LMFDB - Embedded newform 483.8.a.h.1.3

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			1.3
Root			$-18.2300$ 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)

$f(q)$	$=$	$q-17.2300 q^{2} +27.0000 q^{3} +168.872 q^{4} +35.0910 q^{5} -465.209 q^{6} +343.000 q^{7} -704.224 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-17.2300 q^{2} +27.0000 q^{3} +168.872 q^{4} +35.0910 q^{5} -465.209 q^{6} +343.000 q^{7} -704.224 q^{8} +729.000 q^{9} -604.618 q^{10} -5137.97 q^{11} +4559.54 q^{12} +8528.45 q^{13} -5909.88 q^{14} +947.458 q^{15} -9481.86 q^{16} +853.400 q^{17} -12560.7 q^{18} -15031.6 q^{19} +5925.89 q^{20} +9261.00 q^{21} +88527.0 q^{22} -12167.0 q^{23} -19014.0 q^{24} -76893.6 q^{25} -146945. q^{26} +19683.0 q^{27} +57923.1 q^{28} +205172. q^{29} -16324.7 q^{30} -117450. q^{31} +253513. q^{32} -138725. q^{33} -14704.1 q^{34} +12036.2 q^{35} +123108. q^{36} -282497. q^{37} +258994. q^{38} +230268. q^{39} -24711.9 q^{40} -343269. q^{41} -159567. q^{42} -276907. q^{43} -867659. q^{44} +25581.4 q^{45} +209637. q^{46} +1.15649e6 q^{47} -256010. q^{48} +117649. q^{49} +1.32488e6 q^{50} +23041.8 q^{51} +1.44022e6 q^{52} -88398.7 q^{53} -339138. q^{54} -180297. q^{55} -241549. q^{56} -405852. q^{57} -3.53512e6 q^{58} +2.69771e6 q^{59} +159999. q^{60} +1.25611e6 q^{61} +2.02366e6 q^{62} +250047. q^{63} -3.15434e6 q^{64} +299272. q^{65} +2.39023e6 q^{66} +2.35484e6 q^{67} +144115. q^{68} -328509. q^{69} -207384. q^{70} -3.35073e6 q^{71} -513379. q^{72} +791900. q^{73} +4.86741e6 q^{74} -2.07613e6 q^{75} -2.53841e6 q^{76} -1.76232e6 q^{77} -3.96752e6 q^{78} +7.24612e6 q^{79} -332728. q^{80} +531441. q^{81} +5.91452e6 q^{82} +5.57635e6 q^{83} +1.56392e6 q^{84} +29946.7 q^{85} +4.77109e6 q^{86} +5.53966e6 q^{87} +3.61828e6 q^{88} -6.50296e6 q^{89} -440766. q^{90} +2.92526e6 q^{91} -2.05467e6 q^{92} -3.17114e6 q^{93} -1.99263e7 q^{94} -527473. q^{95} +6.84485e6 q^{96} -4.08451e6 q^{97} -2.02709e6 q^{98} -3.74558e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−17.2300	−1.52293	−0.761464	−	0.648207i	$-0.775519\pi$
$2$	−17.2300	−1.52293	−0.761464	+	0.648207i	$0.775519\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	168.872	1.31931
$5$	35.0910	0.125546	0.0627728	−	0.998028i	$-0.480006\pi$
$5$	35.0910	0.125546	0.0627728	+	0.998028i	$0.480006\pi$
$6$	−465.209	−0.879263
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−704.224	−0.486290
$9$	729.000	0.333333
$10$	−604.618	−0.191197
$11$	−5137.97	−1.16390	−0.581951	−	0.813223i	$-0.697711\pi$
$11$	−5137.97	−1.16390	−0.581951	+	0.813223i	$0.697711\pi$
$12$	4559.54	0.761706
$13$	8528.45	1.07664	0.538318	−	0.842742i	$-0.319060\pi$
$13$	8528.45	1.07664	0.538318	+	0.842742i	$0.319060\pi$
$14$	−5909.88	−0.575613
$15$	947.458	0.0724837
$16$	−9481.86	−0.578727
$17$	853.400	0.0421290	0.0210645	−	0.999778i	$-0.493294\pi$
$17$	853.400	0.0421290	0.0210645	+	0.999778i	$0.493294\pi$
$18$	−12560.7	−0.507643
$19$	−15031.6	−0.502767	−0.251383	−	0.967888i	$-0.580886\pi$
$19$	−15031.6	−0.502767	−0.251383	+	0.967888i	$0.580886\pi$
$20$	5925.89	0.165634
$21$	9261.00	0.218218
$22$	88527.0	1.77254
$23$	−12167.0	−0.208514
$23$	−12167.0	−0.208514
$24$	−19014.0	−0.280760
$25$	−76893.6	−0.984238
$26$	−146945.	−1.63964
$27$	19683.0	0.192450
$28$	57923.1	0.498653
$29$	205172.	1.56216	0.781081	−	0.624430i	$-0.214669\pi$
$29$	205172.	1.56216	0.781081	+	0.624430i	$0.214669\pi$
$30$	−16324.7	−0.110388
$31$	−117450.	−0.708086	−0.354043	−	0.935229i	$-0.615193\pi$
$31$	−117450.	−0.708086	−0.354043	+	0.935229i	$0.615193\pi$
$32$	253513.	1.36765
$33$	−138725.	−0.671980
$34$	−14704.1	−0.0641595
$35$	12036.2	0.0474517
$36$	123108.	0.439771
$37$	−282497.	−0.916870	−0.458435	−	0.888728i	$-0.651590\pi$
$37$	−282497.	−0.916870	−0.458435	+	0.888728i	$0.651590\pi$
$38$	258994.	0.765678
$39$	230268.	0.621596
$40$	−24711.9	−0.0610516
$41$	−343269.	−0.777842	−0.388921	−	0.921271i	$-0.627152\pi$
$41$	−343269.	−0.777842	−0.388921	+	0.921271i	$0.627152\pi$
$42$	−159567.	−0.332330
$43$	−276907.	−0.531121	−0.265561	−	0.964094i	$-0.585557\pi$
$43$	−276907.	−0.531121	−0.265561	+	0.964094i	$0.585557\pi$
$44$	−867659.	−1.53555
$45$	25581.4	0.0418485
$46$	209637.	0.317553
$47$	1.15649e6	1.62480	0.812398	−	0.583104i	$-0.198162\pi$
$47$	1.15649e6	1.62480	0.812398	+	0.583104i	$0.198162\pi$
$48$	−256010.	−0.334128
$49$	117649.	0.142857
$50$	1.32488e6	1.49893
$51$	23041.8	0.0243232
$52$	1.44022e6	1.42042
$53$	−88398.7	−0.0815606	−0.0407803	−	0.999168i	$-0.512984\pi$
$53$	−88398.7	−0.0815606	−0.0407803	+	0.999168i	$0.512984\pi$
$54$	−339138.	−0.293088
$55$	−180297.	−0.146123
$56$	−241549.	−0.183801
$57$	−405852.	−0.290273
$58$	−3.53512e6	−2.37906
$59$	2.69771e6	1.71007	0.855034	−	0.518572i	$-0.173536\pi$
$59$	2.69771e6	1.71007	0.855034	+	0.518572i	$0.173536\pi$
$60$	159999.	0.0956287
$61$	1.25611e6	0.708553	0.354276	−	0.935141i	$-0.384727\pi$
$61$	1.25611e6	0.708553	0.354276	+	0.935141i	$0.384727\pi$
$62$	2.02366e6	1.07836
$63$	250047.	0.125988
$64$	−3.15434e6	−1.50411
$65$	299272.	0.135167
$66$	2.39023e6	1.02338
$67$	2.35484e6	0.956531	0.478265	−	0.878215i	$-0.341266\pi$
$67$	2.35484e6	0.956531	0.478265	+	0.878215i	$0.341266\pi$
$68$	144115.	0.0555814
$69$	−328509.	−0.120386
$70$	−207384.	−0.0722656
$71$	−3.35073e6	−1.11106	−0.555528	−	0.831498i	$-0.687484\pi$
$71$	−3.35073e6	−1.11106	−0.555528	+	0.831498i	$0.687484\pi$
$72$	−513379.	−0.162097
$73$	791900.	0.238254	0.119127	−	0.992879i	$-0.461990\pi$
$73$	791900.	0.238254	0.119127	+	0.992879i	$0.461990\pi$
$74$	4.86741e6	1.39633
$75$	−2.07613e6	−0.568250
$76$	−2.53841e6	−0.663307
$77$	−1.76232e6	−0.439914
$78$	−3.96752e6	−0.946646
$79$	7.24612e6	1.65352	0.826762	−	0.562552i	$-0.190180\pi$
$79$	7.24612e6	1.65352	0.826762	+	0.562552i	$0.190180\pi$
$80$	−332728.	−0.0726566
$81$	531441.	0.111111
$82$	5.91452e6	1.18460
