LMFDB - Embedded newform 483.8.a.h.1.13

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			1.13
Root			$8.23051$ 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)

$f(q)$	$=$	$q+9.23051 q^{2} +27.0000 q^{3} -42.7976 q^{4} +406.225 q^{5} +249.224 q^{6} +343.000 q^{7} -1576.55 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+9.23051 q^{2} +27.0000 q^{3} -42.7976 q^{4} +406.225 q^{5} +249.224 q^{6} +343.000 q^{7} -1576.55 q^{8} +729.000 q^{9} +3749.67 q^{10} +1005.36 q^{11} -1155.54 q^{12} +9628.90 q^{13} +3166.07 q^{14} +10968.1 q^{15} -9074.27 q^{16} -11670.7 q^{17} +6729.05 q^{18} +33692.2 q^{19} -17385.5 q^{20} +9261.00 q^{21} +9280.03 q^{22} -12167.0 q^{23} -42566.8 q^{24} +86894.1 q^{25} +88879.7 q^{26} +19683.0 q^{27} -14679.6 q^{28} +20614.7 q^{29} +101241. q^{30} +68688.6 q^{31} +118038. q^{32} +27144.8 q^{33} -107727. q^{34} +139335. q^{35} -31199.4 q^{36} -553979. q^{37} +310997. q^{38} +259980. q^{39} -640435. q^{40} +519082. q^{41} +85483.8 q^{42} +318063. q^{43} -43027.2 q^{44} +296138. q^{45} -112308. q^{46} -213559. q^{47} -245005. q^{48} +117649. q^{49} +802077. q^{50} -315110. q^{51} -412094. q^{52} -510941. q^{53} +181684. q^{54} +408404. q^{55} -540757. q^{56} +909691. q^{57} +190285. q^{58} +3.10816e6 q^{59} -469408. q^{60} -285227. q^{61} +634031. q^{62} +250047. q^{63} +2.25106e6 q^{64} +3.91150e6 q^{65} +250561. q^{66} -1.25165e6 q^{67} +499480. q^{68} -328509. q^{69} +1.28614e6 q^{70} +472948. q^{71} -1.14930e6 q^{72} +2.57244e6 q^{73} -5.11351e6 q^{74} +2.34614e6 q^{75} -1.44195e6 q^{76} +344840. q^{77} +2.39975e6 q^{78} +3.62065e6 q^{79} -3.68620e6 q^{80} +531441. q^{81} +4.79139e6 q^{82} -2.77576e6 q^{83} -396349. q^{84} -4.74095e6 q^{85} +2.93589e6 q^{86} +556598. q^{87} -1.58501e6 q^{88} -2.11122e6 q^{89} +2.73351e6 q^{90} +3.30271e6 q^{91} +520718. q^{92} +1.85459e6 q^{93} -1.97126e6 q^{94} +1.36866e7 q^{95} +3.18703e6 q^{96} -5.84030e6 q^{97} +1.08596e6 q^{98} +732910. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	9.23051	0.815870	0.407935	−	0.913011i	$-0.366249\pi$
$2$	9.23051	0.815870	0.407935	+	0.913011i	$0.366249\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	−42.7976	−0.334356
$5$	406.225	1.45336	0.726678	−	0.686978i	$-0.241063\pi$
$5$	406.225	1.45336	0.726678	+	0.686978i	$0.241063\pi$
$6$	249.224	0.471043
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−1576.55	−1.08866
$9$	729.000	0.333333
$10$	3749.67	1.18575
$11$	1005.36	0.227745	0.113872	−	0.993495i	$-0.463674\pi$
$11$	1005.36	0.227745	0.113872	+	0.993495i	$0.463674\pi$
$12$	−1155.54	−0.193041
$13$	9628.90	1.21556	0.607778	−	0.794107i	$-0.292061\pi$
$13$	9628.90	1.21556	0.607778	+	0.794107i	$0.292061\pi$
$14$	3166.07	0.308370
$15$	10968.1	0.839096
$16$	−9074.27	−0.553850
$17$	−11670.7	−0.576139	−0.288069	−	0.957610i	$-0.593013\pi$
$17$	−11670.7	−0.576139	−0.288069	+	0.957610i	$0.593013\pi$
$18$	6729.05	0.271957
$19$	33692.2	1.12692	0.563459	−	0.826144i	$-0.309470\pi$
$19$	33692.2	1.12692	0.563459	+	0.826144i	$0.309470\pi$
$20$	−17385.5	−0.485939
$21$	9261.00	0.218218
$22$	9280.03	0.185810
$23$	−12167.0	−0.208514
$23$	−12167.0	−0.208514
$24$	−42566.8	−0.628539
$25$	86894.1	1.11224
$26$	88879.7	0.991736
$27$	19683.0	0.192450
$28$	−14679.6	−0.126375
$29$	20614.7	0.156958	0.0784792	−	0.996916i	$-0.474994\pi$
$29$	20614.7	0.156958	0.0784792	+	0.996916i	$0.474994\pi$
$30$	101241.	0.684593
$31$	68688.6	0.414113	0.207057	−	0.978329i	$-0.433612\pi$
$31$	68688.6	0.414113	0.207057	+	0.978329i	$0.433612\pi$
$32$	118038.	0.636792
$33$	27144.8	0.131489
$34$	−107727.	−0.470054
$35$	139335.	0.549317
$36$	−31199.4	−0.111452
$37$	−553979.	−1.79799	−0.898995	−	0.437958i	$-0.855702\pi$
$37$	−553979.	−1.79799	−0.898995	+	0.437958i	$0.855702\pi$
$38$	310997.	0.919419
$39$	259980.	0.701802
$40$	−640435.	−1.58221
$41$	519082.	1.17623	0.588115	−	0.808777i	$-0.299870\pi$
$41$	519082.	1.17623	0.588115	+	0.808777i	$0.299870\pi$
$42$	85483.8	0.178037
$43$	318063.	0.610062	0.305031	−	0.952342i	$-0.401333\pi$
$43$	318063.	0.610062	0.305031	+	0.952342i	$0.401333\pi$
$44$	−43027.2	−0.0761480
$45$	296138.	0.484452
$46$	−112308.	−0.170121
$47$	−213559.	−0.300038	−0.150019	−	0.988683i	$-0.547933\pi$
$47$	−213559.	−0.300038	−0.150019	+	0.988683i	$0.547933\pi$
$48$	−245005.	−0.319765
$49$	117649.	0.142857
$50$	802077.	0.907447
$51$	−315110.	−0.332634
$52$	−412094.	−0.406429
$53$	−510941.	−0.471417	−0.235708	−	0.971824i	$-0.575741\pi$
$53$	−510941.	−0.471417	−0.235708	+	0.971824i	$0.575741\pi$
$54$	181684.	0.157014
$55$	408404.	0.330995
$56$	−540757.	−0.411475
$57$	909691.	0.650626
$58$	190285.	0.128058
$59$	3.10816e6	1.97025	0.985126	−	0.171832i	$-0.0549687\pi$
$59$	3.10816e6	1.97025	0.985126	+	0.171832i	$0.0549687\pi$
$60$	−469408.	−0.280557
$61$	−285227.	−0.160893	−0.0804464	−	0.996759i	$-0.525635\pi$
$61$	−285227.	−0.160893	−0.0804464	+	0.996759i	$0.525635\pi$
$62$	634031.	0.337862
$63$	250047.	0.125988
$64$	2.25106e6	1.07339
$65$	3.91150e6	1.76664
$66$	250561.	0.107278
$67$	−1.25165e6	−0.508417	−0.254209	−	0.967149i	$-0.581815\pi$
$67$	−1.25165e6	−0.508417	−0.254209	+	0.967149i	$0.581815\pi$
$68$	499480.	0.192636
$69$	−328509.	−0.120386
$70$	1.28614e6	0.448171
$71$	472948.	0.156823	0.0784114	−	0.996921i	$-0.475015\pi$
$71$	472948.	0.156823	0.0784114	+	0.996921i	$0.475015\pi$
$72$	−1.14930e6	−0.362887
$73$	2.57244e6	0.773954	0.386977	−	0.922089i	$-0.373519\pi$
$73$	2.57244e6	0.773954	0.386977	+	0.922089i	$0.373519\pi$
$74$	−5.11351e6	−1.46693
$75$	2.34614e6	0.642155
$76$	−1.44195e6	−0.376792
$77$	344840.	0.0860795
$78$	2.39975e6	0.572579
$79$	3.62065e6	0.826212	0.413106	−	0.910683i	$-0.364444\pi$
$79$	3.62065e6	0.826212	0.413106	+	0.910683i	$0.364444\pi$
$80$	−3.68620e6	−0.804941
$81$	531441.	0.111111
$82$	4.79139e6	0.959651
$83$	−2.77576e6	−0.532855	−0.266428	−	0.963855i	$-0.585843\pi$
