LMFDB - Embedded newform 33.8.d.b.32.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [33,8,Mod(32,33)] 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("33.32"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	33.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] 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:	$10.3087058410$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			32.2
Character	$\chi$	$=$	33.32
Dual form			33.8.d.b.32.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-21.2791 q^{2} +(13.2650 + 44.8446i) q^{3} +324.799 q^{4} -116.081i q^{5} +(-282.268 - 954.252i) q^{6} +73.6975i q^{7} -4187.71 q^{8} +(-1835.08 + 1189.73i) q^{9} +2470.10i q^{10} +(1337.24 - 4207.01i) q^{11} +(4308.48 + 14565.5i) q^{12} -11437.6i q^{13} -1568.22i q^{14} +(5205.60 - 1539.82i) q^{15} +47536.4 q^{16} +19264.4 q^{17} +(39048.8 - 25316.4i) q^{18} +42528.5i q^{19} -37703.0i q^{20} +(-3304.93 + 977.600i) q^{21} +(-28455.2 + 89521.4i) q^{22} -38757.4i q^{23} +(-55550.2 - 187796. i) q^{24} +64650.2 q^{25} +243381. i q^{26} +(-77695.4 - 66511.5i) q^{27} +23936.9i q^{28} +115979. q^{29} +(-110771. + 32765.9i) q^{30} +157493. q^{31} -475503. q^{32} +(206400. + 4161.63i) q^{33} -409928. q^{34} +8554.87 q^{35} +(-596032. + 386424. i) q^{36} -205289. q^{37} -904967. i q^{38} +(512913. - 151720. i) q^{39} +486114. i q^{40} +457481. q^{41} +(70326.0 - 20802.4i) q^{42} -215319. i q^{43} +(434334. - 1.36644e6i) q^{44} +(138105. + 213018. i) q^{45} +824722. i q^{46} +682721. i q^{47} +(630572. + 2.13175e6i) q^{48} +818112. q^{49} -1.37570e6 q^{50} +(255543. + 863903. i) q^{51} -3.71491e6i q^{52} -1.29875e6i q^{53} +(1.65329e6 + 1.41530e6i) q^{54} +(-488354. - 155228. i) q^{55} -308624. i q^{56} +(-1.90717e6 + 564142. i) q^{57} -2.46794e6 q^{58} +2.61276e6i q^{59} +(1.69078e6 - 500132. i) q^{60} -1.67910e6i q^{61} -3.35131e6 q^{62} +(-87680.2 - 135241. i) q^{63} +4.03362e6 q^{64} -1.32768e6 q^{65} +(-4.39201e6 - 88555.7i) q^{66} +2.45218e6 q^{67} +6.25706e6 q^{68} +(1.73806e6 - 514118. i) q^{69} -182040. q^{70} -658125. i q^{71} +(7.68478e6 - 4.98225e6i) q^{72} -1.22508e6i q^{73} +4.36836e6 q^{74} +(857588. + 2.89921e6i) q^{75} +1.38132e7i q^{76} +(310046. + 98551.0i) q^{77} +(-1.09143e7 + 3.22845e6i) q^{78} -6.39822e6i q^{79} -5.51807e6i q^{80} +(1.95205e6 - 4.36650e6i) q^{81} -9.73478e6 q^{82} -8.51697e6 q^{83} +(-1.07344e6 + 317524. i) q^{84} -2.23623e6i q^{85} +4.58180e6i q^{86} +(1.53847e6 + 5.20105e6i) q^{87} +(-5.59996e6 + 1.76178e7i) q^{88} -2.50924e6i q^{89} +(-2.93875e6 - 4.53282e6i) q^{90} +842919. q^{91} -1.25884e7i q^{92} +(2.08915e6 + 7.06272e6i) q^{93} -1.45277e7i q^{94} +4.93675e6 q^{95} +(-6.30757e6 - 2.13238e7i) q^{96} +5.77174e6 q^{97} -1.74087e7 q^{98} +(2.55128e6 + 9.31115e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9} - 6936 q^{12} + 23160 q^{15} + 5844 q^{16} - 17556 q^{22} - 34704 q^{25} + 7560 q^{27} + 131328 q^{31} + 28644 q^{33} - 436080 q^{34} - 302832 q^{36} + 1072488 q^{37}+ \cdots + 53650080 q^{99}+O(q^{100}) $ 24 * q + 120 * q^3 + 1788 * q^4 - 5940 * q^9 - 6936 * q^12 + 23160 * q^15 + 5844 * q^16 - 17556 * q^22 - 34704 * q^25 + 7560 * q^27 + 131328 * q^31 + 28644 * q^33 - 436080 * q^34 - 302832 * q^36 + 1072488 * q^37 - 100296 * q^42 - 1854252 * q^45 + 3172548 * q^48 - 1169304 * q^49 - 4401936 * q^55 - 2920440 * q^58 + 1981452 * q^60 + 14578596 * q^64 + 2895156 * q^66 + 7729200 * q^67 - 4614108 * q^69 - 6924504 * q^70 - 4375800 * q^75 - 26237448 * q^78 + 22367340 * q^81 - 23600232 * q^82 - 25179660 * q^88 + 9380640 * q^91 + 25396908 * q^93 + 72948360 * q^97 + 53650080 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−21.2791			−1.88082			−0.940412	−	0.340038i	$-0.889560\pi$
$2$	−21.2791			−1.88082			−0.940412	+	0.340038i	$0.889560\pi$
$3$	13.2650	+	44.8446i	0.283651	+	0.958928i
$3$	13.2650	+	44.8446i	0.283651	+	0.958928i
$4$	324.799			2.53750
$5$		−	116.081i		−	0.415304i	−0.978203	−	0.207652i	$-0.933418\pi$
$5$		−	116.081i		−	0.415304i	0.978203	−	0.207652i	$-0.0665821\pi$
$6$	−282.268	−	954.252i	−0.533497	−	1.80357i
$7$			73.6975i			0.0812100i	0.999175	+	0.0406050i	$0.0129285\pi$
$7$			73.6975i			0.0812100i	−0.999175	+	0.0406050i	$0.987071\pi$
$8$	−4187.71			−2.89176
$9$	−1835.08	+	1189.73i	−0.839084	+	0.544001i
$10$			2470.10i			0.781113i
$11$	1337.24	−	4207.01i	0.302924	−	0.953015i
$11$	1337.24	−	4207.01i	0.302924	−	0.953015i
$12$	4308.48	+	14565.5i	0.719763	+	2.43327i
$13$		−	11437.6i		−	1.44388i	−0.691955	−	0.721940i	$-0.743250\pi$
$13$		−	11437.6i		−	1.44388i	0.691955	−	0.721940i	$-0.256750\pi$
$14$		−	1568.22i		−	0.152742i
$15$	5205.60	−	1539.82i	0.398246	−	0.117801i
$16$	47536.4			2.90139
$17$	19264.4			0.951007			0.475503	−	0.879714i	$-0.342266\pi$
$17$	19264.4			0.951007			0.475503	+	0.879714i	$0.342266\pi$
$18$	39048.8	−	25316.4i	1.57817	−	1.02317i
$19$			42528.5i			1.42247i	0.702956	+	0.711234i	$0.251863\pi$
$19$			42528.5i			1.42247i	−0.702956	+	0.711234i	$0.748137\pi$
$20$		−	37703.0i		−	1.05383i
$21$	−3304.93	+	977.600i	−0.0778745	+	0.0230353i
$22$	−28455.2	+	89521.4i	−0.569747	+	1.79245i
$23$		−	38757.4i		−	0.664212i	−0.943242	−	0.332106i	$-0.892241\pi$
$23$		−	38757.4i		−	0.664212i	0.943242	−	0.332106i	$-0.107759\pi$
$24$	−55550.2	−	187796.i	−0.820250	−	2.77299i
$25$	64650.2			0.827523
$26$			243381.i			2.71568i
$27$	−77695.4	−	66511.5i	−0.759665	−	0.650315i
$28$			23936.9i			0.206070i
$29$	115979.			0.883056			0.441528	−	0.897247i	$-0.354437\pi$
$29$	115979.			0.883056			0.441528	+	0.897247i	$0.354437\pi$
$30$	−110771.	+	32765.9i	−0.749031	+	0.221563i
$31$	157493.			0.949502			0.474751	−	0.880120i	$-0.342538\pi$
$31$	157493.			0.949502			0.474751	+	0.880120i	$0.342538\pi$
$32$	−475503.			−2.56524
$33$	206400.	+	4161.63i	0.999797	+	0.0201588i
$34$	−409928.			−1.78868
$35$	8554.87			0.0337268
$36$	−596032.	+	386424.i	−2.12917	+	1.38040i
$37$	−205289.			−0.666284			−0.333142	−	0.942877i	$-0.608109\pi$
$37$	−205289.			−0.666284			−0.333142	+	0.942877i	$0.608109\pi$
$38$		−	904967.i		−	2.67541i
$39$	512913.	−	151720.i	1.38458	−	0.409558i
$40$			486114.i			1.20096i
$41$	457481.			1.03664			0.518322	−	0.855185i	$-0.326557\pi$
$41$	457481.			1.03664			0.518322	+	0.855185i	$0.326557\pi$
$42$	70326.0	−	20802.4i	0.146468	−	0.0433253i
$43$		−	215319.i		−	0.412994i	−0.978447	−	0.206497i	$-0.933794\pi$
$43$		−	215319.i		−	0.412994i	0.978447	−	0.206497i	$-0.0662063\pi$
$44$	434334.	−	1.36644e6i	0.768669	−	2.41827i
$45$	138105.	+	213018.i	0.225926	+	0.348475i
$46$			824722.i			1.24927i
$47$			682721.i			0.959181i	0.877492	+	0.479591i	$0.159215\pi$
$47$			682721.i			0.959181i	−0.877492	+	0.479591i	$0.840785\pi$
$48$	630572.	+	2.13175e6i	0.822982	+	2.78222i
$49$	818112.			0.993405
$50$	−1.37570e6			−1.55642
$51$	255543.	+	863903.i	0.269754	+	0.911947i
$52$		−	3.71491e6i		−	3.66384i
$53$		−	1.29875e6i		−	1.19829i	−0.800642	−	0.599143i	$-0.795508\pi$
$53$		−	1.29875e6i		−	1.19829i	0.800642	−	0.599143i	$-0.204492\pi$
$54$	1.65329e6	+	1.41530e6i	1.42880	+	1.22313i
$55$	−488354.	−	155228.i	−0.395791	−	0.125806i
$56$		−	308624.i		−	0.234840i
$57$	−1.90717e6	+	564142.i	−1.36404	+	0.403484i
$58$	−2.46794e6			−1.66087
$59$			2.61276e6i			1.65622i	0.560567	+	0.828109i	$0.310583\pi$
$59$			2.61276e6i			1.65622i	−0.560567	+	0.828109i	$0.689417\pi$
$60$	1.69078e6	−	500132.i	1.01055	−	0.298920i
$61$		−	1.67910e6i		−	0.947156i	−0.880752	−	0.473578i	$-0.842962\pi$
$61$		−	1.67910e6i		−	0.947156i	0.880752	−	0.473578i	$-0.157038\pi$
$62$	−3.35131e6			−1.78585
$63$	−87680.2	−	135241.i	−0.0441783	−	0.0681420i
$64$	4.03362e6			1.92338
$65$	−1.32768e6			−0.599649
$66$	−4.39201e6	−	88555.7i	−1.88044	−	0.0379152i
$67$	2.45218e6			0.996070			0.498035	−	0.867157i	$-0.334055\pi$
$67$	2.45218e6			0.996070			0.498035	+	0.867157i	$0.334055\pi$
$68$	6.25706e6			2.41318
$69$	1.73806e6	−	514118.i	0.636932	−	0.188404i
$70$	−182040.			−0.0634342
