LMFDB - Embedded newform 25.5.f.a.3.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,5,Mod(2,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("25.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	25.f (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.58424907710$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			3.3
Character	$\chi$	$=$	25.3
Dual form			25.5.f.a.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.14039 - 4.20075i) q^{2} +(-0.349755 - 2.20827i) q^{3} +(-3.66045 + 5.03818i) q^{4} +(-17.0385 - 18.2946i) q^{5} +(-8.52776 + 6.19578i) q^{6} +(-46.9663 + 46.9663i) q^{7} +(-45.5061 - 7.20746i) q^{8} +(72.2815 - 23.4857i) q^{9} +O(q^{10})$	\(q+(-2.14039 - 4.20075i) q^{2} +(-0.349755 - 2.20827i) q^{3} +(-3.66045 + 5.03818i) q^{4} +(-17.0385 - 18.2946i) q^{5} +(-8.52776 + 6.19578i) q^{6} +(-46.9663 + 46.9663i) q^{7} +(-45.5061 - 7.20746i) q^{8} +(72.2815 - 23.4857i) q^{9} +(-40.3819 + 110.732i) q^{10} +(44.7709 - 137.791i) q^{11} +(12.4059 + 6.32113i) q^{12} +(109.439 - 214.786i) q^{13} +(297.820 + 96.7675i) q^{14} +(-34.4400 + 44.0241i) q^{15} +(97.9146 + 301.350i) q^{16} +(-4.04094 + 25.5135i) q^{17} +(-253.368 - 253.368i) q^{18} +(-5.30919 - 7.30747i) q^{19} +(154.540 - 18.8765i) q^{20} +(120.141 + 87.2875i) q^{21} +(-674.650 + 106.854i) q^{22} +(279.342 - 142.332i) q^{23} +103.011i q^{24} +(-44.3812 + 623.422i) q^{25} -1136.50 q^{26} +(-159.361 - 312.763i) q^{27} +(-64.7068 - 408.543i) q^{28} +(573.163 - 788.891i) q^{29} +(258.649 + 50.4450i) q^{30} +(-521.353 + 378.785i) q^{31} +(535.060 - 535.060i) q^{32} +(-319.937 - 50.6731i) q^{33} +(115.825 - 37.6338i) q^{34} +(1659.46 + 58.9936i) q^{35} +(-146.258 + 450.135i) q^{36} +(-1433.07 - 730.185i) q^{37} +(-19.3331 + 37.9434i) q^{38} +(-512.581 - 166.548i) q^{39} +(643.497 + 955.318i) q^{40} +(717.809 + 2209.19i) q^{41} +(109.525 - 691.511i) q^{42} +(2196.50 + 2196.50i) q^{43} +(530.332 + 729.939i) q^{44} +(-1661.23 - 922.197i) q^{45} +(-1195.80 - 868.798i) q^{46} +(617.769 - 97.8450i) q^{47} +(631.216 - 321.621i) q^{48} -2010.67i q^{49} +(2713.83 - 1147.93i) q^{50} +57.7540 q^{51} +(681.534 + 1337.59i) q^{52} +(-429.515 - 2711.85i) q^{53} +(-972.745 + 1338.87i) q^{54} +(-3283.64 + 1528.68i) q^{55} +(2475.76 - 1798.75i) q^{56} +(-14.2799 + 14.2799i) q^{57} +(-4540.72 - 719.179i) q^{58} +(-2183.28 + 709.390i) q^{59} +(-95.7356 - 334.663i) q^{60} +(1655.25 - 5094.34i) q^{61} +(2707.08 + 1379.33i) q^{62} +(-2291.76 + 4497.83i) q^{63} +(1428.71 + 464.217i) q^{64} +(-5794.08 + 1657.49i) q^{65} +(471.925 + 1452.44i) q^{66} +(-459.046 + 2898.30i) q^{67} +(-113.750 - 113.750i) q^{68} +(-412.007 - 567.080i) q^{69} +(-3304.07 - 7097.25i) q^{70} +(-608.681 - 442.232i) q^{71} +(-3458.52 + 547.776i) q^{72} +(5420.42 - 2761.84i) q^{73} +7582.84i q^{74} +(1392.21 - 120.040i) q^{75} +56.2504 q^{76} +(4368.79 + 8574.24i) q^{77} +(397.498 + 2509.70i) q^{78} +(913.900 - 1257.88i) q^{79} +(3844.75 - 6925.85i) q^{80} +(4345.46 - 3157.16i) q^{81} +(7743.85 - 7743.85i) q^{82} +(2922.11 + 462.816i) q^{83} +(-879.541 + 285.780i) q^{84} +(535.609 - 360.784i) q^{85} +(4525.57 - 13928.3i) q^{86} +(-1942.55 - 989.778i) q^{87} +(-3030.47 + 5947.63i) q^{88} +(-6467.26 - 2101.34i) q^{89} +(-318.251 + 8952.25i) q^{90} +(4947.76 + 15227.6i) q^{91} +(-305.424 + 1928.37i) q^{92} +(1018.81 + 1018.81i) q^{93} +(-1733.29 - 2385.66i) q^{94} +(-43.2265 + 221.637i) q^{95} +(-1368.70 - 994.416i) q^{96} +(1629.76 - 258.129i) q^{97} +(-8446.32 + 4303.62i) q^{98} -11011.2i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9}+O(q^{10}) $ 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9	\( 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9} - 6 q^{11} - 178 q^{12} - 288 q^{13} - 10 q^{14} + 410 q^{15} + 762 q^{16} + 1042 q^{17} - 28 q^{18} - 1310 q^{19} - 3790 q^{20} - 6 q^{21} - 3226 q^{22} - 578 q^{23} + 1110 q^{25} - 976 q^{26} + 5120 q^{27} + 10318 q^{28} + 3290 q^{29} + 5270 q^{30} - 6 q^{31} - 1298 q^{32} - 2806 q^{33} - 8010 q^{34} - 5360 q^{35} - 2758 q^{36} + 4692 q^{37} + 14480 q^{38} + 8790 q^{39} + 2540 q^{40} + 1434 q^{41} - 23886 q^{42} - 14958 q^{43} - 22060 q^{44} - 23420 q^{45} - 6 q^{46} - 12158 q^{47} - 14168 q^{48} + 8050 q^{50} - 16 q^{51} + 29372 q^{52} + 22852 q^{53} + 53940 q^{54} + 18070 q^{55} - 1030 q^{56} + 34150 q^{57} + 23000 q^{58} + 23240 q^{59} + 40610 q^{60} + 2634 q^{61} - 13716 q^{62} - 42428 q^{63} - 66060 q^{64} - 41870 q^{65} + 5178 q^{66} - 25558 q^{67} - 71982 q^{68} - 39560 q^{69} - 38130 q^{70} + 7974 q^{71} - 37860 q^{72} - 4228 q^{73} + 21210 q^{75} - 1040 q^{76} + 34374 q^{77} + 51844 q^{78} + 26590 q^{79} + 110710 q^{80} - 14368 q^{81} + 145614 q^{82} + 99832 q^{83} + 149990 q^{84} + 48860 q^{85} - 6 q^{86} - 31320 q^{87} - 95490 q^{88} - 93760 q^{89} - 207250 q^{90} - 6 q^{91} - 199958 q^{92} - 134396 q^{93} - 130410 q^{94} - 50290 q^{95} + 17694 q^{96} - 40108 q^{97} - 25052 q^{98}+O(q^{100}) \) 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9 - 6 * q^11 - 178 * q^12 - 288 * q^13 - 10 * q^14 + 410 * q^15 + 762 * q^16 + 1042 * q^17 - 28 * q^18 - 1310 * q^19 - 3790 * q^20 - 6 * q^21 - 3226 * q^22 - 578 * q^23 + 1110 * q^25 - 976 * q^26 + 5120 * q^27 + 10318 * q^28 + 3290 * q^29 + 5270 * q^30 - 6 * q^31 - 1298 * q^32 - 2806 * q^33 - 8010 * q^34 - 5360 * q^35 - 2758 * q^36 + 4692 * q^37 + 14480 * q^38 + 8790 * q^39 + 2540 * q^40 + 1434 * q^41 - 23886 * q^42 - 14958 * q^43 - 22060 * q^44 - 23420 * q^45 - 6 * q^46 - 12158 * q^47 - 14168 * q^48 + 8050 * q^50 - 16 * q^51 + 29372 * q^52 + 22852 * q^53 + 53940 * q^54 + 18070 * q^55 - 1030 * q^56 + 34150 * q^57 + 23000 * q^58 + 23240 * q^59 + 40610 * q^60 + 2634 * q^61 - 13716 * q^62 - 42428 * q^63 - 66060 * q^64 - 41870 * q^65 + 5178 * q^66 - 25558 * q^67 - 71982 * q^68 - 39560 * q^69 - 38130 * q^70 + 7974 * q^71 - 37860 * q^72 - 4228 * q^73 + 21210 * q^75 - 1040 * q^76 + 34374 * q^77 + 51844 * q^78 + 26590 * q^79 + 110710 * q^80 - 14368 * q^81 + 145614 * q^82 + 99832 * q^83 + 149990 * q^84 + 48860 * q^85 - 6 * q^86 - 31320 * q^87 - 95490 * q^88 - 93760 * q^89 - 207250 * q^90 - 6 * q^91 - 199958 * q^92 - 134396 * q^93 - 130410 * q^94 - 50290 * q^95 + 17694 * q^96 - 40108 * q^97 - 25052 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−2.14039	−	4.20075i	−0.535097	−	1.05019i	−0.987388	−	0.158317i	$-0.949393\pi$
$2$	−2.14039	−	4.20075i	−0.535097	−	1.05019i	0.452292	−	0.891870i	$-0.350607\pi$
$3$	−0.349755	−	2.20827i	−0.0388617	−	0.245363i	0.960609	−	0.277905i	$-0.0896399\pi$
$3$	−0.349755	−	2.20827i	−0.0388617	−	0.245363i	−0.999470	+	0.0325415i	$0.989640\pi$
$4$	−3.66045	+	5.03818i	−0.228778	+	0.314886i
$5$	−17.0385	−	18.2946i	−0.681539	−	0.731782i
$5$	−17.0385	−	18.2946i	−0.681539	−	0.731782i
$6$	−8.52776	+	6.19578i	−0.236882	+	0.172105i
$7$	−46.9663	+	46.9663i	−0.958496	+	0.958496i	−0.999172	−	0.0406760i	$-0.987049\pi$
$7$	−46.9663	+	46.9663i	−0.958496	+	0.958496i	0.0406760	+	0.999172i	$0.487049\pi$
$8$	−45.5061	−	7.20746i	−0.711033	−	0.112617i
$9$	72.2815	−	23.4857i	0.892364	−	0.289947i
$10$	−40.3819	+	110.732i	−0.403819	+	1.10732i
$11$	44.7709	−	137.791i	0.370007	−	1.13876i	−0.576779	−	0.816900i	$-0.695691\pi$
$11$	44.7709	−	137.791i	0.370007	−	1.13876i	0.946786	−	0.321864i	$-0.104309\pi$
$12$	12.4059	+	6.32113i	0.0861522	+	0.0438967i
$13$	109.439	−	214.786i	0.647567	−	1.27092i	−0.300782	−	0.953693i	$-0.597248\pi$
$13$	109.439	−	214.786i	0.647567	−	1.27092i	0.948349	−	0.317229i	$-0.102752\pi$
$14$	297.820	+	96.7675i	1.51949	+	0.493712i
$15$	−34.4400	+	44.0241i	−0.153067	+	0.195663i
$16$	97.9146	+	301.350i	0.382479	+	1.17715i
$17$	−4.04094	+	25.5135i	−0.0139825	+	0.0882820i	−0.993693	−	0.112137i	$-0.964230\pi$
$17$	−4.04094	+	25.5135i	−0.0139825	+	0.0882820i	0.979710	+	0.200419i	$0.0642304\pi$
$18$	−253.368	−	253.368i	−0.781999	−	0.781999i
$19$	−5.30919	−	7.30747i	−0.0147069	−	0.0202423i	0.801600	−	0.597860i	$-0.203982\pi$
$19$	−5.30919	−	7.30747i	−0.0147069	−	0.0202423i	−0.816307	+	0.577618i	$0.803982\pi$
$20$	154.540	−	18.8765i	0.386349	−	0.0471914i
$21$	120.141	+	87.2875i	0.272428	+	0.197931i
$22$	−674.650	+	106.854i	−1.39391	+	0.220773i
$23$	279.342	−	142.332i	0.528056	−	0.269058i	−0.169573	−	0.985518i	$-0.554239\pi$
$23$	279.342	−	142.332i	0.528056	−	0.269058i	0.697628	+	0.716460i	$0.254239\pi$
$24$			103.011i			0.178838i
$25$	−44.3812	+	623.422i	−0.0710100	+	0.997476i
$26$	−1136.50			−1.68122
$27$	−159.361	−	312.763i	−0.218602	−	0.429031i
$28$	−64.7068	−	408.543i	−0.0825342	−	0.521101i
$29$	573.163	−	788.891i	0.681525	−	0.938039i	−0.318426	−	0.947948i	$-0.603154\pi$
$29$	573.163	−	788.891i	0.681525	−	0.938039i	0.999951	+	0.00990906i	$0.00315420\pi$
$30$	258.649	+	50.4450i	0.287388	+	0.0560500i
$31$	−521.353	+	378.785i	−0.542511	+	0.394157i	−0.825017	−	0.565108i	$-0.808834\pi$
$31$	−521.353	+	378.785i	−0.542511	+	0.394157i	0.282506	+	0.959266i	$0.408834\pi$
$32$	535.060	−	535.060i	0.522520	−	0.522520i
$33$	−319.937	−	50.6731i	−0.293790	−	0.0465317i
$34$	115.825	−	37.6338i	0.100195	−	0.0325552i
$35$	1659.46	+	58.9936i	1.35466	+	0.0481581i
$36$	−146.258	+	450.135i	−0.112853	+	0.347327i
$37$	−1433.07	−	730.185i	−1.04680	−	0.533371i	−0.155995	−	0.987758i	$-0.549859\pi$
$37$	−1433.07	−	730.185i	−1.04680	−	0.533371i	−0.890805	+	0.454387i	$0.849859\pi$
$38$	−19.3331	+	37.9434i	−0.0133886	+	0.0262766i
$39$	−512.581	−	166.548i	−0.337003	−	0.109499i
$40$	643.497	+	955.318i	0.402186	+	0.597074i
$41$	717.809	+	2209.19i	0.427013	+	1.31421i	0.901054	+	0.433707i	$0.142795\pi$
$41$	717.809	+	2209.19i	0.427013	+	1.31421i	−0.474041	+	0.880503i	$0.657205\pi$
$42$	109.525	−	691.511i	0.0620887	−	0.392013i
$43$	2196.50	+	2196.50i	1.18794	+	1.18794i	0.977637	+	0.210301i	$0.0674445\pi$
$43$	2196.50	+	2196.50i	1.18794	+	1.18794i	0.210301	+	0.977637i	$0.432556\pi$
$44$	530.332	+	729.939i	0.273932	+	0.377035i
$45$	−1661.23	−	922.197i	−0.820358	−	0.455406i
