LMFDB - Embedded newform 252.2.n.b.187.38

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [252,2,Mod(31,252)] 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("252.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(252, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [84] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			187.38
Character	$\chi$	$=$	252.187
Dual form			252.2.n.b.31.38

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.30137 - 0.553558i) q^{2} +(1.49040 - 0.882451i) q^{3} +(1.38715 - 1.44077i) q^{4} +4.05112i q^{5} +(1.45107 - 1.97342i) q^{6} +(-2.21649 - 1.44470i) q^{7} +(1.00765 - 2.64285i) q^{8} +(1.44256 - 2.63040i) q^{9} +(2.24253 + 5.27202i) q^{10} +0.543883i q^{11} +(0.795990 - 3.37141i) q^{12} +(-1.01063 + 0.583488i) q^{13} +(-3.68421 - 0.653137i) q^{14} +(3.57492 + 6.03778i) q^{15} +(-0.151642 - 3.99712i) q^{16} +(-5.05773 + 2.92008i) q^{17} +(0.421231 - 4.22168i) q^{18} +(1.16501 - 2.01785i) q^{19} +(5.83674 + 5.61950i) q^{20} +(-4.57833 - 0.197227i) q^{21} +(0.301071 + 0.707796i) q^{22} +1.61483i q^{23} +(-0.830389 - 4.82809i) q^{24} -11.4116 q^{25} +(-0.992214 + 1.31878i) q^{26} +(-0.171215 - 5.19333i) q^{27} +(-5.15609 + 1.18945i) q^{28} +(2.40001 - 4.15694i) q^{29} +(7.99456 + 5.87848i) q^{30} +(-2.24515 + 3.88871i) q^{31} +(-2.40998 - 5.11781i) q^{32} +(0.479950 + 0.810602i) q^{33} +(-4.96557 + 6.59987i) q^{34} +(5.85265 - 8.97929i) q^{35} +(-1.78876 - 5.72716i) q^{36} +(-1.48498 + 2.57206i) q^{37} +(0.399112 - 3.27088i) q^{38} +(-0.991340 + 1.76146i) q^{39} +(10.7065 + 4.08210i) q^{40} +(3.89836 - 2.25072i) q^{41} +(-6.06729 + 2.27770i) q^{42} +(-2.89521 - 1.67155i) q^{43} +(0.783611 + 0.754447i) q^{44} +(10.6561 + 5.84399i) q^{45} +(0.893904 + 2.10150i) q^{46} +(4.29074 + 7.43179i) q^{47} +(-3.75327 - 5.82348i) q^{48} +(2.82569 + 6.40433i) q^{49} +(-14.8507 + 6.31697i) q^{50} +(-4.96120 + 8.81528i) q^{51} +(-0.561221 + 2.26547i) q^{52} +(5.84343 + 10.1211i) q^{53} +(-3.09762 - 6.66369i) q^{54} -2.20334 q^{55} +(-6.05157 + 4.40211i) q^{56} +(-0.0443331 - 4.03546i) q^{57} +(0.822204 - 6.73827i) q^{58} +(6.43904 - 11.1527i) q^{59} +(13.6580 + 3.22465i) q^{60} +(1.80408 - 1.04158i) q^{61} +(-0.769151 + 6.30348i) q^{62} +(-6.99757 + 3.74621i) q^{63} +(-5.96929 - 5.32612i) q^{64} +(-2.36378 - 4.09419i) q^{65} +(1.07331 + 0.789215i) q^{66} +(-6.14549 - 3.54810i) q^{67} +(-2.80865 + 11.3376i) q^{68} +(1.42501 + 2.40674i) q^{69} +(2.64594 - 14.9252i) q^{70} -5.17264i q^{71} +(-5.49816 - 6.46299i) q^{72} +(5.58686 - 3.22558i) q^{73} +(-0.508730 + 4.16923i) q^{74} +(-17.0078 + 10.0702i) q^{75} +(-1.29122 - 4.47756i) q^{76} +(0.785748 - 1.20551i) q^{77} +(-0.315035 + 2.84108i) q^{78} +(3.48731 - 2.01340i) q^{79} +(16.1928 - 0.614320i) q^{80} +(-4.83804 - 7.58903i) q^{81} +(3.82732 - 5.08700i) q^{82} +(-2.76985 + 4.79753i) q^{83} +(-6.63498 + 6.32274i) q^{84} +(-11.8296 - 20.4895i) q^{85} +(-4.69305 - 0.572646i) q^{86} +(-0.0913299 - 8.31337i) q^{87} +(1.43740 + 0.548043i) q^{88} +(-7.63381 - 4.40738i) q^{89} +(17.1025 + 1.70646i) q^{90} +(3.08302 + 0.166760i) q^{91} +(2.32661 + 2.24001i) q^{92} +(0.0854368 + 7.77695i) q^{93} +(9.69779 + 7.29636i) q^{94} +(8.17456 + 4.71958i) q^{95} +(-8.10804 - 5.50087i) q^{96} +(13.8033 + 7.96935i) q^{97} +(7.22244 + 6.77025i) q^{98} +(1.43063 + 0.784585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - q^{2} + q^{4} - 16 q^{8} - 14 q^{9} - 18 q^{10} + 9 q^{12} - 18 q^{13} - 25 q^{14} - 7 q^{16} + 6 q^{17} - 13 q^{18} + 24 q^{20} + 4 q^{21} + 6 q^{22} + 6 q^{24} - 32 q^{25} - 30 q^{26} - 4 q^{28}+ \cdots + 21 q^{98}+O(q^{100}) $ 84 * q - q^2 + q^4 - 16 * q^8 - 14 * q^9 - 18 * q^10 + 9 * q^12 - 18 * q^13 - 25 * q^14 - 7 * q^16 + 6 * q^17 - 13 * q^18 + 24 * q^20 + 4 * q^21 + 6 * q^22 + 6 * q^24 - 32 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 14 * q^30 + 9 * q^32 - 6 * q^33 + 24 * q^34 - 38 * q^36 + 2 * q^37 - 6 * q^41 + 7 * q^42 - 13 * q^44 - 18 * q^45 + 10 * q^46 - 9 * q^48 + 2 * q^49 - 17 * q^50 - 2 * q^53 - 42 * q^54 - 32 * q^56 + 6 * q^57 + 26 * q^58 + 8 * q^60 - 24 * q^61 - 8 * q^64 + 50 * q^65 + 27 * q^66 + 18 * q^69 - 4 * q^70 - 7 * q^72 + 30 * q^73 + 46 * q^74 + 46 * q^77 + 15 * q^78 + 3 * q^80 - 26 * q^81 - 18 * q^82 + 29 * q^84 - 50 * q^85 + 18 * q^86 - 2 * q^88 - 102 * q^89 + 39 * q^90 + 28 * q^92 - 24 * q^93 + 3 * q^94 - 30 * q^96 - 6 * q^97 + 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.30137	−	0.553558i	0.920210	−	0.391424i
$2$	1.30137	−	0.553558i	0.920210	−	0.391424i
$3$	1.49040	−	0.882451i	0.860481	−	0.509483i
$3$	1.49040	−	0.882451i	0.860481	−	0.509483i
$4$	1.38715	−	1.44077i	0.693574	−	0.720385i
$5$			4.05112i			1.81172i	0.423581	+	0.905858i	$0.360773\pi$
$5$			4.05112i			1.81172i	−0.423581	+	0.905858i	$0.639227\pi$
$6$	1.45107	−	1.97342i	0.592399	−	0.805645i
$7$	−2.21649	−	1.44470i	−0.837756	−	0.546045i
$7$	−2.21649	−	1.44470i	−0.837756	−	0.546045i
$8$	1.00765	−	2.64285i	0.356257	−	0.934388i
$9$	1.44256	−	2.63040i	0.480853	−	0.876801i
$10$	2.24253	+	5.27202i	0.709150	+	1.66716i
$11$			0.543883i			0.163987i	0.996633	+	0.0819935i	$0.0261287\pi$
$11$			0.543883i			0.163987i	−0.996633	+	0.0819935i	$0.973871\pi$
$12$	0.795990	−	3.37141i	0.229782	−	0.973242i
$13$	−1.01063	+	0.583488i	−0.280298	+	0.161830i	−0.633558	−	0.773695i	$-0.718406\pi$
$13$	−1.01063	+	0.583488i	−0.280298	+	0.161830i	0.353260	+	0.935525i	$0.385073\pi$
$14$	−3.68421	−	0.653137i	−0.984647	−	0.174558i
$15$	3.57492	+	6.03778i	0.923039	+	1.55895i
$16$	−0.151642	−	3.99712i	−0.0379105	−	0.999281i
$17$	−5.05773	+	2.92008i	−1.22668	+	0.708224i	−0.966334	−	0.257291i	$-0.917170\pi$
$17$	−5.05773	+	2.92008i	−1.22668	+	0.708224i	−0.260347	+	0.965515i	$0.583837\pi$
$18$	0.421231	−	4.22168i	0.0992850	−	0.995059i
$19$	1.16501	−	2.01785i	0.267271	−	0.462927i	−0.700885	−	0.713274i	$-0.747212\pi$
$19$	1.16501	−	2.01785i	0.267271	−	0.462927i	0.968156	+	0.250347i	$0.0805448\pi$
$20$	5.83674	+	5.61950i	1.30513	+	1.25656i
$21$	−4.57833	−	0.197227i	−0.999073	−	0.0430384i
$22$	0.301071	+	0.707796i	0.0641885	+	0.150903i
$23$			1.61483i			0.336716i	0.985726	+	0.168358i	$0.0538465\pi$
$23$			1.61483i			0.336716i	−0.985726	+	0.168358i	$0.946153\pi$
$24$	−0.830389	−	4.82809i	−0.169502	−	0.985530i
$25$	−11.4116			−2.28232
$26$	−0.992214	+	1.31878i	−0.194589	+	0.258634i
$27$	−0.171215	−	5.19333i	−0.0329504	−	0.999457i
$28$	−5.15609	+	1.18945i	−0.974408	+	0.224785i
$29$	2.40001	−	4.15694i	0.445670	−	0.771924i	−0.552428	−	0.833560i	$-0.686299\pi$
$29$	2.40001	−	4.15694i	0.445670	−	0.771924i	0.998099	+	0.0616368i	$0.0196320\pi$
$30$	7.99456	+	5.87848i	1.45960	+	1.07326i
$31$	−2.24515	+	3.88871i	−0.403240	+	0.698433i	−0.994115	−	0.108331i	$-0.965449\pi$
$31$	−2.24515	+	3.88871i	−0.403240	+	0.698433i	0.590875	+	0.806763i	$0.298783\pi$
$32$	−2.40998	−	5.11781i	−0.426029	−	0.904710i
$33$	0.479950	+	0.810602i	0.0835486	+	0.141108i
$34$	−4.96557	+	6.59987i	−0.851588	+	1.13187i
$35$	5.85265	−	8.97929i	0.989279	−	1.51778i
$36$	−1.78876	−	5.72716i	−0.298127	−	0.954526i
$37$	−1.48498	+	2.57206i	−0.244129	+	0.422844i	−0.961886	−	0.273450i	$-0.911835\pi$
$37$	−1.48498	+	2.57206i	−0.244129	+	0.422844i	0.717757	+	0.696293i	$0.245169\pi$
$38$	0.399112	−	3.27088i	0.0647446	−	0.530606i
$39$	−0.991340	+	1.76146i	−0.158741	+	0.282059i
$40$	10.7065	+	4.08210i	1.69285	+	0.645437i
$41$	3.89836	−	2.25072i	0.608822	−	0.351504i	−0.163682	−	0.986513i	$-0.552337\pi$
$41$	3.89836	−	2.25072i	0.608822	−	0.351504i	0.772504	+	0.635010i	$0.219004\pi$
$42$	−6.06729	+	2.27770i	−0.936204	+	0.351457i
$43$	−2.89521	−	1.67155i	−0.441515	−	0.254909i	0.262725	−	0.964871i	$-0.415379\pi$
$43$	−2.89521	−	1.67155i	−0.441515	−	0.254909i	−0.704240	+	0.709962i	$0.748712\pi$
$44$	0.783611	+	0.754447i	0.118134	+	0.113737i
$45$	10.6561	+	5.84399i	1.58851	+	0.871170i
$46$	0.893904	+	2.10150i	0.131799	+	0.309850i
$47$	4.29074	+	7.43179i	0.625869	+	1.08404i	0.988372	+	0.152055i	$0.0485890\pi$
$47$	4.29074	+	7.43179i	0.625869	+	1.08404i	−0.362503	+	0.931983i	$0.618078\pi$
$48$	−3.75327	−	5.82348i	−0.541738	−	0.840547i
$49$	2.82569	+	6.40433i	0.403670	+	0.914905i
$50$	−14.8507	+	6.31697i	−2.10021	+	0.893355i
$51$	−4.96120	+	8.81528i	−0.694706	+	1.23439i
$52$	−0.561221	+	2.26547i	−0.0778274	+	0.314164i
$53$	5.84343	+	10.1211i	0.802658	+	1.39024i	0.917861	+	0.396902i	$0.129915\pi$
$53$	5.84343	+	10.1211i	0.802658	+	1.39024i	−0.115204	+	0.993342i	$0.536752\pi$
$54$	−3.09762	−	6.66369i	−0.421533	−	0.906813i
$55$	−2.20334			−0.297098
$56$	−6.05157	+	4.40211i	−0.808675	+	0.588256i
$57$	−0.0443331	−	4.03546i	−0.00587207	−	0.534509i
$58$	0.822204	−	6.73827i	0.107961	−	0.884778i
$59$	6.43904	−	11.1527i	0.838292	−	1.45196i	−0.0530303	−	0.998593i	$-0.516888\pi$
$59$	6.43904	−	11.1527i	0.838292	−	1.45196i	0.891322	−	0.453371i	$-0.149779\pi$
$60$	13.6580	+	3.22465i	1.76324	+	0.416301i
$61$	1.80408	−	1.04158i	0.230988	−	0.133361i	−0.380040	−	0.924970i	$-0.624090\pi$
$61$	1.80408	−	1.04158i	0.230988	−	0.133361i	0.611028	+	0.791609i	$0.290756\pi$
$62$	−0.769151	+	6.30348i	−0.0976823	+	0.800543i
$63$	−6.99757	+	3.74621i	−0.881611	+	0.471978i
$64$	−5.96929	−	5.32612i	−0.746161	−	0.665765i
$65$	−2.36378	−	4.09419i	−0.293191	−	0.507821i
$66$	1.07331	+	0.789215i	0.132115	+	0.0971457i
$67$	−6.14549	−	3.54810i	−0.750791	−	0.433470i	0.0751884	−	0.997169i	$-0.476044\pi$
