LMFDB - Embedded newform 25.5.f.a.12.8

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			12.8
Character	$\chi$	$=$	25.12
Dual form			25.5.f.a.23.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.01425 + 6.40375i) q^{2} +(-7.85334 - 4.00148i) q^{3} +(-24.7624 + 8.04580i) q^{4} +(-19.2679 + 15.9295i) q^{5} +(17.6592 - 54.3493i) q^{6} +(33.7104 + 33.7104i) q^{7} +(-29.5430 - 57.9814i) q^{8} +(-1.94750 - 2.68050i) q^{9} +O(q^{10})$	\(q+(1.01425 + 6.40375i) q^{2} +(-7.85334 - 4.00148i) q^{3} +(-24.7624 + 8.04580i) q^{4} +(-19.2679 + 15.9295i) q^{5} +(17.6592 - 54.3493i) q^{6} +(33.7104 + 33.7104i) q^{7} +(-29.5430 - 57.9814i) q^{8} +(-1.94750 - 2.68050i) q^{9} +(-121.551 - 107.230i) q^{10} +(73.7487 + 53.5816i) q^{11} +(226.663 + 35.8998i) q^{12} +(-36.3627 + 229.585i) q^{13} +(-181.682 + 250.064i) q^{14} +(215.059 - 47.9993i) q^{15} +(4.30744 - 3.12954i) q^{16} +(362.032 - 184.465i) q^{17} +(15.1900 - 15.1900i) q^{18} +(-451.899 - 146.831i) q^{19} +(348.955 - 549.478i) q^{20} +(-129.848 - 399.631i) q^{21} +(-268.323 + 526.614i) q^{22} +(472.222 - 74.7927i) q^{23} +573.563i q^{24} +(117.505 - 613.855i) q^{25} -1507.09 q^{26} +(116.252 + 733.989i) q^{27} +(-1105.98 - 563.525i) q^{28} +(706.169 - 229.448i) q^{29} +(525.500 + 1328.50i) q^{30} +(-284.279 + 874.921i) q^{31} +(-711.819 - 711.819i) q^{32} +(-364.768 - 715.898i) q^{33} +(1548.46 + 2131.27i) q^{34} +(-1186.52 - 112.541i) q^{35} +(69.7915 + 50.7065i) q^{36} +(84.7001 + 13.4152i) q^{37} +(481.928 - 3042.77i) q^{38} +(1204.25 - 1657.50i) q^{39} +(1492.84 + 646.576i) q^{40} +(677.916 - 492.535i) q^{41} +(2427.44 - 1236.84i) q^{42} +(-380.214 + 380.214i) q^{43} +(-2257.30 - 733.442i) q^{44} +(80.2231 + 20.6251i) q^{45} +(957.908 + 2948.14i) q^{46} +(-1862.00 + 3654.39i) q^{47} +(-46.3506 + 7.34121i) q^{48} -128.213i q^{49} +(4050.15 + 129.867i) q^{50} -3581.29 q^{51} +(-946.766 - 5977.65i) q^{52} +(2351.03 + 1197.91i) q^{53} +(-4582.37 + 1488.90i) q^{54} +(-2274.51 + 142.372i) q^{55} +(958.670 - 2950.48i) q^{56} +(2961.38 + 2961.38i) q^{57} +(2185.56 + 4289.41i) q^{58} +(528.407 + 727.290i) q^{59} +(-4939.18 + 2918.90i) q^{60} +(2086.81 + 1516.16i) q^{61} +(-5891.11 - 933.059i) q^{62} +(24.7098 - 156.012i) q^{63} +(3886.42 - 5349.20i) q^{64} +(-2956.53 - 5002.86i) q^{65} +(4214.46 - 3061.99i) q^{66} +(2962.83 - 1509.64i) q^{67} +(-7480.63 + 7480.63i) q^{68} +(-4007.80 - 1302.21i) q^{69} +(-482.749 - 7712.32i) q^{70} +(-1144.14 - 3521.31i) q^{71} +(-97.8842 + 192.109i) q^{72} +(-4816.28 + 762.823i) q^{73} +556.005i q^{74} +(-3379.13 + 4350.62i) q^{75} +12371.5 q^{76} +(679.843 + 4292.36i) q^{77} +(11835.7 + 6030.57i) q^{78} +(5880.69 - 1910.75i) q^{79} +(-33.1435 + 128.915i) q^{80} +(1941.14 - 5974.20i) q^{81} +(3841.65 + 3841.65i) q^{82} +(335.858 + 659.159i) q^{83} +(6430.70 + 8851.10i) q^{84} +(-4037.19 + 9321.23i) q^{85} +(-2820.43 - 2049.16i) q^{86} +(-6463.92 - 1023.78i) q^{87} +(927.976 - 5859.01i) q^{88} +(6076.75 - 8363.93i) q^{89} +(-50.7111 + 534.648i) q^{90} +(-8965.21 + 6513.61i) q^{91} +(-11091.6 + 5651.45i) q^{92} +(5733.51 - 5733.51i) q^{93} +(-25290.3 - 8217.33i) q^{94} +(11046.1 - 4369.38i) q^{95} +(2741.83 + 8438.48i) q^{96} +(6484.17 - 12725.9i) q^{97} +(821.043 - 130.040i) q^{98} -302.033i 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 $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{20}\right)$

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 $

$2$	1.01425	+	6.40375i	0.253564	+	1.60094i	0.705382	+	0.708828i	$0.250776\pi$
$2$	1.01425	+	6.40375i	0.253564	+	1.60094i	−0.451818	+	0.892110i	$0.649224\pi$
$3$	−7.85334	−	4.00148i	−0.872593	−	0.444608i	−0.0404579	−	0.999181i	$-0.512882\pi$
$3$	−7.85334	−	4.00148i	−0.872593	−	0.444608i	−0.832135	+	0.554573i	$0.812882\pi$
$4$	−24.7624	+	8.04580i	−1.54765	+	0.502862i
$5$	−19.2679	+	15.9295i	−0.770716	+	0.637178i
$5$	−19.2679	+	15.9295i	−0.770716	+	0.637178i
$6$	17.6592	−	54.3493i	0.490533	−	1.50970i
$7$	33.7104	+	33.7104i	0.687968	+	0.687968i	0.961783	−	0.273814i	$-0.0882854\pi$
$7$	33.7104	+	33.7104i	0.687968	+	0.687968i	−0.273814	+	0.961783i	$0.588285\pi$
$8$	−29.5430	−	57.9814i	−0.461609	−	0.905959i
$9$	−1.94750	−	2.68050i	−0.0240432	−	0.0330926i
$10$	−121.551	−	107.230i	−1.21551	−	1.07230i
$11$	73.7487	+	53.5816i	0.609494	+	0.442823i	0.849236	−	0.528014i	$-0.177063\pi$
$11$	73.7487	+	53.5816i	0.609494	+	0.442823i	−0.239742	+	0.970837i	$0.577063\pi$
$12$	226.663	+	35.8998i	1.57405	+	0.249304i
$13$	−36.3627	+	229.585i	−0.215164	+	1.35849i	0.609463	+	0.792814i	$0.291385\pi$
$13$	−36.3627	+	229.585i	−0.215164	+	1.35849i	−0.824627	+	0.565677i	$0.808615\pi$
$14$	−181.682	+	250.064i	−0.926951	+	1.27584i
$15$	215.059	−	47.9993i	0.955817	−	0.213330i
$16$	4.30744	−	3.12954i	0.0168259	−	0.0122248i
$17$	362.032	−	184.465i	1.25271	−	0.638286i	0.303468	−	0.952842i	$-0.401855\pi$
$17$	362.032	−	184.465i	1.25271	−	0.638286i	0.949239	+	0.314555i	$0.101855\pi$
$18$	15.1900	−	15.1900i	0.0468827	−	0.0468827i
$19$	−451.899	−	146.831i	−1.25180	−	0.406734i	−0.393233	−	0.919439i	$-0.628644\pi$
$19$	−451.899	−	146.831i	−1.25180	−	0.406734i	−0.858565	+	0.512705i	$0.828644\pi$
$20$	348.955	−	549.478i	0.872387	−	1.37369i
$21$	−129.848	−	399.631i	−0.294440	−	0.906193i
$22$	−268.323	+	526.614i	−0.554387	+	1.08805i
$23$	472.222	−	74.7927i	0.892670	−	0.141385i	0.306785	−	0.951779i	$-0.400747\pi$
$23$	472.222	−	74.7927i	0.892670	−	0.141385i	0.585885	+	0.810394i	$0.300747\pi$
$24$			573.563i			0.995769i
$25$	117.505	−	613.855i	0.188008	−	0.982168i
$26$	−1507.09			−2.22942
$27$	116.252	+	733.989i	0.159468	+	1.00684i
$28$	−1105.98	−	563.525i	−1.41069	−	0.718781i
$29$	706.169	−	229.448i	0.839678	−	0.272828i	0.142562	−	0.989786i	$-0.454466\pi$
$29$	706.169	−	229.448i	0.839678	−	0.272828i	0.697116	+	0.716958i	$0.254466\pi$
$30$	525.500	+	1328.50i	0.583889	+	1.47611i
$31$	−284.279	+	874.921i	−0.295816	+	0.910427i	0.687130	+	0.726534i	$0.258870\pi$
$31$	−284.279	+	874.921i	−0.295816	+	0.910427i	−0.982946	+	0.183893i	$0.941130\pi$
$32$	−711.819	−	711.819i	−0.695136	−	0.695136i
$33$	−364.768	−	715.898i	−0.334957	−	0.657390i
$34$	1548.46	+	2131.27i	1.33950	+	1.84366i
$35$	−1186.52	−	112.541i	−0.968587	−	0.0918700i
$36$	69.7915	+	50.7065i	0.0538515	+	0.0391254i
$37$	84.7001	+	13.4152i	0.0618701	+	0.00979926i	0.187293	−	0.982304i	$-0.440029\pi$
$37$	84.7001	+	13.4152i	0.0618701	+	0.00979926i	−0.125423	+	0.992103i	$0.540029\pi$
$38$	481.928	−	3042.77i	0.333745	−	2.10718i
$39$	1204.25	−	1657.50i	0.791747	−	1.08975i
$40$	1492.84	+	646.576i	0.933027	+	0.404110i
$41$	677.916	−	492.535i	0.403281	−	0.293001i	−0.367595	−	0.929986i	$-0.619819\pi$
$41$	677.916	−	492.535i	0.403281	−	0.293001i	0.770876	+	0.636985i	$0.219819\pi$
$42$	2427.44	−	1236.84i	1.37610	−	0.701157i
$43$	−380.214	+	380.214i	−0.205632	+	0.205632i	−0.802408	−	0.596776i	$-0.796448\pi$
$43$	−380.214	+	380.214i	−0.205632	+	0.205632i	0.596776	+	0.802408i	$0.296448\pi$
$44$	−2257.30	−	733.442i	−1.16596	−	0.378844i
$45$	80.2231	+	20.6251i	0.0396164	+	0.0101852i
$46$	957.908	+	2948.14i	0.452697	+	1.39326i
$47$	−1862.00	+	3654.39i	−0.842917	+	1.65432i	−0.0902463	+	0.995919i	$0.528765\pi$
$47$	−1862.00	+	3654.39i	−0.842917	+	1.65432i	−0.752670	+	0.658398i	$0.771235\pi$
$48$	−46.3506	+	7.34121i	−0.0201174	+	0.00318629i
$49$		−	128.213i		−	0.0533998i
$50$	4050.15	+	129.867i	1.62006	+	0.0519467i
$51$	−3581.29			−1.37689
$52$	−946.766	−	5977.65i	−0.350135	−	2.21067i
$53$	2351.03	+	1197.91i	0.836964	+	0.426454i	0.819283	−	0.573389i	$-0.194372\pi$
$53$	2351.03	+	1197.91i	0.836964	+	0.426454i	0.0176807	+	0.999844i	$0.494372\pi$
$54$	−4582.37	+	1488.90i	−1.57146	+	0.510598i
$55$	−2274.51	+	142.372i	−0.751904	+	0.0470651i
$56$	958.670	−	2950.48i	0.305698	−	0.940843i
$57$	2961.38	+	2961.38i	0.911473	+	0.911473i
$58$	2185.56	+	4289.41i	0.649692	+	1.27509i
$59$	528.407	+	727.290i	0.151797	+	0.208931i	0.878143	−	0.478399i	$-0.158783\pi$
$59$	528.407	+	727.290i	0.151797	+	0.208931i	−0.726345	+	0.687330i	$0.758783\pi$
$60$	−4939.18	+	2918.90i	−1.37199	+	0.810805i
$61$	2086.81	+	1516.16i	0.560820	+	0.407460i	0.831759	−	0.555137i	$-0.187334\pi$
$61$	2086.81	+	1516.16i	0.560820	+	0.407460i	−0.270939	+	0.962597i	$0.587334\pi$
$62$	−5891.11	−	933.059i	−1.53255	−	0.242731i
$63$	24.7098	−	156.012i	0.00622571	−	0.0393076i
$64$	3886.42	−	5349.20i	0.948832	−	1.30596i
$65$	−2956.53	−	5002.86i	−0.699771	−	1.18411i
$66$	4214.46	−	3061.99i	0.967508	−	0.702936i
$67$	2962.83	−	1509.64i	0.660021	−	0.336297i	−0.0916927	−	0.995787i	$-0.529228\pi$
$67$	2962.83	−	1509.64i	0.660021	−	0.336297i	0.751713	+	0.659490i	$0.229228\pi$
$68$	−7480.63	+	7480.63i	−1.61778	+	1.61778i
$69$	−4007.80	−	1302.21i	−0.841799	−	0.273517i
$70$	−482.749	−	7712.32i	−0.0985202	−	1.57394i
$71$	−1144.14	−	3521.31i	−0.226967	−	0.698534i	−0.998086	−	0.0618422i	$-0.980302\pi$
$71$	−1144.14	−	3521.31i	−0.226967	−	0.698534i	0.771119	−	0.636692i	$-0.219698\pi$
$72$	−97.8842	+	192.109i	−0.0188820	+	0.0370580i
$73$	−4816.28	+	762.823i	−0.903786	+	0.143146i	−0.590994	−	0.806676i	$-0.701264\pi$
$73$	−4816.28	+	762.823i	−0.903786	+	0.143146i	−0.312792	+	0.949822i	$0.601264\pi$
$74$			556.005i			0.101535i