$46$	−1195.80	−	868.798i	−0.565122	−	0.410585i
$47$	617.769	−	97.8450i	0.279660	−	0.0442938i	−0.0150288	−	0.999887i	$-0.504784\pi$
$47$	617.769	−	97.8450i	0.279660	−	0.0442938i	0.294689	+	0.955593i	$0.404784\pi$
$48$	631.216	−	321.621i	0.273965	−	0.139592i
$49$		−	2010.67i		−	0.837431i
$50$	2713.83	−	1147.93i	1.08553	−	0.459172i
$51$	57.7540			0.0222045
$52$	681.534	+	1337.59i	0.252047	+	0.494669i
$53$	−429.515	−	2711.85i	−0.152907	−	0.965416i	−0.938150	−	0.346229i	$-0.887462\pi$
$53$	−429.515	−	2711.85i	−0.152907	−	0.965416i	0.785243	−	0.619187i	$-0.212538\pi$
$54$	−972.745	+	1338.87i	−0.333589	+	0.459146i
$55$	−3283.64	+	1528.68i	−1.08550	+	0.505348i
$56$	2475.76	−	1798.75i	0.789465	−	0.573580i
$57$	−14.2799	+	14.2799i	−0.00439518	+	0.00439518i
$58$	−4540.72	−	719.179i	−1.34980	−	0.213787i
$59$	−2183.28	+	709.390i	−0.627198	+	0.203789i	−0.605334	−	0.795972i	$-0.706960\pi$
$59$	−2183.28	+	709.390i	−0.627198	+	0.203789i	−0.0218646	+	0.999761i	$0.506960\pi$
$60$	−95.7356	−	334.663i	−0.0265932	−	0.0929620i
$61$	1655.25	−	5094.34i	0.444841	−	1.36908i	−0.437818	−	0.899064i	$-0.644249\pi$
$61$	1655.25	−	5094.34i	0.444841	−	1.36908i	0.882658	−	0.470015i	$-0.155751\pi$
$62$	2707.08	+	1379.33i	0.704235	+	0.358826i
$63$	−2291.76	+	4497.83i	−0.577415	+	1.13324i
$64$	1428.71	+	464.217i	0.348807	+	0.113334i
$65$	−5794.08	+	1657.49i	−1.37138	+	0.392304i
$66$	471.925	+	1452.44i	0.108339	+	0.333433i
$67$	−459.046	+	2898.30i	−0.102260	+	0.645646i	0.882312	+	0.470665i	$0.155986\pi$
$67$	−459.046	+	2898.30i	−0.102260	+	0.645646i	−0.984572	+	0.174980i	$0.944014\pi$
$68$	−113.750	−	113.750i	−0.0245999	−	0.0245999i
$69$	−412.007	−	567.080i	−0.0865380	−	0.119109i
$70$	−3304.07	−	7097.25i	−0.674301	−	1.44842i
$71$	−608.681	−	442.232i	−0.120746	−	0.0877271i	0.525773	−	0.850625i	$-0.323776\pi$
$71$	−608.681	−	442.232i	−0.120746	−	0.0877271i	−0.646519	+	0.762898i	$0.723776\pi$
$72$	−3458.52	+	547.776i	−0.667153	+	0.105667i
$73$	5420.42	−	2761.84i	1.01716	−	0.518267i	0.135808	−	0.990735i	$-0.456637\pi$
$73$	5420.42	−	2761.84i	1.01716	−	0.518267i	0.881348	+	0.472468i	$0.156637\pi$
$74$			7582.84i			1.38474i
$75$	1392.21	−	120.040i	0.247503	−	0.0213404i
$76$	56.2504			0.00973864
$77$	4368.79	+	8574.24i	0.736851	+	1.44615i
$78$	397.498	+	2509.70i	0.0653349	+	0.412508i
$79$	913.900	−	1257.88i	0.146435	−	0.201550i	−0.729498	−	0.683982i	$-0.760246\pi$
$79$	913.900	−	1257.88i	0.146435	−	0.201550i	0.875933	+	0.482432i	$0.160246\pi$
$80$	3844.75	−	6925.85i	0.600742	−	1.08216i
$81$	4345.46	−	3157.16i	0.662317	−	0.481201i
$82$	7743.85	−	7743.85i	1.15167	−	1.15167i
$83$	2922.11	+	462.816i	0.424170	+	0.0671819i	0.364870	−	0.931058i	$-0.381113\pi$
$83$	2922.11	+	462.816i	0.424170	+	0.0671819i	0.0592996	+	0.998240i	$0.481113\pi$
$84$	−879.541	+	285.780i	−0.124651	+	0.0405017i
$85$	535.609	−	360.784i	0.0741328	−	0.0499355i
$86$	4525.57	−	13928.3i	0.611895	−	1.88322i
$87$	−1942.55	−	989.778i	−0.256645	−	0.130767i
$88$	−3030.47	+	5947.63i	−0.391331	+	0.768030i
$89$	−6467.26	−	2101.34i	−0.816470	−	0.265287i	−0.129134	−	0.991627i	$-0.541220\pi$
$89$	−6467.26	−	2101.34i	−0.816470	−	0.265287i	−0.687336	+	0.726340i	$0.741220\pi$
$90$	−318.251	+	8952.25i	−0.0392903	+	1.10522i
$91$	4947.76	+	15227.6i	0.597483	+	1.83886i
$92$	−305.424	+	1928.37i	−0.0360851	+	0.227832i
$93$	1018.81	+	1018.81i	0.117795	+	0.117795i
$94$	−1733.29	−	2385.66i	−0.196162	−	0.269994i
$95$	−43.2265	+	221.637i	−0.00478964	+	0.0245582i
$96$	−1368.70	−	994.416i	−0.148513	−	0.107901i
$97$	1629.76	−	258.129i	0.173213	−	0.0274343i	−0.0692252	−	0.997601i	$-0.522053\pi$
$97$	1629.76	−	258.129i	0.173213	−	0.0274343i	0.242439	+	0.970167i	$0.422053\pi$
$98$	−8446.32	+	4303.62i	−0.879459	+	0.448107i
$99$		−	11011.2i		−	1.12347i
$100$	−2978.46	−	2505.61i	−0.297846	−	0.250561i
$101$	−14168.4			−1.38892			−0.694460	−	0.719532i	$-0.744357\pi$
$101$	−14168.4			−1.38892			−0.694460	+	0.719532i	$0.744357\pi$
$102$	−123.616	−	242.610i	−0.0118816	−	0.0233189i
$103$	209.540	+	1322.98i	0.0197512	+	0.124704i	0.995594	−	0.0937705i	$-0.0298920\pi$
$103$	209.540	+	1322.98i	0.0197512	+	0.124704i	−0.975843	+	0.218474i	$0.929892\pi$
$104$	−6528.19	+	8985.29i	−0.603568	+	0.830740i
$105$	−450.132	−	3685.17i	−0.0408283	−	0.334256i
$106$	−10472.5	+	7608.70i	−0.932047	+	0.677172i
$107$	8267.87	−	8267.87i	0.722148	−	0.722148i	−0.246895	−	0.969042i	$-0.579410\pi$
$107$	8267.87	−	8267.87i	0.722148	−	0.722148i	0.969042	+	0.246895i	$0.0794101\pi$
$108$	2159.09	+	341.966i	0.185107	+	0.0293181i
$109$	4803.68	−	1560.81i	0.404316	−	0.131370i	−0.0997973	−	0.995008i	$-0.531819\pi$
$109$	4803.68	−	1560.81i	0.404316	−	0.131370i	0.504113	+	0.863638i	$0.331819\pi$
$110$	13449.9	+	10521.8i	1.11156	+	0.869569i
$111$	−1111.22	+	3419.99i	−0.0901892	+	0.277574i
$112$	−18752.0	−	9554.62i	−1.49490	−	0.761689i
$113$	5136.15	−	10080.3i	0.402236	−	0.789433i	−0.597688	−	0.801729i	$-0.703914\pi$
$113$	5136.15	−	10080.3i	0.402236	−	0.789433i	0.999924	+	0.0122959i	$0.00391399\pi$
$114$	90.5510	+	29.4218i	0.00696761	+	0.00226391i
$115$	−7363.44	−	2685.32i	−0.556782	−	0.203048i
$116$	1876.54	+	5775.39i	0.139457	+	0.429206i
$117$	2866.01	−	18095.3i	0.209366	−	1.32188i
$118$	7653.03	+	7653.03i	0.549628	+	0.549628i
$119$	−1008.49	−	1388.06i	−0.0712158	−	0.0980201i
$120$	1884.53	−	1755.14i	0.130870	−	0.121885i
$121$	−5136.98	−	3732.23i	−0.350862	−	0.254916i
$122$	−24942.9	+	3950.57i	−1.67582	+	0.265424i
$123$	4627.42	−	2357.79i	0.305864	−	0.155846i
$124$		−	4013.20i		−	0.261004i
$125$	12161.4	−	9810.23i	0.778331	−	0.627854i
$126$	23799.5			1.49909
$127$	13813.6	+	27110.8i	0.856446	+	1.68087i	0.724131	+	0.689662i	$0.242241\pi$
$127$	13813.6	+	27110.8i	0.856446	+	1.68087i	0.132315	+	0.991208i	$0.457759\pi$
$128$	−3001.90	−	18953.2i	−0.183221	−	1.15681i
$129$	4082.22	−	5618.69i	0.245311	−	0.337641i
$130$	19364.3	+	20791.8i	1.14581	+	1.23028i
$131$	−20709.6	+	15046.4i	−1.20678	+	0.876779i	−0.994935	−	0.100523i	$-0.967948\pi$
$131$	−20709.6	+	15046.4i	−1.20678	+	0.876779i	−0.211848	+	0.977303i	$0.567948\pi$
$132$	1426.42	−	1426.42i	0.0818650	−	0.0818650i
$133$	592.558	+	93.8520i	0.0334987	+	0.00530567i
$134$	13157.6	−	4275.15i	0.732768	−	0.238091i
$135$	−3006.60	+	8244.44i	−0.164971	+	0.452370i
$136$	367.775	−	1131.89i	0.0198840	−	0.0611967i
$137$	−1983.40	−	1010.59i	−0.105674	−	0.0538438i	0.400354	−	0.916360i	$-0.368887\pi$
$137$	−1983.40	−	1010.59i	−0.105674	−	0.0538438i	−0.506029	+	0.862517i	$0.668887\pi$
$138$	−1500.30	+	2944.51i	−0.0787808	+	0.154616i
$139$	21103.2	+	6856.84i	1.09224	+	0.354890i	0.799112	−	0.601183i	$-0.205304\pi$
$139$	21103.2	+	6856.84i	1.09224	+	0.354890i	0.293129	+	0.956073i	$0.405304\pi$
$140$	−6371.60	+	8144.73i	−0.325082	+	0.415547i
$141$	−432.136	−	1329.98i	−0.0217361	−	0.0668969i
$142$	−554.894	+	3503.46i	−0.0275190	+	0.173748i
$143$	−24695.8	−	24695.8i	−1.20768	−	1.20768i
$144$	14154.8	+	19482.4i	0.682621	+	0.939547i
$145$	−24198.2	+	2955.73i	−1.15093	+	0.140582i
$146$	−23203.6	−	16858.4i	−1.08855	−	0.790881i
$147$	−4440.10	+	703.243i	−0.205475	+	0.0325440i
$148$	8924.49	−	4547.25i	0.407437	−	0.207599i
$149$			23822.7i			1.07305i	0.843885	+	0.536524i	$0.180263\pi$
$149$			23822.7i			1.07305i	−0.843885	+	0.536524i	$0.819737\pi$
$150$	−3484.12	−	5591.37i	−0.154850	−	0.248505i
$151$	30063.9			1.31853			0.659267	−	0.751909i	$-0.270867\pi$
$151$	30063.9			1.31853			0.659267	+	0.751909i	$0.270867\pi$
$152$	188.932	+	370.800i	0.00817747	+	0.0160492i
$153$	307.116	+	1939.06i	0.0131196	+	0.0828338i
$154$	26667.3	−	36704.4i	1.12444	−	1.54766i
$155$	15812.8	+	3084.00i	0.658180	+	0.128366i
$156$	2715.38	−	1972.84i	0.111579	−	0.0810666i
$157$	−3973.96	+	3973.96i	−0.161222	+	0.161222i	−0.783108	−	0.621886i	$-0.786367\pi$
$157$	−3973.96	+	3973.96i	−0.161222	+	0.161222i	0.621886	+	0.783108i	$0.286367\pi$
$158$	−7240.12	−	1146.72i	−0.290022	−	0.0459350i
$159$	−5838.27	+	1896.97i	−0.230935	+	0.0750354i
$160$	−18905.3	−	672.081i	−0.738488	−	0.0262532i
$161$	−6434.85	+	19804.4i	−0.248249	+	0.764031i
$162$	−22563.4	−	11496.6i	−0.859755	−	0.438067i
$163$	15120.1	−	29674.9i	0.569088	−	1.11690i	−0.409738	−	0.912203i	$-0.634380\pi$
$163$	15120.1	−	29674.9i	0.569088	−	1.11690i	0.978826	−	0.204695i	$-0.0656203\pi$
$164$	−13757.8	−	4470.18i	−0.511518	−	0.166202i
$165$	4524.20	+	6716.50i	0.166178	+	0.246703i
$166$	−4310.27	−	13265.6i	−0.156419	−	0.481407i
$167$	−4227.86	+	26693.7i	−0.151596	+	0.957139i	0.788204	+	0.615414i	$0.211011\pi$
$167$	−4227.86	+	26693.7i	−0.151596	+	0.957139i	−0.939800	+	0.341725i	$0.888989\pi$
$168$	−4838.03	−	4838.03i	−0.171415	−	0.171415i
$169$	−17368.3	−	23905.4i	−0.608113	−	0.836996i
$170$	−2661.97	−	1477.74i	−0.0921098	−	0.0511330i
$171$	−555.377	−	403.505i	−0.0189931	−	0.0137993i
$172$	−19106.5	+	3026.18i	−0.645840	+	0.102291i
$173$	−4168.82	+	2124.12i	−0.139290	+	0.0709719i	−0.522247	−	0.852795i	$-0.674906\pi$
$173$	−4168.82	+	2124.12i	−0.139290	+	0.0709719i	0.382956	+	0.923766i	$0.374906\pi$
$174$			10278.7i			0.339499i
$175$	−27195.4	−	31364.3i	−0.888014	−	1.02414i
$176$	45906.9			1.48202
$177$	2330.13	+	4573.15i	0.0743763	+	0.145972i
$178$	5015.24	+	31665.0i	0.158289	+	0.999400i
$179$	−32821.0	+	45174.2i	−1.02434	+	1.40989i	−0.115229	+	0.993339i	$0.536760\pi$
$179$	−32821.0	+	45174.2i	−1.02434	+	1.40989i	−0.909114	+	0.416548i	$0.863240\pi$
$180$	10727.0	−	4993.89i	0.331081	−	0.154133i
$181$	−32155.0	+	23362.0i	−0.981502	+	0.713103i	−0.958044	−	0.286622i	$-0.907468\pi$
$181$	−32155.0	+	23362.0i	−0.981502	+	0.713103i	−0.0234584	+	0.999725i	$0.507468\pi$
$182$	53377.3	−	53377.3i	1.61144	−	1.61144i
$183$	−11828.6	−	1873.47i	−0.353209	−	0.0559427i
$184$	−13737.6	+	4463.62i	−0.405765	+	0.131841i
$185$	11058.9	+	38658.6i	0.323123	+	1.12954i
$186$	2099.11	−	6460.38i	0.0606748	−	0.186738i
$187$	3334.60	+	1699.06i	0.0953588	+	0.0485877i
$188$	−1768.35	+	3470.59i	−0.0500326	+	0.0981946i