$67$	−6.14549	−	3.54810i	−0.750791	−	0.433470i	−0.825980	+	0.563700i	$0.809378\pi$
$68$	−2.80865	+	11.3376i	−0.340599	+	1.37489i
$69$	1.42501	+	2.40674i	0.171551	+	0.289738i
$70$	2.64594	−	14.9252i	0.316250	−	1.78390i
$71$		−	5.17264i		−	0.613879i	−0.951729	−	0.306940i	$-0.900695\pi$
$71$		−	5.17264i		−	0.613879i	0.951729	−	0.306940i	$-0.0993049\pi$
$72$	−5.49816	−	6.46299i	−0.647965	−	0.761670i
$73$	5.58686	−	3.22558i	0.653893	−	0.377525i	−0.136053	−	0.990702i	$-0.543442\pi$
$73$	5.58686	−	3.22558i	0.653893	−	0.377525i	0.789946	+	0.613176i	$0.210108\pi$
$74$	−0.508730	+	4.16923i	−0.0591386	+	0.484663i
$75$	−17.0078	+	10.0702i	−1.96389	+	1.16280i
$76$	−1.29122	−	4.47756i	−0.148114	−	0.513612i
$77$	0.785748	−	1.20551i	0.0895443	−	0.137381i
$78$	−0.315035	+	2.84108i	−0.0356706	+	0.321689i
$79$	3.48731	−	2.01340i	0.392353	−	0.226525i	−0.290826	−	0.956776i	$-0.593930\pi$
$79$	3.48731	−	2.01340i	0.392353	−	0.226525i	0.683179	+	0.730251i	$0.260597\pi$
$80$	16.1928	−	0.614320i	1.81041	−	0.0686830i
$81$	−4.83804	−	7.58903i	−0.537560	−	0.843226i
$82$	3.82732	−	5.08700i	0.422657	−	0.561765i
$83$	−2.76985	+	4.79753i	−0.304031	+	0.526597i	−0.977045	−	0.213033i	$-0.931666\pi$
$83$	−2.76985	+	4.79753i	−0.304031	+	0.526597i	0.673014	+	0.739630i	$0.264999\pi$
$84$	−6.63498	+	6.32274i	−0.723936	+	0.689868i
$85$	−11.8296	−	20.4895i	−1.28310	−	2.22240i
$86$	−4.69305	−	0.572646i	−0.506064	−	0.0617500i
$87$	−0.0913299	−	8.31337i	−0.00979159	−	0.891287i
$88$	1.43740	+	0.548043i	0.153227	+	0.0584216i
$89$	−7.63381	−	4.40738i	−0.809183	−	0.467182i	0.0374893	−	0.999297i	$-0.488064\pi$
$89$	−7.63381	−	4.40738i	−0.809183	−	0.467182i	−0.846672	+	0.532115i	$0.821397\pi$
$90$	17.1025	+	1.70646i	1.80276	+	0.179876i
$91$	3.08302	+	0.166760i	0.323188	+	0.0174812i
$92$	2.32661	+	2.24001i	0.242566	+	0.233538i
$93$	0.0854368	+	7.77695i	0.00885938	+	0.806432i
$94$	9.69779	+	7.29636i	1.00025	+	0.752562i
$95$	8.17456	+	4.71958i	0.838692	+	0.484219i
$96$	−8.10804	−	5.50087i	−0.827524	−	0.561431i
$97$	13.8033	+	7.96935i	1.40151	+	0.809165i	0.994548	−	0.104278i	$-0.0332533\pi$
$97$	13.8033	+	7.96935i	1.40151	+	0.809165i	0.406966	+	0.913443i	$0.366587\pi$
$98$	7.22244	+	6.77025i	0.729577	+	0.683899i
$99$	1.43063	+	0.784585i	0.143784	+	0.0788537i
$100$	−15.8296	+	16.4415i	−1.58296	+	1.64415i
$101$			7.40581i			0.736905i	0.929646	+	0.368453i	$0.120112\pi$
$101$			7.40581i			0.736905i	−0.929646	+	0.368453i	$0.879888\pi$
$102$	−1.57660	+	14.2183i	−0.156107	+	1.40782i
$103$	−6.46062			−0.636584			−0.318292	−	0.947993i	$-0.603109\pi$
$103$	−6.46062			−0.636584			−0.318292	+	0.947993i	$0.603109\pi$
$104$	0.523709	+	3.25889i	0.0513539	+	0.319561i
$105$	0.798990	−	18.5474i	0.0779734	−	1.81004i
$106$	13.2071	+	9.93669i	1.28279	+	0.965137i
$107$	9.62572	+	5.55741i	0.930553	+	0.537255i	0.886987	−	0.461795i	$-0.152795\pi$
$107$	9.62572	+	5.55741i	0.930553	+	0.537255i	0.0435667	+	0.999051i	$0.486128\pi$
$108$	−7.71990	−	6.95724i	−0.742848	−	0.669460i
$109$	−1.67348	−	2.89856i	−0.160291	−	0.277632i	0.774682	−	0.632351i	$-0.217910\pi$
$109$	−1.67348	−	2.89856i	−0.160291	−	0.277632i	−0.934973	+	0.354719i	$0.884576\pi$
$110$	−2.86737	+	1.21967i	−0.273393	+	0.116291i
$111$	0.0565093	+	5.14381i	0.00536363	+	0.488228i
$112$	−5.43853	+	9.07868i	−0.513893	+	0.857854i
$113$	−1.36060	−	2.35662i	−0.127994	−	0.221692i	0.794905	−	0.606734i	$-0.207521\pi$
$113$	−1.36060	−	2.35662i	−0.127994	−	0.221692i	−0.922899	+	0.385041i	$0.874187\pi$
$114$	−2.29155	−	5.22710i	−0.214624	−	0.489563i
$115$	−6.54189			−0.610035
$116$	−2.66003	−	9.22415i	−0.246977	−	0.856441i
$117$	0.0769123	+	3.50008i	0.00711055	+	0.323583i
$118$	2.20591	−	18.0783i	0.203071	−	1.66424i
$119$	15.4291	+	0.834556i	1.41438	+	0.0765037i
$120$	19.5592	−	3.36401i	1.78550	−	0.307090i
$121$	10.7042			0.973108
$122$	1.77120	−	2.35415i	0.160357	−	0.213135i
$123$	3.82395	−	6.79458i	0.344794	−	0.612647i
$124$	2.48839	+	8.62896i	0.223464	+	0.774903i
$125$		−	25.9741i		−	2.32320i
$126$	−7.03271	+	8.74877i	−0.626524	+	0.779402i
$127$		−	14.2111i		−	1.26103i	−0.776178	−	0.630513i	$-0.782844\pi$
$127$		−	14.2111i		−	1.26103i	0.776178	−	0.630513i	$-0.217156\pi$
$128$	−10.7166	−	3.62693i	−0.947222	−	0.320578i
$129$	−5.79007	+	0.0636091i	−0.509787	+	0.00560047i
$130$	−5.34253	−	4.01958i	−0.468571	−	0.352540i
$131$	−15.9099			−1.39006			−0.695029	−	0.718982i	$-0.744608\pi$
$131$	−15.9099			−1.39006			−0.695029	+	0.718982i	$0.744608\pi$
$132$	1.83365	+	0.432926i	0.159599	+	0.0376813i
$133$	−5.49742	+	2.78947i	−0.476686	+	0.241878i
$134$	−9.96166	−	1.21552i	−0.860556	−	0.105005i
$135$	21.0388	−	0.693614i	1.81073	−	0.0596968i
$136$	2.62092	+	16.3092i	0.224742	+	1.39851i
$137$	12.5593			1.07301			0.536507	−	0.843896i	$-0.319743\pi$
$137$	12.5593			1.07301			0.536507	+	0.843896i	$0.319743\pi$
$138$	3.18675	+	2.34325i	0.271274	+	0.199470i
$139$	−7.10577	−	12.3076i	−0.602704	−	1.04391i	−0.992410	−	0.122974i	$-0.960757\pi$
$139$	−7.10577	−	12.3076i	−0.602704	−	1.04391i	0.389706	−	0.920939i	$-0.372577\pi$
$140$	−4.81860	−	20.8879i	−0.407246	−	1.76535i
$141$	12.9531	+	7.28993i	1.09085	+	0.613923i
$142$	−2.86335	−	6.73153i	−0.240287	−	0.564898i
$143$	−0.317349	−	0.549665i	−0.0265381	−	0.0459653i
$144$	−10.7328	−	5.36721i	−0.894400	−	0.447268i
$145$	16.8403	+	9.72272i	1.39851	+	0.807428i
$146$	5.48505	−	7.29033i	0.453946	−	0.603352i
$147$	9.86291	+	7.05146i	0.813479	+	0.581595i
$148$	1.64586	+	5.70734i	0.135289	+	0.469140i
$149$	−4.23296			−0.346778			−0.173389	−	0.984853i	$-0.555472\pi$
$149$	−4.23296			−0.346778			−0.173389	+	0.984853i	$0.555472\pi$
$150$	−16.5591	+	22.5198i	−1.35204	+	1.83874i
$151$		−	8.70659i		−	0.708532i	−0.935145	−	0.354266i	$-0.884731\pi$
$151$		−	8.70659i		−	0.708532i	0.935145	−	0.354266i	$-0.115269\pi$
$152$	−4.15896	−	5.11222i	−0.337336	−	0.414656i
$153$	0.384911	+	17.5163i	0.0311182	+	1.41611i
$154$	0.355230	−	2.00378i	0.0286253	−	0.161469i
$155$	−15.7536	−	9.09537i	−1.26536	−	0.730557i
$156$	1.16272	+	3.87170i	0.0930924	+	0.309984i
$157$	−6.61453	−	3.81890i	−0.527897	−	0.304782i	0.212262	−	0.977213i	$-0.431917\pi$
$157$	−6.61453	−	3.81890i	−0.527897	−	0.304782i	−0.740160	+	0.672431i	$0.765250\pi$
$158$	3.42376	−	4.55061i	0.272380	−	0.362027i
$159$	17.6404	+	9.92794i	1.39898	+	0.787337i
$160$	20.7329	−	9.76313i	1.63908	−	0.771843i
$161$	2.33295	−	3.57927i	0.183862	−	0.282086i
$162$	−10.4971	−	7.19803i	−0.824727	−	0.565531i
$163$	13.1093	+	7.56865i	1.02680	+	0.592822i	0.916066	−	0.401028i	$-0.131347\pi$
$163$	13.1093	+	7.56865i	1.02680	+	0.592822i	0.110732	+	0.993850i	$0.464680\pi$
$164$	2.16483	−	8.73873i	0.169045	−	0.682380i
$165$	−3.28385	+	1.94434i	−0.255647	+	0.151366i
$166$	−0.948907	+	7.77665i	−0.0736495	+	0.603585i
$167$	−1.88524	−	3.26533i	−0.145884	−	0.252679i	0.783818	−	0.620990i	$-0.213269\pi$
$167$	−1.88524	−	3.26533i	−0.145884	−	0.252679i	−0.929702	+	0.368311i	$0.879936\pi$
$168$	−5.13459	+	11.9011i	−0.396142	+	0.918189i
$169$	−5.81908	+	10.0790i	−0.447622	+	0.775304i
$170$	−26.7369	−	20.1161i	−2.05062	−	1.54284i
$171$	−3.62717	−	5.97531i	−0.277376	−	0.456943i
$172$	−6.42440	+	1.85265i	−0.489856	+	0.141263i
$173$	−5.42558	+	3.13246i	−0.412499	+	0.238157i	−0.691863	−	0.722029i	$-0.743210\pi$
$173$	−5.42558	+	3.13246i	−0.412499	+	0.238157i	0.279364	+	0.960185i	$0.409877\pi$
$174$	−4.72078	−	10.7682i	−0.357882	−	0.816339i
$175$	25.2937	+	16.4863i	1.91202	+	1.24625i
$176$	2.17397	−	0.0824755i	0.163869	−	0.00621682i
$177$	−0.245031	−	22.3041i	−0.0184177	−	1.67648i
$178$	−12.3742	−	1.50990i	−0.927485	−	0.113172i
$179$	−8.63863	+	4.98752i	−0.645682	+	0.372785i	−0.786800	−	0.617208i	$-0.788264\pi$
$179$	−8.63863	+	4.98752i	−0.645682	+	0.372785i	0.141118	+	0.989993i	$0.454930\pi$
$180$	23.2014	−	7.24650i	1.72933	−	0.540122i
$181$		−	5.34622i		−	0.397382i	−0.980062	−	0.198691i	$-0.936331\pi$
$181$		−	5.34622i		−	0.397382i	0.980062	−	0.198691i	$-0.0636690\pi$
$182$	4.10447	−	1.48961i	0.304244	−	0.110417i
$183$	1.76964	−	3.14438i	0.130816	−	0.232440i
$184$	4.26776	+	1.62719i	0.314624	+	0.119958i
$185$	−10.4197	−	6.01583i	−0.766073	−	0.442292i
$186$	4.41618	+	10.0734i	0.323810	+	0.738619i
$187$	−1.58819	−	2.75082i	−0.116140	−	0.201160i
$188$	16.6594	+	4.12701i	1.21501	+	0.300993i
$189$	−7.12330	+	11.7583i	−0.518144	+	0.855293i
$190$	13.2507	+	1.61685i	0.961308	+	0.117299i
$191$	−19.0615	+	11.0052i	−1.37924	+	0.796307i	−0.992068	−	0.125700i	$-0.959882\pi$
$191$	−19.0615	+	11.0052i	−1.37924	+	0.796307i	−0.387175	+	0.922006i	$0.626549\pi$
$192$	−13.5966	−	2.67042i	−0.981254	−	0.192721i
$193$	2.91719	−	5.05272i	0.209984	−	0.363703i	−0.741725	−	0.670704i	$-0.765992\pi$
$193$	2.91719	−	5.05272i	0.209984	−	0.363703i	0.951709	+	0.307001i	$0.0993255\pi$
$194$	22.3748	+	2.73017i	1.60641	+	0.196015i
$195$	−7.13588	−	4.01604i	−0.511011	−	0.287594i
$196$	13.1468	+	4.81259i	0.939059	+	0.343756i
$197$	14.2652			1.01636			0.508178	−	0.861252i	$-0.330319\pi$
$197$	14.2652			1.01636			0.508178	+	0.861252i	$0.330319\pi$
$198$	2.29610	+	0.229100i	0.163177	+	0.0162815i
$199$	−2.14848	−	3.72128i	−0.152302	−	0.263794i	0.779771	−	0.626064i	$-0.215335\pi$
$199$	−2.14848	−	3.72128i	−0.152302	−	0.263794i	−0.932073	+	0.362270i	$0.882002\pi$
$200$	−11.4989	+	30.1591i	−0.813092	+	2.13257i
$201$	−12.2902	+	0.135019i	−0.866887	+	0.00952353i
