LMFDB - Embedded newform 483.8.a.h.1.12

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			1.12
Root			$5.08154$ 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)

$f(q)$	$=$	$q+6.08154 q^{2} +27.0000 q^{3} -91.0149 q^{4} +440.690 q^{5} +164.202 q^{6} +343.000 q^{7} -1331.95 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+6.08154 q^{2} +27.0000 q^{3} -91.0149 q^{4} +440.690 q^{5} +164.202 q^{6} +343.000 q^{7} -1331.95 q^{8} +729.000 q^{9} +2680.07 q^{10} +6337.99 q^{11} -2457.40 q^{12} -15114.8 q^{13} +2085.97 q^{14} +11898.6 q^{15} +3549.61 q^{16} +21161.0 q^{17} +4433.44 q^{18} -14018.4 q^{19} -40109.3 q^{20} +9261.00 q^{21} +38544.7 q^{22} -12167.0 q^{23} -35962.6 q^{24} +116082. q^{25} -91921.1 q^{26} +19683.0 q^{27} -31218.1 q^{28} +127341. q^{29} +72361.9 q^{30} +78628.9 q^{31} +192076. q^{32} +171126. q^{33} +128692. q^{34} +151157. q^{35} -66349.8 q^{36} +98709.4 q^{37} -85253.7 q^{38} -408099. q^{39} -586976. q^{40} +104723. q^{41} +56321.1 q^{42} -463986. q^{43} -576851. q^{44} +321263. q^{45} -73994.1 q^{46} +810921. q^{47} +95839.5 q^{48} +117649. q^{49} +705960. q^{50} +571348. q^{51} +1.37567e6 q^{52} +588730. q^{53} +119703. q^{54} +2.79309e6 q^{55} -456858. q^{56} -378498. q^{57} +774429. q^{58} -1.86953e6 q^{59} -1.08295e6 q^{60} +2.02175e6 q^{61} +478185. q^{62} +250047. q^{63} +713770. q^{64} -6.66093e6 q^{65} +1.04071e6 q^{66} -1.21344e6 q^{67} -1.92597e6 q^{68} -328509. q^{69} +919265. q^{70} +628331. q^{71} -970990. q^{72} +1.14120e6 q^{73} +600305. q^{74} +3.13422e6 q^{75} +1.27589e6 q^{76} +2.17393e6 q^{77} -2.48187e6 q^{78} -2.45505e6 q^{79} +1.56428e6 q^{80} +531441. q^{81} +636874. q^{82} +5.53752e6 q^{83} -842889. q^{84} +9.32545e6 q^{85} -2.82175e6 q^{86} +3.43821e6 q^{87} -8.44187e6 q^{88} +7.12729e6 q^{89} +1.95377e6 q^{90} -5.18437e6 q^{91} +1.10738e6 q^{92} +2.12298e6 q^{93} +4.93165e6 q^{94} -6.17778e6 q^{95} +5.18606e6 q^{96} -4.16914e6 q^{97} +715487. q^{98} +4.62039e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	6.08154	0.537537	0.268769	−	0.963205i	$-0.413383\pi$
$2$	6.08154	0.537537	0.268769	+	0.963205i	$0.413383\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	−91.0149	−0.711054
$5$	440.690	1.57666	0.788330	−	0.615253i	$-0.210946\pi$
$5$	440.690	1.57666	0.788330	+	0.615253i	$0.210946\pi$
$6$	164.202	0.310347
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−1331.95	−0.919755
$9$	729.000	0.333333
$10$	2680.07	0.847513
$11$	6337.99	1.43574	0.717872	−	0.696175i	$-0.245116\pi$
$11$	6337.99	1.43574	0.717872	+	0.696175i	$0.245116\pi$
$12$	−2457.40	−0.410527
$13$	−15114.8	−1.90810	−0.954048	−	0.299655i	$-0.903128\pi$
$13$	−15114.8	−1.90810	−0.954048	+	0.299655i	$0.903128\pi$
$14$	2085.97	0.203170
$15$	11898.6	0.910285
$16$	3549.61	0.216651
$17$	21161.0	1.04464	0.522319	−	0.852750i	$-0.325067\pi$
$17$	21161.0	1.04464	0.522319	+	0.852750i	$0.325067\pi$
$18$	4433.44	0.179179
$19$	−14018.4	−0.468880	−0.234440	−	0.972131i	$-0.575326\pi$
$19$	−14018.4	−0.468880	−0.234440	+	0.972131i	$0.575326\pi$
$20$	−40109.3	−1.12109
$21$	9261.00	0.218218
$22$	38544.7	0.771766
$23$	−12167.0	−0.208514
$23$	−12167.0	−0.208514
$24$	−35962.6	−0.531021
$25$	116082.	1.48585
$26$	−91921.1	−1.02567
$27$	19683.0	0.192450
$28$	−31218.1	−0.268753
$29$	127341.	0.969561	0.484780	−	0.874636i	$-0.338900\pi$
$29$	127341.	0.969561	0.484780	+	0.874636i	$0.338900\pi$
$30$	72361.9	0.489312
$31$	78628.9	0.474041	0.237021	−	0.971505i	$-0.423829\pi$
$31$	78628.9	0.474041	0.237021	+	0.971505i	$0.423829\pi$
$32$	192076.	1.03621
$33$	171126.	0.828927
$34$	128692.	0.561532
$35$	151157.	0.595921
$36$	−66349.8	−0.237018
$37$	98709.4	0.320371	0.160185	−	0.987087i	$-0.448791\pi$
$37$	98709.4	0.320371	0.160185	+	0.987087i	$0.448791\pi$
$38$	−85253.7	−0.252041
$39$	−408099.	−1.10164
$40$	−586976.	−1.45014
$41$	104723.	0.237299	0.118650	−	0.992936i	$-0.462143\pi$
$41$	104723.	0.237299	0.118650	+	0.992936i	$0.462143\pi$
$42$	56321.1	0.117300
$43$	−463986.	−0.889950	−0.444975	−	0.895543i	$-0.646787\pi$
$43$	−463986.	−0.889950	−0.444975	+	0.895543i	$0.646787\pi$
$44$	−576851.	−1.02089
$45$	321263.	0.525553
$46$	−73994.1	−0.112084
$47$	810921.	1.13930	0.569648	−	0.821889i	$-0.307080\pi$
$47$	810921.	1.13930	0.569648	+	0.821889i	$0.307080\pi$
$48$	95839.5	0.125084
$49$	117649.	0.142857
$50$	705960.	0.798702