$75$	−3379.13	+	4350.62i	−0.600734	+	0.773443i
$76$	12371.5			2.14188
$77$	679.843	+	4292.36i	0.114664	+	0.723960i
$78$	11835.7	+	6030.57i	1.94537	+	0.991218i
$79$	5880.69	−	1910.75i	0.942268	−	0.306161i	0.202698	−	0.979241i	$-0.435029\pi$
$79$	5880.69	−	1910.75i	0.942268	−	0.306161i	0.739570	+	0.673080i	$0.235029\pi$
$80$	−33.1435	+	128.915i	−0.00517868	+	0.0201429i
$81$	1941.14	−	5974.20i	0.295860	−	0.910563i
$82$	3841.65	+	3841.65i	0.571334	+	0.571334i
$83$	335.858	+	659.159i	0.0487528	+	0.0956828i	0.914098	−	0.405494i	$-0.132901\pi$
$83$	335.858	+	659.159i	0.0487528	+	0.0956828i	−0.865345	+	0.501177i	$0.832901\pi$
$84$	6430.70	+	8851.10i	0.911380	+	1.25441i
$85$	−4037.19	+	9321.23i	−0.558780	+	1.29014i
$86$	−2820.43	−	2049.16i	−0.381346	−	0.277064i
$87$	−6463.92	−	1023.78i	−0.853999	−	0.135260i
$88$	927.976	−	5859.01i	0.119832	−	0.756587i
$89$	6076.75	−	8363.93i	0.767170	−	1.05592i	−0.229414	−	0.973329i	$-0.573681\pi$
$89$	6076.75	−	8363.93i	0.767170	−	1.05592i	0.996584	−	0.0825898i	$-0.0263191\pi$
$90$	−50.7111	+	534.648i	−0.00626063	+	0.0660059i
$91$	−8965.21	+	6513.61i	−1.08262	+	0.786573i
$92$	−11091.6	+	5651.45i	−1.31044	+	0.667705i
$93$	5733.51	−	5733.51i	0.662910	−	0.662910i
$94$	−25290.3	−	8217.33i	−2.86219	−	0.929983i
$95$	11046.1	−	4369.38i	1.22394	−	0.484142i
$96$	2741.83	+	8438.48i	0.297507	+	0.915634i
$97$	6484.17	−	12725.9i	0.689146	−	1.35253i	−0.235566	−	0.971858i	$-0.575694\pi$
$97$	6484.17	−	12725.9i	0.689146	−	1.35253i	0.924712	−	0.380667i	$-0.124306\pi$
$98$	821.043	−	130.040i	0.0854897	−	0.0135402i
$99$		−	302.033i		−	0.0308166i
$100$	2029.25	+	16145.9i	0.202925	+	1.61459i
$101$	−466.088			−0.0456905			−0.0228452	−	0.999739i	$-0.507272\pi$
$101$	−466.088			−0.0456905			−0.0228452	+	0.999739i	$0.507272\pi$
$102$	−3632.34	−	22933.7i	−0.349130	−	2.20432i
$103$	−4753.67	−	2422.12i	−0.448079	−	0.228308i	0.215365	−	0.976534i	$-0.430906\pi$
$103$	−4753.67	−	2422.12i	−0.448079	−	0.228308i	−0.663444	+	0.748226i	$0.730906\pi$
$104$	14385.9	−	4674.27i	1.33006	−	0.432162i
$105$	8867.80	+	5631.65i	0.804336	+	0.510807i
$106$	−5286.58	+	16270.4i	−0.470503	+	1.44806i
$107$	625.709	+	625.709i	0.0546519	+	0.0546519i	0.733905	−	0.679253i	$-0.237696\pi$
$107$	625.709	+	625.709i	0.0546519	+	0.0546519i	−0.679253	+	0.733905i	$0.737696\pi$
$108$	−8784.21	−	17240.0i	−0.753105	−	1.47805i
$109$	3255.83	+	4481.27i	0.274037	+	0.377180i	0.923747	−	0.383002i	$-0.125110\pi$
$109$	3255.83	+	4481.27i	0.274037	+	0.377180i	−0.649710	+	0.760182i	$0.725110\pi$
$110$	−3218.65	−	14421.0i	−0.266004	−	1.19182i
$111$	−611.498	−	444.279i	−0.0496306	−	0.0360587i
$112$	250.704	+	39.7076i	0.0199860	+	0.00316546i
$113$	−34.2641	+	216.335i	−0.00268338	+	0.0169422i	−0.988994	−	0.147958i	$-0.952730\pi$
$113$	−34.2641	+	216.335i	−0.00268338	+	0.0169422i	0.986310	+	0.164900i	$0.0527301\pi$
$114$	−15960.3	+	21967.5i	−1.22810	+	1.69033i
$115$	−7907.33	+	8963.35i	−0.597908	+	0.677758i
$116$	−15640.4	+	11363.4i	−1.16233	+	0.844485i
$117$	686.219	−	349.646i	0.0501292	−	0.0255421i
$118$	−4121.44	+	4121.44i	−0.295996	+	0.295996i
$119$	18422.7	+	5985.88i	1.30094	+	0.422702i
$120$	−9136.54	−	11051.4i	−0.634482	−	0.767455i
$121$	−1956.43	−	6021.27i	−0.133627	−	0.411261i
$122$	−7592.54	+	14901.2i	−0.510114	+	1.00116i
$123$	−7294.77	+	1155.38i	−0.482171	+	0.0763684i
$124$		−	23952.4i		−	1.55778i
$125$	7514.30	+	13699.5i	0.480915	+	0.876767i
$126$	1024.12			0.0645076
$127$	3820.39	+	24121.0i	0.236864	+	1.49550i	0.763720	+	0.645548i	$0.223371\pi$
$127$	3820.39	+	24121.0i	0.236864	+	1.49550i	−0.526855	+	0.849955i	$0.676629\pi$
$128$	23845.6	+	12150.0i	1.45542	+	0.741574i
$129$	4507.37	−	1464.53i	0.270859	−	0.0880075i
$130$	29038.4	−	24007.1i	1.71825	−	1.42054i
$131$	4956.76	−	15255.3i	0.288839	−	0.888954i	−0.696383	−	0.717670i	$-0.745208\pi$
$131$	4956.76	−	15255.3i	0.288839	−	0.888954i	0.985222	−	0.171284i	$-0.0547915\pi$
$132$	14792.5	+	14792.5i	0.848973	+	0.848973i
$133$	−10284.0	−	20183.5i	−0.581377	−	1.14102i
$134$	12672.4	+	17442.1i	0.705748	+	0.971379i
$135$	−13932.0	−	12290.6i	−0.764443	−	0.674381i
$136$	−21391.0	−	15541.5i	−1.15652	−	0.840263i
$137$	8924.44	+	1413.49i	0.475488	+	0.0753099i	0.389579	−	0.920993i	$-0.372620\pi$
$137$	8924.44	+	1413.49i	0.475488	+	0.0753099i	0.0859092	+	0.996303i	$0.472620\pi$
$138$	4274.12	−	26985.8i	0.224434	−	1.41702i
$139$	−14899.1	+	20506.8i	−0.771132	+	1.06137i	0.225073	+	0.974342i	$0.427738\pi$
$139$	−14899.1	+	20506.8i	−0.771132	+	1.06137i	−0.996206	+	0.0870309i	$0.972262\pi$
$140$	30286.6	−	6759.71i	1.54523	−	0.344883i
$141$	29245.9	−	21248.4i	1.47105	−	1.06878i
$142$	21389.1	−	10898.3i	1.06076	−	0.540484i
$143$	−14983.2	+	14983.2i	−0.732712	+	0.732712i
$144$	−16.7775	−	5.45133i	−0.000809098	−	0.000262892i
$145$	−9951.42	+	15669.9i	−0.473314	+	0.745297i
$146$	−9769.86	−	30068.5i	−0.458335	−	1.41061i
$147$	−513.040	+	1006.90i	−0.0237420	+	0.0465963i
$148$	−2205.32	+	349.288i	−0.100681	+	0.0159463i
$149$			18028.4i			0.812052i	0.913862	+	0.406026i	$0.133086\pi$
$149$			18028.4i			0.812052i	−0.913862	+	0.406026i	$0.866914\pi$
$150$	−31287.6	−	17226.5i	−1.39056	−	0.765621i
$151$	−5721.36			−0.250926			−0.125463	−	0.992098i	$-0.540042\pi$
$151$	−5721.36			−0.250926			−0.125463	+	0.992098i	$0.540042\pi$
$152$	4836.99	+	30539.6i	0.209357	+	1.32183i
$153$	−1199.52	−	611.183i	−0.0512416	−	0.0261089i
$154$	−26797.7	+	8707.09i	−1.12994	+	0.367140i
$155$	−8459.55	−	21386.3i	−0.352114	−	0.890169i
$156$	−16484.1	+	50732.9i	−0.677356	+	2.08469i
$157$	−25987.3	−	25987.3i	−1.05429	−	1.05429i	−0.998439	−	0.0558554i	$-0.982211\pi$
$157$	−25987.3	−	25987.3i	−1.05429	−	1.05429i	−0.0558554	−	0.998439i	$-0.517789\pi$
$158$	18200.5	+	35720.5i	0.729070	+	1.43088i
$159$	−13670.0	−	18815.2i	−0.540724	−	0.744242i
$160$	25054.1	+	2376.37i	0.978678	+	0.0928271i
$161$	18440.1	+	13397.5i	0.711397	+	0.516860i
$162$	40226.1	+	6371.19i	1.53277	+	0.242767i
$163$	−1532.48	+	9675.68i	−0.0576792	+	0.364172i	0.941919	+	0.335839i	$0.109020\pi$
$163$	−1532.48	+	9675.68i	−0.0576792	+	0.364172i	−0.999599	+	0.0283328i	$0.990980\pi$
$164$	−12824.0	+	17650.7i	−0.476800	+	0.656259i
$165$	18432.2	+	7983.30i	0.677032	+	0.293234i
$166$	−3880.45	+	2819.31i	−0.140820	+	0.102312i
$167$	7746.43	−	3947.00i	0.277759	−	0.141525i	−0.309562	−	0.950879i	$-0.600182\pi$
$167$	7746.43	−	3947.00i	0.277759	−	0.141525i	0.587321	+	0.809354i	$0.300182\pi$
$168$	−19335.1	+	19335.1i	−0.685057	+	0.685057i
$169$	−24223.9	−	7870.82i	−0.848146	−	0.275579i
$170$	−63785.6	−	16399.0i	−2.20711	−	0.567441i
$171$	486.492	+	1497.27i	0.0166373	+	0.0512044i
$172$	6355.90	−	12474.2i	0.214842	−	0.421652i
$173$	−50964.1	+	8071.92i	−1.70283	+	0.269702i	−0.930706	−	0.365767i	$-0.880807\pi$
$173$	−50964.1	+	8071.92i	−1.70283	+	0.269702i	−0.772126	+	0.635469i	$0.780807\pi$
$174$		−	42431.7i		−	1.40150i
$175$	24654.5	−	16732.2i	0.805043	−	0.546357i
$176$	485.354			0.0156687
$177$	−1239.53	−	7826.06i	−0.0395648	−	0.249802i
$178$	59723.9	+	30430.9i	1.88499	+	0.960449i
$179$	16502.5	−	5361.99i	0.515044	−	0.167348i	−0.0399512	−	0.999202i	$-0.512720\pi$
$179$	16502.5	−	5361.99i	0.515044	−	0.167348i	0.554995	+	0.831854i	$0.312720\pi$
$180$	−2152.46	+	134.732i	−0.0664341	+	0.00415841i
$181$	8780.02	−	27022.1i	0.268002	−	0.824826i	−0.722984	−	0.690864i	$-0.757230\pi$
$181$	8780.02	−	27022.1i	0.268002	−	0.824826i	0.990987	−	0.133961i	$-0.0427698\pi$
$182$	−50804.5	−	50804.5i	−1.53377	−	1.53377i
$183$	−10321.6	−	20257.2i	−0.308208	−	0.604892i
$184$	−18287.4	−	25170.5i	−0.540154	−	0.743458i
$185$	−1845.69	+	1090.74i	−0.0539282	+	0.0318698i
$186$	42531.2	+	30900.7i	1.22937	+	0.893188i
$187$	36583.3	+	5794.23i	1.04616	+	0.165696i
$188$	16705.2	−	105473.i	0.472647	−	2.98418i
$189$	−20824.2	+	28662.0i	−0.582967	+	0.802385i
$190$	39184.0	+	66304.8i	1.08543	+	1.83670i
$191$	−12800.6	+	9300.20i	−0.350885	+	0.254933i	−0.749240	−	0.662299i	$-0.769581\pi$
$191$	−12800.6	+	9300.20i	−0.350885	+	0.254933i	0.398355	+	0.917231i	$0.369581\pi$
$192$	−51926.0	+	26457.6i	−1.40858	+	0.717709i
$193$	12770.0	−	12770.0i	0.342829	−	0.342829i	−0.514601	−	0.857430i	$-0.672060\pi$
$193$	12770.0	−	12770.0i	0.342829	−	0.342829i	0.857430	+	0.514601i	$0.172060\pi$
$194$	88070.2	+	28615.7i	2.34005	+	0.760329i
$195$	3199.81	+	51119.6i	0.0841502	+	1.34437i
$196$	1031.57	+	3174.86i	0.0268527	+	0.0826442i
$197$	−2031.18	+	3986.42i	−0.0523379	+	0.102719i	−0.915694	−	0.401876i	$-0.868358\pi$
$197$	−2031.18	+	3986.42i	−0.0523379	+	0.102719i	0.863356	+	0.504595i	$0.168358\pi$
$198$	1934.15	−	306.339i	0.0493355	−	0.00781397i
$199$		−	13188.8i		−	0.333042i	−0.986038	−	0.166521i	$-0.946747\pi$
$199$		−	13188.8i		−	0.333042i	0.986038	−	0.166521i	$-0.0532534\pi$
$200$	−39063.6	+	11322.0i	−0.976590	+	0.283050i
$201$	−29308.9			−0.725450
$202$	−472.732	−	2984.71i	−0.0115854	−	0.0731476i
$203$	31540.1	+	16070.5i	0.765368	+	0.389975i
$204$	88681.5	−	28814.4i	2.13095	−	0.692387i
$205$	−5216.21	+	20289.0i	−0.124122	+	0.482783i
$206$	10689.2	−	32898.0i	0.251890	−	0.775237i
$207$	−1120.13	−	1120.13i	−0.0261414	−	0.0261414i
$208$	561.865	+	1102.72i	0.0129869	+	0.0254882i
$209$	−25459.6	−	35042.1i	−0.582852	−	0.802227i
$210$	−27069.5	+	62499.1i	−0.613820	+	1.41721i