$202$	4.09954	+	9.63772i	0.288443	+	0.678108i
$203$	−11.3251	+	5.74653i	−0.794868	+	0.403328i
$204$	5.81889	+	19.3760i	0.407404	+	1.35659i
$205$	9.11794	+	15.7927i	0.636825	+	1.10301i
$206$	−8.40769	+	3.57633i	−0.585791	+	0.249175i
$207$	4.24767	+	2.32950i	0.295233	+	0.161911i
$208$	2.48553	+	3.95113i	0.172340	+	0.273962i
$209$	1.09748	+	0.633628i	0.0759139	+	0.0438289i
$210$	−9.22725	−	24.5793i	−0.636741	−	1.69614i
$211$	−0.0869189	+	0.0501826i	−0.00598374	+	0.00345472i	−0.502989	−	0.864293i	$-0.667766\pi$
$211$	−0.0869189	+	0.0501826i	−0.00598374	+	0.00345472i	0.497005	+	0.867748i	$0.334433\pi$
$212$	22.6879	+	5.62045i	1.55821	+	0.386014i
$213$	−4.56460	−	7.70928i	−0.312761	−	0.528231i
$214$	15.6030	+	1.90388i	1.06660	+	0.130146i
$215$	6.77165	−	11.7288i	0.461823	−	0.799901i
$216$	−13.8977	−	4.78055i	−0.945619	−	0.325275i
$217$	10.5944	−	5.37574i	0.719193	−	0.364929i
$218$	−3.78235	−	2.84574i	−0.256173	−	0.192738i
$219$	5.48022	−	9.73752i	0.370319	−	0.658001i
$220$	−3.05635	+	3.17450i	−0.206059	+	0.214025i
$221$	3.40767	−	5.90225i	0.229224	−	0.397028i
$222$	2.92093	+	6.66273i	0.196040	+	0.447173i
$223$	−6.41092	+	11.1040i	−0.429307	+	0.743582i	−0.996812	−	0.0797885i	$-0.974575\pi$
$223$	−6.41092	+	11.1040i	−0.429307	+	0.743582i	0.567505	+	0.823370i	$0.307909\pi$
$224$	−2.05199	+	14.8253i	−0.137104	+	0.990557i
$225$	−16.4619	+	30.0171i	−1.09746	+	2.00114i
$226$	−3.07517	−	2.31368i	−0.204557	−	0.153904i
$227$	18.7851			1.24681			0.623406	−	0.781898i	$-0.285748\pi$
$227$	18.7851			1.24681			0.623406	+	0.781898i	$0.285748\pi$
$228$	−5.87567	−	5.53390i	−0.389126	−	0.366492i
$229$		−	18.0895i		−	1.19539i	−0.801725	−	0.597693i	$-0.796084\pi$
$229$		−	18.0895i		−	1.19539i	0.801725	−	0.597693i	$-0.203916\pi$
$230$	−8.51345	+	3.62131i	−0.561360	+	0.238782i
$231$	0.107268	−	2.49008i	0.00705774	−	0.163835i
$232$	−8.56779	−	10.5316i	−0.562503	−	0.691432i
$233$	−5.88363	+	10.1908i	−0.385450	+	0.667618i	−0.991831	−	0.127555i	$-0.959287\pi$
$233$	−5.88363	+	10.1908i	−0.385450	+	0.667618i	0.606382	+	0.795174i	$0.292620\pi$
$234$	2.03759	+	4.51234i	0.133201	+	0.294981i
$235$	−30.1071	+	17.3823i	−1.96397	+	1.13390i
$236$	−7.13665	−	24.7477i	−0.464556	−	1.61094i
$237$	3.42074	−	6.07814i	0.222201	−	0.394817i
$238$	20.5410	−	7.45482i	1.33147	−	0.483224i
$239$	1.69786	−	0.980260i	0.109825	−	0.0634077i	−0.444081	−	0.895987i	$-0.646470\pi$
$239$	1.69786	−	0.980260i	0.109825	−	0.0634077i	0.553907	+	0.832579i	$0.313136\pi$
$240$	23.5916	−	15.2050i	1.52283	−	0.981476i
$241$			6.85575i			0.441618i	0.975317	+	0.220809i	$0.0708697\pi$
$241$			6.85575i			0.441618i	−0.975317	+	0.220809i	$0.929130\pi$
$242$	13.9302	−	5.92539i	0.895464	−	0.380898i
$243$	−13.9075	−	7.04133i	−0.892169	−	0.451701i
$244$	1.00184	−	4.04409i	0.0641361	−	0.258897i
$245$	−25.9447	+	11.4472i	−1.65755	+	0.731335i
$246$	1.21520	−	10.9591i	0.0774784	−	0.698725i
$247$			2.71907i			0.173010i
$248$	8.01495	+	9.85203i	0.508950	+	0.625605i
$249$	0.105404	+	9.59448i	0.00667971	+	0.608025i
$250$	−14.3782	−	33.8020i	−0.909355	−	2.13783i
$251$	−17.0335			−1.07515			−0.537574	−	0.843217i	$-0.680659\pi$
$251$	−17.0335			−1.07515			−0.537574	+	0.843217i	$0.680659\pi$
$252$	−4.30924	+	15.2784i	−0.271456	+	0.962451i
$253$	−0.878282			−0.0552171
$254$	−7.86664	−	18.4939i	−0.493597	−	1.16041i
$255$	−35.7118	−	20.0984i	−2.23636	−	1.25861i
$256$	−15.9540	+	1.21226i	−0.997126	+	0.0757664i
$257$			20.7823i			1.29636i	0.761486	+	0.648182i	$0.224470\pi$
$257$			20.7823i			1.29636i	−0.761486	+	0.648182i	$0.775530\pi$
$258$	−7.49983	+	3.28792i	−0.466919	+	0.204697i
$259$	7.00730	−	3.55560i	0.435412	−	0.220934i
$260$	−9.17769	−	2.27358i	−0.569176	−	0.141001i
$261$	−7.47226	−	12.3096i	−0.462521	−	0.761946i
$262$	−20.7048	+	8.80707i	−1.27915	+	0.544102i
$263$			9.81930i			0.605484i	0.953073	+	0.302742i	$0.0979021\pi$
$263$			9.81930i			0.605484i	−0.953073	+	0.302742i	$0.902098\pi$
$264$	2.62592	−	0.451635i	0.161614	−	0.0277962i
$265$	−41.0019	+	23.6725i	−2.51873	+	1.45419i
$266$	−5.61006	+	6.67328i	−0.343975	+	0.409165i
$267$	−15.2667	+	0.167719i	−0.934307	+	0.0102642i
$268$	−13.6367	+	3.93251i	−0.832994	+	0.240216i
$269$	4.88843	−	2.82234i	0.298053	−	0.172081i	−0.343515	−	0.939147i	$-0.611618\pi$
$269$	4.88843	−	2.82234i	0.298053	−	0.172081i	0.641568	+	0.767066i	$0.278284\pi$
$270$	26.9954	−	12.5488i	1.64289	−	0.763699i
$271$	−11.3288	+	19.6221i	−0.688177	+	1.19196i	0.284251	+	0.958750i	$0.408255\pi$
$271$	−11.3288	+	19.6221i	−0.688177	+	1.19196i	−0.972427	+	0.233207i	$0.925078\pi$
$272$	12.4389	+	19.7736i	0.754219	+	1.19895i
$273$	4.74208	−	2.47207i	0.287004	−	0.149617i
$274$	16.3444	−	6.95230i	0.987399	−	0.420004i
$275$		−	6.20657i		−	0.374270i
$276$	5.44427	+	1.28539i	0.327706	+	0.0773715i
$277$	11.5327			0.692931			0.346466	−	0.938063i	$-0.387382\pi$
$277$	11.5327			0.692931			0.346466	+	0.938063i	$0.387382\pi$
$278$	−16.0602	−	12.0833i	−0.963227	−	0.724707i
$279$	6.99011	+	11.5153i	0.418487	+	0.689405i
$280$	−17.8335	−	24.5156i	−1.06575	−	1.46509i
$281$	0.625840	−	1.08399i	0.0373345	−	0.0646652i	−0.846754	−	0.531984i	$-0.821447\pi$
$281$	0.625840	−	1.08399i	0.0373345	−	0.0646652i	0.884089	+	0.467319i	$0.154780\pi$
$282$	20.8922	+	2.31664i	1.24411	+	0.137954i
$283$	−0.475742	+	0.824009i	−0.0282799	+	0.0489822i	−0.879819	−	0.475309i	$-0.842336\pi$
$283$	−0.475742	+	0.824009i	−0.0282799	+	0.0489822i	0.851539	+	0.524291i	$0.175670\pi$
$284$	−7.45258	−	7.17521i	−0.442230	−	0.425770i
$285$	16.3481	−	0.179599i	0.968380	−	0.0106385i
$286$	−0.717261	−	0.539648i	−0.0424125	−	0.0319101i
$287$	−11.8923	−	0.643253i	−0.701981	−	0.0379700i
$288$	−16.9384	−	1.04353i	−0.998108	−	0.0614905i
$289$	8.55378	−	14.8156i	0.503164	−	0.871505i
$290$	27.2976	+	3.33085i	1.60297	+	0.195594i
$291$	27.6050	−	0.303265i	1.61823	−	0.0177777i
$292$	3.10249	−	12.5237i	0.181559	−	0.732897i
$293$	−14.3254	+	8.27078i	−0.836900	+	0.483184i	−0.856209	−	0.516629i	$-0.827187\pi$
$293$	−14.3254	+	8.27078i	−0.836900	+	0.483184i	0.0193095	+	0.999814i	$0.493853\pi$
$294$	16.7387	+	3.71690i	0.976222	+	0.216774i
$295$	45.1811	+	26.0853i	2.63055	+	1.51875i
$296$	5.30122	+	6.51630i	0.308127	+	0.378752i
$297$	2.82457	−	0.0931212i	0.163898	−	0.00540344i
$298$	−5.50867	+	2.34319i	−0.319109	+	0.135737i
$299$	−0.942236	−	1.63200i	−0.0544909	−	0.0943810i
$300$	−9.08351	+	38.4731i	−0.524436	+	2.22125i
$301$	4.00233	+	7.88769i	0.230690	+	0.454639i
$302$	−4.81960	−	11.3305i	−0.277337	−	0.651999i
$303$	6.53526	+	11.0376i	0.375441	+	0.634093i
$304$	−8.24226	−	4.35069i	−0.472726	−	0.249529i
$305$	4.21959	+	7.30854i	0.241613	+	0.418486i
$306$	10.1972	+	22.5822i	0.582934	+	1.29094i
$307$	27.1061			1.54702			0.773512	−	0.633781i	$-0.218498\pi$
$307$	27.1061			1.54702			0.773512	+	0.633781i	$0.218498\pi$
$308$	−0.646921	−	2.80431i	−0.0368618	−	0.159790i
$309$	−9.62889	+	5.70118i	−0.547768	+	0.324329i
$310$	−25.5362	−	3.11593i	−1.45036	−	0.176973i
$311$	−6.23017	+	10.7910i	−0.353281	+	0.611900i	−0.986822	−	0.161809i	$-0.948267\pi$
$311$	−6.23017	+	10.7910i	−0.353281	+	0.611900i	0.633541	+	0.773709i	$0.281601\pi$
$312$	3.65635	+	4.39489i	0.207000	+	0.248812i
$313$	−16.4616	+	9.50414i	−0.930467	+	0.537206i	−0.886959	−	0.461847i	$-0.847187\pi$
$313$	−16.4616	+	9.50414i	−0.930467	+	0.537206i	−0.0435081	+	0.999053i	$0.513853\pi$
$314$	−10.7220	−	1.30829i	−0.605075	−	0.0738313i
$315$	−15.1763	−	28.3480i	−0.855090	−	1.59723i
$316$	1.93657	−	7.81729i	0.108940	−	0.439757i
$317$	10.2693	+	17.7870i	0.576784	+	0.999018i	0.995845	+	0.0910607i	$0.0290257\pi$
$317$	10.2693	+	17.7870i	0.576784	+	0.999018i	−0.419062	+	0.907958i	$0.637641\pi$
$318$	28.4525	+	3.15497i	1.59554	+	0.176922i
$319$	2.26089	+	1.30532i	0.126585	+	0.0730841i
$320$	21.5768	−	24.1823i	1.20618	−	1.35183i
$321$	19.2503	−	0.211482i	1.07445	−	0.0118038i
$322$	1.05471	−	5.94939i	0.0587766	−	0.331547i
$323$			13.6077i			0.757151i
$324$	−17.6451	−	3.55660i	−0.980285	−	0.197589i
$325$	11.5329	−	6.65852i	0.639730	−	0.369348i
$326$	21.2498	+	2.59290i	1.17692	+	0.143607i
$327$	−5.05199	−	2.84323i	−0.279376	−	0.157231i
$328$	−2.02013	−	12.5707i	−0.111543	−	0.694102i
$329$	1.22629	−	22.6713i	0.0676075	−	1.24991i
$330$	−3.19721	+	4.34811i	−0.176000	+	0.239355i
$331$	−9.93630	+	5.73673i	−0.546149	+	0.315319i	−0.747567	−	0.664186i	$-0.768778\pi$
$331$	−9.93630	+	5.73673i	−0.546149	+	0.315319i	0.201419	+	0.979505i	$0.435445\pi$
$332$	3.06994	+	10.6456i	0.168485	+	0.584254i
$333$	4.62338	+	7.61644i	0.253360	+	0.417378i
$334$	−4.26095	−	3.20583i	−0.233149	−	0.175415i
$335$	14.3738	−	24.8961i	0.785324	−	1.36022i
$336$	−0.0940739	+	18.3301i	−0.00513215	+	0.999987i
$337$	−4.74216	−	8.21367i	−0.258322	−	0.447427i	0.707470	−	0.706743i	$-0.249836\pi$
$337$	−4.74216	−	8.21367i	−0.258322	−	0.447427i	−0.965793	+	0.259316i	$0.916503\pi$
$338$	−1.99352	+	16.3377i	−0.108433	+	0.888653i
$339$	−4.10743	−	2.31164i	−0.223085	−	0.125551i
$340$	−45.9301	−	11.3782i	−2.49091	−	0.617069i
$341$	−2.11500	−	1.22110i	−0.114534	−	0.0661262i
$342$	−8.02798	−	5.76826i	−0.434103	−	0.311912i
$343$	2.98921	−	18.2774i	0.161402	−	0.986889i
$344$	−7.33500	+	5.96726i	−0.395477	+	0.321733i
$345$	−9.75001	+	5.77290i	−0.524923	+	0.310802i
$346$	−5.32671	+	7.07988i	−0.286366	+	0.380617i
$347$	1.98409	+	1.14551i	0.106511	+	0.0614943i	0.552309	−	0.833639i	$-0.313747\pi$
