LMFDB - Embedded newform 700.2.bj.a.323.44

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(127,700)] 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("700.127"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$90$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			323.44
Character	$\chi$	$=$	700.323
Dual form			700.2.bj.a.687.44

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0542309 + 1.41317i) q^{2} +(0.700808 + 1.37541i) q^{3} +(-1.99412 - 0.153275i) q^{4} +(0.861206 - 2.06357i) q^{5} +(-1.98170 + 0.915773i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.324747 - 2.80972i) q^{8} +(0.362727 - 0.499251i) q^{9} +(2.86948 + 1.32894i) q^{10} +(-0.460480 - 0.633796i) q^{11} +(-1.18668 - 2.85015i) q^{12} +(0.683366 + 4.31460i) q^{13} +(-1.03761 + 0.960917i) q^{14} +(3.44180 - 0.261653i) q^{15} +(3.95301 + 0.611298i) q^{16} +(2.27386 + 1.15859i) q^{17} +(0.685857 + 0.539671i) q^{18} +(2.34307 + 7.21123i) q^{19} +(-2.03364 + 3.98300i) q^{20} +(-0.477018 + 1.46811i) q^{21} +(0.920635 - 0.616366i) q^{22} +(-1.03667 + 6.54529i) q^{23} +(4.09211 - 1.52241i) q^{24} +(-3.51665 - 3.55432i) q^{25} +(-6.13434 + 0.731729i) q^{26} +(5.51485 + 0.873466i) q^{27} +(-1.30167 - 1.51844i) q^{28} +(-4.49990 - 1.46211i) q^{29} +(0.183108 + 4.87805i) q^{30} +(4.02459 - 1.30767i) q^{31} +(-1.07825 + 5.55314i) q^{32} +(0.549023 - 1.07752i) q^{33} +(-1.76060 + 3.15052i) q^{34} +(2.06813 - 0.850200i) q^{35} +(-0.799843 + 0.939968i) q^{36} +(6.40412 - 1.01431i) q^{37} +(-10.3178 + 2.92009i) q^{38} +(-5.45545 + 3.96362i) q^{39} +(-5.51839 - 3.08989i) q^{40} +(-5.06229 - 3.67797i) q^{41} +(-2.04882 - 0.753726i) q^{42} +(3.22208 - 3.22208i) q^{43} +(0.821105 + 1.33444i) q^{44} +(-0.717857 - 1.17847i) q^{45} +(-9.19342 - 1.81996i) q^{46} +(4.56461 - 2.32578i) q^{47} +(1.92952 + 5.86543i) q^{48} +1.00000i q^{49} +(5.21358 - 4.77688i) q^{50} +3.93944i q^{51} +(-0.701390 - 8.70857i) q^{52} +(3.28279 - 1.67266i) q^{53} +(-1.53343 + 7.74607i) q^{54} +(-1.70445 + 0.404403i) q^{55} +(2.21640 - 1.75714i) q^{56} +(-8.27637 + 8.27637i) q^{57} +(2.31024 - 6.27984i) q^{58} +(1.50129 + 1.09075i) q^{59} +(-6.90346 - 0.00577712i) q^{60} +(1.54026 - 1.11907i) q^{61} +(1.62970 + 5.75835i) q^{62} +(0.609510 - 0.0965369i) q^{63} +(-7.78908 - 1.82490i) q^{64} +(9.49200 + 2.30559i) q^{65} +(1.49295 + 0.834300i) q^{66} +(1.82622 - 3.58416i) q^{67} +(-4.35675 - 2.65889i) q^{68} +(-9.72899 + 3.16114i) q^{69} +(1.08932 + 2.96873i) q^{70} +(-3.85061 - 1.25114i) q^{71} +(-1.28496 - 1.18129i) q^{72} +(-5.29495 - 0.838637i) q^{73} +(1.08610 + 9.10514i) q^{74} +(2.42416 - 7.32774i) q^{75} +(-3.56706 - 14.7392i) q^{76} +(0.122553 - 0.773769i) q^{77} +(-5.30542 - 7.92445i) q^{78} +(-2.14212 + 6.59276i) q^{79} +(4.66582 - 7.63087i) q^{80} +(2.09138 + 6.43661i) q^{81} +(5.47214 - 6.95443i) q^{82} +(-12.3604 - 6.29793i) q^{83} +(1.17625 - 2.85447i) q^{84} +(4.34908 - 3.69448i) q^{85} +(4.37862 + 4.72809i) q^{86} +(-1.14257 - 7.21387i) q^{87} +(-1.93033 + 1.08800i) q^{88} +(-10.0422 - 13.8219i) q^{89} +(1.70431 - 0.950546i) q^{90} +(-2.56767 + 3.53410i) q^{91} +(3.07048 - 12.8932i) q^{92} +(4.61904 + 4.61904i) q^{93} +(3.03919 + 6.57671i) q^{94} +(16.8987 + 1.37526i) q^{95} +(-8.39351 + 2.40865i) q^{96} +(-2.21821 - 4.35347i) q^{97} +(-1.41317 - 0.0542309i) q^{98} -0.483451 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q + 16 q^{10} + 16 q^{12} + 4 q^{13} + 20 q^{17} - 28 q^{18} - 20 q^{20} - 4 q^{22} + 20 q^{25} + 4 q^{30} - 20 q^{37} - 64 q^{40} - 80 q^{42} - 140 q^{44} - 20 q^{45} - 236 q^{48} - 40 q^{50} - 16 q^{52}+ \cdots - 20 q^{97}+O(q^{100}) $ 720 * q + 16 * q^10 + 16 * q^12 + 4 * q^13 + 20 * q^17 - 28 * q^18 - 20 * q^20 - 4 * q^22 + 20 * q^25 + 4 * q^30 - 20 * q^37 - 64 * q^40 - 80 * q^42 - 140 * q^44 - 20 * q^45 - 236 * q^48 - 40 * q^50 - 16 * q^52 + 44 * q^53 - 260 * q^54 + 16 * q^57 - 136 * q^58 - 140 * q^60 - 140 * q^62 - 4 * q^65 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 76 * q^78 + 20 * q^80 + 180 * q^81 + 24 * q^82 - 80 * q^85 + 160 * q^88 - 260 * q^89 + 16 * q^90 + 256 * q^92 - 112 * q^93 + 320 * q^94 - 40 * q^96 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	−0.0542309	+	1.41317i	−0.0383470	+	0.999264i
$2$	−0.0542309	+	1.41317i	−0.0383470	+	0.999264i
$3$	0.700808	+	1.37541i	0.404612	+	0.794095i	0.999956	−	0.00937562i	$-0.00298440\pi$
$3$	0.700808	+	1.37541i	0.404612	+	0.794095i	−0.595344	+	0.803471i	$0.702984\pi$
$4$	−1.99412	−	0.153275i	−0.997059	−	0.0766376i
$5$	0.861206	−	2.06357i	0.385143	−	0.922857i
$5$	0.861206	−	2.06357i	0.385143	−	0.922857i
$6$	−1.98170	+	0.915773i	−0.809027	+	0.373863i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	0.324747	−	2.80972i	0.114816	−	0.993387i
$9$	0.362727	−	0.499251i	0.120909	−	0.166417i
$10$	2.86948	+	1.32894i	0.907409	+	0.420249i
$11$	−0.460480	−	0.633796i	−0.138840	−	0.191097i	0.733935	−	0.679220i	$-0.237682\pi$
$11$	−0.460480	−	0.633796i	−0.138840	−	0.191097i	−0.872775	+	0.488123i	$0.837682\pi$
$12$	−1.18668	−	2.85015i	−0.342564	−	0.822768i
$13$	0.683366	+	4.31460i	0.189532	+	1.19665i	0.880598	+	0.473864i	$0.157141\pi$
$13$	0.683366	+	4.31460i	0.189532	+	1.19665i	−0.691067	+	0.722791i	$0.742859\pi$
$14$	−1.03761	+	0.960917i	−0.277313	+	0.256816i
$15$	3.44180	−	0.261653i	0.888669	−	0.0675584i
$16$	3.95301	+	0.611298i	0.988253	+	0.152824i
$17$	2.27386	+	1.15859i	0.551491	+	0.280999i	0.707448	−	0.706765i	$-0.249846\pi$
$17$	2.27386	+	1.15859i	0.551491	+	0.280999i	−0.155957	+	0.987764i	$0.549846\pi$
$18$	0.685857	+	0.539671i	0.161658	+	0.127202i
$19$	2.34307	+	7.21123i	0.537537	+	1.65437i	0.738102	+	0.674689i	$0.235722\pi$
$19$	2.34307	+	7.21123i	0.537537	+	1.65437i	−0.200565	+	0.979680i	$0.564278\pi$
$20$	−2.03364	+	3.98300i	−0.454736	+	0.890626i
$21$	−0.477018	+	1.46811i	−0.104094	+	0.320368i
$22$	0.920635	−	0.616366i	0.196280	−	0.131410i
$23$	−1.03667	+	6.54529i	−0.216161	+	1.36479i	0.605969	+	0.795488i	$0.292786\pi$
$23$	−1.03667	+	6.54529i	−0.216161	+	1.36479i	−0.822130	+	0.569300i	$0.807214\pi$
$24$	4.09211	−	1.52241i	0.835299	−	0.310761i
$25$	−3.51665	−	3.55432i	−0.703330	−	0.710864i
$26$	−6.13434	+	0.731729i	−1.20304	+	0.143504i
$27$	5.51485	+	0.873466i	1.06133	+	0.168099i
$28$	−1.30167	−	1.51844i	−0.245993	−	0.286958i
$29$	−4.49990	−	1.46211i	−0.835610	−	0.271506i	−0.140203	−	0.990123i	$-0.544776\pi$
$29$	−4.49990	−	1.46211i	−0.835610	−	0.271506i	−0.695407	+	0.718617i	$0.744776\pi$
$30$	0.183108	+	4.87805i	0.0334309	+	0.890606i
$31$	4.02459	−	1.30767i	0.722837	−	0.234864i	0.0755843	−	0.997139i	$-0.475918\pi$
$31$	4.02459	−	1.30767i	0.722837	−	0.234864i	0.647253	+	0.762275i	$0.275918\pi$
$32$	−1.07825	+	5.55314i	−0.190609	+	0.981666i
$33$	0.549023	−	1.07752i	0.0955726	−	0.187572i
$34$	−1.76060	+	3.15052i	−0.301940	+	0.540310i
$35$	2.06813	−	0.850200i	0.349578	−	0.143710i
$36$	−0.799843	+	0.939968i	−0.133307	+	0.156661i
$37$	6.40412	−	1.01431i	1.05283	−	0.166752i	0.394051	−	0.919088i	$-0.371073\pi$
$37$	6.40412	−	1.01431i	1.05283	−	0.166752i	0.658779	+	0.752336i	$0.271073\pi$
$38$	−10.3178	+	2.92009i	−1.67377	+	0.473702i
$39$	−5.45545	+	3.96362i	−0.873571	+	0.634686i
$40$	−5.51839	−	3.08989i	−0.872533	−	0.488554i
$41$	−5.06229	−	3.67797i	−0.790596	−	0.574402i	0.117544	−	0.993068i	$-0.462498\pi$
$41$	−5.06229	−	3.67797i	−0.790596	−	0.574402i	−0.908140	+	0.418666i	$0.862498\pi$
$42$	−2.04882	−	0.753726i	−0.316140	−	0.116302i
$43$	3.22208	−	3.22208i	0.491362	−	0.491362i	−0.417373	−	0.908735i	$-0.637049\pi$
$43$	3.22208	−	3.22208i	0.491362	−	0.491362i	0.908735	+	0.417373i	$0.137049\pi$
$44$	0.821105	+	1.33444i	0.123786	+	0.201175i
$45$	−0.717857	−	1.17847i	−0.107012	−	0.175676i
$46$	−9.19342	−	1.81996i	−1.35550	−	0.268338i
$47$	4.56461	−	2.32578i	0.665816	−	0.339250i	−0.0882032	−	0.996103i	$-0.528112\pi$
$47$	4.56461	−	2.32578i	0.665816	−	0.339250i	0.754019	+	0.656852i	$0.228112\pi$
$48$	1.92952	+	5.86543i	0.278502	+	0.846602i
$49$			1.00000i			0.142857i
$50$	5.21358	−	4.77688i	0.737312	−	0.675553i
$51$			3.93944i			0.551632i
$52$	−0.701390	−	8.70857i	−0.0972653	−	1.20766i
$53$	3.28279	−	1.67266i	0.450925	−	0.229758i	−0.213753	−	0.976888i	$-0.568569\pi$
$53$	3.28279	−	1.67266i	0.450925	−	0.229758i	0.664678	+	0.747130i	$0.268569\pi$
$54$	−1.53343	+	7.74607i	−0.208674	+	1.05411i
$55$	−1.70445	+	0.404403i	−0.229828	+	0.0545297i
$56$	2.21640	−	1.75714i	0.296180	−	0.234808i
$57$	−8.27637	+	8.27637i	−1.09623	+	1.09623i
$58$	2.31024	−	6.27984i	0.303350	−	0.824584i
$59$	1.50129	+	1.09075i	0.195451	+	0.142003i	0.681207	−	0.732091i	$-0.261456\pi$
$59$	1.50129	+	1.09075i	0.195451	+	0.142003i	−0.485756	+	0.874095i	$0.661456\pi$
$60$	−6.90346	−	0.00577712i	−0.891233	−	0.000745823i
$61$	1.54026	−	1.11907i	0.197210	−	0.143282i	−0.484798	−	0.874626i	$-0.661107\pi$
$61$	1.54026	−	1.11907i	0.197210	−	0.143282i	0.682008	+	0.731345i	$0.261107\pi$
$62$	1.62970	+	5.75835i	0.206973	+	0.731312i
$63$	0.609510	−	0.0965369i	0.0767911	−	0.0121625i
$64$	−7.78908	−	1.82490i	−0.973635	−	0.228112i
$65$	9.49200	+	2.30559i	1.17734	+	0.285973i
$66$	1.49295	+	0.834300i	0.183769	+	0.102695i
$67$	1.82622	−	3.58416i	0.223109	−	0.437875i	−0.752135	−	0.659009i	$-0.770976\pi$
$67$	1.82622	−	3.58416i	0.223109	−	0.437875i	0.975243	+	0.221134i	$0.0709758\pi$
$68$	−4.35675	−	2.65889i	−0.528334	−	0.322437i
$69$	−9.72899	+	3.16114i	−1.17123	+	0.380557i
$70$	1.08932	+	2.96873i	0.130199	+	0.354831i