$211$	−7407.20	−	5381.65i	−0.166375	−	0.120879i	0.501482	−	0.865168i	$-0.332788\pi$
$211$	−7407.20	−	5381.65i	−0.166375	−	0.120879i	−0.667857	+	0.744289i	$0.732788\pi$
$212$	−67855.4	−	10747.2i	−1.50978	−	0.239125i
$213$	−5105.09	+	32232.3i	−0.112524	+	0.710447i
$214$	−3372.26	+	4641.51i	−0.0736365	+	0.101352i
$215$	1269.33	−	13382.5i	0.0274598	−	0.289509i
$216$	39123.2	−	28424.7i	0.838546	−	0.609240i
$217$	−39077.1	+	19910.8i	−0.829857	+	0.422833i
$218$	−25394.7	+	25394.7i	−0.534355	+	0.534355i
$219$	40876.3	+	13281.5i	0.852281	+	0.276923i
$220$	55176.9	−	21825.7i	1.14002	−	0.450944i
$221$	29185.9	+	89824.8i	0.597569	+	1.83913i
$222$	2224.84	−	4366.50i	0.0451433	−	0.0885986i
$223$	46744.1	−	7403.54i	0.939977	−	0.148878i	0.332400	−	0.943138i	$-0.392142\pi$
$223$	46744.1	−	7403.54i	0.939977	−	0.148878i	0.607577	+	0.794261i	$0.292142\pi$
$224$		−	47991.4i		−	0.956462i
$225$	−1874.28	+	880.509i	−0.0370228	+	0.0173928i
$226$	−1420.11			−0.0278038
$227$	3331.97	+	21037.2i	0.0646621	+	0.408260i	0.998695	+	0.0510732i	$0.0162642\pi$
$227$	3331.97	+	21037.2i	0.0646621	+	0.408260i	−0.934033	+	0.357187i	$0.883736\pi$
$228$	−97157.5	−	49504.2i	−1.86899	−	0.952297i
$229$	49800.6	−	16181.2i	0.949649	−	0.308560i	0.207076	−	0.978325i	$-0.433605\pi$
$229$	49800.6	−	16181.2i	0.949649	−	0.308560i	0.742573	+	0.669765i	$0.233605\pi$
$230$	−65419.1	−	41545.5i	−1.23666	−	0.785359i
$231$	11836.7	−	36429.7i	0.221824	−	0.682703i
$232$	−34166.1	−	34166.1i	−0.634774	−	0.634774i
$233$	21312.3	+	41827.7i	0.392570	+	0.770463i	0.999709	−	0.0241333i	$-0.00768262\pi$
$233$	21312.3	+	41827.7i	0.392570	+	0.770463i	−0.607138	+	0.794596i	$0.707683\pi$
$234$	2935.05	+	4039.75i	0.0536023	+	0.0737772i
$235$	−22335.5	−	100073.i	−0.404445	−	1.81210i
$236$	−18936.3	−	13758.0i	−0.339993	−	0.247019i
$237$	−53828.9	−	8525.66i	−0.958338	−	0.151786i
$238$	−19646.8	+	124045.i	−0.346848	+	2.18991i
$239$	−3249.15	+	4472.07i	−0.0568818	+	0.0782911i	−0.836510	−	0.547951i	$-0.815408\pi$
$239$	−3249.15	+	4472.07i	−0.0568818	+	0.0782911i	0.779628	+	0.626242i	$0.215408\pi$
$240$	776.137	−	879.789i	0.0134746	−	0.0152741i
$241$	−46945.8	+	34108.2i	−0.808282	+	0.587251i	−0.913332	−	0.407216i	$-0.866500\pi$
$241$	−46945.8	+	34108.2i	−0.808282	+	0.587251i	0.105050	+	0.994467i	$0.466500\pi$
$242$	36574.4	−	18635.6i	0.624521	−	0.318209i
$243$	3413.69	−	3413.69i	0.0578112	−	0.0578112i
$244$	−63873.2	−	20753.7i	−1.07285	−	0.348590i
$245$	2042.36	+	2470.39i	0.0340252	+	0.0411561i
$246$	−14797.5	−	45542.0i	−0.244522	−	0.752562i
$247$	50142.5	−	98410.1i	0.821886	−	1.61304i
$248$	59127.5	−	9364.88i	0.961361	−	0.152265i
$249$		−	6520.53i		−	0.105168i
$250$	−80106.7	+	62014.5i	−1.28171	+	0.992232i
$251$	−19192.3			−0.304634			−0.152317	−	0.988332i	$-0.548673\pi$
$251$	−19192.3			−0.304634			−0.152317	+	0.988332i	$0.548673\pi$
$252$	643.364	+	4062.04i	0.0101311	+	0.0639651i
$253$	38833.3	+	19786.6i	0.606685	+	0.309122i
$254$	−150590.	+	48929.6i	−2.33415	+	0.758411i
$255$	69004.0	−	57048.1i	1.06119	−	0.877325i
$256$	−20928.4	+	64411.0i	−0.319342	+	0.982833i
$257$	65874.8	+	65874.8i	0.997363	+	0.997363i	0.999997	−	0.00263390i	$-0.000838396\pi$
$257$	65874.8	+	65874.8i	0.997363	+	0.997363i	−0.00263390	+	0.999997i	$0.500838\pi$
$258$	13950.1	+	27378.7i	0.209575	+	0.411313i
$259$	2403.05	+	3307.51i	0.0358231	+	0.0493062i
$260$	113463.	+	100095.i	1.67844	+	1.48070i
$261$	−1990.30	−	1446.04i	−0.0292171	−	0.0212275i
$262$	102719.	+	16269.1i	1.49640	+	0.237006i
$263$	10750.2	−	67874.1i	0.155419	−	0.981279i	−0.779496	−	0.626408i	$-0.784525\pi$
$263$	10750.2	−	67874.1i	0.155419	−	0.981279i	0.934915	−	0.354872i	$-0.115475\pi$
$264$	−30732.4	+	42299.5i	−0.440949	+	0.606915i
$265$	−64381.5	+	14369.4i	−0.916789	+	0.204620i
$266$	118819.	−	86327.2i	1.67928	−	1.22007i
$267$	−81190.9	+	41368.8i	−1.13890	+	0.580297i
$268$	−61220.6	+	61220.6i	−0.852370	+	0.852370i
$269$	−98834.5	−	32113.3i	−1.36585	−	0.443793i	−0.467861	−	0.883802i	$-0.654975\pi$
$269$	−98834.5	−	32113.3i	−1.36585	−	0.443793i	−0.897993	+	0.440009i	$0.854975\pi$
$270$	64575.3	−	101683.i	0.885807	−	1.39482i
$271$	23362.3	+	71901.9i	0.318110	+	0.979043i	0.974455	+	0.224582i	$0.0721016\pi$
$271$	23362.3	+	71901.9i	0.318110	+	0.979043i	−0.656345	+	0.754461i	$0.727898\pi$
$272$	982.143	−	1927.57i	0.0132751	−	0.0260538i
$273$	96470.9	−	15279.5i	1.29441	−	0.205014i
$274$			58583.5i			0.780323i
$275$	41557.1	−	38974.9i	0.549516	−	0.515371i
$276$	109720.			1.44035
$277$	−5666.53	−	35777.1i	−0.0738513	−	0.466279i	−0.996704	−	0.0811254i	$-0.974149\pi$
$277$	−5666.53	−	35777.1i	−0.0738513	−	0.466279i	0.922853	−	0.385153i	$-0.125851\pi$
$278$	−146432.	−	74610.7i	−1.89472	−	0.965410i
$279$	2898.86	−	941.896i	0.0372408	−	0.0121003i
$280$	28528.0	+	72120.8i	0.363878	+	0.919908i
$281$	41940.1	−	129078.i	0.531150	−	1.63471i	−0.220674	−	0.975348i	$-0.570826\pi$
$281$	41940.1	−	129078.i	0.531150	−	1.63471i	0.751824	−	0.659364i	$-0.229174\pi$
$282$	165732.	+	165732.i	2.08405	+	2.08405i
$283$	−13405.0	−	26308.9i	−0.167377	−	0.328495i	0.792049	−	0.610458i	$-0.209015\pi$
$283$	−13405.0	−	26308.9i	−0.167377	−	0.328495i	−0.959425	+	0.281963i	$0.909015\pi$
$284$	56663.5	+	77990.6i	0.702533	+	0.966953i
$285$	−104233.	−	9886.42i	−1.28326	−	0.121716i
$286$	−111146.	−	80752.1i	−1.35882	−	0.987237i
$287$	39456.4	+	6249.28i	0.479020	+	0.0758693i
$288$	−521.765	+	3294.30i	−0.00629057	+	0.0397171i
$289$	47947.8	−	65994.5i	0.574081	−	0.790155i
$290$	−110439.	−	47833.2i	−1.31319	−	0.568765i
$291$	−101845.	+	73994.6i	−1.20269	+	0.873804i
$292$	113125.	−	57640.1i	1.32676	−	0.676019i
$293$	102243.	−	102243.i	1.19096	−	1.19096i	0.214167	−	0.976797i	$-0.431296\pi$
$293$	102243.	−	102243.i	1.19096	−	1.19096i	0.976797	−	0.214167i	$-0.0687037\pi$
$294$	−6968.28	−	2264.13i	−0.0806178	−	0.0261943i
$295$	−21766.6	−	5596.12i	−0.250119	−	0.0643047i
$296$	−1724.46	−	5307.35i	−0.0196821	−	0.0605752i
$297$	−30754.8	+	60359.7i	−0.348658	+	0.684281i
$298$	−115449.	+	18285.3i	−1.30004	+	0.205907i
$299$			111135.i			1.24311i
$300$	48671.3	−	134920.i	0.540792	−	1.49911i
$301$	−25634.4			−0.282937
$302$	−5802.91	−	36638.2i	−0.0636257	−	0.401717i
$303$	3660.35	+	1865.04i	0.0398692	+	0.0203144i
$304$	−2406.04	+	781.770i	−0.0260349	+	0.00845925i
$305$	−64360.1	+	4028.59i	−0.691858	+	0.0433065i
$306$	2697.25	−	8301.29i	0.0288057	−	0.0886549i
$307$	4979.69	+	4979.69i	0.0528354	+	0.0528354i	0.733031	−	0.680195i	$-0.238105\pi$
$307$	4979.69	+	4979.69i	0.0528354	+	0.0528354i	−0.680195	+	0.733031i	$0.738105\pi$
$308$	−51370.0	−	100819.i	−0.541512	−	1.06278i
$309$	27640.1	+	38043.4i	0.289483	+	0.398439i
$310$	128372.	−	75864.0i	1.33582	−	0.789428i
$311$	52844.6	+	38393.8i	0.546361	+	0.396955i	0.826442	−	0.563022i	$-0.190361\pi$
$311$	52844.6	+	38393.8i	0.546361	+	0.396955i	−0.280081	+	0.959976i	$0.590361\pi$
$312$	−131681.	−	20856.3i	−1.35274	−	0.214253i
$313$	−23979.0	+	151397.i	−0.244761	+	1.54536i	0.492838	+	0.870121i	$0.335960\pi$
$313$	−23979.0	+	151397.i	−0.244761	+	1.54536i	−0.737599	+	0.675239i	$0.764040\pi$
$314$	140058.	−	192774.i	1.42053	−	1.95519i
$315$	2009.08	+	3399.64i	0.0202477	+	0.0342619i
$316$	−130247.	+	94629.7i	−1.30434	+	0.947662i
$317$	32746.0	−	16684.9i	0.325866	−	0.166037i	−0.283402	−	0.959001i	$-0.591463\pi$
$317$	32746.0	−	16684.9i	0.325866	−	0.166037i	0.609269	+	0.792964i	$0.291463\pi$
$318$	106623.	−	106623.i	1.05438	−	1.05438i
$319$	64373.3	+	20916.1i	0.632593	+	0.205542i
$320$	10326.6	+	164976.i	0.100846	+	1.61110i
$321$	−2410.15	−	7417.66i	−0.0233902	−	0.0719875i
$322$	−67091.5	+	131674.i	−0.647077	+	1.26996i
$323$	−190687.	+	30201.9i	−1.82775	+	0.289487i
$324$			163554.i			1.55801i
$325$	136659.	+	49298.8i	1.29381	+	0.466734i
$326$	−63515.0			−0.597642
$327$	−7637.47	−	48221.1i	−0.0714256	−	0.450964i
$328$	−48585.5	−	24755.6i	−0.451605	−	0.230104i
$329$	−185960.	+	60422.0i	−1.71802	+	0.558218i
$330$	−32428.1	+	126132.i	−0.297779	+	1.15824i
$331$	−47767.2	+	147012.i	−0.435987	+	1.34183i	0.456085	+	0.889936i	$0.349251\pi$
$331$	−47767.2	+	147012.i	−0.435987	+	1.34183i	−0.892072	+	0.451894i	$0.850749\pi$
$332$	−13620.1	−	13620.1i	−0.123568	−	0.123568i
$333$	−128.994	−	253.165i	−0.00116327	−	0.00228305i
$334$	33132.5	+	45602.9i	0.297003	+	0.408790i
$335$	−33039.9	+	76283.9i	−0.294407	+	0.679741i
$336$	−1809.97	−	1315.02i	−0.0160322	−	0.0116481i
$337$	−222423.	−	35228.4i	−1.95849	−	0.310194i	−0.999656	−	0.0262098i	$-0.991656\pi$
$337$	−222423.	−	35228.4i	−1.95849	−	0.310194i	−0.958829	−	0.283984i	$-0.908344\pi$
$338$	25833.6	−	163107.i	0.226126	−	1.42771i
$339$	1134.75	−	1561.84i	0.00987415	−	0.0135906i
$340$	24973.8	−	263299.i	0.216036	−	2.27767i
$341$	−67844.8	+	49292.2i	−0.583456	+	0.423906i
$342$	−9094.71	+	4633.99i	−0.0777565	+	0.0396189i
$343$	85260.9	−	85260.9i	0.724705	−	0.724705i
$344$	33278.0	+	10812.7i	0.281216	+	0.0913727i
$345$	97965.6	−	38751.2i	0.823067	−	0.325572i
$346$	−103381.	−	318174.i	−0.863553	−	2.65774i
$347$	18895.7	−	37085.0i	0.156930	−	0.307992i	−0.799133	−	0.601154i	$-0.794708\pi$
$347$	18895.7	−	37085.0i	0.156930	−	0.307992i	0.956063	+	0.293163i	$0.0947077\pi$
$348$	168299.	−	26656.0i	1.38971	−	0.220108i
