LMFDB - Embedded newform 110.5.e.a.23.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,5,Mod(23,110)] 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("110.23"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 0])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	110.e (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,-40] 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:	$11.3706959392$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 595 x^{18} + 794 x^{17} + 135593 x^{16} + 104156 x^{15} - 14736226 x^{14} + \cdots + 68253675578125 $ x^20 - 4x^19 - 595x^18 + 794x^17 + 135593x^16 + 104156x^15 - 14736226x^14 - 31156068x^13 + 848840747x^12 + 2660048600x^11 - 26176251827x^10 - 109185859846x^9 + 382200503919x^8 + 2275960010348x^7 - 1063937227432x^6 - 21722280452880x^5 - 26853692727465x^4 + 61112468225900x^3 + 191565356825375x^2 + 188014429658750*x + 68253675578125
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{9}\cdot 5^{5}\cdot 11^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.8
Root			$16.0782 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	110.23
Dual form			110.5.e.a.67.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 + 2.00000i) q^{2} +(3.29205 + 3.29205i) q^{3} -8.00000i q^{4} +(10.5135 + 22.6819i) q^{5} -13.1682 q^{6} +(57.4046 - 57.4046i) q^{7} +(16.0000 + 16.0000i) q^{8} -59.3248i q^{9} +(-66.3907 - 24.3368i) q^{10} +36.4829 q^{11} +(26.3364 - 26.3364i) q^{12} +(32.7610 + 32.7610i) q^{13} +229.619i q^{14} +(-40.0590 + 109.281i) q^{15} -64.0000 q^{16} +(168.824 - 168.824i) q^{17} +(118.650 + 118.650i) q^{18} -181.017i q^{19} +(181.455 - 84.1077i) q^{20} +377.958 q^{21} +(-72.9657 + 72.9657i) q^{22} +(369.401 + 369.401i) q^{23} +105.346i q^{24} +(-403.934 + 476.930i) q^{25} -131.044 q^{26} +(461.957 - 461.957i) q^{27} +(-459.237 - 459.237i) q^{28} +1600.80i q^{29} +(-138.444 - 298.680i) q^{30} +906.950 q^{31} +(128.000 - 128.000i) q^{32} +(120.104 + 120.104i) q^{33} +675.296i q^{34} +(1905.57 + 698.523i) q^{35} -474.598 q^{36} +(-1197.14 + 1197.14i) q^{37} +(362.034 + 362.034i) q^{38} +215.702i q^{39} +(-194.694 + 531.125i) q^{40} +1669.56 q^{41} +(-755.917 + 755.917i) q^{42} +(-1279.83 - 1279.83i) q^{43} -291.863i q^{44} +(1345.60 - 623.709i) q^{45} -1477.60 q^{46} +(56.3821 - 56.3821i) q^{47} +(-210.691 - 210.691i) q^{48} -4189.58i q^{49} +(-145.992 - 1761.73i) q^{50} +1111.56 q^{51} +(262.088 - 262.088i) q^{52} +(-3790.83 - 3790.83i) q^{53} +1847.83i q^{54} +(383.561 + 827.500i) q^{55} +1836.95 q^{56} +(595.918 - 595.918i) q^{57} +(-3201.60 - 3201.60i) q^{58} +1050.34i q^{59} +(874.247 + 320.472i) q^{60} +2198.55 q^{61} +(-1813.90 + 1813.90i) q^{62} +(-3405.52 - 3405.52i) q^{63} +512.000i q^{64} +(-398.650 + 1087.51i) q^{65} -480.414 q^{66} +(-1849.11 + 1849.11i) q^{67} +(-1350.59 - 1350.59i) q^{68} +2432.18i q^{69} +(-5208.18 + 2414.09i) q^{70} -2182.76 q^{71} +(949.196 - 949.196i) q^{72} +(-1754.00 - 1754.00i) q^{73} -4788.54i q^{74} +(-2899.85 + 240.306i) q^{75} -1448.14 q^{76} +(2094.29 - 2094.29i) q^{77} +(-431.404 - 431.404i) q^{78} -4099.30i q^{79} +(-672.862 - 1451.64i) q^{80} -1763.73 q^{81} +(-3339.11 + 3339.11i) q^{82} +(6077.02 + 6077.02i) q^{83} -3023.67i q^{84} +(5604.17 + 2054.32i) q^{85} +5119.34 q^{86} +(-5269.93 + 5269.93i) q^{87} +(583.726 + 583.726i) q^{88} -10526.4i q^{89} +(-1443.78 + 3938.61i) q^{90} +3761.27 q^{91} +(2955.21 - 2955.21i) q^{92} +(2985.73 + 2985.73i) q^{93} +225.528i q^{94} +(4105.81 - 1903.12i) q^{95} +842.766 q^{96} +(5967.87 - 5967.87i) q^{97} +(8379.17 + 8379.17i) q^{98} -2164.34i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 40 q^{2} - 26 q^{3} + 8 q^{5} + 104 q^{6} - 48 q^{7} + 320 q^{8} - 132 q^{10} - 208 q^{12} + 20 q^{13} + 700 q^{15} - 1280 q^{16} + 1080 q^{17} - 376 q^{18} + 464 q^{20} - 1536 q^{21} - 1998 q^{23}+ \cdots + 16776 q^{98}+O(q^{100}) $ 20 * q - 40 * q^2 - 26 * q^3 + 8 * q^5 + 104 * q^6 - 48 * q^7 + 320 * q^8 - 132 * q^10 - 208 * q^12 + 20 * q^13 + 700 * q^15 - 1280 * q^16 + 1080 * q^17 - 376 * q^18 + 464 * q^20 - 1536 * q^21 - 1998 * q^23 + 1242 * q^25 - 80 * q^26 + 1558 * q^27 + 384 * q^28 - 2284 * q^30 - 1256 * q^31 + 2560 * q^32 + 1210 * q^33 + 3636 * q^35 + 1504 * q^36 - 286 * q^37 + 736 * q^38 - 800 * q^40 - 5112 * q^41 + 3072 * q^42 - 3048 * q^43 - 3274 * q^45 + 7992 * q^46 + 6636 * q^47 + 1664 * q^48 - 260 * q^50 - 2384 * q^51 + 160 * q^52 - 4212 * q^53 - 726 * q^55 - 1536 * q^56 - 21984 * q^57 - 8528 * q^58 + 3536 * q^60 + 8456 * q^61 + 2512 * q^62 - 5788 * q^63 + 13640 * q^65 - 4840 * q^66 + 8870 * q^67 - 8640 * q^68 - 6776 * q^70 - 14396 * q^71 - 3008 * q^72 + 23020 * q^73 + 6204 * q^75 - 2944 * q^76 - 2048 * q^78 - 512 * q^80 - 808 * q^81 + 10224 * q^82 + 20288 * q^83 - 1332 * q^85 + 12192 * q^86 - 1904 * q^87 - 12352 * q^90 - 27072 * q^91 - 15984 * q^92 + 13386 * q^93 + 21916 * q^95 - 6656 * q^96 + 6754 * q^97 + 16776 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−2.00000	+	2.00000i	−0.500000	+	0.500000i
$2$	−2.00000	+	2.00000i	−0.500000	+	0.500000i
$3$	3.29205	+	3.29205i	0.365784	+	0.365784i	0.865937	−	0.500153i	$-0.166723\pi$
$3$	3.29205	+	3.29205i	0.365784	+	0.365784i	−0.500153	+	0.865937i	$0.666723\pi$
$4$		−	8.00000i		−	0.500000i
$5$	10.5135	+	22.6819i	0.420539	+	0.907275i
$5$	10.5135	+	22.6819i	0.420539	+	0.907275i
$6$	−13.1682			−0.365784
$7$	57.4046	−	57.4046i	1.17152	−	1.17152i	0.189676	−	0.981847i	$-0.439256\pi$
$7$	57.4046	−	57.4046i	1.17152	−	1.17152i	0.981847	−	0.189676i	$-0.0607439\pi$
$8$	16.0000	+	16.0000i	0.250000	+	0.250000i
$9$		−	59.3248i		−	0.732404i
$10$	−66.3907	−	24.3368i	−0.663907	−	0.243368i
$11$	36.4829			0.301511
$11$	36.4829			0.301511
$12$	26.3364	−	26.3364i	0.182892	−	0.182892i
$13$	32.7610	+	32.7610i	0.193852	+	0.193852i	0.797358	−	0.603506i	$-0.206230\pi$
$13$	32.7610	+	32.7610i	0.193852	+	0.193852i	−0.603506	+	0.797358i	$0.706230\pi$
$14$			229.619i			1.17152i
$15$	−40.0590	+	109.281i	−0.178040	+	0.485693i
$16$	−64.0000			−0.250000
$17$	168.824	−	168.824i	0.584166	−	0.584166i	−0.351879	−	0.936045i	$-0.614457\pi$
$17$	168.824	−	168.824i	0.584166	−	0.584166i	0.936045	+	0.351879i	$0.114457\pi$
$18$	118.650	+	118.650i	0.366202	+	0.366202i
$19$		−	181.017i		−	0.501432i	−0.968061	−	0.250716i	$-0.919334\pi$
$19$		−	181.017i		−	0.501432i	0.968061	−	0.250716i	$-0.0806661\pi$
$20$	181.455	−	84.1077i	0.453637	−	0.210269i
$21$	377.958			0.857048
$22$	−72.9657	+	72.9657i	−0.150756	+	0.150756i
$23$	369.401	+	369.401i	0.698301	+	0.698301i	0.964044	−	0.265743i	$-0.0856173\pi$
$23$	369.401	+	369.401i	0.698301	+	0.698301i	−0.265743	+	0.964044i	$0.585617\pi$
$24$			105.346i			0.182892i
$25$	−403.934	+	476.930i	−0.646295	+	0.763088i
$26$	−131.044			−0.193852
$27$	461.957	−	461.957i	0.633686	−	0.633686i
$28$	−459.237	−	459.237i	−0.585762	−	0.585762i
$29$			1600.80i			1.90345i	0.306952	+	0.951725i	$0.400691\pi$
$29$			1600.80i			1.90345i	−0.306952	+	0.951725i	$0.599309\pi$
$30$	−138.444	−	298.680i	−0.153826	−	0.331866i
$31$	906.950			0.943757			0.471878	−	0.881664i	$-0.343576\pi$
$31$	906.950			0.943757			0.471878	+	0.881664i	$0.343576\pi$
$32$	128.000	−	128.000i	0.125000	−	0.125000i
$33$	120.104	+	120.104i	0.110288	+	0.110288i
$34$			675.296i			0.584166i
$35$	1905.57	+	698.523i	1.55556	+	0.570223i
$36$	−474.598			−0.366202
$37$	−1197.14	+	1197.14i	−0.874460	+	0.874460i	−0.992955	−	0.118495i	$-0.962193\pi$
$37$	−1197.14	+	1197.14i	−0.874460	+	0.874460i	0.118495	+	0.992955i	$0.462193\pi$
$38$	362.034	+	362.034i	0.250716	+	0.250716i
$39$			215.702i			0.141816i
$40$	−194.694	+	531.125i	−0.121684	+	0.331953i
$41$	1669.56			0.993192			0.496596	−	0.867982i	$-0.334583\pi$
$41$	1669.56			0.993192			0.496596	+	0.867982i	$0.334583\pi$
$42$	−755.917	+	755.917i	−0.428524	+	0.428524i
$43$	−1279.83	−	1279.83i	−0.692176	−	0.692176i	0.270534	−	0.962710i	$-0.412800\pi$
$43$	−1279.83	−	1279.83i	−0.692176	−	0.692176i	−0.962710	+	0.270534i	$0.912800\pi$
$44$		−	291.863i		−	0.150756i
$45$	1345.60	−	623.709i	0.664492	−	0.308004i
$46$	−1477.60			−0.698301
$47$	56.3821	−	56.3821i	0.0255238	−	0.0255238i	−0.694230	−	0.719754i	$-0.744255\pi$
$47$	56.3821	−	56.3821i	0.0255238	−	0.0255238i	0.719754	+	0.694230i	$0.244255\pi$
$48$	−210.691	−	210.691i	−0.0914460	−	0.0914460i
$49$		−	4189.58i		−	1.74493i
$50$	−145.992	−	1761.73i	−0.0583966	−	0.704691i
$51$	1111.56			0.427357
$52$	262.088	−	262.088i	0.0969261	−	0.0969261i
$53$	−3790.83	−	3790.83i	−1.34953	−	1.34953i	−0.886170	−	0.463360i	$-0.846644\pi$
