−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
$223$	−21.7537	+	12.5595i	−1.45673	+	0.841046i	−0.998849	−	0.0479660i	$-0.984726\pi$
$223$	−21.7537	+	12.5595i	−1.45673	+	0.841046i	−0.457885	+	0.889012i	$0.651393\pi$
$224$	3.19321	−	1.84360i	0.213355	−	0.123181i
$225$	−3.98208	+	3.02375i	−0.265472	+	0.201583i
$226$	5.75129	−	5.75129i	0.382570	−	0.382570i
$227$	−9.03882	+	15.6557i	−0.599928	+	1.03910i	0.392904	+	0.919580i	$0.371471\pi$
$227$	−9.03882	+	15.6557i	−0.599928	+	1.03910i	−0.992831	+	0.119525i	$0.961863\pi$
$228$	4.05597	−	7.02514i	0.268613	−	0.465251i
$229$	8.19344	−	8.19344i	0.541437	−	0.541437i	−0.382513	−	0.923950i	$-0.624941\pi$
$229$	8.19344	−	8.19344i	0.541437	−	0.541437i	0.923950	+	0.382513i	$0.124941\pi$
$230$	−12.2979	−	10.8400i	−0.810896	−	0.714765i
$231$	9.40764	−	5.43150i	0.618977	−	0.357367i
$232$	4.63913	−	2.67840i	0.304574	−	0.175846i
$233$	20.2207	+	20.2207i	1.32470	+	1.32470i	0.909919	+	0.414785i	$0.136143\pi$
$233$	20.2207	+	20.2207i	1.32470	+	1.32470i	0.414785	+	0.909919i	$0.363857\pi$
$234$	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
$237$	2.80024	−	10.4506i	0.181895	−	0.678842i
$238$	14.0098	−	3.75391i	0.908119	−	0.243330i
$239$	−3.98481	−	3.98481i	−0.257756	−	0.257756i	0.566385	−	0.824141i	$-0.308342\pi$
$239$	−3.98481	−	3.98481i	−0.257756	−	0.257756i	−0.824141	+	0.566385i	$0.808342\pi$
$240$	−1.47858	+	1.67744i	−0.0954419	+	0.108278i
$241$	−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	$0.545835\pi$
$242$		−	2.32027i		−	0.149153i
$243$	−0.258819	−	0.965926i	−0.0166032	−	0.0619642i
$244$	4.93418	+	8.54626i	0.315879	+	0.547118i
$245$	−6.55618	+	13.2105i	−0.418859	+	0.843986i
$246$		−	2.90115i		−	0.184971i
$247$	29.1792	−	2.00437i	1.85663	−	0.127535i
$248$	−2.94395	+	2.94395i	−0.186941	+	0.186941i
$249$	2.70843	−	10.1080i	0.171640	−	0.640569i
$250$	7.30786	+	8.46139i	0.462190	+	0.535146i
$251$	−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	$0.677512\pi$
$252$	3.68720			0.232272
$253$	−18.7054	−	10.7995i	−1.17600	−	0.678962i
$254$	3.57670	+	13.3484i	0.224422	+	0.837555i
$255$	−7.32575	+	4.86821i	−0.458756	+	0.304859i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.02566	−	1.34662i	−0.313492	−	0.0840000i	0.0986424	−	0.995123i	$-0.468550\pi$
$257$	−5.02566	−	1.34662i	−0.313492	−	0.0840000i	−0.412135	+	0.911123i	$0.635217\pi$
$258$	−1.89370	−	3.27998i	−0.117896	−	0.204203i
$259$	8.35261			0.519006
$260$	−7.99392	−	1.04746i	−0.495762	−	0.0649605i
$261$	5.35680			0.331578
$262$	5.13642	+	8.89655i	0.317329	+	0.549631i
$263$	10.1069	+	2.70814i	0.623220	+	0.166991i	0.556591	−	0.830787i	$-0.312109\pi$
$263$	10.1069	+	2.70814i	0.623220	+	0.166991i	0.0666287	+	0.997778i	$0.478776\pi$
$264$	−1.47307	+	2.55143i	−0.0906611	+	0.157030i
$265$	−2.95138	−	0.594814i	−0.181302	−	0.0365391i
$266$	7.74136	+	28.8912i	0.474653	+	1.77143i
$267$	8.58599	+	4.95712i	0.525454	+	0.303371i
$268$	−13.1374			−0.802496
$269$	−11.6065	−	6.70100i	−0.707659	−	0.408567i	0.102535	−	0.994729i	$-0.467305\pi$
$269$	−11.6065	−	6.70100i	−0.707659	−	0.408567i	−0.810194	+	0.586162i	$0.800638\pi$
$270$	−2.11921	+	0.713415i	−0.128971	+	0.0434170i
$271$	−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
$273$	7.42058	+	11.0307i	0.449114	+	0.667607i
$274$			3.76591i			0.227507i
$275$	11.6412	+	9.02635i	0.701993	+	0.544309i
$276$	−3.66566	−	6.34911i	−0.220647	−	0.382172i
$277$	1.48757	+	5.55169i	0.0893794	+	0.333569i	0.996107	−	0.0881474i	$-0.0280946\pi$
$277$	1.48757	+	5.55169i	0.0893794	+	0.333569i	−0.906728	+	0.421716i	$0.861428\pi$
$278$			5.80636i			0.348243i
$279$	−4.02151	+	1.07756i	−0.240762	+	0.0645119i
$280$	−0.518473	−	8.22851i	−0.0309847	−	0.491748i
$281$	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	$0.476048\pi$
$282$	11.9262	−	3.19563i	0.710197	−	0.190297i
$283$	2.37477	−	8.86275i	0.141165	−	0.526836i	−0.858731	−	0.512427i	$-0.828747\pi$
$283$	2.37477	−	8.86275i	0.141165	−	0.526836i	0.999896	−	0.0144091i	$-0.00458671\pi$
$284$	−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
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	1.32223	−	0.763387i	0.0777780	−	0.0449051i
$290$	−0.753244	−	11.9545i	−0.0442320	−	0.701991i
$291$	2.26797	−	2.26797i	0.132951	−	0.132951i
$292$	−4.33793	+	7.51351i	−0.253858	+	0.439695i
$293$	−5.56995	+	9.64744i	−0.325400	+	0.563610i	−0.981593	−	0.190983i	$-0.938832\pi$
$293$	−5.56995	+	9.64744i	−0.325400	+	0.563610i	0.656193	+	0.754593i	$0.272166\pi$
$294$	−4.66369	+	4.66369i	−0.271992	+	0.271992i
$295$	−10.0922	+	11.4495i	−0.587590	+	0.666617i
$296$	−1.96180	+	1.13265i	−0.114028	+	0.0658339i
$297$	−2.55143	+	1.47307i	−0.148049	+	0.0854761i
$298$	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
$302$	1.64834	−	6.15168i	0.0948512	−	0.353989i
$303$	−7.61532	+	2.04052i	−0.437489	+	0.117225i
$304$	−5.73600	−	5.73600i	−0.328982	−	0.328982i
$305$	22.0227	−	1.38763i	1.26101	−	0.0794557i
$306$	−3.79957	+	1.01809i	−0.217207	+	0.0582004i
$307$			31.8543i			1.81802i	0.416773	+	0.909010i	$0.363161\pi$
$307$			31.8543i			1.81802i	−0.416773	+	0.909010i	$0.636839\pi$
$308$	−2.81155	−	10.4929i	−0.160203	−	0.597886i
$309$	1.62068	+	2.80710i	0.0921974	+	0.159691i
$310$	2.97021	+	8.82306i	0.168697	+	0.501116i
$311$		−	9.69424i		−	0.549710i	−0.961486	−	0.274855i	$-0.911370\pi$
$311$		−	9.69424i		−	0.549710i	0.961486	−	0.274855i	$-0.0886298\pi$
$312$	−3.23870	−	1.58455i	−0.183355	−	0.0897076i
$313$	12.1109	−	12.1109i	0.684549	−	0.684549i	−0.276472	−	0.961022i	$-0.589165\pi$
$313$	12.1109	−	12.1109i	0.684549	−	0.684549i	0.961022	+	0.276472i	$0.0891654\pi$
$314$	−0.669620	+	2.49905i	−0.0377888	+	0.141030i
$315$	3.66525	−	7.38534i	0.206513	−	0.416117i
$316$	−9.36978	−	5.40965i	−0.527091	−	0.304316i
$317$	0.342702			0.0192480			0.00962402	−	0.999954i	$-0.496937\pi$
$317$	0.342702			0.0192480			0.00962402	+	0.999954i	$0.496937\pi$
$318$	−1.16605	−	0.673219i	−0.0653888	−	0.0377522i
$319$	−4.08465	−	15.2441i	−0.228697	−	0.853507i
$320$	1.23760	+	1.86235i	0.0691838	+	0.104109i
$321$	−8.86873	+	15.3611i	−0.495004	+	0.857373i
$322$	26.1110	+	6.99642i	1.45511	+	0.389895i
$323$	−15.9546	−	27.6341i	−0.887736	−	1.53760i
$324$	−1.00000			−0.0555556