$347$	1.98409	+	1.14551i	0.106511	+	0.0614943i	−0.445798	+	0.895134i	$0.647080\pi$
$348$	−12.1044	−	11.4003i	−0.648861	−	0.611120i
$349$	−28.3807	−	16.3856i	−1.51918	−	0.877100i	−0.999745	−	0.0225916i	$-0.992808\pi$
$349$	−28.3807	−	16.3856i	−1.51918	−	0.877100i	−0.519437	−	0.854509i	$-0.673858\pi$
$350$	42.0427	+	7.45333i	2.24728	+	0.398397i
$351$	3.20328	+	5.14863i	0.170978	+	0.274814i
$352$	2.78349	−	1.31075i	0.148361	−	0.0698631i
$353$		−	21.0983i		−	1.12295i	−0.827494	−	0.561474i	$-0.810235\pi$
$353$		−	21.0983i		−	1.12295i	0.827494	−	0.561474i	$-0.189765\pi$
$354$	−12.6655	−	28.8904i	−0.673164	−	1.53551i
$355$	20.9550			1.11217
$356$	−16.9393	+	4.88488i	−0.897779	+	0.258898i
$357$	23.7319	−	12.3716i	1.25602	−	0.654774i
$358$	−8.48121	+	11.2726i	−0.448246	+	0.595776i
$359$	25.9102	+	14.9593i	1.36749	+	0.789519i	0.990607	−	0.136742i	$-0.0436632\pi$
$359$	25.9102	+	14.9593i	1.36749	+	0.789519i	0.376881	+	0.926262i	$0.376997\pi$
$360$	26.1824	−	22.2737i	1.37993	−	1.17393i
$361$	6.78552	+	11.7529i	0.357133	+	0.618572i
$362$	−2.95944	−	6.95744i	−0.155545	−	0.365675i
$363$	15.9535	−	9.44592i	0.837341	−	0.495782i
$364$	4.51687	−	4.21060i	0.236748	−	0.220696i
$365$	13.0672	+	22.6331i	0.683969	+	1.18467i
$366$	0.562369	−	5.07162i	0.0293955	−	0.265098i
$367$	20.1276			1.05065			0.525325	−	0.850901i	$-0.323944\pi$
$367$	20.1276			1.05065			0.525325	+	0.850901i	$0.323944\pi$
$368$	6.45470	−	0.244877i	0.336474	−	0.0127651i
$369$	−0.296679	−	13.5011i	−0.0154445	−	0.702837i
$370$	−16.8901	−	2.06093i	−0.878072	−	0.107142i
$371$	1.67005	−	30.8754i	0.0867045	−	1.60297i
$372$	11.3233	+	10.6647i	0.587087	+	0.552938i
$373$	−10.9412			−0.566511			−0.283256	−	0.959044i	$-0.591415\pi$
$373$	−10.9412			−0.566511			−0.283256	+	0.959044i	$0.591415\pi$
$374$	−3.58956	−	2.70069i	−0.185612	−	0.139649i
$375$	−22.9209	−	38.7117i	−1.18363	−	1.99906i
$376$	23.9646	−	3.85116i	1.23588	−	0.198608i
$377$			5.60150i			0.288492i
$378$	−2.76116	+	19.2452i	−0.142019	+	0.989864i
$379$		−	15.9358i		−	0.818566i	−0.912407	−	0.409283i	$-0.865779\pi$
$379$		−	15.9358i		−	0.818566i	0.912407	−	0.409283i	$-0.134221\pi$
$380$	18.1392	−	5.23091i	0.930519	−	0.268340i
$381$	−12.5406	−	21.1801i	−0.642472	−	1.08509i
$382$	−18.7142	+	24.8735i	−0.957500	+	1.27264i
$383$	−23.4896			−1.20026			−0.600130	−	0.799902i	$-0.704885\pi$
$383$	−23.4896			−1.20026			−0.600130	+	0.799902i	$0.704885\pi$
$384$	−19.1726	+	4.05131i	−0.978395	+	0.206743i
$385$	4.88368	+	3.18316i	0.248896	+	0.162229i
$386$	0.999382	−	8.19031i	0.0508672	−	0.416876i
$387$	−8.57336	+	5.20426i	−0.435809	+	0.264547i
$388$	30.6292	−	8.83275i	1.55496	−	0.448415i
$389$	−8.13354			−0.412387			−0.206193	−	0.978511i	$-0.566108\pi$
$389$	−8.13354			−0.412387			−0.206193	+	0.978511i	$0.566108\pi$
$390$	−11.5096	−	1.27624i	−0.582809	−	0.0646251i
$391$	−4.71545	−	8.16740i	−0.238471	−	0.413043i
$392$	19.7730	−	1.01455i	0.998686	−	0.0512425i
$393$	−23.7121	+	14.0397i	−1.19612	+	0.708211i
$394$	18.5644	−	7.89663i	0.935261	−	0.397826i
$395$	8.15652	+	14.1275i	0.410399	+	0.710832i
$396$	3.11491	−	0.972879i	0.156530	−	0.0488890i
$397$	−23.7199	−	13.6947i	−1.19047	−	0.687318i	−0.232057	−	0.972702i	$-0.574545\pi$
$397$	−23.7199	−	13.6947i	−1.19047	−	0.687318i	−0.958413	+	0.285384i	$0.907879\pi$
$398$	−4.85592	−	3.65347i	−0.243405	−	0.183132i
$399$	−5.73176	+	9.00861i	−0.286947	+	0.450995i
$400$	1.73047	+	45.6135i	0.0865237	+	2.28068i
$401$	18.8493			0.941289			0.470644	−	0.882323i	$-0.344021\pi$
$401$	18.8493			0.941289			0.470644	+	0.882323i	$0.344021\pi$
$402$	−15.9195	+	6.97907i	−0.793990	+	0.348084i
$403$		−	5.24006i		−	0.261026i
$404$	10.6701	+	10.2730i	0.530856	+	0.511098i
$405$	30.7441	−	19.5995i	1.52769	−	0.973906i
$406$	−11.5572	+	13.7475i	−0.573573	+	0.682277i
$407$	−1.39890	−	0.807655i	−0.0693409	−	0.0400340i
$408$	18.2983	+	21.9944i	0.905902	+	1.08888i
$409$	16.5259	+	9.54123i	0.817153	+	0.471784i	0.849434	−	0.527695i	$-0.176944\pi$
$409$	16.5259	+	9.54123i	0.817153	+	0.471784i	−0.0322805	+	0.999479i	$0.510277\pi$
$410$	20.6080	+	15.5050i	1.01776	+	0.765735i
$411$	18.7184	−	11.0830i	0.923308	−	0.546683i
$412$	−8.96184	+	9.30828i	−0.441518	+	0.458586i
$413$	−30.3845	+	15.4175i	−1.49512	+	0.758646i
$414$	6.81731	+	0.680218i	0.335053	+	0.0334309i
$415$	−19.4354	−	11.2210i	−0.954045	−	0.550818i
$416$	5.42178	+	3.76602i	0.265825	+	0.184644i
$417$	−21.4512	−	12.0726i	−1.05047	−	0.591200i
$418$	1.77898	+	0.217071i	0.0870125	+	0.0106173i
$419$	12.7212	+	22.0338i	0.621473	+	1.07642i	0.989212	+	0.146493i	$0.0467986\pi$
$419$	12.7212	+	22.0338i	0.621473	+	1.07642i	−0.367739	+	0.929929i	$0.619868\pi$
$420$	−25.6142	−	26.8791i	−1.24984	−	1.31157i
$421$	10.2492	−	17.7521i	0.499514	−	0.865183i	−0.500486	−	0.865745i	$-0.666845\pi$
$421$	10.2492	−	17.7521i	0.499514	−	0.865183i	1.00000		0.000561434i	$0.000178710\pi$
$422$	−0.0853350	+	0.113421i	−0.00415404	+	0.00552125i
$423$	25.7383	−	0.565584i	1.25144	−	0.0274996i
$424$	32.6367	−	5.24478i	1.58498	−	0.254709i
$425$	57.7168	−	33.3228i	2.79967	−	1.61639i
$426$	−10.2078	−	7.50588i	−0.494568	−	0.363661i
$427$	−5.50350	−	0.297684i	−0.266333	−	0.0144059i
$428$	21.3592	−	6.15950i	1.03244	−	0.297731i
$429$	−0.958028	−	0.539173i	−0.0462540	−	0.0260315i
$430$	2.31986	−	19.0121i	0.111874	−	0.916845i
$431$	−15.2031	+	8.77752i	−0.732308	+	0.422798i	−0.819266	−	0.573414i	$-0.805619\pi$
$431$	−15.2031	+	8.77752i	−0.732308	+	0.422798i	0.0869578	+	0.996212i	$0.472285\pi$
$432$	−20.7324	+	1.47190i	−0.997489	+	0.0708166i
$433$			15.2009i			0.730507i	0.930908	+	0.365254i	$0.119018\pi$
$433$			15.2009i			0.730507i	−0.930908	+	0.365254i	$0.880982\pi$
$434$	10.8115	−	12.8604i	0.518967	−	0.617321i
$435$	33.6785	−	0.369988i	1.61476	−	0.0177396i
$436$	−6.49753	−	1.60962i	−0.311175	−	0.0770869i
$437$	3.25849	+	1.88129i	0.155875	+	0.0899944i
$438$	1.74154	−	15.7058i	0.0832141	−	0.750451i
$439$	7.28455	+	12.6172i	0.347673	+	0.602187i	0.985836	−	0.167715i	$-0.0536387\pi$
$439$	7.28455	+	12.6172i	0.347673	+	0.602187i	−0.638163	+	0.769901i	$0.720305\pi$
$440$	−2.22019	+	5.82309i	−0.105843	+	0.277605i
$441$	20.9222	+	1.80594i	0.996295	+	0.0859971i
$442$	1.16741	−	9.56737i	0.0555281	−	0.455074i
$443$	−20.8085	+	12.0138i	−0.988639	+	0.570791i	−0.904867	−	0.425694i	$-0.860030\pi$
$443$	−20.8085	+	12.0138i	−0.988639	+	0.570791i	−0.0837721	+	0.996485i	$0.526697\pi$
$444$	7.48943	+	7.05380i	0.355433	+	0.334759i
$445$	17.8549	−	30.9255i	0.846401	−	1.46601i
$446$	−2.19628	+	17.9993i	−0.103997	+	0.852293i
$447$	−6.30879	+	3.73538i	−0.298396	+	0.176678i
$448$	5.53625	+	20.4291i	0.261563	+	0.965186i
$449$	36.1930			1.70806			0.854028	−	0.520228i	$-0.174153\pi$
$449$	36.1930			1.70806			0.854028	+	0.520228i	$0.174153\pi$
$450$	−4.80691	+	48.1760i	−0.226600	+	2.27104i
$451$	1.22413	+	2.12025i	0.0576420	+	0.0998389i
$452$	−5.28270	−	1.30868i	−0.248477	−	0.0615549i
$453$	−7.68314	−	12.9763i	−0.360985	−	0.609678i
$454$	24.4465	−	10.3986i	1.14733	−	0.488033i
$455$	−0.675565	+	12.4897i	−0.0316710	+	0.585525i
$456$	−10.7098	−	3.94916i	−0.501531	−	0.184936i
$457$	−10.2859	−	17.8158i	−0.481156	−	0.833386i	0.518610	−	0.855011i	$-0.326450\pi$
$457$	−10.2859	−	17.8158i	−0.481156	−	0.833386i	−0.999766	+	0.0216244i	$0.993116\pi$
$458$	−10.0136	−	23.5412i	−0.467903	−	1.10001i
$459$	16.0309	+	25.7665i	0.748260	+	1.20268i
$460$	−9.07457	+	9.42537i	−0.423104	+	0.439460i
$461$	−20.0785	−	11.5923i	−0.935149	−	0.539908i	−0.0467125	−	0.998908i	$-0.514874\pi$
$461$	−20.0785	−	11.5923i	−0.935149	−	0.539908i	−0.888436	+	0.459000i	$0.848208\pi$
$462$	−1.23880	−	3.29990i	−0.0576344	−	0.153525i
$463$	−11.0442	+	6.37637i	−0.513268	+	0.296335i	−0.734176	−	0.678959i	$-0.762431\pi$
$463$	−11.0442	+	6.37637i	−0.513268	+	0.296335i	0.220908	+	0.975295i	$0.429098\pi$
$464$	−16.9797	−	8.96277i	−0.788264	−	0.416086i
$465$	−31.5054	+	0.346115i	−1.46103	+	0.0160507i
$466$	−2.01564	+	16.5189i	−0.0933726	+	0.765224i
$467$	−10.3847	+	17.9868i	−0.480545	+	0.832329i	−0.999751	−	0.0223206i	$-0.992895\pi$
$467$	−10.3847	+	17.9868i	−0.480545	+	0.832329i	0.519206	+	0.854649i	$0.326228\pi$
$468$	5.14950	+	4.74432i	0.238036	+	0.219306i
$469$	8.49550	+	16.7427i	0.392286	+	0.773108i
$470$	−29.5584	+	39.2869i	−1.36343	+	1.81217i
$471$	−13.2283	+	0.145324i	−0.609527	+	0.00669620i
$472$	−22.9867	−	28.2554i	−1.05805	−	1.30056i
$473$	0.909128	−	1.57466i	0.0418018	−	0.0724028i
$474$	1.08707	−	9.80351i	0.0499306	−	0.450290i
$475$	−13.2946	+	23.0269i	−0.609997	+	1.05655i
$476$	22.6048	−	21.0721i	1.03609	−	0.965839i
$477$	35.0521	−	0.770252i	1.60493	−	0.0352674i
$478$	1.66692	−	2.21555i	0.0762431	−	0.101337i
$479$	−18.2347			−0.833166			−0.416583	−	0.909098i	$-0.636772\pi$
$479$	−18.2347			−0.833166			−0.416583	+	0.909098i	$0.636772\pi$
$480$	22.2847	−	32.8467i	1.01715	−	1.49924i
$481$		−	3.46587i		−	0.158030i
$482$	3.79505	+	8.92189i	0.172860	+	0.406381i
$483$	0.318489	−	7.39325i	0.0144917	−	0.336404i
$484$	14.8483	−	15.4223i	0.674923	−	0.701013i
$485$	−32.2848	+	55.9189i	−1.46598	+	2.53915i
$486$	−21.9967	−	1.46477i	−0.997790	−	0.0664435i
$487$	8.32199	−	4.80470i	0.377105	−	0.217722i	−0.299453	−	0.954111i	$-0.596804\pi$
$487$	8.32199	−	4.80470i	0.377105	−	0.217722i	0.676558	+	0.736389i	$0.263471\pi$
$488$	−0.934875	−	5.81745i	−0.0423198	−	0.263344i
$489$	26.2170	−	0.288017i	1.18557	−	0.0130246i
$490$	−27.4271	+	29.2590i	−1.23903	+	1.32179i
