LMFDB - Embedded newform 930.2.j.c.497.4

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			497.4
Root			$0.692297i$ of defining polynomial
Character	$\chi$	$=$	930.497
Dual form			930.2.j.c.683.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.292893 - 1.70711i) q^{3} -1.00000i q^{4} +(1.19663 - 1.88893i) q^{5} +(-1.41421 - 1.00000i) q^{6} +(3.59604 + 3.59604i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 + 1.00000i) q^{9} +(-0.489528 - 2.18183i) q^{10} -1.67135i q^{11} +(-1.70711 + 0.292893i) q^{12} +(-0.721916 + 0.721916i) q^{13} +5.08557 q^{14} +(-3.57510 - 1.48953i) q^{15} -1.00000 q^{16} +(5.06462 - 5.06462i) q^{17} +(-1.29289 + 2.70711i) q^{18} -7.32821i q^{19} +(-1.88893 - 1.19663i) q^{20} +(5.08557 - 7.19208i) q^{21} +(-1.18183 - 1.18183i) q^{22} +(3.01025 + 3.01025i) q^{23} +(-1.00000 + 1.41421i) q^{24} +(-2.13613 - 4.52072i) q^{25} +1.02094i q^{26} +(2.53553 + 4.53553i) q^{27} +(3.59604 - 3.59604i) q^{28} -10.0205 q^{29} +(-3.58123 + 1.47472i) q^{30} +1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.85318 + 0.489528i) q^{33} -7.16246i q^{34} +(11.0958 - 2.48953i) q^{35} +(1.00000 + 2.82843i) q^{36} +(-2.00000 - 2.00000i) q^{37} +(-5.18183 - 5.18183i) q^{38} +(1.44383 + 1.02094i) q^{39} +(-2.18183 + 0.489528i) q^{40} +10.6359i q^{41} +(-1.48953 - 8.68161i) q^{42} +(-5.28834 + 5.28834i) q^{43} -1.67135 q^{44} +(-1.49566 + 6.53934i) q^{45} +4.25714 q^{46} +(1.86387 - 1.86387i) q^{47} +(0.292893 + 1.70711i) q^{48} +18.8630i q^{49} +(-4.70711 - 1.68616i) q^{50} +(-10.1292 - 7.16246i) q^{51} +(0.721916 + 0.721916i) q^{52} +(0.190501 + 0.190501i) q^{53} +(5.00000 + 1.41421i) q^{54} +(-3.15707 - 2.00000i) q^{55} -5.08557i q^{56} +(-12.5100 + 2.14638i) q^{57} +(-7.08557 + 7.08557i) q^{58} +3.00868 q^{59} +(-1.48953 + 3.57510i) q^{60} +9.83710 q^{61} +(0.707107 - 0.707107i) q^{62} +(-13.7672 - 6.57510i) q^{63} +1.00000i q^{64} +(0.499781 + 2.22752i) q^{65} +(-1.67135 + 2.36365i) q^{66} +(1.37233 + 1.37233i) q^{67} +(-5.06462 - 5.06462i) q^{68} +(4.25714 - 6.02051i) q^{69} +(6.08557 - 9.60629i) q^{70} -1.32821i q^{71} +(2.70711 + 1.29289i) q^{72} +(-0.424905 + 0.424905i) q^{73} -2.82843 q^{74} +(-7.09170 + 4.97069i) q^{75} -7.32821 q^{76} +(6.01025 - 6.01025i) q^{77} +(1.74286 - 0.299028i) q^{78} -1.39909i q^{79} +(-1.19663 + 1.88893i) q^{80} +(7.00000 - 5.65685i) q^{81} +(7.52072 + 7.52072i) q^{82} +(-7.37010 - 7.37010i) q^{83} +(-7.19208 - 5.08557i) q^{84} +(-3.50623 - 15.6272i) q^{85} +7.47884i q^{86} +(2.93494 + 17.1061i) q^{87} +(-1.18183 + 1.18183i) q^{88} +3.30770 q^{89} +(3.56642 + 5.68161i) q^{90} -5.19208 q^{91} +(3.01025 - 3.01025i) q^{92} +(-0.292893 - 1.70711i) q^{93} -2.63591i q^{94} +(-13.8425 - 8.76919i) q^{95} +(1.41421 + 1.00000i) q^{96} +(5.96456 + 5.96456i) q^{97} +(13.3382 + 13.3382i) q^{98} +(1.67135 + 4.72730i) 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^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

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
$5$	1.19663	−	1.88893i	0.535151	−	0.844756i
$5$	1.19663	−	1.88893i	0.535151	−	0.844756i
$6$	−1.41421	−	1.00000i	−0.577350	−	0.408248i
$7$	3.59604	+	3.59604i	1.35917	+	1.35917i	0.874935	+	0.484239i	$0.160904\pi$
$7$	3.59604	+	3.59604i	1.35917	+	1.35917i	0.484239	+	0.874935i	$0.339096\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.82843	+	1.00000i	−0.942809	+	0.333333i
$10$	−0.489528	−	2.18183i	−0.154802	−	0.689954i
$11$		−	1.67135i		−	0.503932i	−0.967736	−	0.251966i	$-0.918923\pi$
$11$		−	1.67135i		−	0.503932i	0.967736	−	0.251966i	$-0.0810771\pi$
$12$	−1.70711	+	0.292893i	−0.492799	+	0.0845510i
$13$	−0.721916	+	0.721916i	−0.200224	+	0.200224i	−0.800096	−	0.599872i	$-0.795218\pi$
$13$	−0.721916	+	0.721916i	−0.200224	+	0.200224i	0.599872	+	0.800096i	$0.295218\pi$
$14$	5.08557			1.35917
$15$	−3.57510	−	1.48953i	−0.923086	−	0.384595i
$16$	−1.00000			−0.250000
$17$	5.06462	−	5.06462i	1.22835	−	1.22835i	0.263764	−	0.964587i	$-0.415036\pi$
$17$	5.06462	−	5.06462i	1.22835	−	1.22835i	0.964587	−	0.263764i	$-0.0849642\pi$
$18$	−1.29289	+	2.70711i	−0.304738	+	0.638071i
$19$		−	7.32821i		−	1.68121i	−0.541652	−	0.840603i	$-0.682201\pi$
$19$		−	7.32821i		−	1.68121i	0.541652	−	0.840603i	$-0.317799\pi$
$20$	−1.88893	−	1.19663i	−0.422378	−	0.267576i
$21$	5.08557	−	7.19208i	1.10976	−	1.56944i
$22$	−1.18183	−	1.18183i	−0.251966	−	0.251966i
$23$	3.01025	+	3.01025i	0.627681	+	0.627681i	0.947484	−	0.319803i	$-0.103617\pi$
$23$	3.01025	+	3.01025i	0.627681	+	0.627681i	−0.319803	+	0.947484i	$0.603617\pi$
$24$	−1.00000	+	1.41421i	−0.204124	+	0.288675i
$25$	−2.13613	−	4.52072i	−0.427226	−	0.904145i
$26$			1.02094i			0.200224i
$27$	2.53553	+	4.53553i	0.487964	+	0.872864i
$28$	3.59604	−	3.59604i	0.679587	−	0.679587i
$29$	−10.0205			−1.86076			−0.930381	−	0.366595i	$-0.880523\pi$
$29$	−10.0205			−1.86076			−0.930381	+	0.366595i	$0.880523\pi$
$30$	−3.58123	+	1.47472i	−0.653840	+	0.269246i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−2.85318	+	0.489528i	−0.496675	+	0.0852159i
$34$		−	7.16246i		−	1.22835i
$35$	11.0958	−	2.48953i	1.87554	−	0.420807i
$36$	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	$0.824689\pi$
$38$	−5.18183	−	5.18183i	−0.840603	−	0.840603i
$39$	1.44383	+	1.02094i	0.231198	+	0.163482i
$40$	−2.18183	+	0.489528i	−0.344977	+	0.0774012i
$41$			10.6359i			1.66105i	0.556981	+	0.830525i	$0.311960\pi$
$41$			10.6359i			1.66105i	−0.556981	+	0.830525i	$0.688040\pi$
$42$	−1.48953	−	8.68161i	−0.229839	−	1.33960i
$43$	−5.28834	+	5.28834i	−0.806464	+	0.806464i	−0.984097	−	0.177633i	$-0.943156\pi$
$43$	−5.28834	+	5.28834i	−0.806464	+	0.806464i	0.177633	+	0.984097i	$0.443156\pi$
$44$	−1.67135			−0.251966
$45$	−1.49566	+	6.53934i	−0.222960	+	0.974828i
$46$	4.25714			0.627681
$47$	1.86387	−	1.86387i	0.271873	−	0.271873i	−0.557981	−	0.829854i	$-0.688424\pi$
$47$	1.86387	−	1.86387i	0.271873	−	0.271873i	0.829854	+	0.557981i	$0.188424\pi$
$48$	0.292893	+	1.70711i	0.0422755	+	0.246400i
$49$			18.8630i			2.69471i
$50$	−4.70711	−	1.68616i	−0.665685	−	0.238459i
$51$	−10.1292	−	7.16246i	−1.41838	−	1.00294i
$52$	0.721916	+	0.721916i	0.100112	+	0.100112i
$53$	0.190501	+	0.190501i	0.0261673	+	0.0261673i	0.720069	−	0.693902i	$-0.244110\pi$
$53$	0.190501	+	0.190501i	0.0261673	+	0.0261673i	−0.693902	+	0.720069i	$0.744110\pi$
$54$	5.00000	+	1.41421i	0.680414	+	0.192450i
$55$	−3.15707	−	2.00000i	−0.425700	−	0.269680i
$56$		−	5.08557i		−	0.679587i
$57$	−12.5100	+	2.14638i	−1.65699	+	0.284295i
$58$	−7.08557	+	7.08557i	−0.930381	+	0.930381i
$59$	3.00868			0.391696			0.195848	−	0.980634i	$-0.437254\pi$
$59$	3.00868			0.391696			0.195848	+	0.980634i	$0.437254\pi$
$60$	−1.48953	+	3.57510i	−0.192297	+	0.461543i
$61$	9.83710			1.25951			0.629756	−	0.776793i	$-0.283155\pi$
$61$	9.83710			1.25951			0.629756	+	0.776793i	$0.283155\pi$
$62$	0.707107	−	0.707107i	0.0898027	−	0.0898027i
$63$	−13.7672	−	6.57510i	−1.73450	−	0.828384i
$64$			1.00000i			0.125000i
$65$	0.499781	+	2.22752i	0.0619902	+	0.276290i
$66$	−1.67135	+	2.36365i	−0.205729	+	0.290945i
$67$	1.37233	+	1.37233i	0.167656	+	0.167656i	0.785948	−	0.618292i	$-0.212175\pi$
$67$	1.37233	+	1.37233i	0.167656	+	0.167656i	−0.618292	+	0.785948i	$0.712175\pi$
$68$	−5.06462	−	5.06462i	−0.614176	−	0.614176i
$69$	4.25714	−	6.02051i	0.512499	−	0.724784i
$70$	6.08557	−	9.60629i	0.727364	−	1.14817i
$71$		−	1.32821i		−	0.157629i	−0.996889	−	0.0788146i	$-0.974886\pi$
$71$		−	1.32821i		−	0.157629i	0.996889	−	0.0788146i	$-0.0251135\pi$
$72$	2.70711	+	1.29289i	0.319036	+	0.152369i
$73$	−0.424905	+	0.424905i	−0.0497313	+	0.0497313i	−0.731535	−	0.681804i	$-0.761196\pi$
$73$	−0.424905	+	0.424905i	−0.0497313	+	0.0497313i	0.681804	+	0.731535i	$0.261196\pi$
$74$	−2.82843			−0.328798
$75$	−7.09170	+	4.97069i	−0.818879	+	0.573966i
$76$	−7.32821			−0.840603
$77$	6.01025	−	6.01025i	0.684932	−	0.684932i
$78$	1.74286	−	0.299028i	0.197340	−	0.0338582i
$79$		−	1.39909i		−	0.157410i	−0.996898	−	0.0787052i	$-0.974921\pi$
$79$		−	1.39909i		−	0.157410i	0.996898	−	0.0787052i	$-0.0250786\pi$
$80$	−1.19663	+	1.88893i	−0.133788	+	0.211189i
$81$	7.00000	−	5.65685i	0.777778	−	0.628539i
$82$	7.52072	+	7.52072i	0.830525	+	0.830525i
$83$	−7.37010	−	7.37010i	−0.808973	−	0.808973i	0.175505	−	0.984478i	$-0.443844\pi$
$83$	−7.37010	−	7.37010i	−0.808973	−	0.808973i	−0.984478	+	0.175505i	$0.943844\pi$
$84$	−7.19208	−	5.08557i	−0.784720	−	0.554881i
