LMFDB - Embedded newform 31.5.f.a.23.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,5,Mod(15,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.15"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	31.f (of order $10$, degree $4$, 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:	$3.20446885560$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			23.6
Character	$\chi$	$=$	31.23
Dual form			31.5.f.a.27.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.416650 - 1.28232i) q^{2} +(-7.95500 + 2.58474i) q^{3} +(11.4735 + 8.33601i) q^{4} +20.3736 q^{5} +11.2778i q^{6} +(51.5849 + 37.4786i) q^{7} +(32.9227 - 23.9197i) q^{8} +(-8.92916 + 6.48742i) q^{9} +(8.48864 - 26.1253i) q^{10} +(28.4574 - 39.1683i) q^{11} +(-112.818 - 36.6569i) q^{12} +(-105.739 + 34.3566i) q^{13} +(69.5523 - 50.5327i) q^{14} +(-162.072 + 52.6603i) q^{15} +(53.1646 + 163.624i) q^{16} +(-25.4504 - 35.0295i) q^{17} +(4.59859 + 14.1530i) q^{18} +(72.3785 - 222.758i) q^{19} +(233.757 + 169.834i) q^{20} +(-507.231 - 164.809i) q^{21} +(-38.3694 - 52.8109i) q^{22} +(-382.527 - 526.503i) q^{23} +(-200.074 + 275.378i) q^{24} -209.918 q^{25} +149.905i q^{26} +(452.497 - 622.808i) q^{27} +(279.439 + 860.025i) q^{28} +(596.191 + 193.714i) q^{29} +229.768i q^{30} +(146.525 - 949.764i) q^{31} +883.084 q^{32} +(-125.139 + 385.139i) q^{33} +(-55.5228 + 18.0404i) q^{34} +(1050.97 + 763.573i) q^{35} -156.528 q^{36} +1972.98i q^{37} +(-255.490 - 185.624i) q^{38} +(752.348 - 546.613i) q^{39} +(670.753 - 487.330i) q^{40} +(60.3154 - 185.632i) q^{41} +(-422.675 + 581.762i) q^{42} +(-2708.26 - 879.966i) q^{43} +(653.015 - 212.177i) q^{44} +(-181.919 + 132.172i) q^{45} +(-834.524 + 271.153i) q^{46} +(-821.672 - 2528.85i) q^{47} +(-845.848 - 1164.21i) q^{48} +(514.406 + 1583.18i) q^{49} +(-87.4624 + 269.182i) q^{50} +(293.000 + 212.877i) q^{51} +(-1499.59 - 487.247i) q^{52} +(-1091.64 - 1502.52i) q^{53} +(-610.105 - 839.737i) q^{54} +(579.779 - 797.998i) q^{55} +2594.79 q^{56} +1959.12i q^{57} +(496.806 - 683.795i) q^{58} +(1779.59 + 5477.02i) q^{59} +(-2298.51 - 746.832i) q^{60} -3412.06i q^{61} +(-1156.85 - 583.611i) q^{62} -703.750 q^{63} +(-482.696 + 1485.59i) q^{64} +(-2154.27 + 699.965i) q^{65} +(441.731 + 320.936i) q^{66} -5929.67 q^{67} -614.067i q^{68} +(4403.88 + 3199.60i) q^{69} +(1417.03 - 1029.53i) q^{70} +(7886.64 - 5729.98i) q^{71} +(-138.795 + 427.167i) q^{72} +(-2557.84 + 3520.56i) q^{73} +(2529.99 + 822.043i) q^{74} +(1669.90 - 542.584i) q^{75} +(2687.35 - 1952.48i) q^{76} +(2935.95 - 953.948i) q^{77} +(-387.465 - 1192.49i) q^{78} +(4632.43 + 6375.99i) q^{79} +(1083.15 + 3333.60i) q^{80} +(-1713.56 + 5273.78i) q^{81} +(-212.908 - 154.687i) q^{82} +(5544.98 + 1801.67i) q^{83} +(-4445.88 - 6119.22i) q^{84} +(-518.515 - 713.675i) q^{85} +(-2256.79 + 3106.20i) q^{86} -5243.40 q^{87} -1970.22i q^{88} +(3536.06 - 4866.98i) q^{89} +(93.6896 + 288.347i) q^{90} +(-6742.15 - 2190.66i) q^{91} -9229.60i q^{92} +(1289.28 + 7934.10i) q^{93} -3585.13 q^{94} +(1474.61 - 4538.38i) q^{95} +(-7024.93 + 2282.54i) q^{96} +(-505.044 - 366.936i) q^{97} +2244.46 q^{98} +534.356i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 5 q^{3} - 79 q^{4} - 2 q^{5} - 73 q^{7} + 173 q^{8} + 62 q^{9} + 84 q^{10} + 100 q^{11} + 150 q^{12} - 260 q^{13} + 488 q^{14} - 1075 q^{15} + 777 q^{16} - 725 q^{17} - 786 q^{18} - 1581 q^{19}+ \cdots + 74456 q^{98}+O(q^{100}) $ 36 * q - 3 * q^2 - 5 * q^3 - 79 * q^4 - 2 * q^5 - 73 * q^7 + 173 * q^8 + 62 * q^9 + 84 * q^10 + 100 * q^11 + 150 * q^12 - 260 * q^13 + 488 * q^14 - 1075 * q^15 + 777 * q^16 - 725 * q^17 - 786 * q^18 - 1581 * q^19 + 827 * q^20 + 2335 * q^21 - 1030 * q^22 + 1675 * q^23 - 165 * q^24 + 1294 * q^25 - 2855 * q^27 + 352 * q^28 - 575 * q^29 + 895 * q^31 - 5470 * q^32 + 4468 * q^33 + 1815 * q^34 - 3042 * q^35 + 7808 * q^36 - 6604 * q^38 + 595 * q^39 + 1482 * q^40 - 1740 * q^41 + 3840 * q^42 - 10055 * q^43 - 5780 * q^44 + 6774 * q^45 + 16515 * q^46 + 693 * q^47 + 4710 * q^48 - 944 * q^49 - 6240 * q^50 + 12641 * q^51 + 15885 * q^52 - 10835 * q^53 - 25960 * q^54 - 14010 * q^55 - 19976 * q^56 + 4755 * q^58 - 6021 * q^59 + 35 * q^60 - 11088 * q^62 - 15564 * q^63 + 6935 * q^64 + 26645 * q^65 + 23988 * q^66 + 28596 * q^67 - 4229 * q^69 + 8041 * q^70 + 31101 * q^71 + 20690 * q^72 + 6125 * q^73 - 47295 * q^74 - 27475 * q^75 + 12511 * q^76 + 35950 * q^77 + 29801 * q^78 - 29050 * q^79 - 47358 * q^80 - 1965 * q^81 + 9198 * q^82 + 21640 * q^83 - 35875 * q^84 - 55360 * q^85 - 27935 * q^86 - 2262 * q^87 - 11645 * q^89 - 14916 * q^90 + 670 * q^91 - 36224 * q^93 - 52442 * q^94 + 73983 * q^95 + 29810 * q^96 + 55059 * q^97 + 74456 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	0.416650	−	1.28232i	0.104162	−	0.320579i	−0.885371	−	0.464886i	$-0.846095\pi$
$2$	0.416650	−	1.28232i	0.104162	−	0.320579i	0.989533	+	0.144307i	$0.0460953\pi$
$3$	−7.95500	+	2.58474i	−0.883889	+	0.287193i	−0.715571	−	0.698540i	$-0.753834\pi$
$3$	−7.95500	+	2.58474i	−0.883889	+	0.287193i	−0.168318	+	0.985733i	$0.553834\pi$
$4$	11.4735	+	8.33601i	0.717096	+	0.521001i
$5$	20.3736			0.814942			0.407471	−	0.913218i	$-0.366411\pi$
$5$	20.3736			0.814942			0.407471	+	0.913218i	$0.366411\pi$
$6$			11.2778i			0.313271i
$7$	51.5849	+	37.4786i	1.05275	+	0.764870i	0.972734	−	0.231923i	$-0.0745018\pi$
$7$	51.5849	+	37.4786i	1.05275	+	0.764870i	0.0800193	+	0.996793i	$0.474502\pi$
$8$	32.9227	−	23.9197i	0.514417	−	0.373746i
$9$	−8.92916	+	6.48742i	−0.110237	+	0.0800916i
$10$	8.48864	−	26.1253i	0.0848864	−	0.261253i
$11$	28.4574	−	39.1683i	0.235185	−	0.323705i	−0.675069	−	0.737755i	$-0.735886\pi$
$11$	28.4574	−	39.1683i	0.235185	−	0.323705i	0.910254	+	0.414050i	$0.135886\pi$
$12$	−112.818	−	36.6569i	−0.783461	−	0.254562i
$13$	−105.739	+	34.3566i	−0.625672	+	0.203293i	−0.604657	−	0.796486i	$-0.706690\pi$
$13$	−105.739	+	34.3566i	−0.625672	+	0.203293i	−0.0210151	+	0.999779i	$0.506690\pi$
$14$	69.5523	−	50.5327i	0.354859	−	0.257820i
$15$	−162.072	+	52.6603i	−0.720319	+	0.234046i
$16$	53.1646	+	163.624i	0.207674	+	0.639155i
$17$	−25.4504	−	35.0295i	−0.0880637	−	0.121209i	0.762712	−	0.646738i	$-0.223867\pi$
$17$	−25.4504	−	35.0295i	−0.0880637	−	0.121209i	−0.850776	+	0.525529i	$0.823867\pi$
$18$	4.59859	+	14.1530i	0.0141932	+	0.0436821i
$19$	72.3785	−	222.758i	0.200495	−	0.617059i	−0.799374	−	0.600834i	$-0.794835\pi$
$19$	72.3785	−	222.758i	0.200495	−	0.617059i	0.999868	−	0.0162247i	$-0.00516471\pi$
$20$	233.757	+	169.834i	0.584392	+	0.424585i
$21$	−507.231	−	164.809i	−1.15018	−	0.373717i
$22$	−38.3694	−	52.8109i	−0.0792756	−	0.109113i
$23$	−382.527	−	526.503i	−0.723114	−	0.995281i	−0.999415	−	0.0342094i	$-0.989109\pi$
$23$	−382.527	−	526.503i	−0.723114	−	0.995281i	0.276301	−	0.961071i	$-0.410891\pi$
$24$	−200.074	+	275.378i	−0.347351	+	0.478087i
$25$	−209.918			−0.335869
$26$			149.905i			0.221753i
$27$	452.497	−	622.808i	0.620709	−	0.854332i
$28$	279.439	+	860.025i	0.356427	+	1.09697i
$29$	596.191	+	193.714i	0.708908	+	0.230338i	0.641207	−	0.767368i	$-0.278434\pi$
$29$	596.191	+	193.714i	0.708908	+	0.230338i	0.0677003	+	0.997706i	$0.478434\pi$
$30$			229.768i			0.255298i
$31$	146.525	−	949.764i	0.152472	−	0.988308i
$31$	146.525	−	949.764i	0.152472	−	0.988308i
$32$	883.084			0.862386
$33$	−125.139	+	385.139i	−0.114912	+	0.353663i
$34$	−55.5228	+	18.0404i	−0.0480301	+	0.0156059i
$35$	1050.97	+	763.573i	0.857933	+	0.623325i
$36$	−156.528			−0.120778
$37$			1972.98i			1.44119i	0.693359	+	0.720593i	$0.256130\pi$
$37$			1972.98i			1.44119i	−0.693359	+	0.720593i	$0.743870\pi$
$38$	−255.490	−	185.624i	−0.176932	−	0.128549i
$39$	752.348	−	546.613i	0.494641	−	0.359377i
$40$	670.753	−	487.330i	0.419220	−	0.304581i
$41$	60.3154	−	185.632i	0.0358806	−	0.110429i	−0.931512	−	0.363710i	$-0.881510\pi$
$41$	60.3154	−	185.632i	0.0358806	−	0.110429i	0.967393	+	0.253281i	$0.0815098\pi$
$42$	−422.675	+	581.762i	−0.239612	+	0.329797i
$43$	−2708.26	−	879.966i	−1.46471	−	0.475914i	−0.535208	−	0.844721i	$-0.679767\pi$
$43$	−2708.26	−	879.966i	−1.46471	−	0.475914i	−0.929506	+	0.368806i	$0.879767\pi$
$44$	653.015	−	212.177i	0.337301	−	0.109596i
$45$	−181.919	+	132.172i	−0.0898365	+	0.0652700i
$46$	−834.524	+	271.153i	−0.394387	+	0.128144i
$47$	−821.672	−	2528.85i	−0.371966	−	1.14479i	−0.945503	−	0.325613i	$-0.894429\pi$
$47$	−821.672	−	2528.85i	−0.371966	−	1.14479i	0.573537	−	0.819179i	$-0.305571\pi$
$48$	−845.848	−	1164.21i	−0.367122	−	0.505300i
$49$	514.406	+	1583.18i	0.214246	+	0.659383i
$50$	−87.4624	+	269.182i	−0.0349850	+	0.107673i
$51$	293.000	+	212.877i	0.112649	+	0.0818443i
$52$	−1499.59	−	487.247i	−0.554583	−	0.180195i
$53$	−1091.64	−	1502.52i	−0.388624	−	0.534895i	0.569219	−	0.822186i	$-0.307245\pi$
$53$	−1091.64	−	1502.52i	−0.388624	−	0.534895i	−0.957843	+	0.287291i	$0.907245\pi$
$54$	−610.105	−	839.737i	−0.209227	−	0.287976i
$55$	579.779	−	797.998i	0.191663	−	0.263801i
$56$	2594.79			0.827422
$57$			1959.12i			0.602992i
$58$	496.806	−	683.795i	0.147683	−	0.203268i
$59$	1779.59	+	5477.02i	0.511230	+	1.57340i	0.790038	+	0.613058i	$0.210061\pi$
$59$	1779.59	+	5477.02i	0.511230	+	1.57340i	−0.278808	+	0.960347i	$0.589939\pi$
