LMFDB - Embedded newform 45.5.h.a.14.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,5,Mod(14,45)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			14.10
Character	$\chi$	$=$	45.14
Dual form			45.5.h.a.29.10

$q$-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 $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	$-0.210353\pi$
$2$	−0.547257	−	0.947877i	−0.136814	−	0.236969i	−0.926289	+	0.376814i	$0.877020\pi$
$3$	−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	−0.662622	−	0.748954i	$-0.730556\pi$
$7$	−16.9207	+	9.76914i	−0.345319	+	0.199370i	0.317302	+	0.948324i	$0.397223\pi$
$8$	−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	−0.853783	−	0.520629i	$-0.825697\pi$
$11$	−100.405	+	57.9690i	−0.829796	+	0.479083i	0.0239867	+	0.999712i	$0.492364\pi$
$12$	−126.190	+	42.6980i	−0.876322	+	0.296514i
$13$	−158.728	−	91.6418i	−0.939220	−	0.542259i	−0.0495044	−	0.998774i	$-0.515764\pi$
$13$	−158.728	−	91.6418i	−0.939220	−	0.542259i	−0.889716	+	0.456515i	$0.849098\pi$
$14$	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	−0.559012	−	0.829160i	$-0.688819\pi$
$23$	232.002	−	401.839i	0.438567	−	0.759621i	0.997579	+	0.0695388i	$0.0221528\pi$
$24$	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	−0.999966	−	0.00830339i	$-0.997357\pi$
$29$	−1255.41	+	724.811i	−1.49276	+	0.861844i	−0.492792	+	0.870147i	$0.664024\pi$
$30$	−138.819	−	203.411i	−0.154243	−	0.226013i
$31$	767.942	−	1330.11i	0.799107	−	1.38409i	−0.121091	−	0.992641i	$-0.538639\pi$
$31$	767.942	−	1330.11i	0.799107	−	1.38409i	0.920198	−	0.391453i	$-0.128027\pi$
$32$	−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
$40$	589.511	−	602.364i	0.368444	−	0.376478i
$41$	−1195.31	−	690.111i	−0.711069	−	0.410536i	0.100388	−	0.994948i	$-0.467992\pi$
$41$	−1195.31	−	690.111i	−0.711069	−	0.410536i	−0.811457	+	0.584412i	$0.801325\pi$
$42$	−61.6871	−	182.311i	−0.0349700	−	0.103351i
$43$	−1776.09	+	1025.43i	−0.960568	+	0.554584i	−0.896348	−	0.443351i	$-0.853789\pi$
$43$	−1776.09	+	1025.43i	−0.960568	+	0.554584i	−0.0642203	+	0.997936i	$0.520456\pi$
$44$			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	0.701311	−	0.712855i	$-0.252598\pi$
$47$	−589.129	−	1020.40i	−0.266695	−	0.461929i	−0.968006	+	0.250926i	$0.919265\pi$
$48$	−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	0.848766	−	0.528768i	$-0.177346\pi$
$59$	2837.79	+	1638.40i	0.815223	+	0.470669i	−0.0335434	+	0.999437i	$0.510679\pi$
$60$	1443.67	−	3001.30i	0.401019	−	0.833693i
$61$	929.409	+	1609.78i	0.249774	+	0.432621i	0.963463	−	0.267842i	$-0.0863104\pi$
$61$	929.409	+	1609.78i	0.249774	+	0.432621i	−0.713689	+	0.700463i	$0.752977\pi$
$62$	−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	0.987765	+	0.155949i	$0.0498435\pi$
$67$	7257.38	+	4190.05i	1.61670	+	0.933404i	0.628938	+	0.777455i	$0.283490\pi$
$68$	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	$-0.850440\pi$
$71$		−	4564.71i		−	0.905517i	0.891633	−	0.452759i	$-0.149560\pi$
$72$	−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
$75$	−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	0.970654	+	0.240482i	$0.0773054\pi$