$491$	−1.55447	+	0.897475i	−0.0701524	+	0.0405025i	−0.534666	−	0.845064i	$-0.679563\pi$
$491$	−1.55447	+	0.897475i	−0.0701524	+	0.0405025i	0.464514	+	0.885566i	$0.346229\pi$
$492$	−4.48504	−	14.9345i	−0.202201	−	0.673300i
$493$			28.0329i			1.26254i
$494$	1.50516	+	3.53852i	0.0677204	+	0.159206i
$495$	−3.17845	+	5.79567i	−0.142861	+	0.260496i
$496$	15.8841	+	8.38444i	0.713218	+	0.376473i
$497$	−7.47290	+	11.4651i	−0.335206	+	0.514281i
$498$	5.44827	+	12.4277i	0.244143	+	0.556897i
$499$		−	43.9761i		−	1.96864i	−0.176386	−	0.984321i	$-0.556441\pi$
$499$		−	43.9761i		−	1.96864i	0.176386	−	0.984321i	$-0.443559\pi$
$500$	−37.4227	−	36.0299i	−1.67360	−	1.61131i
$501$	−5.69125	−	3.20300i	−0.254266	−	0.143100i
$502$	−22.1670	+	9.42905i	−0.989362	+	0.420839i
$503$	−18.3538			−0.818355			−0.409178	−	0.912455i	$-0.634184\pi$
$503$	−18.3538			−0.818355			−0.409178	+	0.912455i	$0.634184\pi$
$504$	2.84957	+	22.2684i	0.126930	+	0.991912i
$505$	−30.0018			−1.33506
$506$	−1.14297	+	0.486180i	−0.0508113	+	0.0216133i
$507$	0.221439	+	20.1567i	0.00983447	+	0.895190i
$508$	−20.4749	−	19.7128i	−0.908425	−	0.874615i
$509$		−	15.2086i		−	0.674110i	−0.941485	−	0.337055i	$-0.890569\pi$
$509$		−	15.2086i		−	0.674110i	0.941485	−	0.337055i	$-0.109431\pi$
$510$	−57.6000	−	6.38701i	−2.55057	−	0.282821i
$511$	−17.0432	−	0.921866i	−0.753948	−	0.0407809i
$512$	−20.0911	+	10.4091i	−0.887908	+	0.460020i
$513$	−10.6788	−	5.70478i	−0.471482	−	0.251872i
$514$	11.5042	+	27.0455i	0.507428	+	1.19293i
$515$		−	26.1728i		−	1.15331i
$516$	−7.94004	+	8.43040i	−0.349541	+	0.371128i
$517$	−4.04203	+	2.33366i	−0.177768	+	0.102634i
$518$	7.15088	−	8.50611i	0.314192	−	0.373737i
$519$	−5.32202	+	9.45642i	−0.233611	+	0.415091i
$520$	−13.2022	+	2.12161i	−0.578953	+	0.0930388i
$521$	14.2730	−	8.24049i	0.625309	−	0.361023i	−0.153624	−	0.988129i	$-0.549094\pi$
$521$	14.2730	−	8.24049i	0.625309	−	0.361023i	0.778933	+	0.627107i	$0.215761\pi$
$522$	−16.5383	−	11.8831i	−0.723861	−	0.520109i
$523$	7.92785	−	13.7314i	0.346661	−	0.600434i	−0.638993	−	0.769212i	$-0.720649\pi$
$523$	7.92785	−	13.7314i	0.346661	−	0.600434i	0.985654	+	0.168778i	$0.0539822\pi$
$524$	−22.0694	+	22.9226i	−0.964108	+	1.00138i
$525$	52.2460	+	2.25067i	2.28020	+	0.0982273i
$526$	5.43555	+	12.7786i	0.237001	+	0.557173i
$527$		−	26.2241i		−	1.14234i
$528$	3.16729	−	2.04134i	0.137839	−	0.0888380i
$529$	20.3923			0.886622
$530$	−40.2547	+	53.5036i	−1.74855	+	2.32405i
$531$	−20.0475	−	33.0258i	−0.869988	−	1.43320i
$532$	−3.60674	+	11.7899i	−0.156372	+	0.511158i
$533$	−2.62653	+	4.54929i	−0.113768	+	0.197052i
$534$	−19.7749	+	8.66927i	−0.855741	+	0.375156i
$535$	−22.5137	+	38.9950i	−0.973354	+	1.68590i
$536$	−15.5696	+	12.6664i	−0.672504	+	0.547104i
$537$	−8.47375	+	15.0565i	−0.365669	+	0.649738i
$538$	4.79935	−	6.37895i	0.206915	−	0.275016i
$539$	−3.48321	+	1.53684i	−0.150032	+	0.0661966i
$540$	28.1846	−	31.2743i	1.21287	−	1.34583i
$541$	16.3113	−	28.2520i	0.701278	−	1.21465i	−0.266740	−	0.963768i	$-0.585947\pi$
$541$	16.3113	−	28.2520i	0.701278	−	1.21465i	0.968018	−	0.250880i	$-0.0807201\pi$
$542$	−3.88107	+	31.8068i	−0.166706	+	1.36622i
$543$	−4.71778	−	7.96799i	−0.202459	−	0.341939i
$544$	27.1335	+	18.8472i	1.16334	+	0.808066i
$545$	11.7424	−	6.77949i	0.502990	−	0.290401i
$546$	4.80278	−	5.84211i	0.205540	−	0.250019i
$547$	−30.4408	−	17.5750i	−1.30155	−	0.751453i	−0.320884	−	0.947119i	$-0.603980\pi$
$547$	−30.4408	−	17.5750i	−1.30155	−	0.751453i	−0.980671	+	0.195666i	$0.937313\pi$
$548$	17.4216	−	18.0951i	0.744215	−	0.772984i
$549$	−0.137296	−	6.24800i	−0.00585967	−	0.266658i
$550$	−3.43570	−	8.07707i	−0.146499	−	0.344407i
$551$	−5.59205	−	9.68572i	−0.238229	−	0.412625i
$552$	7.79657	−	1.34094i	0.331844	−	0.0570742i
$553$	−10.6383	−	0.575427i	−0.452389	−	0.0244696i
$554$	15.0083	−	6.38400i	0.637642	−	0.271230i
$555$	−20.8382	+	0.228926i	−0.884532	+	0.00971738i
$556$	−27.5891	−	6.83461i	−1.17004	−	0.289852i
$557$	−21.0919	−	36.5322i	−0.893692	−	1.54792i	−0.835415	−	0.549620i	$-0.814773\pi$
$557$	−21.0919	−	36.5322i	−0.893692	−	1.54792i	−0.0582771	−	0.998300i	$-0.518561\pi$
$558$	15.4712	+	11.1163i	0.654946	+	0.470592i
$559$	3.90131			0.165008
$560$	−36.7788	−	22.0321i	−1.55419	−	0.931028i
$561$	−4.79449	−	2.69831i	−0.202423	−	0.113923i
$562$	0.214403	−	1.75711i	0.00904402	−	0.0741192i
$563$	16.2172	−	28.0890i	0.683473	−	1.18381i	−0.290441	−	0.956893i	$-0.593802\pi$
$563$	16.2172	−	28.0890i	0.683473	−	1.18381i	0.973914	−	0.226917i	$-0.0728646\pi$
$564$	28.4710	−	8.55023i	1.19884	−	0.360030i
$565$	9.54696	−	5.51194i	0.401644	−	0.231889i
$566$	−0.162981	+	1.33569i	−0.00685062	+	0.0561434i
$567$	−0.240384	+	23.8105i	−0.0100952	+	0.999949i
$568$	−13.6705	−	5.21220i	−0.573601	−	0.218699i
$569$	−9.74520	−	16.8792i	−0.408540	−	0.707612i	0.586186	−	0.810176i	$-0.300629\pi$
$569$	−9.74520	−	16.8792i	−0.408540	−	0.707612i	−0.994726	+	0.102564i	$0.967295\pi$
$570$	21.1756	−	9.28336i	0.886949	−	0.388837i
$571$	26.1168	+	15.0785i	1.09295	+	0.631017i	0.934361	−	0.356327i	$-0.115971\pi$
$571$	26.1168	+	15.0785i	1.09295	+	0.631017i	0.158593	+	0.987344i	$0.449304\pi$
$572$	−1.23215	−	0.305239i	−0.0515188	−	0.0127627i
$573$	−18.6977	+	33.2229i	−0.781107	+	1.38791i
$574$	−15.8324	+	5.74597i	−0.660832	+	0.239832i
$575$		−	18.4278i		−	0.768493i
$576$	−22.6209	+	8.01839i	−0.942538	+	0.334099i
$577$	−14.9496	+	8.63117i	−0.622361	+	0.359320i	−0.777788	−	0.628527i	$-0.783658\pi$
$577$	−14.9496	+	8.63117i	−0.622361	+	0.359320i	0.155426	+	0.987847i	$0.450325\pi$
$578$	2.93039	−	24.0156i	0.121888	−	0.998919i
$579$	−0.111011	−	10.1048i	−0.00461345	−	0.419942i
$580$	37.3681	−	10.7761i	1.55163	−	0.447453i
$581$	13.0703	−	6.63208i	0.542249	−	0.275145i
$582$	35.7565	−	15.6756i	1.48215	−	0.649775i
$583$	−5.50471	+	3.17815i	−0.227982	+	0.131625i
$584$	−2.89512	−	18.0155i	−0.119801	−	0.745486i
$585$	−14.1793	+	0.311581i	−0.586240	+	0.0128823i
$586$	−14.0644	+	18.6933i	−0.580994	+	0.772214i
$587$	−17.3621	+	30.0720i	−0.716611	+	1.24121i	0.245724	+	0.969340i	$0.420974\pi$
$587$	−17.3621	+	30.0720i	−0.716611	+	1.24121i	−0.962335	+	0.271866i	$0.912359\pi$
$588$	23.8408	−	4.42877i	0.983180	−	0.182639i
$589$	5.23122	+	9.06074i	0.215549	+	0.373341i
$590$	73.2373	+	8.93641i	3.01513	+	0.367906i
$591$	21.2608	−	12.5884i	0.874554	−	0.517816i
$592$	10.5060	+	5.54561i	0.431795	+	0.227923i
$593$	15.7360	+	9.08520i	0.646201	+	0.373085i	0.786999	−	0.616954i	$-0.211633\pi$
$593$	15.7360	+	9.08520i	0.646201	+	0.373085i	−0.140798	+	0.990038i	$0.544967\pi$
$594$	3.62427	−	1.68475i	0.148706	−	0.0691260i
$595$	−3.38089	+	62.5051i	−0.138603	+	2.56246i
$596$	−5.87175	+	6.09873i	−0.240516	+	0.249814i
$597$	−6.48593	−	3.65025i	−0.265452	−	0.149395i
$598$	−2.12961	−	1.60226i	−0.0870861	−	0.0655213i
$599$	24.5378	+	14.1669i	1.00259	+	0.578845i	0.909013	−	0.416767i	$-0.136837\pi$
$599$	24.5378	+	14.1669i	1.00259	+	0.578845i	0.0935756	+	0.995612i	$0.470170\pi$
$600$	9.47606	+	55.0962i	0.386858	+	2.24929i
$601$	−16.3852	−	9.46002i	−0.668368	−	0.385882i	0.127090	−	0.991891i	$-0.459436\pi$
$601$	−16.3852	−	9.46002i	−0.668368	−	0.385882i	−0.795458	+	0.606009i	$0.792770\pi$
$602$	9.57481	+	8.04931i	0.390240	+	0.328065i
$603$	−18.1982	+	11.0468i	−0.741087	+	0.449859i
$604$	−12.5442	−	12.0773i	−0.510416	−	0.491420i
$605$			43.3640i			1.76300i
$606$	14.6148	+	10.7464i	0.593684	+	0.436542i
$607$	6.04655			0.245422			0.122711	−	0.992442i	$-0.460841\pi$
$607$	6.04655			0.245422			0.122711	+	0.992442i	$0.460841\pi$
$608$	−13.1346	−	1.09930i	−0.532679	−	0.0445825i
$609$	−11.8079	+	18.5585i	−0.478480	+	0.752027i
$610$	9.53696	+	7.17535i	0.386140	+	0.290522i
$611$	−8.67271	−	5.00719i	−0.350860	−	0.202569i
$612$	25.7709	+	23.7431i	1.04173	+	0.959758i
$613$	−0.0235058	−	0.0407133i	−0.000949392	−	0.00164439i	0.865550	−	0.500822i	$-0.166969\pi$
$613$	−0.0235058	−	0.0407133i	−0.000949392	−	0.00164439i	−0.866500	+	0.499178i	$0.833636\pi$
$614$	35.2751	−	15.0048i	1.42359	−	0.605543i
$615$	27.5257	+	15.4913i	1.10994	+	0.624669i
$616$	−2.39423	−	3.29135i	−0.0964664	−	0.132612i
$617$	−10.4917	−	18.1721i	−0.422379	−	0.731582i	0.573793	−	0.819001i	$-0.305472\pi$
$617$	−10.4917	−	18.1721i	−0.422379	−	0.731582i	−0.996172	+	0.0874187i	$0.972138\pi$
$618$	−9.37485	+	12.7495i	−0.377112	+	0.512861i
$619$	5.34333			0.214767			0.107383	−	0.994218i	$-0.465753\pi$
$619$	5.34333			0.214767			0.107383	+	0.994218i	$0.465753\pi$
$620$	−34.9570	+	10.0808i	−1.40391	+	0.404853i
$621$	8.38637	−	0.276484i	0.336533	−	0.0110949i
$622$	−2.13436	+	17.4919i	−0.0855799	+	0.701359i
$623$	10.5530	+	20.7975i	0.422795	+	0.833234i
$624$	7.19110	+	3.69540i	0.287874	+	0.147934i
$625$	48.1664			1.92665
$626$	−16.1617	+	21.4809i	−0.645950	+	0.858550i
$627$	2.19482	−	0.0241121i	0.0876526	−	0.000962943i
$628$	−14.6775	+	4.23265i	−0.585696	+	0.168901i
$629$		−	17.3450i		−	0.691592i
$630$	−35.4423	−	28.4904i	−1.41206	−	1.13508i
$631$			23.1548i			0.921776i	0.887458	+	0.460888i	$0.152469\pi$
$631$			23.1548i			0.921776i	−0.887458	+	0.460888i	$0.847531\pi$
$632$	−1.80713	−	11.2452i	−0.0718836	−	0.447311i
$633$	−0.0852598	+	0.151494i	−0.00338877	+	0.00602133i
$634$	23.2104	+	17.4629i	0.921802	+	0.693540i
$635$	57.5707			2.28462
$636$	38.7738	−	11.6443i	1.53748	−	0.461726i
$637$	−6.59257	−	4.82366i	−0.261207	−	0.191120i