$83$	−2.77576e6	−0.532855	−0.266428	+	0.963855i	$0.585843\pi$
$84$	−396349.	−0.0729625
$85$	−4.74095e6	−0.837335
$86$	2.93589e6	0.497731
$87$	556598.	0.0906200
$88$	−1.58501e6	−0.247937
$89$	−2.11122e6	−0.317445	−0.158722	−	0.987323i	$-0.550737\pi$
$89$	−2.11122e6	−0.317445	−0.158722	+	0.987323i	$0.550737\pi$
$90$	2.73351e6	0.395250
$91$	3.30271e6	0.459437
$92$	520718.	0.0697181
$93$	1.85459e6	0.239088
$94$	−1.97126e6	−0.244792
$95$	1.36866e7	1.63781
$96$	3.18703e6	0.367652
$97$	−5.84030e6	−0.649731	−0.324866	−	0.945760i	$-0.605319\pi$
$97$	−5.84030e6	−0.649731	−0.324866	+	0.945760i	$0.605319\pi$
$98$	1.08596e6	0.116553
$99$	732910.	0.0759150
$100$	−3.71886e6	−0.371886
$101$	9.45608e6	0.913243	0.456621	−	0.889661i	$-0.349059\pi$
$101$	9.45608e6	0.913243	0.456621	+	0.889661i	$0.349059\pi$
$102$	−2.90863e6	−0.271386
$103$	−5.23700e6	−0.472229	−0.236114	−	0.971725i	$-0.575874\pi$
$103$	−5.23700e6	−0.472229	−0.236114	+	0.971725i	$0.575874\pi$
$104$	−1.51804e7	−1.32333
$105$	3.76205e6	0.317148
$106$	−4.71624e6	−0.384615
$107$	2.19114e6	0.172913	0.0864563	−	0.996256i	$-0.472446\pi$
$107$	2.19114e6	0.172913	0.0864563	+	0.996256i	$0.472446\pi$
$108$	−842385.	−0.0643469
$109$	−1.00278e7	−0.741672	−0.370836	−	0.928698i	$-0.620929\pi$
$109$	−1.00278e7	−0.741672	−0.370836	+	0.928698i	$0.620929\pi$
$110$	3.76978e6	0.270049
$111$	−1.49574e7	−1.03807
$112$	−3.11248e6	−0.209336
$113$	8.49737e6	0.554000	0.277000	−	0.960870i	$-0.410660\pi$
$113$	8.49737e6	0.554000	0.277000	+	0.960870i	$0.410660\pi$
$114$	8.39691e6	0.530827
$115$	−4.94254e6	−0.303046
$116$	−882261.	−0.0524800
$117$	7.01947e6	0.405185
$118$	2.86900e7	1.60747
$119$	−4.00306e6	−0.217760
$120$	−1.72917e7	−0.913491
$121$	−1.84764e7	−0.948132
$122$	−2.63279e6	−0.131268
$123$	1.40152e7	0.679097
$124$	−2.93971e6	−0.138461
$125$	3.56223e6	0.163131
$126$	2.30806e6	0.102790
$127$	3.99145e7	1.72909	0.864545	−	0.502556i	$-0.167607\pi$
$127$	3.99145e7	1.72909	0.864545	+	0.502556i	$0.167607\pi$
$128$	5.66956e6	0.238954
$129$	8.58771e6	0.352220
$130$	3.61052e7	1.44135
$131$	−3.01288e7	−1.17094	−0.585468	−	0.810696i	$-0.699089\pi$
$131$	−3.01288e7	−1.17094	−0.585468	+	0.810696i	$0.699089\pi$
$132$	−1.16173e6	−0.0439640
$133$	1.15564e7	0.425935
$134$	−1.15533e7	−0.414802
$135$	7.99573e6	0.279699
$136$	1.83995e7	0.627220
$137$	992032.	0.0329613	0.0164806	−	0.999864i	$-0.494754\pi$
$137$	992032.	0.0329613	0.0164806	+	0.999864i	$0.494754\pi$
$138$	−3.03231e6	−0.0982192
$139$	2.03013e7	0.641167	0.320584	−	0.947220i	$-0.396121\pi$
$139$	2.03013e7	0.641167	0.320584	+	0.947220i	$0.396121\pi$
$140$	−5.96322e6	−0.183668
$141$	−5.76610e6	−0.173227
$142$	4.36556e6	0.127947
$143$	9.68055e6	0.276837
$144$	−6.61515e6	−0.184617
$145$	8.37423e6	0.228117
$146$	2.37450e7	0.631446
$147$	3.17652e6	0.0824786
$148$	2.37090e7	0.601169
$149$	4.87150e7	1.20645	0.603227	−	0.797569i	$-0.293881\pi$
$149$	4.87150e7	1.20645	0.603227	+	0.797569i	$0.293881\pi$
$150$	2.16561e7	0.523915
$151$	7.28946e7	1.72296	0.861482	−	0.507789i	$-0.169537\pi$
$151$	7.28946e7	1.72296	0.861482	+	0.507789i	$0.169537\pi$
$152$	−5.31175e7	−1.22683
$153$	−8.50797e6	−0.192046
$154$	3.18305e6	0.0702297
$155$	2.79031e7	0.601854
$156$	−1.11265e7	−0.234652
$157$	−1.69802e7	−0.350182	−0.175091	−	0.984552i	$-0.556022\pi$
$157$	−1.69802e7	−0.350182	−0.175091	+	0.984552i	$0.556022\pi$
$158$	3.34204e7	0.674082
$159$	−1.37954e7	−0.272172
$160$	4.79501e7	0.925485
$161$	−4.17328e6	−0.0788110
$162$	4.90547e6	0.0906522
$163$	5.22130e7	0.944327	0.472163	−	0.881511i	$-0.343473\pi$
$163$	5.22130e7	0.944327	0.472163	+	0.881511i	$0.343473\pi$
$164$	−2.22155e7	−0.393280
$165$	1.10269e7	0.191100
$166$	−2.56217e7	−0.434741
$167$	−2.18118e7	−0.362396	−0.181198	−	0.983447i	$-0.557997\pi$
$167$	−2.18118e7	−0.362396	−0.181198	+	0.983447i	$0.557997\pi$
$168$	−1.46004e7	−0.237565
$169$	2.99672e7	0.477576
$170$	−4.37614e7	−0.683157
$171$	2.45616e7	0.375639
$172$	−1.36123e7	−0.203978
$173$	8.45138e7	1.24098	0.620492	−	0.784213i	$-0.286933\pi$
$173$	8.45138e7	1.24098	0.620492	+	0.784213i	$0.286933\pi$
$174$	5.13768e6	0.0739341
$175$	2.98047e7	0.420389
$176$	−9.12295e6	−0.126137
$177$	8.39204e7	1.13753
$178$	−1.94876e7	−0.258993
$179$	1.24802e8	1.62643	0.813217	−	0.581960i	$-0.197714\pi$
$179$	1.24802e8	1.62643	0.813217	+	0.581960i	$0.197714\pi$
$180$	−1.26740e7	−0.161980
$181$	8.19557e7	1.02732	0.513658	−	0.857995i	$-0.328290\pi$
$181$	8.19557e7	1.02732	0.513658	+	0.857995i	$0.328290\pi$
$182$	3.04857e7	0.374841
$183$	−7.70113e6	−0.0928915
$184$	1.91819e7	0.227002
$185$	−2.25040e8	−2.61312
$186$	1.71188e7	0.195065
$187$	−1.17333e7	−0.131213
$188$	9.13982e6	0.100319
$189$	6.75127e6	0.0727393
$190$	1.26335e8	1.33624
$191$	−1.01157e8	−1.05046	−0.525228	−	0.850962i	$-0.676020\pi$
$191$	−1.01157e8	−1.05046	−0.525228	+	0.850962i	$0.676020\pi$
$192$	6.07786e7	0.619721
$193$	3.84133e7	0.384620	0.192310	−	0.981334i	$-0.438402\pi$
$193$	3.84133e7	0.384620	0.192310	+	0.981334i	$0.438402\pi$
$194$	−5.39089e7	−0.530096
$195$	1.05611e8	1.01997
$196$	−5.03509e6	−0.0477652
$197$	−6.20666e7	−0.578397	−0.289198	−	0.957269i	$-0.593389\pi$
$197$	−6.20666e7	−0.578397	−0.289198	+	0.957269i	$0.593389\pi$
$198$	6.76514e6	0.0619368
$199$	−1.30185e8	−1.17105	−0.585525	−	0.810655i	$-0.699111\pi$
$199$	−1.30185e8	−1.17105	−0.585525	+	0.810655i	$0.699111\pi$
$200$	−1.36993e8	−1.21086
$201$	−3.37945e7	−0.293535
$202$	8.72845e7	0.745087
$203$	7.07085e6	0.0593247
$204$	1.34860e7	0.111218
$205$	2.10864e8	1.70948
$206$	−4.83402e7	−0.385277
$207$	−8.86974e6	−0.0695048
$208$	−8.73753e7	−0.673235
$209$	3.38730e7	0.256650
$210$	3.47257e7	0.258752
$211$	1.62728e7	0.119254	0.0596271	−	0.998221i	$-0.481009\pi$
$211$	1.62728e7	0.119254	0.0596271	+	0.998221i	$0.481009\pi$
$212$	2.18670e7	0.157621
$213$	1.27696e7	0.0905417
$214$	2.02253e7	0.141074
$215$	1.29205e8	0.886638