$60$	−2298.51	−	746.832i	−0.638475	−	0.207453i
$61$		−	3412.06i		−	0.916975i	−0.888701	−	0.458488i	$-0.848391\pi$
$61$		−	3412.06i		−	0.916975i	0.888701	−	0.458488i	$-0.151609\pi$
$62$	−1156.85	−	583.611i	−0.300949	−	0.151824i
$63$	−703.750			−0.177312
$64$	−482.696	+	1485.59i	−0.117846	+	0.362692i
$65$	−2154.27	+	699.965i	−0.509887	+	0.165672i
$66$	441.731	+	320.936i	0.101407	+	0.0736768i
$67$	−5929.67			−1.32093			−0.660467	−	0.750855i	$-0.729642\pi$
$67$	−5929.67			−1.32093			−0.660467	+	0.750855i	$0.729642\pi$
$68$		−	614.067i		−	0.132800i
$69$	4403.88	+	3199.60i	0.924990	+	0.672045i
$70$	1417.03	−	1029.53i	0.289189	−	0.210108i
$71$	7886.64	−	5729.98i	1.56450	−	1.13668i	0.632303	−	0.774721i	$-0.282110\pi$
$71$	7886.64	−	5729.98i	1.56450	−	1.13668i	0.932196	−	0.361954i	$-0.117890\pi$
$72$	−138.795	+	427.167i	−0.0267737	+	0.0824010i
$73$	−2557.84	+	3520.56i	−0.479984	+	0.660642i	−0.978502	−	0.206238i	$-0.933878\pi$
$73$	−2557.84	+	3520.56i	−0.479984	+	0.660642i	0.498518	+	0.866880i	$0.333878\pi$
$74$	2529.99	+	822.043i	0.462014	+	0.150117i
$75$	1669.90	−	542.584i	0.296871	−	0.0964593i
$76$	2687.35	−	1952.48i	0.465262	−	0.338032i
$77$	2935.95	−	953.948i	0.495185	−	0.160895i
$78$	−387.465	−	1192.49i	−0.0636859	−	0.196005i
$79$	4632.43	+	6375.99i	0.742258	+	1.02163i	0.998486	+	0.0550136i	$0.0175202\pi$
$79$	4632.43	+	6375.99i	0.742258	+	1.02163i	−0.256228	+	0.966616i	$0.582480\pi$
$80$	1083.15	+	3333.60i	0.169242	+	0.520874i
$81$	−1713.56	+	5273.78i	−0.261173	+	0.803808i
$82$	−212.908	−	154.687i	−0.0316639	−	0.0230052i
$83$	5544.98	+	1801.67i	0.804904	+	0.261529i	0.682438	−	0.730944i	$-0.260920\pi$
$83$	5544.98	+	1801.67i	0.804904	+	0.261529i	0.122466	+	0.992473i	$0.460920\pi$
$84$	−4445.88	−	6119.22i	−0.630085	−	0.867237i
$85$	−518.515	−	713.675i	−0.0717668	−	0.0987785i
$86$	−2256.79	+	3106.20i	−0.305136	+	0.419984i
$87$	−5243.40			−0.692747
$88$		−	1970.22i		−	0.254419i
$89$	3536.06	−	4866.98i	0.446416	−	0.614440i	−0.525206	−	0.850975i	$-0.676012\pi$
$89$	3536.06	−	4866.98i	0.446416	−	0.614440i	0.971623	+	0.236535i	$0.0760119\pi$
$90$	93.6896	+	288.347i	0.0115666	+	0.0355984i
$91$	−6742.15	−	2190.66i	−0.814171	−	0.264540i
$92$		−	9229.60i		−	1.09045i
$93$	1289.28	+	7934.10i	0.149067	+	0.917344i
$94$	−3585.13			−0.405741
$95$	1474.61	−	4538.38i	0.163391	−	0.502867i
$96$	−7024.93	+	2282.54i	−0.762254	+	0.247671i
$97$	−505.044	−	366.936i	−0.0536767	−	0.0389984i	0.560623	−	0.828071i	$-0.310562\pi$
$97$	−505.044	−	366.936i	−0.0536767	−	0.0389984i	−0.614300	+	0.789072i	$0.710562\pi$
$98$	2244.46			0.233701
$99$			534.356i			0.0545205i
$100$	−2408.50	−	1749.88i	−0.240850	−	0.174988i
$101$	−1104.91	+	802.768i	−0.108314	+	0.0786950i	−0.640624	−	0.767855i	$-0.721324\pi$
$101$	−1104.91	+	802.768i	−0.108314	+	0.0786950i	0.532310	+	0.846550i	$0.321324\pi$
$102$	395.054	−	287.024i	0.0379714	−	0.0275878i
$103$	1479.32	−	4552.88i	0.139440	−	0.429153i	−0.856814	−	0.515626i	$-0.827560\pi$
$103$	1479.32	−	4552.88i	0.139440	−	0.429153i	0.996254	+	0.0864727i	$0.0275595\pi$
$104$	−2659.40	+	3660.35i	−0.245877	+	0.338420i
$105$	−10334.1	−	3357.75i	−0.937333	−	0.304558i
$106$	−2381.54	+	773.809i	−0.211956	+	0.0688688i
$107$	−7516.81	+	5461.28i	−0.656547	+	0.477009i	−0.865495	−	0.500917i	$-0.832996\pi$
$107$	−7516.81	+	5461.28i	−0.656547	+	0.477009i	0.208948	+	0.977927i	$0.432996\pi$
$108$	10383.5	−	3373.79i	0.890215	−	0.289249i
$109$	1622.71	+	4994.20i	0.136581	+	0.420352i	0.995833	−	0.0912009i	$-0.0290706\pi$
$109$	1622.71	+	4994.20i	0.136581	+	0.420352i	−0.859252	+	0.511553i	$0.829071\pi$
$110$	−781.721	−	1075.95i	−0.0646050	−	0.0889212i
$111$	−5099.64	−	15695.1i	−0.413898	−	1.27385i
$112$	−3389.90	+	10433.0i	−0.270241	+	0.831716i
$113$	7512.09	+	5457.85i	0.588307	+	0.427430i	0.841709	−	0.539931i	$-0.181550\pi$
$113$	7512.09	+	5457.85i	0.588307	+	0.427430i	−0.253403	+	0.967361i	$0.581550\pi$
$114$	2512.21	+	816.268i	0.193307	+	0.0628091i
$115$	−7793.44	−	10726.7i	−0.589296	−	0.811096i
$116$	5225.62	+	7192.44i	0.388348	+	0.534516i
$117$	721.272	−	992.746i	0.0526899	−	0.0725214i
$118$	7764.74			0.557652
$119$		−	2760.84i		−	0.194961i
$120$	−4076.22	+	5610.43i	−0.283071	+	0.389613i
$121$	3799.99	+	11695.2i	0.259544	+	0.798795i
$122$	−4375.35	−	1421.64i	−0.293963	−	0.0955144i
$123$			1632.60i			0.107912i
$124$	9598.41	−	9675.71i	0.624246	−	0.629273i
$125$	−17010.3			−1.08866
$126$	−293.217	+	902.430i	−0.0184692	+	0.0568424i
$127$	17953.8	−	5833.53i	1.11313	−	0.361679i	0.305991	−	0.952034i	$-0.401012\pi$
$127$	17953.8	−	5833.53i	1.11313	−	0.361679i	0.807144	+	0.590355i	$0.201012\pi$
$128$	13134.8	+	9542.95i	0.801682	+	0.582456i
$129$	23818.7			1.43132
$130$			3054.10i			0.180716i
$131$	−15853.4	−	11518.2i	−0.923803	−	0.671182i	0.0206648	−	0.999786i	$-0.493422\pi$
$131$	−15853.4	−	11518.2i	−0.923803	−	0.671182i	−0.944468	+	0.328604i	$0.893422\pi$
$132$	−4646.31	+	3375.74i	−0.266662	+	0.193741i
$133$	12082.3	−	8778.31i	0.683041	−	0.496258i
$134$	−2470.60	+	7603.72i	−0.137592	+	0.423464i
$135$	9218.97	−	12688.8i	0.505842	−	0.696232i
$136$	−1675.79	−	544.498i	−0.0906030	−	0.0294387i
$137$	−29448.6	+	9568.44i	−1.56900	+	0.509800i	−0.959194	−	0.282748i	$-0.908754\pi$
$137$	−29448.6	+	9568.44i	−1.56900	+	0.509800i	−0.609809	+	0.792548i	$0.708754\pi$
$138$	5937.78	−	4314.05i	0.311793	−	0.226531i
$139$	22821.1	−	7415.02i	1.18115	−	0.383780i	0.348359	−	0.937361i	$-0.386739\pi$
$139$	22821.1	−	7415.02i	1.18115	−	0.383780i	0.832795	+	0.553581i	$0.186739\pi$
$140$	5693.17	+	17521.8i	0.290468	+	0.893967i
$141$	13072.8	+	17993.2i	0.657553	+	0.905044i
$142$	−4061.68	−	12500.6i	−0.201432	−	0.619945i
$143$	−1663.36	+	5119.30i	−0.0813420	+	0.250345i
$144$	−1536.21	−	1116.12i	−0.0740842	−	0.0538253i
$145$	12146.5	+	3946.65i	0.577719	+	0.187712i
$146$	3448.75	+	4746.80i	0.161792	+	0.222687i
$147$	−8184.20	−	11264.6i	−0.378740	−	0.521291i
$148$	−16446.8	+	22637.1i	−0.750859	+	1.03347i
$149$	−34200.9			−1.54051			−0.770255	−	0.637736i	$-0.779871\pi$
$149$	−34200.9			−1.54051			−0.770255	+	0.637736i	$0.779871\pi$
$150$		−	2367.41i		−	0.105218i
$151$	−13987.5	+	19252.1i	−0.613460	+	0.844355i	−0.996856	−	0.0792291i	$-0.974754\pi$
$151$	−13987.5	+	19252.1i	−0.613460	+	0.844355i	0.383397	+	0.923584i	$0.374754\pi$
$152$	−2945.42	−	9065.08i	−0.127485	−	0.392360i
$153$	454.502	+	147.677i	0.0194157	+	0.00630854i
$154$		−	4162.28i		−	0.175505i
$155$	2985.25	−	19350.1i	0.124256	−	0.805414i
$156$	13188.7			0.541941
$157$	−4043.87	+	12445.7i	−0.164058	+	0.504919i	−0.998966	−	0.0454714i	$-0.985521\pi$
$157$	−4043.87	+	12445.7i	−0.164058	+	0.504919i	0.834908	+	0.550390i	$0.185521\pi$
$158$	10106.1	−	3283.68i	0.404829	−	0.131537i
$159$	12567.7	+	9130.94i	0.497119	+	0.361178i
$160$	17991.6			0.702795
$161$		−	41496.2i		−	1.60087i
$162$	6048.70	+	4394.64i	0.230479	+	0.167453i
$163$	−2105.40	+	1529.66i	−0.0792428	+	0.0575732i	−0.626701	−	0.779260i	$-0.715595\pi$
$163$	−2105.40	+	1529.66i	−0.0792428	+	0.0575732i	0.547459	+	0.836833i	$0.315595\pi$
$164$	2239.46	−	1627.06i	0.0832636	−	0.0604945i
$165$	−2549.53	+	7846.65i	−0.0936467	+	0.288215i
$166$	4620.63	−	6359.76i	0.167682	−	0.230794i
$167$	−21362.2	−	6940.99i	−0.765971	−	0.248879i	−0.100132	−	0.994974i	$-0.531926\pi$
$167$	−21362.2	−	6940.99i	−0.765971	−	0.248879i	−0.665839	+	0.746095i	$0.731926\pi$
$168$	−20641.6	+	6706.86i	−0.731349	+	0.237630i
$169$	−13106.1	+	9522.11i	−0.458879	+	0.333395i
$170$	−1131.20	+	367.548i	−0.0391417	+	0.0127179i
$171$	798.846	+	2458.59i	0.0273194	+	0.0840804i
$172$	−23737.9	−	32672.4i	−0.802389	−	1.10439i
$173$	−11739.8	−	36131.5i	−0.392256	−	1.20724i	−0.931078	−	0.364820i	$-0.881130\pi$
$173$	−11739.8	−	36131.5i	−0.392256	−	1.20724i	0.538822	−	0.842420i	$-0.318870\pi$
$174$	−2184.66	+	6723.70i	−0.0721583	+	0.222080i
$175$	−10828.6	−	7867.45i	−0.353587	−	0.256896i
$176$	7921.79	+	2573.95i	0.255740	+	0.0830948i
$177$	−28313.3	−	38969.9i	−0.903742	−	1.24389i
$178$	−4767.70	−	6562.18i	−0.150477	−	0.207113i
$179$	−19761.1	+	27198.8i	−0.616744	+	0.848875i	−0.997111	−	0.0759609i	$-0.975798\pi$
$179$	−19761.1	+	27198.8i	−0.616744	+	0.848875i	0.380367	+	0.924836i	$0.375798\pi$
$180$	−3189.04			−0.0984271
$181$			18612.8i			0.568139i	0.958804	+	0.284070i	$0.0916847\pi$
$181$			18612.8i			0.568139i	−0.958804	+	0.284070i	$0.908315\pi$
$182$	−5618.24	+	7732.84i	−0.169612	+	0.233451i
$183$	8819.29	+	27143.0i	0.263349	+	0.810504i
$184$	−25187.7	−	8183.97i	−0.743964	−	0.241729i
$185$			40196.7i			1.17448i
$186$	10711.2	+	1652.48i	0.309608	+	0.0477650i
$187$	−2096.30			−0.0599473
$188$	11653.0	−	35864.3i	0.329703	−	1.01472i
$189$	46684.0	−	15168.6i	1.30691	−	0.424640i
$190$	−5205.24	−	3781.83i	−0.144189	−	0.104760i
$191$	56146.3			1.53906			0.769528	−	0.638613i	$-0.220491\pi$
$191$	56146.3			1.53906			0.769528	+	0.638613i	$0.220491\pi$
$192$		−	13065.5i		−	0.354424i
$193$	53261.3	+	38696.6i	1.42987	+	1.03886i	0.990040	+	0.140784i	$0.0449622\pi$
$193$	53261.3	+	38696.6i	1.42987	+	1.03886i	0.439833	+	0.898080i	$0.355038\pi$
$194$	−680.955	+	494.743i	−0.0180932	+	0.0131455i
$195$	15328.0	−	11136.5i	0.403103	−	0.292872i
