LMFDB - Embedded newform 390.2.s.c.77.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(77,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("390.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.4
Character	$\chi$	$=$	390.77
Dual form			390.2.s.c.233.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.805823 + 1.53318i) q^{3} +1.00000i q^{4} +(-1.53706 + 1.62402i) q^{5} +(0.514321 - 1.65393i) q^{6} +(-0.677204 + 0.677204i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.70130 + 2.47095i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.805823 + 1.53318i) q^{3} +1.00000i q^{4} +(-1.53706 + 1.62402i) q^{5} +(0.514321 - 1.65393i) q^{6} +(-0.677204 + 0.677204i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.70130 + 2.47095i) q^{9} +(2.23522 - 0.0614950i) q^{10} -2.37516 q^{11} +(-1.53318 + 0.805823i) q^{12} +(0.799399 - 3.51582i) q^{13} +0.957712 q^{14} +(-3.72852 - 1.04791i) q^{15} -1.00000 q^{16} +(-5.31930 + 5.31930i) q^{17} +(2.95022 - 0.544224i) q^{18} +2.08922 q^{19} +(-1.62402 - 1.53706i) q^{20} +(-1.58398 - 0.492571i) q^{21} +(1.67949 + 1.67949i) q^{22} +(-1.90576 - 1.90576i) q^{23} +(1.65393 + 0.514321i) q^{24} +(-0.274910 - 4.99244i) q^{25} +(-3.05132 + 1.92080i) q^{26} +(-5.15936 - 0.617257i) q^{27} +(-0.677204 - 0.677204i) q^{28} -1.89961 q^{29} +(1.89548 + 3.37745i) q^{30} +8.49906i q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.91396 - 3.64155i) q^{33} +7.52262 q^{34} +(-0.0588945 - 2.14070i) q^{35} +(-2.47095 - 1.70130i) q^{36} +(-2.64183 + 2.64183i) q^{37} +(-1.47730 - 1.47730i) q^{38} +(6.03456 - 1.60750i) q^{39} +(0.0614950 + 2.23522i) q^{40} +8.75503 q^{41} +(0.771746 + 1.46835i) q^{42} +(0.132445 - 0.132445i) q^{43} -2.37516i q^{44} +(-1.39788 - 6.56094i) q^{45} +2.69516i q^{46} +(-2.08023 - 2.08023i) q^{47} +(-0.805823 - 1.53318i) q^{48} +6.08279i q^{49} +(-3.33580 + 3.72458i) q^{50} +(-12.4419 - 3.86904i) q^{51} +(3.51582 + 0.799399i) q^{52} +(5.82795 + 5.82795i) q^{53} +(3.21175 + 4.08468i) q^{54} +(3.65076 - 3.85732i) q^{55} +0.957712i q^{56} +(1.68354 + 3.20315i) q^{57} +(1.34322 + 1.34322i) q^{58} +11.2474i q^{59} +(1.04791 - 3.72852i) q^{60} +9.29389 q^{61} +(6.00974 - 6.00974i) q^{62} +(-0.521209 - 2.82546i) q^{63} -1.00000i q^{64} +(4.48105 + 6.70225i) q^{65} +(-1.22160 + 3.92834i) q^{66} +(-8.47780 + 8.47780i) q^{67} +(-5.31930 - 5.31930i) q^{68} +(1.38618 - 4.45759i) q^{69} +(-1.47206 + 1.55535i) q^{70} +12.4970 q^{71} +(0.544224 + 2.95022i) q^{72} +(-3.69590 - 3.69590i) q^{73} +3.73612 q^{74} +(7.43279 - 4.44451i) q^{75} +2.08922i q^{76} +(1.60847 - 1.60847i) q^{77} +(-5.40375 - 3.13041i) q^{78} -1.03917i q^{79} +(1.53706 - 1.62402i) q^{80} +(-3.21116 - 8.40764i) q^{81} +(-6.19074 - 6.19074i) q^{82} +(0.475749 - 0.475749i) q^{83} +(0.492571 - 1.58398i) q^{84} +(-0.462604 - 16.8147i) q^{85} -0.187305 q^{86} +(-1.53075 - 2.91244i) q^{87} +(-1.67949 + 1.67949i) q^{88} -8.15992i q^{89} +(-3.65083 + 5.62774i) q^{90} +(1.83957 + 2.92228i) q^{91} +(1.90576 - 1.90576i) q^{92} +(-13.0306 + 6.84873i) q^{93} +2.94189i q^{94} +(-3.21124 + 3.39294i) q^{95} +(-0.514321 + 1.65393i) q^{96} +(1.11610 - 1.11610i) q^{97} +(4.30118 - 4.30118i) q^{98} +(4.04086 - 5.86890i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} + 12 q^{9}+O(q^{10}) $ 24 * q + 4 * q^3 + 12 * q^9	$ 24 q + 4 q^{3} + 12 q^{9} + 4 q^{10} - 8 q^{12} - 8 q^{13} + 16 q^{14} - 24 q^{16} - 52 q^{17} + 16 q^{22} + 16 q^{23} + 16 q^{25} - 56 q^{27} + 80 q^{29} + 8 q^{30} - 20 q^{35} + 16 q^{38} + 32 q^{39} - 48 q^{42} + 28 q^{43} - 4 q^{48} - 20 q^{51} - 8 q^{52} - 72 q^{53} + 24 q^{55} - 64 q^{61} + 32 q^{62} + 12 q^{65} + 8 q^{66} - 52 q^{68} + 16 q^{69} + 120 q^{74} + 24 q^{75} - 32 q^{77} - 64 q^{78} + 12 q^{81} + 32 q^{82} - 16 q^{88} - 44 q^{90} + 64 q^{91} - 16 q^{92} - 96 q^{95}+O(q^{100}) $ 24 * q + 4 * q^3 + 12 * q^9 + 4 * q^10 - 8 * q^12 - 8 * q^13 + 16 * q^14 - 24 * q^16 - 52 * q^17 + 16 * q^22 + 16 * q^23 + 16 * q^25 - 56 * q^27 + 80 * q^29 + 8 * q^30 - 20 * q^35 + 16 * q^38 + 32 * q^39 - 48 * q^42 + 28 * q^43 - 4 * q^48 - 20 * q^51 - 8 * q^52 - 72 * q^53 + 24 * q^55 - 64 * q^61 + 32 * q^62 + 12 * q^65 + 8 * q^66 - 52 * q^68 + 16 * q^69 + 120 * q^74 + 24 * q^75 - 32 * q^77 - 64 * q^78 + 12 * q^81 + 32 * q^82 - 16 * q^88 - 44 * q^90 + 64 * q^91 - 16 * q^92 - 96 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.805823	+	1.53318i	0.465242	+	0.885184i
$3$	0.805823	+	1.53318i	0.465242	+	0.885184i
$4$			1.00000i			0.500000i
$5$	−1.53706	+	1.62402i	−0.687393	+	0.726286i
$5$	−1.53706	+	1.62402i	−0.687393	+	0.726286i
$6$	0.514321	−	1.65393i	0.209971	−	0.675213i
$7$	−0.677204	+	0.677204i	−0.255959	+	0.255959i	−0.823408	−	0.567449i	$-0.807930\pi$
$7$	−0.677204	+	0.677204i	−0.255959	+	0.255959i	0.567449	+	0.823408i	$0.307930\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.70130	+	2.47095i	−0.567100	+	0.823649i
$10$	2.23522	−	0.0614950i	0.706839	−	0.0194464i
$11$	−2.37516			−0.716138			−0.358069	−	0.933695i	$-0.616565\pi$
$11$	−2.37516			−0.716138			−0.358069	+	0.933695i	$0.616565\pi$
$12$	−1.53318	+	0.805823i	−0.442592	+	0.232621i
$13$	0.799399	−	3.51582i	0.221713	−	0.975112i
$13$	0.799399	−	3.51582i	0.221713	−	0.975112i
$14$	0.957712			0.255959
$15$	−3.72852	−	1.04791i	−0.962700	−	0.270570i
$16$	−1.00000			−0.250000
$17$	−5.31930	+	5.31930i	−1.29012	+	1.29012i	−0.355407	+	0.934712i	$0.615658\pi$
$17$	−5.31930	+	5.31930i	−1.29012	+	1.29012i	−0.934712	+	0.355407i	$0.884342\pi$
$18$	2.95022	−	0.544224i	0.695374	−	0.128275i
$19$	2.08922			0.479299			0.239649	−	0.970859i	$-0.422967\pi$
$19$	2.08922			0.479299			0.239649	+	0.970859i	$0.422967\pi$
$20$	−1.62402	−	1.53706i	−0.363143	−	0.343696i
$21$	−1.58398	−	0.492571i	−0.345654	−	0.107488i
$22$	1.67949	+	1.67949i	0.358069	+	0.358069i
$23$	−1.90576	−	1.90576i	−0.397379	−	0.397379i	0.479929	−	0.877308i	$-0.340663\pi$
$23$	−1.90576	−	1.90576i	−0.397379	−	0.397379i	−0.877308	+	0.479929i	$0.840663\pi$
$24$	1.65393	+	0.514321i	0.337606	+	0.104985i
$25$	−0.274910	−	4.99244i	−0.0549820	−	0.998487i
$26$	−3.05132	+	1.92080i	−0.598413	+	0.376699i
$27$	−5.15936	−	0.617257i	−0.992919	−	0.118791i
$28$	−0.677204	−	0.677204i	−0.127980	−	0.127980i
$29$	−1.89961			−0.352748			−0.176374	−	0.984323i	$-0.556437\pi$
$29$	−1.89961			−0.352748			−0.176374	+	0.984323i	$0.556437\pi$
$30$	1.89548	+	3.37745i	0.346065	+	0.616635i
$31$			8.49906i			1.52648i	0.646118	+	0.763238i	$0.276392\pi$
$31$			8.49906i			1.52648i	−0.646118	+	0.763238i	$0.723608\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−1.91396	−	3.64155i	−0.333177	−	0.633913i
$34$	7.52262			1.29012
$35$	−0.0588945	−	2.14070i	−0.00995499	−	0.361844i
$36$	−2.47095	−	1.70130i	−0.411825	−	0.283550i
$37$	−2.64183	+	2.64183i	−0.434315	+	0.434315i	−0.890093	−	0.455779i	$-0.849361\pi$
$37$	−2.64183	+	2.64183i	−0.434315	+	0.434315i	0.455779	+	0.890093i	$0.349361\pi$
$38$	−1.47730	−	1.47730i	−0.239649	−	0.239649i
$39$	6.03456	−	1.60750i	0.966303	−	0.257406i
$40$	0.0614950	+	2.23522i	0.00972322	+	0.353420i
$41$	8.75503			1.36731			0.683653	−	0.729807i	$-0.260390\pi$
$41$	8.75503			1.36731			0.683653	+	0.729807i	$0.260390\pi$
$42$	0.771746	+	1.46835i	0.119083	+	0.226571i
$43$	0.132445	−	0.132445i	0.0201977	−	0.0201977i	−0.696936	−	0.717133i	$-0.745454\pi$
$43$	0.132445	−	0.132445i	0.0201977	−	0.0201977i	0.717133	+	0.696936i	$0.245454\pi$
$44$		−	2.37516i		−	0.358069i
$45$	−1.39788	−	6.56094i	−0.208384	−	0.978047i
$46$			2.69516i			0.397379i
$47$	−2.08023	−	2.08023i	−0.303433	−	0.303433i	0.538922	−	0.842356i	$-0.318832\pi$
$47$	−2.08023	−	2.08023i	−0.303433	−	0.303433i	−0.842356	+	0.538922i	$0.818832\pi$
$48$	−0.805823	−	1.53318i	−0.116311	−	0.221296i
$49$			6.08279i			0.868970i
$50$	−3.33580	+	3.72458i	−0.471753	+	0.526735i
$51$	−12.4419	−	3.86904i	−1.74221	−	0.541774i
$52$	3.51582	+	0.799399i	0.487556	+	0.110857i
$53$	5.82795	+	5.82795i	0.800530	+	0.800530i	0.983178	−	0.182648i	$-0.0584669\pi$
$53$	5.82795	+	5.82795i	0.800530	+	0.800530i	−0.182648	+	0.983178i	$0.558467\pi$
$54$	3.21175	+	4.08468i	0.437064	+	0.555855i
$55$	3.65076	−	3.85732i	0.492268	−	0.520121i
$56$			0.957712i			0.127980i
$57$	1.68354	+	3.20315i	0.222990	+	0.424268i
$58$	1.34322	+	1.34322i	0.176374	+	0.176374i
$59$			11.2474i			1.46429i	0.681150	+	0.732144i	$0.261480\pi$
$59$			11.2474i			1.46429i	−0.681150	+	0.732144i	$0.738520\pi$
$60$	1.04791	−	3.72852i	0.135285	−	0.481350i
$61$	9.29389			1.18996			0.594980	−	0.803740i	$-0.297160\pi$
$61$	9.29389			1.18996			0.594980	+	0.803740i	$0.297160\pi$
$62$	6.00974	−	6.00974i	0.763238	−	0.763238i
$63$	−0.521209	−	2.82546i	−0.0656662	−	0.355975i
$64$		−	1.00000i		−	0.125000i
$65$	4.48105	+	6.70225i	0.555806	+	0.831312i
$66$	−1.22160	+	3.92834i	−0.150368	+	0.483545i
$67$	−8.47780	+	8.47780i	−1.03573	+	1.03573i	−0.0363899	+	0.999338i	$0.511586\pi$
