LMFDB - Embedded newform 390.2.bn.c.67.8

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			67.8
Character	$\chi$	$=$	390.67
Dual form			390.2.bn.c.163.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.04880 - 0.895783i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-1.39412 - 0.804897i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.04880 - 0.895783i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-1.39412 - 0.804897i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +(-1.80017 - 1.32642i) q^{10} +(0.837189 - 3.12443i) q^{11} +(-0.707107 + 0.707107i) q^{12} +(-0.932870 - 3.48278i) q^{13} +1.60979i q^{14} +(2.21083 - 0.334992i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.84812 + 6.89728i) q^{17} -1.00000i q^{18} +(5.04898 - 1.35287i) q^{19} +(-0.248628 + 2.22220i) q^{20} +(-1.13830 - 1.13830i) q^{21} +(-3.12443 + 0.837189i) q^{22} +(0.676432 - 2.52448i) q^{23} +(0.965926 + 0.258819i) q^{24} +(3.39515 - 3.67056i) q^{25} +(-2.54974 + 2.54928i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.39412 - 0.804897i) q^{28} +(-4.32052 + 2.49445i) q^{29} +(-1.39553 - 1.74714i) q^{30} +(3.38960 - 3.38960i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.61732 - 2.80129i) q^{33} +(5.04916 - 5.04916i) q^{34} +(-3.57729 - 0.400240i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-8.67879 + 5.01070i) q^{37} +(-3.69611 - 3.69611i) q^{38} +(0.000325957 - 3.60555i) q^{39} +(2.04880 - 0.895783i) q^{40} +(3.37590 + 0.904570i) q^{41} +(-0.416645 + 1.55494i) q^{42} +(4.42768 - 1.18639i) q^{43} +(2.28724 + 2.28724i) q^{44} +(2.22220 + 0.248628i) q^{45} +(-2.52448 + 0.676432i) q^{46} +0.302237i q^{47} +(-0.258819 - 0.965926i) q^{48} +(-2.20428 - 3.81793i) q^{49} +(-4.87637 - 1.10501i) q^{50} +7.14059i q^{51} +(3.48261 + 0.933500i) q^{52} +(-6.71181 + 6.71181i) q^{53} +(0.258819 - 0.965926i) q^{54} +(-1.08358 - 7.15127i) q^{55} +(-1.39412 - 0.804897i) q^{56} +5.22708 q^{57} +(4.32052 + 2.49445i) q^{58} +(1.67964 + 6.26852i) q^{59} +(-0.815305 + 2.08213i) q^{60} +(-0.840772 + 1.45626i) q^{61} +(-4.63027 - 1.24068i) q^{62} +(-0.804897 - 1.39412i) q^{63} +1.00000 q^{64} +(-5.03108 - 6.29986i) q^{65} -3.23465 q^{66} +(-5.61225 - 9.72071i) q^{67} +(-6.89728 - 1.84812i) q^{68} +(1.30677 - 2.26339i) q^{69} +(1.44202 + 3.29814i) q^{70} +(0.465764 + 1.73825i) q^{71} +(0.866025 + 0.500000i) q^{72} -9.67009 q^{73} +(8.67879 + 5.01070i) q^{74} +(4.22947 - 2.66676i) q^{75} +(-1.35287 + 5.04898i) q^{76} +(-3.68199 + 3.68199i) q^{77} +(-3.12266 + 1.80249i) q^{78} +11.7501i q^{79} +(-1.80017 - 1.32642i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.904570 - 3.37590i) q^{82} +13.9992i q^{83} +(1.55494 - 0.416645i) q^{84} +(9.96489 + 12.4756i) q^{85} +(-3.24129 - 3.24129i) q^{86} +(-4.81891 + 1.29122i) q^{87} +(0.837189 - 3.12443i) q^{88} +(13.4808 + 3.61218i) q^{89} +(-0.895783 - 2.04880i) q^{90} +(-1.50274 + 5.60628i) q^{91} +(1.84805 + 1.84805i) q^{92} +(4.15139 - 2.39681i) q^{93} +(0.261745 - 0.151118i) q^{94} +(9.13246 - 7.29454i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(-3.45811 + 5.98962i) q^{97} +(-2.20428 + 3.81793i) q^{98} +(2.28724 - 2.28724i) 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
$5$	2.04880	−	0.895783i	0.916250	−	0.400606i
$5$	2.04880	−	0.895783i	0.916250	−	0.400606i
$6$	−0.258819	−	0.965926i	−0.105662	−	0.394338i
$7$	−1.39412	−	0.804897i	−0.526929	−	0.304222i	0.212836	−	0.977088i	$-0.431730\pi$
$7$	−1.39412	−	0.804897i	−0.526929	−	0.304222i	−0.739765	+	0.672866i	$0.765063\pi$
$8$	1.00000			0.353553
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	−1.80017	−	1.32642i	−0.569264	−	0.419451i
$11$	0.837189	−	3.12443i	0.252422	−	0.942051i	−0.717085	−	0.696986i	$-0.754524\pi$
$11$	0.837189	−	3.12443i	0.252422	−	0.942051i	0.969507	−	0.245065i	$-0.0788094\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−0.932870	−	3.48278i	−0.258732	−	0.965949i
$13$	−0.932870	−	3.48278i	−0.258732	−	0.965949i
$14$			1.60979i			0.430235i
$15$	2.21083	−	0.334992i	0.570835	−	0.0864945i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.84812	+	6.89728i	0.448235	+	1.67284i	0.707251	+	0.706963i	$0.249935\pi$
$17$	1.84812	+	6.89728i	0.448235	+	1.67284i	−0.259016	+	0.965873i	$0.583398\pi$
$18$		−	1.00000i		−	0.235702i
$19$	5.04898	−	1.35287i	1.15831	−	0.310369i	0.372022	−	0.928224i	$-0.378665\pi$
$19$	5.04898	−	1.35287i	1.15831	−	0.310369i	0.786292	+	0.617854i	$0.211998\pi$
$20$	−0.248628	+	2.22220i	−0.0555950	+	0.496900i
$21$	−1.13830	−	1.13830i	−0.248396	−	0.248396i
$22$	−3.12443	+	0.837189i	−0.666131	+	0.178489i
$23$	0.676432	−	2.52448i	0.141046	−	0.526390i	−0.858854	−	0.512221i	$-0.828823\pi$
$23$	0.676432	−	2.52448i	0.141046	−	0.526390i	0.999900	−	0.0141693i	$-0.00451039\pi$
$24$	0.965926	+	0.258819i	0.197169	+	0.0528312i
$25$	3.39515	−	3.67056i	0.679029	−	0.734111i
$26$	−2.54974	+	2.54928i	−0.500045	+	0.499955i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	1.39412	−	0.804897i	0.263464	−	0.152111i
$29$	−4.32052	+	2.49445i	−0.802300	+	0.463208i	−0.844275	−	0.535911i	$-0.819968\pi$
$29$	−4.32052	+	2.49445i	−0.802300	+	0.463208i	0.0419749	+	0.999119i	$0.486635\pi$
$30$	−1.39553	−	1.74714i	−0.254787	−	0.318983i
$31$	3.38960	−	3.38960i	0.608789	−	0.608789i	−0.333840	−	0.942630i	$-0.608345\pi$
$31$	3.38960	−	3.38960i	0.608789	−	0.608789i	0.942630	+	0.333840i	$0.108345\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.61732	−	2.80129i	0.281540	−	0.487642i
$34$	5.04916	−	5.04916i	0.865924	−	0.865924i
$35$	−3.57729	−	0.400240i	−0.604672	−	0.0676530i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	−8.67879	+	5.01070i	−1.42678	+	0.823754i	−0.996866	−	0.0791138i	$-0.974791\pi$
$37$	−8.67879	+	5.01070i	−1.42678	+	0.823754i	−0.429918	+	0.902868i	$0.641458\pi$
$38$	−3.69611	−	3.69611i	−0.599588	−	0.599588i
$39$	0.000325957	−	3.60555i	5.21949e−5	−	0.577350i
$40$	2.04880	−	0.895783i	0.323943	−	0.141636i
$41$	3.37590	+	0.904570i	0.527227	+	0.141270i	0.512607	−	0.858623i	$-0.328680\pi$
$41$	3.37590	+	0.904570i	0.527227	+	0.141270i	0.0146195	+	0.999893i	$0.495346\pi$
$42$	−0.416645	+	1.55494i	−0.0642897	+	0.239933i
$43$	4.42768	−	1.18639i	0.675215	−	0.180923i	0.0951120	−	0.995467i	$-0.469679\pi$
$43$	4.42768	−	1.18639i	0.675215	−	0.180923i	0.580103	+	0.814543i	$0.303012\pi$
$44$	2.28724	+	2.28724i	0.344815	+	0.344815i
$45$	2.22220	+	0.248628i	0.331266	+	0.0370633i
$46$	−2.52448	+	0.676432i	−0.372214	+	0.0997345i
$47$			0.302237i			0.0440858i	0.999757	+	0.0220429i	$0.00701704\pi$
$47$			0.302237i			0.0440858i	−0.999757	+	0.0220429i	$0.992983\pi$
$48$	−0.258819	−	0.965926i	−0.0373573	−	0.139419i
$49$	−2.20428	−	3.81793i	−0.314898	−	0.545419i
$50$	−4.87637	−	1.10501i	−0.689623	−	0.156271i
$51$			7.14059i			0.999882i
$52$	3.48261	+	0.933500i	0.482951	+	0.129453i
$53$	−6.71181	+	6.71181i	−0.921938	+	0.921938i	−0.997166	−	0.0752287i	$-0.976031\pi$
$53$	−6.71181	+	6.71181i	−0.921938	+	0.921938i	0.0752287	+	0.997166i	$0.476031\pi$
$54$	0.258819	−	0.965926i	0.0352208	−	0.131446i
$55$	−1.08358	−	7.15127i	−0.146110	−	0.964277i
$56$	−1.39412	−	0.804897i	−0.186297	−	0.107559i
$57$	5.22708			0.692344
$58$	4.32052	+	2.49445i	0.567312	+	0.327538i
$59$	1.67964	+	6.26852i	0.218671	+	0.816092i	0.984842	+	0.173455i	$0.0554930\pi$
$59$	1.67964	+	6.26852i	0.218671	+	0.816092i	−0.766171	+	0.642637i	$0.777840\pi$
$60$	−0.815305	+	2.08213i	−0.105255	+	0.268802i
$61$	−0.840772	+	1.45626i	−0.107650	+	0.186455i	−0.914818	−	0.403867i	$-0.867666\pi$
$61$	−0.840772	+	1.45626i	−0.107650	+	0.186455i	0.807168	+	0.590322i	$0.200999\pi$
$62$	−4.63027	−	1.24068i	−0.588045	−	0.157566i
$63$	−0.804897	−	1.39412i	−0.101407	−	0.175643i
$64$	1.00000			0.125000
$65$	−5.03108	−	6.29986i	−0.624028	−	0.781402i
$66$	−3.23465			−0.398158
$67$	−5.61225	−	9.72071i	−0.685646	−	1.18757i	−0.973233	−	0.229819i	$-0.926187\pi$
$67$	−5.61225	−	9.72071i	−0.685646	−	1.18757i	0.287588	−	0.957754i	$-0.407147\pi$
$68$	−6.89728	−	1.84812i	−0.836418	−	0.224118i
$69$	1.30677	−	2.26339i	0.157316	−	0.272480i
$70$	1.44202	+	3.29814i	0.172355	+	0.394203i
$71$	0.465764	+	1.73825i	0.0552760	+	0.206293i	0.988041	−	0.154193i	$-0.0492777\pi$
$71$	0.465764	+	1.73825i	0.0552760	+	0.206293i	−0.932765	+	0.360486i	$0.882611\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−9.67009			−1.13180			−0.565899	−	0.824474i	$-0.691471\pi$
$73$	−9.67009			−1.13180			−0.565899	+	0.824474i	$0.691471\pi$
$74$	8.67879	+	5.01070i	1.00889	+	0.582482i
$75$	4.22947	−	2.66676i	0.488377	−	0.307930i
$76$	−1.35287	+	5.04898i	−0.155185	+	0.579157i
$77$	−3.68199	+	3.68199i	−0.419601	+	0.419601i
$78$	−3.12266	+	1.80249i	−0.353572	+	0.204092i
$79$			11.7501i			1.32199i	0.750388	+	0.660997i	$0.229867\pi$
$79$			11.7501i			1.32199i	−0.750388	+	0.660997i	$0.770133\pi$
$80$	−1.80017	−	1.32642i	−0.201265	−	0.148298i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−0.904570	−	3.37590i	−0.0998930	−	0.372806i
$83$			13.9992i			1.53661i	0.640083	+	0.768306i	$0.278900\pi$