$71$	−3.85061	−	1.25114i	−0.456984	−	0.148483i	0.0714743	−	0.997442i	$-0.477230\pi$
$71$	−3.85061	−	1.25114i	−0.456984	−	0.148483i	−0.528458	+	0.848959i	$0.677230\pi$
$72$	−1.28496	−	1.18129i	−0.151434	−	0.139217i
$73$	−5.29495	−	0.838637i	−0.619727	−	0.0981551i	−0.161327	−	0.986901i	$-0.551577\pi$
$73$	−5.29495	−	0.838637i	−0.619727	−	0.0981551i	−0.458400	+	0.888746i	$0.651577\pi$
$74$	1.08610	+	9.10514i	0.126256	+	1.05845i
$75$	2.42416	−	7.32774i	0.279918	−	0.846134i
$76$	−3.56706	−	14.7392i	−0.409169	−	1.69070i
$77$	0.122553	−	0.773769i	0.0139662	−	0.0881792i
$78$	−5.30542	−	7.92445i	−0.600721	−	0.897267i
$79$	−2.14212	+	6.59276i	−0.241007	+	0.741743i	0.755261	+	0.655425i	$0.227510\pi$
$79$	−2.14212	+	6.59276i	−0.241007	+	0.741743i	−0.996268	+	0.0863187i	$0.972490\pi$
$80$	4.66582	−	7.63087i	0.521654	−	0.853157i
$81$	2.09138	+	6.43661i	0.232376	+	0.715179i
$82$	5.47214	−	6.95443i	0.604296	−	0.767988i
$83$	−12.3604	−	6.29793i	−1.35673	−	0.691288i	−0.384022	−	0.923324i	$-0.625461\pi$
$83$	−12.3604	−	6.29793i	−1.35673	−	0.691288i	−0.972707	+	0.232036i	$0.925461\pi$
$84$	1.17625	−	2.85447i	0.128340	−	0.311448i
$85$	4.34908	−	3.69448i	0.471724	−	0.400723i
$86$	4.37862	+	4.72809i	0.472159	+	0.509843i
$87$	−1.14257	−	7.21387i	−0.122496	−	0.773408i
$88$	−1.93033	+	1.08800i	−0.205774	+	0.115981i
$89$	−10.0422	−	13.8219i	−1.06447	−	1.46512i	−0.875548	−	0.483131i	$-0.839500\pi$
$89$	−10.0422	−	13.8219i	−1.06447	−	1.46512i	−0.188925	−	0.981991i	$-0.560500\pi$
$90$	1.70431	−	0.950546i	0.179650	−	0.100196i
$91$	−2.56767	+	3.53410i	−0.269165	+	0.370474i
$92$	3.07048	−	12.8932i	0.320120	−	1.34421i
$93$	4.61904	+	4.61904i	0.478973	+	0.478973i
$94$	3.03919	+	6.57671i	0.313469	+	0.678336i
$95$	16.8987	+	1.37526i	1.73377	+	0.141099i
$96$	−8.39351	+	2.40865i	−0.856659	+	0.245832i
$97$	−2.21821	−	4.35347i	−0.225225	−	0.442028i	0.750548	−	0.660816i	$-0.229790\pi$
$97$	−2.21821	−	4.35347i	−0.225225	−	0.442028i	−0.975772	+	0.218788i	$0.929790\pi$
$98$	−1.41317	−	0.0542309i	−0.142752	−	0.00547815i
$99$	−0.483451			−0.0485887
$100$	6.46782	+	7.62675i	0.646782	+	0.762675i
$101$	6.61885			0.658601			0.329300	−	0.944225i	$-0.393187\pi$
$101$	6.61885			0.658601			0.329300	+	0.944225i	$0.393187\pi$
$102$	−5.56711	−	0.213639i	−0.551226	−	0.0211534i
$103$	4.26991	+	8.38017i	0.420727	+	0.825723i	0.999944	+	0.0105500i	$0.00335824\pi$
$103$	4.26991	+	8.38017i	0.420727	+	0.825723i	−0.579217	+	0.815173i	$0.696642\pi$
$104$	12.3448	−	0.518913i	1.21050	−	0.0508836i
$105$	2.61874	+	2.24871i	0.255563	+	0.219451i
$106$	2.18573	+	4.72986i	0.212297	+	0.459404i
$107$	−10.7670	−	10.7670i	−1.04088	−	1.04088i	−0.999128	−	0.0417555i	$-0.986705\pi$
$107$	−10.7670	−	10.7670i	−1.04088	−	1.04088i	−0.0417555	−	0.999128i	$-0.513295\pi$
$108$	−10.8634	−	2.58708i	−1.04533	−	0.248942i
$109$	−5.13278	+	7.06467i	−0.491631	+	0.676672i	−0.980688	−	0.195580i	$-0.937341\pi$
$109$	−5.13278	+	7.06467i	−0.491631	+	0.676672i	0.489057	+	0.872252i	$0.337341\pi$
$110$	−0.479058	−	2.43061i	−0.0456764	−	0.231750i
$111$	5.88315	+	8.09747i	0.558404	+	0.768578i
$112$	2.36295	+	3.22746i	0.223278	+	0.304966i
$113$	1.72707	+	10.9043i	0.162469	+	1.02579i	0.925312	+	0.379207i	$0.123803\pi$
$113$	1.72707	+	10.9043i	0.162469	+	1.02579i	−0.762843	+	0.646584i	$0.776197\pi$
$114$	−11.2471	−	12.1448i	−1.05339	−	1.13746i
$115$	12.6139	+	7.77609i	1.17625	+	0.725125i
$116$	8.74922	+	3.60533i	0.812345	+	0.334747i
$117$	2.40194	+	1.22385i	0.222060	+	0.113145i
$118$	−1.62283	+	2.06243i	−0.149394	+	0.189862i
$119$	0.788614	+	2.42710i	0.0722921	+	0.222492i
$120$	0.382545	−	9.75548i	0.0349214	−	0.890549i
$121$	3.20953	−	9.87792i	0.291776	−	0.897993i
$122$	1.49790	+	2.23735i	0.135614	+	0.202560i
$123$	1.51103	−	9.54028i	0.136245	−	0.860218i
$124$	−8.22593	+	1.99077i	−0.738711	+	0.178777i
$125$	−10.3631	+	4.19585i	−0.926908	+	0.375288i
$126$	0.103369	+	0.866579i	0.00920886	+	0.0772010i
$127$	−14.9474	−	2.36744i	−1.32637	−	0.210077i	−0.547260	−	0.836962i	$-0.684329\pi$
$127$	−14.9474	−	2.36744i	−1.32637	−	0.210077i	−0.779111	+	0.626886i	$0.784329\pi$
$128$	3.00131	−	10.9084i	0.265281	−	0.964171i
$129$	6.68975	+	2.17363i	0.588999	+	0.191377i
$130$	−3.77295	+	13.2888i	−0.330910	+	1.16551i
$131$	13.1960	−	4.28763i	1.15294	−	0.374612i	0.330688	−	0.943740i	$-0.392719\pi$
$131$	13.1960	−	4.28763i	1.15294	−	0.374612i	0.822249	+	0.569128i	$0.192719\pi$
$132$	−1.25997	+	2.06455i	−0.109667	+	0.179696i
$133$	−3.44231	+	6.75591i	−0.298486	+	0.585812i
$134$	4.96601	+	2.77514i	0.428998	+	0.239736i
$135$	6.55188	−	10.6280i	0.563896	−	0.914716i
$136$	3.99374	−	6.01265i	0.342460	−	0.515581i
$137$	16.1864	−	2.56368i	1.38290	−	0.219030i	0.579743	−	0.814799i	$-0.303153\pi$
$137$	16.1864	−	2.56368i	1.38290	−	0.219030i	0.803155	+	0.595770i	$0.203153\pi$
$138$	−3.93963	−	13.9202i	−0.335363	−	1.18496i
$139$	−12.3942	+	9.00490i	−1.05126	+	0.763786i	−0.972452	−	0.233104i	$-0.925112\pi$
$139$	−12.3942	+	9.00490i	−1.05126	+	0.763786i	−0.0788088	+	0.996890i	$0.525112\pi$
$140$	−4.25441	+	1.37841i	−0.359563	+	0.116497i
$141$	6.39782	+	4.64829i	0.538794	+	0.391457i
$142$	1.97690	−	5.37373i	0.165898	−	0.450954i
$143$	2.41990	−	2.41990i	0.202362	−	0.202362i
$144$	1.73906	−	1.75181i	0.144921	−	0.145984i
$145$	−6.89250	+	8.02668i	−0.572391	+	0.666580i
$146$	1.47229	−	7.43720i	0.121848	−	0.615507i
$147$	−1.37541	+	0.700808i	−0.113442	+	0.0578017i
$148$	−12.9260	+	1.04107i	−1.06251	+	0.0855751i
$149$			12.7299i			1.04287i	0.853291	+	0.521435i	$0.174603\pi$
$149$			12.7299i			1.04287i	−0.853291	+	0.521435i	$0.825397\pi$
$150$	10.2239	+	3.82315i	0.834778	+	0.312159i
$151$			18.0245i			1.46681i	0.679790	+	0.733407i	$0.262071\pi$
$151$			18.0245i			1.46681i	−0.679790	+	0.733407i	$0.737929\pi$
$152$	21.0225	−	4.24155i	1.70515	−	0.344035i
$153$	1.40321	−	0.714973i	0.113443	−	0.0578022i
$154$	1.08682	+	0.215151i	0.0875788	+	0.0173374i
$155$	0.767535	−	9.43119i	0.0616499	−	0.757531i
$156$	11.4863	−	7.06773i	0.919643	−	0.565871i
$157$	6.83067	−	6.83067i	0.545147	−	0.545147i	−0.379886	−	0.925033i	$-0.624037\pi$
$157$	6.83067	−	6.83067i	0.545147	−	0.545147i	0.925033	+	0.379886i	$0.124037\pi$
$158$	−9.20054	−	3.38471i	−0.731956	−	0.269273i
$159$	4.60120	+	3.34297i	0.364899	+	0.265115i
$160$	10.5307	+	7.00744i	0.832526	+	0.553986i
$161$	−5.36126	+	3.89518i	−0.422526	+	0.306983i
$162$	−9.20947	+	2.60642i	−0.723564	+	0.204780i
$163$	−0.318331	+	0.0504186i	−0.0249336	+	0.00394909i	−0.168889	−	0.985635i	$-0.554018\pi$
$163$	−0.318331	+	0.0504186i	−0.0249336	+	0.00394909i	0.143955	+	0.989584i	$0.454018\pi$
$164$	9.53105	+	8.11022i	0.744250	+	0.633302i
$165$	−1.75071	−	2.06091i	−0.136293	−	0.160442i
$166$	9.57039	−	17.1258i	0.742806	−	1.32922i
$167$	10.2193	−	20.0565i	0.790794	−	1.55202i	−0.0424403	−	0.999099i	$-0.513513\pi$
$167$	10.2193	−	20.0565i	0.790794	−	1.55202i	0.833234	−	0.552921i	$-0.186487\pi$
$168$	3.97007	+	1.81705i	0.306298	+	0.140189i
$169$	−5.78505	+	1.87968i	−0.445004	+	0.144591i
$170$	4.98508	+	6.34637i	0.382339	+	0.486744i
$171$	4.45011	+	1.44593i	0.340308	+	0.110573i
$172$	−6.91907	+	5.93134i	−0.527574	+	0.452260i
$173$	−0.912277	−	0.144490i	−0.0693591	−	0.0109854i	0.121658	−	0.992572i	$-0.461179\pi$
$173$	−0.912277	−	0.144490i	−0.0693591	−	0.0109854i	−0.191018	+	0.981587i	$0.561179\pi$
$174$	10.2564	−	1.22343i	0.777537	−	0.0927478i
$175$	0.0266379	−	4.99993i	0.00201364	−	0.377959i
$176$	−1.43284	−	2.78689i	−0.108005	−	0.210070i
$177$	−0.448116	+	2.82930i	−0.0336825	+	0.212663i
$178$	20.0774	−	13.4418i	1.50486	−	1.00751i
$179$	4.02350	−	12.3831i	0.300730	−	0.925553i	−0.680506	−	0.732743i	$-0.738240\pi$
$179$	4.02350	−	12.3831i	0.300730	−	0.925553i	0.981236	−	0.192810i	$-0.0617601\pi$
$180$	1.25086	+	2.46004i	0.0932336	+	0.183360i
$181$	−7.32162	−	22.5336i	−0.544211	−	1.67491i	−0.722857	−	0.690997i	$-0.757172\pi$
$181$	−7.32162	−	22.5336i	−0.544211	−	1.67491i	0.178646	−	0.983913i	$-0.442828\pi$
$182$	−4.85504	−	3.82022i	−0.359880	−	0.283174i
$183$	2.61861	+	1.33425i	0.193573	+	0.0986303i
$184$	18.0538	+	5.03833i	1.33094	+	0.371431i
$185$	3.42216	−	14.0889i	0.251602	−	1.03584i
$186$	−6.77801	+	6.27702i	−0.496987	+	0.460253i
$187$	−0.312756	−	1.97467i	−0.0228710	−	0.144402i
$188$	−9.45885	+	3.93824i	−0.689857	+	0.287226i
$189$	3.28195	+	4.51722i	0.238727	+	0.328579i
$190$	−2.85992	+	23.8063i	−0.207480	+	1.72709i
$191$	−4.46143	+	6.14063i	−0.322817	+	0.444320i	−0.939325	−	0.343029i	$-0.888547\pi$
$191$	−4.46143	+	6.14063i	−0.322817	+	0.444320i	0.616507	+	0.787349i	$0.288547\pi$
$192$	−2.94866	−	11.9921i	−0.212801	−	0.865455i
$193$	−13.8661	−	13.8661i	−0.998105	−	0.998105i	0.00189317	−	0.999998i	$-0.499397\pi$
$193$	−13.8661	−	13.8661i	−0.998105	−	0.998105i	−0.999998	+	0.00189317i	$0.999397\pi$
$194$	6.27251	−	2.89862i	0.450340	−	0.208108i
$195$	3.48093	+	14.6712i	0.249275	+	1.05063i
$196$	0.153275	−	1.99412i	0.0109482	−	0.142437i
$197$	−0.209748	−	0.411654i	−0.0149439	−	0.0293291i	0.883414	−	0.468594i	$-0.155239\pi$
$197$	−0.209748	−	0.411654i	−0.0149439	−	0.0293291i	−0.898358	+	0.439264i	$0.855239\pi$
$198$	0.0262180	−	0.683201i	0.00186323	−	0.0485529i
$199$	−8.69771			−0.616564			−0.308282	−	0.951295i	$-0.599754\pi$
$199$	−8.69771			−0.616564			−0.308282	+	0.951295i	$0.599754\pi$
$200$	−11.1287	+	8.72655i	−0.786916	+	0.617060i
$201$	6.20954			0.437987
$202$	−0.358946	+	9.35359i	−0.0252554	+	0.658116i
$203$	−2.14804	−	4.21577i	−0.150763	−	0.295889i
$204$	0.603818	−	7.85570i	0.0422757	−	0.550009i
