LMFDB - Embedded newform 620.2.k.d.63.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [620,2,Mod(63,620)] 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("620.63"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(620, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 620 = 2^{2} \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	620.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [88,2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.95072492532$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.6
Character	$\chi$	$=$	620.63
Dual form			620.2.k.d.187.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.25756 - 0.646956i) q^{2} +(-1.39122 + 1.39122i) q^{3} +(1.16290 + 1.62717i) q^{4} +(-2.16579 - 0.556189i) q^{5} +(2.64960 - 0.849482i) q^{6} +(2.15391 + 2.15391i) q^{7} +(-0.409703 - 2.79860i) q^{8} -0.871005i q^{9} +(2.36378 + 2.10061i) q^{10} +5.67605i q^{11} +(-3.88160 - 0.645904i) q^{12} +(-1.47992 - 1.47992i) q^{13} +(-1.31518 - 4.10215i) q^{14} +(3.78688 - 2.23932i) q^{15} +(-1.29534 + 3.78445i) q^{16} +(1.62859 - 1.62859i) q^{17} +(-0.563502 + 1.09534i) q^{18} +2.82660 q^{19} +(-1.61358 - 4.17089i) q^{20} -5.99314 q^{21} +(3.67216 - 7.13796i) q^{22} +(-0.674653 + 0.674653i) q^{23} +(4.46346 + 3.32348i) q^{24} +(4.38131 + 2.40918i) q^{25} +(0.903640 + 2.81853i) q^{26} +(-2.96191 - 2.96191i) q^{27} +(-0.999996 + 6.00954i) q^{28} +3.16048i q^{29} +(-6.21096 + 0.366121i) q^{30} +1.00000i q^{31} +(4.07734 - 3.92113i) q^{32} +(-7.89666 - 7.89666i) q^{33} +(-3.10167 + 0.994417i) q^{34} +(-3.46694 - 5.86290i) q^{35} +(1.41727 - 1.01289i) q^{36} +(-2.62791 + 2.62791i) q^{37} +(-3.55461 - 1.82869i) q^{38} +4.11780 q^{39} +(-0.669218 + 6.28905i) q^{40} -6.95287 q^{41} +(7.53671 + 3.87729i) q^{42} +(-5.71552 + 5.71552i) q^{43} +(-9.23589 + 6.60066i) q^{44} +(-0.484444 + 1.88642i) q^{45} +(1.28488 - 0.411944i) q^{46} +(-7.76807 - 7.76807i) q^{47} +(-3.46291 - 7.06713i) q^{48} +2.27865i q^{49} +(-3.95111 - 5.86419i) q^{50} +4.53146i q^{51} +(0.687083 - 4.12907i) q^{52} +(-9.46144 - 9.46144i) q^{53} +(1.80854 + 5.64099i) q^{54} +(3.15696 - 12.2932i) q^{55} +(5.14546 - 6.91038i) q^{56} +(-3.93244 + 3.93244i) q^{57} +(2.04469 - 3.97448i) q^{58} -6.38820 q^{59} +(8.04750 + 3.55780i) q^{60} -7.62563 q^{61} +(0.646956 - 1.25756i) q^{62} +(1.87607 - 1.87607i) q^{63} +(-7.66429 + 2.29319i) q^{64} +(2.38208 + 4.02831i) q^{65} +(4.82171 + 15.0393i) q^{66} +(8.48145 + 8.48145i) q^{67} +(4.54386 + 0.756105i) q^{68} -1.87719i q^{69} +(0.566833 + 9.61588i) q^{70} -0.618974i q^{71} +(-2.43759 + 0.356853i) q^{72} +(2.16403 + 2.16403i) q^{73} +(5.00488 - 1.60460i) q^{74} +(-9.44708 + 2.74367i) q^{75} +(3.28705 + 4.59935i) q^{76} +(-12.2257 + 12.2257i) q^{77} +(-5.17837 - 2.66403i) q^{78} +6.50460 q^{79} +(4.91032 - 7.47588i) q^{80} +10.8544 q^{81} +(8.74362 + 4.49820i) q^{82} +(-1.57085 + 1.57085i) q^{83} +(-6.96940 - 9.75183i) q^{84} +(-4.43299 + 2.62138i) q^{85} +(10.8853 - 3.48990i) q^{86} +(-4.39693 - 4.39693i) q^{87} +(15.8850 - 2.32550i) q^{88} -0.579869i q^{89} +(1.82964 - 2.05886i) q^{90} -6.37523i q^{91} +(-1.88232 - 0.313221i) q^{92} +(-1.39122 - 1.39122i) q^{93} +(4.74319 + 14.7944i) q^{94} +(-6.12183 - 1.57213i) q^{95} +(-0.217320 + 11.1277i) q^{96} +(8.85186 - 8.85186i) q^{97} +(1.47418 - 2.86553i) q^{98} +4.94387 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 2 q^{2} + 2 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{8} - 10 q^{10} - 12 q^{12} - 6 q^{13} + 22 q^{14} - 2 q^{15} + 8 q^{16} - 2 q^{17} - 24 q^{18} + 8 q^{19} + 8 q^{20} - 16 q^{21} - 16 q^{22} + 10 q^{23}+ \cdots - 8 q^{99}+O(q^{100}) $ 88 * q + 2 * q^2 + 2 * q^3 - 2 * q^5 + 4 * q^7 - 4 * q^8 - 10 * q^10 - 12 * q^12 - 6 * q^13 + 22 * q^14 - 2 * q^15 + 8 * q^16 - 2 * q^17 - 24 * q^18 + 8 * q^19 + 8 * q^20 - 16 * q^21 - 16 * q^22 + 10 * q^23 - 44 * q^24 - 4 * q^25 - 8 * q^26 + 8 * q^27 + 46 * q^28 + 16 * q^30 - 8 * q^32 - 8 * q^33 + 40 * q^34 - 12 * q^35 - 20 * q^36 + 10 * q^37 - 64 * q^38 + 8 * q^39 + 8 * q^41 + 28 * q^42 + 10 * q^43 - 16 * q^44 + 6 * q^45 - 24 * q^46 - 64 * q^47 + 88 * q^48 - 14 * q^50 + 20 * q^52 + 18 * q^53 + 36 * q^54 + 40 * q^55 - 24 * q^56 - 24 * q^57 - 52 * q^58 - 32 * q^60 + 20 * q^61 + 2 * q^62 - 4 * q^63 - 150 * q^64 - 18 * q^65 + 8 * q^66 + 116 * q^67 + 68 * q^68 - 6 * q^70 - 26 * q^72 + 38 * q^73 + 36 * q^74 - 70 * q^75 - 8 * q^76 + 40 * q^77 - 152 * q^78 + 32 * q^79 + 68 * q^80 - 60 * q^81 + 14 * q^82 - 14 * q^83 - 120 * q^84 + 6 * q^85 + 4 * q^86 - 44 * q^87 + 52 * q^88 - 68 * q^90 - 92 * q^92 + 2 * q^93 + 112 * q^94 + 104 * q^95 - 20 * q^96 + 16 * q^97 - 62 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/620\mathbb{Z}\right)^\times$.

$n$	$311$	$497$	$561$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.25756	−	0.646956i	−0.889227	−	0.457467i
$2$	−1.25756	−	0.646956i	−0.889227	−	0.457467i
$3$	−1.39122	+	1.39122i	−0.803223	+	0.803223i	−0.983598	−	0.180375i	$-0.942269\pi$
$3$	−1.39122	+	1.39122i	−0.803223	+	0.803223i	0.180375	+	0.983598i	$0.442269\pi$
$4$	1.16290	+	1.62717i	0.581448	+	0.813583i
$5$	−2.16579	−	0.556189i	−0.968571	−	0.248735i
$5$	−2.16579	−	0.556189i	−0.968571	−	0.248735i
$6$	2.64960	−	0.849482i	1.08170	−	0.346800i
$7$	2.15391	+	2.15391i	0.814101	+	0.814101i	0.985246	−	0.171145i	$-0.0547466\pi$
$7$	2.15391	+	2.15391i	0.814101	+	0.814101i	−0.171145	+	0.985246i	$0.554747\pi$
$8$	−0.409703	−	2.79860i	−0.144852	−	0.989453i
$9$		−	0.871005i		−	0.290335i
$10$	2.36378	+	2.10061i	0.747491	+	0.664271i
$11$			5.67605i			1.71139i	0.517476	+	0.855697i	$0.326872\pi$
$11$			5.67605i			1.71139i	−0.517476	+	0.855697i	$0.673128\pi$
$12$	−3.88160	−	0.645904i	−1.12052	−	0.186456i
$13$	−1.47992	−	1.47992i	−0.410456	−	0.410456i	0.471441	−	0.881897i	$-0.343734\pi$
$13$	−1.47992	−	1.47992i	−0.410456	−	0.410456i	−0.881897	+	0.471441i	$0.843734\pi$
$14$	−1.31518	−	4.10215i	−0.351496	−	1.09634i
$15$	3.78688	−	2.23932i	0.977769	−	0.578189i
$16$	−1.29534	+	3.78445i	−0.323836	+	0.946113i
$17$	1.62859	−	1.62859i	0.394991	−	0.394991i	−0.481471	−	0.876462i	$-0.659897\pi$
$17$	1.62859	−	1.62859i	0.394991	−	0.394991i	0.876462	+	0.481471i	$0.159897\pi$
$18$	−0.563502	+	1.09534i	−0.132819	+	0.258174i
$19$	2.82660			0.648467			0.324234	−	0.945977i	$-0.394894\pi$
$19$	2.82660			0.648467			0.324234	+	0.945977i	$0.394894\pi$
$20$	−1.61358	−	4.17089i	−0.360807	−	0.932640i
$21$	−5.99314			−1.30781
$22$	3.67216	−	7.13796i	0.782906	−	1.52182i
$23$	−0.674653	+	0.674653i	−0.140675	+	0.140675i	−0.773937	−	0.633262i	$-0.781715\pi$
$23$	−0.674653	+	0.674653i	−0.140675	+	0.140675i	0.633262	+	0.773937i	$0.281715\pi$
$24$	4.46346	+	3.32348i	0.911100	+	0.678404i
$25$	4.38131	+	2.40918i	0.876261	+	0.481836i
$26$	0.903640	+	2.81853i	0.177218	+	0.552758i
$27$	−2.96191	−	2.96191i	−0.570019	−	0.570019i
$28$	−0.999996	+	6.00954i	−0.188981	+	1.13570i
$29$			3.16048i			0.586886i	0.955977	+	0.293443i	$0.0948011\pi$
$29$			3.16048i			0.586886i	−0.955977	+	0.293443i	$0.905199\pi$
$30$	−6.21096	+	0.366121i	−1.13396	+	0.0668443i
$31$			1.00000i			0.179605i
$31$			1.00000i			0.179605i
$32$	4.07734	−	3.92113i	0.720779	−	0.693165i
$33$	−7.89666	−	7.89666i	−1.37463	−	1.37463i
$34$	−3.10167	+	0.994417i	−0.531931	+	0.170541i
$35$	−3.46694	−	5.86290i	−0.586019	−	0.991011i
$36$	1.41727	−	1.01289i	0.236212	−	0.168815i
$37$	−2.62791	+	2.62791i	−0.432025	+	0.432025i	−0.889317	−	0.457292i	$-0.848820\pi$
$37$	−2.62791	+	2.62791i	−0.432025	+	0.432025i	0.457292	+	0.889317i	$0.348820\pi$
$38$	−3.55461	−	1.82869i	−0.576634	−	0.296652i
$39$	4.11780			0.659376
$40$	−0.669218	+	6.28905i	−0.105813	+	0.994386i
$41$	−6.95287			−1.08586			−0.542928	−	0.839779i	$-0.682684\pi$
$41$	−6.95287			−1.08586			−0.542928	+	0.839779i	$0.682684\pi$
$42$	7.53671	+	3.87729i	1.16294	+	0.598280i
$43$	−5.71552	+	5.71552i	−0.871609	+	0.871609i	−0.992648	−	0.121039i	$-0.961378\pi$
$43$	−5.71552	+	5.71552i	−0.871609	+	0.871609i	0.121039	+	0.992648i	$0.461378\pi$
$44$	−9.23589	+	6.60066i	−1.39236	+	0.995088i
$45$	−0.484444	+	1.88642i	−0.0722166	+	0.281210i
$46$	1.28488	−	0.411944i	0.189446	−	0.0607378i
$47$	−7.76807	−	7.76807i	−1.13309	−	1.13309i	−0.989661	−	0.143429i	$-0.954187\pi$
$47$	−7.76807	−	7.76807i	−1.13309	−	1.13309i	−0.143429	−	0.989661i	$-0.545813\pi$
$48$	−3.46291	−	7.06713i	−0.499828	−	1.02005i
$49$			2.27865i			0.325521i
$50$	−3.95111	−	5.86419i	−0.558771	−	0.829322i
$51$			4.53146i			0.634531i
$52$	0.687083	−	4.12907i	0.0952813	−	0.572599i
$53$	−9.46144	−	9.46144i	−1.29963	−	1.29963i	−0.928636	−	0.370992i	$-0.879018\pi$
$53$	−9.46144	−	9.46144i	−1.29963	−	1.29963i	−0.370992	−	0.928636i	$-0.620982\pi$
$54$	1.80854	+	5.64099i	0.246111	+	0.767641i
$55$	3.15696	−	12.2932i	0.425684	−	1.65761i
$56$	5.14546	−	6.91038i	0.687591	−	0.923439i
$57$	−3.93244	+	3.93244i	−0.520864	+	0.520864i
$58$	2.04469	−	3.97448i	0.268481	−	0.521875i
$59$	−6.38820			−0.831673			−0.415836	−	0.909439i	$-0.636511\pi$