$83$			13.9992i			1.53661i	−0.640083	+	0.768306i	$0.721100\pi$
$84$	1.55494	−	0.416645i	0.169658	−	0.0454597i
$85$	9.96489	+	12.4756i	1.08084	+	1.35317i
$86$	−3.24129	−	3.24129i	−0.349517	−	0.349517i
$87$	−4.81891	+	1.29122i	−0.516641	+	0.138434i
$88$	0.837189	−	3.12443i	0.0892446	−	0.333065i
$89$	13.4808	+	3.61218i	1.42897	+	0.382890i	0.888655	−	0.458576i	$-0.151640\pi$
$89$	13.4808	+	3.61218i	1.42897	+	0.382890i	0.540310	+	0.841466i	$0.318307\pi$
$90$	−0.895783	−	2.04880i	−0.0944238	−	0.215962i
$91$	−1.50274	+	5.60628i	−0.157530	+	0.587698i
$92$	1.84805	+	1.84805i	0.192672	+	0.192672i
$93$	4.15139	−	2.39681i	0.430479	−	0.248537i
$94$	0.261745	−	0.151118i	0.0269969	−	0.0155867i
$95$	9.13246	−	7.29454i	0.936970	−	0.748404i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	−3.45811	+	5.98962i	−0.351118	+	0.608154i	−0.986446	−	0.164089i	$-0.947532\pi$
$97$	−3.45811	+	5.98962i	−0.351118	+	0.608154i	0.635328	+	0.772242i	$0.280865\pi$
$98$	−2.20428	+	3.81793i	−0.222666	+	0.385669i
$99$	2.28724	−	2.28724i	0.229876	−	0.229876i
$100$	1.48122	+	4.77556i	0.148122	+	0.477556i
$101$	−10.5683	+	6.10159i	−1.05158	+	0.607131i	−0.923092	−	0.384580i	$-0.874346\pi$
$101$	−10.5683	+	6.10159i	−1.05158	+	0.607131i	−0.128490	+	0.991711i	$0.541013\pi$
$102$	6.18393	−	3.57029i	0.612300	−	0.353512i
$103$	2.69782	+	2.69782i	0.265824	+	0.265824i	0.827415	−	0.561591i	$-0.189811\pi$
$103$	2.69782	+	2.69782i	0.265824	+	0.265824i	−0.561591	+	0.827415i	$0.689811\pi$
$104$	−0.932870	−	3.48278i	−0.0914755	−	0.341515i
$105$	−3.35180	−	1.31247i	−0.327103	−	0.128084i
$106$	9.16850	+	2.45669i	0.890523	+	0.238615i
$107$	−3.52356	+	13.1501i	−0.340635	+	1.27127i	0.556994	+	0.830517i	$0.311955\pi$
$107$	−3.52356	+	13.1501i	−0.340635	+	1.27127i	−0.897629	+	0.440751i	$0.854712\pi$
$108$	−0.965926	+	0.258819i	−0.0929463	+	0.0249049i
$109$	11.2429	+	11.2429i	1.07688	+	1.07688i	0.996788	+	0.0800905i	$0.0255209\pi$
$109$	11.2429	+	11.2429i	1.07688	+	1.07688i	0.0800905	+	0.996788i	$0.474479\pi$
$110$	−5.65139	+	4.51404i	−0.538839	+	0.430397i
$111$	−9.67993	+	2.59373i	−0.918778	+	0.246186i
$112$			1.60979i			0.152111i
$113$	−1.29827	−	4.84521i	−0.122131	−	0.455799i	0.877590	−	0.479412i	$-0.159150\pi$
$113$	−1.29827	−	4.84521i	−0.122131	−	0.455799i	−0.999721	+	0.0236123i	$0.992483\pi$
$114$	−2.61354	−	4.52679i	−0.244781	−	0.423973i
$115$	−0.875512	−	5.77808i	−0.0816419	−	0.538809i
$116$		−	4.98890i		−	0.463208i
$117$	0.933500	−	3.48261i	0.0863021	−	0.321967i
$118$	4.58887	−	4.58887i	0.422440	−	0.422440i
$119$	2.97509	−	11.1032i	0.272726	−	1.01783i
$120$	2.21083	−	0.334992i	0.201820	−	0.0305804i
$121$	0.465095	+	0.268523i	0.0422814	+	0.0244112i
$122$	1.68154			0.152240
$123$	3.02675	+	1.74749i	0.272913	+	0.157566i
$124$	1.24068	+	4.63027i	0.111416	+	0.415811i
$125$	3.66795	−	10.5615i	0.328071	−	0.944653i
$126$	−0.804897	+	1.39412i	−0.0717059	+	0.124198i
$127$	−9.88261	−	2.64804i	−0.876940	−	0.234975i	−0.207853	−	0.978160i	$-0.566648\pi$
$127$	−9.88261	−	2.64804i	−0.876940	−	0.234975i	−0.669086	+	0.743185i	$0.733314\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	4.58387			0.403587
$130$	−2.94030	+	7.50697i	−0.257882	+	0.658405i
$131$	14.3337			1.25234			0.626169	−	0.779687i	$-0.284622\pi$
$131$	14.3337			1.25234			0.626169	+	0.779687i	$0.284622\pi$
$132$	1.61732	+	2.80129i	0.140770	+	0.243821i
$133$	−8.12781	−	2.17784i	−0.704770	−	0.188843i
$134$	−5.61225	+	9.72071i	−0.484825	+	0.839741i
$135$	2.08213	+	0.815305i	0.179201	+	0.0701703i
$136$	1.84812	+	6.89728i	0.158475	+	0.591437i
$137$	−5.48815	−	3.16859i	−0.468885	−	0.270711i	0.246888	−	0.969044i	$-0.420592\pi$
$137$	−5.48815	−	3.16859i	−0.468885	−	0.270711i	−0.715773	+	0.698333i	$0.753925\pi$
$138$	−2.61353			−0.222479
$139$	−14.8328	−	8.56372i	−1.25810	−	0.726365i	−0.285396	−	0.958410i	$-0.592125\pi$
$139$	−14.8328	−	8.56372i	−1.25810	−	0.726365i	−0.972705	+	0.232044i	$0.925459\pi$
$140$	2.13526	−	2.89790i	0.180463	−	0.244917i
$141$	−0.0782246	+	0.291938i	−0.00658770	+	0.0245856i
$142$	1.27249	−	1.27249i	0.106785	−	0.106785i
$143$	−11.6627	−	0.00105436i	−0.975283	−	8.81698e-5i
$144$		−	1.00000i		−	0.0833333i
$145$	−6.61738	+	8.98087i	−0.549543	+	0.745821i
$146$	4.83505	+	8.37454i	0.400151	+	0.693082i
$147$	−1.14102	−	4.25835i	−0.0941098	−	0.351223i
$148$		−	10.0214i		−	0.823754i
$149$	6.04714	−	1.62033i	0.495401	−	0.132742i	−0.00246394	−	0.999997i	$-0.500784\pi$
$149$	6.04714	−	1.62033i	0.495401	−	0.132742i	0.497865	+	0.867255i	$0.334118\pi$
$150$	−4.42421	−	2.32945i	−0.361235	−	0.190199i
$151$	−3.81978	−	3.81978i	−0.310849	−	0.310849i	0.534389	−	0.845239i	$-0.320542\pi$
$151$	−3.81978	−	3.81978i	−0.310849	−	0.310849i	−0.845239	+	0.534389i	$0.820542\pi$
$152$	5.04898	−	1.35287i	0.409526	−	0.109732i
$153$	−1.84812	+	6.89728i	−0.149412	+	0.557612i
$154$	5.02969	+	1.34770i	0.405304	+	0.108601i
$155$	3.90826	−	9.98094i	0.313919	−	0.801688i
$156$	3.12234	+	1.80306i	0.249987	+	0.144360i
$157$	−12.2093	−	12.2093i	−0.974409	−	0.974409i	0.0252715	−	0.999681i	$-0.491955\pi$
$157$	−12.2093	−	12.2093i	−0.974409	−	0.974409i	−0.999681	+	0.0252715i	$0.991955\pi$
$158$	10.1759	−	5.87507i	0.809553	−	0.467396i
$159$	−8.22025	+	4.74596i	−0.651908	+	0.376379i
$160$	−0.248628	+	2.22220i	−0.0196558	+	0.175681i
$161$	−2.97497	+	2.97497i	−0.234461	+	0.234461i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	2.14934	−	3.72277i	0.168350	−	0.291590i	−0.769490	−	0.638659i	$-0.779490\pi$
$163$	2.14934	−	3.72277i	0.168350	−	0.291590i	0.937840	+	0.347069i	$0.112823\pi$
$164$	−2.47133	+	2.47133i	−0.192978	+	0.192978i
$165$	0.804226	−	7.18805i	0.0626089	−	0.559589i
$166$	12.1237	−	6.99960i	0.940978	−	0.543274i
$167$	8.67762	−	5.01003i	0.671494	−	0.387688i	−0.125148	−	0.992138i	$-0.539941\pi$
$167$	8.67762	−	5.01003i	0.671494	−	0.387688i	0.796643	+	0.604451i	$0.206607\pi$
$168$	−1.13830	−	1.13830i	−0.0878214	−	0.0878214i
$169$	−11.2595	+	6.49796i	−0.866116	+	0.499843i
$170$	5.82176	−	14.8677i	0.446508	−	1.14030i
$171$	5.04898	+	1.35287i	0.386105	+	0.103456i
$172$	−1.18639	+	4.42768i	−0.0904616	+	0.337607i
$173$	2.50448	−	0.671072i	0.190412	−	0.0510207i	−0.162353	−	0.986733i	$-0.551908\pi$
$173$	2.50448	−	0.671072i	0.190412	−	0.0510207i	0.352765	+	0.935712i	$0.385242\pi$
$174$	3.52769	+	3.52769i	0.267433	+	0.267433i
$175$	−7.68767	+	2.38446i	−0.581133	+	0.180248i
$176$	−3.12443	+	0.837189i	−0.235513	+	0.0631055i
$177$			6.48965i			0.487792i
$178$	−3.61218	−	13.4808i	−0.270744	−	1.01043i
$179$	−7.23031	−	12.5233i	−0.540418	−	0.936032i	−0.998880	−	0.0473179i	$-0.984933\pi$
$179$	−7.23031	−	12.5233i	−0.540418	−	0.936032i	0.458461	−	0.888714i	$-0.348401\pi$
$180$	−1.32642	+	1.80017i	−0.0988655	+	0.134177i
$181$			8.93732i			0.664306i	0.943226	+	0.332153i	$0.107775\pi$
$181$			8.93732i			0.664306i	−0.943226	+	0.332153i	$0.892225\pi$
$182$	5.60656	−	1.50173i	0.415586	−	0.111316i
$183$	−1.18903	+	1.18903i	−0.0878957	+	0.0878957i
$184$	0.676432	−	2.52448i	0.0498672	−	0.186107i
$185$	−13.2926	+	18.0402i	−0.977290	+	1.32634i
$186$	−4.15139	−	2.39681i	−0.304395	−	0.175742i
$187$	23.0973			1.68904
$188$	−0.261745	−	0.151118i	−0.0190897	−	0.0110214i
$189$	−0.416645	−	1.55494i	−0.0303065	−	0.113105i
$190$	−10.8835	−	4.26167i	−0.789571	−	0.309174i
$191$	−4.01556	+	6.95516i	−0.290556	+	0.503257i	−0.973941	−	0.226800i	$-0.927174\pi$
$191$	−4.01556	+	6.95516i	−0.290556	+	0.503257i	0.683385	+	0.730058i	$0.260507\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	5.38346	+	9.32442i	0.387510	+	0.671186i	0.992114	−	0.125340i	$-0.0400020\pi$
$193$	5.38346	+	9.32442i	0.387510	+	0.671186i	−0.604604	+	0.796526i	$0.706669\pi$
$194$	6.91621			0.496555
$195$	−3.22912	−	7.38734i	−0.231242	−	0.529018i
$196$	4.40857			0.314898
$197$	−8.15048	−	14.1170i	−0.580698	−	1.00580i	−0.995397	−	0.0958394i	$-0.969446\pi$
$197$	−8.15048	−	14.1170i	−0.580698	−	1.00580i	0.414699	−	0.909959i	$-0.363887\pi$
$198$	−3.12443	−	0.837189i	−0.222044	−	0.0594964i
$199$	8.15165	−	14.1191i	0.577855	−	1.00087i	−0.417870	−	0.908507i	$-0.637223\pi$
$199$	8.15165	−	14.1191i	0.577855	−	1.00087i	0.995725	−	0.0923673i	$-0.0294434\pi$
$200$	3.39515	−	3.67056i	0.240073	−	0.259547i
$201$	−2.90512	−	10.8420i	−0.204911	−	0.764738i
$202$	10.5683	+	6.10159i	0.743580	+	0.429306i
$203$	8.03110			0.563673
$204$	−6.18393	−	3.57029i	−0.432962	−	0.249971i
$205$	7.72683	−	1.17079i	0.539666	−	0.0817717i
$206$	0.987470	−	3.68529i	0.0688003	−	0.256766i
$207$	1.84805	−	1.84805i	0.128448	−	0.128448i
$208$	−2.54974	+	2.54928i	−0.176793	+	0.176761i
$209$		−	16.9078i		−	1.16954i
$210$	0.539267	+	3.55898i	0.0372130	+	0.245593i
$211$	−11.4183	−	19.7772i	−0.786071	−	1.36152i	−0.928357	−	0.371690i	$-0.878778\pi$
$211$	−11.4183	−	19.7772i	−0.786071	−	1.36152i	0.142285	−	0.989826i	$-0.454555\pi$
$212$	−2.45669	−	9.16850i	−0.168726	−	0.629695i
$213$			1.79957i			0.123305i
$214$	13.1501	−	3.52356i	0.898922	−	0.240865i
