LMFDB - Embedded newform 70.5.f.a.43.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [70,5,Mod(43,70)] 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("70.43"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(70, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 0])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	70.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,-24] 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:	$7.23589741587$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 334x^{10} + 34233x^{8} + 1144512x^{6} + 13607616x^{4} + 38549504x^{2} + 31360000 $ x^12 + 334x^10 + 34233x^8 + 1144512x^6 + 13607616x^4 + 38549504*x^2 + 31360000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5^{2}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.3
Root			$-1.27116i$ of defining polynomial
Character	$\chi$	$=$	70.43
Dual form			70.5.f.a.57.3

$q$-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} +(-6.14353 - 6.14353i) q^{3} -8.00000i q^{4} +(22.5891 + 10.7113i) q^{5} +24.5741 q^{6} +(-13.0958 + 13.0958i) q^{7} +(16.0000 + 16.0000i) q^{8} -5.51396i q^{9} +(-66.6008 + 23.7557i) q^{10} -107.742 q^{11} +(-49.1483 + 49.1483i) q^{12} +(-156.484 - 156.484i) q^{13} -52.3832i q^{14} +(-72.9719 - 204.582i) q^{15} -64.0000 q^{16} +(-345.450 + 345.450i) q^{17} +(11.0279 + 11.0279i) q^{18} -553.780i q^{19} +(85.6903 - 180.713i) q^{20} +160.909 q^{21} +(215.483 - 215.483i) q^{22} +(-313.375 - 313.375i) q^{23} -196.593i q^{24} +(395.537 + 483.917i) q^{25} +625.937 q^{26} +(-531.502 + 531.502i) q^{27} +(104.766 + 104.766i) q^{28} -154.098i q^{29} +(555.108 + 263.221i) q^{30} -1056.04 q^{31} +(128.000 - 128.000i) q^{32} +(661.915 + 661.915i) q^{33} -1381.80i q^{34} +(-436.096 + 155.550i) q^{35} -44.1117 q^{36} +(-1009.72 + 1009.72i) q^{37} +(1107.56 + 1107.56i) q^{38} +1922.73i q^{39} +(190.045 + 532.807i) q^{40} +2590.16 q^{41} +(-321.818 + 321.818i) q^{42} +(-826.179 - 826.179i) q^{43} +861.934i q^{44} +(59.0617 - 124.556i) q^{45} +1253.50 q^{46} +(1700.19 - 1700.19i) q^{47} +(393.186 + 393.186i) q^{48} -343.000i q^{49} +(-1758.91 - 176.761i) q^{50} +4244.57 q^{51} +(-1251.87 + 1251.87i) q^{52} +(770.758 + 770.758i) q^{53} -2126.01i q^{54} +(-2433.79 - 1154.05i) q^{55} -419.066 q^{56} +(-3402.17 + 3402.17i) q^{57} +(308.197 + 308.197i) q^{58} -5567.45i q^{59} +(-1636.66 + 583.775i) q^{60} +3899.53 q^{61} +(2112.09 - 2112.09i) q^{62} +(72.2098 + 72.2098i) q^{63} +512.000i q^{64} +(-1858.69 - 5210.99i) q^{65} -2647.66 q^{66} +(-3509.44 + 3509.44i) q^{67} +(2763.60 + 2763.60i) q^{68} +3850.46i q^{69} +(561.092 - 1183.29i) q^{70} -3076.44 q^{71} +(88.2234 - 88.2234i) q^{72} +(-2473.70 - 2473.70i) q^{73} -4038.87i q^{74} +(542.969 - 5402.95i) q^{75} -4430.24 q^{76} +(1410.96 - 1410.96i) q^{77} +(-3845.46 - 3845.46i) q^{78} +4246.96i q^{79} +(-1445.70 - 685.522i) q^{80} +6083.97 q^{81} +(-5180.32 + 5180.32i) q^{82} +(572.593 + 572.593i) q^{83} -1287.27i q^{84} +(-11503.6 + 4103.20i) q^{85} +3304.72 q^{86} +(-946.709 + 946.709i) q^{87} +(-1723.87 - 1723.87i) q^{88} +3337.76i q^{89} +(130.988 + 367.235i) q^{90} +4098.57 q^{91} +(-2507.00 + 2507.00i) q^{92} +(6487.83 + 6487.83i) q^{93} +6800.75i q^{94} +(5931.70 - 12509.4i) q^{95} -1572.74 q^{96} +(6884.42 - 6884.42i) q^{97} +(686.000 + 686.000i) q^{98} +594.084i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{2} - 20 q^{3} + 8 q^{5} + 80 q^{6} + 192 q^{8} - 144 q^{10} + 4 q^{11} - 160 q^{12} - 180 q^{13} - 736 q^{15} - 768 q^{16} - 236 q^{17} - 464 q^{18} + 512 q^{20} - 196 q^{21} - 8 q^{22} - 1232 q^{23}+ \cdots + 8232 q^{98}+O(q^{100}) $ 12 * q - 24 * q^2 - 20 * q^3 + 8 * q^5 + 80 * q^6 + 192 * q^8 - 144 * q^10 + 4 * q^11 - 160 * q^12 - 180 * q^13 - 736 * q^15 - 768 * q^16 - 236 * q^17 - 464 * q^18 + 512 * q^20 - 196 * q^21 - 8 * q^22 - 1232 * q^23 + 944 * q^25 + 720 * q^26 - 908 * q^27 - 632 * q^30 - 992 * q^31 + 1536 * q^32 + 6268 * q^33 - 784 * q^35 + 1856 * q^36 + 2200 * q^37 - 2880 * q^38 - 896 * q^40 + 176 * q^41 + 392 * q^42 + 1436 * q^43 + 3436 * q^45 + 4928 * q^46 + 5708 * q^47 + 1280 * q^48 - 1352 * q^50 + 6028 * q^51 - 1440 * q^52 - 9868 * q^53 - 7036 * q^55 - 5676 * q^57 - 4376 * q^58 + 8416 * q^60 - 1512 * q^61 + 1984 * q^62 - 3920 * q^63 + 7888 * q^65 - 25072 * q^66 - 11340 * q^67 + 1888 * q^68 + 4312 * q^70 - 14544 * q^71 - 3712 * q^72 + 24744 * q^73 - 6468 * q^75 + 11520 * q^76 - 9016 * q^77 + 10152 * q^78 - 512 * q^80 + 15740 * q^81 - 352 * q^82 - 30368 * q^83 - 27972 * q^85 - 5744 * q^86 + 2084 * q^87 + 64 * q^88 - 5168 * q^90 + 11172 * q^91 - 9856 * q^92 + 34508 * q^93 + 30436 * q^95 - 5120 * q^96 + 56180 * q^97 + 8232 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−2.00000	+	2.00000i	−0.500000	+	0.500000i
$2$	−2.00000	+	2.00000i	−0.500000	+	0.500000i
$3$	−6.14353	−	6.14353i	−0.682615	−	0.682615i	0.277974	−	0.960589i	$-0.410337\pi$
$3$	−6.14353	−	6.14353i	−0.682615	−	0.682615i	−0.960589	+	0.277974i	$0.910337\pi$
$4$		−	8.00000i		−	0.500000i
$5$	22.5891	+	10.7113i	0.903565	+	0.428452i
$5$	22.5891	+	10.7113i	0.903565	+	0.428452i
$6$	24.5741			0.682615
$7$	−13.0958	+	13.0958i	−0.267261	+	0.267261i
$7$	−13.0958	+	13.0958i	−0.267261	+	0.267261i
$8$	16.0000	+	16.0000i	0.250000	+	0.250000i
$9$		−	5.51396i		−	0.0680736i
$10$	−66.6008	+	23.7557i	−0.666008	+	0.237557i
$11$	−107.742			−0.890427			−0.445214	−	0.895424i	$-0.646872\pi$
$11$	−107.742			−0.890427			−0.445214	+	0.895424i	$0.646872\pi$
$12$	−49.1483	+	49.1483i	−0.341307	+	0.341307i
$13$	−156.484	−	156.484i	−0.925942	−	0.925942i	0.0714989	−	0.997441i	$-0.477222\pi$
$13$	−156.484	−	156.484i	−0.925942	−	0.925942i	−0.997441	+	0.0714989i	$0.977222\pi$
$14$		−	52.3832i		−	0.267261i
$15$	−72.9719	−	204.582i	−0.324319	−	0.909254i
$16$	−64.0000			−0.250000
$17$	−345.450	+	345.450i	−1.19533	+	1.19533i	−0.219781	+	0.975549i	$0.570534\pi$
$17$	−345.450	+	345.450i	−1.19533	+	1.19533i	−0.975549	+	0.219781i	$0.929466\pi$
$18$	11.0279	+	11.0279i	0.0340368	+	0.0340368i
$19$		−	553.780i		−	1.53402i	−0.641637	−	0.767009i	$-0.721744\pi$
$19$		−	553.780i		−	1.53402i	0.641637	−	0.767009i	$-0.278256\pi$
$20$	85.6903	−	180.713i	0.214226	−	0.451782i
$21$	160.909			0.364873
$22$	215.483	−	215.483i	0.445214	−	0.445214i
$23$	−313.375	−	313.375i	−0.592391	−	0.592391i	0.345886	−	0.938277i	$-0.387579\pi$
$23$	−313.375	−	313.375i	−0.592391	−	0.592391i	−0.938277	+	0.345886i	$0.887579\pi$
$24$		−	196.593i		−	0.341307i
$25$	395.537	+	483.917i	0.632859	+	0.774267i
$26$	625.937			0.925942
$27$	−531.502	+	531.502i	−0.729083	+	0.729083i
$28$	104.766	+	104.766i	0.133631	+	0.133631i
$29$		−	154.098i		−	0.183232i	−0.995794	−	0.0916162i	$-0.970797\pi$
$29$		−	154.098i		−	0.183232i	0.995794	−	0.0916162i	$-0.0292033\pi$
$30$	555.108	+	263.221i	0.616787	+	0.292467i
$31$	−1056.04			−1.09890			−0.549450	−	0.835527i	$-0.685163\pi$
$31$	−1056.04			−1.09890			−0.549450	+	0.835527i	$0.685163\pi$
$32$	128.000	−	128.000i	0.125000	−	0.125000i
$33$	661.915	+	661.915i	0.607819	+	0.607819i
$34$		−	1381.80i		−	1.19533i
$35$	−436.096	+	155.550i	−0.355996	+	0.126979i
$36$	−44.1117			−0.0340368
$37$	−1009.72	+	1009.72i	−0.737559	+	0.737559i	−0.972105	−	0.234546i	$-0.924640\pi$
$37$	−1009.72	+	1009.72i	−0.737559	+	0.737559i	0.234546	+	0.972105i	$0.424640\pi$
$38$	1107.56	+	1107.56i	0.767009	+	0.767009i
$39$			1922.73i			1.26412i
$40$	190.045	+	532.807i	0.118778	+	0.333004i
$41$	2590.16			1.54084			0.770422	−	0.637534i	$-0.220045\pi$
$41$	2590.16			1.54084			0.770422	+	0.637534i	$0.220045\pi$
$42$	−321.818	+	321.818i	−0.182437	+	0.182437i
$43$	−826.179	−	826.179i	−0.446825	−	0.446825i	0.447473	−	0.894298i	$-0.352324\pi$
$43$	−826.179	−	826.179i	−0.446825	−	0.446825i	−0.894298	+	0.447473i	$0.852324\pi$
$44$			861.934i			0.445214i
$45$	59.0617	−	124.556i	0.0291663	−	0.0615089i
$46$	1253.50			0.592391
$47$	1700.19	−	1700.19i	0.769664	−	0.769664i	−0.208383	−	0.978047i	$-0.566820\pi$
$47$	1700.19	−	1700.19i	0.769664	−	0.769664i	0.978047	+	0.208383i	$0.0668201\pi$
$48$	393.186	+	393.186i	0.170654	+	0.170654i
$49$		−	343.000i		−	0.142857i
$50$	−1758.91	−	176.761i	−0.703563	−	0.0707044i
$51$	4244.57			1.63190
$52$	−1251.87	+	1251.87i	−0.462971	+	0.462971i
$53$	770.758	+	770.758i	0.274389	+	0.274389i	0.830864	−	0.556475i	$-0.187847\pi$
$53$	770.758	+	770.758i	0.274389	+	0.274389i	−0.556475	+	0.830864i	$0.687847\pi$
$54$		−	2126.01i		−	0.729083i
$55$	−2433.79	−	1154.05i	−0.804559	−	0.381505i
$56$	−419.066			−0.133631
