LMFDB - Embedded newform 930.2.j.f.683.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(497,930)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [8,0,8,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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			683.2
Root			$1.69230i$ of defining polynomial
Character	$\chi$	$=$	930.683
Dual form			930.2.j.f.497.2

$q$-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} +(1.70711 - 0.292893i) 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} +(0.292893 + 1.70711i) q^{12} +(-3.10651 - 3.10651i) q^{13} +0.671354 q^{14} +(1.47472 + 3.58123i) q^{15} -1.00000 q^{16} +(4.06462 + 4.06462i) q^{17} +(-2.70711 - 1.29289i) 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} +(4.53553 - 2.53553i) q^{27} +(-0.474719 - 0.474719i) q^{28} +1.87899 q^{29} +(1.48953 - 3.57510i) q^{30} +1.00000 q^{31} +(0.707107 + 0.707107i) q^{32} +(1.19663 + 6.97450i) 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} +(1.14607 - 0.196635i) q^{42} +(1.16702 + 1.16702i) q^{43} -4.08557 q^{44} +(3.56642 + 5.68161i) q^{45} -1.49978 q^{46} +(0.520724 + 0.520724i) q^{47} +(-1.70711 + 0.292893i) 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} +(0.460219 + 2.68235i) q^{57} +(-1.32865 - 1.32865i) q^{58} -4.40554 q^{59} +(-3.58123 + 1.47472i) q^{60} +11.2340 q^{61} +(-0.707107 - 0.707107i) q^{62} +(-0.867988 + 1.81743i) 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} +(1.29289 - 2.70711i) q^{72} +(-7.86799 - 7.86799i) q^{73} +2.82843 q^{74} +(-7.09170 + 4.97069i) q^{75} -1.57129 q^{76} +(-1.93949 - 1.93949i) q^{77} +(1.28676 + 7.49978i) 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} +(3.20764 - 0.550343i) q^{87} +(2.88893 + 2.88893i) q^{88} -5.69230 q^{89} +(1.49566 - 6.53934i) q^{90} +2.94944 q^{91} +(1.06051 + 1.06051i) q^{92} +(1.70711 - 0.292893i) 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} + 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}+ \cdots + 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^30 + 8 * q^31 - 24 * q^35 + 8 * q^36 - 16 * q^37 + 28 * q^38 - 8 * q^39 - 4 * q^40 - 16 * q^42 - 8 * q^43 - 4 * q^44 - 4 * 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 - 32 * q^57 - 28 * q^58 - 24 * q^59 + 56 * q^61 + 20 * 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 + 12 * q^78 + 56 * q^81 + 28 * q^82 + 12 * q^83 + 8 * q^84 + 32 * q^85 + 36 * q^87 + 4 * q^88 - 36 * q^89 + 12 * q^90 + 8 * q^91 + 12 * q^92 + 8 * q^93 + 36 * q^95 + 12 * q^97 - 32 * q^98 + 4 * q^99

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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
$3$	1.70711	−	0.292893i	0.985599	−	0.169102i
$3$	1.70711	−	0.292893i	0.985599	−	0.169102i
$4$			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	−0.791106	−	0.611679i	$-0.790494\pi$
$7$	−0.474719	+	0.474719i	−0.179427	+	0.179427i	0.611679	+	0.791106i	$0.290494\pi$
$8$	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	$0.788783\pi$
$12$	0.292893	+	1.70711i	0.0845510	+	0.492799i
$13$	−3.10651	−	3.10651i	−0.861591	−	0.861591i	0.129932	−	0.991523i	$-0.458524\pi$
$13$	−3.10651	−	3.10651i	−0.861591	−	0.861591i	−0.991523	+	0.129932i	$0.958524\pi$
$14$	0.671354			0.179427
$15$	1.47472	+	3.58123i	0.380771	+	0.924669i
$16$	−1.00000			−0.250000
$17$	4.06462	+	4.06462i	0.985816	+	0.985816i	0.999901	−	0.0140848i	$-0.00448349\pi$
$17$	4.06462	+	4.06462i	0.985816	+	0.985816i	−0.0140848	+	0.999901i	$0.504483\pi$
$18$	−2.70711	−	1.29289i	−0.638071	−	0.304738i
$19$			1.57129i			0.360478i	0.983623	+	0.180239i	$0.0576871\pi$
$19$			1.57129i			0.360478i	−0.983623	+	0.180239i	$0.942313\pi$
$20$	−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	$-0.700023\pi$
$23$	1.06051	−	1.06051i	0.221131	−	0.221131i	0.808974	+	0.587844i	$0.200023\pi$
$24$	1.00000	−	1.41421i	0.204124	−	0.288675i
$25$	−4.52072	+	2.13613i	−0.904145	+	0.427226i
$26$			4.39327i			0.861591i
$27$	4.53553	−	2.53553i	0.872864	−	0.487964i
$28$	−0.474719	−	0.474719i	−0.0897134	−	0.0897134i
$29$	1.87899			0.348920			0.174460	−	0.984664i	$-0.444182\pi$
$29$	1.87899			0.348920			0.174460	+	0.984664i	$0.444182\pi$
$30$	1.48953	−	3.57510i	0.271949	−	0.652720i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	1.19663	+	6.97450i	0.208307	+	1.21410i
$34$		−	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	−0.852129	−	0.523331i	$-0.824689\pi$
$37$	−2.00000	+	2.00000i	−0.328798	+	0.328798i	0.523331	+	0.852129i	$0.324689\pi$
$38$	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	$0.808030\pi$
$42$	1.14607	−	0.196635i	0.176843	−	0.0303414i
$43$	1.16702	+	1.16702i	0.177968	+	0.177968i	0.790470	−	0.612501i	$-0.209837\pi$
$43$	1.16702	+	1.16702i	0.177968	+	0.177968i	−0.612501	+	0.790470i	$0.709837\pi$
$44$	−4.08557			−0.615922
$45$	3.56642	+	5.68161i	0.531651	+	0.846964i
$46$	−1.49978			−0.221131
$47$	0.520724	+	0.520724i	0.0759555	+	0.0759555i	0.744064	−	0.668108i	$-0.232896\pi$
$47$	0.520724	+	0.520724i	0.0759555	+	0.0759555i	−0.668108	+	0.744064i	$0.732896\pi$
$48$	−1.70711	+	0.292893i	−0.246400	+	0.0422755i
$49$			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	$-0.672456\pi$
$53$	2.48339	−	2.48339i	0.341120	−	0.341120i	0.856788	+	0.515668i	$0.172456\pi$
$54$	−5.00000	−	1.41421i	−0.680414	−	0.192450i
$55$	−8.91399	+	2.00000i	−1.20196	+	0.269680i
$56$			0.671354i			0.0897134i
$57$	0.460219	+	2.68235i	0.0609575	+	0.355287i
$58$	−1.32865	−	1.32865i	−0.174460	−	0.174460i
$59$	−4.40554			−0.573552			−0.286776	−	0.957998i	$-0.592584\pi$
$59$	−4.40554			−0.573552			−0.286776	+	0.957998i	$0.592584\pi$
$60$	−3.58123	+	1.47472i	−0.462335	+	0.190385i
$61$	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
$63$	−0.867988	+	1.81743i	−0.109356	+	0.228974i
$64$		−	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	−0.954511	−	0.298177i	$-0.903622\pi$
$67$	−5.37233	+	5.37233i	−0.656334	+	0.656334i	0.298177	+	0.954511i	$0.403622\pi$
$68$	−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	$0.915355\pi$