$71$		−	658125.i		−	0.218225i	−0.994029	−	0.109112i	$-0.965199\pi$
$71$		−	658125.i		−	0.218225i	0.994029	−	0.109112i	$-0.0348009\pi$
$72$	7.68478e6	−	4.98225e6i	2.42643	−	1.57312i
$73$		−	1.22508e6i		−	0.368583i	−0.982872	−	0.184291i	$-0.941001\pi$
$73$		−	1.22508e6i		−	0.368583i	0.982872	−	0.184291i	$-0.0589990\pi$
$74$	4.36836e6			1.25316
$75$	857588.	+	2.89921e6i	0.234728	+	0.793534i
$76$			1.38132e7i			3.60950i
$77$	310046.	+	98551.0i	0.0773943	+	0.0246005i
$78$	−1.09143e7	+	3.22845e6i	−2.60415	+	0.770306i
$79$		−	6.39822e6i		−	1.46004i	−0.683426	−	0.730020i	$-0.739511\pi$
$79$		−	6.39822e6i		−	1.46004i	0.683426	−	0.730020i	$-0.260489\pi$
$80$		−	5.51807e6i		−	1.20496i
$81$	1.95205e6	−	4.36650e6i	0.408125	−	0.912926i
$82$	−9.73478e6			−1.94975
$83$	−8.51697e6			−1.63498			−0.817488	−	0.575945i	$-0.804634\pi$
$83$	−8.51697e6			−1.63498			−0.817488	+	0.575945i	$0.804634\pi$
$84$	−1.07344e6	+	317524.i	−0.197606	+	0.0584520i
$85$		−	2.23623e6i		−	0.394957i
$86$			4.58180e6i			0.776768i
$87$	1.53847e6	+	5.20105e6i	0.250480	+	0.846787i
$88$	−5.59996e6	+	1.76178e7i	−0.875983	+	2.75589i
$89$		−	2.50924e6i		−	0.377292i	−0.982045	−	0.188646i	$-0.939590\pi$
$89$		−	2.50924e6i		−	0.377292i	0.982045	−	0.188646i	$-0.0604099\pi$
$90$	−2.93875e6	−	4.53282e6i	−0.424927	−	0.655420i
$91$	842919.			0.117258
$92$		−	1.25884e7i		−	1.68544i
$93$	2.08915e6	+	7.06272e6i	0.269327	+	0.910504i
$94$		−	1.45277e7i		−	1.80405i
$95$	4.93675e6			0.590756
$96$	−6.30757e6	−	2.13238e7i	−0.727634	−	2.45988i
$97$	5.77174e6			0.642104			0.321052	−	0.947062i	$-0.395964\pi$
$97$	5.77174e6			0.642104			0.321052	+	0.947062i	$0.395964\pi$
$98$	−1.74087e7			−1.86842
$99$	2.55128e6	+	9.31115e6i	0.264262	+	0.964451i
$100$	2.09984e7			2.09984
$101$	−4.05710e6			−0.391823			−0.195912	−	0.980622i	$-0.562767\pi$
$101$	−4.05710e6			−0.391823			−0.195912	+	0.980622i	$0.562767\pi$
$102$	−5.43771e6	−	1.83831e7i	−0.507359	−	1.71521i
$103$	−1.06050e7			−0.956267			−0.478133	−	0.878287i	$-0.658686\pi$
$103$	−1.06050e7			−0.956267			−0.478133	+	0.878287i	$0.658686\pi$
$104$			4.78972e7i			4.17535i
$105$	113481.	+	383640.i	0.00956664	+	0.0323416i
$106$			2.76362e7i			2.25376i
$107$	1.68359e7			1.32860			0.664298	−	0.747468i	$-0.268731\pi$
$107$	1.68359e7			1.32860			0.664298	+	0.747468i	$0.268731\pi$
$108$	−2.52354e7	−	2.16029e7i	−1.92765	−	1.65017i
$109$			4.01015e6i			0.296597i	0.988943	+	0.148299i	$0.0473797\pi$
$109$			4.01015e6i			0.296597i	−0.988943	+	0.148299i	$0.952620\pi$
$110$	1.03917e7	+	3.30310e6i	0.744412	+	0.236618i
$111$	−2.72317e6	−	9.20610e6i	−0.188992	−	0.638918i
$112$			3.50331e6i			0.235622i
$113$		−	3.24480e6i		−	0.211550i	−0.994390	−	0.105775i	$-0.966268\pi$
$113$		−	3.24480e6i		−	0.211550i	0.994390	−	0.105775i	$-0.0337324\pi$
$114$	4.05829e7	−	1.20044e7i	2.56552	−	0.758882i
$115$	−4.49899e6			−0.275850
$116$	3.76701e7			2.24075
$117$	1.36076e7	+	2.09888e7i	0.785473	+	1.21154i
$118$		−	5.55972e7i		−	3.11505i
$119$			1.41974e6i			0.0772313i
$120$	−2.17996e7	+	6.44832e6i	−1.15163	+	0.340653i
$121$	−1.59108e7	−	1.12515e7i	−0.816474	−	0.577382i
$122$			3.57297e7i			1.78143i
$123$	6.06851e6	+	2.05156e7i	0.294045	+	0.994067i
$124$	5.11537e7			2.40936
$125$		−	1.65735e7i		−	0.758977i
$126$	1.86575e6	+	2.87780e6i	0.0830917	+	0.128163i
$127$		−	2.48533e7i		−	1.07664i	−0.842739	−	0.538322i	$-0.819059\pi$
$127$		−	2.48533e7i		−	1.07664i	0.842739	−	0.538322i	$-0.180941\pi$
$128$	−2.49673e7			−1.05229
$129$	9.65591e6	−	2.85622e6i	0.396031	−	0.117146i
$130$	2.82519e7			1.12783
$131$	2.73219e7			1.06185			0.530924	−	0.847420i	$-0.321845\pi$
$131$	2.73219e7			1.06185			0.530924	+	0.847420i	$0.321845\pi$
$132$	6.70387e7	+	1.35170e6i	2.53698	+	0.0511529i
$133$	−3.13424e6			−0.115519
$134$	−5.21801e7			−1.87343
$135$	−7.72072e6	+	9.01895e6i	−0.270078	+	0.315492i
$136$	−8.06737e7			−2.75008
$137$		−	1.91331e7i		−	0.635716i	−0.948138	−	0.317858i	$-0.897036\pi$
$137$		−	1.91331e7i		−	0.635716i	0.948138	−	0.317858i	$-0.102964\pi$
$138$	−3.69843e7	+	1.09400e7i	−1.19796	+	0.354355i
$139$		−	8.95211e6i		−	0.282731i	−0.989957	−	0.141366i	$-0.954851\pi$
$139$		−	8.95211e6i		−	0.282731i	0.989957	−	0.141366i	$-0.0451493\pi$
$140$	2.77862e6			0.0855817
$141$	−3.06164e7	+	9.05632e6i	−0.919786	+	0.272073i
$142$			1.40043e7i			0.410442i
$143$	−4.81180e7	−	1.52947e7i	−1.37604	−	0.437386i
$144$	−8.72329e7	+	5.65555e7i	−2.43451	+	1.57836i
$145$		−	1.34630e7i		−	0.366737i
$146$			2.60686e7i			0.693239i
$147$	1.08523e7	+	3.66879e7i	0.281780	+	0.952603i
$148$	−6.66778e7			−1.69069
$149$	96814.2			0.00239766			0.00119883	−	0.999999i	$-0.499618\pi$
$149$	96814.2			0.00239766			0.00119883	+	0.999999i	$0.499618\pi$
$150$	−1.82487e7	−	6.16926e7i	−0.441481	−	1.49250i
$151$			6.10092e7i			1.44204i	0.692917	+	0.721018i	$0.256325\pi$
$151$			6.10092e7i			1.44204i	−0.692917	+	0.721018i	$0.743675\pi$
$152$		−	1.78097e8i		−	4.11343i
$153$	−3.53516e7	+	2.29194e7i	−0.797975	+	0.517349i
$154$	−6.59750e6	−	2.09707e6i	−0.145565	−	0.0462691i
$155$		−	1.82820e7i		−	0.394332i
$156$	1.66594e8	−	4.92784e7i	3.51336	−	1.03925i
$157$	−1.55235e7			−0.320141			−0.160071	−	0.987106i	$-0.551172\pi$
$157$	−1.55235e7			−0.320141			−0.160071	+	0.987106i	$0.551172\pi$
$158$			1.36148e8i			2.74608i
$159$	5.82420e7	−	1.72280e7i	1.14907	−	0.339895i
$160$			5.51969e7i			1.06536i
$161$	2.85632e6			0.0539407
$162$	−4.15378e7	+	9.29151e7i	−0.767611	+	1.71705i
$163$	1.97076e7			0.356432			0.178216	−	0.983991i	$-0.442967\pi$
$163$	1.97076e7			0.356432			0.178216	+	0.983991i	$0.442967\pi$
$164$	1.48590e8			2.63048
$165$	483086.	−	2.39592e7i	0.00837203	−	0.415219i
$166$	1.81233e8			3.07510
$167$	−4.16534e7			−0.692058			−0.346029	−	0.938224i	$-0.612470\pi$
$167$	−4.16534e7			−0.692058			−0.346029	+	0.938224i	$0.612470\pi$
$168$	1.38401e7	−	4.09391e6i	0.225194	−	0.0666125i
$169$	−6.80691e7			−1.08479
$170$			4.75849e7i			0.742844i
$171$	−5.05974e7	−	7.80431e7i	−0.773824	−	1.19357i
$172$		−	6.99356e7i		−	1.04797i
$173$	−5.29067e7			−0.776871			−0.388436	−	0.921476i	$-0.626984\pi$
$173$	−5.29067e7			−0.776871			−0.388436	+	0.921476i	$0.626984\pi$
$174$	−3.27373e7	−	1.10674e8i	−0.471108	−	1.59266i
$175$			4.76456e6i			0.0672031i
$176$	6.35674e7	−	1.99986e8i	0.878901	−	2.76507i
$177$	−1.17168e8	+	3.46584e7i	−1.58819	+	0.469788i
$178$			5.33944e7i			0.709620i
$179$			1.87430e7i			0.244260i	0.992514	+	0.122130i	$0.0389725\pi$
$179$			1.87430e7i			0.244260i	−0.992514	+	0.122130i	$0.961027\pi$
$180$	4.48565e7	+	6.91880e7i	0.573286	+	0.884254i
$181$	1.34869e7			0.169059			0.0845293	−	0.996421i	$-0.473061\pi$
$181$	1.34869e7			0.169059			0.0845293	+	0.996421i	$0.473061\pi$
$182$	−1.79365e7			−0.220541
$183$	7.52985e7	−	2.22733e7i	0.908254	−	0.268662i
$184$			1.62305e8i			1.92074i
$185$			2.38301e7i			0.276710i
$186$	−4.44553e7	−	1.50288e8i	−0.506557	−	1.71250i
$187$	2.57610e7	−	8.10455e7i	0.288083	−	0.906323i
$188$			2.21747e8i			2.43392i
$189$	4.90173e6	−	5.72595e6i	0.0528121	−	0.0616924i
$190$	−1.05049e8			−1.11111
$191$		−	8.65128e7i		−	0.898387i	−0.893434	−	0.449194i	$-0.851711\pi$
$191$		−	8.65128e7i		−	0.898387i	0.893434	−	0.449194i	$-0.148289\pi$
$192$	5.35061e7	+	1.80886e8i	0.545568	+	1.84438i
$193$			1.50178e8i			1.50368i	0.659347	+	0.751838i	$0.270833\pi$
$193$			1.50178e8i			1.50368i	−0.659347	+	0.751838i	$0.729167\pi$
$194$	−1.22817e8			−1.20768
$195$	−1.76118e7	−	5.95394e7i	−0.170091	−	0.575020i
$196$	2.65722e8			2.52076
$197$	−8.80966e7			−0.820971			−0.410485	−	0.911867i	$-0.634641\pi$
$197$	−8.80966e7			−0.820971			−0.410485	+	0.911867i	$0.634641\pi$
$198$	−5.42890e7	−	1.98133e8i	−0.497031	−	1.81396i
$199$	−6.12483e6			−0.0550945			−0.0275472	−	0.999621i	$-0.508770\pi$
$199$	−6.12483e6			−0.0550945			−0.0275472	+	0.999621i	$0.508770\pi$
$200$	−2.70737e8			−2.39300
$201$	3.25282e7	+	1.09967e8i	0.282536	+	0.955159i
$202$	8.63313e7			0.736951
$203$			8.54740e6i			0.0717130i