$349$		−	154218.i		−	1.26614i	−0.774093	−	0.633072i	$-0.781794\pi$
$349$		−	154218.i		−	1.26614i	0.774093	−	0.633072i	$-0.218206\pi$
$350$	132155.	+	140910.i	1.07881	+	1.15029i
$351$	−172740.			−1.40210
$352$	−14355.3	−	90636.1i	−0.115859	−	0.731503i
$353$	194961.	+	99337.5i	1.56458	+	0.797193i	0.999610	−	0.0279181i	$-0.00888777\pi$
$353$	194961.	+	99337.5i	1.56458	+	0.797193i	0.564970	+	0.825112i	$0.308888\pi$
$354$	48858.9	−	15875.2i	0.389886	−	0.126682i
$355$	78137.8	+	49622.7i	0.620018	+	0.393753i
$356$	−83180.6	+	256004.i	−0.656330	+	2.01997i
$357$	−120727.	−	120727.i	−0.947257	−	0.947257i
$358$	51074.6	+	100240.i	0.398510	+	0.782120i
$359$	−12968.7	−	17849.8i	−0.100625	−	0.138499i	0.755735	−	0.654877i	$-0.227280\pi$
$359$	−12968.7	−	17849.8i	−0.100625	−	0.138499i	−0.856360	+	0.516379i	$0.827280\pi$
$360$	−1174.16	−	5260.77i	−0.00905988	−	0.0405924i
$361$	77221.7	+	56104.8i	0.592550	+	0.430512i
$362$	181948.	+	28817.7i	1.38845	+	0.219909i
$363$	−8729.47	+	55115.7i	−0.0662483	+	0.418275i
$364$	169593.	−	233425.i	1.27999	−	1.76175i
$365$	80648.2	−	91418.7i	0.605353	−	0.686197i
$366$	119254.	−	86642.8i	0.890244	−	0.646800i
$367$	206115.	−	105021.i	1.53030	−	0.779727i	0.532527	−	0.846413i	$-0.321243\pi$
$367$	206115.	−	105021.i	1.53030	−	0.779727i	0.997774	+	0.0666861i	$0.0212426\pi$
$368$	1800.00	−	1800.00i	0.0132916	−	0.0132916i
$369$	−2640.48	−	857.944i	−0.0193923	−	0.00630095i
$370$	−8856.86	−	10713.1i	−0.0646958	−	0.0782546i
$371$	38872.2	+	119636.i	0.282417	+	0.869191i
$372$	−95845.0	+	188106.i	−0.692601	+	1.35931i
$373$	−23215.1	+	3676.91i	−0.166860	+	0.0264281i	−0.239306	−	0.970944i	$-0.576920\pi$
$373$	−23215.1	+	3676.91i	−0.166860	+	0.0264281i	0.0724452	+	0.997372i	$0.476920\pi$
$374$			240147.i			1.71686i
$375$	−4194.17	−	137655.i	−0.0298252	−	0.978880i
$376$	266895.			1.88784
$377$	26999.7	+	170469.i	0.189966	+	1.19940i
$378$	−204665.	−	104282.i	−1.43239	−	0.729838i
$379$	−108124.	+	35131.6i	−0.752737	+	0.244579i	−0.660158	−	0.751126i	$-0.729511\pi$
$379$	−108124.	+	35131.6i	−0.752737	+	0.244579i	−0.0925785	+	0.995705i	$0.529511\pi$
$380$	−238373.	+	197071.i	−1.65078	+	1.36476i
$381$	66516.7	−	204717.i	0.458227	−	1.41028i
$382$	−72539.2	−	72539.2i	−0.497103	−	0.497103i
$383$	−56849.4	−	111573.i	−0.387551	−	0.760611i	0.611992	−	0.790864i	$-0.290369\pi$
$383$	−56849.4	−	111573.i	−0.387551	−	0.760611i	−0.999542	+	0.0302533i	$0.990369\pi$
$384$	−138650.	−	190835.i	−0.940281	−	1.29419i
$385$	−81474.1	−	71875.3i	−0.549665	−	0.484907i
$386$	94728.2	+	68824.1i	0.635777	+	0.461919i
$387$	1759.63	+	278.698i	0.0117490	+	0.00186085i
$388$	−58173.8	+	367295.i	−0.386424	+	2.43978i
$389$	68040.5	−	93649.8i	0.449644	−	0.618881i	−0.522677	−	0.852531i	$-0.675067\pi$
$389$	68040.5	−	93649.8i	0.449644	−	0.618881i	0.972321	+	0.233649i	$0.0750667\pi$
$390$	−324112.	+	72339.1i	−2.13091	+	0.475602i
$391$	157163.	−	114186.i	1.02801	−	0.746893i
$392$	−7433.95	+	3787.79i	−0.0483780	+	0.0246498i
$393$	−99971.0	+	99971.0i	−0.647275	+	0.647275i
$394$	−27588.2	−	8963.93i	−0.177717	−	0.0577439i
$395$	−82871.4	+	130492.i	−0.531142	+	0.836356i
$396$	2430.10	+	7479.08i	0.0154965	+	0.0476933i
$397$	−26316.7	+	51649.4i	−0.166975	+	0.327706i	−0.959298	−	0.282395i	$-0.908871\pi$
$397$	−26316.7	+	51649.4i	−0.166975	+	0.327706i	0.792324	+	0.610101i	$0.208871\pi$
$398$	84457.8	−	13376.8i	0.533180	−	0.0844473i
$399$			199659.i			1.25413i
$400$	−1414.94	−	3011.88i	−0.00884336	−	0.0188242i
$401$	287826.			1.78995			0.894977	−	0.446112i	$-0.147192\pi$
$401$	287826.			1.78995			0.894977	+	0.446112i	$0.147192\pi$
$402$	−29726.7	−	187687.i	−0.183948	−	1.16140i
$403$	−190531.	−	97080.6i	−1.17316	−	0.597754i
$404$	11541.5	−	3750.05i	0.0707129	−	0.0229760i
$405$	57764.1	+	146032.i	0.352167	+	0.890301i
$406$	−70921.6	+	218274.i	−0.430256	+	1.32419i
$407$	5527.72	+	5527.72i	0.0333701	+	0.0333701i
$408$	105802.	+	207648.i	0.635585	+	1.24741i
$409$	29282.0	+	40303.2i	0.175047	+	0.240931i	0.887521	−	0.460767i	$-0.152426\pi$
$409$	29282.0	+	40303.2i	0.175047	+	0.240931i	−0.712475	+	0.701698i	$0.752426\pi$
$410$	−135216.	−	12825.2i	−0.804378	−	0.0762949i
$411$	−64430.6	−	46811.6i	−0.381424	−	0.277121i
$412$	137200.	+	21730.4i	0.808277	+	0.128019i
$413$	−6704.43	+	42330.1i	−0.0393062	+	0.248170i
$414$	6036.96	−	8309.16i	0.0352223	−	0.0484793i
$415$	−16971.3	−	7350.58i	−0.0985416	−	0.0426801i
$416$	189307.	−	137539.i	1.09390	−	0.794767i
$417$	199065.	−	101429.i	1.14478	−	0.583295i
$418$	198578.	−	198578.i	1.13653	−	1.13653i
$419$	−245070.	−	79628.2i	−1.39593	−	0.453564i	−0.488056	−	0.872812i	$-0.662294\pi$
$419$	−245070.	−	79628.2i	−1.39593	−	0.453564i	−0.907872	+	0.419248i	$0.862294\pi$
$420$	−264899.	−	68104.6i	−1.50170	−	0.386081i
$421$	−72962.6	−	224556.i	−0.411658	−	1.26695i	−0.915206	−	0.402985i	$-0.867973\pi$
$421$	−72962.6	−	224556.i	−0.411658	−	1.26695i	0.503549	−	0.863967i	$-0.332027\pi$
$422$	26949.9	−	52892.2i	0.151333	−	0.297007i
$423$	13421.8	−	2125.81i	0.0750121	−	0.0118807i
$424$		−	171706.i		−	0.955110i
$425$	−70694.0	−	243911.i	−0.391385	−	1.35037i
$426$	−211585.			−1.16591
$427$	19237.0	+	121458.i	0.105507	+	0.666146i
$428$	−20528.4	−	10459.7i	−0.112064	−	0.0570996i
$429$	177623.	−	57713.3i	0.965129	−	0.313590i
$430$	86985.9	−	5444.84i	0.470448	−	0.0294475i
$431$	75467.0	−	232264.i	0.406259	−	1.25034i	−0.513581	−	0.858041i	$-0.671681\pi$
$431$	75467.0	−	232264.i	0.406259	−	1.25034i	0.919840	−	0.392295i	$-0.128319\pi$
$432$	2797.80	+	2797.80i	0.0149916	+	0.0149916i
$433$	5735.79	+	11257.1i	0.0305927	+	0.0600415i	0.905797	−	0.423712i	$-0.139273\pi$
$433$	5735.79	+	11257.1i	0.0305927	+	0.0600415i	−0.875204	+	0.483754i	$0.839273\pi$
$434$	−167138.	−	230046.i	−0.887351	−	1.22133i
$435$	140854.	−	83240.5i	0.744376	−	0.439902i
$436$	−116678.	−	84771.4i	−0.613783	−	0.445940i
$437$	−224379.	−	35538.1i	−1.17495	−	0.186094i
$438$	−43592.5	+	275232.i	−0.227229	+	1.43467i
$439$	−173528.	+	238841.i	−0.900412	+	1.23931i	0.0699245	+	0.997552i	$0.477724\pi$
$439$	−173528.	+	238841.i	−0.900412	+	1.23931i	−0.970336	+	0.241758i	$0.922276\pi$
$440$	75450.7	+	127673.i	0.389725	+	0.659468i
$441$	−343.675	+	249.694i	−0.00176714	+	0.00128390i
$442$	−545614.	+	278004.i	−2.79281	+	1.42301i
$443$	−128280.	+	128280.i	−0.653658	+	0.653658i	−0.953872	−	0.300214i	$-0.902942\pi$
$443$	−128280.	+	128280.i	−0.653658	+	0.653658i	0.300214	+	0.953872i	$0.402942\pi$
$444$	18716.8	+	6081.44i	0.0949434	+	0.0308490i
$445$	16146.6	+	257955.i	0.0815380	+	1.30264i
$446$	94820.9	+	291829.i	0.476688	+	1.46710i
$447$	72140.0	−	141583.i	0.361045	−	0.708591i
$448$	311337.	−	49310.9i	1.55122	−	0.245690i
$449$		−	145028.i		−	0.719381i	−0.933072	−	0.359690i	$-0.882882\pi$
$449$		−	145028.i		−	0.719381i	0.933072	−	0.359690i	$-0.117118\pi$
$450$	−7539.56	−	11109.4i	−0.0372324	−	0.0548610i
$451$	76386.2			0.375545
$452$	−892.126	−	5632.66i	−0.00436666	−	0.0275700i
$453$	44931.8	+	22893.9i	0.218956	+	0.111564i
$454$	−131338.	+	42674.2i	−0.637203	+	0.207040i
$455$	68982.7	−	268315.i	0.333209	−	1.29605i
$456$	84216.8	−	259193.i	0.405013	−	1.24650i
$457$	80041.7	+	80041.7i	0.383251	+	0.383251i	0.872272	−	0.489021i	$-0.162646\pi$
$457$	80041.7	+	80041.7i	0.383251	+	0.383251i	−0.489021	+	0.872272i	$0.662646\pi$
$458$	154131.	+	302499.i	0.734782	+	1.44209i
$459$	177482.	+	244283.i	0.842421	+	1.15949i
$460$	123687.	−	285575.i	0.584534	−	1.34960i
$461$	194833.	+	141554.i	0.916769	+	0.666071i	0.942718	−	0.333592i	$-0.108261\pi$
$461$	194833.	+	141554.i	0.916769	+	0.666071i	−0.0259490	+	0.999663i	$0.508261\pi$
$462$	245292.	+	38850.5i	1.14921	+	0.182017i
$463$	−12003.8	+	75788.9i	−0.0559959	+	0.353544i	0.943743	+	0.330681i	$0.107278\pi$
$463$	−12003.8	+	75788.9i	−0.0559959	+	0.353544i	−0.999739	+	0.0228636i	$0.992722\pi$
$464$	2323.71	−	3198.32i	0.0107931	−	0.0148554i
$465$	−19141.1	+	201805.i	−0.0885239	+	0.933308i
$466$	−246238.	+	178902.i	−1.13392	+	0.823842i
$467$	75436.7	−	38436.9i	0.345899	−	0.176244i	−0.272407	−	0.962182i	$-0.587820\pi$
$467$	75436.7	−	38436.9i	0.345899	−	0.176244i	0.618305	+	0.785938i	$0.287820\pi$
$468$	−14179.3	+	14179.3i	−0.0647384	+	0.0647384i
$469$	150769.	+	48987.8i	0.685435	+	0.222711i
$470$	618189.	−	244530.i	2.79850	−	1.10697i
$471$	100099.	+	308075.i	0.451222	+	1.38872i
$472$	26558.5	−	52124.1i	0.119212	−	0.233967i
$473$	−48412.8	+	7667.83i	−0.216390	+	0.0342729i
$474$		−	353354.i		−	1.57273i
$475$	−143233.	+	260147.i	−0.634829	+	1.15301i
$476$	−504351.			−2.22597
$477$	−1367.63	−	8634.87i	−0.00601079	−	0.0379506i
$478$	−31933.5	−	16270.9i	−0.139762	−	0.0712125i
$479$	33016.9	−	10727.8i	0.143901	−	0.0467564i	−0.236181	−	0.971709i	$-0.575896\pi$
$479$	33016.9	−	10727.8i	0.143901	−	0.0467564i	0.380082	+	0.924953i	$0.375896\pi$
$480$	−187250.	−	118916.i	−0.812716	−	0.516129i
$481$	−6159.85	+	18958.1i	−0.0266244	+	0.0819415i
$482$	−266035.	−	266035.i	−1.14510	−	1.14510i
$483$	−91206.6	−	179003.i	−0.390960	−	0.767302i
$484$	96891.9	+	133360.i	0.413615	+	0.569293i
$485$	77780.3	+	348491.i	0.330663	+	1.48152i
$486$	25322.8	+	18398.1i	0.107211	+	0.0778933i
$487$	−242588.	−	38422.1i	−1.02285	−	0.162003i	−0.377594	−	0.925971i	$-0.623248\pi$