$53$	−3790.83	−	3790.83i	−1.34953	−	1.34953i	−0.463360	−	0.886170i	$-0.653356\pi$
$54$			1847.83i			0.633686i
$55$	383.561	+	827.500i	0.126797	+	0.273554i
$56$	1836.95			0.585762
$57$	595.918	−	595.918i	0.183416	−	0.183416i
$58$	−3201.60	−	3201.60i	−0.951725	−	0.951725i
$59$			1050.34i			0.301736i	0.988554	+	0.150868i	$0.0482069\pi$
$59$			1050.34i			0.301736i	−0.988554	+	0.150868i	$0.951793\pi$
$60$	874.247	+	320.472i	0.242846	+	0.0890201i
$61$	2198.55			0.590848			0.295424	−	0.955366i	$-0.404539\pi$
$61$	2198.55			0.590848			0.295424	+	0.955366i	$0.404539\pi$
$62$	−1813.90	+	1813.90i	−0.471878	+	0.471878i
$63$	−3405.52	−	3405.52i	−0.858029	−	0.858029i
$64$			512.000i			0.125000i
$65$	−398.650	+	1087.51i	−0.0943549	+	0.257400i
$66$	−480.414			−0.110288
$67$	−1849.11	+	1849.11i	−0.411920	+	0.411920i	−0.882407	−	0.470487i	$-0.844078\pi$
$67$	−1849.11	+	1849.11i	−0.411920	+	0.411920i	0.470487	+	0.882407i	$0.344078\pi$
$68$	−1350.59	−	1350.59i	−0.292083	−	0.292083i
$69$			2432.18i			0.510854i
$70$	−5208.18	+	2414.09i	−1.06289	+	0.492671i
$71$	−2182.76			−0.433001			−0.216500	−	0.976283i	$-0.569464\pi$
$71$	−2182.76			−0.433001			−0.216500	+	0.976283i	$0.569464\pi$
$72$	949.196	−	949.196i	0.183101	−	0.183101i
$73$	−1754.00	−	1754.00i	−0.329143	−	0.329143i	0.523118	−	0.852261i	$-0.324769\pi$
$73$	−1754.00	−	1754.00i	−0.329143	−	0.329143i	−0.852261	+	0.523118i	$0.824769\pi$
$74$		−	4788.54i		−	0.874460i
$75$	−2899.85	+	240.306i	−0.515529	+	0.0427211i
$76$	−1448.14			−0.250716
$77$	2094.29	−	2094.29i	0.353227	−	0.353227i
$78$	−431.404	−	431.404i	−0.0709080	−	0.0709080i
$79$		−	4099.30i		−	0.656834i	−0.944533	−	0.328417i	$-0.893485\pi$
$79$		−	4099.30i		−	0.656834i	0.944533	−	0.328417i	$-0.106515\pi$
$80$	−672.862	−	1451.64i	−0.105135	−	0.226819i
$81$	−1763.73			−0.268821
$82$	−3339.11	+	3339.11i	−0.496596	+	0.496596i
$83$	6077.02	+	6077.02i	0.882134	+	0.882134i	0.993751	−	0.111617i	$-0.0356030\pi$
$83$	6077.02	+	6077.02i	0.882134	+	0.882134i	−0.111617	+	0.993751i	$0.535603\pi$
$84$		−	3023.67i		−	0.428524i
$85$	5604.17	+	2054.32i	0.775663	+	0.284335i
$86$	5119.34			0.692176
$87$	−5269.93	+	5269.93i	−0.696251	+	0.696251i
$88$	583.726	+	583.726i	0.0753778	+	0.0753778i
$89$		−	10526.4i		−	1.32892i	−0.747323	−	0.664461i	$-0.768661\pi$
$89$		−	10526.4i		−	1.32892i	0.747323	−	0.664461i	$-0.231339\pi$
$90$	−1443.78	+	3938.61i	−0.178244	+	0.486248i
$91$	3761.27			0.454205
$92$	2955.21	−	2955.21i	0.349150	−	0.349150i
$93$	2985.73	+	2985.73i	0.345211	+	0.345211i
$94$			225.528i			0.0255238i
$95$	4105.81	−	1903.12i	0.454937	−	0.210872i
$96$	842.766			0.0914460
$97$	5967.87	−	5967.87i	0.634272	−	0.634272i	−0.314865	−	0.949137i	$-0.601959\pi$
$97$	5967.87	−	5967.87i	0.634272	−	0.634272i	0.949137	+	0.314865i	$0.101959\pi$
$98$	8379.17	+	8379.17i	0.872466	+	0.872466i
$99$		−	2164.34i		−	0.220828i
$100$	3815.44	+	3231.47i	0.381544	+	0.323147i
$101$	3805.45			0.373047			0.186524	−	0.982450i	$-0.440278\pi$
$101$	3805.45			0.373047			0.186524	+	0.982450i	$0.440278\pi$
$102$	−2223.11	+	2223.11i	−0.213679	+	0.213679i
$103$	−3008.03	−	3008.03i	−0.283535	−	0.283535i	0.550982	−	0.834517i	$-0.314253\pi$
$103$	−3008.03	−	3008.03i	−0.283535	−	0.283535i	−0.834517	+	0.550982i	$0.814253\pi$
$104$			1048.35i			0.0969261i
$105$	3973.65	+	8572.80i	0.360422	+	0.777578i
$106$	15163.3			1.34953
$107$	−15655.8	+	15655.8i	−1.36744	+	1.36744i	−0.503360	+	0.864077i	$0.667903\pi$
$107$	−15655.8	+	15655.8i	−1.36744	+	1.36744i	−0.864077	+	0.503360i	$0.832097\pi$
$108$	−3695.65	−	3695.65i	−0.316843	−	0.316843i
$109$			19945.9i			1.67880i	0.543510	+	0.839402i	$0.317095\pi$
$109$			19945.9i			1.67880i	−0.543510	+	0.839402i	$0.682905\pi$
$110$	−2422.12	−	887.877i	−0.200175	−	0.0733782i
$111$	−7882.07			−0.639727
$112$	−3673.90	+	3673.90i	−0.292881	+	0.292881i
$113$	−6331.12	−	6331.12i	−0.495820	−	0.495820i	0.414314	−	0.910134i	$-0.364021\pi$
$113$	−6331.12	−	6331.12i	−0.495820	−	0.495820i	−0.910134	+	0.414314i	$0.864021\pi$
$114$			2383.67i			0.183416i
$115$	−4495.02	+	12262.4i	−0.339888	+	0.927213i
$116$	12806.4			0.951725
$117$	1943.54	−	1943.54i	0.141978	−	0.141978i
$118$	−2100.69	−	2100.69i	−0.150868	−	0.150868i
$119$		−	19382.6i		−	1.36873i
$120$	−2389.44	+	1107.55i	−0.165933	+	0.0769131i
$121$	1331.00			0.0909091
$122$	−4397.09	+	4397.09i	−0.295424	+	0.295424i
$123$	5496.27	+	5496.27i	0.363294	+	0.363294i
$124$		−	7255.60i		−	0.471878i
$125$	−15064.4	−	4147.80i	−0.964122	−	0.265459i
$126$	13622.1			0.858029
$127$	−9733.35	+	9733.35i	−0.603469	+	0.603469i	−0.941231	−	0.337763i	$-0.890330\pi$
$127$	−9733.35	+	9733.35i	−0.603469	+	0.603469i	0.337763	+	0.941231i	$0.390330\pi$
$128$	−1024.00	−	1024.00i	−0.0625000	−	0.0625000i
$129$		−	8426.57i		−	0.506374i
$130$	−1377.73	−	2972.33i	−0.0815224	−	0.175877i
$131$	28037.7			1.63380			0.816901	−	0.576778i	$-0.195690\pi$
$131$	28037.7			1.63380			0.816901	+	0.576778i	$0.195690\pi$
$132$	960.829	−	960.829i	0.0551440	−	0.0551440i
$133$	−10391.2	−	10391.2i	−0.587440	−	0.587440i
$134$		−	7396.43i		−	0.411920i
$135$	15334.8	+	5621.28i	0.841416	+	0.308438i
$136$	5402.37			0.292083
$137$	15583.4	−	15583.4i	0.830271	−	0.830271i	−0.157282	−	0.987554i	$-0.550273\pi$
$137$	15583.4	−	15583.4i	0.830271	−	0.830271i	0.987554	+	0.157282i	$0.0502733\pi$
$138$	−4864.36	−	4864.36i	−0.255427	−	0.255427i
$139$			23317.4i			1.20684i	0.797423	+	0.603421i	$0.206196\pi$
$139$			23317.4i			1.20684i	−0.797423	+	0.603421i	$0.793804\pi$
$140$	5588.18	−	15244.5i	0.285111	−	0.777782i
$141$	371.226			0.0186724
$142$	4365.51	−	4365.51i	0.216500	−	0.216500i
$143$	1195.22	+	1195.22i	0.0584487	+	0.0584487i
$144$			3796.78i			0.183101i
$145$	−36309.2	+	16830.0i	−1.72695	+	0.800474i
$146$	7016.01			0.329143
$147$	13792.3	−	13792.3i	0.638268	−	0.638268i
$148$	9577.09	+	9577.09i	0.437230	+	0.437230i
$149$			12667.4i			0.570578i	0.958442	+	0.285289i	$0.0920895\pi$
$149$			12667.4i			0.570578i	−0.958442	+	0.285289i	$0.907910\pi$
$150$	5319.09	−	6280.32i	0.236404	−	0.279125i
$151$	−14238.4			−0.624464			−0.312232	−	0.950006i	$-0.601077\pi$
$151$	−14238.4			−0.624464			−0.312232	+	0.950006i	$0.601077\pi$
$152$	2896.27	−	2896.27i	0.125358	−	0.125358i
$153$	−10015.4	−	10015.4i	−0.427846	−	0.427846i
$154$			8377.14i			0.353227i
$155$	9535.19	+	20571.3i	0.396886	+	0.856247i
$156$	1725.62			0.0709080
$157$	−7969.33	+	7969.33i	−0.323313	+	0.323313i	−0.850036	−	0.526724i	$-0.823420\pi$
$157$	−7969.33	+	7969.33i	−0.323313	+	0.323313i	0.526724	+	0.850036i	$0.323420\pi$
$158$	8198.60	+	8198.60i	0.328417	+	0.328417i
$159$		−	24959.2i		−	0.987272i
$160$	4249.00	+	1557.56i	0.165977	+	0.0608420i
$161$	42410.7			1.63615
$162$	3527.46	−	3527.46i	0.134410	−	0.134410i
$163$	−15896.4	−	15896.4i	−0.598307	−	0.598307i	0.341555	−	0.939862i	$-0.389047\pi$
$163$	−15896.4	−	15896.4i	−0.598307	−	0.598307i	−0.939862	+	0.341555i	$0.889047\pi$
$164$		−	13356.4i		−	0.496596i
$165$	−1461.47	+	3986.88i	−0.0536811	+	0.146442i
$166$	−24308.1			−0.882134
$167$	−4487.35	+	4487.35i	−0.160900	+	0.160900i	−0.782965	−	0.622065i	$-0.786294\pi$
$167$	−4487.35	+	4487.35i	−0.160900	+	0.160900i	0.622065	+	0.782965i	$0.286294\pi$
$168$	6047.33	+	6047.33i	0.214262	+	0.214262i
$169$		−	26414.4i		−	0.924843i
$170$	−15317.0	+	7099.70i	−0.529999	+	0.245664i
$171$	−10738.8			−0.367251
$172$	−10238.7	+	10238.7i	−0.346088	+	0.346088i
$173$	−38917.5	−	38917.5i	−1.30033	−	1.30033i	−0.928169	−	0.372159i	$-0.878618\pi$
$173$	−38917.5	−	38917.5i	−1.30033	−	1.30033i	−0.372159	−	0.928169i	$-0.621382\pi$
$174$		−	21079.7i		−	0.696251i
$175$	4190.29	+	50565.7i	0.136826	+	1.65112i
$176$	−2334.90			−0.0753778
$177$	−3457.79	+	3457.79i	−0.110370	+	0.110370i
$178$	21052.8	+	21052.8i	0.664461	+	0.664461i
$179$		−	9880.94i		−	0.308384i	−0.988041	−	0.154192i	$-0.950723\pi$
$179$		−	9880.94i		−	0.308384i	0.988041	−	0.154192i	$-0.0492775\pi$
$180$	−4989.67	−	10764.8i	−0.154002	−	0.332246i
$181$	−35122.5			−1.07208			−0.536041	−	0.844192i	$-0.680081\pi$
$181$	−35122.5			−1.07208			−0.536041	+	0.844192i	$0.680081\pi$
$182$	−7522.54	+	7522.54i	−0.227102	+	0.227102i
$183$	7237.74	+	7237.74i	0.216123	+	0.216123i
$184$			11820.8i			0.349150i
$185$	−39739.3	−	14567.2i	−1.16112	−	0.425631i
$186$	−11942.9			−0.345211
$187$	6159.18	−	6159.18i	0.176133	−	0.176133i
$188$	−451.057	−	451.057i	−0.0127619	−	0.0127619i
$189$		−	53036.9i		−	1.48475i
$190$	−4405.38	+	12017.8i	−0.122033	+	0.332904i