$57$	−3402.17	+	3402.17i	−1.04714	+	1.04714i
$58$	308.197	+	308.197i	0.0916162	+	0.0916162i
$59$		−	5567.45i		−	1.59938i	−0.600411	−	0.799692i	$-0.704996\pi$
$59$		−	5567.45i		−	1.59938i	0.600411	−	0.799692i	$-0.295004\pi$
$60$	−1636.66	+	583.775i	−0.454627	+	0.162160i
$61$	3899.53			1.04798			0.523990	−	0.851725i	$-0.324443\pi$
$61$	3899.53			1.04798			0.523990	+	0.851725i	$0.324443\pi$
$62$	2112.09	−	2112.09i	0.549450	−	0.549450i
$63$	72.2098	+	72.2098i	0.0181934	+	0.0181934i
$64$			512.000i			0.125000i
$65$	−1858.69	−	5210.99i	−0.439927	−	1.23337i
$66$	−2647.66			−0.607819
$67$	−3509.44	+	3509.44i	−0.781786	+	0.781786i	−0.980132	−	0.198346i	$-0.936443\pi$
$67$	−3509.44	+	3509.44i	−0.781786	+	0.781786i	0.198346	+	0.980132i	$0.436443\pi$
$68$	2763.60	+	2763.60i	0.597665	+	0.597665i
$69$			3850.46i			0.808750i
$70$	561.092	−	1183.29i	0.114508	−	0.241488i
$71$	−3076.44			−0.610284			−0.305142	−	0.952307i	$-0.598704\pi$
$71$	−3076.44			−0.610284			−0.305142	+	0.952307i	$0.598704\pi$
$72$	88.2234	−	88.2234i	0.0170184	−	0.0170184i
$73$	−2473.70	−	2473.70i	−0.464196	−	0.464196i	0.435832	−	0.900028i	$-0.356454\pi$
$73$	−2473.70	−	2473.70i	−0.464196	−	0.464196i	−0.900028	+	0.435832i	$0.856454\pi$
$74$		−	4038.87i		−	0.737559i
$75$	542.969	−	5402.95i	0.0965278	−	0.960525i
$76$	−4430.24			−0.767009
$77$	1410.96	−	1410.96i	0.237977	−	0.237977i
$78$	−3845.46	−	3845.46i	−0.632062	−	0.632062i
$79$			4246.96i			0.680493i	0.940336	+	0.340246i	$0.110511\pi$
$79$			4246.96i			0.680493i	−0.940336	+	0.340246i	$0.889489\pi$
$80$	−1445.70	−	685.522i	−0.225891	−	0.107113i
$81$	6083.97			0.927292
$82$	−5180.32	+	5180.32i	−0.770422	+	0.770422i
$83$	572.593	+	572.593i	0.0831169	+	0.0831169i	0.747443	−	0.664326i	$-0.231281\pi$
$83$	572.593	+	572.593i	0.0831169	+	0.0831169i	−0.664326	+	0.747443i	$0.731281\pi$
$84$		−	1287.27i		−	0.182437i
$85$	−11503.6	+	4103.20i	−1.59220	+	0.567917i
$86$	3304.72			0.446825
$87$	−946.709	+	946.709i	−0.125077	+	0.125077i
$88$	−1723.87	−	1723.87i	−0.222607	−	0.222607i
$89$			3337.76i			0.421381i	0.977553	+	0.210691i	$0.0675713\pi$
$89$			3337.76i			0.421381i	−0.977553	+	0.210691i	$0.932429\pi$
$90$	130.988	+	367.235i	0.0161713	+	0.0453376i
$91$	4098.57			0.494937
$92$	−2507.00	+	2507.00i	−0.296196	+	0.296196i
$93$	6487.83	+	6487.83i	0.750125	+	0.750125i
$94$			6800.75i			0.769664i
$95$	5931.70	−	12509.4i	0.657252	−	1.38608i
$96$	−1572.74			−0.170654
$97$	6884.42	−	6884.42i	0.731684	−	0.731684i	−0.239269	−	0.970953i	$-0.576908\pi$
$97$	6884.42	−	6884.42i	0.731684	−	0.731684i	0.970953	+	0.239269i	$0.0769078\pi$
$98$	686.000	+	686.000i	0.0714286	+	0.0714286i
$99$			594.084i			0.0606146i
$100$	3871.34	−	3164.29i	0.387134	−	0.316429i
$101$	−8844.81			−0.867053			−0.433527	−	0.901141i	$-0.642731\pi$
$101$	−8844.81			−0.867053			−0.433527	+	0.901141i	$0.642731\pi$
$102$	−8489.15	+	8489.15i	−0.815950	+	0.815950i
$103$	5142.53	+	5142.53i	0.484732	+	0.484732i	0.906639	−	0.421907i	$-0.138639\pi$
$103$	5142.53	+	5142.53i	0.484732	+	0.484732i	−0.421907	+	0.906639i	$0.638639\pi$
$104$		−	5007.49i		−	0.462971i
$105$	3634.79	+	1723.54i	0.329686	+	0.156330i
$106$	−3083.03			−0.274389
$107$	6900.66	−	6900.66i	0.602731	−	0.602731i	−0.338306	−	0.941036i	$-0.609854\pi$
$107$	6900.66	−	6900.66i	0.602731	−	0.602731i	0.941036	+	0.338306i	$0.109854\pi$
$108$	4252.01	+	4252.01i	0.364542	+	0.364542i
$109$			3830.12i			0.322373i	0.986924	+	0.161187i	$0.0515321\pi$
$109$			3830.12i			0.322373i	−0.986924	+	0.161187i	$0.948468\pi$
$110$	7175.69	−	2559.48i	0.593032	−	0.211527i
$111$	12406.5			1.00694
$112$	838.131	−	838.131i	0.0668153	−	0.0668153i
$113$	6819.26	+	6819.26i	0.534048	+	0.534048i	0.921775	−	0.387726i	$-0.126739\pi$
$113$	6819.26	+	6819.26i	0.534048	+	0.534048i	−0.387726	+	0.921775i	$0.626739\pi$
$114$		−	13608.7i		−	1.04714i
$115$	−3722.21	−	10435.5i	−0.281453	−	0.789075i
$116$	−1232.79			−0.0916162
$117$	−862.848	+	862.848i	−0.0630322	+	0.0630322i
$118$	11134.9	+	11134.9i	0.799692	+	0.799692i
$119$		−	9047.90i		−	0.638931i
$120$	2105.77	−	4440.87i	0.146234	−	0.308393i
$121$	−3032.73			−0.207139
$122$	−7799.06	+	7799.06i	−0.523990	+	0.523990i
$123$	−15912.7	−	15912.7i	−1.05180	−	1.05180i
$124$			8448.34i			0.549450i
$125$	3751.45	+	15168.0i	0.240093	+	0.970750i
$126$	−288.839			−0.0181934
$127$	−16078.4	+	16078.4i	−0.996864	+	0.996864i	−0.999995	−	0.00313125i	$-0.999003\pi$
$127$	−16078.4	+	16078.4i	−0.996864	+	0.996864i	0.00313125	+	0.999995i	$0.499003\pi$
$128$	−1024.00	−	1024.00i	−0.0625000	−	0.0625000i
$129$			10151.3i			0.610018i
$130$	14139.4	+	6704.59i	0.836648	+	0.396721i
$131$	20737.3			1.20840			0.604198	−	0.796834i	$-0.293494\pi$
$131$	20737.3			1.20840			0.604198	+	0.796834i	$0.293494\pi$
$132$	5295.32	−	5295.32i	0.303909	−	0.303909i
$133$	7252.20	+	7252.20i	0.409983	+	0.409983i
$134$		−	14037.7i		−	0.781786i
$135$	−17699.2	+	6313.09i	−0.971150	+	0.346397i
$136$	−11054.4			−0.597665
$137$	64.1999	−	64.1999i	0.00342053	−	0.00342053i	−0.705394	−	0.708815i	$-0.749230\pi$
$137$	64.1999	−	64.1999i	0.00342053	−	0.00342053i	0.708815	+	0.705394i	$0.249230\pi$
$138$	−7700.92	−	7700.92i	−0.404375	−	0.404375i
$139$		−	12074.6i		−	0.624949i	−0.949926	−	0.312475i	$-0.898842\pi$
$139$		−	12074.6i		−	0.624949i	0.949926	−	0.312475i	$-0.101158\pi$
$140$	1244.40	+	3488.76i	0.0634897	+	0.177998i
$141$	−20890.3			−1.05077
$142$	6152.88	−	6152.88i	0.305142	−	0.305142i
$143$	16859.9	+	16859.9i	0.824484	+	0.824484i
$144$			352.894i			0.0170184i
$145$	1650.59	−	3480.95i	0.0785062	−	0.165562i
$146$	9894.80			0.464196
$147$	−2107.23	+	2107.23i	−0.0975164	+	0.0975164i
$148$	8077.74	+	8077.74i	0.368779	+	0.368779i
$149$			14865.6i			0.669590i	0.942291	+	0.334795i	$0.108667\pi$
$149$			14865.6i			0.669590i	−0.942291	+	0.334795i	$0.891333\pi$
$150$	9719.97	+	11891.8i	0.431999	+	0.528527i
$151$	−32311.0			−1.41709			−0.708544	−	0.705666i	$-0.750648\pi$
$151$	−32311.0			−1.41709			−0.708544	+	0.705666i	$0.750648\pi$
$152$	8860.48	−	8860.48i	0.383504	−	0.383504i
$153$	1904.80	+	1904.80i	0.0813705	+	0.0813705i
$154$			5643.86i			0.237977i
$155$	−23855.1	−	11311.6i	−0.992927	−	0.470825i
$156$	15381.9			0.632062
$157$	20962.0	−	20962.0i	0.850420	−	0.850420i	−0.139765	−	0.990185i	$-0.544635\pi$
$157$	20962.0	−	20962.0i	0.850420	−	0.850420i	0.990185	+	0.139765i	$0.0446347\pi$
$158$	−8493.91	−	8493.91i	−0.340246	−	0.340246i
$159$		−	9470.35i		−	0.374604i
$160$	4262.45	−	1520.36i	0.166502	−	0.0593892i
$161$	8207.79			0.316646
$162$	−12167.9	+	12167.9i	−0.463646	+	0.463646i
$163$	−4876.07	−	4876.07i	−0.183525	−	0.183525i	0.609365	−	0.792890i	$-0.291424\pi$
$163$	−4876.07	−	4876.07i	−0.183525	−	0.183525i	−0.792890	+	0.609365i	$0.791424\pi$
$164$		−	20721.3i		−	0.770422i
$165$	7862.11	+	22042.0i	0.288783	+	0.809625i
$166$	−2290.37			−0.0831169
$167$	17701.4	−	17701.4i	0.634711	−	0.634711i	−0.314535	−	0.949246i	$-0.601849\pi$
$167$	17701.4	−	17701.4i	0.634711	−	0.634711i	0.949246	+	0.314535i	$0.101849\pi$
$168$	2574.54	+	2574.54i	0.0912183	+	0.0912183i
$169$			20413.6i			0.714736i
$170$	14800.9	−	31213.7i	0.512141	−	1.08006i
$171$	−3053.52			−0.104426
$172$	−6609.43	+	6609.43i	−0.223412	+	0.223412i
$173$	−37244.1	−	37244.1i	−1.24442	−	1.24442i	−0.958150	−	0.286265i	$-0.907586\pi$
$173$	−37244.1	−	37244.1i	−1.24442	−	1.24442i	−0.286265	−	0.958150i	$-0.592414\pi$
$174$		−	3786.84i		−	0.125077i
$175$	−11517.2	−	1157.41i	−0.376070	−	0.0377931i
$176$	6895.47			0.222607
$177$	−34203.8	+	34203.8i	−1.09176	+	1.09176i
$178$	−6675.52	−	6675.52i	−0.210691	−	0.210691i
$179$			9674.30i			0.301935i	0.988539	+	0.150968i	$0.0482389\pi$
$179$			9674.30i			0.301935i	−0.988539	+	0.150968i	$0.951761\pi$
$180$	−996.445	−	472.493i	−0.0307545	−	0.0145831i
$181$	−29963.0			−0.914593			−0.457297	−	0.889314i	$-0.651182\pi$
$181$	−29963.0			−0.914593			−0.457297	+	0.889314i	$0.651182\pi$
$182$	−8197.14	+	8197.14i	−0.247468	+	0.247468i
$183$	−23956.9	−	23956.9i	−0.715366	−	0.715366i
$184$		−	10028.0i		−	0.296196i
$185$	−33624.0	+	11993.3i	−0.982440	+	0.350424i
$186$	−25951.3			−0.750125
$187$	37219.4	−	37219.4i	1.06435	−	1.06435i
$188$	−13601.5	−	13601.5i	−0.384832	−	0.384832i
$189$		−	13920.9i		−	0.389711i
$190$	13155.4	+	36882.2i	0.364416	+	1.02167i
$191$	−12935.5			−0.354581			−0.177291	−	0.984159i	$-0.556733\pi$
$191$	−12935.5			−0.354581			−0.177291	+	0.984159i	$0.556733\pi$
$192$	3145.49	−	3145.49i	0.0853269	−	0.0853269i