$51$	571348.	0.603122
$52$	1.37567e6	1.35676
$53$	588730.	0.543189	0.271594	−	0.962412i	$-0.412449\pi$
$53$	588730.	0.543189	0.271594	+	0.962412i	$0.412449\pi$
$54$	119703.	0.103449
$55$	2.79309e6	2.26368
$56$	−456858.	−0.347635
$57$	−378498.	−0.270708
$58$	774429.	0.521175
$59$	−1.86953e6	−1.18509	−0.592543	−	0.805539i	$-0.701876\pi$
$59$	−1.86953e6	−1.18509	−0.592543	+	0.805539i	$0.701876\pi$
$60$	−1.08295e6	−0.647261
$61$	2.02175e6	1.14044	0.570220	−	0.821492i	$-0.306858\pi$
$61$	2.02175e6	1.14044	0.570220	+	0.821492i	$0.306858\pi$
$62$	478185.	0.254815
$63$	250047.	0.125988
$64$	713770.	0.340352
$65$	−6.66093e6	−3.00842
$66$	1.04071e6	0.445579
$67$	−1.21344e6	−0.492897	−0.246448	−	0.969156i	$-0.579264\pi$
$67$	−1.21344e6	−0.492897	−0.246448	+	0.969156i	$0.579264\pi$
$68$	−1.92597e6	−0.742794
$69$	−328509.	−0.120386
$70$	919265.	0.320330
$71$	628331.	0.208346	0.104173	−	0.994559i	$-0.466781\pi$
$71$	628331.	0.208346	0.104173	+	0.994559i	$0.466781\pi$
$72$	−970990.	−0.306585
$73$	1.14120e6	0.343344	0.171672	−	0.985154i	$-0.445083\pi$
$73$	1.14120e6	0.343344	0.171672	+	0.985154i	$0.445083\pi$
$74$	600305.	0.172211
$75$	3.13422e6	0.857859
$76$	1.27589e6	0.333399
$77$	2.17393e6	0.542660
$78$	−2.48187e6	−0.592172
$79$	−2.45505e6	−0.560230	−0.280115	−	0.959966i	$-0.590373\pi$
$79$	−2.45505e6	−0.560230	−0.280115	+	0.959966i	$0.590373\pi$
$80$	1.56428e6	0.341585
$81$	531441.	0.111111
$82$	636874.	0.127557
$83$	5.53752e6	1.06302	0.531511	−	0.847051i	$-0.321624\pi$
$83$	5.53752e6	1.06302	0.531511	+	0.847051i	$0.321624\pi$
$84$	−842889.	−0.155165
$85$	9.32545e6	1.64704
$86$	−2.82175e6	−0.478381
$87$	3.43821e6	0.559776
$88$	−8.44187e6	−1.32053
$89$	7.12729e6	1.07167	0.535833	−	0.844324i	$-0.319998\pi$
$89$	7.12729e6	1.07167	0.535833	+	0.844324i	$0.319998\pi$
$90$	1.95377e6	0.282504
$91$	−5.18437e6	−0.721192
$92$	1.10738e6	0.148265
$93$	2.12298e6	0.273688
$94$	4.93165e6	0.612414
$95$	−6.17778e6	−0.739265
$96$	5.18606e6	0.598258
$97$	−4.16914e6	−0.463816	−0.231908	−	0.972738i	$-0.574497\pi$
$97$	−4.16914e6	−0.463816	−0.231908	+	0.972738i	$0.574497\pi$
$98$	715487.	0.0767910
$99$	4.62039e6	0.478581
$100$	−1.05652e7	−1.05652
$101$	−1.06779e7	−1.03124	−0.515619	−	0.856818i	$-0.672438\pi$
$101$	−1.06779e7	−1.03124	−0.515619	+	0.856818i	$0.672438\pi$
$102$	3.47468e6	0.324200
$103$	−6.12899e6	−0.552661	−0.276330	−	0.961063i	$-0.589118\pi$
$103$	−6.12899e6	−0.552661	−0.276330	+	0.961063i	$0.589118\pi$
$104$	2.01321e7	1.75498
$105$	4.08123e6	0.344055
$106$	3.58039e6	0.291984
$107$	−1.75330e7	−1.38361	−0.691804	−	0.722085i	$-0.743184\pi$
$107$	−1.75330e7	−1.38361	−0.691804	+	0.722085i	$0.743184\pi$
$108$	−1.79145e6	−0.136842
$109$	1.00742e7	0.745103	0.372552	−	0.928011i	$-0.378483\pi$
$109$	1.00742e7	0.745103	0.372552	+	0.928011i	$0.378483\pi$
$110$	1.69863e7	1.21681
$111$	2.66515e6	0.184966
$112$	1.21752e6	0.0818864
$113$	6.64358e6	0.433139	0.216570	−	0.976267i	$-0.430513\pi$
$113$	6.64358e6	0.433139	0.216570	+	0.976267i	$0.430513\pi$
$114$	−2.30185e6	−0.145516
$115$	−5.36187e6	−0.328756
$116$	−1.15899e7	−0.689410
$117$	−1.10187e7	−0.636032
$118$	−1.13696e7	−0.637028
$119$	7.25824e6	0.394836
$120$	−1.58483e7	−0.837239
$121$	2.06829e7	1.06136
$122$	1.22953e7	0.613029
$123$	2.82751e6	0.137005
$124$	−7.15640e6	−0.337069
$125$	1.67274e7	0.766027
$126$	1.52067e6	0.0677233
$127$	3.61361e7	1.56541	0.782705	−	0.622393i	$-0.213839\pi$
$127$	3.61361e7	1.56541	0.782705	+	0.622393i	$0.213839\pi$
$128$	−2.02450e7	−0.853261
$129$	−1.25276e7	−0.513813
$130$	−4.05087e7	−1.61714
$131$	2.56576e7	0.997165	0.498582	−	0.866842i	$-0.333854\pi$
$131$	2.56576e7	0.997165	0.498582	+	0.866842i	$0.333854\pi$
$132$	−1.55750e7	−0.589412
$133$	−4.80832e6	−0.177220
$134$	−7.37958e6	−0.264950
$135$	8.67409e6	0.303428
$136$	−2.81854e7	−0.960811
$137$	5.12274e7	1.70208	0.851041	−	0.525099i	$-0.175972\pi$
$137$	5.12274e7	1.70208	0.851041	+	0.525099i	$0.175972\pi$
$138$	−1.99784e6	−0.0647119
$139$	1.98679e7	0.627481	0.313741	−	0.949509i	$-0.398418\pi$
$139$	1.98679e7	0.627481	0.313741	+	0.949509i	$0.398418\pi$
$140$	−1.37575e7	−0.423732
$141$	2.18949e7	0.657772
$142$	3.82122e6	0.111994
$143$	−9.57973e7	−2.73954
$144$	2.58767e6	0.0722170
$145$	5.61178e7	1.52867
$146$	6.94022e6	0.184560
$147$	3.17652e6	0.0824786
$148$	−8.98403e6	−0.227801
$149$	−8.32985e6	−0.206293	−0.103147	−	0.994666i	$-0.532891\pi$
