LMFDB - Embedded newform 483.8.a.h.1.20

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			1.20
Root			$20.5538$ 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)

$f(q)$	$=$	$q+21.5538 q^{2} +27.0000 q^{3} +336.565 q^{4} +164.789 q^{5} +581.952 q^{6} +343.000 q^{7} +4495.37 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+21.5538 q^{2} +27.0000 q^{3} +336.565 q^{4} +164.789 q^{5} +581.952 q^{6} +343.000 q^{7} +4495.37 q^{8} +729.000 q^{9} +3551.82 q^{10} +7190.66 q^{11} +9087.26 q^{12} -990.823 q^{13} +7392.94 q^{14} +4449.30 q^{15} +53811.8 q^{16} -3827.03 q^{17} +15712.7 q^{18} +19215.1 q^{19} +55462.2 q^{20} +9261.00 q^{21} +154986. q^{22} -12167.0 q^{23} +121375. q^{24} -50969.6 q^{25} -21356.0 q^{26} +19683.0 q^{27} +115442. q^{28} -97147.0 q^{29} +95899.2 q^{30} -157466. q^{31} +584440. q^{32} +194148. q^{33} -82487.0 q^{34} +56522.6 q^{35} +245356. q^{36} -361395. q^{37} +414158. q^{38} -26752.2 q^{39} +740787. q^{40} +18859.6 q^{41} +199609. q^{42} -210418. q^{43} +2.42013e6 q^{44} +120131. q^{45} -262245. q^{46} +162055. q^{47} +1.45292e6 q^{48} +117649. q^{49} -1.09859e6 q^{50} -103330. q^{51} -333477. q^{52} -1.34110e6 q^{53} +424243. q^{54} +1.18494e6 q^{55} +1.54191e6 q^{56} +518808. q^{57} -2.09388e6 q^{58} -177157. q^{59} +1.49748e6 q^{60} +1.86304e6 q^{61} -3.39398e6 q^{62} +250047. q^{63} +5.70897e6 q^{64} -163277. q^{65} +4.18462e6 q^{66} -109037. q^{67} -1.28805e6 q^{68} -328509. q^{69} +1.21828e6 q^{70} -823425. q^{71} +3.27712e6 q^{72} +771110. q^{73} -7.78944e6 q^{74} -1.37618e6 q^{75} +6.46713e6 q^{76} +2.46640e6 q^{77} -576611. q^{78} -3.58974e6 q^{79} +8.86758e6 q^{80} +531441. q^{81} +406495. q^{82} +4.40614e6 q^{83} +3.11693e6 q^{84} -630653. q^{85} -4.53531e6 q^{86} -2.62297e6 q^{87} +3.23247e7 q^{88} +3.98198e6 q^{89} +2.58928e6 q^{90} -339852. q^{91} -4.09499e6 q^{92} -4.25157e6 q^{93} +3.49289e6 q^{94} +3.16644e6 q^{95} +1.57799e7 q^{96} +90719.7 q^{97} +2.53578e6 q^{98} +5.24199e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	21.5538	1.90510	0.952551	−	0.304378i	$-0.0984487\pi$
$2$	21.5538	1.90510	0.952551	+	0.304378i	$0.0984487\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	336.565	2.62942
$5$	164.789	0.589567	0.294783	−	0.955564i	$-0.404752\pi$
$5$	164.789	0.589567	0.294783	+	0.955564i	$0.404752\pi$
$6$	581.952	1.09991
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	4495.37	3.10420
$9$	729.000	0.333333
$10$	3551.82	1.12319
$11$	7190.66	1.62890	0.814450	−	0.580233i	$-0.197039\pi$
$11$	7190.66	1.62890	0.814450	+	0.580233i	$0.197039\pi$
$12$	9087.26	1.51809
$13$	−990.823	−0.125082	−0.0625409	−	0.998042i	$-0.519920\pi$
$13$	−990.823	−0.125082	−0.0625409	+	0.998042i	$0.519920\pi$
$14$	7392.94	0.720061
$15$	4449.30	0.340387
$16$	53811.8	3.28441
$17$	−3827.03	−0.188926	−0.0944628	−	0.995528i	$-0.530113\pi$
$17$	−3827.03	−0.188926	−0.0944628	+	0.995528i	$0.530113\pi$
$18$	15712.7	0.635034
$19$	19215.1	0.642695	0.321348	−	0.946961i	$-0.395864\pi$
$19$	19215.1	0.642695	0.321348	+	0.946961i	$0.395864\pi$
$20$	55462.2	1.55022
$21$	9261.00	0.218218
$22$	154986.	3.10322
$23$	−12167.0	−0.208514
$23$	−12167.0	−0.208514
$24$	121375.	1.79221
$25$	−50969.6	−0.652411
$26$	−21356.0	−0.238294
$27$	19683.0	0.192450
$28$	115442.	0.993826
$29$	−97147.0	−0.739667	−0.369834	−	0.929098i	$-0.620585\pi$
$29$	−97147.0	−0.739667	−0.369834	+	0.929098i	$0.620585\pi$
$30$	95899.2	0.648471
$31$	−157466.	−0.949335	−0.474668	−	0.880165i	$-0.657432\pi$
$31$	−157466.	−0.949335	−0.474668	+	0.880165i	$0.657432\pi$
$32$	584440.	3.15293
$33$	194148.	0.940446
$34$	−82487.0	−0.359923
$35$	56522.6	0.222835
$36$	245356.	0.876472
$37$	−361395.	−1.17294	−0.586471	−	0.809970i	$-0.699483\pi$
$37$	−361395.	−1.17294	−0.586471	+	0.809970i	$0.699483\pi$
$38$	414158.	1.22440
$39$	−26752.2	−0.0722161
$40$	740787.	1.83014
$41$	18859.6	0.0427354	0.0213677	−	0.999772i	$-0.493198\pi$
$41$	18859.6	0.0427354	0.0213677	+	0.999772i	$0.493198\pi$
$42$	199609.	0.415727
$43$	−210418.	−0.403593	−0.201797	−	0.979427i	$-0.564678\pi$
$43$	−210418.	−0.403593	−0.201797	+	0.979427i	$0.564678\pi$
$44$	2.42013e6	4.28306
$45$	120131.	0.196522
$46$	−262245.	−0.397241
$47$	162055.	0.227677	0.113839	−	0.993499i	$-0.463685\pi$
$47$	162055.	0.227677	0.113839	+	0.993499i	$0.463685\pi$
$48$	1.45292e6	1.89625
$49$	117649.	0.142857
$50$	−1.09859e6	−1.24291
$51$	−103330.	−0.109076
$52$	−333477.	−0.328892
$53$	−1.34110e6	−1.23736	−0.618679	−	0.785644i	$-0.712332\pi$
$53$	−1.34110e6	−1.23736	−0.618679	+	0.785644i	$0.712332\pi$
$54$	424243.	0.366637
$55$	1.18494e6	0.960346
$56$	1.54191e6	1.17328
$57$	518808.	0.371060
$58$	−2.09388e6	−1.40914
$59$	−177157.	−0.112299	−0.0561495	−	0.998422i	$-0.517882\pi$
$59$	−177157.	−0.112299	−0.0561495	+	0.998422i	$0.517882\pi$
$60$	1.49748e6	0.895018
$61$	1.86304e6	1.05091	0.525457	−	0.850820i	$-0.323894\pi$
$61$	1.86304e6	1.05091	0.525457	+	0.850820i	$0.323894\pi$
$62$	−3.39398e6	−1.80858
$63$	250047.	0.125988
$64$	5.70897e6	2.72225
$65$	−163277.	−0.0737441
$66$	4.18462e6	1.79165
$67$	−109037.	−0.0442905	−0.0221452	−	0.999755i	$-0.507050\pi$
$67$	−109037.	−0.0442905	−0.0221452	+	0.999755i	$0.507050\pi$
$68$	−1.28805e6	−0.496764
$69$	−328509.	−0.120386
$70$	1.21828e6	0.424524
$71$	−823425.	−0.273036	−0.136518	−	0.990638i	$-0.543591\pi$
$71$	−823425.	−0.273036	−0.136518	+	0.990638i	$0.543591\pi$
$72$	3.27712e6	1.03473
$73$	771110.	0.231999	0.116000	−	0.993249i	$-0.462993\pi$
$73$	771110.	0.231999	0.116000	+	0.993249i	$0.462993\pi$
$74$	−7.78944e6	−2.23458
$75$	−1.37618e6	−0.376670
$76$	6.46713e6	1.68991
$77$	2.46640e6	0.615667
$78$	−576611.	−0.137579
$79$	−3.58974e6	−0.819159	−0.409579	−	0.912274i	$-0.634325\pi$
$79$	−3.58974e6	−0.819159	−0.409579	+	0.912274i	$0.634325\pi$
$80$	8.86758e6	1.93638
$81$	531441.	0.111111
$82$	406495.	0.0814154