$79$	4328.70	+	7497.52i	0.693590	+	1.20133i	−0.277063	+	0.960852i	$0.589361\pi$
$80$	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	$-0.0887243\pi$
$83$	1670.06	+	2892.62i	0.242424	+	0.419890i	−0.718981	+	0.695030i	$0.755391\pi$
$84$	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	$-0.778165\pi$
$89$		−	10168.3i		−	1.28371i	0.766825	−	0.641856i	$-0.221835\pi$
$90$	−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	−0.973340	−	0.229365i	$-0.926335\pi$
$97$	−11868.3	+	6852.15i	−1.26137	+	0.728255i	−0.288034	+	0.957620i	$0.593002\pi$
$98$	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	−0.167422	−	0.985885i	$-0.553544\pi$
$101$	6147.82	−	3549.45i	0.602668	−	0.347951i	0.770091	+	0.637935i	$0.220211\pi$
$102$	−171.924	+	859.916i	−0.0165248	+	0.0826525i
$103$	4058.54	+	2343.20i	0.382557	+	0.220869i	0.678930	−	0.734203i	$-0.262444\pi$
$103$	4058.54	+	2343.20i	0.382557	+	0.220869i	−0.296373	+	0.955072i	$0.595777\pi$
$104$	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	−0.992711	−	0.120517i	$-0.961545\pi$
$113$	−5005.26	+	8669.36i	−0.391985	+	0.678938i	0.600726	+	0.799455i	$0.294878\pi$
$114$	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	$0.207640\pi$
$127$			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
$130$	−3584.29	−	3507.81i	−0.212088	−	0.207563i
$131$	−24663.9	−	14239.7i	−1.43721	−	0.829773i	−0.439553	−	0.898216i	$-0.644863\pi$
$131$	−24663.9	−	14239.7i	−1.43721	−	0.829773i	−0.997655	+	0.0684439i	$0.978197\pi$
$132$	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	−0.968837	−	0.247698i	$-0.920326\pi$
$137$	−13118.2	−	22721.5i	−0.698931	−	1.21058i	0.269906	−	0.962887i	$-0.413007\pi$
$138$	3433.50	+	3017.06i	0.180293	+	0.158426i
$139$	16654.1	−	28845.7i	0.861967	−	1.49297i	−0.00805999	−	0.999968i	$-0.502566\pi$
$139$	16654.1	−	28845.7i	0.861967	−	1.49297i	0.870027	−	0.493004i	$-0.164101\pi$
$140$	−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	0.393806	−	0.919194i	$-0.371158\pi$
$149$	−4558.66	−	2631.94i	−0.205336	−	0.118551i	−0.599142	+	0.800643i	$0.704491\pi$
$150$	6061.79	+	1076.54i	0.269413	+	0.0478462i
$151$	−5636.90	−	9763.41i	−0.247222	−	0.428201i	0.715532	−	0.698580i	$-0.246184\pi$
$151$	−5636.90	−	9763.41i	−0.247222	−	0.428201i	−0.962754	+	0.270379i	$0.912851\pi$
$152$	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	0.810162	−	0.586207i	$-0.199379\pi$
$157$	17441.0	+	10069.5i	0.707573	+	0.408517i	−0.102589	+	0.994724i	$0.532713\pi$
$158$	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	$-0.906478\pi$
$163$		−	15388.7i		−	0.579197i	0.957148	−	0.289598i	$-0.0935218\pi$
$164$	−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	−0.977403	−	0.211383i	$-0.932203\pi$
$167$	−8523.96	+	14763.9i	−0.305639	+	0.529382i	0.671765	+	0.740765i	$0.265537\pi$
$168$	−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	$-0.271777\pi$
$173$	−9704.36	−	16808.4i	−0.324246	−	0.561610i	−0.981359	+	0.192181i	$0.938444\pi$
$174$	−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	$-0.966862\pi$
$179$		−	6659.35i		−	0.207838i	0.994586	−	0.103919i	$-0.0331383\pi$
$180$	−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	−0.110847	−	0.993837i	$-0.535357\pi$