$325$	−10.0443	+	14.9703i	−0.557160	+	0.830405i
$326$	17.1079			0.947520
$327$	4.56247	+	7.90243i	0.252305	+	0.437005i
$328$	−2.80230	−	0.750873i	−0.154731	−	0.0414600i
$329$	−22.7629	+	39.4264i	−1.25496	+	2.17365i
$330$	3.64613	+	5.48675i	0.200713	+	0.302035i
$331$	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	$0.650959\pi$
$332$	−9.06259	−	5.23229i	−0.497374	−	0.287159i
$333$	−2.26530			−0.124138
$334$	−1.98761	−	1.14754i	−0.108757	−	0.0627908i
$335$	−13.0592	+	26.3138i	−0.713500	+	1.43768i
$336$	0.954318	−	3.56156i	0.0520623	−	0.194299i
$337$	1.69270	−	1.69270i	0.0922074	−	0.0922074i	−0.659498	−	0.751706i	$-0.729231\pi$
$337$	1.69270	−	1.69270i	0.0922074	−	0.0922074i	0.751706	+	0.659498i	$0.229231\pi$
$338$	−1.77759	−	12.8779i	−0.0966883	−	0.700465i
$339$		−	8.13356i		−	0.441754i
$340$	2.80629	+	8.33612i	0.152192	+	0.452089i
$341$	6.13294	+	10.6226i	0.332117	+	0.575244i
$342$	−2.09952	−	7.83553i	−0.113529	−	0.423697i
$343$			1.49165i			0.0805415i
$344$	−3.65834	+	0.980250i	−0.197245	+	0.0528515i
$345$	−16.3609	+	1.03089i	−0.880841	+	0.0555012i
$346$	−15.1002	−	15.1002i	−0.811790	−	0.811790i
$347$	−3.81806	+	1.02305i	−0.204964	+	0.0549201i	−0.359840	−	0.933014i	$-0.617169\pi$
$347$	−3.81806	+	1.02305i	−0.204964	+	0.0549201i	0.154876	+	0.987934i	$0.450502\pi$
$348$	1.38644	−	5.17428i	0.0743211	−	0.277370i
$349$	−6.30915	−	1.69053i	−0.337721	−	0.0904921i	0.0859729	−	0.996297i	$-0.472600\pi$
$349$	−6.30915	−	1.69053i	−0.337721	−	0.0904921i	−0.423694	+	0.905805i	$0.639267\pi$
$350$	−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
$353$	−23.7777	+	13.7281i	−1.26556	+	0.730671i	−0.974144	−	0.225926i	$-0.927459\pi$
$353$	−23.7777	+	13.7281i	−1.26556	+	0.730671i	−0.291414	+	0.956597i	$0.594126\pi$
$354$	−5.91114	+	3.41280i	−0.314173	+	0.181388i
$355$	−3.54700	+	4.02405i	−0.188255	+	0.213574i
$356$	7.01043	−	7.01043i	0.371552	−	0.371552i
$357$	7.25199	−	12.5608i	0.383816	−	0.664789i
$358$	0.651952	−	1.12921i	0.0344567	−	0.0596808i
$359$	2.54684	−	2.54684i	0.134417	−	0.134417i	−0.636697	−	0.771114i	$-0.719700\pi$
$359$	2.54684	−	2.54684i	0.134417	−	0.134417i	0.771114	+	0.636697i	$0.219700\pi$
$360$	0.140614	+	2.23164i	0.00741103	+	0.117618i
$361$	40.5330	−	23.4017i	2.13332	−	1.23167i
$362$	12.6002	−	7.27474i	0.662253	−	0.382352i
$363$	−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
$367$	−3.11318	+	11.6185i	−0.162506	+	0.606482i	0.835839	+	0.548975i	$0.184982\pi$
$367$	−3.11318	+	11.6185i	−0.162506	+	0.606482i	−0.998345	+	0.0575071i	$0.981685\pi$
$368$	−7.08152	+	1.89749i	−0.369150	+	0.0989133i
$369$	−2.05142	−	2.05142i	−0.106793	−	0.106793i
$370$	0.318533	+	5.05533i	0.0165598	+	0.262814i
$371$	4.79542	−	1.28493i	0.248966	−	0.0667102i
$372$			4.16338i			0.215861i
$373$	7.90723	+	29.5102i	0.409421	+	1.52798i	0.795753	+	0.605621i	$0.207075\pi$
$373$	7.90723	+	29.5102i	0.409421	+	1.52798i	−0.386332	+	0.922360i	$0.626258\pi$
$374$	5.79447	+	10.0363i	0.299625	+	0.518965i
$375$	11.1505	+	0.815673i	0.575812	+	0.0421211i
$376$		−	12.3470i		−	0.636746i
$377$	18.2697	−	6.26564i	0.940936	−	0.322697i
$378$	2.60724	−	2.60724i	0.134102	−	0.134102i
$379$	6.78244	−	25.3124i	0.348391	−	1.30021i	−0.540210	−	0.841530i	$-0.681655\pi$
$379$	6.78244	−	25.3124i	0.348391	−	1.30021i	0.888601	−	0.458682i	$-0.151678\pi$
$380$	−17.1909	+	5.78717i	−0.881873	+	0.296876i
$381$	11.9679	+	6.90965i	0.613133	+	0.353992i
$382$	−11.8337			−0.605462
$383$	18.0734	+	10.4347i	0.923507	+	0.533187i	0.884752	−	0.466062i	$-0.154328\pi$
$383$	18.0734	+	10.4347i	0.923507	+	0.533187i	0.0387549	+	0.999249i	$0.487661\pi$
$384$	0.258819	+	0.965926i	0.0132078	+	0.0492922i
$385$	−23.8116	−	4.79893i	−1.21355	−	0.244576i
$386$	2.54585	−	4.40954i	0.129580	−	0.224440i
$387$	−3.65834	−	0.980250i	−0.185964	−	0.0498289i
$388$	−1.60370	−	2.77769i	−0.0814155	−	0.141016i
$389$	−19.1719			−0.972054			−0.486027	−	0.873944i	$-0.661554\pi$
$389$	−19.1719			−0.972054			−0.486027	+	0.873944i	$0.661554\pi$
$390$	−6.39322	+	4.91189i	−0.323733	+	0.248723i
$391$	−28.8385			−1.45843
$392$	3.29773	+	5.71183i	0.166560	+	0.288491i
$393$	9.92281	+	2.65881i	0.500540	+	0.134119i
$394$	1.75942	−	3.04740i	0.0886381	−	0.153526i
$395$	−20.1493	+	13.3899i	−1.01382	+	0.673720i
$396$	0.762517	+	2.84575i	0.0383179	+	0.143004i
$397$	−8.64291	−	4.98999i	−0.433775	−	0.250440i	0.267178	−	0.963647i	$-0.413909\pi$
$397$	−8.64291	−	4.98999i	−0.433775	−	0.250440i	−0.700954	+	0.713207i	$0.747242\pi$
$398$	−12.3949			−0.621299
$399$	25.9031	+	14.9552i	1.29678	+	0.748695i
$400$	4.96046	−	0.627602i	0.248023	−	0.0313801i
$401$	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
$403$	−12.4552	+	8.37889i	−0.620438	+	0.417382i
$404$			7.88396i			0.392241i
$405$	−0.994046	+	2.00297i	−0.0493945	+	0.0995282i
$406$	9.87581	+	17.1054i	0.490128	+	0.848927i
$407$	1.72733	+	6.44647i	0.0856204	+	0.319540i
$408$			3.93360i			0.194742i
$409$	5.77688	−	1.54791i	0.285648	−	0.0765393i	−0.113150	−	0.993578i	$-0.536094\pi$
$409$	5.77688	−	1.54791i	0.285648	−	0.0765393i	0.398798	+	0.917039i	$0.369427\pi$
$410$	−4.28959	+	4.86650i	−0.211848	+	0.240340i
$411$	2.66290	+	2.66290i	0.131351	+	0.131351i
$412$	3.13092	−	0.838927i	0.154249	−	0.0413310i
$413$	6.51379	−	24.3098i	0.320522	−	1.19621i
$414$	−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
$418$	−20.6970	+	11.9494i	−1.01233	+	0.584466i
$419$	4.96010	−	2.86371i	0.242317	−	0.139902i	−0.373924	−	0.927459i	$-0.621988\pi$
$419$	4.96010	−	2.86371i	0.242317	−	0.139902i	0.616241	+	0.787558i	$0.288655\pi$
$420$	−6.18505	−	5.45182i	−0.301800	−	0.266022i
$421$	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	$-0.0731751\pi$
$422$	−13.4158	+	23.2369i	−0.653072	+	1.13115i
$423$	6.17348	−	10.6928i	0.300165	−	0.519901i
$424$	−0.952075	+	0.952075i	−0.0462369	+	0.0462369i
$425$	19.4865	+	2.66558i	0.945236	+	0.129300i
$426$	−2.07753	+	1.19946i	−0.100657	+	0.0581141i
$427$	−31.5118	+	18.1933i	−1.52496	+	0.880437i
$428$	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	$0.545762\pi$
$432$	−0.258819	+	0.965926i	−0.0124524	+	0.0464731i
$433$	3.96274	−	1.06181i	0.190437	−	0.0510274i	−0.162340	−	0.986735i	$-0.551904\pi$
