LMFDB - Embedded newform 390.2.s.b.233.7

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			233.7
Character	$\chi$	$=$	390.233
Dual form			390.2.s.b.77.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.53318 + 0.805823i) q^{3} -1.00000i q^{4} +(1.53706 + 1.62402i) q^{5} +(-0.514321 + 1.65393i) q^{6} +(-0.677204 - 0.677204i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.70130 - 2.47095i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.53318 + 0.805823i) 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} +(0.805823 + 1.53318i) q^{12} +(0.799399 + 3.51582i) q^{13} -0.957712 q^{14} +(-3.66527 - 1.25133i) q^{15} -1.00000 q^{16} +(5.31930 + 5.31930i) q^{17} +(-0.544224 - 2.95022i) 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} +(-0.617257 + 5.15936i) q^{27} +(-0.677204 + 0.677204i) q^{28} +1.89961 q^{29} +(-3.47656 + 1.70691i) q^{30} -8.49906i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.64155 + 1.91396i) 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} +(-4.05875 - 4.74621i) q^{39} +(0.0614950 - 2.23522i) q^{40} -8.75503 q^{41} +(1.46835 - 0.771746i) q^{42} +(0.132445 + 0.132445i) q^{43} -2.37516i q^{44} +(6.62787 - 1.03504i) q^{45} -2.69516i q^{46} +(2.08023 - 2.08023i) q^{47} +(1.53318 - 0.805823i) 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} +(-3.20315 + 1.68354i) q^{57} +(1.34322 - 1.34322i) q^{58} +11.2474i q^{59} +(-1.25133 + 3.66527i) q^{60} +9.29389 q^{61} +(-6.00974 - 6.00974i) q^{62} +(-2.82546 + 0.521209i) 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} +(-2.95022 + 0.544224i) q^{72} +(-3.69590 + 3.69590i) q^{73} -3.73612 q^{74} +(-3.60153 - 7.87585i) q^{75} -2.08922i q^{76} +(-1.60847 - 1.60847i) q^{77} +(-6.22605 - 0.486111i) 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} +(-2.91244 + 1.53075i) q^{87} +(-1.67949 - 1.67949i) q^{88} -8.15992i q^{89} +(3.95473 - 5.41850i) q^{90} +(1.83957 - 2.92228i) q^{91} +(-1.90576 - 1.90576i) q^{92} +(6.84873 + 13.0306i) 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 - 8 q^{3} - 12 q^{9}+O(q^{10}) $ 24 * q - 8 * q^3 - 12 * q^9	$ 24 q - 8 q^{3} - 12 q^{9} + 4 q^{10} + 4 q^{12} - 8 q^{13} - 16 q^{14} - 24 q^{16} + 52 q^{17} + 16 q^{22} - 16 q^{23} + 16 q^{25} + 40 q^{27} - 80 q^{29} + 20 q^{35} - 16 q^{38} - 32 q^{39} - 4 q^{42} + 28 q^{43} + 8 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} - 104 q^{75} + 32 q^{77} + 44 q^{78} + 12 q^{81} + 32 q^{82} - 32 q^{87} - 16 q^{88} + 64 q^{90} + 64 q^{91} + 16 q^{92} + 96 q^{95}+O(q^{100}) $ 24 * q - 8 * q^3 - 12 * q^9 + 4 * q^10 + 4 * q^12 - 8 * q^13 - 16 * q^14 - 24 * q^16 + 52 * q^17 + 16 * q^22 - 16 * q^23 + 16 * q^25 + 40 * q^27 - 80 * q^29 + 20 * q^35 - 16 * q^38 - 32 * q^39 - 4 * q^42 + 28 * q^43 + 8 * 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 - 104 * q^75 + 32 * q^77 + 44 * q^78 + 12 * q^81 + 32 * q^82 - 32 * q^87 - 16 * q^88 + 64 * 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 $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

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

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
$3$	−1.53318	+	0.805823i	−0.885184	+	0.465242i
$3$	−1.53318	+	0.805823i	−0.885184	+	0.465242i
$4$		−	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	0.567449	−	0.823408i	$-0.307930\pi$
$7$	−0.677204	−	0.677204i	−0.255959	−	0.255959i	−0.823408	+	0.567449i	$0.807930\pi$
$8$	−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	$-0.383435\pi$
$11$	2.37516			0.716138			0.358069	+	0.933695i	$0.383435\pi$
$12$	0.805823	+	1.53318i	0.232621	+	0.442592i
$13$	0.799399	+	3.51582i	0.221713	+	0.975112i
$13$	0.799399	+	3.51582i	0.221713	+	0.975112i
$14$	−0.957712			−0.255959
$15$	−3.66527	−	1.25133i	−0.946368	−	0.323092i
$16$	−1.00000			−0.250000
$17$	5.31930	+	5.31930i	1.29012	+	1.29012i	0.934712	+	0.355407i	$0.115658\pi$
$17$	5.31930	+	5.31930i	1.29012	+	1.29012i	0.355407	+	0.934712i	$0.384342\pi$
$18$	−0.544224	−	2.95022i	−0.128275	−	0.695374i
$19$	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	$-0.659337\pi$
$23$	1.90576	−	1.90576i	0.397379	−	0.397379i	0.877308	+	0.479929i	$0.159337\pi$
$24$	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
$27$	−0.617257	+	5.15936i	−0.118791	+	0.992919i
$28$	−0.677204	+	0.677204i	−0.127980	+	0.127980i
$29$	1.89961			0.352748			0.176374	−	0.984323i	$-0.443563\pi$
$29$	1.89961			0.352748			0.176374	+	0.984323i	$0.443563\pi$
$30$	−3.47656	+	1.70691i	−0.634730	+	0.311638i
$31$		−	8.49906i		−	1.52648i	−0.646118	−	0.763238i	$-0.723608\pi$
$31$		−	8.49906i		−	1.52648i	0.646118	−	0.763238i	$-0.276392\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−3.64155	+	1.91396i	−0.633913	+	0.333177i
$34$	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	0.455779	−	0.890093i	$-0.349361\pi$
$37$	−2.64183	−	2.64183i	−0.434315	−	0.434315i	−0.890093	+	0.455779i	$0.849361\pi$
$38$	1.47730	−	1.47730i	0.239649	−	0.239649i
$39$	−4.05875	−	4.74621i	−0.649920	−	0.760003i
$40$	0.0614950	−	2.23522i	0.00972322	−	0.353420i
$41$	−8.75503			−1.36731			−0.683653	−	0.729807i	$-0.739610\pi$
$41$	−8.75503			−1.36731			−0.683653	+	0.729807i	$0.739610\pi$
$42$	1.46835	−	0.771746i	0.226571	−	0.119083i
$43$	0.132445	+	0.132445i	0.0201977	+	0.0201977i	0.717133	−	0.696936i	$-0.245454\pi$
$43$	0.132445	+	0.132445i	0.0201977	+	0.0201977i	−0.696936	+	0.717133i	$0.745454\pi$
$44$		−	2.37516i		−	0.358069i
$45$	6.62787	−	1.03504i	0.988025	−	0.154294i
$46$		−	2.69516i		−	0.397379i
$47$	2.08023	−	2.08023i	0.303433	−	0.303433i	−0.538922	−	0.842356i	$-0.681168\pi$
$47$	2.08023	−	2.08023i	0.303433	−	0.303433i	0.842356	+	0.538922i	$0.181168\pi$
$48$	1.53318	−	0.805823i	0.221296	−	0.116311i
$49$		−	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	$-0.941533\pi$
$53$	−5.82795	+	5.82795i	−0.800530	+	0.800530i	0.182648	+	0.983178i	$0.441533\pi$
$54$	3.21175	+	4.08468i	0.437064	+	0.555855i
$55$	3.65076	+	3.85732i	0.492268	+	0.520121i
$56$			0.957712i			0.127980i
$57$	−3.20315	+	1.68354i	−0.424268	+	0.222990i
$58$	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	$0.738520\pi$
$60$	−1.25133	+	3.66527i	−0.161546	+	0.473184i
$61$	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
$63$	−2.82546	+	0.521209i	−0.355975	+	0.0656662i
