LMFDB - Embedded newform 930.2.j.f.497.1

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			497.1
Root			$0.692297i$ of defining polynomial
Character	$\chi$	$=$	930.497
Dual form			930.2.j.f.683.1

$q$-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} +(-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} +(0.292893 - 1.70711i) q^{12} +(-0.721916 + 0.721916i) q^{13} -5.08557 q^{14} +(-2.59604 + 2.87412i) q^{15} -1.00000 q^{16} +(-5.06462 + 5.06462i) q^{17} +(-2.70711 + 1.29289i) 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} +(4.53553 + 2.53553i) q^{27} +(3.59604 - 3.59604i) q^{28} +10.0205 q^{29} +(-0.196635 - 3.86799i) q^{30} +1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.489528 + 2.85318i) 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} +(-8.68161 - 1.48953i) q^{42} +(-5.28834 + 5.28834i) q^{43} +1.67135 q^{44} +(-5.27353 + 4.14607i) q^{45} +4.25714 q^{46} +(-1.86387 + 1.86387i) q^{47} +(-1.70711 - 0.292893i) 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} +(2.14638 - 12.5100i) q^{57} +(-7.08557 + 7.08557i) q^{58} -3.00868 q^{59} +(2.87412 + 2.59604i) q^{60} +9.83710 q^{61} +(-0.707107 + 0.707107i) q^{62} +(6.57510 + 13.7672i) 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} +(1.29289 + 2.70711i) q^{72} +(-0.424905 + 0.424905i) q^{73} +2.82843 q^{74} +(-2.32251 - 8.34302i) q^{75} -7.32821 q^{76} +(-6.01025 + 6.01025i) q^{77} +(0.299028 - 1.74286i) 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} +(17.1061 + 2.93494i) q^{87} +(-1.18183 + 1.18183i) q^{88} -3.30770 q^{89} +(0.797231 - 6.66066i) q^{90} -5.19208 q^{91} +(-3.01025 + 3.01025i) q^{92} +(1.70711 + 0.292893i) 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^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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

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

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
$3$	1.70711	+	0.292893i	0.985599	+	0.169102i
$3$	1.70711	+	0.292893i	0.985599	+	0.169102i
$4$		−	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	$0.0810771\pi$
$11$			1.67135i			0.503932i	−0.967736	+	0.251966i	$0.918923\pi$
$12$	0.292893	−	1.70711i	0.0845510	−	0.492799i
$13$	−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
$15$	−2.59604	+	2.87412i	−0.670294	+	0.742095i
$16$	−1.00000			−0.250000
$17$	−5.06462	+	5.06462i	−1.22835	+	1.22835i	−0.263764	+	0.964587i	$0.584964\pi$
$17$	−5.06462	+	5.06462i	−1.22835	+	1.22835i	−0.964587	+	0.263764i	$0.915036\pi$
$18$	−2.70711	+	1.29289i	−0.638071	+	0.304738i
$19$		−	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	0.319803	−	0.947484i	$-0.396383\pi$
$23$	−3.01025	−	3.01025i	−0.627681	−	0.627681i	−0.947484	+	0.319803i	$0.896383\pi$
$24$	1.00000	+	1.41421i	0.204124	+	0.288675i
$25$	−2.13613	−	4.52072i	−0.427226	−	0.904145i
$26$		−	1.02094i		−	0.200224i
$27$	4.53553	+	2.53553i	0.872864	+	0.487964i
$28$	3.59604	−	3.59604i	0.679587	−	0.679587i
$29$	10.0205			1.86076			0.930381	−	0.366595i	$-0.119477\pi$
$29$	10.0205			1.86076			0.930381	+	0.366595i	$0.119477\pi$
$30$	−0.196635	−	3.86799i	−0.0359005	−	0.706195i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.489528	+	2.85318i	−0.0852159	+	0.496675i
$34$		−	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	$-0.688040\pi$
$41$		−	10.6359i		−	1.66105i	0.556981	−	0.830525i	$-0.311960\pi$
$42$	−8.68161	−	1.48953i	−1.33960	−	0.229839i
$43$	−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
$45$	−5.27353	+	4.14607i	−0.786131	+	0.618060i
$46$	4.25714			0.627681
$47$	−1.86387	+	1.86387i	−0.271873	+	0.271873i	−0.829854	−	0.557981i	$-0.811576\pi$
$47$	−1.86387	+	1.86387i	−0.271873	+	0.271873i	0.557981	+	0.829854i	$0.311576\pi$
$48$	−1.70711	−	0.292893i	−0.246400	−	0.0422755i
$49$			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	0.693902	−	0.720069i	$-0.255890\pi$
$53$	−0.190501	−	0.190501i	−0.0261673	−	0.0261673i	−0.720069	+	0.693902i	$0.755890\pi$
$54$	−5.00000	+	1.41421i	−0.680414	+	0.192450i
$55$	−3.15707	−	2.00000i	−0.425700	−	0.269680i
$56$			5.08557i			0.679587i
$57$	2.14638	−	12.5100i	0.284295	−	1.65699i
$58$	−7.08557	+	7.08557i	−0.930381	+	0.930381i
$59$	−3.00868			−0.391696			−0.195848	−	0.980634i	$-0.562746\pi$
$59$	−3.00868			−0.391696			−0.195848	+	0.980634i	$0.562746\pi$
$60$	2.87412	+	2.59604i	0.371048	+	0.335147i
$61$	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
$63$	6.57510	+	13.7672i	0.828384	+	1.73450i
$64$			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	$0.0251135\pi$
$71$			1.32821i			0.157629i	−0.996889	+	0.0788146i	$0.974886\pi$
$72$	1.29289	+	2.70711i	0.152369	+	0.319036i
$73$	−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
$75$	−2.32251	−	8.34302i	−0.268181	−	0.963369i
$76$	−7.32821			−0.840603
$77$	−6.01025	+	6.01025i	−0.684932	+	0.684932i