$205$	−11.9494	+	7.27890i	−0.834583	+	0.508380i
$206$	−12.0742	+	5.57966i	−0.841249	+	0.388753i
$207$	2.89171	+	2.89171i	0.200988	+	0.200988i
$208$	0.0638467	+	17.4734i	0.00442697	+	1.21156i
$209$	3.49151	−	4.80565i	0.241513	−	0.332414i
$210$	−3.31983	+	3.57878i	−0.229090	+	0.246959i
$211$	0.125593	+	0.172865i	0.00864621	+	0.0119005i	0.813318	−	0.581819i	$-0.197659\pi$
$211$	0.125593	+	0.172865i	0.00864621	+	0.0119005i	−0.804672	+	0.593720i	$0.797659\pi$
$212$	−6.80264	+	2.83232i	−0.467207	+	0.194524i
$213$	−0.977706	−	6.17299i	−0.0669913	−	0.422966i
$214$	15.7995	−	14.6317i	1.08003	−	1.00020i
$215$	−3.87411	−	9.42386i	−0.264212	−	0.642702i
$216$	4.24513	−	15.2115i	0.288844	−	1.03501i
$217$	3.77047	+	1.92115i	0.255956	+	0.130416i
$218$	−9.70524	−	7.63663i	−0.657322	−	0.517218i
$219$	−2.55727	−	7.87046i	−0.172804	−	0.531837i
$220$	3.46086	−	0.545178i	0.233331	−	0.0367559i
$221$	−3.44497	+	10.6025i	−0.231734	+	0.713202i
$222$	−11.7622	+	7.87478i	−0.789425	+	0.528521i
$223$	−1.52735	+	9.64330i	−0.102279	+	0.645763i	0.882282	+	0.470721i	$0.156006\pi$
$223$	−1.52735	+	9.64330i	−0.102279	+	0.645763i	−0.984561	+	0.175042i	$0.943994\pi$
$224$	−4.68910	+	3.16423i	−0.313304	+	0.211419i
$225$	−3.05008	+	0.466442i	−0.203339	+	0.0310961i
$226$	−15.5033	+	1.84930i	−1.03127	+	0.123014i
$227$	−16.0643	−	2.54434i	−1.06623	−	0.168874i	−0.401424	−	0.915892i	$-0.631485\pi$
$227$	−16.0643	−	2.54434i	−1.06623	−	0.168874i	−0.664804	+	0.747018i	$0.731485\pi$
$228$	17.7726	−	15.2355i	1.17702	−	1.00900i
$229$	15.1516	+	4.92305i	1.00125	+	0.325324i	0.763363	−	0.645969i	$-0.223547\pi$
$229$	15.1516	+	4.92305i	1.00125	+	0.325324i	0.237882	+	0.971294i	$0.423547\pi$
$230$	−11.6730	+	17.4039i	−0.769697	+	1.14758i
$231$	1.15014	−	0.373703i	0.0756736	−	0.0245878i
$232$	−5.56944	+	12.1686i	−0.365652	+	0.798911i
$233$	5.29482	−	10.3917i	0.346875	−	0.680781i	−0.649986	−	0.759946i	$-0.725225\pi$
$233$	5.29482	−	10.3917i	0.346875	−	0.680781i	0.996862	+	0.0791650i	$0.0252254\pi$
$234$	−1.85977	+	3.32799i	−0.121577	+	0.217558i
$235$	−0.868350	−	11.4224i	−0.0566449	−	0.745113i
$236$	−2.82656	−	2.40519i	−0.183993	−	0.156565i
$237$	−10.5690	+	1.67396i	−0.686529	+	0.108736i
$238$	−3.47269	+	0.982824i	−0.225101	+	0.0637070i
$239$	−13.8288	+	10.0472i	−0.894511	+	0.649901i	−0.937050	−	0.349194i	$-0.886455\pi$
$239$	−13.8288	+	10.0472i	−0.894511	+	0.649901i	0.0425390	+	0.999095i	$0.486455\pi$
$240$	13.7654	+	1.06965i	0.888555	+	0.0690456i
$241$	12.7028	+	9.22911i	0.818258	+	0.594499i	0.916213	−	0.400692i	$-0.131230\pi$
$241$	12.7028	+	9.22911i	0.818258	+	0.594499i	−0.0979551	+	0.995191i	$0.531230\pi$
$242$	13.7852	+	5.07131i	0.886144	+	0.325996i
$243$	4.45725	−	4.45725i	0.285932	−	0.285932i
$244$	−3.24299	+	1.99547i	−0.207611	+	0.127747i
$245$	2.06357	+	0.861206i	0.131837	+	0.0550204i
$246$	13.4001	+	2.65273i	0.854361	+	0.169132i
$247$	−29.5124	+	15.0373i	−1.87783	+	0.956802i
$248$	−2.36721	−	11.7326i	−0.150318	−	0.745023i
$249$		−	21.4143i		−	1.35708i
$250$	−5.36746	−	14.8725i	−0.339468	−	0.940618i
$251$		−	23.3167i		−	1.47174i	−0.677123	−	0.735870i	$-0.736773\pi$
$251$		−	23.3167i		−	1.47174i	0.677123	−	0.735870i	$-0.263227\pi$
$252$	−1.23023	+	0.0990832i	−0.0774973	+	0.00624166i
$253$	4.62575	−	2.35694i	0.290818	−	0.148179i
$254$	4.15622	−	20.9949i	0.260784	−	1.31734i
$255$	8.12931	+	3.39267i	0.509077	+	0.212457i
$256$	15.2526	+	4.83294i	0.953289	+	0.302059i
$257$	7.20754	−	7.20754i	0.449594	−	0.449594i	−0.445625	−	0.895220i	$-0.647019\pi$
$257$	7.20754	−	7.20754i	0.449594	−	0.449594i	0.895220	+	0.445625i	$0.147019\pi$
$258$	−3.43451	+	9.33589i	−0.213823	+	0.581227i
$259$	5.24562	+	3.81117i	0.325947	+	0.236814i
$260$	−18.5748	−	6.05250i	−1.15196	−	0.375360i
$261$	−2.36219	+	1.71623i	−0.146216	+	0.106232i
$262$	5.34353	+	18.8807i	0.330125	+	1.16645i
$263$	−20.4791	+	3.24357i	−1.26279	+	0.200007i	−0.751693	−	0.659513i	$-0.770762\pi$
$263$	−20.4791	+	3.24357i	−1.26279	+	0.200007i	−0.511102	+	0.859520i	$0.670762\pi$
$264$	−2.84923	−	1.89252i	−0.175358	−	0.116477i
$265$	−0.624503	−	8.21477i	−0.0383629	−	0.504629i
$266$	−9.36059	−	5.23096i	−0.573935	−	0.320731i
$267$	11.9732	−	23.4987i	0.732748	−	1.43810i
$268$	−4.19107	+	6.86733i	−0.256010	+	0.419489i
$269$	18.7068	−	6.07822i	1.14058	−	0.370595i	0.322990	−	0.946402i	$-0.395312\pi$
$269$	18.7068	−	6.07822i	1.14058	−	0.370595i	0.817586	+	0.575807i	$0.195312\pi$
$270$	14.6640	+	9.83531i	0.892420	+	0.598558i
$271$	−24.0920	−	7.82795i	−1.46348	−	0.475514i	−0.534351	−	0.845263i	$-0.679444\pi$
$271$	−24.0920	−	7.82795i	−1.46348	−	0.475514i	−0.929132	+	0.369749i	$0.879444\pi$
$272$	8.28034	+	5.96991i	0.502069	+	0.361979i
$273$	−6.66028	−	1.05489i	−0.403099	−	0.0638446i
$274$	2.74511	+	23.0132i	0.165838	+	1.39028i
$275$	−0.633368	+	3.86553i	−0.0381935	+	0.233100i
$276$	19.8853	−	4.81247i	1.19695	−	0.289677i
$277$	−1.43201	+	9.04137i	−0.0860413	+	0.543243i	0.906585	+	0.422024i	$0.138680\pi$
$277$	−1.43201	+	9.04137i	−0.0860413	+	0.543243i	−0.992626	+	0.121219i	$0.961320\pi$
$278$	−12.0533	−	18.0035i	−0.722911	−	1.07978i
$279$	0.806972	−	2.48360i	0.0483121	−	0.148689i
$280$	−1.71721	−	6.08697i	−0.102623	−	0.363766i
$281$	1.04298	+	3.20998i	0.0622193	+	0.191491i	0.977334	−	0.211701i	$-0.0679005\pi$
$281$	1.04298	+	3.20998i	0.0622193	+	0.191491i	−0.915115	+	0.403193i	$0.867900\pi$
$282$	−6.91580	+	8.78915i	−0.411830	+	0.523386i
$283$	10.4174	+	5.30794i	0.619252	+	0.315525i	0.735323	−	0.677716i	$-0.237030\pi$
$283$	10.4174	+	5.30794i	0.619252	+	0.315525i	−0.116072	+	0.993241i	$0.537030\pi$
$284$	7.48681	+	3.08512i	0.444260	+	0.183068i
$285$	9.95122	+	24.2065i	0.589459	+	1.43387i
$286$	3.28850	+	3.55097i	0.194453	+	0.209973i
$287$	−0.978862	−	6.18029i	−0.0577804	−	0.364811i
$288$	2.38130	+	2.55259i	0.140320	+	0.150413i
$289$	−6.16426	−	8.48437i	−0.362603	−	0.499081i
$290$	−10.9693	−	10.1756i	−0.644140	−	0.597531i
$291$	4.43329	−	6.10190i	0.259884	−	0.357699i
$292$	10.4302	+	2.48393i	0.610382	+	0.145361i
$293$	−16.0271	−	16.0271i	−0.936314	−	0.936314i	0.0617764	−	0.998090i	$-0.480323\pi$
$293$	−16.0271	−	16.0271i	−0.936314	−	0.936314i	−0.998090	+	0.0617764i	$0.980323\pi$
$294$	−0.915773	−	1.98170i	−0.0534090	−	0.115575i
$295$	3.54376	−	2.15865i	0.206325	−	0.125682i
$296$	−0.770217	−	18.3232i	−0.0447679	−	1.06501i
$297$	−1.98588	−	3.89750i	−0.115232	−	0.226156i
$298$	−17.9895	−	0.690351i	−1.04210	−	0.0399910i
$299$	−28.9488			−1.67415
$300$	−5.95723	+	14.2408i	−0.343941	+	0.822194i
$301$	4.55671			0.262644
$302$	−25.4718	−	0.977485i	−1.46573	−	0.0562479i
$303$	4.63854	+	9.10366i	0.266477	+	0.522991i
$304$	4.85398	+	29.9384i	0.278395	+	1.71708i
$305$	−0.982788	−	4.14219i	−0.0562743	−	0.237181i
$306$	0.934284	+	2.02176i	0.0534094	+	0.115576i
$307$	−11.3832	−	11.3832i	−0.649673	−	0.649673i	0.303241	−	0.952914i	$-0.401931\pi$
$307$	−11.3832	−	11.3832i	−0.649673	−	0.649673i	−0.952914	+	0.303241i	$0.901931\pi$
$308$	−0.362985	+	1.52420i	−0.0206830	+	0.0868495i
$309$	−8.53381	+	11.7458i	−0.485472	+	0.668194i
$310$	13.2863	+	1.59612i	0.754610	+	0.0906536i
$311$	5.91950	+	8.14750i	0.335664	+	0.462002i	0.943169	−	0.332314i	$-0.107829\pi$
$311$	5.91950	+	8.14750i	0.335664	+	0.462002i	−0.607505	+	0.794316i	$0.707829\pi$
$312$	9.36502	+	16.6155i	0.530190	+	0.940666i
$313$	1.60689	+	10.1455i	0.0908266	+	0.573457i	0.990567	+	0.137031i	$0.0437559\pi$
$313$	1.60689	+	10.1455i	0.0908266	+	0.573457i	−0.899740	+	0.436426i	$0.856244\pi$
$314$	9.28249	+	10.0234i	0.523841	+	0.565650i
$315$	0.325703	−	1.34091i	0.0183513	−	0.0755515i
$316$	5.28214	−	12.8184i	0.297144	−	0.721092i
$317$	22.4962	+	11.4624i	1.26351	+	0.643791i	0.951897	−	0.306418i	$-0.0991304\pi$
$317$	22.4962	+	11.4624i	1.26351	+	0.643791i	0.311614	+	0.950209i	$0.399130\pi$
$318$	−4.97372	+	6.32101i	−0.278913	+	0.354464i
$319$	1.14543	+	3.52529i	0.0641320	+	0.197378i
$320$	−10.4738	+	14.5017i	−0.585504	+	0.810670i
$321$	7.26346	−	22.3546i	0.405407	−	1.24771i
$322$	−5.21382	−	7.78763i	−0.290555	−	0.433988i
$323$	−3.02703	+	19.1119i	−0.168429	+	1.06342i
$324$	−3.18389	−	13.1559i	−0.176883	−	0.730884i
$325$	12.9323	−	17.6018i	0.717356	−	0.976374i
$326$	−0.0539869	−	0.452591i	−0.00299006	−	0.0250667i
$327$	−13.3139	−	2.10872i	−0.736262	−	0.116612i
$328$	−11.9780	+	13.0292i	−0.661376	+	0.719418i
$329$	4.87224	+	1.58309i	0.268615	+	0.0872784i
$330$	3.00737	−	2.36230i	0.165550	−	0.130040i
$331$	19.1335	−	6.21685i	1.05167	−	0.341709i	0.268347	−	0.963322i	$-0.413523\pi$
$331$	19.1335	−	6.21685i	1.05167	−	0.341709i	0.783324	+	0.621614i	$0.213523\pi$
$332$	23.6828	+	14.4534i	1.29976	+	0.793232i
$333$	1.81655	−	3.56518i	0.0995463	−	0.195371i
$334$	27.7891	+	15.5293i	1.52055	+	0.849727i
$335$	−5.82342	−	6.85524i	−0.318167	−	0.374542i
$336$	−2.78311	+	5.51186i	−0.151831	+	0.300696i
$337$	−18.7510	+	2.96987i	−1.02143	+	0.161779i	−0.644614	−	0.764508i	$-0.722982\pi$
$337$	−18.7510	+	2.96987i	−1.02143	+	0.161779i	−0.376819	+	0.926287i	$0.622982\pi$
$338$	−2.34258	−	8.27722i	−0.127420	−	0.450221i
$339$	−13.7876	+	10.0173i	−0.748839	+	0.544063i
$340$	−9.23886	+	6.70062i	−0.501048	+	0.363392i
$341$	−2.68203	−	1.94861i	−0.145240	−	0.105523i
$342$	−2.28468	+	6.21036i	−0.123541	+	0.335818i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−8.00678	−	10.0995i	−0.431697	−	0.544529i
$345$	−1.85543	+	22.7989i	−0.0998930	+	1.22745i
$346$	0.253664	−	1.28137i	0.0136370	−	0.0688868i