$67$	−8.47780	+	8.47780i	−1.03573	+	1.03573i	−0.999338	+	0.0363899i	$0.988414\pi$
$68$	−5.31930	−	5.31930i	−0.645059	−	0.645059i
$69$	1.38618	−	4.45759i	0.166876	−	0.536631i
$70$	−1.47206	+	1.55535i	−0.175945	+	0.185900i
$71$	12.4970			1.48312			0.741560	−	0.670887i	$-0.234086\pi$
$71$	12.4970			1.48312			0.741560	+	0.670887i	$0.234086\pi$
$72$	0.544224	+	2.95022i	0.0641374	+	0.347687i
$73$	−3.69590	−	3.69590i	−0.432573	−	0.432573i	0.456930	−	0.889503i	$-0.348949\pi$
$73$	−3.69590	−	3.69590i	−0.432573	−	0.432573i	−0.889503	+	0.456930i	$0.848949\pi$
$74$	3.73612			0.434315
$75$	7.43279	−	4.44451i	0.858265	−	0.513207i
$76$			2.08922i			0.239649i
$77$	1.60847	−	1.60847i	0.183302	−	0.183302i
$78$	−5.40375	−	3.13041i	−0.611855	−	0.354449i
$79$		−	1.03917i		−	0.116916i	−0.998290	−	0.0584581i	$-0.981382\pi$
$79$		−	1.03917i		−	0.116916i	0.998290	−	0.0584581i	$-0.0186184\pi$
$80$	1.53706	−	1.62402i	0.171848	−	0.181571i
$81$	−3.21116	−	8.40764i	−0.356796	−	0.934182i
$82$	−6.19074	−	6.19074i	−0.683653	−	0.683653i
$83$	0.475749	−	0.475749i	0.0522202	−	0.0522202i	−0.680514	−	0.732735i	$-0.738244\pi$
$83$	0.475749	−	0.475749i	0.0522202	−	0.0522202i	0.732735	+	0.680514i	$0.238244\pi$
$84$	0.492571	−	1.58398i	0.0537439	−	0.172827i
$85$	−0.462604	−	16.8147i	−0.0501764	−	1.82381i
$86$	−0.187305			−0.0201977
$87$	−1.53075	−	2.91244i	−0.164113	−	0.312247i
$88$	−1.67949	+	1.67949i	−0.179034	+	0.179034i
$89$		−	8.15992i		−	0.864950i	−0.901646	−	0.432475i	$-0.857640\pi$
$89$		−	8.15992i		−	0.864950i	0.901646	−	0.432475i	$-0.142360\pi$
$90$	−3.65083	+	5.62774i	−0.384831	+	0.593216i
$91$	1.83957	+	2.92228i	0.192839	+	0.306338i
$92$	1.90576	−	1.90576i	0.198689	−	0.198689i
$93$	−13.0306	+	6.84873i	−1.35121	+	0.710181i
$94$			2.94189i			0.303433i
$95$	−3.21124	+	3.39294i	−0.329467	+	0.348108i
$96$	−0.514321	+	1.65393i	−0.0524927	+	0.168803i
$97$	1.11610	−	1.11610i	0.113323	−	0.113323i	−0.648172	−	0.761494i	$-0.724466\pi$
$97$	1.11610	−	1.11610i	0.113323	−	0.113323i	0.761494	+	0.648172i	$0.224466\pi$
$98$	4.30118	−	4.30118i	0.434485	−	0.434485i
$99$	4.04086	−	5.86890i	0.406122	−	0.589846i
$100$	4.99244	−	0.274910i	0.499244	−	0.0274910i
$101$		−	17.6200i		−	1.75325i	−0.481171	−	0.876627i	$-0.659788\pi$
$101$		−	17.6200i		−	1.75325i	0.481171	−	0.876627i	$-0.340212\pi$
$102$	6.06190	+	11.5336i	0.600217	+	1.14199i
$103$	−1.63440	+	1.63440i	−0.161042	+	0.161042i	−0.783028	−	0.621986i	$-0.786326\pi$
$103$	−1.63440	+	1.63440i	−0.161042	+	0.161042i	0.621986	+	0.783028i	$0.286326\pi$
$104$	−1.92080	−	3.05132i	−0.188350	−	0.299206i
$105$	3.23462	−	1.81532i	0.315667	−	0.177157i
$106$		−	8.24196i		−	0.800530i
$107$	4.52629	−	4.52629i	0.437573	−	0.437573i	−0.453622	−	0.891194i	$-0.649868\pi$
$107$	4.52629	−	4.52629i	0.437573	−	0.437573i	0.891194	+	0.453622i	$0.149868\pi$
$108$	0.617257	−	5.15936i	0.0593955	−	0.496460i
$109$	17.1190			1.63970			0.819851	−	0.572577i	$-0.194056\pi$
$109$	17.1190			1.63970			0.819851	+	0.572577i	$0.194056\pi$
$110$	−5.30901	+	0.146061i	−0.506194	+	0.0139263i
$111$	−6.17926	−	1.92156i	−0.586510	−	0.182387i
$112$	0.677204	−	0.677204i	0.0639898	−	0.0639898i
$113$	−1.12282	−	1.12282i	−0.105626	−	0.105626i	0.652319	−	0.757945i	$-0.273796\pi$
$113$	−1.12282	−	1.12282i	−0.105626	−	0.105626i	−0.757945	+	0.652319i	$0.773796\pi$
$114$	1.07453	−	3.45541i	0.100639	−	0.323629i
$115$	6.02427	−	0.165739i	0.561766	−	0.0154552i
$116$		−	1.89961i		−	0.176374i
$117$	7.32738	+	7.95673i	0.677416	+	0.735600i
$118$	7.95312	−	7.95312i	0.732144	−	0.732144i
$119$		−	7.20450i		−	0.660436i
$120$	−3.37745	+	1.89548i	−0.308318	+	0.173033i
$121$	−5.35861			−0.487147
$122$	−6.57177	−	6.57177i	−0.594980	−	0.594980i
$123$	7.05501	+	13.4231i	0.636129	+	1.21032i
$124$	−8.49906			−0.763238
$125$	8.53039	+	7.22720i	0.762981	+	0.646420i
$126$	−1.62935	+	2.36646i	−0.145154	+	0.210821i
$127$	−7.66011	−	7.66011i	−0.679725	−	0.679725i	0.280213	−	0.959938i	$-0.409595\pi$
$127$	−7.66011	−	7.66011i	−0.679725	−	0.679725i	−0.959938	+	0.280213i	$0.909595\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	0.309789	+	0.0963351i	0.0272754	+	0.00848183i
$130$	1.57063	−	7.90779i	0.137753	−	0.693559i
$131$			21.9129i			1.91454i	0.289200	+	0.957269i	$0.406611\pi$
$131$			21.9129i			1.91454i	−0.289200	+	0.957269i	$0.593389\pi$
$132$	3.64155	−	1.91396i	0.316957	−	0.166589i
$133$	−1.41483	+	1.41483i	−0.122681	+	0.122681i
$134$	11.9894			1.03573
$135$	8.93267	−	7.43017i	0.768802	−	0.639487i
$136$			7.52262i			0.645059i
$137$	−5.92464	−	5.92464i	−0.506176	−	0.506176i	0.407174	−	0.913351i	$-0.366514\pi$
$137$	−5.92464	−	5.92464i	−0.506176	−	0.506176i	−0.913351	+	0.407174i	$0.866514\pi$
$138$	−4.13217	+	2.17182i	−0.351753	+	0.184877i
$139$			13.3375i			1.13127i	0.824655	+	0.565636i	$0.191369\pi$
$139$			13.3375i			1.13127i	−0.824655	+	0.565636i	$0.808631\pi$
$140$	2.14070	−	0.0588945i	0.180922	−	0.00497749i
$141$	1.51308	−	4.86568i	0.127424	−	0.409764i
$142$	−8.83670	−	8.83670i	−0.741560	−	0.741560i
$143$	−1.89870	+	8.35063i	−0.158777	+	0.698314i
$144$	1.70130	−	2.47095i	0.141775	−	0.205912i
$145$	2.91980	−	3.08501i	0.242477	−	0.256196i
$146$			5.22680i			0.432573i
$147$	−9.32603	+	4.90165i	−0.769198	+	0.404281i
$148$	−2.64183	−	2.64183i	−0.217157	−	0.217157i
$149$		−	5.50449i		−	0.450945i	−0.974250	−	0.225473i	$-0.927607\pi$
$149$		−	5.50449i		−	0.450945i	0.974250	−	0.225473i	$-0.0723926\pi$
$150$	−8.39852	−	2.11303i	−0.685736	−	0.172529i
$151$			13.8469i			1.12684i	0.826169	+	0.563422i	$0.190516\pi$
$151$			13.8469i			1.12684i	−0.826169	+	0.563422i	$0.809484\pi$
$152$	1.47730	−	1.47730i	0.119825	−	0.119825i
$153$	−4.09399	−	22.1934i	−0.330979	−	1.79423i
$154$	−2.27472			−0.183302
$155$	−13.8027	−	13.0635i	−1.10866	−	1.04929i
$156$	1.60750	+	6.03456i	0.128703	+	0.483152i
$157$	6.58993	+	6.58993i	0.525934	+	0.525934i	0.919357	−	0.393424i	$-0.128709\pi$
$157$	6.58993	+	6.58993i	0.525934	+	0.525934i	−0.393424	+	0.919357i	$0.628709\pi$
$158$	−0.734807	+	0.734807i	−0.0584581	+	0.0584581i
$159$	−4.23902	+	13.6316i	−0.336176	+	1.08106i
$160$	−2.23522	+	0.0614950i	−0.176710	+	0.00486161i
$161$	2.58118			0.203426
$162$	−3.67447	+	8.21574i	−0.288693	+	0.645489i
$163$	6.28194	+	6.28194i	0.492039	+	0.492039i	0.908948	−	0.416909i	$-0.136887\pi$
$163$	6.28194	+	6.28194i	0.492039	+	0.492039i	−0.416909	+	0.908948i	$0.636887\pi$
$164$			8.75503i			0.683653i
$165$	8.85584	+	2.48896i	0.689426	+	0.193766i
$166$	−0.672810			−0.0522202
$167$	−2.35390	−	2.35390i	−0.182150	−	0.182150i	0.610142	−	0.792292i	$-0.291112\pi$
$167$	−2.35390	−	2.35390i	−0.182150	−	0.182150i	−0.792292	+	0.610142i	$0.791112\pi$
$168$	−1.46835	+	0.771746i	−0.113285	+	0.0595415i
$169$	−11.7219	−	5.62108i	−0.901686	−	0.432391i
$170$	−11.5627	+	12.2169i	−0.886818	+	0.936995i
$171$	−3.55438	+	5.16234i	−0.271810	+	0.394774i
$172$	0.132445	+	0.132445i	0.0100988	+	0.0100988i
$173$	13.8181	+	13.8181i	1.05057	+	1.05057i	0.998651	+	0.0519185i	$0.0165336\pi$
$173$	13.8181	+	13.8181i	1.05057	+	1.05057i	0.0519185	+	0.998651i	$0.483466\pi$
$174$	−0.977008	+	3.14181i	−0.0740668	+	0.238180i
$175$	3.56707	+	3.19473i	0.269645	+	0.241499i
$176$	2.37516			0.179034
$177$	−17.2443	+	9.06342i	−1.29616	+	0.681248i
$178$	−5.76993	+	5.76993i	−0.432475	+	0.432475i
$179$	−9.07466			−0.678272			−0.339136	−	0.940737i	$-0.610135\pi$
$179$	−9.07466			−0.678272			−0.339136	+	0.940737i	$0.610135\pi$
$180$	6.56094	−	1.39788i	0.489024	−	0.104192i
$181$	1.89872			0.141131			0.0705653	−	0.997507i	$-0.477520\pi$
$181$	1.89872			0.141131			0.0705653	+	0.997507i	$0.477520\pi$
$182$	0.765594	−	3.36714i	0.0567496	−	0.249589i
$183$	7.48923	+	14.2492i	0.553620	+	1.05333i
$184$	−2.69516			−0.198689
$185$	−0.229753	−	8.35105i	−0.0168917	−	0.613981i
$186$	14.0568	+	4.37125i	1.03070	+	0.320515i
$187$	12.6342	−	12.6342i	0.923903	−	0.923903i
$188$	2.08023	−	2.08023i	0.151717	−	0.151717i
$189$	3.91195	−	3.07593i	0.284552	−	0.223741i
$190$	4.66986	−	0.128476i	0.338787	−	0.00932066i
$191$			14.2651i			1.03219i	0.856532	+	0.516094i	$0.172614\pi$
$191$			14.2651i			1.03219i	−0.856532	+	0.516094i	$0.827386\pi$
$192$	1.53318	−	0.805823i	0.110648	−	0.0581553i
$193$	−9.53551	−	9.53551i	−0.686381	−	0.686381i	0.275049	−	0.961430i	$-0.411306\pi$
$193$	−9.53551	−	9.53551i	−0.686381	−	0.686381i	−0.961430	+	0.275049i	$0.911306\pi$
$194$	−1.57840			−0.113323
$195$	−6.66485	+	12.2711i	−0.477280	+	0.878751i
$196$	−6.08279			−0.434485
$197$	−8.00501	−	8.00501i	−0.570334	−	0.570334i	0.361888	−	0.932222i	$-0.382132\pi$
$197$	−8.00501	−	8.00501i	−0.570334	−	0.570334i	−0.932222	+	0.361888i	$0.882132\pi$
$198$	−7.00725	+	1.29262i	−0.497984	+	0.0918624i
$199$			10.2380i			0.725753i	0.931837	+	0.362877i	$0.118205\pi$
$199$			10.2380i			0.725753i	−0.931837	+	0.362877i	$0.881795\pi$
$200$	−3.72458	−	3.33580i	−0.263367	−	0.235876i
$201$	−19.8296	−	6.16641i	−1.39867	−	0.434945i