$215$	8.00867	−	6.39692i	0.546187	−	0.436266i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	−7.45379	+	1.99724i	−0.505996	+	0.135581i
$218$	4.11520	−	15.3581i	0.278717	−	1.04018i
$219$	−9.34059	−	2.50280i	−0.631179	−	0.169124i
$220$	6.73497	+	2.63723i	0.454072	+	0.177802i
$221$	22.2976	−	12.8709i	1.49990	−	0.865788i
$222$	7.08620	+	7.08620i	0.475595	+	0.475595i
$223$	21.0808	−	12.1710i	1.41167	−	0.815029i	0.416126	−	0.909307i	$-0.363388\pi$
$223$	21.0808	−	12.1710i	1.41167	−	0.815029i	0.995546	+	0.0942781i	$0.0300543\pi$
$224$	1.39412	−	0.804897i	0.0931487	−	0.0537794i
$225$	4.77556	−	1.48122i	0.318371	−	0.0987481i
$226$	−3.54694	+	3.54694i	−0.235939	+	0.235939i
$227$	−0.401227	+	0.694946i	−0.0266304	+	0.0461252i	−0.879033	−	0.476760i	$-0.841811\pi$
$227$	−0.401227	+	0.694946i	−0.0266304	+	0.0461252i	0.852403	+	0.522885i	$0.175144\pi$
$228$	−2.61354	+	4.52679i	−0.173086	+	0.299794i
$229$	−6.37716	+	6.37716i	−0.421415	+	0.421415i	−0.885691	−	0.464276i	$-0.846315\pi$
$229$	−6.37716	+	6.37716i	−0.421415	+	0.421415i	0.464276	+	0.885691i	$0.346315\pi$
$230$	−4.56621	+	3.64726i	−0.301087	+	0.240493i
$231$	−4.50950	+	2.60356i	−0.296703	+	0.171302i
$232$	−4.32052	+	2.49445i	−0.283656	+	0.163769i
$233$	12.7968	+	12.7968i	0.838349	+	0.838349i	0.988642	−	0.150293i	$-0.0480216\pi$
$233$	12.7968	+	12.7968i	0.838349	+	0.838349i	−0.150293	+	0.988642i	$0.548022\pi$
$234$	−3.48278	+	0.932870i	−0.227676	+	0.0609837i
$235$	0.270739	+	0.619222i	0.0176610	+	0.0403936i
$236$	−6.26852	−	1.67964i	−0.408046	−	0.109336i
$237$	−3.04116	+	11.3498i	−0.197545	+	0.737247i
$238$	−11.1032	+	2.97509i	−0.719713	+	0.192847i
$239$	−18.1883	−	18.1883i	−1.17650	−	1.17650i	−0.980629	−	0.195873i	$-0.937246\pi$
$239$	−18.1883	−	18.1883i	−1.17650	−	1.17650i	−0.195873	−	0.980629i	$-0.562754\pi$
$240$	−1.39553	−	1.74714i	−0.0900809	−	0.112777i
$241$	20.5529	−	5.50713i	1.32393	−	0.354745i	0.473479	−	0.880805i	$-0.342998\pi$
$241$	20.5529	−	5.50713i	1.32393	−	0.354745i	0.850448	+	0.526060i	$0.176331\pi$
$242$		−	0.537046i		−	0.0345226i
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	−0.840772	−	1.45626i	−0.0538249	−	0.0932275i
$245$	−7.93617	−	5.84761i	−0.507023	−	0.373590i
$246$		−	3.49499i		−	0.222832i
$247$	−9.42179	−	16.3224i	−0.599494	−	1.03857i
$248$	3.38960	−	3.38960i	0.215240	−	0.215240i
$249$	−3.62326	+	13.5222i	−0.229615	+	0.856934i
$250$	−10.9805	+	2.10423i	−0.694470	+	0.133083i
$251$	−3.15024	−	1.81879i	−0.198842	−	0.114801i	0.397273	−	0.917700i	$-0.369956\pi$
$251$	−3.15024	−	1.81879i	−0.198842	−	0.114801i	−0.596115	+	0.802899i	$0.703290\pi$
$252$	1.60979			0.101407
$253$	−7.32126	−	4.22693i	−0.460284	−	0.265745i
$254$	2.64804	+	9.88261i	0.166153	+	0.620090i
$255$	6.39642	+	14.6296i	0.400559	+	0.916143i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	12.4452	+	3.33469i	0.776311	+	0.208012i	0.625158	−	0.780498i	$-0.285035\pi$
$257$	12.4452	+	3.33469i	0.776311	+	0.208012i	0.151153	+	0.988510i	$0.451701\pi$
$258$	−2.29194	−	3.96975i	−0.142690	−	0.247146i
$259$	16.1324			1.00242
$260$	7.97138	−	1.20711i	0.494364	−	0.0748617i
$261$	−4.98890			−0.308805
$262$	−7.16683	−	12.4133i	−0.442768	−	0.766897i
$263$	4.24589	+	1.13768i	0.261813	+	0.0701525i	0.387338	−	0.921938i	$-0.373395\pi$
$263$	4.24589	+	1.13768i	0.261813	+	0.0701525i	−0.125525	+	0.992090i	$0.540061\pi$
$264$	1.61732	−	2.80129i	0.0995394	−	0.172407i
$265$	−7.73882	+	19.7635i	−0.475392	+	1.21406i
$266$	2.17784	+	8.12781i	0.133532	+	0.498348i
$267$	12.0866	+	6.97819i	0.739687	+	0.427058i
$268$	11.2245			0.685646
$269$	9.17607	+	5.29781i	0.559475	+	0.323013i	0.752935	−	0.658095i	$-0.228638\pi$
$269$	9.17607	+	5.29781i	0.559475	+	0.323013i	−0.193460	+	0.981108i	$0.561971\pi$
$270$	−0.334992	−	2.21083i	−0.0203869	−	0.134547i
$271$	−2.99813	+	11.1892i	−0.182123	+	0.679694i	0.813105	+	0.582118i	$0.197776\pi$
$271$	−2.99813	+	11.1892i	−0.182123	+	0.679694i	−0.995228	+	0.0975763i	$0.968891\pi$
$272$	5.04916	−	5.04916i	0.306150	−	0.306150i
$273$	−2.90255	+	5.02632i	−0.175670	+	0.304206i
$274$			6.33718i			0.382843i
$275$	−8.62602	−	13.6808i	−0.520169	−	0.824986i
$276$	1.30677	+	2.26339i	0.0786581	+	0.136240i
$277$	0.351691	+	1.31253i	0.0211311	+	0.0788622i	0.975686	−	0.219172i	$-0.0703356\pi$
$277$	0.351691	+	1.31253i	0.0211311	+	0.0788622i	−0.954555	+	0.298034i	$0.903669\pi$
$278$			17.1274i			1.02724i
$279$	4.63027	−	1.24068i	0.277207	−	0.0742775i
$280$	−3.57729	−	0.400240i	−0.213784	−	0.0239189i
$281$	1.44877	+	1.44877i	0.0864265	+	0.0864265i	0.748998	−	0.662572i	$-0.230535\pi$
$281$	1.44877	+	1.44877i	0.0864265	+	0.0864265i	−0.662572	+	0.748998i	$0.730535\pi$
$282$	0.291938	−	0.0782246i	0.0173847	−	0.00465821i
$283$	−1.93668	+	7.22777i	−0.115123	+	0.429646i	−0.999296	−	0.0375138i	$-0.988056\pi$
$283$	−1.93668	+	7.22777i	−0.115123	+	0.429646i	0.884173	+	0.467160i	$0.154723\pi$
$284$	−1.73825	−	0.465764i	−0.103146	−	0.0276380i
$285$	10.7092	−	4.68233i	0.634361	−	0.277357i
$286$	5.83043	+	10.1007i	0.344761	+	0.597268i
$287$	−3.97833	−	3.97833i	−0.234833	−	0.234833i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	−29.4345	+	16.9940i	−1.73144	+	0.999647i
$290$	11.0864	+	1.24038i	0.651013	+	0.0728378i
$291$	−4.89050	+	4.89050i	−0.286686	+	0.286686i
$292$	4.83505	−	8.37454i	0.282950	−	0.490083i
$293$	−14.7846	+	25.6077i	−0.863725	+	1.49601i	0.00458335	+	0.999989i	$0.498541\pi$
$293$	−14.7846	+	25.6077i	−0.863725	+	1.49601i	−0.868308	+	0.496025i	$0.834792\pi$
$294$	−3.11733	+	3.11733i	−0.181806	+	0.181806i
$295$	9.05648	+	11.3383i	0.527289	+	0.660143i
$296$	−8.67879	+	5.01070i	−0.504444	+	0.291241i
$297$	2.80129	−	1.61732i	0.162547	−	0.0938467i
$298$	−4.42681	−	4.42681i	−0.256438	−	0.256438i
$299$	−9.42323		0.000851899i	−0.544959		4.92666e-5i
$300$	0.194744	+	4.99621i	0.0112435	+	0.288456i
$301$	−7.12765	−	1.90985i	−0.410831	−	0.110082i
$302$	−1.39814	+	5.21792i	−0.0804537	+	0.300257i
$303$	−11.7874	+	3.15841i	−0.677166	+	0.181446i
$304$	−3.69611	−	3.69611i	−0.211986	−	0.211986i
$305$	−0.418080	+	3.73673i	−0.0239392	+	0.213965i
$306$	6.89728	−	1.84812i	0.394291	−	0.105650i
$307$			19.1490i			1.09289i	0.837495	+	0.546445i	$0.184019\pi$
$307$			19.1490i			1.09289i	−0.837495	+	0.546445i	$0.815981\pi$
$308$	−1.34770	−	5.02969i	−0.0767924	−	0.286593i
$309$	1.90764	+	3.30414i	0.108522	+	0.187966i
$310$	−10.5979	+	1.60582i	−0.601919	+	0.0912045i
$311$		−	2.43834i		−	0.138266i	−0.997607	−	0.0691328i	$-0.977977\pi$
$311$		−	2.43834i		−	0.138266i	0.997607	−	0.0691328i	$-0.0220232\pi$
$312$	0.000325957	−	3.60555i	1.84537e−5	−	0.204124i
$313$	22.4839	−	22.4839i	1.27086	−	1.27086i	0.325226	−	0.945636i	$-0.394560\pi$
$313$	22.4839	−	22.4839i	1.27086	−	1.27086i	0.945636	−	0.325226i	$-0.105440\pi$
$314$	−4.46892	+	16.6782i	−0.252196	+	0.941207i
$315$	−2.89790	−	2.13526i	−0.163278	−	0.120308i
$316$	−10.1759	−	5.87507i	−0.572440	−	0.330499i
$317$	5.98914			0.336384			0.168192	−	0.985754i	$-0.446207\pi$
$317$	5.98914			0.336384			0.168192	+	0.985754i	$0.446207\pi$
$318$	8.22025	+	4.74596i	0.460969	+	0.266140i
$319$	4.17665	+	15.5875i	0.233848	+	0.872731i
$320$	2.04880	−	0.895783i	0.114531	−	0.0500758i
$321$	−6.80699	+	11.7901i	−0.379929	+	0.658057i
$322$	4.06389	+	1.08892i	0.226472	+	0.0606829i
$323$	18.6622	+	32.3239i	1.03839	+	1.79855i
$324$	−1.00000			−0.0555556
$325$	−15.9510	−	8.40039i	−0.884801	−	0.465970i
$326$	−4.29869			−0.238082
$327$	7.94996	+	13.7697i	0.439634	+	0.761468i
$328$	3.37590	+	0.904570i	0.186403	+	0.0499465i
$329$	0.243269	−	0.421355i	0.0134119	−	0.0232301i
$330$	−6.62714	+	2.89754i	−0.364812	+	0.159504i
$331$	−4.74108	−	17.6940i	−0.260593	−	0.972548i	−0.964893	−	0.262644i	$-0.915405\pi$
$331$	−4.74108	−	17.6940i	−0.260593	−	0.972548i	0.704299	−	0.709903i	$-0.251261\pi$
$332$	−12.1237	−	6.99960i	−0.665372	−	0.384153i
$333$	−10.0214			−0.549169
$334$	−8.67762	−	5.01003i	−0.474818	−	0.274136i
$335$	−20.2060	−	14.8884i	−1.10397	−	0.813440i
$336$	−0.416645	+	1.55494i	−0.0227299	+	0.0848290i
$337$	−13.5343	+	13.5343i	−0.737258	+	0.737258i	−0.972046	−	0.234788i	$-0.924560\pi$
$337$	−13.5343	+	13.5343i	−0.737258	+	0.737258i	0.234788	+	0.972046i	$0.424560\pi$
$338$	11.2572	+	6.50204i	0.612309	+	0.353664i
$339$		−	5.01613i		−	0.272439i
$340$	−15.7866	+	2.39204i	−0.856151	+	0.129726i
$341$	−7.75283	−	13.4283i	−0.419839	−	0.727183i
$342$	−1.35287	−	5.04898i	−0.0731548	−	0.273017i
$343$			18.3654i			0.991640i
$344$	4.42768	−	1.18639i	0.238724	−	0.0639660i
$345$	0.649798	−	5.80780i	0.0349840	−	0.312681i
$346$	−1.83340	−	1.83340i	−0.0985644	−	0.0985644i
$347$	31.4472	−	8.42626i	1.68818	−	0.452346i	0.718258	−	0.695776i	$-0.244940\pi$
$347$	31.4472	−	8.42626i	1.68818	−	0.452346i	0.969918	+	0.243431i	$0.0782729\pi$
$348$	1.29122	−	4.81891i	0.0692168	−	0.258321i
$349$	−2.75155	−	0.737276i	−0.147287	−	0.0394655i	0.184422	−	0.982847i	$-0.440959\pi$
$349$	−2.75155	−	0.737276i	−0.147287	−	0.0394655i	−0.331709	+	0.943382i	$0.607625\pi$
$350$	5.90884	+	5.46548i	0.315841	+	0.292142i
