LMFDB - Embedded newform 99.8.f.b.37.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [99,8,Mod(37,99)] 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("99.37"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(99, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,6] 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:	$30.9261175229$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			37.6
Character	$\chi$	$=$	99.37
Dual form			99.8.f.b.91.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(12.1293 + 8.81245i) q^{2} +(29.9064 + 92.0423i) q^{4} +(3.10808 - 2.25815i) q^{5} +(300.631 + 925.246i) q^{7} +(144.646 - 445.175i) q^{8} +57.5987 q^{10} +(3928.96 - 2012.57i) q^{11} +(7881.27 + 5726.08i) q^{13} +(-4507.24 + 13871.9i) q^{14} +(15699.4 - 11406.3i) q^{16} +(-29814.1 + 21661.2i) q^{17} +(-3261.53 + 10037.9i) q^{19} +(300.797 + 218.542i) q^{20} +(65391.2 + 10212.7i) q^{22} +13400.6 q^{23} +(-24137.4 + 74287.3i) q^{25} +(45133.5 + 138907. i) q^{26} +(-76171.0 + 55341.5i) q^{28} +(12789.3 + 39361.5i) q^{29} +(76358.0 + 55477.3i) q^{31} +231025. q^{32} -552512. q^{34} +(3023.73 + 2196.87i) q^{35} +(145533. + 447903. i) q^{37} +(-128019. + 93011.2i) q^{38} +(-555.701 - 1710.27i) q^{40} +(-13634.9 + 41964.0i) q^{41} +321422. q^{43} +(302743. + 301442. i) q^{44} +(162540. + 118092. i) q^{46} +(59337.5 - 182622. i) q^{47} +(-99441.1 + 72248.2i) q^{49} +(-947422. + 688342. i) q^{50} +(-291341. + 896657. i) q^{52} +(-701340. - 509553. i) q^{53} +(7666.82 - 15127.4i) q^{55} +455381. q^{56} +(-191746. + 590133. i) q^{58} +(-953474. - 2.93449e6i) q^{59} +(-370998. + 269546. i) q^{61} +(437277. + 1.34580e6i) q^{62} +(792649. + 575893. i) q^{64} +37426.0 q^{65} -1.21931e6 q^{67} +(-2.88538e6 - 2.09635e6i) q^{68} +(17315.9 + 53292.9i) q^{70} +(-721185. + 523972. i) q^{71} +(-910226. - 2.80139e6i) q^{73} +(-2.18192e6 + 6.71525e6i) q^{74} -1.02146e6 q^{76} +(3.04329e6 + 3.03021e6i) q^{77} +(5.31286e6 + 3.86002e6i) q^{79} +(23037.9 - 70903.3i) q^{80} +(-535188. + 388837. i) q^{82} +(6.31652e6 - 4.58922e6i) q^{83} +(-43750.3 + 134649. i) q^{85} +(3.89862e6 + 2.83251e6i) q^{86} +(-327638. - 2.04018e6i) q^{88} +1.00202e7 q^{89} +(-2.92868e6 + 9.01355e6i) q^{91} +(400763. + 1.23342e6i) q^{92} +(2.32907e6 - 1.69217e6i) q^{94} +(12530.1 + 38563.8i) q^{95} +(821688. + 596991. i) q^{97} -1.84283e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 6 q^{2} + 160 q^{4} - 773 q^{5} + 1289 q^{7} - 2956 q^{8} - 10640 q^{10} - 13209 q^{11} + 13499 q^{13} + 3318 q^{14} - 113196 q^{16} - 30296 q^{17} - 6858 q^{19} - 76725 q^{20} - 48859 q^{22} + 166984 q^{23}+ \cdots - 140532178 q^{98}+O(q^{100}) $ 28 * q + 6 * q^2 + 160 * q^4 - 773 * q^5 + 1289 * q^7 - 2956 * q^8 - 10640 * q^10 - 13209 * q^11 + 13499 * q^13 + 3318 * q^14 - 113196 * q^16 - 30296 * q^17 - 6858 * q^19 - 76725 * q^20 - 48859 * q^22 + 166984 * q^23 + 99832 * q^25 - 340424 * q^26 + 657387 * q^28 - 192014 * q^29 + 396068 * q^31 + 303498 * q^32 - 1229124 * q^34 + 725859 * q^35 + 811053 * q^37 - 1548798 * q^38 - 1427263 * q^40 - 1041497 * q^41 - 5265288 * q^43 + 5341085 * q^44 + 1198651 * q^46 - 1667505 * q^47 + 2968140 * q^49 - 11247432 * q^50 + 2325763 * q^52 + 1625736 * q^53 - 8338690 * q^55 + 18201906 * q^56 + 14965553 * q^58 + 2587454 * q^59 + 5801619 * q^61 - 15631121 * q^62 - 3732846 * q^64 + 15368174 * q^65 - 7141262 * q^67 - 17394545 * q^68 - 4329200 * q^70 - 3569199 * q^71 + 125008 * q^73 + 13691530 * q^74 - 19690428 * q^76 + 6038739 * q^77 + 17075485 * q^79 - 26606436 * q^80 + 19886007 * q^82 + 4645575 * q^83 + 12002715 * q^85 + 12296287 * q^86 - 50905990 * q^88 - 9601664 * q^89 - 14129477 * q^91 + 90776021 * q^92 + 1047679 * q^94 - 58935661 * q^95 - 22170261 * q^97 - 140532178 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	12.1293	+	8.81245i	1.07209	+	0.778918i	0.976286	−	0.216483i	$-0.0694585\pi$
$2$	12.1293	+	8.81245i	1.07209	+	0.778918i	0.0958018	+	0.995400i	$0.469458\pi$
$3$		0			0
$3$		0			0
$4$	29.9064	+	92.0423i	0.233643	+	0.719081i
$5$	3.10808	−	2.25815i	0.0111198	−	0.00807901i	−0.582211	−	0.813037i	$-0.697812\pi$
$5$	3.10808	−	2.25815i	0.0111198	−	0.00807901i	0.593331	+	0.804958i	$0.297812\pi$
$6$		0			0
$7$	300.631	+	925.246i	0.331276	+	1.01956i	0.968527	+	0.248907i	$0.0800713\pi$
$7$	300.631	+	925.246i	0.331276	+	1.01956i	−0.637251	+	0.770656i	$0.719929\pi$
$8$	144.646	−	445.175i	0.0998830	−	0.307408i
$9$		0			0
$10$	57.5987			0.0182143
$11$	3928.96	−	2012.57i	0.890027	−	0.455908i
$11$	3928.96	−	2012.57i	0.890027	−	0.455908i
$12$		0			0
$13$	7881.27	+	5726.08i	0.994935	+	0.722862i	0.960996	−	0.276562i	$-0.0891950\pi$
$13$	7881.27	+	5726.08i	0.994935	+	0.722862i	0.0339384	+	0.999424i	$0.489195\pi$
$14$	−4507.24	+	13871.9i	−0.438999	+	1.35110i
$15$		0			0
$16$	15699.4	−	11406.3i	0.958216	−	0.696185i
$17$	−29814.1	+	21661.2i	−1.47180	+	1.06933i	−0.491719	+	0.870754i	$0.663631\pi$
$17$	−29814.1	+	21661.2i	−1.47180	+	1.06933i	−0.980086	+	0.198575i	$0.936369\pi$
$18$		0			0
$19$	−3261.53	+	10037.9i	−0.109090	+	0.335743i	−0.990669	−	0.136293i	$-0.956481\pi$
$19$	−3261.53	+	10037.9i	−0.109090	+	0.335743i	0.881579	+	0.472037i	$0.156481\pi$
$20$	300.797	+	218.542i	0.00840753	+	0.00610843i
$21$		0			0
$22$	65391.2	+	10212.7i	1.30930	+	0.204484i
$23$	13400.6			0.229655			0.114828	−	0.993385i	$-0.463368\pi$
$23$	13400.6			0.229655			0.114828	+	0.993385i	$0.463368\pi$
$24$		0			0
$25$	−24137.4	+	74287.3i	−0.308959	+	0.950877i
$26$	45133.5	+	138907.i	0.503607	+	1.54994i
$27$		0			0
$28$	−76171.0	+	55341.5i	−0.655748	+	0.476429i
$29$	12789.3	+	39361.5i	0.0973766	+	0.299694i	0.987866	−	0.155310i	$-0.0496376\pi$
$29$	12789.3	+	39361.5i	0.0973766	+	0.299694i	−0.890489	+	0.455004i	$0.849638\pi$
$30$		0			0
$31$	76358.0	+	55477.3i	0.460350	+	0.334464i	0.793669	−	0.608350i	$-0.208168\pi$
$31$	76358.0	+	55477.3i	0.460350	+	0.334464i	−0.333318	+	0.942814i	$0.608168\pi$
$32$	231025.			1.24633
$33$		0			0
$34$	−552512.			−2.41082
$35$	3023.73	+	2196.87i	0.0119208	+	0.00866096i
$36$		0			0
$37$	145533.	+	447903.i	0.472340	+	1.45371i	0.849512	+	0.527569i	$0.176896\pi$
$37$	145533.	+	447903.i	0.472340	+	1.45371i	−0.377173	+	0.926143i	$0.623104\pi$
$38$	−128019.	+	93011.2i	−0.378470	+	0.274975i
$39$		0			0
$40$	−555.701	−	1710.27i	−0.00137288	−	0.00422528i
$41$	−13634.9	+	41964.0i	−0.0308965	+	0.0950898i	−0.965316	−	0.261086i	$-0.915919\pi$
$41$	−13634.9	+	41964.0i	−0.0308965	+	0.0950898i	0.934419	+	0.356176i	$0.115919\pi$
$42$		0			0
$43$	321422.			0.616504			0.308252	−	0.951305i	$-0.400256\pi$
$43$	321422.			0.616504			0.308252	+	0.951305i	$0.400256\pi$
$44$	302743.	+	301442.i	0.535784	+	0.533481i
$45$		0			0
$46$	162540.	+	118092.i	0.246211	+	0.178883i
$47$	59337.5	−	182622.i	0.0833656	−	0.256573i	−0.900682	−	0.434479i	$-0.856932\pi$
$47$	59337.5	−	182622.i	0.0833656	−	0.256573i	0.984047	+	0.177906i	$0.0569324\pi$
$48$		0			0
$49$	−99441.1	+	72248.2i	−0.120748	+	0.0877285i
$50$	−947422.	+	688342.i	−1.07189	+	0.778771i
$51$		0			0
$52$	−291341.	+	896657.i	−0.287336	+	0.884330i
$53$	−701340.	−	509553.i	−0.647088	−	0.470137i	0.215190	−	0.976572i	$-0.430963\pi$
$53$	−701340.	−	509553.i	−0.647088	−	0.470137i	−0.862278	+	0.506435i	$0.830963\pi$
$54$		0			0
$55$	7666.82	−	15127.4i	0.00621364	−	0.0122601i
$56$	455381.			0.346511
$57$		0			0
$58$	−191746.	+	590133.i	−0.129041	+	0.397147i
$59$	−953474.	−	2.93449e6i	−0.604403	−	1.86016i	−0.500844	−	0.865538i	$-0.666977\pi$
$59$	−953474.	−	2.93449e6i	−0.604403	−	1.86016i	−0.103559	−	0.994623i	$-0.533023\pi$
$60$		0			0
$61$	−370998.	+	269546.i	−0.209275	+	0.152047i	−0.687486	−	0.726198i	$-0.741286\pi$
$61$	−370998.	+	269546.i	−0.209275	+	0.152047i	0.478211	+	0.878245i	$0.341286\pi$
$62$	437277.	+	1.34580e6i	0.233016	+	0.717150i
$63$		0			0
$64$	792649.	+	575893.i	0.377964	+	0.274607i
$65$	37426.0			0.0169035
$66$		0			0
$67$	−1.21931e6			−0.495282			−0.247641	−	0.968852i	$-0.579655\pi$
$67$	−1.21931e6			−0.495282			−0.247641	+	0.968852i	$0.579655\pi$
