LMFDB - Embedded newform 45.5.h.a.29.10

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			29.10
Character	$\chi$	$=$	45.29
Dual form			45.5.h.a.14.10

$q$-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} +(-17.4860 - 17.8673i) 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} +(224.363 + 16.9161i) q^{15} +(-99.9665 + 173.147i) q^{16} +89.0232 q^{17} +(70.4409 + 53.8322i) q^{18} -52.2295 q^{19} +(99.6252 - 356.388i) 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} +(-13.4788 + 624.855i) q^{25} -200.607i q^{26} +(406.791 + 604.948i) q^{27} -289.206i q^{28} +(-1255.41 - 724.811i) q^{29} +(-138.819 + 203.411i) 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} +(589.511 + 602.364i) q^{40} +(-1195.31 + 690.111i) q^{41} +(-61.6871 + 182.311i) q^{42} +(-1776.09 - 1025.43i) q^{43} -1716.12i q^{44} +(-1617.36 + 1218.52i) q^{45} -507.859 q^{46} +(-589.129 + 1020.40i) q^{47} +(-352.774 - 1764.48i) q^{48} +(-1009.63 - 1748.73i) q^{49} +(-584.909 - 354.732i) 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} +(1443.67 + 3001.30i) q^{60} +(929.409 - 1609.78i) q^{61} -1681.05 q^{62} +(-960.964 + 1257.45i) q^{63} -2369.02 q^{64} +(4412.91 + 1233.59i) 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} +(-514.884 - 143.931i) q^{70} +4564.71i q^{71} +(-351.131 + 2708.11i) q^{72} +8077.75i q^{73} +(-608.027 - 351.045i) q^{74} +(-3620.97 - 4304.55i) 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} +(-1556.66 - 1590.60i) q^{85} +(1943.96 - 1122.34i) q^{86} +(12793.4 - 2557.80i) q^{87} +(3384.99 + 1954.33i) q^{88} +10168.3i q^{89} +(-269.896 - 2199.90i) q^{90} +3581.05 q^{91} +(-3434.10 + 5948.04i) q^{92} +(-13093.7 - 4430.42i) q^{93} +(-644.811 - 1116.84i) q^{94} +(913.285 + 933.198i) 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	−0.926289	−	0.376814i	$-0.877020\pi$
$2$	−0.547257	+	0.947877i	−0.136814	+	0.236969i	0.789475	+	0.613783i	$0.210353\pi$
$3$	−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
$5$	−17.4860	−	17.8673i	−0.699440	−	0.714691i
$5$	−17.4860	−	17.8673i	−0.699440	−	0.714691i
$6$	−1.93123	−	9.65947i	−0.0536452	−	0.268318i
$7$	−16.9207	−	9.76914i	−0.345319	−	0.199370i	0.317302	−	0.948324i	$-0.397223\pi$
$7$	−16.9207	−	9.76914i	−0.345319	−	0.199370i	−0.662622	+	0.748954i	$0.730556\pi$
$8$	−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	−0.889716	−	0.456515i	$-0.849098\pi$
$13$	−158.728	+	91.6418i	−0.939220	+	0.542259i	−0.0495044	+	0.998774i	$0.515764\pi$
$14$	18.5199	−	10.6925i	0.0944893	−	0.0545534i
$15$	224.363	+	16.9161i	0.997170	+	0.0751829i
$16$	−99.9665	+	173.147i	−0.390494	+	0.676355i
$17$	89.0232			0.308039			0.154019	−	0.988068i	$-0.450778\pi$
$17$	89.0232			0.308039			0.154019	+	0.988068i	$0.450778\pi$
$18$	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	$0.523047\pi$
$20$	99.6252	−	356.388i	0.249063	−	0.890970i
$21$	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	0.997579	−	0.0695388i	$-0.0221528\pi$
$23$	232.002	+	401.839i	0.438567	+	0.759621i	−0.559012	+	0.829160i	$0.688819\pi$
$24$	227.927	−	200.282i	0.395706	−	0.347711i
$25$	−13.4788	+	624.855i	−0.0215660	+	0.999767i
$26$		−	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	$0.997357\pi$
$30$	−138.819	+	203.411i	−0.154243	+	0.226013i
$31$	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	$0.0752736\pi$
$37$			641.462i			0.468562i	−0.972169	+	0.234281i	$0.924726\pi$
$38$	28.5830	−	49.5071i	0.0197943	−	0.0342847i
$39$	528.700	−	1562.53i	0.347601	−	1.02730i
$40$	589.511	+	602.364i	0.368444	+	0.376478i
$41$	−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	−0.0642203	−	0.997936i	$-0.520456\pi$
$43$	−1776.09	−	1025.43i	−0.960568	−	0.554584i	−0.896348	+	0.443351i	$0.853789\pi$
$44$		−	1716.12i		−	0.886426i
$45$	−1617.36	+	1218.52i	−0.798694	+	0.601737i
$46$	−507.859			−0.240009
$47$	−589.129	+	1020.40i	−0.266695	+	0.461929i	−0.968006	−	0.250926i	$-0.919265\pi$
$47$	−589.129	+	1020.40i	−0.266695	+	0.461929i	0.701311	+	0.712855i	$0.252598\pi$
$48$	−352.774	−	1764.48i	−0.153114	−	0.765832i
$49$	−1009.63	−	1748.73i	−0.420503	−	0.728333i
$50$	−584.909	−	354.732i	−0.233964	−	0.141893i
$51$	−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	$-0.503650\pi$
$53$	−64.4267			−0.0229358			−0.0114679	+	0.999934i	$0.503650\pi$
$54$	−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	$0.177346\pi$
$60$	1443.67	+	3001.30i	0.401019	+	0.833693i
$61$	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
$65$	4412.91	+	1233.59i	1.04448	+	0.291974i
$66$	−366.044	+	1081.81i	−0.0840322	+	0.248350i
$67$	7257.38	−	4190.05i	1.61670	−	0.933404i	0.628938	−	0.777455i	$-0.283490\pi$
$67$	7257.38	−	4190.05i	1.61670	−	0.933404i	0.987765	−	0.155949i	$-0.0498435\pi$
$68$	658.862	+	1141.18i	0.142488	+	0.246796i
