LMFDB - Embedded newform 483.8.a.h.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,8,Mod(1,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("483.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	483.a (trivial)

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:	yes
Analytic conductor:	$150.881967309$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 2001 x^{18} + 9297 x^{17} + 1659337 x^{16} - 8672053 x^{15} - 738401777 x^{14} + \cdots - 22\!\cdots\!64 $ x^20 - 4x^19 - 2001x^18 + 9297x^17 + 1659337x^16 - 8672053x^15 - 738401777x^14 + 4248573317x^13 + 190725569395x^12 - 1191766077909x^11 - 28809268305651x^10 + 194059760420751x^9 + 2416325036841643x^8 - 17542703161820151x^7 - 96562220978595987x^6 + 769676768580639007x^5 + 1106866539128328056x^4 - 11190813130219227259x^3 + 3800031563479945160x^2 + 10696825777367791356*x - 2276660808569002464
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	multiple of $ 2^{16}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Root			$18.8751$ of defining polynomial
Character	$\chi$	$=$	483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+19.8751 q^{2} +27.0000 q^{3} +267.021 q^{4} +443.021 q^{5} +536.629 q^{6} +343.000 q^{7} +2763.06 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+19.8751 q^{2} +27.0000 q^{3} +267.021 q^{4} +443.021 q^{5} +536.629 q^{6} +343.000 q^{7} +2763.06 q^{8} +729.000 q^{9} +8805.11 q^{10} -3729.03 q^{11} +7209.57 q^{12} +472.823 q^{13} +6817.17 q^{14} +11961.6 q^{15} +20737.6 q^{16} -16542.6 q^{17} +14489.0 q^{18} +9339.90 q^{19} +118296. q^{20} +9261.00 q^{21} -74115.0 q^{22} -12167.0 q^{23} +74602.7 q^{24} +118143. q^{25} +9397.42 q^{26} +19683.0 q^{27} +91588.2 q^{28} +197433. q^{29} +237738. q^{30} +307025. q^{31} +58489.9 q^{32} -100684. q^{33} -328787. q^{34} +151956. q^{35} +194658. q^{36} +277220. q^{37} +185632. q^{38} +12766.2 q^{39} +1.22410e6 q^{40} +43551.7 q^{41} +184064. q^{42} -585.889 q^{43} -995730. q^{44} +322963. q^{45} -241821. q^{46} +1.01643e6 q^{47} +559914. q^{48} +117649. q^{49} +2.34811e6 q^{50} -446651. q^{51} +126254. q^{52} -46957.0 q^{53} +391202. q^{54} -1.65204e6 q^{55} +947731. q^{56} +252177. q^{57} +3.92401e6 q^{58} -2.61753e6 q^{59} +3.19399e6 q^{60} -1.97260e6 q^{61} +6.10216e6 q^{62} +250047. q^{63} -1.49191e6 q^{64} +209471. q^{65} -2.00110e6 q^{66} +1.51984e6 q^{67} -4.41723e6 q^{68} -328509. q^{69} +3.02015e6 q^{70} +3.58087e6 q^{71} +2.01427e6 q^{72} -6.16605e6 q^{73} +5.50978e6 q^{74} +3.18986e6 q^{75} +2.49395e6 q^{76} -1.27906e6 q^{77} +253730. q^{78} -3.22372e6 q^{79} +9.18719e6 q^{80} +531441. q^{81} +865595. q^{82} -981033. q^{83} +2.47288e6 q^{84} -7.32873e6 q^{85} -11644.6 q^{86} +5.33070e6 q^{87} -1.03035e7 q^{88} -1.54313e6 q^{89} +6.41892e6 q^{90} +162178. q^{91} -3.24885e6 q^{92} +8.28966e6 q^{93} +2.02018e7 q^{94} +4.13777e6 q^{95} +1.57923e6 q^{96} +1.09117e7 q^{97} +2.33829e6 q^{98} -2.71846e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 24 q^{2} + 540 q^{3} + 1486 q^{4} + 1069 q^{5} + 648 q^{6} + 6860 q^{7} + 2127 q^{8} + 14580 q^{9}+O(q^{10}) $ 20 * q + 24 * q^2 + 540 * q^3 + 1486 * q^4 + 1069 * q^5 + 648 * q^6 + 6860 * q^7 + 2127 * q^8 + 14580 * q^9	\( 20 q + 24 q^{2} + 540 q^{3} + 1486 q^{4} + 1069 q^{5} + 648 q^{6} + 6860 q^{7} + 2127 q^{8} + 14580 q^{9} - 1949 q^{10} + 10073 q^{11} + 40122 q^{12} + 13391 q^{13} + 8232 q^{14} + 28863 q^{15} + 133122 q^{16} + 62626 q^{17} + 17496 q^{18} + 9895 q^{19} + 106064 q^{20} + 185220 q^{21} + 28599 q^{22} - 243340 q^{23} + 57429 q^{24} + 265365 q^{25} + 594400 q^{26} + 393660 q^{27} + 509698 q^{28} + 594658 q^{29} - 52623 q^{30} + 514862 q^{31} + 832720 q^{32} + 271971 q^{33} - 106257 q^{34} + 366667 q^{35} + 1083294 q^{36} + 891864 q^{37} + 680125 q^{38} + 361557 q^{39} + 44594 q^{40} + 296689 q^{41} + 222264 q^{42} - 704949 q^{43} + 2001503 q^{44} + 779301 q^{45} - 292008 q^{46} + 2102453 q^{47} + 3594294 q^{48} + 2352980 q^{49} + 4129604 q^{50} + 1690902 q^{51} + 4416739 q^{52} + 5841486 q^{53} + 472392 q^{54} + 4290005 q^{55} + 729561 q^{56} + 267165 q^{57} + 7165650 q^{58} + 7015980 q^{59} + 2863728 q^{60} + 2474138 q^{61} + 4418145 q^{62} + 5000940 q^{63} + 12695973 q^{64} + 6582462 q^{65} + 772173 q^{66} + 2305855 q^{67} + 10253157 q^{68} - 6570180 q^{69} - 668507 q^{70} + 12287349 q^{71} + 1550583 q^{72} + 9140922 q^{73} - 832604 q^{74} + 7164855 q^{75} + 290029 q^{76} + 3455039 q^{77} + 16048800 q^{78} - 1444882 q^{79} + 2254323 q^{80} + 10628820 q^{81} + 6031922 q^{82} + 4284072 q^{83} + 13761846 q^{84} + 15450581 q^{85} + 19710382 q^{86} + 16055766 q^{87} - 4553328 q^{88} + 36265659 q^{89} - 1420821 q^{90} + 4593113 q^{91} - 18080162 q^{92} + 13901274 q^{93} + 11807737 q^{94} + 35752199 q^{95} + 22483440 q^{96} + 15575692 q^{97} + 2823576 q^{98} + 7343217 q^{99}+O(q^{100}) \) 20 * q + 24 * q^2 + 540 * q^3 + 1486 * q^4 + 1069 * q^5 + 648 * q^6 + 6860 * q^7 + 2127 * q^8 + 14580 * q^9 - 1949 * q^10 + 10073 * q^11 + 40122 * q^12 + 13391 * q^13 + 8232 * q^14 + 28863 * q^15 + 133122 * q^16 + 62626 * q^17 + 17496 * q^18 + 9895 * q^19 + 106064 * q^20 + 185220 * q^21 + 28599 * q^22 - 243340 * q^23 + 57429 * q^24 + 265365 * q^25 + 594400 * q^26 + 393660 * q^27 + 509698 * q^28 + 594658 * q^29 - 52623 * q^30 + 514862 * q^31 + 832720 * q^32 + 271971 * q^33 - 106257 * q^34 + 366667 * q^35 + 1083294 * q^36 + 891864 * q^37 + 680125 * q^38 + 361557 * q^39 + 44594 * q^40 + 296689 * q^41 + 222264 * q^42 - 704949 * q^43 + 2001503 * q^44 + 779301 * q^45 - 292008 * q^46 + 2102453 * q^47 + 3594294 * q^48 + 2352980 * q^49 + 4129604 * q^50 + 1690902 * q^51 + 4416739 * q^52 + 5841486 * q^53 + 472392 * q^54 + 4290005 * q^55 + 729561 * q^56 + 267165 * q^57 + 7165650 * q^58 + 7015980 * q^59 + 2863728 * q^60 + 2474138 * q^61 + 4418145 * q^62 + 5000940 * q^63 + 12695973 * q^64 + 6582462 * q^65 + 772173 * q^66 + 2305855 * q^67 + 10253157 * q^68 - 6570180 * q^69 - 668507 * q^70 + 12287349 * q^71 + 1550583 * q^72 + 9140922 * q^73 - 832604 * q^74 + 7164855 * q^75 + 290029 * q^76 + 3455039 * q^77 + 16048800 * q^78 - 1444882 * q^79 + 2254323 * q^80 + 10628820 * q^81 + 6031922 * q^82 + 4284072 * q^83 + 13761846 * q^84 + 15450581 * q^85 + 19710382 * q^86 + 16055766 * q^87 - 4553328 * q^88 + 36265659 * q^89 - 1420821 * q^90 + 4593113 * q^91 - 18080162 * q^92 + 13901274 * q^93 + 11807737 * q^94 + 35752199 * q^95 + 22483440 * q^96 + 15575692 * q^97 + 2823576 * q^98 + 7343217 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	19.8751	1.75673	0.878365	−	0.477990i	$-0.158634\pi$
$2$	19.8751	1.75673	0.878365	+	0.477990i	$0.158634\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	267.021	2.08610
$5$	443.021	1.58500	0.792501	−	0.609871i	$-0.208779\pi$
$5$	443.021	1.58500	0.792501	+	0.609871i	$0.208779\pi$
$6$	536.629	1.01425