$149$	−8.32985e6	−0.206293	−0.103147	+	0.994666i	$0.532891\pi$
$150$	1.90609e7	0.461131
$151$	−2.77678e7	−0.656329	−0.328164	−	0.944621i	$-0.606430\pi$
$151$	−2.77678e7	−0.656329	−0.328164	+	0.944621i	$0.606430\pi$
$152$	1.86718e7	0.431255
$153$	1.54264e7	0.348213
$154$	1.32208e7	0.291700
$155$	3.46509e7	0.747401
$156$	3.71431e7	0.783325
$157$	5.33595e7	1.10043	0.550216	−	0.835022i	$-0.314545\pi$
$157$	5.33595e7	1.10043	0.550216	+	0.835022i	$0.314545\pi$
$158$	−1.49305e7	−0.301144
$159$	1.58957e7	0.313610
$160$	8.46461e7	1.63376
$161$	−4.17328e6	−0.0788110
$162$	3.23198e6	0.0597264
$163$	4.22644e7	0.764396	0.382198	−	0.924081i	$-0.375167\pi$
$163$	4.22644e7	0.764396	0.382198	+	0.924081i	$0.375167\pi$
$164$	−9.53131e6	−0.168733
$165$	7.54133e7	1.30694
$166$	3.36767e7	0.571414
$167$	3.05136e7	0.506975	0.253487	−	0.967339i	$-0.418422\pi$
$167$	3.05136e7	0.506975	0.253487	+	0.967339i	$0.418422\pi$
$168$	−1.23352e7	−0.200707
$169$	1.65708e8	2.64083
$170$	5.67131e7	0.885344
$171$	−1.02194e7	−0.156293
$172$	4.22297e7	0.632802
$173$	−1.06619e8	−1.56557	−0.782787	−	0.622290i	$-0.786202\pi$
$173$	−1.06619e8	−1.56557	−0.782787	+	0.622290i	$0.786202\pi$
$174$	2.09096e7	0.300901
$175$	3.98163e7	0.561600
$176$	2.24974e7	0.311055
$177$	−5.04773e7	−0.684210
$178$	4.33449e7	0.576060
$179$	−3.98722e7	−0.519618	−0.259809	−	0.965660i	$-0.583660\pi$
$179$	−3.98722e7	−0.519618	−0.259809	+	0.965660i	$0.583660\pi$
$180$	−2.92397e7	−0.373696
$181$	1.48670e8	1.86358	0.931789	−	0.363000i	$-0.118248\pi$
$181$	1.48670e8	1.86358	0.931789	+	0.363000i	$0.118248\pi$
$182$	−3.15289e7	−0.387668
$183$	5.45872e7	0.658434
$184$	1.62058e7	0.191782
$185$	4.35002e7	0.505115
$186$	1.29110e7	0.147117
$187$	1.34118e8	1.49983
$188$	−7.38059e7	−0.810100
$189$	6.75127e6	0.0727393
$190$	−3.75704e7	−0.397382
$191$	1.70355e8	1.76904	0.884520	−	0.466502i	$-0.154486\pi$
$191$	1.70355e8	1.76904	0.884520	+	0.466502i	$0.154486\pi$
$192$	1.92718e7	0.196502
$193$	−3.58285e7	−0.358738	−0.179369	−	0.983782i	$-0.557406\pi$
$193$	−3.58285e7	−0.358738	−0.179369	+	0.983782i	$0.557406\pi$
$194$	−2.53548e7	−0.249318
$195$	−1.79845e8	−1.73691
$196$	−1.07078e7	−0.101579
$197$	−1.47948e8	−1.37872	−0.689362	−	0.724417i	$-0.742109\pi$
$197$	−1.47948e8	−1.37872	−0.689362	+	0.724417i	$0.742109\pi$
$198$	2.80991e7	0.257255
$199$	−3.83118e7	−0.344625	−0.172312	−	0.985042i	$-0.555124\pi$
$199$	−3.83118e7	−0.344625	−0.172312	+	0.985042i	$0.555124\pi$
$200$	−1.54616e8	−1.36662
$201$	−3.27628e7	−0.284574
$202$	−6.49378e7	−0.554329
$203$	4.36779e7	0.366460
$204$	−5.20012e7	−0.428852
$205$	4.61501e7	0.374140
$206$	−3.72737e7	−0.297076
$207$	−8.86974e6	−0.0695048
$208$	−5.36516e7	−0.413391
$209$	−8.88487e7	−0.673192
$210$	2.48201e7	0.184943
$211$	−1.54272e7	−0.113057	−0.0565287	−	0.998401i	$-0.518003\pi$
$211$	−1.54272e7	−0.113057	−0.0565287	+	0.998401i	$0.518003\pi$
$212$	−5.35832e7	−0.386236
$213$	1.69649e7	0.120288
$214$	−1.06628e8	−0.743741
$215$	−2.04474e8	−1.40315
$216$	−2.62167e7	−0.177007
$217$	2.69697e7	0.179171
$218$	6.12665e7	0.400521
$219$	3.08123e7	0.198230
$220$	−2.54212e8	−1.60960
$221$	−3.19844e8	−1.99327
$222$	1.62082e7	0.0994261
$223$	1.77155e8	1.06976	0.534880	−	0.844928i	$-0.320357\pi$
$223$	1.77155e8	1.06976	0.534880	+	0.844928i	$0.320357\pi$
$224$	6.58822e7	0.391652
$225$	8.46241e7	0.495285
$226$	4.04032e7	0.232829
$227$	6.69063e7	0.379644	0.189822	−	0.981819i	$-0.439209\pi$
$227$	6.69063e7	0.379644	0.189822	+	0.981819i	$0.439209\pi$
$228$	3.44489e7	0.192488
$229$	−1.93715e8	−1.06595	−0.532977	−	0.846130i	$-0.678927\pi$
$229$	−1.93715e8	−1.06595	−0.532977	+	0.846130i	$0.678927\pi$
$230$	−3.26084e7	−0.176719
$231$	5.86961e7	0.313305
$232$	−1.69611e8	−0.891759
$233$	−7.16576e7	−0.371122	−0.185561	−	0.982633i	$-0.559410\pi$
$233$	−7.16576e7	−0.371122	−0.185561	+	0.982633i	$0.559410\pi$
$234$	−6.70105e7	−0.341891
$235$	3.57365e8	1.79628
$236$	1.70155e8	0.842660
$237$	−6.62865e7	−0.323449
$238$	4.41412e7	0.212239
$239$	−1.96261e8	−0.929913	−0.464956	−	0.885334i	$-0.653930\pi$
$239$	−1.96261e8	−0.929913	−0.464956	+	0.885334i	$0.653930\pi$
$240$	4.22355e7	0.197214
$241$	1.10755e8	0.509685	0.254843	−	0.966983i	$-0.417976\pi$
$241$	1.10755e8	0.509685	0.254843	+	0.966983i	$0.417976\pi$
$242$	1.25784e8	0.570521
$243$	1.43489e7	0.0641500
$244$	−1.84009e8	−0.810915