$204$	8.30001e7	+	2.80595e8i	0.684499	+	2.31406i
$205$		−	5.31049e7i		−	0.430522i
$206$	2.25664e8			1.79857
$207$	4.61109e7	+	7.11228e7i	0.361332	+	0.557330i
$208$		−	5.43700e8i		−	4.18926i
$209$	1.78918e8	+	5.68706e7i	1.35563	+	0.430900i
$210$	−2.41477e6	−	8.16351e6i	−0.0179932	−	0.0608288i
$211$			1.45369e8i			1.06533i	0.846327	+	0.532664i	$0.178809\pi$
$211$			1.45369e8i			1.06533i	−0.846327	+	0.532664i	$0.821191\pi$
$212$		−	4.21834e8i		−	3.04065i
$213$	2.95134e7	−	8.73006e6i	0.209262	−	0.0618997i
$214$	−3.58253e8			−2.49885
$215$	−2.49945e7			−0.171518
$216$	3.25366e8	+	2.78531e8i	2.19677	+	1.88055i
$217$			1.16069e7i			0.0771091i
$218$		−	8.53322e7i		−	0.557847i
$219$	5.49383e7	−	1.62508e7i	0.353444	−	0.104549i
$220$	−1.58617e8	−	5.04179e7i	−1.00432	−	0.319231i
$221$		−	2.20337e8i		−	1.37314i
$222$	5.79465e7	+	1.95897e8i	0.355461	+	1.20169i
$223$	2.55101e8			1.54044			0.770220	−	0.637778i	$-0.220146\pi$
$223$	2.55101e8			1.54044			0.770220	+	0.637778i	$0.220146\pi$
$224$		−	3.50434e7i		−	0.208323i
$225$	−1.18638e8	+	7.69164e7i	−0.694361	+	0.450173i
$226$			6.90464e7i			0.397889i
$227$	3.50553e7			0.198913			0.0994564	−	0.995042i	$-0.468290\pi$
$227$	3.50553e7			0.198913			0.0994564	+	0.995042i	$0.468290\pi$
$228$	−6.19449e8	+	1.83233e8i	−3.46125	+	1.02384i
$229$	−9.43843e7			−0.519369			−0.259684	−	0.965694i	$-0.583618\pi$
$229$	−9.43843e7			−0.519369			−0.259684	+	0.965694i	$0.583618\pi$
$230$	9.57345e7			0.518825
$231$	−306702.	+	1.52112e7i	−0.00163710	+	0.0811935i
$232$	−4.85689e8			−2.55358
$233$	1.32885e7			0.0688227			0.0344114	−	0.999408i	$-0.489044\pi$
$233$	1.32885e7			0.0688227			0.0344114	+	0.999408i	$0.489044\pi$
$234$	−2.89558e8	−	4.46622e8i	−1.47734	−	2.27869i
$235$	7.92509e7			0.398352
$236$			8.48623e8i			4.20265i
$237$	2.86926e8	−	8.48727e7i	1.40007	−	0.414141i
$238$		−	3.02107e7i		−	0.145258i
$239$	1.59568e8			0.756053			0.378026	−	0.925795i	$-0.376603\pi$
$239$	1.59568e8			0.756053			0.378026	+	0.925795i	$0.376603\pi$
$240$	2.47456e8	−	7.31974e7i	1.15547	−	0.341788i
$241$			2.64943e8i			1.21925i	0.792689	+	0.609626i	$0.208680\pi$
$241$			2.64943e8i			1.21925i	−0.792689	+	0.609626i	$0.791320\pi$
$242$	3.38567e8	+	2.39423e8i	1.53564	+	1.08595i
$243$	2.21708e8	+	2.96172e7i	0.991195	+	0.132410i
$244$		−	5.45370e8i		−	2.40340i
$245$		−	9.49672e7i		−	0.412565i
$246$	−1.29132e8	−	4.36553e8i	−0.553047	−	1.86966i
$247$	4.86422e8			2.05387
$248$	−6.59536e8			−2.74573
$249$	−1.12978e8	−	3.81940e8i	−0.463763	−	1.56782i
$250$			3.52669e8i			1.42750i
$251$			7.51774e7i			0.300075i	0.988680	+	0.150037i	$0.0479394\pi$
$251$			7.51774e7i			0.300075i	−0.988680	+	0.150037i	$0.952061\pi$
$252$	−2.84785e7	−	4.39261e7i	−0.112102	−	0.172910i
$253$	−1.63053e8	−	5.18278e7i	−0.633004	−	0.201206i
$254$			5.28856e8i			2.02498i
$255$	1.00283e8	−	2.96636e7i	0.378735	−	0.112030i
$256$	1.49782e7			0.0557980
$257$		−	1.43540e8i		−	0.527482i	−0.964593	−	0.263741i	$-0.915044\pi$
$257$		−	1.43540e8i		−	0.527482i	0.964593	−	0.263741i	$-0.0849565\pi$
$258$	−2.05469e8	+	6.07777e7i	−0.744864	+	0.220331i
$259$		−	1.51293e7i		−	0.0541090i
$260$	−4.31230e8			−1.52161
$261$	−2.12831e8	+	1.37984e8i	−0.740958	+	0.480384i
$262$	−5.81386e8			−1.99715
$263$	−1.37060e8			−0.464585			−0.232293	−	0.972646i	$-0.574623\pi$
$263$	−1.37060e8			−0.464585			−0.232293	+	0.972646i	$0.574623\pi$
$264$	−8.64346e8	−	1.74277e7i	−2.89117	−	0.0582944i
$265$	−1.50760e8			−0.497653
$266$	6.66938e7			0.217270
$267$	1.12526e8	−	3.32852e7i	0.361796	−	0.107019i
$268$	7.96466e8			2.52752
$269$		−	5.97463e7i		−	0.187145i	−0.995612	−	0.0935725i	$-0.970171\pi$
$269$		−	5.97463e7i		−	0.187145i	0.995612	−	0.0935725i	$-0.0298287\pi$
$270$	1.64290e8	−	1.91915e8i	0.507969	−	0.593384i
$271$		−	5.05492e8i		−	1.54284i	−0.636325	−	0.771421i	$-0.719546\pi$
$271$		−	5.05492e8i		−	1.54284i	0.636325	−	0.771421i	$-0.280454\pi$
$272$	9.15758e8			2.75924
$273$	1.11814e7	+	3.78004e7i	0.0332602	+	0.112442i
$274$			4.07135e8i			1.19567i
$275$	8.64526e7	−	2.71984e8i	0.250677	−	0.788641i
$276$	5.64521e8	−	1.66985e8i	1.61621	−	0.478076i
$277$			4.20567e8i			1.18893i	0.804121	+	0.594465i	$0.202636\pi$
$277$			4.20567e8i			1.18893i	−0.804121	+	0.594465i	$0.797364\pi$
$278$			1.90493e8i			0.531767i
$279$	−2.89012e8	+	1.87375e8i	−0.796712	+	0.516530i
$280$	−3.58254e7			−0.0975298
$281$	2.17377e8			0.584442			0.292221	−	0.956351i	$-0.405606\pi$
$281$	2.17377e8			0.584442			0.292221	+	0.956351i	$0.405606\pi$
$282$	6.51488e8	−	1.92710e8i	1.72995	−	0.511721i
$283$		−	1.24453e8i		−	0.326403i	−0.986593	−	0.163202i	$-0.947818\pi$
$283$		−	1.24453e8i		−	0.326403i	0.986593	−	0.163202i	$-0.0521821\pi$
$284$		−	2.13759e8i		−	0.553745i
$285$	6.54861e7	+	2.21386e8i	0.167568	+	0.566492i
$286$	1.02391e9	+	3.25457e8i	2.58809	+	0.822646i
$287$			3.37152e7i			0.0841859i
$288$	8.72585e8	−	5.65721e8i	2.15246	−	1.39550i
$289$	−3.92227e7			−0.0955862
$290$			2.86481e8i			0.689767i
$291$	7.65623e7	+	2.58831e8i	0.182133	+	0.615731i
$292$		−	3.97906e8i		−	0.935277i
$293$	−7.39068e8			−1.71651			−0.858257	−	0.513220i	$-0.828453\pi$
$293$	−7.39068e8			−1.71651			−0.858257	+	0.513220i	$0.828453\pi$
$294$	−2.30927e8	−	7.80685e8i	−0.529979	−	1.79168i
$295$	3.03292e8			0.687834
$296$	8.59691e8			1.92673
$297$	−3.83712e8	+	2.37924e8i	−0.849880	+	0.526976i
$298$	−2.06012e6			−0.00450957
$299$	−4.43290e8			−0.959044
$300$	2.78544e8	+	9.41663e8i	0.595620	+	2.01359i
$301$	1.58685e7			0.0335392
$302$		−	1.29822e9i		−	2.71221i
$303$	−5.38175e7	−	1.81939e8i	−0.111141	−	0.375730i
$304$			2.02165e9i			4.12713i
$305$	−1.94911e8			−0.393358
$306$	7.52250e8	−	4.87704e8i	1.50085	−	0.973042i
$307$			6.55755e8i			1.29347i	0.762713	+	0.646737i	$0.223867\pi$
$307$			6.55755e8i			1.29347i	−0.762713	+	0.646737i	$0.776133\pi$
$308$	1.00703e8	+	3.20093e7i	0.196388	+	0.0624236i
$309$	−1.40675e8	−	4.75576e8i	−0.271246	−	0.916991i
$310$			3.89023e8i			0.741669i
$311$			6.55393e8i			1.23549i	0.786377	+	0.617746i	$0.211954\pi$
$311$			6.55393e8i			1.23549i	−0.786377	+	0.617746i	$0.788046\pi$
$312$	−2.14793e9	+	6.35358e8i	−4.00386	+	1.18434i
$313$	−8.32166e8			−1.53393			−0.766963	−	0.641691i	$-0.778233\pi$
$313$	−8.32166e8			−1.53393			−0.766963	+	0.641691i	$0.778233\pi$
$314$	3.30326e8			0.602129
$315$	−1.56989e7	+	1.01780e7i	−0.0282997	+	0.0183474i
$316$		−	2.07814e9i		−	3.70484i
$317$		−	7.71297e7i		−	0.135992i	−0.997686	−	0.0679961i	$-0.978339\pi$
$317$		−	7.71297e7i		−	0.135992i	0.997686	−	0.0679961i	$-0.0216605\pi$
$318$	−1.23934e9	+	3.66596e8i	−2.16120	+	0.639282i
$319$	1.55092e8	−	4.87927e8i	0.267499	−	0.841565i
$320$		−	4.68226e8i		−	0.798787i
$321$	2.23329e8	+	7.54999e8i	0.376858	+	1.27403i
$322$	−6.07799e7			−0.101453
$323$			8.19284e8i			1.35278i
$324$	6.34025e8	−	1.41824e9i	1.03562	−	2.31655i
$325$		−	7.39440e8i		−	1.19484i
$326$	−4.19359e8			−0.670386
$327$	−1.79833e8	+	5.31947e7i	−0.284416	+	0.0841301i
$328$	−1.91580e9			−2.99773
$329$	−5.03148e7			−0.0778951
$330$	−1.02796e7	+	5.09829e8i	−0.0157463	+	0.780954i
$331$	−6.98515e8			−1.05871			−0.529356	−	0.848400i	$-0.677566\pi$
$331$	−6.98515e8			−1.05871			−0.529356	+	0.848400i	$0.677566\pi$
$332$	−2.76631e9			−4.14875
$333$	3.76721e8	−	2.44239e8i	0.559069	−	0.362460i
$334$	8.86346e8			1.30164
$335$		−	2.84651e8i		−	0.413672i
$336$	−1.57105e8	+	4.64716e7i	−0.225944	+	0.0668344i
$337$		−	5.36311e8i		−	0.763330i	−0.924301	−	0.381665i	$-0.875351\pi$
$337$		−	5.36311e8i		−	0.763330i	0.924301	−	0.381665i	$-0.124649\pi$
$338$	1.44845e9			2.04030
$339$	1.45512e8	−	4.30424e7i	0.202861	−	0.0600064i
$340$		−	7.26325e8i		−	1.00220i
$341$	2.10606e8	−	6.62576e8i	0.287627	−	0.904889i
$342$	1.07667e9	+	1.66068e9i	1.45543	+	2.24489i
$343$			1.20986e8i			0.161884i
$344$			9.01695e8i			1.19428i
$345$	−5.96793e7	−	2.01756e8i	−0.0782451	−	0.264520i
$346$	1.12581e9			1.46116
$347$	5.95942e8			0.765687			0.382843	−	0.923813i	$-0.374945\pi$
$347$	5.95942e8			0.765687			0.382843	+	0.923813i	$0.374945\pi$