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	2763.06	1.90799
$9$	729.000	0.333333
$10$	8805.11	2.78442
$11$	−3729.03	−0.844737	−0.422368	−	0.906424i	$-0.638801\pi$
$11$	−3729.03	−0.844737	−0.422368	+	0.906424i	$0.638801\pi$
$12$	7209.57	1.20441
$13$	472.823	0.0596893	0.0298447	−	0.999555i	$-0.490499\pi$
$13$	472.823	0.0596893	0.0298447	+	0.999555i	$0.490499\pi$
$14$	6817.17	0.663982
$15$	11961.6	0.915101
$16$	20737.6	1.26572
$17$	−16542.6	−0.816644	−0.408322	−	0.912838i	$-0.633886\pi$
$17$	−16542.6	−0.816644	−0.408322	+	0.912838i	$0.633886\pi$
$18$	14489.0	0.585577
$19$	9339.90	0.312395	0.156198	−	0.987726i	$-0.450076\pi$
$19$	9339.90	0.312395	0.156198	+	0.987726i	$0.450076\pi$
$20$	118296.	3.30647
$21$	9261.00	0.218218
$22$	−74115.0	−1.48398
$23$	−12167.0	−0.208514
$23$	−12167.0	−0.208514
$24$	74602.7	1.10158
$25$	118143.	1.51223
$26$	9397.42	0.104858
$27$	19683.0	0.192450
$28$	91588.2	0.788473
$29$	197433.	1.50324	0.751618	−	0.659598i	$-0.229274\pi$
$29$	197433.	1.50324	0.751618	+	0.659598i	$0.229274\pi$
$30$	237738.	1.60759
$31$	307025.	1.85100	0.925502	−	0.378743i	$-0.123644\pi$
$31$	307025.	1.85100	0.925502	+	0.378743i	$0.123644\pi$
$32$	58489.9	0.315541
$33$	−100684.	−0.487709
$34$	−328787.	−1.43462
$35$	151956.	0.599074
$36$	194658.	0.695367
$37$	277220.	0.899742	0.449871	−	0.893094i	$-0.351470\pi$
$37$	277220.	0.899742	0.449871	+	0.893094i	$0.351470\pi$
$38$	185632.	0.548794
$39$	12766.2	0.0344616
$40$	1.22410e6	3.02417
$41$	43551.7	0.0986873	0.0493436	−	0.998782i	$-0.484287\pi$
$41$	43551.7	0.0986873	0.0493436	+	0.998782i	$0.484287\pi$
$42$	184064.	0.383350
$43$	−585.889	−0.00112377	−0.000561883	−	1.00000i	$-0.500179\pi$
$43$	−585.889	−0.00112377	−0.000561883		1.00000i	$0.500179\pi$
$44$	−995730.	−1.76221
$45$	322963.	0.528334
$46$	−241821.	−0.366304
$47$	1.01643e6	1.42803	0.714014	−	0.700131i	$-0.246875\pi$
$47$	1.01643e6	1.42803	0.714014	+	0.700131i	$0.246875\pi$
$48$	559914.	0.730764
$49$	117649.	0.142857
$50$	2.34811e6	2.65658
$51$	−446651.	−0.471490
$52$	126254.	0.124518
$53$	−46957.0	−0.0433246	−0.0216623	−	0.999765i	$-0.506896\pi$
$53$	−46957.0	−0.0433246	−0.0216623	+	0.999765i	$0.506896\pi$
$54$	391202.	0.338083
$55$	−1.65204e6	−1.33891
$56$	947731.	0.721152
$57$	252177.	0.180361
$58$	3.92401e6	2.64078
$59$	−2.61753e6	−1.65924	−0.829621	−	0.558327i	$-0.811444\pi$
$59$	−2.61753e6	−1.65924	−0.829621	+	0.558327i	$0.811444\pi$
$60$	3.19399e6	1.90899
$61$	−1.97260e6	−1.11272	−0.556359	−	0.830942i	$-0.687802\pi$
$61$	−1.97260e6	−1.11272	−0.556359	+	0.830942i	$0.687802\pi$
$62$	6.10216e6	3.25171
$63$	250047.	0.125988
$64$	−1.49191e6	−0.711400
$65$	209471.	0.0946076
$66$	−2.00110e6	−0.856773
$67$	1.51984e6	0.617355	0.308677	−	0.951167i	$-0.400114\pi$
$67$	1.51984e6	0.617355	0.308677	+	0.951167i	$0.400114\pi$
$68$	−4.41723e6	−1.70360
$69$	−328509.	−0.120386
$70$	3.02015e6	1.05241
$71$	3.58087e6	1.18737	0.593683	−	0.804699i	$-0.297673\pi$
$71$	3.58087e6	1.18737	0.593683	+	0.804699i	$0.297673\pi$
$72$	2.01427e6	0.635996
$73$	−6.16605e6	−1.85514	−0.927571	−	0.373647i	$-0.878107\pi$
$73$	−6.16605e6	−1.85514	−0.927571	+	0.373647i	$0.878107\pi$
$74$	5.50978e6	1.58060
$75$	3.18986e6	0.873086
$76$	2.49395e6	0.651689
$77$	−1.27906e6	−0.319281
$78$	253730.	0.0605398
$79$	−3.22372e6	−0.735636	−0.367818	−	0.929898i	$-0.619895\pi$
$79$	−3.22372e6	−0.735636	−0.367818	+	0.929898i	$0.619895\pi$
$80$	9.18719e6	2.00617
$81$	531441.	0.111111
$82$	865595.	0.173367
$83$	−981033.	−0.188326	−0.0941630	−	0.995557i	$-0.530017\pi$
$83$	−981033.	−0.188326	−0.0941630	+	0.995557i	$0.530017\pi$
$84$	2.47288e6	0.455225
$85$	−7.32873e6	−1.29438
$86$	−11644.6	−0.00197415
$87$	5.33070e6	0.867894
$88$	−1.03035e7	−1.61175
$89$	−1.54313e6	−0.232026	−0.116013	−	0.993248i	$-0.537011\pi$
$89$	−1.54313e6	−0.232026	−0.116013	+	0.993248i	$0.537011\pi$
$90$	6.41892e6	0.928140
$91$	162178.	0.0225604
$92$	−3.24885e6	−0.434982
$93$	8.28966e6	1.06868
$94$	2.02018e7	2.50866
$95$	4.13777e6	0.495147
$96$	1.57923e6	0.182178
$97$	1.09117e7	1.21393	0.606964	−	0.794730i	$-0.292387\pi$
$97$	1.09117e7	1.21393	0.606964	+	0.794730i	$0.292387\pi$
$98$	2.33829e6	0.250962
$99$	−2.71846e6	−0.281579
$100$	3.15466e7	3.15466
$101$	9.80494e6	0.946935	0.473468	−	0.880811i	$-0.343002\pi$
$101$	9.80494e6	0.946935	0.473468	+	0.880811i	$0.343002\pi$
$102$	−8.87724e6	−0.828280
$103$	−1.46206e7	−1.31836	−0.659181	−	0.751984i	$-0.729097\pi$
$103$	−1.46206e7	−1.31836	−0.659181	+	0.751984i	$0.729097\pi$
$104$	1.30644e6	0.113887
$105$	4.10282e6	0.345876
$106$	−933276.	−0.0761097
$107$	−1.05971e7	−0.836263	−0.418132	−	0.908386i	$-0.637315\pi$
$107$	−1.05971e7	−0.836263	−0.418132	+	0.908386i	$0.637315\pi$
$108$	5.25578e6	0.401471
$109$	4.79841e6	0.354899	0.177449	−	0.984130i	$-0.443215\pi$
$109$	4.79841e6	0.354899	0.177449	+	0.984130i	$0.443215\pi$
$110$	−3.28345e7	−2.35210
$111$	7.48493e6	0.519466
$112$	7.11299e6	0.478397
$113$	−2.19612e7	−1.43180	−0.715898	−	0.698205i	$-0.753982\pi$
$113$	−2.19612e7	−1.43180	−0.715898	+	0.698205i	$0.753982\pi$
$114$	5.01206e6	0.316847
$115$	−5.39024e6	−0.330496
$116$	5.27188e7	3.13591
$117$	344688.	0.0198964
$118$	−5.20238e7	−2.91484
$119$	−5.67412e6	−0.308662
$120$	3.30506e7	1.74600
$121$	−5.58151e6	−0.286420
$122$	−3.92057e7	−1.95475
$123$	1.17589e6	0.0569771
$124$	8.19821e7	3.86138
$125$	1.77288e7	0.811883
$126$	4.96972e6	0.221327
$127$	−4.20973e7	−1.82365	−0.911824	−	0.410581i	$-0.865326\pi$
$127$	−4.20973e7	−1.82365	−0.911824	+	0.410581i	$0.865326\pi$
$128$	−3.71387e7	−1.56528
$129$	−15819.0	−0.000648806 0
$130$	4.16326e6	0.166200
$131$	−2.23002e7	−0.866683	−0.433341	−	0.901230i	$-0.642666\pi$
$131$	−2.23002e7	−0.866683	−0.433341	+	0.901230i	$0.642666\pi$
$132$	−2.68847e7	−1.01741
$133$	3.20358e6	0.118074
$134$	3.02069e7	1.08453
$135$	8.71999e6	0.305034
$136$	−4.57083e7	−1.55815
$137$	2.18005e7	0.724343	0.362171	−	0.932112i	$-0.382036\pi$
$137$	2.18005e7	0.724343	0.362171	+	0.932112i	$0.382036\pi$
$138$	−6.52916e6	−0.211486
$139$	−3.28412e7	−1.03721	−0.518605	−	0.855014i	$-0.673548\pi$
$139$	−3.28412e7	−1.03721	−0.518605	+	0.855014i	$0.673548\pi$
$140$	4.05755e7	1.24973
$141$	2.74437e7	0.824472
$142$	7.11703e7	2.08588
$143$	−1.76317e6	−0.0504218
$144$	1.51177e7	0.421907
$145$	8.74671e7	2.38263
$146$	−1.22551e8	−3.25898
$147$	3.17652e6	0.0824786
$148$	7.40235e7	1.87695
$149$	−5.27485e7	−1.30635	−0.653173	−	0.757208i	$-0.726563\pi$
$149$	−5.27485e7	−1.30635	−0.653173	+	0.757208i	$0.726563\pi$
$150$	6.33989e7	1.53378
$151$	6.01165e7	1.42093	0.710467	−	0.703730i	$-0.248484\pi$
$151$	6.01165e7	1.42093	0.710467	+	0.703730i	$0.248484\pi$
$152$	2.58067e7	0.596047
$153$	−1.20596e7	−0.272215
$154$	−2.54214e7	−0.560890
$155$	1.36018e8	2.93384
$156$	3.40885e6	0.0718905
$157$	−9.43107e7	−1.94497	−0.972483	−	0.232972i	$-0.925155\pi$