$83$	5.57635e6	1.07047	0.535237	−	0.844702i	$-0.320222\pi$
$83$	5.57635e6	1.07047	0.535237	+	0.844702i	$0.320222\pi$
$84$	1.56392e6	0.287898
$85$	29946.7	0.00528911
$86$	4.77109e6	0.808860
$87$	5.53966e6	0.901915
$88$	3.61828e6	0.565995
$89$	−6.50296e6	−0.977792	−0.488896	−	0.872342i	$-0.662600\pi$
$89$	−6.50296e6	−0.977792	−0.488896	+	0.872342i	$0.662600\pi$
$90$	−440766.	−0.0637323
$91$	2.92526e6	0.406930
$92$	−2.05467e6	−0.275096
$93$	−3.17114e6	−0.408814
$94$	−1.99263e7	−2.47445
$95$	−527473.	−0.0631201
$96$	6.84485e6	0.789613
$97$	−4.08451e6	−0.454401	−0.227200	−	0.973848i	$-0.572957\pi$
$97$	−4.08451e6	−0.454401	−0.227200	+	0.973848i	$0.572957\pi$
$98$	−2.02709e6	−0.217561
$99$	−3.74558e6	−0.387968
$100$	−1.29852e7	−1.29852
$101$	2.28739e6	0.220910	0.110455	−	0.993881i	$-0.464769\pi$
$101$	2.28739e6	0.220910	0.110455	+	0.993881i	$0.464769\pi$
$102$	−397010.	−0.0370425
$103$	−1.86414e7	−1.68092	−0.840462	−	0.541871i	$-0.817716\pi$
$103$	−1.86414e7	−1.68092	−0.840462	+	0.541871i	$0.817716\pi$
$104$	−6.00594e6	−0.523557
$105$	324978.	0.0273963
$106$	1.52311e6	0.124211
$107$	−1.19130e7	−0.940107	−0.470053	−	0.882638i	$-0.655765\pi$
$107$	−1.19130e7	−0.940107	−0.470053	+	0.882638i	$0.655765\pi$
$108$	3.32391e6	0.253902
$109$	4.92927e6	0.364578	0.182289	−	0.983245i	$-0.441649\pi$
$109$	4.92927e6	0.364578	0.182289	+	0.983245i	$0.441649\pi$
$110$	3.10651e6	0.222535
$111$	−7.62742e6	−0.529355
$112$	−3.25228e6	−0.218738
$113$	1.17781e7	0.767895	0.383947	−	0.923355i	$-0.374564\pi$
$113$	1.17781e7	0.767895	0.383947	+	0.923355i	$0.374564\pi$
$114$	6.99283e6	0.442065
$115$	−426953.	−0.0261781
$116$	3.46479e7	2.06098
$117$	6.21724e6	0.358878
$118$	−4.64815e7	−2.60431
$119$	292716.	0.0159233
$120$	−667223.	−0.0352482
$121$	6.91152e6	0.354670
$122$	−2.16427e7	−1.07908
$123$	−9.26827e6	−0.449087
$124$	−1.98340e7	−0.934187
$125$	−5.43976e6	−0.249112
$126$	−4.30830e6	−0.191871
$127$	2.50242e7	1.08404	0.542022	−	0.840364i	$-0.317659\pi$
$127$	2.50242e7	1.08404	0.542022	+	0.840364i	$0.317659\pi$
$128$	2.18996e7	0.922998
$129$	−7.47648e6	−0.306643
$130$	−5.15645e6	−0.205849
$131$	6.90446e6	0.268337	0.134168	−	0.990959i	$-0.457164\pi$
$131$	6.90446e6	0.268337	0.134168	+	0.990959i	$0.457164\pi$
$132$	−2.34268e7	−0.886551
$133$	−5.15583e6	−0.190028
$134$	−4.05738e7	−1.45673
$135$	690697.	0.0241612
$136$	−600985.	−0.0204869
$137$	−1.11363e7	−0.370014	−0.185007	−	0.982737i	$-0.559231\pi$
$137$	−1.11363e7	−0.370014	−0.185007	+	0.982737i	$0.559231\pi$
$138$	5.66020e6	0.183339
$139$	3.35702e6	0.106024	0.0530118	−	0.998594i	$-0.483118\pi$
$139$	3.35702e6	0.106024	0.0530118	+	0.998594i	$0.483118\pi$
$140$	2.03258e6	0.0626037
$141$	3.12252e7	0.938076
$142$	5.77330e7	1.69206
$143$	−4.38189e7	−1.25310
$144$	−6.91228e6	−0.192909
$145$	7.19972e6	0.196122
$146$	−1.36444e7	−0.362844
$147$	3.17652e6	0.0824786
$148$	−4.77058e7	−1.20964
$149$	−9.95910e6	−0.246643	−0.123321	−	0.992367i	$-0.539355\pi$
$149$	−9.95910e6	−0.246643	−0.123321	+	0.992367i	$0.539355\pi$
$150$	3.57716e7	0.865405
$151$	−3.54483e7	−0.837869	−0.418934	−	0.908016i	$-0.637596\pi$
$151$	−3.54483e7	−0.837869	−0.418934	+	0.908016i	$0.637596\pi$
$152$	1.05856e7	0.244491
$153$	622129.	0.0140430
$154$	3.03648e7	0.669958
$155$	−4.12143e6	−0.0888970
$156$	3.88859e7	0.820079
$157$	−8.05644e7	−1.66148	−0.830738	−	0.556663i	$-0.812081\pi$
$157$	−8.05644e7	−1.66148	−0.830738	+	0.556663i	$0.812081\pi$
$158$	−1.24850e8	−2.51820
$159$	−2.38676e6	−0.0470890
$160$	8.89603e6	0.171702
$161$	−4.17328e6	−0.0788110
$162$	−9.15671e6	−0.169214
$163$	−8.31483e7	−1.50382	−0.751911	−	0.659264i	$-0.770868\pi$
$163$	−8.31483e7	−1.50382	−0.751911	+	0.659264i	$0.770868\pi$
$164$	−5.79686e7	−1.02622
$165$	−4.86801e6	−0.0843640
$166$	−9.60803e7	−1.63026
$167$	3.85547e7	0.640575	0.320287	−	0.947320i	$-0.396221\pi$
$167$	3.85547e7	0.640575	0.320287	+	0.947320i	$0.396221\pi$
$168$	−6.52182e6	−0.106117
$169$	9.98599e6	0.159143
$170$	−515981.	−0.00805494
$171$	−1.09580e7	−0.167589
$172$	−4.67618e7	−0.700715
$173$	−2.23010e7	−0.327464	−0.163732	−	0.986505i	$-0.552353\pi$
$173$	−2.23010e7	−0.327464	−0.163732	+	0.986505i	$0.552353\pi$
$174$	−9.54482e7	−1.37355
$175$	−2.63745e7	−0.372007
$176$	4.87175e7	0.673582
$177$	7.28382e7	0.987308
$178$	1.12046e8	1.48911
$179$	−4.89856e6	−0.0638385	−0.0319193	−	0.999490i	$-0.510162\pi$
$179$	−4.89856e6	−0.0638385	−0.0319193	+	0.999490i	$0.510162\pi$
$180$	4.31998e6	0.0552113
$181$	3.78366e7	0.474282	0.237141	−	0.971475i	$-0.423790\pi$
$181$	3.78366e7	0.474282	0.237141	+	0.971475i	$0.423790\pi$
$182$	−5.04021e7	−0.619725
$183$	3.39149e7	0.409083
$184$	8.56829e6	0.101399
$185$	−9.91311e6	−0.115109
$186$	5.46387e7	0.622594
$187$	−4.38474e6	−0.0490341
$188$	1.95298e8	2.14361
$189$	6.75127e6	0.0727393
$190$	9.08835e6	0.0961275
$191$	1.23964e8	1.28729	0.643647	−	0.765322i	$-0.277420\pi$
$191$	1.23964e8	1.28729	0.643647	+	0.765322i	$0.277420\pi$
$192$	−8.51672e7	−0.868397
$193$	6.86466e7	0.687335	0.343668	−	0.939091i	$-0.388331\pi$
$193$	6.86466e7	0.687335	0.343668	+	0.939091i	$0.388331\pi$
$194$	7.03760e7	0.692020
$195$	8.08035e6	0.0780385
$196$	1.98676e7	0.188473
$197$	2.02774e8	1.88965	0.944823	−	0.327580i	$-0.106233\pi$
$197$	2.02774e8	1.88965	0.944823	+	0.327580i	$0.106233\pi$
$198$	6.45362e7	0.590847
$199$	3.35908e7	0.302159	0.151079	−	0.988522i	$-0.451725\pi$
$199$	3.35908e7	0.302159	0.151079	+	0.988522i	$0.451725\pi$
$200$	5.41503e7	0.478626
$201$	6.35806e7	0.552253
$202$	−3.94117e7	−0.336431
$203$	7.03742e7	0.590442
$204$	3.89112e6	0.0320899
$205$	−1.20457e7	−0.0976546
$206$	3.21191e8	2.55993
$207$	−8.86974e6	−0.0695048
$208$	−8.08656e7	−0.623078
$209$	7.72317e7	0.585172
$210$	−5.59936e6	−0.0417226
$211$	−1.42727e8	−1.04597	−0.522983	−	0.852343i	$-0.675181\pi$
$211$	−1.42727e8	−1.04597	−0.522983	+	0.852343i	$0.675181\pi$
$212$	−1.49281e7	−0.107604
