LMFDB - Embedded newform 62.6.g.a.41.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,6,Mod(7,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.7"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,-56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$9.94379682840$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			41.1
Character	$\chi$	$=$	62.41
Dual form			62.6.g.a.59.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.23607 - 2.35114i) q^{2} +(-2.85659 - 27.1786i) q^{3} +(4.94427 + 15.2169i) q^{4} +(38.2269 + 66.2110i) q^{5} +(-54.6567 + 94.6681i) q^{6} +(-128.247 - 27.2597i) q^{7} +(19.7771 - 60.8676i) q^{8} +(-492.827 + 104.754i) q^{9} +(31.9664 - 304.140i) q^{10} +(-495.944 + 550.801i) q^{11} +(399.451 - 177.847i) q^{12} +(760.197 + 338.462i) q^{13} +(350.924 + 389.741i) q^{14} +(1690.32 - 1228.09i) q^{15} +(-207.108 + 150.473i) q^{16} +(83.9872 + 93.2773i) q^{17} +(1841.11 + 819.717i) q^{18} +(-176.907 + 78.7642i) q^{19} +(-818.522 + 909.061i) q^{20} +(-374.533 + 3563.44i) q^{21} +(2899.92 - 616.397i) q^{22} +(-110.851 + 341.164i) q^{23} +(-1710.79 - 363.640i) q^{24} +(-1360.10 + 2355.76i) q^{25} +(-1664.28 - 2882.62i) q^{26} +(2202.75 + 6779.37i) q^{27} +(-219.279 - 2086.30i) q^{28} +(-2394.92 - 1740.01i) q^{29} -8357.42 q^{30} +(696.395 - 5305.11i) q^{31} +1024.00 q^{32} +(16386.7 + 11905.7i) q^{33} +(-52.4804 - 499.317i) q^{34} +(-3097.59 - 9533.40i) q^{35} +(-4030.70 - 6981.38i) q^{36} +(-7728.21 + 13385.7i) q^{37} +(757.669 + 161.048i) q^{38} +(7027.35 - 21628.0i) q^{39} +(4786.12 - 1017.32i) q^{40} +(-1651.10 + 15709.2i) q^{41} +(9590.17 - 10651.0i) q^{42} +(-5338.05 + 2376.65i) q^{43} +(-10833.6 - 4823.42i) q^{44} +(-25775.1 - 28626.2i) q^{45} +(1160.84 - 843.403i) q^{46} +(3049.69 - 2215.73i) q^{47} +(4681.27 + 5199.08i) q^{48} +(350.196 + 155.917i) q^{49} +(9940.08 - 4425.61i) q^{50} +(2295.23 - 2549.11i) q^{51} +(-1391.72 + 13241.3i) q^{52} +(-901.444 + 191.608i) q^{53} +(8811.00 - 27117.5i) q^{54} +(-55427.5 - 11781.5i) q^{55} +(-4195.58 + 7266.96i) q^{56} +(2646.05 + 4583.10i) q^{57} +(3659.11 + 11261.6i) q^{58} +(4488.06 + 42701.0i) q^{59} +(27045.2 + 19649.5i) q^{60} -22791.1 q^{61} +(-14726.6 + 15530.4i) q^{62} +66059.1 q^{63} +(-3313.73 - 2407.57i) q^{64} +(6650.13 + 63271.8i) q^{65} +(-25036.7 - 77055.0i) q^{66} +(-34298.0 - 59405.8i) q^{67} +(-1004.14 + 1739.21i) q^{68} +(9589.01 + 2038.21i) q^{69} +(-12390.4 + 38133.6i) q^{70} +(16436.6 - 3493.71i) q^{71} +(-3370.58 + 32069.0i) q^{72} +(11875.1 - 13188.7i) q^{73} +(56480.6 - 25146.8i) q^{74} +(67911.4 + 30236.1i) q^{75} +(-2073.22 - 2302.55i) q^{76} +(78617.9 - 57119.2i) q^{77} +(-73591.4 + 53467.3i) q^{78} +(-651.100 - 723.120i) q^{79} +(-17880.1 - 7960.73i) q^{80} +(66113.9 - 29435.8i) q^{81} +(42277.6 - 46954.0i) q^{82} +(-8443.81 + 80337.5i) q^{83} +(-56076.3 + 11919.4i) q^{84} +(-2965.41 + 9126.58i) q^{85} +(22862.1 + 4859.50i) q^{86} +(-40449.8 + 70061.1i) q^{87} +(23717.6 + 41080.2i) q^{88} +(-2411.45 - 7421.67i) q^{89} +(16105.9 + 153237. i) q^{90} +(-88266.5 - 64129.4i) q^{91} -5739.53 q^{92} +(-146175. - 3772.55i) q^{93} -15078.5 q^{94} +(-11977.7 - 8702.29i) q^{95} +(-2925.15 - 27830.9i) q^{96} +(19935.9 + 61356.5i) q^{97} +(-766.675 - 1327.92i) q^{98} +(186716. - 323402. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 56 q^{2} + 11 q^{3} - 224 q^{4} - 33 q^{5} - 136 q^{6} + 104 q^{7} - 896 q^{8} + 524 q^{9} + 448 q^{10} - 795 q^{11} + 176 q^{12} + 764 q^{13} - 1384 q^{14} - 3208 q^{15} - 3584 q^{16} + 2440 q^{17}+ \cdots - 168255 q^{99}+O(q^{100}) $ 56 * q - 56 * q^2 + 11 * q^3 - 224 * q^4 - 33 * q^5 - 136 * q^6 + 104 * q^7 - 896 * q^8 + 524 * q^9 + 448 * q^10 - 795 * q^11 + 176 * q^12 + 764 * q^13 - 1384 * q^14 - 3208 * q^15 - 3584 * q^16 + 2440 * q^17 + 2716 * q^18 - 2747 * q^19 + 1952 * q^20 + 4909 * q^21 + 7500 * q^22 - 11297 * q^23 + 384 * q^24 - 21385 * q^25 - 14064 * q^26 - 12466 * q^27 + 1424 * q^28 - 11901 * q^29 + 20008 * q^30 - 4745 * q^31 + 57344 * q^32 + 2812 * q^33 + 7160 * q^34 + 17912 * q^35 - 38496 * q^36 - 54498 * q^37 + 9552 * q^38 - 38158 * q^39 + 7808 * q^40 + 56747 * q^41 + 61396 * q^42 + 69670 * q^43 - 22320 * q^44 + 54688 * q^45 + 22412 * q^46 - 63503 * q^47 + 1536 * q^48 + 9721 * q^49 + 16580 * q^50 + 87134 * q^51 + 12224 * q^52 + 48127 * q^53 - 49864 * q^54 - 150047 * q^55 - 6464 * q^56 - 142312 * q^57 - 36764 * q^58 - 105890 * q^59 - 51328 * q^60 + 383664 * q^61 - 10700 * q^62 - 236690 * q^63 - 57344 * q^64 + 284638 * q^65 + 46348 * q^66 - 59674 * q^67 - 75120 * q^68 + 213337 * q^69 + 71648 * q^70 - 186679 * q^71 + 43456 * q^72 - 132007 * q^73 - 29932 * q^74 + 186494 * q^75 + 97728 * q^76 + 208527 * q^77 + 71688 * q^78 - 229841 * q^79 - 82688 * q^80 - 503164 * q^81 - 234012 * q^82 - 634514 * q^83 - 165056 * q^84 + 129149 * q^85 + 60740 * q^86 + 297951 * q^87 - 33600 * q^88 + 78674 * q^89 + 290652 * q^90 + 127680 * q^91 + 182208 * q^92 + 427164 * q^93 + 143528 * q^94 + 293666 * q^95 + 11264 * q^96 - 94321 * q^97 - 291156 * q^98 - 168255 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

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 $

$2$	−3.23607	−	2.35114i	−0.572061	−	0.415627i
$2$	−3.23607	−	2.35114i	−0.572061	−	0.415627i
$3$	−2.85659	−	27.1786i	−0.183250	−	1.74351i	−0.570287	−	0.821445i	$-0.693168\pi$
$3$	−2.85659	−	27.1786i	−0.183250	−	1.74351i	0.387037	−	0.922064i	$-0.373498\pi$
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	38.2269	+	66.2110i	0.683824	+	1.18442i	0.973805	+	0.227386i	$0.0730178\pi$
$5$	38.2269	+	66.2110i	0.683824	+	1.18442i	−0.289981	+	0.957032i	$0.593649\pi$
$6$	−54.6567	+	94.6681i	−0.619819	+	1.07356i
$7$	−128.247	−	27.2597i	−0.989240	−	0.210269i	−0.315249	−	0.949009i	$-0.602088\pi$
$7$	−128.247	−	27.2597i	−0.989240	−	0.210269i	−0.673991	+	0.738740i	$0.735421\pi$
$8$	19.7771	−	60.8676i	0.109254	−	0.336249i
$9$	−492.827	+	104.754i	−2.02810	+	0.431085i
$10$	31.9664	−	304.140i	0.101087	−	0.961776i
$11$	−495.944	+	550.801i	−1.23581	+	1.37250i	−0.332731	+	0.943022i	$0.607970\pi$
$11$	−495.944	+	550.801i	−1.23581	+	1.37250i	−0.903076	+	0.429481i	$0.858697\pi$
$12$	399.451	−	177.847i	0.800774	−	0.356528i
$13$	760.197	+	338.462i	1.24758	+	0.555458i	0.920945	−	0.389693i	$-0.127419\pi$
$13$	760.197	+	338.462i	1.24758	+	0.555458i	0.326634	+	0.945151i	$0.394086\pi$
$14$	350.924	+	389.741i	0.478512	+	0.531442i
$15$	1690.32	−	1228.09i	1.93973	−	1.40930i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	83.9872	+	93.2773i	0.0704841	+	0.0782805i	0.777355	−	0.629062i	$-0.216561\pi$
$17$	83.9872	+	93.2773i	0.0704841	+	0.0782805i	−0.706871	+	0.707342i	$0.749894\pi$
$18$	1841.11	+	819.717i	1.33937	+	0.596324i
$19$	−176.907	+	78.7642i	−0.112425	+	0.0500547i	−0.462178	−	0.886787i	$-0.652932\pi$
$19$	−176.907	+	78.7642i	−0.112425	+	0.0500547i	0.349754	+	0.936842i	$0.386265\pi$
$20$	−818.522	+	909.061i	−0.457568	+	0.508180i
$21$	−374.533	+	3563.44i	−0.185328	+	1.76328i
$22$	2899.92	−	616.397i	1.27741	−	0.271521i
$23$	−110.851	+	341.164i	−0.0436937	+	0.134476i	−0.970524	−	0.241006i	$-0.922523\pi$
$23$	−110.851	+	341.164i	−0.0436937	+	0.134476i	0.926830	+	0.375482i	$0.122523\pi$
$24$	−1710.79	−	363.640i	−0.606275	−	0.128868i
$25$	−1360.10	+	2355.76i	−0.435231	+	0.753842i
$26$	−1664.28	−	2882.62i	−0.482828	−	0.836283i
$27$	2202.75	+	6779.37i	0.581508	+	1.78970i
$28$	−219.279	−	2086.30i	−0.0528569	−	0.502900i
$29$	−2394.92	−	1740.01i	−0.528805	−	0.384200i	0.291105	−	0.956691i	$-0.405977\pi$
$29$	−2394.92	−	1740.01i	−0.528805	−	0.384200i	−0.819911	+	0.572491i	$0.805977\pi$
$30$	−8357.42			−1.69539
$31$	696.395	−	5305.11i	0.130152	−	0.991494i
$31$	696.395	−	5305.11i	0.130152	−	0.991494i
$32$	1024.00			0.176777
$33$	16386.7	+	11905.7i	2.61943	+	1.90313i
$34$	−52.4804	−	499.317i	−0.00778574	−	0.0740763i
$35$	−3097.59	−	9533.40i	−0.427419	−	1.31546i
$36$	−4030.70	−	6981.38i	−0.518351	−	0.897811i
$37$	−7728.21	+	13385.7i	−0.928057	+	1.60744i	−0.141489	+	0.989940i	$0.545189\pi$
$37$	−7728.21	+	13385.7i	−0.928057	+	1.60744i	−0.786569	+	0.617503i	$0.788144\pi$
$38$	757.669	+	161.048i	0.0851179	+	0.0180924i
$39$	7027.35	−	21628.0i	0.739827	−	2.27695i
$40$	4786.12	−	1017.32i	0.472970	−	0.100533i
$41$	−1651.10	+	15709.2i	−0.153396	+	1.45947i	0.598997	+	0.800751i	$0.295566\pi$
$41$	−1651.10	+	15709.2i	−0.153396	+	1.45947i	−0.752393	+	0.658715i	$0.771100\pi$
$42$	9590.17	−	10651.0i	0.838886	−	0.931677i
$43$	−5338.05	+	2376.65i	−0.440262	+	0.196017i	−0.614883	−	0.788618i	$-0.710797\pi$
$43$	−5338.05	+	2376.65i	−0.440262	+	0.196017i	0.174621	+	0.984636i	$0.444130\pi$
$44$	−10833.6	−	4823.42i	−0.843606	−	0.375598i
$45$	−25775.1	−	28626.2i	−1.89745	−	2.10733i
$46$	1160.84	−	843.403i	0.0808871	−	0.0587679i
$47$	3049.69	−	2215.73i	0.201377	−	0.146309i	−0.482526	−	0.875881i	$-0.660281\pi$
$47$	3049.69	−	2215.73i	0.201377	−	0.146309i	0.683904	+	0.729572i	$0.260281\pi$
$48$	4681.27	+	5199.08i	0.293265	+	0.325704i
$49$	350.196	+	155.917i	0.0208363	+	0.00927693i
$50$	9940.08	−	4425.61i	0.562296	−	0.250350i
$51$	2295.23	−	2549.11i	0.123567	−	0.137235i
$52$	−1391.72	+	13241.3i	−0.0713744	+	0.679082i
$53$	−901.444	+	191.608i	−0.0440808	+	0.00936965i	−0.229899	−	0.973214i	$-0.573840\pi$
$53$	−901.444	+	191.608i	−0.0440808	+	0.00936965i	0.185819	+	0.982584i	$0.440506\pi$
$54$	8811.00	−	27117.5i	0.411189	−	1.26551i
$55$	−55427.5	−	11781.5i	−2.47069	−	0.525162i
$56$	−4195.58	+	7266.96i	−0.178781	+	0.309658i
$57$	2646.05	+	4583.10i	0.107873	+	0.186841i
$58$	3659.11	+	11261.6i	0.142825	+	0.439572i
$59$	4488.06	+	42701.0i	0.167853	+	1.59701i	0.676768	+	0.736196i	$0.263380\pi$
$59$	4488.06	+	42701.0i	0.167853	+	1.59701i	−0.508916	+	0.860816i	$0.669954\pi$
$60$	27045.2	+	19649.5i	0.969867	+	0.704649i
$61$	−22791.1			−0.784223			−0.392112	−	0.919918i	$-0.628255\pi$
$61$	−22791.1			−0.784223			−0.392112	+	0.919918i	$0.628255\pi$