$245$	5.18467e7	0.225237
$246$	1.71956e7	0.0736452
$247$	2.11886e8	0.894668
$248$	−1.04730e8	−0.436002
$249$	1.49513e8	0.613736
$250$	1.01729e8	0.411768
$251$	3.02113e8	1.20590	0.602951	−	0.797778i	$-0.293992\pi$
$251$	3.02113e8	1.20590	0.602951	+	0.797778i	$0.293992\pi$
$252$	−2.27580e7	−0.0895843
$253$	−7.71143e7	−0.299373
$254$	2.19763e8	0.841466
$255$	2.51787e8	0.950918
$256$	−2.14483e8	−0.799012
$257$	−1.84004e8	−0.676178	−0.338089	−	0.941114i	$-0.609780\pi$
$257$	−1.84004e8	−0.676178	−0.338089	+	0.941114i	$0.609780\pi$
$258$	−7.61873e7	−0.276194
$259$	3.38573e7	0.121089
$260$	6.06243e8	2.13915
$261$	9.28315e7	0.323187
$262$	1.56038e8	0.536013
$263$	−3.08182e8	−1.04463	−0.522314	−	0.852753i	$-0.674931\pi$
$263$	−3.08182e8	−1.04463	−0.522314	+	0.852753i	$0.674931\pi$
$264$	−2.27930e8	−0.762410
$265$	2.59447e8	0.856424
$266$	−2.92420e7	−0.0952624
$267$	1.92437e8	0.618726
$268$	1.10441e8	0.350476
$269$	−5.87454e8	−1.84010	−0.920048	−	0.391805i	$-0.871851\pi$
$269$	−5.87454e8	−1.84010	−0.920048	+	0.391805i	$0.871851\pi$
$270$	5.27519e7	0.163104
$271$	2.71901e8	0.829887	0.414943	−	0.909847i	$-0.363801\pi$
$271$	2.71901e8	0.829887	0.414943	+	0.909847i	$0.363801\pi$
$272$	7.51134e7	0.226322
$273$	−1.39978e8	−0.416380
$274$	3.11542e8	0.914933
$275$	7.35729e8	2.13331
$276$	2.98992e7	0.0856008
$277$	5.24004e8	1.48134	0.740671	−	0.671868i	$-0.234508\pi$
$277$	5.24004e8	1.48134	0.740671	+	0.671868i	$0.234508\pi$
$278$	1.20828e8	0.337295
$279$	5.73204e7	0.158014
$280$	−2.01333e8	−0.548102
$281$	5.84533e8	1.57158	0.785791	−	0.618492i	$-0.212256\pi$
$281$	5.84533e8	1.57158	0.785791	+	0.618492i	$0.212256\pi$
$282$	1.33155e8	0.353577
$283$	3.30137e8	0.865848	0.432924	−	0.901431i	$-0.357482\pi$
$283$	3.30137e8	0.865848	0.432924	+	0.901431i	$0.357482\pi$
$284$	−5.71875e7	−0.148145
$285$	−1.66800e8	−0.426815
$286$	−5.82595e8	−1.47260
$287$	3.59198e7	0.0896907
$288$	1.40024e8	0.345404
$289$	3.74508e7	0.0912680
$290$	3.41283e8	0.821716
$291$	−1.12567e8	−0.267784
$292$	−1.03866e8	−0.244136
$293$	−5.11993e8	−1.18912	−0.594562	−	0.804050i	$-0.702675\pi$
$293$	−5.11993e8	−1.18912	−0.594562	+	0.804050i	$0.702675\pi$
$294$	1.93182e7	0.0443353
$295$	−8.23882e8	−1.86848
$296$	−1.31476e8	−0.294662
$297$	1.24751e8	0.276309
$298$	−5.06583e7	−0.110890
$299$	1.83901e8	0.397865
$300$	−2.85261e8	−0.609984
$301$	−1.59147e8	−0.336369
$302$	−1.68871e8	−0.352801
$303$	−2.88302e8	−0.595386
$304$	−4.97600e7	−0.101583
$305$	8.90964e8	1.79809
$306$	9.38162e7	0.187177
$307$	−3.11180e8	−0.613801	−0.306901	−	0.951742i	$-0.599292\pi$
$307$	−3.11180e8	−0.613801	−0.306901	+	0.951742i	$0.599292\pi$
$308$	−1.97860e8	−0.385861
$309$	−1.65483e8	−0.319079
$310$	2.10731e8	0.401756
$311$	3.16422e7	0.0596492	0.0298246	−	0.999555i	$-0.490505\pi$
$311$	3.16422e7	0.0596492	0.0298246	+	0.999555i	$0.490505\pi$
$312$	5.43566e8	1.01324
$313$	2.17969e8	0.401782	0.200891	−	0.979614i	$-0.435616\pi$
$313$	2.17969e8	0.401782	0.200891	+	0.979614i	$0.435616\pi$
$314$	3.24508e8	0.591523
$315$	1.10193e8	0.198640
$316$	2.23446e8	0.398354
$317$	7.70884e8	1.35919	0.679597	−	0.733585i	$-0.262155\pi$
$317$	7.70884e8	1.35919	0.679597	+	0.733585i	$0.262155\pi$
$318$	9.66704e7	0.168577
$319$	8.07085e8	1.39204
$320$	3.14551e8	0.536619
$321$	−4.73391e8	−0.798826
$322$	−2.53800e7	−0.0423639
$323$	−2.96645e8	−0.489810
$324$	−4.83690e7	−0.0790060
$325$	−1.75456e9	−2.83515
$326$	2.57033e8	0.410891
$327$	2.72003e8	0.430186
$328$	−1.39485e8	−0.218257
$329$	2.78146e8	0.430613
$330$	4.58629e8	0.702527
$331$	6.49363e8	0.984214	0.492107	−	0.870535i	$-0.336227\pi$
$331$	6.49363e8	0.984214	0.492107	+	0.870535i	$0.336227\pi$
$332$	−5.03997e8	−0.755866
$333$	7.19592e7	0.106790
$334$	1.85570e8	0.272518
$335$	−5.34750e8	−0.777131
$336$	3.28729e7	0.0472771
$337$	−5.30396e8	−0.754911	−0.377455	−	0.926028i	$-0.623201\pi$
$337$	−5.30396e8	−0.754911	−0.377455	+	0.926028i	$0.623201\pi$
$338$	1.00776e9	1.41954
$339$	1.79377e8	0.250073
$340$	−8.48755e8	−1.17113
$341$	4.98349e8	0.680602
$342$	−6.21499e7	−0.0840135
$343$	4.03536e7	0.0539949
$344$	6.18006e8	0.818536
$345$	−1.44771e8	−0.189807
$346$	−6.48408e8	−0.841554
$347$	1.29413e9	1.66274	0.831368	−	0.555722i	$-0.187558\pi$
$347$	1.29413e9	1.66274	0.831368	+	0.555722i	$0.187558\pi$
$348$	−3.12928e8	−0.398031
$349$	−7.34008e8	−0.924297	−0.462149	−	0.886803i	$-0.652921\pi$