$196$	−7295.34	+	22452.7i	−0.189904	+	0.584463i
$197$	−45331.6	+	62393.6i	−1.16807	+	1.60771i	−0.492793	+	0.870146i	$0.664024\pi$
$197$	−45331.6	+	62393.6i	−1.16807	+	1.60771i	−0.675277	+	0.737564i	$0.735976\pi$
$198$	685.213	+	222.639i	0.0174781	+	0.00567899i
$199$	47008.3	−	15273.9i	1.18705	−	0.385695i	0.352068	−	0.935975i	$-0.385479\pi$
$199$	47008.3	−	15273.9i	1.18705	−	0.385695i	0.834981	+	0.550279i	$0.185479\pi$
$200$	−6911.08	+	5021.19i	−0.172777	+	0.125530i
$201$	47170.6	−	15326.6i	1.16756	−	0.379363i
$202$	569.040	+	1751.32i	0.0139457	+	0.0429204i
$203$	23494.3	+	32337.2i	0.570126	+	0.784712i
$204$	1587.20	+	4884.90i	0.0381392	+	0.117380i
$205$	1228.84	−	3781.97i	0.0292406	−	0.0899935i
$206$	−5221.88	−	3793.92i	−0.123053	−	0.0894033i
$207$	6831.30	+	2219.62i	0.159427	+	0.0518010i
$208$	−11243.1	−	15474.8i	−0.259872	−	0.357683i
$209$	−6665.35	−	9174.07i	−0.152592	−	0.210024i
$210$	−8611.40	+	11852.6i	−0.195270	+	0.268766i
$211$	−25563.4			−0.574188			−0.287094	−	0.957902i	$-0.592689\pi$
$211$	−25563.4			−0.574188			−0.287094	+	0.957902i	$0.592689\pi$
$212$		−	26339.2i		−	0.586044i
$213$	−47927.8	+	65966.9i	−1.05640	+	1.45401i
$214$	3871.21	+	11914.4i	0.0845317	+	0.260162i
$215$	−55176.8	−	17928.0i	−1.19366	−	0.387843i
$216$		−	31328.1i		−	0.671471i
$217$	43154.4	−	43501.9i	0.916442	−	0.923823i
$218$	7080.24			0.148983
$219$	11247.9	−	34617.4i	0.234521	−	0.721782i
$220$	13304.2	−	4322.81i	0.274881	−	0.0893142i
$221$	3894.58	+	2829.58i	0.0797400	+	0.0579345i
$222$	−22250.8			−0.451482
$223$		−	1133.03i		−	0.0227840i	−0.999935	−	0.0113920i	$-0.996374\pi$
$223$		−	1133.03i		−	0.0227840i	0.999935	−	0.0113920i	$-0.00362627\pi$
$224$	45553.8	+	33096.8i	0.907880	+	0.659614i
$225$	1874.39	−	1361.83i	0.0370251	−	0.0269003i
$226$	10128.6	−	7358.86i	0.198305	−	0.144077i
$227$	−1354.20	+	4167.78i	−0.0262803	+	0.0808823i	−0.963336	−	0.268296i	$-0.913539\pi$
$227$	−1354.20	+	4167.78i	−0.0262803	+	0.0808823i	0.937056	+	0.349179i	$0.113539\pi$
$228$	−16331.3	+	22478.0i	−0.314159	+	0.432403i
$229$	38889.5	+	12636.0i	0.741585	+	0.240956i	0.655356	−	0.755320i	$-0.272518\pi$
$229$	38889.5	+	12636.0i	0.741585	+	0.240956i	0.0862286	+	0.996275i	$0.472518\pi$
$230$	−17002.2	+	5524.36i	−0.321403	+	0.104430i
$231$	−20889.8	+	15177.3i	−0.391480	+	0.284427i
$232$	24261.8	−	7883.15i	0.450762	−	0.146462i
$233$	−17818.9	−	54841.0i	−0.328223	−	1.01017i	−0.969964	−	0.243247i	$-0.921788\pi$
$233$	−17818.9	−	54841.0i	−0.328223	−	1.01017i	0.641741	−	0.766921i	$-0.278212\pi$
$234$	−972.496	−	1338.53i	−0.0177605	−	0.0244453i
$235$	−16740.4	−	51521.6i	−0.303130	−	0.932940i
$236$	−25238.3	+	77675.5i	−0.453144	+	1.39463i
$237$	−53331.3	−	38747.4i	−0.949479	−	0.689837i
$238$	−3540.27	−	1150.30i	−0.0625003	−	0.0203076i
$239$	15737.4	+	21660.7i	0.275510	+	0.379207i	0.924240	−	0.381812i	$-0.124700\pi$
$239$	15737.4	+	21660.7i	0.275510	+	0.379207i	−0.648730	+	0.761018i	$0.724700\pi$
$240$	−17232.9	−	23719.1i	−0.299183	−	0.411790i
$241$	−268.043	+	368.930i	−0.00461499	+	0.00635199i	−0.811318	−	0.584605i	$-0.801250\pi$
$241$	−268.043	+	368.930i	−0.00461499	+	0.00635199i	0.806703	+	0.590957i	$0.201250\pi$
$242$	16580.2			0.283112
$243$			15974.5i			0.270529i
$244$	28443.0	−	39148.4i	0.477745	−	0.657559i
$245$	10480.3	+	32255.0i	0.174599	+	0.537359i
$246$	2093.51	+	680.222i	0.0345943	+	0.0112404i
$247$			26040.8i			0.426836i
$248$	−17894.1	−	34773.6i	−0.290942	−	0.565388i
$249$	−48767.2			−0.786555
$250$	−7087.32	+	21812.5i	−0.113397	+	0.349000i
$251$	−9961.57	+	3236.71i	−0.158118	+	0.0513755i	−0.387006	−	0.922077i	$-0.626491\pi$
$251$	−9961.57	+	3236.71i	−0.158118	+	0.0513755i	0.228889	+	0.973453i	$0.426491\pi$
$252$	−8074.50	−	5866.47i	−0.127149	−	0.0923795i
$253$	−31508.0			−0.492243
$254$		−	25452.9i		−	0.394521i
$255$	5969.45	+	4337.06i	0.0918024	+	0.0666984i
$256$	−2509.76	+	1823.45i	−0.0382960	+	0.0278236i
$257$	97371.4	−	70744.5i	1.47423	−	1.07109i	0.494870	−	0.868967i	$-0.335216\pi$
$257$	97371.4	−	70744.5i	1.47423	−	1.07109i	0.979360	−	0.202124i	$-0.0647843\pi$
$258$	9924.04	−	30543.1i	0.149090	−	0.458853i
$259$	−73944.7	+	101776.i	−1.10232	+	1.51721i
$260$	−30552.0	−	9926.95i	−0.451953	−	0.146848i
$261$	−6580.20	+	2138.04i	−0.0965957	+	0.0313858i
$262$	−21375.2	+	15530.0i	−0.311393	+	0.226240i
$263$	−5077.96	+	1649.93i	−0.0734138	+	0.0238536i	−0.345494	−	0.938421i	$-0.612289\pi$
$263$	−5077.96	+	1649.93i	−0.0734138	+	0.0238536i	0.272080	+	0.962275i	$0.412289\pi$
$264$	5092.50	+	15673.1i	0.0730674	+	0.224878i
$265$	−22240.7	−	30611.7i	−0.316706	−	0.435909i
$266$	−6222.48	−	19150.8i	−0.0879428	−	0.270660i
$267$	−15549.6	+	47856.6i	−0.218120	+	0.671304i
$268$	−68034.3	−	49429.8i	−0.947236	−	0.688208i
$269$	36057.1	+	11715.7i	0.498294	+	0.161906i	0.547372	−	0.836889i	$-0.315628\pi$
$269$	36057.1	+	11715.7i	0.498294	+	0.161906i	−0.0490778	+	0.998795i	$0.515628\pi$
$270$	−12430.0	−	17108.4i	−0.170508	−	0.234684i
$271$	−45357.8	−	62429.6i	−0.617608	−	0.850065i	0.379568	−	0.925164i	$-0.376073\pi$
$271$	−45357.8	−	62429.6i	−0.617608	−	0.850065i	−0.997176	+	0.0750992i	$0.976073\pi$
$272$	4378.59	−	6026.62i	0.0591830	−	0.0814584i
$273$	59296.1			0.795612
$274$			41749.2i			0.556092i
$275$	−5973.74	+	8222.14i	−0.0789916	+	0.108723i
$276$	23856.1	+	73421.5i	0.313171	+	0.963841i
$277$	−49096.4	−	15952.4i	−0.639868	−	0.207906i	−0.0289267	−	0.999582i	$-0.509209\pi$
$277$	−49096.4	−	15952.4i	−0.639868	−	0.207906i	−0.610941	+	0.791676i	$0.709209\pi$
$278$		−	32353.3i		−	0.418629i
$279$	4853.16	+	9431.17i	0.0623471	+	0.121159i
$280$	52865.2			0.674301
$281$	−3891.11	+	11975.6i	−0.0492789	+	0.151665i	−0.972668	−	0.232201i	$-0.925407\pi$
$281$	−3891.11	+	11975.6i	−0.0492789	+	0.151665i	0.923389	+	0.383866i	$0.125407\pi$
$282$	28519.7	−	9266.62i	0.358630	−	0.116526i
$283$	70569.0	+	51271.4i	0.881133	+	0.640180i	0.933551	−	0.358445i	$-0.116693\pi$
$283$	70569.0	+	51271.4i	0.881133	+	0.640180i	−0.0524182	+	0.998625i	$0.516693\pi$
$284$	138253.			1.71410
$285$			39914.3i			0.491404i
$286$	5871.53	+	4265.91i	0.0717825	+	0.0521531i
$287$	10068.6	−	7315.25i	0.122237	−	0.0888107i
$288$	−7885.20	+	5728.93i	−0.0950665	+	0.0690699i
$289$	25230.1	−	77650.2i	0.302081	−	0.929708i
$290$	10121.7	−	13931.3i	0.120353	−	0.165652i
$291$	4966.06	+	1613.57i	0.0586444	+	0.0190547i
$292$	−58694.8	+	19071.1i	−0.688390	+	0.223671i
$293$	108916.	−	79132.3i	1.26870	−	0.921762i	0.269546	−	0.962987i	$-0.413126\pi$
$293$	108916.	−	79132.3i	1.26870	−	0.921762i	0.999150	+	0.0412259i	$0.0131263\pi$
$294$	−17854.7	+	5801.35i	−0.206566	+	0.0671172i
$295$	36256.6	+	111586.i	0.416623	+	1.28223i
$296$	47193.3	+	64955.9i	0.538637	+	0.741371i
$297$	−11517.4	−	35447.1i	−0.130570	−	0.401853i
$298$	−14249.8	+	43856.3i	−0.160463	+	0.493855i
$299$	58536.7	+	42529.4i	0.654766	+	0.475715i
$300$	23682.6	+	7694.96i	0.263140	+	0.0854995i
$301$	−106725.	−	146895.i	−1.17797	−	1.62134i
$302$	18859.4	+	25957.8i	0.206783	+	0.284612i
$303$	6714.66	−	9241.93i	0.0731373	−	0.100665i
$304$	40296.5			0.436034
$305$		−	69515.9i		−	0.747282i
$306$	378.736	−	521.286i	0.00404477	−	0.00556715i
$307$	32033.0	+	98587.4i	0.339876	+	1.04603i	0.964270	+	0.264922i	$0.0853461\pi$
$307$	32033.0	+	98587.4i	0.339876	+	1.04603i	−0.624394	+	0.781110i	$0.714654\pi$
$308$	41637.8	+	13529.0i	0.438921	+	0.142614i
$309$			40041.9i			0.419370i
$310$	−23569.1	−	11890.2i	−0.245256	−	0.123728i
$311$	−95052.5			−0.982749			−0.491375	−	0.870948i	$-0.663505\pi$
$311$	−95052.5			−0.982749			−0.491375	+	0.870948i	$0.663505\pi$
$312$	11694.5	−	35992.0i	0.120136	−	0.369740i
$313$	−120203.	+	39056.4i	−1.22695	+	0.398661i	−0.849609	−	0.527413i	$-0.823162\pi$
$313$	−120203.	+	39056.4i	−1.22695	+	0.398661i	−0.377342	+	0.926074i	$0.623162\pi$
$314$	14274.5	+	10371.0i	0.144778	+	0.105187i
$315$	−14337.9			−0.144499
$316$			111771.i			1.11932i
$317$	−53514.3	−	38880.4i	−0.532539	−	0.386912i	0.288768	−	0.957399i	$-0.406755\pi$
$317$	−53514.3	−	38880.4i	−0.532539	−	0.386912i	−0.821307	+	0.570487i	$0.806755\pi$
$318$	16945.1	−	12311.3i	0.167567	−	0.121745i
$319$	24553.5	−	17839.2i	0.241286	−	0.175305i
$320$	−9834.24	+	30266.7i	−0.0960375	+	0.295573i
$321$	45680.3	−	62873.5i	0.443321	−	0.610179i
$322$	−53211.3	−	17289.4i	−0.513206	−	0.166751i
$323$	−9645.17	+	3133.90i	−0.0924495	+	0.0300387i
$324$	−63622.8	+	46224.7i	−0.606070	+	0.440336i
$325$	22196.5	−	7212.07i	0.210144	−	0.0682799i
$326$	1084.30	+	3337.12i	0.0102027	+	0.0314005i
$327$	−25817.4	−	35534.6i	−0.241444	−	0.332319i
$328$	−2454.52	−	7554.22i	−0.0228149	−	0.0702170i
$329$	52391.8	−	161245.i	0.484029	−	1.48969i
$330$	8999.63	+	6538.61i	0.0826412	+	0.0600424i
$331$	1515.50	+	492.415i	0.0138325	+	0.00449444i	0.315925	−	0.948784i	$-0.397685\pi$
$331$	1515.50	+	492.415i	0.0138325	+	0.00449444i	−0.302093	+	0.953279i	$0.597685\pi$
$332$	48601.8	+	66894.6i	0.440937	+	0.606897i
$333$	−12799.6	−	17617.1i	−0.115427	−	0.158871i
$334$	−17801.1	+	24501.1i	−0.159571	+	0.219630i
$335$	−120809.			−1.07648
$336$		−	91757.0i		−	0.812756i
$337$	51602.7	−	71025.0i	0.454373	−	0.625391i	−0.518957	−	0.854800i	$-0.673680\pi$
$337$	51602.7	−	71025.0i	0.454373	−	0.625391i	0.973330	+	0.229410i	$0.0736795\pi$