$85$	−3.50623	−	15.6272i	−0.380304	−	1.69501i
$86$			7.47884i			0.806464i
$87$	2.93494	+	17.1061i	0.314658	+	1.83396i
$88$	−1.18183	+	1.18183i	−0.125983	+	0.125983i
$89$	3.30770			0.350616			0.175308	−	0.984514i	$-0.443908\pi$
$89$	3.30770			0.350616			0.175308	+	0.984514i	$0.443908\pi$
$90$	3.56642	+	5.68161i	0.375934	+	0.598894i
$91$	−5.19208			−0.544278
$92$	3.01025	−	3.01025i	0.313841	−	0.313841i
$93$	−0.292893	−	1.70711i	−0.0303716	−	0.177019i
$94$		−	2.63591i		−	0.271873i
$95$	−13.8425	−	8.76919i	−1.42021	−	0.899700i
$96$	1.41421	+	1.00000i	0.144338	+	0.102062i
$97$	5.96456	+	5.96456i	0.605609	+	0.605609i	0.941795	−	0.336186i	$-0.109137\pi$
$97$	5.96456	+	5.96456i	0.605609	+	0.605609i	−0.336186	+	0.941795i	$0.609137\pi$
$98$	13.3382	+	13.3382i	1.34736	+	1.34736i
$99$	1.67135	+	4.72730i	0.167977	+	0.475112i
$100$	−4.52072	+	2.13613i	−0.452072	+	0.213613i
$101$			9.46972i			0.942273i	0.882060	+	0.471136i	$0.156156\pi$
$101$			9.46972i			0.942273i	−0.882060	+	0.471136i	$0.843844\pi$
$102$	−12.2271	+	2.09784i	−1.21066	+	0.207717i
$103$	1.93494	−	1.93494i	0.190655	−	0.190655i	−0.605324	−	0.795979i	$-0.706956\pi$
$103$	1.93494	−	1.93494i	0.190655	−	0.190655i	0.795979	+	0.605324i	$0.206956\pi$
$104$	1.02094			0.100112
$105$	−7.49978	−	18.2126i	−0.731904	−	1.77737i
$106$	0.269409			0.0261673
$107$	0.0543708	−	0.0543708i	0.00525622	−	0.00525622i	−0.704474	−	0.709730i	$-0.748817\pi$
$107$	0.0543708	−	0.0543708i	0.00525622	−	0.00525622i	0.709730	+	0.704474i	$0.248817\pi$
$108$	4.53553	−	2.53553i	0.436432	−	0.243982i
$109$			6.07974i			0.582334i	0.956672	+	0.291167i	$0.0940435\pi$
$109$			6.07974i			0.582334i	−0.956672	+	0.291167i	$0.905957\pi$
$110$	−3.64660	+	0.818175i	−0.347690	+	0.0780099i
$111$	−2.82843	+	4.00000i	−0.268462	+	0.379663i
$112$	−3.59604	−	3.59604i	−0.339794	−	0.339794i
$113$	−2.23239	−	2.23239i	−0.210005	−	0.210005i	0.594264	−	0.804270i	$-0.297443\pi$
$113$	−2.23239	−	2.23239i	−0.210005	−	0.210005i	−0.804270	+	0.594264i	$0.797443\pi$
$114$	−7.32821	+	10.3637i	−0.686350	+	0.970645i
$115$	9.28834	−	2.08399i	0.866142	−	0.194333i
$116$			10.0205i			0.930381i
$117$	1.31997	−	2.76380i	0.122031	−	0.255514i
$118$	2.12745	−	2.12745i	0.195848	−	0.195848i
$119$	36.4252			3.33909
$120$	1.47472	+	3.58123i	0.134623	+	0.326920i
$121$	8.20658			0.746052
$122$	6.95588	−	6.95588i	0.629756	−	0.629756i
$123$	18.1566	−	3.11519i	1.63713	−	0.280887i
$124$		−	1.00000i		−	0.0898027i
$125$	−11.0955	−	1.37465i	−0.992413	−	0.122953i
$126$	−14.3842	+	5.08557i	−1.28144	+	0.453058i
$127$	−9.51384	−	9.51384i	−0.844217	−	0.844217i	0.145187	−	0.989404i	$-0.453622\pi$
$127$	−9.51384	−	9.51384i	−0.844217	−	0.844217i	−0.989404	+	0.145187i	$0.953622\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	10.5767	+	7.47884i	0.931224	+	0.658475i
$130$	1.92849	+	1.22170i	0.169140	+	0.107150i
$131$			4.47704i			0.391161i	0.980688	+	0.195581i	$0.0626591\pi$
$131$			4.47704i			0.391161i	−0.980688	+	0.195581i	$0.937341\pi$
$132$	0.489528	+	2.85318i	0.0426080	+	0.248337i
$133$	26.3525	−	26.3525i	2.28505	−	2.28505i
$134$	1.94076			0.167656
$135$	11.6014	+	0.637927i	0.998492	+	0.0549040i
$136$	−7.16246			−0.614176
$137$	−4.29859	+	4.29859i	−0.367253	+	0.367253i	−0.866475	−	0.499221i	$-0.833619\pi$
$137$	−4.29859	+	4.29859i	−0.367253	+	0.367253i	0.499221	+	0.866475i	$0.333619\pi$
$138$	−1.24689	−	7.26739i	−0.106142	−	0.618642i
$139$			8.18340i			0.694107i	0.937845	+	0.347054i	$0.112818\pi$
$139$			8.18340i			0.694107i	−0.937845	+	0.347054i	$0.887182\pi$
$140$	−2.48953	−	11.0958i	−0.210404	−	0.937768i
$141$	−3.72774	−	2.63591i	−0.313932	−	0.221984i
$142$	−0.939185	−	0.939185i	−0.0788146	−	0.0788146i
$143$	1.20658	+	1.20658i	0.100899	+	0.100899i
$144$	2.82843	−	1.00000i	0.235702	−	0.0833333i
$145$	−11.9909	+	18.9281i	−0.995789	+	1.57189i
$146$			0.600906i			0.0497313i
$147$	32.2011	−	5.52484i	2.65591	−	0.455681i
$148$	−2.00000	+	2.00000i	−0.164399	+	0.164399i
$149$	15.9667			1.30804			0.654020	−	0.756478i	$-0.273081\pi$
$149$	15.9667			1.30804			0.654020	+	0.756478i	$0.273081\pi$
$150$	−1.49978	+	8.52940i	−0.122457	+	0.696423i
$151$	10.3004			0.838233			0.419117	−	0.907932i	$-0.362340\pi$
$151$	10.3004			0.838233			0.419117	+	0.907932i	$0.362340\pi$
$152$	−5.18183	+	5.18183i	−0.420302	+	0.420302i
$153$	−9.26029	+	19.3895i	−0.748650	+	1.56755i
$154$		−	8.49978i		−	0.684932i
$155$	1.19663	−	1.88893i	0.0961160	−	0.151723i
$156$	1.02094	−	1.44383i	0.0817409	−	0.115599i
$157$	4.58377	+	4.58377i	0.365825	+	0.365825i	0.865952	−	0.500127i	$-0.166713\pi$
$157$	4.58377	+	4.58377i	0.365825	+	0.365825i	−0.500127	+	0.865952i	$0.666713\pi$
$158$	−0.989309	−	0.989309i	−0.0787052	−	0.0787052i
$159$	0.269409	−	0.381001i	0.0213655	−	0.0302154i
$160$	0.489528	+	2.18183i	0.0387006	+	0.172488i
$161$			21.6500i			1.70626i
$162$	0.949747	−	8.94975i	0.0746192	−	0.703159i
$163$	3.08557	−	3.08557i	0.241680	−	0.241680i	−0.575865	−	0.817545i	$-0.695335\pi$
$163$	3.08557	−	3.08557i	0.241680	−	0.241680i	0.817545	+	0.575865i	$0.195335\pi$
$164$	10.6359			0.830525
$165$	−2.48953	+	5.97525i	−0.193810	+	0.465172i
$166$	−10.4229			−0.808973
$167$	−10.8177	+	10.8177i	−0.837102	+	0.837102i	−0.988476	−	0.151375i	$-0.951630\pi$
$167$	−10.8177	+	10.8177i	−0.837102	+	0.837102i	0.151375	+	0.988476i	$0.451630\pi$
$168$	−8.68161	+	1.48953i	−0.669800	+	0.114920i
$169$			11.9577i			0.919821i
$170$	−13.5294	−	8.57085i	−1.03766	−	0.657354i
$171$	7.32821	+	20.7273i	0.560402	+	1.58506i
$172$	5.28834	+	5.28834i	0.403232	+	0.403232i
$173$	−6.45251	−	6.45251i	−0.490575	−	0.490575i	0.417912	−	0.908487i	$-0.362762\pi$
$173$	−6.45251	−	6.45251i	−0.490575	−	0.490575i	−0.908487	+	0.417912i	$0.862762\pi$
$174$	14.1711	+	10.0205i	1.07431	+	0.759653i
$175$	8.57510	−	23.9383i	0.648216	−	1.80957i
$176$			1.67135i			0.125983i
$177$	−0.881221	−	5.13613i	−0.0662366	−	0.386055i
$178$	2.33890	−	2.33890i	0.175308	−	0.175308i
$179$	−16.5843			−1.23957			−0.619784	−	0.784772i	$-0.712780\pi$
$179$	−16.5843			−1.23957			−0.619784	+	0.784772i	$0.712780\pi$
$180$	6.53934	+	1.49566i	0.487414	+	0.111480i
$181$	1.87211			0.139153			0.0695763	−	0.997577i	$-0.477835\pi$
$181$	1.87211			0.139153			0.0695763	+	0.997577i	$0.477835\pi$
$182$	−3.67135	+	3.67135i	−0.272139	+	0.272139i
$183$	−2.88122	−	16.7930i	−0.212986	−	1.24137i
$184$		−	4.25714i		−	0.313841i
$185$	−6.17113	+	1.38459i	−0.453711	+	0.101797i
$186$	−1.41421	−	1.00000i	−0.103695	−	0.0733236i
$187$	−8.46478	−	8.46478i	−0.619006	−	0.619006i
$188$	−1.86387	−	1.86387i	−0.135937	−	0.135937i
$189$	−7.19208	+	25.4278i	−0.523147	+	1.84960i
$190$	−15.9889	+	3.58736i	−1.15995	+	0.260255i
$191$			17.4430i			1.26213i	0.775731	+	0.631064i	$0.217381\pi$
$191$			17.4430i			1.26213i	−0.775731	+	0.631064i	$0.782619\pi$
$192$	1.70711	−	0.292893i	0.123200	−	0.0211377i
$193$	−1.90216	+	1.90216i	−0.136921	+	0.136921i	−0.772245	−	0.635325i	$-0.780866\pi$
$193$	−1.90216	+	1.90216i	−0.136921	+	0.136921i	0.635325	+	0.772245i	$0.280866\pi$
$194$	8.43516			0.605609
$195$	3.65623	−	1.50560i	0.261828	−	0.107819i
$196$	18.8630			1.34736
$197$	2.69768	−	2.69768i	0.192202	−	0.192202i	−0.604445	−	0.796647i	$-0.706605\pi$
$197$	2.69768	−	2.69768i	0.192202	−	0.192202i	0.796647	+	0.604445i	$0.206605\pi$
$198$	4.52453	+	2.16088i	0.321545	+	0.153567i
$199$		−	24.1848i		−	1.71441i	−0.514974	−	0.857206i	$-0.672198\pi$
$199$		−	24.1848i		−	1.71441i	0.514974	−	0.857206i	$-0.327802\pi$
$200$	−1.68616	+	4.70711i	−0.119230	+	0.332843i
$201$	1.94076	−	2.74465i	0.136891	−	0.193593i
$202$	6.69611	+	6.69611i	0.471136	+	0.471136i
$203$	−36.0341	−	36.0341i	−2.52910	−	2.52910i
$204$	−7.16246	+	10.1292i	−0.501472	+	0.709189i
$205$	20.0905	+	12.7273i	1.40318	+	0.888913i
$206$		−	2.73642i		−	0.190655i
$207$	−11.5245	−	5.50403i	−0.801010	−	0.382556i
$208$	0.721916	−	0.721916i	0.0500559	−	0.0500559i
$209$	−12.2480			−0.847214
$210$	−18.1814	−	7.57510i	−1.25463	−	0.522731i
$211$	−14.6009			−1.00517			−0.502584	−	0.864528i	$-0.667617\pi$
$211$	−14.6009			−1.00517			−0.502584	+	0.864528i	$0.667617\pi$
$212$	0.190501	−	0.190501i	0.0130836	−	0.0130836i
$213$	−2.26739	+	0.389023i	−0.155359	+	0.0266554i
$214$		−	0.0768919i		−	0.00525622i
$215$	3.66110	+	16.3175i	0.249685	+	1.11285i
$216$	1.41421	−	5.00000i	0.0962250	−	0.340207i
$217$	3.59604	+	3.59604i	0.244115	+	0.244115i
$218$	4.29903	+	4.29903i	0.291167	+	0.291167i
