LMFDB - Embedded newform 70.5.f.a.57.3

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)

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")

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);

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			57.3
Root			$1.27116i$ of defining polynomial
Character	$\chi$	$=$	70.57
Dual form			70.5.f.a.43.3

$q$-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 $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

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

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	−0.960589	−	0.277974i	$-0.910337\pi$
$3$	−6.14353	+	6.14353i	−0.682615	+	0.682615i	0.277974	+	0.960589i	$0.410337\pi$
$4$			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	−0.997441	−	0.0714989i	$-0.977222\pi$
$13$	−156.484	+	156.484i	−0.925942	+	0.925942i	0.0714989	+	0.997441i	$0.477222\pi$
$14$			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	−0.975549	−	0.219781i	$-0.929466\pi$
$17$	−345.450	−	345.450i	−1.19533	−	1.19533i	−0.219781	−	0.975549i	$-0.570534\pi$
$18$	11.0279	−	11.0279i	0.0340368	−	0.0340368i
$19$			553.780i			1.53402i	0.641637	+	0.767009i	$0.278256\pi$
$19$			553.780i			1.53402i	−0.641637	+	0.767009i	$0.721744\pi$
$20$	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	−0.938277	−	0.345886i	$-0.887579\pi$
$23$	−313.375	+	313.375i	−0.592391	+	0.592391i	0.345886	+	0.938277i	$0.387579\pi$
$24$			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	$0.0292033\pi$
$29$			154.098i			0.183232i	−0.995794	+	0.0916162i	$0.970797\pi$
$30$	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	0.234546	−	0.972105i	$-0.424640\pi$
$37$	−1009.72	−	1009.72i	−0.737559	−	0.737559i	−0.972105	+	0.234546i	$0.924640\pi$
$38$	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	−0.894298	−	0.447473i	$-0.852324\pi$
$43$	−826.179	+	826.179i	−0.446825	+	0.446825i	0.447473	+	0.894298i	$0.352324\pi$
$44$		−	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	0.978047	−	0.208383i	$-0.0668201\pi$
$47$	1700.19	+	1700.19i	0.769664	+	0.769664i	−0.208383	+	0.978047i	$0.566820\pi$
$48$	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	−0.556475	−	0.830864i	$-0.687847\pi$
$53$	770.758	−	770.758i	0.274389	−	0.274389i	0.830864	+	0.556475i	$0.187847\pi$
$54$			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	$0.295004\pi$
$59$			5567.45i			1.59938i	−0.600411	+	0.799692i	$0.704996\pi$
$60$	−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	0.198346	−	0.980132i	$-0.436443\pi$
$67$	−3509.44	−	3509.44i	−0.781786	−	0.781786i	−0.980132	+	0.198346i	$0.936443\pi$
$68$	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	−0.900028	−	0.435832i	$-0.856454\pi$
$73$	−2473.70	+	2473.70i	−0.464196	+	0.464196i	0.435832	+	0.900028i	$0.356454\pi$
$74$			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	$-0.889489\pi$
$79$		−	4246.96i		−	0.680493i	0.940336	−	0.340246i	$-0.110511\pi$
$80$	−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	−0.664326	−	0.747443i	$-0.731281\pi$
$83$	572.593	−	572.593i	0.0831169	−	0.0831169i	0.747443	+	0.664326i	$0.231281\pi$
$84$			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	$-0.932429\pi$
$89$		−	3337.76i		−	0.421381i	0.977553	−	0.210691i	$-0.0675713\pi$
$90$	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	0.970953	−	0.239269i	$-0.0769078\pi$
$97$	6884.42	+	6884.42i	0.731684	+	0.731684i	−0.239269	+	0.970953i	$0.576908\pi$
$98$	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	−0.421907	−	0.906639i	$-0.638639\pi$
$103$	5142.53	−	5142.53i	0.484732	−	0.484732i	0.906639	+	0.421907i	$0.138639\pi$
$104$			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	0.941036	−	0.338306i	$-0.109854\pi$
$107$	6900.66	+	6900.66i	0.602731	+	0.602731i	−0.338306	+	0.941036i	$0.609854\pi$
