LMFDB - Embedded newform 31.5.f.a.27.2

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			27.2
Character	$\chi$	$=$	31.27
Dual form			31.5.f.a.23.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.60665 - 4.94476i) q^{2} +(-15.6281 - 5.07789i) q^{3} +(-8.92504 + 6.48442i) q^{4} +30.2396 q^{5} +85.4357i q^{6} +(-52.6343 + 38.2411i) q^{7} +(-20.8969 - 15.1825i) q^{8} +(152.923 + 111.105i) q^{9} +(-48.5844 - 149.527i) q^{10} +(-51.5717 - 70.9824i) q^{11} +(172.409 - 56.0190i) q^{12} +(-132.954 - 43.1994i) q^{13} +(273.658 + 198.824i) q^{14} +(-472.588 - 153.553i) q^{15} +(-96.0447 + 295.595i) q^{16} +(-138.618 + 190.791i) q^{17} +(303.694 - 934.675i) q^{18} +(-103.377 - 318.162i) q^{19} +(-269.889 + 196.086i) q^{20} +(1016.76 - 330.365i) q^{21} +(-268.133 + 369.054i) q^{22} +(14.2811 - 19.6562i) q^{23} +(249.485 + 343.386i) q^{24} +289.432 q^{25} +726.832i q^{26} +(-1043.37 - 1436.07i) q^{27} +(221.792 - 682.606i) q^{28} +(-762.379 + 247.712i) q^{29} +2583.54i q^{30} +(630.290 - 725.434i) q^{31} +1202.68 q^{32} +(445.529 + 1371.20i) q^{33} +(1166.13 + 378.897i) q^{34} +(-1591.64 + 1156.39i) q^{35} -2085.30 q^{36} -2507.85i q^{37} +(-1407.14 + 1022.35i) q^{38} +(1858.46 + 1350.25i) q^{39} +(-631.913 - 459.112i) q^{40} +(-178.276 - 548.678i) q^{41} +(-3267.15 - 4496.85i) q^{42} +(-1694.83 + 550.683i) q^{43} +(920.559 + 299.108i) q^{44} +(4624.33 + 3359.77i) q^{45} +(-120.140 - 39.0358i) q^{46} +(-444.930 + 1369.35i) q^{47} +(3002.00 - 4131.90i) q^{48} +(566.042 - 1742.10i) q^{49} +(-465.016 - 1431.17i) q^{50} +(3135.15 - 2277.82i) q^{51} +(1466.74 - 476.574i) q^{52} +(807.406 - 1111.30i) q^{53} +(-5424.71 + 7466.47i) q^{54} +(-1559.51 - 2146.48i) q^{55} +1680.49 q^{56} +5497.22i q^{57} +(2449.75 + 3371.79i) q^{58} +(237.883 - 732.129i) q^{59} +(5213.57 - 1693.99i) q^{60} -3145.37i q^{61} +(-4599.75 - 1951.12i) q^{62} -12297.8 q^{63} +(-395.565 - 1217.42i) q^{64} +(-4020.47 - 1306.33i) q^{65} +(6064.43 - 4406.07i) q^{66} +962.501 q^{67} -2601.68i q^{68} +(-322.999 + 234.672i) q^{69} +(8275.29 + 6012.35i) q^{70} +(3529.45 + 2564.29i) q^{71} +(-1508.77 - 4643.51i) q^{72} +(-853.858 - 1175.23i) q^{73} +(-12400.7 + 4029.23i) q^{74} +(-4523.28 - 1469.70i) q^{75} +(2985.74 + 2169.27i) q^{76} +(5428.89 + 1763.95i) q^{77} +(3690.77 - 11359.0i) q^{78} +(-5850.11 + 8051.98i) q^{79} +(-2904.35 + 8938.68i) q^{80} +(4282.35 + 13179.7i) q^{81} +(-2426.65 + 1763.07i) q^{82} +(8033.97 - 2610.40i) q^{83} +(-6932.40 + 9541.62i) q^{84} +(-4191.75 + 5769.44i) q^{85} +(5445.99 + 7495.76i) q^{86} +13172.4 q^{87} +2266.30i q^{88} +(-2769.04 - 3811.26i) q^{89} +(9183.59 - 28264.2i) q^{90} +(8649.94 - 2810.53i) q^{91} +268.037i q^{92} +(-13533.9 + 8136.64i) q^{93} +7485.97 q^{94} +(-3126.08 - 9621.09i) q^{95} +(-18795.6 - 6107.06i) q^{96} +(9460.32 - 6873.32i) q^{97} -9523.69 q^{98} -16584.7i 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 $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−1.60665	−	4.94476i	−0.401662	−	1.23619i	−0.923650	−	0.383237i	$-0.874809\pi$
$2$	−1.60665	−	4.94476i	−0.401662	−	1.23619i	0.521988	−	0.852953i	$-0.325191\pi$
$3$	−15.6281	−	5.07789i	−1.73646	−	0.564210i	−0.742101	−	0.670288i	$-0.766171\pi$
$3$	−15.6281	−	5.07789i	−1.73646	−	0.564210i	−0.994358	+	0.106078i	$0.966171\pi$
$4$	−8.92504	+	6.48442i	−0.557815	+	0.405276i
$5$	30.2396			1.20958			0.604792	−	0.796384i	$-0.293256\pi$
$5$	30.2396			1.20958			0.604792	+	0.796384i	$0.293256\pi$
$6$			85.4357i			2.37321i
$7$	−52.6343	+	38.2411i	−1.07417	+	0.780430i	−0.976657	−	0.214804i	$-0.931089\pi$
$7$	−52.6343	+	38.2411i	−1.07417	+	0.780430i	−0.0975127	+	0.995234i	$0.531089\pi$
$8$	−20.8969	−	15.1825i	−0.326514	−	0.237226i
$9$	152.923	+	111.105i	1.88794	+	1.37167i
$10$	−48.5844	−	149.527i	−0.485844	−	1.49527i
$11$	−51.5717	−	70.9824i	−0.426213	−	0.586631i	0.540866	−	0.841109i	$-0.318097\pi$
$11$	−51.5717	−	70.9824i	−0.426213	−	0.586631i	−0.967079	+	0.254477i	$0.918097\pi$
$12$	172.409	−	56.0190i	1.19728	−	0.389021i
$13$	−132.954	−	43.1994i	−0.786710	−	0.255618i	−0.112008	−	0.993707i	$-0.535728\pi$
$13$	−132.954	−	43.1994i	−0.786710	−	0.255618i	−0.674703	+	0.738090i	$0.735728\pi$
$14$	273.658	+	198.824i	1.39621	+	1.01441i
$15$	−472.588	−	153.553i	−2.10039	−	0.682459i
$16$	−96.0447	+	295.595i	−0.375175	+	1.15467i
$17$	−138.618	+	190.791i	−0.479647	+	0.660177i	−0.978437	−	0.206546i	$-0.933778\pi$
$17$	−138.618	+	190.791i	−0.479647	+	0.660177i	0.498790	+	0.866723i	$0.333778\pi$
$18$	303.694	−	934.675i	0.937328	−	2.88480i
$19$	−103.377	−	318.162i	−0.286363	−	0.881336i	−0.985987	−	0.166824i	$-0.946649\pi$
$19$	−103.377	−	318.162i	−0.286363	−	0.881336i	0.699623	−	0.714512i	$-0.253351\pi$
$20$	−269.889	+	196.086i	−0.674723	+	0.490215i
$21$	1016.76	−	330.365i	2.30558	−	0.749128i
$22$	−268.133	+	369.054i	−0.553994	+	0.762507i
$23$	14.2811	−	19.6562i	0.0269964	−	0.0371573i	−0.795305	−	0.606209i	$-0.792690\pi$
$23$	14.2811	−	19.6562i	0.0269964	−	0.0371573i	0.822302	+	0.569052i	$0.192690\pi$
$24$	249.485	+	343.386i	0.433133	+	0.596156i
$25$	289.432			0.463091
$26$			726.832i			1.07520i
$27$	−1043.37	−	1436.07i	−1.43123	−	1.96992i
$28$	221.792	−	682.606i	0.282898	−	0.870671i
$29$	−762.379	+	247.712i	−0.906514	+	0.294544i	−0.724923	−	0.688830i	$-0.758125\pi$
$29$	−762.379	+	247.712i	−0.906514	+	0.294544i	−0.181591	+	0.983374i	$0.558125\pi$
$30$			2583.54i			2.87060i
$31$	630.290	−	725.434i	0.655869	−	0.754874i
$31$	630.290	−	725.434i	0.655869	−	0.754874i
$32$	1202.68			1.17449
$33$	445.529	+	1371.20i	0.409118	+	1.25913i
$34$	1166.13	+	378.897i	1.00876	+	0.327766i
$35$	−1591.64	+	1156.39i	−1.29930	+	0.943995i
$36$	−2085.30			−1.60903
$37$		−	2507.85i		−	1.83188i	−0.401314	−	0.915941i	$-0.631446\pi$
$37$		−	2507.85i		−	1.83188i	0.401314	−	0.915941i	$-0.368554\pi$
$38$	−1407.14	+	1022.35i	−0.974477	+	0.707999i
$39$	1858.46	+	1350.25i	1.22187	+	0.887739i
$40$	−631.913	−	459.112i	−0.394946	−	0.286945i
$41$	−178.276	−	548.678i	−0.106054	−	0.326400i	0.883923	−	0.467633i	$-0.154893\pi$
$41$	−178.276	−	548.678i	−0.106054	−	0.326400i	−0.989976	+	0.141234i	$0.954893\pi$
$42$	−3267.15	−	4496.85i	−1.85213	−	2.54924i
$43$	−1694.83	+	550.683i	−0.916619	+	0.297827i	−0.729079	−	0.684430i	$-0.760051\pi$
$43$	−1694.83	+	550.683i	−0.916619	+	0.297827i	−0.187540	+	0.982257i	$0.560051\pi$
$44$	920.559	+	299.108i	0.475496	+	0.154498i
$45$	4624.33	+	3359.77i	2.28362	+	1.65915i
$46$	−120.140	−	39.0358i	−0.0567769	−	0.0184479i
$47$	−444.930	+	1369.35i	−0.201417	+	0.619898i	0.798425	+	0.602095i	$0.205667\pi$
$47$	−444.930	+	1369.35i	−0.201417	+	0.619898i	−0.999842	+	0.0178028i	$0.994333\pi$
$48$	3002.00	−	4131.90i	1.30295	−	1.79336i
$49$	566.042	−	1742.10i	0.235753	−	0.725573i
$50$	−465.016	−	1431.17i	−0.186006	−	0.572468i
$51$	3135.15	−	2277.82i	1.20537	−	0.875749i
$52$	1466.74	−	476.574i	0.542435	−	0.176248i
$53$	807.406	−	1111.30i	0.287435	−	0.395621i	−0.640744	−	0.767755i	$-0.721374\pi$
$53$	807.406	−	1111.30i	0.287435	−	0.395621i	0.928179	+	0.372134i	$0.121374\pi$
$54$	−5424.71	+	7466.47i	−1.86032	+	2.56052i
$55$	−1559.51	−	2146.48i	−0.515540	−	0.709579i
$56$	1680.49			0.535870
$57$			5497.22i			1.69197i
$58$	2449.75	+	3371.79i	0.728225	+	1.00232i
$59$	237.883	−	732.129i	0.0683375	−	0.210321i	−0.911056	−	0.412283i	$-0.864732\pi$
$59$	237.883	−	732.129i	0.0683375	−	0.210321i	0.979393	+	0.201961i	$0.0647316\pi$
$60$	5213.57	−	1693.99i	1.44821	−	0.470553i
$61$		−	3145.37i		−	0.845303i	−0.906292	−	0.422652i	$-0.861099\pi$
$61$		−	3145.37i		−	0.845303i	0.906292	−	0.422652i	$-0.138901\pi$
$62$	−4599.75	−	1951.12i	−1.19661	−	0.507574i
$63$	−12297.8			−3.09846
$64$	−395.565	−	1217.42i	−0.0965735	−	0.297223i
$65$	−4020.47	−	1306.33i	−0.951591	−	0.309191i
$66$	6064.43	−	4406.07i	1.39220	−	1.01149i
$67$	962.501			0.214413			0.107207	−	0.994237i	$-0.465809\pi$
$67$	962.501			0.214413			0.107207	+	0.994237i	$0.465809\pi$
$68$		−	2601.68i		−	0.562646i
$69$	−322.999	+	234.672i	−0.0678426	+	0.0492906i
$70$	8275.29	+	6012.35i	1.68884	+	1.22701i
$71$	3529.45	+	2564.29i	0.700148	+	0.508687i	0.879980	−	0.475010i	$-0.157556\pi$
$71$	3529.45	+	2564.29i	0.700148	+	0.508687i	−0.179832	+	0.983697i	$0.557556\pi$
$72$	−1508.77	−	4643.51i	−0.291043	−	0.895739i
$73$	−853.858	−	1175.23i	−0.160229	−	0.220536i	0.721353	−	0.692568i	$-0.243521\pi$
$73$	−853.858	−	1175.23i	−0.160229	−	0.220536i	−0.881581	+	0.472032i	$0.843521\pi$
$74$	−12400.7	+	4029.23i	−2.26455	+	0.735798i
$75$	−4523.28	−	1469.70i	−0.804139	−	0.261281i
$76$	2985.74	+	2169.27i	0.516922	+	0.375566i
$77$	5428.89	+	1763.95i	0.915650	+	0.297513i
$78$	3690.77	−	11359.0i	0.606636	−	1.86703i