$78$	0.299028	−	1.74286i	0.0338582	−	0.197340i
$79$		−	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	0.984478	−	0.175505i	$-0.0561560\pi$
$83$	7.37010	+	7.37010i	0.808973	+	0.808973i	−0.175505	+	0.984478i	$0.556156\pi$
$84$	7.19208	−	5.08557i	0.784720	−	0.554881i
$85$	−3.50623	−	15.6272i	−0.380304	−	1.69501i
$86$		−	7.47884i		−	0.806464i
$87$	17.1061	+	2.93494i	1.83396	+	0.314658i
$88$	−1.18183	+	1.18183i	−0.125983	+	0.125983i
$89$	−3.30770			−0.350616			−0.175308	−	0.984514i	$-0.556092\pi$
$89$	−3.30770			−0.350616			−0.175308	+	0.984514i	$0.556092\pi$
$90$	0.797231	−	6.66066i	0.0840355	−	0.702095i
$91$	−5.19208			−0.544278
$92$	−3.01025	+	3.01025i	−0.313841	+	0.313841i
$93$	1.70711	+	0.292893i	0.177019	+	0.0303716i
$94$		−	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	$-0.843844\pi$
$101$		−	9.46972i		−	0.942273i	0.882060	−	0.471136i	$-0.156156\pi$
$102$	2.09784	−	12.2271i	0.207717	−	1.21066i
$103$	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
$105$	−19.6709	+	1.00000i	−1.91968	+	0.0975900i
$106$	0.269409			0.0261673
$107$	−0.0543708	+	0.0543708i	−0.00525622	+	0.00525622i	−0.709730	−	0.704474i	$-0.751183\pi$
$107$	−0.0543708	+	0.0543708i	−0.00525622	+	0.00525622i	0.704474	+	0.709730i	$0.251183\pi$
$108$	2.53553	−	4.53553i	0.243982	−	0.436432i
$109$			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	0.804270	−	0.594264i	$-0.202557\pi$
$113$	2.23239	+	2.23239i	0.210005	+	0.210005i	−0.594264	+	0.804270i	$0.702557\pi$
$114$	7.32821	+	10.3637i	0.686350	+	0.970645i
$115$	9.28834	−	2.08399i	0.866142	−	0.194333i
$116$		−	10.0205i		−	0.930381i
$117$	−2.76380	+	1.31997i	−0.255514	+	0.122031i
$118$	2.12745	−	2.12745i	0.195848	−	0.195848i
$119$	−36.4252			−3.33909
$120$	−3.86799	+	0.196635i	−0.353097	+	0.0179502i
$121$	8.20658			0.746052
$122$	−6.95588	+	6.95588i	−0.629756	+	0.629756i
$123$	3.11519	−	18.1566i	0.280887	−	1.63713i
$124$		−	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	$-0.937341\pi$
$131$		−	4.47704i		−	0.391161i	0.980688	−	0.195581i	$-0.0626591\pi$
$132$	2.85318	+	0.489528i	0.248337	+	0.0426080i
$133$	26.3525	−	26.3525i	2.28505	−	2.28505i
$134$	−1.94076			−0.167656
$135$	−10.2168	+	5.53321i	−0.879325	+	0.476223i
$136$	−7.16246			−0.614176
$137$	4.29859	−	4.29859i	0.367253	−	0.367253i	−0.499221	−	0.866475i	$-0.666381\pi$
$137$	4.29859	−	4.29859i	0.367253	−	0.367253i	0.866475	+	0.499221i	$0.166381\pi$
$138$	7.26739	+	1.24689i	0.618642	+	0.106142i
$139$			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
$147$	−5.52484	+	32.2011i	−0.455681	+	2.65591i
$148$	−2.00000	+	2.00000i	−0.164399	+	0.164399i
$149$	−15.9667			−1.30804			−0.654020	−	0.756478i	$-0.726919\pi$
$149$	−15.9667			−1.30804			−0.654020	+	0.756478i	$0.726919\pi$
$150$	7.54167	+	4.25714i	0.615775	+	0.347594i
$151$	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
$153$	−19.3895	+	9.26029i	−1.56755	+	0.748650i
$154$		−	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
$162$	−8.94975	+	0.949747i	−0.703159	+	0.0746192i
$163$	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
$165$	−4.80368	−	4.33890i	−0.373966	−	0.337783i
$166$	−10.4229			−0.808973
$167$	10.8177	−	10.8177i	0.837102	−	0.837102i	−0.151375	−	0.988476i	$-0.548370\pi$
$167$	10.8177	−	10.8177i	0.837102	−	0.837102i	0.988476	+	0.151375i	$0.0483701\pi$
$168$	−1.48953	+	8.68161i	−0.114920	+	0.669800i
$169$			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	0.908487	−	0.417912i	$-0.137238\pi$
$173$	6.45251	+	6.45251i	0.490575	+	0.490575i	−0.417912	+	0.908487i	$0.637238\pi$
$174$	−14.1711	+	10.0205i	−1.07431	+	0.759653i
$175$	8.57510	−	23.9383i	0.648216	−	1.80957i
$176$		−	1.67135i		−	0.125983i
$177$	−5.13613	−	0.881221i	−0.386055	−	0.0662366i
$178$	2.33890	−	2.33890i	0.175308	−	0.175308i
$179$	16.5843			1.23957			0.619784	−	0.784772i	$-0.287220\pi$
$179$	16.5843			1.23957			0.619784	+	0.784772i	$0.287220\pi$
$180$	4.14607	+	5.27353i	0.309030	+	0.393065i
$181$	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
$183$	16.7930	+	2.88122i	1.24137	+	0.212986i
$184$		−	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	$-0.782619\pi$
$191$		−	17.4430i		−	1.26213i	0.775731	−	0.631064i	$-0.217381\pi$
$192$	−0.292893	+	1.70711i	−0.0211377	+	0.123200i
$193$	−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
$195$	−0.200753	−	3.94900i	−0.0143762	−	0.282794i
$196$	18.8630			1.34736
$197$	−2.69768	+	2.69768i	−0.192202	+	0.192202i	−0.796647	−	0.604445i	$-0.793395\pi$
$197$	−2.69768	+	2.69768i	−0.192202	+	0.192202i	0.604445	+	0.796647i	$0.293395\pi$
$198$	−2.16088	−	4.52453i	−0.153567	−	0.321545i
$199$		−	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
$207$	−5.50403	−	11.5245i	−0.382556	−	0.801010i
$208$	0.721916	−	0.721916i	0.0500559	−	0.0500559i
$209$	12.2480			0.847214
$210$	13.2023	−	14.6165i	0.911047	−	1.00864i