$349$	−7.34008e8	−0.924297	−0.462149	+	0.886803i	$0.652921\pi$
$350$	2.42144e8	0.301881
$351$	−2.97504e8	−0.367213
$352$	1.21738e9	1.48774
$353$	−2.24725e8	−0.271919	−0.135959	−	0.990714i	$-0.543412\pi$
$353$	−2.24725e8	−0.271919	−0.135959	+	0.990714i	$0.543412\pi$
$354$	−3.06980e8	−0.367788
$355$	2.76899e8	0.328490
$356$	−6.48689e8	−0.762012
$357$	1.95972e8	0.227959
$358$	−2.42484e8	−0.279314
$359$	3.47626e8	0.396535	0.198268	−	0.980148i	$-0.436468\pi$
$359$	3.47626e8	0.396535	0.198268	+	0.980148i	$0.436468\pi$
$360$	−4.27905e8	−0.483380
$361$	−6.97355e8	−0.780151
$362$	9.04141e8	1.00174
$363$	5.58439e8	0.612777
$364$	4.71855e8	0.512806
$365$	5.02913e8	0.541337
$366$	3.31974e8	0.353933
$367$	1.06644e9	1.12617	0.563087	−	0.826398i	$-0.309614\pi$
$367$	1.06644e9	1.12617	0.563087	+	0.826398i	$0.309614\pi$
$368$	−4.31881e7	−0.0451749
$369$	7.63427e7	0.0790998
$370$	2.64548e8	0.271518
$371$	2.01934e8	0.205306
$372$	−1.93223e8	−0.194607
$373$	−3.91967e8	−0.391082	−0.195541	−	0.980696i	$-0.562646\pi$
$373$	−3.91967e8	−0.391082	−0.195541	+	0.980696i	$0.562646\pi$
$374$	8.15646e8	0.806216
$375$	4.51641e8	0.442266
$376$	−1.08010e9	−1.04787
$377$	−1.92473e9	−1.85001
$378$	4.10581e7	0.0391001
$379$	−2.85769e8	−0.269636	−0.134818	−	0.990870i	$-0.543045\pi$
$379$	−2.85769e8	−0.269636	−0.134818	+	0.990870i	$0.543045\pi$
$380$	5.62270e8	0.525657
$381$	9.75674e8	0.903790
$382$	1.03602e9	0.950925
$383$	9.09293e8	0.827005	0.413502	−	0.910503i	$-0.364305\pi$
$383$	9.09293e8	0.827005	0.413502	+	0.910503i	$0.364305\pi$
$384$	−5.46614e8	−0.492631
$385$	9.58028e8	0.855590
$386$	−2.17892e8	−0.192835
$387$	−3.38246e8	−0.296650
$388$	3.79454e8	0.329798
$389$	8.19270e8	0.705673	0.352836	−	0.935685i	$-0.385217\pi$
$389$	8.19270e8	0.705673	0.352836	+	0.935685i	$0.385217\pi$
$390$	−1.09373e9	−0.933654
$391$	−2.57466e8	−0.217822
$392$	−1.56702e8	−0.131394
$393$	6.92756e8	0.575713
$394$	−8.99752e8	−0.741115
$395$	−1.08192e9	−0.883292
$396$	−4.20524e8	−0.340297
$397$	1.07139e9	0.859368	0.429684	−	0.902979i	$-0.358625\pi$
$397$	1.07139e9	0.859368	0.429684	+	0.902979i	$0.358625\pi$
$398$	−2.32994e8	−0.185249
$399$	−1.29825e8	−0.102318
$400$	4.12047e8	0.321912
$401$	−1.94534e9	−1.50657	−0.753287	−	0.657692i	$-0.771533\pi$
$401$	−1.94534e9	−1.50657	−0.753287	+	0.657692i	$0.771533\pi$
$402$	−1.99249e8	−0.152969
$403$	−1.18846e9	−0.904516
$404$	9.71843e8	0.733266
$405$	2.34201e8	0.175184
$406$	2.65629e8	0.196986
$407$	6.25619e8	0.459970
$408$	−7.61006e8	−0.554724
$409$	−2.23036e9	−1.61192	−0.805960	−	0.591970i	$-0.798350\pi$
$409$	−2.23036e9	−1.61192	−0.805960	+	0.591970i	$0.798350\pi$
$410$	2.80664e8	0.201114
$411$	1.38314e9	0.982698
$412$	5.57829e8	0.392972
$413$	−6.41248e8	−0.447921
$414$	−5.39417e7	−0.0373614
$415$	2.44033e9	1.67602
$416$	−2.90319e9	−1.97719
$417$	5.36434e8	0.362276
$418$	−5.40337e8	−0.361866
$419$	−8.73043e8	−0.579811	−0.289906	−	0.957055i	$-0.593624\pi$
$419$	−8.73043e8	−0.579811	−0.289906	+	0.957055i	$0.593624\pi$
$420$	−3.71452e8	−0.244642
$421$	6.78986e8	0.443479	0.221740	−	0.975106i	$-0.428826\pi$
$421$	6.78986e8	0.443479	0.221740	+	0.975106i	$0.428826\pi$
$422$	−9.38213e7	−0.0607726
$423$	5.91162e8	0.379765
$424$	−7.84158e8	−0.499601
$425$	2.45642e9	1.55218
$426$	1.03173e8	0.0646595
$427$	6.93460e8	0.431046
$428$	1.59576e9	0.983819
$429$	−2.58653e9	−1.58167
$430$	−1.24352e9	−0.754244
$431$	−1.17106e9	−0.704545	−0.352272	−	0.935898i	$-0.614591\pi$
$431$	−1.17106e9	−0.704545	−0.352272	+	0.935898i	$0.614591\pi$
$432$	6.98670e7	0.0416945
$433$	−9.72412e8	−0.575629	−0.287815	−	0.957686i	$-0.592929\pi$
$433$	−9.72412e8	−0.575629	−0.287815	+	0.957686i	$0.592929\pi$
$434$	1.64017e8	0.0963109
$435$	1.51518e9	0.882576
$436$	−9.16899e8	−0.529809
$437$	1.70562e8	0.0977683
$438$	1.87386e8	0.106556
$439$	−1.10147e9	−0.621363	−0.310681	−	0.950514i	$-0.600557\pi$
$439$	−1.10147e9	−0.621363	−0.310681	+	0.950514i	$0.600557\pi$
$440$	−3.72024e9	−2.08203
$441$	8.57661e7	0.0476190
$442$	−1.94515e9	−1.07146
$443$	−2.34426e9	−1.28113	−0.640564	−	0.767905i	$-0.721299\pi$
$443$	−2.34426e9	−1.28113	−0.640564	+	0.767905i	$0.721299\pi$
$444$	−2.42569e8	−0.131521
$445$	3.14092e9	1.68965
$446$	1.07737e9	0.575036
$447$	−2.24906e8	−0.119103
$448$	2.44823e8	0.128641
$449$	−2.55326e9	−1.33117	−0.665584	−	0.746323i	$-0.731818\pi$