$219$	0.849810	+	0.600906i	0.0574248	+	0.0406055i
$220$	−2.00000	+	3.15707i	−0.134840	+	0.212850i
$221$			7.31247i			0.491890i
$222$	0.828427	+	4.82843i	0.0556004	+	0.324063i
$223$	12.2654	−	12.2654i	0.821350	−	0.821350i	−0.164951	−	0.986302i	$-0.552747\pi$
$223$	12.2654	−	12.2654i	0.821350	−	0.821350i	0.986302	+	0.164951i	$0.0527467\pi$
$224$	−5.08557			−0.339794
$225$	10.5626	+	10.6504i	0.704174	+	0.710027i
$226$	−3.15707			−0.210005
$227$	4.98392	−	4.98392i	0.330795	−	0.330795i	−0.522094	−	0.852888i	$-0.674849\pi$
$227$	4.98392	−	4.98392i	0.330795	−	0.330795i	0.852888	+	0.522094i	$0.174849\pi$
$228$	2.14638	+	12.5100i	0.142148	+	0.828497i
$229$			12.3993i			0.819367i	0.912228	+	0.409684i	$0.134361\pi$
$229$			12.3993i			0.819367i	−0.912228	+	0.409684i	$0.865639\pi$
$230$	5.09424	−	8.04145i	0.335904	−	0.530237i
$231$	−12.0205	−	8.49978i	−0.790891	−	0.559245i
$232$	7.08557	+	7.08557i	0.465190	+	0.465190i
$233$	19.3438	+	19.3438i	1.26726	+	1.26726i	0.947499	+	0.319758i	$0.103602\pi$
$233$	19.3438	+	19.3438i	1.26726	+	1.26726i	0.319758	+	0.947499i	$0.396398\pi$
$234$	−1.02094	−	2.88767i	−0.0667412	−	0.188773i
$235$	−1.29035	−	5.75110i	−0.0841733	−	0.375160i
$236$		−	3.00868i		−	0.195848i
$237$	−2.38840	+	0.409785i	−0.155143	+	0.0266184i
$238$	25.7565	−	25.7565i	1.66954	−	1.66954i
$239$	8.86716			0.573569			0.286784	−	0.957995i	$-0.407414\pi$
$239$	8.86716			0.573569			0.286784	+	0.957995i	$0.407414\pi$
$240$	3.57510	+	1.48953i	0.230771	+	0.0961486i
$241$	−6.97906			−0.449561			−0.224780	−	0.974409i	$-0.572166\pi$
$241$	−6.97906			−0.449561			−0.224780	+	0.974409i	$0.572166\pi$
$242$	5.80293	−	5.80293i	0.373026	−	0.373026i
$243$	−11.7071	−	10.2929i	−0.751011	−	0.660289i
$244$		−	9.83710i		−	0.629756i
$245$	35.6309	+	22.5721i	2.27638	+	1.44208i
$246$	10.6359	−	15.0414i	0.678121	−	0.959008i
$247$	5.29035	+	5.29035i	0.336617	+	0.336617i
$248$	−0.707107	−	0.707107i	−0.0449013	−	0.0449013i
$249$	−10.4229	+	14.7402i	−0.660524	+	0.934122i
$250$	−8.81774	+	6.87368i	−0.557683	+	0.434730i
$251$		−	17.0941i		−	1.07897i	−0.841995	−	0.539485i	$-0.818619\pi$
$251$		−	17.0941i		−	1.07897i	0.841995	−	0.539485i	$-0.181381\pi$
$252$	−6.57510	+	13.7672i	−0.414192	+	0.867250i
$253$	5.03120	−	5.03120i	0.316309	−	0.316309i
$254$	−13.4546			−0.844217
$255$	−25.6504	+	10.5626i	−1.60629	+	0.661456i
$256$	1.00000			0.0625000
$257$	−17.3020	+	17.3020i	−1.07927	+	1.07927i	−0.0826913	+	0.996575i	$0.526352\pi$
$257$	−17.3020	+	17.3020i	−1.07927	+	1.07927i	−0.996575	+	0.0826913i	$0.973648\pi$
$258$	12.7672	−	2.19050i	0.794849	−	0.136375i
$259$		−	14.3842i		−	0.893788i
$260$	2.22752	−	0.499781i	0.138145	−	0.0309951i
$261$	28.3423	−	10.0205i	1.75434	−	0.620254i
$262$	3.16575	+	3.16575i	0.195581	+	0.195581i
$263$	1.22752	+	1.22752i	0.0756922	+	0.0756922i	0.743939	−	0.668247i	$-0.232955\pi$
$263$	1.22752	+	1.22752i	0.0756922	+	0.0756922i	−0.668247	+	0.743939i	$0.732955\pi$
$264$	2.36365	+	1.67135i	0.145473	+	0.102865i
$265$	0.587802	−	0.131883i	0.0361084	−	0.00810151i
$266$		−	37.2681i		−	2.28505i
$267$	−0.968804	−	5.64660i	−0.0592898	−	0.345566i
$268$	1.37233	−	1.37233i	0.0838282	−	0.0838282i
$269$	−0.283908			−0.0173102			−0.00865508	−	0.999963i	$-0.502755\pi$
$269$	−0.283908			−0.0173102			−0.00865508	+	0.999963i	$0.502755\pi$
$270$	8.65453	−	7.75236i	0.526698	−	0.471794i
$271$	21.0688			1.27984			0.639920	−	0.768441i	$-0.278967\pi$
$271$	21.0688			1.27984			0.639920	+	0.768441i	$0.278967\pi$
$272$	−5.06462	+	5.06462i	−0.307088	+	0.307088i
$273$	1.52072	+	8.86343i	0.0920384	+	0.536439i
$274$			6.07912i			0.367253i
$275$	−7.55573	+	3.57023i	−0.455628	+	0.215293i
$276$	−6.02051	−	4.25714i	−0.362392	−	0.256250i
$277$	−11.3481	−	11.3481i	−0.681841	−	0.681841i	0.278574	−	0.960415i	$-0.410138\pi$
$277$	−11.3481	−	11.3481i	−0.681841	−	0.681841i	−0.960415	+	0.278574i	$0.910138\pi$
$278$	5.78654	+	5.78654i	0.347054	+	0.347054i
$279$	−2.82843	+	1.00000i	−0.169334	+	0.0598684i
$280$	−9.60629	−	6.08557i	−0.574086	−	0.363682i
$281$			17.1288i			1.02182i	0.859634	+	0.510910i	$0.170691\pi$
$281$			17.1288i			1.02182i	−0.859634	+	0.510910i	$0.829309\pi$
$282$	−4.49978	+	0.772040i	−0.267958	+	0.0459743i
$283$	19.5708	−	19.5708i	1.16337	−	1.16337i	0.179632	−	0.983734i	$-0.442509\pi$
$283$	19.5708	−	19.5708i	1.16337	−	1.16337i	0.983734	−	0.179632i	$-0.0574908\pi$
$284$	−1.32821			−0.0788146
$285$	−10.9156	+	26.1990i	−0.646583	+	1.55190i
$286$	1.70636			0.100899
$287$	−38.2471	+	38.2471i	−2.25766	+	2.25766i
$288$	1.29289	−	2.70711i	0.0761845	−	0.159518i
$289$		−	34.3008i		−	2.01770i
$290$	4.90532	+	21.8630i	0.288050	+	1.28384i
$291$	8.43516	−	11.9291i	0.494478	−	0.699297i
$292$	0.424905	+	0.424905i	0.0248657	+	0.0248657i
$293$	7.32282	+	7.32282i	0.427804	+	0.427804i	0.887880	−	0.460076i	$-0.152178\pi$
$293$	7.32282	+	7.32282i	0.427804	+	0.427804i	−0.460076	+	0.887880i	$0.652178\pi$
$294$	18.8630	−	26.6763i	1.10011	−	1.55579i
$295$	3.60029	−	5.68318i	0.209617	−	0.330888i
$296$			2.82843i			0.164399i
$297$	7.58048	−	4.23777i	0.439864	−	0.245901i
$298$	11.2901	−	11.2901i	0.654020	−	0.654020i
$299$	−4.34630			−0.251353
$300$	4.97069	+	7.09170i	0.286983	+	0.409440i
$301$	−38.0341			−2.19225
$302$	7.28347	−	7.28347i	0.419117	−	0.419117i
$303$	16.1658	−	2.77362i	0.928703	−	0.159340i
$304$			7.32821i			0.420302i
$305$	11.7714	−	18.5816i	0.674030	−	1.06398i
$306$	7.16246	+	20.2585i	0.409451	+	1.15810i
$307$	18.7355	+	18.7355i	1.06929	+	1.06929i	0.997413	+	0.0718804i	$0.0229000\pi$
$307$	18.7355	+	18.7355i	1.06929	+	1.06929i	0.0718804	+	0.997413i	$0.477100\pi$
$308$	−6.01025	−	6.01025i	−0.342466	−	0.342466i
$309$	−3.86988	−	2.73642i	−0.220150	−	0.155669i
$310$	−0.489528	−	2.18183i	−0.0278033	−	0.123919i
$311$		−	3.21704i		−	0.182422i	−0.995832	−	0.0912109i	$-0.970926\pi$
$311$		−	3.21704i		−	0.182422i	0.995832	−	0.0912109i	$-0.0290737\pi$
$312$	−0.299028	−	1.74286i	−0.0169291	−	0.0986700i
$313$	−11.4423	+	11.4423i	−0.646759	+	0.646759i	−0.952208	−	0.305449i	$-0.901193\pi$
$313$	−11.4423	+	11.4423i	−0.646759	+	0.646759i	0.305449	+	0.952208i	$0.401193\pi$
$314$	6.48243			0.365825
$315$	−28.8942	+	18.1373i	−1.62800	+	1.02192i
$316$	−1.39909			−0.0787052
$317$	5.94299	−	5.94299i	0.333792	−	0.333792i	−0.520233	−	0.854025i	$-0.674155\pi$
$317$	5.94299	−	5.94299i	0.333792	−	0.333792i	0.854025	+	0.520233i	$0.174155\pi$
$318$	−0.0789079	−	0.459909i	−0.00442494	−	0.0257904i
$319$			16.7478i			0.937697i
$320$	1.88893	+	1.19663i	0.105595	+	0.0668939i
$321$	−0.108742	−	0.0768919i	−0.00606936	−	0.00429169i
$322$	15.3088	+	15.3088i	0.853128	+	0.853128i
$323$	−37.1146	−	37.1146i	−2.06511	−	2.06511i
$324$	−5.65685	−	7.00000i	−0.314270	−	0.388889i
$325$	4.80569	+	1.72148i	0.266572	+	0.0954904i
$326$		−	4.36365i		−	0.241680i
$327$	10.3788	−	1.78072i	0.573947	−	0.0984738i
$328$	7.52072	−	7.52072i	0.415263	−	0.415263i
$329$	13.4051			0.739047
$330$	2.46478	+	5.98550i	0.135681	+	0.329491i
$331$	−11.5358			−0.634067			−0.317034	−	0.948414i	$-0.602687\pi$
$331$	−11.5358			−0.634067			−0.317034	+	0.948414i	$0.602687\pi$
$332$	−7.37010	+	7.37010i	−0.404487	+	0.404487i
$333$	7.65685	+	3.65685i	0.419593	+	0.200394i
$334$			15.2986i			0.837102i
$335$	4.23440	−	0.950058i	0.231350	−	0.0519072i
$336$	−5.08557	+	7.19208i	−0.277440	+	0.392360i
$337$	9.50560	+	9.50560i	0.517803	+	0.517803i	0.916906	−	0.399103i	$-0.130678\pi$
$337$	9.50560	+	9.50560i	0.517803	+	0.517803i	−0.399103	+	0.916906i	$0.630678\pi$
$338$	8.45535	+	8.45535i	0.459911	+	0.459911i
$339$	−3.15707	+	4.46478i	−0.171469	+	0.242493i
$340$	−15.6272	+	3.50623i	−0.847506	+	0.190152i
$341$		−	1.67135i		−	0.0905089i
$342$	19.8382	+	9.47459i	1.07273	+	0.512327i
$343$	−42.6598	+	42.6598i	−2.30341	+	2.30341i
$344$	7.47884			0.403232
$345$	−6.27808	−	15.2458i	−0.338001	−	0.820806i
$346$	−9.12522			−0.490575
$347$	4.39104	−	4.39104i	0.235723	−	0.235723i	−0.579353	−	0.815077i	$-0.696695\pi$
$347$	4.39104	−	4.39104i	0.235723	−	0.235723i	0.815077	+	0.579353i	$0.196695\pi$
$348$	17.1061	−	2.93494i	0.916982	−	0.157329i
$349$		−	15.3708i		−	0.822782i	−0.911459	−	0.411391i	$-0.865043\pi$
$349$		−	15.3708i		−	0.822782i	0.911459	−	0.411391i	$-0.134957\pi$
$350$	−10.8634	−	22.9904i	−0.580675	−	1.22889i
$351$	−5.10472	−	1.44383i	−0.272470	−	0.0770661i
$352$	1.18183	+	1.18183i	0.0629915	+	0.0629915i
$353$	−3.94944	−	3.94944i	−0.210207	−	0.210207i	0.594148	−	0.804356i	$-0.297489\pi$