$62$	−14726.6	+	15530.4i	−0.486547	+	0.513101i
$63$	66059.1			2.09692
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	6650.13	+	63271.8i	0.195230	+	1.85749i
$66$	−25036.7	−	77055.0i	−0.707485	−	2.17741i
$67$	−34298.0	−	59405.8i	−0.933429	−	1.61675i	−0.777411	−	0.628993i	$-0.783467\pi$
$67$	−34298.0	−	59405.8i	−0.933429	−	1.61675i	−0.156018	−	0.987754i	$-0.549866\pi$
$68$	−1004.14	+	1739.21i	−0.0263342	+	0.0456122i
$69$	9589.01	+	2038.21i	0.242466	+	0.0515378i
$70$	−12390.4	+	38133.6i	−0.302231	+	0.930171i
$71$	16436.6	−	3493.71i	0.386960	−	0.0822509i	−0.0103237	−	0.999947i	$-0.503286\pi$
$71$	16436.6	−	3493.71i	0.386960	−	0.0822509i	0.397284	+	0.917696i	$0.369953\pi$
$72$	−3370.58	+	32069.0i	−0.0766256	+	0.729044i
$73$	11875.1	−	13188.7i	0.260814	−	0.289663i	−0.598488	−	0.801132i	$-0.704232\pi$
$73$	11875.1	−	13188.7i	0.260814	−	0.289663i	0.859302	+	0.511468i	$0.170898\pi$
$74$	56480.6	−	25146.8i	1.19900	−	0.533830i
$75$	67911.4	+	30236.1i	1.39409	+	0.620687i
$76$	−2073.22	−	2302.55i	−0.0411730	−	0.0457272i
$77$	78617.9	−	57119.2i	1.51110	−	1.09788i
$78$	−73591.4	+	53467.3i	−1.36959	+	0.995065i
$79$	−651.100	−	723.120i	−0.0117376	−	0.0130360i	0.737247	−	0.675623i	$-0.236125\pi$
$79$	−651.100	−	723.120i	−0.0117376	−	0.0130360i	−0.748985	+	0.662587i	$0.769459\pi$
$80$	−17880.1	−	7960.73i	−0.312352	−	0.139068i
$81$	66113.9	−	29435.8i	1.11965	−	0.498498i
$82$	42277.6	−	46954.0i	0.694345	−	0.771149i
$83$	−8443.81	+	80337.5i	−0.134537	+	1.28004i	0.693947	+	0.720026i	$0.255870\pi$
$83$	−8443.81	+	80337.5i	−0.134537	+	1.28004i	−0.828484	+	0.560012i	$0.810797\pi$
$84$	−56076.3	+	11919.4i	−0.867124	+	0.184313i
$85$	−2965.41	+	9126.58i	−0.0445181	+	0.137013i
$86$	22862.1	+	4859.50i	0.333327	+	0.0708509i
$87$	−40449.8	+	70061.1i	−0.572952	+	0.992382i
$88$	23717.6	+	41080.2i	0.326486	+	0.565491i
$89$	−2411.45	−	7421.67i	−0.0322703	−	0.0993177i	0.933624	−	0.358254i	$-0.116628\pi$
$89$	−2411.45	−	7421.67i	−0.0322703	−	0.0993177i	−0.965894	+	0.258937i	$0.916628\pi$
$90$	16105.9	+	153237.i	0.209594	+	1.99415i
$91$	−88266.5	−	64129.4i	−1.11736	−	0.811809i
$92$	−5739.53			−0.0706980
$93$	−146175.	−	3772.55i	−1.75253	−	0.0452302i
$94$	−15078.5			−0.176010
$95$	−11977.7	−	8702.29i	−0.136164	−	0.0989292i
$96$	−2925.15	−	27830.9i	−0.0323944	−	0.308212i
$97$	19935.9	+	61356.5i	0.215133	+	0.662111i	0.999144	+	0.0413645i	$0.0131705\pi$
$97$	19935.9	+	61356.5i	0.215133	+	0.662111i	−0.784011	+	0.620747i	$0.786830\pi$
$98$	−766.675	−	1327.92i	−0.00806392	−	0.0139671i
$99$	186716.	−	323402.i	1.91467	−	3.31631i
$100$	−42572.0	−	9048.96i	−0.425720	−	0.0904896i
$101$	19215.7	−	59139.8i	0.187436	−	0.576868i	−0.812546	−	0.582897i	$-0.801919\pi$
$101$	19215.7	−	59139.8i	0.187436	−	0.576868i	0.999982	+	0.00602882i	$0.00191905\pi$
$102$	−13420.8	+	2852.69i	−0.127726	+	0.0271490i
$103$	−17857.1	+	169899.i	−0.165851	+	1.57797i	0.522533	+	0.852619i	$0.324987\pi$
$103$	−17857.1	+	169899.i	−0.165851	+	1.57797i	−0.688384	+	0.725346i	$0.741680\pi$
$104$	35635.8	−	39577.6i	0.323075	−	0.358811i
$105$	−250256.	+	111421.i	−2.21519	+	0.986267i
$106$	3367.63	+	1499.37i	0.0291112	+	0.0129611i
$107$	−93352.4	−	103678.i	−0.788254	−	0.875445i	0.206426	−	0.978462i	$-0.433817\pi$
$107$	−93352.4	−	103678.i	−0.788254	−	0.875445i	−0.994680	+	0.103018i	$0.967150\pi$
$108$	−92270.0	+	67038.1i	−0.761204	+	0.553047i
$109$	−110299.	+	80137.3i	−0.889216	+	0.646053i	−0.935673	−	0.352867i	$-0.885207\pi$
$109$	−110299.	+	80137.3i	−0.889216	+	0.646053i	0.0464577	+	0.998920i	$0.485207\pi$
$110$	151667.	+	168444.i	1.19512	+	1.32731i
$111$	385880.	+	171805.i	2.97266	+	1.32351i
$112$	30662.8	−	13652.0i	0.230976	−	0.102837i
$113$	126162.	−	140117.i	0.929463	−	1.03227i	−0.0699340	−	0.997552i	$-0.522279\pi$
$113$	126162.	−	140117.i	0.929463	−	1.03227i	0.999397	−	0.0347216i	$-0.0110544\pi$
$114$	2212.70	−	21052.5i	0.0159463	−	0.151719i
$115$	−26826.3	+	5702.10i	−0.189154	+	0.0402059i
$116$	14636.4	−	45046.3i	0.100993	−	0.310824i
$117$	−410101.	−	87169.7i	−2.76966	−	0.588709i
$118$	85872.5	−	148735.i	0.567739	−	0.983353i
$119$	−8228.39	−	14252.0i	−0.0532656	−	0.0922588i
$120$	−41321.4	−	127174.i	−0.261952	−	0.806205i
$121$	−40587.5	−	386164.i	−0.252016	−	2.39777i
$122$	73753.4	+	53585.0i	0.448624	+	0.325944i
$123$	431671.			2.57270
$124$	84170.5	−	15632.9i	0.491593	−	0.0913032i
$125$	30949.1			0.177163
$126$	−213772.	−	155314.i	−1.19957	−	0.871535i
$127$	−25349.7	−	241186.i	−0.139464	−	1.32691i	−0.810609	−	0.585588i	$-0.800864\pi$
$127$	−25349.7	−	241186.i	−0.139464	−	1.32691i	0.671145	−	0.741327i	$-0.265803\pi$
$128$	5062.93	+	15582.1i	0.0273135	+	0.0840623i
$129$	79842.8	+	138292.i	0.422436	+	0.731681i
$130$	127241.	−	220387.i	0.660339	−	1.14374i
$131$	183322.	+	38966.3i	0.933331	+	0.198386i	0.649390	−	0.760456i	$-0.275024\pi$
$131$	183322.	+	38966.3i	0.933331	+	0.198386i	0.283942	+	0.958842i	$0.408358\pi$
$132$	−100147.	+	308220.i	−0.500267	+	1.53966i
$133$	24834.9	−	5278.82i	0.121740	−	0.0258766i
$134$	−28680.9	+	272881.i	−0.137985	+	1.31284i
$135$	−364664.	+	405001.i	−1.72210	+	1.91259i
$136$	7338.59	−	3267.35i	0.0340224	−	0.0151478i
$137$	−113710.	−	50626.9i	−0.517603	−	0.230452i	0.131272	−	0.991346i	$-0.458094\pi$
$137$	−113710.	−	50626.9i	−0.517603	−	0.230452i	−0.648876	+	0.760894i	$0.724760\pi$
$138$	−26238.6	−	29140.9i	−0.117285	−	0.130258i
$139$	39609.7	−	28778.2i	0.173886	−	0.126336i	−0.497438	−	0.867499i	$-0.665726\pi$
$139$	39609.7	−	28778.2i	0.173886	−	0.126336i	0.671324	+	0.741164i	$0.265726\pi$
$140$	129754.	−	94271.5i	0.559499	−	0.406500i
$141$	−68932.2	−	76556.9i	−0.291994	−	0.324292i
$142$	−61404.2	−	27338.9i	−0.255551	−	0.113778i
$143$	−563440.	+	250860.i	−2.30413	+	1.02587i
$144$	86306.1	−	95852.6i	0.346845	−	0.385210i
$145$	23657.4	−	225085.i	0.0934431	−	0.889052i
$146$	−69437.1	+	14759.3i	−0.269594	+	0.0573039i
$147$	3237.25	−	9963.24i	0.0123562	−	0.0380283i
$148$	−241899.	−	51417.2i	−0.907777	−	0.192954i
$149$	−66512.7	+	115203.i	−0.245436	+	0.425108i	−0.962254	−	0.272152i	$-0.912265\pi$
$149$	−66512.7	+	115203.i	−0.245436	+	0.425108i	0.716818	+	0.697261i	$0.245598\pi$
$150$	−148677.	−	257515.i	−0.539529	−	0.934491i
$151$	−72703.7	−	223759.i	−0.259486	−	0.798616i	−0.992913	−	0.118847i	$-0.962080\pi$
$151$	−72703.7	−	223759.i	−0.259486	−	0.798616i	0.733426	−	0.679769i	$-0.237920\pi$
$152$	1295.48	+	12325.6i	0.00454800	+	0.0432714i
$153$	−51162.4	−	37171.6i	−0.176694	−	0.128376i
$154$	−388708.			−1.32075
$155$	377878.	−	156689.i	1.26334	−	0.523853i
$156$	363856.			1.19707
$157$	253652.	+	184289.i	0.821275	+	0.596692i	0.917078	−	0.398709i	$-0.130542\pi$
$157$	253652.	+	184289.i	0.821275	+	0.596692i	−0.0958021	+	0.995400i	$0.530542\pi$
$158$	406.848	+	3870.90i	0.00129655	+	0.0123358i
$159$	7782.69	+	23952.7i	0.0244139	+	0.0751382i
$160$	39144.4	+	67800.0i	0.120884	+	0.209378i
$161$	23516.3	−	40731.4i	0.0714997	−	0.123841i
$162$	−283157.	−	60186.9i	−0.847695	−	0.180183i
$163$	−148166.	+	456007.i	−0.436796	+	1.34432i	0.454439	+	0.890778i	$0.349840\pi$
$163$	−148166.	+	456007.i	−0.436796	+	1.34432i	−0.891235	+	0.453542i	$0.850160\pi$
$164$	−247209.	+	52545.8i	−0.717718	+	0.152556i
$165$	−161871.	+	1.54010e6i	−0.462870	+	4.40391i
$166$	216209.	−	240125.i	0.608982	−	0.676343i
$167$	216805.	−	96527.6i	0.601558	−	0.267831i	−0.0832802	−	0.996526i	$-0.526540\pi$
$167$	216805.	−	96527.6i	0.601558	−	0.267831i	0.684838	+	0.728695i	$0.259873\pi$
$168$	209491.	+	93271.4i	0.572654	+	0.254962i
$169$	214900.	+	238671.i	0.578789	+	0.642810i
$170$	31054.1	−	22562.2i	0.0824133	−	0.0598767i
$171$	78933.9	−	57348.8i	0.206430	−	0.149980i
$172$	−62558.1	−	69477.8i	−0.161236	−	0.179071i
$173$	569173.	+	253412.i	1.44587	+	0.643742i	0.971598	−	0.236637i	$-0.0760452\pi$
$173$	569173.	+	253412.i	1.44587	+	0.643742i	0.474271	+	0.880379i	$0.342712\pi$
$174$	295622.	−	131619.i	0.740224	−	0.329569i
$175$	238645.	−	265042.i	0.589057	−	0.654214i
$176$	19833.3	−	188702.i	0.0482630	−	0.459192i
$177$	1.14773e6	−	243958.i	2.75365	−	0.585306i
$178$	−9645.79	+	29686.7i	−0.0228185	+	0.0702282i
$179$	236428.	+	50254.4i	0.551527	+	0.117231i	0.475242	−	0.879855i	$-0.342361\pi$
$179$	236428.	+	50254.4i	0.551527	+	0.117231i	0.0762854	+	0.997086i	$0.475694\pi$
$180$	308163.	−	533753.i	0.708922	−	1.22789i
$181$	−311712.	−	539901.i	−0.707225	−	1.22495i	−0.965883	−	0.258980i	$-0.916614\pi$
$181$	−311712.	−	539901.i	−0.707225	−	1.22495i	0.258658	−	0.965969i	$-0.416720\pi$
$182$	134859.	+	415054.i	0.301788	+	0.928809i
$183$	65104.7	+	619429.i	0.143709	+	1.36730i
$184$	18573.5	+	13494.4i	0.0404436	+	0.0293840i
$185$	−1.18170e6			−2.53851
$186$	464162.	+	355886.i	0.983756	+	0.754273i
$187$	−93030.2			−0.194545
$188$	48795.0	+	35451.7i	0.100689	+	0.0731546i
$189$	−97692.2	−	929479.i	−0.198932	−	1.89271i
$190$	18300.3	+	56322.4i	0.0367767	+	0.113187i
$191$	−118162.	−	204663.i	−0.234366	−	0.405934i	0.724722	−	0.689041i	$-0.241968\pi$
$191$	−118162.	−	204663.i	−0.234366	−	0.405934i	−0.959088	+	0.283107i	$0.908635\pi$
$192$	−55968.4	+	96940.1i	−0.109570	+	0.189780i
$193$	−449927.	−	95634.9i	−0.869458	−	0.184809i	−0.248480	−	0.968637i	$-0.579931\pi$
$193$	−449927.	−	95634.9i	−0.869458	−	0.184809i	−0.620978	+	0.783828i	$0.713264\pi$
$194$	79743.7	−	245426.i	0.152122	−	0.468183i
$195$	1.70064e6	−	361483.i	3.20278	−	0.680771i
$196$	−641.115	+	6099.80i	−0.00119205	+	0.0113416i
$197$	−120853.	+	134221.i	−0.221866	+	0.246407i	−0.843794	−	0.536667i	$-0.819683\pi$
$197$	−120853.	+	134221.i	−0.221866	+	0.246407i	0.621928	+	0.783075i	$0.286350\pi$
$198$	−1.36459e6	+	607554.i	−2.47365	+	1.10134i
$199$	−123919.	−	55172.2i	−0.221822	−	0.0987615i	0.292817	−	0.956169i	$-0.405407\pi$
$199$	−123919.	−	55172.2i	−0.221822	−	0.0987615i	−0.514639	+	0.857407i	$0.672074\pi$
$200$	116490.	+	129376.i	0.205928	+	0.228706i