$72$	1.29289	−	2.70711i	0.152369	−	0.319036i
$73$	−7.86799	−	7.86799i	−0.920878	−	0.920878i	0.0762132	−	0.997092i	$-0.475717\pi$
$73$	−7.86799	−	7.86799i	−0.920878	−	0.920878i	−0.997092	+	0.0762132i	$0.975717\pi$
$74$	2.82843			0.328798
$75$	−7.09170	+	4.97069i	−0.818879	+	0.573966i
$76$	−1.57129			−0.180239
$77$	−1.93949	−	1.93949i	−0.221026	−	0.221026i
$78$	1.28676	+	7.49978i	0.145697	+	0.849183i
$79$		−	9.12702i		−	1.02687i	−0.858129	−	0.513435i	$-0.828373\pi$
$79$		−	9.12702i		−	1.02687i	0.858129	−	0.513435i	$-0.171627\pi$
$80$	−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	$-0.525316\pi$
$83$	8.35783	−	8.35783i	0.917391	−	0.917391i	0.996839	+	0.0794483i	$0.0253159\pi$
$84$	−0.949437	−	0.671354i	−0.103592	−	0.0732507i
$85$	−6.87855	+	10.8580i	−0.746084	+	1.17772i
$86$		−	1.65041i		−	0.177968i
$87$	3.20764	−	0.550343i	0.343895	−	0.0590030i
$88$	2.88893	+	2.88893i	0.307961	+	0.307961i
$89$	−5.69230			−0.603382			−0.301691	−	0.953406i	$-0.597551\pi$
$89$	−5.69230			−0.603382			−0.301691	+	0.953406i	$0.597551\pi$
$90$	1.49566	−	6.53934i	0.157657	−	0.689307i
$91$	2.94944			0.309185
$92$	1.06051	+	1.06051i	0.110565	+	0.110565i
$93$	1.70711	−	0.292893i	0.177019	−	0.0303716i
$94$		−	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	−0.142121	−	0.989849i	$-0.545392\pi$
$97$	8.34915	−	8.34915i	0.847728	−	0.847728i	0.989849	+	0.142121i	$0.0453923\pi$
$98$	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	$-0.215061\pi$
$102$	−1.68362	−	9.81287i	−0.166703	−	0.971619i
$103$	−0.449657	−	0.449657i	−0.0443060	−	0.0443060i	0.684607	−	0.728913i	$-0.259974\pi$
$103$	−0.449657	−	0.449657i	−0.0443060	−	0.0443060i	−0.728913	+	0.684607i	$0.759974\pi$
$104$	−4.39327			−0.430796
$105$	−2.40015	−	1.00000i	−0.234231	−	0.0975900i
$106$	−3.51205			−0.341120
$107$	5.00412	+	5.00412i	0.483766	+	0.483766i	0.906332	−	0.422566i	$-0.138870\pi$
$107$	5.00412	+	5.00412i	0.483766	+	0.483766i	−0.422566	+	0.906332i	$0.638870\pi$
$108$	2.53553	+	4.53553i	0.243982	+	0.436432i
$109$		−	7.47661i		−	0.716129i	−0.933697	−	0.358064i	$-0.883437\pi$
$109$		−	7.47661i		−	0.716129i	0.933697	−	0.358064i	$-0.116563\pi$
$110$	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	$-0.612283\pi$
$113$	6.30315	−	6.30315i	0.592950	−	0.592950i	0.938427	+	0.345477i	$0.112283\pi$
$114$	1.57129	−	2.22214i	0.147165	−	0.208122i
$115$	2.83298	+	1.79469i	0.264177	+	0.167356i
$116$			1.87899i			0.174460i
$117$	−11.8931	−	5.68003i	−1.09951	−	0.525119i
$118$	3.11519	+	3.11519i	0.286776	+	0.286776i
$119$	−3.85911			−0.353764
$120$	3.57510	+	1.48953i	0.326360	+	0.135975i
$121$	−5.69186			−0.517442
$122$	−7.94361	−	7.94361i	−0.719181	−	0.719181i
$123$	2.12745	+	12.3997i	0.191826	+	1.11804i
$124$			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	0.224741	−	0.974419i	$-0.427846\pi$
$127$	13.5138	−	13.5138i	1.19916	−	1.19916i	0.974419	−	0.224741i	$-0.0721536\pi$
$128$	−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	$0.779951\pi$
$132$	−6.97450	+	1.19663i	−0.607052	+	0.104154i
$133$	−0.745919	−	0.745919i	−0.0646794	−	0.0646794i
$134$	7.59762			0.656334
$135$	7.75236	+	8.65453i	0.667217	+	0.744863i
$136$	5.74825			0.492908
$137$	−6.22752	−	6.22752i	−0.532053	−	0.532053i	0.389130	−	0.921183i	$-0.372776\pi$
$137$	−6.22752	−	6.22752i	−0.532053	−	0.532053i	−0.921183	+	0.389130i	$0.872776\pi$
$138$	−2.56029	+	0.439276i	−0.217946	+	0.0373936i
$139$			1.35498i			0.114928i	0.998348	+	0.0574638i	$0.0183014\pi$
$139$			1.35498i			0.114928i	−0.998348	+	0.0574638i	$0.981699\pi$
$140$	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
$147$	1.91824	+	11.1803i	0.158214	+	0.922138i
$148$	−2.00000	−	2.00000i	−0.164399	−	0.164399i
$149$	20.3809			1.66967			0.834833	−	0.550504i	$-0.185564\pi$
$149$	20.3809			1.66967			0.834833	+	0.550504i	$0.185564\pi$
$150$	8.52940	+	1.49978i	0.696423	+	0.122457i
$151$	−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
$153$	15.5611	+	7.43187i	1.25804	+	0.600831i
$154$			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	−0.763053	−	0.646336i	$-0.776300\pi$
$157$	−1.46245	+	1.46245i	−0.116716	+	0.116716i	0.646336	+	0.763053i	$0.276300\pi$
$158$	−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
$162$	−8.94975	−	0.949747i	−0.703159	−	0.0746192i
$163$	−2.67135	−	2.67135i	−0.209237	−	0.209237i	0.594706	−	0.803943i	$-0.297268\pi$
$163$	−2.67135	−	2.67135i	−0.209237	−	0.209237i	−0.803943	+	0.594706i	$0.797268\pi$
$164$	−7.26358			−0.567191
$165$	−14.6314	+	6.02506i	−1.13905	+	0.469050i
$166$	−11.8198			−0.917391
$167$	3.37465	+	3.37465i	0.261138	+	0.261138i	0.825516	−	0.564378i	$-0.190884\pi$
$167$	3.37465	+	3.37465i	0.261138	+	0.261138i	−0.564378	+	0.825516i	$0.690884\pi$
$168$	0.196635	+	1.14607i	0.0151707	+	0.0884214i
$169$			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	$-0.512683\pi$
$173$	12.6186	−	12.6186i	0.959371	−	0.959371i	0.999206	+	0.0398349i	$0.0126832\pi$
$174$	−2.65729	−	1.87899i	−0.201449	−	0.142446i
$175$	1.13201	−	3.16013i	0.0855720	−	0.238884i
$176$		−	4.08557i		−	0.307961i
$177$	−7.52072	+	1.29035i	−0.565292	+	0.0969888i
$178$	4.02506	+	4.02506i	0.301691	+	0.301691i
$179$	−22.7264			−1.69865			−0.849326	−	0.527868i	$-0.822992\pi$
$179$	−22.7264			−1.69865			−0.849326	+	0.527868i	$0.822992\pi$
$180$	−5.68161	+	3.56642i	−0.423482	+	0.265825i
$181$	−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
$183$	19.1776	−	3.29035i	1.41765	−	0.243230i
$184$		−	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	$-0.00939314\pi$
$192$	−0.292893	−	1.70711i	−0.0211377	−	0.123200i
$193$	−5.68362	−	5.68362i	−0.409116	−	0.409116i	0.472314	−	0.881430i	$-0.343419\pi$
$193$	−5.68362	−	5.68362i	−0.409116	−	0.409116i	−0.881430	+	0.472314i	$0.843419\pi$
$194$	−11.8075			−0.847728
$195$	6.54390	−	15.7064i	0.468618	−	1.12476i
$196$	−6.54928			−0.467806
$197$	18.3545	+	18.3545i	1.30771	+	1.30771i	0.923067	+	0.384640i	$0.125674\pi$
$197$	18.3545	+	18.3545i	1.30771	+	1.30771i	0.384640	+	0.923067i	$0.374326\pi$