$191$	−4383.68			−0.120163			−0.0600817	−	0.998193i	$-0.519136\pi$
$191$	−4383.68			−0.120163			−0.0600817	+	0.998193i	$0.519136\pi$
$192$	−1685.53	+	1685.53i	−0.0457230	+	0.0457230i
$193$	−26448.3	−	26448.3i	−0.710040	−	0.710040i	0.256503	−	0.966543i	$-0.417430\pi$
$193$	−26448.3	−	26448.3i	−0.710040	−	0.710040i	−0.966543	+	0.256503i	$0.917430\pi$
$194$			23871.5i			0.634272i
$195$	−4892.53	+	2267.78i	−0.128666	+	0.0596391i
$196$	−33516.7			−0.872466
$197$	32508.2	−	32508.2i	0.837646	−	0.837646i	−0.150903	−	0.988549i	$-0.548218\pi$
$197$	32508.2	−	32508.2i	0.837646	−	0.837646i	0.988549	+	0.150903i	$0.0482180\pi$
$198$	4328.67	+	4328.67i	0.110414	+	0.110414i
$199$			58365.4i			1.47384i	0.675982	+	0.736918i	$0.263720\pi$
$199$			58365.4i			1.47384i	−0.675982	+	0.736918i	$0.736280\pi$
$200$	−14093.8	+	1167.93i	−0.352346	+	0.0291983i
$201$	−12174.7			−0.301347
$202$	−7610.91	+	7610.91i	−0.186524	+	0.186524i
$203$	91893.4	+	91893.4i	2.22994	+	2.22994i
$204$		−	8892.44i		−	0.213679i
$205$	17552.8	+	37868.6i	0.417675	+	0.901098i
$206$	12032.1			0.283535
$207$	21914.6	−	21914.6i	0.511439	−	0.511439i
$208$	−2096.71	−	2096.71i	−0.0484631	−	0.0484631i
$209$		−	6604.02i		−	0.151188i
$210$	−25092.9	−	9198.30i	−0.569000	−	0.208578i
$211$	−54742.1			−1.22958			−0.614789	−	0.788691i	$-0.710759\pi$
$211$	−54742.1			−1.22958			−0.614789	+	0.788691i	$0.710759\pi$
$212$	−30326.6	+	30326.6i	−0.674765	+	0.674765i
$213$	−7185.75	−	7185.75i	−0.158385	−	0.158385i
$214$		−	62623.1i		−	1.36744i
$215$	15573.5	−	42484.5i	0.336907	−	0.919081i
$216$	14782.6			0.316843
$217$	52063.2	−	52063.2i	1.10563	−	1.10563i
$218$	−39891.8	−	39891.8i	−0.839402	−	0.839402i
$219$		−	11548.5i		−	0.240790i
$220$	6620.00	−	3068.49i	0.136777	−	0.0633986i
$221$	11061.7			0.226484
$222$	15764.1	−	15764.1i	0.319863	−	0.319863i
$223$	−11144.1	−	11144.1i	−0.224097	−	0.224097i	0.586124	−	0.810221i	$-0.300653\pi$
$223$	−11144.1	−	11144.1i	−0.224097	−	0.224097i	−0.810221	+	0.586124i	$0.800653\pi$
$224$		−	14695.6i		−	0.292881i
$225$	28293.8	+	23963.3i	0.558889	+	0.473349i
$226$	25324.5			0.495820
$227$	−12095.7	+	12095.7i	−0.234736	+	0.234736i	−0.814666	−	0.579930i	$-0.803080\pi$
$227$	−12095.7	+	12095.7i	−0.234736	+	0.234736i	0.579930	+	0.814666i	$0.303080\pi$
$228$	−4767.35	−	4767.35i	−0.0917079	−	0.0917079i
$229$		−	13110.8i		−	0.250011i	−0.992156	−	0.125005i	$-0.960105\pi$
$229$		−	13110.8i		−	0.250011i	0.992156	−	0.125005i	$-0.0398948\pi$
$230$	−15534.7	−	33514.8i	−0.293662	−	0.633551i
$231$	13789.0			0.258410
$232$	−25612.8	+	25612.8i	−0.475862	+	0.475862i
$233$	−38967.4	−	38967.4i	−0.717776	−	0.717776i	0.250373	−	0.968149i	$-0.419447\pi$
$233$	−38967.4	−	38967.4i	−0.717776	−	0.717776i	−0.968149	+	0.250373i	$0.919447\pi$
$234$			7774.16i			0.141978i
$235$	1871.62	+	686.080i	0.0338909	+	0.0124234i
$236$	8402.76			0.150868
$237$	13495.1	−	13495.1i	0.240259	−	0.240259i
$238$	38765.1	+	38765.1i	0.684364	+	0.684364i
$239$			60444.6i			1.05819i	0.848564	+	0.529093i	$0.177468\pi$
$239$			60444.6i			1.05819i	−0.848564	+	0.529093i	$0.822532\pi$
$240$	2563.78	−	6993.97i	0.0445101	−	0.121423i
$241$	26519.0			0.456587			0.228293	−	0.973592i	$-0.426685\pi$
$241$	26519.0			0.456587			0.228293	+	0.973592i	$0.426685\pi$
$242$	−2662.00	+	2662.00i	−0.0454545	+	0.0454545i
$243$	−43224.8	−	43224.8i	−0.732016	−	0.732016i
$244$		−	17588.4i		−	0.295424i
$245$	95027.6	−	44047.0i	1.58313	−	0.733811i
$246$	−21985.1			−0.363294
$247$	5930.31	−	5930.31i	0.0972038	−	0.0972038i
$248$	14511.2	+	14511.2i	0.235939	+	0.235939i
$249$			40011.8i			0.645341i
$250$	38424.4	−	21833.2i	0.614791	−	0.349332i
$251$	−114262.			−1.81366			−0.906829	−	0.421499i	$-0.861504\pi$
$251$	−114262.			−1.81366			−0.906829	+	0.421499i	$0.861504\pi$
$252$	−27244.1	+	27244.1i	−0.429014	+	0.429014i
$253$	13476.8	+	13476.8i	0.210546	+	0.210546i
$254$		−	38933.4i		−	0.603469i
$255$	11686.3	+	25212.2i	0.179720	+	0.387730i
$256$	4096.00			0.0625000
$257$	−75385.0	+	75385.0i	−1.14135	+	1.14135i	−0.153146	+	0.988204i	$0.548940\pi$
$257$	−75385.0	+	75385.0i	−1.14135	+	1.14135i	−0.988204	+	0.153146i	$0.951060\pi$
$258$	16853.1	+	16853.1i	0.253187	+	0.253187i
$259$			137442.i			2.04890i
$260$	8700.11	+	3189.20i	0.128700	+	0.0471775i
$261$	94967.1			1.39410
$262$	−56075.4	+	56075.4i	−0.816901	+	0.816901i
$263$	81024.9	+	81024.9i	1.17140	+	1.17140i	0.981875	+	0.189529i	$0.0606962\pi$
$263$	81024.9	+	81024.9i	1.17140	+	1.17140i	0.189529	+	0.981875i	$0.439304\pi$
$264$			3843.32i			0.0551440i
$265$	46128.3	−	125838.i	0.656865	−	1.79192i
$266$	41564.9			0.587440
$267$	34653.5	−	34653.5i	0.486098	−	0.486098i
$268$	14792.9	+	14792.9i	0.205960	+	0.205960i
$269$			96608.6i			1.33509i	0.744568	+	0.667546i	$0.232655\pi$
$269$			96608.6i			1.33509i	−0.744568	+	0.667546i	$0.767345\pi$
$270$	−41912.2	+	19427.1i	−0.574927	+	0.266489i
$271$	63412.9			0.863454			0.431727	−	0.902004i	$-0.357904\pi$
$271$	63412.9			0.863454			0.431727	+	0.902004i	$0.357904\pi$
$272$	−10804.7	+	10804.7i	−0.146042	+	0.146042i
$273$	12382.3	+	12382.3i	0.166141	+	0.166141i
$274$			62333.4i			0.830271i
$275$	−14736.7	+	17399.8i	−0.194865	+	0.230080i
$276$	19457.4			0.255427
$277$	33000.0	−	33000.0i	0.430085	−	0.430085i	−0.458572	−	0.888657i	$-0.651639\pi$
$277$	33000.0	−	33000.0i	0.430085	−	0.430085i	0.888657	+	0.458572i	$0.151639\pi$
$278$	−46634.8	−	46634.8i	−0.603421	−	0.603421i
$279$		−	53804.6i		−	0.691212i
$280$	19312.7	+	41665.4i	0.246335	+	0.531447i
$281$	−48286.4			−0.611522			−0.305761	−	0.952108i	$-0.598911\pi$
$281$	−48286.4			−0.611522			−0.305761	+	0.952108i	$0.598911\pi$
$282$	−742.452	+	742.452i	−0.00933620	+	0.00933620i
$283$	−24472.9	−	24472.9i	−0.305571	−	0.305571i	0.537618	−	0.843189i	$-0.319324\pi$
$283$	−24472.9	−	24472.9i	−0.305571	−	0.305571i	−0.843189	+	0.537618i	$0.819324\pi$
$284$			17462.1i			0.216500i
$285$	19781.7	+	7251.37i	0.243542	+	0.0892751i
$286$	−4780.87			−0.0584487
$287$	95840.2	−	95840.2i	1.16355	−	1.16355i
$288$	−7593.57	−	7593.57i	−0.0915505	−	0.0915505i
$289$			26517.9i			0.317500i
$290$	38958.4	−	106278.i	0.463239	−	1.26371i
$291$	39293.1			0.464013
$292$	−14032.0	+	14032.0i	−0.164571	+	0.164571i
$293$	10067.4	+	10067.4i	0.117268	+	0.117268i	0.763306	−	0.646037i	$-0.223575\pi$
$293$	10067.4	+	10067.4i	0.117268	+	0.117268i	−0.646037	+	0.763306i	$0.723575\pi$
$294$			55169.3i			0.638268i
$295$	−23823.8	+	11042.8i	−0.273758	+	0.126892i
$296$	−38308.3			−0.437230
$297$	16853.5	−	16853.5i	0.191063	−	0.191063i
$298$	−25334.8	−	25334.8i	−0.285289	−	0.285289i
$299$			24203.9i			0.270734i
$300$	1922.45	+	23198.8i	0.0213605	+	0.257765i
$301$	−146937.			−1.62180
$302$	28476.8	−	28476.8i	0.312232	−	0.312232i
$303$	12527.8	+	12527.8i	0.136455	+	0.136455i
$304$			11585.1i			0.125358i
$305$	23114.3	+	49867.2i	0.248475	+	0.536062i
$306$	40061.8			0.427846
$307$	20163.8	−	20163.8i	0.213942	−	0.213942i	−0.591998	−	0.805940i	$-0.701661\pi$
$307$	20163.8	−	20163.8i	0.213942	−	0.213942i	0.805940	+	0.591998i	$0.201661\pi$
$308$	−16754.3	−	16754.3i	−0.176614	−	0.176614i
$309$		−	19805.2i		−	0.207425i
$310$	−60213.0	−	22072.3i	−0.626566	−	0.229680i
$311$	48107.7			0.497386			0.248693	−	0.968582i	$-0.419999\pi$
$311$	48107.7			0.497386			0.248693	+	0.968582i	$0.419999\pi$
$312$	−3451.24	+	3451.24i	−0.0354540	+	0.0354540i
$313$	91323.7	+	91323.7i	0.932169	+	0.932169i	0.997841	−	0.0656722i	$-0.0209192\pi$
$313$	91323.7	+	91323.7i	0.932169	+	0.932169i	−0.0656722	+	0.997841i	$0.520919\pi$
$314$		−	31877.3i		−	0.323313i
$315$	41439.7	−	113047.i	0.417634	−	1.13930i
$316$	−32794.4			−0.328417
$317$	−45916.0	+	45916.0i	−0.456926	+	0.456926i	−0.897645	−	0.440719i	$-0.854723\pi$
$317$	−45916.0	+	45916.0i	−0.456926	+	0.456926i	0.440719	+	0.897645i	$0.354723\pi$
$318$	49918.5	+	49918.5i	0.493636	+	0.493636i
$319$			58401.8i			0.573912i
$320$	−11613.1	+	5382.89i	−0.113409	+	0.0525673i
$321$	−103079.			−1.00037
$322$	−84821.4	+	84821.4i	−0.818076	+	0.818076i
$323$	−30560.0	−	30560.0i	−0.292920	−	0.292920i
$324$			14109.9i			0.134410i
$325$	−28858.0	+	2391.42i	−0.273212	+	0.0226406i
$326$	63585.7			0.598307
$327$	−65662.9	+	65662.9i	−0.614080	+	0.614080i
$328$	26712.9	+	26712.9i	0.248298	+	0.248298i
$329$		−	6473.19i		−	0.0598035i
$330$	−5050.82	−	10896.7i	−0.0463803	−	0.100061i
$331$	−195697.			−1.78620			−0.893098	−	0.449862i	$-0.851473\pi$
$331$	−195697.			−1.78620			−0.893098	+	0.449862i	$0.851473\pi$
$332$	48616.2	−	48616.2i	0.441067	−	0.441067i
