LMFDB - Embedded newform 31.6.g.a.9.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,6,Mod(7,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.7"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	31.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.97189841420$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.7
Character	$\chi$	$=$	31.9
Dual form			31.6.g.a.7.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.326144 - 1.00377i) q^{2} +(-7.10263 - 1.50971i) q^{3} +(24.9874 + 18.1544i) q^{4} +(-45.3815 - 78.6031i) q^{5} +(-3.83188 + 6.63701i) q^{6} +(143.301 - 63.8015i) q^{7} +(53.6957 - 39.0122i) q^{8} +(-173.823 - 77.3912i) q^{9} +(-93.7002 + 19.9166i) q^{10} +(68.8142 - 654.723i) q^{11} +(-150.068 - 166.667i) q^{12} +(-39.0657 + 43.3868i) q^{13} +(-17.3053 - 164.649i) q^{14} +(203.660 + 626.801i) q^{15} +(283.772 + 873.359i) q^{16} +(27.7520 + 264.042i) q^{17} +(-134.374 + 149.238i) q^{18} +(1065.14 + 1182.96i) q^{19} +(293.026 - 2787.96i) q^{20} +(-1114.13 + 236.816i) q^{21} +(-634.747 - 282.608i) q^{22} +(-750.831 + 545.511i) q^{23} +(-440.278 + 196.024i) q^{24} +(-2556.46 + 4427.92i) q^{25} +(30.8093 + 53.3633i) q^{26} +(2545.27 + 1849.25i) q^{27} +(4738.98 + 1007.30i) q^{28} +(-1183.13 + 3641.30i) q^{29} +695.586 q^{30} +(-312.855 - 5341.47i) q^{31} +3093.09 q^{32} +(-1477.20 + 4546.37i) q^{33} +(274.089 + 58.2593i) q^{34} +(-11518.2 - 8368.45i) q^{35} +(-2938.40 - 5089.46i) q^{36} +(4597.72 - 7963.48i) q^{37} +(1534.81 - 683.340i) q^{38} +(342.970 - 249.183i) q^{39} +(-5503.27 - 2450.21i) q^{40} +(8142.47 - 1730.74i) q^{41} +(-125.659 + 1195.57i) q^{42} +(-6716.88 - 7459.85i) q^{43} +(13605.6 - 15110.5i) q^{44} +(1805.18 + 17175.2i) q^{45} +(302.687 + 931.576i) q^{46} +(7147.70 + 21998.4i) q^{47} +(-697.005 - 6631.56i) q^{48} +(5218.33 - 5795.55i) q^{49} +(3610.83 + 4010.24i) q^{50} +(201.515 - 1917.29i) q^{51} +(-1763.81 + 374.909i) q^{52} +(-19968.7 - 8890.63i) q^{53} +(2686.34 - 1951.74i) q^{54} +(-54586.1 + 24303.3i) q^{55} +(5205.58 - 9016.34i) q^{56} +(-5779.38 - 10010.2i) q^{57} +(3269.15 + 2375.18i) q^{58} +(36613.1 + 7782.36i) q^{59} +(-6290.26 + 19359.4i) q^{60} +56005.2 q^{61} +(-5463.63 - 1428.05i) q^{62} -29846.7 q^{63} +(-8071.90 + 24842.8i) q^{64} +(5183.20 + 1101.72i) q^{65} +(4081.72 + 2965.54i) q^{66} +(22557.2 + 39070.2i) q^{67} +(-4100.08 + 7101.54i) q^{68} +(6156.43 - 2741.02i) q^{69} +(-12156.6 + 8832.27i) q^{70} +(-29077.8 - 12946.3i) q^{71} +(-12352.8 + 2625.66i) q^{72} +(706.672 - 6723.53i) q^{73} +(-6493.97 - 7212.29i) q^{74} +(24842.5 - 27590.3i) q^{75} +(5139.18 + 48896.0i) q^{76} +(-31911.2 - 98212.7i) q^{77} +(-138.264 - 425.533i) q^{78} +(1208.85 + 11501.4i) q^{79} +(55770.7 - 61939.7i) q^{80} +(15651.9 + 17383.2i) q^{81} +(918.362 - 8737.63i) q^{82} +(-30347.8 + 6450.63i) q^{83} +(-32138.5 - 14309.0i) q^{84} +(19495.1 - 14164.0i) q^{85} +(-9678.63 + 4309.21i) q^{86} +(13900.6 - 24076.6i) q^{87} +(-21847.2 - 37840.4i) q^{88} +(59042.1 + 42896.6i) q^{89} +(17828.7 + 3789.60i) q^{90} +(-2829.99 + 8709.81i) q^{91} -28664.7 q^{92} +(-5841.97 + 38410.8i) q^{93} +24412.5 q^{94} +(44646.5 - 137408. i) q^{95} +(-21969.1 - 4669.67i) q^{96} +(-81444.2 - 59172.7i) q^{97} +(-4115.46 - 7128.18i) q^{98} +(-62631.3 + 108481. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 6 q^{2} - 20 q^{3} - 346 q^{4} - 33 q^{5} + 283 q^{6} - 66 q^{7} - 271 q^{8} + 658 q^{9} + 896 q^{10} + 41 q^{11} - 1169 q^{12} + 149 q^{13} - 2 q^{14} + 4906 q^{15} - 2450 q^{16} - 3152 q^{17} - 3 q^{18}+ \cdots + 674326 q^{99}+O(q^{100}) $ 96 * q - 6 * q^2 - 20 * q^3 - 346 * q^4 - 33 * q^5 + 283 * q^6 - 66 * q^7 - 271 * q^8 + 658 * q^9 + 896 * q^10 + 41 * q^11 - 1169 * q^12 + 149 * q^13 - 2 * q^14 + 4906 * q^15 - 2450 * q^16 - 3152 * q^17 - 3 * q^18 - 5216 * q^19 + 7943 * q^20 - 14003 * q^21 - 8471 * q^22 + 13925 * q^23 + 25478 * q^24 - 18843 * q^25 + 12637 * q^26 + 3409 * q^27 - 10560 * q^28 + 6386 * q^29 - 25530 * q^30 - 39101 * q^31 + 31482 * q^32 + 17969 * q^33 - 18136 * q^34 + 5943 * q^35 - 9713 * q^36 + 40836 * q^37 + 18746 * q^38 + 55889 * q^39 + 15841 * q^40 - 46266 * q^41 + 8917 * q^42 - 137449 * q^43 + 28951 * q^44 + 69269 * q^45 - 97978 * q^46 + 5774 * q^47 - 112102 * q^48 - 146686 * q^49 + 58913 * q^50 + 149254 * q^51 + 263153 * q^52 + 62548 * q^53 + 144508 * q^54 + 13077 * q^55 - 103466 * q^56 + 68345 * q^57 - 52881 * q^58 - 149116 * q^59 + 65951 * q^60 - 204972 * q^61 - 62393 * q^62 - 80326 * q^63 - 205193 * q^64 - 296504 * q^65 - 268720 * q^66 - 105499 * q^67 + 497808 * q^68 + 448358 * q^69 + 351230 * q^70 + 93454 * q^71 + 192637 * q^72 + 74644 * q^73 - 83209 * q^74 - 323995 * q^75 - 446776 * q^76 - 249590 * q^77 - 588829 * q^78 + 396670 * q^79 - 236822 * q^80 + 616675 * q^81 + 449670 * q^82 + 518776 * q^83 + 578676 * q^84 + 463509 * q^85 - 95508 * q^86 - 360817 * q^87 + 238379 * q^88 + 239175 * q^89 - 1232679 * q^90 - 178840 * q^91 - 1350224 * q^92 - 65783 * q^93 + 580620 * q^94 - 276050 * q^95 - 1587604 * q^96 - 611799 * q^97 + 200092 * q^98 + 674326 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{15}\right)$

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 $

$2$	0.326144	−	1.00377i	0.0576547	−	0.177443i	−0.918082	−	0.396391i	$-0.870263\pi$
$2$	0.326144	−	1.00377i	0.0576547	−	0.177443i	0.975737	+	0.218948i	$0.0702625\pi$
$3$	−7.10263	−	1.50971i	−0.455634	−	0.0968479i	−0.0256229	−	0.999672i	$-0.508157\pi$
$3$	−7.10263	−	1.50971i	−0.455634	−	0.0968479i	−0.430011	+	0.902824i	$0.641490\pi$
$4$	24.9874	+	18.1544i	0.780855	+	0.567324i
$5$	−45.3815	−	78.6031i	−0.811809	−	1.40609i	−0.911597	−	0.411086i	$-0.865150\pi$
$5$	−45.3815	−	78.6031i	−0.811809	−	1.40609i	0.0997879	−	0.995009i	$-0.468184\pi$
$6$	−3.83188	+	6.63701i	−0.0434544	+	0.0752652i
$7$	143.301	−	63.8015i	1.10536	−	0.492137i	0.228819	−	0.973469i	$-0.426514\pi$
$7$	143.301	−	63.8015i	1.10536	−	0.492137i	0.876538	+	0.481332i	$0.159847\pi$
$8$	53.6957	−	39.0122i	0.296630	−	0.215514i
$9$	−173.823	−	77.3912i	−0.715323	−	0.318482i
$10$	−93.7002	+	19.9166i	−0.296306	+	0.0629818i
$11$	68.8142	−	654.723i	0.171473	−	1.63146i	−0.483174	−	0.875524i	$-0.660516\pi$
$11$	68.8142	−	654.723i	0.171473	−	1.63146i	0.654647	−	0.755934i	$-0.272817\pi$
$12$	−150.068	−	166.667i	−0.300840	−	0.334116i
$13$	−39.0657	+	43.3868i	−0.0641117	+	0.0712032i	−0.774347	−	0.632761i	$-0.781922\pi$
$13$	−39.0657	+	43.3868i	−0.0641117	+	0.0712032i	0.710236	+	0.703964i	$0.248588\pi$
$14$	−17.3053	−	164.649i	−0.0235971	−	0.224512i
$15$	203.660	+	626.801i	0.233710	+	0.719286i
$16$	283.772	+	873.359i	0.277121	+	0.852890i
$17$	27.7520	+	264.042i	0.0232901	+	0.221590i	0.999976	+	0.00691747i	$0.00220192\pi$
$17$	27.7520	+	264.042i	0.0232901	+	0.221590i	−0.976686	+	0.214673i	$0.931131\pi$
$18$	−134.374	+	149.238i	−0.0977542	+	0.108567i
$19$	1065.14	+	1182.96i	0.676898	+	0.751771i	0.979522	−	0.201339i	$-0.0645292\pi$
$19$	1065.14	+	1182.96i	0.676898	+	0.751771i	−0.302624	+	0.953110i	$0.597863\pi$
$20$	293.026	−	2787.96i	0.163807	−	1.55851i
$21$	−1114.13	+	236.816i	−0.551300	+	0.117183i
$22$	−634.747	−	282.608i	−0.279605	−	0.124488i
$23$	−750.831	+	545.511i	−0.295953	+	0.215022i	−0.725846	−	0.687858i	$-0.758551\pi$
$23$	−750.831	+	545.511i	−0.295953	+	0.215022i	0.429893	+	0.902880i	$0.358551\pi$
$24$	−440.278	+	196.024i	−0.156027	+	0.0694675i
$25$	−2556.46	+	4427.92i	−0.818067	+	1.41693i
$26$	30.8093	+	53.3633i	0.00893817	+	0.0154814i
$27$	2545.27	+	1849.25i	0.671931	+	0.488187i
$28$	4738.98	+	1007.30i	1.14233	+	0.242809i
$29$	−1183.13	+	3641.30i	−0.261238	+	0.804009i	0.731298	+	0.682058i	$0.238915\pi$
$29$	−1183.13	+	3641.30i	−0.261238	+	0.804009i	−0.992536	+	0.121951i	$0.961085\pi$
$30$	695.586			0.141107
$31$	−312.855	−	5341.47i	−0.0584709	−	0.998289i
$31$	−312.855	−	5341.47i	−0.0584709	−	0.998289i
$32$	3093.09			0.533971
$33$	−1477.20	+	4546.37i	−0.236132	+	0.726741i
$34$	274.089	+	58.2593i	0.0406625	+	0.00864307i
$35$	−11518.2	−	8368.45i	−1.58933	−	1.15472i
$36$	−2938.40	−	5089.46i	−0.377881	−	0.654509i
$37$	4597.72	−	7963.48i	0.552126	−	0.956310i	−0.445995	−	0.895035i	$-0.647150\pi$
$37$	4597.72	−	7963.48i	0.552126	−	0.956310i	0.998121	−	0.0612745i	$-0.0195165\pi$
$38$	1534.81	−	683.340i	0.172423	−	0.0767676i
$39$	342.970	−	249.183i	0.0361073	−	0.0262335i
$40$	−5503.27	−	2450.21i	−0.543840	−	0.242133i
$41$	8142.47	−	1730.74i	0.756479	−	0.160795i	0.186501	−	0.982455i	$-0.440285\pi$
$41$	8142.47	−	1730.74i	0.756479	−	0.160795i	0.569978	+	0.821660i	$0.306952\pi$
$42$	−125.659	+	1195.57i	−0.0109919	+	0.104580i
$43$	−6716.88	−	7459.85i	−0.553983	−	0.615260i	0.399491	−	0.916737i	$-0.369187\pi$
$43$	−6716.88	−	7459.85i	−0.553983	−	0.615260i	−0.953473	+	0.301477i	$0.902520\pi$
$44$	13605.6	−	15110.5i	1.05946	−	1.17665i
$45$	1805.18	+	17175.2i	0.132889	+	1.26436i
$46$	302.687	+	931.576i	0.0210911	+	0.0649118i
$47$	7147.70	+	21998.4i	0.471978	+	1.45260i	0.849990	+	0.526799i	$0.176608\pi$
$47$	7147.70	+	21998.4i	0.471978	+	1.45260i	−0.378012	+	0.925801i	$0.623392\pi$
$48$	−697.005	−	6631.56i	−0.0436649	−	0.415444i
$49$	5218.33	−	5795.55i	0.310486	−	0.344829i
$50$	3610.83	+	4010.24i	0.204260	+	0.226853i
$51$	201.515	−	1917.29i	0.0108488	−	0.103220i
$52$	−1763.81	+	374.909i	−0.0904572	+	0.0192273i
$53$	−19968.7	−	8890.63i	−0.976472	−	0.434753i	−0.144460	−	0.989511i	$-0.546144\pi$
$53$	−19968.7	−	8890.63i	−0.976472	−	0.434753i	−0.832012	+	0.554757i	$0.812811\pi$
$54$	2686.34	−	1951.74i	0.125365	−	0.0910832i
$55$	−54586.1	+	24303.3i	−2.43319	+	1.08333i
$56$	5205.58	−	9016.34i	0.221819	−	0.384202i
$57$	−5779.38	−	10010.2i	−0.235610	−	0.408089i
$58$	3269.15	+	2375.18i	0.127604	+	0.0927098i
$59$	36613.1	+	7782.36i	1.36933	+	0.291059i	0.833150	−	0.553047i	$-0.186535\pi$
$59$	36613.1	+	7782.36i	1.36933	+	0.291059i	0.536176	+	0.844106i	$0.319868\pi$
$60$	−6290.26	+	19359.4i	−0.225575	+	0.694248i
$61$	56005.2			1.92710			0.963549	−	0.267533i	$-0.0862085\pi$