$351$	1.80306	−	3.12234i	0.0962401	−	0.166658i
$352$	2.28724	+	2.28724i	0.121910	+	0.121910i
$353$	25.6455	−	14.8064i	1.36497	−	0.788066i	0.374690	−	0.927150i	$-0.377749\pi$
$353$	25.6455	−	14.8064i	1.36497	−	0.788066i	0.990281	+	0.139084i	$0.0444159\pi$
$354$	5.62020	−	3.24482i	0.298710	−	0.172460i
$355$	2.51135	+	3.14411i	0.133289	+	0.166872i
$356$	−9.86865	+	9.86865i	−0.523038	+	0.523038i
$357$	5.74744	−	9.95485i	0.304187	−	0.526867i
$358$	−7.23031	+	12.5233i	−0.382134	+	0.661875i
$359$	6.13464	−	6.13464i	0.323774	−	0.323774i	−0.526439	−	0.850213i	$-0.676473\pi$
$359$	6.13464	−	6.13464i	0.323774	−	0.323774i	0.850213	+	0.526439i	$0.176473\pi$
$360$	2.22220	+	0.248628i	0.117120	+	0.0131039i
$361$	7.20742	−	4.16121i	0.379338	−	0.219011i
$362$	7.73995	−	4.46866i	0.406803	−	0.234868i
$363$	0.379749	+	0.379749i	0.0199316	+	0.0199316i
$364$	−4.10381	−	4.10455i	−0.215098	−	0.215137i
$365$	−19.8121	+	8.66230i	−1.03701	+	0.453406i
$366$	1.62425	+	0.435216i	0.0849007	+	0.0227491i
$367$	5.45699	−	20.3658i	0.284852	−	1.06308i	−0.664095	−	0.747648i	$-0.731183\pi$
$367$	5.45699	−	20.3658i	0.284852	−	1.06308i	0.948947	−	0.315435i	$-0.102150\pi$
$368$	−2.52448	+	0.676432i	−0.131598	+	0.0352615i
$369$	2.47133	+	2.47133i	0.128652	+	0.128652i
$370$	22.2696	+	2.49161i	1.15774	+	0.129532i
$371$	14.7594	−	3.95477i	0.766269	−	0.205321i
$372$			4.79361i			0.248537i
$373$	2.38267	+	8.89223i	0.123370	+	0.460422i	0.999776	−	0.0211498i	$-0.00673269\pi$
$373$	2.38267	+	8.89223i	0.123370	+	0.460422i	−0.876407	+	0.481572i	$0.840066\pi$
$374$	−11.5486	−	20.0028i	−0.597166	−	1.03432i
$375$	6.27650	−	9.25233i	0.324117	−	0.477788i
$376$			0.302237i			0.0155867i
$377$	12.7181	+	12.7204i	0.655016	+	0.655134i
$378$	−1.13830	+	1.13830i	−0.0585476	+	0.0585476i
$379$	2.65698	−	9.91598i	0.136480	−	0.509350i	−0.863508	−	0.504336i	$-0.831737\pi$
$379$	2.65698	−	9.91598i	0.136480	−	0.509350i	0.999987	−	0.00501389i	$-0.00159598\pi$
$380$	1.75103	+	11.5562i	0.0898259	+	0.592821i
$381$	−8.86050	−	5.11561i	−0.453937	−	0.262081i
$382$	8.03112			0.410908
$383$	−18.5766	−	10.7252i	−0.949222	−	0.548034i	−0.0563828	−	0.998409i	$-0.517957\pi$
$383$	−18.5766	−	10.7252i	−0.949222	−	0.548034i	−0.892839	+	0.450376i	$0.851290\pi$
$384$	−0.258819	−	0.965926i	−0.0132078	−	0.0492922i
$385$	−4.24539	+	10.8419i	−0.216365	+	0.552555i
$386$	5.38346	−	9.32442i	0.274011	−	0.474600i
$387$	4.42768	+	1.18639i	0.225072	+	0.0603077i
$388$	−3.45811	−	5.98962i	−0.175559	−	0.304077i
$389$	−2.24554			−0.113854			−0.0569268	−	0.998378i	$-0.518130\pi$
$389$	−2.24554			−0.113854			−0.0569268	+	0.998378i	$0.518130\pi$
$390$	−4.78306	+	6.49017i	−0.242200	+	0.328643i
$391$	18.6622			0.943786
$392$	−2.20428	−	3.81793i	−0.111333	−	0.192835i
$393$	13.8453	+	3.70983i	0.698401	+	0.187136i
$394$	−8.15048	+	14.1170i	−0.410615	+	0.711207i
$395$	10.5256	+	24.0737i	0.529599	+	1.21128i
$396$	0.837189	+	3.12443i	0.0420703	+	0.157009i
$397$	−28.2852	−	16.3305i	−1.41959	−	0.819603i	−0.423331	−	0.905975i	$-0.639139\pi$
$397$	−28.2852	−	16.3305i	−1.41959	−	0.819603i	−0.996263	+	0.0863726i	$0.972472\pi$
$398$	−16.3033			−0.817210
$399$	−7.28719	−	4.20726i	−0.364816	−	0.210627i
$400$	−4.87637	−	1.10501i	−0.243818	−	0.0552503i
$401$	2.47105	−	9.22208i	0.123398	−	0.460529i	−0.876379	−	0.481622i	$-0.840048\pi$
$401$	2.47105	−	9.22208i	0.123398	−	0.460529i	0.999778	+	0.0210930i	$0.00671461\pi$
$402$	−7.93692	+	7.93692i	−0.395858	+	0.395858i
$403$	−14.9673	−	8.64316i	−0.745573	−	0.430547i
$404$		−	12.2032i		−	0.607131i
$405$	1.80017	+	1.32642i	0.0894511	+	0.0659103i
$406$	−4.01555	−	6.95514i	−0.199288	−	0.345178i
$407$	8.38980	+	31.3112i	0.415867	+	1.55204i
$408$			7.14059i			0.353512i
$409$	−2.51038	+	0.672655i	−0.124130	+	0.0332606i	−0.320349	−	0.947299i	$-0.603800\pi$
$409$	−2.51038	+	0.672655i	−0.124130	+	0.0332606i	0.196219	+	0.980560i	$0.437134\pi$
$410$	−4.87735	−	6.10624i	−0.240875	−	0.301566i
$411$	−4.48106	−	4.48106i	−0.221034	−	0.221034i
$412$	−3.68529	+	0.987470i	−0.181561	+	0.0486491i
$413$	2.70388	−	10.0910i	0.133049	−	0.496547i
$414$	−2.52448	−	0.676432i	−0.124071	−	0.0332448i
$415$	12.5402	+	28.6815i	0.615576	+	1.40792i
$416$	3.48261	+	0.933500i	0.170749	+	0.0457686i
$417$	−12.1109	−	12.1109i	−0.593075	−	0.593075i
$418$	−14.6426	+	8.45389i	−0.716192	+	0.413493i
$419$	−15.9488	+	9.20806i	−0.779151	+	0.449843i	−0.836129	−	0.548532i	$-0.815187\pi$
$419$	−15.9488	+	9.20806i	−0.779151	+	0.449843i	0.0569781	+	0.998375i	$0.481853\pi$
$420$	2.81254	−	2.24651i	0.137238	−	0.109619i
$421$	9.24742	−	9.24742i	0.450692	−	0.450692i	−0.444892	−	0.895584i	$-0.646758\pi$
$421$	9.24742	−	9.24742i	0.450692	−	0.450692i	0.895584	+	0.444892i	$0.146758\pi$
$422$	−11.4183	+	19.7772i	−0.555836	+	0.962737i
$423$	−0.151118	+	0.261745i	−0.00734763	+	0.0127265i
$424$	−6.71181	+	6.71181i	−0.325954	+	0.325954i
$425$	31.5915	+	16.6336i	1.53241	+	0.806850i
$426$	1.55848	−	0.899786i	0.0755084	−	0.0435948i
$427$	2.34428	−	1.35347i	0.113448	−	0.0654990i
$428$	−9.62654	−	9.62654i	−0.465316	−	0.465316i
$429$	−11.2650	−	3.01955i	−0.543880	−	0.145785i
$430$	−9.54423	−	3.73725i	−0.460264	−	0.180226i
$431$	−0.913591	−	0.244796i	−0.0440061	−	0.0117914i	0.236749	−	0.971571i	$-0.423918\pi$
$431$	−0.913591	−	0.244796i	−0.0440061	−	0.0117914i	−0.280755	+	0.959779i	$0.590585\pi$
$432$	0.258819	−	0.965926i	0.0124524	−	0.0464731i
$433$	28.1868	−	7.55262i	1.35457	−	0.362956i	0.492750	−	0.870171i	$-0.335992\pi$
$433$	28.1868	−	7.55262i	1.35457	−	0.362956i	0.861819	+	0.507215i	$0.169325\pi$
$434$	5.45655	+	5.45655i	0.261923	+	0.261923i
$435$	−8.71632	+	6.96215i	−0.417915	+	0.333810i
$436$	−15.3581	+	4.11520i	−0.735521	+	0.197082i
$437$		−	13.6612i		−	0.653502i
$438$	2.50280	+	9.34059i	0.119589	+	0.446311i
$439$	4.82036	+	8.34911i	0.230063	+	0.398481i	0.957826	−	0.287347i	$-0.0927734\pi$
$439$	4.82036	+	8.34911i	0.230063	+	0.398481i	−0.727763	+	0.685828i	$0.759440\pi$
$440$	−1.08358	−	7.15127i	−0.0516577	−	0.340923i
$441$		−	4.40857i		−	0.209932i
$442$	−22.2953	−	12.8749i	−1.06048	−	0.612396i
$443$	−12.4480	+	12.4480i	−0.591422	+	0.591422i	−0.938015	−	0.346594i	$-0.887338\pi$
$443$	−12.4480	+	12.4480i	−0.591422	+	0.591422i	0.346594	+	0.938015i	$0.387338\pi$
$444$	2.59373	−	9.67993i	0.123093	−	0.459389i
$445$	30.8552	−	4.67527i	1.46268	−	0.221629i
$446$	−21.0808	−	12.1710i	−0.998203	−	0.576313i
$447$	6.26046			0.296109
$448$	−1.39412	−	0.804897i	−0.0658661	−	0.0380278i
$449$	−4.62541	−	17.2623i	−0.218287	−	0.814656i	−0.984984	−	0.172647i	$-0.944768\pi$
$449$	−4.62541	−	17.2623i	−0.218287	−	0.814656i	0.766697	−	0.642009i	$-0.221899\pi$
$450$	−3.67056	−	3.39515i	−0.173032	−	0.160049i
$451$	5.65253	−	9.79047i	0.266167	−	0.461015i
$452$	4.84521	+	1.29827i	0.227900	+	0.0610655i
$453$	−2.70099	−	4.67826i	−0.126904	−	0.219804i
$454$	0.802455			0.0376611
$455$	1.94320	+	12.8323i	0.0910984	+	0.601586i
$456$	5.22708			0.244781
$457$	0.805048	+	1.39438i	0.0376585	+	0.0652265i	0.884240	−	0.467032i	$-0.154677\pi$
$457$	0.805048	+	1.39438i	0.0376585	+	0.0652265i	−0.846582	+	0.532259i	$0.821343\pi$
$458$	8.71136	+	2.33420i	0.407055	+	0.109070i
$459$	−3.57029	+	6.18393i	−0.166647	+	0.288641i
$460$	5.44172	+	2.13083i	0.253722	+	0.0993503i
$461$	−3.98137	−	14.8587i	−0.185431	−	0.692037i	−0.994538	−	0.104376i	$-0.966716\pi$
$461$	−3.98137	−	14.8587i	−0.185431	−	0.692037i	0.809107	−	0.587661i	$-0.199951\pi$
$462$	4.50950	+	2.60356i	0.209801	+	0.121128i
$463$	1.25368			0.0582634			0.0291317	−	0.999576i	$-0.490726\pi$
$463$	1.25368			0.0582634			0.0291317	+	0.999576i	$0.490726\pi$
$464$	4.32052	+	2.49445i	0.200575	+	0.115802i
$465$	6.35834	−	8.62932i	0.294861	−	0.400175i
$466$	4.68397	−	17.4808i	0.216981	−	0.809783i
$467$	−27.3399	+	27.3399i	−1.26514	+	1.26514i	−0.316572	+	0.948568i	$0.602532\pi$
$467$	−27.3399	+	27.3399i	−1.26514	+	1.26514i	−0.948568	+	0.316572i	$0.897468\pi$
$468$	2.54928	+	2.54974i	0.117840	+	0.117862i
$469$			18.0691i			0.834355i
$470$	0.400893	−	0.544078i	0.0184918	−	0.0250964i
$471$	−8.63329	−	14.9533i	−0.397801	−	0.689011i
$472$	1.67964	+	6.26852i	0.0773119	+	0.288532i
$473$		−	14.8272i		−	0.681756i
$474$	11.3498	−	3.04116i	0.521312	−	0.139685i
$475$	12.1762	−	23.1257i	0.558684	−	1.06108i
$476$	8.12810	+	8.12810i	0.372551	+	0.372551i
$477$	−9.16850	+	2.45669i	−0.419797	+	0.112484i
$478$	−6.65737	+	24.8457i	−0.304501	+	1.13641i
$479$	−30.5800	−	8.19388i	−1.39723	−	0.374388i	−0.519884	−	0.854237i	$-0.674025\pi$
$479$	−30.5800	−	8.19388i	−1.39723	−	0.374388i	−0.877351	+	0.479849i	$0.840691\pi$
$480$	−0.815305	+	2.08213i	−0.0372134	+	0.0950359i
$481$	25.5473	+	25.5520i	1.16486	+	1.16507i
$482$	−15.0457	−	15.0457i	−0.685315	−	0.685315i
$483$	−3.64358	+	2.10362i	−0.165789	+	0.0957182i
$484$	−0.465095	+	0.268523i	−0.0211407	+	0.0122056i
$485$	−1.71957	+	15.3692i	−0.0780815	+	0.697881i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	18.2868	−	31.6737i	0.828655	−	1.43527i	−0.0704390	−	0.997516i	$-0.522440\pi$