$202$	−12.4592	+	12.4592i	−0.876627	+	0.876627i
$203$	1.28642	−	1.28642i	0.0902891	−	0.0902891i
$204$	3.86904	−	12.4419i	0.270887	−	0.871105i
$205$	−13.4570	+	14.2184i	−0.939877	+	0.993055i
$206$	2.31139			0.161042
$207$	7.95131	−	1.46677i	0.552654	−	0.101947i
$208$	−0.799399	+	3.51582i	−0.0554283	+	0.243778i
$209$	−4.96222			−0.343244
$210$	−3.57085	−	1.00360i	−0.246412	−	0.0692549i
$211$	−3.79498			−0.261257			−0.130629	−	0.991431i	$-0.541700\pi$
$211$	−3.79498			−0.261257			−0.130629	+	0.991431i	$0.541700\pi$
$212$	−5.82795	+	5.82795i	−0.400265	+	0.400265i
$213$	10.0704	+	19.1602i	0.690010	+	1.31283i
$214$	−6.40114			−0.437573
$215$	0.0115183	+	0.418669i	0.000785545	+	0.0285530i
$216$	−4.08468	+	3.21175i	−0.277928	+	0.218532i
$217$	−5.75560	−	5.75560i	−0.390716	−	0.390716i
$218$	−12.1050	−	12.1050i	−0.819851	−	0.819851i
$219$	2.68825	−	8.64474i	0.181655	−	0.584157i
$220$	3.85732	+	3.65076i	0.260060	+	0.246134i
$221$	14.4494	+	22.9539i	0.971974	+	1.54405i
$222$	3.01065	+	5.72815i	0.202061	+	0.384448i
$223$	−0.0933672	−	0.0933672i	−0.00625233	−	0.00625233i	0.703974	−	0.710226i	$-0.251407\pi$
$223$	−0.0933672	−	0.0933672i	−0.00625233	−	0.00625233i	−0.710226	+	0.703974i	$0.751407\pi$
$224$	−0.957712			−0.0639898
$225$	12.8038	+	7.81434i	0.853584	+	0.520956i
$226$			1.58790i			0.105626i
$227$	10.9359	+	10.9359i	0.725841	+	0.725841i	0.969788	−	0.243947i	$-0.0784424\pi$
$227$	10.9359	+	10.9359i	0.725841	+	0.725841i	−0.243947	+	0.969788i	$0.578442\pi$
$228$	−3.20315	+	1.68354i	−0.212134	+	0.111495i
$229$	3.93272			0.259881			0.129941	−	0.991522i	$-0.458521\pi$
$229$	3.93272			0.259881			0.129941	+	0.991522i	$0.458521\pi$
$230$	−4.37700	−	4.14261i	−0.288611	−	0.273155i
$231$	3.76222	+	1.16994i	0.247536	+	0.0769761i
$232$	−1.34322	+	1.34322i	−0.0881870	+	0.0881870i
$233$	−2.63212	−	2.63212i	−0.172436	−	0.172436i	0.615613	−	0.788049i	$-0.288908\pi$
$233$	−2.63212	−	2.63212i	−0.172436	−	0.172436i	−0.788049	+	0.615613i	$0.788908\pi$
$234$	0.445016	−	10.8075i	0.0290916	−	0.706508i
$235$	6.57579	−	0.180912i	0.428957	−	0.0118014i
$236$	−11.2474			−0.732144
$237$	1.59324	−	0.837390i	0.103492	−	0.0543943i
$238$	−5.09435	+	5.09435i	−0.330218	+	0.330218i
$239$			1.55998i			0.100907i	0.998726	+	0.0504535i	$0.0160667\pi$
$239$			1.55998i			0.100907i	−0.998726	+	0.0504535i	$0.983933\pi$
$240$	3.72852	+	1.04791i	0.240675	+	0.0676425i
$241$		−	7.65343i		−	0.493001i	−0.969143	−	0.246501i	$-0.920719\pi$
$241$		−	7.65343i		−	0.493001i	0.969143	−	0.246501i	$-0.0792807\pi$
$242$	3.78911	+	3.78911i	0.243573	+	0.243573i
$243$	10.3028	−	11.6984i	0.660926	−	0.750451i
$244$			9.29389i			0.594980i
$245$	−9.87860	−	9.34959i	−0.631120	−	0.597324i
$246$	4.50290	−	14.4802i	0.287094	−	0.923223i
$247$	1.67012	−	7.34530i	0.106267	−	0.467370i
$248$	6.00974	+	6.00974i	0.381619	+	0.381619i
$249$	1.11278	+	0.346041i	0.0705195	+	0.0219294i
$250$	−0.921495	−	11.1423i	−0.0582805	−	0.704701i
$251$		−	3.75378i		−	0.236937i	−0.992958	−	0.118468i	$-0.962202\pi$
$251$		−	3.75378i		−	0.236937i	0.992958	−	0.118468i	$-0.0377984\pi$
$252$	2.82546	−	0.521209i	0.177987	−	0.0328331i
$253$	4.52649	+	4.52649i	0.284578	+	0.284578i
$254$			10.8330i			0.679725i
$255$	25.4073	−	14.2589i	1.59107	−	0.892930i
$256$	1.00000			0.0625000
$257$	3.00645	−	3.00645i	0.187537	−	0.187537i	−0.607093	−	0.794631i	$-0.707665\pi$
$257$	3.00645	−	3.00645i	0.187537	−	0.187537i	0.794631	+	0.607093i	$0.207665\pi$
$258$	−0.150935	−	0.287173i	−0.00939680	−	0.0178786i
$259$		−	3.57812i		−	0.222334i
$260$	−6.70225	+	4.48105i	−0.415656	+	0.277903i
$261$	3.23180	−	4.69383i	0.200043	−	0.290541i
$262$	15.4947	−	15.4947i	0.957269	−	0.957269i
$263$	11.5352	+	11.5352i	0.711294	+	0.711294i	0.966806	−	0.255512i	$-0.0822440\pi$
$263$	11.5352	+	11.5352i	0.711294	+	0.711294i	−0.255512	+	0.966806i	$0.582244\pi$
$264$	−3.92834	−	1.22160i	−0.241773	−	0.0751840i
$265$	−18.4226	+	0.506840i	−1.13169	+	0.0311349i
$266$	2.00087			0.122681
$267$	12.5106	−	6.57545i	0.765639	−	0.402411i
$268$	−8.47780	−	8.47780i	−0.517864	−	0.517864i
$269$	−15.9555			−0.972825			−0.486412	−	0.873729i	$-0.661695\pi$
$269$	−15.9555			−0.972825			−0.486412	+	0.873729i	$0.661695\pi$
$270$	−11.5703	−	1.06243i	−0.704144	−	0.0646575i
$271$		−	27.1560i		−	1.64961i	−0.565420	−	0.824803i	$-0.691286\pi$
$271$		−	27.1560i		−	1.64961i	0.565420	−	0.824803i	$-0.308714\pi$
$272$	5.31930	−	5.31930i	0.322530	−	0.322530i
$273$	−2.99803	+	5.17524i	−0.181449	+	0.313220i
$274$			8.37871i			0.506176i
$275$	0.652956	+	11.8578i	0.0393747	+	0.715055i
$276$	4.45759	+	1.38618i	0.268315	+	0.0834379i
$277$	10.6914	+	10.6914i	0.642384	+	0.642384i	0.951141	−	0.308757i	$-0.0999129\pi$
$277$	10.6914	+	10.6914i	0.642384	+	0.642384i	−0.308757	+	0.951141i	$0.599913\pi$
$278$	9.43104	−	9.43104i	0.565636	−	0.565636i
$279$	−21.0007	−	14.4594i	−1.25728	−	0.865664i
$280$	−1.55535	−	1.47206i	−0.0929498	−	0.0879723i
$281$	−17.6198			−1.05111			−0.525556	−	0.850759i	$-0.676143\pi$
$281$	−17.6198			−1.05111			−0.525556	+	0.850759i	$0.676143\pi$
$282$	−4.51046	+	2.37065i	−0.268594	+	0.141170i
$283$	−17.2344	+	17.2344i	−1.02448	+	1.02448i	−0.0247857	+	0.999693i	$0.507890\pi$
$283$	−17.2344	+	17.2344i	−1.02448	+	1.02448i	−0.999693	+	0.0247857i	$0.992110\pi$
$284$			12.4970i			0.741560i
$285$	−7.78969	−	2.18932i	−0.461421	−	0.129684i
$286$	7.24737	−	4.56220i	0.428546	−	0.269769i
$287$	−5.92895	+	5.92895i	−0.349975	+	0.349975i
$288$	−2.95022	+	0.544224i	−0.173844	+	0.0320687i
$289$		−	39.5898i		−	2.32881i
$290$	−4.24604	+	0.116816i	−0.249336	+	0.00685969i
$291$	2.61056	+	0.811805i	0.153034	+	0.0475888i
$292$	3.69590	−	3.69590i	0.216286	−	0.216286i
$293$	8.39295	−	8.39295i	0.490321	−	0.490321i	−0.418086	−	0.908407i	$-0.637299\pi$
$293$	8.39295	−	8.39295i	0.490321	−	0.490321i	0.908407	+	0.418086i	$0.137299\pi$
$294$	10.0605	+	3.12851i	0.586740	+	0.182458i
$295$	−18.2661	−	17.2879i	−1.06349	−	1.00654i
$296$			3.73612i			0.217157i
$297$	12.2543	+	1.46608i	0.711067	+	0.0850708i
$298$	−3.89226	+	3.89226i	−0.225473	+	0.225473i
$299$	−8.22377	+	5.17685i	−0.475593	+	0.299385i
$300$	4.44451	+	7.43279i	0.256604	+	0.429132i
$301$			0.179384i			0.0103395i
$302$	9.79124	−	9.79124i	0.563422	−	0.563422i
$303$	27.0147	−	14.1986i	1.55195	−	0.815687i
$304$	−2.08922			−0.119825
$305$	−14.2852	+	15.0935i	−0.817970	+	0.864251i
$306$	−12.7982	+	18.5880i	−0.731626	+	1.06261i
$307$	−15.1124	+	15.1124i	−0.862512	+	0.862512i	−0.991629	−	0.129118i	$-0.958786\pi$
$307$	−15.1124	+	15.1124i	−0.862512	+	0.862512i	0.129118	+	0.991629i	$0.458786\pi$
$308$	1.60847	+	1.60847i	0.0916510	+	0.0916510i
$309$	−3.82286	−	1.18879i	−0.217475	−	0.0676282i
$310$	0.522650	+	18.9973i	0.0296845	+	1.07897i
$311$		−	32.5293i		−	1.84457i	−0.386513	−	0.922284i	$-0.626321\pi$
$311$		−	32.5293i		−	1.84457i	0.386513	−	0.922284i	$-0.373679\pi$
$312$	3.13041	−	5.40375i	0.177224	−	0.305927i
$313$	5.87745	−	5.87745i	0.332213	−	0.332213i	−0.521213	−	0.853426i	$-0.674520\pi$
$313$	5.87745	−	5.87745i	0.332213	−	0.332213i	0.853426	+	0.521213i	$0.174520\pi$
$314$		−	9.31957i		−	0.525934i
$315$	5.38975	+	3.49644i	0.303678	+	0.197002i
$316$	1.03917			0.0584581
$317$	−16.6705	−	16.6705i	−0.936311	−	0.936311i	0.0617787	−	0.998090i	$-0.480323\pi$
$317$	−16.6705	−	16.6705i	−0.936311	−	0.936311i	−0.998090	+	0.0617787i	$0.980323\pi$
$318$	12.6364	−	6.64156i	0.708616	−	0.372440i
$319$	4.51187			0.252616
$320$	1.62402	+	1.53706i	0.0907857	+	0.0859241i
$321$	10.5870	+	3.29224i	0.590909	+	0.183755i
$322$	−1.82517	−	1.82517i	−0.101713	−	0.101713i
$323$	−11.1132	+	11.1132i	−0.618353	+	0.618353i
$324$	8.40764	−	3.21116i	0.467091	−	0.178398i
$325$	−17.7723	−	3.02442i	−0.985827	−	0.167764i
$326$		−	8.88400i		−	0.492039i
$327$	13.7949	+	26.2465i	0.762858	+	1.45144i
$328$	6.19074	−	6.19074i	0.341827	−	0.341827i
$329$	2.81749			0.155333
$330$	−4.50206	−	8.02199i	−0.247830	−	0.441596i
$331$		−	13.6672i		−	0.751219i	−0.926778	−	0.375610i	$-0.877433\pi$
$331$		−	13.6672i		−	0.751219i	0.926778	−	0.375610i	$-0.122567\pi$
$332$	0.475749	+	0.475749i	0.0261101	+	0.0261101i
$333$	−2.03328	−	11.0224i	−0.111423	−	0.604023i
$334$			3.32892i			0.182150i
$335$	−0.737289	−	26.7990i	−0.0402824	−	1.46419i
$336$	1.58398	+	0.492571i	0.0864135	+	0.0268720i
$337$	19.0461	+	19.0461i	1.03751	+	1.03751i	0.999269	+	0.0382377i	$0.0121744\pi$
$337$	19.0461	+	19.0461i	1.03751	+	1.03751i	0.0382377	+	0.999269i	$0.487826\pi$
$338$	4.31395	+	12.2634i	0.234648	+	0.667039i
$339$	0.816692	−	2.62628i	0.0443566	−	0.142640i
$340$	16.8147	−	0.462604i	0.911907	−	0.0250882i
$341$		−	20.1866i		−	1.09317i
$342$	6.16365	−	1.13700i	0.333292	−	0.0614819i
$343$	−8.85972	−	8.85972i	−0.478380	−	0.478380i
$344$		−	0.187305i		−	0.0100988i
$345$	5.10860	+	9.10275i	0.275038	+	0.490076i
$346$		−	19.5417i		−	1.05057i
$347$	15.6314	−	15.6314i	0.839135	−	0.839135i	−0.149610	−	0.988745i	$-0.547802\pi$