$333$	71019.8	+	71019.8i	0.640458	+	0.640458i
$334$		−	17949.4i		−	0.160900i
$335$	−61381.7	−	22500.7i	−0.546952	−	0.200496i
$336$	−24189.3			−0.214262
$337$	−86291.9	+	86291.9i	−0.759819	+	0.759819i	−0.976289	−	0.216470i	$-0.930546\pi$
$337$	−86291.9	+	86291.9i	−0.759819	+	0.759819i	0.216470	+	0.976289i	$0.430546\pi$
$338$	52828.9	+	52828.9i	0.462421	+	0.462421i
$339$		−	41684.8i		−	0.362726i
$340$	16434.5	−	44833.3i	0.142167	−	0.387832i
$341$	33088.2			0.284553
$342$	21477.6	−	21477.6i	0.183626	−	0.183626i
$343$	−102673.	−	102673.i	−0.872706	−	0.872706i
$344$		−	40954.7i		−	0.346088i
$345$	−55166.3	+	25570.6i	−0.463485	+	0.214834i
$346$	155670.			1.30033
$347$	124508.	−	124508.i	1.03404	−	1.03404i	0.0346438	−	0.999400i	$-0.488970\pi$
$347$	124508.	−	124508.i	1.03404	−	1.03404i	0.999400	−	0.0346438i	$-0.0110297\pi$
$348$	42159.4	+	42159.4i	0.348126	+	0.348126i
$349$		−	104109.i		−	0.854744i	−0.904076	−	0.427372i	$-0.859439\pi$
$349$		−	104109.i		−	0.854744i	0.904076	−	0.427372i	$-0.140561\pi$
$350$	−109512.	−	92750.8i	−0.893975	−	0.757149i
$351$	30268.4			0.245683
$352$	4669.81	−	4669.81i	0.0376889	−	0.0376889i
$353$	−76938.5	−	76938.5i	−0.617440	−	0.617440i	0.327434	−	0.944874i	$-0.393816\pi$
$353$	−76938.5	−	76938.5i	−0.617440	−	0.617440i	−0.944874	+	0.327434i	$0.893816\pi$
$354$		−	13831.2i		−	0.110370i
$355$	−22948.3	−	49509.0i	−0.182094	−	0.392851i
$356$	−84211.2			−0.664461
$357$	63808.4	−	63808.4i	0.500659	−	0.500659i
$358$	19761.9	+	19761.9i	0.154192	+	0.154192i
$359$			72390.2i			0.561682i	0.959754	+	0.280841i	$0.0906134\pi$
$359$			72390.2i			0.561682i	−0.959754	+	0.280841i	$0.909387\pi$
$360$	31508.9	+	11550.2i	0.243124	+	0.0891219i
$361$	97553.8			0.748565
$362$	70244.9	−	70244.9i	0.536041	−	0.536041i
$363$	4381.72	+	4381.72i	0.0332531	+	0.0332531i
$364$		−	30090.2i		−	0.227102i
$365$	21343.4	−	58224.7i	0.160206	−	0.437040i
$366$	−28950.9			−0.216123
$367$	20973.4	−	20973.4i	0.155717	−	0.155717i	−0.624949	−	0.780666i	$-0.714880\pi$
$367$	20973.4	−	20973.4i	0.155717	−	0.155717i	0.780666	+	0.624949i	$0.214880\pi$
$368$	−23641.7	−	23641.7i	−0.174575	−	0.174575i
$369$		−	99046.0i		−	0.727418i
$370$	108613.	−	50344.2i	0.793376	−	0.367744i
$371$	−435222.			−3.16201
$372$	23885.8	−	23885.8i	0.172606	−	0.172606i
$373$	−126422.	−	126422.i	−0.908671	−	0.908671i	0.0874941	−	0.996165i	$-0.472114\pi$
$373$	−126422.	−	126422.i	−0.908671	−	0.908671i	−0.996165	+	0.0874941i	$0.972114\pi$
$374$			24636.7i			0.176133i
$375$	−35938.1	−	63247.6i	−0.255560	−	0.449761i
$376$	1804.23			0.0127619
$377$	−52443.9	+	52443.9i	−0.368988	+	0.368988i
$378$	106074.	+	106074.i	0.742377	+	0.742377i
$379$			84258.2i			0.586589i	0.956022	+	0.293294i	$0.0947516\pi$
$379$			84258.2i			0.586589i	−0.956022	+	0.293294i	$0.905248\pi$
$380$	−15224.9	−	32846.5i	−0.105436	−	0.227468i
$381$	−64085.4			−0.441478
$382$	8767.36	−	8767.36i	0.0600817	−	0.0600817i
$383$	−78026.0	−	78026.0i	−0.531915	−	0.531915i	0.389227	−	0.921142i	$-0.372742\pi$
$383$	−78026.0	−	78026.0i	−0.531915	−	0.531915i	−0.921142	+	0.389227i	$0.872742\pi$
$384$		−	6742.13i		−	0.0457230i
$385$	69520.5	+	25484.1i	0.469020	+	0.171929i
$386$	105793.			0.710040
$387$	−75925.8	+	75925.8i	−0.506953	+	0.506953i
$388$	−47742.9	−	47742.9i	−0.317136	−	0.317136i
$389$		−	50793.5i		−	0.335667i	−0.985815	−	0.167834i	$-0.946323\pi$
$389$		−	50793.5i		−	0.335667i	0.985815	−	0.167834i	$-0.0536771\pi$
$390$	5249.50	−	14320.6i	0.0345135	−	0.0941526i
$391$	124728.			0.815847
$392$	67033.3	−	67033.3i	0.436233	−	0.436233i
$393$	92301.6	+	92301.6i	0.597618	+	0.597618i
$394$			130033.i			0.837646i
$395$	92979.8	−	43097.9i	0.595929	−	0.276224i
$396$	−17314.7			−0.110414
$397$	−35190.7	+	35190.7i	−0.223278	+	0.223278i	−0.809877	−	0.586599i	$-0.800466\pi$
$397$	−35190.7	+	35190.7i	−0.223278	+	0.223278i	0.586599	+	0.809877i	$0.300466\pi$
$398$	−116731.	−	116731.i	−0.736918	−	0.736918i
$399$		−	68416.9i		−	0.429752i
$400$	25851.8	−	30523.5i	0.161574	−	0.190772i
$401$	−255749.			−1.59047			−0.795235	−	0.606301i	$-0.792653\pi$
$401$	−255749.			−1.59047			−0.795235	+	0.606301i	$0.792653\pi$
$402$	24349.5	−	24349.5i	0.150674	−	0.150674i
$403$	29712.6	+	29712.6i	0.182949	+	0.182949i
$404$		−	30443.6i		−	0.186524i
$405$	−18542.9	−	40004.7i	−0.113049	−	0.243894i
$406$	−367574.			−2.22994
$407$	−43675.0	+	43675.0i	−0.263660	+	0.263660i
$408$	17784.9	+	17784.9i	0.106839	+	0.106839i
$409$			77635.6i			0.464103i	0.972704	+	0.232051i	$0.0745438\pi$
$409$			77635.6i			0.464103i	−0.972704	+	0.232051i	$0.925456\pi$
$410$	−110843.	−	40631.7i	−0.659387	−	0.241711i
$411$	102603.			0.607400
$412$	−24064.2	+	24064.2i	−0.141768	+	0.141768i
$413$	60294.6	+	60294.6i	0.353491	+	0.353491i
$414$			87658.5i			0.511439i
$415$	−73947.7	+	201729.i	−0.429367	+	1.17131i
$416$	8386.83			0.0484631
$417$	−76762.2	+	76762.2i	−0.441443	+	0.441443i
$418$	13208.0	+	13208.0i	0.0755938	+	0.0755938i
$419$			297750.i			1.69599i	0.530003	+	0.847996i	$0.322191\pi$
$419$			297750.i			1.69599i	−0.530003	+	0.847996i	$0.677809\pi$
$420$	68582.4	−	31789.2i	0.388789	−	0.180211i
$421$	217165.			1.22526			0.612628	−	0.790372i	$-0.290113\pi$
$421$	217165.			1.22526			0.612628	+	0.790372i	$0.290113\pi$
$422$	109484.	−	109484.i	0.614789	−	0.614789i
$423$	−3344.85	−	3344.85i	−0.0186938	−	0.0186938i
$424$		−	121307.i		−	0.674765i
$425$	12323.4	+	148711.i	0.0682266	+	0.823313i
$426$	28743.0			0.158385
$427$	126207.	−	126207.i	0.692193	−	0.692193i
$428$	125246.	+	125246.i	0.683718	+	0.683718i
$429$			7869.44i			0.0427592i
$430$	53822.0	+	116116.i	0.291087	+	0.627994i
$431$	82952.2			0.446554			0.223277	−	0.974755i	$-0.428325\pi$
$431$	82952.2			0.446554			0.223277	+	0.974755i	$0.428325\pi$
$432$	−29565.2	+	29565.2i	−0.158421	+	0.158421i
$433$	−144496.	−	144496.i	−0.770688	−	0.770688i	0.207539	−	0.978227i	$-0.433455\pi$
$433$	−144496.	−	144496.i	−0.770688	−	0.770688i	−0.978227	+	0.207539i	$0.933455\pi$
$434$			208253.i			1.10563i
$435$	−174937.	−	64126.6i	−0.924492	−	0.338891i
$436$	159567.			0.839402
$437$	66867.9	−	66867.9i	0.350151	−	0.350151i
$438$	23097.1	+	23097.1i	0.120395	+	0.120395i
$439$		−	296938.i		−	1.54077i	−0.637582	−	0.770383i	$-0.720065\pi$
$439$		−	296938.i		−	1.54077i	0.637582	−	0.770383i	$-0.279935\pi$
$440$	−7103.01	+	19377.0i	−0.0366891	+	0.100088i
$441$	−248546.			−1.27800
$442$	−22123.4	+	22123.4i	−0.113242	+	0.113242i
$443$	197150.	+	197150.i	1.00459	+	1.00459i	0.999989	+	0.00460145i	$0.00146469\pi$
$443$	197150.	+	197150.i	1.00459	+	1.00459i	0.00460145	+	0.999989i	$0.498535\pi$
$444$			63056.6i			0.319863i
$445$	238758.	−	110669.i	1.20570	−	0.558863i
$446$	44576.5			0.224097
$447$	−41701.8	+	41701.8i	−0.208708	+	0.208708i
$448$	29391.2	+	29391.2i	0.146440	+	0.146440i
$449$			203408.i			1.00897i	0.863422	+	0.504483i	$0.168317\pi$
$449$			203408.i			1.00897i	−0.863422	+	0.504483i	$0.831683\pi$
$450$	−104514.	+	8660.91i	−0.516119	+	0.0427699i
$451$	60910.2			0.299459
$452$	−50649.0	+	50649.0i	−0.247910	+	0.247910i
$453$	−46873.6	−	46873.6i	−0.228419	−	0.228419i
$454$		−	48382.8i		−	0.234736i
$455$	39544.0	+	85312.6i	0.191011	+	0.412089i
$456$	19069.4			0.0917079
$457$	157632.	−	157632.i	0.754764	−	0.754764i	−0.220600	−	0.975364i	$-0.570802\pi$
$457$	157632.	−	157632.i	0.754764	−	0.754764i	0.975364	+	0.220600i	$0.0708016\pi$
$458$	26221.6	+	26221.6i	0.125005	+	0.125005i
$459$		−	155979.i		−	0.740355i
$460$	98099.2	+	35960.2i	0.463607	+	0.169944i
$461$	309715.			1.45734			0.728669	−	0.684866i	$-0.240139\pi$
$461$	309715.			1.45734			0.728669	+	0.684866i	$0.240139\pi$
$462$	−27578.0	+	27578.0i	−0.129205	+	0.129205i
$463$	48756.8	+	48756.8i	0.227443	+	0.227443i	0.811624	−	0.584181i	$-0.198584\pi$
$463$	48756.8	+	48756.8i	0.227443	+	0.227443i	−0.584181	+	0.811624i	$0.698584\pi$
$464$		−	102451.i		−	0.475862i
$465$	−36331.6	+	99112.3i	−0.168027	+	0.458376i
$466$	155869.			0.717776
$467$	9644.17	−	9644.17i	0.0442213	−	0.0442213i	−0.684650	−	0.728872i	$-0.740045\pi$
$467$	9644.17	−	9644.17i	0.0442213	−	0.0442213i	0.728872	+	0.684650i	$0.240045\pi$
$468$	−15548.3	−	15548.3i	−0.0709891	−	0.0709891i
$469$			212295.i			0.965147i
$470$	−5115.41	+	2371.08i	−0.0231571	+	0.0107337i
$471$	−52471.0			−0.236525
$472$	−16805.5	+	16805.5i	−0.0754341	+	0.0754341i
$473$	−46692.0	−	46692.0i	−0.208699	−	0.208699i
$474$			53980.5i			0.240259i
$475$	86332.5	+	73119.0i	0.382637	+	0.324073i
$476$	−155060.			−0.684364
$477$	−224890.	+	224890.i	−0.988402	+	0.988402i