$433$	3.96274	−	1.06181i	0.190437	−	0.0510274i	0.352777	+	0.935707i	$0.385237\pi$
$434$	−10.8549	−	10.8549i	−0.521054	−	0.521054i
$435$	−8.98571	−	7.92046i	−0.430832	−	0.379757i
$436$	8.81402	−	2.36171i	0.422115	−	0.113105i
$437$		−	59.4712i		−	2.84490i
$438$	2.24548	+	8.38023i	0.107293	+	0.400423i
$439$	−0.444561	−	0.770002i	−0.0212177	−	0.0367502i	0.855222	−	0.518263i	$-0.173421\pi$
$439$	−0.444561	−	0.770002i	−0.0212177	−	0.0367502i	−0.876439	+	0.481512i	$0.840088\pi$
$440$	6.24348	−	2.10182i	0.297646	−	0.100200i
$441$			6.59545i			0.314069i
$442$	−11.7678	+	7.91646i	−0.559738	+	0.376548i
$443$	2.43706	−	2.43706i	0.115788	−	0.115788i	−0.646839	−	0.762627i	$-0.723909\pi$
$443$	2.43706	−	2.43706i	0.115788	−	0.115788i	0.762627	+	0.646839i	$0.223909\pi$
$444$	−0.586302	+	2.18811i	−0.0278247	+	0.103843i
$445$	−7.07297	−	21.0103i	−0.335291	−	0.995986i
$446$	21.7537	+	12.5595i	1.03007	+	0.594709i
$447$	7.39571			0.349805
$448$	−3.19321	−	1.84360i	−0.150865	−	0.0871019i
$449$	3.19285	+	11.9159i	0.150680	+	0.562344i	0.999437	+	0.0335612i	$0.0106849\pi$
$449$	3.19285	+	11.9159i	0.150680	+	0.562344i	−0.848757	+	0.528783i	$0.822648\pi$
$450$	4.60968	+	1.93671i	0.217302	+	0.0912973i
$451$	−4.27360	+	7.40209i	−0.201236	+	0.348551i
$452$	−7.85641	−	2.10512i	−0.369535	−	0.0990165i
$453$	−3.18434	−	5.51545i	−0.149614	−	0.259138i
$454$	18.0776			0.848426
$455$	3.86218	−	29.4752i	0.181062	−	1.38182i
$456$	−8.11193			−0.379876
$457$	9.04457	+	15.6657i	0.423087	+	0.732808i	0.996240	−	0.0866404i	$-0.0276131\pi$
$457$	9.04457	+	15.6657i	0.423087	+	0.732808i	−0.573153	+	0.819449i	$0.694280\pi$
$458$	−11.1924	−	2.99901i	−0.522988	−	0.140134i
$459$	−1.96680	+	3.40660i	−0.0918024	+	0.159006i
$460$	−3.23875	+	16.0702i	−0.151007	+	0.749278i
$461$	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	$0.788350\pi$
$462$	−9.40764	−	5.43150i	−0.437683	−	0.252696i
$463$	8.14963			0.378745			0.189373	−	0.981905i	$-0.439355\pi$
$463$	8.14963			0.378745			0.189373	+	0.981905i	$0.439355\pi$
$464$	−4.63913	−	2.67840i	−0.215366	−	0.124342i
$465$	8.33910	+	4.13859i	0.386717	+	0.191922i
$466$	7.40130	−	27.6220i	0.342859	−	1.27957i
$467$	13.9799	−	13.9799i	0.646912	−	0.646912i	−0.305333	−	0.952246i	$-0.598768\pi$
$467$	13.9799	−	13.9799i	0.646912	−	0.646912i	0.952246	+	0.305333i	$0.0987679\pi$
$468$	−3.41056	+	1.16966i	−0.157653	+	0.0540676i
$469$		−	48.4403i		−	2.23677i
$470$	−24.7305	−	12.2734i	−1.14073	−	0.566131i
$471$	1.29361	+	2.24059i	0.0596062	+	0.103241i
$472$	1.76659	+	6.59302i	0.0813141	+	0.303468i
$473$			11.1582i			0.513054i
$474$	−10.4506	+	2.80024i	−0.480014	+	0.128619i
$475$	−5.49700	+	40.1854i	−0.252220	+	1.84383i
$476$	−10.2559	−	10.2559i	−0.470077	−	0.470077i
$477$	−1.30056	+	0.348484i	−0.0595485	+	0.0159560i
$478$	−1.45854	+	5.44335i	−0.0667122	+	0.248973i
$479$	2.72948	+	0.731362i	0.124713	+	0.0334168i	0.320636	−	0.947203i	$-0.396103\pi$
$479$	2.72948	+	0.731362i	0.124713	+	0.0334168i	−0.195923	+	0.980619i	$0.562770\pi$
$480$	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
$483$	23.4105	−	13.5160i	1.06521	−	0.615001i
$484$	−2.00941	+	1.16013i	−0.0913369	+	0.0527334i
$485$	−7.15777	+	0.451006i	−0.325017	+	0.0204791i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	6.12135	−	10.6025i	0.277385	−	0.480445i	−0.693349	−	0.720602i	$-0.743866\pi$
$487$	6.12135	−	10.6025i	0.277385	−	0.480445i	0.970734	+	0.240157i	$0.0771989\pi$
$488$	4.93418	−	8.54626i	0.223360	−	0.386871i
$489$	12.0971	−	12.0971i	0.547051	−	0.547051i
$490$	14.7187	−	0.927415i	0.664923	−	0.0418964i
$491$	−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	$0.611738\pi$
$492$	−2.51247	+	1.45058i	−0.113271	+	0.0653970i
$493$	−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
$497$	2.28934	−	8.54392i	0.102691	−	0.383247i
$498$	−10.1080	+	2.70843i	−0.452951	+	0.121368i
$499$	13.5016	+	13.5016i	0.604414	+	0.604414i	0.941481	−	0.337067i	$-0.109435\pi$
$499$	13.5016	+	13.5016i	0.604414	+	0.604414i	−0.337067	+	0.941481i	$0.609435\pi$
$500$	3.67385	−	10.5595i	0.164300	−	0.472235i
$501$	−2.21689	+	0.594013i	−0.0990431	+	0.0265385i
$502$			1.07935i			0.0481739i
$503$	−0.375901	−	1.40288i	−0.0167606	−	0.0625515i	0.957039	−	0.289959i	$-0.0936417\pi$
$503$	−0.375901	−	1.40288i	−0.0167606	−	0.0625515i	−0.973800	+	0.227408i	$0.926975\pi$
$504$	−1.84360	−	3.19321i	−0.0821205	−	0.142237i
$505$	15.7913	+	7.83701i	0.702704	+	0.348742i
$506$			21.5991i			0.960197i
$507$	−10.3630	−	7.84910i	−0.460237	−	0.348591i
$508$	9.77173	−	9.77173i	0.433550	−	0.433550i
$509$	−0.337646	+	1.26011i	−0.0149659	+	0.0558534i	−0.973005	−	0.230784i	$-0.925871\pi$
$509$	−0.337646	+	1.26011i	−0.0149659	+	0.0558534i	0.958039	+	0.286638i	$0.0925375\pi$
$510$	7.87887	+	3.91018i	0.348882	+	0.173146i
$511$	−27.7038	−	15.9948i	−1.22555	−	0.707569i
$512$	1.00000			0.0441942
$513$	−7.02514	−	4.05597i	−0.310168	−	0.179075i
$514$	1.34662	+	5.02566i	0.0593970	+	0.221672i
$515$	1.43193	−	7.10505i	0.0630985	−	0.313086i
$516$	−1.89370	+	3.27998i	−0.0833654	+	0.144393i
$517$	−35.1364	−	9.41476i	−1.54530	−	0.414061i
$518$	−4.17630	−	7.23357i	−0.183496	−	0.317825i
$519$	−21.3549			−0.937375
$520$	3.08984	+	7.44667i	0.135498	+	0.326558i
$521$	−5.16162			−0.226135			−0.113067	−	0.993587i	$-0.536068\pi$
$521$	−5.16162			−0.226135			−0.113067	+	0.993587i	$0.536068\pi$
$522$	−2.67840	−	4.63913i	−0.117230	−	0.203049i
$523$	23.9820	+	6.42597i	1.04866	+	0.280988i	0.741698	−	0.670734i	$-0.234021\pi$
$523$	23.9820	+	6.42597i	1.04866	+	0.280988i	0.306963	+	0.951721i	$0.400687\pi$
$524$	5.13642	−	8.89655i	0.224386	−	0.388647i
$525$	−17.0680	+	6.96909i	−0.744910	+	0.304156i
$526$	−2.70814	−	10.1069i	−0.118081	−	0.440683i
$527$	14.1830	+	8.18853i	0.617819	+	0.356698i
$528$	2.94614			0.128214
$529$	−26.6288	−	15.3742i	−1.15778	−	0.668442i
$530$	0.960568	+	2.85338i	0.0417244	+	0.123943i
$531$	−1.76659	+	6.59302i	−0.0766636	+	0.286113i
$532$	21.1498	−	21.1498i	0.916960	−	0.916960i
$533$	−9.39597	−	4.59703i	−0.406985	−	0.199119i
$534$		−	9.91424i		−	0.429031i
$535$	37.5894	−	12.6542i	1.62513	−	0.547087i
$536$	6.56871	+	11.3773i	0.283725	+	0.491426i
$537$	−0.337475	−	1.25947i	−0.0145631	−	0.0543503i