$201$	−1.51659e6	+	1.10187e6i	−2.64776	+	1.92371i
$202$	−201229.	+	146202.i	−0.346987	+	0.252101i
$203$	259709.	+	288436.i	0.442330	+	0.491257i
$204$	50137.8	+	22322.8i	0.0843510	+	0.0375555i
$205$	−1.10324e6	+	491193.i	−1.83351	+	0.816333i
$206$	457243.	−	507820.i	0.750722	−	0.833761i
$207$	18892.2	−	179747.i	0.0306447	−	0.291565i
$208$	−208373.	+	44291.0i	−0.333951	+	0.0709834i
$209$	44352.6	−	136503.i	0.0702350	−	0.216161i
$210$	1.07181e6	+	227821.i	1.67715	+	0.356488i
$211$	−129638.	+	224539.i	−0.200459	+	0.347205i	−0.948676	−	0.316249i	$-0.897577\pi$
$211$	−129638.	+	224539.i	−0.200459	+	0.347205i	0.748217	+	0.663454i	$0.230910\pi$
$212$	−7372.66	−	12769.8i	−0.0112664	−	0.0195140i
$213$	−141907.	−	436744.i	−0.214316	−	0.659596i
$214$	58332.3	+	554995.i	0.0870713	+	0.828428i
$215$	−361418.	−	262585.i	−0.533229	−	0.387413i
$216$	456208.			0.665317
$217$	−233926.	+	661380.i	−0.337233	+	0.953458i
$218$	545351.			0.777203
$219$	−392372.	−	285075.i	−0.552825	−	0.401651i
$220$	−94771.0	−	901686.i	−0.132014	−	1.25603i
$221$	32276.1	+	99335.6i	0.0444529	+	0.136812i
$222$	−844797.	−	1.46323e6i	−1.15046	−	1.99265i
$223$	262654.	−	454930.i	0.353689	−	0.612608i	−0.633203	−	0.773985i	$-0.718260\pi$
$223$	262654.	−	454930.i	0.353689	−	0.612608i	0.986893	+	0.161378i	$0.0515937\pi$
$224$	−131325.	−	27913.9i	−0.174875	−	0.0371707i
$225$	423519.	−	1.30346e6i	0.557720	−	1.71649i
$226$	−737703.	+	156804.i	−0.960750	+	0.204214i
$227$	8498.32	−	80856.2i	0.0109463	−	0.104147i	−0.987684	−	0.156459i	$-0.949992\pi$
$227$	8498.32	−	80856.2i	0.0109463	−	0.104147i	0.998631	+	0.0523114i	$0.0166588\pi$
$228$	−56657.7	+	62924.8i	−0.0721809	+	0.0801650i
$229$	1.12390e6	−	500391.i	1.41624	−	0.630551i	0.451146	−	0.892450i	$-0.351015\pi$
$229$	1.12390e6	−	500391.i	1.41624	−	0.630551i	0.965095	+	0.261898i	$0.0843486\pi$
$230$	100218.	+	44620.0i	0.124918	+	0.0556173i
$231$	−1.77700e6	−	1.97356e6i	−2.19108	−	2.43344i
$232$	−153275.	+	111361.i	−0.186961	+	0.135835i
$233$	139360.	−	101251.i	0.168169	−	0.122182i	−0.500517	−	0.865727i	$-0.666857\pi$
$233$	139360.	−	101251.i	0.168169	−	0.122182i	0.668687	+	0.743544i	$0.266857\pi$
$234$	1.12217e6	+	1.24629e6i	1.33973	+	1.48792i
$235$	263286.	+	117222.i	0.310998	+	0.138465i
$236$	−627587.	+	279420.i	−0.733490	+	0.326571i
$237$	−17793.5	+	19761.7i	−0.0205774	+	0.0228535i
$238$	−6880.80	+	65466.5i	−0.00787402	+	0.0749163i
$239$	40319.6	−	8570.19i	0.0456584	−	0.00970500i	−0.185026	−	0.982734i	$-0.559237\pi$
$239$	40319.6	−	8570.19i	0.0456584	−	0.00970500i	0.230684	+	0.973029i	$0.425904\pi$
$240$	−165286.	+	508697.i	−0.185228	+	0.570073i
$241$	−70126.9	−	14905.9i	−0.0777754	−	0.0165317i	0.168860	−	0.985640i	$-0.445992\pi$
$241$	−70126.9	−	14905.9i	−0.0777754	−	0.0165317i	−0.246635	+	0.969108i	$0.579325\pi$
$242$	−776582.	+	1.34508e6i	−0.852411	+	1.47642i
$243$	−122803.	−	212700.i	−0.133411	−	0.231075i
$244$	−112685.	−	346809.i	−0.121169	−	0.372920i
$245$	3063.48	+	29147.1i	0.00326062	+	0.0310227i
$246$	−1.39692e6	−	1.01492e6i	−1.47174	−	1.06928i
$247$	−161143.			−0.168062
$248$	−309137.	−	147308.i	−0.319169	−	0.152088i
$249$	2.20758e6			2.25641
$250$	−100153.	−	72765.7i	−0.101348	−	0.0736337i
$251$	−51596.9	−	490911.i	−0.0516939	−	0.491834i	−0.989485	−	0.144635i	$-0.953799\pi$
$251$	−51596.9	−	490911.i	−0.0516939	−	0.491834i	0.937791	−	0.347200i	$-0.112867\pi$
$252$	326614.	+	1.00522e6i	0.323992	+	0.997143i
$253$	−132938.	−	230255.i	−0.130571	−	0.226156i
$254$	−485029.	+	840095.i	−0.471719	+	0.817042i
$255$	256519.	+	54524.8i	0.247041	+	0.0525102i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	1.19285e6	−	253547.i	1.12655	−	0.239456i	0.393299	−	0.919411i	$-0.371334\pi$
$257$	1.19285e6	−	253547.i	1.12655	−	0.239456i	0.733255	+	0.679954i	$0.238000\pi$
$258$	66766.7	−	635243.i	0.0624469	−	0.594142i
$259$	1.35601e6	−	1.50600e6i	1.25607	−	1.39500i
$260$	−929920.	+	414027.i	−0.853124	+	0.379835i
$261$	1.36255e6	+	606648.i	1.23809	+	0.551234i
$262$	−501627.	−	557113.i	−0.451468	−	0.501406i
$263$	−514347.	+	373695.i	−0.458529	+	0.333141i	−0.792954	−	0.609282i	$-0.791458\pi$
$263$	−514347.	+	373695.i	−0.458529	+	0.333141i	0.334425	+	0.942422i	$0.391458\pi$
$264$	1.04875e6	−	761962.i	0.926109	−	0.672858i
$265$	−47146.0	−	52360.9i	−0.0412411	−	0.0458028i
$266$	−92778.6	−	41307.7i	−0.0803977	−	0.0357954i
$267$	−194822.	+	86740.5i	−0.167248	+	0.0744635i
$268$	734394.	−	815628.i	0.624586	−	0.693673i
$269$	−128956.	+	1.22694e6i	−0.108658	+	1.03381i	0.795307	+	0.606207i	$0.207310\pi$
$269$	−128956.	+	1.22694e6i	−0.108658	+	1.03381i	−0.903965	+	0.427606i	$0.859357\pi$
$270$	2.13229e6	−	453233.i	1.78007	−	0.378366i
$271$	−637402.	+	1.96172e6i	−0.527218	+	1.62261i	0.232670	+	0.972556i	$0.425254\pi$
$271$	−637402.	+	1.96172e6i	−0.527218	+	1.62261i	−0.759888	+	0.650054i	$0.774746\pi$
$272$	−31430.2	−	6680.69i	−0.0257587	−	0.00547519i
$273$	−1.49081e6	+	2.58215e6i	−1.21064	+	2.09689i
$274$	248942.	+	431180.i	0.200319	+	0.346963i
$275$	−623022.	−	1.91746e6i	−0.496789	−	1.52896i
$276$	16395.5	+	155993.i	0.0129554	+	0.123263i
$277$	−384698.	−	279499.i	−0.301245	−	0.218867i	0.426886	−	0.904306i	$-0.359611\pi$
$277$	−384698.	−	279499.i	−0.301245	−	0.218867i	−0.728131	+	0.685438i	$0.759611\pi$
$278$	−195841.			−0.151982
$279$	212527.	+	2.68745e6i	0.163457	+	2.06695i
$280$	−641537.			−0.489020
$281$	834823.	+	606535.i	0.630709	+	0.458237i	0.856646	−	0.515905i	$-0.172544\pi$
$281$	834823.	+	606535.i	0.630709	+	0.458237i	−0.225937	+	0.974142i	$0.572544\pi$
$282$	43073.0	+	409813.i	0.0322539	+	0.306876i
$283$	−11187.4	−	34431.3i	−0.00830354	−	0.0255557i	0.946819	−	0.321767i	$-0.104277\pi$
$283$	−11187.4	−	34431.3i	−0.00830354	−	0.0255557i	−0.955122	+	0.296211i	$0.904277\pi$
$284$	134430.	+	232840.i	0.0989013	+	0.171302i
$285$	−202301.	+	350395.i	−0.147532	+	0.255533i
$286$	2.41314e6	+	512928.i	1.74448	+	0.370801i
$287$	639976.	−	1.96964e6i	0.458627	−	1.41151i
$288$	−504655.	+	107268.i	−0.358520	+	0.0762058i
$289$	146769.	−	1.39641e6i	0.103369	−	0.983487i
$290$	−605764.	+	672769.i	−0.422969	+	0.469755i
$291$	1.61064e6	−	717101.i	1.11497	−	0.496418i
$292$	259404.	+	115494.i	0.178041	+	0.0792690i
$293$	489939.	+	544132.i	0.333406	+	0.370285i	0.886416	−	0.462890i	$-0.153188\pi$
$293$	489939.	+	544132.i	0.333406	+	0.370285i	−0.553010	+	0.833175i	$0.686521\pi$
$294$	−33901.0	+	24630.5i	−0.0228741	+	0.0166190i
$295$	−2.65571e6	+	1.92949e6i	−1.77675	+	1.29088i
$296$	661912.	+	735127.i	0.439107	+	0.487678i
$297$	−4.82653e6	−	2.14891e6i	−3.17500	−	1.41360i
$298$	486099.	−	216425.i	0.317091	−	0.141178i
$299$	−199739.	+	221833.i	−0.129207	+	0.143499i
$300$	−124328.	+	1.18290e6i	−0.0797561	+	0.758829i
$301$	749375.	−	159285.i	0.476741	−	0.101334i
$302$	−290815.	+	895036.i	−0.183484	+	0.564707i
$303$	−1.66223e6	−	353318.i	−1.04012	−	0.221085i
$304$	24787.1	−	42932.5i	0.0153830	−	0.0266442i
$305$	−871232.	−	1.50902e6i	−0.536271	−	0.928848i
$306$	78169.1	+	240580.i	0.0477234	+	0.146878i
$307$	229656.	+	2.18503e6i	0.139070	+	1.32316i	0.812089	+	0.583534i	$0.198331\pi$
$307$	229656.	+	2.18503e6i	0.139070	+	1.32316i	−0.673019	+	0.739625i	$0.735003\pi$
$308$	1.25789e6	+	913908.i	0.755552	+	0.548941i
$309$	4.66863e6			2.78159
$310$	−1.59124e6	−	381387.i	−0.940438	−	0.225404i
$311$	−2.31072e6			−1.35471			−0.677355	−	0.735656i	$-0.736874\pi$
$311$	−2.31072e6			−1.35471			−0.677355	+	0.735656i	$0.736874\pi$
$312$	−1.17746e6	−	855476.i	−0.684795	−	0.497533i
$313$	−273932.	−	2.60628e6i	−0.158045	−	1.50370i	−0.730019	−	0.683427i	$-0.760489\pi$
$313$	−273932.	−	2.60628e6i	−0.158045	−	1.50370i	0.571973	−	0.820272i	$-0.306178\pi$
$314$	−387545.	−	1.19274e6i	−0.221819	−	0.682688i
$315$	2.52524e6	+	4.37384e6i	1.43392	+	2.48363i
$316$	7784.44	−	13483.0i	0.00438540	−	0.00759574i
$317$	−784115.	−	166669.i	−0.438260	−	0.0931550i	−0.0165027	−	0.999864i	$-0.505253\pi$
$317$	−784115.	−	166669.i	−0.438260	−	0.0931550i	−0.421757	+	0.906709i	$0.638587\pi$
$318$	31130.8	−	95810.6i	0.0172632	−	0.0531307i
$319$	2.14614e6	−	456177.i	1.18082	−	0.250990i
$320$	32733.6	−	311440.i	0.0178698	−	0.170020i
$321$	−2.55117e6	+	2.83336e6i	−1.38190	+	1.53475i
$322$	−171866.	+	76519.5i	−0.0923739	+	0.0411275i
$323$	−22204.9	−	9886.24i	−0.0118425	−	0.00527260i
$324$	774807.	+	860511.i	0.410045	+	0.455401i
$325$	−1.83127e6	+	1.33050e6i	−0.961712	+	0.698725i
$326$	1.55161e6	−	1.12731e6i	0.808610	−	0.587490i
$327$	2.49310e6	+	2.76887e6i	1.28935	+	1.43197i
$328$	923527.	+	411181.i	0.473985	+	0.211032i
$329$	−451513.	+	201027.i	−0.229975	+	0.102391i
$330$	4.14481e6	−	4.60328e6i	2.09517	−	2.32693i
$331$	48478.5	−	461242.i	0.0243209	−	0.231398i	−0.975609	−	0.219518i	$-0.929552\pi$
$331$	48478.5	−	461242.i	0.0243209	−	0.231398i	0.999929	−	0.0118801i	$-0.00378165\pi$
$332$	−1.26424e6	+	268722.i	−0.629481	+	0.133800i
$333$	2.40648e6	−	7.40638e6i	1.18925	−	3.66012i
$334$	−928545.	−	197368.i	−0.455446	−	0.0968080i
$335$	2.62221e6	−	4.54180e6i	1.27660	−	2.21114i
$336$	−458633.	−	794376.i	−0.221624	−	0.383864i
$337$	893457.	+	2.74978e6i	0.428547	+	1.31893i	0.899556	+	0.436805i	$0.143890\pi$
$337$	893457.	+	2.74978e6i	0.428547	+	1.31893i	−0.471009	+	0.882129i	$0.656110\pi$
$338$	−134283.	−	1.27762e6i	−0.0639336	−	0.608287i
$339$	−4.16858e6	−	3.02865e6i	−1.97010	−	1.43136i
$340$	−153540.			−0.0720318
$341$	2.57669e6	+	3.01461e6i	1.19999	+	1.40393i
$342$	−390271.			−0.180427
$343$	1.74209e6	+	1.26570e6i	0.799530	+	0.580892i
$344$	39090.1	+	371918.i	0.0178103	+	0.169454i
$345$	231607.	+	712812.i	0.104762	+	0.322424i
$346$	−1.24607e6	−	2.15826e6i	−0.559569	−	0.969202i
$347$	−915906.	+	1.58640e6i	−0.408345	+	0.707275i	−0.994704	−	0.102777i	$-0.967227\pi$
$347$	−915906.	+	1.58640e6i	−0.408345	+	0.707275i	0.586359	+	0.810051i	$0.300561\pi$
$348$	−1.26611e6	−	269119.i	−0.560431	−	0.119123i
$349$	652884.	−	2.00937e6i	0.286928	−	0.883073i	−0.698887	−	0.715233i	$-0.746321\pi$