$108$	4252.01	−	4252.01i	0.364542	−	0.364542i
$109$		−	3830.12i		−	0.322373i	−0.986924	−	0.161187i	$-0.948468\pi$
$109$		−	3830.12i		−	0.322373i	0.986924	−	0.161187i	$-0.0515321\pi$
$110$	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	−0.387726	−	0.921775i	$-0.626739\pi$
$113$	6819.26	−	6819.26i	0.534048	−	0.534048i	0.921775	+	0.387726i	$0.126739\pi$
$114$			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	0.00313125	−	0.999995i	$-0.499003\pi$
$127$	−16078.4	−	16078.4i	−0.996864	−	0.996864i	−0.999995	+	0.00313125i	$0.999003\pi$
$128$	−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	0.708815	−	0.705394i	$-0.249230\pi$
$137$	64.1999	+	64.1999i	0.00342053	+	0.00342053i	−0.705394	+	0.708815i	$0.749230\pi$
$138$	−7700.92	+	7700.92i	−0.404375	+	0.404375i
$139$			12074.6i			0.624949i	0.949926	+	0.312475i	$0.101158\pi$
$139$			12074.6i			0.624949i	−0.949926	+	0.312475i	$0.898842\pi$
$140$	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	$-0.891333\pi$
$149$		−	14865.6i		−	0.669590i	0.942291	−	0.334795i	$-0.108667\pi$
$150$	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	0.990185	−	0.139765i	$-0.0446347\pi$
$157$	20962.0	+	20962.0i	0.850420	+	0.850420i	−0.139765	+	0.990185i	$0.544635\pi$
$158$	−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	−0.792890	−	0.609365i	$-0.791424\pi$
$163$	−4876.07	+	4876.07i	−0.183525	+	0.183525i	0.609365	+	0.792890i	$0.291424\pi$
$164$			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	0.949246	−	0.314535i	$-0.101849\pi$
$167$	17701.4	+	17701.4i	0.634711	+	0.634711i	−0.314535	+	0.949246i	$0.601849\pi$
$168$	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	−0.286265	+	0.958150i	$0.592414\pi$
$173$	−37244.1	+	37244.1i	−1.24442	+	1.24442i	−0.958150	+	0.286265i	$0.907586\pi$
$174$			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	$-0.951761\pi$
$179$		−	9674.30i		−	0.301935i	0.988539	−	0.150968i	$-0.0482389\pi$
$180$	−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	−0.538507	+	0.842621i	$0.681012\pi$
$193$	−51445.6	+	51445.6i	−1.38113	+	1.38113i	−0.842621	+	0.538507i	$0.818988\pi$
$194$		−	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	0.899273	+	0.437387i	$0.144096\pi$
$197$	51874.5	+	51874.5i	1.33666	+	1.33666i	0.437387	+	0.899273i	$0.355904\pi$
$198$	−1188.17	+	1188.17i	−0.0303073	+	0.0303073i
$199$		−	6717.24i		−	0.169623i	−0.996397	−	0.0848115i	$-0.972971\pi$
$199$		−	6717.24i		−	0.169623i	0.996397	−	0.0848115i	$-0.0270288\pi$
$200$	−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	−0.849945	−	0.526872i	$-0.823365\pi$
$223$	−16066.1	+	16066.1i	−0.323073	+	0.323073i	0.526872	+	0.849945i	$0.323365\pi$
$224$		−	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	0.999496	−	0.0317436i	$-0.0101060\pi$
$227$	49867.3	+	49867.3i	0.967752	+	0.967752i	−0.0317436	+	0.999496i	$0.510106\pi$
$228$	27217.3	−	27217.3i	0.523572	−	0.523572i
$229$		−	55646.5i		−	1.06113i	−0.847645	−	0.530563i	$-0.821980\pi$
$229$		−	55646.5i		−	1.06113i	0.847645	−	0.530563i	$-0.178020\pi$
$230$	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	−0.711499	−	0.702687i	$-0.751983\pi$
$233$	−478.359	+	478.359i	−0.00881134	+	0.00881134i	0.702687	+	0.711499i	$0.251983\pi$
$234$			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	$-0.867356\pi$
$239$		−	46240.3i		−	0.809515i	0.914424	−	0.404758i	$-0.132644\pi$
$240$	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	0.218262	−	0.975890i	$-0.429961\pi$
$257$	−50040.6	−	50040.6i	−0.757628	−	0.757628i	−0.975890	+	0.218262i	$0.929961\pi$
$258$	−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	−0.313390	−	0.949625i	$-0.601465\pi$
$263$	44007.7	−	44007.7i	0.636235	−	0.636235i	0.949625	+	0.313390i	$0.101465\pi$