$348$	4.99695e8	+	1.68930e9i	0.635591	+	2.14872i
$349$		−	7.19204e8i		−	0.905655i	−0.891598	−	0.452828i	$-0.850415\pi$
$349$		−	7.19204e8i		−	0.905655i	0.891598	−	0.452828i	$-0.149585\pi$
$350$		−	1.01385e8i		−	0.126397i
$351$	−7.60729e8	+	8.88645e8i	−0.938977	+	1.09687i
$352$	−6.35860e8	+	2.00045e9i	−0.777074	+	2.44471i
$353$			1.09245e8i			0.132188i	0.997813	+	0.0660938i	$0.0210536\pi$
$353$			1.09245e8i			0.132188i	−0.997813	+	0.0660938i	$0.978946\pi$
$354$	2.49323e9	−	7.37498e8i	2.98711	−	0.883588i
$355$	−7.63958e7			−0.0906296
$356$		−	8.15001e8i		−	0.957378i
$357$	−6.36675e7	+	1.88328e7i	−0.0740592	+	0.0219067i
$358$		−	3.98833e8i		−	0.459410i
$359$	1.53339e9			1.74913			0.874567	−	0.484904i	$-0.161146\pi$
$359$	1.53339e9			1.74913			0.874567	+	0.484904i	$0.161146\pi$
$360$	−5.78345e8	−	8.92056e8i	−0.653323	−	1.00771i
$361$	−9.14800e8			−1.02341
$362$	−2.86989e8			−0.317970
$363$	2.93514e8	−	8.62764e8i	0.322074	−	0.946714i
$364$	2.73780e8			0.297541
$365$	−1.42209e8			−0.153074
$366$	−1.60228e9	+	4.73955e8i	−1.70827	+	0.505305i
$367$	−4.93917e8			−0.521582			−0.260791	−	0.965395i	$-0.583983\pi$
$367$	−4.93917e8			−0.521582			−0.260791	+	0.965395i	$0.583983\pi$
$368$		−	1.84239e9i		−	1.92714i
$369$	−8.39514e8	+	5.44280e8i	−0.869832	+	0.563936i
$370$		−	5.07084e8i		−	0.520443i
$371$	9.57147e7			0.0973128
$372$	6.78556e8	+	2.29397e9i	0.683416	+	2.31040i
$373$			1.69102e9i			1.68721i	0.536965	+	0.843605i	$0.319571\pi$
$373$			1.69102e9i			1.68721i	−0.536965	+	0.843605i	$0.680429\pi$
$374$	−5.48171e8	+	1.72457e9i	−0.541833	+	1.70463i
$375$	7.43231e8	−	2.19848e8i	0.727804	−	0.215285i
$376$		−	2.85904e9i		−	2.77372i
$377$		−	1.32652e9i		−	1.27503i
$378$	−1.04304e8	+	1.21843e8i	−0.0993301	+	0.116032i
$379$	9.30338e8			0.877817			0.438908	−	0.898532i	$-0.355365\pi$
$379$	9.30338e8			0.877817			0.438908	+	0.898532i	$0.355365\pi$
$380$	1.60345e9			1.49904
$381$	1.11454e9	−	3.29681e8i	1.03242	−	0.305391i
$382$			1.84091e9i			1.68971i
$383$			2.08513e8i			0.189643i	0.995494	+	0.0948214i	$0.0302280\pi$
$383$			2.08513e8i			0.189643i	−0.995494	+	0.0948214i	$0.969772\pi$
$384$	−3.31192e8	−	1.11965e9i	−0.298484	−	1.00907i
$385$	1.14399e7	−	3.59905e7i	0.0102167	−	0.0321422i
$386$		−	3.19564e9i		−	2.82815i
$387$	2.56172e8	+	3.95127e8i	0.224669	+	0.346536i
$388$	1.87466e9			1.62934
$389$		−	6.01312e8i		−	0.517936i	−0.965886	−	0.258968i	$-0.916618\pi$
$389$		−	6.01312e8i		−	0.517936i	0.965886	−	0.258968i	$-0.0833825\pi$
$390$	3.74762e8	+	1.26694e9i	0.319911	+	1.08151i
$391$		−	7.46637e8i		−	0.631671i
$392$	−3.42602e9			−2.87269
$393$	3.62427e8	+	1.22524e9i	0.301194	+	1.01823i
$394$	1.87462e9			1.54410
$395$	−7.42712e8			−0.606360
$396$	8.28655e8	+	3.02426e9i	0.670565	+	2.44729i
$397$	−2.59934e8			−0.208495			−0.104248	−	0.994551i	$-0.533243\pi$
$397$	−2.59934e8			−0.208495			−0.104248	+	0.994551i	$0.533243\pi$
$398$	1.30331e8			0.103623
$399$	−4.15758e7	−	1.40554e8i	−0.0327669	−	0.110774i
$400$	3.07324e9			2.40097
$401$			1.85389e9i			1.43575i	0.696174	+	0.717873i	$0.254884\pi$
$401$			1.85389e9i			1.43575i	−0.696174	+	0.717873i	$0.745116\pi$
$402$	−6.92171e8	−	2.34000e9i	−0.531401	−	1.79649i
$403$		−	1.80134e9i		−	1.37097i
$404$	−1.31774e9			−0.994250
$405$	−5.06867e8	−	2.26596e8i	−0.379142	−	0.169496i
$406$		−	1.81881e8i		−	0.134879i
$407$	−2.74520e8	+	8.63654e8i	−0.201834	+	0.634979i
$408$	−1.07014e9	−	3.61778e9i	−0.780063	−	2.63713i
$409$			4.43794e8i			0.320738i	0.987057	+	0.160369i	$0.0512684\pi$
$409$			4.43794e8i			0.320738i	−0.987057	+	0.160369i	$0.948732\pi$
$410$			1.13002e9i			0.809737i
$411$	8.58016e8	−	2.53801e8i	0.609606	−	0.180321i
$412$	−3.44449e9			−2.42652
$413$	−1.92554e8			−0.134501
$414$	−9.81197e8	−	1.51343e9i	−0.679602	−	1.04824i
$415$			9.88658e8i			0.679012i
$416$			5.43859e9i			3.70391i
$417$	4.01454e8	−	1.18750e8i	0.271119	−	0.0801969i
$418$	−3.80721e9	−	1.21016e9i	−2.54970	−	0.810446i
$419$			9.87687e8i			0.655950i	0.944686	+	0.327975i	$0.106366\pi$
$419$			9.87687e8i			0.655950i	−0.944686	+	0.327975i	$0.893634\pi$
$420$	3.68585e7	+	1.24606e8i	0.0242753	+	0.0820666i
$421$	2.40008e8			0.156761			0.0783805	−	0.996924i	$-0.475025\pi$
$421$	2.40008e8			0.156761			0.0783805	+	0.996924i	$0.475025\pi$
$422$		−	3.09332e9i		−	2.00369i
$423$	−8.12254e8	−	1.25285e9i	−0.521796	−	0.804834i
$424$			5.43880e9i			3.46515i
$425$	1.24545e9			0.786980
$426$	−6.28017e8	+	1.85768e8i	−0.393585	+	0.116422i
$427$	1.23745e8			0.0769185
$428$	5.46829e9			3.37131
$429$	4.75989e7	−	2.36072e9i	0.0291069	−	1.44359i
$430$	5.31859e8			0.322595
$431$	−5.62589e8			−0.338470			−0.169235	−	0.985576i	$-0.554130\pi$
$431$	−5.62589e8			−0.338470			−0.169235	+	0.985576i	$0.554130\pi$
$432$	−3.69336e9	−	3.16172e9i	−2.20408	−	1.88682i
$433$	6.74068e8			0.399021			0.199511	−	0.979896i	$-0.436065\pi$
$433$	6.74068e8			0.399021			0.199511	+	0.979896i	$0.436065\pi$
$434$		−	2.46983e8i		−	0.145029i
$435$	6.03743e8	−	1.78587e8i	0.351674	−	0.104025i
$436$			1.30249e9i			0.752615i
$437$	1.64829e9			0.944820
$438$	−1.16904e9	+	3.45801e8i	−0.664766	+	0.196638i
$439$			1.29876e9i			0.732661i	0.930485	+	0.366331i	$0.119386\pi$
$439$			1.29876e9i			0.732661i	−0.930485	+	0.366331i	$0.880614\pi$
$440$	2.04509e9	+	6.50049e8i	1.14453	+	0.363799i
$441$	−1.50130e9	+	9.73333e8i	−0.833551	+	0.540414i
$442$			4.68858e9i			2.58263i
$443$		−	9.82222e8i		−	0.536780i	−0.963310	−	0.268390i	$-0.913508\pi$
$443$		−	9.82222e8i		−	0.536780i	0.963310	−	0.268390i	$-0.0864917\pi$
$444$	−8.84483e8	−	2.99014e9i	−0.479567	−	1.62125i
$445$	−2.91275e8			−0.156691
$446$	−5.42831e9			−2.89730
$447$	1.28424e6	+	4.34159e6i	0.000680098	+	0.00229918i
$448$			2.97268e8i			0.156198i
$449$			3.16711e9i			1.65120i	0.564253	+	0.825602i	$0.309164\pi$
$449$			3.16711e9i			1.65120i	−0.564253	+	0.825602i	$0.690836\pi$
$450$	2.52451e9	−	1.63671e9i	1.30597	−	0.846697i
$451$	6.11761e8	−	1.92463e9i	0.314025	−	0.987937i
$452$		−	1.05391e9i		−	0.536808i
$453$	−2.73593e9	+	8.09289e8i	−1.38281	+	0.409035i
$454$	−7.45944e8			−0.374120
$455$		−	9.78468e7i		−	0.0486975i
$456$	7.98669e9	−	2.36246e9i	3.94448	−	1.16678i
$457$		−	3.03618e9i		−	1.48806i	−0.668146	−	0.744031i	$-0.732912\pi$
$457$		−	3.03618e9i		−	1.48806i	0.668146	−	0.744031i	$-0.267088\pi$
$458$	2.00841e9			0.976840
$459$	−1.49675e9	−	1.28130e9i	−0.722446	−	0.618454i
$460$	−1.46127e9			−0.699968
$461$	−1.09519e9			−0.520637			−0.260319	−	0.965523i	$-0.583828\pi$
$461$	−1.09519e9			−0.520637			−0.260319	+	0.965523i	$0.583828\pi$
$462$	6.52634e6	−	3.23680e8i	0.00307909	−	0.152711i
$463$	3.57109e9			1.67212			0.836060	−	0.548639i	$-0.184854\pi$
$463$	3.57109e9			1.67212			0.836060	+	0.548639i	$0.184854\pi$
$464$	5.51324e9			2.56209
$465$	8.19847e8	−	2.42511e8i	0.378136	−	0.111853i
$466$	−2.82768e8			−0.129443
$467$			9.84786e8i			0.447438i	0.974654	+	0.223719i	$0.0718198\pi$
$467$			9.84786e8i			0.447438i	−0.974654	+	0.223719i	$0.928180\pi$
$468$	4.41974e9	+	6.81715e9i	1.99313	+	3.07427i
$469$			1.80719e8i			0.0808909i
$470$	−1.68639e9			−0.749229
$471$	−2.05920e8	−	6.96146e8i	−0.0908083	−	0.306992i
$472$		−	1.09415e10i		−	4.78938i
$473$	−9.05851e8	−	2.87933e8i	−0.393589	−	0.125106i
$474$	−6.10552e9	+	1.80601e9i	−2.63329	+	0.778927i
$475$			2.74948e9i			1.17712i
$476$			4.61129e8i			0.195974i
$477$	1.54516e9	+	2.38331e9i	0.651869	+	1.00546i
$478$	−3.39545e9			−1.42200
$479$	−1.72008e9			−0.715113			−0.357556	−	0.933892i	$-0.616390\pi$
$479$	−1.72008e9			−0.715113			−0.357556	+	0.933892i	$0.616390\pi$
$480$	−2.47528e9	+	7.32189e8i	−1.02160	+	0.302189i
$481$			2.34800e9i			0.962035i
$482$		−	5.63775e9i		−	2.29320i
$483$	3.78892e7	+	1.28091e8i	0.0153003	+	0.0517252i
$484$	−5.16781e9	−	3.65450e9i	−2.07180	−	1.46511i
$485$		−	6.69989e8i		−	0.266668i
$486$	−4.71774e9	−	6.30226e8i	−1.86426	−	0.249040i
$487$	−1.16488e9			−0.457015			−0.228508	−	0.973542i	$-0.573385\pi$
