LMFDB - Embedded newform 25.5.f.a.22.1

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			22.1
Character	$\chi$	$=$	25.22
Dual form			25.5.f.a.8.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.66808 + 3.39756i) q^{2} +(11.5382 - 1.82747i) q^{3} +(23.5154 - 32.3661i) q^{4} +(-4.94350 + 24.5064i) q^{5} +(-70.7286 + 51.3874i) q^{6} +(32.8567 + 32.8567i) q^{7} +(-28.1051 + 177.449i) q^{8} +(52.7545 - 17.1410i) q^{9} +O(q^{10})$	\(q+(-6.66808 + 3.39756i) q^{2} +(11.5382 - 1.82747i) q^{3} +(23.5154 - 32.3661i) q^{4} +(-4.94350 + 24.5064i) q^{5} +(-70.7286 + 51.3874i) q^{6} +(32.8567 + 32.8567i) q^{7} +(-28.1051 + 177.449i) q^{8} +(52.7545 - 17.1410i) q^{9} +(-50.2981 - 180.206i) q^{10} +(-14.0800 + 43.3336i) q^{11} +(212.177 - 416.420i) q^{12} +(146.690 + 74.7423i) q^{13} +(-330.724 - 107.459i) q^{14} +(-12.2544 + 291.793i) q^{15} +(-217.681 - 669.953i) q^{16} +(226.533 + 35.8793i) q^{17} +(-293.534 + 293.534i) q^{18} +(-212.222 - 292.098i) q^{19} +(676.928 + 736.278i) q^{20} +(439.151 + 319.062i) q^{21} +(-53.3423 - 336.790i) q^{22} +(-234.973 - 461.160i) q^{23} +2098.80i q^{24} +(-576.124 - 242.294i) q^{25} -1232.08 q^{26} +(-265.742 + 135.402i) q^{27} +(1836.08 - 290.807i) q^{28} +(666.506 - 917.366i) q^{29} +(-909.670 - 1987.33i) q^{30} +(589.653 - 428.408i) q^{31} +(1695.09 + 1695.09i) q^{32} +(-83.2662 + 525.722i) q^{33} +(-1632.44 + 530.412i) q^{34} +(-967.625 + 642.771i) q^{35} +(685.754 - 2110.53i) q^{36} +(-211.836 + 415.751i) q^{37} +(2407.53 + 1226.70i) q^{38} +(1829.12 + 594.319i) q^{39} +(-4209.69 - 1565.97i) q^{40} +(-52.7851 - 162.456i) q^{41} +(-4012.33 - 635.490i) q^{42} +(-499.789 + 499.789i) q^{43} +(1071.45 + 1474.72i) q^{44} +(159.271 + 1377.56i) q^{45} +(3133.64 + 2276.72i) q^{46} +(-255.065 - 1610.42i) q^{47} +(-3735.96 - 7332.24i) q^{48} -241.877i q^{49} +(4664.85 - 341.774i) q^{50} +2679.35 q^{51} +(5868.58 - 2990.19i) q^{52} +(-3644.13 + 577.174i) q^{53} +(1311.95 - 1805.75i) q^{54} +(-992.346 - 559.268i) q^{55} +(-6753.82 + 4906.94i) q^{56} +(-2982.45 - 2982.45i) q^{57} +(-1327.51 + 8381.56i) q^{58} +(-829.044 + 269.373i) q^{59} +(9156.04 + 7258.25i) q^{60} +(664.208 - 2044.22i) q^{61} +(-2476.32 + 4860.04i) q^{62} +(2296.53 + 1170.14i) q^{63} +(-6342.93 - 2060.94i) q^{64} +(-2556.82 + 3225.35i) q^{65} +(-1230.95 - 3788.46i) q^{66} +(3106.69 + 492.052i) q^{67} +(6488.27 - 6488.27i) q^{68} +(-3553.92 - 4891.55i) q^{69} +(4268.35 - 7573.61i) q^{70} +(4257.89 + 3093.54i) q^{71} +(1558.97 + 9842.96i) q^{72} +(4230.54 + 8302.90i) q^{73} -3491.99i q^{74} +(-7090.21 - 1742.79i) q^{75} -14444.6 q^{76} +(-1886.42 + 961.179i) q^{77} +(-14216.0 + 2251.59i) q^{78} +(3270.95 - 4502.08i) q^{79} +(17494.2 - 2022.66i) q^{80} +(-6453.67 + 4688.86i) q^{81} +(903.929 + 903.929i) q^{82} +(2086.10 - 13171.1i) q^{83} +(20653.6 - 6710.76i) q^{84} +(-1999.14 + 5374.13i) q^{85} +(1634.57 - 5030.70i) q^{86} +(6013.81 - 11802.8i) q^{87} +(-7293.78 - 3716.37i) q^{88} +(-11038.2 - 3586.52i) q^{89} +(-5742.36 - 8644.53i) q^{90} +(2363.96 + 7275.53i) q^{91} +(-20451.4 - 3239.19i) q^{92} +(6020.63 - 6020.63i) q^{93} +(7172.29 + 9871.81i) q^{94} +(8207.38 - 3756.80i) q^{95} +(22656.0 + 16460.6i) q^{96} +(666.885 + 4210.55i) q^{97} +(821.793 + 1612.86i) q^{98} +2527.39i 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 $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{20}\right)$

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 $

$2$	−6.66808	+	3.39756i	−1.66702	+	0.849389i	−0.673068	+	0.739581i	$0.735024\pi$
$2$	−6.66808	+	3.39756i	−1.66702	+	0.849389i	−0.993953	+	0.109809i	$0.964976\pi$
$3$	11.5382	−	1.82747i	1.28202	−	0.203052i	0.521997	−	0.852947i	$-0.325187\pi$
$3$	11.5382	−	1.82747i	1.28202	−	0.203052i	0.760024	+	0.649895i	$0.225187\pi$
$4$	23.5154	−	32.3661i	1.46971	−	2.02288i
$5$	−4.94350	+	24.5064i	−0.197740	+	0.980255i
$5$	−4.94350	+	24.5064i	−0.197740	+	0.980255i
$6$	−70.7286	+	51.3874i	−1.96468	+	1.42743i
$7$	32.8567	+	32.8567i	0.670544	+	0.670544i	0.957842	−	0.287297i	$-0.0927567\pi$
$7$	32.8567	+	32.8567i	0.670544	+	0.670544i	−0.287297	+	0.957842i	$0.592757\pi$
$8$	−28.1051	+	177.449i	−0.439143	+	2.77264i
$9$	52.7545	−	17.1410i	0.651290	−	0.211617i
$10$	−50.2981	−	180.206i	−0.502981	−	1.80206i
$11$	−14.0800	+	43.3336i	−0.116363	+	0.358129i	−0.992229	−	0.124426i	$-0.960291\pi$
$11$	−14.0800	+	43.3336i	−0.116363	+	0.358129i	0.875866	+	0.482555i	$0.160291\pi$
$12$	212.177	−	416.420i	1.47345	−	2.89180i
$13$	146.690	+	74.7423i	0.867988	+	0.442262i	0.830489	−	0.557035i	$-0.188061\pi$
$13$	146.690	+	74.7423i	0.867988	+	0.442262i	0.0374987	+	0.999297i	$0.488061\pi$
$14$	−330.724	−	107.459i	−1.68736	−	0.548258i
$15$	−12.2544	+	291.793i	−0.0544640	+	1.29686i
$16$	−217.681	−	669.953i	−0.850317	−	2.61701i
$17$	226.533	+	35.8793i	0.783851	+	0.124150i	0.535517	−	0.844525i	$-0.320117\pi$
$17$	226.533	+	35.8793i	0.783851	+	0.124150i	0.248334	+	0.968674i	$0.420117\pi$
$18$	−293.534	+	293.534i	−0.905968	+	0.905968i
$19$	−212.222	−	292.098i	−0.587872	−	0.809136i	0.406659	−	0.913580i	$-0.366694\pi$
$19$	−212.222	−	292.098i	−0.587872	−	0.809136i	−0.994531	+	0.104444i	$0.966694\pi$
$20$	676.928	+	736.278i	1.69232	+	1.84069i
$21$	439.151	+	319.062i	0.995807	+	0.723496i
$22$	−53.3423	−	336.790i	−0.110211	−	0.695847i
$23$	−234.973	−	461.160i	−0.444183	−	0.871759i	−0.999203	−	0.0399213i	$-0.987289\pi$
$23$	−234.973	−	461.160i	−0.444183	−	0.871759i	0.555020	−	0.831837i	$-0.312711\pi$
$24$			2098.80i			3.64375i
$25$	−576.124	−	242.294i	−0.921798	−	0.387671i
$26$	−1232.08			−1.82261
$27$	−265.742	+	135.402i	−0.364530	+	0.185737i
$28$	1836.08	−	290.807i	2.34194	−	0.370927i
$29$	666.506	−	917.366i	0.792516	−	1.09080i	−0.201275	−	0.979535i	$-0.564508\pi$
$29$	666.506	−	917.366i	0.792516	−	1.09080i	0.993790	−	0.111269i	$-0.0354916\pi$
$30$	−909.670	−	1987.33i	−1.01074	−	2.20815i
$31$	589.653	−	428.408i	0.613583	−	0.445794i	−0.237091	−	0.971487i	$-0.576194\pi$
$31$	589.653	−	428.408i	0.613583	−	0.445794i	0.850674	+	0.525693i	$0.176194\pi$
$32$	1695.09	+	1695.09i	1.65536	+	1.65536i
$33$	−83.2662	+	525.722i	−0.0764612	+	0.482757i
$34$	−1632.44	+	530.412i	−1.41215	+	0.458834i
$35$	−967.625	+	642.771i	−0.789898	+	0.524711i
$36$	685.754	−	2110.53i	0.529131	−	1.62850i
$37$	−211.836	+	415.751i	−0.154738	+	0.303690i	−0.955341	−	0.295505i	$-0.904512\pi$
$37$	−211.836	+	415.751i	−0.154738	+	0.303690i	0.800604	+	0.599194i	$0.204512\pi$
$38$	2407.53	+	1226.70i	1.66727	+	0.849515i
$39$	1829.12	+	594.319i	1.20258	+	0.390742i
$40$	−4209.69	−	1565.97i	−2.63105	−	0.978733i
$41$	−52.7851	−	162.456i	−0.0314010	−	0.0966425i	0.934128	−	0.356939i	$-0.116180\pi$
$41$	−52.7851	−	162.456i	−0.0314010	−	0.0966425i	−0.965529	+	0.260297i	$0.916180\pi$
$42$	−4012.33	−	635.490i	−2.27456	−	0.360255i
$43$	−499.789	+	499.789i	−0.270302	+	0.270302i	−0.829222	−	0.558919i	$-0.811216\pi$
$43$	−499.789	+	499.789i	−0.270302	+	0.270302i	0.558919	+	0.829222i	$0.311216\pi$
$44$	1071.45	+	1474.72i	0.553433	+	0.761735i
$45$	159.271	+	1377.56i	0.0786523	+	0.680275i
$46$	3133.64	+	2276.72i	1.48093	+	1.07595i
$47$	−255.065	−	1610.42i	−0.115466	−	0.729027i	−0.975697	−	0.219122i	$-0.929681\pi$
$47$	−255.065	−	1610.42i	−0.115466	−	0.729027i	0.860231	−	0.509905i	$-0.170319\pi$
$48$	−3735.96	−	7332.24i	−1.62151	−	3.18240i
$49$		−	241.877i		−	0.100740i
$50$	4664.85	−	341.774i	1.86594	−	0.136710i
$51$	2679.35			1.03012
$52$	5868.58	−	2990.19i	2.17033	−	1.10584i
$53$	−3644.13	+	577.174i	−1.29731	+	0.205473i	−0.766623	−	0.642097i	$-0.778065\pi$
$53$	−3644.13	+	577.174i	−1.29731	+	0.205473i	−0.530683	+	0.847570i	$0.678065\pi$
$54$	1311.95	−	1805.75i	0.449916	−	0.619256i
$55$	−992.346	−	559.268i	−0.328048	−	0.184882i
$56$	−6753.82	+	4906.94i	−2.15364	+	1.56471i
$57$	−2982.45	−	2982.45i	−0.917961	−	0.917961i
$58$	−1327.51	+	8381.56i	−0.394622	+	2.49155i
$59$	−829.044	+	269.373i	−0.238163	+	0.0773837i	−0.425666	−	0.904880i	$-0.639960\pi$
$59$	−829.044	+	269.373i	−0.238163	+	0.0773837i	0.187504	+	0.982264i	$0.439960\pi$
$60$	9156.04	+	7258.25i	2.54334	+	2.01618i
$61$	664.208	−	2044.22i	0.178502	−	0.549374i	−0.821274	−	0.570534i	$-0.806736\pi$
$61$	664.208	−	2044.22i	0.178502	−	0.549374i	0.999776	+	0.0211605i	$0.00673609\pi$
$62$	−2476.32	+	4860.04i	−0.644203	+	1.26432i
$63$	2296.53	+	1170.14i	0.578617	+	0.294820i
$64$	−6342.93	−	2060.94i	−1.54857	−	0.503160i
$65$	−2556.82	+	3225.35i	−0.605165	+	0.763396i
$66$	−1230.95	−	3788.46i	−0.282586	−	0.869711i
$67$	3106.69	+	492.052i	0.692068	+	0.109613i	0.492554	−	0.870282i	$-0.336064\pi$
$67$	3106.69	+	492.052i	0.692068	+	0.109613i	0.199514	+	0.979895i	$0.436064\pi$
$68$	6488.27	−	6488.27i	1.40317	−	1.40317i
$69$	−3553.92	−	4891.55i	−0.746464	−	1.02742i
$70$	4268.35	−	7573.61i	0.871092	−	1.54563i
$71$	4257.89	+	3093.54i	0.844652	+	0.613676i	0.923666	−	0.383198i	$-0.125177\pi$
$71$	4257.89	+	3093.54i	0.844652	+	0.613676i	−0.0790140	+	0.996874i	$0.525177\pi$
$72$	1558.97	+	9842.96i	0.300728	+	1.89872i
$73$	4230.54	+	8302.90i	0.793871	+	1.55806i	0.829376	+	0.558690i	$0.188696\pi$
$73$	4230.54	+	8302.90i	0.793871	+	1.55806i	−0.0355052	+	0.999369i	$0.511304\pi$