$189$	22173.9	+	7204.75i	0.620753	+	0.201695i
$190$	1023.56	−	292.806i	0.0283536	−	0.00811098i
$191$	−12835.6	−	39504.1i	−0.351845	−	1.08287i	−0.957816	−	0.287381i	$-0.907216\pi$
$191$	−12835.6	−	39504.1i	−0.351845	−	1.08287i	0.605972	−	0.795486i	$-0.292784\pi$
$192$	525.416	−	3317.34i	0.0142528	−	0.0899887i
$193$	30495.9	+	30495.9i	0.818705	+	0.818705i	0.985920	−	0.167216i	$-0.0534777\pi$
$193$	30495.9	+	30495.9i	0.818705	+	0.818705i	−0.167216	+	0.985920i	$0.553478\pi$
$194$	−4572.66	−	6293.73i	−0.121497	−	0.167226i
$195$	5686.68	+	12215.2i	0.149551	+	0.321240i
$196$	10130.1	+	7359.97i	0.263696	+	0.191586i
$197$	11755.7	−	1861.92i	0.302911	−	0.0479764i	−0.00312869	−	0.999995i	$-0.500996\pi$
$197$	11755.7	−	1861.92i	0.302911	−	0.0479764i	0.306040	+	0.952019i	$0.400996\pi$
$198$	−46255.2	+	23568.2i	−1.17986	+	0.601168i
$199$		−	64011.1i		−	1.61640i	−0.588907	−	0.808201i	$-0.700441\pi$
$199$		−	64011.1i		−	1.61640i	0.588907	−	0.808201i	$-0.299559\pi$
$200$	6512.91	−	28049.6i	0.162823	−	0.701241i
$201$	6560.78			0.162392
$202$	30325.8	+	59517.7i	0.743206	+	1.45862i
$203$	10132.0	+	63970.6i	0.245867	+	1.55235i
$204$	−211.406	+	290.975i	−0.00507991	+	0.00699190i
$205$	28185.7	−	50773.2i	0.670690	−	1.20817i
$206$	5109.03	−	3711.92i	0.120394	−	0.0874711i
$207$	16848.5	−	16848.5i	0.393205	−	0.393205i
$208$	75441.4	+	11948.7i	1.74374	+	0.276182i
$209$	−1244.60	+	404.394i	−0.0284929	+	0.00925790i
$210$	−14517.0	+	9778.58i	−0.329184	+	0.221737i
$211$	5713.11	−	17583.1i	0.128324	−	0.394941i	−0.866168	−	0.499753i	$-0.833424\pi$
$211$	5713.11	−	17583.1i	0.128324	−	0.394941i	0.994492	+	0.104812i	$0.0334242\pi$
$212$	15235.0	+	7762.64i	0.338978	+	0.172718i
$213$	−763.678	+	1498.80i	−0.0168326	+	0.0330358i
$214$	−52427.7	−	17034.8i	−1.14481	−	0.371971i
$215$	2758.98	−	77608.9i	0.0596860	−	1.67894i
$216$	4997.66	+	15381.2i	0.107117	+	0.329673i
$217$	6695.89	−	42276.2i	0.142197	−	0.897794i
$218$	−16838.3	−	16838.3i	−0.354311	−	0.354311i
$219$	−7994.71	−	11003.8i	−0.166692	−	0.229432i
$220$	4317.87	−	22139.2i	0.0892122	−	0.457422i
$221$	5037.70	+	3660.10i	0.103145	+	0.0749391i
$222$	16744.9	−	2652.14i	0.339764	−	0.0538134i
$223$	−35981.5	+	18333.5i	−0.723552	+	0.368668i	−0.776660	−	0.629921i	$-0.783087\pi$
$223$	−35981.5	+	18333.5i	−0.723552	+	0.368668i	0.0531073	+	0.998589i	$0.483087\pi$
$224$			50259.6i			1.00167i
$225$	11433.5	+	46104.2i	0.225848	+	0.910700i
$226$	−53338.0			−1.04429
$227$	−14084.0	−	27641.5i	−0.273323	−	0.536426i	0.713018	−	0.701146i	$-0.247328\pi$
$227$	−14084.0	−	27641.5i	−0.273323	−	0.536426i	−0.986340	+	0.164720i	$0.947328\pi$
$228$	−19.6739	−	124.216i	−0.000378460	−	0.00238950i
$229$	−34986.5	+	48154.8i	−0.667160	+	0.918266i	−0.999692	−	0.0248255i	$-0.992097\pi$
$229$	−34986.5	+	48154.8i	−0.667160	+	0.918266i	0.332532	+	0.943092i	$0.392097\pi$
$230$	4480.29	+	36679.6i	0.0846937	+	0.693376i
$231$	17406.2	−	12646.3i	0.326197	−	0.236996i
$232$	−31768.3	+	31768.3i	−0.590225	+	0.590225i
$233$	19453.3	+	3081.10i	0.358329	+	0.0567537i	0.333004	−	0.942926i	$-0.391938\pi$
$233$	19453.3	+	3081.10i	0.358329	+	0.0567537i	0.0253252	+	0.999679i	$0.491938\pi$
$234$	−82148.0	+	26691.5i	−1.50026	+	0.487463i
$235$	−12315.9	−	9634.68i	−0.223013	−	0.174462i
$236$	4417.75	−	13596.4i	0.0793190	−	0.244119i
$237$	−3097.37	−	1578.19i	−0.0551437	−	0.0280971i
$238$	−3672.35	+	7207.39i	−0.0648321	+	0.127240i
$239$	−19134.7	−	6217.24i	−0.334985	−	0.108843i	0.136694	−	0.990613i	$-0.456352\pi$
$239$	−19134.7	−	6217.24i	−0.334985	−	0.108843i	−0.471680	+	0.881770i	$0.656352\pi$
$240$	−16638.9	−	6067.89i	−0.288869	−	0.105345i
$241$	1775.32	+	5463.87i	0.0305662	+	0.0940732i	0.965176	−	0.261602i	$-0.0842509\pi$
$241$	1775.32	+	5463.87i	0.0305662	+	0.0940732i	−0.934610	+	0.355675i	$0.884251\pi$
$242$	−4683.04	+	29567.6i	−0.0799645	+	0.504876i
$243$	−28596.7	−	28596.7i	−0.484288	−	0.484288i
$244$	19607.2	+	26987.1i	0.329334	+	0.453290i
$245$	−36784.3	+	34258.8i	−0.612817	+	0.570741i
$246$	−19808.9	−	14392.0i	−0.327334	−	0.237822i
$247$	−2150.57	+	340.617i	−0.0352501	+	0.00558306i
$248$	26454.8	−	13479.4i	0.430132	−	0.219163i
$249$		−	6614.67i		−	0.106686i
$250$	−67240.4	−	30089.4i	−1.07585	−	0.481430i
$251$	102586.			1.62832			0.814161	−	0.580639i	$-0.197197\pi$
$251$	102586.			1.62832			0.814161	+	0.580639i	$0.197197\pi$
$252$	−14272.0	−	28010.4i	−0.224742	−	0.441081i
$253$	−7105.59	−	44862.9i	−0.111009	−	0.700885i
$254$	84318.9	−	116055.i	1.30695	−	1.79886i
$255$	−984.039	−	1056.58i	−0.0151332	−	0.0162489i
$256$	−53747.2	+	39049.6i	−0.820117	+	0.595850i
$257$	−28328.0	+	28328.0i	−0.428894	+	0.428894i	−0.888251	−	0.459358i	$-0.848080\pi$
$257$	−28328.0	+	28328.0i	−0.428894	+	0.428894i	0.459358	+	0.888251i	$0.348080\pi$
$258$	−32340.2	−	5122.19i	−0.485852	−	0.0769513i
$259$	101600.	−	33011.9i	1.51459	−	0.492120i
$260$	12858.2	−	35258.8i	0.190211	−	0.521579i
$261$	22901.4	−	70483.3i	0.336187	−	1.03468i
$262$	107533.	+	54790.7i	1.56653	+	0.798186i
$263$	−21824.7	+	42833.5i	−0.315528	+	0.619258i	−0.993241	−	0.116068i	$-0.962971\pi$
$263$	−21824.7	+	42833.5i	−0.315528	+	0.619258i	0.677714	+	0.735326i	$0.262971\pi$
$264$	14193.9	+	4611.87i	0.203654	+	0.0661712i
$265$	−42293.9	+	54063.6i	−0.602262	+	0.769863i
$266$	−874.056	−	2690.07i	−0.0123531	−	0.0380189i
$267$	−2378.36	+	15016.4i	−0.0333623	+	0.210641i
$268$	−12921.9	−	12921.9i	−0.179910	−	0.179910i
$269$	49185.1	+	67697.5i	0.679719	+	0.935553i	0.999930	−	0.0117931i	$-0.00375395\pi$
$269$	49185.1	+	67697.5i	0.679719	+	0.935553i	−0.320211	+	0.947346i	$0.603754\pi$
$270$	41068.1	−	5016.34i	0.563348	−	0.0688112i
$271$	−2246.04	−	1631.84i	−0.0305829	−	0.0222198i	0.572389	−	0.819982i	$-0.306017\pi$
$271$	−2246.04	−	1631.84i	−0.0305829	−	0.0222198i	−0.602972	+	0.797763i	$0.706017\pi$
$272$	−8084.16	+	1280.41i	−0.109269	+	0.0173065i
$273$	31896.2	−	16251.9i	0.427970	−	0.218062i
$274$			10494.8i			0.139789i
$275$	83914.7	+	34026.5i	1.10962	+	0.449937i
$276$	4365.18			0.0573039
$277$	9223.97	+	18103.1i	0.120215	+	0.235935i	0.943270	−	0.332026i	$-0.107732\pi$
$277$	9223.97	+	18103.1i	0.120215	+	0.235935i	−0.823055	+	0.567961i	$0.807732\pi$
$278$	−16365.1	−	103325.i	−0.211753	−	1.33696i
$279$	−28788.1	+	39623.5i	−0.369833	+	0.509031i
$280$	−75090.5	−	14645.1i	−0.957787	−	0.186799i
$281$	104877.	−	76197.4i	1.32821	−	0.965001i	0.328419	−	0.944532i	$-0.393484\pi$
$281$	104877.	−	76197.4i	1.32821	−	0.965001i	0.999790	−	0.0204688i	$-0.00651587\pi$
$282$	−4661.96	+	4661.96i	−0.0586233	+	0.0586233i
$283$	−45722.5	−	7241.73i	−0.570896	−	0.0904211i	−0.135689	−	0.990751i	$-0.543325\pi$
$283$	−45722.5	−	7241.73i	−0.570896	−	0.0904211i	−0.435207	+	0.900330i	$0.643325\pi$
$284$	4456.10	−	1447.87i	0.0552482	−	0.0179512i
$285$	504.553	+	17.9368i	0.00621180	+	0.000220829i
$286$	−50882.2	+	156599.i	−0.622062	+	1.91451i
$287$	−137470.	−	70044.6i	−1.66896	−	0.850376i
$288$	26108.7	−	51241.2i	0.314775	−	0.617781i
$289$	78798.6	+	25603.2i	0.943458	+	0.306548i
$290$	64209.8	+	95324.1i	0.763494	+	1.13346i
$291$	−1140.04	−	3508.67i	−0.0134627	−	0.0414340i
$292$	−5926.54	+	37418.7i	−0.0695081	+	0.438857i
$293$	53176.2	+	53176.2i	0.619416	+	0.619416i	0.945382	−	0.325966i	$-0.105689\pi$
$293$	53176.2	+	53176.2i	0.619416	+	0.619416i	−0.325966	+	0.945382i	$0.605689\pi$
$294$	12457.7	+	17146.5i	0.144126	+	0.198373i
$295$	50177.7	+	27855.2i	0.576589	+	0.320082i
$296$	59950.6	+	43556.7i	0.684243	+	0.497132i
$297$	−50230.5	+	7955.73i	−0.569449	+	0.0901919i
$298$	100073.	−	50989.9i	1.12690	−	0.574185i
$299$		−	75575.2i		−	0.845350i
$300$	−4491.32	+	7453.58i	−0.0499036	+	0.0828176i
$301$	−206323.			−2.27727
$302$	−64348.4	−	126291.i	−0.705543	−	1.38471i
$303$	4955.46	+	31287.5i	0.0539758	+	0.340790i
$304$	1682.26	−	2315.43i	0.0182031	−	0.0250545i
$305$	−121402.	+	56517.7i	−1.30504	+	0.607554i
$306$	7488.14	−	5440.45i	0.0799707	−	0.0581021i
$307$	−74129.5	+	74129.5i	−0.786528	+	0.786528i	−0.980923	−	0.194395i	$-0.937726\pi$
$307$	−74129.5	+	74129.5i	−0.786528	+	0.786528i	0.194395	+	0.980923i	$0.437726\pi$
$308$	−59190.3	−	9374.83i	−0.623949	−	0.0988238i
$309$	2848.22	−	925.441i	0.0298302	−	0.00969241i
$310$	−20890.3	−	73026.4i	−0.217381	−	0.759900i
$311$	−19933.1	+	61347.8i	−0.206089	+	0.634276i	0.793578	+	0.608468i	$0.208216\pi$
$311$	−19933.1	+	61347.8i	−0.206089	+	0.634276i	−0.999667	+	0.0258077i	$0.991784\pi$
$312$	22125.2	+	11273.3i	0.227289	+	0.115809i
$313$	7519.31	−	14757.5i	0.0767519	−	0.150634i	−0.849442	−	0.527683i	$-0.823061\pi$
$313$	7519.31	−	14757.5i	0.0767519	−	0.150634i	0.926193	+	0.377049i	$0.123061\pi$
$314$	25199.4	+	8187.80i	0.255583	+	0.0830439i
$315$	121334.	−	34709.4i	1.22282	−	0.349805i
$316$	2992.12	+	9208.79i	0.0299643	+	0.0922207i
$317$	17037.2	−	107569.i	0.169543	−	1.07045i	−0.745325	−	0.666701i	$-0.767706\pi$
$317$	17037.2	−	107569.i	0.169543	−	1.07045i	0.914868	−	0.403752i	$-0.132294\pi$
$318$	20464.9	+	20464.9i	0.202374	+	0.202374i
$319$	−83040.7	−	114296.i	−0.816036	−	1.12318i
$320$	−15850.4	−	34047.2i	−0.154789	−	0.332492i
$321$	−21149.4	−	15365.9i	−0.205252	−	0.149125i
$322$	96966.5	−	15358.0i	0.935212	−	0.148123i
$323$	207.893	−	105.927i	0.00199267	−	0.00101532i
$324$			33449.9i			0.318643i
$325$	129045.	+	77759.0i	1.22173	+	0.736180i
$326$	−157020.			−1.47747
$327$	−5126.80	−	10061.9i	−0.0479458	−	0.0940989i
$328$	−16742.0	−	105705.i	−0.155618	−	0.982536i
$329$	−24418.9	+	33609.8i	−0.225598	+	0.310509i
$330$	18530.8	−	33380.9i	0.170163	−	0.306528i
$331$	14496.8	−	10532.5i	0.132317	−	0.0961339i	−0.519658	−	0.854374i	$-0.673941\pi$
$331$	14496.8	−	10532.5i	0.132317	−	0.0961339i	0.651975	+	0.758240i	$0.273941\pi$
$332$	−13028.0	+	13028.0i	−0.118196	+	0.118196i
$333$	−120733.	−	19122.3i	−1.08878	−	0.172445i
$334$	121183.	−	39374.6i	1.08629	−	0.352958i
$335$	60844.6	−	40984.6i	0.542166	−	0.365200i
$336$	−14540.6	+	44751.2i	−0.128796	+	0.396393i
$337$	−50824.7	−	25896.5i	−0.447523	−	0.228024i	0.215680	−	0.976464i	$-0.430803\pi$