$216$	−3.10312e7	−0.209513
$217$	2.35602e7	0.156520
$218$	−9.25616e7	−0.605108
$219$	6.94559e7	0.446843
$220$	−1.74787e7	−0.110670
$221$	−1.12376e8	−0.700329
$222$	−1.38065e8	−0.846930
$223$	−2.16600e8	−1.30795	−0.653977	−	0.756515i	$-0.726901\pi$
$223$	−2.16600e8	−1.30795	−0.653977	+	0.756515i	$0.726901\pi$
$224$	4.04871e7	0.240685
$225$	6.33458e7	0.370748
$226$	7.84351e7	0.451992
$227$	−1.69900e6	−0.00964055	−0.00482027	−	0.999988i	$-0.501534\pi$
$227$	−1.69900e6	−0.00964055	−0.00482027	+	0.999988i	$0.501534\pi$
$228$	−3.89326e7	−0.217541
$229$	1.90192e8	1.04657	0.523284	−	0.852158i	$-0.324707\pi$
$229$	1.90192e8	1.04657	0.523284	+	0.852158i	$0.324707\pi$
$230$	−4.56222e7	−0.247246
$231$	9.31067e6	0.0496980
$232$	−3.25001e7	−0.170875
$233$	3.29461e7	0.170631	0.0853155	−	0.996354i	$-0.472810\pi$
$233$	3.29461e7	0.170631	0.0853155	+	0.996354i	$0.472810\pi$
$234$	6.47933e7	0.330579
$235$	−8.67531e7	−0.436061
$236$	−1.33022e8	−0.658766
$237$	9.77575e7	0.477014
$238$	−3.69503e7	−0.177664
$239$	4.55472e6	0.0215809	0.0107904	−	0.999942i	$-0.496565\pi$
$239$	4.55472e6	0.0215809	0.0107904	+	0.999942i	$0.496565\pi$
$240$	−9.95274e7	−0.464733
$241$	−3.32932e8	−1.53213	−0.766067	−	0.642761i	$-0.777789\pi$
$241$	−3.32932e8	−1.53213	−0.766067	+	0.642761i	$0.777789\pi$
$242$	−1.70547e8	−0.773553
$243$	1.43489e7	0.0641500
$244$	1.22070e7	0.0537955
$245$	4.77920e7	0.207622
$246$	1.29368e8	0.554055
$247$	3.24419e8	1.36983
$248$	−1.08291e8	−0.450829
$249$	−7.49456e7	−0.307644
$250$	3.28812e7	0.133094
$251$	−4.46806e8	−1.78345	−0.891725	−	0.452578i	$-0.850504\pi$
$251$	−4.46806e8	−1.78345	−0.891725	+	0.452578i	$0.850504\pi$
$252$	−1.07014e7	−0.0421249
$253$	−1.22323e7	−0.0474881
$254$	3.68431e8	1.41071
$255$	−1.28006e8	−0.483436
$256$	−2.35803e8	−0.878434
$257$	1.68337e8	0.618606	0.309303	−	0.950963i	$-0.399904\pi$
$257$	1.68337e8	0.618606	0.309303	+	0.950963i	$0.399904\pi$
$258$	7.92690e7	0.287365
$259$	−1.90015e8	−0.679577
$260$	−1.67403e8	−0.590686
$261$	1.50281e7	0.0523195
$262$	−2.78105e8	−0.955331
$263$	2.74360e8	0.929986	0.464993	−	0.885314i	$-0.346057\pi$
$263$	2.74360e8	0.929986	0.464993	+	0.885314i	$0.346057\pi$
$264$	−4.27952e7	−0.143147
$265$	−2.07557e8	−0.685136
$266$	1.06672e8	0.347508
$267$	−5.70029e7	−0.183277
$268$	5.35675e7	0.169992
$269$	3.88757e8	1.21771	0.608857	−	0.793280i	$-0.291628\pi$
$269$	3.88757e8	1.21771	0.608857	+	0.793280i	$0.291628\pi$
$270$	7.38047e7	0.228198
$271$	2.90761e8	0.887450	0.443725	−	0.896163i	$-0.353657\pi$
$271$	2.90761e8	0.887450	0.443725	+	0.896163i	$0.353657\pi$
$272$	1.05904e8	0.319094
$273$	8.91732e7	0.265256
$274$	9.15697e6	0.0268921
$275$	8.73602e7	0.253308
$276$	1.40594e7	0.0402518
$277$	2.13994e8	0.604955	0.302478	−	0.953156i	$-0.402186\pi$
$277$	2.13994e8	0.604955	0.302478	+	0.953156i	$0.402186\pi$
$278$	1.87391e8	0.523109
$279$	5.00740e7	0.138038
$280$	−2.19669e8	−0.598020
$281$	1.19740e8	0.321935	0.160968	−	0.986960i	$-0.448539\pi$
$281$	1.19740e8	0.321935	0.160968	+	0.986960i	$0.448539\pi$
$282$	−5.32240e7	−0.141331
$283$	2.13990e8	0.561231	0.280616	−	0.959820i	$-0.409461\pi$
$283$	2.13990e8	0.561231	0.280616	+	0.959820i	$0.409461\pi$
$284$	−2.02410e7	−0.0524347
$285$	3.69539e8	0.945592
$286$	8.93564e7	0.225863
$287$	1.78045e8	0.444573
$288$	8.60498e7	0.212264
$289$	−2.74132e8	−0.668064
$290$	7.72984e7	0.186113
$291$	−1.57688e8	−0.375123
$292$	−1.10094e8	−0.258776
$293$	3.18231e8	0.739105	0.369553	−	0.929210i	$-0.379511\pi$
$293$	3.18231e8	0.739105	0.369553	+	0.929210i	$0.379511\pi$
$294$	2.93209e7	0.0672918
$295$	1.26262e9	2.86348
$296$	8.73376e8	1.95740
$297$	1.97886e7	0.0438295
$298$	4.49665e8	0.984310
$299$	−1.17155e8	−0.253461
$300$	−1.00409e8	−0.214708
$301$	1.09096e8	0.230582
$302$	6.72855e8	1.40571
$303$	2.55314e8	0.527261
$304$	−3.05733e8	−0.624143
$305$	−1.15867e8	−0.233834
$306$	−7.85329e7	−0.156685
$307$	4.55192e8	0.897863	0.448931	−	0.893566i	$-0.351805\pi$
$307$	4.55192e8	0.897863	0.448931	+	0.893566i	$0.351805\pi$
$308$	−1.47583e7	−0.0287812
$309$	−1.41399e8	−0.272641
$310$	2.57560e8	0.491034
$311$	−4.18952e8	−0.789775	−0.394887	−	0.918730i	$-0.629216\pi$
$311$	−4.18952e8	−0.789775	−0.394887	+	0.918730i	$0.629216\pi$
$312$	−4.09872e8	−0.764024
$313$	−5.24661e8	−0.967105	−0.483553	−	0.875315i	$-0.660654\pi$
$313$	−5.24661e8	−0.967105	−0.483553	+	0.875315i	$0.660654\pi$
$314$	−1.56736e8	−0.285703
$315$	1.01575e8	0.183106
$316$	−1.54955e8	−0.276249
$317$	−3.96542e8	−0.699169	−0.349584	−	0.936905i	$-0.613677\pi$
$317$	−3.96542e8	−0.699169	−0.349584	+	0.936905i	$0.613677\pi$
$318$	−1.27339e8	−0.222057
$319$	2.07253e7	0.0357465
$320$	9.14438e8	1.56002
$321$	5.91607e7	0.0998311
$322$	−3.85215e7	−0.0642996
$323$	−3.93213e8	−0.649261
$324$	−2.27444e7	−0.0371507
$325$	8.36694e8	1.35200
$326$	4.81953e8	0.770448
$327$	−2.70750e8	−0.428205
$328$	−8.18359e8	−1.28052
$329$	−7.32508e7	−0.113404
$330$	1.01784e8	0.155913
$331$	1.85934e8	0.281813	0.140907	−	0.990023i	$-0.454998\pi$
$331$	1.85934e8	0.281813	0.140907	+	0.990023i	$0.454998\pi$
$332$	1.18796e8	0.178163
$333$	−4.03851e8	−0.599330
$334$	−2.01334e8	−0.295668
$335$	−5.08451e8	−0.738911
$336$	−8.40369e7	−0.120860
$337$	−2.13605e8	−0.304024	−0.152012	−	0.988379i	$-0.548575\pi$
$337$	−2.13605e8	−0.304024	−0.152012	+	0.988379i	$0.548575\pi$
$338$	2.76613e8	0.389640
$339$	2.29429e8	0.319852
$340$	2.02901e8	0.279968
$341$	6.90571e7	0.0943122
$342$	2.26717e8	0.306473
$343$	4.03536e7	0.0539949
$344$	−5.01443e8	−0.664151
$345$	−1.33449e8	−0.174964
$346$	7.80106e8	1.01248
$347$	−1.10235e9	−1.41633	−0.708165	−	0.706047i	$-0.750477\pi$
$347$	−1.10235e9	−1.41633	−0.708165	+	0.706047i	$0.750477\pi$
$348$	−2.38210e7	−0.0302994
$349$	−1.37822e9	−1.73552	−0.867759	−	0.496985i	$-0.834440\pi$
$349$	−1.37822e9	−1.73552	−0.867759	+	0.496985i	$0.834440\pi$
$350$	2.75112e8	0.342983
$351$	1.89526e8	0.233934
$352$	1.18671e8	0.145026