$69$	−3955.73	−	1338.47i	−0.830861	−	0.281132i
$70$	−514.884	−	143.931i	−0.105078	−	0.0293738i
$71$			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	$0.273777\pi$
$73$			8077.75i			1.51581i	−0.652365	+	0.757905i	$0.726223\pi$
$74$	−608.027	−	351.045i	−0.111035	−	0.0641060i
$75$	−3620.97	−	4304.55i	−0.643728	−	0.765254i
$76$	−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	−0.718981	−	0.695030i	$-0.755391\pi$
$83$	1670.06	−	2892.62i	0.242424	−	0.419890i	0.961404	+	0.275140i	$0.0887243\pi$
$84$	1718.10	+	1955.25i	0.243495	+	0.277105i
$85$	−1556.66	−	1590.60i	−0.215455	−	0.220152i
$86$	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	$0.778165\pi$
$90$	−269.896	−	2199.90i	−0.0333204	−	0.271592i
$91$	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
$95$	913.285	+	933.198i	0.101195	+	0.103401i
$96$	6464.17	+	2187.23i	0.701407	+	0.237329i
$97$	−11868.3	−	6852.15i	−1.26137	−	0.728255i	−0.288034	−	0.957620i	$-0.593002\pi$
$97$	−11868.3	−	6852.15i	−1.26137	−	0.728255i	−0.973340	+	0.229365i	$0.926335\pi$
$98$	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	−0.296373	−	0.955072i	$-0.595777\pi$
$103$	4058.54	−	2343.20i	0.382557	−	0.220869i	0.678930	+	0.734203i	$0.262444\pi$
$104$	5351.25	−	3089.54i	0.494753	−	0.285646i
$105$	−3631.12	−	2478.07i	−0.329353	−	0.224768i
$106$	35.2580	−	61.0686i	0.00313795	−	0.00543509i
$107$	−20235.1			−1.76741			−0.883705	−	0.468044i	$-0.844959\pi$
$107$	−20235.1			−1.76741			−0.883705	+	0.468044i	$0.844959\pi$
$108$	−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	$0.469617\pi$
$110$	−3055.27	−	854.074i	−0.252502	−	0.0705846i
$111$	−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	0.600726	−	0.799455i	$-0.294878\pi$
$113$	−5005.26	−	8669.36i	−0.391985	−	0.678938i	−0.992711	+	0.120517i	$0.961545\pi$
$114$	100.867	+	504.509i	0.00776139	+	0.0388203i
$115$	3122.98	−	11171.8i	0.236142	−	0.844749i
$116$		−	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
$120$	−7564.02	−	570.299i	−0.525279	−	0.0396041i
$121$	−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	$-0.792360\pi$
$127$		−	19581.7i		−	1.21406i	0.794677	−	0.607032i	$-0.207640\pi$
$128$	7362.40	−	12752.0i	0.449365	−	0.778323i
$129$	18099.5	−	3618.65i	1.08764	−	0.217454i
$130$	−3584.29	+	3507.81i	−0.212088	+	0.207563i
$131$	−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
$135$	3695.63	−	17846.4i	0.202778	−	0.979225i
$136$	−3001.26			−0.162266
$137$	−13118.2	+	22721.5i	−0.698931	+	1.21058i	0.269906	+	0.962887i	$0.413007\pi$
$137$	−13118.2	+	22721.5i	−0.698931	+	1.21058i	−0.968837	+	0.247698i	$0.920326\pi$
$138$	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	$0.502566\pi$
$140$	−5167.33	+	5057.07i	−0.263639	+	0.258014i
$141$	−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	$0.371158\pi$
$150$	6061.79	−	1076.54i	0.269413	−	0.0478462i
$151$	−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
$155$	10337.3	−	36979.4i	0.430271	−	1.53921i
$156$	23942.9	−	4786.93i	0.983847	−	0.196702i
$157$	17441.0	−	10069.5i	0.707573	−	0.408517i	−0.102589	−	0.994724i	$-0.532713\pi$
$157$	17441.0	−	10069.5i	0.707573	−	0.408517i	0.810162	+	0.586207i	$0.199379\pi$
$158$	4737.82	+	8206.15i	0.189786	+	0.328719i
$159$	435.572	−	382.742i	0.0172292	−	0.0151395i
$160$	−5103.35	+	18256.2i	−0.199350	+	0.713131i
$161$		−	9065.85i		−	0.349749i
$162$	5057.87	−	5097.67i	0.192725	−	0.194241i
$163$			15388.7i			0.579197i	0.957148	+	0.289598i	$0.0935218\pi$
$163$			15388.7i			0.579197i	−0.957148	+	0.289598i	$0.906478\pi$
$164$	−17693.0	−	10215.1i	−0.657830	−	0.379798i
$165$	−21546.7	−	14704.6i	−0.791429	−	0.540114i
$166$	1827.90	+	3166.02i	0.0663340	+	0.114894i
$167$	−8523.96	−	14763.9i	−0.305639	−	0.529382i	0.671765	−	0.740765i	$-0.265537\pi$
$167$	−8523.96	−	14763.9i	−0.305639	−	0.529382i	−0.977403	+	0.211383i	$0.932203\pi$
$168$	−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	−0.981359	−	0.192181i	$-0.938444\pi$
$173$	−9704.36	+	16808.4i	−0.324246	+	0.561610i	0.657114	+	0.753792i	$0.271777\pi$
$174$	−4576.80	+	13526.4i	−0.151169	+	0.446768i
$175$	6332.36	−	10441.3i	0.206771	−	0.340940i
$176$	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	$0.966862\pi$
$180$	−27590.2	−	11714.5i	−0.851549	−	0.361559i
$181$	−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
$185$	11461.2	−	11216.6i	0.334877	−	0.327731i
$186$	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	−0.908113	−	0.418725i	$-0.862477\pi$
$193$	−37232.0	+	21495.9i	−0.999543	+	0.577086i	−0.0914300	+	0.995812i	$0.529144\pi$
$194$	12990.0	−	7499.78i	0.345148	−	0.199271i
$195$	−37163.0	+	17876.0i	−0.977331	+	0.470111i
$196$	14944.5	−	25884.7i	0.389019	−	0.673800i
$197$	−48322.8			−1.24514			−0.622571	−	0.782563i	$-0.713912\pi$
$197$	−48322.8			−1.24514			−0.622571	+	0.782563i	$0.713912\pi$