$478$	−120889.	−	120889.i	−0.529093	−	0.529093i
$479$		−	122729.i		−	0.534904i	−0.963571	−	0.267452i	$-0.913818\pi$
$479$		−	122729.i		−	0.534904i	0.963571	−	0.267452i	$-0.0861816\pi$
$480$	8860.39	+	19115.5i	0.0384565	+	0.0829666i
$481$	−78438.8			−0.339032
$482$	−53038.0	+	53038.0i	−0.228293	+	0.228293i
$483$	139618.	+	139618.i	0.598478	+	0.598478i
$484$		−	10648.0i		−	0.0454545i
$485$	198105.	+	72619.4i	0.842195	+	0.308723i
$486$	172899.			0.732016
$487$	121645.	−	121645.i	0.512903	−	0.512903i	−0.402512	−	0.915415i	$-0.631863\pi$
$487$	121645.	−	121645.i	0.512903	−	0.512903i	0.915415	+	0.402512i	$0.131863\pi$
$488$	35176.8	+	35176.8i	0.147712	+	0.147712i
$489$		−	104664.i		−	0.437702i
$490$	−101961.	+	278149.i	−0.424661	+	1.15847i
$491$	117310.			0.486598			0.243299	−	0.969951i	$-0.421770\pi$
$491$	117310.			0.486598			0.243299	+	0.969951i	$0.421770\pi$
$492$	43970.1	−	43970.1i	0.181647	−	0.181647i
$493$	270254.	+	270254.i	1.11193	+	1.11193i
$494$			23721.2i			0.0972038i
$495$	49091.2	−	22754.7i	0.200352	−	0.0928668i
$496$	−58044.8			−0.235939
$497$	−125300.	+	125300.i	−0.507270	+	0.507270i
$498$	−80023.5	−	80023.5i	−0.322670	−	0.322670i
$499$		−	279864.i		−	1.12395i	−0.827155	−	0.561974i	$-0.810042\pi$
$499$		−	279864.i		−	1.12395i	0.827155	−	0.561974i	$-0.189958\pi$
$500$	−33182.4	+	120515.i	−0.132729	+	0.482061i
$501$	−29545.2			−0.117709
$502$	228525.	−	228525.i	0.906829	−	0.906829i
$503$	140765.	+	140765.i	0.556363	+	0.556363i	0.928270	−	0.371907i	$-0.121296\pi$
$503$	140765.	+	140765.i	0.556363	+	0.556363i	−0.371907	+	0.928270i	$0.621296\pi$
$504$		−	108976.i		−	0.429014i
$505$	40008.5	+	86314.8i	0.156881	+	0.338456i
$506$	−53907.3			−0.210546
$507$	86957.7	−	86957.7i	0.338292	−	0.338292i
$508$	77866.8	+	77866.8i	0.301734	+	0.301734i
$509$			21739.3i			0.0839093i	0.999120	+	0.0419546i	$0.0133585\pi$
$509$			21739.3i			0.0839093i	−0.999120	+	0.0419546i	$0.986642\pi$
$510$	−73796.9	−	27051.7i	−0.283725	−	0.104005i
$511$	−201376.			−0.771197
$512$	−8192.00	+	8192.00i	−0.0312500	+	0.0312500i
$513$	−83622.1	−	83622.1i	−0.317750	−	0.317750i
$514$		−	301540.i		−	1.14135i
$515$	36602.9	−	99852.4i	0.138007	−	0.376482i
$516$	−67412.5			−0.253187
$517$	2056.98	−	2056.98i	0.00769572	−	0.00769572i
$518$	−274885.	−	274885.i	−1.02445	−	1.02445i
$519$		−	256237.i		−	0.951278i
$520$	−23778.6	+	11021.8i	−0.0879386	+	0.0407612i
$521$	313803.			1.15606			0.578031	−	0.816015i	$-0.303821\pi$
$521$	313803.			1.15606			0.578031	+	0.816015i	$0.303821\pi$
$522$	−189934.	+	189934.i	−0.697048	+	0.697048i
$523$	339221.	+	339221.i	1.24017	+	1.24017i	0.959932	+	0.280235i	$0.0904122\pi$
$523$	339221.	+	339221.i	1.24017	+	1.24017i	0.280235	+	0.959932i	$0.409588\pi$
$524$		−	224301.i		−	0.816901i
$525$	−152670.	+	180260.i	−0.553906	+	0.654003i
$526$	−324099.			−1.17140
$527$	153115.	−	153115.i	0.551311	−	0.551311i
$528$	−7686.63	−	7686.63i	−0.0275720	−	0.0275720i
$529$		−	6926.54i		−	0.0247517i
$530$	159419.	+	343932.i	0.567529	+	1.22439i
$531$	62311.4			0.220993
$532$	−83129.8	+	83129.8i	−0.293720	+	0.293720i
$533$	54696.4	+	54696.4i	0.192533	+	0.192533i
$534$			138614.i			0.486098i
$535$	−519699.	−	190506.i	−1.81570	−	0.665581i
$536$	−59171.4			−0.205960
$537$	32528.6	−	32528.6i	0.112802	−	0.112802i
$538$	−193217.	−	193217.i	−0.667546	−	0.667546i
$539$		−	152848.i		−	0.526117i
$540$	44970.2	−	122678.i	0.154219	−	0.420708i
$541$	112228.			0.383449			0.191724	−	0.981449i	$-0.438592\pi$
$541$	112228.			0.383449			0.191724	+	0.981449i	$0.438592\pi$
$542$	−126826.	+	126826.i	−0.431727	+	0.431727i
$543$	−115625.	−	115625.i	−0.392150	−	0.392150i
$544$		−	43218.9i		−	0.146042i
$545$	−452410.	+	209700.i	−1.52314	+	0.706002i
$546$	−49529.2			−0.166141
$547$	265724.	−	265724.i	0.888090	−	0.888090i	−0.106250	−	0.994339i	$-0.533884\pi$
$547$	265724.	−	265724.i	0.888090	−	0.888090i	0.994339	+	0.106250i	$0.0338843\pi$
$548$	−124667.	−	124667.i	−0.415136	−	0.415136i
$549$		−	130428.i		−	0.432740i
$550$	−5326.19	−	64272.9i	−0.0176072	−	0.212472i
$551$	289772.			0.954452
$552$	−38914.8	+	38914.8i	−0.127714	+	0.127714i
$553$	−235319.	−	235319.i	−0.769496	−	0.769496i
$554$			132000.i			0.430085i
$555$	−82867.9	−	178780.i	−0.269030	−	0.580408i
$556$	186539.			0.603421
$557$	42009.1	−	42009.1i	0.135405	−	0.135405i	−0.636156	−	0.771561i	$-0.719476\pi$
$557$	42009.1	−	42009.1i	0.135405	−	0.135405i	0.771561	+	0.636156i	$0.219476\pi$
$558$	107609.	+	107609.i	0.345606	+	0.345606i
$559$		−	83857.4i		−	0.268360i
$560$	−121956.	−	44705.5i	−0.388891	−	0.142556i
$561$	40552.7			0.128853
$562$	96572.8	−	96572.8i	0.305761	−	0.305761i
$563$	−205773.	−	205773.i	−0.649190	−	0.649190i	0.303607	−	0.952797i	$-0.401809\pi$
$563$	−205773.	−	205773.i	−0.649190	−	0.649190i	−0.952797	+	0.303607i	$0.901809\pi$
$564$		−	2969.81i		−	0.00933620i
$565$	77039.7	−	210164.i	0.241333	−	0.658356i
$566$	97891.6			0.305571
$567$	−101246.	+	101246.i	−0.314929	+	0.314929i
$568$	−34924.1	−	34924.1i	−0.108250	−	0.108250i
$569$			218016.i			0.673387i	0.941614	+	0.336693i	$0.109309\pi$
$569$			218016.i			0.673387i	−0.941614	+	0.336693i	$0.890691\pi$
$570$	−54066.2	+	25060.7i	−0.166409	+	0.0771335i
$571$	−54907.8			−0.168408			−0.0842039	−	0.996449i	$-0.526835\pi$
$571$	−54907.8			−0.168408			−0.0842039	+	0.996449i	$0.526835\pi$
$572$	9561.73	−	9561.73i	0.0292243	−	0.0292243i
$573$	−14431.3	−	14431.3i	−0.0439538	−	0.0439538i
$574$			383361.i			1.16355i
$575$	−325392.	+	26964.7i	−0.984173	+	0.0815568i
$576$	30374.3			0.0915505
$577$	−212675.	+	212675.i	−0.638800	+	0.638800i	−0.950260	−	0.311459i	$-0.899182\pi$
$577$	−212675.	+	212675.i	−0.638800	+	0.638800i	0.311459	+	0.950260i	$0.399182\pi$
$578$	−53035.8	−	53035.8i	−0.158750	−	0.158750i
$579$		−	174138.i		−	0.519443i
$580$	134640.	+	290473.i	0.400237	+	0.863476i
$581$	697698.			2.06688
$582$	−78586.2	+	78586.2i	−0.232006	+	0.232006i
$583$	−138300.	−	138300.i	−0.406899	−	0.406899i
$584$		−	56128.1i		−	0.164571i
$585$	64516.5	+	23649.8i	0.188521	+	0.0691060i
$586$	−40269.5			−0.117268
$587$	−381382.	+	381382.i	−1.10684	+	1.10684i	−0.113274	+	0.993564i	$0.536134\pi$
$587$	−381382.	+	381382.i	−1.10684	+	1.10684i	−0.993564	+	0.113274i	$0.963866\pi$
$588$	−110339.	−	110339.i	−0.319134	−	0.319134i
$589$		−	164174.i		−	0.473230i
$590$	25562.0	−	69733.1i	0.0734330	−	0.200325i
$591$	214038.			0.612795
$592$	76616.7	−	76616.7i	0.218615	−	0.218615i
$593$	288518.	+	288518.i	0.820471	+	0.820471i	0.986175	−	0.165705i	$-0.0529899\pi$
$593$	288518.	+	288518.i	0.820471	+	0.820471i	−0.165705	+	0.986175i	$0.552990\pi$
$594$			67414.0i			0.191063i
$595$	439633.	−	203778.i	1.24181	−	0.575603i
$596$	101339.			0.285289
$597$	−192142.	+	192142.i	−0.539105	+	0.539105i
$598$	−48407.9	−	48407.9i	−0.135367	−	0.135367i
$599$		−	82163.0i		−	0.228993i	−0.993424	−	0.114497i	$-0.963475\pi$
$599$		−	82163.0i		−	0.228993i	0.993424	−	0.114497i	$-0.0365255\pi$
$600$	−50242.5	−	42552.7i	−0.139563	−	0.118202i
$601$	−615756.			−1.70475			−0.852373	−	0.522935i	$-0.824837\pi$
$601$	−615756.			−1.70475			−0.852373	+	0.522935i	$0.824837\pi$
$602$	293874.	−	293874.i	0.810901	−	0.810901i
$603$	109698.	+	109698.i	0.301692	+	0.301692i
$604$			113907.i			0.312232i
$605$	13993.4	+	30189.6i	0.0382308	+	0.0824795i
$606$	−50111.0			−0.136455
$607$	−82585.7	+	82585.7i	−0.224144	+	0.224144i	−0.810241	−	0.586097i	$-0.800664\pi$
$607$	−82585.7	+	82585.7i	−0.224144	+	0.224144i	0.586097	+	0.810241i	$0.300664\pi$
$608$	−23170.2	−	23170.2i	−0.0626791	−	0.0626791i
$609$			605036.i			1.63135i
$610$	−145963.	−	53505.6i	−0.392268	−	0.143794i
$611$	3694.27			0.00989570
$612$	−80123.5	+	80123.5i	−0.213923	+	0.213923i
$613$	−292820.	−	292820.i	−0.779256	−	0.779256i	0.200448	−	0.979704i	$-0.435760\pi$
$613$	−292820.	−	292820.i	−0.779256	−	0.779256i	−0.979704	+	0.200448i	$0.935760\pi$
$614$			80655.1i			0.213942i
$615$	−66880.8	+	182450.i	−0.176828	+	0.482386i
$616$	67017.1			0.176614
$617$	−292611.	+	292611.i	−0.768635	+	0.768635i	−0.977866	−	0.209231i	$-0.932904\pi$
$617$	−292611.	+	292611.i	−0.768635	+	0.768635i	0.209231	+	0.977866i	$0.432904\pi$
$618$	39610.3	+	39610.3i	0.103713	+	0.103713i
$619$		−	367533.i		−	0.959213i	−0.877484	−	0.479606i	$-0.840779\pi$
$619$		−	367533.i		−	0.959213i	0.877484	−	0.479606i	$-0.159221\pi$
$620$	164571.	−	76281.5i	0.428123	−	0.198443i
$621$	341295.			0.885006
$622$	−96215.4	+	96215.4i	−0.248693	+	0.248693i
$623$	−604264.	−	604264.i	−1.55686	−	1.55686i