$347$	15.6314	−	15.6314i	0.839135	−	0.839135i	0.988745	+	0.149610i	$0.0478019\pi$
$348$	2.91244	−	1.53075i	0.156123	−	0.0820566i
$349$	17.3180			0.927010			0.463505	−	0.886094i	$-0.346592\pi$
$349$	17.3180			0.927010			0.463505	+	0.886094i	$0.346592\pi$
$350$	−0.263285	−	4.78131i	−0.0140732	−	0.255572i
$351$	−6.29455	+	17.6459i	−0.335978	+	0.941870i
$352$	−1.67949	−	1.67949i	−0.0895172	−	0.0895172i
$353$	25.9079	−	25.9079i	1.37894	−	1.37894i	0.532525	−	0.846414i	$-0.321243\pi$
$353$	25.9079	−	25.9079i	1.37894	−	1.37894i	0.846414	−	0.532525i	$-0.178757\pi$
$354$	18.6024	+	5.78478i	0.988706	+	0.307458i
$355$	−19.2086	+	20.2954i	−1.01949	+	1.07717i
$356$	8.15992			0.432475
$357$	11.0458	−	5.80555i	0.584607	−	0.307262i
$358$	6.41675	+	6.41675i	0.339136	+	0.339136i
$359$			32.6510i			1.72326i	0.507540	+	0.861628i	$0.330555\pi$
$359$			32.6510i			1.72326i	−0.507540	+	0.861628i	$0.669445\pi$
$360$	−5.62774	−	3.65083i	−0.296608	−	0.192416i
$361$	−14.6352			−0.770272
$362$	−1.34260	−	1.34260i	−0.0705653	−	0.0705653i
$363$	−4.31809	−	8.21573i	−0.226641	−	0.431214i
$364$	−2.92228	+	1.83957i	−0.153169	+	0.0964196i
$365$	11.6831	−	0.321422i	0.611519	−	0.0168240i
$366$	4.78004	−	15.3714i	0.249857	−	0.803477i
$367$	−2.00117	−	2.00117i	−0.104460	−	0.104460i	0.652945	−	0.757405i	$-0.273533\pi$
$367$	−2.00117	−	2.00117i	−0.104460	−	0.104460i	−0.757405	+	0.652945i	$0.773533\pi$
$368$	1.90576	+	1.90576i	0.0993447	+	0.0993447i
$369$	−14.8949	+	21.6332i	−0.775399	+	1.12618i
$370$	−5.74262	+	6.06754i	−0.298545	+	0.315437i
$371$	−7.89342			−0.409806
$372$	−6.84873	−	13.0306i	−0.355090	−	0.675606i
$373$	−12.1573	+	12.1573i	−0.629480	+	0.629480i	−0.947937	−	0.318457i	$-0.896835\pi$
$373$	−12.1573	+	12.1573i	−0.629480	+	0.629480i	0.318457	+	0.947937i	$0.396835\pi$
$374$	−17.8674			−0.923903
$375$	−4.20664	+	18.9025i	−0.217230	+	0.976121i
$376$	−2.94189			−0.151717
$377$	−1.51854	+	6.67867i	−0.0782090	+	0.343969i
$378$	−4.94118	−	0.591154i	−0.254147	−	0.0304057i
$379$	−20.5970			−1.05800			−0.528999	−	0.848623i	$-0.677432\pi$
$379$	−20.5970			−1.05800			−0.528999	+	0.848623i	$0.677432\pi$
$380$	−3.39294	−	3.21124i	−0.174054	−	0.164733i
$381$	5.57166	−	17.9170i	0.285445	−	0.917918i
$382$	10.0870	−	10.0870i	0.516094	−	0.516094i
$383$	1.71164	−	1.71164i	0.0874607	−	0.0874607i	−0.662023	−	0.749484i	$-0.730302\pi$
$383$	1.71164	−	1.71164i	0.0874607	−	0.0874607i	0.749484	+	0.662023i	$0.230302\pi$
$384$	−1.65393	−	0.514321i	−0.0844016	−	0.0262463i
$385$	0.139884	+	5.08450i	0.00712914	+	0.259130i
$386$			13.4852i			0.686381i
$387$	0.101936	+	0.552593i	0.00518170	+	0.0280899i
$388$	1.11610	+	1.11610i	0.0566613	+	0.0566613i
$389$	22.7607			1.15401			0.577007	−	0.816739i	$-0.304221\pi$
$389$	22.7607			1.15401			0.577007	+	0.816739i	$0.304221\pi$
$390$	13.3897	−	3.96422i	0.678016	−	0.200736i
$391$	20.2746			1.02533
$392$	4.30118	+	4.30118i	0.217242	+	0.217242i
$393$	−33.5965	+	17.6579i	−1.69472	+	0.890723i
$394$			11.3208i			0.570334i
$395$	1.68764	+	1.59727i	0.0849146	+	0.0803674i
$396$	5.86890	+	4.04086i	0.294923	+	0.203061i
$397$	19.2632	−	19.2632i	0.966794	−	0.966794i	−0.0326724	−	0.999466i	$-0.510402\pi$
$397$	19.2632	−	19.2632i	0.966794	−	0.966794i	0.999466	+	0.0326724i	$0.0104018\pi$
$398$	7.23937	−	7.23937i	0.362877	−	0.362877i
$399$	−3.30929	−	1.02909i	−0.165672	−	0.0515188i
$400$	0.274910	+	4.99244i	0.0137455	+	0.249622i
$401$	22.1388			1.10556			0.552779	−	0.833328i	$-0.313568\pi$
$401$	22.1388			1.10556			0.552779	+	0.833328i	$0.313568\pi$
$402$	9.66134	+	18.3820i	0.481864	+	0.916809i
$403$	29.8811	+	6.79414i	1.48848	+	0.338440i
$404$	17.6200			0.876627
$405$	18.5900	+	7.70802i	0.923742	+	0.383015i
$406$	−1.81928			−0.0902891
$407$	6.27478	−	6.27478i	0.311029	−	0.311029i
$408$	−11.5336	+	6.06190i	−0.570996	+	0.300109i
$409$	−23.0621			−1.14035			−0.570173	−	0.821525i	$-0.693124\pi$
$409$	−23.0621			−1.14035			−0.570173	+	0.821525i	$0.693124\pi$
$410$	19.5694	−	0.538391i	0.966466	−	0.0265892i
$411$	4.30935	−	13.8578i	0.212564	−	0.683554i
$412$	−1.63440	−	1.63440i	−0.0805210	−	0.0805210i
$413$	−7.61679	−	7.61679i	−0.374798	−	0.374798i
$414$	−6.65959	−	4.58526i	−0.327301	−	0.225353i
$415$	0.0413745	+	1.50388i	0.00203099	+	0.0738226i
$416$	3.05132	−	1.92080i	0.149603	−	0.0941748i
$417$	−20.4488	+	10.7477i	−1.00138	+	0.526315i
$418$	3.50882	+	3.50882i	0.171622	+	0.171622i
$419$	−25.3285			−1.23738			−0.618688	−	0.785637i	$-0.712335\pi$
$419$	−25.3285			−1.23738			−0.618688	+	0.785637i	$0.712335\pi$
$420$	1.81532	+	3.23462i	0.0885785	+	0.157833i
$421$			25.2669i			1.23143i	0.787968	+	0.615716i	$0.211133\pi$
$421$			25.2669i			1.23143i	−0.787968	+	0.615716i	$0.788867\pi$
$422$	2.68346	+	2.68346i	0.130629	+	0.130629i
$423$	8.67925	−	1.60105i	0.422000	−	0.0778456i
$424$	8.24196			0.400265
$425$	28.0186	+	25.0939i	1.35910	+	1.21723i
$426$	6.42746	−	20.6691i	0.311412	−	1.00142i
$427$	−6.29386	+	6.29386i	−0.304581	+	0.304581i
$428$	4.52629	+	4.52629i	0.218786	+	0.218786i
$429$	−14.3331	+	3.81807i	−0.692006	+	0.184338i
$430$	0.287899	−	0.304188i	0.0138837	−	0.0146693i
$431$	−26.8636			−1.29397			−0.646987	−	0.762501i	$-0.723971\pi$
$431$	−26.8636			−1.29397			−0.646987	+	0.762501i	$0.723971\pi$
$432$	5.15936	+	0.617257i	0.248230	+	0.0296978i
$433$	−3.38479	+	3.38479i	−0.162663	+	0.162663i	−0.783745	−	0.621083i	$-0.786693\pi$
$433$	−3.38479	+	3.38479i	−0.162663	+	0.162663i	0.621083	+	0.783745i	$0.286693\pi$
$434$			8.13965i			0.390716i
$435$	7.08272	+	1.99062i	0.339591	+	0.0954431i
$436$			17.1190i			0.819851i
$437$	−3.98155	−	3.98155i	−0.190463	−	0.190463i
$438$	−8.01363	+	4.21187i	−0.382906	+	0.201251i
$439$		−	28.3140i		−	1.35136i	−0.737197	−	0.675678i	$-0.763851\pi$
$439$		−	28.3140i		−	1.35136i	0.737197	−	0.675678i	$-0.236149\pi$
$440$	−0.146061	−	5.30901i	−0.00696316	−	0.253097i
$441$	−15.0303	−	10.3486i	−0.715726	−	0.492793i
$442$	6.01358	−	26.4481i	0.286037	−	1.25801i
$443$	5.20707	+	5.20707i	0.247395	+	0.247395i	0.819901	−	0.572505i	$-0.194028\pi$
$443$	5.20707	+	5.20707i	0.247395	+	0.247395i	−0.572505	+	0.819901i	$0.694028\pi$
$444$	1.92156	−	6.17926i	0.0911934	−	0.293255i
$445$	13.2519	+	12.5423i	0.628201	+	0.594560i
$446$			0.132041i			0.00625233i
$447$	8.43938	−	4.43564i	0.399169	−	0.209799i
$448$	0.677204	+	0.677204i	0.0319949	+	0.0319949i
$449$			23.9066i			1.12822i	0.825699	+	0.564110i	$0.190781\pi$
$449$			23.9066i			1.12822i	−0.825699	+	0.564110i	$0.809219\pi$
$450$	−3.52805	−	14.5792i	−0.166314	−	0.687270i
$451$	−20.7946			−0.979180
$452$	1.12282	−	1.12282i	0.0528129	−	0.0528129i
$453$	−21.2298	+	11.1582i	−0.997465	+	0.524256i
$454$		−	15.4657i		−	0.725841i
$455$	−7.57338	−	1.50421i	−0.355046	−	0.0705184i
$456$	3.45541	+	1.07453i	0.161814	+	0.0503194i
$457$	−24.0463	+	24.0463i	−1.12484	+	1.12484i	−0.133837	+	0.991003i	$0.542730\pi$
$457$	−24.0463	+	24.0463i	−1.12484	+	1.12484i	−0.991003	+	0.133837i	$0.957270\pi$
$458$	−2.78085	−	2.78085i	−0.129941	−	0.129941i
$459$	30.7275	−	24.1608i	1.43424	−	1.12773i
$460$	0.165739	+	6.02427i	0.00772760	+	0.280883i
$461$	19.8148			0.922867			0.461433	−	0.887175i	$-0.347335\pi$
$461$	19.8148			0.922867			0.461433	+	0.887175i	$0.347335\pi$
$462$	−1.83302	−	3.48756i	−0.0852798	−	0.162256i
$463$	−5.15121	−	5.15121i	−0.239397	−	0.239397i	0.577203	−	0.816600i	$-0.304144\pi$
$463$	−5.15121	−	5.15121i	−0.239397	−	0.239397i	−0.816600	+	0.577203i	$0.804144\pi$
$464$	1.89961			0.0881870
$465$	8.90628	−	31.6889i	0.413019	−	1.46954i
$466$			3.72237i			0.172436i
$467$	4.55792	−	4.55792i	0.210915	−	0.210915i	−0.593741	−	0.804656i	$-0.702350\pi$
$467$	4.55792	−	4.55792i	0.210915	−	0.210915i	0.804656	+	0.593741i	$0.202350\pi$
$468$	−7.95673	+	7.32738i	−0.367800	+	0.338708i
$469$		−	11.4824i		−	0.530208i
$470$	−4.77771	−	4.52186i	−0.220379	−	0.208578i
$471$	−4.79325	+	15.4139i	−0.220861	+	0.710234i
$472$	7.95312	+	7.95312i	0.366072	+	0.366072i
$473$	−0.314578	+	0.314578i	−0.0144643	+	0.0144643i
$474$	−1.71872	−	0.534469i	−0.0789433	−	0.0245490i
$475$	−0.574347	−	10.4303i	−0.0263528	−	0.478574i
$476$	7.20450			0.330218
$477$	−24.3156	+	4.48547i	−1.11334	+	0.205376i
$478$	1.10307	−	1.10307i	0.0504535	−	0.0504535i
$479$		−	15.9309i		−	0.727903i	−0.931418	−	0.363951i	$-0.881427\pi$
$479$		−	15.9309i		−	0.727903i	0.931418	−	0.363951i	$-0.118573\pi$
$480$	−1.89548	−	3.37745i	−0.0865163	−	0.154159i
$481$	7.17632	+	11.4001i	0.327212	+	0.519799i
$482$	−5.41180	+	5.41180i	−0.246501	+	0.246501i
$483$	2.07997	+	3.95742i	0.0946421	+	0.180069i
$484$		−	5.35861i		−	0.243573i
$485$	0.0970638	+	3.52807i	0.00440744	+	0.160202i
$486$	−15.5572	+	0.986800i	−0.705689	+	0.0447622i
$487$	20.8304	−	20.8304i	0.943914	−	0.943914i	−0.0545949	−	0.998509i	$-0.517387\pi$
$487$	20.8304	−	20.8304i	0.943914	−	0.943914i	0.998509	+	0.0545949i	$0.0173867\pi$
$488$	6.57177	−	6.57177i	0.297490	−	0.297490i