$198$	−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	$0.458705\pi$
$200$	454.413	−	21065.9i	0.0113603	−	0.526647i
$201$	−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
$205$	33231.6	+	9289.59i	0.790757	+	0.221049i
$206$			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
$210$	4336.06	−	2085.71i	0.0983233	−	0.0472950i
$211$	−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
$220$	−30662.4	+	30008.1i	−0.633520	+	0.620002i
$221$	−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	0.857887	−	0.513839i	$-0.171777\pi$
$223$	41863.5	+	24169.9i	0.841833	+	0.486032i	−0.0160539	+	0.999871i	$0.505110\pi$
$224$			14814.7i			0.295256i
$225$	50052.7	+	7590.72i	0.988695	+	0.149940i
$226$	10956.7			0.214517
$227$	−9830.70	+	17027.3i	−0.190780	+	0.330441i	−0.945509	−	0.325596i	$-0.894435\pi$
$227$	−9830.70	+	17027.3i	−0.190780	+	0.330441i	0.754729	+	0.656037i	$0.227768\pi$
$228$	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	$-0.452945\pi$
$230$	8880.43	+	9074.06i	0.167872	+	0.171532i
$231$	−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	$-0.389601\pi$
$233$	36907.6			0.679837			0.339918	+	0.940455i	$0.389601\pi$
$234$	−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	$0.258189\pi$
$240$	−25357.8	+	37156.8i	−0.440239	+	0.645083i
$241$	−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
$245$	−13590.6	+	48617.5i	−0.226416	+	0.809955i
$246$	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
$250$	3889.63	+	16653.6i	0.0622341	+	0.266457i
$251$		−	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
$255$	19973.5	+	1505.93i	0.307167	+	0.0231592i
$256$	−10893.9	−	18868.8i	−0.166228	−	0.287915i
$257$	28510.3	+	49381.3i	0.431654	+	0.747647i	0.997016	−	0.0771960i	$-0.0245967\pi$
$257$	28510.3	+	49381.3i	0.431654	+	0.747647i	−0.565362	+	0.824843i	$0.691263\pi$
$258$	−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	−0.567210	−	0.823573i	$-0.691977\pi$
$263$	29717.1	−	51471.5i	0.429630	−	0.744142i	0.996840	+	0.0794316i	$0.0253105\pi$
$264$	−34495.2	+	6896.67i	−0.494938	+	0.0989535i
$265$	1126.57	+	1151.13i	0.0160422	+	0.0163920i
$266$	−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	$-0.267185\pi$
$270$	14893.7	+	13269.6i	0.204303	+	0.182024i
$271$	−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
$275$	37575.6	−	61957.4i	0.496867	−	0.819271i
$276$	−12118.7	−	60614.3i	−0.159088	−	0.795714i
$277$	−23205.3	−	13397.6i	−0.302432	−	0.174609i	0.341103	−	0.940026i	$-0.389200\pi$
$277$	−23205.3	−	13397.6i	−0.302432	−	0.174609i	−0.643535	+	0.765417i	$0.722533\pi$
$278$	−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	−0.796972	−	0.604016i	$-0.793566\pi$
$283$	−53849.1	+	31089.8i	−0.672366	+	0.388190i	0.124607	+	0.992206i	$0.460233\pi$
$284$	−58514.8	+	33783.5i	−0.725486	+	0.418859i
$285$	−11718.4	−	883.521i	−0.144271	−	0.0108775i
$286$	−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
$290$	−38201.3	−	10678.8i	−0.454236	−	0.126978i
$291$	120945.	−	24180.7i	1.42824	−	0.285551i
$292$	−103548.	+	59783.6i	−1.21444	+	0.701159i
$293$	−8608.02	−	14909.5i	−0.100269	−	0.173672i	0.811526	−	0.584316i	$-0.198637\pi$
$293$	−8608.02	−	14909.5i	−0.100269	−	0.173672i	−0.911796	+	0.410644i	$0.865304\pi$
$294$	−14941.9	+	13129.7i	−0.172867	+	0.151900i
$295$	−78895.4	−	22054.5i	−0.906583	−	0.253427i
$296$		−	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
$300$	28380.9	−	78275.1i	0.315344	−	0.869724i
$301$	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	$0.192940\pi$
$307$			107387.i			1.13940i	−0.821854	+	0.569698i	$0.807060\pi$
$308$	−16765.0	+	29037.9i	−0.176727	+	0.306100i
$309$	−13518.4	+	39952.5i	−0.141582	+	0.418434i
$310$	29394.8	+	30035.7i	0.305877	+	0.312547i
$311$	−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	0.0199154	−	0.999802i	$-0.493660\pi$
$313$	−81900.2	−	47285.1i	−0.835981	−	0.482654i	−0.855896	+	0.517148i	$0.826994\pi$
$314$			22042.5i			0.223564i
$315$	39270.6	−	4817.93i	0.395773	−	0.0485556i
$316$	128147.			1.28332
$317$	70757.2	−	122555.i	0.704129	−	1.21959i	−0.262876	−	0.964830i	$-0.584671\pi$
$317$	70757.2	−	122555.i	0.704129	−	1.21959i	0.967005	−	0.254758i	$-0.0819957\pi$
$318$	124.423	+	622.328i	0.00123040	+	0.00615411i
$319$	84033.2	+	145550.i	0.825790	+	1.43031i
$320$	41424.7	+	42327.9i	0.404538	+	0.413359i
$321$	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
$330$	25729.7	−	12376.4i	0.236269	−	0.113649i
$331$	−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
$335$	−201767.	−	56402.3i	−1.79788	−	0.502582i
$336$	−11268.3	+	33302.4i	−0.0998110	+	0.294983i
$337$	72053.4	−	41600.0i	0.634446	−	0.366297i	−0.148026	−	0.988983i	$-0.547292\pi$
$337$	72053.4	−	41600.0i	0.634446	−	0.366297i	0.782472	+	0.622686i	$0.213959\pi$
