LMFDB - Embedded newform 45.5.h.a.29.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(14,45)] 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("45.14"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.h (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.65164833877$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.13
Character	$\chi$	$=$	45.29
Dual form			45.5.h.a.14.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.547257 - 0.947877i) q^{2} +(6.76074 - 5.94074i) q^{3} +(7.40102 + 12.8189i) q^{4} +(6.73050 + 24.0770i) q^{5} +(-1.93123 - 9.65947i) q^{6} +(16.9207 + 9.76914i) q^{7} +33.7133 q^{8} +(10.4152 - 80.3276i) q^{9} +(26.5053 + 6.79660i) q^{10} +(-100.405 - 57.9690i) q^{11} +(126.190 + 42.6980i) q^{12} +(158.728 - 91.6418i) q^{13} +(18.5199 - 10.6925i) q^{14} +(188.538 + 122.794i) q^{15} +(-99.9665 + 173.147i) q^{16} -89.0232 q^{17} +(-70.4409 - 53.8322i) q^{18} -52.2295 q^{19} +(-258.829 + 264.472i) q^{20} +(172.432 - 34.4745i) q^{21} +(-109.895 + 63.4480i) q^{22} +(-232.002 - 401.839i) q^{23} +(227.927 - 200.282i) q^{24} +(-534.401 + 324.100i) q^{25} -200.607i q^{26} +(-406.791 - 604.948i) q^{27} +289.206i q^{28} +(-1255.41 - 724.811i) q^{29} +(219.572 - 111.511i) q^{30} +(767.942 + 1330.11i) q^{31} +(379.121 + 656.657i) q^{32} +(-1023.19 + 204.568i) q^{33} +(-48.7186 + 84.3831i) q^{34} +(-121.327 + 473.149i) q^{35} +(1106.80 - 460.994i) q^{36} -641.462i q^{37} +(-28.5830 + 49.5071i) q^{38} +(528.700 - 1562.53i) q^{39} +(226.907 + 811.713i) q^{40} +(-1195.31 + 690.111i) q^{41} +(61.6871 - 182.311i) q^{42} +(1776.09 + 1025.43i) q^{43} -1716.12i q^{44} +(2004.14 - 289.878i) q^{45} -507.859 q^{46} +(589.129 - 1020.40i) q^{47} +(352.774 + 1764.48i) q^{48} +(-1009.63 - 1748.73i) q^{49} +(14.7527 + 683.912i) q^{50} +(-601.863 + 528.864i) q^{51} +(2349.50 + 1356.49i) q^{52} +64.4267 q^{53} +(-796.036 + 54.5254i) q^{54} +(719.940 - 2807.62i) q^{55} +(570.451 + 329.350i) q^{56} +(-353.110 + 310.282i) q^{57} +(-1374.06 + 793.316i) q^{58} +(2837.79 - 1638.40i) q^{59} +(-178.714 + 3325.66i) q^{60} +(929.409 - 1609.78i) q^{61} +1681.05 q^{62} +(960.964 - 1257.45i) q^{63} -2369.02 q^{64} +(3274.78 + 3204.90i) q^{65} +(-366.044 + 1081.81i) q^{66} +(-7257.38 + 4190.05i) q^{67} +(-658.862 - 1141.18i) q^{68} +(-3955.73 - 1338.47i) q^{69} +(382.090 + 373.937i) q^{70} +4564.71i q^{71} +(351.131 - 2708.11i) q^{72} -8077.75i q^{73} +(-608.027 - 351.045i) q^{74} +(-1687.55 + 5365.89i) q^{75} +(-386.551 - 669.527i) q^{76} +(-1132.62 - 1961.75i) q^{77} +(-1191.75 - 1356.25i) q^{78} +(4328.70 - 7497.52i) q^{79} +(-4841.68 - 1241.52i) q^{80} +(-6344.05 - 1673.26i) q^{81} +1510.67i q^{82} +(-1670.06 + 2892.62i) q^{83} +(1718.10 + 1955.25i) q^{84} +(-599.171 - 2143.41i) q^{85} +(1943.96 - 1122.34i) q^{86} +(-12793.4 + 2557.80i) q^{87} +(-3384.99 - 1954.33i) q^{88} +10168.3i q^{89} +(822.014 - 2058.32i) q^{90} +3581.05 q^{91} +(3434.10 - 5948.04i) q^{92} +(13093.7 + 4430.42i) q^{93} +(-644.811 - 1116.84i) q^{94} +(-351.531 - 1257.53i) q^{95} +(6464.17 + 2187.23i) q^{96} +(11868.3 + 6852.15i) q^{97} -2210.10 q^{98} +(-5702.26 + 7461.56i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) $ 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.547257	−	0.947877i	0.136814	−	0.236969i	−0.789475	−	0.613783i	$-0.789647\pi$
$2$	0.547257	−	0.947877i	0.136814	−	0.236969i	0.926289	+	0.376814i	$0.122980\pi$
$3$	6.76074	−	5.94074i	0.751193	−	0.660082i
$3$	6.76074	−	5.94074i	0.751193	−	0.660082i
$4$	7.40102	+	12.8189i	0.462564	+	0.801184i
$5$	6.73050	+	24.0770i	0.269220	+	0.963079i
$5$	6.73050	+	24.0770i	0.269220	+	0.963079i
$6$	−1.93123	−	9.65947i	−0.0536452	−	0.268318i
$7$	16.9207	+	9.76914i	0.345319	+	0.199370i	0.662622	−	0.748954i	$-0.269444\pi$
$7$	16.9207	+	9.76914i	0.345319	+	0.199370i	−0.317302	+	0.948324i	$0.602777\pi$
$8$	33.7133			0.526770
$9$	10.4152	−	80.3276i	0.128583	−	0.991699i
$10$	26.5053	+	6.79660i	0.265053	+	0.0679660i
$11$	−100.405	−	57.9690i	−0.829796	−	0.479083i	0.0239867	−	0.999712i	$-0.492364\pi$
$11$	−100.405	−	57.9690i	−0.829796	−	0.479083i	−0.853783	+	0.520629i	$0.825697\pi$
$12$	126.190	+	42.6980i	0.876322	+	0.296514i
$13$	158.728	−	91.6418i	0.939220	−	0.542259i	0.0495044	−	0.998774i	$-0.484236\pi$
$13$	158.728	−	91.6418i	0.939220	−	0.542259i	0.889716	+	0.456515i	$0.150902\pi$
$14$	18.5199	−	10.6925i	0.0944893	−	0.0545534i
$15$	188.538	+	122.794i	0.837947	+	0.545751i
$16$	−99.9665	+	173.147i	−0.390494	+	0.676355i
$17$	−89.0232			−0.308039			−0.154019	−	0.988068i	$-0.549222\pi$
$17$	−89.0232			−0.308039			−0.154019	+	0.988068i	$0.549222\pi$
$18$	−70.4409	−	53.8322i	−0.217410	−	0.166149i
$19$	−52.2295			−0.144680			−0.0723400	−	0.997380i	$-0.523047\pi$
$19$	−52.2295			−0.144680			−0.0723400	+	0.997380i	$0.523047\pi$
$20$	−258.829	+	264.472i	−0.647072	+	0.661180i
$21$	172.432	−	34.4745i	0.391002	−	0.0781736i
$22$	−109.895	+	63.4480i	−0.227056	+	0.131091i
$23$	−232.002	−	401.839i	−0.438567	−	0.759621i	0.559012	−	0.829160i	$-0.311181\pi$
$23$	−232.002	−	401.839i	−0.438567	−	0.759621i	−0.997579	+	0.0695388i	$0.977847\pi$
$24$	227.927	−	200.282i	0.395706	−	0.347711i
$25$	−534.401	+	324.100i	−0.855041	+	0.518560i
$26$		−	200.607i		−	0.296755i
$27$	−406.791	−	604.948i	−0.558012	−	0.829833i
$28$			289.206i			0.368886i
$29$	−1255.41	−	724.811i	−1.49276	−	0.861844i	−0.492792	−	0.870147i	$-0.664024\pi$
$29$	−1255.41	−	724.811i	−1.49276	−	0.861844i	−0.999966	+	0.00830339i	$0.997357\pi$
$30$	219.572	−	111.511i	0.243969	−	0.123901i
$31$	767.942	+	1330.11i	0.799107	+	1.38409i	0.920198	+	0.391453i	$0.128027\pi$
$31$	767.942	+	1330.11i	0.799107	+	1.38409i	−0.121091	+	0.992641i	$0.538639\pi$
$32$	379.121	+	656.657i	0.370235	+	0.641266i
$33$	−1023.19	+	204.568i	−0.939572	+	0.187850i
$34$	−48.7186	+	84.3831i	−0.0421441	+	0.0729957i
$35$	−121.327	+	473.149i	−0.0990423	+	0.386244i
$36$	1106.80	−	460.994i	0.854011	−	0.355705i
$37$		−	641.462i		−	0.468562i	−0.972169	−	0.234281i	$-0.924726\pi$
$37$		−	641.462i		−	0.468562i	0.972169	−	0.234281i	$-0.0752736\pi$
$38$	−28.5830	+	49.5071i	−0.0197943	+	0.0342847i
$39$	528.700	−	1562.53i	0.347601	−	1.02730i
$40$	226.907	+	811.713i	0.141817	+	0.507321i
$41$	−1195.31	+	690.111i	−0.711069	+	0.410536i	−0.811457	−	0.584412i	$-0.801325\pi$
$41$	−1195.31	+	690.111i	−0.711069	+	0.410536i	0.100388	+	0.994948i	$0.467992\pi$
$42$	61.6871	−	182.311i	0.0349700	−	0.103351i
$43$	1776.09	+	1025.43i	0.960568	+	0.554584i	0.896348	−	0.443351i	$-0.146211\pi$
$43$	1776.09	+	1025.43i	0.960568	+	0.554584i	0.0642203	+	0.997936i	$0.479544\pi$
$44$		−	1716.12i		−	0.886426i
$45$	2004.14	−	289.878i	0.989701	−	0.143150i
$46$	−507.859			−0.240009
$47$	589.129	−	1020.40i	0.266695	−	0.461929i	−0.701311	−	0.712855i	$-0.747402\pi$
$47$	589.129	−	1020.40i	0.266695	−	0.461929i	0.968006	+	0.250926i	$0.0807350\pi$
$48$	352.774	+	1764.48i	0.153114	+	0.765832i
$49$	−1009.63	−	1748.73i	−0.420503	−	0.728333i
$50$	14.7527	+	683.912i	0.00590108	+	0.273565i
$51$	−601.863	+	528.864i	−0.231397	+	0.203331i
$52$	2349.50	+	1356.49i	0.868898	+	0.501659i
$53$	64.4267			0.0229358			0.0114679	−	0.999934i	$-0.496350\pi$
$53$	64.4267			0.0229358			0.0114679	+	0.999934i	$0.496350\pi$
$54$	−796.036	+	54.5254i	−0.272989	+	0.0186987i
$55$	719.940	−	2807.62i	0.237997	−	0.928138i
$56$	570.451	+	329.350i	0.181904	+	0.105022i
$57$	−353.110	+	310.282i	−0.108683	+	0.0955007i
$58$	−1374.06	+	793.316i	−0.408461	+	0.235825i
$59$	2837.79	−	1638.40i	0.815223	−	0.470669i	−0.0335434	−	0.999437i	$-0.510679\pi$
$59$	2837.79	−	1638.40i	0.815223	−	0.470669i	0.848766	+	0.528768i	$0.177346\pi$
$60$	−178.714	+	3325.66i	−0.0496427	+	0.923794i
$61$	929.409	−	1609.78i	0.249774	−	0.432621i	−0.713689	−	0.700463i	$-0.752977\pi$
$61$	929.409	−	1609.78i	0.249774	−	0.432621i	0.963463	+	0.267842i	$0.0863104\pi$
$62$	1681.05			0.437317
$63$	960.964	−	1257.45i	0.242117	−	0.316817i
$64$	−2369.02			−0.578374
$65$	3274.78	+	3204.90i	0.775095	+	0.758556i
$66$	−366.044	+	1081.81i	−0.0840322	+	0.248350i
$67$	−7257.38	+	4190.05i	−1.61670	+	0.933404i	−0.628938	+	0.777455i	$0.716510\pi$
$67$	−7257.38	+	4190.05i	−1.61670	+	0.933404i	−0.987765	+	0.155949i	$0.950156\pi$
$68$	−658.862	−	1141.18i	−0.142488	−	0.246796i
$69$	−3955.73	−	1338.47i	−0.830861	−	0.281132i
$70$	382.090	+	373.937i	0.0779777	+	0.0763137i
$71$			4564.71i			0.905517i	0.891633	+	0.452759i	$0.149560\pi$
$71$			4564.71i			0.905517i	−0.891633	+	0.452759i	$0.850440\pi$
$72$	351.131	−	2708.11i	0.0677337	−	0.522397i
$73$		−	8077.75i		−	1.51581i	−0.652365	−	0.757905i	$-0.726223\pi$
$73$		−	8077.75i		−	1.51581i	0.652365	−	0.757905i	$-0.273777\pi$
$74$	−608.027	−	351.045i	−0.111035	−	0.0641060i
$75$	−1687.55	+	5365.89i	−0.300009	+	0.953936i
$76$	−386.551	−	669.527i	−0.0669237	−	0.115915i
$77$	−1132.62	−	1961.75i	−0.191030	−	0.330873i