$83$	4.40614e6	0.845834	0.422917	−	0.906168i	$-0.361006\pi$
$83$	4.40614e6	0.845834	0.422917	+	0.906168i	$0.361006\pi$
$84$	3.11693e6	0.573785
$85$	−630653.	−0.111384
$86$	−4.53531e6	−0.768887
$87$	−2.62297e6	−0.427047
$88$	3.23247e7	5.05644
$89$	3.98198e6	0.598734	0.299367	−	0.954138i	$-0.403225\pi$
$89$	3.98198e6	0.598734	0.299367	+	0.954138i	$0.403225\pi$
$90$	2.58928e6	0.374395
$91$	−339852.	−0.0472765
$92$	−4.09499e6	−0.548271
$93$	−4.25157e6	−0.548099
$94$	3.49289e6	0.433748
$95$	3.16644e6	0.378912
$96$	1.57799e7	1.82035
$97$	90719.7	0.0100925	0.00504627	−	0.999987i	$-0.498394\pi$
$97$	90719.7	0.0100925	0.00504627	+	0.999987i	$0.498394\pi$
$98$	2.53578e6	0.272157
$99$	5.24199e6	0.542967
$100$	−1.71546e7	−1.71546
$101$	−1.17891e7	−1.13856	−0.569279	−	0.822144i	$-0.692778\pi$
$101$	−1.17891e7	−1.13856	−0.569279	+	0.822144i	$0.692778\pi$
$102$	−2.22715e6	−0.207801
$103$	1.93006e7	1.74036	0.870181	−	0.492731i	$-0.164001\pi$
$103$	1.93006e7	1.74036	0.870181	+	0.492731i	$0.164001\pi$
$104$	−4.45411e6	−0.388280
$105$	1.52611e6	0.128654
$106$	−2.89058e7	−2.35729
$107$	5.09650e6	0.402187	0.201094	−	0.979572i	$-0.435550\pi$
$107$	5.09650e6	0.402187	0.201094	+	0.979572i	$0.435550\pi$
$108$	6.62461e6	0.506031
$109$	9.71304e6	0.718394	0.359197	−	0.933262i	$-0.383051\pi$
$109$	9.71304e6	0.718394	0.359197	+	0.933262i	$0.383051\pi$
$110$	2.55400e7	1.82956
$111$	−9.75768e6	−0.677199
$112$	1.84574e7	1.24139
$113$	−7.85519e6	−0.512133	−0.256066	−	0.966659i	$-0.582427\pi$
$113$	−7.85519e6	−0.512133	−0.256066	+	0.966659i	$0.582427\pi$
$114$	1.11823e7	0.706908
$115$	−2.00499e6	−0.122933
$116$	−3.26963e7	−1.94489
$117$	−722310.	−0.0416940
$118$	−3.81840e6	−0.213941
$119$	−1.31267e6	−0.0714072
$120$	2.00012e7	1.05663
$121$	3.22185e7	1.65332
$122$	4.01555e7	2.00210
$123$	509208.	0.0246733
$124$	−5.29974e7	−2.49620
$125$	−2.12734e7	−0.974207
$126$	5.38946e6	0.240020
$127$	2.04461e7	0.885722	0.442861	−	0.896590i	$-0.353964\pi$
$127$	2.04461e7	0.885722	0.442861	+	0.896590i	$0.353964\pi$
$128$	4.82417e7	2.03323
$129$	−5.68130e6	−0.233015
$130$	−3.51923e6	−0.140490
$131$	2.40934e7	0.936373	0.468187	−	0.883630i	$-0.344907\pi$
$131$	2.40934e7	0.936373	0.468187	+	0.883630i	$0.344907\pi$
$132$	6.53434e7	2.47282
$133$	6.59078e6	0.242916
$134$	−2.35015e6	−0.0843779
$135$	3.24354e6	0.113462
$136$	−1.72039e7	−0.586464
$137$	−5.17468e7	−1.71934	−0.859669	−	0.510851i	$-0.829330\pi$
$137$	−5.17468e7	−1.71934	−0.859669	+	0.510851i	$0.829330\pi$
$138$	−7.08061e6	−0.229347
$139$	−3.69140e7	−1.16584	−0.582921	−	0.812529i	$-0.698090\pi$
$139$	−3.69140e7	−1.16584	−0.582921	+	0.812529i	$0.698090\pi$
$140$	1.90235e7	0.585927
$141$	4.37548e6	0.131449
$142$	−1.77479e7	−0.520162
$143$	−7.12468e6	−0.203746
$144$	3.92288e7	1.09480
$145$	−1.60087e7	−0.436083
$146$	1.66203e7	0.441982
$147$	3.17652e6	0.0824786
$148$	−1.21633e8	−3.08415
$149$	−2.40730e7	−0.596181	−0.298090	−	0.954538i	$-0.596350\pi$
$149$	−2.40730e7	−0.596181	−0.298090	+	0.954538i	$0.596350\pi$
$150$	−2.96619e7	−0.717594
$151$	1.47529e7	0.348705	0.174352	−	0.984683i	$-0.444217\pi$
$151$	1.47529e7	0.348705	0.174352	+	0.984683i	$0.444217\pi$
$152$	8.63789e7	1.99506
$153$	−2.78991e6	−0.0629752
$154$	5.31602e7	1.17291
$155$	−2.59486e7	−0.559697
$156$	−9.00387e6	−0.189886
$157$	−2.04171e6	−0.0421060	−0.0210530	−	0.999778i	$-0.506702\pi$
$157$	−2.04171e6	−0.0421060	−0.0210530	+	0.999778i	$0.506702\pi$
$158$	−7.73724e7	−1.56058
$159$	−3.62097e7	−0.714389
$160$	9.63092e7	1.85886
$161$	−4.17328e6	−0.0788110
$162$	1.14546e7	0.211678
$163$	−4.53649e7	−0.820471	−0.410236	−	0.911980i	$-0.634554\pi$
$163$	−4.53649e7	−0.820471	−0.410236	+	0.911980i	$0.634554\pi$
$164$	6.34747e6	0.112369
$165$	3.19934e7	0.554456
$166$	9.49690e7	1.61140
$167$	−6.06935e6	−0.100840	−0.0504202	−	0.998728i	$-0.516056\pi$
$167$	−6.06935e6	−0.100840	−0.0504202	+	0.998728i	$0.516056\pi$
$168$	4.16316e7	0.677393
$169$	−6.17668e7	−0.984355
$170$	−1.35929e7	−0.212198
$171$	1.40078e7	0.214232
$172$	−7.08195e7	−1.06121
$173$	5.70558e7	0.837796	0.418898	−	0.908033i	$-0.362416\pi$
$173$	5.70558e7	0.837796	0.418898	+	0.908033i	$0.362416\pi$
$174$	−5.65349e7	−0.813568
$175$	−1.74826e7	−0.246588
$176$	3.86942e8	5.34998
$177$	−4.78324e6	−0.0648359
$178$	8.58266e7	1.14065
$179$	1.11978e8	1.45931	0.729657	−	0.683814i	$-0.239680\pi$
$179$	1.11978e8	1.45931	0.729657	+	0.683814i	$0.239680\pi$
$180$	4.04320e7	0.516739
$181$	−1.17037e7	−0.146706	−0.0733529	−	0.997306i	$-0.523370\pi$
$181$	−1.17037e7	−0.146706	−0.0733529	+	0.997306i	$0.523370\pi$
$182$	−7.32510e6	−0.0900666
$183$	5.03020e7	0.606746
$184$	−5.46951e7	−0.647271
$185$	−5.95540e7	−0.691528
$186$	−9.16374e7	−1.04418
$187$	−2.75189e7	−0.307741
$188$	5.45420e7	0.598657
$189$	6.75127e6	0.0727393
$190$	6.82486e7	0.721866
$191$	−7.81017e7	−0.811043	−0.405521	−	0.914086i	$-0.632910\pi$
$191$	−7.81017e7	−0.811043	−0.405521	+	0.914086i	$0.632910\pi$
$192$	1.54142e8	1.57169
$193$	−1.38643e8	−1.38819	−0.694095	−	0.719884i	$-0.744195\pi$
$193$	−1.38643e8	−1.38819	−0.694095	+	0.719884i	$0.744195\pi$
$194$	1.95535e6	0.0192273
$195$	−4.40847e6	−0.0425762
$196$	3.95966e7	0.375631
$197$	2.03914e8	1.90027	0.950135	−	0.311840i	$-0.100945\pi$
$197$	2.03914e8	1.90027	0.950135	+	0.311840i	$0.100945\pi$
$198$	1.12985e8	1.03441
$199$	−5.22326e6	−0.0469846	−0.0234923	−	0.999724i	$-0.507479\pi$
$199$	−5.22326e6	−0.0469846	−0.0234923	+	0.999724i	$0.507479\pi$
$200$	−2.29127e8	−2.02522
$201$	−2.94399e6	−0.0255711
$202$	−2.54099e8	−2.16907
$203$	−3.33214e7	−0.279568
$204$	−3.47772e7	−0.286807
$205$	3.10785e6	0.0251954
$206$	4.16000e8	3.31557
$207$	−8.86974e6	−0.0695048
$208$	−5.33179e7	−0.410820
$209$	1.38169e8	1.04689
$210$	3.28934e7	0.245099
$211$	1.69794e8	1.24432	0.622161	−	0.782889i	$-0.286255\pi$
$211$	1.69794e8	1.24432	0.622161	+	0.782889i	$0.286255\pi$
$212$	−4.51367e8	−3.25353