$338$	2753.72	+	4769.59i	0.0241039	+	0.0417491i
$339$	85341.6	+	28876.4i	0.742611	+	0.251271i
$340$	8868.95	−	31726.8i	0.0767210	−	0.274453i
$341$		−	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
$345$	45255.2	+	94082.5i	0.380216	+	0.790444i
$346$	−10621.6	−	18397.1i	−0.0887230	−	0.153673i
$347$	−51814.1	−	89744.7i	−0.430317	−	0.745332i	0.566583	−	0.824005i	$-0.308265\pi$
$347$	−51814.1	−	89744.7i	−0.430317	−	0.745332i	−0.996900	+	0.0786729i	$0.974932\pi$
$348$	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	−0.907016	−	0.421096i	$-0.861646\pi$
$353$	−11068.8	+	19171.8i	−0.0888286	+	0.153856i	0.818188	+	0.574951i	$0.194979\pi$
$354$	−21306.5	−	24247.4i	−0.170022	−	0.193490i
$355$	81558.9	−	79818.6i	0.647165	−	0.633355i
$356$	−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	$0.885245\pi$
$360$	54526.4	−	41080.2i	0.420728	−	0.316977i
$361$	−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
$365$	144327.	−	141248.i	1.08334	−	1.06022i
$366$	−17344.5	−	5868.73i	−0.129479	−	0.0438109i
$367$	17103.7	+	9874.80i	0.126986	+	0.0733156i	0.562148	−	0.827037i	$-0.309975\pi$
$367$	17103.7	+	9874.80i	0.126986	+	0.0733156i	−0.435161	+	0.900353i	$0.643309\pi$
$368$	−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	−0.119464	−	0.992839i	$-0.538118\pi$
$373$	94695.0	−	54672.2i	0.680627	−	0.392960i	0.800091	+	0.599878i	$0.204784\pi$
$374$	9783.21	−	5648.34i	0.0699420	−	0.0403811i
$375$	−13594.3	+	139966.i	−0.0966704	+	0.995316i
$376$	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	$0.415283\pi$
$380$	−5203.37	+	18614.0i	−0.0360344	+	0.128906i
$381$	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	$0.0971389\pi$
$383$	108125.	+	187277.i	0.737100	+	1.27670i	−0.216695	+	0.976239i	$0.569528\pi$
$384$	25981.3	+	129951.i	0.176197	+	0.881289i
$385$	15246.2	−	54539.9i	0.102858	−	0.367954i
$386$		−	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	$0.606833\pi$
$390$	3393.49	−	45008.7i	0.0223109	−	0.295915i
$391$	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	$0.299082\pi$
$397$			254481.i			1.61464i	−0.590117	+	0.807318i	$0.700918\pi$
$398$	−5607.39	+	9712.29i	−0.0353993	+	0.0613134i
$399$	−9006.04	+	1800.59i	−0.0565702	+	0.0113102i
$400$	−106844.	−	64798.3i	−0.667777	−	0.404990i
$401$	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
$405$	81035.5	+	142609.i	0.494043	+	0.869437i
$406$	−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	$0.932263\pi$
$410$	−26991.6	+	26415.6i	−0.160569	+	0.157142i
$411$	−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	$0.386534\pi$
$420$	4892.26	−	64887.3i	0.0277339	−	0.367842i
$421$	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
$425$	−1199.92	+	55626.6i	−0.00664317	+	0.307967i
$426$	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
$430$	−54045.3	−	15107.9i	−0.292295	−	0.0817084i
$431$		−	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	$0.0880895\pi$
$433$			102452.i			0.546445i	−0.961951	+	0.273222i	$0.911910\pi$
$434$	28444.4	+	16422.4i	0.151014	+	0.0871880i
$435$	−269407.	−	183858.i	−1.42374	−	0.971634i
$436$	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	$0.383983\pi$
$443$	−123815.	+	214453.i	−0.630906	+	1.09276i	−0.987367	+	0.158451i	$0.949350\pi$
$444$	27389.1	−	80946.3i	0.138935	−	0.410611i
$445$	181679.	−	177803.i	0.917457	−	0.897880i
$446$	−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	$0.936995\pi$
$450$	−34586.8	+	43289.7i	−0.170799	+	0.213776i
$451$	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
$455$	−62618.2	−	63983.5i	−0.302467	−	0.309062i
$456$	−11904.5	+	10460.6i	−0.0572508	+	0.0503069i
$457$	101766.	+	58754.5i	0.487270	+	0.281325i	0.723441	−	0.690386i	$-0.242559\pi$
$457$	101766.	+	58754.5i	0.487270	+	0.281325i	−0.236171	+	0.971711i	$0.575893\pi$
$458$	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	−0.301672	−	0.953412i	$-0.597545\pi$
$463$	79996.4	−	46185.9i	0.373171	−	0.215451i	0.674843	+	0.737961i	$0.264211\pi$
$464$	250998.	−	144914.i	1.16583	−	0.673090i
$465$	149797.	+	311419.i	0.692785	+	1.44026i
$466$	−20198.0	+	34983.9i	−0.0930114	+	0.161100i
$467$	−82073.0			−0.376328			−0.188164	−	0.982138i	$-0.560254\pi$
$467$	−82073.0			−0.376328			−0.188164	+	0.982138i	$0.560254\pi$
$468$	−133434.	+	174602.i	−0.609220	+	0.797181i
$469$	−163733.			−0.744372
$470$	−8679.80	+	31050.2i	−0.0392929	+	0.140562i
$471$	−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
$475$	703.989	−	32635.8i	0.00312017	−	0.144646i
$476$		−	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	$0.730014\pi$
$480$	−73952.7	−	153743.i	−0.320975	−	0.667287i
$481$	−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	$0.169032\pi$
$487$			240214.i			1.01284i	−0.862287	+	0.506421i	$0.830968\pi$
$488$	−31333.4	+	54271.1i	−0.131573	+	0.227892i