$79$	−5850.11	+	8051.98i	−0.937367	+	1.29017i	0.0195488	+	0.999809i	$0.493777\pi$
$79$	−5850.11	+	8051.98i	−0.937367	+	1.29017i	−0.956916	+	0.290366i	$0.906223\pi$
$80$	−2904.35	+	8938.68i	−0.453805	+	1.39667i
$81$	4282.35	+	13179.7i	0.652697	+	2.00880i
$82$	−2426.65	+	1763.07i	−0.360894	+	0.262205i
$83$	8033.97	−	2610.40i	1.16620	−	0.378922i	0.338979	−	0.940794i	$-0.389919\pi$
$83$	8033.97	−	2610.40i	1.16620	−	0.378922i	0.827224	+	0.561872i	$0.189919\pi$
$84$	−6932.40	+	9541.62i	−0.982482	+	1.35227i
$85$	−4191.75	+	5769.44i	−0.580172	+	0.798539i
$86$	5445.99	+	7495.76i	0.736342	+	1.01349i
$87$	13172.4			1.74031
$88$			2266.30i			0.292652i
$89$	−2769.04	−	3811.26i	−0.349583	−	0.481159i	0.597627	−	0.801774i	$-0.296110\pi$
$89$	−2769.04	−	3811.26i	−0.349583	−	0.481159i	−0.947210	+	0.320615i	$0.896110\pi$
$90$	9183.59	−	28264.2i	1.13378	−	3.48941i
$91$	8649.94	−	2810.53i	1.04455	−	0.339396i
$92$			268.037i			0.0316679i
$93$	−13533.9	+	8136.64i	−1.56480	+	0.940761i
$94$	7485.97			0.847213
$95$	−3126.08	−	9621.09i	−0.346380	−	1.06605i
$96$	−18795.6	−	6107.06i	−2.03945	−	0.662659i
$97$	9460.32	−	6873.32i	1.00545	−	0.730505i	0.0422035	−	0.999109i	$-0.486562\pi$
$97$	9460.32	−	6873.32i	1.00545	−	0.730505i	0.963251	+	0.268604i	$0.0865622\pi$
$98$	−9523.69			−0.991638
$99$		−	16584.7i		−	1.69215i
$100$	−2583.19	+	1876.80i	−0.258319	+	0.187680i
$101$	−5662.91	−	4114.35i	−0.555133	−	0.403328i	0.274541	−	0.961575i	$-0.411474\pi$
$101$	−5662.91	−	4114.35i	−0.555133	−	0.403328i	−0.829674	+	0.558248i	$0.811474\pi$
$102$	−16300.4	−	11842.9i	−1.56674	−	1.13830i
$103$	−2067.12	−	6361.95i	−0.194846	−	0.599675i	−0.999978	−	0.00657925i	$-0.997906\pi$
$103$	−2067.12	−	6361.95i	−0.194846	−	0.599675i	0.805132	−	0.593095i	$-0.202094\pi$
$104$	2122.45	+	2921.31i	0.196233	+	0.270091i
$105$	30746.4	−	9990.11i	2.78879	−	0.906132i
$106$	−6792.32	−	2206.96i	−0.604514	−	0.196419i
$107$	8967.84	+	6515.52i	0.783286	+	0.569091i	0.905963	−	0.423356i	$-0.139148\pi$
$107$	8967.84	+	6515.52i	0.783286	+	0.569091i	−0.122677	+	0.992447i	$0.539148\pi$
$108$	18624.2	+	6051.37i	1.59672	+	0.518807i
$109$	−6455.77	+	19868.8i	−0.543369	+	1.67232i	0.181467	+	0.983397i	$0.441915\pi$
$109$	−6455.77	+	19868.8i	−0.543369	+	1.67232i	−0.724836	+	0.688921i	$0.758085\pi$
$110$	−8108.23	+	11160.0i	−0.670102	+	0.922316i
$111$	−12734.6	+	39192.9i	−1.03357	+	3.18099i
$112$	−6248.63	−	19231.3i	−0.498137	−	1.53311i
$113$	−4596.65	+	3339.66i	−0.359985	+	0.261544i	−0.753046	−	0.657968i	$-0.771416\pi$
$113$	−4596.65	+	3339.66i	−0.359985	+	0.261544i	0.393061	+	0.919512i	$0.371416\pi$
$114$	27182.4	−	8832.10i	2.09160	−	0.679602i
$115$	431.854	−	594.396i	0.0326544	−	0.0449449i
$116$	5197.99	−	7154.42i	0.386295	−	0.531690i
$117$	−15532.1	−	21378.1i	−1.13464	−	1.56170i
$118$	−4002.39			−0.287446
$119$		−	15343.1i		−	1.08347i
$120$	7544.31	+	10383.8i	0.523910	+	0.721101i
$121$	2145.46	−	6603.05i	0.146538	−	0.450997i
$122$	−15553.1	+	5053.51i	−1.04496	+	0.339527i
$123$			9480.07i			0.626616i
$124$	−921.345	+	10561.6i	−0.0599210	+	0.686889i
$125$	−10147.4			−0.649436
$126$	19758.2	+	60809.6i	1.24453	+	3.83028i
$127$	−12126.7	−	3940.19i	−0.751855	−	0.244292i	−0.0920757	−	0.995752i	$-0.529350\pi$
$127$	−12126.7	−	3940.19i	−0.751855	−	0.244292i	−0.659779	+	0.751460i	$0.729350\pi$
$128$	10183.4	−	7398.71i	0.621548	−	0.451581i
$129$	29283.3			1.75971
$130$			21979.1i			1.30054i
$131$	5543.35	−	4027.48i	0.323020	−	0.234688i	−0.414443	−	0.910075i	$-0.636024\pi$
$131$	5543.35	−	4027.48i	0.323020	−	0.234688i	0.737463	+	0.675387i	$0.236024\pi$
$132$	−12867.8	−	9348.99i	−0.738509	−	0.536558i
$133$	17608.1	+	12793.0i	0.995424	+	0.723218i
$134$	−1546.40	−	4759.33i	−0.0861217	−	0.265055i
$135$	−31551.0	−	43426.2i	−1.73119	−	2.38278i
$136$	5793.37	−	1882.38i	0.313223	−	0.101772i
$137$	10520.5	+	3418.32i	0.560526	+	0.182126i	0.575558	−	0.817761i	$-0.304785\pi$
$137$	10520.5	+	3418.32i	0.560526	+	0.182126i	−0.0150321	+	0.999887i	$0.504785\pi$
$138$	1679.34	+	1220.11i	0.0881823	+	0.0640682i
$139$	−23492.7	−	7633.24i	−1.21591	−	0.395075i	−0.370322	−	0.928903i	$-0.620753\pi$
$139$	−23492.7	−	7633.24i	−1.21591	−	0.395075i	−0.845593	+	0.533829i	$0.820753\pi$
$140$	6706.90	−	20641.7i	0.342189	−	1.05315i
$141$	13906.9	−	19141.1i	0.699505	−	0.962786i
$142$	7009.22	−	21572.2i	0.347611	−	1.06984i
$143$	3790.27	+	11665.3i	0.185353	+	0.570456i
$144$	−47529.6	+	34532.3i	−2.29213	+	1.66533i
$145$	−23054.0	+	7490.70i	−1.09650	+	0.356276i
$146$	−4439.40	+	6110.31i	−0.208266	+	0.286654i
$147$	−17692.4	+	24351.5i	−0.818750	+	1.12691i
$148$	16261.9	+	22382.6i	0.742418	+	1.02185i
$149$	29591.3			1.33288			0.666440	−	0.745558i	$-0.267817\pi$
$149$	29591.3			1.33288			0.666440	+	0.745558i	$0.267817\pi$
$150$			24727.8i			1.09901i
$151$	−20779.9	−	28601.1i	−0.911359	−	1.25438i	−0.966701	−	0.255910i	$-0.917625\pi$
$151$	−20779.9	−	28601.1i	−0.911359	−	1.25438i	0.0553421	−	0.998467i	$-0.482375\pi$
$152$	−2670.23	+	8218.13i	−0.115574	+	0.355701i
$153$	−42395.8	+	13775.2i	−1.81109	+	0.588458i
$154$		−	29678.6i		−	1.25142i
$155$	19059.7	−	21936.8i	0.793328	−	0.913083i
$156$	−25342.4			−1.04136
$157$	−8097.29	−	24920.9i	−0.328504	−	1.01103i	−0.969834	−	0.243766i	$-0.921617\pi$
$157$	−8097.29	−	24920.9i	−0.328504	−	1.01103i	0.641330	−	0.767265i	$-0.278383\pi$
$158$	49214.2	+	15990.7i	1.97141	+	0.640548i
$159$	−18261.3	+	13267.6i	−0.722333	+	0.524805i
$160$	36368.5			1.42064
$161$			1580.72i			0.0609821i
$162$	58290.2	−	42350.3i	2.22109	−	1.61372i
$163$	18860.7	+	13703.1i	0.709877	+	0.515756i	0.883134	−	0.469121i	$-0.155429\pi$
$163$	18860.7	+	13703.1i	0.709877	+	0.515756i	−0.173257	+	0.984877i	$0.555429\pi$
$164$	5148.98	+	3740.95i	0.191440	+	0.139090i
$165$	13472.6	+	41464.4i	0.494862	+	1.52303i
$166$	−25815.6	−	35532.1i	−0.936840	−	1.28945i
$167$	9172.13	−	2980.21i	0.328880	−	0.106860i	−0.139923	−	0.990162i	$-0.544685\pi$
$167$	9172.13	−	2980.21i	0.328880	−	0.106860i	0.468803	+	0.883303i	$0.344685\pi$
$168$	−26262.9	−	8533.33i	−0.930517	−	0.302343i
$169$	−7295.74	−	5300.67i	−0.255444	−	0.185591i
$170$	35263.2	+	11457.7i	1.22018	+	0.396460i
$171$	19540.7	−	60140.1i	0.668264	−	2.05671i
$172$	11555.5	−	15904.8i	0.390601	−	0.537616i
$173$	−7994.50	+	24604.5i	−0.267115	+	0.822097i	0.724083	+	0.689713i	$0.242263\pi$
$173$	−7994.50	+	24604.5i	−0.267115	+	0.822097i	−0.991199	+	0.132384i	$0.957737\pi$
$174$	−21163.4	−	65134.4i	−0.699017	−	2.15135i
$175$	−15234.1	+	11068.2i	−0.497439	+	0.361410i
$176$	25935.3	−	8426.87i	0.837269	−	0.272045i
$177$	−7435.33	+	10233.9i	−0.237331	+	0.326658i
$178$	−14396.9	+	19815.6i	−0.454390	+	0.625414i
$179$	11514.1	+	15847.8i	0.359355	+	0.494610i	0.949969	−	0.312344i	$-0.101114\pi$
$179$	11514.1	+	15847.8i	0.359355	+	0.494610i	−0.590614	+	0.806954i	$0.701114\pi$
$180$	−63058.5			−1.94625
$181$			5753.52i			0.175621i	0.996137	+	0.0878105i	$0.0279870\pi$
$181$			5753.52i			0.175621i	−0.996137	+	0.0878105i	$0.972013\pi$
$182$	−27794.8	−	38256.3i	−0.839115	−	1.15494i
$183$	−15971.9	+	49156.3i	−0.476928	+	1.46783i
$184$	−596.861	+	193.932i	−0.0176294	+	0.00572814i
$185$		−	75836.2i		−	2.21581i
$186$	61978.0	+	53849.3i	1.79148	+	1.55652i
$187$	20691.6			0.591712
$188$	−4908.45	−	15106.7i	−0.138876	−	0.427418i
$189$	109834.	+	35687.2i	3.07477	+	0.999054i
$190$	−42551.4	+	30915.4i	−1.17871	+	0.856383i
$191$	−46796.3			−1.28276			−0.641380	−	0.767224i	$-0.721638\pi$
$191$	−46796.3			−1.28276			−0.641380	+	0.767224i	$0.721638\pi$
$192$			21034.7i			0.570603i
$193$	−10734.4	+	7799.02i	−0.288180	+	0.209375i	−0.722478	−	0.691394i	$-0.756997\pi$
$193$	−10734.4	+	7799.02i	−0.288180	+	0.209375i	0.434297	+	0.900770i	$0.356997\pi$
$194$	−49186.3	−	35736.0i	−1.30690	−	0.949516i
$195$	56199.1	+	40831.0i	1.47795	+	1.07379i
$196$	6244.55	+	19218.8i	0.162551	+	0.500280i
$197$	23757.4	+	32699.2i	0.612162	+	0.842568i	0.996753	−	0.0805186i	$-0.0256576\pi$
$197$	23757.4	+	32699.2i	0.612162	+	0.842568i	−0.384591	+	0.923087i	$0.625658\pi$
$198$	−82007.5	+	26645.9i	−2.09182	+	0.679672i
$199$	15708.9	+	5104.12i	0.396679	+	0.128889i	0.500562	−	0.865701i	$-0.333127\pi$
$199$	15708.9	+	5104.12i	0.396679	+	0.128889i	−0.103883	+	0.994590i	$0.533127\pi$
$200$	−6048.23	−	4394.30i	−0.151206	−	0.109857i
$201$	−15042.1	−	4887.47i	−0.372320	−	0.120974i
$202$	−11246.1	+	34612.0i	−0.275613	+	0.848251i
$203$	30654.5	−	42192.3i	0.743879	−	1.02386i
$204$	−13211.0	+	40659.3i	−0.317450	+	0.977012i
$205$	−5391.00	−	16591.8i	−0.128281	−	0.394807i
$206$	−28137.1	+	20442.8i	−0.663049	+	0.481733i
$207$	4367.82	−	1419.19i	0.101935	−	0.0331207i
$208$	25539.1	−	35151.5i	0.590308	−	0.812489i
$209$	−17252.6	+	23746.1i	−0.394967	+	0.543626i