$191$	25333.0	−	14626.0i	0.694417	−	0.400922i	0.805265	+	0.592915i	$0.202023\pi$
$192$	16016.3	+	14073.7i	0.434471	+	0.381774i
$193$	−37232.0	−	21495.9i	−0.999543	−	0.577086i	−0.0914300	−	0.995812i	$-0.529144\pi$
$193$	−37232.0	−	21495.9i	−0.999543	−	0.577086i	−0.908113	+	0.418725i	$0.862477\pi$
$194$	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	−0.921749	−	0.387786i	$-0.873240\pi$
$211$	−5566.99	+	9642.31i	−0.125042	+	0.216579i	0.796707	+	0.604365i	$0.206573\pi$
$212$	−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	−0.0160539	−	0.999871i	$-0.505110\pi$
$223$	41863.5	−	24169.9i	0.841833	−	0.486032i	0.857887	+	0.513839i	$0.171777\pi$
$224$		−	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	0.754729	−	0.656037i	$-0.227768\pi$
$227$	−9830.70	−	17027.3i	−0.190780	−	0.330441i	−0.945509	+	0.325596i	$0.894435\pi$
$228$	6590.86	−	2230.09i	0.126786	−	0.0428996i
$229$	−41057.9	+	71114.4i	−0.782935	+	1.35608i	0.147290	+	0.989093i	$0.452945\pi$
$229$	−41057.9	+	71114.4i	−0.782935	+	1.35608i	−0.930225	+	0.366990i	$0.880388\pi$
$230$	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	0.688684	−	0.725061i	$-0.258189\pi$
$239$	23140.0	+	13359.9i	0.405105	+	0.233888i	−0.283579	+	0.958949i	$0.591522\pi$
$240$	−25357.8	−	37156.8i	−0.440239	−	0.645083i
$241$	−7637.82	−	13229.1i	−0.131503	−	0.227770i	0.792753	−	0.609543i	$-0.208647\pi$
$241$	−7637.82	−	13229.1i	−0.131503	−	0.227770i	−0.924256	+	0.381773i	$0.875314\pi$
$242$	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	$0.0443642\pi$
$251$			17504.6i			0.277847i	−0.990303	+	0.138923i	$0.955636\pi$
$252$	−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	−0.565362	−	0.824843i	$-0.691263\pi$
$257$	28510.3	−	49381.3i	0.431654	−	0.747647i	0.997016	+	0.0771960i	$0.0245967\pi$
$258$	−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	$-0.0253105\pi$
$263$	29717.1	+	51471.5i	0.429630	+	0.744142i	−0.567210	+	0.823573i	$0.691977\pi$
$264$	−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	$0.267185\pi$
$269$			107707.i			1.48847i	−0.667919	+	0.744234i	$0.732815\pi$
$270$	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	−0.643535	−	0.765417i	$-0.722533\pi$
$277$	−23205.3	+	13397.6i	−0.302432	+	0.174609i	0.341103	+	0.940026i	$0.389200\pi$
$278$	−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	−0.241821	−	0.970321i	$-0.577745\pi$
$281$	37711.0	−	21772.5i	0.477591	−	0.275737i	0.719412	+	0.694584i	$0.244411\pi$
$282$	10994.3	−	3720.05i	0.138251	−	0.0467789i
$283$	−53849.1	−	31089.8i	−0.672366	−	0.388190i	0.124607	−	0.992206i	$-0.460233\pi$
$283$	−53849.1	−	31089.8i	−0.672366	−	0.388190i	−0.796972	+	0.604016i	$0.793566\pi$
$284$	−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	−0.911796	−	0.410644i	$-0.865304\pi$
$293$	−8608.02	+	14909.5i	−0.100269	+	0.173672i	0.811526	+	0.584316i	$0.198637\pi$
$294$	−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	$-0.807060\pi$
$307$		−	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
$310$	29394.8	−	30035.7i	0.305877	−	0.312547i
$311$	−118121.	−	68197.1i	−1.22125	−	0.705091i	−0.256068	−	0.966659i	$-0.582427\pi$
