LMFDB - Embedded newform 930.2.j.c.497.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(497,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("930.497");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.3
Root			$-1.69230i$ of defining polynomial
Character	$\chi$	$=$	930.497
Dual form			930.2.j.c.683.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.292893 - 1.70711i) q^{3} -1.00000i q^{4} +(-0.489528 + 2.18183i) q^{5} +(-1.41421 - 1.00000i) q^{6} +(-0.474719 - 0.474719i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 + 1.00000i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.292893 - 1.70711i) q^{3} -1.00000i q^{4} +(-0.489528 + 2.18183i) q^{5} +(-1.41421 - 1.00000i) q^{6} +(-0.474719 - 0.474719i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 + 1.00000i) q^{9} +(1.19663 + 1.88893i) q^{10} +4.08557i q^{11} +(-1.70711 + 0.292893i) q^{12} +(-3.10651 + 3.10651i) q^{13} -0.671354 q^{14} +(3.86799 + 0.196635i) q^{15} -1.00000 q^{16} +(-4.06462 + 4.06462i) q^{17} +(-1.29289 + 2.70711i) q^{18} -1.57129i q^{19} +(2.18183 + 0.489528i) q^{20} +(-0.671354 + 0.949437i) q^{21} +(2.88893 + 2.88893i) q^{22} +(-1.06051 - 1.06051i) q^{23} +(-1.00000 + 1.41421i) q^{24} +(-4.52072 - 2.13613i) q^{25} +4.39327i q^{26} +(2.53553 + 4.53553i) q^{27} +(-0.474719 + 0.474719i) q^{28} -1.87899 q^{29} +(2.87412 - 2.59604i) q^{30} +1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(6.97450 - 1.19663i) q^{33} +5.74825i q^{34} +(1.26814 - 0.803365i) q^{35} +(1.00000 + 2.82843i) q^{36} +(-2.00000 - 2.00000i) q^{37} +(-1.11107 - 1.11107i) q^{38} +(6.21302 + 4.39327i) q^{39} +(1.88893 - 1.19663i) q^{40} +7.26358i q^{41} +(0.196635 + 1.14607i) q^{42} +(1.16702 - 1.16702i) q^{43} +4.08557 q^{44} +(-0.797231 - 6.66066i) q^{45} -1.49978 q^{46} +(-0.520724 + 0.520724i) q^{47} +(0.292893 + 1.70711i) q^{48} -6.54928i q^{49} +(-4.70711 + 1.68616i) q^{50} +(8.12925 + 5.74825i) q^{51} +(3.10651 + 3.10651i) q^{52} +(-2.48339 - 2.48339i) q^{53} +(5.00000 + 1.41421i) q^{54} +(-8.91399 - 2.00000i) q^{55} +0.671354i q^{56} +(-2.68235 + 0.460219i) q^{57} +(-1.32865 + 1.32865i) q^{58} +4.40554 q^{59} +(0.196635 - 3.86799i) q^{60} +11.2340 q^{61} +(0.707107 - 0.707107i) q^{62} +(1.81743 + 0.867988i) q^{63} +1.00000i q^{64} +(-5.25714 - 8.29859i) q^{65} +(4.08557 - 5.77786i) q^{66} +(-5.37233 - 5.37233i) q^{67} +(4.06462 + 4.06462i) q^{68} +(-1.49978 + 2.12101i) q^{69} +(0.328646 - 1.46478i) q^{70} +4.42871i q^{71} +(2.70711 + 1.29289i) q^{72} +(-7.86799 + 7.86799i) q^{73} -2.82843 q^{74} +(-2.32251 + 8.34302i) q^{75} -1.57129 q^{76} +(1.93949 - 1.93949i) q^{77} +(7.49978 - 1.28676i) q^{78} +9.12702i q^{79} +(0.489528 - 2.18183i) q^{80} +(7.00000 - 5.65685i) q^{81} +(5.13613 + 5.13613i) q^{82} +(-8.35783 - 8.35783i) q^{83} +(0.949437 + 0.671354i) q^{84} +(-6.87855 - 10.8580i) q^{85} -1.65041i q^{86} +(0.550343 + 3.20764i) q^{87} +(2.88893 - 2.88893i) q^{88} +5.69230 q^{89} +(-5.27353 - 4.14607i) q^{90} +2.94944 q^{91} +(-1.06051 + 1.06051i) q^{92} +(-0.292893 - 1.70711i) q^{93} +0.736416i q^{94} +(3.42827 + 0.769189i) q^{95} +(1.41421 + 1.00000i) q^{96} +(8.34915 + 8.34915i) q^{97} +(-4.63104 - 4.63104i) q^{98} +(-4.08557 - 11.5557i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} + 4 q^{7}+O(q^{10}) $ 8 * q - 8 * q^3 + 4 * q^7	$ 8 q - 8 q^{3} + 4 q^{7} - 8 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{15} - 8 q^{16} + 4 q^{17} - 16 q^{18} + 4 q^{20} + 12 q^{21} + 4 q^{22} - 12 q^{23} - 8 q^{24} - 4 q^{25} - 8 q^{27} + 4 q^{28} - 8 q^{29} + 8 q^{31} + 8 q^{33} + 24 q^{35} + 8 q^{36} - 16 q^{37} - 28 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{42} - 8 q^{43} + 4 q^{44} - 12 q^{45} + 28 q^{46} + 28 q^{47} + 8 q^{48} - 32 q^{50} - 8 q^{51} + 4 q^{52} - 12 q^{53} + 40 q^{54} - 20 q^{55} - 24 q^{57} - 28 q^{58} + 24 q^{59} - 8 q^{60} + 56 q^{61} - 28 q^{63} - 36 q^{65} + 4 q^{66} - 16 q^{67} - 4 q^{68} + 28 q^{69} + 20 q^{70} + 16 q^{72} - 36 q^{73} - 32 q^{75} + 4 q^{76} + 12 q^{77} + 20 q^{78} + 56 q^{81} + 28 q^{82} - 12 q^{83} - 8 q^{84} + 32 q^{85} - 20 q^{87} + 4 q^{88} + 36 q^{89} - 4 q^{90} + 8 q^{91} - 12 q^{92} - 8 q^{93} - 36 q^{95} + 12 q^{97} + 32 q^{98} - 4 q^{99}+O(q^{100}) $ 8 * q - 8 * q^3 + 4 * q^7 - 8 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^15 - 8 * q^16 + 4 * q^17 - 16 * q^18 + 4 * q^20 + 12 * q^21 + 4 * q^22 - 12 * q^23 - 8 * q^24 - 4 * q^25 - 8 * q^27 + 4 * q^28 - 8 * q^29 + 8 * q^31 + 8 * q^33 + 24 * q^35 + 8 * q^36 - 16 * q^37 - 28 * q^38 + 8 * q^39 - 4 * q^40 - 8 * q^42 - 8 * q^43 + 4 * q^44 - 12 * q^45 + 28 * q^46 + 28 * q^47 + 8 * q^48 - 32 * q^50 - 8 * q^51 + 4 * q^52 - 12 * q^53 + 40 * q^54 - 20 * q^55 - 24 * q^57 - 28 * q^58 + 24 * q^59 - 8 * q^60 + 56 * q^61 - 28 * q^63 - 36 * q^65 + 4 * q^66 - 16 * q^67 - 4 * q^68 + 28 * q^69 + 20 * q^70 + 16 * q^72 - 36 * q^73 - 32 * q^75 + 4 * q^76 + 12 * q^77 + 20 * q^78 + 56 * q^81 + 28 * q^82 - 12 * q^83 - 8 * q^84 + 32 * q^85 - 20 * q^87 + 4 * q^88 + 36 * q^89 - 4 * q^90 + 8 * q^91 - 12 * q^92 - 8 * q^93 - 36 * q^95 + 12 * q^97 + 32 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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
$3$	−0.292893	−	1.70711i	−0.169102	−	0.985599i
$3$	−0.292893	−	1.70711i	−0.169102	−	0.985599i
$4$		−	1.00000i		−	0.500000i
$5$	−0.489528	+	2.18183i	−0.218924	+	0.975742i
$5$	−0.489528	+	2.18183i	−0.218924	+	0.975742i
$6$	−1.41421	−	1.00000i	−0.577350	−	0.408248i
$7$	−0.474719	−	0.474719i	−0.179427	−	0.179427i	0.611679	−	0.791106i	$-0.290494\pi$
$7$	−0.474719	−	0.474719i	−0.179427	−	0.179427i	−0.791106	+	0.611679i	$0.790494\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.82843	+	1.00000i	−0.942809	+	0.333333i
$10$	1.19663	+	1.88893i	0.378409	+	0.597333i
$11$			4.08557i			1.23184i	0.787807	+	0.615922i	$0.211217\pi$
$11$			4.08557i			1.23184i	−0.787807	+	0.615922i	$0.788783\pi$
$12$	−1.70711	+	0.292893i	−0.492799	+	0.0845510i
$13$	−3.10651	+	3.10651i	−0.861591	+	0.861591i	−0.991523	−	0.129932i	$-0.958524\pi$
$13$	−3.10651	+	3.10651i	−0.861591	+	0.861591i	0.129932	+	0.991523i	$0.458524\pi$
$14$	−0.671354			−0.179427
$15$	3.86799	+	0.196635i	0.998710	+	0.0507709i
$16$	−1.00000			−0.250000
$17$	−4.06462	+	4.06462i	−0.985816	+	0.985816i	−0.999901	−	0.0140848i	$-0.995517\pi$
$17$	−4.06462	+	4.06462i	−0.985816	+	0.985816i	0.0140848	+	0.999901i	$0.495517\pi$
$18$	−1.29289	+	2.70711i	−0.304738	+	0.638071i
$19$		−	1.57129i		−	0.360478i	−0.983623	−	0.180239i	$-0.942313\pi$
$19$		−	1.57129i		−	0.360478i	0.983623	−	0.180239i	$-0.0576871\pi$
$20$	2.18183	+	0.489528i	0.487871	+	0.109462i
$21$	−0.671354	+	0.949437i	−0.146501	+	0.207184i
$22$	2.88893	+	2.88893i	0.615922	+	0.615922i
$23$	−1.06051	−	1.06051i	−0.221131	−	0.221131i	0.587844	−	0.808974i	$-0.299977\pi$
$23$	−1.06051	−	1.06051i	−0.221131	−	0.221131i	−0.808974	+	0.587844i	$0.799977\pi$
$24$	−1.00000	+	1.41421i	−0.204124	+	0.288675i
$25$	−4.52072	−	2.13613i	−0.904145	−	0.427226i
$26$			4.39327i			0.861591i
$27$	2.53553	+	4.53553i	0.487964	+	0.872864i
$28$	−0.474719	+	0.474719i	−0.0897134	+	0.0897134i
$29$	−1.87899			−0.348920			−0.174460	−	0.984664i	$-0.555818\pi$
$29$	−1.87899			−0.348920			−0.174460	+	0.984664i	$0.555818\pi$
$30$	2.87412	−	2.59604i	0.524741	−	0.473970i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	6.97450	−	1.19663i	1.21410	−	0.208307i
$34$			5.74825i			0.985816i
$35$	1.26814	−	0.803365i	0.214355	−	0.135793i
$36$	1.00000	+	2.82843i	0.166667	+	0.471405i
$37$	−2.00000	−	2.00000i	−0.328798	−	0.328798i	0.523331	−	0.852129i	$-0.324689\pi$
$37$	−2.00000	−	2.00000i	−0.328798	−	0.328798i	−0.852129	+	0.523331i	$0.824689\pi$
$38$	−1.11107	−	1.11107i	−0.180239	−	0.180239i
$39$	6.21302	+	4.39327i	0.994880	+	0.703486i
$40$	1.88893	−	1.19663i	0.298666	−	0.189205i
$41$			7.26358i			1.13438i	0.823587	+	0.567191i	$0.191970\pi$
$41$			7.26358i			1.13438i	−0.823587	+	0.567191i	$0.808030\pi$
$42$	0.196635	+	1.14607i	0.0303414	+	0.176843i
$43$	1.16702	−	1.16702i	0.177968	−	0.177968i	−0.612501	−	0.790470i	$-0.709837\pi$
$43$	1.16702	−	1.16702i	0.177968	−	0.177968i	0.790470	+	0.612501i	$0.209837\pi$
$44$	4.08557			0.615922
$45$	−0.797231	−	6.66066i	−0.118844	−	0.992913i
$46$	−1.49978			−0.221131
$47$	−0.520724	+	0.520724i	−0.0759555	+	0.0759555i	−0.744064	−	0.668108i	$-0.767104\pi$
$47$	−0.520724	+	0.520724i	−0.0759555	+	0.0759555i	0.668108	+	0.744064i	$0.267104\pi$
$48$	0.292893	+	1.70711i	0.0422755	+	0.246400i
$49$		−	6.54928i		−	0.935612i
$50$	−4.70711	+	1.68616i	−0.665685	+	0.238459i
$51$	8.12925	+	5.74825i	1.13832	+	0.804915i
$52$	3.10651	+	3.10651i	0.430796	+	0.430796i
$53$	−2.48339	−	2.48339i	−0.341120	−	0.341120i	0.515668	−	0.856788i	$-0.327544\pi$
$53$	−2.48339	−	2.48339i	−0.341120	−	0.341120i	−0.856788	+	0.515668i	$0.827544\pi$
$54$	5.00000	+	1.41421i	0.680414	+	0.192450i
$55$	−8.91399	−	2.00000i	−1.20196	−	0.269680i
$56$			0.671354i			0.0897134i
$57$	−2.68235	+	0.460219i	−0.355287	+	0.0609575i