$213$	−2.22325e7	−0.157637
$214$	1.09849e8	0.766208
$215$	−3.46746e7	−0.237945
$216$	8.84823e7	0.597404
$217$	−5.40107e7	−0.358815
$218$	2.09353e8	1.36861
$219$	2.08200e7	0.133945
$220$	3.98810e8	2.52515
$221$	3.79191e6	0.0236312
$222$	−2.10315e8	−1.29013
$223$	2.94330e7	0.177733	0.0888663	−	0.996044i	$-0.471676\pi$
$223$	2.94330e7	0.177733	0.0888663	+	0.996044i	$0.471676\pi$
$224$	2.00463e8	1.19170
$225$	−3.71568e7	−0.217470
$226$	−1.69309e8	−0.975665
$227$	9.33859e7	0.529896	0.264948	−	0.964263i	$-0.414645\pi$
$227$	9.33859e7	0.529896	0.264948	+	0.964263i	$0.414645\pi$
$228$	1.74613e8	0.975671
$229$	−2.36331e7	−0.130046	−0.0650229	−	0.997884i	$-0.520712\pi$
$229$	−2.36331e7	−0.130046	−0.0650229	+	0.997884i	$0.520712\pi$
$230$	−4.32150e7	−0.234200
$231$	6.65927e7	0.355455
$232$	−4.36711e8	−2.29608
$233$	−2.62112e8	−1.35750	−0.678752	−	0.734368i	$-0.737479\pi$
$233$	−2.62112e8	−1.35750	−0.678752	+	0.734368i	$0.737479\pi$
$234$	−1.55685e7	−0.0794313
$235$	2.67048e7	0.134231
$236$	−5.96249e7	−0.295281
$237$	−9.69230e7	−0.472942
$238$	−2.82930e7	−0.136038
$239$	1.60349e8	0.759757	0.379879	−	0.925036i	$-0.375966\pi$
$239$	1.60349e8	0.759757	0.379879	+	0.925036i	$0.375966\pi$
$240$	2.39425e8	1.11797
$241$	1.95706e8	0.900628	0.450314	−	0.892870i	$-0.351312\pi$
$241$	1.95706e8	0.900628	0.450314	+	0.892870i	$0.351312\pi$
$242$	6.94430e8	3.14974
$243$	1.43489e7	0.0641500
$244$	6.27034e8	2.76329
$245$	1.93873e7	0.0842238
$246$	1.09754e7	0.0470052
$247$	−1.90388e7	−0.0803895
$248$	−7.07865e8	−2.94693
$249$	1.18966e8	0.488343
$250$	−4.58521e8	−1.85596
$251$	−2.28136e8	−0.910617	−0.455309	−	0.890334i	$-0.650471\pi$
$251$	−2.28136e8	−0.910617	−0.455309	+	0.890334i	$0.650471\pi$
$252$	8.41571e7	0.331275
$253$	−8.74888e7	−0.339649
$254$	4.40691e8	1.68739
$255$	−1.70276e7	−0.0643078
$256$	3.09041e8	1.15127
$257$	−1.73516e8	−0.637637	−0.318819	−	0.947816i	$-0.603286\pi$
$257$	−1.73516e8	−0.637637	−0.318819	+	0.947816i	$0.603286\pi$
$258$	−1.22453e8	−0.443917
$259$	−1.23959e8	−0.443331
$260$	−5.49532e7	−0.193904
$261$	−7.08202e7	−0.246556
$262$	5.19304e8	1.78389
$263$	3.61583e8	1.22564	0.612820	−	0.790223i	$-0.290035\pi$
$263$	3.61583e8	1.22564	0.612820	+	0.790223i	$0.290035\pi$
$264$	8.72766e8	2.91934
$265$	−2.20998e8	−0.729505
$266$	1.42056e8	0.462780
$267$	1.07513e8	0.345679
$268$	−3.66979e7	−0.116458
$269$	−5.65782e8	−1.77221	−0.886107	−	0.463480i	$-0.846600\pi$
$269$	−5.65782e8	−1.77221	−0.886107	+	0.463480i	$0.846600\pi$
$270$	6.99105e7	0.216157
$271$	2.10092e8	0.641236	0.320618	−	0.947209i	$-0.396109\pi$
$271$	2.10092e8	0.641236	0.320618	+	0.947209i	$0.396109\pi$
$272$	−2.05939e8	−0.620509
$273$	−9.17601e6	−0.0272951
$274$	−1.11534e9	−3.27552
$275$	−3.66505e8	−1.06271
$276$	−1.10565e8	−0.316544
$277$	3.05607e8	0.863940	0.431970	−	0.901888i	$-0.357819\pi$
$277$	3.05607e8	0.863940	0.431970	+	0.901888i	$0.357819\pi$
$278$	−7.95637e8	−2.22105
$279$	−1.14792e8	−0.316445
$280$	2.54090e8	0.691726
$281$	−3.10858e8	−0.835776	−0.417888	−	0.908498i	$-0.637230\pi$
$281$	−3.10858e8	−0.835776	−0.417888	+	0.908498i	$0.637230\pi$
$282$	9.43081e7	0.250425
$283$	3.39603e8	0.890674	0.445337	−	0.895363i	$-0.353084\pi$
$283$	3.39603e8	0.890674	0.445337	+	0.895363i	$0.353084\pi$
$284$	−2.77136e8	−0.717925
$285$	8.54938e7	0.218765
$286$	−1.53564e8	−0.388157
$287$	6.46883e6	0.0161525
$288$	4.26057e8	1.05098
$289$	−3.95692e8	−0.964307
$290$	−3.45049e8	−0.830783
$291$	2.44943e6	0.00582693
$292$	2.59529e8	0.610022
$293$	−5.58952e8	−1.29819	−0.649094	−	0.760708i	$-0.724852\pi$
$293$	−5.58952e8	−1.29819	−0.649094	+	0.760708i	$0.724852\pi$
$294$	6.84661e7	0.157130
$295$	−2.91935e7	−0.0662078
$296$	−1.62460e9	−3.64105
$297$	1.41534e8	0.313482
$298$	−5.18864e8	−1.13579
$299$	1.20553e7	0.0260814
$300$	−4.63174e8	−0.990421
$301$	−7.21735e7	−0.152544
$302$	3.17980e8	0.664318
$303$	−3.18305e8	−0.657347
$304$	1.03400e9	2.11087
$305$	3.07008e8	0.619584
$306$	−6.01330e7	−0.119974
$307$	3.22454e7	0.0636039	0.0318019	−	0.999494i	$-0.489875\pi$
$307$	3.22454e7	0.0636039	0.0318019	+	0.999494i	$0.489875\pi$
$308$	8.30104e8	1.61884
$309$	5.21115e8	1.00480
$310$	−5.59290e8	−1.06628
$311$	5.06461e8	0.954739	0.477370	−	0.878703i	$-0.341590\pi$
$311$	5.06461e8	0.954739	0.477370	+	0.878703i	$0.341590\pi$
$312$	−1.20261e8	−0.224173
$313$	−1.05335e9	−1.94163	−0.970817	−	0.239821i	$-0.922911\pi$
$313$	−1.05335e9	−1.94163	−0.970817	+	0.239821i	$0.922911\pi$
$314$	−4.40065e7	−0.0802163
$315$	4.12050e7	0.0742784
$316$	−1.20818e9	−2.15391
$317$	−5.66763e8	−0.999296	−0.499648	−	0.866229i	$-0.666537\pi$
$317$	−5.66763e8	−0.999296	−0.499648	+	0.866229i	$0.666537\pi$
$318$	−7.80455e8	−1.36098
$319$	−6.98551e8	−1.20484
$320$	9.40776e8	1.60495
$321$	1.37605e8	0.232203
$322$	−8.99500e7	−0.150143
$323$	−7.35368e7	−0.121422
$324$	1.78865e8	0.292157
$325$	5.05019e7	0.0816048
$326$	−9.77785e8	−1.56308
$327$	2.62252e8	0.414765
$328$	8.47806e7	0.132659
$329$	5.55848e7	0.0860538
$330$	6.89579e8	1.05630
$331$	−7.09925e7	−0.107601	−0.0538003	−	0.998552i	$-0.517133\pi$
$331$	−7.09925e7	−0.107601	−0.0538003	+	0.998552i	$0.517133\pi$
$332$	1.48295e9	2.22405
$333$	−2.63457e8	−0.390981
$334$	−1.30817e8	−0.192111
$335$	−1.79680e7	−0.0261122
$336$	4.98351e8	0.716717
$337$	6.54611e8	0.931706	0.465853	−	0.884862i	$-0.345748\pi$
$337$	6.54611e8	0.931706	0.465853	+	0.884862i	$0.345748\pi$
$338$	−1.33131e9	−1.87530
$339$	−2.12090e8	−0.295680
$340$	−2.12256e8	−0.292876
$341$	−1.13228e9	−1.54637
$342$	3.01921e8	0.408133
$343$	4.03536e7	0.0539949
$344$	−9.45907e8	−1.25284
$345$	−5.41346e7	−0.0709755
$346$	1.22977e9	1.59609
$347$	−9.15412e7	−0.117615	−0.0588076	−	0.998269i	$-0.518730\pi$
$347$	−9.15412e7	−0.117615	−0.0588076	+	0.998269i	$0.518730\pi$
$348$	−8.82800e8	−1.12288
$349$	1.02877e9	1.29548	0.647740	−	0.761861i	$-0.275714\pi$
$349$	1.02877e9	1.29548	0.647740	+	0.761861i	$0.275714\pi$