$193$	−51445.6	−	51445.6i	−1.38113	−	1.38113i	−0.842621	−	0.538507i	$-0.818988\pi$
$193$	−51445.6	−	51445.6i	−1.38113	−	1.38113i	−0.538507	−	0.842621i	$-0.681012\pi$
$194$			27537.7i			0.731684i
$195$	−20594.9	+	43432.8i	−0.541616	+	1.14222i
$196$	−2744.00			−0.0714286
$197$	51874.5	−	51874.5i	1.33666	−	1.33666i	0.437387	−	0.899273i	$-0.355904\pi$
$197$	51874.5	−	51874.5i	1.33666	−	1.33666i	0.899273	−	0.437387i	$-0.144096\pi$
$198$	−1188.17	−	1188.17i	−0.0303073	−	0.0303073i
$199$			6717.24i			0.169623i	0.996397	+	0.0848115i	$0.0270288\pi$
$199$			6717.24i			0.169623i	−0.996397	+	0.0848115i	$0.972971\pi$
$200$	−1414.09	+	14071.3i	−0.0353522	+	0.351781i
$201$	43120.7			1.06732
$202$	17689.6	−	17689.6i	0.433527	−	0.433527i
$203$	2018.04	+	2018.04i	0.0489709	+	0.0489709i
$204$		−	33956.6i		−	0.815950i
$205$	58509.4	+	27744.0i	1.39225	+	0.660177i
$206$	−20570.1			−0.484732
$207$	−1727.94	+	1727.94i	−0.0403262	+	0.0403262i
$208$	10015.0	+	10015.0i	0.231485	+	0.231485i
$209$			59665.2i			1.36593i
$210$	−10716.7	+	3822.50i	−0.243008	+	0.0866780i
$211$	66873.2			1.50206			0.751030	−	0.660269i	$-0.229558\pi$
$211$	66873.2			1.50206			0.751030	+	0.660269i	$0.229558\pi$
$212$	6166.06	−	6166.06i	0.137194	−	0.137194i
$213$	18900.2	+	18900.2i	0.416589	+	0.416589i
$214$			27602.6i			0.602731i
$215$	−9813.21	−	27512.1i	−0.212292	−	0.595178i
$216$	−17008.0			−0.364542
$217$	13829.7	−	13829.7i	0.293693	−	0.293693i
$218$	−7660.24	−	7660.24i	−0.161187	−	0.161187i
$219$			30394.5i			0.633734i
$220$	−9232.42	+	19470.3i	−0.190752	+	0.402279i
$221$	108115.			2.21361
$222$	−24812.9	+	24812.9i	−0.503469	+	0.503469i
$223$	−16066.1	−	16066.1i	−0.323073	−	0.323073i	0.526872	−	0.849945i	$-0.323365\pi$
$223$	−16066.1	−	16066.1i	−0.323073	−	0.323073i	−0.849945	+	0.526872i	$0.823365\pi$
$224$			3352.53i			0.0668153i
$225$	2668.30	−	2180.97i	0.0527072	−	0.0430810i
$226$	−27277.1			−0.534048
$227$	49867.3	−	49867.3i	0.967752	−	0.967752i	−0.0317436	−	0.999496i	$-0.510106\pi$
$227$	49867.3	−	49867.3i	0.967752	−	0.967752i	0.999496	+	0.0317436i	$0.0101060\pi$
$228$	27217.3	+	27217.3i	0.523572	+	0.523572i
$229$			55646.5i			1.06113i	0.847645	+	0.530563i	$0.178020\pi$
$229$			55646.5i			1.06113i	−0.847645	+	0.530563i	$0.821980\pi$
$230$	28315.5	+	13426.6i	0.535264	+	0.253811i
$231$	−17336.6			−0.324893
$232$	2465.57	−	2465.57i	0.0458081	−	0.0458081i
$233$	−478.359	−	478.359i	−0.00881134	−	0.00881134i	0.702687	−	0.711499i	$-0.251983\pi$
$233$	−478.359	−	478.359i	−0.00881134	−	0.00881134i	−0.711499	+	0.702687i	$0.751983\pi$
$234$		−	3451.39i		−	0.0630322i
$235$	56616.9	−	20194.5i	1.02521	−	0.365678i
$236$	−44539.6			−0.799692
$237$	26091.3	−	26091.3i	0.464515	−	0.464515i
$238$	18095.8	+	18095.8i	0.319465	+	0.319465i
$239$			46240.3i			0.809515i	0.914424	+	0.404758i	$0.132644\pi$
$239$			46240.3i			0.809515i	−0.914424	+	0.404758i	$0.867356\pi$
$240$	4670.20	+	13093.3i	0.0810798	+	0.227314i
$241$	−43109.0			−0.742221			−0.371111	−	0.928589i	$-0.621023\pi$
$241$	−43109.0			−0.742221			−0.371111	+	0.928589i	$0.621023\pi$
$242$	6065.45	−	6065.45i	0.103570	−	0.103570i
$243$	5674.57	+	5674.57i	0.0960994	+	0.0960994i
$244$		−	31196.2i		−	0.523990i
$245$	3673.97	−	7748.07i	0.0612074	−	0.129081i
$246$	63651.0			1.05180
$247$	−86657.8	+	86657.8i	−1.42041	+	1.42041i
$248$	−16896.7	−	16896.7i	−0.274725	−	0.274725i
$249$		−	7035.48i		−	0.113474i
$250$	−37838.8	−	22833.0i	−0.605421	−	0.365329i
$251$	−81263.7			−1.28988			−0.644940	−	0.764233i	$-0.723118\pi$
$251$	−81263.7			−1.28988			−0.644940	+	0.764233i	$0.723118\pi$
$252$	577.678	−	577.678i	0.00909672	−	0.00909672i
$253$	33763.5	+	33763.5i	0.527481	+	0.527481i
$254$		−	64313.7i		−	0.996864i
$255$	95881.2	+	45464.8i	1.47453	+	0.699190i
$256$	4096.00			0.0625000
$257$	−50040.6	+	50040.6i	−0.757628	+	0.757628i	−0.975890	−	0.218262i	$-0.929961\pi$
$257$	−50040.6	+	50040.6i	−0.757628	+	0.757628i	0.218262	+	0.975890i	$0.429961\pi$
$258$	−20302.6	−	20302.6i	−0.305009	−	0.305009i
$259$		−	26446.1i		−	0.394242i
$260$	−41687.9	+	14869.5i	−0.616685	+	0.219964i
$261$	−849.693			−0.0124733
$262$	−41474.6	+	41474.6i	−0.604198	+	0.604198i
$263$	44007.7	+	44007.7i	0.636235	+	0.636235i	0.949625	−	0.313390i	$-0.101465\pi$
$263$	44007.7	+	44007.7i	0.636235	+	0.636235i	−0.313390	+	0.949625i	$0.601465\pi$
$264$			21181.3i			0.303909i
$265$	9154.93	+	25666.5i	0.130366	+	0.365490i
$266$	−29008.8			−0.409983
$267$	20505.7	−	20505.7i	0.287641	−	0.287641i
$268$	28075.5	+	28075.5i	0.390893	+	0.390893i
$269$		−	83460.6i		−	1.15339i	−0.816959	−	0.576696i	$-0.804342\pi$
$269$		−	83460.6i		−	1.15339i	0.816959	−	0.576696i	$-0.195658\pi$
$270$	22772.3	−	48024.6i	0.312377	−	0.658774i
$271$	23355.4			0.318016			0.159008	−	0.987277i	$-0.449170\pi$
$271$	23355.4			0.318016			0.159008	+	0.987277i	$0.449170\pi$
$272$	22108.8	−	22108.8i	0.298833	−	0.298833i
$273$	−25179.7	−	25179.7i	−0.337851	−	0.337851i
$274$			256.800i			0.00342053i
$275$	−42615.8	−	52138.1i	−0.563515	−	0.689429i
$276$	30803.7			0.404375
$277$	70680.6	−	70680.6i	0.921173	−	0.921173i	−0.0759399	−	0.997112i	$-0.524196\pi$
$277$	70680.6	−	70680.6i	0.921173	−	0.921173i	0.997112	+	0.0759399i	$0.0241957\pi$
$278$	24149.3	+	24149.3i	0.312475	+	0.312475i
$279$			5822.98i			0.0748061i
$280$	−9466.32	−	4488.73i	−0.120744	−	0.0572542i
$281$	−90444.8			−1.14544			−0.572718	−	0.819752i	$-0.694111\pi$
$281$	−90444.8			−1.14544			−0.572718	+	0.819752i	$0.694111\pi$
$282$	41780.7	−	41780.7i	0.525384	−	0.525384i
$283$	−17338.8	−	17338.8i	−0.216494	−	0.216494i	0.590525	−	0.807019i	$-0.298921\pi$
$283$	−17338.8	−	17338.8i	−0.216494	−	0.216494i	−0.807019	+	0.590525i	$0.798921\pi$
$284$			24611.5i			0.305142i
$285$	−113294.	+	40410.4i	−1.39481	+	0.497512i
$286$	−67439.5			−0.824484
$287$	−33920.2	+	33920.2i	−0.411808	+	0.411808i
$288$	−705.787	−	705.787i	−0.00850920	−	0.00850920i
$289$		−	155151.i		−	1.85763i
$290$	3660.71	+	10263.1i	0.0435281	+	0.122034i
$291$	−84589.3			−0.998917
$292$	−19789.6	+	19789.6i	−0.232098	+	0.232098i
$293$	−57740.9	−	57740.9i	−0.672587	−	0.672587i	0.285725	−	0.958312i	$-0.407766\pi$
$293$	−57740.9	−	57740.9i	−0.672587	−	0.672587i	−0.958312	+	0.285725i	$0.907766\pi$
$294$		−	8428.93i		−	0.0975164i
$295$	59634.6	−	125764.i	0.685258	−	1.44515i
$296$	−32311.0			−0.368779
$297$	57264.9	−	57264.9i	0.649195	−	0.649195i
$298$	−29731.1	−	29731.1i	−0.334795	−	0.334795i
$299$			98076.4i			1.09704i
$300$	−43223.6	−	4343.75i	−0.480263	−	0.0482639i
$301$	21638.9			0.238838
$302$	64622.1	−	64622.1i	0.708544	−	0.708544i
$303$	54338.4	+	54338.4i	0.591864	+	0.591864i
$304$			35441.9i			0.383504i
$305$	88087.0	+	41769.0i	0.946917	+	0.449008i
$306$	−7619.20			−0.0813705
$307$	−21949.4	+	21949.4i	−0.232887	+	0.232887i	−0.813897	−	0.581010i	$-0.802658\pi$
$307$	−21949.4	+	21949.4i	−0.232887	+	0.232887i	0.581010	+	0.813897i	$0.302658\pi$
$308$	−11287.7	−	11287.7i	−0.118988	−	0.118988i
$309$		−	63186.6i		−	0.661771i
$310$	70333.3	−	25087.0i	0.731876	−	0.261051i
$311$	−19879.8			−0.205538			−0.102769	−	0.994705i	$-0.532770\pi$
$311$	−19879.8			−0.205538			−0.102769	+	0.994705i	$0.532770\pi$
$312$	−30763.7	+	30763.7i	−0.316031	+	0.316031i
$313$	−127683.	−	127683.i	−1.30330	−	1.30330i	−0.926155	−	0.377143i	$-0.876906\pi$
$313$	−127683.	−	127683.i	−1.30330	−	1.30330i	−0.377143	−	0.926155i	$-0.623094\pi$
$314$			83848.0i			0.850420i
$315$	857.696	+	2404.62i	0.00864395	+	0.0242340i
$316$	33975.7			0.340246
$317$	−82092.3	+	82092.3i	−0.816928	+	0.816928i	−0.985662	−	0.168734i	$-0.946032\pi$
$317$	−82092.3	+	82092.3i	−0.816928	+	0.816928i	0.168734	+	0.985662i	$0.446032\pi$
$318$	18940.7	+	18940.7i	0.187302	+	0.187302i
$319$			16602.8i			0.163155i
$320$	−5484.18	+	11565.6i	−0.0535564	+	0.112946i
$321$	−84788.9			−0.822866
$322$	−16415.6	+	16415.6i	−0.158323	+	0.158323i
$323$	191304.	+	191304.i	1.83366	+	1.83366i
$324$		−	48671.7i		−	0.463646i
$325$	13830.2	−	137621.i	0.130936	−	1.30292i
$326$	19504.3			0.183525
$327$	23530.5	−	23530.5i	0.220057	−	0.220057i
$328$	41442.6	+	41442.6i	0.385211	+	0.385211i
$329$			44530.6i			0.411403i
$330$	−59808.3	−	28359.8i	−0.549204	−	0.260421i
$331$	−51918.8			−0.473880			−0.236940	−	0.971524i	$-0.576144\pi$
$331$	−51918.8			−0.473880			−0.236940	+	0.971524i	$0.576144\pi$
$332$	4580.74	−	4580.74i	0.0415585	−	0.0415585i
$333$	5567.55	+	5567.55i	0.0502083	+	0.0502083i
$334$			70805.8i			0.634711i
$335$	−116866.	+	41684.5i	−1.04135	+	0.371437i
$336$	−10298.2			−0.0912183