$68$	−2.88538e6	−	2.09635e6i	−1.11281	−	0.808505i
$69$		0			0
$70$	17315.9	+	53292.9i	0.00603396	+	0.0185706i
$71$	−721185.	+	523972.i	−0.239135	+	0.173741i	−0.700898	−	0.713262i	$-0.747217\pi$
$71$	−721185.	+	523972.i	−0.239135	+	0.173741i	0.461763	+	0.887003i	$0.347217\pi$
$72$		0			0
$73$	−910226.	−	2.80139e6i	−0.273854	−	0.842836i	−0.989520	−	0.144394i	$-0.953877\pi$
$73$	−910226.	−	2.80139e6i	−0.273854	−	0.842836i	0.715666	−	0.698443i	$-0.246123\pi$
$74$	−2.18192e6	+	6.71525e6i	−0.625932	+	1.92642i
$75$		0			0
$76$	−1.02146e6			−0.266915
$77$	3.04329e6	+	3.03021e6i	0.759672	+	0.756407i
$78$		0			0
$79$	5.31286e6	+	3.86002e6i	1.21237	+	0.880835i	0.995443	−	0.0953541i	$-0.0303983\pi$
$79$	5.31286e6	+	3.86002e6i	1.21237	+	0.880835i	0.216922	+	0.976189i	$0.430398\pi$
$80$	23037.9	−	70903.3i	0.00503069	−	0.0154829i
$81$		0			0
$82$	−535188.	+	388837.i	−0.107191	+	0.0778788i
$83$	6.31652e6	−	4.58922e6i	1.21256	−	0.880978i	0.217102	−	0.976149i	$-0.430340\pi$
$83$	6.31652e6	−	4.58922e6i	1.21256	−	0.880978i	0.995461	+	0.0951705i	$0.0303396\pi$
$84$		0			0
$85$	−43750.3	+	134649.i	−0.00772706	+	0.0237814i
$86$	3.89862e6	+	2.83251e6i	0.660947	+	0.480206i
$87$		0			0
$88$	−327638.	−	2.04018e6i	−0.0512514	−	0.319139i
$89$	1.00202e7			1.50665			0.753326	−	0.657647i	$-0.228448\pi$
$89$	1.00202e7			1.50665			0.753326	+	0.657647i	$0.228448\pi$
$90$		0			0
$91$	−2.92868e6	+	9.01355e6i	−0.407406	+	1.25387i
$92$	400763.	+	1.23342e6i	0.0536574	+	0.165141i
$93$		0			0
$94$	2.32907e6	−	1.69217e6i	0.289224	−	0.210134i
$95$	12530.1	+	38563.8i	0.00149942	+	0.00461474i
$96$		0			0
$97$	821688.	+	596991.i	0.0914126	+	0.0664151i	0.632553	−	0.774517i	$-0.282007\pi$
$97$	821688.	+	596991.i	0.0914126	+	0.0664151i	−0.541140	+	0.840932i	$0.682007\pi$
$98$	−1.84283e6			−0.197786
$99$		0			0
$100$	−7.55943e6			−0.755943
$101$	−1.03730e7	−	7.53646e6i	−1.00180	−	0.727851i	−0.0393272	−	0.999226i	$-0.512521\pi$
$101$	−1.03730e7	−	7.53646e6i	−1.00180	−	0.727851i	−0.962474	+	0.271376i	$0.912521\pi$
$102$		0			0
$103$	−5.76942e6	−	1.77565e7i	−0.520238	−	1.60113i	−0.773545	−	0.633742i	$-0.781518\pi$
$103$	−5.76942e6	−	1.77565e7i	−0.520238	−	1.60113i	0.253307	−	0.967386i	$-0.418482\pi$
$104$	3.68910e6	−	2.68029e6i	0.321591	−	0.233650i
$105$		0			0
$106$	−4.01635e6	−	1.23610e7i	−0.327537	−	1.00806i
$107$	−2.73931e6	+	8.43073e6i	−0.216171	+	0.665307i	0.782897	+	0.622151i	$0.213741\pi$
$107$	−2.73931e6	+	8.43073e6i	−0.216171	+	0.665307i	−0.999068	+	0.0431557i	$0.986259\pi$
$108$		0			0
$109$	1.21609e7			0.899440			0.449720	−	0.893170i	$-0.351524\pi$
$109$	1.21609e7			0.899440			0.449720	+	0.893170i	$0.351524\pi$
$110$	226303.	−	115922.i	0.0162112	−	0.00830404i
$111$		0			0
$112$	1.52733e7	+	1.10967e7i	1.02724	+	0.746332i
$113$	1.76527e6	−	5.43293e6i	0.115089	−	0.354209i	−0.876876	−	0.480716i	$-0.840377\pi$
$113$	1.76527e6	−	5.43293e6i	0.115089	−	0.354209i	0.991966	+	0.126507i	$0.0403767\pi$
$114$		0			0
$115$	41650.1	−	30260.6i	0.00255372	−	0.00185539i
$116$	−3.24044e6	+	2.35432e6i	−0.192753	+	0.140043i
$117$		0			0
$118$	1.42951e7	−	4.39957e7i	0.800939	−	2.46504i
$119$	−2.90050e7	−	2.10733e7i	−1.57782	−	1.14635i
$120$		0			0
$121$	1.13863e7	−	1.58146e7i	0.584296	−	0.811541i
$122$	−6.87530e6			−0.342793
$123$		0			0
$124$	−2.82267e6	+	8.68729e6i	−0.132949	+	0.409174i
$125$	185479.	+	570847.i	0.00849397	+	0.0261418i
$126$		0			0
$127$	−9.87717e6	+	7.17618e6i	−0.427878	+	0.310871i	−0.780800	−	0.624781i	$-0.785188\pi$
$127$	−9.87717e6	+	7.17618e6i	−0.427878	+	0.310871i	0.352922	+	0.935653i	$0.385188\pi$
$128$	−4.59877e6	−	1.41536e7i	−0.193824	−	0.596528i
$129$		0			0
$130$	453951.	+	329814.i	0.0181220	+	0.0131664i
$131$	−567295.			−0.0220475			−0.0110237	−	0.999939i	$-0.503509\pi$
$131$	−567295.			−0.0220475			−0.0110237	+	0.999939i	$0.503509\pi$
$132$		0			0
$133$	−1.02681e7			−0.378450
$134$	−1.47894e7	−	1.07451e7i	−0.530986	−	0.385784i
$135$		0			0
$136$	5.33053e6	+	1.64057e7i	0.181712	+	0.559253i
$137$	4.09822e7	−	2.97753e7i	1.36167	−	0.989315i	0.363338	−	0.931657i	$-0.381637\pi$
$137$	4.09822e7	−	2.97753e7i	1.36167	−	0.989315i	0.998336	−	0.0576575i	$-0.0183631\pi$
$138$		0			0
$139$	−1.48420e7	−	4.56788e7i	−0.468748	−	1.44266i	−0.854207	−	0.519933i	$-0.825957\pi$
$139$	−1.48420e7	−	4.56788e7i	−0.468748	−	1.44266i	0.385459	−	0.922725i	$-0.374043\pi$
$140$	−111776.	+	344012.i	−0.00344271	+	0.0105956i
$141$		0			0
$142$	−1.33649e7			−0.391704
$143$	4.24893e7	+	6.63589e6i	1.21508	+	0.189768i
$144$		0			0
$145$	128635.	+	93458.5i	0.00350404	+	0.00254584i
$146$	1.36467e7	−	4.20002e7i	0.362904	−	1.11690i
$147$		0			0
$148$	−3.68737e7	+	2.67903e7i	−0.934977	+	0.679300i
$149$	−4.29481e7	+	3.12036e7i	−1.06363	+	0.772775i	−0.974757	−	0.223267i	$-0.928328\pi$
$149$	−4.29481e7	+	3.12036e7i	−1.06363	+	0.772775i	−0.0888769	+	0.996043i	$0.528328\pi$
$150$		0			0
$151$	−2.12772e7	+	6.54844e7i	−0.502915	+	1.54781i	0.301332	+	0.953519i	$0.402569\pi$
$151$	−2.12772e7	+	6.54844e7i	−0.502915	+	1.54781i	−0.804247	+	0.594295i	$0.797431\pi$
$152$	3.99688e6	+	2.90390e6i	0.0923141	+	0.0670701i
$153$		0			0
$154$	1.02094e7	+	6.35732e7i	0.225256	+	1.40266i
$155$	362603.			0.00782115
$156$		0			0
$157$	1.92919e7	−	5.93743e7i	0.397856	−	1.22448i	−0.528859	−	0.848710i	$-0.677380\pi$
$157$	1.92919e7	−	5.93743e7i	0.397856	−	1.22448i	0.926715	−	0.375765i	$-0.122620\pi$
$158$	3.04250e7	+	9.36386e7i	0.613665	+	1.88867i
$159$		0			0
$160$	718045.	−	521690.i	0.0138590	−	0.0100691i
$161$	4.02863e6	+	1.23988e7i	0.0760793	+	0.234148i
$162$		0			0
$163$	−5.66777e7	−	4.11788e7i	−1.02508	−	0.744761i	−0.0577580	−	0.998331i	$-0.518395\pi$
$163$	−5.66777e7	−	4.11788e7i	−1.02508	−	0.744761i	−0.967317	+	0.253570i	$0.918395\pi$
$164$	−4.27024e6			−0.0755960
$165$		0			0
$166$	1.17057e8			1.98618
$167$	2.14118e7	+	1.55565e7i	0.355750	+	0.258467i	0.751277	−	0.659987i	$-0.229438\pi$
$167$	2.14118e7	+	1.55565e7i	0.355750	+	0.258467i	−0.395527	+	0.918454i	$0.629438\pi$
$168$		0			0
$169$	9.93610e6	+	3.05802e7i	0.158348	+	0.487345i
$170$	−1.71725e6	+	1.24766e6i	−0.0268079	+	0.0194771i
$171$		0			0
$172$	9.61256e6	+	2.95844e7i	0.144042	+	0.443316i
$173$	−3.37909e7	+	1.03998e8i	−0.496180	+	1.52708i	0.318931	+	0.947778i	$0.396676\pi$
$173$	−3.37909e7	+	1.03998e8i	−0.496180	+	1.52708i	−0.815110	+	0.579306i	$0.803324\pi$
$174$		0			0
$175$	−7.59904e7			−1.07183
$176$	3.87263e7	−	7.64110e7i	0.535442	−	1.05648i
$177$		0			0
$178$	1.21538e8	+	8.83028e7i	1.61526	+	1.17356i
$179$	−5.80543e6	+	1.78673e7i	−0.0756569	+	0.232848i	−0.981732	−	0.190269i	$-0.939064\pi$
$179$	−5.80543e6	+	1.78673e7i	−0.0756569	+	0.232848i	0.906075	+	0.423117i	$0.139064\pi$
$180$		0			0
$181$	−7.93024e7	+	5.76166e7i	−0.994057	+	0.722225i	−0.960806	−	0.277222i	$-0.910586\pi$
$181$	−7.93024e7	+	5.76166e7i	−0.994057	+	0.722225i	−0.0332516	+	0.999447i	$0.510586\pi$
$182$	−1.14954e8	+	8.35192e7i	−1.41343	+	1.02692i
$183$		0			0
$184$	1.93834e6	−	5.96560e6i	0.0229387	−	0.0705979i
$185$	1.46376e6	+	1.06348e6i	0.0169969	+	0.0123490i
$186$		0			0
$187$	−7.35436e7	+	1.45109e8i	−0.822430	+	1.62274i
$188$	1.85835e7			0.203974
$189$		0			0
$190$	−187860.	+	578172.i	−0.00198699	+	0.00611533i
$191$	1.48145e7	+	4.55943e7i	0.153840	+	0.473471i	0.998042	−	0.0625550i	$-0.0199249\pi$
$191$	1.48145e7	+	4.55943e7i	0.153840	+	0.473471i	−0.844201	+	0.536026i	$0.819925\pi$
$192$		0			0
$193$	4.65794e7	−	3.38419e7i	0.466383	−	0.338847i	−0.329647	−	0.944104i	$-0.606930\pi$
$193$	4.65794e7	−	3.38419e7i	0.466383	−	0.338847i	0.796030	+	0.605257i	$0.206930\pi$
$194$	4.70554e6	+	1.44822e7i	0.0462704	+	0.142406i
$195$		0			0
$196$	−9.62382e6	−	6.99211e6i	−0.0912959	−	0.0663303i
$197$	−6.71674e7			−0.625931			−0.312966	−	0.949764i	$-0.601322\pi$
$197$	−6.71674e7			−0.625931			−0.312966	+	0.949764i	$0.601322\pi$
$198$		0			0
$199$	−1.04918e7			−0.0943768			−0.0471884	−	0.998886i	$-0.515026\pi$
$199$	−1.04918e7			−0.0943768			−0.0471884	+	0.998886i	$0.515026\pi$