$350$	−3.76815e8	−0.469776
$351$	−1.95024e7	−0.0240720
$352$	4.20251e9	5.13581
$353$	6.77333e8	0.819579	0.409790	−	0.912180i	$-0.365602\pi$
$353$	6.77333e8	0.819579	0.409790	+	0.912180i	$0.365602\pi$
$354$	−1.03097e8	−0.123519
$355$	−1.35691e8	−0.160973
$356$	1.34019e9	1.57432
$357$	−3.54421e7	−0.0412270
$358$	2.41356e9	2.78014
$359$	7.78557e8	0.888095	0.444048	−	0.896003i	$-0.353542\pi$
$359$	7.78557e8	0.888095	0.444048	+	0.896003i	$0.353542\pi$
$360$	5.40033e8	0.610045
$361$	−5.24652e8	−0.586943
$362$	−2.52258e8	−0.279490
$363$	8.69899e8	0.954543
$364$	−1.14382e8	−0.124310
$365$	1.27070e8	0.136779
$366$	1.08420e9	1.15591
$367$	4.48369e8	0.473483	0.236742	−	0.971573i	$-0.423921\pi$
$367$	4.48369e8	0.473483	0.236742	+	0.971573i	$0.423921\pi$
$368$	−6.54728e8	−0.684847
$369$	1.37486e7	0.0142451
$370$	−1.28361e9	−1.31743
$371$	−4.59997e8	−0.467677
$372$	−1.43093e9	−1.44118
$373$	1.08121e9	1.07877	0.539386	−	0.842059i	$-0.318656\pi$
$373$	1.08121e9	1.07877	0.539386	+	0.842059i	$0.318656\pi$
$374$	−5.93136e8	−0.586278
$375$	−5.74381e8	−0.562458
$376$	7.28495e8	0.706756
$377$	9.62555e7	0.0925190
$378$	1.45515e8	0.138576
$379$	1.34730e9	1.27124	0.635619	−	0.772003i	$-0.280745\pi$
$379$	1.34730e9	1.27124	0.635619	+	0.772003i	$0.280745\pi$
$380$	1.06571e9	0.996316
$381$	5.52045e8	0.511372
$382$	−1.68339e9	−1.54512
$383$	−8.93705e8	−0.812828	−0.406414	−	0.913689i	$-0.633221\pi$
$383$	−8.93705e8	−0.812828	−0.406414	+	0.913689i	$0.633221\pi$
$384$	1.30252e9	1.17389
$385$	4.06435e8	0.362977
$386$	−2.98829e9	−2.64464
$387$	−1.53395e8	−0.134531
$388$	3.05331e7	0.0265375
$389$	−1.55064e9	−1.33563	−0.667816	−	0.744326i	$-0.732771\pi$
$389$	−1.55064e9	−1.33563	−0.667816	+	0.744326i	$0.732771\pi$
$390$	−9.50192e7	−0.0811120
$391$	4.65635e7	0.0393937
$392$	5.28875e8	0.443458
$393$	6.50523e8	0.540615
$394$	4.39511e9	3.62021
$395$	−5.91549e8	−0.482949
$396$	1.76427e9	1.42769
$397$	2.13587e9	1.71320	0.856600	−	0.515981i	$-0.172573\pi$
$397$	2.13587e9	1.71320	0.856600	+	0.515981i	$0.172573\pi$
$398$	−1.12581e8	−0.0895105
$399$	1.77951e8	0.140248
$400$	−2.74276e9	−2.14278
$401$	−1.04261e9	−0.807448	−0.403724	−	0.914881i	$-0.632284\pi$
$401$	−1.04261e9	−0.807448	−0.403724	+	0.914881i	$0.632284\pi$
$402$	−6.34541e7	−0.0487156
$403$	1.56020e8	0.118745
$404$	−3.96780e9	−2.99374
$405$	8.75756e7	0.0655074
$406$	−7.18202e8	−0.532606
$407$	−2.59867e9	−1.91061
$408$	−4.64506e8	−0.338595
$409$	−1.72668e9	−1.24790	−0.623951	−	0.781464i	$-0.714473\pi$
$409$	−1.72668e9	−1.24790	−0.623951	+	0.781464i	$0.714473\pi$
$410$	6.69858e7	0.0479998
$411$	−1.39716e9	−0.992660
$412$	6.49590e9	4.57614
$413$	−6.07648e7	−0.0424451
$414$	−1.91176e8	−0.132414
$415$	7.26084e8	0.498676
$416$	−5.79076e8	−0.394375
$417$	−9.96679e8	−0.673099
$418$	2.97807e9	1.99443
$419$	1.60855e9	1.06828	0.534141	−	0.845395i	$-0.320635\pi$
$419$	1.60855e9	1.06828	0.534141	+	0.845395i	$0.320635\pi$
$420$	5.13636e8	0.338285
$421$	−1.56259e9	−1.02061	−0.510304	−	0.859994i	$-0.670467\pi$
$421$	−1.56259e9	−1.02061	−0.510304	+	0.859994i	$0.670467\pi$
$422$	3.65969e9	2.37056
$423$	1.18138e8	0.0758923
$424$	−6.02873e9	−3.84101
$425$	1.95062e8	0.123257
$426$	−4.79194e8	−0.300315
$427$	6.39022e8	0.397208
$428$	1.71530e9	1.05752
$429$	−1.92366e8	−0.117633
$430$	−7.47369e8	−0.453310
$431$	−2.05137e9	−1.23417	−0.617083	−	0.786898i	$-0.711686\pi$
$431$	−2.05137e9	−1.23417	−0.617083	+	0.786898i	$0.711686\pi$
$432$	1.05918e9	0.632085
$433$	−1.59168e8	−0.0942212	−0.0471106	−	0.998890i	$-0.515001\pi$
$433$	−1.59168e8	−0.0942212	−0.0471106	+	0.998890i	$0.515001\pi$
$434$	−1.16413e9	−0.683579
$435$	−4.32236e8	−0.251773
$436$	3.26907e9	1.88896
$437$	−2.33790e8	−0.134011
$438$	4.48749e8	0.255178
$439$	1.24125e9	0.700219	0.350110	−	0.936709i	$-0.386144\pi$
$439$	1.24125e9	0.700219	0.350110	+	0.936709i	$0.386144\pi$
$440$	5.32675e9	2.98111
$441$	8.57661e7	0.0476190
$442$	8.17300e7	0.0450198
$443$	1.73354e9	0.947374	0.473687	−	0.880693i	$-0.342923\pi$
$443$	1.73354e9	0.947374	0.473687	+	0.880693i	$0.342923\pi$
$444$	−3.28409e9	−1.78064
$445$	6.56186e8	0.352993
$446$	6.34392e8	0.338599
$447$	−6.49971e8	−0.344205
$448$	1.95818e9	1.02891
$449$	8.10946e8	0.422795	0.211397	−	0.977400i	$-0.432199\pi$
$449$	8.10946e8	0.422795	0.211397	+	0.977400i	$0.432199\pi$
$450$	−8.00870e8	−0.414303
$451$	1.35613e8	0.0696118
$452$	−2.64378e9	−1.34661
$453$	3.98328e8	0.201325
$454$	2.01282e9	1.00951
$455$	−5.60039e7	−0.0278727
$456$	2.33223e9	1.15185
$457$	−2.64317e9	−1.29545	−0.647723	−	0.761876i	$-0.724278\pi$
$457$	−2.64317e9	−1.29545	−0.647723	+	0.761876i	$0.724278\pi$
$458$	−5.09382e8	−0.247750
$459$	−7.53275e7	−0.0363588
$460$	−6.74809e8	−0.323242
$461$	3.67177e9	1.74551	0.872755	−	0.488158i	$-0.162331\pi$
$461$	3.67177e9	1.74551	0.872755	+	0.488158i	$0.162331\pi$
$462$	1.43532e9	0.677179
$463$	3.63871e9	1.70378	0.851891	−	0.523720i	$-0.175456\pi$
$463$	3.63871e9	1.70378	0.851891	+	0.523720i	$0.175456\pi$
$464$	−5.22765e9	−2.42937
$465$	−7.00612e8	−0.323141
$466$	−5.64950e9	−2.58618
$467$	−2.19065e9	−0.995321	−0.497661	−	0.867372i	$-0.665807\pi$
$467$	−2.19065e9	−0.995321	−0.497661	+	0.867372i	$0.665807\pi$
$468$	−2.43104e8	−0.109631
$469$	−3.73996e7	−0.0167402
$470$	5.75590e8	0.255723
$471$	−5.51261e7	−0.0243099
$472$	−7.96385e8	−0.348599
$473$	−1.51305e9	−0.657413
$474$	−2.08906e9	−0.901002
$475$	−9.79386e8	−0.419301
$476$	−4.41800e8	−0.187759
$477$	−9.77661e8	−0.412453
$478$	3.45613e9	1.44741
$479$	4.30228e9	1.78865	0.894323	−	0.447422i	$-0.147658\pi$
$479$	4.30228e9	1.78865	0.894323	+	0.447422i	$0.147658\pi$
$480$	2.60035e9	1.07322
$481$	3.58079e8	0.146714
$482$	4.21821e9	1.71579
$483$	−1.12679e8	−0.0455016
$484$	1.08436e10	4.34726
$485$	1.49496e7	0.00595022
$486$	3.09273e8	0.122212
$487$	−1.73358e9	−0.680131	−0.340066	−	0.940402i	$-0.610449\pi$