$211$	−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
$213$	−0.389023	+	2.26739i	−0.0266554	+	0.155359i
$214$		−	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
$222$	4.82843	+	0.828427i	0.324063	+	0.0556004i
$223$	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
$225$	−1.52116	−	14.9227i	−0.101411	−	0.994845i
$226$	−3.15707			−0.210005
$227$	−4.98392	+	4.98392i	−0.330795	+	0.330795i	−0.852888	−	0.522094i	$-0.825151\pi$
$227$	−4.98392	+	4.98392i	−0.330795	+	0.330795i	0.522094	+	0.852888i	$0.325151\pi$
$228$	−12.5100	−	2.14638i	−0.828497	−	0.142148i
$229$			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	$-0.896398\pi$
$233$	−19.3438	−	19.3438i	−1.26726	−	1.26726i	−0.319758	−	0.947499i	$-0.603602\pi$
$234$	1.02094	−	2.88767i	0.0667412	−	0.188773i
$235$	−1.29035	−	5.75110i	−0.0841733	−	0.375160i
$236$			3.00868i			0.195848i
$237$	0.409785	−	2.38840i	0.0266184	−	0.155143i
$238$	25.7565	−	25.7565i	1.66954	−	1.66954i
$239$	−8.86716			−0.573569			−0.286784	−	0.957995i	$-0.592586\pi$
$239$	−8.86716			−0.573569			−0.286784	+	0.957995i	$0.592586\pi$
$240$	2.59604	−	2.87412i	0.167574	−	0.185524i
$241$	−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
$243$	10.2929	+	11.7071i	0.660289	+	0.751011i
$244$		−	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	$0.181381\pi$
$251$			17.0941i			1.07897i	−0.841995	+	0.539485i	$0.818619\pi$
$252$	13.7672	−	6.57510i	0.867250	−	0.414192i
$253$	5.03120	−	5.03120i	0.316309	−	0.316309i
$254$	13.4546			0.844217
$255$	−1.40839	−	27.7043i	−0.0881968	−	1.73491i
$256$	1.00000			0.0625000
$257$	17.3020	−	17.3020i	1.07927	−	1.07927i	0.0826913	−	0.996575i	$-0.473648\pi$
$257$	17.3020	−	17.3020i	1.07927	−	1.07927i	0.996575	−	0.0826913i	$-0.0263515\pi$
$258$	2.19050	−	12.7672i	0.136375	−	0.794849i
$259$		−	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	0.668247	−	0.743939i	$-0.267045\pi$
$263$	−1.22752	−	1.22752i	−0.0756922	−	0.0756922i	−0.743939	+	0.668247i	$0.767045\pi$
$264$	−2.36365	+	1.67135i	−0.145473	+	0.102865i
$265$	0.587802	−	0.131883i	0.0361084	−	0.00810151i
$266$			37.2681i			2.28505i
$267$	−5.64660	−	0.968804i	−0.345566	−	0.0592898i
$268$	1.37233	−	1.37233i	0.0838282	−	0.0838282i
$269$	0.283908			0.0173102			0.00865508	−	0.999963i	$-0.497245\pi$
$269$	0.283908			0.0173102			0.00865508	+	0.999963i	$0.497245\pi$
$270$	3.31182	−	11.1370i	0.201551	−	0.677774i
$271$	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
$273$	−8.86343	−	1.52072i	−0.536439	−	0.0920384i
$274$			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	$-0.829309\pi$
$281$		−	17.1288i		−	1.02182i	0.859634	−	0.510910i	$-0.170691\pi$
$282$	0.772040	−	4.49978i	0.0459743	−	0.267958i
$283$	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
$285$	21.0622	+	19.0243i	1.24762	+	1.12690i
$286$	1.70636			0.100899
$287$	38.2471	−	38.2471i	2.25766	−	2.25766i
$288$	2.70711	−	1.29289i	0.159518	−	0.0761845i
$289$		−	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	0.460076	−	0.887880i	$-0.347822\pi$
$293$	−7.32282	−	7.32282i	−0.427804	−	0.427804i	−0.887880	+	0.460076i	$0.847822\pi$
$294$	−18.8630	−	26.6763i	−1.10011	−	1.55579i
$295$	3.60029	−	5.68318i	0.209617	−	0.330888i
$296$		−	2.82843i		−	0.164399i
$297$	−4.23777	+	7.58048i	−0.245901	+	0.439864i
$298$	11.2901	−	11.2901i	0.654020	−	0.654020i
$299$	4.34630			0.251353
$300$	−8.34302	+	2.32251i	−0.481684	+	0.134090i
$301$	−38.0341			−2.19225
$302$	−7.28347	+	7.28347i	−0.419117	+	0.419117i
$303$	2.77362	−	16.1658i	0.159340	−	0.928703i
$304$			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	$0.0290737\pi$
$311$			3.21704i			0.182422i	−0.995832	+	0.0912109i	$0.970926\pi$
$312$	−1.74286	−	0.299028i	−0.0986700	−	0.0169291i
$313$	−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
$315$	−33.8732	−	4.05437i	−1.90854	−	0.228438i
$316$	−1.39909			−0.0787052
$317$	−5.94299	+	5.94299i	−0.333792	+	0.333792i	−0.854025	−	0.520233i	$-0.825845\pi$
$317$	−5.94299	+	5.94299i	−0.333792	+	0.333792i	0.520233	+	0.854025i	$0.325845\pi$
$318$	0.459909	+	0.0789079i	0.0257904	+	0.00442494i
$319$			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
$327$	−1.78072	+	10.3788i	−0.0984738	+	0.573947i
$328$	7.52072	−	7.52072i	0.415263	−	0.415263i
$329$	−13.4051			−0.739047
$330$	6.46478	−	0.328646i	0.355874	−	0.0180914i
$331$	−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
$333$	−3.65685	−	7.65685i	−0.200394	−	0.419593i
$334$			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
$342$	9.47459	+	19.8382i	0.512327	+	1.07273i
$343$	−42.6598	+	42.6598i	−2.30341	+	2.30341i
$344$	−7.47884			−0.403232
$345$	16.4666	−	0.837102i	0.886530	−	0.0450681i
$346$	−9.12522			−0.490575
$347$	−4.39104	+	4.39104i	−0.235723	+	0.235723i	−0.815077	−	0.579353i	$-0.803305\pi$
$347$	−4.39104	+	4.39104i	−0.235723	+	0.235723i	0.579353	+	0.815077i	$0.303305\pi$