$638$	3.66483	+	0.447183i	0.145092	+	0.0177041i
$639$	−13.6061	−	7.46184i	−0.538250	−	0.295186i
$640$	14.6931	−	43.4142i	0.580797	−	1.71610i
$641$	−16.3966			−0.647628			−0.323814	−	0.946121i	$-0.604965\pi$
$641$	−16.3966			−0.647628			−0.323814	+	0.946121i	$0.604965\pi$
$642$	24.9347	−	10.9314i	0.984096	−	0.431426i
$643$	4.77787	+	8.27551i	0.188421	+	0.326354i	0.944724	−	0.327867i	$-0.106330\pi$
$643$	4.77787	+	8.27551i	0.188421	+	0.326354i	−0.756303	+	0.654221i	$0.772996\pi$
$644$	−1.92076	−	8.32622i	−0.0756886	−	0.328099i
$645$	−0.257688	−	23.4563i	−0.0101465	−	0.923590i
$646$	7.53263	+	17.7087i	0.296367	+	0.696738i
$647$	−10.7329	−	18.5900i	−0.421956	−	0.730849i	0.574175	−	0.818733i	$-0.305323\pi$
$647$	−10.7329	−	18.5900i	−0.421956	−	0.730849i	−0.996131	+	0.0878838i	$0.971990\pi$
$648$	−24.9317	+	5.13913i	−0.979409	+	0.201884i
$649$	6.06579	+	3.50209i	0.238103	+	0.137469i
$650$	11.3227	−	15.0493i	0.444114	−	0.590284i
$651$	11.0460	−	17.3610i	0.432926	−	0.680431i
$652$	29.0892	−	8.38864i	1.13922	−	0.328525i
$653$	−3.15237			−0.123362			−0.0616808	−	0.998096i	$-0.519646\pi$
$653$	−3.15237			−0.123362			−0.0616808	+	0.998096i	$0.519646\pi$
$654$	−8.14842	−	0.903542i	−0.318628	−	0.0353313i
$655$		−	64.4531i		−	2.51839i
$656$	−9.58757	−	15.2409i	−0.374332	−	0.595059i
$657$	−0.425179	−	19.3488i	−0.0165878	−	0.754868i
$658$	−10.9540	−	30.1827i	−0.427033	−	1.17664i
$659$	−9.56754	−	5.52382i	−0.372698	−	0.215178i	0.301938	−	0.953327i	$-0.402366\pi$
$659$	−9.56754	−	5.52382i	−0.372698	−	0.215178i	−0.674637	+	0.738150i	$0.735700\pi$
$660$	−1.75383	+	7.42835i	−0.0682679	+	0.289148i
$661$	24.5803	+	14.1914i	0.956063	+	0.551983i	0.894959	−	0.446148i	$-0.147205\pi$
$661$	24.5803	+	14.1914i	0.956063	+	0.551983i	0.0611040	+	0.998131i	$0.480538\pi$
$662$	−9.75524	+	12.9659i	−0.379148	+	0.503936i
$663$	−0.129675	−	11.8038i	−0.00503617	−	0.458421i
$664$	9.88810	+	12.1545i	0.383733	+	0.471687i
$665$	−11.3005	−	22.2707i	−0.438214	−	0.863621i
$666$	10.2329	+	7.35253i	0.396516	+	0.284905i
$667$	6.71276	+	3.87562i	0.259919	+	0.150064i
$668$	−7.31970	−	1.81330i	−0.283208	−	0.0701586i
$669$	0.243961	+	22.2067i	0.00943208	+	0.858562i
$670$	4.92423	−	40.3559i	0.190240	−	1.55908i
$671$	0.566500	+	0.981208i	0.0218695	+	0.0378791i
$672$	10.0243	+	23.9063i	0.386697	+	0.922207i
$673$	14.8049	−	25.6429i	0.570688	−	0.988461i	−0.425807	−	0.904814i	$-0.640010\pi$
$673$	14.8049	−	25.6429i	0.570688	−	0.988461i	0.996495	−	0.0836470i	$-0.0266568\pi$
$674$	−10.7181	−	8.06399i	−0.412845	−	0.310613i
$675$	1.95384	+	59.2641i	0.0752033	+	2.28108i
$676$	6.44953	+	22.3650i	0.248059	+	0.860191i
$677$	−17.0249	+	9.82935i	−0.654321	+	0.377772i	−0.790110	−	0.612965i	$-0.789976\pi$
$677$	−17.0249	+	9.82935i	−0.654321	+	0.377772i	0.135789	+	0.990738i	$0.456643\pi$
$678$	−6.62493	−	0.734608i	−0.254429	−	0.0282125i
$679$	−19.0817	−	37.6057i	−0.732287	−	1.44317i
$680$	−66.0707	+	10.6177i	−2.53370	+	0.407169i
$681$	27.9973	−	16.5770i	1.07286	−	0.635230i
$682$	−3.42836	−	0.418329i	−0.131279	−	0.0160186i
$683$	4.93427	−	2.84880i	0.188804	−	0.109006i	−0.402618	−	0.915368i	$-0.631900\pi$
$683$	4.93427	−	2.84880i	0.188804	−	0.109006i	0.591423	+	0.806362i	$0.298566\pi$
$684$	−13.6405	−	3.06272i	−0.521556	−	0.117106i
$685$			50.8793i			1.94400i
$686$	−6.22753	−	25.4405i	−0.237768	−	0.971322i
$687$	−15.9631	−	26.9605i	−0.609030	−	1.02861i
$688$	−6.24236	+	11.8260i	−0.237988	+	0.450862i
$689$	−11.8111	−	6.81914i	−0.449967	−	0.259789i
$690$	−9.49277	+	12.9099i	−0.361384	+	0.491471i
$691$	−8.90268	−	15.4199i	−0.338674	−	0.586600i	0.645510	−	0.763752i	$-0.276645\pi$
$691$	−8.90268	−	15.4199i	−0.338674	−	0.586600i	−0.984184	+	0.177152i	$0.943312\pi$
$692$	−3.01293	+	12.1622i	−0.114534	+	0.462338i
$693$	−2.03750	−	3.80586i	−0.0773982	−	0.144573i
$694$	3.21614	+	0.392434i	0.122083	+	0.0148966i
$695$	49.8594	−	28.7863i	1.89128	−	1.09193i
$696$	−22.0630	−	8.13558i	−0.836296	−	0.308378i
$697$	−13.1446	+	22.7671i	−0.497887	+	0.862365i
$698$	−46.0042	−	5.61344i	−1.74129	−	0.212472i
$699$	0.223896	+	20.3803i	0.00846851	+	0.770853i
$700$	58.8391	−	13.5735i	2.22391	−	0.513030i
$701$	9.77794			0.369308			0.184654	−	0.982804i	$-0.440884\pi$
$701$	9.77794			0.369308			0.184654	+	0.982804i	$0.440884\pi$
$702$	7.01873	+	4.92710i	0.264905	+	0.185961i
$703$	3.46002	+	5.99293i	0.130497	+	0.226028i
$704$	2.89679	−	3.24660i	0.109177	−	0.122361i
$705$	−29.5324	+	52.4746i	−1.11225	+	1.97631i
$706$	−11.6791	−	27.4567i	−0.439549	−	1.03335i
$707$	10.6992	−	16.4149i	0.402384	−	0.617347i
$708$	−32.4751	−	30.5861i	−1.22049	−	1.14950i
$709$	6.52938	+	11.3092i	0.245216	+	0.424726i	0.962192	−	0.272371i	$-0.0878078\pi$
$709$	6.52938	+	11.3092i	0.245216	+	0.424726i	−0.716976	+	0.697097i	$0.754474\pi$
$710$	27.2703	−	11.5998i	1.02343	−	0.435332i
$711$	−0.265396	−	12.0775i	−0.00995312	−	0.452941i
$712$	−19.3402	+	15.7339i	−0.724806	+	0.589653i
$713$	−6.27962	−	3.62554i	−0.235174	−	0.135778i
$714$	24.0357	−	29.2370i	0.899513	−	1.09417i
$715$	2.22676	−	1.28562i	0.0832761	−	0.0480795i
$716$	−4.79719	+	19.3647i	−0.179279	+	0.723693i
$717$	1.66545	−	2.95925i	0.0621974	−	0.110515i
$718$	41.9997	+	5.12480i	1.56741	+	0.191256i
$719$	15.4289	−	26.7237i	0.575401	−	0.996624i	−0.420597	−	0.907248i	$-0.638179\pi$
$719$	15.4289	−	26.7237i	0.575401	−	0.996624i	0.995998	−	0.0893766i	$-0.0284875\pi$
$720$	21.7432	−	43.4799i	0.810323	−	1.62040i
$721$	14.3199	+	9.33366i	0.533302	+	0.347604i
$722$	15.3364	+	11.5387i	0.570761	+	0.429426i
$723$	6.04986	+	10.2178i	0.224997	+	0.380003i
$724$	−7.70269	−	7.41600i	−0.286268	−	0.275614i
$725$	−27.3879	+	47.4372i	−1.01716	+	1.76177i
$726$	15.5326	−	21.1239i	0.576468	−	0.783980i
$727$	−1.75480	+	3.03940i	−0.0650819	+	0.112725i	−0.896730	−	0.442577i	$-0.854064\pi$
$727$	−1.75480	+	3.03940i	−0.0650819	+	0.112725i	0.831648	+	0.555303i	$0.187398\pi$
$728$	3.54732	−	7.97992i	0.131472	−	0.295755i
$729$	−26.9414	+	1.77836i	−0.997829	+	0.0658650i
$730$	29.5340	+	22.2206i	1.09310	+	0.822422i
$731$	19.5243			0.722131
$732$	−2.07558	−	6.91137i	−0.0767157	−	0.255452i
$733$		−	2.53898i		−	0.0937793i	−0.998900	−	0.0468897i	$-0.985069\pi$
$733$		−	2.53898i		−	0.0937793i	0.998900	−	0.0468897i	$-0.0149309\pi$
$734$	26.1935	−	11.1418i	0.966820	−	0.411250i
$735$	−28.5663	+	39.9558i	−1.05368	+	1.47379i
$736$	8.26442	−	3.89172i	0.304631	−	0.143451i
$737$	1.92975	−	3.34243i	0.0710834	−	0.123120i
$738$	−7.85971	−	17.4057i	−0.289320	−	0.640713i
$739$	−7.43557	+	4.29293i	−0.273522	+	0.157918i	−0.630487	−	0.776200i	$-0.717145\pi$
$739$	−7.43557	+	4.29293i	−0.273522	+	0.157918i	0.356965	+	0.934118i	$0.383812\pi$
$740$	−23.1211	+	6.66759i	−0.849949	+	0.245105i
$741$	2.39944	+	4.05249i	0.0881458	+	0.148872i
$742$	−14.9180	−	41.1049i	−0.547656	−	1.50901i
$743$	0.852403	−	0.492135i	0.0312716	−	0.0180547i	−0.484283	−	0.874912i	$-0.660919\pi$
$743$	0.852403	−	0.492135i	0.0312716	−	0.0180547i	0.515554	+	0.856857i	$0.327586\pi$
$744$	20.6394	+	7.61063i	0.756677	+	0.279019i
$745$		−	17.1482i		−	0.628263i
$746$	−14.2385	+	6.05656i	−0.521310	+	0.221746i
$747$	8.62375	+	14.2066i	0.315526	+	0.519791i
$748$	−6.16635	−	1.52758i	−0.225464	−	0.0558538i
$749$	−13.3066	−	26.2242i	−0.486211	−	0.958213i
$750$	−51.2578	−	37.6904i	−1.87167	−	1.37626i
$751$		−	4.82883i		−	0.176207i	−0.996111	−	0.0881033i	$-0.971919\pi$
$751$		−	4.82883i		−	0.176207i	0.996111	−	0.0881033i	$-0.0280806\pi$
$752$	29.0551	−	18.2776i	1.05953	−	0.666516i
$753$	−25.3867	+	15.0313i	−0.925144	+	0.547770i
$754$	3.10075	+	7.28964i	0.112923	+	0.265473i
$755$	35.2715			1.28366
$756$	7.06000	+	26.5736i	0.256770	+	0.966473i
$757$	−39.8457			−1.44822			−0.724109	−	0.689686i	$-0.757749\pi$
$757$	−39.8457			−1.44822			−0.724109	+	0.689686i	$0.757749\pi$
$758$	−8.82138	−	20.7384i	−0.320407	−	0.753253i
$759$	−1.30899	+	0.775041i	−0.0475132	+	0.0281322i
$760$	20.7102	−	16.8484i	0.751239	−	0.611157i
$761$			23.6541i			0.857460i	0.903433	+	0.428730i	$0.141039\pi$
$761$			23.6541i			0.857460i	−0.903433	+	0.428730i	$0.858961\pi$
$762$	−28.0444	−	20.6213i	−1.01594	−	0.747031i
$763$	−0.478280	+	8.84232i	−0.0173149	+	0.320113i
$764$	−10.5852	+	42.7291i	−0.382960	+	1.54588i
$765$	−70.9606	+	1.55932i	−2.56558	+	0.0563773i
$766$	−30.5687	+	13.0028i	−1.10449	+	0.469811i
$767$			15.0284i			0.542644i
$768$	−22.7080	+	15.8854i	−0.819405	+	0.573214i
$769$	1.86343	−	1.07585i	0.0671971	−	0.0387963i	−0.466025	−	0.884772i	$-0.654314\pi$
$769$	1.86343	−	1.07585i	0.0671971	−	0.0387963i	0.533222	+	0.845975i	$0.320981\pi$
$770$	8.11756	+	1.43908i	0.292537	+	0.0518609i
$771$	18.3394	+	30.9738i	0.660476	+	1.11550i
$772$	−3.23324	−	11.2119i	−0.116367	−	0.403524i
$773$	24.9256	−	14.3908i	0.896513	−	0.517602i	0.0204456	−	0.999791i	$-0.493491\pi$
$773$	24.9256	−	14.3908i	0.896513	−	0.517602i	0.876067	+	0.482189i	$0.160158\pi$
$774$	−8.27630	+	11.5185i	−0.297485	+	0.414025i
$775$	25.6207	−	44.3763i	0.920323	−	1.59405i
$776$	34.9707	−	28.4498i	1.25537	−	1.02129i
$777$	7.30600	−	11.4829i	0.262101	−	0.411945i
$778$	−10.5848	+	4.50238i	−0.379483	+	0.161418i
$779$		−	10.4884i		−	0.375787i
$780$	−15.6847	+	4.71034i	−0.561603	+	0.168657i
$781$	2.81331			0.100668
$782$	−10.6577	−	8.01857i	−0.381118	−	0.286744i
$783$	−21.9993	−	11.7523i	−0.786190	−	0.419993i
$784$	25.1704	−	12.2658i	0.898944	−	0.438064i
$785$	15.4708	−	26.7963i	0.552178	−	0.956400i