$338$	6749.72	+	20773.5i	0.0590816	+	0.181834i
$339$	−73865.8	−	24000.5i	−0.642753	−	0.208843i
$340$		−	12510.7i		−	0.108224i
$341$	−33030.9	−	32767.0i	−0.284061	−	0.281792i
$342$	3485.53			0.0298001
$343$	14508.8	−	44653.4i	0.123322	−	0.379548i
$344$	−110212.	+	35809.9i	−0.931345	+	0.302612i
$345$	89722.6	+	65187.3i	0.753813	+	0.547678i
$346$	−51223.4			−0.427874
$347$			112465.i			0.934028i	0.884250	+	0.467014i	$0.154670\pi$
$347$			112465.i			0.934028i	−0.884250	+	0.467014i	$0.845330\pi$
$348$	−60160.4	−	43709.1i	−0.496766	−	0.360922i
$349$	−98564.6	+	71611.4i	−0.809226	+	0.587937i	−0.913606	−	0.406600i	$-0.866714\pi$
$349$	−98564.6	+	71611.4i	−0.809226	+	0.587937i	0.104380	+	0.994538i	$0.466714\pi$
$350$	−14600.3	+	10607.7i	−0.119186	+	0.0865938i
$351$	−26448.8	+	81401.1i	−0.214680	+	0.660718i
$352$	25130.3	−	34588.9i	0.202821	−	0.279159i
$353$	−1674.73	−	544.153i	−0.0134399	−	0.00436688i	0.302289	−	0.953216i	$-0.402249\pi$
$353$	−1674.73	−	544.153i	−0.0134399	−	0.00436688i	−0.315729	+	0.948849i	$0.602249\pi$
$354$	−61768.6	+	20069.8i	−0.492902	+	0.160154i
$355$	160679.	−	116740.i	1.27498	−	0.926325i
$356$	81142.3	−	26364.7i	0.640247	−	0.208029i
$357$	7136.04	+	21962.5i	0.0559914	+	0.172324i
$358$	26644.0	+	36672.3i	0.207890	+	0.286136i
$359$	−24710.7	−	76051.6i	−0.191732	−	0.590092i	−0.999999	−	0.00127530i	$-0.999594\pi$
$359$	−24710.7	−	76051.6i	−0.191732	−	0.590092i	0.808267	−	0.588817i	$-0.200406\pi$
$360$	−2827.74	+	8702.90i	−0.0218190	+	0.0671520i
$361$	61049.3	+	44354.9i	0.468454	+	0.340352i
$362$	23867.5	+	7755.03i	0.182134	+	0.0591788i
$363$	−60457.8	−	83213.1i	−0.458817	−	0.631507i
$364$	−59095.0	−	81337.3i	−0.446013	−	0.613885i
$365$	−52112.2	+	71726.3i	−0.391159	+	0.538385i
$366$	38480.4			0.287262
$367$			197962.i			1.46977i	0.678190	+	0.734887i	$0.262765\pi$
$367$			197962.i			1.46977i	−0.678190	+	0.734887i	$0.737235\pi$
$368$	65811.5	−	90581.8i	0.485967	−	0.668876i
$369$	665.704	+	2048.83i	0.00488909	+	0.0150471i
$370$	51544.9	+	16747.9i	0.376515	+	0.122337i
$371$		−	118421.i		−	0.860360i
$372$	−51346.2	+	101780.i	−0.371041	+	0.735487i
$373$	−11227.3			−0.0806967			−0.0403483	−	0.999186i	$-0.512847\pi$
$373$	−11227.3			−0.0806967			−0.0403483	+	0.999186i	$0.512847\pi$
$374$	−873.423	+	2688.12i	−0.00624426	+	0.0192179i
$375$	135317.	−	43967.0i	0.962252	−	0.312654i
$376$	−87541.0	−	63602.3i	−0.619207	−	0.449880i
$377$	−69695.8			−0.490370
$378$		−	66183.7i		−	0.463199i
$379$	−60118.7	−	43678.8i	−0.418534	−	0.304083i	0.358514	−	0.933525i	$-0.383284\pi$
$379$	−60118.7	−	43678.8i	−0.418534	−	0.304083i	−0.777048	+	0.629442i	$0.783284\pi$
$380$	54750.9	−	39778.9i	0.379161	−	0.275477i
$381$	−127744.	+	92811.5i	−0.880016	+	0.639369i
$382$	23393.4	−	71997.3i	0.160312	−	0.493389i
$383$	−46119.3	+	63477.8i	−0.314402	+	0.432737i	−0.936748	−	0.350005i	$-0.886180\pi$
$383$	−46119.3	+	63477.8i	−0.314402	+	0.432737i	0.622346	+	0.782742i	$0.286180\pi$
$384$	−129153.	−	41964.4i	−0.875875	−	0.284589i
$385$	59815.7	−	19435.3i	0.403547	−	0.131120i
$386$	71812.6	−	52174.9i	0.481977	−	0.350177i
$387$	29891.2	−	9712.23i	0.199582	−	0.0648481i
$388$	−2735.86	−	8420.11i	−0.0181732	−	0.0559312i
$389$	57942.3	+	79750.7i	0.382910	+	0.527030i	0.956352	−	0.292216i	$-0.0943925\pi$
$389$	57942.3	+	79750.7i	0.382910	+	0.527030i	−0.573443	+	0.819246i	$0.694392\pi$
$390$	−7894.04	−	24295.4i	−0.0519003	−	0.159733i
$391$	−8707.67	+	26799.5i	−0.0569572	+	0.175296i
$392$	54804.9	+	39818.1i	0.356654	+	0.259124i
$393$	155885.	+	50650.1i	1.00930	+	0.327941i
$394$	61121.0	+	84125.8i	0.393729	+	0.541922i
$395$	94379.1	+	129902.i	0.604897	+	0.832569i
$396$	−4454.39	+	6130.95i	−0.0284052	+	0.0390964i
$397$	170179.			1.07975			0.539876	−	0.841744i	$-0.318471\pi$
$397$	170179.			1.07975			0.539876	+	0.841744i	$0.318471\pi$
$398$		−	66643.4i		−	0.420718i
$399$	−73425.2	+	101061.i	−0.461211	+	0.634802i
$400$	−11160.2	−	34347.6i	−0.0697513	−	0.214672i
$401$	124119.	+	40328.7i	0.771879	+	0.250799i	0.668369	−	0.743830i	$-0.266993\pi$
$401$	124119.	+	40328.7i	0.771879	+	0.250799i	0.103510	+	0.994628i	$0.466993\pi$
$402$		−	66873.4i		−	0.413811i
$403$	17137.2	+	105461.i	0.105519	+	0.649353i
$404$	−19369.2			−0.118672
$405$	−34911.2	+	107446.i	−0.212841	+	0.655057i
$406$	51255.4	−	16653.9i	0.310948	−	0.101033i
$407$	77278.4	+	56146.0i	0.466519	+	0.338946i
$408$	14738.3			0.0885376
$409$		−	163184.i		−	0.975511i	−0.872980	−	0.487755i	$-0.837816\pi$
$409$		−	163184.i		−	0.975511i	0.872980	−	0.487755i	$-0.162184\pi$
$410$	−4337.69	−	3151.52i	−0.0258042	−	0.0187479i
$411$	209532.	−	152234.i	1.24041	−	0.901214i
$412$	54925.9	−	39906.0i	0.323581	−	0.235095i
$413$	−113471.	+	349228.i	−0.665251	+	2.04743i
$414$	5692.52	−	7835.08i	0.0332127	−	0.0457133i
$415$	112971.	+	36706.5i	0.655950	+	0.213131i
$416$	−93376.0	+	30339.7i	−0.539571	+	0.175317i
$417$	−162376.	+	117973.i	−0.933791	+	0.678439i
$418$	−14541.2	+	4724.72i	−0.0832237	+	0.0270410i
$419$	−57804.8	−	177905.i	−0.329258	−	1.01335i	−0.969482	−	0.245163i	$-0.921159\pi$
$419$	−57804.8	−	177905.i	−0.329258	−	1.01335i	0.640224	−	0.768188i	$-0.278841\pi$
$420$	−90578.3	−	124670.i	−0.513482	−	0.706748i
$421$	75775.7	+	233214.i	0.427529	+	1.31580i	0.900551	+	0.434749i	$0.143163\pi$
$421$	75775.7	+	233214.i	0.427529	+	1.31580i	−0.473022	+	0.881051i	$0.656837\pi$
$422$	−10651.0	+	32780.4i	−0.0598089	+	0.184073i
$423$	23742.5	+	17250.0i	0.132692	+	0.0964067i
$424$	−71879.8	−	23355.2i	−0.399830	−	0.129913i
$425$	5342.50	+	7353.33i	0.0295779	+	0.0407105i
$426$	64621.3	+	88943.7i	0.356088	+	0.490112i
$427$	127880.	−	176011.i	0.701367	−	0.965349i
$428$	−131770.			−0.719329
$429$		−	45023.4i		−	0.244638i
$430$	−45978.8	+	63284.4i	−0.248669	+	0.342263i
$431$	−106712.	−	328426.i	−0.574458	−	1.76800i	−0.638017	−	0.770023i	$-0.720245\pi$
$431$	−106712.	−	328426.i	−0.574458	−	1.76800i	0.0635582	−	0.997978i	$-0.479755\pi$
$432$	125963.	+	40927.9i	0.674956	+	0.219306i
$433$			1311.51i			0.00699515i	0.999994	+	0.00349757i	$0.00111331\pi$
$433$			1311.51i			0.00699515i	−0.999994	+	0.00349757i	$0.998887\pi$
$434$	−37803.0	−	73462.6i	−0.200700	−	0.390020i
$435$	−106827.			−0.564549
$436$	−23013.4	+	70828.0i	−0.121062	+	0.372591i
$437$	−144970.	+	47103.5i	−0.759127	+	0.246655i
$438$	−39704.0	−	28846.7i	−0.206960	−	0.150365i
$439$	−263145.			−1.36542			−0.682711	−	0.730689i	$-0.739199\pi$
$439$	−263145.			−1.36542			−0.682711	+	0.730689i	$0.739199\pi$
$440$		−	40140.4i		−	0.207337i
$441$	−14864.0	−	10799.3i	−0.0764288	−	0.0555288i
$442$	5251.09	−	3815.14i	0.0268785	−	0.0195284i
$443$	−51866.9	+	37683.5i	−0.264291	+	0.192019i	−0.712037	−	0.702142i	$-0.752227\pi$
$443$	−51866.9	+	37683.5i	−0.264291	+	0.192019i	0.447745	+	0.894161i	$0.352227\pi$
$444$	72323.5	−	222589.i	0.366871	−	1.12911i
$445$	72042.2	−	99157.6i	0.363804	−	0.500733i
$446$	−1452.90	−	472.075i	−0.00730408	−	0.00237324i
$447$	272068.	−	88400.2i	1.36164	−	0.442424i
$448$	−80577.6	+	58543.1i	−0.401475	+	0.291689i
$449$	−46523.0	+	15116.3i	−0.230768	+	0.0749810i	−0.422118	−	0.906541i	$-0.638713\pi$
$449$	−46523.0	+	15116.3i	−0.230768	+	0.0749810i	0.191350	+	0.981522i	$0.438713\pi$
$450$	−965.327	−	2970.97i	−0.00476705	−	0.0146715i
$451$	−5554.45	−	7645.05i	−0.0273079	−	0.0375861i
$452$	40693.5	+	125242.i	0.199181	+	0.613016i
$453$	61508.8	−	189305.i	0.299738	−	0.922497i
$454$	4780.19	+	3473.01i	0.0231918	+	0.0168498i
$455$	−137362.	−	44631.5i	−0.663503	−	0.215585i
$456$	46861.7	+	64499.6i	0.225366	+	0.310190i
$457$	−25506.2	−	35106.3i	−0.122127	−	0.168094i	0.743576	−	0.668652i	$-0.233128\pi$
$457$	−25506.2	−	35106.3i	−0.122127	−	0.168094i	−0.865703	+	0.500558i	$0.833128\pi$
$458$	32406.6	−	44603.8i	0.154491	−	0.212638i
$459$	−33332.9			−0.158215
$460$		−	188040.i		−	0.888657i
$461$	−95882.0	+	131970.i	−0.451165	+	0.620975i	−0.972647	−	0.232287i	$-0.925379\pi$
$461$	−95882.0	+	131970.i	−0.451165	+	0.620975i	0.521483	+	0.853262i	$0.325379\pi$
$462$	10758.4	+	33110.9i	0.0504038	+	0.155127i
$463$	−98998.7	−	32166.6i	−0.461814	−	0.150053i	0.0688636	−	0.997626i	$-0.478063\pi$
$463$	−98998.7	−	32166.6i	−0.461814	−	0.150053i	−0.530678	+	0.847573i	$0.678063\pi$
$464$			107850.i			0.500937i
$465$	26267.2	+	161646.i	0.121481	+	0.747582i
$466$	−77747.8			−0.358027
$467$	24921.6	−	76700.8i	0.114273	−	0.351695i	−0.877522	−	0.479536i	$-0.840805\pi$
$467$	24921.6	−	76700.8i	0.114273	−	0.351695i	0.991795	+	0.127841i	$0.0408048\pi$
$468$	16551.1	−	5377.77i	0.0755674	−	0.0245533i
$469$	−305882.	−	222236.i	−1.39062	−	1.01034i
$470$	−73041.9			−0.330656
$471$		−	109458.i		−	0.493409i
$472$	189598.	+	137751.i	0.851039	+	0.618316i
$473$	−111537.	+	81036.2i	−0.498535	+	0.362207i
$474$	−71906.9	+	52243.4i	−0.320047	+	0.232528i
$475$	−15193.6	+	46761.0i	−0.0673399	+	0.207251i
$476$	23014.4	−	31676.6i	0.101575	−	0.139806i
$477$	19495.0	+	6334.29i	0.0856812	+	0.0278395i
$478$	34332.8	−	11155.4i	0.150263	−	0.0488236i
$479$	−69026.4	+	50150.6i	−0.300846	+	0.218577i	−0.727959	−	0.685621i	$-0.759531\pi$
$479$	−69026.4	+	50150.6i	−0.300846	+	0.218577i	0.427113	+	0.904198i	$0.359531\pi$