$337$	−99346.7	+	99346.7i	−0.874770	+	0.874770i	−0.992988	−	0.118218i	$-0.962282\pi$
$337$	−99346.7	+	99346.7i	−0.874770	+	0.874770i	0.118218	+	0.992988i	$0.462282\pi$
$338$	−40827.2	−	40827.2i	−0.357368	−	0.357368i
$339$		−	83788.8i		−	0.729099i
$340$	32825.6	+	92029.1i	0.283959	+	0.796100i
$341$	113780.			0.978490
$342$	6107.05	−	6107.05i	0.0522131	−	0.0522131i
$343$	4491.86	+	4491.86i	0.0381802	+	0.0381802i
$344$		−	26437.7i		−	0.223412i
$345$	−41243.4	+	86978.5i	−0.346510	+	0.730758i
$346$	148976.			1.24442
$347$	−87398.0	+	87398.0i	−0.725843	+	0.725843i	−0.969789	−	0.243946i	$-0.921558\pi$
$347$	−87398.0	+	87398.0i	−0.725843	+	0.725843i	0.243946	+	0.969789i	$0.421558\pi$
$348$	7573.67	+	7573.67i	0.0625386	+	0.0625386i
$349$		−	44483.3i		−	0.365213i	−0.983186	−	0.182606i	$-0.941547\pi$
$349$		−	44483.3i		−	0.365213i	0.983186	−	0.182606i	$-0.0584534\pi$
$350$	25349.1	−	20719.5i	0.206932	−	0.169139i
$351$	166343.			1.35018
$352$	−13790.9	+	13790.9i	−0.111303	+	0.111303i
$353$	58237.1	+	58237.1i	0.467359	+	0.467359i	0.901058	−	0.433699i	$-0.142792\pi$
$353$	58237.1	+	58237.1i	0.467359	+	0.467359i	−0.433699	+	0.901058i	$0.642792\pi$
$354$		−	136815.i		−	1.09176i
$355$	−69494.1	−	32952.6i	−0.551431	−	0.261477i
$356$	26702.1			0.210691
$357$	−55586.1	+	55586.1i	−0.436144	+	0.436144i
$358$	−19348.6	−	19348.6i	−0.150968	−	0.150968i
$359$			28354.8i			0.220008i	0.993931	+	0.110004i	$0.0350863\pi$
$359$			28354.8i			0.220008i	−0.993931	+	0.110004i	$0.964914\pi$
$360$	2937.88	−	1047.90i	0.0226688	−	0.00808567i
$361$	−176352.			−1.35321
$362$	59926.0	−	59926.0i	0.457297	−	0.457297i
$363$	18631.7	+	18631.7i	0.141396	+	0.141396i
$364$		−	32788.6i		−	0.247468i
$365$	−29382.2	−	82375.2i	−0.220546	−	0.618316i
$366$	95827.6			0.715366
$367$	−118283.	+	118283.i	−0.878191	+	0.878191i	−0.993347	−	0.115157i	$-0.963263\pi$
$367$	−118283.	+	118283.i	−0.878191	+	0.878191i	0.115157	+	0.993347i	$0.463263\pi$
$368$	20056.0	+	20056.0i	0.148098	+	0.148098i
$369$		−	14282.1i		−	0.104891i
$370$	43261.5	−	91234.5i	0.316008	−	0.666432i
$371$	−20187.4			−0.146667
$372$	51902.7	−	51902.7i	0.375063	−	0.375063i
$373$	13634.2	+	13634.2i	0.0979971	+	0.0979971i	0.754406	−	0.656409i	$-0.227925\pi$
$373$	13634.2	+	13634.2i	0.0979971	+	0.0979971i	−0.656409	+	0.754406i	$0.727925\pi$
$374$			148878.i			1.06435i
$375$	70137.8	−	116232.i	0.498758	−	0.826539i
$376$	54406.0			0.384832
$377$	−24114.0	+	24114.0i	−0.169662	+	0.169662i
$378$	27841.8	+	27841.8i	0.194856	+	0.194856i
$379$			219026.i			1.52482i	0.647097	+	0.762408i	$0.275983\pi$
$379$			219026.i			1.52482i	−0.647097	+	0.762408i	$0.724017\pi$
$380$	−100075.	−	47453.6i	−0.693042	−	0.328626i
$381$	197557.			1.36095
$382$	25870.9	−	25870.9i	0.177291	−	0.177291i
$383$	38144.2	+	38144.2i	0.260034	+	0.260034i	0.825068	−	0.565034i	$-0.191137\pi$
$383$	38144.2	+	38144.2i	0.260034	+	0.260034i	−0.565034	+	0.825068i	$0.691137\pi$
$384$			12582.0i			0.0853269i
$385$	46985.7	−	16759.2i	0.316989	−	0.113066i
$386$	205783.			1.38113
$387$	−4555.52	+	4555.52i	−0.0304170	+	0.0304170i
$388$	−55075.3	−	55075.3i	−0.365842	−	0.365842i
$389$		−	157406.i		−	1.04021i	−0.854101	−	0.520107i	$-0.825892\pi$
$389$		−	157406.i		−	1.04021i	0.854101	−	0.520107i	$-0.174108\pi$
$390$	−45675.8	−	128055.i	−0.300301	−	0.841916i
$391$	216511.			1.41621
$392$	5488.00	−	5488.00i	0.0357143	−	0.0357143i
$393$	−127400.	−	127400.i	−0.824869	−	0.824869i
$394$			207498.i			1.33666i
$395$	−45490.4	+	95935.0i	−0.291558	+	0.614869i
$396$	4752.67			0.0303073
$397$	131252.	−	131252.i	0.832772	−	0.832772i	−0.155123	−	0.987895i	$-0.549577\pi$
$397$	131252.	−	131252.i	0.832772	−	0.832772i	0.987895	+	0.155123i	$0.0495774\pi$
$398$	−13434.5	−	13434.5i	−0.0848115	−	0.0848115i
$399$		−	89108.2i		−	0.559722i
$400$	−25314.3	−	30970.7i	−0.158215	−	0.193567i
$401$	102718.			0.638789			0.319394	−	0.947622i	$-0.396521\pi$
$401$	102718.			0.638789			0.319394	+	0.947622i	$0.396521\pi$
$402$	−86241.4	+	86241.4i	−0.533659	+	0.533659i
$403$	165254.	+	165254.i	1.01752	+	1.01752i
$404$			70758.5i			0.433527i
$405$	137431.	+	65167.1i	0.837869	+	0.397300i
$406$	−8072.17			−0.0489709
$407$	108789.	−	108789.i	0.656742	−	0.656742i
$408$	67913.2	+	67913.2i	0.407975	+	0.407975i
$409$		−	141379.i		−	0.845157i	−0.906326	−	0.422578i	$-0.861125\pi$
$409$		−	141379.i		−	0.845157i	0.906326	−	0.422578i	$-0.138875\pi$
$410$	−172507.	+	61531.0i	−1.02622	+	0.366038i
$411$	−788.829			−0.00466981
$412$	41140.2	−	41140.2i	0.242366	−	0.242366i
$413$	72910.3	+	72910.3i	0.427453	+	0.427453i
$414$		−	6911.75i		−	0.0403262i
$415$	6801.16	+	19067.6i	0.0394900	+	0.110713i
$416$	−40059.9			−0.231485
$417$	−74181.0	+	74181.0i	−0.426600	+	0.426600i
$418$	−119330.	−	119330.i	−0.682965	−	0.682965i
$419$			166898.i			0.950657i	0.879808	+	0.475328i	$0.157671\pi$
$419$			166898.i			0.950657i	−0.879808	+	0.475328i	$0.842329\pi$
$420$	13788.3	−	29078.3i	0.0781652	−	0.164843i
$421$	82494.6			0.465438			0.232719	−	0.972544i	$-0.425238\pi$
$421$	82494.6			0.465438			0.232719	+	0.972544i	$0.425238\pi$
$422$	−133746.	+	133746.i	−0.751030	+	0.751030i
$423$	−9374.77	−	9374.77i	−0.0523938	−	0.0523938i
$424$			24664.2i			0.137194i
$425$	−303808.	−	30531.1i	−1.68198	−	0.169030i
$426$	−75600.9			−0.416589
$427$	−51067.5	+	51067.5i	−0.280084	+	0.280084i
$428$	−55205.3	−	55205.3i	−0.301365	−	0.301365i
$429$		−	207158.i		−	1.12561i
$430$	74650.6	+	35397.8i	0.403735	+	0.191443i
$431$	−196664.			−1.05869			−0.529346	−	0.848406i	$-0.677563\pi$
$431$	−196664.			−1.05869			−0.529346	+	0.848406i	$0.677563\pi$
$432$	34016.1	−	34016.1i	0.182271	−	0.182271i
$433$	−60507.3	−	60507.3i	−0.322725	−	0.322725i	0.527087	−	0.849811i	$-0.323284\pi$
$433$	−60507.3	−	60507.3i	−0.322725	−	0.322725i	−0.849811	+	0.527087i	$0.823284\pi$
$434$			55318.9i			0.293693i
$435$	−31525.8	+	11244.8i	−0.166605	+	0.0594258i
$436$	30641.0			0.161187
$437$	−173541.	+	173541.i	−0.908738	+	0.908738i
$438$	−60789.0	−	60789.0i	−0.316867	−	0.316867i
$439$		−	251676.i		−	1.30591i	−0.757397	−	0.652954i	$-0.773529\pi$
$439$		−	251676.i		−	1.30591i	0.757397	−	0.652954i	$-0.226471\pi$
$440$	−20475.8	−	57405.5i	−0.105763	−	0.296516i
$441$	−1891.29			−0.00972480
$442$	−216230.	+	216230.i	−1.10681	+	1.10681i
$443$	−40354.8	−	40354.8i	−0.205630	−	0.205630i	0.596777	−	0.802407i	$-0.296448\pi$
$443$	−40354.8	−	40354.8i	−0.205630	−	0.205630i	−0.802407	+	0.596777i	$0.796448\pi$
$444$		−	99251.8i		−	0.503469i
$445$	−35751.7	+	75397.1i	−0.180541	+	0.380745i
$446$	64264.3			0.323073
$447$	91327.1	−	91327.1i	0.457072	−	0.457072i
$448$	−6705.05	−	6705.05i	−0.0334077	−	0.0334077i
$449$		−	35102.5i		−	0.174119i	−0.996203	−	0.0870594i	$-0.972253\pi$
$449$		−	35102.5i		−	0.174119i	0.996203	−	0.0870594i	$-0.0277470\pi$
$450$	−974.654	+	9698.55i	−0.00481311	+	0.0478941i
$451$	−279068.			−1.37201
$452$	54554.1	−	54554.1i	0.267024	−	0.267024i
$453$	198504.	+	198504.i	0.967326	+	0.967326i
$454$			199469.i			0.967752i
$455$	92583.1	+	43901.0i	0.447207	+	0.212056i
$456$	−108869.			−0.523572
$457$	−17668.8	+	17668.8i	−0.0846007	+	0.0846007i	−0.748141	−	0.663540i	$-0.769053\pi$
$457$	−17668.8	+	17668.8i	−0.0846007	+	0.0846007i	0.663540	+	0.748141i	$0.269053\pi$
$458$	−111293.	−	111293.i	−0.530563	−	0.530563i
$459$		−	367215.i		−	1.74299i
$460$	−83484.1	+	29777.7i	−0.394537	+	0.140726i
$461$	311286.			1.46473			0.732365	−	0.680912i	$-0.238417\pi$
$461$	311286.			1.46473			0.732365	+	0.680912i	$0.238417\pi$
$462$	34673.2	−	34673.2i	0.162446	−	0.162446i
$463$	−68332.5	−	68332.5i	−0.318761	−	0.318761i	0.529530	−	0.848291i	$-0.322368\pi$
$463$	−68332.5	−	68332.5i	−0.318761	−	0.318761i	−0.848291	+	0.529530i	$0.822368\pi$
$464$			9862.30i			0.0458081i
$465$	77061.4	+	216048.i	0.356395	+	0.999179i
$466$	1913.44			0.00881134
$467$	−17162.8	+	17162.8i	−0.0786962	+	0.0786962i	−0.745359	−	0.666663i	$-0.767722\pi$
$467$	−17162.8	+	17162.8i	−0.0786962	+	0.0786962i	0.666663	+	0.745359i	$0.267722\pi$
$468$	6902.78	+	6902.78i	0.0315161	+	0.0315161i
$469$		−	91917.8i		−	0.417882i
$470$	−72844.8	+	153623.i	−0.329764	+	0.695441i
$471$	−257562.			−1.16102
$472$	89079.3	−	89079.3i	0.399846	−	0.399846i
$473$	89013.9	+	89013.9i	0.397865	+	0.397865i
$474$			104365.i			0.464515i
$475$	267984.	−	219040.i	1.18774	−	0.970816i
$476$	−72383.2			−0.319465
$477$	4249.93	−	4249.93i	0.0186786	−	0.0186786i
$478$	−92480.6	−	92480.6i	−0.404758	−	0.404758i
$479$			26855.2i			0.117046i	0.998286	+	0.0585230i	$0.0186391\pi$