$58$	−1.32865	+	1.32865i	−0.174460	+	0.174460i
$59$	4.40554			0.573552			0.286776	−	0.957998i	$-0.407416\pi$
$59$	4.40554			0.573552			0.286776	+	0.957998i	$0.407416\pi$
$60$	0.196635	−	3.86799i	0.0253855	−	0.499355i
$61$	11.2340			1.43836			0.719181	−	0.694823i	$-0.244517\pi$
$61$	11.2340			1.43836			0.719181	+	0.694823i	$0.244517\pi$
$62$	0.707107	−	0.707107i	0.0898027	−	0.0898027i
$63$	1.81743	+	0.867988i	0.228974	+	0.109356i
$64$			1.00000i			0.125000i
$65$	−5.25714	−	8.29859i	−0.652068	−	1.02931i
$66$	4.08557	−	5.77786i	0.502899	−	0.711206i
$67$	−5.37233	−	5.37233i	−0.656334	−	0.656334i	0.298177	−	0.954511i	$-0.403622\pi$
$67$	−5.37233	−	5.37233i	−0.656334	−	0.656334i	−0.954511	+	0.298177i	$0.903622\pi$
$68$	4.06462	+	4.06462i	0.492908	+	0.492908i
$69$	−1.49978	+	2.12101i	−0.180552	+	0.255340i
$70$	0.328646	−	1.46478i	0.0392808	−	0.175074i
$71$			4.42871i			0.525592i	0.964851	+	0.262796i	$0.0846445\pi$
$71$			4.42871i			0.525592i	−0.964851	+	0.262796i	$0.915355\pi$
$72$	2.70711	+	1.29289i	0.319036	+	0.152369i
$73$	−7.86799	+	7.86799i	−0.920878	+	0.920878i	−0.997092	−	0.0762132i	$-0.975717\pi$
$73$	−7.86799	+	7.86799i	−0.920878	+	0.920878i	0.0762132	+	0.997092i	$0.475717\pi$
$74$	−2.82843			−0.328798
$75$	−2.32251	+	8.34302i	−0.268181	+	0.963369i
$76$	−1.57129			−0.180239
$77$	1.93949	−	1.93949i	0.221026	−	0.221026i
$78$	7.49978	−	1.28676i	0.849183	−	0.145697i
$79$			9.12702i			1.02687i	0.858129	+	0.513435i	$0.171627\pi$
$79$			9.12702i			1.02687i	−0.858129	+	0.513435i	$0.828373\pi$
$80$	0.489528	−	2.18183i	0.0547309	−	0.243935i
$81$	7.00000	−	5.65685i	0.777778	−	0.628539i
$82$	5.13613	+	5.13613i	0.567191	+	0.567191i
$83$	−8.35783	−	8.35783i	−0.917391	−	0.917391i	0.0794483	−	0.996839i	$-0.474684\pi$
$83$	−8.35783	−	8.35783i	−0.917391	−	0.917391i	−0.996839	+	0.0794483i	$0.974684\pi$
$84$	0.949437	+	0.671354i	0.103592	+	0.0732507i
$85$	−6.87855	−	10.8580i	−0.746084	−	1.17772i
$86$		−	1.65041i		−	0.177968i
$87$	0.550343	+	3.20764i	0.0590030	+	0.343895i
$88$	2.88893	−	2.88893i	0.307961	−	0.307961i
$89$	5.69230			0.603382			0.301691	−	0.953406i	$-0.402449\pi$
$89$	5.69230			0.603382			0.301691	+	0.953406i	$0.402449\pi$
$90$	−5.27353	−	4.14607i	−0.555879	−	0.437034i
$91$	2.94944			0.309185
$92$	−1.06051	+	1.06051i	−0.110565	+	0.110565i
$93$	−0.292893	−	1.70711i	−0.0303716	−	0.177019i
$94$			0.736416i			0.0759555i
$95$	3.42827	+	0.769189i	0.351734	+	0.0789172i
$96$	1.41421	+	1.00000i	0.144338	+	0.102062i
$97$	8.34915	+	8.34915i	0.847728	+	0.847728i	0.989849	−	0.142121i	$-0.0453923\pi$
$97$	8.34915	+	8.34915i	0.847728	+	0.847728i	−0.142121	+	0.989849i	$0.545392\pi$
$98$	−4.63104	−	4.63104i	−0.467806	−	0.467806i
$99$	−4.08557	−	11.5557i	−0.410615	−	1.16139i
$100$	−2.13613	+	4.52072i	−0.213613	+	0.452072i
$101$		−	12.5702i		−	1.25078i	−0.780311	−	0.625392i	$-0.784939\pi$
$101$		−	12.5702i		−	1.25078i	0.780311	−	0.625392i	$-0.215061\pi$
$102$	9.81287	−	1.68362i	0.971619	−	0.166703i
$103$	−0.449657	+	0.449657i	−0.0443060	+	0.0443060i	−0.728913	−	0.684607i	$-0.759974\pi$
$103$	−0.449657	+	0.449657i	−0.0443060	+	0.0443060i	0.684607	+	0.728913i	$0.259974\pi$
$104$	4.39327			0.430796
$105$	−1.74286	−	1.92955i	−0.170086	−	0.188305i
$106$	−3.51205			−0.341120
$107$	−5.00412	+	5.00412i	−0.483766	+	0.483766i	−0.906332	−	0.422566i	$-0.861130\pi$
$107$	−5.00412	+	5.00412i	−0.483766	+	0.483766i	0.422566	+	0.906332i	$0.361130\pi$
$108$	4.53553	−	2.53553i	0.436432	−	0.243982i
$109$			7.47661i			0.716129i	0.933697	+	0.358064i	$0.116563\pi$
$109$			7.47661i			0.716129i	−0.933697	+	0.358064i	$0.883437\pi$
$110$	−7.71736	+	4.88893i	−0.735821	+	0.466141i
$111$	−2.82843	+	4.00000i	−0.268462	+	0.379663i
$112$	0.474719	+	0.474719i	0.0448567	+	0.0448567i
$113$	−6.30315	−	6.30315i	−0.592950	−	0.592950i	0.345477	−	0.938427i	$-0.387717\pi$
$113$	−6.30315	−	6.30315i	−0.592950	−	0.592950i	−0.938427	+	0.345477i	$0.887717\pi$
$114$	−1.57129	+	2.22214i	−0.147165	+	0.208122i
$115$	2.83298	−	1.79469i	0.264177	−	0.167356i
$116$			1.87899i			0.174460i
$117$	5.68003	−	11.8931i	0.525119	−	1.09951i
$118$	3.11519	−	3.11519i	0.286776	−	0.286776i
$119$	3.85911			0.353764
$120$	−2.59604	−	2.87412i	−0.236985	−	0.262370i
$121$	−5.69186			−0.517442
$122$	7.94361	−	7.94361i	0.719181	−	0.719181i
$123$	12.3997	−	2.12745i	1.11804	−	0.191826i
$124$		−	1.00000i		−	0.0898027i
$125$	6.87368	−	8.81774i	0.614801	−	0.788682i
$126$	1.89887	−	0.671354i	0.169165	−	0.0598089i
$127$	13.5138	+	13.5138i	1.19916	+	1.19916i	0.974419	+	0.224741i	$0.0721536\pi$
$127$	13.5138	+	13.5138i	1.19916	+	1.19916i	0.224741	+	0.974419i	$0.427846\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−2.33403	−	1.65041i	−0.205500	−	0.145310i
$130$	−9.58535	−	2.15063i	−0.840691	−	0.188623i
$131$			14.5940i			1.27509i	0.770415	+	0.637543i	$0.220049\pi$
$131$			14.5940i			1.27509i	−0.770415	+	0.637543i	$0.779951\pi$
$132$	−1.19663	−	6.97450i	−0.104154	−	0.607052i
$133$	−0.745919	+	0.745919i	−0.0646794	+	0.0646794i
$134$	−7.59762			−0.656334
$135$	−11.1370	+	3.31182i	−0.958517	+	0.285036i
$136$	5.74825			0.492908
$137$	6.22752	−	6.22752i	0.532053	−	0.532053i	−0.389130	−	0.921183i	$-0.627224\pi$
$137$	6.22752	−	6.22752i	0.532053	−	0.532053i	0.921183	+	0.389130i	$0.127224\pi$
$138$	0.439276	+	2.56029i	0.0373936	+	0.217946i
$139$		−	1.35498i		−	0.114928i	−0.998348	−	0.0574638i	$-0.981699\pi$
$139$		−	1.35498i		−	0.114928i	0.998348	−	0.0574638i	$-0.0183014\pi$
$140$	−0.803365	−	1.26814i	−0.0678967	−	0.107178i
$141$	1.04145	+	0.736416i	0.0877058	+	0.0620174i
$142$	3.13157	+	3.13157i	0.262796	+	0.262796i
$143$	−12.6919	−	12.6919i	−1.06135	−	1.06135i
$144$	2.82843	−	1.00000i	0.235702	−	0.0833333i
$145$	0.919818	−	4.09963i	0.0763868	−	0.340456i
$146$			11.1270i			0.920878i
$147$	−11.1803	+	1.91824i	−0.922138	+	0.158214i
$148$	−2.00000	+	2.00000i	−0.164399	+	0.164399i
$149$	−20.3809			−1.66967			−0.834833	−	0.550504i	$-0.814436\pi$
$149$	−20.3809			−1.66967			−0.834833	+	0.550504i	$0.814436\pi$
$150$	4.25714	+	7.54167i	0.347594	+	0.615775i
$151$	−19.4720			−1.58461			−0.792303	−	0.610128i	$-0.791118\pi$
$151$	−19.4720			−1.58461			−0.792303	+	0.610128i	$0.791118\pi$
$152$	−1.11107	+	1.11107i	−0.0901195	+	0.0901195i
$153$	7.43187	−	15.5611i	0.600831	−	1.25804i
$154$		−	2.74286i		−	0.221026i
$155$	−0.489528	+	2.18183i	−0.0393198	+	0.175248i
$156$	4.39327	−	6.21302i	0.351743	−	0.497440i
$157$	−1.46245	−	1.46245i	−0.116716	−	0.116716i	0.646336	−	0.763053i	$-0.276300\pi$
$157$	−1.46245	−	1.46245i	−0.116716	−	0.116716i	−0.763053	+	0.646336i	$0.776300\pi$
$158$	6.45377	+	6.45377i	0.513435	+	0.513435i
$159$	−3.51205	+	4.96679i	−0.278524	+	0.393892i
$160$	−1.19663	−	1.88893i	−0.0946023	−	0.149333i
$161$			1.00688i			0.0793535i
$162$	0.949747	−	8.94975i	0.0746192	−	0.703159i
$163$	−2.67135	+	2.67135i	−0.209237	+	0.209237i	−0.803943	−	0.594706i	$-0.797268\pi$
$163$	−2.67135	+	2.67135i	−0.209237	+	0.209237i	0.594706	+	0.803943i	$0.297268\pi$
$164$	7.26358			0.567191
$165$	−0.803365	+	15.8029i	−0.0625419	+	1.23026i
$166$	−11.8198			−0.917391
$167$	−3.37465	+	3.37465i	−0.261138	+	0.261138i	−0.825516	−	0.564378i	$-0.809116\pi$
$167$	−3.37465	+	3.37465i	−0.261138	+	0.261138i	0.564378	+	0.825516i	$0.309116\pi$
$168$	1.14607	−	0.196635i	0.0884214	−	0.0151707i
$169$		−	6.30082i		−	0.484678i
$170$	−12.5417	−	2.81393i	−0.961902	−	0.215818i
$171$	1.57129	+	4.44427i	0.120159	+	0.339862i
$172$	−1.16702	−	1.16702i	−0.0889841	−	0.0889841i
$173$	−12.6186	−	12.6186i	−0.959371	−	0.959371i	0.0398349	−	0.999206i	$-0.487317\pi$
$173$	−12.6186	−	12.6186i	−0.959371	−	0.959371i	−0.999206	+	0.0398349i	$0.987317\pi$
$174$	2.65729	+	1.87899i	0.201449	+	0.142446i
$175$	1.13201	+	3.16013i	0.0855720	+	0.238884i
$176$		−	4.08557i		−	0.307961i
$177$	−1.29035	−	7.52072i	−0.0969888	−	0.565292i
$178$	4.02506	−	4.02506i	0.301691	−	0.301691i
$179$	22.7264			1.69865			0.849326	−	0.527868i	$-0.177008\pi$
$179$	22.7264			1.69865			0.849326	+	0.527868i	$0.177008\pi$
$180$	−6.66066	+	0.797231i	−0.496456	+	0.0594221i
$181$	−10.6295			−0.790082			−0.395041	−	0.918663i	$-0.629270\pi$
$181$	−10.6295			−0.790082			−0.395041	+	0.918663i	$0.629270\pi$
$182$	2.08557	−	2.08557i	0.154593	−	0.154593i
$183$	−3.29035	−	19.1776i	−0.243230	−	1.41765i
$184$			1.49978i			0.110565i
$185$	5.34271	−	3.38459i	0.392804	−	0.248840i
$186$	−1.41421	−	1.00000i	−0.103695	−	0.0733236i
$187$	−16.6063	−	16.6063i	−1.21437	−	1.21437i
$188$	0.520724	+	0.520724i	0.0379777	+	0.0379777i
$189$	0.949437	−	3.35677i	0.0690614	−	0.244169i
$190$	2.96805	−	1.88026i	0.215325	−	0.136408i
$191$		−	0.815538i		−	0.0590103i	−0.999565	−	0.0295051i	$-0.990607\pi$
$191$		−	0.815538i		−	0.0590103i	0.999565	−	0.0295051i	$-0.00939314\pi$
$192$	1.70711	−	0.292893i	0.123200	−	0.0211377i
$193$	−5.68362	+	5.68362i	−0.409116	+	0.409116i	−0.881430	−	0.472314i	$-0.843419\pi$
$193$	−5.68362	+	5.68362i	−0.409116	+	0.409116i	0.472314	+	0.881430i	$0.343419\pi$