$337$	−50824.7	−	25896.5i	−0.447523	−	0.228024i	−0.663203	+	0.748440i	$0.730803\pi$
$338$	−63245.8	+	124127.i	−0.553603	+	1.08651i
$339$	−24056.3	−	7816.37i	−0.209329	−	0.0680152i
$340$	−142.879	+	4019.13i	−0.00123598	+	0.0347676i
$341$	28851.6	+	88796.1i	0.248120	+	0.763634i
$342$	−506.300	+	3196.65i	−0.00432869	+	0.0273302i
$343$	−18332.3	−	18332.3i	−0.155822	−	0.155822i
$344$	−84122.9	−	115785.i	−0.710881	−	0.978444i
$345$	−3354.49	+	17199.7i	−0.0281831	+	0.144505i
$346$	17845.8	+	12965.7i	0.149068	+	0.108304i
$347$	110362.	−	17479.6i	0.916560	−	0.145169i	0.319704	−	0.947517i	$-0.396417\pi$
$347$	110362.	−	17479.6i	0.916560	−	0.145169i	0.596856	+	0.802349i	$0.296417\pi$
$348$	12097.3	−	6163.88i	0.0998917	−	0.0508974i
$349$			55696.8i			0.457277i	0.973511	+	0.228639i	$0.0734274\pi$
$349$			55696.8i			0.457277i	−0.973511	+	0.228639i	$0.926573\pi$
$350$	−73544.6	+	181373.i	−0.600364	+	1.48059i
$351$	−84617.3			−0.686823
$352$	−49771.1	−	97681.4i	−0.401691	−	0.788363i
$353$	14748.5	+	93118.4i	0.118358	+	0.747285i	0.973466	+	0.228834i	$0.0734912\pi$
$353$	14748.5	+	93118.4i	0.118358	+	0.747285i	−0.855107	+	0.518451i	$0.826509\pi$
$354$	14223.2	−	19576.6i	0.113499	−	0.156218i
$355$	2280.54	+	18670.5i	0.0180960	+	0.148149i
$356$	34260.0	−	24891.4i	0.270326	−	0.196403i
$357$	−2712.49	+	2712.49i	−0.0212830	+	0.0212830i
$358$	260015.	+	41182.3i	2.02877	+	0.321325i
$359$	−144753.	+	47033.1i	−1.12315	+	0.364934i	−0.810970	−	0.585088i	$-0.801060\pi$
$359$	−144753.	+	47033.1i	−1.12315	+	0.364934i	−0.312183	+	0.950022i	$0.601060\pi$
$360$	68949.2	+	53938.8i	0.532015	+	0.416195i
$361$	40246.2	−	123865.i	0.308824	−	0.950461i
$362$	166962.	+	85071.3i	1.27409	+	0.649181i
$363$	−6445.08	+	12649.2i	−0.0489120	+	0.0959952i
$364$	−94830.6	−	30812.3i	−0.715724	−	0.232553i
$365$	−142882.	−	52106.6i	−1.07249	−	0.391118i
$366$	17447.8	+	53698.9i	0.130250	+	0.400870i
$367$	−6691.45	+	42248.2i	−0.0496808	+	0.313672i	0.950316	+	0.311286i	$0.100760\pi$
$367$	−6691.45	+	42248.2i	−0.0496808	+	0.313672i	−0.999997	+	0.00238631i	$0.999240\pi$
$368$	70243.3	+	70243.3i	0.518692	+	0.518692i
$369$	103769.	+	142825.i	0.762101	+	1.04894i
$370$	138725.	−	129200.i	1.01333	−	0.943755i
$371$	147539.	+	107193.i	1.07191	+	0.778787i
$372$	−8862.22	+	1403.64i	−0.0640408	+	0.0101431i
$373$	82155.4	−	41860.3i	0.590498	−	0.300874i	−0.133092	−	0.991104i	$-0.542491\pi$
$373$	82155.4	−	41860.3i	0.590498	−	0.300874i	0.723590	+	0.690230i	$0.242491\pi$
$374$		−	17644.5i		−	0.126144i
$375$	−25917.1	−	23424.5i	−0.184300	−	0.166574i
$376$	−28817.5			−0.203836
$377$	−106716.	−	209442.i	−0.750841	−	1.47361i
$378$	−17195.5	−	108568.i	−0.120346	−	0.759833i
$379$	−25896.4	+	35643.3i	−0.180285	+	0.248142i	−0.889589	−	0.456761i	$-0.849009\pi$
$379$	−25896.4	+	35643.3i	−0.180285	+	0.248142i	0.709304	+	0.704903i	$0.249009\pi$
$380$	−958.421	−	1029.08i	−0.00663726	−	0.00712657i
$381$	55036.4	−	39986.3i	0.379141	−	0.275462i
$382$	−138473.	+	138473.i	−0.948941	+	0.948941i
$383$	−159535.	−	25267.9i	−1.08757	−	0.172255i	−0.413197	−	0.910642i	$-0.635588\pi$
$383$	−159535.	−	25267.9i	−1.08757	−	0.172255i	−0.674377	+	0.738387i	$0.735588\pi$
$384$	−40803.9	+	13258.0i	−0.276719	+	0.0899115i
$385$	82424.3	−	226017.i	0.556076	−	1.52482i
$386$	62832.6	−	193379.i	0.421706	−	1.29788i
$387$	210352.	+	107180.i	1.40451	+	0.715634i
$388$	−4665.17	+	9155.92i	−0.0309888	+	0.0608189i
$389$	102797.	+	33400.6i	0.679328	+	0.220727i	0.628301	−	0.777970i	$-0.283751\pi$
$389$	102797.	+	33400.6i	0.679328	+	0.220727i	0.0510270	+	0.998697i	$0.483751\pi$
$390$	39141.1	−	50033.5i	0.257338	−	0.328951i
$391$	2502.57	+	7702.13i	0.0163694	+	0.0503799i
$392$	−14491.8	+	91497.8i	−0.0943086	+	0.595441i
$393$	40469.8	+	40469.8i	0.262027	+	0.262027i
$394$	−32983.2	−	45397.4i	−0.212471	−	0.292441i
$395$	−38583.7	+	4712.88i	−0.247292	+	0.0302059i
$396$	55476.3	+	40305.9i	0.353767	+	0.257027i
$397$	228881.	−	36251.2i	1.45221	−	0.230007i	0.620058	−	0.784556i	$-0.287109\pi$
$397$	228881.	−	36251.2i	1.45221	−	0.230007i	0.832152	+	0.554548i	$0.187109\pi$
$398$	−268895.	+	137009.i	−1.69752	+	0.864932i
$399$		−	1341.35i		−	0.00842553i
$400$	−192214.	+	47667.9i	−1.20134	+	0.297924i
$401$	−132892.			−0.826440			−0.413220	−	0.910631i	$-0.635596\pi$
$401$	−132892.			−0.826440			−0.413220	+	0.910631i	$0.635596\pi$
$402$	−14042.6	−	27560.2i	−0.0868952	−	0.170541i
$403$	24301.4	+	153433.i	0.149631	+	0.944732i
$404$	51862.6	−	71382.8i	0.317755	−	0.437352i
$405$	−131799.	−	25705.1i	−0.803529	−	0.156714i
$406$	247038.	−	179484.i	1.49869	−	1.08886i
$407$	−164772.	+	164772.i	−0.994708	+	0.994708i
$408$	−2628.16	−	416.259i	−0.0157881	−	0.00250060i
$409$	110258.	−	35825.1i	0.659121	−	0.214161i	0.0396895	−	0.999212i	$-0.487363\pi$
$409$	110258.	−	35825.1i	0.659121	−	0.214161i	0.619432	+	0.785051i	$0.287363\pi$
$410$	−273614.	−	9726.93i	−1.62768	−	0.0578639i
$411$	−1537.96	+	4733.34i	−0.00910459	+	0.0280211i
$412$	−7432.45	−	3787.02i	−0.0437862	−	0.0223102i
$413$	69223.1	−	135858.i	0.405836	−	0.796498i
$414$	−106838.	−	34713.9i	−0.623342	−	0.202536i
$415$	−41321.2	−	61344.3i	−0.239926	−	0.356187i
$416$	−56367.0	−	173480.i	−0.325715	−	1.00245i
$417$	7760.79	−	48999.7i	0.0446307	−	0.281787i
$418$	4362.68	+	4362.68i	0.0249690	+	0.0249690i
$419$	89477.1	+	123155.i	0.509664	+	0.701492i	0.983863	−	0.178925i	$-0.0572621\pi$
$419$	89477.1	+	123155.i	0.509664	+	0.701492i	−0.474199	+	0.880418i	$0.657262\pi$
$420$	20214.2	+	11221.5i	0.114593	+	0.0636142i
$421$	−112763.	−	81926.8i	−0.636211	−	0.462234i	0.222336	−	0.974970i	$-0.428632\pi$
$421$	−112763.	−	81926.8i	−0.636211	−	0.462234i	−0.858546	+	0.512736i	$0.828632\pi$
$422$	−86090.6	+	13635.4i	−0.483427	+	0.0765673i
$423$	42355.3	−	21581.1i	0.236716	−	0.120613i
$424$			126502.i			0.703662i
$425$	−15726.3	−	3651.53i	−0.0870662	−	0.0202161i
$426$	7930.66			0.0437009
$427$	161521.	+	317004.i	0.885879	+	1.73863i
$428$	11390.9	+	71919.2i	0.0621827	+	0.392606i
$429$	−45897.4	+	63172.3i	−0.249387	+	0.343251i
$430$	−331921.	+	154523.i	−1.79514	+	0.835713i
$431$	67259.9	−	48867.2i	0.362078	−	0.263065i	−0.391841	−	0.920033i	$-0.628162\pi$
$431$	67259.9	−	48867.2i	0.362078	−	0.263065i	0.753918	+	0.656968i	$0.228162\pi$
$432$	78647.5	−	78647.5i	0.421422	−	0.421422i
$433$	−211867.	−	33556.5i	−1.13003	−	0.178979i	−0.436703	−	0.899606i	$-0.643854\pi$
$433$	−211867.	−	33556.5i	−1.13003	−	0.178979i	−0.693323	+	0.720627i	$0.743854\pi$
$434$	−191923.	+	62359.7i	−1.01894	+	0.331074i
$435$	14990.5	+	52402.3i	0.0792205	+	0.276931i
$436$	−9719.99	+	29915.1i	−0.0511320	+	0.157368i
$437$	−2523.16	−	1285.61i	−0.0132124	−	0.00673206i
$438$	−29112.3	+	57136.1i	−0.151750	+	0.297826i
$439$	−170618.	−	55437.0i	−0.885309	−	0.287654i	−0.169149	−	0.985591i	$-0.554102\pi$
$439$	−170618.	−	55437.0i	−0.885309	−	0.287654i	−0.716160	+	0.697936i	$0.754102\pi$
$440$	160444.	−	45897.4i	0.828738	−	0.237073i
$441$	−47222.0	−	145334.i	−0.242810	−	0.747293i
$442$	4592.54	−	28996.1i	0.0235076	−	0.148421i
$443$	−109049.	−	109049.i	−0.555667	−	0.555667i	0.372404	−	0.928071i	$-0.378534\pi$
$443$	−109049.	−	109049.i	−0.555667	−	0.555667i	−0.928071	+	0.372404i	$0.878534\pi$
$444$	−13162.9	−	18117.2i	−0.0667709	−	0.0919022i
$445$	71749.1	+	154119.i	0.362323	+	0.778281i
$446$	154029.	+	111909.i	0.774341	+	0.562592i
$447$	52607.0	−	8332.13i	0.263286	−	0.0417005i
$448$	−88904.0	+	45298.8i	−0.442961	+	0.225700i
$449$		−	102054.i		−	0.506220i	−0.967438	−	0.253110i	$-0.918547\pi$
$449$		−	102054.i		−	0.506220i	0.967438	−	0.253110i	$-0.0814534\pi$
$450$	169200.	−	146710.i	0.835555	−	0.724495i
$451$	336542.			1.65457
$452$	31985.6	+	62775.2i	0.156559	+	0.307264i
$453$	−10515.0	−	66389.1i	−0.0512405	−	0.323519i
$454$	−85969.6	+	118327.i	−0.417093	+	0.574080i
$455$	194281.	−	349973.i	0.938440	−	1.69048i
$456$	752.746	−	546.902i	0.00362009	−	0.00263015i
$457$	53323.8	−	53323.8i	0.255322	−	0.255322i	−0.567826	−	0.823149i	$-0.692215\pi$
$457$	53323.8	−	53323.8i	0.255322	−	0.255322i	0.823149	+	0.567826i	$0.192215\pi$
$458$	277171.	+	43899.6i	1.32135	+	0.209281i
$459$	8623.65	−	2801.99i	0.0409323	−	0.0132997i
$460$	40482.7	−	27268.9i	0.191317	−	0.128870i
$461$	−89757.1	+	276244.i	−0.422345	+	1.29984i	0.483170	+	0.875527i	$0.339485\pi$
$461$	−89757.1	+	276244.i	−0.422345	+	1.29984i	−0.905514	+	0.424316i	$0.860515\pi$
$462$	−90380.1	−	46051.0i	−0.423437	−	0.215752i
$463$	11933.1	−	23420.0i	0.0556661	−	0.109251i	−0.861497	−	0.507762i	$-0.830473\pi$
$463$	11933.1	−	23420.0i	0.0556661	−	0.109251i	0.917164	+	0.398511i	$0.130473\pi$
$464$	293853.	+	95478.7i	1.36488	+	0.443477i
$465$	1279.71	−	35997.5i	0.00591840	−	0.166482i
$466$	−28694.7	−	88313.2i	−0.132139	−	0.406681i
$467$	2361.24	−	14908.3i	0.0108270	−	0.0683587i	−0.981683	−	0.190520i	$-0.938983\pi$
$467$	2361.24	−	14908.3i	0.0108270	−	0.0683587i	0.992510	+	0.122161i	$0.0389826\pi$
$468$	80676.4	+	80676.4i	0.368345	+	0.368345i
$469$	−114563.	−	157682.i	−0.520833	−	0.716865i
$470$	−14112.1	+	72357.8i	−0.0638846	+	0.327559i
$471$	10165.5	+	7385.66i	0.0458233	+	0.0332926i
$472$	104465.	−	16545.7i	0.468909	−	0.0742678i
$473$	400995.	−	204317.i	1.79233	−	0.913236i
$474$			16389.2i			0.0729459i
$475$	4791.27	−	2985.55i	0.0212355	−	0.0132324i
$476$	10684.8			0.0471578
$477$	−94735.7	−	185929.i	−0.416368	−	0.817167i
$478$	14838.6	+	93687.3i	0.0649438	+	0.410039i
$479$	65667.4	−	90383.4i	0.286206	−	0.393929i	−0.641571	−	0.767064i	$-0.721717\pi$
$479$	65667.4	−	90383.4i	0.286206	−	0.393929i	0.927777	+	0.373135i	$0.121717\pi$
$480$	5128.09	+	41983.0i	0.0222573	+	0.182218i
$481$	−313667.	+	227892.i	−1.35575	+	0.985007i
$482$	19152.5	−	19152.5i	0.0824386	−	0.0824386i
$483$	45984.1	+	7283.17i	0.197112	+	0.0312195i
$484$	37607.3	−	12219.4i	0.160539	−	0.0521624i
$485$	−32491.1	−	25417.7i	−0.138128	−	0.108057i
$486$	−58919.6	+	181336.i	−0.249452	+	0.767734i