$78$	−1191.75	−	1356.25i	−0.195883	−	0.222921i
$79$	4328.70	−	7497.52i	0.693590	−	1.20133i	−0.277063	−	0.960852i	$-0.589361\pi$
$79$	4328.70	−	7497.52i	0.693590	−	1.20133i	0.970654	−	0.240482i	$-0.0773054\pi$
$80$	−4841.68	−	1241.52i	−0.756512	−	0.193988i
$81$	−6344.05	−	1673.26i	−0.966933	−	0.255031i
$82$			1510.67i			0.224669i
$83$	−1670.06	+	2892.62i	−0.242424	+	0.419890i	−0.961404	−	0.275140i	$-0.911276\pi$
$83$	−1670.06	+	2892.62i	−0.242424	+	0.419890i	0.718981	+	0.695030i	$0.244609\pi$
$84$	1718.10	+	1955.25i	0.243495	+	0.277105i
$85$	−599.171	−	2143.41i	−0.0829302	−	0.296666i
$86$	1943.96	−	1122.34i	0.262839	−	0.151750i
$87$	−12793.4	+	2557.80i	−1.69024	+	0.337931i
$88$	−3384.99	−	1954.33i	−0.437112	−	0.252367i
$89$			10168.3i			1.28371i	0.766825	+	0.641856i	$0.221835\pi$
$89$			10168.3i			1.28371i	−0.766825	+	0.641856i	$0.778165\pi$
$90$	822.014	−	2058.32i	0.101483	−	0.254114i
$91$	3581.05			0.432441
$92$	3434.10	−	5948.04i	0.405731	−	0.702746i
$93$	13093.7	+	4430.42i	1.51390	+	0.512246i
$94$	−644.811	−	1116.84i	−0.0729754	−	0.126397i
$95$	−351.531	−	1257.53i	−0.0389508	−	0.139338i
$96$	6464.17	+	2187.23i	0.701407	+	0.237329i
$97$	11868.3	+	6852.15i	1.26137	+	0.728255i	0.973340	−	0.229365i	$-0.0736649\pi$
$97$	11868.3	+	6852.15i	1.26137	+	0.728255i	0.288034	+	0.957620i	$0.406998\pi$
$98$	−2210.10			−0.230123
$99$	−5702.26	+	7461.56i	−0.581804	+	0.761306i
$100$	−8109.73	−	4451.78i	−0.810973	−	0.445178i
$101$	6147.82	+	3549.45i	0.602668	+	0.347951i	0.770091	−	0.637935i	$-0.220211\pi$
$101$	6147.82	+	3549.45i	0.602668	+	0.347951i	−0.167422	+	0.985885i	$0.553544\pi$
$102$	171.924	+	859.916i	0.0165248	+	0.0826525i
$103$	−4058.54	+	2343.20i	−0.382557	+	0.220869i	−0.678930	−	0.734203i	$-0.737556\pi$
$103$	−4058.54	+	2343.20i	−0.382557	+	0.220869i	0.296373	+	0.955072i	$0.404223\pi$
$104$	5351.25	−	3089.54i	0.494753	−	0.285646i
$105$	1990.60	+	3919.61i	0.180553	+	0.355520i
$106$	35.2580	−	61.0686i	0.00313795	−	0.00543509i
$107$	20235.1			1.76741			0.883705	−	0.468044i	$-0.155041\pi$
$107$	20235.1			1.76741			0.883705	+	0.468044i	$0.155041\pi$
$108$	4744.13	−	9691.86i	0.406733	−	0.830921i
$109$	2264.65			0.190611			0.0953053	−	0.995448i	$-0.469617\pi$
$109$	2264.65			0.190611			0.0953053	+	0.995448i	$0.469617\pi$
$110$	−2267.28	−	2218.90i	−0.187379	−	0.183380i
$111$	−3810.76	−	4336.76i	−0.309290	−	0.351981i
$112$	−3383.00	+	1953.17i	−0.269690	+	0.155706i
$113$	5005.26	+	8669.36i	0.391985	+	0.678938i	0.992711	−	0.120517i	$-0.0384552\pi$
$113$	5005.26	+	8669.36i	0.391985	+	0.678938i	−0.600726	+	0.799455i	$0.705122\pi$
$114$	100.867	+	504.509i	0.00776139	+	0.0388203i
$115$	8113.58	−	8290.49i	0.613503	−	0.626880i
$116$		−	21457.4i		−	1.59463i
$117$	−5708.17	−	13704.7i	−0.416990	−	1.00115i
$118$		−	3586.50i		−	0.257577i
$119$	−1506.33	−	869.680i	−0.106372	−	0.0614138i
$120$	6356.24	+	4139.79i	0.441406	+	0.287485i
$121$	−599.679	−	1038.67i	−0.0409588	−	0.0709428i
$122$	−1017.25	−	1761.93i	−0.0683453	−	0.118378i
$123$	−3981.39	+	11766.7i	−0.263163	+	0.777756i
$124$	−11367.1	+	19688.4i	−0.739276	+	1.28046i
$125$	−11400.1	−	10685.4i	−0.729609	−	0.683865i
$126$	−666.011	−	1599.02i	−0.0419508	−	0.100720i
$127$			19581.7i			1.21406i	0.794677	+	0.607032i	$0.207640\pi$
$127$			19581.7i			1.21406i	−0.794677	+	0.607032i	$0.792360\pi$
$128$	−7362.40	+	12752.0i	−0.449365	+	0.778323i
$129$	18099.5	−	3618.65i	1.08764	−	0.217454i
$130$	4830.00	−	1350.18i	0.285799	−	0.0798925i
$131$	−24663.9	+	14239.7i	−1.43721	+	0.829773i	−0.997655	−	0.0684439i	$-0.978197\pi$
$131$	−24663.9	+	14239.7i	−1.43721	+	0.829773i	−0.439553	+	0.898216i	$0.644863\pi$
$132$	−10195.0	−	11602.2i	−0.585114	−	0.665877i
$133$	−883.757	−	510.237i	−0.0499608	−	0.0288449i
$134$			9172.14i			0.510812i
$135$	11827.4	−	13865.9i	0.648966	−	0.760817i
$136$	−3001.26			−0.162266
$137$	13118.2	−	22721.5i	0.698931	−	1.21058i	−0.269906	−	0.962887i	$-0.586993\pi$
$137$	13118.2	−	22721.5i	0.698931	−	1.21058i	0.968837	−	0.247698i	$-0.0796740\pi$
$138$	−3433.50	+	3017.06i	−0.180293	+	0.158426i
$139$	16654.1	+	28845.7i	0.861967	+	1.49297i	0.870027	+	0.493004i	$0.164101\pi$
$139$	16654.1	+	28845.7i	0.861967	+	1.49297i	−0.00805999	+	0.999968i	$0.502566\pi$
$140$	−6963.21	+	1946.51i	−0.355266	+	0.0993115i
$141$	−2078.99	−	10398.5i	−0.104572	−	0.523039i
$142$	4326.79	+	2498.07i	0.214580	+	0.123888i
$143$	−21249.5			−1.03915
$144$	12867.3	+	9833.43i	0.620530	+	0.474220i
$145$	9001.71	−	35104.8i	0.428143	−	1.66967i
$146$	−7656.72	−	4420.61i	−0.359201	−	0.207385i
$147$	−17214.6	−	5824.75i	−0.796638	−	0.269552i
$148$	8222.86	−	4747.47i	0.375405	−	0.216740i
$149$	−4558.66	+	2631.94i	−0.205336	+	0.118551i	−0.599142	−	0.800643i	$-0.704491\pi$
$149$	−4558.66	+	2631.94i	−0.205336	+	0.118551i	0.393806	+	0.919194i	$0.371158\pi$
$150$	4162.68	+	4536.11i	0.185008	+	0.201605i
$151$	−5636.90	+	9763.41i	−0.247222	+	0.428201i	−0.962754	−	0.270379i	$-0.912851\pi$
$151$	−5636.90	+	9763.41i	−0.247222	+	0.428201i	0.715532	+	0.698580i	$0.246184\pi$
$152$	−1760.83			−0.0762131
$153$	−927.197	+	7151.02i	−0.0396086	+	0.305482i
$154$	−2479.33			−0.104542
$155$	−26856.5	+	27442.1i	−1.11786	+	1.14223i
$156$	23942.9	−	4786.93i	0.983847	−	0.196702i
$157$	−17441.0	+	10069.5i	−0.707573	+	0.408517i	−0.810162	−	0.586207i	$-0.800621\pi$
$157$	−17441.0	+	10069.5i	−0.707573	+	0.408517i	0.102589	+	0.994724i	$0.467287\pi$
$158$	−4737.82	−	8206.15i	−0.189786	−	0.328719i
$159$	435.572	−	382.742i	0.0172292	−	0.0151395i
$160$	−13258.6	+	13547.7i	−0.517915	+	0.529208i
$161$		−	9065.85i		−	0.349749i
$162$	−5057.87	+	5097.67i	−0.192725	+	0.194241i
$163$		−	15388.7i		−	0.579197i	−0.957148	−	0.289598i	$-0.906478\pi$
$163$		−	15388.7i		−	0.579197i	0.957148	−	0.289598i	$-0.0935218\pi$
$164$	−17693.0	−	10215.1i	−0.657830	−	0.379798i
$165$	−11812.0	−	23258.5i	−0.433866	−	0.854308i
$166$	1827.90	+	3166.02i	0.0663340	+	0.114894i
$167$	8523.96	+	14763.9i	0.305639	+	0.529382i	0.977403	−	0.211383i	$-0.0677967\pi$
$167$	8523.96	+	14763.9i	0.305639	+	0.529382i	−0.671765	+	0.740765i	$0.734463\pi$
$168$	5813.25	−	1162.25i	0.205968	−	0.0411795i
$169$	2515.93	−	4357.72i	0.0880898	−	0.152576i
$170$	−2359.59	−	605.055i	−0.0816467	−	0.0209362i
$171$	−543.982	+	4195.47i	−0.0186034	+	0.143479i
$172$			30356.8i			1.02612i
$173$	9704.36	−	16808.4i	0.324246	−	0.561610i	−0.657114	−	0.753792i	$-0.728223\pi$
$173$	9704.36	−	16808.4i	0.324246	−	0.561610i	0.981359	+	0.192181i	$0.0615561\pi$
$174$	−4576.80	+	13526.4i	−0.151169	+	0.446768i
$175$	−12208.6	+	263.352i	−0.398648	+	0.00859925i
$176$	20074.3	−	11589.9i	0.648061	−	0.374158i
$177$	9452.27	−	27935.4i	0.301710	−	0.891678i
$178$	9638.28	+	5564.66i	0.304200	+	0.175630i
$179$			6659.35i			0.207838i	0.994586	+	0.103919i	$0.0331383\pi$
$179$			6659.35i			0.207838i	−0.994586	+	0.103919i	$0.966862\pi$
$180$	18548.6	+	23545.6i	0.572489	+	0.726717i
$181$	−15739.8			−0.480443			−0.240221	−	0.970718i	$-0.577220\pi$
$181$	−15739.8			−0.480443			−0.240221	+	0.970718i	$0.577220\pi$
$182$	1959.75	−	3394.39i	0.0591642	−	0.102475i
$183$	−3279.81	−	16404.7i	−0.0979370	−	0.489853i
$184$	−7821.55	−	13547.3i	−0.231024	−	0.400145i
$185$	15444.5	−	4317.36i	0.451262	−	0.126146i
$186$	11365.1	−	9986.66i	0.328510	−	0.288665i
$187$	8938.40	+	5160.59i	0.255609	+	0.147576i
$188$	17440.6			0.493454
$189$	−973.338	−	14210.1i	−0.0272483	−	0.397808i
$190$	−1384.36	−	354.983i	−0.0383479	−	0.00983332i
$191$	25333.0	+	14626.0i	0.694417	+	0.400922i	0.805265	−	0.592915i	$-0.202023\pi$
$191$	25333.0	+	14626.0i	0.694417	+	0.400922i	−0.110847	+	0.993837i	$0.535357\pi$
$192$	−16016.3	+	14073.7i	−0.434471	+	0.381774i
$193$	37232.0	−	21495.9i	0.999543	−	0.577086i	0.0914300	−	0.995812i	$-0.470856\pi$
$193$	37232.0	−	21495.9i	0.999543	−	0.577086i	0.908113	+	0.418725i	$0.137523\pi$
$194$	12990.0	−	7499.78i	0.345148	−	0.199271i
$195$	41179.4	+	2212.89i	1.08296	+	0.0581957i
$196$	14944.5	−	25884.7i	0.389019	−	0.673800i
$197$	48322.8			1.24514			0.622571	−	0.782563i	$-0.286088\pi$
$197$	48322.8			1.24514			0.622571	+	0.782563i	$0.286088\pi$
$198$	3952.04	+	9488.43i	0.100807	+	0.242027i
$199$	10246.4			0.258740			0.129370	−	0.991596i	$-0.458705\pi$
$199$	10246.4			0.258740			0.129370	+	0.991596i	$0.458705\pi$
$200$	−18016.4	+	10926.5i	−0.450410	+	0.273162i
$201$	−24173.3	+	71442.1i	−0.598333	+	1.76832i
$202$	6728.88	−	3884.92i	0.164907	−	0.0952093i
$203$	−14161.6	−	24528.5i	−0.343652	−	0.595223i
$204$	−11233.9	−	3801.11i	−0.269941	−	0.0913378i
$205$	−24660.8	−	24134.6i	−0.586813	−	0.574291i
$206$			5129.34i			0.120872i
$207$	−34695.1	+	14450.9i	−0.809707	+	0.337252i
$208$			36644.4i			0.846996i
$209$	5244.12	+	3027.69i	0.120055	+	0.0693137i
$210$	4804.68	+	258.193i	0.108950	+	0.00585471i
$211$	−5566.99	−	9642.31i	−0.125042	−	0.216579i	0.796707	−	0.604365i	$-0.206573\pi$