$61$	56005.2			1.92710			0.963549	+	0.267533i	$0.0862085\pi$
$62$	−5463.63	−	1428.05i	−0.180510	−	0.0471808i
$63$	−29846.7			−0.947424
$64$	−8071.90	+	24842.8i	−0.246335	+	0.758141i
$65$	5183.20	+	1101.72i	0.152165	+	0.0323436i
$66$	4081.72	+	2965.54i	0.115341	+	0.0838000i
$67$	22557.2	+	39070.2i	0.613900	+	1.06331i	0.990576	+	0.136961i	$0.0437335\pi$
$67$	22557.2	+	39070.2i	0.613900	+	1.06331i	−0.376676	+	0.926345i	$0.622933\pi$
$68$	−4100.08	+	7101.54i	−0.107528	+	0.186243i
$69$	6156.43	−	2741.02i	0.155671	−	0.0693090i
$70$	−12156.6	+	8832.27i	−0.296528	+	0.215441i
$71$	−29077.8	−	12946.3i	−0.684567	−	0.304789i	0.0348247	−	0.999393i	$-0.488913\pi$
$71$	−29077.8	−	12946.3i	−0.684567	−	0.304789i	−0.719392	+	0.694605i	$0.755579\pi$
$72$	−12352.8	+	2625.66i	−0.280823	+	0.0596909i
$73$	706.672	−	6723.53i	0.0155207	−	0.147669i	−0.984017	−	0.178075i	$-0.943013\pi$
$73$	706.672	−	6723.53i	0.0155207	−	0.147669i	0.999538	+	0.0304053i	$0.00967980\pi$
$74$	−6493.97	−	7212.29i	−0.137858	−	0.153107i
$75$	24842.5	−	27590.3i	0.509966	−	0.566375i
$76$	5139.18	+	48896.0i	0.102061	+	0.971045i
$77$	−31911.2	−	98212.7i	−0.613362	−	1.88773i
$78$	−138.264	−	425.533i	−0.00257319	−	0.00791947i
$79$	1208.85	+	11501.4i	0.0217924	+	0.207340i	1.00000		0.000288806i	$-9.19298e-5\pi$
$79$	1208.85	+	11501.4i	0.0217924	+	0.207340i	−0.978208	+	0.207629i	$0.933425\pi$
$80$	55770.7	−	61939.7i	0.974275	−	1.08204i
$81$	15651.9	+	17383.2i	0.265067	+	0.294387i
$82$	918.362	−	8737.63i	0.0150827	−	0.143502i
$83$	−30347.8	+	6450.63i	−0.483540	+	0.102780i	−0.443230	−	0.896408i	$-0.646168\pi$
$83$	−30347.8	+	6450.63i	−0.483540	+	0.102780i	−0.0403093	+	0.999187i	$0.512834\pi$
$84$	−32138.5	−	14309.0i	−0.496966	−	0.221264i
$85$	19495.1	−	14164.0i	0.292670	−	0.212637i
$86$	−9678.63	+	4309.21i	−0.141113	+	0.0628277i
$87$	13900.6	−	24076.6i	0.196896	−	0.341033i
$88$	−21847.2	−	37840.4i	−0.300738	−	0.520894i
$89$	59042.1	+	42896.6i	0.790109	+	0.574048i	0.907996	−	0.418979i	$-0.137612\pi$
$89$	59042.1	+	42896.6i	0.790109	+	0.574048i	−0.117887	+	0.993027i	$0.537612\pi$
$90$	17828.7	+	3789.60i	0.232013	+	0.0493159i
$91$	−2829.99	+	8709.81i	−0.0358246	+	0.110257i
$92$	−28664.7			−0.353084
$93$	−5841.97	+	38410.8i	−0.0700409	+	0.460517i
$94$	24412.5			0.284965
$95$	44646.5	−	137408.i	0.507550	−	1.56208i
$96$	−21969.1	−	4669.67i	−0.243295	−	0.0517140i
$97$	−81444.2	−	59172.7i	−0.878883	−	0.638546i	0.0540728	−	0.998537i	$-0.482780\pi$
$97$	−81444.2	−	59172.7i	−0.878883	−	0.638546i	−0.932956	+	0.359991i	$0.882780\pi$
$98$	−4115.46	−	7128.18i	−0.0432866	−	0.0749745i
$99$	−62631.3	+	108481.i	−0.642249	+	1.11241i
$100$	−144265.	+	64231.1i	−1.44265	+	0.642311i
$101$	155908.	−	113274.i	1.52077	−	1.10491i	0.559672	−	0.828714i	$-0.310927\pi$
$101$	155908.	−	113274.i	1.52077	−	1.10491i	0.961102	−	0.276193i	$-0.0890728\pi$
$102$	−1858.79	−	827.588i	−0.0176901	−	0.00787615i
$103$	9250.94	−	1966.35i	0.0859197	−	0.0182628i	−0.164751	−	0.986335i	$-0.552682\pi$
$103$	9250.94	−	1966.35i	0.0859197	−	0.0182628i	0.250671	+	0.968072i	$0.419349\pi$
$104$	−405.043	+	3853.73i	−0.00367213	+	0.0349379i
$105$	69175.4	+	76827.1i	0.612320	+	0.680051i
$106$	−15436.8	+	17144.3i	−0.133442	+	0.148203i
$107$	−3432.66	−	32659.6i	−0.0289849	−	0.275773i	−0.999409	−	0.0343675i	$-0.989058\pi$
$107$	−3432.66	−	32659.6i	−0.0289849	−	0.275773i	0.970424	−	0.241405i	$-0.0776083\pi$
$108$	30027.7	+	92415.7i	0.247721	+	0.762406i
$109$	5792.98	+	17829.0i	0.0467020	+	0.143734i	0.971688	−	0.236266i	$-0.0759238\pi$
$109$	5792.98	+	17829.0i	0.0467020	+	0.143734i	−0.924986	+	0.380000i	$0.875924\pi$
$110$	6591.95	+	62718.3i	0.0519437	+	0.494211i
$111$	−44678.4	+	49620.4i	−0.344184	+	0.382255i
$112$	96386.3	+	107048.i	0.726056	+	0.806367i
$113$	−888.243	+	8451.07i	−0.00654388	+	0.0622609i	−0.997306	−	0.0733468i	$-0.976632\pi$
$113$	−888.243	+	8451.07i	−0.00654388	+	0.0622609i	0.990763	+	0.135608i	$0.0432987\pi$
$114$	−11932.8	+	2536.40i	−0.0859964	+	0.0182791i
$115$	76952.6	+	34261.5i	0.542599	+	0.241581i
$116$	−95668.8	+	69507.4i	−0.660123	+	0.479608i
$117$	10148.3	−	4518.31i	0.0685375	−	0.0305149i
$118$	19752.9	−	34212.9i	0.130594	−	0.226196i
$119$	20823.2	+	36066.8i	0.134797	+	0.233475i
$120$	35388.6	+	25711.3i	0.224342	+	0.162994i
$121$	−266396.	−	56624.1i	−1.65411	−	0.351591i
$122$	18265.8	−	56216.3i	0.111106	−	0.341950i
$123$	−60445.9			−0.360250
$124$	89153.6	−	139149.i	0.520697	−	0.812691i
$125$	180430.			1.03284
$126$	−9734.32	+	29959.2i	−0.0546235	+	0.168114i
$127$	−281745.	−	59886.8i	−1.55006	−	0.329475i	−0.648186	−	0.761482i	$-0.724472\pi$
$127$	−281745.	−	59886.8i	−1.55006	−	0.329475i	−0.901870	+	0.432007i	$0.857805\pi$
$128$	102379.	+	74383.0i	0.552316	+	0.401281i
$129$	36445.3	+	63125.0i	0.192827	+	0.333985i
$130$	2796.34	−	4843.41i	0.0145122	−	0.0251358i
$131$	9308.20	−	4144.28i	0.0473901	−	0.0210994i	−0.382905	−	0.923788i	$-0.625076\pi$
$131$	9308.20	−	4144.28i	0.0473901	−	0.0210994i	0.430295	+	0.902688i	$0.358410\pi$
$132$	−119448.	+	86784.0i	−0.596683	+	0.433516i
$133$	228110.	+	101561.i	1.11819	+	0.497850i
$134$	46574.3	−	9899.67i	0.224070	−	0.0476276i
$135$	29848.3	−	283988.i	0.140957	−	1.34111i
$136$	11791.0	+	13095.3i	0.0546644	+	0.0607110i
$137$	−264667.	+	293942.i	−1.20475	+	1.33801i	−0.278812	+	0.960346i	$0.589941\pi$
$137$	−264667.	+	293942.i	−1.20475	+	1.33801i	−0.925941	+	0.377668i	$0.876726\pi$
$138$	−743.466	−	7073.61i	−0.00332325	−	0.0316186i
$139$	42119.9	+	129632.i	0.184906	+	0.569081i	0.999947	−	0.0103219i	$-0.00328562\pi$
$139$	42119.9	+	129632.i	0.184906	+	0.569081i	−0.815041	+	0.579403i	$0.803286\pi$
$140$	−135885.	−	418211.i	−0.585938	−	1.80333i
$141$	−17556.3	−	167037.i	−0.0743679	−	0.707563i
$142$	−22478.6	+	24965.1i	−0.0935511	+	0.103899i
$143$	25718.1	+	28562.8i	0.105172	+	0.116805i
$144$	18264.1	−	173772.i	0.0733995	−	0.698350i
$145$	339909.	−	72249.9i	1.34259	−	0.285376i
$146$	−6518.40	−	2902.18i	−0.0253081	−	0.0112679i
$147$	−45813.5	+	33285.4i	−0.174864	+	0.127046i
$148$	259457.	−	115518.i	0.973668	−	0.433505i
$149$	55436.4	−	96018.7i	0.204564	−	0.354315i	−0.745430	−	0.666584i	$-0.767756\pi$
$149$	55436.4	−	96018.7i	0.204564	−	0.354315i	0.949994	+	0.312269i	$0.101089\pi$
$150$	−19592.1	−	33934.5i	−0.0710973	−	0.123144i
$151$	−274164.	−	199192.i	−0.978517	−	0.710934i	−0.0211403	−	0.999777i	$-0.506730\pi$
$151$	−274164.	−	199192.i	−0.978517	−	0.710934i	−0.957377	+	0.288842i	$0.906730\pi$
$152$	103343.	+	21966.3i	0.362805	+	0.0771166i
$153$	15610.6	−	48044.5i	0.0539127	−	0.165926i
$154$	−108990.			−0.370328
$155$	−405658.	+	266995.i	−1.35622	+	0.892636i
$156$	13093.7			0.0430775
$157$	−29451.6	+	90642.9i	−0.0953587	+	0.293484i	−0.987347	−	0.158575i	$-0.949310\pi$
$157$	−29451.6	+	90642.9i	−0.0953587	+	0.293484i	0.891988	+	0.452059i	$0.149310\pi$
$158$	11939.0	+	2537.72i	0.0380475	+	0.00808725i
$159$	128408.	+	93293.8i	0.402809	+	0.292658i
$160$	−140369.	−	243126.i	−0.433482	−	0.750814i
$161$	−72790.1	+	126076.i	−0.221313	+	0.383326i
$162$	22553.5	−	10041.5i	0.0675192	−	0.0300615i
$163$	215193.	−	156347.i	0.634393	−	0.460914i	−0.223526	−	0.974698i	$-0.571757\pi$
$163$	215193.	−	156347.i	0.634393	−	0.460914i	0.857920	+	0.513784i	$0.171757\pi$
$164$	234879.	+	104575.i	0.681923	+	0.303612i
$165$	424396.	−	90208.1i	1.21356	−	0.257950i
$166$	−3422.83	+	32566.0i	−0.00964084	+	0.0917264i
$167$	−188569.	−	209427.i	−0.523214	−	0.581088i	0.422387	−	0.906415i	$-0.361192\pi$
$167$	−188569.	−	209427.i	−0.523214	−	0.581088i	−0.945601	+	0.325327i	$0.894525\pi$
$168$	−50585.4	+	56180.8i	−0.138278	+	0.153573i
$169$	38454.4	+	365869.i	0.103569	+	0.985392i
$170$	−7859.19	−	24188.1i	−0.0208572	−	0.0641918i
$171$	−93595.9	−	288059.i	−0.244775	−	0.753339i
$172$	−32408.1	−	308343.i	−0.0835281	−	0.794717i
$173$	−5522.56	+	6133.43i	−0.0140290	+	0.0155807i	−0.750118	−	0.661303i	$-0.770004\pi$
$173$	−5522.56	+	6133.43i	−0.0140290	+	0.0155807i	0.736090	+	0.676884i	$0.236670\pi$
$174$	−19633.7	−	21805.5i	−0.0491620	−	0.0545999i
$175$	−83834.2	+	797629.i	−0.206931	+	1.96882i
$176$	591336.	−	125692.i	1.43897	−	0.305863i
$177$	−248300.	−	110550.i	−0.595722	−	0.265233i
$178$	62314.6	−	45274.2i	0.147414	−	0.107103i
$179$	−313835.	+	139728.i	−0.732097	+	0.325951i	−0.738706	−	0.674027i	$-0.764563\pi$
$179$	−313835.	+	139728.i	−0.732097	+	0.325951i	0.00660892	+	0.999978i	$0.497896\pi$
$180$	−266698.	+	461935.i	−0.613534	+	1.06267i
$181$	229121.	+	396849.i	0.519838	+	0.900387i	0.999734	+	0.0230611i	$0.00734122\pi$
$181$	229121.	+	396849.i	0.519838	+	0.900387i	−0.479896	+	0.877326i	$0.659325\pi$
$182$	7819.65	+	5681.31i	0.0174988	+	0.0127136i
$183$	−397784.	−	84551.6i	−0.878050	−	0.186635i
$184$	−19034.8	+	58583.2i	−0.0414481	+	0.127564i
$185$	−834605.			−1.79288
$186$	36650.2	+	18391.4i	0.0776773	+	0.0389792i
$187$	174784.			0.365509
$188$	−220765.	+	679443.i	−0.455549	+	1.40203i
$189$	482724.	+	102606.i	0.982979	+	0.208939i
$190$	−123364.	−	89629.5i	−0.247917	−	0.180122i
$191$	277105.	+	479960.i	0.549618	+	0.951967i	0.998301	+	0.0582755i	$0.0185602\pi$
$191$	277105.	+	479960.i	0.549618	+	0.951967i	−0.448682	+	0.893691i	$0.648106\pi$
$192$	94837.0	−	164263.i	0.185663	−	0.321577i
$193$	680316.	−	302896.i	1.31467	−	0.585330i	0.374879	−	0.927074i	$-0.377684\pi$
$193$	680316.	−	302896.i	1.31467	−	0.585330i	0.939793	+	0.341744i	$0.111018\pi$
$194$	−85958.3	+	62452.3i	−0.163977	+	0.119136i
$195$	−35151.0	−	15650.2i	−0.0661990	−	0.0294737i
$196$	235607.	−	50079.8i	0.438074	−	0.0931156i
$197$	73709.9	−	701303.i	0.135319	−	1.28748i	−0.690413	−	0.723416i	$-0.742571\pi$
$197$	73709.9	−	701303.i	0.135319	−	1.28748i	0.825732	−	0.564062i	$-0.190762\pi$
$198$	88462.7	+	98247.7i	0.160360	+	0.178098i
$199$	−392267.	+	435657.i	−0.702181	+	0.779851i	−0.983722	−	0.179698i	$-0.942488\pi$
$199$	−392267.	+	435657.i	−0.702181	+	0.779851i	0.281541	+	0.959549i	$0.409154\pi$