$210$	−98797.3	−	135983.i	−2.24030	−	3.08351i
$211$	−23180.7			−0.520669			−0.260334	−	0.965519i	$-0.583833\pi$
$211$	−23180.7			−0.520669			−0.260334	+	0.965519i	$0.583833\pi$
$212$			15153.9i			0.337174i
$213$	−42137.5	−	57997.2i	−0.928772	−	1.27834i
$214$	17809.5	−	54812.0i	0.388887	−	1.19687i
$215$	−51250.9	+	16652.4i	−1.10873	+	0.360247i
$216$			45850.4i			0.982733i
$217$	−5433.52	+	62285.7i	−0.115388	+	1.32272i
$218$	108619.			2.28555
$219$	7376.50	+	22702.5i	0.153802	+	0.473354i
$220$	27837.3	+	9044.90i	0.575151	+	0.186878i
$221$	26671.9	−	19378.2i	0.546096	−	0.396762i
$222$	214260.			4.34745
$223$			12932.5i			0.260059i	0.991510	+	0.130029i	$0.0415072\pi$
$223$			12932.5i			0.260059i	−0.991510	+	0.130029i	$0.958493\pi$
$224$	−63302.1	+	45991.7i	−1.26160	+	0.916607i
$225$	44260.9	+	32157.4i	0.874289	+	0.635208i
$226$	23899.0	+	17363.7i	0.467911	+	0.339957i
$227$	−11390.3	−	35055.7i	−0.221046	−	0.680310i	−0.998669	−	0.0515788i	$-0.983575\pi$
$227$	−11390.3	−	35055.7i	−0.221046	−	0.680310i	0.777623	−	0.628731i	$-0.216425\pi$
$228$	−35646.3	−	49062.9i	−0.685716	−	0.943807i
$229$	10833.0	−	3519.87i	0.206576	−	0.0671205i	−0.203901	−	0.978991i	$-0.565362\pi$
$229$	10833.0	−	3519.87i	0.206576	−	0.0671205i	0.410477	+	0.911871i	$0.365362\pi$
$230$	−3632.98	−	1180.43i	−0.0686764	−	0.0223143i
$231$	−75886.2	−	55134.6i	−1.42213	−	1.03324i
$232$	19692.2	+	6398.39i	0.365863	+	0.118876i
$233$	−24465.4	+	75296.7i	−0.450651	+	1.38696i	0.425515	+	0.904951i	$0.360093\pi$
$233$	−24465.4	+	75296.7i	−0.450651	+	1.38696i	−0.876166	+	0.482009i	$0.839907\pi$
$234$	−80754.8	+	111149.i	−1.47481	+	2.02990i
$235$	−13454.5	+	41408.7i	−0.243631	+	0.749818i
$236$	2624.31	+	8076.81i	0.0471185	+	0.145016i
$237$	132313.	−	96131.2i	2.35563	−	1.71146i
$238$	−75867.7	+	24650.9i	−1.33938	+	0.435190i
$239$	−35223.7	+	48481.3i	−0.616651	+	0.848747i	−0.997104	−	0.0760532i	$-0.975768\pi$
$239$	−35223.7	+	48481.3i	−0.616651	+	0.848747i	0.380453	+	0.924800i	$0.375768\pi$
$240$	90779.2	−	124947.i	1.57603	−	2.16922i
$241$	3582.61	+	4931.04i	0.0616830	+	0.0848994i	0.838744	−	0.544526i	$-0.183290\pi$
$241$	3582.61	+	4931.04i	0.0616830	+	0.0848994i	−0.777061	+	0.629425i	$0.783290\pi$
$242$	−36097.5			−0.616377
$243$		−	83937.7i		−	1.42149i
$244$	20395.9	+	28072.6i	0.342581	+	0.471523i
$245$	17116.9	−	52680.4i	0.285163	−	0.877640i
$246$	46876.7	−	15231.2i	0.774616	−	0.251688i
$247$			46766.8i			0.766555i
$248$	−24185.0	+	5589.95i	−0.393227	+	0.0908876i
$249$	−138811.			−2.23886
$250$	16303.4	+	50176.6i	0.260854	+	0.802826i
$251$	−11440.1	−	3717.12i	−0.181586	−	0.0590010i	0.216812	−	0.976213i	$-0.430434\pi$
$251$	−11440.1	−	3717.12i	−0.181586	−	0.0590010i	−0.398399	+	0.917212i	$0.630434\pi$
$252$	109758.	−	79744.0i	1.72837	−	1.25573i
$253$	−2131.75			−0.0333039
$254$			66293.9i			1.02756i
$255$	94805.8	−	68880.4i	1.45799	−	1.05929i
$256$	−69515.7	−	50506.1i	−1.06073	−	0.770662i
$257$	−98382.7	−	71479.3i	−1.48954	−	1.08222i	−0.974322	−	0.225157i	$-0.927710\pi$
$257$	−98382.7	−	71479.3i	−1.48954	−	1.08222i	−0.515219	−	0.857058i	$-0.672290\pi$
$258$	−47048.0	−	144799.i	−0.706808	−	2.17533i
$259$	95902.7	+	131999.i	1.42966	+	1.96775i
$260$	44353.7	−	14411.4i	0.656120	−	0.213186i
$261$	−144107.	−	46823.3i	−2.11546	−	0.687355i
$262$	−28821.2	−	20939.8i	−0.419864	−	0.305049i
$263$	130451.	+	42386.1i	1.88597	+	0.612790i	0.983157	+	0.182764i	$0.0585045\pi$
$263$	130451.	+	42386.1i	1.88597	+	0.612790i	0.902817	+	0.430026i	$0.141495\pi$
$264$	11508.0	−	35418.0i	0.165117	−	0.508179i
$265$	24415.6	−	33605.2i	0.347677	−	0.478536i
$266$	34968.3	−	107621.i	0.494210	−	1.52102i
$267$	23921.8	+	73623.8i	0.335561	+	1.03275i
$268$	−8590.36	+	6241.26i	−0.119603	+	0.0868966i
$269$	44679.6	−	14517.3i	0.617454	−	0.200623i	0.0164443	−	0.999865i	$-0.494765\pi$
$269$	44679.6	−	14517.3i	0.617454	−	0.200623i	0.601010	+	0.799242i	$0.294765\pi$
$270$	−164041.	+	225783.i	−2.25022	+	3.09716i
$271$	−26536.4	+	36524.3i	−0.361330	+	0.497328i	−0.950519	−	0.310667i	$-0.899448\pi$
$271$	−26536.4	+	36524.3i	−0.361330	+	0.497328i	0.589189	+	0.807996i	$0.299448\pi$
$272$	−43083.4	−	59299.3i	−0.582335	−	0.801515i
$273$	−149454.			−2.00531
$274$		−	57513.4i		−	0.766069i
$275$	−14926.5	−	20544.6i	−0.197375	−	0.271664i
$276$	1361.06	−	4188.92i	0.0178673	−	0.0549900i
$277$	−55663.1	+	18086.0i	−0.725450	+	0.235713i	−0.648385	−	0.761313i	$-0.724555\pi$
$277$	−55663.1	+	18086.0i	−0.725450	+	0.235713i	−0.0770657	+	0.997026i	$0.524555\pi$
$278$			128430.i			1.66179i
$279$	176986.	−	40907.2i	2.27368	−	0.525522i
$280$	50817.3			0.648180
$281$	−33430.3	−	102888.i	−0.423377	−	1.30302i	−0.904540	−	0.426389i	$-0.859785\pi$
$281$	−33430.3	−	102888.i	−0.423377	−	1.30302i	0.481163	−	0.876631i	$-0.340215\pi$
$282$	−116992.	−	38012.9i	−1.47115	−	0.478006i
$283$	108960.	−	79164.1i	1.36049	−	0.988452i	0.362073	−	0.932150i	$-0.382069\pi$
$283$	108960.	−	79164.1i	1.36049	−	0.988452i	0.998414	−	0.0563021i	$-0.0179310\pi$
$284$	−48128.4			−0.596712
$285$			166234.i			2.04658i
$286$	51592.3	−	37484.0i	0.630743	−	0.458262i
$287$	30365.5	+	22061.8i	0.368652	+	0.267841i
$288$	183917.	+	133624.i	2.21737	+	1.61101i
$289$	8623.06	+	26539.1i	0.103244	+	0.317753i
$290$	74079.4	+	101962.i	0.880849	+	1.21238i
$291$	−182749.	+	59378.8i	−2.15809	+	0.701205i
$292$	15241.4	+	4952.24i	0.178756	+	0.0580813i
$293$	15165.8	+	11018.6i	0.176656	+	0.128348i	0.672600	−	0.740007i	$-0.265178\pi$
$293$	15165.8	+	11018.6i	0.176656	+	0.128348i	−0.495943	+	0.868355i	$0.665178\pi$
$294$	148838.	+	48360.2i	1.72194	+	0.559492i
$295$	7193.48	−	22139.3i	0.0826599	−	0.254401i
$296$	−38075.3	+	52406.2i	−0.434571	+	0.598135i
$297$	−48127.6	+	148122.i	−0.545609	+	1.67921i
$298$	−47542.8	−	146322.i	−0.535368	−	1.64769i
$299$	−2747.87	+	1996.44i	−0.0307364	+	0.0223313i
$300$	49900.6	−	16213.7i	0.554451	−	0.180152i
$301$	68147.4	−	93796.9i	0.752171	−	1.03527i
$302$	−108039.	+	148703.i	−1.18459	+	1.63045i
$303$	67608.5	+	93055.2i	0.736404	+	1.01357i
$304$	103976.			1.12509
$305$		−	95114.8i		−	1.02246i
$306$	136230.	+	187505.i	1.45489	+	2.00249i
$307$	37244.5	−	114627.i	0.395171	−	1.21621i	−0.533657	−	0.845701i	$-0.679183\pi$
$307$	37244.5	−	114627.i	0.395171	−	1.21621i	0.928828	−	0.370511i	$-0.120817\pi$
$308$	−59891.2	+	19459.8i	−0.631338	+	0.205134i
$309$			109922.i			1.15124i
$310$	−139095.	−	59000.9i	−1.44739	−	0.613953i
$311$	17612.1			0.182092			0.0910460	−	0.995847i	$-0.470979\pi$
$311$	17612.1			0.182092			0.0910460	+	0.995847i	$0.470979\pi$
$312$	−18335.9	−	56432.1i	−0.188362	−	0.579719i
$313$	−136146.	−	44236.5i	−1.38969	−	0.451536i	−0.483844	−	0.875154i	$-0.660760\pi$
$313$	−136146.	−	44236.5i	−1.38969	−	0.451536i	−0.905841	+	0.423618i	$0.860760\pi$
$314$	−110218.	+	80078.3i	−1.11788	+	0.812186i
$315$	−371880.			−3.74785
$316$		−	109799.i		−	1.09957i
$317$	−43544.2	+	31636.7i	−0.433323	+	0.314828i	−0.782976	−	0.622051i	$-0.786299\pi$
$317$	−43544.2	+	31636.7i	−0.433323	+	0.314828i	0.349653	+	0.936879i	$0.386299\pi$
$318$	94944.6	+	68981.3i	0.938893	+	0.682146i
$319$	56900.4	+	41340.5i	0.559157	+	0.406251i
$320$	−11961.7	−	36814.4i	−0.116814	−	0.359516i
$321$	−107066.	−	147363.i	−1.03906	−	1.43014i
$322$	7816.26	−	2539.66i	0.0753854	−	0.0244942i
$323$	75032.5	+	24379.5i	0.719191	+	0.233679i
$324$	−123683.	−	89860.9i	−1.17820	−	0.856014i
$325$	−38481.1	−	12503.3i	−0.364319	−	0.118374i
$326$	37456.0	−	115278.i	0.352441	−	1.08470i
$327$	201783.	−	277731.i	1.88708	−	2.59734i
$328$	−4604.87	+	14172.3i	−0.0428026	+	0.131733i
$329$	−28947.0	−	89089.6i	−0.267431	−	0.823067i
$330$	183386.	−	133238.i	1.68398	−	1.22349i
$331$	−1183.57	+	384.564i	−0.0108028	+	0.00351005i	−0.314413	−	0.949286i	$-0.601808\pi$
$331$	−1183.57	+	384.564i	−0.0108028	+	0.00351005i	0.303611	+	0.952796i	$0.401808\pi$
$332$	−54776.6	+	75393.5i	−0.496957	+	0.684003i
$333$	278635.	−	383508.i	2.51274	−	3.45848i
$334$	−29472.8	−	40565.8i	−0.264197	−	0.363637i
$335$	29105.6			0.259351
$336$			332279.i			2.94323i
$337$	81001.7	+	111489.i	0.713238	+	0.981687i	0.999721	+	0.0236023i	$0.00751353\pi$
$337$	81001.7	+	111489.i	0.713238	+	0.981687i	−0.286484	+	0.958085i	$0.592486\pi$
$338$	−14488.8	+	44592.0i	−0.126823	+	0.390323i
$339$	88795.4	−	28851.4i	0.772665	−	0.251054i
$340$		−	78673.6i		−	0.680567i
$341$	−83998.2	−	7327.62i	−0.722373	−	0.0630165i
$342$	−328773.			−2.81089
$343$	−11444.5	−	35222.4i	−0.0972763	−	0.299386i
$344$	43777.4	+	14224.1i	0.369941	+	0.120201i
$345$	−9767.35	+	7096.39i	−0.0820613	+	0.0596210i
$346$	134508.			1.12356
$347$			32191.7i			0.267353i	0.991025	+	0.133676i	$0.0426783\pi$
$347$			32191.7i			0.267353i	−0.991025	+	0.133676i	$0.957322\pi$