$213$	−9.04698e7	−0.641468
$214$	2.05260e8	1.43172
$215$	−9.71694e6	−0.0666799
$216$	−1.38612e7	−0.0935866
$217$	−4.02852e7	−0.267631
$218$	−8.49313e7	−0.555226
$219$	2.13813e7	0.137556
$220$	−3.04470e7	−0.192782
$221$	7.27818e6	0.0453576
$222$	1.31420e8	0.806170
$223$	−5.84857e7	−0.353169	−0.176584	−	0.984286i	$-0.556505\pi$
$223$	−5.84857e7	−0.353169	−0.176584	+	0.984286i	$0.556505\pi$
$224$	8.69549e7	0.516923
$225$	−5.60554e7	−0.328079
$226$	−2.02937e8	−1.16945
$227$	6.16524e7	0.349832	0.174916	−	0.984583i	$-0.444035\pi$
$227$	6.16524e7	0.349832	0.174916	+	0.984583i	$0.444035\pi$
$228$	−6.85371e7	−0.382960
$229$	2.88252e8	1.58616	0.793082	−	0.609115i	$-0.208475\pi$
$229$	2.88252e8	1.58616	0.793082	+	0.609115i	$0.208475\pi$
$230$	7.35638e6	0.0398673
$231$	−4.75827e7	−0.253984
$232$	−1.44487e8	−0.759665
$233$	3.42297e8	1.77279	0.886396	−	0.462928i	$-0.153201\pi$
$233$	3.42297e8	1.77279	0.886396	+	0.462928i	$0.153201\pi$
$234$	−1.07123e8	−0.546546
$235$	4.05824e7	0.203986
$236$	4.55568e8	2.25611
$237$	1.95645e8	0.954662
$238$	−5.04349e6	−0.0242500
$239$	3.21357e8	1.52263	0.761317	−	0.648380i	$-0.224553\pi$
$239$	3.21357e8	1.52263	0.761317	+	0.648380i	$0.224553\pi$
$240$	−8.98366e6	−0.0419483
$241$	2.51240e8	1.15619	0.578095	−	0.815970i	$-0.303796\pi$
$241$	2.51240e8	1.15619	0.578095	+	0.815970i	$0.303796\pi$
$242$	−1.19085e8	−0.540137
$243$	1.43489e7	0.0641500
$244$	2.12121e8	0.934803
$245$	4.12843e6	0.0179351
$246$	1.59692e8	0.683928
$247$	−1.28196e8	−0.541297
$248$	8.27109e7	0.344335
$249$	1.50561e8	0.618039
$250$	9.37270e7	0.379380
$251$	2.47491e8	0.987873	0.493937	−	0.869498i	$-0.335558\pi$
$251$	2.47491e8	0.987873	0.493937	+	0.869498i	$0.335558\pi$
$252$	4.22259e7	0.166218
$253$	6.25136e7	0.242691
$254$	−4.31166e8	−1.65092
$255$	808561.	0.00305367
$256$	2.64265e7	0.0984463
$257$	2.65918e8	0.977197	0.488598	−	0.872509i	$-0.337508\pi$
$257$	2.65918e8	0.977197	0.488598	+	0.872509i	$0.337508\pi$
$258$	1.28820e8	0.466995
$259$	−9.68964e7	−0.346544
$260$	5.05387e7	0.178327
$261$	1.49571e8	0.520721
$262$	−1.18964e8	−0.408658
$263$	−7.20871e7	−0.244350	−0.122175	−	0.992509i	$-0.538987\pi$
$263$	−7.20871e7	−0.244350	−0.122175	+	0.992509i	$0.538987\pi$
$264$	9.76935e7	0.326777
$265$	−3.10200e6	−0.0102396
$266$	8.88348e7	0.289399
$267$	−1.75580e8	−0.564528
$268$	3.97666e8	1.26196
$269$	3.24038e8	1.01499	0.507496	−	0.861654i	$-0.330571\pi$
$269$	3.24038e8	1.01499	0.507496	+	0.861654i	$0.330571\pi$
$270$	−1.19007e7	−0.0367959
$271$	1.97030e7	0.0601368	0.0300684	−	0.999548i	$-0.490427\pi$
$271$	1.97030e7	0.0601368	0.0300684	+	0.999548i	$0.490427\pi$
$272$	−8.09182e6	−0.0243812
$273$	7.89820e7	0.234941
$274$	1.91878e8	0.563506
$275$	3.95077e8	1.14556
$276$	−5.54760e7	−0.158827
$277$	−6.55214e7	−0.185227	−0.0926134	−	0.995702i	$-0.529522\pi$
$277$	−6.55214e7	−0.185227	−0.0926134	+	0.995702i	$0.529522\pi$
$278$	−5.78414e7	−0.161466
$279$	−8.56208e7	−0.236029
$280$	−8.47620e6	−0.0230753
$281$	5.21410e8	1.40187	0.700935	−	0.713226i	$-0.252766\pi$
$281$	5.21410e8	1.40187	0.700935	+	0.713226i	$0.252766\pi$
$282$	−5.38009e8	−1.42862
$283$	−1.89167e8	−0.496128	−0.248064	−	0.968744i	$-0.579794\pi$
$283$	−1.89167e8	−0.496128	−0.248064	+	0.968744i	$0.579794\pi$
$284$	−5.65845e8	−1.46583
$285$	−1.42418e7	−0.0364424
$286$	7.54998e8	1.90838
$287$	−1.17741e8	−0.293997
$288$	1.84811e8	0.455883
$289$	−4.09610e8	−0.998225
$290$	−1.24051e8	−0.298681
$291$	−1.10282e8	−0.262348
$292$	1.33730e8	0.314331
$293$	−4.53492e8	−1.05325	−0.526627	−	0.850097i	$-0.676543\pi$
$293$	−4.53492e8	−1.05325	−0.526627	+	0.850097i	$0.676543\pi$
$294$	−5.47314e7	−0.125609
$295$	9.46655e7	0.214691
$296$	1.98941e8	0.445865
$297$	−1.01131e8	−0.223993
$298$	1.71595e8	0.375619
$299$	−1.03766e8	−0.224494
$300$	−3.50600e8	−0.749700
$301$	−9.49789e7	−0.200745
$302$	6.10773e8	1.27601
$303$	6.17596e7	0.127543
$304$	1.42527e8	0.290965
$305$	4.40781e7	0.0889556
$306$	−1.07193e7	−0.0213865
$307$	5.99075e8	1.18167	0.590836	−	0.806792i	$-0.298798\pi$
$307$	5.99075e8	1.18167	0.590836	+	0.806792i	$0.298798\pi$
$308$	−2.97607e8	−0.580384
$309$	−5.03318e8	−0.970482
$310$	7.10122e7	0.135384
$311$	5.30192e8	0.999475	0.499737	−	0.866177i	$-0.333430\pi$
$311$	5.30192e8	0.999475	0.499737	+	0.866177i	$0.333430\pi$
$312$	−1.62160e8	−0.302276
$313$	−4.17385e8	−0.769364	−0.384682	−	0.923049i	$-0.625689\pi$
$313$	−4.17385e8	−0.769364	−0.384682	+	0.923049i	$0.625689\pi$
$314$	1.38812e9	2.53031
$315$	8.77441e6	0.0158172
$316$	1.22367e9	2.18151
$317$	−6.23516e7	−0.109936	−0.0549680	−	0.998488i	$-0.517506\pi$
$317$	−6.23516e7	−0.109936	−0.0549680	+	0.998488i	$0.517506\pi$
$318$	4.11239e7	0.0717132
$319$	−1.05417e9	−1.81821
$320$	−1.10689e8	−0.188834
$321$	−3.21650e8	−0.542771
$322$	7.19055e7	0.120024
$323$	−1.28279e7	−0.0211811
$324$	8.97455e7	0.146590
$325$	−6.55784e8	−1.05967
$326$	1.43264e9	2.29022
$327$	1.33090e8	0.210489
$328$	2.41738e8	0.378257
$329$	3.96675e8	0.614115
$330$	8.38756e7	0.128480
$331$	−4.11779e8	−0.624117	−0.312059	−	0.950063i	$-0.601018\pi$
$331$	−4.11779e8	−0.624117	−0.312059	+	0.950063i	$0.601018\pi$
$332$	9.41689e8	1.41229
$333$	−2.05940e8	−0.305623
$334$	−6.64297e8	−0.975550
$335$	8.26337e7	0.120088
$336$	−8.78115e7	−0.126289
$337$	1.07824e9	1.53465	0.767325	−	0.641258i	$-0.221587\pi$
$337$	1.07824e9	1.53465	0.767325	+	0.641258i	$0.221587\pi$
$338$	−1.72058e8	−0.242364
$339$	3.18009e8	0.443344
$340$	5.05716e6	0.00697799
$341$	6.03453e8	0.824143
$342$	1.88806e8	0.255226
$343$	4.03536e7	0.0539949
$344$	1.95004e8	0.258279
$345$	−1.15277e7	−0.0151139
$346$	3.84246e8	0.498704
$347$	−3.19902e8	−0.411020	−0.205510	−	0.978655i	$-0.565885\pi$
$347$	−3.19902e8	−0.411020	−0.205510	+	0.978655i	$0.565885\pi$
$348$	9.35493e8	1.18991
$349$	6.64446e8	0.836702	0.418351	−	0.908286i	$-0.362608\pi$
$349$	6.64446e8	0.836702	0.418351	+	0.908286i	$0.362608\pi$