$487$	45226.9	+	23044.3i	0.190695	+	0.0971639i	0.546731	−	0.837308i	$-0.315872\pi$
$487$	45226.9	+	23044.3i	0.190695	+	0.0971639i	−0.356036	+	0.934472i	$0.615872\pi$
$488$	−112041.	+	219893.i	−0.470477	+	0.923364i
$489$	−70818.4	−	23010.3i	−0.296161	−	0.0962287i
$490$	222645.	+	81194.6i	0.927302	+	0.338170i
$491$	−61076.0	−	187973.i	−0.253342	−	0.779707i	−0.994152	−	0.107992i	$-0.965558\pi$
$491$	−61076.0	−	187973.i	−0.253342	−	0.779707i	0.740809	−	0.671715i	$-0.234442\pi$
$492$	−5059.49	+	31944.4i	−0.0209015	+	0.131967i
$493$	17811.2	+	17811.2i	0.0732825	+	0.0732825i
$494$	6033.90	+	8304.96i	0.0247255	+	0.0340317i
$495$	−201444.	+	187614.i	−0.822138	+	0.765691i
$496$	−165195.	−	120021.i	−0.671481	−	0.487860i
$497$	49357.5	−	7817.47i	0.199821	−	0.0316485i
$498$	−27786.5	+	14158.0i	−0.112041	+	0.0570876i
$499$		−	5504.19i		−	0.0221051i	−0.999939	−	0.0110525i	$-0.996482\pi$
$499$		−	5504.19i		−	0.0221051i	0.999939	−	0.0110525i	$-0.00351820\pi$
$500$	4909.39	+	97181.3i	0.0196376	+	0.388725i
$501$	60425.5			0.240738
$502$	−219574.	−	430937.i	−0.871310	−	1.71004i
$503$	4281.70	+	27033.6i	0.0169231	+	0.106848i	0.994704	−	0.102781i	$-0.0327742\pi$
$503$	4281.70	+	27033.6i	0.0169231	+	0.106848i	−0.977781	+	0.209630i	$0.932774\pi$
$504$	136707.	−	188161.i	0.538182	−	0.740745i
$505$	241407.	+	259204.i	0.946602	+	1.01639i
$506$	−173249.	+	125873.i	−0.676659	+	0.491622i
$507$	−46715.0	+	46715.0i	−0.181736	+	0.181736i
$508$	−187153.	−	29642.1i	−0.725219	−	0.114863i
$509$	−116420.	+	37827.1i	−0.449357	+	0.146005i	−0.524948	−	0.851134i	$-0.675915\pi$
$509$	−116420.	+	37827.1i	−0.449357	+	0.146005i	0.0755918	+	0.997139i	$0.475915\pi$
$510$	−2332.21	+	6395.20i	−0.00896660	+	0.0245874i
$511$	−124864.	+	384291.i	−0.478183	+	1.47170i
$512$	5509.85	+	2807.41i	0.0210184	+	0.0107094i
$513$	−1439.43	+	2825.04i	−0.00546961	+	0.0107347i
$514$	179632.	+	58365.8i	0.679918	+	0.220919i
$515$	20633.2	−	26375.1i	0.0777949	−	0.0994441i
$516$	13365.2	+	41133.9i	0.0501969	+	0.154490i
$517$	14175.9	−	89503.3i	0.0530360	−	0.334856i
$518$	−356138.	−	356138.i	−1.32727	−	1.32727i
$519$	6148.69	+	8462.94i	0.0228269	+	0.0314186i
$520$	275612.	−	33665.2i	1.01928	−	0.124501i
$521$	−159137.	−	115620.i	−0.586267	−	0.425948i	0.254711	−	0.967017i	$-0.418020\pi$
$521$	−159137.	−	115620.i	−0.586267	−	0.425948i	−0.840978	+	0.541069i	$0.818020\pi$
$522$	−345100.	+	54658.5i	−1.26650	+	0.200593i
$523$	−403830.	+	205762.i	−1.47637	+	0.752249i	−0.992425	−	0.122849i	$-0.960797\pi$
$523$	−403830.	+	205762.i	−1.47637	+	0.752249i	−0.483946	+	0.875098i	$0.660797\pi$
$524$		−	159415.i		−	0.580588i
$525$	−59749.0	+	71024.6i	−0.216776	+	0.257686i
$526$	226646.			0.819175
$527$	−7557.38	−	14832.2i	−0.0272113	−	0.0534053i
$528$	−16056.2	−	101375.i	−0.0575936	−	0.363632i
$529$	−106713.	+	146878.i	−0.381334	+	0.524862i
$530$	317633.	+	61948.7i	1.13077	+	0.220536i
$531$	−141150.	+	102551.i	−0.500601	+	0.363708i
$532$	−2641.88	+	2641.88i	−0.00933446	+	0.00933446i
$533$	553058.	+	87595.8i	1.94678	+	0.308339i
$534$	68170.7	−	22150.0i	0.239064	−	0.0776767i
$535$	−292129.	−	10385.1i	−1.02063	−	0.0362831i
$536$	41778.8	−	128582.i	0.145421	−	0.447559i
$537$	111236.	+	56677.6i	0.385742	+	0.196545i
$538$	179105.	−	351513.i	0.618790	−	1.21444i
$539$	−277051.	−	90019.5i	−0.953636	−	0.309855i
$540$	−30531.5	−	45326.2i	−0.104703	−	0.155440i
$541$	−7753.70	−	23863.4i	−0.0264920	−	0.0815339i	0.936936	−	0.349500i	$-0.113649\pi$
$541$	−7753.70	−	23863.4i	−0.0264920	−	0.0815339i	−0.963428	+	0.267966i	$0.913649\pi$
$542$	−2047.56	+	12927.8i	−0.00697010	+	0.0440075i
$543$	62835.9	+	62835.9i	0.213112	+	0.213112i
$544$	11489.1	+	15813.4i	0.0388230	+	0.0534352i
$545$	−110402.	−	61287.3i	−0.371691	−	0.206337i
$546$	−136540.	−	99202.4i	−0.458011	−	0.332764i
$547$	−453588.	+	71841.2i	−1.51596	+	0.240104i	−0.858274	−	0.513192i	$-0.828463\pi$
$547$	−453588.	+	71841.2i	−1.51596	+	0.240104i	−0.657682	+	0.753296i	$0.728463\pi$
$548$	12351.7	−	6293.51i	0.0411307	−	0.0209571i
$549$		−	407101.i		−	1.35070i
$550$	−36673.4	−	425334.i	−0.121234	−	1.40606i
$551$	−8807.82			−0.0290112
$552$	14661.7	+	28775.1i	0.0481177	+	0.0944363i
$553$	16155.3	+	102000.i	0.0528280	+	0.333543i
$554$	56303.5	−	77495.1i	0.183449	−	0.252496i
$555$	81500.6	−	37942.0i	0.264591	−	0.123178i
$556$	−111793.	+	81222.5i	−0.361631	+	0.262740i
$557$	189866.	−	189866.i	0.611978	−	0.611978i	−0.331483	−	0.943461i	$-0.607549\pi$
$557$	189866.	−	189866.i	0.611978	−	0.611978i	0.943461	+	0.331483i	$0.107549\pi$
$558$	228066.	+	36122.1i	0.732474	+	0.116012i
$559$	712158.	−	231394.i	2.27904	−	0.740507i
$560$	144708.	+	505856.i	0.461441	+	1.61306i
$561$	2585.69	−	7957.95i	0.00821583	−	0.0252857i
$562$	−544563.	−	277469.i	−1.72415	−	0.878499i
$563$	171622.	−	336828.i	0.541448	−	1.06265i	−0.444528	−	0.895765i	$-0.646628\pi$
$563$	171622.	−	336828.i	0.541448	−	1.06265i	0.985976	−	0.166887i	$-0.0533715\pi$
$564$	8282.48	+	2691.14i	0.0260377	+	0.00846015i
$565$	−271926.	+	77788.7i	−0.851832	+	0.243680i
$566$	67443.2	+	207569.i	0.210526	+	0.647932i
$567$	−55810.0	+	352371.i	−0.173599	+	1.09606i
$568$	24511.3	+	24511.3i	0.0759749	+	0.0759749i
$569$	318584.	+	438494.i	0.984011	+	1.35437i	0.934640	+	0.355594i	$0.115721\pi$
$569$	318584.	+	438494.i	0.984011	+	1.35437i	0.0493703	+	0.998781i	$0.484279\pi$
$570$	−1004.59	−	2157.89i	−0.00309200	−	0.00664171i
$571$	469488.	+	341103.i	1.43997	+	1.04620i	0.988050	+	0.154136i	$0.0492593\pi$
$571$	469488.	+	341103.i	1.43997	+	1.04620i	0.451916	+	0.892061i	$0.350741\pi$
$572$	214819.	−	34024.1i	0.656571	−	0.103991i
$573$	−82746.2	+	42161.3i	−0.252022	+	0.128412i
$574$			727400.i			2.20775i
$575$	76335.2	+	180465.i	0.230881	+	0.545829i
$576$	114172.			0.344124
$577$	113274.	+	222312.i	0.340233	+	0.667746i	0.996205	−	0.0870401i	$-0.0277408\pi$
$577$	113274.	+	222312.i	0.340233	+	0.667746i	−0.655971	+	0.754786i	$0.727741\pi$
$578$	−61106.9	−	385814.i	−0.182909	−	1.15484i
$579$	56677.1	−	78009.3i	0.169064	−	0.232696i
$580$	73684.9	−	132734.i	0.219040	−	0.394573i
$581$	−158977.	+	115504.i	−0.470959	+	0.342172i
$582$	−12298.9	+	12298.9i	−0.0363096	+	0.0363096i
$583$	−392897.	−	62228.8i	−1.15596	−	0.183086i
$584$	−266568.	+	86613.3i	−0.781597	+	0.253956i
$585$	−379877.	+	255883.i	−1.11002	+	0.747705i
$586$	109562.	−	337198.i	0.319055	−	0.981950i
$587$	144746.	+	73751.9i	0.420079	+	0.214041i	0.651236	−	0.758875i	$-0.274251\pi$
$587$	144746.	+	73751.9i	0.420079	+	0.214041i	−0.231156	+	0.972917i	$0.574251\pi$
$588$	12709.7	−	24944.2i	0.0367605	−	0.0721465i
$589$	5535.93	+	1798.73i	0.0159573	+	0.00518484i
$590$	9612.84	−	270404.i	0.0276152	−	0.776801i
$591$	−8223.22	−	25308.5i	−0.0235433	−	0.0724588i
$592$	79723.1	−	503352.i	0.227479	−	1.43624i
$593$	−222222.	−	222222.i	−0.631943	−	0.631943i	0.316612	−	0.948555i	$-0.397455\pi$
$593$	−222222.	−	222222.i	−0.631943	−	0.631943i	−0.948555	+	0.316612i	$0.897455\pi$
$594$	140933.	+	193977.i	0.399429	+	0.549766i
$595$	−8210.92	+	42100.3i	−0.0231931	+	0.118919i
$596$	−120023.	−	87202.1i	−0.337888	−	0.245490i
$597$	−141354.	+	22388.2i	−0.396605	+	0.0628161i
$598$	−317472.	+	161760.i	−0.887776	+	0.452344i
$599$		−	295772.i		−	0.824334i	−0.911108	−	0.412167i	$-0.864772\pi$
$599$		−	295772.i		−	0.824334i	0.911108	−	0.412167i	$-0.135228\pi$
$600$	−64219.0	−	4571.73i	−0.178386	−	0.0126993i
$601$	222079.			0.614835			0.307417	−	0.951575i	$-0.400535\pi$
$601$	222079.			0.614835			0.307417	+	0.951575i	$0.400535\pi$
$602$	441611.	+	866710.i	1.21856	+	2.39156i
$603$	34888.1	+	220275.i	0.0959494	+	0.605801i
$604$	−110047.	+	151467.i	−0.301652	+	0.415188i
$605$	19246.7	+	157570.i	0.0525830	+	0.430490i
$606$	120824.	−	87784.1i	0.329010	−	0.239040i
$607$	127560.	−	127560.i	0.346207	−	0.346207i	−0.512487	−	0.858695i	$-0.671276\pi$
$607$	127560.	−	127560.i	0.346207	−	0.346207i	0.858695	+	0.512487i	$0.171276\pi$
$608$	−6750.68	−	1069.20i	−0.0182617	−	0.00289236i
$609$	137721.	−	44748.1i	0.371334	−	0.120654i
$610$	497263.	+	389008.i	1.33637	+	1.04544i
$611$	46592.2	−	143396.i	0.124805	−	0.384109i
$612$	−10893.5	−	5550.52i	−0.0290847	−	0.0148194i
$613$	182869.	−	358900.i	0.486651	−	0.955107i	−0.508894	−	0.860829i	$-0.669946\pi$
$613$	182869.	−	358900.i	0.486651	−	0.955107i	0.995546	−	0.0942783i	$-0.0300544\pi$
$614$	470065.	+	152733.i	1.24687	+	0.405133i
$615$	−121979.	−	44483.5i	−0.322503	−	0.117611i
$616$	−137008.	−	421668.i	−0.361065	−	1.11124i
$617$	−53243.4	+	336166.i	−0.139861	+	0.883046i	0.813577	+	0.581457i	$0.197517\pi$
$617$	−53243.4	+	336166.i	−0.139861	+	0.883046i	−0.953438	+	0.301589i	$0.902483\pi$
$618$	−9983.83	−	9983.83i	−0.0261409	−	0.0261409i
$619$	−408163.	−	561788.i	−1.06525	−	1.46619i	−0.874792	−	0.484499i	$-0.839002\pi$
$619$	−408163.	−	561788.i	−1.06525	−	1.46619i	−0.190460	−	0.981695i	$-0.560998\pi$
$620$	−73419.7	+	68378.8i	−0.190998	+	0.177884i
$621$	−89032.2	−	64685.7i	−0.230868	−	0.167735i
$622$	300371.	−	47574.1i	0.776386	−	0.122967i
$623$	402435.	−	205051.i	1.03686	−	0.528307i
$624$		−	170774.i		−	0.438584i
$625$	−386686.	−	55336.5i	−0.989915	−	0.141661i
$626$	−78086.6			−0.199264
$627$	1328.31	+	2606.96i	0.00337883	+	0.00663132i
$628$	−5475.04	−	34568.1i	−0.0138825	−	0.0876508i
$629$	24420.5	−	33612.0i	0.0617239	−	0.0849557i
$630$	−405507.	−	435401.i	−1.02169	−	1.09700i
$631$	463323.	−	336624.i	1.16366	−	0.845446i	0.173420	−	0.984848i	$-0.444518\pi$
$631$	463323.	−	336624.i	1.16366	−	0.845446i	0.990236	+	0.139402i	$0.0445181\pi$
$632$	−50654.1	+	50654.1i	−0.126818	+	0.126818i
$633$	−40826.5	−	6466.28i	−0.101891	−	0.0161379i
$634$	−488336.	+	158670.i	−1.21490	+	0.394744i
$635$	260616.	−	714640.i	0.646329	−	1.77231i
$636$	11813.4	−	36358.0i	0.0292053	−	0.0898848i
$637$	−431864.	−	220045.i	−1.06431	−	0.542292i
$638$	−302388.	+	593470.i	−0.742888	+	1.45800i
$639$	−54382.5	−	17669.9i	−0.133186	−	0.0432746i
$640$	−295593.	+	377853.i	−0.721663	+	0.922492i