$538$			13.4020i			0.577801i
$539$	18.7690	−	5.02914i	0.808439	−	0.216620i
$540$	1.67744	+	1.47858i	0.0721855	+	0.0636280i
$541$	−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	$0.761751\pi$
$542$	4.88695	−	1.30945i	0.209913	−	0.0562459i
$543$	3.76568	−	14.0537i	0.161601	−	0.603103i
$544$	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	0.926955	+	0.375172i	$0.122416\pi$
$547$	30.4542	+	30.4542i	1.30213	+	1.30213i	0.375172	+	0.926955i	$0.377584\pi$
$548$	3.26137	−	1.88296i	0.139319	−	0.0804359i
$549$	8.54626	−	4.93418i	0.364745	−	0.210586i
$550$	1.99643	−	14.5948i	0.0851281	−	0.622323i
$551$	30.7266	−	30.7266i	1.30900	−	1.30900i
$552$	−3.66566	+	6.34911i	−0.156021	+	0.270236i
$553$	19.9465	−	34.5483i	0.848210	−	1.46914i
$554$	4.06412	−	4.06412i	0.172668	−	0.172668i
$555$	3.79990	+	3.34942i	0.161297	+	0.142175i
$556$	5.02846	−	2.90318i	0.213254	−	0.123122i
$557$	−23.9313	+	13.8168i	−1.01400	+	0.585435i	−0.912361	−	0.409387i	$-0.865743\pi$
$557$	−23.9313	+	13.8168i	−1.01400	+	0.585435i	−0.101641	+	0.994821i	$0.532409\pi$
$558$	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
$562$	6.57961	−	24.5554i	0.277544	−	1.03581i
$563$	−6.88207	+	1.84404i	−0.290045	+	0.0777172i	−0.400908	−	0.916118i	$-0.631305\pi$
$563$	−6.88207	+	1.84404i	−0.290045	+	0.0777172i	0.110863	+	0.993836i	$0.464639\pi$
$564$	−8.73061	−	8.73061i	−0.367625	−	0.367625i
$565$	−12.0261	+	13.6435i	−0.505943	+	0.573988i
$566$	−8.86275	+	2.37477i	−0.372529	+	0.0998189i
$567$		−	3.68720i		−	0.154848i
$568$	0.620887	+	2.31718i	0.0260519	+	0.0972268i
$569$	6.40701	+	11.0973i	0.268596	+	0.465222i	0.968499	−	0.249016i	$-0.0801070\pi$
$569$	6.40701	+	11.0973i	0.268596	+	0.465222i	−0.699904	+	0.714237i	$0.746774\pi$
$570$	−8.06363	+	16.2479i	−0.337748	+	0.680551i
$571$			27.7231i			1.16018i	0.814554	+	0.580088i	$0.196982\pi$
$571$			27.7231i			1.16018i	−0.814554	+	0.580088i	$0.803018\pi$
$572$	5.92917	+	8.81371i	0.247911	+	0.368520i
$573$	−8.36766	+	8.36766i	−0.349564	+	0.349564i
$574$	2.76862	−	10.3326i	0.115560	−	0.431276i
$575$	28.9687	+	22.4616i	1.20808	+	0.936715i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$	13.4871			0.561474			0.280737	−	0.959785i	$-0.409421\pi$
$577$	13.4871			0.561474			0.280737	+	0.959785i	$0.409421\pi$
$578$	−1.32223	−	0.763387i	−0.0549973	−	0.0317527i
$579$	−1.31783	−	4.91821i	−0.0547671	−	0.204394i
$580$	−9.97625	+	6.62956i	−0.414241	+	0.275278i
$581$	19.2925	−	33.4156i	0.800388	−	1.38631i
$582$	−3.09811	−	0.830136i	−0.128421	−	0.0344102i
$583$	1.98340	+	3.43534i	0.0821439	+	0.142277i
$584$	8.67586			0.359009
$585$	−1.04746	+	7.99392i	−0.0433070	+	0.330508i
$586$	11.1399			0.460185
$587$	5.08942	+	8.81513i	0.210063	+	0.363839i	0.951734	−	0.306924i	$-0.0992998\pi$
$587$	5.08942	+	8.81513i	0.210063	+	0.363839i	−0.741671	+	0.670764i	$0.765966\pi$
$588$	6.37072	+	1.70703i	0.262724	+	0.0703967i
$589$	−16.8865	+	29.2483i	−0.695797	+	1.20516i
$590$	14.9617	+	3.01533i	0.615962	+	0.124139i
$591$	−0.910741	−	3.39893i	−0.0374629	−	0.139813i
$592$	1.96180	+	1.13265i	0.0806297	+	0.0465516i
$593$	2.71984			0.111690			0.0558452	−	0.998439i	$-0.482215\pi$
$593$	2.71984			0.111690			0.0558452	+	0.998439i	$0.482215\pi$
$594$	2.55143	+	1.47307i	0.104686	+	0.0604408i
$595$	−30.7369	+	10.3474i	−1.26009	+	0.424200i
$596$	1.91415	−	7.14371i	0.0784067	−	0.292618i
$597$	−8.76450	+	8.76450i	−0.358707	+	0.358707i
$598$	−26.3713	+	1.81149i	−1.07840	+	0.0740773i
$599$		−	14.9558i		−	0.611079i	−0.952179	−	0.305540i	$-0.901163\pi$
$599$		−	14.9558i		−	0.611079i	0.952179	−	0.305540i	$-0.0988369\pi$
$600$	3.06379	−	3.95135i	0.125079	−	0.161313i
$601$	−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	$-0.392097\pi$
$602$	−3.61438	−	13.4890i	−0.147311	−	0.549772i
$603$			13.1374i			0.534997i
$604$	−6.15168	+	1.64834i	−0.250308	+	0.0670699i
$605$	0.326263	+	5.17801i	0.0132645	+	0.210516i
$606$	5.57480	+	5.57480i	0.226461	+	0.226461i
$607$	−34.6067	+	9.27282i	−1.40464	+	0.376372i	−0.880009	−	0.474957i	$-0.842464\pi$
$607$	−34.6067	+	9.27282i	−1.40464	+	0.376372i	−0.524632	+	0.851329i	$0.675797\pi$
$608$	−2.09952	+	7.83553i	−0.0851469	+	0.317773i
$609$	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
$613$	6.85777	−	3.95933i	0.276983	−	0.159916i	−0.355074	−	0.934838i	$-0.615544\pi$
$613$	6.85777	−	3.95933i	0.276983	−	0.159916i	0.632057	+	0.774922i	$0.282211\pi$
$614$	27.5866	−	15.9272i	1.11331	−	0.642767i
$615$	0.407944	+	6.47433i	0.0164499	+	0.261070i
$616$	−7.68130	+	7.68130i	−0.309489	+	0.309489i
$617$	20.8739	−	36.1546i	0.840350	−	1.45553i	−0.0492496	−	0.998787i	$-0.515683\pi$
$617$	20.8739	−	36.1546i	0.840350	−	1.45553i	0.889599	−	0.456742i	$-0.150984\pi$
$618$	1.62068	−	2.80710i	0.0651934	−	0.112918i
$619$	−14.0868	+	14.0868i	−0.566197	+	0.566197i	−0.931061	−	0.364864i	$-0.881116\pi$
$619$	−14.0868	+	14.0868i	−0.566197	+	0.566197i	0.364864	+	0.931061i	$0.381116\pi$
$620$	6.15588	−	6.98381i	0.247226	−	0.280476i
$621$	−6.34911	+	3.66566i	−0.254781	+	0.147098i
$622$	−8.39546	+	4.84712i	−0.336627	+	0.194352i
$623$	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
$627$	−6.18549	+	23.0845i	−0.247024	+	0.921908i
$628$	2.49905	−	0.669620i	0.0997231	−	0.0267207i
$629$	6.30087	+	6.30087i	0.251232	+	0.251232i
$630$	−8.22851	+	0.518473i	−0.327832	+	0.0206565i
$631$	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	$0.344742\pi$
$632$			10.8193i			0.430368i
$633$	6.94454	+	25.9174i	0.276021	+	1.03012i
$634$	−0.171351	−	0.296788i	−0.00680521	−	0.0117870i
$635$	−9.85890	−	29.2860i	−0.391238	−	1.16218i
$636$			1.34644i			0.0533897i
$637$	7.71444	+	22.4942i	0.305657	+	0.891251i
$638$	−11.1595	+	11.1595i	−0.441808	+	0.441808i
$639$	−0.620887	+	2.31718i	−0.0245619	+	0.0916663i
$640$	0.994046	−	2.00297i	0.0392931	−	0.0791742i
$641$	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	$0.387406\pi$
$642$	17.7375			0.700042
$643$	−24.5681	−	14.1844i	−0.968873	−	0.559379i	−0.0699802	−	0.997548i	$-0.522294\pi$
$643$	−24.5681	−	14.1844i	−0.968873	−	0.559379i	−0.898892	+	0.438170i	$0.855627\pi$
$644$	−6.99642	−	26.1110i	−0.275697	−	1.02892i
$645$	4.68727	+	7.05346i	0.184561	+	0.277730i
$646$	−15.9546	+	27.6341i	−0.627724	+	1.08725i