$264$		−	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	$0.195658\pi$
$269$			83460.6i			1.15339i	−0.816959	+	0.576696i	$0.804342\pi$
$270$	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	0.997112	−	0.0759399i	$-0.0241957\pi$
$277$	70680.6	+	70680.6i	0.921173	+	0.921173i	−0.0759399	+	0.997112i	$0.524196\pi$
$278$	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	−0.807019	−	0.590525i	$-0.798921\pi$
$283$	−17338.8	+	17338.8i	−0.216494	+	0.216494i	0.590525	+	0.807019i	$0.298921\pi$
$284$		−	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	−0.958312	−	0.285725i	$-0.907766\pi$
$293$	−57740.9	+	57740.9i	−0.672587	+	0.672587i	0.285725	+	0.958312i	$0.407766\pi$
$294$			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	0.581010	−	0.813897i	$-0.302658\pi$
$307$	−21949.4	−	21949.4i	−0.232887	−	0.232887i	−0.813897	+	0.581010i	$0.802658\pi$
$308$	−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	−0.377143	+	0.926155i	$0.623094\pi$
$313$	−127683.	+	127683.i	−1.30330	+	1.30330i	−0.926155	+	0.377143i	$0.876906\pi$
$314$		−	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	0.168734	−	0.985662i	$-0.446032\pi$
$317$	−82092.3	−	82092.3i	−0.816928	−	0.816928i	−0.985662	+	0.168734i	$0.946032\pi$
$318$	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	0.118218	−	0.992988i	$-0.462282\pi$
$337$	−99346.7	−	99346.7i	−0.874770	−	0.874770i	−0.992988	+	0.118218i	$0.962282\pi$
$338$	−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	0.243946	−	0.969789i	$-0.421558\pi$
$347$	−87398.0	−	87398.0i	−0.725843	−	0.725843i	−0.969789	+	0.243946i	$0.921558\pi$
$348$	7573.67	−	7573.67i	0.0625386	−	0.0625386i
$349$			44483.3i			0.365213i	0.983186	+	0.182606i	$0.0584534\pi$
$349$			44483.3i			0.365213i	−0.983186	+	0.182606i	$0.941547\pi$
$350$	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	−0.433699	−	0.901058i	$-0.642792\pi$
$353$	58237.1	−	58237.1i	0.467359	−	0.467359i	0.901058	+	0.433699i	$0.142792\pi$
$354$			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	$-0.964914\pi$
$359$		−	28354.8i		−	0.220008i	0.993931	−	0.110004i	$-0.0350863\pi$
$360$	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	0.115157	−	0.993347i	$-0.463263\pi$
$367$	−118283.	−	118283.i	−0.878191	−	0.878191i	−0.993347	+	0.115157i	$0.963263\pi$
$368$	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	−0.656409	−	0.754406i	$-0.727925\pi$
$373$	13634.2	−	13634.2i	0.0979971	−	0.0979971i	0.754406	+	0.656409i	$0.227925\pi$
$374$		−	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	$-0.724017\pi$
$379$		−	219026.i		−	1.52482i	0.647097	−	0.762408i	$-0.275983\pi$
$380$	−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	−0.565034	−	0.825068i	$-0.691137\pi$
$383$	38144.2	−	38144.2i	0.260034	−	0.260034i	0.825068	+	0.565034i	$0.191137\pi$
$384$		−	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	$0.174108\pi$
$389$			157406.i			1.04021i	−0.854101	+	0.520107i	$0.825892\pi$
$390$	−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	0.987895	−	0.155123i	$-0.0495774\pi$
$397$	131252.	+	131252.i	0.832772	+	0.832772i	−0.155123	+	0.987895i	$0.549577\pi$
$398$	−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	$0.138875\pi$
$409$			141379.i			0.845157i	−0.906326	+	0.422578i	$0.861125\pi$
$410$	−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	$-0.842329\pi$
$419$		−	166898.i		−	0.950657i	0.879808	−	0.475328i	$-0.157671\pi$
$420$	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	−0.849811	−	0.527087i	$-0.823284\pi$
$433$	−60507.3	+	60507.3i	−0.322725	+	0.322725i	0.527087	+	0.849811i	$0.323284\pi$
$434$		−	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	$0.226471\pi$
$439$			251676.i			1.30591i	−0.757397	+	0.652954i	$0.773529\pi$
$440$	−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	−0.802407	−	0.596777i	$-0.796448\pi$