$480$	−143123.	+	46503.4i	−0.621193	+	0.201838i
$481$	−67784.9	−	208620.i	−0.292983	−	0.901710i
$482$	361.405	+	497.431i	0.00155561	+	0.00214111i
$483$	107257.	+	330103.i	0.459760	+	1.41499i
$484$	−53891.7	+	165862.i	−0.230055	+	0.708035i
$485$	−10289.5	−	7475.79i	−0.0437434	−	0.0317815i
$486$	20484.3	+	6655.76i	0.0867259	+	0.0281790i
$487$	201919.	+	277917.i	0.851371	+	1.17181i	0.983559	+	0.180587i	$0.0577998\pi$
$487$	201919.	+	277917.i	0.851371	+	1.17181i	−0.132188	+	0.991225i	$0.542200\pi$
$488$	−81615.7	−	112334.i	−0.342716	−	0.471708i
$489$	12794.7	−	17610.4i	0.0535072	−	0.0736463i
$490$	45727.7			0.190453
$491$		−	28221.3i		−	0.117061i	−0.998286	−	0.0585307i	$-0.981358\pi$
$491$		−	28221.3i		−	0.117061i	0.998286	−	0.0585307i	$-0.0186415\pi$
$492$	−13609.4	+	18731.7i	−0.0562222	+	0.0773832i
$493$	−8387.60	−	25814.4i	−0.0345099	−	0.106211i
$494$	33392.6	+	10849.9i	0.136835	+	0.0444603i
$495$			10886.7i			0.0444311i
$496$	163194.	−	26518.7i	0.663346	−	0.107793i
$497$	621584.			2.51644
$498$	−20318.9	+	62535.0i	−0.0819296	+	0.252153i
$499$	212870.	−	69165.6i	0.854895	−	0.277772i	0.151400	−	0.988473i	$-0.451622\pi$
$499$	212870.	−	69165.6i	0.854895	−	0.277772i	0.703495	+	0.710700i	$0.251622\pi$
$500$	−195168.	−	141798.i	−0.780671	−	0.567191i
$501$	187877.			0.748510
$502$			14122.5i			0.0560406i
$503$	−174250.	−	126600.i	−0.688711	−	0.500378i	0.187525	−	0.982260i	$-0.439953\pi$
$503$	−174250.	−	126600.i	−0.688711	−	0.500378i	−0.876236	+	0.481882i	$0.839953\pi$
$504$	−23169.3	+	16833.5i	−0.0912122	+	0.0662695i
$505$	−22511.0	+	16355.2i	−0.0882699	+	0.0641319i
$506$	−13127.8	+	40403.2i	−0.0512733	+	0.157803i
$507$	79646.6	−	109624.i	0.309850	−	0.426472i
$508$	254621.	+	82731.5i	0.986660	+	0.320585i
$509$	59234.0	−	19246.3i	0.228631	−	0.0742868i	−0.192461	−	0.981305i	$-0.561647\pi$
$509$	59234.0	−	19246.3i	0.228631	−	0.0742868i	0.421092	+	0.907018i	$0.361647\pi$
$510$	8048.66	−	5847.69i	0.0309445	−	0.0224825i
$511$	−263892.	+	85743.6i	−1.01061	+	0.328367i
$512$	81565.0	+	251031.i	0.311146	+	0.957608i
$513$	−105985.	−	145875.i	−0.402724	−	0.554303i
$514$	−50147.0	−	154337.i	−0.189810	−	0.584175i
$515$	30139.0	−	92758.4i	0.113636	−	0.349735i
$516$	273284.	+	198553.i	1.02640	+	0.745721i
$517$	−122433.	−	39781.0i	−0.458056	−	0.148831i
$518$	99700.2	+	137226.i	0.371566	+	0.511417i
$519$	186781.	+	257082.i	0.693422	+	0.954413i
$520$	−54181.4	+	74574.4i	−0.200375	+	0.275793i
$521$	−304010.			−1.11999			−0.559993	−	0.828497i	$-0.689196\pi$
$521$	−304010.			−1.11999			−0.559993	+	0.828497i	$0.689196\pi$
$522$			9328.71i			0.0342358i
$523$	277267.	−	381625.i	1.01367	−	1.39519i	0.0971138	−	0.995273i	$-0.469039\pi$
$523$	277267.	−	381625.i	1.01367	−	1.39519i	0.916551	−	0.399917i	$-0.130961\pi$
$524$	−85878.8	−	264308.i	−0.312769	−	0.962604i
$525$	106477.	+	34596.5i	0.386311	+	0.125520i
$526$			7198.99i			0.0260196i
$527$	−36998.9	+	19039.2i	−0.133219	+	0.0685530i
$528$	−69670.8			−0.249910
$529$	−44403.2	+	136659.i	−0.158673	+	0.488345i
$530$	−48520.4	+	15765.2i	−0.172732	+	0.0561241i
$531$	−51422.0	−	37360.3i	−0.182373	−	0.132502i
$532$	211803.			0.748357
$533$			21700.6i			0.0763868i
$534$	54888.6	+	39878.9i	0.192486	+	0.139849i
$535$	−153144.	+	111266.i	−0.535048	+	0.388735i
$536$	−195221.	+	141836.i	−0.679511	+	0.493694i
$537$	86897.7	−	267444.i	0.301342	−	0.927436i
$538$	30046.4	−	41355.3i	0.103807	−	0.142878i
$539$	76649.1	+	24904.8i	0.263833	+	0.0857246i
$540$	211548.	−	68736.2i	0.725474	−	0.235721i
$541$	−63773.8	+	46334.4i	−0.217895	+	0.158310i	−0.691379	−	0.722493i	$-0.742996\pi$
$541$	−63773.8	+	46334.4i	−0.217895	+	0.158310i	0.473483	+	0.880803i	$0.342996\pi$
$542$	−98952.8	+	32151.7i	−0.336845	+	0.109447i
$543$	−48109.2	−	148065.i	−0.163166	−	0.502172i
$544$	−22474.8	−	30934.0i	−0.0759449	−	0.104529i
$545$	33060.4	+	101750.i	0.111305	+	0.342562i
$546$	24705.7	−	76036.4i	0.0828729	−	0.255056i
$547$	−254868.	−	185173.i	−0.851807	−	0.618874i	0.0738364	−	0.997270i	$-0.476476\pi$
$547$	−254868.	−	185173.i	−0.851807	−	0.618874i	−0.925644	+	0.378396i	$0.876476\pi$
$548$	−417642.	−	135700.i	−1.39073	−	0.451876i
$549$	22135.5	+	30466.9i	0.0734420	+	0.101084i
$550$	8054.43	+	11086.0i	0.0266262	+	0.0366479i
$551$	86302.9	−	118786.i	0.284264	−	0.391256i
$552$	221521.			0.727005
$553$			502522.i			1.64326i
$554$	−40912.1	+	56310.6i	−0.133301	+	0.183472i
$555$	−103898.	−	319765.i	−0.337303	−	1.03811i
$556$	323650.	+	105160.i	1.04695	+	0.340175i
$557$			264207.i			0.851597i	0.904818	+	0.425798i	$0.140007\pi$
$557$			264207.i			0.851597i	−0.904818	+	0.425798i	$0.859993\pi$
$558$	14115.8	−	2293.80i	0.0453354	−	0.00736693i
$559$	316600.			1.01318
$560$	−69064.4	+	212558.i	−0.220231	+	0.677801i
$561$	16676.1	−	5418.38i	0.0529868	−	0.0172165i
$562$	13735.3	+	9979.27i	0.0434876	+	0.0315956i
$563$	−256502.			−0.809234			−0.404617	−	0.914486i	$-0.632595\pi$
$563$	−256502.			−0.809234			−0.404617	+	0.914486i	$0.632595\pi$
$564$			315420.i			0.991589i
$565$	153048.	+	111196.i	0.479436	+	0.348331i
$566$	95148.7	−	69129.6i	0.297009	−	0.215790i
$567$	−286048.	+	207826.i	−0.889759	+	0.646448i
$568$	122590.	−	377293.i	0.379978	−	1.16945i
$569$	264078.	−	363472.i	0.815657	−	1.12266i	−0.174769	−	0.984610i	$-0.555918\pi$
$569$	264078.	−	363472.i	0.815657	−	1.12266i	0.990426	−	0.138046i	$-0.0440823\pi$
$570$	51182.7	+	16630.3i	0.157534	+	0.0511858i
$571$	−168954.	+	54896.4i	−0.518198	+	0.168373i	−0.556427	−	0.830896i	$-0.687828\pi$
$571$	−168954.	+	54896.4i	−0.518198	+	0.168373i	0.0382294	+	0.999269i	$0.487828\pi$
$572$	−61759.2	+	44870.7i	−0.188760	+	0.137142i
$573$	−446644.	+	145123.i	−1.36036	+	0.442006i
$574$	−5185.39	−	15959.0i	−0.0157383	−	0.0484375i
$575$	80299.4	+	110523.i	0.242872	+	0.334284i
$576$	−5327.54	−	16396.5i	−0.0160577	−	0.0494204i
$577$	154018.	−	474017.i	0.462614	−	1.42378i	−0.399345	−	0.916801i	$-0.630763\pi$
$577$	154018.	−	474017.i	0.462614	−	1.42378i	0.861959	−	0.506978i	$-0.169237\pi$
$578$	−89060.0	−	64705.9i	−0.266580	−	0.193681i
$579$	−523715.	−	170165.i	−1.56220	−	0.507591i
$580$	106464.	+	146536.i	0.316482	+	0.435599i
$581$	218513.	+	300758.i	0.647330	+	0.890973i
$582$	4138.22	−	5695.77i	0.0122171	−	0.0168154i
$583$	−89916.6			−0.264547
$584$			177089.i			0.519238i
$585$	14694.9	−	20225.8i	0.0429392	−	0.0591008i
$586$	−56092.7	−	172636.i	−0.163347	−	0.502730i
$587$	−309805.	−	100662.i	−0.899108	−	0.292138i	−0.177239	−	0.984168i	$-0.556717\pi$
$587$	−309805.	−	100662.i	−0.899108	−	0.292138i	−0.721869	+	0.692030i	$0.756717\pi$
$588$		−	197468.i		−	0.571140i
$589$	−200962.	−	101382.i	−0.579274	−	0.292234i
$590$	158195.			0.454454
$591$	199342.	−	613512.i	0.570721	−	1.75650i
$592$	−322827.	+	104893.i	−0.921141	+	0.299297i
$593$	240298.	+	174587.i	0.683346	+	0.496480i	0.874466	−	0.485087i	$-0.161212\pi$
$593$	240298.	+	174587.i	0.683346	+	0.496480i	−0.191120	+	0.981567i	$0.561212\pi$
$594$	−50253.1			−0.142426
$595$		−	56248.1i		−	0.158882i
$596$	−392405.	−	285099.i	−1.10469	−	0.802606i
$597$	−334472.	+	243008.i	−0.938450	+	0.681824i
$598$	78925.5	−	57342.7i	0.220706	−	0.160353i
$599$	64534.9	−	198618.i	0.179863	−	0.553560i	−0.819960	−	0.572422i	$-0.806004\pi$
$599$	64534.9	−	198618.i	0.179863	−	0.553560i	0.999822	+	0.0188614i	$0.00600411\pi$
$600$	41999.2	−	57806.9i	0.116664	−	0.160575i
$601$	−147605.	−	47959.8i	−0.408650	−	0.132779i	0.0974760	−	0.995238i	$-0.468923\pi$
$601$	−147605.	−	47959.8i	−0.408650	−	0.132779i	−0.506126	+	0.862459i	$0.668923\pi$
$602$	−232833.	+	75651.9i	−0.642467	+	0.208750i
$603$	52947.0	−	38468.3i	0.145615	−	0.105796i
$604$	−320972.	+	104290.i	−0.879819	+	0.285870i
$605$	77419.3	+	238272.i	0.211514	+	0.650972i
$606$	−9053.42	−	12461.0i	−0.0246529	−	0.0339318i
$607$	125971.	+	387700.i	0.341896	+	1.05225i	0.963224	+	0.268698i	$0.0865934\pi$
$607$	125971.	+	387700.i	0.341896	+	1.05225i	−0.621328	+	0.783550i	$0.713407\pi$
$608$	63916.3	−	196714.i	0.172904	−	0.532143i
$609$	−270481.	−	196516.i	−0.729292	−	0.529862i
$610$	−89141.4	−	28963.8i	−0.239563	−	0.0778387i
$611$	173765.	+	239167.i	0.465457	+	0.640647i
$612$	3983.71	+	5483.10i	0.0106362	+	0.0146394i
$613$	174764.	−	240542.i	0.465084	−	0.640133i	−0.510470	−	0.859896i	$-0.670528\pi$
$613$	174764.	−	240542.i	0.465084	−	0.640133i	0.975553	+	0.219763i	$0.0705284\pi$
$614$	139767.			0.370738
$615$			33261.8i			0.0879420i
$616$	73841.2	−	101634.i	0.194598	−	0.267841i
$617$	−63672.2	−	195963.i	−0.167255	−	0.514758i	0.831940	−	0.554865i	$-0.187230\pi$
$617$	−63672.2	−	195963.i	−0.167255	−	0.514758i	−0.999195	+	0.0401069i	$0.987230\pi$
$618$	51346.3	+	16683.4i	0.134441	+	0.0436826i
$619$			727184.i			1.89786i	0.315493	+	0.948928i	$0.397830\pi$
$619$			727184.i			1.89786i	−0.315493	+	0.948928i	$0.602170\pi$
$620$	195554.	−	197129.i	0.508724	−	0.512822i
$621$	−501003.			−1.29914
$622$	−39603.6	+	121887.i	−0.102366	+	0.315049i
$623$	364815.	−	118536.i	0.939933	−	0.305403i
$624$	129437.	+	94041.6i	0.332422	+	0.241519i
$625$	−215360.			−0.551323
$626$			170411.i			0.434860i
$627$	76735.5	+	55751.6i	0.195192	+	0.141815i
$628$	−150145.	+	109087.i	−0.380708	+	0.276601i
$629$	69112.6	−	50213.2i	0.174685	−	0.126916i