$487$	−1.16488e9			−0.457015			−0.228508	+	0.973542i	$0.573385\pi$
$488$			7.03158e9i			2.73895i
$489$	2.61422e8	+	8.83779e8i	0.101102	+	0.341793i
$490$			2.02081e9i			0.775962i
$491$	−2.41653e9			−0.921313			−0.460657	−	0.887578i	$-0.652386\pi$
$491$	−2.41653e9			−0.921313			−0.460657	+	0.887578i	$0.652386\pi$
$492$	1.97105e9	+	6.66345e9i	0.746138	+	2.52244i
$493$	2.23427e9			0.839792
$494$	−1.03506e10			−3.86297
$495$	1.08085e9	−	2.96155e8i	0.400540	−	0.109749i
$496$	7.48666e9			2.75488
$497$	4.85022e7			0.0177220
$498$	2.40407e9	+	8.12733e9i	0.872255	+	2.94880i
$499$	−3.43329e9			−1.23697			−0.618484	−	0.785797i	$-0.712253\pi$
$499$	−3.43329e9			−1.23697			−0.618484	+	0.785797i	$0.712253\pi$
$500$		−	5.38306e9i		−	1.92590i
$501$	−5.52534e8	−	1.86793e9i	−0.196303	−	0.663634i
$502$		−	1.59971e9i		−	0.564387i
$503$	1.05168e9			0.368464			0.184232	−	0.982883i	$-0.441020\pi$
$503$	1.05168e9			0.368464			0.184232	+	0.982883i	$0.441020\pi$
$504$	3.67179e8	+	5.66349e8i	0.127753	+	0.197050i
$505$			4.70952e8i			0.162726i
$506$	3.46962e9	+	1.10285e9i	1.19057	+	0.378433i
$507$	−9.02939e8	−	3.05253e9i	−0.307702	−	1.04024i
$508$		−	8.07235e9i		−	2.73198i
$509$			7.06309e7i			0.0237401i	0.999930	+	0.0118700i	$0.00377844\pi$
$509$			7.06309e7i			0.0237401i	−0.999930	+	0.0118700i	$0.996222\pi$
$510$	−2.13392e9	+	6.31215e8i	−0.712333	+	0.210708i
$511$	9.02855e7			0.0299326
$512$	2.87709e9			0.947347
$513$	2.82863e9	−	3.30427e9i	0.925051	−	1.08060i
$514$			3.05441e9i			0.992101i
$515$			1.23103e9i			0.397141i
$516$	3.13623e9	−	9.27698e8i	1.00493	−	0.297257i
$517$	2.87222e9	+	9.12959e8i	0.914114	+	0.290559i
$518$			3.21937e8i			0.101769i
$519$	−7.01809e8	−	2.37258e9i	−0.220360	−	0.744963i
$520$	5.55995e9			1.73404
$521$			3.88780e9i			1.20440i	0.798344	+	0.602202i	$0.205710\pi$
$521$			3.88780e9i			1.20440i	−0.798344	+	0.602202i	$0.794290\pi$
$522$	4.52886e9	−	2.93618e9i	1.39361	−	0.903517i
$523$			1.58766e9i			0.485292i	0.970115	+	0.242646i	$0.0780153\pi$
$523$			1.58766e9i			0.485292i	−0.970115	+	0.242646i	$0.921985\pi$
$524$	8.87415e9			2.69443
$525$	−2.13665e8	+	6.32020e7i	−0.0644429	+	0.0190622i
$526$	2.91651e9			0.873802
$527$	3.03401e9			0.902983
$528$	9.81153e9	+	1.97829e8i	2.90080	+	0.0584886i
$529$	1.90269e9			0.558822
$530$	3.20804e9			0.935997
$531$	−3.10848e9	−	4.79462e9i	−0.900985	−	1.38971i
$532$	−1.01800e9			−0.293128
$533$		−	5.23247e9i		−	1.49679i
$534$	−2.39445e9	+	7.08279e8i	−0.680474	+	0.201284i
$535$		−	1.95433e9i		−	0.551771i
$536$	−1.02690e10			−2.88039
$537$	−8.40521e8	+	2.48626e8i	−0.234228	+	0.0692847i
$538$			1.27135e9i			0.351987i
$539$	1.09401e9	−	3.44181e9i	0.300926	−	0.946729i
$540$	−2.50769e9	+	2.92935e9i	−0.685322	+	0.800559i
$541$		−	5.30861e8i		−	0.144142i	−0.997400	−	0.0720709i	$-0.977039\pi$
$541$		−	5.30861e8i		−	0.144142i	0.997400	−	0.0720709i	$-0.0229608\pi$
$542$			1.07564e10i			2.90181i
$543$	1.78904e8	+	6.04815e8i	0.0479536	+	0.162115i
$544$	−9.16027e9			−2.43956
$545$	4.65502e8			0.123178
$546$	−2.37929e8	−	8.04357e8i	−0.0625566	−	0.211483i
$547$			3.43126e9i			0.896391i	0.893936	+	0.448195i	$0.147933\pi$
$547$			3.43126e9i			0.896391i	−0.893936	+	0.448195i	$0.852067\pi$
$548$		−	6.21442e9i		−	1.61313i
$549$	1.99767e9	+	3.08127e9i	0.515254	+	0.794744i
$550$	−1.83963e9	+	5.78758e9i	−0.471478	+	1.48329i
$551$			4.93243e9i			1.25612i
$552$	−7.27849e9	+	2.15298e9i	−1.84185	+	0.544820i
$553$	4.71533e8			0.118570
$554$		−	8.94929e9i		−	2.23617i
$555$	−1.06865e9	+	3.16108e8i	−0.265345	+	0.0784892i
$556$		−	2.90764e9i		−	0.717429i
$557$	1.86574e9			0.457464			0.228732	−	0.973489i	$-0.426542\pi$
$557$	1.86574e9			0.457464			0.228732	+	0.973489i	$0.426542\pi$
$558$	6.14992e9	−	3.98716e9i	1.49848	−	0.971502i
$559$	−2.46273e9			−0.596313
$560$	4.06668e8			0.0978547
$561$	3.97617e9	+	8.01712e7i	0.950813	+	0.0191712i
$562$	−4.62558e9			−1.09923
$563$	5.10827e9			1.20641			0.603204	−	0.797587i	$-0.293890\pi$
$563$	5.10827e9			1.20641			0.603204	+	0.797587i	$0.293890\pi$
$564$	−9.94418e9	+	2.94149e9i	−2.33395	+	0.690383i
$565$	−3.76660e8			−0.0878576
$566$			2.64825e9i			0.613906i
$567$	3.21800e8	+	1.43861e8i	0.0741387	+	0.0331438i
$568$			2.75604e9i			0.631054i
$569$	1.72525e8			0.0392607			0.0196303	−	0.999807i	$-0.493751\pi$
$569$	1.72525e8			0.0392607			0.0196303	+	0.999807i	$0.493751\pi$
$570$	−1.39349e9	−	4.71090e9i	−0.315167	−	1.06547i
$571$			2.09567e9i			0.471083i	0.971864	+	0.235541i	$0.0756863\pi$
$571$			2.09567e9i			0.471083i	−0.971864	+	0.235541i	$0.924314\pi$
$572$	−1.56287e10	−	4.96771e9i	−3.49170	−	1.10987i
$573$	3.87963e9	−	1.14760e9i	0.861488	−	0.254828i
$574$		−	7.17429e8i		−	0.158339i
$575$		−	2.50567e9i		−	0.549651i
$576$	−7.40200e9	+	4.79892e9i	−1.61388	+	1.04632i
$577$	9.05678e8			0.196272			0.0981360	−	0.995173i	$-0.468712\pi$
$577$	9.05678e8			0.196272			0.0981360	+	0.995173i	$0.468712\pi$
$578$	8.34624e8			0.179781
$579$	−6.73465e9	+	1.99211e9i	−1.44192	+	0.426519i
$580$		−	4.37278e9i		−	0.930592i
$581$		−	6.27679e8i		−	0.132776i
$582$	−1.62918e9	−	5.50769e9i	−0.342561	−	1.15808i
$583$	−5.46386e9	−	1.73674e9i	−1.14198	−	0.362990i
$584$			5.13029e9i			1.06585i
$585$	2.43640e9	−	1.57958e9i	0.503156	−	0.326210i
$586$	1.57267e10			3.22846
$587$			2.37789e9i			0.485241i	0.970121	+	0.242621i	$0.0780070\pi$
$587$			2.37789e9i			0.485241i	−0.970121	+	0.242621i	$0.921993\pi$
$588$	3.52482e9	+	1.19162e10i	0.715016	+	2.41723i
$589$			6.69795e9i			1.35064i
$590$	−6.45377e9			−1.29369
$591$	−1.16861e9	−	3.95066e9i	−0.232869	−	0.787251i
$592$	−9.75869e9			−1.93315
$593$	−6.48663e9			−1.27740			−0.638701	−	0.769455i	$-0.720528\pi$
$593$	−6.48663e9			−1.27740			−0.638701	+	0.769455i	$0.720528\pi$
$594$	8.16504e9	−	5.06281e9i	1.59847	−	0.991148i
$595$	1.64804e8			0.0320744
$596$	3.14452e7			0.00608405
$597$	−8.12461e7	−	2.74666e8i	−0.0156276	−	0.0528316i
$598$	9.43280e9			1.80379
$599$			1.63992e9i			0.311767i	0.987775	+	0.155883i	$0.0498224\pi$
$599$			1.63992e9i			0.311767i	−0.987775	+	0.155883i	$0.950178\pi$
$600$	−3.59133e9	−	1.21411e10i	−0.678775	−	2.29471i
$601$			2.98244e9i			0.560416i	0.959939	+	0.280208i	$0.0904035\pi$
$601$			2.98244e9i			0.560416i	−0.959939	+	0.280208i	$0.909597\pi$
$602$	−3.37667e8			−0.0630813
$603$	−4.49994e9	+	2.91743e9i	−0.835787	+	0.541864i
$604$			1.98157e10i			3.65916i
$605$	−1.30609e9	+	1.84694e9i	−0.239789	+	0.339085i
$606$	1.14519e9	+	3.87149e9i	0.209037	+	0.706682i
$607$			8.17709e9i			1.48402i	0.670391	+	0.742008i	$0.266126\pi$
$607$			8.17709e9i			1.48402i	−0.670391	+	0.742008i	$0.733874\pi$
$608$		−	2.02224e10i		−	3.64897i
$609$	−3.83305e8	+	1.13382e8i	−0.0687676	+	0.0203414i
$610$	4.14753e9			0.739836
$611$	7.80866e9			1.38494
$612$	−1.14822e10	+	7.44421e9i	−2.02486	+	1.31277i
$613$		−	1.01160e10i		−	1.77378i	−0.461985	−	0.886888i	$-0.652863\pi$
$613$		−	1.01160e10i		−	1.77378i	0.461985	−	0.886888i	$-0.347137\pi$
$614$		−	1.39539e10i		−	2.43279i
$615$	2.38147e9	−	7.04438e8i	0.412840	−	0.122118i
$616$	−1.29839e9	−	4.12703e8i	−0.223806	−	0.0711386i
$617$		−	1.05718e10i		−	1.81198i	−0.423303	−	0.905988i	$-0.639130\pi$
$617$		−	1.05718e10i		−	1.81198i	0.423303	−	0.905988i	$-0.360870\pi$
$618$	2.99344e9	+	1.01198e10i	0.510166	+	1.72470i
$619$	−6.19329e9			−1.04955			−0.524776	−	0.851240i	$-0.675851\pi$
$619$	−6.19329e9			−1.04955			−0.524776	+	0.851240i	$0.675851\pi$
$620$		−	5.93797e9i		−	1.00062i
$621$	−2.57781e9	+	3.01127e9i	−0.431947	+	0.504579i
$622$		−	1.39462e10i		−	2.32374i
$623$	1.84925e8			0.0306399
$624$	2.43820e10	−	7.21220e9i	4.01720	−	1.18829i
$625$	3.12693e9			0.512317
$626$	1.77077e10			2.88504
$627$	−1.76988e8	+	8.77790e9i	−0.0286753	+	1.42218i
$628$	−5.04203e9			−0.812357
$629$	−3.95476e9			−0.633641
$630$	3.34057e8	−	2.16579e8i	0.0532266	−	0.0345083i
$631$	−3.29651e9			−0.522338			−0.261169	−	0.965293i	$-0.584108\pi$
$631$	−3.29651e9			−0.522338			−0.261169	+	0.965293i	$0.584108\pi$
$632$			2.67939e10i			4.22208i