$350$	4.54432e8	0.566540
$351$	1.67866e8	0.207199
$352$	−1.30254e9	−1.59181
$353$	−8.87564e8	−1.07396	−0.536980	−	0.843595i	$-0.680435\pi$
$353$	−8.87564e8	−1.07396	−0.536980	+	0.843595i	$0.680435\pi$
$354$	−1.25500e9	−1.50360
$355$	−1.17581e8	−0.139488
$356$	−1.09817e9	−1.29001
$357$	7.90334e6	0.00919331
$358$	8.44021e7	0.0972215
$359$	7.51235e8	0.856929	0.428465	−	0.903558i	$-0.359055\pi$
$359$	7.51235e8	0.856929	0.428465	+	0.903558i	$0.359055\pi$
$360$	−1.80150e7	−0.0203505
$361$	−6.67924e8	−0.747225
$362$	−6.51923e8	−0.722298
$363$	1.86611e8	0.204769
$364$	4.93994e8	0.536868
$365$	2.77886e7	0.0299117
$366$	−5.84353e8	−0.623005
$367$	−2.56329e8	−0.270687	−0.135343	−	0.990799i	$-0.543214\pi$
$367$	−2.56329e8	−0.270687	−0.135343	+	0.990799i	$0.543214\pi$
$368$	1.15366e8	0.120673
$369$	−2.50243e8	−0.259281
$370$	1.70803e8	0.175303
$371$	−3.03207e7	−0.0308270
$372$	−5.35517e8	−0.539353
$373$	−6.42252e8	−0.640803	−0.320401	−	0.947282i	$-0.603818\pi$
$373$	−6.42252e8	−0.640803	−0.320401	+	0.947282i	$0.603818\pi$
$374$	7.55490e7	0.0746755
$375$	−1.46874e8	−0.143825
$376$	−8.14426e8	−0.790122
$377$	1.74980e9	1.68188
$378$	−1.16324e8	−0.110777
$379$	1.29046e9	1.21761	0.608803	−	0.793321i	$-0.291650\pi$
$379$	1.29046e9	1.21761	0.608803	+	0.793321i	$0.291650\pi$
$380$	−8.90755e7	−0.0832752
$381$	6.75653e8	0.625873
$382$	−2.13589e9	−1.96046
$383$	−1.94863e9	−1.77229	−0.886145	−	0.463408i	$-0.846626\pi$
$383$	−1.94863e9	−1.77229	−0.886145	+	0.463408i	$0.846626\pi$
$384$	5.91289e8	0.532893
$385$	−6.18417e7	−0.0552292
$386$	−1.18278e9	−1.04676
$387$	−2.01865e8	−0.177040
$388$	−6.89760e8	−0.599497
$389$	7.25175e8	0.624625	0.312313	−	0.949979i	$-0.398896\pi$
$389$	7.25175e8	0.624625	0.312313	+	0.949979i	$0.398896\pi$
$390$	−1.39224e8	−0.118847
$391$	−1.03833e7	−0.00878451
$392$	−8.28512e7	−0.0694701
$393$	1.86420e8	0.154924
$394$	−3.49379e9	−2.87780
$395$	2.54274e8	0.207593
$396$	−6.32523e8	−0.511851
$397$	1.14254e9	0.916443	0.458221	−	0.888838i	$-0.348487\pi$
$397$	1.14254e9	0.916443	0.458221	+	0.888838i	$0.348487\pi$
$398$	−5.78769e8	−0.460166
$399$	−1.39207e8	−0.109713
$400$	7.29095e8	0.569605
$401$	5.81652e8	0.450461	0.225231	−	0.974305i	$-0.427686\pi$
$401$	5.81652e8	0.450461	0.225231	+	0.974305i	$0.427686\pi$
$402$	−1.09549e9	−0.841042
$403$	−1.00166e9	−0.762350
$404$	3.86277e8	0.291450
$405$	1.86488e7	0.0139495
$406$	−1.21255e9	−0.899201
$407$	1.45146e9	1.06715
$408$	−1.62266e7	−0.0118281
$409$	2.27930e9	1.64729	0.823645	−	0.567106i	$-0.191937\pi$
$409$	2.27930e9	1.64729	0.823645	+	0.567106i	$0.191937\pi$
$410$	2.07547e8	0.148721
$411$	−3.00680e8	−0.213628
$412$	−3.14801e9	−2.21766
$413$	9.25315e8	0.646345
$414$	1.52825e8	0.105851
$415$	1.95680e8	0.134393
$416$	2.16207e9	1.47246
$417$	9.06396e7	0.0612127
$418$	−1.33070e9	−0.891175
$419$	−5.25538e8	−0.349024	−0.174512	−	0.984655i	$-0.555835\pi$
$419$	−5.25538e8	−0.349024	−0.174512	+	0.984655i	$0.555835\pi$
$420$	5.48797e7	0.0361443
$421$	2.01013e8	0.131291	0.0656457	−	0.997843i	$-0.479089\pi$
$421$	2.01013e8	0.131291	0.0656457	+	0.997843i	$0.479089\pi$
$422$	2.45918e9	1.59293
$423$	8.43080e8	0.541598
$424$	6.22525e7	0.0396621
$425$	−6.56210e7	−0.0414650
$426$	1.55879e9	0.976910
$427$	4.30845e8	0.267808
$428$	−2.01177e9	−1.24029
$429$	−1.18311e9	−0.723477
$430$	1.67423e8	0.101549
$431$	−1.72629e9	−1.03859	−0.519293	−	0.854596i	$-0.673805\pi$
$431$	−1.72629e9	−1.03859	−0.519293	+	0.854596i	$0.673805\pi$
$432$	−1.86631e8	−0.111376
$433$	6.64140e8	0.393145	0.196572	−	0.980489i	$-0.437019\pi$
$433$	6.64140e8	0.393145	0.196572	+	0.980489i	$0.437019\pi$
$434$	6.94114e8	0.407584
$435$	1.94392e8	0.113231
$436$	8.32417e8	0.480992
$437$	1.82889e8	0.104834
$438$	−3.68399e8	−0.209488
$439$	−5.11832e8	−0.288736	−0.144368	−	0.989524i	$-0.546115\pi$
$439$	−5.11832e8	−0.288736	−0.144368	+	0.989524i	$0.546115\pi$
$440$	1.26969e8	0.0710581
$441$	8.57661e7	0.0476190
$442$	−1.25403e8	−0.0690764
$443$	−1.05570e9	−0.576933	−0.288467	−	0.957490i	$-0.593145\pi$
$443$	−1.05570e9	−0.576933	−0.288467	+	0.957490i	$0.593145\pi$
$444$	−1.28806e9	−0.698385
$445$	−2.28196e8	−0.122757
$446$	1.00771e9	0.537851
$447$	−2.68896e8	−0.142399
$448$	−1.08194e9	−0.568499
$449$	3.28127e9	1.71072	0.855362	−	0.518031i	$-0.173335\pi$
$449$	3.28127e9	1.71072	0.855362	+	0.518031i	$0.173335\pi$
$450$	9.65834e8	0.499642
$451$	1.76371e9	0.905333
$452$	1.98900e9	1.01309
$453$	−9.57104e8	−0.483744
$454$	−1.06227e9	−0.532769
$455$	1.02650e8	0.0510882
$456$	2.85811e8	0.141157
$457$	3.52761e9	1.72892	0.864458	−	0.502705i	$-0.167662\pi$
$457$	3.52761e9	1.72892	0.864458	+	0.502705i	$0.167662\pi$
$458$	−4.96657e9	−2.41561
$459$	1.67975e7	0.00810773
$460$	−7.21004e7	−0.0345370
$461$	−1.98344e9	−0.942902	−0.471451	−	0.881892i	$-0.656270\pi$
$461$	−1.98344e9	−0.942902	−0.471451	+	0.881892i	$0.656270\pi$
$462$	8.19849e8	0.386800
$463$	2.66767e8	0.124910	0.0624552	−	0.998048i	$-0.480107\pi$
$463$	2.66767e8	0.124910	0.0624552	+	0.998048i	$0.480107\pi$
$464$	−1.94542e9	−0.904065
$465$	−1.11279e8	−0.0513247
$466$	−5.89777e9	−2.69984
$467$	−3.73783e9	−1.69828	−0.849142	−	0.528165i	$-0.822880\pi$
$467$	−3.73783e9	−1.69828	−0.849142	+	0.528165i	$0.822880\pi$
$468$	1.04992e9	0.473473
$469$	8.07709e8	0.361535
$470$	−6.99233e8	−0.310656
$471$	−2.17524e9	−0.959254
$472$	−1.89979e9	−0.831590
$473$	1.42274e9	0.618174
$474$	−3.37096e9	−1.45388
$475$	1.15583e9	0.494843
$476$	4.94316e7	0.0210078
$477$	−6.44426e7	−0.0271869
$478$	−5.53698e9	−2.31886
$479$	9.35936e8	0.389110	0.194555	−	0.980892i	$-0.437674\pi$
$479$	9.35936e8	0.389110	0.194555	+	0.980892i	$0.437674\pi$
$480$	2.40193e8	0.0991324
$481$	−2.40926e9	−0.987134
$482$	−4.32886e9	−1.76079
$483$	−1.12679e8	−0.0455016
$484$	1.16716e9	0.467921
$485$	−1.43330e8	−0.0570480
$486$	−2.47231e8	−0.0976959
$487$	3.17790e9	1.24678	0.623389	−	0.781912i	$-0.285756\pi$