$64$			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	−0.999338	−	0.0363899i	$-0.988414\pi$
$67$	−8.47780	−	8.47780i	−1.03573	−	1.03573i	−0.0363899	−	0.999338i	$-0.511586\pi$
$68$	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	$-0.765914\pi$
$71$	−12.4970			−1.48312			−0.741560	+	0.670887i	$0.765914\pi$
$72$	−2.95022	+	0.544224i	−0.347687	+	0.0641374i
$73$	−3.69590	+	3.69590i	−0.432573	+	0.432573i	−0.889503	−	0.456930i	$-0.848949\pi$
$73$	−3.69590	+	3.69590i	−0.432573	+	0.432573i	0.456930	+	0.889503i	$0.348949\pi$
$74$	−3.73612			−0.434315
$75$	−3.60153	−	7.87585i	−0.415869	−	0.909424i
$76$		−	2.08922i		−	0.239649i
$77$	−1.60847	−	1.60847i	−0.183302	−	0.183302i
$78$	−6.22605	−	0.486111i	−0.704961	−	0.0550413i
$79$			1.03917i			0.116916i	0.998290	+	0.0584581i	$0.0186184\pi$
$79$			1.03917i			0.116916i	−0.998290	+	0.0584581i	$0.981382\pi$
$80$	−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	$-0.261756\pi$
$83$	−0.475749	−	0.475749i	−0.0522202	−	0.0522202i	−0.732735	+	0.680514i	$0.761756\pi$
$84$	0.492571	−	1.58398i	0.0537439	−	0.172827i
$85$	−0.462604	+	16.8147i	−0.0501764	+	1.82381i
$86$	0.187305			0.0201977
$87$	−2.91244	+	1.53075i	−0.312247	+	0.164113i
$88$	−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	$-0.142360\pi$
$90$	3.95473	−	5.41850i	0.416865	−	0.571160i
$91$	1.83957	−	2.92228i	0.192839	−	0.306338i
$92$	−1.90576	−	1.90576i	−0.198689	−	0.198689i
$93$	6.84873	+	13.0306i	0.710181	+	1.35121i
$94$		−	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	0.761494	−	0.648172i	$-0.224466\pi$
$97$	1.11610	+	1.11610i	0.113323	+	0.113323i	−0.648172	+	0.761494i	$0.724466\pi$
$98$	−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	$-0.340212\pi$
$102$	−11.5336	+	6.06190i	−1.14199	+	0.600217i
$103$	−1.63440	−	1.63440i	−0.161042	−	0.161042i	0.621986	−	0.783028i	$-0.286326\pi$
$103$	−1.63440	−	1.63440i	−0.161042	−	0.161042i	−0.783028	+	0.621986i	$0.786326\pi$
$104$	1.92080	−	3.05132i	0.188350	−	0.299206i
$105$	1.63473	+	3.32954i	0.159533	+	0.324930i
$106$			8.24196i			0.800530i
$107$	−4.52629	−	4.52629i	−0.437573	−	0.437573i	0.453622	−	0.891194i	$-0.350132\pi$
$107$	−4.52629	−	4.52629i	−0.437573	−	0.437573i	−0.891194	+	0.453622i	$0.850132\pi$
$108$	5.15936	+	0.617257i	0.496460	+	0.0593955i
$109$	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	$-0.726204\pi$
$113$	1.12282	−	1.12282i	0.105626	−	0.105626i	0.757945	+	0.652319i	$0.226204\pi$
$114$	−1.07453	+	3.45541i	−0.100639	+	0.323629i
$115$	6.02427	+	0.165739i	0.561766	+	0.0154552i
$116$		−	1.89961i		−	0.176374i
$117$	10.0474	+	4.00618i	0.928884	+	0.370372i
$118$	7.95312	+	7.95312i	0.732144	+	0.732144i
$119$		−	7.20450i		−	0.660436i
$120$	1.70691	+	3.47656i	0.155819	+	0.317365i
$121$	−5.35861			−0.487147
$122$	6.57177	−	6.57177i	0.594980	−	0.594980i
$123$	13.4231	−	7.05501i	1.21032	−	0.636129i
$124$	−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	−0.959938	−	0.280213i	$-0.909595\pi$
$127$	−7.66011	+	7.66011i	−0.679725	+	0.679725i	0.280213	+	0.959938i	$0.409595\pi$
$128$	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	$0.593389\pi$
$132$	1.91396	+	3.64155i	0.166589	+	0.316957i
$133$	−1.41483	−	1.41483i	−0.122681	−	0.122681i
$134$	−11.9894			−1.03573
$135$	−9.32768	+	6.92779i	−0.802799	+	0.596249i
$136$		−	7.52262i		−	0.645059i
$137$	5.92464	−	5.92464i	0.506176	−	0.506176i	−0.407174	−	0.913351i	$-0.633486\pi$
$137$	5.92464	−	5.92464i	0.506176	−	0.506176i	0.913351	+	0.407174i	$0.133486\pi$
$138$	2.17182	+	4.13217i	0.184877	+	0.351753i
$139$		−	13.3375i		−	1.13127i	−0.824655	−	0.565636i	$-0.808631\pi$
$139$		−	13.3375i		−	1.13127i	0.824655	−	0.565636i	$-0.191369\pi$
$140$	−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
$147$	4.90165	+	9.32603i	0.404281	+	0.769198i
$148$	−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	$-0.0723926\pi$
$150$	−8.11573	−	3.02240i	−0.662647	−	0.246778i
$151$		−	13.8469i		−	1.12684i	−0.826169	−	0.563422i	$-0.809484\pi$
$151$		−	13.8469i		−	1.12684i	0.826169	−	0.563422i	$-0.190516\pi$
$152$	−1.47730	−	1.47730i	−0.119825	−	0.119825i
$153$	22.1934	−	4.09399i	1.79423	−	0.330979i
$154$	−2.27472			−0.183302
$155$	13.8027	−	13.0635i	1.10866	−	1.04929i
$156$	−4.74621	+	4.05875i	−0.380001	+	0.324960i
$157$	6.58993	−	6.58993i	0.525934	−	0.525934i	−0.393424	−	0.919357i	$-0.628709\pi$
$157$	6.58993	−	6.58993i	0.525934	−	0.525934i	0.919357	+	0.393424i	$0.128709\pi$
$158$	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
$162$	−8.21574	−	3.67447i	−0.645489	−	0.288693i
$163$	6.28194	−	6.28194i	0.492039	−	0.492039i	−0.416909	−	0.908948i	$-0.636887\pi$
$163$	6.28194	−	6.28194i	0.492039	−	0.492039i	0.908948	+	0.416909i	$0.136887\pi$
$164$			8.75503i			0.683653i
$165$	−8.70559	−	2.97211i	−0.677730	−	0.231378i
$166$	−0.672810			−0.0522202
$167$	2.35390	−	2.35390i	0.182150	−	0.182150i	−0.610142	−	0.792292i	$-0.708888\pi$
$167$	2.35390	−	2.35390i	0.182150	−	0.182150i	0.792292	+	0.610142i	$0.208888\pi$
$168$	−0.771746	−	1.46835i	−0.0595415	−	0.113285i
$169$	−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	−0.0519185	+	0.998651i	$0.516534\pi$
$173$	−13.8181	+	13.8181i	−1.05057	+	1.05057i	−0.998651	+	0.0519185i	$0.983466\pi$
$174$	−0.977008	+	3.14181i	−0.0740668	+	0.238180i
$175$	3.56707	−	3.19473i	0.269645	−	0.241499i
$176$	−2.37516			−0.179034
$177$	−9.06342	−	17.2443i	−0.681248	−	1.29616i
$178$	−5.76993	−	5.76993i	−0.432475	−	0.432475i
$179$	9.07466			0.678272			0.339136	−	0.940737i	$-0.389865\pi$
$179$	9.07466			0.678272			0.339136	+	0.940737i	$0.389865\pi$
$180$	−1.03504	−	6.62787i	−0.0771471	−	0.494012i
$181$	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
$183$	−14.2492	+	7.48923i	−1.05333	+	0.553620i
$184$	−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	$0.827386\pi$
$192$	−0.805823	−	1.53318i	−0.0581553	−	0.110648i
$193$	−9.53551	+	9.53551i	−0.686381	+	0.686381i	−0.961430	−	0.275049i	$-0.911306\pi$
$193$	−9.53551	+	9.53551i	−0.686381	+	0.686381i	0.275049	+	0.961430i	$0.411306\pi$
$194$	1.57840			0.113323
$195$	1.46944	−	13.8867i	0.105229	−	0.994448i
$196$	−6.08279			−0.434485
$197$	8.00501	−	8.00501i	0.570334	−	0.570334i	−0.361888	−	0.932222i	$-0.617868\pi$
$197$	8.00501	−	8.00501i	0.570334	−	0.570334i	0.932222	+	0.361888i	$0.117868\pi$