$353$	−3.94944	−	3.94944i	−0.210207	−	0.210207i	−0.804356	+	0.594148i	$0.797489\pi$
$354$	−4.25491	−	3.00868i	−0.226146	−	0.159909i
$355$	−2.50889	−	1.58938i	−0.133158	−	0.0843555i
$356$		−	3.30770i		−	0.175308i
$357$	−10.6687	−	62.1816i	−0.564647	−	3.29100i
$358$	−11.7269	+	11.7269i	−0.619784	+	0.619784i
$359$	7.94361			0.419248			0.209624	−	0.977782i	$-0.432776\pi$
$359$	7.94361			0.419248			0.209624	+	0.977782i	$0.432776\pi$
$360$	5.68161	−	3.56642i	0.299447	−	0.187967i
$361$	−34.7026			−1.82645
$362$	1.32378	−	1.32378i	0.0695763	−	0.0695763i
$363$	−2.40365	−	14.0095i	−0.126159	−	0.735308i
$364$			5.19208i			0.272139i
$365$	0.294160	+	1.31107i	0.0153971	+	0.0686247i
$366$	−13.9118	−	9.83710i	−0.727180	−	0.514194i
$367$	−1.04145	−	1.04145i	−0.0543632	−	0.0543632i	0.679403	−	0.733766i	$-0.262239\pi$
$367$	−1.04145	−	1.04145i	−0.0543632	−	0.0543632i	−0.733766	+	0.679403i	$0.762239\pi$
$368$	−3.01025	−	3.01025i	−0.156920	−	0.156920i
$369$	−10.6359	−	30.0829i	−0.553683	−	1.56605i
$370$	−3.38459	+	5.34271i	−0.175957	+	0.277754i
$371$			1.37010i			0.0711318i
$372$	−1.70711	+	0.292893i	−0.0885094	+	0.0151858i
$373$	−4.50403	+	4.50403i	−0.233210	+	0.233210i	−0.814031	−	0.580821i	$-0.802731\pi$
$373$	−4.50403	+	4.50403i	−0.233210	+	0.233210i	0.580821	+	0.814031i	$0.302731\pi$
$374$	−11.9710			−0.619006
$375$	0.903121	+	19.3438i	0.0466370	+	0.998912i
$376$	−2.63591			−0.135937
$377$	7.23397	−	7.23397i	0.372568	−	0.372568i
$378$	12.8946	+	23.0658i	0.663228	+	1.18637i
$379$			25.4703i			1.30832i	0.756355	+	0.654162i	$0.226978\pi$
$379$			25.4703i			1.30832i	−0.756355	+	0.654162i	$0.773022\pi$
$380$	−8.76919	+	13.8425i	−0.449850	+	0.710105i
$381$	−13.4546	+	19.0277i	−0.689300	+	0.974818i
$382$	12.3340	+	12.3340i	0.631064	+	0.631064i
$383$	−2.60896	−	2.60896i	−0.133312	−	0.133312i	0.637302	−	0.770614i	$-0.280050\pi$
$383$	−2.60896	−	2.60896i	−0.133312	−	0.133312i	−0.770614	+	0.637302i	$0.780050\pi$
$384$	1.00000	−	1.41421i	0.0510310	−	0.0721688i
$385$	−4.16088	−	18.5450i	−0.212058	−	0.945143i
$386$			2.69007i			0.136921i
$387$	9.66934	−	20.2460i	0.491520	−	1.02916i
$388$	5.96456	−	5.96456i	0.302805	−	0.302805i
$389$	7.76113			0.393505			0.196753	−	0.980453i	$-0.436960\pi$
$389$	7.76113			0.393505			0.196753	+	0.980453i	$0.436960\pi$
$390$	1.52072	−	3.64997i	0.0770049	−	0.184823i
$391$	30.4916			1.54203
$392$	13.3382	−	13.3382i	0.673678	−	0.673678i
$393$	7.64279	−	1.31130i	0.385528	−	0.0661461i
$394$		−	3.81510i		−	0.192202i
$395$	−2.64279	−	1.67420i	−0.132973	−	0.0842384i
$396$	4.72730	−	1.67135i	0.237556	−	0.0839887i
$397$	6.71705	+	6.71705i	0.337119	+	0.337119i	0.855282	−	0.518163i	$-0.173384\pi$
$397$	6.71705	+	6.71705i	0.337119	+	0.337119i	−0.518163	+	0.855282i	$0.673384\pi$
$398$	−17.1012	−	17.1012i	−0.857206	−	0.857206i
$399$	−52.7050	−	37.2681i	−2.63855	−	1.86574i
$400$	2.13613	+	4.52072i	0.106806	+	0.226036i
$401$			34.9927i			1.74745i	0.486419	+	0.873725i	$0.338303\pi$
$401$			34.9927i			1.74745i	−0.486419	+	0.873725i	$0.661697\pi$
$402$	−0.568436	−	3.31309i	−0.0283510	−	0.165242i
$403$	−0.721916	+	0.721916i	−0.0359612	+	0.0359612i
$404$	9.46972			0.471136
$405$	−2.30897	−	19.9917i	−0.114734	−	0.993396i
$406$	−50.9600			−2.52910
$407$	−3.34271	+	3.34271i	−0.165692	+	0.165692i
$408$	2.09784	+	12.2271i	0.103858	+	0.605331i
$409$			32.7857i			1.62115i	0.585637	+	0.810573i	$0.300844\pi$
$409$			32.7857i			1.62115i	−0.585637	+	0.810573i	$0.699156\pi$
$410$	23.2057	−	5.20658i	1.14605	−	0.257135i
$411$	8.59718	+	6.07912i	0.424068	+	0.299861i
$412$	−1.93494	−	1.93494i	−0.0953276	−	0.0953276i
$413$	10.8193	+	10.8193i	0.532384	+	0.532384i
$414$	−12.0410	+	4.25714i	−0.591783	+	0.209227i
$415$	−22.7409	+	5.10230i	−1.11631	+	0.250462i
$416$		−	1.02094i		−	0.0500559i
$417$	13.9699	−	2.39686i	0.684111	−	0.117375i
$418$	−8.66066	+	8.66066i	−0.423607	+	0.423607i
$419$	−7.13118			−0.348381			−0.174191	−	0.984712i	$-0.555731\pi$
$419$	−7.13118			−0.348381			−0.174191	+	0.984712i	$0.555731\pi$
$420$	−18.2126	+	7.49978i	−0.888683	+	0.365952i
$421$	−4.65642			−0.226940			−0.113470	−	0.993541i	$-0.536197\pi$
$421$	−4.65642			−0.226940			−0.113470	+	0.993541i	$0.536197\pi$
$422$	−10.3244	+	10.3244i	−0.502584	+	0.502584i
$423$	−3.40795	+	7.13569i	−0.165700	+	0.346949i
$424$		−	0.269409i		−	0.0130836i
$425$	−33.7145	−	12.0771i	−1.63539	−	0.585824i
$426$	−1.32821	+	1.87837i	−0.0643519	+	0.0910073i
$427$	35.3746	+	35.3746i	1.71190	+	1.71190i
$428$	−0.0543708	−	0.0543708i	−0.00262811	−	0.00262811i
$429$	1.70636	−	2.41315i	0.0823837	−	0.116508i
$430$	14.1270	+	8.94944i	0.681265	+	0.431580i
$431$		−	20.2121i		−	0.973585i	−0.873518	−	0.486792i	$-0.838167\pi$
$431$		−	20.2121i		−	0.973585i	0.873518	−	0.486792i	$-0.161833\pi$
$432$	−2.53553	−	4.53553i	−0.121991	−	0.218216i
$433$	−23.9174	+	23.9174i	−1.14940	+	1.14940i	−0.162723	+	0.986672i	$0.552028\pi$
$433$	−23.9174	+	23.9174i	−1.14940	+	1.14940i	−0.986672	+	0.162723i	$0.947972\pi$
$434$	5.08557			0.244115
$435$	35.8243	+	14.9258i	1.71764	+	0.715638i
$436$	6.07974			0.291167
$437$	22.0598	−	22.0598i	1.05526	−	1.05526i
$438$	1.02581	−	0.176001i	0.0490151	−	0.00840967i
$439$		−	12.5477i		−	0.598868i	−0.954117	−	0.299434i	$-0.903202\pi$
$439$		−	12.5477i		−	0.598868i	0.954117	−	0.299434i	$-0.0967978\pi$
$440$	0.818175	+	3.64660i	0.0390049	+	0.173845i
$441$	−18.8630	−	53.3526i	−0.898238	−	2.54060i
$442$	5.17070	+	5.17070i	0.245945	+	0.245945i
$443$	14.0922	+	14.0922i	0.669542	+	0.669542i	0.957610	−	0.288068i	$-0.0930129\pi$
$443$	14.0922	+	14.0922i	0.669542	+	0.669542i	−0.288068	+	0.957610i	$0.593013\pi$
$444$	4.00000	+	2.82843i	0.189832	+	0.134231i
$445$	3.95811	−	6.24803i	0.187633	−	0.296185i
$446$		−	17.3459i		−	0.821350i
$447$	−4.67652	−	27.2568i	−0.221192	−	1.28920i
$448$	−3.59604	+	3.59604i	−0.169897	+	0.169897i
$449$	−10.0174			−0.472748			−0.236374	−	0.971662i	$-0.575959\pi$
$449$	−10.0174			−0.472748			−0.236374	+	0.971662i	$0.575959\pi$
$450$	14.9999	+	0.0620825i	0.707101	+	0.00292660i
$451$	17.7764			0.837056
$452$	−2.23239	+	2.23239i	−0.105003	+	0.105003i
$453$	−3.01691	−	17.5839i	−0.141747	−	0.826161i
$454$		−	7.04833i		−	0.330795i
$455$	−6.21302	+	9.80748i	−0.291271	+	0.459782i
$456$	10.3637	+	7.32821i	0.485322	+	0.343175i
$457$	−21.2949	−	21.2949i	−0.996132	−	0.996132i	0.00386099	−	0.999993i	$-0.498771\pi$
$457$	−21.2949	−	21.2949i	−0.996132	−	0.996132i	−0.999993	+	0.00386099i	$0.998771\pi$
$458$	8.76761	+	8.76761i	0.409684	+	0.409684i
$459$	35.8123	+	10.1292i	1.67157	+	0.472793i
$460$	−2.08399	−	9.28834i	−0.0971665	−	0.433071i
$461$		−	24.5134i		−	1.14170i	−0.821053	−	0.570851i	$-0.806613\pi$
$461$		−	24.5134i		−	1.14170i	0.821053	−	0.570851i	$-0.193387\pi$
$462$	−14.5100	+	2.48953i	−0.675068	+	0.115823i
$463$	8.63306	−	8.63306i	0.401212	−	0.401212i	−0.477448	−	0.878660i	$-0.658438\pi$
$463$	8.63306	−	8.63306i	0.401212	−	0.401212i	0.878660	+	0.477448i	$0.158438\pi$
$464$	10.0205			0.465190
$465$	−3.57510	−	1.48953i	−0.165791	−	0.0690752i
$466$	27.3563			1.26726
$467$	−21.3541	+	21.3541i	−0.988150	+	0.988150i	−0.999931	−	0.0117808i	$-0.996250\pi$
$467$	−21.3541	+	21.3541i	−0.988150	+	0.988150i	0.0117808	+	0.999931i	$0.496250\pi$
$468$	−2.76380	−	1.31997i	−0.127757	−	0.0610157i
$469$			9.86988i			0.455749i
$470$	−4.97906	−	3.15422i	−0.229667	−	0.145493i
$471$	6.48243	−	9.16754i	0.298695	−	0.422418i
$472$	−2.12745	−	2.12745i	−0.0979240	−	0.0979240i
$473$	8.83868	+	8.83868i	0.406403	+	0.406403i
$474$	−1.39909	+	1.97862i	−0.0642625	+	0.0908809i
$475$	−33.1288	+	15.6540i	−1.52005	+	0.718255i
$476$		−	36.4252i		−	1.66954i
$477$	−0.729318	−	0.348317i	−0.0333932	−	0.0159483i
$478$	6.27003	−	6.27003i	0.286784	−	0.286784i
$479$	−7.69589			−0.351634			−0.175817	−	0.984423i	$-0.556257\pi$
$479$	−7.69589			−0.351634			−0.175817	+	0.984423i	$0.556257\pi$
$480$	3.58123	−	1.47472i	0.163460	−	0.0673114i
$481$	2.88767			0.131666
$482$	−4.93494	+	4.93494i	−0.224780	+	0.224780i
$483$	36.9588	−	6.34113i	1.68168	−	0.288531i
$484$		−	8.20658i		−	0.373026i
$485$	18.4040	−	4.12925i	0.835684	−	0.187499i
$486$	−15.5563	+	1.00000i	−0.705650	+	0.0453609i
$487$	−10.0281	−	10.0281i	−0.454418	−	0.454418i	0.442400	−	0.896818i	$-0.354127\pi$
$487$	−10.0281	−	10.0281i	−0.454418	−	0.454418i	−0.896818	+	0.442400i	$0.854127\pi$
$488$	−6.95588	−	6.95588i	−0.314878	−	0.314878i
$489$	−6.17113	−	4.36365i	−0.279068	−	0.197331i