$348$	2.93494	−	17.1061i	0.157329	−	0.916982i
$349$		−	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	0.804356	−	0.594148i	$-0.202511\pi$
$353$	3.94944	+	3.94944i	0.210207	+	0.210207i	−0.594148	+	0.804356i	$0.702511\pi$
$354$	4.25491	−	3.00868i	0.226146	−	0.159909i
$355$	−2.50889	−	1.58938i	−0.133158	−	0.0843555i
$356$			3.30770i			0.175308i
$357$	−62.1816	−	10.6687i	−3.29100	−	0.564647i
$358$	−11.7269	+	11.7269i	−0.619784	+	0.619784i
$359$	−7.94361			−0.419248			−0.209624	−	0.977782i	$-0.567224\pi$
$359$	−7.94361			−0.419248			−0.209624	+	0.977782i	$0.567224\pi$
$360$	−6.66066	−	0.797231i	−0.351048	−	0.0420178i
$361$	−34.7026			−1.82645
$362$	−1.32378	+	1.32378i	−0.0695763	+	0.0695763i
$363$	14.0095	+	2.40365i	0.735308	+	0.126159i
$364$			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
$372$	0.292893	−	1.70711i	0.0151858	−	0.0885094i
$373$	−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
$375$	18.5386	+	5.59648i	0.957329	+	0.289001i
$376$	−2.63591			−0.135937
$377$	−7.23397	+	7.23397i	−0.372568	+	0.372568i
$378$	−23.0658	−	12.8946i	−1.18637	−	0.663228i
$379$			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	0.770614	−	0.637302i	$-0.219950\pi$
$383$	2.60896	+	2.60896i	0.133312	+	0.133312i	−0.637302	+	0.770614i	$0.719950\pi$
$384$	−1.00000	−	1.41421i	−0.0510310	−	0.0721688i
$385$	−4.16088	−	18.5450i	−0.212058	−	0.945143i
$386$		−	2.69007i		−	0.136921i
$387$	−20.2460	+	9.66934i	−1.02916	+	0.491520i
$388$	5.96456	−	5.96456i	0.302805	−	0.302805i
$389$	−7.76113			−0.393505			−0.196753	−	0.980453i	$-0.563040\pi$
$389$	−7.76113			−0.393505			−0.196753	+	0.980453i	$0.563040\pi$
$390$	2.93432	+	2.65041i	0.148585	+	0.134209i
$391$	30.4916			1.54203
$392$	−13.3382	+	13.3382i	−0.673678	+	0.673678i
$393$	1.31130	−	7.64279i	0.0661461	−	0.385528i
$394$		−	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	$-0.661697\pi$
$401$		−	34.9927i		−	1.74745i	0.486419	−	0.873725i	$-0.338303\pi$
$402$	−3.31309	−	0.568436i	−0.165242	−	0.0283510i
$403$	−0.721916	+	0.721916i	−0.0359612	+	0.0359612i
$404$	−9.46972			−0.471136
$405$	−19.0619	+	6.45334i	−0.947191	+	0.320669i
$406$	−50.9600			−2.52910
$407$	3.34271	−	3.34271i	0.165692	−	0.165692i
$408$	−12.2271	−	2.09784i	−0.605331	−	0.103858i
$409$			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
$417$	−2.39686	+	13.9699i	−0.117375	+	0.684111i
$418$	−8.66066	+	8.66066i	−0.423607	+	0.423607i
$419$	7.13118			0.348381			0.174191	−	0.984712i	$-0.444269\pi$
$419$	7.13118			0.348381			0.174191	+	0.984712i	$0.444269\pi$
$420$	1.00000	+	19.6709i	0.0487950	+	0.959842i
$421$	−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
$423$	−7.13569	+	3.40795i	−0.346949	+	0.165700i
$424$		−	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	$0.161833\pi$
$431$			20.2121i			0.973585i	−0.873518	+	0.486792i	$0.838167\pi$
$432$	−4.53553	−	2.53553i	−0.218216	−	0.121991i
$433$	−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
$435$	−26.0136	+	28.8002i	−1.24726	+	1.38086i
$436$	6.07974			0.291167
$437$	−22.0598	+	22.0598i	−1.05526	+	1.05526i
$438$	0.176001	−	1.02581i	0.00840967	−	0.0490151i
$439$		−	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	0.288068	−	0.957610i	$-0.406987\pi$
$443$	−14.0922	−	14.0922i	−0.669542	−	0.669542i	−0.957610	+	0.288068i	$0.906987\pi$
$444$	−4.00000	+	2.82843i	−0.189832	+	0.134231i
$445$	3.95811	−	6.24803i	0.187633	−	0.296185i
$446$			17.3459i			0.821350i
$447$	−27.2568	−	4.67652i	−1.28920	−	0.221192i
$448$	−3.59604	+	3.59604i	−0.169897	+	0.169897i
$449$	10.0174			0.472748			0.236374	−	0.971662i	$-0.424041\pi$
$449$	10.0174			0.472748			0.236374	+	0.971662i	$0.424041\pi$
$450$	11.6275	+	9.47630i	0.548128	+	0.446717i
$451$	17.7764			0.837056
$452$	2.23239	−	2.23239i	0.105003	−	0.105003i
$453$	17.5839	+	3.01691i	0.826161	+	0.141747i
$454$		−	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	$0.193387\pi$
$461$			24.5134i			1.14170i	−0.821053	+	0.570851i	$0.806613\pi$
$462$	2.48953	−	14.5100i	0.115823	−	0.675068i
$463$	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
$465$	−2.59604	+	2.87412i	−0.120388	+	0.133284i
$466$	27.3563			1.26726
$467$	21.3541	−	21.3541i	0.988150	−	0.988150i	−0.0117808	−	0.999931i	$-0.503750\pi$
$467$	21.3541	−	21.3541i	0.988150	−	0.988150i	0.999931	+	0.0117808i	$0.00375002\pi$
$468$	1.31997	+	2.76380i	0.0610157	+	0.127757i
$469$			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
$477$	−0.348317	−	0.729318i	−0.0159483	−	0.0333932i
$478$	6.27003	−	6.27003i	0.286784	−	0.286784i
$479$	7.69589			0.351634			0.175817	−	0.984423i	$-0.443743\pi$
$479$	7.69589			0.351634			0.175817	+	0.984423i	$0.443743\pi$
$480$	0.196635	+	3.86799i	0.00897511	+	0.176549i
$481$	2.88767			0.131666
$482$	4.93494	−	4.93494i	0.224780	−	0.224780i
$483$	6.34113	−	36.9588i	0.288531	−	1.68168i