$311$	−118121.	−	68197.1i	−1.22125	−	0.705091i	−0.965185	+	0.261568i	$0.915760\pi$
$312$	−17824.2	−	52678.0i	−0.183105	−	0.541153i
$313$	−81900.2	+	47285.1i	−0.835981	+	0.482654i	−0.855896	−	0.517148i	$-0.826994\pi$
$313$	−81900.2	+	47285.1i	−0.835981	+	0.482654i	0.0199154	+	0.999802i	$0.493660\pi$
$314$		−	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	0.967005	+	0.254758i	$0.0819957\pi$
$317$	70757.2	+	122555.i	0.704129	+	1.21959i	−0.262876	+	0.964830i	$0.584671\pi$
$318$	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	0.613071	−	0.790028i	$-0.289934\pi$
$331$	−41375.6	−	71664.7i	−0.377649	−	0.654108i	−0.990720	+	0.135921i	$0.956601\pi$
$332$	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	0.782472	−	0.622686i	$-0.213959\pi$
$337$	72053.4	+	41600.0i	0.634446	+	0.366297i	−0.148026	+	0.988983i	$0.547292\pi$
$338$	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	−0.996900	−	0.0786729i	$-0.974932\pi$
$347$	−51814.1	+	89744.7i	−0.430317	+	0.745332i	0.566583	+	0.824005i	$0.308265\pi$
$348$	127473.	−	145068.i	1.05259	−	1.19788i
$349$	−75356.4	−	130521.i	−0.618685	−	1.07159i	−0.989726	−	0.142977i	$-0.954332\pi$
$349$	−75356.4	−	130521.i	−0.618685	−	1.07159i	0.371041	−	0.928616i	$-0.379001\pi$
$350$	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	$-0.194979\pi$
$353$	−11068.8	−	19171.8i	−0.0888286	−	0.153856i	−0.907016	+	0.421096i	$0.861646\pi$
$354$	−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	$-0.885245\pi$
$359$		−	90926.7i		−	0.705509i	0.935716	−	0.352755i	$-0.114755\pi$
$360$	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	−0.435161	−	0.900353i	$-0.643309\pi$
$367$	17103.7	−	9874.80i	0.126986	−	0.0733156i	0.562148	+	0.827037i	$0.309975\pi$
$368$	−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	$-0.204784\pi$
$373$	94695.0	+	54672.2i	0.680627	+	0.392960i	−0.119464	+	0.992839i	$0.538118\pi$
$374$	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	−0.216695	−	0.976239i	$-0.569528\pi$
$383$	108125.	−	187277.i	0.737100	−	1.27670i	0.953796	−	0.300456i	$-0.0971389\pi$
$384$	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	−0.329360	−	0.944205i	$-0.606833\pi$
$389$	48977.4	−	28277.1i	0.323666	−	0.186868i	0.653025	+	0.757336i	$0.273500\pi$
$390$	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	$-0.700918\pi$
$397$		−	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
$400$	−106844.	+	64798.3i	−0.667777	+	0.404990i
$401$	48697.9	+	28115.7i	0.302846	+	0.174848i	0.643721	−	0.765261i	$-0.277390\pi$
$401$	48697.9	+	28115.7i	0.302846	+	0.174848i	−0.340875	+	0.940109i	$0.610723\pi$
$402$	−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	−0.977443	−	0.211201i	$-0.932263\pi$
$409$	−51157.2	+	88606.9i	−0.305816	+	0.529689i	0.671627	+	0.740890i	$0.265596\pi$
$410$	−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	0.348962	−	0.937137i	$-0.386534\pi$
$419$	−50586.4	−	29206.1i	−0.288142	−	0.166359i	−0.637103	+	0.770778i	$0.719868\pi$
$420$	4892.26	+	64887.3i	0.0277339	+	0.367842i
$421$	117518.	+	203548.i	0.663043	+	1.14842i	0.979812	+	0.199921i	$0.0640685\pi$