$200$	35472.0	+	337493.i	0.0627062	+	0.596610i
$201$	−101231.	−	311556.i	−0.176735	−	0.543933i
$202$	−62852.2	−	193439.i	−0.108378	−	0.333554i
$203$	62777.2	+	597285.i	0.106921	+	1.01728i
$204$	39842.6	−	44249.7i	0.0670304	−	0.0744448i
$205$	−505559.	−	561480.i	−0.840209	−	0.933146i
$206$	1043.38	−	9927.12i	0.00171307	−	0.0162988i
$207$	172730.	−	36714.8i	0.280183	−	0.0595547i
$208$	−48978.0	−	21806.4i	−0.0784952	−	0.0349483i
$209$	847808.	−	615968.i	1.34255	−	0.975422i
$210$	99677.8	−	44379.4i	0.155973	−	0.0694438i
$211$	125868.	−	218011.i	0.194630	−	0.337110i	−0.752149	−	0.658993i	$-0.770983\pi$
$211$	125868.	−	218011.i	0.194630	−	0.337110i	0.946779	+	0.321883i	$0.104316\pi$
$212$	−337561.	−	584673.i	−0.515837	−	0.893456i
$213$	186984.	+	135852.i	0.282394	+	0.205171i
$214$	−33902.2	−	7206.14i	−0.0506051	−	0.0107564i
$215$	−281545.	+	866506.i	−0.415386	+	1.27843i
$216$	208813.			0.304526
$217$	−385626.	−	745474.i	−0.555926	−	1.07469i
$218$	19785.5			0.0281972
$219$	−15169.8	+	46687.9i	−0.0213732	+	0.0657800i
$220$	−1.80518e6	−	383702.i	−2.51456	−	0.534487i
$221$	−12540.1	−	9110.92i	−0.0172711	−	0.0125482i
$222$	35235.8	+	61030.2i	0.0479846	+	0.0831117i
$223$	492944.	−	853804.i	0.663797	−	1.14973i	−0.315813	−	0.948822i	$-0.602277\pi$
$223$	492944.	−	853804.i	0.663797	−	1.14973i	0.979610	−	0.200909i	$-0.0643896\pi$
$224$	443242.	−	197344.i	0.590229	−	0.262787i
$225$	787055.	−	571829.i	1.03645	−	0.753026i
$226$	8193.22	+	3647.86i	0.0106705	+	0.00475080i
$227$	−1.08442e6	+	230500.i	−1.39679	+	0.296897i	−0.843965	−	0.536398i	$-0.819785\pi$
$227$	−1.08442e6	+	230500.i	−1.39679	+	0.296897i	−0.552828	+	0.833296i	$0.686451\pi$
$228$	37317.1	−	355049.i	0.0475413	−	0.452325i
$229$	298139.	+	331117.i	0.375691	+	0.417247i	0.901106	−	0.433599i	$-0.142757\pi$
$229$	298139.	+	331117.i	0.375691	+	0.417247i	−0.525415	+	0.850846i	$0.676090\pi$
$230$	59488.3	−	66068.5i	0.0741501	−	0.0823521i
$231$	78380.9	+	745744.i	0.0966452	+	0.919518i
$232$	78526.1	+	241678.i	0.0957842	+	0.294794i
$233$	296732.	+	913248.i	0.358076	+	1.10204i	0.954204	+	0.299155i	$0.0967049\pi$
$233$	296732.	+	913248.i	0.358076	+	1.10204i	−0.596129	+	0.802889i	$0.703295\pi$
$234$	−1225.53	−	11660.2i	−0.00146314	−	0.0139208i
$235$	1.40477e6	−	1.56015e6i	1.65934	−	1.84288i
$236$	773581.	+	859149.i	0.904120	+	1.00413i
$237$	8777.81	−	83515.3i	0.0101512	−	0.0965818i
$238$	42994.1	−	9138.67i	0.0492001	−	0.0104578i
$239$	−651107.	−	289891.i	−0.737322	−	0.328277i	0.00348558	−	0.999994i	$-0.498891\pi$
$239$	−651107.	−	289891.i	−0.737322	−	0.328277i	−0.740808	+	0.671717i	$0.765557\pi$
$240$	−489630.	+	355737.i	−0.548706	+	0.398658i
$241$	−283063.	+	126028.i	−0.313936	+	0.139773i	−0.557656	−	0.830072i	$-0.688299\pi$
$241$	−283063.	+	126028.i	−0.313936	+	0.139773i	0.243720	+	0.969846i	$0.421632\pi$
$242$	−143721.	+	248932.i	−0.157754	+	0.273239i
$243$	−467181.	−	809181.i	−0.507539	−	0.879083i
$244$	1.39942e6	+	1.01674e6i	1.50478	+	1.09329i
$245$	−692363.	−	147166.i	−0.736917	−	0.156637i
$246$	−19714.1	+	60673.7i	−0.0207701	+	0.0639238i
$247$	−92935.3			−0.0969256
$248$	−225181.	−	274609.i	−0.232490	−	0.283521i
$249$	225288.			0.230271
$250$	58846.1	−	181110.i	0.0595481	−	0.183270i
$251$	−837277.	−	177969.i	−0.838851	−	0.178303i	−0.231598	−	0.972812i	$-0.574395\pi$
$251$	−837277.	−	177969.i	−0.838851	−	0.178303i	−0.607253	+	0.794508i	$0.707729\pi$
$252$	−745790.	−	541848.i	−0.739801	−	0.537497i
$253$	305491.	+	529125.i	0.300052	+	0.519706i
$254$	−152002.	+	263275.i	−0.147831	+	0.256051i
$255$	−159850.	+	71169.8i	−0.153944	+	0.0685402i
$256$	−568186.	+	412812.i	−0.541865	+	0.393688i
$257$	−659347.	−	293560.i	−0.622704	−	0.277246i	0.0710333	−	0.997474i	$-0.477370\pi$
$257$	−659347.	−	293560.i	−0.622704	−	0.277246i	−0.693737	+	0.720228i	$0.744037\pi$
$258$	75249.4	−	15994.7i	0.0703807	−	0.0149599i
$259$	150773.	−	1.43451e6i	0.139661	−	1.32879i
$260$	109513.	+	121627.i	0.100469	+	0.111583i
$261$	487460.	−	541379.i	0.442933	−	0.491926i
$262$	−1124.08	−	10694.9i	−0.00101168	−	0.00962551i
$263$	113808.	+	350264.i	0.101457	+	0.312252i	0.988883	−	0.148699i	$-0.0475084\pi$
$263$	113808.	+	350264.i	0.101457	+	0.312252i	−0.887426	+	0.460951i	$0.847508\pi$
$264$	98044.3	+	301749.i	0.0865790	+	0.266463i
$265$	207378.	+	1.97307e6i	0.181405	+	1.72595i
$266$	176341.	−	195846.i	0.152809	−	0.169711i
$267$	−354593.	−	393815.i	−0.304405	−	0.338076i
$268$	−145650.	+	1.38577e6i	−0.123873	+	1.17857i
$269$	229580.	−	48798.7i	0.193443	−	0.0411176i	−0.110171	−	0.993913i	$-0.535140\pi$
$269$	229580.	−	48798.7i	0.193443	−	0.0411176i	0.303614	+	0.952795i	$0.401807\pi$
$270$	−275323.	−	122582.i	−0.229844	−	0.102333i
$271$	1.20386e6	−	874656.i	0.995756	−	0.723459i	0.0345821	−	0.999402i	$-0.488990\pi$
$271$	1.20386e6	−	874656.i	0.995756	−	0.723459i	0.961174	+	0.275943i	$0.0889900\pi$
$272$	−222729.	+	99165.1i	−0.182538	+	0.0812712i
$273$	33249.6	−	57590.0i	0.0270010	−	0.0467671i
$274$	208730.	+	361532.i	0.167961	+	0.290918i
$275$	2.72314e6	+	1.97848e6i	2.17139	+	1.57761i
$276$	203595.	+	43275.4i	0.160877	+	0.0341954i
$277$	−711664.	+	2.19028e6i	−0.557282	+	1.71514i	0.132556	+	0.991176i	$0.457682\pi$
$277$	−711664.	+	2.19028e6i	−0.557282	+	1.71514i	−0.689838	+	0.723963i	$0.742318\pi$
$278$	143857.			0.111640
$279$	−359001.	+	952685.i	−0.276112	+	0.732721i
$280$	−944949.			−0.720300
$281$	−180242.	+	554728.i	−0.136173	+	0.419097i	−0.995771	−	0.0918743i	$-0.970714\pi$
$281$	−180242.	+	554728.i	−0.136173	+	0.419097i	0.859598	+	0.510971i	$0.170714\pi$
$282$	−173393.	−	36855.7i	−0.129840	−	0.0275983i
$283$	−898105.	−	652512.i	−0.666594	−	0.484309i	0.202290	−	0.979326i	$-0.435162\pi$
$283$	−898105.	−	652512.i	−0.666594	−	0.484309i	−0.868883	+	0.495017i	$0.835162\pi$
$284$	−491546.	−	851383.i	−0.361633	−	0.626368i
$285$	−524553.	+	908553.i	−0.382541	+	0.662580i
$286$	37058.3	−	16499.4i	0.0267899	−	0.0119276i
$287$	1.05640e6	−	767518.i	0.757047	−	0.550027i
$288$	−537652.	−	239378.i	−0.381962	−	0.170060i
$289$	1.31988e6	−	280549.i	0.929588	−	0.197590i
$290$	38337.2	−	364754.i	0.0267686	−	0.254686i
$291$	489134.	+	543239.i	0.338607	+	0.376061i
$292$	139719.	−	155174.i	0.0958959	−	0.106503i
$293$	228958.	+	2.17839e6i	0.155807	+	1.48240i	0.740998	+	0.671507i	$0.234353\pi$
$293$	228958.	+	2.17839e6i	0.155807	+	1.48240i	−0.585191	+	0.810895i	$0.698981\pi$
$294$	18469.1	+	56842.0i	0.0124617	+	0.0383531i
$295$	−1.04984e6	−	3.23108e6i	−0.702374	−	2.16169i
$296$	−63795.3	−	606972.i	−0.0423213	−	0.402661i
$297$	1.38590e6	−	1.53919e6i	0.911675	−	1.01252i
$298$	−78300.3	−	86961.3i	−0.0510767	−	0.0567264i
$299$	5663.74	−	53886.9i	0.00366375	−	0.0348582i
$300$	1.12163e6	−	238410.i	0.719528	−	0.152940i
$301$	−1.43848e6	−	640453.i	−0.915141	−	0.407447i
$302$	−289360.	+	210232.i	−0.182566	+	0.132642i
$303$	−1.27837e6	+	569165.i	−0.799924	+	0.356149i
$304$	−730892.	+	1.26594e6i	−0.453596	+	0.785651i
$305$	−2.54160e6	−	4.40218e6i	−1.56443	−	2.70968i
$306$	−43134.3	−	31338.9i	−0.0263341	−	0.0191329i
$307$	−727385.	−	154611.i	−0.440472	−	0.0936253i	−0.0176631	−	0.999844i	$-0.505623\pi$
$307$	−727385.	−	154611.i	−0.440472	−	0.0936253i	−0.422809	+	0.906219i	$0.638956\pi$
$308$	985613.	−	3.03340e6i	0.592011	−	1.82202i
$309$	−68674.6			−0.0409166
$310$	135698.	+	494266.i	0.0801993	+	0.292117i
$311$	−28797.0			−0.0168829			−0.00844143	−	0.999964i	$-0.502687\pi$
$311$	−28797.0			−0.0168829			−0.00844143	+	0.999964i	$0.502687\pi$
$312$	8694.88	−	26760.1i	0.00505681	−	0.0155633i
$313$	−1.20299e6	−	255703.i	−0.694066	−	0.147528i	−0.152647	−	0.988281i	$-0.548780\pi$
$313$	−1.20299e6	−	255703.i	−0.694066	−	0.147528i	−0.541420	+	0.840752i	$0.682113\pi$
$314$	81379.0	+	59125.3i	0.0465788	+	0.0338415i
$315$	1.35449e6	+	2.34604e6i	0.769127	+	1.33217i
$316$	−178595.	+	309336.i	−0.100613	+	0.174266i
$317$	−128726.	+	57312.5i	−0.0719479	+	0.0320333i	−0.442395	−	0.896820i	$-0.645871\pi$
$317$	−128726.	+	57312.5i	−0.0719479	+	0.0320333i	0.370447	+	0.928854i	$0.379204\pi$
$318$	135525.	−	98464.6i	0.0751538	−	0.0546025i
$319$	2.30263e6	+	1.02520e6i	1.26691	+	0.564066i
$320$	2.31903e6	−	492925.i	1.26599	−	0.269095i
$321$	−24925.6	+	237151.i	−0.0135015	+	0.128459i
$322$	102811.	+	114183.i	0.0552587	+	0.0613710i
$323$	−282791.	+	314072.i	−0.150820	+	0.167503i
$324$	75518.7	+	718512.i	0.0399661	+	0.380252i
$325$	−92243.5	−	283896.i	−0.0484426	−	0.149091i
$326$	−86752.1	−	266995.i	−0.0452101	−	0.139142i
$327$	−14228.8	−	135378.i	−0.00735867	−	0.0700131i
$328$	369696.	−	410589.i	0.189741	−	0.210728i
$329$	2.42780e6	+	2.69634e6i	1.23658	+	1.37336i
$330$	47866.2	−	455416.i	0.0241960	−	0.230210i
$331$	1.61888e6	−	344103.i	0.812165	−	0.172631i	0.216935	−	0.976186i	$-0.430394\pi$
$331$	1.61888e6	−	344103.i	0.812165	−	0.172631i	0.595231	+	0.803555i	$0.297061\pi$
$332$	−875419.	−	389762.i	−0.435884	−	0.194068i
$333$	−1.41549e6	+	1.02842e6i	−0.699516	+	0.508228i
$334$	−271717.	+	120976.i	−0.133276	+	0.0593382i
$335$	2.04736e6	−	3.54613e6i	0.996739	−	1.72640i
$336$	−522985.	−	905836.i	−0.252721	−	0.437725i
$337$	−2.94524e6	−	2.13984e6i	−1.41269	−	1.02638i	−0.992925	−	0.118745i	$-0.962113\pi$
$337$	−2.94524e6	−	2.13984e6i	−1.41269	−	1.02638i	−0.419764	−	0.907633i	$-0.637887\pi$
$338$	379790.	+	80726.8i	0.180822	+	0.0384349i
$339$	19067.5	−	58683.8i	0.00901145	−	0.0277344i
$340$	744270.			0.349167
$341$	−3.51871e6	−	162735.i	−1.63869	−	0.0757871i
$342$	−319670.			−0.147787
$343$	−436661.	+	1.34390e6i	−0.200405	+	0.616783i
$344$	−651693.	−	138522.i	−0.296925	−	0.0631133i
$345$	−494841.	−	359523.i	−0.223830	−	0.162622i
$346$	4355.39	+	7543.76i	0.00195586	+	0.00338764i
$347$	−542464.	+	939575.i	−0.241851	+	0.418898i	−0.961241	−	0.275708i	$-0.911088\pi$
$347$	−542464.	+	939575.i	−0.241851	+	0.418898i	0.719391	+	0.694606i	$0.244421\pi$
$348$	784436.	−	349253.i	0.347224	−	0.154594i
$349$	−796847.	+	578943.i	−0.350196	+	0.254432i	−0.748951	−	0.662625i	$-0.769442\pi$