$641$	86645.6	+	266668.i	0.210878	+	0.649014i	0.999421	+	0.0340348i	$0.0108357\pi$
$641$	86645.6	+	266668.i	0.210878	+	0.649014i	−0.788543	+	0.614979i	$0.789164\pi$
$642$	−19280.5	+	121732.i	−0.0467787	+	0.295349i
$643$	99235.7	+	99235.7i	0.240019	+	0.240019i	0.816858	−	0.576839i	$-0.195714\pi$
$643$	99235.7	+	99235.7i	0.240019	+	0.240019i	−0.576839	+	0.816858i	$0.695714\pi$
$644$	−76223.9	−	104913.i	−0.183789	−	0.252964i
$645$	−172346.	+	21051.5i	−0.414269	+	0.0506016i
$646$	−889.944	−	646.582i	−0.00213254	−	0.00154938i
$647$	−265439.	+	42041.4i	−0.634097	+	0.100431i	−0.465204	−	0.885203i	$-0.654019\pi$
$647$	−265439.	+	42041.4i	−0.634097	+	0.100431i	−0.168893	+	0.985634i	$0.554019\pi$
$648$	−220500.	+	112350.i	−0.525120	+	0.267562i
$649$			332595.i			0.789634i
$650$	50439.4	−	708521.i	0.119383	−	1.67697i
$651$	−95699.1			−0.225811
$652$	94161.0	+	184801.i	0.221501	+	0.434720i
$653$	125764.	+	794041.i	0.294937	+	1.86216i	0.477045	+	0.878879i	$0.341708\pi$
$653$	125764.	+	794041.i	0.294937	+	1.86216i	−0.182109	+	0.983278i	$0.558292\pi$
$654$	−31294.2	+	43072.7i	−0.0731658	+	0.100704i
$655$	628127.	+	122505.i	1.46408	+	0.285543i
$656$	−595455.	+	432624.i	−1.38370	+	1.00532i
$657$	326932.	−	326932.i	0.757403	−	0.757403i
$658$	193452.	+	30639.8i	0.446809	+	0.0707675i
$659$	−645819.	+	209839.i	−1.48710	+	0.483188i	−0.936225	−	0.351401i	$-0.885705\pi$
$659$	−645819.	+	209839.i	−1.48710	+	0.483188i	−0.550874	+	0.834589i	$0.685705\pi$
$660$	−50399.6	−	1791.70i	−0.115701	−	0.00411317i
$661$	214402.	−	659862.i	0.490711	−	1.51025i	−0.332824	−	0.942989i	$-0.608002\pi$
$661$	214402.	−	659862.i	0.490711	−	1.51025i	0.823535	−	0.567265i	$-0.191998\pi$
$662$	−75273.2	−	38353.6i	−0.171761	−	0.0875166i
$663$	6320.52	−	12404.7i	0.0143789	−	0.0282202i
$664$	−129638.	−	42121.9i	−0.294033	−	0.0955371i
$665$	−8379.30	−	12439.7i	−0.0189481	−	0.0281298i
$666$	178088.	+	548099.i	0.401501	+	1.23569i
$667$	47824.0	−	301949.i	0.107497	−	0.678706i
$668$	−119012.	−	119012.i	−0.266708	−	0.266708i
$669$	53070.0	+	73044.6i	0.118576	+	0.163206i
$670$	−302397.	−	167870.i	−0.673640	−	0.373958i
$671$	−627845.	−	456156.i	−1.39446	−	1.01314i
$672$	110987.	−	17578.6i	0.245772	−	0.0389265i
$673$	330785.	−	168544.i	0.730325	−	0.372119i	−0.0489502	−	0.998801i	$-0.515588\pi$
$673$	330785.	−	168544.i	0.730325	−	0.372119i	0.779275	+	0.626682i	$0.215588\pi$
$674$			268930.i			0.591998i
$675$	202056.	−	85468.3i	0.443470	−	0.187585i
$676$	184016.			0.402682
$677$	52407.8	+	102856.i	0.114345	+	0.224416i	0.941086	−	0.338168i	$-0.109807\pi$
$677$	52407.8	+	102856.i	0.114345	+	0.224416i	−0.826740	+	0.562584i	$0.809807\pi$
$678$	18655.2	+	117785.i	0.0405828	+	0.256229i
$679$	−64420.7	+	88667.4i	−0.139729	+	0.192320i
$680$	−26973.8	+	12557.5i	−0.0583344	+	0.0271572i
$681$	−56113.9	+	40769.1i	−0.120997	+	0.0879097i
$682$	311256.	−	311256.i	0.669190	−	0.669190i
$683$	−310872.	−	49237.2i	−0.666407	−	0.105549i	−0.185940	−	0.982561i	$-0.559533\pi$
$683$	−310872.	−	49237.2i	−0.666407	−	0.105549i	−0.480467	+	0.877013i	$0.659533\pi$
$684$	4065.86	−	1321.08i	0.00869041	−	0.00282369i
$685$	15305.8	+	53504.4i	0.0326193	+	0.114027i
$686$	−37771.1	+	116248.i	−0.0802623	+	0.247022i
$687$	118575.	+	60417.2i	0.251236	+	0.128011i
$688$	−446846.	+	876984.i	−0.944019	+	1.85274i
$689$	−629473.	−	204528.i	−1.32599	−	0.430839i
$690$	79431.3	−	22722.6i	0.166837	−	0.0477265i
$691$	192276.	+	591766.i	0.402689	+	1.23935i	0.922810	+	0.385256i	$0.125887\pi$
$691$	192276.	+	591766.i	0.402689	+	1.23935i	−0.520121	+	0.854093i	$0.674113\pi$
$692$	4558.07	−	28778.5i	0.00951850	−	0.0600974i
$693$	517154.	+	517154.i	1.07685	+	1.07685i
$694$	−309645.	−	426190.i	−0.642903	−	0.884879i
$695$	−234123.	−	502903.i	−0.484702	−	1.04115i
$696$	81264.0	+	59041.8i	0.167757	+	0.121882i
$697$	−59264.7	+	9386.61i	−0.121992	+	0.0193216i
$698$	233968.	−	119213.i	0.480227	−	0.244688i
$699$		−	44035.7i		−	0.0901262i
$700$	257567.	−	22208.0i	0.525646	−	0.0453225i
$701$	533524.			1.08572			0.542860	−	0.839823i	$-0.317341\pi$
$701$	533524.			1.08572			0.542860	+	0.839823i	$0.317341\pi$
$702$	181114.	+	355456.i	0.367517	+	0.721293i
$703$	2272.63	+	14348.8i	0.00459852	+	0.0290339i
$704$	127929.	−	176080.i	0.258122	−	0.355275i
$705$	−16968.4	+	30566.5i	−0.0341399	+	0.0614989i
$706$	359599.	−	261264.i	0.721456	−	0.524168i
$707$	665436.	−	665436.i	1.33127	−	1.33127i
$708$	−31569.7	−	5000.15i	−0.0629802	−	0.00997508i
$709$	403838.	−	131215.i	0.803369	−	0.261030i	0.121582	−	0.992581i	$-0.461203\pi$
$709$	403838.	−	131215.i	0.803369	−	0.261030i	0.681787	+	0.731551i	$0.261203\pi$
$710$	73548.8	−	49542.1i	0.145901	−	0.0982783i
$711$	36516.0	−	112385.i	0.0722344	−	0.222315i
$712$	279154.	+	142236.i	0.550661	+	0.280576i
$713$	−91722.5	+	180016.i	−0.180425	+	0.354104i
$714$	17200.3	+	5588.71i	0.0337395	+	0.0109626i
$715$	−31020.0	+	872576.i	−0.0606777	+	1.70683i
$716$	−107456.	−	330716.i	−0.209607	−	0.645103i
$717$	−7036.87	+	44429.0i	−0.0136880	+	0.0864229i
$718$	507402.	+	507402.i	0.984245	+	0.984245i
$719$	−26144.0	−	35984.1i	−0.0505725	−	0.0696070i	0.782982	−	0.622045i	$-0.213698\pi$
$719$	−26144.0	−	35984.1i	−0.0505725	−	0.0696070i	−0.833554	+	0.552438i	$0.813698\pi$
$720$	115246.	−	590907.i	0.222311	−	1.13987i
$721$	−71977.0	−	52294.4i	−0.138460	−	0.100597i
$722$	−606468.	+	96055.1i	−1.16341	+	0.184266i
$723$	11444.8	−	5831.39i	0.0218942	−	0.0111557i
$724$		−	247518.i		−	0.472204i
$725$	466374.	+	392334.i	0.887276	+	0.746415i
$726$	66931.0			0.126986
$727$	23865.4	+	46838.5i	0.0451544	+	0.0886205i	0.912481	−	0.409118i	$-0.134164\pi$
$727$	23865.4	+	46838.5i	0.0451544	+	0.0886205i	−0.867327	+	0.497739i	$0.834164\pi$
$728$	−115401.	−	728611.i	−0.217744	−	1.37478i
$729$	202583.	−	278831.i	0.381195	−	0.524670i
$730$	86936.9	+	711741.i	0.163139	+	1.33560i
$731$	−64916.2	+	47164.4i	−0.121484	+	0.0882632i
$732$	52736.9	−	52736.9i	0.0984221	−	0.0984221i
$733$	−841575.	−	133292.i	−1.56634	−	0.248083i	−0.687850	−	0.725853i	$-0.741445\pi$
$733$	−841575.	−	133292.i	−1.56634	−	0.248083i	−0.878485	+	0.477770i	$0.841445\pi$
$734$	191796.	−	62318.3i	0.355998	−	0.115671i
$735$	88518.0	+	69247.5i	0.163854	+	0.128183i
$736$	73308.6	−	225621.i	0.135332	−	0.416508i
$737$	378807.	+	193012.i	0.697401	+	0.355344i
$738$	377867.	−	741606.i	0.693788	−	1.36163i
$739$	−248337.	−	80689.7i	−0.454730	−	0.147751i	0.0726918	−	0.997354i	$-0.476841\pi$
$739$	−248337.	−	80689.7i	−0.454730	−	0.147751i	−0.527421	+	0.849604i	$0.676841\pi$
$740$	−235250.	−	85791.3i	−0.429601	−	0.156668i
$741$	1504.35	+	4629.91i	0.00273976	+	0.00843210i
$742$	134501.	−	849207.i	0.244297	−	1.54243i
$743$	375591.	+	375591.i	0.680359	+	0.680359i	0.960081	−	0.279722i	$-0.0902423\pi$
$743$	375591.	+	375591.i	0.680359	+	0.680359i	−0.279722	+	0.960081i	$0.590242\pi$
$744$	−39018.9	−	53704.9i	−0.0704902	−	0.0970215i
$745$	435827.	−	405903.i	0.785238	−	0.731324i
$746$	−351689.	−	255517.i	−0.631948	−	0.459137i
$747$	222084.	−	35174.6i	0.397993	−	0.0630359i
$748$	−20766.3	+	10581.0i	−0.0371156	+	0.0189114i
$749$			776623.i			1.38435i
$750$	−42927.7	+	159009.i	−0.0763159	+	0.282682i
$751$	−584701.			−1.03670			−0.518351	−	0.855168i	$-0.673454\pi$
$751$	−584701.			−1.03670			−0.518351	+	0.855168i	$0.673454\pi$
$752$	89974.2	+	176584.i	0.159104	+	0.312260i
$753$	−35880.0	−	226537.i	−0.0632793	−	0.399530i
$754$	−651400.	+	896576.i	−1.14579	+	1.57705i
$755$	−512243.	−	550005.i	−0.898632	−	0.964879i
$756$	−117465.	+	85343.7i	−0.205526	+	0.149323i
$757$	−715032.	+	715032.i	−1.24777	+	1.24777i	−0.291063	+	0.956704i	$0.594009\pi$
$757$	−715032.	+	715032.i	−1.24777	+	1.24777i	−0.956704	+	0.291063i	$0.905991\pi$
$758$	205157.	+	32493.6i	0.357065	+	0.0565536i
$759$	−96584.1	+	31382.1i	−0.167657	+	0.0544751i
$760$	3564.51	−	9774.30i	0.00617124	−	0.0169223i
$761$	−40082.8	+	123362.i	−0.0692132	+	0.213016i	−0.979680	−	0.200565i	$-0.935722\pi$
$761$	−40082.8	+	123362.i	−0.0692132	+	0.213016i	0.910467	+	0.413581i	$0.135722\pi$
$762$	−285772.	−	145608.i	−0.492163	−	0.250770i
$763$	−152306.	+	298916.i	−0.261617	+	0.513453i
$764$	246013.	+	79934.4i	0.421474	+	0.136945i
$765$	30241.4	−	38657.1i	0.0516748	−	0.0660551i
$766$	235323.	+	724250.i	0.401058	+	1.23433i
$767$	−86568.4	+	546571.i	−0.147153	+	0.929087i
$768$	105030.	+	105030.i	0.178071	+	0.178071i
$769$	632504.	+	870566.i	1.06957	+	1.47214i	0.870508	+	0.492154i	$0.163790\pi$
$769$	632504.	+	870566.i	1.06957	+	1.47214i	0.199065	+	0.979986i	$0.436210\pi$
$770$	−1.12586e6	+	137520.i	−1.89890	+	0.231945i
$771$	72463.7	+	52647.9i	0.121902	+	0.0885671i
$772$	−265273.	+	42015.1i	−0.445101	+	0.0704970i
$773$	−24766.3	+	12619.1i	−0.0414479	+	0.0211188i	−0.474592	−	0.880206i	$-0.657404\pi$
$773$	−24766.3	+	12619.1i	−0.0414479	+	0.0211188i	0.433144	+	0.901325i	$0.357404\pi$
$774$		−	1.11304e6i		−	1.85793i
$775$	−213005.	−	341834.i	−0.354639	−	0.569131i
$776$	−76024.7			−0.126250
$777$	−108434.	−	212814.i	−0.179607	−	0.352499i
$778$	−79716.9	−	503313.i	−0.131702	−	0.831532i
$779$	12332.6	−	16974.4i	0.0203226	−	0.0279717i
$780$	−82358.0	−	16062.5i	−0.135368	−	0.0264012i
$781$	−88186.6	+	64071.3i	−0.144577	+	0.105042i
$782$	26998.2	−	26998.2i	0.0441491	−	0.0441491i
$783$	−338076.	−	53545.9i	−0.551430	−	0.0873379i
$784$	605916.	−	196874.i	0.985781	−	0.320300i
$785$	140412.	+	4991.63i	0.227859	+	0.00810034i
$786$	83382.3	−	256624.i	0.134967	−	0.415387i
$787$	−890436.	−	453700.i	−1.43765	−	0.732519i	−0.450569	−	0.892742i	$-0.648779\pi$
$787$	−890436.	−	453700.i	−1.43765	−	0.732519i	−0.987081	+	0.160222i	$0.948779\pi$
$788$	−33650.4	+	66042.7i	−0.0541924	+	0.106359i
$789$	102221.	+	33213.6i	0.164205	+	0.0533534i
$790$	102382.	+	151993.i	0.164047	+	0.243540i
$791$	232207.	+	714659.i	0.371127	+	1.14221i
$792$	−79362.6	+	501076.i	−0.126522	+	0.798827i
$793$	−913043.	−	913043.i	−1.45193	−	1.45193i
$794$	−642177.	−	883881.i	−1.01862	−	1.40202i
$795$	134179.	+	74487.1i	0.212301	+	0.117855i