$211$	−5566.99	−	9642.31i	−0.125042	−	0.216579i	−0.921749	+	0.387786i	$0.873240\pi$
$212$	476.823	+	825.882i	0.0106093	+	0.0183758i
$213$	27117.8	+	30860.8i	0.597716	+	0.680218i
$214$	11073.8	−	19180.4i	0.241807	−	0.418822i
$215$	−12735.2	+	49664.5i	−0.275504	+	1.07441i
$216$	−13714.2	−	20394.8i	−0.293944	−	0.437131i
$217$			30008.5i			0.637273i
$218$	1239.34	−	2146.61i	0.0260783	−	0.0451689i
$219$	−47987.8	−	54611.6i	−1.00056	−	1.13867i
$220$	41319.0	−	11550.4i	0.853698	−	0.238644i
$221$	−14130.5	+	8158.24i	−0.289316	+	0.167037i
$222$	−6196.18	+	1238.81i	−0.125724	+	0.0251361i
$223$	−41863.5	−	24169.9i	−0.841833	−	0.486032i	0.0160539	−	0.999871i	$-0.494890\pi$
$223$	−41863.5	−	24169.9i	−0.841833	−	0.486032i	−0.857887	+	0.513839i	$0.828223\pi$
$224$			14814.7i			0.295256i
$225$	20468.3	+	46302.7i	0.404312	+	0.914621i
$226$	10956.7			0.214517
$227$	9830.70	−	17027.3i	0.190780	−	0.330441i	−0.754729	−	0.656037i	$-0.772232\pi$
$227$	9830.70	−	17027.3i	0.190780	−	0.330441i	0.945509	+	0.325596i	$0.105565\pi$
$228$	−6590.86	−	2230.09i	−0.126786	−	0.0428996i
$229$	−41057.9	−	71114.4i	−0.782935	−	1.35608i	−0.930225	−	0.366990i	$-0.880388\pi$
$229$	−41057.9	−	71114.4i	−0.782935	−	1.35608i	0.147290	−	0.989093i	$-0.452945\pi$
$230$	−3418.15	−	12227.7i	−0.0646153	−	0.231148i
$231$	−19311.6	−	6534.30i	−0.361904	−	0.122455i
$232$	−42323.9	−	24435.7i	−0.786340	−	0.453993i
$233$	−36907.6			−0.679837			−0.339918	−	0.940455i	$-0.610399\pi$
$233$	−36907.6			−0.679837			−0.339918	+	0.940455i	$0.610399\pi$
$234$	−16114.2	−	2089.36i	−0.294292	−	0.0381577i
$235$	28533.3	+	7316.63i	0.516674	+	0.132488i
$236$	42005.1	+	24251.7i	0.754185	+	0.435429i
$237$	−15275.6	−	76404.5i	−0.271958	−	1.36026i
$238$	−1648.70	+	951.878i	−0.0291064	+	0.0168046i
$239$	23140.0	−	13359.9i	0.405105	−	0.233888i	−0.283579	−	0.958949i	$-0.591522\pi$
$239$	23140.0	−	13359.9i	0.405105	−	0.233888i	0.688684	+	0.725061i	$0.258189\pi$
$240$	−40108.9	+	20369.5i	−0.696335	+	0.353638i
$241$	−7637.82	+	13229.1i	−0.131503	+	0.227770i	−0.924256	−	0.381773i	$-0.875314\pi$
$241$	−7637.82	+	13229.1i	−0.131503	+	0.227770i	0.792753	+	0.609543i	$0.208647\pi$
$242$	−1312.71			−0.0224150
$243$	−52830.9	+	26375.8i	−0.894695	+	0.446677i
$244$	27514.3			0.462145
$245$	35308.7	−	36078.6i	0.588234	−	0.601059i
$246$	8974.52	+	10213.3i	0.148300	+	0.168770i
$247$	−8290.29	+	4786.40i	−0.135886	+	0.0784540i
$248$	25889.8	+	44842.5i	0.420946	+	0.729099i
$249$	5893.50	+	29477.6i	0.0950549	+	0.475438i
$250$	−16367.2	+	4958.28i	−0.261876	+	0.0793324i
$251$		−	17504.6i		−	0.277847i	−0.990303	−	0.138923i	$-0.955636\pi$
$251$		−	17504.6i		−	0.277847i	0.990303	−	0.138923i	$-0.0443642\pi$
$252$	23231.3	+	3012.15i	0.365824	+	0.0474325i
$253$			53795.8i			0.840441i
$254$	18561.0	+	10716.2i	0.287696	+	0.166101i
$255$	−16784.3	−	10931.5i	−0.258120	−	0.168112i
$256$	−10893.9	−	18868.8i	−0.166228	−	0.287915i
$257$	−28510.3	−	49381.3i	−0.431654	−	0.747647i	0.565362	−	0.824843i	$-0.308737\pi$
$257$	−28510.3	−	49381.3i	−0.431654	−	0.747647i	−0.997016	+	0.0771960i	$0.975403\pi$
$258$	6475.03	−	19136.4i	0.0972753	−	0.287489i
$259$	6266.53	−	10854.0i	0.0934174	−	0.161804i
$260$	−16846.7	+	65698.7i	−0.249212	+	0.971874i
$261$	−71297.7	+	93294.9i	−1.04663	+	1.36955i
$262$			31171.2i			0.454099i
$263$	−29717.1	+	51471.5i	−0.429630	+	0.744142i	−0.996840	−	0.0794316i	$-0.974689\pi$
$263$	−29717.1	+	51471.5i	−0.429630	+	0.744142i	0.567210	+	0.823573i	$0.308023\pi$
$264$	−34495.2	+	6896.67i	−0.494938	+	0.0989535i
$265$	433.624	+	1551.20i	0.00617479	+	0.0220890i
$266$	−967.285	+	558.462i	−0.0136707	+	0.00789279i
$267$	60407.1	+	68745.1i	0.847355	+	0.964316i
$268$	−107424.	−	62021.3i	−1.49566	−	0.863518i
$269$		−	107707.i		−	1.48847i	−0.667919	−	0.744234i	$-0.732815\pi$
$269$		−	107707.i		−	1.48847i	0.667919	−	0.744234i	$-0.267185\pi$
$270$	−6670.53	−	18799.1i	−0.0915025	−	0.257876i
$271$	−11971.8			−0.163012			−0.0815059	−	0.996673i	$-0.525973\pi$
$271$	−11971.8			−0.163012			−0.0815059	+	0.996673i	$0.525973\pi$
$272$	8899.33	−	15414.1i	0.120287	−	0.208344i
$273$	24210.5	−	21274.1i	0.324847	−	0.285447i
$274$	−14358.1	−	24869.0i	−0.191248	−	0.331251i
$275$	72444.5	−	1562.70i	0.957943	−	0.0206638i
$276$	−12118.7	−	60614.3i	−0.159088	−	0.795714i
$277$	23205.3	+	13397.6i	0.302432	+	0.174609i	0.643535	−	0.765417i	$-0.277467\pi$
$277$	23205.3	+	13397.6i	0.302432	+	0.174609i	−0.341103	+	0.940026i	$0.610800\pi$
$278$	36456.2			0.471718
$279$	114843.	−	47833.5i	1.47536	−	0.614502i
$280$	−4090.32	+	15951.4i	−0.0521725	+	0.203462i
$281$	37711.0	+	21772.5i	0.477591	+	0.275737i	0.719412	−	0.694584i	$-0.244411\pi$
$281$	37711.0	+	21772.5i	0.477591	+	0.275737i	−0.241821	+	0.970321i	$0.577745\pi$
$282$	−10994.3	−	3720.05i	−0.138251	−	0.0467789i
$283$	53849.1	−	31089.8i	0.672366	−	0.388190i	−0.124607	−	0.992206i	$-0.539767\pi$
$283$	53849.1	−	31089.8i	0.672366	−	0.388190i	0.796972	+	0.604016i	$0.206434\pi$
$284$	−58514.8	+	33783.5i	−0.725486	+	0.418859i
$285$	−9847.25	−	6413.46i	−0.121234	−	0.0789592i
$286$	−11629.0	+	20142.0i	−0.142170	+	0.246246i
$287$	−26967.2			−0.327395
$288$	56696.3	−	23614.6i	0.683549	−	0.284706i
$289$	−75595.9			−0.905112
$290$	−28348.8	−	27743.9i	−0.337084	−	0.329891i
$291$	120945.	−	24180.7i	1.42824	−	0.285551i
$292$	103548.	−	59783.6i	1.21444	−	0.701159i
$293$	8608.02	+	14909.5i	0.100269	+	0.173672i	0.911796	−	0.410644i	$-0.134696\pi$
$293$	8608.02	+	14909.5i	0.100269	+	0.173672i	−0.811526	+	0.584316i	$0.801363\pi$
$294$	−14941.9	+	13129.7i	−0.172867	+	0.151900i
$295$	58547.5	+	57298.1i	0.672766	+	0.658410i
$296$		−	21625.8i		−	0.246825i
$297$	5775.68	+	84321.3i	0.0654773	+	0.955926i
$298$			5761.40i			0.0648777i
$299$	−73650.6	−	42522.2i	−0.823822	−	0.475634i
$300$	−81274.6	+	18080.5i	−0.903052	+	0.200894i
$301$	20035.1	+	34701.8i	0.221135	+	0.383017i
$302$	6169.67	+	10686.2i	0.0676470	+	0.117168i
$303$	62650.1	−	12525.7i	0.682397	−	0.136432i
$304$	5221.20	−	9043.38i	0.0564967	−	0.0978551i
$305$	45014.1	+	11542.7i	0.483892	+	0.124082i
$306$	6270.87	+	4792.32i	0.0669708	+	0.0511803i
$307$		−	107387.i		−	1.13940i	−0.821854	−	0.569698i	$-0.807060\pi$
$307$		−	107387.i		−	1.13940i	0.821854	−	0.569698i	$-0.192940\pi$
$308$	16765.0	−	29037.9i	0.176727	−	0.306100i
$309$	−13518.4	+	39952.5i	−0.141582	+	0.418434i
$310$	11314.3	+	40474.5i	0.117735	+	0.421171i
$311$	−118121.	+	68197.1i	−1.22125	+	0.705091i	−0.965185	−	0.261568i	$-0.915760\pi$
$311$	−118121.	+	68197.1i	−1.22125	+	0.705091i	−0.256068	+	0.966659i	$0.582427\pi$
$312$	17824.2	−	52678.0i	0.183105	−	0.541153i
$313$	81900.2	+	47285.1i	0.835981	+	0.482654i	0.855896	−	0.517148i	$-0.173006\pi$
$313$	81900.2	+	47285.1i	0.835981	+	0.482654i	−0.0199154	+	0.999802i	$0.506340\pi$
$314$			22042.5i			0.223564i
$315$	36743.3	+	14673.8i	0.370303	+	0.147885i
$316$	128147.			1.28332
$317$	−70757.2	+	122555.i	−0.704129	+	1.21959i	0.262876	+	0.964830i	$0.415329\pi$
$317$	−70757.2	+	122555.i	−0.704129	+	1.21959i	−0.967005	+	0.254758i	$0.918004\pi$
$318$	−124.423	−	622.328i	−0.00123040	−	0.00615411i
$319$	84033.2	+	145550.i	0.825790	+	1.43031i
$320$	−15944.7	−	57038.8i	−0.155710	−	0.557020i
$321$	136804.	−	120211.i	1.32767	−	1.16664i
$322$	−8593.31	−	4961.35i	−0.0828798	−	0.0478507i
$323$	4649.64			0.0445670
$324$	−25503.0	−	93707.8i	−0.242941	−	0.892659i
$325$	−55123.3	+	100417.i	−0.521878	+	0.950696i
$326$	−14586.6	−	8421.57i	−0.137252	−	0.0792424i
$327$	15310.7	−	13453.7i	0.143185	−	0.125819i
$328$	−40297.7	+	23265.9i	−0.374570	+	0.216258i
$329$	19936.9	−	11510.6i	0.184190	−	0.106342i
$330$	−28510.4	−	1532.09i	−0.261804	−	0.0140688i
$331$	−41375.6	+	71664.7i	−0.377649	+	0.654108i	−0.990720	−	0.135921i	$-0.956601\pi$
$331$	−41375.6	+	71664.7i	−0.377649	+	0.654108i	0.613071	+	0.790028i	$0.289934\pi$
$332$	−49440.5			−0.448545
$333$	−51527.1	−	6680.97i	−0.464673	−	0.0602492i
$334$	18659.2			0.167263
$335$	−149730.	−	146535.i	−1.33419	−	1.30572i
$336$	−11268.3	+	33302.4i	−0.0998110	+	0.294983i
$337$	−72053.4	+	41600.0i	−0.634446	+	0.366297i	−0.782472	−	0.622686i	$-0.786041\pi$
$337$	−72053.4	+	41600.0i	−0.634446	+	0.366297i	0.148026	+	0.988983i	$0.452708\pi$
$338$	−2753.72	−	4769.59i	−0.0241039	−	0.0417491i
$339$	85341.6	+	28876.4i	0.742611	+	0.251271i
$340$	23041.8	−	23544.1i	0.199323	−	0.203669i
$341$		−	178067.i		−	1.53135i
$342$	3679.09	+	2811.63i	0.0314549	+	0.0240384i
$343$		−	86364.2i		−	0.734084i
$344$	59877.8	+	34570.5i	0.505998	+	0.292138i
$345$	5602.19	−	104251.i	0.0470674	−	0.875871i
$346$	−10621.6	−	18397.1i	−0.0887230	−	0.153673i
$347$	51814.1	+	89744.7i	0.430317	+	0.745332i	0.996900	−	0.0786729i	$-0.0250683\pi$
$347$	51814.1	+	89744.7i	0.430317	+	0.745332i	−0.566583	+	0.824005i	$0.691735\pi$
$348$	−127473.	−	145068.i	−1.05259	−	1.19788i
$349$	−75356.4	+	130521.i	−0.618685	+	1.07159i	0.371041	+	0.928616i	$0.379001\pi$