$624$		−	13804.9i		−	0.0354540i
$625$	−64299.4	−	385297.i	−0.164606	−	0.986359i
$626$	−365295.			−0.932169
$627$	21740.8	−	21740.8i	0.0553020	−	0.0553020i
$628$	63754.7	+	63754.7i	0.161656	+	0.161656i
$629$			404211.i			1.02166i
$630$	143215.	+	308974.i	0.360834	+	0.778468i
$631$	165282.			0.415113			0.207557	−	0.978223i	$-0.433449\pi$
$631$	165282.			0.415113			0.207557	+	0.978223i	$0.433449\pi$
$632$	65588.8	−	65588.8i	0.164209	−	0.164209i
$633$	−180214.	−	180214.i	−0.449760	−	0.449760i
$634$		−	183664.i		−	0.456926i
$635$	−323102.	−	118439.i	−0.801294	−	0.293730i
$636$	−199674.			−0.493636
$637$	137255.	−	137255.i	0.338259	−	0.338259i
$638$	−116804.	−	116804.i	−0.286956	−	0.286956i
$639$			129492.i			0.317132i
$640$	12460.4	−	33992.0i	0.0304210	−	0.0829883i
$641$	730293.			1.77738			0.888692	−	0.458505i	$-0.151615\pi$
$641$	730293.			1.77738			0.888692	+	0.458505i	$0.151615\pi$
$642$	206159.	−	206159.i	0.500186	−	0.500186i
$643$	−378424.	−	378424.i	−0.915285	−	0.915285i	0.0813969	−	0.996682i	$-0.474062\pi$
$643$	−378424.	−	378424.i	−0.915285	−	0.915285i	−0.996682	+	0.0813969i	$0.974062\pi$
$644$		−	339285.i		−	0.818076i
$645$	191130.	−	88592.4i	0.459420	−	0.212950i
$646$	122240.			0.292920
$647$	−305253.	+	305253.i	−0.729207	+	0.729207i	−0.970462	−	0.241255i	$-0.922441\pi$
$647$	−305253.	+	305253.i	−0.729207	+	0.729207i	0.241255	+	0.970462i	$0.422441\pi$
$648$	−28219.7	−	28219.7i	−0.0672051	−	0.0672051i
$649$			38319.6i			0.0909770i
$650$	52933.2	−	62498.9i	0.125286	−	0.147926i
$651$	342789.			0.808845
$652$	−127171.	+	127171.i	−0.299154	+	0.299154i
$653$	−151818.	−	151818.i	−0.356038	−	0.356038i	0.506312	−	0.862350i	$-0.331008\pi$
$653$	−151818.	−	151818.i	−0.356038	−	0.356038i	−0.862350	+	0.506312i	$0.831008\pi$
$654$		−	262652.i		−	0.614080i
$655$	294773.	+	635947.i	0.687077	+	1.48231i
$656$	−106852.			−0.248298
$657$	−104056.	+	104056.i	−0.241066	+	0.241066i
$658$	12946.4	+	12946.4i	0.0299017	+	0.0299017i
$659$			397358.i			0.914979i	0.889215	+	0.457490i	$0.151251\pi$
$659$			397358.i			0.914979i	−0.889215	+	0.457490i	$0.848749\pi$
$660$	31895.0	+	11691.8i	0.0732209	+	0.0268406i
$661$	509480.			1.16607			0.583035	−	0.812447i	$-0.301865\pi$
$661$	509480.			1.16607			0.583035	+	0.812447i	$0.301865\pi$
$662$	391395.	−	391395.i	0.893098	−	0.893098i
$663$	36415.7	+	36415.7i	0.0828441	+	0.0828441i
$664$			194465.i			0.441067i
$665$	126445.	−	344940.i	0.285928	−	0.780010i
$666$	−284079.			−0.640458
$667$	−591338.	+	591338.i	−1.32918	+	1.32918i
$668$	35898.8	+	35898.8i	0.0804501	+	0.0804501i
$669$		−	73374.1i		−	0.163942i
$670$	167765.	−	77762.1i	0.373724	−	0.173228i
$671$	80209.3			0.178148
$672$	48378.7	−	48378.7i	0.107131	−	0.107131i
$673$	−83140.6	−	83140.6i	−0.183562	−	0.183562i	0.609344	−	0.792906i	$-0.291433\pi$
$673$	−83140.6	−	83140.6i	−0.183562	−	0.183562i	−0.792906	+	0.609344i	$0.791433\pi$
$674$		−	345168.i		−	0.759819i
$675$	33720.9	+	406921.i	0.0740102	+	0.893105i
$676$	−211315.			−0.462421
$677$	−258103.	+	258103.i	−0.563140	+	0.563140i	−0.930198	−	0.367058i	$-0.880365\pi$
$677$	−258103.	+	258103.i	−0.563140	+	0.563140i	0.367058	+	0.930198i	$0.380365\pi$
$678$	83369.6	+	83369.6i	0.181363	+	0.181363i
$679$		−	685166.i		−	1.48613i
$680$	56797.6	+	122536.i	0.122832	+	0.265000i
$681$	−79639.4			−0.171725
$682$	−66176.3	+	66176.3i	−0.142277	+	0.142277i
$683$	234321.	+	234321.i	0.502308	+	0.502308i	0.912154	−	0.409847i	$-0.134418\pi$
$683$	234321.	+	234321.i	0.502308	+	0.502308i	−0.409847	+	0.912154i	$0.634418\pi$
$684$			85910.4i			0.183626i
$685$	517295.	+	189625.i	1.10245	+	0.404123i
$686$	410692.			0.872706
$687$	43161.5	−	43161.5i	0.0914498	−	0.0914498i
$688$	81909.4	+	81909.4i	0.173044	+	0.173044i
$689$		−	248383.i		−	0.523219i
$690$	59191.4	−	161474.i	0.124326	−	0.339160i
$691$	−231471.			−0.484776			−0.242388	−	0.970179i	$-0.577931\pi$
$691$	−231471.			−0.484776			−0.242388	+	0.970179i	$0.577931\pi$
$692$	−311340.	+	311340.i	−0.650164	+	0.650164i
$693$	−124243.	−	124243.i	−0.258705	−	0.258705i
$694$			498033.i			1.03404i
$695$	−528882.	+	245147.i	−1.09494	+	0.507524i
$696$	−168638.			−0.348126
$697$	281861.	−	281861.i	0.580189	−	0.580189i
$698$	208217.	+	208217.i	0.427372	+	0.427372i
$699$		−	256565.i		−	0.525102i
$700$	404525.	−	33522.4i	0.825562	−	0.0684130i
$701$	218394.			0.444432			0.222216	−	0.974997i	$-0.428671\pi$
$701$	218394.			0.444432			0.222216	+	0.974997i	$0.428671\pi$
$702$	−60536.7	+	60536.7i	−0.122841	+	0.122841i
$703$	216702.	+	216702.i	0.438483	+	0.438483i
$704$			18679.2i			0.0376889i
$705$	3902.87	+	8420.10i	0.00785246	+	0.0169410i
$706$	307754.			0.617440
$707$	218451.	−	218451.i	0.437033	−	0.437033i
$708$	27662.3	+	27662.3i	0.0551852	+	0.0551852i
$709$		−	465461.i		−	0.925958i	−0.886369	−	0.462979i	$-0.846781\pi$
$709$		−	465461.i		−	0.925958i	0.886369	−	0.462979i	$-0.153219\pi$
$710$	144915.	+	53121.3i	0.287472	+	0.105379i
$711$	−243190.			−0.481068
$712$	168422.	−	168422.i	0.332231	−	0.332231i
$713$	335029.	+	335029.i	0.659026	+	0.659026i
$714$			255234.i			0.500659i
$715$	−14543.9	+	39675.6i	−0.0284491	+	0.0776089i
$716$	−79047.6			−0.154192
$717$	−198987.	+	198987.i	−0.387067	+	0.387067i
$718$	−144780.	−	144780.i	−0.280841	−	0.280841i
$719$		−	198562.i		−	0.384095i	−0.981386	−	0.192047i	$-0.938487\pi$
$719$		−	198562.i		−	0.384095i	0.981386	−	0.192047i	$-0.0615127\pi$
$720$	−86118.2	+	39917.4i	−0.166123	+	0.0770011i
$721$	−345349.			−0.664336
$722$	−195108.	+	195108.i	−0.374283	+	0.374283i
$723$	87302.1	+	87302.1i	0.167012	+	0.167012i
$724$			280980.i			0.536041i
$725$	−763470.	−	646618.i	−1.45250	−	1.23019i
$726$	−17526.9			−0.0332531
$727$	−27750.7	+	27750.7i	−0.0525056	+	0.0525056i	−0.732872	−	0.680366i	$-0.761821\pi$
$727$	−27750.7	+	27750.7i	−0.0525056	+	0.0525056i	0.680366	+	0.732872i	$0.261821\pi$
$728$	60180.3	+	60180.3i	0.113551	+	0.113551i
$729$		−	141735.i		−	0.266699i
$730$	73762.6	+	159136.i	0.138417	+	0.298623i
$731$	−432133.			−0.808692
$732$	57901.9	−	57901.9i	0.108061	−	0.108061i
$733$	−217489.	−	217489.i	−0.404789	−	0.404789i	0.475128	−	0.879917i	$-0.342402\pi$
$733$	−217489.	−	217489.i	−0.404789	−	0.404789i	−0.879917	+	0.475128i	$0.842402\pi$
$734$			83893.7i			0.155717i
$735$	457841.	+	167831.i	0.847501	+	0.310668i
$736$	94566.7			0.174575
$737$	−67460.8	+	67460.8i	−0.124198	+	0.124198i
$738$	198092.	+	198092.i	0.363709	+	0.363709i
$739$		−	476409.i		−	0.872350i	−0.899862	−	0.436175i	$-0.856333\pi$
$739$		−	476409.i		−	0.872350i	0.899862	−	0.436175i	$-0.143667\pi$
$740$	−116538.	+	317915.i	−0.212816	+	0.580560i
$741$	39045.8			0.0711112
$742$	870445.	−	870445.i	1.58101	−	1.58101i
$743$	−236181.	−	236181.i	−0.427827	−	0.427827i	0.460061	−	0.887887i	$-0.347828\pi$
$743$	−236181.	−	236181.i	−0.427827	−	0.427827i	−0.887887	+	0.460061i	$0.847828\pi$
$744$			95543.4i			0.172606i
$745$	−287320.	+	133178.i	−0.517671	+	0.239950i
$746$	505690.			0.908671
$747$	360518.	−	360518.i	0.646079	−	0.646079i
$748$	−49273.5	−	49273.5i	−0.0880663	−	0.0880663i
$749$			1.79743e6i			3.20397i
$750$	198371.	+	54619.1i	0.352660	+	0.0971006i
$751$	593025.			1.05146			0.525730	−	0.850651i	$-0.323792\pi$
$751$	593025.			1.05146			0.525730	+	0.850651i	$0.323792\pi$
$752$	−3608.45	+	3608.45i	−0.00638095	+	0.00638095i
$753$	−376158.	−	376158.i	−0.663407	−	0.663407i
$754$		−	209776.i		−	0.368988i
$755$	−149695.	−	322954.i	−0.262611	−	0.566560i
$756$	−424295.			−0.742377
$757$	300574.	−	300574.i	0.524517	−	0.524517i	−0.394415	−	0.918932i	$-0.629053\pi$
$757$	300574.	−	300574.i	0.524517	−	0.524517i	0.918932	+	0.394415i	$0.129053\pi$
$758$	−168516.	−	168516.i	−0.293294	−	0.293294i
$759$			88732.8i			0.154028i
$760$	96142.8	+	35243.0i	0.166452	+	0.0610163i
$761$	730201.			1.26088			0.630439	−	0.776239i	$-0.282875\pi$
$761$	730201.			1.26088			0.630439	+	0.776239i	$0.282875\pi$
$762$	128171.	−	128171.i	0.220739	−	0.220739i
$763$	1.14499e6	+	1.14499e6i	1.96676	+	1.96676i
$764$			35069.4i			0.0600817i
$765$	121872.	−	332466.i	0.208248	−	0.568099i
$766$	312104.			0.531915
$767$	−34410.4	+	34410.4i	−0.0584923	+	0.0584923i
$768$	13484.3	+	13484.3i	0.0228615	+	0.0228615i
$769$			250411.i			0.423448i	0.977330	+	0.211724i	$0.0679078\pi$
$769$			250411.i			0.423448i	−0.977330	+	0.211724i	$0.932092\pi$
$770$	−190009.	+	88072.8i	−0.320474	+	0.148546i
$771$	−496343.			−0.834974
$772$	−211586.	+	211586.i	−0.355020	+	0.355020i
$773$	−113443.	−	113443.i	−0.189853	−	0.189853i	0.605780	−	0.795633i	$-0.292861\pi$