$157$	−9.43107e7	−1.94497	−0.972483	+	0.232972i	$0.925155\pi$
$158$	−6.40719e7	−1.29231
$159$	−1.26784e6	−0.0250135
$160$	2.59123e7	0.500133
$161$	−4.17328e6	−0.0788110
$162$	1.05625e7	0.195192
$163$	4.05377e7	0.733167	0.366583	−	0.930385i	$-0.380527\pi$
$163$	4.05377e7	0.733167	0.366583	+	0.930385i	$0.380527\pi$
$164$	1.16292e7	0.205872
$165$	−4.46051e7	−0.773019
$166$	−1.94982e7	−0.330838
$167$	−3.20443e7	−0.532406	−0.266203	−	0.963917i	$-0.585769\pi$
$167$	−3.20443e7	−0.532406	−0.266203	+	0.963917i	$0.585769\pi$
$168$	2.55887e7	0.416357
$169$	−6.25250e7	−0.996437
$170$	−1.45660e8	−2.27388
$171$	6.80878e6	0.104132
$172$	−156445.	−0.00234429
$173$	8.33625e7	1.22408	0.612039	−	0.790827i	$-0.290349\pi$
$173$	8.33625e7	1.22408	0.612039	+	0.790827i	$0.290349\pi$
$174$	1.05948e8	1.52466
$175$	4.05230e7	0.571569
$176$	−7.73310e7	−1.06920
$177$	−7.06733e7	−0.957964
$178$	−3.06699e7	−0.407608
$179$	6.31833e7	0.823411	0.411705	−	0.911317i	$-0.364933\pi$
$179$	6.31833e7	0.823411	0.411705	+	0.911317i	$0.364933\pi$
$180$	8.62378e7	1.10216
$181$	−1.77510e7	−0.222509	−0.111254	−	0.993792i	$-0.535487\pi$
$181$	−1.77510e7	−0.222509	−0.111254	+	0.993792i	$0.535487\pi$
$182$	3.22331e6	0.0396326
$183$	−5.32602e7	−0.642428
$184$	−3.36182e7	−0.397843
$185$	1.22814e8	1.42609
$186$	1.64758e8	1.87738
$187$	6.16879e7	0.689849
$188$	2.71409e8	2.97901
$189$	6.75127e6	0.0727393
$190$	8.22388e7	0.869840
$191$	1.41060e7	0.146483	0.0732416	−	0.997314i	$-0.476666\pi$
$191$	1.41060e7	0.146483	0.0732416	+	0.997314i	$0.476666\pi$
$192$	−4.02817e7	−0.410727
$193$	−9.45023e7	−0.946219	−0.473109	−	0.881004i	$-0.656868\pi$
$193$	−9.45023e7	−0.946219	−0.473109	+	0.881004i	$0.656868\pi$
$194$	2.16872e8	2.13254
$195$	5.65570e6	0.0546217
$196$	3.14148e7	0.298015
$197$	6.26327e7	0.583673	0.291836	−	0.956468i	$-0.405734\pi$
$197$	6.26327e7	0.583673	0.291836	+	0.956468i	$0.405734\pi$
$198$	−5.40298e7	−0.494658
$199$	3.68824e7	0.331767	0.165884	−	0.986145i	$-0.446952\pi$
$199$	3.68824e7	0.331767	0.165884	+	0.986145i	$0.446952\pi$
$200$	3.26436e8	2.88532
$201$	4.10356e7	0.356430
$202$	1.94875e8	1.66351
$203$	6.77196e7	0.568170
$204$	−1.19265e8	−0.983576
$205$	1.92943e7	0.156419
$206$	−2.90586e8	−2.31601
$207$	−8.86974e6	−0.0695048
$208$	9.80519e6	0.0755500
$209$	−3.48288e7	−0.263892
$210$	8.15441e7	0.607610
$211$	−6.57606e7	−0.481922	−0.240961	−	0.970535i	$-0.577463\pi$
$211$	−6.57606e7	−0.481922	−0.240961	+	0.970535i	$0.577463\pi$
$212$	−1.25385e7	−0.0903796
$213$	9.66835e7	0.685526
$214$	−2.10618e8	−1.46909
$215$	−259561.	−0.00178117
$216$	5.43854e7	0.367193
$217$	1.05309e8	0.699614
$218$	9.53691e7	0.623462
$219$	−1.66483e8	−1.07107
$220$	−4.41129e8	−2.79310
$221$	−7.82172e6	−0.0487449
$222$	1.48764e8	0.912562
$223$	−5.59315e7	−0.337745	−0.168873	−	0.985638i	$-0.554013\pi$
$223$	−5.59315e7	−0.337745	−0.168873	+	0.985638i	$0.554013\pi$
$224$	2.00620e7	0.119263
$225$	8.61262e7	0.504076
$226$	−4.36481e8	−2.51528
$227$	−1.09071e8	−0.618895	−0.309448	−	0.950917i	$-0.600144\pi$
$227$	−1.09071e8	−0.618895	−0.309448	+	0.950917i	$0.600144\pi$
$228$	6.73366e7	0.376253
$229$	−4.33868e7	−0.238745	−0.119372	−	0.992850i	$-0.538088\pi$
$229$	−4.33868e7	−0.238745	−0.119372	+	0.992850i	$0.538088\pi$
$230$	−1.07132e8	−0.580592
$231$	−3.45345e7	−0.184337
$232$	5.45521e8	2.86816
$233$	2.25089e8	1.16576	0.582879	−	0.812559i	$-0.301926\pi$
$233$	2.25089e8	1.16576	0.582879	+	0.812559i	$0.301926\pi$
$234$	6.85072e6	0.0349527
$235$	4.50302e8	2.26343
$236$	−6.98936e8	−3.46135
$237$	−8.70405e7	−0.424719
$238$	−1.12774e8	−0.542237
$239$	2.05487e8	0.973625	0.486813	−	0.873506i	$-0.338159\pi$
$239$	2.05487e8	0.973625	0.486813	+	0.873506i	$0.338159\pi$
$240$	2.48054e8	1.15826
$241$	3.20946e8	1.47697	0.738485	−	0.674269i	$-0.235541\pi$
$241$	3.20946e8	1.47697	0.738485	+	0.674269i	$0.235541\pi$
$242$	−1.10933e8	−0.503162
$243$	1.43489e7	0.0641500
$244$	−5.26726e8	−2.32124
$245$	5.21210e7	0.226429
$246$	2.33711e7	0.100093
$247$	4.41611e6	0.0186467
$248$	8.48329e8	3.53170
$249$	−2.64879e7	−0.108730
$250$	3.52362e8	1.42626
$251$	−8.35360e7	−0.333438	−0.166719	−	0.986004i	$-0.553317\pi$
$251$	−8.35360e7	−0.333438	−0.166719	+	0.986004i	$0.553317\pi$
$252$	6.67678e7	0.262824
$253$	4.53711e7	0.176140
$254$	−8.36689e8	−3.20366
$255$	−1.97876e8	−0.747312
$256$	−5.47172e8	−2.03837
$257$	−2.66355e8	−0.978803	−0.489401	−	0.872059i	$-0.662785\pi$
$257$	−2.66355e8	−0.978803	−0.489401	+	0.872059i	$0.662785\pi$
$258$	−314405.	−0.00113978
$259$	9.50863e7	0.340070
$260$	5.59330e7	0.197361
$261$	1.43929e8	0.501079
$262$	−4.43220e8	−1.52253
$263$	−2.87161e8	−0.973374	−0.486687	−	0.873576i	$-0.661795\pi$
$263$	−2.87161e8	−0.973374	−0.486687	+	0.873576i	$0.661795\pi$
$264$	−2.78196e8	−0.930544
$265$	−2.08029e7	−0.0686695
$266$	6.36717e7	0.207425
$267$	−4.16645e7	−0.133961
$268$	4.05828e8	1.28787
$269$	−1.76284e8	−0.552179	−0.276089	−	0.961132i	$-0.589039\pi$
$269$	−1.76284e8	−0.552179	−0.276089	+	0.961132i	$0.589039\pi$
$270$	1.73311e8	0.535862
$271$	−5.45576e7	−0.166519	−0.0832593	−	0.996528i	$-0.526533\pi$
$271$	−5.45576e7	−0.166519	−0.0832593	+	0.996528i	$0.526533\pi$
$272$	−3.43054e8	−1.03364
$273$	4.37881e6	0.0130253
$274$	4.33287e8	1.27247
$275$	−4.40558e8	−1.27744
$276$	−8.77188e7	−0.251137
$277$	−1.96150e8	−0.554511	−0.277255	−	0.960796i	$-0.589425\pi$
$277$	−1.96150e8	−0.554511	−0.277255	+	0.960796i	$0.589425\pi$
$278$	−6.52722e8	−1.82210
$279$	2.23821e8	0.617001
$280$	4.19865e8	1.14303
$281$	−4.07501e7	−0.109561	−0.0547806	−	0.998498i	$-0.517446\pi$
$281$	−4.07501e7	−0.109561	−0.0547806	+	0.998498i	$0.517446\pi$
$282$	5.45448e8	1.44838
$283$	1.12571e8	0.295238	0.147619	−	0.989044i	$-0.452839\pi$
$283$	1.12571e8	0.295238	0.147619	+	0.989044i	$0.452839\pi$
$284$	9.56168e8	2.47697
$285$	1.11720e8	0.285873
$286$	−3.50432e7	−0.0885775
$287$	1.49382e7	0.0373003
$288$	4.26391e7	0.105180
$289$	−1.36681e8	−0.333092
$290$	1.73842e9	4.18564
$291$	2.94617e8	0.700861
$292$	−1.64647e9	−3.87002
$293$	8.27380e7	0.192162	0.0960812	−	0.995373i	$-0.469369\pi$
$293$	8.27380e7	0.192162	0.0960812	+	0.995373i	$0.469369\pi$
$294$	6.31338e7	0.144893
$295$	−1.15962e9	−2.62990
$296$	7.65975e8	1.71670
$297$	−7.33985e7	−0.162570
$298$	−1.04838e9	−2.29490
$299$	−5.75283e6	−0.0124461
$300$	8.51759e8	1.82135
$301$	−200960.	−0.000424743 0
$302$	1.19482e9	2.49620
$303$	2.64733e8	0.546713
$304$	1.93687e8	0.395405
$305$	−8.73905e8	−1.76366
$306$	−2.39685e8	−0.478208
$307$	1.27166e8	0.250834	0.125417	−	0.992104i	$-0.459973\pi$
$307$	1.27166e8	0.250834	0.125417	+	0.992104i	$0.459973\pi$
$308$	−3.41535e8	−0.666052
$309$	−3.94756e8	−0.761157
$310$	2.70339e9	5.15397
$311$	−9.41607e7	−0.177504	−0.0887520	−	0.996054i	$-0.528288\pi$
$311$	−9.41607e7	−0.177504	−0.0887520	+	0.996054i	$0.528288\pi$
$312$	3.52739e7	0.0657524