$349$	652884.	−	2.00937e6i	0.286928	−	0.883073i	0.985814	−	0.167840i	$-0.0536792\pi$
$350$	−1.39542e6	+	296607.i	−0.608886	+	0.129423i
$351$	−620032.	+	5.89921e6i	−0.268625	+	2.55579i
$352$	−507846.	+	564020.i	−0.218462	+	0.242626i
$353$	2.47299e6	−	1.10104e6i	1.05629	−	0.470293i	0.196272	−	0.980549i	$-0.437116\pi$
$353$	2.47299e6	−	1.10104e6i	1.05629	−	0.470293i	0.860022	+	0.510257i	$0.170450\pi$
$354$	−4.28773e6	−	1.90902e6i	−1.81852	−	0.809659i
$355$	859643.	+	954730.i	0.362032	+	0.402077i
$356$	101012.	−	73389.5i	0.0422424	−	0.0306909i
$357$	−363844.	+	264348.i	−0.151093	+	0.109776i
$358$	−646943.	−	718503.i	−0.266783	−	0.296293i
$359$	1.29099e6	+	574785.i	0.528672	+	0.235380i	0.653674	−	0.756777i	$-0.273227\pi$
$359$	1.29099e6	+	574785.i	0.528672	+	0.235380i	−0.125002	+	0.992157i	$0.539894\pi$
$360$	−2.25216e6	+	1.00273e6i	−0.915891	+	0.407781i
$361$	−1.63174e6	+	1.81223e6i	−0.658997	+	0.731890i
$362$	−260662.	+	2.48004e6i	−0.104546	+	0.994688i
$363$	−1.03795e7	+	2.20622e6i	−4.13436	+	0.878785i
$364$	539437.	−	1.66022e6i	0.213397	−	0.656767i
$365$	1.32718e6	+	282102.i	0.521434	+	0.110834i
$366$	1.24568e6	−	2.15759e6i	0.486077	−	0.841909i
$367$	148186.	+	256665.i	0.0574303	+	0.0994723i	0.893311	−	0.449439i	$-0.148376\pi$
$367$	148186.	+	256665.i	0.0574303	+	0.0994723i	−0.835881	+	0.548911i	$0.815043\pi$
$368$	−28377.8	−	87337.9i	−0.0109234	−	0.0336189i
$369$	−831887.	−	7.91488e6i	−0.318052	−	3.02607i
$370$	3.82407e6	+	2.77835e6i	1.45218	+	1.05507i
$371$	120830.			0.0455766
$372$	−665322.	−	2.24298e6i	−0.249272	−	0.840366i
$373$	2.39111e6			0.889873			0.444936	−	0.895562i	$-0.353226\pi$
$373$	2.39111e6			0.889873			0.444936	+	0.895562i	$0.353226\pi$
$374$	301052.	+	218727.i	0.111292	+	0.0808581i
$375$	−88408.8	−	841154.i	−0.0324652	−	0.308885i
$376$	−74552.2	−	229448.i	−0.0271951	−	0.0836979i
$377$	−1.23168e6	−	2.13334e6i	−0.446320	−	0.773048i
$378$	−1.86920e6	+	3.23755e6i	−0.672862	+	1.16543i
$379$	−484915.	−	103072.i	−0.173407	−	0.0368589i	0.120390	−	0.992727i	$-0.461586\pi$
$379$	−484915.	−	103072.i	−0.173407	−	0.0368589i	−0.293797	+	0.955868i	$0.594919\pi$
$380$	73201.0	−	225290.i	0.0260051	−	0.0800354i
$381$	−6.48269e6	+	1.37794e6i	−2.28793	+	0.486315i
$382$	−98810.5	+	940120.i	−0.0346453	+	0.329628i
$383$	−1.85968e6	+	2.06539e6i	−0.647802	+	0.719457i	−0.974178	−	0.225783i	$-0.927506\pi$
$383$	−1.85968e6	+	2.06539e6i	−0.647802	+	0.719457i	0.326376	+	0.945240i	$0.394173\pi$
$384$	409038.	−	182115.i	0.141558	−	0.0630258i
$385$	6.78724e6	+	3.02187e6i	2.33368	+	1.03902i
$386$	1.23114e6	+	1.36732e6i	0.420572	+	0.467092i
$387$	2.38177e6	−	1.73046e6i	0.808394	−	0.587333i
$388$	−835087.	+	606726.i	−0.281613	+	0.204604i
$389$	−393163.	−	436651.i	−0.131734	−	0.146306i	0.673669	−	0.739034i	$-0.264718\pi$
$389$	−393163.	−	436651.i	−0.131734	−	0.146306i	−0.805403	+	0.592728i	$0.798051\pi$
$390$	−6.35329e6	−	2.82867e6i	−2.11513	−	0.941717i
$391$	−41132.9	+	18313.5i	−0.0136065	+	0.00605801i
$392$	16416.2	−	18232.0i	0.00539581	−	0.00599266i
$393$	535374.	−	5.09374e6i	0.174854	−	1.66363i
$394$	706660.	−	150205.i	0.229335	−	0.0487466i
$395$	22988.9	−	70752.7i	0.00741355	−	0.0228166i
$396$	5.84435e6	+	1.24226e6i	1.87283	+	0.398082i
$397$	−1.31014e6	+	2.26922e6i	−0.417196	+	0.722605i	−0.995656	−	0.0931058i	$-0.970321\pi$
$397$	−1.31014e6	+	2.26922e6i	−0.417196	+	0.722605i	0.578460	+	0.815711i	$0.303654\pi$
$398$	271292.	+	469892.i	0.0858479	+	0.148693i
$399$	−214414.	−	659898.i	−0.0674250	−	0.207513i
$400$	−72790.4	−	692554.i	−0.0227470	−	0.216423i
$401$	1.15721e6	+	840761.i	0.359377	+	0.261103i	0.752792	−	0.658258i	$-0.228706\pi$
$401$	1.15721e6	+	840761.i	0.359377	+	0.261103i	−0.393415	+	0.919361i	$0.628706\pi$
$402$	7.49845e6			2.31423
$403$	2.32497e6	−	3.79723e6i	0.713108	−	1.16467i
$404$	994933.			0.303278
$405$	4.47631e6	+	3.25223e6i	1.35607	+	0.985243i
$406$	−162282.	−	1.54401e6i	−0.0488602	−	0.464873i
$407$	−3.54008e6	−	1.08952e7i	−1.05932	−	3.26025i
$408$	−109765.	−	190119.i	−0.0326449	−	0.0565426i
$409$	457031.	−	791600.i	0.135094	−	0.233990i	−0.790539	−	0.612411i	$-0.790200\pi$
$409$	457031.	−	791600.i	0.135094	−	0.233990i	0.925633	+	0.378421i	$0.123533\pi$
$410$	4.72501e6	+	1.00433e6i	1.38817	+	0.295065i
$411$	−1.05115e6	+	3.23510e6i	−0.306944	+	0.944677i
$412$	−2.67363e6	+	568297.i	−0.775992	+	0.164942i
$413$	588438.	−	5.59861e6i	0.169756	−	1.61512i
$414$	−483746.	+	537255.i	−0.138713	+	0.154056i
$415$	−5.64200e6	+	2.51198e6i	−1.60810	+	0.715972i
$416$	778442.	+	346585.i	0.220543	+	0.0981920i
$417$	−895300.	−	994331.i	−0.252132	−	0.280021i
$418$	−464467.	+	337455.i	−0.130021	+	0.0944658i
$419$	−353446.	+	256793.i	−0.0983530	+	0.0714576i	−0.635875	−	0.771792i	$-0.719361\pi$
$419$	−353446.	+	256793.i	−0.0983530	+	0.0714576i	0.537522	+	0.843250i	$0.319361\pi$
$420$	−2.93282e6	−	3.25723e6i	−0.811264	−	0.901000i
$421$	605925.	+	269775.i	0.166615	+	0.0741816i	0.488349	−	0.872648i	$-0.337599\pi$
$421$	605925.	+	269775.i	0.166615	+	0.0741816i	−0.321735	+	0.946830i	$0.604266\pi$
$422$	947440.	−	421827.i	0.258983	−	0.115306i
$423$	−1.27086e6	+	1.41144e6i	−0.345341	+	0.383540i
$424$	−6165.22	+	58658.2i	−0.00166546	+	0.0158458i
$425$	−333969.	+	70987.3i	−0.0896880	+	0.0190638i
$426$	−567627.	+	1.74698e6i	−0.151544	+	0.466405i
$427$	2.92288e6	+	621277.i	0.775785	+	0.164898i
$428$	1.11610e6	−	1.93315e6i	0.294507	−	0.510101i
$429$	8.42754e6	+	1.45969e7i	2.21084	+	3.82929i
$430$	552197.	+	1.69949e6i	0.144020	+	0.443248i
$431$	274084.	+	2.60773e6i	0.0710706	+	0.676192i	0.970824	+	0.239793i	$0.0770796\pi$
$431$	274084.	+	2.60773e6i	0.0710706	+	0.676192i	−0.899753	+	0.436399i	$0.856254\pi$
$432$	−1.47632e6	−	1.07261e6i	−0.380602	−	0.276524i
$433$	1.22586e6			0.314210			0.157105	−	0.987582i	$-0.449784\pi$
$433$	1.22586e6			0.314210			0.157105	+	0.987582i	$0.449784\pi$
$434$	2.31200e6	−	1.59028e6i	0.589201	−	0.405274i
$435$	−6.18508e6			−1.56719
$436$	−1.76479e6	−	1.28220e6i	−0.444608	−	0.323027i
$437$	−7261.17	−	69085.4i	−0.00181887	−	0.0173054i
$438$	599491.	+	1.84504e6i	0.149313	+	0.459538i
$439$	763663.	+	1.32270e6i	0.189121	+	0.327568i	0.944958	−	0.327193i	$-0.106103\pi$
$439$	763663.	+	1.32270e6i	0.189121	+	0.327568i	−0.755836	+	0.654761i	$0.772769\pi$
$440$	−1.81330e6	+	3.14074e6i	−0.446518	+	0.773392i
$441$	−188919.	−	40156.0i	−0.0462572	−	0.00983228i
$442$	129104.	−	397342.i	0.0314330	−	0.0967407i
$443$	−2.52757e6	+	537252.i	−0.611920	+	0.130068i	−0.503439	−	0.864031i	$-0.667932\pi$
$443$	−2.52757e6	+	537252.i	−0.611920	+	0.130068i	−0.108481	+	0.994099i	$0.534599\pi$
$444$	−706442.	+	6.72135e6i	−0.170067	+	1.61808i
$445$	399214.	−	443372.i	0.0955665	−	0.106137i
$446$	−1.91957e6	+	854648.i	−0.456948	+	0.203447i
$447$	3.32107e6	+	1.47864e6i	0.786157	+	0.350020i
$448$	359346.	+	399094.i	0.0845898	+	0.0939465i
$449$	507339.	−	368603.i	0.118763	−	0.0862866i	−0.526818	−	0.849978i	$-0.676615\pi$
$449$	507339.	−	368603.i	0.118763	−	0.0862866i	0.645581	+	0.763691i	$0.276615\pi$
$450$	−4.43514e6	+	3.22232e6i	−1.03247	+	0.750132i
$451$	−7.83379e6	−	8.70030e6i	−1.81355	−	2.01415i
$452$	2.75593e6	+	1.22702e6i	0.634485	+	0.282491i
$453$	−5.87377e6	+	2.61517e6i	−1.34484	+	0.598763i
$454$	−217605.	+	241675.i	−0.0495484	+	0.0550291i
$455$	871911.	−	8.29568e6i	0.197444	−	1.87855i
$456$	331293.	−	70418.6i	0.0746106	−	0.0158590i
$457$	296704.	−	913160.i	0.0664557	−	0.204530i	−0.912315	−	0.409490i	$-0.865707\pi$
$457$	296704.	−	913160.i	0.0664557	−	0.204530i	0.978770	+	0.204961i	$0.0657066\pi$
$458$	−4.81349e6	−	1.02314e6i	−1.07225	−	0.227914i
$459$	−447358.	+	774847.i	−0.0991114	+	0.171666i
$460$	−219405.	−	380020.i	−0.0483450	−	0.0837359i
$461$	1.01905e6	+	3.13632e6i	0.223329	+	0.687335i	0.998457	+	0.0555310i	$0.0176852\pi$
$461$	1.01905e6	+	3.13632e6i	0.223329	+	0.687335i	−0.775128	+	0.631804i	$0.782315\pi$
$462$	1.11038e6	+	1.05646e7i	0.242028	+	2.30275i
$463$	5.41727e6	+	3.93588e6i	1.17443	+	0.853276i	0.991533	−	0.129856i	$-0.0414514\pi$
$463$	5.41727e6	+	3.93588e6i	1.17443	+	0.853276i	0.182901	+	0.983131i	$0.441451\pi$
$464$	757832.			0.163410
$465$	−5.33803e6	−	9.82259e6i	−1.14485	−	2.10666i
$466$	−689032.			−0.146985
$467$	6.00385e6	+	4.36205e6i	1.27391	+	0.925548i	0.999351	−	0.0360231i	$-0.0114690\pi$
$467$	6.00385e6	+	4.36205e6i	1.27391	+	0.925548i	0.274556	+	0.961571i	$0.411469\pi$
$468$	−701199.	−	6.67146e6i	−0.147988	−	1.40801i
$469$	2.77922e6	+	8.55356e6i	0.583433	+	1.79562i
$470$	−576404.	−	998362.i	−0.120360	−	0.208470i
$471$	4.28414e6	−	7.42034e6i	0.889838	−	1.54125i
$472$	2.68787e6	+	571324.i	0.555333	+	0.118040i
$473$	1.33831e6	−	4.11889e6i	0.275045	−	0.846501i
$474$	104043.	−	22115.1i	0.0212701	−	0.00452109i
$475$	55061.7	−	523877.i	0.0111974	−	0.106536i
$476$	176188.	−	195676.i	0.0356417	−	0.0395841i
$477$	424185.	−	188859.i	0.0853609	−	0.0380051i
$478$	−150627.	−	67063.3i	−0.0301531	−	0.0134250i
$479$	−1.82995e6	−	2.03236e6i	−0.364418	−	0.404727i	0.532853	−	0.846208i	$-0.321120\pi$
$479$	−1.82995e6	−	2.03236e6i	−0.364418	−	0.404727i	−0.897271	+	0.441481i	$0.854453\pi$
$480$	1.73089e6	−	1.25757e6i	0.342900	−	0.249131i
$481$	−1.04055e7	+	7.56004e6i	−2.05069	+	1.48991i
$482$	191890.	+	213115.i	0.0376213	+	0.0417827i
$483$	−1.17420e6	−	522787.i	−0.229020	−	0.101966i
$484$	5.67554e6	−	2.52692e6i	1.10127	−	0.490317i
$485$	−3.30038e6	+	3.66545e6i	−0.637103	+	0.707575i
$486$	−102691.	+	977039.i	−0.0197216	+	0.187638i
$487$	138282.	−	29392.8i	0.0264207	−	0.00561589i	−0.194682	−	0.980866i	$-0.562368\pi$
$487$	138282.	−	29392.8i	0.0264207	−	0.00561589i	0.221103	+	0.975250i	$0.429034\pi$
$488$	−450741.	+	1.38724e6i	−0.0856796	+	0.263695i
$489$	1.28169e7	+	2.72432e6i	2.42388	+	0.515211i
$490$	58615.3	−	101525.i	0.0110286	−	0.0191021i
$491$	833349.	+	1.44340e6i	0.155999	+	0.270199i	0.933423	−	0.358779i	$-0.116807\pi$