$487$	18.2868	−	31.6737i	0.828655	−	1.43527i	0.899094	−	0.437756i	$-0.144227\pi$
$488$	−0.840772	+	1.45626i	−0.0380600	+	0.0659218i
$489$	3.03963	−	3.03963i	0.137457	−	0.137457i
$490$	−1.09609	+	9.79673i	−0.0495165	+	0.442571i
$491$	−33.5648	+	19.3787i	−1.51476	+	0.874547i	−0.514909	+	0.857245i	$0.672174\pi$
$491$	−33.5648	+	19.3787i	−1.51476	+	0.874547i	−0.999850	+	0.0173022i	$0.994492\pi$
$492$	−3.02675	+	1.74749i	−0.136456	+	0.0787831i
$493$	−25.1898	−	25.1898i	−1.13449	−	1.13449i
$494$	−9.42474	+	16.3207i	−0.424039	+	0.734304i
$495$	2.63723	−	6.73497i	0.118534	−	0.302714i
$496$	−4.63027	−	1.24068i	−0.207905	−	0.0557081i
$497$	0.749783	−	2.79823i	0.0336324	−	0.125518i
$498$	13.5222	−	3.62326i	0.605944	−	0.162362i
$499$	3.24347	+	3.24347i	0.145198	+	0.145198i	0.775969	−	0.630771i	$-0.217261\pi$
$499$	3.24347	+	3.24347i	0.145198	+	0.145198i	−0.630771	+	0.775969i	$0.717261\pi$
$500$	7.31259	+	8.45731i	0.327029	+	0.378222i
$501$	9.67863	−	2.59338i	0.432409	−	0.115864i
$502$			3.63759i			0.162353i
$503$	−2.78347	−	10.3880i	−0.124109	−	0.463180i	0.875698	−	0.482860i	$-0.160402\pi$
$503$	−2.78347	−	10.3880i	−0.124109	−	0.463180i	−0.999806	+	0.0196799i	$0.993735\pi$
$504$	−0.804897	−	1.39412i	−0.0358529	−	0.0620991i
$505$	−16.1865	+	21.9678i	−0.720291	+	0.977554i
$506$			8.45386i			0.375820i
$507$	−12.5576	+	3.36238i	−0.557705	+	0.149328i
$508$	7.23457	−	7.23457i	0.320982	−	0.320982i
$509$	6.59468	−	24.6117i	0.292304	−	1.09089i	−0.651031	−	0.759051i	$-0.725663\pi$
$509$	6.59468	−	24.6117i	0.292304	−	1.09089i	0.943335	−	0.331842i	$-0.107670\pi$
$510$	9.47142	−	12.8543i	0.419401	−	0.569197i
$511$	13.4813	+	7.78342i	0.596377	+	0.344318i
$512$	1.00000			0.0441942
$513$	4.52679	+	2.61354i	0.199863	+	0.115391i
$514$	−3.33469	−	12.4452i	−0.147087	−	0.548935i
$515$	7.94394	+	3.11062i	0.350052	+	0.137070i
$516$	−2.29194	+	3.96975i	−0.100897	+	0.174758i
$517$	0.944318	+	0.253029i	0.0415311	+	0.0111282i
$518$	−8.06619	−	13.9711i	−0.354408	−	0.613853i
$519$	2.59282			0.113812
$520$	−5.03108	−	6.29986i	−0.220627	−	0.276267i
$521$	5.33735			0.233834			0.116917	−	0.993142i	$-0.462699\pi$
$521$	5.33735			0.233834			0.116917	+	0.993142i	$0.462699\pi$
$522$	2.49445	+	4.32052i	0.109179	+	0.189104i
$523$	3.80359	+	1.01917i	0.166319	+	0.0445651i	0.341018	−	0.940057i	$-0.389228\pi$
$523$	3.80359	+	1.01917i	0.166319	+	0.0445651i	−0.174698	+	0.984622i	$0.555895\pi$
$524$	−7.16683	+	12.4133i	−0.313085	+	0.542278i
$525$	−8.04286	+	0.313497i	−0.351019	+	0.0136821i
$526$	−1.13768	−	4.24589i	−0.0496053	−	0.185130i
$527$	29.6434	+	17.1146i	1.29129	+	0.745524i
$528$	−3.23465			−0.140770
$529$	14.0032	+	8.08472i	0.608833	+	0.351510i
$530$	20.9851	−	3.17972i	0.911533	−	0.138118i
$531$	−1.67964	+	6.26852i	−0.0728904	+	0.272031i
$532$	5.94997	−	5.94997i	0.257964	−	0.257964i
$533$	0.00113922	−	12.6014i	4.93449e−5	−	0.545826i
$534$		−	13.9564i		−	0.603952i
$535$	4.56057	+	30.0982i	0.197171	+	1.30126i
$536$	−5.61225	−	9.72071i	−0.242412	−	0.419871i
$537$	−3.74268	−	13.9679i	−0.161509	−	0.602758i
$538$		−	10.5956i		−	0.456809i
$539$	−13.7743	+	3.69080i	−0.593299	+	0.158974i
$540$	−1.74714	+	1.39553i	−0.0751850	+	0.0600539i
$541$	4.26612	+	4.26612i	0.183415	+	0.183415i	0.792842	−	0.609427i	$-0.208601\pi$
$541$	4.26612	+	4.26612i	0.183415	+	0.183415i	−0.609427	+	0.792842i	$0.708601\pi$
$542$	11.1892	−	2.99813i	0.480616	−	0.128781i
$543$	−2.31315	+	8.63279i	−0.0992667	+	0.370469i
$544$	−6.89728	−	1.84812i	−0.295718	−	0.0792375i
$545$	33.1057	+	12.9633i	1.41809	+	0.555286i
$546$	5.80419		0.000524724i	0.248396		2.24561e-5i
$547$	9.84706	+	9.84706i	0.421030	+	0.421030i	0.885558	−	0.464528i	$-0.153776\pi$
$547$	9.84706	+	9.84706i	0.421030	+	0.421030i	−0.464528	+	0.885558i	$0.653776\pi$
$548$	5.48815	−	3.16859i	0.234442	−	0.135355i
$549$	−1.45626	+	0.840772i	−0.0621517	+	0.0358833i
$550$	−7.53495	+	14.3108i	−0.321292	+	0.610214i
$551$	−18.4395	+	18.4395i	−0.785550	+	0.785550i
$552$	1.30677	−	2.26339i	0.0556197	−	0.0963361i
$553$	9.45765	−	16.3811i	0.402180	−	0.696597i
$554$	0.960838	−	0.960838i	0.0408221	−	0.0408221i
$555$	−17.5088	+	13.9851i	−0.743207	+	0.593636i
$556$	14.8328	−	8.56372i	0.629051	−	0.363183i
$557$	36.7446	−	21.2145i	1.55692	−	0.898887i	0.559369	−	0.828919i	$-0.311043\pi$
$557$	36.7446	−	21.2145i	1.55692	−	0.898887i	0.997549	−	0.0699688i	$-0.0222900\pi$
$558$	−3.38960	−	3.38960i	−0.143493	−	0.143493i
$559$	−8.26240	−	14.3139i	−0.349462	−	0.605413i
$560$	1.44202	+	3.29814i	0.0609367	+	0.139372i
$561$	22.3103	+	5.97802i	0.941941	+	0.252392i
$562$	0.530287	−	1.97906i	0.0223688	−	0.0834815i
$563$	−23.9893	+	6.42791i	−1.01103	+	0.270904i	−0.726059	−	0.687632i	$-0.758650\pi$
$563$	−23.9893	+	6.42791i	−1.01103	+	0.270904i	−0.284970	+	0.958537i	$0.591983\pi$
$564$	−0.213714	−	0.213714i	−0.00899897	−	0.00899897i
$565$	−7.00015	−	8.76390i	−0.294499	−	0.368700i
$566$	7.22777	−	1.93668i	0.303806	−	0.0814045i
$567$		−	1.60979i		−	0.0676050i
$568$	0.465764	+	1.73825i	0.0195430	+	0.0729355i
$569$	6.22248	+	10.7776i	0.260860	+	0.451822i	0.966471	−	0.256777i	$-0.0826606\pi$
$569$	6.22248	+	10.7776i	0.260860	+	0.451822i	−0.705611	+	0.708600i	$0.749327\pi$
$570$	−9.40964	−	6.93331i	−0.394126	−	0.290404i
$571$		−	32.4233i		−	1.35687i	−0.734659	−	0.678436i	$-0.762658\pi$
$571$		−	32.4233i		−	1.35687i	0.734659	−	0.678436i	$-0.237342\pi$
$572$	5.83226	−	10.0997i	0.243859	−	0.422288i
$573$	−5.67886	+	5.67886i	−0.237238	+	0.237238i
$574$	−1.45617	+	5.43450i	−0.0607794	+	0.226832i
$575$	−6.96965	−	11.0539i	−0.290655	−	0.460978i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$	−11.3316			−0.471743			−0.235871	−	0.971784i	$-0.575794\pi$
$577$	−11.3316			−0.471743			−0.235871	+	0.971784i	$0.575794\pi$
$578$	29.4345	+	16.9940i	1.22431	+	0.706857i
$579$	2.78668	+	10.4000i	0.115811	+	0.432211i
$580$	−4.46897	−	10.2213i	−0.185564	−	0.424414i
$581$	11.2679	−	19.5166i	0.467471	−	0.809684i
$582$	6.68055	+	1.79005i	0.276918	+	0.0741999i
$583$	15.3515	+	26.5896i	0.635795	+	1.10123i
$584$	−9.67009			−0.400151
$585$	−1.20711	−	7.97138i	−0.0499078	−	0.329576i
$586$	29.5692			1.22149
$587$	−18.6492	−	32.3014i	−0.769736	−	1.33322i	−0.937706	−	0.347429i	$-0.887055\pi$
$587$	−18.6492	−	32.3014i	−0.769736	−	1.33322i	0.167971	−	0.985792i	$-0.446279\pi$
$588$	4.25835	+	1.14102i	0.175611	+	0.0470549i
$589$	12.5283	−	21.6997i	0.516220	−	0.894119i
$590$	5.29104	−	13.5123i	0.217829	−	0.556293i
$591$	−4.21900	−	15.7455i	−0.173546	−	0.647684i
$592$	8.67879	+	5.01070i	0.356696	+	0.205939i
$593$	−35.2605			−1.44798			−0.723988	−	0.689813i	$-0.757693\pi$
$593$	−35.2605			−1.44798			−0.723988	+	0.689813i	$0.757693\pi$
$594$	−2.80129	−	1.61732i	−0.114938	−	0.0663596i
$595$	−3.85069	−	25.4132i	−0.157863	−	1.04184i
$596$	−1.62033	+	6.04714i	−0.0663711	+	0.247700i
$597$	11.5282	−	11.5282i	0.471817	−	0.471817i
$598$	4.71087	+	8.16118i	0.192642	+	0.333735i
$599$			40.8880i			1.67064i	0.549766	+	0.835319i	$0.314717\pi$
$599$			40.8880i			1.67064i	−0.549766	+	0.835319i	$0.685283\pi$
$600$	4.22947	−	2.66676i	0.172667	−	0.108870i
$601$	10.6495	+	18.4454i	0.434401	+	0.752405i	0.997247	−	0.0741571i	$-0.0236266\pi$
$601$	10.6495	+	18.4454i	0.434401	+	0.752405i	−0.562845	+	0.826562i	$0.690293\pi$
$602$	1.90985	+	7.12765i	0.0778396	+	0.290501i
$603$		−	11.2245i		−	0.457097i
$604$	5.21792	−	1.39814i	0.212314	−	0.0568894i
$605$	1.19342	+	0.133525i	0.0485196	+	0.00542856i
$606$	8.62895	+	8.62895i	0.350527	+	0.350527i
$607$	21.1299	−	5.66175i	0.857637	−	0.229803i	0.196903	−	0.980423i	$-0.436912\pi$
$607$	21.1299	−	5.66175i	0.857637	−	0.229803i	0.660734	+	0.750620i	$0.270245\pi$
$608$	−1.35287	+	5.04898i	−0.0548661	+	0.204763i
$609$	7.75745	+	2.07860i	0.314348	+	0.0842292i
$610$	3.44514	−	1.50630i	0.139490	−	0.0609882i
$611$	1.05262	−	0.281948i	0.0425846	−	0.0114064i
$612$	−5.04916	−	5.04916i	−0.204100	−	0.204100i
$613$	19.3964	−	11.1985i	0.783415	−	0.452305i	−0.0542241	−	0.998529i	$-0.517269\pi$
$613$	19.3964	−	11.1985i	0.783415	−	0.452305i	0.837639	+	0.546224i	$0.183935\pi$
$614$	16.5835	−	9.57449i	0.669256	−	0.386395i
$615$	7.76657	+	0.868954i	0.313178	+	0.0350396i
$616$	−3.68199	+	3.68199i	−0.148351	+	0.148351i
$617$	−20.7823	+	35.9960i	−0.836665	+	1.44915i	0.0560035	+	0.998431i	$0.482164\pi$
$617$	−20.7823	+	35.9960i	−0.836665	+	1.44915i	−0.892668	+	0.450715i	$0.851169\pi$
$618$	1.90764	−	3.30414i	0.0767367	−	0.132912i
$619$	7.03762	−	7.03762i	0.282866	−	0.282866i	−0.551385	−	0.834251i	$-0.685900\pi$
$619$	7.03762	−	7.03762i	0.282866	−	0.282866i	0.834251	+	0.551385i	$0.185900\pi$
$620$	6.68962	+	8.37512i	0.268662	+	0.336353i
$621$	2.26339	−	1.30677i	0.0908265	−	0.0524387i
$622$	−2.11166	+	1.21917i	−0.0846700	+	0.0488842i
$623$	−15.8865	−	15.8865i	−0.636479	−	0.636479i
$624$	−3.12266	+	1.80249i	−0.125007	+	0.0721575i
$625$	−1.94596	−	24.9241i	−0.0778383	−	0.996966i
$626$	−30.7135	−	8.22966i	−1.22756	−	0.328923i
$627$	4.37606	−	16.3317i	0.174763	−	0.652224i
$628$	16.6782	−	4.46892i	0.665534	−	0.178329i