$313$	6.47846e8	1.19417	0.597086	−	0.802177i	$-0.296325\pi$
$313$	6.47846e8	1.19417	0.597086	+	0.802177i	$0.296325\pi$
$314$	−1.87444e9	−3.41678
$315$	1.10776e8	0.199691
$316$	−8.60802e8	−1.53461
$317$	6.48239e7	0.114295	0.0571475	−	0.998366i	$-0.481799\pi$
$317$	6.48239e7	0.114295	0.0571475	+	0.998366i	$0.481799\pi$
$318$	−2.51985e7	−0.0439419
$319$	−7.36235e8	−1.26984
$320$	−6.60950e8	−1.12757
$321$	−2.86121e8	−0.482817
$322$	−8.29445e7	−0.138450
$323$	−1.54506e8	−0.255116
$324$	1.41906e8	0.231789
$325$	5.58606e7	0.0902639
$326$	8.05693e8	1.28798
$327$	1.29557e8	0.204901
$328$	1.20336e8	0.188294
$329$	3.48637e8	0.539744
$330$	−8.86532e8	−1.35799
$331$	1.11966e8	0.169702	0.0848509	−	0.996394i	$-0.472959\pi$
$331$	1.11966e8	0.169702	0.0848509	+	0.996394i	$0.472959\pi$
$332$	−2.61957e8	−0.392867
$333$	2.02093e8	0.299914
$334$	−6.36885e8	−0.935294
$335$	6.73320e8	0.978508
$336$	1.92051e8	0.276203
$337$	−5.57696e7	−0.0793767	−0.0396883	−	0.999212i	$-0.512637\pi$
$337$	−5.57696e7	−0.0793767	−0.0396883	+	0.999212i	$0.512637\pi$
$338$	−1.24269e9	−1.75047
$339$	−5.92952e8	−0.826648
$340$	−1.95693e9	−2.70021
$341$	−1.14490e9	−1.56361
$342$	1.35326e8	0.182931
$343$	4.03536e7	0.0539949
$344$	−1.61885e6	−0.00214413
$345$	−1.45536e8	−0.190812
$346$	1.65684e9	2.15038
$347$	−8.86157e8	−1.13856	−0.569282	−	0.822142i	$-0.692779\pi$
$347$	−8.86157e8	−1.13856	−0.569282	+	0.822142i	$0.692779\pi$
$348$	1.42341e9	1.81052
$349$	1.21957e9	1.53574	0.767872	−	0.640604i	$-0.221316\pi$
$349$	1.21957e9	1.53574	0.767872	+	0.640604i	$0.221316\pi$
$350$	8.05400e8	1.00409
$351$	9.30657e6	0.0114872
$352$	−2.18111e8	−0.266549
$353$	−7.57443e7	−0.0916513	−0.0458257	−	0.998949i	$-0.514592\pi$
$353$	−7.57443e7	−0.0916513	−0.0458257	+	0.998949i	$0.514592\pi$
$354$	−1.40464e9	−1.68288
$355$	1.58640e9	1.88198
$356$	−4.12048e8	−0.484031
$357$	−1.53201e8	−0.178206
$358$	1.25578e9	1.44651
$359$	−1.45850e9	−1.66370	−0.831852	−	0.554997i	$-0.812719\pi$
$359$	−1.45850e9	−1.66370	−0.831852	+	0.554997i	$0.812719\pi$
$360$	8.92366e8	1.00806
$361$	−8.06638e8	−0.902409
$362$	−3.52803e8	−0.390888
$363$	−1.50701e8	−0.165364
$364$	4.33050e7	0.0470634
$365$	−2.73169e9	−2.94040
$366$	−1.05855e9	−1.12857
$367$	1.38635e9	1.46400	0.731999	−	0.681305i	$-0.238587\pi$
$367$	1.38635e9	1.46400	0.731999	+	0.681305i	$0.238587\pi$
$368$	−2.52314e8	−0.263921
$369$	3.17492e7	0.0328958
$370$	2.44095e9	2.50526
$371$	−1.61062e7	−0.0163752
$372$	2.21352e9	2.22937
$373$	1.87504e9	1.87081	0.935406	−	0.353576i	$-0.115034\pi$
$373$	1.87504e9	1.87081	0.935406	+	0.353576i	$0.115034\pi$
$374$	1.22606e9	1.21188
$375$	4.78677e8	0.468741
$376$	2.80847e9	2.72466
$377$	9.33509e7	0.0897272
$378$	1.34182e8	0.127783
$379$	−2.12461e8	−0.200467	−0.100233	−	0.994964i	$-0.531959\pi$
$379$	−2.12461e8	−0.200467	−0.100233	+	0.994964i	$0.531959\pi$
$380$	1.10487e9	1.03293
$381$	−1.13663e9	−1.05288
$382$	2.80359e8	0.257332
$383$	1.34032e9	1.21902	0.609511	−	0.792777i	$-0.291366\pi$
$383$	1.34032e9	1.21902	0.609511	+	0.792777i	$0.291366\pi$
$384$	−1.00275e9	−0.903714
$385$	−5.66650e8	−0.506060
$386$	−1.87825e9	−1.66225
$387$	−427113.	−0.000374588 0
$388$	2.91366e9	2.53238
$389$	4.07958e8	0.351392	0.175696	−	0.984444i	$-0.443782\pi$
$389$	4.07958e8	0.351392	0.175696	+	0.984444i	$0.443782\pi$
$390$	1.12408e8	0.0959557
$391$	2.01274e8	0.170282
$392$	3.25072e8	0.272570
$393$	−6.02107e8	−0.500379
$394$	1.24483e9	1.02536
$395$	−1.42818e9	−1.16598
$396$	−7.25887e8	−0.587403
$397$	−1.95797e9	−1.57051	−0.785253	−	0.619175i	$-0.787467\pi$
$397$	−1.95797e9	−1.57051	−0.785253	+	0.619175i	$0.787467\pi$
$398$	7.33043e8	0.582826
$399$	8.64968e7	0.0681702
$400$	2.45000e9	1.91406
$401$	−9.84097e7	−0.0762137	−0.0381068	−	0.999274i	$-0.512133\pi$
$401$	−9.84097e7	−0.0762137	−0.0381068	+	0.999274i	$0.512133\pi$
$402$	8.15587e8	0.626151
$403$	1.45168e8	0.110485
$404$	2.61813e9	1.97540
$405$	2.35440e8	0.176111
$406$	1.34594e9	0.998122
$407$	−1.03376e9	−0.760045
$408$	−1.23412e9	−0.899597
$409$	3.60189e8	0.260315	0.130158	−	0.991493i	$-0.458452\pi$
$409$	3.60189e8	0.260315	0.130158	+	0.991493i	$0.458452\pi$
$410$	3.83477e8	0.274787
$411$	5.88613e8	0.418199
$412$	−3.90401e9	−2.75024
$413$	−8.97813e8	−0.627135
$414$	−1.76287e8	−0.122101
$415$	−4.34619e8	−0.298497
$416$	2.76554e7	0.0188344
$417$	−8.86711e8	−0.598833
$418$	−6.92226e8	−0.463587
$419$	1.49875e9	0.995360	0.497680	−	0.867361i	$-0.334185\pi$
$419$	1.49875e9	0.995360	0.497680	+	0.867361i	$0.334185\pi$
$420$	1.09554e9	0.721532
$421$	1.32709e9	0.866789	0.433394	−	0.901204i	$-0.357316\pi$
$421$	1.32709e9	0.866789	0.433394	+	0.901204i	$0.357316\pi$
$422$	−1.30700e9	−0.846607
$423$	7.40981e8	0.476009
$424$	−1.29745e8	−0.0826629
$425$	−1.95439e9	−1.23495
$426$	1.92160e9	1.20428
$427$	−6.76602e8	−0.420568
$428$	−2.82964e9	−1.74453
$429$	−4.76056e7	−0.0291110
$430$	−5.15881e6	−0.00312903
$431$	−3.01125e9	−1.81166	−0.905828	−	0.423646i	$-0.860750\pi$
$431$	−3.01125e9	−1.81166	−0.905828	+	0.423646i	$0.860750\pi$
$432$	4.08178e8	0.243588
$433$	2.55564e9	1.51284	0.756419	−	0.654088i	$-0.226947\pi$
$433$	2.55564e9	1.51284	0.756419	+	0.654088i	$0.226947\pi$
$434$	2.09304e9	1.22903
$435$	2.36161e9	1.37561
$436$	1.28128e9	0.740356
$437$	−1.13639e8	−0.0651389
$438$	−3.30888e9	−1.88158
$439$	−1.92868e8	−0.108801	−0.0544006	−	0.998519i	$-0.517325\pi$
$439$	−1.92868e8	−0.108801	−0.0544006	+	0.998519i	$0.517325\pi$
$440$	−4.56469e9	−2.55462
$441$	8.57661e7	0.0476190
$442$	−1.55458e8	−0.0856317
$443$	−2.27943e9	−1.24570	−0.622849	−	0.782342i	$-0.714025\pi$
$443$	−2.27943e9	−1.24570	−0.622849	+	0.782342i	$0.714025\pi$
$444$	1.99863e9	1.08366
$445$	−6.83639e8	−0.367762
$446$	−1.11165e9	−0.593328
$447$	−1.42421e9	−0.754220
$448$	−5.11727e8	−0.268884
$449$	1.49028e9	0.776972	0.388486	−	0.921455i	$-0.372998\pi$
$449$	1.49028e9	0.776972	0.388486	+	0.921455i	$0.372998\pi$
$450$	1.71177e9	0.885526
$451$	−1.62405e8	−0.0833648
$452$	−5.86410e9	−2.98687
$453$	1.62314e9	0.820377
$454$	−2.16779e9	−1.08723
$455$	7.18484e7	0.0357583
$456$	6.96782e8	0.344128
$457$	3.03066e9	1.48536	0.742679	−	0.669648i	$-0.233555\pi$
$457$	3.03066e9	1.48536	0.742679	+	0.669648i	$0.233555\pi$
$458$	−8.62319e8	−0.419410
$459$	−3.25608e8	−0.157163
$460$	−1.43931e9	−0.689448
$461$	3.50328e9	1.66541	0.832706	−	0.553716i	$-0.186791\pi$
$461$	3.50328e9	1.66541	0.832706	+	0.553716i	$0.186791\pi$
$462$	−6.86379e8	−0.323830
$463$	8.37582e8	0.392187	0.196094	−	0.980585i	$-0.437174\pi$
$463$	8.37582e8	0.392187	0.196094	+	0.980585i	$0.437174\pi$
$464$	4.09429e9	1.90268
$465$	3.67250e9	1.69386
$466$	4.47367e9	2.04792
$467$	3.26301e9	1.48255	0.741276	−	0.671201i	$-0.234221\pi$
$467$	3.26301e9	1.48255	0.741276	+	0.671201i	$0.234221\pi$
$468$	9.20389e7	0.0415060
$469$	5.21304e8	0.233338
$470$	8.94981e9	3.97623
$471$	−2.54639e9	−1.12293