$198$	−1.29262	−	7.00725i	−0.0918624	−	0.497984i
$199$		−	10.2380i		−	0.725753i	−0.931837	−	0.362877i	$-0.881795\pi$
$199$		−	10.2380i		−	0.725753i	0.931837	−	0.362877i	$-0.118205\pi$
$200$	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
$207$	−1.46677	−	7.95131i	−0.101947	−	0.552654i
$208$	−0.799399	−	3.51582i	−0.0554283	−	0.243778i
$209$	4.96222			0.343244
$210$	3.51027	+	1.19841i	0.242231	+	0.0826984i
$211$	−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
$213$	19.1602	−	10.0704i	1.31283	−	0.690010i
$214$	−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
$222$	5.72815	−	3.01065i	0.384448	−	0.202061i
$223$	−0.0933672	+	0.0933672i	−0.00625233	+	0.00625233i	−0.710226	−	0.703974i	$-0.751407\pi$
$223$	−0.0933672	+	0.0933672i	−0.00625233	+	0.00625233i	0.703974	+	0.710226i	$0.251407\pi$
$224$	0.957712			0.0639898
$225$	11.8683	+	9.17292i	0.791223	+	0.611528i
$226$		−	1.58790i		−	0.105626i
$227$	−10.9359	+	10.9359i	−0.725841	+	0.725841i	−0.969788	−	0.243947i	$-0.921558\pi$
$227$	−10.9359	+	10.9359i	−0.725841	+	0.725841i	0.243947	+	0.969788i	$0.421558\pi$
$228$	1.68354	+	3.20315i	0.111495	+	0.212134i
$229$	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	$-0.711092\pi$
$233$	2.63212	−	2.63212i	0.172436	−	0.172436i	0.788049	+	0.615613i	$0.211092\pi$
$234$	9.93739	−	4.27180i	0.649628	−	0.279256i
$235$	6.57579	+	0.180912i	0.428957	+	0.0118014i
$236$	11.2474			0.732144
$237$	−0.837390	−	1.59324i	−0.0543943	−	0.103492i
$238$	−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	$0.983933\pi$
$240$	3.66527	+	1.25133i	0.236592	+	0.0807730i
$241$			7.65343i			0.493001i	0.969143	+	0.246501i	$0.0792807\pi$
$241$			7.65343i			0.493001i	−0.969143	+	0.246501i	$0.920719\pi$
$242$	−3.78911	+	3.78911i	−0.243573	+	0.243573i
$243$	11.6984	+	10.3028i	0.750451	+	0.660926i
$244$		−	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	$-0.0377984\pi$
$252$	0.521209	+	2.82546i	0.0328331	+	0.177987i
$253$	4.52649	−	4.52649i	0.284578	−	0.284578i
$254$			10.8330i			0.679725i
$255$	−12.8404	−	26.1528i	−0.804099	−	1.63775i
$256$	1.00000			0.0625000
$257$	−3.00645	−	3.00645i	−0.187537	−	0.187537i	0.607093	−	0.794631i	$-0.292335\pi$
$257$	−3.00645	−	3.00645i	−0.187537	−	0.187537i	−0.794631	+	0.607093i	$0.792335\pi$
$258$	−0.287173	+	0.150935i	−0.0178786	+	0.00939680i
$259$			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	$-0.917756\pi$
$263$	−11.5352	+	11.5352i	−0.711294	+	0.711294i	0.255512	+	0.966806i	$0.417756\pi$
$264$	3.92834	+	1.22160i	0.241773	+	0.0751840i
$265$	−18.4226	−	0.506840i	−1.13169	−	0.0311349i
$266$	−2.00087			−0.122681
$267$	6.57545	+	12.5106i	0.402411	+	0.765639i
$268$	−8.47780	+	8.47780i	−0.517864	+	0.517864i
$269$	15.9555			0.972825			0.486412	−	0.873729i	$-0.338305\pi$
$269$	15.9555			0.972825			0.486412	+	0.873729i	$0.338305\pi$
$270$	−1.69698	+	11.4944i	−0.103275	+	0.699524i
$271$			27.1560i			1.64961i	0.565420	+	0.824803i	$0.308714\pi$
$271$			27.1560i			1.64961i	−0.565420	+	0.824803i	$0.691286\pi$
$272$	−5.31930	−	5.31930i	−0.322530	−	0.322530i
$273$	−0.465554	+	5.96276i	−0.0281766	+	0.360883i
$274$		−	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	−0.308757	−	0.951141i	$-0.599913\pi$
$277$	10.6914	−	10.6914i	0.642384	−	0.642384i	0.951141	+	0.308757i	$0.0999129\pi$
$278$	−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	$-0.323857\pi$
$281$	17.6198			1.05111			0.525556	+	0.850759i	$0.323857\pi$
$282$	2.37065	+	4.51046i	0.141170	+	0.268594i
$283$	−17.2344	−	17.2344i	−1.02448	−	1.02448i	−0.999693	−	0.0247857i	$-0.992110\pi$
$283$	−17.2344	−	17.2344i	−1.02448	−	1.02448i	−0.0247857	−	0.999693i	$-0.507890\pi$
$284$			12.4970i			0.741560i
$285$	−7.65753	−	2.61430i	−0.453593	−	0.154858i
$286$	7.24737	+	4.56220i	0.428546	+	0.269769i
$287$	5.92895	+	5.92895i	0.349975	+	0.349975i
$288$	0.544224	+	2.95022i	0.0320687	+	0.173844i
$289$			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	$-0.362701\pi$
$293$	−8.39295	−	8.39295i	−0.490321	−	0.490321i	−0.908407	+	0.418086i	$0.862701\pi$
$294$	10.0605	+	3.12851i	0.586740	+	0.182458i
$295$	−18.2661	+	17.2879i	−1.06349	+	1.00654i
$296$			3.73612i			0.217157i
$297$	−1.46608	+	12.2543i	−0.0850708	+	0.711067i
$298$	−3.89226	−	3.89226i	−0.225473	−	0.225473i
$299$	8.22377	+	5.17685i	0.475593	+	0.299385i
$300$	−7.87585	+	3.60153i	−0.454712	+	0.207935i
$301$		−	0.179384i		−	0.0103395i
$302$	−9.79124	−	9.79124i	−0.563422	−	0.563422i
$303$	14.1986	+	27.0147i	0.815687	+	1.55195i
$304$	−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	0.129118	−	0.991629i	$-0.458786\pi$
$307$	−15.1124	−	15.1124i	−0.862512	−	0.862512i	−0.991629	+	0.129118i	$0.958786\pi$
$308$	−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	$-0.373679\pi$
$312$	−0.486111	+	6.22605i	−0.0275206	+	0.352481i
$313$	5.87745	+	5.87745i	0.332213	+	0.332213i	0.853426	−	0.521213i	$-0.174520\pi$
$313$	5.87745	+	5.87745i	0.332213	+	0.332213i	−0.521213	+	0.853426i	$0.674520\pi$
$314$		−	9.31957i		−	0.525934i
$315$	−5.18936	−	3.78749i	−0.292387	−	0.213401i
$316$	1.03917			0.0584581
$317$	16.6705	−	16.6705i	0.936311	−	0.936311i	−0.0617787	−	0.998090i	$-0.519677\pi$
$317$	16.6705	−	16.6705i	0.936311	−	0.936311i	0.998090	+	0.0617787i	$0.0196773\pi$
$318$	−6.64156	−	12.6364i	−0.372440	−	0.708616i
$319$	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
$327$	−26.2465	+	13.7949i	−1.45144	+	0.762858i
$328$	6.19074	+	6.19074i	0.341827	+	0.341827i
$329$	−2.81749			−0.155333
$330$	−8.25738	+	4.05418i	−0.454554	+	0.223176i
$331$			13.6672i			0.751219i	0.926778	+	0.375610i	$0.122567\pi$
$331$			13.6672i			0.751219i	−0.926778	+	0.375610i	$0.877433\pi$
$332$	−0.475749	+	0.475749i	−0.0261101	+	0.0261101i
$333$	−11.0224	+	2.03328i	−0.604023	+	0.111423i
$334$		−	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	0.0382377	−	0.999269i	$-0.487826\pi$
$337$	19.0461	−	19.0461i	1.03751	−	1.03751i	0.999269	−	0.0382377i	$-0.0121744\pi$
$338$	−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
$342$	−1.13700	−	6.16365i	−0.0614819	−	0.333292i
$343$	−8.85972	+	8.85972i	−0.478380	+	0.478380i
$344$		−	0.187305i		−	0.0100988i
$345$	−9.36986	+	4.60039i	−0.504457	+	0.247677i
$346$			19.5417i			1.05057i