$194$	11.8075			0.847728
$195$	−12.6268	+	11.4051i	−0.904224	+	0.816736i
$196$	−6.54928			−0.467806
$197$	−18.3545	+	18.3545i	−1.30771	+	1.30771i	−0.384640	+	0.923067i	$0.625674\pi$
$197$	−18.3545	+	18.3545i	−1.30771	+	1.30771i	−0.923067	+	0.384640i	$0.874326\pi$
$198$	−11.0601	−	5.28220i	−0.786005	−	0.375390i
$199$			16.1137i			1.14227i	0.820856	+	0.571135i	$0.193497\pi$
$199$			16.1137i			1.14227i	−0.820856	+	0.571135i	$0.806503\pi$
$200$	1.68616	+	4.70711i	0.119230	+	0.332843i
$201$	−7.59762	+	10.7447i	−0.535895	+	0.757869i
$202$	−8.88849	−	8.88849i	−0.625392	−	0.625392i
$203$	0.891992	+	0.891992i	0.0626055	+	0.0626055i
$204$	5.74825	−	8.12925i	0.402458	−	0.569161i
$205$	−15.8479	−	3.55573i	−1.10686	−	0.248343i
$206$			0.635910i			0.0443060i
$207$	4.06007	+	1.93906i	0.282194	+	0.134774i
$208$	3.10651	−	3.10651i	0.215398	−	0.215398i
$209$	6.41960			0.444053
$210$	−2.59679	−	0.132012i	−0.179195	−	0.00910966i
$211$	−25.1270			−1.72982			−0.864908	−	0.501931i	$-0.832623\pi$
$211$	−25.1270			−1.72982			−0.864908	+	0.501931i	$0.832623\pi$
$212$	−2.48339	+	2.48339i	−0.170560	+	0.170560i
$213$	7.56029	−	1.29714i	0.518022	−	0.0888786i
$214$			7.07689i			0.483766i
$215$	1.97494	+	3.11751i	0.134690	+	0.212613i
$216$	1.41421	−	5.00000i	0.0962250	−	0.340207i
$217$	−0.474719	−	0.474719i	−0.0322260	−	0.0322260i
$218$	5.28676	+	5.28676i	0.358064	+	0.358064i
$219$	15.7360	+	11.1270i	1.06334	+	0.751894i
$220$	−2.00000	+	8.91399i	−0.134840	+	0.600981i
$221$		−	25.2536i		−	1.69874i
$222$	0.828427	+	4.82843i	0.0556004	+	0.324063i
$223$	−3.60852	+	3.60852i	−0.241645	+	0.241645i	−0.817530	−	0.575886i	$-0.804657\pi$
$223$	−3.60852	+	3.60852i	−0.241645	+	0.241645i	0.575886	+	0.817530i	$0.304657\pi$
$224$	0.671354			0.0448567
$225$	14.9227	+	1.52116i	0.994845	+	0.101411i
$226$	−8.91399			−0.592950
$227$	16.2085	−	16.2085i	1.07579	−	1.07579i	0.0789120	−	0.996882i	$-0.474855\pi$
$227$	16.2085	−	16.2085i	1.07579	−	1.07579i	0.996882	−	0.0789120i	$-0.0251446\pi$
$228$	0.460219	+	2.68235i	0.0304788	+	0.177643i
$229$			6.64235i			0.438939i	0.975619	+	0.219470i	$0.0704327\pi$
$229$			6.64235i			0.438939i	−0.975619	+	0.219470i	$0.929567\pi$
$230$	0.734185	−	3.27226i	0.0484107	−	0.215766i
$231$	−3.87899	−	2.74286i	−0.255219	−	0.180467i
$232$	1.32865	+	1.32865i	0.0872299	+	0.0872299i
$233$	−9.15146	−	9.15146i	−0.599532	−	0.599532i	0.340656	−	0.940188i	$-0.389351\pi$
$233$	−9.15146	−	9.15146i	−0.599532	−	0.599532i	−0.940188	+	0.340656i	$0.889351\pi$
$234$	−4.39327	−	12.4260i	−0.287197	−	0.812316i
$235$	−0.881221	−	1.39104i	−0.0574845	−	0.0907414i
$236$		−	4.40554i		−	0.286776i
$237$	15.5808	−	2.67324i	1.01208	−	0.173646i
$238$	2.72880	−	2.72880i	0.176882	−	0.176882i
$239$	26.5471			1.71719			0.858593	−	0.512658i	$-0.171339\pi$
$239$	26.5471			1.71719			0.858593	+	0.512658i	$0.171339\pi$
$240$	−3.86799	−	0.196635i	−0.249678	−	0.0126927i
$241$	−3.60673			−0.232330			−0.116165	−	0.993230i	$-0.537060\pi$
$241$	−3.60673			−0.232330			−0.116165	+	0.993230i	$0.537060\pi$
$242$	−4.02475	+	4.02475i	−0.258721	+	0.258721i
$243$	−11.7071	−	10.2929i	−0.751011	−	0.660289i
$244$		−	11.2340i		−	0.719181i
$245$	14.2894	+	3.20606i	0.912916	+	0.204828i
$246$	7.26358	−	10.2723i	0.463109	−	0.654935i
$247$	4.88122	+	4.88122i	0.310585	+	0.310585i
$248$	−0.707107	−	0.707107i	−0.0449013	−	0.0449013i
$249$	−11.8198	+	16.7157i	−0.749046	+	1.05931i
$250$	−1.37465	−	11.0955i	−0.0869406	−	0.701742i
$251$			18.2657i			1.15292i	0.817126	+	0.576460i	$0.195566\pi$
$251$			18.2657i			1.15292i	−0.817126	+	0.576460i	$0.804434\pi$
$252$	0.867988	−	1.81743i	0.0546781	−	0.114487i
$253$	4.33276	−	4.33276i	0.272399	−	0.272399i
$254$	19.1115			1.19916
$255$	−16.5212	+	14.9227i	−1.03460	+	0.934494i
$256$	1.00000			0.0625000
$257$	17.9380	−	17.9380i	1.11894	−	1.11894i	0.127045	−	0.991897i	$-0.459451\pi$
$257$	17.9380	−	17.9380i	1.11894	−	1.11894i	0.991897	−	0.127045i	$-0.0405491\pi$
$258$	−2.81743	+	0.483394i	−0.175405	+	0.0300948i
$259$			1.89887i			0.117990i
$260$	−8.29859	+	5.25714i	−0.514657	+	0.326034i
$261$	5.31459	−	1.87899i	0.328965	−	0.116307i
$262$	10.3195	+	10.3195i	0.637543	+	0.637543i
$263$	−9.29859	−	9.29859i	−0.573376	−	0.573376i	0.359695	−	0.933070i	$-0.382881\pi$
$263$	−9.29859	−	9.29859i	−0.573376	−	0.573376i	−0.933070	+	0.359695i	$0.882881\pi$
$264$	−5.77786	−	4.08557i	−0.355603	−	0.251449i
$265$	6.63402	−	4.20264i	0.407525	−	0.258166i
$266$			1.05489i			0.0646794i
$267$	−1.66724	−	9.71736i	−0.102033	−	0.594693i
$268$	−5.37233	+	5.37233i	−0.328167	+	0.328167i
$269$	9.25447			0.564255			0.282128	−	0.959377i	$-0.408960\pi$
$269$	9.25447			0.564255			0.282128	+	0.959377i	$0.408960\pi$
$270$	−5.53321	+	10.2168i	−0.336740	+	0.621776i
$271$	28.8012			1.74955			0.874775	−	0.484530i	$-0.161009\pi$
$271$	28.8012			1.74955			0.874775	+	0.484530i	$0.161009\pi$
$272$	4.06462	−	4.06462i	0.246454	−	0.246454i
$273$	−0.863870	−	5.03500i	−0.0522838	−	0.304732i
$274$		−	8.80704i		−	0.532053i
$275$	8.72730	−	18.4697i	0.526276	−	1.11377i
$276$	2.12101	+	1.49978i	0.127670	+	0.0902762i
$277$	18.8334	+	18.8334i	1.13159	+	1.13159i	0.989913	+	0.141674i	$0.0452486\pi$
$277$	18.8334	+	18.8334i	1.13159	+	1.13159i	0.141674	+	0.989913i	$0.454751\pi$
$278$	−0.958112	−	0.958112i	−0.0574638	−	0.0574638i
$279$	−2.82843	+	1.00000i	−0.169334	+	0.0598684i
$280$	−1.46478	−	0.328646i	−0.0875371	−	0.0196404i
$281$		−	12.6435i		−	0.754250i	−0.926162	−	0.377125i	$-0.876913\pi$
$281$		−	12.6435i		−	0.754250i	0.926162	−	0.377125i	$-0.123087\pi$
$282$	1.25714	−	0.215691i	0.0748616	−	0.0128442i
$283$	13.8139	−	13.8139i	0.821153	−	0.821153i	−0.165121	−	0.986273i	$-0.552801\pi$
$283$	13.8139	−	13.8139i	0.821153	−	0.821153i	0.986273	+	0.165121i	$0.0528013\pi$
$284$	4.42871			0.262796
$285$	0.308970	−	6.07772i	0.0183018	−	0.360013i
$286$	−17.9490			−1.06135
$287$	3.44816	−	3.44816i	0.203538	−	0.203538i
$288$	1.29289	−	2.70711i	0.0761845	−	0.159518i
$289$		−	16.0423i		−	0.943666i
$290$	−2.24846	−	3.54928i	−0.132034	−	0.208421i
$291$	11.8075	−	16.6983i	0.692167	−	0.978872i
$292$	7.86799	+	7.86799i	0.460439	+	0.460439i
$293$	20.2335	+	20.2335i	1.18206	+	1.18206i	0.979211	+	0.202844i	$0.0650185\pi$
$293$	20.2335	+	20.2335i	1.18206	+	1.18206i	0.202844	+	0.979211i	$0.434981\pi$
$294$	−6.54928	+	9.26209i	−0.381962	+	0.540176i
$295$	−2.15663	+	9.61212i	−0.125564	+	0.559639i
$296$			2.82843i			0.164399i
$297$	−18.5302	+	10.3591i	−1.07523	+	0.601096i
$298$	−14.4114	+	14.4114i	−0.834833	+	0.834833i
$299$	6.58894			0.381048
$300$	8.34302	+	2.32251i	0.481684	+	0.134090i
$301$	−1.10801			−0.0638645
$302$	−13.7688	+	13.7688i	−0.792303	+	0.792303i
$303$	−21.4587	+	3.68173i	−1.23277	+	0.211510i
$304$			1.57129i			0.0901195i
$305$	−5.49934	+	24.5106i	−0.314891	+	1.40347i
$306$	−5.74825	−	16.2585i	−0.328605	−	0.929436i
$307$	−7.66447	−	7.66447i	−0.437434	−	0.437434i	0.453713	−	0.891148i	$-0.350099\pi$
$307$	−7.66447	−	7.66447i	−0.437434	−	0.437434i	−0.891148	+	0.453713i	$0.850099\pi$
$308$	−1.93949	−	1.93949i	−0.110513	−	0.110513i
$309$	0.899313	+	0.635910i	0.0511601	+	0.0361757i
$310$	1.19663	+	1.88893i	0.0679643	+	0.107284i
$311$			28.5308i			1.61783i	0.587925	+	0.808915i	$0.299945\pi$
$311$			28.5308i			1.61783i	−0.587925	+	0.808915i	$0.700055\pi$
$312$	−1.28676	−	7.49978i	−0.0728484	−	0.424591i
$313$	23.0992	−	23.0992i	1.30564	−	1.30564i	0.381116	−	0.924527i	$-0.375540\pi$
$313$	23.0992	−	23.0992i	1.30564	−	1.30564i	0.924527	−	0.381116i	$-0.124460\pi$
$314$	−2.06822			−0.116716
$315$	−2.78348	+	3.54040i	−0.156831	+	0.199479i
$316$	9.12702			0.513435
$317$	−11.3278	+	11.3278i	−0.636231	+	0.636231i	−0.949624	−	0.313393i	$-0.898534\pi$
$317$	−11.3278	+	11.3278i	−0.636231	+	0.636231i	0.313393	+	0.949624i	$0.398534\pi$
$318$	1.02866	+	5.99544i	0.0576841	+	0.336208i
$319$		−	7.67674i		−	0.429815i
$320$	−2.18183	−	0.489528i	−0.121968	−	0.0273655i
$321$	10.0082	+	7.07689i	0.558605	+	0.394994i
$322$	0.711974	+	0.711974i	0.0396768	+	0.0396768i
$323$	6.38669	+	6.38669i	0.355365	+	0.355365i
$324$	−5.65685	−	7.00000i	−0.314270	−	0.388889i
$325$	20.6796	−	7.40777i	1.14710	−	0.410909i
$326$			3.77786i			0.209237i
$327$	12.7634	−	2.18985i	0.705816	−	0.121099i
$328$	5.13613	−	5.13613i	0.283595	−	0.283595i
$329$	0.494395			0.0272569
$330$	10.6063	+	11.7424i	0.583857	+	0.646399i
$331$	−19.6774			−1.08157			−0.540783	−	0.841162i	$-0.681872\pi$
$331$	−19.6774			−1.08157			−0.540783	+	0.841162i	$0.681872\pi$
$332$	−8.35783	+	8.35783i	−0.458695	+	0.458695i
$333$	7.65685	+	3.65685i	0.419593	+	0.200394i
$334$			4.77248i			0.261138i
$335$	14.3514	−	9.09157i	0.784100	−	0.496726i
$336$	0.671354	−	0.949437i	0.0366253	−	0.0517961i
$337$	−3.40510	−	3.40510i	−0.185488	−	0.185488i	0.608254	−	0.793742i	$-0.291870\pi$
$337$	−3.40510	−	3.40510i	−0.185488	−	0.185488i	−0.793742	+	0.608254i	$0.791870\pi$
$338$	−4.45535	−	4.45535i	−0.242339	−	0.242339i
$339$	−8.91399	+	12.6063i	−0.484142	+	0.684680i