$472$	−7.23240e9	−3.16582
$473$	2.18480e6	0.000949286 0
$474$	−1.72994e9	−0.746118
$475$	1.10344e9	0.472413
$476$	−1.51511e9	−0.643902
$477$	−3.42316e7	−0.0144415
$478$	4.08408e9	1.71040
$479$	−3.50275e9	−1.45625	−0.728124	−	0.685446i	$-0.759607\pi$
$479$	−3.50275e9	−1.45625	−0.728124	+	0.685446i	$0.759607\pi$
$480$	6.99631e8	0.288752
$481$	1.31076e8	0.0537050
$482$	6.37884e9	2.59464
$483$	−1.12679e8	−0.0455016
$484$	−1.49038e9	−0.597501
$485$	4.83413e9	1.92408
$486$	2.85187e8	0.112694
$487$	−1.54705e9	−0.606950	−0.303475	−	0.952839i	$-0.598147\pi$
$487$	−1.54705e9	−0.606950	−0.303475	+	0.952839i	$0.598147\pi$
$488$	−5.45042e9	−2.12305
$489$	1.09452e9	0.423294
$490$	1.03591e9	0.397774
$491$	8.52600e8	0.325057	0.162529	−	0.986704i	$-0.448035\pi$
$491$	8.52600e8	0.325057	0.162529	+	0.986704i	$0.448035\pi$
$492$	3.13989e8	0.118860
$493$	−3.26606e9	−1.22761
$494$	8.77709e7	0.0327572
$495$	−1.20434e9	−0.446303
$496$	6.36694e9	2.34285
$497$	1.22824e9	0.448782
$498$	−5.26451e8	−0.191009
$499$	−1.98801e9	−0.716252	−0.358126	−	0.933673i	$-0.616584\pi$
$499$	−1.98801e9	−0.716252	−0.358126	+	0.933673i	$0.616584\pi$
$500$	4.73396e9	1.69367
$501$	−8.65196e8	−0.307385
$502$	−1.66029e9	−0.585762
$503$	2.60183e9	0.911571	0.455786	−	0.890090i	$-0.349358\pi$
$503$	2.60183e9	0.911571	0.455786	+	0.890090i	$0.349358\pi$
$504$	6.90896e8	0.240384
$505$	4.34380e9	1.50089
$506$	9.01757e8	0.309430
$507$	−1.68817e9	−0.575293
$508$	−1.12409e10	−3.80432
$509$	3.06624e9	1.03061	0.515304	−	0.857007i	$-0.327679\pi$
$509$	3.06624e9	1.03061	0.515304	+	0.857007i	$0.327679\pi$
$510$	−3.93281e9	−1.31283
$511$	−2.11496e9	−0.701178
$512$	−6.12136e9	−2.01559
$513$	1.83837e8	0.0601205
$514$	−5.29385e9	−1.71949
$515$	−6.47723e9	−2.08961
$516$	−4.22401e6	−0.00135348
$517$	−3.79031e9	−1.20631
$518$	1.88985e9	0.597412
$519$	2.25079e9	0.706722
$520$	5.78780e8	0.180510
$521$	−1.24479e9	−0.385624	−0.192812	−	0.981236i	$-0.561761\pi$
$521$	−1.24479e9	−0.385624	−0.192812	+	0.981236i	$0.561761\pi$
$522$	2.86061e9	0.880261
$523$	1.06169e9	0.324519	0.162260	−	0.986748i	$-0.448122\pi$
$523$	1.06169e9	0.324519	0.162260	+	0.986748i	$0.448122\pi$
$524$	−5.95464e9	−1.80799
$525$	1.09412e9	0.329995
$526$	−5.70736e9	−1.70996
$527$	−5.07899e9	−1.51161
$528$	−2.08794e9	−0.617304
$529$	1.48036e8	0.0434783
$530$	−4.13461e8	−0.120634
$531$	−1.90818e9	−0.553081
$532$	8.55425e8	0.246315
$533$	2.05922e7	0.00589058
$534$	−8.28088e8	−0.235333
$535$	−4.69473e9	−1.32548
$536$	4.19940e9	1.17791
$537$	1.70595e9	0.475397
$538$	−3.50367e9	−0.970030
$539$	−4.38717e8	−0.120677
$540$	2.32842e9	0.636331
$541$	−5.32115e9	−1.44482	−0.722412	−	0.691463i	$-0.756966\pi$
$541$	−5.32115e9	−1.44482	−0.722412	+	0.691463i	$0.756966\pi$
$542$	−1.08434e9	−0.292528
$543$	−4.79277e8	−0.128466
$544$	−9.67576e8	−0.257685
$545$	2.12580e9	0.562515
$546$	8.70295e7	0.0228819
$547$	5.27634e9	1.37841	0.689203	−	0.724568i	$-0.257961\pi$
$547$	5.27634e9	1.37841	0.689203	+	0.724568i	$0.257961\pi$
$548$	5.82119e9	1.51105
$549$	−1.43803e9	−0.370906
$550$	−8.75616e9	−2.24411
$551$	1.84401e9	0.469604
$552$	−9.07691e8	−0.229695
$553$	−1.10574e9	−0.278044
$554$	−3.89852e9	−0.974126
$555$	3.31598e9	0.823355
$556$	−8.76928e9	−2.16373
$557$	2.73206e8	0.0669880	0.0334940	−	0.999439i	$-0.489337\pi$
$557$	2.73206e8	0.0669880	0.0334940	+	0.999439i	$0.489337\pi$
$558$	4.44847e9	1.08390
$559$	−277021.	−6.70768e−5 0
$560$	3.15120e9	0.758261
$561$	1.66557e9	0.398285
$562$	−8.09914e8	−0.192470
$563$	−3.05265e9	−0.720937	−0.360469	−	0.932771i	$-0.617383\pi$
$563$	−3.05265e9	−0.720937	−0.360469	+	0.932771i	$0.617383\pi$
$564$	7.32805e9	1.71993
$565$	−9.72927e9	−2.26940
$566$	2.23736e9	0.518654
$567$	1.82284e8	0.0419961
$568$	9.89417e9	2.26548
$569$	−3.10601e9	−0.706823	−0.353411	−	0.935468i	$-0.614978\pi$
$569$	−3.10601e9	−0.706823	−0.353411	+	0.935468i	$0.614978\pi$
$570$	2.22045e9	0.502202
$571$	−4.81905e9	−1.08327	−0.541633	−	0.840615i	$-0.682194\pi$
$571$	−4.81905e9	−1.08327	−0.541633	+	0.840615i	$0.682194\pi$
$572$	−4.70804e8	−0.105185
$573$	3.80863e8	0.0845721
$574$	2.96899e8	0.0655266
$575$	−1.43744e9	−0.315322
$576$	−1.08761e9	−0.237133
$577$	7.11603e9	1.54213	0.771067	−	0.636754i	$-0.219723\pi$
$577$	7.11603e9	1.54213	0.771067	+	0.636754i	$0.219723\pi$
$578$	−2.71655e9	−0.585154
$579$	−2.55156e9	−0.546300
$580$	2.33556e10	4.97041
$581$	−3.36494e8	−0.0711805
$582$	5.85555e9	1.23122
$583$	1.75104e8	0.0365979
$584$	−1.70372e10	−3.53959
$585$	1.52704e8	0.0315359
$586$	1.64443e9	0.337578
$587$	4.57721e9	0.934045	0.467022	−	0.884245i	$-0.345327\pi$
$587$	4.57721e9	0.934045	0.467022	+	0.884245i	$0.345327\pi$
$588$	8.48199e8	0.172059
$589$	2.86758e9	0.578245
$590$	−2.30476e10	−4.62003
$591$	1.69108e9	0.336984
$592$	5.74886e9	1.13882
$593$	−7.44086e9	−1.46532	−0.732659	−	0.680596i	$-0.761721\pi$
$593$	−7.44086e9	−1.46532	−0.732659	+	0.680596i	$0.761721\pi$
$594$	−1.45881e9	−0.285591
$595$	−2.51375e9	−0.489230
$596$	−1.40850e10	−2.72517
$597$	9.95825e8	0.191546
$598$	−1.14338e8	−0.0218644
$599$	4.55488e8	0.0865931	0.0432965	−	0.999062i	$-0.486214\pi$
$599$	4.55488e8	0.0865931	0.0432965	+	0.999062i	$0.486214\pi$
$600$	8.81378e9	1.66584
$601$	1.03752e9	0.194956	0.0974782	−	0.995238i	$-0.468922\pi$
$601$	1.03752e9	0.194956	0.0974782	+	0.995238i	$0.468922\pi$
$602$	−3.99410e6	−0.000746160 0
$603$	1.10796e9	0.205785
$604$	1.60524e10	2.96422
$605$	−2.47273e9	−0.453975
$606$	5.26161e9	0.960428
$607$	−3.51343e9	−0.637634	−0.318817	−	0.947816i	$-0.603286\pi$
$607$	−3.51343e9	−0.637634	−0.318817	+	0.947816i	$0.603286\pi$
$608$	5.46290e8	0.0985736
$609$	1.82843e9	0.328033
$610$	−1.73690e10	−3.09827
$611$	4.80593e8	0.0852380
$612$	−3.22016e9	−0.567868
$613$	−1.07863e10	−1.89131	−0.945655	−	0.325171i	$-0.894578\pi$
$613$	−1.07863e10	−1.89131	−0.945655	+	0.325171i	$0.894578\pi$
$614$	2.52744e9	0.440647
$615$	5.20946e8	0.0903088
$616$	−3.53412e9	−0.609184
$617$	−4.14123e9	−0.709792	−0.354896	−	0.934906i	$-0.615484\pi$
$617$	−4.14123e9	−0.709792	−0.354896	+	0.934906i	$0.615484\pi$
$618$	−7.84583e9	−1.33715
$619$	−7.67868e9	−1.30127	−0.650637	−	0.759388i	$-0.725498\pi$
$619$	−7.67868e9	−1.30127	−0.650637	+	0.759388i	$0.725498\pi$
$620$	3.63198e10	6.12030
$621$	−2.39483e8	−0.0401286
$622$	−1.87146e9	−0.311827
$623$	−5.29294e8	−0.0876977
$624$	2.64740e8	0.0436188
$625$	−1.37569e9	−0.225393
$626$	1.28760e10	2.09784
$627$	−9.40376e8	−0.152358
$628$	−2.51829e10	−4.05740
$629$	−4.58594e9	−0.734769
$630$	2.20169e9	0.350804
$631$	−3.08332e9	−0.488557	−0.244279	−	0.969705i	$-0.578551\pi$
$631$	−3.08332e9	−0.488557	−0.244279	+	0.969705i	$0.578551\pi$
$632$	−8.90735e9	−1.40359
$633$	−1.77554e9	−0.278238
$634$	1.28838e9	0.200786
$635$	−1.86500e10	−2.89048
$636$	−3.38540e8	−0.0521807
$637$	5.56271e7	0.00852704
$638$	−1.46328e10	−2.23077
$639$	2.61045e9	0.395788