$59$	−6.38820			−0.831673			−0.415836	+	0.909439i	$0.636511\pi$
$60$	8.04750	+	3.55780i	1.03893	+	0.459310i
$61$	−7.62563			−0.976362			−0.488181	−	0.872742i	$-0.662339\pi$
$61$	−7.62563			−0.976362			−0.488181	+	0.872742i	$0.662339\pi$
$62$	0.646956	−	1.25756i	0.0821635	−	0.159710i
$63$	1.87607	−	1.87607i	0.236362	−	0.236362i
$64$	−7.66429	+	2.29319i	−0.958036	+	0.286648i
$65$	2.38208	+	4.02831i	0.295461	+	0.499651i
$66$	4.82171	+	15.0393i	0.593511	+	1.85121i
$67$	8.48145	+	8.48145i	1.03617	+	1.03617i	0.999321	+	0.0368535i	$0.0117335\pi$
$67$	8.48145	+	8.48145i	1.03617	+	1.03617i	0.0368535	+	0.999321i	$0.488266\pi$
$68$	4.54386	+	0.756105i	0.551024	+	0.0916912i
$69$		−	1.87719i		−	0.225987i
$70$	0.566833	+	9.61588i	0.0677495	+	1.14932i
$71$		−	0.618974i		−	0.0734587i	−0.999325	−	0.0367294i	$-0.988306\pi$
$71$		−	0.618974i		−	0.0734587i	0.999325	−	0.0367294i	$-0.0116940\pi$
$72$	−2.43759	+	0.356853i	−0.287273	+	0.0420556i
$73$	2.16403	+	2.16403i	0.253281	+	0.253281i	0.822314	−	0.569034i	$-0.192683\pi$
$73$	2.16403	+	2.16403i	0.253281	+	0.253281i	−0.569034	+	0.822314i	$0.692683\pi$
$74$	5.00488	−	1.60460i	0.581805	−	0.186531i
$75$	−9.44708	+	2.74367i	−1.09086	+	0.316812i
$76$	3.28705	+	4.59935i	0.377050	+	0.527582i
$77$	−12.2257	+	12.2257i	−1.39325	+	1.39325i
$78$	−5.17837	−	2.66403i	−0.586334	−	0.301642i
$79$	6.50460			0.731825			0.365913	−	0.930649i	$-0.380757\pi$
$79$	6.50460			0.731825			0.365913	+	0.930649i	$0.380757\pi$
$80$	4.91032	−	7.47588i	0.548990	−	0.835829i
$81$	10.8544			1.20604
$82$	8.74362	+	4.49820i	0.965572	+	0.496743i
$83$	−1.57085	+	1.57085i	−0.172423	+	0.172423i	−0.788043	−	0.615620i	$-0.788906\pi$
$83$	−1.57085	+	1.57085i	−0.172423	+	0.172423i	0.615620	+	0.788043i	$0.288906\pi$
$84$	−6.96940	−	9.75183i	−0.760424	−	1.06401i
$85$	−4.43299	+	2.62138i	−0.480825	+	0.284329i
$86$	10.8853	−	3.48990i	1.17379	−	0.376326i
$87$	−4.39693	−	4.39693i	−0.471401	−	0.471401i
$88$	15.8850	−	2.32550i	1.69335	−	0.247899i
$89$		−	0.579869i		−	0.0614660i	−0.999528	−	0.0307330i	$-0.990216\pi$
$89$		−	0.579869i		−	0.0614660i	0.999528	−	0.0307330i	$-0.00978415\pi$
$90$	1.82964	−	2.05886i	0.192861	−	0.217023i
$91$		−	6.37523i		−	0.668305i
$92$	−1.88232	−	0.313221i	−0.196246	−	0.0326556i
$93$	−1.39122	−	1.39122i	−0.144263	−	0.144263i
$94$	4.74319	+	14.7944i	0.489222	+	1.52592i
$95$	−6.12183	−	1.57213i	−0.628087	−	0.161297i
$96$	−0.217320	+	11.1277i	−0.0221802	+	1.13571i
$97$	8.85186	−	8.85186i	0.898770	−	0.898770i	−0.0965572	−	0.995327i	$-0.530783\pi$
$97$	8.85186	−	8.85186i	0.898770	−	0.898770i	0.995327	+	0.0965572i	$0.0307831\pi$
$98$	1.47418	−	2.86553i	0.148915	−	0.289462i
$99$	4.94387			0.496878
$100$	1.17487	+	9.93074i	0.117487	+	0.993074i
$101$	13.2880			1.32221			0.661105	−	0.750294i	$-0.270088\pi$
$101$	13.2880			1.32221			0.661105	+	0.750294i	$0.270088\pi$
$102$	2.93165	−	5.69857i	0.290277	−	0.564242i
$103$	−9.60352	+	9.60352i	−0.946263	+	0.946263i	−0.998628	−	0.0523646i	$-0.983324\pi$
$103$	−9.60352	+	9.60352i	−0.946263	+	0.946263i	0.0523646	+	0.998628i	$0.483324\pi$
$104$	−3.53537	+	4.74803i	−0.346672	+	0.465582i
$105$	12.9799	+	3.33332i	1.26671	+	0.325299i
$106$	5.77716	+	18.0194i	0.561127	+	1.75020i
$107$	−7.74367	−	7.74367i	−0.748609	−	0.748609i	0.225609	−	0.974218i	$-0.427563\pi$
$107$	−7.74367	−	7.74367i	−0.748609	−	0.748609i	−0.974218	+	0.225609i	$0.927563\pi$
$108$	1.37513	−	8.26391i	0.132322	−	0.795195i
$109$		−	7.84932i		−	0.751829i	−0.926654	−	0.375914i	$-0.877329\pi$
$109$		−	7.84932i		−	0.751829i	0.926654	−	0.375914i	$-0.122671\pi$
$110$	−11.9232	+	13.4169i	−1.13683	+	1.27925i
$111$		−	7.31201i		−	0.694025i
$112$	−10.9414	+	5.36131i	−1.03387	+	0.506597i
$113$	12.1117	+	12.1117i	1.13937	+	1.13937i	0.988563	+	0.150811i	$0.0481886\pi$
$113$	12.1117	+	12.1117i	1.13937	+	1.13937i	0.150811	+	0.988563i	$0.451811\pi$
$114$	7.48937	−	2.40115i	0.701444	−	0.224888i
$115$	1.83639	−	1.08592i	0.171244	−	0.101263i
$116$	−5.14263	+	3.67531i	−0.477481	+	0.341244i
$117$	−1.28902	+	1.28902i	−0.119170	+	0.119170i
$118$	8.03352	+	4.13288i	0.739546	+	0.380463i
$119$	7.01566			0.643125
$120$	−7.81844	−	9.68051i	−0.713723	−	0.883705i
$121$	−21.2176			−1.92887
$122$	9.58967	+	4.93345i	0.868208	+	0.446653i
$123$	9.67299	−	9.67299i	0.872184	−	0.872184i
$124$	−1.62717	+	1.16290i	−0.146124	+	0.104431i
$125$	−8.14904	−	7.65462i	−0.728872	−	0.684650i
$126$	−3.57299	+	1.14553i	−0.318307	+	0.102052i
$127$	−12.3197	−	12.3197i	−1.09320	−	1.09320i	−0.995185	−	0.0980137i	$-0.968751\pi$
$127$	−12.3197	−	12.3197i	−1.09320	−	1.09320i	−0.0980137	−	0.995185i	$-0.531249\pi$
$128$	11.1219	+	2.07464i	0.983043	+	0.183374i
$129$		−	15.9031i		−	1.40019i
$130$	−0.389463	−	6.60694i	−0.0341582	−	0.579467i
$131$			3.82981i			0.334612i	0.985905	+	0.167306i	$0.0535068\pi$
$131$			3.82981i			0.334612i	−0.985905	+	0.167306i	$0.946493\pi$
$132$	3.66619	−	22.0322i	0.319100	−	1.91766i
$133$	6.08824	+	6.08824i	0.527918	+	0.527918i
$134$	−5.17878	−	16.1530i	−0.447378	−	1.39541i
$135$	4.76749	+	8.06225i	0.410321	+	0.693888i
$136$	−5.22500	−	3.89052i	−0.448040	−	0.333610i
$137$	1.74294	−	1.74294i	0.148910	−	0.148910i	−0.628721	−	0.777631i	$-0.716421\pi$
$137$	1.74294	−	1.74294i	0.148910	−	0.148910i	0.777631	+	0.628721i	$0.216421\pi$
$138$	−1.21446	+	2.36067i	−0.103381	+	0.200953i
$139$	12.9731			1.10036			0.550181	−	0.835046i	$-0.314559\pi$
$139$	12.9731			1.10036			0.550181	+	0.835046i	$0.314559\pi$
$140$	5.50822	−	12.4592i	0.465530	−	1.05300i
$141$	21.6142			1.82025
$142$	−0.400449	+	0.778395i	−0.0336049	+	0.0653215i
$143$	8.40011	−	8.40011i	0.702452	−	0.702452i
$144$	3.29628	+	1.12825i	0.274690	+	0.0940209i
$145$	1.75782	−	6.84494i	0.145979	−	0.568441i
$146$	−1.32136	−	4.12142i	−0.109356	−	0.341091i
$147$	−3.17011	−	3.17011i	−0.261466	−	0.261466i
$148$	−7.33202	−	1.22006i	−0.602689	−	0.100288i
$149$			13.0122i			1.06600i	0.846116	+	0.532999i	$0.178935\pi$
$149$			13.0122i			1.06600i	−0.846116	+	0.532999i	$0.821065\pi$
$150$	13.6553	+	2.66153i	1.11495	+	0.217313i
$151$			7.69229i			0.625989i	0.949755	+	0.312995i	$0.101332\pi$
$151$			7.69229i			0.625989i	−0.949755	+	0.312995i	$0.898668\pi$
$152$	−1.15807	−	7.91052i	−0.0939317	−	0.641628i
$153$	−1.41851	−	1.41851i	−0.114680	−	0.114680i
$154$	23.2840	−	7.46502i	1.87628	−	0.601549i
$155$	0.556189	−	2.16579i	0.0446742	−	0.173961i
$156$	4.78857	+	6.70035i	0.383393	+	0.536457i
$157$	4.32575	−	4.32575i	0.345232	−	0.345232i	−0.513098	−	0.858330i	$-0.671502\pi$
$157$	4.32575	−	4.32575i	0.345232	−	0.345232i	0.858330	+	0.513098i	$0.171502\pi$
$158$	−8.17991	−	4.20819i	−0.650758	−	0.334786i
$159$	26.3259			2.08778
$160$	−11.0116	+	6.22458i	−0.870541	+	0.492097i
$161$	−2.90628			−0.229047
$162$	−13.6500	−	7.02229i	−1.07244	−	0.551724i
$163$	−16.3868	+	16.3868i	−1.28352	+	1.28352i	−0.344863	+	0.938653i	$0.612074\pi$
$163$	−16.3868	+	16.3868i	−1.28352	+	1.28352i	−0.938653	+	0.344863i	$0.887926\pi$
$164$	−8.08546	−	11.3135i	−0.631369	−	0.883434i
$165$	12.7105	+	21.4946i	0.989510	+	1.67335i
$166$	2.99170	−	0.959160i	0.232201	−	0.0744452i
$167$	13.8935	+	13.8935i	1.07511	+	1.07511i	0.996940	+	0.0781747i	$0.0249092\pi$
$167$	13.8935	+	13.8935i	1.07511	+	1.07511i	0.0781747	+	0.996940i	$0.475091\pi$
$168$	2.45541	+	16.7724i	0.189439	+	1.29402i
$169$		−	8.61967i		−	0.663052i
$170$	7.27065	−	0.428587i	0.557633	−	0.0328711i
$171$		−	2.46199i		−	0.188273i
$172$	−15.9467	−	2.65355i	−1.21592	−	0.202331i
$173$	0.654048	+	0.654048i	0.0497263	+	0.0497263i	0.731533	−	0.681806i	$-0.238805\pi$
$173$	0.654048	+	0.654048i	0.0497263	+	0.0497263i	−0.681806	+	0.731533i	$0.738805\pi$
$174$	2.68477	+	8.37401i	0.203532	+	0.634832i
$175$	4.24778	+	14.6261i	0.321102	+	1.10563i
$176$	−21.4808	−	7.35244i	−1.61917	−	0.554211i
$177$	8.88741	−	8.88741i	0.668019	−	0.668019i
$178$	−0.375150	+	0.729218i	−0.0281186	+	0.0546572i
$179$	4.16341			0.311188			0.155594	−	0.987821i	$-0.450271\pi$
$179$	4.16341			0.311188			0.155594	+	0.987821i	$0.450271\pi$
$180$	−3.63287	+	1.40544i	−0.270778	+	0.104755i
$181$	−6.14138			−0.456485			−0.228242	−	0.973604i	$-0.573298\pi$
$181$	−6.14138			−0.456485			−0.228242	+	0.973604i	$0.573298\pi$
$182$	−4.12449	+	8.01721i	−0.305728	+	0.594275i
$183$	10.6090	−	10.6090i	0.784237	−	0.784237i
$184$	2.16449	+	1.61167i	0.159568	+	0.118814i
$185$	7.15311	−	4.22988i	0.525907	−	0.310987i
$186$	0.849482	+	2.64960i	0.0622870	+	0.194278i
$187$	9.24395	+	9.24395i	0.675985	+	0.675985i
$188$	3.60648	−	21.6734i	0.263030	−	1.58070i
$189$		−	12.7594i		−	0.928107i
$190$	6.68145	+	5.93759i	0.484724	+	0.430758i
$191$		−	6.76334i		−	0.489378i	−0.969602	−	0.244689i	$-0.921314\pi$
$191$		−	6.76334i		−	0.489378i	0.969602	−	0.244689i	$-0.0786858\pi$
$192$	7.47240	−	13.8531i	0.539274	−	0.999759i
$193$	0.437408	+	0.437408i	0.0314853	+	0.0314853i	0.722674	−	0.691189i	$-0.242913\pi$
$193$	0.437408	+	0.437408i	0.0314853	+	0.0314853i	−0.691189	+	0.722674i	$0.742913\pi$
$194$	−16.8585	+	5.40495i	−1.21037	+	0.388053i
$195$	−8.91830	−	2.29028i	−0.638652	−	0.164010i