$347$	−14.4663	+	7.37096i	−0.776593	+	0.395694i	−0.796909	−	0.604100i	$-0.793533\pi$
$347$	−14.4663	+	7.37096i	−0.776593	+	0.395694i	0.0203155	+	0.999794i	$0.493533\pi$
$348$	1.17270	+	14.5604i	0.0628634	+	0.780521i
$349$		−	19.9298i		−	1.06682i	−0.845858	−	0.533409i	$-0.820911\pi$
$349$		−	19.9298i		−	1.06682i	0.845858	−	0.533409i	$-0.179089\pi$
$350$	7.06432	+	0.308795i	0.377604	+	0.0165058i
$351$			24.3913i			1.30191i
$352$	4.01607	−	1.87372i	0.214057	−	0.0998697i
$353$	−0.890656	+	0.453812i	−0.0474048	+	0.0241540i	−0.477532	−	0.878614i	$-0.658469\pi$
$353$	−0.890656	+	0.453812i	−0.0474048	+	0.0241540i	0.430127	+	0.902768i	$0.358469\pi$
$354$	−3.97398	−	0.786701i	−0.211215	−	0.0418127i
$355$	−5.89799	+	6.86852i	−0.313033	+	0.364543i
$356$	17.9068	+	29.1018i	0.949059	+	1.54239i
$357$	−2.78560	+	2.78560i	−0.147430	+	0.147430i
$358$	17.2812	+	6.35744i	0.913340	+	0.336001i
$359$	−29.9944	−	21.7922i	−1.58304	−	1.15015i	−0.913099	−	0.407738i	$-0.866318\pi$
$359$	−29.9944	−	21.7922i	−1.58304	−	1.15015i	−0.669945	−	0.742411i	$-0.733682\pi$
$360$	−3.54430	+	1.63427i	−0.186801	+	0.0861337i
$361$	−31.1405	+	22.6249i	−1.63897	+	1.19078i
$362$	32.2410	−	9.12469i	1.69455	−	0.479583i
$363$	15.8355	−	2.50809i	0.831147	−	0.131641i
$364$	5.66193	−	6.65384i	0.296766	−	0.348756i
$365$	−6.29063	+	10.2043i	−0.329267	+	0.534115i
$366$	−2.02753	+	3.62819i	−0.105981	+	0.189648i
$367$	−1.75256	+	3.43959i	−0.0914827	+	0.179545i	−0.932214	−	0.361908i	$-0.882125\pi$
$367$	−1.75256	+	3.43959i	−0.0914827	+	0.179545i	0.840731	+	0.541453i	$0.182125\pi$
$368$	−8.09911	+	25.2399i	−0.422195	+	1.31572i
$369$	−3.67245	+	1.19325i	−0.191180	+	0.0621183i
$370$	19.7244	+	5.60016i	1.02543	+	0.291138i
$371$	3.50403	+	1.13853i	0.181920	+	0.0591095i
$372$	−8.50293	−	9.91890i	−0.440857	−	0.514271i
$373$	24.7301	+	3.91686i	1.28047	+	0.202807i	0.759355	−	0.650676i	$-0.225515\pi$
$373$	24.7301	+	3.91686i	1.28047	+	0.202807i	0.521120	+	0.853484i	$0.325515\pi$
$374$	2.80751	−	0.334891i	0.145173	−	0.0173168i
$375$	−13.0336	−	11.3131i	−0.673052	−	0.584207i
$376$	−5.05246	−	13.5806i	−0.260561	−	0.700364i
$377$	3.23333	−	20.4144i	0.166525	−	1.05140i
$378$	−6.56160	+	4.39300i	−0.337492	+	0.225951i
$379$	−9.48845	+	29.2024i	−0.487389	+	1.50003i	0.341102	+	0.940026i	$0.389200\pi$
$379$	−9.48845	+	29.2024i	−0.487389	+	1.50003i	−0.828491	+	0.560002i	$0.810800\pi$
$380$	−33.4873	−	5.33260i	−1.71786	−	0.273556i
$381$	−7.21908	−	22.2180i	−0.369845	−	1.13826i
$382$	−8.43582	−	6.63778i	−0.431614	−	0.339618i
$383$	32.0116	+	16.3107i	1.63572	+	0.833440i	0.998003	+	0.0631671i	$0.0201201\pi$
$383$	32.0116	+	16.3107i	1.63572	+	0.833440i	0.637715	+	0.770273i	$0.279880\pi$
$384$	17.1068	−	3.51662i	0.872979	−	0.179457i
$385$	−1.49118	−	0.919272i	−0.0759978	−	0.0468504i
$386$	20.3472	−	18.8433i	1.03565	−	0.959097i
$387$	−0.439891	−	2.77736i	−0.0223609	−	0.141181i
$388$	3.75608	+	9.02133i	0.190686	+	0.457989i
$389$	−4.08693	−	5.62517i	−0.207215	−	0.285208i	0.692742	−	0.721186i	$-0.256403\pi$
$389$	−4.08693	−	5.62517i	−0.207215	−	0.285208i	−0.899957	+	0.435978i	$0.856403\pi$
$390$	−20.9217	+	4.12353i	−1.05941	+	0.208803i
$391$	−9.94054	+	13.6820i	−0.502715	+	0.691927i
$392$	2.80972	+	0.324747i	0.141912	+	0.0164022i
$393$	15.1451	+	15.1451i	0.763969	+	0.763969i
$394$	0.593113	−	0.274086i	0.0298806	−	0.0138082i
$395$	11.7598	+	10.0981i	0.591701	+	0.508092i
$396$	0.964059	+	0.0741011i	0.0484458	+	0.00372372i
$397$	8.40097	+	16.4878i	0.421633	+	0.827500i	0.999932	+	0.0116757i	$0.00371658\pi$
$397$	8.40097	+	16.4878i	0.421633	+	0.827500i	−0.578299	+	0.815825i	$0.696283\pi$
$398$	0.471685	−	12.2914i	0.0236434	−	0.616111i
$399$	−11.7046			−0.585961
$400$	−11.7286	−	16.2000i	−0.586430	−	0.810000i
$401$	−17.3313			−0.865483			−0.432741	−	0.901518i	$-0.642454\pi$
$401$	−17.3313			−0.865483			−0.432741	+	0.901518i	$0.642454\pi$
$402$	−0.336749	+	8.77515i	−0.0167955	+	0.437665i
$403$	8.39233	+	16.4709i	0.418052	+	0.820472i
$404$	−13.1988	−	1.01451i	−0.656664	−	0.0504736i
$405$	15.0835	+	1.22754i	0.749506	+	0.0609967i
$406$	6.07411	−	2.80693i	0.301453	−	0.139306i
$407$	−3.59183	−	3.59183i	−0.178040	−	0.178040i
$408$	11.0687	+	1.27932i	0.547983	+	0.0633359i
$409$	2.31641	−	3.18827i	0.114539	−	0.157650i	−0.747898	−	0.663813i	$-0.768937\pi$
$409$	2.31641	−	3.18827i	0.114539	−	0.157650i	0.862437	+	0.506164i	$0.168937\pi$
$410$	−9.63832	−	17.2813i	−0.476003	−	0.853464i
$411$	14.8697	+	20.4664i	0.733467	+	1.00953i
$412$	−7.23024	−	17.3655i	−0.356208	−	0.855538i
$413$	0.290294	+	1.83285i	0.0142845	+	0.0901885i
$414$	−4.24331	+	3.92967i	−0.208547	+	0.193133i
$415$	−23.6411	+	20.0827i	−1.16049	+	0.985822i
$416$	−24.6964	−	0.857372i	−1.21084	−	0.0420361i
$417$	−21.0714	−	10.7364i	−1.03187	−	0.525764i
$418$	6.60187	+	5.19472i	0.322908	+	0.254082i
$419$	−1.42752	−	4.39347i	−0.0697391	−	0.214635i	0.910113	−	0.414361i	$-0.135995\pi$
$419$	−1.42752	−	4.39347i	−0.0697391	−	0.214635i	−0.979852	+	0.199726i	$0.935995\pi$
$420$	−4.87740	−	4.88557i	−0.237993	−	0.238391i
$421$	−2.20857	+	6.79729i	−0.107639	+	0.331280i	−0.990341	−	0.138654i	$-0.955722\pi$
$421$	−2.20857	+	6.79729i	−0.107639	+	0.331280i	0.882702	+	0.469934i	$0.155722\pi$
$422$	−0.251099	+	0.168111i	−0.0122233	+	0.00818350i
$423$	0.494556	−	3.12251i	0.0240462	−	0.151821i
$424$	−3.63364	−	9.76691i	−0.176465	−	0.474323i
$425$	−3.87836	−	12.1564i	−0.188128	−	0.589670i
$426$	8.77653	−	1.04690i	0.425224	−	0.0507225i
$427$	1.88043	+	0.297831i	0.0910003	+	0.0144130i
$428$	19.8203	+	23.1209i	0.958051	+	1.11759i
$429$	5.02424	+	1.63248i	0.242573	+	0.0788167i
$430$	13.5276	−	4.96373i	0.652361	−	0.239372i
$431$	−27.7348	+	9.01158i	−1.33594	+	0.434072i	−0.887939	−	0.459962i	$-0.847863\pi$
$431$	−27.7348	+	9.01158i	−1.33594	+	0.434072i	−0.447999	+	0.894034i	$0.647863\pi$
$432$	21.2663	+	6.82404i	1.02318	+	0.328322i
$433$	−3.21744	+	6.31459i	−0.154620	+	0.303460i	−0.955303	−	0.295630i	$-0.904471\pi$
$433$	−3.21744	+	6.31459i	−0.154620	+	0.303460i	0.800682	+	0.599089i	$0.204471\pi$
$434$	−2.91940	+	5.22415i	−0.140136	+	0.250767i
$435$	−15.8703	−	3.85487i	−0.760924	−	0.184827i
$436$	11.3182	−	13.3011i	0.542044	−	0.637005i
$437$	−49.6286	+	7.86040i	−2.37406	+	0.376014i
$438$	11.2610	−	3.18704i	0.538072	−	0.152283i
$439$	−19.7759	+	14.3681i	−0.943854	+	0.685750i	−0.949345	−	0.314235i	$-0.898252\pi$
$439$	−19.7759	+	14.3681i	−0.943854	+	0.685750i	0.00549123	+	0.999985i	$0.498252\pi$
$440$	0.582745	+	4.92036i	0.0277813	+	0.234569i
$441$	0.499251	+	0.362727i	0.0237738	+	0.0172727i
$442$	−14.7964	−	5.44332i	−0.703792	−	0.258912i
$443$	19.5321	−	19.5321i	0.928000	−	0.928000i	−0.0695765	−	0.997577i	$-0.522165\pi$
$443$	19.5321	−	19.5321i	0.928000	−	0.928000i	0.997577	+	0.0695765i	$0.0221648\pi$
$444$	−10.4906	−	17.0490i	−0.497860	−	0.809112i
$445$	−37.1710	+	8.81930i	−1.76207	+	0.418075i
$446$	−13.5448	−	2.68137i	−0.641366	−	0.126967i
$447$	−17.5088	+	8.92119i	−0.828138	+	0.421958i
$448$	−4.21731	−	6.79811i	−0.199249	−	0.321180i
$449$			37.4647i			1.76807i	0.467422	+	0.884034i	$0.345183\pi$
$449$			37.4647i			1.76807i	−0.467422	+	0.884034i	$0.654817\pi$
$450$	−0.493755	−	4.33559i	−0.0232758	−	0.204382i
$451$			4.90208i			0.230830i
$452$	−1.77263	−	22.0092i	−0.0833773	−	1.03523i
$453$	−24.7911	+	12.6317i	−1.16479	+	0.593490i
$454$	4.46678	−	22.5637i	0.209636	−	1.05897i
$455$	5.08156	+	8.34216i	0.238227	+	0.391086i
$456$	20.5666	+	25.9420i	0.963118	+	1.21485i
$457$	20.7551	−	20.7551i	0.970884	−	0.970884i	−0.0287039	−	0.999588i	$-0.509138\pi$
$457$	20.7551	−	20.7551i	0.970884	−	0.970884i	0.999588	+	0.0287039i	$0.00913799\pi$
$458$	−7.77881	+	21.1449i	−0.363480	+	0.988034i
$459$	11.5280	+	8.37557i	0.538080	+	0.390938i
$460$	−23.9617	−	17.4398i	−1.11722	−	0.813137i
$461$	−3.87840	+	2.81782i	−0.180635	+	0.131239i	−0.674428	−	0.738340i	$-0.735610\pi$
$461$	−3.87840	+	2.81782i	−0.180635	+	0.131239i	0.493793	+	0.869579i	$0.335610\pi$
$462$	0.465734	+	1.64561i	0.0216679	+	0.0765608i
$463$	−5.40415	+	0.855933i	−0.251152	+	0.0397786i	−0.280741	−	0.959784i	$-0.590580\pi$
$463$	−5.40415	+	0.855933i	−0.251152	+	0.0397786i	0.0295889	+	0.999562i	$0.490580\pi$
$464$	−16.8944	−	8.53050i	−0.784302	−	0.396019i
$465$	13.5097	−	5.55378i	0.626496	−	0.257550i
$466$	14.3981	+	8.04605i	0.666978	+	0.372726i
$467$	9.59363	−	18.8286i	0.443940	−	0.871282i	−0.555275	−	0.831667i	$-0.687387\pi$
$467$	9.59363	−	18.8286i	0.443940	−	0.871282i	0.999215	−	0.0396147i	$-0.0126131\pi$
$468$	−4.60217	−	2.80866i	−0.212735	−	0.129830i
$469$	3.82572	−	1.24305i	0.176655	−	0.0573988i
$470$	16.1889	−	0.607685i	0.746737	−	0.0280304i
$471$	14.1820	+	4.60800i	0.653471	+	0.212326i
$472$	3.55224	−	3.86398i	0.163505	−	0.177854i
$473$	−3.52584	−	0.558438i	−0.162118	−	0.0256770i
$474$	−1.79243	−	15.0266i	−0.0823292	−	0.690194i
$475$	17.3913	−	33.6874i	0.797966	−	1.54568i
$476$	−1.20057	−	4.96081i	−0.0550282	−	0.227378i
$477$	0.355677	−	2.24565i	0.0162853	−	0.102821i
$478$	−13.4485	−	20.0874i	−0.615121	−	0.918775i
$479$	12.8318	−	39.4923i	0.586302	−	1.80445i	−0.00767753	−	0.999971i	$-0.502444\pi$
$479$	12.8318	−	39.4923i	0.586302	−	1.80445i	0.593979	−	0.804480i	$-0.297556\pi$
$480$	−2.25811	+	19.3949i	−0.103068	+	0.885254i
$481$	8.75271	+	26.9381i	0.399089	+	1.22827i
$482$	−13.7312	+	17.4507i	−0.625440	+	0.794859i
$483$	−9.11470	−	4.64417i	−0.414733	−	0.211317i
$484$	−7.91423	+	19.2058i	−0.359738	+	0.872991i
$485$	−10.8940	+	0.828186i	−0.494672	+	0.0376060i
$486$	6.05714	+	6.54058i	0.274757	+	0.296687i