$349$	−796847.	+	578943.i	−0.350196	+	0.254432i	0.398755	+	0.917057i	$0.369442\pi$
$350$	773293.	+	344292.i	0.337423	+	0.150230i
$351$	−179666.	+	38189.2i	−0.0778391	+	0.0165452i
$352$	212849.	−	2.02512e6i	0.0915617	−	0.871152i
$353$	172619.	+	191712.i	0.0737311	+	0.0818867i	0.778882	−	0.627171i	$-0.215787\pi$
$353$	172619.	+	191712.i	0.0737311	+	0.0818867i	−0.705151	+	0.709058i	$0.749121\pi$
$354$	−191949.	+	213181.i	−0.0814099	+	0.0904148i
$355$	301978.	+	2.87313e6i	0.127176	+	1.21000i
$356$	696546.	+	2.14375e6i	0.291289	+	0.896496i
$357$	−93448.8	−	287606.i	−0.0388064	−	0.119434i
$358$	37899.5	+	360589.i	0.0156288	+	0.148698i
$359$	188480.	−	209328.i	0.0771842	−	0.0857218i	−0.703316	−	0.710878i	$-0.748298\pi$
$359$	188480.	−	209328.i	0.0771842	−	0.0857218i	0.780500	+	0.625156i	$0.214965\pi$
$360$	766973.	+	851809.i	0.311906	+	0.346407i
$361$	−6043.76	+	57502.5i	−0.00244084	+	0.0232230i
$362$	473071.	−	100554.i	0.189738	−	0.0403301i
$363$	1.80662e6	+	804360.i	0.719616	+	0.320394i
$364$	−228835.	+	166258.i	−0.0905251	+	0.0657704i
$365$	−560560.	+	249577.i	−0.220237	+	0.0980558i
$366$	−214605.	+	371707.i	−0.0837409	+	0.145043i
$367$	1.66135e6	+	2.87754e6i	0.643866	+	1.11521i	0.984562	+	0.175035i	$0.0560038\pi$
$367$	1.66135e6	+	2.87754e6i	0.643866	+	1.11521i	−0.340697	+	0.940173i	$0.610663\pi$
$368$	−689491.	−	500945.i	−0.265405	−	0.192828i
$369$	−1.54930e6	−	329313.i	−0.592337	−	0.125905i
$370$	−272202.	+	837751.i	−0.103368	+	0.318134i
$371$	−3.42876e6			−1.29331
$372$	−843299.	+	853726.i	−0.315954	+	0.319861i
$373$	4.09267e6			1.52312			0.761562	−	0.648092i	$-0.224433\pi$
$373$	4.09267e6			1.52312			0.761562	+	0.648092i	$0.224433\pi$
$374$	57004.9	−	175443.i	0.0210733	−	0.0648571i
$375$	−1.28152e6	−	272396.i	−0.470596	−	0.100028i
$376$	1.24201e6	+	902370.i	0.453058	+	0.329166i
$377$	−111765.	−	193582.i	−0.0404996	−	0.0701474i
$378$	260430.	−	451079.i	0.0937480	−	0.162376i
$379$	1.67306e6	−	744896.i	0.598294	−	0.266378i	−0.0851646	−	0.996367i	$-0.527142\pi$
$379$	1.67306e6	−	744896.i	0.598294	−	0.266378i	0.683459	+	0.729989i	$0.260475\pi$
$380$	3.61015e6	−	2.62293e6i	1.28253	−	0.931810i
$381$	1.91072e6	+	850708.i	0.674349	+	0.300240i
$382$	572145.	−	121613.i	0.200608	−	0.0426405i
$383$	−108699.	+	1.03420e6i	−0.0378642	+	0.360254i	0.959142	+	0.282927i	$0.0913053\pi$
$383$	−108699.	+	1.03420e6i	−0.0378642	+	0.360254i	−0.997006	+	0.0773272i	$0.975361\pi$
$384$	−614866.	−	682878.i	−0.212791	−	0.236328i
$385$	−6.27164e6	+	6.96536e6i	−2.15640	+	2.39492i
$386$	−82156.6	−	781668.i	−0.0280656	−	0.267026i
$387$	590224.	+	1.81652e6i	0.200327	+	0.616543i
$388$	−960833.	−	2.95714e6i	−0.324018	−	0.997223i
$389$	−52151.9	−	496192.i	−0.0174741	−	0.166255i	0.982305	−	0.187290i	$-0.0599705\pi$
$389$	−52151.9	−	496192.i	−0.0174741	−	0.166255i	−0.999779	+	0.0210350i	$0.993304\pi$
$390$	−27173.5	+	30179.3i	−0.00904658	+	0.0100473i
$391$	−164875.	−	183112.i	−0.0545397	−	0.0605725i
$392$	54105.0	−	514775.i	0.0177837	−	0.169201i
$393$	−72369.3	+	15382.6i	−0.0236359	+	0.00502398i
$394$	−679906.	−	302713.i	−0.220652	−	0.0982406i
$395$	849188.	−	616971.i	0.273849	−	0.198963i
$396$	−3.53439e6	+	1.57361e6i	−1.13260	+	0.504266i
$397$	−616254.	+	1.06738e6i	−0.196238	+	0.339894i	−0.947306	−	0.320331i	$-0.896206\pi$
$397$	−616254.	+	1.06738e6i	−0.196238	+	0.339894i	0.751068	+	0.660225i	$0.229539\pi$
$398$	309363.	+	535832.i	0.0978950	+	0.169559i
$399$	−1.46685e6	−	1.06573e6i	−0.461269	−	0.335131i
$400$	−4.59262e6	−	976191.i	−1.43519	−	0.305060i
$401$	347851.	−	1.07057e6i	0.108027	−	0.332473i	−0.882402	−	0.470496i	$-0.844075\pi$
$401$	347851.	−	1.07057e6i	0.108027	−	0.332473i	0.990429	+	0.138024i	$0.0440750\pi$
$402$	−345746.			−0.106707
$403$	243971.	+	195094.i	0.0748301	+	0.0598387i
$404$	5.95214e6			1.81434
$405$	656067.	−	2.01917e6i	0.198752	−	0.611695i
$406$	620011.	+	131787.i	0.186674	+	0.0396788i
$407$	−4.89749e6	−	3.55823e6i	−1.46551	−	1.06475i
$408$	−63977.2	−	110812.i	−0.0190272	−	0.0329561i
$409$	1.21910e6	−	2.11154e6i	0.360355	−	0.624153i	−0.627664	−	0.778484i	$-0.715989\pi$
$409$	1.21910e6	−	2.11154e6i	0.360355	−	0.624153i	0.988019	+	0.154331i	$0.0493222\pi$
$410$	−728481.	+	324341.i	−0.214022	+	0.0952888i
$411$	2.32360e6	−	1.68819e6i	0.678510	−	0.492966i
$412$	266854.	+	118811.i	0.0774518	+	0.0344838i
$413$	5.74321e6	−	1.22076e6i	1.65684	−	0.352171i
$414$	19481.6	−	185355.i	0.00558630	−	0.0531500i
$415$	1.88427e6	+	2.09269e6i	0.537060	+	0.596465i
$416$	−120834.	+	134199.i	−0.0342338	+	0.0380205i
$417$	−103456.	−	984315.i	−0.0291349	−	0.277200i
$418$	−341782.	−	1.05190e6i	−0.0956773	−	0.294464i
$419$	−250056.	−	769593.i	−0.0695829	−	0.214154i	0.910218	−	0.414129i	$-0.135914\pi$
$419$	−250056.	−	769593.i	−0.0695829	−	0.214154i	−0.979801	+	0.199975i	$0.935914\pi$
$420$	333763.	+	3.17554e6i	0.0923241	+	0.878405i
$421$	−607183.	+	674345.i	−0.166961	+	0.185429i	−0.820819	−	0.571188i	$-0.806483\pi$
$421$	−607183.	+	674345.i	−0.166961	+	0.185429i	0.653858	+	0.756617i	$0.273149\pi$
$422$	−177781.	−	197446.i	−0.0485964	−	0.0539717i
$423$	460041.	−	4.37700e6i	0.125010	−	1.18939i
$424$	−1.41908e6	+	301634.i	−0.383346	+	0.0814827i
$425$	−1.24010e6	−	552130.i	−0.333032	−	0.148275i
$426$	197347.	−	143381.i	0.0526875	−	0.0382797i
$427$	8.02557e6	−	3.57322e6i	2.13013	−	0.948396i
$428$	507142.	−	878395.i	0.133820	−	0.231782i
$429$	−139544.	−	241698.i	−0.0366074	−	0.0634059i
$430$	777948.	+	565212.i	0.202899	+	0.147415i
$431$	2.67687e6	+	568985.i	0.694118	+	0.147539i	0.541444	−	0.840737i	$-0.317878\pi$
$431$	2.67687e6	+	568985.i	0.694118	+	0.147539i	0.152675	+	0.988277i	$0.451211\pi$
$432$	−892783.	+	2.74770e6i	−0.230163	+	0.708370i
$433$	−3.30134e6			−0.846196			−0.423098	−	0.906084i	$-0.639057\pi$
$433$	−3.30134e6			−0.846196			−0.423098	+	0.906084i	$0.639057\pi$
$434$	−874054.	+	143947.i	−0.222748	+	0.0366842i
$435$	−2.52332e6			−0.639367
$436$	−178922.	+	550666.i	−0.0450763	+	0.138731i
$437$	−1.44506e6	−	307157.i	−0.361978	−	0.0769407i
$438$	41916.3	+	30454.0i	0.0104399	+	0.00758505i
$439$	−803308.	−	1.39137e6i	−0.198939	−	0.344573i	0.749245	−	0.662293i	$-0.230416\pi$
$439$	−803308.	−	1.39137e6i	−0.198939	−	0.344573i	−0.948185	+	0.317719i	$0.897083\pi$
$440$	−1.98292e6	+	3.43451e6i	−0.488284	+	0.845733i
$441$	−1.35559e6	+	603549.i	−0.331920	+	0.147780i
$442$	−13235.1	+	9615.89i	−0.00322235	+	0.00234118i
$443$	111390.	+	49594.0i	0.0269673	+	0.0120066i	0.420176	−	0.907443i	$-0.361968\pi$
$443$	111390.	+	49594.0i	0.0269673	+	0.0120066i	−0.393209	+	0.919449i	$0.628635\pi$
$444$	−2.01722e6	+	428774.i	−0.485620	+	0.103222i
$445$	692385.	−	6.58761e6i	0.165748	−	1.57699i
$446$	−696251.	−	773265.i	−0.165741	−	0.184074i
$447$	−538704.	+	598292.i	−0.127521	+	0.141626i
$448$	428298.	+	4.07498e6i	0.100821	+	0.959247i
$449$	−1.86945e6	−	5.75358e6i	−0.437621	−	1.34686i	−0.890377	−	0.455224i	$-0.849559\pi$
$449$	−1.86945e6	−	5.75358e6i	−0.437621	−	1.34686i	0.452756	−	0.891634i	$-0.350441\pi$
$450$	−317290.	−	976520.i	−0.0738628	−	0.227326i
$451$	−572836.	−	5.45017e6i	−0.132614	−	1.26174i
$452$	−175619.	+	195044.i	−0.0404320	+	0.0449042i
$453$	1.64656e6	+	1.82869e6i	0.376993	+	0.418693i
$454$	−122308.	+	1.16368e6i	−0.0278493	+	0.264969i
$455$	813047.	−	172818.i	0.184114	−	0.0391346i
$456$	−700847.	−	312037.i	−0.157838	−	0.0702739i
$457$	−559382.	+	406415.i	−0.125291	+	0.0910289i	−0.648666	−	0.761073i	$-0.724673\pi$
$457$	−559382.	+	406415.i	−0.125291	+	0.0910289i	0.523375	+	0.852102i	$0.324673\pi$
$458$	429601.	−	191271.i	0.0956978	−	0.0426074i
$459$	−417644.	+	723380.i	−0.0925282	+	0.160264i
$460$	1.30085e6	+	2.25313e6i	0.286637	+	0.496469i
$461$	4.79916e6	+	3.48679e6i	1.05175	+	0.764141i	0.972545	−	0.232717i	$-0.0747616\pi$
$461$	4.79916e6	+	3.48679e6i	1.05175	+	0.764141i	0.0792058	+	0.996858i	$0.474762\pi$
$462$	774119.	+	164544.i	0.168734	+	0.0358655i
$463$	−84148.9	+	258984.i	−0.0182430	+	0.0561462i	−0.959764	−	0.280809i	$-0.909397\pi$
$463$	−84148.9	+	258984.i	−0.0182430	+	0.0561462i	0.941521	+	0.336955i	$0.109397\pi$
$464$	−3.51590e6			−0.758126
$465$	3.28432e6	−	1.28394e6i	0.704390	−	0.275368i
$466$	1.01347e6			0.216195
$467$	−1.46758e6	+	4.51676e6i	−0.311394	+	0.958373i	0.665819	+	0.746113i	$0.268082\pi$
$467$	−1.46758e6	+	4.51676e6i	−0.311394	+	0.958373i	−0.977213	+	0.212260i	$0.931918\pi$
$468$	335606.	+	71335.3i	0.0708297	+	0.0150553i
$469$	5.72519e6	+	4.15959e6i	1.20187	+	0.873210i
$470$	−1.10787e6	−	1.91889e6i	−0.231337	−	0.400688i
$471$	346028.	−	599339.i	0.0718720	−	0.124486i
$472$	2.26957e6	−	1.01048e6i	0.468910	−	0.208772i
$473$	−5.34635e6	+	3.88435e6i	−1.09876	+	0.798299i
$474$	−80967.2	−	36048.9i	−0.0165525	−	0.00736965i
$475$	−7.96104e6	+	1.69217e6i	−1.61896	+	0.344120i
$476$	−134454.	+	1.27925e6i	−0.0271992	+	0.258783i
$477$	2.78297e6	+	3.09080e6i	0.560032	+	0.621978i
$478$	−503339.	+	559014.i	−0.100761	+	0.111906i
$479$	333584.	+	3.17384e6i	0.0664304	+	0.632043i	0.976191	+	0.216911i	$0.0695980\pi$
$479$	333584.	+	3.17384e6i	0.0664304	+	0.632043i	−0.909761	+	0.415132i	$0.863735\pi$
$480$	629939.	+	1.93875e6i	0.124794	+	0.384078i
$481$	165897.	+	510579.i	0.0326946	+	0.100624i
$482$	34183.4	+	325234.i	0.00670190	+	0.0637643i
$483$	707339.	−	785580.i	0.137962	−	0.153222i
$484$	−5.62855e6	−	6.25114e6i	−1.09215	−	1.21296i
$485$	−955094.	+	9.08711e6i	−0.184371	+	1.75417i
$486$	−964599.	+	205032.i	−0.185249	+	0.0393759i
$487$	8.48232e6	+	3.77657e6i	1.62066	+	0.721565i	0.998136	−	0.0610352i	$-0.0194402\pi$
$487$	8.48232e6	+	3.77657e6i	1.62066	+	0.721565i	0.622525	+	0.782600i	$0.286107\pi$
$488$	3.00724e6	−	2.18489e6i	0.571634	−	0.415317i
$489$	−1.76447e6	+	785594.i	−0.333690	+	0.148568i
$490$	−373531.	+	646975.i	−0.0702808	+	0.121730i
$491$	−763454.	−	1.32234e6i	−0.142916	−	0.247537i	0.785678	−	0.618636i	$-0.212314\pi$
$491$	−763454.	−	1.32234e6i	−0.142916	−	0.247537i	−0.928593	+	0.371099i	$0.878981\pi$