$489$	−4.56923	+	14.6935i	−0.206628	+	0.664462i
$490$	0.374061	+	13.5964i	0.0168984	+	0.614222i
$491$			24.8807i			1.12285i	0.827527	+	0.561426i	$0.189747\pi$
$491$			24.8807i			1.12285i	−0.827527	+	0.561426i	$0.810253\pi$
$492$	−13.4231	+	7.05501i	−0.605159	+	0.318064i
$493$	10.1046	−	10.1046i	0.455087	−	0.455087i
$494$	−6.37486	+	4.01296i	−0.286819	+	0.180552i
$495$	3.32020	+	15.5833i	0.149232	+	0.700416i
$496$		−	8.49906i		−	0.381619i
$497$	−8.46301	+	8.46301i	−0.379618	+	0.379618i
$498$	−0.542166	−	1.03154i	−0.0242950	−	0.0462245i
$499$	−41.1465			−1.84197			−0.920985	−	0.389598i	$-0.872614\pi$
$499$	−41.1465			−1.84197			−0.920985	+	0.389598i	$0.872614\pi$
$500$	−7.22720	+	8.53039i	−0.323210	+	0.381491i
$501$	1.71213	−	5.50578i	0.0764924	−	0.245980i
$502$	−2.65432	+	2.65432i	−0.118468	+	0.118468i
$503$	−15.8407	−	15.8407i	−0.706300	−	0.706300i	0.259455	−	0.965755i	$-0.416457\pi$
$503$	−15.8407	−	15.8407i	−0.706300	−	0.706300i	−0.965755	+	0.259455i	$0.916457\pi$
$504$	−2.36646	−	1.62935i	−0.105410	−	0.0725772i
$505$	28.6153	+	27.0829i	1.27336	+	1.20517i
$506$		−	6.40143i		−	0.284578i
$507$	−0.827651	−	22.5014i	−0.0367573	−	0.999324i
$508$	7.66011	−	7.66011i	0.339862	−	0.339862i
$509$			4.84314i			0.214668i	0.994223	+	0.107334i	$0.0342314\pi$
$509$			4.84314i			0.214668i	−0.994223	+	0.107334i	$0.965769\pi$
$510$	−28.0483	−	7.88306i	−1.24200	−	0.349068i
$511$	5.00576			0.221442
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−10.7790	−	1.28958i	−0.475905	−	0.0569364i
$514$	−4.25176			−0.187537
$515$	−0.142139	−	5.16646i	−0.00626338	−	0.227662i
$516$	−0.0963351	+	0.309789i	−0.00424092	+	0.0136377i
$517$	4.94089	+	4.94089i	0.217300	+	0.217300i
$518$	−2.53011	+	2.53011i	−0.111167	+	0.111167i
$519$	−10.0507	+	32.3206i	−0.441178	+	1.41872i
$520$	7.90779	+	1.57063i	0.346779	+	0.0688766i
$521$		−	1.67217i		−	0.0732593i	−0.999329	−	0.0366296i	$-0.988338\pi$
$521$		−	1.67217i		−	0.0732593i	0.999329	−	0.0366296i	$-0.0116622\pi$
$522$	−5.60426	+	1.03381i	−0.245292	+	0.0452487i
$523$	15.2663	−	15.2663i	0.667550	−	0.667550i	−0.289599	−	0.957148i	$-0.593522\pi$
$523$	15.2663	−	15.2663i	0.667550	−	0.667550i	0.957148	+	0.289599i	$0.0935218\pi$
$524$	−21.9129			−0.957269
$525$	−2.02368	+	8.04336i	−0.0883205	+	0.351041i
$526$		−	16.3133i		−	0.711294i
$527$	−45.2090	−	45.2090i	−1.96934	−	1.96934i
$528$	1.91396	+	3.64155i	0.0832943	+	0.158478i
$529$		−	15.7361i		−	0.684180i
$530$	13.3851	+	12.6684i	0.581414	+	0.550279i
$531$	−27.7917	−	19.1352i	−1.20606	−	0.830397i
$532$	−1.41483	−	1.41483i	−0.0613405	−	0.0613405i
$533$	6.99877	−	30.7811i	0.303150	−	1.33328i
$534$	−13.4959	−	4.19682i	−0.584025	−	0.181614i
$535$	0.393638	+	14.3080i	0.0170185	+	0.618587i
$536$			11.9894i			0.517864i
$537$	−7.31256	−	13.9131i	−0.315560	−	0.600395i
$538$	11.2823	+	11.2823i	0.486412	+	0.486412i
$539$		−	14.4476i		−	0.622302i
$540$	7.43017	+	8.93267i	0.319743	+	0.384401i
$541$		−	29.0935i		−	1.25083i	−0.780293	−	0.625414i	$-0.784930\pi$
$541$		−	29.0935i		−	1.25083i	0.780293	−	0.625414i	$-0.215070\pi$
$542$	−19.2022	+	19.2022i	−0.824803	+	0.824803i
$543$	1.53003	+	2.91108i	0.0656599	+	0.124926i
$544$	−7.52262			−0.322530
$545$	−26.3129	+	27.8017i	−1.12712	+	1.19089i
$546$	5.77937	−	1.53952i	0.247334	−	0.0658854i
$547$	7.13810	+	7.13810i	0.305203	+	0.305203i	0.843045	−	0.537842i	$-0.180760\pi$
$547$	7.13810	+	7.13810i	0.305203	+	0.305203i	−0.537842	+	0.843045i	$0.680760\pi$
$548$	5.92464	−	5.92464i	0.253088	−	0.253088i
$549$	−15.8117	+	22.9647i	−0.674826	+	0.980110i
$550$	7.92305	−	8.84647i	0.337840	−	0.377215i
$551$	−3.96869			−0.169072
$552$	−2.17182	−	4.13217i	−0.0924387	−	0.175877i
$553$	0.703733	+	0.703733i	0.0299258	+	0.0299258i
$554$		−	15.1199i		−	0.642384i
$555$	12.6185	−	7.08172i	0.535627	−	0.300602i
$556$	−13.3375			−0.565636
$557$	4.94545	+	4.94545i	0.209546	+	0.209546i	0.804074	−	0.594529i	$-0.202661\pi$
$557$	4.94545	+	4.94545i	0.209546	+	0.209546i	−0.594529	+	0.804074i	$0.702661\pi$
$558$	4.62539	+	25.0741i	0.195808	+	1.06147i
$559$	−0.359775	−	0.571528i	−0.0152169	−	0.0241731i
$560$	0.0588945	+	2.14070i	0.00248875	+	0.0904610i
$561$	29.5514	+	9.18960i	1.24766	+	0.387985i
$562$	12.4591	+	12.4591i	0.525556	+	0.525556i
$563$	4.14895	+	4.14895i	0.174857	+	0.174857i	0.789110	−	0.614252i	$-0.210542\pi$
$563$	4.14895	+	4.14895i	0.174857	+	0.174857i	−0.614252	+	0.789110i	$0.710542\pi$
$564$	4.86568	+	1.51308i	0.204882	+	0.0637121i
$565$	3.54932	−	0.0976482i	0.149321	−	0.00410809i
$566$	24.3731			1.02448
$567$	7.86830	+	3.51908i	0.330438	+	0.147787i
$568$	8.83670	−	8.83670i	0.370780	−	0.370780i
$569$	26.2934			1.10228			0.551139	−	0.834414i	$-0.314194\pi$
$569$	26.2934			1.10228			0.551139	+	0.834414i	$0.314194\pi$
$570$	3.96006	+	7.05622i	0.165869	+	0.295553i
$571$	29.9043			1.25145			0.625727	−	0.780042i	$-0.284802\pi$
$571$	29.9043			1.25145			0.625727	+	0.780042i	$0.284802\pi$
$572$	−8.35063	−	1.89870i	−0.349157	−	0.0793887i
$573$	−21.8710	+	11.4952i	−0.913676	+	0.480217i
$574$	8.38480			0.349975
$575$	−8.99048	+	10.0383i	−0.374929	+	0.418627i
$576$	2.47095	+	1.70130i	0.102956	+	0.0708875i
$577$	4.56357	−	4.56357i	0.189984	−	0.189984i	−0.605705	−	0.795689i	$-0.707109\pi$
$577$	4.56357	−	4.56357i	0.189984	−	0.189984i	0.795689	+	0.605705i	$0.207109\pi$
$578$	−27.9942	+	27.9942i	−1.16441	+	1.16441i
$579$	6.93575	−	22.3036i	0.288240	−	0.926907i
$580$	3.08501	+	2.91980i	0.128098	+	0.121238i
$581$			0.644358i			0.0267325i
$582$	−1.27191	−	2.41998i	−0.0527224	−	0.100311i
$583$	−13.8423	−	13.8423i	−0.573290	−	0.573290i
$584$	−5.22680			−0.216286
$585$	−24.1845	−	0.330102i	−0.999907	−	0.0136481i
$586$	−11.8694			−0.490321
$587$	0.204915	+	0.204915i	0.00845773	+	0.00845773i	0.711323	−	0.702865i	$-0.248096\pi$
$587$	0.204915	+	0.204915i	0.00845773	+	0.00845773i	−0.702865	+	0.711323i	$0.748096\pi$
$588$	−4.90165	−	9.32603i	−0.202141	−	0.384599i
$589$			17.7564i			0.731638i
$590$	0.691660	+	25.1405i	0.0284752	+	1.03502i
$591$	5.82253	−	18.7238i	0.239507	−	0.770193i
$592$	2.64183	−	2.64183i	0.108579	−	0.108579i
$593$	−11.2316	+	11.2316i	−0.461226	+	0.461226i	−0.899057	−	0.437831i	$-0.855747\pi$
$593$	−11.2316	+	11.2316i	−0.461226	+	0.461226i	0.437831	+	0.899057i	$0.355747\pi$
$594$	−7.62843	−	9.70178i	−0.312998	−	0.398069i
$595$	11.7003	+	11.0737i	0.479665	+	0.453979i
$596$	5.50449			0.225473
$597$	−15.6967	+	8.25002i	−0.642425	+	0.337651i
$598$	9.47567	+	2.15450i	0.387489	+	0.0881042i
$599$	24.5114			1.00151			0.500755	−	0.865589i	$-0.333056\pi$
$599$	24.5114			1.00151			0.500755	+	0.865589i	$0.333056\pi$
$600$	2.11303	−	8.39852i	0.0862643	−	0.342868i
$601$	25.9192			1.05727			0.528634	−	0.848850i	$-0.322704\pi$
$601$	25.9192			1.05727			0.528634	+	0.848850i	$0.322704\pi$
$602$	0.126844	−	0.126844i	0.00516977	−	0.00516977i
$603$	−6.52492	−	35.3715i	−0.265715	−	1.44044i
$604$	−13.8469			−0.563422
$605$	8.23650	−	8.70252i	0.334861	−	0.353808i
$606$	−29.1422	−	9.06233i	−1.18382	−	0.368132i
$607$	28.1226	+	28.1226i	1.14146	+	1.14146i	0.988183	+	0.153276i	$0.0489824\pi$
$607$	28.1226	+	28.1226i	1.14146	+	1.14146i	0.153276	+	0.988183i	$0.451018\pi$
$608$	1.47730	+	1.47730i	0.0599124	+	0.0599124i
$609$	3.00895	+	0.935692i	0.121929	+	0.0379161i
$610$	20.7739	−	0.571528i	0.841111	−	0.0231405i
$611$	−8.97666	+	5.65078i	−0.363157	+	0.228606i
$612$	22.1934	−	4.09399i	0.897116	−	0.165490i
$613$	27.8570	+	27.8570i	1.12513	+	1.12513i	0.990958	+	0.134175i	$0.0428383\pi$
$613$	27.8570	+	27.8570i	1.12513	+	1.12513i	0.134175	+	0.990958i	$0.457162\pi$
$614$	21.3722			0.862512
$615$	−32.6433	−	9.17452i	−1.31631	−	0.369952i
$616$		−	2.27472i		−	0.0916510i
$617$	−8.65622	−	8.65622i	−0.348486	−	0.348486i	0.511059	−	0.859546i	$-0.329253\pi$
$617$	−8.65622	−	8.65622i	−0.348486	−	0.348486i	−0.859546	+	0.511059i	$0.829253\pi$
$618$	1.86257	+	3.54378i	0.0749235	+	0.142552i
$619$	24.1462			0.970516			0.485258	−	0.874371i	$-0.338726\pi$
$619$	24.1462			0.970516			0.485258	+	0.874371i	$0.338726\pi$
$620$	13.0635	−	13.8027i	0.524644	−	0.554329i
$621$	8.65617	+	11.0089i	0.347360	+	0.441770i
$622$	−23.0017	+	23.0017i	−0.922284	+	0.922284i
$623$	5.52593	+	5.52593i	0.221392	+	0.221392i
$624$	−6.03456	+	1.60750i	−0.241576	+	0.0643515i
$625$	−24.8488	+	2.74494i	−0.993954	+	0.109798i
$626$	−8.31197			−0.332213
$627$	−3.99867	−	7.60799i	−0.159692	−	0.303834i
$628$	−6.58993	+	6.58993i	−0.262967	+	0.262967i
$629$		−	28.1054i		−	1.12064i
$630$	−1.33877	−	6.28349i	−0.0533379	−	0.250340i
$631$			37.6669i			1.49950i	0.661723	+	0.749749i	$0.269826\pi$
$631$			37.6669i			1.49950i	−0.661723	+	0.749749i	$0.730174\pi$
$632$	−0.734807	−	0.734807i	−0.0292291	−	0.0292291i
$633$	−3.05808	−	5.81840i	−0.121548	−	0.231261i
$634$			23.5757i			0.936311i
$635$	24.2142	−	0.666177i	0.960912	−	0.0264364i
$636$	−13.6316	−	4.23902i	−0.540528	−	0.168088i