$491$	833349.	+	1.44340e6i	0.155999	+	0.270199i	−0.777423	+	0.628978i	$0.783474\pi$
$492$	2.13430e6	+	6.56869e6i	0.397504	+	1.22339i
$493$	−38839.2	−	369530.i	−0.00719702	−	0.0684751i
$494$	521470.	+	378870.i	0.0961417	+	0.0698510i
$495$	2.85503e7			5.23719
$496$	654047.	+	1.20352e6i	0.119373	+	0.219659i
$497$	−2.20318e6			−0.400091
$498$	−7.14388e6	−	5.19034e6i	−1.29081	−	0.937826i
$499$	760050.	+	7.23139e6i	0.136644	+	1.30008i	0.820998	+	0.570931i	$0.193418\pi$
$499$	760050.	+	7.23139e6i	0.136644	+	1.30008i	−0.684354	+	0.729150i	$0.739916\pi$
$500$	153021.	+	470950.i	0.0273732	+	0.0842460i
$501$	−3.24281e6	−	5.61671e6i	−0.577201	−	0.999742i
$502$	−987231.	+	1.70993e6i	−0.174848	+	0.302845i
$503$	−6.42703e6	−	1.36611e6i	−1.13264	−	0.240749i	−0.396797	−	0.917906i	$-0.629878\pi$
$503$	−6.42703e6	−	1.36611e6i	−1.13264	−	0.240749i	−0.735838	+	0.677157i	$0.763212\pi$
$504$	1.30646e6	−	4.02086e6i	0.229097	−	0.705087i
$505$	4.65026e6	−	988444.i	0.811426	−	0.172474i
$506$	−111166.	+	1.05767e6i	−0.0193017	+	0.183644i
$507$	5.87287e6	−	6.52248e6i	1.01468	−	1.12692i
$508$	3.54477e6	−	1.57823e6i	0.609437	−	0.271339i
$509$	−2.38057e6	−	1.05990e6i	−0.407274	−	0.181330i	0.192866	−	0.981225i	$-0.438222\pi$
$509$	−2.38057e6	−	1.05990e6i	−0.407274	−	0.181330i	−0.600140	+	0.799895i	$0.704888\pi$
$510$	−701917.	−	779558.i	−0.119498	−	0.132716i
$511$	−1.88247e6	+	1.36769e6i	−0.318915	+	0.231705i
$512$	−212079.	+	154084.i	−0.0357538	+	0.0259767i
$513$	−923654.	−	1.02582e6i	−0.154959	−	0.172099i
$514$	−4.45626e6	−	1.98405e6i	−0.743982	−	0.331242i
$515$	−1.19318e7	+	5.31238e6i	−1.98238	+	0.882614i
$516$	−1.70961e6	+	1.89871e6i	−0.282665	+	0.313931i
$517$	−292048.	+	2.77865e6i	−0.0480538	+	0.457201i
$518$	−7.92895e6	+	1.68535e6i	−1.29835	+	0.275973i
$519$	5.26150e6	−	1.61932e7i	0.857415	−	2.63885i
$520$	3.98272e6	+	846554.i	0.645909	+	0.137292i
$521$	−329773.	+	571184.i	−0.0532257	+	0.0921896i	−0.891411	−	0.453196i	$-0.850284\pi$
$521$	−329773.	+	571184.i	−0.0532257	+	0.0921896i	0.838185	+	0.545386i	$0.183617\pi$
$522$	−2.98300e6	−	5.16671e6i	−0.479157	−	0.829923i
$523$	−924810.	−	2.84627e6i	−0.147842	−	0.455011i	0.849523	−	0.527551i	$-0.176890\pi$
$523$	−924810.	−	2.84627e6i	−0.147842	−	0.455011i	−0.997366	+	0.0725396i	$0.976890\pi$
$524$	313447.	+	2.98225e6i	0.0498696	+	0.474478i
$525$	−7.88520e6	−	5.72893e6i	−1.24857	−	0.907142i
$526$	2.54307e6			0.400769
$527$	553334.	−	380604.i	0.0867883	−	0.0596962i
$528$	−5.18531e6			−0.809449
$529$	5.10301e6	+	3.70755e6i	0.792842	+	0.576034i
$530$	29459.7	+	280290.i	0.00455553	+	0.0433429i
$531$	−6.68493e6	−	2.05741e7i	−1.02887	−	3.16654i
$532$	203118.	+	351810.i	0.0311149	+	0.0538926i
$533$	−6.57212e6	+	1.13832e7i	−1.00205	+	1.73559i
$534$	834397.	+	177357.i	0.126625	+	0.0269150i
$535$	3.29607e6	−	1.01443e7i	0.497866	−	1.53227i
$536$	−4.29421e6	+	912762.i	−0.645611	+	0.137229i
$537$	690467.	−	6.56935e6i	0.103325	−	0.983075i
$538$	3.30202e6	−	3.66726e6i	0.491840	−	0.546243i
$539$	−259557.	+	115562.i	−0.0384823	+	0.0171334i
$540$	−7.96586e6	−	3.54663e6i	−1.17557	−	0.523397i
$541$	−827791.	−	919355.i	−0.121598	−	0.135049i	0.679272	−	0.733887i	$-0.262296\pi$
$541$	−827791.	−	919355.i	−0.121598	−	0.135049i	−0.800870	+	0.598838i	$0.795629\pi$
$542$	6.67496e6	−	4.84964e6i	0.976001	−	0.709106i
$543$	−1.37833e7	+	1.00142e7i	−2.00611	+	1.45752i
$544$	86002.9	+	95515.9i	0.0124599	+	0.0138382i
$545$	−9.52238e6	−	4.23963e6i	−1.37326	−	0.611417i
$546$	1.08954e7	−	4.85093e6i	1.56408	−	0.696375i
$547$	−1.32499e6	+	1.47155e6i	−0.189340	+	0.210284i	−0.830340	−	0.557258i	$-0.811854\pi$
$547$	−1.32499e6	+	1.47155e6i	−0.189340	+	0.210284i	0.640999	+	0.767542i	$0.278520\pi$
$548$	208172.	−	1.98063e6i	0.0296123	−	0.281742i
$549$	1.12321e7	−	2.38745e6i	1.59048	−	0.338067i
$550$	−2.49209e6	+	7.66986e6i	−0.351283	+	1.08114i
$551$	560729.	+	119187.i	0.0786817	+	0.0167243i
$552$	313704.	−	543351.i	0.0438199	−	0.0758984i
$553$	63789.5	+	110487.i	0.00887026	+	0.0153637i
$554$	587766.	+	1.80896e6i	0.0813636	+	0.250411i
$555$	3.37564e6	+	3.21171e7i	0.465183	+	4.42592i
$556$	633756.	+	460451.i	0.0869431	+	0.0631679i
$557$	−7.93502e6			−1.08370			−0.541851	−	0.840475i	$-0.682276\pi$
$557$	−7.93502e6			−1.08370			−0.541851	+	0.840475i	$0.682276\pi$
$558$	5.63083e6	−	9.19646e6i	0.765574	−	1.25036i
$559$	−4.86238e6			−0.658141
$560$	2.07606e6	+	1.50834e6i	0.279749	+	0.203250i
$561$	265749.	+	2.52843e6i	0.0356504	+	0.339191i
$562$	−1.27550e6	−	3.92557e6i	−0.170349	−	0.524279i
$563$	3.80536e6	+	6.59107e6i	0.505970	+	0.876365i	0.999976	+	0.00690709i	$0.00219861\pi$
$563$	3.80536e6	+	6.59107e6i	0.505970	+	0.876365i	−0.494006	+	0.869458i	$0.664468\pi$
$564$	824140.	−	1.42745e6i	0.109095	−	0.188957i
$565$	1.41001e7	+	2.99706e6i	1.85823	+	0.394979i
$566$	−44749.6	+	137725.i	−0.00587149	+	0.0180706i
$567$	−9.28131e6	+	1.97280e6i	−1.21242	+	0.257707i
$568$	112414.	−	1.06955e6i	0.0146201	−	0.139101i
$569$	−8.95142e6	+	9.94156e6i	−1.15907	+	1.28728i	−0.208067	+	0.978115i	$0.566717\pi$
$569$	−8.95142e6	+	9.94156e6i	−1.15907	+	1.28728i	−0.951008	+	0.309168i	$0.899950\pi$
$570$	1.47849e6	−	658266.i	0.190603	−	0.0848621i
$571$	−1.13451e7	−	5.05115e6i	−1.45619	−	0.648336i	−0.482431	−	0.875934i	$-0.660246\pi$
$571$	−1.13451e7	−	5.05115e6i	−1.45619	−	0.648336i	−0.973755	+	0.227599i	$0.926913\pi$
$572$	−6.60311e6	−	7.33350e6i	−0.843837	−	0.937176i
$573$	−5.22492e6	+	3.79612e6i	−0.664803	+	0.483008i
$574$	−6.70192e6	+	4.86923e6i	−0.849023	+	0.616851i
$575$	−652931.	−	725153.i	−0.0823564	−	0.0914660i
$576$	1.88530e6	+	839390.i	0.236769	+	0.105416i
$577$	6.90749e6	−	3.07541e6i	0.863735	−	0.384560i	0.0734501	−	0.997299i	$-0.476599\pi$
$577$	6.90749e6	−	3.07541e6i	0.863735	−	0.384560i	0.790285	+	0.612739i	$0.209932\pi$
$578$	−3.75811e6	+	4.17381e6i	−0.467897	+	0.519652i
$579$	−1.31397e6	+	1.25016e7i	−0.162888	+	1.54977i
$580$	3.54207e6	−	752890.i	0.437207	−	0.0929312i
$581$	3.27287e6	−	1.00728e7i	0.402243	−	1.23798i
$582$	−6.89813e6	−	1.46624e6i	−0.844158	−	0.179431i
$583$	341528.	−	591543.i	0.0416154	−	0.0720800i
$584$	−567907.	−	983644.i	−0.0689041	−	0.119345i
$585$	−9.90532e6	−	3.04854e7i	−1.19668	−	3.68301i
$586$	−306144.	−	2.91277e6i	−0.0368283	−	0.350398i
$587$	−8.99365e6	−	6.53427e6i	−1.07731	−	0.782712i	−0.100098	−	0.994978i	$-0.531916\pi$
$587$	−8.99365e6	−	6.53427e6i	−1.07731	−	0.782712i	−0.977212	+	0.212266i	$0.931916\pi$
$588$	167616.			0.0199927
$589$	294655.	+	993363.i	0.0349966	+	0.117983i
$590$	1.31306e7			1.55294
$591$	3.99316e6	+	2.90120e6i	0.470271	+	0.341672i
$592$	−413603.	−	3.93517e6i	−0.0485042	−	0.461487i
$593$	−664518.	−	2.04518e6i	−0.0776015	−	0.238833i	0.904729	−	0.425988i	$-0.140073\pi$
$593$	−664518.	−	2.04518e6i	−0.0776015	−	0.238833i	−0.982330	+	0.187155i	$0.940073\pi$
$594$	1.05666e7	+	1.83019e7i	1.22876	+	2.12828i
$595$	629092.	−	1.08962e6i	0.0728487	−	0.126178i
$596$	−2.08190e6	−	442521.i	−0.240073	−	0.0510291i
$597$	−1.14552e6	+	3.52555e6i	−0.131543	+	0.404847i
$598$	1.16793e6	−	248251.i	0.133556	−	0.0283882i
$599$	378938.	−	3.60536e6i	0.0431520	−	0.410564i	−0.951529	−	0.307560i	$-0.900488\pi$
$599$	378938.	−	3.60536e6i	0.0431520	−	0.410564i	0.994681	−	0.103005i	$-0.0328457\pi$
$600$	3.18349e6	−	3.53562e6i	0.361015	−	0.400948i
$601$	−1.20618e7	+	5.37027e6i	−1.36216	+	0.606471i	−0.952155	−	0.305615i	$-0.901138\pi$
$601$	−1.20618e7	+	5.37027e6i	−1.36216	+	0.606471i	−0.410000	+	0.912086i	$0.634471\pi$
$602$	−2.79953e6	−	1.24643e6i	−0.314843	−	0.140177i
$603$	2.31260e7	+	2.56840e7i	2.59004	+	2.87653i
$604$	3.04545e6	−	2.21265e6i	0.339672	−	0.246786i
$605$	2.40168e7	−	1.74492e7i	2.66763	−	1.93815i
$606$	4.54839e6	+	5.05150e6i	0.503125	+	0.558777i
$607$	−1.60221e6	−	713351.i	−0.176501	−	0.0785835i	0.316584	−	0.948565i	$-0.397464\pi$
$607$	−1.60221e6	−	713351.i	−0.176501	−	0.0785835i	−0.493085	+	0.869981i	$0.664131\pi$
$608$	−181153.	+	80654.5i	−0.0198741	+	0.00884850i
$609$	7.09740e6	−	7.88246e6i	0.775454	−	0.861229i
$610$	−728548.	+	6.93167e6i	−0.0792745	+	0.754247i
$611$	3.06830e6	−	652188.i	0.332503	−	0.0706757i
$612$	312677.	−	962319.i	0.0337456	−	0.103858i
$613$	−6.44175e6	−	1.36924e6i	−0.692393	−	0.147173i	−0.151742	−	0.988420i	$-0.548488\pi$
$613$	−6.44175e6	−	1.36924e6i	−0.692393	−	0.147173i	−0.540650	+	0.841248i	$0.681822\pi$
$614$	4.39414e6	−	7.61087e6i	0.470384	−	0.814729i
$615$	1.65014e7	+	2.85813e7i	1.75928	+	3.04716i
$616$	−1.92188e6	−	5.91493e6i	−0.204068	−	0.628056i
$617$	1.03317e6	+	9.82997e6i	0.109260	+	1.03953i	0.902519	+	0.430651i	$0.141716\pi$
$617$	1.03317e6	+	9.82997e6i	0.109260	+	1.03953i	−0.793259	+	0.608884i	$0.791617\pi$
$618$	−1.51080e7	−	1.09766e7i	−1.59124	−	1.15610i
$619$	474073.			0.0497300			0.0248650	−	0.999691i	$-0.492084\pi$
$619$	474073.			0.0497300			0.0248650	+	0.999691i	$0.492084\pi$
$620$	4.25265e6	+	4.97541e6i	0.444304	+	0.519816i
$621$	−2.55705e6			−0.266079
$622$	7.47765e6	+	5.43283e6i	0.774978	+	0.563054i
$623$	106948.	+	1.01754e6i	0.0110396	+	0.105034i
$624$	1.79900e6	+	5.53676e6i	0.184957	+	0.569238i
$625$	5.43339e6	+	9.41091e6i	0.556379	+	0.963677i
$626$	−5.24128e6	+	9.07817e6i	−0.534566	+	0.925896i
$627$	−3.83667e6	−	815509.i	−0.389749	−	0.0828438i
$628$	−1.55018e6	+	4.77097e6i	−0.156850	+	0.482734i
$629$	−1.89765e6	+	403358.i	−0.191245	+	0.0406503i
$630$	2.11167e6	−	2.00912e7i	0.211970	−	2.01676i
$631$	1.07382e7	−	1.19259e7i	1.07363	−	1.19239i	0.0931795	−	0.995649i	$-0.470297\pi$
$631$	1.07382e7	−	1.19259e7i	1.07363	−	1.19239i	0.980455	−	0.196743i	$-0.0630364\pi$
$632$	−56891.5	+	25329.7i	−0.00566571	+	0.00252254i
$633$	6.47299e6	+	2.88196e6i	0.642089	+	0.285877i
$634$	2.14559e6	+	2.38292e6i	0.211994	+	0.235443i
$635$	1.50001e7	−	1.08982e7i	1.47625	−	1.07256i
$636$	−326006.	+	236857.i	−0.0319582	+	0.0232190i
$637$	213446.	+	237056.i	0.0208420	+	0.0231474i
$638$	−8.01761e6	−	3.56967e6i	−0.779818	−	0.347197i