$74$		−	3491.99i		−	0.637689i
$75$	−7090.21	−	1742.79i	−1.26048	−	0.309829i
$76$	−14444.6			−2.50079
$77$	−1886.42	+	961.179i	−0.318168	+	0.162115i
$78$	−14216.0	+	2251.59i	−2.33662	+	0.370084i
$79$	3270.95	−	4502.08i	0.524107	−	0.721372i	−0.462111	−	0.886822i	$-0.652908\pi$
$79$	3270.95	−	4502.08i	0.524107	−	0.721372i	0.986218	+	0.165450i	$0.0529077\pi$
$80$	17494.2	−	2022.66i	2.73347	−	0.316040i
$81$	−6453.67	+	4688.86i	−0.983641	+	0.714657i
$82$	903.929	+	903.929i	0.134433	+	0.134433i
$83$	2086.10	−	13171.1i	0.302816	−	1.91191i	−0.0969522	−	0.995289i	$-0.530909\pi$
$83$	2086.10	−	13171.1i	0.302816	−	1.91191i	0.399768	−	0.916616i	$-0.369091\pi$
$84$	20653.6	−	6710.76i	2.92710	−	0.951071i
$85$	−1999.14	+	5374.13i	−0.276697	+	0.743824i
$86$	1634.57	−	5030.70i	0.221008	−	0.680192i
$87$	6013.81	−	11802.8i	0.794531	−	1.55935i
$88$	−7293.78	−	3716.37i	−0.941862	−	0.479903i
$89$	−11038.2	−	3586.52i	−1.39353	−	0.452786i	−0.486439	−	0.873715i	$-0.661704\pi$
$89$	−11038.2	−	3586.52i	−1.39353	−	0.452786i	−0.907094	+	0.420928i	$0.861704\pi$
$90$	−5742.36	−	8644.53i	−0.708933	−	1.06723i
$91$	2363.96	+	7275.53i	0.285468	+	0.878581i
$92$	−20451.4	−	3239.19i	−2.41629	−	0.382702i
$93$	6020.63	−	6020.63i	0.696107	−	0.696107i
$94$	7172.29	+	9871.81i	0.811712	+	1.11723i
$95$	8207.38	−	3756.80i	0.909405	−	0.416266i
$96$	22656.0	+	16460.6i	2.45833	+	1.78608i
$97$	666.885	+	4210.55i	0.0708774	+	0.447502i	0.997449	+	0.0713836i	$0.0227414\pi$
$97$	666.885	+	4210.55i	0.0708774	+	0.447502i	−0.926572	+	0.376119i	$0.877259\pi$
$98$	821.793	+	1612.86i	0.0855677	+	0.167936i
$99$			2527.39i			0.257870i
$100$	−21389.9	+	12949.2i	−2.13899	+	1.29492i
$101$	8271.32			0.810834			0.405417	−	0.914132i	$-0.367126\pi$
$101$	8271.32			0.810834			0.405417	+	0.914132i	$0.367126\pi$
$102$	−17866.1	+	9103.23i	−1.71723	+	0.874974i
$103$	−3965.04	+	628.001i	−0.373743	+	0.0591951i	−0.340481	−	0.940252i	$-0.610590\pi$
$103$	−3965.04	+	628.001i	−0.373743	+	0.0591951i	−0.0332625	+	0.999447i	$0.510590\pi$
$104$	−17385.7	+	23929.3i	−1.60740	+	2.21240i
$105$	−9989.99	+	9184.71i	−0.906121	+	0.833080i
$106$	22338.4	−	16229.8i	1.98811	−	1.44445i
$107$	6406.55	+	6406.55i	0.559573	+	0.559573i	0.929186	−	0.369613i	$-0.120510\pi$
$107$	6406.55	+	6406.55i	0.559573	+	0.559573i	−0.369613	+	0.929186i	$0.620510\pi$
$108$	−1866.57	+	11785.1i	−0.160029	+	1.01038i
$109$	−14441.2	+	4692.24i	−1.21549	+	0.394936i	−0.845437	−	0.534075i	$-0.820660\pi$
$109$	−14441.2	+	4692.24i	−1.21549	+	0.394936i	−0.370052	+	0.929011i	$0.620660\pi$
$110$	8517.19	+	357.695i	0.703900	+	0.0295616i
$111$	−1684.43	+	5184.14i	−0.136712	+	0.420756i
$112$	14860.2	−	29164.7i	1.18464	−	2.32499i
$113$	−5.14684	−	2.62245i	−0.000403073	−	0.000205376i	0.453789	−	0.891109i	$-0.350072\pi$
$113$	−5.14684	−	2.62245i	−0.000403073	−	0.000205376i	−0.454192	+	0.890904i	$0.650072\pi$
$114$	30020.3	+	9754.19i	2.30997	+	0.750553i
$115$	12462.9	−	3478.59i	0.942378	−	0.263031i
$116$	−14018.5	−	43144.4i	−1.04180	−	3.20633i
$117$	9019.70	+	1428.58i	0.658902	+	0.104360i
$118$	4612.92	−	4612.92i	0.331293	−	0.331293i
$119$	6264.24	+	8621.99i	0.442359	+	0.608855i
$120$	−51433.9	−	10375.4i	−3.57180	−	0.720514i
$121$	10165.3	+	7385.49i	0.694301	+	0.504439i
$122$	2516.37	+	15887.7i	0.169065	+	1.06744i
$123$	−905.928	−	1777.98i	−0.0598802	−	0.117522i
$124$		−	29159.0i		−	1.89640i
$125$	8785.82	−	12920.9i	0.562293	−	0.826938i
$126$	−19289.1			−1.21498
$127$	5336.84	−	2719.26i	0.330885	−	0.168594i	−0.280653	−	0.959809i	$-0.590551\pi$
$127$	5336.84	−	2719.26i	0.330885	−	0.168594i	0.611538	+	0.791215i	$0.290551\pi$
$128$	11414.0	−	1807.81i	0.696657	−	0.110340i
$129$	−4853.31	+	6680.01i	−0.291648	+	0.401419i
$130$	6090.80	−	30193.8i	0.360402	−	1.78662i
$131$	−15903.7	+	11554.7i	−0.926736	+	0.673313i	−0.945191	−	0.326517i	$-0.894125\pi$
$131$	−15903.7	+	11554.7i	−0.926736	+	0.673313i	0.0184555	+	0.999830i	$0.494125\pi$
$132$	15057.6	+	15057.6i	0.864185	+	0.864185i
$133$	2624.47	−	16570.3i	0.148368	−	0.936756i
$134$	−22387.5	+	7274.13i	−1.24680	+	0.405108i
$135$	−2004.53	−	7181.74i	−0.109988	−	0.394060i
$136$	−12733.5	+	39189.6i	−0.688444	+	2.11881i
$137$	−5146.28	+	10100.1i	−0.274190	+	0.538129i	−0.986505	−	0.163731i	$-0.947647\pi$
$137$	−5146.28	+	10100.1i	−0.274190	+	0.538129i	0.712315	+	0.701860i	$0.247647\pi$
$138$	40317.1	+	20542.6i	2.11705	+	1.07869i
$139$	18667.0	+	6065.27i	0.966149	+	0.313921i	0.749261	−	0.662275i	$-0.230409\pi$
$139$	18667.0	+	6065.27i	0.966149	+	0.313921i	0.216889	+	0.976196i	$0.430409\pi$
$140$	−1950.05	+	46433.2i	−0.0994924	+	2.36904i
$141$	−5885.98	−	18115.2i	−0.296061	−	0.911181i
$142$	−38902.5	−	6161.54i	−1.92930	−	0.305572i
$143$	−5304.24	+	5304.24i	−0.259389	+	0.259389i
$144$	−22967.3	−	31611.8i	−1.10760	−	1.52449i
$145$	19186.4	+	20868.6i	0.912554	+	0.992562i
$146$	−56419.2	−	40990.9i	−2.64680	−	1.92301i
$147$	−442.023	−	2790.83i	−0.0204555	−	0.129151i
$148$	8474.86	+	16632.8i	0.386909	+	0.759352i
$149$		−	7557.91i		−	0.340431i	−0.985407	−	0.170215i	$-0.945554\pi$
$149$		−	7557.91i		−	0.340431i	0.985407	−	0.170215i	$-0.0544464\pi$
$150$	53199.3	−	12468.3i	2.36441	−	0.554148i
$151$	−23162.4			−1.01585			−0.507925	−	0.861401i	$-0.669587\pi$
$151$	−23162.4			−1.01585			−0.507925	+	0.861401i	$0.669587\pi$
$152$	57797.0	−	29449.0i	2.50160	−	1.27463i
$153$	12565.6	−	1990.20i	0.536786	−	0.0850185i
$154$	9313.14	−	12818.4i	0.392694	−	0.540498i
$155$	7583.78	+	16568.1i	0.315662	+	0.689619i
$156$	62248.3	−	45226.1i	2.55787	−	1.85840i
$157$	−6263.87	−	6263.87i	−0.254123	−	0.254123i	0.568536	−	0.822658i	$-0.307510\pi$
$157$	−6263.87	−	6263.87i	−0.254123	−	0.254123i	−0.822658	+	0.568536i	$0.807510\pi$
$158$	−6514.91	+	41133.5i	−0.260972	+	1.64771i
$159$	−40991.9	+	13319.1i	−1.62145	+	0.526842i
$160$	−49920.2	+	33160.8i	−1.95001	+	1.29535i
$161$	7431.77	−	22872.6i	0.286708	−	0.882397i
$162$	27102.9	−	53192.4i	1.03273	−	2.02684i
$163$	−42906.5	−	21861.9i	−1.61491	−	0.822836i	−0.999398	−	0.0347066i	$-0.988950\pi$
$163$	−42906.5	−	21861.9i	−1.61491	−	0.822836i	−0.615509	−	0.788130i	$-0.711050\pi$
$164$	−6499.33	−	2111.76i	−0.241647	−	0.0785158i
$165$	−12471.9	−	4639.46i	−0.458105	−	0.170412i
$166$	30839.3	+	94913.7i	1.11915	+	3.44439i
$167$	36380.5	+	5762.11i	1.30448	+	0.206609i	0.769711	−	0.638392i	$-0.220400\pi$
$167$	36380.5	+	5762.11i	1.30448	+	0.206609i	0.534765	+	0.845001i	$0.320400\pi$
$168$	−68959.5	+	68959.5i	−2.44329	+	2.44329i
$169$	−856.199	−	1178.46i	−0.0299779	−	0.0412610i
$170$	−4928.50	−	42627.3i	−0.170536	−	1.47499i
$171$	−16202.5	−	11771.8i	−0.554102	−	0.402578i
$172$	4423.51	+	27929.0i	0.149524	+	0.944057i
$173$	−14975.7	−	29391.4i	−0.500373	−	0.982037i	−0.993687	−	0.112186i	$-0.964215\pi$
$173$	−14975.7	−	29391.4i	−0.500373	−	0.982037i	0.493315	−	0.869851i	$-0.335785\pi$
$174$			99134.0i			3.27434i
$175$	−10968.5	−	26890.5i	−0.358156	−	0.878057i
$176$	32096.5			1.03617
$177$	−9073.39	+	4623.12i	−0.289616	+	0.147567i
$178$	85788.9	−	13587.6i	2.70764	−	0.428848i
$179$	5739.11	−	7899.20i	0.179118	−	0.246534i	−0.710012	−	0.704189i	$-0.751311\pi$
$179$	5739.11	−	7899.20i	0.179118	−	0.246534i	0.889130	+	0.457655i	$0.151311\pi$
$180$	48331.5	+	27238.8i	1.49171	+	0.840702i
$181$	7454.85	−	5416.26i	0.227552	−	0.165327i	−0.468167	−	0.883640i	$-0.655086\pi$
$181$	7454.85	−	5416.26i	0.227552	−	0.165327i	0.695720	+	0.718313i	$0.255086\pi$
$182$	−40482.1	−	40482.1i	−1.22214	−	1.22214i
$183$	3928.00	−	24800.4i	0.117292	−	0.740554i
$184$	88436.3	−	28734.7i	2.61213	−	0.848732i
$185$	−9141.34	−	7246.59i	−0.267095	−	0.211734i
$186$	−19690.6	+	60601.5i	−0.569159	+	1.75169i
$187$	−4744.35	+	9311.31i	−0.135673	+	0.266273i
$188$	−58121.0	−	29614.1i	−1.64444	−	0.837883i
$189$	−13180.3	−	4282.54i	−0.368979	−	0.119888i
$190$	−41963.6	+	52935.7i	−1.16243	+	1.46636i
$191$	−2339.54	−	7200.37i	−0.0641304	−	0.197373i	0.913857	−	0.406035i	$-0.133089\pi$
$191$	−2339.54	−	7200.37i	−0.0641304	−	0.197373i	−0.977988	+	0.208662i	$0.933089\pi$
$192$	−76952.2	−	12188.0i	−2.08746	−	0.330622i
$193$	−21713.7	+	21713.7i	−0.582933	+	0.582933i	−0.935708	−	0.352775i	$-0.885238\pi$
$193$	−21713.7	+	21713.7i	−0.582933	+	0.582933i	0.352775	+	0.935708i	$0.385238\pi$
$194$	−18752.4	−	25810.5i	−0.498258	−	0.685793i
$195$	−23606.9	+	41887.2i	−0.620825	+	1.10157i
$196$	−7828.63	−	5687.84i	−0.203786	−	0.148059i
$197$	10646.1	+	67216.8i	0.274320	+	1.73199i	0.612114	+	0.790770i	$0.290319\pi$
$197$	10646.1	+	67216.8i	0.274320	+	1.73199i	−0.337794	+	0.941220i	$0.609681\pi$
$198$	−8586.94	−	16852.8i	−0.219032	−	0.429875i
$199$		−	51934.2i		−	1.31144i	−0.755005	−	0.655719i	$-0.772366\pi$
$199$		−	51934.2i		−	1.31144i	0.755005	−	0.655719i	$-0.227634\pi$
$200$	59186.9	−	95422.7i	1.47967	−	2.38557i
$201$	36744.8			0.909502
$202$	−55153.8	+	28102.3i	−1.35168	+	0.688714i
$203$	52040.8	−	8242.45i	1.26285	−	0.200016i
$204$	63005.8	−	86720.0i	1.51398	−	2.08381i
$205$	4242.15	−	490.471i	0.100943	−	0.0116709i
$206$	24305.5	−	17659.0i	0.572758	−	0.416133i
$207$	−20300.6	−	20300.6i	−0.473771	−	0.473771i
$208$	18142.2	−	114545.i	0.419337	−	2.64759i
$209$	15645.7	−	5083.61i	0.358182	−	0.116380i
$210$	35408.5	−	95186.0i	0.802913	−	2.15841i