$633$	−6.51902e9	+	1.92833e9i	−1.02157	+	0.302181i
$634$			1.64125e9i			0.255777i
$635$	−2.88500e9			−0.447134
$636$	1.89170e10	−	5.59564e9i	2.91576	−	0.862482i
$637$		−	9.35720e9i		−	1.43436i
$638$	−3.30022e9	+	1.03826e10i	−0.503118	+	1.58284i
$639$	7.82992e8	+	1.20771e9i	0.118715	+	0.183109i
$640$			2.89823e9i			0.437021i
$641$		−	1.09738e10i		−	1.64571i	−0.568253	−	0.822854i	$-0.692380\pi$
$641$		−	1.09738e10i		−	1.64571i	0.568253	−	0.822854i	$-0.307620\pi$
$642$	−4.75223e9	−	1.60657e10i	−0.708802	−	2.39622i
$643$	−8.87778e9			−1.31694			−0.658470	−	0.752607i	$-0.728796\pi$
$643$	−8.87778e9			−1.31694			−0.658470	+	0.752607i	$0.728796\pi$
$644$	9.27732e8			0.136874
$645$	−3.31553e8	−	1.12087e9i	−0.0486512	−	0.164473i
$646$		−	1.74336e10i		−	2.54433i
$647$			1.21358e10i			1.76159i	0.473498	+	0.880795i	$0.342991\pi$
$647$			1.21358e10i			1.76159i	−0.473498	+	0.880795i	$0.657009\pi$
$648$	−8.17462e9	+	1.82856e10i	−1.18020	+	2.63996i
$649$	1.09919e10	+	3.49388e9i	1.57840	+	0.501708i
$650$			1.57346e10i			2.24729i
$651$	−5.20505e8	+	1.53965e8i	−0.0739420	+	0.0218721i
$652$	6.40101e9			0.904445
$653$			1.91875e9i			0.269663i	0.990869	+	0.134832i	$0.0430493\pi$
$653$			1.91875e9i			0.269663i	−0.990869	+	0.134832i	$0.956951\pi$
$654$	3.82669e9	−	1.13194e9i	0.534935	−	0.158234i
$655$		−	3.17156e9i		−	0.440989i
$656$	2.17470e10			3.00771
$657$	1.45752e9	+	2.24812e9i	0.200510	+	0.309272i
$658$	1.07065e9			0.146507
$659$	−1.08084e10			−1.47117			−0.735587	−	0.677431i	$-0.763093\pi$
$659$	−1.08084e10			−1.47117			−0.735587	+	0.677431i	$0.763093\pi$
$660$	1.56906e8	−	7.78192e9i	0.0212440	−	1.05362i
$661$	−6.26254e9			−0.843423			−0.421711	−	0.906730i	$-0.638570\pi$
$661$	−6.26254e9			−0.843423			−0.421711	+	0.906730i	$0.638570\pi$
$662$	1.48638e10			1.99125
$663$	9.88094e9	−	2.92278e9i	1.31674	−	0.389493i
$664$	3.56666e10			4.72796
$665$			3.63826e8i			0.0479753i
$666$	−8.01628e9	+	5.19717e9i	−1.05151	+	0.681722i
$667$		−	4.49506e9i		−	0.586537i
$668$	−1.35290e10			−1.75610
$669$	3.38392e9	+	1.14399e10i	0.436947	+	1.47717i
$670$			6.05711e9i			0.778044i
$671$	−7.06399e9	−	2.24535e9i	−0.902654	−	0.286916i
$672$	1.57151e9	−	4.64852e8i	0.199767	−	0.0590911i
$673$		−	1.29760e10i		−	1.64093i	−0.571699	−	0.820463i	$-0.693716\pi$
$673$		−	1.29760e10i		−	1.64093i	0.571699	−	0.820463i	$-0.306284\pi$
$674$			1.14122e10i			1.43569i
$675$	−5.02302e9	−	4.29998e9i	−0.628640	−	0.538150i
$676$	−2.21088e10			−2.75266
$677$	1.37621e10			1.70461			0.852305	−	0.523045i	$-0.175204\pi$
$677$	1.37621e10			1.70461			0.852305	+	0.523045i	$0.175204\pi$
$678$	−3.09636e9	+	9.15903e8i	−0.381546	+	0.112861i
$679$			4.25362e8i			0.0521453i
$680$			9.36467e9i			1.14212i
$681$	4.65010e8	+	1.57204e9i	0.0564218	+	0.190743i
$682$	−4.48150e9	+	1.40990e10i	−0.540976	+	1.70194i
$683$		−	4.38092e9i		−	0.526130i	−0.964778	−	0.263065i	$-0.915267\pi$
$683$		−	4.38092e9i		−	0.526130i	0.964778	−	0.263065i	$-0.0847334\pi$
$684$	−1.64340e10	−	2.53483e10i	−1.96358	−	3.02868i
$685$	−2.22099e9			−0.264015
$686$		−	2.57447e9i		−	0.304476i
$687$	−1.25201e9	−	4.23263e9i	−0.147319	−	0.498037i
$688$		−	1.02355e10i		−	1.19826i
$689$	−1.48545e10			−1.73018
$690$	1.26992e9	+	4.29318e9i	0.147165	+	0.497516i
$691$	−1.01743e10			−1.17309			−0.586544	−	0.809917i	$-0.699512\pi$
$691$	−1.01743e10			−1.17309			−0.586544	+	0.809917i	$0.699512\pi$
$692$	−1.71841e10			−1.97131
$693$	−6.86208e8	+	1.88023e8i	−0.0783231	+	0.0214607i
$694$	−1.26811e10			−1.44012
$695$	−1.03917e9			−0.117419
$696$	−6.44268e9	−	2.17805e10i	−0.724326	−	2.44870i
$697$	8.81309e9			0.985856
$698$			1.53040e10i			1.70338i
$699$	1.76273e8	+	5.95920e8i	0.0195216	+	0.0659960i
$700$			1.54753e9i			0.170528i
$701$	−7.87337e9			−0.863272			−0.431636	−	0.902048i	$-0.642063\pi$
$701$	−7.87337e9			−0.863272			−0.431636	+	0.902048i	$0.642063\pi$
$702$	1.61876e10	−	1.89096e10i	1.76605	−	2.06301i
$703$		−	8.73063e9i		−	0.947768i
$704$	5.39390e9	−	1.69695e10i	0.582638	−	1.83301i
$705$	1.05127e9	+	3.55398e9i	0.112993	+	0.381991i
$706$		−	2.32464e9i		−	0.248621i
$707$		−	2.98998e8i		−	0.0318200i
$708$	−3.80562e10	+	1.12570e10i	−4.03003	+	1.19208i
$709$	1.55379e10			1.63731			0.818654	−	0.574287i	$-0.194721\pi$
$709$	1.55379e10			1.63731			0.818654	+	0.574287i	$0.194721\pi$
$710$	1.62563e9			0.170458
$711$	7.61216e9	+	1.17412e10i	0.794263	+	1.22510i
$712$			1.05080e10i			1.09104i
$713$		−	6.10403e9i		−	0.630671i
$714$	1.35479e9	−	4.00746e8i	0.139292	−	0.0412027i
$715$	−1.77542e9	+	5.58558e9i	−0.181648	+	0.571475i
$716$			6.08771e9i			0.619810i
$717$	2.11667e9	+	7.15575e9i	0.214455	+	0.725000i
$718$	−3.26292e10			−3.28981
$719$		−	7.61998e8i		−	0.0764545i	−0.999269	−	0.0382272i	$-0.987829\pi$
$719$		−	7.61998e8i		−	0.0764545i	0.999269	−	0.0382272i	$-0.0121711\pi$
$720$	6.56502e9	+	1.01261e10i	0.655499	+	1.01106i
$721$		−	7.81559e8i		−	0.0776584i
$722$	1.94661e10			1.92486
$723$	−1.18813e10	+	3.51448e9i	−1.16917	+	0.345842i
$724$	4.38054e9			0.428986
$725$	7.49810e9			0.730749
$726$	−6.24571e9	+	1.83588e10i	−0.605765	+	1.78060i
$727$	1.10918e10			1.07061			0.535307	−	0.844658i	$-0.320196\pi$
$727$	1.10918e10			1.07061			0.535307	+	0.844658i	$0.320196\pi$
$728$	−3.52990e9			−0.339081
$729$	1.61279e9	+	1.03353e10i	0.154182	+	0.988043i
$730$	3.02607e9			0.287905
$731$		−	4.14799e9i		−	0.392760i
$732$	2.44569e10	−	7.23435e9i	2.30469	−	0.681728i
$733$			1.36766e10i			1.28267i	0.767262	+	0.641333i	$0.221618\pi$
$733$			1.36766e10i			1.28267i	−0.767262	+	0.641333i	$0.778382\pi$
$734$	1.05101e10			0.981003
$735$	4.25877e9	−	1.25974e9i	0.395620	−	0.117024i
$736$			1.84293e10i			1.70387i
$737$	3.27914e9	−	1.03163e10i	0.301734	−	0.949270i
$738$	1.78641e10	−	1.15818e10i	1.63600	−	1.06066i
$739$		−	1.59670e10i		−	1.45536i	−0.685919	−	0.727678i	$-0.740600\pi$
$739$		−	1.59670e10i		−	1.45536i	0.685919	−	0.727678i	$-0.259400\pi$
$740$			7.74002e9i			0.702152i
$741$	6.45240e9	+	2.18134e10i	0.582583	+	1.96952i
$742$	−2.03672e9			−0.183028
$743$	−1.12516e10			−1.00636			−0.503180	−	0.864182i	$-0.667837\pi$
$743$	−1.12516e10			−1.00636			−0.503180	+	0.864182i	$0.667837\pi$
$744$	−8.74878e9	−	2.95767e10i	−0.778829	−	2.63296i
$745$		−	1.12383e7i		−	0.000995756i
$746$		−	3.59834e10i		−	3.17334i
$747$	1.56293e10	−	1.01329e10i	1.37188	−	0.889430i
$748$	8.36717e9	−	2.63235e10i	0.731009	−	2.29979i
$749$			1.24076e9i			0.107895i
$750$	−1.58153e10	+	4.67816e9i	−1.36887	+	0.404912i
$751$	1.39812e10			1.20449			0.602246	−	0.798310i	$-0.294273\pi$
$751$	1.39812e10			1.20449			0.602246	+	0.798310i	$0.294273\pi$
$752$			3.24541e10i			2.78296i
$753$	−3.37130e9	+	9.97231e8i	−0.287750	+	0.0851164i
$754$			2.82272e10i			2.39810i
$755$	7.08200e9			0.598883
$756$	1.59208e9	−	1.85979e9i	0.134010	−	0.156544i
$757$	−2.10157e10			−1.76079			−0.880397	−	0.474237i	$-0.842724\pi$
$757$	−2.10157e10			−1.76079			−0.880397	+	0.474237i	$0.842724\pi$
$758$	−1.97968e10			−1.65102
$759$	1.61294e8	−	7.99954e9i	0.0133897	−	0.664077i
$760$	−2.06737e10			−1.70832
$761$	2.06241e10			1.69640			0.848200	−	0.529676i	$-0.177686\pi$
$761$	2.06241e10			1.69640			0.848200	+	0.529676i	$0.177686\pi$
$762$	−2.37164e10	+	7.01530e9i	−1.94181	+	0.574386i
$763$	−2.95538e8			−0.0240867
$764$		−	2.80993e10i		−	2.27965i
$765$	2.66051e9	+	4.10365e9i	0.214857	+	0.331402i
$766$		−	4.43696e9i		−	0.356685i
$767$	2.98836e10			2.39138
$768$	1.98686e8	+	6.71690e8i	0.0158272	+	0.0535063i
$769$		−	8.45536e9i		−	0.670487i	−0.942132	−	0.335243i	$-0.891181\pi$
$769$		−	8.45536e9i		−	0.670487i	0.942132	−	0.335243i	$-0.108819\pi$
$770$	−2.43430e8	+	7.65845e8i	−0.0192157	+	0.0604537i
$771$	6.43701e9	−	1.90407e9i	0.505817	−	0.149621i
$772$			4.87776e10i			3.81557i
$773$		−	3.75493e9i		−	0.292397i	−0.989255	−	0.146199i	$-0.953296\pi$
$773$		−	3.75493e9i		−	0.292397i	0.989255	−	0.146199i	$-0.0467038\pi$
$774$	−5.45110e9	−	8.40795e9i	−0.422563	−	0.651774i
$775$	1.01820e10			0.785735