$484$		−	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	$-0.911454\pi$
$491$		−	12.1695i		−	0.549203i	0.961558	−	0.274601i	$-0.0885459\pi$
$492$	−18.1566	−	3.11519i	−0.818564	−	0.140443i
$493$	−50.7501	+	50.7501i	−2.28567	+	2.28567i
$494$	−7.48169			−0.336617
$495$	−6.92955	−	8.81393i	−0.311460	−	0.396157i
$496$	−1.00000			−0.0449013
$497$	−4.77629	+	4.77629i	−0.214246	+	0.214246i
$498$	−17.7930	−	3.05279i	−0.797323	−	0.136799i
$499$		−	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	0.767207	−	0.641400i	$-0.221646\pi$
$503$	2.82154	+	2.82154i	0.125806	+	0.125806i	−0.641400	+	0.767207i	$0.721646\pi$
$504$	−5.08557	+	14.3842i	−0.226529	+	0.640721i
$505$	17.8877	+	11.3318i	0.795991	+	0.504259i
$506$			7.11519i			0.316309i
$507$	−3.50232	+	20.4130i	−0.155544	+	0.906574i
$508$	−9.51384	+	9.51384i	−0.422108	+	0.422108i
$509$	−10.2585			−0.454700			−0.227350	−	0.973813i	$-0.573006\pi$
$509$	−10.2585			−0.454700			−0.227350	+	0.973813i	$0.573006\pi$
$510$	20.5858	+	18.5940i	0.911554	+	0.823357i
$511$	−3.05595			−0.135187
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	18.5809	−	33.2373i	0.820368	−	1.46746i
$514$			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	$-0.873351\pi$
$521$		−	17.6881i		−	0.774931i	0.921884	−	0.387466i	$-0.126649\pi$
$522$	−27.1266	+	12.9554i	−1.18730	+	0.567044i
$523$	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
$525$	21.6500	−	38.3537i	0.944882	−	1.67389i
$526$	1.73598			0.0756922
$527$	−5.06462	+	5.06462i	−0.220618	+	0.220618i
$528$	0.489528	−	2.85318i	0.0213040	−	0.124169i
$529$		−	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
$537$	28.3112	+	4.85743i	1.22172	+	0.209613i
$538$	−0.200753	+	0.200753i	−0.00865508	+	0.00865508i
$539$	−31.5267			−1.35795
$540$	5.53321	+	10.2168i	0.238111	+	0.439662i
$541$	−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
$543$	3.19589	+	0.548327i	0.137149	+	0.0235310i
$544$			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
$552$	1.24689	−	7.26739i	0.0530711	−	0.309321i
$553$	5.03120	−	5.03120i	0.213948	−	0.213948i
$554$	16.0486			0.681841
$555$	10.9403	−	0.556167i	0.464391	−	0.0236080i
$556$	8.18340			0.347054
$557$	12.0399	−	12.0399i	0.510146	−	0.510146i	−0.404425	−	0.914571i	$-0.632528\pi$
$557$	12.0399	−	12.0399i	0.510146	−	0.510146i	0.914571	+	0.404425i	$0.132528\pi$
$558$	−2.70711	+	1.29289i	−0.114601	+	0.0547325i
$559$		−	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	0.995975	−	0.0896326i	$-0.0285693\pi$
$563$	21.5053	+	21.5053i	0.906342	+	0.906342i	−0.0896326	+	0.995975i	$0.528569\pi$
$564$	2.63591	+	3.72774i	0.110992	+	0.156966i
$565$	−6.88818	+	1.54548i	−0.289788	+	0.0650187i
$566$			27.6774i			1.16337i
$567$	4.83000	+	45.5145i	0.202841	+	1.91143i
$568$	−0.939185	+	0.939185i	−0.0394073	+	0.0394073i
$569$	−1.35317			−0.0567280			−0.0283640	−	0.999598i	$-0.509030\pi$
$569$	−1.35317			−0.0567280			−0.0283640	+	0.999598i	$0.509030\pi$
$570$	−28.3454	+	1.44098i	−1.18726	+	0.0603561i
$571$	−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
$573$	5.10892	−	29.7770i	0.213428	−	1.24395i
$574$			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
$582$	−14.3997	−	2.47060i	−0.596887	−	0.102410i
$583$	0.318394	−	0.318394i	0.0131865	−	0.0131865i
$584$	−0.600906			−0.0248657
$585$	0.813928	−	6.80016i	0.0336518	−	0.281152i
$586$	10.3560			0.427804
$587$	−31.6919	+	31.6919i	−1.30806	+	1.30806i	−0.385251	+	0.922812i	$0.625885\pi$
$587$	−31.6919	+	31.6919i	−1.30806	+	1.30806i	−0.922812	+	0.385251i	$0.874115\pi$
$588$	32.2011	+	5.52484i	1.32795	+	0.227841i
$589$		−	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	0.766361	−	0.642410i	$-0.222065\pi$
$593$	3.01841	+	3.01841i	0.123951	+	0.123951i	−0.642410	+	0.766361i	$0.722065\pi$
$594$	−2.36365	−	8.35677i	−0.0969818	−	0.342882i
$595$	43.5876	−	68.8047i	1.78692	−	2.82072i
$596$			15.9667i			0.654020i
$597$	7.08355	−	41.2860i	0.289910	−	1.68972i
$598$	−3.07330	+	3.07330i	−0.125677	+	0.125677i
$599$	45.0422			1.84037			0.920187	−	0.391479i	$-0.128037\pi$
$599$	45.0422			1.84037			0.920187	+	0.391479i	$0.128037\pi$
$600$	4.25714	−	7.54167i	0.173797	−	0.307887i
$601$	−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
$603$	2.50920	+	5.25385i	0.102182	+	0.213953i
$604$		−	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
$612$	9.26029	+	19.3895i	0.374325	+	0.783776i
$613$	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
$615$	30.5689	+	27.6112i	1.23266	+	1.11339i
$616$	−8.49978			−0.342466
$617$	−24.9415	+	24.9415i	−1.00411	+	1.00411i	−0.00411392	+	0.999992i	$0.501310\pi$
$617$	−24.9415	+	24.9415i	−1.00411	+	1.00411i	−0.999992	+	0.00411392i	$0.998690\pi$
$618$	−0.801478	+	4.67135i	−0.0322402	+	0.187909i
$619$			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
$627$	20.9087	+	3.58736i	0.835013	+	0.143266i
$628$	4.58377	−	4.58377i	0.182912	−	0.182912i