$198$	5.28220	−	11.0601i	0.375390	−	0.786005i
$199$		−	16.1137i		−	1.14227i	−0.820856	−	0.571135i	$-0.806503\pi$
$199$		−	16.1137i		−	1.14227i	0.820856	−	0.571135i	$-0.193497\pi$
$200$	−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
$207$	1.93906	−	4.06007i	0.134774	−	0.282194i
$208$	3.10651	+	3.10651i	0.215398	+	0.215398i
$209$	−6.41960			−0.444053
$210$	0.990058	+	2.40427i	0.0683205	+	0.165910i
$211$	−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
$213$	1.29714	+	7.56029i	0.0888786	+	0.518022i
$214$		−	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
$222$	4.82843	−	0.828427i	0.324063	−	0.0556004i
$223$	−3.60852	−	3.60852i	−0.241645	−	0.241645i	0.575886	−	0.817530i	$-0.304657\pi$
$223$	−3.60852	−	3.60852i	−0.241645	−	0.241645i	−0.817530	+	0.575886i	$0.804657\pi$
$224$	−0.671354			−0.0448567
$225$	−10.6504	+	10.5626i	−0.710027	+	0.704174i
$226$	−8.91399			−0.592950
$227$	−16.2085	−	16.2085i	−1.07579	−	1.07579i	−0.996882	−	0.0789120i	$-0.974855\pi$
$227$	−16.2085	−	16.2085i	−1.07579	−	1.07579i	−0.0789120	−	0.996882i	$-0.525145\pi$
$228$	−2.68235	+	0.460219i	−0.177643	+	0.0304788i
$229$		−	6.64235i		−	0.438939i	−0.975619	−	0.219470i	$-0.929567\pi$
$229$		−	6.64235i		−	0.438939i	0.975619	−	0.219470i	$-0.0704327\pi$
$230$	−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	$-0.610649\pi$
$233$	9.15146	−	9.15146i	0.599532	−	0.599532i	0.940188	+	0.340656i	$0.110649\pi$
$234$	4.39327	+	12.4260i	0.287197	+	0.812316i
$235$	−0.881221	+	1.39104i	−0.0574845	+	0.0907414i
$236$		−	4.40554i		−	0.286776i
$237$	−2.67324	−	15.5808i	−0.173646	−	1.01208i
$238$	2.72880	+	2.72880i	0.176882	+	0.176882i
$239$	−26.5471			−1.71719			−0.858593	−	0.512658i	$-0.828661\pi$
$239$	−26.5471			−1.71719			−0.858593	+	0.512658i	$0.828661\pi$
$240$	−1.47472	−	3.58123i	−0.0951927	−	0.231167i
$241$	−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
$243$	10.2929	−	11.7071i	0.660289	−	0.751011i
$244$			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	$0.804434\pi$
$252$	−1.81743	−	0.867988i	−0.114487	−	0.0546781i
$253$	4.33276	+	4.33276i	0.272399	+	0.272399i
$254$	−19.1115			−1.19916
$255$	−8.56217	+	20.5505i	−0.536184	+	1.28692i
$256$	1.00000			0.0625000
$257$	−17.9380	−	17.9380i	−1.11894	−	1.11894i	−0.991897	−	0.127045i	$-0.959451\pi$
$257$	−17.9380	−	17.9380i	−1.11894	−	1.11894i	−0.127045	−	0.991897i	$-0.540549\pi$
$258$	−0.483394	−	2.81743i	−0.0300948	−	0.175405i
$259$		−	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	$-0.617119\pi$
$263$	9.29859	−	9.29859i	0.573376	−	0.573376i	0.933070	+	0.359695i	$0.117119\pi$
$264$	5.77786	+	4.08557i	0.355603	+	0.251449i
$265$	6.63402	+	4.20264i	0.407525	+	0.258166i
$266$			1.05489i			0.0646794i
$267$	−9.71736	+	1.66724i	−0.594693	+	0.102033i
$268$	−5.37233	−	5.37233i	−0.328167	−	0.328167i
$269$	−9.25447			−0.564255			−0.282128	−	0.959377i	$-0.591040\pi$
$269$	−9.25447			−0.564255			−0.282128	+	0.959377i	$0.591040\pi$
$270$	0.637927	−	11.6014i	0.0388230	−	0.706040i
$271$	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
$273$	5.03500	−	0.863870i	0.304732	−	0.0522838i
$274$			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	0.141674	−	0.989913i	$-0.454751\pi$
$277$	18.8334	−	18.8334i	1.13159	−	1.13159i	0.989913	−	0.141674i	$-0.0452486\pi$
$278$	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	$-0.123087\pi$
$282$	−0.215691	−	1.25714i	−0.0128442	−	0.0748616i
$283$	13.8139	+	13.8139i	0.821153	+	0.821153i	0.986273	−	0.165121i	$-0.0528013\pi$
$283$	13.8139	+	13.8139i	0.821153	+	0.821153i	−0.165121	+	0.986273i	$0.552801\pi$
$284$	−4.42871			−0.262796
$285$	−5.62714	+	2.31721i	−0.333323	+	0.137259i
$286$	−17.9490			−1.06135
$287$	−3.44816	−	3.44816i	−0.203538	−	0.203538i
$288$	2.70711	+	1.29289i	0.159518	+	0.0761845i
$289$			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	−0.202844	+	0.979211i	$0.565019\pi$
$293$	−20.2335	+	20.2335i	−1.18206	+	1.18206i	−0.979211	+	0.202844i	$0.934981\pi$
$294$	6.54928	−	9.26209i	0.381962	−	0.540176i
$295$	−2.15663	−	9.61212i	−0.125564	−	0.559639i
$296$			2.82843i			0.164399i
$297$	10.3591	+	18.5302i	0.601096	+	1.07523i
$298$	−14.4114	−	14.4114i	−0.834833	−	0.834833i
$299$	−6.58894			−0.381048
$300$	−4.97069	−	7.09170i	−0.286983	−	0.409440i
$301$	−1.10801			−0.0638645
$302$	13.7688	+	13.7688i	0.792303	+	0.792303i
$303$	−3.68173	−	21.4587i	−0.211510	−	1.23277i
$304$		−	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	−0.891148	−	0.453713i	$-0.850099\pi$
$307$	−7.66447	+	7.66447i	−0.437434	+	0.437434i	0.453713	+	0.891148i	$0.350099\pi$
$308$	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	$0.700055\pi$
$312$	−7.49978	+	1.28676i	−0.424591	+	0.0728484i
$313$	23.0992	+	23.0992i	1.30564	+	1.30564i	0.924527	+	0.381116i	$0.124460\pi$
$313$	23.0992	+	23.0992i	1.30564	+	1.30564i	0.381116	+	0.924527i	$0.375540\pi$
$314$	2.06822			0.116716
$315$	−4.39021	−	1.00412i	−0.247360	−	0.0565757i
$316$	9.12702			0.513435
$317$	11.3278	+	11.3278i	0.636231	+	0.636231i	0.949624	−	0.313393i	$-0.101466\pi$
$317$	11.3278	+	11.3278i	0.636231	+	0.636231i	−0.313393	+	0.949624i	$0.601466\pi$
$318$	−5.99544	+	1.02866i	−0.336208	+	0.0576841i
$319$			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
$327$	−2.18985	−	12.7634i	−0.121099	−	0.705816i
$328$	5.13613	+	5.13613i	0.283595	+	0.283595i
$329$	−0.494395			−0.0272569
$330$	14.6063	+	6.08557i	0.804050	+	0.334999i
$331$	−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
$333$	−3.65685	+	7.65685i	−0.200394	+	0.419593i
$334$		−	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	−0.793742	−	0.608254i	$-0.791870\pi$
$337$	−3.40510	+	3.40510i	−0.185488	+	0.185488i	0.608254	+	0.793742i	$0.291870\pi$
$338$	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
$342$	2.03151	−	4.25364i	0.109851	−	0.230011i
$343$	−6.43210	−	6.43210i	−0.347301	−	0.347301i
$344$	1.65041			0.0889841
$345$	5.36186	+	2.23397i	0.288673	+	0.120273i
$346$	−17.8453			−0.959371