$211$	−18595.9	+	57232.3i	−0.417688	+	1.28551i	0.492136	+	0.870518i	$0.336216\pi$
$211$	−18595.9	+	57232.3i	−0.417688	+	1.28551i	−0.909824	+	0.414994i	$0.863784\pi$
$212$	−67012.3	+	131519.i	−1.49102	+	2.92629i
$213$	54781.7	+	27912.7i	1.20747	+	0.615237i
$214$	−64486.1	−	20952.8i	−1.40812	−	0.457524i
$215$	−9777.31	−	14718.7i	−0.211516	−	0.318415i
$216$	−16558.3	−	50961.2i	−0.354902	−	1.09227i
$217$	33450.1	+	5297.98i	0.710360	+	0.112510i
$218$	80353.1	−	80353.1i	1.69079	−	1.69079i
$219$	63986.0	+	88069.2i	1.33413	+	1.83627i
$220$	−41436.7	+	18967.0i	−0.856130	+	0.391880i
$221$	30548.4	+	22194.7i	0.625466	+	0.454428i
$222$	−6381.50	−	40291.2i	−0.129484	−	0.817531i
$223$	−1927.07	−	3782.09i	−0.0387515	−	0.0760541i	0.870819	−	0.491604i	$-0.163589\pi$
$223$	−1927.07	−	3782.09i	−0.0387515	−	0.0760541i	−0.909570	+	0.415550i	$0.863589\pi$
$224$			111390.i			2.21999i
$225$	−34546.2	−	2906.80i	−0.682395	−	0.0574182i
$226$	43.2295			0.000846376
$227$	−251.496	+	128.144i	−0.00488067	+	0.00248683i	−0.456429	−	0.889760i	$-0.650872\pi$
$227$	−251.496	+	128.144i	−0.00488067	+	0.00248683i	0.451548	+	0.892247i	$0.350872\pi$
$228$	−166664.	+	26397.0i	−3.20606	+	0.507790i
$229$	−26745.4	+	36811.9i	−0.510010	+	0.701969i	−0.983921	−	0.178604i	$-0.942842\pi$
$229$	−26745.4	+	36811.9i	−0.510010	+	0.701969i	0.473911	+	0.880573i	$0.342842\pi$
$230$	−71285.3	+	65539.1i	−1.34755	+	1.23892i
$231$	−20009.3	+	14537.6i	−0.374980	+	0.272439i
$232$	144053.	+	144053.i	2.67638	+	2.67638i
$233$	−8361.82	+	52794.4i	−0.154024	+	0.972470i	0.782699	+	0.622400i	$0.213842\pi$
$233$	−8361.82	+	52794.4i	−0.154024	+	0.972470i	−0.936723	+	0.350070i	$0.886158\pi$
$234$	−64997.8	+	21119.1i	−1.18704	+	0.385694i
$235$	40726.4	+	1710.38i	0.737464	+	0.0309712i
$236$	−10776.7	+	33167.3i	−0.193492	+	0.595507i
$237$	29513.5	−	57923.4i	0.525440	−	1.03123i
$238$	−71064.2	−	36209.0i	−1.25458	−	0.639238i
$239$	47126.2	+	15312.2i	0.825024	+	0.268067i	0.690948	−	0.722905i	$-0.257193\pi$
$239$	47126.2	+	15312.2i	0.825024	+	0.268067i	0.134076	+	0.990971i	$0.457193\pi$
$240$	198155.	−	55307.9i	3.44020	−	0.960207i
$241$	−19465.9	−	59910.0i	−0.335152	−	1.03149i	−0.966647	−	0.256111i	$-0.917559\pi$
$241$	−19465.9	−	59910.0i	−0.335152	−	1.03149i	0.631496	−	0.775379i	$-0.282441\pi$
$242$	−92875.4	−	14710.0i	−1.58588	−	0.251179i
$243$	−48812.4	+	48812.4i	−0.826642	+	0.826642i
$244$	−50544.4	−	69568.4i	−0.848972	−	1.16851i
$245$	5927.54	+	1195.72i	0.0987511	+	0.0199204i
$246$	12081.6	+	8777.80i	0.199643	+	0.145049i
$247$	−9298.72	−	58709.8i	−0.152416	−	0.962314i
$248$	59448.2	+	116674.i	0.966575	+	1.89701i
$249$		−	155783.i		−	2.51259i
$250$	−14685.0	+	116008.i	−0.234961	+	1.85613i
$251$	42492.0			0.674466			0.337233	−	0.941421i	$-0.390509\pi$
$251$	42492.0			0.674466			0.337233	+	0.941421i	$0.390509\pi$
$252$	91876.7	−	46813.5i	1.44679	−	0.737174i
$253$	23292.2	−	3689.12i	0.363889	−	0.0576343i
$254$	−26347.7	+	36264.5i	−0.408390	+	0.562101i
$255$	−13245.3	+	65661.0i	−0.203696	+	1.00978i
$256$	16362.3	−	11887.9i	0.249669	−	0.181395i
$257$	−32432.0	−	32432.0i	−0.491030	−	0.491030i	0.417601	−	0.908631i	$-0.362871\pi$
$257$	−32432.0	−	32432.0i	−0.491030	−	0.491030i	−0.908631	+	0.417601i	$0.862871\pi$
$258$	9666.56	−	61032.3i	0.145222	−	0.916896i
$259$	−20620.4	+	6699.98i	−0.307396	+	0.0998790i
$260$	44267.4	+	158600.i	0.654843	+	2.34615i
$261$	19436.6	−	59819.7i	0.285325	−	0.878139i
$262$	66789.4	−	131082.i	0.972983	−	1.90959i
$263$	−28449.9	−	14495.9i	−0.411310	−	0.209573i	0.236077	−	0.971734i	$-0.424138\pi$
$263$	−28449.9	−	14495.9i	−0.411310	−	0.209573i	−0.647387	+	0.762162i	$0.724138\pi$
$264$	−90948.5	−	29551.0i	−1.30493	−	0.423998i
$265$	3870.34	−	92157.8i	0.0551134	−	1.31232i
$266$	38798.3	+	119409.i	0.548339	+	1.68761i
$267$	−133915.	−	21210.0i	−1.87848	−	0.297521i
$268$	88980.8	−	88980.8i	1.23887	−	1.23887i
$269$	60514.9	+	83291.7i	0.836292	+	1.15106i	0.986719	+	0.162436i	$0.0519352\pi$
$269$	60514.9	+	83291.7i	0.836292	+	1.15106i	−0.150427	+	0.988621i	$0.548065\pi$
$270$	37766.7	+	41078.0i	0.518062	+	0.563484i
$271$	−13310.5	−	9670.62i	−0.181240	−	0.131679i	0.493466	−	0.869765i	$-0.335730\pi$
$271$	−13310.5	−	9670.62i	−0.181240	−	0.131679i	−0.674706	+	0.738086i	$0.735730\pi$
$272$	−25274.5	−	159577.i	−0.341621	−	2.15691i
$273$	40571.6	+	79626.3i	0.544374	+	1.06839i
$274$		−	84833.4i		−	1.12997i
$275$	18611.3	−	21554.0i	0.246100	−	0.285012i
$276$	−241892.			−3.17544
$277$	−109759.	+	55924.9i	−1.43047	+	0.728862i	−0.985971	−	0.166916i	$-0.946619\pi$
$277$	−109759.	+	55924.9i	−1.43047	+	0.728862i	−0.444502	+	0.895778i	$0.646619\pi$
$278$	−145080.	+	22978.4i	−1.87723	+	0.297324i
$279$	23763.5	−	32707.7i	0.305283	−	0.420186i
$280$	−86863.7	−	189769.i	−1.10795	−	2.42052i
$281$	−1715.73	+	1246.55i	−0.0217289	+	0.0157869i	−0.598597	−	0.801051i	$-0.704275\pi$
$281$	−1715.73	+	1246.55i	−0.0217289	+	0.0157869i	0.576868	+	0.816838i	$0.304275\pi$
$282$	100796.	+	100796.i	1.26749	+	1.26749i
$283$	−18320.9	+	115674.i	−0.228757	+	1.44431i	0.559430	+	0.828878i	$0.311020\pi$
$283$	−18320.9	+	115674.i	−0.228757	+	1.44431i	−0.788187	+	0.615436i	$0.788980\pi$
$284$	200252.	−	65065.8i	2.48279	−	0.806707i
$285$	87832.9	−	58345.3i	1.08135	−	0.718317i
$286$	17347.7	−	53390.6i	0.212084	−	0.652729i
$287$	3603.42	−	7072.11i	0.0437473	−	0.0858589i
$288$	118479.	+	60368.1i	1.42842	+	0.727818i
$289$	−29403.4	−	9553.75i	−0.352048	−	0.114387i
$290$	−198839.	−	73966.7i	−2.36432	−	0.879509i
$291$	15389.3	+	47363.4i	0.181732	+	0.559315i
$292$	368215.	+	58319.6i	4.31853	+	0.683988i
$293$	−73976.8	+	73976.8i	−0.861708	+	0.861708i	−0.991536	−	0.129828i	$-0.958557\pi$
$293$	−73976.8	+	73976.8i	−0.861708	+	0.861708i	0.129828	+	0.991536i	$0.458557\pi$
$294$	12429.4	+	17107.7i	0.143799	+	0.197923i
$295$	−2502.97	−	21648.5i	−0.0287615	−	0.248762i
$296$	−67820.9	−	49274.7i	−0.774069	−	0.562394i
$297$	−2125.84	−	13422.0i	−0.0241001	−	0.152162i
$298$	25678.4	+	50396.8i	0.289158	+	0.567505i
$299$		−	85210.0i		−	0.953121i
$300$	−223136.	+	188500.i	−2.47929	+	2.09445i
$301$	−32842.8			−0.362500
$302$	154449.	−	78695.5i	1.69344	−	0.862852i
$303$	95436.0	−	15115.6i	1.03951	−	0.164642i
$304$	−149496.	+	205763.i	−1.61764	+	2.22649i
$305$	46812.9	+	26382.9i	0.503229	+	0.283611i
$306$	−77026.8	+	55963.2i	−0.822619	+	0.597668i
$307$	−86101.0	−	86101.0i	−0.913548	−	0.913548i	0.0830013	−	0.996549i	$-0.473549\pi$
$307$	−86101.0	−	86101.0i	−0.913548	−	0.913548i	−0.996549	+	0.0830013i	$0.973549\pi$
$308$	−13250.2	+	83658.6i	−0.139676	+	0.881879i
$309$	−44601.7	+	14492.0i	−0.467127	+	0.151779i
$310$	−106860.	−	84711.1i	−1.11197	−	0.881489i
$311$	27057.5	−	83274.4i	0.279748	−	0.860975i	−0.708176	−	0.706036i	$-0.750482\pi$
$311$	27057.5	−	83274.4i	0.279748	−	0.860975i	0.987924	−	0.154939i	$-0.0495183\pi$
$312$	−156869.	+	307873.i	−1.61149	+	3.16273i
$313$	56080.2	+	28574.3i	0.572428	+	0.291667i	0.716144	−	0.697952i	$-0.245905\pi$
$313$	56080.2	+	28574.3i	0.572428	+	0.291667i	−0.143716	+	0.989619i	$0.545905\pi$
$314$	63049.9	+	20486.1i	0.639477	+	0.207779i
$315$	−40028.8	+	50495.0i	−0.403415	+	0.508894i
$316$	−68797.3	−	211736.i	−0.688965	−	2.12042i
$317$	97697.8	+	15473.8i	0.972224	+	0.153985i	0.622288	−	0.782789i	$-0.286203\pi$
$317$	97697.8	+	15473.8i	0.972224	+	0.153985i	0.349936	+	0.936774i	$0.386203\pi$
$318$	228085.	−	228085.i	2.25550	−	2.25550i
$319$	30368.4	+	41798.6i	0.298429	+	0.410752i
$320$	81862.5	−	145254.i	0.799438	−	1.41850i
$321$	85627.7	+	62212.2i	0.831007	+	0.603762i
$322$	28155.4	+	177766.i	0.271550	+	1.71450i
$323$	−37594.9	−	73784.2i	−0.360350	−	0.707226i
$324$			319140.i			3.04013i
$325$	−66401.9	−	78602.9i	−0.628657	−	0.744170i
$326$	360381.			3.39099
$327$	−158051.	+	80530.8i	−1.47809	+	0.753124i
$328$	30311.1	−	4800.81i	0.281744	−	0.0446239i
$329$	44532.4	−	61293.6i	0.411419	−	0.566270i
$330$	98926.6	−	11437.7i	0.908417	−	0.105030i
$331$	−60578.1	+	44012.5i	−0.552916	+	0.401717i	−0.828860	−	0.559457i	$-0.811010\pi$
$331$	−60578.1	+	44012.5i	−0.552916	+	0.401717i	0.275943	+	0.961174i	$0.411010\pi$
$332$	−377243.	−	377243.i	−3.42251	−	3.42251i
$333$	−4048.91	+	25563.8i	−0.0365132	+	0.230535i
$334$	−262166.	+	85182.7i	−2.35008	+	0.763587i
$335$	−27416.3	+	73701.3i	−0.244298	+	0.656728i
$336$	118162.	−	363664.i	1.04664	−	3.22123i
$337$	60096.9	−	117947.i	0.529166	−	1.03855i	−0.459466	−	0.888195i	$-0.651959\pi$
$337$	60096.9	−	117947.i	0.529166	−	1.03855i	0.988633	−	0.150352i	$-0.0480406\pi$
$338$	9713.08	+	4949.06i	0.0850205	+	0.0433201i
$339$	−64.1776	−	20.8526i	−0.000558450	−	0.000181451i
$340$	126929.	+	191079.i	1.09800	+	1.65293i
$341$	10262.2	+	31583.8i	0.0882534	+	0.271616i
$342$	148035.	+	23446.4i	1.26564	+	0.200458i
$343$	86836.2	−	86836.2i	0.738095	−	0.738095i
$344$	−74640.4	−	102734.i	−0.630749	−	0.868152i
$345$	137443.	−	62912.2i	1.15474	−	0.528563i
$346$	199718.	+	145103.i	1.66826	+	1.21206i
$347$	22842.0	+	144219.i	0.189703	+	1.19774i	0.880270	+	0.474472i	$0.157361\pi$
$347$	22842.0	+	144219.i	0.189703	+	1.19774i	−0.690567	+	0.723268i	$0.742639\pi$
$348$	−240593.	−	472190.i	−1.98666	−	3.89904i