$492$	−1.51038e6	−	1.09736e6i	−0.281303	−	0.204379i
$493$	−994290.	−	211343.i	−0.184245	−	0.0391625i
$494$	−30310.3	+	93285.6i	−0.00558822	+	0.0171988i
$495$	1.13692e7			2.08554
$496$	4.57624e6	−	1.78899e6i	0.835227	−	0.326516i
$497$	−4.99286e6			−0.906689
$498$	73476.3	−	226137.i	0.0132762	−	0.0408600i
$499$	−5.42337e6	−	1.15277e6i	−0.975030	−	0.207249i	−0.307267	−	0.951623i	$-0.599415\pi$
$499$	−5.42337e6	−	1.15277e6i	−0.975030	−	0.207249i	−0.667763	+	0.744374i	$0.732748\pi$
$500$	4.50846e6	+	3.27559e6i	0.806498	+	0.585955i
$501$	1.02316e6	+	1.77217e6i	0.182117	+	0.315435i
$502$	−451712.	+	782389.i	−0.0800023	+	0.138568i
$503$	−1.84510e6	+	821492.i	−0.325162	+	0.144772i	−0.562825	−	0.826576i	$-0.690285\pi$
$503$	−1.84510e6	+	821492.i	−0.325162	+	0.144772i	0.237662	+	0.971348i	$0.423619\pi$
$504$	−1.60264e6	+	1.16438e6i	−0.281034	+	0.204183i
$505$	−1.59790e7	−	7.11431e6i	−2.78818	−	1.24138i
$506$	630754.	−	134071.i	0.109517	−	0.0232787i
$507$	279229.	−	2.65669e6i	0.0482437	−	0.459008i
$508$	−5.95287e6	−	6.61133e6i	−1.02345	−	1.13666i
$509$	3.23496e6	−	3.59279e6i	0.553445	−	0.614663i	−0.399895	−	0.916561i	$-0.630953\pi$
$509$	3.23496e6	−	3.59279e6i	0.553445	−	0.614663i	0.953340	+	0.301898i	$0.0976202\pi$
$510$	19303.9	+	183664.i	0.00328639	+	0.0312679i
$511$	−327705.	−	1.00857e6i	−0.0555177	−	0.170866i
$512$	1.48043e6	+	4.55630e6i	0.249582	+	0.768134i
$513$	523489.	+	4.98066e6i	0.0878242	+	0.835591i
$514$	−509709.	+	566089.i	−0.0850971	+	0.0945099i
$515$	−574383.	−	637916.i	−0.0954296	−	0.105985i
$516$	−235325.	+	2.23897e6i	−0.0389085	+	0.370189i
$517$	1.48947e7	−	3.16597e6i	2.45079	−	0.520931i
$518$	−1.39074e6	−	619199.i	−0.227731	−	0.101393i
$519$	48484.4	−	35226.0i	0.00790103	−	0.00574043i
$520$	321296.	−	143050.i	0.0521071	−	0.0231996i
$521$	1.80506e6	−	3.12645e6i	0.291338	−	0.504612i	−0.682789	−	0.730616i	$-0.739233\pi$
$521$	1.80506e6	−	3.12645e6i	0.291338	−	0.504612i	0.974126	+	0.226004i	$0.0725663\pi$
$522$	−384437.	−	665865.i	−0.0617517	−	0.106957i
$523$	3.78504e6	+	2.74999e6i	0.605084	+	0.439619i	0.847680	−	0.530508i	$-0.177999\pi$
$523$	3.78504e6	+	2.74999e6i	0.605084	+	0.439619i	−0.242596	+	0.970128i	$0.577999\pi$
$524$	307824.	+	65430.0i	0.0489750	+	0.0104100i
$525$	1.79963e6	−	5.53870e6i	0.284961	−	0.877020i
$526$	388702.			0.0612565
$527$	1.40169e6	−	230843.i	0.219850	−	0.0362068i
$528$	−4.38980e6			−0.685267
$529$	−1.72277e6	+	5.30215e6i	−0.267663	+	0.823784i
$530$	2.04814e6	+	435346.i	0.316716	+	0.0673201i
$531$	−5.76193e6	−	4.18629e6i	−0.886813	−	0.644307i
$532$	3.85609e6	+	6.67894e6i	0.590701	+	1.02312i
$533$	−243000.	+	420889.i	−0.0370500	+	0.0641725i
$534$	−510948.	+	227489.i	−0.0775396	+	0.0345228i
$535$	−2.41137e6	+	1.75196e6i	−0.364232	+	0.264630i
$536$	2.73544e6	+	1.21789e6i	0.411258	+	0.183104i
$537$	2.44000e6	−	518639.i	0.365136	−	0.0776120i
$538$	25893.6	−	246361.i	0.00385688	−	0.0366958i
$539$	−3.43538e6	−	3.81538e6i	−0.509335	−	0.565674i
$540$	5.90146e6	−	6.55423e6i	0.870913	−	0.967247i
$541$	−923362.	−	8.78520e6i	−0.135637	−	1.29050i	−0.824605	−	0.565709i	$-0.808602\pi$
$541$	−923362.	−	8.78520e6i	−0.135637	−	1.29050i	0.688968	−	0.724792i	$-0.258064\pi$
$542$	−485320.	−	1.49366e6i	−0.0709627	−	0.218401i
$543$	−1.02823e6	−	3.16458e6i	−0.149655	−	0.460592i
$544$	85839.3	+	816707.i	0.0124362	+	0.118323i
$545$	1.13852e6	−	1.26445e6i	0.164190	−	0.182352i
$546$	−46962.9	−	52157.6i	−0.00674176	−	0.00748749i
$547$	−570793.	+	5.43074e6i	−0.0815663	+	0.776051i	0.874919	+	0.484270i	$0.160915\pi$
$547$	−570793.	+	5.43074e6i	−0.0815663	+	0.776051i	−0.956485	+	0.291781i	$0.905752\pi$
$548$	−1.19497e7	+	2.53998e6i	−1.69983	+	0.361309i
$549$	−9.73502e6	−	4.33431e6i	−1.37850	−	0.613746i
$550$	2.87407e6	−	2.08814e6i	0.405127	−	0.294342i
$551$	−5.56770e6	+	2.47890e6i	−0.781263	+	0.347841i
$552$	223641.	−	387357.i	0.0312394	−	0.0541083i
$553$	907037.	+	1.57103e6i	0.126128	+	0.218460i
$554$	1.96643e6	+	1.42869e6i	0.272209	+	0.197772i
$555$	5.92789e6	+	1.26001e6i	0.816898	+	0.173637i
$556$	−1.30092e6	+	4.00382e6i	−0.178469	+	0.549272i
$557$	6.27848e6			0.857465			0.428732	−	0.903431i	$-0.358960\pi$
$557$	6.27848e6			0.857465			0.428732	+	0.903431i	$0.358960\pi$
$558$	839189.	+	671067.i	0.114097	+	0.0912389i
$559$	586059.			0.0793253
$560$	4.04013e6	−	1.24342e7i	0.544409	−	1.67552i
$561$	−1.24143e6	−	263874.i	−0.166538	−	0.0353988i
$562$	498034.	+	361843.i	0.0665148	+	0.0483258i
$563$	−5.14756e6	−	8.91583e6i	−0.684432	−	1.18547i	−0.973615	−	0.228197i	$-0.926717\pi$
$563$	−5.14756e6	−	8.91583e6i	−0.684432	−	1.18547i	0.289183	−	0.957274i	$-0.406616\pi$
$564$	2.59377e6	−	4.49254e6i	0.343347	−	0.594695i
$565$	704589.	−	313703.i	0.0928571	−	0.0413426i
$566$	−947883.	+	688677.i	−0.124369	+	0.0903597i
$567$	3.35201e6	+	1.49241e6i	0.437872	+	0.194953i
$568$	−2.06642e6	+	439230.i	−0.268749	+	0.0571244i
$569$	−1.52233e6	+	1.44840e7i	−0.197118	+	1.87546i	0.232711	+	0.972546i	$0.425240\pi$
$569$	−1.52233e6	+	1.44840e7i	−0.197118	+	1.87546i	−0.429829	+	0.902910i	$0.641426\pi$
$570$	740897.	+	822850.i	0.0955148	+	0.106080i
$571$	7.22122e6	−	8.01997e6i	0.926873	−	1.02940i	−0.0726139	−	0.997360i	$-0.523134\pi$
$571$	7.22122e6	−	8.01997e6i	0.926873	−	1.02940i	0.999487	−	0.0320364i	$-0.0101993\pi$
$572$	124087.	+	1.18061e6i	0.0158575	+	0.150874i
$573$	−1.24357e6	−	3.82733e6i	−0.158229	−	0.486978i
$574$	−425872.	−	1.31070e6i	−0.0539510	−	0.166044i
$575$	−496007.	−	4.71920e6i	−0.0625631	−	0.595249i
$576$	3.32570e6	−	3.69356e6i	0.417663	−	0.463862i
$577$	−5.61452e6	−	6.23556e6i	−0.702059	−	0.779715i	0.281644	−	0.959519i	$-0.409120\pi$
$577$	−5.61452e6	−	6.23556e6i	−0.702059	−	0.779715i	−0.983702	+	0.179804i	$0.942454\pi$
$578$	148865.	−	1.41636e6i	0.0185342	−	0.176341i
$579$	−5.28932e6	+	1.12428e6i	−0.655697	+	0.139373i
$580$	9.80509e6	+	4.36551e6i	1.21027	+	0.538846i
$581$	−3.93730e6	+	2.86061e6i	−0.483903	+	0.351576i
$582$	704814.	−	313804.i	0.0862516	−	0.0384017i
$583$	−7.19503e6	+	1.24622e7i	−0.876721	+	1.51853i
$584$	−224355.	−	388594.i	−0.0272209	−	0.0471480i
$585$	−815698.	−	592639.i	−0.0985461	−	0.0715980i
$586$	2.26127e6	+	480648.i	0.272025	+	0.0578207i
$587$	−4.51401e6	+	1.38927e7i	−0.540713	+	1.66414i	0.190257	+	0.981734i	$0.439068\pi$
$587$	−4.51401e6	+	1.38927e7i	−0.540713	+	1.66414i	−0.730970	+	0.682410i	$0.760932\pi$
$588$	−1.74903e6			−0.208620
$589$	5.98550e6	−	6.05951e6i	0.710906	−	0.719697i
$590$	−3.58566e6			−0.424071
$591$	−1.58230e6	+	4.86981e6i	−0.186346	+	0.573513i
$592$	8.25968e6	+	1.75565e6i	0.968632	+	0.205889i
$593$	825819.	+	599993.i	0.0964380	+	0.0700663i	0.634959	−	0.772546i	$-0.281017\pi$
$593$	825819.	+	599993.i	0.0964380	+	0.0700663i	−0.538521	+	0.842612i	$0.681017\pi$
$594$	−1.09299e6	−	1.89312e6i	−0.127102	−	0.220147i
$595$	1.88997e6	−	3.27353e6i	0.218858	−	0.379074i
$596$	3.12837e6	−	1.39284e6i	0.360747	−	0.160615i
$597$	3.44384e6	−	2.50210e6i	0.395464	−	0.287322i
$598$	−52242.8	−	23260.0i	−0.00597412	−	0.00265985i
$599$	−7.80984e6	+	1.66003e6i	−0.889355	+	0.189038i	−0.629862	−	0.776707i	$-0.716889\pi$
$599$	−7.80984e6	+	1.66003e6i	−0.889355	+	0.189038i	−0.259493	+	0.965745i	$0.583555\pi$
$600$	257573.	−	2.45064e6i	0.0292094	−	0.277908i
$601$	4.70093e6	+	5.22091e6i	0.530882	+	0.589604i	0.947611	−	0.319427i	$-0.103490\pi$
$601$	4.70093e6	+	5.22091e6i	0.530882	+	0.589604i	−0.416729	+	0.909031i	$0.636824\pi$
$602$	−1.11202e6	+	1.23502e6i	−0.125061	+	0.138894i
$603$	−897279.	−	8.53704e6i	−0.100493	−	0.956123i
$604$	−3.23443e6	−	9.95456e6i	−0.360750	−	1.11027i
$605$	7.63860e6	+	2.35092e7i	0.848448	+	2.61126i
$606$	154379.	+	1.46881e6i	0.0170768	+	0.162474i
$607$	−1.02607e7	+	1.13957e7i	−1.13033	+	1.25536i	−0.167324	+	0.985902i	$0.553513\pi$
$607$	−1.02607e7	+	1.13957e7i	−1.13033	+	1.25536i	−0.963011	+	0.269462i	$0.913154\pi$
$608$	3.29458e6	+	3.65900e6i	0.361444	+	0.401424i
$609$	455844.	−	4.33707e6i	0.0498050	−	0.473863i
$610$	−5.24770e6	+	1.11543e6i	−0.571011	+	0.121372i
$611$	−1.23367e6	−	549265.i	−0.133689	−	0.0595222i
$612$	1.26229e6	−	917104.i	0.136232	−	0.0989784i
$613$	1.13217e7	−	5.04074e6i	1.21691	−	0.541805i	0.305066	−	0.952331i	$-0.401322\pi$
$613$	1.13217e7	−	5.04074e6i	1.21691	−	0.541805i	0.911849	+	0.410526i	$0.134655\pi$
$614$	−392426.	+	679701.i	−0.0420084	+	0.0727608i
$615$	2.74312e6	+	4.75123e6i	0.292454	+	0.506545i
$616$	−5.54499e6	−	4.02867e6i	−0.588774	−	0.427770i
$617$	8.93581e6	+	1.89937e6i	0.944977	+	0.200861i	0.654535	−	0.756032i	$-0.272864\pi$
$617$	8.93581e6	+	1.89937e6i	0.944977	+	0.200861i	0.290442	+	0.956893i	$0.406198\pi$
$618$	−22397.8	+	68933.4i	−0.00235904	+	0.00726037i
$619$	−7.73822e6			−0.811736			−0.405868	−	0.913932i	$-0.633031\pi$
$619$	−7.73822e6			−0.811736			−0.405868	+	0.913932i	$0.633031\pi$
$620$	−1.49835e7	−	692961.i	−1.56543	−	0.0723986i
$621$	−2.91985e6			−0.303831
$622$	−9391.97	+	28905.5i	−0.000973376	+	0.00299574i
$623$	1.11976e7	+	2.38013e6i	1.15586	+	0.245686i
$624$	314951.	+	228826.i	0.0323804	+	0.0235257i
$625$	−199228.	−	345073.i	−0.0204010	−	0.0353355i
$626$	−649015.	+	1.12413e6i	−0.0661941	+	0.114651i
$627$	−6.95160e6	+	3.09505e6i	−0.706180	+	0.314412i
$628$	−2.38148e6	+	1.73025e6i	−0.240962	+	0.175069i
$629$	2.23029e6	+	992990.i	0.224768	+	0.100073i
$630$	2.79664e6	−	594444.i	0.280728	−	0.0596705i
$631$	−539258.	+	5.13070e6i	−0.0539167	+	0.512983i	0.933919	+	0.357484i	$0.116365\pi$
$631$	−539258.	+	5.13070e6i	−0.0539167	+	0.512983i	−0.987836	+	0.155499i	$0.950301\pi$
$632$	513606.	+	570417.i	0.0511490	+	0.0568067i
$633$	−1.22313e6	+	1.35842e6i	−0.121329	+	0.134749i
$634$	15545.3	+	147903.i	0.00153594	+	0.0146135i
$635$	8.07874e6	+	2.48638e7i	0.795077	+	2.44700i
$636$	1.51488e6	+	4.66233e6i	0.148503	+	0.457046i
$637$	47592.7	+	452814.i	0.00464720	+	0.0442152i
$638$	1.78005e6	−	1.97694e6i	0.173133	−	0.192284i
$639$	4.05248e6	+	4.50073e6i	0.392617	+	0.436045i
$640$	1.20060e6	−	1.14229e7i	0.115864	−	1.10237i