$490$	41.1558	−	9.23397i	1.85923	−	0.417148i
$491$			12.1695i			0.549203i	0.961558	+	0.274601i	$0.0885459\pi$
$491$			12.1695i			0.549203i	−0.961558	+	0.274601i	$0.911454\pi$
$492$	−3.11519	−	18.1566i	−0.140443	−	0.818564i
$493$	−50.7501	+	50.7501i	−2.28567	+	2.28567i
$494$	7.48169			0.336617
$495$	10.9296	+	2.49978i	0.491247	+	0.112357i
$496$	−1.00000			−0.0449013
$497$	4.77629	−	4.77629i	0.214246	−	0.214246i
$498$	3.05279	+	17.7930i	0.136799	+	0.797323i
$499$		−	29.7110i		−	1.33005i	−0.746822	−	0.665024i	$-0.768421\pi$
$499$		−	29.7110i		−	1.33005i	0.746822	−	0.665024i	$-0.231579\pi$
$500$	−1.37465	+	11.0955i	−0.0614763	+	0.496206i
$501$	21.6355	+	15.2986i	0.966602	+	0.683491i
$502$	−12.0874	−	12.0874i	−0.539485	−	0.539485i
$503$	−2.82154	−	2.82154i	−0.125806	−	0.125806i	0.641400	−	0.767207i	$-0.278354\pi$
$503$	−2.82154	−	2.82154i	−0.125806	−	0.125806i	−0.767207	+	0.641400i	$0.778354\pi$
$504$	5.08557	+	14.3842i	0.226529	+	0.640721i
$505$	17.8877	+	11.3318i	0.795991	+	0.504259i
$506$		−	7.11519i		−	0.316309i
$507$	20.4130	−	3.50232i	0.906574	−	0.155544i
$508$	−9.51384	+	9.51384i	−0.422108	+	0.422108i
$509$	10.2585			0.454700			0.227350	−	0.973813i	$-0.426994\pi$
$509$	10.2585			0.454700			0.227350	+	0.973813i	$0.426994\pi$
$510$	−10.6687	+	25.6065i	−0.472417	+	1.13387i
$511$	−3.05595			−0.135187
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	33.2373	−	18.5809i	1.46746	−	0.820368i
$514$			24.4687i			1.07927i
$515$	−1.33955	−	5.97038i	−0.0590277	−	0.263086i
$516$	7.47884	−	10.5767i	0.329237	−	0.465612i
$517$	−3.11519	−	3.11519i	−0.137006	−	0.137006i
$518$	−10.1711	−	10.1711i	−0.446894	−	0.446894i
$519$	−9.12522	+	12.9050i	−0.400553	+	0.566467i
$520$	1.22170	−	1.92849i	0.0535750	−	0.0845700i
$521$			17.6881i			0.774931i	0.921884	+	0.387466i	$0.126649\pi$
$521$			17.6881i			0.774931i	−0.921884	+	0.387466i	$0.873351\pi$
$522$	12.9554	−	27.1266i	0.567044	−	1.18730i
$523$	8.57689	−	8.57689i	0.375041	−	0.375041i	−0.494268	−	0.869309i	$-0.664564\pi$
$523$	8.57689	−	8.57689i	0.375041	−	0.375041i	0.869309	+	0.494268i	$0.164564\pi$
$524$	4.47704			0.195581
$525$	−43.3768	−	7.62724i	−1.89312	−	0.332880i
$526$	1.73598			0.0756922
$527$	5.06462	−	5.06462i	0.220618	−	0.220618i
$528$	2.85318	−	0.489528i	0.124169	−	0.0213040i
$529$		−	4.87676i		−	0.212033i
$530$	0.322384	−	0.508895i	0.0140035	−	0.0221050i
$531$	−8.50982	+	3.00868i	−0.369295	+	0.130565i
$532$	−26.3525	−	26.3525i	−1.14253	−	1.14253i
$533$	−7.67824	−	7.67824i	−0.332581	−	0.332581i
$534$	−4.67780	−	3.30770i	−0.202428	−	0.143138i
$535$	−0.0376408	−	0.167765i	−0.00162735	−	0.00725310i
$536$		−	1.94076i		−	0.0838282i
$537$	4.85743	+	28.3112i	0.209613	+	1.22172i
$538$	−0.200753	+	0.200753i	−0.00865508	+	0.00865508i
$539$	31.5267			1.35795
$540$	0.637927	−	11.6014i	0.0274520	−	0.499246i
$541$	−32.1779			−1.38343			−0.691717	−	0.722168i	$-0.743146\pi$
$541$	−32.1779			−1.38343			−0.691717	+	0.722168i	$0.743146\pi$
$542$	14.8979	−	14.8979i	0.639920	−	0.639920i
$543$	−0.548327	−	3.19589i	−0.0235310	−	0.137149i
$544$			7.16246i			0.307088i
$545$	11.4842	+	7.27523i	0.491930	+	0.311637i
$546$	7.34271	+	5.19208i	0.314239	+	0.222200i
$547$	−12.5918	−	12.5918i	−0.538386	−	0.538386i	0.384669	−	0.923055i	$-0.374316\pi$
$547$	−12.5918	−	12.5918i	−0.538386	−	0.538386i	−0.923055	+	0.384669i	$0.874316\pi$
$548$	4.29859	+	4.29859i	0.183627	+	0.183627i
$549$	−27.8235	+	9.83710i	−1.18748	+	0.419837i
$550$	−2.81817	+	7.86724i	−0.120167	+	0.335460i
$551$			73.4323i			3.12832i
$552$	−7.26739	+	1.24689i	−0.309321	+	0.0530711i
$553$	5.03120	−	5.03120i	0.213948	−	0.213948i
$554$	−16.0486			−0.681841
$555$	4.17113	+	10.1292i	0.177055	+	0.429963i
$556$	8.18340			0.347054
$557$	−12.0399	+	12.0399i	−0.510146	+	0.510146i	−0.914571	−	0.404425i	$-0.867472\pi$
$557$	−12.0399	+	12.0399i	−0.510146	+	0.510146i	0.404425	+	0.914571i	$0.367472\pi$
$558$	−1.29289	+	2.70711i	−0.0547325	+	0.114601i
$559$		−	7.63547i		−	0.322946i
$560$	−11.0958	+	2.48953i	−0.468884	+	0.105202i
$561$	−11.9710	+	16.9296i	−0.505416	+	0.714766i
$562$	12.1119	+	12.1119i	0.510910	+	0.510910i
$563$	−21.5053	−	21.5053i	−0.906342	−	0.906342i	0.0896326	−	0.995975i	$-0.471431\pi$
$563$	−21.5053	−	21.5053i	−0.906342	−	0.906342i	−0.995975	+	0.0896326i	$0.971431\pi$
$564$	−2.63591	+	3.72774i	−0.110992	+	0.156966i
$565$	−6.88818	+	1.54548i	−0.289788	+	0.0650187i
$566$		−	27.6774i		−	1.16337i
$567$	45.5145	+	4.83000i	1.91143	+	0.202841i
$568$	−0.939185	+	0.939185i	−0.0394073	+	0.0394073i
$569$	1.35317			0.0567280			0.0283640	−	0.999598i	$-0.490970\pi$
$569$	1.35317			0.0567280			0.0283640	+	0.999598i	$0.490970\pi$
$570$	10.8070	+	26.2440i	0.452657	+	1.09924i
$571$	−15.6166			−0.653535			−0.326768	−	0.945105i	$-0.605959\pi$
$571$	−15.6166			−0.653535			−0.326768	+	0.945105i	$0.605959\pi$
$572$	1.20658	−	1.20658i	0.0504495	−	0.0504495i
$573$	29.7770	−	5.10892i	1.24395	−	0.213428i
$574$			54.0896i			2.25766i
$575$	7.17823	−	20.0388i	0.299353	−	0.835676i
$576$	−1.00000	−	2.82843i	−0.0416667	−	0.117851i
$577$	−27.1671	−	27.1671i	−1.13098	−	1.13098i	−0.990014	−	0.140967i	$-0.954979\pi$
$577$	−27.1671	−	27.1671i	−1.13098	−	1.13098i	−0.140967	−	0.990014i	$-0.545021\pi$
$578$	−24.2543	−	24.2543i	−1.00885	−	1.00885i
$579$	3.80433	+	2.69007i	0.158103	+	0.111795i
$580$	18.9281	+	11.9909i	0.785945	+	0.497894i
$581$		−	53.0063i		−	2.19907i
$582$	−2.47060	−	14.3997i	−0.102410	−	0.596887i
$583$	0.318394	−	0.318394i	0.0131865	−	0.0131865i
$584$	0.600906			0.0248657
$585$	−3.64111	−	5.80060i	−0.150542	−	0.239825i
$586$	10.3560			0.427804
$587$	31.6919	−	31.6919i	1.30806	−	1.30806i	0.385251	−	0.922812i	$-0.374115\pi$
$587$	31.6919	−	31.6919i	1.30806	−	1.30806i	0.922812	−	0.385251i	$-0.125885\pi$
$588$	−5.52484	−	32.2011i	−0.227841	−	1.32795i
$589$		−	7.32821i		−	0.301954i
$590$	−1.47283	−	6.56440i	−0.0606355	−	0.270252i
$591$	−5.39537	−	3.81510i	−0.221936	−	0.156932i
$592$	2.00000	+	2.00000i	0.0821995	+	0.0821995i
$593$	−3.01841	−	3.01841i	−0.123951	−	0.123951i	0.642410	−	0.766361i	$-0.277935\pi$
$593$	−3.01841	−	3.01841i	−0.123951	−	0.123951i	−0.766361	+	0.642410i	$0.777935\pi$
$594$	2.36365	−	8.35677i	0.0969818	−	0.342882i
$595$	43.5876	−	68.8047i	1.78692	−	2.82072i
$596$		−	15.9667i		−	0.654020i
$597$	−41.2860	+	7.08355i	−1.68972	+	0.289910i
$598$	−3.07330	+	3.07330i	−0.125677	+	0.125677i
$599$	−45.0422			−1.84037			−0.920187	−	0.391479i	$-0.871963\pi$
$599$	−45.0422			−1.84037			−0.920187	+	0.391479i	$0.871963\pi$
$600$	8.52940	+	1.49978i	0.348211	+	0.0612283i
$601$	−19.9056			−0.811967			−0.405983	−	0.913880i	$-0.633071\pi$
$601$	−19.9056			−0.811967			−0.405983	+	0.913880i	$0.633071\pi$
$602$	−26.8942	+	26.8942i	−1.09613	+	1.09613i
$603$	−5.25385	−	2.50920i	−0.213953	−	0.102182i
$604$		−	10.3004i		−	0.419117i
$605$	9.82028	−	15.5017i	0.399251	−	0.630232i
$606$	9.46972	−	13.3922i	0.384681	−	0.544021i
$607$	−32.7744	−	32.7744i	−1.33027	−	1.33027i	−0.905126	−	0.425144i	$-0.860223\pi$
$607$	−32.7744	−	32.7744i	−1.33027	−	1.33027i	−0.425144	−	0.905126i	$-0.639777\pi$
$608$	5.18183	+	5.18183i	0.210151	+	0.210151i
$609$	−50.9600	+	72.0683i	−2.06500	+	2.92035i
$610$	−4.81554	−	21.4628i	−0.194975	−	0.869005i
$611$			2.69112i			0.108871i
$612$	19.3895	+	9.26029i	0.783776	+	0.374325i
$613$	6.91802	−	6.91802i	0.279416	−	0.279416i	−0.553460	−	0.832876i	$-0.686693\pi$
$613$	6.91802	−	6.91802i	0.279416	−	0.279416i	0.832876	+	0.553460i	$0.186693\pi$
$614$	26.4961			1.06929
$615$	15.8425	−	38.0244i	0.638831	−	1.53329i
$616$	−8.49978			−0.342466
$617$	24.9415	−	24.9415i	1.00411	−	1.00411i	0.00411392	−	0.999992i	$-0.498690\pi$
$617$	24.9415	−	24.9415i	1.00411	−	1.00411i	0.999992	−	0.00411392i	$-0.00130951\pi$
$618$	−4.67135	+	0.801478i	−0.187909	+	0.0322402i
$619$			25.7810i			1.03623i	0.855312	+	0.518113i	$0.173365\pi$
$619$			25.7810i			1.03623i	−0.855312	+	0.518113i	$0.826635\pi$
$620$	−1.88893	−	1.19663i	−0.0758613	−	0.0480580i
$621$	−6.02051	+	21.2857i	−0.241595	+	0.854166i
$622$	−2.27479	−	2.27479i	−0.0912109	−	0.0912109i
$623$	11.8946	+	11.8946i	0.476548	+	0.476548i
$624$	−1.44383	−	1.02094i	−0.0577996	−	0.0408705i
$625$	−15.8739	+	19.3137i	−0.634956	+	0.772548i
$626$			16.1819i			0.646759i
$627$	3.58736	+	20.9087i	0.143266	+	0.835013i
$628$	4.58377	−	4.58377i	0.182912	−	0.182912i
$629$	−20.2585			−0.807759
$630$	−7.60629	+	33.2563i	−0.303042	+	1.32496i