$449$	−2.55326e9	−1.33117	−0.665584	+	0.746323i	$0.731818\pi$
$450$	5.14645e8	0.266234
$451$	6.63730e8	0.340701
$452$	−6.04665e8	−0.307985
$453$	−7.49729e8	−0.378932
$454$	4.06893e8	0.204073
$455$	−2.28470e9	−1.13707
$456$	5.04139e8	0.248985
$457$	−1.55298e9	−0.761132	−0.380566	−	0.924754i	$-0.624271\pi$
$457$	−1.55298e9	−0.761132	−0.380566	+	0.924754i	$0.624271\pi$
$458$	−1.17808e9	−0.572990
$459$	4.16513e8	0.201041
$460$	4.88010e8	0.233763
$461$	−3.51016e9	−1.66868	−0.834340	−	0.551250i	$-0.814151\pi$
$461$	−3.51016e9	−1.66868	−0.834340	+	0.551250i	$0.814151\pi$
$462$	3.56963e8	0.168413
$463$	−3.47421e9	−1.62676	−0.813379	−	0.581735i	$-0.802374\pi$
$463$	−3.47421e9	−1.62676	−0.813379	+	0.581735i	$0.802374\pi$
$464$	4.52011e8	0.210056
$465$	9.35575e8	0.431512
$466$	−4.35789e8	−0.199492
$467$	−2.09086e8	−0.0949982	−0.0474991	−	0.998871i	$-0.515125\pi$
$467$	−2.09086e8	−0.0949982	−0.0474991	+	0.998871i	$0.515125\pi$
$468$	1.00286e9	0.452253
$469$	−4.16210e8	−0.186298
$470$	2.17333e9	0.965568
$471$	1.44071e9	0.635335
$472$	2.49011e9	1.08999
$473$	−2.94074e9	−1.27774
$474$	−4.03124e8	−0.173866
$475$	−1.62729e9	−0.696688
$476$	−6.60607e8	−0.280750
$477$	4.29184e8	0.181063
$478$	−1.19357e9	−0.499863
$479$	9.85319e8	0.409640	0.204820	−	0.978800i	$-0.434339\pi$
$479$	9.85319e8	0.409640	0.204820	+	0.978800i	$0.434339\pi$
$480$	2.28544e9	0.943249
$481$	−1.49197e9	−0.611298
$482$	6.73558e8	0.273975
$483$	−1.12679e8	−0.0455016
$484$	−1.88245e9	−0.754684
$485$	−1.83730e9	−0.731280
$486$	8.72634e7	0.0344830
$487$	−4.40685e9	−1.72893	−0.864465	−	0.502693i	$-0.832342\pi$
$487$	−4.40685e9	−1.72893	−0.864465	+	0.502693i	$0.832342\pi$
$488$	−2.69286e9	−1.04893
$489$	1.14114e9	0.441324
$490$	3.15308e8	0.121073
$491$	2.18452e9	0.832858	0.416429	−	0.909168i	$-0.363281\pi$
$491$	2.18452e9	0.832858	0.416429	+	0.909168i	$0.363281\pi$
$492$	−2.57345e8	−0.0974178
$493$	2.69467e9	1.01284
$494$	1.28859e9	0.480918
$495$	2.03616e9	0.754560
$496$	2.79102e8	0.102702
$497$	2.15518e8	0.0787472
$498$	9.09270e8	0.329906
$499$	−1.92608e9	−0.693941	−0.346971	−	0.937876i	$-0.612790\pi$
$499$	−1.92608e9	−0.693941	−0.346971	+	0.937876i	$0.612790\pi$
$500$	−1.52245e9	−0.544687
$501$	8.23868e8	0.292702
$502$	1.83731e9	0.648217
$503$	1.40342e9	0.491698	0.245849	−	0.969308i	$-0.420933\pi$
$503$	1.40342e9	0.491698	0.245849	+	0.969308i	$0.420933\pi$
$504$	−3.33050e8	−0.115878
$505$	−4.70562e9	−1.62591
$506$	−4.68974e8	−0.160924
$507$	4.47412e9	1.52468
$508$	−3.28892e9	−1.11309
$509$	1.64074e9	0.551476	0.275738	−	0.961233i	$-0.411078\pi$
$509$	1.64074e9	0.551476	0.275738	+	0.961233i	$0.411078\pi$
$510$	1.53125e9	0.511154
$511$	3.91430e8	0.129772
$512$	1.28697e9	0.423763
$513$	−2.75925e8	−0.0902361
$514$	−1.11903e9	−0.363471
$515$	−2.70098e9	−0.871358
$516$	1.14020e9	0.365349
$517$	5.13961e9	1.63574
$518$	2.05905e8	0.0650897
$519$	−2.87871e9	−0.903884
$520$	8.87201e9	2.76701
$521$	−2.87695e9	−0.891251	−0.445625	−	0.895220i	$-0.647019\pi$
$521$	−2.87695e9	−0.891251	−0.445625	+	0.895220i	$0.647019\pi$
$522$	5.64559e8	0.173725
$523$	−2.97829e9	−0.910357	−0.455178	−	0.890400i	$-0.650425\pi$
$523$	−2.97829e9	−0.910357	−0.455178	+	0.890400i	$0.650425\pi$
$524$	−2.33523e9	−0.709038
$525$	1.07504e9	0.324240
$526$	−1.87422e9	−0.561526
$527$	1.66387e9	0.495201
$528$	6.07429e8	0.179588
$529$	1.48036e8	0.0434783
$530$	1.57784e9	0.460360
$531$	−1.36289e9	−0.395029
$532$	4.37629e8	0.126013
$533$	−1.58286e9	−0.452790
$534$	1.17031e9	0.332588
$535$	−7.72661e9	−2.18148
$536$	1.61624e9	0.453344
$537$	−1.07655e9	−0.300002
$538$	−3.57262e9	−0.989121
$539$	7.45658e8	0.205106
$540$	−7.89472e8	−0.215754
$541$	−6.98300e9	−1.89606	−0.948029	−	0.318185i	$-0.896927\pi$
$541$	−6.98300e9	−1.89606	−0.948029	+	0.318185i	$0.896927\pi$
$542$	1.65358e9	0.446095
$543$	4.01408e9	1.07594
$544$	4.06454e9	1.08247
$545$	4.43958e9	1.17477
$546$	−8.51281e8	−0.223820
$547$	4.56989e9	1.19385	0.596926	−	0.802297i	$-0.296389\pi$
$547$	4.56989e9	1.19385	0.596926	+	0.802297i	$0.296389\pi$
$548$	−4.66246e9	−1.21027
$549$	1.47385e9	0.380147
$550$	4.47436e9	1.14673
$551$	−1.78512e9	−0.454608
$552$	4.37557e8	0.110726
$553$	−8.42084e8	−0.211747
$554$	3.18675e9	0.796276
$555$	1.17451e9	0.291628
$556$	−1.80828e9	−0.446173
$557$	3.96752e9	0.972805	0.486402	−	0.873735i	$-0.338309\pi$
$557$	3.96752e9	0.972805	0.486402	+	0.873735i	$0.338309\pi$