$347$	−15.6314	−	15.6314i	−0.839135	−	0.839135i	0.149610	−	0.988745i	$-0.452198\pi$
$347$	−15.6314	−	15.6314i	−0.839135	−	0.839135i	−0.988745	+	0.149610i	$0.952198\pi$
$348$	1.53075	+	2.91244i	0.0820566	+	0.156123i
$349$	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
$351$	−18.6328	+	1.95423i	−0.994545	+	0.104309i
$352$	−1.67949	+	1.67949i	−0.0895172	+	0.0895172i
$353$	−25.9079	−	25.9079i	−1.37894	−	1.37894i	−0.846414	−	0.532525i	$-0.821243\pi$
$353$	−25.9079	−	25.9079i	−1.37894	−	1.37894i	−0.532525	−	0.846414i	$-0.678757\pi$
$354$	−18.6024	−	5.78478i	−0.988706	−	0.307458i
$355$	−19.2086	−	20.2954i	−1.01949	−	1.07717i
$356$	−8.15992			−0.432475
$357$	5.80555	+	11.0458i	0.307262	+	0.584607i
$358$	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	$0.669445\pi$
$360$	−5.41850	−	3.95473i	−0.285580	−	0.208433i
$361$	−14.6352			−0.770272
$362$	1.34260	−	1.34260i	0.0705653	−	0.0705653i
$363$	8.21573	−	4.31809i	0.431214	−	0.226641i
$364$	−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	−0.757405	−	0.652945i	$-0.773533\pi$
$367$	−2.00117	+	2.00117i	−0.104460	+	0.104460i	0.652945	+	0.757405i	$0.273533\pi$
$368$	−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
$372$	13.0306	−	6.84873i	0.675606	−	0.355090i
$373$	−12.1573	−	12.1573i	−0.629480	−	0.629480i	0.318457	−	0.947937i	$-0.396835\pi$
$373$	−12.1573	−	12.1573i	−0.629480	−	0.629480i	−0.947937	+	0.318457i	$0.896835\pi$
$374$	17.8674			0.923903
$375$	7.25481	−	17.9546i	0.374637	−	0.927172i
$376$	−2.94189			−0.151717
$377$	1.51854	+	6.67867i	0.0782090	+	0.343969i
$378$	0.591154	−	4.94118i	0.0304057	−	0.254147i
$379$	−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	$-0.269698\pi$
$383$	−1.71164	−	1.71164i	−0.0874607	−	0.0874607i	−0.749484	+	0.662023i	$0.769698\pi$
$384$	−1.65393	−	0.514321i	−0.0844016	−	0.0262463i
$385$	0.139884	−	5.08450i	0.00712914	−	0.259130i
$386$			13.4852i			0.686381i
$387$	0.552593	−	0.101936i	0.0280899	−	0.00518170i
$388$	1.11610	−	1.11610i	0.0566613	−	0.0566613i
$389$	−22.7607			−1.15401			−0.577007	−	0.816739i	$-0.695779\pi$
$389$	−22.7607			−1.15401			−0.577007	+	0.816739i	$0.695779\pi$
$390$	−8.78034	−	10.8584i	−0.444610	−	0.549838i
$391$	20.2746			1.02533
$392$	−4.30118	+	4.30118i	−0.217242	+	0.217242i
$393$	−17.6579	−	33.5965i	−0.890723	−	1.69472i
$394$		−	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	0.999466	−	0.0326724i	$-0.0104018\pi$
$397$	19.2632	+	19.2632i	0.966794	+	0.966794i	−0.0326724	+	0.999466i	$0.510402\pi$
$398$	−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	$-0.686432\pi$
$401$	−22.1388			−1.10556			−0.552779	+	0.833328i	$0.686432\pi$
$402$	18.3820	−	9.66134i	0.916809	−	0.481864i
$403$	29.8811	−	6.79414i	1.48848	−	0.338440i
$404$	−17.6200			−0.876627
$405$	8.71847	−	18.1380i	0.433224	−	0.901286i
$406$	−1.81928			−0.0902891
$407$	−6.27478	−	6.27478i	−0.311029	−	0.311029i
$408$	6.06190	+	11.5336i	0.300109	+	0.570996i
$409$	−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
$417$	10.7477	+	20.4488i	0.526315	+	1.00138i
$418$	3.50882	−	3.50882i	0.171622	−	0.171622i
$419$	25.3285			1.23738			0.618688	−	0.785637i	$-0.287665\pi$
$419$	25.3285			1.23738			0.618688	+	0.785637i	$0.287665\pi$
$420$	3.32954	−	1.63473i	0.162465	−	0.0797665i
$421$		−	25.2669i		−	1.23143i	−0.787968	−	0.615716i	$-0.788867\pi$
$421$		−	25.2669i		−	1.23143i	0.787968	−	0.615716i	$-0.211133\pi$
$422$	−2.68346	+	2.68346i	−0.130629	+	0.130629i
$423$	−1.60105	−	8.67925i	−0.0778456	−	0.422000i
$424$	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
$429$	−9.64018	−	11.2730i	−0.465432	−	0.544267i
$430$	0.287899	+	0.304188i	0.0138837	+	0.0146693i
$431$	26.8636			1.29397			0.646987	−	0.762501i	$-0.276029\pi$
$431$	26.8636			1.29397			0.646987	+	0.762501i	$0.276029\pi$
$432$	0.617257	−	5.15936i	0.0296978	−	0.248230i
$433$	−3.38479	−	3.38479i	−0.162663	−	0.162663i	0.621083	−	0.783745i	$-0.286693\pi$
$433$	−3.38479	−	3.38479i	−0.162663	−	0.162663i	−0.783745	+	0.621083i	$0.786693\pi$
$434$			8.13965i			0.390716i
$435$	−6.96256	−	2.37704i	−0.333829	−	0.113970i
$436$		−	17.1190i		−	0.819851i
$437$	3.98155	−	3.98155i	0.190463	−	0.190463i
$438$	−4.21187	−	8.01363i	−0.201251	−	0.382906i
$439$			28.3140i			1.35136i	0.737197	+	0.675678i	$0.236149\pi$
$439$			28.3140i			1.35136i	−0.737197	+	0.675678i	$0.763851\pi$
$440$	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	$-0.805972\pi$
$443$	−5.20707	+	5.20707i	−0.247395	+	0.247395i	0.572505	+	0.819901i	$0.305972\pi$
$444$	1.92156	−	6.17926i	0.0911934	−	0.293255i
$445$	13.2519	−	12.5423i	0.628201	−	0.594560i
$446$			0.132041i			0.00625233i
$447$	4.43564	+	8.43938i	0.209799	+	0.399169i
$448$	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	$0.809219\pi$
$450$	14.8784	−	1.90596i	0.701375	−	0.0898476i
$451$	−20.7946			−0.979180
$452$	−1.12282	−	1.12282i	−0.0528129	−	0.0528129i
$453$	11.1582	+	21.2298i	0.524256	+	0.997465i
$454$			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	−0.991003	−	0.133837i	$-0.957270\pi$
$457$	−24.0463	−	24.0463i	−1.12484	−	1.12484i	−0.133837	−	0.991003i	$-0.542730\pi$
$458$	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	$-0.652665\pi$
$461$	−19.8148			−0.922867			−0.461433	+	0.887175i	$0.652665\pi$
$462$	3.48756	−	1.83302i	0.162256	−	0.0852798i
$463$	−5.15121	+	5.15121i	−0.239397	+	0.239397i	−0.816600	−	0.577203i	$-0.804144\pi$
$463$	−5.15121	+	5.15121i	−0.239397	+	0.239397i	0.577203	+	0.816600i	$0.304144\pi$
$464$	−1.89961			−0.0881870
$465$	−10.6351	+	31.1513i	−0.493192	+	1.44461i
$466$		−	3.72237i		−	0.172436i
$467$	−4.55792	−	4.55792i	−0.210915	−	0.210915i	0.593741	−	0.804656i	$-0.297650\pi$
$467$	−4.55792	−	4.55792i	−0.210915	−	0.210915i	−0.804656	+	0.593741i	$0.797650\pi$
$468$	4.00618	−	10.0474i	0.185186	−	0.464442i
$469$			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
$477$	4.48547	+	24.3156i	0.205376	+	1.11334i
$478$	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	$-0.118573\pi$
$480$	3.47656	−	1.70691i	0.158682	−	0.0779094i
$481$	7.17632	−	11.4001i	0.327212	−	0.519799i
$482$	5.41180	+	5.41180i	0.246501	+	0.246501i
$483$	3.95742	−	2.07997i	0.180069	−	0.0946421i
$484$			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	0.998509	−	0.0545949i	$-0.0173867\pi$