$487$	−1.73358e9	−0.680131	−0.340066	+	0.940402i	$0.610449\pi$
$488$	8.37504e9	3.26225
$489$	−1.22485e9	−0.473699
$490$	4.17868e8	0.160455
$491$	−9.17931e8	−0.349965	−0.174983	−	0.984572i	$-0.555987\pi$
$491$	−9.17931e8	−0.349965	−0.174983	+	0.984572i	$0.555987\pi$
$492$	1.71382e8	0.0648764
$493$	3.71785e8	0.139742
$494$	−4.10357e8	−0.153150
$495$	8.63823e8	0.320115
$496$	−8.47350e9	−3.11801
$497$	−2.82435e8	−0.103198
$498$	2.56416e9	0.930343
$499$	3.02404e9	1.08952	0.544761	−	0.838591i	$-0.316620\pi$
$499$	3.02404e9	1.08952	0.544761	+	0.838591i	$0.316620\pi$
$500$	−7.15987e9	−2.56159
$501$	−1.63872e8	−0.0582202
$502$	−4.91719e9	−1.73482
$503$	−3.07038e9	−1.07573	−0.537867	−	0.843030i	$-0.680770\pi$
$503$	−3.07038e9	−1.07573	−0.537867	+	0.843030i	$0.680770\pi$
$504$	1.12405e9	0.391093
$505$	−1.94271e9	−0.671256
$506$	−1.88571e9	−0.647067
$507$	−1.66770e9	−0.568317
$508$	6.88144e9	2.32893
$509$	−7.91111e8	−0.265904	−0.132952	−	0.991122i	$-0.542446\pi$
$509$	−7.91111e8	−0.265904	−0.132952	+	0.991122i	$0.542446\pi$
$510$	−3.67009e8	−0.122513
$511$	2.64491e8	0.0876874
$512$	4.86071e8	0.160050
$513$	3.78211e8	0.123687
$514$	−3.73992e9	−1.21476
$515$	3.18052e9	1.02606
$516$	−1.91213e9	−0.612692
$517$	1.16528e9	0.370863
$518$	−2.67178e9	−0.844590
$519$	1.54051e9	0.483702
$520$	−7.33988e8	−0.228917
$521$	−5.98943e9	−1.85547	−0.927734	−	0.373242i	$-0.878246\pi$
$521$	−5.98943e9	−1.85547	−0.927734	+	0.373242i	$0.878246\pi$
$522$	−1.52644e9	−0.469714
$523$	−6.24113e9	−1.90769	−0.953844	−	0.300301i	$-0.902913\pi$
$523$	−6.24113e9	−1.90769	−0.953844	+	0.300301i	$0.902913\pi$
$524$	8.10901e9	2.46211
$525$	−4.72030e8	−0.142368
$526$	7.79348e9	2.33497
$527$	6.02626e8	0.179354
$528$	1.04474e10	3.08881
$529$	1.48036e8	0.0434783
$530$	−4.76335e9	−1.38978
$531$	−1.29147e8	−0.0374330
$532$	2.21823e9	0.638727
$533$	−1.86865e7	−0.00534543
$534$	2.31732e9	0.658554
$535$	8.39846e8	0.237116
$536$	−4.90159e8	−0.137487
$537$	3.02342e9	0.842535
$538$	−1.21947e10	−3.37625
$539$	8.45974e8	0.232700
$540$	1.09166e9	0.298339
$541$	−7.78362e8	−0.211345	−0.105672	−	0.994401i	$-0.533699\pi$
$541$	−7.78362e8	−0.211345	−0.105672	+	0.994401i	$0.533699\pi$
$542$	4.52829e9	1.22162
$543$	−3.15999e8	−0.0847006
$544$	−2.23667e9	−0.595670
$545$	1.60060e9	0.423541
$546$	−1.97778e8	−0.0520000
$547$	−4.48427e9	−1.17148	−0.585742	−	0.810498i	$-0.699197\pi$
$547$	−4.48427e9	−1.17148	−0.585742	+	0.810498i	$0.699197\pi$
$548$	−1.74162e10	−4.52085
$549$	1.35815e9	0.350305
$550$	−7.89957e9	−2.02458
$551$	−1.86669e9	−0.475381
$552$	−1.47677e9	−0.373702
$553$	−1.23128e9	−0.309613
$554$	6.58698e9	1.64590
$555$	−1.60796e9	−0.399254
$556$	−1.24240e10	−3.06548
$557$	−2.62106e8	−0.0642664	−0.0321332	−	0.999484i	$-0.510230\pi$
$557$	−2.62106e8	−0.0642664	−0.0321332	+	0.999484i	$0.510230\pi$
$558$	−2.47421e9	−0.602860
$559$	2.08487e8	0.0504822
$560$	3.04158e9	0.731882
$561$	−7.43011e8	−0.177674
$562$	−6.70017e9	−1.59224
$563$	−1.44267e9	−0.340712	−0.170356	−	0.985383i	$-0.554492\pi$
$563$	−1.44267e9	−0.340712	−0.170356	+	0.985383i	$0.554492\pi$
$564$	1.47263e9	0.345635
$565$	−1.29445e9	−0.301936
$566$	7.31972e9	1.69683
$567$	1.82284e8	0.0419961
$568$	−3.70160e9	−0.847559
$569$	−3.02715e9	−0.688876	−0.344438	−	0.938809i	$-0.611931\pi$
$569$	−3.02715e9	−0.688876	−0.344438	+	0.938809i	$0.611931\pi$
$570$	1.84271e9	0.416769
$571$	−5.46830e9	−1.22921	−0.614605	−	0.788835i	$-0.710684\pi$
$571$	−5.46830e9	−1.22921	−0.614605	+	0.788835i	$0.710684\pi$
$572$	−2.39792e9	−0.535733
$573$	−2.10875e9	−0.468256
$574$	1.39428e8	0.0307721
$575$	6.20147e8	0.136037
$576$	4.16184e9	0.907417
$577$	−3.90545e9	−0.846362	−0.423181	−	0.906045i	$-0.639086\pi$
$577$	−3.90545e9	−0.846362	−0.423181	+	0.906045i	$0.639086\pi$
$578$	−8.52867e9	−1.83710
$579$	−3.74337e9	−0.801472
$580$	−5.38799e9	−1.14664
$581$	1.51131e9	0.319695
$582$	5.27945e7	0.0111009
$583$	−9.64340e9	−2.01553
$584$	3.46642e9	0.720172
$585$	−1.19029e8	−0.0245814
$586$	−1.20475e10	−2.47318
$587$	−7.98053e8	−0.162854	−0.0814270	−	0.996679i	$-0.525948\pi$
$587$	−7.98053e8	−0.162854	−0.0814270	+	0.996679i	$0.525948\pi$
$588$	1.06911e9	0.216871
$589$	−3.02572e9	−0.610133
$590$	−6.29230e8	−0.126133
$591$	5.50568e9	1.09712
$592$	−1.94473e10	−3.85242
$593$	8.47336e9	1.66865	0.834323	−	0.551275i	$-0.185859\pi$
$593$	8.47336e9	1.66865	0.834323	+	0.551275i	$0.185859\pi$
$594$	3.05059e9	0.597215
$595$	−2.16314e8	−0.0420993
$596$	−8.10213e9	−1.56761
$597$	−1.41028e8	−0.0271266
$598$	2.59838e8	0.0496877
$599$	−6.04158e9	−1.14857	−0.574284	−	0.818656i	$-0.694719\pi$
$599$	−6.04158e9	−1.14857	−0.574284	+	0.818656i	$0.694719\pi$
$600$	−6.18643e9	−1.16926
$601$	6.32153e9	1.18785	0.593925	−	0.804520i	$-0.297577\pi$
$601$	6.32153e9	1.18785	0.593925	+	0.804520i	$0.297577\pi$
$602$	−1.55561e9	−0.290612
$603$	−7.94877e7	−0.0147635
$604$	4.96531e9	0.916890
$605$	5.30925e9	0.974741
$606$	−6.86068e9	−1.25231
$607$	6.16023e9	1.11799	0.558993	−	0.829172i	$-0.311188\pi$
$607$	6.16023e9	1.11799	0.558993	+	0.829172i	$0.311188\pi$
$608$	1.12301e10	2.02637
$609$	−8.99678e8	−0.161409
$610$	6.61718e9	1.18037
$611$	−1.60568e8	−0.0284783
$612$	−9.38985e8	−0.165588
$613$	3.34351e9	0.586261	0.293131	−	0.956072i	$-0.405303\pi$
$613$	3.34351e9	0.586261	0.293131	+	0.956072i	$0.405303\pi$
$614$	6.95010e8	0.121172
$615$	8.39119e7	0.0145466
$616$	1.10874e10	1.91115
$617$	−3.68416e9	−0.631452	−0.315726	−	0.948850i	$-0.602248\pi$
$617$	−3.68416e9	−0.631452	−0.315726	+	0.948850i	$0.602248\pi$
$618$	1.12320e10	1.91424
$619$	−7.19102e9	−1.21863	−0.609317	−	0.792927i	$-0.708556\pi$
$619$	−7.19102e9	−1.21863	−0.609317	+	0.792927i	$0.708556\pi$
$620$	−8.73339e9	−1.47167
$621$	−2.39483e8	−0.0401286
$622$	1.09162e10	1.81888
$623$	1.36582e9	0.226300
$624$	−1.43958e9	−0.237187
$625$	4.76386e8	0.0780510
$626$	−2.27037e10	−3.69901
$627$	3.73057e9	0.604420