$196$	−3.70774	+	2.64983i	−0.264838	+	0.189274i
$197$	−16.6229	+	16.6229i	−1.18434	+	1.18434i	−0.205725	+	0.978610i	$0.565955\pi$
$197$	−16.6229	+	16.6229i	−1.18434	+	1.18434i	−0.978610	+	0.205725i	$0.934045\pi$
$198$	−6.21720	−	3.19847i	−0.441837	−	0.227305i
$199$	0.793619			0.0562581			0.0281291	−	0.999604i	$-0.491045\pi$
$199$	0.793619			0.0562581			0.0281291	+	0.999604i	$0.491045\pi$
$200$	4.94729	−	13.2486i	0.349826	−	0.936815i
$201$	−23.5992			−1.66456
$202$	−16.7105	−	8.59677i	−1.17574	−	0.604867i
$203$	−6.80738	+	6.80738i	−0.477785	+	0.477785i
$204$	−7.37344	+	5.26962i	−0.516244	+	0.368947i
$205$	15.0585	+	3.86711i	1.05173	+	0.270091i
$206$	18.2900	−	5.86392i	1.27433	−	0.408559i
$207$	0.587626	+	0.587626i	0.0408429	+	0.0408429i
$208$	7.51769	−	3.68368i	0.521258	−	0.255418i
$209$			16.0440i			1.10978i
$210$	−14.1664	−	12.5892i	−0.977577	−	0.868741i
$211$		−	21.1971i		−	1.45927i	−0.683836	−	0.729636i	$-0.739690\pi$
$211$		−	21.1971i		−	1.45927i	0.683836	−	0.729636i	$-0.260310\pi$
$212$	4.39266	−	26.3980i	0.301689	−	1.81302i
$213$	0.861132	+	0.861132i	0.0590038	+	0.0590038i
$214$	4.72829	+	14.7479i	0.323219	+	1.00815i
$215$	15.5575	−	9.19972i	1.06102	−	0.627416i
$216$	−7.07568	+	9.50269i	−0.481439	+	0.646576i
$217$	−2.15391	+	2.15391i	−0.146217	+	0.146217i
$218$	−5.07817	+	9.87097i	−0.343937	+	0.668546i
$219$	−6.02130			−0.406882
$220$	23.6742	−	9.15876i	1.59612	−	0.617484i
$221$	−4.82036			−0.324253
$222$	−4.73055	+	9.19526i	−0.317493	+	0.617146i
$223$	3.15928	−	3.15928i	0.211561	−	0.211561i	−0.593369	−	0.804930i	$-0.702203\pi$
$223$	3.15928	−	3.15928i	0.211561	−	0.211561i	0.804930	+	0.593369i	$0.202203\pi$
$224$	17.2280	+	0.336458i	1.15109	+	0.0224806i
$225$	2.09841	−	3.81614i	0.139894	−	0.254409i
$226$	−7.39542	−	23.0669i	−0.491936	−	1.53439i
$227$	4.40305	+	4.40305i	0.292240	+	0.292240i	0.837965	−	0.545724i	$-0.183745\pi$
$227$	4.40305	+	4.40305i	0.292240	+	0.292240i	−0.545724	+	0.837965i	$0.683745\pi$
$228$	−10.9717	−	1.82571i	−0.726622	−	0.120911i
$229$		−	26.0581i		−	1.72197i	−0.508631	−	0.860984i	$-0.669848\pi$
$229$		−	26.0581i		−	1.72197i	0.508631	−	0.860984i	$-0.330152\pi$
$230$	−3.01191	+	0.177545i	−0.198600	+	0.0117070i
$231$		−	34.0174i		−	2.23818i
$232$	8.84491	−	1.29486i	0.580697	−	0.0850116i
$233$	16.3473	+	16.3473i	1.07095	+	1.07095i	0.997283	+	0.0736622i	$0.0234687\pi$
$233$	16.3473	+	16.3473i	1.07095	+	1.07095i	0.0736622	+	0.997283i	$0.476531\pi$
$234$	2.45495	−	0.787076i	0.160485	−	0.0514527i
$235$	12.5035	+	21.1445i	0.815639	+	1.37932i
$236$	−7.42882	−	10.3947i	−0.483575	−	0.676635i
$237$	−9.04936	+	9.04936i	−0.587819	+	0.587819i
$238$	−8.82259	−	4.53882i	−0.571883	−	0.294208i
$239$	−19.5701			−1.26589			−0.632944	−	0.774198i	$-0.718153\pi$
$239$	−19.5701			−1.26589			−0.632944	+	0.774198i	$0.718153\pi$
$240$	3.56927	+	17.2320i	0.230396	+	1.11232i
$241$	−24.7132			−1.59192			−0.795960	−	0.605349i	$-0.793034\pi$
$241$	−24.7132			−1.59192			−0.795960	+	0.605349i	$0.793034\pi$
$242$	26.6823	+	13.7268i	1.71520	+	0.882395i
$243$	−6.21513	+	6.21513i	−0.398701	+	0.398701i
$244$	−8.86782	−	12.4082i	−0.567704	−	0.794352i
$245$	1.26736	−	4.93507i	0.0809685	−	0.315290i
$246$	−18.4223	+	5.90634i	−1.17456	+	0.376574i
$247$	−4.18315	−	4.18315i	−0.266167	−	0.266167i
$248$	2.79860	−	0.409703i	0.177711	−	0.0260162i
$249$		−	4.37080i		−	0.276988i
$250$	5.29568	+	14.8982i	0.334928	+	0.942244i
$251$			25.0804i			1.58306i	0.611129	+	0.791531i	$0.290716\pi$
$251$			25.0804i			1.58306i	−0.611129	+	0.791531i	$0.709284\pi$
$252$	5.23434	+	0.871002i	0.329733	+	0.0548680i
$253$	−3.82937	−	3.82937i	−0.240750	−	0.240750i
$254$	7.52243	+	23.4631i	0.471999	+	1.47220i
$255$	2.52035	−	9.81420i	0.157830	−	0.614589i
$256$	−12.6442	−	9.80433i	−0.790261	−	0.612771i
$257$	2.15050	−	2.15050i	0.134145	−	0.134145i	−0.636846	−	0.770991i	$-0.719761\pi$
$257$	2.15050	−	2.15050i	0.134145	−	0.134145i	0.770991	+	0.636846i	$0.219761\pi$
$258$	−10.2886	+	19.9991i	−0.640542	+	1.24509i
$259$	−11.3205			−0.703424
$260$	−3.78462	+	8.56056i	−0.234712	+	0.530903i
$261$	2.75279			0.170394
$262$	2.47772	−	4.81620i	0.153074	−	0.297546i
$263$	−9.01487	+	9.01487i	−0.555881	+	0.555881i	−0.928132	−	0.372251i	$-0.878586\pi$
$263$	−9.01487	+	9.01487i	−0.555881	+	0.555881i	0.372251	+	0.928132i	$0.378586\pi$
$264$	−18.8643	+	25.3349i	−1.16102	+	1.55925i
$265$	15.2292	+	25.7539i	0.935519	+	1.58205i
$266$	−3.71749	−	11.5951i	−0.227934	−	0.710943i
$267$	0.806727	+	0.806727i	0.0493709	+	0.0493709i
$268$	−3.93769	+	23.6638i	−0.240532	+	1.44550i
$269$			3.34273i			0.203810i	0.994794	+	0.101905i	$0.0324938\pi$
$269$			3.34273i			0.203810i	−0.994794	+	0.101905i	$0.967506\pi$
$270$	−0.779470	−	13.2231i	−0.0474370	−	0.804732i
$271$			16.6539i			1.01166i	0.862635	+	0.505828i	$0.168813\pi$
$271$			16.6539i			1.01166i	−0.862635	+	0.505828i	$0.831187\pi$
$272$	4.05373	+	8.27290i	0.245794	+	0.501618i
$273$	8.86936	+	8.86936i	0.536798	+	0.536798i
$274$	−3.31946	+	1.06424i	−0.200536	+	0.0642932i
$275$	−13.6746	+	24.8685i	−0.824612	+	1.49963i
$276$	3.05449	−	2.18297i	0.183859	−	0.131400i
$277$	9.33332	−	9.33332i	0.560785	−	0.560785i	−0.368746	−	0.929530i	$-0.620213\pi$
$277$	9.33332	−	9.33332i	0.560785	−	0.560785i	0.929530	+	0.368746i	$0.120213\pi$
$278$	−16.3144	−	8.39300i	−0.978471	−	0.503379i
$279$	0.871005			0.0521457
$280$	−14.9875	+	12.1046i	−0.895673	+	0.723389i
$281$	−3.74535			−0.223429			−0.111714	−	0.993740i	$-0.535634\pi$
$281$	−3.74535			−0.223429			−0.111714	+	0.993740i	$0.535634\pi$
$282$	−27.1811	−	13.9835i	−1.61861	−	0.832703i
$283$	−20.3323	+	20.3323i	−1.20863	+	1.20863i	−0.237160	+	0.971471i	$0.576217\pi$
$283$	−20.3323	+	20.3323i	−1.20863	+	1.20863i	−0.971471	+	0.237160i	$0.923783\pi$
$284$	1.00717	−	0.719803i	0.0597648	−	0.0427125i
$285$	10.7040	−	6.32966i	0.634051	−	0.374937i
$286$	−15.9981	+	5.12911i	−0.945988	+	0.303291i
$287$	−14.9758	−	14.9758i	−0.883996	−	0.883996i
$288$	−3.41533	−	3.55139i	−0.201250	−	0.209267i
$289$			11.6954i			0.687965i
$290$	−6.63894	+	7.47066i	−0.389852	+	0.438692i
$291$			24.6298i			1.44383i
$292$	−1.00469	+	6.03778i	−0.0587953	+	0.353334i
$293$	14.2039	+	14.2039i	0.829801	+	0.829801i	0.987489	−	0.157688i	$-0.0504041\pi$
$293$	14.2039	+	14.2039i	0.829801	+	0.829801i	−0.157688	+	0.987489i	$0.550404\pi$
$294$	1.93567	+	6.03751i	0.112890	+	0.352114i
$295$	13.8355	+	3.55305i	0.805535	+	0.206866i
$296$	8.43111	+	6.27779i	0.490048	+	0.364889i
$297$	16.8119	−	16.8119i	0.975528	−	0.975528i
$298$	8.41829	−	16.3635i	0.487659	−	0.947914i
$299$	1.99687			0.115482
$300$	−15.4504	−	12.1814i	−0.892029	−	0.703292i
$301$	−24.6214			−1.41916
$302$	4.97657	−	9.67349i	0.286369	−	0.556647i
$303$	−18.4866	+	18.4866i	−1.06203	+	1.06203i
$304$	−3.66142	+	10.6971i	−0.209997	+	0.613523i
$305$	16.5155	+	4.24130i	0.945677	+	0.242856i
$306$	0.866142	+	2.70157i	0.0495141	+	0.154438i
$307$	0.585176	+	0.585176i	0.0333978	+	0.0333978i	0.723608	−	0.690211i	$-0.242482\pi$
$307$	0.585176	+	0.585176i	0.0333978	+	0.0333978i	−0.690211	+	0.723608i	$0.742482\pi$
$308$	−34.1105	−	5.67603i	−1.94363	−	0.323422i
$309$		−	26.7213i		−	1.52012i
$310$	−2.10061	+	2.36378i	−0.119307	+	0.134253i
$311$			23.1745i			1.31410i	0.753845	+	0.657052i	$0.228197\pi$
$311$			23.1745i			1.31410i	−0.753845	+	0.657052i	$0.771803\pi$
$312$	−1.68707	−	11.5241i	−0.0955118	−	0.652421i
$313$	6.95553	+	6.95553i	0.393150	+	0.393150i	0.875808	−	0.482659i	$-0.160329\pi$
$313$	6.95553	+	6.95553i	0.393150	+	0.393150i	−0.482659	+	0.875808i	$0.660329\pi$
$314$	−8.23843	+	2.64130i	−0.464922	+	0.149057i
$315$	−5.10662	+	3.01972i	−0.287725	+	0.170142i
$316$	7.56418	+	10.5841i	0.425518	+	0.595401i
$317$	12.4563	−	12.4563i	0.699615	−	0.699615i	−0.264712	−	0.964327i	$-0.585277\pi$
$317$	12.4563	−	12.4563i	0.699615	−	0.699615i	0.964327	+	0.264712i	$0.0852770\pi$
$318$	−33.1064	−	17.0317i	−1.85651	−	0.955092i
$319$	−17.9391			−1.00439
$320$	17.8747	−	0.703772i	0.999226	−	0.0393420i
$321$	21.5463			1.20260
$322$	3.65481	+	1.88024i	0.203675	+	0.104781i
$323$	4.60337	−	4.60337i	0.256138	−	0.256138i
$324$	12.6225	+	17.6619i	0.701250	+	0.981215i
$325$	−2.91859	−	10.0494i	−0.161894	−	0.557439i
$326$	31.2089	−	10.0058i	1.72850	−	0.554171i
$327$	10.9202	+	10.9202i	0.603886	+	0.603886i
$328$	2.84861	+	19.4583i	0.157288	+	1.07440i
$329$		−	33.4634i		−	1.84490i
$330$	−2.07812	−	35.2537i	−0.114397	−	1.94065i
$331$			7.12833i			0.391808i	0.980623	+	0.195904i	$0.0627641\pi$
$331$			7.12833i			0.391808i	−0.980623	+	0.195904i	$0.937236\pi$
$332$	−4.38276	−	0.729297i	−0.240535	−	0.0400254i
$333$	2.28892	+	2.28892i	0.125432	+	0.125432i
$334$	−8.48340	−	26.4604i	−0.464191	−	1.44785i
$335$	−13.6518	−	23.0863i	−0.745876	−	1.26134i
$336$	7.76317	−	22.6807i	0.423516	−	1.23734i
$337$	−18.1802	+	18.1802i	−0.990340	+	0.990340i	−0.999954	−	0.00961397i	$-0.996940\pi$
$337$	−18.1802	+	18.1802i	−0.990340	+	0.990340i	0.00961397	+	0.999954i	$0.496940\pi$