$558$	3.48597e8	0.0849383
$559$	7.01305e9	1.69811
$560$	5.36547e8	0.129107
$561$	3.62120e9	0.865928
$562$	3.55486e9	0.844784
$563$	−3.43943e9	−0.812283	−0.406142	−	0.913810i	$-0.633126\pi$
$563$	−3.43943e9	−0.812283	−0.406142	+	0.913810i	$0.633126\pi$
$564$	−1.99276e9	−0.467711
$565$	2.92776e9	0.682913
$566$	2.00774e9	0.465425
$567$	1.82284e8	0.0419961
$568$	−8.36904e8	−0.191627
$569$	−7.74018e9	−1.76140	−0.880700	−	0.473675i	$-0.842927\pi$
$569$	−7.74018e9	−1.76140	−0.880700	+	0.473675i	$0.842927\pi$
$570$	−1.01440e9	−0.229429
$571$	−7.58234e9	−1.70442	−0.852211	−	0.523199i	$-0.824739\pi$
$571$	−7.58234e9	−1.70442	−0.852211	+	0.523199i	$0.824739\pi$
$572$	8.71898e9	1.94796
$573$	4.59958e9	1.02136
$574$	2.18448e8	0.0482121
$575$	−1.41237e9	−0.309822
$576$	5.20338e8	0.113451
$577$	−1.63676e9	−0.354706	−0.177353	−	0.984147i	$-0.556753\pi$
$577$	−1.63676e9	−0.354706	−0.177353	+	0.984147i	$0.556753\pi$
$578$	2.27758e8	0.0490599
$579$	−9.67368e8	−0.207118
$580$	−5.10756e9	−1.08696
$581$	1.89937e9	0.401785
$582$	−6.84580e8	−0.143944
$583$	3.73136e9	0.779880
$584$	−1.52001e9	−0.315793
$585$	−4.85582e9	−1.00281
$586$	−3.11371e9	−0.639199
$587$	−4.63175e9	−0.945174	−0.472587	−	0.881284i	$-0.656680\pi$
$587$	−4.63175e9	−0.945174	−0.472587	+	0.881284i	$0.656680\pi$
$588$	−2.89111e8	−0.0586467
$589$	−1.10225e9	−0.222269
$590$	−5.01047e9	−1.00438
$591$	−3.99460e9	−0.796007
$592$	3.50380e8	0.0694086
$593$	2.38584e9	0.469841	0.234920	−	0.972015i	$-0.424517\pi$
$593$	2.38584e9	0.469841	0.234920	+	0.972015i	$0.424517\pi$
$594$	7.58676e8	0.148526
$595$	3.19863e9	0.622522
$596$	7.58140e8	0.146686
$597$	−1.03442e9	−0.198969
$598$	1.11840e9	0.213867
$599$	−8.55270e9	−1.62596	−0.812979	−	0.582293i	$-0.802156\pi$
$599$	−8.55270e9	−1.62596	−0.812979	+	0.582293i	$0.802156\pi$
$600$	−4.17462e9	−0.789020
$601$	−3.83189e9	−0.720034	−0.360017	−	0.932946i	$-0.617229\pi$
$601$	−3.83189e9	−0.720034	−0.360017	+	0.932946i	$0.617229\pi$
$602$	−9.67861e8	−0.180811
$603$	−8.84597e8	−0.164299
$604$	2.52728e9	0.466685
$605$	9.11474e9	1.67340
$606$	−1.75332e9	−0.320042
$607$	−6.02745e9	−1.09389	−0.546944	−	0.837169i	$-0.684209\pi$
$607$	−6.02745e9	−1.09389	−0.546944	+	0.837169i	$0.684209\pi$
$608$	−2.69261e9	−0.485860
$609$	1.17930e9	0.211576
$610$	5.41843e9	0.966539
$611$	−1.22569e10	−2.17388
$612$	−1.40403e9	−0.247598
$613$	9.21736e9	1.61620	0.808100	−	0.589046i	$-0.200496\pi$
$613$	9.21736e9	1.61620	0.808100	+	0.589046i	$0.200496\pi$
$614$	−1.89246e9	−0.329941
$615$	1.24605e9	0.216010
$616$	−2.89556e9	−0.499114
$617$	1.14497e10	1.96245	0.981223	−	0.192878i	$-0.0617823\pi$
$617$	1.14497e10	1.96245	0.981223	+	0.192878i	$0.0617823\pi$
$618$	−1.00639e9	−0.171517
$619$	−1.08449e10	−1.83784	−0.918919	−	0.394447i	$-0.870936\pi$
$619$	−1.08449e10	−1.83784	−0.918919	+	0.394447i	$0.870936\pi$
$620$	−3.15375e9	−0.531443
$621$	−2.39483e8	−0.0401286
$622$	1.92433e8	0.0320637
$623$	2.44466e9	0.405051
$624$	−1.44859e9	−0.238671
$625$	−1.69733e9	−0.278091
$626$	1.32559e9	0.215973
$627$	−2.39891e9	−0.388668
$628$	−4.85651e9	−0.782466
$629$	2.08879e9	0.334671
$630$	6.70144e8	0.106777
$631$	−4.24628e9	−0.672831	−0.336416	−	0.941714i	$-0.609215\pi$
$631$	−4.24628e9	−0.672831	−0.336416	+	0.941714i	$0.609215\pi$
$632$	3.27000e9	0.515274
$633$	−4.16535e8	−0.0652738
$634$	4.68816e9	0.730618
$635$	1.59248e10	2.46812
$636$	−1.44675e9	−0.222994
$637$	−1.77824e9	−0.272585
$638$	4.90832e9	0.748274
$639$	4.58053e8	0.0694485
$640$	−8.92174e9	−1.34530
$641$	1.23460e10	1.85149	0.925745	−	0.378148i	$-0.123439\pi$
$641$	1.23460e10	1.85149	0.925745	+	0.378148i	$0.123439\pi$
$642$	−2.87895e9	−0.429399
$643$	7.63260e9	1.13223	0.566114	−	0.824327i	$-0.308446\pi$
$643$	7.63260e9	1.13223	0.566114	+	0.824327i	$0.308446\pi$
$644$	3.79831e8	0.0560389
$645$	−5.52080e9	−0.810108
$646$	−1.80406e9	−0.263291
$647$	−6.40238e9	−0.929344	−0.464672	−	0.885483i	$-0.653828\pi$
$647$	−6.40238e9	−0.929344	−0.464672	+	0.885483i	$0.653828\pi$
$648$	−7.07852e8	−0.102195
$649$	−1.18491e10	−1.70148
$650$	−1.06704e10	−1.52400
$651$	7.28182e8	0.103444
$652$	−3.84669e9	−0.543526
$653$	1.38481e10	1.94622	0.973111	−	0.230336i	$-0.0739824\pi$
$653$	1.38481e10	1.94622	0.973111	+	0.230336i	$0.0739824\pi$
$654$	1.65419e9	0.231241
$655$	1.13071e10	1.57219
$656$	3.71724e8	0.0514112
$657$	8.31931e8	0.114448