$353$	−9.75886e8	−1.18083	−0.590415	−	0.807100i	$-0.701036\pi$
$353$	−9.75886e8	−1.18083	−0.590415	+	0.807100i	$0.701036\pi$
$354$	7.74629e8	0.928073
$355$	1.92124e8	0.227920
$356$	9.03550e7	0.106140
$357$	−1.08083e8	−0.125724
$358$	1.15199e9	1.32696
$359$	5.73952e8	0.654704	0.327352	−	0.944902i	$-0.393844\pi$
$359$	5.73952e8	0.654704	0.327352	+	0.944902i	$0.393844\pi$
$360$	−4.66877e8	−0.527404
$361$	2.41296e8	0.269944
$362$	7.56493e8	0.838157
$363$	−4.98863e8	−0.547404
$364$	−1.41348e8	−0.153616
$365$	1.04499e9	1.12483
$366$	−7.10854e7	−0.0757873
$367$	−1.62431e9	−1.71529	−0.857645	−	0.514242i	$-0.828073\pi$
$367$	−1.62431e9	−1.71529	−0.857645	+	0.514242i	$0.828073\pi$
$368$	1.10407e8	0.115486
$369$	3.78411e8	0.392077
$370$	−2.07724e9	−2.13197
$371$	−1.75253e8	−0.178179
$372$	−7.93721e7	−0.0799406
$373$	1.18457e9	1.18189	0.590946	−	0.806711i	$-0.298754\pi$
$373$	1.18457e9	1.18189	0.590946	+	0.806711i	$0.298754\pi$
$374$	−1.08305e8	−0.107053
$375$	9.61801e7	0.0941837
$376$	3.36687e8	0.326639
$377$	1.98497e8	0.190792
$378$	6.23177e7	0.0593458
$379$	−4.10564e7	−0.0387386	−0.0193693	−	0.999812i	$-0.506166\pi$
$379$	−4.10564e7	−0.0387386	−0.0193693	+	0.999812i	$0.506166\pi$
$380$	−5.85755e8	−0.547613
$381$	1.07769e9	0.998290
$382$	−9.33728e8	−0.857035
$383$	1.88237e9	1.71203	0.856013	−	0.516955i	$-0.172935\pi$
$383$	1.88237e9	1.71203	0.856013	+	0.516955i	$0.172935\pi$
$384$	1.53078e8	0.137960
$385$	1.40083e8	0.125104
$386$	3.54575e8	0.313800
$387$	2.31868e8	0.203354
$388$	2.49951e8	0.217242
$389$	−6.45800e8	−0.556256	−0.278128	−	0.960544i	$-0.589714\pi$
$389$	−6.45800e8	−0.556256	−0.278128	+	0.960544i	$0.589714\pi$
$390$	9.74840e8	0.832161
$391$	1.41998e8	0.120133
$392$	−1.85480e8	−0.155523
$393$	−8.13479e8	−0.676040
$394$	−5.72906e8	−0.471897
$395$	1.47080e9	1.20078
$396$	−3.13668e7	−0.0253827
$397$	5.68136e8	0.455707	0.227853	−	0.973695i	$-0.426829\pi$
$397$	5.68136e8	0.455707	0.227853	+	0.973695i	$0.426829\pi$
$398$	−1.20167e9	−0.955424
$399$	3.12024e8	0.245914
$400$	−7.88501e8	−0.616016
$401$	2.38475e8	0.184687	0.0923437	−	0.995727i	$-0.470564\pi$
$401$	2.38475e8	0.184687	0.0923437	+	0.995727i	$0.470564\pi$
$402$	−3.11940e8	−0.239486
$403$	6.61396e8	0.503378
$404$	−4.04697e8	−0.305348
$405$	2.15885e8	0.161484
$406$	6.52676e7	0.0484013
$407$	−5.56951e8	−0.409483
$408$	4.96787e8	0.362126
$409$	−6.56133e8	−0.474199	−0.237099	−	0.971485i	$-0.576197\pi$
$409$	−6.56133e8	−0.474199	−0.237099	+	0.971485i	$0.576197\pi$
$410$	1.94639e9	1.39472
$411$	2.67849e7	0.0190302
$412$	2.24131e8	0.157893
$413$	1.06610e9	0.744685
$414$	−8.18723e7	−0.0567069
$415$	−1.12759e9	−0.774428
$416$	1.13658e9	0.774056
$417$	5.48134e8	0.370178
$418$	3.12665e8	0.209393
$419$	−1.85164e9	−1.22972	−0.614862	−	0.788634i	$-0.710788\pi$
$419$	−1.85164e9	−1.22972	−0.614862	+	0.788634i	$0.710788\pi$
$420$	−1.61007e8	−0.106041
$421$	−1.91815e8	−0.125284	−0.0626421	−	0.998036i	$-0.519953\pi$
$421$	−1.91815e8	−0.125284	−0.0626421	+	0.998036i	$0.519953\pi$
$422$	1.50206e8	0.0972960
$423$	−1.55685e8	−0.100013
$424$	8.05523e8	0.513213
$425$	−1.01412e9	−0.640807
$426$	1.17870e8	0.0738703
$427$	−9.78329e7	−0.0608117
$428$	−9.37754e7	−0.0578144
$429$	2.61375e8	0.159832
$430$	1.19263e9	0.723381
$431$	−1.82043e9	−1.09523	−0.547613	−	0.836732i	$-0.684463\pi$
$431$	−1.82043e9	−1.09523	−0.547613	+	0.836732i	$0.684463\pi$
$432$	−1.78609e8	−0.106588
$433$	−2.11867e8	−0.125416	−0.0627082	−	0.998032i	$-0.519974\pi$
$433$	−2.11867e8	−0.125416	−0.0627082	+	0.998032i	$0.519974\pi$
$434$	2.17473e8	0.127700
$435$	2.26104e8	0.131703
$436$	4.29165e8	0.247983
$437$	−4.09934e8	−0.234979
$438$	6.41114e8	0.364566
$439$	−2.84257e9	−1.60356	−0.801781	−	0.597618i	$-0.796114\pi$
$439$	−2.84257e9	−1.60356	−0.801781	+	0.597618i	$0.796114\pi$
$440$	−6.43870e8	−0.360341
$441$	8.57661e7	0.0476190
$442$	−1.03729e9	−0.571377
$443$	−2.74638e9	−1.50089	−0.750444	−	0.660935i	$-0.770160\pi$
$443$	−2.74638e9	−1.50089	−0.750444	+	0.660935i	$0.770160\pi$
$444$	6.40142e8	0.347085
$445$	−8.57630e8	−0.461360
$446$	−1.99933e9	−1.06712
$447$	1.31531e9	0.696547
$448$	7.72114e8	0.405703
$449$	−2.06248e9	−1.07530	−0.537648	−	0.843170i	$-0.680687\pi$
$449$	−2.06248e9	−1.07530	−0.537648	+	0.843170i	$0.680687\pi$
$450$	5.84714e8	0.302482
$451$	5.21866e8	0.267881
$452$	−3.63667e8	−0.185233
$453$	1.96815e9	0.994753
$454$	−1.56826e7	−0.00786543
$455$	1.34165e9	0.667726
$456$	−1.43417e9	−0.708312
$457$	3.24746e9	1.59161	0.795805	−	0.605553i	$-0.207048\pi$
$457$	3.24746e9	1.59161	0.795805	+	0.605553i	$0.207048\pi$
$458$	1.75557e9	0.853863
$459$	−2.29715e8	−0.110878
$460$	2.11529e8	0.101325
$461$	−2.47492e9	−1.17654	−0.588272	−	0.808663i	$-0.700191\pi$
$461$	−2.47492e9	−1.17654	−0.588272	+	0.808663i	$0.700191\pi$
$462$	8.59423e7	0.0405471
$463$	−1.47032e9	−0.688460	−0.344230	−	0.938885i	$-0.611860\pi$
$463$	−1.47032e9	−0.688460	−0.344230	+	0.938885i	$0.611860\pi$
$464$	−1.87064e8	−0.0869314
$465$	7.53383e8	0.347480
$466$	3.04109e8	0.139213
$467$	2.57805e9	1.17134	0.585669	−	0.810550i	$-0.300832\pi$
$467$	2.57805e9	1.17134	0.585669	+	0.810550i	$0.300832\pi$
$468$	−3.00416e8	−0.135476
$469$	−4.29315e8	−0.192164
$470$	−8.00776e8	−0.355769
$471$	−4.58465e8	−0.202178
$472$	−4.90017e9	−2.14494
$473$	3.19769e8	0.138939
$474$	9.02352e8	0.389181
$475$	2.92766e9	1.25341
$476$	1.71322e8	0.0728094
$477$	−3.72476e8	−0.157139
$478$	4.20424e7	0.0176072
$479$	−4.59766e9	−1.91145	−0.955723	−	0.294267i	$-0.904925\pi$
$479$	−4.59766e9	−1.91145	−0.955723	+	0.294267i	$0.904925\pi$
$480$	1.29465e9	0.534329
$481$	−5.33421e9	−2.18556
$482$	−3.07314e9	−1.25002
$483$	−1.12679e8	−0.0455016
$484$	7.90746e8	0.317014
$485$	−2.37248e9	−0.944291
$486$	1.32448e8	0.0523381
$487$	2.33731e9	0.916990	0.458495	−	0.888697i	$-0.348389\pi$
$487$	2.33731e9	0.916990	0.458495	+	0.888697i	$0.348389\pi$
$488$	4.49675e8	0.175158