$348$	−117564.	+	85415.4i	−0.970771	+	0.705306i
$349$	−24763.6	−	17991.8i	−0.203312	−	0.147715i	0.481471	−	0.876462i	$-0.340103\pi$
$349$	−24763.6	−	17991.8i	−0.203312	−	0.147715i	−0.684783	+	0.728747i	$0.740103\pi$
$350$	79205.3	+	57546.0i	0.646574	+	0.469763i
$351$	76682.5	+	236005.i	0.622418	+	1.91561i
$352$	−62024.2	−	85368.9i	−0.500582	−	0.688992i
$353$	−61959.5	+	20131.9i	−0.497231	+	0.161560i	−0.546887	−	0.837206i	$-0.684187\pi$
$353$	−61959.5	+	20131.9i	−0.497231	+	0.161560i	0.0496562	+	0.998766i	$0.484187\pi$
$354$	62549.9	+	20323.7i	0.499138	+	0.162180i
$355$	106729.	+	77543.1i	0.846887	+	0.615299i
$356$	49427.7	+	16060.0i	0.390005	+	0.126720i
$357$	−77910.3	+	239783.i	−0.611306	+	1.88141i
$358$	59864.4	−	82396.3i	0.467092	−	0.642897i
$359$	16279.7	−	50103.6i	0.126315	−	0.388759i	−0.867823	−	0.496873i	$-0.834481\pi$
$359$	16279.7	−	50103.6i	0.126315	−	0.388759i	0.994138	+	0.108114i	$0.0344813\pi$
$360$	−45624.5	−	140418.i	−0.352041	−	1.08347i
$361$	14891.6	−	10819.4i	0.114268	−	0.0830209i
$362$	28449.8	−	9243.89i	0.217101	−	0.0705404i
$363$	−67059.1	+	92298.9i	−0.508914	+	0.700460i
$364$	−58976.3	+	81174.0i	−0.445118	+	0.612652i
$365$	−25820.3	−	35538.6i	−0.193810	−	0.266756i
$366$	268727.			2.00609
$367$		−	31847.8i		−	0.236455i	−0.992987	−	0.118227i	$-0.962279\pi$
$367$		−	31847.8i		−	0.236455i	0.992987	−	0.118227i	$-0.0377211\pi$
$368$	4438.66	+	6109.30i	0.0327761	+	0.0451124i
$369$	33698.4	−	103713.i	0.247489	−	0.761693i
$370$	−374992.	+	121842.i	−2.73916	+	0.890008i
$371$			89368.5i			0.649287i
$372$	68029.5	−	160380.i	0.491600	−	1.15895i
$373$	20845.9			0.149832			0.0749158	−	0.997190i	$-0.476131\pi$
$373$	20845.9			0.149832			0.0749158	+	0.997190i	$0.476131\pi$
$374$	−33244.1	−	102315.i	−0.237668	−	0.731468i
$375$	158585.	+	51527.5i	1.12772	+	0.366418i
$376$	30087.9	−	21860.1i	0.212822	−	0.154624i
$377$	112062.			0.788455
$378$		−	600439.i		−	4.20228i
$379$	−141917.	+	103109.i	−0.988000	+	0.717824i	−0.959482	−	0.281769i	$-0.909079\pi$
$379$	−141917.	+	103109.i	−0.988000	+	0.717824i	−0.0285182	+	0.999593i	$0.509079\pi$
$380$	90287.6	+	65597.8i	0.625260	+	0.454278i
$381$	169509.	+	123156.i	1.16773	+	0.848408i
$382$	75185.3	+	231397.i	0.515236	+	1.58573i
$383$	28773.3	+	39603.0i	0.196152	+	0.269980i	0.895751	−	0.444555i	$-0.146638\pi$
$383$	28773.3	+	39603.0i	0.196152	+	0.269980i	−0.699600	+	0.714535i	$0.746638\pi$
$384$	−196718.	+	63917.6i	−1.33408	+	0.433469i
$385$	164167.	+	53341.2i	1.10755	+	0.359866i
$386$	55810.7	+	40548.9i	0.374579	+	0.272147i
$387$	−320362.	−	104092.i	−2.13904	−	0.695017i
$388$	−39864.2	+	122689.i	−0.264801	+	0.814974i
$389$	23735.6	−	32669.2i	0.156856	−	0.215894i	−0.723355	−	0.690476i	$-0.757401\pi$
$389$	23735.6	−	32669.2i	0.156856	−	0.215894i	0.880211	+	0.474583i	$0.157401\pi$
$390$	111607.	−	343492.i	0.733776	−	2.25833i
$391$	1770.62	+	5449.41i	0.0115817	+	0.0356448i
$392$	−38277.9	+	27810.6i	−0.249102	+	0.180983i
$393$	−107083.	+	34793.5i	−0.693325	+	0.225275i
$394$	123520.	−	170011.i	0.795692	−	1.09518i
$395$	−176905.	+	243488.i	−1.13382	+	1.56057i
$396$	107542.	+	148019.i	0.685787	+	0.943905i
$397$	−231014.			−1.46574			−0.732871	−	0.680367i	$-0.761820\pi$
$397$	−231014.			−1.46574			−0.732871	+	0.680367i	$0.761820\pi$
$398$		−	85877.1i		−	0.542140i
$399$	−210220.	−	289342.i	−1.32047	−	1.81747i
$400$	−27798.4	+	85554.7i	−0.173740	+	0.534717i
$401$	144442.	−	46932.0i	0.898264	−	0.291864i	0.176744	−	0.984257i	$-0.443444\pi$
$401$	144442.	−	46932.0i	0.898264	−	0.291864i	0.721520	+	0.692393i	$0.243444\pi$
$402$			82231.9i			0.508848i
$403$	−115138.	+	69221.3i	−0.708938	+	0.426216i
$404$	77220.9			0.473121
$405$	129496.	+	398549.i	0.789492	+	2.42981i
$406$	−257882.	−	83790.9i	−1.56448	−	0.508329i
$407$	−178013.	+	129334.i	−1.07464	+	0.780771i
$408$	−100098.			−0.601319
$409$		−	65916.3i		−	0.394045i	−0.980399	−	0.197023i	$-0.936873\pi$
$409$		−	65916.3i		−	0.394045i	0.980399	−	0.197023i	$-0.0631273\pi$
$410$	−73380.9	+	53314.3i	−0.436531	+	0.317158i
$411$	−147058.	−	106844.i	−0.870573	−	0.632508i
$412$	59702.7	+	43376.5i	0.351722	+	0.255541i
$413$	15476.6	+	47632.0i	0.0907350	+	0.279254i
$414$	−14035.1	−	19317.7i	−0.0818870	−	0.112708i
$415$	242944.	−	78937.3i	1.41062	−	0.458338i
$416$	−159901.	−	51954.9i	−0.923983	−	0.300220i
$417$	328386.	+	238586.i	1.88848	+	1.37206i
$418$	145138.	+	47158.1i	0.830668	+	0.269901i
$419$	80368.6	−	247349.i	0.457781	−	1.40891i	−0.410057	−	0.912060i	$-0.634491\pi$
$419$	80368.6	−	247349.i	0.457781	−	1.40891i	0.867838	−	0.496846i	$-0.165509\pi$
$420$	−209633.	+	288535.i	−1.18839	+	1.63568i
$421$	37944.7	−	116782.i	0.214085	−	0.658887i	−0.785132	−	0.619328i	$-0.787405\pi$
$421$	37944.7	−	116782.i	0.214085	−	0.658887i	0.999217	−	0.0395582i	$-0.0125950\pi$
$422$	37243.2	+	114623.i	0.209133	+	0.643645i
$423$	−220182.	+	159972.i	−1.23056	+	0.894053i
$424$	−33744.6	+	10964.3i	−0.187703	+	0.0609885i
$425$	−40120.4	+	55221.1i	−0.222120	+	0.305722i
$426$	−219082.	+	301541.i	−1.20722	+	1.66160i
$427$	120282.	+	165555.i	0.659700	+	0.907999i
$428$	−122288.			−0.667567
$429$		−	201553.i		−	1.09515i
$430$	164684.	+	226669.i	0.890667	+	1.22590i
$431$	86241.9	−	265425.i	0.464263	−	1.42885i	−0.395645	−	0.918404i	$-0.629479\pi$
$431$	86241.9	−	265425.i	0.464263	−	1.42885i	0.859907	−	0.510450i	$-0.170521\pi$
$432$	524706.	−	170487.i	2.81157	−	0.913534i
$433$			190941.i			1.01841i	0.860645	+	0.509205i	$0.170060\pi$
$433$			190941.i			1.01841i	−0.860645	+	0.509205i	$0.829940\pi$
$434$	316718.	−	73203.9i	1.68148	−	0.388646i
$435$	398328.			2.10505
$436$	−71219.8	−	219192.i	−0.374652	−	1.15306i
$437$	−7730.21	−	2511.70i	−0.0404789	−	0.0131524i
$438$	100407.	−	72950.0i	0.523379	−	0.380257i
$439$	−95224.4			−0.494105			−0.247053	−	0.969002i	$-0.579462\pi$
$439$	−95224.4			−0.494105			−0.247053	+	0.969002i	$0.579462\pi$
$440$			68531.9i			0.353987i
$441$	280117.	−	203517.i	1.44033	−	1.04646i
$442$	−138673.	−	100752.i	−0.709819	−	0.515714i
$443$	−270148.	−	196274.i	−1.37656	−	1.00013i	−0.997193	−	0.0748777i	$-0.976143\pi$
$443$	−270148.	−	196274.i	−1.37656	−	1.00013i	−0.379362	−	0.925248i	$-0.623857\pi$
$444$	−140487.	−	432375.i	−0.712640	−	2.19328i
$445$	−83734.7	−	115251.i	−0.422849	−	0.582002i
$446$	63947.9	−	20777.9i	0.321482	−	0.104456i
$447$	−462456.	−	150261.i	−2.31449	−	0.752024i
$448$	67375.9	+	48951.5i	0.335698	+	0.243899i
$449$	−327612.	−	106447.i	−1.62505	−	0.528011i	−0.651924	−	0.758285i	$-0.726038\pi$
$449$	−327612.	−	106447.i	−1.62505	−	0.528011i	−0.973126	+	0.230274i	$0.926038\pi$
$450$	87898.9	−	270525.i	0.434068	−	1.33593i
$451$	−29752.4	+	40950.7i	−0.146275	+	0.201330i
$452$	19369.5	−	59613.2i	0.0948073	−	0.291787i
$453$	179518.	+	552499.i	0.874805	+	2.69237i
$454$	−155042.	+	112644.i	−0.752206	+	0.546510i
$455$	261570.	−	84989.4i	1.26347	−	0.410527i
$456$	83461.4	−	114875.i	0.401380	−	0.552453i
$457$	201919.	−	277917.i	0.966816	−	1.33071i	0.0231767	−	0.999731i	$-0.492622\pi$
$457$	201919.	−	277917.i	0.966816	−	1.33071i	0.943639	−	0.330976i	$-0.107378\pi$
$458$	−34809.8	−	47911.5i	−0.165947	−	0.228407i
$459$	418619.			1.98698
$460$			8105.33i			0.0383050i
$461$	−31279.2	−	43052.2i	−0.147182	−	0.202578i	0.729060	−	0.684449i	$-0.239957\pi$
$461$	−31279.2	−	43052.2i	−0.147182	−	0.202578i	−0.876242	+	0.481871i	$0.839957\pi$
$462$	−150705.	+	463821.i	−0.706061	+	2.17303i
$463$	−292512.	+	95042.8i	−1.36452	+	0.443361i	−0.897551	−	0.440911i	$-0.854656\pi$
$463$	−292512.	+	95042.8i	−1.36452	+	0.443361i	−0.466973	+	0.884272i	$0.654656\pi$
$464$		−	249147.i		−	1.15723i
$465$	−409260.	+	246049.i	−1.89275	+	1.13793i
$466$	411631.			1.89556
$467$	−84285.1	−	259403.i	−0.386471	−	1.18944i	−0.935407	−	0.353572i	$-0.884967\pi$
$467$	−84285.1	−	259403.i	−0.386471	−	1.18944i	0.548936	−	0.835864i	$-0.315033\pi$
$468$	277249.	+	90083.6i	1.26584	+	0.411296i
$469$	−50660.6	+	36807.1i	−0.230316	+	0.167334i
$470$	226373.			1.02477
$471$			430584.i			1.94096i
$472$	−16086.6	+	11687.6i	−0.0722069	+	0.0524614i
$473$	126494.	+	91903.3i	0.565389	+	0.410779i
$474$	−687927.	−	499808.i	−3.06186	−	2.22457i
$475$	−29920.7	−	92086.3i	−0.132612	−	0.408139i
$476$	99490.9	+	136937.i	0.439106	+	0.604377i
$477$	246942.	−	80236.4i	1.08532	−	0.352642i
$478$	296320.	+	96280.3i	1.29690	+	0.421388i
$479$	96057.5	+	69789.8i	0.418659	+	0.304173i	0.777098	−	0.629380i	$-0.216691\pi$
$479$	96057.5	+	69789.8i	0.418659	+	0.304173i	−0.358439	+	0.933553i	$0.616691\pi$
$480$	−568371.	−	184675.i	−2.46689	−	0.801541i
$481$	−108337.	+	333428.i	−0.468261	+	1.44116i
$482$	18626.8	−	25637.6i	0.0801760	−	0.110353i
$483$	8026.70	−	24703.6i	0.0344067	−	0.105893i