$776$	−2.41704e10			−1.85681
$777$	6.78467e8	−	2.00690e8i	0.0518866	−	0.0153481i
$778$			1.27954e10i			0.974147i
$779$			1.94560e10i			1.47459i
$780$	−5.72029e9	−	1.93384e10i	−0.431605	−	1.45911i
$781$	−2.76874e9	−	8.80069e8i	−0.207972	−	0.0661056i
$782$			1.58877e10i			1.18806i
$783$	−9.01107e9	−	7.71397e9i	−0.670827	−	0.574264i
$784$	3.88901e10			2.88226
$785$			1.80199e9i			0.132956i
$786$	−7.71211e9	−	2.60720e10i	−0.566492	−	1.91512i
$787$			9.67085e9i			0.707218i	0.935393	+	0.353609i	$0.115046\pi$
$787$			9.67085e9i			0.707218i	−0.935393	+	0.353609i	$0.884954\pi$
$788$	−2.86137e10			−2.08321
$789$	−1.81810e9	−	6.14640e9i	−0.131780	−	0.445504i
$790$	1.58042e10			1.14046
$791$	2.39134e8			0.0171800
$792$	−1.06840e10	−	3.89924e10i	−0.764183	−	2.78896i
$793$	−1.92048e10			−1.36758
$794$	5.53116e9			0.392143
$795$	−1.99984e9	−	6.76079e9i	−0.141160	−	0.477213i
$796$	−1.98934e9			−0.139802
$797$		−	2.79433e9i		−	0.195512i	−0.995210	−	0.0977559i	$-0.968834\pi$
$797$		−	2.79433e9i		−	0.195512i	0.995210	−	0.0977559i	$-0.0311665\pi$
$798$	8.84696e8	+	2.99086e9i	0.0616288	+	0.208346i
$799$			1.31522e10i			0.912188i
$800$	−3.07414e10			−2.12280
$801$	2.98533e9	+	4.60466e9i	0.205248	+	0.316580i
$802$		−	3.94490e10i		−	2.70038i
$803$	−5.15394e9	−	1.63822e9i	−0.351265	−	0.111653i
$804$	1.05652e10	+	3.57172e10i	0.716935	+	2.42371i
$805$		−	3.31565e8i		−	0.0224018i
$806$			3.83308e10i			2.57855i
$807$	2.67930e9	−	7.92537e8i	0.179459	−	0.0530838i
$808$	1.69900e10			1.13306
$809$	−1.68092e10			−1.11616			−0.558081	−	0.829787i	$-0.688462\pi$
$809$	−1.68092e10			−1.11616			−0.558081	+	0.829787i	$0.688462\pi$
$810$	1.07857e10	+	4.82175e9i	0.713098	+	0.318792i
$811$		−	4.67476e9i		−	0.307742i	−0.988091	−	0.153871i	$-0.950826\pi$
$811$		−	4.67476e9i		−	0.307742i	0.988091	−	0.153871i	$-0.0491740\pi$
$812$			2.77619e9i			0.181971i
$813$	2.26686e10	−	6.70537e9i	1.47947	−	0.437629i
$814$	5.84153e9	−	1.83778e10i	0.379613	−	1.19428i
$815$		−	2.28768e9i		−	0.148028i
$816$	1.21476e10	+	4.10668e10i	0.782661	+	2.64591i
$817$	9.15720e9			0.587470
$818$		−	9.44354e9i		−	0.603251i
$819$	−1.54682e9	+	1.00285e9i	−0.0983890	+	0.0637883i
$820$		−	1.72484e10i		−	1.09245i
$821$	−1.33329e10			−0.840862			−0.420431	−	0.907325i	$-0.638121\pi$
$821$	−1.33329e10			−0.840862			−0.420431	+	0.907325i	$0.638121\pi$
$822$	−1.82578e10	+	5.40066e9i	−1.14656	+	0.339153i
$823$	2.50853e10			1.56863			0.784314	−	0.620364i	$-0.213015\pi$
$823$	2.50853e10			1.56863			0.784314	+	0.620364i	$0.213015\pi$
$824$	4.44106e10			2.76529
$825$	1.33438e10	+	2.69050e8i	0.827355	+	0.0166819i
$826$	4.09737e9			0.252974
$827$	−1.67010e9			−0.102677			−0.0513385	−	0.998681i	$-0.516349\pi$
$827$	−1.67010e9			−0.102677			−0.0513385	+	0.998681i	$0.516349\pi$
$828$	1.49768e10	+	2.31006e10i	0.916880	+	1.41422i
$829$	−1.58908e10			−0.968734			−0.484367	−	0.874865i	$-0.660950\pi$
$829$	−1.58908e10			−0.968734			−0.484367	+	0.874865i	$0.660950\pi$
$830$		−	2.10377e10i		−	1.27710i
$831$	−1.88602e10	+	5.57884e9i	−1.14010	+	0.337241i
$832$		−	4.61347e10i		−	2.77713i
$833$	1.57604e10			0.944735
$834$	−8.54257e9	+	2.52689e9i	−0.509926	+	0.150836i
$835$			4.83517e9i			0.287415i
$836$	5.81125e10	+	1.84716e10i	3.43991	+	1.09341i
$837$	−1.22365e10	−	1.04751e10i	−0.721303	−	0.617475i
$838$		−	2.10171e10i		−	1.23373i
$839$		−	2.09530e10i		−	1.22484i	−0.790533	−	0.612419i	$-0.790197\pi$
$839$		−	2.09530e10i		−	1.22484i	0.790533	−	0.612419i	$-0.209803\pi$
$840$	−4.75225e8	−	1.60657e9i	−0.0276644	−	0.0935240i
$841$	−3.79863e9			−0.220212
$842$	−5.10714e9			−0.294840
$843$	2.88351e9	+	9.74818e9i	0.165777	+	0.560438i
$844$			4.72158e10i			2.70327i
$845$			7.90153e9i			0.450518i
$846$	1.72840e10	+	2.66594e10i	0.981406	+	1.51375i
$847$	8.29211e8	−	1.17258e9i	0.0468892	−	0.0663059i
$848$		−	6.17379e10i		−	3.47669i
$849$	5.58106e9	−	1.65088e9i	0.312997	−	0.0925845i
$850$	−2.65019e10			−1.48017
$851$			7.95646e9i			0.442554i
$852$	9.58593e9	−	2.83552e9i	0.531001	−	0.157070i
$853$			1.13843e10i			0.628038i	0.949417	+	0.314019i	$0.101676\pi$
$853$			1.13843e10i			0.628038i	−0.949417	+	0.314019i	$0.898324\pi$
$854$	−2.63319e9			−0.144670
$855$	−9.05931e9	+	5.87340e9i	−0.495694	+	0.321372i
$856$	−7.05039e10			−3.84198
$857$	−9.61380e9			−0.521749			−0.260875	−	0.965373i	$-0.584011\pi$
$857$	−9.61380e9			−0.521749			−0.260875	+	0.965373i	$0.584011\pi$
$858$	−1.01286e9	+	5.02339e10i	−0.0547450	+	2.71513i
$859$	9.04935e9			0.487126			0.243563	−	0.969885i	$-0.421684\pi$
$859$	9.04935e9			0.487126			0.243563	+	0.969885i	$0.421684\pi$
$860$	−8.11819e9			−0.435226
$861$	−1.51195e9	+	4.47234e8i	−0.0807282	+	0.0238794i
$862$	1.19714e10			0.636603
$863$			2.62910e10i			1.39242i	0.717840	+	0.696208i	$0.245131\pi$
$863$			2.62910e10i			1.39242i	−0.717840	+	0.696208i	$0.754869\pi$
$864$	3.69444e10	+	3.16264e10i	1.94873	+	1.66822i
$865$			6.14146e9i			0.322638i
$866$	−1.43435e10			−0.750488
$867$	−5.20291e8	−	1.75893e9i	−0.0271131	−	0.0916603i
$868$			3.76990e9i			0.195664i
$869$	−2.69174e10	−	8.55594e9i	−1.39144	−	0.442281i
$870$	−1.28471e10	+	3.80018e9i	−0.661436	+	0.195653i
$871$		−	2.80469e10i		−	1.43821i
$872$		−	1.67933e10i		−	0.857688i
$873$	−1.05916e10	+	6.86681e9i	−0.538780	+	0.349305i
$874$	−3.50742e10			−1.77704
$875$	1.22142e9			0.0616365
$876$	1.78439e10	−	5.27824e9i	0.896863	−	0.265292i
$877$			2.46243e10i			1.23272i	0.787464	+	0.616361i	$0.211394\pi$
$877$			2.46243e10i			1.23272i	−0.787464	+	0.616361i	$0.788606\pi$
$878$		−	2.76364e10i		−	1.37801i
$879$	−9.80376e9	−	3.31432e10i	−0.486891	−	1.64601i
$880$	−2.32146e10	−	7.37896e9i	−1.14834	−	0.365011i
$881$		−	2.84916e10i		−	1.40379i	−0.712282	−	0.701893i	$-0.752338\pi$
$881$		−	2.84916e10i		−	1.40379i	0.712282	−	0.701893i	$-0.247662\pi$
$882$	3.19463e10	−	2.07116e10i	1.56776	−	1.01642i
$883$	1.42961e10			0.698802			0.349401	−	0.936973i	$-0.386385\pi$
$883$	1.42961e10			0.698802			0.349401	+	0.936973i	$0.386385\pi$
$884$		−	7.15654e10i		−	3.48434i
$885$	4.02318e9	+	1.36010e10i	0.195105	+	0.659583i
$886$			2.09008e10i			1.00959i
$887$	2.01976e9			0.0971780			0.0485890	−	0.998819i	$-0.484528\pi$
$887$	2.01976e9			0.0971780			0.0485890	+	0.998819i	$0.484528\pi$
$888$	1.14038e10	+	3.85525e10i	0.546520	+	1.84760i
$889$	1.83163e9			0.0874342
$890$	6.19808e9			0.294708
$891$	−1.57596e10	−	1.40513e10i	−0.746401	−	0.665497i
$892$	8.28566e10			3.90886
$893$	−2.90351e10			−1.36440
$894$	−2.73275e7	−	9.23852e7i	−0.00127914	−	0.00432435i
$895$	2.17570e9			0.101442
$896$		−	1.84003e9i		−	0.0854567i
$897$	−5.88025e9	−	1.98791e10i	−0.272034	−	0.919654i
$898$		−	6.73932e10i		−	3.10562i
$899$	1.82660e10			0.838463
$900$	−3.85336e10	+	2.49824e10i	−1.76194	+	1.14231i
$901$		−	2.50196e10i		−	1.13958i
$902$	−1.30177e10	+	4.09544e10i	−0.590625	+	1.85814i
$903$	2.10496e8	+	7.11616e8i	0.00951342	+	0.0321617i
$904$			1.35883e10i			0.611752i
$905$		−	1.56557e9i		−	0.0702107i
$906$	5.82181e10	−	1.72209e10i	2.60082	−	0.769322i
$907$	−1.89029e10			−0.841208			−0.420604	−	0.907244i	$-0.638182\pi$
$907$	−1.89029e10			−0.841208			−0.420604	+	0.907244i	$0.638182\pi$
$908$	1.13859e10			0.504741
$909$	7.44509e9	−	4.82685e9i	0.328773	−	0.213152i
$910$			2.08209e9i			0.0915914i
$911$			1.87105e10i			0.819918i	0.912104	+	0.409959i	$0.134457\pi$
$911$			1.87105e10i			0.819918i	−0.912104	+	0.409959i	$0.865543\pi$
$912$	−9.06601e10	+	2.68173e10i	−3.95762	+	1.17066i
$913$	−1.13892e10	+	3.58310e10i	−0.495274	+	1.55816i
$914$			6.46071e10i			2.79878i
$915$	−2.58551e9	−	8.74072e9i	−0.111576	−	0.377201i
$916$	−3.06560e10			−1.31790
$917$			2.01356e9i			0.0862326i
$918$	3.18495e10	+	2.72649e10i	1.35879	+	1.16320i
$919$		−	6.43421e9i		−	0.273458i	−0.990608	−	0.136729i	$-0.956341\pi$
$919$		−	6.43421e9i		−	0.273458i	0.990608	−	0.136729i	$-0.0436590\pi$
$920$	1.88405e10			0.797691
$921$	−2.94071e10	+	8.69862e9i	−1.24035	+	0.366895i
$922$	2.33046e10			0.979226
$923$	−7.52734e9			−0.315091