$347$	−8.75110	−	8.75110i	−0.469783	−	0.469783i	0.432061	−	0.901844i	$-0.357787\pi$
$347$	−8.75110	−	8.75110i	−0.469783	−	0.469783i	−0.901844	+	0.432061i	$0.857787\pi$
$348$	0.550343	+	3.20764i	0.0295015	+	0.171947i
$349$		−	30.6845i		−	1.64251i	−0.570564	−	0.821253i	$-0.693276\pi$
$349$		−	30.6845i		−	1.64251i	0.570564	−	0.821253i	$-0.306724\pi$
$350$	−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	$-0.800431\pi$
$353$	−4.19208	+	4.19208i	−0.223122	+	0.223122i	0.586690	+	0.809812i	$0.300431\pi$
$354$	6.23037	+	4.40554i	0.331141	+	0.234152i
$355$	−9.66268	+	2.16798i	−0.512842	+	0.115064i
$356$		−	5.69230i		−	0.301691i
$357$	−6.58790	+	1.13031i	−0.348669	+	0.0598221i
$358$	16.0700	+	16.0700i	0.849326	+	0.849326i
$359$	−6.95588			−0.367117			−0.183559	−	0.983009i	$-0.558762\pi$
$359$	−6.95588			−0.367117			−0.183559	+	0.983009i	$0.558762\pi$
$360$	6.53934	+	1.49566i	0.344654	+	0.0788283i
$361$	16.5311			0.870056
$362$	7.51617	+	7.51617i	0.395041	+	0.395041i
$363$	−9.71661	+	1.66711i	−0.509990	+	0.0875004i
$364$			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	−0.603088	−	0.797675i	$-0.706063\pi$
$367$	3.72774	−	3.72774i	0.194586	−	0.194586i	0.797675	+	0.603088i	$0.206063\pi$
$368$	−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
$372$	0.292893	+	1.70711i	0.0151858	+	0.0885094i
$373$	2.93906	+	2.93906i	0.152179	+	0.152179i	0.779090	−	0.626912i	$-0.215681\pi$
$373$	2.93906	+	2.93906i	0.152179	+	0.152179i	−0.626912	+	0.779090i	$0.715681\pi$
$374$	23.4848			1.21437
$375$	−14.3168	−	13.0396i	−0.739315	−	0.673360i
$376$	0.736416			0.0379777
$377$	−5.83710	−	5.83710i	−0.300626	−	0.300626i
$378$	3.04495	−	1.70224i	0.156615	−	0.0875538i
$379$		−	19.7134i		−	1.01261i	−0.862354	−	0.506305i	$-0.831011\pi$
$379$		−	19.7134i		−	1.01261i	0.862354	−	0.506305i	$-0.168989\pi$
$380$	−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	$-0.770153\pi$
$383$	−1.75110	+	1.75110i	−0.0894769	+	0.0894769i	0.660952	+	0.750428i	$0.270153\pi$
$384$	−1.00000	+	1.41421i	−0.0510310	+	0.0721688i
$385$	3.28220	−	5.18108i	0.167277	−	0.264052i
$386$			8.03786i			0.409116i
$387$	4.46784	+	2.13380i	0.227113	+	0.108467i
$388$	8.34915	+	8.34915i	0.423864	+	0.423864i
$389$	−13.1089			−0.664649			−0.332324	−	0.943165i	$-0.607833\pi$
$389$	−13.1089			−0.664649			−0.332324	+	0.943165i	$0.607833\pi$
$390$	−15.7333	+	6.47884i	−0.796687	+	0.328069i
$391$	8.62111			0.435988
$392$	4.63104	+	4.63104i	0.233903	+	0.233903i
$393$	4.27449	+	24.9136i	0.215620	+	1.25672i
$394$		−	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	−0.831429	−	0.555631i	$-0.812477\pi$
$397$	−5.49522	+	5.49522i	−0.275797	+	0.275797i	0.555631	+	0.831429i	$0.312477\pi$
$398$	−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	$0.977443\pi$
$402$	12.9699	−	2.22529i	0.646882	−	0.110987i
$403$	−3.10651	−	3.10651i	−0.154746	−	0.154746i
$404$	12.5702			0.625392
$405$	15.7690	+	12.5036i	0.783566	+	0.621308i
$406$	1.26147			0.0626055
$407$	−8.17113	−	8.17113i	−0.405028	−	0.405028i
$408$	9.81287	−	1.68362i	0.485809	−	0.0833517i
$409$		−	3.01333i		−	0.148999i	−0.997221	−	0.0744997i	$-0.976264\pi$
$409$		−	3.01333i		−	0.148999i	0.997221	−	0.0744997i	$-0.0237360\pi$
$410$	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
$417$	0.396863	+	2.31309i	0.0194345	+	0.113272i
$418$	4.53934	+	4.53934i	0.222026	+	0.222026i
$419$	39.6972			1.93934			0.969669	−	0.244423i	$-0.0785986\pi$
$419$	39.6972			1.93934			0.969669	+	0.244423i	$0.0785986\pi$
$420$	1.00000	−	2.40015i	0.0487950	−	0.117115i
$421$	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
$423$	1.99356	+	0.952107i	0.0969300	+	0.0462930i
$424$		−	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	$0.941525\pi$
$432$	−4.53553	+	2.53553i	−0.218216	+	0.121991i
$433$	6.55340	+	6.55340i	0.314936	+	0.314936i	0.846818	−	0.531882i	$-0.178515\pi$
$433$	6.55340	+	6.55340i	0.314936	+	0.314936i	−0.531882	+	0.846818i	$0.678515\pi$
$434$	0.671354			0.0322260
$435$	2.77098	+	6.72909i	0.132858	+	0.322635i
$436$	7.47661			0.358064
$437$	1.66636	+	1.66636i	0.0797127	+	0.0797127i
$438$	3.25903	+	18.9950i	0.155722	+	0.907616i
$439$			11.1508i			0.532199i	0.963946	+	0.266100i	$0.0857350\pi$
$439$			11.1508i			0.532199i	−0.963946	+	0.266100i	$0.914265\pi$
$440$	−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	$-0.789518\pi$
$443$	−3.68595	+	3.68595i	−0.175125	+	0.175125i	0.614102	+	0.789227i	$0.289518\pi$
$444$	−4.00000	−	2.82843i	−0.189832	−	0.134231i
$445$	−2.78654	−	12.4196i	−0.132095	−	0.588745i
$446$			5.10322i			0.241645i
$447$	34.7923	−	5.96942i	1.64562	−	0.282344i
$448$	0.474719	+	0.474719i	0.0224283	+	0.0224283i
$449$	12.8111			0.604592			0.302296	−	0.953214i	$-0.402247\pi$
$449$	12.8111			0.604592			0.302296	+	0.953214i	$0.402247\pi$
$450$	14.9999	+	0.0620825i	0.707101	+	0.00292660i
$451$	−29.6759			−1.39738
$452$	6.30315	+	6.30315i	0.296475	+	0.296475i
$453$	−33.2407	+	5.70320i	−1.56178	+	0.267960i
$454$			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	−0.0262250	−	0.999656i	$-0.508349\pi$
$457$	20.8096	−	20.8096i	0.973431	−	0.973431i	0.999656	+	0.0262250i	$0.00834864\pi$
$458$	−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	$0.924973\pi$
$462$	0.803365	+	4.68235i	0.0373759	+	0.217843i
$463$	−3.28991	−	3.28991i	−0.152895	−	0.152895i	0.626515	−	0.779410i	$-0.284481\pi$
$463$	−3.28991	−	3.28991i	−0.152895	−	0.152895i	−0.779410	+	0.626515i	$0.784481\pi$
$464$	−1.87899			−0.0872299
$465$	1.47472	+	3.58123i	0.0683884	+	0.166076i
$466$	−12.9421			−0.599532
$467$	−11.2120	−	11.2120i	−0.518828	−	0.518828i	0.398389	−	0.917217i	$-0.369569\pi$
$467$	−11.2120	−	11.2120i	−0.518828	−	0.518828i	−0.917217	+	0.398389i	$0.869569\pi$
$468$	5.68003	−	11.8931i	0.262559	−	0.549756i
$469$		−	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
$477$	4.54070	−	9.50749i	0.207905	−	0.435318i
$478$	18.7716	+	18.7716i	0.858593	+	0.858593i
$479$	5.88990			0.269116			0.134558	−	0.990906i	$-0.457039\pi$