$628$	−6.87167e8	−0.110714
$629$	1.38307e9	0.221599
$630$	8.88123e8	0.141508
$631$	8.28681e9	1.31306	0.656530	−	0.754300i	$-0.272024\pi$
$631$	8.28681e9	1.31306	0.656530	+	0.754300i	$0.272024\pi$
$632$	−1.61372e10	−2.54284
$633$	4.58443e9	0.718410
$634$	−1.22159e10	−1.90376
$635$	3.36929e9	0.522192
$636$	−1.21869e10	−1.87843
$637$	−1.16569e8	−0.0178688
$638$	−1.50564e10	−2.29535
$639$	−6.00277e8	−0.0910120
$640$	7.94969e9	1.19873
$641$	−1.96665e9	−0.294934	−0.147467	−	0.989067i	$-0.547112\pi$
$641$	−1.96665e9	−0.294934	−0.147467	+	0.989067i	$0.547112\pi$
$642$	2.96592e9	0.442371
$643$	−1.43510e9	−0.212884	−0.106442	−	0.994319i	$-0.533946\pi$
$643$	−1.43510e9	−0.212884	−0.106442	+	0.994319i	$0.533946\pi$
$644$	−1.40458e9	−0.207227
$645$	−9.36215e8	−0.137378
$646$	−1.58500e9	−0.231321
$647$	1.14322e10	1.65946	0.829729	−	0.558166i	$-0.188495\pi$
$647$	1.14322e10	1.65946	0.829729	+	0.558166i	$0.188495\pi$
$648$	2.38902e9	0.344911
$649$	−1.27388e9	−0.182924
$650$	1.08851e9	0.155465
$651$	−1.45829e9	−0.207162
$652$	−1.52682e10	−2.15736
$653$	−1.22526e10	−1.72200	−0.861001	−	0.508603i	$-0.830162\pi$
$653$	−1.22526e10	−1.72200	−0.861001	+	0.508603i	$0.830162\pi$
$654$	5.65252e9	0.790169
$655$	3.97033e9	0.552055
$656$	1.01487e9	0.140361
$657$	5.62139e8	0.0773330
$658$	1.19806e9	0.163941
$659$	−1.39958e10	−1.90502	−0.952512	−	0.304502i	$-0.901510\pi$
$659$	−1.39958e10	−1.90502	−0.952512	+	0.304502i	$0.901510\pi$
$660$	1.07679e10	1.45789
$661$	−2.06828e9	−0.278551	−0.139276	−	0.990254i	$-0.544477\pi$
$661$	−2.06828e9	−0.278551	−0.139276	+	0.990254i	$0.544477\pi$
$662$	−1.53016e9	−0.204990
$663$	1.02382e8	0.0136435
$664$	1.98072e10	2.62564
$665$	1.08609e9	0.143215
$666$	−5.67850e9	−0.744858
$667$	1.18199e9	0.154231
$668$	−2.04273e9	−0.265151
$669$	7.94690e8	0.102614
$670$	−3.87279e8	−0.0497464
$671$	1.33965e10	1.71184
$672$	5.41250e9	0.688026
$673$	−4.18491e9	−0.529216	−0.264608	−	0.964356i	$-0.585243\pi$
$673$	−4.18491e9	−0.529216	−0.264608	+	0.964356i	$0.585243\pi$
$674$	1.41093e10	1.77500
$675$	−1.00323e9	−0.125557
$676$	−2.07885e10	−2.58828
$677$	1.08895e10	1.34880	0.674399	−	0.738368i	$-0.264403\pi$
$677$	1.08895e10	1.34880	0.674399	+	0.738368i	$0.264403\pi$
$678$	−4.57134e9	−0.563300
$679$	3.11168e7	0.00381462
$680$	−2.83501e9	−0.345759
$681$	2.52142e9	0.305936
$682$	−2.44049e10	−2.94600
$683$	4.62092e9	0.554952	0.277476	−	0.960733i	$-0.410502\pi$
$683$	4.62092e9	0.554952	0.277476	+	0.960733i	$0.410502\pi$
$684$	4.71454e9	0.563304
$685$	−8.52730e9	−1.01366
$686$	8.69773e8	0.102866
$687$	−6.38093e8	−0.0750819
$688$	−1.13230e10	−1.32557
$689$	1.32879e9	0.154771
$690$	−1.16681e9	−0.135216
$691$	1.06136e10	1.22374	0.611869	−	0.790959i	$-0.290418\pi$
$691$	1.06136e10	1.22374	0.611869	+	0.790959i	$0.290418\pi$
$692$	1.92030e10	2.20291
$693$	1.79800e9	0.205222
$694$	−1.97306e9	−0.224069
$695$	−6.08302e9	−0.687342
$696$	−1.17912e10	−1.32564
$697$	−7.21762e7	−0.00807382
$698$	2.21740e10	2.46802
$699$	−7.07702e9	−0.783755
$700$	−5.88403e9	−0.648383
$701$	−5.47178e9	−0.599950	−0.299975	−	0.953947i	$-0.596978\pi$
$701$	−5.47178e9	−0.599950	−0.299975	+	0.953947i	$0.596978\pi$
$702$	−4.20350e8	−0.0458597
$703$	−6.94425e9	−0.753844
$704$	4.10513e10	4.43428
$705$	7.21030e8	0.0774982
$706$	1.45991e10	1.56138
$707$	−4.04366e9	−0.430335
$708$	−1.60987e9	−0.170481
$709$	−7.13976e9	−0.752353	−0.376176	−	0.926548i	$-0.622761\pi$
$709$	−7.13976e9	−0.752353	−0.376176	+	0.926548i	$0.622761\pi$
$710$	−2.92466e9	−0.306670
$711$	−2.61692e9	−0.273053
$712$	1.79004e10	1.85859
$713$	1.91588e9	0.197950
$714$	−7.63912e8	−0.0785416
$715$	−1.17407e9	−0.120122
$716$	3.76880e10	3.83714
$717$	4.32943e9	0.438646
$718$	1.67808e10	1.69191
$719$	3.29169e9	0.330269	0.165135	−	0.986271i	$-0.447194\pi$
$719$	3.29169e9	0.330269	0.165135	+	0.986271i	$0.447194\pi$
$720$	6.46447e9	0.645460
$721$	6.62009e9	0.657795
$722$	−1.13082e10	−1.11819
$723$	5.28407e9	0.519978
$724$	−3.93905e9	−0.385751
$725$	4.95154e9	0.482567
$726$	1.87496e10	1.81850
$727$	−1.45423e10	−1.40366	−0.701830	−	0.712345i	$-0.747633\pi$
$727$	−1.45423e10	−1.40366	−0.701830	+	0.712345i	$0.747633\pi$
$728$	−1.52776e9	−0.146756
$729$	3.87420e8	0.0370370
$730$	2.73885e9	0.260578
$731$	8.05278e8	0.0762491
$732$	1.69299e10	1.59539
$733$	1.18109e10	1.10769	0.553844	−	0.832621i	$-0.313160\pi$
$733$	1.18109e10	1.10769	0.553844	+	0.832621i	$0.313160\pi$
$734$	9.66405e9	0.902034
$735$	5.23456e8	0.0486267
$736$	−7.11088e9	−0.657432
$737$	−7.84046e8	−0.0721448
$738$	2.96335e8	0.0271385
$739$	−9.48510e9	−0.864542	−0.432271	−	0.901744i	$-0.642288\pi$
$739$	−9.48510e9	−0.864542	−0.432271	+	0.901744i	$0.642288\pi$
$740$	−2.00438e10	−1.81831
$741$	−5.14047e8	−0.0464129
$742$	−9.91467e9	−0.890973
$743$	8.08215e8	0.0722879	0.0361440	−	0.999347i	$-0.488493\pi$
$743$	8.08215e8	0.0722879	0.0361440	+	0.999347i	$0.488493\pi$
$744$	−1.91124e10	−1.70141
$745$	−3.96696e9	−0.351488
$746$	2.33042e10	2.05517
$747$	3.21208e9	0.281945
$748$	−9.26191e9	−0.809179
$749$	1.74810e9	0.152013
$750$	−1.23801e10	−1.07154
$751$	−6.86614e9	−0.591525	−0.295763	−	0.955261i	$-0.595574\pi$
$751$	−6.86614e9	−0.591525	−0.295763	+	0.955261i	$0.595574\pi$
$752$	8.72045e9	0.747785
$753$	−6.15967e9	−0.525745
$754$	2.07467e9	0.176258
$755$	2.43111e9	0.205585
$756$	2.27224e9	0.191262
$757$	−1.86595e9	−0.156338	−0.0781692	−	0.996940i	$-0.524907\pi$
$757$	−1.86595e9	−0.156338	−0.0781692	+	0.996940i	$0.524907\pi$
$758$	2.90394e10	2.42184
$759$	−2.36220e9	−0.196097
$760$	1.42343e10	1.17622
$761$	8.04839e9	0.662007	0.331004	−	0.943630i	$-0.392613\pi$
$761$	8.04839e9	0.662007	0.331004	+	0.943630i	$0.392613\pi$
$762$	1.18986e10	0.974216
$763$	3.33157e9	0.271527
$764$	−2.62863e10	−2.13257
$765$	−4.59746e8	−0.0371281
$766$	−1.92627e10	−1.54852
$767$	1.75531e8	0.0140466
$768$	8.34411e9	0.664685