$338$	−5.57655	+	10.8397i	−0.303324	+	0.589603i
$339$	−33.7002			−1.83034
$340$	−9.42052	−	4.16481i	−0.510900	−	0.225869i
$341$	−5.67605			−0.307376
$342$	−1.59280	+	3.09609i	−0.0861285	+	0.167417i
$343$	10.1694	−	10.1694i	0.549094	−	0.549094i
$344$	18.3371	+	13.6538i	0.988671	+	0.736162i
$345$	−1.04407	+	4.06559i	−0.0562109	+	0.218884i
$346$	−0.399362	−	1.24564i	−0.0214698	−	0.0669662i
$347$	−17.3201	−	17.3201i	−0.929792	−	0.929792i	0.0679003	−	0.997692i	$-0.478370\pi$
$347$	−17.3201	−	17.3201i	−0.929792	−	0.929792i	−0.997692	+	0.0679003i	$0.978370\pi$
$348$	2.04137	−	12.2677i	0.109429	−	0.657619i
$349$		−	20.0853i		−	1.07514i	−0.843218	−	0.537571i	$-0.819342\pi$
$349$		−	20.0853i		−	1.07514i	0.843218	−	0.537571i	$-0.180658\pi$
$350$	4.12061	−	21.1413i	0.220256	−	1.13005i
$351$			8.76677i			0.467936i
$352$	22.2566	+	23.1432i	1.18628	+	1.23354i
$353$	11.7907	+	11.7907i	0.627556	+	0.627556i	0.947453	−	0.319896i	$-0.103648\pi$
$353$	11.7907	+	11.7907i	0.627556	+	0.627556i	−0.319896	+	0.947453i	$0.603648\pi$
$354$	−16.9262	+	5.42666i	−0.899617	+	0.288424i
$355$	−0.344267	+	1.34057i	−0.0182718	+	0.0711500i
$356$	0.943543	−	0.674327i	0.0500077	−	0.0357393i
$357$	−9.76035	+	9.76035i	−0.516573	+	0.516573i
$358$	−5.23573	−	2.69354i	−0.276717	−	0.142358i
$359$	5.69369			0.300501			0.150251	−	0.988648i	$-0.451992\pi$
$359$	5.69369			0.300501			0.150251	+	0.988648i	$0.451992\pi$
$360$	5.47780	+	0.582892i	0.288705	+	0.0307211i
$361$	−11.0103			−0.579490
$362$	7.72313	+	3.97320i	0.405919	+	0.208827i
$363$	29.5184	−	29.5184i	1.54932	−	1.54932i
$364$	10.3736	−	7.41373i	0.543722	−	0.388585i
$365$	−3.48323	−	5.89045i	−0.182321	−	0.308320i
$366$	−20.2049	+	6.47784i	−1.05613	+	0.338602i
$367$	16.1841	+	16.1841i	0.844805	+	0.844805i	0.989479	−	0.144674i	$-0.0462135\pi$
$367$	16.1841	+	16.1841i	0.844805	+	0.844805i	−0.144674	+	0.989479i	$0.546213\pi$
$368$	−1.67928	−	3.42710i	−0.0875388	−	0.178650i
$369$			6.05598i			0.315262i
$370$	−11.7320	+	0.691572i	−0.609917	+	0.0359531i
$371$		−	40.7581i		−	2.11606i
$372$	0.645904	−	3.88160i	0.0334886	−	0.201252i
$373$	−10.0251	−	10.0251i	−0.519080	−	0.519080i	0.398213	−	0.917293i	$-0.369631\pi$
$373$	−10.0251	−	10.0251i	−0.519080	−	0.519080i	−0.917293	+	0.398213i	$0.869631\pi$
$374$	−5.64436	−	17.6052i	−0.291863	−	0.910344i
$375$	21.9864	−	0.687851i	1.13537	−	0.0355205i
$376$	−18.5571	+	24.9223i	−0.957009	+	1.28527i
$377$	4.67726	−	4.67726i	0.240891	−	0.240891i
$378$	−8.25474	+	16.0456i	−0.424578	+	0.825297i
$379$	24.6560			1.26649			0.633246	−	0.773951i	$-0.281722\pi$
$379$	24.6560			1.26649			0.633246	+	0.773951i	$0.281722\pi$
$380$	−4.56095	−	11.7895i	−0.233972	−	0.604787i
$381$	34.2790			1.75617
$382$	−4.37558	+	8.50528i	−0.223874	+	0.435168i
$383$	12.5151	−	12.5151i	0.639491	−	0.639491i	−0.310939	−	0.950430i	$-0.600643\pi$
$383$	12.5151	−	12.5151i	0.639491	−	0.639491i	0.950430	+	0.310939i	$0.100643\pi$
$384$	−18.3593	+	12.5867i	−0.936894	+	0.642313i
$385$	33.2781	−	19.6785i	1.69601	−	1.00291i
$386$	−0.267082	−	0.833049i	−0.0135941	−	0.0424011i
$387$	4.97825	+	4.97825i	0.253059	+	0.253059i
$388$	24.6972	+	4.10966i	1.25381	+	0.208636i
$389$			23.7495i			1.20415i	0.798440	+	0.602074i	$0.205659\pi$
$389$			23.7495i			1.20415i	−0.798440	+	0.602074i	$0.794341\pi$
$390$	9.73355	+	8.64989i	0.492878	+	0.438004i
$391$			2.19746i			0.111131i
$392$	6.37701	−	0.933568i	0.322088	−	0.0471523i
$393$	−5.32812	−	5.32812i	−0.268768	−	0.268768i
$394$	31.6586	−	10.1500i	1.59494	−	0.511348i
$395$	−14.0876	−	3.61779i	−0.708825	−	0.182031i
$396$	5.74921	+	8.04451i	0.288909	+	0.404252i
$397$	6.40962	−	6.40962i	0.321690	−	0.321690i	−0.527725	−	0.849415i	$-0.676955\pi$
$397$	6.40962	−	6.40962i	0.321690	−	0.321690i	0.849415	+	0.527725i	$0.176955\pi$
$398$	−0.998020	−	0.513436i	−0.0500262	−	0.0257362i
$399$	−16.9402			−0.848072
$400$	−14.7927	+	13.4601i	−0.739636	+	0.673007i
$401$	19.5380			0.975683			0.487841	−	0.872932i	$-0.337784\pi$
$401$	19.5380			0.975683			0.487841	+	0.872932i	$0.337784\pi$
$402$	29.6773	+	15.2676i	1.48017	+	0.761480i
$403$	1.47992	−	1.47992i	0.0737201	−	0.0737201i
$404$	15.4526	+	21.6219i	0.768796	+	1.07573i
$405$	−23.5083	−	6.03708i	−1.16814	−	0.299985i
$406$	12.9647	−	4.15659i	0.643430	−	0.206288i
$407$	−14.9161	−	14.9161i	−0.739365	−	0.739365i
$408$	12.6817	−	1.85655i	0.627839	−	0.0919130i
$409$		−	9.83106i		−	0.486115i	−0.970012	−	0.243057i	$-0.921850\pi$
$409$		−	9.83106i		−	0.486115i	0.970012	−	0.243057i	$-0.0781503\pi$
$410$	−16.4350	−	14.6053i	−0.811668	−	0.721303i
$411$			4.84965i			0.239216i
$412$	−26.7944	−	4.45863i	−1.32007	−	0.219661i
$413$	−13.7596	−	13.7596i	−0.677066	−	0.677066i
$414$	−0.358805	−	1.11914i	−0.0176343	−	0.0550028i
$415$	4.27581	−	2.52844i	0.209891	−	0.124116i
$416$	−11.8371	−	0.231176i	−0.580362	−	0.0113343i
$417$	−18.0484	+	18.0484i	−0.883836	+	0.883836i
$418$	10.3797	−	20.1762i	0.507689	−	0.986849i
$419$	−14.3319			−0.700160			−0.350080	−	0.936720i	$-0.613846\pi$
$419$	−14.3319			−0.700160			−0.350080	+	0.936720i	$0.613846\pi$
$420$	9.67040	+	24.9967i	0.471867	+	1.21972i
$421$	27.5506			1.34273			0.671367	−	0.741125i	$-0.265707\pi$
$421$	27.5506			1.34273			0.671367	+	0.741125i	$0.265707\pi$
$422$	−13.7136	+	26.6566i	−0.667568	+	1.29762i
$423$	−6.76603	+	6.76603i	−0.328976	+	0.328976i
$424$	−22.6024	+	30.3551i	−1.09767	+	1.47418i
$425$	11.0589	−	3.21178i	0.536436	−	0.155794i
$426$	−0.525808	−	1.64004i	−0.0254755	−	0.0794600i
$427$	−16.4249	−	16.4249i	−0.794858	−	0.794858i
$428$	3.59515	−	21.6053i	0.173778	−	1.04433i
$429$			23.3729i			1.12845i
$430$	−25.5163	+	1.50412i	−1.23051	+	0.0725353i
$431$		−	5.20598i		−	0.250763i	−0.992109	−	0.125382i	$-0.959984\pi$
$431$		−	5.20598i		−	0.250763i	0.992109	−	0.125382i	$-0.0400155\pi$
$432$	15.0459	−	7.37251i	0.723896	−	0.354710i
$433$	0.996539	+	0.996539i	0.0478906	+	0.0478906i	0.730647	−	0.682756i	$-0.239219\pi$
$433$	0.996539	+	0.996539i	0.0478906	+	0.0478906i	−0.682756	+	0.730647i	$0.739219\pi$
$434$	4.10215	−	1.31518i	0.196909	−	0.0631306i
$435$	7.07731	+	11.9684i	0.339331	+	0.573839i
$436$	12.7722	−	9.12795i	0.611675	−	0.437150i
$437$	−1.90698	+	1.90698i	−0.0912230	+	0.0912230i
$438$	7.57212	+	3.89551i	0.361810	+	0.186135i
$439$	15.7193			0.750240			0.375120	−	0.926976i	$-0.377602\pi$
$439$	15.7193			0.750240			0.375120	+	0.926976i	$0.377602\pi$
$440$	−35.6970	−	3.79852i	−1.70179	−	0.181087i
$441$	1.98471			0.0945101
$442$	6.06188	+	3.11856i	0.288334	+	0.148335i
$443$	−2.99207	+	2.99207i	−0.142157	+	0.142157i	−0.774604	−	0.632447i	$-0.782051\pi$
$443$	−2.99207	+	2.99207i	−0.142157	+	0.142157i	0.632447	+	0.774604i	$0.282051\pi$
$444$	11.8979	−	8.50311i	0.564647	−	0.403540i
$445$	−0.322517	+	1.25588i	−0.0152888	+	0.0595342i
$446$	−6.01689	+	1.92906i	−0.284908	+	0.0913436i
$447$	−18.1028	−	18.1028i	−0.856234	−	0.856234i
$448$	−21.4475	−	11.5689i	−1.01330	−	0.546577i
$449$			14.6277i			0.690323i	0.938543	+	0.345162i	$0.112176\pi$
$449$			14.6277i			0.690323i	−0.938543	+	0.345162i	$0.887824\pi$
$450$	−5.10774	+	3.44144i	−0.240781	+	0.162231i
$451$		−	39.4649i		−	1.85833i
$452$	−5.62311	+	33.7924i	−0.264489	+	1.58946i
$453$	−10.7017	−	10.7017i	−0.502809	−	0.502809i
$454$	−2.68850	−	8.38565i	−0.126178	−	0.393558i
$455$	−3.54583	+	13.8074i	−0.166231	+	0.647302i
$456$	12.6164	+	9.39417i	0.590819	+	0.439922i
$457$	−26.5331	+	26.5331i	−1.24117	+	1.24117i	−0.281651	+	0.959517i	$0.590882\pi$
$457$	−26.5331	+	26.5331i	−1.24117	+	1.24117i	−0.959517	+	0.281651i	$0.909118\pi$
$458$	−16.8584	+	32.7696i	−0.787744	+	1.53122i
$459$	−9.64745			−0.450305
$460$	3.90251	+	1.72530i	0.181956	+	0.0804426i
$461$	1.60077			0.0745551			0.0372776	−	0.999305i	$-0.488131\pi$
$461$	1.60077			0.0745551			0.0372776	+	0.999305i	$0.488131\pi$
$462$	−22.0077	+	42.7788i	−1.02389	+	1.99025i
$463$	−1.63630	+	1.63630i	−0.0760454	+	0.0760454i	−0.744106	−	0.668061i	$-0.767124\pi$
$463$	−1.63630	+	1.63630i	−0.0760454	+	0.0760454i	0.668061	+	0.744106i	$0.267124\pi$
$464$	−11.9607	−	4.09391i	−0.555261	−	0.190055i
$465$	2.23932	+	3.78688i	0.103846	+	0.175613i
$466$	−9.98166	−	31.1336i	−0.462391	−	1.44224i
$467$	7.34693	+	7.34693i	0.339975	+	0.339975i	0.856358	−	0.516383i	$-0.172722\pi$
$467$	7.34693	+	7.34693i	0.339975	+	0.339975i	−0.516383	+	0.856358i	$0.672722\pi$
$468$	−3.59644	−	0.598453i	−0.166246	−	0.0276635i
$469$			36.5365i			1.68710i
$470$	−2.04428	−	34.6797i	−0.0942957	−	1.59965i
$471$			12.0362i			0.554597i
$472$	2.61726	+	17.8780i	0.120469	+	0.822901i
$473$	−32.4416	−	32.4416i	−1.49167	−	1.49167i
$474$	17.2346	−	5.52554i	0.791612	−	0.253797i
$475$	12.3842	+	6.80979i	0.568227	+	0.312455i
$476$	8.15849	+	11.4156i	0.373944	+	0.523235i
$477$	−8.24096	+	8.24096i	−0.377328	+	0.377328i
$478$	24.6106	+	12.6610i	1.12566	+	0.579101i
$479$	15.1513			0.692282			0.346141	−	0.938183i	$-0.387492\pi$
$479$	15.1513			0.692282			0.346141	+	0.938183i	$0.387492\pi$
$480$	6.65976	−	23.9793i	0.303975	−	1.09450i
$481$	7.77818			0.354655