$629$	20.2585			0.807759
$630$	26.8189	−	21.0851i	1.06849	−	0.840052i
$631$	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
$633$	−24.9253	−	4.27651i	−0.990692	−	0.169976i
$634$		−	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	$0.210615\pi$
$641$			31.1123i			1.22886i	−0.788970	+	0.614432i	$0.789385\pi$
$642$	0.0225211	−	0.131263i	0.000888838	−	0.00518053i
$643$	−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
$645$	−1.47060	−	28.9281i	−0.0579048	−	1.13904i
$646$	−52.4880			−2.06511
$647$	16.5241	−	16.5241i	0.649629	−	0.649629i	−0.303274	−	0.952903i	$-0.598080\pi$
$647$	16.5241	−	16.5241i	0.649629	−	0.649629i	0.952903	+	0.303274i	$0.0980798\pi$
$648$	0.949747	+	8.94975i	0.0373096	+	0.351579i
$649$		−	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	0.694811	−	0.719192i	$-0.255488\pi$
$653$	−0.623022	−	0.623022i	−0.0243807	−	0.0243807i	−0.719192	+	0.694811i	$0.755488\pi$
$654$	−6.07974	−	8.59806i	−0.237737	−	0.336211i
$655$	8.45683	+	5.35739i	0.330436	+	0.209330i
$656$			10.6359i			0.415263i
$657$	−1.62672	+	0.776907i	−0.0634643	+	0.0303100i
$658$	9.47884	−	9.47884i	0.369524	−	0.369524i
$659$	3.37145			0.131333			0.0656665	−	0.997842i	$-0.479083\pi$
$659$	3.37145			0.131333			0.0656665	+	0.997842i	$0.479083\pi$
$660$	−4.33890	+	4.80368i	−0.168891	+	0.186983i
$661$	−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
$663$	2.14177	−	12.4832i	0.0831795	−	0.484806i
$664$			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
$672$	8.68161	+	1.48953i	0.334900	+	0.0574598i
$673$	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
$675$	1.77396	−	25.9201i	0.0682798	−	0.997666i
$676$	11.9577			0.459911
$677$	19.7632	−	19.7632i	0.759560	−	0.759560i	−0.216683	−	0.976242i	$-0.569524\pi$
$677$	19.7632	−	19.7632i	0.759560	−	0.759560i	0.976242	+	0.216683i	$0.0695237\pi$
$678$	−5.38946	−	0.924685i	−0.206981	−	0.0355123i
$679$			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	0.173717	−	0.984796i	$-0.444422\pi$
$683$	−21.1969	−	21.1969i	−0.811079	−	0.811079i	−0.984796	+	0.173717i	$0.944422\pi$
$684$	−20.7273	−	7.32821i	−0.792528	−	0.280201i
$685$	2.97590	+	13.2636i	0.113703	+	0.506776i
$686$		−	60.3300i		−	2.30341i
$687$	−3.63166	+	21.1669i	−0.138557	+	0.807567i
$688$	5.28834	−	5.28834i	0.201616	−	0.201616i
$689$	0.275051			0.0104786
$690$	−11.0517	+	12.2355i	−0.420731	+	0.465799i
$691$	−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
$693$	−23.0098	+	10.9893i	−0.874071	+	0.417449i
$694$		−	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	$-0.843428\pi$
$701$		−	25.0090i		−	0.944576i	0.881444	−	0.472288i	$-0.156572\pi$
$702$	2.58864	−	4.63053i	0.0977018	−	0.174768i
$703$	−14.6564	+	14.6564i	−0.552777	+	0.552777i
$704$	−1.67135			−0.0629915
$705$	−0.518312	−	10.1957i	−0.0195208	−	0.383991i
$706$	−5.58535			−0.210207
$707$	34.0535	−	34.0535i	1.28071	−	1.28071i
$708$	−0.881221	+	5.13613i	−0.0331183	+	0.193028i
$709$		−	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
$717$	−15.1372	−	2.59713i	−0.565309	−	0.0969916i
$718$	5.61698	−	5.61698i	0.209624	−	0.209624i
$719$	21.5174			0.802465			0.401232	−	0.915976i	$-0.368582\pi$
$719$	21.5174			0.802465			0.401232	+	0.915976i	$0.368582\pi$
$720$	5.27353	−	4.14607i	0.196533	−	0.154515i
$721$	13.9162			0.518267
$722$	24.5385	−	24.5385i	0.913227	−	0.913227i
$723$	−11.9140	−	2.04412i	−0.443086	−	0.0760216i
$724$		−	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
$732$	2.88122	−	16.7930i	0.106493	−	0.620687i
$733$	−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
$735$	−54.2146	−	48.9691i	−1.99973	−	1.80625i
$736$	−4.25714			−0.156920
$737$	−2.29364	+	2.29364i	−0.0844874	+	0.0844874i
$738$	13.7511	+	28.7925i	0.506185	+	1.05987i
$739$			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	0.988680	−	0.150041i	$-0.0479407\pi$
$743$	22.8596	+	22.8596i	0.838638	+	0.838638i	−0.150041	+	0.988680i	$0.547941\pi$
$744$	1.00000	+	1.41421i	0.0366618	+	0.0518476i
$745$	19.1063	−	30.1599i	0.699999	−	1.10497i
$746$		−	6.36966i		−	0.233210i
$747$	13.4757	+	28.2159i	0.493049	+	1.03236i
$748$	−8.46478	+	8.46478i	−0.309503	+	0.309503i
$749$	−0.391039			−0.0142883
$750$	−17.0661	+	9.15146i	−0.623165	+	0.334164i
$751$	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
$753$	−5.00675	+	29.1815i	−0.182456	+	1.06343i
$754$		−	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	$0.0786574\pi$
$761$			13.4953i			0.489205i	−0.969623	+	0.244602i	$0.921343\pi$
$762$	22.9684	+	3.94076i	0.832059	+	0.142759i
$763$	−21.8630	+	21.8630i	−0.791493	+	0.791493i
$764$	−17.4430			−0.631064
$765$	5.71013	−	47.7067i	0.206450	−	1.72484i
$766$	−3.68963			−0.133312
$767$	2.17201	−	2.17201i	0.0784268	−	0.0784268i
$768$	1.70711	+	0.292893i	0.0615999	+	0.0105689i
$769$			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	0.824958	−	0.565193i	$-0.191198\pi$