$769$	2.36466e10	1.87511	0.937555	−	0.347837i	$-0.113084\pi$
$769$	2.36466e10	1.87511	0.937555	+	0.347837i	$0.113084\pi$
$770$	8.76021e9	0.691508
$771$	−4.68493e9	−0.368140
$772$	−4.66626e10	−3.65013
$773$	2.04615e9	0.159334	0.0796671	−	0.996822i	$-0.474614\pi$
$773$	2.04615e9	0.159334	0.0796671	+	0.996822i	$0.474614\pi$
$774$	−3.30624e9	−0.256296
$775$	8.02596e9	0.619357
$776$	4.07818e8	0.0313293
$777$	−3.34688e9	−0.255957
$778$	−3.34221e10	−2.54452
$779$	3.62388e8	0.0274659
$780$	−1.48374e9	−0.111950
$781$	−5.92097e9	−0.444749
$782$	1.00362e9	0.0750491
$783$	−1.91214e9	−0.142349
$784$	6.33090e9	0.469201
$785$	−3.36451e8	−0.0248243
$786$	1.40212e10	1.02993
$787$	−1.77353e10	−1.29696	−0.648481	−	0.761231i	$-0.724595\pi$
$787$	−1.77353e10	−1.29696	−0.648481	+	0.761231i	$0.724595\pi$
$788$	6.86303e10	4.99660
$789$	9.76274e9	0.707623
$790$	−1.27501e10	−0.920067
$791$	−2.69433e9	−0.193568
$792$	2.35647e10	1.68548
$793$	−1.84594e9	−0.131450
$794$	4.60361e10	3.26382
$795$	−5.96696e9	−0.421180
$796$	−1.75797e9	−0.123542
$797$	1.22200e10	0.855003	0.427501	−	0.904015i	$-0.359394\pi$
$797$	1.22200e10	0.855003	0.427501	+	0.904015i	$0.359394\pi$
$798$	3.83552e9	0.267186
$799$	−6.20189e8	−0.0430140
$800$	−2.97887e10	−2.05701
$801$	2.90286e9	0.199578
$802$	−2.24721e10	−1.53827
$803$	5.54479e9	0.377904
$804$	−9.90844e8	−0.0672371
$805$	−6.87711e8	−0.0464644
$806$	3.36283e9	0.226221
$807$	−1.52761e10	−1.02319
$808$	−5.29963e10	−3.53432
$809$	9.33616e9	0.619938	0.309969	−	0.950747i	$-0.399681\pi$
$809$	9.33616e9	0.619938	0.309969	+	0.950747i	$0.399681\pi$
$810$	1.88758e9	0.124798
$811$	−1.29585e10	−0.853061	−0.426531	−	0.904473i	$-0.640264\pi$
$811$	−1.29585e10	−0.853061	−0.426531	+	0.904473i	$0.640264\pi$
$812$	−1.12148e10	−0.735100
$813$	5.67250e9	0.370218
$814$	−5.60112e10	−3.63990
$815$	−7.47563e9	−0.483723
$816$	−5.56036e9	−0.358251
$817$	−4.04321e9	−0.259387
$818$	−3.72165e10	−2.37738
$819$	−2.47752e8	−0.0157588
$820$	1.04599e9	0.0662492
$821$	−1.49829e10	−0.944920	−0.472460	−	0.881352i	$-0.656634\pi$
$821$	−1.49829e10	−0.944920	−0.472460	+	0.881352i	$0.656634\pi$
$822$	−3.01141e10	−1.89112
$823$	2.34444e10	1.46602	0.733009	−	0.680219i	$-0.238115\pi$
$823$	2.34444e10	1.46602	0.733009	+	0.680219i	$0.238115\pi$
$824$	8.67631e10	5.40244
$825$	−9.89564e9	−0.613557
$826$	−1.30971e9	−0.0808622
$827$	−4.86551e9	−0.299130	−0.149565	−	0.988752i	$-0.547787\pi$
$827$	−4.86551e9	−0.299130	−0.149565	+	0.988752i	$0.547787\pi$
$828$	−2.98525e9	−0.182757
$829$	−1.63612e10	−0.997412	−0.498706	−	0.866771i	$-0.666191\pi$
$829$	−1.63612e10	−0.997412	−0.498706	+	0.866771i	$0.666191\pi$
$830$	1.56498e10	0.950028
$831$	8.25138e9	0.498796
$832$	−5.65658e9	−0.340504
$833$	−4.50247e8	−0.0269894
$834$	−2.14822e10	−1.28232
$835$	−1.00016e9	−0.0594522
$836$	4.65030e10	2.75270
$837$	−3.09939e9	−0.182700
$838$	3.46704e10	2.03519
$839$	2.80045e10	1.63705	0.818523	−	0.574474i	$-0.194793\pi$
$839$	2.80045e10	1.63705	0.818523	+	0.574474i	$0.194793\pi$
$840$	6.86042e9	0.399368
$841$	−7.81234e9	−0.452892
$842$	−3.36798e10	−1.94436
$843$	−8.39317e9	−0.482536
$844$	5.71466e10	3.27184
$845$	−1.01785e10	−0.580343
$846$	2.54632e9	0.144583
$847$	1.10509e10	0.624895
$848$	−7.21669e10	−4.06399
$849$	9.16928e9	0.514231
$850$	4.20433e9	0.234818
$851$	4.39710e9	0.244575
$852$	−7.48268e9	−0.414494
$853$	4.49480e9	0.247964	0.123982	−	0.992284i	$-0.460433\pi$
$853$	4.49480e9	0.247964	0.123982	+	0.992284i	$0.460433\pi$
$854$	1.37733e10	0.756723
$855$	2.30833e9	0.126304
$856$	2.29106e10	1.24847
$857$	1.38068e10	0.749310	0.374655	−	0.927164i	$-0.377761\pi$
$857$	1.38068e10	0.749310	0.374655	+	0.927164i	$0.377761\pi$
$858$	−4.14622e9	−0.224103
$859$	3.75224e9	0.201983	0.100992	−	0.994887i	$-0.467799\pi$
$859$	3.75224e9	0.201983	0.100992	+	0.994887i	$0.467799\pi$
$860$	−1.16703e10	−0.625657
$861$	1.74658e8	0.00932564
$862$	−4.42148e10	−2.35121
$863$	2.42630e10	1.28501	0.642506	−	0.766281i	$-0.277895\pi$
$863$	2.42630e10	1.28501	0.642506	+	0.766281i	$0.277895\pi$
$864$	1.15035e10	0.606782
$865$	9.40217e9	0.493937
$866$	−3.43068e9	−0.179501
$867$	−1.06837e10	−0.556743
$868$	−1.81781e10	−0.943474
$869$	−2.58126e10	−1.33433
$870$	−9.31632e9	−0.479653
$871$	1.08036e8	0.00553994
$872$	4.36637e10	2.23004
$873$	6.61346e7	0.00336418
$874$	−5.03906e9	−0.255305
$875$	−7.29676e9	−0.368216
$876$	7.00728e9	0.352196
$877$	1.44528e10	0.723525	0.361762	−	0.932270i	$-0.382175\pi$
$877$	1.44528e10	0.723525	0.361762	+	0.932270i	$0.382175\pi$
$878$	2.67537e10	1.33399
$879$	−1.50917e10	−0.749509
$880$	6.37638e10	3.15417
$881$	1.21598e10	0.599115	0.299558	−	0.954078i	$-0.403161\pi$
$881$	1.21598e10	0.599115	0.299558	+	0.954078i	$0.403161\pi$
$882$	1.84858e9	0.0907192
$883$	2.59186e10	1.26692	0.633459	−	0.773776i	$-0.281634\pi$
$883$	2.59186e10	1.26692	0.633459	+	0.773776i	$0.281634\pi$
$884$	1.27623e9	0.0621362
$885$	−7.88225e8	−0.0382251
$886$	3.73644e10	1.80484
$887$	−2.40445e10	−1.15686	−0.578432	−	0.815731i	$-0.696335\pi$
$887$	−2.40445e10	−1.15686	−0.578432	+	0.815731i	$0.696335\pi$
$888$	−4.38643e10	−2.10216
$889$	7.01301e9	0.334771
$890$	1.41433e10	0.672489
$891$	3.82141e9	0.180989
$892$	9.90611e9	0.467333
$893$	3.11390e9	0.146327
$894$	−1.40093e10	−0.655746
$895$	1.84528e10	0.860363
$896$	1.65469e10	0.768490
$897$	3.25494e8	0.0150581
$898$	1.74789e10	0.805467
$899$	1.52973e10	0.702192
$900$	−1.25057e10	−0.571820
$901$	5.13243e9	0.233769
$902$	2.92297e9	0.132618
$903$	−1.94868e9	−0.0880713
$904$	−3.53120e10	−1.58976
$905$	−1.92864e9	−0.0864929
$906$	8.58547e9	0.383544
$907$	2.31516e10	1.03028	0.515140	−	0.857106i	$-0.327740\pi$
$907$	2.31516e10	1.03028	0.515140	+	0.857106i	$0.327740\pi$
$908$	3.14304e10	1.39332
$909$	−8.59425e9	−0.379520
$910$	−1.20710e9	−0.0531003
$911$	2.82330e10	1.23721	0.618605	−	0.785703i	$-0.287698\pi$
$911$	2.82330e10	1.23721	0.618605	+	0.785703i	$0.287698\pi$