$421$	117518.	+	203548.i	0.663043	+	1.14842i	−0.316770	+	0.948503i	$0.602598\pi$
$422$	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	$0.0374429\pi$
$431$			43601.5i			0.234718i	−0.993090	+	0.117359i	$0.962557\pi$
$432$	−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
$435$	−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	0.967782	−	0.251789i	$-0.0810189\pi$
$439$	51232.1	+	88736.5i	0.265835	+	0.460440i	−0.701947	+	0.712229i	$0.747686\pi$
$440$	−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	−0.987367	−	0.158451i	$-0.949350\pi$
$443$	−123815.	−	214453.i	−0.630906	−	1.09276i	0.356461	−	0.934310i	$-0.383983\pi$
$444$	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	$-0.936995\pi$
$449$		−	79287.5i		−	0.393289i	0.980475	−	0.196645i	$-0.0630045\pi$
$450$	−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	−0.236171	−	0.971711i	$-0.575893\pi$
$457$	101766.	−	58754.5i	0.487270	−	0.281325i	0.723441	+	0.690386i	$0.242559\pi$
$458$	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	0.495901	−	0.868379i	$-0.334838\pi$
$461$	317908.	−	183544.i	1.49589	−	0.863653i	0.999989	+	0.00472615i	$0.00150439\pi$
$462$	16762.1	+	14729.0i	0.0785316	+	0.0690066i
$463$	79996.4	+	46185.9i	0.373171	+	0.215451i	0.674843	−	0.737961i	$-0.264211\pi$
$463$	79996.4	+	46185.9i	0.373171	+	0.215451i	−0.301672	+	0.953412i	$0.597545\pi$
$464$	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	−0.661345	−	0.750082i	$-0.730014\pi$
$479$	−78567.0	+	45360.7i	−0.342428	+	0.197701i	0.318917	+	0.947783i	$0.396681\pi$
$480$	−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	$-0.830968\pi$
$487$		−	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
$490$	−38645.9	+	39488.5i	−0.160958	+	0.164467i
$491$	−198232.	−	114449.i	−0.822264	−	0.474734i	0.0289325	−	0.999581i	$-0.490789\pi$
$491$	−198232.	−	114449.i	−0.822264	−	0.474734i	−0.851197	+	0.524847i	$0.824123\pi$
$492$	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	−0.876341	−	0.481692i	$-0.840022\pi$
$499$	−5232.25	+	9062.53i	−0.0210130	+	0.0363956i	0.855328	+	0.518087i	$0.173356\pi$
$500$	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	0.848972	−	0.528437i	$-0.177222\pi$
$509$	211363.	+	122031.i	0.815819	+	0.471013i	−0.0331537	+	0.999450i	$0.510555\pi$
$510$	−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	$0.217229\pi$
$521$			342391.i			1.26138i	−0.776034	+	0.630692i	$0.782771\pi$
$522$	−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
$525$	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	−0.950430	−	0.310939i	$-0.899357\pi$
$547$	−345995.	+	199760.i	−1.15636	+	0.667627i	−0.205934	+	0.978566i	$0.566023\pi$
$548$	−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	−0.0519165	+	0.998651i	$0.516533\pi$
$563$	−282361.	+	489064.i	−0.890816	+	1.54294i	−0.838899	+	0.544287i	$0.816800\pi$
$564$	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	−0.999587	−	0.0287503i	$-0.990847\pi$
$569$	−477380.	+	275615.i	−1.47448	+	0.851292i	−0.474895	+	0.880043i	$0.657514\pi$
$570$	7250.43	+	10624.1i	0.0223159	+	0.0326995i
$571$	107836.	−	186778.i	0.330744	−	0.572865i	−0.651914	−	0.758293i	$-0.726034\pi$