$487$	−0.666780	−	4.20988i	−0.0302147	−	0.190768i	0.967964	−	0.251087i	$-0.0807881\pi$
$487$	−0.666780	−	4.20988i	−0.0302147	−	0.190768i	−0.998179	+	0.0603193i	$0.980788\pi$
$488$	−2.64407	−	4.69112i	−0.119691	−	0.212357i
$489$	−0.292435	−	0.402502i	−0.0132244	−	0.0182018i
$490$	−1.32894	+	2.86948i	−0.0600355	+	0.129630i
$491$	−0.799482	+	1.10039i	−0.0360801	+	0.0496600i	−0.826676	−	0.562678i	$-0.809771\pi$
$491$	−0.799482	+	1.10039i	−0.0360801	+	0.0496600i	0.790596	+	0.612338i	$0.209771\pi$
$492$	−4.47546	+	18.7928i	−0.201770	+	0.847247i
$493$	−8.53814	−	8.53814i	−0.384538	−	0.384538i
$494$	−19.6499	−	42.5216i	−0.884089	−	1.91314i
$495$	−0.416351	+	0.997636i	−0.0187136	+	0.0448404i
$496$	16.7086	−	2.70901i	0.750239	−	0.121638i
$497$	−1.83811	−	3.60748i	−0.0824503	−	0.161818i
$498$	30.2621	+	1.16132i	1.35608	+	0.0520398i
$499$	29.0713			1.30141			0.650704	−	0.759331i	$-0.274474\pi$
$499$	29.0713			1.30141			0.650704	+	0.759331i	$0.274474\pi$
$500$	21.3085	−	6.77860i	0.952943	−	0.303148i
$501$	34.7478			1.55242
$502$	32.9506	+	1.26449i	1.47066	+	0.0564369i
$503$	11.4258	+	22.4244i	0.509451	+	0.999854i	0.992266	+	0.124131i	$0.0396144\pi$
$503$	11.4258	+	22.4244i	0.509451	+	0.999854i	−0.482815	+	0.875722i	$0.660386\pi$
$504$	−0.0733052	−	1.74390i	−0.00326527	−	0.0776797i
$505$	5.70020	−	13.6585i	0.253655	−	0.607794i
$506$	3.07990	+	6.66480i	0.136918	+	0.296286i
$507$	−6.63954	−	6.63954i	−0.294873	−	0.294873i
$508$	29.4441	+	7.01204i	1.30637	+	0.311109i
$509$	21.9980	−	30.2777i	0.975045	−	1.34203i	0.0355879	−	0.999367i	$-0.488670\pi$
$509$	21.9980	−	30.2777i	0.975045	−	1.34203i	0.939457	−	0.342667i	$-0.111330\pi$
$510$	−5.23529	+	11.3041i	−0.231822	+	0.500555i
$511$	−3.15109	−	4.33710i	−0.139396	−	0.191862i
$512$	−7.65694	+	21.2925i	−0.338392	+	0.941005i
$513$	6.62291	+	41.8154i	0.292409	+	1.84620i
$514$	9.79463	+	10.5764i	0.432023	+	0.466504i
$515$	20.9704	−	1.59421i	0.924064	−	0.0702492i
$516$	−13.0070	−	5.35985i	−0.572600	−	0.235954i
$517$	−3.57598	−	1.82205i	−0.157271	−	0.0801337i
$518$	−5.67032	+	7.20629i	−0.249139	+	0.316626i
$519$	−0.440597	−	1.35602i	−0.0193400	−	0.0595225i
$520$	9.56056	−	25.9212i	0.419258	−	1.13672i
$521$	−9.52891	+	29.3270i	−0.417469	+	1.28484i	0.492555	+	0.870281i	$0.336063\pi$
$521$	−9.52891	+	29.3270i	−0.417469	+	1.28484i	−0.910024	+	0.414556i	$0.863937\pi$
$522$	−2.29723	−	3.43126i	−0.100547	−	0.150182i
$523$	0.0908352	−	0.573511i	0.00397195	−	0.0250779i	−0.985623	−	0.168961i	$-0.945959\pi$
$523$	0.0908352	−	0.573511i	0.00397195	−	0.0250779i	0.989595	+	0.143883i	$0.0459589\pi$
$524$	−26.9715	+	6.52742i	−1.17826	+	0.285152i
$525$	6.89563	−	3.46735i	0.300950	−	0.151328i
$526$	−3.47313	−	29.1164i	−0.151435	−	1.26954i
$527$	10.6664	+	1.68939i	0.464635	+	0.0735909i
$528$	2.82898	−	3.92383i	0.123116	−	0.170763i
$529$	−19.8919	−	6.46326i	−0.864864	−	0.281012i
$530$	11.6428	−	0.437037i	0.505729	−	0.0189837i
$531$	1.08911	−	0.353875i	0.0472636	−	0.0153569i
$532$	7.89988	−	12.9445i	0.342503	−	0.561213i
$533$	12.4096	−	24.3551i	0.537518	−	1.05494i
$534$	32.5585	+	18.1946i	1.40894	+	0.787356i
$535$	−31.4910	+	12.9458i	−1.36148	+	0.559697i
$536$	−9.47744	−	6.29513i	−0.409363	−	0.271908i
$537$	19.8515	−	3.14417i	0.856656	−	0.135681i
$538$	7.57509	+	26.7656i	0.326585	+	1.15395i
$539$	0.633796	−	0.460480i	0.0272995	−	0.0198343i
$540$	−14.6942	+	20.1893i	−0.632339	+	0.868811i
$541$	−2.11776	−	1.53864i	−0.0910494	−	0.0661513i	0.541329	−	0.840811i	$-0.317921\pi$
$541$	−2.11776	−	1.53864i	−0.0910494	−	0.0661513i	−0.632379	+	0.774659i	$0.717921\pi$
$542$	12.3688	−	33.6216i	0.531285	−	1.44417i
$543$	25.8620	−	25.8620i	1.10984	−	1.10984i
$544$	−8.88557	+	11.3778i	−0.380966	+	0.487819i
$545$	10.1581	+	16.6760i	0.435123	+	0.714321i
$546$	1.85193	−	9.35493i	0.0792552	−	0.400354i
$547$	40.4155	−	20.5927i	1.72804	−	0.880481i	0.753134	−	0.657868i	$-0.228541\pi$
$547$	40.4155	−	20.5927i	1.72804	−	0.880481i	0.974907	−	0.222613i	$-0.0714586\pi$
$548$	−32.6706	+	2.63130i	−1.39562	+	0.112403i
$549$		−	1.17489i		−	0.0501432i
$550$	−5.42831	−	1.10469i	−0.231464	−	0.0471041i
$551$		−	35.8756i		−	1.52835i
$552$	5.72246	+	28.3623i	0.243564	+	1.20718i
$553$	−6.17649	+	3.14708i	−0.262651	+	0.133827i
$554$	−12.6994	−	2.51400i	−0.539544	−	0.106810i
$555$	21.7763	−	5.16672i	0.924353	−	0.219315i
$556$	26.0957	−	16.0571i	1.10670	−	0.680973i
$557$	−6.10546	+	6.10546i	−0.258697	+	0.258697i	−0.824524	−	0.565827i	$-0.808557\pi$
$557$	−6.10546	+	6.10546i	−0.258697	+	0.258697i	0.565827	+	0.824524i	$0.308557\pi$
$558$	3.46600	+	1.27508i	0.146728	+	0.0539784i
$559$	16.1038	+	11.7001i	0.681120	+	0.494862i
$560$	8.69507	−	2.09661i	0.367434	−	0.0885979i
$561$	2.49680	−	1.81403i	0.105415	−	0.0765884i
$562$	−4.59282	+	1.29984i	−0.193736	+	0.0548304i
$563$	16.7081	−	2.64631i	0.704164	−	0.111529i	0.205924	−	0.978568i	$-0.433980\pi$
$563$	16.7081	−	2.64631i	0.704164	−	0.111529i	0.498240	+	0.867039i	$0.333980\pi$
$564$	−12.0455	−	10.2499i	−0.507209	−	0.431597i
$565$	23.9892	+	5.82692i	1.00923	+	0.245140i
$566$	−8.06599	+	14.4338i	−0.339039	+	0.606697i
$567$	−3.07254	+	6.03020i	−0.129035	+	0.253245i
$568$	−4.76583	+	10.4128i	−0.199970	+	0.436913i
$569$	−0.190116	+	0.0617726i	−0.00797009	+	0.00258964i	−0.312999	−	0.949753i	$-0.601334\pi$
$569$	−0.190116	+	0.0617726i	−0.00797009	+	0.00258964i	0.305029	+	0.952343i	$0.401334\pi$
$570$	−34.7477	+	12.7501i	−1.45542	+	0.534041i
$571$	−21.6834	−	7.04538i	−0.907424	−	0.294840i	−0.182126	−	0.983275i	$-0.558298\pi$
$571$	−21.6834	−	7.04538i	−0.907424	−	0.294840i	−0.725298	+	0.688435i	$0.758298\pi$
$572$	−5.19648	+	4.45465i	−0.217276	+	0.186258i
$573$	−11.5725	−	1.83290i	−0.483448	−	0.0765706i
$574$	8.78691	−	1.04814i	0.366758	−	0.0437485i
$575$	26.9097	−	19.3328i	1.12221	−	0.806235i
$576$	−3.73639	+	3.22676i	−0.155683	+	0.134448i
$577$	5.41792	−	34.2074i	0.225551	−	1.42407i	−0.571719	−	0.820450i	$-0.693723\pi$
$577$	5.41792	−	34.2074i	0.225551	−	1.42407i	0.797270	−	0.603623i	$-0.206277\pi$
$578$	12.3242	−	8.25105i	0.512618	−	0.343198i
$579$	9.35415	−	28.7891i	0.388745	−	1.19644i
$580$	14.9747	−	14.9497i	0.621792	−	0.620753i
$581$	−4.28681	−	13.1934i	−0.177847	−	0.547356i
$582$	8.38262	+	6.59591i	0.347471	+	0.273409i
$583$	−2.57178	−	1.31039i	−0.106512	−	0.0542707i
$584$	−4.07586	+	14.6050i	−0.168660	+	0.604359i
$585$	4.59407	−	3.90259i	0.189941	−	0.161352i
$586$	23.5182	−	21.7799i	0.971530	−	0.899720i
$587$	5.57697	+	35.2116i	0.230186	+	1.45334i	0.784032	+	0.620720i	$0.213160\pi$
$587$	5.57697	+	35.2116i	0.230186	+	1.45334i	−0.553846	+	0.832619i	$0.686840\pi$
$588$	2.85015	−	1.18668i	0.117538	−	0.0489377i
$589$	18.8598	+	25.9583i	0.777104	+	1.06959i
$590$	2.85837	+	5.12501i	0.117677	+	0.210993i
$591$	0.419201	−	0.576980i	0.0172436	−	0.0237338i
$592$	25.9356	−	0.0947670i	1.06595	−	0.00389490i
$593$	−14.8874	−	14.8874i	−0.611351	−	0.611351i	0.331947	−	0.943298i	$-0.392295\pi$
$593$	−14.8874	−	14.8874i	−0.611351	−	0.611351i	−0.943298	+	0.331947i	$0.892295\pi$
$594$	5.61554	−	2.59502i	0.230408	−	0.106475i
$595$	5.68766	+	0.462876i	0.233171	+	0.0189761i
$596$	1.95117	−	25.3848i	0.0799231	−	1.03980i
$597$	−6.09542	−	11.9629i	−0.249469	−	0.489611i
$598$	1.56992	−	40.9096i	0.0641987	−	1.67292i
$599$	17.3116			0.707333			0.353666	−	0.935372i	$-0.384935\pi$
$599$	17.3116			0.707333			0.353666	+	0.935372i	$0.384935\pi$
$600$	−19.8017	−	9.19089i	−0.808400	−	0.375216i
$601$	−18.0392			−0.735835			−0.367917	−	0.929859i	$-0.619929\pi$
$601$	−18.0392			−0.735835			−0.367917	+	0.929859i	$0.619929\pi$
$602$	−0.247114	+	6.43942i	−0.0100716	+	0.262451i
$603$	−1.12698	−	2.21182i	−0.0458940	−	0.0900721i
$604$	2.76271	−	35.9430i	0.112413	−	1.46250i
$605$	−17.6197	−	15.1300i	−0.716344	−	0.615123i
$606$	−13.1166	+	6.06137i	−0.532825	+	0.246226i
$607$	7.55686	+	7.55686i	0.306724	+	0.306724i	0.843637	−	0.536914i	$-0.180410\pi$
$607$	7.55686	+	7.55686i	0.306724	+	0.306724i	−0.536914	+	0.843637i	$0.680410\pi$
$608$	−42.5714	+	5.23593i	−1.72650	+	0.212345i
$609$	4.29306	−	5.90889i	0.173964	−	0.239440i
$610$	5.90692	−	1.16422i	0.239164	−	0.0471377i
$611$	13.1541	+	18.1051i	0.532159	+	0.732453i
$612$	−2.90776	+	1.21066i	−0.117539	+	0.0489382i
$613$	−6.94305	−	43.8367i	−0.280427	−	1.77055i	−0.578186	−	0.815905i	$-0.696239\pi$
$613$	−6.94305	−	43.8367i	−0.280427	−	1.77055i	0.297759	−	0.954641i	$-0.403761\pi$
$614$	16.7037	−	15.4691i	0.674108	−	0.624282i
$615$	−18.3857	−	11.3343i	−0.741384	−	0.457042i
$616$	−2.13428	−	0.595620i	−0.0859925	−	0.0239982i
$617$	6.33155	+	3.22608i	0.254898	+	0.129877i	0.576771	−	0.816906i	$-0.304312\pi$
$617$	6.33155	+	3.22608i	0.254898	+	0.129877i	−0.321873	+	0.946783i	$0.604312\pi$
$618$	−16.1360	−	12.6967i	−0.649086	−	0.510738i
$619$	−9.05146	−	27.8575i	−0.363809	−	1.11969i	−0.950723	−	0.310040i	$-0.899658\pi$
$619$	−9.05146	−	27.8575i	−0.363809	−	1.11969i	0.586914	−	0.809649i	$-0.300342\pi$
$620$	−2.97612	+	18.6893i	−0.119524	+	0.750579i
$621$	−11.4342	+	35.1908i	−0.458838	+	1.41216i
$622$	−11.8348	+	7.92344i	−0.474534	+	0.317701i
$623$	2.67266	−	16.8745i	0.107078	−	0.676063i
$624$	−23.9884	+	12.3333i	−0.960305	+	0.493728i
$625$	−0.266375	+	24.9986i	−0.0106550	+	0.999943i
$626$	−14.4245	+	1.72061i	−0.576518	+	0.0687695i
$627$	9.05663	+	1.43443i	0.361687	+	0.0572856i
$628$	−14.6681	+	12.5742i	−0.585322	+	0.501765i
$629$	15.7372	+	5.11333i	0.627484	+	0.203882i
$630$	1.87727	+	0.532994i	0.0747922	+	0.0212350i