$631$	3.45745			0.137639			0.0688195	−	0.997629i	$-0.478077\pi$
$631$	3.45745			0.137639			0.0688195	+	0.997629i	$0.478077\pi$
$632$	−0.989309	+	0.989309i	−0.0393526	+	0.0393526i
$633$	4.27651	+	24.9253i	0.169976	+	0.990692i
$634$		−	8.40466i		−	0.333792i
$635$	−29.3556	+	6.58641i	−1.16494	+	0.261374i
$636$	−0.381001	−	0.269409i	−0.0151077	−	0.0106827i
$637$	−13.6175	−	13.6175i	−0.539545	−	0.539545i
$638$	11.8425	+	11.8425i	0.468849	+	0.468849i
$639$	1.32821	+	3.75674i	0.0525431	+	0.148614i
$640$	2.18183	−	0.489528i	0.0862442	−	0.0193503i
$641$		−	31.1123i		−	1.22886i	−0.788970	−	0.614432i	$-0.789385\pi$
$641$		−	31.1123i		−	1.22886i	0.788970	−	0.614432i	$-0.210615\pi$
$642$	−0.131263	+	0.0225211i	−0.00518053	+	0.000888838i
$643$	−6.93380	+	6.93380i	−0.273442	+	0.273442i	−0.830484	−	0.557042i	$-0.811936\pi$
$643$	−6.93380	+	6.93380i	−0.273442	+	0.273442i	0.557042	+	0.830484i	$0.311936\pi$
$644$	21.6500			0.853128
$645$	26.7834	−	11.0292i	1.05460	−	0.434274i
$646$	−52.4880			−2.06511
$647$	−16.5241	+	16.5241i	−0.649629	+	0.649629i	−0.952903	−	0.303274i	$-0.901920\pi$
$647$	−16.5241	+	16.5241i	−0.649629	+	0.649629i	0.303274	+	0.952903i	$0.401920\pi$
$648$	−8.94975	−	0.949747i	−0.351579	−	0.0373096i
$649$		−	5.02856i		−	0.197388i
$650$	4.61541	−	2.18087i	0.181031	−	0.0855407i
$651$	5.08557	−	7.19208i	0.199319	−	0.281880i
$652$	−3.08557	−	3.08557i	−0.120840	−	0.120840i
$653$	0.623022	+	0.623022i	0.0243807	+	0.0243807i	0.719192	−	0.694811i	$-0.244512\pi$
$653$	0.623022	+	0.623022i	0.0243807	+	0.0243807i	−0.694811	+	0.719192i	$0.744512\pi$
$654$	6.07974	−	8.59806i	0.237737	−	0.336211i
$655$	8.45683	+	5.35739i	0.330436	+	0.209330i
$656$		−	10.6359i		−	0.415263i
$657$	0.776907	−	1.62672i	0.0303100	−	0.0634643i
$658$	9.47884	−	9.47884i	0.369524	−	0.369524i
$659$	−3.37145			−0.131333			−0.0656665	−	0.997842i	$-0.520917\pi$
$659$	−3.37145			−0.131333			−0.0656665	+	0.997842i	$0.520917\pi$
$660$	5.97525	+	2.48953i	0.232586	+	0.0969048i
$661$	−2.09797			−0.0816016			−0.0408008	−	0.999167i	$-0.512991\pi$
$661$	−2.09797			−0.0816016			−0.0408008	+	0.999167i	$0.512991\pi$
$662$	−8.15707	+	8.15707i	−0.317034	+	0.317034i
$663$	12.4832	−	2.14177i	0.484806	−	0.0831795i
$664$			10.4229i			0.404487i
$665$	−18.2438	−	81.3125i	−0.707463	−	3.15316i
$666$	8.00000	−	2.82843i	0.309994	−	0.109599i
$667$	−30.1643	−	30.1643i	−1.16796	−	1.16796i
$668$	10.8177	+	10.8177i	0.418551	+	0.418551i
$669$	−24.5308	−	17.3459i	−0.948414	−	0.670630i
$670$	2.32238	−	3.66597i	0.0897215	−	0.141629i
$671$		−	16.4413i		−	0.634708i
$672$	1.48953	+	8.68161i	0.0574598	+	0.334900i
$673$	29.1402	−	29.1402i	1.12327	−	1.12327i	0.132026	−	0.991246i	$-0.457852\pi$
$673$	29.1402	−	29.1402i	1.12327	−	1.12327i	0.991246	−	0.132026i	$-0.0421482\pi$
$674$	13.4430			0.517803
$675$	15.0877	−	21.1509i	0.580725	−	0.814100i
$676$	11.9577			0.459911
$677$	−19.7632	+	19.7632i	−0.759560	+	0.759560i	−0.976242	−	0.216683i	$-0.930476\pi$
$677$	−19.7632	+	19.7632i	−0.759560	+	0.759560i	0.216683	+	0.976242i	$0.430476\pi$
$678$	0.924685	+	5.38946i	0.0355123	+	0.206981i
$679$			42.8976i			1.64626i
$680$	−8.57085	+	13.5294i	−0.328677	+	0.518829i
$681$	−9.96785	−	7.04833i	−0.381969	−	0.270093i
$682$	−1.18183	−	1.18183i	−0.0452544	−	0.0452544i
$683$	21.1969	+	21.1969i	0.811079	+	0.811079i	0.984796	−	0.173717i	$-0.0555778\pi$
$683$	21.1969	+	21.1969i	0.811079	+	0.811079i	−0.173717	+	0.984796i	$0.555578\pi$
$684$	20.7273	−	7.32821i	0.792528	−	0.280201i
$685$	2.97590	+	13.2636i	0.113703	+	0.506776i
$686$			60.3300i			2.30341i
$687$	21.1669	−	3.63166i	0.807567	−	0.138557i
$688$	5.28834	−	5.28834i	0.201616	−	0.201616i
$689$	−0.275051			−0.0104786
$690$	−15.2197	−	6.34113i	−0.579403	−	0.241403i
$691$	−25.9726			−0.988045			−0.494022	−	0.869449i	$-0.664474\pi$
$691$	−25.9726			−0.988045			−0.494022	+	0.869449i	$0.664474\pi$
$692$	−6.45251	+	6.45251i	−0.245288	+	0.245288i
$693$	−10.9893	+	23.0098i	−0.417449	+	0.874071i
$694$		−	6.20987i		−	0.235723i
$695$	15.4579	+	9.79255i	0.586351	+	0.371452i
$696$	10.0205	−	14.1711i	0.379826	−	0.537155i
$697$	53.8669	+	53.8669i	2.04035	+	2.04035i
$698$	−10.8688	−	10.8688i	−0.411391	−	0.411391i
$699$	27.3563	−	38.6877i	1.03471	−	1.46330i
$700$	−23.9383	−	8.57510i	−0.904783	−	0.324108i
$701$			25.0090i			0.944576i	0.881444	+	0.472288i	$0.156572\pi$
$701$			25.0090i			0.944576i	−0.881444	+	0.472288i	$0.843428\pi$
$702$	−4.63053	+	2.58864i	−0.174768	+	0.0977018i
$703$	−14.6564	+	14.6564i	−0.552777	+	0.552777i
$704$	1.67135			0.0629915
$705$	−9.43980	+	3.88723i	−0.355523	+	0.146401i
$706$	−5.58535			−0.210207
$707$	−34.0535	+	34.0535i	−1.28071	+	1.28071i
$708$	−5.13613	+	0.881221i	−0.193028	+	0.0331183i
$709$		−	45.1020i		−	1.69384i	−0.531718	−	0.846921i	$-0.678453\pi$
$709$		−	45.1020i		−	1.69384i	0.531718	−	0.846921i	$-0.321547\pi$
$710$	−2.89792	+	0.650195i	−0.108757	+	0.0244014i
$711$	1.39909	+	3.95724i	0.0524701	+	0.148408i
$712$	−2.33890	−	2.33890i	−0.0876539	−	0.0876539i
$713$	3.01025	+	3.01025i	0.112735	+	0.112735i
$714$	−51.5130	−	36.4252i	−1.92782	−	1.36318i
$715$	3.72298	−	0.835310i	0.139231	−	0.0312388i
$716$			16.5843i			0.619784i
$717$	−2.59713	−	15.1372i	−0.0969916	−	0.565309i
$718$	5.61698	−	5.61698i	0.209624	−	0.209624i
$719$	−21.5174			−0.802465			−0.401232	−	0.915976i	$-0.631418\pi$
$719$	−21.5174			−0.802465			−0.401232	+	0.915976i	$0.631418\pi$
$720$	1.49566	−	6.53934i	0.0557400	−	0.243707i
$721$	13.9162			0.518267
$722$	−24.5385	+	24.5385i	−0.913227	+	0.913227i
$723$	2.04412	+	11.9140i	0.0760216	+	0.443086i
$724$		−	1.87211i		−	0.0695763i
$725$	21.4051	+	45.2999i	0.794965	+	1.68240i
$726$	−11.6059	−	8.20658i	−0.430734	−	0.304575i
$727$	−20.7172	−	20.7172i	−0.768360	−	0.768360i	0.209458	−	0.977818i	$-0.432830\pi$
$727$	−20.7172	−	20.7172i	−0.768360	−	0.768360i	−0.977818	+	0.209458i	$0.932830\pi$
$728$	3.67135	+	3.67135i	0.136069	+	0.136069i
$729$	−14.1421	+	23.0000i	−0.523783	+	0.851852i
$730$	1.13507	+	0.719065i	0.0420109	+	0.0266138i
$731$			53.5669i			1.98124i
$732$	−16.7930	+	2.88122i	−0.620687	+	0.106493i
$733$	−10.2304	+	10.2304i	−0.377867	+	0.377867i	−0.870332	−	0.492465i	$-0.836096\pi$
$733$	−10.2304	+	10.2304i	−0.377867	+	0.377867i	0.492465	+	0.870332i	$0.336096\pi$
$734$	−1.47283			−0.0543632
$735$	28.0970	−	67.4370i	1.03637	−	2.48745i
$736$	−4.25714			−0.156920
$737$	2.29364	−	2.29364i	0.0844874	−	0.0844874i
$738$	−28.7925	−	13.7511i	−1.05987	−	0.506185i
$739$			32.5957i			1.19905i	0.800355	+	0.599526i	$0.204644\pi$
$739$			32.5957i			1.19905i	−0.800355	+	0.599526i	$0.795356\pi$
$740$	1.38459	+	6.17113i	0.0508987	+	0.226855i
$741$	7.48169	−	10.5807i	0.274847	−	0.388692i
$742$	0.968804	+	0.968804i	0.0355659	+	0.0355659i
$743$	−22.8596	−	22.8596i	−0.838638	−	0.838638i	0.150041	−	0.988680i	$-0.452059\pi$
$743$	−22.8596	−	22.8596i	−0.838638	−	0.838638i	−0.988680	+	0.150041i	$0.952059\pi$
$744$	−1.00000	+	1.41421i	−0.0366618	+	0.0518476i
$745$	19.1063	−	30.1599i	0.699999	−	1.10497i
$746$			6.36966i			0.233210i
$747$	28.2159	+	13.4757i	1.03236	+	0.493049i
$748$	−8.46478	+	8.46478i	−0.309503	+	0.309503i
$749$	0.391039			0.0142883
$750$	14.3168	+	13.0396i	0.522774	+	0.476137i
$751$	48.8210			1.78150			0.890751	−	0.454491i	$-0.150179\pi$
$751$	48.8210			1.78150			0.890751	+	0.454491i	$0.150179\pi$
$752$	−1.86387	+	1.86387i	−0.0679684	+	0.0679684i
$753$	−29.1815	+	5.00675i	−1.06343	+	0.182456i
$754$		−	10.2304i		−	0.372568i
$755$	12.3258	−	19.4567i	0.448582	−	0.708103i
$756$	25.4278	+	7.19208i	0.924801	+	0.261573i
$757$	10.4100	+	10.4100i	0.378360	+	0.378360i	0.870510	−	0.492151i	$-0.163789\pi$
$757$	10.4100	+	10.4100i	0.378360	+	0.378360i	−0.492151	+	0.870510i	$0.663789\pi$
$758$	18.0103	+	18.0103i	0.654162	+	0.654162i
$759$	−10.0624	−	7.11519i	−0.365242	−	0.258265i
$760$	3.58736	+	15.9889i	0.130127	+	0.579977i
$761$		−	13.4953i		−	0.489205i	−0.969623	−	0.244602i	$-0.921343\pi$
$761$		−	13.4953i		−	0.489205i	0.969623	−	0.244602i	$-0.0786574\pi$
$762$	3.94076	+	22.9684i	0.142759	+	0.832059i
$763$	−21.8630	+	21.8630i	−0.791493	+	0.791493i
$764$	17.4430			0.631064
$765$	25.5443	+	40.6943i	0.923557	+	1.47130i
$766$	−3.68963			−0.133312
$767$	−2.17201	+	2.17201i	−0.0784268	+	0.0784268i
$768$	−0.292893	−	1.70711i	−0.0105689	−	0.0615999i
$769$			37.0453i			1.33589i	0.744211	+	0.667945i	$0.232826\pi$
$769$			37.0453i			1.33589i	−0.744211	+	0.667945i	$0.767174\pi$