$647$	6.69072	+	1.79277i	0.263040	+	0.0704812i	0.387928	−	0.921690i	$-0.373191\pi$
$647$	6.69072	+	1.79277i	0.263040	+	0.0704812i	−0.124889	+	0.992171i	$0.539857\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	20.1091			0.789353
$650$	17.9869	+	1.21349i	0.705503	+	0.0475969i
$651$	−15.3512			−0.601661
$652$	−8.55396	−	14.8159i	−0.334999	−	0.580235i
$653$	−18.9740	−	5.08406i	−0.742508	−	0.198954i	−0.132316	−	0.991208i	$-0.542241\pi$
$653$	−18.9740	−	5.08406i	−0.742508	−	0.198954i	−0.610193	+	0.792253i	$0.708908\pi$
$654$	4.56247	−	7.90243i	0.178407	−	0.309009i
$655$	−12.7136	−	19.1317i	−0.496763	−	0.747536i
$656$	0.750873	+	2.80230i	0.0293167	+	0.109411i
$657$	7.51351	+	4.33793i	0.293130	+	0.169239i
$658$	45.5257			1.77478
$659$	−0.440581	−	0.254370i	−0.0171626	−	0.00990883i	0.491394	−	0.870937i	$-0.336487\pi$
$659$	−0.440581	−	0.254370i	−0.0171626	−	0.00990883i	−0.508557	+	0.861028i	$0.669821\pi$
$660$	2.92860	−	5.90102i	0.113995	−	0.229697i
$661$	−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
$663$	−2.72332	+	13.9189i	−0.105765	+	0.540565i
$664$			10.4646i			0.406104i
$665$	−21.3385	−	63.3862i	−0.827470	−	2.45801i
$666$	1.13265	+	1.96180i	0.0438892	+	0.0760184i
$667$	−10.1645	−	37.9343i	−0.393570	−	1.46882i
$668$			2.29509i			0.0887997i
$669$	24.2631	−	6.50127i	0.938064	−	0.251354i
$670$	29.3180	−	1.84731i	1.13265	−	0.0713678i
$671$	−20.5581	−	20.5581i	−0.793638	−	0.793638i
$672$	−3.56156	+	0.954318i	−0.137390	+	0.0368136i
$673$	−6.87456	+	25.6562i	−0.264995	+	0.988974i	0.697259	+	0.716819i	$0.254403\pi$
$673$	−6.87456	+	25.6562i	−0.264995	+	0.988974i	−0.962254	+	0.272154i	$0.912264\pi$
$674$	−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	0.540614	−	0.841271i	$-0.318192\pi$
$677$	−7.82287	−	7.82287i	−0.300657	−	0.300657i	−0.841271	+	0.540614i	$0.818192\pi$
$678$	−7.04387	+	4.06678i	−0.270518	+	0.156184i
$679$	10.2419	−	5.91316i	0.393048	−	0.226926i
$680$	5.81615	−	6.59838i	0.223039	−	0.253036i
$681$	12.7828	−	12.7828i	0.489839	−	0.489839i
$682$	6.13294	−	10.6226i	0.234842	−	0.406759i
$683$	10.0979	−	17.4901i	0.386387	−	0.669241i	−0.605574	−	0.795789i	$-0.707056\pi$
$683$	10.0979	−	17.4901i	0.386387	−	0.669241i	0.991961	+	0.126548i	$0.0403897\pi$
$684$	−5.73600	+	5.73600i	−0.219322	+	0.219322i
$685$	−0.529541	−	8.40417i	−0.0202327	−	0.321107i
$686$	1.29181	−	0.745825i	0.0493214	−	0.0284757i
$687$	−10.0349	+	5.79363i	−0.382854	+	0.221041i
$688$	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	$0.657424\pi$
$692$	−5.52705	+	20.6272i	−0.210107	+	0.784129i
$693$	−10.4929	+	2.81155i	−0.398591	+	0.106802i
$694$	2.79502	+	2.79502i	0.106097	+	0.106097i
$695$	−0.816458	−	12.9577i	−0.0309700	−	0.491515i
$696$	−5.17428	+	1.38644i	−0.196130	+	0.0525530i
$697$			11.4120i			0.432259i
$698$	1.69053	+	6.30915i	0.0639876	+	0.238805i
$699$	−14.2982	−	24.7652i	−0.540808	−	0.936708i
$700$	2.31409	+	18.2902i	0.0874646	+	0.691304i
$701$			12.7429i			0.481293i	0.970613	+	0.240647i	$0.0773595\pi$
$701$			12.7429i			0.481293i	−0.970613	+	0.240647i	$0.922641\pi$
$702$	−1.58455	+	3.23870i	−0.0598051	+	0.122237i
$703$	−12.9938	+	12.9938i	−0.490069	+	0.490069i
$704$	0.762517	−	2.84575i	0.0287384	−	0.107253i
$705$	−26.1658	+	8.80850i	−0.985459	+	0.331747i
$706$	23.7777	+	13.7281i	0.894885	+	0.516662i
$707$	−29.0697			−1.09328
$708$	5.91114	+	3.41280i	0.222154	+	0.128261i
$709$	−2.41602	−	9.01670i	−0.0907355	−	0.338629i	0.905603	−	0.424126i	$-0.139419\pi$
$709$	−2.41602	−	9.01670i	−0.0907355	−	0.338629i	−0.996338	+	0.0854972i	$0.972752\pi$
$710$	5.25843	+	1.05977i	0.197345	+	0.0397724i
$711$	−5.40965	+	9.36978i	−0.202878	+	0.351394i
$712$	−9.57642	−	2.56600i	−0.358892	−	0.0961647i
$713$	15.2615	+	26.4338i	0.571549	+	0.989952i
$714$	−14.5040			−0.542798
$715$	23.5474	−	3.11470i	0.880624	−	0.116483i
$716$	−1.30390			−0.0487292
$717$	2.81769	+	4.88038i	0.105228	+	0.182261i
$718$	−3.47904	−	0.932207i	−0.129837	−	0.0347897i
$719$	−18.9523	+	32.8264i	−0.706802	+	1.22422i	0.259235	+	0.965814i	$0.416530\pi$
$719$	−18.9523	+	32.8264i	−0.706802	+	1.22422i	−0.966037	+	0.258403i	$0.916804\pi$
$720$	1.86235	−	1.23760i	0.0694058	−	0.0461225i
$721$	3.09329	+	11.5443i	0.115200	+	0.429933i
$722$	−40.5330	−	23.4017i	−1.50848	−	0.870923i
$723$	12.2563			0.455816
$724$	−12.6002	−	7.27474i	−0.468283	−	0.270363i
$725$	3.36194	+	26.5722i	0.124859	+	0.986866i
$726$	−0.600530	+	2.24121i	−0.0222878	+	0.0831790i
$727$	−8.59009	+	8.59009i	−0.318589	+	0.318589i	−0.848225	−	0.529636i	$-0.822328\pi$
$727$	−8.59009	+	8.59009i	−0.318589	+	0.318589i	0.529636	+	0.848225i	$0.322328\pi$
$728$	−10.0227	−	8.73423i	−0.371465	−	0.323712i
$729$			1.00000i			0.0370370i
$730$	8.62420	−	17.3774i	0.319196	−	0.643168i
$731$	7.44905	+	12.9021i	0.275513	+	0.477203i
$732$	−2.55412	−	9.53211i	−0.0944031	−	0.352317i
$733$		−	50.9118i		−	1.88047i	−0.340526	−	0.940235i	$-0.610605\pi$
$733$		−	50.9118i		−	1.88047i	0.340526	−	0.940235i	$-0.389395\pi$
$734$	11.6185	−	3.11318i	0.428848	−	0.114909i
$735$	9.75190	−	11.0635i	0.359704	−	0.408082i
$736$	5.18403	+	5.18403i	0.191086	+	0.191086i
$737$	37.3858	−	10.0175i	1.37712	−	0.368999i
$738$	−0.750873	+	2.80230i	−0.0276400	+	0.103154i
$739$	37.0613	+	9.93055i	1.36332	+	0.365301i	0.865035	−	0.501711i	$-0.167296\pi$
$739$	37.0613	+	9.93055i	1.36332	+	0.365301i	0.498287	+	0.867012i	$0.333963\pi$
$740$	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
$743$	−36.5195	+	21.0845i	−1.33977	+	0.773517i	−0.986773	−	0.162107i	$-0.948171\pi$
$743$	−36.5195	+	21.0845i	−1.33977	+	0.773517i	−0.352997	+	0.935624i	$0.614838\pi$
$744$	3.60559	−	2.08169i	0.132187	−	0.0763184i
$745$	−12.4059	−	10.9352i	−0.454515	−	0.400633i
$746$	21.6030	−	21.6030i	0.790941	−	0.790941i
$747$	−5.23229	+	9.06259i	−0.191439	+	0.331583i
$748$	5.79447	−	10.0363i	0.211867	−	0.366964i
$749$	−46.2459	+	46.2459i	−1.68979	+	1.68979i
$750$	−4.86888	−	10.0645i	−0.177786	−	0.367503i
$751$	−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	$0.492931\pi$
$752$	−10.6928	+	6.17348i	−0.389925	+	0.225124i
$753$	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
$757$	1.23449	−	4.60716i	0.0448681	−	0.167450i	−0.939856	−	0.341570i	$-0.889041\pi$