$639$	−7.73443e6	+	3.44359e6i	−0.749335	+	0.333626i
$640$	−838166.	+	930878.i	−0.0808873	+	0.0898344i
$641$	−570493.	+	5.42788e6i	−0.0548410	+	0.521777i	0.932273	+	0.361756i	$0.117823\pi$
$641$	−570493.	+	5.42788e6i	−0.0548410	+	0.521777i	−0.987114	+	0.160021i	$0.948844\pi$
$642$	1.49174e7	−	3.17078e6i	1.42842	−	0.303619i
$643$	2.71640e6	−	8.36022e6i	0.259099	−	0.797426i	−0.733895	−	0.679263i	$-0.762299\pi$
$643$	2.71640e6	−	8.36022e6i	0.259099	−	0.797426i	0.992994	−	0.118163i	$-0.0377005\pi$
$644$	736077.	+	156458.i	0.0699372	+	0.0148656i
$645$	−6.10429e6	+	1.05729e7i	−0.577744	+	1.00068i
$646$	48612.5	+	84199.3i	0.00458318	+	0.00793829i
$647$	6.05748e6	+	1.86430e7i	0.568894	+	1.75087i	0.656089	+	0.754684i	$0.272210\pi$
$647$	6.05748e6	+	1.86430e7i	0.568894	+	1.75087i	−0.0871953	+	0.996191i	$0.527790\pi$
$648$	−484147.	−	4.60635e6i	−0.0452939	−	0.430943i
$649$	−2.57456e7	−	1.87053e7i	−2.39934	−	1.74322i
$650$	9.05432e6			0.840567
$651$	1.86436e7	+	4.46850e6i	1.72416	+	0.413247i
$652$	−7.67159e6			−0.706751
$653$	1.13592e7	+	8.25296e6i	1.04248	+	0.757403i	0.970767	−	0.240023i	$-0.0771550\pi$
$653$	1.13592e7	+	8.25296e6i	1.04248	+	0.757403i	0.0717080	+	0.997426i	$0.477155\pi$
$654$	−1.55784e6	−	1.48219e7i	−0.142423	−	1.35506i
$655$	4.42784e6	+	1.36275e7i	0.403263	+	1.24112i
$656$	−2.02185e6	−	3.50195e6i	−0.183438	−	0.317724i
$657$	−4.47083e6	+	7.74370e6i	−0.404087	+	0.699898i
$658$	1.93377e6	+	411035.i	0.174116	+	0.0370096i
$659$	−3.95496e6	+	1.21721e7i	−0.354755	+	1.09182i	0.601396	+	0.798951i	$0.294611\pi$
$659$	−3.95496e6	+	1.21721e7i	−0.354755	+	1.09182i	−0.956151	+	0.292873i	$0.905389\pi$
$660$	−2.42359e7	+	5.15149e6i	−2.16570	+	0.460334i
$661$	−1.10198e6	+	1.04847e7i	−0.0981004	+	0.933363i	0.829177	+	0.558987i	$0.188810\pi$
$661$	−1.10198e6	+	1.04847e7i	−0.0981004	+	0.933363i	−0.927277	+	0.374376i	$0.877857\pi$
$662$	−1.24132e6	+	1.37863e6i	−0.110088	+	0.122265i
$663$	2.60761e6	−	1.16098e6i	0.230387	−	0.102575i
$664$	4.72296e6	+	2.10280e6i	0.415713	+	0.185087i
$665$	1.29888e6	+	1.44255e6i	0.113897	+	0.126496i
$666$	−2.52010e7	+	1.83096e7i	−2.20157	+	1.59953i
$667$	859107.	−	624178.i	0.0747709	−	0.0543242i
$668$	2.54079e6	+	2.82184e6i	0.220307	+	0.244676i
$669$	−1.31147e7	−	5.83903e6i	−1.13290	−	0.504400i
$670$	−1.91641e7	+	8.53240e6i	−1.64931	+	0.734318i
$671$	1.13031e7	−	1.25533e7i	0.969149	−	1.07635i
$672$	−383522.	+	3.64896e6i	−0.0327617	+	0.311707i
$673$	−1.20143e7	+	2.55373e6i	−1.02250	+	0.217339i	−0.688501	−	0.725236i	$-0.741731\pi$
$673$	−1.20143e7	+	2.55373e6i	−1.02250	+	0.217339i	−0.333997	+	0.942574i	$0.608397\pi$
$674$	3.57383e6	−	1.09991e7i	0.303029	−	0.932627i
$675$	−1.89665e7	−	4.03145e6i	−1.60224	−	0.340567i
$676$	−2.56931e6	+	4.45017e6i	−0.216247	+	0.374550i
$677$	−5.53473e6	−	9.58643e6i	−0.464114	−	0.803869i	0.535047	−	0.844822i	$-0.320294\pi$
$677$	−5.53473e6	−	9.58643e6i	−0.464114	−	0.803869i	−0.999161	+	0.0409533i	$0.986961\pi$
$678$	6.36902e6	+	1.96018e7i	0.532106	+	1.63766i
$679$	−884160.	−	8.41222e6i	−0.0735964	−	0.700223i
$680$	496866.	+	360994.i	0.0412066	+	0.0299384i
$681$	−2.22183e6			−0.183588
$682$	−1.25056e6	−	1.58136e7i	−0.102954	−	1.30188i
$683$	1.92798e7			1.58144			0.790718	−	0.612181i	$-0.209708\pi$
$683$	1.92798e7			1.58144			0.790718	+	0.612181i	$0.209708\pi$
$684$	1.26294e6	+	917581.i	0.103215	+	0.0749902i
$685$	−994723.	−	9.46416e6i	−0.0809983	−	0.770647i
$686$	−2.66167e6	−	8.19178e6i	−0.215946	−	0.664612i
$687$	−1.68104e7	−	2.91165e7i	−1.35890	−	2.35368i
$688$	747933.	−	1.29546e6i	0.0602409	−	0.104340i
$689$	−750127.	−	159444.i	−0.0601987	−	0.0127956i
$690$	926427.	−	2.85125e6i	0.0740779	−	0.227988i
$691$	2.37763e7	−	5.05381e6i	1.89430	−	0.402646i	0.895225	−	0.445615i	$-0.147015\pi$
$691$	2.37763e7	−	5.05381e6i	1.89430	−	0.402646i	0.999076	+	0.0429688i	$0.0136816\pi$
$692$	−1.04200e6	+	9.91399e6i	−0.0827186	+	0.787015i
$693$	−3.27616e7	+	3.63854e7i	−2.59138	+	2.87802i
$694$	6.69378e6	−	2.98026e6i	0.527561	−	0.234885i
$695$	3.41959e6	+	1.52250e6i	0.268542	+	0.119563i
$696$	3.46447e6	+	3.84769e6i	0.271090	+	0.301076i
$697$	−1.60398e6	+	1.16536e6i	−0.125060	+	0.0908612i
$698$	−6.83709e6	+	4.96744e6i	−0.531169	+	0.385917i
$699$	−3.14995e6	−	3.49837e6i	−0.243843	−	0.270815i
$700$	5.21305e6	+	2.32100e6i	0.402112	+	0.179032i
$701$	4.39260e6	−	1.95571e6i	0.337619	−	0.150318i	−0.230923	−	0.972972i	$-0.574174\pi$
$701$	4.39260e6	−	1.95571e6i	0.337619	−	0.150318i	0.568542	+	0.822654i	$0.307508\pi$
$702$	1.58763e7	−	1.76325e7i	1.21593	−	1.35042i
$703$	312867.	−	2.97673e6i	0.0238765	−	0.227170i
$704$	2.96952e6	−	631190.i	0.225816	−	0.0479986i
$705$	2.43384e6	−	7.49060e6i	0.184425	−	0.567602i
$706$	−1.05915e7	−	2.25129e6i	−0.799732	−	0.169988i
$707$	−4.07649e6	+	7.06068e6i	−0.306717	+	0.531249i
$708$	9.38700e6	+	1.62588e7i	0.703791	+	1.21900i
$709$	−4.54220e6	−	1.39794e7i	−0.339352	−	1.04442i	−0.964538	−	0.263942i	$-0.914977\pi$
$709$	−4.54220e6	−	1.39794e7i	−0.339352	−	1.04442i	0.625187	−	0.780475i	$-0.285023\pi$
$710$	−537158.	−	5.11071e6i	−0.0399904	−	0.380483i
$711$	396630.	+	288168.i	0.0294246	+	0.0213783i
$712$	−499431.			−0.0369212
$713$	1.73271e6	+	825660.i	0.127645	+	0.0608244i
$714$	1.79894e6			0.132060
$715$	−3.81483e7	−	2.77163e7i	−2.79068	−	2.02755i
$716$	404250.	+	3.84618e6i	0.0294691	+	0.280380i
$717$	−348102.	−	1.07135e6i	−0.0252877	−	0.0778275i
$718$	−2.82633e6	−	4.89534e6i	−0.204603	−	0.354382i
$719$	5.68294e6	−	9.84315e6i	0.409969	−	0.710087i	−0.584917	−	0.811093i	$-0.698873\pi$
$719$	5.68294e6	−	9.84315e6i	0.409969	−	0.710087i	0.994886	+	0.101006i	$0.0322061\pi$
$720$	9.64571e6	+	2.05026e6i	0.693431	+	0.147393i
$721$	6.92151e6	−	2.13022e7i	0.495864	−	1.52611i
$722$	9.54124e6	−	2.02805e6i	0.681180	−	0.144789i
$723$	−204799.	+	1.94853e6i	−0.0145708	+	0.138632i
$724$	6.67444e6	−	7.41271e6i	0.473226	−	0.525570i
$725$	7.35636e6	−	3.27526e6i	0.519778	−	0.231420i
$726$	3.87758e7	+	1.72641e7i	2.73035	+	1.21563i
$727$	46346.0	+	51472.4i	0.00325219	+	0.00361192i	0.744769	−	0.667323i	$-0.232560\pi$
$727$	46346.0	+	51472.4i	0.00325219	+	0.00361192i	−0.741517	+	0.670935i	$0.765893\pi$
$728$	−5.64906e6	+	4.10428e6i	−0.395046	+	0.287018i
$729$	8.79733e6	−	6.39164e6i	0.613101	−	0.445444i
$730$	−3.63160e6	−	4.03330e6i	−0.252226	−	0.280126i
$731$	−670016.	−	298310.i	−0.0463758	−	0.0206478i
$732$	−9.10390e6	+	4.05332e6i	−0.627986	+	0.279597i
$733$	−8.28576e6	+	9.20227e6i	−0.569603	+	0.632608i	−0.957272	−	0.289191i	$-0.906614\pi$
$733$	−8.28576e6	+	9.20227e6i	−0.569603	+	0.632608i	0.387668	+	0.921799i	$0.373281\pi$
$734$	123917.	−	1.17899e6i	0.00848967	−	0.0807739i
$735$	783426.	−	166522.i	0.0534909	−	0.0113698i
$736$	−113511.	+	349352.i	−0.00772403	+	0.0237721i
$737$	4.97307e7	+	1.05706e7i	3.37253	+	0.716853i
$738$	−1.59169e7	+	2.75690e7i	−1.07577	+	1.86329i
$739$	−7.51595e6	−	1.30180e7i	−0.506259	−	0.876866i	−0.999974	−	0.00724250i	$-0.997695\pi$
$739$	−7.51595e6	−	1.30180e7i	−0.506259	−	0.876866i	0.493715	−	0.869624i	$-0.335639\pi$
$740$	−5.84266e6	−	1.79819e7i	−0.392222	−	1.20713i
$741$	460319.	+	4.37965e6i	0.0307974	+	0.293017i
$742$	−391016.	−	284089.i	−0.0260726	−	0.0189429i
$743$	−2.04515e7			−1.35911			−0.679553	−	0.733626i	$-0.737826\pi$
$743$	−2.04515e7			−1.35911			−0.679553	+	0.733626i	$0.737826\pi$
$744$	−3.12054e6	+	8.82271e6i	−0.206679	+	0.584345i
$745$	−1.01703e7			−0.671341
$746$	−7.73780e6	−	5.62184e6i	−0.509062	−	0.369855i
$747$	−4.25431e6	−	4.04770e7i	−0.278951	−	2.65404i
$748$	−459966.	−	1.41563e6i	−0.0300588	−	0.0925116i
$749$	9.14591e6	+	1.58412e7i	0.595693	+	1.03177i
$750$	−1.69157e6	+	2.92989e6i	−0.109809	+	0.190195i
$751$	−3.88802e6	−	826424.i	−0.251552	−	0.0534691i	0.0804095	−	0.996762i	$-0.474377\pi$
$751$	−3.88802e6	−	826424.i	−0.251552	−	0.0534691i	−0.331962	+	0.943293i	$0.607711\pi$
$752$	−298209.	+	917792.i	−0.0192298	+	0.0591834i
$753$	−1.31949e7	+	2.80466e6i	−0.848045	+	0.180258i
$754$	−1.02997e6	+	9.79950e6i	−0.0659775	+	0.627734i
$755$	1.20361e7	−	1.33674e7i	0.768452	−	0.853453i
$756$	1.36608e7	−	6.08217e6i	0.869303	−	0.387038i
$757$	2.43868e7	+	1.08577e7i	1.54673	+	0.688651i	0.989873	−	0.141955i	$-0.0453387\pi$
$757$	2.43868e7	+	1.08577e7i	1.54673	+	0.688651i	0.556862	+	0.830605i	$0.312005\pi$
$758$	1.32688e6	+	1.47365e6i	0.0838802	+	0.0931584i
$759$	−5.87826e6	+	4.27080e6i	−0.370377	+	0.269095i
$760$	−766571.	+	556946.i	−0.0481414	+	0.0349767i
$761$	−1.42705e7	−	1.58489e7i	−0.893256	−	0.992062i	0.106741	−	0.994287i	$-0.465958\pi$
$761$	−1.42705e7	−	1.58489e7i	−0.893256	−	0.992062i	−0.999998	+	0.00222520i	$0.999292\pi$
$762$	2.42182e7	+	1.07826e7i	1.51096	+	0.672724i
$763$	1.63301e7	−	7.27062e6i	1.01549	−	0.452126i
$764$	2.53011e6	−	2.80997e6i	0.156822	−	0.174168i
$765$	505390.	−	4.80847e6i	0.0312229	−	0.297066i
$766$	1.08741e7	−	2.31136e6i	0.669608	−	0.142330i
$767$	−1.10409e7	+	3.39802e7i	−0.677664	+	2.08563i
$768$	−1.75185e6	−	372368.i	−0.107175	−	0.0227808i
$769$	−9.62949e6	+	1.66788e7i	−0.587202	+	1.01706i	0.407395	+	0.913252i	$0.366437\pi$
$769$	−9.62949e6	+	1.66788e7i	−0.587202	+	1.01706i	−0.994597	+	0.103811i	$0.966896\pi$
$770$	−1.48591e7	−	2.57367e7i	−0.903163	−	1.56432i
$771$	−1.02985e7	−	3.16956e7i	−0.623936	−	1.92028i
$772$	−769293.	−	7.31934e6i	−0.0464567	−	0.442006i
$773$	2.13970e7	+	1.55459e7i	1.28797	+	0.935764i	0.999762	−	0.0218049i	$-0.00694127\pi$
$773$	2.13970e7	+	1.55459e7i	1.28797	+	0.935764i	0.288206	+	0.957568i	$0.406941\pi$
$774$	−1.17761e7			−0.706562
$775$	1.15504e7	+	8.85600e6i	0.690783	+	0.529643i
$776$	4.12890e6			0.246139
$777$	−4.48045e7	−	3.25524e7i	−2.66238	−	1.93433i
$778$	245672.	+	2.33741e6i	0.0145515	+	0.138448i
$779$	−945229.	−	2.90912e6i	−0.0558076	−	0.171758i
$780$	1.39091e7	+	2.40912e7i	0.818582	+	1.41783i
$781$	−6.22729e6	+	1.07860e7i	−0.365318	+	0.632750i
$782$	176166.	+	37445.3i	0.0103016	+	0.00218968i