$489$	−91420.2	−	104039.i	−0.382318	−	0.435089i
$490$	−38645.9	−	39488.5i	−0.160958	−	0.164467i
$491$	−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
$495$	233027.	−	28589.1i	0.951035	−	0.116678i
$496$	−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	$0.840022\pi$
$500$	221348.	+	67054.9i	0.885392	+	0.268220i
$501$	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	$-0.444800\pi$
$503$	87312.8			0.345097			0.172549	+	0.985001i	$0.444800\pi$
$504$	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	$0.177222\pi$
$510$	−12358.1	+	18108.3i	−0.0475129	+	0.0696206i
$511$	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
$515$	−112834.	−	31541.9i	−0.425429	−	0.118925i
$516$	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
$520$	−148774.	−	41588.4i	−0.550199	−	0.153803i
$521$		−	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	$0.194503\pi$
$523$			313862.i			1.14746i	−0.819046	+	0.573728i	$0.805497\pi$
$524$	−365076.	−	210777.i	−1.32960	−	0.767645i
$525$	19217.4	+	108210.i	0.0697230	+	0.392597i
$526$	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
$535$	353831.	+	361546.i	1.23620	+	1.26315i
$536$	−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
$540$	256123.	−	84707.3i	0.878337	−	0.290491i
$541$	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
$545$	−39599.6	−	40463.0i	−0.133321	−	0.136228i
$546$	−6915.82	−	34591.0i	−0.0231984	−	0.116032i
$547$	−345995.	−	199760.i	−1.15636	−	0.667627i	−0.205934	−	0.978566i	$-0.566023\pi$
$547$	−345995.	−	199760.i	−1.15636	−	0.667627i	−0.950430	+	0.310939i	$0.899357\pi$
$548$	−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
$555$	−10851.1	+	143920.i	−0.0352279	+	0.467236i
$556$	−246514.	+	426975.i	−0.797430	+	1.38119i
$557$	−464065.			−1.49578			−0.747892	−	0.663821i	$-0.768934\pi$
$557$	−464065.			−1.49578			−0.747892	+	0.663821i	$0.768934\pi$
$558$	−17508.5	+	135034.i	−0.0562316	+	0.433687i
$559$	375888.			1.20291
$560$	−94053.0	−	26291.7i	−0.299914	−	0.0838383i
$561$	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	$-0.816800\pi$
$563$	−282361.	−	489064.i	−0.890816	−	1.54294i	−0.0519165	−	0.998651i	$-0.516533\pi$
$564$	117912.	−	103610.i	0.370679	−	0.325720i
$565$	−67375.8	+	241023.i	−0.211061	+	0.755025i
$566$		−	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	$0.990847\pi$
$570$	7250.43	−	10624.1i	0.0223159	−	0.0326995i
$571$	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	$-0.849896\pi$
$577$		−	302487.i		−	0.908562i	0.890858	−	0.454281i	$-0.150104\pi$
$578$	41370.4	−	71655.6i	0.123832	−	0.214484i
$579$	124014.	−	366514.i	0.369926	−	1.09328i
$580$	−383384.	+	375203.i	−1.13967	+	1.11535i
$581$	−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
$585$	145053.	−	341630.i	0.423852	−	0.998263i
$586$	18843.2			0.0548731
$587$	−67877.0	+	117566.i	−0.196991	+	0.341198i	−0.947551	−	0.319603i	$-0.896450\pi$
$587$	−67877.0	+	117566.i	−0.196991	+	0.341198i	0.750560	+	0.660802i	$0.229784\pi$
$588$	52738.1	+	263782.i	0.152535	+	0.762939i
$589$	−40109.2	−	69471.2i	−0.115615	−	0.200251i
$590$	64081.0	−	62713.7i	0.184088	−	0.180160i
$591$	326698.	−	287073.i	0.935343	−	0.821897i
$592$	−111067.	−	64124.7i	−0.316915	−	0.182971i
$593$	612873.			1.74285			0.871427	−	0.490525i	$-0.163195\pi$
$593$	612873.			1.74285			0.871427	+	0.490525i	$0.163195\pi$
$594$	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	$0.412364\pi$
$600$	122075.	+	145121.i	0.339097	+	0.403113i
$601$	−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
$605$	−8072.28	+	28876.9i	−0.0220539	+	0.0788932i
$606$	22412.9	−	66239.4i	0.0610313	−	0.180373i
$607$	189924.	−	109653.i	0.515470	−	0.297607i	−0.219609	−	0.975588i	$-0.570478\pi$
$607$	189924.	−	109653.i	0.515470	−	0.297607i	0.735079	+	0.677981i	$0.237145\pi$
$608$	19801.3	+	34296.8i	0.0535656	+	0.0927784i
$609$	−241460.	−	81701.0i	−0.651045	−	0.220289i
$610$	13693.2	−	48984.7i	0.0367999	−	0.131644i
$611$		−	215955.i		−	0.578471i
$612$	98530.7	−	41039.1i	0.263068	−	0.109571i
$613$		−	75985.1i		−	0.202212i	−0.994876	−	0.101106i	$-0.967762\pi$
$613$		−	75985.1i		−	0.202212i	0.994876	−	0.101106i	$-0.0322382\pi$
$614$	−101790.	−	58768.3i	−0.270002	−	0.155886i
$615$	−279857.	+	134616.i	−0.739922	+	0.355914i
$616$	−38184.2	−	66137.0i	−0.100629	−	0.174294i
$617$	−242066.	−	419271.i	−0.635863	−	1.10135i	−0.986331	−	0.164773i	$-0.947311\pi$
$617$	−242066.	−	419271.i	−0.635863	−	1.10135i	0.350468	−	0.936575i	$-0.386023\pi$
$618$	−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
$625$	−390262.	−	16844.5i	−0.999070	−	0.0431220i
$626$	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
$630$	−16924.3	+	39860.4i	−0.0426412	+	0.100429i
$631$	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
$635$	−349871.	+	342405.i	−0.867681	+	0.849166i