$757$	1.23449	−	4.60716i	0.0448681	−	0.167450i	0.984724	+	0.174120i	$0.0557080\pi$
$758$	−25.3124	+	6.78244i	−0.919389	+	0.246349i
$759$	15.2729	+	15.2729i	0.554370	+	0.554370i
$760$	13.6073	+	11.9941i	0.493588	+	0.435073i
$761$	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	$0.345047\pi$
$762$		−	13.8193i		−	0.500621i
$763$	8.70809	+	32.4991i	0.315254	+	1.17654i
$764$	5.91683	+	10.2482i	0.214063	+	0.370768i
$765$	8.33612	−	2.80629i	0.301393	−	0.101462i
$766$		−	20.8694i		−	0.754040i
$767$	1.68653	+	24.5522i	0.0608970	+	0.886527i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−13.6011	+	50.7601i	−0.490470	+	1.83046i	0.0635845	+	0.997976i	$0.479747\pi$
$769$	−13.6011	+	50.7601i	−0.490470	+	1.83046i	−0.554054	+	0.832481i	$0.686920\pi$
$770$	7.74983	+	23.0210i	0.279284	+	0.829618i
$771$	4.50589	+	2.60147i	0.162276	+	0.0936898i
$772$	−5.09170			−0.183254
$773$	6.99165	+	4.03663i	0.251472	+	0.145188i	0.620438	−	0.784255i	$-0.286955\pi$
$773$	6.99165	+	4.03663i	0.251472	+	0.145188i	−0.368966	+	0.929443i	$0.620288\pi$
$774$	0.980250	+	3.65834i	0.0352344	+	0.131496i
$775$	−7.86910	−	19.2723i	−0.282666	−	0.692280i
$776$	−1.60370	+	2.77769i	−0.0575694	+	0.0997132i
$777$	−8.06800	−	2.16181i	−0.289438	−	0.0775546i
$778$	9.58595	+	16.6034i	0.343673	+	0.595259i
$779$	−23.5340			−0.843191
$780$	7.45044	+	3.08075i	0.266768	+	0.110308i
$781$	7.06756			0.252897
$782$	14.4193	+	24.9749i	0.515632	+	0.893100i
$783$	−5.17428	−	1.38644i	−0.184914	−	0.0495474i
$784$	3.29773	−	5.71183i	0.117776	−	0.203994i
$785$	1.14295	−	5.67115i	0.0407936	−	0.202412i
$786$	−2.65881	−	9.92281i	−0.0948366	−	0.353935i
$787$	45.2450	+	26.1222i	1.61281	+	0.931157i	0.988715	+	0.149810i	$0.0478661\pi$
$787$	45.2450	+	26.1222i	1.61281	+	0.931157i	0.624096	+	0.781347i	$0.285467\pi$
$788$	−3.51883			−0.125353
$789$	−9.06162	−	5.23173i	−0.322602	−	0.186255i
$790$	21.6707	+	10.7549i	0.771008	+	0.382641i
$791$	7.76200	−	28.9682i	0.275985	−	1.02999i
$792$	2.08323	−	2.08323i	0.0740245	−	0.0740245i
$793$	23.3762	−	26.8245i	0.830112	−	0.952567i
$794$			9.97998i			0.354176i
$795$	2.69687	+	1.33842i	0.0956481	+	0.0474689i
$796$	6.19744	+	10.7343i	0.219662	+	0.380467i
$797$	−11.1091	−	41.4597i	−0.393504	−	1.46858i	−0.824313	−	0.566135i	$-0.808438\pi$
$797$	−11.1091	−	41.4597i	−0.393504	−	1.46858i	0.430809	−	0.902443i	$-0.358228\pi$
$798$		−	29.9103i		−	1.05881i
$799$	−46.9131	+	12.5703i	−1.65967	+	0.444706i
$800$	−3.02375	−	3.98208i	−0.106906	−	0.140788i
$801$	−7.01043	−	7.01043i	−0.247701	−	0.247701i
$802$	−10.3491	+	2.77303i	−0.365439	+	0.0979191i
$803$	6.61549	−	24.6893i	0.233455	−	0.871267i
$804$	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
$808$	6.82771	−	3.94198i	0.240198	−	0.138678i
$809$	−2.44761	+	1.41313i	−0.0860534	+	0.0496829i	−0.542409	−	0.840114i	$-0.682488\pi$
$809$	−2.44761	+	1.41313i	−0.0860534	+	0.0496829i	0.456356	+	0.889797i	$0.349154\pi$
$810$	2.23164	−	0.140614i	0.0784119	−	0.00494069i
$811$	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	$0.172015\pi$
$812$	9.87581	−	17.1054i	0.346573	−	0.600282i
$813$	2.52967	−	4.38152i	0.0887195	−	0.153667i
$814$	4.71914	−	4.71914i	0.165406	−	0.165406i
$815$	−38.1788	+	2.40562i	−1.33734	+	0.0842652i
$816$	3.40660	−	1.96680i	0.119255	−	0.0688518i
$817$	−26.6070	+	15.3615i	−0.930860	+	0.537433i
$818$	−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	$0.991791\pi$
$822$	0.974690	−	3.63759i	0.0339962	−	0.126876i
$823$	−5.35052	+	1.43367i	−0.186507	+	0.0499745i	−0.350864	−	0.936427i	$-0.614112\pi$
$823$	−5.35052	+	1.43367i	−0.186507	+	0.0499745i	0.164356	+	0.986401i	$0.447445\pi$
$824$	−2.29199	−	2.29199i	−0.0798453	−	0.0798453i
$825$	−8.90838	−	11.7318i	−0.310150	−	0.408447i
$826$	−24.3098	+	6.51379i	−0.845845	+	0.226644i
$827$			31.8131i			1.10625i	0.833098	+	0.553126i	$0.186565\pi$
$827$			31.8131i			1.10625i	−0.833098	+	0.553126i	$0.813435\pi$
$828$	1.89749	+	7.08152i	0.0659422	+	0.246100i
$829$	−5.52347	−	9.56694i	−0.191838	−	0.332274i	0.754021	−	0.656850i	$-0.228112\pi$
$829$	−5.52347	−	9.56694i	−0.191838	−	0.332274i	−0.945859	+	0.324577i	$0.894778\pi$
$830$	20.9602	+	10.4023i	0.727539	+	0.361068i
$831$		−	5.74753i		−	0.199380i
$832$	3.53846	+	0.692322i	0.122674	+	0.0240019i
$833$	18.3451	−	18.3451i	0.635620	−	0.635620i
$834$	1.50280	−	5.60852i	0.0520376	−	0.194207i
$835$	4.59699	+	2.28142i	0.159085	+	0.0789519i
$836$	20.6970	+	11.9494i	0.715822	+	0.413280i
$837$	4.16338			0.143907
$838$	−4.96010	−	2.86371i	−0.171344	−	0.0989253i
$839$	−7.14130	−	26.6517i	−0.246545	−	0.920118i	−0.972601	−	0.232482i	$-0.925315\pi$
$839$	−7.14130	−	26.6517i	−0.246545	−	0.920118i	0.726056	−	0.687636i	$-0.241351\pi$
$840$	−1.62889	+	8.08233i	−0.0562020	+	0.278867i
$841$	−0.152327	+	0.263838i	−0.00525266	+	0.00909787i
$842$	−33.6779	−	9.02397i	−1.16062	−	0.310986i
$843$	−12.7108	−	22.0158i	−0.437784	−	0.758264i
$844$	26.8316			0.923583
$845$	5.77777	+	28.4889i	0.198761	+	0.980048i
$846$	−12.3470			−0.424497
$847$	−4.27765	−	7.40911i	−0.146982	−	0.254580i
$848$	1.30056	+	0.348484i	0.0446614	+	0.0119670i
$849$	−4.58770	+	7.94612i	−0.157449	+	0.272710i
$850$	−7.43481	−	18.2086i	−0.255012	−	0.624551i
$851$	4.29837	+	16.0417i	0.147346	+	0.549904i
$852$	2.07753	+	1.19946i	0.0711750	+	0.0410929i
$853$	4.04387			0.138460			0.0692298	−	0.997601i	$-0.477946\pi$
$853$	4.04387			0.138460			0.0692298	+	0.997601i	$0.477946\pi$
$854$	31.5118	+	18.1933i	1.07831	+	0.622563i
$855$	5.78717	+	17.1909i	0.197917	+	0.587915i
$856$	4.59079	−	17.1331i	0.156910	−	0.585597i
$857$	6.00540	−	6.00540i	0.205141	−	0.205141i	−0.597058	−	0.802198i	$-0.703664\pi$
$857$	6.00540	−	6.00540i	0.205141	−	0.205141i	0.802198	+	0.597058i	$0.203664\pi$
$858$	10.4248	+	2.03968i	0.355896	+	0.0696334i
$859$			14.6934i			0.501332i	0.968074	+	0.250666i	$0.0806496\pi$
$859$			14.6934i			0.501332i	−0.968074	+	0.250666i	$0.919350\pi$
$860$	8.02627	−	2.70198i	0.273694	−	0.0921368i
$861$	−5.34857	−	9.26399i	−0.182279	−	0.315716i
$862$	−1.26549	−	4.72288i	−0.0431028	−	0.160862i
$863$			37.9938i			1.29332i	0.762777	+	0.646662i	$0.223836\pi$
$863$			37.9938i			1.29332i	−0.762777	+	0.646662i	$0.776164\pi$