$487$	20.8304	+	20.8304i	0.943914	+	0.943914i	−0.0545949	+	0.998509i	$0.517387\pi$
$488$	−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	$0.810253\pi$
$492$	−7.05501	−	13.4231i	−0.318064	−	0.605159i
$493$	10.1046	+	10.1046i	0.455087	+	0.455087i
$494$	6.37486	+	4.01296i	0.286819	+	0.180552i
$495$	15.7423	−	2.45838i	0.707562	−	0.110496i
$496$			8.49906i			0.381619i
$497$	8.46301	+	8.46301i	0.379618	+	0.379618i
$498$	1.03154	−	0.542166i	0.0462245	−	0.0242950i
$499$	−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	$-0.583543\pi$
$503$	15.8407	−	15.8407i	0.706300	−	0.706300i	0.965755	+	0.259455i	$0.0835429\pi$
$504$	2.36646	+	1.62935i	0.105410	+	0.0725772i
$505$	28.6153	−	27.0829i	1.27336	−	1.20517i
$506$		−	6.40143i		−	0.284578i
$507$	13.4423	−	18.0639i	0.596992	−	0.802248i
$508$	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	$0.965769\pi$
$510$	−27.5724	−	9.41328i	−1.22093	−	0.416827i
$511$	5.00576			0.221442
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−1.28958	+	10.7790i	−0.0569364	+	0.475905i
$514$	−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	$-0.0116622\pi$
$522$	−1.03381	−	5.60426i	−0.0452487	−	0.245292i
$523$	15.2663	+	15.2663i	0.667550	+	0.667550i	0.957148	−	0.289599i	$-0.0935218\pi$
$523$	15.2663	+	15.2663i	0.667550	+	0.667550i	−0.289599	+	0.957148i	$0.593522\pi$
$524$	21.9129			0.957269
$525$	−2.89458	+	7.77253i	−0.126330	+	0.339221i
$526$			16.3133i			0.711294i
$527$	45.2090	−	45.2090i	1.96934	−	1.96934i
$528$	3.64155	−	1.91396i	0.158478	−	0.0832943i
$529$			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
$537$	−13.9131	+	7.31256i	−0.600395	+	0.315560i
$538$	11.2823	−	11.2823i	0.486412	−	0.486412i
$539$		−	14.4476i		−	0.622302i
$540$	6.92779	+	9.32768i	0.298125	+	0.401400i
$541$			29.0935i			1.25083i	0.780293	+	0.625414i	$0.215070\pi$
$541$			29.0935i			1.25083i	−0.780293	+	0.625414i	$0.784930\pi$
$542$	19.2022	+	19.2022i	0.824803	+	0.824803i
$543$	−2.91108	+	1.53003i	−0.124926	+	0.0656599i
$544$	−7.52262			−0.322530
$545$	26.3129	+	27.8017i	1.12712	+	1.19089i
$546$	3.88711	+	4.54550i	0.166353	+	0.194530i
$547$	7.13810	−	7.13810i	0.305203	−	0.305203i	−0.537842	−	0.843045i	$-0.680760\pi$
$547$	7.13810	−	7.13810i	0.305203	−	0.305203i	0.843045	+	0.537842i	$0.180760\pi$
$548$	−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
$552$	4.13217	−	2.17182i	0.175877	−	0.0924387i
$553$	0.703733	−	0.703733i	0.0299258	−	0.0299258i
$554$		−	15.1199i		−	0.642384i
$555$	6.37721	+	12.9888i	0.270698	+	0.551345i
$556$	−13.3375			−0.565636
$557$	−4.94545	+	4.94545i	−0.209546	+	0.209546i	−0.804074	−	0.594529i	$-0.797339\pi$
$557$	−4.94545	+	4.94545i	−0.209546	+	0.209546i	0.594529	+	0.804074i	$0.297339\pi$
$558$	−25.0741	+	4.62539i	−1.06147	+	0.195808i
$559$	−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	$-0.789458\pi$
$563$	−4.14895	+	4.14895i	−0.174857	+	0.174857i	0.614252	+	0.789110i	$0.289458\pi$
$564$	4.86568	+	1.51308i	0.204882	+	0.0637121i
$565$	3.54932	+	0.0976482i	0.149321	+	0.00410809i
$566$	−24.3731			−1.02448
$567$	−3.51908	+	7.86830i	−0.147787	+	0.330438i
$568$	8.83670	+	8.83670i	0.370780	+	0.370780i
$569$	−26.2934			−1.10228			−0.551139	−	0.834414i	$-0.685806\pi$
$569$	−26.2934			−1.10228			−0.551139	+	0.834414i	$0.685806\pi$
$570$	−7.26328	+	3.56610i	−0.304225	+	0.149368i
$571$	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
$573$	−11.4952	−	21.8710i	−0.480217	−	0.913676i
$574$	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	0.795689	−	0.605705i	$-0.207109\pi$
$577$	4.56357	+	4.56357i	0.189984	+	0.189984i	−0.605705	+	0.795689i	$0.707109\pi$
$578$	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
$582$	−2.41998	+	1.27191i	−0.100311	+	0.0527224i
$583$	−13.8423	+	13.8423i	−0.573290	+	0.573290i
$584$	5.22680			0.216286
$585$	8.93731	+	22.4750i	0.369512	+	0.929226i
$586$	−11.8694			−0.490321
$587$	−0.204915	+	0.204915i	−0.00845773	+	0.00845773i	−0.711323	−	0.702865i	$-0.751904\pi$
$587$	−0.204915	+	0.204915i	−0.00845773	+	0.00845773i	0.702865	+	0.711323i	$0.251904\pi$
$588$	9.32603	−	4.90165i	0.384599	−	0.202141i
$589$		−	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	$-0.144253\pi$
$593$	11.2316	+	11.2316i	0.461226	+	0.461226i	−0.437831	+	0.899057i	$0.644253\pi$
$594$	7.62843	+	9.70178i	0.312998	+	0.398069i
$595$	11.7003	−	11.0737i	0.479665	−	0.453979i
$596$	−5.50449			−0.225473
$597$	8.25002	+	15.6967i	0.337651	+	0.642425i
$598$	9.47567	−	2.15450i	0.387489	−	0.0881042i
$599$	−24.5114			−1.00151			−0.500755	−	0.865589i	$-0.666944\pi$
$599$	−24.5114			−1.00151			−0.500755	+	0.865589i	$0.666944\pi$
$600$	−3.02240	+	8.11573i	−0.123389	+	0.331323i
$601$	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
$603$	−35.3715	+	6.52492i	−1.44044	+	0.265715i
$604$	−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	0.153276	−	0.988183i	$-0.451018\pi$
$607$	28.1226	−	28.1226i	1.14146	−	1.14146i	0.988183	−	0.153276i	$-0.0489824\pi$
$608$	−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
$612$	−4.09399	−	22.1934i	−0.165490	−	0.897116i
$613$	27.8570	−	27.8570i	1.12513	−	1.12513i	0.134175	−	0.990958i	$-0.457162\pi$
$613$	27.8570	−	27.8570i	1.12513	−	1.12513i	0.990958	−	0.134175i	$-0.0428383\pi$
$614$	−21.3722			−0.862512
$615$	32.0895	+	10.9554i	1.29397	+	0.441766i
$616$			2.27472i			0.0916510i
$617$	8.65622	−	8.65622i	0.348486	−	0.348486i	−0.511059	−	0.859546i	$-0.670747\pi$
$617$	8.65622	−	8.65622i	0.348486	−	0.348486i	0.859546	+	0.511059i	$0.170747\pi$
$618$	3.54378	−	1.86257i	0.142552	−	0.0749235i
$619$	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
$624$	4.05875	+	4.74621i	0.162480	+	0.190001i
$625$	−24.8488	−	2.74494i	−0.993954	−	0.109798i
$626$	8.31197			0.332213
$627$	−7.60799	+	3.99867i	−0.303834	+	0.159692i
$628$	−6.58993	−	6.58993i	−0.262967	−	0.262967i
$629$		−	28.1054i		−	1.12064i
$630$	−6.34759	+	0.991267i	−0.252894	+	0.0394930i
$631$		−	37.6669i		−	1.49950i	−0.661723	−	0.749749i	$-0.730174\pi$
$631$		−	37.6669i		−	1.49950i	0.661723	−	0.749749i	$-0.269826\pi$
$632$	0.734807	−	0.734807i	0.0292291	−	0.0292291i
$633$	5.81840	−	3.05808i	0.231261	−	0.121548i
$634$		−	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	$-0.0379762\pi$
$642$	9.81411	−	5.15818i	0.387332	−	0.203577i