$484$	23668.6	+	72844.5i	0.101037	+	0.310961i
$485$	286076.	−	207846.i	1.21618	−	0.883607i
$486$	−415052.	+	134859.i	−1.75723	+	0.570960i
$487$	−37745.2	+	51951.8i	−0.159149	+	0.219050i	−0.881143	−	0.472849i	$-0.843226\pi$
$487$	−37745.2	+	51951.8i	−0.159149	+	0.219050i	0.721995	+	0.691899i	$0.243226\pi$
$488$	−47754.6	+	65728.6i	−0.200528	+	0.276003i
$489$	−225175.	−	309927.i	−0.941678	−	1.29611i
$490$	−287992.			−1.19947
$491$			38515.8i			0.159763i	0.996804	+	0.0798814i	$0.0254542\pi$
$491$			38515.8i			0.159763i	−0.996804	+	0.0798814i	$0.974546\pi$
$492$	−61472.8	−	84610.0i	−0.253953	−	0.349536i
$493$	58418.1	−	179792.i	0.240355	−	0.739737i
$494$	231250.	−	75137.8i	0.947608	−	0.307896i
$495$		−	501516.i		−	2.04679i
$496$	153899.	+	255985.i	0.625565	+	1.04052i
$497$	−283831.			−1.14907
$498$	223021.	+	686388.i	0.899264	+	2.76765i
$499$	54706.0	+	17775.1i	0.219702	+	0.0713855i	0.416800	−	0.908998i	$-0.363152\pi$
$499$	54706.0	+	17775.1i	0.219702	+	0.0713855i	−0.197098	+	0.980384i	$0.563152\pi$
$500$	90566.3	−	65800.2i	0.362265	−	0.263201i
$501$	−158476.			−0.631378
$502$			62540.8i			0.248174i
$503$	−15050.0	+	10934.5i	−0.0594841	+	0.0432178i	−0.617130	−	0.786861i	$-0.711705\pi$
$503$	−15050.0	+	10934.5i	−0.0594841	+	0.0432178i	0.557646	+	0.830079i	$0.311705\pi$
$504$	256986.	+	186711.i	1.01169	+	0.735037i
$505$	−171244.	−	124416.i	−0.671479	−	0.487858i
$506$	3424.97	+	10541.0i	0.0133769	+	0.0411699i
$507$	87102.7	+	119887.i	0.338856	+	0.466396i
$508$	133781.	−	43468.0i	0.518402	−	0.168439i
$509$	270059.	+	87747.6i	1.04237	+	0.338688i	0.779671	−	0.626189i	$-0.215386\pi$
$509$	270059.	+	87747.6i	1.04237	+	0.338688i	0.262703	+	0.964877i	$0.415386\pi$
$510$	−492917.	−	358125.i	−1.89510	−	1.37687i
$511$	89884.5	+	29205.2i	0.344225	+	0.111846i
$512$	−75817.5	+	233342.i	−0.289221	+	0.890130i
$513$	−349044.	+	480417.i	−1.32631	+	1.82551i
$514$	−195381.	+	601321.i	−0.739531	+	2.27604i
$515$	−62508.9	−	192383.i	−0.235682	−	0.725356i
$516$	−261355.	+	189885.i	−0.981591	+	0.713168i
$517$	120146.	−	39037.7i	0.449498	−	0.146051i
$518$	498620.	−	686291.i	1.85828	−	2.55770i
$519$	249878.	−	343928.i	0.927670	−	1.27683i
$520$	64182.1	+	88339.1i	0.237360	+	0.326698i
$521$	435906.			1.60590			0.802949	−	0.596048i	$-0.203263\pi$
$521$	435906.			1.60590			0.802949	+	0.596048i	$0.203263\pi$
$522$			787805.i			2.89120i
$523$	−108962.	−	149973.i	−0.398356	−	0.548290i	0.561974	−	0.827155i	$-0.310042\pi$
$523$	−108962.	−	149973.i	−0.398356	−	0.548290i	−0.960330	+	0.278865i	$0.910042\pi$
$524$	−23358.8	+	71890.9i	−0.0850721	+	0.261825i
$525$	294283.	−	95618.3i	1.06769	−	0.346914i
$526$		−	713148.i		−	2.57756i
$527$	51036.9	+	220812.i	0.183765	+	0.795063i
$528$	−448110.			−1.60737
$529$	86293.2	+	265583.i	0.308365	+	0.949050i
$530$	−205397.	−	66737.5i	−0.731210	−	0.237585i
$531$	117721.	−	85529.4i	0.417509	−	0.303338i
$532$	−240108.			−0.848365
$533$			80650.3i			0.283891i
$534$	325618.	−	236575.i	1.14189	−	0.829635i
$535$	271184.	+	197026.i	0.947449	+	0.688362i
$536$	−20113.3	−	14613.2i	−0.0700089	−	0.0508645i
$537$	−99470.5	−	306139.i	−0.344942	−	1.06162i
$538$	−143569.	−	197606.i	−0.496016	−	0.682707i
$539$	−152850.	+	49664.0i	−0.526124	+	0.170948i
$540$	563188.	+	182991.i	1.93137	+	0.627541i
$541$	−203893.	−	148137.i	−0.696638	−	0.506137i	0.182197	−	0.983262i	$-0.441679\pi$
$541$	−203893.	−	148137.i	−0.696638	−	0.506137i	−0.878836	+	0.477125i	$0.841679\pi$
$542$	223239.	+	72534.6i	0.759925	+	0.246915i
$543$	29215.7	−	89916.8i	0.0990871	−	0.304959i
$544$	−166713.	+	229460.i	−0.563340	+	0.775371i
$545$	−195220.	+	600825.i	−0.657250	+	2.02281i
$546$	240120.	+	739014.i	0.805458	+	2.47895i
$547$	−140925.	+	102388.i	−0.470993	+	0.342196i	−0.797828	−	0.602885i	$-0.794018\pi$
$547$	−140925.	+	102388.i	−0.470993	+	0.342196i	0.326835	+	0.945081i	$0.394018\pi$
$548$	−116062.	+	37710.7i	−0.386481	+	0.125575i
$549$	349467.	−	481001.i	1.15948	−	1.59588i
$550$	−77606.3	+	106816.i	−0.256550	+	0.353110i
$551$	157625.	+	216952.i	0.519185	+	0.714597i
$552$	10312.6			0.0338446
$553$		−	647525.i		−	2.11742i
$554$	178862.	+	246183.i	0.582772	+	0.802117i
$555$	−385088.	+	1.18518e6i	−1.25018	+	3.84767i
$556$	259170.	−	84209.5i	0.838370	−	0.272403i
$557$		−	260021.i		−	0.838105i	−0.907962	−	0.419052i	$-0.862362\pi$
$557$		−	260021.i		−	0.838105i	0.907962	−	0.419052i	$-0.137638\pi$
$558$	−486630.	−	809427.i	−1.56290	−	2.59962i
$559$	249123.			0.797243
$560$	−188956.	−	581547.i	−0.602538	−	1.85442i
$561$	−323371.	−	105070.i	−1.02748	−	0.333850i
$562$	−455044.	+	330609.i	−1.44073	+	1.04675i
$563$	11668.9			0.0368139			0.0184069	−	0.999831i	$-0.494141\pi$
$563$	11668.9			0.0368139			0.0184069	+	0.999831i	$0.494141\pi$
$564$			261013.i			0.820549i
$565$	−139001.	+	100990.i	−0.435432	+	0.316360i
$566$	−566508.	−	411592.i	−1.76837	−	1.28480i
$567$	−729405.	−	529944.i	−2.26883	−	1.64840i
$568$	−34822.1	−	107172.i	−0.107934	−	0.332187i
$569$	249335.	+	343181.i	0.770122	+	1.05998i	0.996304	+	0.0858969i	$0.0273756\pi$
$569$	249335.	+	343181.i	0.770122	+	1.05998i	−0.226182	+	0.974085i	$0.572624\pi$
$570$	821985.	−	267079.i	2.52996	−	0.822034i
$571$	83742.9	+	27209.7i	0.256848	+	0.0834549i	0.434611	−	0.900618i	$-0.356886\pi$
$571$	83742.9	+	27209.7i	0.256848	+	0.0834549i	−0.177763	+	0.984073i	$0.556886\pi$
$572$	−109471.	−	79535.2i	−0.334585	−	0.243090i
$573$	731339.	+	237627.i	2.22746	+	0.723745i
$574$	60303.6	−	185595.i	0.183029	−	0.563305i
$575$	4133.40	−	5689.14i	0.0125018	−	0.0172072i
$576$	74771.1	−	230122.i	0.225366	−	0.693606i
$577$	−87504.5	−	269311.i	−0.262832	−	0.808915i	−0.992185	−	0.124777i	$-0.960179\pi$
$577$	−87504.5	−	269311.i	−0.262832	−	0.808915i	0.729353	−	0.684138i	$-0.239821\pi$
$578$	117375.	−	85277.9i	0.351334	−	0.255259i
$579$	207362.	−	67375.9i	0.618545	−	0.200977i
$580$	157185.	−	216347.i	0.467256	−	0.643123i
$581$	−323038.	+	444624.i	−0.956978	+	1.31717i
$582$	587227.	+	808249.i	1.73365	+	2.38616i
$583$	−120522.			−0.354592
$584$			37522.5i			0.110018i
$585$	−469683.	−	646464.i	−1.37244	−	1.88900i
$586$	30118.1	−	92694.0i	0.0877067	−	0.269933i
$587$	−130632.	+	42444.8i	−0.379116	+	0.123182i	−0.492375	−	0.870383i	$-0.663871\pi$
$587$	−130632.	+	42444.8i	−0.379116	+	0.123182i	0.113259	+	0.993566i	$0.463871\pi$
$588$		−	332063.i		−	0.960429i
$589$	−295963.	−	125541.i	−0.853115	−	0.361873i
$590$	−121031.			−0.347689
$591$	−205240.	−	631665.i	−0.587608	−	1.80847i
$592$	741307.	+	240865.i	2.11522	+	0.687276i
$593$	−282044.	+	204917.i	−0.802062	+	0.582732i	−0.911518	−	0.411259i	$-0.865089\pi$
$593$	−282044.	+	204917.i	−0.802062	+	0.582732i	0.109456	+	0.993992i	$0.465089\pi$
$594$	809749.			2.29497
$595$		−	463968.i		−	1.31055i
$596$	−264103.	+	191882.i	−0.743501	+	0.540185i
$597$	−219582.	−	159536.i	−0.616096	−	0.447620i
$598$	14286.8	+	10379.9i	0.0399514	+	0.0290264i
$599$	−33742.5	−	103849.i	−0.0940423	−	0.289432i	0.892961	−	0.450135i	$-0.148624\pi$
$599$	−33742.5	−	103849.i	−0.0940423	−	0.289432i	−0.987003	+	0.160702i	$0.948624\pi$
$600$	72208.8	+	99386.9i	0.200580	+	0.276075i
$601$	359670.	−	116864.i	0.995760	−	0.323542i	0.234590	−	0.972094i	$-0.424625\pi$
$601$	359670.	−	116864.i	0.995760	−	0.323542i	0.761170	+	0.648552i	$0.224625\pi$
$602$	−573292.	−	186274.i	−1.58191	−	0.513995i
$603$	147189.	+	106939.i	0.404799	+	0.294104i
$604$	370923.	+	120520.i	1.01674	+	0.330358i
$605$	64877.8	−	199673.i	0.177250	−	0.545518i
$606$	351512.	−	483815.i	0.957183	−	1.31745i
$607$	145868.	−	448936.i	0.395898	−	1.21845i	−0.532362	−	0.846517i	$-0.678696\pi$
$607$	145868.	−	448936.i	0.395898	−	1.21845i	0.928260	−	0.371932i	$-0.121304\pi$
$608$	−124329.	−	382646.i	−0.336331	−	1.03512i
$609$	−693321.	+	503727.i	−1.86939	+	1.35819i
$610$	−470320.	+	152816.i	−1.26396	+	0.410686i
$611$	118311.	−	162840.i	0.316914	−	0.436194i
$612$	289060.	−	397856.i	0.771764	−	1.06224i
$613$	−203327.	−	279856.i	−0.541096	−	0.744755i	0.447674	−	0.894197i	$-0.352252\pi$
$613$	−203327.	−	279856.i	−0.541096	−	0.744755i	−0.988771	+	0.149441i	$0.952252\pi$
$614$	−626640.			−1.66219
$615$			286673.i			0.757944i
$616$	−86665.7	−	119285.i	−0.228395	−	0.314358i
$617$	−154290.	+	474857.i	−0.405292	+	1.24736i	0.515358	+	0.856975i	$0.327659\pi$
$617$	−154290.	+	474857.i	−0.405292	+	1.24736i	−0.920651	+	0.390387i	$0.872341\pi$
$618$	543537.	−	176606.i	1.42316	−	0.462411i
$619$			704235.i			1.83796i	0.394302	+	0.918981i	$0.370986\pi$
$619$			704235.i			1.83796i	−0.394302	+	0.918981i	$0.629014\pi$
$620$	−27861.1	+	319378.i	−0.0724794	+	0.830849i
$621$	−43128.2			−0.111835
$622$	−28296.5	−	87087.7i	−0.0731395	−	0.225100i
$623$	291494.	+	94712.0i	0.751022	+	0.244022i