$443$	−40354.8	+	40354.8i	−0.205630	+	0.205630i	0.596777	+	0.802407i	$0.296448\pi$
$444$			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	$0.0277470\pi$
$449$			35102.5i			0.174119i	−0.996203	+	0.0870594i	$0.972253\pi$
$450$	−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	0.663540	−	0.748141i	$-0.269053\pi$
$457$	−17668.8	−	17668.8i	−0.0846007	−	0.0846007i	−0.748141	+	0.663540i	$0.769053\pi$
$458$	−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	−0.848291	−	0.529530i	$-0.822368\pi$
$463$	−68332.5	+	68332.5i	−0.318761	+	0.318761i	0.529530	+	0.848291i	$0.322368\pi$
$464$		−	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	0.666663	−	0.745359i	$-0.267722\pi$
$467$	−17162.8	−	17162.8i	−0.0786962	−	0.0786962i	−0.745359	+	0.666663i	$0.767722\pi$
$468$	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	$-0.981361\pi$
$479$		−	26855.2i		−	0.117046i	0.998286	−	0.0585230i	$-0.0186391\pi$
$480$	−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	0.322391	−	0.946607i	$-0.395513\pi$
$487$	−148045.	−	148045.i	−0.624216	−	0.624216i	−0.946607	+	0.322391i	$0.895513\pi$
$488$	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	$0.259816\pi$
$499$			362831.i			1.45715i	−0.684968	+	0.728574i	$0.740184\pi$
$500$	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	−0.288486	+	0.957484i	$0.593152\pi$
$503$	−315242.	+	315242.i	−1.24597	+	1.24597i	−0.957484	+	0.288486i	$0.906848\pi$
$504$		−	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	$-0.714309\pi$
$509$		−	405092.i		−	1.56357i	0.623546	−	0.781786i	$-0.285691\pi$
$510$	−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	−0.936960	−	0.349437i	$-0.886373\pi$
$523$	−160705.	+	160705.i	−0.587523	+	0.587523i	0.349437	+	0.936960i	$0.386373\pi$
$524$			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	0.709341	−	0.704865i	$-0.248993\pi$
$547$	1339.21	+	1339.21i	0.00447583	+	0.00447583i	−0.704865	+	0.709341i	$0.748993\pi$
$548$	−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	0.713632	−	0.700520i	$-0.247049\pi$
$557$	4068.01	+	4068.01i	0.0131121	+	0.0131121i	−0.700520	+	0.713632i	$0.747049\pi$
$558$	−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	0.00620147	−	0.999981i	$-0.498026\pi$
$563$	318929.	−	318929.i	1.00618	−	1.00618i	0.999981	−	0.00620147i	$-0.00197400\pi$
$564$		−	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	$0.278275\pi$
$569$			496680.i			1.53410i	−0.641590	+	0.767048i	$0.721725\pi$
$570$	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	−0.939416	−	0.342780i	$-0.888632\pi$
$577$	−426880.	−	426880.i	−1.28220	−	1.28220i	−0.342780	−	0.939416i	$-0.611368\pi$
$578$	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	0.980645	−	0.195796i	$-0.0627290\pi$
$587$	270435.	+	270435.i	0.784849	+	0.784849i	−0.195796	+	0.980645i	$0.562729\pi$
$588$	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	−0.452311	−	0.891860i	$-0.649400\pi$
$593$	154567.	−	154567.i	0.439550	−	0.439550i	0.891860	+	0.452311i	$0.149400\pi$
$594$		−	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	$-0.893820\pi$
$599$		−	234959.i		−	0.654844i	0.944878	−	0.327422i	$-0.106180\pi$
$600$	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	0.992776	+	0.119979i	$0.0382826\pi$
$607$	409993.	+	409993.i	1.11275	+	1.11275i	0.119979	+	0.992776i	$0.461717\pi$
$608$	−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	−0.115784	+	0.993274i	$0.536938\pi$
$613$	−416750.	+	416750.i	−1.10906	+	1.10906i	−0.993274	+	0.115784i	$0.963062\pi$
$614$			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	0.597893	−	0.801576i	$-0.296005\pi$
$617$	−77539.7	−	77539.7i	−0.203683	−	0.203683i	−0.801576	+	0.597893i	$0.796005\pi$
$618$	126373.	−	126373.i	0.330886	−	0.330886i