$349$			141569.i			1.16230i	0.813797	+	0.581149i	$0.197397\pi$
$349$			141569.i			1.16230i	−0.813797	+	0.581149i	$0.802603\pi$
$350$	164501.	+	142042.i	1.34287	+	1.15953i
$351$	−49102.0			−0.398552
$352$	−97321.3	+	49587.7i	−0.785457	+	0.400210i
$353$	−182451.	+	28897.4i	−1.46419	+	0.231905i	−0.837103	−	0.547045i	$-0.815753\pi$
$353$	−182451.	+	28897.4i	−1.46419	+	0.231905i	−0.627086	+	0.778950i	$0.715753\pi$
$354$	44794.8	−	61654.7i	0.357455	−	0.491994i
$355$	−96860.3	+	89052.5i	−0.768580	+	0.706626i
$356$	−375648.	+	272925.i	−2.96402	+	2.15349i
$357$	88034.4	+	88034.4i	0.690742	+	0.690742i
$358$	−11430.8	+	72171.5i	−0.0891892	+	0.563118i
$359$	79379.8	−	25792.1i	0.615916	−	0.200123i	0.0155896	−	0.999878i	$-0.495037\pi$
$359$	79379.8	−	25792.1i	0.615916	−	0.200123i	0.600326	+	0.799755i	$0.295037\pi$
$360$	−248922.	−	10453.9i	−1.92069	−	0.0806632i
$361$	−11.8780	+	36.5568i	−9.11443e−5	+	0.000280513i
$362$	−31307.5	+	61444.4i	−0.238908	+	0.468883i
$363$	130785.	+	66638.5i	0.992535	+	0.505722i
$364$	291070.	+	94574.4i	2.19682	+	0.713790i
$365$	−224388.	+	62629.7i	−1.68428	+	0.470105i
$366$	58068.6	+	178717.i	0.433490	+	1.33415i
$367$	−42423.3	−	6719.18i	−0.314972	−	0.0498867i	−0.00305290	−	0.999995i	$-0.500972\pi$
$367$	−42423.3	−	6719.18i	−0.314972	−	0.0498867i	−0.311919	+	0.950109i	$0.600972\pi$
$368$	−257807.	+	257807.i	−1.90370	+	1.90370i
$369$	−5569.30	−	7665.49i	−0.0409023	−	0.0562972i
$370$	85575.9	+	17262.6i	0.625098	+	0.126097i
$371$	−138698.	−	100770.i	−1.00768	−	0.732123i
$372$	−53287.1	−	336442.i	−0.385067	−	2.43122i
$373$	−80194.2	−	157390.i	−0.576402	−	1.13125i	−0.976648	−	0.214844i	$-0.931076\pi$
$373$	−80194.2	−	157390.i	−0.576402	−	1.13125i	0.400247	−	0.916407i	$-0.368924\pi$
$374$		−	78207.8i		−	0.559122i
$375$	77759.9	−	165140.i	0.552959	−	1.17433i
$376$	292936.			2.07203
$377$	166336.	−	84752.3i	1.17031	−	0.596305i
$378$	102437.	−	16224.5i	0.716927	−	0.113550i
$379$	−45512.3	+	62642.4i	−0.316848	+	0.436104i	−0.937502	−	0.347981i	$-0.886867\pi$
$379$	−45512.3	+	62642.4i	−0.316848	+	0.436104i	0.620654	+	0.784085i	$0.286867\pi$
$380$	71406.7	−	353984.i	0.494506	−	2.45141i
$381$	56608.1	−	41128.2i	0.389968	−	0.283328i
$382$	40063.9	+	40063.9i	0.274553	+	0.274553i
$383$	40585.9	−	256249.i	0.276680	−	1.74689i	−0.322771	−	0.946477i	$-0.604614\pi$
$383$	40585.9	−	256249.i	0.276680	−	1.74689i	0.599451	−	0.800411i	$-0.295386\pi$
$384$	128394.	−	41717.6i	0.870724	−	0.282915i
$385$	−14229.5	−	50980.9i	−0.0959992	−	0.343942i
$386$	71015.1	−	218562.i	0.476624	−	1.46690i
$387$	−17799.2	+	34933.0i	−0.118845	+	0.233246i
$388$	151961.	+	77428.1i	1.00941	+	0.514322i
$389$	−41400.1	−	13451.7i	−0.273591	−	0.0888951i	0.169008	−	0.985615i	$-0.445944\pi$
$389$	−41400.1	−	13451.7i	−0.273591	−	0.0888951i	−0.442599	+	0.896720i	$0.645944\pi$
$390$	15098.4	−	359513.i	0.0992664	−	2.36366i
$391$	−36683.0	−	112899.i	−0.239945	−	0.738474i
$392$	42920.9	+	6798.00i	0.279316	+	0.0442393i
$393$	−162384.	+	162384.i	−1.05138	+	1.05138i
$394$	−299362.	−	412036.i	−1.92843	−	2.65426i
$395$	94159.7	+	102415.i	0.603491	+	0.656403i
$396$	81801.7	+	59432.4i	0.521641	+	0.378995i
$397$	28932.1	+	182670.i	0.183569	+	1.15901i	0.891599	+	0.452825i	$0.149584\pi$
$397$	28932.1	+	182670.i	0.183569	+	1.15901i	−0.708031	+	0.706181i	$0.750416\pi$
$398$	176450.	+	346302.i	1.11392	+	2.18619i
$399$		−	195987.i		−	1.23107i
$400$	−36914.8	+	438719.i	−0.230717	+	2.74199i
$401$	−210969.			−1.31199			−0.655993	−	0.754767i	$-0.727750\pi$
$401$	−210969.			−1.31199			−0.655993	+	0.754767i	$0.727750\pi$
$402$	−245017.	+	124843.i	−1.51616	+	0.772522i
$403$	118516.	−	18771.2i	0.729741	−	0.115580i
$404$	194503.	−	267710.i	1.19169	−	1.64022i
$405$	−83003.3	−	181335.i	−0.506040	−	1.10553i
$406$	−319008.	+	231773.i	−1.93530	+	1.40608i
$407$	−15033.4	−	15033.4i	−0.0907544	−	0.0907544i
$408$	−75303.3	+	475447.i	−0.452370	+	2.85615i
$409$	−158373.	+	51458.5i	−0.946748	+	0.307617i	−0.741393	−	0.671071i	$-0.765835\pi$
$409$	−158373.	+	51458.5i	−0.946748	+	0.307617i	−0.205354	+	0.978688i	$0.565835\pi$
$410$	−26620.6	+	17683.4i	−0.158362	+	0.105196i
$411$	−40921.0	+	125942.i	−0.242249	+	0.745567i
$412$	−72913.4	+	143101.i	−0.429549	+	0.843038i
$413$	−36090.3	−	18388.9i	−0.211588	−	0.107809i
$414$	204339.	+	66393.6i	1.19220	+	0.387370i
$415$	312463.	+	116234.i	1.81427	+	0.674897i
$416$	121958.	+	375348.i	0.704731	+	2.16894i
$417$	226467.	+	35868.9i	1.30237	+	0.206274i
$418$	−87055.3	+	87055.3i	−0.498245	+	0.498245i
$419$	90167.3	+	124105.i	0.513595	+	0.706903i	0.984520	−	0.175270i	$-0.0560798\pi$
$419$	90167.3	+	124105.i	0.513595	+	0.706903i	−0.470925	+	0.882173i	$0.656080\pi$
$420$	62355.3	+	539319.i	0.353488	+	3.05736i
$421$	−20037.1	−	14557.8i	−0.113050	−	0.0821357i	0.529824	−	0.848108i	$-0.322258\pi$
$421$	−20037.1	−	14557.8i	−0.113050	−	0.0821357i	−0.642874	+	0.765972i	$0.722258\pi$
$422$	−70451.0	−	444810.i	−0.395606	−	2.49776i
$423$	−41060.0	−	80584.7i	−0.229476	−	0.450373i
$424$		−	662869.i		−	3.68719i
$425$	−121818.	−	75558.5i	−0.674422	−	0.418317i
$426$	−460124.			−2.53545
$427$	88990.0	−	45342.6i	0.488074	−	0.248686i
$428$	358008.	−	56702.8i	1.95436	−	0.309540i
$429$	−51508.0	+	70894.6i	−0.279872	+	0.385211i
$430$	115204.	+	64926.7i	0.623059	+	0.351145i
$431$	229271.	−	166575.i	1.23423	−	0.896719i	0.237027	−	0.971503i	$-0.423827\pi$
$431$	229271.	−	166575.i	1.23423	−	0.896719i	0.997200	+	0.0747845i	$0.0238269\pi$
$432$	148560.	+	148560.i	0.796041	+	0.796041i
$433$	−4639.49	+	29292.6i	−0.0247454	+	0.156236i	−0.996967	−	0.0778263i	$-0.975202\pi$
$433$	−4639.49	+	29292.6i	−0.0247454	+	0.156236i	0.972222	+	0.234062i	$0.0752020\pi$
$434$	−241048.	+	78321.4i	−1.27975	+	0.415816i
$435$	259513.	+	205723.i	1.37145	+	1.08719i
$436$	−187721.	+	577746.i	−0.987507	+	3.03923i
$437$	−84837.7	+	166503.i	−0.444249	+	0.871887i
$438$	−725884.	−	369857.i	−3.78372	−	1.92790i
$439$	294734.	+	95764.9i	1.52933	+	0.496909i	0.948409	−	0.317050i	$-0.102692\pi$
$439$	294734.	+	95764.9i	1.52933	+	0.496909i	0.580921	+	0.813960i	$0.302692\pi$
$440$	127131.	−	160372.i	0.656671	−	0.828369i
$441$	−4146.01	−	12760.1i	−0.0213183	−	0.0656111i
$442$	−279107.	−	44206.2i	−1.42865	−	0.226276i
$443$	18940.9	−	18940.9i	0.0965148	−	0.0965148i	−0.657201	−	0.753716i	$-0.728260\pi$
$443$	18940.9	−	18940.9i	0.0965148	−	0.0965148i	0.753716	+	0.657201i	$0.228260\pi$
$444$	128180.	+	176425.i	0.650213	+	0.894942i
$445$	142460.	−	252776.i	0.719403	−	1.27648i
$446$	25699.8	+	18672.0i	0.129199	+	0.0938686i
$447$	−13811.8	−	87204.5i	−0.0691252	−	0.436439i
$448$	−140692.	−	276123.i	−0.700992	−	1.37577i
$449$			308660.i			1.53104i	0.643410	+	0.765521i	$0.277519\pi$
$449$			308660.i			1.53104i	−0.643410	+	0.765521i	$0.722481\pi$
$450$	240233.	−	97990.1i	1.18634	−	0.483902i
$451$	7783.02			0.0382644
$452$	−205.908	+	104.916i	−0.00100785	+	0.000513526i
$453$	−267252.	+	42328.5i	−1.30234	+	0.206270i
$454$	1241.62	−	1708.94i	0.00602389	−	0.00829118i
$455$	−189983.	+	21965.5i	−0.917681	+	0.106101i
$456$	613055.	−	445411.i	2.94829	−	2.14206i
$457$	−15641.5	−	15641.5i	−0.0748940	−	0.0748940i	0.668668	−	0.743562i	$-0.266865\pi$
$457$	−15641.5	−	15641.5i	−0.0748940	−	0.0748940i	−0.743562	+	0.668668i	$0.766865\pi$
$458$	53270.1	−	336334.i	0.253953	−	1.60339i
$459$	−65057.5	+	21138.5i	−0.308796	+	0.100334i
$460$	180482.	−	485178.i	0.852942	−	2.29290i
$461$	12380.9	−	38104.6i	0.0582575	−	0.179298i	−0.917693	−	0.397290i	$-0.869951\pi$
$461$	12380.9	−	38104.6i	0.0582575	−	0.179298i	0.975951	+	0.217992i	$0.0699507\pi$
$462$	84031.4	−	164921.i	0.393693	−	0.772666i
$463$	226168.	+	115239.i	1.05504	+	0.537571i	0.893392	−	0.449277i	$-0.148318\pi$
$463$	226168.	+	115239.i	1.05504	+	0.537571i	0.161650	+	0.986848i	$0.448318\pi$
$464$	−759678.	−	246834.i	−3.52853	−	1.14649i
$465$	117781.	+	177307.i	0.544714	+	0.820010i
$466$	−123615.	−	380447.i	−0.569245	−	1.75195i
$467$	10566.3	+	1673.53i	0.0484493	+	0.00767362i	0.180612	−	0.983554i	$-0.442192\pi$
$467$	10566.3	+	1673.53i	0.0484493	+	0.00767362i	−0.132163	+	0.991228i	$0.542192\pi$
$468$	258339.	−	258339.i	1.17950	−	1.17950i
$469$	85908.4	+	118243.i	0.390562	+	0.537563i
$470$	−277378.	+	126965.i	−1.25567	+	0.574764i
$471$	−83720.7	−	60826.7i	−0.377391	−	0.274190i
$472$	−24499.5	−	154684.i	−0.109970	−	0.694321i
$473$	−14620.7	−	28694.7i	−0.0653499	−	0.128256i
$474$			486512.i			2.16539i
$475$	51492.2	+	219705.i	0.228220	+	0.973761i
$476$	426366.			1.88178
$477$	−182351.	+	92912.5i	−0.801441	+	0.408355i
$478$	−366266.	+	58010.8i	−1.60302	+	0.253894i
$479$	27261.9	−	37522.8i	0.118819	−	0.163540i	−0.745465	−	0.666545i	$-0.767772\pi$
$479$	27261.9	−	37522.8i	0.118819	−	0.163540i	0.864283	+	0.503005i	$0.167772\pi$
$480$	−515388.	+	473844.i	−2.23693	+	2.05661i
$481$	−62148.4	+	45153.4i	−0.268621	+	0.195164i
$482$	333348.	+	333348.i	1.43484	+	1.43484i
$483$	43950.1	−	277490.i	0.188393	−	1.18947i
$484$	478080.	−	155337.i	2.04084	−	0.663110i
$485$	−106482.	−	4471.91i	−0.452681	−	0.0190112i
$486$	159642.	−	491328.i	0.675888	−	2.08017i
$487$	109136.	−	214191.i	0.460161	−	0.903117i	−0.538026	−	0.842928i	$-0.680830\pi$