$349$	−75356.4	+	130521.i	−0.618685	+	1.07159i	−0.989726	+	0.142977i	$0.954332\pi$
$350$	−6431.61	+	11716.4i	−0.0525030	+	0.0956438i
$351$	−120008.	−	58743.3i	−0.974081	−	0.476809i
$352$		−	87909.1i		−	0.709494i
$353$	11068.8	−	19171.8i	0.0888286	−	0.153856i	−0.818188	−	0.574951i	$-0.805021\pi$
$353$	11068.8	−	19171.8i	0.0888286	−	0.153856i	0.907016	+	0.421096i	$0.138354\pi$
$354$	−21306.5	−	24247.4i	−0.170022	−	0.193490i
$355$	−109904.	+	30722.8i	−0.872084	+	0.243783i
$356$	−130347.	+	75255.6i	−1.02849	+	0.593798i
$357$	−15350.5	+	3069.03i	−0.120444	+	0.0240805i
$358$	6312.25	+	3644.38i	0.0492513	+	0.0284353i
$359$			90926.7i			0.705509i	0.935716	+	0.352755i	$0.114755\pi$
$359$			90926.7i			0.705509i	−0.935716	+	0.352755i	$0.885245\pi$
$360$	67566.3	−	9772.74i	0.521345	−	0.0754070i
$361$	−127593.			−0.979068
$362$	−8613.71	+	14919.4i	−0.0657314	+	0.113850i
$363$	−10224.8	−	3459.67i	−0.0775961	−	0.0262556i
$364$	26503.4	+	45905.2i	0.200032	+	0.346465i
$365$	194488.	−	54367.3i	1.45984	−	0.408087i
$366$	−17344.5	−	5868.73i	−0.129479	−	0.0438109i
$367$	−17103.7	−	9874.80i	−0.126986	−	0.0733156i	0.435161	−	0.900353i	$-0.356691\pi$
$367$	−17103.7	−	9874.80i	−0.126986	−	0.0733156i	−0.562148	+	0.827037i	$0.690025\pi$
$368$	92769.7			0.685032
$369$	42985.6	+	103204.i	0.315697	+	0.757954i
$370$	4359.76	−	17002.2i	0.0318463	−	0.124194i
$371$	1090.14	+	629.394i	0.00792019	+	0.00457272i
$372$	40113.6	+	200637.i	0.289872	+	1.44986i
$373$	−94695.0	+	54672.2i	−0.680627	+	0.392960i	−0.800091	−	0.599878i	$-0.795216\pi$
$373$	−94695.0	+	54672.2i	−0.680627	+	0.392960i	0.119464	+	0.992839i	$0.461882\pi$
$374$	9783.21	−	5648.34i	0.0699420	−	0.0403811i
$375$	−140552.	−	4515.89i	−0.999484	−	0.0321130i
$376$	19861.5	−	34401.1i	0.140487	−	0.243331i
$377$	−265692.			−1.86937
$378$	−14002.1	−	6853.98i	−0.0979964	−	0.0479689i
$379$	75560.0			0.526034			0.263017	−	0.964791i	$-0.415283\pi$
$379$	75560.0			0.526034			0.263017	+	0.964791i	$0.415283\pi$
$380$	13518.5	−	13813.2i	0.0936183	−	0.0956595i
$381$	116329.	+	132386.i	0.801383	+	0.911997i
$382$	27727.4	−	16008.4i	0.190012	−	0.109704i
$383$	−108125.	−	187277.i	−0.737100	−	1.27670i	−0.953796	−	0.300456i	$-0.902861\pi$
$383$	−108125.	−	187277.i	−0.737100	−	1.27670i	0.216695	−	0.976239i	$-0.430472\pi$
$384$	25981.3	+	129951.i	0.176197	+	0.881289i
$385$	39609.9	−	40473.5i	0.267228	−	0.273055i
$386$		−	47055.1i		−	0.315815i
$387$	100868.	−	131989.i	0.673493	−	0.881284i
$388$			202852.i			1.34746i
$389$	48977.4	+	28277.1i	0.323666	+	0.186868i	0.653025	−	0.757336i	$-0.273500\pi$
$389$	48977.4	+	28277.1i	0.323666	+	0.186868i	−0.329360	+	0.944205i	$0.606833\pi$
$390$	24633.3	−	37822.0i	0.161954	−	0.248665i
$391$	20653.6	+	35773.0i	0.135096	+	0.233993i
$392$	−34037.9	−	58955.3i	−0.221508	−	0.383664i
$393$	−82151.9	+	242793.i	−0.531903	+	1.57200i
$394$	26445.0	−	45804.0i	0.170353	−	0.295061i
$395$	209652.	+	53759.8i	1.34371	+	0.344559i
$396$	−137852.	−	17873.8i	−0.879067	−	0.113979i
$397$		−	254481.i		−	1.61464i	−0.590117	−	0.807318i	$-0.700918\pi$
$397$		−	254481.i		−	1.61464i	0.590117	−	0.807318i	$-0.299082\pi$
$398$	5607.39	−	9712.29i	0.0353993	−	0.0613134i
$399$	−9006.04	+	1800.59i	−0.0565702	+	0.0113102i
$400$	−2694.85	−	124929.i	−0.0168428	−	0.780806i
$401$	48697.9	−	28115.7i	0.302846	−	0.174848i	−0.340875	−	0.940109i	$-0.610723\pi$
$401$	48697.9	−	28115.7i	0.302846	−	0.174848i	0.643721	+	0.765261i	$0.277390\pi$
$402$	54489.3	+	62010.5i	0.337178	+	0.383719i
$403$	243788.	+	140751.i	1.50107	+	0.866646i
$404$			105078.i			0.643797i
$405$	−2411.60	−	164007.i	−0.0147026	−	0.999892i
$406$	−31000.1			−0.188066
$407$	−37184.9	+	64406.2i	−0.224480	+	0.388811i
$408$	−20290.8	+	17829.7i	−0.121893	+	0.107109i
$409$	−51157.2	−	88606.9i	−0.305816	−	0.529689i	0.671627	−	0.740890i	$-0.265596\pi$
$409$	−51157.2	−	88606.9i	−0.305816	−	0.529689i	−0.977443	+	0.211201i	$0.932263\pi$
$410$	−36372.4	+	10167.6i	−0.216374	+	0.0604854i
$411$	−46293.2	−	231546.i	−0.274053	−	1.37073i
$412$	−60074.7	−	34684.2i	−0.353914	−	0.204332i
$413$	64023.0			0.375350
$414$	−5289.47	+	40795.1i	−0.0308611	+	0.238017i
$415$	−80885.9	−	20741.1i	−0.469652	−	0.120430i
$416$	120354.	+	69486.6i	0.695465	+	0.401527i
$417$	283959.	+	96080.8i	1.63299	+	0.552541i
$418$	5739.76	−	3313.85i	0.0328505	−	0.0189662i
$419$	−50586.4	+	29206.1i	−0.288142	+	0.166359i	−0.637103	−	0.770778i	$-0.719868\pi$
$419$	−50586.4	+	29206.1i	−0.288142	+	0.166359i	0.348962	+	0.937137i	$0.386534\pi$
$420$	−35512.8	+	54526.5i	−0.201320	+	0.309107i
$421$	117518.	−	203548.i	0.663043	−	1.14842i	−0.316770	−	0.948503i	$-0.602598\pi$
$421$	117518.	−	203548.i	0.663043	−	1.14842i	0.979812	−	0.199921i	$-0.0640685\pi$
$422$	−12186.3			−0.0684301
$423$	−75830.5	−	57951.1i	−0.423802	−	0.323877i
$424$	2172.04			0.0120819
$425$	47574.1	−	28852.4i	0.263386	−	0.159737i
$426$	44092.7	−	8815.50i	0.242967	−	0.0485767i
$427$	31452.4	−	18159.1i	0.172504	−	0.0995950i
$428$	149760.	+	259392.i	0.817540	+	1.41602i
$429$	−143663.	+	126238.i	−0.780601	+	0.685923i
$430$	40106.4	+	39250.6i	0.216909	+	0.212280i
$431$		−	43601.5i		−	0.234718i	−0.993090	−	0.117359i	$-0.962557\pi$
$431$		−	43601.5i		−	0.234718i	0.993090	−	0.117359i	$-0.0374429\pi$
$432$	145410.	−	9960.05i	0.779162	−	0.0533696i
$433$		−	102452.i		−	0.546445i	−0.961951	−	0.273222i	$-0.911910\pi$
$433$		−	102452.i		−	0.546445i	0.961951	−	0.273222i	$-0.0880895\pi$
$434$	28444.4	+	16422.4i	0.151014	+	0.0871880i
$435$	−147690.	−	290811.i	−0.780500	−	1.53685i
$436$	16760.7	+	29030.4i	0.0881696	+	0.152714i
$437$	12117.3	+	20987.9i	0.0634519	+	0.109902i
$438$	−78026.8	+	15600.0i	−0.406720	+	0.0813160i
$439$	51232.1	−	88736.5i	0.265835	−	0.460440i	−0.701947	−	0.712229i	$-0.747686\pi$
$439$	51232.1	−	88736.5i	0.265835	−	0.460440i	0.967782	+	0.251789i	$0.0810189\pi$
$440$	24271.5	−	94654.0i	0.125370	−	0.488915i
$441$	−150986.	+	62887.6i	−0.776356	+	0.323361i
$442$			17858.6i			0.0914121i
$443$	123815.	−	214453.i	0.630906	−	1.09276i	−0.356461	−	0.934310i	$-0.616017\pi$
$443$	123815.	−	214453.i	0.630906	−	1.09276i	0.987367	−	0.158451i	$-0.0506500\pi$
$444$	27389.1	−	80946.3i	0.138935	−	0.410611i
$445$	−244821.	+	68437.7i	−1.23632	+	0.345601i
$446$	−45820.2	+	26454.3i	−0.230350	+	0.132992i
$447$	−15184.2	+	44875.7i	−0.0759937	+	0.224593i
$448$	−40085.4	−	23143.3i	−0.199724	−	0.115311i
$449$			79287.5i			0.393289i	0.980475	+	0.196645i	$0.0630045\pi$
$449$			79287.5i			0.393289i	−0.980475	+	0.196645i	$0.936995\pi$
$450$	55090.7	+	5938.05i	0.272053	+	0.0293237i
$451$	160020.			0.786723
$452$	−74088.0	+	128324.i	−0.362636	+	0.628104i
$453$	19892.2	+	99495.2i	0.0969363	+	0.484848i
$454$	−10759.8	−	18636.6i	−0.0522029	−	0.0904180i
$455$	24102.3	+	86220.7i	0.116422	+	0.416475i
$456$	−11904.5	+	10460.6i	−0.0572508	+	0.0503069i
$457$	−101766.	−	58754.5i	−0.487270	−	0.281325i	0.236171	−	0.971711i	$-0.424107\pi$
$457$	−101766.	−	58754.5i	−0.487270	−	0.281325i	−0.723441	+	0.690386i	$0.757441\pi$
$458$	−89876.9			−0.428467
$459$	36213.8	+	53854.4i	0.171889	+	0.255621i
$460$	166324.	+	42649.5i	0.786030	+	0.201557i
$461$	317908.	+	183544.i	1.49589	+	0.863653i	0.999989	−	0.00472615i	$-0.00150439\pi$
$461$	317908.	+	183544.i	1.49589	+	0.863653i	0.495901	+	0.868379i	$0.334838\pi$
$462$	−16762.1	+	14729.0i	−0.0785316	+	0.0690066i
$463$	−79996.4	+	46185.9i	−0.373171	+	0.215451i	−0.674843	−	0.737961i	$-0.735789\pi$
$463$	−79996.4	+	46185.9i	−0.373171	+	0.215451i	0.301672	+	0.953412i	$0.402455\pi$
$464$	250998.	−	144914.i	1.16583	−	0.673090i
$465$	−18543.6	+	345076.i	−0.0857608	+	1.59591i
$466$	−20198.0	+	34983.9i	−0.0930114	+	0.161100i
$467$	82073.0			0.376328			0.188164	−	0.982138i	$-0.439746\pi$
$467$	82073.0			0.376328			0.188164	+	0.982138i	$0.439746\pi$
$468$	133434.	−	174602.i	0.609220	−	0.797181i
$469$	−163733.			−0.744372
$470$	22550.3	−	23042.0i	0.102084	−	0.104310i
$471$	−58093.3	+	171690.i	−0.261869	+	0.773932i
$472$	95671.2	−	55235.8i	0.429435	−	0.247934i
$473$	−118886.	−	205917.i	−0.531384	−	0.920384i
$474$	−80781.8	−	27333.5i	−0.359548	−	0.121657i
$475$	27911.5	−	16927.6i	0.123707	−	0.0750253i
$476$		−	25746.1i		−	0.113631i
$477$	671.019	−	5175.24i	0.00294916	−	0.0227454i
$478$		−	29245.2i		−	0.127997i
$479$	−78567.0	−	45360.7i	−0.342428	−	0.197701i	0.318917	−	0.947783i	$-0.396681\pi$
$479$	−78567.0	−	45360.7i	−0.342428	−	0.197701i	−0.661345	+	0.750082i	$0.730014\pi$
$480$	−9154.70	+	170359.i	−0.0397339	+	0.739404i
$481$	−58784.7	−	101818.i	−0.254082	−	0.440083i
$482$	8359.71	+	14479.4i	0.0359830	+	0.0623243i
$483$	−53857.8	−	61291.8i	−0.230863	−	0.262729i
$484$	8876.46	−	15374.5i	0.0378922	−	0.0656311i
$485$	−85099.6	+	331871.i	−0.361779	+	1.41086i
$486$	−3911.00	+	64511.5i	−0.0165583	+	0.273127i
$487$		−	240214.i		−	1.01284i	−0.862287	−	0.506421i	$-0.830968\pi$