$340$	−10.8580	+	6.87855i	−0.588860	+	0.373042i
$341$			4.08557i			0.221246i
$342$	4.25364	+	2.03151i	0.230011	+	0.109851i
$343$	−6.43210	+	6.43210i	−0.347301	+	0.347301i
$344$	−1.65041			−0.0889841
$345$	−3.89349	−	4.31055i	−0.209618	−	0.232072i
$346$	−17.8453			−0.959371
$347$	8.75110	−	8.75110i	0.469783	−	0.469783i	−0.432061	−	0.901844i	$-0.642213\pi$
$347$	8.75110	−	8.75110i	0.469783	−	0.469783i	0.901844	+	0.432061i	$0.142213\pi$
$348$	3.20764	−	0.550343i	0.171947	−	0.0295015i
$349$			30.6845i			1.64251i	0.570564	+	0.821253i	$0.306724\pi$
$349$			30.6845i			1.64251i	−0.570564	+	0.821253i	$0.693276\pi$
$350$	3.03500	+	1.43410i	0.162228	+	0.0766558i
$351$	−21.9663	−	6.21302i	−1.17248	−	0.331627i
$352$	−2.88893	−	2.88893i	−0.153981	−	0.153981i
$353$	4.19208	+	4.19208i	0.223122	+	0.223122i	0.809812	−	0.586690i	$-0.199569\pi$
$353$	4.19208	+	4.19208i	0.223122	+	0.223122i	−0.586690	+	0.809812i	$0.699569\pi$
$354$	−6.23037	−	4.40554i	−0.331141	−	0.234152i
$355$	−9.66268	−	2.16798i	−0.512842	−	0.115064i
$356$		−	5.69230i		−	0.301691i
$357$	−1.13031	−	6.58790i	−0.0598221	−	0.348669i
$358$	16.0700	−	16.0700i	0.849326	−	0.849326i
$359$	6.95588			0.367117			0.183559	−	0.983009i	$-0.441238\pi$
$359$	6.95588			0.367117			0.183559	+	0.983009i	$0.441238\pi$
$360$	−4.14607	+	5.27353i	−0.218517	+	0.277939i
$361$	16.5311			0.870056
$362$	−7.51617	+	7.51617i	−0.395041	+	0.395041i
$363$	1.66711	+	9.71661i	0.0875004	+	0.509990i
$364$		−	2.94944i		−	0.154593i
$365$	−13.3150	−	21.0182i	−0.696938	−	1.10014i
$366$	−15.8872	−	11.2340i	−0.830439	−	0.587209i
$367$	3.72774	+	3.72774i	0.194586	+	0.194586i	0.797675	−	0.603088i	$-0.206063\pi$
$367$	3.72774	+	3.72774i	0.194586	+	0.194586i	−0.603088	+	0.797675i	$0.706063\pi$
$368$	1.06051	+	1.06051i	0.0552826	+	0.0552826i
$369$	−7.26358	−	20.5445i	−0.378127	−	1.06950i
$370$	1.38459	−	6.17113i	0.0719816	−	0.320822i
$371$			2.35783i			0.122412i
$372$	−1.70711	+	0.292893i	−0.0885094	+	0.0151858i
$373$	2.93906	−	2.93906i	0.152179	−	0.152179i	−0.626912	−	0.779090i	$-0.715681\pi$
$373$	2.93906	−	2.93906i	0.152179	−	0.152179i	0.779090	+	0.626912i	$0.215681\pi$
$374$	−23.4848			−1.21437
$375$	−17.0661	−	9.15146i	−0.881288	−	0.472579i
$376$	0.736416			0.0379777
$377$	5.83710	−	5.83710i	0.300626	−	0.300626i
$378$	−1.70224	−	3.04495i	−0.0875538	−	0.156615i
$379$			19.7134i			1.01261i	0.862354	+	0.506305i	$0.168989\pi$
$379$			19.7134i			1.01261i	−0.862354	+	0.506305i	$0.831011\pi$
$380$	0.769189	−	3.42827i	0.0394586	−	0.175867i
$381$	19.1115	−	27.0277i	0.979110	−	1.38467i
$382$	−0.576673	−	0.576673i	−0.0295051	−	0.0295051i
$383$	1.75110	+	1.75110i	0.0894769	+	0.0894769i	0.750428	−	0.660952i	$-0.229847\pi$
$383$	1.75110	+	1.75110i	0.0894769	+	0.0894769i	−0.660952	+	0.750428i	$0.729847\pi$
$384$	1.00000	−	1.41421i	0.0510310	−	0.0721688i
$385$	3.28220	+	5.18108i	0.167277	+	0.264052i
$386$			8.03786i			0.409116i
$387$	−2.13380	+	4.46784i	−0.108467	+	0.227113i
$388$	8.34915	−	8.34915i	0.423864	−	0.423864i
$389$	13.1089			0.664649			0.332324	−	0.943165i	$-0.392167\pi$
$389$	13.1089			0.664649			0.332324	+	0.943165i	$0.392167\pi$
$390$	−0.863870	+	16.9931i	−0.0437438	+	0.860480i
$391$	8.62111			0.435988
$392$	−4.63104	+	4.63104i	−0.233903	+	0.233903i
$393$	24.9136	−	4.27449i	1.25672	−	0.215620i
$394$			25.9572i			1.30771i
$395$	−19.9136	−	4.46793i	−1.00196	−	0.224806i
$396$	−11.5557	+	4.08557i	−0.580697	+	0.205307i
$397$	−5.49522	−	5.49522i	−0.275797	−	0.275797i	0.555631	−	0.831429i	$-0.312477\pi$
$397$	−5.49522	−	5.49522i	−0.275797	−	0.275797i	−0.831429	+	0.555631i	$0.812477\pi$
$398$	11.3941	+	11.3941i	0.571135	+	0.571135i
$399$	1.49184	+	1.05489i	0.0746853	+	0.0528105i
$400$	4.52072	+	2.13613i	0.226036	+	0.106806i
$401$			2.83575i			0.141611i	0.997490	+	0.0708053i	$0.0225569\pi$
$401$			2.83575i			0.141611i	−0.997490	+	0.0708053i	$0.977443\pi$
$402$	2.22529	+	12.9699i	0.110987	+	0.646882i
$403$	−3.10651	+	3.10651i	−0.154746	+	0.154746i
$404$	−12.5702			−0.625392
$405$	8.91557	+	18.0420i	0.443018	+	0.896513i
$406$	1.26147			0.0626055
$407$	8.17113	−	8.17113i	0.405028	−	0.405028i
$408$	−1.68362	−	9.81287i	−0.0833517	−	0.485809i
$409$			3.01333i			0.148999i	0.997221	+	0.0744997i	$0.0237360\pi$
$409$			3.01333i			0.148999i	−0.997221	+	0.0744997i	$0.976264\pi$
$410$	−13.7204	+	8.69186i	−0.677603	+	0.429260i
$411$	−12.4550	−	8.80704i	−0.614362	−	0.434419i
$412$	0.449657	+	0.449657i	0.0221530	+	0.0221530i
$413$	−2.09139	−	2.09139i	−0.102911	−	0.102911i
$414$	4.24202	−	1.49978i	0.208484	−	0.0737102i
$415$	22.3267	−	14.1439i	1.09598	−	0.694298i
$416$		−	4.39327i		−	0.215398i
$417$	−2.31309	+	0.396863i	−0.113272	+	0.0194345i
$418$	4.53934	−	4.53934i	0.222026	−	0.222026i
$419$	−39.6972			−1.93934			−0.969669	−	0.244423i	$-0.921401\pi$
$419$	−39.6972			−1.93934			−0.969669	+	0.244423i	$0.921401\pi$
$420$	−1.92955	+	1.74286i	−0.0941525	+	0.0850429i
$421$	6.85743			0.334210			0.167105	−	0.985939i	$-0.446558\pi$
$421$	6.85743			0.334210			0.167105	+	0.985939i	$0.446558\pi$
$422$	−17.7675	+	17.7675i	−0.864908	+	0.864908i
$423$	0.952107	−	1.99356i	0.0462930	−	0.0969300i
$424$			3.51205i			0.170560i
$425$	27.0576	−	9.69248i	1.31249	−	0.470154i
$426$	4.42871	−	6.26315i	0.214572	−	0.303450i
$427$	−5.33297	−	5.33297i	−0.258081	−	0.258081i
$428$	5.00412	+	5.00412i	0.241883	+	0.241883i
$429$	−17.9490	+	25.3837i	−0.866586	+	1.22554i
$430$	3.60091	+	0.807922i	0.173651	+	0.0389615i
$431$			7.58473i			0.365343i	0.983174	+	0.182672i	$0.0584746\pi$
$431$			7.58473i			0.365343i	−0.983174	+	0.182672i	$0.941525\pi$
$432$	−2.53553	−	4.53553i	−0.121991	−	0.218216i
$433$	6.55340	−	6.55340i	0.314936	−	0.314936i	−0.531882	−	0.846818i	$-0.678515\pi$
$433$	6.55340	−	6.55340i	0.314936	−	0.314936i	0.846818	+	0.531882i	$0.178515\pi$
$434$	−0.671354			−0.0322260
$435$	−7.26791	−	0.369475i	−0.348470	−	0.0177150i
$436$	7.47661			0.358064
$437$	−1.66636	+	1.66636i	−0.0797127	+	0.0797127i
$438$	18.9950	−	3.25903i	0.907616	−	0.155722i
$439$		−	11.1508i		−	0.532199i	−0.963946	−	0.266100i	$-0.914265\pi$
$439$		−	11.1508i		−	0.532199i	0.963946	−	0.266100i	$-0.0857350\pi$
$440$	4.88893	+	7.71736i	0.233071	+	0.367911i
$441$	6.54928	+	18.5242i	0.311871	+	0.882104i
$442$	−17.8570	−	17.8570i	−0.849370	−	0.849370i
$443$	3.68595	+	3.68595i	0.175125	+	0.175125i	0.789227	−	0.614102i	$-0.210482\pi$
$443$	3.68595	+	3.68595i	0.175125	+	0.175125i	−0.614102	+	0.789227i	$0.710482\pi$
$444$	4.00000	+	2.82843i	0.189832	+	0.134231i
$445$	−2.78654	+	12.4196i	−0.132095	+	0.588745i
$446$			5.10322i			0.241645i
$447$	5.96942	+	34.7923i	0.282344	+	1.64562i
$448$	0.474719	−	0.474719i	0.0224283	−	0.0224283i
$449$	−12.8111			−0.604592			−0.302296	−	0.953214i	$-0.597753\pi$
$449$	−12.8111			−0.604592			−0.302296	+	0.953214i	$0.597753\pi$
$450$	11.6275	−	9.47630i	0.548128	−	0.446717i
$451$	−29.6759			−1.39738
$452$	−6.30315	+	6.30315i	−0.296475	+	0.296475i
$453$	5.70320	+	33.2407i	0.267960	+	1.56178i
$454$		−	22.9222i		−	1.07579i
$455$	−1.44383	+	6.43516i	−0.0676879	+	0.301685i
$456$	2.22214	+	1.57129i	0.104061	+	0.0735823i
$457$	20.8096	+	20.8096i	0.973431	+	0.973431i	0.999656	−	0.0262250i	$-0.00834864\pi$
$457$	20.8096	+	20.8096i	0.973431	+	0.973431i	−0.0262250	+	0.999656i	$0.508349\pi$
$458$	4.69685	+	4.69685i	0.219470	+	0.219470i
$459$	−28.7412	−	8.12925i	−1.34153	−	0.379441i
$460$	−1.79469	−	2.83298i	−0.0836778	−	0.132089i
$461$			10.0281i			0.467056i	0.972350	+	0.233528i	$0.0750271\pi$
$461$			10.0281i			0.467056i	−0.972350	+	0.233528i	$0.924973\pi$
$462$	−4.68235	+	0.803365i	−0.217843	+	0.0373759i
$463$	−3.28991	+	3.28991i	−0.152895	+	0.152895i	−0.779410	−	0.626515i	$-0.784481\pi$
$463$	−3.28991	+	3.28991i	−0.152895	+	0.152895i	0.626515	+	0.779410i	$0.284481\pi$
$464$	1.87899			0.0872299
$465$	3.86799	+	0.196635i	0.179374	+	0.00911873i
$466$	−12.9421			−0.599532
$467$	11.2120	−	11.2120i	0.518828	−	0.518828i	−0.398389	−	0.917217i	$-0.630431\pi$
$467$	11.2120	−	11.2120i	0.518828	−	0.518828i	0.917217	+	0.398389i	$0.130431\pi$
$468$	−11.8931	−	5.68003i	−0.549756	−	0.262559i
$469$			5.10069i			0.235528i
$470$	−1.60673	−	0.360496i	−0.0741129	−	0.0166284i
$471$	−2.06822	+	2.92490i	−0.0952984	+	0.134772i
$472$	−3.11519	−	3.11519i	−0.143388	−	0.143388i
$473$	4.76792	+	4.76792i	0.219229	+	0.219229i
$474$	9.12702	−	12.9075i	0.419218	−	0.592863i
$475$	−3.35647	+	7.10336i	−0.154006	+	0.325924i
$476$		−	3.85911i		−	0.176882i
$477$	9.50749	+	4.54070i	0.435318	+	0.207905i
$478$	18.7716	−	18.7716i	0.858593	−	0.858593i
$479$	−5.88990			−0.269116			−0.134558	−	0.990906i	$-0.542961\pi$
$479$	−5.88990			−0.269116			−0.134558	+	0.990906i	$0.542961\pi$
$480$	−2.87412	+	2.59604i	−0.131185	+	0.118492i
$481$	12.4260			0.566579
$482$	−2.55034	+	2.55034i	−0.116165	+	0.116165i
$483$	1.71886	−	0.294909i	0.0782107	−	0.0134188i
$484$			5.69186i			0.258721i
$485$	−22.3035	+	14.1292i	−1.01275	+	0.641576i
$486$	−15.5563	+	1.00000i	−0.705650	+	0.0453609i