$643$	−0.846729	+	0.846729i	−0.0333917	+	0.0333917i	−0.723606	−	0.690214i	$-0.757516\pi$
$643$	−0.846729	+	0.846729i	−0.0333917	+	0.0333917i	0.690214	+	0.723606i	$0.257516\pi$
$644$			2.58118i			0.101713i
$645$	−0.319713	−	0.651178i	−0.0125887	−	0.0256401i
$646$	15.7164			0.618353
$647$	−3.77881	−	3.77881i	−0.148560	−	0.148560i	0.628914	−	0.777475i	$-0.283500\pi$
$647$	−3.77881	−	3.77881i	−0.148560	−	0.148560i	−0.777475	+	0.628914i	$0.783500\pi$
$648$	−3.67447	+	8.21574i	−0.144347	+	0.322745i
$649$			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	$-0.770285\pi$
$653$	−2.30151	+	2.30151i	−0.0900649	+	0.0900649i	0.660639	+	0.750704i	$0.270285\pi$
$654$	−8.80466	+	28.3136i	−0.344289	+	1.10715i
$655$	−35.5871	+	33.6814i	−1.39050	+	1.31604i
$656$	8.75503			0.341827
$657$	2.84455	+	15.4202i	0.110976	+	0.601600i
$658$	−1.99226	+	1.99226i	−0.0776665	+	0.0776665i
$659$	23.4178			0.912228			0.456114	−	0.889921i	$-0.349241\pi$
$659$	23.4178			0.912228			0.456114	+	0.889921i	$0.349241\pi$
$660$	−2.97211	+	8.70559i	−0.115689	+	0.338865i
$661$			18.6057i			0.723679i	0.932240	+	0.361840i	$0.117851\pi$
$661$			18.6057i			0.723679i	−0.932240	+	0.361840i	$0.882149\pi$
$662$	9.66419	+	9.66419i	0.375610	+	0.375610i
$663$	3.65683	−	46.8362i	0.142020	−	1.81897i
$664$			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
$672$	−1.46835	+	0.771746i	−0.0566427	+	0.0297707i
$673$	−24.7786	−	24.7786i	−0.955145	−	0.955145i	0.0438911	−	0.999036i	$-0.486025\pi$
$673$	−24.7786	−	24.7786i	−0.955145	−	0.955145i	−0.999036	+	0.0438911i	$0.986025\pi$
$674$		−	26.9352i		−	1.03751i
$675$	−25.5881	−	4.49997i	−0.984886	−	0.173204i
$676$	5.62108	+	11.7219i	0.216195	+	0.450843i
$677$	2.48540	+	2.48540i	0.0955215	+	0.0955215i	0.753253	−	0.657731i	$-0.228484\pi$
$677$	2.48540	+	2.48540i	0.0955215	+	0.0955215i	−0.657731	+	0.753253i	$0.728484\pi$
$678$	1.27957	+	2.43455i	0.0491416	+	0.0934982i
$679$		−	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	0.985623	+	0.168961i	$0.0540413\pi$
$683$	30.1742	+	30.1742i	1.15458	+	1.15458i	0.168961	+	0.985623i	$0.445959\pi$
$684$	−5.16234	−	3.55438i	−0.197387	−	0.135905i
$685$	18.7283	+	0.515249i	0.715571	+	0.0196867i
$686$			12.5295i			0.478380i
$687$	−6.02957	+	3.16907i	−0.230043	+	0.120908i
$688$	−0.132445	−	0.132445i	−0.00504941	−	0.00504941i
$689$	−25.1488	−	15.8311i	−0.958095	−	0.603118i
$690$	−3.37253	+	9.87846i	−0.128390	+	0.376067i
$691$			2.84295i			0.108151i	0.998537	+	0.0540754i	$0.0172211\pi$
$691$			2.84295i			0.108151i	−0.998537	+	0.0540754i	$0.982779\pi$
$692$	13.8181	+	13.8181i	0.525285	+	0.525285i
$693$	−6.71093	+	1.23796i	−0.254927	+	0.0470260i
$694$	−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	$-0.0484455\pi$
$702$	−11.7935	+	14.5572i	−0.445118	+	0.549427i
$703$	−5.51936	−	5.51936i	−0.208167	−	0.208167i
$704$			2.37516i			0.0895172i
$705$	−10.2277	+	5.02155i	−0.385196	+	0.189123i
$706$	−36.6393			−1.37894
$707$	−11.9323	+	11.9323i	−0.448761	+	0.448761i
$708$	−17.2443	+	9.06342i	−0.648082	+	0.340624i
$709$	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
$717$	−1.25707	−	2.39174i	−0.0469461	−	0.0893211i
$718$	23.0878	+	23.0878i	0.861628	+	0.861628i
$719$	9.03729			0.337034			0.168517	−	0.985699i	$-0.446102\pi$
$719$	9.03729			0.337034			0.168517	+	0.985699i	$0.446102\pi$
$720$	−6.62787	+	1.03504i	−0.247006	+	0.0385735i
$721$			2.21364i			0.0824403i
$722$	−10.3486	+	10.3486i	−0.385136	+	0.385136i
$723$	−6.16731	−	11.7341i	−0.229365	−	0.436396i
$724$		−	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	−0.499440	+	0.866349i	$0.666461\pi$
$727$	−36.8257	+	36.8257i	−1.36579	+	1.36579i	−0.866349	+	0.499440i	$0.833539\pi$
$728$	−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
$732$	7.48923	+	14.2492i	0.276810	+	0.526667i
$733$	33.7479	−	33.7479i	1.24651	−	1.24651i	0.289256	−	0.957252i	$-0.406592\pi$
$733$	33.7479	−	33.7479i	1.24651	−	1.24651i	0.957252	−	0.289256i	$-0.0934079\pi$
$734$			2.83009i			0.104460i
$735$	−7.61158	+	22.2950i	−0.280757	+	0.822365i
$736$			2.69516i			0.0993447i
$737$	−20.1361	−	20.1361i	−0.741724	−	0.741724i
$738$	4.76470	+	25.8293i	0.175391	+	0.950790i
$739$	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
$741$	−8.47960	−	9.91587i	−0.311506	−	0.364268i
$742$	5.58149	−	5.58149i	0.204903	−	0.204903i
$743$	17.2290	+	17.2290i	0.632070	+	0.632070i	0.948587	−	0.316517i	$-0.102513\pi$
$743$	17.2290	+	17.2290i	0.632070	+	0.632070i	−0.316517	+	0.948587i	$0.602513\pi$
$744$	4.37125	−	14.0568i	0.160258	−	0.515348i
$745$	8.93942	−	8.46071i	0.327515	−	0.309976i
$746$	−17.1930			−0.629480
$747$	−1.98494	+	0.366159i	−0.0726252	+	0.0133971i
$748$	12.6342	−	12.6342i	0.461951	−	0.461951i
$749$			6.13044i			0.224001i
$750$	−7.56590	−	17.8257i	−0.276268	−	0.650904i
$751$	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
$753$	3.02488	+	5.75523i	0.110233	+	0.209732i
$754$	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	−0.924232	−	0.381831i	$-0.875293\pi$
$757$	−14.9234	+	14.9234i	−0.542401	+	0.542401i	0.381831	+	0.924232i	$0.375293\pi$
$758$	−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	$-0.589627\pi$
$761$	−15.3305			−0.555729			−0.277864	+	0.960620i	$0.589627\pi$
$762$	−8.72950	−	16.6090i	−0.316236	−	0.601681i
$763$	−11.5931	−	11.5931i	−0.419697	−	0.419697i
$764$	14.2651			0.516094
$765$	40.7613	+	29.7500i	1.47373	+	1.07561i
$766$	−2.42062			−0.0874607
$767$	−39.5438	+	8.99116i	−1.42784	+	0.324652i
$768$	−1.53318	+	0.805823i	−0.0553240	+	0.0290776i
$769$	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	$-0.128179\pi$
$773$	14.6833	+	14.6833i	0.528122	+	0.528122i	−0.391890	+	0.920012i	$0.628179\pi$
$774$	0.318662	−	0.462822i	0.0114541	−	0.0166358i
$775$	42.4310	+	2.33648i	1.52417	+	0.0839287i
$776$		−	1.57840i		−	0.0566613i
$777$	−2.88333	−	5.48592i	−0.103439	−	0.196806i
$778$	−16.0943	+	16.0943i	−0.577007	+	0.577007i
$779$	−18.2912			−0.655349
$780$	−13.8867	−	1.46944i	−0.497224	−	0.0526143i
$781$	−29.6823			−1.06212
$782$	14.3363	−	14.3363i	0.512666	−	0.512666i
$783$	−1.17254	+	9.80075i	−0.0419033	+	0.350250i
$784$			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	0.997028	−	0.0770443i	$-0.0245483\pi$