$487$		−	240214.i		−	1.01284i	0.862287	−	0.506421i	$-0.169032\pi$
$488$	31333.4	−	54271.1i	0.131573	−	0.227892i
$489$	−91420.2	−	104039.i	−0.382318	−	0.435089i
$490$	−14875.1	−	53212.6i	−0.0619538	−	0.221627i
$491$	−198232.	+	114449.i	−0.822264	+	0.474734i	−0.851197	−	0.524847i	$-0.824123\pi$
$491$	−198232.	+	114449.i	−0.822264	+	0.474734i	0.0289325	+	0.999581i	$0.490789\pi$
$492$	−180303.	+	36048.1i	−0.744855	+	0.148920i
$493$	111761.	+	64525.0i	0.459827	+	0.265481i
$494$			10477.6i			0.0429345i
$495$	−218031.	−	87073.0i	−0.889831	−	0.355364i
$496$	−307074.			−1.24819
$497$	−44593.3	+	77237.9i	−0.180533	+	0.312693i
$498$	31166.4	+	10545.5i	0.125669	+	0.0425216i
$499$	−5232.25	−	9062.53i	−0.0210130	−	0.0363956i	0.855328	−	0.518087i	$-0.173356\pi$
$499$	−5232.25	−	9062.53i	−0.0210130	−	0.0363956i	−0.876341	+	0.481692i	$0.840022\pi$
$500$	52602.7	−	225220.i	0.210411	−	0.900882i
$501$	145337.	+	49176.5i	0.579030	+	0.195922i
$502$	−16592.2	−	9579.54i	−0.0658412	−	0.0380134i
$503$	−87312.8			−0.345097			−0.172549	−	0.985001i	$-0.555200\pi$
$503$	−87312.8			−0.345097			−0.172549	+	0.985001i	$0.555200\pi$
$504$	32397.3	−	42392.7i	0.127540	−	0.166890i
$505$	−44081.9	+	171910.i	−0.172853	+	0.674092i
$506$	50991.8	+	29440.1i	0.199159	+	0.114984i
$507$	−8878.53	−	44407.9i	−0.0345402	−	0.172761i
$508$	−251016.	+	144924.i	−0.972689	+	0.561582i
$509$	211363.	−	122031.i	0.815819	−	0.471013i	−0.0331537	−	0.999450i	$-0.510555\pi$
$509$	211363.	−	122031.i	0.815819	−	0.471013i	0.848972	+	0.528437i	$0.177222\pi$
$510$	−19547.0	+	9927.08i	−0.0751520	+	0.0381664i
$511$	78912.7	−	136681.i	0.302207	−	0.523439i
$512$	−259444.			−0.989700
$513$	21246.5	+	31596.1i	0.0807332	+	0.120060i
$514$	−62409.9			−0.236226
$515$	−83733.2	−	81946.5i	−0.315706	−	0.308970i
$516$	180342.	+	205234.i	0.677325	+	0.770816i
$517$	−118303.	+	68302.6i	−0.442605	+	0.255538i
$518$	−6858.81	−	11879.8i	−0.0255617	−	0.0442741i
$519$	−34245.9	−	171289.i	−0.127138	−	0.635907i
$520$	110403.	+	108048.i	0.408297	+	0.399584i
$521$		−	342391.i		−	1.26138i	−0.776034	−	0.630692i	$-0.782771\pi$
$521$		−	342391.i		−	1.26138i	0.776034	−	0.630692i	$-0.217229\pi$
$522$	49414.0	+	118638.i	0.181346	+	0.435394i
$523$		−	313862.i		−	1.14746i	−0.819046	−	0.573728i	$-0.805497\pi$
$523$		−	313862.i		−	1.14746i	0.819046	−	0.573728i	$-0.194503\pi$
$524$	−365076.	−	210777.i	−1.32960	−	0.767645i
$525$	−80974.6	+	74308.5i	−0.293785	+	0.269600i
$526$	32525.8	+	56336.3i	0.117559	+	0.203618i
$527$	−68364.6	−	118411.i	−0.246156	−	0.426355i
$528$	66864.7	−	197613.i	0.239844	−	0.708839i
$529$	32270.6	−	55894.3i	0.115318	−	0.199736i
$530$	1707.65	+	437.883i	0.00607922	+	0.00155886i
$531$	−102052.	−	245017.i	−0.361938	−	0.868976i
$532$		−	15105.1i		−	0.0533704i
$533$	−126486.	+	219080.i	−0.445234	+	0.771167i
$534$	98220.1	−	19637.3i	0.344444	−	0.0688650i
$535$	136192.	+	487199.i	0.475823	+	1.70216i
$536$	−244670.	+	141260.i	−0.851631	+	0.491689i
$537$	39561.5	+	45022.1i	0.137190	+	0.156127i
$538$	−102093.	−	58943.5i	−0.352721	−	0.203644i
$539$			234109.i			0.805823i
$540$	265281.	+	48993.1i	0.909743	+	0.168015i
$541$	81438.3			0.278249			0.139125	−	0.990275i	$-0.455571\pi$
$541$	81438.3			0.278249			0.139125	+	0.990275i	$0.455571\pi$
$542$	−6551.63	+	11347.8i	−0.0223024	+	0.0386288i
$543$	−106413.	+	93506.0i	−0.360905	+	0.317132i
$544$	−33750.6	−	58457.7i	−0.114047	−	0.197535i
$545$	15242.2	+	54525.8i	0.0513162	+	0.183573i
$546$	−6915.82	−	34591.0i	−0.0231984	−	0.116032i
$547$	345995.	+	199760.i	1.15636	+	0.667627i	0.950430	−	0.310939i	$-0.100643\pi$
$547$	345995.	+	199760.i	1.15636	+	0.667627i	0.205934	+	0.978566i	$0.433977\pi$
$548$	388353.			1.29320
$549$	−119630.	−	91423.4i	−0.396913	−	0.303328i
$550$	38164.5	−	69523.7i	0.126164	−	0.229830i
$551$	65569.4	+	37856.5i	0.215972	+	0.124692i
$552$	−133361.	−	45124.1i	−0.437673	−	0.148092i
$553$	146489.	−	84575.3i	0.479020	−	0.276563i
$554$	25398.6	−	14663.9i	0.0827541	−	0.0477781i
$555$	78767.6	−	120940.i	0.255718	−	0.392631i
$556$	−246514.	+	426975.i	−0.797430	+	1.38119i
$557$	464065.			1.49578			0.747892	−	0.663821i	$-0.231066\pi$
$557$	464065.			1.49578			0.747892	+	0.663821i	$0.231066\pi$
$558$	17508.5	−	135034.i	0.0562316	−	0.433687i
$559$	375888.			1.20291
$560$	−69795.8	−	68306.4i	−0.222563	−	0.217814i
$561$	91088.0	−	18211.3i	0.289424	−	0.0578650i
$562$	41275.3	−	23830.3i	0.130682	−	0.0754496i
$563$	282361.	+	489064.i	0.890816	+	1.54294i	0.838899	+	0.544287i	$0.183200\pi$
$563$	282361.	+	489064.i	0.890816	+	1.54294i	0.0519165	+	0.998651i	$0.483467\pi$
$564$	117912.	−	103610.i	0.370679	−	0.325720i
$565$	−175044.	+	178861.i	−0.548340	+	0.560296i
$566$		−	68056.4i		−	0.212440i
$567$	−90999.1	−	90288.6i	−0.283055	−	0.280845i
$568$			153891.i			0.476999i
$569$	−477380.	−	275615.i	−1.47448	−	0.851292i	−0.474895	−	0.880043i	$-0.657514\pi$
$569$	−477380.	−	275615.i	−1.47448	−	0.851292i	−0.999587	+	0.0287503i	$0.990847\pi$
$570$	−11468.2	+	5824.17i	−0.0352975	+	0.0179260i
$571$	107836.	+	186778.i	0.330744	+	0.572865i	0.982658	−	0.185428i	$-0.0593670\pi$
$571$	107836.	+	186778.i	0.330744	+	0.572865i	−0.651914	+	0.758293i	$0.726034\pi$
$572$	−157268.	−	272397.i	−0.480672	−	0.832549i
$573$	258160.	−	51614.1i	0.786283	−	0.157202i
$574$	−14758.0	+	25561.6i	−0.0447923	+	0.0775825i
$575$	254218.	+	139551.i	0.768902	+	0.422083i
$576$	−24673.9	+	190298.i	−0.0743691	+	0.573573i
$577$			302487.i			0.908562i	0.890858	+	0.454281i	$0.150104\pi$
$577$			302487.i			0.908562i	−0.890858	+	0.454281i	$0.849896\pi$
$578$	−41370.4	+	71655.6i	−0.123832	+	0.214484i
$579$	124014.	−	366514.i	0.369926	−	1.09328i
$580$	516628.	−	144419.i	1.53575	−	0.429307i
$581$	−56516.9	+	32630.0i	−0.167427	+	0.0966641i
$582$	43267.8	−	127874.i	0.127738	−	0.377518i
$583$	−6468.79	−	3734.76i	−0.0190321	−	0.0109882i
$584$		−	272327.i		−	0.798483i
$585$	291549.	−	229675.i	0.851923	−	0.671123i
$586$	18843.2			0.0548731
$587$	67877.0	−	117566.i	0.196991	−	0.341198i	−0.750560	−	0.660802i	$-0.770216\pi$
$587$	67877.0	−	117566.i	0.196991	−	0.341198i	0.947551	+	0.319603i	$0.103550\pi$
$588$	−52738.1	−	263782.i	−0.152535	−	0.762939i
$589$	−40109.2	−	69471.2i	−0.115615	−	0.200251i
$590$	86352.1	−	24139.0i	0.248067	−	0.0693450i
$591$	326698.	−	287073.i	0.935343	−	0.821897i
$592$	111067.	+	64124.7i	0.316915	+	0.182971i
$593$	−612873.			−1.74285			−0.871427	−	0.490525i	$-0.836805\pi$
$593$	−612873.			−1.74285			−0.871427	+	0.490525i	$0.836805\pi$
$594$	83087.0	+	40670.8i	0.235483	+	0.115268i
$595$	10800.9	−	42121.3i	0.0305089	−	0.118978i
$596$	−67477.4	−	38958.1i	−0.189962	−	0.109674i
$597$	69272.9	−	60870.9i	0.194364	−	0.170790i
$598$	−80611.6	+	46541.1i	−0.225421	+	0.130147i
$599$	−152718.	+	88171.6i	−0.425634	+	0.245740i	−0.697485	−	0.716600i	$-0.745697\pi$
$599$	−152718.	+	88171.6i	−0.425634	+	0.245740i	0.271851	+	0.962339i	$0.412364\pi$
$600$	−56892.8	+	180902.i	−0.158036	+	0.502505i
$601$	−55051.5	+	95352.0i	−0.152412	+	0.263986i	−0.932114	−	0.362165i	$-0.882038\pi$
$601$	−55051.5	+	95352.0i	−0.152412	+	0.263986i	0.779701	+	0.626152i	$0.215371\pi$
$602$	43857.4			0.121018
$603$	260989.	+	626608.i	0.717775	+	1.72330i
$604$	−166875.			−0.457423
$605$	20972.0	−	21429.2i	0.0572966	−	0.0585458i
$606$	22412.9	−	66239.4i	0.0610313	−	0.180373i
$607$	−189924.	+	109653.i	−0.515470	+	0.297607i	−0.735079	−	0.677981i	$-0.762855\pi$
$607$	−189924.	+	109653.i	−0.515470	+	0.297607i	0.219609	+	0.975588i	$0.429522\pi$
$608$	−19801.3	−	34296.8i	−0.0535656	−	0.0927784i
$609$	−241460.	−	81701.0i	−0.651045	−	0.220289i
$610$	35575.3	−	36351.0i	0.0956069	−	0.0976915i
$611$		−	215955.i		−	0.578471i
$612$	−98530.7	+	41039.1i	−0.263068	+	0.109571i
$613$			75985.1i			0.202212i	0.994876	+	0.101106i	$0.0322382\pi$
$613$			75985.1i			0.202212i	−0.994876	+	0.101106i	$0.967762\pi$
$614$	−101790.	−	58768.3i	−0.270002	−	0.155886i
$615$	−310103.	−	16664.2i	−0.819889	−	0.0440590i
$616$	−38184.2	−	66137.0i	−0.100629	−	0.174294i
$617$	242066.	+	419271.i	0.635863	+	1.10135i	0.986331	+	0.164773i	$0.0526892\pi$
$617$	242066.	+	419271.i	0.635863	+	1.10135i	−0.350468	+	0.936575i	$0.613977\pi$
$618$	30472.0	+	34678.1i	0.0797856	+	0.0907984i
$619$	−23051.5	+	39926.4i	−0.0601614	+	0.104203i	−0.894537	−	0.446993i	$-0.852495\pi$
$619$	−23051.5	+	39926.4i	−0.0601614	+	0.104203i	0.834376	+	0.551196i	$0.185828\pi$
$620$	−550543.	−	141173.i	−1.43221	−	0.367254i
$621$	−148716.	+	303814.i	−0.385633	+	0.787815i
$622$			149285.i			0.385866i
$623$	−99335.4	+	172054.i	−0.255934	+	0.443291i
$624$	217695.	+	247743.i	0.559087	+	0.636258i
$625$	180543.	−	346399.i	0.462190	−	0.886781i
$626$	89640.9	−	51754.2i	0.228748	−	0.132068i
$627$	53440.9	−	10684.5i	0.135937	−	0.0271781i
$628$	−258162.	−	149050.i	−0.654595	−	0.377930i
$629$			57105.0i			0.144335i
$630$	34017.0	−	26797.8i	0.0857068	−	0.0675177i