$487$	24.5134	+	24.5134i	1.11081	+	1.11081i	0.993041	+	0.117767i	$0.0375736\pi$
$487$	24.5134	+	24.5134i	1.11081	+	1.11081i	0.117767	+	0.993041i	$0.462426\pi$
$488$	−7.94361	−	7.94361i	−0.359590	−	0.359590i
$489$	5.34271	+	3.77786i	0.241606	+	0.170841i
$490$	12.3712	−	7.83710i	0.558872	−	0.354044i
$491$			24.6711i			1.11339i	0.830717	+	0.556696i	$0.187931\pi$
$491$			24.6711i			1.11339i	−0.830717	+	0.556696i	$0.812069\pi$
$492$	−2.12745	−	12.3997i	−0.0959131	−	0.559022i
$493$	7.63739	−	7.63739i	0.343971	−	0.343971i
$494$	6.90309			0.310585
$495$	27.2126	−	3.25714i	1.22311	−	0.146398i
$496$	−1.00000			−0.0449013
$497$	2.10239	−	2.10239i	0.0943052	−	0.0943052i
$498$	3.46193	+	20.1776i	0.155133	+	0.904179i
$499$		−	38.4311i		−	1.72041i	−0.509945	−	0.860207i	$-0.670334\pi$
$499$		−	38.4311i		−	1.72041i	0.509945	−	0.860207i	$-0.329666\pi$
$500$	−8.81774	−	6.87368i	−0.394341	−	0.307400i
$501$	6.74930	+	4.77248i	0.301537	+	0.213219i
$502$	12.9158	+	12.9158i	0.576460	+	0.576460i
$503$	17.8215	+	17.8215i	0.794623	+	0.794623i	0.982242	−	0.187619i	$-0.0600769\pi$
$503$	17.8215	+	17.8215i	0.794623	+	0.794623i	−0.187619	+	0.982242i	$0.560077\pi$
$504$	−0.671354	−	1.89887i	−0.0299045	−	0.0845826i
$505$	27.4260	+	6.15348i	1.22044	+	0.273826i
$506$		−	6.12745i		−	0.272399i
$507$	−10.7562	+	1.84547i	−0.477698	+	0.0819601i
$508$	13.5138	−	13.5138i	0.599580	−	0.599580i
$509$	−26.2585			−1.16389			−0.581944	−	0.813229i	$-0.697708\pi$
$509$	−26.2585			−1.16389			−0.581944	+	0.813229i	$0.697708\pi$
$510$	−1.13031	+	22.2341i	−0.0500508	+	0.984545i
$511$	7.47016			0.330460
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	7.12663	−	3.98405i	0.314648	−	0.175900i
$514$		−	25.3682i		−	1.11894i
$515$	−0.760953	−	1.20119i	−0.0335316	−	0.0529308i
$516$	−1.65041	+	2.33403i	−0.0726552	+	0.102750i
$517$	−2.12745	−	2.12745i	−0.0935653	−	0.0935653i
$518$	1.34271	+	1.34271i	0.0589952	+	0.0589952i
$519$	−17.8453	+	25.2371i	−0.783323	+	1.10779i
$520$	−2.15063	+	9.58535i	−0.0943113	+	0.420345i
$521$		−	27.7886i		−	1.21744i	−0.793384	−	0.608721i	$-0.791683\pi$
$521$		−	27.7886i		−	1.21744i	0.793384	−	0.608721i	$-0.208317\pi$
$522$	2.42933	−	5.08663i	0.106329	−	0.222636i
$523$	−18.1124	+	18.1124i	−0.792001	+	0.792001i	−0.981819	−	0.189818i	$-0.939210\pi$
$523$	−18.1124	+	18.1124i	−0.792001	+	0.792001i	0.189818	+	0.981819i	$0.439210\pi$
$524$	14.5940			0.637543
$525$	5.06313	−	2.85805i	0.220973	−	0.124735i
$526$	−13.1502			−0.573376
$527$	−4.06462	+	4.06462i	−0.177058	+	0.177058i
$528$	−6.97450	+	1.19663i	−0.303526	+	0.0520768i
$529$		−	20.7507i		−	0.902203i
$530$	1.71925	−	7.66268i	0.0746793	−	0.332845i
$531$	−12.4607	+	4.40554i	−0.540750	+	0.191184i
$532$	0.745919	+	0.745919i	0.0323397	+	0.0323397i
$533$	−22.5644	−	22.5644i	−0.977373	−	0.977373i
$534$	−8.05012	−	5.69230i	−0.348363	−	0.246330i
$535$	−8.46846	−	13.3678i	−0.366123	−	0.577939i
$536$			7.59762i			0.328167i
$537$	−6.65642	−	38.7964i	−0.287246	−	1.67419i
$538$	6.54390	−	6.54390i	0.282128	−	0.282128i
$539$	26.7575			1.15253
$540$	3.31182	+	11.1370i	0.142518	+	0.479258i
$541$	28.7637			1.23665			0.618323	−	0.785924i	$-0.287812\pi$
$541$	28.7637			1.23665			0.618323	+	0.785924i	$0.287812\pi$
$542$	20.3655	−	20.3655i	0.874775	−	0.874775i
$543$	3.11330	+	18.1456i	0.133604	+	0.778704i
$544$		−	5.74825i		−	0.246454i
$545$	−16.3126	−	3.66001i	−0.698757	−	0.156778i
$546$	−4.17113	−	2.94944i	−0.178508	−	0.126224i
$547$	−10.2072	−	10.2072i	−0.436428	−	0.436428i	0.454380	−	0.890808i	$-0.349861\pi$
$547$	−10.2072	−	10.2072i	−0.436428	−	0.436428i	−0.890808	+	0.454380i	$0.849861\pi$
$548$	−6.22752	−	6.22752i	−0.266027	−	0.266027i
$549$	−31.7745	+	11.2340i	−1.35610	+	0.479454i
$550$	−6.88893	−	19.2312i	−0.293745	−	0.820021i
$551$			2.95243i			0.125778i
$552$	2.56029	−	0.439276i	0.108973	−	0.0186968i
$553$	4.33276	−	4.33276i	0.184248	−	0.184248i
$554$	26.6344			1.13159
$555$	−7.34271	−	8.12925i	−0.311681	−	0.345067i
$556$	−1.35498			−0.0574638
$557$	−12.7383	+	12.7383i	−0.539739	+	0.539739i	−0.923452	−	0.383713i	$-0.874645\pi$
$557$	−12.7383	+	12.7383i	−0.539739	+	0.539739i	0.383713	+	0.923452i	$0.374645\pi$
$558$	−1.29289	+	2.70711i	−0.0547325	+	0.114601i
$559$			7.25070i			0.306672i
$560$	−1.26814	+	0.803365i	−0.0535888	+	0.0339484i
$561$	−23.4848	+	33.2126i	−0.991531	+	1.40224i
$562$	−8.94032	−	8.94032i	−0.377125	−	0.377125i
$563$	−1.84999	−	1.84999i	−0.0779678	−	0.0779678i	0.667047	−	0.745015i	$-0.267558\pi$
$563$	−1.84999	−	1.84999i	−0.0779678	−	0.0779678i	−0.745015	+	0.667047i	$0.767558\pi$
$564$	0.736416	−	1.04145i	0.0310087	−	0.0438529i
$565$	16.8379	−	10.6668i	0.708377	−	0.448756i
$566$		−	19.5358i		−	0.821153i
$567$	−6.00844	−	0.637616i	−0.252331	−	0.0267774i
$568$	3.13157	−	3.13157i	0.131398	−	0.131398i
$569$	−28.0100			−1.17424			−0.587121	−	0.809499i	$-0.699739\pi$
$569$	−28.0100			−1.17424			−0.587121	+	0.809499i	$0.699739\pi$
$570$	−4.07912	−	4.51607i	−0.170856	−	0.189157i
$571$	41.3740			1.73145			0.865724	−	0.500522i	$-0.166859\pi$
$571$	41.3740			1.73145			0.865724	+	0.500522i	$0.166859\pi$
$572$	−12.6919	+	12.6919i	−0.530673	+	0.530673i
$573$	−1.39221	+	0.238866i	−0.0581604	+	0.00997875i
$574$		−	4.87643i		−	0.203538i
$575$	2.52887	+	7.05963i	0.105461	+	0.294407i
$576$	−1.00000	−	2.82843i	−0.0416667	−	0.117851i
$577$	−3.56082	−	3.56082i	−0.148239	−	0.148239i	0.629092	−	0.777331i	$-0.283427\pi$
$577$	−3.56082	−	3.56082i	−0.148239	−	0.148239i	−0.777331	+	0.629092i	$0.783427\pi$
$578$	−11.3436	−	11.3436i	−0.471833	−	0.471833i
$579$	11.3672	+	8.03786i	0.472407	+	0.334042i
$580$	−4.09963	−	0.919818i	−0.170228	−	0.0381934i
$581$			7.93523i			0.329209i
$582$	−3.45833	−	20.1566i	−0.143352	−	0.835519i
$583$	10.1461	−	10.1461i	0.420207	−	0.420207i
$584$	11.1270			0.460439
$585$	23.1680	+	18.2148i	0.957880	+	0.753090i
$586$	28.6145			1.18206
$587$	17.7934	−	17.7934i	0.734413	−	0.734413i	−0.237078	−	0.971491i	$-0.576190\pi$
$587$	17.7934	−	17.7934i	0.734413	−	0.734413i	0.971491	+	0.237078i	$0.0761896\pi$
$588$	1.91824	+	11.1803i	0.0791069	+	0.461069i
$589$		−	1.57129i		−	0.0647438i
$590$	5.27182	+	8.32176i	0.217037	+	0.342602i
$591$	36.7091	+	25.9572i	1.51001	+	1.06774i
$592$	2.00000	+	2.00000i	0.0821995	+	0.0821995i
$593$	−33.6090	−	33.6090i	−1.38016	−	1.38016i	−0.844325	−	0.535832i	$-0.819998\pi$
$593$	−33.6090	−	33.6090i	−1.38016	−	1.38016i	−0.535832	−	0.844325i	$-0.680002\pi$
$594$	−5.77786	+	20.4278i	−0.237069	+	0.838164i
$595$	−1.88914	+	8.41989i	−0.0774472	+	0.345182i
$596$			20.3809i			0.834833i
$597$	27.5078	−	4.71959i	1.12582	−	0.193160i
$598$	4.65908	−	4.65908i	0.190524	−	0.190524i
$599$	6.77010			0.276619			0.138309	−	0.990389i	$-0.455833\pi$
$599$	6.77010			0.276619			0.138309	+	0.990389i	$0.455833\pi$
$600$	7.54167	−	4.25714i	0.307887	−	0.173797i
$601$	45.8051			1.86843			0.934215	−	0.356711i	$-0.116102\pi$
$601$	45.8051			1.86843			0.934215	+	0.356711i	$0.116102\pi$
$602$	−0.783480	+	0.783480i	−0.0319323	+	0.0319323i
$603$	20.5676	+	9.82291i	0.837576	+	0.400020i
$604$			19.4720i			0.792303i
$605$	2.78632	−	12.4186i	0.113280	−	0.504890i
$606$	−12.5702	+	17.7770i	−0.510631	+	0.722141i
$607$	20.7241	+	20.7241i	0.841165	+	0.841165i	0.989010	−	0.147845i	$-0.0472338\pi$
$607$	20.7241	+	20.7241i	0.841165	+	0.841165i	−0.147845	+	0.989010i	$0.547234\pi$
$608$	1.11107	+	1.11107i	0.0450597	+	0.0450597i
$609$	1.26147	−	1.78398i	0.0511172	−	0.0722906i
$610$	13.4430	+	21.2202i	0.544289	+	0.859181i
$611$		−	3.23527i		−	0.130885i
$612$	−15.5611	−	7.43187i	−0.629021	−	0.300415i
$613$	−25.8175	+	25.8175i	−1.04276	+	1.04276i	−0.0437155	+	0.999044i	$0.513920\pi$
$613$	−25.8175	+	25.8175i	−1.04276	+	1.04276i	−0.999044	+	0.0437155i	$0.986080\pi$
$614$	−10.8392			−0.437434
$615$	−1.42827	+	28.0955i	−0.0575936	+	1.13292i
$616$	−2.74286			−0.110513
$617$	−13.0922	+	13.0922i	−0.527073	+	0.527073i	−0.919698	−	0.392626i	$-0.871567\pi$
$617$	−13.0922	+	13.0922i	−0.527073	+	0.527073i	0.392626	+	0.919698i	$0.371567\pi$
$618$	1.08557	−	0.186254i	0.0436679	−	0.00749223i
$619$			6.70426i			0.269467i	0.990882	+	0.134734i	$0.0430178\pi$
$619$			6.70426i			0.269467i	−0.990882	+	0.134734i	$0.956982\pi$
$620$	2.18183	+	0.489528i	0.0876242	+	0.0196599i
$621$	2.12101	−	7.49890i	0.0851132	−	0.300921i
$622$	20.1743	+	20.1743i	0.808915	+	0.808915i
$623$	−2.70224	−	2.70224i	−0.108263	−	0.108263i
$624$	−6.21302	−	4.39327i	−0.248720	−	0.175872i
$625$	15.8739	+	19.3137i	0.634956	+	0.772548i
$626$		−	32.6672i		−	1.30564i
$627$	−1.88026	−	10.9589i	−0.0750902	−	0.437658i
$628$	−1.46245	+	1.46245i	−0.0583581	+	0.0583581i
$629$	16.2585			0.648269
$630$	0.535224	+	4.47166i	0.0213238	+	0.178155i
$631$	−20.5580			−0.818399			−0.409200	−	0.912445i	$-0.634192\pi$
$631$	−20.5580			−0.818399			−0.409200	+	0.912445i	$0.634192\pi$
$632$	6.45377	−	6.45377i	0.256717	−	0.256717i
$633$	7.35953	+	42.8945i	0.292515	+	1.70490i
$634$			16.0199i			0.636231i
$635$	−36.1002	+	22.8694i	−1.43259	+	0.907546i