$864$	0.965926	−	0.258819i	0.0328615	−	0.00880520i
$865$	35.8215	+	31.5749i	1.21797	+	1.07358i
$866$	−2.90093	−	2.90093i	−0.0985774	−	0.0985774i
$867$	−1.47475	+	0.395158i	−0.0500852	+	0.0134203i
$868$	−3.97318	+	14.8281i	−0.134859	+	0.503299i
$869$	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
$873$	−2.77769	+	1.60370i	−0.0940105	+	0.0542770i
$874$	−51.5036	+	29.7356i	−1.74214	+	1.00582i
$875$	38.9350	+	13.5462i	1.31624	+	0.457946i
$876$	6.13476	−	6.13476i	0.207274	−	0.207274i
$877$	26.7231	−	46.2858i	0.902375	−	1.56296i	0.0779723	−	0.996956i	$-0.475155\pi$
$877$	26.7231	−	46.2858i	0.902375	−	1.56296i	0.824403	−	0.566004i	$-0.191511\pi$
$878$	−0.444561	+	0.770002i	−0.0150032	+	0.0259863i
$879$	7.87710	−	7.87710i	0.265688	−	0.265688i
$880$	−4.94197	−	4.35610i	−0.166594	−	0.146844i
$881$	−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	$0.478535\pi$
$882$	5.71183	−	3.29773i	0.192327	−	0.111040i
$883$	2.17489	+	2.17489i	0.0731907	+	0.0731907i	0.742755	−	0.669564i	$-0.233519\pi$
$883$	2.17489	+	2.17489i	0.0731907	+	0.0731907i	−0.669564	+	0.742755i	$0.733519\pi$
$884$	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
$887$	−9.39478	+	35.0618i	−0.315446	+	1.17726i	0.608128	+	0.793839i	$0.291921\pi$
$887$	−9.39478	+	35.0618i	−0.315446	+	1.17726i	−0.923574	+	0.383421i	$0.874746\pi$
$888$	2.18811	−	0.586302i	0.0734281	−	0.0196750i
$889$	36.0303	+	36.0303i	1.20842	+	1.20842i
$890$	−14.6590	+	16.6305i	−0.491371	+	0.557457i
$891$	2.84575	−	0.762517i	0.0953362	−	0.0255453i
$892$		−	25.1190i		−	0.841046i
$893$	−25.9227	−	96.7449i	−0.867471	−	3.23744i
$894$	−3.69786	−	6.40487i	−0.123675	−	0.214211i
$895$	−1.29614	+	2.61167i	−0.0433252	+	0.0872987i
$896$			3.68720i			0.123181i
$897$	−17.3664	+	19.9283i	−0.579848	+	0.665385i
$898$	8.72302	−	8.72302i	0.291091	−	0.291091i
$899$	−5.77228	+	21.5425i	−0.192516	+	0.718481i
$900$	−0.627602	−	4.96046i	−0.0209201	−	0.165349i
$901$	4.58677	+	2.64818i	0.152808	+	0.0882235i
$902$	8.54719			0.284590
$903$	−12.0939	−	6.98244i	−0.402461	−	0.232361i
$904$	2.10512	+	7.85641i	0.0700152	+	0.261300i
$905$	−27.0962	+	18.0064i	−0.900710	+	0.598552i
$906$	−3.18434	+	5.51545i	−0.105793	+	0.183238i
$907$	7.17611	+	1.92283i	0.238279	+	0.0638466i	0.375982	−	0.926627i	$-0.377305\pi$
$907$	7.17611	+	1.92283i	0.238279	+	0.0638466i	−0.137703	+	0.990474i	$0.543972\pi$
$908$	−9.03882	−	15.6557i	−0.299964	−	0.519552i
$909$	7.88396			0.261494
$910$	−27.4574	+	11.3929i	−0.910203	+	0.377669i
$911$	−41.1547			−1.36352			−0.681759	−	0.731577i	$-0.738785\pi$
$911$	−41.1547			−1.36352			−0.681759	+	0.731577i	$0.738785\pi$
$912$	4.05597	+	7.02514i	0.134306	+	0.232626i
$913$	29.7796	+	7.97942i	0.985560	+	0.264080i
$914$	9.04457	−	15.6657i	0.299168	−	0.518174i
$915$	−21.6314	−	4.35953i	−0.715112	−	0.144122i
$916$	2.99901	+	11.1924i	0.0990899	+	0.369809i
$917$	32.8034	+	18.9390i	1.08326	+	0.625422i
$918$	3.93360			0.129828
$919$	−2.96561	−	1.71220i	−0.0978264	−	0.0564801i	0.450289	−	0.892883i	$-0.351321\pi$
$919$	−2.96561	−	1.71220i	−0.0978264	−	0.0564801i	−0.548115	+	0.836403i	$0.684654\pi$
$920$	15.5366	−	5.23028i	0.512227	−	0.172437i
$921$	8.24450	−	30.7689i	0.271665	−	1.01387i
$922$	11.9116	−	11.9116i	0.392288	−	0.392288i
$923$	0.592747	+	8.62911i	0.0195105	+	0.284031i
$924$			10.8630i			0.357367i
$925$	−1.42171	−	11.2369i	−0.0467454	−	0.369467i
$926$	−4.07481	−	7.05778i	−0.133907	−	0.231933i
$927$	−0.838927	−	3.13092i	−0.0275540	−	0.102833i
$928$			5.35680i			0.175846i
$929$	24.8807	−	6.66677i	0.816310	−	0.218730i	0.173578	−	0.984820i	$-0.444467\pi$
$929$	24.8807	−	6.66677i	0.816310	−	0.218730i	0.642733	+	0.766091i	$0.277801\pi$
$930$	−0.585431	−	9.29117i	−0.0191970	−	0.304669i
$931$	37.8315	+	37.8315i	1.23988	+	1.23988i
$932$	−27.6220	+	7.40130i	−0.904790	+	0.242438i
$933$	−2.50905	+	9.36392i	−0.0821427	+	0.306561i
$934$	−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	0.250965	−	0.967996i	$-0.419252\pi$
$937$	−21.9487	−	21.9487i	−0.717031	−	0.717031i	−0.967996	+	0.250965i	$0.919252\pi$
$938$	−41.9505	+	24.2202i	−1.36973	+	0.790816i
$939$	−14.8328	+	8.56371i	−0.484050	+	0.279466i
$940$	1.73616	+	27.5540i	0.0566273	+	0.898712i
$941$	−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	$0.335745\pi$
$942$	1.29361	−	2.24059i	0.0421480	−	0.0730024i
$943$	−10.6346	+	18.4197i	−0.346312	+	0.599829i
$944$	4.82642	−	4.82642i	0.157087	−	0.157087i
$945$	−5.45182	+	6.18505i	−0.177348	+	0.201200i
$946$	9.66327	−	5.57909i	0.314180	−	0.181392i
$947$	0.715640	−	0.413175i	0.0232552	−	0.0134264i	−0.488327	−	0.872661i	$-0.662393\pi$
$947$	0.715640	−	0.413175i	0.0232552	−	0.0134264i	0.511583	+	0.859234i	$0.329059\pi$
$948$	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
$952$	−3.75391	+	14.0098i	−0.121665	+	0.454059i
$953$	42.9151	−	11.4991i	1.39016	−	0.372492i	0.515357	−	0.856975i	$-0.327659\pi$
$953$	42.9151	−	11.4991i	1.39016	−	0.372492i	0.874800	+	0.484484i	$0.160993\pi$
$954$	0.952075	+	0.952075i	0.0308246	+	0.0308246i
$955$	26.4085	−	1.66398i	0.854558	−	0.0538452i
$956$	5.44335	−	1.45854i	0.176051	−	0.0471726i
$957$			15.7819i			0.510156i
$958$	−0.731362	−	2.72948i	−0.0236292	−	0.0881855i
$959$	6.94284	+	12.0253i	0.224196	+	0.388319i
$960$	−0.713415	−	2.11921i	−0.0230254	−	0.0683971i
$961$			13.6663i			0.440848i
$962$	6.15761	+	5.36603i	0.198529	+	0.173008i
$963$	12.5423	−	12.5423i	0.404169	−	0.404169i
$964$	3.17216	−	11.8387i	0.102168	−	0.381298i
$965$	−5.06138	+	10.1985i	−0.162932	+	0.328302i
$966$	−23.4105	−	13.5160i	−0.753219	−	0.434871i
$967$	−16.8946			−0.543295			−0.271647	−	0.962397i	$-0.587568\pi$
$967$	−16.8946			−0.543295			−0.271647	+	0.962397i	$0.587568\pi$
$968$	2.00941	+	1.16013i	0.0645850	+	0.0372881i
$969$	8.25869	+	30.8218i	0.265307	+	0.990140i
$970$	3.96947	+	5.97330i	0.127452	+	0.191791i
$971$	−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	$0.832120\pi$
$972$	0.965926	+	0.258819i	0.0309821	+	0.00830162i
$973$	10.7046	+	18.5409i	0.343174	+	0.594395i
$974$	−12.2427			−0.392282
$975$	13.5767	−	11.8606i	0.434802	−	0.379842i
$976$	−9.86837			−0.315879
$977$	7.47231	+	12.9424i	0.239060	+	0.414065i	0.960445	−	0.278470i	$-0.0898273\pi$