$631$	240096.			0.603013			0.301507	−	0.953464i	$-0.402510\pi$
$631$	240096.			0.603013			0.301507	+	0.953464i	$0.402510\pi$
$632$	145935.	−	252766.i	0.365362	−	0.632826i
$633$	−94919.4	−	32117.1i	−0.236890	−	0.0801547i
$634$	77444.8	+	134138.i	0.192670	+	0.333714i
$635$	−471467.	+	131794.i	−1.16924	+	0.326851i
$636$	8130.03	+	2750.89i	0.0200992	+	0.00680079i
$637$	−320513.	−	185048.i	−0.789890	−	0.456043i
$638$	183951.			0.451919
$639$	366672.	+	47542.5i	0.898000	+	0.116434i
$640$	−356583.	−	91436.5i	−0.870565	−	0.223234i
$641$	480663.	+	277511.i	1.16984	+	0.675405i	0.953641	−	0.300945i	$-0.0973021\pi$
$641$	480663.	+	277511.i	1.16984	+	0.675405i	0.216195	+	0.976350i	$0.430635\pi$
$642$	−39078.6	−	195460.i	−0.0948131	−	0.474229i
$643$	560077.	−	323360.i	1.35465	−	0.782105i	0.365749	−	0.930713i	$-0.380813\pi$
$643$	560077.	−	323360.i	1.35465	−	0.782105i	0.988896	+	0.148609i	$0.0474794\pi$
$644$	116215.	−	67096.5i	0.280213	−	0.161781i
$645$	208945.	+	411425.i	0.502241	+	0.988943i
$646$	2544.55	−	4407.28i	0.00609741	−	0.0105610i
$647$	−347688.			−0.830579			−0.415289	−	0.909689i	$-0.636320\pi$
$647$	−347688.			−0.830579			−0.415289	+	0.909689i	$0.636320\pi$
$648$	−213879.	−	56411.1i	−0.509351	−	0.134343i
$649$	−379906.			−0.901959
$650$	65016.6	+	107204.i	0.153885	+	0.253738i
$651$	178273.	+	202880.i	0.420652	+	0.478715i
$652$	197267.	−	113892.i	0.464043	−	0.267915i
$653$	−304539.	−	527478.i	−0.714196	−	1.23702i	−0.963269	−	0.268538i	$-0.913459\pi$
$653$	−304539.	−	527478.i	−0.714196	−	1.23702i	0.249073	−	0.968485i	$-0.419874\pi$
$654$	−4373.55	−	21875.3i	−0.0102254	−	0.0511444i
$655$	−508850.	−	497992.i	−1.18606	−	1.16075i
$656$		−	275952.i		−	0.641247i
$657$	−648866.	−	84131.6i	−1.50323	−	0.194907i
$658$		−	25197.0i		−	0.0581965i
$659$	540048.	+	311797.i	1.24354	+	0.717961i	0.969814	−	0.243845i	$-0.0784090\pi$
$659$	540048.	+	311797.i	1.24354	+	0.717961i	0.273731	+	0.961806i	$0.411742\pi$
$660$	210729.	−	323554.i	0.483768	−	0.742778i
$661$	−184642.	−	319810.i	−0.422598	−	0.731962i	0.573594	−	0.819140i	$-0.305549\pi$
$661$	−184642.	−	319810.i	−0.422598	−	0.731962i	−0.996193	+	0.0871775i	$0.972215\pi$
$662$	45286.2	+	78438.0i	0.103336	+	0.178983i
$663$	−47066.6	+	139101.i	−0.107074	+	0.316449i
$664$	−56303.1	+	97519.8i	−0.127701	+	0.221185i
$665$	6336.84	−	24712.3i	0.0143294	−	0.0558818i
$666$	−34531.3	+	45185.1i	−0.0778511	+	0.101870i
$667$			672630.i			1.51191i
$668$	−126172.	+	218536.i	−0.282755	+	0.489746i
$669$	−426615.	+	85293.7i	−0.953201	+	0.190575i
$670$	−220837.	+	61733.2i	−0.491952	+	0.137521i
$671$	−186635.	+	107754.i	−0.414523	+	0.239325i
$672$	88010.6	+	100159.i	0.194893	+	0.221794i
$673$	−130097.	−	75111.4i	−0.287234	−	0.165835i	0.349460	−	0.936951i	$-0.386365\pi$
$673$	−130097.	−	75111.4i	−0.287234	−	0.165835i	−0.636694	+	0.771117i	$0.719699\pi$
$674$			91063.7i			0.200459i
$675$	413453.	+	191444.i	0.907442	+	0.420178i
$676$	74481.8			0.162988
$677$	290147.	−	502550.i	0.633055	−	1.09648i	−0.353869	−	0.935295i	$-0.615134\pi$
$677$	290147.	−	502550.i	0.633055	−	1.09648i	0.986924	−	0.161188i	$-0.0515326\pi$
$678$	74075.1	−	65090.6i	0.161143	−	0.141599i
$679$	133879.	+	231886.i	0.290385	+	0.502961i
$680$	−20200.0	−	72261.3i	−0.0436852	−	0.156274i
$681$	−34691.8	−	173519.i	−0.0748053	−	0.374155i
$682$	−168786.	−	97448.7i	−0.362884	−	0.209511i
$683$	−11404.6			−0.0244477			−0.0122238	−	0.999925i	$-0.503891\pi$
$683$	−11404.6			−0.0244477			−0.0122238	+	0.999925i	$0.503891\pi$
$684$	−57807.5	+	24077.5i	−0.123558	+	0.0514634i
$685$	635356.	+	162921.i	1.35405	+	0.347212i
$686$	−81862.7	−	47263.4i	−0.173955	−	0.100433i
$687$	−700054.	−	236871.i	−1.48326	−	0.501879i
$688$	−355099.	+	205017.i	−0.750192	+	0.433124i
$689$	10226.3	−	5904.18i	0.0215418	−	0.0124372i
$690$	−95750.9	−	62362.0i	−0.201115	−	0.130985i
$691$	50403.6	−	87301.6i	0.105562	−	0.182838i	−0.808406	−	0.588625i	$-0.799669\pi$
$691$	50403.6	−	87301.6i	0.105562	−	0.182838i	0.913967	+	0.405787i	$0.133003\pi$
$692$	287289.			0.599938
$693$	−169379.	+	70548.3i	−0.352690	+	0.146899i
$694$	113423.			0.235494
$695$	−582427.	+	595126.i	−1.20579	+	1.23208i
$696$	−431308.	+	86231.8i	−0.890366	+	0.178012i
$697$	106410.	−	61435.9i	0.219037	−	0.126461i
$698$	82478.7	+	142857.i	0.169290	+	0.293219i
$699$	−249523.	+	219259.i	−0.510689	+	0.448748i
$700$	−93731.9	−	154552.i	−0.191290	−	0.315412i
$701$			220659.i			0.449040i	0.974469	+	0.224520i	$0.0720814\pi$
$701$			220659.i			0.449040i	−0.974469	+	0.224520i	$0.927919\pi$
$702$	−121357.	+	81604.9i	−0.246257	+	0.165593i
$703$			33503.2i			0.0677916i
$704$	237862.	+	137330.i	0.479933	+	0.277089i
$705$	236373.	−	120043.i	0.475575	−	0.241524i
$706$	−12115.0	−	20983.8i	−0.0243060	−	0.0420993i
$707$	69350.1	+	120118.i	0.138742	+	0.240308i
$708$	428058.	−	85582.2i	0.853958	−	0.170733i
$709$	64731.1	−	112118.i	0.128772	−	0.223039i	−0.794429	−	0.607357i	$-0.792230\pi$
$709$	64731.1	−	112118.i	0.128772	−	0.223039i	0.923201	+	0.384318i	$0.125563\pi$
$710$	−31024.5	+	120989.i	−0.0615444	+	0.240010i
$711$	−557174.	−	425802.i	−1.10218	−	0.842304i
$712$			342806.i			0.676221i
$713$	356328.	−	617179.i	0.700924	−	1.21404i
$714$	−5491.58	+	16229.9i	−0.0107721	+	0.0318361i
$715$	−143020.	−	511625.i	−0.279760	−	1.00078i
$716$	−85365.8	+	49286.0i	−0.166517	+	0.0961385i
$717$	77076.0	−	227792.i	0.149927	−	0.443097i
$718$	86187.4	+	49760.3i	0.167184	+	0.0965238i
$719$			354459.i			0.685659i	0.939398	+	0.342829i	$0.111385\pi$
$719$			354459.i			0.685659i	−0.939398	+	0.342829i	$0.888615\pi$
$720$	−150156.	+	375990.i	−0.289652	+	0.725289i
$721$	−91564.3			−0.176139
$722$	−69826.2	+	120943.i	−0.133950	+	0.232009i
$723$	26953.3	+	134813.i	0.0515626	+	0.257902i
$724$	−116490.	−	201767.i	−0.222235	−	0.384923i
$725$	905803.	−	19539.1i	1.72329	−	0.0371731i
$726$	−8874.92	+	7798.49i	−0.0168380	+	0.0147958i
$727$	−173161.	−	99974.6i	−0.327628	−	0.189156i	0.327159	−	0.944969i	$-0.393909\pi$
$727$	−173161.	−	99974.6i	−0.327628	−	0.189156i	−0.654788	+	0.755813i	$0.727242\pi$
$728$	120729.			0.227797
$729$	−200484.	+	492175.i	−0.377245	+	0.926113i
$730$	54901.3	−	214103.i	0.103024	−	0.401770i
$731$	−158113.	−	91286.7i	−0.295892	−	0.170833i
$732$	186017.	−	163455.i	0.347161	−	0.305054i
$733$	746774.	−	431150.i	1.38989	−	0.802455i	0.396590	−	0.917996i	$-0.370193\pi$
$733$	746774.	−	431150.i	1.38989	−	0.802455i	0.993303	+	0.115541i	$0.0368600\pi$
$734$	−18720.2	+	10808.1i	−0.0347471	+	0.0200612i
$735$	24379.7	−	453678.i	0.0451287	−	0.839794i
$736$	175914.	−	304691.i	0.324746	−	0.562477i
$737$	971573.			1.78871
$738$	121349.	+	15734.0i	0.222804	+	0.0288886i
$739$	684605.			1.25358			0.626789	−	0.779189i	$-0.284369\pi$
$739$	684605.			1.25358			0.626789	+	0.779189i	$0.284369\pi$
$740$	169649.	+	166029.i	0.309804	+	0.303193i
$741$	−27613.7	+	81610.1i	−0.0502908	+	0.148630i
$742$	1193.18	−	688.881i	0.00216719	−	0.00125123i
$743$	−400928.	−	694427.i	−0.726254	−	1.25791i	−0.958456	−	0.285241i	$-0.907926\pi$
$743$	−400928.	−	694427.i	−0.726254	−	1.25791i	0.232202	−	0.972668i	$-0.425407\pi$
$744$	441432.	+	149364.i	0.797477	+	0.269836i
$745$	−94051.3	−	92044.4i	−0.169454	−	0.165838i
$746$			119679.i			0.215050i
$747$	214963.	+	164279.i	0.385233	+	0.294402i
$748$			152775.i			0.273053i
$749$	342391.	+	197679.i	0.610321	+	0.352369i
$750$	−81198.9	+	130755.i	−0.144354	+	0.232454i
$751$	−254539.	−	440875.i	−0.451310	−	0.781692i	0.547158	−	0.837030i	$-0.315710\pi$
$751$	−254539.	−	440875.i	−0.451310	−	0.781692i	−0.998468	+	0.0553377i	$0.982376\pi$
$752$	117786.	+	204012.i	0.208286	+	0.360761i
$753$	−103990.	−	118344.i	−0.183402	−	0.208717i
$754$	−145402.	+	251843.i	−0.255757	+	0.442983i
$755$	−273012.	−	70006.9i	−0.478948	−	0.122814i
$756$	174955.	−	117647.i	0.306114	−	0.205843i
$757$			766769.i			1.33805i	0.743239	+	0.669026i	$0.233288\pi$
$757$			766769.i			1.33805i	−0.743239	+	0.669026i	$0.766712\pi$
$758$	41350.8	−	71621.6i	0.0719689	−	0.124654i
$759$	319587.	+	363699.i	0.554760	+	0.631333i
$760$	−11851.3	−	42395.4i	−0.0205181	−	0.0733992i
$761$	283879.	−	163898.i	0.490190	−	0.283011i	−0.234463	−	0.972125i	$-0.575333\pi$
$761$	283879.	−	163898.i	0.490190	−	0.283011i	0.724653	+	0.689114i	$0.242000\pi$
$762$	189148.	−	37816.6i	0.325756	−	0.0651288i
$763$	38319.3	+	22123.6i	0.0658216	+	0.0380021i
$764$			432990.i			0.741808i
$765$	−178415.	+	25805.9i	−0.304866	+	0.0440957i
$766$	−236688.			−0.403384
$767$	300292.	−	520120.i	0.510449	−	0.884124i
$768$	−185746.	−	62849.2i	−0.314917	−	0.106556i
$769$	−197438.	−	341972.i	−0.333870	−	0.578280i	0.649397	−	0.760449i	$-0.275021\pi$
$769$	−197438.	−	341972.i	−0.333870	−	0.578280i	−0.983267	+	0.182170i	$0.941688\pi$
$770$	−16687.1	−	59694.7i	−0.0281449	−	0.100683i
$771$	−486113.	−	164482.i	−0.817764	−	0.276700i
$772$	551109.	+	318183.i	0.924705	+	0.533878i