$640$	−1.64532e10	−2.48097
$641$	1.67015e8	0.0250468	0.0125234	−	0.999922i	$-0.496014\pi$
$641$	1.67015e8	0.0250468	0.0125234	+	0.999922i	$0.496014\pi$
$642$	−5.68670e9	−0.848179
$643$	3.81183e9	0.565452	0.282726	−	0.959201i	$-0.408761\pi$
$643$	3.81183e9	0.565452	0.282726	+	0.959201i	$0.408761\pi$
$644$	−1.11435e9	−0.164408
$645$	−7.00815e6	−0.00102836
$646$	−3.07083e9	−0.448170
$647$	−1.77415e9	−0.257529	−0.128764	−	0.991675i	$-0.541101\pi$
$647$	−1.77415e9	−0.257529	−0.128764	+	0.991675i	$0.541101\pi$
$648$	1.46841e9	0.211999
$649$	9.76085e9	1.40162
$650$	1.11024e9	0.158569
$651$	2.84336e9	0.403922
$652$	1.08244e10	1.52946
$653$	1.05990e10	1.48959	0.744796	−	0.667292i	$-0.232547\pi$
$653$	1.05990e10	1.48959	0.744796	+	0.667292i	$0.232547\pi$
$654$	2.57497e9	0.359956
$655$	−9.87948e9	−1.37369
$656$	9.03156e8	0.124911
$657$	−4.49505e9	−0.618381
$658$	6.92921e9	0.948185
$659$	−5.40242e9	−0.735342	−0.367671	−	0.929956i	$-0.619845\pi$
$659$	−5.40242e9	−0.735342	−0.367671	+	0.929956i	$0.619845\pi$
$660$	−1.19105e10	−1.61260
$661$	−7.49994e9	−1.01007	−0.505037	−	0.863098i	$-0.668521\pi$
$661$	−7.49994e9	−1.01007	−0.505037	+	0.863098i	$0.668521\pi$
$662$	2.22533e9	0.298120
$663$	−2.11186e8	−0.0281429
$664$	−2.71066e9	−0.359324
$665$	1.41926e9	0.187148
$666$	4.01663e9	0.526868
$667$	−2.40217e9	−0.313446
$668$	−8.55650e9	−1.11065
$669$	−1.51015e9	−0.194997
$670$	1.33823e10	1.71897
$671$	7.35589e9	0.939954
$672$	5.41675e8	0.0688567
$673$	1.10697e10	1.39985	0.699927	−	0.714214i	$-0.253216\pi$
$673$	1.10697e10	1.39985	0.699927	+	0.714214i	$0.253216\pi$
$674$	−1.10843e9	−0.139443
$675$	2.32541e9	0.291029
$676$	−1.66955e10	−2.07867
$677$	1.07908e10	1.33657	0.668285	−	0.743906i	$-0.267029\pi$
$677$	1.07908e10	1.33657	0.668285	+	0.743906i	$0.267029\pi$
$678$	−1.17850e10	−1.45220
$679$	3.74272e9	0.458821
$680$	−2.02497e10	−2.46967
$681$	−2.94490e9	−0.357319
$682$	−2.27551e10	−2.74684
$683$	−1.14197e10	−1.37145	−0.685726	−	0.727859i	$-0.740515\pi$
$683$	−1.14197e10	−1.37145	−0.685726	+	0.727859i	$0.740515\pi$
$684$	1.81809e9	0.217230
$685$	9.65808e9	1.14808
$686$	8.02034e8	0.0948545
$687$	−1.17144e9	−0.137839
$688$	−1.21499e7	−0.00142237
$689$	−2.22023e7	−0.00258602
$690$	−2.89256e9	−0.335205
$691$	6.53411e9	0.753379	0.376689	−	0.926340i	$-0.377062\pi$
$691$	6.53411e9	0.753379	0.376689	+	0.926340i	$0.377062\pi$
$692$	2.22595e10	2.55355
$693$	−9.32433e8	−0.106427
$694$	−1.76125e10	−2.00015
$695$	−1.45493e10	−1.64398
$696$	1.47291e10	1.65593
$697$	−7.20458e8	−0.0805924
$698$	2.42392e10	2.69789
$699$	6.07740e9	0.673051
$700$	1.08205e10	1.19235
$701$	3.61317e9	0.396165	0.198082	−	0.980185i	$-0.436529\pi$
$701$	3.61317e9	0.396165	0.198082	+	0.980185i	$0.436529\pi$
$702$	1.84969e8	0.0201799
$703$	2.58920e9	0.281075
$704$	5.56339e9	0.600946
$705$	1.21582e10	1.30679
$706$	−1.50543e9	−0.161007
$707$	3.36309e9	0.357908
$708$	−1.88713e10	−1.99841
$709$	−1.77189e9	−0.186713	−0.0933565	−	0.995633i	$-0.529760\pi$
$709$	−1.77189e9	−0.186713	−0.0933565	+	0.995633i	$0.529760\pi$
$710$	3.15299e10	3.30612
$711$	−2.35009e9	−0.245212
$712$	−4.26377e9	−0.442704
$713$	−3.73557e9	−0.385961
$714$	−3.04489e9	−0.313061
$715$	−7.81122e8	−0.0799186
$716$	1.68713e10	1.71772
$717$	5.54815e9	0.562123
$718$	−2.89879e10	−2.92268
$719$	1.86117e10	1.86739	0.933694	−	0.358072i	$-0.116566\pi$
$719$	1.86117e10	1.86739	0.933694	+	0.358072i	$0.116566\pi$
$720$	6.69746e9	0.668723
$721$	−5.01486e9	−0.498294
$722$	−1.60320e10	−1.58529
$723$	8.66553e9	0.852730
$724$	−4.73989e9	−0.464176
$725$	2.33253e10	2.27324
$726$	−2.99520e9	−0.290501
$727$	−1.18521e10	−1.14399	−0.571997	−	0.820256i	$-0.693831\pi$
$727$	−1.18521e10	−1.14399	−0.571997	+	0.820256i	$0.693831\pi$
$728$	4.48109e8	0.0430451
$729$	3.87420e8	0.0370370
$730$	−5.42928e10	−5.16549
$731$	9.69213e6	0.000917716 0
$732$	−1.42216e10	−1.34017
$733$	1.14086e10	1.06996	0.534982	−	0.844863i	$-0.320318\pi$
$733$	1.14086e10	1.06996	0.534982	+	0.844863i	$0.320318\pi$
$734$	2.75538e10	2.57185
$735$	1.40727e9	0.130729
$736$	−7.11647e8	−0.0657949
$737$	−5.66751e9	−0.521502
$738$	6.31019e8	0.0577890
$739$	1.35598e10	1.23594	0.617969	−	0.786202i	$-0.287956\pi$
$739$	1.35598e10	1.23594	0.617969	+	0.786202i	$0.287956\pi$
$740$	3.27940e10	2.97497
$741$	1.19235e8	0.0107657
$742$	−3.20114e8	−0.0287667
$743$	2.44262e9	0.218471	0.109236	−	0.994016i	$-0.465160\pi$
$743$	2.44262e9	0.218471	0.109236	+	0.994016i	$0.465160\pi$
$744$	2.29049e10	2.03903
$745$	−2.33687e10	−2.07056
$746$	3.72667e10	3.28651
$747$	−7.15173e8	−0.0627753
$748$	1.64720e10	1.43910
$749$	−3.63480e9	−0.316078
$750$	9.51377e9	0.823452
$751$	−3.93139e9	−0.338693	−0.169347	−	0.985557i	$-0.554166\pi$
$751$	−3.93139e9	−0.338693	−0.169347	+	0.985557i	$0.554166\pi$
$752$	2.10784e10	1.80748
$753$	−2.25547e9	−0.192511
$754$	1.85536e9	0.157626
$755$	2.66329e10	2.25218
$756$	1.80273e9	0.151742
$757$	−1.20353e10	−1.00837	−0.504186	−	0.863595i	$-0.668207\pi$
$757$	−1.20353e10	−1.00837	−0.504186	+	0.863595i	$0.668207\pi$
$758$	−4.22270e9	−0.352166
$759$	1.22502e9	0.101694
$760$	1.14329e10	0.944735
$761$	1.54532e10	1.27108	0.635540	−	0.772068i	$-0.280777\pi$
$761$	1.54532e10	1.27108	0.635540	+	0.772068i	$0.280777\pi$
$762$	−2.25906e10	−1.84963
$763$	1.64586e9	0.134139
$764$	3.76661e9	0.305579
$765$	−5.34264e9	−0.431461
$766$	2.66390e10	2.14149
$767$	−1.23763e9	−0.0990390
$768$	−1.47736e10	−1.17686
$769$	−5.75796e9	−0.456590	−0.228295	−	0.973592i	$-0.573315\pi$
$769$	−5.75796e9	−0.456590	−0.228295	+	0.973592i	$0.573315\pi$
$770$	−1.12622e10	−0.889011
$771$	−7.19159e9	−0.565112
$772$	−2.52341e10	−1.97391
$773$	8.39283e9	0.653552	0.326776	−	0.945102i	$-0.394038\pi$
$773$	8.39283e9	0.653552	0.326776	+	0.945102i	$0.394038\pi$
$774$	−8.48893e6	−0.000658051 0
$775$	3.62728e10	2.79914
$776$	3.01498e10	2.31616
$777$	2.56733e9	0.196340
$778$	8.10823e9	0.617302
$779$	4.06768e8	0.0308294
$780$	1.51019e9	0.113947
$781$	−1.33532e10	−1.00301
$782$	4.00035e9	0.299140
$783$	3.88608e9	0.289298
$784$	2.43975e9	0.180817
$785$	−4.17816e10	−3.08277
$786$	−1.19670e10	−0.879032
$787$	−2.02422e10	−1.48029	−0.740144	−	0.672449i	$-0.765243\pi$
$787$	−2.02422e10	−1.48029	−0.740144	+	0.672449i	$0.765243\pi$
$788$	1.67243e10	1.21760
$789$	−7.75334e9	−0.561978
$790$	−2.83852e10	−2.04832
$791$	−7.53268e9	−0.541168
$792$	−7.51129e9	−0.537250
$793$	−9.32691e8	−0.0664173
$794$	−3.89149e10	−2.75896
$795$	−5.61679e8	−0.0396464
$796$	9.84838e9	0.692101
$797$	3.57718e9	0.250286	0.125143	−	0.992139i	$-0.460061\pi$
$797$	3.57718e9	0.250286	0.125143	+	0.992139i	$0.460061\pi$
$798$	1.71914e9	0.119757
$799$	−1.68145e10	−1.16619
$800$	6.91017e9	0.477170
$801$	−1.12494e9	−0.0773421
$802$	−1.95591e9	−0.133887
$803$	2.29934e10	1.56711
$804$	1.09574e10	0.743549
$805$	−1.84885e9	−0.124916
$806$	2.88524e9	0.194093