$619$		−	423255.i		−	1.10464i	−0.833632	−	0.552320i	$-0.813743\pi$
$619$		−	423255.i		−	1.10464i	0.833632	−	0.552320i	$-0.186257\pi$
$620$	−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	−0.751112	−	0.660175i	$-0.770482\pi$
$643$	−37597.7	+	37597.7i	−0.0909367	+	0.0909367i	0.660175	+	0.751112i	$0.270482\pi$
$644$			65662.3i			0.158323i
$645$	−108734.	−	229309.i	−0.261363	−	0.551191i
$646$	−765214.			−1.83366
$647$	119710.	+	119710.i	0.285970	+	0.285970i	0.835484	−	0.549514i	$-0.185187\pi$
$647$	119710.	+	119710.i	0.285970	+	0.285970i	−0.549514	+	0.835484i	$0.685187\pi$
$648$	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	−0.506204	−	0.862414i	$-0.668952\pi$
$653$	151891.	−	151891.i	0.356210	−	0.356210i	0.862414	+	0.506204i	$0.168952\pi$
$654$		−	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	$0.185380\pi$
$659$			477726.i			1.10004i	−0.835152	+	0.550019i	$0.814620\pi$
$660$	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	−0.398620	+	0.917116i	$0.630511\pi$
$673$	−595935.	+	595935.i	−1.31574	+	1.31574i	−0.917116	+	0.398620i	$0.869489\pi$
$674$			397387.i			0.874770i
$675$	−467431.	+	46974.4i	−1.02591	+	0.103099i
$676$	163309.			0.357368
$677$	631754.	+	631754.i	1.37839	+	1.37839i	0.847347	+	0.531039i	$0.178198\pi$
$677$	631754.	+	631754.i	1.37839	+	1.37839i	0.531039	+	0.847347i	$0.321802\pi$
$678$	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	−0.872324	−	0.488928i	$-0.837388\pi$
$683$	−178850.	+	178850.i	−0.383397	+	0.383397i	0.488928	+	0.872324i	$0.337388\pi$
$684$		−	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	$-0.730766\pi$
$709$		−	752530.i		−	1.49703i	0.663116	−	0.748517i	$-0.269234\pi$
$710$	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	$-0.878868\pi$
$719$		−	384030.i		−	0.742860i	0.928461	−	0.371430i	$-0.121132\pi$
$720$	−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	0.446334	−	0.894867i	$-0.352729\pi$
$727$	−237063.	−	237063.i	−0.448533	−	0.448533i	−0.894867	+	0.446334i	$0.852729\pi$
$728$	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	−0.716928	−	0.697147i	$-0.754453\pi$
$733$	−10628.5	+	10628.5i	−0.0197817	+	0.0197817i	0.697147	+	0.716928i	$0.254453\pi$
$734$			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	$0.325603\pi$
$739$			932369.i			1.70726i	−0.520882	+	0.853629i	$0.674397\pi$
$740$	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	−0.0583506	−	0.998296i	$-0.518584\pi$
$743$	518896.	−	518896.i	0.939946	−	0.939946i	0.998296	+	0.0583506i	$0.0185841\pi$
$744$		−	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	0.630770	−	0.775970i	$-0.282739\pi$
$757$	−83206.5	−	83206.5i	−0.145200	−	0.145200i	−0.775970	+	0.630770i	$0.782739\pi$
$758$	−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	$-0.761398\pi$
$769$		−	805835.i		−	1.36268i	0.731968	−	0.681339i	$-0.238602\pi$
$770$	−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	−0.112064	−	0.993701i	$-0.535746\pi$
$773$	526804.	−	526804.i	0.881638	−	0.881638i	0.993701	+	0.112064i	$0.0357460\pi$
$774$			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	0.956839	+	0.290618i	$0.0938609\pi$
$787$	772636.	+	772636.i	1.24746	+	1.24746i	0.290618	+	0.956839i	$0.406139\pi$
$788$	−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	0.823870	−	0.566779i	$-0.191811\pi$
$797$	163306.	+	163306.i	0.257091	+	0.257091i	−0.566779	+	0.823870i	$0.691811\pi$
$798$	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	$-0.964034\pi$
$809$		−	147585.i		−	0.225499i	0.993623	−	0.112750i	$-0.0359658\pi$
$810$	−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	−0.784568	−	0.620043i	$-0.787115\pi$
$823$	−111438.	+	111438.i	−0.164525	+	0.164525i	0.620043	+	0.784568i	$0.287115\pi$
$824$		−	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	0.846130	−	0.532976i	$-0.178926\pi$