$487$	3.17790e9	1.24678	0.623389	+	0.781912i	$0.285756\pi$
$488$	−8.84581e8	−0.344563
$489$	−2.24500e9	−0.868233
$490$	−7.11327e7	−0.0273138
$491$	4.69640e9	1.79052	0.895262	−	0.445539i	$-0.146988\pi$
$491$	4.69640e9	1.79052	0.895262	+	0.445539i	$0.146988\pi$
$492$	−1.56515e9	−0.592487
$493$	1.75094e8	0.0658124
$494$	2.20881e9	0.824356
$495$	−1.31436e8	−0.0487076
$496$	1.11364e9	0.409788
$497$	−1.14930e9	−0.419939
$498$	−2.59417e9	−0.941229
$499$	2.60154e8	0.0937300	0.0468650	−	0.998901i	$-0.485077\pi$
$499$	2.60154e8	0.0937300	0.0468650	+	0.998901i	$0.485077\pi$
$500$	−9.18624e8	−0.328657
$501$	1.04098e9	0.369836
$502$	−4.26426e9	−1.50446
$503$	6.36072e8	0.222853	0.111426	−	0.993773i	$-0.464458\pi$
$503$	6.36072e8	0.222853	0.111426	+	0.993773i	$0.464458\pi$
$504$	−1.76089e8	−0.0612668
$505$	8.02670e7	0.0277343
$506$	−1.07711e9	−0.369600
$507$	2.69622e8	0.0918813
$508$	4.22589e9	1.43019
$509$	1.78419e9	0.599692	0.299846	−	0.953988i	$-0.403065\pi$
$509$	1.78419e9	0.599692	0.299846	+	0.953988i	$0.403065\pi$
$510$	−1.39315e7	−0.00465052
$511$	2.71622e8	0.0900515
$512$	−3.25847e9	−1.07293
$513$	−2.95866e8	−0.0967576
$514$	−4.58176e9	−1.48820
$515$	−6.54146e8	−0.211032
$516$	−1.26257e9	−0.404558
$517$	−5.94200e9	−1.89110
$518$	1.66952e9	0.527762
$519$	−6.02127e8	−0.189061
$520$	−2.10755e8	−0.0657303
$521$	3.33567e9	1.03336	0.516680	−	0.856179i	$-0.327168\pi$
$521$	3.33567e9	1.03336	0.516680	+	0.856179i	$0.327168\pi$
$522$	−2.57710e9	−0.793021
$523$	1.57482e9	0.481366	0.240683	−	0.970604i	$-0.422629\pi$
$523$	1.57482e9	0.481366	0.240683	+	0.970604i	$0.422629\pi$
$524$	1.16597e9	0.354020
$525$	−7.12112e8	−0.214778
$526$	1.24206e9	0.372128
$527$	−1.00232e8	−0.0298310
$528$	1.31537e9	0.388893
$529$	1.48036e8	0.0434783
$530$	5.34474e7	0.0155941
$531$	1.96663e9	0.570023
$532$	−8.70675e8	−0.250706
$533$	−2.92756e9	−0.837452
$534$	3.02524e9	0.859737
$535$	−4.18039e8	−0.118026
$536$	−1.65833e9	−0.465152
$537$	−1.32261e8	−0.0368572
$538$	−5.58316e9	−1.54576
$539$	−6.04477e8	−0.166272
$540$	1.16639e8	0.0318762
$541$	−5.57535e9	−1.51385	−0.756923	−	0.653504i	$-0.773298\pi$
$541$	−5.57535e9	−1.51385	−0.756923	+	0.653504i	$0.773298\pi$
$542$	−3.39482e8	−0.0915840
$543$	1.02159e9	0.273827
$544$	2.16348e8	0.0576178
$545$	1.72973e8	0.0457711
$546$	−1.36086e9	−0.357799
$547$	3.33963e9	0.872456	0.436228	−	0.899836i	$-0.356314\pi$
$547$	3.33963e9	0.872456	0.436228	+	0.899836i	$0.356314\pi$
$548$	−1.88061e9	−0.488165
$549$	9.15702e8	0.236184
$550$	−6.80716e9	−1.74460
$551$	−3.08406e9	−0.785404
$552$	2.31344e8	0.0585425
$553$	2.48542e9	0.624973
$554$	1.12893e9	0.282087
$555$	−2.67654e8	−0.0664581
$556$	5.66907e8	0.139878
$557$	−2.76668e9	−0.678369	−0.339185	−	0.940720i	$-0.610151\pi$
$557$	−2.76668e9	−0.678369	−0.339185	+	0.940720i	$0.610151\pi$
$558$	1.47524e9	0.359455
$559$	−2.36158e9	−0.571824
$560$	−1.14126e8	−0.0274616
$561$	−1.18388e8	−0.0283099
$562$	−8.98389e9	−2.13495
$563$	2.19612e9	0.518652	0.259326	−	0.965790i	$-0.416500\pi$
$563$	2.19612e9	0.518652	0.259326	+	0.965790i	$0.416500\pi$
$564$	5.27306e9	1.23762
$565$	4.13307e8	0.0964057
$566$	3.25935e9	0.755568
$567$	1.82284e8	0.0419961
$568$	2.35967e9	0.540296
$569$	6.93029e9	1.57710	0.788549	−	0.614972i	$-0.210833\pi$
$569$	6.93029e9	1.57710	0.788549	+	0.614972i	$0.210833\pi$
$570$	2.45386e8	0.0554992
$571$	−2.34996e9	−0.528244	−0.264122	−	0.964489i	$-0.585082\pi$
$571$	−2.34996e9	−0.528244	−0.264122	+	0.964489i	$0.585082\pi$
$572$	−7.39979e9	−1.65323
$573$	3.34702e9	0.743220
$574$	2.02868e9	0.447736
$575$	9.35565e8	0.205228
$576$	−2.29952e9	−0.501369
$577$	1.72368e9	0.373543	0.186771	−	0.982403i	$-0.440198\pi$
$577$	1.72368e9	0.373543	0.186771	+	0.982403i	$0.440198\pi$
$578$	7.05758e9	1.52023
$579$	1.85346e9	0.396833
$580$	1.21583e9	0.258747
$581$	1.91269e9	0.404601
$582$	1.90015e9	0.399538
$583$	4.54189e8	0.0949286
$584$	−5.57675e8	−0.115861
$585$	2.18169e8	0.0450556
$586$	7.81366e9	1.60403
$587$	2.57975e9	0.526435	0.263217	−	0.964737i	$-0.415216\pi$
$587$	2.57975e9	0.526435	0.263217	+	0.964737i	$0.415216\pi$
$588$	5.36426e8	0.108815
$589$	1.76545e9	0.356002
$590$	−1.63108e9	−0.326960
$591$	5.47490e9	1.09099
$592$	2.67860e9	0.530617
$593$	4.92540e9	0.969951	0.484976	−	0.874528i	$-0.338828\pi$
$593$	4.92540e9	0.969951	0.484976	+	0.874528i	$0.338828\pi$
$594$	1.74248e9	0.341126
$595$	1.02717e7	0.00199910
$596$	−1.68181e9	−0.325399
$597$	9.06952e8	0.174451
$598$	1.78788e9	0.341888
$599$	−8.60849e9	−1.63656	−0.818282	−	0.574817i	$-0.805073\pi$
$599$	−8.60849e9	−1.63656	−0.818282	+	0.574817i	$0.805073\pi$
$600$	1.46206e9	0.276335
$601$	−3.49104e9	−0.655985	−0.327993	−	0.944680i	$-0.606372\pi$
$601$	−3.49104e9	−0.655985	−0.327993	+	0.944680i	$0.606372\pi$
$602$	1.63648e9	0.305720
$603$	1.71668e9	0.318844
$604$	−5.98623e9	−1.10541
$605$	2.42532e8	0.0445273
$606$	−1.06412e9	−0.194238
$607$	5.85282e9	1.06220	0.531099	−	0.847310i	$-0.321779\pi$
$607$	5.85282e9	1.06220	0.531099	+	0.847310i	$0.321779\pi$
$608$	−3.81070e9	−0.687609
$609$	1.90010e9	0.340892
$610$	−7.59465e8	−0.135473
$611$	9.86305e9	1.74931
$612$	1.05060e8	0.0185271
$613$	7.26562e9	1.27397	0.636987	−	0.770874i	$-0.280180\pi$
$613$	7.26562e9	1.27397	0.636987	+	0.770874i	$0.280180\pi$
$614$	−1.03220e10	−1.79960
$615$	−3.25233e8	−0.0563809
$616$	1.24107e9	0.213926
$617$	1.19372e9	0.204599	0.102299	−	0.994754i	$-0.467380\pi$
$617$	1.19372e9	0.204599	0.102299	+	0.994754i	$0.467380\pi$
$618$	8.67215e9	1.47797
$619$	−3.68439e9	−0.624379	−0.312189	−	0.950020i	$-0.601062\pi$
$619$	−3.68439e9	−0.624379	−0.312189	+	0.950020i	$0.601062\pi$
$620$	−6.95995e8	−0.117283
$621$	−2.39483e8	−0.0401286
$622$	−9.13520e9	−1.52213
$623$	−2.23052e9	−0.369571
$624$	−2.18337e9	−0.359734
$625$	5.81643e9	0.952963
$626$	7.19154e9	1.17169
$627$	2.08526e9	0.337849
$628$	−1.36051e10	−2.19201
$629$	−2.41083e8	−0.0386268