$200$	2.95794e7	+	2.14907e7i	0.261448	+	0.189953i
$201$		0			0
$202$	−5.94031e7	−	1.82824e8i	−0.507083	−	1.56064i
$203$	−3.25742e7	+	2.36666e7i	−0.273299	+	0.198563i
$204$		0			0
$205$	52382.7	+	161217.i	0.000424668	+	0.00130699i
$206$	8.64988e7	−	2.66216e8i	0.689406	−	2.12177i
$207$		0			0
$208$	1.89045e8			1.45661
$209$	7.38770e6	+	4.60028e7i	0.0559754	+	0.348555i
$210$		0			0
$211$	1.59514e8	+	1.15894e8i	1.16899	+	0.849319i	0.990887	−	0.134693i	$-0.0430049\pi$
$211$	1.59514e8	+	1.15894e8i	1.16899	+	0.849319i	0.178100	+	0.984012i	$0.443005\pi$
$212$	2.59259e7	−	7.97919e7i	0.186878	−	0.575153i
$213$		0			0
$214$	−1.07521e8	+	7.81188e7i	−0.749974	+	0.544888i
$215$	999005.	−	725820.i	0.00685540	−	0.00498074i
$216$		0			0
$217$	−2.83746e7	+	8.73281e7i	−0.188504	+	0.580156i
$218$	1.47503e8	+	1.07167e8i	0.964279	+	0.700590i
$219$		0			0
$220$	1.62165e6	+	253266.i	0.0102678	+	0.00160360i
$221$	−3.59007e8			−2.23733
$222$		0			0
$223$	2.61370e7	−	8.04413e7i	0.157829	−	0.485749i	−0.840607	−	0.541645i	$-0.817802\pi$
$223$	2.61370e7	−	8.04413e7i	0.157829	−	0.485749i	0.998437	+	0.0558962i	$0.0178016\pi$
$224$	6.94533e7	+	2.13755e8i	0.412881	+	1.27072i
$225$		0			0
$226$	6.92888e7	−	5.03413e7i	0.399286	−	0.290098i
$227$	−7.32485e7	−	2.25436e8i	−0.415631	−	1.27918i	−0.911685	−	0.410890i	$-0.865218\pi$
$227$	−7.32485e7	−	2.25436e8i	−0.415631	−	1.27918i	0.496054	−	0.868292i	$-0.334782\pi$
$228$		0			0
$229$	−2.50219e8	−	1.81795e8i	−1.37688	−	1.00036i	−0.997164	−	0.0752610i	$-0.976021\pi$
$229$	−2.50219e8	−	1.81795e8i	−1.37688	−	1.00036i	−0.379718	−	0.925102i	$-0.623979\pi$
$230$	771856.			0.00418301
$231$		0			0
$232$	1.93727e7			0.101855
$233$	−1.40253e8	−	1.01900e8i	−0.726383	−	0.527748i	0.162034	−	0.986785i	$-0.448194\pi$
$233$	−1.40253e8	−	1.01900e8i	−0.726383	−	0.527748i	−0.888417	+	0.459037i	$0.848194\pi$
$234$		0			0
$235$	−227963.	−	701597.i	−0.00114585	−	0.00352655i
$236$	2.41582e8	−	1.75520e8i	1.19639	−	0.869229i
$237$		0			0
$238$	−1.66102e8	−	5.11209e8i	−0.798648	−	2.45799i
$239$	4.15422e7	−	1.27854e8i	0.196833	−	0.605789i	−0.803118	−	0.595820i	$-0.796827\pi$
$239$	4.15422e7	−	1.27854e8i	0.196833	−	0.605789i	0.999950	−	0.00996816i	$-0.00317302\pi$
$240$		0			0
$241$	−8.52837e7			−0.392470			−0.196235	−	0.980557i	$-0.562871\pi$
$241$	−8.52837e7			−0.392470			−0.196235	+	0.980557i	$0.562871\pi$
$242$	2.77473e8	−	9.14795e7i	1.25854	−	0.414925i
$243$		0			0
$244$	−3.59048e7	−	2.60864e7i	−0.158230	−	0.114961i
$245$	−145924.	+	449106.i	−0.000633934	+	0.00195105i
$246$		0			0
$247$	−8.31831e7	+	6.04360e7i	−0.351233	+	0.255186i
$248$	3.57420e7	−	2.59681e7i	0.148798	−	0.108108i
$249$		0			0
$250$	−2.78083e6	+	8.55850e6i	−0.0112560	+	0.0346424i
$251$	−1.24212e8	−	9.02451e7i	−0.495798	−	0.360218i	0.311612	−	0.950209i	$-0.399131\pi$
$251$	−1.24212e8	−	9.02451e7i	−0.495798	−	0.360218i	−0.807410	+	0.589991i	$0.799131\pi$
$252$		0			0
$253$	5.26503e7	−	2.69697e7i	0.204399	−	0.104702i
$254$	−1.83043e8			−0.700866
$255$		0			0
$256$	1.07702e8	−	3.31471e8i	0.401220	−	1.23483i
$257$	−4.93355e7	−	1.51839e8i	−0.181298	−	0.557979i	0.818567	−	0.574412i	$-0.194769\pi$
$257$	−4.93355e7	−	1.51839e8i	−0.181298	−	0.557979i	−0.999865	+	0.0164326i	$0.994769\pi$
$258$		0			0
$259$	−3.70669e8	+	2.69307e8i	−1.32568	+	0.963160i
$260$	1.11927e6	+	3.44477e6i	0.00394939	+	0.0121550i
$261$		0			0
$262$	−6.88088e6	−	4.99925e6i	−0.0236369	−	0.0171732i
$263$	4.05134e8			1.37326			0.686631	−	0.727006i	$-0.259089\pi$
$263$	4.05134e8			1.37326			0.686631	+	0.727006i	$0.259089\pi$
$264$		0			0
$265$	−3.33047e6			−0.0109937
$266$	−1.24545e8	−	9.04870e7i	−0.405732	−	0.294782i
$267$		0			0
$268$	−3.64652e7	−	1.12228e8i	−0.115719	−	0.356148i
$269$	−1.28630e8	+	9.34552e7i	−0.402911	+	0.292732i	−0.770726	−	0.637167i	$-0.780106\pi$
$269$	−1.28630e8	+	9.34552e7i	−0.402911	+	0.292732i	0.367815	+	0.929899i	$0.380106\pi$
$270$		0			0
$271$	8.22457e7	+	2.53126e8i	0.251027	+	0.772582i	0.994586	+	0.103912i	$0.0331361\pi$
$271$	8.22457e7	+	2.53126e8i	0.251027	+	0.772582i	−0.743559	+	0.668670i	$0.766864\pi$
$272$	−2.20990e8	+	6.80136e8i	−0.665856	+	2.04930i
$273$		0			0
$274$	7.59479e8			2.23043
$275$	5.46737e7	+	3.40450e8i	0.158531	+	0.987163i
$276$		0			0
$277$	3.64036e8	+	2.64488e8i	1.02912	+	0.747699i	0.968132	−	0.250440i	$-0.0805752\pi$
$277$	3.64036e8	+	2.64488e8i	1.02912	+	0.747699i	0.0609870	+	0.998139i	$0.480575\pi$
$278$	2.22520e8	−	6.84846e8i	0.621172	−	1.91177i
$279$		0			0
$280$	1.41536e6	−	1.02832e6i	0.00385313	−	0.00279947i
$281$	−1.55424e8	+	1.12922e8i	−0.417876	+	0.303604i	−0.776783	−	0.629769i	$-0.783150\pi$
$281$	−1.55424e8	+	1.12922e8i	−0.417876	+	0.303604i	0.358907	+	0.933373i	$0.383150\pi$
$282$		0			0
$283$	1.41068e8	−	4.34163e8i	0.369979	−	1.13868i	−0.576825	−	0.816867i	$-0.695709\pi$
$283$	1.41068e8	−	4.34163e8i	0.369979	−	1.13868i	0.946804	−	0.321810i	$-0.104291\pi$
$284$	−6.97956e7	−	5.07095e7i	−0.180806	−	0.131364i
$285$		0			0
$286$	4.56887e8	+	4.54924e8i	1.15486	+	1.14989i
$287$	−4.29262e7			−0.107185
$288$		0			0
$289$	2.92870e8	−	9.01362e8i	0.713728	−	2.19663i
$290$	736648.	+	2.26717e6i	0.00177365	+	0.00545872i
$291$		0			0
$292$	2.30625e8	−	1.67559e8i	0.542083	−	0.393846i
$293$	2.58616e8	+	7.95938e8i	0.600646	+	1.84860i	0.524330	+	0.851515i	$0.324316\pi$
$293$	2.58616e8	+	7.95938e8i	0.600646	+	1.84860i	0.0763166	+	0.997084i	$0.475684\pi$
$294$		0			0
$295$	−9.59000e6	−	6.96754e6i	−0.0217491	−	0.0158016i
$296$	2.20446e8			0.494062
$297$		0			0
$298$	−7.95911e8			−1.74224
$299$	1.05614e8	+	7.67328e7i	0.228492	+	0.166009i
$300$		0			0
$301$	9.66293e7	+	2.97394e8i	0.204233	+	0.628565i
$302$	−8.35155e8	+	6.06776e8i	−1.74479	+	1.26766i
$303$		0			0
$304$	6.32917e7	+	1.94792e8i	0.129208	+	0.397661i
$305$	−544416.	+	1.67554e6i	−0.00109871	+	0.00338147i
$306$		0			0
$307$	−4.79231e8			−0.945281			−0.472641	−	0.881255i	$-0.656699\pi$
$307$	−4.79231e8			−0.945281			−0.472641	+	0.881255i	$0.656699\pi$
$308$	−1.87894e8	+	3.70734e8i	−0.366425	+	0.722995i
$309$		0			0
$310$	4.39812e6	+	3.19542e6i	0.00838496	+	0.00609203i
$311$	2.10610e8	−	6.48190e8i	0.397024	−	1.22192i	−0.530350	−	0.847779i	$-0.677939\pi$
$311$	2.10610e8	−	6.48190e8i	0.397024	−	1.22192i	0.927374	−	0.374136i	$-0.122061\pi$
$312$		0			0
$313$	−2.29633e8	+	1.66838e8i	−0.423282	+	0.307532i	−0.778957	−	0.627077i	$-0.784251\pi$
$313$	−2.29633e8	+	1.66838e8i	−0.423282	+	0.307532i	0.355675	+	0.934610i	$0.384251\pi$
$314$	7.57230e8	−	5.50160e8i	1.38030	−	1.00285i
$315$		0			0
$316$	−1.96397e8	+	6.04447e8i	−0.350130	+	1.07759i
$317$	5.04864e7	+	3.66805e7i	0.0890158	+	0.0646738i	0.631403	−	0.775455i	$-0.282479\pi$
$317$	5.04864e7	+	3.66805e7i	0.0890158	+	0.0646738i	−0.542387	+	0.840129i	$0.682479\pi$
$318$		0			0
$319$	1.29467e8	+	1.28910e8i	0.223301	+	0.222341i
$320$	3.76407e6			0.00642145
$321$		0			0
$322$	−6.03997e7	+	1.85891e8i	−0.100818	+	0.310287i
$323$	−1.20195e8	−	3.69921e8i	−0.198461	−	0.610801i
$324$		0			0
$325$	−6.15608e8	+	4.47265e8i	−0.994747	+	0.722726i
$326$	−3.24575e8	−	9.98939e8i	−0.518864	−	1.59690i
$327$		0			0
$328$	1.67091e7	+	1.21399e7i	0.0261454	+	0.0189957i
$329$	1.86809e8			0.289209
$330$		0			0
$331$	−7.79464e8			−1.18140			−0.590702	−	0.806890i	$-0.701149\pi$
$331$	−7.79464e8			−1.18140			−0.590702	+	0.806890i	$0.701149\pi$
$332$	6.11306e8	+	4.44140e8i	0.916802	+	0.666096i
$333$		0			0
$334$	1.22618e8	+	3.77380e8i	0.180070	+	0.554200i
$335$	−3.78972e6	+	2.75339e6i	−0.00550744	+	0.00400139i
$336$		0			0
$337$	−3.63029e8	−	1.11729e9i	−0.516698	−	1.59023i	−0.780172	−	0.625565i	$-0.784868\pi$
$337$	−3.63029e8	−	1.11729e9i	−0.516698	−	1.59023i	0.263474	−	0.964666i	$-0.415132\pi$
$338$	−1.48968e8	+	4.58477e8i	−0.209839	+	0.645817i
$339$		0			0
$340$	−1.37019e7			−0.0189062
$341$	4.11660e8	+	6.42921e7i	0.562209	+	0.0878046i
$342$		0			0
$343$	5.51436e8	+	4.00642e8i	0.737846	+	0.536077i
$344$	4.64924e7	−	1.43089e8i	0.0615783	−	0.189519i
$345$		0			0