$487$	−242588.	−	38422.1i	−1.02285	−	0.162003i	−0.645254	+	0.763968i	$0.723248\pi$
$488$	26258.2	−	165788.i	0.110262	−	0.696167i
$489$	50752.1	−	69854.2i	0.212244	−	0.292129i
$490$	−13748.3	+	15584.4i	−0.0572608	+	0.0649079i
$491$	−35485.3	+	25781.6i	−0.147192	+	0.106942i	−0.658944	−	0.752192i	$-0.728997\pi$
$491$	−35485.3	+	25781.6i	−0.147192	+	0.106942i	0.511752	+	0.859133i	$0.328997\pi$
$492$	171340.	−	87302.2i	0.707830	−	0.360658i
$493$	213331.	−	213331.i	0.877728	−	0.877728i
$494$	681051.	+	221287.i	2.79078	+	0.906780i
$495$	4811.23	+	5819.55i	0.0196357	+	0.0237509i
$496$	1513.58	+	4658.33i	0.00615238	+	0.0189351i
$497$	80135.3	−	157274.i	0.324423	−	0.636715i
$498$	41755.8	−	6613.48i	0.168368	−	0.0266668i
$499$		−	111889.i		−	0.449351i	−0.974434	−	0.224675i	$-0.927868\pi$
$499$		−	111889.i		−	0.449351i	0.974434	−	0.224675i	$-0.0721322\pi$
$500$	−296296.	−	278774.i	−1.18518	−	1.11510i
$501$	−76629.1			−0.305294
$502$	−19465.8	−	122902.i	−0.0772441	−	0.487700i
$503$	−375743.	−	191450.i	−1.48510	−	0.756694i	−0.491628	−	0.870806i	$-0.663598\pi$
$503$	−375743.	−	191450.i	−1.48510	−	0.756694i	−0.993468	+	0.114112i	$0.963598\pi$
$504$	−9775.78	+	3176.34i	−0.0384849	+	0.0125045i
$505$	8980.55	−	7424.54i	0.0352144	−	0.0291130i
$506$	−87321.4	+	268747.i	−0.341051	+	1.04965i
$507$	158744.	+	158744.i	0.617561	+	0.617561i
$508$	−288674.	−	566556.i	−1.11862	−	2.19541i
$509$	−129248.	−	177894.i	−0.498870	−	0.686635i	0.483123	−	0.875552i	$-0.339502\pi$
$509$	−129248.	−	177894.i	−0.498870	−	0.686635i	−0.981993	+	0.188917i	$0.939502\pi$
$510$	435309.	+	384024.i	1.67362	+	1.47645i
$511$	−188074.	−	136644.i	−0.720256	−	0.523296i
$512$	−10769.1	−	1705.66i	−0.0410808	−	0.00650657i
$513$	55237.9	−	348758.i	0.209895	−	1.32523i
$514$	−355032.	+	488660.i	−1.34382	+	1.84961i
$515$	130176.	−	29054.3i	0.490815	−	0.109546i
$516$	−99830.0	+	72530.8i	−0.374940	+	0.272410i
$517$	−333128.	+	169737.i	−1.24632	+	0.635033i
$518$	−18743.2	+	18743.2i	−0.0698528	+	0.0698528i
$519$	432538.	+	140540.i	1.60579	+	0.521753i
$520$	−202728.	+	319223.i	−0.749734	+	1.18056i
$521$	−140863.	−	433533.i	−0.518947	−	1.59715i	−0.775984	−	0.630753i	$-0.782746\pi$
$521$	−140863.	−	433533.i	−0.518947	−	1.59715i	0.257037	−	0.966402i	$-0.417254\pi$
$522$	7241.39	−	14212.0i	0.0265755	−	0.0521573i
$523$	−99474.6	+	15755.2i	−0.363671	+	0.0575998i	−0.335596	−	0.942006i	$-0.608938\pi$
$523$	−99474.6	+	15755.2i	−0.363671	+	0.0575998i	−0.0280750	+	0.999606i	$0.508938\pi$
$524$			417640.i			1.52104i
$525$	−260573.	+	32749.2i	−0.945390	+	0.118818i
$526$	445552.			1.61038
$527$	58473.8	+	369189.i	0.210543	+	1.32931i
$528$	−3811.65	−	1942.13i	−0.0136724	−	0.00696644i
$529$	−48744.5	+	15838.0i	−0.174186	+	0.0565966i
$530$	−157317.	−	397709.i	−0.560048	−	1.41584i
$531$	920.429	−	2832.79i	0.00326439	−	0.0100467i
$532$	417048.	+	417048.i	1.47354	+	1.47354i
$533$	88427.8	+	173549.i	0.311268	+	0.610897i
$534$	−347264.	−	477968.i	−1.21780	−	1.67616i
$535$	−22023.3	−	2088.90i	−0.0769441	−	0.00729811i
$536$	−175062.	−	127190.i	−0.609343	−	0.442714i
$537$	−151056.	−	23924.9i	−0.523828	−	0.0829662i
$538$	105402.	−	665483.i	0.364154	−	2.29918i
$539$	6869.85	−	9455.53i	0.0236466	−	0.0325468i
$540$	443877.	+	192251.i	1.52221	+	0.659296i
$541$	−309533.	+	224889.i	−1.05758	+	0.768375i	−0.973639	−	0.228096i	$-0.926750\pi$
$541$	−309533.	+	224889.i	−1.05758	+	0.768375i	−0.0839384	+	0.996471i	$0.526750\pi$
$542$	−436746.	+	222533.i	−1.48673	+	0.757524i
$543$	−177081.	+	177081.i	−0.600581	+	0.600581i
$544$	−389007.	−	126396.i	−1.31450	−	0.427106i
$545$	−134117.	−	34481.1i	−0.451536	−	0.116088i
$546$	195692.	+	602278.i	0.656429	+	2.02028i
$547$	160459.	−	314919.i	0.536277	−	1.05250i	−0.450855	−	0.892597i	$-0.648881\pi$
$547$	160459.	−	314919.i	0.536277	−	1.05250i	0.987132	−	0.159906i	$-0.0511192\pi$
$548$	−232363.	+	36802.7i	−0.773761	+	0.122552i
$549$		−	8546.41i		−	0.0283556i
$550$	291735.	+	226591.i	0.964414	+	0.749061i
$551$	−352807.			−1.16208
$552$	42898.3	+	270849.i	0.140787	+	0.888893i
$553$	262653.	+	133828.i	0.858879	+	0.437621i
$554$	223360.	−	72574.2i	0.727757	−	0.236463i
$555$	18859.4	−	1180.50i	0.0612269	−	0.00383247i
$556$	203943.	−	627672.i	0.659720	−	2.03041i
$557$	121828.	+	121828.i	0.392678	+	0.392678i	0.875641	−	0.482963i	$-0.160439\pi$
$557$	121828.	+	121828.i	0.392678	+	0.392678i	−0.482963	+	0.875641i	$0.660439\pi$
$558$	8971.85	+	17608.2i	0.0288147	+	0.0565520i
$559$	−73465.9	−	101117.i	−0.235105	−	0.323594i
$560$	−5463.06	+	3228.49i	−0.0174205	+	0.0102949i
$561$	−264116.	−	191891.i	−0.839206	−	0.609719i
$562$	869125.	+	137656.i	2.75175	+	0.435835i
$563$	−3146.41	+	19865.6i	−0.00992655	+	0.0626738i	−0.992154	−	0.125019i	$-0.960101\pi$
$563$	−3146.41	+	19865.6i	−0.00992655	+	0.0626738i	0.982228	+	0.187693i	$0.0601009\pi$
$564$	−553239.	+	761467.i	−1.73922	+	2.39383i
$565$	−2785.90	−	4714.13i	−0.00872708	−	0.0147674i
$566$	154879.	−	112526.i	0.483460	−	0.351254i
$567$	266829.	−	135956.i	0.829980	−	0.422896i
$568$	−170369.	+	170369.i	−0.528073	+	0.528073i
$569$	−16958.5	−	5510.16i	−0.0523798	−	0.0170192i	0.282710	−	0.959205i	$-0.408767\pi$
$569$	−16958.5	−	5510.16i	−0.0523798	−	0.0170192i	−0.335090	+	0.942186i	$0.608767\pi$
$570$	−42408.3	−	677507.i	−0.130527	−	2.08528i
$571$	53554.1	+	164823.i	0.164256	+	0.505528i	0.998981	−	0.0451397i	$-0.0143733\pi$
$571$	53554.1	+	164823.i	0.164256	+	0.505528i	−0.834725	+	0.550667i	$0.814373\pi$
$572$	250469.	−	491573.i	0.765529	−	1.50244i
$573$	137742.	−	21816.2i	0.419525	−	0.0664462i
$574$			259007.i			0.786119i
$575$	9576.57	−	298664.i	0.0289651	−	0.903333i
$576$	−21907.3			−0.0660304
$577$	7421.08	+	46854.9i	0.0222903	+	0.140735i	0.996324	−	0.0856693i	$-0.0273028\pi$
$577$	7421.08	+	46854.9i	0.0222903	+	0.140735i	−0.974033	+	0.226405i	$0.927303\pi$
$578$	471244.	+	240111.i	1.41055	+	0.718713i
$579$	−151386.	+	49188.4i	−0.451575	+	0.146726i
$580$	120345.	−	468091.i	0.357742	−	1.39147i
$581$	−10898.6	+	33542.5i	−0.0322863	+	0.0993671i
$582$	−577140.	−	577140.i	−1.70386	−	1.70386i
$583$	109200.	+	214316.i	0.321280	+	0.630548i
$584$	186517.	+	256718.i	0.546880	+	0.752716i
$585$	−7652.33	+	17668.0i	−0.0223605	+	0.0516270i
$586$	758440.	+	551039.i	2.20864	+	1.60467i
$587$	345342.	+	54696.8i	1.00224	+	0.158740i	0.635926	−	0.771750i	$-0.280618\pi$
$587$	345342.	+	54696.8i	1.00224	+	0.158740i	0.366318	+	0.930490i	$0.380618\pi$
$588$	4602.82	−	29061.1i	0.0133128	−	0.0840537i
$589$	256931.	−	353635.i	0.740603	−	1.01935i
$590$	13759.3	−	145064.i	0.0395267	−	0.416731i
$591$	31903.1	−	23179.0i	0.0913393	−	0.0663619i
$592$	406.824	−	207.287i	0.00116082	−	0.000591465i
$593$	−217412.	+	217412.i	−0.618263	+	0.618263i	−0.945086	−	0.326823i	$-0.894022\pi$
$593$	−217412.	+	217412.i	−0.618263	+	0.618263i	0.326823	+	0.945086i	$0.394022\pi$
$594$	−417722.	−	135726.i	−1.18390	−	0.384672i
$595$	−450318.	+	178127.i	−1.27199	+	0.503149i
$596$	−145053.	−	446426.i	−0.408350	−	1.25677i
$597$	−52774.6	+	103576.i	−0.148073	+	0.290610i
$598$	−711680.	+	112719.i	−1.99013	+	0.315206i
$599$		−	380215.i		−	1.05968i	−0.848097	−	0.529841i	$-0.822251\pi$
$599$		−	380215.i		−	1.05968i	0.848097	−	0.529841i	$-0.177749\pi$
$600$	352084.	+	67396.4i	0.978012	+	0.187212i
$601$	610086.			1.68905			0.844524	−	0.535518i	$-0.179884\pi$
$601$	610086.			1.68905			0.844524	+	0.535518i	$0.179884\pi$
$602$	−25999.8	−	164156.i	−0.0717425	−	0.452965i
$603$	−9816.69	−	5001.86i	−0.0269979	−	0.0137561i
$604$	141675.	−	46032.9i	0.388346	−	0.126181i
$605$	133612.	+	84852.5i	0.365035	+	0.231822i
$606$	−8230.74	+	25331.6i	−0.0224127	+	0.0689791i
$607$	53794.4	+	53794.4i	0.146002	+	0.146002i	0.776330	−	0.630327i	$-0.217079\pi$
$607$	53794.4	+	53794.4i	0.146002	+	0.146002i	−0.630327	+	0.776330i	$0.717079\pi$
$608$	217153.	+	426187.i	0.587434	+	1.15290i
$609$	−183389.	−	252414.i	−0.494469	−	0.680578i
$610$	−91075.6	−	408060.i	−0.244761	−	1.09664i
$611$	−771285.	−	560371.i	−2.06601	−	1.50104i
$612$	34620.4	+	5483.33i	0.0924333	+	0.0146400i
$613$	−14106.0	+	89062.0i	−0.0375391	+	0.237013i	−0.999323	−	0.0367981i	$-0.988284\pi$
$613$	−14106.0	+	89062.0i	−0.0375391	+	0.237013i	0.961784	+	0.273811i	$0.0882842\pi$
$614$	−26838.0	+	36939.3i	−0.0711891	+	0.0979834i
$615$	122150.	−	138463.i	0.322957	−	0.366087i
$616$	228792.	−	166227.i	0.602948	−	0.438068i
$617$	−202062.	+	102956.i	−0.530781	+	0.270446i	−0.698775	−	0.715342i	$-0.746271\pi$
$617$	−202062.	+	102956.i	−0.530781	+	0.270446i	0.167994	+	0.985788i	$0.446271\pi$
$618$	−215586.	+	215586.i	−0.564474	+	0.564474i
$619$	548401.	+	178186.i	1.43125	+	0.465043i	0.919159	−	0.393886i	$-0.128870\pi$
$619$	548401.	+	178186.i	1.43125	+	0.465043i	0.512095	+	0.858929i	$0.328870\pi$
$620$	381549.	+	461513.i	0.992583	+	1.20061i
$621$	109794.	+	337911.i	0.284705	+	0.876232i
$622$	−192267.	+	377345.i	−0.496962	+	0.975343i
$623$	486802.	−	77101.8i	1.25423	−	0.198650i
$624$		−	10908.3i		−	0.0280149i
$625$	−363010.	−	144262.i	−0.929306	−	0.369310i
$626$	−993832.			−2.53609
$627$	59722.5	+	377073.i	0.151916	+	0.959158i
$628$	852597.	+	434420.i	2.16184	+	1.10151i
$629$	33138.8	−	10767.5i	0.0837598	−	0.0272152i
$630$	−19732.7	+	16313.7i	−0.0497171	+	0.0411029i