$977$	7.47231	+	12.9424i	0.239060	+	0.414065i	−0.721385	+	0.692535i	$0.756494\pi$
$978$	−16.5250	−	4.42786i	−0.528411	−	0.141587i
$979$	−14.6044	+	25.2955i	−0.466758	+	0.808448i
$980$	−8.16251	−	12.2831i	−0.260742	−	0.392368i
$981$	−2.36171	−	8.81402i	−0.0754036	−	0.281410i
$982$	29.4491	+	17.0024i	0.939758	+	0.542570i
$983$	−26.7656			−0.853689			−0.426844	−	0.904325i	$-0.640375\pi$
$983$	−26.7656			−0.853689			−0.426844	+	0.904325i	$0.640375\pi$
$984$	2.51247	+	1.45058i	0.0800947	+	0.0462427i
$985$	−3.49788	+	7.04810i	−0.111452	+	0.224571i
$986$	−5.45371	+	20.3535i	−0.173682	+	0.648189i
$987$	32.1915	−	32.1915i	1.02467	−	1.02467i
$988$	−12.8538	+	26.2721i	−0.408933	+	0.835828i
$989$			27.7666i			0.882927i
$990$	−2.10182	−	6.24348i	−0.0668002	−	0.198431i
$991$	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	$0.614576\pi$
$992$	−1.07756	−	4.02151i	−0.0342126	−	0.127683i
$993$		−	26.9672i		−	0.855778i
$994$	−8.54392	+	2.28934i	−0.270997	+	0.0726133i
$995$	27.6609	−	1.74290i	0.876911	−	0.0552536i
$996$	7.39957	+	7.39957i	0.234464	+	0.234464i
$997$	55.9256	−	14.9852i	1.77118	−	0.474586i	0.782250	−	0.622965i	$-0.214072\pi$
$997$	55.9256	−	14.9852i	1.77118	−	0.474586i	0.988931	+	0.148378i	$0.0474054\pi$
$998$	4.94192	−	18.4435i	0.156434	−	0.583819i
$999$	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.bn.c.67.4	yes	32
5.3	odd	4		390.2.bd.c.223.5	yes	32
13.7	odd	12		390.2.bd.c.7.5	✓	32
65.33	even	12	inner	390.2.bn.c.163.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.c.7.5	✓	32	13.7	odd	12
390.2.bd.c.223.5	yes	32	5.3	odd	4
390.2.bn.c.67.4	yes	32	1.1	even	1	trivial
390.2.bn.c.163.4	yes	32	65.33	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.23760 + 1.86235i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-3.19321 - 1.84360i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.23760 + 1.86235i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-3.19321 - 1.84360i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +(0.994046 - 2.00297i) q^{10} +(0.762517 - 2.84575i) q^{11} +(0.707107 - 0.707107i) q^{12} +(3.53846 + 0.692322i) q^{13} +3.68720i q^{14} +(-0.713415 - 2.11921i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.01809 - 3.79957i) q^{17} -1.00000i q^{18} +(7.83553 - 2.09952i) q^{19} +(-2.23164 + 0.140614i) q^{20} +(2.60724 + 2.60724i) q^{21} +(-2.84575 + 0.762517i) q^{22} +(1.89749 - 7.08152i) 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} +(3.19321 - 1.84360i) q^{28} +(4.63913 - 2.67840i) q^{29} +(-1.47858 + 1.67744i) q^{30} +(-2.94395 + 2.94395i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.47307 + 2.55143i) q^{33} +(-2.78148 + 2.78148i) q^{34} +(-0.518473 - 8.22851i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-1.96180 + 1.13265i) 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} +(0.954318 - 3.56156i) q^{42} +(-3.65834 + 0.980250i) q^{43} +(2.08323 + 2.08323i) q^{44} +(0.140614 + 2.23164i) q^{45} +(-7.08152 + 1.89749i) q^{46} -12.3470i q^{47} +(0.258819 + 0.965926i) q^{48} +(3.29773 + 5.71183i) q^{49} +(4.96046 - 0.627602i) q^{50} +3.93360i q^{51} +(-2.36880 + 2.71823i) q^{52} +(-0.952075 + 0.952075i) q^{53} +(-0.258819 + 0.965926i) q^{54} +(6.24348 - 2.10182i) q^{55} +(-3.19321 - 1.84360i) q^{56} -8.11193 q^{57} +(-4.63913 - 2.67840i) q^{58} +(1.76659 + 6.59302i) q^{59} +(2.19199 + 0.441768i) q^{60} +(4.93418 - 8.54626i) q^{61} +(4.02151 + 1.07756i) q^{62} +(-1.84360 - 3.19321i) q^{63} +1.00000 q^{64} +(3.08984 + 7.44667i) q^{65} +2.94614 q^{66} +(6.56871 + 11.3773i) q^{67} +(3.79957 + 1.01809i) q^{68} +(-3.66566 + 6.34911i) q^{69} +(-6.86687 + 4.56327i) q^{70} +(0.620887 + 2.31718i) q^{71} +(0.866025 + 0.500000i) q^{72} +8.67586 q^{73} +(1.96180 + 1.13265i) q^{74} +(3.06379 - 3.95135i) q^{75} +(-2.09952 + 7.83553i) q^{76} +(-7.68130 + 7.68130i) q^{77} +(0.247089 + 3.59707i) q^{78} +10.8193i q^{79} +(0.994046 - 2.00297i) q^{80} +(0.500000 + 0.866025i) q^{81} +(0.750873 + 2.80230i) q^{82} +10.4646i q^{83} +(-3.56156 + 0.954318i) q^{84} +(5.81615 - 6.59838i) q^{85} +(2.67809 + 2.67809i) q^{86} +(-5.17428 + 1.38644i) q^{87} +(0.762517 - 2.84575i) 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} +(3.60559 - 2.08169i) q^{93} +(-10.6928 + 6.17348i) q^{94} +(13.6073 + 11.9941i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-1.60370 + 2.77769i) q^{97} +(3.29773 - 5.71183i) q^{98} +(2.08323 - 2.08323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8	\( 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8} - 4 q^{11} + 8 q^{13} - 4 q^{15} - 16 q^{16} - 4 q^{17} + 20 q^{19} + 8 q^{21} + 8 q^{22} - 16 q^{23} - 8 q^{25} - 4 q^{26} + 12 q^{28} + 24 q^{29} + 8 q^{30} + 12 q^{31} - 16 q^{32} - 16 q^{34} + 12 q^{35} - 24 q^{37} - 4 q^{38} - 20 q^{39} - 28 q^{41} - 16 q^{42} + 4 q^{43} - 4 q^{44} - 4 q^{46} + 20 q^{49} - 8 q^{50} - 4 q^{52} - 4 q^{53} + 68 q^{55} - 12 q^{56} + 16 q^{57} - 24 q^{58} + 36 q^{59} - 4 q^{60} - 28 q^{61} - 48 q^{62} + 32 q^{64} - 28 q^{65} - 28 q^{67} + 20 q^{68} - 20 q^{69} - 24 q^{70} - 4 q^{71} - 48 q^{73} + 24 q^{74} + 24 q^{75} - 16 q^{76} + 20 q^{77} + 4 q^{78} + 16 q^{81} + 44 q^{82} + 8 q^{84} + 64 q^{85} - 8 q^{86} + 20 q^{87} - 4 q^{88} - 16 q^{89} - 40 q^{91} + 20 q^{92} - 24 q^{93} - 24 q^{94} + 68 q^{95} + 8 q^{97} + 20 q^{98} - 4 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8 - 4 * q^11 + 8 * q^13 - 4 * q^15 - 16 * q^16 - 4 * q^17 + 20 * q^19 + 8 * q^21 + 8 * q^22 - 16 * q^23 - 8 * q^25 - 4 * q^26 + 12 * q^28 + 24 * q^29 + 8 * q^30 + 12 * q^31 - 16 * q^32 - 16 * q^34 + 12 * q^35 - 24 * q^37 - 4 * q^38 - 20 * q^39 - 28 * q^41 - 16 * q^42 + 4 * q^43 - 4 * q^44 - 4 * q^46 + 20 * q^49 - 8 * q^50 - 4 * q^52 - 4 * q^53 + 68 * q^55 - 12 * q^56 + 16 * q^57 - 24 * q^58 + 36 * q^59 - 4 * q^60 - 28 * q^61 - 48 * q^62 + 32 * q^64 - 28 * q^65 - 28 * q^67 + 20 * q^68 - 20 * q^69 - 24 * q^70 - 4 * q^71 - 48 * q^73 + 24 * q^74 + 24 * q^75 - 16 * q^76 + 20 * q^77 + 4 * q^78 + 16 * q^81 + 44 * q^82 + 8 * q^84 + 64 * q^85 - 8 * q^86 + 20 * q^87 - 4 * q^88 - 16 * q^89 - 40 * q^91 + 20 * q^92 - 24 * q^93 - 24 * q^94 + 68 * q^95 + 8 * q^97 + 20 * q^98 - 4 * q^99

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