$636$	4.96679	+	3.51205i	0.196946	+	0.139262i
$637$	20.3454	+	20.3454i	0.806115	+	0.806115i
$638$	−5.42827	−	5.42827i	−0.214907	−	0.214907i
$639$	−4.42871	−	12.5263i	−0.175197	−	0.495532i
$640$	−1.88893	+	1.19663i	−0.0746666	+	0.0473011i
$641$		−	21.5740i		−	0.852120i	−0.904695	−	0.426060i	$-0.859901\pi$
$641$		−	21.5740i		−	0.852120i	0.904695	−	0.426060i	$-0.140099\pi$
$642$	12.0810	−	2.07277i	0.476799	−	0.0818059i
$643$	−21.5307	+	21.5307i	−0.849087	+	0.849087i	−0.990019	−	0.140933i	$-0.954990\pi$
$643$	−21.5307	+	21.5307i	−0.849087	+	0.849087i	0.140933	+	0.990019i	$0.454990\pi$
$644$	1.00688			0.0396768
$645$	4.74348	−	4.28453i	0.186774	−	0.168703i
$646$	9.03214			0.355365
$647$	10.5743	−	10.5743i	0.415720	−	0.415720i	−0.468005	−	0.883726i	$-0.655027\pi$
$647$	10.5743	−	10.5743i	0.415720	−	0.415720i	0.883726	+	0.468005i	$0.155027\pi$
$648$	−8.94975	−	0.949747i	−0.351579	−	0.0373096i
$649$			17.9991i			0.706527i
$650$	9.38459	−	19.8608i	0.368094	−	0.779003i
$651$	−0.671354	+	0.949437i	−0.0263124	+	0.0372114i
$652$	2.67135	+	2.67135i	0.104618	+	0.104618i
$653$	−21.0078	−	21.0078i	−0.822099	−	0.822099i	0.164310	−	0.986409i	$-0.447460\pi$
$653$	−21.0078	−	21.0078i	−0.822099	−	0.822099i	−0.986409	+	0.164310i	$0.947460\pi$
$654$	7.47661	−	10.5735i	0.292358	−	0.413457i
$655$	−31.8416	−	7.14418i	−1.24415	−	0.279146i
$656$		−	7.26358i		−	0.283595i
$657$	14.3860	−	30.1220i	0.561253	−	1.17517i
$658$	0.349590	−	0.349590i	0.0136284	−	0.0136284i
$659$	26.4009			1.02843			0.514216	−	0.857661i	$-0.328083\pi$
$659$	26.4009			1.02843			0.514216	+	0.857661i	$0.328083\pi$
$660$	15.8029	+	0.803365i	0.615128	+	0.0312709i
$661$	−29.3162			−1.14027			−0.570135	−	0.821551i	$-0.693109\pi$
$661$	−29.3162			−1.14027			−0.570135	+	0.821551i	$0.693109\pi$
$662$	−13.9140	+	13.9140i	−0.540783	+	0.540783i
$663$	−43.1106	+	7.39661i	−1.67428	+	0.287260i
$664$			11.8198i			0.458695i
$665$	−1.26232	−	1.99261i	−0.0489506	−	0.0772703i
$666$	8.00000	−	2.82843i	0.309994	−	0.109599i
$667$	1.99268	+	1.99268i	0.0771568	+	0.0771568i
$668$	3.37465	+	3.37465i	0.130569	+	0.130569i
$669$	7.21704	+	5.10322i	0.279027	+	0.197302i
$670$	3.71925	−	16.5767i	0.143687	−	0.640413i
$671$			45.8971i			1.77184i
$672$	−0.196635	−	1.14607i	−0.00758536	−	0.0442107i
$673$	−21.6844	+	21.6844i	−0.835870	+	0.835870i	−0.988312	−	0.152442i	$-0.951286\pi$
$673$	−21.6844	+	21.6844i	−0.835870	+	0.835870i	0.152442	+	0.988312i	$0.451286\pi$
$674$	−4.81554			−0.185488
$675$	−1.77396	−	25.9201i	−0.0682798	−	0.997666i
$676$	−6.30082			−0.242339
$677$	−31.1572	+	31.1572i	−1.19747	+	1.19747i	−0.222544	+	0.974923i	$0.571436\pi$
$677$	−31.1572	+	31.1572i	−1.19747	+	1.19747i	−0.974923	+	0.222544i	$0.928564\pi$
$678$	2.61085	+	15.2171i	0.100269	+	0.584411i
$679$		−	7.92700i		−	0.304210i
$680$	−2.81393	+	12.5417i	−0.107909	+	0.480951i
$681$	−32.4169	−	22.9222i	−1.24222	−	0.878382i
$682$	2.88893	+	2.88893i	0.110623	+	0.110623i
$683$	27.6523	+	27.6523i	1.05809	+	1.05809i	0.998206	+	0.0598802i	$0.0190719\pi$
$683$	27.6523	+	27.6523i	1.05809	+	1.05809i	0.0598802	+	0.998206i	$0.480928\pi$
$684$	4.44427	−	1.57129i	0.169931	−	0.0600797i
$685$	10.5388	+	16.6359i	0.402668	+	0.635625i
$686$			9.09636i			0.347301i
$687$	11.3392	−	1.94550i	0.432618	−	0.0742255i
$688$	−1.16702	+	1.16702i	−0.0444921	+	0.0444921i
$689$	15.4294			0.587813
$690$	−5.80113	−	0.294909i	−0.220845	−	0.0112270i
$691$	−13.4710			−0.512462			−0.256231	−	0.966616i	$-0.582481\pi$
$691$	−13.4710			−0.512462			−0.256231	+	0.966616i	$0.582481\pi$
$692$	−12.6186	+	12.6186i	−0.479686	+	0.479686i
$693$	−3.54623	+	7.42521i	−0.134710	+	0.282061i
$694$		−	12.3759i		−	0.469783i
$695$	2.95632	+	0.663299i	0.112140	+	0.0251604i
$696$	1.87899	−	2.65729i	0.0712229	−	0.100724i
$697$	−29.5237	−	29.5237i	−1.11829	−	1.11829i
$698$	21.6972	+	21.6972i	0.821253	+	0.821253i
$699$	−12.9421	+	18.3029i	−0.489516	+	0.692280i
$700$	3.16013	−	1.13201i	0.119442	−	0.0427860i
$701$			6.91995i			0.261363i	0.991424	+	0.130682i	$0.0417165\pi$
$701$			6.91995i			0.261363i	−0.991424	+	0.130682i	$0.958283\pi$
$702$	−19.9258	+	11.1393i	−0.752052	+	0.420425i
$703$	−3.14257	+	3.14257i	−0.118524	+	0.118524i
$704$	−4.08557			−0.153981
$705$	−2.11655	+	1.91176i	−0.0797138	+	0.0720012i
$706$	5.92849			0.223122
$707$	−5.96732	+	5.96732i	−0.224424	+	0.224424i
$708$	−7.52072	+	1.29035i	−0.282646	+	0.0484944i
$709$		−	19.1112i		−	0.717735i	−0.933389	−	0.358867i	$-0.883163\pi$
$709$		−	19.1112i		−	0.717735i	0.933389	−	0.358867i	$-0.116837\pi$
$710$	−8.36554	+	5.29955i	−0.313953	+	0.198889i
$711$	−9.12702	−	25.8151i	−0.342290	−	0.968142i
$712$	−4.02506	−	4.02506i	−0.150846	−	0.150846i
$713$	−1.06051	−	1.06051i	−0.0397162	−	0.0397162i
$714$	−5.45760	−	3.85911i	−0.204245	−	0.144423i
$715$	33.9044	−	21.4784i	1.26795	−	0.803247i
$716$		−	22.7264i		−	0.849326i
$717$	−7.77545	−	45.3187i	−0.290380	−	1.69246i
$718$	4.91855	−	4.91855i	0.183559	−	0.183559i
$719$	40.0027			1.49185			0.745925	−	0.666030i	$-0.232008\pi$
$719$	40.0027			1.49185			0.745925	+	0.666030i	$0.232008\pi$
$720$	0.797231	+	6.66066i	0.0297110	+	0.248228i
$721$	0.426921			0.0158994
$722$	11.6892	−	11.6892i	0.435028	−	0.435028i
$723$	1.05639	+	6.15707i	0.0392874	+	0.228984i
$724$			10.6295i			0.395041i
$725$	8.49440	+	4.01377i	0.315474	+	0.149068i
$726$	8.04950	+	5.69186i	0.298745	+	0.211245i
$727$	−13.2741	−	13.2741i	−0.492311	−	0.492311i	0.416723	−	0.909034i	$-0.363179\pi$
$727$	−13.2741	−	13.2741i	−0.492311	−	0.492311i	−0.909034	+	0.416723i	$0.863179\pi$
$728$	−2.08557	−	2.08557i	−0.0772963	−	0.0772963i
$729$	−14.1421	+	23.0000i	−0.523783	+	0.851852i
$730$	−24.2772	−	5.44699i	−0.898540	−	0.201602i
$731$			9.48696i			0.350888i
$732$	−19.1776	+	3.29035i	−0.708824	+	0.121615i
$733$	−8.25491	+	8.25491i	−0.304902	+	0.304902i	−0.842928	−	0.538026i	$-0.819170\pi$
$733$	−8.25491	+	8.25491i	−0.304902	+	0.304902i	0.538026	+	0.842928i	$0.319170\pi$
$734$	5.27182			0.194586
$735$	1.28782	−	25.3326i	0.0475019	−	0.934405i
$736$	1.49978			0.0552826
$737$	21.9490	−	21.9490i	0.808502	−	0.808502i
$738$	−19.6633	−	9.39104i	−0.723816	−	0.345689i
$739$		−	27.7673i		−	1.02143i	−0.859749	−	0.510717i	$-0.829380\pi$
$739$		−	27.7673i		−	1.02143i	0.859749	−	0.510717i	$-0.170620\pi$
$740$	−3.38459	−	5.34271i	−0.124420	−	0.196402i
$741$	6.90309	−	9.76244i	0.253591	−	0.358632i
$742$	1.66724	+	1.66724i	0.0612061	+	0.0612061i
$743$	−22.1612	−	22.1612i	−0.813015	−	0.813015i	0.172070	−	0.985085i	$-0.444955\pi$
$743$	−22.1612	−	22.1612i	−0.813015	−	0.813015i	−0.985085	+	0.172070i	$0.944955\pi$
$744$	−1.00000	+	1.41421i	−0.0366618	+	0.0518476i
$745$	9.97701	−	44.4675i	0.365529	−	1.62916i
$746$		−	4.15645i		−	0.152179i
$747$	31.9973	+	15.2817i	1.17072	+	0.559127i
$748$	−16.6063	+	16.6063i	−0.607186	+	0.607186i
$749$	4.75110			0.173601
$750$	−18.5386	+	5.59648i	−0.676934	+	0.204354i
$751$	−14.3357			−0.523117			−0.261558	−	0.965188i	$-0.584236\pi$
$751$	−14.3357			−0.523117			−0.261558	+	0.965188i	$0.584236\pi$
$752$	0.520724	−	0.520724i	0.0189889	−	0.0189889i
$753$	31.1815	−	5.34989i	1.13632	−	0.194961i
$754$		−	8.25491i		−	0.300626i
$755$	9.53207	−	42.4844i	0.346908	−	1.54617i
$756$	−3.35677	−	0.949437i	−0.122084	−	0.0345307i
$757$	−32.6821	−	32.6821i	−1.18785	−	1.18785i	−0.977660	−	0.210192i	$-0.932591\pi$
$757$	−32.6821	−	32.6821i	−1.18785	−	1.18785i	−0.210192	−	0.977660i	$-0.567409\pi$
$758$	13.9395	+	13.9395i	0.506305	+	0.506305i
$759$	−8.66553	−	6.12745i	−0.314539	−	0.222413i
$760$	−1.88026	−	2.96805i	−0.0682041	−	0.107663i
$761$			15.8679i			0.575211i	0.957749	+	0.287605i	$0.0928591\pi$
$761$			15.8679i			0.575211i	−0.957749	+	0.287605i	$0.907141\pi$
$762$	−5.59762	−	32.6253i	−0.202780	−	1.18189i
$763$	3.54928	−	3.54928i	0.128493	−	0.128493i
$764$	−0.815538			−0.0295051
$765$	30.3135	+	23.8326i	1.09599	+	0.861671i
$766$	2.47642			0.0894769
$767$	−13.6859	+	13.6859i	−0.494168	+	0.494168i
$768$	−0.292893	−	1.70711i	−0.0105689	−	0.0615999i
$769$		−	25.7022i		−	0.926845i	−0.886138	−	0.463422i	$-0.846621\pi$
$769$		−	25.7022i		−	0.926845i	0.886138	−	0.463422i	$-0.153379\pi$
$770$	5.98444	+	1.34271i	0.215664	+	0.0483878i
$771$	−35.8760	−	25.3682i	−1.29204	−	0.913612i
$772$	5.68362	+	5.68362i	0.204558	+	0.204558i
$773$	29.4146	+	29.4146i	1.05797	+	1.05797i	0.998213	+	0.0597568i	$0.0190325\pi$
$773$	29.4146	+	29.4146i	1.05797	+	1.05797i	0.0597568	+	0.998213i	$0.480967\pi$
$774$	1.65041	+	4.66806i	0.0593228	+	0.167790i
$775$	−4.52072	−	2.13613i	−0.162389	−	0.0767320i
$776$		−	11.8075i		−	0.423864i
$777$	3.24158	−	0.556167i	0.116291	−	0.0199524i
$778$	9.26941	−	9.26941i	0.332324	−	0.332324i
$779$	11.4132			0.408919
$780$	11.4051	+	12.6268i	0.408368	+	0.452112i
$781$	−18.0938			−0.647447
$782$	6.09604	−	6.09604i	0.217994	−	0.217994i
$783$	−4.76424	−	8.52222i	−0.170260	−	0.304559i
$784$			6.54928i			0.233903i
$785$	3.90672	−	2.47490i	0.139437	−	0.0883330i
$786$	14.5940	−	20.6391i	0.520552	−	0.736171i