$787$	25.8088	+	25.8088i	0.919983	+	0.919983i	−0.0770443	+	0.997028i	$0.524548\pi$
$788$	−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
$792$	−7.00725	+	1.29262i	−0.248992	+	0.0459312i
$793$	7.42953	+	32.6756i	0.263830	+	1.16034i
$794$	27.2423			0.966794
$795$	28.6537	−	14.0683i	1.01624	−	0.498951i
$796$	−10.2380			−0.362877
$797$	−6.38493	−	6.38493i	−0.226166	−	0.226166i	0.584923	−	0.811089i	$-0.301125\pi$
$797$	−6.38493	−	6.38493i	−0.226166	−	0.226166i	−0.811089	+	0.584923i	$0.801125\pi$
$798$	3.06769	−	1.61234i	0.108595	−	0.0570763i
$799$	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
$807$	−24.4627	+	12.8573i	−0.861128	+	0.452599i
$808$	−12.4592	+	12.4592i	−0.438313	+	0.438313i
$809$	−19.9820			−0.702530			−0.351265	−	0.936276i	$-0.614248\pi$
$809$	−19.9820			−0.702530			−0.351265	+	0.936276i	$0.614248\pi$
$810$	−6.66063	−	18.9904i	−0.234031	−	0.667255i
$811$			8.19667i			0.287824i	0.989590	+	0.143912i	$0.0459682\pi$
$811$			8.19667i			0.287824i	−0.989590	+	0.143912i	$0.954032\pi$
$812$	−1.28642	+	1.28642i	−0.0451446	+	0.0451446i
$813$	−21.8829	−	41.6350i	−0.767466	−	1.46020i
$814$	−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
$819$	−4.09115	−	9.51716i	−0.142956	−	0.332556i
$820$	−14.2184	+	13.4570i	−0.496528	+	0.469938i
$821$	3.86982			0.135058			0.0675288	−	0.997717i	$-0.478489\pi$
$821$	3.86982			0.135058			0.0675288	+	0.997717i	$0.478489\pi$
$822$	6.75176	+	12.8461i	0.235495	+	0.448059i
$823$	−17.2535	−	17.2535i	−0.601420	−	0.601420i	0.339269	−	0.940689i	$-0.389820\pi$
$823$	−17.2535	−	17.2535i	−0.601420	−	0.601420i	−0.940689	+	0.339269i	$0.889820\pi$
$824$			2.31139i			0.0805210i
$825$	−8.55422	−	18.7064i	−0.297820	−	0.651273i
$826$		−	10.7718i		−	0.374798i
$827$	−27.8990	+	27.8990i	−0.970143	+	0.970143i	−0.999567	−	0.0294237i	$-0.990633\pi$
$827$	−27.8990	+	27.8990i	−0.970143	+	0.970143i	0.0294237	+	0.999567i	$0.490633\pi$
$828$	−7.95131	+	1.46677i	−0.276327	+	0.0509737i
$829$		−	37.1965i		−	1.29189i	−0.763386	−	0.645943i	$-0.776464\pi$
$829$		−	37.1965i		−	1.29189i	0.763386	−	0.645943i	$-0.223536\pi$
$830$	−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
$837$	43.8497	+	5.24610i	1.51567	+	0.181332i
$838$	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	$0.917809\pi$
$840$	1.19841	−	3.51027i	0.0413492	−	0.121116i
$841$	−25.3915			−0.875569
$842$	−17.8664	−	17.8664i	−0.615716	−	0.615716i
$843$	−27.0144	+	14.1985i	−0.930426	+	0.489021i
$844$			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
$852$	−10.0704	−	19.1602i	−0.345005	−	0.656416i
$853$	−25.7170	+	25.7170i	−0.880533	+	0.880533i	−0.993589	−	0.113056i	$-0.963936\pi$
$853$	−25.7170	+	25.7170i	−0.880533	+	0.880533i	0.113056	+	0.993589i	$0.463936\pi$
$854$	−8.90087			−0.304581
$855$	13.8471	−	2.16241i	0.473559	−	0.0739530i
$856$			6.40114i			0.218786i
$857$	26.4247	+	26.4247i	0.902650	+	0.902650i	0.995665	−	0.0930149i	$-0.0296504\pi$
$857$	26.4247	+	26.4247i	0.902650	+	0.902650i	−0.0930149	+	0.995665i	$0.529650\pi$
$858$	−14.7879	−	1.15459i	−0.504849	−	0.0394171i
$859$			27.8865i			0.951475i	0.879587	+	0.475738i	$0.157819\pi$
$859$			27.8865i			0.951475i	−0.879587	+	0.475738i	$0.842181\pi$
$860$	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	$-0.318171\pi$
$863$	−8.82969	−	8.82969i	−0.300566	−	0.300566i	−0.841235	+	0.540669i	$0.818171\pi$
$864$	−3.21175	−	4.08468i	−0.109266	−	0.138964i
$865$	−43.6801	−	1.20172i	−1.48517	−	0.0408597i
$866$	−4.78682			−0.162663
$867$	−31.9024	−	60.6984i	−1.08346	−	2.06143i
$868$	5.75560	+	5.75560i	0.195358	+	0.195358i
$869$			2.46821i			0.0837281i
$870$	−6.60409	+	3.24246i	−0.223900	+	0.109930i
$871$	23.0292	−	36.5835i	0.780316	−	1.23958i
$872$	−12.1050	−	12.1050i	−0.409926	−	0.409926i
$873$	4.65663	−	0.859003i	0.157603	−	0.0290728i
$874$		−	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	0.230584	−	0.973053i	$-0.425937\pi$
$877$	−21.9876	−	21.9876i	−0.742469	−	0.742469i	−0.973053	+	0.230584i	$0.925937\pi$
$878$	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	$0.856734\pi$
$882$	−17.9456	+	3.31040i	−0.604259	+	0.111467i
$883$	32.7661	+	32.7661i	1.10267	+	1.10267i	0.994088	+	0.108581i	$0.0346306\pi$
$883$	32.7661	+	32.7661i	1.10267	+	1.10267i	0.108581	+	0.994088i	$0.465369\pi$
$884$	22.9539	+	14.4494i	0.772023	+	0.485987i
$885$	14.0742	−	41.2247i	0.473100	−	1.38575i
$886$			7.36391i			0.247395i
$887$	−15.9624	−	15.9624i	−0.535966	−	0.535966i	0.386376	−	0.922341i	$-0.373727\pi$
$887$	−15.9624	−	15.9624i	−0.535966	−	0.535966i	−0.922341	+	0.386376i	$0.873727\pi$
$888$	−3.01065	−	5.72815i	−0.101031	−	0.192224i
$889$	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
$897$	−16.7802	−	1.31014i	−0.560274	−	0.0437445i
$898$	16.9045	+	16.9045i	0.564110	+	0.564110i
$899$		−	16.1449i		−	0.538461i
$900$	9.17292	−	11.8683i	0.305764	−	0.395611i
$901$	−62.0012			−2.06556
$902$	−14.7040	+	14.7040i	−0.489590	+	0.489590i
$903$	0.144552	+	0.275029i	0.00481039	+	0.00915240i
$904$	−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	−0.644492	−	0.764611i	$-0.722931\pi$
$907$	3.61754	−	3.61754i	0.120118	−	0.120118i	0.764611	+	0.644492i	$0.222931\pi$
$908$	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	$-0.248994\pi$
$912$	3.20315	−	1.68354i	0.106067	−	0.0557475i
$913$	−1.12998	−	1.12998i	−0.0373969	−	0.0373969i
$914$	−34.0067			−1.12484
$915$	−34.0646	−	11.6297i	−1.12614	−	0.384467i
$916$		−	3.93272i		−	0.129941i
$917$	14.8395	−	14.8395i	0.490043	−	0.490043i
$918$	−4.64339	+	38.8119i	−0.153255	+	1.28098i
$919$		−	30.8672i		−	1.01822i	−0.860703	−	0.509108i	$-0.829975\pi$
$919$		−	30.8672i		−	1.01822i	0.860703	−	0.509108i	$-0.170025\pi$
$920$	−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
$927$	−6.81911	+	1.25791i	−0.223969	+	0.0413152i
$928$	−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	$0.807578\pi$
$930$	14.5071	+	29.5475i	0.475707	+	0.968900i
$931$		−	12.7083i		−	0.416496i
$932$	−2.63212	−	2.63212i	−0.0862178	−	0.0862178i
$933$	26.2129	+	49.8734i	0.858171	+	1.63278i
$934$	−6.44587			−0.210915
$935$	−1.09876	+	39.9377i	−0.0359332	+	1.30610i
$936$	−4.27180	−	9.93739i	−0.139628	−	0.324814i
$937$	−10.4252	+	10.4252i	−0.340577	+	0.340577i	−0.856584	−	0.516007i	$-0.827418\pi$
$937$	−10.4252	+	10.4252i	−0.340577	+	0.340577i	0.516007	+	0.856584i	$0.327418\pi$