$637$	21.3860	+	4.86257i	0.847343	+	0.192662i
$638$	−3.19037	−	3.19037i	−0.126308	−	0.126308i
$639$	−21.2611	+	30.8794i	−0.841077	+	1.22157i
$640$	−0.0614950	−	2.23522i	−0.00243080	−	0.0883549i
$641$		−	6.02684i		−	0.238046i	−0.992892	−	0.119023i	$-0.962024\pi$
$641$		−	6.02684i		−	0.238046i	0.992892	−	0.119023i	$-0.0379762\pi$
$642$	−5.15818	−	9.81411i	−0.203577	−	0.387332i
$643$	−0.846729	−	0.846729i	−0.0333917	−	0.0333917i	0.690214	−	0.723606i	$-0.257516\pi$
$643$	−0.846729	−	0.846729i	−0.0333917	−	0.0333917i	−0.723606	+	0.690214i	$0.757516\pi$
$644$			2.58118i			0.101713i
$645$	−0.632614	+	0.355033i	−0.0249092	+	0.0139794i
$646$	15.7164			0.618353
$647$	3.77881	−	3.77881i	0.148560	−	0.148560i	−0.628914	−	0.777475i	$-0.716500\pi$
$647$	3.77881	−	3.77881i	0.148560	−	0.148560i	0.777475	+	0.628914i	$0.216500\pi$
$648$	−8.21574	−	3.67447i	−0.322745	−	0.144347i
$649$		−	26.7144i		−	1.04863i
$650$	10.4283	+	14.7055i	0.409031	+	0.576796i
$651$	4.18639	−	13.4624i	0.164078	−	0.527632i
$652$	−6.28194	+	6.28194i	−0.246020	+	0.246020i
$653$	2.30151	+	2.30151i	0.0900649	+	0.0900649i	0.750704	−	0.660639i	$-0.229715\pi$
$653$	2.30151	+	2.30151i	0.0900649	+	0.0900649i	−0.660639	+	0.750704i	$0.729715\pi$
$654$	8.80466	−	28.3136i	0.344289	−	1.10715i
$655$	−35.5871	−	33.6814i	−1.39050	−	1.31604i
$656$	−8.75503			−0.341827
$657$	15.4202	−	2.84455i	0.601600	−	0.110976i
$658$	−1.99226	−	1.99226i	−0.0776665	−	0.0776665i
$659$	−23.4178			−0.912228			−0.456114	−	0.889921i	$-0.650759\pi$
$659$	−23.4178			−0.912228			−0.456114	+	0.889921i	$0.650759\pi$
$660$	−2.48896	+	8.85584i	−0.0968828	+	0.344713i
$661$		−	18.6057i		−	0.723679i	−0.932240	−	0.361840i	$-0.882149\pi$
$661$		−	18.6057i		−	0.723679i	0.932240	−	0.361840i	$-0.117851\pi$
$662$	−9.66419	+	9.66419i	−0.375610	+	0.375610i
$663$	−23.5489	+	40.6504i	−0.914562	+	1.57873i
$664$		−	0.672810i		−	0.0261101i
$665$	−0.123043	−	4.47238i	−0.00477142	−	0.173431i
$666$	−6.35625	+	9.23175i	−0.246300	+	0.357723i
$667$	3.62020	+	3.62020i	0.140175	+	0.140175i
$668$	2.35390	−	2.35390i	0.0910751	−	0.0910751i
$669$	0.0679116	−	0.218386i	0.00262561	−	0.00844331i
$670$	−18.4284	+	19.4711i	−0.711952	+	0.752234i
$671$	−22.0745			−0.852176
$672$	−0.771746	−	1.46835i	−0.0297707	−	0.0566427i
$673$	−24.7786	+	24.7786i	−0.955145	+	0.955145i	−0.999036	−	0.0438911i	$-0.986025\pi$
$673$	−24.7786	+	24.7786i	−0.955145	+	0.955145i	0.0438911	+	0.999036i	$0.486025\pi$
$674$		−	26.9352i		−	1.03751i
$675$	−1.66325	+	25.9275i	−0.0640187	+	0.997949i
$676$	5.62108	−	11.7219i	0.216195	−	0.450843i
$677$	−2.48540	+	2.48540i	−0.0955215	+	0.0955215i	−0.753253	−	0.657731i	$-0.771516\pi$
$677$	−2.48540	+	2.48540i	−0.0955215	+	0.0955215i	0.657731	+	0.753253i	$0.271516\pi$
$678$	−2.43455	+	1.27957i	−0.0934982	+	0.0491416i
$679$			1.51165i			0.0580119i
$680$	−12.2169	−	11.5627i	−0.468497	−	0.443409i
$681$	−7.95433	+	25.5791i	−0.304811	+	0.980194i
$682$	−14.2741	+	14.2741i	−0.546583	+	0.546583i
$683$	−30.1742	+	30.1742i	−1.15458	+	1.15458i	−0.168961	+	0.985623i	$0.554041\pi$
$683$	−30.1742	+	30.1742i	−1.15458	+	1.15458i	−0.985623	+	0.168961i	$0.945959\pi$
$684$	−5.16234	−	3.55438i	−0.197387	−	0.135905i
$685$	18.7283	−	0.515249i	0.715571	−	0.0196867i
$686$			12.5295i			0.478380i
$687$	3.16907	+	6.02957i	0.120908	+	0.230043i
$688$	−0.132445	+	0.132445i	−0.00504941	+	0.00504941i
$689$	25.1488	−	15.8311i	0.958095	−	0.603118i
$690$	2.82429	−	10.0489i	0.107519	−	0.382557i
$691$		−	2.84295i		−	0.108151i	−0.998537	−	0.0540754i	$-0.982779\pi$
$691$		−	2.84295i		−	0.108151i	0.998537	−	0.0540754i	$-0.0172211\pi$
$692$	−13.8181	+	13.8181i	−0.525285	+	0.525285i
$693$	1.23796	+	6.71093i	0.0470260	+	0.254927i
$694$	−22.1061			−0.839135
$695$	−21.6604	−	20.5005i	−0.821627	−	0.777629i
$696$	−3.14181	−	0.977008i	−0.119090	−	0.0370334i
$697$	−46.5706	+	46.5706i	−1.76399	+	1.76399i
$698$	−12.2457	−	12.2457i	−0.463505	−	0.463505i
$699$	1.91450	−	6.15653i	0.0724129	−	0.232862i
$700$	−3.19473	+	3.56707i	−0.120749	+	0.134823i
$701$		−	8.02812i		−	0.303218i	−0.988441	−	0.151609i	$-0.951555\pi$
$701$		−	8.02812i		−	0.303218i	0.988441	−	0.151609i	$-0.0484455\pi$
$702$	16.9285	−	8.02664i	0.638924	−	0.302946i
$703$	−5.51936	+	5.51936i	−0.208167	+	0.208167i
$704$			2.37516i			0.0895172i
$705$	5.57629	+	9.93610i	0.210015	+	0.374215i
$706$	−36.6393			−1.37894
$707$	11.9323	+	11.9323i	0.448761	+	0.448761i
$708$	−9.06342	−	17.2443i	−0.340624	−	0.648082i
$709$	29.4941			1.10767			0.553837	−	0.832625i	$-0.313163\pi$
$709$	29.4941			1.10767			0.553837	+	0.832625i	$0.313163\pi$
$710$	27.9335	−	0.768503i	1.04833	−	0.0288414i
$711$	2.56774	+	1.76795i	0.0962980	+	0.0663032i
$712$	−5.76993	−	5.76993i	−0.216237	−	0.216237i
$713$	16.1972	−	16.1972i	0.606589	−	0.606589i
$714$	−11.9157	−	3.70543i	−0.445934	−	0.138672i
$715$	−10.6432	−	15.9189i	−0.398033	−	0.595334i
$716$		−	9.07466i		−	0.339136i
$717$	−2.39174	+	1.25707i	−0.0893211	+	0.0469461i
$718$	23.0878	−	23.0878i	0.861628	−	0.861628i
$719$	−9.03729			−0.337034			−0.168517	−	0.985699i	$-0.553898\pi$
$719$	−9.03729			−0.337034			−0.168517	+	0.985699i	$0.553898\pi$
$720$	1.39788	+	6.56094i	0.0520961	+	0.244512i
$721$		−	2.21364i		−	0.0824403i
$722$	10.3486	+	10.3486i	0.385136	+	0.385136i
$723$	11.7341	−	6.16731i	0.436396	−	0.229365i
$724$			1.89872i			0.0705653i
$725$	0.522221	+	9.48367i	0.0193948	+	0.352214i
$726$	−2.75605	+	8.86275i	−0.102287	+	0.328928i
$727$	−36.8257	−	36.8257i	−1.36579	−	1.36579i	−0.866349	−	0.499440i	$-0.833539\pi$
$727$	−36.8257	−	36.8257i	−1.36579	−	1.36579i	−0.499440	−	0.866349i	$-0.666461\pi$
$728$	3.36714	+	0.765594i	0.124794	+	0.0283748i
$729$	26.2380	+	6.36930i	0.971777	+	0.235900i
$730$	−8.48844	−	8.03389i	−0.314171	−	0.297347i
$731$			1.40903i			0.0521147i
$732$	−14.2492	+	7.48923i	−0.526667	+	0.276810i
$733$	33.7479	+	33.7479i	1.24651	+	1.24651i	0.957252	+	0.289256i	$0.0934079\pi$
$733$	33.7479	+	33.7479i	1.24651	+	1.24651i	0.289256	+	0.957252i	$0.406592\pi$
$734$			2.83009i			0.104460i
$735$	6.37424	−	22.6798i	0.235117	−	0.836557i
$736$		−	2.69516i		−	0.0993447i
$737$	20.1361	−	20.1361i	0.741724	−	0.741724i
$738$	25.8293	−	4.76470i	0.950790	−	0.175391i
$739$	28.6230			1.05292			0.526458	−	0.850201i	$-0.323520\pi$
$739$	28.6230			1.05292			0.526458	+	0.850201i	$0.323520\pi$
$740$	8.35105	−	0.229753i	0.306991	−	0.00844587i
$741$	12.6075	−	3.35841i	0.463148	−	0.123374i
$742$	5.58149	+	5.58149i	0.204903	+	0.204903i
$743$	−17.2290	+	17.2290i	−0.632070	+	0.632070i	−0.948587	−	0.316517i	$-0.897487\pi$
$743$	−17.2290	+	17.2290i	−0.632070	+	0.632070i	0.316517	+	0.948587i	$0.397487\pi$
$744$	−4.37125	+	14.0568i	−0.160258	+	0.515348i
$745$	8.93942	+	8.46071i	0.327515	+	0.309976i
$746$	17.1930			0.629480
$747$	0.366159	+	1.98494i	0.0133971	+	0.0726252i
$748$	12.6342	+	12.6342i	0.461951	+	0.461951i
$749$			6.13044i			0.224001i
$750$	16.3406	−	10.3915i	0.596675	−	0.379445i
$751$	46.3660			1.69192			0.845960	−	0.533247i	$-0.179028\pi$
$751$	46.3660			1.69192			0.845960	+	0.533247i	$0.179028\pi$
$752$	2.08023	+	2.08023i	0.0758583	+	0.0758583i
$753$	5.75523	−	3.02488i	0.209732	−	0.110233i
$754$	5.79630	−	3.64876i	0.211089	−	0.132880i
$755$	−22.4877	−	21.2835i	−0.818411	−	0.774585i
$756$	3.07593	+	3.91195i	0.111871	+	0.142276i
$757$	−14.9234	−	14.9234i	−0.542401	−	0.542401i	0.381831	−	0.924232i	$-0.375293\pi$
$757$	−14.9234	−	14.9234i	−0.542401	−	0.542401i	−0.924232	+	0.381831i	$0.875293\pi$
$758$	14.5643	+	14.5643i	0.528999	+	0.528999i
$759$	−3.29239	+	10.5875i	−0.119506	+	0.384301i
$760$	0.128476	+	4.66986i	0.00466033	+	0.169394i
$761$	15.3305			0.555729			0.277864	−	0.960620i	$-0.410373\pi$
$761$	15.3305			0.555729			0.277864	+	0.960620i	$0.410373\pi$
$762$	−16.6090	+	8.72950i	−0.601681	+	0.316236i
$763$	−11.5931	+	11.5931i	−0.419697	+	0.419697i
$764$	−14.2651			−0.516094
$765$	42.3353	+	27.4638i	1.53064	+	0.992956i
$766$	−2.42062			−0.0874607
$767$	39.5438	+	8.99116i	1.42784	+	0.324652i
$768$	0.805823	+	1.53318i	0.0290776	+	0.0553240i
$769$	36.6299			1.32091			0.660454	−	0.750866i	$-0.270364\pi$
$769$	36.6299			1.32091			0.660454	+	0.750866i	$0.270364\pi$
$770$	3.49637	−	3.69420i	0.126001	−	0.133130i
$771$	7.03210	+	2.18677i	0.253255	+	0.0787547i
$772$	9.53551	−	9.53551i	0.343191	−	0.343191i
$773$	−14.6833	+	14.6833i	−0.528122	+	0.528122i	−0.920012	−	0.391890i	$-0.871821\pi$
$773$	−14.6833	+	14.6833i	−0.528122	+	0.528122i	0.391890	+	0.920012i	$0.371821\pi$
$774$	0.318662	−	0.462822i	0.0114541	−	0.0166358i
$775$	42.4310	−	2.33648i	1.52417	−	0.0839287i
$776$		−	1.57840i		−	0.0566613i
$777$	5.48592	−	2.88333i	0.196806	−	0.103439i
$778$	−16.0943	−	16.0943i	−0.577007	−	0.577007i
$779$	18.2912			0.655349
$780$	−12.2711	−	6.66485i	−0.439376	−	0.238640i
$781$	−29.6823			−1.06212
$782$	−14.3363	−	14.3363i	−0.512666	−	0.512666i
$783$	9.80075	+	1.17254i	0.350250	+	0.0419033i