$489$	1.40975e9	0.545207
$490$	4.41145e8	0.169393
$491$	−9.51832e8	−0.362890	−0.181445	−	0.983401i	$-0.558077\pi$
$491$	−9.51832e8	−0.362890	−0.181445	+	0.983401i	$0.558077\pi$
$492$	−5.99817e8	−0.227060
$493$	−2.40589e8	−0.0904299
$494$	2.99456e9	1.11760
$495$	2.97727e8	0.110332
$496$	−6.23299e8	−0.229356
$497$	1.62221e8	0.0592735
$498$	−6.91787e8	−0.250998
$499$	−3.33268e9	−1.20072	−0.600360	−	0.799730i	$-0.704976\pi$
$499$	−3.33268e9	−1.20072	−0.600360	+	0.799730i	$0.704976\pi$
$500$	−1.52455e8	−0.0545438
$501$	−5.88917e8	−0.209229
$502$	−4.12425e9	−1.45506
$503$	−1.57251e9	−0.550942	−0.275471	−	0.961309i	$-0.588834\pi$
$503$	−1.57251e9	−0.550942	−0.275471	+	0.961309i	$0.588834\pi$
$504$	−3.94212e8	−0.137158
$505$	3.84130e9	1.32727
$506$	−1.12910e8	−0.0387441
$507$	8.09115e8	0.275729
$508$	−1.70824e9	−0.578132
$509$	1.41374e9	0.475181	0.237590	−	0.971365i	$-0.423642\pi$
$509$	1.41374e9	0.475181	0.237590	+	0.971365i	$0.423642\pi$
$510$	−1.18156e9	−0.394421
$511$	8.82347e8	0.292527
$512$	−2.90228e9	−0.955642
$513$	6.63164e8	0.216875
$514$	1.55384e9	0.504702
$515$	−2.12740e9	−0.686316
$516$	−3.67533e8	−0.117767
$517$	−2.14705e8	−0.0683320
$518$	−1.75394e9	−0.554446
$519$	2.28187e9	0.716482
$520$	−6.16668e9	−1.92327
$521$	−1.22652e9	−0.379966	−0.189983	−	0.981787i	$-0.560843\pi$
$521$	−1.22652e9	−0.379966	−0.189983	+	0.981787i	$0.560843\pi$
$522$	1.38717e8	0.0426859
$523$	−1.03018e9	−0.314890	−0.157445	−	0.987528i	$-0.550326\pi$
$523$	−1.03018e9	−0.314890	−0.157445	+	0.987528i	$0.550326\pi$
$524$	1.28944e9	0.391509
$525$	8.04726e8	0.242712
$526$	2.53249e9	0.758748
$527$	−8.01647e8	−0.238587
$528$	−2.46320e8	−0.0728249
$529$	1.48036e8	0.0434783
$530$	−1.91586e9	−0.558982
$531$	2.26585e9	0.656751
$532$	−4.94588e8	−0.142414
$533$	4.99819e9	1.42977
$534$	−5.26166e8	−0.149530
$535$	8.90096e8	0.251304
$536$	1.97328e9	0.553494
$537$	3.36966e9	0.939023
$538$	3.58843e9	0.993497
$539$	1.18280e8	0.0325350
$540$	−3.42198e8	−0.0935189
$541$	4.74130e9	1.28738	0.643690	−	0.765286i	$-0.277403\pi$
$541$	4.74130e9	1.28738	0.643690	+	0.765286i	$0.277403\pi$
$542$	2.68388e9	0.724044
$543$	2.21280e9	0.593121
$544$	−1.37759e9	−0.366881
$545$	−4.07354e9	−1.07791
$546$	8.23115e8	0.216414
$547$	−2.26525e9	−0.591780	−0.295890	−	0.955222i	$-0.595616\pi$
$547$	−2.26525e9	−0.591780	−0.295890	+	0.955222i	$0.595616\pi$
$548$	−4.24566e7	−0.0110208
$549$	−2.07931e8	−0.0536309
$550$	8.06379e8	0.206666
$551$	6.94557e8	0.176879
$552$	5.17911e8	0.131059
$553$	1.24188e9	0.312279
$554$	1.97528e9	0.493565
$555$	−6.07609e9	−1.50869
$556$	−8.68846e8	−0.214378
$557$	−2.32061e8	−0.0568995	−0.0284498	−	0.999595i	$-0.509057\pi$
$557$	−2.32061e8	−0.0568995	−0.0284498	+	0.999595i	$0.509057\pi$
$558$	4.62209e8	0.112621
$559$	3.06260e9	0.741565
$560$	−1.26437e9	−0.304239
$561$	−3.16800e8	−0.0757557
$562$	1.10527e9	0.262657
$563$	−5.26086e9	−1.24245	−0.621223	−	0.783634i	$-0.713364\pi$
$563$	−5.26086e9	−1.24245	−0.621223	+	0.783634i	$0.713364\pi$
$564$	2.46775e8	0.0579194
$565$	3.45185e9	0.805159
$566$	1.97524e9	0.457892
$567$	1.82284e8	0.0419961
$568$	−7.45626e8	−0.170727
$569$	6.94781e8	0.158108	0.0790542	−	0.996870i	$-0.474810\pi$
$569$	6.94781e8	0.158108	0.0790542	+	0.996870i	$0.474810\pi$
$570$	3.41104e9	0.771480
$571$	−5.95133e9	−1.33779	−0.668894	−	0.743357i	$-0.733232\pi$
$571$	−5.95133e9	−1.33779	−0.668894	+	0.743357i	$0.733232\pi$
$572$	−4.14304e8	−0.0925621
$573$	−2.73123e9	−0.606481
$574$	1.64345e9	0.362714
$575$	−1.05724e9	−0.231919
$576$	1.64102e9	0.357796
$577$	−7.41310e9	−1.60651	−0.803257	−	0.595633i	$-0.796901\pi$
$577$	−7.41310e9	−1.60651	−0.803257	+	0.595633i	$0.796901\pi$
$578$	−2.53038e9	−0.545053
$579$	1.03716e9	0.222060
$580$	−3.58397e8	−0.0762722
$581$	−9.52087e8	−0.201400
$582$	−1.45554e9	−0.306051
$583$	−5.13681e8	−0.107363
$584$	−4.05558e9	−0.842574
$585$	2.85149e9	0.588879
$586$	2.93744e9	0.603014
$587$	−6.19145e9	−1.26345	−0.631727	−	0.775191i	$-0.717654\pi$
$587$	−6.19145e9	−1.26345	−0.631727	+	0.775191i	$0.717654\pi$
$588$	−1.35948e8	−0.0275772
$589$	2.31427e9	0.466671
$590$	1.16546e10	2.33623
$591$	−1.67580e9	−0.333938
$592$	5.02696e9	0.995817
$593$	9.61806e9	1.89407	0.947035	−	0.321130i	$-0.104063\pi$
$593$	9.61806e9	1.89407	0.947035	+	0.321130i	$0.104063\pi$
$594$	1.82659e8	0.0357592
$595$	−1.62615e9	−0.316483
$596$	−2.08489e9	−0.403386
$597$	−3.51500e9	−0.676106
$598$	−1.08140e9	−0.206791
$599$	−1.09673e9	−0.208500	−0.104250	−	0.994551i	$-0.533244\pi$
$599$	−1.09673e9	−0.208500	−0.104250	+	0.994551i	$0.533244\pi$
$600$	−3.69881e9	−0.699089
$601$	8.64848e9	1.62510	0.812548	−	0.582894i	$-0.198080\pi$
$601$	8.64848e9	1.62510	0.812548	+	0.582894i	$0.198080\pi$
$602$	1.00701e9	0.188125
$603$	−9.12451e8	−0.169472
$604$	−3.11971e9	−0.576083
$605$	−7.50559e9	−1.37797
$606$	2.35668e9	0.430176
$607$	−2.79123e9	−0.506565	−0.253282	−	0.967392i	$-0.581510\pi$
$607$	−2.79123e9	−0.506565	−0.253282	+	0.967392i	$0.581510\pi$
$608$	3.97697e9	0.717612
$609$	1.90913e8	0.0342511
$610$	−1.06951e9	−0.190778
$611$	−2.05634e9	−0.364712
$612$	3.64121e8	0.0642119
$613$	−3.09905e9	−0.543397	−0.271699	−	0.962382i	$-0.587585\pi$
$613$	−3.09905e9	−0.543397	−0.271699	+	0.962382i	$0.587585\pi$
$614$	4.20165e9	0.732539
$615$	5.69334e9	0.986970
$616$	−5.43657e8	−0.0937114
$617$	−6.56087e7	−0.0112451	−0.00562255	−	0.999984i	$-0.501790\pi$
$617$	−6.56087e7	−0.0112451	−0.00562255	+	0.999984i	$0.501790\pi$
$618$	−1.30519e9	−0.222440
$619$	−7.88282e9	−1.33587	−0.667935	−	0.744219i	$-0.732822\pi$
$619$	−7.88282e9	−1.33587	−0.667935	+	0.744219i	$0.732822\pi$
$620$	−1.19418e9	−0.201234
$621$	−2.39483e8	−0.0401286
$622$	−3.86715e9	−0.644354
$623$	−7.24148e8	−0.119983
$624$	−2.35913e9	−0.388693
$625$	−5.34153e9	−0.875157
$626$	−4.84289e9	−0.789032
$627$	9.14570e8	0.148177
$628$	7.26711e8	0.117085
$629$	6.46535e9	1.03589