$346$	−1.32634e9	+	9.63639e8i	−1.72142	+	1.25069i
$347$	2.04810e8	−	1.48803e8i	0.263147	−	0.191187i	−0.448386	−	0.893840i	$-0.648001\pi$
$347$	2.04810e8	−	1.48803e8i	0.263147	−	0.191187i	0.711533	+	0.702652i	$0.248001\pi$
$348$		0			0
$349$	3.35012e8	−	1.03106e9i	0.421863	−	1.29836i	−0.484103	−	0.875011i	$-0.660854\pi$
$349$	3.35012e8	−	1.03106e9i	0.421863	−	1.29836i	0.905966	−	0.423350i	$-0.139146\pi$
$350$	−9.21710e8	−	6.69662e8i	−1.14910	−	0.834867i
$351$		0			0
$352$	9.07689e8	−	4.64955e8i	1.10927	−	0.568214i
$353$	−9.31667e7			−0.112733			−0.0563663	−	0.998410i	$-0.517951\pi$
$353$	−9.31667e7			−0.112733			−0.0563663	+	0.998410i	$0.517951\pi$
$354$		0			0
$355$	−1.05829e6	+	3.25709e6i	−0.00125547	+	0.00386394i
$356$	2.99669e8	+	9.22286e8i	0.352019	+	1.08340i
$357$		0			0
$358$	−2.27870e8	+	1.65557e8i	−0.262480	+	0.190703i
$359$	1.73493e7	+	5.33955e7i	0.0197902	+	0.0609080i	0.960464	−	0.278405i	$-0.0898056\pi$
$359$	1.73493e7	+	5.33955e7i	0.0197902	+	0.0609080i	−0.940674	+	0.339313i	$0.889806\pi$
$360$		0			0
$361$	6.33035e8	+	4.59927e8i	0.708194	+	0.514533i
$362$	−1.46963e9			−1.62827
$363$		0			0
$364$	−9.17214e8			−0.996818
$365$	−9.15502e6	−	6.65151e6i	−0.00985449	−	0.00715971i
$366$		0			0
$367$	2.88719e8	+	8.88584e8i	0.304890	+	0.938356i	0.979718	+	0.200381i	$0.0642178\pi$
$367$	2.88719e8	+	8.88584e8i	0.304890	+	0.938356i	−0.674828	+	0.737975i	$0.735782\pi$
$368$	2.10381e8	−	1.52851e8i	0.220059	−	0.159882i
$369$		0			0
$370$	8.38248e6	+	2.57986e7i	0.00860333	+	0.0264783i
$371$	2.60618e8	−	8.02100e8i	0.264969	−	0.815492i
$372$		0			0
$373$	1.08253e9			1.08009			0.540043	−	0.841637i	$-0.318408\pi$
$373$	1.08253e9			1.08009			0.540043	+	0.841637i	$0.318408\pi$
$374$	−2.17080e9	+	1.11197e9i	−2.14570	+	1.09911i
$375$		0			0
$376$	−7.27158e7	−	5.28311e7i	−0.0705458	−	0.0512545i
$377$	−1.24591e8	+	3.83451e8i	−0.119754	+	0.368566i
$378$		0			0
$379$	1.24586e9	−	9.05168e8i	1.17552	−	0.854067i	0.183863	−	0.982952i	$-0.441140\pi$
$379$	1.24586e9	−	9.05168e8i	1.17552	−	0.854067i	0.991660	+	0.128885i	$0.0411399\pi$
$380$	−3.17477e6	+	2.30660e6i	−0.00296804	+	0.00215641i
$381$		0			0
$382$	−2.22108e8	+	6.83578e8i	−0.203865	+	0.627432i
$383$	5.52491e8	+	4.01409e8i	0.502493	+	0.365082i	0.809968	−	0.586474i	$-0.199484\pi$
$383$	5.52491e8	+	4.01409e8i	0.502493	+	0.365082i	−0.307476	+	0.951556i	$0.599484\pi$
$384$		0			0
$385$	1.63015e7	+	2.54593e6i	0.0145584	+	0.00227370i
$386$	8.63205e8			0.763938
$387$		0			0
$388$	−3.03748e7	+	9.34839e7i	−0.0263999	+	0.0812505i
$389$	−2.50863e8	−	7.72076e8i	−0.216079	−	0.665023i	−0.999075	−	0.0429965i	$-0.986310\pi$
$389$	−2.50863e8	−	7.72076e8i	−0.216079	−	0.665023i	0.782996	−	0.622027i	$-0.213690\pi$
$390$		0			0
$391$	−3.99526e8	+	2.90273e8i	−0.338008	+	0.245577i
$392$	1.77793e7	+	5.47191e7i	0.0149078	+	0.0458815i
$393$		0			0
$394$	−8.14693e8	−	5.91909e8i	−0.671053	−	0.487549i
$395$	2.52293e7			0.0205975
$396$		0			0
$397$	1.73977e8			0.139549			0.0697744	−	0.997563i	$-0.477772\pi$
$397$	1.73977e8			0.139549			0.0697744	+	0.997563i	$0.477772\pi$
$398$	−1.27258e8	−	9.24587e7i	−0.101180	−	0.0735118i
$399$		0			0
$400$	4.68399e8	+	1.44158e9i	0.365937	+	1.12624i
$401$	−1.02157e9	+	7.42211e8i	−0.791154	+	0.574807i	−0.908306	−	0.418307i	$-0.862624\pi$
$401$	−1.02157e9	+	7.42211e8i	−0.791154	+	0.574807i	0.117152	+	0.993114i	$0.462624\pi$
$402$		0			0
$403$	2.84130e8	+	8.74464e8i	0.216247	+	0.665540i
$404$	3.83453e8	−	1.18015e9i	0.289319	−	0.890433i
$405$		0			0
$406$	−6.03663e8			−0.447665
$407$	1.47323e9	+	1.46690e9i	1.08315	+	1.07850i
$408$		0			0
$409$	2.18898e8	+	1.59038e8i	0.158201	+	0.114940i	0.664070	−	0.747671i	$-0.268828\pi$
$409$	2.18898e8	+	1.59038e8i	0.158201	+	0.114940i	−0.505868	+	0.862611i	$0.668828\pi$
$410$	−785355.	+	2.41707e6i	−0.000562759	+	0.00173199i
$411$		0			0
$412$	1.46180e9	−	1.06206e9i	1.02979	−	0.748186i
$413$	2.42848e9	−	1.76440e9i	1.69633	−	1.23245i
$414$		0			0
$415$	9.26908e6	−	2.85273e7i	0.00636603	−	0.0195926i
$416$	1.82077e9	+	1.32287e9i	1.24002	+	0.900928i
$417$		0			0
$418$	−3.15789e8	+	6.23085e8i	−0.211485	+	0.417282i
$419$	−2.39255e9			−1.58896			−0.794479	−	0.607292i	$-0.792256\pi$
$419$	−2.39255e9			−1.58896			−0.794479	+	0.607292i	$0.792256\pi$
$420$		0			0
$421$	8.11970e8	−	2.49899e9i	0.530338	−	1.63221i	−0.223175	−	0.974778i	$-0.571642\pi$
$421$	8.11970e8	−	2.49899e9i	0.530338	−	1.63221i	0.753513	−	0.657433i	$-0.228358\pi$
$422$	9.13484e8	+	2.81142e9i	0.591708	+	1.82109i
$423$		0			0
$424$	−3.28286e8	+	2.38514e8i	−0.209157	+	0.151961i
$425$	−8.89517e8	−	2.73765e9i	−0.562073	−	1.72988i
$426$		0			0
$427$	−3.60930e8	−	2.62231e8i	−0.224349	−	0.162999i
$428$	−8.57907e8			−0.528916
$429$		0			0
$430$	1.85135e7			0.0112292
$431$	1.45063e9	+	1.05395e9i	0.872744	+	0.634086i	0.931322	−	0.364197i	$-0.118657\pi$
$431$	1.45063e9	+	1.05395e9i	0.872744	+	0.634086i	−0.0585777	+	0.998283i	$0.518657\pi$
$432$		0			0
$433$	3.35539e8	+	1.03268e9i	0.198625	+	0.611306i	0.999915	+	0.0130297i	$0.00414760\pi$
$433$	3.35539e8	+	1.03268e9i	0.198625	+	0.611306i	−0.801290	+	0.598277i	$0.795852\pi$
$434$	−1.11374e9	+	8.09178e8i	−0.653987	+	0.475149i
$435$		0			0
$436$	3.63688e8	+	1.11932e9i	0.210148	+	0.646770i
$437$	−4.37064e7	+	1.34514e8i	−0.0250530	+	0.0771052i
$438$		0			0
$439$	−9.49338e8			−0.535544			−0.267772	−	0.963482i	$-0.586287\pi$
$439$	−9.49338e8			−0.535544			−0.267772	+	0.963482i	$0.586287\pi$
$440$	−5.62537e6	−	5.60120e6i	−0.00314823	−	0.00313470i
$441$		0			0
$442$	−4.35450e9	−	3.16373e9i	−2.39861	−	1.74269i
$443$	−3.89212e8	+	1.19787e9i	−0.212703	+	0.654631i	0.786606	+	0.617455i	$0.211836\pi$
$443$	−3.89212e8	+	1.19787e9i	−0.212703	+	0.654631i	−0.999309	+	0.0371763i	$0.988164\pi$
$444$		0			0
$445$	3.11437e7	−	2.26272e7i	0.0167537	−	0.0121723i
$446$	1.02591e9	−	7.45366e8i	0.547566	−	0.397830i
$447$		0			0
$448$	−2.94548e8	+	9.06526e8i	−0.154769	+	0.476329i
$449$	9.80528e8	+	7.12395e8i	0.511208	+	0.371414i	0.813282	−	0.581870i	$-0.197679\pi$
$449$	9.80528e8	+	7.12395e8i	0.511208	+	0.371414i	−0.302074	+	0.953285i	$0.597679\pi$
$450$		0			0
$451$	3.08846e7	+	1.92316e8i	0.0158534	+	0.0987184i
$452$	5.52852e8			0.281595
$453$		0			0
$454$	1.09819e9	−	3.37987e9i	0.550784	−	1.69514i
$455$	1.12514e7	+	3.46282e7i	0.00559972	+	0.0172342i
$456$		0			0
$457$	1.86626e9	−	1.35592e9i	0.914674	−	0.664550i	−0.0275186	−	0.999621i	$-0.508761\pi$
$457$	1.86626e9	−	1.35592e9i	0.914674	−	0.664550i	0.942193	+	0.335072i	$0.108761\pi$
$458$	−1.43293e9	−	4.41009e9i	−0.696938	−	2.14496i
$459$		0			0
$460$	4.03085e6	+	2.92859e6i	0.00193083	+	0.00140283i
$461$	−1.28878e9			−0.612667			−0.306334	−	0.951924i	$-0.599102\pi$
$461$	−1.28878e9			−0.612667			−0.306334	+	0.951924i	$0.599102\pi$
$462$		0			0
$463$	1.95406e9			0.914963			0.457482	−	0.889219i	$-0.348752\pi$
$463$	1.95406e9			0.914963			0.457482	+	0.889219i	$0.348752\pi$
$464$	6.49754e8	+	4.72074e8i	0.301950	+	0.219380i
$465$		0			0
$466$	−8.03182e8	−	2.47194e9i	−0.367674	−	1.13158i
$467$	1.46789e9	−	1.06649e9i	0.666937	−	0.484558i	−0.202061	−	0.979373i	$-0.564764\pi$
$467$	1.46789e9	−	1.06649e9i	0.666937	−	0.484558i	0.868999	+	0.494815i	$0.164764\pi$
$468$		0			0
$469$	−3.66562e8	−	1.12816e9i	−0.164075	−	0.504971i
$470$	3.41776e6	−	1.05188e7i	0.00151845	−	0.00467329i
$471$		0			0
$472$	−1.44428e9			−0.632199
$473$	1.26285e9	−	6.46885e8i	0.548705	−	0.281069i
$474$		0			0
$475$	−6.66967e8	−	4.84580e8i	−0.285546	−	0.207462i
$476$	1.07221e9	−	3.29991e9i	0.455674	−	1.40242i
$477$		0			0
$478$	1.63058e9	−	1.18469e9i	0.682881	−	0.496142i
$479$	−1.04380e9	+	7.58366e8i	−0.433954	+	0.315286i	−0.783228	−	0.621735i	$-0.786428\pi$
$479$	−1.04380e9	+	7.58366e8i	−0.433954	+	0.315286i	0.349274	+	0.937021i	$0.386428\pi$
$480$		0			0
$481$	−1.41775e9	+	4.36338e9i	−0.580886	+	1.78778i
$482$	−1.03443e9	−	7.51558e8i	−0.420762	−	0.305702i
$483$		0			0
$484$	1.79614e9	+	5.75060e8i	0.720080	+	0.230544i
$485$	3.90197e6			0.00155306
$486$		0			0