$479$	5.88990			0.269116			0.134558	+	0.990906i	$0.457039\pi$
$480$	−1.48953	+	3.57510i	−0.0679873	+	0.163180i
$481$	12.4260			0.566579
$482$	2.55034	+	2.55034i	0.116165	+	0.116165i
$483$	0.294909	+	1.71886i	0.0134188	+	0.0782107i
$484$		−	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	0.117767	−	0.993041i	$-0.462426\pi$
$487$	24.5134	−	24.5134i	1.11081	−	1.11081i	0.993041	−	0.117767i	$-0.0375736\pi$
$488$	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	$0.812069\pi$
$492$	−12.3997	+	2.12745i	−0.559022	+	0.0959131i
$493$	7.63739	+	7.63739i	0.343971	+	0.343971i
$494$	−6.90309			−0.310585
$495$	−23.2126	+	14.5708i	−1.04333	+	0.654911i
$496$	−1.00000			−0.0449013
$497$	−2.10239	−	2.10239i	−0.0943052	−	0.0943052i
$498$	−20.1776	+	3.46193i	−0.904179	+	0.155133i
$499$			38.4311i			1.72041i	0.509945	+	0.860207i	$0.329666\pi$
$499$			38.4311i			1.72041i	−0.509945	+	0.860207i	$0.670334\pi$
$500$	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	$-0.939923\pi$
$503$	−17.8215	+	17.8215i	−0.794623	+	0.794623i	0.187619	+	0.982242i	$0.439923\pi$
$504$	0.671354	+	1.89887i	0.0299045	+	0.0845826i
$505$	27.4260	−	6.15348i	1.22044	−	0.273826i
$506$		−	6.12745i		−	0.272399i
$507$	1.84547	+	10.7562i	0.0819601	+	0.477698i
$508$	13.5138	+	13.5138i	0.599580	+	0.599580i
$509$	26.2585			1.16389			0.581944	−	0.813229i	$-0.302292\pi$
$509$	26.2585			1.16389			0.581944	+	0.813229i	$0.302292\pi$
$510$	20.5858	−	8.47704i	0.911554	−	0.375370i
$511$	7.47016			0.330460
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	3.98405	+	7.12663i	0.175900	+	0.314648i
$514$			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	$-0.208317\pi$
$522$	−5.08663	−	2.42933i	−0.222636	−	0.106329i
$523$	−18.1124	−	18.1124i	−0.792001	−	0.792001i	0.189818	−	0.981819i	$-0.439210\pi$
$523$	−18.1124	−	18.1124i	−0.792001	−	0.792001i	−0.981819	+	0.189818i	$0.939210\pi$
$524$	−14.5940			−0.637543
$525$	1.00688	−	5.72624i	0.0439440	−	0.249914i
$526$	−13.1502			−0.573376
$527$	4.06462	+	4.06462i	0.177058	+	0.177058i
$528$	−1.19663	−	6.97450i	−0.0520768	−	0.303526i
$529$			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
$537$	−38.7964	+	6.65642i	−1.67419	+	0.287246i
$538$	6.54390	+	6.54390i	0.282128	+	0.282128i
$539$	−26.7575			−1.15253
$540$	−8.65453	+	7.75236i	−0.372432	+	0.333609i
$541$	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
$543$	−18.1456	+	3.11330i	−0.778704	+	0.133604i
$544$			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	−0.890808	−	0.454380i	$-0.849861\pi$
$547$	−10.2072	+	10.2072i	−0.436428	+	0.436428i	0.454380	+	0.890808i	$0.349861\pi$
$548$	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
$552$	−0.439276	−	2.56029i	−0.0186968	−	0.108973i
$553$	4.33276	+	4.33276i	0.184248	+	0.184248i
$554$	−26.6344			−1.13159
$555$	−10.1119	−	4.21302i	−0.429226	−	0.178833i
$556$	−1.35498			−0.0574638
$557$	12.7383	+	12.7383i	0.539739	+	0.539739i	0.923452	−	0.383713i	$-0.125355\pi$
$557$	12.7383	+	12.7383i	0.539739	+	0.539739i	−0.383713	+	0.923452i	$0.625355\pi$
$558$	−2.70711	−	1.29289i	−0.114601	−	0.0547325i
$559$		−	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	$-0.732442\pi$
$563$	1.84999	−	1.84999i	0.0779678	−	0.0779678i	0.745015	+	0.667047i	$0.232442\pi$
$564$	−0.736416	+	1.04145i	−0.0310087	+	0.0438529i
$565$	16.8379	+	10.6668i	0.708377	+	0.448756i
$566$		−	19.5358i		−	0.821153i
$567$	−0.637616	+	6.00844i	−0.0267774	+	0.252331i
$568$	3.13157	+	3.13157i	0.131398	+	0.131398i
$569$	28.0100			1.17424			0.587121	−	0.809499i	$-0.300261\pi$
$569$	28.0100			1.17424			0.587121	+	0.809499i	$0.300261\pi$
$570$	5.61750	+	2.34048i	0.235291	+	0.0980318i
$571$	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
$573$	−0.238866	−	1.39221i	−0.00997875	−	0.0581604i
$574$			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	−0.777331	−	0.629092i	$-0.783427\pi$
$577$	−3.56082	+	3.56082i	−0.148239	+	0.148239i	0.629092	+	0.777331i	$0.283427\pi$
$578$	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
$582$	−20.1566	+	3.45833i	−0.835519	+	0.143352i
$583$	10.1461	+	10.1461i	0.420207	+	0.420207i
$584$	−11.1270			−0.460439
$585$	6.57085	−	28.7291i	0.271671	−	1.18780i
$586$	28.6145			1.18206
$587$	−17.7934	−	17.7934i	−0.734413	−	0.734413i	0.237078	−	0.971491i	$-0.423810\pi$
$587$	−17.7934	−	17.7934i	−0.734413	−	0.734413i	−0.971491	+	0.237078i	$0.923810\pi$
$588$	−11.1803	+	1.91824i	−0.461069	+	0.0791069i
$589$			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	0.535832	−	0.844325i	$-0.319998\pi$
$593$	33.6090	−	33.6090i	1.38016	−	1.38016i	0.844325	−	0.535832i	$-0.180002\pi$
$594$	5.77786	−	20.4278i	0.237069	−	0.838164i
$595$	−1.88914	−	8.41989i	−0.0774472	−	0.345182i
$596$			20.3809i			0.834833i
$597$	−4.71959	−	27.5078i	−0.193160	−	1.12582i
$598$	4.65908	+	4.65908i	0.190524	+	0.190524i
$599$	−6.77010			−0.276619			−0.138309	−	0.990389i	$-0.544167\pi$
$599$	−6.77010			−0.276619			−0.138309	+	0.990389i	$0.544167\pi$
$600$	−1.49978	+	8.52940i	−0.0612283	+	0.348211i
$601$	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
$603$	−9.82291	+	20.5676i	−0.400020	+	0.837576i
$604$		−	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	−0.147845	−	0.989010i	$-0.547234\pi$
$607$	20.7241	−	20.7241i	0.841165	−	0.841165i	0.989010	+	0.147845i	$0.0472338\pi$
$608$	−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
$612$	−7.43187	+	15.5611i	−0.300415	+	0.629021i
$613$	−25.8175	−	25.8175i	−1.04276	−	1.04276i	−0.999044	−	0.0437155i	$-0.986080\pi$
$613$	−25.8175	−	25.8175i	−1.04276	−	1.04276i	−0.0437155	−	0.999044i	$-0.513920\pi$
$614$	10.8392			0.437434
$615$	−26.0126	+	10.7117i	−1.04893	+	0.431939i
$616$	−2.74286			−0.110513
$617$	13.0922	+	13.0922i	0.527073	+	0.527073i	0.919698	−	0.392626i	$-0.128433\pi$
$617$	13.0922	+	13.0922i	0.527073	+	0.527073i	−0.392626	+	0.919698i	$0.628433\pi$
$618$	0.186254	+	1.08557i	0.00749223	+	0.0436679i
$619$		−	6.70426i		−	0.269467i	−0.990882	−	0.134734i	$-0.956982\pi$