$630$	−1.51183e8	−0.0240885
$631$	5.35601e9	0.848670	0.424335	−	0.905505i	$-0.360508\pi$
$631$	5.35601e9	0.848670	0.424335	+	0.905505i	$0.360508\pi$
$632$	−5.10289e9	−0.804093
$633$	−3.85363e9	−0.603889
$634$	1.07432e9	0.167425
$635$	8.78125e8	0.136097
$636$	−4.03058e8	−0.0621251
$637$	1.00336e9	0.153805
$638$	1.81633e10	2.76900
$639$	−2.44268e9	−0.370352
$640$	7.68479e8	0.115878
$641$	6.01890e9	0.902639	0.451319	−	0.892362i	$-0.350954\pi$
$641$	6.01890e9	0.902639	0.451319	+	0.892362i	$0.350954\pi$
$642$	5.54203e9	0.826601
$643$	1.55056e9	0.230012	0.115006	−	0.993365i	$-0.463311\pi$
$643$	1.55056e9	0.230012	0.115006	+	0.993365i	$0.463311\pi$
$644$	−7.04750e8	−0.103976
$645$	−2.62357e8	−0.0384977
$646$	2.21025e8	0.0322573
$647$	1.23453e10	1.79200	0.896000	−	0.444055i	$-0.146461\pi$
$647$	1.23453e10	1.79200	0.896000	+	0.444055i	$0.146461\pi$
$648$	−3.74253e8	−0.0540323
$649$	−1.38607e10	−1.99035
$650$	1.12991e10	1.61380
$651$	−1.08770e9	−0.154517
$652$	−1.40414e10	−1.98401
$653$	8.94045e9	1.25650	0.628251	−	0.778011i	$-0.283771\pi$
$653$	8.94045e9	1.25650	0.628251	+	0.778011i	$0.283771\pi$
$654$	−2.29314e9	−0.320560
$655$	2.42285e8	0.0336885
$656$	3.25483e9	0.450158
$657$	5.77295e8	0.0794180
$658$	−6.83471e9	−0.935253
$659$	2.58682e9	0.352101	0.176050	−	0.984381i	$-0.443668\pi$
$659$	2.58682e9	0.352101	0.176050	+	0.984381i	$0.443668\pi$
$660$	−8.22070e8	−0.111303
$661$	−9.09918e9	−1.22545	−0.612727	−	0.790294i	$-0.709928\pi$
$661$	−9.09918e9	−1.22545	−0.612727	+	0.790294i	$0.709928\pi$
$662$	7.09494e9	0.950486
$663$	1.96511e8	0.0261872
$664$	−3.92700e9	−0.520562
$665$	−1.80923e8	−0.0238572
$666$	3.54834e9	0.465442
$667$	−2.49633e9	−0.325733
$668$	6.51081e9	0.845118
$669$	−1.57911e9	−0.203902
$670$	−1.42378e9	−0.182886
$671$	−6.45384e9	−0.824687
$672$	2.34778e9	0.298446
$673$	8.17202e9	1.03342	0.516710	−	0.856161i	$-0.327157\pi$
$673$	8.17202e9	1.03342	0.516710	+	0.856161i	$0.327157\pi$
$674$	−1.85780e10	−2.33716
$675$	−1.51350e9	−0.189417
$676$	1.68635e9	0.209959
$677$	−3.50961e9	−0.434708	−0.217354	−	0.976093i	$-0.569743\pi$
$677$	−3.50961e9	−0.434708	−0.217354	+	0.976093i	$0.569743\pi$
$678$	−5.47929e9	−0.675182
$679$	−1.40099e9	−0.171747
$680$	−2.10892e7	−0.00257204
$681$	1.66461e9	0.201975
$682$	−1.03975e10	−1.25511
$683$	−1.33334e10	−1.60128	−0.800640	−	0.599146i	$-0.795507\pi$
$683$	−1.33334e10	−1.60128	−0.800640	+	0.599146i	$0.795507\pi$
$684$	−1.85050e9	−0.221102
$685$	−3.90784e8	−0.0464537
$686$	−6.95292e8	−0.0822304
$687$	7.78280e9	0.915772
$688$	2.62559e9	0.307374
$689$	−7.53904e8	−0.0878110
$690$	1.98622e8	0.0230174
$691$	8.14518e9	0.939134	0.469567	−	0.882897i	$-0.344410\pi$
$691$	8.14518e9	0.939134	0.469567	+	0.882897i	$0.344410\pi$
$692$	−3.76602e9	−0.432027
$693$	−1.28473e9	−0.146638
$694$	5.51190e9	0.625955
$695$	1.17801e8	0.0133108
$696$	−3.90116e9	−0.438593
$697$	−2.92946e8	−0.0327697
$698$	−1.14484e10	−1.27424
$699$	9.24203e9	1.02352
$700$	−4.45392e9	−0.490794
$701$	−1.17908e10	−1.29280	−0.646401	−	0.762998i	$-0.723727\pi$
$701$	−1.17908e10	−1.29280	−0.646401	+	0.762998i	$0.723727\pi$
$702$	−2.89232e9	−0.315549
$703$	4.24637e9	0.460972
$704$	1.62069e10	1.75064
$705$	1.09572e9	0.117771
$706$	1.52927e10	1.63557
$707$	7.84576e8	0.0834963
$708$	1.23003e10	1.30257
$709$	−8.62141e9	−0.908483	−0.454241	−	0.890879i	$-0.650090\pi$
$709$	−8.62141e9	−0.908483	−0.454241	+	0.890879i	$0.650090\pi$
$710$	2.02591e9	0.212430
$711$	5.28242e9	0.551175
$712$	4.57954e9	0.475491
$713$	1.42901e9	0.147646
$714$	−1.36174e8	−0.0140008
$715$	−1.53765e9	−0.157321
$716$	−8.27230e8	−0.0842230
$717$	8.67665e9	0.879093
$718$	−1.29438e10	−1.30504
$719$	9.80299e8	0.0983575	0.0491787	−	0.998790i	$-0.484340\pi$
$719$	9.80299e8	0.0983575	0.0491787	+	0.998790i	$0.484340\pi$
$720$	−2.42559e8	−0.0242189
$721$	−6.39400e9	−0.635330
$722$	1.15083e10	1.13797
$723$	6.78348e9	0.667526
$724$	6.38954e9	0.625727
$725$	−1.57765e10	−1.53754
$726$	−3.21530e9	−0.311849
$727$	8.32462e8	0.0803515	0.0401757	−	0.999193i	$-0.487208\pi$
$727$	8.32462e8	0.0803515	0.0401757	+	0.999193i	$0.487208\pi$
$728$	−2.06004e9	−0.197886
$729$	3.87420e8	0.0370370
$730$	−4.78796e8	−0.0455534
$731$	−2.36312e8	−0.0223756
$732$	5.72728e9	0.539709
$733$	−3.05409e8	−0.0286430	−0.0143215	−	0.999897i	$-0.504559\pi$
$733$	−3.05409e8	−0.0286430	−0.0143215	+	0.999897i	$0.504559\pi$
$734$	4.41655e9	0.412237
$735$	1.11467e8	0.0103548
$736$	−3.08449e9	−0.285175
$737$	−1.20991e10	−1.11331
$738$	4.31169e9	0.394866
$739$	7.63045e9	0.695496	0.347748	−	0.937588i	$-0.386946\pi$
$739$	7.63045e9	0.695496	0.347748	+	0.937588i	$0.386946\pi$
$740$	−1.67405e9	−0.151865
$741$	−3.46129e9	−0.312518
$742$	5.22426e8	0.0469473
$743$	9.19625e9	0.822527	0.411263	−	0.911517i	$-0.365088\pi$
$743$	9.19625e9	0.822527	0.411263	+	0.911517i	$0.365088\pi$
$744$	2.23319e9	0.198802
$745$	−3.49475e8	−0.0309649
$746$	1.10660e10	0.975897
$747$	4.06516e9	0.356825
$748$	−7.40460e8	−0.0646913
$749$	−4.08615e9	−0.355327
$750$	2.53063e9	0.219035
$751$	−4.47930e9	−0.385896	−0.192948	−	0.981209i	$-0.561805\pi$
$751$	−4.47930e9	−0.385896	−0.192948	+	0.981209i	$0.561805\pi$
$752$	−1.09657e10	−0.940312
$753$	6.68225e9	0.570349
$754$	−3.01491e10	−2.56138
$755$	−1.24392e9	−0.105191
$756$	1.14010e9	0.0959659
$757$	−1.57067e10	−1.31598	−0.657991	−	0.753026i	$-0.728594\pi$
$757$	−1.57067e10	−1.31598	−0.657991	+	0.753026i	$0.728594\pi$
$758$	−2.22346e10	−1.85433
$759$	1.68787e9	0.140117
$760$	3.71459e8	0.0306947
$761$	−9.66120e9	−0.794667	−0.397333	−	0.917674i	$-0.630064\pi$
$761$	−9.66120e9	−0.794667	−0.397333	+	0.917674i	$0.630064\pi$
$762$	−1.16415e10	−0.953161
$763$	1.69074e9	0.137797
$764$	2.09340e10	1.69834
$765$	2.18311e7	0.00176304
$766$	3.35749e10	2.69907
$767$	2.30073e10	1.84112
$768$	7.13515e8	0.0568380
$769$	9.86620e9	0.782362	0.391181	−	0.920314i	$-0.372067\pi$