$641$	−1.46861e7	+	3.12162e6i	−1.41176	+	0.300079i	−0.849808	−	0.527092i	$-0.823282\pi$
$641$	−1.46861e7	+	3.12162e6i	−1.41176	+	0.300079i	−0.561951	+	0.827170i	$0.689949\pi$
$642$	229916.	+	102365.i	0.0220156	+	0.00980199i
$643$	−2.58131e6	+	1.87543e6i	−0.246214	+	0.178885i	−0.704047	−	0.710153i	$-0.748626\pi$
$643$	−2.58131e6	+	1.87543e6i	−0.246214	+	0.178885i	0.457833	+	0.889038i	$0.348626\pi$
$644$	−4.10767e6	+	1.82885e6i	−0.390284	+	0.173766i
$645$	3.30788e6	−	5.72942e6i	0.313077	−	0.542265i
$646$	223025.	+	386290.i	0.0210267	+	0.0364193i
$647$	−8.63394e6	−	6.27293e6i	−0.810865	−	0.589128i	0.103216	−	0.994659i	$-0.467087\pi$
$647$	−8.63394e6	−	6.27293e6i	−0.810865	−	0.589128i	−0.914081	+	0.405531i	$0.867087\pi$
$648$	1.51860e6	+	322788.i	0.142071	+	0.0301982i
$649$	7.61480e6	−	2.34359e7i	0.709654	−	2.18409i
$650$	−315051.			−0.0292481
$651$	1.61351e6	+	5.87701e6i	0.149217	+	0.543506i
$652$	8.21548e6			0.756857
$653$	2.70907e6	−	8.33765e6i	0.248620	−	0.765175i	−0.746400	−	0.665498i	$-0.768219\pi$
$653$	2.70907e6	−	8.33765e6i	0.248620	−	0.765175i	0.995020	−	0.0996767i	$-0.0317809\pi$
$654$	−140529.	−	29870.4i	−0.0128476	−	0.00273084i
$655$	−748173.	−	543579.i	−0.0681394	−	0.0495062i
$656$	3.82216e6	+	6.62017e6i	0.346776	+	0.600634i
$657$	−643179.	+	1.11402e6i	−0.0581324	+	0.100688i
$658$	3.49832e6	−	1.55755e6i	0.314988	−	0.140242i
$659$	2.85024e6	−	2.07082e6i	0.255663	−	0.185750i	−0.452570	−	0.891729i	$-0.649493\pi$
$659$	2.85024e6	−	2.07082e6i	0.255663	−	0.185750i	0.708233	+	0.705979i	$0.249493\pi$
$660$	1.22422e7	+	5.45058e6i	1.09396	+	0.487061i
$661$	−7.01219e6	+	1.49049e6i	−0.624238	+	0.132686i	−0.509162	−	0.860671i	$-0.670045\pi$
$661$	−7.01219e6	+	1.49049e6i	−0.624238	+	0.132686i	−0.115076	+	0.993357i	$0.536711\pi$
$662$	182588.	−	1.73721e6i	0.0161930	−	0.154066i
$663$	75312.9	+	83643.4i	0.00665404	+	0.00739006i
$664$	−1.37789e6	+	1.53031e6i	−0.121282	+	0.134697i
$665$	−2.36896e6	−	2.25391e7i	−0.207732	−	1.97644i
$666$	570637.	+	1.75624e6i	0.0498511	+	0.153426i
$667$	−1.09804e6	−	3.37941e6i	−0.0955657	−	0.294121i
$668$	−909823.	−	8.65639e6i	−0.0788889	−	0.750578i
$669$	−4.79019e6	+	5.32005e6i	−0.413797	+	0.459569i
$670$	−2.89176e6	−	3.21162e6i	−0.248871	−	0.276400i
$671$	3.85395e6	−	3.66679e7i	0.330446	−	3.14398i
$672$	−3.44611e6	+	732493.i	−0.294378	+	0.0625721i
$673$	−1.40081e7	−	6.23679e6i	−1.19218	−	0.530791i	−0.287867	−	0.957670i	$-0.592946\pi$
$673$	−1.40081e7	−	6.23679e6i	−1.19218	−	0.530791i	−0.904308	+	0.426880i	$0.859613\pi$
$674$	−3.10848e6	+	2.25845e6i	−0.263572	+	0.191496i
$675$	−1.46952e7	+	6.54273e6i	−1.24141	+	0.552713i
$676$	−5.68125e6	+	9.84022e6i	−0.478165	+	0.828205i
$677$	3.29930e6	+	5.71455e6i	0.276662	+	0.479193i	0.970553	−	0.240887i	$-0.0774383\pi$
$677$	3.29930e6	+	5.71455e6i	0.276662	+	0.479193i	−0.693891	+	0.720080i	$0.744105\pi$
$678$	−52686.2	−	38278.8i	−0.00440172	−	0.00319804i
$679$	−1.54463e7	−	3.28321e6i	−1.28573	−	0.273291i
$680$	494233.	−	1.52109e6i	0.0409883	−	0.126149i
$681$	8.05020e6			0.665180
$682$	−1.31096e6	+	3.47890e6i	−0.107926	+	0.286405i
$683$	−1.09720e7			−0.899984			−0.449992	−	0.893033i	$-0.648573\pi$
$683$	−1.09720e7			−0.899984			−0.449992	+	0.893033i	$0.648573\pi$
$684$	2.89081e6	−	8.89700e6i	0.236254	−	0.727115i
$685$	3.51157e7	+	7.46408e6i	2.85940	+	0.607785i
$686$	1.20655e6	+	876613.i	0.0978896	+	0.0711209i
$687$	−1.61768e6	−	2.80190e6i	−0.130768	−	0.226496i
$688$	4.60907e6	−	7.98314e6i	0.371229	−	0.642988i
$689$	1.16583e6	−	519060.i	0.0935591	−	0.0416552i
$690$	−522267.	+	379449.i	−0.0417609	+	0.0303411i
$691$	570734.	+	254107.i	0.0454714	+	0.0202452i	0.429346	−	0.903140i	$-0.358744\pi$
$691$	570734.	+	254107.i	0.0454714	+	0.0202452i	−0.383875	+	0.923385i	$0.625411\pi$
$692$	−249343.	+	52999.5i	−0.0197939	+	0.00420733i
$693$	−2.05387e6	+	1.95413e7i	−0.162458	+	1.54568i
$694$	766195.	+	850945.i	0.0603866	+	0.0670661i
$695$	8.27799e6	−	9.19364e6i	0.650074	−	0.721980i
$696$	−192877.	−	1.83510e6i	−0.0150924	−	0.143594i
$697$	682957.	+	2.10193e6i	0.0532490	+	0.163884i
$698$	321238.	+	988669.i	0.0249568	+	0.0768091i
$699$	−728839.	−	6.93444e6i	−0.0564207	−	0.536807i
$700$	−1.65753e7	+	1.84087e7i	−1.27854	+	1.41997i
$701$	1.17587e7	+	1.30594e7i	0.903785	+	1.00376i	0.999965	+	0.00839116i	$0.00267102\pi$
$701$	1.17587e7	+	1.30594e7i	0.903785	+	1.00376i	−0.0961796	+	0.995364i	$0.530662\pi$
$702$	−20263.9	+	192798.i	−0.00155196	+	0.0147659i
$703$	1.43177e7	−	3.04332e6i	1.09266	−	0.232252i
$704$	1.57097e7	+	6.99439e6i	1.19464	+	0.531886i
$705$	−1.23329e7	+	8.96038e6i	−0.934528	+	0.678974i
$706$	248733.	−	110743.i	0.0187812	−	0.00836191i
$707$	1.51147e7	−	2.61793e7i	1.13723	−	1.96975i
$708$	−4.19739e6	−	7.27010e6i	−0.314700	−	0.545076i
$709$	−7.94180e6	−	5.77006e6i	−0.593340	−	0.431087i	0.250169	−	0.968202i	$-0.419514\pi$
$709$	−7.94180e6	−	5.77006e6i	−0.593340	−	0.431087i	−0.843509	+	0.537116i	$0.819514\pi$
$710$	2.98244e6	+	633938.i	0.222038	+	0.0471955i
$711$	679983.	−	2.09277e6i	0.0504457	−	0.155256i
$712$	4.84380e6			0.358085
$713$	3.14873e6	+	3.83987e6i	0.231959	+	0.282874i
$714$	−319168.			−0.0234300
$715$	1.07800e6	−	3.31775e6i	0.0788595	−	0.242705i
$716$	−1.03786e7	−	2.20604e6i	−0.756582	−	0.160816i
$717$	4.18692e6	+	3.04197e6i	0.304156	+	0.220982i
$718$	−148645.	−	257461.i	−0.0107607	−	0.0186381i
$719$	962229.	−	1.66663e6i	0.0694154	−	0.120231i	−0.829229	−	0.558909i	$-0.811220\pi$
$719$	962229.	−	1.66663e6i	0.0694154	−	0.120231i	0.898644	+	0.438678i	$0.144553\pi$
$720$	−1.44878e7	+	6.45040e6i	−1.04153	+	0.463720i
$721$	1.20021e6	−	872003.i	0.0859842	−	0.0624712i
$722$	55748.1	+	24820.6i	0.00398004	+	0.00177203i
$723$	2.20076e6	−	467786.i	0.156577	−	0.0332814i
$724$	−1.47942e6	+	1.40758e7i	−0.104893	+	0.997989i
$725$	−1.30987e7	−	1.45476e7i	−0.925518	−	1.02789i
$726$	1.39661e6	−	1.55109e6i	0.0983408	−	0.109219i
$727$	−1.68531e6	−	1.60347e7i	−0.118262	−	1.12519i	−0.879230	−	0.476398i	$-0.841942\pi$
$727$	−1.68531e6	−	1.60347e7i	−0.118262	−	1.12519i	0.760968	−	0.648789i	$-0.224724\pi$
$728$	187831.	+	578083.i	0.0131352	+	0.0404261i
$729$	340093.	+	1.04670e6i	0.0237017	+	0.0729462i
$730$	67694.6	+	644071.i	0.00470161	+	0.0447329i
$731$	1.78331e6	−	1.98056e6i	0.123434	−	0.137087i
$732$	−8.40459e6	−	9.33424e6i	−0.579747	−	0.643875i
$733$	−2.35773e6	+	2.24323e7i	−0.162082	+	1.54211i	0.547091	+	0.837073i	$0.315735\pi$
$733$	−2.35773e6	+	2.24323e7i	−0.162082	+	1.54211i	−0.709173	+	0.705034i	$0.750932\pi$
$734$	3.43022e6	−	729116.i	0.235008	−	0.0499524i
$735$	4.69542e6	+	2.09054e6i	0.320595	+	0.142738i
$736$	−2.32239e6	+	1.68731e6i	−0.158030	+	0.114816i
$737$	2.71324e7	−	1.20801e7i	1.84001	−	0.819224i
$738$	−835849.	+	1.44773e6i	−0.0564920	+	0.0978470i
$739$	6.24495e6	+	1.08166e7i	0.420647	+	0.728582i	0.996003	−	0.0893212i	$-0.0284698\pi$
$739$	6.24495e6	+	1.08166e7i	0.420647	+	0.728582i	−0.575356	+	0.817903i	$0.695136\pi$
$740$	−2.08546e7	−	1.51517e7i	−1.39998	−	1.01715i
$741$	660085.	+	140305.i	0.0441626	+	0.00938704i
$742$	−1.11827e6	+	3.44168e6i	−0.0745653	+	0.229489i
$743$	−1.07245e7			−0.712697			−0.356349	−	0.934353i	$-0.615978\pi$
$743$	−1.07245e7			−0.712697			−0.356349	+	0.934353i	$0.615978\pi$
$744$	1.18480e6	+	2.29040e6i	0.0784717	+	0.151698i
$745$	−1.00631e7			−0.664268
$746$	1.33480e6	−	4.10810e6i	0.0878152	−	0.270268i
$747$	5.77438e6	+	1.22738e6i	0.378621	+	0.0804783i
$748$	4.36740e6	+	3.17310e6i	0.285410	+	0.207362i
$749$	−2.57563e6	−	4.46113e6i	−0.167757	−	0.290563i
$750$	−691385.	+	1.19751e6i	−0.0448814	+	0.0777369i
$751$	−1.68783e7	+	7.51470e6i	−1.09202	+	0.486197i	−0.872103	−	0.489323i	$-0.837244\pi$
$751$	−1.68783e7	+	7.51470e6i	−1.09202	+	0.486197i	−0.219913	+	0.975520i	$0.570577\pi$
$752$	−1.71842e7	+	1.24850e7i	−1.10811	+	0.805091i
$753$	5.67818e6	+	2.52809e6i	0.364940	+	0.162482i
$754$	−230763.	+	49050.2i	−0.0147822	+	0.00314204i
$755$	−3.21511e6	+	3.05898e7i	−0.205272	+	1.95303i
$756$	1.01992e7	+	1.13274e7i	0.649028	+	0.720819i
$757$	−9.61547e6	+	1.06791e7i	−0.609861	+	0.677319i	−0.966424	−	0.256952i	$-0.917282\pi$
$757$	−9.61547e6	+	1.06791e7i	−0.609861	+	0.677319i	0.356563	+	0.934271i	$0.383948\pi$
$758$	−202043.	−	1.92231e6i	−0.0127724	−	0.121521i
$759$	−1.37096e6	−	4.21938e6i	−0.0863815	−	0.265855i
$760$	−2.96326e6	−	9.11997e6i	−0.186095	−	0.572742i
$761$	−1.59203e6	−	1.51471e7i	−0.0996526	−	0.948132i	−0.924089	−	0.382177i	$-0.875174\pi$
$761$	−1.59203e6	−	1.51471e7i	−0.0996526	−	0.948132i	0.824436	−	0.565954i	$-0.191492\pi$
$762$	1.47708e6	−	1.64047e6i	0.0921548	−	0.102348i
$763$	1.96765e6	+	2.18530e6i	0.122359	+	0.135894i
$764$	−1.78925e6	+	1.70236e7i	−0.110902	+	1.05516i
$765$	−4.48488e6	+	953290.i	−0.277075	+	0.0588941i
$766$	1.00265e6	+	446408.i	0.0617414	+	0.0274891i
$767$	−1.76797e6	+	1.28450e6i	−0.108514	+	0.0788401i
$768$	4.65884e6	−	2.07425e6i	0.285020	−	0.126899i
$769$	−1.27686e6	+	2.21158e6i	−0.0778622	+	0.134861i	−0.902327	−	0.431051i	$-0.858143\pi$
$769$	−1.27686e6	+	2.21158e6i	−0.0778622	+	0.134861i	0.824465	+	0.565913i	$0.191476\pi$
$770$	4.94615e6	+	8.56698e6i	0.300636	+	0.520716i
$771$	4.23991e6	+	3.08047e6i	0.256874	+	0.186630i
$772$	2.24982e7	+	4.78214e6i	1.35864	+	0.288788i
$773$	8.78607e6	−	2.70408e7i	0.528866	−	1.62768i	−0.227674	−	0.973737i	$-0.573112\pi$
$773$	8.78607e6	−	2.70408e7i	0.528866	−	1.62768i	0.756541	−	0.653946i	$-0.226888\pi$
$774$	2.01587e6			0.120951
$775$	2.44514e7	+	1.22700e7i	1.46234	+	0.733818i
$776$	−6.68166e6			−0.398318
$777$	−3.23658e6	+	9.96118e6i	−0.192324	+	0.591914i
$778$	−515071.	−	109482.i	−0.0305083	−	0.00648474i
$779$	1.07203e7	+	7.78874e6i	0.632940	+	0.459858i
$780$	−594211.	−	1.02920e6i	−0.0349707	−	0.0605710i
$781$	−1.04772e7	+	1.81470e7i	−0.614635	+	1.06458i
$782$	−237575.	+	105775.i	−0.0138926	+	0.00618539i
$783$	−9.74505e6	+	7.08019e6i	−0.568041	+	0.412706i
$784$	6.54241e6	+	2.91287e6i	0.380143	+	0.169251i