$619$		−	6.70426i		−	0.269467i	0.990882	−	0.134734i	$-0.0430178\pi$
$620$	−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
$627$	−10.9589	+	1.88026i	−0.437658	+	0.0750902i
$628$	−1.46245	−	1.46245i	−0.0583581	−	0.0583581i
$629$	−16.2585			−0.648269
$630$	2.39433	+	3.81437i	0.0953923	+	0.151968i
$631$	−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
$633$	−42.8945	+	7.35953i	−1.70490	+	0.292515i
$634$		−	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	$-0.140099\pi$
$642$	−2.07277	−	12.0810i	−0.0818059	−	0.476799i
$643$	−21.5307	−	21.5307i	−0.849087	−	0.849087i	0.140933	−	0.990019i	$-0.454990\pi$
$643$	−21.5307	−	21.5307i	−0.849087	−	0.849087i	−0.990019	+	0.140933i	$0.954990\pi$
$644$	−1.00688			−0.0396768
$645$	−2.45833	+	5.90037i	−0.0967967	+	0.232327i
$646$	9.03214			0.355365
$647$	−10.5743	−	10.5743i	−0.415720	−	0.415720i	0.468005	−	0.883726i	$-0.344973\pi$
$647$	−10.5743	−	10.5743i	−0.415720	−	0.415720i	−0.883726	+	0.468005i	$0.844973\pi$
$648$	0.949747	−	8.94975i	0.0373096	−	0.351579i
$649$		−	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	$-0.552540\pi$
$653$	21.0078	−	21.0078i	0.822099	−	0.822099i	0.986409	+	0.164310i	$0.0525398\pi$
$654$	−7.47661	+	10.5735i	−0.292358	+	0.413457i
$655$	−31.8416	+	7.14418i	−1.24415	+	0.279146i
$656$		−	7.26358i		−	0.283595i
$657$	−30.1220	−	14.3860i	−1.17517	−	0.561253i
$658$	0.349590	+	0.349590i	0.0136284	+	0.0136284i
$659$	−26.4009			−1.02843			−0.514216	−	0.857661i	$-0.671917\pi$
$659$	−26.4009			−1.02843			−0.514216	+	0.857661i	$0.671917\pi$
$660$	−6.02506	−	14.6314i	−0.234525	−	0.569525i
$661$	−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
$663$	−7.39661	−	43.1106i	−0.287260	−	1.67428i
$664$		−	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
$672$	−1.14607	+	0.196635i	−0.0442107	+	0.00758536i
$673$	−21.6844	−	21.6844i	−0.835870	−	0.835870i	0.152442	−	0.988312i	$-0.451286\pi$
$673$	−21.6844	−	21.6844i	−0.835870	−	0.835870i	−0.988312	+	0.152442i	$0.951286\pi$
$674$	4.81554			0.185488
$675$	−15.0877	+	21.1509i	−0.580725	+	0.814100i
$676$	−6.30082			−0.242339
$677$	31.1572	+	31.1572i	1.19747	+	1.19747i	0.974923	+	0.222544i	$0.0714362\pi$
$677$	31.1572	+	31.1572i	1.19747	+	1.19747i	0.222544	+	0.974923i	$0.428564\pi$
$678$	−15.2171	+	2.61085i	−0.584411	+	0.100269i
$679$			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	−0.0598802	+	0.998206i	$0.519072\pi$
$683$	−27.6523	+	27.6523i	−1.05809	+	1.05809i	−0.998206	+	0.0598802i	$0.980928\pi$
$684$	−4.44427	+	1.57129i	−0.169931	+	0.0600797i
$685$	10.5388	−	16.6359i	0.402668	−	0.635625i
$686$			9.09636i			0.347301i
$687$	−1.94550	−	11.3392i	−0.0742255	−	0.432618i
$688$	−1.16702	−	1.16702i	−0.0444921	−	0.0444921i
$689$	−15.4294			−0.587813
$690$	−2.21175	−	5.37106i	−0.0842001	−	0.204473i
$691$	−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
$693$	−7.42521	−	3.54623i	−0.282061	−	0.134710i
$694$			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	$0.958283\pi$
$702$	11.1393	+	19.9258i	0.420425	+	0.752052i
$703$	−3.14257	−	3.14257i	−0.118524	−	0.118524i
$704$	4.08557			0.153981
$705$	−1.09691	+	2.63276i	−0.0413121	+	0.0991553i
$706$	5.92849			0.223122
$707$	5.96732	+	5.96732i	0.224424	+	0.224424i
$708$	−1.29035	−	7.52072i	−0.0484944	−	0.282646i
$709$			19.1112i			0.717735i	0.933389	+	0.358867i	$0.116837\pi$
$709$			19.1112i			0.717735i	−0.933389	+	0.358867i	$0.883163\pi$
$710$	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
$717$	−45.3187	+	7.77545i	−1.69246	+	0.290380i
$718$	4.91855	+	4.91855i	0.183559	+	0.183559i
$719$	−40.0027			−1.49185			−0.745925	−	0.666030i	$-0.767992\pi$
$719$	−40.0027			−1.49185			−0.745925	+	0.666030i	$0.767992\pi$
$720$	−3.56642	−	5.68161i	−0.132913	−	0.211741i
$721$	0.426921			0.0158994
$722$	−11.6892	−	11.6892i	−0.435028	−	0.435028i
$723$	−6.15707	+	1.05639i	−0.228984	+	0.0392874i
$724$		−	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	−0.909034	−	0.416723i	$-0.863179\pi$
$727$	−13.2741	+	13.2741i	−0.492311	+	0.492311i	0.416723	+	0.909034i	$0.363179\pi$
$728$	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
$732$	3.29035	+	19.1776i	0.121615	+	0.708824i
$733$	−8.25491	−	8.25491i	−0.304902	−	0.304902i	0.538026	−	0.842928i	$-0.319170\pi$
$733$	−8.25491	−	8.25491i	−0.304902	−	0.304902i	−0.842928	+	0.538026i	$0.819170\pi$
$734$	−5.27182			−0.194586
$735$	−23.4545	+	9.65835i	−0.865132	+	0.356254i
$736$	1.49978			0.0552826
$737$	−21.9490	−	21.9490i	−0.808502	−	0.808502i
$738$	9.39104	−	19.6633i	0.345689	−	0.723816i
$739$			27.7673i			1.02143i	0.859749	+	0.510717i	$0.170620\pi$
$739$			27.7673i			1.02143i	−0.859749	+	0.510717i	$0.829380\pi$
$740$	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	$-0.555045\pi$
$743$	22.1612	−	22.1612i	0.813015	−	0.813015i	0.985085	+	0.172070i	$0.0550454\pi$
$744$	1.00000	−	1.41421i	0.0366618	−	0.0518476i
$745$	9.97701	+	44.4675i	0.365529	+	1.62916i
$746$		−	4.15645i		−	0.152179i
$747$	15.2817	−	31.9973i	0.559127	−	1.17072i
$748$	−16.6063	−	16.6063i	−0.607186	−	0.607186i
$749$	−4.75110			−0.173601
$750$	0.903121	+	19.3438i	0.0329773	+	0.706337i
$751$	−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
$753$	5.34989	+	31.1815i	0.194961	+	1.13632i
$754$			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	−0.210192	+	0.977660i	$0.567409\pi$
$757$	−32.6821	+	32.6821i	−1.18785	+	1.18785i	−0.977660	+	0.210192i	$0.932591\pi$
$758$	−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	$0.907141\pi$
$762$	−32.6253	+	5.59762i	−1.18189	+	0.202780i
$763$	3.54928	+	3.54928i	0.128493	+	0.128493i
$764$	0.815538			0.0295051
$765$	−8.59743	+	37.5897i	−0.310841	+	1.35906i
$766$	2.47642			0.0894769
$767$	13.6859	+	13.6859i	0.494168	+	0.494168i
$768$	1.70711	−	0.292893i	0.0615999	−	0.0105689i
$769$			25.7022i			0.926845i	0.886138	+	0.463422i	$0.153379\pi$
$769$			25.7022i			0.926845i	−0.886138	+	0.463422i	$0.846621\pi$
$770$	−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	−0.0597568	+	0.998213i	$0.519033\pi$