$769$	9.86620e9	0.782362	0.391181	+	0.920314i	$0.372067\pi$
$770$	1.06553e9	0.0841102
$771$	7.17979e9	0.564185
$772$	1.15925e10	0.906810
$773$	−2.23241e10	−1.73838	−0.869192	−	0.494474i	$-0.835361\pi$
$773$	−2.23241e10	−1.73838	−0.869192	+	0.494474i	$0.835361\pi$
$774$	3.47813e9	0.269620
$775$	9.03113e9	0.696925
$776$	2.87641e9	0.220971
$777$	−2.61620e9	−0.200077
$778$	−1.24948e10	−0.951260
$779$	5.15988e9	0.391073
$780$	1.36455e9	0.102957
$781$	1.72160e10	1.29316
$782$	1.78904e8	0.0133782
$783$	4.03841e9	0.300638
$784$	−1.11553e9	−0.0826753
$785$	−2.82709e9	−0.208591
$786$	−3.21202e9	−0.235939
$787$	−2.70286e10	−1.97657	−0.988285	−	0.152622i	$-0.951228\pi$
$787$	−2.70286e10	−1.97657	−0.988285	+	0.152622i	$0.951228\pi$
$788$	3.42429e10	2.49303
$789$	−1.94635e9	−0.141075
$790$	−4.38113e9	−0.316149
$791$	4.03990e9	0.290237
$792$	2.63772e9	0.188665
$793$	1.07127e10	0.762853
$794$	−1.96860e10	−1.39568
$795$	−8.37540e7	−0.00591182
$796$	5.67255e9	0.398642
$797$	1.47929e10	1.03502	0.517511	−	0.855677i	$-0.326859\pi$
$797$	1.47929e10	1.03502	0.517511	+	0.855677i	$0.326859\pi$
$798$	2.39854e9	0.167085
$799$	9.86947e8	0.0684510
$800$	−1.94935e10	−1.34609
$801$	−4.74066e9	−0.325931
$802$	−1.00218e10	−0.686021
$803$	−4.06875e9	−0.277304
$804$	1.07370e10	0.728595
$805$	−1.46445e8	−0.00989437
$806$	1.72586e10	1.16101
$807$	8.74902e9	0.586006
$808$	−1.61084e9	−0.107427
$809$	−2.33250e9	−0.154883	−0.0774413	−	0.996997i	$-0.524675\pi$
$809$	−2.33250e9	−0.154883	−0.0774413	+	0.996997i	$0.524675\pi$
$810$	−3.21319e8	−0.0212441
$811$	5.41056e9	0.356179	0.178090	−	0.984014i	$-0.443008\pi$
$811$	5.41056e9	0.356179	0.178090	+	0.984014i	$0.443008\pi$
$812$	1.18842e10	0.778977
$813$	5.31981e8	0.0347200
$814$	−2.50086e10	−1.62519
$815$	−2.91776e9	−0.188798
$816$	−2.18479e8	−0.0140765
$817$	4.16234e9	0.267030
$818$	−3.92723e10	−2.50871
$819$	2.13251e9	0.135643
$820$	−2.03418e9	−0.128837
$821$	9.97001e9	0.628774	0.314387	−	0.949295i	$-0.398201\pi$
$821$	9.97001e9	0.628774	0.314387	+	0.949295i	$0.398201\pi$
$822$	5.18071e9	0.325340
$823$	−1.80926e10	−1.13136	−0.565682	−	0.824624i	$-0.691387\pi$
$823$	−1.80926e10	−1.13136	−0.565682	+	0.824624i	$0.691387\pi$
$824$	1.31277e10	0.817417
$825$	1.06671e10	0.661388
$826$	−1.59432e10	−0.984338
$827$	3.65871e8	0.0224936	0.0112468	−	0.999937i	$-0.496420\pi$
$827$	3.65871e8	0.0224936	0.0112468	+	0.999937i	$0.496420\pi$
$828$	−1.49785e9	−0.0916986
$829$	3.04544e10	1.85656	0.928279	−	0.371884i	$-0.121288\pi$
$829$	3.04544e10	1.85656	0.928279	+	0.371884i	$0.121288\pi$
$830$	−3.37156e9	−0.204671
$831$	−1.76908e9	−0.106941
$832$	−2.69017e10	−1.61937
$833$	1.00402e8	0.00601843
$834$	−1.56172e9	−0.0932226
$835$	1.35292e9	0.0804213
$836$	1.30423e10	0.772025
$837$	−2.31176e9	−0.136271
$838$	9.05500e9	0.531538
$839$	−2.82316e10	−1.65032	−0.825162	−	0.564896i	$-0.808916\pi$
$839$	−2.82316e10	−1.65032	−0.825162	+	0.564896i	$0.808916\pi$
$840$	−2.28857e8	−0.0133225
$841$	2.48459e10	1.44035
$842$	−3.46344e9	−0.199947
$843$	1.40781e10	0.809370
$844$	−2.41026e10	−1.37996
$845$	3.50419e8	0.0199797
$846$	−1.45262e10	−0.824816
$847$	2.37065e9	0.134053
$848$	8.38184e8	0.0472013
$849$	−5.10752e9	−0.286440
$850$	1.13065e9	0.0631483
$851$	3.43714e9	0.191181
$852$	−1.52778e10	−0.846297
$853$	−2.40881e9	−0.132887	−0.0664434	−	0.997790i	$-0.521165\pi$
$853$	−2.40881e9	−0.132887	−0.0664434	+	0.997790i	$0.521165\pi$
$854$	−7.42344e9	−0.407852
$855$	−3.84528e8	−0.0210400
$856$	8.38940e9	0.457165
$857$	1.43053e10	0.776363	0.388182	−	0.921583i	$-0.373103\pi$
$857$	1.43053e10	0.776363	0.388182	+	0.921583i	$0.373103\pi$
$858$	2.03850e10	1.10180
$859$	−3.20961e10	−1.72773	−0.863866	−	0.503722i	$-0.831964\pi$
$859$	−3.20961e10	−1.72773	−0.863866	+	0.503722i	$0.831964\pi$
$860$	−1.64092e9	−0.0879716
$861$	−3.17902e9	−0.169739
$862$	2.97439e10	1.58169
$863$	2.27176e10	1.20317	0.601583	−	0.798810i	$-0.294537\pi$
$863$	2.27176e10	1.20317	0.601583	+	0.798810i	$0.294537\pi$
$864$	4.98989e9	0.263204
$865$	−7.82566e8	−0.0411116
$866$	−1.14431e10	−0.598731
$867$	−1.10595e10	−0.576326
$868$	−6.80305e9	−0.353089
$869$	−3.72303e10	−1.92454
$870$	−3.34937e9	−0.172443
$871$	2.00831e10	1.02983
$872$	−3.47131e9	−0.177291
$873$	−2.97761e9	−0.151467
$874$	−3.15117e9	−0.159655
$875$	−1.86584e9	−0.0941556
$876$	3.61070e9	0.181479
$877$	4.88484e9	0.244541	0.122271	−	0.992497i	$-0.460982\pi$
$877$	4.88484e9	0.244541	0.122271	+	0.992497i	$0.460982\pi$
$878$	8.81885e9	0.439725
$879$	−1.22443e10	−0.608096
$880$	1.70955e9	0.0845652
$881$	−3.65486e10	−1.80076	−0.900378	−	0.435109i	$-0.856710\pi$
$881$	−3.65486e10	−1.80076	−0.900378	+	0.435109i	$0.856710\pi$
$882$	−1.47775e9	−0.0725204
$883$	1.81596e10	0.887655	0.443828	−	0.896112i	$-0.353620\pi$
$883$	1.81596e10	0.887655	0.443828	+	0.896112i	$0.353620\pi$
$884$	1.22908e9	0.0598408
$885$	2.55597e9	0.123952
$886$	1.81896e10	0.878628
$887$	−2.63306e10	−1.26686	−0.633429	−	0.773801i	$-0.718353\pi$
$887$	−2.63306e10	−1.26686	−0.633429	+	0.773801i	$0.718353\pi$
$888$	5.37141e9	0.257420
$889$	8.58330e9	0.409730
$890$	3.93181e9	0.186951
$891$	−2.73053e9	−0.129323
$892$	−9.87659e9	−0.465940
$893$	−1.73838e10	−0.816893
$894$	4.63307e9	0.216864
$895$	−1.71896e8	−0.00801464
$896$	7.51156e9	0.348861
$897$	−2.80167e9	−0.129612
$898$	−5.65362e10	−2.60531
$899$	−2.40974e10	−1.10615
$900$	−9.46620e9	−0.432839
$901$	−7.54394e7	−0.00343607
$902$	−3.03886e10	−1.37876
$903$	−2.56443e9	−0.115900
$904$	−8.29444e9	−0.373420
$905$	1.32772e9	0.0595440
$906$	1.64909e10	0.736708
$907$	4.54731e9	0.202362	0.101181	−	0.994868i	$-0.467738\pi$
$907$	4.54731e9	0.202362	0.101181	+	0.994868i	$0.467738\pi$
$908$	1.04114e10	0.461537
$909$	1.66751e9	0.0736368
$910$	−1.76866e9	−0.0778037
$911$	3.73260e10	1.63567	0.817837	−	0.575449i	$-0.195173\pi$
$911$	3.73260e10	1.63567	0.817837	+	0.575449i	$0.195173\pi$
$912$	3.84824e9	0.167989