$487$	−7.41150e8	+	2.28103e9i	−0.290773	+	0.894909i	0.693835	+	0.720134i	$0.255920\pi$
$487$	−7.41150e8	+	2.28103e9i	−0.290773	+	0.894909i	−0.984608	+	0.174775i	$0.944080\pi$
$488$	6.63316e7	+	2.04148e8i	0.0258375	+	0.0795198i
$489$		0			0
$490$	−5.72768e6	+	4.16140e6i	−0.00219934	+	0.00159791i
$491$	−1.08288e8	−	3.33276e8i	−0.0412852	−	0.127063i	0.928290	−	0.371858i	$-0.121279\pi$
$491$	−1.08288e8	−	3.33276e8i	−0.0412852	−	0.127063i	−0.969575	+	0.244795i	$0.921279\pi$
$492$		0			0
$493$	−1.23392e9	−	8.96495e8i	−0.463791	−	0.336964i
$494$	−1.54154e9			−0.575322
$495$		0			0
$496$	1.83157e9			0.673964
$497$	−7.01613e8	−	5.09752e8i	−0.256360	−	0.186256i
$498$		0			0
$499$	8.49899e8	+	2.61572e9i	0.306207	+	0.942409i	0.979224	+	0.202782i	$0.0649982\pi$
$499$	8.49899e8	+	2.61572e9i	0.306207	+	0.942409i	−0.673017	+	0.739627i	$0.735002\pi$
$500$	−4.69951e7	+	3.41439e7i	−0.0168135	+	0.0122157i
$501$		0			0
$502$	−7.11320e8	−	2.18922e9i	−0.250959	−	0.772371i
$503$	3.86725e8	−	1.19022e9i	0.135492	−	0.417002i	−0.860174	−	0.510001i	$-0.829645\pi$
$503$	3.86725e8	−	1.19022e9i	0.135492	−	0.417002i	0.995666	+	0.0929983i	$0.0296451\pi$
$504$		0			0
$505$	−4.92587e7			−0.0170201
$506$	8.76280e8	+	1.36856e8i	0.300688	+	0.0469608i
$507$		0			0
$508$	−9.55903e8	−	6.94504e8i	−0.323512	−	0.235045i
$509$	−1.03978e9	+	3.20011e9i	−0.349485	+	1.07560i	0.609654	+	0.792667i	$0.291308\pi$
$509$	−1.03978e9	+	3.20011e9i	−0.349485	+	1.07560i	−0.959139	+	0.282936i	$0.908692\pi$
$510$		0			0
$511$	2.31833e9	−	1.68437e9i	0.768604	−	0.558423i
$512$	2.68633e9	−	1.95173e9i	0.884535	−	0.642652i
$513$		0			0
$514$	7.39670e8	−	2.27647e9i	0.240252	−	0.739419i
$515$	−5.80286e7	−	4.21602e7i	−0.0187205	−	0.0136012i
$516$		0			0
$517$	−1.34406e8	−	8.36936e8i	−0.0427760	−	0.266364i
$518$	−6.86921e9			−2.17146
$519$		0			0
$520$	5.41352e6	−	1.66611e7i	0.00168837	−	0.00519627i
$521$	−8.94675e8	−	2.75353e9i	−0.277162	−	0.853016i	−0.988639	−	0.150307i	$-0.951974\pi$
$521$	−8.94675e8	−	2.75353e9i	−0.277162	−	0.853016i	0.711478	−	0.702709i	$-0.248026\pi$
$522$		0			0
$523$	4.66077e9	−	3.38625e9i	1.42463	−	1.03505i	0.433643	−	0.901085i	$-0.357228\pi$
$523$	4.66077e9	−	3.38625e9i	1.42463	−	1.03505i	0.990986	−	0.133969i	$-0.0427721\pi$
$524$	−1.69657e7	−	5.22151e7i	−0.00515125	−	0.0158539i
$525$		0			0
$526$	4.91399e9	+	3.57022e9i	1.47226	+	1.06966i
$527$	−3.47825e9			−1.03520
$528$		0			0
$529$	−3.22525e9			−0.947258
$530$	−4.03963e7	−	2.93496e7i	−0.0117862	−	0.00856321i
$531$		0			0
$532$	−3.07081e8	−	9.45099e8i	−0.0884224	−	0.272136i
$533$	−3.47750e8	+	2.52655e8i	−0.0994769	+	0.0722742i
$534$		0			0
$535$	1.05239e7	+	3.23892e7i	0.00297124	+	0.00914453i
$536$	−1.76369e8	+	5.42807e8i	−0.0494703	+	0.152254i
$537$		0			0
$538$	−2.38376e9			−0.659971
$539$	−2.45295e8	+	4.83993e8i	−0.0674728	+	0.133131i
$540$		0			0
$541$	−1.01713e9	−	7.38990e8i	−0.276177	−	0.200654i	0.441071	−	0.897472i	$-0.354599\pi$
$541$	−1.01713e9	−	7.38990e8i	−0.276177	−	0.200654i	−0.717248	+	0.696818i	$0.754599\pi$
$542$	−1.23308e9	+	3.79503e9i	−0.332655	+	1.02381i
$543$		0			0
$544$	−6.88780e9	+	5.00428e9i	−1.83436	+	1.33274i
$545$	3.77970e7	−	2.74611e7i	0.0100016	−	0.00726659i
$546$		0			0
$547$	3.74175e8	−	1.15159e9i	0.0977505	−	0.300845i	−0.890210	−	0.455550i	$-0.849443\pi$
$547$	3.74175e8	−	1.15159e9i	0.0977505	−	0.300845i	0.987961	+	0.154705i	$0.0494426\pi$
$548$	3.96622e9	+	2.88163e9i	1.02954	+	0.748007i
$549$		0			0
$550$	−2.33704e9	+	4.61123e9i	−0.598959	+	1.18181i
$551$	−4.36822e8			−0.111243
$552$		0			0
$553$	−1.97426e9	+	6.07614e9i	−0.496439	+	1.52788i
$554$	2.08472e9	+	6.41610e9i	0.520911	+	1.60320i
$555$		0			0
$556$	3.76052e9	−	2.73218e9i	0.927867	−	0.674135i
$557$	−8.51549e8	−	2.62080e9i	−0.208793	−	0.642599i	−0.999536	−	0.0304511i	$-0.990306\pi$
$557$	−8.51549e8	−	2.62080e9i	−0.208793	−	0.642599i	0.790743	−	0.612148i	$-0.209694\pi$
$558$		0			0
$559$	2.53321e9	+	1.84049e9i	0.613381	+	0.445648i
$560$	7.25289e7			0.0174523
$561$		0			0
$562$	−2.88031e9			−0.684482
$563$	−1.88263e9	−	1.36781e9i	−0.444616	−	0.323033i	0.342850	−	0.939390i	$-0.388608\pi$
$563$	−1.88263e9	−	1.36781e9i	−0.444616	−	0.323033i	−0.787467	+	0.616357i	$0.788608\pi$
$564$		0			0
$565$	−6.78179e6	−	2.08722e7i	−0.00158189	−	0.00486854i
$566$	5.53710e9	−	4.02294e9i	1.28359	−	0.932580i
$567$		0			0
$568$	1.28942e8	+	3.96844e8i	0.0295241	+	0.0908658i
$569$	−1.96545e9	+	6.04902e9i	−0.447269	+	1.37655i	0.432708	+	0.901534i	$0.357558\pi$
$569$	−1.96545e9	+	6.04902e9i	−0.447269	+	1.37655i	−0.879977	+	0.475017i	$0.842442\pi$
$570$		0			0
$571$	−1.08891e9			−0.244775			−0.122387	−	0.992482i	$-0.539055\pi$
$571$	−1.08891e9			−0.244775			−0.122387	+	0.992482i	$0.539055\pi$
$572$	6.59919e8	+	4.10927e9i	0.147436	+	0.918077i
$573$		0			0
$574$	−5.20664e8	−	3.78284e8i	−0.114912	−	0.0834885i
$575$	−3.23455e8	+	9.95493e8i	−0.0709540	+	0.218374i
$576$		0			0
$577$	3.68643e8	−	2.67835e8i	0.0798897	−	0.0580433i	−0.547124	−	0.837052i	$-0.684277\pi$
$577$	3.68643e8	−	2.67835e8i	0.0798897	−	0.0580433i	0.627013	+	0.779009i	$0.284277\pi$
$578$	1.14955e10	−	8.35198e9i	2.47617	−	1.79904i
$579$		0			0
$580$	−4.75514e6	+	1.46348e7i	−0.00101197	+	0.00311451i
$581$	6.14509e9	+	4.46467e9i	1.29991	+	0.944437i
$582$		0			0
$583$	−3.78105e9	−	5.90516e8i	−0.790265	−	0.123422i
$584$	−1.37877e9			−0.286448
$585$		0			0
$586$	−3.87733e9	+	1.19332e10i	−0.795961	+	2.44972i
$587$	2.00905e9	+	6.18323e9i	0.409976	+	1.26178i	0.916668	+	0.399649i	$0.130868\pi$
$587$	2.00905e9	+	6.18323e9i	0.409976	+	1.26178i	−0.506693	+	0.862127i	$0.669132\pi$
$588$		0			0
$589$	−8.05922e8	+	5.85537e8i	−0.162514	+	0.118073i
$590$	−5.49188e7	−	1.69023e8i	−0.0110088	−	0.0338815i
$591$		0			0
$592$	7.39369e9	+	5.37183e9i	1.46465	+	1.06413i
$593$	4.63931e9			0.913612			0.456806	−	0.889566i	$-0.348993\pi$
$593$	4.63931e9			0.913612			0.456806	+	0.889566i	$0.348993\pi$
$594$		0			0
$595$	−1.37737e8			−0.0268065
$596$	−4.15648e9	−	3.01986e9i	−0.804199	−	0.584285i
$597$		0			0
$598$	6.04815e8	+	1.86143e9i	0.115656	+	0.355953i
$599$	−3.65908e9	+	2.65848e9i	−0.695629	+	0.505404i	−0.878506	−	0.477732i	$-0.841459\pi$
$599$	−3.65908e9	+	2.65848e9i	−0.695629	+	0.505404i	0.182877	+	0.983136i	$0.441459\pi$
$600$		0			0
$601$	−1.93979e8	−	5.97007e8i	−0.0364498	−	0.112181i	0.931176	−	0.364570i	$-0.118784\pi$
$601$	−1.93979e8	−	5.97007e8i	−0.0364498	−	0.112181i	−0.967626	+	0.252389i	$0.918784\pi$
$602$	−1.44873e9	+	4.45873e9i	−0.270644	+	0.832958i
$603$		0			0
$604$	−6.66366e9			−1.23051
$605$	−322422.	−	7.48651e7i	−5.91944e−5	−	0.0137447i
$606$		0			0
$607$	4.97237e9	+	3.61264e9i	0.902408	+	0.655638i	0.939083	−	0.343690i	$-0.111677\pi$
$607$	4.97237e9	+	3.61264e9i	0.902408	+	0.655638i	−0.0366755	+	0.999327i	$0.511677\pi$
$608$	−7.53495e8	+	2.31902e9i	−0.135962	+	0.418448i
$609$		0			0
$610$	−2.13690e7	+	1.55255e7i	−0.00381180	+	0.00276943i
$611$	1.51336e9	−	1.09952e9i	0.268410	−	0.195011i
$612$		0			0
$613$	9.61637e8	−	2.95961e9i	0.168616	−	0.518948i	−0.830668	−	0.556768i	$-0.812041\pi$
$613$	9.61637e8	−	2.95961e9i	0.168616	−	0.518948i	0.999285	+	0.0378201i	$0.0120414\pi$
$614$	−5.81274e9	−	4.22320e9i	−1.01342	−	0.736296i
$615$		0			0
$616$	1.78917e9	−	9.16488e8i	0.308404	−	0.157977i
$617$	5.30557e9			0.909355			0.454678	−	0.890656i	$-0.349754\pi$
$617$	5.30557e9			0.909355			0.454678	+	0.890656i	$0.349754\pi$
$618$		0			0
$619$	−1.98122e9	+	6.09756e9i	−0.335749	+	1.03333i	0.630603	+	0.776105i	$0.282808\pi$
$619$	−1.98122e9	+	6.09756e9i	−0.335749	+	1.03333i	−0.966352	+	0.257223i	$0.917192\pi$
$620$	1.08441e7	+	3.33748e7i	0.00182736	+	0.00562403i
$621$		0			0
$622$	8.26669e9	−	6.00610e9i	1.37742	−	1.00075i
$623$	3.01239e9	+	9.27118e9i	0.499118	+	1.53613i
$624$		0			0
$625$	−4.93505e9	−	3.58552e9i	−0.808559	−	0.587452i
$626$	−4.25554e9			−0.693338
$627$		0			0
$628$	6.04190e9			0.973453
$629$	−1.40410e10	−	1.02014e10i	−2.24969	−	1.63449i
$630$		0			0
$631$	8.59403e7	+	2.64497e8i	0.0136174	+	0.0419100i	0.957634	−	0.287987i	$-0.0929860\pi$