$571$	107836.	−	186778.i	0.330744	−	0.572865i	0.982658	+	0.185428i	$0.0593670\pi$
$572$	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
$580$	−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	0.750560	−	0.660802i	$-0.229784\pi$
$587$	−67877.0	−	117566.i	−0.196991	−	0.341198i	−0.947551	+	0.319603i	$0.896450\pi$
$588$	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	0.271851	−	0.962339i	$-0.412364\pi$
$599$	−152718.	−	88171.6i	−0.425634	−	0.245740i	−0.697485	+	0.716600i	$0.745697\pi$
$600$	122075.	−	145121.i	0.339097	−	0.403113i
$601$	−55051.5	−	95352.0i	−0.152412	−	0.263986i	0.779701	−	0.626152i	$-0.215371\pi$
$601$	−55051.5	−	95352.0i	−0.152412	−	0.263986i	−0.932114	+	0.362165i	$0.882038\pi$
$602$	−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	0.735079	−	0.677981i	$-0.237145\pi$
$607$	189924.	+	109653.i	0.515470	+	0.297607i	−0.219609	+	0.975588i	$0.570478\pi$
$608$	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	$0.0322382\pi$
$613$			75985.1i			0.202212i	−0.994876	+	0.101106i	$0.967762\pi$
$614$	−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	0.350468	+	0.936575i	$0.386023\pi$
$617$	−242066.	+	419271.i	−0.635863	+	1.10135i	−0.986331	+	0.164773i	$0.947311\pi$
$618$	−30472.0	+	34678.1i	−0.0797856	+	0.0907984i
$619$	−23051.5	−	39926.4i	−0.0601614	−	0.104203i	0.834376	−	0.551196i	$-0.185828\pi$
$619$	−23051.5	−	39926.4i	−0.0601614	−	0.104203i	−0.894537	+	0.446993i	$0.852495\pi$
$620$	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	0.216195	−	0.976350i	$-0.430635\pi$
$641$	480663.	−	277511.i	1.16984	−	0.675405i	0.953641	+	0.300945i	$0.0973021\pi$
$642$	39078.6	−	195460.i	0.0948131	−	0.474229i
$643$	−560077.	−	323360.i	−1.35465	−	0.782105i	−0.365749	−	0.930713i	$-0.619187\pi$
$643$	−560077.	−	323360.i	−1.35465	−	0.782105i	−0.988896	+	0.148609i	$0.952521\pi$
$644$	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	−0.249073	−	0.968485i	$-0.580126\pi$
$653$	304539.	−	527478.i	0.714196	−	1.23702i	0.963269	−	0.268538i	$-0.0865406\pi$
$654$	−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	0.273731	−	0.961806i	$-0.411742\pi$
$659$	540048.	−	311797.i	1.24354	−	0.717961i	0.969814	+	0.243845i	$0.0784090\pi$
$660$	29030.1	+	385034.i	0.0666440	+	0.883917i
$661$	−184642.	+	319810.i	−0.422598	+	0.731962i	−0.996193	−	0.0871775i	$-0.972215\pi$
$661$	−184642.	+	319810.i	−0.422598	+	0.731962i	0.573594	+	0.819140i	$0.305549\pi$
$662$	−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	−0.349460	−	0.936951i	$-0.613635\pi$
$673$	130097.	−	75111.4i	0.287234	−	0.165835i	0.636694	+	0.771117i	$0.280301\pi$
$674$		−	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	−0.986924	−	0.161188i	$-0.948467\pi$
$677$	−290147.	−	502550.i	−0.633055	−	1.09648i	0.353869	−	0.935295i	$-0.384866\pi$
$678$	−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	0.913967	−	0.405787i	$-0.133003\pi$
$691$	50403.6	+	87301.6i	0.105562	+	0.182838i	−0.808406	+	0.588625i	$0.799669\pi$
$692$	−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	$-0.927919\pi$
$701$		−	220659.i		−	0.449040i	0.974469	−	0.224520i	$-0.0720814\pi$
$702$	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	0.923201	−	0.384318i	$-0.125563\pi$