$487$	109136.	−	214191.i	0.460161	−	0.903117i	0.998187	−	0.0601890i	$-0.0191703\pi$
$488$	344077.	+	175316.i	1.44483	+	0.736176i
$489$	−535015.	−	173837.i	−2.23742	−	0.726983i
$490$	−43587.8	+	12166.0i	−0.181540	+	0.0506705i
$491$	8877.84	+	27323.2i	0.0368251	+	0.113336i	0.967779	−	0.251800i	$-0.0810225\pi$
$491$	8877.84	+	27323.2i	0.0368251	+	0.113336i	−0.930954	+	0.365136i	$0.881022\pi$
$492$	−78849.7	−	12488.6i	−0.325739	−	0.0515920i
$493$	183900.	−	183900.i	0.756637	−	0.756637i
$494$	261475.	+	359889.i	1.07146	+	1.47474i
$495$	−61937.0	−	12494.1i	−0.252778	−	0.0509913i
$496$	−415370.	−	301784.i	−1.68839	−	1.22668i
$497$	38256.8	+	241544.i	0.154880	+	0.977874i
$498$	529282.	+	1.03877e6i	2.13417	+	4.18854i
$499$		−	165444.i		−	0.664433i	−0.943203	−	0.332216i	$-0.892204\pi$
$499$		−	165444.i		−	0.664433i	0.943203	−	0.332216i	$-0.107796\pi$
$500$	−211598.	−	588203.i	−0.846392	−	2.35281i
$501$	430295.			1.71432
$502$	−283340.	+	144369.i	−1.12435	+	0.572884i
$503$	−230967.	+	36581.5i	−0.912879	+	0.144586i	−0.595167	−	0.803602i	$-0.702914\pi$
$503$	−230967.	+	36581.5i	−0.912879	+	0.144586i	−0.317711	+	0.948188i	$0.602914\pi$
$504$	−272184.	+	374630.i	−1.07152	+	1.47483i
$505$	−40889.3	+	202700.i	−0.160334	+	0.794824i
$506$	−142780.	+	103736.i	−0.557656	+	0.405161i
$507$	−12032.6	−	12032.6i	−0.0468104	−	0.0468104i
$508$	37486.0	−	236677.i	0.145259	−	0.917126i
$509$	80760.9	−	26240.8i	0.311721	−	0.101284i	−0.148979	−	0.988840i	$-0.547599\pi$
$509$	80760.9	−	26240.8i	0.311721	−	0.101284i	0.460699	+	0.887556i	$0.347599\pi$
$510$	−134766.	−	482835.i	−0.518132	−	1.85634i
$511$	−133804.	+	411807.i	−0.512422	+	1.57707i
$512$	−152659.	+	299609.i	−0.582346	+	1.14292i
$513$	95947.1	+	48887.5i	0.364584	+	0.185765i
$514$	326449.	+	106070.i	1.23563	+	0.401481i
$515$	4211.16	−	100273.i	0.0158777	−	0.378069i
$516$	102079.	+	314166.i	0.383385	+	1.17994i
$517$	73376.6	+	11621.7i	0.274522	+	0.0434800i
$518$	114735.	−	114735.i	0.427599	−	0.427599i
$519$	−226504.	−	311756.i	−0.840892	−	1.15739i
$520$	−500474.	−	544354.i	−1.85087	−	2.01314i
$521$	−94745.0	−	68836.3i	−0.349045	−	0.253596i	0.399424	−	0.916767i	$-0.369210\pi$
$521$	−94745.0	−	68836.3i	−0.349045	−	0.253596i	−0.748468	+	0.663171i	$0.769210\pi$
$522$	73636.0	+	464920.i	0.270240	+	1.70623i
$523$	16492.7	+	32368.8i	0.0602961	+	0.118338i	0.919188	−	0.393819i	$-0.128846\pi$
$523$	16492.7	+	32368.8i	0.0602961	+	0.118338i	−0.858892	+	0.512157i	$0.828846\pi$
$524$			786455.i			2.86425i
$525$	−175698.	−	290223.i	−0.637454	−	1.05296i
$526$	238957.			0.863670
$527$	148947.	−	75892.2i	0.536303	−	0.273260i
$528$	370335.	−	58655.3i	1.32839	−	0.210397i
$529$	7029.89	−	9675.81i	0.0251210	−	0.0345761i
$530$	287304.	+	627665.i	1.02280	+	2.23448i
$531$	−39118.5	+	28421.2i	−0.138737	+	0.100798i
$532$	−474600.	−	474600.i	−1.67689	−	1.67689i
$533$	4399.28	−	27775.9i	0.0154856	−	0.0977720i
$534$	965017.	−	313553.i	3.38417	−	1.09958i
$535$	−188672.	+	125331.i	−0.659174	+	0.437874i
$536$	−174628.	+	537450.i	−0.607833	+	1.87072i
$537$	51783.3	−	101630.i	0.179573	−	0.352432i
$538$	−686507.	−	349793.i	−2.37181	−	1.20850i
$539$	10481.4	+	3405.62i	0.0360780	+	0.0117225i
$540$	−279582.	−	104003.i	−0.958787	−	0.356662i
$541$	137252.	+	422417.i	0.468946	+	1.44327i	0.853951	+	0.520354i	$0.174200\pi$
$541$	137252.	+	422417.i	0.468946	+	1.44327i	−0.385005	+	0.922915i	$0.625800\pi$
$542$	121612.	+	19261.4i	0.413978	+	0.0655676i
$543$	76117.3	−	76117.3i	0.258157	−	0.258157i
$544$	323175.	+	444813.i	1.09204	+	1.50307i
$545$	−43599.5	−	377098.i	−0.146787	−	1.26958i
$546$	−541070.	−	393110.i	−1.81496	−	1.31865i
$547$	−56405.2	−	356128.i	−0.188514	−	1.19023i	−0.882524	−	0.470267i	$-0.844157\pi$
$547$	−56405.2	−	356128.i	−0.188514	−	1.19023i	0.694010	−	0.719966i	$-0.255843\pi$
$548$	205886.	+	404074.i	0.685591	+	1.34555i
$549$		−	119227.i		−	0.395576i
$550$	−50870.5	+	206957.i	−0.168167	+	0.684156i
$551$	−409408.			−1.34851
$552$	967882.	−	493161.i	3.17647	−	1.61849i
$553$	255396.	−	40450.8i	0.835149	−	0.132275i
$554$	541872.	−	745823.i	1.76554	−	2.43006i
$555$	−118717.	−	66907.0i	−0.385415	−	0.217213i
$556$	635270.	−	461551.i	2.05498	−	1.49303i
$557$	37956.8	+	37956.8i	0.122343	+	0.122343i	0.765627	−	0.643284i	$-0.222429\pi$
$557$	37956.8	+	37956.8i	0.122343	+	0.122343i	−0.643284	+	0.765627i	$0.722429\pi$
$558$	−47330.9	+	298835.i	−0.152011	+	0.959762i
$559$	−110669.	+	35958.7i	−0.354164	+	0.115075i
$560$	641260.	+	508344.i	2.04483	+	1.62100i
$561$	−37725.1	+	116106.i	−0.119868	+	0.368917i
$562$	7205.41	−	14141.4i	0.0228132	−	0.0447734i
$563$	−88595.9	−	45141.9i	−0.279510	−	0.142417i	0.308616	−	0.951187i	$-0.400134\pi$
$563$	−88595.9	−	45141.9i	−0.279510	−	0.142417i	−0.588126	+	0.808769i	$0.700134\pi$
$564$	−724730.	−	235479.i	−2.27834	−	0.740276i
$565$	89.7100	−	113.166i	0.000281024	−	0.000354503i
$566$	−270843.	−	833568.i	−0.845443	−	2.60200i
$567$	−366106.	−	57985.6i	−1.13878	−	0.180366i
$568$	−668613.	+	668613.i	−2.07242	+	2.07242i
$569$	−243749.	−	335492.i	−0.752867	−	1.03623i	−0.997774	−	0.0666861i	$-0.978757\pi$
$569$	−243749.	−	335492.i	−0.752867	−	1.03623i	0.244907	−	0.969547i	$-0.421243\pi$
$570$	−387445.	+	687469.i	−1.19251	+	2.11594i
$571$	142475.	+	103514.i	0.436984	+	0.317488i	0.784435	−	0.620210i	$-0.212953\pi$
$571$	142475.	+	103514.i	0.436984	+	0.317488i	−0.347451	+	0.937698i	$0.612953\pi$
$572$	46946.6	+	296409.i	0.143487	+	0.905939i
$573$	−40152.5	−	78803.7i	−0.122293	−	0.240014i
$574$			59400.2i			0.180287i
$575$	23636.9	+	322618.i	0.0714915	+	0.975782i
$576$	−369944.			−1.11504
$577$	335946.	−	171173.i	1.00906	−	0.514143i	0.130336	−	0.991470i	$-0.458394\pi$
$577$	335946.	−	171173.i	1.00906	−	0.514143i	0.878726	+	0.477327i	$0.158394\pi$
$578$	228524.	−	36194.6i	0.684031	−	0.108340i
$579$	−210855.	+	290217.i	−0.628966	+	0.865697i
$580$	1.12661e6	−	130257.i	3.34903	−	0.387209i
$581$	501301.	−	364217.i	1.48507	−	1.07897i
$582$	−263537.	−	263537.i	−0.778028	−	0.778028i
$583$	26298.2	−	166040.i	0.0773729	−	0.488513i
$584$	−1.59224e6	+	517350.i	−4.66856	+	1.51691i
$585$	−79598.2	+	213978.i	−0.232590	+	0.625255i
$586$	241943.	−	744624.i	0.704560	−	2.16841i
$587$	−90536.3	+	177687.i	−0.262752	+	0.515680i	−0.984260	−	0.176726i	$-0.943449\pi$
$587$	−90536.3	+	177687.i	−0.262752	+	0.515680i	0.721508	+	0.692406i	$0.243449\pi$
$588$	−100723.	−	51320.7i	−0.291321	−	0.148436i
$589$	−250275.	−	81319.2i	−0.721417	−	0.234403i
$590$	90242.0	+	135850.i	0.259242	+	0.390261i
$591$	245673.	+	756104.i	0.703368	+	2.16475i
$592$	324646.	+	51419.0i	0.926333	+	0.146717i
$593$	−370586.	+	370586.i	−1.05385	+	1.05385i	−0.0553861	+	0.998465i	$0.517639\pi$
$593$	−370586.	+	370586.i	−1.05385	+	1.05385i	−0.998465	+	0.0553861i	$0.982361\pi$
$594$	59777.5	+	82276.6i	0.169420	+	0.233187i
$595$	−242261.	+	110891.i	−0.684304	+	0.313229i
$596$	−244620.	−	177727.i	−0.688652	−	0.500335i
$597$	−94908.2	−	599227.i	−0.266290	−	1.68129i
$598$	289506.	+	568187.i	0.809571	+	1.58887i
$599$		−	441417.i		−	1.23026i	−0.788427	−	0.615128i	$-0.789104\pi$
$599$		−	441417.i		−	1.23026i	0.788427	−	0.615128i	$-0.210896\pi$
$600$	508527.	−	1.20917e6i	1.41257	−	3.35880i
$601$	39914.9			0.110506			0.0552530	−	0.998472i	$-0.482403\pi$
$601$	39914.9			0.110506			0.0552530	+	0.998472i	$0.482403\pi$
$602$	218999.	−	111585.i	0.604294	−	0.307903i
$603$	172326.	−	27293.8i	0.473933	−	0.0750635i
$604$	−544672.	+	749677.i	−1.49300	+	2.05494i
$605$	−231244.	+	212603.i	−0.631770	+	0.580844i
$606$	−585019.	+	425041.i	−1.59303	+	1.15741i
$607$	−52.3851	−	52.3851i	−0.000142177	−	0.000142177i	0.707036	−	0.707178i	$-0.250032\pi$
$607$	−52.3851	−	52.3851i	−0.000142177	−	0.000142177i	−0.707178	+	0.707036i	$0.750032\pi$
$608$	135398.	−	854869.i	0.366273	−	2.31256i
$609$	585393.	−	190206.i	1.57839	−	0.512848i
$610$	−401790.	−	16873.9i	−1.07979	−	0.0453478i
$611$	82950.9	−	255297.i	0.222197	−	0.683853i
$612$	231070.	−	453501.i	0.616937	−	1.21081i
$613$	433740.	+	221002.i	1.15427	+	0.588132i	0.923016	−	0.384761i	$-0.125716\pi$
$613$	433740.	+	221002.i	1.15427	+	0.588132i	0.231257	+	0.972893i	$0.425716\pi$
$614$	866662.	+	281595.i	2.29886	+	0.746945i
$615$	48050.4	−	13411.5i	0.127042	−	0.0354591i
$616$	−117542.	−	361757.i	−0.309764	−	0.953357i
$617$	−7627.90	−	1208.14i	−0.0200371	−	0.00317356i	0.146408	−	0.989224i	$-0.453229\pi$
$617$	−7627.90	−	1208.14i	−0.0200371	−	0.00317356i	−0.166445	+	0.986051i	$0.553229\pi$
$618$	248171.	−	248171.i	0.649790	−	0.649790i
$619$	186675.	+	256936.i	0.487197	+	0.670570i	0.979868	−	0.199646i	$-0.0639793\pi$
$619$	186675.	+	256936.i	0.487197	+	0.670570i	−0.492671	+	0.870216i	$0.663979\pi$
$620$	714580.	+	144147.i	1.85895	+	0.374993i
$621$	124885.	+	90733.9i	0.323836	+	0.235281i
$622$	102508.	+	647210.i	0.264958	+	1.67288i
$623$	−244837.	−	480519.i	−0.630812	−	1.23804i
$624$		−	1.35480e6i		−	3.47941i
$625$	273212.	+	279183.i	0.699422	+	0.714709i
$626$	−471030.			−1.20199
$627$	171233.	−	87247.8i	0.435565	−	0.221932i
$628$	−350034.	+	55440.0i	−0.887547	+	0.140574i
$629$	−62904.6	+	86580.7i	−0.158994	+	0.218837i
$630$	95355.6	−	472705.i	0.240251	−	1.19099i
$631$	−308574.	+	224192.i	−0.774998	+	0.563069i	−0.903474	−	0.428644i	$-0.858992\pi$