$631$	−27.1105	+	8.80875i	−1.07925	+	0.350671i	−0.794085	−	0.607807i	$-0.792050\pi$
$631$	−27.1105	+	8.80875i	−1.07925	+	0.350671i	−0.285168	+	0.958477i	$0.592050\pi$
$632$	17.8282	+	8.15974i	0.709167	+	0.324577i
$633$	−0.149743	+	0.293888i	−0.00595176	+	0.0116810i
$634$	−17.4183	+	31.1694i	−0.691769	+	1.23789i
$635$	−17.7582	+	28.8063i	−0.704713	+	1.14314i
$636$	−8.66295	−	7.37153i	−0.343508	−	0.292300i
$637$	−4.31460	+	0.683366i	−0.170951	+	0.0270759i
$638$	−5.04396	+	1.42752i	−0.199692	+	0.0565160i
$639$	−2.02135	+	1.46860i	−0.0799635	+	0.0580969i
$640$	−19.9254	−	15.5878i	−0.787621	−	0.616160i
$641$	3.82658	+	2.78017i	0.151141	+	0.109810i	0.660786	−	0.750575i	$-0.270223\pi$
$641$	3.82658	+	2.78017i	0.151141	+	0.109810i	−0.509645	+	0.860385i	$0.670223\pi$
$642$	31.1971	+	11.4768i	1.23125	+	0.452955i
$643$	19.8105	−	19.8105i	0.781251	−	0.781251i	−0.198791	−	0.980042i	$-0.563702\pi$
$643$	19.8105	−	19.8105i	0.781251	−	0.781251i	0.980042	+	0.198791i	$0.0637016\pi$
$644$	11.2880	−	6.94571i	0.444810	−	0.273699i
$645$	10.2467	−	11.9328i	0.403463	−	0.469854i
$646$	−26.8443	−	5.31418i	−1.05618	−	0.209084i
$647$	−24.8943	+	12.6843i	−0.978696	+	0.498671i	−0.868741	−	0.495266i	$-0.835071\pi$
$647$	−24.8943	+	12.6843i	−0.978696	+	0.498671i	−0.109955	+	0.993937i	$0.535071\pi$
$648$	18.7643	−	3.78593i	0.737130	−	0.148725i
$649$		−	1.45378i		−	0.0570657i
$650$	24.1731	+	19.2302i	0.948147	+	0.754269i
$651$			6.53232i			0.256022i
$652$	0.642517	−	0.0517485i	0.0251629	−	0.00202663i
$653$	15.3319	−	7.81197i	0.599982	−	0.305706i	−0.127494	−	0.991839i	$-0.540693\pi$
$653$	15.3319	−	7.81197i	0.599982	−	0.305706i	0.727476	+	0.686133i	$0.240693\pi$
$654$	3.70201	−	18.7005i	0.144760	−	0.731249i
$655$	2.51662	−	30.9233i	0.0983325	−	1.20827i
$656$	−17.7629	−	17.6336i	−0.693527	−	0.688477i
$657$	−2.33931	+	2.33931i	−0.0912652	+	0.0912652i
$658$	−2.50140	+	6.79947i	−0.0975148	+	0.265071i
$659$	−9.52354	−	6.91926i	−0.370984	−	0.269536i	0.386635	−	0.922233i	$-0.373637\pi$
$659$	−9.52354	−	6.91926i	−0.370984	−	0.269536i	−0.757619	+	0.652697i	$0.773637\pi$
$660$	3.17524	+	4.37805i	0.123596	+	0.170415i
$661$	1.10614	−	0.803661i	0.0430240	−	0.0312588i	−0.566065	−	0.824360i	$-0.691535\pi$
$661$	1.10614	−	0.803661i	0.0430240	−	0.0312588i	0.609089	+	0.793102i	$0.291535\pi$
$662$	7.74785	+	27.3761i	0.301129	+	1.06400i
$663$	−16.9971	+	2.69208i	−0.660113	+	0.104552i
$664$	−21.7095	+	32.6840i	−0.842490	+	1.26839i
$665$	10.9768	+	12.9217i	0.425660	+	0.501081i
$666$	4.93970	+	2.76044i	0.191410	+	0.106965i
$667$	14.2348	−	27.9374i	0.551175	−	1.08174i
$668$	−23.4527	+	38.4287i	−0.907411	+	1.48685i
$669$	−14.3339	+	4.65737i	−0.554180	+	0.180064i
$670$	10.0035	−	7.85774i	0.386467	−	0.303571i
$671$	−1.41852	−	0.460904i	−0.0547613	−	0.0177930i
$672$	−7.63828	−	4.23193i	−0.294653	−	0.163250i
$673$	48.6142	+	7.69974i	1.87394	+	0.296803i	0.986455	−	0.164033i	$-0.0524502\pi$
$673$	48.6142	+	7.69974i	1.87394	+	0.296803i	0.887486	+	0.460836i	$0.152450\pi$
$674$	−3.18006	−	26.6595i	−0.122491	−	1.02689i
$675$	−16.2892	−	22.6732i	−0.626972	−	0.872692i
$676$	11.8242	−	2.86159i	0.454776	−	0.110061i
$677$	−4.57557	+	28.8890i	−0.175854	+	1.11030i	0.728982	+	0.684533i	$0.239994\pi$
$677$	−4.57557	+	28.8890i	−0.175854	+	1.11030i	−0.904835	+	0.425762i	$0.860006\pi$
$678$	−13.4084	−	20.0275i	−0.514947	−	0.769151i
$679$	1.50986	−	4.64688i	0.0579432	−	0.178331i
$680$	−8.96811	−	13.4195i	−0.343911	−	0.514614i
$681$	−7.75850	−	23.8782i	−0.297306	−	0.915015i
$682$	2.89917	−	3.68450i	0.111015	−	0.141087i
$683$	1.04046	+	0.530142i	0.0398122	+	0.0202853i	0.473783	−	0.880641i	$-0.342888\pi$
$683$	1.04046	+	0.530142i	0.0398122	+	0.0202853i	−0.433971	+	0.900927i	$0.642888\pi$
$684$	−8.65241	−	3.56544i	−0.330833	−	0.136328i
$685$	8.64951	−	35.6097i	0.330481	−	1.36058i
$686$	−0.960917	−	1.03761i	−0.0366880	−	0.0396162i
$687$	3.84713	+	24.2898i	0.146777	+	0.926714i
$688$	14.7066	−	10.7673i	0.560683	−	0.410498i
$689$	9.46021	+	13.0209i	0.360405	+	0.496056i
$690$	−32.1181	−	3.85845i	−1.22272	−	0.146888i
$691$	−11.9723	+	16.4785i	−0.455449	+	0.626871i	−0.973557	−	0.228443i	$-0.926636\pi$
$691$	−11.9723	+	16.4785i	−0.455449	+	0.626871i	0.518108	+	0.855315i	$0.326636\pi$
$692$	1.79704	+	0.427960i	0.0683132	+	0.0162686i
$693$	−0.341852	−	0.341852i	−0.0129859	−	0.0129859i
$694$	−9.63193	−	20.8432i	−0.365623	−	0.791196i
$695$	7.90830	+	33.3313i	0.299979	+	1.26433i
$696$	−20.6400	+	0.867605i	−0.782358	+	0.0328865i
$697$	−7.24966	−	14.2283i	−0.274601	−	0.538934i
$698$	28.1643	+	1.08081i	1.06603	+	0.0409093i
$699$	18.0035			0.680954
$700$	−0.819485	+	9.96637i	−0.0309736	+	0.376693i
$701$	37.2713			1.40772			0.703860	−	0.710339i	$-0.251458\pi$
$701$	37.2713			1.40772			0.703860	+	0.710339i	$0.251458\pi$
$702$	−34.4691	−	1.32276i	−1.30095	−	0.0499244i
$703$	22.3197	+	43.8049i	0.841805	+	1.65213i
$704$	2.43010	+	5.77701i	0.0915877	+	0.217729i
$705$	15.1019	−	9.19922i	0.568771	−	0.346463i
$706$	−0.593014	−	1.28326i	−0.0223184	−	0.0482962i
$707$	4.68024	+	4.68024i	0.176018	+	0.176018i
$708$	1.32726	−	5.57326i	0.0498814	−	0.209456i
$709$	−14.9401	+	20.5633i	−0.561088	+	0.772271i	−0.991464	−	0.130378i	$-0.958381\pi$
$709$	−14.9401	+	20.5633i	−0.561088	+	0.772271i	0.430376	+	0.902649i	$0.358381\pi$
$710$	−9.38656	−	8.70737i	−0.352271	−	0.326782i
$711$	2.51444	+	3.46083i	0.0942987	+	0.129791i
$712$	−42.0970	+	23.7272i	−1.57765	+	0.889215i
$713$	4.38689	+	27.6977i	0.164290	+	1.03729i
$714$	−3.78547	−	4.08761i	−0.141668	−	0.152975i
$715$	−2.90960	−	7.07767i	−0.108813	−	0.264690i
$716$	−9.92135	+	24.0766i	−0.370778	+	0.899784i
$717$	−23.5104	−	11.9792i	−0.878012	−	0.447370i
$718$	32.4228	−	41.2055i	1.21001	−	1.53777i
$719$	−1.15764	−	3.56286i	−0.0431728	−	0.132872i	0.927147	−	0.374698i	$-0.122254\pi$
$719$	−1.15764	−	3.56286i	−0.0431728	−	0.132872i	−0.970320	+	0.241826i	$0.922254\pi$
$720$	−2.11730	−	5.09733i	−0.0789071	−	0.189966i
$721$	−2.90639	+	8.94496i	−0.108240	+	0.333128i
$722$	−30.2841	−	45.2339i	−1.12706	−	1.68343i
$723$	−3.79163	+	23.9394i	−0.141012	+	0.890316i
$724$	11.1463	+	46.0569i	0.414250	+	1.71169i
$725$	10.6278	+	21.1358i	0.394705	+	0.784963i
$726$	2.68560	+	22.5143i	0.0996720	+	0.835584i
$727$	10.7704	+	1.70586i	0.399452	+	0.0632669i	0.352929	−	0.935650i	$-0.385186\pi$
$727$	10.7704	+	1.70586i	0.399452	+	0.0632669i	0.0465231	+	0.998917i	$0.485186\pi$
$728$	9.09598	+	8.36213i	0.337120	+	0.309921i
$729$	28.5641	+	9.28103i	1.05793	+	0.343742i
$730$	−14.0792	−	9.44314i	−0.521096	−	0.349506i
$731$	11.0596	−	3.59348i	0.409054	−	0.132910i
$732$	−5.01730	−	3.06201i	−0.185445	−	0.113175i
$733$	−3.70017	+	7.26200i	−0.136669	+	0.268228i	−0.949190	−	0.314704i	$-0.898095\pi$
$733$	−3.70017	+	7.26200i	−0.136669	+	0.268228i	0.812521	+	0.582932i	$0.198095\pi$
$734$	−4.76569	−	2.66320i	−0.175905	−	0.0983004i
$735$	0.261653	+	3.44180i	0.00965120	+	0.126953i
$736$	−35.2292	−	12.8142i	−1.29856	−	0.472339i
$737$	−3.11257	+	0.492982i	−0.114653	+	0.0181592i
$738$	−1.48711	−	5.25453i	−0.0547414	−	0.193422i
$739$	−28.0866	+	20.4061i	−1.03318	+	0.750651i	−0.968943	−	0.247284i	$-0.920462\pi$
$739$	−28.0866	+	20.4061i	−1.03318	+	0.750651i	−0.0642391	+	0.997935i	$0.520462\pi$
$740$	−8.98367	+	27.5704i	−0.330246	+	1.01351i
$741$	−41.3650	−	30.0535i	−1.51958	−	1.10404i
$742$	−1.79897	+	4.89006i	−0.0660421	+	0.179520i
$743$	16.0055	−	16.0055i	0.587185	−	0.587185i	−0.349683	−	0.936868i	$-0.613711\pi$
$743$	16.0055	−	16.0055i	0.587185	−	0.587185i	0.936868	+	0.349683i	$0.113711\pi$
$744$	14.4783	−	11.4782i	0.530799	−	0.420812i
$745$	26.2690	+	10.9630i	0.962420	+	0.401654i
$746$	−6.87633	+	34.7355i	−0.251760	+	1.27176i
$747$	−7.62770	+	3.88651i	−0.279083	+	0.142200i
$748$	0.321006	+	3.98565i	0.0117371	+	0.145730i
$749$		−	15.2268i		−	0.556376i
$750$	16.6942	−	17.8052i	0.609587	−	0.650155i
$751$		−	12.5470i		−	0.457845i	−0.973445	−	0.228923i	$-0.926480\pi$
$751$		−	12.5470i		−	0.457845i	0.973445	−	0.228923i	$-0.0735202\pi$
$752$	19.4657	−	6.40352i	0.709841	−	0.233512i
$753$	32.0702	−	16.3406i	1.16870	−	0.595483i
$754$	28.6738	+	5.67634i	1.04424	+	0.206720i
$755$	37.1948	+	15.5228i	1.35366	+	0.564933i
$756$	−5.85222	−	9.51091i	−0.212843	−	0.345909i
$757$	−14.4886	+	14.4886i	−0.526597	+	0.526597i	−0.919556	−	0.392959i	$-0.871451\pi$
$757$	−14.4886	+	14.4886i	−0.526597	+	0.526597i	0.392959	+	0.919556i	$0.371451\pi$
$758$	−40.7535	−	14.9925i	−1.48024	−	0.544552i
$759$	6.48352	+	4.71055i	0.235337	+	0.170982i
$760$	9.35193	−	47.0342i	0.339230	−	1.70611i
$761$	−15.2041	+	11.0464i	−0.551149	+	0.400433i	−0.828209	−	0.560420i	$-0.810640\pi$
$761$	−15.2041	+	11.0464i	−0.551149	+	0.400433i	0.277060	+	0.960853i	$0.410640\pi$
$762$	31.7894	−	8.99690i	1.15161	−	0.325923i
$763$	−8.62490	+	1.36605i	−0.312242	+	0.0494543i
$764$	9.83781	−	11.5613i	0.355920	−	0.418273i
$765$	−0.266941	−	3.51137i	−0.00965128	−	0.126954i
$766$	−24.7859	+	44.3534i	−0.895552	+	1.60255i
$767$	−3.68022	+	7.22284i	−0.132885	+	0.260801i
$768$	4.04188	+	24.3656i	0.145849	+	0.879219i
$769$	−12.3628	+	4.01692i	−0.445814	+	0.144854i	−0.523317	−	0.852138i	$-0.675305\pi$
$769$	−12.3628	+	4.01692i	−0.445814	+	0.144854i	0.0775023	+	0.996992i	$0.475305\pi$
$770$	1.37996	−	2.05745i	0.0497303	−	0.0741453i
$771$	14.9644	+	4.86224i	0.538931	+	0.175109i
$772$	25.5253	+	29.7760i	0.918677	+	1.07166i
$773$	8.99951	+	1.42538i	0.323690	+	0.0512674i	0.316165	−	0.948704i	$-0.397605\pi$