$636$	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	−0.988896	−	0.148609i	$-0.952521\pi$
$643$	−560077.	+	323360.i	−1.35465	+	0.782105i	−0.365749	+	0.930713i	$0.619187\pi$
$644$	116215.	−	67096.5i	0.280213	−	0.161781i
$645$	−381143.	−	260113.i	−0.916154	−	0.625233i
$646$	2544.55	−	4407.28i	0.00609741	−	0.0105610i
$647$	347688.			0.830579			0.415289	−	0.909689i	$-0.363680\pi$
$647$	347688.			0.830579			0.415289	+	0.909689i	$0.363680\pi$
$648$	213879.	+	56411.1i	0.509351	+	0.134343i
$649$	−379906.			−0.901959
$650$	125350.	+	2703.93i	0.296686	+	0.00639983i
$651$	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	$0.0865406\pi$
$653$	304539.	+	527478.i	0.714196	+	1.23702i	−0.249073	+	0.968485i	$0.580126\pi$
$654$	−4373.55	−	21875.3i	−0.0102254	−	0.0511444i
$655$	685699.	+	191681.i	1.59827	+	0.446783i
$656$		−	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	$0.411742\pi$
$660$	29030.1	−	385034.i	0.0666440	−	0.883917i
$661$	−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
$670$	163881.	−	160384.i	0.365073	−	0.357283i
$671$	−186635.	+	107754.i	−0.414523	+	0.239325i
$672$	−88010.6	−	100159.i	−0.194893	−	0.221794i
$673$	130097.	+	75111.4i	0.287234	+	0.165835i	0.636694	−	0.771117i	$-0.280301\pi$
$673$	130097.	+	75111.4i	0.287234	+	0.165835i	−0.349460	+	0.936951i	$0.613635\pi$
$674$			91063.7i			0.200459i
$675$	−383488.	+	246031.i	−0.841674	+	0.539986i
$676$	74481.8			0.162988
$677$	−290147.	+	502550.i	−0.633055	+	1.09648i	0.353869	+	0.935295i	$0.384866\pi$
$677$	−290147.	+	502550.i	−0.633055	+	1.09648i	−0.986924	+	0.161188i	$0.948467\pi$
$678$	−74075.1	+	65090.6i	−0.161143	+	0.141599i
$679$	133879.	+	231886.i	0.290385	+	0.502961i
$680$	52480.1	+	53624.4i	0.113495	+	0.115970i
$681$	−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	$-0.496109\pi$
$683$	11404.6			0.0244477			0.0122238	+	0.999925i	$0.496109\pi$
$684$	−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
$690$	−113945.	−	8591.02i	−0.239330	−	0.0180446i
$691$	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
$695$	224181.	−	801959.i	0.464118	−	1.66028i
$696$	−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
$700$	180712.	+	3898.15i	0.368800	+	0.00795540i
$701$			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
$705$	−149440.	+	218975.i	−0.300669	+	0.440571i
$706$	−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
$715$	−371570.	−	379671.i	−0.726823	−	0.742670i
$716$	−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	$0.888615\pi$
$720$	−49301.3	−	401851.i	−0.0951029	−	0.775176i
$721$	−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
$725$	469823.	−	774679.i	0.893836	−	1.47382i
$726$	−8874.92	+	7798.49i	−0.0168380	+	0.0147958i
$727$	173161.	+	99974.6i	0.327628	+	0.189156i	0.654788	−	0.755813i	$-0.272758\pi$
$727$	173161.	+	99974.6i	0.327628	+	0.189156i	−0.327159	+	0.944969i	$0.606091\pi$
$728$	−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	−0.993303	−	0.115541i	$-0.963140\pi$
$733$	−746774.	+	431150.i	−1.38989	+	0.802455i	−0.396590	+	0.917996i	$0.629807\pi$
$734$	−18720.2	+	10808.1i	−0.0347471	+	0.0200612i
$735$	−196942.	−	409429.i	−0.364555	−	0.757886i
$736$	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	$0.284369\pi$
$740$	228609.	+	63905.8i	0.417475	+	0.116702i
$741$	−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	$0.0920737\pi$
$743$	400928.	+	694427.i	0.726254	+	1.25791i	−0.232202	+	0.972668i	$0.574593\pi$
$744$	441432.	+	149364.i	0.797477	+	0.269836i
$745$	126738.	+	35428.6i	0.228347	+	0.0638324i
$746$			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
$750$	−125231.	−	89483.3i	−0.222634	−	0.159081i
$751$	−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	$-0.766712\pi$
$757$		−	766769.i		−	1.33805i	0.743239	−	0.669026i	$-0.233288\pi$
$758$	−41350.8	+	71621.6i	−0.0719689	+	0.124654i
$759$	319587.	+	363699.i	0.554760	+	0.631333i
$760$	−30789.8	−	31461.2i	−0.0533065	−	0.0544688i
$761$	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
$765$	−143982.	+	108476.i	−0.246029	+	0.185358i
$766$	−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	$0.941688\pi$
$770$	43353.6	+	44298.8i	0.0731212	+	0.0747155i
$771$	−486113.	−	164482.i	−0.817764	−	0.276700i
$772$	−551109.	−	318183.i	−0.924705	−	0.533878i
$773$	121076.			0.202628			0.101314	−	0.994855i	$-0.467695\pi$
$773$	121076.			0.202628			0.101314	+	0.994855i	$0.467695\pi$
$774$	−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
$780$	−504195.	−	344090.i	−0.828723	−	0.565565i
$781$	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
$785$	−484888.	−	135546.i	−0.786868	−	0.219962i
$786$	185180.	+	210740.i	0.299743	+	0.341116i
$787$	523274.	−	302112.i	0.844849	−	0.487774i	−0.0140603	−	0.999901i	$-0.504476\pi$