$631$	−308574.	+	224192.i	−0.774998	+	0.563069i	0.128476	+	0.991713i	$0.458992\pi$
$632$	706958.	+	706958.i	1.76994	+	1.76994i
$633$	−109973.	+	694340.i	−0.274459	+	1.73287i
$634$	−704030.	+	228753.i	−1.75151	+	0.569100i
$635$	40256.4	+	144229.i	0.0998362	+	0.357689i
$636$	−532853.	+	1.63995e6i	−1.31733	+	4.05431i
$637$	18078.5	−	35481.0i	0.0445536	−	0.0874414i
$638$	−344512.	−	175538.i	−0.846376	−	0.431250i
$639$	277649.	+	90213.6i	0.679977	+	0.220938i
$640$	−12122.5	+	288653.i	−0.0295960	+	0.704720i
$641$	−99218.1	−	305362.i	−0.241477	−	0.743188i	−0.996196	−	0.0871407i	$-0.972227\pi$
$641$	−99218.1	−	305362.i	−0.241477	−	0.743188i	0.754719	−	0.656048i	$-0.227773\pi$
$642$	−782342.	−	123911.i	−1.89813	−	0.300635i
$643$	−530154.	+	530154.i	−1.28227	+	1.28227i	−0.342901	+	0.939372i	$0.611410\pi$
$643$	−530154.	+	530154.i	−1.28227	+	1.28227i	−0.939372	+	0.342901i	$0.888590\pi$
$644$	−565537.	−	778395.i	−1.36361	−	1.87685i
$645$	−139710.	−	151960.i	−0.335822	−	0.365266i
$646$	501372.	+	364268.i	1.20142	+	0.872883i
$647$	−3628.95	−	22912.3i	−0.00866908	−	0.0547344i	0.982975	−	0.183742i	$-0.0588210\pi$
$647$	−3628.95	−	22912.3i	−0.00866908	−	0.0547344i	−0.991644	+	0.129007i	$0.958821\pi$
$648$	−650652.	−	1.27698e6i	−1.54953	−	3.04111i
$649$		−	39718.2i		−	0.0942976i
$650$	709831.	+	298527.i	1.68007	+	0.706572i
$651$	395636.			0.933541
$652$	−1.71655e6	+	874624.i	−4.03795	+	2.05744i
$653$	467642.	−	74067.2i	1.09670	−	0.173700i	0.418238	−	0.908337i	$-0.362648\pi$
$653$	467642.	−	74067.2i	1.09670	−	0.173700i	0.678460	+	0.734638i	$0.262648\pi$
$654$	780286.	−	1.07397e6i	1.82431	−	2.51095i
$655$	−204544.	−	446863.i	−0.476765	−	1.04158i
$656$	−97347.6	+	70727.2i	−0.226213	+	0.164353i
$657$	365500.	+	365500.i	0.846752	+	0.846752i
$658$	−88697.3	+	560013.i	−0.204861	+	1.29344i
$659$	566959.	−	184216.i	1.30551	−	0.424187i	0.428016	−	0.903771i	$-0.359213\pi$
$659$	566959.	−	184216.i	1.30551	−	0.424187i	0.877496	+	0.479584i	$0.159213\pi$
$660$	−443443.	+	294569.i	−1.01800	+	0.676237i
$661$	178804.	−	550304.i	0.409237	−	1.25950i	−0.508067	−	0.861317i	$-0.669640\pi$
$661$	178804.	−	550304.i	0.409237	−	1.25950i	0.917305	−	0.398186i	$-0.130360\pi$
$662$	254404.	−	499297.i	0.580508	−	1.13931i
$663$	393033.	+	200260.i	0.894133	+	0.455583i
$664$	2.27857e6	+	740352.i	5.16804	+	1.67920i
$665$	393103.	+	146231.i	0.888921	+	0.330672i
$666$	−59856.0	−	184218.i	−0.134946	−	0.415320i
$667$	−579664.	−	91809.7i	−1.30294	−	0.206365i
$668$	1.04200e6	−	1.04200e6i	2.33515	−	2.33515i
$669$	−29146.6	−	40116.8i	−0.0651232	−	0.0896343i
$670$	−67590.0	−	584595.i	−0.150568	−	1.30228i
$671$	79231.5	+	57565.1i	0.175976	+	0.127854i
$672$	203562.	+	1.28524e6i	0.450773	+	2.84607i
$673$	−40186.4	−	78870.3i	−0.0887257	−	0.174134i	0.842379	−	0.538885i	$-0.181154\pi$
$673$	−40186.4	−	78870.3i	−0.0887257	−	0.174134i	−0.931105	+	0.364751i	$0.881154\pi$
$674$			990661.i			2.18075i
$675$	185908.	−	13620.7i	0.408028	−	0.0298945i
$676$	−58275.9			−0.127525
$677$	−573297.	+	292109.i	−1.25084	+	0.637335i	−0.948775	−	0.315952i	$-0.897676\pi$
$677$	−573297.	+	292109.i	−1.25084	+	0.637335i	−0.302066	+	0.953287i	$0.597676\pi$
$678$	498.790	−	79.0005i	0.00108507	−	0.000171858i
$679$	−116433.	+	160256.i	−0.252544	+	0.347596i
$680$	−897446.	−	505785.i	−1.94084	−	1.09382i
$681$	−2667.63	+	1938.15i	−0.00575216	+	0.00417919i
$682$	−175737.	−	175737.i	−0.377828	−	0.377828i
$683$	−30055.7	+	189764.i	−0.0644296	+	0.406792i	0.934304	+	0.356478i	$0.116022\pi$
$683$	−30055.7	+	189764.i	−0.0644296	+	0.406792i	−0.998733	+	0.0503146i	$0.983978\pi$
$684$	−762015.	+	247594.i	−1.62874	+	0.529209i
$685$	−222077.	−	176047.i	−0.473285	−	0.375186i
$686$	−284000.	+	874062.i	−0.603490	+	1.85735i
$687$	−241321.	+	473619.i	−0.511307	+	1.00350i
$688$	443630.	+	226041.i	0.937226	+	0.477540i
$689$	−577697.	−	187705.i	−1.21692	−	0.395401i
$690$	−702732.	+	886474.i	−1.47602	+	1.86195i
$691$	−106536.	−	327885.i	−0.223121	−	0.686696i	−0.998477	−	0.0551717i	$-0.982429\pi$
$691$	−106536.	−	327885.i	−0.223121	−	0.686696i	0.775356	−	0.631525i	$-0.217571\pi$
$692$	−1.30344e6	−	206445.i	−2.72195	−	0.431114i
$693$	−83041.5	+	83041.5i	−0.172913	+	0.172913i
$694$	−642304.	−	884056.i	−1.33359	−	1.83553i
$695$	−240918.	+	427476.i	−0.498769	+	0.884997i
$696$	1.92537e6	+	1.39886e6i	3.97461	+	2.88773i
$697$	−6128.76	−	38695.5i	−0.0126156	−	0.0796517i
$698$	−480989.	−	943995.i	−0.987244	−	1.93758i
$699$			624433.i			1.27800i
$700$	−1.12827e6	−	277331.i	−2.30259	−	0.565982i
$701$	547440.			1.11404			0.557020	−	0.830499i	$-0.311945\pi$
$701$	547440.			1.11404			0.557020	+	0.830499i	$0.311945\pi$
$702$	327416.	−	166827.i	0.664395	−	0.338526i
$703$	166396.	−	26354.6i	0.336692	−	0.0533268i
$704$	178616.	−	245844.i	0.360393	−	0.496038i
$705$	473035.	−	54691.6i	0.951733	−	0.110038i
$706$	1.11842e6	−	812579.i	2.24386	−	1.63026i
$707$	271768.	+	271768.i	0.543700	+	0.543700i
$708$	−63731.5	+	402385.i	−0.127142	+	0.802740i
$709$	626250.	−	203481.i	1.24582	−	0.404791i	0.389398	−	0.921069i	$-0.372683\pi$
$709$	626250.	−	203481.i	1.24582	−	0.404791i	0.856421	+	0.516278i	$0.172683\pi$
$710$	343311.	−	922898.i	0.681038	−	1.83078i
$711$	95387.4	−	293572.i	0.188691	−	0.580732i
$712$	946653.	−	1.85791e6i	1.86737	−	3.66492i
$713$	−336117.	−	171260.i	−0.661168	−	0.336882i
$714$	−886122.	−	287919.i	−1.73819	−	0.564772i
$715$	−103766.	−	156209.i	−0.202975	−	0.305559i
$716$	−120709.	−	371505.i	−0.235459	−	0.724668i
$717$	571733.	+	90553.7i	1.11213	+	0.176144i
$718$	−441681.	+	441681.i	−0.856762	+	0.856762i
$719$	398389.	+	548335.i	0.770636	+	1.06069i	0.996254	+	0.0864733i	$0.0275597\pi$
$719$	398389.	+	548335.i	0.770636	+	1.06069i	−0.225618	+	0.974216i	$0.572440\pi$
$720$	888228.	−	406572.i	1.71340	−	0.784282i
$721$	−150912.	−	109644.i	−0.290304	−	0.210918i
$722$	−45.0001	−	284.120i	−8.63256e−5	−	0.000545038i
$723$	−334085.	−	655679.i	−0.639117	−	1.25434i
$724$		−	368650.i		−	0.703294i
$725$	−606262.	+	367026.i	−1.15341	+	0.698265i
$726$	−1.09850e6			−2.08413
$727$	595924.	−	303638.i	1.12751	−	0.574497i	0.212195	−	0.977227i	$-0.431939\pi$
$727$	595924.	−	303638.i	1.12751	−	0.574497i	0.915319	+	0.402730i	$0.131939\pi$
$728$	−1.35747e6	+	215003.i	−2.56135	+	0.405677i
$729$	−94205.3	+	129662.i	−0.177264	+	0.243983i
$730$	1.28345e6	−	1.17999e6i	2.40842	−	2.21428i
$731$	−131151.	+	95286.6i	−0.245435	+	0.178319i
$732$	−710325.	−	710325.i	−1.32567	−	1.32567i
$733$	41372.7	−	261217.i	0.0770027	−	0.486176i	−0.918806	−	0.394710i	$-0.870845\pi$
$733$	41372.7	−	261217.i	0.0770027	−	0.486176i	0.995808	−	0.0914655i	$-0.0291551\pi$
$734$	305711.	−	99331.4i	0.567438	−	0.184372i
$735$	70578.1	+	2964.06i	0.130646	+	0.00548672i
$736$	383408.	−	1.18001e6i	0.707792	−	2.17836i
$737$	−65064.5	+	127696.i	−0.119787	+	0.235095i
$738$	63180.5	+	32192.1i	0.116003	+	0.0591066i
$739$	−99814.2	−	32431.6i	−0.182769	−	0.0593854i	0.216202	−	0.976349i	$-0.430633\pi$
$739$	−99814.2	−	32431.6i	−0.182769	−	0.0593854i	−0.398972	+	0.916963i	$0.630633\pi$
$740$	−449506.	+	125463.i	−0.820865	+	0.229115i
$741$	−214581.	−	660411.i	−0.390800	−	1.20276i
$742$	1.26722e6	+	200708.i	2.30168	+	0.364551i
$743$	−2313.23	+	2313.23i	−0.00419027	+	0.00419027i	−0.709199	−	0.705009i	$-0.750943\pi$
$743$	−2313.23	+	2313.23i	−0.00419027	+	0.00419027i	0.705009	+	0.709199i	$0.250943\pi$
$744$	899142.	+	1.23756e6i	1.62436	+	2.23574i
$745$	185217.	+	37362.5i	0.333709	+	0.0673168i
$746$	1.06948e6	+	777025.i	1.92175	+	1.39623i
$747$	−115715.	−	730593.i	−0.207370	−	1.30928i
$748$	189806.	+	372515.i	0.339240	+	0.665795i
$749$			420996.i			0.750437i
$750$	42562.4	+	1.36536e6i	0.0756666	+	2.42730i
$751$	−620684.			−1.10050			−0.550251	−	0.835000i	$-0.685468\pi$
$751$	−620684.			−1.10050			−0.550251	+	0.835000i	$0.685468\pi$
$752$	−1.02338e6	+	521440.i	−1.80968	+	0.922080i
$753$	490281.	−	77652.8i	0.864679	−	0.136952i
$754$	−821189.	+	1.13027e6i	−1.44444	+	1.98811i
$755$	114503.	−	567626.i	0.200874	−	0.995791i
$756$	−448548.	+	325889.i	−0.784812	+	0.570199i
$757$	−624617.	−	624617.i	−1.08999	−	1.08999i	−0.995529	−	0.0944594i	$-0.969888\pi$
$757$	−624617.	−	624617.i	−1.08999	−	1.08999i	−0.0944594	−	0.995529i	$-0.530112\pi$
$758$	90649.0	−	572335.i	0.157770	−	0.996121i
$759$	262007.	−	85131.4i	0.454810	−	0.147777i
$760$	435969.	+	1.56198e6i	0.754795	+	2.70425i
$761$	−204796.	+	630296.i	−0.353632	+	1.08837i	0.603166	+	0.797615i	$0.293905\pi$
$761$	−204796.	+	630296.i	−0.353632	+	1.08837i	−0.956798	+	0.290752i	$0.906095\pi$
$762$	−237732.	+	466576.i	−0.409429	+	0.803549i
$763$	−628662.	−	320319.i	−1.07986	−	0.550217i
$764$	−288063.	−	93597.4i	−0.493516	−	0.160353i
$765$	−13345.6	+	317776.i	−0.0228042	+	0.542998i
$766$	599992.	+	1.84658e6i	1.02256	+	3.14711i
$767$	−141746.	−	22450.4i	−0.240946	−	0.0381621i
$768$	167066.	−	167066.i	0.283248	−	0.283248i
$769$	−659803.	−	908140.i	−1.11574	−	1.53568i	−0.812684	−	0.582704i	$-0.801995\pi$
$769$	−659803.	−	908140.i	−1.11574	−	1.53568i	−0.303051	−	0.952974i	$-0.598005\pi$
$770$	268094.	+	291599.i	0.452174	+	0.491819i
$771$	−433475.	−	314938.i	−0.729214	−	0.529805i
$772$	192182.	+	1.21339e6i	0.322462	+	2.03595i