$630$	9.37594e8	0.149390
$631$	−1.18049e10	−1.87050	−0.935252	−	0.353982i	$-0.884827\pi$
$631$	−1.18049e10	−1.87050	−0.935252	+	0.353982i	$0.884827\pi$
$632$	−5.70813e9	−0.899465
$633$	4.39366e8	0.0688515
$634$	−3.66029e9	−0.570431
$635$	1.62143e10	2.51298
$636$	5.90410e8	0.0910025
$637$	1.13283e9	0.173651
$638$	1.91305e8	0.0291645
$639$	3.44779e8	0.0522743
$640$	2.30312e9	0.347285
$641$	2.51387e8	0.0376998	0.0188499	−	0.999822i	$-0.494000\pi$
$641$	2.51387e8	0.0376998	0.0188499	+	0.999822i	$0.494000\pi$
$642$	5.46084e8	0.0814492
$643$	−1.61030e9	−0.238874	−0.119437	−	0.992842i	$-0.538109\pi$
$643$	−1.61030e9	−0.238874	−0.119437	+	0.992842i	$0.538109\pi$
$644$	1.78606e8	0.0263510
$645$	3.48855e9	0.511900
$646$	−3.62956e9	−0.529713
$647$	−9.47289e9	−1.37505	−0.687523	−	0.726162i	$-0.741302\pi$
$647$	−9.47289e9	−1.37505	−0.687523	+	0.726162i	$0.741302\pi$
$648$	−8.37843e8	−0.120962
$649$	3.12484e9	0.448715
$650$	7.72312e9	1.10305
$651$	6.36125e8	0.0903669
$652$	−2.23459e9	−0.315741
$653$	−4.53190e9	−0.636919	−0.318460	−	0.947936i	$-0.603166\pi$
$653$	−4.53190e9	−0.636919	−0.318460	+	0.947936i	$0.603166\pi$
$654$	−2.49916e9	−0.349359
$655$	−1.22391e10	−1.70179
$656$	−4.71029e9	−0.651455
$657$	1.87531e9	0.257985
$658$	−6.76142e8	−0.0925225
$659$	2.77377e8	0.0377548	0.0188774	−	0.999822i	$-0.493991\pi$
$659$	2.77377e8	0.0377548	0.0188774	+	0.999822i	$0.493991\pi$
$660$	−4.71926e8	−0.0638954
$661$	−8.06233e9	−1.08581	−0.542907	−	0.839793i	$-0.682676\pi$
$661$	−8.06233e9	−1.08581	−0.542907	+	0.839793i	$0.682676\pi$
$662$	1.71627e9	0.229923
$663$	−3.03416e9	−0.404335
$664$	4.37613e9	0.580099
$665$	4.69452e9	0.619035
$666$	−3.72775e9	−0.488976
$667$	−2.50819e8	−0.0327281
$668$	9.33491e8	0.121169
$669$	−5.84821e9	−0.755147
$670$	−4.69326e9	−0.602855
$671$	−2.86757e8	−0.0366425
$672$	1.09315e9	0.138959
$673$	−5.69978e9	−0.720785	−0.360392	−	0.932801i	$-0.617357\pi$
$673$	−5.69978e9	−0.720785	−0.360392	+	0.932801i	$0.617357\pi$
$674$	−1.97169e9	−0.248044
$675$	1.71034e9	0.214052
$676$	−1.28252e9	−0.159681
$677$	3.36844e9	0.417223	0.208611	−	0.977999i	$-0.433106\pi$
$677$	3.36844e9	0.417223	0.208611	+	0.977999i	$0.433106\pi$
$678$	2.11775e9	0.260958
$679$	−2.00322e9	−0.245575
$680$	7.47435e9	0.911574
$681$	−4.58729e7	−0.00556597
$682$	6.37432e8	0.0769465
$683$	1.56433e10	1.87869	0.939346	−	0.342971i	$-0.111433\pi$
$683$	1.56433e10	1.87869	0.939346	+	0.342971i	$0.111433\pi$
$684$	−1.05118e9	−0.125597
$685$	4.02989e8	0.0479044
$686$	3.72485e8	0.0440528
$687$	5.13518e9	0.604236
$688$	−2.88619e9	−0.337883
$689$	−4.91980e9	−0.573033
$690$	−1.23180e9	−0.142747
$691$	−1.23089e10	−1.41921	−0.709605	−	0.704599i	$-0.751127\pi$
$691$	−1.23089e10	−1.41921	−0.709605	+	0.704599i	$0.751127\pi$
$692$	−3.61699e9	−0.414931
$693$	2.51388e8	0.0286932
$694$	−1.01752e10	−1.15554
$695$	8.24689e9	0.931845
$696$	−8.77504e8	−0.0986545
$697$	−6.05807e9	−0.677672
$698$	−1.27217e10	−1.41596
$699$	8.89543e8	0.0985138
$700$	−1.27557e9	−0.140560
$701$	−1.22111e10	−1.33888	−0.669439	−	0.742867i	$-0.733465\pi$
$701$	−1.22111e10	−1.33888	−0.669439	+	0.742867i	$0.733465\pi$
$702$	1.74942e9	0.190860
$703$	−1.86648e10	−2.02619
$704$	2.26313e9	0.244459
$705$	−2.34233e9	−0.251760
$706$	−9.00793e9	−0.963404
$707$	3.24343e9	0.345173
$708$	−3.59159e9	−0.380339
$709$	−8.42070e9	−0.887333	−0.443666	−	0.896192i	$-0.646322\pi$
$709$	−8.42070e9	−0.887333	−0.443666	+	0.896192i	$0.646322\pi$
$710$	1.77340e9	0.185953
$711$	2.63945e9	0.275404
$712$	3.32844e9	0.345590
$713$	−8.35734e8	−0.0863485
$714$	−9.97659e8	−0.102574
$715$	3.93248e9	0.402342
$716$	−5.34123e9	−0.543809
$717$	1.22977e8	0.0124597
$718$	5.29788e9	0.534154
$719$	−5.94291e8	−0.0596277	−0.0298139	−	0.999555i	$-0.509491\pi$
$719$	−5.94291e8	−0.0596277	−0.0298139	+	0.999555i	$0.509491\pi$
$720$	−2.68724e9	−0.268314
$721$	−1.79629e9	−0.178486
$722$	2.22728e9	0.220239
$723$	−8.98918e9	−0.884578
$724$	−3.50751e9	−0.343490
$725$	1.79130e9	0.174576
$726$	−4.60476e9	−0.446611
$727$	1.56604e10	1.51158	0.755790	−	0.654814i	$-0.227253\pi$
$727$	1.56604e10	1.51158	0.755790	+	0.654814i	$0.227253\pi$
$728$	−5.20689e9	−0.500171
$729$	3.87420e8	0.0370370
$730$	9.64580e9	0.917716
$731$	−3.71204e9	−0.351481
$732$	3.29590e8	0.0310588
$733$	−1.26810e9	−0.118930	−0.0594649	−	0.998230i	$-0.518939\pi$
$733$	−1.26810e9	−0.118930	−0.0594649	+	0.998230i	$0.518939\pi$
$734$	−1.49932e10	−1.39945
$735$	1.29038e9	0.119871
$736$	−1.43617e9	−0.132780
$737$	−1.25836e9	−0.115789
$738$	3.49293e9	0.319884
$739$	−7.07144e9	−0.644543	−0.322272	−	0.946647i	$-0.604446\pi$
$739$	−7.07144e9	−0.644543	−0.322272	+	0.946647i	$0.604446\pi$
$740$	9.63119e9	0.873713
$741$	8.75932e9	0.790873
$742$	−1.61767e9	−0.145371
$743$	−2.71852e9	−0.243149	−0.121574	−	0.992582i	$-0.538794\pi$
$743$	−2.71852e9	−0.243149	−0.121574	+	0.992582i	$0.538794\pi$
$744$	−2.92386e9	−0.260286
$745$	1.97893e10	1.75341
$746$	1.09341e10	0.964271
$747$	−2.02353e9	−0.177618
$748$	5.02159e8	0.0438718
$749$	7.51560e8	0.0653548
$750$	8.87792e8	0.0768416
$751$	5.37743e9	0.463271	0.231635	−	0.972803i	$-0.425592\pi$
$751$	5.37743e9	0.463271	0.231635	+	0.972803i	$0.425592\pi$
$752$	1.93789e9	0.166176
$753$	−1.20638e10	−1.02968
$754$	1.83223e9	0.155661
$755$	2.96116e10	2.50408
$756$	−2.88938e8	−0.0243208
$757$	−1.74896e9	−0.146536	−0.0732679	−	0.997312i	$-0.523343\pi$
$757$	−1.74896e9	−0.146536	−0.0732679	+	0.997312i	$0.523343\pi$
$758$	−3.78972e8	−0.0316056
$759$	−3.30271e8	−0.0274173
$760$	−2.15777e10	−1.78302
$761$	6.33313e9	0.520921	0.260460	−	0.965485i	$-0.416126\pi$
$761$	6.33313e9	0.520921	0.260460	+	0.965485i	$0.416126\pi$
$762$	9.94764e9	0.814475
$763$	−3.43953e9	−0.280326
$764$	4.32926e9	0.351226
$765$	−3.45615e9	−0.279112
$766$	1.73753e10	1.39679
$767$	2.99282e10	2.39495
$768$	−6.36667e9	−0.507164
$769$	−1.58726e10	−1.25865	−0.629327	−	0.777141i	$-0.716669\pi$