$773$	−121076.			−0.202628			−0.101314	−	0.994855i	$-0.532305\pi$
$773$	−121076.			−0.202628			−0.101314	+	0.994855i	$0.532305\pi$
$774$	−69908.4	−	167843.i	−0.116694	−	0.280170i
$775$	−841479.	−	461924.i	−1.40101	−	0.769072i
$776$	400118.	+	231008.i	0.664454	+	0.383623i
$777$	−22114.1	−	110609.i	−0.0366292	−	0.183209i
$778$	53606.5	−	30949.7i	0.0885642	−	0.0511326i
$779$	62430.3	−	36044.1i	0.102878	−	0.0593964i
$780$	276403.	+	544254.i	0.454311	+	0.894566i
$781$	264612.	−	458321.i	0.433818	−	0.751395i
$782$	45211.3			0.0739321
$783$	72215.7	+	1.05430e6i	0.117790	+	1.71966i
$784$	403716.			0.656816
$785$	−359830.	−	352152.i	−0.583927	−	0.571467i
$786$	185180.	+	210740.i	0.299743	+	0.341116i
$787$	−523274.	+	302112.i	−0.844849	+	0.487774i	−0.858910	−	0.512127i	$-0.828858\pi$
$787$	−523274.	+	302112.i	−0.844849	+	0.487774i	0.0140603	+	0.999901i	$0.495524\pi$
$788$	357638.	+	619446.i	0.575958	+	0.997588i
$789$	104869.	+	524527.i	0.168459	+	0.842586i
$790$	165691.	−	169304.i	0.265488	−	0.271277i
$791$			195588.i			0.312601i
$792$	−192242.	+	251554.i	−0.306477	+	0.401033i
$793$		−	340691.i		−	0.541769i
$794$	−241217.	−	139267.i	−0.382619	−	0.220905i
$795$	12146.9	+	7911.21i	0.0192190	+	0.0125172i
$796$	75833.5	+	131347.i	0.119684	+	0.207298i
$797$	−444851.	−	770505.i	−0.700322	−	1.21299i	−0.968353	−	0.249584i	$-0.919706\pi$
$797$	−444851.	−	770505.i	−0.700322	−	1.21299i	0.268031	−	0.963410i	$-0.413627\pi$
$798$	−3221.88	+	9522.00i	−0.00505946	+	0.0149528i
$799$	−52446.2	+	90839.5i	−0.0821524	+	0.142292i
$800$	−415425.	−	228045.i	−0.649102	−	0.356320i
$801$	816793.	+	105905.i	1.27306	+	0.165064i
$802$		−	61546.2i		−	0.0956868i
$803$	−468260.	+	811049.i	−0.726199	+	1.25781i
$804$	−1.09472e6	+	218868.i	−1.69352	+	0.338587i
$805$	218278.	−	61017.7i	0.336836	−	0.0941595i
$806$	266830.	−	154054.i	0.410737	−	0.237139i
$807$	−639860.	−	728180.i	−0.982512	−	1.11813i
$808$	207263.	+	119663.i	0.317468	+	0.183290i
$809$		−	351052.i		−	0.536382i	−0.963366	−	0.268191i	$-0.913574\pi$
$809$		−	351052.i		−	0.536382i	0.963366	−	0.268191i	$-0.0864258\pi$
$810$	−156779.	−	87468.3i	−0.238955	−	0.133315i
$811$	−316054.			−0.480529			−0.240264	−	0.970707i	$-0.577234\pi$
$811$	−316054.			−0.480529			−0.240264	+	0.970707i	$0.577234\pi$
$812$	209620.	−	363072.i	0.317922	−	0.550657i
$813$	−80937.9	+	71121.1i	−0.122453	+	0.107601i
$814$	40699.4	+	70493.5i	0.0614242	+	0.106390i
$815$	370513.	−	103574.i	0.557812	−	0.155932i
$816$	−31405.1	−	157079.i	−0.0471649	−	0.235906i
$817$	−92764.3	−	53557.5i	−0.138975	−	0.0802373i
$818$	−111985.			−0.167360
$819$	37297.4	−	287657.i	0.0556046	−	0.428852i
$820$	126865.	−	494746.i	0.188674	−	0.735791i
$821$	−853848.	−	492970.i	−1.26676	−	0.731364i	−0.292387	−	0.956300i	$-0.594449\pi$
$821$	−853848.	−	492970.i	−1.26676	−	0.731364i	−0.974374	+	0.224936i	$0.927783\pi$
$822$	−244811.	−	82834.9i	−0.362316	−	0.122594i
$823$	−547461.	+	316077.i	−0.808264	+	0.466651i	−0.846353	−	0.532623i	$-0.821206\pi$
$823$	−547461.	+	316077.i	−0.808264	+	0.466651i	0.0380887	+	0.999274i	$0.487873\pi$
$824$	−136827.	+	78997.0i	−0.201519	+	0.116347i
$825$	480495.	−	440939.i	0.705961	−	0.647844i
$826$	35037.1	−	60686.0i	0.0513532	−	0.0889464i
$827$	309027.			0.451840			0.225920	−	0.974146i	$-0.427461\pi$
$827$	309027.			0.451840			0.225920	+	0.974146i	$0.427461\pi$
$828$	−442025.	−	337803.i	−0.644742	−	0.492724i
$829$	−832364.			−1.21117			−0.605584	−	0.795782i	$-0.707060\pi$
$829$	−832364.			−1.21117			−0.605584	+	0.795782i	$0.707060\pi$
$830$	−63925.4	+	65319.2i	−0.0927934	+	0.0948166i
$831$	236477.	−	47279.1i	0.342442	−	0.0684647i
$832$	−376030.	+	217101.i	−0.543221	+	0.313629i
$833$	89880.3	+	155677.i	0.129531	+	0.224355i
$834$	246471.	−	216577.i	0.354351	−	0.311373i
$835$	−298100.	+	304600.i	−0.427552	+	0.436875i
$836$			89632.1i			0.128248i
$837$	492259.	−	1.00564e6i	0.702656	−	1.43547i
$838$			63933.0i			0.0910410i
$839$	718506.	+	414830.i	1.02072	+	0.589313i	0.914312	−	0.405010i	$-0.132732\pi$
$839$	718506.	+	414830.i	1.02072	+	0.589313i	0.106407	+	0.994323i	$0.466065\pi$
$840$	67109.6	+	132143.i	0.0951099	+	0.187277i
$841$	697061.	+	1.20734e6i	0.985550	+	1.70702i
$842$	−128626.	−	222786.i	−0.181427	−	0.314241i
$843$	384299.	−	76833.4i	0.540772	−	0.108117i
$844$	82402.8	−	142726.i	0.115680	−	0.200363i
$845$	121854.	+	31246.3i	0.170658	+	0.0437608i
$846$	−96429.3	+	40163.9i	−0.134731	+	0.0561171i
$847$		−	23433.4i		−	0.0326639i
$848$	−6440.51	+	11155.3i	−0.00895630	+	0.0155128i
$849$	179363.	−	530093.i	0.248839	−	0.735423i
$850$	−1313.33	−	60884.1i	−0.00181776	−	0.0842686i
$851$	−257765.	+	148820.i	−0.355930	+	0.205496i
$852$	−194904.	+	576023.i	−0.268498	+	0.793524i
$853$	−607611.	−	350804.i	−0.835079	−	0.482133i	0.0205095	−	0.999790i	$-0.493471\pi$
$853$	−607611.	−	350804.i	−0.835079	−	0.482133i	−0.855588	+	0.517657i	$0.826805\pi$
$854$		−	39750.7i		−	0.0545041i
$855$	−104675.	+	15140.2i	−0.143190	+	0.0207109i
$856$	682191.			0.931019
$857$	−542612.	+	939831.i	−0.738801	+	1.27964i	0.214234	+	0.976782i	$0.431274\pi$
$857$	−542612.	+	939831.i	−0.738801	+	1.27964i	−0.953035	+	0.302859i	$0.902059\pi$
$858$	41037.7	+	205259.i	0.0557454	+	0.278823i
$859$	442391.	+	766243.i	0.599542	+	1.03844i	0.992889	+	0.119047i	$0.0379839\pi$
$859$	442391.	+	766243.i	0.599542	+	1.03844i	−0.393347	+	0.919390i	$0.628683\pi$
$860$	−730900.	+	204317.i	−0.988236	+	0.276253i
$861$	−182318.	+	160205.i	−0.245937	+	0.216107i
$862$	−41328.9	−	23861.2i	−0.0556210	−	0.0321128i
$863$	−848540.			−1.13933			−0.569667	−	0.821876i	$-0.692928\pi$
$863$	−848540.			−1.13933			−0.569667	+	0.821876i	$0.692928\pi$
$864$	243020.	−	496470.i	0.325548	−	0.665068i
$865$	470011.	+	120522.i	0.628169	+	0.161077i
$866$	−97112.3	−	56067.8i	−0.129491	−	0.0747615i
$867$	−511084.	+	449095.i	−0.679914	+	0.597448i
$868$	−384678.	+	222094.i	−0.510573	+	0.294779i
$869$	−869248.	+	501861.i	−1.15108	+	0.664575i
$870$	−356478.	−	19156.3i	−0.470971	−	0.0253089i
$871$	−767967.	+	1.33016e6i	−1.01229	+	1.75334i
$872$	76348.6			0.100408
$873$	674028.	−	881983.i	0.884401	−	1.15726i
$874$	26525.2			0.0347245
$875$	−88510.7	−	292173.i	−0.115606	−	0.381614i
$876$	344904.	−	1.01933e6i	0.449459	−	1.32834i
$877$	445046.	−	256947.i	0.578636	−	0.334076i	−0.181955	−	0.983307i	$-0.558243\pi$
$877$	445046.	−	256947.i	0.578636	−	0.334076i	0.760591	+	0.649231i	$0.224909\pi$
$878$	−56074.2	−	97123.4i	−0.0727402	−	0.125990i
$879$	146770.	+	49661.4i	0.189959	+	0.0642749i
$880$	414161.	+	405323.i	0.534815	+	0.523403i
$881$			222212.i			0.286297i	0.989701	+	0.143148i	$0.0457226\pi$
$881$			222212.i			0.286297i	−0.989701	+	0.143148i	$0.954277\pi$
$882$	−23018.7	+	177532.i	−0.0295900	+	0.228213i
$883$		−	248366.i		−	0.318545i	−0.987235	−	0.159272i	$-0.949085\pi$
$883$		−	248366.i		−	0.318545i	0.987235	−	0.159272i	$-0.0509148\pi$
$884$	−209160.	−	120759.i	−0.267654	−	0.154530i
$885$	736218.	+	39562.7i	0.939982	+	0.0505126i
$886$	−135517.	−	234722.i	−0.172634	−	0.299011i
$887$	432263.	+	748702.i	0.549415	+	0.951616i	0.998315	+	0.0580331i	$0.0184829\pi$
$887$	432263.	+	748702.i	0.549415	+	0.951616i	−0.448899	+	0.893582i	$0.648184\pi$
$888$	−128473.	−	146206.i	−0.162924	−	0.185413i
$889$	−191296.	+	331334.i	−0.242048	+	0.419240i
$890$	−69109.7	+	269514.i	−0.0872488	+	0.340252i
$891$	539979.	+	535763.i	0.680176	+	0.674865i
$892$		−	715528.i		−	0.899284i
$893$	−30769.9	+	53295.1i	−0.0385855	+	0.0668320i
$894$	34227.0	+	38951.3i	0.0428246	+	0.0487357i
$895$	−160337.	+	44820.8i	−0.200165	+	0.0559543i
$896$	−249153.	+	143849.i	−0.310349	+	0.179180i
$897$	−750545.	+	150057.i	−0.932808	+	0.186497i
$898$	75154.8	+	43390.7i	0.0931975	+	0.0538076i
$899$		−	2.22645e6i		−	2.75482i
$900$	−442065.	+	605069.i	−0.545760	+	0.746999i
$901$	−5735.47			−0.00706512
$902$	87572.3	−	151680.i	0.107635	−	0.186429i
$903$	341606.	+	115586.i	0.418938	+	0.141753i
$904$	168744.	+	292272.i	0.206486	+	0.357644i
$905$	−105937.	−	378966.i	−0.129345	−	0.462704i
$906$	105195.	+	35594.1i	0.128156	+	0.0433633i
$907$	929719.	+	536773.i	1.13015	+	0.652494i	0.943973	−	0.330022i	$-0.107056\pi$
$907$	929719.	+	536773.i	1.13015	+	0.652494i	0.186179	+	0.982516i	$0.440390\pi$
$908$	291029.			0.352992
$909$	349149.	−	456871.i	0.422555	−	0.552925i
$910$	94916.8	+	24338.9i	0.114620	+	0.0293913i
$911$	−872700.	−	503854.i	−1.05155	−	0.607110i	−0.128464	−	0.991714i	$-0.541005\pi$
$911$	−872700.	−	503854.i	−1.05155	−	0.607110i	−0.923082	+	0.384604i	$0.874338\pi$
$912$	−18425.2	−	92157.7i	−0.0221525	−	0.110801i
$913$	335365.	−	193623.i	0.402324	−	0.232282i
$914$	−111384.	+	64307.7i	−0.133331	+	0.0769787i
$915$	372901.	−	189380.i	0.445401	−	0.226199i
$916$	607741.	−	1.05264e6i	0.724315	−	1.25455i
$917$	−556440.			−0.661728
$918$	70865.7	−	4854.02i	0.0840912	−	0.00575992i
$919$	−576271.			−0.682332			−0.341166	−	0.940003i	$-0.610822\pi$