$773$	−72775.2	−	142829.i	−0.121794	−	0.239033i	0.822058	−	0.569404i	$-0.192826\pi$
$773$	−72775.2	−	142829.i	−0.121794	−	0.239033i	−0.943851	+	0.330371i	$0.892826\pi$
$774$		−	293410.i		−	0.489771i
$775$	−443514.	+	103946.i	−0.738421	+	0.173064i
$776$	−765899.			−1.27189
$777$	−225678.	+	114989.i	−0.373807	+	0.190464i
$778$	321762.	−	50962.1i	0.531589	−	0.0841954i
$779$	−36250.9	+	49895.1i	−0.0597371	+	0.0822211i
$780$	800602.	+	1.74906e6i	1.31591	+	2.87484i
$781$	−194005.	+	140953.i	−0.318062	+	0.231085i
$782$	628185.	+	628185.i	1.02724	+	1.02724i
$783$	−52905.1	+	334030.i	−0.0862927	+	0.544830i
$784$	−162047.	+	52652.1i	−0.263638	+	0.0856611i
$785$	184470.	−	122539.i	0.299355	−	0.198855i
$786$	531081.	−	1.63450e6i	0.859638	−	2.64570i
$787$	−330520.	+	648681.i	−0.533639	+	1.04733i	0.454062	+	0.890970i	$0.349975\pi$
$787$	−330520.	+	648681.i	−0.533639	+	1.04733i	−0.987701	+	0.156356i	$0.950025\pi$
$788$	2.42589e6	+	1.23605e6i	3.90678	+	1.99061i
$789$	−354751.	−	115265.i	−0.569861	−	0.185159i
$790$	−975826.	−	363000.i	−1.56357	−	0.581638i
$791$	−82.9432	−	255.273i	−0.000132565	−	0.000407992i
$792$	−448482.	−	71032.5i	−0.714981	−	0.113242i
$793$	250222.	−	250222.i	0.397905	−	0.397905i
$794$	−813553.	−	1.11976e6i	−1.29046	−	1.77617i
$795$	−123759.	−	1.07041e6i	−0.195813	−	1.69361i
$796$	−1.68091e6	−	1.22125e6i	−2.65288	−	1.92743i
$797$	149108.	+	941428.i	0.234738	+	1.48208i	0.770355	+	0.637615i	$0.220079\pi$
$797$	149108.	+	941428.i	0.234738	+	1.48208i	−0.535617	+	0.844461i	$0.679921\pi$
$798$	665877.	+	1.30686e6i	1.04566	+	2.05221i
$799$		−	373964.i		−	0.585783i
$800$	−565871.	−	1.38729e6i	−0.884174	−	2.16765i
$801$	−643789.			−1.00341
$802$	1.40676e6	−	716778.i	2.18711	−	1.11439i
$803$	−419361.	+	66420.2i	−0.650364	+	0.103008i
$804$	864067.	−	1.18929e6i	1.33670	−	1.83982i
$805$	523786.	+	295196.i	0.808280	+	0.455532i
$806$	−726501.	+	527834.i	−1.11832	+	0.812508i
$807$	850445.	+	850445.i	1.30587	+	1.30587i
$808$	−232466.	+	1.46774e6i	−0.356072	+	2.24815i
$809$	579495.	−	188289.i	0.885427	−	0.287693i	0.169218	−	0.985579i	$-0.445876\pi$
$809$	579495.	−	188289.i	0.885427	−	0.287693i	0.716209	+	0.697886i	$0.245876\pi$
$810$	1.16957e6	+	927150.i	1.78261	+	1.41312i
$811$	−26308.0	+	80967.6i	−0.0399987	+	0.123103i	−0.969062	−	0.246818i	$-0.920615\pi$
$811$	−26308.0	+	80967.6i	−0.0399987	+	0.123103i	0.929063	+	0.369921i	$0.120615\pi$
$812$	956981.	−	1.87818e6i	1.45141	−	2.84856i
$813$	−171251.	−	87256.9i	−0.259091	−	0.132014i
$814$	151321.	+	49167.0i	0.228375	+	0.0742036i
$815$	747865.	−	943407.i	1.12592	−	1.42031i
$816$	−583243.	−	1.79504e6i	−0.875929	−	2.69583i
$817$	252054.	+	39921.4i	0.377615	+	0.0598083i
$818$	881210.	−	881210.i	1.31696	−	1.31696i
$819$	249419.	+	343296.i	0.371845	+	0.511801i
$820$	83881.0	−	148835.i	0.124749	−	0.221350i
$821$	507444.	+	368680.i	0.752839	+	0.546969i	0.896705	−	0.442628i	$-0.145954\pi$
$821$	507444.	+	368680.i	0.752839	+	0.546969i	−0.143867	+	0.989597i	$0.545954\pi$
$822$	−155030.	−	978823.i	−0.229442	−	1.44864i
$823$	173691.	+	340888.i	0.256435	+	0.503283i	0.982951	−	0.183867i	$-0.0588616\pi$
$823$	173691.	+	340888.i	0.256435	+	0.503283i	−0.726516	+	0.687150i	$0.758862\pi$
$824$		−	721242.i		−	1.06225i
$825$	175351.	−	282706.i	0.257633	−	0.415362i
$826$	303131.			0.444293
$827$	943406.	−	480689.i	1.37939	−	0.702835i	0.402271	−	0.915521i	$-0.368221\pi$
$827$	943406.	−	480689.i	1.37939	−	0.702835i	0.977121	+	0.212686i	$0.0682211\pi$
$828$	−1.13443e6	+	179676.i	−1.65469	+	0.262077i
$829$	−81982.0	+	112839.i	−0.119292	+	0.164191i	−0.864487	−	0.502656i	$-0.832356\pi$
$829$	−81982.0	+	112839.i	−0.119292	+	0.164191i	0.745195	+	0.666846i	$0.232356\pi$
$830$	−2.47844e6	+	286554.i	−3.59768	+	0.415959i
$831$	−1.16422e6	+	845852.i	−1.68590	+	1.22488i
$832$	−776405.	−	776405.i	−1.12161	−	1.12161i
$833$	8678.39	−	54793.2i	0.0125069	−	0.0789653i
$834$	−1.63197e6	+	530258.i	−2.34628	+	0.762352i
$835$	−321056.	+	863070.i	−0.460476	+	1.23786i
$836$	203379.	−	625935.i	0.291000	−	0.895606i
$837$	−98688.4	+	193687.i	−0.140869	+	0.276471i
$838$	−1.02290e6	−	521191.i	−1.45661	−	0.742180i
$839$	−518041.	−	168322.i	−0.735937	−	0.239120i	−0.0830178	−	0.996548i	$-0.526456\pi$
$839$	−518041.	−	168322.i	−0.735937	−	0.239120i	−0.652919	+	0.757428i	$0.726456\pi$
$840$	−1.34905e6	−	2.03085e6i	−1.91191	−	2.87819i
$841$	−178769.	−	550195.i	−0.252756	−	0.777902i
$842$	183070.	+	28995.5i	0.258222	+	0.0408983i
$843$	−17518.4	+	17518.4i	−0.0246513	+	0.0246513i
$844$	1.41510e6	+	1.94772e6i	1.98656	+	2.73427i
$845$	33112.3	−	15156.6i	0.0463741	−	0.0212270i
$846$	547583.	+	397842.i	0.765084	+	0.555866i
$847$	91333.9	+	576659.i	0.127311	+	0.803808i
$848$	1.17994e6	+	2.31576e6i	1.64085	+	3.22034i
$849$			1.36814e6i			1.89809i
$850$	1.06900e6	+	89948.3i	1.47959	+	0.124496i
$851$	241504.			0.333476
$852$	2.19164e6	−	1.11669e6i	3.01918	−	1.53835i
$853$	154434.	−	24460.0i	0.212249	−	0.0336169i	−0.0494044	−	0.998779i	$-0.515732\pi$
$853$	154434.	−	24460.0i	0.212249	−	0.0336169i	0.261653	+	0.965162i	$0.415732\pi$
$854$	−439338.	+	604697.i	−0.602397	+	0.829129i
$855$	368581.	−	338870.i	0.504197	−	0.463555i
$856$	−1.31689e6	+	956778.i	−1.79723	+	1.30576i
$857$	−140133.	−	140133.i	−0.190800	−	0.190800i	0.605242	−	0.796042i	$-0.293077\pi$
$857$	−140133.	−	140133.i	−0.190800	−	0.190800i	−0.796042	+	0.605242i	$0.793077\pi$
$858$	102591.	−	647733.i	0.139359	−	0.879876i
$859$	−47304.8	+	15370.3i	−0.0641090	+	0.0208303i	−0.340896	−	0.940101i	$-0.610730\pi$
$859$	−47304.8	+	15370.3i	−0.0641090	+	0.0208303i	0.276787	+	0.960931i	$0.410730\pi$
$860$	−706305.	−	29662.6i	−0.954983	−	0.0401063i
$861$	28652.9	−	88184.4i	0.0386511	−	0.118956i
$862$	−962850.	+	1.88970e6i	−1.29582	+	2.54319i
$863$	437502.	+	222918.i	0.587433	+	0.299312i	0.722331	−	0.691547i	$-0.243071\pi$
$863$	437502.	+	222918.i	0.587433	+	0.299312i	−0.134898	+	0.990859i	$0.543071\pi$
$864$	−679977.	−	220938.i	−0.910892	−	0.295967i
$865$	794308.	−	221703.i	1.06159	−	0.296305i
$866$	−68586.7	−	211088.i	−0.0914543	−	0.281467i
$867$	−356721.	−	56499.1i	−0.474559	−	0.0751628i
$868$	958067.	−	958067.i	1.27162	−	1.27162i
$869$	149037.	+	205131.i	0.197358	+	0.271639i
$870$	−2.42941e6	−	490069.i	−3.20969	−	0.647469i
$871$	418944.	+	304380.i	0.552229	+	0.401218i
$872$	−426759.	−	2.69445e6i	−0.561242	−	3.54354i
$873$	107354.	+	210694.i	0.140861	+	0.276455i
$874$		−	1.39850e6i		−	1.83079i
$875$	713211.	−	135865.i	0.931541	−	0.177457i
$876$	4.35511e6			5.67533
$877$	−967125.	+	492775.i	−1.25743	+	0.640692i	−0.950406	−	0.311011i	$-0.899333\pi$
$877$	−967125.	+	492775.i	−1.25743	+	0.640692i	−0.307022	+	0.951702i	$0.599333\pi$
$878$	−2.29068e6	+	362808.i	−2.97149	+	0.470638i
$879$	−718367.	+	988748.i	−0.929756	+	1.27970i
$880$	−158669.	+	786567.i	−0.204893	+	1.01571i
$881$	826113.	−	600206.i	1.06436	−	0.773301i	0.0894682	−	0.995990i	$-0.471483\pi$
$881$	826113.	−	600206.i	1.06436	−	0.773301i	0.974890	+	0.222688i	$0.0714832\pi$
$882$	70999.2	+	70999.2i	0.0912675	+	0.0912675i
$883$	112090.	−	707709.i	0.143763	−	0.907681i	−0.805363	−	0.592782i	$-0.798030\pi$
$883$	112090.	−	707709.i	0.143763	−	0.907681i	0.949125	−	0.314899i	$-0.101970\pi$
$884$	1.43671e6	−	466816.i	1.83851	−	0.597367i
$885$	−68441.6	−	245210.i	−0.0873844	−	0.313078i
$886$	−61946.8	+	190653.i	−0.0789135	+	0.242871i
$887$	−22165.6	+	43502.4i	−0.0281729	+	0.0552924i	−0.904664	−	0.426126i	$-0.859878\pi$
$887$	−22165.6	+	43502.4i	−0.0281729	+	0.0552924i	0.876491	+	0.481418i	$0.159878\pi$
$888$	−872577.	−	444600.i	−1.10657	−	0.563825i
$889$	264697.	+	86005.2i	0.334923	+	0.108823i
$890$	−91114.1	+	2.16954e6i	−0.115028	+	2.73898i
$891$	−112318.	−	345680.i	−0.141480	−	0.435430i
$892$	−167728.	−	26565.4i	−0.210802	−	0.0333878i
$893$	−416270.	+	416270.i	−0.522002	+	0.522002i
$894$	388381.	+	534560.i	0.485940	+	0.668839i
$895$	165209.	+	179694.i	0.206248	+	0.224330i
$896$	434426.	+	315629.i	0.541127	+	0.393152i
$897$	−155719.	−	983168.i	−0.193533	−	1.22192i
$898$	−1.04869e6	−	2.05817e6i	−1.30045	−	2.55228i
$899$		−	826465.i		−	1.02260i
$900$	−906449.	+	1.04977e6i	−1.11907	+	1.29602i
$901$	−846225.			−1.04240
$902$	−51897.8	+	26443.3i	−0.0637876	+	0.0325014i
$903$	−378947.	+	60019.2i	−0.464732	+	0.0736063i
$904$	610.003	−	839.597i	0.000746440	−	0.00102739i
$905$	95879.9	+	209466.i	0.117066	+	0.255751i
$906$	1.63824e6	−	1.19025e6i	1.99582	−	1.45005i
$907$	−911565.	−	911565.i	−1.10809	−	1.10809i	−0.993402	−	0.114683i	$-0.963415\pi$
$907$	−911565.	−	911565.i	−1.10809	−	1.10809i	−0.114683	−	0.993402i	$-0.536585\pi$
$908$	−1766.51	+	11153.3i	−0.00214261	+	0.0135279i
$909$	436349.	−	141778.i	0.528088	−	0.171586i
$910$	1.19219e6	−	791946.i	1.43967	−	0.956341i
$911$	215515.	−	663288.i	0.259682	−	0.799218i	−0.733189	−	0.680025i	$-0.761969\pi$
$911$	215515.	−	663288.i	0.259682	−	0.799218i	0.992871	−	0.119194i	$-0.0380309\pi$
$912$	−1.34888e6	+	2.64733e6i	−1.62175	+	3.18286i
$913$	541380.	+	275847.i	0.649472	+	0.330923i
$914$	157442.	+	51156.1i	0.188464	+	0.0612357i
$915$	588350.	+	218862.i	0.702738	+	0.261413i
$916$	562531.	+	1.73129e6i	0.670433	+	2.06338i