$796$	322500.	+	234310.i	0.508983	+	0.369798i
$797$	−430575.	+	68196.4i	−0.677848	+	0.107361i	−0.485860	−	0.874037i	$-0.661493\pi$
$797$	−430575.	+	68196.4i	−0.677848	+	0.107361i	−0.191988	+	0.981397i	$0.561493\pi$
$798$	−5634.68	+	2871.01i	−0.00884838	+	0.00450847i
$799$			16156.8i			0.0253083i
$800$	309822.	+	357315.i	0.484097	+	0.558305i
$801$	−516814.			−0.805507
$802$	284441.	+	558247.i	0.442225	+	0.867916i
$803$	−137879.	−	870533.i	−0.213829	−	1.35006i
$804$	−24015.4	+	33054.4i	−0.0371517	+	0.0511349i
$805$	471953.	−	219715.i	0.728295	−	0.339053i
$806$	592519.	−	430490.i	0.912078	−	0.662664i
$807$	132292.	−	132292.i	0.203135	−	0.203135i
$808$	644747.	+	102118.i	0.987567	+	0.156415i
$809$	251694.	−	81780.3i	0.384570	−	0.124954i	−0.110350	−	0.993893i	$-0.535197\pi$
$809$	251694.	−	81780.3i	0.384570	−	0.124954i	0.494920	+	0.868938i	$0.335197\pi$
$810$	174120.	+	608673.i	0.265387	+	0.927713i
$811$	266960.	−	821620.i	0.405887	−	1.24919i	−0.514265	−	0.857631i	$-0.671935\pi$
$811$	266960.	−	821620.i	0.405887	−	1.24919i	0.920152	−	0.391560i	$-0.128065\pi$
$812$	−359383.	−	183115.i	−0.545062	−	0.277723i
$813$	−2817.98	+	5530.60i	−0.00426341	+	0.00836741i
$814$	1.04484e6	+	339490.i	1.57689	+	0.512364i
$815$	−800512.	+	228999.i	−1.20518	+	0.344761i
$816$	5654.96	+	17404.2i	0.00849276	+	0.0261380i
$817$	4389.22	−	27712.5i	0.00657572	−	0.0415175i
$818$	−386488.	−	386488.i	−0.577603	−	0.577603i
$819$	715262.	+	984474.i	1.06634	+	1.46770i
$820$	152632.	+	327858.i	0.226996	+	0.487593i
$821$	−124052.	−	90129.1i	−0.184042	−	0.133715i	0.491949	−	0.870624i	$-0.336285\pi$
$821$	−124052.	−	90129.1i	−0.184042	−	0.133715i	−0.675992	+	0.736909i	$0.736285\pi$
$822$	23175.4	−	3670.62i	0.0342992	−	0.00543246i
$823$	46115.6	−	23497.1i	0.0680845	−	0.0346908i	−0.419617	−	0.907701i	$-0.637836\pi$
$823$	46115.6	−	23497.1i	0.0680845	−	0.0346908i	0.487701	+	0.873011i	$0.337836\pi$
$824$		−	61714.1i		−	0.0908929i
$825$	45789.9	−	197207.i	0.0672763	−	0.289744i
$826$	−718869.			−1.05363
$827$	−204200.	−	400766.i	−0.298570	−	0.585976i	0.692173	−	0.721732i	$-0.256654\pi$
$827$	−204200.	−	400766.i	−0.298570	−	0.585976i	−0.990742	+	0.135756i	$0.956654\pi$
$828$	23212.6	+	146559.i	0.0338581	+	0.213772i
$829$	39228.5	−	53993.3i	0.0570811	−	0.0785654i	−0.779522	−	0.626375i	$-0.784538\pi$
$829$	39228.5	−	53993.3i	0.0570811	−	0.0785654i	0.836603	+	0.547809i	$0.184538\pi$
$830$	−169249.	+	304881.i	−0.245679	+	0.442562i
$831$	36750.3	−	26700.6i	0.0532180	−	0.0386651i
$832$	256064.	−	256064.i	0.369915	−	0.369915i
$833$	51299.2	+	8125.00i	0.0739300	+	0.0117094i
$834$	−222446.	+	72277.2i	−0.319811	+	0.103913i
$835$	560385.	−	377472.i	0.803736	−	0.541392i
$836$	2518.38	−	7750.77i	0.00360337	−	0.0110900i
$837$	201553.	+	102697.i	0.287700	+	0.146590i
$838$	325826.	−	639470.i	0.463978	−	0.910609i
$839$	887965.	+	288517.i	1.26145	+	0.409872i	0.862013	−	0.506887i	$-0.169204\pi$
$839$	887965.	+	288517.i	1.26145	+	0.409872i	0.399442	+	0.916758i	$0.369204\pi$
$840$	−6076.97	+	170942.i	−0.00861248	+	0.242265i
$841$	−75271.2	−	231661.i	−0.106423	−	0.327537i
$842$	−102798.	+	649042.i	−0.144998	+	0.915480i
$843$	−204946.	−	204946.i	−0.288392	−	0.288392i
$844$	67674.5	+	93146.0i	0.0950037	+	0.130761i
$845$	−141410.	+	725058.i	−0.198046	+	1.01545i
$846$	−181313.	−	131732.i	−0.253332	−	0.184056i
$847$	416554.	−	65975.7i	0.580637	−	0.0919639i
$848$	775162.	−	394965.i	1.07795	−	0.549245i
$849$			103500.i			0.143591i
$850$	18321.3	+	73878.1i	0.0253582	+	0.102253i
$851$	−504244.			−0.696277
$852$	−4755.83	−	9333.85i	−0.00655160	−	0.0128582i
$853$	−8969.78	−	56633.0i	−0.0123277	−	0.0778343i	0.980757	−	0.195230i	$-0.0625454\pi$
$853$	−8969.78	−	56633.0i	−0.0123277	−	0.0778343i	−0.993085	+	0.117396i	$0.962545\pi$
$854$	985933.	−	1.35702e6i	1.35186	−	1.86068i
$855$	2080.83	+	17035.5i	0.00284645	+	0.0233035i
$856$	−435829.	+	316648.i	−0.594797	+	0.432145i
$857$	−98979.9	+	98979.9i	−0.134768	+	0.134768i	−0.771273	−	0.636505i	$-0.780379\pi$
$857$	−98979.9	+	98979.9i	−0.134768	+	0.134768i	0.636505	+	0.771273i	$0.280379\pi$
$858$	363609.	+	57590.0i	0.493924	+	0.0782299i
$859$	184366.	−	59904.1i	0.249859	−	0.0811840i	−0.181410	−	0.983408i	$-0.558066\pi$
$859$	184366.	−	59904.1i	0.249859	−	0.0811840i	0.431269	+	0.902224i	$0.358066\pi$
$860$	380908.	+	297984.i	0.515020	+	0.402899i
$861$	−106596.	+	328070.i	−0.143792	+	0.442547i
$862$	−349241.	−	177947.i	−0.470014	−	0.239484i
$863$	−319060.	+	626190.i	−0.428401	+	0.840784i	0.571397	+	0.820674i	$0.306402\pi$
$863$	−319060.	+	626190.i	−0.428401	+	0.840784i	−0.999798	+	0.0201099i	$0.993598\pi$
$864$	−252615.	−	82079.6i	−0.338401	−	0.109953i
$865$	109890.	+	40074.9i	0.146868	+	0.0535600i
$866$	312516.	+	961825.i	0.416713	+	1.28251i
$867$	28978.5	−	182963.i	0.0385512	−	0.243403i
$868$	188485.	+	188485.i	0.250171	+	0.250171i
$869$	−132407.	−	182243.i	−0.175336	−	0.241330i
$870$	188043.	−	175133.i	0.248439	−	0.231381i
$871$	572277.	+	415783.i	0.754344	+	0.548063i
$872$	−229846.	+	36404.0i	−0.302276	+	0.0478759i
$873$	111739.	−	56934.1i	0.146615	−	0.0747040i
$874$			13350.9i			0.0174778i
$875$	−110427.	+	1.03193e6i	−0.144231	+	1.34782i
$876$	84703.3			0.110380
$877$	−32821.5	−	64415.9i	−0.0426736	−	0.0837517i	0.868685	−	0.495365i	$-0.164966\pi$
$877$	−32821.5	−	64415.9i	−0.0426736	−	0.0837517i	−0.911359	+	0.411613i	$0.864966\pi$
$878$	132311.	+	835378.i	0.171635	+	1.08366i
$879$	98828.7	−	136026.i	0.127910	−	0.176053i
$880$	−782184.	−	839847.i	−1.01005	−	1.08451i
$881$	−4823.43	+	3504.42i	−0.00621447	+	0.00451507i	−0.590888	−	0.806753i	$-0.701223\pi$
$881$	−4823.43	+	3504.42i	−0.00621447	+	0.00451507i	0.584674	+	0.811269i	$0.301223\pi$
$882$	−509439.	+	509439.i	−0.654870	+	0.654870i
$883$	−480265.	−	76066.5i	−0.615970	−	0.0975600i	−0.159350	−	0.987222i	$-0.550940\pi$
$883$	−480265.	−	76066.5i	−0.615970	−	0.0975600i	−0.456619	+	0.889662i	$0.650940\pi$
$884$	−36880.5	+	11983.2i	−0.0471946	+	0.0153345i
$885$	43961.7	−	120548.i	0.0561291	−	0.153913i
$886$	−224680.	+	691495.i	−0.286219	+	0.880890i
$887$	136080.	+	69336.3i	0.172961	+	0.0881279i	0.538327	−	0.842736i	$-0.319056\pi$
$887$	136080.	+	69336.3i	0.172961	+	0.0881279i	−0.365367	+	0.930864i	$0.619056\pi$
$888$	75216.8	−	147621.i	0.0953869	−	0.187207i
$889$	−1.92207e6	−	624518.i	−2.43201	−	0.790208i
$890$	493845.	−	631274.i	0.623463	−	0.796963i
$891$	−240477.	−	740112.i	−0.302913	−	0.932271i
$892$	39341.2	−	248390.i	0.0494445	−	0.312180i
$893$	−3994.85	−	3994.85i	−0.00500954	−	0.00500954i
$894$	−147601.	−	203155.i	−0.184677	−	0.254186i
$895$	1.38566e6	−	169254.i	1.72986	−	0.211297i
$896$	1.03115e6	+	749176.i	1.28442	+	0.933185i
$897$	−166890.	+	26432.8i	−0.207418	+	0.0328517i
$898$	−428705.	+	218436.i	−0.531625	+	0.270877i
$899$			628396.i			0.777525i
$900$	−274133.	−	111158.i	−0.338436	−	0.137232i
$901$	70924.5			0.0873668
$902$	−720330.	−	1.41373e6i	−0.885357	−	1.73761i
$903$	72162.5	+	455616.i	0.0884985	+	0.558758i
$904$	−306379.	+	421695.i	−0.374906	+	0.516014i
$905$	975269.	+	190209.i	1.19077	+	0.232238i
$906$	−256378.	+	186269.i	−0.312337	+	0.226926i
$907$	268134.	−	268134.i	0.325940	−	0.325940i	−0.525100	−	0.851040i	$-0.675972\pi$
$907$	268134.	−	268134.i	0.325940	−	0.325940i	0.851040	+	0.525100i	$0.175972\pi$
$908$	190817.	+	30222.4i	0.231444	+	0.0366571i
$909$	−1.02411e6	+	332754.i	−1.23942	+	0.402712i
$910$	−1.88598e6	−	67046.4i	−2.27748	−	0.0809641i
$911$	12149.1	−	37391.1i	0.0146389	−	0.0450538i	−0.943470	−	0.331457i	$-0.892460\pi$
$911$	12149.1	−	37391.1i	0.0146389	−	0.0450538i	0.958109	+	0.286403i	$0.0924598\pi$
$912$	−5701.48	−	2905.05i	−0.00685485	−	0.00349272i
$913$	194597.	−	381918.i	0.233450	−	0.458172i
$914$	−338134.	−	109866.i	−0.404759	−	0.131514i
$915$	167267.	+	248320.i	0.199787	+	0.296599i
$916$	−114546.	−	352537.i	−0.136518	−	0.420159i
$917$	265979.	−	1.67933e6i	0.316307	−	1.99709i
$918$	−30228.4	−	30228.4i	−0.0358699	−	0.0358699i
$919$	426668.	+	587258.i	0.505195	+	0.695342i	0.983100	−	0.183070i	$-0.0586036\pi$
$919$	426668.	+	587258.i	0.505195	+	0.695342i	−0.477905	+	0.878412i	$0.658604\pi$
$920$	315727.	+	175270.i	0.373024	+	0.207077i
$921$	189625.	+	137771.i	0.223551	+	0.162419i
$922$	1.35255e6	−	214222.i	1.59107	−	0.252001i
$923$	−161599.	+	82338.6i	−0.189685	+	0.0966495i
$924$			133987.i			0.156935i
$925$	518815.	−	861001.i	0.606358	−	1.00628i
$926$	−123923.			−0.144521
$927$	46217.0	+	90706.1i	0.0537827	+	0.105555i
$928$	−115428.	−	728781.i	−0.134034	−	0.846254i
$929$	383460.	−	527787.i	0.444312	−	0.611543i	−0.526852	−	0.849957i	$-0.676628\pi$
$929$	383460.	−	527787.i	0.444312	−	0.611543i	0.971164	+	0.238414i	$0.0766276\pi$
$930$	−153955.	+	71672.8i	−0.178004	+	0.0828683i
$931$	−14692.9	+	10675.0i	−0.0169515	+	0.0123160i
$932$	−86731.1	+	86731.1i	−0.0998488	+	0.0998488i
$933$	142444.	+	22560.9i	0.163637	+	0.0259175i
$934$	−67679.9	+	21990.5i	−0.0775829	+	0.0252082i
$935$	−25732.9	−	89954.5i	−0.0294351	−	0.102896i
$936$	−260842.	+	802789.i	−0.297732	+	0.916325i
$937$	823802.	+	419748.i	0.938304	+	0.478090i	0.855112	−	0.518444i	$-0.173488\pi$
$937$	823802.	+	419748.i	0.938304	+	0.478090i	0.0831923	+	0.996534i	$0.473488\pi$
$938$	−417175.	+	818751.i	−0.474146	+	0.930564i
$939$	−35218.4	−	11443.1i	−0.0399427	−	0.0129782i
$940$	93622.9	−	26782.3i	0.105956	−	0.0303104i
$941$	−371858.	−	1.14446e6i	−0.419950	−	1.29247i	−0.907747	−	0.419517i	$-0.862199\pi$
$941$	−371858.	−	1.14446e6i	−0.419950	−	1.29247i	0.487797	−	0.872957i	$-0.337801\pi$
$942$	9267.21	−	58510.8i	0.0104435	−	0.0659378i
$943$	514951.	+	514951.i	0.579085	+	0.579085i
$944$	−427549.	−	588471.i	−0.479780	−	0.660361i
$945$	−246002.	−	528420.i	−0.275471	−	0.591719i
$946$	−1.71657e6	−	1.24716e6i	−1.91814	−	1.39361i
$947$	−1.18673e6	+	187959.i	−1.32328	+	0.209587i	−0.777787	−	0.628528i	$-0.783658\pi$
$947$	−1.18673e6	+	187959.i	−1.32328	+	0.209587i	−0.545493	+	0.838115i	$0.683658\pi$