$631$	8.59403e7	+	2.64497e8i	0.0136174	+	0.0419100i	−0.944017	+	0.329897i	$0.892986\pi$
$632$	2.48687e9	−	1.80681e9i	0.391871	−	0.284711i
$633$		0			0
$634$	2.89119e8	+	8.89818e8i	0.0450573	+	0.138672i
$635$	−1.44941e7	+	4.46083e7i	−0.00224638	+	0.00691365i
$636$		0			0
$637$	−1.19742e9			−0.183552
$638$	4.34324e8	+	2.70451e9i	0.0662127	+	0.412303i
$639$		0			0
$640$	−4.62542e7	−	3.36057e7i	−0.00697463	−	0.00506737i
$641$	2.93551e9	−	9.03458e9i	0.440231	−	1.35489i	−0.447398	−	0.894335i	$-0.647649\pi$
$641$	2.93551e9	−	9.03458e9i	0.440231	−	1.35489i	0.887630	−	0.460558i	$-0.152351\pi$
$642$		0			0
$643$	1.04789e10	−	7.61335e9i	1.55445	−	1.12937i	0.614066	−	0.789255i	$-0.289533\pi$
$643$	1.04789e10	−	7.61335e9i	1.55445	−	1.12937i	0.940383	−	0.340118i	$-0.110467\pi$
$644$	−1.02074e9	+	7.41608e8i	−0.150596	+	0.109414i
$645$		0			0
$646$	1.80203e9	−	5.54609e9i	0.262996	−	0.809418i
$647$	5.45579e9	+	3.96386e9i	0.791940	+	0.575378i	0.908539	−	0.417801i	$-0.137199\pi$
$647$	5.45579e9	+	3.96386e9i	0.791940	+	0.575378i	−0.116598	+	0.993179i	$0.537199\pi$
$648$		0			0
$649$	−9.65203e9	−	9.61056e9i	−1.38600	−	1.38004i
$650$	−1.14084e10			−1.62940
$651$		0			0
$652$	2.09517e9	−	6.44826e9i	0.296041	−	0.911120i
$653$	1.99079e8	+	6.12701e8i	0.0279788	+	0.0861097i	0.964071	−	0.265645i	$-0.0855850\pi$
$653$	1.99079e8	+	6.12701e8i	0.0279788	+	0.0861097i	−0.936092	+	0.351755i	$0.885585\pi$
$654$		0			0
$655$	−1.76320e6	+	1.28104e6i	−0.000245164	+	0.000178122i
$656$	2.64593e8	+	8.14335e8i	0.0365945	+	0.112626i
$657$		0			0
$658$	2.26586e9	+	1.64624e9i	0.310058	+	0.225270i
$659$	−1.09725e10			−1.49350			−0.746752	−	0.665102i	$-0.768388\pi$
$659$	−1.09725e10			−1.49350			−0.746752	+	0.665102i	$0.768388\pi$
$660$		0			0
$661$	−7.47730e9			−1.00702			−0.503512	−	0.863988i	$-0.667959\pi$
$661$	−7.47730e9			−1.00702			−0.503512	+	0.863988i	$0.667959\pi$
$662$	−9.45435e9	−	6.86899e9i	−1.26657	−	0.920216i
$663$		0			0
$664$	−1.12934e9	−	3.47577e9i	−0.149706	−	0.460747i
$665$	−3.19140e7	+	2.31869e7i	−0.00420829	+	0.00305750i
$666$		0			0
$667$	1.71384e8	+	5.27467e8i	0.0223631	+	0.0688264i
$668$	−7.91513e8	+	2.43603e9i	−0.102740	+	0.316202i
$669$		0			0
$670$	−7.02307e7			−0.00902121
$671$	−9.15156e8	+	1.80570e9i	−0.116941	+	0.230736i
$672$		0			0
$673$	−6.47607e9	−	4.70514e9i	−0.818952	−	0.595004i	0.0974600	−	0.995239i	$-0.468928\pi$
$673$	−6.47607e9	−	4.70514e9i	−0.818952	−	0.595004i	−0.916412	+	0.400236i	$0.868928\pi$
$674$	5.44276e9	−	1.67511e10i	0.684714	−	2.10733i
$675$		0			0
$676$	−2.51752e9	+	1.82908e9i	−0.313443	+	0.227730i
$677$	7.91124e9	−	5.74785e9i	0.979905	−	0.711943i	0.0222176	−	0.999753i	$-0.492927\pi$
$677$	7.91124e9	−	5.74785e9i	0.979905	−	0.711943i	0.957687	+	0.287811i	$0.0929273\pi$
$678$		0			0
$679$	−3.05339e8	+	9.39738e8i	−0.0374316	+	0.115203i
$680$	5.36142e7	+	3.89530e7i	0.00653881	+	0.00475073i
$681$		0			0
$682$	4.42657e9	+	4.40755e9i	0.534345	+	0.532049i
$683$	5.12646e9			0.615666			0.307833	−	0.951440i	$-0.400396\pi$
$683$	5.12646e9			0.615666			0.307833	+	0.951440i	$0.400396\pi$
$684$		0			0
$685$	6.01388e7	−	1.85088e8i	0.00714887	−	0.0220020i
$686$	3.15790e9	+	9.71901e9i	0.373477	+	1.14944i
$687$		0			0
$688$	5.04613e9	−	3.66623e9i	0.590744	−	0.429201i
$689$	−2.60971e9	−	8.03186e9i	−0.303966	−	0.935511i
$690$		0			0
$691$	6.27785e9	+	4.56112e9i	0.723832	+	0.525894i	0.887606	−	0.460603i	$-0.152367\pi$
$691$	6.27785e9	+	4.56112e9i	0.723832	+	0.525894i	−0.163774	+	0.986498i	$0.552367\pi$
$692$	−1.05828e10			−1.21403
$693$		0			0
$694$	3.79552e9			0.431036
$695$	−1.49280e8	−	1.08458e8i	−0.0168676	−	0.0122551i
$696$		0			0
$697$	−5.02478e8	−	1.54647e9i	−0.0562086	−	0.172992i
$698$	1.31496e10	−	9.55377e9i	1.46359	−	1.06336i
$699$		0			0
$700$	−2.27260e9	−	6.99434e9i	−0.250426	−	0.770732i
$701$	5.46246e9	−	1.68117e10i	0.598929	−	1.84331i	0.0648202	−	0.997897i	$-0.479353\pi$
$701$	5.46246e9	−	1.68117e10i	0.598929	−	1.84331i	0.534109	−	0.845416i	$-0.320647\pi$
$702$		0			0
$703$	−4.97069e9			−0.539601
$704$	4.27331e9	+	6.67397e8i	0.461594	+	0.0720908i
$705$		0			0
$706$	−1.13005e9	−	8.21027e8i	−0.120859	−	0.0878094i
$707$	3.85462e9	−	1.18633e10i	0.410217	−	1.26252i
$708$		0			0
$709$	−1.27810e10	+	9.28593e9i	−1.34680	+	0.978506i	−0.347633	+	0.937631i	$0.613015\pi$
$709$	−1.27810e10	+	9.28593e9i	−1.34680	+	0.978506i	−0.999164	+	0.0408753i	$0.986985\pi$
$710$	−4.15393e7	+	3.01801e7i	−0.00435567	+	0.00316458i
$711$		0			0
$712$	1.44939e9	−	4.46076e9i	0.150489	−	0.463157i
$713$	1.02324e9	+	7.43429e8i	0.105722	+	0.0768114i
$714$		0			0
$715$	1.47045e8	−	7.53225e7i	0.0150446	−	0.00770644i
$716$	−1.81816e9			−0.185113
$717$		0			0
$718$	−2.60111e8	+	8.00539e8i	−0.0262255	+	0.0807137i
$719$	4.09431e9	+	1.26010e10i	0.410799	+	1.26431i	0.915955	+	0.401282i	$0.131435\pi$
$719$	4.09431e9	+	1.26010e10i	0.410799	+	1.26431i	−0.505155	+	0.863028i	$0.668565\pi$
$720$		0			0
$721$	1.46946e10	−	1.06763e10i	1.46011	−	1.06083i
$722$	3.62518e9	+	1.11572e10i	0.358468	+	1.10325i
$723$		0			0
$724$	−7.67481e9	−	5.57608e9i	−0.751593	−	0.546064i
$725$	−3.23276e9			−0.315058
$726$		0			0
$727$	−1.39564e10			−1.34711			−0.673557	−	0.739135i	$-0.735234\pi$
$727$	−1.39564e10			−1.34711			−0.673557	+	0.739135i	$0.735234\pi$
$728$	3.58898e9	+	2.60755e9i	0.344756	+	0.250480i
$729$		0			0
$730$	−5.24278e7	−	1.61356e8i	−0.00498806	−	0.0153517i
$731$	−9.58290e9	+	6.96238e9i	−0.907374	+	0.659246i
$732$		0			0
$733$	−5.29135e9	−	1.62851e10i	−0.496252	−	1.52731i	−0.814996	−	0.579467i	$-0.803261\pi$
$733$	−5.29135e9	−	1.62851e10i	−0.496252	−	1.52731i	0.318743	−	0.947841i	$-0.396739\pi$
$734$	−4.32865e9	+	1.33222e10i	−0.404033	+	1.24348i
$735$		0			0
$736$	3.09587e9			0.286227
$737$	−4.79062e9	+	2.45395e9i	−0.440814	+	0.225803i
$738$		0			0
$739$	1.33441e10	+	9.69504e9i	1.21628	+	0.883678i	0.995786	−	0.0917111i	$-0.0292336\pi$
$739$	1.33441e10	+	9.69504e9i	1.21628	+	0.883678i	0.220492	+	0.975389i	$0.429234\pi$
$740$	−5.41098e7	+	1.66533e8i	−0.00490868	+	0.0151074i
$741$		0			0
$742$	1.02296e10	−	7.43222e9i	0.919272	−	0.667890i
$743$	−2.84548e9	+	2.06736e9i	−0.254504	+	0.184908i	−0.707721	−	0.706492i	$-0.750276\pi$
$743$	−2.84548e9	+	2.06736e9i	−0.254504	+	0.184908i	0.453217	+	0.891400i	$0.350276\pi$
$744$		0			0
$745$	−6.30236e7	+	1.93967e8i	−0.00558414	+	0.0171862i
$746$	1.31303e10	+	9.53973e9i	1.15795	+	0.841298i
$747$		0			0
$748$	−1.55556e10	−	2.42944e9i	−1.35904	−	0.212251i
$749$	−8.62402e9			−0.749935
$750$		0			0
$751$	−3.98758e8	+	1.22725e9i	−0.0343534	+	0.105729i	−0.966763	−	0.255675i	$-0.917702\pi$
$751$	−3.98758e8	+	1.22725e9i	−0.0343534	+	0.105729i	0.932409	+	0.361404i	$0.117702\pi$
$752$	−1.15148e9	−	3.54388e9i	−0.0987398	−	0.303890i
$753$		0			0
$754$	−4.89035e9	+	3.55304e9i	−0.415470	+	0.301857i
$755$	8.17426e7	+	2.51578e8i	0.00691249	+	0.0212744i
$756$		0			0
$757$	1.60174e10	+	1.16373e10i	1.34201	+	0.975031i	0.999367	+	0.0355669i	$0.0113237\pi$
$757$	1.60174e10	+	1.16373e10i	1.34201	+	0.975031i	0.342648	+	0.939464i	$0.388676\pi$
$758$	2.30881e10			1.92551
$759$		0			0
$760$	1.89801e7			0.00156837
$761$	8.35908e9	+	6.07323e9i	0.687563	+	0.499544i	0.875858	−	0.482569i	$-0.160296\pi$
$761$	8.35908e9	+	6.07323e9i	0.687563	+	0.499544i	−0.188295	+	0.982112i	$0.560296\pi$
$762$		0			0
$763$	3.65593e9	+	1.12518e10i	0.297963	+	0.917036i
$764$	−3.75356e9	+	2.72712e9i	−0.304520	+	0.221247i
$765$		0			0
$766$	3.16394e9	+	9.73760e9i	0.254348	+	0.782801i
$767$	9.28854e9	−	2.85872e10i	0.743299	−	2.28764i
$768$		0			0
$769$	9.99627e9			0.792676			0.396338	−	0.918105i	$-0.370281\pi$
$769$	9.99627e9			0.792676			0.396338	+	0.918105i	$0.370281\pi$
$770$	1.75289e8	+	1.74536e8i	0.0138369	+	0.0137774i
$771$		0			0
$772$	4.50791e9	+	3.27518e9i	0.352626	+	0.256198i
$773$	−6.02412e9	+	1.85403e10i	−0.469100	+	1.44374i	0.384652	+	0.923062i	$0.374321\pi$
$773$	−6.02412e9	+	1.85403e10i	−0.469100	+	1.44374i	−0.853752	+	0.520680i	$0.825679\pi$