$919$	−576271.			−0.682332			−0.341166	+	0.940003i	$0.610822\pi$
$920$	273535.	−	279500.i	0.323175	−	0.330222i
$921$	−637958.	−	726015.i	−0.752095	−	0.855907i
$922$	347955.	−	200892.i	0.409318	−	0.236320i
$923$	418318.	+	724549.i	0.491025	+	0.850480i
$924$	−59162.5	−	295914.i	−0.0692951	−	0.346595i
$925$	207898.	+	342798.i	0.242978	+	0.400640i
$926$			101102.i			0.117907i
$927$	145953.	+	350418.i	0.169845	+	0.407781i
$928$		−	1.09916e6i		−	1.27634i
$929$	−889734.	−	513688.i	−1.03093	−	0.595207i	−0.113679	−	0.993518i	$-0.536263\pi$
$929$	−889734.	−	513688.i	−1.03093	−	0.595207i	−0.917251	+	0.398310i	$0.869597\pi$
$930$	316942.	+	206422.i	0.366449	+	0.238666i
$931$	52732.3	+	91335.1i	0.0608384	+	0.105375i
$932$	−273154.	−	473117.i	−0.314468	−	0.544674i
$933$	−393443.	+	1.16279e6i	−0.451979	+	1.33579i
$934$	44915.0	−	77795.1i	0.0514870	−	0.0891782i
$935$	−64091.4	+	249943.i	−0.0733122	+	0.285902i
$936$	−192441.	−	462031.i	−0.219658	−	0.527375i
$937$			358312.i			0.408115i	0.978959	+	0.204057i	$0.0654129\pi$
$937$			358312.i			0.408115i	−0.978959	+	0.204057i	$0.934587\pi$
$938$	−89604.0	+	155199.i	−0.101841	+	0.176393i
$939$	834614.	−	166865.i	0.946574	−	0.189250i
$940$	117384.	+	419918.i	0.132848	+	0.475235i
$941$	634781.	−	366491.i	0.716877	−	0.413889i	−0.0967250	−	0.995311i	$-0.530837\pi$
$941$	634781.	−	366491.i	0.716877	−	0.413889i	0.813602	+	0.581422i	$0.197503\pi$
$942$	130949.	+	149024.i	0.147571	+	0.167940i
$943$	554628.	+	320214.i	0.623703	+	0.360095i
$944$			655140.i			0.735174i
$945$	335585.	−	119076.i	0.375785	−	0.133340i
$946$	−260245.			−0.290804
$947$	361257.	−	625716.i	0.402825	−	0.697713i	−0.591241	−	0.806495i	$-0.701362\pi$
$947$	361257.	−	625716.i	0.402825	−	0.697713i	0.994066	+	0.108782i	$0.0346950\pi$
$948$	866369.	−	761288.i	0.964020	−	0.847096i
$949$	−740260.	−	1.28217e6i	−0.821962	−	1.42368i
$950$	−770.526	−	35720.4i	−0.000853768	−	0.0395794i
$951$	249697.	+	1.24891e6i	0.276091	+	1.38093i
$952$	−50783.3	−	29319.8i	−0.0560335	−	0.0323509i
$953$	686812.			0.756227			0.378113	−	0.925759i	$-0.376573\pi$
$953$	686812.			0.756227			0.378113	+	0.925759i	$0.376573\pi$
$954$	−4538.28	−	3468.23i	−0.00498648	−	0.00381076i
$955$	−181646.	+	708383.i	−0.199168	+	0.776715i
$956$	342519.	+	197754.i	0.374774	+	0.216376i
$957$	1.43280e6	+	484805.i	1.56445	+	0.529350i
$958$	−85992.7	+	49647.9i	−0.0936980	+	0.0540966i
$959$	443938.	−	256308.i	0.482709	−	0.278692i
$960$	−446651.	−	290901.i	−0.484647	−	0.315648i
$961$	−717709.	+	1.24311e6i	−0.777144	+	1.34605i
$962$	−128681.			−0.139048
$963$	210753.	−	1.62544e6i	0.227259	−	1.75274i
$964$	−226111.			−0.243314
$965$	768146.	+	751755.i	0.824877	+	0.807275i
$966$	−87571.2	+	17508.2i	−0.0938441	+	0.0187624i
$967$	−217686.	+	125681.i	−0.232797	+	0.134406i	−0.611862	−	0.790965i	$-0.709579\pi$
$967$	−217686.	+	125681.i	−0.232797	+	0.134406i	0.379064	+	0.925370i	$0.376246\pi$
$968$	−20217.1	−	35017.1i	−0.0215759	−	0.0373705i
$969$	31435.0	−	27622.3i	0.0334785	−	0.0294179i
$970$	268001.	+	262282.i	0.284835	+	0.278757i
$971$			299319.i			0.317465i	0.987322	+	0.158733i	$0.0507408\pi$
$971$			299319.i			0.317465i	−0.987322	+	0.158733i	$0.949259\pi$
$972$	−729113.	−	482027.i	−0.771724	−	0.510199i
$973$			650784.i			0.687403i
$974$	−227694.	−	131459.i	−0.240012	−	0.138571i
$975$	223878.	+	1.00637e6i	0.235507	+	1.05864i
$976$	185819.	+	321849.i	0.195070	+	0.337872i
$977$	352133.	+	609912.i	0.368907	+	0.638966i	0.989395	−	0.145250i	$-0.0463986\pi$
$977$	352133.	+	609912.i	0.368907	+	0.638966i	−0.620488	+	0.784216i	$0.713065\pi$
$978$	−148646.	+	29719.1i	−0.155409	+	0.0310712i
$979$	589446.	−	1.02095e6i	0.615004	−	1.06522i
$980$	723810.	+	185602.i	0.753654	+	0.193255i
$981$	23586.8	−	181914.i	0.0245093	−	0.189028i
$982$			250533.i			0.259802i
$983$	343643.	−	595207.i	0.355632	−	0.615972i	−0.631594	−	0.775299i	$-0.717599\pi$
$983$	343643.	−	595207.i	0.355632	−	0.615972i	0.987226	+	0.159327i	$0.0509324\pi$
$984$	−134226.	+	396693.i	−0.138626	+	0.409699i
$985$	325237.	+	1.16347e6i	0.335218	+	1.19917i
$986$	122323.	−	70623.5i	0.125822	−	0.0726433i
$987$	66406.9	−	196260.i	0.0681678	−	0.201464i
$988$	−122713.	−	70848.5i	−0.125712	−	0.0725800i
$989$		−	951604.i		−	0.972890i
$990$	−201853.	+	159015.i	−0.205952	+	0.162244i
$991$	315848.			0.321611			0.160806	−	0.986986i	$-0.448591\pi$
$991$	315848.			0.321611			0.160806	+	0.986986i	$0.448591\pi$
$992$	−582286.	+	1.00855e6i	−0.591715	+	1.02488i
$993$	146011.	+	730308.i	0.148077	+	0.740641i
$994$	48808.0	+	84538.0i	0.0493990	+	0.0855617i
$995$	68963.1	+	246701.i	0.0696580	+	0.249187i
$996$	−334254.	+	293713.i	−0.336944	+	0.296077i
$997$	−458423.	−	264671.i	−0.461186	−	0.266266i	0.251357	−	0.967895i	$-0.419123\pi$
$997$	−458423.	−	264671.i	−0.461186	−	0.266266i	−0.712543	+	0.701629i	$0.752457\pi$
$998$	−11453.6			−0.0114995
$999$	−388051.	+	260941.i	−0.388828	+	0.261463i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.h.a.29.13	yes	44
3.2	odd	2		135.5.h.a.89.10		44
5.4	even	2	inner	45.5.h.a.29.10	yes	44
9.2	odd	6		405.5.d.a.404.25		44
9.4	even	3		135.5.h.a.44.13		44
9.5	odd	6	inner	45.5.h.a.14.10	✓	44
9.7	even	3		405.5.d.a.404.19		44
15.14	odd	2		135.5.h.a.89.13		44
45.4	even	6		135.5.h.a.44.10		44
45.14	odd	6	inner	45.5.h.a.14.13	yes	44
45.29	odd	6		405.5.d.a.404.20		44
45.34	even	6		405.5.d.a.404.26		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.10	✓	44	9.5	odd	6	inner
45.5.h.a.14.13	yes	44	45.14	odd	6	inner
45.5.h.a.29.10	yes	44	5.4	even	2	inner
45.5.h.a.29.13	yes	44	1.1	even	1	trivial
135.5.h.a.44.10		44	45.4	even	6
135.5.h.a.44.13		44	9.4	even	3
135.5.h.a.89.10		44	3.2	odd	2
135.5.h.a.89.13		44	15.14	odd	2
405.5.d.a.404.19		44	9.7	even	3
405.5.d.a.404.20		44	45.29	odd	6
405.5.d.a.404.25		44	9.2	odd	6
405.5.d.a.404.26		44	45.34	even	6

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	45.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.547257 - 0.947877i) q^{2} +(6.76074 - 5.94074i) q^{3} +(7.40102 + 12.8189i) q^{4} +(6.73050 + 24.0770i) q^{5} +(-1.93123 - 9.65947i) q^{6} +(16.9207 + 9.76914i) q^{7} +33.7133 q^{8} +(10.4152 - 80.3276i) q^{9} +(26.5053 + 6.79660i) q^{10} +(-100.405 - 57.9690i) q^{11} +(126.190 + 42.6980i) q^{12} +(158.728 - 91.6418i) q^{13} +(18.5199 - 10.6925i) q^{14} +(188.538 + 122.794i) q^{15} +(-99.9665 + 173.147i) q^{16} -89.0232 q^{17} +(-70.4409 - 53.8322i) q^{18} -52.2295 q^{19} +(-258.829 + 264.472i) q^{20} +(172.432 - 34.4745i) q^{21} +(-109.895 + 63.4480i) q^{22} +(-232.002 - 401.839i) q^{23} +(227.927 - 200.282i) q^{24} +(-534.401 + 324.100i) q^{25} -200.607i q^{26} +(-406.791 - 604.948i) q^{27} +289.206i q^{28} +(-1255.41 - 724.811i) q^{29} +(219.572 - 111.511i) q^{30} +(767.942 + 1330.11i) q^{31} +(379.121 + 656.657i) q^{32} +(-1023.19 + 204.568i) q^{33} +(-48.7186 + 84.3831i) q^{34} +(-121.327 + 473.149i) q^{35} +(1106.80 - 460.994i) q^{36} -641.462i q^{37} +(-28.5830 + 49.5071i) q^{38} +(528.700 - 1562.53i) q^{39} +(226.907 + 811.713i) q^{40} +(-1195.31 + 690.111i) q^{41} +(61.6871 - 182.311i) q^{42} +(1776.09 + 1025.43i) q^{43} -1716.12i q^{44} +(2004.14 - 289.878i) q^{45} -507.859 q^{46} +(589.129 - 1020.40i) q^{47} +(352.774 + 1764.48i) q^{48} +(-1009.63 - 1748.73i) q^{49} +(14.7527 + 683.912i) q^{50} +(-601.863 + 528.864i) q^{51} +(2349.50 + 1356.49i) q^{52} +64.4267 q^{53} +(-796.036 + 54.5254i) q^{54} +(719.940 - 2807.62i) q^{55} +(570.451 + 329.350i) q^{56} +(-353.110 + 310.282i) q^{57} +(-1374.06 + 793.316i) q^{58} +(2837.79 - 1638.40i) q^{59} +(-178.714 + 3325.66i) q^{60} +(929.409 - 1609.78i) q^{61} +1681.05 q^{62} +(960.964 - 1257.45i) q^{63} -2369.02 q^{64} +(3274.78 + 3204.90i) q^{65} +(-366.044 + 1081.81i) q^{66} +(-7257.38 + 4190.05i) q^{67} +(-658.862 - 1141.18i) q^{68} +(-3955.73 - 1338.47i) q^{69} +(382.090 + 373.937i) q^{70} +4564.71i q^{71} +(351.131 - 2708.11i) q^{72} -8077.75i q^{73} +(-608.027 - 351.045i) q^{74} +(-1687.55 + 5365.89i) q^{75} +(-386.551 - 669.527i) q^{76} +(-1132.62 - 1961.75i) q^{77} +(-1191.75 - 1356.25i) q^{78} +(4328.70 - 7497.52i) q^{79} +(-4841.68 - 1241.52i) q^{80} +(-6344.05 - 1673.26i) q^{81} +1510.67i q^{82} +(-1670.06 + 2892.62i) q^{83} +(1718.10 + 1955.25i) q^{84} +(-599.171 - 2143.41i) q^{85} +(1943.96 - 1122.34i) q^{86} +(-12793.4 + 2557.80i) q^{87} +(-3384.99 - 1954.33i) q^{88} +10168.3i q^{89} +(822.014 - 2058.32i) q^{90} +3581.05 q^{91} +(3434.10 - 5948.04i) q^{92} +(13093.7 + 4430.42i) q^{93} +(-644.811 - 1116.84i) q^{94} +(-351.531 - 1257.53i) q^{95} +(6464.17 + 2187.23i) q^{96} +(11868.3 + 6852.15i) q^{97} -2210.10 q^{98} +(-5702.26 + 7461.56i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) \) 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * q^99

Introduction

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