$773$	−29.4146	+	29.4146i	−1.05797	+	1.05797i	−0.998213	+	0.0597568i	$0.980967\pi$
$774$	−1.65041	−	4.66806i	−0.0593228	−	0.167790i
$775$	−4.52072	+	2.13613i	−0.162389	+	0.0767320i
$776$		−	11.8075i		−	0.423864i
$777$	−0.556167	−	3.24158i	−0.0199524	−	0.116291i
$778$	9.26941	+	9.26941i	0.332324	+	0.332324i
$779$	−11.4132			−0.408919
$780$	15.7064	+	6.54390i	0.562378	+	0.234309i
$781$	−18.0938			−0.647447
$782$	−6.09604	−	6.09604i	−0.217994	−	0.217994i
$783$	8.52222	−	4.76424i	0.304559	−	0.170260i
$784$		−	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	−0.601194	−	0.799103i	$-0.705308\pi$
$787$	5.55205	−	5.55205i	0.197909	−	0.197909i	0.799103	+	0.601194i	$0.205308\pi$
$788$	−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
$792$	11.0601	+	5.28220i	0.393002	+	0.187695i
$793$	−34.8984	−	34.8984i	−1.23928	−	1.23928i
$794$	7.77142			0.275797
$795$	12.5559	+	5.23130i	0.445312	+	0.185535i
$796$	16.1137			0.571135
$797$	1.64459	+	1.64459i	0.0582542	+	0.0582542i	0.735634	−	0.677380i	$-0.236884\pi$
$797$	1.64459	+	1.64459i	0.0582542	+	0.0582542i	−0.677380	+	0.735634i	$0.736884\pi$
$798$	0.308970	+	1.80081i	0.0109374	+	0.0637479i
$799$			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
$807$	−15.7984	+	2.71057i	−0.556129	+	0.0954166i
$808$	−8.88849	−	8.88849i	−0.312696	−	0.312696i
$809$	36.8202			1.29453			0.647265	−	0.762265i	$-0.275913\pi$
$809$	36.8202			1.29453			0.647265	+	0.762265i	$0.275913\pi$
$810$	−2.30897	−	19.9917i	−0.0811289	−	0.702437i
$811$	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
$813$	49.1668	−	8.43568i	1.72435	−	0.295852i
$814$			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	$-0.150466\pi$
$822$	2.57952	+	15.0346i	0.0899712	+	0.524391i
$823$	1.58219	+	1.58219i	0.0551518	+	0.0551518i	0.734145	−	0.678993i	$-0.237583\pi$
$823$	1.58219	+	1.58219i	0.0551518	+	0.0551518i	−0.678993	+	0.734145i	$0.737583\pi$
$824$	−0.635910			−0.0221530
$825$	−20.3081	−	28.9736i	−0.707037	−	1.00873i
$826$	−2.95767			−0.102911
$827$	32.0545	+	32.0545i	1.11464	+	1.11464i	0.992514	+	0.122128i	$0.0389719\pi$
$827$	32.0545	+	32.0545i	1.11464	+	1.11464i	0.122128	+	0.992514i	$0.461028\pi$
$828$	4.06007	+	1.93906i	0.141097	+	0.0673869i
$829$		−	19.2021i		−	0.666917i	−0.942765	−	0.333458i	$-0.891784\pi$
$829$		−	19.2021i		−	0.666917i	0.942765	−	0.333458i	$-0.108216\pi$
$830$	−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
$837$	4.53553	−	2.53553i	0.156771	−	0.0876409i
$838$	−28.0702	−	28.0702i	−0.969669	−	0.969669i
$839$	4.58696			0.158359			0.0791797	−	0.996860i	$-0.474770\pi$
$839$	4.58696			0.158359			0.0791797	+	0.996860i	$0.474770\pi$
$840$	−2.40427	+	0.990058i	−0.0829552	+	0.0341602i
$841$	−25.4694			−0.878255
$842$	−4.84893	−	4.84893i	−0.167105	−	0.167105i
$843$	−3.70320	−	21.5839i	−0.127545	−	0.743387i
$844$		−	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
$852$	−7.56029	+	1.29714i	−0.259011	+	0.0444393i
$853$	−28.9519	−	28.9519i	−0.991296	−	0.991296i	0.00866672	−	0.999962i	$-0.497241\pi$
$853$	−28.9519	−	28.9519i	−0.991296	−	0.991296i	−0.999962	+	0.00866672i	$0.997241\pi$
$854$	7.54196			0.258081
$855$	−8.92743	+	5.60387i	−0.305312	+	0.191648i
$856$	7.07689			0.241883
$857$	−20.9236	−	20.9236i	−0.714736	−	0.714736i	0.252786	−	0.967522i	$-0.418653\pi$
$857$	−20.9236	−	20.9236i	−0.714736	−	0.714736i	−0.967522	+	0.252786i	$0.918653\pi$
$858$	−30.6409	+	5.25714i	−1.04606	+	0.179476i
$859$			41.8628i			1.42834i	0.699971	+	0.714171i	$0.253196\pi$
$859$			41.8628i			1.42834i	−0.699971	+	0.714171i	$0.746804\pi$
$860$	−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	$-0.640000\pi$
$863$	14.0730	−	14.0730i	0.479049	−	0.479049i	0.904827	+	0.425778i	$0.140000\pi$
$864$	5.00000	+	1.41421i	0.170103	+	0.0481125i
$865$	33.7086	+	21.3544i	1.14613	+	0.726070i
$866$		−	9.26791i		−	0.314936i
$867$	4.69869	+	27.3860i	0.159576	+	0.930076i
$868$	−0.474719	−	0.474719i	−0.0161130	−	0.0161130i
$869$	37.2890			1.26494
$870$	2.79881	−	6.71757i	0.0948885	−	0.227747i
$871$	33.3784			1.13098
$872$	−5.28676	−	5.28676i	−0.179032	−	0.179032i
$873$	15.2658	−	31.9641i	0.516670	−	1.08182i
$874$		−	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	−0.990116	−	0.140248i	$-0.955210\pi$
$877$	−25.1682	+	25.1682i	−0.849868	+	0.849868i	0.140248	+	0.990116i	$0.455210\pi$
$878$	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	$0.610722\pi$
$882$	8.46753	−	17.7296i	0.285116	−	0.596987i
$883$	11.1283	+	11.1283i	0.374497	+	0.374497i	0.869112	−	0.494615i	$-0.164691\pi$
$883$	11.1283	+	11.1283i	0.374497	+	0.374497i	−0.494615	+	0.869112i	$0.664691\pi$
$884$	25.2536			0.849370
$885$	−6.49693	−	15.7772i	−0.218392	−	0.530346i
$886$	5.21272			0.175125
$887$	−27.8846	−	27.8846i	−0.936272	−	0.936272i	0.0618158	−	0.998088i	$-0.480311\pi$
$887$	−27.8846	−	27.8846i	−0.936272	−	0.936272i	−0.998088	+	0.0618158i	$0.980311\pi$
$888$	0.828427	+	4.82843i	0.0278002	+	0.162031i
$889$			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
$897$	−11.2480	+	1.92986i	−0.375561	+	0.0644360i
$898$	−9.05880	−	9.05880i	−0.302296	−	0.302296i
$899$	1.87899			0.0626678
$900$	−10.5626	−	10.6504i	−0.352087	−	0.355014i
$901$	20.1881			0.672564
$902$	20.9840	+	20.9840i	0.698691	+	0.698691i
$903$	−1.89149	+	0.324528i	−0.0629448	+	0.0107996i
$904$		−	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	−0.982575	−	0.185866i	$-0.940491\pi$
$907$	−23.9940	+	23.9940i	−0.796709	+	0.796709i	0.185866	+	0.982575i	$0.440491\pi$
$908$	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	$0.972648\pi$
$912$	−0.460219	−	2.68235i	−0.0152394	−	0.0888216i
$913$	34.1465	+	34.1465i	1.13008	+	1.13008i
$914$	−29.4292			−0.973431
$915$	16.5669	+	40.2314i	0.547686	+	1.33001i
$916$	6.64235			0.219470
$917$	−6.92805	−	6.92805i	−0.228785	−	0.228785i
$918$	−14.5749	−	26.0714i	−0.481042	−	0.860483i
$919$		−	37.4389i		−	1.23500i	−0.786573	−	0.617498i	$-0.788146\pi$
$919$		−	37.4389i		−	1.23500i	0.786573	−	0.617498i	$-0.211854\pi$