$773$	8.99951	+	1.42538i	0.323690	+	0.0512674i	0.00752496	+	0.999972i	$0.497605\pi$
$774$	3.94875	−	0.471023i	0.141935	−	0.0169306i
$775$	−18.8009	−	9.70606i	−0.675349	−	0.348652i
$776$	−12.9524	+	4.81876i	−0.464964	+	0.172983i
$777$	−1.56576	+	9.88579i	−0.0561712	+	0.354651i
$778$	8.17098	−	5.47048i	0.292944	−	0.196126i
$779$	14.6614	−	45.1230i	0.525298	−	1.61670i
$780$	−4.69266	−	29.7896i	−0.168024	−	1.06664i
$781$	0.980161	+	3.01663i	0.0350729	+	0.107943i
$782$	−18.7959	−	14.7897i	−0.672141	−	0.528878i
$783$	−23.5392	−	11.9938i	−0.841221	−	0.428623i
$784$	−0.611298	+	3.95301i	−0.0218321	+	0.141179i
$785$	−8.21295	−	19.9782i	−0.293133	−	0.713052i
$786$	−22.2240	+	20.5813i	−0.792703	+	0.734111i
$787$	−4.43126	−	27.9779i	−0.157957	−	0.997304i	−0.931548	−	0.363618i	$-0.881541\pi$
$787$	−4.43126	−	27.9779i	−0.157957	−	0.997304i	0.773591	−	0.633686i	$-0.218459\pi$
$788$	0.355166	+	0.853035i	0.0126523	+	0.0303881i
$789$	−18.8131	−	25.8941i	−0.669766	−	0.921854i
$790$	−14.9082	+	16.0710i	−0.530409	+	0.571782i
$791$	−6.48929	+	8.93174i	−0.230732	+	0.317576i
$792$	−0.157000	+	1.35836i	−0.00557873	+	0.0482674i
$793$	5.88088	+	5.88088i	0.208836	+	0.208836i
$794$	−23.7558	+	10.9779i	−0.843060	+	0.389590i
$795$	10.8610	−	6.61592i	0.385201	−	0.234643i
$796$	17.3443	+	1.33314i	0.614751	+	0.0472520i
$797$	−3.38478	−	6.64300i	−0.119895	−	0.235307i	0.823257	−	0.567669i	$-0.192155\pi$
$797$	−3.38478	−	6.64300i	−0.119895	−	0.235307i	−0.943152	+	0.332362i	$0.892155\pi$
$798$	0.634749	−	16.5406i	0.0224699	−	0.585530i
$799$	13.0739			0.462520
$800$	23.5295	−	15.6960i	0.831892	−	0.554938i
$801$	−10.5432			−0.372526
$802$	0.939891	−	24.4921i	0.0331887	−	0.864846i
$803$	1.90669	+	3.74209i	0.0672856	+	0.132056i
$804$	−12.3825	−	0.951768i	−0.436699	−	0.0335663i
$805$	3.42084	+	14.4179i	0.120569	+	0.508164i
$806$	−23.7313	+	10.9666i	−0.835900	+	0.386281i
$807$	21.4699	+	21.4699i	0.755778	+	0.755778i
$808$	2.14946	−	18.5971i	0.0756176	−	0.654245i
$809$	19.6048	−	26.9837i	0.689268	−	0.948697i	−0.310730	−	0.950498i	$-0.600573\pi$
$809$	19.6048	−	26.9837i	0.689268	−	0.948697i	0.999998	+	0.00180166i	$0.000573487\pi$
$810$	−2.55271	+	21.2491i	−0.0896932	+	0.746616i
$811$	0.846410	+	1.16498i	0.0297215	+	0.0409081i	0.823619	−	0.567143i	$-0.191951\pi$
$811$	0.846410	+	1.16498i	0.0297215	+	0.0409081i	−0.793898	+	0.608051i	$0.791951\pi$
$812$	3.63728	+	8.73599i	0.127643	+	0.306573i
$813$	−6.11717	−	38.6223i	−0.214538	−	1.35454i
$814$	5.27067	−	4.88109i	0.184737	−	0.171082i
$815$	−0.170106	+	0.700319i	−0.00595855	+	0.0245311i
$816$	−2.40817	+	15.5726i	−0.0843028	+	0.545152i
$817$	30.7847	+	15.6856i	1.07702	+	0.548769i
$818$	4.37995	+	3.44639i	0.153141	+	0.120500i
$819$	0.833037	+	2.56382i	0.0291087	+	0.0895872i
$820$	24.9442	−	12.6834i	0.871090	−	0.442925i
$821$	7.86164	−	24.1956i	0.274373	−	0.844434i	−0.715011	−	0.699113i	$-0.753579\pi$
$821$	7.86164	−	24.1956i	0.274373	−	0.844434i	0.989385	−	0.145321i	$-0.0464215\pi$
$822$	−29.7289	+	19.9035i	−1.03691	+	0.694215i
$823$	−0.841102	+	5.31051i	−0.0293190	+	0.185113i	−0.998002	−	0.0631897i	$-0.979873\pi$
$823$	−0.841102	+	5.31051i	−0.0293190	+	0.185113i	0.968683	+	0.248302i	$0.0798727\pi$
$824$	24.9326	−	9.27583i	0.868568	−	0.323139i
$825$	−5.76057	+	1.83785i	−0.200557	+	0.0639857i
$826$	−2.60587	+	0.310839i	−0.0906699	+	0.0108155i
$827$	54.1186	+	8.57155i	1.88189	+	0.298062i	0.988500	−	0.151221i	$-0.0483206\pi$
$827$	54.1186	+	8.57155i	1.88189	+	0.298062i	0.893389	+	0.449283i	$0.148321\pi$
$828$	−5.32319	−	6.20965i	−0.184994	−	0.215800i
$829$	−25.4926	−	8.28305i	−0.885395	−	0.287682i	−0.169199	−	0.985582i	$-0.554118\pi$
$829$	−25.4926	−	8.28305i	−0.885395	−	0.287682i	−0.716195	+	0.697900i	$0.754118\pi$
$830$	−27.0983	−	34.4980i	−0.940596	−	1.19744i
$831$	−13.4392	+	4.36665i	−0.466200	+	0.151478i
$832$	2.55092	−	34.8538i	0.0884374	−	1.20834i
$833$	−1.15859	+	2.27386i	−0.0401427	+	0.0787844i
$834$	16.3151	−	29.1953i	0.564947	−	1.01095i
$835$	−32.5871	−	38.3611i	−1.12772	−	1.32754i
$836$	−7.69907	+	9.04787i	−0.266278	+	0.312927i
$837$	23.3372	−	3.69625i	0.806651	−	0.127761i
$838$	6.28615	−	1.77908i	0.217151	−	0.0614572i
$839$	−7.07927	+	5.14339i	−0.244404	+	0.177570i	−0.703243	−	0.710950i	$-0.748265\pi$
$839$	−7.07927	+	5.14339i	−0.244404	+	0.177570i	0.458839	+	0.888519i	$0.348265\pi$
$840$	7.16866	−	6.62766i	0.247342	−	0.228676i
$841$	−5.35017	−	3.88712i	−0.184489	−	0.134039i
$842$	−9.48598	−	3.48972i	−0.326908	−	0.120264i
$843$	−3.68411	+	3.68411i	−0.126888	+	0.126888i
$844$	−0.223952	−	0.363963i	−0.00770876	−	0.0125281i
$845$	−1.10328	+	13.5567i	−0.0379538	+	0.466363i
$846$	4.38582	+	0.868230i	0.150788	+	0.0298504i
$847$	9.25423	−	4.71526i	0.317979	−	0.162018i
$848$	13.9994	−	4.60530i	0.480741	−	0.158147i
$849$			18.0481i			0.619410i
$850$	17.3894	−	4.82154i	0.596450	−	0.165378i
$851$			42.9683i			1.47294i
$852$	1.00349	+	12.4595i	0.0343791	+	0.426857i
$853$	−33.6030	+	17.1216i	−1.15054	+	0.586232i	−0.921957	−	0.387292i	$-0.873411\pi$
$853$	−33.6030	+	17.1216i	−1.15054	+	0.586232i	−0.228587	+	0.973523i	$0.573411\pi$
$854$	−0.522864	+	2.64122i	−0.0178920	+	0.0903807i
$855$	6.81623	−	7.93787i	0.233110	−	0.271469i
$856$	−33.7488	+	26.7557i	−1.15351	+	0.914490i
$857$	−34.8301	+	34.8301i	−1.18977	+	1.18977i	−0.212644	+	0.977130i	$0.568207\pi$
$857$	−34.8301	+	34.8301i	−1.18977	+	1.18977i	−0.977130	+	0.212644i	$0.931793\pi$
$858$	−2.57944	+	7.01160i	−0.0880607	+	0.239372i
$859$	32.9337	+	23.9277i	1.12368	+	0.816404i	0.984763	−	0.173900i	$-0.0556368\pi$
$859$	32.9337	+	23.9277i	1.12368	+	0.816404i	0.138920	+	0.990304i	$0.455637\pi$
$860$	6.28099	+	19.3861i	0.214180	+	0.661060i
$861$	7.81446	−	5.67754i	0.266316	−	0.193490i
$862$	−11.2308	−	39.6828i	−0.382524	−	1.35160i
$863$	20.5327	−	3.25206i	0.698942	−	0.110702i	0.203156	−	0.979146i	$-0.434880\pi$
$863$	20.5327	−	3.25206i	0.698942	−	0.110702i	0.495786	+	0.868445i	$0.334880\pi$
$864$	−10.7968	+	29.6829i	−0.367316	+	1.00983i
$865$	−1.08382	+	1.75811i	−0.0368511	+	0.0597776i
$866$	−8.74912	−	4.88925i	−0.297307	−	0.166144i
$867$	7.34955	−	14.4243i	0.249604	−	0.489875i
$868$	−7.22430	−	4.40892i	−0.245209	−	0.149649i
$869$	5.16486	−	1.67817i	0.175206	−	0.0569279i
$870$	6.30826	−	22.2185i	0.213870	−	0.753276i
$871$	16.7122	+	5.43013i	0.566272	+	0.183993i
$872$	18.1829	+	16.7159i	0.615751	+	0.566072i
$873$	−2.97808	−	0.471681i	−0.100793	−	0.0159640i
$874$	−8.41670	−	70.5601i	−0.284699	−	2.38673i
$875$	−10.2948	−	4.36094i	−0.348027	−	0.147427i
$876$	3.89315	+	16.0866i	0.131537	+	0.543516i
$877$	−2.29142	+	14.4674i	−0.0773757	+	0.488531i	0.918319	+	0.395840i	$0.129547\pi$
$877$	−2.29142	+	14.4674i	−0.0773757	+	0.488531i	−0.995695	+	0.0926903i	$0.970453\pi$
$878$	−19.2321	−	28.7260i	−0.649052	−	0.969456i
$879$	10.8120	−	33.2758i	0.364679	−	1.12237i
$880$	−6.98492	+	0.556685i	−0.235462	+	0.0187658i
$881$	−11.6721	−	35.9230i	−0.393243	−	1.21028i	−0.930321	−	0.366745i	$-0.880472\pi$
$881$	−11.6721	−	35.9230i	−0.393243	−	1.21028i	0.537079	−	0.843532i	$-0.319528\pi$
$882$	−0.539671	+	0.685857i	−0.0181717	+	0.0230940i
$883$	−35.3957	−	18.0350i	−1.19116	−	0.606926i	−0.257915	−	0.966168i	$-0.583035\pi$
$883$	−35.3957	−	18.0350i	−1.19116	−	0.606926i	−0.933245	+	0.359242i	$0.883035\pi$
$884$	8.49477	−	20.6146i	0.285710	−	0.693345i
$885$	5.45253	+	3.36133i	0.183285	+	0.112990i
$886$	26.5431	+	28.6615i	0.891732	+	0.962904i
$887$	8.47198	+	53.4900i	0.284461	+	1.79602i	0.553459	+	0.832876i	$0.313307\pi$
$887$	8.47198	+	53.4900i	0.284461	+	1.79602i	−0.268998	+	0.963141i	$0.586693\pi$
$888$	24.6622	−	13.9004i	0.827608	−	0.466467i
$889$	−8.89541	−	12.2435i	−0.298342	−	0.410633i
$890$	−10.4474	−	53.0073i	−0.350197	−	1.77681i
$891$	3.11646	−	4.28944i	0.104405	−	0.143702i
$892$	4.52379	−	18.9958i	0.151468	−	0.636026i
$893$	27.4669	+	27.4669i	0.919146	+	0.919146i
$894$	−11.6577	−	25.2268i	−0.389891	−	0.843710i
$895$	−22.0882	−	18.9671i	−0.738329	−	0.634001i
$896$	9.83562	−	5.59112i	0.328585	−	0.186786i
$897$	−20.2875	−	39.8165i	−0.677380	−	1.32943i
$898$	−52.9441	−	2.03174i	−1.76677	−	0.0678002i
$899$	−20.0222			−0.667777
$900$	6.15371	−	0.462638i	0.205124	−	0.0154213i
$901$	9.40251			0.313243
$902$	−6.92749	−	0.265844i	−0.230660	−	0.00885165i
$903$	3.19338	+	6.26735i	0.106269	+	0.208564i
$904$	31.1989	−	1.31145i	1.03766	−	0.0436182i
$905$	−52.8051	−	4.29742i	−1.75530	−	0.142851i
$906$	−16.5064	−	35.7192i	−0.548387	−	1.18669i
$907$	1.10773	+	1.10773i	0.0367816	+	0.0367816i	0.725258	−	0.688477i	$-0.241720\pi$
$907$	1.10773	+	1.10773i	0.0367816	+	0.0367816i	−0.688477	+	0.725258i	$0.741720\pi$
$908$	31.6442	+	7.53598i	1.05015	+	0.250090i
$909$	2.40084	−	3.30447i	0.0796307	−	0.109602i
$910$	−12.0645	+	6.72873i	−0.399934	+	0.223055i
$911$	−10.1621	−	13.9869i	−0.336684	−	0.463406i	0.606785	−	0.794866i	$-0.292459\pi$
$911$	−10.1621	−	13.9869i	−0.336684	−	0.463406i	−0.943469	+	0.331460i	$0.892459\pi$
$912$	−37.7759	+	27.6573i	−1.25089	+	0.915824i
$913$	1.70010	+	10.7340i	0.0562652	+	0.355245i
$914$	28.2050	+	30.4562i	0.932939	+	1.00740i
$915$	5.00847	−	4.25462i	0.165575	−	0.140653i
$916$	−29.4595	−	12.1395i	−0.973369	−	0.401101i
$917$	12.3628	+	6.29915i	0.408255	+	0.208016i
$918$	−12.4613	+	15.8368i	−0.411284	+	0.522693i
$919$	10.3350	+	31.8078i	0.340920	+	1.04924i	0.963732	+	0.266871i	$0.0859899\pi$
$919$	10.3350	+	31.8078i	0.340920	+	1.04924i	−0.622813	+	0.782371i	$0.714010\pi$
$920$	25.9450	−	32.9163i	0.855381	−	1.08522i