$482$	31.0783	+	15.9884i	1.41558	+	0.728251i
$483$	4.04329	−	4.04329i	0.183976	−	0.183976i
$484$	−24.6739	−	34.5246i	−1.12154	−	1.56930i
$485$	−24.0946	+	14.2480i	−1.09408	+	0.646967i
$486$	11.8368	−	3.79496i	0.536927	−	0.172143i
$487$	−7.00072	−	7.00072i	−0.317233	−	0.317233i	0.530470	−	0.847703i	$-0.322015\pi$
$487$	−7.00072	−	7.00072i	−0.317233	−	0.317233i	−0.847703	+	0.530470i	$0.822015\pi$
$488$	3.12425	+	21.3411i	0.141428	+	0.966065i
$489$		−	45.5955i		−	2.06190i
$490$	−4.78655	+	5.38621i	−0.216234	+	0.243324i
$491$			1.30059i			0.0586950i	0.999569	+	0.0293475i	$0.00934294\pi$
$491$			1.30059i			0.0586950i	−0.999569	+	0.0293475i	$0.990657\pi$
$492$	26.9883	+	4.49088i	1.21672	+	0.202465i
$493$	5.14712	+	5.14712i	0.231815	+	0.231815i
$494$	2.55423	+	7.96685i	0.114920	+	0.358446i
$495$	−10.7074	−	2.74973i	−0.481262	−	0.123591i
$496$	−3.78445	−	1.29534i	−0.169927	−	0.0581626i
$497$	1.33321	−	1.33321i	0.0598028	−	0.0598028i
$498$	−2.82771	+	5.49652i	−0.126713	+	0.246305i
$499$	10.6573			0.477085			0.238542	−	0.971132i	$-0.423330\pi$
$499$	10.6573			0.477085			0.238542	+	0.971132i	$0.423330\pi$
$500$	2.97885	−	22.1614i	0.133218	−	0.991087i
$501$	−38.6580			−1.72711
$502$	16.2259	−	31.5401i	0.724199	−	1.40770i
$503$	10.7661	−	10.7661i	0.480037	−	0.480037i	−0.425106	−	0.905143i	$-0.639763\pi$
$503$	10.7661	−	10.7661i	0.480037	−	0.480037i	0.905143	+	0.425106i	$0.139763\pi$
$504$	−6.01898	−	4.48172i	−0.268107	−	0.199632i
$505$	−28.7791	−	7.39066i	−1.28065	−	0.328880i
$506$	2.33821	+	7.29308i	0.103946	+	0.324217i
$507$	11.9919	+	11.9919i	0.532579	+	0.532579i
$508$	5.71968	−	34.3728i	0.253770	−	1.52505i
$509$		−	34.9774i		−	1.55035i	−0.631749	−	0.775173i	$-0.717663\pi$
$509$		−	34.9774i		−	1.55035i	0.631749	−	0.775173i	$-0.282337\pi$
$510$	−9.51883	+	10.7114i	−0.421501	+	0.474307i
$511$			9.32225i			0.412392i
$512$	9.55779	+	20.5097i	0.422398	+	0.906410i
$513$	−8.37214	−	8.37214i	−0.369639	−	0.369639i
$514$	−4.09566	+	1.31310i	−0.180652	+	0.0579183i
$515$	26.1406	−	15.4579i	1.15189	−	0.681155i
$516$	25.8771	−	18.4937i	1.13917	−	0.814140i
$517$	44.0920	−	44.0920i	1.93916	−	1.93916i
$518$	14.2362	+	7.32389i	0.625503	+	0.321793i
$519$	−1.81985			−0.0798827
$520$	10.2977	−	8.31690i	0.451583	−	0.364720i
$521$	−28.8962			−1.26597			−0.632983	−	0.774166i	$-0.718170\pi$
$521$	−28.8962			−1.26597			−0.632983	+	0.774166i	$0.718170\pi$
$522$	−3.46179	−	1.78094i	−0.151519	−	0.0779495i
$523$	−5.68758	+	5.68758i	−0.248701	+	0.248701i	−0.820437	−	0.571737i	$-0.806270\pi$
$523$	−5.68758	+	5.68758i	−0.248701	+	0.248701i	0.571737	+	0.820437i	$0.306270\pi$
$524$	−6.23174	+	4.45367i	−0.272235	+	0.194559i
$525$	−26.2578	−	14.4385i	−1.14598	−	0.630150i
$526$	17.1689	−	5.50449i	0.748601	−	0.240007i
$527$	1.62859	+	1.62859i	0.0709424	+	0.0709424i
$528$	40.1134	−	19.6557i	1.74571	−	0.855402i
$529$			22.0897i			0.960421i
$530$	−2.48992	−	42.2395i	−0.108155	−	1.83477i
$531$			5.56416i			0.241464i
$532$	−2.82659	+	16.9866i	−0.122548	+	0.736462i
$533$	10.2897	+	10.2897i	0.445696	+	0.445696i
$534$	−0.492588	−	1.53642i	−0.0213164	−	0.0664875i
$535$	12.4642	+	21.0781i	0.538875	+	0.911286i
$536$	20.2613	−	27.2110i	0.875154	−	1.17534i
$537$	−5.79224	+	5.79224i	−0.249954	+	0.249954i
$538$	2.16260	−	4.20368i	0.0932363	−	0.181233i
$539$	−12.9337			−0.557095
$540$	−7.57453	+	17.1331i	−0.325956	+	0.737290i
$541$	18.1551			0.780550			0.390275	−	0.920698i	$-0.372380\pi$
$541$	18.1551			0.780550			0.390275	+	0.920698i	$0.372380\pi$
$542$	10.7744	−	20.9433i	0.462799	−	0.899591i
$543$	8.54403	−	8.54403i	0.366659	−	0.366659i
$544$	0.254399	−	13.0262i	0.0109073	−	0.558495i
$545$	−4.36571	+	17.0000i	−0.187006	+	0.728200i
$546$	−5.41564	−	16.8918i	−0.231768	−	0.722903i
$547$	15.9461	+	15.9461i	0.681806	+	0.681806i	0.960407	−	0.278601i	$-0.0898708\pi$
$547$	15.9461	+	15.9461i	0.681806	+	0.681806i	−0.278601	+	0.960407i	$0.589871\pi$
$548$	4.86292	+	0.809197i	0.207734	+	0.0345672i
$549$			6.64197i			0.283472i
$550$	33.2855	−	22.4267i	1.41930	−	0.956278i
$551$			8.93342i			0.380576i
$552$	−5.25349	+	0.769089i	−0.223603	+	0.0327346i
$553$	14.0103	+	14.0103i	0.595779	+	0.595779i
$554$	−17.7754	+	5.69893i	−0.755205	+	0.242124i
$555$	−4.06686	+	15.8363i	−0.172629	+	0.672213i
$556$	15.0863	+	21.1094i	0.639803	+	0.895236i
$557$	−24.7792	+	24.7792i	−1.04993	+	1.04993i	−0.0512441	+	0.998686i	$0.516319\pi$
$557$	−24.7792	+	24.7792i	−1.04993	+	1.04993i	−0.998686	+	0.0512441i	$0.983681\pi$
$558$	−1.09534	−	0.563502i	−0.0463694	−	0.0238549i
$559$	16.9170			0.715515
$560$	26.6787	−	5.52599i	1.12738	−	0.233516i
$561$	−25.7208			−1.08593
$562$	4.70999	+	2.42308i	0.198679	+	0.102211i
$563$	−25.9944	+	25.9944i	−1.09553	+	1.09553i	−0.100607	+	0.994926i	$0.532079\pi$
$563$	−25.9944	+	25.9944i	−1.09553	+	1.09553i	−0.994926	+	0.100607i	$0.967921\pi$
$564$	25.1351	+	35.1700i	1.05838	+	1.48092i
$565$	−19.4950	−	32.9678i	−0.820163	−	1.38697i
$566$	38.7231	−	12.4149i	1.62766	−	0.521838i
$567$	23.3793	+	23.3793i	0.981839	+	0.981839i
$568$	−1.73226	+	0.253596i	−0.0726840	+	0.0106406i
$569$			18.8164i			0.788826i	0.918933	+	0.394413i	$0.129052\pi$
$569$			18.8164i			0.788826i	−0.918933	+	0.394413i	$0.870948\pi$
$570$	−17.5559	+	1.03488i	−0.735336	+	0.0433463i
$571$		−	5.60289i		−	0.234474i	−0.993104	−	0.117237i	$-0.962596\pi$
$571$		−	5.60289i		−	0.234474i	0.993104	−	0.117237i	$-0.0374036\pi$
$572$	23.4368	+	3.89992i	0.979943	+	0.163064i
$573$	9.40931	+	9.40931i	0.393080	+	0.393080i
$574$	9.14426	+	28.5217i	0.381674	+	1.19047i
$575$	−4.58122	+	1.33050i	−0.191050	+	0.0554858i
$576$	1.99738	+	6.67563i	0.0832241	+	0.278151i
$577$	−27.5007	+	27.5007i	−1.14487	+	1.14487i	−0.157323	+	0.987547i	$0.550286\pi$
$577$	−27.5007	+	27.5007i	−1.14487	+	1.14487i	−0.987547	+	0.157323i	$0.949714\pi$
$578$	7.56641	−	14.7076i	0.314721	−	0.611757i
$579$	−1.21707			−0.0505795
$580$	13.1820	−	5.09968i	0.547354	−	0.211753i
$581$	−6.76692			−0.280739
$582$	15.9344	−	30.9734i	0.660503	−	1.28389i
$583$	53.7036	−	53.7036i	2.22418	−	2.22418i
$584$	5.16964	−	6.94286i	0.213921	−	0.287297i
$585$	3.50868	−	2.07481i	0.145066	−	0.0857827i
$586$	−8.67291	−	27.0515i	−0.358275	−	1.11749i
$587$	−11.7090	−	11.7090i	−0.483284	−	0.483284i	0.422895	−	0.906179i	$-0.361014\pi$
$587$	−11.7090	−	11.7090i	−0.483284	−	0.483284i	−0.906179	+	0.422895i	$0.861014\pi$
$588$	1.47179	−	8.84480i	0.0606954	−	0.364753i
$589$			2.82660i			0.116468i
$590$	−15.1003	−	13.4191i	−0.621668	−	0.552456i
$591$		−	46.2524i		−	1.90257i
$592$	−6.54115	−	13.3492i	−0.268839	−	0.548650i
$593$	15.8990	+	15.8990i	0.652895	+	0.652895i	0.953689	−	0.300794i	$-0.0972518\pi$
$593$	15.8990	+	15.8990i	0.652895	+	0.652895i	−0.300794	+	0.953689i	$0.597252\pi$
$594$	−32.0186	+	10.2654i	−1.31374	+	0.421194i
$595$	−15.1945	−	3.90203i	−0.622912	−	0.159968i
$596$	−21.1730	+	15.1318i	−0.867278	+	0.619823i
$597$	−1.10410	+	1.10410i	−0.0451878	+	0.0451878i
$598$	−2.51117	−	1.29188i	−0.102689	−	0.0528290i
$599$	−25.4620			−1.04035			−0.520175	−	0.854060i	$-0.674133\pi$
$599$	−25.4620			−1.04035			−0.520175	+	0.854060i	$0.674133\pi$
$600$	11.5489	+	25.3145i	0.471483	+	1.03346i
$601$	−31.7318			−1.29437			−0.647184	−	0.762334i	$-0.724054\pi$
$601$	−31.7318			−1.29437			−0.647184	+	0.762334i	$0.724054\pi$
$602$	30.9628	+	15.9290i	1.26195	+	0.649217i
$603$	7.38739	−	7.38739i	0.300838	−	0.300838i
$604$	−12.5166	+	8.94533i	−0.509295	+	0.363980i
$605$	45.9529	+	11.8010i	1.86825	+	0.479779i
$606$	35.2080	−	11.2880i	1.43023	−	0.458542i
$607$	−12.1917	−	12.1917i	−0.494847	−	0.494847i	0.414982	−	0.909829i	$-0.363788\pi$
$607$	−12.1917	−	12.1917i	−0.494847	−	0.494847i	−0.909829	+	0.414982i	$0.863788\pi$
$608$	11.5250	−	11.0835i	0.467401	−	0.449495i
$609$		−	18.9412i		−	0.767535i
$610$	−18.0253	−	16.0185i	−0.729823	−	0.648570i
$611$			22.9922i			0.930167i
$612$	0.658572	−	3.95773i	0.0266212	−	0.159982i
$613$	26.9794	+	26.9794i	1.08969	+	1.08969i	0.995560	+	0.0941281i	$0.0300063\pi$
$613$	26.9794	+	26.9794i	1.08969	+	1.08969i	0.0941281	+	0.995560i	$0.469994\pi$
$614$	−0.357309	−	1.11448i	−0.0144198	−	0.0449766i
$615$	−26.3297	+	15.5697i	−1.06172	+	0.627830i
$616$	39.2237	+	29.2059i	1.58037	+	1.17674i
$617$	27.4484	−	27.4484i	1.10503	−	1.10503i	0.111238	−	0.993794i	$-0.464518\pi$
$617$	27.4484	−	27.4484i	1.10503	−	1.10503i	0.993794	−	0.111238i	$-0.0354817\pi$
$618$	−17.2875	+	33.6035i	−0.695405	+	1.35173i
$619$	14.9682			0.601621			0.300810	−	0.953684i	$-0.402743\pi$
$619$	14.9682			0.601621			0.300810	+	0.953684i	$0.402743\pi$
$620$	4.17089	−	1.61358i	0.167507	−	0.0648029i
$621$	3.99652			0.160375
$622$	14.9929	−	29.1432i	0.601159	−	1.16854i
$623$	1.24898	−	1.24898i	0.0500395	−	0.0500395i
$624$	−5.33397	+	15.5836i	−0.213530	+	0.623844i
$625$	13.3917	+	21.1107i	0.535668	+	0.844429i
$626$	−4.24705	−	13.2469i	−0.169746	−	0.529452i
$627$	−22.3207	−	22.3207i	−0.891404	−	0.891404i
$628$	12.0691	+	2.00832i	0.481610	+	0.0801405i
$629$			8.55955i			0.341292i
$630$	8.37548	−	0.493715i	0.333687	−	0.0196701i