$769$	−1.58726e10	−1.25865	−0.629327	+	0.777141i	$0.716669\pi$
$770$	1.29304e9	0.102069
$771$	4.54511e9	0.357153
$772$	−1.64400e9	−0.128600
$773$	8.33352e9	0.648934	0.324467	−	0.945897i	$-0.394815\pi$
$773$	8.33352e9	0.648934	0.324467	+	0.945897i	$0.394815\pi$
$774$	2.14026e9	0.165910
$775$	5.96864e9	0.460595
$776$	9.20752e9	0.707337
$777$	−5.13040e9	−0.392354
$778$	−5.96107e9	−0.453833
$779$	1.74890e10	1.32552
$780$	−4.51988e9	−0.341033
$781$	4.75485e8	0.0357156
$782$	1.31071e9	0.0980131
$783$	4.05760e8	0.0302067
$784$	−1.06758e9	−0.0791214
$785$	−6.89778e9	−0.508939
$786$	−7.50883e9	−0.551560
$787$	2.31135e10	1.69027	0.845133	−	0.534557i	$-0.179521\pi$
$787$	2.31135e10	1.69027	0.845133	+	0.534557i	$0.179521\pi$
$788$	2.65630e9	0.193391
$789$	7.40773e9	0.536928
$790$	1.35762e10	0.979681
$791$	2.91460e9	0.209392
$792$	−1.15547e9	−0.0826457
$793$	−2.74642e9	−0.195574
$794$	5.24418e9	0.371797
$795$	−5.60404e9	−0.395564
$796$	5.57161e9	0.391548
$797$	8.07603e9	0.565059	0.282530	−	0.959259i	$-0.408826\pi$
$797$	8.07603e9	0.565059	0.282530	+	0.959259i	$0.408826\pi$
$798$	2.88014e9	0.200634
$799$	2.49239e9	0.172863
$800$	1.02568e10	0.708268
$801$	−1.53908e9	−0.105815
$802$	2.20125e9	0.150681
$803$	2.58624e9	0.176264
$804$	1.44632e9	0.0981452
$805$	−1.69529e9	−0.114541
$806$	6.10502e9	0.410691
$807$	1.04964e10	0.703048
$808$	−1.49080e10	−0.994212
$809$	9.70365e9	0.644340	0.322170	−	0.946682i	$-0.395588\pi$
$809$	9.70365e9	0.644340	0.322170	+	0.946682i	$0.395588\pi$
$810$	1.99273e9	0.131750
$811$	2.40385e10	1.58246	0.791232	−	0.611516i	$-0.209440\pi$
$811$	2.40385e10	1.58246	0.791232	+	0.611516i	$0.209440\pi$
$812$	−3.02615e8	−0.0198356
$813$	7.85055e9	0.512370
$814$	−5.14094e9	−0.334085
$815$	2.12103e10	1.37244
$816$	2.85939e9	0.184229
$817$	1.07163e10	0.687490
$818$	−6.05645e9	−0.386884
$819$	2.40768e9	0.153146
$820$	−9.02449e9	−0.571576
$821$	−8.31415e9	−0.524345	−0.262172	−	0.965021i	$-0.584439\pi$
$821$	−8.31415e9	−0.524345	−0.262172	+	0.965021i	$0.584439\pi$
$822$	2.47238e8	0.0155262
$823$	−1.19574e10	−0.747718	−0.373859	−	0.927486i	$-0.621966\pi$
$823$	−1.19574e10	−0.747718	−0.373859	+	0.927486i	$0.621966\pi$
$824$	8.25639e9	0.514097
$825$	2.35872e9	0.146247
$826$	9.84065e9	0.607566
$827$	−1.38513e9	−0.0851572	−0.0425786	−	0.999093i	$-0.513557\pi$
$827$	−1.38513e9	−0.0851572	−0.0425786	+	0.999093i	$0.513557\pi$
$828$	3.79604e8	0.0232394
$829$	5.34364e7	0.00325759	0.00162879	−	0.999999i	$-0.499482\pi$
$829$	5.34364e7	0.00325759	0.00162879	+	0.999999i	$0.499482\pi$
$830$	−1.04082e10	−0.631833
$831$	5.77785e9	0.349271
$832$	2.16752e10	1.30476
$833$	−1.37305e9	−0.0823056
$834$	5.05956e9	0.302017
$835$	−8.86049e9	−0.526690
$836$	−1.44968e9	−0.0858125
$837$	1.35200e9	0.0796961
$838$	−1.70916e10	−1.00330
$839$	−3.22599e10	−1.88580	−0.942900	−	0.333075i	$-0.891914\pi$
$839$	−3.22599e10	−1.88580	−0.942900	+	0.333075i	$0.891914\pi$
$840$	−5.93106e9	−0.345267
$841$	−1.68249e10	−0.975364
$842$	−1.77055e9	−0.102216
$843$	3.23299e9	0.185869
$844$	−6.96437e8	−0.0398734
$845$	1.21734e10	0.694089
$846$	−1.43705e9	−0.0815972
$847$	−6.33741e9	−0.358360
$848$	4.63641e9	0.261094
$849$	5.77774e9	0.324027
$850$	−9.36083e9	−0.522815
$851$	6.74026e9	0.374907
$852$	−5.46508e8	−0.0302732
$853$	8.60172e8	0.0474530	0.0237265	−	0.999718i	$-0.492447\pi$
$853$	8.60172e8	0.0474530	0.0237265	+	0.999718i	$0.492447\pi$
$854$	−9.03048e8	−0.0496145
$855$	9.97756e9	0.545938
$856$	−3.45444e9	−0.188243
$857$	3.31024e10	1.79650	0.898250	−	0.439485i	$-0.144839\pi$
$857$	3.31024e10	1.79650	0.898250	+	0.439485i	$0.144839\pi$
$858$	2.41262e9	0.130402
$859$	3.01439e8	0.0162264	0.00811322	−	0.999967i	$-0.497417\pi$
$859$	3.01439e8	0.0162264	0.00811322	+	0.999967i	$0.497417\pi$
$860$	−5.52968e9	−0.296453
$861$	4.80722e9	0.256675
$862$	−1.68035e10	−0.893562
$863$	2.27867e10	1.20682	0.603411	−	0.797430i	$-0.293808\pi$
$863$	2.27867e10	1.20682	0.603411	+	0.797430i	$0.293808\pi$
$864$	2.32334e9	0.122551
$865$	3.43316e10	1.80359
$866$	−1.95564e9	−0.102324
$867$	−7.40158e9	−0.385707
$868$	−1.00832e9	−0.0523334
$869$	3.64007e9	0.188166
$870$	2.08706e9	0.107453
$871$	−1.20520e10	−0.618009
$872$	1.58093e10	0.807430
$873$	−4.25758e9	−0.216577
$874$	−3.78390e9	−0.191712
$875$	1.22184e9	0.0616577
$876$	−2.97255e9	−0.149405
$877$	4.10930e9	0.205716	0.102858	−	0.994696i	$-0.467201\pi$
$877$	4.10930e9	0.205716	0.102858	+	0.994696i	$0.467201\pi$
$878$	−2.62384e10	−1.30830
$879$	8.59225e9	0.426723
$880$	−3.70597e9	−0.183321
$881$	1.93514e10	0.953449	0.476725	−	0.879053i	$-0.341824\pi$
$881$	1.93514e10	0.953449	0.476725	+	0.879053i	$0.341824\pi$
$882$	7.91665e8	0.0388510
$883$	−9.74420e9	−0.476303	−0.238152	−	0.971228i	$-0.576542\pi$
$883$	−9.74420e9	−0.476303	−0.238152	+	0.971228i	$0.576542\pi$
$884$	4.80944e9	0.234159
$885$	3.40906e10	1.65323
$886$	−2.53505e10	−1.22453
$887$	2.60570e10	1.25369	0.626847	−	0.779143i	$-0.284345\pi$
$887$	2.60570e10	1.25369	0.626847	+	0.779143i	$0.284345\pi$
$888$	2.35811e10	1.13011
$889$	1.36907e10	0.653534
$890$	−7.91637e9	−0.376410
$891$	5.34292e8	0.0253050
$892$	9.26998e9	0.437322
$893$	−7.19529e9	−0.338118
$894$	1.21409e10	0.568292
$895$	5.06978e10	2.36379
$896$	1.94466e9	0.0903162
$897$	−3.16318e9	−0.146336
$898$	−1.90378e10	−0.877301
$899$	1.41600e9	0.0649985
$900$	−2.71105e9	−0.123962
$901$	5.96305e9	0.271601
$902$	4.81709e9	0.218556
$903$	2.94558e9	0.133126
$904$	−1.33965e10	−0.603118
$905$	3.32925e10	1.49306
$906$	1.81671e10	0.811589
$907$	1.91550e10	0.852424	0.426212	−	0.904623i	$-0.359848\pi$
$907$	1.91550e10	0.852424	0.426212	+	0.904623i	$0.359848\pi$
$908$	7.27129e7	0.00322338
$909$	6.89348e9	0.304414
$910$	1.23841e10	0.544777
$911$	1.12394e10	0.492525	0.246263	−	0.969203i	$-0.420797\pi$
$911$	1.12394e10	0.492525	0.246263	+	0.969203i	$0.420797\pi$
$912$	−8.25478e9	−0.360349
$913$	−2.79065e9	−0.121355