$479$			26855.2i			0.117046i	−0.998286	+	0.0585230i	$0.981361\pi$
$480$	−35526.9	−	16846.1i	−0.154197	−	0.0731169i
$481$	316010.			1.36587
$482$	86217.9	−	86217.9i	0.371111	−	0.371111i
$483$	−50424.8	−	50424.8i	−0.216148	−	0.216148i
$484$			24261.8i			0.103570i
$485$	229254.	−	81771.9i	0.974615	−	0.347633i
$486$	−22698.3			−0.0960994
$487$	−148045.	+	148045.i	−0.624216	+	0.624216i	−0.946607	−	0.322391i	$-0.895513\pi$
$487$	−148045.	+	148045.i	−0.624216	+	0.624216i	0.322391	+	0.946607i	$0.395513\pi$
$488$	62392.5	+	62392.5i	0.261995	+	0.261995i
$489$			59912.7i			0.250554i
$490$	8148.19	+	22844.1i	0.0339367	+	0.0951440i
$491$	−265155.			−1.09986			−0.549930	−	0.835211i	$-0.685346\pi$
$491$	−265155.			−1.09986			−0.549930	+	0.835211i	$0.685346\pi$
$492$	−127302.	+	127302.i	−0.525902	+	0.525902i
$493$	53233.4	+	53233.4i	0.219023	+	0.219023i
$494$		−	346631.i		−	1.42041i
$495$	−6363.40	+	13419.8i	−0.0259704	+	0.0547692i
$496$	67586.7			0.274725
$497$	40288.5	−	40288.5i	0.163105	−	0.163105i
$498$	14071.0	+	14071.0i	0.0567369	+	0.0567369i
$499$		−	362831.i		−	1.45715i	−0.684968	−	0.728574i	$-0.740184\pi$
$499$		−	362831.i		−	1.45715i	0.684968	−	0.728574i	$-0.259816\pi$
$500$	121344.	−	30011.6i	0.485375	−	0.120046i
$501$	−217499.			−0.866526
$502$	162527.	−	162527.i	0.644940	−	0.644940i
$503$	−315242.	−	315242.i	−1.24597	−	1.24597i	−0.957484	−	0.288486i	$-0.906848\pi$
$503$	−315242.	−	315242.i	−1.24597	−	1.24597i	−0.288486	−	0.957484i	$-0.593152\pi$
$504$			2310.71i			0.00909672i
$505$	−199796.	−	94739.3i	−0.783439	−	0.371490i
$506$	−135054.			−0.527481
$507$	125412.	−	125412.i	0.487890	−	0.487890i
$508$	128627.	+	128627.i	0.498432	+	0.498432i
$509$			405092.i			1.56357i	0.623546	+	0.781786i	$0.285691\pi$
$509$			405092.i			1.56357i	−0.623546	+	0.781786i	$0.714309\pi$
$510$	−282692.	+	100833.i	−1.08686	+	0.387669i
$511$	64790.1			0.248123
$512$	−8192.00	+	8192.00i	−0.0312500	+	0.0312500i
$513$	294335.	+	294335.i	1.11843	+	1.11843i
$514$		−	200162.i		−	0.757628i
$515$	61082.1	+	171248.i	0.230303	+	0.645672i
$516$	81210.5			0.305009
$517$	−183181.	+	183181.i	−0.685330	+	0.685330i
$518$	52892.3	+	52892.3i	0.197121	+	0.197121i
$519$			457621.i			1.69891i
$520$	53636.7	−	113115.i	0.198361	−	0.418324i
$521$	−214681.			−0.790896			−0.395448	−	0.918488i	$-0.629411\pi$
$521$	−214681.			−0.790896			−0.395448	+	0.918488i	$0.629411\pi$
$522$	1699.39	−	1699.39i	0.00623665	−	0.00623665i
$523$	−160705.	−	160705.i	−0.587523	−	0.587523i	0.349437	−	0.936960i	$-0.386373\pi$
$523$	−160705.	−	160705.i	−0.587523	−	0.587523i	−0.936960	+	0.349437i	$0.886373\pi$
$524$		−	165898.i		−	0.604198i
$525$	63645.4	+	77866.6i	0.230913	+	0.282509i
$526$	−176031.			−0.636235
$527$	364810.	−	364810.i	1.31355	−	1.31355i
$528$	−42362.6	−	42362.6i	−0.151955	−	0.151955i
$529$		−	83433.4i		−	0.298146i
$530$	−69642.9	−	33023.2i	−0.247928	−	0.117562i
$531$	−30698.7			−0.108876
$532$	58017.6	−	58017.6i	0.204992	−	0.204992i
$533$	−405319.	−	405319.i	−1.42673	−	1.42673i
$534$			82022.6i			0.287641i
$535$	229795.	−	81964.9i	0.802847	−	0.286365i
$536$	−112302.			−0.390893
$537$	59434.4	−	59434.4i	0.206105	−	0.206105i
$538$	166921.	+	166921.i	0.576696	+	0.576696i
$539$			36955.4i			0.127204i
$540$	50504.7	+	141594.i	0.173198	+	0.485575i
$541$	482776.			1.64950			0.824749	−	0.565500i	$-0.191317\pi$
$541$	482776.			1.64950			0.824749	+	0.565500i	$0.191317\pi$
$542$	−46710.8	+	46710.8i	−0.159008	+	0.159008i
$543$	184079.	+	184079.i	0.624315	+	0.624315i
$544$			88435.3i			0.298833i
$545$	−41025.5	+	86519.0i	−0.138121	+	0.291285i
$546$	100719.			0.337851
$547$	1339.21	−	1339.21i	0.00447583	−	0.00447583i	−0.704865	−	0.709341i	$-0.748993\pi$
$547$	1339.21	−	1339.21i	0.00447583	−	0.00447583i	0.709341	+	0.704865i	$0.248993\pi$
$548$	−513.599	−	513.599i	−0.00171026	−	0.00171026i
$549$		−	21501.9i		−	0.0713398i
$550$	189508.	+	19044.5i	0.626472	+	0.0629572i
$551$	−85336.6			−0.281082
$552$	−61607.3	+	61607.3i	−0.202188	+	0.202188i
$553$	−55617.3	−	55617.3i	−0.181869	−	0.181869i
$554$			282723.i			0.921173i
$555$	280251.	+	132889.i	0.909833	+	0.431424i
$556$	−96597.1			−0.312475
$557$	4068.01	−	4068.01i	0.0131121	−	0.0131121i	−0.700520	−	0.713632i	$-0.747049\pi$
$557$	4068.01	−	4068.01i	0.0131121	−	0.0131121i	0.713632	+	0.700520i	$0.247049\pi$
$558$	−11646.0	−	11646.0i	−0.0374030	−	0.0374030i
$559$			258568.i			0.827467i
$560$	27910.1	−	9955.18i	0.0889991	−	0.0317448i
$561$	−457318.			−1.45309
$562$	180890.	−	180890.i	0.572718	−	0.572718i
$563$	318929.	+	318929.i	1.00618	+	1.00618i	0.999981	+	0.00620147i	$0.00197400\pi$
$563$	318929.	+	318929.i	1.00618	+	1.00618i	0.00620147	+	0.999981i	$0.498026\pi$
$564$			167123.i			0.525384i
$565$	80998.1	+	227084.i	0.253733	+	0.711361i
$566$	69355.1			0.216494
$567$	−79674.4	+	79674.4i	−0.247829	+	0.247829i
$568$	−49223.1	−	49223.1i	−0.152571	−	0.152571i
$569$		−	496680.i		−	1.53410i	−0.641590	−	0.767048i	$-0.721725\pi$
$569$		−	496680.i		−	1.53410i	0.641590	−	0.767048i	$-0.278275\pi$
$570$	145766.	−	307408.i	0.448650	−	0.946162i
$571$	66636.3			0.204380			0.102190	−	0.994765i	$-0.467415\pi$
$571$	66636.3			0.204380			0.102190	+	0.994765i	$0.467415\pi$
$572$	134879.	−	134879.i	0.412242	−	0.412242i
$573$	79469.5	+	79469.5i	0.242042	+	0.242042i
$574$		−	135681.i		−	0.411808i
$575$	27696.2	−	275599.i	0.0837694	−	0.833569i
$576$	2823.15			0.00850920
$577$	−426880.	+	426880.i	−1.28220	+	1.28220i	−0.342780	+	0.939416i	$0.611368\pi$
$577$	−426880.	+	426880.i	−1.28220	+	1.28220i	−0.939416	+	0.342780i	$0.888632\pi$
$578$	310302.	+	310302.i	0.928814	+	0.928814i
$579$			632116.i			1.88556i
$580$	−27847.6	−	13204.7i	−0.0827811	−	0.0392531i
$581$	−14997.1			−0.0444279
$582$	169179.	−	169179.i	0.499459	−	0.499459i
$583$	−83042.7	−	83042.7i	−0.244323	−	0.244323i
$584$		−	79158.4i		−	0.232098i
$585$	−28733.2	+	10248.8i	−0.0839599	+	0.0299474i
$586$	230964.			0.672587
$587$	270435.	−	270435.i	0.784849	−	0.784849i	−0.195796	−	0.980645i	$-0.562729\pi$
$587$	270435.	−	270435.i	0.784849	−	0.784849i	0.980645	+	0.195796i	$0.0627290\pi$
$588$	16857.9	+	16857.9i	0.0487582	+	0.0487582i
$589$			584816.i			1.68573i
$590$	132259.	+	370797.i	0.379944	+	1.06520i
$591$	−637385.			−1.82485
$592$	64621.9	−	64621.9i	0.184390	−	0.184390i
$593$	154567.	+	154567.i	0.439550	+	0.439550i	0.891860	−	0.452311i	$-0.149400\pi$
$593$	154567.	+	154567.i	0.439550	+	0.439550i	−0.452311	+	0.891860i	$0.649400\pi$
$594$			229060.i			0.649195i
$595$	96914.7	−	204384.i	0.273751	−	0.577315i
$596$	118924.			0.334795
$597$	41267.6	−	41267.6i	0.115787	−	0.115787i
$598$	−196153.	−	196153.i	−0.548520	−	0.548520i
$599$			234959.i			0.654844i	0.944878	+	0.327422i	$0.106180\pi$
$599$			234959.i			0.654844i	−0.944878	+	0.327422i	$0.893820\pi$
$600$	95134.8	−	77759.8i	0.264263	−	0.215999i
$601$	427818.			1.18443			0.592216	−	0.805779i	$-0.298253\pi$
$601$	427818.			1.18443			0.592216	+	0.805779i	$0.298253\pi$
$602$	−43277.9	+	43277.9i	−0.119419	+	0.119419i
$603$	19350.9	+	19350.9i	0.0532190	+	0.0532190i
$604$			258488.i			0.708544i
$605$	−68506.6	−	32484.4i	−0.187164	−	0.0887491i
$606$	−217354.			−0.591864
$607$	409993.	−	409993.i	1.11275	−	1.11275i	0.119979	−	0.992776i	$-0.461717\pi$
$607$	409993.	−	409993.i	1.11275	−	1.11275i	0.992776	−	0.119979i	$-0.0382826\pi$
$608$	−70883.9	−	70883.9i	−0.191752	−	0.191752i
$609$		−	24795.8i		−	0.0668565i
$610$	−259712.	+	92635.9i	−0.697963	+	0.248954i
$611$	−532105.			−1.42533
$612$	15238.4	−	15238.4i	0.0406852	−	0.0406852i
$613$	−416750.	−	416750.i	−1.10906	−	1.10906i	−0.993274	−	0.115784i	$-0.963062\pi$
$613$	−416750.	−	416750.i	−1.10906	−	1.10906i	−0.115784	−	0.993274i	$-0.536938\pi$
$614$		−	87797.5i		−	0.232887i
$615$	−189009.	−	529901.i	−0.499726	−	1.40102i
$616$	45150.8			0.118988
$617$	−77539.7	+	77539.7i	−0.203683	+	0.203683i	−0.801576	−	0.597893i	$-0.796005\pi$
$617$	−77539.7	+	77539.7i	−0.203683	+	0.203683i	0.597893	+	0.801576i	$0.296005\pi$
$618$	126373.	+	126373.i	0.330886	+	0.330886i
$619$			423255.i			1.10464i	0.833632	+	0.552320i	$0.186257\pi$
$619$			423255.i			1.10464i	−0.833632	+	0.552320i	$0.813743\pi$
$620$	−90492.6	+	190841.i	−0.235413	+	0.496464i
$621$	333118.			0.863805
$622$	39759.6	−	39759.6i	0.102769	−	0.102769i
$623$	−43710.7	−	43710.7i	−0.112619	−	0.112619i
$624$		−	123055.i		−	0.316031i
$625$	−77726.6	+	382814.i	−0.198980	+	0.980004i
$626$	510731.			1.30330
$627$	366555.	−	366555.i	0.932405	−	0.932405i