$912$	2.79180e10	1.21871
$913$	3.16831e10	1.37778
$914$	−5.69704e10	−2.46796
$915$	8.28922e9	0.357717
$916$	−7.95407e9	−0.341944
$917$	8.26405e9	0.353916
$918$	−1.62359e9	−0.0692672
$919$	1.20968e10	0.514123	0.257062	−	0.966395i	$-0.417246\pi$
$919$	1.20968e10	0.514123	0.257062	+	0.966395i	$0.417246\pi$
$920$	−9.01315e9	−0.381610
$921$	8.70626e8	0.0367217
$922$	7.91405e10	3.32538
$923$	8.15869e8	0.0341519
$924$	2.24128e10	0.934640
$925$	1.84202e10	0.765240
$926$	7.84279e10	3.24588
$927$	1.40701e10	0.580121
$928$	−5.67766e10	−2.33212
$929$	−1.36433e10	−0.558294	−0.279147	−	0.960248i	$-0.590052\pi$
$929$	−1.36433e10	−0.558294	−0.279147	+	0.960248i	$0.590052\pi$
$930$	−1.51008e10	−0.615617
$931$	2.26064e9	0.0918136
$932$	−8.82177e10	−3.56944
$933$	1.36745e10	0.551219
$934$	−4.72167e10	−1.89619
$935$	−4.53481e9	−0.181434
$936$	−3.24705e9	−0.129427
$937$	3.40873e10	1.35364	0.676821	−	0.736148i	$-0.263357\pi$
$937$	3.40873e10	1.35364	0.676821	+	0.736148i	$0.263357\pi$
$938$	−8.06102e8	−0.0318919
$939$	−2.84404e10	−1.12100
$940$	8.98791e9	0.352949
$941$	4.28634e10	1.67696	0.838481	−	0.544932i	$-0.183444\pi$
$941$	4.28634e10	1.67696	0.838481	+	0.544932i	$0.183444\pi$
$942$	−1.18817e9	−0.0463129
$943$	−2.29464e8	−0.00891095
$944$	−9.53313e9	−0.368836
$945$	1.11253e9	0.0428847
$946$	−3.26119e10	−1.25244
$947$	−5.53374e9	−0.211735	−0.105868	−	0.994380i	$-0.533762\pi$
$947$	−5.53374e9	−0.211735	−0.105868	+	0.994380i	$0.533762\pi$
$948$	−3.26209e10	−1.24356
$949$	−7.64034e8	−0.0290189
$950$	−2.11095e10	−0.798812
$951$	−1.53026e10	−0.576944
$952$	−5.90094e9	−0.221662
$953$	3.36613e10	1.25981	0.629907	−	0.776671i	$-0.283093\pi$
$953$	3.36613e10	1.25981	0.629907	+	0.776671i	$0.283093\pi$
$954$	−2.10723e10	−0.785765
$955$	−1.28703e10	−0.478164
$956$	5.39680e10	1.99772
$957$	−1.88609e10	−0.695617
$958$	9.27304e10	3.40755
$959$	−1.77491e10	−0.649849
$960$	2.54009e10	0.926618
$961$	−2.71722e9	−0.0987625
$962$	7.71795e9	0.279505
$963$	3.71535e9	0.134062
$964$	6.58680e10	2.36813
$965$	−2.28469e10	−0.818431
$966$	−2.42865e9	−0.0866852
$967$	4.92834e10	1.75270	0.876351	−	0.481673i	$-0.159971\pi$
$967$	4.92834e10	1.75270	0.876351	+	0.481673i	$0.159971\pi$
$968$	1.44834e11	5.13223
$969$	−1.98549e9	−0.0701028
$970$	3.22220e8	0.0113358
$971$	2.56120e10	0.897793	0.448896	−	0.893584i	$-0.351817\pi$
$971$	2.56120e10	0.897793	0.448896	+	0.893584i	$0.351817\pi$
$972$	4.82934e9	0.168677
$973$	−1.26615e10	−0.440647
$974$	−3.73652e10	−1.29572
$975$	1.36355e9	0.0471145
$976$	1.00253e11	3.45163
$977$	2.47618e10	0.849475	0.424737	−	0.905317i	$-0.360366\pi$
$977$	2.47618e10	0.849475	0.424737	+	0.905317i	$0.360366\pi$
$978$	−2.64002e10	−0.902446
$979$	2.86331e10	0.975278
$980$	6.52507e9	0.221459
$981$	7.08081e9	0.239465
$982$	−1.97849e10	−0.666719
$983$	−2.11745e10	−0.711010	−0.355505	−	0.934674i	$-0.615691\pi$
$983$	−2.11745e10	−0.711010	−0.355505	+	0.934674i	$0.615691\pi$
$984$	2.28908e9	0.0765910
$985$	3.36028e10	1.12034
$986$	8.01336e9	0.266223
$987$	1.50079e9	0.0496832
$988$	−6.40778e9	−0.211377
$989$	2.56016e9	0.0841550
$990$	1.86186e10	0.609852
$991$	−5.53778e9	−0.180750	−0.0903750	−	0.995908i	$-0.528807\pi$
$991$	−5.53778e9	−0.180750	−0.0903750	+	0.995908i	$0.528807\pi$
$992$	−9.20291e10	−2.99319
$993$	−1.91680e9	−0.0621232
$994$	−6.08754e9	−0.196603
$995$	−8.60735e8	−0.0277006
$996$	4.00398e10	1.28406
$997$	8.60175e9	0.274887	0.137443	−	0.990510i	$-0.456112\pi$
$997$	8.60175e9	0.274887	0.137443	+	0.990510i	$0.456112\pi$
$998$	6.51795e10	2.07565
$999$	−7.11335e9	−0.225733

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.8.a.h.1.20	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.8.a.h.1.20	✓	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)

\(f(q)\)	\(=\)	\(q+21.5538 q^{2} +27.0000 q^{3} +336.565 q^{4} +164.789 q^{5} +581.952 q^{6} +343.000 q^{7} +4495.37 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+21.5538 q^{2} +27.0000 q^{3} +336.565 q^{4} +164.789 q^{5} +581.952 q^{6} +343.000 q^{7} +4495.37 q^{8} +729.000 q^{9} +3551.82 q^{10} +7190.66 q^{11} +9087.26 q^{12} -990.823 q^{13} +7392.94 q^{14} +4449.30 q^{15} +53811.8 q^{16} -3827.03 q^{17} +15712.7 q^{18} +19215.1 q^{19} +55462.2 q^{20} +9261.00 q^{21} +154986. q^{22} -12167.0 q^{23} +121375. q^{24} -50969.6 q^{25} -21356.0 q^{26} +19683.0 q^{27} +115442. q^{28} -97147.0 q^{29} +95899.2 q^{30} -157466. q^{31} +584440. q^{32} +194148. q^{33} -82487.0 q^{34} +56522.6 q^{35} +245356. q^{36} -361395. q^{37} +414158. q^{38} -26752.2 q^{39} +740787. q^{40} +18859.6 q^{41} +199609. q^{42} -210418. q^{43} +2.42013e6 q^{44} +120131. q^{45} -262245. q^{46} +162055. q^{47} +1.45292e6 q^{48} +117649. q^{49} -1.09859e6 q^{50} -103330. q^{51} -333477. q^{52} -1.34110e6 q^{53} +424243. q^{54} +1.18494e6 q^{55} +1.54191e6 q^{56} +518808. q^{57} -2.09388e6 q^{58} -177157. q^{59} +1.49748e6 q^{60} +1.86304e6 q^{61} -3.39398e6 q^{62} +250047. q^{63} +5.70897e6 q^{64} -163277. q^{65} +4.18462e6 q^{66} -109037. q^{67} -1.28805e6 q^{68} -328509. q^{69} +1.21828e6 q^{70} -823425. q^{71} +3.27712e6 q^{72} +771110. q^{73} -7.78944e6 q^{74} -1.37618e6 q^{75} +6.46713e6 q^{76} +2.46640e6 q^{77} -576611. q^{78} -3.58974e6 q^{79} +8.86758e6 q^{80} +531441. q^{81} +406495. q^{82} +4.40614e6 q^{83} +3.11693e6 q^{84} -630653. q^{85} -4.53531e6 q^{86} -2.62297e6 q^{87} +3.23247e7 q^{88} +3.98198e6 q^{89} +2.58928e6 q^{90} -339852. q^{91} -4.09499e6 q^{92} -4.25157e6 q^{93} +3.49289e6 q^{94} +3.16644e6 q^{95} +1.57799e7 q^{96} +90719.7 q^{97} +2.53578e6 q^{98} +5.24199e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 24 q^{2} + 540 q^{3} + 1486 q^{4} + 1069 q^{5} + 648 q^{6} + 6860 q^{7} + 2127 q^{8} + 14580 q^{9}+O(q^{10}) \) 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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