$774$		0			0
$775$	−5.96434e9	+	4.33335e9i	−0.460263	+	0.334401i
$776$	3.84620e8	−	2.79442e8i	0.0295471	−	0.0214672i
$777$		0			0
$778$	3.76109e9	−	1.15755e10i	0.286342	−	0.881271i
$779$	−3.76762e8	−	2.73734e8i	−0.0285553	−	0.0207466i
$780$		0			0
$781$	−1.77898e9	+	3.51010e9i	−0.133626	+	0.263658i
$782$	−7.40398e9			−0.553658
$783$		0			0
$784$	−7.37083e8	+	2.26851e9i	−0.0546274	+	0.168126i
$785$	−7.41155e7	−	2.28104e8i	−0.00546847	−	0.0168302i
$786$		0			0
$787$	3.82358e9	−	2.77799e9i	0.279614	−	0.203151i	−0.439135	−	0.898421i	$-0.644715\pi$
$787$	3.82358e9	−	2.77799e9i	0.279614	−	0.203151i	0.718749	+	0.695270i	$0.244715\pi$
$788$	−2.00873e9	−	6.18224e9i	−0.146245	−	0.450095i
$789$		0			0
$790$	3.06014e8	+	2.22332e8i	0.0220824	+	0.0160438i
$791$	5.55749e9			0.399265
$792$		0			0
$793$	−4.46738e9			−0.318124
$794$	2.11022e9	+	1.53317e9i	0.149609	+	0.108697i
$795$		0			0
$796$	−3.13772e8	−	9.65692e8i	−0.0220505	−	0.0678645i
$797$	−2.96367e8	+	2.15323e8i	−0.0207360	+	0.0150656i	−0.598105	−	0.801418i	$-0.704079\pi$
$797$	−2.96367e8	+	2.15323e8i	−0.0207360	+	0.0150656i	0.577369	+	0.816483i	$0.304079\pi$
$798$		0			0
$799$	2.18672e9	+	6.73003e9i	0.151663	+	0.466770i
$800$	−5.57635e9	+	1.71622e10i	−0.385066	+	1.18511i
$801$		0			0
$802$	−1.89316e10			−1.29591
$803$	−9.21424e9	−	9.17464e9i	−0.627994	−	0.625295i
$804$		0			0
$805$	4.05198e7	+	2.94393e7i	0.00273767	+	0.00198903i
$806$	−4.25986e9	+	1.31105e10i	−0.286565	+	0.881956i
$807$		0			0
$808$	−4.85546e9	+	3.52770e9i	−0.323810	+	0.235262i
$809$	−1.85830e10	+	1.35013e10i	−1.23394	+	0.896513i	−0.997179	−	0.0750538i	$-0.976087\pi$
$809$	−1.85830e10	+	1.35013e10i	−1.23394	+	0.896513i	−0.236765	+	0.971567i	$0.576087\pi$
$810$		0			0
$811$	−5.87298e9	+	1.80752e10i	−0.386621	+	1.18990i	0.548676	+	0.836035i	$0.315132\pi$
$811$	−5.87298e9	+	1.80752e10i	−0.386621	+	1.18990i	−0.935297	+	0.353863i	$0.884868\pi$
$812$	−3.15250e9	−	2.29043e9i	−0.206637	−	0.150131i
$813$		0			0
$814$	4.94227e9	+	3.07752e10i	0.321174	+	1.99993i
$815$	−2.69147e8			−0.0174156
$816$		0			0
$817$	−1.04833e9	+	3.22642e9i	−0.0672542	+	0.206987i
$818$	1.25356e9	+	3.85805e9i	0.0800769	+	0.246451i
$819$		0			0
$820$	−1.32722e7	+	9.64285e6i	−0.000840613	+	0.000610741i
$821$	−5.68227e9	−	1.74882e10i	−0.358361	−	1.10292i	−0.954035	−	0.299696i	$-0.903115\pi$
$821$	−5.68227e9	−	1.74882e10i	−0.358361	−	1.10292i	0.595674	−	0.803226i	$-0.296885\pi$
$822$		0			0
$823$	−1.87043e10	−	1.35895e10i	−1.16961	−	0.849774i	−0.178651	−	0.983912i	$-0.557173\pi$
$823$	−1.87043e10	−	1.35895e10i	−1.16961	−	0.849774i	−0.990963	+	0.134138i	$0.957173\pi$
$824$	−8.73925e9			−0.544163
$825$		0			0
$826$	4.50044e10			2.77859
$827$	4.07116e9	+	2.95787e9i	0.250293	+	0.181849i	0.705857	−	0.708355i	$-0.250562\pi$
$827$	4.07116e9	+	2.95787e9i	0.250293	+	0.181849i	−0.455563	+	0.890203i	$0.650562\pi$
$828$		0			0
$829$	−6.51647e9	−	2.00556e10i	−0.397257	−	1.22263i	−0.927190	−	0.374592i	$-0.877783\pi$
$829$	−6.51647e9	−	2.00556e10i	−0.397257	−	1.22263i	0.529932	−	0.848040i	$-0.322217\pi$
$830$	3.63823e8	−	2.64333e8i	0.0220860	−	0.0160464i
$831$		0			0
$832$	2.94947e9	+	9.07754e9i	0.177547	+	0.546433i
$833$	1.39976e9	−	4.30803e9i	0.0839068	−	0.258238i
$834$		0			0
$835$	1.01678e8			0.00604403
$836$	−4.01326e9	+	2.05576e9i	−0.237561	+	0.121689i
$837$		0			0
$838$	−2.90200e10	−	2.10842e10i	−1.70350	−	1.23767i
$839$	−2.57022e9	+	7.91032e9i	−0.150246	+	0.462410i	−0.997648	−	0.0685416i	$-0.978165\pi$
$839$	−2.57022e9	+	7.91032e9i	−0.150246	+	0.462410i	0.847402	+	0.530952i	$0.178165\pi$
$840$		0			0
$841$	1.25697e10	−	9.13241e9i	0.728682	−	0.529419i
$842$	3.18708e10	−	2.31555e10i	1.83993	−	1.33679i
$843$		0			0
$844$	−5.89664e9	+	1.81480e10i	−0.337603	+	1.03903i
$845$	9.99368e7	+	7.26084e7i	0.00569806	+	0.00413988i
$846$		0			0
$847$	1.80555e10	+	5.78074e9i	1.02098	+	0.326882i
$848$	−1.68227e10			−0.947352
$849$		0			0
$850$	1.33362e10	−	4.10446e10i	0.744845	−	2.29240i
$851$	1.95022e9	+	6.00217e9i	0.108475	+	0.333852i
$852$		0			0
$853$	−1.31047e10	+	9.52113e9i	−0.722946	+	0.525251i	−0.887324	−	0.461147i	$-0.847438\pi$
$853$	−1.31047e10	+	9.52113e9i	−0.722946	+	0.525251i	0.164378	+	0.986397i	$0.447438\pi$
$854$	−2.06693e9	−	6.36135e9i	−0.113559	−	0.349500i
$855$		0			0
$856$	3.35692e9	+	2.43894e9i	0.182929	+	0.132906i
$857$	−3.85272e9			−0.209091			−0.104545	−	0.994520i	$-0.533339\pi$
$857$	−3.85272e9			−0.209091			−0.104545	+	0.994520i	$0.533339\pi$
$858$		0			0
$859$	−9.83291e9			−0.529305			−0.264653	−	0.964344i	$-0.585257\pi$
$859$	−9.83291e9			−0.529305			−0.264653	+	0.964344i	$0.585257\pi$
$860$	9.66827e7	+	7.02441e7i	0.00518328	+	0.00376587i
$861$		0			0
$862$	8.30730e9	+	2.55673e10i	0.441758	+	1.35959i
$863$	−7.57316e9	+	5.50222e9i	−0.401087	+	0.291407i	−0.769984	−	0.638063i	$-0.779736\pi$
$863$	−7.57316e9	+	5.50222e9i	−0.401087	+	0.291407i	0.368896	+	0.929471i	$0.379736\pi$
$864$		0			0
$865$	1.29818e8	+	3.99539e8i	0.00681991	+	0.0209895i
$866$	−5.03061e9	+	1.54826e10i	−0.263213	+	0.810087i
$867$		0			0
$868$	−8.88646e9			−0.461222
$869$	2.86426e10	+	4.47334e9i	1.48062	+	0.231240i
$870$		0			0
$871$	−9.60972e9	−	6.98187e9i	−0.492773	−	0.358021i
$872$	1.75902e9	−	5.41372e9i	0.0898388	−	0.276495i
$873$		0			0
$874$	−1.71553e9	+	1.24640e9i	−0.0869176	+	0.0631494i
$875$	−4.72413e8	+	3.43228e8i	−0.0238393	+	0.0173203i
$876$		0			0
$877$	−5.11518e9	+	1.57429e10i	−0.256072	+	0.788109i	0.737544	+	0.675299i	$0.235985\pi$
$877$	−5.11518e9	+	1.57429e10i	−0.256072	+	0.788109i	−0.993617	+	0.112810i	$0.964015\pi$
$878$	−1.15148e10	−	8.36599e9i	−0.574150	−	0.417145i
$879$		0			0
$880$	−5.21832e7	−	3.24942e8i	−0.00258132	−	0.0160737i
$881$	−2.32328e10			−1.14469			−0.572343	−	0.820015i	$-0.693965\pi$
$881$	−2.32328e10			−1.14469			−0.572343	+	0.820015i	$0.693965\pi$
$882$		0			0
$883$	−4.41527e9	+	1.35888e10i	−0.215822	+	0.664231i	0.783272	+	0.621679i	$0.213549\pi$
$883$	−4.41527e9	+	1.35888e10i	−0.215822	+	0.664231i	−0.999094	+	0.0425525i	$0.986451\pi$
$884$	−1.07366e10	−	3.30438e10i	−0.522737	−	1.60882i
$885$		0			0
$886$	−1.52770e10	+	1.10994e10i	−0.737940	+	0.536145i
$887$	4.16055e8	+	1.28049e9i	0.0200179	+	0.0616087i	0.960566	−	0.278050i	$-0.0896883\pi$
$887$	4.16055e8	+	1.28049e9i	0.0200179	+	0.0616087i	−0.940549	+	0.339659i	$0.889688\pi$
$888$		0			0
$889$	−9.60912e9	−	6.98143e9i	−0.458698	−	0.333264i
$890$	5.77152e8			0.0274426
$891$		0			0
$892$	8.18567e9			0.386169
$893$	1.63962e9	+	1.19125e9i	0.0770483	+	0.0559789i
$894$		0			0
$895$	2.23033e7	+	6.86424e7i	0.00103989	+	0.00320046i
$896$	1.17130e10	−	8.50999e9i	0.543989	−	0.395231i
$897$		0			0
$898$	5.61516e9	+	1.72817e10i	0.258759	+	0.796378i
$899$	−1.20710e9	+	3.71508e9i	−0.0554097	+	0.170533i
$900$		0			0
$901$	3.19473e10			1.45512
$902$	−1.32017e9	+	2.60483e9i	−0.0598973	+	0.118183i
$903$		0			0
$904$	−2.16326e9	−	1.57170e9i	−0.0973913	−	0.0707589i
$905$	−1.16371e8	+	3.58154e8i	−0.00521886	+	0.0160620i
$906$		0			0
$907$	−2.84628e10	+	2.06794e10i	−1.26664	+	0.920266i	−0.999063	−	0.0432712i	$-0.986222\pi$
$907$	−2.84628e10	+	2.06794e10i	−1.26664	+	0.920266i	−0.267574	+	0.963537i	$0.586222\pi$
$908$	1.85590e10	−	1.34839e10i	0.822725	−	0.597745i
$909$		0			0
$910$	−1.68688e8	+	5.19168e8i	−0.00742061	+	0.0228383i
$911$	3.28326e10	+	2.38542e10i	1.43877	+	1.04533i	0.988298	+	0.152533i	$0.0487430\pi$
$911$	3.28326e10	+	2.38542e10i	1.43877	+	1.04533i	0.450468	+	0.892792i	$0.351257\pi$
$912$		0			0
$913$	1.55812e10	−	3.07433e10i	0.677568	−	1.33691i
$914$	3.45854e10			1.49824
$915$		0			0
$916$	9.24968e9	−	2.84676e10i	0.397642	−	1.22382i
$917$	−1.70546e8	−	5.24887e8i	−0.00730381	−	0.0224788i
$918$		0			0
$919$	−2.14866e10	+	1.56110e10i	−0.913196	+	0.663476i	−0.941821	−	0.336114i	$-0.890887\pi$
$919$	−2.14866e10	+	1.56110e10i	−0.913196	+	0.663476i	0.0286249	+	0.999590i	$0.490887\pi$
$920$	−7.44672e6	−	2.29186e7i	−0.000315288	−	0.000970357i
$921$		0			0
$922$	−1.56320e10	−	1.13573e10i	−0.656833	−	0.477217i