$773$	−113443.	−	113443.i	−0.189853	−	0.189853i	−0.795633	+	0.605780i	$0.792861\pi$
$774$		−	303703.i		−	0.506953i
$775$	−366348.	+	432552.i	−0.609945	+	0.720169i
$776$	190972.			0.317136
$777$	−452468.	+	452468.i	−0.749455	+	0.749455i
$778$	101587.	+	101587.i	0.167834	+	0.167834i
$779$		−	302218.i		−	0.498019i
$780$	18142.2	+	39140.2i	0.0298196	+	0.0643331i
$781$	−79633.2			−0.130555
$782$	−249455.	+	249455.i	−0.407924	+	0.407924i
$783$	739501.	+	739501.i	1.20619	+	1.20619i
$784$			268133.i			0.436233i
$785$	−264545.	−	96974.1i	−0.429299	−	0.157368i
$786$	−369206.			−0.597618
$787$	425730.	−	425730.i	0.687361	−	0.687361i	−0.274287	−	0.961648i	$-0.588442\pi$
$787$	425730.	−	425730.i	0.687361	−	0.687361i	0.961648	+	0.274287i	$0.0884417\pi$
$788$	−260066.	−	260066.i	−0.418823	−	0.418823i
$789$			533477.i			0.856962i
$790$	−99763.9	+	272155.i	−0.159852	+	0.436077i
$791$	−726872.			−1.16173
$792$	34629.4	−	34629.4i	0.0552071	−	0.0552071i
$793$	72026.7	+	72026.7i	0.114537	+	0.114537i
$794$		−	140763.i		−	0.223278i
$795$	566122.	−	262408.i	0.895727	−	0.415186i
$796$	466923.			0.736918
$797$	−38391.8	+	38391.8i	−0.0604396	+	0.0604396i	−0.736681	−	0.676241i	$-0.763608\pi$
$797$	−38391.8	+	38391.8i	−0.0604396	+	0.0604396i	0.676241	+	0.736681i	$0.263608\pi$
$798$	136834.	+	136834.i	0.214876	+	0.214876i
$799$		−	19037.3i		−	0.0298203i
$800$	9343.46	+	112751.i	0.0145992	+	0.176173i
$801$	−624476.			−0.973309
$802$	511498.	−	511498.i	0.795235	−	0.795235i
$803$	−63991.1	−	63991.1i	−0.0992403	−	0.0992403i
$804$			97397.8i			0.150674i
$805$	445883.	+	961953.i	0.688065	+	1.48444i
$806$	−118851.			−0.182949
$807$	−318041.	+	318041.i	−0.488355	+	0.488355i
$808$	60887.3	+	60887.3i	0.0932618	+	0.0932618i
$809$		−	777628.i		−	1.18816i	−0.804406	−	0.594080i	$-0.797516\pi$
$809$		−	777628.i		−	1.18816i	0.804406	−	0.594080i	$-0.202484\pi$
$810$	117095.	+	42923.6i	0.178472	+	0.0654223i
$811$	330668.			0.502748			0.251374	−	0.967890i	$-0.419118\pi$
$811$	330668.			0.502748			0.251374	+	0.967890i	$0.419118\pi$
$812$	735147.	−	735147.i	1.11497	−	1.11497i
$813$	208759.	+	208759.i	0.315838	+	0.315838i
$814$		−	174700.i		−	0.263660i
$815$	193434.	−	527687.i	0.291218	−	0.794440i
$816$	−71139.6			−0.106839
$817$	−231672.	+	231672.i	−0.347080	+	0.347080i
$818$	−155271.	−	155271.i	−0.232051	−	0.232051i
$819$		−	223136.i		−	0.332662i
$820$	302949.	−	140422.i	0.450549	−	0.208838i
$821$	277852.			0.412218			0.206109	−	0.978529i	$-0.433920\pi$
$821$	277852.			0.412218			0.206109	+	0.978529i	$0.433920\pi$
$822$	−205205.	+	205205.i	−0.303700	+	0.303700i
$823$	512130.	+	512130.i	0.756103	+	0.756103i	0.975611	−	0.219508i	$-0.0704452\pi$
$823$	512130.	+	512130.i	0.756103	+	0.756103i	−0.219508	+	0.975611i	$0.570445\pi$
$824$		−	96256.8i		−	0.141768i
$825$	−105795.	+	8767.05i	−0.155438	+	0.0128809i
$826$	−241179.			−0.353491
$827$	−644659.	+	644659.i	−0.942582	+	0.942582i	−0.998439	−	0.0558565i	$-0.982211\pi$
$827$	−644659.	+	644659.i	−0.942582	+	0.942582i	0.0558565	+	0.998439i	$0.482211\pi$
$828$	−175317.	−	175317.i	−0.255719	−	0.255719i
$829$		−	790.834i		−	0.00115074i	−1.00000		0.000575369i	$-0.999817\pi$
$829$		−	790.834i		−	0.00115074i	1.00000		0.000575369i	$-0.000183146\pi$
$830$	−255562.	−	551353.i	−0.370971	−	0.800338i
$831$	217276.			0.314637
$832$	−16773.7	+	16773.7i	−0.0242315	+	0.0242315i
$833$	−707302.	−	707302.i	−1.01933	−	1.01933i
$834$		−	307049.i		−	0.441443i
$835$	−148959.	−	54603.8i	−0.213645	−	0.0783159i
$836$	−52832.2			−0.0755938
$837$	418972.	−	418972.i	0.598045	−	0.598045i
$838$	−595500.	−	595500.i	−0.847996	−	0.847996i
$839$			925136.i			1.31426i	0.753777	+	0.657130i	$0.228230\pi$
$839$			925136.i			1.31426i	−0.753777	+	0.657130i	$0.771770\pi$
$840$	−73586.4	+	200743.i	−0.104289	+	0.284500i
$841$	−1.85528e6			−2.62312
$842$	−434331.	+	434331.i	−0.612628	+	0.612628i
$843$	−158962.	−	158962.i	−0.223685	−	0.223685i
$844$			437937.i			0.614789i
$845$	599129.	−	277707.i	0.839086	−	0.388932i
$846$	13379.4			0.0186938
$847$	76405.6	−	76405.6i	0.106502	−	0.106502i
$848$	242613.	+	242613.i	0.337382	+	0.337382i
$849$		−	161132.i		−	0.223546i
$850$	−322069.	−	272775.i	−0.445770	−	0.377543i
$851$	−884447.			−1.22127
$852$	−57486.0	+	57486.0i	−0.0791923	+	0.0791923i
$853$	107179.	+	107179.i	0.147303	+	0.147303i	0.776912	−	0.629609i	$-0.216785\pi$
$853$	107179.	+	107179.i	0.147303	+	0.147303i	−0.629609	+	0.776912i	$0.716785\pi$
$854$			504827.i			0.692193i
$855$	−112902.	−	243576.i	−0.154443	−	0.333198i
$856$	−500985.			−0.683718
$857$	85320.0	−	85320.0i	0.116169	−	0.116169i	−0.646633	−	0.762801i	$-0.723823\pi$
$857$	85320.0	−	85320.0i	0.116169	−	0.116169i	0.762801	+	0.646633i	$0.223823\pi$
$858$	−15738.9	−	15738.9i	−0.0213796	−	0.0213796i
$859$		−	1.21206e6i		−	1.64262i	−0.570485	−	0.821308i	$-0.693245\pi$
$859$		−	1.21206e6i		−	1.64262i	0.570485	−	0.821308i	$-0.306755\pi$
$860$	−339876.	−	124588.i	−0.459540	−	0.168454i
$861$	631023.			0.851214
$862$	−165904.	+	165904.i	−0.223277	+	0.223277i
$863$	1.00528e6	+	1.00528e6i	1.34979	+	1.34979i	0.885887	+	0.463901i	$0.153551\pi$
$863$	1.00528e6	+	1.00528e6i	1.34979	+	1.34979i	0.463901	+	0.885887i	$0.346449\pi$
$864$		−	118261.i		−	0.158421i
$865$	473564.	−	1.29188e6i	0.632917	−	1.72659i
$866$	577982.			0.770688
$867$	−87298.4	+	87298.4i	−0.116136	+	0.116136i
$868$	−416505.	−	416505.i	−0.552816	−	0.552816i
$869$		−	149554.i		−	0.198043i
$870$	478127.	−	221621.i	0.631691	−	0.292800i
$871$	−121157.			−0.159703
$872$	−319134.	+	319134.i	−0.419701	+	0.419701i
$873$	−354042.	−	354042.i	−0.464544	−	0.464544i
$874$			267472.i			0.350151i
$875$	−1.10287e6	+	626664.i	−1.44048	+	0.818500i
$876$	−92388.4			−0.120395
$877$	−185547.	+	185547.i	−0.241243	+	0.241243i	−0.817364	−	0.576121i	$-0.804566\pi$
$877$	−185547.	+	185547.i	−0.241243	+	0.241243i	0.576121	+	0.817364i	$0.304566\pi$
$878$	593876.	+	593876.i	0.770383	+	0.770383i
$879$			66284.7i			0.0857898i
$880$	−24547.9	−	52960.0i	−0.0316993	−	0.0683884i
$881$	−838842.			−1.08076			−0.540379	−	0.841422i	$-0.681719\pi$
$881$	−838842.			−1.08076			−0.540379	+	0.841422i	$0.681719\pi$
$882$	497092.	−	497092.i	0.638998	−	0.638998i
$883$	−853023.	−	853023.i	−1.09406	−	1.09406i	−0.995091	−	0.0989647i	$-0.968447\pi$
$883$	−853023.	−	853023.i	−1.09406	−	1.09406i	−0.0989647	−	0.995091i	$-0.531553\pi$
$884$		−	88493.6i		−	0.113242i
$885$	−114783.	−	42075.8i	−0.146551	−	0.0537212i
$886$	−788600.			−1.00459
$887$	1.00870e6	−	1.00870e6i	1.28208	−	1.28208i	0.342603	−	0.939480i	$-0.388691\pi$
$887$	1.00870e6	−	1.00870e6i	1.28208	−	1.28208i	0.939480	−	0.342603i	$-0.111309\pi$
$888$	−126113.	−	126113.i	−0.159932	−	0.159932i
$889$			1.11748e6i			1.41396i
$890$	−256179.	+	698854.i	−0.323417	+	0.882280i
$891$	−64346.0			−0.0810524
$892$	−89153.0	+	89153.0i	−0.112049	+	0.112049i
$893$	−10206.1	−	10206.1i	−0.0127985	−	0.0127985i
$894$		−	166807.i		−	0.208708i
$895$	224118.	−	103883.i	0.279789	−	0.129688i
$896$	−117565.			−0.146440
$897$	−79680.7	+	79680.7i	−0.0990303	+	0.0990303i
$898$	−406817.	−	406817.i	−0.504483	−	0.504483i
$899$			1.45185e6i			1.79639i
$900$	191706.	−	226350.i	0.236675	−	0.279444i
$901$	−1.27997e6			−1.57670
$902$	−121820.	+	121820.i	−0.149729	+	0.149729i
$903$	−483724.	−	483724.i	−0.593229	−	0.593229i
$904$		−	202596.i		−	0.247910i
$905$	−369259.	−	796643.i	−0.450852	−	0.972673i
$906$	187494.			0.228419
$907$	469619.	−	469619.i	0.570861	−	0.570861i	−0.361508	−	0.932369i	$-0.617738\pi$
$907$	469619.	−	469619.i	0.570861	−	0.570861i	0.932369	+	0.361508i	$0.117738\pi$
$908$	96765.6	+	96765.6i	0.117368	+	0.117368i
$909$		−	225758.i		−	0.273221i
$910$	−249713.	−	91537.3i	−0.301550	−	0.110539i
$911$	117127.			0.141130			0.0705652	−	0.997507i	$-0.477520\pi$
$911$	117127.			0.141130			0.0705652	+	0.997507i	$0.477520\pi$
$912$	−38138.8	+	38138.8i	−0.0458540	+	0.0458540i
$913$	221707.	+	221707.i	0.265973	+	0.265973i
$914$			630527.i			0.754764i
$915$	−88071.7	+	240259.i	−0.105195	+	0.286971i
$916$	−104886.			−0.125005
$917$	1.60949e6	−	1.60949e6i	1.91404	−	1.91404i
$918$	311958.	+	311958.i	0.370178	+	0.370178i
$919$			473921.i			0.561145i	0.959833	+	0.280572i	$0.0905243\pi$
$919$			473921.i			0.561145i	−0.959833	+	0.280572i	$0.909476\pi$
$920$	−268119.	+	124278.i	−0.316775	+	0.146831i
$921$	132761.			0.156513
$922$	−619430.	+	619430.i	−0.728669	+	0.728669i
$923$	−71509.4	−	71509.4i	−0.0839382	−	0.0839382i
$924$		−	110312.i		−	0.129205i