$624$	−577623.	+	419668.i	−1.48346	+	1.07780i
$625$	−487749.			−1.24864
$626$			744282.i			1.89928i
$627$	390206.	−	283501.i	0.992564	−	0.721140i
$628$	233866.	+	169914.i	0.592991	+	0.430833i
$629$	478475.	+	347632.i	1.20937	+	0.878656i
$630$	597481.	+	1.83886e6i	1.50537	+	4.63305i
$631$	−156910.	−	215969.i	−0.394088	−	0.542415i	0.565160	−	0.824981i	$-0.308814\pi$
$631$	−156910.	−	215969.i	−0.394088	−	0.542415i	−0.959248	+	0.282566i	$0.908814\pi$
$632$	244498.	−	79442.3i	0.612127	−	0.198892i
$633$	362271.	+	117709.i	0.904120	+	0.293766i
$634$	226396.	+	164486.i	0.563236	+	0.409215i
$635$	−366705.	−	119150.i	−0.909431	−	0.295492i
$636$	76950.0	−	236828.i	0.190237	−	0.585489i
$637$	−150515.	+	207166.i	−0.370938	+	0.510553i
$638$	113000.	−	347778.i	0.277611	−	0.854400i
$639$	254828.	+	784280.i	0.624087	+	1.92074i
$640$	307943.	−	223734.i	0.751814	−	0.546225i
$641$	286517.	−	93095.1i	0.697325	−	0.226574i	0.0611601	−	0.998128i	$-0.480520\pi$
$641$	286517.	−	93095.1i	0.697325	−	0.226574i	0.636164	+	0.771554i	$0.280520\pi$
$642$	−556658.	+	766174.i	−1.35057	+	1.85891i
$643$	−61486.1	+	84628.4i	−0.148715	+	0.204689i	−0.876875	−	0.480719i	$-0.840376\pi$
$643$	−61486.1	+	84628.4i	−0.148715	+	0.204689i	0.728160	+	0.685407i	$0.240376\pi$
$644$	−10250.0	−	14108.0i	−0.0247146	−	0.0340167i
$645$	885515.			2.12851
$646$		−	410187.i		−	0.982916i
$647$	432205.	+	594880.i	1.03248	+	1.42109i	0.903069	+	0.429496i	$0.141309\pi$
$647$	432205.	+	594880.i	1.03248	+	1.42109i	0.129411	+	0.991591i	$0.458691\pi$
$648$	110613.	−	340432.i	0.263424	−	0.810737i
$649$	−64236.3	+	20871.6i	−0.152507	+	0.0495527i
$650$			210368.i			0.497913i
$651$	401196.	−	945819.i	0.946661	−	2.23175i
$652$	−257189.			−0.605003
$653$	232757.	+	716352.i	0.545853	+	1.67996i	0.718952	+	0.695059i	$0.244622\pi$
$653$	232757.	+	716352.i	0.545853	+	1.67996i	−0.173099	+	0.984904i	$0.555378\pi$
$654$	−1.69751e6	−	551553.i	−3.96877	−	1.28953i
$655$	167629.	−	121789.i	0.390720	−	0.283875i
$656$	179309.			0.416672
$657$		−	274589.i		−	0.636139i
$658$	−394019.	+	286272.i	−0.910050	+	0.661190i
$659$	−607414.	−	441312.i	−1.39867	−	1.01619i	−0.994851	−	0.101350i	$-0.967684\pi$
$659$	−607414.	−	441312.i	−1.39867	−	1.01619i	−0.403815	−	0.914841i	$-0.632316\pi$
$660$	−389116.	−	282710.i	−0.893288	−	0.649012i
$661$	−126873.	−	390476.i	−0.290380	−	0.893699i	−0.984734	−	0.174065i	$-0.944310\pi$
$661$	−126873.	−	390476.i	−0.290380	−	0.893699i	0.694354	−	0.719634i	$-0.255690\pi$
$662$	3803.16	+	5234.60i	0.00867817	+	0.0119445i
$663$	−515232.	+	167409.i	−1.17213	+	0.380848i
$664$	−207517.	−	67426.5i	−0.470672	−	0.152931i
$665$	532460.	+	386855.i	1.20405	+	0.874792i
$666$	−2.34402e6	−	761619.i	−5.28461	−	1.71707i
$667$	−6018.51	+	18523.1i	−0.0135281	+	0.0416353i
$668$	−62536.7	+	86074.4i	−0.140147	+	0.192895i
$669$	65669.6	−	202110.i	0.146728	−	0.451582i
$670$	−46762.5	−	143920.i	−0.104171	−	0.320606i
$671$	−223266.	+	162212.i	−0.495882	+	0.360279i
$672$	1.22283e6	−	397323.i	2.70788	−	0.879843i
$673$	412081.	−	567180.i	0.909813	−	1.25225i	−0.0574178	−	0.998350i	$-0.518287\pi$
$673$	412081.	−	567180.i	0.909813	−	1.25225i	0.967231	−	0.253900i	$-0.0817133\pi$
$674$	421146.	−	579658.i	0.927071	−	1.27600i
$675$	−301984.	−	415645.i	−0.662791	−	0.912253i
$676$	99486.6			0.217706
$677$			590615.i			1.28863i	0.764762	+	0.644313i	$0.222857\pi$
$677$			590615.i			1.28863i	−0.764762	+	0.644313i	$0.777143\pi$
$678$	−285326.	−	392718.i	−0.620701	−	0.854322i
$679$	−235094.	+	723546.i	−0.509920	+	1.56937i
$680$	175189.	−	56922.4i	0.378869	−	0.123102i
$681$			605693.i			1.30605i
$682$	98722.4	+	427124.i	0.212250	+	0.918301i
$683$	−257573.			−0.552152			−0.276076	−	0.961136i	$-0.589034\pi$
$683$	−257573.			−0.552152			−0.276076	+	0.961136i	$0.589034\pi$
$684$	215572.	+	663463.i	0.460766	+	1.41809i
$685$	318136.	+	103369.i	0.678002	+	0.220296i
$686$	−155779.	+	113180.i	−0.331025	+	0.240504i
$687$	−187174.			−0.396580
$688$		−	553873.i		−	1.17013i
$689$	−155355.	+	112872.i	−0.327256	+	0.237765i
$690$	50782.6	+	36895.8i	0.106664	+	0.0774958i
$691$	355965.	+	258624.i	0.745506	+	0.541642i	0.894431	−	0.447207i	$-0.147581\pi$
$691$	355965.	+	258624.i	0.745506	+	0.541642i	−0.148925	+	0.988849i	$0.547581\pi$
$692$	−88194.9	−	271436.i	−0.184175	−	0.566833i
$693$	634218.	+	872927.i	1.32060	+	1.81765i
$694$	159180.	−	51720.8i	0.330499	−	0.107386i
$695$	−710409.	−	230826.i	−1.47075	−	0.477876i
$696$	−275262.	−	199990.i	−0.568236	−	0.412847i
$697$	129395.	+	42043.0i	0.266350	+	0.0865423i
$698$	−49178.7	+	151357.i	−0.100941	+	0.310664i
$699$	764697.	−	1.05251e6i	1.56507	−	2.15414i
$700$	64193.8	−	197568.i	0.131008	−	0.403200i
$701$	43604.5	+	134201.i	0.0887350	+	0.273098i	0.985570	−	0.169266i	$-0.0541397\pi$
$701$	43604.5	+	134201.i	0.0887350	+	0.273098i	−0.896835	+	0.442365i	$0.854140\pi$
$702$	1.04378e6	−	758353.i	2.11805	−	1.53885i
$703$	−797902.	+	259254.i	−1.61450	+	0.524584i
$704$	−66015.7	+	90862.9i	−0.133199	+	0.183333i
$705$	420537.	−	578820.i	0.846109	−	1.16457i
$706$	199094.	+	274030.i	0.399438	+	0.549779i
$707$	455401.			0.911076
$708$		−	139551.i		−	0.278399i
$709$	255655.	+	351879.i	0.508583	+	0.700005i	0.983680	−	0.179929i	$-0.0575869\pi$
$709$	255655.	+	351879.i	0.508583	+	0.700005i	−0.475097	+	0.879934i	$0.657587\pi$
$710$	211956.	−	652333.i	0.420464	−	1.29406i
$711$	−1.78923e6	+	581357.i	−3.53939	+	1.15002i
$712$			121685.i			0.240035i
$713$	−5258.07	−	22749.1i	−0.0103430	−	0.0447492i
$714$	1.31085e6			2.57131
$715$	114616.	+	352753.i	0.224199	+	0.690014i
$716$	−205528.	−	66780.0i	−0.400907	−	0.130263i
$717$	796663.	−	578810.i	1.54966	−	1.12589i
$718$	−273906.			−0.531316
$719$		−	698940.i		−	1.35202i	−0.736894	−	0.676009i	$-0.763708\pi$
$719$		−	698940.i		−	1.35202i	0.736894	−	0.676009i	$-0.236292\pi$
$720$	−1.43728e6	+	1.04424e6i	−2.77252	+	2.01436i
$721$	352089.	+	255808.i	0.677302	+	0.492089i
$722$	−77424.7	−	56252.3i	−0.148527	−	0.107911i
$723$	−30950.2	−	95255.1i	−0.0592090	−	0.182226i
$724$	−37308.3	−	51350.4i	−0.0711750	−	0.0979640i
$725$	−220657.	+	71695.7i	−0.419799	+	0.136401i
$726$	564136.	+	183299.i	1.07031	+	0.347766i
$727$	708778.	+	514958.i	1.34104	+	0.974322i	0.999405	+	0.0344893i	$0.0109805\pi$
$727$	708778.	+	514958.i	1.34104	+	0.974322i	0.341634	+	0.939833i	$0.389020\pi$
$728$	−223428.	−	72596.1i	−0.421575	−	0.136978i
$729$	−79356.3	+	244234.i	−0.149323	+	0.459569i
$730$	−134246.	+	184773.i	−0.251915	+	0.346732i
$731$	129868.	−	399693.i	0.243034	−	0.747983i
$732$	−176201.	−	542290.i	−0.328841	−	1.01207i
$733$	215462.	−	156542.i	0.401017	−	0.291356i	−0.368938	−	0.929454i	$-0.620279\pi$
$733$	215462.	−	156542.i	0.401017	−	0.291356i	0.769955	+	0.638098i	$0.220279\pi$
$734$	−157480.	+	51168.3i	−0.292303	+	0.0949749i
$735$	−535010.	+	736378.i	−0.990346	+	1.36309i
$736$	17175.5	−	23640.1i	0.0317070	−	0.0436409i
$737$	−49637.8	−	68320.6i	−0.0913856	−	0.125781i
$738$	−566977.			−1.04100
$739$			386604.i			0.707909i	0.935263	+	0.353955i	$0.115163\pi$
$739$			386604.i			0.707909i	−0.935263	+	0.353955i	$0.884837\pi$
$740$	491754.	+	676841.i	0.898016	+	1.23601i
$741$	237476.	−	730877.i	0.432498	−	1.33109i
$742$	441906.	−	143584.i	0.802642	−	0.260794i
$743$		−	597383.i		−	1.08212i	−0.840984	−	0.541060i	$-0.818023\pi$
$743$		−	597383.i		−	1.08212i	0.840984	−	0.541060i	$-0.181977\pi$
$744$	406352.	+	35448.3i	0.734102	+	0.0640397i
$745$	894828.			1.61223
$746$	−33492.1	−	103078.i	−0.0601817	−	0.185220i
$747$	1.51861e6	+	493426.i	2.72148	+	0.884262i
$748$	−184673.	+	134173.i	−0.330066	+	0.239807i
$749$	−721177.			−1.28552
$750$		−	866953.i		−	1.54125i
$751$	243742.	−	177089.i	0.432165	−	0.313986i	−0.350349	−	0.936619i	$-0.613937\pi$
$751$	243742.	−	177089.i	0.432165	−	0.313986i	0.782514	+	0.622633i	$0.213937\pi$
$752$	−362041.	−	263038.i	−0.640210	−	0.465140i
$753$	159913.	+	116183.i	0.282028	+	0.204906i
$754$	−180045.	−	554121.i	−0.316693	−	0.974680i
$755$	−628375.	−	864884.i	−1.10236	−	1.51727i
$756$	−1.21168e6	+	393700.i	−2.12005	+	0.688845i
$757$	−295884.	−	96138.7i	−0.516333	−	0.167767i	0.0392472	−	0.999230i	$-0.487504\pi$
$757$	−295884.	−	96138.7i	−0.516333	−	0.167767i	−0.555581	+	0.831463i	$0.687504\pi$
$758$	737861.	+	536087.i	1.28421	+	0.933033i
$759$	33315.2	+	10824.8i	0.0578308	+	0.0187904i
$760$	−80746.7	+	248513.i	−0.139797	+	0.430250i
$761$	−296392.	+	407949.i	−0.511797	+	0.704428i	−0.984221	−	0.176944i	$-0.943379\pi$
$761$	−296392.	+	407949.i	−0.511797	+	0.704428i	0.472424	+	0.881371i	$0.343379\pi$
$762$	336633.	−	1.03605e6i	0.579758	−	1.78431i
$763$	−420010.	−	1.29266e6i	−0.721457	−	2.22042i
$764$	417659.	−	303447.i	0.715542	−	0.519872i