$773$	7.22222	+	7.22222i	0.259765	+	0.259765i	−0.565193	+	0.824958i	$0.691198\pi$
$774$	7.47884	−	21.1533i	0.268821	−	0.760341i
$775$	−2.13613	−	4.52072i	−0.0767320	−	0.162389i
$776$			8.43516i			0.302805i
$777$	4.21302	−	24.5553i	0.151141	−	0.880916i
$778$	5.48795	−	5.48795i	0.196753	−	0.196753i
$779$	−77.9422			−2.79257
$780$	−3.94900	+	0.200753i	−0.141397	+	0.00718812i
$781$	−2.21990			−0.0794344
$782$	−21.5608	+	21.5608i	−0.771013	+	0.771013i
$783$	45.4483	+	25.4073i	1.62419	+	0.907984i
$784$		−	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
$792$	−4.52453	+	2.16088i	−0.160772	+	0.0767836i
$793$	−7.10156	+	7.10156i	−0.252184	+	0.252184i
$794$	−9.49934			−0.337119
$795$	1.04207	−	0.0529751i	0.0369584	−	0.00187883i
$796$	−24.1848			−0.857206
$797$	−0.330877	+	0.330877i	−0.0117203	+	0.0117203i	−0.712943	−	0.701222i	$-0.752638\pi$
$797$	−0.330877	+	0.330877i	−0.0117203	+	0.0117203i	0.701222	+	0.712943i	$0.252638\pi$
$798$	−10.9156	+	63.6206i	−0.386407	+	2.25215i
$799$		−	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
$807$	0.484661	+	0.0831547i	0.0170609	+	0.00292718i
$808$	6.69611	−	6.69611i	0.235568	−	0.235568i
$809$	−18.3644			−0.645657			−0.322829	−	0.946457i	$-0.604634\pi$
$809$	−18.3644			−0.645657			−0.322829	+	0.946457i	$0.604634\pi$
$810$	8.91557	−	18.0420i	0.313261	−	0.633930i
$811$	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
$813$	35.9668	+	6.17092i	1.26141	+	0.216424i
$814$			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	$0.0358234\pi$
$821$			6.43578i			0.224610i	−0.993674	+	0.112305i	$0.964177\pi$
$822$	−1.78053	+	10.3777i	−0.0621032	+	0.361964i
$823$	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
$825$	13.9441	−	3.88174i	0.485472	−	0.135145i
$826$	15.3008			0.532384
$827$	−17.7824	+	17.7824i	−0.618354	+	0.618354i	−0.945109	−	0.326755i	$-0.894045\pi$
$827$	−17.7824	+	17.7824i	−0.618354	+	0.618354i	0.326755	+	0.945109i	$0.394045\pi$
$828$	−11.5245	+	5.50403i	−0.400505	+	0.191278i
$829$		−	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
$837$	4.53553	+	2.53553i	0.156771	+	0.0876409i
$838$	−5.04251	+	5.04251i	−0.174191	+	0.174191i
$839$	−30.9423			−1.06825			−0.534123	−	0.845407i	$-0.679358\pi$
$839$	−30.9423			−1.06825			−0.534123	+	0.845407i	$0.679358\pi$
$840$	−14.6165	−	13.2023i	−0.504319	−	0.455524i
$841$	71.4105			2.46243
$842$	3.29258	−	3.29258i	0.113470	−	0.113470i
$843$	5.01691	−	29.2407i	0.172792	−	1.00710i
$844$			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
$852$	2.26739	+	0.389023i	0.0776796	+	0.0133277i
$853$	−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
$855$	30.3833	+	38.6455i	1.03909	+	1.32165i
$856$	−0.0768919			−0.00262811
$857$	−13.3607	+	13.3607i	−0.456392	+	0.456392i	−0.897469	−	0.441077i	$-0.854597\pi$
$857$	−13.3607	+	13.3607i	−0.456392	+	0.456392i	0.441077	+	0.897469i	$0.354597\pi$
$858$	2.91294	+	0.499781i	0.0994460	+	0.0170622i
$859$			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	0.932148	−	0.362078i	$-0.117933\pi$
$863$	16.7468	+	16.7468i	0.570069	+	0.570069i	−0.362078	+	0.932148i	$0.617933\pi$
$864$	5.00000	−	1.41421i	0.170103	−	0.0481125i
$865$	−19.9096	+	4.46705i	−0.676948	+	0.151884i
$866$		−	33.8243i		−	1.14940i
$867$	10.0465	−	58.5552i	0.341196	−	1.98864i
$868$	3.59604	−	3.59604i	0.122058	−	0.122058i
$869$	2.33838			0.0793241
$870$	−1.97038	−	38.7592i	−0.0668022	−	1.31406i
$871$	−1.98141			−0.0671375
$872$	−4.29903	+	4.29903i	−0.145583	+	0.145583i
$873$	10.9058	+	22.8349i	0.369104	+	0.772843i
$874$		−	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	$0.153817\pi$
$881$			27.5826i			0.929282i	−0.885499	+	0.464641i	$0.846183\pi$
$882$	−24.3878	−	51.0641i	−0.821181	−	1.71942i
$883$	−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
$885$	7.81064	−	8.64730i	0.262552	−	0.290676i
$886$	19.9294			0.669542
$887$	−22.1276	+	22.1276i	−0.742973	+	0.742973i	−0.973149	−	0.230176i	$-0.926070\pi$
$887$	−22.1276	+	22.1276i	−0.742973	+	0.742973i	0.230176	+	0.973149i	$0.426070\pi$
$888$	0.828427	−	4.82843i	0.0278002	−	0.162031i
$889$		−	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
$897$	7.41960	+	1.27300i	0.247733	+	0.0425043i
$898$	−7.08334	+	7.08334i	−0.236374	+	0.236374i
$899$	10.0205			0.334203
$900$	−14.9227	+	1.52116i	−0.497422	+	0.0507054i
$901$	1.92963			0.0642852
$902$	−12.5698	+	12.5698i	−0.418528	+	0.418528i
$903$	−64.9283	−	11.1399i	−2.16068	−	0.370714i
$904$			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	$-0.903114\pi$
$911$		−	18.0914i		−	0.599395i	0.954034	−	0.299697i	$-0.0968857\pi$
$912$	−2.14638	+	12.5100i	−0.0710738	+	0.414249i
$913$	−12.3180	+	12.3180i	−0.407667	+	0.407667i
$914$	30.1155			0.996132
$915$	−25.5375	+	28.2730i	−0.844244	+	0.934678i
$916$	12.3993			0.409684
$917$	16.0996	−	16.0996i	0.531657	−	0.531657i