$920$	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
$927$	−1.72148	−	0.822164i	−0.0565407	−	0.0270034i
$928$	1.32865	+	1.32865i	0.0436150	+	0.0436150i
$929$	−10.3349			−0.339079			−0.169539	−	0.985523i	$-0.554228\pi$
$929$	−10.3349			−0.339079			−0.169539	+	0.985523i	$0.554228\pi$
$930$	1.48953	−	3.57510i	0.0488436	−	0.117232i
$931$	−10.2908			−0.337268
$932$	9.15146	+	9.15146i	0.299766	+	0.299766i
$933$	8.35646	+	48.7050i	0.273578	+	1.59453i
$934$			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	−0.398298	−	0.917256i	$-0.630399\pi$
$937$	15.8855	−	15.8855i	0.518958	−	0.518958i	0.917256	+	0.398298i	$0.130399\pi$
$938$	−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	$-0.156548\pi$
$942$	3.53067	−	0.605767i	0.115035	−	0.0197369i
$943$	7.70307	+	7.70307i	0.250846	+	0.250846i
$944$	4.40554			0.143388
$945$	−7.78866	−	0.428274i	−0.253365	−	0.0139318i
$946$	6.74286			0.219229
$947$	34.7182	+	34.7182i	1.12819	+	1.12819i	0.990471	+	0.137718i	$0.0439768\pi$
$947$	34.7182	+	34.7182i	1.12819	+	1.12819i	0.137718	+	0.990471i	$0.456023\pi$
$948$	15.5808	−	2.67324i	0.506041	−	0.0868228i
$949$			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	$-0.772299\pi$
$953$	−3.05595	+	3.05595i	−0.0989919	+	0.0989919i	0.655876	+	0.754868i	$0.272299\pi$
$954$	−9.93358	+	3.51205i	−0.321611	+	0.113707i
$955$	1.77936	−	0.399229i	0.0575788	−	0.0129187i
$956$		−	26.5471i		−	0.858593i
$957$	2.24846	+	13.1050i	0.0726825	+	0.423625i
$958$	−4.16479	−	4.16479i	−0.134558	−	0.134558i
$959$	5.91264			0.190929
$960$	3.58123	−	1.47472i	0.115584	−	0.0475963i
$961$	1.00000			0.0322581
$962$	−8.78654	−	8.78654i	−0.283289	−	0.283289i
$963$	19.1579	+	9.14967i	0.617355	+	0.294844i
$964$		−	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	−0.0927884	+	0.995686i	$0.529578\pi$
$967$	−33.8479	+	33.8479i	−1.08847	+	1.08847i	−0.995686	+	0.0927884i	$0.970422\pi$
$968$	−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	$-0.384892\pi$
$972$	11.7071	+	10.2929i	0.375506	+	0.330145i
$973$	−0.643232	−	0.643232i	−0.0206211	−	0.0206211i
$974$	−34.6672			−1.11081
$975$	37.4720	+	6.58894i	1.20006	+	0.211015i
$976$	−11.2340			−0.359590
$977$	−1.11995	−	1.11995i	−0.0358304	−	0.0358304i	0.688965	−	0.724795i	$-0.258066\pi$
$977$	−1.11995	−	1.11995i	−0.0358304	−	0.0358304i	−0.724795	+	0.688965i	$0.758066\pi$
$978$	1.10651	+	6.44922i	0.0353823	+	0.206223i
$979$		−	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	−0.187087	+	0.982343i	$0.559905\pi$
$983$	−36.6650	+	36.6650i	−1.16943	+	1.16943i	−0.982343	+	0.187087i	$0.940095\pi$
$984$	10.2723	+	7.26358i	0.327468	+	0.231555i
$985$	−31.0613	+	49.0315i	−0.989696	+	1.56227i
$986$		−	10.8009i		−	0.343971i
$987$	−0.843985	+	0.144805i	−0.0268644	+	0.00460919i
$988$	4.88122	+	4.88122i	0.155292	+	0.155292i
$989$	2.47525			0.0787085
$990$	26.7169	+	6.11063i	0.849119	+	0.194209i
$991$	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
$993$	−33.5914	+	5.76337i	−1.06599	+	0.182895i
$994$			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	−0.903875	−	0.427796i	$-0.859290\pi$
$997$	−15.0323	+	15.0323i	−0.476079	+	0.476079i	0.427796	+	0.903875i	$0.359290\pi$
$998$	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.f.683.2	yes	8
3.2	odd	2		930.2.j.c.683.3	yes	8
5.2	odd	4		930.2.j.c.497.3	✓	8
15.2	even	4	inner	930.2.j.f.497.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.c.497.3	✓	8	5.2	odd	4
930.2.j.c.683.3	yes	8	3.2	odd	2
930.2.j.f.497.2	yes	8	15.2	even	4	inner
930.2.j.f.683.2	yes	8	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

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} +(1.70711 - 0.292893i) 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} +(0.292893 + 1.70711i) q^{12} +(-3.10651 - 3.10651i) q^{13} +0.671354 q^{14} +(1.47472 + 3.58123i) q^{15} -1.00000 q^{16} +(4.06462 + 4.06462i) q^{17} +(-2.70711 - 1.29289i) 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} +(4.53553 - 2.53553i) q^{27} +(-0.474719 - 0.474719i) q^{28} +1.87899 q^{29} +(1.48953 - 3.57510i) q^{30} +1.00000 q^{31} +(0.707107 + 0.707107i) q^{32} +(1.19663 + 6.97450i) 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} +(1.14607 - 0.196635i) q^{42} +(1.16702 + 1.16702i) q^{43} -4.08557 q^{44} +(3.56642 + 5.68161i) q^{45} -1.49978 q^{46} +(0.520724 + 0.520724i) q^{47} +(-1.70711 + 0.292893i) 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} +(0.460219 + 2.68235i) q^{57} +(-1.32865 - 1.32865i) q^{58} -4.40554 q^{59} +(-3.58123 + 1.47472i) q^{60} +11.2340 q^{61} +(-0.707107 - 0.707107i) q^{62} +(-0.867988 + 1.81743i) 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} +(1.29289 - 2.70711i) q^{72} +(-7.86799 - 7.86799i) q^{73} +2.82843 q^{74} +(-7.09170 + 4.97069i) q^{75} -1.57129 q^{76} +(-1.93949 - 1.93949i) q^{77} +(1.28676 + 7.49978i) 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} +(3.20764 - 0.550343i) q^{87} +(2.88893 + 2.88893i) q^{88} -5.69230 q^{89} +(1.49566 - 6.53934i) q^{90} +2.94944 q^{91} +(1.06051 + 1.06051i) q^{92} +(1.70711 - 0.292893i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} + 4 q^{7} + 8 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{15} - 8 q^{16} - 4 q^{17} - 16 q^{18} - 4 q^{20} + 12 q^{21} + 4 q^{22} + 12 q^{23} + 8 q^{24} - 4 q^{25} + 8 q^{27} + 4 q^{28} + 8 q^{29}+ \cdots + 4 q^{99}+O(q^{100}) \) 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^30 + 8 * q^31 - 24 * q^35 + 8 * q^36 - 16 * q^37 + 28 * q^38 - 8 * q^39 - 4 * q^40 - 16 * q^42 - 8 * q^43 - 4 * q^44 - 4 * 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 - 32 * q^57 - 28 * q^58 - 24 * q^59 + 56 * q^61 + 20 * 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 + 12 * q^78 + 56 * q^81 + 28 * q^82 + 12 * q^83 + 8 * q^84 + 32 * q^85 + 36 * q^87 + 4 * q^88 - 36 * q^89 + 12 * q^90 + 8 * q^91 + 12 * q^92 + 8 * q^93 + 36 * q^95 + 12 * q^97 - 32 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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