$765$	−1.28203e6	+	416557.i	−2.19066	+	0.711789i
$766$	149599.	−	205905.i	0.254959	−	0.350921i
$767$	−63255.0	+	87063.1i	−0.107524	+	0.147994i
$768$	829936.	+	1.14231e6i	1.40709	+	1.93669i
$769$	−1.09375e6			−1.84955			−0.924776	−	0.380512i	$-0.875748\pi$
$769$	−1.09375e6			−1.84955			−0.924776	+	0.380512i	$0.875748\pi$
$770$		−	897468.i		−	1.51369i
$771$	1.17457e6	+	1.61666e6i	1.97593	+	2.71964i
$772$	45233.1	−	139213.i	0.0758964	−	0.233585i
$773$	169601.	−	55106.8i	0.283838	−	0.0922245i	−0.163638	−	0.986520i	$-0.552323\pi$
$773$	169601.	−	55106.8i	0.283838	−	0.0922245i	0.447476	+	0.894296i	$0.352323\pi$
$774$			1.75135e6i			2.92342i
$775$	182426.	−	209964.i	0.303727	−	0.349576i
$776$	−302046.			−0.501590
$777$	−828505.	−	2.54988e6i	−1.37231	−	4.22355i
$778$	−199676.	−	64878.8i	−0.329889	−	0.107187i
$779$	−156139.	+	113441.i	−0.257298	+	0.186938i
$780$	−766345.			−1.25961
$781$		−	382774.i		−	0.627538i
$782$	24101.2	−	17510.6i	0.0394118	−	0.0286343i
$783$	1.15117e6	+	836377.i	1.87766	+	1.36420i
$784$	460591.	+	334639.i	0.749348	+	0.544433i
$785$	−244859.	−	753597.i	−0.397353	−	1.22293i
$786$	344091.	+	473600.i	0.556965	+	0.766597i
$787$	−288985.	+	93896.9i	−0.466580	+	0.151601i	−0.532866	−	0.846200i	$-0.678885\pi$
$787$	−288985.	+	93896.9i	−0.466580	+	0.151601i	0.0662862	+	0.997801i	$0.478885\pi$
$788$	−424071.	−	137789.i	−0.682946	−	0.221903i
$789$	−1.82347e6	−	1.32483e6i	−2.92917	−	2.12817i
$790$	1.48822e6	+	483551.i	2.38458	+	0.774797i
$791$	114229.	−	351562.i	0.182568	−	0.561886i
$792$	−251798.	+	346570.i	−0.401422	+	0.552510i
$793$	−135878.	+	418190.i	−0.216074	+	0.665009i
$794$	371159.	+	1.14231e6i	0.588734	+	1.81194i
$795$	−552214.	+	401207.i	−0.873721	+	0.634796i
$796$	−173300.	+	56308.5i	−0.273509	+	0.0888684i
$797$	−622161.	+	856331.i	−0.979459	+	1.34811i	−0.0423379	+	0.999103i	$0.513481\pi$
$797$	−622161.	+	856331.i	−0.979459	+	1.34811i	−0.937121	+	0.349006i	$0.886519\pi$
$798$	−1.09298e6	+	1.50436e6i	−1.71635	+	2.36235i
$799$	−199585.	−	274706.i	−0.312633	−	0.430303i
$800$	348093.			0.543896
$801$		−	890486.i		−	1.38791i
$802$	−464134.	−	638826.i	−0.721598	−	0.993194i
$803$	−39386.0	+	121218.i	−0.0610817	+	0.187990i
$804$	165944.	−	53918.4i	0.256713	−	0.0834112i
$805$			47800.2i			0.0737629i
$806$	527269.	+	458115.i	0.811637	+	0.705187i
$807$	−771975.			−1.18538
$808$	55871.3	+	171954.i	0.0855788	+	0.263384i
$809$	−901896.	−	293044.i	−1.37803	−	0.447750i	−0.476010	−	0.879440i	$-0.657918\pi$
$809$	−901896.	−	293044.i	−1.37803	−	0.447750i	−0.902022	+	0.431690i	$0.857918\pi$
$810$	1.76267e6	−	1.28066e6i	2.68659	−	1.95192i
$811$	−776534.			−1.18064			−0.590321	−	0.807168i	$-0.700999\pi$
$811$	−776534.			−1.18064			−0.590321	+	0.807168i	$0.700999\pi$
$812$			575345.i			0.872602i
$813$	600181.	−	436057.i	0.908033	−	0.659724i
$814$	925529.	+	672436.i	1.39682	+	1.01485i
$815$	570340.	+	414376.i	0.858655	+	0.623849i
$816$	372199.	+	1.14551e6i	0.558978	+	1.72036i
$817$	350413.	+	482302.i	0.524972	+	0.722562i
$818$	−325940.	+	105904.i	−0.487115	+	0.158273i
$819$	1.63504e6	+	531257.i	2.43759	+	0.792021i
$820$	155703.	+	113125.i	0.231563	+	0.168240i
$821$	492107.	+	159895.i	0.730085	+	0.237219i	0.650390	−	0.759600i	$-0.274605\pi$
$821$	492107.	+	159895.i	0.730085	+	0.237219i	0.0796947	+	0.996819i	$0.474605\pi$
$822$	−292047.	+	898827.i	−0.432224	+	1.33025i
$823$	137191.	−	188827.i	0.202547	−	0.278782i	−0.695645	−	0.718386i	$-0.744881\pi$
$823$	137191.	−	188827.i	0.202547	−	0.278782i	0.898192	+	0.439604i	$0.144881\pi$
$824$	−53393.7	+	164329.i	−0.0786386	+	0.242025i
$825$	128950.	+	396868.i	0.189459	+	0.583094i
$826$	210663.	−	153056.i	0.308765	−	0.224331i
$827$	182986.	−	59455.9i	0.267552	−	0.0869329i	−0.172169	−	0.985067i	$-0.555077\pi$
$827$	182986.	−	59455.9i	0.267552	−	0.0869329i	0.439721	+	0.898135i	$0.355077\pi$
$828$	−29780.3	+	40989.1i	−0.0434379	+	0.0597871i
$829$	−192338.	+	264731.i	−0.279870	+	0.385208i	−0.925691	−	0.378281i	$-0.876515\pi$
$829$	−192338.	+	264731.i	−0.279870	+	0.385208i	0.645821	+	0.763489i	$0.276515\pi$
$830$	−780651.	−	1.07447e6i	−1.13319	−	1.55970i
$831$	961749.			1.39271
$832$			178950.i			0.258514i
$833$	253914.	+	349482.i	0.365928	+	0.503657i
$834$	652151.	−	2.00711e6i	0.937597	−	2.88563i
$835$	277361.	−	90120.2i	0.397808	−	0.129256i
$836$		−	323808.i		−	0.463314i
$837$	−1.69940e6	−	148248.i	−2.42574	−	0.211611i
$838$	−1.35221e6			−1.92555
$839$	327423.	+	1.00770e6i	0.465141	+	1.43156i	0.858805	+	0.512303i	$0.171208\pi$
$839$	327423.	+	1.00770e6i	0.465141	+	1.43156i	−0.393663	+	0.919255i	$0.628792\pi$
$840$	−794179.	−	258044.i	−1.12554	−	0.365709i
$841$	−52342.4	+	38029.0i	−0.0740052	+	0.0537679i
$842$	−638421.			−0.900499
$843$			1.77770e6i			2.50151i
$844$	206889.	−	150313.i	0.290437	−	0.211015i
$845$	−220620.	−	160290.i	−0.308981	−	0.224488i
$846$	1.14478e6	+	831730.i	1.59949	+	1.16210i
$847$	139583.	+	429592.i	0.194565	+	0.598810i
$848$	250948.	+	345400.i	0.348973	+	0.480320i
$849$	−2.10483e6	+	683900.i	−2.92012	+	0.948806i
$850$	337514.	+	109665.i	0.467148	+	0.151786i
$851$	−49294.8	−	35814.8i	−0.0680678	−	0.0494542i
$852$	752157.	+	244391.i	1.03617	+	0.336671i
$853$	−123376.	+	379713.i	−0.169564	+	0.521864i	−0.999344	−	0.0362268i	$-0.988466\pi$
$853$	−123376.	+	379713.i	−0.169564	+	0.521864i	0.829780	+	0.558091i	$0.188466\pi$
$854$	625376.	−	860756.i	0.857483	−	1.18022i
$855$	590903.	−	1.81861e6i	0.808321	−	2.48776i
$856$	−88478.3	−	272308.i	−0.120751	−	0.371632i
$857$	944576.	−	686274.i	1.28610	−	0.934407i	0.286382	−	0.958116i	$-0.407547\pi$
$857$	944576.	−	686274.i	1.28610	−	0.934407i	0.999719	+	0.0237085i	$0.00754737\pi$
$858$	−996630.	+	323825.i	−1.35382	+	0.439881i
$859$	564527.	−	777005.i	0.765065	−	1.05302i	−0.231711	−	0.972785i	$-0.574432\pi$
$859$	564527.	−	777005.i	0.765065	−	1.05302i	0.996776	−	0.0802372i	$-0.0255678\pi$
$860$	349435.	−	480956.i	0.472465	−	0.650292i
$861$	−362528.	−	498977.i	−0.489030	−	0.673092i
$862$	−1.45102e6			−1.95281
$863$		−	1.19431e6i		−	1.60360i	−0.597595	−	0.801798i	$-0.703877\pi$
$863$		−	1.19431e6i		−	1.60360i	0.597595	−	0.801798i	$-0.296123\pi$
$864$	−1.25484e6	−	1.72713e6i	−1.68097	−	2.31365i
$865$	−241750.	+	744030.i	−0.323098	+	0.994394i
$866$	944155.	−	306775.i	1.25895	−	0.409057i
$867$		−	458543.i		−	0.610017i
$868$	−355392.	−	591136.i	−0.471703	−	0.784599i
$869$	873249.			1.15637
$870$	−639973.	−	1.96964e6i	−0.845519	−	2.60224i
$871$	−127968.	−	41579.4i	−0.168681	−	0.0548078i
$872$	436564.	−	317182.i	0.574136	−	0.417134i
$873$	2.21036e6			2.90025
$874$			42259.4i			0.0553224i
$875$	534103.	−	388049.i	0.697604	−	0.506839i
$876$	−213048.	−	154789.i	−0.277632	−	0.201712i
$877$	−454124.	−	329940.i	−0.590439	−	0.428979i	0.252033	−	0.967719i	$-0.418901\pi$
$877$	−454124.	−	329940.i	−0.590439	−	0.428979i	−0.842473	+	0.538739i	$0.818901\pi$
$878$	152992.	+	470862.i	0.198463	+	0.610807i
$879$	−181061.	−	249210.i	−0.234341	−	0.322543i
$880$	784271.	−	254825.i	1.01275	−	0.329061i
$881$	484412.	+	157395.i	0.624113	+	0.202787i	0.603966	−	0.797010i	$-0.293586\pi$
$881$	484412.	+	157395.i	0.624113	+	0.202787i	0.0201476	+	0.999797i	$0.493586\pi$
$882$	−1.45639e6	−	1.05813e6i	−1.87215	−	1.36020i
$883$	−125793.	−	40872.7i	−0.161338	−	0.0524219i	0.227234	−	0.973840i	$-0.427032\pi$
$883$	−125793.	−	40872.7i	−0.161338	−	0.0524219i	−0.388572	+	0.921418i	$0.627032\pi$
$884$	−112391.	+	345903.i	−0.143822	+	0.442639i
$885$	−224841.	+	309468.i	−0.287071	+	0.395120i
$886$	−536494.	+	1.65116e6i	−0.683435	+	2.10340i
$887$	272811.	+	839627.i	0.346749	+	1.06718i	0.960641	+	0.277794i	$0.0896032\pi$
$887$	272811.	+	839627.i	0.346749	+	1.06718i	−0.613892	+	0.789390i	$0.710397\pi$
$888$	861159.	−	625669.i	1.09209	−	0.793448i
$889$	788956.	−	256347.i	0.998273	−	0.324359i
$890$	−435356.	+	599216.i	−0.549622	+	0.756490i
$891$	714679.	−	983672.i	0.900235	−	1.23907i
$892$	−83859.6	−	115423.i	−0.105396	−	0.145065i
$893$	481672.			0.604016
$894$			2.52815e6i			3.16321i
$895$	348181.	+	479231.i	0.434670	+	0.598272i
$896$	−253064.	+	778852.i	−0.315221	+	0.970150i
$897$	53081.7	−	17247.3i	0.0659720	−	0.0214356i
$898$			1.79098e6i			2.22095i
$899$	−300821.	+	709186.i	−0.372211	+	0.877487i
$900$	−603552.			−0.745126
$901$	100105.	+	308092.i	0.123312	+	0.379516i
$902$	250293.	+	81325.2i	0.307635	+	0.0999567i
$903$	−1.54131e6	+	1.11982e6i	−1.89023	+	1.37333i
$904$	146760.			0.179585
$905$			173984.i			0.212428i
$906$	2.44355e6	−	1.77534e6i	2.97691	−	2.16285i
$907$	−782134.	−	568254.i	−0.950751	−	0.690761i	0.000233648	−	1.00000i	$-0.499926\pi$
$907$	−782134.	−	568254.i	−0.950751	−	0.690761i	−0.950984	+	0.309239i	$0.899926\pi$