$827$	214175.	+	214175.i	0.313154	+	0.313154i	−0.532976	+	0.846130i	$0.678926\pi$
$828$	13823.5	−	13823.5i	0.0201631	−	0.0201631i
$829$			1.24165e6i			1.80671i	0.428890	+	0.903357i	$0.358905\pi$
$829$			1.24165e6i			1.80671i	−0.428890	+	0.903357i	$0.641095\pi$
$830$	−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	$0.0157512\pi$
$839$			69636.9i			0.0989271i	−0.998776	+	0.0494635i	$0.984249\pi$
$840$	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	−0.740526	−	0.672028i	$-0.765423\pi$
$853$	−49839.7	+	49839.7i	−0.0684980	+	0.0684980i	0.672028	+	0.740526i	$0.265423\pi$
$854$			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	0.523153	−	0.852239i	$-0.324755\pi$
$857$	−241696.	−	241696.i	−0.329085	−	0.329085i	−0.852239	+	0.523153i	$0.824755\pi$
$858$	414317.	−	414317.i	0.562805	−	0.562805i
$859$		−	623485.i		−	0.844967i	−0.906371	−	0.422484i	$-0.861158\pi$
$859$		−	623485.i		−	0.844967i	0.906371	−	0.422484i	$-0.138842\pi$
$860$	−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	−0.961344	−	0.275349i	$-0.911207\pi$
$863$	−510908.	+	510908.i	−0.685995	+	0.685995i	0.275349	+	0.961344i	$0.411207\pi$
$864$		−	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	0.723714	−	0.690100i	$-0.242434\pi$
$877$	25852.8	+	25852.8i	0.0336131	+	0.0336131i	−0.690100	+	0.723714i	$0.742434\pi$
$878$	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	−0.608314	−	0.793696i	$-0.708154\pi$
$883$	144540.	−	144540.i	0.185382	−	0.185382i	0.793696	+	0.608314i	$0.208154\pi$
$884$			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	0.175774	−	0.984430i	$-0.443757\pi$
$887$	−636225.	−	636225.i	−0.808656	−	0.808656i	−0.984430	+	0.175774i	$0.943757\pi$
$888$	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	0.617006	−	0.786958i	$-0.288345\pi$
$907$	−139811.	−	139811.i	−0.169952	−	0.169952i	−0.786958	+	0.617006i	$0.788345\pi$
$908$	−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	$-0.660489\pi$
$919$		−	1.47894e6i		−	1.75113i	0.483099	−	0.875566i	$-0.339511\pi$
$920$	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	$-0.908392\pi$
$929$		−	489931.i		−	0.567679i	0.958872	−	0.283840i	$-0.0916084\pi$
$930$	−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	0.487545	−	0.873098i	$-0.337893\pi$
$937$	−338504.	−	338504.i	−0.385553	−	0.385553i	−0.873098	+	0.487545i	$0.837893\pi$
$938$	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	0.714025	−	0.700120i	$-0.246870\pi$
$947$	12469.5	+	12469.5i	0.0139043	+	0.0139043i	−0.700120	+	0.714025i	$0.746870\pi$
$948$	−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	−0.873822	−	0.486246i	$-0.838366\pi$
$953$	−352000.	+	352000.i	−0.387576	+	0.387576i	0.486246	+	0.873822i	$0.338366\pi$
$954$		−	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	0.814142	−	0.580666i	$-0.197208\pi$
$967$	218321.	+	218321.i	0.233476	+	0.233476i	−0.580666	+	0.814142i	$0.697208\pi$
$968$	−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	0.842089	−	0.539339i	$-0.181326\pi$
$977$	288983.	+	288983.i	0.302749	+	0.302749i	−0.539339	+	0.842089i	$0.681326\pi$
$978$	−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	−0.203940	−	0.978983i	$-0.565375\pi$
$983$	748916.	−	748916.i	0.775043	−	0.775043i	0.978983	+	0.203940i	$0.0653749\pi$
$984$			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	0.819928	−	0.572467i	$-0.194013\pi$
$997$	245978.	+	245978.i	0.247461	+	0.247461i	−0.572467	+	0.819928i	$0.694013\pi$
$998$	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.57.3	yes	12
5.2	odd	4		350.5.f.d.43.4		12
5.3	odd	4	inner	70.5.f.a.43.3	✓	12
5.4	even	2		350.5.f.d.57.4		12

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

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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