$917$	−902193.	−	142893.i	−1.07290	−	0.169931i
$918$	361990.	−	361990.i	0.429547	−	0.429547i
$919$	137777.	+	189634.i	0.163134	+	0.224535i	0.882757	−	0.469831i	$-0.155685\pi$
$919$	137777.	+	189634.i	0.163134	+	0.224535i	−0.719622	+	0.694366i	$0.755685\pi$
$920$	266998.	+	2.30930e6i	0.315451	+	2.72838i
$921$	−1.15080e6	−	836102.i	−1.35669	−	0.985689i
$922$	46905.5	+	296150.i	0.0551775	+	0.348377i
$923$	393372.	+	772036.i	0.461743	+	0.906221i
$924$			989482.i			1.15895i
$925$	222778.	−	188197.i	0.260368	−	0.219953i
$926$	−1.89964e6			−2.21538
$927$	−198409.	+	101094.i	−0.230888	+	0.117643i
$928$	2.68481e6	−	425232.i	3.11758	−	0.493776i
$929$	76222.2	−	104911.i	0.0883182	−	0.121560i	−0.762572	−	0.646904i	$-0.776063\pi$
$929$	76222.2	−	104911.i	0.0883182	−	0.121560i	0.850890	+	0.525344i	$0.176063\pi$
$930$	−1.38778e6	−	782129.i	−1.60456	−	0.904299i
$931$	−70652.0	+	51331.7i	−0.0815126	+	0.0592224i
$932$	1.51212e6	+	1.51212e6i	1.74082	+	1.74082i
$933$	160013.	−	1.01028e6i	0.183820	−	1.16059i
$934$	−76142.6	+	24740.2i	−0.0872839	+	0.0283603i
$935$	−204733.	−	162297.i	−0.234188	−	0.185647i
$936$	−507000.	+	1.56038e6i	−0.578703	+	1.78107i
$937$	188224.	−	369410.i	0.214386	−	0.420755i	−0.758621	−	0.651532i	$-0.774127\pi$
$937$	188224.	−	369410.i	0.214386	−	0.420755i	0.973007	+	0.230777i	$0.0741266\pi$
$938$	−974581.	−	496574.i	−1.10768	−	0.564389i
$939$	699282.	+	227211.i	0.793088	+	0.257690i
$940$	1.01306e6	−	1.27794e6i	1.14651	−	1.44628i
$941$	90054.6	+	277160.i	0.101701	+	0.313005i	0.988942	−	0.148302i	$-0.0473808\pi$
$941$	90054.6	+	277160.i	0.101701	+	0.313005i	−0.887241	+	0.461307i	$0.847381\pi$
$942$	764919.	+	121151.i	0.862012	+	0.136529i
$943$	−62515.2	+	62515.2i	−0.0703011	+	0.0703011i
$944$	360934.	+	496783.i	0.405027	+	0.557472i
$945$	170106.	−	301830.i	0.190483	−	0.337986i
$946$	194984.	+	141664.i	0.217879	+	0.158299i
$947$	−63384.0	−	400191.i	−0.0706772	−	0.446238i	−0.997496	−	0.0707285i	$-0.977468\pi$
$947$	−63384.0	−	400191.i	−0.0706772	−	0.446238i	0.926818	−	0.375510i	$-0.122532\pi$
$948$	−1.18074e6	−	2.31733e6i	−1.31382	−	2.57852i
$949$			1.53415e6i			1.70348i
$950$	−1.08981e6	−	1.29006e6i	−1.20755	−	1.42943i
$951$	1.15553e6			1.27768
$952$	−1.70602e6	+	869260.i	−1.88239	+	0.959126i
$953$	87927.4	−	13926.3i	0.0968141	−	0.0153338i	−0.107839	−	0.994168i	$-0.534393\pi$
$953$	87927.4	−	13926.3i	0.0968141	−	0.0153338i	0.204653	+	0.978834i	$0.434393\pi$
$954$	900256.	−	1.23910e6i	0.989166	−	1.36147i
$955$	188020.	−	21738.6i	0.206157	−	0.0238356i
$956$	1.60379e6	−	1.16522e6i	1.75481	−	1.27495i
$957$	426782.	+	426782.i	0.465996	+	0.465996i
$958$	−54298.8	+	342829.i	−0.0591642	+	0.373548i
$959$	−500947.	+	162767.i	−0.544696	+	0.176983i
$960$	679098.	−	1.82557e6i	0.736868	−	1.98087i
$961$	−121226.	+	373096.i	−0.131265	+	0.403993i
$962$	260999.	−	512239.i	0.282026	−	0.553507i
$963$	447789.	+	228160.i	0.482859	+	0.246029i
$964$	−2.39680e6	−	778769.i	−2.57916	−	0.838020i
$965$	−424781.	−	639464.i	−0.456153	−	0.686691i
$966$	649725.	+	1.99965e6i	0.696266	+	2.14289i
$967$	−262123.	−	41516.3i	−0.280319	−	0.0443982i	0.0146917	−	0.999892i	$-0.495323\pi$
$967$	−262123.	−	41516.3i	−0.280319	−	0.0443982i	−0.295011	+	0.955494i	$0.595323\pi$
$968$	−1.59624e6	+	1.59624e6i	−1.70352	+	1.70352i
$969$	−568615.	−	782632.i	−0.605579	−	0.833508i
$970$	725224.	−	331960.i	0.770777	−	0.352811i
$971$	485785.	+	352943.i	0.515235	+	0.374340i	0.814806	−	0.579734i	$-0.196844\pi$
$971$	485785.	+	352943.i	0.515235	+	0.374340i	−0.299571	+	0.954074i	$0.596844\pi$
$972$	432027.	+	2.72771e6i	0.457276	+	2.88712i
$973$	414050.	+	812619.i	0.437348	+	0.858344i
$974$			1.79904e6i			1.89637i
$975$	−909802.	−	785588.i	−0.957057	−	0.826391i
$976$	−1.51412e6			−1.58950
$977$	−466605.	+	237747.i	−0.488833	+	0.249073i	−0.680992	−	0.732291i	$-0.738451\pi$
$977$	−466605.	+	237747.i	−0.488833	+	0.249073i	0.192159	+	0.981364i	$0.438451\pi$
$978$	4.15814e6	−	658585.i	4.34732	−	0.688548i
$979$	310834.	−	427826.i	0.324312	−	0.446377i
$980$	178089.	−	163734.i	0.185432	−	0.170485i
$981$	−681409.	+	495073.i	−0.708060	+	0.514436i
$982$	−152030.	−	152030.i	−0.157655	−	0.157655i
$983$	−230984.	+	1.45838e6i	−0.239042	+	1.50925i	0.517712	+	0.855555i	$0.326784\pi$
$983$	−230984.	+	1.45838e6i	−0.239042	+	1.50925i	−0.756755	+	0.653699i	$0.773216\pi$
$984$	340962.	−	110785.i	0.352141	−	0.114417i
$985$	−1.69987e6	−	71389.2i	−1.75204	−	0.0735800i
$986$	−601449.	+	1.85107e6i	−0.618650	+	1.90401i
$987$	401811.	−	788599.i	0.412466	−	0.809509i
$988$	−2.11887e6	−	1.07962e6i	−2.17065	−	1.10600i
$989$	347920.	+	113046.i	0.355702	+	0.115575i
$990$	455451.	−	127123.i	0.464698	−	0.129704i
$991$	−289694.	−	891588.i	−0.294980	−	0.907856i	−0.983228	−	0.182380i	$-0.941620\pi$
$991$	−289694.	−	891588.i	−0.294980	−	0.907856i	0.688248	−	0.725476i	$-0.258380\pi$
$992$	1.72571e6	+	273325.i	1.75365	+	0.277752i
$993$	−618529.	+	618529.i	−0.627280	+	0.627280i
$994$	−1.07576e6	−	1.48065e6i	−1.08878	−	1.49858i
$995$	1.27272e6	+	256737.i	1.28554	+	0.259324i
$996$	−5.04209e6	−	3.66329e6i	−5.08267	−	3.69278i
$997$	46548.7	+	293897.i	0.0468293	+	0.295669i	0.999977	−	0.00683795i	$-0.00217660\pi$
$997$	46548.7	+	293897.i	0.0468293	+	0.295669i	−0.953147	+	0.302506i	$0.902177\pi$
$998$	562107.	+	1.10320e6i	0.564362	+	1.10762i
$999$		−	139166.i		−	0.139445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.5.f.a.22.1	yes	72
5.2	odd	4		125.5.f.a.118.1		72
5.3	odd	4		125.5.f.b.118.9		72
5.4	even	2		125.5.f.c.7.9		72
25.6	even	5		125.5.f.b.107.9		72
25.8	odd	20	inner	25.5.f.a.8.1	✓	72
25.17	odd	20		125.5.f.c.18.9		72
25.19	even	10		125.5.f.a.107.1		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.5.f.a.8.1	✓	72	25.8	odd	20	inner
25.5.f.a.22.1	yes	72	1.1	even	1	trivial
125.5.f.a.107.1		72	25.19	even	10
125.5.f.a.118.1		72	5.2	odd	4
125.5.f.b.107.9		72	25.6	even	5
125.5.f.b.118.9		72	5.3	odd	4
125.5.f.c.7.9		72	5.4	even	2
125.5.f.c.18.9		72	25.17	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)

\(f(q)\)	\(=\)	\(q+(-6.66808 + 3.39756i) q^{2} +(11.5382 - 1.82747i) q^{3} +(23.5154 - 32.3661i) q^{4} +(-4.94350 + 24.5064i) q^{5} +(-70.7286 + 51.3874i) q^{6} +(32.8567 + 32.8567i) q^{7} +(-28.1051 + 177.449i) q^{8} +(52.7545 - 17.1410i) q^{9} +O(q^{10})\)	\(q+(-6.66808 + 3.39756i) q^{2} +(11.5382 - 1.82747i) q^{3} +(23.5154 - 32.3661i) q^{4} +(-4.94350 + 24.5064i) q^{5} +(-70.7286 + 51.3874i) q^{6} +(32.8567 + 32.8567i) q^{7} +(-28.1051 + 177.449i) q^{8} +(52.7545 - 17.1410i) q^{9} +(-50.2981 - 180.206i) q^{10} +(-14.0800 + 43.3336i) q^{11} +(212.177 - 416.420i) q^{12} +(146.690 + 74.7423i) q^{13} +(-330.724 - 107.459i) q^{14} +(-12.2544 + 291.793i) q^{15} +(-217.681 - 669.953i) q^{16} +(226.533 + 35.8793i) q^{17} +(-293.534 + 293.534i) q^{18} +(-212.222 - 292.098i) q^{19} +(676.928 + 736.278i) q^{20} +(439.151 + 319.062i) q^{21} +(-53.3423 - 336.790i) q^{22} +(-234.973 - 461.160i) q^{23} +2098.80i q^{24} +(-576.124 - 242.294i) q^{25} -1232.08 q^{26} +(-265.742 + 135.402i) q^{27} +(1836.08 - 290.807i) q^{28} +(666.506 - 917.366i) q^{29} +(-909.670 - 1987.33i) q^{30} +(589.653 - 428.408i) q^{31} +(1695.09 + 1695.09i) q^{32} +(-83.2662 + 525.722i) q^{33} +(-1632.44 + 530.412i) q^{34} +(-967.625 + 642.771i) q^{35} +(685.754 - 2110.53i) q^{36} +(-211.836 + 415.751i) q^{37} +(2407.53 + 1226.70i) q^{38} +(1829.12 + 594.319i) q^{39} +(-4209.69 - 1565.97i) q^{40} +(-52.7851 - 162.456i) q^{41} +(-4012.33 - 635.490i) q^{42} +(-499.789 + 499.789i) q^{43} +(1071.45 + 1474.72i) q^{44} +(159.271 + 1377.56i) q^{45} +(3133.64 + 2276.72i) q^{46} +(-255.065 - 1610.42i) q^{47} +(-3735.96 - 7332.24i) q^{48} -241.877i q^{49} +(4664.85 - 341.774i) q^{50} +2679.35 q^{51} +(5868.58 - 2990.19i) q^{52} +(-3644.13 + 577.174i) q^{53} +(1311.95 - 1805.75i) q^{54} +(-992.346 - 559.268i) q^{55} +(-6753.82 + 4906.94i) q^{56} +(-2982.45 - 2982.45i) q^{57} +(-1327.51 + 8381.56i) q^{58} +(-829.044 + 269.373i) q^{59} +(9156.04 + 7258.25i) q^{60} +(664.208 - 2044.22i) q^{61} +(-2476.32 + 4860.04i) q^{62} +(2296.53 + 1170.14i) q^{63} +(-6342.93 - 2060.94i) q^{64} +(-2556.82 + 3225.35i) q^{65} +(-1230.95 - 3788.46i) q^{66} +(3106.69 + 492.052i) q^{67} +(6488.27 - 6488.27i) q^{68} +(-3553.92 - 4891.55i) q^{69} +(4268.35 - 7573.61i) q^{70} +(4257.89 + 3093.54i) q^{71} +(1558.97 + 9842.96i) q^{72} +(4230.54 + 8302.90i) q^{73} -3491.99i q^{74} +(-7090.21 - 1742.79i) q^{75} -14444.6 q^{76} +(-1886.42 + 961.179i) q^{77} +(-14216.0 + 2251.59i) q^{78} +(3270.95 - 4502.08i) q^{79} +(17494.2 - 2022.66i) q^{80} +(-6453.67 + 4688.86i) q^{81} +(903.929 + 903.929i) q^{82} +(2086.10 - 13171.1i) q^{83} +(20653.6 - 6710.76i) q^{84} +(-1999.14 + 5374.13i) q^{85} +(1634.57 - 5030.70i) q^{86} +(6013.81 - 11802.8i) q^{87} +(-7293.78 - 3716.37i) q^{88} +(-11038.2 - 3586.52i) q^{89} +(-5742.36 - 8644.53i) q^{90} +(2363.96 + 7275.53i) q^{91} +(-20451.4 - 3239.19i) q^{92} +(6020.63 - 6020.63i) q^{93} +(7172.29 + 9871.81i) q^{94} +(8207.38 - 3756.80i) q^{95} +(22656.0 + 16460.6i) q^{96} +(666.885 + 4210.55i) q^{97} +(821.793 + 1612.86i) q^{98} +2527.39i 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more