$785$	8.46137e6	−	1.79852e6i	0.490079	−	0.104170i
$786$	−8162.29	+	77659.0i	−0.000471254	+	0.00448369i
$787$	3.16093e6	+	3.51057e6i	0.181919	+	0.202041i	0.827206	−	0.561899i	$-0.189929\pi$
$787$	3.16093e6	+	3.51057e6i	0.181919	+	0.202041i	−0.645287	+	0.763940i	$0.723262\pi$
$788$	1.45735e7	−	1.61855e7i	0.836083	−	0.928564i
$789$	−279536.	−	2.65961e6i	−0.0159862	−	0.152099i
$790$	−342339.	−	1.05361e6i	−0.0195159	−	0.0600637i
$791$	411905.	+	1.26771e6i	0.0234076	+	0.0720410i
$792$	869037.	+	8.26833e6i	0.0492295	+	0.468387i
$793$	−2.18788e6	+	2.42989e6i	−0.123549	+	0.137216i
$794$	870418.	+	966697.i	0.0489978	+	0.0544176i
$795$	1.50583e6	−	1.43271e7i	0.0845006	−	0.803969i
$796$	−1.77108e7	+	3.76454e6i	−0.990730	+	0.210586i
$797$	6.84413e6	+	3.04720e6i	0.381656	+	0.169924i	0.588592	−	0.808430i	$-0.299682\pi$
$797$	6.84413e6	+	3.04720e6i	0.381656	+	0.169924i	−0.206936	+	0.978355i	$0.566349\pi$
$798$	−1.54815e6	+	1.12480e6i	−0.0860610	+	0.0625270i
$799$	−5.61014e6	+	2.49779e6i	−0.310890	+	0.138417i
$800$	−7.90736e6	+	1.36960e7i	−0.436824	+	0.756602i
$801$	−6.94309e6	−	1.20258e7i	−0.382359	−	0.662265i
$802$	−961159.	−	698323.i	−0.0527667	−	0.0383372i
$803$	−4.35343e6	−	925349.i	−0.238255	−	0.0506427i
$804$	3.12661e6	−	9.62273e6i	0.170582	−	0.524999i
$805$	1.32133e7			0.718656
$806$	275399.	−	181262.i	0.0149323	−	0.00982808i
$807$	−1.70429e6			−0.0921214
$808$	3.95253e6	−	1.21646e7i	0.212984	−	0.655496i
$809$	−5.26567e6	−	1.11925e6i	−0.282867	−	0.0601252i	0.0642934	−	0.997931i	$-0.479521\pi$
$809$	−5.26567e6	−	1.11925e6i	−0.282867	−	0.0601252i	−0.347160	+	0.937806i	$0.612854\pi$
$810$	−1.81280e6	−	1.31708e6i	−0.0970819	−	0.0705342i
$811$	−1.18853e7	−	2.05860e7i	−0.634539	−	1.09905i	−0.986613	−	0.163082i	$-0.947857\pi$
$811$	−1.18853e7	−	2.05860e7i	−0.634539	−	1.09905i	0.352073	−	0.935972i	$-0.385477\pi$
$812$	−9.27471e6	+	1.60643e7i	−0.493640	+	0.855009i
$813$	−9.87105e6	+	4.39487e6i	−0.523766	+	0.233195i
$814$	−5.16893e6	+	3.75545e6i	−0.273426	+	0.198656i
$815$	−2.20551e7	−	9.81956e6i	−1.16309	−	0.517843i
$816$	1.73167e6	−	368077.i	0.0910415	−	0.0193515i
$817$	1.67027e6	−	1.58916e7i	0.0875452	−	0.832937i
$818$	−1.72190e6	−	1.91236e6i	−0.0899754	−	0.0999278i
$819$	1.16598e6	−	1.29495e6i	0.0607410	−	0.0674597i
$820$	−2.43926e6	−	2.32080e7i	−0.126685	−	1.20532i
$821$	−2.68273e6	−	8.25659e6i	−0.138905	−	0.427507i	0.857272	−	0.514864i	$-0.172158\pi$
$821$	−2.68273e6	−	8.25659e6i	−0.138905	−	0.427507i	−0.996177	+	0.0873577i	$0.972158\pi$
$822$	−936727.	−	2.88295e6i	−0.0483541	−	0.148819i
$823$	974845.	+	9.27503e6i	0.0501690	+	0.477327i	0.990545	+	0.137189i	$0.0438069\pi$
$823$	974845.	+	9.27503e6i	0.0501690	+	0.477327i	−0.940376	+	0.340137i	$0.889526\pi$
$824$	420024.	−	466484.i	0.0215504	−	0.0239342i
$825$	−1.63545e7	−	1.81635e7i	−0.836572	−	0.929107i
$826$	647757.	−	6.16299e6i	0.0330341	−	0.314298i
$827$	−13916.8	+	2958.11i	−0.000707580	+	0.000150401i	−0.208265	−	0.978072i	$-0.566782\pi$
$827$	−13916.8	+	2958.11i	−0.000707580	+	0.000150401i	0.207558	+	0.978223i	$0.433448\pi$
$828$	4.98260e6	+	2.21839e6i	0.252569	+	0.112451i
$829$	2.75799e7	−	2.00379e7i	1.39382	−	1.01267i	0.398383	−	0.917219i	$-0.369572\pi$
$829$	2.75799e7	−	2.00379e7i	1.39382	−	1.01267i	0.995434	−	0.0954480i	$-0.0304284\pi$
$830$	2.71512e6	−	1.20885e6i	0.136803	−	0.0609084i
$831$	8.36136e6	−	1.44823e7i	0.420024	−	0.727503i
$832$	−762514.	−	1.32071e6i	−0.0381891	−	0.0661455i
$833$	1.67509e6	+	1.21702e6i	0.0836421	+	0.0607696i
$834$	−1.02177e6	−	217183.i	−0.0508670	−	0.0108121i
$835$	−7.90407e6	+	2.43262e7i	−0.392315	+	1.20742i
$836$	3.23670e7			1.60172
$837$	9.08140e6	−	1.41740e7i	0.448063	−	0.699326i
$838$	−854048.			−0.0420119
$839$	2.75513e6	−	8.47940e6i	0.135125	−	0.415873i	−0.860484	−	0.509477i	$-0.829839\pi$
$839$	2.75513e6	−	8.47940e6i	0.135125	−	0.415873i	0.995609	+	0.0936044i	$0.0298389\pi$
$840$	6.71162e6	+	1.42660e6i	0.328193	+	0.0697595i
$841$	4.73462e6	+	3.43990e6i	0.230832	+	0.167709i
$842$	478857.	+	829405.i	0.0232769	+	0.0403169i
$843$	2.11767e6	−	3.66792e6i	0.102634	−	0.177767i
$844$	7.10297e6	−	3.16244e6i	0.343229	−	0.152815i
$845$	2.70133e7	−	1.96263e7i	1.30148	−	0.945578i
$846$	−4.24346e6	−	1.88931e6i	−0.203842	−	0.0907564i
$847$	−4.17873e7	+	8.88217e6i	−2.00141	+	0.425413i
$848$	2.09817e6	−	1.99628e7i	0.100196	−	0.953303i
$849$	5.39380e6	+	5.99043e6i	0.256818	+	0.285226i
$850$	−958664.	+	1.06470e6i	−0.0455113	+	0.0505454i
$851$	892054.	+	8.48733e6i	0.0422248	+	0.401742i
$852$	2.20593e6	+	6.78915e6i	0.104110	+	0.320418i
$853$	6.22939e6	+	1.91721e7i	0.293138	+	0.902187i	0.983840	+	0.179048i	$0.0573017\pi$
$853$	6.22939e6	+	1.91721e7i	0.293138	+	0.902187i	−0.690702	+	0.723140i	$0.742698\pi$
$854$	−969188.	−	9.22120e6i	−0.0454740	−	0.432656i
$855$	−1.83948e7	+	2.04295e7i	−0.860556	+	0.955744i
$856$	−1.45844e6	−	1.61976e6i	−0.0680307	−	0.0755558i
$857$	−809720.	+	7.70397e6i	−0.0376602	+	0.358313i	0.959422	+	0.281975i	$0.0909895\pi$
$857$	−809720.	+	7.70397e6i	−0.0376602	+	0.358313i	−0.997082	+	0.0763380i	$0.975677\pi$
$858$	−288121.	+	61241.9i	−0.0133615	+	0.00284008i
$859$	1.97512e7	+	8.79381e6i	0.913294	+	0.406625i	0.808924	−	0.587914i	$-0.200051\pi$
$859$	1.97512e7	+	8.79381e6i	0.913294	+	0.406625i	0.104371	+	0.994538i	$0.466717\pi$
$860$	−2.27659e7	+	1.65404e7i	−1.04964	+	0.762607i
$861$	−8.66193e6	+	3.85654e6i	−0.398205	+	0.177292i
$862$	1.44417e6	−	2.50138e6i	0.0661990	−	0.114660i
$863$	1.42488e7	+	2.46797e7i	0.651257	+	1.12801i	0.982818	+	0.184576i	$0.0590913\pi$
$863$	1.42488e7	+	2.46797e7i	0.651257	+	1.12801i	−0.331561	+	0.943434i	$0.607575\pi$
$864$	7.87276e6	+	5.71989e6i	0.358792	+	0.260678i
$865$	732728.	+	155746.i	0.0332968	+	0.00707746i
$866$	−1.07671e6	+	3.31378e6i	−0.0487872	+	0.150151i
$867$	−9.79817e6			−0.442688
$868$	3.89785e6	−	2.56282e7i	0.175601	−	1.15457i
$869$	7.61344e6			0.342004
$870$	−822968.	+	2.53283e6i	−0.0368625	+	0.113451i
$871$	−2.57634e6	−	547618.i	−0.115069	−	0.0244587i
$872$	1.00660e6	+	731341.i	0.0448299	+	0.0325708i
$873$	9.57747e6	+	1.65887e7i	0.425320	+	0.736675i
$874$	−779611.	+	1.35033e6i	−0.0345223	+	0.0597944i
$875$	2.58557e7	−	1.15117e7i	1.14166	−	0.508298i
$876$	−1.22664e6	+	891209.i	−0.0540080	+	0.0392391i
$877$	−3.52551e7	−	1.56966e7i	−1.54783	−	0.689139i	−0.557798	−	0.829977i	$-0.688354\pi$
$877$	−3.52551e7	−	1.56966e7i	−1.54783	−	0.689139i	−0.990033	+	0.140838i	$0.955020\pi$
$878$	−1.65861e6	+	352548.i	−0.0726119	+	0.0154341i
$879$	1.66253e6	−	1.58179e7i	0.0725768	−	0.690522i
$880$	−3.67155e7	−	4.07767e7i	−1.59824	−	1.77503i
$881$	−1.76857e6	+	1.96420e6i	−0.0767685	+	0.0852600i	−0.780305	−	0.625399i	$-0.784936\pi$
$881$	−1.76857e6	+	1.96420e6i	−0.0767685	+	0.0852600i	0.703537	+	0.710659i	$0.251603\pi$
$882$	163705.	+	1.55755e6i	0.00708581	+	0.0674170i
$883$	−1.03957e7	−	3.19946e7i	−0.448695	−	1.38094i	−0.878381	−	0.477962i	$-0.841376\pi$
$883$	−1.03957e7	−	3.19946e7i	−0.448695	−	1.38094i	0.429686	−	0.902978i	$-0.358624\pi$
$884$	−147941.	−	455316.i	−0.00636734	−	0.0195967i
$885$	2.57864e6	+	2.45341e7i	0.110671	+	1.05296i
$886$	86110.1	−	95635.0i	0.00368527	−	0.00409291i
$887$	−1.41969e7	−	1.57673e7i	−0.605878	−	0.672896i	0.359682	−	0.933075i	$-0.382885\pi$
$887$	−1.41969e7	−	1.57673e7i	−0.605878	−	0.672896i	−0.965560	+	0.260179i	$0.916218\pi$
$888$	−463237.	+	4.40741e6i	−0.0197138	+	0.187565i
$889$	−4.41951e7	+	9.39397e6i	−1.87551	+	0.398653i
$890$	−6.38662e6	−	2.84350e6i	−0.270269	−	0.120331i
$891$	1.24583e7	−	9.05147e6i	0.525731	−	0.381966i
$892$	2.78177e7	−	1.23852e7i	1.17060	−	0.521185i
$893$	−1.84099e7	+	3.18868e7i	−0.772542	+	1.33808i
$894$	424851.	+	735864.i	0.0177784	+	0.0307931i
$895$	2.52254e7	+	1.83273e7i	1.05264	+	0.764788i
$896$	1.94168e7	+	4.12716e6i	0.807992	+	0.171744i
$897$	−121581.	+	374188.i	−0.00504528	+	0.0155278i
$898$	−6.38497e6			−0.264221
$899$	1.98200e7	+	5.18045e6i	0.817909	+	0.213780i
$900$	3.00476e7			1.23653
$901$	1.79333e6	−	5.51931e6i	0.0735951	−	0.226502i
$902$	−5.65754e6	−	1.20255e6i	−0.231532	−	0.0492136i
$903$	9.25010e6	+	6.72059e6i	0.377509	+	0.274276i
$904$	282000.	+	488438.i	0.0114770	+	0.0198787i
$905$	2.07957e7	−	3.60192e7i	0.844019	−	1.46188i
$906$	2.37260e6	−	1.05635e6i	0.0960295	−	0.0427551i
$907$	−3.81671e7	+	2.77300e7i	−1.54053	+	1.11926i	−0.590533	+	0.807014i	$0.701082\pi$
$907$	−3.81671e7	+	2.77300e7i	−1.54053	+	1.11926i	−0.950000	+	0.312249i	$0.898918\pi$
$908$	−3.12813e7	−	1.39273e7i	−1.25913	−	0.560601i
$909$	−3.58668e7	+	7.62373e6i	−1.43974	+	0.306026i
$910$	91700.8	−	872474.i	0.00367087	−	0.0349260i
$911$	1.28893e7	+	1.43150e7i	0.514557	+	0.571473i	0.943295	−	0.331956i	$-0.107708\pi$
$911$	1.28893e7	+	1.43150e7i	0.514557	+	0.571473i	−0.428738	+	0.903429i	$0.641042\pi$
$912$	7.10245e6	−	7.88807e6i	0.282762	−	0.314039i
$913$	2.13502e6	+	2.03133e7i	0.0847665	+	0.806499i
$914$	225507.	+	694040.i	0.00892885	+	0.0274802i
$915$	1.14060e7	+	3.51041e7i	0.450382	+	1.38613i
$916$	1.43849e6	+	1.36863e7i	0.0566457	+	0.538948i
$917$	1.06946e6	−	1.18775e6i	0.0419992	−	0.0466448i
$918$	589894.	+	655144.i	0.0231029	+	0.0256584i
$919$	591695.	−	5.62960e6i	0.0231105	−	0.219882i	−0.976871	−	0.213829i	$-0.931407\pi$
$919$	591695.	−	5.62960e6i	0.0231105	−	0.219882i	0.999982	−	0.00605303i	$-0.00192675\pi$
$920$	5.46864e6	−	1.16240e6i	0.213015	−	0.0452777i
$921$	4.93293e6	+	2.19628e6i	0.191627	+	0.0853177i
$922$	5.06515e6	−	3.68005e6i	0.196230	−	0.142569i
$923$	1.69764e6	−	755839.i	0.0655907	−	0.0292029i
$924$	−1.15800e7	+	2.00571e7i	−0.446199	+	0.772839i
$925$	2.35078e7	+	4.07166e7i	0.903352	+	1.56465i
$926$	232515.	+	168932.i	0.00891094	+	0.00647418i
$927$	−1.76021e6	−	374144.i	−0.0672767	−	0.0143001i
$928$	−3.65953e6	+	1.12629e7i	−0.139494	+	0.429318i
$929$	−7.17274e6			−0.272675			−0.136338	−	0.990662i	$-0.543533\pi$
$929$	−7.17274e6			−0.272675			−0.136338	+	0.990662i	$0.543533\pi$
$930$	−217618.	−	3.71545e6i	−0.00825063	−	0.140865i
$931$	1.24142e7			0.469400