$938$	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	$-0.451562\pi$
$941$	9.29998			0.303171			0.151585	+	0.988444i	$0.451562\pi$
$942$	7.50992	+	14.2886i	0.244686	+	0.465548i
$943$	−16.6850	+	16.6850i	−0.543339	+	0.543339i
$944$		−	11.2474i		−	0.366072i
$945$	11.0083	+	1.62522i	0.358099	+	0.0528683i
$946$	0.444880			0.0144643
$947$	−39.1313	+	39.1313i	−1.27160	+	1.27160i	−0.326344	+	0.945251i	$0.605817\pi$
$947$	−39.1313	+	39.1313i	−1.27160	+	1.27160i	−0.945251	+	0.326344i	$0.894183\pi$
$948$	−1.59324	+	0.837390i	−0.0517462	+	0.0271972i
$949$	−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	$-0.558155\pi$
$953$	24.7482	−	24.7482i	0.801673	−	0.801673i	0.983357	+	0.181684i	$0.0581547\pi$
$954$	20.3655	+	14.0220i	0.659356	+	0.453980i
$955$	−23.1669	+	21.9263i	−0.749663	+	0.709518i
$956$	1.55998			0.0504535
$957$	−6.91752	+	3.63577i	−0.223612	+	0.117528i
$958$	−11.2649	−	11.2649i	−0.363951	−	0.363951i
$959$	−8.02439			−0.259121
$960$	1.25133	−	3.66527i	0.0403865	−	0.118296i
$961$	−41.2340			−1.33013
$962$	−2.98665	−	13.1355i	−0.0962934	−	0.423505i
$963$	−18.8848	+	3.48365i	−0.608554	+	0.112259i
$964$	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	0.913226	−	0.407454i	$-0.133583\pi$
$967$	15.7278	+	15.7278i	0.505772	+	0.505772i	−0.407454	+	0.913226i	$0.633583\pi$
$968$	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	$0.894969\pi$
$972$	10.3028	−	11.6984i	0.330463	−	0.375225i
$973$	−9.03222	+	9.03222i	−0.289560	+	0.289560i
$974$	29.4586			0.943914
$975$	24.8110	−	18.9583i	0.794587	−	0.607150i
$976$	−9.29389			−0.297490
$977$	−37.9379	+	37.9379i	−1.21374	+	1.21374i	−0.243954	+	0.969787i	$0.578445\pi$
$977$	−37.9379	+	37.9379i	−1.21374	+	1.21374i	−0.969787	+	0.243954i	$0.921555\pi$
$978$	7.15893	+	13.6208i	0.228917	+	0.435545i
$979$		−	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	$-0.238369\pi$
$983$	1.61981	+	1.61981i	0.0516638	+	0.0516638i	−0.680803	+	0.732467i	$0.738369\pi$
$984$	−14.4802	−	4.50290i	−0.461611	−	0.143547i
$985$	25.3045	+	0.696173i	0.806268	+	0.0221819i
$986$	14.2900			0.455087
$987$	4.31972	−	2.27040i	0.137498	−	0.0722675i
$988$	7.34530	−	1.67012i	0.233685	−	0.0531335i
$989$	0.504817			0.0160522
$990$	9.39312	−	12.8698i	0.298533	−	0.409029i
$991$	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
$993$	−11.0134	−	20.9544i	−0.349499	−	0.664967i
$994$	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	−0.683421	−	0.730024i	$-0.739509\pi$
$997$	1.47150	−	1.47150i	0.0466030	−	0.0466030i	0.730024	+	0.683421i	$0.239509\pi$
$998$	−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.b.233.7	yes	24
3.2	odd	2		390.2.s.c.233.4	yes	24
5.2	odd	4		390.2.s.c.77.10	yes	24
13.12	even	2	inner	390.2.s.b.233.1	yes	24
15.2	even	4	inner	390.2.s.b.77.1	✓	24
39.38	odd	2		390.2.s.c.233.10	yes	24
65.12	odd	4		390.2.s.c.77.4	yes	24
195.77	even	4	inner	390.2.s.b.77.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.s.b.77.1	✓	24	15.2	even	4	inner
390.2.s.b.77.7	yes	24	195.77	even	4	inner
390.2.s.b.233.1	yes	24	13.12	even	2	inner
390.2.s.b.233.7	yes	24	1.1	even	1	trivial
390.2.s.c.77.4	yes	24	65.12	odd	4
390.2.s.c.77.10	yes	24	5.2	odd	4
390.2.s.c.233.4	yes	24	3.2	odd	2
390.2.s.c.233.10	yes	24	39.38	odd	2

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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.53318 + 0.805823i) q^{3} -1.00000i q^{4} +(1.53706 + 1.62402i) q^{5} +(-0.514321 + 1.65393i) q^{6} +(-0.677204 - 0.677204i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.70130 - 2.47095i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.53318 + 0.805823i) 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} +(0.805823 + 1.53318i) q^{12} +(0.799399 + 3.51582i) q^{13} -0.957712 q^{14} +(-3.66527 - 1.25133i) q^{15} -1.00000 q^{16} +(5.31930 + 5.31930i) q^{17} +(-0.544224 - 2.95022i) 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} +(-0.617257 + 5.15936i) q^{27} +(-0.677204 + 0.677204i) q^{28} +1.89961 q^{29} +(-3.47656 + 1.70691i) q^{30} -8.49906i q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.64155 + 1.91396i) 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} +(-4.05875 - 4.74621i) q^{39} +(0.0614950 - 2.23522i) q^{40} -8.75503 q^{41} +(1.46835 - 0.771746i) q^{42} +(0.132445 + 0.132445i) q^{43} -2.37516i q^{44} +(6.62787 - 1.03504i) q^{45} -2.69516i q^{46} +(2.08023 - 2.08023i) q^{47} +(1.53318 - 0.805823i) 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} +(-3.20315 + 1.68354i) q^{57} +(1.34322 - 1.34322i) q^{58} +11.2474i q^{59} +(-1.25133 + 3.66527i) q^{60} +9.29389 q^{61} +(-6.00974 - 6.00974i) q^{62} +(-2.82546 + 0.521209i) 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} +(-2.95022 + 0.544224i) q^{72} +(-3.69590 + 3.69590i) q^{73} -3.73612 q^{74} +(-3.60153 - 7.87585i) q^{75} -2.08922i q^{76} +(-1.60847 - 1.60847i) q^{77} +(-6.22605 - 0.486111i) 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} +(-2.91244 + 1.53075i) q^{87} +(-1.67949 - 1.67949i) q^{88} -8.15992i q^{89} +(3.95473 - 5.41850i) q^{90} +(1.83957 - 2.92228i) q^{91} +(-1.90576 - 1.90576i) q^{92} +(6.84873 + 13.0306i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{3} - 12 q^{9}+O(q^{10}) \) 24 * q - 8 * q^3 - 12 * q^9	\( 24 q - 8 q^{3} - 12 q^{9} + 4 q^{10} + 4 q^{12} - 8 q^{13} - 16 q^{14} - 24 q^{16} + 52 q^{17} + 16 q^{22} - 16 q^{23} + 16 q^{25} + 40 q^{27} - 80 q^{29} + 20 q^{35} - 16 q^{38} - 32 q^{39} - 4 q^{42} + 28 q^{43} + 8 q^{48} - 20 q^{51} - 8 q^{52} + 72 q^{53} + 24 q^{55} - 64 q^{61} - 32 q^{62} - 12 q^{65} + 8 q^{66} + 52 q^{68} - 16 q^{69} - 120 q^{74} - 104 q^{75} + 32 q^{77} + 44 q^{78} + 12 q^{81} + 32 q^{82} - 32 q^{87} - 16 q^{88} + 64 q^{90} + 64 q^{91} + 16 q^{92} + 96 q^{95}+O(q^{100}) \) 24 * q - 8 * q^3 - 12 * q^9 + 4 * q^10 + 4 * q^12 - 8 * q^13 - 16 * q^14 - 24 * q^16 + 52 * q^17 + 16 * q^22 - 16 * q^23 + 16 * q^25 + 40 * q^27 - 80 * q^29 + 20 * q^35 - 16 * q^38 - 32 * q^39 - 4 * q^42 + 28 * q^43 + 8 * 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 - 104 * q^75 + 32 * q^77 + 44 * q^78 + 12 * q^81 + 32 * q^82 - 32 * q^87 - 16 * q^88 + 64 * q^90 + 64 * q^91 + 16 * q^92 + 96 * q^95

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