$629$	−50.5996	−	50.5996i	−2.01754	−	2.01754i
$630$	−0.400240	+	3.57729i	−0.0159460	+	0.142523i
$631$	−41.3136	+	11.0699i	−1.64467	+	0.440687i	−0.958113	−	0.286391i	$-0.907544\pi$
$631$	−41.3136	+	11.0699i	−1.64467	+	0.440687i	−0.686554	+	0.727078i	$0.740878\pi$
$632$			11.7501i			0.467396i
$633$	−5.91057	−	22.0586i	−0.234924	−	0.876749i
$634$	−2.99457	−	5.18675i	−0.118930	−	0.205992i
$635$	−22.6195	+	3.42738i	−0.897629	+	0.136011i
$636$		−	9.49193i		−	0.376379i
$637$	−11.2407	+	11.2387i	−0.445373	+	0.445292i
$638$	11.4108	−	11.4108i	0.451759	−	0.451759i
$639$	−0.465764	+	1.73825i	−0.0184253	+	0.0687643i
$640$	−1.80017	−	1.32642i	−0.0711580	−	0.0524313i
$641$	−1.13935	−	0.657806i	−0.0450018	−	0.0259818i	0.477330	−	0.878724i	$-0.341605\pi$
$641$	−1.13935	−	0.657806i	−0.0450018	−	0.0259818i	−0.522332	+	0.852742i	$0.674938\pi$
$642$	13.6140			0.537301
$643$	−0.0963617	−	0.0556344i	−0.00380013	−	0.00219401i	0.498099	−	0.867120i	$-0.334032\pi$
$643$	−0.0963617	−	0.0556344i	−0.00380013	−	0.00219401i	−0.501899	+	0.864926i	$0.667365\pi$
$644$	−1.08892	−	4.06389i	−0.0429093	−	0.160140i
$645$	9.39143	−	4.10615i	0.369787	−	0.161680i
$646$	18.6622	−	32.3239i	0.734256	−	1.27177i
$647$	26.6818	+	7.14936i	1.04897	+	0.281070i	0.741825	−	0.670593i	$-0.233960\pi$
$647$	26.6818	+	7.14936i	1.04897	+	0.281070i	0.307143	+	0.951663i	$0.400627\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	20.9917			0.823998
$650$	0.700529	+	18.0141i	0.0274770	+	0.706573i
$651$	−7.71673			−0.302442
$652$	2.14934	+	3.72277i	0.0841748	+	0.145795i
$653$	−27.9429	−	7.48728i	−1.09349	−	0.293000i	−0.333379	−	0.942793i	$-0.608189\pi$
$653$	−27.9429	−	7.48728i	−1.09349	−	0.293000i	−0.760111	+	0.649793i	$0.774856\pi$
$654$	7.94996	−	13.7697i	0.310868	−	0.538439i
$655$	29.3668	−	12.8399i	1.14746	−	0.501694i
$656$	−0.904570	−	3.37590i	−0.0353175	−	0.131807i
$657$	−8.37454	−	4.83505i	−0.326722	−	0.188633i
$658$	−0.486539			−0.0189673
$659$	27.0057	+	15.5917i	1.05199	+	0.607368i	0.923207	−	0.384304i	$-0.125559\pi$
$659$	27.0057	+	15.5917i	1.05199	+	0.607368i	0.128786	+	0.991672i	$0.458892\pi$
$660$	5.82292	+	4.29050i	0.226657	+	0.167008i
$661$	0.686777	−	2.56309i	0.0267125	−	0.0996925i	−0.951283	−	0.308320i	$-0.900233\pi$
$661$	0.686777	−	2.56309i	0.0267125	−	0.0996925i	0.977995	+	0.208628i	$0.0668998\pi$
$662$	−12.9529	+	12.9529i	−0.503428	+	0.503428i
$663$	24.8691	−	6.66124i	0.965836	−	0.258701i
$664$			13.9992i			0.543274i
$665$	−18.6031	+	2.81880i	−0.721398	+	0.109308i
$666$	5.01070	+	8.67879i	0.194161	+	0.336296i
$667$	3.37465	+	12.5944i	0.130667	+	0.487656i
$668$			10.0201i			0.387688i
$669$	23.5125	−	6.30016i	0.909047	−	0.243578i
$670$	−2.79073	+	24.9431i	−0.107815	+	0.963637i
$671$	3.84610	+	3.84610i	0.148477	+	0.148477i
$672$	1.55494	−	0.416645i	0.0599831	−	0.0160724i
$673$	−6.21821	+	23.2067i	−0.239694	+	0.894551i	0.736282	+	0.676675i	$0.236580\pi$
$673$	−6.21821	+	23.2067i	−0.239694	+	0.894551i	−0.975976	+	0.217876i	$0.930087\pi$
$674$	18.4881	+	4.95388i	0.712137	+	0.190816i
$675$	4.99621	−	0.194744i	0.192304	−	0.00749568i
$676$	0.00235051	−	13.0000i	9.04042e−5	−	0.500000i
$677$	−19.7316	−	19.7316i	−0.758349	−	0.758349i	0.217673	−	0.976022i	$-0.430153\pi$
$677$	−19.7316	−	19.7316i	−0.758349	−	0.758349i	−0.976022	+	0.217673i	$0.930153\pi$
$678$	−4.34410	+	2.50807i	−0.166834	+	0.0963217i
$679$	9.64205	−	5.56684i	0.370028	−	0.213636i
$680$	9.96489	+	12.4756i	0.382136	+	0.478418i
$681$	−0.567421	+	0.567421i	−0.0217436	+	0.0217436i
$682$	−7.75283	+	13.4283i	−0.296871	+	0.514196i
$683$	1.72111	−	2.98106i	0.0658566	−	0.114067i	−0.831217	−	0.555948i	$-0.812355\pi$
$683$	1.72111	−	2.98106i	0.0658566	−	0.114067i	0.897074	+	0.441881i	$0.145689\pi$
$684$	−3.69611	+	3.69611i	−0.141324	+	0.141324i
$685$	−14.0825	−	1.57560i	−0.538064	−	0.0602007i
$686$	15.9049	−	9.18272i	0.607253	−	0.350598i
$687$	−7.81040	+	4.50933i	−0.297985	+	0.172042i
$688$	−3.24129	−	3.24129i	−0.123573	−	0.123573i
$689$	29.6370	+	17.1145i	1.12908	+	0.652010i
$690$	−5.35460	+	2.34116i	−0.203846	+	0.0891263i
$691$	25.6450	+	6.87155i	0.975581	+	0.261406i	0.711183	−	0.703007i	$-0.248160\pi$
$691$	25.6450	+	6.87155i	0.975581	+	0.261406i	0.264399	+	0.964413i	$0.414827\pi$
$692$	−0.671072	+	2.50448i	−0.0255103	+	0.0952059i
$693$	−5.02969	+	1.34770i	−0.191062	+	0.0511949i
$694$	−23.0210	−	23.0210i	−0.873865	−	0.873865i
$695$	−38.0606	−	4.25837i	−1.44372	−	0.161529i
$696$	−4.81891	+	1.29122i	−0.182660	+	0.0489437i
$697$			24.9563i			0.945286i
$698$	0.737276	+	2.75155i	0.0279063	+	0.104148i
$699$	9.04873	+	15.6729i	0.342254	+	0.592802i
$700$	1.77883	−	7.84994i	0.0672335	−	0.296700i
$701$		−	14.1107i		−	0.532954i	−0.963841	−	0.266477i	$-0.914140\pi$
$701$		−	14.1107i		−	0.532954i	0.963841	−	0.266477i	$-0.0858596\pi$
$702$	−3.60555		0.000325957i	−0.136083		1.23025e-5i
$703$	−37.0402	+	37.0402i	−1.39700	+	1.39700i
$704$	0.837189	−	3.12443i	0.0315527	−	0.117756i
$705$	0.101247	+	0.668195i	0.00381318	+	0.0251657i
$706$	−25.6455	−	14.8064i	−0.965180	−	0.557247i
$707$	19.6446			0.738811
$708$	−5.62020	−	3.24482i	−0.211220	−	0.121948i
$709$	−9.01486	−	33.6439i	−0.338560	−	1.26352i	−0.899958	−	0.435977i	$-0.856403\pi$
$709$	−9.01486	−	33.6439i	−0.338560	−	1.26352i	0.561398	−	0.827546i	$-0.310264\pi$
$710$	1.46720	−	3.74695i	0.0550631	−	0.140621i
$711$	−5.87507	+	10.1759i	−0.220332	+	0.381627i
$712$	13.4808	+	3.61218i	0.505216	+	0.135372i
$713$	−6.26413	−	10.8498i	−0.234594	−	0.406328i
$714$	−11.4949			−0.430185
$715$	−23.8954	+	10.4451i	−0.893639	+	0.390624i
$716$	14.4606			0.540418
$717$	−12.8611	−	22.2760i	−0.480305	−	0.831913i
$718$	−8.38007	−	2.24543i	−0.312741	−	0.0837988i
$719$	−5.55899	+	9.62846i	−0.207315	+	0.359081i	−0.950868	−	0.309597i	$-0.899806\pi$
$719$	−5.55899	+	9.62846i	−0.207315	+	0.359081i	0.743553	+	0.668678i	$0.233139\pi$
$720$	−0.895783	−	2.04880i	−0.0333839	−	0.0763542i
$721$	−1.58962	−	5.93255i	−0.0592006	−	0.220940i
$722$	−7.20742	−	4.16121i	−0.268232	−	0.154864i
$723$	21.2779			0.791334
$724$	−7.73995	−	4.46866i	−0.287653	−	0.166077i
$725$	−5.51276	+	24.3277i	−0.204739	+	0.903509i
$726$	0.138998	−	0.518746i	0.00515869	−	0.0192525i
$727$	−22.7582	+	22.7582i	−0.844055	+	0.844055i	−0.989383	−	0.145329i	$-0.953576\pi$
$727$	−22.7582	+	22.7582i	−0.844055	+	0.844055i	0.145329	+	0.989383i	$0.453576\pi$
$728$	−1.50274	+	5.60628i	−0.0556953	+	0.207783i
$729$			1.00000i			0.0370370i
$730$	17.4078	+	12.8266i	0.644292	+	0.474734i
$731$	16.3658	+	28.3463i	0.605310	+	1.04843i
$732$	−0.435216	−	1.62425i	−0.0160860	−	0.0600339i
$733$		−	8.74883i		−	0.323145i	−0.986861	−	0.161573i	$-0.948343\pi$
$733$		−	8.74883i		−	0.323145i	0.986861	−	0.161573i	$-0.0516566\pi$
$734$	−20.3658	+	5.45699i	−0.751714	+	0.201421i
$735$	−6.15227	−	7.70239i	−0.226930	−	0.284107i
$736$	1.84805	+	1.84805i	0.0681199	+	0.0681199i
$737$	−35.0702	+	9.39703i	−1.29183	+	0.346144i
$738$	0.904570	−	3.37590i	0.0332977	−	0.124269i
$739$	−24.1116	−	6.46068i	−0.886959	−	0.237660i	−0.213552	−	0.976932i	$-0.568503\pi$
$739$	−24.1116	−	6.46068i	−0.886959	−	0.237660i	−0.673407	+	0.739272i	$0.735170\pi$
$740$	−8.97700	−	20.5318i	−0.330001	−	0.754765i
$741$	−4.87619	−	18.2048i	−0.179131	−	0.668769i
$742$	−10.8046	−	10.8046i	−0.396650	−	0.396650i
$743$	0.807394	−	0.466149i	0.0296204	−	0.0171014i	−0.485117	−	0.874449i	$-0.661223\pi$
$743$	0.807394	−	0.466149i	0.0296204	−	0.0171014i	0.514737	+	0.857348i	$0.327890\pi$
$744$	4.15139	−	2.39681i	0.152197	−	0.0878712i
$745$	10.9379	−	8.73664i	0.400734	−	0.320086i
$746$	6.50956	−	6.50956i	0.238332	−	0.238332i
$747$	−6.99960	+	12.1237i	−0.256102	+	0.443581i
$748$	−11.5486	+	20.0028i	−0.422260	+	0.731377i
$749$	15.4967	−	15.4967i	0.566239	−	0.566239i
$750$	−11.1510	−	0.809439i	−0.407177	−	0.0295565i
$751$	−27.9998	+	16.1657i	−1.02173	+	0.589895i	−0.914604	−	0.404351i	$-0.867498\pi$
$751$	−27.9998	+	16.1657i	−1.02173	+	0.589895i	−0.107124	+	0.994246i	$0.534164\pi$
$752$	0.261745	−	0.151118i	0.00954485	−	0.00551072i
$753$	−2.57216	−	2.57216i	−0.0937348	−	0.0937348i
$754$	4.65714	−	17.3744i	0.169603	−	0.632739i
$755$	−11.2477	−	4.40427i	−0.409344	−	0.160288i
$756$	1.55494	+	0.416645i	0.0565527	+	0.0151532i
$757$	2.84736	−	10.6265i	0.103489	−	0.386226i	−0.894680	−	0.446707i	$-0.852597\pi$
$757$	2.84736	−	10.6265i	0.103489	−	0.386226i	0.998169	+	0.0604807i	$0.0192633\pi$
$758$	−9.91598	+	2.65698i	−0.360165	+	0.0965058i
$759$	−5.97778	−	5.97778i	−0.216980	−	0.216980i
$760$	9.13246	−	7.29454i	0.331269	−	0.264601i
$761$	−19.9306	+	5.34040i	−0.722485	+	0.193589i	−0.601280	−	0.799038i	$-0.705342\pi$
$761$	−19.9306	+	5.34040i	−0.722485	+	0.193589i	−0.121205	+	0.992628i	$0.538676\pi$
$762$			10.2312i			0.370638i
$763$	−6.62462	−	24.7234i	−0.239827	−	0.895048i
$764$	−4.01556	−	6.95516i	−0.145278	−	0.251629i
$765$	2.39204	+	15.7866i	0.0864843	+	0.570767i
$766$			21.4505i			0.775036i