$709$	64731.1	+	112118.i	0.128772	+	0.223039i	−0.794429	+	0.607357i	$0.792230\pi$
$710$	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	$-0.888615\pi$
$719$		−	354459.i		−	0.685659i	0.939398	−	0.342829i	$-0.111385\pi$
$720$	−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	−0.327159	−	0.944969i	$-0.606091\pi$
$727$	173161.	−	99974.6i	0.327628	−	0.189156i	0.654788	+	0.755813i	$0.272758\pi$
$728$	−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	$-0.629807\pi$
$733$	−746774.	−	431150.i	−1.38989	−	0.802455i	−0.993303	+	0.115541i	$0.963140\pi$
$734$	−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	−0.232202	−	0.972668i	$-0.574593\pi$
$743$	400928.	−	694427.i	0.726254	−	1.25791i	0.958456	−	0.285241i	$-0.0920737\pi$
$744$	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	−0.998468	−	0.0553377i	$-0.982376\pi$
$751$	−254539.	+	440875.i	−0.451310	+	0.781692i	0.547158	+	0.837030i	$0.315710\pi$
$752$	−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
$760$	−30789.8	+	31461.2i	−0.0533065	+	0.0544688i
$761$	283879.	+	163898.i	0.490190	+	0.283011i	0.724653	−	0.689114i	$-0.242000\pi$
$761$	283879.	+	163898.i	0.490190	+	0.283011i	−0.234463	+	0.972125i	$0.575333\pi$
$762$	−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	−0.983267	−	0.182170i	$-0.941688\pi$
$769$	−197438.	+	341972.i	−0.333870	+	0.578280i	0.649397	+	0.760449i	$0.275021\pi$
$770$	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	0.858910	−	0.512127i	$-0.171142\pi$
$787$	523274.	+	302112.i	0.844849	+	0.487774i	−0.0140603	+	0.999901i	$0.504476\pi$
$788$	−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	−0.268031	−	0.963410i	$-0.586373\pi$
$797$	444851.	−	770505.i	0.700322	−	1.21299i	0.968353	−	0.249584i	$-0.0802937\pi$
$798$	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	$0.0864258\pi$
$809$			351052.i			0.536382i	−0.963366	+	0.268191i	$0.913574\pi$
$810$	−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	−0.974374	−	0.224936i	$-0.927783\pi$
$821$	−853848.	+	492970.i	−1.26676	+	0.731364i	−0.292387	+	0.956300i	$0.594449\pi$
$822$	244811.	−	82834.9i	0.362316	−	0.122594i
$823$	547461.	+	316077.i	0.808264	+	0.466651i	0.846353	−	0.532623i	$-0.178794\pi$
$823$	547461.	+	316077.i	0.808264	+	0.466651i	−0.0380887	+	0.999274i	$0.512127\pi$
$824$	−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	0.106407	−	0.994323i	$-0.466065\pi$
$839$	718506.	−	414830.i	1.02072	−	0.589313i	0.914312	+	0.405010i	$0.132732\pi$
$840$	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	−0.0205095	−	0.999790i	$-0.506529\pi$
$853$	607611.	−	350804.i	0.835079	−	0.482133i	0.855588	+	0.517657i	$0.173195\pi$
$854$			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	0.953035	+	0.302859i	$0.0979411\pi$
$857$	542612.	+	939831.i	0.738801	+	1.27964i	−0.214234	+	0.976782i	$0.568726\pi$
$858$	−41037.7	+	205259.i	−0.0557454	+	0.278823i
$859$	442391.	−	766243.i	0.599542	−	1.03844i	−0.393347	−	0.919390i	$-0.628683\pi$
$859$	442391.	−	766243.i	0.599542	−	1.03844i	0.992889	−	0.119047i	$-0.0379839\pi$
$860$	−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	0.181955	−	0.983307i	$-0.441757\pi$