$630$	−5973.88	+	18385.7i	−0.0150513	+	0.0463233i
$631$	257508.	−	354429.i	0.646743	−	0.890166i	−0.352209	−	0.935921i	$-0.614569\pi$
$631$	257508.	−	354429.i	0.646743	−	0.890166i	0.998953	+	0.0457554i	$0.0145695\pi$
$632$	305024.	+	99108.4i	0.763660	+	0.248128i
$633$	203357.	−	66074.8i	0.507519	−	0.164903i
$634$	−72153.7	+	52422.8i	−0.179507	+	0.130419i
$635$	365782.	−	118850.i	0.907141	−	0.294748i
$636$	68079.9	+	209528.i	0.168308	+	0.517998i
$637$	−108785.	−	149730.i	−0.268096	−	0.369003i
$638$	−12645.3	−	38918.1i	−0.0310661	−	0.0956115i
$639$	−33248.3	+	102328.i	−0.0814270	+	0.250606i
$640$	267602.	+	194424.i	0.653324	+	0.474668i
$641$	559704.	+	181859.i	1.36220	+	0.442607i	0.896779	−	0.442480i	$-0.145901\pi$
$641$	559704.	+	181859.i	1.36220	+	0.442607i	0.465426	+	0.885087i	$0.345901\pi$
$642$	−61591.0	−	84772.8i	−0.149433	−	0.205677i
$643$	198899.	+	273761.i	0.481073	+	0.662140i	0.978711	−	0.205245i	$-0.0657992\pi$
$643$	198899.	+	273761.i	0.481073	+	0.662140i	−0.497638	+	0.867385i	$0.665799\pi$
$644$	345913.	−	476108.i	0.834056	−	1.14798i
$645$	485271.			1.16645
$646$			13673.9i			0.0327663i
$647$	413590.	−	569258.i	0.988011	−	1.35988i	0.0556116	−	0.998452i	$-0.482289\pi$
$647$	413590.	−	569258.i	0.988011	−	1.35988i	0.932400	−	0.361429i	$-0.117711\pi$
$648$	69732.6	+	214615.i	0.166068	+	0.511105i
$649$	265168.	+	86158.4i	0.629553	+	0.204554i
$650$		−	31467.8i		−	0.0744800i
$651$	−230852.	+	457601.i	−0.544718	+	1.07975i
$652$	−36907.7			−0.0868204
$653$	−179369.	+	552041.i	−0.420650	+	1.29463i	0.486448	+	0.873709i	$0.338292\pi$
$653$	−179369.	+	552041.i	−0.420650	+	1.29463i	−0.907098	+	0.420919i	$0.861708\pi$
$654$	−56323.4	+	18300.6i	−0.131684	+	0.0427867i
$655$	−322990.	−	234666.i	−0.752846	−	0.546975i
$656$	33580.4			0.0780329
$657$		−	48029.4i		−	0.111270i
$658$	−184939.	−	134366.i	−0.427146	−	0.310339i
$659$	−8773.73	+	6374.49i	−0.0202029	+	0.0146783i	−0.597841	−	0.801615i	$-0.703975\pi$
$659$	−8773.73	+	6374.49i	−0.0202029	+	0.0146783i	0.577638	+	0.816293i	$0.303975\pi$
$660$	−94661.9	+	68775.9i	−0.217314	+	0.157888i
$661$	−263748.	+	811733.i	−0.603651	+	1.85785i	−0.0978423	+	0.995202i	$0.531194\pi$
$661$	−263748.	+	811733.i	−0.603651	+	1.85785i	−0.505809	+	0.862646i	$0.668806\pi$
$662$	1262.86	−	1738.18i	0.00288165	−	0.00396625i
$663$	−38295.1	−	12442.8i	−0.0871197	−	0.0283069i
$664$	225651.	−	73318.6i	0.511802	−	0.166295i
$665$	246160.	−	178845.i	0.556639	−	0.404422i
$666$	−27923.6	+	9072.93i	−0.0629540	+	0.0204550i
$667$	−126068.	−	387998.i	−0.283370	−	0.872123i
$668$	−187239.	−	257713.i	−0.419608	−	0.577541i
$669$	2928.58	+	9013.23i	0.00654341	+	0.0201386i
$670$	−50334.9	+	154915.i	−0.112129	+	0.345099i
$671$	−133645.	−	97098.6i	−0.296829	−	0.215659i
$672$	−447927.	−	145540.i	−0.991902	−	0.322288i
$673$	89313.0	+	122929.i	0.197190	+	0.271409i	0.896149	−	0.443753i	$-0.146353\pi$
$673$	89313.0	+	122929.i	0.197190	+	0.271409i	−0.698959	+	0.715161i	$0.746353\pi$
$674$	−69576.3	−	95763.5i	−0.153159	−	0.210805i
$675$	−94987.3	+	130739.i	−0.208477	+	0.286944i
$676$	−229749.			−0.502760
$677$			324964.i			0.709020i	0.935052	+	0.354510i	$0.115352\pi$
$677$			324964.i			0.709020i	−0.935052	+	0.354510i	$0.884648\pi$
$678$	−61552.3	+	84719.5i	−0.133901	+	0.184300i
$679$	−12300.4	−	37856.7i	−0.0266796	−	0.0821115i
$680$	−34141.8	−	11093.4i	−0.0738362	−	0.0239908i
$681$		−	36655.0i		−	0.0790385i
$682$	−55780.0	+	28703.7i	−0.119925	+	0.0617119i
$683$	482539.			1.03441			0.517203	−	0.855863i	$-0.326973\pi$
$683$	482539.			1.03441			0.517203	+	0.855863i	$0.326973\pi$
$684$	−11329.3	+	34867.9i	−0.0242153	+	0.0745271i
$685$	−599973.	+	194943.i	−1.27865	+	0.415458i
$686$	−51214.7	−	37209.7i	−0.108829	−	0.0790692i
$687$	−342026.			−0.724680
$688$		−	489918.i		−	1.03501i
$689$	167050.	+	121369.i	0.351892	+	0.255664i
$690$	120974.	−	87892.5i	0.254093	−	0.184609i
$691$	−309330.	+	224741.i	−0.647837	+	0.470681i	−0.862534	−	0.505999i	$-0.831124\pi$
$691$	−309330.	+	224741.i	−0.647837	+	0.470681i	0.214696	+	0.976681i	$0.431124\pi$
$692$	166495.	−	512419.i	0.347688	−	1.07007i
$693$	−20026.9	+	27564.7i	−0.0417011	+	0.0573967i
$694$	144216.	+	46858.7i	0.299430	+	0.0972906i
$695$	464947.	−	151070.i	0.962572	−	0.312759i
$696$	−172627.	+	125421.i	−0.356361	+	0.258912i
$697$	−8037.63	+	2611.58i	−0.0165448	+	0.00537574i
$698$	50761.5	+	156228.i	0.104189	+	0.320662i
$699$	283499.	+	390203.i	0.580226	+	0.798613i
$700$	−58659.3	−	180535.i	−0.119713	−	0.368439i
$701$	167316.	−	514947.i	0.340488	−	1.04792i	−0.623466	−	0.781850i	$-0.714276\pi$
$701$	167316.	−	514947.i	0.340488	−	1.04792i	0.963955	−	0.266066i	$-0.0857238\pi$
$702$	93362.1	+	67831.5i	0.189451	+	0.137644i
$703$	439498.	+	142802.i	0.889296	+	0.288950i
$704$	44451.6	+	61182.4i	0.0896896	+	0.123447i
$705$	266340.	+	366585.i	0.535868	+	0.737558i
$706$	−1395.55	+	1920.81i	−0.00279986	+	0.00385368i
$707$	−87083.6			−0.174220
$708$		−	683143.i		−	1.36284i
$709$	195029.	−	268435.i	0.387979	−	0.534007i	−0.569698	−	0.821854i	$-0.692940\pi$
$709$	195029.	−	268435.i	0.387979	−	0.534007i	0.957676	+	0.287848i	$0.0929397\pi$
$710$	−82750.8	−	254681.i	−0.164156	−	0.505219i
$711$	−82727.5	−	26879.8i	−0.163648	−	0.0531724i
$712$		−	244816.i		−	0.482925i
$713$	−556104.	+	286164.i	−1.09390	+	0.562907i
$714$	31136.1			0.0610756
$715$	−33888.6	+	104298.i	−0.0662890	+	0.204017i
$716$	−453459.	+	147338.i	−0.884528	+	0.287401i
$717$	−181178.	−	131634.i	−0.352426	−	0.256052i
$718$	−107818.			−0.209142
$719$			784447.i			1.51742i	0.651428	+	0.758710i	$0.274170\pi$
$719$			784447.i			1.51742i	−0.651428	+	0.758710i	$0.725830\pi$
$720$	−31298.1	−	22739.4i	−0.0603744	−	0.0438645i
$721$	246947.	−	179417.i	0.475042	−	0.345139i
$722$	82313.3	−	59804.1i	0.157905	−	0.114725i
$723$	1178.70	−	3627.66i	0.00225489	−	0.00693985i
$724$	−155157.	+	213555.i	−0.296001	+	0.407410i
$725$	−125151.	−	40664.2i	−0.238100	−	0.0773635i
$726$	−131895.	+	42855.4i	−0.250239	+	0.0813077i
$727$	247513.	−	179829.i	0.468305	−	0.340244i	−0.328475	−	0.944513i	$-0.606535\pi$
$727$	247513.	−	179829.i	0.468305	−	0.340244i	0.796780	+	0.604269i	$0.206535\pi$
$728$	−274370.	+	89148.2i	−0.517695	+	0.168209i
$729$	−180088.	−	554253.i	−0.338867	−	1.04293i
$730$	70263.3	+	96709.1i	0.131851	+	0.181477i
$731$	38101.5	+	117264.i	0.0713029	+	0.219448i
$732$	−125076.	+	384944.i	−0.233427	+	0.718414i
$733$	−15661.4	−	11378.7i	−0.0291490	−	0.0211780i	0.573115	−	0.819475i	$-0.305735\pi$
$733$	−15661.4	−	11378.7i	−0.0291490	−	0.0211780i	−0.602264	+	0.798297i	$0.705735\pi$
$734$	253850.	+	82481.0i	0.471179	+	0.153095i
$735$	−166741.	−	229500.i	−0.308651	−	0.424822i
$736$	−337803.	−	464947.i	−0.623603	−	0.858316i
$737$	−168743.	+	232255.i	−0.310665	+	0.427593i
$738$	2904.61			0.00533304
$739$		−	597226.i		−	1.09358i	−0.837270	−	0.546789i	$-0.815850\pi$
$739$		−	597226.i		−	1.09358i	0.837270	−	0.546789i	$-0.184150\pi$
$740$	−335080.	+	461198.i	−0.611906	+	0.842217i
$741$	−67308.7	−	207155.i	−0.122584	−	0.377275i
$742$	−151853.	−	49340.0i	−0.275813	−	0.0896172i
$743$		−	672799.i		−	1.21873i	−0.792890	−	0.609365i	$-0.791424\pi$
$743$		−	672799.i		−	1.21873i	0.792890	−	0.609365i	$-0.208576\pi$
$744$	232228.	+	230373.i	0.419536	+	0.416184i
$745$	−696793.			−1.25543
$746$	−4677.83	+	14396.9i	−0.00840557	+	0.0258697i
$747$	−61200.3	+	19885.2i	−0.109676	+	0.0356359i
$748$	−24052.0	−	17474.8i	−0.0429880	−	0.0312326i
$749$	−592435.			−1.05603
$750$		−	191838.i		−	0.341045i
$751$	−276810.	−	201115.i	−0.490798	−	0.356585i	0.314693	−	0.949193i	$-0.398098\pi$
$751$	−276810.	−	201115.i	−0.490798	−	0.356585i	−0.805491	+	0.592608i	$0.798098\pi$
$752$	370095.	−	268890.i	0.654452	−	0.475487i
$753$	70878.3	−	51496.1i	0.125004	−	0.0908205i
$754$	−29038.7	+	89372.1i	−0.0510781	+	0.157202i
$755$	−284975.	+	392234.i	−0.499934	+	0.688100i
$756$	662076.	+	215121.i	1.15841	+	0.376392i
$757$	374271.	−	121608.i	0.653123	−	0.212212i	0.0363321	−	0.999340i	$-0.488433\pi$
$757$	374271.	−	121608.i	0.653123	−	0.212212i	0.616790	+	0.787127i	$0.288433\pi$
$758$	−81058.5	+	58892.4i	−0.141078	+	0.102499i
$759$	250646.	−	81439.9i	0.435088	−	0.141369i
$760$	−60008.7	−	184688.i	−0.103893	−	0.319750i
$761$	−238121.	−	327746.i	−0.411177	−	0.565937i	0.552328	−	0.833627i	$-0.313740\pi$
$761$	−238121.	−	327746.i	−0.411177	−	0.565937i	−0.963505	+	0.267690i	$0.913740\pi$
$762$	65789.1	+	202478.i	0.113304	+	0.348713i
$763$	−103468.	+	318442.i	−0.177729	+	0.546993i
$764$	644197.	+	468036.i	1.10365	+	0.801849i
$765$	9259.82	+	3008.70i	0.0158227	+	0.00514109i
$766$	62183.0	+	85587.6i	0.105978	+	0.145866i
$767$	−376343.	−	517992.i	−0.639725	−	0.880506i
$768$	15252.0	−	20992.6i	0.0258586	−	0.0355914i
$769$	455348.			0.770001			0.385000	−	0.922916i	$-0.374201\pi$
$769$	455348.			0.770001			0.385000	+	0.922916i	$0.374201\pi$
$770$		−	84800.4i		−	0.143027i
$771$	−591734.	+	814452.i	−0.995446	+	1.37011i
$772$	288520.	+	887974.i	0.484107	+	1.48993i
$773$	756672.	+	245858.i	1.26634	+	0.411457i	0.863748	−	0.503924i	$-0.168111\pi$
$773$	756672.	+	245858.i	1.26634	+	0.411457i	0.402587	+	0.915382i	$0.368111\pi$
$774$		−	42376.5i		−	0.0707365i