$628$	−167696.	−	167696.i	−0.425210	−	0.425210i
$629$		−	697615.i		−	1.76325i
$630$	−6524.62	−	3093.84i	−0.0164390	−	0.00779501i
$631$	232217.			0.583225			0.291612	−	0.956537i	$-0.405808\pi$
$631$	232217.			0.583225			0.291612	+	0.956537i	$0.405808\pi$
$632$	−67951.3	+	67951.3i	−0.170123	+	0.170123i
$633$	−410838.	−	410838.i	−1.02533	−	1.02533i
$634$		−	328369.i		−	0.816928i
$635$	−535418.	+	190977.i	−1.32784	+	0.473623i
$636$	−75762.8			−0.187302
$637$	−53674.1	+	53674.1i	−0.132277	+	0.132277i
$638$	−33205.6	−	33205.6i	−0.0815775	−	0.0815775i
$639$			16963.4i			0.0415442i
$640$	−12162.9	−	34099.6i	−0.0296946	−	0.0832510i
$641$	182295.			0.443668			0.221834	−	0.975084i	$-0.428796\pi$
$641$	182295.			0.443668			0.221834	+	0.975084i	$0.428796\pi$
$642$	169578.	−	169578.i	0.411433	−	0.411433i
$643$	−37597.7	−	37597.7i	−0.0909367	−	0.0909367i	0.660175	−	0.751112i	$-0.270482\pi$
$643$	−37597.7	−	37597.7i	−0.0909367	−	0.0909367i	−0.751112	+	0.660175i	$0.770482\pi$
$644$		−	65662.3i		−	0.158323i
$645$	−108734.	+	229309.i	−0.261363	+	0.551191i
$646$	−765214.			−1.83366
$647$	119710.	−	119710.i	0.285970	−	0.285970i	−0.549514	−	0.835484i	$-0.685187\pi$
$647$	119710.	−	119710.i	0.285970	−	0.285970i	0.835484	+	0.549514i	$0.185187\pi$
$648$	97343.4	+	97343.4i	0.231823	+	0.231823i
$649$			599847.i			1.42413i
$650$	247581.	+	302901.i	0.585990	+	0.716927i
$651$	−169927.			−0.400959
$652$	−39008.6	+	39008.6i	−0.0917625	+	0.0917625i
$653$	151891.	+	151891.i	0.356210	+	0.356210i	0.862414	−	0.506204i	$-0.168952\pi$
$653$	151891.	+	151891.i	0.356210	+	0.356210i	−0.506204	+	0.862414i	$0.668952\pi$
$654$			94121.9i			0.220057i
$655$	468437.	+	222123.i	1.09186	+	0.517739i
$656$	−165770.			−0.385211
$657$	−13639.9	+	13639.9i	−0.0315995	+	0.0315995i
$658$	−89061.3	−	89061.3i	−0.205701	−	0.205701i
$659$		−	477726.i		−	1.10004i	−0.835152	−	0.550019i	$-0.814620\pi$
$659$		−	477726.i		−	1.10004i	0.835152	−	0.550019i	$-0.185380\pi$
$660$	176336.	−	62896.9i	0.404812	−	0.144391i
$661$	−246683.			−0.564593			−0.282297	−	0.959327i	$-0.591096\pi$
$661$	−246683.			−0.564593			−0.282297	+	0.959327i	$0.591096\pi$
$662$	103838.	−	103838.i	0.236940	−	0.236940i
$663$	−664208.	−	664208.i	−1.51104	−	1.51104i
$664$			18323.0i			0.0415585i
$665$	86140.3	+	241501.i	0.194789	+	0.546104i
$666$	−22270.2			−0.0502083
$667$	−48290.6	+	48290.6i	−0.108545	+	0.108545i
$668$	−141612.	−	141612.i	−0.317355	−	0.317355i
$669$			197405.i			0.441068i
$670$	150362.	−	317100.i	0.334957	−	0.706394i
$671$	−420142.			−0.933149
$672$	20596.4	−	20596.4i	0.0456091	−	0.0456091i
$673$	−595935.	−	595935.i	−1.31574	−	1.31574i	−0.917116	−	0.398620i	$-0.869489\pi$
$673$	−595935.	−	595935.i	−1.31574	−	1.31574i	−0.398620	−	0.917116i	$-0.630511\pi$
$674$		−	397387.i		−	0.874770i
$675$	−467431.	−	46974.4i	−1.02591	−	0.103099i
$676$	163309.			0.357368
$677$	631754.	−	631754.i	1.37839	−	1.37839i	0.531039	−	0.847347i	$-0.321802\pi$
$677$	631754.	−	631754.i	1.37839	−	1.37839i	0.847347	−	0.531039i	$-0.178198\pi$
$678$	167578.	+	167578.i	0.364549	+	0.364549i
$679$			180314.i			0.391102i
$680$	−249709.	−	118407.i	−0.540029	−	0.256071i
$681$	−612723.			−1.32120
$682$	−227560.	+	227560.i	−0.489245	+	0.489245i
$683$	−178850.	−	178850.i	−0.383397	−	0.383397i	0.488928	−	0.872324i	$-0.337388\pi$
$683$	−178850.	−	178850.i	−0.383397	−	0.383397i	−0.872324	+	0.488928i	$0.837388\pi$
$684$			24428.2i			0.0522131i
$685$	2137.88	−	762.556i	0.00455620	−	0.00162514i
$686$	−17967.4			−0.0381802
$687$	341866.	−	341866.i	0.724341	−	0.724341i
$688$	52875.4	+	52875.4i	0.111706	+	0.111706i
$689$		−	241223.i		−	0.508136i
$690$	−91470.2	−	256444.i	−0.192124	−	0.538634i
$691$	−280026.			−0.586466			−0.293233	−	0.956041i	$-0.594731\pi$
$691$	−280026.			−0.586466			−0.293233	+	0.956041i	$0.594731\pi$
$692$	−297953.	+	297953.i	−0.622208	+	0.622208i
$693$	−7780.00	−	7780.00i	−0.0161999	−	0.0161999i
$694$		−	349592.i		−	0.725843i
$695$	129335.	−	272756.i	0.267760	−	0.564682i
$696$	−30294.7			−0.0625386
$697$	−894772.	+	894772.i	−1.84182	+	1.84182i
$698$	88966.6	+	88966.6i	0.182606	+	0.182606i
$699$			5877.63i			0.0120295i
$700$	−9259.31	+	92137.2i	−0.0188966	+	0.188035i
$701$	752353.			1.53104			0.765519	−	0.643414i	$-0.222482\pi$
$701$	752353.			1.53104			0.765519	+	0.643414i	$0.222482\pi$
$702$	−332686.	+	332686.i	−0.675088	+	0.675088i
$703$	559162.	+	559162.i	1.13143	+	1.13143i
$704$		−	55163.8i		−	0.111303i
$705$	−471894.	−	223762.i	−0.949437	−	0.450203i
$706$	−232948.			−0.467359
$707$	115830.	−	115830.i	0.231730	−	0.231730i
$708$	273631.	+	273631.i	0.545881	+	0.545881i
$709$			752530.i			1.49703i	0.663116	+	0.748517i	$0.269234\pi$
$709$			752530.i			1.49703i	−0.663116	+	0.748517i	$0.730766\pi$
$710$	204893.	−	73082.9i	0.406454	−	0.144977i
$711$	23417.6			0.0463236
$712$	−53404.2	+	53404.2i	−0.105345	+	0.105345i
$713$	330937.	+	330937.i	0.650978	+	0.650978i
$714$		−	222344.i		−	0.436144i
$715$	200259.	+	561441.i	0.391723	+	1.09823i
$716$	77394.4			0.150968
$717$	284079.	−	284079.i	0.552587	−	0.552587i
$718$	−56709.6	−	56709.6i	−0.110004	−	0.110004i
$719$			384030.i			0.742860i	0.928461	+	0.371430i	$0.121132\pi$
$719$			384030.i			0.742860i	−0.928461	+	0.371430i	$0.878868\pi$
$720$	−3779.95	+	7971.56i	−0.00729156	+	0.0153772i
$721$	−134691.			−0.259100
$722$	352703.	−	352703.i	0.676604	−	0.676604i
$723$	264841.	+	264841.i	0.506651	+	0.506651i
$724$			239704.i			0.457297i
$725$	74570.9	−	60951.6i	0.141871	−	0.115960i
$726$	−74526.6			−0.141396
$727$	−237063.	+	237063.i	−0.448533	+	0.448533i	−0.894867	−	0.446334i	$-0.852729\pi$
$727$	−237063.	+	237063.i	−0.448533	+	0.448533i	0.446334	+	0.894867i	$0.352729\pi$
$728$	65577.1	+	65577.1i	0.123734	+	0.123734i
$729$		−	562525.i		−	1.05849i
$730$	223515.	+	105986.i	0.419431	+	0.198885i
$731$	570808.			1.06821
$732$	−191655.	+	191655.i	−0.357683	+	0.357683i
$733$	−10628.5	−	10628.5i	−0.0197817	−	0.0197817i	0.697147	−	0.716928i	$-0.254453\pi$
$733$	−10628.5	−	10628.5i	−0.0197817	−	0.0197817i	−0.716928	+	0.697147i	$0.754453\pi$
$734$		−	473130.i		−	0.878191i
$735$	−70171.7	+	25029.3i	−0.129893	+	0.0463313i
$736$	−80224.0			−0.148098
$737$	378113.	−	378113.i	0.696123	−	0.696123i
$738$	28564.1	+	28564.1i	0.0524455	+	0.0524455i
$739$		−	932369.i		−	1.70726i	−0.520882	−	0.853629i	$-0.674397\pi$
$739$		−	932369.i		−	1.70726i	0.520882	−	0.853629i	$-0.325603\pi$
$740$	95946.1	+	268992.i	0.175212	+	0.491220i
$741$	1.06477e6			1.93919
$742$	40374.8	−	40374.8i	0.0733334	−	0.0733334i
$743$	518896.	+	518896.i	0.939946	+	0.939946i	0.998296	−	0.0583506i	$-0.0185841\pi$
$743$	518896.	+	518896.i	0.939946	+	0.939946i	−0.0583506	+	0.998296i	$0.518584\pi$
$744$			207611.i			0.375063i
$745$	−159229.	+	335800.i	−0.286887	+	0.605018i
$746$	−54537.0			−0.0979971
$747$	3157.25	−	3157.25i	0.00565807	−	0.00565807i
$748$	−297755.	−	297755.i	−0.532177	−	0.532177i
$749$			180739.i			0.322173i
$750$	92188.6	+	372740.i	0.163891	+	0.662648i
$751$	636485.			1.12852			0.564259	−	0.825598i	$-0.309162\pi$
$751$	636485.			1.12852			0.564259	+	0.825598i	$0.309162\pi$
$752$	−108812.	+	108812.i	−0.192416	+	0.192416i
$753$	499247.	+	499247.i	0.880492	+	0.880492i
$754$		−	96455.8i		−	0.169662i
$755$	−729878.	−	346093.i	−1.28043	−	0.607154i
$756$	−111367.			−0.194856
$757$	−83206.5	+	83206.5i	−0.145200	+	0.145200i	−0.775970	−	0.630770i	$-0.782739\pi$
$757$	−83206.5	+	83206.5i	−0.145200	+	0.145200i	0.630770	+	0.775970i	$0.282739\pi$
$758$	−438052.	−	438052.i	−0.762408	−	0.762408i
$759$		−	414855.i		−	0.720133i
$760$	295058.	−	105243.i	0.510834	−	0.182208i
$761$	861240.			1.48715			0.743575	−	0.668653i	$-0.233129\pi$
$761$	861240.			1.48715			0.743575	+	0.668653i	$0.233129\pi$
$762$	−395113.	+	395113.i	−0.680474	+	0.680474i
$763$	−50158.5	−	50158.5i	−0.0861579	−	0.0861579i
$764$			103484.i			0.177291i
$765$	22624.9	+	63430.7i	0.0386602	+	0.108387i
$766$	−152577.			−0.260034
$767$	−871218.	+	871218.i	−1.48094	+	1.48094i
$768$	−25163.9	−	25163.9i	−0.0426634	−	0.0426634i
$769$			805835.i			1.36268i	0.731968	+	0.681339i	$0.238602\pi$
$769$			805835.i			1.36268i	−0.731968	+	0.681339i	$0.761398\pi$
$770$	−60453.0	+	127490.i	−0.101961	+	0.215027i
$771$	614852.			1.03434
$772$	−411565.	+	411565.i	−0.690564	+	0.690564i
$773$	526804.	+	526804.i	0.881638	+	0.881638i	0.993701	−	0.112064i	$-0.0357460\pi$
$773$	526804.	+	526804.i	0.881638	+	0.881638i	−0.112064	+	0.993701i	$0.535746\pi$
$774$		−	18222.1i		−	0.0304170i