$948$	19289.0	−	9828.22i	0.0214631	−	0.0109360i
$949$		−	1.46648e6i		−	1.62834i
$950$	−22796.7	−	13736.7i	−0.0252595	−	0.0152207i
$951$	−243500.			−0.269239
$952$	35887.9	+	70434.0i	0.0395981	+	0.0777156i
$953$	232557.	+	1.46831e6i	0.256061	+	1.61671i	0.695563	+	0.718465i	$0.255155\pi$
$953$	232557.	+	1.46831e6i	0.256061	+	1.61671i	−0.439502	+	0.898242i	$0.644845\pi$
$954$	−578271.	+	795921.i	−0.635381	+	0.874527i
$955$	−504009.	+	907911.i	−0.552627	+	0.995489i
$956$	101365.	−	73646.2i	0.110911	−	0.0805813i
$957$	−223351.	+	223351.i	−0.243874	+	0.243874i
$958$	−520232.	−	82396.6i	−0.566847	−	0.0897797i
$959$	140617.	−	45689.2i	0.152898	−	0.0496794i
$960$	−69641.6	+	46910.2i	−0.0755660	+	0.0509008i
$961$	−157053.	+	483359.i	−0.170059	+	0.523387i
$962$	1.62869e6	+	829857.i	1.75990	+	0.896712i
$963$	403437.	−	791790.i	0.435034	−	0.853803i
$964$	−34026.4	−	11055.9i	−0.0366153	−	0.0118970i
$965$	38305.4	−	1.07751e6i	0.0411345	−	1.15709i
$966$	−67829.1	−	208756.i	−0.0726878	−	0.223710i
$967$	−251192.	+	1.58596e6i	−0.268629	+	1.69606i	0.372022	+	0.928224i	$0.378664\pi$
$967$	−251192.	+	1.58596e6i	−0.268629	+	1.69606i	−0.640651	+	0.767832i	$0.721336\pi$
$968$	206864.	+	206864.i	0.220767	+	0.220767i
$969$	−306.627	−	422.035i	−0.000326560	−	0.000449471i
$970$	−37229.8	+	190890.i	−0.0395683	+	0.202881i
$971$	−264637.	−	192270.i	−0.280680	−	0.203926i	0.438534	−	0.898715i	$-0.355498\pi$
$971$	−264637.	−	192270.i	−0.280680	−	0.203926i	−0.719214	+	0.694789i	$0.755498\pi$
$972$	248753.	−	39398.5i	0.263290	−	0.0417011i
$973$	−1.31318e6	+	669098.i	−1.38707	+	0.706747i
$974$		−	239311.i		−	0.252257i
$975$	126579.	−	312163.i	0.133153	−	0.328376i
$976$	1.69725e6			1.78175
$977$	−149939.	−	294272.i	−0.157082	−	0.308290i	0.799031	−	0.601290i	$-0.205346\pi$
$977$	−149939.	−	294272.i	−0.157082	−	0.308290i	−0.956112	+	0.293000i	$0.905346\pi$
$978$	54918.4	+	346741.i	0.0574170	+	0.362516i
$979$	−579089.	+	797048.i	−0.604199	+	0.831609i
$980$	−37954.5	−	310729.i	−0.0395195	−	0.323541i
$981$	310560.	−	225635.i	0.322706	−	0.234460i
$982$	−658899.	+	658899.i	−0.683276	+	0.683276i
$983$	1.60976e6	+	254962.i	1.66592	+	0.263857i	0.917026	−	0.398828i	$-0.130583\pi$
$983$	1.60976e6	+	254962.i	1.66592	+	0.263857i	0.748899	+	0.662684i	$0.230583\pi$
$984$	−227570.	+	73941.8i	−0.235030	+	0.0763660i
$985$	−234362.	−	183341.i	−0.241554	−	0.188967i
$986$	36697.6	−	112943.i	0.0377471	−	0.116174i
$987$	82760.0	+	42168.3i	0.0849544	+	0.0432864i
$988$	6155.98	−	12081.8i	0.00630642	−	0.0123771i
$989$	926204.	+	300942.i	0.946922	+	0.307673i
$990$	1.21929e6	+	444652.i	1.24404	+	0.453680i
$991$	−200778.	−	617930.i	−0.204441	−	0.629205i	−0.999736	−	0.0229819i	$-0.992684\pi$
$991$	−200778.	−	617930.i	−0.204441	−	0.629205i	0.795295	−	0.606223i	$-0.207316\pi$
$992$	−76282.5	+	481629.i	−0.0775178	+	0.489428i
$993$	−28329.0	−	28329.0i	−0.0287298	−	0.0287298i
$994$	−138483.	−	190606.i	−0.140160	−	0.192914i
$995$	−1.17106e6	+	1.09065e6i	−1.18285	+	1.10164i
$996$	33325.9	+	24212.7i	0.0335941	+	0.0244076i
$997$	1.16632e6	−	184726.i	1.17334	−	0.185840i	0.460825	−	0.887491i	$-0.347554\pi$
$997$	1.16632e6	−	184726.i	1.17334	−	0.185840i	0.712520	+	0.701652i	$0.247554\pi$
$998$	−23121.7	+	11781.1i	−0.0232145	+	0.0118284i
$999$			564574.i			0.565705i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.5.f.a.3.3	✓	72
5.2	odd	4		125.5.f.b.7.7		72
5.3	odd	4		125.5.f.a.7.3		72
5.4	even	2		125.5.f.c.118.7		72
25.6	even	5		125.5.f.b.18.7		72
25.8	odd	20		125.5.f.c.107.7		72
25.17	odd	20	inner	25.5.f.a.17.3	yes	72
25.19	even	10		125.5.f.a.18.3		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.5.f.a.3.3	✓	72	1.1	even	1	trivial
25.5.f.a.17.3	yes	72	25.17	odd	20	inner
125.5.f.a.7.3		72	5.3	odd	4
125.5.f.a.18.3		72	25.19	even	10
125.5.f.b.7.7		72	5.2	odd	4
125.5.f.b.18.7		72	25.6	even	5
125.5.f.c.107.7		72	25.8	odd	20
125.5.f.c.118.7		72	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	25.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.14039 - 4.20075i) q^{2} +(-0.349755 - 2.20827i) q^{3} +(-3.66045 + 5.03818i) q^{4} +(-17.0385 - 18.2946i) q^{5} +(-8.52776 + 6.19578i) q^{6} +(-46.9663 + 46.9663i) q^{7} +(-45.5061 - 7.20746i) q^{8} +(72.2815 - 23.4857i) q^{9} +O(q^{10})\)	\(q+(-2.14039 - 4.20075i) q^{2} +(-0.349755 - 2.20827i) q^{3} +(-3.66045 + 5.03818i) q^{4} +(-17.0385 - 18.2946i) q^{5} +(-8.52776 + 6.19578i) q^{6} +(-46.9663 + 46.9663i) q^{7} +(-45.5061 - 7.20746i) q^{8} +(72.2815 - 23.4857i) q^{9} +(-40.3819 + 110.732i) q^{10} +(44.7709 - 137.791i) q^{11} +(12.4059 + 6.32113i) q^{12} +(109.439 - 214.786i) q^{13} +(297.820 + 96.7675i) q^{14} +(-34.4400 + 44.0241i) q^{15} +(97.9146 + 301.350i) q^{16} +(-4.04094 + 25.5135i) q^{17} +(-253.368 - 253.368i) q^{18} +(-5.30919 - 7.30747i) q^{19} +(154.540 - 18.8765i) q^{20} +(120.141 + 87.2875i) q^{21} +(-674.650 + 106.854i) q^{22} +(279.342 - 142.332i) q^{23} +103.011i q^{24} +(-44.3812 + 623.422i) q^{25} -1136.50 q^{26} +(-159.361 - 312.763i) q^{27} +(-64.7068 - 408.543i) q^{28} +(573.163 - 788.891i) q^{29} +(258.649 + 50.4450i) q^{30} +(-521.353 + 378.785i) q^{31} +(535.060 - 535.060i) q^{32} +(-319.937 - 50.6731i) q^{33} +(115.825 - 37.6338i) q^{34} +(1659.46 + 58.9936i) q^{35} +(-146.258 + 450.135i) q^{36} +(-1433.07 - 730.185i) q^{37} +(-19.3331 + 37.9434i) q^{38} +(-512.581 - 166.548i) q^{39} +(643.497 + 955.318i) q^{40} +(717.809 + 2209.19i) q^{41} +(109.525 - 691.511i) q^{42} +(2196.50 + 2196.50i) q^{43} +(530.332 + 729.939i) q^{44} +(-1661.23 - 922.197i) q^{45} +(-1195.80 - 868.798i) q^{46} +(617.769 - 97.8450i) q^{47} +(631.216 - 321.621i) q^{48} -2010.67i q^{49} +(2713.83 - 1147.93i) q^{50} +57.7540 q^{51} +(681.534 + 1337.59i) q^{52} +(-429.515 - 2711.85i) q^{53} +(-972.745 + 1338.87i) q^{54} +(-3283.64 + 1528.68i) q^{55} +(2475.76 - 1798.75i) q^{56} +(-14.2799 + 14.2799i) q^{57} +(-4540.72 - 719.179i) q^{58} +(-2183.28 + 709.390i) q^{59} +(-95.7356 - 334.663i) q^{60} +(1655.25 - 5094.34i) q^{61} +(2707.08 + 1379.33i) q^{62} +(-2291.76 + 4497.83i) q^{63} +(1428.71 + 464.217i) q^{64} +(-5794.08 + 1657.49i) q^{65} +(471.925 + 1452.44i) q^{66} +(-459.046 + 2898.30i) q^{67} +(-113.750 - 113.750i) q^{68} +(-412.007 - 567.080i) q^{69} +(-3304.07 - 7097.25i) q^{70} +(-608.681 - 442.232i) q^{71} +(-3458.52 + 547.776i) q^{72} +(5420.42 - 2761.84i) q^{73} +7582.84i q^{74} +(1392.21 - 120.040i) q^{75} +56.2504 q^{76} +(4368.79 + 8574.24i) q^{77} +(397.498 + 2509.70i) q^{78} +(913.900 - 1257.88i) q^{79} +(3844.75 - 6925.85i) q^{80} +(4345.46 - 3157.16i) q^{81} +(7743.85 - 7743.85i) q^{82} +(2922.11 + 462.816i) q^{83} +(-879.541 + 285.780i) q^{84} +(535.609 - 360.784i) q^{85} +(4525.57 - 13928.3i) q^{86} +(-1942.55 - 989.778i) q^{87} +(-3030.47 + 5947.63i) q^{88} +(-6467.26 - 2101.34i) q^{89} +(-318.251 + 8952.25i) q^{90} +(4947.76 + 15227.6i) q^{91} +(-305.424 + 1928.37i) q^{92} +(1018.81 + 1018.81i) q^{93} +(-1733.29 - 2385.66i) q^{94} +(-43.2265 + 221.637i) q^{95} +(-1368.70 - 994.416i) q^{96} +(1629.76 - 258.129i) q^{97} +(-8446.32 + 4303.62i) q^{98} -11011.2i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9}+O(q^{10}) \) 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9	\( 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9} - 6 q^{11} - 178 q^{12} - 288 q^{13} - 10 q^{14} + 410 q^{15} + 762 q^{16} + 1042 q^{17} - 28 q^{18} - 1310 q^{19} - 3790 q^{20} - 6 q^{21} - 3226 q^{22} - 578 q^{23} + 1110 q^{25} - 976 q^{26} + 5120 q^{27} + 10318 q^{28} + 3290 q^{29} + 5270 q^{30} - 6 q^{31} - 1298 q^{32} - 2806 q^{33} - 8010 q^{34} - 5360 q^{35} - 2758 q^{36} + 4692 q^{37} + 14480 q^{38} + 8790 q^{39} + 2540 q^{40} + 1434 q^{41} - 23886 q^{42} - 14958 q^{43} - 22060 q^{44} - 23420 q^{45} - 6 q^{46} - 12158 q^{47} - 14168 q^{48} + 8050 q^{50} - 16 q^{51} + 29372 q^{52} + 22852 q^{53} + 53940 q^{54} + 18070 q^{55} - 1030 q^{56} + 34150 q^{57} + 23000 q^{58} + 23240 q^{59} + 40610 q^{60} + 2634 q^{61} - 13716 q^{62} - 42428 q^{63} - 66060 q^{64} - 41870 q^{65} + 5178 q^{66} - 25558 q^{67} - 71982 q^{68} - 39560 q^{69} - 38130 q^{70} + 7974 q^{71} - 37860 q^{72} - 4228 q^{73} + 21210 q^{75} - 1040 q^{76} + 34374 q^{77} + 51844 q^{78} + 26590 q^{79} + 110710 q^{80} - 14368 q^{81} + 145614 q^{82} + 99832 q^{83} + 149990 q^{84} + 48860 q^{85} - 6 q^{86} - 31320 q^{87} - 95490 q^{88} - 93760 q^{89} - 207250 q^{90} - 6 q^{91} - 199958 q^{92} - 134396 q^{93} - 130410 q^{94} - 50290 q^{95} + 17694 q^{96} - 40108 q^{97} - 25052 q^{98}+O(q^{100}) \) 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9 - 6 * q^11 - 178 * q^12 - 288 * q^13 - 10 * q^14 + 410 * q^15 + 762 * q^16 + 1042 * q^17 - 28 * q^18 - 1310 * q^19 - 3790 * q^20 - 6 * q^21 - 3226 * q^22 - 578 * q^23 + 1110 * q^25 - 976 * q^26 + 5120 * q^27 + 10318 * q^28 + 3290 * q^29 + 5270 * q^30 - 6 * q^31 - 1298 * q^32 - 2806 * q^33 - 8010 * q^34 - 5360 * q^35 - 2758 * q^36 + 4692 * q^37 + 14480 * q^38 + 8790 * q^39 + 2540 * q^40 + 1434 * q^41 - 23886 * q^42 - 14958 * q^43 - 22060 * q^44 - 23420 * q^45 - 6 * q^46 - 12158 * q^47 - 14168 * q^48 + 8050 * q^50 - 16 * q^51 + 29372 * q^52 + 22852 * q^53 + 53940 * q^54 + 18070 * q^55 - 1030 * q^56 + 34150 * q^57 + 23000 * q^58 + 23240 * q^59 + 40610 * q^60 + 2634 * q^61 - 13716 * q^62 - 42428 * q^63 - 66060 * q^64 - 41870 * q^65 + 5178 * q^66 - 25558 * q^67 - 71982 * q^68 - 39560 * q^69 - 38130 * q^70 + 7974 * q^71 - 37860 * q^72 - 4228 * q^73 + 21210 * q^75 - 1040 * q^76 + 34374 * q^77 + 51844 * q^78 + 26590 * q^79 + 110710 * q^80 - 14368 * q^81 + 145614 * q^82 + 99832 * q^83 + 149990 * q^84 + 48860 * q^85 - 6 * q^86 - 31320 * q^87 - 95490 * q^88 - 93760 * q^89 - 207250 * q^90 - 6 * q^91 - 199958 * q^92 - 134396 * q^93 - 130410 * q^94 - 50290 * q^95 + 17694 * q^96 - 40108 * q^97 - 25052 * q^98

Introduction

L-functions

Modular forms

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