$807$	−4.75967e9	−0.318801
$808$	2.70917e10	1.80674
$809$	2.00655e10	1.33239	0.666193	−	0.745780i	$-0.267923\pi$
$809$	2.00655e10	1.33239	0.666193	+	0.745780i	$0.267923\pi$
$810$	4.67940e9	0.309380
$811$	1.28076e9	0.0843131	0.0421565	−	0.999111i	$-0.486577\pi$
$811$	1.28076e9	0.0843131	0.0421565	+	0.999111i	$0.486577\pi$
$812$	1.80826e10	1.18526
$813$	−1.47306e9	−0.0961396
$814$	−2.05461e10	−1.33519
$815$	1.79591e10	1.16207
$816$	−9.26245e9	−0.596774
$817$	−5.47214e6	−0.000351059 0
$818$	7.15882e9	0.457304
$819$	1.18228e8	0.00752015
$820$	5.15199e9	0.326307
$821$	1.82281e10	1.14958	0.574791	−	0.818301i	$-0.305083\pi$
$821$	1.82281e10	1.14958	0.574791	+	0.818301i	$0.305083\pi$
$822$	1.16988e10	0.734664
$823$	1.38540e10	0.866316	0.433158	−	0.901318i	$-0.357399\pi$
$823$	1.38540e10	0.866316	0.433158	+	0.901318i	$0.357399\pi$
$824$	−4.03976e10	−2.51542
$825$	−1.18951e10	−0.737528
$826$	−1.78442e10	−1.10171
$827$	1.17555e10	0.722721	0.361360	−	0.932426i	$-0.382312\pi$
$827$	1.17555e10	0.722721	0.361360	+	0.932426i	$0.382312\pi$
$828$	−2.36841e9	−0.144994
$829$	1.57196e10	0.958301	0.479150	−	0.877733i	$-0.340945\pi$
$829$	1.57196e10	0.958301	0.479150	+	0.877733i	$0.340945\pi$
$830$	−8.63810e9	−0.524379
$831$	−5.29606e9	−0.320147
$832$	−7.05411e8	−0.0424630
$833$	−1.94622e9	−0.116663
$834$	−1.76235e10	−1.05199
$835$	−1.41963e10	−0.843864
$836$	−9.30001e9	−0.550505
$837$	6.04317e9	0.356226
$838$	2.97879e10	1.74858
$839$	1.03089e9	0.0602624	0.0301312	−	0.999546i	$-0.490407\pi$
$839$	1.03089e9	0.0602624	0.0301312	+	0.999546i	$0.490407\pi$
$840$	1.13364e10	0.659927
$841$	2.17300e10	1.25972
$842$	2.63761e10	1.52271
$843$	−1.10025e9	−0.0632552
$844$	−1.75595e10	−1.00534
$845$	−2.76999e10	−1.57935
$846$	1.47271e10	0.836220
$847$	−1.91446e9	−0.108256
$848$	−9.73774e8	−0.0548368
$849$	3.03941e9	0.170456
$850$	−3.88438e10	−2.16948
$851$	−3.37293e9	−0.187609
$852$	2.58165e10	1.43008
$853$	2.62081e10	1.44582	0.722908	−	0.690944i	$-0.242805\pi$
$853$	2.62081e10	1.44582	0.722908	+	0.690944i	$0.242805\pi$
$854$	−1.34476e10	−0.738824
$855$	3.01644e9	0.165049
$856$	−2.92804e10	−1.59558
$857$	2.35667e10	1.27899	0.639494	−	0.768796i	$-0.279144\pi$
$857$	2.35667e10	1.27899	0.639494	+	0.768796i	$0.279144\pi$
$858$	−9.46168e8	−0.0511402
$859$	2.42543e10	1.30561	0.652803	−	0.757528i	$-0.273593\pi$
$859$	2.42543e10	1.30561	0.652803	+	0.757528i	$0.273593\pi$
$860$	−6.93083e7	−0.00371570
$861$	4.03332e8	0.0215353
$862$	−5.98489e10	−3.18259
$863$	1.27570e10	0.675631	0.337816	−	0.941212i	$-0.390312\pi$
$863$	1.27570e10	0.675631	0.337816	+	0.941212i	$0.390312\pi$
$864$	1.15126e9	0.0607259
$865$	3.69314e10	1.94017
$866$	5.07937e10	2.65765
$867$	−3.69038e9	−0.192311
$868$	2.81198e10	1.45947
$869$	1.20214e10	0.621419
$870$	4.69374e10	2.41658
$871$	7.18613e8	0.0368495
$872$	1.32583e10	0.677143
$873$	7.95465e9	0.404642
$874$	−2.25858e9	−0.114432
$875$	6.08097e9	0.306863
$876$	−4.44546e10	−2.23435
$877$	−2.72841e9	−0.136588	−0.0682938	−	0.997665i	$-0.521756\pi$
$877$	−2.72841e9	−0.136588	−0.0682938	+	0.997665i	$0.521756\pi$
$878$	−3.83327e9	−0.191134
$879$	2.23393e9	0.110945
$880$	−3.42593e10	−1.69468
$881$	−8.73462e9	−0.430356	−0.215178	−	0.976575i	$-0.569033\pi$
$881$	−8.73462e9	−0.430356	−0.215178	+	0.976575i	$0.569033\pi$
$882$	1.70461e9	0.0836538
$883$	−2.15569e10	−1.05372	−0.526859	−	0.849953i	$-0.676630\pi$
$883$	−2.15569e10	−1.05372	−0.526859	+	0.849953i	$0.676630\pi$
$884$	−2.08856e9	−0.101687
$885$	−3.13098e10	−1.51837
$886$	−4.53039e10	−2.18835
$887$	−8.14998e9	−0.392124	−0.196062	−	0.980591i	$-0.562815\pi$
$887$	−8.14998e9	−0.392124	−0.196062	+	0.980591i	$0.562815\pi$
$888$	2.06813e10	0.991136
$889$	−1.44394e10	−0.689274
$890$	−1.35874e10	−0.646059
$891$	−1.98176e9	−0.0938597
$892$	−1.49349e10	−0.704571
$893$	9.49339e9	0.446109
$894$	−2.83064e10	−1.32496
$895$	2.79915e10	1.30511
$896$	−1.27386e10	−0.591620
$897$	−1.55327e8	−0.00718575
$898$	2.96195e10	1.36493
$899$	6.06169e10	2.78250
$900$	2.29975e10	1.05155
$901$	7.76791e8	0.0353808
$902$	−3.22783e9	−0.146449
$903$	−5.42592e6	−0.000245226 0
$904$	−6.06801e10	−2.73185
$905$	−7.86406e9	−0.352677
$906$	3.22602e10	1.44118
$907$	6.36015e9	0.283036	0.141518	−	0.989936i	$-0.454802\pi$
$907$	6.36015e9	0.283036	0.141518	+	0.989936i	$0.454802\pi$
$908$	−2.91241e10	−1.29108
$909$	7.14780e9	0.315645
$910$	1.42800e9	0.0628177
$911$	−2.88581e10	−1.26460	−0.632300	−	0.774724i	$-0.717889\pi$
$911$	−2.88581e10	−1.26460	−0.632300	+	0.774724i	$0.717889\pi$
$912$	5.22954e9	0.228287
$913$	3.65830e9	0.159086
$914$	6.02349e10	2.60937
$915$	−2.35954e10	−1.01825
$916$	−1.15852e10	−0.498046
$917$	−7.64898e9	−0.327575
$918$	−6.47151e9	−0.276093
$919$	−1.96804e10	−0.836432	−0.418216	−	0.908348i	$-0.637344\pi$
$919$	−1.96804e10	−0.836432	−0.418216	+	0.908348i	$0.637344\pi$
$920$	−1.48936e10	−0.630582
$921$	3.43348e9	0.144819
$922$	6.96282e10	2.92568
$923$	1.69312e9	0.0708730
$924$	−9.22145e9	−0.384545
$925$	3.27515e10	1.36062
$926$	1.66470e10	0.688968
$927$	−1.06584e10	−0.439454
$928$	1.15479e10	0.474333
$929$	−1.82282e9	−0.0745912	−0.0372956	−	0.999304i	$-0.511874\pi$
$929$	−1.82282e9	−0.0745912	−0.0372956	+	0.999304i	$0.511874\pi$
$930$	7.29914e10	2.97565
$931$	1.09883e9	0.0446279
$932$	6.01035e10	2.43189
$933$	−2.54234e9	−0.102482
$934$	6.48528e10	2.60444
$935$	2.73291e10	1.09341
$936$	9.52394e8	0.0379622
$937$	−4.30455e10	−1.70938	−0.854690	−	0.519138i	$-0.826253\pi$
$937$	−4.30455e10	−1.70938	−0.854690	+	0.519138i	$0.826253\pi$
$938$	1.03610e10	0.409912
$939$	1.74918e10	0.689455
$940$	1.20240e11	4.72174
$941$	−2.77374e10	−1.08518	−0.542590	−	0.839998i	$-0.682556\pi$
$941$	−2.77374e10	−1.08518	−0.542590	+	0.839998i	$0.682556\pi$
$942$	−5.06098e10	−1.97268
$943$	−5.29893e8	−0.0205777
$944$	−5.42812e10	−2.10014
$945$	2.99096e9	0.115292
$946$	4.34231e7	0.00166764
$947$	2.08630e10	0.798272	0.399136	−	0.916892i	$-0.369310\pi$
$947$	2.08630e10	0.798272	0.399136	+	0.916892i	$0.369310\pi$
$948$	−2.32417e10	−0.886008
$949$	−2.91545e9	−0.110732
$950$	2.19311e10	0.829903
$951$	1.75024e9	0.0659883
$952$	−1.56779e10	−0.588925
$953$	2.64363e10	0.989410	0.494705	−	0.869061i	$-0.335276\pi$
$953$	2.64363e10	0.989410	0.494705	+	0.869061i	$0.335276\pi$
$954$	−6.80358e8	−0.0253699
$955$	6.24927e9	0.232176
$956$	5.48694e10	2.03108
$957$	−1.98783e10	−0.733142
$958$	−6.96177e10	−2.55823
$959$	7.47756e9	0.273776
$960$	−1.78456e10	−0.651003
$961$	6.67515e10	2.42621
$962$	2.60515e9	0.0943452
$963$	−7.72527e9	−0.278754
$964$	8.56993e10	3.08111
$965$	−4.18665e10	−1.49976
$966$	−2.23950e9	−0.0799340
$967$	9.18510e9	0.326656	0.163328	−	0.986572i	$-0.447777\pi$
$967$	9.18510e9	0.326656	0.163328	+	0.986572i	$0.447777\pi$
$968$	−1.54221e10	−0.546485
$969$	−4.17167e9	−0.147291
$970$	9.60790e10	3.38008
$971$	2.62598e10	0.920501	0.460250	−	0.887789i	$-0.347760\pi$