$924$	−9.96166e7	+	4.94059e9i	−0.00415413	+	0.206028i
$925$	−1.32720e10			−0.551365
$926$	−7.59895e10			−3.14496
$927$	1.94609e10	−	1.26171e10i	0.802388	−	0.520210i
$928$	−5.51486e10			−2.26525
$929$			4.41197e9i			0.180542i	0.995917	+	0.0902708i	$0.0287733\pi$
$929$			4.41197e9i			0.180542i	−0.995917	+	0.0902708i	$0.971227\pi$
$930$	−1.74456e10	+	5.16041e9i	−0.711206	+	0.210375i
$931$			3.47930e10i			1.41309i
$932$	4.31611e9			0.174637
$933$	−2.93908e10	+	8.69381e9i	−1.18475	+	0.350449i
$934$		−	2.09553e10i		−	0.841551i
$935$	−9.40784e9	−	2.99036e9i	−0.376400	−	0.119642i
$936$	−5.69848e10	−	8.78951e10i	−2.27140	−	3.50347i
$937$		−	2.10425e8i		−	0.00835619i	−0.999991	−	0.00417809i	$-0.998670\pi$
$937$		−	2.10425e8i		−	0.00835619i	0.999991	−	0.00417809i	$-0.00132993\pi$
$938$		−	3.84554e9i		−	0.152141i
$939$	−1.10387e10	−	3.73181e10i	−0.435100	−	1.47092i
$940$	2.57407e10			1.01082
$941$	3.06020e10			1.19725			0.598627	−	0.801028i	$-0.295713\pi$
$941$	3.06020e10			1.19725			0.598627	+	0.801028i	$0.295713\pi$
$942$	4.38179e9	+	1.48134e10i	0.170794	+	0.577398i
$943$		−	1.77308e10i		−	0.688552i
$944$			1.24201e11i			4.80534i
$945$	−6.64674e8	−	5.68998e8i	−0.0256211	−	0.0219331i
$946$	1.92757e10	+	6.12694e9i	0.740271	+	0.235302i
$947$			1.68029e10i			0.642925i	0.946922	+	0.321463i	$0.104174\pi$
$947$			1.68029e10i			0.642925i	−0.946922	+	0.321463i	$0.895826\pi$
$948$	9.31934e10	−	2.75666e10i	3.55268	−	1.05088i
$949$	−1.40119e10			−0.532190
$950$		−	5.85063e10i		−	2.21396i
$951$	3.45885e9	−	1.02313e9i	0.130407	−	0.0385743i
$952$		−	5.94545e9i		−	0.223334i
$953$	4.57844e8			0.0171353			0.00856767	−	0.999963i	$-0.497273\pi$
$953$	4.57844e8			0.0171353			0.00856767	+	0.999963i	$0.497273\pi$
$954$	−3.28797e10	−	5.07146e10i	−1.22605	−	1.89110i
$955$	−1.00425e10			−0.373104
$956$	5.18275e10			1.91848
$957$	2.39382e10	+	4.82664e8i	0.882876	+	0.0178014i
$958$	3.66017e10			1.34500
$959$	1.41006e9			0.0516265
$960$	2.09974e10	−	6.21104e9i	0.765979	−	0.226577i
$961$	−2.70850e9			−0.0984457
$962$		−	4.99634e10i		−	1.80942i
$963$	−3.08952e10	+	2.00302e10i	−1.11480	+	0.722758i
$964$			8.60535e10i			3.09385i
$965$	1.74328e10			0.624483
$966$	−8.06248e8	−	2.72565e9i	−0.0287772	−	0.0972860i
$967$			1.99002e10i			0.707726i	0.935297	+	0.353863i	$0.115132\pi$
$967$			1.99002e10i			0.707726i	−0.935297	+	0.353863i	$0.884868\pi$
$968$	6.66297e10	+	4.71182e10i	2.36105	+	1.66965i
$969$	−3.67405e10	+	1.08678e10i	−1.29721	+	0.383716i
$970$			1.42567e10i			0.501556i
$971$			2.59685e10i			0.910291i	0.890417	+	0.455145i	$0.150413\pi$
$971$			2.59685e10i			0.910291i	−0.890417	+	0.455145i	$0.849587\pi$
$972$	7.20106e10	+	9.61964e9i	2.51515	+	0.335990i
$973$	6.59748e8			0.0229606
$974$	2.47876e10			0.859564
$975$	3.31599e10	−	9.80870e9i	1.14577	−	0.338919i
$976$		−	7.98182e10i		−	2.74807i
$977$		−	2.89249e10i		−	0.992296i	−0.868238	−	0.496148i	$-0.834747\pi$
$977$		−	2.89249e10i		−	0.992296i	0.868238	−	0.496148i	$-0.165253\pi$
$978$	−5.56282e9	−	1.88060e10i	−0.190156	−	0.642851i
$979$	−1.05564e10	−	3.35545e9i	−0.359565	−	0.114291i
$980$		−	3.08453e10i		−	1.04688i
$981$	−4.77099e9	−	7.35893e9i	−0.161349	−	0.248870i
$982$	5.14216e10			1.73283
$983$			5.49184e10i			1.84408i	0.387089	+	0.922042i	$0.373481\pi$
$983$			5.49184e10i			1.84408i	−0.387089	+	0.922042i	$0.626519\pi$
$984$	−2.54132e10	−	8.59133e10i	−0.850307	−	2.87460i
$985$			1.02263e10i			0.340952i
$986$	−4.75433e10			−1.57950
$987$	−6.67428e8	−	2.25635e9i	−0.0220950	−	0.0746958i
$988$	1.57990e11			5.21170
$989$	−8.34521e9			−0.274315
$990$	−2.29994e10	+	6.30191e9i	−0.753345	+	0.206419i
$991$	5.40673e10			1.76472			0.882362	−	0.470571i	$-0.155952\pi$
$991$	5.40673e10			1.76472			0.882362	+	0.470571i	$0.155952\pi$
$992$	−7.48885e10			−2.43570
$993$	−9.26583e9	−	3.13246e10i	−0.300304	−	1.01523i
$994$	−1.03208e9			−0.0333320
$995$			7.10976e8i			0.0228810i
$996$	−3.66952e10	−	1.24054e11i	−1.17680	−	3.97835i
$997$			3.57762e10i			1.14330i	0.820497	+	0.571651i	$0.193697\pi$
$997$			3.57762e10i			1.14330i	−0.820497	+	0.571651i	$0.806303\pi$
$998$	7.30573e10			2.32652
$999$	1.59500e10	+	1.36541e10i	0.506153	+	0.433294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.8.d.b.32.2	yes	24
3.2	odd	2	inner	33.8.d.b.32.23	yes	24
11.10	odd	2	inner	33.8.d.b.32.24	yes	24
33.32	even	2	inner	33.8.d.b.32.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.d.b.32.1	✓	24	33.32	even	2	inner
33.8.d.b.32.2	yes	24	1.1	even	1	trivial
33.8.d.b.32.23	yes	24	3.2	odd	2	inner
33.8.d.b.32.24	yes	24	11.10	odd	2	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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	33.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-21.2791 q^{2} +(13.2650 + 44.8446i) q^{3} +324.799 q^{4} -116.081i q^{5} +(-282.268 - 954.252i) q^{6} +73.6975i q^{7} -4187.71 q^{8} +(-1835.08 + 1189.73i) q^{9} +2470.10i q^{10} +(1337.24 - 4207.01i) q^{11} +(4308.48 + 14565.5i) q^{12} -11437.6i q^{13} -1568.22i q^{14} +(5205.60 - 1539.82i) q^{15} +47536.4 q^{16} +19264.4 q^{17} +(39048.8 - 25316.4i) q^{18} +42528.5i q^{19} -37703.0i q^{20} +(-3304.93 + 977.600i) q^{21} +(-28455.2 + 89521.4i) q^{22} -38757.4i q^{23} +(-55550.2 - 187796. i) q^{24} +64650.2 q^{25} +243381. i q^{26} +(-77695.4 - 66511.5i) q^{27} +23936.9i q^{28} +115979. q^{29} +(-110771. + 32765.9i) q^{30} +157493. q^{31} -475503. q^{32} +(206400. + 4161.63i) q^{33} -409928. q^{34} +8554.87 q^{35} +(-596032. + 386424. i) q^{36} -205289. q^{37} -904967. i q^{38} +(512913. - 151720. i) q^{39} +486114. i q^{40} +457481. q^{41} +(70326.0 - 20802.4i) q^{42} -215319. i q^{43} +(434334. - 1.36644e6i) q^{44} +(138105. + 213018. i) q^{45} +824722. i q^{46} +682721. i q^{47} +(630572. + 2.13175e6i) q^{48} +818112. q^{49} -1.37570e6 q^{50} +(255543. + 863903. i) q^{51} -3.71491e6i q^{52} -1.29875e6i q^{53} +(1.65329e6 + 1.41530e6i) q^{54} +(-488354. - 155228. i) q^{55} -308624. i q^{56} +(-1.90717e6 + 564142. i) q^{57} -2.46794e6 q^{58} +2.61276e6i q^{59} +(1.69078e6 - 500132. i) q^{60} -1.67910e6i q^{61} -3.35131e6 q^{62} +(-87680.2 - 135241. i) q^{63} +4.03362e6 q^{64} -1.32768e6 q^{65} +(-4.39201e6 - 88555.7i) q^{66} +2.45218e6 q^{67} +6.25706e6 q^{68} +(1.73806e6 - 514118. i) q^{69} -182040. q^{70} -658125. i q^{71} +(7.68478e6 - 4.98225e6i) q^{72} -1.22508e6i q^{73} +4.36836e6 q^{74} +(857588. + 2.89921e6i) q^{75} +1.38132e7i q^{76} +(310046. + 98551.0i) q^{77} +(-1.09143e7 + 3.22845e6i) q^{78} -6.39822e6i q^{79} -5.51807e6i q^{80} +(1.95205e6 - 4.36650e6i) q^{81} -9.73478e6 q^{82} -8.51697e6 q^{83} +(-1.07344e6 + 317524. i) q^{84} -2.23623e6i q^{85} +4.58180e6i q^{86} +(1.53847e6 + 5.20105e6i) q^{87} +(-5.59996e6 + 1.76178e7i) q^{88} -2.50924e6i q^{89} +(-2.93875e6 - 4.53282e6i) q^{90} +842919. q^{91} -1.25884e7i q^{92} +(2.08915e6 + 7.06272e6i) q^{93} -1.45277e7i q^{94} +4.93675e6 q^{95} +(-6.30757e6 - 2.13238e7i) q^{96} +5.77174e6 q^{97} -1.74087e7 q^{98} +(2.55128e6 + 9.31115e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9} - 6936 q^{12} + 23160 q^{15} + 5844 q^{16} - 17556 q^{22} - 34704 q^{25} + 7560 q^{27} + 131328 q^{31} + 28644 q^{33} - 436080 q^{34} - 302832 q^{36} + 1072488 q^{37}+ \cdots + 53650080 q^{99}+O(q^{100}) \) 24 * q + 120 * q^3 + 1788 * q^4 - 5940 * q^9 - 6936 * q^12 + 23160 * q^15 + 5844 * q^16 - 17556 * q^22 - 34704 * q^25 + 7560 * q^27 + 131328 * q^31 + 28644 * q^33 - 436080 * q^34 - 302832 * q^36 + 1072488 * q^37 - 100296 * q^42 - 1854252 * q^45 + 3172548 * q^48 - 1169304 * q^49 - 4401936 * q^55 - 2920440 * q^58 + 1981452 * q^60 + 14578596 * q^64 + 2895156 * q^66 + 7729200 * q^67 - 4614108 * q^69 - 6924504 * q^70 - 4375800 * q^75 - 26237448 * q^78 + 22367340 * q^81 - 23600232 * q^82 - 25179660 * q^88 + 9380640 * q^91 + 25396908 * q^93 + 72948360 * q^97 + 53650080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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