$786$	−23.0865	+	31.3970i	−0.823468	+	1.11989i
$787$	5.56484	−	9.63859i	0.198365	−	0.343579i	−0.749633	−	0.661853i	$-0.769770\pi$
$787$	5.56484	−	9.63859i	0.198365	−	0.343579i	0.947999	+	0.318275i	$0.103103\pi$
$788$	19.7880	−	20.5529i	0.704918	−	0.732168i
$789$	8.66505	+	14.6347i	0.308484	+	0.521007i
$790$	18.4351	+	13.8701i	0.655890	+	0.493475i
$791$	−0.388857	+	7.18909i	−0.0138262	+	0.255615i
$792$	3.51511	−	2.99036i	0.124904	−	0.106258i
$793$	−1.21550	+	2.10531i	−0.0431638	+	0.0747619i
$794$	−38.4493	−	4.69159i	−1.36452	−	0.166498i
$795$	−40.2193	+	71.4635i	−1.42643	+	2.53455i
$796$	−8.34177	−	2.06649i	−0.295666	−	0.0732449i
$797$	25.2083	−	14.5540i	0.892923	−	0.515529i	0.0180253	−	0.999838i	$-0.494262\pi$
$797$	25.2083	−	14.5540i	0.892923	−	0.515529i	0.874897	+	0.484308i	$0.160929\pi$
$798$	−2.47237	+	14.8964i	−0.0875210	+	0.527328i
$799$	−43.4029	−	25.0587i	−1.53548	−	0.886512i
$800$	27.5017	+	58.4023i	0.972332	+	2.06483i
$801$	−22.6054	+	13.7221i	−0.798724	+	0.484846i
$802$	24.5300	−	10.4342i	0.866184	−	0.368443i
$803$	1.75434	+	3.03860i	0.0619092	+	0.107230i
$804$	−16.8539	+	17.8947i	−0.594389	+	0.631098i
$805$	14.5001	+	9.45107i	0.511060	+	0.333106i
$806$	−2.90068	−	6.81928i	−0.102172	−	0.240199i
$807$	4.79513	−	8.52021i	0.168796	−	0.299925i
$808$	19.5724	+	7.46245i	0.688555	+	0.262528i
$809$	11.9462	+	20.6915i	0.420007	+	0.727474i	0.995940	−	0.0900232i	$-0.0286941\pi$
$809$	11.9462	+	20.6915i	0.420007	+	0.727474i	−0.575932	+	0.817497i	$0.695361\pi$
$810$	29.1601	−	42.5249i	1.02458	−	1.49417i
$811$	20.7873			0.729940			0.364970	−	0.931019i	$-0.381079\pi$
$811$	20.7873			0.729940			0.364970	+	0.931019i	$0.381079\pi$
$812$	−7.43019	+	24.2882i	−0.260748	+	0.852349i
$813$	0.431107	+	39.2418i	0.0151196	+	1.37627i
$814$	−2.26757	−	0.276690i	−0.0794785	−	0.00969796i
$815$	−30.6615	+	53.1073i	−1.07403	+	1.86027i
$816$	35.9881	+	18.4938i	1.25984	+	0.647411i
$817$	−6.74588	+	3.89473i	−0.236008	+	0.136259i
$818$	26.7880	+	3.26867i	0.936621	+	0.114286i
$819$	4.88609	−	7.86902i	0.170734	−	0.274966i
$820$	35.4017	+	8.77000i	1.23628	+	0.306262i
$821$	2.89057	+	5.00661i	0.100881	+	0.174732i	0.912048	−	0.410083i	$-0.134500\pi$
$821$	2.89057	+	5.00661i	0.100881	+	0.174732i	−0.811167	+	0.584815i	$0.801167\pi$
$822$	18.2245	−	24.7848i	0.635653	−	0.864469i
$823$	16.5191	+	9.53730i	0.575819	+	0.332449i	0.759470	−	0.650542i	$-0.225458\pi$
$823$	16.5191	+	9.53730i	0.575819	+	0.332449i	−0.183651	+	0.982992i	$0.558792\pi$
$824$	−6.51004	+	17.0744i	−0.226788	+	0.594817i
$825$	−5.47699	−	9.25025i	−0.190684	−	0.322052i
$826$	−31.0071	+	36.8835i	−1.07887	+	1.28334i
$827$			14.6270i			0.508631i	0.967121	+	0.254315i	$0.0818501\pi$
$827$			14.6270i			0.508631i	−0.967121	+	0.254315i	$0.918150\pi$
$828$	9.24841	−	2.88856i	0.321405	−	0.100384i
$829$	3.92858	−	2.26817i	0.136445	−	0.0787767i	−0.430223	−	0.902722i	$-0.641565\pi$
$829$	3.92858	−	2.26817i	0.136445	−	0.0787767i	0.566669	+	0.823946i	$0.308232\pi$
$830$	−31.5042	−	3.84414i	−1.09353	−	0.133432i
$831$	17.1883	−	10.1770i	0.596254	−	0.353037i
$832$	9.14047	+	1.89973i	0.316889	+	0.0658613i
$833$	−32.9928	−	24.1402i	−1.14313	−	0.836407i
$834$	−34.5990	−	3.83652i	−1.19806	−	0.132848i
$835$	13.2283	−	7.63734i	0.457783	−	0.264301i
$836$	2.43527	−	0.702275i	0.0842257	−	0.0242887i
$837$	20.5798	+	10.9940i	0.711341	+	0.380008i
$838$	28.7521	+	21.6323i	0.993223	+	0.747275i
$839$	12.4814	−	21.6184i	0.430906	−	0.746351i	−0.566046	−	0.824374i	$-0.691527\pi$
$839$	12.4814	−	21.6184i	0.430906	−	0.746351i	0.996952	+	0.0780231i	$0.0248608\pi$
$840$	−48.2128	−	20.8008i	−1.66350	−	0.717697i
$841$	2.97992	+	5.16138i	0.102756	+	0.177978i
$842$	3.51120	−	28.7756i	0.121004	−	0.991672i
$843$	−0.0238157	−	2.16784i	−0.000820256	−	0.0746644i
$844$	−0.0482676	+	0.194841i	−0.00166144	+	0.00670670i
$845$	−40.8311	−	23.5738i	−1.40463	−	0.810964i
$846$	33.1820	−	14.9836i	1.14082	−	0.515148i
$847$	−23.7258	−	15.4643i	−0.815227	−	0.531361i
$848$	39.5693	−	24.8917i	1.35882	−	0.854785i
$849$	0.0181039	+	1.64792i	0.000621323	+	0.0565564i
$850$	56.6650	−	75.3150i	1.94359	−	2.58328i
$851$	−4.15345	−	2.39799i	−0.142378	−	0.0822022i
$852$	−17.4391	−	4.11737i	−0.597453	−	0.141059i
$853$	13.2403	+	7.64427i	0.453338	+	0.261735i	0.709239	−	0.704968i	$-0.249039\pi$
$853$	13.2403	+	7.64427i	0.453338	+	0.261735i	−0.255901	+	0.966703i	$0.582372\pi$
$854$	−7.32690	+	2.65911i	−0.250721	+	0.0909928i
$855$	24.2067	−	14.6941i	0.827852	−	0.502527i
$856$	24.3867	−	19.8394i	0.833521	−	0.678097i
$857$			48.5172i			1.65732i	0.559756	+	0.828658i	$0.310895\pi$
$857$			48.5172i			1.65732i	−0.559756	+	0.828658i	$0.689105\pi$
$858$	−1.54522	−	0.171342i	−0.0527528	−	0.00584952i
$859$	−51.7445			−1.76550			−0.882751	−	0.469842i	$-0.844311\pi$
$859$	−51.7445			−1.76550			−0.882751	+	0.469842i	$0.844311\pi$
$860$	−7.50530	−	26.0260i	−0.255928	−	0.887481i
$861$	−18.2919	+	9.53568i	−0.623386	+	0.324975i
$862$	−14.9261	+	19.8386i	−0.508384	+	0.675707i
$863$	−38.8024	−	22.4026i	−1.32085	−	0.762592i	−0.336984	−	0.941510i	$-0.609407\pi$
$863$	−38.8024	−	22.4026i	−1.32085	−	0.762592i	−0.983864	+	0.178919i	$0.942740\pi$
$864$	−26.1659	+	13.3921i	−0.890181	+	0.455608i
$865$	−12.6900	−	21.9797i	−0.431472	−	0.747332i
$866$	8.41456	+	19.7820i	0.285938	+	0.672220i
$867$	−0.325506	−	29.6294i	−0.0110547	−	1.00627i
$868$	6.95075	−	22.7210i	0.235924	−	0.771201i
$869$	1.09505	+	1.89669i	0.0371471	+	0.0643407i
$870$	43.6235	−	19.1245i	1.47897	−	0.648380i
$871$	8.28109			0.280594
$872$	−9.34673	+	1.50204i	−0.316520	+	0.0508653i
$873$	40.8747	−	24.8120i	1.38340	−	0.839760i
$874$	5.28192	+	0.644501i	0.178664	+	0.0218006i
$875$	−37.5248	+	57.5715i	−1.26857	+	1.94627i
$876$	−6.42765	−	21.4031i	−0.217170	−	0.723145i
$877$	−36.8194			−1.24330			−0.621651	−	0.783294i	$-0.713538\pi$
$877$	−36.8194			−1.24330			−0.621651	+	0.783294i	$0.713538\pi$
$878$	16.4643	+	12.3873i	0.555643	+	0.418051i
$879$	−14.0520	+	24.9682i	−0.473962	+	0.842157i
$880$	0.334118	+	8.80701i	0.0112631	+	0.296884i
$881$		−	50.8325i		−	1.71259i	−0.516486	−	0.856295i	$-0.672760\pi$
$881$		−	50.8325i		−	1.71259i	0.516486	−	0.856295i	$-0.327240\pi$
$882$	28.2273	−	9.23144i	0.950463	−	0.310839i
$883$		−	28.5456i		−	0.960635i	−0.877095	−	0.480317i	$-0.840521\pi$
$883$		−	28.5456i		−	0.960635i	0.877095	−	0.480317i	$-0.159479\pi$
$884$	−3.77685	−	13.0970i	−0.127029	−	0.440498i
$885$	90.3568	−	0.992651i	3.03731	−	0.0333676i
$886$	−20.4293	+	27.1531i	−0.686335	+	0.912226i
$887$	1.83342			0.0615601			0.0307800	−	0.999526i	$-0.490201\pi$
$887$	1.83342			0.0615601			0.0307800	+	0.999526i	$0.490201\pi$
$888$	13.6512	+	5.03380i	0.458106	+	0.168923i
$889$	−20.5307	+	31.4987i	−0.688577	+	1.05643i
$890$	6.11678	−	50.1293i	0.205035	−	1.68034i
$891$	4.12755	−	2.63133i	0.138278	−	0.0881528i
$892$	7.10548	+	24.6396i	0.237909	+	0.824995i
$893$	19.9950			0.669107
$894$	−6.14235	+	8.35341i	−0.205431	+	0.279380i
$895$	−20.2050	−	34.9962i	−0.675380	−	1.16979i
$896$	18.5134	+	23.5213i	0.618491	+	0.785792i
$897$	−2.84447	−	1.60085i	−0.0949739	−	0.0534508i
$898$	47.1007	−	20.0349i	1.57177	−	0.668574i
$899$	10.7767	+	18.6659i	0.359425	+	0.622542i
$900$	20.4126	+	65.3559i	0.680421	+	2.17853i
$901$	−59.1091	−	34.1266i	−1.96921	−	1.13692i
$902$	2.76673	+	2.08162i	0.0921221	+	0.0693103i
$903$	12.9255	+	8.22392i	0.430135	+	0.273675i
$904$	−7.59920	+	1.22120i	−0.252745	+	0.0406166i
$905$	21.6582			0.719943
$906$	−17.1818	−	12.6339i	−0.570825	−	0.419734i
$907$			34.1303i			1.13328i	0.823966	+	0.566640i	$0.191757\pi$
$907$			34.1303i			1.13328i	−0.823966	+	0.566640i	$0.808243\pi$
$908$	26.0577	−	27.0651i	0.864757	−	0.898186i
$909$	19.4803	+	10.6833i	0.646119	+	0.354344i
$910$	6.03460	+	16.6277i	0.200045	+	0.551203i
$911$	46.1098	+	26.6215i	1.52769	+	0.882010i	0.999458	+	0.0329076i	$0.0104767\pi$
$911$	46.1098	+	26.6215i	1.52769	+	0.882010i	0.528228	+	0.849103i	$0.322857\pi$
$912$	−16.1235	+	0.789149i	−0.533903	+	0.0261313i
$913$	−2.60930	−	1.50648i	−0.0863551	−	0.0498571i
$914$	−23.2479	−	17.4911i	−0.768972	−	0.578554i
$915$	12.7383	+	7.16904i	0.421115	+	0.237001i
$916$	−26.0628	−	25.0928i	−0.861139	−	0.829089i
$917$	35.2643	+	22.9851i	1.16453	+	0.759034i
$918$	35.1255	+	24.6578i	1.15931	+	0.813830i
$919$	−13.4852	−	7.78568i	−0.444836	−	0.256826i	0.260811	−	0.965390i	$-0.416010\pi$
$919$	−13.4852	−	7.78568i	−0.444836	−	0.256826i	−0.705647	+	0.708564i	$0.749343\pi$
$920$	−6.59192	+	17.2892i	−0.217329	+	0.570009i
$921$	40.3988	−	23.9198i	1.33118	−	0.788183i
$922$	−32.5467	−	3.97134i	−1.07187	−	0.130789i
$923$	3.01817	+	5.22762i	0.0993442	+	0.172069i
$924$	−3.43883	−	3.60865i	−0.113129	−	0.118716i
$925$	16.9460	−	29.3513i	0.557180	−	0.965063i
$926$	−10.8429	+	14.4116i	−0.356321	+	0.473596i
$927$	−9.31984	+	16.9940i	−0.306104	+	0.558158i
$928$	−27.0584	−	2.26465i	−0.888235	−	0.0743407i
$929$	−5.33592	+	3.08070i	−0.175066	+	0.101074i	−0.584972	−	0.811053i	$-0.698895\pi$
$929$	−5.33592	+	3.08070i	−0.175066	+	0.101074i	0.409906	+	0.912128i	$0.365561\pi$
$930$	−40.8087	+	17.8905i	−1.33817	+	0.586651i
$931$	16.2149	+	1.75927i	0.531423	+	0.0576579i
$932$	6.52107	+	22.6130i	0.213605	+	0.740715i
$933$	0.237083	+	21.5806i	0.00776174	+	0.706519i
$934$	−3.55762	+	29.1560i	−0.116409	+	0.954015i
$935$	11.1439	−	6.43393i	0.364444	−	0.210412i
$936$	9.32768	+	3.32358i	0.304885	+	0.108635i