$787$	5.55205	+	5.55205i	0.197909	+	0.197909i	0.799103	−	0.601194i	$-0.205308\pi$
$787$	5.55205	+	5.55205i	0.197909	+	0.197909i	−0.601194	+	0.799103i	$0.705308\pi$
$788$	18.3545	+	18.3545i	0.653853	+	0.653853i
$789$	−13.1502	+	18.5972i	−0.468159	+	0.662077i
$790$	−17.2403	+	10.9217i	−0.613383	+	0.388577i
$791$			5.98444i			0.212782i
$792$	−5.28220	+	11.0601i	−0.187695	+	0.393002i
$793$	−34.8984	+	34.8984i	−1.23928	+	1.23928i
$794$	−7.77142			−0.275797
$795$	−9.11742	−	10.0941i	−0.323361	−	0.357999i
$796$	16.1137			0.571135
$797$	−1.64459	+	1.64459i	−0.0582542	+	0.0582542i	−0.735634	−	0.677380i	$-0.763116\pi$
$797$	−1.64459	+	1.64459i	−0.0582542	+	0.0582542i	0.677380	+	0.735634i	$0.263116\pi$
$798$	1.80081	−	0.308970i	0.0637479	−	0.0109374i
$799$		−	4.23310i		−	0.149756i
$800$	4.70711	−	1.68616i	0.166421	−	0.0596149i
$801$	−16.1002	+	5.69230i	−0.568874	+	0.201127i
$802$	2.00518	+	2.00518i	0.0708053	+	0.0708053i
$803$	−32.1452	−	32.1452i	−1.13438	−	1.13438i
$804$	10.7447	+	7.59762i	0.378935	+	0.267947i
$805$	−2.19684	−	0.492898i	−0.0774285	−	0.0173724i
$806$			4.39327i			0.154746i
$807$	−2.71057	−	15.7984i	−0.0954166	−	0.556129i
$808$	−8.88849	+	8.88849i	−0.312696	+	0.312696i
$809$	−36.8202			−1.29453			−0.647265	−	0.762265i	$-0.724087\pi$
$809$	−36.8202			−1.29453			−0.647265	+	0.762265i	$0.724087\pi$
$810$	19.0619	+	6.45334i	0.669765	+	0.226747i
$811$	51.4403			1.80631			0.903156	−	0.429312i	$-0.141244\pi$
$811$	51.4403			1.80631			0.903156	+	0.429312i	$0.141244\pi$
$812$	0.891992	−	0.891992i	0.0313028	−	0.0313028i
$813$	−8.43568	−	49.1668i	−0.295852	−	1.72435i
$814$		−	11.5557i		−	0.405028i
$815$	−4.52072	−	7.13613i	−0.158354	−	0.249968i
$816$	−8.12925	−	5.74825i	−0.284581	−	0.201229i
$817$	−1.83372	−	1.83372i	−0.0641536	−	0.0641536i
$818$	2.13074	+	2.13074i	0.0744997	+	0.0744997i
$819$	−8.34227	+	2.94944i	−0.291502	+	0.103062i
$820$	−3.55573	+	15.8479i	−0.124171	+	0.553432i
$821$		−	26.0911i		−	0.910587i	−0.890341	−	0.455293i	$-0.849534\pi$
$821$		−	26.0911i		−	0.910587i	0.890341	−	0.455293i	$-0.150466\pi$
$822$	−15.0346	+	2.57952i	−0.524391	+	0.0899712i
$823$	1.58219	−	1.58219i	0.0551518	−	0.0551518i	−0.678993	−	0.734145i	$-0.737583\pi$
$823$	1.58219	−	1.58219i	0.0551518	−	0.0551518i	0.734145	+	0.678993i	$0.237583\pi$
$824$	0.635910			0.0221530
$825$	−34.0860	−	9.48878i	−1.18672	−	0.330357i
$826$	−2.95767			−0.102911
$827$	−32.0545	+	32.0545i	−1.11464	+	1.11464i	−0.122128	+	0.992514i	$0.538972\pi$
$827$	−32.0545	+	32.0545i	−1.11464	+	1.11464i	−0.992514	+	0.122128i	$0.961028\pi$
$828$	1.93906	−	4.06007i	0.0673869	−	0.141097i
$829$			19.2021i			0.666917i	0.942765	+	0.333458i	$0.108216\pi$
$829$			19.2021i			0.666917i	−0.942765	+	0.333458i	$0.891784\pi$
$830$	5.78610	−	25.7886i	0.200838	−	0.895137i
$831$	26.6344	−	37.6667i	0.923938	−	1.30665i
$832$	−3.10651	−	3.10651i	−0.107699	−	0.107699i
$833$	26.6204	+	26.6204i	0.922341	+	0.922341i
$834$	−1.35498	+	1.91622i	−0.0469190	+	0.0663534i
$835$	−5.71091	−	9.01489i	−0.197634	−	0.311973i
$836$		−	6.41960i		−	0.222026i
$837$	2.53553	+	4.53553i	0.0876409	+	0.156771i
$838$	−28.0702	+	28.0702i	−0.969669	+	0.969669i
$839$	−4.58696			−0.158359			−0.0791797	−	0.996860i	$-0.525230\pi$
$839$	−4.58696			−0.158359			−0.0791797	+	0.996860i	$0.525230\pi$
$840$	−0.132012	+	2.59679i	−0.00455483	+	0.0895977i
$841$	−25.4694			−0.878255
$842$	4.84893	−	4.84893i	0.167105	−	0.167105i
$843$	−21.5839	+	3.70320i	−0.743387	+	0.127545i
$844$			25.1270i			0.864908i
$845$	13.7473	+	3.08443i	0.472921	+	0.106108i
$846$	−0.736416	−	2.08290i	−0.0253185	−	0.0716115i
$847$	2.70203	+	2.70203i	0.0928429	+	0.0928429i
$848$	2.48339	+	2.48339i	0.0852801	+	0.0852801i
$849$	−27.6279	−	19.5358i	−0.948186	−	0.670468i
$850$	12.2790	−	25.9862i	0.421166	−	0.891320i
$851$			4.24202i			0.145415i
$852$	−1.29714	−	7.56029i	−0.0444393	−	0.259011i
$853$	−28.9519	+	28.9519i	−0.991296	+	0.991296i	−0.999962	−	0.00866672i	$-0.997241\pi$
$853$	−28.9519	+	28.9519i	−0.991296	+	0.991296i	0.00866672	+	0.999962i	$0.497241\pi$
$854$	−7.54196			−0.258081
$855$	−10.4658	+	1.25268i	−0.357923	+	0.0428407i
$856$	7.07689			0.241883
$857$	20.9236	−	20.9236i	0.714736	−	0.714736i	−0.252786	−	0.967522i	$-0.581347\pi$
$857$	20.9236	−	20.9236i	0.714736	−	0.714736i	0.967522	+	0.252786i	$0.0813468\pi$
$858$	5.25714	+	30.6409i	0.179476	+	1.04606i
$859$		−	41.8628i		−	1.42834i	−0.699971	−	0.714171i	$-0.746804\pi$
$859$		−	41.8628i		−	1.42834i	0.699971	−	0.714171i	$-0.253196\pi$
$860$	3.11751	−	1.97494i	0.106306	−	0.0673448i
$861$	−6.89632	−	4.87643i	−0.235026	−	0.166188i
$862$	5.36321	+	5.36321i	0.182672	+	0.182672i
$863$	−14.0730	−	14.0730i	−0.479049	−	0.479049i	0.425778	−	0.904827i	$-0.360000\pi$
$863$	−14.0730	−	14.0730i	−0.479049	−	0.479049i	−0.904827	+	0.425778i	$0.860000\pi$
$864$	−5.00000	−	1.41421i	−0.170103	−	0.0481125i
$865$	33.7086	−	21.3544i	1.14613	−	0.726070i
$866$		−	9.26791i		−	0.314936i
$867$	−27.3860	+	4.69869i	−0.930076	+	0.159576i
$868$	−0.474719	+	0.474719i	−0.0161130	+	0.0161130i
$869$	−37.2890			−1.26494
$870$	−5.40045	+	4.87793i	−0.183092	+	0.165377i
$871$	33.3784			1.13098
$872$	5.28676	−	5.28676i	0.179032	−	0.179032i
$873$	−31.9641	−	15.2658i	−1.08182	−	0.516670i
$874$			2.35659i			0.0797127i
$875$	−7.44901	+	0.922878i	−0.251822	+	0.0311990i
$876$	11.1270	−	15.7360i	0.375947	−	0.531669i
$877$	−25.1682	−	25.1682i	−0.849868	−	0.849868i	0.140248	−	0.990116i	$-0.455210\pi$
$877$	−25.1682	−	25.1682i	−0.849868	−	0.849868i	−0.990116	+	0.140248i	$0.955210\pi$
$878$	−7.88481	−	7.88481i	−0.266100	−	0.266100i
$879$	28.6145	−	40.4671i	0.965144	−	1.36492i
$880$	8.91399	+	2.00000i	0.300491	+	0.0674200i
$881$			55.8080i			1.88022i	0.340872	+	0.940110i	$0.389278\pi$
$881$			55.8080i			1.88022i	−0.340872	+	0.940110i	$0.610722\pi$
$882$	17.7296	+	8.46753i	0.596987	+	0.285116i
$883$	11.1283	−	11.1283i	0.374497	−	0.374497i	−0.494615	−	0.869112i	$-0.664691\pi$
$883$	11.1283	−	11.1283i	0.374497	−	0.374497i	0.869112	+	0.494615i	$0.164691\pi$
$884$	−25.2536			−0.849370
$885$	17.0406	+	0.866283i	0.572813	+	0.0291198i
$886$	5.21272			0.175125
$887$	27.8846	−	27.8846i	0.936272	−	0.936272i	−0.0618158	−	0.998088i	$-0.519689\pi$
$887$	27.8846	−	27.8846i	0.936272	−	0.936272i	0.998088	+	0.0618158i	$0.0196891\pi$
$888$	4.82843	−	0.828427i	0.162031	−	0.0278002i
$889$		−	12.8305i		−	0.430323i
$890$	6.81160	+	10.7524i	0.228325	+	0.360420i
$891$	23.1115	+	28.5990i	0.774263	+	0.958102i
$892$	3.60852	+	3.60852i	0.120822	+	0.120822i
$893$	0.818208	+	0.818208i	0.0273803	+	0.0273803i
$894$	28.8229	+	20.3809i	0.963982	+	0.681638i
$895$	−11.1252	+	49.5851i	−0.371875	+	1.65745i
$896$		−	0.671354i		−	0.0224283i
$897$	−1.92986	−	11.2480i	−0.0644360	−	0.375561i
$898$	−9.05880	+	9.05880i	−0.302296	+	0.302296i
$899$	−1.87899			−0.0626678
$900$	1.52116	−	14.9227i	0.0507054	−	0.497422i
$901$	20.1881			0.672564
$902$	−20.9840	+	20.9840i	−0.698691	+	0.698691i
$903$	0.324528	+	1.89149i	0.0107996	+	0.0629448i
$904$			8.91399i			0.296475i
$905$	5.20342	−	23.1916i	0.172968	−	0.770916i
$906$	27.5375	+	19.4720i	0.914872	+	0.646912i
$907$	−23.9940	−	23.9940i	−0.796709	−	0.796709i	0.185866	−	0.982575i	$-0.440491\pi$
$907$	−23.9940	−	23.9940i	−0.796709	−	0.796709i	−0.982575	+	0.185866i	$0.940491\pi$
$908$	−16.2085	−	16.2085i	−0.537897	−	0.537897i
$909$	12.5702	+	35.5540i	0.416928	+	1.17925i
$910$	3.52940	+	5.57129i	0.116998	+	0.184686i
$911$			5.18069i			0.171644i	0.996310	+	0.0858219i	$0.0273516\pi$
$911$			5.18069i			0.171644i	−0.996310	+	0.0858219i	$0.972648\pi$
$912$	2.68235	−	0.460219i	0.0888216	−	0.0152394i
$913$	34.1465	−	34.1465i	1.13008	−	1.13008i
$914$	29.4292			0.973431
$915$	43.4528	+	2.20899i	1.43651	+	0.0730269i
$916$	6.64235			0.219470
$917$	6.92805	−	6.92805i	0.228785	−	0.228785i
$918$	−26.0714	+	14.5749i	−0.860483	+	0.481042i
$919$			37.4389i			1.23500i	0.786573	+	0.617498i	$0.211854\pi$
$919$			37.4389i			1.23500i	−0.786573	+	0.617498i	$0.788146\pi$
$920$	−3.27226	−	0.734185i	−0.107883	−	0.0242054i
$921$	−10.8392	+	15.3289i	−0.357164	+	0.505106i
$922$	7.09095	+	7.09095i	0.233528	+	0.233528i
$923$	−13.7578	−	13.7578i	−0.452845	−	0.452845i
$924$	−2.74286	+	3.87899i	−0.0902335	+	0.127609i
$925$	4.76919	+	13.3137i	0.156810	+	0.437752i
$926$			4.65264i			0.152895i
$927$	0.822164	−	1.72148i	0.0270034	−	0.0565407i
$928$	1.32865	−	1.32865i	0.0436150	−	0.0436150i
$929$	10.3349			0.339079			0.169539	−	0.985523i	$-0.445772\pi$
$929$	10.3349			0.339079			0.169539	+	0.985523i	$0.445772\pi$
$930$	2.87412	−	2.59604i	0.0942462	−	0.0851275i
$931$	−10.2908			−0.337268
$932$	−9.15146	+	9.15146i	−0.299766	+	0.299766i
$933$	48.7050	−	8.35646i	1.59453	−	0.273578i
$934$		−	15.8561i		−	0.518828i
$935$	44.3613	−	28.1028i	1.45077	−	0.919059i
$936$	−12.4260	+	4.39327i	−0.406158	+	0.143599i
$937$	15.8855	+	15.8855i	0.518958	+	0.518958i	0.917256	−	0.398298i	$-0.130399\pi$
$937$	15.8855	+	15.8855i	0.518958	+	0.518958i	−0.398298	+	0.917256i	$0.630399\pi$