$932$	−9.16490e6	+	2.82067e7i	−0.345611	+	1.06368i
$933$	204534.	+	43475.1i	0.00769240	+	0.00163507i
$934$	4.05514e6	+	2.94623e6i	0.152103	+	0.110509i
$935$	−7.93198e6	−	1.37386e7i	−0.296724	−	0.513941i
$936$	368650.	−	638521.i	0.0137539	−	0.0238224i
$937$	1.81114e6	−	806371.i	0.0673912	−	0.0300045i	−0.372764	−	0.927926i	$-0.621590\pi$
$937$	1.81114e6	−	806371.i	0.0673912	−	0.0300045i	0.440155	+	0.897922i	$0.354923\pi$
$938$	6.04251e6	−	4.39014e6i	0.224239	−	0.162919i
$939$	8.15835e6	+	3.63233e6i	0.301952	+	0.134438i
$940$	6.34249e7	−	1.34814e7i	2.34121	−	0.497640i
$941$	−3.93293e6	+	3.74194e7i	−0.144791	+	1.37760i	0.644982	+	0.764198i	$0.276865\pi$
$941$	−3.93293e6	+	3.74194e7i	−0.144791	+	1.37760i	−0.789773	+	0.613399i	$0.789802\pi$
$942$	−488742.	−	542804.i	−0.0179454	−	0.0199304i
$943$	−5.16949e6	+	5.74130e6i	−0.189308	+	0.210247i
$944$	3.59297e6	+	3.41848e7i	0.131227	+	1.24854i
$945$	−1.38416e7	−	4.26000e7i	−0.504204	−	1.55178i
$946$	2.15531e6	+	6.63336e6i	0.0783036	+	0.240994i
$947$	−4.61333e6	−	4.38929e7i	−0.167163	−	1.59045i	−0.680820	−	0.732451i	$-0.738376\pi$
$947$	−4.61333e6	−	4.38929e7i	−0.167163	−	1.59045i	0.513657	−	0.857996i	$-0.328290\pi$
$948$	1.73550e6	−	1.92747e6i	0.0627198	−	0.0696574i
$949$	264106.	+	293320.i	0.00951948	+	0.0105725i
$950$	−897899.	+	8.54293e6i	−0.0322789	+	0.307113i
$951$	1.00082e6	−	212730.i	0.0358842	−	0.00762743i
$952$	2.52516e6	+	1.12427e6i	0.0903018	+	0.0402050i
$953$	−1.37255e7	+	9.97218e6i	−0.489550	+	0.355679i	−0.805011	−	0.593260i	$-0.797841\pi$
$953$	−1.37255e7	+	9.97218e6i	−0.489550	+	0.355679i	0.315462	+	0.948938i	$0.397841\pi$
$954$	4.01010e6	−	1.78541e6i	0.142654	−	0.0635137i
$955$	2.51509e7	−	4.35626e7i	0.892370	−	1.54563i
$956$	−1.10066e7	−	1.90641e7i	−0.389502	−	0.674638i
$957$	−1.48069e7	−	1.07579e7i	−0.522619	−	0.379705i
$958$	3.29460e6	+	700289.i	0.115982	+	0.0246526i
$959$	−1.91729e7	+	5.90082e7i	−0.673197	+	2.07189i
$960$	−1.72154e7			−0.602891
$961$	−2.84334e7	+	3.34221e6i	−0.993162	+	0.116742i
$962$	566610.			0.0197400
$963$	−1.93089e6	+	5.94266e6i	−0.0670952	+	0.206498i
$964$	−9.36097e6	−	1.98974e6i	−0.324435	−	0.0689609i
$965$	−5.46823e7	−	3.97290e7i	−1.89029	−	1.37338i
$966$	−557846.	−	966217.i	−0.0192341	−	0.0333144i
$967$	1.72419e7	−	2.98639e7i	0.592952	−	1.02702i	−0.400880	−	0.916130i	$-0.631296\pi$
$967$	1.72419e7	−	2.98639e7i	0.592952	−	1.02702i	0.993832	−	0.110893i	$-0.0353710\pi$
$968$	−1.65133e7	+	7.35221e6i	−0.566430	+	0.252191i
$969$	2.48272e6	−	1.80380e6i	0.0849412	−	0.0617134i
$970$	8.80986e6	+	3.92240e6i	0.300635	+	0.133851i
$971$	−6.48229e6	+	1.37785e6i	−0.220638	+	0.0468981i	−0.316904	−	0.948458i	$-0.602643\pi$
$971$	−6.48229e6	+	1.37785e6i	−0.220638	+	0.0468981i	0.0962660	+	0.995356i	$0.469310\pi$
$972$	3.01656e6	−	2.87007e7i	0.102411	−	0.974376i
$973$	1.43065e7	+	1.58890e7i	0.484453	+	0.538039i
$974$	6.55726e6	−	7.28258e6i	0.221475	−	0.245973i
$975$	226570.	+	2.15567e6i	0.00763293	+	0.0726225i
$976$	1.58927e7	+	4.89126e7i	0.534039	+	1.64360i
$977$	−3.22976e6	−	9.94017e6i	−0.108251	−	0.333164i	0.882228	−	0.470822i	$-0.156042\pi$
$977$	−3.22976e6	−	9.94017e6i	−0.108251	−	0.333164i	−0.990480	+	0.137658i	$0.956042\pi$
$978$	213082.	+	2.02734e6i	0.00712360	+	0.0677765i
$979$	3.21484e7	−	3.57044e7i	1.07202	−	1.19060i
$980$	−1.46286e7	−	1.62467e7i	−0.486562	−	0.540382i
$981$	372848.	−	3.54742e6i	0.0123697	−	0.117690i
$982$	−1.57632e6	+	335058.i	−0.0521634	+	0.0110877i
$983$	1.47487e7	+	6.56655e6i	0.486822	+	0.216747i	0.635444	−	0.772147i	$-0.280817\pi$
$983$	1.47487e7	+	6.56655e6i	0.486822	+	0.216747i	−0.148622	+	0.988894i	$0.547484\pi$
$984$	−3.24568e6	+	2.35813e6i	−0.106861	+	0.0776389i
$985$	−5.84696e7	+	2.60323e7i	−1.92017	+	0.854914i
$986$	−536422.	+	929109.i	−0.0175717	+	0.0304351i
$987$	−1.31731e7	−	2.28164e7i	−0.430421	−	0.745511i
$988$	−2.32221e6	−	1.68718e6i	−0.0756848	−	0.0549883i
$989$	9.11267e6	+	1.93696e6i	0.296248	+	0.0629694i
$990$	3.70800e6	−	1.14121e7i	0.120241	−	0.370063i
$991$	2.35186e7			0.760725			0.380362	−	0.924838i	$-0.375799\pi$
$991$	2.35186e7			0.760725			0.380362	+	0.924838i	$0.375799\pi$
$992$	−967690.	−	1.65216e7i	−0.0312217	−	0.533057i
$993$	−1.20178e7			−0.386769
$994$	−1.62839e6	+	5.01168e6i	−0.0522749	+	0.160886i
$995$	5.20456e7	+	1.10626e7i	1.66658	+	0.354243i
$996$	5.62935e6	+	4.08996e6i	0.179808	+	0.130638i
$997$	4.58687e6	+	7.94468e6i	0.146143	+	0.253127i	0.929799	−	0.368068i	$-0.119981\pi$
$997$	4.58687e6	+	7.94468e6i	0.146143	+	0.253127i	−0.783656	+	0.621195i	$0.786647\pi$
$998$	−2.92592e6	+	5.06784e6i	−0.0929899	+	0.161063i
$999$	2.64289e7	−	1.17669e7i	0.837848	−	0.373034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.6.g.a.9.7	yes	96
31.7	even	15	inner	31.6.g.a.7.7	✓	96
31.10	even	15		961.6.a.j.1.27		48
31.21	odd	30		961.6.a.k.1.27		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.6.g.a.7.7	✓	96	31.7	even	15	inner
31.6.g.a.9.7	yes	96	1.1	even	1	trivial
961.6.a.j.1.27		48	31.10	even	15
961.6.a.k.1.27		48	31.21	odd	30

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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	31.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.326144 - 1.00377i) q^{2} +(-7.10263 - 1.50971i) q^{3} +(24.9874 + 18.1544i) q^{4} +(-45.3815 - 78.6031i) q^{5} +(-3.83188 + 6.63701i) q^{6} +(143.301 - 63.8015i) q^{7} +(53.6957 - 39.0122i) q^{8} +(-173.823 - 77.3912i) q^{9} +(-93.7002 + 19.9166i) q^{10} +(68.8142 - 654.723i) q^{11} +(-150.068 - 166.667i) q^{12} +(-39.0657 + 43.3868i) q^{13} +(-17.3053 - 164.649i) q^{14} +(203.660 + 626.801i) q^{15} +(283.772 + 873.359i) q^{16} +(27.7520 + 264.042i) q^{17} +(-134.374 + 149.238i) q^{18} +(1065.14 + 1182.96i) q^{19} +(293.026 - 2787.96i) q^{20} +(-1114.13 + 236.816i) q^{21} +(-634.747 - 282.608i) q^{22} +(-750.831 + 545.511i) q^{23} +(-440.278 + 196.024i) q^{24} +(-2556.46 + 4427.92i) q^{25} +(30.8093 + 53.3633i) q^{26} +(2545.27 + 1849.25i) q^{27} +(4738.98 + 1007.30i) q^{28} +(-1183.13 + 3641.30i) q^{29} +695.586 q^{30} +(-312.855 - 5341.47i) q^{31} +3093.09 q^{32} +(-1477.20 + 4546.37i) q^{33} +(274.089 + 58.2593i) q^{34} +(-11518.2 - 8368.45i) q^{35} +(-2938.40 - 5089.46i) q^{36} +(4597.72 - 7963.48i) q^{37} +(1534.81 - 683.340i) q^{38} +(342.970 - 249.183i) q^{39} +(-5503.27 - 2450.21i) q^{40} +(8142.47 - 1730.74i) q^{41} +(-125.659 + 1195.57i) q^{42} +(-6716.88 - 7459.85i) q^{43} +(13605.6 - 15110.5i) q^{44} +(1805.18 + 17175.2i) q^{45} +(302.687 + 931.576i) q^{46} +(7147.70 + 21998.4i) q^{47} +(-697.005 - 6631.56i) q^{48} +(5218.33 - 5795.55i) q^{49} +(3610.83 + 4010.24i) q^{50} +(201.515 - 1917.29i) q^{51} +(-1763.81 + 374.909i) q^{52} +(-19968.7 - 8890.63i) q^{53} +(2686.34 - 1951.74i) q^{54} +(-54586.1 + 24303.3i) q^{55} +(5205.58 - 9016.34i) q^{56} +(-5779.38 - 10010.2i) q^{57} +(3269.15 + 2375.18i) q^{58} +(36613.1 + 7782.36i) q^{59} +(-6290.26 + 19359.4i) q^{60} +56005.2 q^{61} +(-5463.63 - 1428.05i) q^{62} -29846.7 q^{63} +(-8071.90 + 24842.8i) q^{64} +(5183.20 + 1101.72i) q^{65} +(4081.72 + 2965.54i) q^{66} +(22557.2 + 39070.2i) q^{67} +(-4100.08 + 7101.54i) q^{68} +(6156.43 - 2741.02i) q^{69} +(-12156.6 + 8832.27i) q^{70} +(-29077.8 - 12946.3i) q^{71} +(-12352.8 + 2625.66i) q^{72} +(706.672 - 6723.53i) q^{73} +(-6493.97 - 7212.29i) q^{74} +(24842.5 - 27590.3i) q^{75} +(5139.18 + 48896.0i) q^{76} +(-31911.2 - 98212.7i) q^{77} +(-138.264 - 425.533i) q^{78} +(1208.85 + 11501.4i) q^{79} +(55770.7 - 61939.7i) q^{80} +(15651.9 + 17383.2i) q^{81} +(918.362 - 8737.63i) q^{82} +(-30347.8 + 6450.63i) q^{83} +(-32138.5 - 14309.0i) q^{84} +(19495.1 - 14164.0i) q^{85} +(-9678.63 + 4309.21i) q^{86} +(13900.6 - 24076.6i) q^{87} +(-21847.2 - 37840.4i) q^{88} +(59042.1 + 42896.6i) q^{89} +(17828.7 + 3789.60i) q^{90} +(-2829.99 + 8709.81i) q^{91} -28664.7 q^{92} +(-5841.97 + 38410.8i) q^{93} +24412.5 q^{94} +(44646.5 - 137408. i) q^{95} +(-21969.1 - 4669.67i) q^{96} +(-81444.2 - 59172.7i) q^{97} +(-4115.46 - 7128.18i) q^{98} +(-62631.3 + 108481. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 6 q^{2} - 20 q^{3} - 346 q^{4} - 33 q^{5} + 283 q^{6} - 66 q^{7} - 271 q^{8} + 658 q^{9} + 896 q^{10} + 41 q^{11} - 1169 q^{12} + 149 q^{13} - 2 q^{14} + 4906 q^{15} - 2450 q^{16} - 3152 q^{17} - 3 q^{18}+ \cdots + 674326 q^{99}+O(q^{100}) \) 96 * q - 6 * q^2 - 20 * q^3 - 346 * q^4 - 33 * q^5 + 283 * q^6 - 66 * q^7 - 271 * q^8 + 658 * q^9 + 896 * q^10 + 41 * q^11 - 1169 * q^12 + 149 * q^13 - 2 * q^14 + 4906 * q^15 - 2450 * q^16 - 3152 * q^17 - 3 * q^18 - 5216 * q^19 + 7943 * q^20 - 14003 * q^21 - 8471 * q^22 + 13925 * q^23 + 25478 * q^24 - 18843 * q^25 + 12637 * q^26 + 3409 * q^27 - 10560 * q^28 + 6386 * q^29 - 25530 * q^30 - 39101 * q^31 + 31482 * q^32 + 17969 * q^33 - 18136 * q^34 + 5943 * q^35 - 9713 * q^36 + 40836 * q^37 + 18746 * q^38 + 55889 * q^39 + 15841 * q^40 - 46266 * q^41 + 8917 * q^42 - 137449 * q^43 + 28951 * q^44 + 69269 * q^45 - 97978 * q^46 + 5774 * q^47 - 112102 * q^48 - 146686 * q^49 + 58913 * q^50 + 149254 * q^51 + 263153 * q^52 + 62548 * q^53 + 144508 * q^54 + 13077 * q^55 - 103466 * q^56 + 68345 * q^57 - 52881 * q^58 - 149116 * q^59 + 65951 * q^60 - 204972 * q^61 - 62393 * q^62 - 80326 * q^63 - 205193 * q^64 - 296504 * q^65 - 268720 * q^66 - 105499 * q^67 + 497808 * q^68 + 448358 * q^69 + 351230 * q^70 + 93454 * q^71 + 192637 * q^72 + 74644 * q^73 - 83209 * q^74 - 323995 * q^75 - 446776 * q^76 - 249590 * q^77 - 588829 * q^78 + 396670 * q^79 - 236822 * q^80 + 616675 * q^81 + 449670 * q^82 + 518776 * q^83 + 578676 * q^84 + 463509 * q^85 - 95508 * q^86 - 360817 * q^87 + 238379 * q^88 + 239175 * q^89 - 1232679 * q^90 - 178840 * q^91 - 1350224 * q^92 - 65783 * q^93 + 580620 * q^94 - 276050 * q^95 - 1587604 * q^96 - 611799 * q^97 + 200092 * q^98 + 674326 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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