$775$	−30758.4	+	199373.i	−0.0512106	+	0.331942i
$776$	−25404.4			−0.0421877
$777$	325166.	−	1.00076e6i	0.538596	−	1.65763i
$778$	126407.	−	41072.2i	0.208840	−	0.0678561i
$779$	−36985.4	−	26871.5i	−0.0609475	−	0.0442809i
$780$	268700.			0.441650
$781$		−	471967.i		−	0.773766i
$782$	30737.3	+	22332.0i	0.0502635	+	0.0365186i
$783$	390422.	−	283658.i	0.636810	−	0.462670i
$784$	−231697.	+	168338.i	−0.376954	+	0.273873i
$785$	−82388.0	+	253564.i	−0.133698	+	0.411480i
$786$	129899.	−	178791.i	0.210262	−	0.289401i
$787$	−617568.	−	200660.i	−0.997093	−	0.323975i	−0.235390	−	0.971901i	$-0.575637\pi$
$787$	−617568.	−	200660.i	−0.997093	−	0.323975i	−0.761703	+	0.647926i	$0.775637\pi$
$788$	−1.04023e6	+	337991.i	−1.67524	+	0.544317i
$789$	36130.5	−	26250.4i	0.0580391	−	0.0421679i
$790$	205898.	−	66900.3i	0.329912	−	0.107195i
$791$	182958.	+	563086.i	0.292414	+	0.899956i
$792$	12781.6	+	17592.4i	0.0203768	+	0.0280463i
$793$	117227.	+	360787.i	0.186415	+	0.573726i
$794$	70904.9	−	218223.i	0.112470	−	0.346146i
$795$	256048.	+	186030.i	0.405123	+	0.294339i
$796$	666675.	+	216616.i	1.05218	+	0.341872i
$797$	25085.0	+	34526.6i	0.0394910	+	0.0543547i	0.828306	−	0.560276i	$-0.189305\pi$
$797$	25085.0	+	34526.6i	0.0394910	+	0.0543547i	−0.788815	+	0.614631i	$0.789305\pi$
$798$	98999.7	+	136261.i	0.155463	+	0.213977i
$799$	−67672.3	+	93142.9i	−0.106003	+	0.145900i
$800$	−185375.			−0.289649
$801$			66398.0i			0.103488i
$802$	103428.	−	142357.i	0.160802	−	0.221324i
$803$	65104.9	+	200372.i	0.100968	+	0.310747i
$804$	668976.	+	217364.i	1.03490	+	0.336260i
$805$		−	845426.i		−	1.30462i
$806$	142374.	+	21964.9i	0.219160	+	0.0338111i
$807$	−317116.			−0.486935
$808$	−17174.8	+	52858.6i	−0.0263068	+	0.0809641i
$809$	496159.	−	161212.i	0.758095	−	0.246320i	0.0956344	−	0.995417i	$-0.469512\pi$
$809$	496159.	−	161212.i	0.758095	−	0.246320i	0.662461	+	0.749096i	$0.269512\pi$
$810$	123234.	+	89534.5i	0.187827	+	0.136465i
$811$	191861.			0.291705			0.145853	−	0.989306i	$-0.453407\pi$
$811$	191861.			0.291705			0.145853	+	0.989306i	$0.453407\pi$
$812$			566871.i			0.859750i
$813$	522185.	+	379390.i	0.790030	+	0.573990i
$814$	104195.	−	75702.1i	0.157253	−	0.114251i
$815$	−42894.5	+	31164.7i	−0.0645783	+	0.0469189i
$816$	−19254.5	+	59259.3i	−0.0289169	+	0.0889971i
$817$	−392039.	+	539596.i	−0.587334	+	0.808396i
$818$	−209254.	−	67990.8i	−0.312728	−	0.101612i
$819$	74413.5	−	24178.4i	0.110939	−	0.0360463i
$820$	45625.7	−	33149.0i	0.0678550	−	0.0492995i
$821$	1.16130e6	−	377330.i	1.72289	−	0.559802i	0.730501	−	0.682911i	$-0.239286\pi$
$821$	1.16130e6	−	377330.i	1.72289	−	0.559802i	0.992393	+	0.123109i	$0.0392864\pi$
$822$	−107911.	−	332115.i	−0.159706	−	0.491524i
$823$	394079.	+	542403.i	0.581814	+	0.800798i	0.993893	−	0.110350i	$-0.0351973\pi$
$823$	394079.	+	542403.i	0.581814	+	0.800798i	−0.412079	+	0.911148i	$0.635197\pi$
$824$	−60200.5	−	185278.i	−0.0886637	−	0.272879i
$825$	26269.0	−	80847.7i	0.0385954	−	0.118785i
$826$	400544.	+	291012.i	0.587070	+	0.426531i
$827$	−430694.	−	139941.i	−0.629736	−	0.204614i	−0.0232777	−	0.999729i	$-0.507410\pi$
$827$	−430694.	−	139941.i	−0.629736	−	0.204614i	−0.606458	+	0.795116i	$0.707410\pi$
$828$	59876.3	+	82412.7i	0.0873362	+	0.120208i
$829$	−293669.	−	404201.i	−0.427317	−	0.588151i	0.540018	−	0.841653i	$-0.318417\pi$
$829$	−293669.	−	404201.i	−0.427317	−	0.588151i	−0.967335	+	0.253503i	$0.918417\pi$
$830$	94138.7	−	129571.i	0.136651	−	0.188084i
$831$	431795.			0.625282
$832$		−	173668.i		−	0.250884i
$833$	42366.1	−	58311.9i	0.0610560	−	0.0840363i
$834$	83624.8	+	257371.i	0.120227	+	0.370022i
$835$	−435223.	−	141413.i	−0.624222	−	0.202822i
$836$		−	160821.i		−	0.230108i
$837$	−525218.	−	521022.i	−0.749703	−	0.743713i
$838$	−252215.			−0.359156
$839$	−218115.	+	671288.i	−0.309857	+	0.953641i	0.667963	+	0.744194i	$0.267166\pi$
$839$	−218115.	+	671288.i	−0.309857	+	0.953641i	−0.977820	+	0.209447i	$0.932834\pi$
$840$	−420543.	+	136643.i	−0.596007	+	0.193655i
$841$	−254283.	−	184748.i	−0.359523	−	0.261208i
$842$	330626.			0.466351
$843$		−	105323.i		−	0.148207i
$844$	−293303.	−	213097.i	−0.411748	−	0.299152i
$845$	−267017.	+	193999.i	−0.373960	+	0.271698i
$846$	32012.2	−	23258.2i	0.0447276	−	0.0324965i
$847$	−242297.	+	745712.i	−0.337738	+	1.03945i
$848$	187811.	−	258500.i	0.261174	−	0.359475i
$849$	−693900.	−	225462.i	−0.962679	−	0.312793i
$850$	11655.2	−	3787.02i	0.0161318	−	0.00524155i
$851$	1.03878e6	−	754720.i	1.43438	−	1.04214i
$852$	−1.09980e6	+	357347.i	−1.51508	+	0.492279i
$853$	27227.0	+	83796.2i	0.0374199	+	0.115167i	0.968022	−	0.250867i	$-0.0807156\pi$
$853$	27227.0	+	83796.2i	0.0374199	+	0.115167i	−0.930602	+	0.366033i	$0.880716\pi$
$854$	−172421.	−	237317.i	−0.236415	−	0.325397i
$855$	16275.3	+	50090.3i	0.0222637	+	0.0685206i
$856$	−116841.	+	359600.i	−0.159459	+	0.490764i
$857$	−526905.	−	382819.i	−0.717416	−	0.521233i	0.168142	−	0.985763i	$-0.446223\pi$
$857$	−526905.	−	382819.i	−0.717416	−	0.521233i	−0.885558	+	0.464530i	$0.846223\pi$
$858$	−57734.3	−	18759.0i	−0.0784258	−	0.0254821i
$859$	−286901.	−	394886.i	−0.388818	−	0.535162i	0.569076	−	0.822285i	$-0.307301\pi$
$859$	−286901.	−	394886.i	−0.388818	−	0.535162i	−0.957894	+	0.287123i	$0.907301\pi$
$860$	−483625.	−	665652.i	−0.653900	−	0.900017i
$861$	−61187.6	+	84217.5i	−0.0825386	+	0.113605i
$862$	−465607.			−0.626621
$863$			276759.i			0.371604i	0.982587	+	0.185802i	$0.0594882\pi$
$863$			276759.i			0.371604i	−0.982587	+	0.185802i	$0.940512\pi$
$864$	399592.	−	549992.i	0.535291	−	0.736765i
$865$	−239182.	−	736127.i	−0.319666	−	0.983831i
$866$	1681.77	+	546.442i	0.00224250	+	0.000728632i
$867$			682920.i			0.908515i
$868$	857765.	−	139385.i	1.13849	−	0.185003i
$869$	381564.			0.505275
$870$	−44509.4	+	136986.i	−0.0588048	+	0.180983i
$871$	626995.	−	203723.i	0.826472	−	0.268537i
$872$	172884.	+	125608.i	0.227364	+	0.165190i
$873$	6890.09			0.00904058
$874$			205523.i			0.269052i
$875$	−877473.	−	637521.i	−1.14609	−	0.832681i
$876$	417624.	−	303422.i	0.544223	−	0.395401i
$877$	500861.	−	363897.i	0.651206	−	0.473129i	−0.212476	−	0.977166i	$-0.568153\pi$
$877$	500861.	−	363897.i	0.651206	−	0.473129i	0.863682	+	0.504038i	$0.168153\pi$
$878$	−109639.	+	337436.i	−0.142226	+	0.437726i
$879$	−661893.	+	911018.i	−0.856663	+	1.17910i
$880$	161395.	+	52440.4i	0.208413	+	0.0677175i
$881$	−472239.	+	153440.i	−0.608429	+	0.197691i	−0.596996	−	0.802244i	$-0.703639\pi$
$881$	−472239.	+	153440.i	−0.608429	+	0.197691i	−0.0114330	+	0.999935i	$0.503639\pi$
$882$	−20041.2	+	14560.8i	−0.0257624	+	0.0187175i
$883$	−135000.	+	43864.2i	−0.173146	+	0.0562585i	−0.394307	−	0.918979i	$-0.629015\pi$
$883$	−135000.	+	43864.2i	−0.173146	+	0.0562585i	0.221161	+	0.975237i	$0.429015\pi$
$884$	21097.2	+	64930.6i	0.0269973	+	0.0830892i
$885$	−576843.	−	793956.i	−0.736497	−	1.01370i
$886$	26711.8	+	82210.6i	0.0340280	+	0.104727i
$887$	11981.4	−	36874.9i	0.0152286	−	0.0468688i	−0.943153	−	0.332358i	$-0.892156\pi$
$887$	11981.4	−	36874.9i	0.0152286	−	0.0468688i	0.958382	+	0.285489i	$0.0921559\pi$
$888$	−543317.	−	394743.i	−0.689012	−	0.500597i
$889$	1.14478e6	+	371960.i	1.44849	+	0.470644i
$890$	−97135.0	−	133695.i	−0.122630	−	0.168785i
$891$	157802.	+	217195.i	0.198772	+	0.273587i
$892$	9444.92	−	12999.8i	0.0118705	−	0.0163383i
$893$	−622793.			−0.780981
$894$		−	385709.i		−	0.482597i
$895$	−402603.	+	554136.i	−0.502610	+	0.691784i
$896$	319898.	+	984545.i	0.398470	+	1.22636i
$897$	−575587.	−	187020.i	−0.715363	−	0.232435i
$898$			65955.5i			0.0817896i
$899$	271340.	−	537857.i	0.335733	−	0.665499i
$900$	32858.1			0.0405656
$901$	−24849.7	+	76479.5i	−0.0306106	+	0.0942097i
$902$	−12117.6	+	3937.26i	−0.0148938	+	0.00483928i
$903$	1.22868e6	+	892691.i	1.50683	+	1.09478i
$904$	377869.			0.462385
$905$			379209.i			0.463001i
$906$	−217121.	−	157748.i	−0.264512	−	0.192179i
$907$	−129671.	+	94211.4i	−0.157626	+	0.114522i	−0.663802	−	0.747908i	$-0.731058\pi$
$907$	−129671.	+	94211.4i	−0.157626	+	0.114522i	0.506177	+	0.862430i	$0.331058\pi$
$908$	−50280.1	+	36530.6i	−0.0609852	+	0.0443083i
$909$	4658.08	−	14336.1i	0.00563740	−	0.0173501i
$910$	−114463.	+	157545.i	−0.138224	+	0.190249i
$911$	−1.17329e6	−	381224.i	−1.41373	−	0.459349i	−0.500127	−	0.865952i	$-0.666713\pi$
$911$	−1.17329e6	−	381224.i	−1.41373	−	0.459349i	−0.913605	+	0.406603i	$0.866713\pi$
$912$	−320559.	+	104156.i	−0.385405	+	0.125226i
$913$	228365.	−	165917.i	0.273960	−	0.199044i
$914$	−55644.5	+	18080.0i	−0.0666085	+	0.0216424i
$915$	179680.	+	552999.i	0.214614	+	0.660514i
$916$	340866.	+	469162.i	0.406249	+	0.559154i
$917$	−386111.	−	1.18833e6i	−0.459170	−	1.41318i
$918$	−13888.1	+	42743.3i	−0.0164801	+	0.0507204i
$919$	−167688.	−	121833.i	−0.198551	−	0.144256i	0.484068	−	0.875031i	$-0.339159\pi$
$919$	−167688.	−	121833.i	−0.198551	−	0.144256i	−0.682619	+	0.730775i	$0.739159\pi$
$920$	−513162.	−	166736.i	−0.606288	−	0.196995i
$921$	−509645.	−	701466.i	−0.600826	−	0.826966i
$922$	129278.	+	177936.i	0.152077	+	0.209316i
$923$	−637060.	+	876838.i	−0.747785	+	1.02924i
$924$	−366198.			−0.428916
$925$		−	414165.i		−	0.484050i