$775$	−417704.	−	511037.i	−0.695448	−	0.850842i
$776$	220301.			0.365842
$777$	−162473.	+	162473.i	−0.269115	+	0.269115i
$778$	314812.	+	314812.i	0.520107	+	0.520107i
$779$		−	1.43438e6i		−	2.36368i
$780$	347463.	+	164759.i	0.571109	+	0.270808i
$781$	331461.			0.543413
$782$	−433022.	+	433022.i	−0.708103	+	0.708103i
$783$	81903.5	+	81903.5i	0.133592	+	0.133592i
$784$			21952.0i			0.0357143i
$785$	698043.	−	248983.i	1.13277	−	0.404046i
$786$	509601.			0.824869
$787$	772636.	−	772636.i	1.24746	−	1.24746i	0.290618	−	0.956839i	$-0.406139\pi$
$787$	772636.	−	772636.i	1.24746	−	1.24746i	0.956839	−	0.290618i	$-0.0938609\pi$
$788$	−414996.	−	414996.i	−0.668330	−	0.668330i
$789$		−	540726.i		−	0.868607i
$790$	−100889.	−	282851.i	−0.161656	−	0.453214i
$791$	−178607.			−0.285461
$792$	−9505.34	+	9505.34i	−0.0151537	+	0.0151537i
$793$	−610215.	−	610215.i	−0.970368	−	0.970368i
$794$			525010.i			0.832772i
$795$	101440.	−	213927.i	0.160499	−	0.338479i
$796$	53737.9			0.0848115
$797$	163306.	−	163306.i	0.257091	−	0.257091i	−0.566779	−	0.823870i	$-0.691811\pi$
$797$	163306.	−	163306.i	0.257091	−	0.257091i	0.823870	+	0.566779i	$0.191811\pi$
$798$	178216.	+	178216.i	0.279861	+	0.279861i
$799$			1.17466e6i			1.84001i
$800$	112570.	+	11312.7i	0.175891	+	0.0176761i
$801$	18404.3			0.0286850
$802$	−205436.	+	205436.i	−0.319394	+	0.319394i
$803$	266521.	+	266521.i	0.413333	+	0.413333i
$804$		−	344965.i		−	0.533659i
$805$	185407.	+	87916.0i	0.286110	+	0.135668i
$806$	−661016.			−1.01752
$807$	−512743.	+	512743.i	−0.787323	+	0.787323i
$808$	−141517.	−	141517.i	−0.216763	−	0.216763i
$809$			147585.i			0.225499i	0.993623	+	0.112750i	$0.0359658\pi$
$809$			147585.i			0.225499i	−0.993623	+	0.112750i	$0.964034\pi$
$810$	−405197.	+	144529.i	−0.617584	+	0.220284i
$811$	−698858.			−1.06255			−0.531273	−	0.847201i	$-0.678286\pi$
$811$	−698858.			−1.06255			−0.531273	+	0.847201i	$0.678286\pi$
$812$	16144.3	−	16144.3i	0.0244855	−	0.0244855i
$813$	−143485.	−	143485.i	−0.217083	−	0.217083i
$814$			435155.i			0.656742i
$815$	−57917.2	−	162375.i	−0.0871951	−	0.244458i
$816$	−271653.			−0.407975
$817$	−457521.	+	457521.i	−0.685437	+	0.685437i
$818$	282757.	+	282757.i	0.422578	+	0.422578i
$819$		−	22599.4i		−	0.0336921i
$820$	221952.	−	468076.i	0.330089	−	0.696127i
$821$	−704426.			−1.04508			−0.522540	−	0.852615i	$-0.675015\pi$
$821$	−704426.			−1.04508			−0.522540	+	0.852615i	$0.675015\pi$
$822$	1577.66	−	1577.66i	0.00233490	−	0.00233490i
$823$	−111438.	−	111438.i	−0.164525	−	0.164525i	0.620043	−	0.784568i	$-0.287115\pi$
$823$	−111438.	−	111438.i	−0.164525	−	0.164525i	−0.784568	+	0.620043i	$0.787115\pi$
$824$			164561.i			0.242366i
$825$	−58500.4	+	582124.i	−0.0859510	+	0.855278i
$826$	−291641.			−0.427453
$827$	214175.	−	214175.i	0.313154	−	0.313154i	−0.532976	−	0.846130i	$-0.678926\pi$
$827$	214175.	−	214175.i	0.313154	−	0.313154i	0.846130	+	0.532976i	$0.178926\pi$
$828$	13823.5	+	13823.5i	0.0201631	+	0.0201631i
$829$		−	1.24165e6i		−	1.80671i	−0.428890	−	0.903357i	$-0.641095\pi$
$829$		−	1.24165e6i		−	1.80671i	0.428890	−	0.903357i	$-0.358905\pi$
$830$	−51737.4	−	24532.8i	−0.0751015	−	0.0356116i
$831$	−868458.			−1.25761
$832$	80119.9	−	80119.9i	0.115743	−	0.115743i
$833$	118489.	+	118489.i	0.170761	+	0.170761i
$834$		−	296724.i		−	0.426600i
$835$	589465.	−	210255.i	0.845445	−	0.301559i
$836$	477322.			0.682965
$837$	561288.	−	561288.i	0.801189	−	0.801189i
$838$	−333797.	−	333797.i	−0.475328	−	0.475328i
$839$		−	69636.9i		−	0.0989271i	−0.998776	−	0.0494635i	$-0.984249\pi$
$839$		−	69636.9i		−	0.0989271i	0.998776	−	0.0494635i	$-0.0157512\pi$
$840$	30580.0	+	85733.4i	0.0433390	+	0.121504i
$841$	683535.			0.966426
$842$	−164989.	+	164989.i	−0.232719	+	0.232719i
$843$	555651.	+	555651.i	0.781892	+	0.781892i
$844$		−	534985.i		−	0.751030i
$845$	−218656.	+	461125.i	−0.306230	+	0.645811i
$846$	37499.1			0.0523938
$847$	39716.0	−	39716.0i	0.0553603	−	0.0553603i
$848$	−49328.5	−	49328.5i	−0.0685972	−	0.0685972i
$849$			213043.i			0.295564i
$850$	668677.	−	546553.i	0.925505	−	0.756475i
$851$	632840.			0.873846
$852$	151202.	−	151202.i	0.208294	−	0.208294i
$853$	−49839.7	−	49839.7i	−0.0684980	−	0.0684980i	0.672028	−	0.740526i	$-0.265423\pi$
$853$	−49839.7	−	49839.7i	−0.0684980	−	0.0684980i	−0.740526	+	0.672028i	$0.765423\pi$
$854$		−	204270.i		−	0.280084i
$855$	−68976.4	−	32707.2i	−0.0943558	−	0.0447415i
$856$	220821.			0.301365
$857$	−241696.	+	241696.i	−0.329085	+	0.329085i	−0.852239	−	0.523153i	$-0.824755\pi$
$857$	−241696.	+	241696.i	−0.329085	+	0.329085i	0.523153	+	0.852239i	$0.324755\pi$
$858$	414317.	+	414317.i	0.562805	+	0.562805i
$859$			623485.i			0.844967i	0.906371	+	0.422484i	$0.138842\pi$
$859$			623485.i			0.844967i	−0.906371	+	0.422484i	$0.861158\pi$
$860$	−220097.	+	78505.7i	−0.297589	+	0.106146i
$861$	416780.			0.562213
$862$	393327.	−	393327.i	0.529346	−	0.529346i
$863$	−510908.	−	510908.i	−0.685995	−	0.685995i	0.275349	−	0.961344i	$-0.411207\pi$
$863$	−510908.	−	510908.i	−0.685995	−	0.685995i	−0.961344	+	0.275349i	$0.911207\pi$
$864$			136064.i			0.182271i
$865$	−442379.	−	1.24024e6i	−0.591238	−	1.65758i
$866$	242029.			0.322725
$867$	−953175.	+	953175.i	−1.26804	+	1.26804i
$868$	−110638.	−	110638.i	−0.146847	−	0.146847i
$869$		−	457574.i		−	0.605929i
$870$	40561.9	−	85541.3i	0.0535895	−	0.113015i
$871$	1.09834e6			1.44778
$872$	−61281.9	+	61281.9i	−0.0805934	+	0.0805934i
$873$	−37960.4	−	37960.4i	−0.0498084	−	0.0498084i
$874$		−	694163.i		−	0.908738i
$875$	−247765.	−	149508.i	−0.323611	−	0.195276i
$876$	243156.			0.316867
$877$	25852.8	−	25852.8i	0.0336131	−	0.0336131i	−0.690100	−	0.723714i	$-0.742434\pi$
$877$	25852.8	−	25852.8i	0.0336131	−	0.0336131i	0.723714	+	0.690100i	$0.242434\pi$
$878$	503352.	+	503352.i	0.652954	+	0.652954i
$879$			709466.i			0.918236i
$880$	155763.	+	73859.4i	0.201140	+	0.0953762i
$881$	−580513.			−0.747929			−0.373965	−	0.927443i	$-0.622002\pi$
$881$	−580513.			−0.747929			−0.373965	+	0.927443i	$0.622002\pi$
$882$	3782.58	−	3782.58i	0.00486240	−	0.00486240i
$883$	144540.	+	144540.i	0.185382	+	0.185382i	0.793696	−	0.608314i	$-0.208154\pi$
$883$	144540.	+	144540.i	0.185382	+	0.185382i	−0.608314	+	0.793696i	$0.708154\pi$
$884$		−	864920.i		−	1.10681i
$885$	−1.13900e6	+	406267.i	−1.45425	+	0.518711i
$886$	161419.			0.205630
$887$	−636225.	+	636225.i	−0.808656	+	0.808656i	−0.984430	−	0.175774i	$-0.943757\pi$
$887$	−636225.	+	636225.i	−0.808656	+	0.808656i	0.175774	+	0.984430i	$0.443757\pi$
$888$	198504.	+	198504.i	0.251734	+	0.251734i
$889$		−	421119.i		−	0.532846i
$890$	−79290.7	−	222298.i	−0.100102	−	0.280643i
$891$	−655497.			−0.825686
$892$	−128529.	+	128529.i	−0.161536	+	0.161536i
$893$	−941530.	−	941530.i	−1.18068	−	1.18068i
$894$			365308.i			0.457072i
$895$	−103624.	+	218534.i	−0.129365	+	0.272818i
$896$	26820.2			0.0334077
$897$	602536.	−	602536.i	0.748855	−	0.748855i
$898$	70205.0	+	70205.0i	0.0870594	+	0.0870594i
$899$			162734.i			0.201354i
$900$	−17447.8	−	21346.4i	−0.0215405	−	0.0263536i
$901$	−532517.			−0.655970
$902$	558137.	−	558137.i	0.686005	−	0.686005i
$903$	−132940.	−	132940.i	−0.163034	−	0.163034i
$904$			218216.i			0.267024i
$905$	−676837.	−	320942.i	−0.826394	−	0.391859i
$906$	−794016.			−0.967326
$907$	−139811.	+	139811.i	−0.169952	+	0.169952i	−0.786958	−	0.617006i	$-0.788345\pi$
$907$	−139811.	+	139811.i	−0.169952	+	0.169952i	0.617006	+	0.786958i	$0.288345\pi$
$908$	−398939.	−	398939.i	−0.483876	−	0.483876i
$909$			48770.0i			0.0590235i
$910$	−272968.	+	97364.3i	−0.329632	+	0.117575i
$911$	46524.9			0.0560595			0.0280297	−	0.999607i	$-0.491077\pi$
$911$	46524.9			0.0560595			0.0280297	+	0.999607i	$0.491077\pi$
$912$	217739.	−	217739.i	0.261786	−	0.261786i
$913$	−61692.1	−	61692.1i	−0.0740096	−	0.0740096i
$914$		−	70675.1i		−	0.0846007i
$915$	−284556.	−	797775.i	−0.339880	−	0.952880i
$916$	445172.			0.530563
$917$	−271571.	+	271571.i	−0.322957	+	0.322957i
$918$	734430.	+	734430.i	0.871495	+	0.871495i
$919$			1.47894e6i			1.75113i	0.483099	+	0.875566i	$0.339511\pi$
$919$			1.47894e6i			1.75113i	−0.483099	+	0.875566i	$0.660489\pi$
$920$	107413.	−	226524.i	0.126905	−	0.267632i
$921$	269693.			0.317944
$922$	−622572.	+	622572.i	−0.732365	+	0.732365i
$923$	481414.	+	481414.i	0.565087	+	0.565087i
$924$			138693.i			0.162446i
$925$	−888000.	−	89239.4i	−1.03784	−	0.104297i
$926$	273330.			0.318761
$927$	28355.7	−	28355.7i	0.0329975	−	0.0329975i
$928$	−19724.6	−	19724.6i	−0.0229040	−	0.0229040i