$787$	523274.	−	302112.i	0.844849	−	0.487774i	0.858910	+	0.512127i	$0.171142\pi$
$788$	−357638.	−	619446.i	−0.575958	−	0.997588i
$789$	104869.	+	524527.i	0.168459	+	0.842586i
$790$	63775.9	−	228145.i	0.102189	−	0.365558i
$791$			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
$795$	−14455.0	−	1089.85i	−0.0228709	−	0.00172438i
$796$	75833.5	+	131347.i	0.119684	+	0.207298i
$797$	444851.	+	770505.i	0.700322	+	1.21299i	0.968353	+	0.249584i	$0.0802937\pi$
$797$	444851.	+	770505.i	0.700322	+	1.21299i	−0.268031	+	0.963410i	$0.586373\pi$
$798$	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
$805$	−161982.	+	158525.i	−0.249962	+	0.244629i
$806$	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	$-0.0864258\pi$
$810$	−179524.	−	1232.36i	−0.273622	−	0.00187832i
$811$	−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
$815$	274954.	−	269087.i	0.413947	−	0.405114i
$816$	−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	−0.0380887	−	0.999274i	$-0.512127\pi$
$823$	547461.	−	316077.i	0.808264	−	0.466651i	0.846353	+	0.532623i	$0.178794\pi$
$824$	−136827.	+	78997.0i	−0.201519	+	0.116347i
$825$	114034.	+	642105.i	0.167543	+	0.943404i
$826$	35037.1	−	60686.0i	0.0513532	−	0.0889464i
$827$	−309027.			−0.451840			−0.225920	−	0.974146i	$-0.572539\pi$
$827$	−309027.			−0.451840			−0.225920	+	0.974146i	$0.572539\pi$
$828$	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	$0.707060\pi$
$830$	24605.4	−	88020.6i	0.0357169	−	0.127770i
$831$	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
$835$	−114741.	+	410462.i	−0.164568	+	0.588709i
$836$			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	$0.466065\pi$
$840$	122417.	+	83543.8i	0.173493	+	0.118401i
$841$	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
$850$	−52070.5	−	31579.4i	−0.0720699	−	0.0437085i
$851$	−257765.	+	148820.i	−0.355930	+	0.205496i
$852$	194904.	−	576023.i	0.268498	−	0.793524i
$853$	607611.	+	350804.i	0.835079	+	0.482133i	0.855588	−	0.517657i	$-0.173195\pi$
$853$	607611.	+	350804.i	0.835079	+	0.482133i	−0.0205095	+	0.999790i	$0.506529\pi$
$854$		−	39750.7i		−	0.0545041i
$855$	84473.7	−	63642.5i	0.115555	−	0.0870593i
$856$	682191.			0.931019
$857$	542612.	−	939831.i	0.738801	−	1.27964i	−0.214234	−	0.976782i	$-0.568726\pi$
$857$	542612.	−	939831.i	0.738801	−	1.27964i	0.953035	−	0.302859i	$-0.0979411\pi$
$858$	−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	$0.628683\pi$
$860$	−542393.	+	530819.i	−0.733360	+	0.717711i
$861$	−182318.	+	160205.i	−0.245937	+	0.216107i
$862$	41328.9	+	23861.2i	0.0556210	+	0.0321128i
$863$	848540.			1.13933			0.569667	−	0.821876i	$-0.307072\pi$
$863$	848540.			1.13933			0.569667	+	0.821876i	$0.307072\pi$
$864$	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
$870$	321709.	−	154747.i	0.425035	−	0.204448i
$871$	−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
$875$	−297285.	+	69434.2i	−0.388290	+	0.0906895i
$876$	344904.	−	1.01933e6i	0.449459	−	1.32834i
$877$	−445046.	+	256947.i	−0.578636	+	0.334076i	−0.760591	−	0.649231i	$-0.775091\pi$
$877$	−445046.	+	256947.i	−0.578636	+	0.334076i	0.181955	+	0.983307i	$0.441757\pi$
$878$	56074.2	+	97123.4i	0.0727402	+	0.125990i
$879$	146770.	+	49661.4i	0.189959	+	0.0642749i
$880$	−558100.	−	156012.i	−0.720687	−	0.201462i
$881$			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	$0.0509148\pi$
$883$			248366.i			0.318545i	−0.987235	+	0.159272i	$0.949085\pi$
$884$	−209160.	−	120759.i	−0.267654	−	0.154530i
$885$	664411.	−	319592.i	0.848302	−	0.408046i
$886$	−135517.	−	234722.i	−0.172634	−	0.299011i
$887$	−432263.	−	748702.i	−0.549415	−	0.951616i	−0.998315	−	0.0580331i	$-0.981517\pi$
$887$	−432263.	−	748702.i	−0.549415	−	0.951616i	0.448899	−	0.893582i	$-0.351816\pi$
$888$	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
$895$	118984.	−	116445.i	0.148540	−	0.145371i
$896$	−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
$900$	273136.	+	697802.i	0.337205	+	0.861483i
$901$	−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
$905$	275226.	+	281227.i	0.336041	+	0.343368i
$906$	105195.	+	35594.1i	0.128156	+	0.0433633i
$907$	−929719.	−	536773.i	−1.13015	−	0.652494i	−0.186179	−	0.982516i	$-0.559610\pi$
$907$	−929719.	−	536773.i	−1.13015	−	0.652494i	−0.943973	+	0.330022i	$0.892944\pi$
$908$	−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
$915$	235756.	−	345454.i	0.281593	−	0.412618i
$916$	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	$0.610822\pi$
$920$	−105286.	+	376638.i	−0.124393	+	0.444989i
$921$	−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
$925$	−400820.	−	8646.11i	−0.468453	−	0.0101050i
$926$			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	$0.869597\pi$
$930$	−377165.	−	28436.8i	−0.436079	−	0.0328787i
$931$	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	$-0.934587\pi$