$926$	−82495.6	+	113545.i	−0.0962075	+	0.132418i
$927$	16327.4	+	50250.4i	0.0190001	+	0.0584763i
$928$	526487.	+	171066.i	0.611352	+	0.198640i
$929$			1.39368e6i			1.61485i	0.589969	+	0.807426i	$0.299140\pi$
$929$			1.39368e6i			1.61485i	−0.589969	+	0.807426i	$0.700860\pi$
$930$	218225.	+	33666.9i	0.252313	+	0.0389258i
$931$	389898.			0.449833
$932$	252709.	−	777759.i	0.290930	−	0.895392i
$933$	756143.	−	245686.i	0.868641	−	0.282239i
$934$	−87971.2	−	63914.8i	−0.100843	−	0.0732669i
$935$	−42709.1			−0.0488536
$936$		−	49936.5i		−	0.0569989i
$937$	633067.	+	459950.i	0.721059	+	0.523880i	0.886722	−	0.462303i	$-0.152977\pi$
$937$	633067.	+	459950.i	0.721059	+	0.523880i	−0.165664	+	0.986182i	$0.552977\pi$
$938$	−412423.	+	299643.i	−0.468745	+	0.340563i
$939$	855266.	−	621387.i	0.969996	−	0.704744i
$940$	237413.	−	730683.i	0.268689	−	0.826938i
$941$	552661.	−	760673.i	0.624137	−	0.859051i	−0.373509	−	0.927627i	$-0.621846\pi$
$941$	552661.	−	760673.i	0.624137	−	0.859051i	0.997646	+	0.0685758i	$0.0218455\pi$
$942$	−140360.	−	45605.8i	−0.158177	−	0.0513947i
$943$	−120808.	+	39252.9i	−0.135854	+	0.0441416i
$944$	−801559.	+	582367.i	−0.899480	+	0.653511i
$945$	951119.	−	309037.i	1.06505	−	0.346057i
$946$	57442.3	+	176789.i	0.0641874	+	0.197548i
$947$	510698.	+	702916.i	0.569462	+	0.783797i	0.992491	−	0.122319i	$-0.0390332\pi$
$947$	510698.	+	702916.i	0.569462	+	0.783797i	−0.423029	+	0.906116i	$0.639033\pi$
$948$	−288899.	−	889140.i	−0.321462	−	0.989358i
$949$	149508.	−	460138.i	0.166009	−	0.510923i
$950$	53632.0	+	38965.9i	0.0594260	+	0.0431756i
$951$	526202.	+	170973.i	0.581824	+	0.189046i
$952$	−66038.6	−	90894.3i	−0.0728658	−	0.100291i
$953$	−188936.	−	260048.i	−0.208031	−	0.286330i	0.692233	−	0.721674i	$-0.256627\pi$
$953$	−188936.	−	260048.i	−0.208031	−	0.286330i	−0.900264	+	0.435343i	$0.856627\pi$
$954$	16245.1	−	22359.5i	0.0178495	−	0.0245678i
$955$	1.14390e6			1.25424
$956$			379711.i			0.415468i
$957$	−149214.	+	205375.i	−0.162924	+	0.224246i
$958$	35549.1	+	109409.i	0.0387345	+	0.119213i
$959$	−1.87772e6	−	610107.i	−2.04170	−	0.663390i
$960$		−	266190.i		−	0.288835i
$961$	−880582.	−	278329.i	−0.953505	−	0.301378i
$962$	−295760.			−0.319587
$963$	31689.2	−	97529.3i	0.0341711	−	0.105168i
$964$	−6150.81	+	1998.52i	−0.00661878	+	0.00215057i
$965$	1.08512e6	+	788388.i	1.16526	+	0.846614i
$966$	467985.			0.501507
$967$		−	605377.i		−	0.647400i	−0.946160	−	0.323700i	$-0.895073\pi$
$967$		−	605377.i		−	0.647400i	0.946160	−	0.323700i	$-0.104927\pi$
$968$	404851.	+	294142.i	0.432061	+	0.313910i
$969$	68627.0	−	49860.4i	0.0730882	−	0.0531017i
$970$	−13873.5	+	10079.7i	−0.0147449	+	0.0107128i
$971$	75814.6	−	233333.i	0.0804108	−	0.247479i	−0.902767	−	0.430130i	$-0.858468\pi$
$971$	75814.6	−	233333.i	0.0804108	−	0.247479i	0.983178	+	0.182651i	$0.0584678\pi$
$972$	−133163.	+	183284.i	−0.140946	+	0.193995i
$973$	1.45513e6	+	472800.i	1.53701	+	0.499404i
$974$	440508.	−	143130.i	0.464339	−	0.150873i
$975$	−157932.	+	114744.i	−0.166135	+	0.120704i
$976$	558295.	−	181401.i	0.586089	−	0.190432i
$977$	106207.	+	326870.i	0.111266	+	0.342441i	0.991150	−	0.132747i	$-0.0423798\pi$
$977$	106207.	+	326870.i	0.111266	+	0.342441i	−0.879884	+	0.475189i	$0.842380\pi$
$978$	−17251.2	−	23744.2i	−0.0180360	−	0.0248245i
$979$	−90003.8	−	277003.i	−0.0939065	−	0.289015i
$980$	−148632.	+	457442.i	−0.154760	+	0.476304i
$981$	−46888.9	−	34066.8i	−0.0487228	−	0.0353992i
$982$	−36188.6	−	11758.4i	−0.0375274	−	0.0121934i
$983$	−473982.	−	652380.i	−0.490517	−	0.675139i	0.489966	−	0.871742i	$-0.337009\pi$
$983$	−473982.	−	652380.i	−0.490517	−	0.675139i	−0.980483	+	0.196602i	$0.937009\pi$
$984$	39051.4	+	53749.6i	0.0403316	+	0.0555117i
$985$	−923567.	+	1.27118e6i	−0.951910	+	1.31019i
$986$	−36596.9			−0.0376435
$987$			1.41813e6i			1.45573i
$988$	−217076.	+	298780.i	−0.222382	+	0.306082i
$989$	572676.	+	1.76252e6i	0.585486	+	1.80194i
$990$	13960.2	+	4535.95i	0.0142437	+	0.00462805i
$991$			269677.i			0.274597i	0.990530	+	0.137299i	$0.0438420\pi$
$991$			269677.i			0.274597i	−0.990530	+	0.137299i	$0.956158\pi$
$992$	129394.	−	838721.i	0.131490	−	0.852303i
$993$	−13328.6			−0.0135171
$994$	258983.	−	797067.i	0.262119	−	0.806718i
$995$	957726.	−	311184.i	0.967376	−	0.314319i
$996$	−559532.	−	406524.i	−0.564036	−	0.409796i
$997$	235239.			0.236657			0.118328	−	0.992975i	$-0.462246\pi$
$997$	235239.			0.236657			0.118328	+	0.992975i	$0.462246\pi$
$998$		−	301784.i		−	0.302995i
$999$	1.22879e6	+	892768.i	1.23125	+	0.894557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.5.f.a.23.6	✓	36
31.27	odd	10	inner	31.5.f.a.27.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.5.f.a.23.6	✓	36	1.1	even	1	trivial
31.5.f.a.27.6	yes	36	31.27	odd	10	inner

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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	31.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.416650 - 1.28232i) q^{2} +(-7.95500 + 2.58474i) q^{3} +(11.4735 + 8.33601i) q^{4} +20.3736 q^{5} +11.2778i q^{6} +(51.5849 + 37.4786i) q^{7} +(32.9227 - 23.9197i) q^{8} +(-8.92916 + 6.48742i) q^{9} +(8.48864 - 26.1253i) q^{10} +(28.4574 - 39.1683i) q^{11} +(-112.818 - 36.6569i) q^{12} +(-105.739 + 34.3566i) q^{13} +(69.5523 - 50.5327i) q^{14} +(-162.072 + 52.6603i) q^{15} +(53.1646 + 163.624i) q^{16} +(-25.4504 - 35.0295i) q^{17} +(4.59859 + 14.1530i) q^{18} +(72.3785 - 222.758i) q^{19} +(233.757 + 169.834i) q^{20} +(-507.231 - 164.809i) q^{21} +(-38.3694 - 52.8109i) q^{22} +(-382.527 - 526.503i) q^{23} +(-200.074 + 275.378i) q^{24} -209.918 q^{25} +149.905i q^{26} +(452.497 - 622.808i) q^{27} +(279.439 + 860.025i) q^{28} +(596.191 + 193.714i) q^{29} +229.768i q^{30} +(146.525 - 949.764i) q^{31} +883.084 q^{32} +(-125.139 + 385.139i) q^{33} +(-55.5228 + 18.0404i) q^{34} +(1050.97 + 763.573i) q^{35} -156.528 q^{36} +1972.98i q^{37} +(-255.490 - 185.624i) q^{38} +(752.348 - 546.613i) q^{39} +(670.753 - 487.330i) q^{40} +(60.3154 - 185.632i) q^{41} +(-422.675 + 581.762i) q^{42} +(-2708.26 - 879.966i) q^{43} +(653.015 - 212.177i) q^{44} +(-181.919 + 132.172i) q^{45} +(-834.524 + 271.153i) q^{46} +(-821.672 - 2528.85i) q^{47} +(-845.848 - 1164.21i) q^{48} +(514.406 + 1583.18i) q^{49} +(-87.4624 + 269.182i) q^{50} +(293.000 + 212.877i) q^{51} +(-1499.59 - 487.247i) q^{52} +(-1091.64 - 1502.52i) q^{53} +(-610.105 - 839.737i) q^{54} +(579.779 - 797.998i) q^{55} +2594.79 q^{56} +1959.12i q^{57} +(496.806 - 683.795i) q^{58} +(1779.59 + 5477.02i) q^{59} +(-2298.51 - 746.832i) q^{60} -3412.06i q^{61} +(-1156.85 - 583.611i) q^{62} -703.750 q^{63} +(-482.696 + 1485.59i) q^{64} +(-2154.27 + 699.965i) q^{65} +(441.731 + 320.936i) q^{66} -5929.67 q^{67} -614.067i q^{68} +(4403.88 + 3199.60i) q^{69} +(1417.03 - 1029.53i) q^{70} +(7886.64 - 5729.98i) q^{71} +(-138.795 + 427.167i) q^{72} +(-2557.84 + 3520.56i) q^{73} +(2529.99 + 822.043i) q^{74} +(1669.90 - 542.584i) q^{75} +(2687.35 - 1952.48i) q^{76} +(2935.95 - 953.948i) q^{77} +(-387.465 - 1192.49i) q^{78} +(4632.43 + 6375.99i) q^{79} +(1083.15 + 3333.60i) q^{80} +(-1713.56 + 5273.78i) q^{81} +(-212.908 - 154.687i) q^{82} +(5544.98 + 1801.67i) q^{83} +(-4445.88 - 6119.22i) q^{84} +(-518.515 - 713.675i) q^{85} +(-2256.79 + 3106.20i) q^{86} -5243.40 q^{87} -1970.22i q^{88} +(3536.06 - 4866.98i) q^{89} +(93.6896 + 288.347i) q^{90} +(-6742.15 - 2190.66i) q^{91} -9229.60i q^{92} +(1289.28 + 7934.10i) q^{93} -3585.13 q^{94} +(1474.61 - 4538.38i) q^{95} +(-7024.93 + 2282.54i) q^{96} +(-505.044 - 366.936i) q^{97} +2244.46 q^{98} +534.356i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 5 q^{3} - 79 q^{4} - 2 q^{5} - 73 q^{7} + 173 q^{8} + 62 q^{9} + 84 q^{10} + 100 q^{11} + 150 q^{12} - 260 q^{13} + 488 q^{14} - 1075 q^{15} + 777 q^{16} - 725 q^{17} - 786 q^{18} - 1581 q^{19}+ \cdots + 74456 q^{98}+O(q^{100}) \) 36 * q - 3 * q^2 - 5 * q^3 - 79 * q^4 - 2 * q^5 - 73 * q^7 + 173 * q^8 + 62 * q^9 + 84 * q^10 + 100 * q^11 + 150 * q^12 - 260 * q^13 + 488 * q^14 - 1075 * q^15 + 777 * q^16 - 725 * q^17 - 786 * q^18 - 1581 * q^19 + 827 * q^20 + 2335 * q^21 - 1030 * q^22 + 1675 * q^23 - 165 * q^24 + 1294 * q^25 - 2855 * q^27 + 352 * q^28 - 575 * q^29 + 895 * q^31 - 5470 * q^32 + 4468 * q^33 + 1815 * q^34 - 3042 * q^35 + 7808 * q^36 - 6604 * q^38 + 595 * q^39 + 1482 * q^40 - 1740 * q^41 + 3840 * q^42 - 10055 * q^43 - 5780 * q^44 + 6774 * q^45 + 16515 * q^46 + 693 * q^47 + 4710 * q^48 - 944 * q^49 - 6240 * q^50 + 12641 * q^51 + 15885 * q^52 - 10835 * q^53 - 25960 * q^54 - 14010 * q^55 - 19976 * q^56 + 4755 * q^58 - 6021 * q^59 + 35 * q^60 - 11088 * q^62 - 15564 * q^63 + 6935 * q^64 + 26645 * q^65 + 23988 * q^66 + 28596 * q^67 - 4229 * q^69 + 8041 * q^70 + 31101 * q^71 + 20690 * q^72 + 6125 * q^73 - 47295 * q^74 - 27475 * q^75 + 12511 * q^76 + 35950 * q^77 + 29801 * q^78 - 29050 * q^79 - 47358 * q^80 - 1965 * q^81 + 9198 * q^82 + 21640 * q^83 - 35875 * q^84 - 55360 * q^85 - 27935 * q^86 - 2262 * q^87 - 11645 * q^89 - 14916 * q^90 + 670 * q^91 - 36224 * q^93 - 52442 * q^94 + 73983 * q^95 + 29810 * q^96 + 55059 * q^97 + 74456 * q^98

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