$929$			489931.i			0.567679i	0.958872	+	0.283840i	$0.0916084\pi$
$929$			489931.i			0.567679i	−0.958872	+	0.283840i	$0.908392\pi$
$930$	−586218.	−	277972.i	−0.677787	−	0.321392i
$931$	−189947.			−0.219145
$932$	−3826.87	+	3826.87i	−0.00440567	+	0.00440567i
$933$	122132.	+	122132.i	0.140303	+	0.140303i
$934$		−	68651.1i		−	0.0786962i
$935$	1.23942e6	−	442086.i	1.41774	−	0.505689i
$936$	−27611.1			−0.0315161
$937$	−338504.	+	338504.i	−0.385553	+	0.385553i	−0.873098	−	0.487545i	$-0.837893\pi$
$937$	−338504.	+	338504.i	−0.385553	+	0.385553i	0.487545	+	0.873098i	$0.337893\pi$
$938$	183836.	+	183836.i	0.208941	+	0.208941i
$939$			1.56885e6i			1.77930i
$940$	−161556.	−	452936.i	−0.182839	−	0.512603i
$941$	−1.11345e6			−1.25746			−0.628728	−	0.777625i	$-0.716424\pi$
$941$	−1.11345e6			−1.25746			−0.628728	+	0.777625i	$0.716424\pi$
$942$	515123.	−	515123.i	0.580509	−	0.580509i
$943$	−811691.	−	811691.i	−0.912783	−	0.912783i
$944$			356317.i			0.399846i
$945$	149111.	−	314460.i	0.166972	−	0.352129i
$946$	−356056.			−0.397865
$947$	12469.5	−	12469.5i	0.0139043	−	0.0139043i	−0.700120	−	0.714025i	$-0.746870\pi$
$947$	12469.5	−	12469.5i	0.0139043	−	0.0139043i	0.714025	+	0.700120i	$0.246870\pi$
$948$	−208731.	−	208731.i	−0.232257	−	0.232257i
$949$			774190.i			0.859637i
$950$	−97886.8	+	974048.i	−0.108462	+	1.07928i
$951$	1.00867e6			1.11529
$952$	144766.	−	144766.i	0.159733	−	0.159733i
$953$	−352000.	−	352000.i	−0.387576	−	0.387576i	0.486246	−	0.873822i	$-0.338366\pi$
$953$	−352000.	−	352000.i	−0.387576	−	0.387576i	−0.873822	+	0.486246i	$0.838366\pi$
$954$			16999.7i			0.0186786i
$955$	−292201.	−	138556.i	−0.320387	−	0.151921i
$956$	369923.			0.404758
$957$	102000.	−	102000.i	0.111372	−	0.111372i
$958$	−53710.3	−	53710.3i	−0.0585230	−	0.0585230i
$959$			1681.50i			0.00182835i
$960$	104746.	−	37361.6i	0.113657	−	0.0405399i
$961$	191705.			0.207581
$962$	−632019.	+	632019.i	−0.682936	+	0.682936i
$963$	−38050.0	−	38050.0i	−0.0410301	−	0.0410301i
$964$			344872.i			0.371111i
$965$	−611063.	−	1.71316e6i	−0.656192	−	1.83969i
$966$	201699.			0.216148
$967$	218321.	−	218321.i	0.233476	−	0.233476i	−0.580666	−	0.814142i	$-0.697208\pi$
$967$	218321.	−	218321.i	0.233476	−	0.233476i	0.814142	+	0.580666i	$0.197208\pi$
$968$	−48523.6	−	48523.6i	−0.0517848	−	0.0517848i
$969$		−	2.35056e6i		−	2.50336i
$970$	−294964.	+	622052.i	−0.313491	+	0.661124i
$971$	−1.31269e6			−1.39227			−0.696134	−	0.717912i	$-0.745098\pi$
$971$	−1.31269e6			−1.39227			−0.696134	+	0.717912i	$0.745098\pi$
$972$	45396.6	−	45396.6i	0.0480497	−	0.0480497i
$973$	158127.	+	158127.i	0.167025	+	0.167025i
$974$		−	592178.i		−	0.624216i
$975$	−930443.	+	760511.i	−0.978770	+	0.800011i
$976$	−249570.			−0.261995
$977$	288983.	−	288983.i	0.302749	−	0.302749i	−0.539339	−	0.842089i	$-0.681326\pi$
$977$	288983.	−	288983.i	0.302749	−	0.302749i	0.842089	+	0.539339i	$0.181326\pi$
$978$	−119825.	−	119825.i	−0.125277	−	0.125277i
$979$		−	359616.i		−	0.375209i
$980$	−61984.5	−	29391.8i	−0.0645403	−	0.0306037i
$981$	21119.1			0.0219451
$982$	530311.	−	530311.i	0.549930	−	0.549930i
$983$	748916.	+	748916.i	0.775043	+	0.775043i	0.978983	−	0.203940i	$-0.0653749\pi$
$983$	748916.	+	748916.i	0.775043	+	0.775043i	−0.203940	+	0.978983i	$0.565375\pi$
$984$		−	509208.i		−	0.525902i
$985$	1.72744e6	−	616156.i	1.78045	−	0.635065i
$986$	−212933.			−0.219023
$987$	273576.	−	273576.i	0.280830	−	0.280830i
$988$	693263.	+	693263.i	0.710205	+	0.710205i
$989$			517807.i			0.529390i
$990$	−14112.9	−	39566.5i	−0.0143994	−	0.0403698i
$991$	122183.			0.124412			0.0622062	−	0.998063i	$-0.480186\pi$
$991$	122183.			0.124412			0.0622062	+	0.998063i	$0.480186\pi$
$992$	−135173.	+	135173.i	−0.137362	+	0.137362i
$993$	318965.	+	318965.i	0.323477	+	0.323477i
$994$			161154.i			0.163105i
$995$	−71950.3	+	151737.i	−0.0726752	+	0.153265i
$996$	−56283.9			−0.0567369
$997$	245978.	−	245978.i	0.247461	−	0.247461i	−0.572467	−	0.819928i	$-0.694013\pi$
$997$	245978.	−	245978.i	0.247461	−	0.247461i	0.819928	+	0.572467i	$0.194013\pi$
$998$	725662.	+	725662.i	0.728574	+	0.728574i
$999$		−	1.07333e6i		−	1.07548i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.5.f.a.43.3	✓	12
5.2	odd	4	inner	70.5.f.a.57.3	yes	12
5.3	odd	4		350.5.f.d.57.4		12
5.4	even	2		350.5.f.d.43.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.5.f.a.43.3	✓	12	1.1	even	1	trivial
70.5.f.a.57.3	yes	12	5.2	odd	4	inner
350.5.f.d.43.4		12	5.4	even	2
350.5.f.d.57.4		12	5.3	odd	4

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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	70.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 2.00000i) q^{2} +(-6.14353 - 6.14353i) q^{3} -8.00000i q^{4} +(22.5891 + 10.7113i) q^{5} +24.5741 q^{6} +(-13.0958 + 13.0958i) q^{7} +(16.0000 + 16.0000i) q^{8} -5.51396i q^{9} +(-66.6008 + 23.7557i) q^{10} -107.742 q^{11} +(-49.1483 + 49.1483i) q^{12} +(-156.484 - 156.484i) q^{13} -52.3832i q^{14} +(-72.9719 - 204.582i) q^{15} -64.0000 q^{16} +(-345.450 + 345.450i) q^{17} +(11.0279 + 11.0279i) q^{18} -553.780i q^{19} +(85.6903 - 180.713i) q^{20} +160.909 q^{21} +(215.483 - 215.483i) q^{22} +(-313.375 - 313.375i) q^{23} -196.593i q^{24} +(395.537 + 483.917i) q^{25} +625.937 q^{26} +(-531.502 + 531.502i) q^{27} +(104.766 + 104.766i) q^{28} -154.098i q^{29} +(555.108 + 263.221i) q^{30} -1056.04 q^{31} +(128.000 - 128.000i) q^{32} +(661.915 + 661.915i) q^{33} -1381.80i q^{34} +(-436.096 + 155.550i) q^{35} -44.1117 q^{36} +(-1009.72 + 1009.72i) q^{37} +(1107.56 + 1107.56i) q^{38} +1922.73i q^{39} +(190.045 + 532.807i) q^{40} +2590.16 q^{41} +(-321.818 + 321.818i) q^{42} +(-826.179 - 826.179i) q^{43} +861.934i q^{44} +(59.0617 - 124.556i) q^{45} +1253.50 q^{46} +(1700.19 - 1700.19i) q^{47} +(393.186 + 393.186i) q^{48} -343.000i q^{49} +(-1758.91 - 176.761i) q^{50} +4244.57 q^{51} +(-1251.87 + 1251.87i) q^{52} +(770.758 + 770.758i) q^{53} -2126.01i q^{54} +(-2433.79 - 1154.05i) q^{55} -419.066 q^{56} +(-3402.17 + 3402.17i) q^{57} +(308.197 + 308.197i) q^{58} -5567.45i q^{59} +(-1636.66 + 583.775i) q^{60} +3899.53 q^{61} +(2112.09 - 2112.09i) q^{62} +(72.2098 + 72.2098i) q^{63} +512.000i q^{64} +(-1858.69 - 5210.99i) q^{65} -2647.66 q^{66} +(-3509.44 + 3509.44i) q^{67} +(2763.60 + 2763.60i) q^{68} +3850.46i q^{69} +(561.092 - 1183.29i) q^{70} -3076.44 q^{71} +(88.2234 - 88.2234i) q^{72} +(-2473.70 - 2473.70i) q^{73} -4038.87i q^{74} +(542.969 - 5402.95i) q^{75} -4430.24 q^{76} +(1410.96 - 1410.96i) q^{77} +(-3845.46 - 3845.46i) q^{78} +4246.96i q^{79} +(-1445.70 - 685.522i) q^{80} +6083.97 q^{81} +(-5180.32 + 5180.32i) q^{82} +(572.593 + 572.593i) q^{83} -1287.27i q^{84} +(-11503.6 + 4103.20i) q^{85} +3304.72 q^{86} +(-946.709 + 946.709i) q^{87} +(-1723.87 - 1723.87i) q^{88} +3337.76i q^{89} +(130.988 + 367.235i) q^{90} +4098.57 q^{91} +(-2507.00 + 2507.00i) q^{92} +(6487.83 + 6487.83i) q^{93} +6800.75i q^{94} +(5931.70 - 12509.4i) q^{95} -1572.74 q^{96} +(6884.42 - 6884.42i) q^{97} +(686.000 + 686.000i) q^{98} +594.084i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{2} - 20 q^{3} + 8 q^{5} + 80 q^{6} + 192 q^{8} - 144 q^{10} + 4 q^{11} - 160 q^{12} - 180 q^{13} - 736 q^{15} - 768 q^{16} - 236 q^{17} - 464 q^{18} + 512 q^{20} - 196 q^{21} - 8 q^{22} - 1232 q^{23}+ \cdots + 8232 q^{98}+O(q^{100}) \) 12 * q - 24 * q^2 - 20 * q^3 + 8 * q^5 + 80 * q^6 + 192 * q^8 - 144 * q^10 + 4 * q^11 - 160 * q^12 - 180 * q^13 - 736 * q^15 - 768 * q^16 - 236 * q^17 - 464 * q^18 + 512 * q^20 - 196 * q^21 - 8 * q^22 - 1232 * q^23 + 944 * q^25 + 720 * q^26 - 908 * q^27 - 632 * q^30 - 992 * q^31 + 1536 * q^32 + 6268 * q^33 - 784 * q^35 + 1856 * q^36 + 2200 * q^37 - 2880 * q^38 - 896 * q^40 + 176 * q^41 + 392 * q^42 + 1436 * q^43 + 3436 * q^45 + 4928 * q^46 + 5708 * q^47 + 1280 * q^48 - 1352 * q^50 + 6028 * q^51 - 1440 * q^52 - 9868 * q^53 - 7036 * q^55 - 5676 * q^57 - 4376 * q^58 + 8416 * q^60 - 1512 * q^61 + 1984 * q^62 - 3920 * q^63 + 7888 * q^65 - 25072 * q^66 - 11340 * q^67 + 1888 * q^68 + 4312 * q^70 - 14544 * q^71 - 3712 * q^72 + 24744 * q^73 - 6468 * q^75 + 11520 * q^76 - 9016 * q^77 + 10152 * q^78 - 512 * q^80 + 15740 * q^81 - 352 * q^82 - 30368 * q^83 - 27972 * q^85 - 5744 * q^86 + 2084 * q^87 + 64 * q^88 - 5168 * q^90 + 11172 * q^91 - 9856 * q^92 + 34508 * q^93 + 30436 * q^95 - 5120 * q^96 + 56180 * q^97 + 8232 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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