$913$	−2.86511e10	−1.24593
$914$	−6.07807e10	−2.63302
$915$	1.19011e9	0.0513586
$916$	4.86777e10	2.09265
$917$	2.36823e9	0.101422
$918$	−2.89420e8	−0.0123475
$919$	−3.91993e10	−1.66600	−0.832998	−	0.553276i	$-0.813377\pi$
$919$	−3.91993e10	−1.66600	−0.832998	+	0.553276i	$0.813377\pi$
$920$	3.00670e8	0.0127301
$921$	1.61750e10	0.682238
$922$	3.41747e10	1.43597
$923$	−2.85766e10	−1.19620
$924$	−8.03539e9	−0.335085
$925$	2.17222e10	0.902418
$926$	−4.59639e9	−0.190230
$927$	−1.35896e10	−0.560308
$928$	5.20139e10	2.13649
$929$	−4.41282e9	−0.180576	−0.0902882	−	0.995916i	$-0.528779\pi$
$929$	−4.41282e9	−0.180576	−0.0902882	+	0.995916i	$0.528779\pi$
$930$	1.91733e9	0.0781639
$931$	−1.76845e9	−0.0718239
$932$	5.78044e10	2.33887
$933$	1.43152e10	0.577047
$934$	6.44027e10	2.58637
$935$	−1.53865e8	−0.00615601
$936$	−4.37833e9	−0.174519
$937$	−1.08055e10	−0.429097	−0.214549	−	0.976713i	$-0.568828\pi$
$937$	−1.08055e10	−0.429097	−0.214549	+	0.976713i	$0.568828\pi$
$938$	−1.39168e10	−0.550592
$939$	−1.12694e10	−0.444193
$940$	6.85323e9	0.269121
$941$	−2.74310e10	−1.07319	−0.536597	−	0.843839i	$-0.680290\pi$
$941$	−2.74310e10	−1.07319	−0.536597	+	0.843839i	$0.680290\pi$
$942$	3.74793e10	1.46088
$943$	4.17656e9	0.162191
$944$	−2.55793e10	−0.989662
$945$	2.36909e8	0.00913209
$946$	−2.45137e10	−0.941434
$947$	5.99306e9	0.229310	0.114655	−	0.993405i	$-0.463424\pi$
$947$	5.99306e9	0.229310	0.114655	+	0.993405i	$0.463424\pi$
$948$	3.30390e10	1.25950
$949$	6.75368e9	0.256513
$950$	−1.99150e10	−0.753610
$951$	−1.68349e9	−0.0634716
$952$	−2.06138e8	−0.00774334
$953$	4.42583e10	1.65642	0.828208	−	0.560421i	$-0.189361\pi$
$953$	4.42583e10	1.65642	0.828208	+	0.560421i	$0.189361\pi$
$954$	1.11035e9	0.0414037
$955$	4.35002e9	0.161614
$956$	5.42683e10	2.00883
$957$	−2.84626e10	−1.04974
$958$	−1.61262e10	−0.592586
$959$	−3.81975e9	−0.139852
$960$	−2.98861e9	−0.109023
$961$	−1.37182e10	−0.498614
$962$	4.15115e10	1.50334
$963$	−8.68456e9	−0.313369
$964$	4.24274e10	1.52538
$965$	2.40888e9	0.0862919
$966$	1.94145e9	0.0692957
$967$	1.58008e10	0.561934	0.280967	−	0.959717i	$-0.409345\pi$
$967$	1.58008e10	0.561934	0.280967	+	0.959717i	$0.409345\pi$
$968$	−4.86726e9	−0.172473
$969$	−3.46354e8	−0.0122289
$970$	2.46957e9	0.0868800
$971$	−1.34322e8	−0.00470848	−0.00235424	−	0.999997i	$-0.500749\pi$
$971$	−1.34322e8	−0.00470848	−0.00235424	+	0.999997i	$0.500749\pi$
$972$	2.42313e9	0.0846339
$973$	1.15146e9	0.0400731
$974$	−5.47551e10	−1.89875
$975$	−1.77062e10	−0.611798
$976$	−1.19102e10	−0.410059
$977$	3.67190e10	1.25968	0.629839	−	0.776725i	$-0.283121\pi$
$977$	3.67190e10	1.25968	0.629839	+	0.776725i	$0.283121\pi$
$978$	3.86814e10	1.32226
$979$	3.34120e10	1.13805
$980$	6.97176e8	0.0236620
$981$	3.59344e9	0.121526
$982$	−8.09189e10	−2.72684
$983$	3.54849e9	0.119154	0.0595768	−	0.998224i	$-0.481025\pi$
$983$	3.54849e9	0.119154	0.0595768	+	0.998224i	$0.481025\pi$
$984$	6.52694e9	0.218387
$985$	7.11555e9	0.237237
$986$	−3.01687e9	−0.100228
$987$	1.07102e10	0.354559
$988$	−2.16487e10	−0.714139
$989$	3.36912e9	0.110746
$990$	2.26464e9	0.0741782
$991$	−2.33506e10	−0.762151	−0.381076	−	0.924544i	$-0.624446\pi$
$991$	−2.33506e10	−0.762151	−0.381076	+	0.924544i	$0.624446\pi$
$992$	−2.97750e10	−0.968414
$993$	−1.11180e10	−0.360334
$994$	1.98024e10	0.639538
$995$	1.17874e9	0.0379346
$996$	2.54256e10	0.815386
$997$	−4.44173e10	−1.41945	−0.709723	−	0.704481i	$-0.751180\pi$
$997$	−4.44173e10	−1.41945	−0.709723	+	0.704481i	$0.751180\pi$
$998$	−4.48245e9	−0.142744
$999$	−5.56039e9	−0.176452

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.8.a.h.1.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.8.a.h.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-17.2300 q^{2} +27.0000 q^{3} +168.872 q^{4} +35.0910 q^{5} -465.209 q^{6} +343.000 q^{7} -704.224 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-17.2300 q^{2} +27.0000 q^{3} +168.872 q^{4} +35.0910 q^{5} -465.209 q^{6} +343.000 q^{7} -704.224 q^{8} +729.000 q^{9} -604.618 q^{10} -5137.97 q^{11} +4559.54 q^{12} +8528.45 q^{13} -5909.88 q^{14} +947.458 q^{15} -9481.86 q^{16} +853.400 q^{17} -12560.7 q^{18} -15031.6 q^{19} +5925.89 q^{20} +9261.00 q^{21} +88527.0 q^{22} -12167.0 q^{23} -19014.0 q^{24} -76893.6 q^{25} -146945. q^{26} +19683.0 q^{27} +57923.1 q^{28} +205172. q^{29} -16324.7 q^{30} -117450. q^{31} +253513. q^{32} -138725. q^{33} -14704.1 q^{34} +12036.2 q^{35} +123108. q^{36} -282497. q^{37} +258994. q^{38} +230268. q^{39} -24711.9 q^{40} -343269. q^{41} -159567. q^{42} -276907. q^{43} -867659. q^{44} +25581.4 q^{45} +209637. q^{46} +1.15649e6 q^{47} -256010. q^{48} +117649. q^{49} +1.32488e6 q^{50} +23041.8 q^{51} +1.44022e6 q^{52} -88398.7 q^{53} -339138. q^{54} -180297. q^{55} -241549. q^{56} -405852. q^{57} -3.53512e6 q^{58} +2.69771e6 q^{59} +159999. q^{60} +1.25611e6 q^{61} +2.02366e6 q^{62} +250047. q^{63} -3.15434e6 q^{64} +299272. q^{65} +2.39023e6 q^{66} +2.35484e6 q^{67} +144115. q^{68} -328509. q^{69} -207384. q^{70} -3.35073e6 q^{71} -513379. q^{72} +791900. q^{73} +4.86741e6 q^{74} -2.07613e6 q^{75} -2.53841e6 q^{76} -1.76232e6 q^{77} -3.96752e6 q^{78} +7.24612e6 q^{79} -332728. q^{80} +531441. q^{81} +5.91452e6 q^{82} +5.57635e6 q^{83} +1.56392e6 q^{84} +29946.7 q^{85} +4.77109e6 q^{86} +5.53966e6 q^{87} +3.61828e6 q^{88} -6.50296e6 q^{89} -440766. q^{90} +2.92526e6 q^{91} -2.05467e6 q^{92} -3.17114e6 q^{93} -1.99263e7 q^{94} -527473. q^{95} +6.84485e6 q^{96} -4.08451e6 q^{97} -2.02709e6 q^{98} -3.74558e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 24 q^{2} + 540 q^{3} + 1486 q^{4} + 1069 q^{5} + 648 q^{6} + 6860 q^{7} + 2127 q^{8} + 14580 q^{9}+O(q^{10}) \) 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

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Database

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