$921$	7.67916	−	23.6340i	0.253037	−	0.778767i
$922$	−3.77174	−	5.63366i	−0.124216	−	0.185535i
$923$	2.76679	−	17.4688i	0.0910701	−	0.574994i
$924$	−2.35079	+	0.568919i	−0.0773354	+	0.0187161i
$925$	−26.1262	−	19.1953i	−0.859025	−	0.631138i
$926$	−0.916510	−	7.68342i	−0.0301184	−	0.252493i
$927$	5.73262	+	0.907958i	0.188284	+	0.0298213i
$928$	12.9713	−	23.4121i	0.425803	−	0.768539i
$929$	−8.63212	−	2.80475i	−0.283211	−	0.0920207i	0.163967	−	0.986466i	$-0.447571\pi$
$929$	−8.63212	−	2.80475i	−0.283211	−	0.0920207i	−0.447178	+	0.894445i	$0.647571\pi$
$930$	7.11581	+	19.3927i	0.233336	+	0.635912i
$931$	−7.21123	+	2.34307i	−0.236338	+	0.0767910i
$932$	−12.1513	+	19.9106i	−0.398028	+	0.652195i
$933$	−7.05774	+	13.8516i	−0.231060	+	0.453481i
$934$	26.0877	+	14.5785i	0.853617	+	0.477025i
$935$	−4.34421	−	1.05520i	−0.142071	−	0.0345087i
$936$	4.21871	−	6.35135i	0.137893	−	0.207600i
$937$	56.4787	−	8.94535i	1.84508	−	0.292232i	0.866666	−	0.498888i	$-0.166258\pi$
$937$	56.4787	−	8.94535i	1.84508	−	0.292232i	0.978414	+	0.206656i	$0.0662582\pi$
$938$	1.54918	+	5.47382i	0.0505824	+	0.178727i
$939$	−12.8281	+	9.32017i	−0.418630	+	0.304152i
$940$	−0.0191726	+	22.9106i	−0.000625342	+	0.747263i
$941$	35.6792	+	25.9224i	1.16311	+	0.845048i	0.990168	−	0.139885i	$-0.0446732\pi$
$941$	35.6792	+	25.9224i	1.16311	+	0.845048i	0.172941	+	0.984932i	$0.444673\pi$
$942$	−7.28101	+	19.7917i	−0.237228	+	0.644848i
$943$	29.3213	−	29.3213i	0.954833	−	0.954833i
$944$	5.26784	+	5.22948i	0.171453	+	0.170205i
$945$	12.1480	−	2.88228i	0.395176	−	0.0937607i
$946$	0.980379	−	4.95234i	0.0318749	−	0.161014i
$947$	−14.4384	+	7.35675i	−0.469186	+	0.239062i	−0.672565	−	0.740038i	$-0.734808\pi$
$947$	−14.4384	+	7.35675i	−0.469186	+	0.239062i	0.203379	+	0.979100i	$0.434808\pi$
$948$	21.3324	−	1.71811i	0.692843	−	0.0558018i
$949$		−	23.4187i		−	0.760203i
$950$	46.6630	+	26.4038i	1.51395	+	0.856651i
$951$			38.9745i			1.26383i
$952$	7.07559	−	1.42759i	0.229321	−	0.0462685i
$953$	−29.6274	+	15.0959i	−0.959724	+	0.489004i	−0.862388	−	0.506248i	$-0.831032\pi$
$953$	−29.6274	+	15.0959i	−0.959724	+	0.489004i	−0.0973361	+	0.995252i	$0.531032\pi$
$954$	3.15421	+	0.624416i	0.102121	+	0.0202162i
$955$	8.82941	+	14.4948i	0.285713	+	0.469041i
$956$	29.1163	−	17.9157i	0.941687	−	0.579436i
$957$	−4.04599	+	4.04599i	−0.130788	+	0.130788i
$958$	55.1136	+	20.2753i	1.78064	+	0.655066i
$959$	13.2583	+	9.63273i	0.428133	+	0.311057i
$960$	−27.2860	−	4.24291i	−0.880650	−	0.136939i
$961$	−10.5922	+	7.69570i	−0.341685	+	0.248248i
$962$	−38.5428	+	10.9082i	−1.24267	+	0.351695i
$963$	−9.28090	+	1.46995i	−0.299073	+	0.0473685i
$964$	−23.9162	−	20.3510i	−0.770290	−	0.655460i
$965$	−40.5553	+	16.6721i	−1.30552	+	0.536695i
$966$	7.05732	−	12.6288i	0.227065	−	0.406325i
$967$	−23.3723	+	45.8708i	−0.751604	+	1.47511i	0.124106	+	0.992269i	$0.460394\pi$
$967$	−23.3723	+	45.8708i	−0.751604	+	1.47511i	−0.875710	+	0.482837i	$0.839606\pi$
$968$	−26.7119	−	12.2257i	−0.858554	−	0.392950i
$969$	−28.4082	+	9.23038i	−0.912602	+	0.296522i
$970$	−0.579577	−	15.4401i	−0.0186091	−	0.495751i
$971$	2.05800	+	0.668684i	0.0660443	+	0.0214591i	0.341853	−	0.939754i	$-0.388946\pi$
$971$	2.05800	+	0.668684i	0.0660443	+	0.0214591i	−0.275809	+	0.961213i	$0.588946\pi$
$972$	−9.57146	+	8.20509i	−0.307005	+	0.263178i
$973$	−15.1314	−	2.39658i	−0.485091	−	0.0768309i
$974$	5.98545	−	0.713970i	0.191786	−	0.0228771i
$975$	33.2728	+	5.45177i	1.06558	+	0.174596i
$976$	6.77276	−	3.48212i	0.216791	−	0.111460i
$977$	−6.51764	+	41.1508i	−0.208518	+	1.31653i	0.632094	+	0.774892i	$0.282196\pi$
$977$	−6.51764	+	41.1508i	−0.208518	+	1.31653i	−0.840612	+	0.541638i	$0.817804\pi$
$978$	0.584665	−	0.391433i	0.0186955	−	0.0125167i
$979$	−4.13604	+	12.7294i	−0.132189	+	0.406835i
$980$	−3.98300	−	2.03364i	−0.127232	−	0.0649623i
$981$	1.66524	+	5.12509i	0.0531671	+	0.163632i
$982$	−1.51169	−	1.18948i	−0.0482399	−	0.0379579i
$983$	−13.6096	−	6.93443i	−0.434078	−	0.221174i	0.223276	−	0.974755i	$-0.428325\pi$
$983$	−13.6096	−	6.93443i	−0.434078	−	0.221174i	−0.657355	+	0.753581i	$0.728325\pi$
$984$	−26.3148	−	7.34376i	−0.838886	−	0.234111i
$985$	−1.03011	+	0.0783112i	−0.0328221	+	0.00249520i
$986$	12.5289	−	11.6028i	0.399002	−	0.369510i
$987$	1.23711	+	7.81078i	0.0393775	+	0.248620i
$988$	61.1560	−	25.4627i	1.94563	−	0.810075i
$989$	17.7492	+	24.4297i	0.564392	+	0.776819i
$990$	−1.38725	−	0.642479i	−0.0440898	−	0.0204193i
$991$	−15.2543	+	20.9957i	−0.484568	+	0.666950i	−0.979375	−	0.202053i	$-0.935239\pi$
$991$	−15.2543	+	20.9957i	−0.484568	+	0.666950i	0.494807	+	0.869003i	$0.335239\pi$
$992$	2.92217	+	23.7591i	0.0927790	+	0.754352i
$993$	21.9596	+	21.9596i	0.696868	+	0.696868i
$994$	5.19768	−	2.40192i	0.164861	−	0.0761844i
$995$	−7.49052	+	17.9483i	−0.237466	+	0.569001i
$996$	−3.28228	+	42.7026i	−0.104003	+	1.35308i
$997$	18.6526	+	36.6078i	0.590734	+	1.15938i	0.972014	+	0.234921i	$0.0754833\pi$
$997$	18.6526	+	36.6078i	0.590734	+	1.15938i	−0.381280	+	0.924460i	$0.624517\pi$
$998$	−1.57656	+	41.0827i	−0.0499052	+	1.30045i
$999$	36.2037			1.14543

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.bj.a.323.44	yes	720
4.3	odd	2	inner	700.2.bj.a.323.37	✓	720
25.12	odd	20	inner	700.2.bj.a.687.37	yes	720
100.87	even	20	inner	700.2.bj.a.687.44	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.bj.a.323.37	✓	720	4.3	odd	2	inner
700.2.bj.a.323.44	yes	720	1.1	even	1	trivial
700.2.bj.a.687.37	yes	720	25.12	odd	20	inner
700.2.bj.a.687.44	yes	720	100.87	even	20	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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0542309 + 1.41317i) q^{2} +(0.700808 + 1.37541i) q^{3} +(-1.99412 - 0.153275i) q^{4} +(0.861206 - 2.06357i) q^{5} +(-1.98170 + 0.915773i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.324747 - 2.80972i) q^{8} +(0.362727 - 0.499251i) q^{9} +(2.86948 + 1.32894i) q^{10} +(-0.460480 - 0.633796i) q^{11} +(-1.18668 - 2.85015i) q^{12} +(0.683366 + 4.31460i) q^{13} +(-1.03761 + 0.960917i) q^{14} +(3.44180 - 0.261653i) q^{15} +(3.95301 + 0.611298i) q^{16} +(2.27386 + 1.15859i) q^{17} +(0.685857 + 0.539671i) q^{18} +(2.34307 + 7.21123i) q^{19} +(-2.03364 + 3.98300i) q^{20} +(-0.477018 + 1.46811i) q^{21} +(0.920635 - 0.616366i) q^{22} +(-1.03667 + 6.54529i) q^{23} +(4.09211 - 1.52241i) q^{24} +(-3.51665 - 3.55432i) q^{25} +(-6.13434 + 0.731729i) q^{26} +(5.51485 + 0.873466i) q^{27} +(-1.30167 - 1.51844i) q^{28} +(-4.49990 - 1.46211i) q^{29} +(0.183108 + 4.87805i) q^{30} +(4.02459 - 1.30767i) q^{31} +(-1.07825 + 5.55314i) q^{32} +(0.549023 - 1.07752i) q^{33} +(-1.76060 + 3.15052i) q^{34} +(2.06813 - 0.850200i) q^{35} +(-0.799843 + 0.939968i) q^{36} +(6.40412 - 1.01431i) q^{37} +(-10.3178 + 2.92009i) q^{38} +(-5.45545 + 3.96362i) q^{39} +(-5.51839 - 3.08989i) q^{40} +(-5.06229 - 3.67797i) q^{41} +(-2.04882 - 0.753726i) q^{42} +(3.22208 - 3.22208i) q^{43} +(0.821105 + 1.33444i) q^{44} +(-0.717857 - 1.17847i) q^{45} +(-9.19342 - 1.81996i) q^{46} +(4.56461 - 2.32578i) q^{47} +(1.92952 + 5.86543i) q^{48} +1.00000i q^{49} +(5.21358 - 4.77688i) q^{50} +3.93944i q^{51} +(-0.701390 - 8.70857i) q^{52} +(3.28279 - 1.67266i) q^{53} +(-1.53343 + 7.74607i) q^{54} +(-1.70445 + 0.404403i) q^{55} +(2.21640 - 1.75714i) q^{56} +(-8.27637 + 8.27637i) q^{57} +(2.31024 - 6.27984i) q^{58} +(1.50129 + 1.09075i) q^{59} +(-6.90346 - 0.00577712i) q^{60} +(1.54026 - 1.11907i) q^{61} +(1.62970 + 5.75835i) q^{62} +(0.609510 - 0.0965369i) q^{63} +(-7.78908 - 1.82490i) q^{64} +(9.49200 + 2.30559i) q^{65} +(1.49295 + 0.834300i) q^{66} +(1.82622 - 3.58416i) q^{67} +(-4.35675 - 2.65889i) q^{68} +(-9.72899 + 3.16114i) q^{69} +(1.08932 + 2.96873i) q^{70} +(-3.85061 - 1.25114i) q^{71} +(-1.28496 - 1.18129i) q^{72} +(-5.29495 - 0.838637i) q^{73} +(1.08610 + 9.10514i) q^{74} +(2.42416 - 7.32774i) q^{75} +(-3.56706 - 14.7392i) q^{76} +(0.122553 - 0.773769i) q^{77} +(-5.30542 - 7.92445i) q^{78} +(-2.14212 + 6.59276i) q^{79} +(4.66582 - 7.63087i) q^{80} +(2.09138 + 6.43661i) q^{81} +(5.47214 - 6.95443i) q^{82} +(-12.3604 - 6.29793i) q^{83} +(1.17625 - 2.85447i) q^{84} +(4.34908 - 3.69448i) q^{85} +(4.37862 + 4.72809i) q^{86} +(-1.14257 - 7.21387i) q^{87} +(-1.93033 + 1.08800i) q^{88} +(-10.0422 - 13.8219i) q^{89} +(1.70431 - 0.950546i) q^{90} +(-2.56767 + 3.53410i) q^{91} +(3.07048 - 12.8932i) q^{92} +(4.61904 + 4.61904i) q^{93} +(3.03919 + 6.57671i) q^{94} +(16.8987 + 1.37526i) q^{95} +(-8.39351 + 2.40865i) q^{96} +(-2.21821 - 4.35347i) q^{97} +(-1.41317 - 0.0542309i) q^{98} -0.483451 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q + 16 q^{10} + 16 q^{12} + 4 q^{13} + 20 q^{17} - 28 q^{18} - 20 q^{20} - 4 q^{22} + 20 q^{25} + 4 q^{30} - 20 q^{37} - 64 q^{40} - 80 q^{42} - 140 q^{44} - 20 q^{45} - 236 q^{48} - 40 q^{50} - 16 q^{52}+ \cdots - 20 q^{97}+O(q^{100}) \) 720 * q + 16 * q^10 + 16 * q^12 + 4 * q^13 + 20 * q^17 - 28 * q^18 - 20 * q^20 - 4 * q^22 + 20 * q^25 + 4 * q^30 - 20 * q^37 - 64 * q^40 - 80 * q^42 - 140 * q^44 - 20 * q^45 - 236 * q^48 - 40 * q^50 - 16 * q^52 + 44 * q^53 - 260 * q^54 + 16 * q^57 - 136 * q^58 - 140 * q^60 - 140 * q^62 - 4 * q^65 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 76 * q^78 + 20 * q^80 + 180 * q^81 + 24 * q^82 - 80 * q^85 + 160 * q^88 - 260 * q^89 + 16 * q^90 + 256 * q^92 - 112 * q^93 + 320 * q^94 - 40 * q^96 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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