$631$	−196949.	+	606148.i	−0.494647	+	1.52237i	0.322858	+	0.946447i	$0.395356\pi$
$631$	−196949.	+	606148.i	−0.494647	+	1.52237i	−0.817506	+	0.575921i	$0.804644\pi$
$632$	−284521.	−	284521.i	−0.712329	−	0.712329i
$633$	36636.7	+	71903.6i	0.0914343	+	0.179450i
$634$	140059.	+	192774.i	0.348443	+	0.479591i
$635$	−457845.	−	403904.i	−1.13546	−	1.00168i
$636$	489886.	+	355923.i	1.21110	+	0.879918i
$637$	29435.7	+	4662.16i	0.0725431	+	0.0114897i
$638$	−68650.9	+	433445.i	−0.168657	+	1.06486i
$639$	−7210.66	+	9924.62i	−0.0176593	+	0.0243059i
$640$	−652998.	+	145744.i	−1.59423	+	0.355820i
$641$	562789.	−	408890.i	1.36971	−	0.995155i	0.371953	−	0.928251i	$-0.378688\pi$
$641$	562789.	−	408890.i	1.36971	−	0.995155i	0.997759	−	0.0669031i	$-0.0213118\pi$
$642$	45056.4	−	22957.4i	0.109317	−	0.0556996i
$643$	238788.	−	238788.i	0.577552	−	0.577552i	−0.356676	−	0.934228i	$-0.616090\pi$
$643$	238788.	−	238788.i	0.577552	−	0.577552i	0.934228	+	0.356676i	$0.116090\pi$
$644$	−564416.	−	183390.i	−1.36090	−	0.442184i
$645$	−63518.4	+	100018.i	−0.152679	+	0.240414i
$646$	−386811.	−	1.19048e6i	−0.926902	−	2.85271i
$647$	−280177.	+	549878.i	−0.669305	+	1.31358i	0.267441	+	0.963574i	$0.413822\pi$
$647$	−280177.	+	549878.i	−0.669305	+	1.31358i	−0.936746	+	0.350010i	$0.886178\pi$
$648$	−403739.	+	63946.0i	−0.961504	+	0.152287i
$649$			81949.6i			0.194562i
$650$	−177090.	+	925132.i	−0.419148	+	2.18966i
$651$	386558.			0.912122
$652$	−39900.7	−	251923.i	−0.0938611	−	0.592616i
$653$	−249840.	−	127300.i	−0.585915	−	0.298539i	0.135792	−	0.990737i	$-0.456642\pi$
$653$	−249840.	−	127300.i	−0.585915	−	0.298539i	−0.721707	+	0.692199i	$0.756642\pi$
$654$	301050.	−	97816.9i	0.703854	−	0.228696i
$655$	147503.	+	372897.i	0.343810	+	0.869173i
$656$	1378.68	−	4243.13i	0.00320372	−	0.00986004i
$657$	11424.4	+	11424.4i	0.0264669	+	0.0264669i
$658$	−575538.	−	1.12956e6i	−1.32930	−	2.60890i
$659$	339079.	+	466702.i	0.780783	+	1.07466i	0.995195	+	0.0979119i	$0.0312163\pi$
$659$	339079.	+	466702.i	0.780783	+	1.07466i	−0.214412	+	0.976743i	$0.568784\pi$
$660$	−520658.	−	49384.1i	−1.19527	−	0.113370i
$661$	−71123.9	−	51674.5i	−0.162784	−	0.118270i	0.503411	−	0.864047i	$-0.332078\pi$
$661$	−71123.9	−	51674.5i	−0.162784	−	0.118270i	−0.666195	+	0.745777i	$0.732078\pi$
$662$	−989878.	−	156781.i	−2.25874	−	0.357749i
$663$	130225.	−	822211.i	0.296257	−	1.87049i
$664$	28296.7	−	38947.1i	0.0641800	−	0.0883361i
$665$	519662.	+	225075.i	1.17511	+	0.508960i
$666$	1490.37	−	1082.82i	0.00336005	−	0.00244122i
$667$	316308.	−	161167.i	0.710982	−	0.362263i
$668$	−160063.	+	160063.i	−0.358707	+	0.358707i
$669$	−396723.	−	128903.i	−0.886410	−	0.288012i
$670$	−522014.	−	134208.i	−1.16287	−	0.298970i
$671$	72661.6	+	223629.i	0.161384	+	0.496688i
$672$	−192037.	+	376893.i	−0.425251	+	0.834602i
$673$	−431107.	+	68280.7i	−0.951821	+	0.150754i	−0.612987	−	0.790093i	$-0.710032\pi$
$673$	−431107.	+	68280.7i	−0.951821	+	0.150754i	−0.338833	+	0.940846i	$0.610032\pi$
$674$		−	1.46007e6i		−	3.21407i
$675$	464223.	+	14885.1i	1.01887	+	0.0326697i
$676$	663169.			1.45121
$677$	44593.1	+	281549.i	0.0972949	+	0.614296i	0.987364	+	0.158470i	$0.0506560\pi$
$677$	44593.1	+	281549.i	0.0972949	+	0.614296i	−0.890069	+	0.455826i	$0.849344\pi$
$678$	11152.6	+	5682.53i	0.0242614	+	0.0123618i
$679$	647580.	−	210412.i	1.40460	−	0.456384i
$680$	659728.	−	41295.4i	1.42675	−	0.0893066i
$681$	58012.9	−	178545.i	0.125092	−	0.384994i
$682$	−384467.	−	384467.i	−0.826590	−	0.826590i
$683$	84071.5	+	165000.i	0.180222	+	0.353705i	0.963390	−	0.268105i	$-0.0863974\pi$
$683$	84071.5	+	165000.i	0.180222	+	0.353705i	−0.783168	+	0.621810i	$0.786397\pi$
$684$	−24093.4	−	33161.8i	−0.0514976	−	0.0708803i
$685$	−194471.	+	114926.i	−0.414453	+	0.244928i
$686$	632466.	+	459513.i	1.34397	+	0.976449i
$687$	−455849.	−	72199.4i	−0.965846	−	0.152975i
$688$	−447.855	+	2827.65i	−0.000946151	+	0.00597376i
$689$	−360512.	+	496202.i	−0.759419	+	1.04525i
$690$	347515.	+	588044.i	0.729920	+	1.23513i
$691$	−104609.	+	76002.8i	−0.219085	+	0.159175i	−0.691915	−	0.721979i	$-0.743233\pi$
$691$	−104609.	+	76002.8i	−0.219085	+	0.159175i	0.472830	+	0.881154i	$0.343233\pi$
$692$	1.19705e6	−	609927.i	2.49977	−	1.27370i
$693$	10181.7	−	10181.7i	0.0212008	−	0.0212008i
$694$	256648.	+	83390.0i	0.532867	+	0.173139i
$695$	−39588.3	−	632457.i	−0.0819592	−	1.30937i
$696$	131603.	+	405032.i	0.271673	+	0.836125i
$697$	154572.	−	303365.i	0.318175	−	0.624454i
$698$	987571.	−	156416.i	2.02702	−	0.321048i
$699$		−	413767.i		−	0.846841i
$700$	−475880.	+	612694.i	−0.971184	+	1.25040i
$701$	190845.			0.388369			0.194184	−	0.980965i	$-0.437794\pi$
$701$	190845.			0.388369			0.194184	+	0.980965i	$0.437794\pi$
$702$	−175202.	−	1.10618e6i	−0.355521	−	2.24467i
$703$	−36306.2	−	18498.9i	−0.0734632	−	0.0374314i
$704$	573237.	−	186256.i	1.15661	−	0.375807i
$705$	−225032.	+	875283.i	−0.452758	+	1.76104i
$706$	−438393.	+	1.34923e6i	−0.879536	+	2.70693i
$707$	−15712.0	−	15712.0i	−0.0314336	−	0.0314336i
$708$	93660.5	+	183819.i	0.186849	+	0.366711i
$709$	303769.	+	418102.i	0.604298	+	0.831745i	0.996093	−	0.0883076i	$-0.0281458\pi$
$709$	303769.	+	418102.i	0.604298	+	0.831745i	−0.391795	+	0.920052i	$0.628146\pi$
$710$	−238520.	+	550705.i	−0.473160	+	1.09245i
$711$	−16574.4	−	12042.0i	−0.0327868	−	0.0238210i
$712$	−664478.	−	105243.i	−1.31075	−	0.207603i
$713$	−68805.2	+	434419.i	−0.135345	+	0.854535i
$714$	650658.	−	895553.i	1.27631	−	1.75669i
$715$	50020.8	−	527370.i	0.0978450	−	1.03158i
$716$	−365501.	+	265552.i	−0.712955	+	0.517992i
$717$	43411.5	−	22119.3i	0.0844436	−	0.0430261i
$718$	101152.	−	101152.i	0.196213	−	0.196213i
$719$	−693720.	−	225403.i	−1.34192	−	0.436016i	−0.451953	−	0.892042i	$-0.649273\pi$
$719$	−693720.	−	225403.i	−1.34192	−	0.436016i	−0.889967	+	0.456026i	$0.849273\pi$
$720$	410.103	−	162.220i	0.000791094	−	0.000312925i
$721$	−78597.7	−	241899.i	−0.151196	−	0.465333i
$722$	−280959.	+	551413.i	−0.538975	+	1.05780i
$723$	505164.	−	80010.2i	0.966398	−	0.153062i
$724$			739775.i			1.41131i
$725$	−57869.6	−	460447.i	−0.110097	−	0.875998i
$726$	−361801.			−0.686431
$727$	−128605.	−	811981.i	−0.243327	−	1.53630i	−0.742526	−	0.669817i	$-0.766372\pi$
$727$	−128605.	−	811981.i	−0.243327	−	1.53630i	0.499199	−	0.866487i	$-0.333628\pi$
$728$	642527.	+	327384.i	1.21235	+	0.617724i
$729$	−524379.	+	170381.i	−0.986712	+	0.320602i
$730$	667220.	+	423729.i	1.25206	+	0.795138i
$731$	−67513.8	+	207786.i	−0.126345	+	0.388849i
$732$	418573.	+	418573.i	0.781176	+	0.781176i
$733$	−102900.	−	201952.i	−0.191516	−	0.375872i	0.775203	−	0.631713i	$-0.217648\pi$
$733$	−102900.	−	201952.i	−0.191516	−	0.375872i	−0.966719	+	0.255841i	$0.917648\pi$
$734$	881579.	+	1.21339e6i	1.63632	+	2.25221i
$735$	−6154.13	−	27573.3i	−0.0113918	−	0.0510404i
$736$	−389376.	−	282898.i	−0.718808	−	0.522245i
$737$	299394.	+	47419.3i	0.551198	+	0.0873012i
$738$	2815.94	−	17779.2i	0.00517024	−	0.0326436i
$739$	577950.	−	795481.i	1.05828	−	1.45660i	0.176882	−	0.984232i	$-0.443399\pi$
$739$	577950.	−	795481.i	1.05828	−	1.45660i	0.881401	−	0.472369i	$-0.156601\pi$
$740$	36927.9	−	41859.5i	0.0674358	−	0.0764418i
$741$	−787571.	+	572204.i	−1.43434	+	1.04211i
$742$	−726695.	+	370270.i	−1.31991	+	0.672528i
$743$	−373582.	+	373582.i	−0.676720	+	0.676720i	−0.959256	−	0.282537i	$-0.908824\pi$
$743$	−373582.	+	373582.i	−0.676720	+	0.676720i	0.282537	+	0.959256i	$0.408824\pi$
$744$	−501822.	−	163052.i	−0.906575	−	0.294564i
$745$	−287182.	−	347369.i	−0.517422	−	0.625861i
$746$	−47092.1	−	144934.i	−0.0846194	−	0.260432i
$747$	1112.79	−	2183.98i	0.00199422	−	0.00391388i
$748$	−952511.	+	150863.i	−1.70242	+	0.269637i
$749$			42185.9i			0.0751975i
$750$	877254.	−	166476.i	1.55956	−	0.295957i
$751$	1.02681e6			1.82057			0.910287	−	0.413977i	$-0.135861\pi$
$751$	1.02681e6			1.82057			0.910287	+	0.413977i	$0.135861\pi$
$752$	3416.08	+	21568.3i	0.00604077	+	0.0381399i
$753$	150723.	+	76797.3i	0.265822	+	0.135443i
$754$	−1.06426e6	+	345798.i	−1.87199	+	0.608247i
$755$	110239.	−	91138.1i	0.193393	−	0.159884i
$756$	285048.	−	877287.i	0.498740	−	1.53496i
$757$	−410554.	−	410554.i	−0.716439	−	0.716439i	0.251435	−	0.967874i	$-0.419097\pi$
$757$	−410554.	−	410554.i	−0.716439	−	0.716439i	−0.967874	+	0.251435i	$0.919097\pi$
$758$	−334639.	−	656766.i	−0.582423	−	1.14307i
$759$	−225796.	−	310781.i	−0.391951	−	0.539475i
$760$	−579677.	−	511383.i	−1.00360	−	0.885358i
$761$	432286.	+	314074.i	0.746452	+	0.542329i	0.894725	−	0.446617i	$-0.147371\pi$
$761$	432286.	+	314074.i	0.746452	+	0.542329i	−0.148273	+	0.988946i	$0.547371\pi$
$762$	1.37842e6	+	218321.i	2.37396	+	0.375998i
$763$	−41310.0	+	260821.i	−0.0709588	+	0.448016i
$764$	242147.	−	333287.i	0.414851	−	0.570993i
$765$	32848.0	−	7331.39i	0.0561288	−	0.0125275i
$766$	656828.	−	477213.i	1.11942	−	0.813308i
$767$	−186189.	+	94868.1i	−0.316493	+	0.161261i
$768$	422097.	−	422097.i	0.715631	−	0.715631i
$769$	−895744.	−	291045.i	−1.51472	−	0.492161i	−0.570447	−	0.821335i	$-0.693230\pi$
$769$	−895744.	−	291045.i	−1.51472	−	0.492161i	−0.944269	+	0.329174i	$0.893230\pi$
$770$	377636.	−	594640.i	0.636930	−	1.00293i
$771$	−253741.	−	780934.i	−0.426856	−	1.31373i
$772$	−213472.	+	418962.i	−0.358184	+	0.702975i