$784$		−	6.08279i		−	0.217242i
$785$	−20.8313	+	0.573107i	−0.743501	+	0.0204551i
$786$	36.2423	+	11.2703i	1.29272	+	0.401997i
$787$	25.8088	−	25.8088i	0.919983	−	0.919983i	−0.0770443	−	0.997028i	$-0.524548\pi$
$787$	25.8088	−	25.8088i	0.919983	−	0.919983i	0.997028	+	0.0770443i	$0.0245483\pi$
$788$	8.00501	−	8.00501i	0.285167	−	0.285167i
$789$	−8.39028	+	26.9810i	−0.298702	+	0.960549i
$790$	−0.0639040	−	2.32279i	−0.00227360	−	0.0826410i
$791$	1.52075			0.0540718
$792$	−1.29262	−	7.00725i	−0.0459312	−	0.248992i
$793$	7.42953	−	32.6756i	0.263830	−	1.16034i
$794$	−27.2423			−0.966794
$795$	−15.6224	−	27.8368i	−0.554071	−	0.987270i
$796$	−10.2380			−0.362877
$797$	6.38493	−	6.38493i	0.226166	−	0.226166i	−0.584923	−	0.811089i	$-0.698875\pi$
$797$	6.38493	−	6.38493i	0.226166	−	0.226166i	0.811089	+	0.584923i	$0.198875\pi$
$798$	1.61234	+	3.06769i	0.0570763	+	0.108595i
$799$	22.1308			0.782930
$800$	3.33580	−	3.72458i	0.117938	−	0.131684i
$801$	20.1627	+	13.8825i	0.712415	+	0.490513i
$802$	−15.6545	−	15.6545i	−0.552779	−	0.552779i
$803$	8.77836	+	8.77836i	0.309782	+	0.309782i
$804$	6.16641	−	19.8296i	0.217472	−	0.699336i
$805$	−3.96742	+	4.19190i	−0.139833	+	0.147745i
$806$	−16.3250	−	25.9333i	−0.575022	−	0.913462i
$807$	−12.8573	−	24.4627i	−0.452599	−	0.861128i
$808$	−12.4592	−	12.4592i	−0.438313	−	0.438313i
$809$	19.9820			0.702530			0.351265	−	0.936276i	$-0.385752\pi$
$809$	19.9820			0.702530			0.351265	+	0.936276i	$0.385752\pi$
$810$	−7.69469	−	18.5955i	−0.270364	−	0.653378i
$811$		−	8.19667i		−	0.287824i	−0.989590	−	0.143912i	$-0.954032\pi$
$811$		−	8.19667i		−	0.287824i	0.989590	−	0.143912i	$-0.0459682\pi$
$812$	1.28642	+	1.28642i	0.0451446	+	0.0451446i
$813$	41.6350	−	21.8829i	1.46020	−	0.767466i
$814$	−8.87388			−0.311029
$815$	−19.8577	+	0.546322i	−0.695585	+	0.0191368i
$816$	12.4419	+	3.86904i	0.435552	+	0.135444i
$817$	0.276706	−	0.276706i	0.00968071	−	0.00968071i
$818$	16.3073	+	16.3073i	0.570173	+	0.570173i
$819$	−10.3505	−	0.426197i	−0.361674	−	0.0148925i
$820$	−14.2184	−	13.4570i	−0.496528	−	0.469938i
$821$	−3.86982			−0.135058			−0.0675288	−	0.997717i	$-0.521511\pi$
$821$	−3.86982			−0.135058			−0.0675288	+	0.997717i	$0.521511\pi$
$822$	−12.8461	+	6.75176i	−0.448059	+	0.235495i
$823$	−17.2535	+	17.2535i	−0.601420	+	0.601420i	−0.940689	−	0.339269i	$-0.889820\pi$
$823$	−17.2535	+	17.2535i	−0.601420	+	0.601420i	0.339269	+	0.940689i	$0.389820\pi$
$824$			2.31139i			0.0805210i
$825$	−17.6541	+	10.5564i	−0.614636	+	0.367527i
$826$			10.7718i			0.374798i
$827$	27.8990	+	27.8990i	0.970143	+	0.970143i	0.999567	−	0.0294237i	$-0.00936722\pi$
$827$	27.8990	+	27.8990i	0.970143	+	0.970143i	−0.0294237	+	0.999567i	$0.509367\pi$
$828$	1.46677	+	7.95131i	0.0509737	+	0.276327i
$829$			37.1965i			1.29189i	0.763386	+	0.645943i	$0.223536\pi$
$829$			37.1965i			1.29189i	−0.763386	+	0.645943i	$0.776464\pi$
$830$	1.03415	−	1.09266i	0.0358958	−	0.0379268i
$831$	−7.77650	+	25.0073i	−0.269764	+	0.867492i
$832$	−3.51582	−	0.799399i	−0.121889	−	0.0277142i
$833$	−32.3562	−	32.3562i	−1.12107	−	1.12107i
$834$	22.0593	+	6.85976i	0.763850	+	0.237534i
$835$	7.44086	−	0.204712i	0.257502	−	0.00708434i
$836$		−	4.96222i		−	0.171622i
$837$	5.24610	−	43.8497i	0.181332	−	1.51567i
$838$	17.9099	+	17.9099i	0.618688	+	0.618688i
$839$			14.7927i			0.510700i	0.966849	+	0.255350i	$0.0821908\pi$
$839$			14.7927i			0.510700i	−0.966849	+	0.255350i	$0.917809\pi$
$840$	1.00360	−	3.57085i	0.0346275	−	0.123206i
$841$	−25.3915			−0.875569
$842$	17.8664	−	17.8664i	0.615716	−	0.615716i
$843$	−14.1985	−	27.0144i	−0.489021	−	0.930426i
$844$		−	3.79498i		−	0.130629i
$845$	27.1460	−	10.3968i	0.933852	−	0.357660i
$846$	−7.26927	−	5.00504i	−0.249923	−	0.172077i
$847$	3.62888	−	3.62888i	0.124690	−	0.124690i
$848$	−5.82795	−	5.82795i	−0.200133	−	0.200133i
$849$	−40.3113	−	12.5356i	−1.38348	−	0.430221i
$850$	−2.06804	−	37.5562i	−0.0709333	−	1.28817i
$851$	10.0694			0.345175
$852$	−19.1602	+	10.0704i	−0.656416	+	0.345005i
$853$	−25.7170	−	25.7170i	−0.880533	−	0.880533i	0.113056	−	0.993589i	$-0.463936\pi$
$853$	−25.7170	−	25.7170i	−0.880533	−	0.880533i	−0.993589	+	0.113056i	$0.963936\pi$
$854$	8.90087			0.304581
$855$	−2.92048	−	13.7072i	−0.0998784	−	0.468777i
$856$		−	6.40114i		−	0.218786i
$857$	−26.4247	+	26.4247i	−0.902650	+	0.902650i	−0.995665	−	0.0930149i	$-0.970350\pi$
$857$	−26.4247	+	26.4247i	−0.902650	+	0.902650i	0.0930149	+	0.995665i	$0.470350\pi$
$858$	12.8348	+	7.43522i	0.438172	+	0.253834i
$859$		−	27.8865i		−	0.951475i	−0.879587	−	0.475738i	$-0.842181\pi$
$859$		−	27.8865i		−	0.951475i	0.879587	−	0.475738i	$-0.157819\pi$
$860$	−0.418669	+	0.0115183i	−0.0142765	+	0.000392772i
$861$	−13.8678	−	4.31248i	−0.472615	−	0.146969i
$862$	18.9954	+	18.9954i	0.646987	+	0.646987i
$863$	8.82969	−	8.82969i	0.300566	−	0.300566i	−0.540669	−	0.841235i	$-0.681829\pi$
$863$	8.82969	−	8.82969i	0.300566	−	0.300566i	0.841235	+	0.540669i	$0.181829\pi$
$864$	−3.21175	−	4.08468i	−0.109266	−	0.138964i
$865$	−43.6801	+	1.20172i	−1.48517	+	0.0408597i
$866$	4.78682			0.162663
$867$	60.6984	−	31.9024i	2.06143	−	1.08346i
$868$	5.75560	−	5.75560i	0.195358	−	0.195358i
$869$			2.46821i			0.0837281i
$870$	−3.60066	−	6.41583i	−0.122074	−	0.217517i
$871$	23.0292	+	36.5835i	0.780316	+	1.23958i
$872$	12.1050	−	12.1050i	0.409926	−	0.409926i
$873$	0.859003	+	4.65663i	0.0290728	+	0.157603i
$874$			5.63076i			0.190463i
$875$	−10.6711	+	0.882527i	−0.360749	+	0.0298348i
$876$	8.64474	+	2.68825i	0.292079	+	0.0908276i
$877$	−21.9876	+	21.9876i	−0.742469	+	0.742469i	−0.973053	−	0.230584i	$-0.925937\pi$
$877$	−21.9876	+	21.9876i	−0.742469	+	0.742469i	0.230584	+	0.973053i	$0.425937\pi$
$878$	−20.0211	+	20.0211i	−0.675678	+	0.675678i
$879$	19.6312	+	6.10469i	0.662142	+	0.205906i
$880$	−3.65076	+	3.85732i	−0.123067	+	0.130030i
$881$			25.8254i			0.870080i	0.900411	+	0.435040i	$0.143266\pi$
$881$			25.8254i			0.870080i	−0.900411	+	0.435040i	$0.856734\pi$
$882$	3.31040	+	17.9456i	0.111467	+	0.604259i
$883$	32.7661	−	32.7661i	1.10267	−	1.10267i	0.108581	−	0.994088i	$-0.465369\pi$
$883$	32.7661	−	32.7661i	1.10267	−	1.10267i	0.994088	−	0.108581i	$-0.0346306\pi$
$884$	−22.9539	+	14.4494i	−0.772023	+	0.485987i
$885$	11.7863	−	41.9362i	0.396193	−	1.40967i
$886$		−	7.36391i		−	0.247395i
$887$	15.9624	−	15.9624i	0.535966	−	0.535966i	−0.386376	−	0.922341i	$-0.626273\pi$
$887$	15.9624	−	15.9624i	0.535966	−	0.535966i	0.922341	+	0.386376i	$0.126273\pi$
$888$	−5.72815	+	3.01065i	−0.192224	+	0.101031i
$889$	10.3749			0.347964
$890$	−0.501795	−	18.2392i	−0.0168202	−	0.611381i
$891$	7.62703	+	19.9695i	0.255515	+	0.669003i
$892$	0.0933672	−	0.0933672i	0.00312617	−	0.00312617i
$893$	−4.34606	−	4.34606i	−0.145435	−	0.145435i
$894$	−9.10402	−	2.83107i	−0.304484	−	0.0946853i
$895$	13.9483	−	14.7375i	0.466239	−	0.492619i
$896$		−	0.957712i		−	0.0319949i
$897$	−14.5640	−	8.43693i	−0.486276	−	0.281701i
$898$	16.9045	−	16.9045i	0.564110	−	0.564110i
$899$		−	16.1449i		−	0.538461i
$900$	−7.81434	+	12.8038i	−0.260478	+	0.426792i
$901$	−62.0012			−2.06556
$902$	14.7040	+	14.7040i	0.489590	+	0.489590i
$903$	−0.275029	+	0.144552i	−0.00915240	+	0.00481039i
$904$	−1.58790			−0.0528129
$905$	−2.91844	+	3.08356i	−0.0970122	+	0.102501i
$906$	22.9018	+	7.12176i	0.760860	+	0.236604i
$907$	3.61754	+	3.61754i	0.120118	+	0.120118i	0.764611	−	0.644492i	$-0.222931\pi$
$907$	3.61754	+	3.61754i	0.120118	+	0.120118i	−0.644492	+	0.764611i	$0.722931\pi$
$908$	−10.9359	+	10.9359i	−0.362921	+	0.362921i
$909$	43.5380	+	29.9769i	1.44407	+	0.994270i
$910$	4.29155	+	6.41883i	0.142264	+	0.212782i
$911$		−	42.5498i		−	1.40974i	−0.709337	−	0.704869i	$-0.751006\pi$
$911$		−	42.5498i		−	1.40974i	0.709337	−	0.704869i	$-0.248994\pi$
$912$	−1.68354	−	3.20315i	−0.0557475	−	0.106067i
$913$	−1.12998	+	1.12998i	−0.0373969	+	0.0373969i
$914$	34.0067			1.12484
$915$	−34.6525	−	9.73920i	−1.14558	−	0.321968i
$916$			3.93272i			0.129941i
$917$	−14.8395	−	14.8395i	−0.490043	−	0.490043i
$918$	−38.8119	−	4.64339i	−1.28098	−	0.153255i
$919$			30.8672i			1.01822i	0.860703	+	0.509108i	$0.170025\pi$
$919$			30.8672i			1.01822i	−0.860703	+	0.509108i	$0.829975\pi$
$920$	4.14261	−	4.37700i	0.136578	−	0.144305i
$921$	−35.3481	−	10.9922i	−1.16476	−	0.362204i
$922$	−14.0112	−	14.0112i	−0.461433	−	0.461433i
$923$	9.99008	−	43.9371i	0.328827	−	1.44621i
$924$	−1.16994	+	3.76222i	−0.0384881	+	0.123768i
$925$	13.9155	+	12.4629i	0.457537	+	0.409778i
$926$			7.28492i			0.239397i
$927$	−1.25791	−	6.81911i	−0.0413152	−	0.223969i
$928$	−1.34322	−	1.34322i	−0.0440935	−	0.0440935i
$929$			34.6466i			1.13672i	0.822780	+	0.568360i	$0.192422\pi$
$929$			34.6466i			1.13672i	−0.822780	+	0.568360i	$0.807578\pi$
$930$	−28.7051	+	16.1098i	−0.941279	+	0.528260i
$931$			12.7083i			0.416496i
$932$	2.63212	−	2.63212i	0.0862178	−	0.0862178i