$925$	−87385.9	−	1.05451e6i	−0.102131	−	1.23245i
$926$	−195027.			−0.227443
$927$	−178450.	+	178450.i	−0.207662	+	0.207662i
$928$	204903.	+	204903.i	0.237931	+	0.237931i
$929$		−	1.07076e6i		−	1.24068i	−0.784333	−	0.620340i	$-0.786995\pi$
$929$		−	1.07076e6i		−	1.24068i	0.784333	−	0.620340i	$-0.213005\pi$
$930$	−125561.	−	270888.i	−0.145175	−	0.313201i
$931$	−758386.			−0.874966
$932$	−311739.	+	311739.i	−0.358888	+	0.358888i
$933$	158373.	+	158373.i	0.181936	+	0.181936i
$934$			38576.7i			0.0442213i
$935$	204456.	+	74947.4i	0.233871	+	0.0857302i
$936$	62193.3			0.0709891
$937$	−250154.	+	250154.i	−0.284923	+	0.284923i	−0.835069	−	0.550146i	$-0.814572\pi$
$937$	−250154.	+	250154.i	−0.284923	+	0.284923i	0.550146	+	0.835069i	$0.314572\pi$
$938$	−424589.	−	424589.i	−0.482573	−	0.482573i
$939$			601285.i			0.681945i
$940$	5488.64	−	14973.0i	0.00621168	−	0.0169454i
$941$	976779.			1.10311			0.551553	−	0.834140i	$-0.314036\pi$
$941$	976779.			1.10311			0.551553	+	0.834140i	$0.314036\pi$
$942$	104942.	−	104942.i	0.118263	−	0.118263i
$943$	616736.	+	616736.i	0.693547	+	0.693547i
$944$		−	67222.0i		−	0.0754341i
$945$	1.20298e6	−	557602.i	1.34708	−	0.624396i
$946$	186768.			0.208699
$947$	676016.	−	676016.i	0.753802	−	0.753802i	−0.221385	−	0.975187i	$-0.571058\pi$
$947$	676016.	−	676016.i	0.753802	−	0.753802i	0.975187	+	0.221385i	$0.0710576\pi$
$948$	−107961.	−	107961.i	−0.120130	−	0.120130i
$949$		−	114926.i		−	0.127610i
$950$	−318903.	+	26427.0i	−0.353355	+	0.0292820i
$951$	−302316.			−0.334272
$952$	310121.	−	310121.i	0.342182	−	0.342182i
$953$	−68685.5	−	68685.5i	−0.0756275	−	0.0756275i	0.668281	−	0.743909i	$-0.267030\pi$
$953$	−68685.5	−	68685.5i	−0.0756275	−	0.0756275i	−0.743909	+	0.668281i	$0.767030\pi$
$954$		−	899560.i		−	0.988402i
$955$	−46087.7	−	99430.0i	−0.0505333	−	0.109021i
$956$	483557.			0.529093
$957$	−192262.	+	192262.i	−0.209928	+	0.209928i
$958$	245458.	+	245458.i	0.267452	+	0.267452i
$959$		−	1.78911e6i		−	1.94536i
$960$	−55951.8	−	20510.2i	−0.0607116	−	0.0222550i
$961$	−100962.			−0.109323
$962$	156878.	−	156878.i	0.169516	−	0.169516i
$963$	928776.	+	928776.i	1.00152	+	1.00152i
$964$		−	212152.i		−	0.228293i
$965$	321833.	−	877960.i	0.345602	−	0.942801i
$966$	−558473.			−0.598478
$967$	359957.	−	359957.i	0.384945	−	0.384945i	−0.487935	−	0.872880i	$-0.662250\pi$
$967$	359957.	−	359957.i	0.384945	−	0.384945i	0.872880	+	0.487935i	$0.162250\pi$
$968$	21296.0	+	21296.0i	0.0227273	+	0.0227273i
$969$		−	201211.i		−	0.214291i
$970$	−541449.	+	250972.i	−0.575459	+	0.266736i
$971$	768941.			0.815557			0.407779	−	0.913081i	$-0.366304\pi$
$971$	768941.			0.815557			0.407779	+	0.913081i	$0.366304\pi$
$972$	−345798.	+	345798.i	−0.366008	+	0.366008i
$973$	1.33853e6	+	1.33853e6i	1.41384	+	1.41384i
$974$			486579.i			0.512903i
$975$	−102875.	−	87129.5i	−0.108218	−	0.0916550i
$976$	−140707.			−0.147712
$977$	766231.	−	766231.i	0.802732	−	0.802732i	−0.180790	−	0.983522i	$-0.557865\pi$
$977$	766231.	−	766231.i	0.802732	−	0.802732i	0.983522	+	0.180790i	$0.0578654\pi$
$978$	209328.	+	209328.i	0.218851	+	0.218851i
$979$		−	384033.i		−	0.400685i
$980$	−352376.	−	760221.i	−0.366906	−	0.791567i
$981$	1.18328e6			1.22956
$982$	−234619.	+	234619.i	−0.243299	+	0.243299i
$983$	194107.	+	194107.i	0.200879	+	0.200879i	0.800377	−	0.599497i	$-0.204633\pi$
$983$	194107.	+	194107.i	0.200879	+	0.200879i	−0.599497	+	0.800377i	$0.704633\pi$
$984$			175881.i			0.181647i
$985$	1.07912e6	+	395573.i	1.11224	+	0.407713i
$986$	−1.08101e6			−1.11193
$987$	21310.1	−	21310.1i	0.0218751	−	0.0218751i
$988$	−47442.5	−	47442.5i	−0.0486019	−	0.0486019i
$989$		−	945544.i		−	0.966695i
$990$	−52673.1	+	143692.i	−0.0537425	+	0.146609i
$991$	571942.			0.582377			0.291189	−	0.956666i	$-0.405949\pi$
$991$	571942.			0.582377			0.291189	+	0.956666i	$0.405949\pi$
$992$	116090.	−	116090.i	0.117970	−	0.117970i
$993$	−644247.	−	644247.i	−0.653362	−	0.653362i
$994$		−	501201.i		−	0.507270i
$995$	−1.32384e6	+	613622.i	−1.33717	+	0.619805i
$996$	320094.			0.322670
$997$	−1.17237e6	+	1.17237e6i	−1.17943	+	1.17943i	−0.199542	+	0.979889i	$0.563945\pi$
$997$	−1.17237e6	+	1.17237e6i	−1.17943	+	1.17943i	−0.979889	+	0.199542i	$0.936055\pi$
$998$	559728.	+	559728.i	0.561974	+	0.561974i
$999$			1.10605e6i			1.10827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.5.e.a.23.8	✓	20
5.2	odd	4	inner	110.5.e.a.67.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.5.e.a.23.8	✓	20	1.1	even	1	trivial
110.5.e.a.67.8	yes	20	5.2	odd	4	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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	110.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 2.00000i) q^{2} +(3.29205 + 3.29205i) q^{3} -8.00000i q^{4} +(10.5135 + 22.6819i) q^{5} -13.1682 q^{6} +(57.4046 - 57.4046i) q^{7} +(16.0000 + 16.0000i) q^{8} -59.3248i q^{9} +(-66.3907 - 24.3368i) q^{10} +36.4829 q^{11} +(26.3364 - 26.3364i) q^{12} +(32.7610 + 32.7610i) q^{13} +229.619i q^{14} +(-40.0590 + 109.281i) q^{15} -64.0000 q^{16} +(168.824 - 168.824i) q^{17} +(118.650 + 118.650i) q^{18} -181.017i q^{19} +(181.455 - 84.1077i) q^{20} +377.958 q^{21} +(-72.9657 + 72.9657i) q^{22} +(369.401 + 369.401i) q^{23} +105.346i q^{24} +(-403.934 + 476.930i) q^{25} -131.044 q^{26} +(461.957 - 461.957i) q^{27} +(-459.237 - 459.237i) q^{28} +1600.80i q^{29} +(-138.444 - 298.680i) q^{30} +906.950 q^{31} +(128.000 - 128.000i) q^{32} +(120.104 + 120.104i) q^{33} +675.296i q^{34} +(1905.57 + 698.523i) q^{35} -474.598 q^{36} +(-1197.14 + 1197.14i) q^{37} +(362.034 + 362.034i) q^{38} +215.702i q^{39} +(-194.694 + 531.125i) q^{40} +1669.56 q^{41} +(-755.917 + 755.917i) q^{42} +(-1279.83 - 1279.83i) q^{43} -291.863i q^{44} +(1345.60 - 623.709i) q^{45} -1477.60 q^{46} +(56.3821 - 56.3821i) q^{47} +(-210.691 - 210.691i) q^{48} -4189.58i q^{49} +(-145.992 - 1761.73i) q^{50} +1111.56 q^{51} +(262.088 - 262.088i) q^{52} +(-3790.83 - 3790.83i) q^{53} +1847.83i q^{54} +(383.561 + 827.500i) q^{55} +1836.95 q^{56} +(595.918 - 595.918i) q^{57} +(-3201.60 - 3201.60i) q^{58} +1050.34i q^{59} +(874.247 + 320.472i) q^{60} +2198.55 q^{61} +(-1813.90 + 1813.90i) q^{62} +(-3405.52 - 3405.52i) q^{63} +512.000i q^{64} +(-398.650 + 1087.51i) q^{65} -480.414 q^{66} +(-1849.11 + 1849.11i) q^{67} +(-1350.59 - 1350.59i) q^{68} +2432.18i q^{69} +(-5208.18 + 2414.09i) q^{70} -2182.76 q^{71} +(949.196 - 949.196i) q^{72} +(-1754.00 - 1754.00i) q^{73} -4788.54i q^{74} +(-2899.85 + 240.306i) q^{75} -1448.14 q^{76} +(2094.29 - 2094.29i) q^{77} +(-431.404 - 431.404i) q^{78} -4099.30i q^{79} +(-672.862 - 1451.64i) q^{80} -1763.73 q^{81} +(-3339.11 + 3339.11i) q^{82} +(6077.02 + 6077.02i) q^{83} -3023.67i q^{84} +(5604.17 + 2054.32i) q^{85} +5119.34 q^{86} +(-5269.93 + 5269.93i) q^{87} +(583.726 + 583.726i) q^{88} -10526.4i q^{89} +(-1443.78 + 3938.61i) q^{90} +3761.27 q^{91} +(2955.21 - 2955.21i) q^{92} +(2985.73 + 2985.73i) q^{93} +225.528i q^{94} +(4105.81 - 1903.12i) q^{95} +842.766 q^{96} +(5967.87 - 5967.87i) q^{97} +(8379.17 + 8379.17i) q^{98} -2164.34i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 40 q^{2} - 26 q^{3} + 8 q^{5} + 104 q^{6} - 48 q^{7} + 320 q^{8} - 132 q^{10} - 208 q^{12} + 20 q^{13} + 700 q^{15} - 1280 q^{16} + 1080 q^{17} - 376 q^{18} + 464 q^{20} - 1536 q^{21} - 1998 q^{23}+ \cdots + 16776 q^{98}+O(q^{100}) \) 20 * q - 40 * q^2 - 26 * q^3 + 8 * q^5 + 104 * q^6 - 48 * q^7 + 320 * q^8 - 132 * q^10 - 208 * q^12 + 20 * q^13 + 700 * q^15 - 1280 * q^16 + 1080 * q^17 - 376 * q^18 + 464 * q^20 - 1536 * q^21 - 1998 * q^23 + 1242 * q^25 - 80 * q^26 + 1558 * q^27 + 384 * q^28 - 2284 * q^30 - 1256 * q^31 + 2560 * q^32 + 1210 * q^33 + 3636 * q^35 + 1504 * q^36 - 286 * q^37 + 736 * q^38 - 800 * q^40 - 5112 * q^41 + 3072 * q^42 - 3048 * q^43 - 3274 * q^45 + 7992 * q^46 + 6636 * q^47 + 1664 * q^48 - 260 * q^50 - 2384 * q^51 + 160 * q^52 - 4212 * q^53 - 726 * q^55 - 1536 * q^56 - 21984 * q^57 - 8528 * q^58 + 3536 * q^60 + 8456 * q^61 + 2512 * q^62 - 5788 * q^63 + 13640 * q^65 - 4840 * q^66 + 8870 * q^67 - 8640 * q^68 - 6776 * q^70 - 14396 * q^71 - 3008 * q^72 + 23020 * q^73 + 6204 * q^75 - 2944 * q^76 - 2048 * q^78 - 512 * q^80 - 808 * q^81 + 10224 * q^82 + 20288 * q^83 - 1332 * q^85 + 12192 * q^86 - 1904 * q^87 - 12352 * q^90 - 27072 * q^91 - 15984 * q^92 + 13386 * q^93 + 21916 * q^95 - 6656 * q^96 + 6754 * q^97 + 16776 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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