$937$		−	20.3159i		−	0.663692i	−0.943334	−	0.331846i	$-0.892329\pi$
$937$		−	20.3159i		−	0.663692i	0.943334	−	0.331846i	$-0.107671\pi$
$938$	20.3239	+	17.0858i	0.663599	+	0.557871i
$939$	−16.1474	+	28.6915i	−0.526952	+	0.936313i
$940$	−16.7190	+	67.4893i	−0.545314	+	2.20126i
$941$	−33.1891	−	19.1617i	−1.08193	−	0.624654i	−0.150515	−	0.988608i	$-0.548093\pi$
$941$	−33.1891	−	19.1617i	−1.08193	−	0.624654i	−0.931417	+	0.363954i	$0.881427\pi$
$942$	−17.1345	+	7.51173i	−0.558272	+	0.244745i
$943$	3.63454	+	6.29521i	0.118357	+	0.205000i
$944$	−45.5553	−	24.0464i	−1.48270	−	0.782644i
$945$	−47.6345	−	28.8574i	−1.54955	−	0.938730i
$946$	0.311453	−	2.55247i	0.0101262	−	0.0829880i
$947$	−11.4438	+	6.60705i	−0.371872	+	0.214700i	−0.674276	−	0.738479i	$-0.735544\pi$
$947$	−11.4438	+	6.60705i	−0.371872	+	0.214700i	0.302404	+	0.953180i	$0.402211\pi$
$948$	−4.01213	−	13.3598i	−0.130308	−	0.433906i
$949$	−3.76417	+	6.51973i	−0.122190	+	0.211639i
$950$	−4.55451	+	37.3259i	−0.147768	+	1.21101i
$951$	31.0016	+	17.4475i	1.00529	+	0.565774i
$952$	17.7527	−	39.9358i	0.575368	−	1.29433i
$953$	11.6066			0.375976			0.187988	−	0.982171i	$-0.439803\pi$
$953$	11.6066			0.375976			0.187988	+	0.982171i	$0.439803\pi$
$954$	45.1896	−	20.4058i	1.46307	−	0.660661i
$955$	−44.5833	−	77.2206i	−1.44268	−	2.49880i
$956$	0.942852	−	3.80599i	0.0304940	−	0.123095i
$957$	4.52150	−	0.0496728i	0.146159	−	0.00160569i
$958$	−23.7302	+	10.0940i	−0.766688	+	0.326121i
$959$	−27.8376	−	18.1444i	−0.898924	−	0.585914i
$960$	10.8182	−	55.0817i	0.349156	−	1.77775i
$961$	5.41862	+	9.38533i	0.174794	+	0.302753i
$962$	−1.91856	−	4.51039i	−0.0618567	−	0.145421i
$963$	28.5039	−	17.3026i	0.918526	−	0.557569i
$964$	9.87756	+	9.50994i	0.318135	+	0.306294i
$965$	20.4692	+	11.8179i	0.658926	+	0.380431i
$966$	−3.67811	−	9.79768i	−0.118341	−	0.315235i
$967$	−40.7431	+	23.5230i	−1.31021	+	0.756449i	−0.982130	−	0.188201i	$-0.939734\pi$
$967$	−40.7431	+	23.5230i	−1.31021	+	0.756449i	−0.328078	+	0.944651i	$0.606401\pi$
$968$	10.7861	−	28.2895i	0.346677	−	0.909261i
$969$	12.0081	+	20.2808i	0.385756	+	0.651514i
$970$	−11.0603	+	90.6429i	−0.355123	+	2.91037i
$971$	17.2692	−	29.9112i	0.554195	−	0.959895i	−0.443770	−	0.896141i	$-0.646359\pi$
$971$	17.2692	−	29.9112i	0.554195	−	0.959895i	0.997966	−	0.0637540i	$-0.0203073\pi$
$972$	−29.4368	+	10.2702i	−0.944184	+	0.329417i
$973$	−2.03082	+	37.5453i	−0.0651051	+	1.20365i
$974$	8.17034	−	10.8594i	0.261795	−	0.347958i
$975$	11.3128	−	20.1010i	0.362298	−	0.643748i
$976$	−4.43692	−	7.05317i	−0.142022	−	0.225767i
$977$	13.6540	−	23.6494i	0.436830	−	0.756611i	−0.560613	−	0.828078i	$-0.689435\pi$
$977$	13.6540	−	23.6494i	0.436830	−	0.756611i	0.997443	+	0.0714666i	$0.0227679\pi$
$978$	33.9587	−	14.8874i	1.08588	−	0.476048i
$979$	2.39710	−	4.15190i	0.0766117	−	0.132695i
$980$	−19.4964	+	53.2594i	−0.622789	+	1.70131i
$981$	−10.0385	+	0.220590i	−0.320504	+	0.00704290i
$982$	−1.52615	+	2.02844i	−0.0487013	+	0.0647302i
$983$	−19.1321			−0.610221			−0.305110	−	0.952317i	$-0.598693\pi$
$983$	−19.1321			−0.610221			−0.305110	+	0.952317i	$0.598693\pi$
$984$	−14.1038	−	16.9527i	−0.449614	−	0.540431i
$985$			57.7902i			1.84135i
$986$	15.5178	+	36.4813i	0.494188	+	1.16180i
$987$	−18.1787	−	34.8714i	−0.578634	−	1.10997i
$988$	3.91755	+	3.77175i	0.124634	+	0.119995i
$989$	2.69928	−	4.67528i	0.0858320	−	0.148665i
$990$	−0.928114	+	9.30178i	−0.0294974	+	0.295630i
$991$	−19.9326	+	11.5081i	−0.633179	+	0.365566i	−0.781982	−	0.623301i	$-0.785791\pi$
$991$	−19.9326	+	11.5081i	−0.633179	+	0.365566i	0.148803	+	0.988867i	$0.452458\pi$
$992$	25.3124	+	2.11852i	0.803671	+	0.0672631i
$993$	−9.74665	+	17.3183i	−0.309300	+	0.549580i
$994$	−3.37844	+	19.0571i	−0.107158	+	0.604454i
$995$	15.0754	−	8.70376i	0.477921	−	0.275928i
$996$	13.9697	+	13.1571i	0.442645	+	0.416899i
$997$		−	60.9745i		−	1.93108i	−0.260252	−	0.965541i	$-0.583806\pi$
$997$		−	60.9745i		−	1.93108i	0.260252	−	0.965541i	$-0.416194\pi$
$998$	−24.3433	−	57.2294i	−0.770575	−	1.81156i
$999$	13.6118	+	7.27161i	0.430658	+	0.230063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.n.b.187.38	yes	84
3.2	odd	2		756.2.n.b.19.5		84
4.3	odd	2	inner	252.2.n.b.187.10	yes	84
7.3	odd	6		252.2.bj.b.115.20	yes	84
9.4	even	3		252.2.bj.b.103.20	yes	84
9.5	odd	6		756.2.bj.b.523.23		84
12.11	even	2		756.2.n.b.19.33		84
21.17	even	6		756.2.bj.b.451.23		84
28.3	even	6		252.2.bj.b.115.19	yes	84
36.23	even	6		756.2.bj.b.523.24		84
36.31	odd	6		252.2.bj.b.103.19	yes	84
63.31	odd	6	inner	252.2.n.b.31.10	✓	84
63.59	even	6		756.2.n.b.199.33		84
84.59	odd	6		756.2.bj.b.451.24		84
252.31	even	6	inner	252.2.n.b.31.38	yes	84
252.59	odd	6		756.2.n.b.199.5		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.10	✓	84	63.31	odd	6	inner
252.2.n.b.31.38	yes	84	252.31	even	6	inner
252.2.n.b.187.10	yes	84	4.3	odd	2	inner
252.2.n.b.187.38	yes	84	1.1	even	1	trivial
252.2.bj.b.103.19	yes	84	36.31	odd	6
252.2.bj.b.103.20	yes	84	9.4	even	3
252.2.bj.b.115.19	yes	84	28.3	even	6
252.2.bj.b.115.20	yes	84	7.3	odd	6
756.2.n.b.19.5		84	3.2	odd	2
756.2.n.b.19.33		84	12.11	even	2
756.2.n.b.199.5		84	252.59	odd	6
756.2.n.b.199.33		84	63.59	even	6
756.2.bj.b.451.23		84	21.17	even	6
756.2.bj.b.451.24		84	84.59	odd	6
756.2.bj.b.523.23		84	9.5	odd	6
756.2.bj.b.523.24		84	36.23	even	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30137 - 0.553558i) q^{2} +(1.49040 - 0.882451i) q^{3} +(1.38715 - 1.44077i) q^{4} +4.05112i q^{5} +(1.45107 - 1.97342i) q^{6} +(-2.21649 - 1.44470i) q^{7} +(1.00765 - 2.64285i) q^{8} +(1.44256 - 2.63040i) q^{9} +(2.24253 + 5.27202i) q^{10} +0.543883i q^{11} +(0.795990 - 3.37141i) q^{12} +(-1.01063 + 0.583488i) q^{13} +(-3.68421 - 0.653137i) q^{14} +(3.57492 + 6.03778i) q^{15} +(-0.151642 - 3.99712i) q^{16} +(-5.05773 + 2.92008i) q^{17} +(0.421231 - 4.22168i) q^{18} +(1.16501 - 2.01785i) q^{19} +(5.83674 + 5.61950i) q^{20} +(-4.57833 - 0.197227i) q^{21} +(0.301071 + 0.707796i) q^{22} +1.61483i q^{23} +(-0.830389 - 4.82809i) q^{24} -11.4116 q^{25} +(-0.992214 + 1.31878i) q^{26} +(-0.171215 - 5.19333i) q^{27} +(-5.15609 + 1.18945i) q^{28} +(2.40001 - 4.15694i) q^{29} +(7.99456 + 5.87848i) q^{30} +(-2.24515 + 3.88871i) q^{31} +(-2.40998 - 5.11781i) q^{32} +(0.479950 + 0.810602i) q^{33} +(-4.96557 + 6.59987i) q^{34} +(5.85265 - 8.97929i) q^{35} +(-1.78876 - 5.72716i) q^{36} +(-1.48498 + 2.57206i) q^{37} +(0.399112 - 3.27088i) q^{38} +(-0.991340 + 1.76146i) q^{39} +(10.7065 + 4.08210i) q^{40} +(3.89836 - 2.25072i) q^{41} +(-6.06729 + 2.27770i) q^{42} +(-2.89521 - 1.67155i) q^{43} +(0.783611 + 0.754447i) q^{44} +(10.6561 + 5.84399i) q^{45} +(0.893904 + 2.10150i) q^{46} +(4.29074 + 7.43179i) q^{47} +(-3.75327 - 5.82348i) q^{48} +(2.82569 + 6.40433i) q^{49} +(-14.8507 + 6.31697i) q^{50} +(-4.96120 + 8.81528i) q^{51} +(-0.561221 + 2.26547i) q^{52} +(5.84343 + 10.1211i) q^{53} +(-3.09762 - 6.66369i) q^{54} -2.20334 q^{55} +(-6.05157 + 4.40211i) q^{56} +(-0.0443331 - 4.03546i) q^{57} +(0.822204 - 6.73827i) q^{58} +(6.43904 - 11.1527i) q^{59} +(13.6580 + 3.22465i) q^{60} +(1.80408 - 1.04158i) q^{61} +(-0.769151 + 6.30348i) q^{62} +(-6.99757 + 3.74621i) q^{63} +(-5.96929 - 5.32612i) q^{64} +(-2.36378 - 4.09419i) q^{65} +(1.07331 + 0.789215i) q^{66} +(-6.14549 - 3.54810i) q^{67} +(-2.80865 + 11.3376i) q^{68} +(1.42501 + 2.40674i) q^{69} +(2.64594 - 14.9252i) q^{70} -5.17264i q^{71} +(-5.49816 - 6.46299i) q^{72} +(5.58686 - 3.22558i) q^{73} +(-0.508730 + 4.16923i) q^{74} +(-17.0078 + 10.0702i) q^{75} +(-1.29122 - 4.47756i) q^{76} +(0.785748 - 1.20551i) q^{77} +(-0.315035 + 2.84108i) q^{78} +(3.48731 - 2.01340i) q^{79} +(16.1928 - 0.614320i) q^{80} +(-4.83804 - 7.58903i) q^{81} +(3.82732 - 5.08700i) q^{82} +(-2.76985 + 4.79753i) q^{83} +(-6.63498 + 6.32274i) q^{84} +(-11.8296 - 20.4895i) q^{85} +(-4.69305 - 0.572646i) q^{86} +(-0.0913299 - 8.31337i) q^{87} +(1.43740 + 0.548043i) q^{88} +(-7.63381 - 4.40738i) q^{89} +(17.1025 + 1.70646i) q^{90} +(3.08302 + 0.166760i) q^{91} +(2.32661 + 2.24001i) q^{92} +(0.0854368 + 7.77695i) q^{93} +(9.69779 + 7.29636i) q^{94} +(8.17456 + 4.71958i) q^{95} +(-8.10804 - 5.50087i) q^{96} +(13.8033 + 7.96935i) q^{97} +(7.22244 + 6.77025i) q^{98} +(1.43063 + 0.784585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - q^{2} + q^{4} - 16 q^{8} - 14 q^{9} - 18 q^{10} + 9 q^{12} - 18 q^{13} - 25 q^{14} - 7 q^{16} + 6 q^{17} - 13 q^{18} + 24 q^{20} + 4 q^{21} + 6 q^{22} + 6 q^{24} - 32 q^{25} - 30 q^{26} - 4 q^{28}+ \cdots + 21 q^{98}+O(q^{100}) \) 84 * q - q^2 + q^4 - 16 * q^8 - 14 * q^9 - 18 * q^10 + 9 * q^12 - 18 * q^13 - 25 * q^14 - 7 * q^16 + 6 * q^17 - 13 * q^18 + 24 * q^20 + 4 * q^21 + 6 * q^22 + 6 * q^24 - 32 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 14 * q^30 + 9 * q^32 - 6 * q^33 + 24 * q^34 - 38 * q^36 + 2 * q^37 - 6 * q^41 + 7 * q^42 - 13 * q^44 - 18 * q^45 + 10 * q^46 - 9 * q^48 + 2 * q^49 - 17 * q^50 - 2 * q^53 - 42 * q^54 - 32 * q^56 + 6 * q^57 + 26 * q^58 + 8 * q^60 - 24 * q^61 - 8 * q^64 + 50 * q^65 + 27 * q^66 + 18 * q^69 - 4 * q^70 - 7 * q^72 + 30 * q^73 + 46 * q^74 + 46 * q^77 + 15 * q^78 + 3 * q^80 - 26 * q^81 - 18 * q^82 + 29 * q^84 - 50 * q^85 + 18 * q^86 - 2 * q^88 - 102 * q^89 + 39 * q^90 + 28 * q^92 - 24 * q^93 + 3 * q^94 - 30 * q^96 - 6 * q^97 + 21 * q^98

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