$937$		−	358312.i		−	0.408115i	0.978959	−	0.204057i	$-0.0654129\pi$
$938$	89604.0	−	155199.i	0.101841	−	0.176393i
$939$	834614.	−	166865.i	0.946574	−	0.189250i
$940$	304967.	+	311617.i	0.345142	+	0.352667i
$941$	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
$945$	−236876.	+	265869.i	−0.265251	+	0.297717i
$946$	−260245.			−0.290804
$947$	−361257.	+	625716.i	−0.402825	+	0.697713i	−0.994066	−	0.108782i	$-0.965305\pi$
$947$	−361257.	+	625716.i	−0.402825	+	0.697713i	0.591241	+	0.806495i	$0.298638\pi$
$948$	−866369.	+	761288.i	−0.964020	+	0.847096i
$949$	−740260.	−	1.28217e6i	−0.821962	−	1.42368i
$950$	30549.5	+	18527.5i	0.0338499	+	0.0205291i
$951$	249697.	+	1.24891e6i	0.276091	+	1.38093i
$952$	50783.3	+	29319.8i	0.0560335	+	0.0323509i
$953$	−686812.			−0.756227			−0.378113	−	0.925759i	$-0.623427\pi$
$953$	−686812.			−0.756227			−0.378113	+	0.925759i	$0.623427\pi$
$954$	−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
$960$	−531521.	−	40074.7i	−0.576737	−	0.0434838i
$961$	−717709.	+	1.24311e6i	−0.777144	+	1.34605i
$962$	128681.			0.139048
$963$	−210753.	+	1.62544e6i	−0.227259	+	1.75274i
$964$	−226111.			−0.243314
$965$	1.03511e6	+	289356.i	1.11156	+	0.310727i
$966$	−87571.2	+	17508.2i	−0.0938441	+	0.0187624i
$967$	217686.	−	125681.i	0.232797	−	0.134406i	−0.379064	−	0.925370i	$-0.623754\pi$
$967$	217686.	−	125681.i	0.232797	−	0.134406i	0.611862	+	0.790965i	$0.290421\pi$
$968$	20217.1	+	35017.1i	0.0215759	+	0.0373705i
$969$	31435.0	−	27622.3i	0.0334785	−	0.0294179i
$970$	−361144.	−	100955.i	−0.383828	−	0.107296i
$971$			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
$975$	969227.	+	351422.i	1.01957	+	0.369675i
$976$	185819.	+	321849.i	0.195070	+	0.337872i
$977$	−352133.	−	609912.i	−0.368907	−	0.638966i	0.620488	−	0.784216i	$-0.286935\pi$
$977$	−352133.	−	609912.i	−0.368907	−	0.638966i	−0.989395	+	0.145250i	$0.953601\pi$
$978$	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	−0.987226	−	0.159327i	$-0.949068\pi$
$983$	−343643.	+	595207.i	−0.355632	+	0.615972i	0.631594	+	0.775299i	$0.282401\pi$
$984$	−134226.	+	396693.i	−0.138626	+	0.409699i
$985$	844972.	+	863396.i	0.870903	+	0.889892i
$986$	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
$990$	−100427.	+	236527.i	−0.102466	+	0.241330i
$991$	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
$995$	−179168.	−	183074.i	−0.180973	−	0.184919i
$996$	−334254.	+	293713.i	−0.336944	+	0.296077i
$997$	458423.	+	264671.i	0.461186	+	0.266266i	0.712543	−	0.701629i	$-0.247543\pi$
$997$	458423.	+	264671.i	0.461186	+	0.266266i	−0.251357	+	0.967895i	$0.580877\pi$
$998$	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.29.10	yes	44
3.2	odd	2		135.5.h.a.89.13		44
5.4	even	2	inner	45.5.h.a.29.13	yes	44
9.2	odd	6		405.5.d.a.404.20		44
9.4	even	3		135.5.h.a.44.10		44
9.5	odd	6	inner	45.5.h.a.14.13	yes	44
9.7	even	3		405.5.d.a.404.26		44
15.14	odd	2		135.5.h.a.89.10		44
45.4	even	6		135.5.h.a.44.13		44
45.14	odd	6	inner	45.5.h.a.14.10	✓	44
45.29	odd	6		405.5.d.a.404.25		44
45.34	even	6		405.5.d.a.404.19		44

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

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} +(-17.4860 - 17.8673i) 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} +(224.363 + 16.9161i) q^{15} +(-99.9665 + 173.147i) q^{16} +89.0232 q^{17} +(70.4409 + 53.8322i) q^{18} -52.2295 q^{19} +(99.6252 - 356.388i) 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} +(-13.4788 + 624.855i) q^{25} -200.607i q^{26} +(406.791 + 604.948i) q^{27} -289.206i q^{28} +(-1255.41 - 724.811i) q^{29} +(-138.819 + 203.411i) 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} +(589.511 + 602.364i) q^{40} +(-1195.31 + 690.111i) q^{41} +(-61.6871 + 182.311i) q^{42} +(-1776.09 - 1025.43i) q^{43} -1716.12i q^{44} +(-1617.36 + 1218.52i) q^{45} -507.859 q^{46} +(-589.129 + 1020.40i) q^{47} +(-352.774 - 1764.48i) q^{48} +(-1009.63 - 1748.73i) q^{49} +(-584.909 - 354.732i) 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} +(1443.67 + 3001.30i) q^{60} +(929.409 - 1609.78i) q^{61} -1681.05 q^{62} +(-960.964 + 1257.45i) q^{63} -2369.02 q^{64} +(4412.91 + 1233.59i) 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} +(-514.884 - 143.931i) q^{70} +4564.71i q^{71} +(-351.131 + 2708.11i) q^{72} +8077.75i q^{73} +(-608.027 - 351.045i) q^{74} +(-3620.97 - 4304.55i) 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} +(-1556.66 - 1590.60i) q^{85} +(1943.96 - 1122.34i) q^{86} +(12793.4 - 2557.80i) q^{87} +(3384.99 + 1954.33i) q^{88} +10168.3i q^{89} +(-269.896 - 2199.90i) q^{90} +3581.05 q^{91} +(-3434.10 + 5948.04i) q^{92} +(-13093.7 - 4430.42i) q^{93} +(-644.811 - 1116.84i) q^{94} +(913.285 + 933.198i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more