$918$	18.1607	−	32.4856i	0.599391	−	1.07218i
$919$		−	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
$927$	7.40777	−	3.53789i	0.243303	−	0.116200i
$928$	7.08557	−	7.08557i	0.232595	−	0.232595i
$929$	44.8497			1.47147			0.735735	−	0.677270i	$-0.236837\pi$
$929$	44.8497			1.47147			0.735735	+	0.677270i	$0.236837\pi$
$930$	−0.196635	−	3.86799i	−0.00644791	−	0.126836i
$931$	138.232			4.53037
$932$	−19.3438	+	19.3438i	−0.633629	+	0.633629i
$933$	−0.942251	+	5.49184i	−0.0308479	+	0.179795i
$934$			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	$0.321930\pi$
$941$			51.9991i			1.69512i	−0.530697	+	0.847561i	$0.678070\pi$
$942$	−11.0662	−	1.89866i	−0.360556	−	0.0618617i
$943$	−32.0168	+	32.0168i	−1.04261	+	1.04261i
$944$	3.00868			0.0979240
$945$	−56.6377	−	16.8425i	−1.84243	−	0.547886i
$946$	12.4998			0.406403
$947$	5.52445	−	5.52445i	0.179521	−	0.179521i	−0.611626	−	0.791147i	$-0.709484\pi$
$947$	5.52445	−	5.52445i	0.179521	−	0.179521i	0.791147	+	0.611626i	$0.209484\pi$
$948$	−2.38840	−	0.409785i	−0.0775717	−	0.0133092i
$949$		−	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	0.817670	−	0.575688i	$-0.195266\pi$
$953$	7.47016	+	7.47016i	0.241982	+	0.241982i	−0.575688	+	0.817670i	$0.695266\pi$
$954$	0.762002	+	0.269409i	0.0246707	+	0.00872242i
$955$	32.9486	+	20.8728i	1.06619	+	0.675430i
$956$			8.86716i			0.286784i
$957$	−4.90532	+	28.5903i	−0.158566	+	0.924193i
$958$	−5.44182	+	5.44182i	−0.175817	+	0.175817i
$959$	30.9158			0.998323
$960$	−2.87412	−	2.59604i	−0.0927619	−	0.0837868i
$961$	1.00000			0.0322581
$962$	−2.04189	+	2.04189i	−0.0658331	+	0.0658331i
$963$	−0.208155	+	0.0994131i	−0.00670769	+	0.00320354i
$964$			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	$0.0454236\pi$
$971$			8.86332i			0.284437i	−0.989835	+	0.142219i	$0.954576\pi$
$972$	11.7071	−	10.2929i	0.375506	−	0.330145i
$973$	−29.4278	+	29.4278i	−0.943413	+	0.943413i
$974$	14.1819			0.454418
$975$	7.69962	+	4.34630i	0.246585	+	0.139193i
$976$	−9.83710			−0.314878
$977$	34.8184	−	34.8184i	1.11394	−	1.11394i	0.121328	−	0.992612i	$-0.461285\pi$
$977$	34.8184	−	34.8184i	1.11394	−	1.11394i	0.992612	−	0.121328i	$-0.0387153\pi$
$978$	−1.27808	+	7.44922i	−0.0408686	+	0.238200i
$979$		−	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	0.774528	−	0.632539i	$-0.217987\pi$
$983$	4.45175	+	4.45175i	0.141989	+	0.141989i	−0.632539	+	0.774528i	$0.717987\pi$
$984$	15.0414	−	10.6359i	0.479504	−	0.339060i
$985$	−1.86760	−	8.32388i	−0.0595066	−	0.265221i
$986$		−	71.7715i		−	2.28567i
$987$	−22.8839	−	3.92626i	−0.728404	−	0.124974i
$988$	5.29035	−	5.29035i	0.168309	−	0.168309i
$989$	31.8385			1.01240
$990$	11.1323	+	1.33245i	0.353808	+	0.0423482i
$991$	−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
$993$	−19.6929	−	3.37877i	−0.624936	−	0.107222i
$994$		−	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.f.497.1	yes	8
3.2	odd	2		930.2.j.c.497.4	✓	8
5.3	odd	4		930.2.j.c.683.4	yes	8
15.8	even	4	inner	930.2.j.f.683.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.c.497.4	✓	8	3.2	odd	2
930.2.j.c.683.4	yes	8	5.3	odd	4
930.2.j.f.497.1	yes	8	1.1	even	1	trivial
930.2.j.f.683.1	yes	8	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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} +(-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} +(0.292893 - 1.70711i) q^{12} +(-0.721916 + 0.721916i) q^{13} -5.08557 q^{14} +(-2.59604 + 2.87412i) q^{15} -1.00000 q^{16} +(-5.06462 + 5.06462i) q^{17} +(-2.70711 + 1.29289i) 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} +(4.53553 + 2.53553i) q^{27} +(3.59604 - 3.59604i) q^{28} +10.0205 q^{29} +(-0.196635 - 3.86799i) q^{30} +1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.489528 + 2.85318i) 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} +(-8.68161 - 1.48953i) q^{42} +(-5.28834 + 5.28834i) q^{43} +1.67135 q^{44} +(-5.27353 + 4.14607i) q^{45} +4.25714 q^{46} +(-1.86387 + 1.86387i) q^{47} +(-1.70711 - 0.292893i) 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} +(2.14638 - 12.5100i) q^{57} +(-7.08557 + 7.08557i) q^{58} -3.00868 q^{59} +(2.87412 + 2.59604i) q^{60} +9.83710 q^{61} +(-0.707107 + 0.707107i) q^{62} +(6.57510 + 13.7672i) 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} +(1.29289 + 2.70711i) q^{72} +(-0.424905 + 0.424905i) q^{73} +2.82843 q^{74} +(-2.32251 - 8.34302i) q^{75} -7.32821 q^{76} +(-6.01025 + 6.01025i) q^{77} +(0.299028 - 1.74286i) 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} +(17.1061 + 2.93494i) q^{87} +(-1.18183 + 1.18183i) q^{88} -3.30770 q^{89} +(0.797231 - 6.66066i) q^{90} -5.19208 q^{91} +(-3.01025 + 3.01025i) q^{92} +(1.70711 + 0.292893i) 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^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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