$631$		−	21.8906i		−	0.871453i	−0.900079	−	0.435726i	$-0.856492\pi$
$631$		−	21.8906i		−	0.871453i	0.900079	−	0.435726i	$-0.143508\pi$
$632$	−2.66496	−	18.2038i	−0.106006	−	0.724107i
$633$	29.4900	+	29.4900i	1.17212	+	1.17212i
$634$	−23.7232	+	7.60582i	−0.942167	+	0.302066i
$635$	19.8299	+	33.5341i	0.786924	+	1.33076i
$636$	30.6144	+	42.8367i	1.21394	+	1.69859i
$637$	3.37221	−	3.37221i	0.133612	−	0.133612i
$638$	22.5594	+	11.6058i	0.893134	+	0.459477i
$639$	−0.539130			−0.0213277
$640$	−22.9337	−	10.6791i	−0.906536	−	0.422129i
$641$	28.8182			1.13825			0.569125	−	0.822251i	$-0.307282\pi$
$641$	28.8182			1.13825			0.569125	+	0.822251i	$0.307282\pi$
$642$	−27.0957	−	13.9395i	−1.06938	−	0.550149i
$643$	−4.69128	+	4.69128i	−0.185006	+	0.185006i	−0.793533	−	0.608527i	$-0.791761\pi$
$643$	−4.69128	+	4.69128i	−0.185006	+	0.185006i	0.608527	+	0.793533i	$0.291761\pi$
$644$	−3.37970	−	4.72901i	−0.133179	−	0.186349i
$645$	−8.84516	+	34.4429i	−0.348278	+	1.35619i
$646$	−8.76718	+	2.81082i	−0.344940	+	0.110590i
$647$	7.87207	+	7.87207i	0.309483	+	0.309483i	0.844709	−	0.535226i	$-0.179774\pi$
$647$	7.87207	+	7.87207i	0.309483	+	0.309483i	−0.535226	+	0.844709i	$0.679774\pi$
$648$	−4.44707	−	30.3770i	−0.174697	−	1.19332i
$649$		−	36.2598i		−	1.42332i
$650$	−2.83121	+	14.5259i	−0.111049	+	0.569751i
$651$		−	5.99314i		−	0.234890i
$652$	−45.7203	−	7.60792i	−1.79055	−	0.297949i
$653$	−8.40205	−	8.40205i	−0.328798	−	0.328798i	0.523331	−	0.852129i	$-0.324689\pi$
$653$	−8.40205	−	8.40205i	−0.328798	−	0.328798i	−0.852129	+	0.523331i	$0.824689\pi$
$654$	−6.66786	−	20.7976i	−0.260734	−	0.813250i
$655$	2.13010	−	8.29457i	0.0832298	−	0.324096i
$656$	9.00635	−	26.3128i	0.351639	−	1.02734i
$657$	1.88488	−	1.88488i	0.0735362	−	0.0735362i
$658$	−21.6494	+	42.0821i	−0.843980	+	1.64053i
$659$	15.5178			0.604488			0.302244	−	0.953231i	$-0.402264\pi$
$659$	15.5178			0.604488			0.302244	+	0.953231i	$0.402264\pi$
$660$	−20.1943	+	45.6780i	−0.786060	+	1.77801i
$661$	8.38984			0.326327			0.163164	−	0.986599i	$-0.447830\pi$
$661$	8.38984			0.326327			0.163164	+	0.986599i	$0.447830\pi$
$662$	4.61171	−	8.96427i	0.179239	−	0.348406i
$663$	6.70620	−	6.70620i	0.260447	−	0.260447i
$664$	5.03974	+	3.75258i	0.195580	+	0.145629i
$665$	−9.79965	−	16.5721i	−0.380014	−	0.642638i
$666$	−1.39762	−	4.35928i	−0.0541565	−	0.168919i
$667$	−2.13223	−	2.13223i	−0.0825601	−	0.0825601i
$668$	−6.45036	+	38.7639i	−0.249572	+	1.49982i
$669$			8.79053i			0.339862i
$670$	2.23202	+	37.8645i	0.0862304	+	1.46283i
$671$		−	43.2835i		−	1.67094i
$672$	−24.4361	+	23.4999i	−0.942642	+	0.906528i
$673$	−24.4326	−	24.4326i	−0.941808	−	0.941808i	0.0565898	−	0.998398i	$-0.481977\pi$
$673$	−24.4326	−	24.4326i	−0.941808	−	0.941808i	−0.998398	+	0.0565898i	$0.981977\pi$
$674$	34.6245	−	11.1009i	1.33368	−	0.427589i
$675$	−5.84126	−	20.1128i	−0.224830	−	0.774142i
$676$	14.0256	−	10.0238i	0.539448	−	0.385530i
$677$	7.54681	−	7.54681i	0.290047	−	0.290047i	−0.547052	−	0.837099i	$-0.684250\pi$
$677$	7.54681	−	7.54681i	0.290047	−	0.290047i	0.837099	+	0.547052i	$0.184250\pi$
$678$	42.3799	+	21.8025i	1.62759	+	0.837321i
$679$	38.1322			1.46338
$680$	9.15239	+	11.3322i	0.350978	+	0.434568i
$681$	−12.2512			−0.469469
$682$	7.13796	+	3.67216i	0.273327	+	0.140614i
$683$	9.92458	−	9.92458i	0.379754	−	0.379754i	−0.491260	−	0.871013i	$-0.663463\pi$
$683$	9.92458	−	9.92458i	0.379754	−	0.379754i	0.871013	+	0.491260i	$0.163463\pi$
$684$	4.00606	−	2.86303i	0.153176	−	0.109471i
$685$	−4.74426	+	2.80545i	−0.181269	+	0.107191i
$686$	−19.3677	+	6.20942i	−0.739462	+	0.237077i
$687$	36.2527	+	36.2527i	1.38313	+	1.38313i
$688$	−14.2266	−	29.0337i	−0.542383	−	1.10690i
$689$			28.0043i			1.06688i
$690$	3.94324	−	4.43725i	0.150116	−	0.168923i
$691$			8.53570i			0.324713i	0.986732	+	0.162357i	$0.0519095\pi$
$691$			8.53570i			0.324713i	−0.986732	+	0.162357i	$0.948091\pi$
$692$	−0.303655	+	1.82484i	−0.0115432	+	0.0693698i
$693$	10.6487	+	10.6487i	0.404509	+	0.404509i
$694$	10.5757	+	32.9863i	0.401447	+	1.25214i
$695$	−28.0970	−	7.21548i	−1.06578	−	0.273699i
$696$	−10.5038	+	14.1067i	−0.398146	+	0.534712i
$697$	−11.3234	+	11.3234i	−0.428903	+	0.428903i
$698$	−12.9943	+	25.2584i	−0.491842	+	0.956046i
$699$	−45.4854			−1.72042
$700$	−18.8594	+	23.9205i	−0.712817	+	0.904109i
$701$	18.7466			0.708048			0.354024	−	0.935236i	$-0.384813\pi$
$701$	18.7466			0.708048			0.354024	+	0.935236i	$0.384813\pi$
$702$	5.67171	−	11.0247i	0.214065	−	0.416101i
$703$	−7.42805	+	7.42805i	−0.280154	+	0.280154i
$704$	−13.0163	−	43.5029i	−0.490569	−	1.63958i
$705$	−46.8119	−	12.0216i	−1.76304	−	0.452760i
$706$	−7.19942	−	22.4556i	−0.270954	−	0.845126i
$707$	28.6212	+	28.6212i	1.07641	+	1.07641i
$708$	24.7964	+	4.12616i	0.931908	+	0.155071i
$709$			44.9932i			1.68976i	0.534960	+	0.844878i	$0.320327\pi$
$709$			44.9932i			1.68976i	−0.534960	+	0.844878i	$0.679673\pi$
$710$	1.30022	−	1.46312i	0.0487965	−	0.0549098i
$711$		−	5.66554i		−	0.212474i
$712$	−1.62282	+	0.237574i	−0.0608177	+	0.00890346i
$713$	−0.674653	−	0.674653i	−0.0252660	−	0.0252660i
$714$	18.5887	−	5.95968i	0.695665	−	0.223035i
$715$	−22.8649	+	13.5208i	−0.855100	+	0.505651i
$716$	4.84162	+	6.77457i	0.180940	+	0.253178i
$717$	27.2264	−	27.2264i	1.01679	−	1.01679i
$718$	−7.16014	−	3.68357i	−0.267214	−	0.137469i
$719$	20.1987			0.753285			0.376643	−	0.926359i	$-0.377078\pi$
$719$	20.1987			0.753285			0.376643	+	0.926359i	$0.377078\pi$
$720$	−6.51153	−	4.27691i	−0.242670	−	0.159391i
$721$	−41.3702			−1.54071
$722$	13.8461	+	7.12319i	0.515298	+	0.265098i
$723$	34.3817	−	34.3817i	1.27867	−	1.27867i
$724$	−7.14179	−	9.99305i	−0.265422	−	0.371389i
$725$	−7.61416	+	13.8470i	−0.282783	+	0.514266i
$726$	−56.2182	+	18.0240i	−2.08645	+	0.668932i
$727$	−26.1506	−	26.1506i	−0.969873	−	0.969873i	0.0296863	−	0.999559i	$-0.490549\pi$
$727$	−26.1506	−	26.1506i	−0.969873	−	0.969873i	−0.999559	+	0.0296863i	$0.990549\pi$
$728$	−17.8417	+	2.61195i	−0.661257	+	0.0968053i
$729$			15.2698i			0.565550i
$730$	0.569497	+	9.66107i	0.0210780	+	0.357572i
$731$			18.6165i			0.688555i
$732$	29.5997	+	4.92543i	1.09404	+	0.182049i
$733$	−31.9609	−	31.9609i	−1.18050	−	1.18050i	−0.979614	−	0.200888i	$-0.935617\pi$
$733$	−31.9609	−	31.9609i	−1.18050	−	1.18050i	−0.200888	−	0.979614i	$-0.564383\pi$
$734$	−9.88204	−	30.8229i	−0.364753	−	1.13769i
$735$	5.10261	+	8.62897i	0.188213	+	0.318284i
$736$	−0.105386	+	5.39619i	−0.00388459	+	0.198906i
$737$	−48.1412	+	48.1412i	−1.77330	+	1.77330i
$738$	3.91795	−	7.61574i	0.144222	−	0.280339i
$739$	−28.3210			−1.04180			−0.520902	−	0.853617i	$-0.674404\pi$
$739$	−28.3210			−1.04180			−0.520902	+	0.853617i	$0.674404\pi$
$740$	15.2011	+	6.72039i	0.558802	+	0.247046i
$741$	11.6394			0.427583
$742$	−26.3687	+	51.2557i	−0.968026	+	1.88165i
$743$	−4.33565	+	4.33565i	−0.159060	+	0.159060i	−0.782150	−	0.623090i	$-0.785877\pi$
$743$	−4.33565	+	4.33565i	−0.159060	+	0.159060i	0.623090	+	0.782150i	$0.285877\pi$
$744$	−3.32348	+	4.46346i	−0.121845	+	0.163638i
$745$	7.23722	−	28.1816i	0.265151	−	1.03250i
$746$	6.12133	+	19.0929i	0.224118	+	0.699042i
$747$	1.36822	+	1.36822i	0.0500604	+	0.0500604i
$748$	−4.29169	+	25.7912i	−0.156920	+	0.943020i
$749$		−	33.3583i		−	1.21889i
$750$	−28.0942	−	13.3592i	−1.02585	−	0.487810i
$751$		−	2.89650i		−	0.105695i	−0.998603	−	0.0528474i	$-0.983170\pi$
$751$		−	2.89650i		−	0.105695i	0.998603	−	0.0528474i	$-0.0168297\pi$
$752$	39.4602	−	19.3356i	1.43897	−	0.705096i
$753$	−34.8925	−	34.8925i	−1.27155	−	1.27155i
$754$	−8.90789	+	2.85594i	−0.324406	+	0.104007i
$755$	4.27837	−	16.6599i	0.155706	−	0.606316i
$756$	20.7616	−	14.8378i	0.755092	−	0.539646i
$757$	−1.42411	+	1.42411i	−0.0517601	+	0.0517601i	−0.732513	−	0.680753i	$-0.761653\pi$
$757$	−1.42411	+	1.42411i	−0.0517601	+	0.0517601i	0.680753	+	0.732513i	$0.261653\pi$
$758$	−31.0063	−	15.9513i	−1.12620	−	0.579378i
$759$	10.6550			0.386752
$760$	−1.89161	+	17.7766i	−0.0686160	+	0.644827i
$761$	−0.830872			−0.0301191			−0.0150595	−	0.999887i	$-0.504794\pi$
$761$	−0.830872			−0.0301191			−0.0150595	+	0.999887i	$0.504794\pi$
$762$	−43.1077	−	22.1770i	−1.56163	−	0.803387i
$763$	16.9067	−	16.9067i	0.612065	−	0.612065i
$764$	11.0051	−	7.86506i	0.398150	−	0.284548i
$765$	2.28324	+	3.86115i	0.0825505	+	0.139600i
$766$	−23.8352	+	7.64173i	−0.861199	+	0.276107i
$767$	9.45403	+	9.45403i	0.341365	+	0.341365i
$768$	31.2309	−	3.95085i	1.12695	−	0.142564i
$769$		−	15.7348i		−	0.567411i	−0.958911	−	0.283706i	$-0.908436\pi$
$769$		−	15.7348i		−	0.567411i	0.958911	−	0.283706i	$-0.0915638\pi$
$770$	−54.5803	+	3.21738i	−1.96694	+	0.115946i
$771$			5.98366i			0.215496i
$772$	−0.203076	+	1.22040i	−0.00730885	+	0.0439230i
$773$	23.7918	+	23.7918i	0.855732	+	0.855732i	0.990832	−	0.135100i	$-0.0431354\pi$
$773$	23.7918	+	23.7918i	0.855732	+	0.855732i	−0.135100	+	0.990832i	$0.543135\pi$
$774$	−3.03972	−	9.48114i	−0.109261	−	0.340793i
$775$	−2.40918	+	4.38131i	−0.0865403	+	0.157381i