$783$	6.52077e6	−	2.00689e7i	0.380097	−	1.16982i
$784$	−95989.9	+	20403.3i	−0.00557745	+	0.00118552i
$785$	−2.50561e6	+	2.38393e7i	−0.145124	+	1.38077i
$786$	−1.37086e7	+	1.52250e7i	−0.791475	+	0.879022i
$787$	1.17854e7	−	5.24719e6i	0.678276	−	0.301988i	−0.0385332	−	0.999257i	$-0.512269\pi$
$787$	1.17854e7	−	5.24719e6i	0.678276	−	0.301988i	0.716809	+	0.697269i	$0.245602\pi$
$788$	−2.63995e6	−	1.17538e6i	−0.151454	−	0.0674316i
$789$	1.16258e7	+	1.29117e7i	0.664860	+	0.738401i
$790$	−240743.	+	174910.i	−0.0137242	+	0.00997120i
$791$	−1.99994e7	+	1.45304e7i	−1.13652	+	0.825728i
$792$	−1.59920e7	−	1.77609e7i	−0.905920	−	1.00613i
$793$	−1.73257e7	−	7.71390e6i	−0.978381	−	0.435603i
$794$	9.57495e6	−	4.26304e6i	0.538996	−	0.239976i
$795$	−1.28842e6	+	1.43094e6i	−0.0723003	+	0.0802976i
$796$	226862.	−	2.15845e6i	0.0126905	−	0.120742i
$797$	−1.29790e7	+	2.75876e6i	−0.723759	+	0.153840i	−0.555039	−	0.831824i	$-0.687297\pi$
$797$	−1.29790e7	+	2.75876e6i	−0.723759	+	0.153840i	−0.168720	+	0.985664i	$0.553963\pi$
$798$	−857656.	+	2.63959e6i	−0.0476767	+	0.146734i
$799$	462812.	+	98373.7i	0.0256471	+	0.00545145i
$800$	−1.39274e6	+	2.41229e6i	−0.0769387	+	0.133262i
$801$	1.96588e6	+	3.40500e6i	0.108262	+	0.187515i
$802$	−1.76806e6	−	5.44152e6i	−0.0970644	−	0.298734i
$803$	1.37494e6	+	1.30817e7i	0.0752479	+	0.715936i
$804$	−2.42655e7	−	1.76299e7i	−1.32388	−	0.961856i
$805$	3.59582e6			0.195573
$806$	−1.64516e7	+	6.82174e6i	−0.892011	+	0.369877i
$807$	3.37149e7			1.82237
$808$	−3.21967e6	−	2.33923e6i	−0.173493	−	0.126050i
$809$	−3.04592e6	−	2.89800e7i	−0.163624	−	1.55678i	−0.700830	−	0.713328i	$-0.747187\pi$
$809$	−3.04592e6	−	2.89800e7i	−0.163624	−	1.55678i	0.537206	−	0.843451i	$-0.319480\pi$
$810$	−6.83919e6	−	2.10489e7i	−0.366262	−	1.12724i
$811$	−2.66328e6	−	4.61294e6i	−0.142189	−	0.246278i	0.786132	−	0.618059i	$-0.212081\pi$
$811$	−2.66328e6	−	4.61294e6i	−0.142189	−	0.246278i	−0.928321	+	0.371781i	$0.878747\pi$
$812$	−3.10503e6	+	5.37806e6i	−0.165263	+	0.286244i
$813$	5.51377e7	+	1.17199e7i	2.92565	+	0.621866i
$814$	−1.41603e7	+	4.35810e7i	−0.749052	+	2.30534i
$815$	−3.58566e7	+	7.62156e6i	−1.89093	+	0.401929i
$816$	−91788.9	+	873313.i	−0.00482575	+	0.0459139i
$817$	757144.	−	840894.i	0.0396847	−	0.0440744i
$818$	−3.34015e6	+	1.48713e6i	−0.174535	+	0.0777079i
$819$	5.02180e7	+	2.23585e7i	2.61607	+	1.16475i
$820$	−1.29291e7	−	1.43593e7i	−0.671483	−	0.745757i
$821$	1.45715e7	−	1.05868e7i	0.754477	−	0.548160i	−0.142734	−	0.989761i	$-0.545589\pi$
$821$	1.45715e7	−	1.05868e7i	0.754477	−	0.548160i	0.897211	+	0.441601i	$0.145589\pi$
$822$	1.10078e7	−	7.99761e6i	0.568224	−	0.412839i
$823$	−449770.	−	499521.i	−0.0231468	−	0.0257071i	0.731460	−	0.681884i	$-0.238839\pi$
$823$	−449770.	−	499521.i	−0.0231468	−	0.0257071i	−0.754607	+	0.656177i	$0.772172\pi$
$824$	9.98818e6	+	4.44702e6i	0.512470	+	0.228166i
$825$	−5.03343e7	+	2.24103e7i	−2.57472	+	1.14634i
$826$	−1.50674e7	+	1.67340e7i	−0.768399	+	0.853394i
$827$	−3.36487e6	+	3.20146e7i	−0.171082	+	1.62774i	0.486028	+	0.873943i	$0.338445\pi$
$827$	−3.36487e6	+	3.20146e7i	−0.171082	+	1.62774i	−0.657110	+	0.753795i	$0.728221\pi$
$828$	2.82860e6	−	601237.i	0.143382	−	0.0304768i
$829$	5.42866e6	−	1.67077e7i	0.274351	−	0.844366i	−0.715039	−	0.699084i	$-0.753591\pi$
$829$	5.42866e6	−	1.67077e7i	0.274351	−	0.844366i	0.989390	−	0.145281i	$-0.0464088\pi$
$830$	2.41639e7	+	5.13620e6i	1.21751	+	0.258790i
$831$	−6.49748e6	+	1.12540e7i	−0.326394	+	0.565331i
$832$	−1.70422e6	−	2.95180e6i	−0.0853528	−	0.147835i
$833$	14868.5	+	45760.4i	0.000742427	+	0.00228495i
$834$	559438.	+	5.32270e6i	0.0278508	+	0.264982i
$835$	1.46790e7	+	1.06649e7i	0.728583	+	0.529347i
$836$	2.29645e6			0.113643
$837$	3.74993e7	−	6.96471e6i	1.85016	−	0.343629i
$838$	1.74753e6			0.0859637
$839$	8.99644e6	+	6.53629e6i	0.441231	+	0.320573i	0.786124	−	0.618069i	$-0.212085\pi$
$839$	8.99644e6	+	6.53629e6i	0.441231	+	0.320573i	−0.344893	+	0.938642i	$0.612085\pi$
$840$	1.83261e6	+	1.74361e7i	0.0896130	+	0.852611i
$841$	−3.63029e6	−	1.11729e7i	−0.176991	−	0.544723i
$842$	−1.32653e6	−	2.29762e6i	−0.0644819	−	0.111686i
$843$	1.41000e7	−	2.44220e7i	0.683362	−	1.18362i
$844$	−4.05776e6	−	862502.i	−0.196078	−	0.0416777i
$845$	−7.58766e6	+	2.33524e7i	−0.365566	+	1.12510i
$846$	7.43109e6	−	1.57953e6i	0.356966	−	0.0758755i
$847$	−5.32150e6	+	5.06307e7i	−0.254874	+	2.42496i
$848$	157865.	−	175327.i	0.00753868	−	0.00837256i
$849$	−903837.	+	402414.i	−0.0430349	+	0.0191604i
$850$	1.24765e6	+	555489.i	0.0592304	+	0.0263711i
$851$	−3.71002e6	−	4.12040e6i	−0.175611	−	0.195036i
$852$	5.94427e6	−	4.31876e6i	0.280543	−	0.203826i
$853$	2.93173e7	−	2.13003e7i	1.37959	−	1.00233i	0.382676	−	0.923882i	$-0.375002\pi$
$853$	2.93173e7	−	2.13003e7i	1.37959	−	1.00233i	0.996918	−	0.0784515i	$-0.0249976\pi$
$854$	−7.99793e6	−	8.88260e6i	−0.375260	−	0.416769i
$855$	6.81452e6	+	3.03402e6i	0.318801	+	0.141939i
$856$	−8.15690e6	+	3.63168e6i	−0.380488	+	0.169404i
$857$	1.32207e7	−	1.46831e7i	0.614899	−	0.682915i	−0.352604	−	0.935773i	$-0.614704\pi$
$857$	1.32207e7	−	1.46831e7i	0.614899	−	0.682915i	0.967503	+	0.252858i	$0.0813705\pi$
$858$	7.04734e6	−	6.70510e7i	0.326819	−	3.10947i
$859$	2.16434e7	−	4.60045e6i	1.00079	−	0.212724i	0.321749	−	0.946825i	$-0.395729\pi$
$859$	2.16434e7	−	4.60045e6i	1.00079	−	0.212724i	0.679040	+	0.734101i	$0.262396\pi$
$860$	2.20879e6	−	6.79795e6i	0.101838	−	0.313424i
$861$	−5.53604e7	−	1.17672e7i	−2.54502	−	0.540961i
$862$	5.24419e6	−	9.08321e6i	0.240387	−	0.416362i
$863$	−4.15538e6	−	7.19733e6i	−0.189926	−	0.328961i	0.755300	−	0.655380i	$-0.227491\pi$
$863$	−4.15538e6	−	7.19733e6i	−0.189926	−	0.328961i	−0.945225	+	0.326419i	$0.894158\pi$
$864$	2.25562e6	+	6.94208e6i	0.102797	+	0.316377i
$865$	4.97907e6	+	4.73727e7i	0.226260	+	2.15272i
$866$	−3.96696e6	−	2.88217e6i	−0.179748	−	0.130594i
$867$	−3.83718e7			−1.73366
$868$	−1.12207e7	−	289591.i	−0.505502	−	0.0130462i
$869$	721205.			0.0323973
$870$	2.00154e7	+	1.45420e7i	0.896531	+	0.651368i
$871$	−5.96663e6	−	5.67687e7i	−0.266492	−	2.53550i
$872$	2.69636e6	+	8.29855e6i	0.120084	+	0.369582i
$873$	−1.62523e7	−	2.81498e7i	−0.721737	−	1.25008i
$874$	−138932.	+	240637.i	−0.00615210	+	0.0106557i
$875$	−3.96912e6	−	843663.i	−0.175257	−	0.0372520i
$876$	2.39796e6	−	7.38018e6i	0.105580	−	0.324942i
$877$	814272.	−	173079.i	0.0357496	−	0.00759880i	−0.190002	−	0.981784i	$-0.560850\pi$
$877$	814272.	−	173079.i	0.0357496	−	0.00759880i	0.225752	+	0.974185i	$0.427516\pi$
$878$	638596.	−	6.07583e6i	0.0279570	−	0.265993i
$879$	1.33892e7	−	1.48702e7i	0.584498	−	0.649151i
$880$	1.32523e7	−	5.90030e6i	0.576878	−	0.256843i
$881$	1.31862e7	+	5.87085e6i	0.572372	+	0.254836i	0.672449	−	0.740143i	$-0.265242\pi$
$881$	1.31862e7	+	5.87085e6i	0.572372	+	0.254836i	−0.100077	+	0.994980i	$0.531909\pi$
$882$	516943.	+	574123.i	0.0223754	+	0.0248504i
$883$	1.15592e6	−	839823.i	0.0498913	−	0.0362482i	−0.562560	−	0.826756i	$-0.690184\pi$
$883$	1.15592e6	−	839823.i	0.0498913	−	0.0362482i	0.612451	+	0.790508i	$0.290184\pi$
$884$	−1.35200e6	+	982285.i	−0.0581896	+	0.0422772i
$885$	6.00271e7	+	6.66668e7i	2.57626	+	2.86122i
$886$	9.44256e6	+	4.20410e6i	0.404115	+	0.179924i
$887$	−3.40083e7	+	1.51415e7i	−1.45136	+	0.646187i	−0.972754	−	0.231842i	$-0.925525\pi$
$887$	−3.40083e7	+	1.51415e7i	−1.45136	+	0.646187i	−0.478607	+	0.878029i	$0.658858\pi$
$888$	1.80889e7	−	2.00898e7i	0.769805	−	0.854955i
$889$	−3.32365e6	+	3.16224e7i	−0.141046	+	1.34196i
$890$	−2.33431e6	+	496174.i	−0.0987835	+	0.0209971i
$891$	−1.65755e7	+	5.10141e7i	−0.699475	+	2.15276i
$892$	8.22126e6	+	1.74748e6i	0.345960	+	0.0735361i
$893$	−364992.	+	632185.i	−0.0153163	+	0.0265287i
$894$	−7.27073e6	−	1.25933e7i	−0.304252	−	0.526981i
$895$	5.71053e6	+	1.75752e7i	0.238297	+	0.733404i
$896$	−224542.	−	2.13637e6i	−0.00934387	−	0.0889010i
$897$	6.59969e6	+	4.79495e6i	0.273869	+	0.198977i
$898$	−2.50842e6			−0.103803
$899$	−1.08988e7	+	1.14936e7i	−0.449757	+	0.474303i
$900$	2.19286e7			0.902410
$901$	−93582.4	−	67991.6i	−0.00384045	−	0.00279025i
$902$	4.89503e6	+	4.65731e7i	0.200327	+	1.90598i
$903$	−6.46979e6	−	1.99120e7i	−0.264041	−	0.812633i
$904$	−6.03347e6	−	1.04503e7i	−0.245554	−	0.425311i
$905$	2.38316e7	−	4.12775e7i	0.967234	−	1.67530i
$906$	2.51566e7	+	5.34720e6i	1.01820	+	0.216424i
$907$	5.44152e6	−	1.67473e7i	0.219635	−	0.675968i	−0.779157	−	0.626829i	$-0.784352\pi$
$907$	5.44152e6	−	1.67473e7i	0.219635	−	0.675968i	0.998792	−	0.0491387i	$-0.0156476\pi$
$908$	1.27240e6	−	270457.i	0.0512163	−	0.0108864i
$909$	−3.27491e6	+	3.11587e7i	−0.131459	+	1.25075i
$910$	−2.23259e7	+	2.47954e7i	−0.893728	+	0.992585i
$911$	−3.50357e7	+	1.55989e7i	−1.39867	+	0.622727i	−0.961035	−	0.276427i	$-0.910850\pi$
$911$	−3.50357e7	+	1.55989e7i	−1.39867	+	0.622727i	−0.437633	+	0.899154i	$0.644183\pi$
$912$	−1.23765e6	−	551038.i	−0.0492733	−	0.0219379i
$913$	−4.00623e7	−	4.44937e7i	−1.59059	−	1.76653i
$914$	−3.10712e6	+	2.25746e6i	−0.123025	+	0.0893827i
$915$	−3.85243e7	+	2.79895e7i	−1.52118	+	1.10520i
$916$	1.31712e7	+	1.46281e7i	0.518666	+	0.576037i
$917$	−2.24482e7	−	9.99460e6i	−0.881574	−	0.392502i
$918$	3.26946e6	−	1.45566e6i	0.128047	−	0.0570101i
$919$	−1.78508e7	+	1.98254e7i	−0.697220	+	0.774341i	−0.982931	−	0.183975i	$-0.941104\pi$
$919$	−1.78508e7	+	1.98254e7i	−0.697220	+	0.774341i	0.285711	+	0.958316i	$0.407770\pi$
$920$	−183472.	+	1.74562e6i	−0.00714662	+	0.0679956i
$921$	5.87302e7	−	1.24835e7i	2.28146	−	0.484938i
$922$	4.07621e6	−	1.25453e7i	0.157917	−	0.486019i
$923$	1.36776e7	+	2.90725e6i	0.528450	+	0.112326i
$924$	2.12455e7	−	3.67983e7i	0.818628	−	1.41791i
$925$	−2.10222e7	−	3.64116e7i	−0.807838	−	1.39922i
$926$	−8.27686e6	−	2.54736e7i	−0.317204	−	0.976252i
$927$	−8.99707e6	−	8.56014e7i	−0.343876	−	3.27176i
$928$	−2.45240e6	−	1.78177e6i	−0.0934805	−	0.0679175i
$929$	2.28894e7			0.870151			0.435076	−	0.900394i	$-0.356722\pi$