$767$	20.2650	−	11.6975i	0.731726	−	0.422374i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	−6.54335	+	24.4201i	−0.235959	+	0.880612i	0.741755	+	0.670671i	$0.233994\pi$
$769$	−6.54335	+	24.4201i	−0.235959	+	0.880612i	−0.977714	+	0.209941i	$0.932673\pi$
$770$	11.5121	−	1.74434i	0.414866	−	0.0628617i
$771$	11.1581	+	6.44212i	0.401848	+	0.232007i
$772$	−10.7669			−0.387510
$773$	33.5205	+	19.3530i	1.20565	+	0.696081i	0.961805	−	0.273735i	$-0.0882590\pi$
$773$	33.5205	+	19.3530i	1.20565	+	0.696081i	0.243842	+	0.969815i	$0.421592\pi$
$774$	−1.18639	−	4.42768i	−0.0426440	−	0.159150i
$775$	−0.933525	−	23.9499i	−0.0335332	−	0.860305i
$776$	−3.45811	+	5.98962i	−0.124139	+	0.215015i
$777$	15.5827	+	4.17537i	0.559026	+	0.149790i
$778$	1.12277	+	1.94470i	0.0402533	+	0.0697208i
$779$	18.2686			0.654541
$780$	8.01218	+	0.897167i	0.286882	+	0.0321237i
$781$	5.82099			0.208291
$782$	−9.33108	−	16.1619i	−0.333679	−	0.577949i
$783$	−4.81891	−	1.29122i	−0.172214	−	0.0461445i
$784$	−2.20428	+	3.81793i	−0.0787244	+	0.136355i
$785$	−35.9513	−	14.0775i	−1.28316	−	0.502448i
$786$	−3.70983	−	13.8453i	−0.132325	−	0.493844i
$787$	−25.7545	−	14.8693i	−0.918047	−	0.530035i	−0.0350357	−	0.999386i	$-0.511155\pi$
$787$	−25.7545	−	14.8693i	−0.918047	−	0.530035i	−0.883012	+	0.469351i	$0.844488\pi$
$788$	16.3010			0.580698
$789$	3.80676	+	2.19783i	0.135524	+	0.0782449i
$790$	15.5856	−	21.1523i	0.554512	−	0.752563i
$791$	−2.08995	+	7.79979i	−0.0743100	+	0.277329i
$792$	2.28724	−	2.28724i	0.0812736	−	0.0812736i
$793$	5.85616	+	1.56972i	0.207958	+	0.0557424i
$794$			32.6609i			1.15909i
$795$	−12.5903	+	17.0871i	−0.446531	+	0.606016i
$796$	8.15165	+	14.1191i	0.288927	+	0.500437i
$797$	4.53303	+	16.9175i	0.160568	+	0.599248i	0.998564	+	0.0535719i	$0.0170606\pi$
$797$	4.53303	+	16.9175i	0.160568	+	0.599248i	−0.837996	+	0.545677i	$0.816273\pi$
$798$			8.41453i			0.297871i
$799$	−2.08461	+	0.558570i	−0.0737483	+	0.0197608i
$800$	1.48122	+	4.77556i	0.0523691	+	0.168842i
$801$	9.86865	+	9.86865i	0.348692	+	0.348692i
$802$	−9.22208	+	2.47105i	−0.325643	+	0.0872558i
$803$	−8.09569	+	30.2135i	−0.285691	+	1.06621i
$804$	10.8420	+	2.90512i	0.382369	+	0.102456i
$805$	−3.43019	+	8.76005i	−0.120898	+	0.308751i
$806$	−0.00156251	+	17.2836i	−5.50371e−5	+	0.608789i
$807$	7.49223	+	7.49223i	0.263739	+	0.263739i
$808$	−10.5683	+	6.10159i	−0.371790	+	0.214653i
$809$	0.509303	−	0.294046i	0.0179062	−	0.0103381i	−0.491020	−	0.871148i	$-0.663376\pi$
$809$	0.509303	−	0.294046i	0.0179062	−	0.0103381i	0.508926	+	0.860810i	$0.330043\pi$
$810$	0.248628	−	2.22220i	0.00873591	−	0.0780802i
$811$	−29.9296	+	29.9296i	−1.05097	+	1.05097i	−0.0523417	+	0.998629i	$0.516668\pi$
$811$	−29.9296	+	29.9296i	−1.05097	+	1.05097i	−0.998629	+	0.0523417i	$0.983332\pi$
$812$	−4.01555	+	6.95514i	−0.140918	+	0.244078i
$813$	−5.79194	+	10.0319i	−0.203132	+	0.351835i
$814$	22.9214	−	22.9214i	0.803394	−	0.803394i
$815$	1.06878	−	9.55255i	0.0374376	−	0.334611i
$816$	6.18393	−	3.57029i	0.216481	−	0.124985i
$817$	20.7502	−	11.9801i	0.725958	−	0.419132i
$818$	1.83773	+	1.83773i	0.0642546	+	0.0642546i
$819$	−4.10455	+	4.10381i	−0.143425	+	0.143399i
$820$	−2.84948	+	7.27703i	−0.0995082	+	0.254125i
$821$	24.8891	+	6.66901i	0.868635	+	0.232750i	0.665497	−	0.746400i	$-0.268220\pi$
$821$	24.8891	+	6.66901i	0.868635	+	0.232750i	0.203137	+	0.979150i	$0.434886\pi$
$822$	−1.64018	+	6.12124i	−0.0572079	+	0.213503i
$823$	25.8453	−	6.92522i	0.900910	−	0.241398i	0.221503	−	0.975160i	$-0.428904\pi$
$823$	25.8453	−	6.92522i	0.900910	−	0.241398i	0.679407	+	0.733762i	$0.262237\pi$
$824$	2.69782	+	2.69782i	0.0939829	+	0.0939829i
$825$	−4.79123	−	15.4473i	−0.166809	−	0.537805i
$826$	−10.0910	+	2.70388i	−0.351111	+	0.0940800i
$827$		−	6.15755i		−	0.214119i	−0.994253	−	0.107059i	$-0.965856\pi$
$827$		−	6.15755i		−	0.214119i	0.994253	−	0.107059i	$-0.0341435\pi$
$828$	0.676432	+	2.52448i	0.0235076	+	0.0877317i
$829$	9.55922	+	16.5571i	0.332006	+	0.575050i	0.982905	−	0.184114i	$-0.0589414\pi$
$829$	9.55922	+	16.5571i	0.332006	+	0.575050i	−0.650899	+	0.759164i	$0.725608\pi$
$830$	18.5688	−	25.2009i	0.644533	−	0.874737i
$831$			1.35883i			0.0471373i
$832$	−0.932870	−	3.48278i	−0.0323415	−	0.120744i
$833$	22.2595	−	22.2595i	0.771248	−	0.771248i
$834$	−4.43291	+	16.5438i	−0.153499	+	0.572866i
$835$	13.2908	−	18.0378i	0.459947	−	0.624224i
$836$	14.6426	+	8.45389i	0.506424	+	0.292384i
$837$	4.79361			0.165692
$838$	15.9488	+	9.20806i	0.550943	+	0.318087i
$839$	−0.774798	−	2.89159i	−0.0267490	−	0.0998287i	0.951261	−	0.308388i	$-0.0997894\pi$
$839$	−0.774798	−	2.89159i	−0.0267490	−	0.0998287i	−0.978010	+	0.208559i	$0.933123\pi$
$840$	−3.35180	−	1.31247i	−0.115648	−	0.0452846i
$841$	−2.05543	+	3.56010i	−0.0708767	+	0.122762i
$842$	−12.6322	−	3.38479i	−0.435335	−	0.116648i
$843$	1.02444	+	1.77438i	0.0352835	+	0.0611127i
$844$	22.8367			0.786071
$845$	−17.2477	+	23.3991i	−0.593339	+	0.804953i
$846$	0.302237			0.0103911
$847$	−0.432266	−	0.748707i	−0.0148528	−	0.0257259i
$848$	9.16850	+	2.45669i	0.314848	+	0.0843631i
$849$	−3.74137	+	6.48024i	−0.128403	+	0.222401i
$850$	−1.39058	−	35.6759i	−0.0476966	−	1.22367i
$851$	6.77880	+	25.2988i	0.232374	+	0.867232i
$852$	−1.55848	−	0.899786i	−0.0533925	−	0.0308262i
$853$	−23.3642			−0.799973			−0.399987	−	0.916521i	$-0.630985\pi$
$853$	−23.3642			−0.799973			−0.399987	+	0.916521i	$0.630985\pi$
$854$	−2.34428	−	1.35347i	−0.0802195	−	0.0463148i
$855$	11.5562	−	1.75103i	0.395214	−	0.0598840i
$856$	−3.52356	+	13.1501i	−0.120433	+	0.449461i
$857$	2.33660	−	2.33660i	0.0798168	−	0.0798168i	−0.666071	−	0.745888i	$-0.732025\pi$
$857$	2.33660	−	2.33660i	0.0798168	−	0.0798168i	0.745888	+	0.666071i	$0.232025\pi$
$858$	3.01751	+	11.2656i	0.103016	+	0.384600i
$859$			3.73933i			0.127584i	0.997963	+	0.0637922i	$0.0203195\pi$
$859$			3.73933i			0.127584i	−0.997963	+	0.0637922i	$0.979681\pi$
$860$	1.53556	+	10.1342i	0.0523621	+	0.345572i
$861$	−2.81310	−	4.87244i	−0.0958704	−	0.166052i
$862$	0.244796	+	0.913591i	0.00833778	+	0.0311170i
$863$		−	24.5878i		−	0.836977i	−0.908222	−	0.418488i	$-0.862560\pi$
$863$		−	24.5878i		−	0.836977i	0.908222	−	0.418488i	$-0.137440\pi$
$864$	−0.965926	+	0.258819i	−0.0328615	+	0.00880520i
$865$	4.53003	−	3.61836i	0.154026	−	0.123028i
$866$	−20.6341	−	20.6341i	−0.701177	−	0.701177i
$867$	−32.8299	+	8.79674i	−1.11496	+	0.298753i
$868$	1.99724	−	7.45379i	0.0677906	−	0.252998i
$869$	36.7125	+	9.83709i	1.24539	+	0.333700i
$870$	10.3876	+	4.06748i	0.352171	+	0.137900i
$871$	−28.6196	+	28.6144i	−0.969737	+	0.969562i
$872$	11.2429	+	11.2429i	0.380734	+	0.380734i
$873$	−5.98962	+	3.45811i	−0.202718	+	0.117039i
$874$	−11.8309	+	6.83058i	−0.400186	+	0.231048i
$875$	−13.6145	+	11.7718i	−0.460255	+	0.397958i
$876$	6.83779	−	6.83779i	0.231027	−	0.231027i
$877$	20.7013	−	35.8557i	0.699034	−	1.21076i	−0.269768	−	0.962925i	$-0.586947\pi$
$877$	20.7013	−	35.8557i	0.699034	−	1.21076i	0.968802	−	0.247836i	$-0.0797195\pi$
$878$	4.82036	−	8.34911i	0.162679	−	0.281769i
$879$	−20.9086	+	20.9086i	−0.705228	+	0.705228i
$880$	−5.65139	+	4.51404i	−0.190508	+	0.152168i
$881$	−45.8910	+	26.4952i	−1.54611	+	0.892645i	−0.547674	+	0.836692i	$0.684487\pi$
$881$	−45.8910	+	26.4952i	−1.54611	+	0.892645i	−0.998433	+	0.0559534i	$0.982180\pi$
$882$	−3.81793	+	2.20428i	−0.128556	+	0.0742221i
$883$	−14.4468	−	14.4468i	−0.486175	−	0.486175i	0.420922	−	0.907097i	$-0.361707\pi$
$883$	−14.4468	−	14.4468i	−0.486175	−	0.486175i	−0.907097	+	0.420922i	$0.861707\pi$
$884$	−0.00232753	+	25.7458i	−7.82832e−5	+	0.865924i
$885$	5.81331	+	13.2960i	0.195412	+	0.446939i
$886$	17.0043	+	4.55628i	0.571270	+	0.153071i
$887$	9.82748	−	36.6767i	0.329975	−	1.23148i	−0.579241	−	0.815156i	$-0.696651\pi$
$887$	9.82748	−	36.6767i	0.329975	−	1.23148i	0.909216	−	0.416325i	$-0.136682\pi$
$888$	−9.67993	+	2.59373i	−0.324837	+	0.0870399i
$889$	11.6462	+	11.6462i	0.390600	+	0.390600i
$890$	−19.4765	−	24.3838i	−0.652854	−	0.817346i
$891$	3.12443	−	0.837189i	0.104672	−	0.0280469i
$892$			24.3420i			0.815029i
$893$	0.408887	+	1.52599i	0.0136829	+	0.0510652i
$894$	−3.13023	−	5.42171i	−0.104690	−	0.181329i
$895$	−26.0316	−	19.1808i	−0.870139	−	0.641145i
$896$			1.60979i			0.0537794i
$897$	−9.10192	−	2.43973i	−0.303904	−	0.0814603i
$898$	−12.6369	+	12.6369i	−0.421697	+	0.421697i
$899$	−6.18962	+	23.1000i	−0.206435	+	0.770428i
$900$	−1.10501	+	4.87637i	−0.0368335	+	0.162546i
$901$	−58.6974	−	33.8890i	−1.95550	−	1.12901i
$902$	−11.3051			−0.376417
$903$	−6.39047	−	3.68954i	−0.212662	−	0.122780i
$904$	−1.29827	−	4.84521i	−0.0431799	−	0.161149i
$905$	8.00590	+	18.3108i	0.266125	+	0.608671i
$906$	−2.70099	+	4.67826i	−0.0897345	+	0.155425i
$907$	33.8859	+	9.07971i	1.12516	+	0.301487i	0.772972	−	0.634441i	$-0.218769\pi$
$907$	33.8859	+	9.07971i	1.12516	+	0.301487i	0.352193	+	0.935927i	$0.385436\pi$
$908$	−0.401227	−	0.694946i	−0.0133152	−	0.0230626i
$909$	−12.2032			−0.404754
$910$	10.1415	−	8.09899i	0.336187	−	0.268479i
$911$	−24.2576			−0.803691			−0.401845	−	0.915708i	$-0.631631\pi$