$933$	49.8734	−	26.2129i	1.63278	−	0.858171i
$934$	−6.44587			−0.210915
$935$	1.09876	+	39.9377i	0.0359332	+	1.30610i
$936$	10.8075	+	0.445016i	0.353254	+	0.0145458i
$937$	−10.4252	−	10.4252i	−0.340577	−	0.340577i	0.516007	−	0.856584i	$-0.327418\pi$
$937$	−10.4252	−	10.4252i	−0.340577	−	0.340577i	−0.856584	+	0.516007i	$0.827418\pi$
$938$	−8.11928	+	8.11928i	−0.265104	+	0.265104i
$939$	13.7474	+	4.27502i	0.448629	+	0.139510i
$940$	0.180912	+	6.57579i	0.00590070	+	0.214479i
$941$	−9.29998			−0.303171			−0.151585	−	0.988444i	$-0.548438\pi$
$941$	−9.29998			−0.303171			−0.151585	+	0.988444i	$0.548438\pi$
$942$	14.2886	−	7.50992i	0.465548	−	0.244686i
$943$	−16.6850	−	16.6850i	−0.543339	−	0.543339i
$944$		−	11.2474i		−	0.366072i
$945$	−1.01750	+	11.0810i	−0.0330993	+	0.360464i
$946$	0.444880			0.0144643
$947$	39.1313	+	39.1313i	1.27160	+	1.27160i	0.945251	+	0.326344i	$0.105817\pi$
$947$	39.1313	+	39.1313i	1.27160	+	1.27160i	0.326344	+	0.945251i	$0.394183\pi$
$948$	0.837390	+	1.59324i	0.0271972	+	0.0517462i
$949$	−15.9486	+	10.0396i	−0.517714	+	0.325900i
$950$	−6.96920	+	7.78144i	−0.226111	+	0.252463i
$951$	12.1255	−	38.9925i	0.393196	−	1.26442i
$952$	−5.09435	−	5.09435i	−0.165109	−	0.165109i
$953$	−24.7482	−	24.7482i	−0.801673	−	0.801673i	0.181684	−	0.983357i	$-0.441845\pi$
$953$	−24.7482	−	24.7482i	−0.801673	−	0.801673i	−0.983357	+	0.181684i	$0.941845\pi$
$954$	20.3655	+	14.0220i	0.659356	+	0.453980i
$955$	−23.1669	−	21.9263i	−0.749663	−	0.709518i
$956$	−1.55998			−0.0504535
$957$	3.63577	+	6.91752i	0.117528	+	0.223612i
$958$	−11.2649	+	11.2649i	−0.363951	+	0.363951i
$959$	8.02439			0.259121
$960$	−1.04791	+	3.72852i	−0.0338213	+	0.120338i
$961$	−41.2340			−1.33013
$962$	2.98665	−	13.1355i	0.0962934	−	0.423505i
$963$	3.48365	+	18.8848i	0.112259	+	0.608554i
$964$	7.65343			0.246501
$965$	30.1425	−	0.829276i	0.970322	−	0.0266953i
$966$	1.32756	−	4.26908i	0.0427134	−	0.137356i
$967$	15.7278	−	15.7278i	0.505772	−	0.505772i	−0.407454	−	0.913226i	$-0.633583\pi$
$967$	15.7278	−	15.7278i	0.505772	−	0.505772i	0.913226	+	0.407454i	$0.133583\pi$
$968$	−3.78911	+	3.78911i	−0.121787	+	0.121787i
$969$	−25.9937	−	8.08327i	−0.835039	−	0.259672i
$970$	2.42609	−	2.56336i	0.0778971	−	0.0823045i
$971$			20.1928i			0.648019i	0.946054	+	0.324009i	$0.105031\pi$
$971$			20.1928i			0.648019i	−0.946054	+	0.324009i	$0.894969\pi$
$972$	11.6984	+	10.3028i	0.375225	+	0.330463i
$973$	−9.03222	−	9.03222i	−0.289560	−	0.289560i
$974$	−29.4586			−0.943914
$975$	−9.68430	−	29.6853i	−0.310146	−	0.950689i
$976$	−9.29389			−0.297490
$977$	37.9379	+	37.9379i	1.21374	+	1.21374i	0.969787	+	0.243954i	$0.0784448\pi$
$977$	37.9379	+	37.9379i	1.21374	+	1.21374i	0.243954	+	0.969787i	$0.421555\pi$
$978$	13.6208	−	7.15893i	0.435545	−	0.228917i
$979$			19.3811i			0.619423i
$980$	9.34959	−	9.87860i	0.298662	−	0.315560i
$981$	−29.1245	+	42.3001i	−0.929875	+	1.35054i
$982$	17.5933	−	17.5933i	0.561426	−	0.561426i
$983$	−1.61981	+	1.61981i	−0.0516638	+	0.0516638i	−0.732467	−	0.680803i	$-0.761631\pi$
$983$	−1.61981	+	1.61981i	−0.0516638	+	0.0516638i	0.680803	+	0.732467i	$0.261631\pi$
$984$	14.4802	+	4.50290i	0.461611	+	0.143547i
$985$	25.3045	−	0.696173i	0.806268	−	0.0221819i
$986$	−14.2900			−0.455087
$987$	2.27040	+	4.31972i	0.0722675	+	0.137498i
$988$	7.34530	+	1.67012i	0.233685	+	0.0531335i
$989$	−0.504817			−0.0160522
$990$	8.67131	−	13.3668i	0.275592	−	0.424824i
$991$	32.4119			1.02960			0.514799	−	0.857311i	$-0.327867\pi$
$991$	32.4119			1.02960			0.514799	+	0.857311i	$0.327867\pi$
$992$	−6.00974	+	6.00974i	−0.190809	+	0.190809i
$993$	20.9544	−	11.0134i	0.664967	−	0.349499i
$994$	11.9685			0.379618
$995$	−16.6268	−	15.7364i	−0.527104	−	0.498878i
$996$	−0.346041	+	1.11278i	−0.0109647	+	0.0352597i
$997$	1.47150	+	1.47150i	0.0466030	+	0.0466030i	0.730024	−	0.683421i	$-0.239509\pi$
$997$	1.47150	+	1.47150i	0.0466030	+	0.0466030i	−0.683421	+	0.730024i	$0.739509\pi$
$998$	29.0950	+	29.0950i	0.920985	+	0.920985i
$999$	15.2609	−	11.9995i	0.482832	−	0.379647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.s.c.77.4	yes	24
3.2	odd	2		390.2.s.b.77.7	yes	24
5.3	odd	4		390.2.s.b.233.1	yes	24
13.12	even	2	inner	390.2.s.c.77.10	yes	24
15.8	even	4	inner	390.2.s.c.233.10	yes	24
39.38	odd	2		390.2.s.b.77.1	✓	24
65.38	odd	4		390.2.s.b.233.7	yes	24
195.38	even	4	inner	390.2.s.c.233.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.s.b.77.1	✓	24	39.38	odd	2
390.2.s.b.77.7	yes	24	3.2	odd	2
390.2.s.b.233.1	yes	24	5.3	odd	4
390.2.s.b.233.7	yes	24	65.38	odd	4
390.2.s.c.77.4	yes	24	1.1	even	1	trivial
390.2.s.c.77.10	yes	24	13.12	even	2	inner
390.2.s.c.233.4	yes	24	195.38	even	4	inner
390.2.s.c.233.10	yes	24	15.8	even	4	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.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.805823 + 1.53318i) q^{3} +1.00000i q^{4} +(-1.53706 + 1.62402i) q^{5} +(0.514321 - 1.65393i) q^{6} +(-0.677204 + 0.677204i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.70130 + 2.47095i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.805823 + 1.53318i) q^{3} +1.00000i q^{4} +(-1.53706 + 1.62402i) q^{5} +(0.514321 - 1.65393i) q^{6} +(-0.677204 + 0.677204i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.70130 + 2.47095i) q^{9} +(2.23522 - 0.0614950i) q^{10} -2.37516 q^{11} +(-1.53318 + 0.805823i) q^{12} +(0.799399 - 3.51582i) q^{13} +0.957712 q^{14} +(-3.72852 - 1.04791i) q^{15} -1.00000 q^{16} +(-5.31930 + 5.31930i) q^{17} +(2.95022 - 0.544224i) q^{18} +2.08922 q^{19} +(-1.62402 - 1.53706i) q^{20} +(-1.58398 - 0.492571i) q^{21} +(1.67949 + 1.67949i) q^{22} +(-1.90576 - 1.90576i) q^{23} +(1.65393 + 0.514321i) q^{24} +(-0.274910 - 4.99244i) q^{25} +(-3.05132 + 1.92080i) q^{26} +(-5.15936 - 0.617257i) q^{27} +(-0.677204 - 0.677204i) q^{28} -1.89961 q^{29} +(1.89548 + 3.37745i) q^{30} +8.49906i q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.91396 - 3.64155i) q^{33} +7.52262 q^{34} +(-0.0588945 - 2.14070i) q^{35} +(-2.47095 - 1.70130i) q^{36} +(-2.64183 + 2.64183i) q^{37} +(-1.47730 - 1.47730i) q^{38} +(6.03456 - 1.60750i) q^{39} +(0.0614950 + 2.23522i) q^{40} +8.75503 q^{41} +(0.771746 + 1.46835i) q^{42} +(0.132445 - 0.132445i) q^{43} -2.37516i q^{44} +(-1.39788 - 6.56094i) q^{45} +2.69516i q^{46} +(-2.08023 - 2.08023i) q^{47} +(-0.805823 - 1.53318i) q^{48} +6.08279i q^{49} +(-3.33580 + 3.72458i) q^{50} +(-12.4419 - 3.86904i) q^{51} +(3.51582 + 0.799399i) q^{52} +(5.82795 + 5.82795i) q^{53} +(3.21175 + 4.08468i) q^{54} +(3.65076 - 3.85732i) q^{55} +0.957712i q^{56} +(1.68354 + 3.20315i) q^{57} +(1.34322 + 1.34322i) q^{58} +11.2474i q^{59} +(1.04791 - 3.72852i) q^{60} +9.29389 q^{61} +(6.00974 - 6.00974i) q^{62} +(-0.521209 - 2.82546i) q^{63} -1.00000i q^{64} +(4.48105 + 6.70225i) q^{65} +(-1.22160 + 3.92834i) q^{66} +(-8.47780 + 8.47780i) q^{67} +(-5.31930 - 5.31930i) q^{68} +(1.38618 - 4.45759i) q^{69} +(-1.47206 + 1.55535i) q^{70} +12.4970 q^{71} +(0.544224 + 2.95022i) q^{72} +(-3.69590 - 3.69590i) q^{73} +3.73612 q^{74} +(7.43279 - 4.44451i) q^{75} +2.08922i q^{76} +(1.60847 - 1.60847i) q^{77} +(-5.40375 - 3.13041i) q^{78} -1.03917i q^{79} +(1.53706 - 1.62402i) q^{80} +(-3.21116 - 8.40764i) q^{81} +(-6.19074 - 6.19074i) q^{82} +(0.475749 - 0.475749i) q^{83} +(0.492571 - 1.58398i) q^{84} +(-0.462604 - 16.8147i) q^{85} -0.187305 q^{86} +(-1.53075 - 2.91244i) q^{87} +(-1.67949 + 1.67949i) q^{88} -8.15992i q^{89} +(-3.65083 + 5.62774i) q^{90} +(1.83957 + 2.92228i) q^{91} +(1.90576 - 1.90576i) q^{92} +(-13.0306 + 6.84873i) q^{93} +2.94189i q^{94} +(-3.21124 + 3.39294i) q^{95} +(-0.514321 + 1.65393i) q^{96} +(1.11610 - 1.11610i) q^{97} +(4.30118 - 4.30118i) q^{98} +(4.04086 - 5.86890i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} + 12 q^{9}+O(q^{10}) \) 24 * q + 4 * q^3 + 12 * q^9	\( 24 q + 4 q^{3} + 12 q^{9} + 4 q^{10} - 8 q^{12} - 8 q^{13} + 16 q^{14} - 24 q^{16} - 52 q^{17} + 16 q^{22} + 16 q^{23} + 16 q^{25} - 56 q^{27} + 80 q^{29} + 8 q^{30} - 20 q^{35} + 16 q^{38} + 32 q^{39} - 48 q^{42} + 28 q^{43} - 4 q^{48} - 20 q^{51} - 8 q^{52} - 72 q^{53} + 24 q^{55} - 64 q^{61} + 32 q^{62} + 12 q^{65} + 8 q^{66} - 52 q^{68} + 16 q^{69} + 120 q^{74} + 24 q^{75} - 32 q^{77} - 64 q^{78} + 12 q^{81} + 32 q^{82} - 16 q^{88} - 44 q^{90} + 64 q^{91} - 16 q^{92} - 96 q^{95}+O(q^{100}) \) 24 * q + 4 * q^3 + 12 * q^9 + 4 * q^10 - 8 * q^12 - 8 * q^13 + 16 * q^14 - 24 * q^16 - 52 * q^17 + 16 * q^22 + 16 * q^23 + 16 * q^25 - 56 * q^27 + 80 * q^29 + 8 * q^30 - 20 * q^35 + 16 * q^38 + 32 * q^39 - 48 * q^42 + 28 * q^43 - 4 * q^48 - 20 * q^51 - 8 * q^52 - 72 * q^53 + 24 * q^55 - 64 * q^61 + 32 * q^62 + 12 * q^65 + 8 * q^66 - 52 * q^68 + 16 * q^69 + 120 * q^74 + 24 * q^75 - 32 * q^77 - 64 * q^78 + 12 * q^81 + 32 * q^82 - 16 * q^88 - 44 * q^90 + 64 * q^91 - 16 * q^92 - 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more