$938$	3.60673	+	3.60673i	0.117764	+	0.117764i
$939$	−46.1984	−	32.6672i	−1.50763	−	1.06605i
$940$	−1.39104	+	0.881221i	−0.0453707	+	0.0287422i
$941$		−	28.9714i		−	0.944442i	−0.881480	−	0.472221i	$-0.843452\pi$
$941$		−	28.9714i		−	0.944442i	0.881480	−	0.472221i	$-0.156548\pi$
$942$	0.605767	+	3.53067i	0.0197369	+	0.115035i
$943$	7.70307	−	7.70307i	0.250846	−	0.250846i
$944$	−4.40554			−0.143388
$945$	6.85911	+	3.71474i	0.223127	+	0.120840i
$946$	6.74286			0.219229
$947$	−34.7182	+	34.7182i	−1.12819	+	1.12819i	−0.137718	+	0.990471i	$0.543977\pi$
$947$	−34.7182	+	34.7182i	−1.12819	+	1.12819i	−0.990471	+	0.137718i	$0.956023\pi$
$948$	−2.67324	−	15.5808i	−0.0868228	−	0.506041i
$949$		−	48.8840i		−	1.58684i
$950$	2.64945	+	7.39622i	0.0859594	+	0.239965i
$951$	22.6555	+	16.0199i	0.734656	+	0.519480i
$952$	−2.72880	−	2.72880i	−0.0884409	−	0.0884409i
$953$	3.05595	+	3.05595i	0.0989919	+	0.0989919i	0.754868	−	0.655876i	$-0.227701\pi$
$953$	3.05595	+	3.05595i	0.0989919	+	0.0989919i	−0.655876	+	0.754868i	$0.727701\pi$
$954$	9.93358	−	3.51205i	0.321611	−	0.113707i
$955$	1.77936	+	0.399229i	0.0575788	+	0.0129187i
$956$		−	26.5471i		−	0.858593i
$957$	−13.1050	+	2.24846i	−0.423625	+	0.0726825i
$958$	−4.16479	+	4.16479i	−0.134558	+	0.134558i
$959$	−5.91264			−0.190929
$960$	−0.196635	+	3.86799i	−0.00634636	+	0.124839i
$961$	1.00000			0.0322581
$962$	8.78654	−	8.78654i	0.283289	−	0.283289i
$963$	9.14967	−	19.1579i	0.294844	−	0.617355i
$964$			3.60673i			0.116165i
$965$	−9.61838	−	15.1830i	−0.309627	−	0.488757i
$966$	1.00688	−	1.42395i	0.0323959	−	0.0458148i
$967$	−33.8479	−	33.8479i	−1.08847	−	1.08847i	−0.995686	−	0.0927884i	$-0.970422\pi$
$967$	−33.8479	−	33.8479i	−1.08847	−	1.08847i	−0.0927884	−	0.995686i	$-0.529578\pi$
$968$	4.02475	+	4.02475i	0.129360	+	0.129360i
$969$	9.03214	−	12.7734i	0.290154	−	0.410340i
$970$	−5.78010	+	25.7619i	−0.185588	+	0.827164i
$971$		−	58.2910i		−	1.87065i	−0.353793	−	0.935324i	$-0.615108\pi$
$971$		−	58.2910i		−	1.87065i	0.353793	−	0.935324i	$-0.384892\pi$
$972$	−10.2929	+	11.7071i	−0.330145	+	0.375506i
$973$	−0.643232	+	0.643232i	−0.0206211	+	0.0206211i
$974$	34.6672			1.11081
$975$	−18.7028	−	33.1326i	−0.598968	−	1.06109i
$976$	−11.2340			−0.359590
$977$	1.11995	−	1.11995i	0.0358304	−	0.0358304i	−0.688965	−	0.724795i	$-0.741934\pi$
$977$	1.11995	−	1.11995i	0.0358304	−	0.0358304i	0.724795	+	0.688965i	$0.241934\pi$
$978$	6.44922	−	1.10651i	0.206223	−	0.0353823i
$979$			23.2563i			0.743273i
$980$	3.20606	−	14.2894i	0.102414	−	0.456458i
$981$	−7.47661	−	21.1470i	−0.238710	−	0.675173i
$982$	17.4451	+	17.4451i	0.556696	+	0.556696i
$983$	36.6650	+	36.6650i	1.16943	+	1.16943i	0.982343	+	0.187087i	$0.0599047\pi$
$983$	36.6650	+	36.6650i	1.16943	+	1.16943i	0.187087	+	0.982343i	$0.440095\pi$
$984$	−10.2723	−	7.26358i	−0.327468	−	0.231555i
$985$	−31.0613	−	49.0315i	−0.989696	−	1.56227i
$986$		−	10.8009i		−	0.343971i
$987$	−0.144805	−	0.843985i	−0.00460919	−	0.0268644i
$988$	4.88122	−	4.88122i	0.155292	−	0.155292i
$989$	−2.47525			−0.0787085
$990$	16.9391	−	21.5453i	0.538359	−	0.684756i
$991$	60.1248			1.90993			0.954964	−	0.296722i	$-0.0958934\pi$
$991$	60.1248			1.90993			0.954964	+	0.296722i	$0.0958934\pi$
$992$	−0.707107	+	0.707107i	−0.0224507	+	0.0224507i
$993$	5.76337	+	33.5914i	0.182895	+	1.06599i
$994$		−	2.97323i		−	0.0943052i
$995$	−35.1573	−	7.88810i	−1.11456	−	0.250070i
$996$	16.7157	+	11.8198i	0.529656	+	0.374523i
$997$	−15.0323	−	15.0323i	−0.476079	−	0.476079i	0.427796	−	0.903875i	$-0.359290\pi$
$997$	−15.0323	−	15.0323i	−0.476079	−	0.476079i	−0.903875	+	0.427796i	$0.859290\pi$
$998$	−27.1749	−	27.1749i	−0.860207	−	0.860207i
$999$	4.00000	−	14.1421i	0.126554	−	0.447437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.c.497.3	✓	8
3.2	odd	2		930.2.j.f.497.2	yes	8
5.3	odd	4		930.2.j.f.683.2	yes	8
15.8	even	4	inner	930.2.j.c.683.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.c.497.3	✓	8	1.1	even	1	trivial
930.2.j.c.683.3	yes	8	15.8	even	4	inner
930.2.j.f.497.2	yes	8	3.2	odd	2
930.2.j.f.683.2	yes	8	5.3	odd	4

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.292893 - 1.70711i) q^{3} -1.00000i q^{4} +(-0.489528 + 2.18183i) q^{5} +(-1.41421 - 1.00000i) q^{6} +(-0.474719 - 0.474719i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 + 1.00000i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.292893 - 1.70711i) q^{3} -1.00000i q^{4} +(-0.489528 + 2.18183i) q^{5} +(-1.41421 - 1.00000i) q^{6} +(-0.474719 - 0.474719i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 + 1.00000i) q^{9} +(1.19663 + 1.88893i) q^{10} +4.08557i q^{11} +(-1.70711 + 0.292893i) q^{12} +(-3.10651 + 3.10651i) q^{13} -0.671354 q^{14} +(3.86799 + 0.196635i) q^{15} -1.00000 q^{16} +(-4.06462 + 4.06462i) q^{17} +(-1.29289 + 2.70711i) q^{18} -1.57129i q^{19} +(2.18183 + 0.489528i) q^{20} +(-0.671354 + 0.949437i) q^{21} +(2.88893 + 2.88893i) q^{22} +(-1.06051 - 1.06051i) q^{23} +(-1.00000 + 1.41421i) q^{24} +(-4.52072 - 2.13613i) q^{25} +4.39327i q^{26} +(2.53553 + 4.53553i) q^{27} +(-0.474719 + 0.474719i) q^{28} -1.87899 q^{29} +(2.87412 - 2.59604i) q^{30} +1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(6.97450 - 1.19663i) q^{33} +5.74825i q^{34} +(1.26814 - 0.803365i) q^{35} +(1.00000 + 2.82843i) q^{36} +(-2.00000 - 2.00000i) q^{37} +(-1.11107 - 1.11107i) q^{38} +(6.21302 + 4.39327i) q^{39} +(1.88893 - 1.19663i) q^{40} +7.26358i q^{41} +(0.196635 + 1.14607i) q^{42} +(1.16702 - 1.16702i) q^{43} +4.08557 q^{44} +(-0.797231 - 6.66066i) q^{45} -1.49978 q^{46} +(-0.520724 + 0.520724i) q^{47} +(0.292893 + 1.70711i) q^{48} -6.54928i q^{49} +(-4.70711 + 1.68616i) q^{50} +(8.12925 + 5.74825i) q^{51} +(3.10651 + 3.10651i) q^{52} +(-2.48339 - 2.48339i) q^{53} +(5.00000 + 1.41421i) q^{54} +(-8.91399 - 2.00000i) q^{55} +0.671354i q^{56} +(-2.68235 + 0.460219i) q^{57} +(-1.32865 + 1.32865i) q^{58} +4.40554 q^{59} +(0.196635 - 3.86799i) q^{60} +11.2340 q^{61} +(0.707107 - 0.707107i) q^{62} +(1.81743 + 0.867988i) q^{63} +1.00000i q^{64} +(-5.25714 - 8.29859i) q^{65} +(4.08557 - 5.77786i) q^{66} +(-5.37233 - 5.37233i) q^{67} +(4.06462 + 4.06462i) q^{68} +(-1.49978 + 2.12101i) q^{69} +(0.328646 - 1.46478i) q^{70} +4.42871i q^{71} +(2.70711 + 1.29289i) q^{72} +(-7.86799 + 7.86799i) q^{73} -2.82843 q^{74} +(-2.32251 + 8.34302i) q^{75} -1.57129 q^{76} +(1.93949 - 1.93949i) q^{77} +(7.49978 - 1.28676i) q^{78} +9.12702i q^{79} +(0.489528 - 2.18183i) q^{80} +(7.00000 - 5.65685i) q^{81} +(5.13613 + 5.13613i) q^{82} +(-8.35783 - 8.35783i) q^{83} +(0.949437 + 0.671354i) q^{84} +(-6.87855 - 10.8580i) q^{85} -1.65041i q^{86} +(0.550343 + 3.20764i) q^{87} +(2.88893 - 2.88893i) q^{88} +5.69230 q^{89} +(-5.27353 - 4.14607i) q^{90} +2.94944 q^{91} +(-1.06051 + 1.06051i) q^{92} +(-0.292893 - 1.70711i) q^{93} +0.736416i q^{94} +(3.42827 + 0.769189i) q^{95} +(1.41421 + 1.00000i) q^{96} +(8.34915 + 8.34915i) q^{97} +(-4.63104 - 4.63104i) q^{98} +(-4.08557 - 11.5557i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} + 4 q^{7}+O(q^{10}) \) 8 * q - 8 * q^3 + 4 * q^7	\( 8 q - 8 q^{3} + 4 q^{7} - 8 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{15} - 8 q^{16} + 4 q^{17} - 16 q^{18} + 4 q^{20} + 12 q^{21} + 4 q^{22} - 12 q^{23} - 8 q^{24} - 4 q^{25} - 8 q^{27} + 4 q^{28} - 8 q^{29} + 8 q^{31} + 8 q^{33} + 24 q^{35} + 8 q^{36} - 16 q^{37} - 28 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{42} - 8 q^{43} + 4 q^{44} - 12 q^{45} + 28 q^{46} + 28 q^{47} + 8 q^{48} - 32 q^{50} - 8 q^{51} + 4 q^{52} - 12 q^{53} + 40 q^{54} - 20 q^{55} - 24 q^{57} - 28 q^{58} + 24 q^{59} - 8 q^{60} + 56 q^{61} - 28 q^{63} - 36 q^{65} + 4 q^{66} - 16 q^{67} - 4 q^{68} + 28 q^{69} + 20 q^{70} + 16 q^{72} - 36 q^{73} - 32 q^{75} + 4 q^{76} + 12 q^{77} + 20 q^{78} + 56 q^{81} + 28 q^{82} - 12 q^{83} - 8 q^{84} + 32 q^{85} - 20 q^{87} + 4 q^{88} + 36 q^{89} - 4 q^{90} + 8 q^{91} - 12 q^{92} - 8 q^{93} - 36 q^{95} + 12 q^{97} + 32 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^3 + 4 * q^7 - 8 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^15 - 8 * q^16 + 4 * q^17 - 16 * q^18 + 4 * q^20 + 12 * q^21 + 4 * q^22 - 12 * q^23 - 8 * q^24 - 4 * q^25 - 8 * q^27 + 4 * q^28 - 8 * q^29 + 8 * q^31 + 8 * q^33 + 24 * q^35 + 8 * q^36 - 16 * q^37 - 28 * q^38 + 8 * q^39 - 4 * q^40 - 8 * q^42 - 8 * q^43 + 4 * q^44 - 12 * q^45 + 28 * q^46 + 28 * q^47 + 8 * q^48 - 32 * q^50 - 8 * q^51 + 4 * q^52 - 12 * q^53 + 40 * q^54 - 20 * q^55 - 24 * q^57 - 28 * q^58 + 24 * q^59 - 8 * q^60 + 56 * q^61 - 28 * q^63 - 36 * q^65 + 4 * q^66 - 16 * q^67 - 4 * q^68 + 28 * q^69 + 20 * q^70 + 16 * q^72 - 36 * q^73 - 32 * q^75 + 4 * q^76 + 12 * q^77 + 20 * q^78 + 56 * q^81 + 28 * q^82 - 12 * q^83 - 8 * q^84 + 32 * q^85 - 20 * q^87 + 4 * q^88 + 36 * q^89 - 4 * q^90 + 8 * q^91 - 12 * q^92 - 8 * q^93 - 36 * q^95 + 12 * q^97 + 32 * q^98 - 4 * q^99

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