$770$	−16.0555	−	10.1711i	−0.578600	−	0.366542i
$771$	34.6039	+	24.4687i	1.24623	+	0.881217i
$772$	1.90216	+	1.90216i	0.0684604	+	0.0684604i
$773$	−7.22222	−	7.22222i	−0.259765	−	0.259765i	0.565193	−	0.824958i	$-0.308802\pi$
$773$	−7.22222	−	7.22222i	−0.259765	−	0.259765i	−0.824958	+	0.565193i	$0.808802\pi$
$774$	−7.47884	−	21.1533i	−0.268821	−	0.760341i
$775$	−2.13613	−	4.52072i	−0.0767320	−	0.162389i
$776$		−	8.43516i		−	0.302805i
$777$	−24.5553	+	4.21302i	−0.880916	+	0.151141i
$778$	5.48795	−	5.48795i	0.196753	−	0.196753i
$779$	77.9422			2.79257
$780$	−1.50560	−	3.65623i	−0.0539093	−	0.130914i
$781$	−2.21990			−0.0794344
$782$	21.5608	−	21.5608i	0.771013	−	0.771013i
$783$	−25.4073	−	45.4483i	−0.907984	−	1.62419i
$784$		−	18.8630i		−	0.673678i
$785$	14.1435	−	3.17333i	0.504804	−	0.113261i
$786$	4.47704	−	6.33150i	0.159691	−	0.225837i
$787$	5.84135	+	5.84135i	0.208222	+	0.208222i	0.803511	−	0.595290i	$-0.202963\pi$
$787$	5.84135	+	5.84135i	0.208222	+	0.208222i	−0.595290	+	0.803511i	$0.702963\pi$
$788$	−2.69768	−	2.69768i	−0.0961010	−	0.0961010i
$789$	1.73598	−	2.45504i	0.0618024	−	0.0874018i
$790$	−3.05258	+	0.684896i	−0.108606	+	0.0243675i
$791$		−	16.0555i		−	0.570868i
$792$	2.16088	−	4.52453i	0.0767836	−	0.160772i
$793$	−7.10156	+	7.10156i	−0.252184	+	0.252184i
$794$	9.49934			0.337119
$795$	−0.397302	−	0.964814i	−0.0140908	−	0.0342184i
$796$	−24.1848			−0.857206
$797$	0.330877	−	0.330877i	0.0117203	−	0.0117203i	−0.701222	−	0.712943i	$-0.747362\pi$
$797$	0.330877	−	0.330877i	0.0117203	−	0.0117203i	0.712943	+	0.701222i	$0.247362\pi$
$798$	−63.6206	+	10.9156i	−2.25215	+	0.386407i
$799$		−	18.8796i		−	0.667912i
$800$	4.70711	+	1.68616i	0.166421	+	0.0596149i
$801$	−9.35560	+	3.30770i	−0.330564	+	0.116872i
$802$	24.7436	+	24.7436i	0.873725	+	0.873725i
$803$	0.710166	+	0.710166i	0.0250612	+	0.0250612i
$804$	−2.74465	−	1.94076i	−0.0967964	−	0.0684454i
$805$	40.8953	+	25.9071i	1.44137	+	0.913106i
$806$			1.02094i			0.0359612i
$807$	0.0831547	+	0.484661i	0.00292718	+	0.0170609i
$808$	6.69611	−	6.69611i	0.235568	−	0.235568i
$809$	18.3644			0.645657			0.322829	−	0.946457i	$-0.395366\pi$
$809$	18.3644			0.645657			0.322829	+	0.946457i	$0.395366\pi$
$810$	−15.7690	−	12.5036i	−0.554065	−	0.439331i
$811$	29.4003			1.03239			0.516193	−	0.856472i	$-0.327349\pi$
$811$	29.4003			1.03239			0.516193	+	0.856472i	$0.327349\pi$
$812$	−36.0341	+	36.0341i	−1.26455	+	1.26455i
$813$	−6.17092	−	35.9668i	−0.216424	−	1.26141i
$814$			4.72730i			0.165692i
$815$	−2.13613	−	9.52072i	−0.0748254	−	0.333496i
$816$	10.1292	+	7.16246i	0.354595	+	0.250736i
$817$	38.7540	+	38.7540i	1.35583	+	1.35583i
$818$	23.1830	+	23.1830i	0.810573	+	0.810573i
$819$	14.6854	−	5.19208i	0.513150	−	0.181426i
$820$	12.7273	−	20.0905i	0.444457	−	0.701591i
$821$		−	6.43578i		−	0.224610i	−0.993674	−	0.112305i	$-0.964177\pi$
$821$		−	6.43578i		−	0.224610i	0.993674	−	0.112305i	$-0.0358234\pi$
$822$	10.3777	−	1.78053i	0.361964	−	0.0621032i
$823$	1.00359	−	1.00359i	0.0349831	−	0.0349831i	−0.689399	−	0.724382i	$-0.742125\pi$
$823$	1.00359	−	1.00359i	0.0349831	−	0.0349831i	0.724382	+	0.689399i	$0.242125\pi$
$824$	−2.73642			−0.0953276
$825$	8.30778	+	11.8527i	0.289240	+	0.412659i
$826$	15.3008			0.532384
$827$	17.7824	−	17.7824i	0.618354	−	0.618354i	−0.326755	−	0.945109i	$-0.605955\pi$
$827$	17.7824	−	17.7824i	0.618354	−	0.618354i	0.945109	+	0.326755i	$0.105955\pi$
$828$	−5.50403	+	11.5245i	−0.191278	+	0.400505i
$829$		−	18.3026i		−	0.635676i	−0.948145	−	0.317838i	$-0.897043\pi$
$829$		−	18.3026i		−	0.635676i	0.948145	−	0.317838i	$-0.102957\pi$
$830$	−12.4724	+	19.6881i	−0.432923	+	0.683385i
$831$	−16.0486	+	22.6962i	−0.556721	+	0.787322i
$832$	−0.721916	−	0.721916i	−0.0250279	−	0.0250279i
$833$	95.5340	+	95.5340i	3.31006	+	3.31006i
$834$	8.18340	−	11.5731i	0.283368	−	0.400743i
$835$	7.48909	+	33.3789i	0.259171	+	1.15512i
$836$			12.2480i			0.423607i
$837$	2.53553	+	4.53553i	0.0876409	+	0.156771i
$838$	−5.04251	+	5.04251i	−0.174191	+	0.174191i
$839$	30.9423			1.06825			0.534123	−	0.845407i	$-0.320642\pi$
$839$	30.9423			1.06825			0.534123	+	0.845407i	$0.320642\pi$
$840$	−7.57510	+	18.1814i	−0.261366	+	0.627317i
$841$	71.4105			2.46243
$842$	−3.29258	+	3.29258i	−0.113470	+	0.113470i
$843$	29.2407	−	5.01691i	1.00710	−	0.172792i
$844$			14.6009i			0.502584i
$845$	22.5872	+	14.3090i	0.777025	+	0.492244i
$846$	2.63591	+	7.45548i	0.0906245	+	0.256325i
$847$	29.5112	+	29.5112i	1.01402	+	1.01402i
$848$	−0.190501	−	0.190501i	−0.00654182	−	0.00654182i
$849$	−39.1417	−	27.6774i	−1.34334	−	0.949885i
$850$	−32.3795	+	15.2999i	−1.11061	+	0.524784i
$851$		−	12.0410i		−	0.412761i
$852$	0.389023	+	2.26739i	0.0133277	+	0.0776796i
$853$	−39.7674	+	39.7674i	−1.36161	+	1.36161i	−0.489739	+	0.871869i	$0.662908\pi$
$853$	−39.7674	+	39.7674i	−1.36161	+	1.36161i	−0.871869	+	0.489739i	$0.837092\pi$
$854$	50.0272			1.71190
$855$	47.9217	+	10.9605i	1.63889	+	0.374842i
$856$	−0.0768919			−0.00262811
$857$	13.3607	−	13.3607i	0.456392	−	0.456392i	−0.441077	−	0.897469i	$-0.645403\pi$
$857$	13.3607	−	13.3607i	0.456392	−	0.456392i	0.897469	+	0.441077i	$0.145403\pi$
$858$	−0.499781	−	2.91294i	−0.0170622	−	0.0994460i
$859$			53.6202i			1.82950i	0.404023	+	0.914749i	$0.367612\pi$
$859$			53.6202i			1.82950i	−0.404023	+	0.914749i	$0.632388\pi$
$860$	16.3175	−	3.66110i	0.556423	−	0.124843i
$861$	76.4943	+	54.0896i	2.60692	+	1.84337i
$862$	−14.2921	−	14.2921i	−0.486792	−	0.486792i
$863$	−16.7468	−	16.7468i	−0.570069	−	0.570069i	0.362078	−	0.932148i	$-0.382067\pi$
$863$	−16.7468	−	16.7468i	−0.570069	−	0.570069i	−0.932148	+	0.362078i	$0.882067\pi$
$864$	−5.00000	−	1.41421i	−0.170103	−	0.0481125i
$865$	−19.9096	+	4.46705i	−0.676948	+	0.151884i
$866$			33.8243i			1.14940i
$867$	−58.5552	+	10.0465i	−1.98864	+	0.341196i
$868$	3.59604	−	3.59604i	0.122058	−	0.122058i
$869$	−2.33838			−0.0793241
$870$	35.8857	−	14.7774i	1.21664	−	0.501002i
$871$	−1.98141			−0.0671375
$872$	4.29903	−	4.29903i	0.145583	−	0.145583i
$873$	−22.8349	−	10.9058i	−0.772843	−	0.369104i
$874$		−	31.1972i		−	1.05526i
$875$	−34.9566	−	44.8432i	−1.18175	−	1.51598i
$876$	0.600906	−	0.849810i	0.0203027	−	0.0287124i
$877$	−29.3588	−	29.3588i	−0.991375	−	0.991375i	0.00858855	−	0.999963i	$-0.497266\pi$
$877$	−29.3588	−	29.3588i	−0.991375	−	0.991375i	−0.999963	+	0.00858855i	$0.997266\pi$
$878$	−8.87255	−	8.87255i	−0.299434	−	0.299434i
$879$	10.3560	−	14.6456i	0.349300	−	0.493985i
$880$	3.15707	+	2.00000i	0.106425	+	0.0674200i
$881$		−	27.5826i		−	0.929282i	−0.885499	−	0.464641i	$-0.846183\pi$
$881$		−	27.5826i		−	0.929282i	0.885499	−	0.464641i	$-0.153817\pi$
$882$	−51.0641	−	24.3878i	−1.71942	−	0.821181i
$883$	−13.0070	+	13.0070i	−0.437719	+	0.437719i	−0.891244	−	0.453525i	$-0.850166\pi$
$883$	−13.0070	+	13.0070i	−0.437719	+	0.437719i	0.453525	+	0.891244i	$0.350166\pi$
$884$	7.31247			0.245945
$885$	−10.7563	−	4.48151i	−0.361569	−	0.150644i
$886$	19.9294			0.669542
$887$	22.1276	−	22.1276i	0.742973	−	0.742973i	−0.230176	−	0.973149i	$-0.573930\pi$
$887$	22.1276	−	22.1276i	0.742973	−	0.742973i	0.973149	+	0.230176i	$0.0739301\pi$
$888$	4.82843	−	0.828427i	0.162031	−	0.0278002i
$889$		−	68.4243i		−	2.29488i
$890$	−1.61921	−	7.21683i	−0.0542762	−	0.241909i
$891$	−9.45460	−	11.6995i	−0.316741	−	0.391947i
$892$	−12.2654	−	12.2654i	−0.410675	−	0.410675i
$893$	−13.6588	−	13.6588i	−0.457075	−	0.457075i
$894$	−22.5803	−	15.9667i	−0.755197	−	0.534005i
$895$	−19.8453	+	31.3266i	−0.663357	+	1.04713i
$896$			5.08557i			0.169897i
$897$	1.27300	+	7.41960i	0.0425043	+	0.247733i
$898$	−7.08334	+	7.08334i	−0.236374	+	0.236374i
$899$	−10.0205			−0.334203
$900$	10.6504	−	10.5626i	0.355014	−	0.352087i
$901$	1.92963			0.0642852
$902$	12.5698	−	12.5698i	0.418528	−	0.418528i
$903$	11.1399	+	64.9283i	0.370714	+	2.16068i
$904$			3.15707i			0.105003i
$905$	2.24023	−	3.53628i	0.0744677	−	0.117550i
$906$	−14.5669	−	10.3004i	−0.483954	−	0.342207i
$907$	−0.148095	−	0.148095i	−0.00491740	−	0.00491740i	0.704644	−	0.709561i	$-0.251107\pi$
$907$	−0.148095	−	0.148095i	−0.00491740	−	0.00491740i	−0.709561	+	0.704644i	$0.751107\pi$
$908$	−4.98392	−	4.98392i	−0.165397	−	0.165397i
$909$	−9.46972	−	26.7844i	−0.314091	−	0.888383i
$910$	2.54167	+	11.3282i	0.0842555	+	0.375526i
$911$			18.0914i			0.599395i	0.954034	+	0.299697i	$0.0968857\pi$
$911$			18.0914i			0.599395i	−0.954034	+	0.299697i	$0.903114\pi$