$914$	2.99757e10	1.29855
$915$	−3.12840e9	−0.135004
$916$	−8.13975e9	−0.349926
$917$	−1.03342e10	−0.442572
$918$	−2.12039e9	−0.0904620
$919$	−7.78126e9	−0.330709	−0.165354	−	0.986234i	$-0.552877\pi$
$919$	−7.78126e9	−0.330709	−0.165354	+	0.986234i	$0.552877\pi$
$920$	7.79217e9	0.329914
$921$	1.22902e10	0.518381
$922$	−2.28448e10	−0.959906
$923$	4.55397e9	0.190627
$924$	−3.98474e8	−0.0166168
$925$	−4.81375e10	−1.99980
$926$	−1.35718e10	−0.561694
$927$	−3.81777e9	−0.157410
$928$	2.43332e9	0.0999498
$929$	2.42604e10	0.992757	0.496379	−	0.868106i	$-0.334663\pi$
$929$	2.42604e10	0.992757	0.496379	+	0.868106i	$0.334663\pi$
$930$	6.95411e9	0.283499
$931$	3.96386e9	0.160988
$932$	−1.41001e9	−0.0570515
$933$	−1.13117e10	−0.455977
$934$	2.37967e10	0.955660
$935$	−4.76638e9	−0.190699
$936$	−1.10665e10	−0.441110
$937$	3.82306e10	1.51818	0.759088	−	0.650988i	$-0.225645\pi$
$937$	3.82306e10	1.51818	0.759088	+	0.650988i	$0.225645\pi$
$938$	−3.96280e9	−0.156780
$939$	−1.41659e10	−0.558358
$940$	3.71283e9	0.145800
$941$	−3.63866e9	−0.142357	−0.0711783	−	0.997464i	$-0.522676\pi$
$941$	−3.63866e9	−0.142357	−0.0711783	+	0.997464i	$0.522676\pi$
$942$	−4.23187e9	−0.164951
$943$	−6.31567e9	−0.245261
$944$	−2.82043e10	−1.09122
$945$	2.74254e9	0.105716
$946$	2.95164e9	0.113356
$947$	2.34624e10	0.897735	0.448867	−	0.893598i	$-0.351828\pi$
$947$	2.34624e10	0.897735	0.448867	+	0.893598i	$0.351828\pi$
$948$	−4.18379e9	−0.159492
$949$	2.47698e10	0.940785
$950$	2.70238e10	1.02262
$951$	−1.07066e10	−0.403665
$952$	6.31103e9	0.237067
$953$	−8.96812e9	−0.335642	−0.167821	−	0.985818i	$-0.553673\pi$
$953$	−8.96812e9	−0.335642	−0.167821	+	0.985818i	$0.553673\pi$
$954$	−3.43814e9	−0.128205
$955$	−4.10924e10	−1.52669
$956$	−1.94931e8	−0.00721570
$957$	5.59583e8	0.0206383
$958$	−4.24387e10	−1.55949
$959$	3.40267e8	0.0124582
$960$	2.46898e10	0.900676
$961$	−2.27945e10	−0.828510
$962$	−4.92375e10	−1.78313
$963$	1.59734e9	0.0576375
$964$	1.42487e10	0.512278
$965$	1.56045e10	0.558989
$966$	−1.04008e9	−0.0371234
$967$	−2.37995e10	−0.846398	−0.423199	−	0.906037i	$-0.639093\pi$
$967$	−2.37995e10	−0.846398	−0.423199	+	0.906037i	$0.639093\pi$
$968$	2.91290e10	1.03219
$969$	−1.06168e10	−0.374851
$970$	−2.18992e10	−0.770419
$971$	−2.41890e10	−0.847911	−0.423955	−	0.905683i	$-0.639359\pi$
$971$	−2.41890e10	−0.847911	−0.423955	+	0.905683i	$0.639359\pi$
$972$	−6.14099e8	−0.0214490
$973$	6.96334e9	0.242339
$974$	2.15746e10	0.748145
$975$	2.25908e10	0.780575
$976$	2.58823e9	0.0891104
$977$	3.81142e10	1.30754	0.653771	−	0.756693i	$-0.273186\pi$
$977$	3.81142e10	1.30754	0.653771	+	0.756693i	$0.273186\pi$
$978$	1.30127e10	0.444818
$979$	−2.12254e9	−0.0722964
$980$	−2.04538e9	−0.0694198
$981$	−7.31025e9	−0.247224
$982$	−8.78590e9	−0.296071
$983$	3.67354e10	1.23352	0.616761	−	0.787150i	$-0.288444\pi$
$983$	3.67354e10	1.23352	0.616761	+	0.787150i	$0.288444\pi$
$984$	−2.20957e10	−0.739307
$985$	−2.52130e10	−0.840617
$986$	−2.22076e9	−0.0737790
$987$	−1.97777e9	−0.0654736
$988$	−1.38844e10	−0.458012
$989$	−3.86988e9	−0.127207
$990$	2.74817e9	0.0900162
$991$	2.70044e10	0.881408	0.440704	−	0.897652i	$-0.354729\pi$
$991$	2.70044e10	0.881408	0.440704	+	0.897652i	$0.354729\pi$
$992$	8.10788e9	0.263704
$993$	5.02023e9	0.162705
$994$	1.49739e9	0.0483594
$995$	−5.28845e10	−1.70195
$996$	3.20749e9	0.102863
$997$	5.01114e10	1.60141	0.800707	−	0.599056i	$-0.204457\pi$
$997$	5.01114e10	1.60141	0.800707	+	0.599056i	$0.204457\pi$
$998$	−3.07623e10	−0.979631
$999$	−1.09040e10	−0.346023

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.8.a.h.1.13	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.8.a.h.1.13	✓	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)

\(f(q)\)	\(=\)	\(q+9.23051 q^{2} +27.0000 q^{3} -42.7976 q^{4} +406.225 q^{5} +249.224 q^{6} +343.000 q^{7} -1576.55 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+9.23051 q^{2} +27.0000 q^{3} -42.7976 q^{4} +406.225 q^{5} +249.224 q^{6} +343.000 q^{7} -1576.55 q^{8} +729.000 q^{9} +3749.67 q^{10} +1005.36 q^{11} -1155.54 q^{12} +9628.90 q^{13} +3166.07 q^{14} +10968.1 q^{15} -9074.27 q^{16} -11670.7 q^{17} +6729.05 q^{18} +33692.2 q^{19} -17385.5 q^{20} +9261.00 q^{21} +9280.03 q^{22} -12167.0 q^{23} -42566.8 q^{24} +86894.1 q^{25} +88879.7 q^{26} +19683.0 q^{27} -14679.6 q^{28} +20614.7 q^{29} +101241. q^{30} +68688.6 q^{31} +118038. q^{32} +27144.8 q^{33} -107727. q^{34} +139335. q^{35} -31199.4 q^{36} -553979. q^{37} +310997. q^{38} +259980. q^{39} -640435. q^{40} +519082. q^{41} +85483.8 q^{42} +318063. q^{43} -43027.2 q^{44} +296138. q^{45} -112308. q^{46} -213559. q^{47} -245005. q^{48} +117649. q^{49} +802077. q^{50} -315110. q^{51} -412094. q^{52} -510941. q^{53} +181684. q^{54} +408404. q^{55} -540757. q^{56} +909691. q^{57} +190285. q^{58} +3.10816e6 q^{59} -469408. q^{60} -285227. q^{61} +634031. q^{62} +250047. q^{63} +2.25106e6 q^{64} +3.91150e6 q^{65} +250561. q^{66} -1.25165e6 q^{67} +499480. q^{68} -328509. q^{69} +1.28614e6 q^{70} +472948. q^{71} -1.14930e6 q^{72} +2.57244e6 q^{73} -5.11351e6 q^{74} +2.34614e6 q^{75} -1.44195e6 q^{76} +344840. q^{77} +2.39975e6 q^{78} +3.62065e6 q^{79} -3.68620e6 q^{80} +531441. q^{81} +4.79139e6 q^{82} -2.77576e6 q^{83} -396349. q^{84} -4.74095e6 q^{85} +2.93589e6 q^{86} +556598. q^{87} -1.58501e6 q^{88} -2.11122e6 q^{89} +2.73351e6 q^{90} +3.30271e6 q^{91} +520718. q^{92} +1.85459e6 q^{93} -1.97126e6 q^{94} +1.36866e7 q^{95} +3.18703e6 q^{96} -5.84030e6 q^{97} +1.08596e6 q^{98} +732910. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 24 q^{2} + 540 q^{3} + 1486 q^{4} + 1069 q^{5} + 648 q^{6} + 6860 q^{7} + 2127 q^{8} + 14580 q^{9}+O(q^{10}) \) 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

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Groups

Database

Properties

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