$908$	328975.	+	239014.i	0.399016	+	0.289902i
$909$	−408865.	−	1.25836e6i	−0.494826	−	1.52292i
$910$	−840504.	−	1.15685e6i	−1.01498	−	1.39700i
$911$	−1.01715e6	+	330491.i	−1.22560	+	0.398220i	−0.849117	−	0.528205i	$-0.822865\pi$
$911$	−1.01715e6	+	330491.i	−1.22560	+	0.398220i	−0.376479	+	0.926425i	$0.622865\pi$
$912$	−1.62495e6	−	527979.i	−1.95367	−	0.634785i
$913$	−599618.	−	435648.i	−0.719338	−	0.522630i
$914$	−1.69864e6	−	551923.i	−2.03334	−	0.660672i
$915$	−482982.	+	1.48647e6i	−0.576885	+	1.77547i
$916$	−73860.9	+	101661.i	−0.0880286	+	0.121161i
$917$	−137755.	+	423968.i	−0.163821	+	0.504190i
$918$	−672575.	−	2.06997e6i	−0.798096	−	2.45629i
$919$	1.28256e6	−	931838.i	1.51862	−	1.10334i	0.556450	−	0.830881i	$-0.312163\pi$
$919$	1.28256e6	−	931838.i	1.51862	−	1.10334i	0.962167	−	0.272459i	$-0.0878369\pi$
$920$	−18048.8	+	5864.42i	−0.0213242	+	0.00692866i
$921$	−1.16412e6	+	1.60228e6i	−1.37240	+	1.88894i
$922$	−162628.	+	223838.i	−0.191308	+	0.263313i
$923$	−358478.	−	493403.i	−0.420784	−	0.579160i
$924$	1.03480e6			1.21203
$925$		−	725851.i		−	0.848328i
$926$	939927.	+	1.29370e6i	1.09616	+	1.50873i
$927$	390735.	−	1.20256e6i	0.454697	−	1.39941i
$928$	−916895.	+	297917.i	−1.06469	+	0.345939i
$929$		−	1.24842e6i		−	1.44653i	−0.690570	−	0.723266i	$-0.742640\pi$
$929$		−	1.24842e6i		−	1.44653i	0.690570	−	0.723266i	$-0.257360\pi$
$930$	1.87419e6	+	1.62838e6i	2.16694	+	1.88274i
$931$	−612786.			−0.706984
$932$	−269901.	−	830670.i	−0.310722	−	0.956306i
$933$	−275245.	−	89432.4i	−0.316195	−	0.102738i
$934$	−1.14727e6	+	833539.i	−1.31514	+	0.955503i
$935$	625705.			0.715725
$936$			682551.i			0.779083i
$937$	109065.	−	79240.7i	0.124225	−	0.0902546i	−0.523938	−	0.851756i	$-0.675538\pi$
$937$	109065.	−	79240.7i	0.124225	−	0.0902546i	0.648163	+	0.761502i	$0.275538\pi$
$938$	263396.	+	191368.i	0.299366	+	0.217502i
$939$	1.90308e6	+	1.38267e6i	2.15837	+	1.56815i
$940$	−148429.	−	456819.i	−0.167983	−	0.516997i
$941$	101417.	+	139589.i	0.114533	+	0.157642i	0.862435	−	0.506168i	$-0.168938\pi$
$941$	101417.	+	139589.i	0.114533	+	0.157642i	−0.747902	+	0.663810i	$0.768938\pi$
$942$	2.12913e6	−	691798.i	2.39939	−	0.779610i
$943$	−13330.9	−	4331.48i	−0.0149912	−	0.00487094i
$944$	193566.	+	140634.i	0.217213	+	0.157814i
$945$	3.32133e6	+	1.07917e6i	3.71919	+	1.20844i
$946$	251208.	−	773139.i	0.280706	−	0.863923i
$947$	637192.	−	877020.i	0.710511	−	0.977934i	−0.289275	−	0.957246i	$-0.593414\pi$
$947$	637192.	−	877020.i	0.710511	−	0.977934i	0.999786	−	0.0206881i	$-0.00658569\pi$
$948$	−557546.	+	1.71595e6i	−0.620389	+	1.90936i
$949$	62754.5	+	193138.i	0.0696806	+	0.214455i
$950$	−407273.	+	295901.i	−0.451271	+	0.327868i
$951$	841162.	−	273310.i	0.930077	−	0.302200i
$952$	−232946.	+	320622.i	−0.257028	+	0.353769i
$953$	−178356.	+	245487.i	−0.196383	+	0.270297i	−0.895840	−	0.444377i	$-0.853425\pi$
$953$	−178356.	+	245487.i	−0.196383	+	0.270297i	0.699457	+	0.714674i	$0.253425\pi$
$954$	−793499.	−	1.09216e6i	−0.871866	−	1.20002i
$955$	−1.41510e6			−1.55160
$956$		−	661103.i		−	0.723358i
$957$	−679324.	−	935009.i	−0.741742	−	1.02092i
$958$	190763.	−	587109.i	0.207857	−	0.639717i
$959$	−684460.	+	222394.i	−0.744236	+	0.241817i
$960$			636081.i			0.690192i
$961$	−128989.	−	914469.i	−0.139671	−	0.990198i
$962$	1.82278e6			1.96963
$963$	647483.	+	1.99275e6i	0.698193	+	2.14882i
$964$	−63949.9	−	20778.6i	−0.0688154	−	0.0223595i
$965$	−324604.	+	235839.i	−0.348578	+	0.253257i
$966$	−135050.			−0.144724
$967$		−	693389.i		−	0.741522i	−0.928728	−	0.370761i	$-0.879097\pi$
$967$		−	693389.i		−	0.741522i	0.928728	−	0.370761i	$-0.120903\pi$
$968$	−145084.	+	105410.i	−0.154835	+	0.112494i
$969$	−1.04882e6	−	762013.i	−1.11700	−	0.811549i
$970$	−1.48737e6	−	1.08064e6i	−1.58080	−	1.14852i
$971$	−251648.	−	774493.i	−0.266904	−	0.821446i	−0.991249	−	0.132008i	$-0.957858\pi$
$971$	−251648.	−	774493.i	−0.266904	−	0.821446i	0.724345	−	0.689438i	$-0.242142\pi$
$972$	544288.	+	749148.i	0.576097	+	0.792930i
$973$	1.52843e6	−	496615.i	1.61443	−	0.524559i
$974$	317532.	+	103172.i	0.334711	+	0.108754i
$975$	537898.	+	390806.i	0.565836	+	0.411104i
$976$	929758.	+	302097.i	0.976046	+	0.317136i
$977$	−69206.3	+	212995.i	−0.0725030	+	0.223141i	−0.980741	−	0.195313i	$-0.937428\pi$
$977$	−69206.3	+	212995.i	−0.0725030	+	0.223141i	0.908238	+	0.418454i	$0.137428\pi$
$978$	−1.17074e6	+	1.61138e6i	−1.22400	+	1.68469i
$979$	−127728.	+	393107.i	−0.133267	+	0.410152i
$980$	188833.	+	581167.i	0.196619	+	0.605130i
$981$	−3.19477e6	+	2.32113e6i	−3.31972	+	2.41192i
$982$	190451.	−	61881.4i	0.197497	−	0.0641707i
$983$	692222.	−	952762.i	0.716372	−	0.986001i	−0.283265	−	0.959042i	$-0.591417\pi$
$983$	692222.	−	952762.i	0.716372	−	0.986001i	0.999637	−	0.0269597i	$-0.00858257\pi$
$984$	143931.	−	198104.i	0.148650	−	0.204599i
$985$	718413.	+	988811.i	0.740460	+	1.01916i
$986$	−982887.			−1.01100
$987$			1.53929e6i			1.58011i
$988$	−303255.	−	417395.i	−0.310667	−	0.427596i
$989$	−13379.6	+	41178.3i	−0.0136789	+	0.0420994i
$990$	−2.47987e6	+	805760.i	−2.53022	+	0.822120i
$991$			663990.i			0.676105i	0.941127	+	0.338053i	$0.109768\pi$
$991$			663990.i			0.676105i	−0.941127	+	0.338053i	$0.890232\pi$
$992$	758036.	−	872463.i	0.770312	−	0.886592i
$993$	20449.7			0.0207391
$994$	456017.	+	1.40348e6i	0.461539	+	1.42047i
$995$	475030.	+	154347.i	0.479816	+	0.155902i
$996$	1.23890e6	−	900111.i	1.24887	−	0.907355i
$997$	−143884.			−0.144751			−0.0723757	−	0.997377i	$-0.523058\pi$
$997$	−143884.			−0.144751			−0.0723757	+	0.997377i	$0.523058\pi$
$998$		−	299066.i		−	0.300266i
$999$	−3.60145e6	+	2.61661e6i	−3.60866	+	2.62185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.5.f.a.27.2	yes	36
31.23	odd	10	inner	31.5.f.a.23.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.5.f.a.23.2	✓	36	31.23	odd	10	inner
31.5.f.a.27.2	yes	36	1.1	even	1	trivial

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+(-1.60665 - 4.94476i) q^{2} +(-15.6281 - 5.07789i) q^{3} +(-8.92504 + 6.48442i) q^{4} +30.2396 q^{5} +85.4357i q^{6} +(-52.6343 + 38.2411i) q^{7} +(-20.8969 - 15.1825i) q^{8} +(152.923 + 111.105i) q^{9} +(-48.5844 - 149.527i) q^{10} +(-51.5717 - 70.9824i) q^{11} +(172.409 - 56.0190i) q^{12} +(-132.954 - 43.1994i) q^{13} +(273.658 + 198.824i) q^{14} +(-472.588 - 153.553i) q^{15} +(-96.0447 + 295.595i) q^{16} +(-138.618 + 190.791i) q^{17} +(303.694 - 934.675i) q^{18} +(-103.377 - 318.162i) q^{19} +(-269.889 + 196.086i) q^{20} +(1016.76 - 330.365i) q^{21} +(-268.133 + 369.054i) q^{22} +(14.2811 - 19.6562i) q^{23} +(249.485 + 343.386i) q^{24} +289.432 q^{25} +726.832i q^{26} +(-1043.37 - 1436.07i) q^{27} +(221.792 - 682.606i) q^{28} +(-762.379 + 247.712i) q^{29} +2583.54i q^{30} +(630.290 - 725.434i) q^{31} +1202.68 q^{32} +(445.529 + 1371.20i) q^{33} +(1166.13 + 378.897i) q^{34} +(-1591.64 + 1156.39i) q^{35} -2085.30 q^{36} -2507.85i q^{37} +(-1407.14 + 1022.35i) q^{38} +(1858.46 + 1350.25i) q^{39} +(-631.913 - 459.112i) q^{40} +(-178.276 - 548.678i) q^{41} +(-3267.15 - 4496.85i) q^{42} +(-1694.83 + 550.683i) q^{43} +(920.559 + 299.108i) q^{44} +(4624.33 + 3359.77i) q^{45} +(-120.140 - 39.0358i) q^{46} +(-444.930 + 1369.35i) q^{47} +(3002.00 - 4131.90i) q^{48} +(566.042 - 1742.10i) q^{49} +(-465.016 - 1431.17i) q^{50} +(3135.15 - 2277.82i) q^{51} +(1466.74 - 476.574i) q^{52} +(807.406 - 1111.30i) q^{53} +(-5424.71 + 7466.47i) q^{54} +(-1559.51 - 2146.48i) q^{55} +1680.49 q^{56} +5497.22i q^{57} +(2449.75 + 3371.79i) q^{58} +(237.883 - 732.129i) q^{59} +(5213.57 - 1693.99i) q^{60} -3145.37i q^{61} +(-4599.75 - 1951.12i) q^{62} -12297.8 q^{63} +(-395.565 - 1217.42i) q^{64} +(-4020.47 - 1306.33i) q^{65} +(6064.43 - 4406.07i) q^{66} +962.501 q^{67} -2601.68i q^{68} +(-322.999 + 234.672i) q^{69} +(8275.29 + 6012.35i) q^{70} +(3529.45 + 2564.29i) q^{71} +(-1508.77 - 4643.51i) q^{72} +(-853.858 - 1175.23i) q^{73} +(-12400.7 + 4029.23i) q^{74} +(-4523.28 - 1469.70i) q^{75} +(2985.74 + 2169.27i) q^{76} +(5428.89 + 1763.95i) q^{77} +(3690.77 - 11359.0i) q^{78} +(-5850.11 + 8051.98i) q^{79} +(-2904.35 + 8938.68i) q^{80} +(4282.35 + 13179.7i) q^{81} +(-2426.65 + 1763.07i) q^{82} +(8033.97 - 2610.40i) q^{83} +(-6932.40 + 9541.62i) q^{84} +(-4191.75 + 5769.44i) q^{85} +(5445.99 + 7495.76i) q^{86} +13172.4 q^{87} +2266.30i q^{88} +(-2769.04 - 3811.26i) q^{89} +(9183.59 - 28264.2i) q^{90} +(8649.94 - 2810.53i) q^{91} +268.037i q^{92} +(-13533.9 + 8136.64i) q^{93} +7485.97 q^{94} +(-3126.08 - 9621.09i) q^{95} +(-18795.6 - 6107.06i) q^{96} +(9460.32 - 6873.32i) q^{97} -9523.69 q^{98} -16584.7i 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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