$773$	−106685.	+	16897.2i	−0.178543	+	0.0282785i	−0.245066	−	0.969506i	$-0.578810\pi$
$773$	−106685.	+	16897.2i	−0.178543	+	0.0282785i	0.0665225	+	0.997785i	$0.478810\pi$
$774$			11550.9i			0.0192812i
$775$	503670.	+	277313.i	0.838577	+	0.461708i
$776$	−929428.			−1.54345
$777$	−5637.02	−	35590.7i	−0.00933700	−	0.0589515i
$778$	668720.	+	340730.i	1.10480	+	0.562926i
$779$	−378669.	+	123037.i	−0.624000	+	0.202750i
$780$	−490533.	−	1.24010e6i	−0.806268	−	2.03830i
$781$	104298.	−	320997.i	0.170992	−	0.526258i
$782$	890621.	+	890621.i	1.45640	+	1.45640i
$783$	250506.	+	491646.i	0.408597	+	0.801916i
$784$	−401.247	−	552.269i	−0.000652799	−	0.000898501i
$785$	914685.	+	86757.4i	1.48434	+	0.140789i
$786$	−741585.	−	538793.i	−1.20037	−	0.872122i
$787$	−297799.	−	47166.8i	−0.480811	−	0.0761529i	−0.0886755	−	0.996061i	$-0.528263\pi$
$787$	−297799.	−	47166.8i	−0.480811	−	0.0761529i	−0.392135	+	0.919908i	$0.628263\pi$
$788$	18223.0	−	115056.i	0.0293473	−	0.185292i
$789$	−356022.	+	490022.i	−0.571903	+	0.787157i
$790$	−919694.	−	398335.i	−1.47363	−	0.638256i
$791$	−8447.81	+	6137.69i	−0.0135018	+	0.00980962i
$792$	−17512.3	+	8922.97i	−0.0279186	+	0.0142252i
$793$	−423969.	+	423969.i	−0.674199	+	0.674199i
$794$	−357442.	−	116140.i	−0.566976	−	0.184222i
$795$	563109.	+	144773.i	0.890960	+	0.229062i
$796$	106114.	+	326587.i	0.167474	+	0.515433i
$797$	162156.	−	318249.i	0.255280	−	0.501015i	−0.727426	−	0.686186i	$-0.759284\pi$
$797$	162156.	−	318249.i	0.255280	−	0.501015i	0.982706	+	0.185170i	$0.0592837\pi$
$798$	−1.27856e6	+	202505.i	−2.00778	+	0.318002i
$799$			1.66648e6i			2.61040i
$800$	−520595.	+	353311.i	−0.813430	+	0.552049i
$801$	−34254.0			−0.0533883
$802$	291929.	+	1.84317e6i	0.453867	+	2.86561i
$803$	−396067.	−	201806.i	−0.614240	−	0.312971i
$804$	725759.	−	235813.i	1.12274	−	0.364801i
$805$	−568718.	+	35598.6i	−0.877617	+	0.0549341i
$806$	428433.	−	1.31858e6i	0.659497	−	2.02972i
$807$	647681.	+	647681.i	0.994521	+	0.994521i
$808$	13769.6	+	27024.4i	0.0210911	+	0.0413937i
$809$	−7769.68	−	10694.0i	−0.0118715	−	0.0163397i	0.803040	−	0.595925i	$-0.203215\pi$
$809$	−7769.68	−	10694.0i	−0.0118715	−	0.0163397i	−0.814911	+	0.579585i	$0.803215\pi$
$810$	−876563.	+	518020.i	−1.33602	+	0.789545i
$811$	−545262.	−	396156.i	−0.829016	−	0.602316i	0.0902645	−	0.995918i	$-0.471229\pi$
$811$	−545262.	−	396156.i	−0.829016	−	0.602316i	−0.919281	+	0.393602i	$0.871229\pi$
$812$	−910308.	−	144179.i	−1.38063	−	0.218670i
$813$	104241.	−	658153.i	0.157710	−	0.995740i
$814$	−29791.6	+	41004.7i	−0.0449620	+	0.0618849i
$815$	−124601.	−	210842.i	−0.187588	−	0.317425i
$816$	−15426.2	+	11207.8i	−0.0231675	+	0.0168322i
$817$	227646.	−	115991.i	0.341048	−	0.173773i
$818$	−228392.	+	228392.i	−0.341330	+	0.341330i
$819$	34919.5	+	11346.0i	0.0520595	+	0.0169151i
$820$	−34074.7	−	544372.i	−0.0506763	−	0.809596i
$821$	245223.	+	754720.i	0.363811	+	1.11969i	0.950722	+	0.310044i	$0.100344\pi$
$821$	245223.	+	754720.i	0.363811	+	1.11969i	−0.586912	+	0.809651i	$0.699656\pi$
$822$	234421.	−	460076.i	0.346938	−	0.680905i
$823$	324949.	−	51466.9i	0.479751	−	0.0759850i	0.0881245	−	0.996109i	$-0.471913\pi$
$823$	324949.	−	51466.9i	0.479751	−	0.0759850i	0.391626	+	0.920124i	$0.371913\pi$
$824$			347181.i			0.511330i
$825$	−482319.	+	139793.i	−0.708642	+	0.205389i
$826$	−277871.			−0.407271
$827$	−42295.9	−	267046.i	−0.0618425	−	0.390458i	−0.999123	−	0.0418810i	$-0.986665\pi$
$827$	−42295.9	−	267046.i	−0.0618425	−	0.390458i	0.937280	−	0.348577i	$-0.113335\pi$
$828$	36749.6	+	18724.9i	0.0536034	+	0.0273123i
$829$	749067.	−	243386.i	1.08996	−	0.354150i	0.291730	−	0.956501i	$-0.405769\pi$
$829$	749067.	−	243386.i	1.08996	−	0.354150i	0.798232	+	0.602351i	$0.205769\pi$
$830$	29858.0	−	116136.i	0.0433416	−	0.168581i
$831$	−98659.9	+	303644.i	−0.142869	+	0.439706i
$832$	1.08677e6	+	1.08677e6i	1.56997	+	1.56997i
$833$	−23650.7	−	46417.2i	−0.0340843	−	0.0668943i
$834$	851425.	+	1.17189e6i	1.22409	+	1.68482i
$835$	−86383.9	+	199447.i	−0.123897	+	0.286058i
$836$	912381.	+	662884.i	1.30546	+	0.948473i
$837$	−675230.	−	106946.i	−0.963831	−	0.152656i
$838$	261355.	−	1.65013e6i	0.372172	−	2.34980i
$839$	−178026.	+	245031.i	−0.252906	+	0.348095i	−0.916526	−	0.399974i	$-0.869019\pi$
$839$	−178026.	+	245031.i	−0.252906	+	0.348095i	0.663620	+	0.748069i	$0.269019\pi$
$840$	64549.2	−	680543.i	0.0914813	−	0.964488i
$841$	−126174.	+	91670.8i	−0.178393	+	0.129610i
$842$	1.36400e6	−	694991.i	1.92393	−	0.980291i
$843$	−845874.	+	845874.i	−1.19028	+	1.19028i
$844$	226720.	+	73665.7i	0.318277	+	0.103414i
$845$	592122.	−	234219.i	0.829273	−	0.328027i
$846$	27226.3	+	83794.0i	0.0380407	+	0.117077i
$847$	137028.	−	268932.i	0.191004	−	0.374865i
$848$	13875.8	−	2197.72i	0.0192960	−	0.00305619i
$849$			260252.i			0.361060i
$850$	1.49024e6	−	700094.i	2.06262	−	0.968989i
$851$	41000.7			0.0566150
$852$	−132920.	−	839224.i	−0.183110	−	1.15611i
$853$	277365.	+	141324.i	0.381200	+	0.194231i	0.634082	−	0.773266i	$-0.281378\pi$
$853$	277365.	+	141324.i	0.381200	+	0.194231i	−0.252881	+	0.967497i	$0.581378\pi$
$854$	−758274.	+	246378.i	−1.03971	+	0.337821i
$855$	−33224.4	−	21099.7i	−0.0454490	−	0.0288632i
$856$	17794.2	−	54764.8i	0.0242845	−	0.0747401i
$857$	−61002.2	−	61002.2i	−0.0830585	−	0.0830585i	0.664357	−	0.747415i	$-0.268705\pi$
$857$	−61002.2	−	61002.2i	−0.0830585	−	0.0830585i	−0.747415	+	0.664357i	$0.768705\pi$
$858$	549737.	+	1.07892e6i	0.746759	+	1.46560i
$859$	−386837.	−	532435.i	−0.524253	−	0.721573i	0.461988	−	0.886886i	$-0.347136\pi$
$859$	−386837.	−	532435.i	−0.524253	−	0.721573i	−0.986241	+	0.165314i	$0.947136\pi$
$860$	76241.6	+	341597.i	0.103085	+	0.461867i
$861$	−284858.	−	206962.i	−0.384258	−	0.279179i
$862$	1.56390e6	+	247698.i	2.10472	+	0.333355i
$863$	38542.9	−	243350.i	0.0517515	−	0.326746i	−0.948207	−	0.317653i	$-0.897105\pi$
$863$	38542.9	−	243350.i	0.0517515	−	0.326746i	0.999959	−	0.00909346i	$-0.00289458\pi$
$864$	439716.	−	605217.i	0.589040	−	0.810744i
$865$	853390.	−	967359.i	1.14055	−	1.29287i
$866$	−66270.3	+	48148.2i	−0.0883656	+	0.0642014i
$867$	−640626.	+	326415.i	−0.852248	+	0.434242i
$868$	807446.	−	807446.i	1.07170	−	1.07170i
$869$	536075.	+	174181.i	0.709881	+	0.230654i
$870$	675914.	+	817570.i	0.893003	+	1.08016i
$871$	238854.	+	735116.i	0.314844	+	0.968991i
$872$	163643.	−	321168.i	0.215211	−	0.422376i
$873$	−46739.7	+	7402.84i	−0.0613278	+	0.00971337i
$874$		−	1.47291e6i		−	1.92821i
$875$	−208505.	+	715126.i	−0.272334	+	0.934042i
$876$	−1.11906e6			−1.45829
$877$	−83816.8	−	529199.i	−0.108976	−	0.688049i	−0.980326	−	0.197386i	$-0.936755\pi$
$877$	−83816.8	−	529199.i	−0.108976	−	0.688049i	0.871350	−	0.490663i	$-0.163245\pi$
$878$	−1.70548e6	−	868986.i	−2.21237	−	1.12726i
$879$	−1.21207e6	+	393826.i	−1.56874	+	0.509714i
$880$	−9351.75	+	7731.42i	−0.0120761	+	0.00998376i
$881$	−161543.	+	497177.i	−0.208130	+	0.640559i	0.791440	+	0.611247i	$0.209332\pi$
$881$	−161543.	+	497177.i	−0.208130	+	0.640559i	−0.999570	+	0.0293121i	$0.990668\pi$
$882$	−1947.55	−	1947.55i	−0.00250353	−	0.00250353i
$883$	−2616.46	−	5135.09i	−0.00335577	−	0.00658608i	0.889323	−	0.457280i	$-0.151176\pi$
$883$	−2616.46	−	5135.09i	−0.00335577	−	0.00658608i	−0.892678	+	0.450694i	$0.851176\pi$
$884$	−1.44542e6	−	1.98946e6i	−1.84966	−	2.54583i
$885$	148548.	+	131047.i	0.189662	+	0.167317i
$886$	−951579.	−	691363.i	−1.21221	−	0.880722i
$887$	−1.11209e6	−	176138.i	−1.41349	−	0.223875i	−0.597466	−	0.801894i	$-0.703826\pi$
$887$	−1.11209e6	−	176138.i	−1.41349	−	0.223875i	−0.816023	+	0.578020i	$0.803826\pi$
$888$	−7694.45	+	48580.8i	−0.00975779	+	0.0616083i
$889$	−684342.	+	941915.i	−0.865903	+	1.19181i
$890$	−1.63550e6	+	365031.i	−2.06477	+	0.460839i
$891$	463263.	−	336581.i	0.583543	−	0.423968i
$892$	−1.09793e6	+	559424.i	−1.37989	+	0.703090i
$893$	1.37801e6	−	1.37801e6i	1.72803	−	1.72803i
$894$	979829.	+	318366.i	1.22596	+	0.398338i
$895$	−232555.	+	366190.i	−0.290322	+	0.457152i
$896$	394266.	+	1.21343e6i	0.491104	+	1.51146i
$897$	444703.	−	872780.i	0.552695	−	1.08473i
$898$	928723.	−	147095.i	1.15168	−	0.182409i
$899$			683069.i			0.845172i
$900$	39327.3	−	36883.6i	0.0485522	−	0.0455353i
$901$	1.07212e6			1.32067
$902$	77475.1	+	489158.i	0.0952246	+	0.601224i
$903$	201315.	+	102575.i	0.246889	+	0.125796i
$904$	13555.7	−	4404.50i	0.0165876	−	0.00538964i
$905$	261275.	+	660520.i	0.319007	+	0.806472i
$906$	−101034.	+	310952.i	−0.123087	+	0.378824i
$907$	−539135.	−	539135.i	−0.655365	−	0.655365i	0.298915	−	0.954280i	$-0.403375\pi$
$907$	−539135.	−	539135.i	−0.655365	−	0.655365i	−0.954280	+	0.298915i	$0.903375\pi$
$908$	−251769.	−	494125.i	−0.305373	−	0.599328i
$909$	907.706	+	1249.35i	0.00109854	+	0.00151202i
$910$	1.78819e6	+	169609.i	2.15938	+	0.204817i
$911$	−118971.	−	86437.3i	−0.143352	−	0.104151i	0.513798	−	0.857911i	$-0.328238\pi$
$911$	−118971.	−	86437.3i	−0.143352	−	0.104151i	−0.657150	+	0.753760i	$0.728238\pi$
$912$	22023.7	+	3488.21i	0.0264789	+	0.00419385i
$913$	−10549.7	+	66608.0i	−0.0126560	+	0.0799069i
$914$	−431384.	+	593750.i	−0.516383	+	0.710740i
$915$	521562.	+	225897.i	0.622965	+	0.269817i
$916$	−1.10299e6	+	801370.i	−1.31456	+	0.955086i