$911$	−24.2576			−0.803691			−0.401845	+	0.915708i	$0.631631\pi$
$912$	−2.61354	−	4.52679i	−0.0865430	−	0.149897i
$913$	43.7395	+	11.7200i	1.44757	+	0.387874i
$914$	0.805048	−	1.39438i	0.0266286	−	0.0461221i
$915$	−1.37097	+	3.50120i	−0.0453229	+	0.115746i
$916$	−2.33420	−	8.71136i	−0.0771242	−	0.287832i
$917$	−19.9829	−	11.5371i	−0.659893	−	0.380989i
$918$	7.14059			0.235675
$919$	28.3273	+	16.3548i	0.934431	+	0.539494i	0.888210	−	0.459437i	$-0.151949\pi$
$919$	28.3273	+	16.3548i	0.934431	+	0.539494i	0.0462207	+	0.998931i	$0.485282\pi$
$920$	−0.875512	−	5.77808i	−0.0288648	−	0.190498i
$921$	−4.95612	+	18.4965i	−0.163310	+	0.609480i
$922$	−10.8773	+	10.8773i	−0.358225	+	0.358225i
$923$	5.61946	−	3.24372i	0.184967	−	0.106768i
$924$		−	5.20712i		−	0.171302i
$925$	−11.0737	+	48.8680i	−0.364101	+	1.60677i
$926$	−0.626839	−	1.08572i	−0.0205992	−	0.0356789i
$927$	0.987470	+	3.68529i	0.0324328	+	0.121041i
$928$		−	4.98890i		−	0.163769i
$929$	1.00512	−	0.269322i	0.0329770	−	0.00883616i	−0.242293	−	0.970203i	$-0.577899\pi$
$929$	1.00512	−	0.269322i	0.0329770	−	0.00883616i	0.275270	+	0.961367i	$0.411233\pi$
$930$	−10.6524	−	1.19183i	−0.349305	−	0.0390816i
$931$	−16.2945	−	16.2945i	−0.534032	−	0.534032i
$932$	−17.4808	+	4.68397i	−0.572603	+	0.153428i
$933$	0.631089	−	2.35525i	0.0206609	−	0.0771076i
$934$	37.3470	+	10.0071i	1.22203	+	0.327443i
$935$	47.3217	−	20.6902i	1.54759	−	0.676641i
$936$	0.933500	−	3.48261i	0.0305124	−	0.113833i
$937$	−29.5795	−	29.5795i	−0.966321	−	0.966321i	0.0331301	−	0.999451i	$-0.489452\pi$
$937$	−29.5795	−	29.5795i	−0.966321	−	0.966321i	−0.999451	+	0.0331301i	$0.989452\pi$
$938$	15.6483	−	9.03457i	0.510936	−	0.294989i
$939$	27.5370	−	15.8985i	0.898635	−	0.518827i
$940$	−0.671631	−	0.0751447i	−0.0219062	−	0.00245095i
$941$	−9.54159	+	9.54159i	−0.311047	+	0.311047i	−0.845315	−	0.534268i	$-0.820587\pi$
$941$	−9.54159	+	9.54159i	−0.311047	+	0.311047i	0.534268	+	0.845315i	$0.320587\pi$
$942$	−8.63329	+	14.9533i	−0.281288	+	0.487205i
$943$	4.56713	−	7.91051i	0.148726	−	0.257602i
$944$	4.58887	−	4.58887i	0.149355	−	0.149355i
$945$	−2.24651	−	2.81254i	−0.0730790	−	0.0914918i
$946$	−12.8407	+	7.41361i	−0.417489	+	0.241037i
$947$	17.1953	−	9.92770i	0.558771	−	0.322607i	−0.193881	−	0.981025i	$-0.562108\pi$
$947$	17.1953	−	9.92770i	0.558771	−	0.322607i	0.752652	+	0.658418i	$0.228774\pi$
$948$	−8.30861	−	8.30861i	−0.269851	−	0.269851i
$949$	9.02094	+	33.6788i	0.292832	+	1.09326i
$950$	−26.1156	+	1.01794i	−0.847302	+	0.0330264i
$951$	5.78507	+	1.55010i	0.187594	+	0.0502656i
$952$	2.97509	−	11.1032i	0.0964233	−	0.359857i
$953$	29.2748	−	7.84417i	0.948305	−	0.254098i	0.248662	−	0.968590i	$-0.420009\pi$
$953$	29.2748	−	7.84417i	0.948305	−	0.254098i	0.699643	+	0.714493i	$0.253342\pi$
$954$	6.71181	+	6.71181i	0.217303	+	0.217303i
$955$	−1.99677	+	17.8468i	−0.0646138	+	0.577508i
$956$	24.8457	−	6.65737i	0.803566	−	0.215315i
$957$			16.1373i			0.521646i
$958$	8.19388	+	30.5800i	0.264732	+	0.987994i
$959$	5.10077	+	8.83479i	0.164712	+	0.285290i
$960$	2.21083	−	0.334992i	0.0713543	−	0.0108118i
$961$			8.02127i			0.258751i
$962$	9.35498	−	34.9006i	0.301617	−	1.12524i
$963$	−9.62654	+	9.62654i	−0.310211	+	0.310211i
$964$	−5.50713	+	20.5529i	−0.177373	+	0.661963i
$965$	19.3823	+	14.2814i	0.623937	+	0.459736i
$966$	3.64358	+	2.10362i	0.117230	+	0.0676830i
$967$	43.3835			1.39512			0.697560	−	0.716527i	$-0.254269\pi$
$967$	43.3835			1.39512			0.697560	+	0.716527i	$0.254269\pi$
$968$	0.465095	+	0.268523i	0.0149487	+	0.00863065i
$969$	9.66028	+	36.0527i	0.310333	+	1.15818i
$970$	14.1699	−	6.19543i	0.454969	−	0.198923i
$971$	19.7430	−	34.1958i	0.633582	−	1.09740i	−0.353232	−	0.935536i	$-0.614917\pi$
$971$	19.7430	−	34.1958i	0.633582	−	1.09740i	0.986814	−	0.161860i	$-0.0517493\pi$
$972$	−0.965926	−	0.258819i	−0.0309821	−	0.00830162i
$973$	13.7858	+	23.8777i	0.441953	+	0.765485i
$974$	−36.5736			−1.17189
$975$	−13.2333	−	12.2426i	−0.423804	−	0.392076i
$976$	1.68154			0.0538249
$977$	24.2778	+	42.0503i	0.776715	+	1.34531i	0.933826	+	0.357728i	$0.116449\pi$
$977$	24.2778	+	42.0503i	0.776715	+	1.34531i	−0.157111	+	0.987581i	$0.550218\pi$
$978$	−4.15221	−	1.11258i	−0.132773	−	0.0355764i
$979$	22.5720	−	39.0959i	0.721404	−	1.24951i
$980$	9.03226	−	3.94912i	0.288525	−	0.126150i
$981$	4.11520	+	15.3581i	0.131388	+	0.490348i
$982$	33.5648	+	19.3787i	1.07110	+	0.618398i
$983$	−20.1288			−0.642008			−0.321004	−	0.947078i	$-0.604020\pi$
$983$	−20.1288			−0.642008			−0.321004	+	0.947078i	$0.604020\pi$
$984$	3.02675	+	1.74749i	0.0964892	+	0.0557081i
$985$	−29.3445	−	21.6219i	−0.934993	−	0.688932i
$986$	−9.22009	+	34.4099i	−0.293628	+	1.09583i
$987$	0.344035	−	0.344035i	0.0109508	−	0.0109508i
$988$	18.8465	+	0.00170381i	0.599588	+	5.42053e-5i
$989$		−	11.9801i		−	0.380945i
$990$	−7.15127	+	1.08358i	−0.227282	+	0.0344385i
$991$	−4.61961	−	8.00139i	−0.146747	−	0.254173i	0.783277	−	0.621673i	$-0.213547\pi$
$991$	−4.61961	−	8.00139i	−0.146747	−	0.254173i	−0.930023	+	0.367501i	$0.880214\pi$
$992$	1.24068	+	4.63027i	0.0393916	+	0.147011i
$993$		−	18.3181i		−	0.581308i
$994$	−2.79823	+	0.749783i	−0.0887544	+	0.0237817i
$995$	4.05346	−	36.2292i	0.128503	−	1.14854i
$996$	−9.89893	−	9.89893i	−0.313659	−	0.313659i
$997$	−54.5558	+	14.6182i	−1.72780	+	0.462963i	−0.979674	−	0.200594i	$-0.935713\pi$
$997$	−54.5558	+	14.6182i	−1.72780	+	0.462963i	−0.748126	+	0.663557i	$0.769046\pi$
$998$	1.18719	−	4.43066i	0.0375799	−	0.140250i
$999$	−9.67993	−	2.59373i	−0.306259	−	0.0820620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bn.c.67.8	yes	32
5.3	odd	4		390.2.bd.c.223.4	yes	32
13.7	odd	12		390.2.bd.c.7.4	✓	32
65.33	even	12	inner	390.2.bn.c.163.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.c.7.4	✓	32	13.7	odd	12
390.2.bd.c.223.4	yes	32	5.3	odd	4
390.2.bn.c.67.8	yes	32	1.1	even	1	trivial
390.2.bn.c.163.8	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.04880 - 0.895783i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-1.39412 - 0.804897i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.04880 - 0.895783i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-1.39412 - 0.804897i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +(-1.80017 - 1.32642i) q^{10} +(0.837189 - 3.12443i) q^{11} +(-0.707107 + 0.707107i) q^{12} +(-0.932870 - 3.48278i) q^{13} +1.60979i q^{14} +(2.21083 - 0.334992i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.84812 + 6.89728i) q^{17} -1.00000i q^{18} +(5.04898 - 1.35287i) q^{19} +(-0.248628 + 2.22220i) q^{20} +(-1.13830 - 1.13830i) q^{21} +(-3.12443 + 0.837189i) q^{22} +(0.676432 - 2.52448i) q^{23} +(0.965926 + 0.258819i) q^{24} +(3.39515 - 3.67056i) q^{25} +(-2.54974 + 2.54928i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.39412 - 0.804897i) q^{28} +(-4.32052 + 2.49445i) q^{29} +(-1.39553 - 1.74714i) q^{30} +(3.38960 - 3.38960i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.61732 - 2.80129i) q^{33} +(5.04916 - 5.04916i) q^{34} +(-3.57729 - 0.400240i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-8.67879 + 5.01070i) q^{37} +(-3.69611 - 3.69611i) q^{38} +(0.000325957 - 3.60555i) q^{39} +(2.04880 - 0.895783i) q^{40} +(3.37590 + 0.904570i) q^{41} +(-0.416645 + 1.55494i) q^{42} +(4.42768 - 1.18639i) q^{43} +(2.28724 + 2.28724i) q^{44} +(2.22220 + 0.248628i) q^{45} +(-2.52448 + 0.676432i) q^{46} +0.302237i q^{47} +(-0.258819 - 0.965926i) q^{48} +(-2.20428 - 3.81793i) q^{49} +(-4.87637 - 1.10501i) q^{50} +7.14059i q^{51} +(3.48261 + 0.933500i) q^{52} +(-6.71181 + 6.71181i) q^{53} +(0.258819 - 0.965926i) q^{54} +(-1.08358 - 7.15127i) q^{55} +(-1.39412 - 0.804897i) q^{56} +5.22708 q^{57} +(4.32052 + 2.49445i) q^{58} +(1.67964 + 6.26852i) q^{59} +(-0.815305 + 2.08213i) q^{60} +(-0.840772 + 1.45626i) q^{61} +(-4.63027 - 1.24068i) q^{62} +(-0.804897 - 1.39412i) q^{63} +1.00000 q^{64} +(-5.03108 - 6.29986i) q^{65} -3.23465 q^{66} +(-5.61225 - 9.72071i) q^{67} +(-6.89728 - 1.84812i) q^{68} +(1.30677 - 2.26339i) q^{69} +(1.44202 + 3.29814i) q^{70} +(0.465764 + 1.73825i) q^{71} +(0.866025 + 0.500000i) q^{72} -9.67009 q^{73} +(8.67879 + 5.01070i) q^{74} +(4.22947 - 2.66676i) q^{75} +(-1.35287 + 5.04898i) q^{76} +(-3.68199 + 3.68199i) q^{77} +(-3.12266 + 1.80249i) q^{78} +11.7501i q^{79} +(-1.80017 - 1.32642i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.904570 - 3.37590i) q^{82} +13.9992i q^{83} +(1.55494 - 0.416645i) q^{84} +(9.96489 + 12.4756i) q^{85} +(-3.24129 - 3.24129i) q^{86} +(-4.81891 + 1.29122i) q^{87} +(0.837189 - 3.12443i) q^{88} +(13.4808 + 3.61218i) q^{89} +(-0.895783 - 2.04880i) q^{90} +(-1.50274 + 5.60628i) q^{91} +(1.84805 + 1.84805i) q^{92} +(4.15139 - 2.39681i) q^{93} +(0.261745 - 0.151118i) q^{94} +(9.13246 - 7.29454i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(-3.45811 + 5.98962i) q^{97} +(-2.20428 + 3.81793i) q^{98} +(2.28724 - 2.28724i) 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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