$971$	2.62598e10	0.920501	0.460250	+	0.887789i	$0.347760\pi$
$972$	3.83146e9	0.133824
$973$	−1.12645e10	−0.392028
$974$	−3.07478e10	−1.06625
$975$	1.50824e9	0.0521139
$976$	−4.09070e10	−1.40839
$977$	1.30892e10	0.449038	0.224519	−	0.974470i	$-0.427919\pi$
$977$	1.30892e10	0.449038	0.224519	+	0.974470i	$0.427919\pi$
$978$	2.17537e10	0.743613
$979$	5.75438e9	0.196001
$980$	1.39174e10	0.472354
$981$	3.49804e9	0.118300
$982$	1.69455e10	0.571038
$983$	1.72279e10	0.578488	0.289244	−	0.957255i	$-0.406596\pi$
$983$	1.72279e10	0.578488	0.289244	+	0.957255i	$0.406596\pi$
$984$	3.24907e9	0.108712
$985$	2.77476e10	0.925122
$986$	−6.49134e10	−2.15658
$987$	9.41320e9	0.311621
$988$	1.17920e9	0.0388988
$989$	7.12851e6	0.000234321 0
$990$	−2.39364e10	−0.784034
$991$	2.69150e10	0.878491	0.439245	−	0.898367i	$-0.355246\pi$
$991$	2.69150e10	0.878491	0.439245	+	0.898367i	$0.355246\pi$
$992$	1.79578e10	0.584068
$993$	3.02307e9	0.0979774
$994$	2.44114e10	0.788389
$995$	1.63397e10	0.525852
$996$	−7.07283e9	−0.226822
$997$	−4.12139e10	−1.31707	−0.658537	−	0.752548i	$-0.728825\pi$
$997$	−4.12139e10	−1.31707	−0.658537	+	0.752548i	$0.728825\pi$
$998$	−3.95119e10	−1.25826
$999$	5.45651e9	0.173155

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.8.a.h.1.18	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.8.a.h.1.18	✓	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)

\(f(q)\)	\(=\)	\(q+19.8751 q^{2} +27.0000 q^{3} +267.021 q^{4} +443.021 q^{5} +536.629 q^{6} +343.000 q^{7} +2763.06 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+19.8751 q^{2} +27.0000 q^{3} +267.021 q^{4} +443.021 q^{5} +536.629 q^{6} +343.000 q^{7} +2763.06 q^{8} +729.000 q^{9} +8805.11 q^{10} -3729.03 q^{11} +7209.57 q^{12} +472.823 q^{13} +6817.17 q^{14} +11961.6 q^{15} +20737.6 q^{16} -16542.6 q^{17} +14489.0 q^{18} +9339.90 q^{19} +118296. q^{20} +9261.00 q^{21} -74115.0 q^{22} -12167.0 q^{23} +74602.7 q^{24} +118143. q^{25} +9397.42 q^{26} +19683.0 q^{27} +91588.2 q^{28} +197433. q^{29} +237738. q^{30} +307025. q^{31} +58489.9 q^{32} -100684. q^{33} -328787. q^{34} +151956. q^{35} +194658. q^{36} +277220. q^{37} +185632. q^{38} +12766.2 q^{39} +1.22410e6 q^{40} +43551.7 q^{41} +184064. q^{42} -585.889 q^{43} -995730. q^{44} +322963. q^{45} -241821. q^{46} +1.01643e6 q^{47} +559914. q^{48} +117649. q^{49} +2.34811e6 q^{50} -446651. q^{51} +126254. q^{52} -46957.0 q^{53} +391202. q^{54} -1.65204e6 q^{55} +947731. q^{56} +252177. q^{57} +3.92401e6 q^{58} -2.61753e6 q^{59} +3.19399e6 q^{60} -1.97260e6 q^{61} +6.10216e6 q^{62} +250047. q^{63} -1.49191e6 q^{64} +209471. q^{65} -2.00110e6 q^{66} +1.51984e6 q^{67} -4.41723e6 q^{68} -328509. q^{69} +3.02015e6 q^{70} +3.58087e6 q^{71} +2.01427e6 q^{72} -6.16605e6 q^{73} +5.50978e6 q^{74} +3.18986e6 q^{75} +2.49395e6 q^{76} -1.27906e6 q^{77} +253730. q^{78} -3.22372e6 q^{79} +9.18719e6 q^{80} +531441. q^{81} +865595. q^{82} -981033. q^{83} +2.47288e6 q^{84} -7.32873e6 q^{85} -11644.6 q^{86} +5.33070e6 q^{87} -1.03035e7 q^{88} -1.54313e6 q^{89} +6.41892e6 q^{90} +162178. q^{91} -3.24885e6 q^{92} +8.28966e6 q^{93} +2.02018e7 q^{94} +4.13777e6 q^{95} +1.57923e6 q^{96} +1.09117e7 q^{97} +2.33829e6 q^{98} -2.71846e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 24 q^{2} + 540 q^{3} + 1486 q^{4} + 1069 q^{5} + 648 q^{6} + 6860 q^{7} + 2127 q^{8} + 14580 q^{9}+O(q^{10}) \) 20 * q + 24 * q^2 + 540 * q^3 + 1486 * q^4 + 1069 * q^5 + 648 * q^6 + 6860 * q^7 + 2127 * q^8 + 14580 * q^9	\( 20 q + 24 q^{2} + 540 q^{3} + 1486 q^{4} + 1069 q^{5} + 648 q^{6} + 6860 q^{7} + 2127 q^{8} + 14580 q^{9} - 1949 q^{10} + 10073 q^{11} + 40122 q^{12} + 13391 q^{13} + 8232 q^{14} + 28863 q^{15} + 133122 q^{16} + 62626 q^{17} + 17496 q^{18} + 9895 q^{19} + 106064 q^{20} + 185220 q^{21} + 28599 q^{22} - 243340 q^{23} + 57429 q^{24} + 265365 q^{25} + 594400 q^{26} + 393660 q^{27} + 509698 q^{28} + 594658 q^{29} - 52623 q^{30} + 514862 q^{31} + 832720 q^{32} + 271971 q^{33} - 106257 q^{34} + 366667 q^{35} + 1083294 q^{36} + 891864 q^{37} + 680125 q^{38} + 361557 q^{39} + 44594 q^{40} + 296689 q^{41} + 222264 q^{42} - 704949 q^{43} + 2001503 q^{44} + 779301 q^{45} - 292008 q^{46} + 2102453 q^{47} + 3594294 q^{48} + 2352980 q^{49} + 4129604 q^{50} + 1690902 q^{51} + 4416739 q^{52} + 5841486 q^{53} + 472392 q^{54} + 4290005 q^{55} + 729561 q^{56} + 267165 q^{57} + 7165650 q^{58} + 7015980 q^{59} + 2863728 q^{60} + 2474138 q^{61} + 4418145 q^{62} + 5000940 q^{63} + 12695973 q^{64} + 6582462 q^{65} + 772173 q^{66} + 2305855 q^{67} + 10253157 q^{68} - 6570180 q^{69} - 668507 q^{70} + 12287349 q^{71} + 1550583 q^{72} + 9140922 q^{73} - 832604 q^{74} + 7164855 q^{75} + 290029 q^{76} + 3455039 q^{77} + 16048800 q^{78} - 1444882 q^{79} + 2254323 q^{80} + 10628820 q^{81} + 6031922 q^{82} + 4284072 q^{83} + 13761846 q^{84} + 15450581 q^{85} + 19710382 q^{86} + 16055766 q^{87} - 4553328 q^{88} + 36265659 q^{89} - 1420821 q^{90} + 4593113 q^{91} - 18080162 q^{92} + 13901274 q^{93} + 11807737 q^{94} + 35752199 q^{95} + 22483440 q^{96} + 15575692 q^{97} + 2823576 q^{98} + 7343217 q^{99}+O(q^{100}) \) 20 * q + 24 * q^2 + 540 * q^3 + 1486 * q^4 + 1069 * q^5 + 648 * q^6 + 6860 * q^7 + 2127 * q^8 + 14580 * q^9 - 1949 * q^10 + 10073 * q^11 + 40122 * q^12 + 13391 * q^13 + 8232 * q^14 + 28863 * q^15 + 133122 * q^16 + 62626 * q^17 + 17496 * q^18 + 9895 * q^19 + 106064 * q^20 + 185220 * q^21 + 28599 * q^22 - 243340 * q^23 + 57429 * q^24 + 265365 * q^25 + 594400 * q^26 + 393660 * q^27 + 509698 * q^28 + 594658 * q^29 - 52623 * q^30 + 514862 * q^31 + 832720 * q^32 + 271971 * q^33 - 106257 * q^34 + 366667 * q^35 + 1083294 * q^36 + 891864 * q^37 + 680125 * q^38 + 361557 * q^39 + 44594 * q^40 + 296689 * q^41 + 222264 * q^42 - 704949 * q^43 + 2001503 * q^44 + 779301 * q^45 - 292008 * q^46 + 2102453 * q^47 + 3594294 * q^48 + 2352980 * q^49 + 4129604 * q^50 + 1690902 * q^51 + 4416739 * q^52 + 5841486 * q^53 + 472392 * q^54 + 4290005 * q^55 + 729561 * q^56 + 267165 * q^57 + 7165650 * q^58 + 7015980 * q^59 + 2863728 * q^60 + 2474138 * q^61 + 4418145 * q^62 + 5000940 * q^63 + 12695973 * q^64 + 6582462 * q^65 + 772173 * q^66 + 2305855 * q^67 + 10253157 * q^68 - 6570180 * q^69 - 668507 * q^70 + 12287349 * q^71 + 1550583 * q^72 + 9140922 * q^73 - 832604 * q^74 + 7164855 * q^75 + 290029 * q^76 + 3455039 * q^77 + 16048800 * q^78 - 1444882 * q^79 + 2254323 * q^80 + 10628820 * q^81 + 6031922 * q^82 + 4284072 * q^83 + 13761846 * q^84 + 15450581 * q^85 + 19710382 * q^86 + 16055766 * q^87 - 4553328 * q^88 + 36265659 * q^89 - 1420821 * q^90 + 4593113 * q^91 - 18080162 * q^92 + 13901274 * q^93 + 11807737 * q^94 + 35752199 * q^95 + 22483440 * q^96 + 15575692 * q^97 + 2823576 * q^98 + 7343217 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more