$877$	−445046.	−	256947.i	−0.578636	−	0.334076i	−0.760591	+	0.649231i	$0.775091\pi$
$878$	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	$-0.954277\pi$
$881$		−	222212.i		−	0.286297i	0.989701	−	0.143148i	$-0.0457226\pi$
$882$	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
$885$	664411.	+	319592.i	0.848302	+	0.408046i
$886$	−135517.	+	234722.i	−0.172634	+	0.299011i
$887$	−432263.	+	748702.i	−0.549415	+	0.951616i	0.448899	+	0.893582i	$0.351816\pi$
$887$	−432263.	+	748702.i	−0.549415	+	0.951616i	−0.998315	+	0.0580331i	$0.981517\pi$
$888$	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	−0.943973	−	0.330022i	$-0.892944\pi$
$907$	−929719.	+	536773.i	−1.13015	+	0.652494i	−0.186179	+	0.982516i	$0.559610\pi$
$908$	−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	−0.923082	−	0.384604i	$-0.874338\pi$
$911$	−872700.	+	503854.i	−1.05155	+	0.607110i	−0.128464	+	0.991714i	$0.541005\pi$
$912$	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	−0.917251	−	0.398310i	$-0.869597\pi$
$929$	−889734.	+	513688.i	−1.03093	+	0.595207i	−0.113679	+	0.993518i	$0.536263\pi$
$930$	−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	$0.0654129\pi$
$937$			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
$940$	304967.	−	311617.i	0.345142	−	0.352667i
$941$	634781.	+	366491.i	0.716877	+	0.413889i	0.813602	−	0.581422i	$-0.197503\pi$
$941$	634781.	+	366491.i	0.716877	+	0.413889i	−0.0967250	+	0.995311i	$0.530837\pi$
$942$	−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	0.591241	−	0.806495i	$-0.298638\pi$
$947$	−361257.	−	625716.i	−0.402825	−	0.697713i	−0.994066	+	0.108782i	$0.965305\pi$
$948$	−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	0.611862	−	0.790965i	$-0.290421\pi$
$967$	217686.	+	125681.i	0.232797	+	0.134406i	−0.379064	+	0.925370i	$0.623754\pi$
$968$	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	$-0.949259\pi$
$971$		−	299319.i		−	0.317465i	0.987322	−	0.158733i	$-0.0507408\pi$
$972$	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	−0.989395	−	0.145250i	$-0.953601\pi$
$977$	−352133.	+	609912.i	−0.368907	+	0.638966i	0.620488	+	0.784216i	$0.286935\pi$
$978$	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	$-0.282401\pi$
$983$	−343643.	−	595207.i	−0.355632	−	0.615972i	−0.987226	+	0.159327i	$0.949068\pi$
$984$	−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	−0.251357	−	0.967895i	$-0.580877\pi$
$997$	458423.	−	264671.i	0.461186	−	0.266266i	0.712543	+	0.701629i	$0.247543\pi$
$998$	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.14.10	✓	44
3.2	odd	2		135.5.h.a.44.13		44
5.4	even	2	inner	45.5.h.a.14.13	yes	44
9.2	odd	6	inner	45.5.h.a.29.13	yes	44
9.4	even	3		405.5.d.a.404.25		44
9.5	odd	6		405.5.d.a.404.19		44
9.7	even	3		135.5.h.a.89.10		44
15.14	odd	2		135.5.h.a.44.10		44
45.4	even	6		405.5.d.a.404.20		44
45.14	odd	6		405.5.d.a.404.26		44
45.29	odd	6	inner	45.5.h.a.29.10	yes	44
45.34	even	6		135.5.h.a.89.13		44

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

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

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