$776$	−28.3994	−	21.1462i	−1.01948	−	0.759103i
$777$	15.7494	−	15.7494i	0.565007	−	0.565007i
$778$	15.3649	−	29.8664i	0.550858	−	1.07076i
$779$	−19.6530			−0.704141
$780$	−6.64439	−	17.1749i	−0.237907	−	0.614960i
$781$	3.51333			0.125717
$782$	1.42166	−	2.76343i	0.0508385	−	0.0988202i
$783$	9.36105	−	9.36105i	0.334536	−	0.334536i
$784$	−8.62343	−	2.95163i	−0.307980	−	0.105415i
$785$	−11.7746	+	6.96273i	−0.420253	+	0.248511i
$786$	3.25335	+	10.1475i	0.116043	+	0.361948i
$787$	19.5630	+	19.5630i	0.697344	+	0.697344i	0.963837	−	0.266493i	$-0.0858649\pi$
$787$	19.5630	+	19.5630i	0.697344	+	0.697344i	−0.266493	+	0.963837i	$0.585865\pi$
$788$	−46.3790	−	7.71754i	−1.65218	−	0.274926i
$789$		−	25.0834i		−	0.892993i
$790$	15.3754	+	13.6636i	0.547033	+	0.486130i
$791$			52.1750i			1.85513i
$792$	−2.02552	−	13.8359i	−0.0719737	−	0.491638i
$793$	11.2853	+	11.2853i	0.400754	+	0.400754i
$794$	−12.2072	+	3.91372i	−0.433217	+	0.138893i
$795$	−57.0165	−	14.6422i	−2.02217	−	0.519306i
$796$	0.922896	+	1.29135i	0.0327112	+	0.0457707i
$797$	−19.0703	+	19.0703i	−0.675506	+	0.675506i	−0.958980	−	0.283474i	$-0.908513\pi$
$797$	−19.0703	+	19.0703i	−0.675506	+	0.675506i	0.283474	+	0.958980i	$0.408513\pi$
$798$	21.3033	+	10.9596i	0.754128	+	0.387965i
$799$	−25.3020			−0.895119
$800$	27.3108	−	7.35664i	0.965583	−	0.260097i
$801$	−0.505069			−0.0178457
$802$	−24.5702	−	12.6402i	−0.867603	−	0.446342i
$803$	−12.2832	+	12.2832i	−0.433463	+	0.433463i
$804$	−27.4434	−	38.3998i	−0.967855	−	1.35426i
$805$	6.29440	+	1.61644i	0.221848	+	0.0569721i
$806$	−2.81853	+	0.903640i	−0.0992784	+	0.0318294i
$807$	−4.65049	−	4.65049i	−0.163705	−	0.163705i
$808$	−5.44415	−	37.1879i	−0.191525	−	1.30826i
$809$		−	31.7258i		−	1.11542i	−0.830036	−	0.557710i	$-0.811680\pi$
$809$		−	31.7258i		−	1.11542i	0.830036	−	0.557710i	$-0.188320\pi$
$810$	25.6573	+	22.8008i	0.901505	+	0.801138i
$811$			6.60070i			0.231782i	0.993262	+	0.115891i	$0.0369723\pi$
$811$			6.60070i			0.231782i	−0.993262	+	0.115891i	$0.963028\pi$
$812$	−18.9930	−	3.16047i	−0.666525	−	0.110911i
$813$	−23.1694	−	23.1694i	−0.812585	−	0.812585i
$814$	9.10780	+	28.4080i	0.319228	+	0.995699i
$815$	44.6046	−	26.3763i	1.56243	−	0.923921i
$816$	−17.1491	−	5.86980i	−0.600338	−	0.205484i
$817$	−16.1555	+	16.1555i	−0.565210	+	0.565210i
$818$	−6.36026	+	12.3631i	−0.222381	+	0.432266i
$819$	−5.55286			−0.194033
$820$	11.2190	+	28.9997i	0.391784	+	1.01271i
$821$	14.7620			0.515196			0.257598	−	0.966252i	$-0.417069\pi$
$821$	14.7620			0.515196			0.257598	+	0.966252i	$0.417069\pi$
$822$	3.13751	−	6.09871i	0.109433	−	0.212717i
$823$	−30.9399	+	30.9399i	−1.07850	+	1.07850i	−0.0818519	+	0.996645i	$0.526083\pi$
$823$	−30.9399	+	30.9399i	−1.07850	+	1.07850i	−0.996645	+	0.0818519i	$0.973917\pi$
$824$	30.8110	+	22.9418i	1.07335	+	0.799215i
$825$	−15.5732	−	53.6222i	−0.542190	−	1.86688i
$826$	8.40162	+	26.2053i	0.292330	+	0.911800i
$827$	38.9123	+	38.9123i	1.35311	+	1.35311i	0.882157	+	0.470955i	$0.156090\pi$
$827$	38.9123	+	38.9123i	1.35311	+	1.35311i	0.470955	+	0.882157i	$0.343910\pi$
$828$	−0.272817	+	1.63951i	−0.00948106	+	0.0569771i
$829$			46.5189i			1.61567i	0.589411	+	0.807834i	$0.299360\pi$
$829$			46.5189i			1.61567i	−0.589411	+	0.807834i	$0.700640\pi$
$830$	−7.01286	+	0.413391i	−0.243420	+	0.0143490i
$831$			25.9695i			0.900871i
$832$	14.7363	+	7.94880i	0.510888	+	0.275575i
$833$	3.71098	+	3.71098i	0.128578	+	0.128578i
$834$	34.3735	−	11.0204i	1.19026	−	0.381605i
$835$	−22.3631	−	37.8179i	−0.773906	−	1.30874i
$836$	−26.1062	+	18.6575i	−0.902901	+	0.645282i
$837$	2.96191	−	2.96191i	0.102378	−	0.102378i
$838$	18.0232	+	9.27212i	0.622601	+	0.320300i
$839$	35.5450			1.22715			0.613575	−	0.789637i	$-0.289731\pi$
$839$	35.5450			1.22715			0.613575	+	0.789637i	$0.289731\pi$
$840$	4.01071	−	37.6911i	0.138383	−	1.30047i
$841$	19.0114			0.655565
$842$	−34.6465	−	17.8240i	−1.19400	−	0.614257i
$843$	5.21062	−	5.21062i	0.179463	−	0.179463i
$844$	34.4913	−	24.6501i	1.18724	−	0.848491i
$845$	−4.79417	+	18.6684i	−0.164924	+	0.642213i
$846$	12.8860	−	4.13134i	0.443029	−	0.142038i
$847$	−45.7008	−	45.7008i	−1.57030	−	1.57030i
$848$	48.0622	−	23.5506i	1.65046	−	0.808729i
$849$		−	56.5736i		−	1.94160i
$850$	−15.9851	−	3.11562i	−0.548284	−	0.106865i
$851$		−	3.54585i		−	0.121550i
$852$	−0.399798	+	2.40261i	−0.0136969	+	0.0823121i
$853$	26.7387	+	26.7387i	0.915515	+	0.915515i	0.996699	−	0.0811842i	$-0.0258702\pi$
$853$	26.7387	+	26.7387i	0.915515	+	0.915515i	−0.0811842	+	0.996699i	$0.525870\pi$
$854$	10.0291	+	31.2815i	0.343188	+	1.07043i
$855$	−1.36933	+	5.33215i	−0.0468301	+	0.182356i
$856$	−18.4988	+	24.8440i	−0.632276	+	0.849151i
$857$	−33.3758	+	33.3758i	−1.14010	+	1.14010i	−0.151663	+	0.988432i	$0.548463\pi$
$857$	−33.3758	+	33.3758i	−1.14010	+	1.14010i	−0.988432	+	0.151663i	$0.951537\pi$
$858$	15.1212	−	29.3927i	0.516229	−	1.00345i
$859$	−43.6364			−1.48885			−0.744427	−	0.667704i	$-0.767277\pi$
$859$	−43.6364			−1.48885			−0.744427	+	0.667704i	$0.767277\pi$
$860$	33.0613	+	14.6164i	1.12738	+	0.498415i
$861$	41.6695			1.42009
$862$	−3.36804	+	6.54681i	−0.114716	+	0.222985i
$863$	−36.9144	+	36.9144i	−1.25658	+	1.25658i	−0.303867	+	0.952714i	$0.598278\pi$
$863$	−36.9144	+	36.9144i	−1.25658	+	1.25658i	−0.952714	+	0.303867i	$0.901722\pi$
$864$	−23.6907	−	0.462674i	−0.805975	−	0.0157405i
$865$	−1.05276	−	1.78031i	−0.0357948	−	0.0605322i
$866$	−0.608488	−	1.89792i	−0.0206773	−	0.0644940i
$867$	−16.2709	−	16.2709i	−0.552589	−	0.552589i
$868$	−6.00954	−	0.999996i	−0.203977	−	0.0339421i
$869$			36.9205i			1.25244i
$870$	−1.15712	−	19.6296i	−0.0392300	−	0.665506i
$871$		−	25.1037i		−	0.850608i
$872$	−21.9671	+	3.21589i	−0.743900	+	0.108904i
$873$	−7.71002	−	7.71002i	−0.260945	−	0.260945i
$874$	3.63186	−	1.16440i	0.122849	−	0.0393864i
$875$	−1.06494	−	34.0396i	−0.0360015	−	1.15075i
$876$	−7.00215	−	9.79766i	−0.236581	−	0.331032i
$877$	14.9606	−	14.9606i	0.505183	−	0.505183i	−0.407861	−	0.913044i	$-0.633725\pi$
$877$	14.9606	−	14.9606i	0.505183	−	0.505183i	0.913044	+	0.407861i	$0.133725\pi$
$878$	−19.7679	−	10.1697i	−0.667133	−	0.343210i
$879$	−39.5216			−1.33303
$880$	42.4335	+	27.8712i	1.43043	+	0.939539i
$881$	−1.69247			−0.0570207			−0.0285104	−	0.999593i	$-0.509076\pi$
$881$	−1.69247			−0.0570207			−0.0285104	+	0.999593i	$0.509076\pi$
$882$	−2.49589	−	1.28402i	−0.0840409	−	0.0432353i
$883$	7.69756	−	7.69756i	0.259043	−	0.259043i	−0.565622	−	0.824665i	$-0.691364\pi$
$883$	7.69756	−	7.69756i	0.259043	−	0.259043i	0.824665	+	0.565622i	$0.191364\pi$
$884$	−5.60558	−	7.84353i	−0.188536	−	0.263807i
$885$	−24.1914	+	14.3052i	−0.813184	+	0.480864i
$886$	5.69842	−	1.82696i	0.191442	−	0.0613778i
$887$	−2.89770	−	2.89770i	−0.0972951	−	0.0972951i	0.656784	−	0.754079i	$-0.271916\pi$
$887$	−2.89770	−	2.89770i	−0.0972951	−	0.0972951i	−0.754079	+	0.656784i	$0.771916\pi$
$888$	−20.4634	+	2.99575i	−0.686705	+	0.100531i
$889$		−	53.0711i		−	1.77995i
$890$	1.21808	−	1.37068i	0.0408301	−	0.0459453i
$891$			61.6100i			2.06401i
$892$	8.81460	+	1.46676i	0.295134	+	0.0491108i
$893$	−21.9572	−	21.9572i	−0.734771	−	0.734771i
$894$	11.0536	+	34.4770i	0.369688	+	1.15309i
$895$	−9.01709	−	2.31565i	−0.301408	−	0.0774035i
$896$	19.4869	+	28.4241i	0.651011	+	0.949582i
$897$	−2.77809	+	2.77809i	−0.0927576	+	0.0927576i
$898$	9.46347	−	18.3951i	0.315800	−	0.613854i
$899$	−3.16048			−0.105408
$900$	8.64973	−	1.02332i	0.288324	−	0.0341106i
$901$	−30.8176			−1.02668
$902$	−25.5320	+	49.6293i	−0.850123	+	1.65247i
$903$	34.2539	−	34.2539i	1.13990	−	1.13990i
$904$	28.9336	−	38.8580i	0.962317	−	1.29240i
$905$	13.3009	+	3.41577i	0.442138	+	0.113544i
$906$	6.53446	+	20.3815i	0.217093	+	0.677130i
$907$	−1.62736	−	1.62736i	−0.0540355	−	0.0540355i	0.679573	−	0.733608i	$-0.262165\pi$
$907$	−1.62736	−	1.62736i	−0.0540355	−	0.0540355i	−0.733608	+	0.679573i	$0.762165\pi$
$908$	−2.04420	+	12.2848i	−0.0678393	+	0.407685i
$909$		−	11.5740i		−	0.383884i
$910$	13.3919	−	15.0696i	0.443936	−	0.499553i
$911$		−	11.1451i		−	0.369252i	−0.982809	−	0.184626i	$-0.940893\pi$
$911$		−	11.1451i		−	0.369252i	0.982809	−	0.184626i	$-0.0591074\pi$
$912$	−9.78826	−	19.9760i	−0.324122	−	0.661471i
$913$	−8.91621	−	8.91621i	−0.295083	−	0.295083i
$914$	50.5327	−	16.2012i	1.67147	−	0.535886i
$915$	−28.8774	+	17.0762i	−0.954657	+	0.564522i
$916$	42.4009	−	30.3029i	1.40097	−	1.00124i
$917$	−8.24906	+	8.24906i	−0.272408	+	0.272408i
$918$	12.1322	+	6.24148i	0.400423	+	0.205999i
$919$	42.7874			1.41143			0.705713	−	0.708498i	$-0.250627\pi$
$919$	42.7874			1.41143			0.705713	+	0.708498i	$0.250627\pi$
$920$	−3.79144	−	4.69442i	−0.125000	−	0.154770i
$921$	−1.62822			−0.0536517
$922$	−2.01305	−	1.03563i	−0.0662964	−	0.0341065i
$923$	−0.916033	+	0.916033i	−0.0301516	+	0.0301516i
$924$	55.3519	−	39.5587i	1.82095	−	1.30139i
$925$	−17.8448	+	5.18257i	−0.586732	+	0.170402i
$926$	3.11636	−	0.999127i	0.102410	−	0.0328333i
$927$	8.36472	+	8.36472i	0.274733	+	0.274733i
$928$	12.3927	+	12.8864i	0.406809	+	0.423015i