$923$	−8.68416e9			−0.363514
$924$		0			0
$925$	−3.67863e10			−1.52823
$926$	2.37013e10	+	1.72200e10i	0.980921	+	0.712681i
$927$		0			0
$928$	2.95466e9	+	9.09350e9i	0.121364	+	0.373519i
$929$	−4.72240e7	+	3.43102e7i	−0.00193245	+	0.00140401i	−0.588751	−	0.808314i	$-0.700380\pi$
$929$	−4.72240e7	+	3.43102e7i	−0.00193245	+	0.00140401i	0.586819	+	0.809718i	$0.300380\pi$
$930$		0			0
$931$	−4.00894e8	−	1.23382e9i	−0.0162819	−	0.0501106i
$932$	5.18462e9	−	1.59566e10i	0.209779	−	0.645633i
$933$		0			0
$934$	2.72028e10			1.09245
$935$	9.90989e7	+	6.17083e8i	0.00396486	+	0.0246890i
$936$		0			0
$937$	−1.18147e9	−	8.58385e8i	−0.0469172	−	0.0340874i	0.564079	−	0.825720i	$-0.309231\pi$
$937$	−1.18147e9	−	8.58385e8i	−0.0469172	−	0.0340874i	−0.610997	+	0.791633i	$0.709231\pi$
$938$	5.49573e9	−	1.69141e10i	0.217428	−	0.669175i
$939$		0			0
$940$	5.77591e7	−	4.19644e7i	0.00226816	−	0.00164791i
$941$	−3.03062e10	+	2.20187e10i	−1.18568	+	0.861447i	−0.992801	−	0.119775i	$-0.961783\pi$
$941$	−3.03062e10	+	2.20187e10i	−1.18568	+	0.861447i	−0.192879	+	0.981222i	$0.561783\pi$
$942$		0			0
$943$	−1.82716e8	+	5.62343e8i	−0.00709555	+	0.0218379i
$944$	−4.84406e10	−	3.51942e10i	−1.87416	−	1.36166i
$945$		0			0
$946$	2.10182e10	+	3.28257e9i	0.807190	+	0.126065i
$947$	1.11017e10			0.424782			0.212391	−	0.977185i	$-0.431875\pi$
$947$	1.11017e10			0.424782			0.212391	+	0.977185i	$0.431875\pi$
$948$		0			0
$949$	8.86723e9	−	2.72905e10i	0.336788	−	1.03653i
$950$	−3.81950e9	−	1.17552e10i	−0.144535	−	0.444834i
$951$		0			0
$952$	−1.35768e10	+	9.86410e9i	−0.509997	+	0.370534i
$953$	−4.03066e9	−	1.24051e10i	−0.150852	−	0.464275i	0.846865	−	0.531808i	$-0.178487\pi$
$953$	−4.03066e9	−	1.24051e10i	−0.150852	−	0.464275i	−0.997717	+	0.0675331i	$0.978487\pi$
$954$		0			0
$955$	1.49003e8	+	1.08257e8i	0.00553585	+	0.00402203i
$956$	1.30103e10			0.481600
$957$		0			0
$958$	−1.93436e10			−0.710818
$959$	3.98700e10	+	2.89673e10i	1.45976	+	1.06058i
$960$		0			0
$961$	−5.74906e9	−	1.76938e10i	−0.208961	−	0.643115i
$962$	−5.56483e10	+	4.04309e10i	−2.01530	+	1.46420i
$963$		0			0
$964$	−2.55052e9	−	7.84971e9i	−0.0916980	−	0.282217i
$965$	6.83522e7	−	2.10367e8i	0.00244854	−	0.00753583i
$966$		0			0
$967$	2.11690e10			0.752850			0.376425	−	0.926447i	$-0.377153\pi$
$967$	2.11690e10			0.752850			0.376425	+	0.926447i	$0.377153\pi$
$968$	−5.39330e9	−	7.35641e9i	−0.191113	−	0.260677i
$969$		0			0
$970$	4.73281e7	+	3.43859e7i	0.00166502	+	0.00120970i
$971$	−9.01566e9	+	2.77474e10i	−0.316031	+	0.972645i	0.659296	+	0.751883i	$0.270854\pi$
$971$	−9.01566e9	+	2.77474e10i	−0.316031	+	0.972645i	−0.975328	+	0.220762i	$0.929146\pi$
$972$		0			0
$973$	3.78022e10	−	2.74649e10i	1.31560	−	0.955836i
$974$	−2.90910e10	+	2.11359e10i	−1.00880	+	0.732933i
$975$		0			0
$976$	−2.74993e9	+	8.46342e9i	−0.0946777	+	0.291388i
$977$	−1.02064e10	−	7.41535e9i	−0.350138	−	0.254390i	0.398789	−	0.917043i	$-0.369431\pi$
$977$	−1.02064e10	−	7.41535e9i	−0.350138	−	0.254390i	−0.748927	+	0.662652i	$0.769431\pi$
$978$		0			0
$979$	3.93691e10	−	2.01665e10i	1.34096	−	0.686895i
$980$	−4.57008e7			−0.00155108
$981$		0			0
$982$	1.62352e9	−	4.99668e9i	0.0547101	−	0.168380i
$983$	−4.53074e9	−	1.39442e10i	−0.152136	−	0.468226i	0.845724	−	0.533621i	$-0.179169\pi$
$983$	−4.53074e9	−	1.39442e10i	−0.152136	−	0.468226i	−0.997859	+	0.0653952i	$0.979169\pi$
$984$		0			0
$985$	−2.08761e8	+	1.51674e8i	−0.00696023	+	0.00505690i
$986$	−7.06626e9	−	2.17477e10i	−0.234758	−	0.722510i
$987$		0			0
$988$	−8.05038e9	−	5.84894e9i	−0.265563	−	0.192943i
$989$	4.30724e9			0.141583
$990$		0			0
$991$	3.86648e9			0.126200			0.0630998	−	0.998007i	$-0.479901\pi$
$991$	3.86648e9			0.126200			0.0630998	+	0.998007i	$0.479901\pi$
$992$	1.76406e10	+	1.28167e10i	0.573750	+	0.416854i
$993$		0			0
$994$	−4.01791e9	−	1.23659e10i	−0.129762	−	0.399367i
$995$	−3.26094e7	+	2.36921e7i	−0.00104945	+	0.000762471i
$996$		0			0
$997$	−9.72287e9	−	2.99239e10i	−0.310715	−	0.956281i	−0.977483	−	0.211016i	$-0.932323\pi$
$997$	−9.72287e9	−	2.99239e10i	−0.310715	−	0.956281i	0.666768	−	0.745265i	$-0.267677\pi$
$998$	−1.27422e10	+	3.92165e10i	−0.405778	+	1.24886i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.f.b.37.6		28
3.2	odd	2		33.8.e.b.4.2	✓	28
11.3	even	5	inner	99.8.f.b.91.6		28
33.5	odd	10		363.8.a.o.1.12		14
33.14	odd	10		33.8.e.b.25.2	yes	28
33.17	even	10		363.8.a.r.1.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.e.b.4.2	✓	28	3.2	odd	2
33.8.e.b.25.2	yes	28	33.14	odd	10
99.8.f.b.37.6		28	1.1	even	1	trivial
99.8.f.b.91.6		28	11.3	even	5	inner
363.8.a.o.1.12		14	33.5	odd	10
363.8.a.r.1.3		14	33.17	even	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(12.1293 + 8.81245i) q^{2} +(29.9064 + 92.0423i) q^{4} +(3.10808 - 2.25815i) q^{5} +(300.631 + 925.246i) q^{7} +(144.646 - 445.175i) q^{8} +57.5987 q^{10} +(3928.96 - 2012.57i) q^{11} +(7881.27 + 5726.08i) q^{13} +(-4507.24 + 13871.9i) q^{14} +(15699.4 - 11406.3i) q^{16} +(-29814.1 + 21661.2i) q^{17} +(-3261.53 + 10037.9i) q^{19} +(300.797 + 218.542i) q^{20} +(65391.2 + 10212.7i) q^{22} +13400.6 q^{23} +(-24137.4 + 74287.3i) q^{25} +(45133.5 + 138907. i) q^{26} +(-76171.0 + 55341.5i) q^{28} +(12789.3 + 39361.5i) q^{29} +(76358.0 + 55477.3i) q^{31} +231025. q^{32} -552512. q^{34} +(3023.73 + 2196.87i) q^{35} +(145533. + 447903. i) q^{37} +(-128019. + 93011.2i) q^{38} +(-555.701 - 1710.27i) q^{40} +(-13634.9 + 41964.0i) q^{41} +321422. q^{43} +(302743. + 301442. i) q^{44} +(162540. + 118092. i) q^{46} +(59337.5 - 182622. i) q^{47} +(-99441.1 + 72248.2i) q^{49} +(-947422. + 688342. i) q^{50} +(-291341. + 896657. i) q^{52} +(-701340. - 509553. i) q^{53} +(7666.82 - 15127.4i) q^{55} +455381. q^{56} +(-191746. + 590133. i) q^{58} +(-953474. - 2.93449e6i) q^{59} +(-370998. + 269546. i) q^{61} +(437277. + 1.34580e6i) q^{62} +(792649. + 575893. i) q^{64} +37426.0 q^{65} -1.21931e6 q^{67} +(-2.88538e6 - 2.09635e6i) q^{68} +(17315.9 + 53292.9i) q^{70} +(-721185. + 523972. i) q^{71} +(-910226. - 2.80139e6i) q^{73} +(-2.18192e6 + 6.71525e6i) q^{74} -1.02146e6 q^{76} +(3.04329e6 + 3.03021e6i) q^{77} +(5.31286e6 + 3.86002e6i) q^{79} +(23037.9 - 70903.3i) q^{80} +(-535188. + 388837. i) q^{82} +(6.31652e6 - 4.58922e6i) q^{83} +(-43750.3 + 134649. i) q^{85} +(3.89862e6 + 2.83251e6i) q^{86} +(-327638. - 2.04018e6i) q^{88} +1.00202e7 q^{89} +(-2.92868e6 + 9.01355e6i) q^{91} +(400763. + 1.23342e6i) q^{92} +(2.32907e6 - 1.69217e6i) q^{94} +(12530.1 + 38563.8i) q^{95} +(821688. + 596991. i) q^{97} -1.84283e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 6 q^{2} + 160 q^{4} - 773 q^{5} + 1289 q^{7} - 2956 q^{8} - 10640 q^{10} - 13209 q^{11} + 13499 q^{13} + 3318 q^{14} - 113196 q^{16} - 30296 q^{17} - 6858 q^{19} - 76725 q^{20} - 48859 q^{22} + 166984 q^{23}+ \cdots - 140532178 q^{98}+O(q^{100}) \) 28 * q + 6 * q^2 + 160 * q^4 - 773 * q^5 + 1289 * q^7 - 2956 * q^8 - 10640 * q^10 - 13209 * q^11 + 13499 * q^13 + 3318 * q^14 - 113196 * q^16 - 30296 * q^17 - 6858 * q^19 - 76725 * q^20 - 48859 * q^22 + 166984 * q^23 + 99832 * q^25 - 340424 * q^26 + 657387 * q^28 - 192014 * q^29 + 396068 * q^31 + 303498 * q^32 - 1229124 * q^34 + 725859 * q^35 + 811053 * q^37 - 1548798 * q^38 - 1427263 * q^40 - 1041497 * q^41 - 5265288 * q^43 + 5341085 * q^44 + 1198651 * q^46 - 1667505 * q^47 + 2968140 * q^49 - 11247432 * q^50 + 2325763 * q^52 + 1625736 * q^53 - 8338690 * q^55 + 18201906 * q^56 + 14965553 * q^58 + 2587454 * q^59 + 5801619 * q^61 - 15631121 * q^62 - 3732846 * q^64 + 15368174 * q^65 - 7141262 * q^67 - 17394545 * q^68 - 4329200 * q^70 - 3569199 * q^71 + 125008 * q^73 + 13691530 * q^74 - 19690428 * q^76 + 6038739 * q^77 + 17075485 * q^79 - 26606436 * q^80 + 19886007 * q^82 + 4645575 * q^83 + 12002715 * q^85 + 12296287 * q^86 - 50905990 * q^88 - 9601664 * q^89 - 14129477 * q^91 + 90776021 * q^92 + 1047679 * q^94 - 58935661 * q^95 - 22170261 * q^97 - 140532178 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more