$929$	2.28894e7			0.870151			0.435076	+	0.900394i	$0.356722\pi$
$930$	−5.82007e6	+	4.43370e7i	−0.220659	+	1.68097i
$931$	−74232.9			−0.00280687
$932$	2.22975e6	+	1.62001e6i	0.0840847	+	0.0610911i
$933$	6.60078e6	+	6.28022e7i	0.248251	+	2.36195i
$934$	−9.17307e6	−	2.82318e7i	−0.344071	−	1.05894i
$935$	−3.55626e6	−	6.15962e6i	−0.133034	−	0.230422i
$936$	−1.34164e7	+	2.32379e7i	−0.500550	+	0.866977i
$937$	−1.43356e7	−	3.04712e6i	−0.533416	−	0.113381i	−0.0666746	−	0.997775i	$-0.521239\pi$
$937$	−1.43356e7	−	3.04712e6i	−0.533416	−	0.113381i	−0.466742	+	0.884394i	$0.654572\pi$
$938$	1.11169e7	−	3.42142e7i	0.412549	−	1.26970i
$939$	−7.00527e7	+	1.48902e7i	−2.59275	+	0.551107i
$940$	−482005.	+	4.58597e6i	−0.0177923	+	0.169282i
$941$	−2.28667e7	+	2.53960e7i	−0.841839	+	0.934957i	−0.998612	−	0.0526773i	$-0.983225\pi$
$941$	−2.28667e7	+	2.53960e7i	−0.841839	+	0.934957i	0.156772	+	0.987635i	$0.449891\pi$
$942$	−3.13100e7	+	1.39401e7i	−1.14963	+	0.511846i
$943$	−5.17638e6	−	2.30467e6i	−0.189560	−	0.0843976i
$944$	−7.35487e6	−	8.16841e6i	−0.268624	−	0.298337i
$945$	5.78073e7	−	4.19994e7i	2.10573	−	1.52990i
$946$	−1.40149e7	+	1.01825e7i	−0.509171	+	0.369934i
$947$	2.75355e7	+	3.05813e7i	0.997741	+	1.10810i	0.994139	+	0.108110i	$0.0344799\pi$
$947$	2.75355e7	+	3.05813e7i	0.997741	+	1.10810i	0.00360213	+	0.999994i	$0.498853\pi$
$948$	−388687.	−	173055.i	−0.0140469	−	0.00625407i
$949$	1.34913e7	−	6.00671e6i	0.486282	−	0.216507i
$950$	−1.40989e6	+	1.56584e6i	−0.0506847	+	0.0562911i
$951$	−2.28994e6	+	2.17873e7i	−0.0821054	+	0.781181i
$952$	−1.03022e6	+	218980.i	−0.0368414	+	0.00783089i
$953$	−233148.	+	717556.i	−0.00831572	+	0.0255932i	−0.955128	−	0.296192i	$-0.904283\pi$
$953$	−233148.	+	717556.i	−0.00831572	+	0.0255932i	0.946813	+	0.321786i	$0.104283\pi$
$954$	−1.81672e6	−	386157.i	−0.0646276	−	0.0137370i
$955$	9.03396e6	−	1.56473e7i	0.320531	−	0.555176i
$956$	329763.	+	571166.i	0.0116696	+	0.0202124i
$957$	−1.85289e7	−	5.70261e7i	−0.653989	−	2.01277i
$958$	1.14346e6	+	1.08793e7i	0.0402539	+	0.382991i
$959$	1.32029e7	+	9.59244e6i	0.463577	+	0.336808i
$960$	−8.55800e6			−0.299705
$961$	−2.76592e7	−	7.38891e6i	−0.966121	−	0.258090i
$962$	5.14476e7			1.79237
$963$	5.68673e7	+	4.13165e7i	1.97605	+	1.43568i
$964$	−119904.	−	1.14081e6i	−0.00415568	−	0.0395387i
$965$	−1.08672e7	−	3.34459e7i	−0.375665	−	1.15618i
$966$	2.57064e6	+	4.45248e6i	0.0886337	+	0.153518i
$967$	−2.34529e7	+	4.06216e7i	−0.806549	+	1.39698i	0.108692	+	0.994075i	$0.465334\pi$
$967$	−2.34529e7	+	4.06216e7i	−0.806549	+	1.39698i	−0.915241	+	0.402908i	$0.868000\pi$
$968$	−2.43076e7	−	5.16674e6i	−0.833784	−	0.177226i
$969$	−205264.	+	631738.i	−0.00702269	+	0.0216136i
$970$	1.92982e7	−	4.10197e6i	0.658550	−	0.139979i
$971$	4.87560e6	−	4.63882e7i	0.165951	−	1.57892i	−0.521862	−	0.853030i	$-0.674762\pi$
$971$	4.87560e6	−	4.63882e7i	0.165951	−	1.57892i	0.687813	−	0.725888i	$-0.258571\pi$
$972$	2.62947e6	−	2.92032e6i	0.0892694	−	0.0991438i
$973$	−5.86431e6	+	2.61096e6i	−0.198580	+	0.0884133i
$974$	−516598.	−	230004.i	−0.0174484	−	0.00776852i
$975$	4.13923e7	+	4.59708e7i	1.39447	+	1.54871i
$976$	4.72022e6	−	3.42944e6i	0.158613	−	0.115239i
$977$	−6.42041e6	+	4.66470e6i	−0.215192	+	0.156346i	−0.690160	−	0.723657i	$-0.742460\pi$
$977$	−6.42041e6	+	4.66470e6i	−0.215192	+	0.156346i	0.474968	+	0.880003i	$0.342460\pi$
$978$	−3.50711e7	−	3.89504e7i	−1.17247	−	1.30216i
$979$	5.28381e6	+	2.35250e6i	0.176194	+	0.0784465i
$980$	−428382.	+	190728.i	−0.0142484	+	0.00634379i
$981$	4.59639e7	−	5.10481e7i	1.52491	−	1.69359i
$982$	696870.	−	6.63027e6i	0.0230607	−	0.219408i
$983$	8.68532e6	−	1.84612e6i	0.286683	−	0.0609364i	−0.0623256	−	0.998056i	$-0.519852\pi$
$983$	8.68532e6	−	1.84612e6i	0.286683	−	0.0609364i	0.349009	+	0.937120i	$0.386518\pi$
$984$	8.53719e6	−	2.62748e7i	0.281078	−	0.865069i
$985$	−1.35067e7	−	2.87094e6i	−0.443567	−	0.0942831i
$986$	−743131.	+	1.28714e6i	−0.0243430	+	0.0421632i
$987$	6.75341e6	+	1.16973e7i	0.220663	+	0.382200i
$988$	−796735.	−	2.45210e6i	−0.0259670	−	0.0799182i
$989$	−219101.	−	2.08460e6i	−0.00712283	−	0.0677692i
$990$	−9.23908e7	−	6.71259e7i	−2.99599	−	2.17672i
$991$	−6.73591e6			−0.217877			−0.108939	−	0.994048i	$-0.534745\pi$
$991$	−6.73591e6			−0.217877			−0.108939	+	0.994048i	$0.534745\pi$
$992$	713109.	−	5.43243e6i	0.0230079	−	0.175273i
$993$	−1.26744e7			−0.407901
$994$	7.12964e6	+	5.17999e6i	0.228877	+	0.166289i
$995$	−1.08403e6	−	1.03139e7i	−0.0347123	−	0.330266i
$996$	1.09149e7	+	3.35926e7i	0.348635	+	1.07299i
$997$	1.74729e7	+	3.02639e7i	0.556707	+	0.964244i	0.997769	+	0.0667674i	$0.0212685\pi$
$997$	1.74729e7	+	3.02639e7i	0.556707	+	0.964244i	−0.441062	+	0.897477i	$0.645398\pi$
$998$	1.45424e7	−	2.51883e7i	0.462180	−	0.800519i
$999$	−1.07770e8	−	2.29072e7i	−3.41651	−	0.726202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.6.g.a.41.1	✓	56
31.28	even	15	inner	62.6.g.a.59.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.g.a.41.1	✓	56	1.1	even	1	trivial
62.6.g.a.59.1	yes	56	31.28	even	15	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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23607 - 2.35114i) q^{2} +(-2.85659 - 27.1786i) q^{3} +(4.94427 + 15.2169i) q^{4} +(38.2269 + 66.2110i) q^{5} +(-54.6567 + 94.6681i) q^{6} +(-128.247 - 27.2597i) q^{7} +(19.7771 - 60.8676i) q^{8} +(-492.827 + 104.754i) q^{9} +(31.9664 - 304.140i) q^{10} +(-495.944 + 550.801i) q^{11} +(399.451 - 177.847i) q^{12} +(760.197 + 338.462i) q^{13} +(350.924 + 389.741i) q^{14} +(1690.32 - 1228.09i) q^{15} +(-207.108 + 150.473i) q^{16} +(83.9872 + 93.2773i) q^{17} +(1841.11 + 819.717i) q^{18} +(-176.907 + 78.7642i) q^{19} +(-818.522 + 909.061i) q^{20} +(-374.533 + 3563.44i) q^{21} +(2899.92 - 616.397i) q^{22} +(-110.851 + 341.164i) q^{23} +(-1710.79 - 363.640i) q^{24} +(-1360.10 + 2355.76i) q^{25} +(-1664.28 - 2882.62i) q^{26} +(2202.75 + 6779.37i) q^{27} +(-219.279 - 2086.30i) q^{28} +(-2394.92 - 1740.01i) q^{29} -8357.42 q^{30} +(696.395 - 5305.11i) q^{31} +1024.00 q^{32} +(16386.7 + 11905.7i) q^{33} +(-52.4804 - 499.317i) q^{34} +(-3097.59 - 9533.40i) q^{35} +(-4030.70 - 6981.38i) q^{36} +(-7728.21 + 13385.7i) q^{37} +(757.669 + 161.048i) q^{38} +(7027.35 - 21628.0i) q^{39} +(4786.12 - 1017.32i) q^{40} +(-1651.10 + 15709.2i) q^{41} +(9590.17 - 10651.0i) q^{42} +(-5338.05 + 2376.65i) q^{43} +(-10833.6 - 4823.42i) q^{44} +(-25775.1 - 28626.2i) q^{45} +(1160.84 - 843.403i) q^{46} +(3049.69 - 2215.73i) q^{47} +(4681.27 + 5199.08i) q^{48} +(350.196 + 155.917i) q^{49} +(9940.08 - 4425.61i) q^{50} +(2295.23 - 2549.11i) q^{51} +(-1391.72 + 13241.3i) q^{52} +(-901.444 + 191.608i) q^{53} +(8811.00 - 27117.5i) q^{54} +(-55427.5 - 11781.5i) q^{55} +(-4195.58 + 7266.96i) q^{56} +(2646.05 + 4583.10i) q^{57} +(3659.11 + 11261.6i) q^{58} +(4488.06 + 42701.0i) q^{59} +(27045.2 + 19649.5i) q^{60} -22791.1 q^{61} +(-14726.6 + 15530.4i) q^{62} +66059.1 q^{63} +(-3313.73 - 2407.57i) q^{64} +(6650.13 + 63271.8i) q^{65} +(-25036.7 - 77055.0i) q^{66} +(-34298.0 - 59405.8i) q^{67} +(-1004.14 + 1739.21i) q^{68} +(9589.01 + 2038.21i) q^{69} +(-12390.4 + 38133.6i) q^{70} +(16436.6 - 3493.71i) q^{71} +(-3370.58 + 32069.0i) q^{72} +(11875.1 - 13188.7i) q^{73} +(56480.6 - 25146.8i) q^{74} +(67911.4 + 30236.1i) q^{75} +(-2073.22 - 2302.55i) q^{76} +(78617.9 - 57119.2i) q^{77} +(-73591.4 + 53467.3i) q^{78} +(-651.100 - 723.120i) q^{79} +(-17880.1 - 7960.73i) q^{80} +(66113.9 - 29435.8i) q^{81} +(42277.6 - 46954.0i) q^{82} +(-8443.81 + 80337.5i) q^{83} +(-56076.3 + 11919.4i) q^{84} +(-2965.41 + 9126.58i) q^{85} +(22862.1 + 4859.50i) q^{86} +(-40449.8 + 70061.1i) q^{87} +(23717.6 + 41080.2i) q^{88} +(-2411.45 - 7421.67i) q^{89} +(16105.9 + 153237. i) q^{90} +(-88266.5 - 64129.4i) q^{91} -5739.53 q^{92} +(-146175. - 3772.55i) q^{93} -15078.5 q^{94} +(-11977.7 - 8702.29i) q^{95} +(-2925.15 - 27830.9i) q^{96} +(19935.9 + 61356.5i) q^{97} +(-766.675 - 1327.92i) q^{98} +(186716. - 323402. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 56 q^{2} + 11 q^{3} - 224 q^{4} - 33 q^{5} - 136 q^{6} + 104 q^{7} - 896 q^{8} + 524 q^{9} + 448 q^{10} - 795 q^{11} + 176 q^{12} + 764 q^{13} - 1384 q^{14} - 3208 q^{15} - 3584 q^{16} + 2440 q^{17}+ \cdots - 168255 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 + 11 * q^3 - 224 * q^4 - 33 * q^5 - 136 * q^6 + 104 * q^7 - 896 * q^8 + 524 * q^9 + 448 * q^10 - 795 * q^11 + 176 * q^12 + 764 * q^13 - 1384 * q^14 - 3208 * q^15 - 3584 * q^16 + 2440 * q^17 + 2716 * q^18 - 2747 * q^19 + 1952 * q^20 + 4909 * q^21 + 7500 * q^22 - 11297 * q^23 + 384 * q^24 - 21385 * q^25 - 14064 * q^26 - 12466 * q^27 + 1424 * q^28 - 11901 * q^29 + 20008 * q^30 - 4745 * q^31 + 57344 * q^32 + 2812 * q^33 + 7160 * q^34 + 17912 * q^35 - 38496 * q^36 - 54498 * q^37 + 9552 * q^38 - 38158 * q^39 + 7808 * q^40 + 56747 * q^41 + 61396 * q^42 + 69670 * q^43 - 22320 * q^44 + 54688 * q^45 + 22412 * q^46 - 63503 * q^47 + 1536 * q^48 + 9721 * q^49 + 16580 * q^50 + 87134 * q^51 + 12224 * q^52 + 48127 * q^53 - 49864 * q^54 - 150047 * q^55 - 6464 * q^56 - 142312 * q^57 - 36764 * q^58 - 105890 * q^59 - 51328 * q^60 + 383664 * q^61 - 10700 * q^62 - 236690 * q^63 - 57344 * q^64 + 284638 * q^65 + 46348 * q^66 - 59674 * q^67 - 75120 * q^68 + 213337 * q^69 + 71648 * q^70 - 186679 * q^71 + 43456 * q^72 - 132007 * q^73 - 29932 * q^74 + 186494 * q^75 + 97728 * q^76 + 208527 * q^77 + 71688 * q^78 - 229841 * q^79 - 82688 * q^80 - 503164 * q^81 - 234012 * q^82 - 634514 * q^83 - 165056 * q^84 + 129149 * q^85 + 60740 * q^86 + 297951 * q^87 - 33600 * q^88 + 78674 * q^89 + 290652 * q^90 + 127680 * q^91 + 182208 * q^92 + 427164 * q^93 + 143528 * q^94 + 293666 * q^95 + 11264 * q^96 - 94321 * q^97 - 291156 * q^98 - 168255 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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