$917$	681359.	−	347170.i	0.810284	−	0.412860i
$918$	−1.38432e6	+	1.38432e6i	−1.64267	+	1.64267i
$919$	−220057.	−	71501.0i	−0.260558	−	0.0846605i	0.175825	−	0.984421i	$-0.443741\pi$
$919$	−220057.	−	71501.0i	−0.260558	−	0.0846605i	−0.436383	+	0.899761i	$0.643741\pi$
$920$	753313.	+	193674.i	0.890020	+	0.228821i
$921$	−19181.1	−	59033.2i	−0.0226128	−	0.0695949i
$922$	−708868.	+	1.39123e6i	−0.833880	+	1.63658i
$923$	850044.	−	134634.i	0.997787	−	0.158034i
$924$			997324.i			1.16813i
$925$	18187.6	−	50417.2i	0.0212566	−	0.0589244i
$926$	−497508.			−0.580201
$927$	2765.28	+	17459.3i	0.00321795	+	0.0203173i
$928$	−665990.	−	339339.i	−0.773342	−	0.394038i
$929$	1.11968e6	−	363807.i	1.29737	−	0.421541i	0.422704	−	0.906268i	$-0.361081\pi$
$929$	1.11968e6	−	363807.i	1.29737	−	0.421541i	0.874666	+	0.484727i	$0.161081\pi$
$930$	−1.31172e6	+	82106.5i	−1.51661	+	0.0949318i
$931$	−18825.6	+	57939.3i	−0.0217195	+	0.0668457i
$932$	−864280.	−	864280.i	−0.994999	−	0.994999i
$933$	−261374.	−	512976.i	−0.300262	−	0.589296i
$934$	322652.	+	444093.i	0.369863	+	0.509073i
$935$	−797183.	+	471110.i	−0.911874	+	0.538889i
$936$	−40545.9	−	29458.3i	−0.0462802	−	0.0336245i
$937$	149515.	+	23680.9i	0.170297	+	0.0269723i	0.241000	−	0.970525i	$-0.422524\pi$
$937$	149515.	+	23680.9i	0.170297	+	0.0269723i	−0.0707037	+	0.997497i	$0.522524\pi$
$938$	−160788.	+	1.01517e6i	−0.182746	+	1.15381i
$939$	794128.	−	1.09302e6i	0.900657	−	1.23965i
$940$	1.35825e6	+	2.29834e6i	1.53718	+	2.60111i
$941$	−174454.	+	126748.i	−0.197016	+	0.143141i	−0.681920	−	0.731427i	$-0.738855\pi$
$941$	−174454.	+	126748.i	−0.197016	+	0.143141i	0.484904	+	0.874568i	$0.338855\pi$
$942$	−1.87131e6	+	953478.i	−2.10884	+	1.07451i
$943$	283289.	−	283289.i	0.318571	−	0.318571i
$944$	4552.16	+	1479.09i	0.00510827	+	0.00165978i
$945$	−55332.0	−	883974.i	−0.0619602	−	0.989865i
$946$	−98205.8	−	302246.i	−0.109737	−	0.337737i
$947$	409631.	−	803946.i	0.456765	−	0.896452i	−0.541673	−	0.840589i	$-0.682209\pi$
$947$	409631.	−	803946.i	0.456765	−	0.896452i	0.998438	−	0.0558630i	$-0.0177910\pi$
$948$	1.40153e6	−	221980.i	1.55950	−	0.247001i
$949$		−	1.13348e6i		−	1.25858i
$950$	−1.81119e6	−	653374.i	−2.00686	−	0.723961i
$951$	−323930.			−0.358170
$952$	−197190.	−	1.24501e6i	−0.217577	−	1.37372i
$953$	−974762.	−	496666.i	−1.07328	−	0.546863i	−0.174228	−	0.984705i	$-0.555743\pi$
$953$	−974762.	−	496666.i	−1.07328	−	0.546863i	−0.899052	+	0.437842i	$0.855743\pi$
$954$	53908.4	−	17515.9i	0.0592325	−	0.0192458i
$955$	98494.2	−	383102.i	0.107995	−	0.420057i
$956$	44475.4	−	136881.i	0.0486636	−	0.149771i
$957$	−421850.	−	421850.i	−0.460610	−	0.460610i
$958$	102186.	+	200551.i	0.111342	+	0.218521i
$959$	253197.	+	348496.i	0.275310	+	0.378932i
$960$	579050.	−	1.33694e6i	0.628310	−	1.45067i
$961$	62472.6	+	45389.0i	0.0676461	+	0.0491477i
$962$	−127650.	−	20217.8i	−0.137934	−	0.0218466i
$963$	458.647	−	2895.78i	0.000494568	−	0.00312258i
$964$	888065.	−	1.22232e6i	0.955632	−	1.31532i
$965$	−42632.2	+	449472.i	−0.0457808	+	0.482667i
$966$	1.05378e6	−	765619.i	1.12927	−	0.820462i
$967$	−893033.	+	455023.i	−0.955025	+	0.486609i	−0.860801	−	0.508942i	$-0.830037\pi$
$967$	−893033.	+	455023.i	−0.955025	+	0.486609i	−0.0942237	+	0.995551i	$0.530037\pi$
$968$	−291323.	+	291323.i	−0.310902	+	0.310902i
$969$	1.61838e6	+	525845.i	1.72359	+	0.560028i
$970$	−2.15276e6	+	851545.i	−2.28798	+	0.905032i
$971$	−239734.	−	737826.i	−0.254268	−	0.782557i	−0.993973	−	0.109625i	$-0.965035\pi$
$971$	−239734.	−	737826.i	−0.254268	−	0.782557i	0.739705	−	0.672931i	$-0.234965\pi$
$972$	−57065.4	+	111997.i	−0.0604005	+	0.118543i
$973$	−1.19355e6	+	189039.i	−1.26071	+	0.199676i
$974$		−	1.59244e6i		−	1.67859i
$975$	−875962.	−	933998.i	−0.921459	−	0.982509i
$976$	13733.7			0.0144174
$977$	268763.	+	1.69690e6i	0.281566	+	1.77774i	0.571412	+	0.820664i	$0.306396\pi$
$977$	268763.	+	1.69690e6i	0.281566	+	1.77774i	−0.289846	+	0.957073i	$0.593604\pi$
$978$	498805.	+	254154.i	0.521498	+	0.265717i
$979$	896305.	−	291227.i	0.935170	−	0.303855i
$980$	−70450.1	−	44740.5i	−0.0733549	−	0.0465853i
$981$	5671.32	−	17454.5i	0.00589313	−	0.0181372i
$982$	−201090.	−	201090.i	−0.208530	−	0.208530i
$983$	161921.	+	317788.i	0.167570	+	0.328875i	0.959487	−	0.281755i	$-0.0909164\pi$
$983$	161921.	+	317788.i	0.167570	+	0.328875i	−0.791916	+	0.610630i	$0.790916\pi$
$984$	282500.	+	388827.i	0.291761	+	0.401575i
$985$	−24364.8	−	109166.i	−0.0251126	−	0.112516i
$986$	1.58249e6	+	1.14975e6i	1.62775	+	1.18263i
$987$	1.70218e6	+	269599.i	1.74732	+	0.276748i
$988$	−449861.	+	2.84031e6i	−0.460855	+	2.90972i
$989$	−151108.	+	207983.i	−0.154489	+	0.212635i
$990$	−32387.2	+	36712.4i	−0.0330448	+	0.0374578i
$991$	208986.	−	151837.i	0.212799	−	0.154608i	−0.476280	−	0.879294i	$-0.658015\pi$
$991$	208986.	−	151837.i	0.212799	−	0.154608i	0.689079	+	0.724686i	$0.258015\pi$
$992$	825140.	−	420430.i	0.838502	−	0.427238i
$993$	963398.	−	963398.i	0.977028	−	0.977028i
$994$	1.08842e6	+	353650.i	1.10160	+	0.357933i
$995$	210090.	+	254121.i	0.212207	+	0.256681i
$996$	52462.8	+	161464.i	0.0528851	+	0.162764i
$997$	−481562.	+	945120.i	−0.484465	+	0.950816i	0.511346	+	0.859375i	$0.329147\pi$
$997$	−481562.	+	945120.i	−0.484465	+	0.950816i	−0.995811	+	0.0914408i	$0.970853\pi$
$998$	716508.	−	113484.i	0.719383	−	0.113939i
$999$			63728.5i			0.0638561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.5.f.a.12.8	✓	72
5.2	odd	4		125.5.f.a.43.2		72
5.3	odd	4		125.5.f.b.43.8		72
5.4	even	2		125.5.f.c.82.2		72
25.2	odd	20		125.5.f.c.93.2		72
25.11	even	5		125.5.f.b.32.8		72
25.14	even	10		125.5.f.a.32.2		72
25.23	odd	20	inner	25.5.f.a.23.8	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.5.f.a.12.8	✓	72	1.1	even	1	trivial
25.5.f.a.23.8	yes	72	25.23	odd	20	inner
125.5.f.a.32.2		72	25.14	even	10
125.5.f.a.43.2		72	5.2	odd	4
125.5.f.b.32.8		72	25.11	even	5
125.5.f.b.43.8		72	5.3	odd	4
125.5.f.c.82.2		72	5.4	even	2
125.5.f.c.93.2		72	25.2	odd	20

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)

\(f(q)\)	\(=\)	\(q+(1.01425 + 6.40375i) q^{2} +(-7.85334 - 4.00148i) q^{3} +(-24.7624 + 8.04580i) q^{4} +(-19.2679 + 15.9295i) q^{5} +(17.6592 - 54.3493i) q^{6} +(33.7104 + 33.7104i) q^{7} +(-29.5430 - 57.9814i) q^{8} +(-1.94750 - 2.68050i) q^{9} +O(q^{10})\)	\(q+(1.01425 + 6.40375i) q^{2} +(-7.85334 - 4.00148i) q^{3} +(-24.7624 + 8.04580i) q^{4} +(-19.2679 + 15.9295i) q^{5} +(17.6592 - 54.3493i) q^{6} +(33.7104 + 33.7104i) q^{7} +(-29.5430 - 57.9814i) q^{8} +(-1.94750 - 2.68050i) q^{9} +(-121.551 - 107.230i) q^{10} +(73.7487 + 53.5816i) q^{11} +(226.663 + 35.8998i) q^{12} +(-36.3627 + 229.585i) q^{13} +(-181.682 + 250.064i) q^{14} +(215.059 - 47.9993i) q^{15} +(4.30744 - 3.12954i) q^{16} +(362.032 - 184.465i) q^{17} +(15.1900 - 15.1900i) q^{18} +(-451.899 - 146.831i) q^{19} +(348.955 - 549.478i) q^{20} +(-129.848 - 399.631i) q^{21} +(-268.323 + 526.614i) q^{22} +(472.222 - 74.7927i) q^{23} +573.563i q^{24} +(117.505 - 613.855i) q^{25} -1507.09 q^{26} +(116.252 + 733.989i) q^{27} +(-1105.98 - 563.525i) q^{28} +(706.169 - 229.448i) q^{29} +(525.500 + 1328.50i) q^{30} +(-284.279 + 874.921i) q^{31} +(-711.819 - 711.819i) q^{32} +(-364.768 - 715.898i) q^{33} +(1548.46 + 2131.27i) q^{34} +(-1186.52 - 112.541i) q^{35} +(69.7915 + 50.7065i) q^{36} +(84.7001 + 13.4152i) q^{37} +(481.928 - 3042.77i) q^{38} +(1204.25 - 1657.50i) q^{39} +(1492.84 + 646.576i) q^{40} +(677.916 - 492.535i) q^{41} +(2427.44 - 1236.84i) q^{42} +(-380.214 + 380.214i) q^{43} +(-2257.30 - 733.442i) q^{44} +(80.2231 + 20.6251i) q^{45} +(957.908 + 2948.14i) q^{46} +(-1862.00 + 3654.39i) q^{47} +(-46.3506 + 7.34121i) q^{48} -128.213i q^{49} +(4050.15 + 129.867i) q^{50} -3581.29 q^{51} +(-946.766 - 5977.65i) q^{52} +(2351.03 + 1197.91i) q^{53} +(-4582.37 + 1488.90i) q^{54} +(-2274.51 + 142.372i) q^{55} +(958.670 - 2950.48i) q^{56} +(2961.38 + 2961.38i) q^{57} +(2185.56 + 4289.41i) q^{58} +(528.407 + 727.290i) q^{59} +(-4939.18 + 2918.90i) q^{60} +(2086.81 + 1516.16i) q^{61} +(-5891.11 - 933.059i) q^{62} +(24.7098 - 156.012i) q^{63} +(3886.42 - 5349.20i) q^{64} +(-2956.53 - 5002.86i) q^{65} +(4214.46 - 3061.99i) q^{66} +(2962.83 - 1509.64i) q^{67} +(-7480.63 + 7480.63i) q^{68} +(-4007.80 - 1302.21i) q^{69} +(-482.749 - 7712.32i) q^{70} +(-1144.14 - 3521.31i) q^{71} +(-97.8842 + 192.109i) q^{72} +(-4816.28 + 762.823i) q^{73} +556.005i q^{74} +(-3379.13 + 4350.62i) q^{75} +12371.5 q^{76} +(679.843 + 4292.36i) q^{77} +(11835.7 + 6030.57i) q^{78} +(5880.69 - 1910.75i) q^{79} +(-33.1435 + 128.915i) q^{80} +(1941.14 - 5974.20i) q^{81} +(3841.65 + 3841.65i) q^{82} +(335.858 + 659.159i) q^{83} +(6430.70 + 8851.10i) q^{84} +(-4037.19 + 9321.23i) q^{85} +(-2820.43 - 2049.16i) q^{86} +(-6463.92 - 1023.78i) q^{87} +(927.976 - 5859.01i) q^{88} +(6076.75 - 8363.93i) q^{89} +(-50.7111 + 534.648i) q^{90} +(-8965.21 + 6513.61i) q^{91} +(-11091.6 + 5651.45i) q^{92} +(5733.51 - 5733.51i) q^{93} +(-25290.3 - 8217.33i) q^{94} +(11046.1 - 4369.38i) q^{95} +(2741.83 + 8438.48i) q^{96} +(6484.17 - 12725.9i) q^{97} +(821.043 - 130.040i) q^{98} -302.033i 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

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