$929$			5.85612i			0.192133i	0.995375	+	0.0960666i	$0.0306262\pi$
$929$			5.85612i			0.192133i	−0.995375	+	0.0960666i	$0.969374\pi$
$930$	−0.366121	−	6.21096i	−0.0120056	−	0.203665i
$931$			6.44083i			0.211090i
$932$	−7.58955	+	45.6099i	−0.248604	+	1.49400i
$933$	−32.2409	−	32.2409i	−1.05552	−	1.05552i
$934$	−4.48604	−	13.9923i	−0.146788	−	0.457843i
$935$	−14.8791	−	25.1619i	−0.486598	−	0.822881i
$936$	4.13556	+	3.07933i	0.135175	+	0.100651i
$937$	17.1554	−	17.1554i	0.560441	−	0.560441i	−0.368992	−	0.929433i	$-0.620297\pi$
$937$	17.1554	−	17.1554i	0.560441	−	0.560441i	0.929433	+	0.368992i	$0.120297\pi$
$938$	23.6375	−	45.9468i	0.771793	−	1.50022i
$939$	−19.3534			−0.631574
$940$	−19.8654	+	44.9342i	−0.647938	+	1.46559i
$941$	15.5488			0.506876			0.253438	−	0.967352i	$-0.418439\pi$
$941$	15.5488			0.506876			0.253438	+	0.967352i	$0.418439\pi$
$942$	7.78686	−	15.1361i	0.253710	−	0.493162i
$943$	4.69077	−	4.69077i	0.152753	−	0.152753i
$944$	8.27491	−	24.1758i	0.269326	−	0.786857i
$945$	−7.09662	+	27.6341i	−0.230853	+	0.898938i
$946$	19.8089	+	61.7855i	0.644042	+	2.00882i
$947$	22.0958	+	22.0958i	0.718017	+	0.718017i	0.968199	−	0.250182i	$-0.0804904\pi$
$947$	22.0958	+	22.0958i	0.718017	+	0.718017i	−0.250182	+	0.968199i	$0.580490\pi$
$948$	−25.2483	−	4.20135i	−0.820026	−	0.136453i
$949$		−	6.40518i		−	0.207921i
$950$	−11.1682	−	16.5757i	−0.362345	−	0.537788i
$951$			34.6590i			1.12389i
$952$	−2.87434	−	19.6340i	−0.0931578	−	0.636342i
$953$	32.7224	+	32.7224i	1.05998	+	1.05998i	0.998082	+	0.0619005i	$0.0197162\pi$
$953$	32.7224	+	32.7224i	1.05998	+	1.05998i	0.0619005	+	0.998082i	$0.480284\pi$
$954$	15.6950	−	5.03194i	0.508145	−	0.162915i
$955$	−3.76169	+	14.6480i	−0.121726	+	0.473997i
$956$	−22.7580	−	31.8439i	−0.736048	−	1.02990i
$957$	24.9572	−	24.9572i	0.806753	−	0.806753i
$958$	−19.0537	−	9.80224i	−0.615596	−	0.316696i
$959$	7.50828			0.242455
$960$	−23.8886	+	25.8468i	−0.771001	+	0.834202i
$961$	−1.00000			−0.0322581
$962$	−9.78150	−	5.03214i	−0.315368	−	0.162243i
$963$	−6.74477	+	6.74477i	−0.217347	+	0.217347i
$964$	−28.7390	−	40.2126i	−0.925619	−	1.29516i
$965$	−0.704054	−	1.19062i	−0.0226643	−	0.0383273i
$966$	−7.70049	+	2.46883i	−0.247759	+	0.0794334i
$967$	−5.60005	−	5.60005i	−0.180085	−	0.180085i	0.611308	−	0.791393i	$-0.290644\pi$
$967$	−5.60005	−	5.60005i	−0.180085	−	0.180085i	−0.791393	+	0.611308i	$0.790644\pi$
$968$	8.69291	+	59.3795i	0.279401	+	1.90853i
$969$			12.8086i			0.411473i
$970$	39.5181	−	2.32950i	1.26885	−	0.0747957i
$971$		−	56.7400i		−	1.82087i	−0.413649	−	0.910436i	$-0.635746\pi$
$971$		−	56.7400i		−	1.82087i	0.413649	−	0.910436i	$-0.364254\pi$
$972$	−17.3406	−	2.88550i	−0.556200	−	0.0925524i
$973$	27.9428	+	27.9428i	0.895806	+	0.895806i
$974$	4.27464	+	13.3330i	0.136968	+	0.427216i
$975$	18.0413	+	9.92052i	0.577785	+	0.317711i
$976$	9.87782	−	28.8589i	0.316181	−	0.923749i
$977$	2.99327	−	2.99327i	0.0957631	−	0.0957631i	−0.657602	−	0.753365i	$-0.728429\pi$
$977$	2.99327	−	2.99327i	0.0957631	−	0.0957631i	0.753365	+	0.657602i	$0.228429\pi$
$978$	−29.4983	+	57.3389i	−0.943251	+	1.83350i
$979$	3.29137			0.105193
$980$	9.50399	−	3.67678i	0.303594	−	0.117450i
$981$	−6.83680			−0.218282
$982$	0.841427	−	1.63557i	0.0268510	−	0.0521931i
$983$	−26.2745	+	26.2745i	−0.838027	+	0.838027i	−0.988599	−	0.150572i	$-0.951888\pi$
$983$	−26.2745	+	26.2745i	−0.838027	+	0.838027i	0.150572	+	0.988599i	$0.451888\pi$
$984$	−31.0339	−	23.1077i	−0.989323	−	0.736648i
$985$	45.2473	−	26.7563i	1.44170	−	0.852527i
$986$	−3.14283	−	9.80275i	−0.100088	−	0.312183i
$987$	46.5551	+	46.5551i	1.48187	+	1.48187i
$988$	1.94211	−	11.6712i	0.0617868	−	0.371312i
$989$		−	7.71199i		−	0.245227i
$990$	11.6862	+	10.3852i	0.371412	+	0.330062i
$991$		−	54.1088i		−	1.71882i	−0.511285	−	0.859411i	$-0.670830\pi$
$991$		−	54.1088i		−	1.71882i	0.511285	−	0.859411i	$-0.329170\pi$
$992$	3.92113	+	4.07734i	0.124496	+	0.129456i
$993$	−9.91709	−	9.91709i	−0.314709	−	0.314709i
$994$	−2.53912	+	0.814062i	−0.0805361	+	0.0258205i
$995$	−1.71881	−	0.441402i	−0.0544900	−	0.0139934i
$996$	7.11201	−	5.08278i	0.225353	−	0.161054i
$997$	35.4706	−	35.4706i	1.12336	−	1.12336i	0.132132	−	0.991232i	$-0.457818\pi$
$997$	35.4706	−	35.4706i	1.12336	−	1.12336i	0.991232	−	0.132132i	$-0.0421823\pi$
$998$	−13.4021	−	6.89478i	−0.424237	−	0.218250i
$999$	15.5672			0.492525

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	620.2.k.d.63.6	yes	88
4.3	odd	2		620.2.k.c.63.28	✓	88
5.2	odd	4		620.2.k.c.187.28	yes	88
20.7	even	4	inner	620.2.k.d.187.6	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
620.2.k.c.63.28	✓	88	4.3	odd	2
620.2.k.c.187.28	yes	88	5.2	odd	4
620.2.k.d.63.6	yes	88	1.1	even	1	trivial
620.2.k.d.187.6	yes	88	20.7	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:	\( N \)	\(=\)	\( 620 = 2^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	620.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25756 - 0.646956i) q^{2} +(-1.39122 + 1.39122i) q^{3} +(1.16290 + 1.62717i) q^{4} +(-2.16579 - 0.556189i) q^{5} +(2.64960 - 0.849482i) q^{6} +(2.15391 + 2.15391i) q^{7} +(-0.409703 - 2.79860i) q^{8} -0.871005i q^{9} +(2.36378 + 2.10061i) q^{10} +5.67605i q^{11} +(-3.88160 - 0.645904i) q^{12} +(-1.47992 - 1.47992i) q^{13} +(-1.31518 - 4.10215i) q^{14} +(3.78688 - 2.23932i) q^{15} +(-1.29534 + 3.78445i) q^{16} +(1.62859 - 1.62859i) q^{17} +(-0.563502 + 1.09534i) q^{18} +2.82660 q^{19} +(-1.61358 - 4.17089i) q^{20} -5.99314 q^{21} +(3.67216 - 7.13796i) q^{22} +(-0.674653 + 0.674653i) q^{23} +(4.46346 + 3.32348i) q^{24} +(4.38131 + 2.40918i) q^{25} +(0.903640 + 2.81853i) q^{26} +(-2.96191 - 2.96191i) q^{27} +(-0.999996 + 6.00954i) q^{28} +3.16048i q^{29} +(-6.21096 + 0.366121i) q^{30} +1.00000i q^{31} +(4.07734 - 3.92113i) q^{32} +(-7.89666 - 7.89666i) q^{33} +(-3.10167 + 0.994417i) q^{34} +(-3.46694 - 5.86290i) q^{35} +(1.41727 - 1.01289i) q^{36} +(-2.62791 + 2.62791i) q^{37} +(-3.55461 - 1.82869i) q^{38} +4.11780 q^{39} +(-0.669218 + 6.28905i) q^{40} -6.95287 q^{41} +(7.53671 + 3.87729i) q^{42} +(-5.71552 + 5.71552i) q^{43} +(-9.23589 + 6.60066i) q^{44} +(-0.484444 + 1.88642i) q^{45} +(1.28488 - 0.411944i) q^{46} +(-7.76807 - 7.76807i) q^{47} +(-3.46291 - 7.06713i) q^{48} +2.27865i q^{49} +(-3.95111 - 5.86419i) q^{50} +4.53146i q^{51} +(0.687083 - 4.12907i) q^{52} +(-9.46144 - 9.46144i) q^{53} +(1.80854 + 5.64099i) q^{54} +(3.15696 - 12.2932i) q^{55} +(5.14546 - 6.91038i) q^{56} +(-3.93244 + 3.93244i) q^{57} +(2.04469 - 3.97448i) q^{58} -6.38820 q^{59} +(8.04750 + 3.55780i) q^{60} -7.62563 q^{61} +(0.646956 - 1.25756i) q^{62} +(1.87607 - 1.87607i) q^{63} +(-7.66429 + 2.29319i) q^{64} +(2.38208 + 4.02831i) q^{65} +(4.82171 + 15.0393i) q^{66} +(8.48145 + 8.48145i) q^{67} +(4.54386 + 0.756105i) q^{68} -1.87719i q^{69} +(0.566833 + 9.61588i) q^{70} -0.618974i q^{71} +(-2.43759 + 0.356853i) q^{72} +(2.16403 + 2.16403i) q^{73} +(5.00488 - 1.60460i) q^{74} +(-9.44708 + 2.74367i) q^{75} +(3.28705 + 4.59935i) q^{76} +(-12.2257 + 12.2257i) q^{77} +(-5.17837 - 2.66403i) q^{78} +6.50460 q^{79} +(4.91032 - 7.47588i) q^{80} +10.8544 q^{81} +(8.74362 + 4.49820i) q^{82} +(-1.57085 + 1.57085i) q^{83} +(-6.96940 - 9.75183i) q^{84} +(-4.43299 + 2.62138i) q^{85} +(10.8853 - 3.48990i) q^{86} +(-4.39693 - 4.39693i) q^{87} +(15.8850 - 2.32550i) q^{88} -0.579869i q^{89} +(1.82964 - 2.05886i) q^{90} -6.37523i q^{91} +(-1.88232 - 0.313221i) q^{92} +(-1.39122 - 1.39122i) q^{93} +(4.74319 + 14.7944i) q^{94} +(-6.12183 - 1.57213i) q^{95} +(-0.217320 + 11.1277i) q^{96} +(8.85186 - 8.85186i) q^{97} +(1.47418 - 2.86553i) q^{98} +4.94387 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 2 q^{2} + 2 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{8} - 10 q^{10} - 12 q^{12} - 6 q^{13} + 22 q^{14} - 2 q^{15} + 8 q^{16} - 2 q^{17} - 24 q^{18} + 8 q^{19} + 8 q^{20} - 16 q^{21} - 16 q^{22} + 10 q^{23}+ \cdots - 8 q^{99}+O(q^{100}) \) 88 * q + 2 * q^2 + 2 * q^3 - 2 * q^5 + 4 * q^7 - 4 * q^8 - 10 * q^10 - 12 * q^12 - 6 * q^13 + 22 * q^14 - 2 * q^15 + 8 * q^16 - 2 * q^17 - 24 * q^18 + 8 * q^19 + 8 * q^20 - 16 * q^21 - 16 * q^22 + 10 * q^23 - 44 * q^24 - 4 * q^25 - 8 * q^26 + 8 * q^27 + 46 * q^28 + 16 * q^30 - 8 * q^32 - 8 * q^33 + 40 * q^34 - 12 * q^35 - 20 * q^36 + 10 * q^37 - 64 * q^38 + 8 * q^39 + 8 * q^41 + 28 * q^42 + 10 * q^43 - 16 * q^44 + 6 * q^45 - 24 * q^46 - 64 * q^47 + 88 * q^48 - 14 * q^50 + 20 * q^52 + 18 * q^53 + 36 * q^54 + 40 * q^55 - 24 * q^56 - 24 * q^57 - 52 * q^58 - 32 * q^60 + 20 * q^61 + 2 * q^62 - 4 * q^63 - 150 * q^64 - 18 * q^65 + 8 * q^66 + 116 * q^67 + 68 * q^68 - 6 * q^70 - 26 * q^72 + 38 * q^73 + 36 * q^74 - 70 * q^75 - 8 * q^76 + 40 * q^77 - 152 * q^78 + 32 * q^79 + 68 * q^80 - 60 * q^81 + 14 * q^82 - 14 * q^83 - 120 * q^84 + 6 * q^85 + 4 * q^86 - 44 * q^87 + 52 * q^88 - 68 * q^90 - 92 * q^92 + 2 * q^93 + 112 * q^94 + 104 * q^95 - 20 * q^96 + 16 * q^97 - 62 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more