$912$	12.5100	−	2.14638i	0.414249	−	0.0710738i
$913$	−12.3180	+	12.3180i	−0.407667	+	0.407667i
$914$	−30.1155			−0.996132
$915$	−35.1686	−	14.6526i	−1.16264	−	0.484401i
$916$	12.3993			0.409684
$917$	−16.0996	+	16.0996i	−0.531657	+	0.531657i
$918$	32.4856	−	18.1607i	1.07218	−	0.599391i
$919$		−	48.1668i		−	1.58888i	−0.607344	−	0.794439i	$-0.707765\pi$
$919$		−	48.1668i		−	1.58888i	0.607344	−	0.794439i	$-0.292235\pi$
$920$	−8.04145	−	5.09424i	−0.265119	−	0.167952i
$921$	26.4961	−	37.4711i	0.873075	−	1.23471i
$922$	−17.3336	−	17.3336i	−0.570851	−	0.570851i
$923$	0.958855	+	0.958855i	0.0315611	+	0.0315611i
$924$	−8.49978	+	12.0205i	−0.279622	+	0.395446i
$925$	−4.76919	+	13.3137i	−0.156810	+	0.437752i
$926$		−	12.2090i		−	0.401212i
$927$	−3.53789	+	7.40777i	−0.116200	+	0.243303i
$928$	7.08557	−	7.08557i	0.232595	−	0.232595i
$929$	−44.8497			−1.47147			−0.735735	−	0.677270i	$-0.763163\pi$
$929$	−44.8497			−1.47147			−0.735735	+	0.677270i	$0.763163\pi$
$930$	−3.58123	+	1.47472i	−0.117433	+	0.0483579i
$931$	138.232			4.53037
$932$	19.3438	−	19.3438i	0.633629	−	0.633629i
$933$	−5.49184	+	0.942251i	−0.179795	+	0.0308479i
$934$			30.1993i			0.988150i
$935$	−26.1186	+	5.86014i	−0.854171	+	0.191647i
$936$	−2.88767	+	1.02094i	−0.0943863	+	0.0333706i
$937$	−30.1698	−	30.1698i	−0.985605	−	0.985605i	0.0142928	−	0.999898i	$-0.495450\pi$
$937$	−30.1698	−	30.1698i	−0.985605	−	0.985605i	−0.999898	+	0.0142928i	$0.995450\pi$
$938$	6.97906	+	6.97906i	0.227874	+	0.227874i
$939$	22.8847	+	16.1819i	0.746813	+	0.528077i
$940$	−5.75110	+	1.29035i	−0.187580	+	0.0420867i
$941$		−	51.9991i		−	1.69512i	−0.530697	−	0.847561i	$-0.678070\pi$
$941$		−	51.9991i		−	1.69512i	0.530697	−	0.847561i	$-0.321930\pi$
$942$	−1.89866	−	11.0662i	−0.0618617	−	0.360556i
$943$	−32.0168	+	32.0168i	−1.04261	+	1.04261i
$944$	−3.00868			−0.0979240
$945$	39.4252	+	44.0132i	1.28250	+	1.43175i
$946$	12.4998			0.406403
$947$	−5.52445	+	5.52445i	−0.179521	+	0.179521i	−0.791147	−	0.611626i	$-0.790516\pi$
$947$	−5.52445	+	5.52445i	−0.179521	+	0.179521i	0.611626	+	0.791147i	$0.290516\pi$
$948$	0.409785	+	2.38840i	0.0133092	+	0.0775717i
$949$		−	0.613491i		−	0.0199148i
$950$	−12.3566	+	34.4947i	−0.400900	+	1.11915i
$951$	−11.8860	−	8.40466i	−0.385429	−	0.272540i
$952$	−25.7565	−	25.7565i	−0.834772	−	0.834772i
$953$	−7.47016	−	7.47016i	−0.241982	−	0.241982i	0.575688	−	0.817670i	$-0.304734\pi$
$953$	−7.47016	−	7.47016i	−0.241982	−	0.241982i	−0.817670	+	0.575688i	$0.804734\pi$
$954$	−0.762002	+	0.269409i	−0.0246707	+	0.00872242i
$955$	32.9486	+	20.8728i	1.06619	+	0.675430i
$956$		−	8.86716i		−	0.286784i
$957$	28.5903	−	4.90532i	0.924193	−	0.158566i
$958$	−5.44182	+	5.44182i	−0.175817	+	0.175817i
$959$	−30.9158			−0.998323
$960$	1.48953	−	3.57510i	0.0480743	−	0.115386i
$961$	1.00000			0.0322581
$962$	2.04189	−	2.04189i	0.0658331	−	0.0658331i
$963$	−0.0994131	+	0.208155i	−0.00320354	+	0.00670769i
$964$			6.97906i			0.224780i
$965$	1.31686	+	5.86926i	0.0423913	+	0.188938i
$966$	21.6500	−	30.6177i	0.696576	−	0.985108i
$967$	2.09051	+	2.09051i	0.0672264	+	0.0672264i	0.739921	−	0.672694i	$-0.234863\pi$
$967$	2.09051	+	2.09051i	0.0672264	+	0.0672264i	−0.672694	+	0.739921i	$0.734863\pi$
$968$	−5.80293	−	5.80293i	−0.186513	−	0.186513i
$969$	−52.4880	+	74.2292i	−1.68616	+	2.38459i
$970$	10.0938	−	15.9334i	0.324093	−	0.511592i
$971$		−	8.86332i		−	0.284437i	−0.989835	−	0.142219i	$-0.954576\pi$
$971$		−	8.86332i		−	0.284437i	0.989835	−	0.142219i	$-0.0454236\pi$
$972$	−10.2929	+	11.7071i	−0.330145	+	0.375506i
$973$	−29.4278	+	29.4278i	−0.943413	+	0.943413i
$974$	−14.1819			−0.454418
$975$	1.53119	−	8.70804i	0.0490374	−	0.278880i
$976$	−9.83710			−0.314878
$977$	−34.8184	+	34.8184i	−1.11394	+	1.11394i	−0.121328	+	0.992612i	$0.538715\pi$
$977$	−34.8184	+	34.8184i	−1.11394	+	1.11394i	−0.992612	+	0.121328i	$0.961285\pi$
$978$	−7.44922	+	1.27808i	−0.238200	+	0.0408686i
$979$		−	5.52834i		−	0.176687i
$980$	22.5721	−	35.6309i	0.721040	−	1.13819i
$981$	−6.07974	−	17.1961i	−0.194111	−	0.549030i
$982$	8.60515	+	8.60515i	0.274601	+	0.274601i
$983$	−4.45175	−	4.45175i	−0.141989	−	0.141989i	0.632539	−	0.774528i	$-0.282013\pi$
$983$	−4.45175	−	4.45175i	−0.141989	−	0.141989i	−0.774528	+	0.632539i	$0.782013\pi$
$984$	−15.0414	−	10.6359i	−0.479504	−	0.339060i
$985$	−1.86760	−	8.32388i	−0.0595066	−	0.265221i
$986$			71.7715i			2.28567i
$987$	−3.92626	−	22.8839i	−0.124974	−	0.728404i
$988$	5.29035	−	5.29035i	0.168309	−	0.168309i
$989$	−31.8385			−1.01240
$990$	9.49597	−	5.96075i	0.301802	−	0.189445i
$991$	−7.97049			−0.253191			−0.126596	−	0.991954i	$-0.540405\pi$
$991$	−7.97049			−0.253191			−0.126596	+	0.991954i	$0.540405\pi$
$992$	−0.707107	+	0.707107i	−0.0224507	+	0.0224507i
$993$	3.37877	+	19.6929i	0.107222	+	0.624936i
$994$		−	6.75469i		−	0.214246i
$995$	−45.6834	−	28.9403i	−1.44826	−	0.917470i
$996$	14.7402	+	10.4229i	0.467061	+	0.330262i
$997$	2.64756	+	2.64756i	0.0838490	+	0.0838490i	0.747787	−	0.663938i	$-0.231116\pi$
$997$	2.64756	+	2.64756i	0.0838490	+	0.0838490i	−0.663938	+	0.747787i	$0.731116\pi$
$998$	−21.0089	−	21.0089i	−0.665024	−	0.665024i
$999$	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.497.4	✓	8
3.2	odd	2		930.2.j.f.497.1	yes	8
5.3	odd	4		930.2.j.f.683.1	yes	8
15.8	even	4	inner	930.2.j.c.683.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.c.497.4	✓	8	1.1	even	1	trivial
930.2.j.c.683.4	yes	8	15.8	even	4	inner
930.2.j.f.497.1	yes	8	3.2	odd	2
930.2.j.f.683.1	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 $\F_{q}$
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} +(-0.292893 - 1.70711i) q^{3} -1.00000i q^{4} +(1.19663 - 1.88893i) q^{5} +(-1.41421 - 1.00000i) q^{6} +(3.59604 + 3.59604i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 + 1.00000i) q^{9} +(-0.489528 - 2.18183i) q^{10} -1.67135i q^{11} +(-1.70711 + 0.292893i) q^{12} +(-0.721916 + 0.721916i) q^{13} +5.08557 q^{14} +(-3.57510 - 1.48953i) q^{15} -1.00000 q^{16} +(5.06462 - 5.06462i) q^{17} +(-1.29289 + 2.70711i) q^{18} -7.32821i q^{19} +(-1.88893 - 1.19663i) q^{20} +(5.08557 - 7.19208i) q^{21} +(-1.18183 - 1.18183i) q^{22} +(3.01025 + 3.01025i) q^{23} +(-1.00000 + 1.41421i) q^{24} +(-2.13613 - 4.52072i) q^{25} +1.02094i q^{26} +(2.53553 + 4.53553i) q^{27} +(3.59604 - 3.59604i) q^{28} -10.0205 q^{29} +(-3.58123 + 1.47472i) q^{30} +1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.85318 + 0.489528i) q^{33} -7.16246i q^{34} +(11.0958 - 2.48953i) q^{35} +(1.00000 + 2.82843i) q^{36} +(-2.00000 - 2.00000i) q^{37} +(-5.18183 - 5.18183i) q^{38} +(1.44383 + 1.02094i) q^{39} +(-2.18183 + 0.489528i) q^{40} +10.6359i q^{41} +(-1.48953 - 8.68161i) q^{42} +(-5.28834 + 5.28834i) q^{43} -1.67135 q^{44} +(-1.49566 + 6.53934i) q^{45} +4.25714 q^{46} +(1.86387 - 1.86387i) q^{47} +(0.292893 + 1.70711i) q^{48} +18.8630i q^{49} +(-4.70711 - 1.68616i) q^{50} +(-10.1292 - 7.16246i) q^{51} +(0.721916 + 0.721916i) q^{52} +(0.190501 + 0.190501i) q^{53} +(5.00000 + 1.41421i) q^{54} +(-3.15707 - 2.00000i) q^{55} -5.08557i q^{56} +(-12.5100 + 2.14638i) q^{57} +(-7.08557 + 7.08557i) q^{58} +3.00868 q^{59} +(-1.48953 + 3.57510i) q^{60} +9.83710 q^{61} +(0.707107 - 0.707107i) q^{62} +(-13.7672 - 6.57510i) q^{63} +1.00000i q^{64} +(0.499781 + 2.22752i) q^{65} +(-1.67135 + 2.36365i) q^{66} +(1.37233 + 1.37233i) q^{67} +(-5.06462 - 5.06462i) q^{68} +(4.25714 - 6.02051i) q^{69} +(6.08557 - 9.60629i) q^{70} -1.32821i q^{71} +(2.70711 + 1.29289i) q^{72} +(-0.424905 + 0.424905i) q^{73} -2.82843 q^{74} +(-7.09170 + 4.97069i) q^{75} -7.32821 q^{76} +(6.01025 - 6.01025i) q^{77} +(1.74286 - 0.299028i) q^{78} -1.39909i q^{79} +(-1.19663 + 1.88893i) q^{80} +(7.00000 - 5.65685i) q^{81} +(7.52072 + 7.52072i) q^{82} +(-7.37010 - 7.37010i) q^{83} +(-7.19208 - 5.08557i) q^{84} +(-3.50623 - 15.6272i) q^{85} +7.47884i q^{86} +(2.93494 + 17.1061i) q^{87} +(-1.18183 + 1.18183i) q^{88} +3.30770 q^{89} +(3.56642 + 5.68161i) q^{90} -5.19208 q^{91} +(3.01025 - 3.01025i) q^{92} +(-0.292893 - 1.70711i) q^{93} -2.63591i q^{94} +(-13.8425 - 8.76919i) q^{95} +(1.41421 + 1.00000i) q^{96} +(5.96456 + 5.96456i) q^{97} +(13.3382 + 13.3382i) q^{98} +(1.67135 + 4.72730i) 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^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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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