$658$	1.69156e9	0.231471
$659$	−4.71882e9	−0.642294	−0.321147	−	0.947029i	$-0.604068\pi$
$659$	−4.71882e9	−0.642294	−0.321147	+	0.947029i	$0.604068\pi$
$660$	−6.86373e9	−0.929301
$661$	4.22987e8	0.0569668	0.0284834	−	0.999594i	$-0.490932\pi$
$661$	4.22987e8	0.0569668	0.0284834	+	0.999594i	$0.490932\pi$
$662$	3.94913e9	0.529051
$663$	−8.63580e9	−1.15081
$664$	−7.37569e9	−0.977720
$665$	−2.11898e9	−0.279416
$666$	4.37623e8	0.0574037
$667$	−1.54936e9	−0.202167
$668$	−2.77719e9	−0.360486
$669$	4.78318e9	0.617626
$670$	−3.25210e9	−0.417737
$671$	1.28138e10	1.63738
$672$	1.77882e9	0.226120
$673$	6.56559e9	0.830273	0.415137	−	0.909759i	$-0.363734\pi$
$673$	6.56559e9	0.830273	0.415137	+	0.909759i	$0.363734\pi$
$674$	−3.22563e9	−0.405793
$675$	2.28485e9	0.285953
$676$	−1.50819e10	−1.87777
$677$	−3.78178e9	−0.468420	−0.234210	−	0.972186i	$-0.575250\pi$
$677$	−3.78178e9	−0.468420	−0.234210	+	0.972186i	$0.575250\pi$
$678$	1.09089e9	0.134424
$679$	−1.43002e9	−0.175306
$680$	−1.24210e10	−1.51487
$681$	1.80647e9	0.219188
$682$	3.03073e9	0.365849
$683$	−1.02332e10	−1.22897	−0.614483	−	0.788930i	$-0.710635\pi$
$683$	−1.02332e10	−1.22897	−0.614483	+	0.788930i	$0.710635\pi$
$684$	9.30121e8	0.111133
$685$	2.25754e10	2.68360
$686$	2.45412e8	0.0290243
$687$	−5.23030e9	−0.615429
$688$	−1.64697e9	−0.192809
$689$	−8.89853e9	−1.03646
$690$	−8.80428e8	−0.102029
$691$	−2.11082e9	−0.243376	−0.121688	−	0.992568i	$-0.538831\pi$
$691$	−2.11082e9	−0.243376	−0.121688	+	0.992568i	$0.538831\pi$
$692$	9.70392e9	1.11321
$693$	1.58479e9	0.180887
$694$	7.87028e9	0.893783
$695$	8.75559e9	0.989324
$696$	−4.57951e9	−0.514857
$697$	2.21604e9	0.247892
$698$	−4.46390e9	−0.496844
$699$	−1.93476e9	−0.214267
$700$	−3.62387e9	−0.399328
$701$	−1.57691e10	−1.72899	−0.864496	−	0.502639i	$-0.832362\pi$
$701$	−1.57691e10	−1.72899	−0.864496	+	0.502639i	$0.832362\pi$
$702$	−1.80928e9	−0.197391
$703$	−1.38375e9	−0.150215
$704$	4.52387e9	0.488658
$705$	9.64885e9	1.03708
$706$	−1.36667e9	−0.146166
$707$	−3.66250e9	−0.389771
$708$	4.59418e9	0.486510
$709$	−1.05682e10	−1.11363	−0.556815	−	0.830637i	$-0.687977\pi$
$709$	−1.05682e10	−1.11363	−0.556815	+	0.830637i	$0.687977\pi$
$710$	1.68397e9	0.176576
$711$	−1.78973e9	−0.186743
$712$	−9.49317e9	−0.985670
$713$	−9.56677e8	−0.0988444
$714$	1.19181e9	0.122536
$715$	−4.22169e10	−4.31931
$716$	3.62896e9	0.369476
$717$	−5.29906e9	−0.536885
$718$	2.11410e9	0.213152
$719$	−3.56964e9	−0.358157	−0.179078	−	0.983835i	$-0.557312\pi$
$719$	−3.56964e9	−0.358157	−0.179078	+	0.983835i	$0.557312\pi$
$720$	1.14036e9	0.113862
$721$	−2.10224e9	−0.208886
$722$	−4.24099e9	−0.419360
$723$	2.99037e9	0.294267
$724$	−1.35312e10	−1.32510
$725$	1.47820e10	1.44063
$726$	3.39617e9	0.329390
$727$	1.44721e10	1.39689	0.698443	−	0.715666i	$-0.253877\pi$
$727$	1.44721e10	1.39689	0.698443	+	0.715666i	$0.253877\pi$
$728$	6.90531e9	0.663320
$729$	3.87420e8	0.0370370
$730$	3.05849e9	0.290989
$731$	−9.81843e9	−0.929675
$732$	−4.96825e9	−0.468182
$733$	−6.49962e9	−0.609570	−0.304785	−	0.952421i	$-0.598585\pi$
$733$	−6.49962e9	−0.609570	−0.304785	+	0.952421i	$0.598585\pi$
$734$	6.48560e9	0.605360
$735$	1.39986e9	0.130041
$736$	−2.33699e9	−0.216065
$737$	−7.69076e9	−0.707674
$738$	4.64281e8	0.0425191
$739$	−2.77190e9	−0.252652	−0.126326	−	0.991989i	$-0.540318\pi$
$739$	−2.77190e9	−0.252652	−0.126326	+	0.991989i	$0.540318\pi$
$740$	−3.95917e9	−0.359164
$741$	5.72091e9	0.516537
$742$	1.22807e9	0.110360
$743$	−1.20760e10	−1.08009	−0.540047	−	0.841635i	$-0.681594\pi$
$743$	−1.20760e10	−1.08009	−0.540047	+	0.841635i	$0.681594\pi$
$744$	−2.82770e9	−0.251726
$745$	−3.67088e9	−0.325254
$746$	−2.38376e9	−0.210221
$747$	4.03685e9	0.354341
$748$	−1.22068e10	−1.06646
$749$	−6.01382e9	−0.522955
$750$	2.74667e9	0.237734
$751$	−1.83521e10	−1.58105	−0.790524	−	0.612431i	$-0.790192\pi$
$751$	−1.83521e10	−1.58105	−0.790524	+	0.612431i	$0.790192\pi$
$752$	2.87846e9	0.246830
$753$	8.15706e9	0.696228
$754$	−1.17053e10	−0.994452
$755$	−1.22370e10	−1.03481
$756$	−6.14466e8	−0.0517215
$757$	7.04324e9	0.590115	0.295058	−	0.955479i	$-0.404661\pi$
$757$	7.04324e9	0.590115	0.295058	+	0.955479i	$0.404661\pi$
$758$	−1.73792e9	−0.144939
$759$	−2.08209e9	−0.172843
$760$	8.22848e9	0.679942
$761$	2.20485e9	0.181356	0.0906781	−	0.995880i	$-0.471097\pi$
$761$	2.20485e9	0.181356	0.0906781	+	0.995880i	$0.471097\pi$
$762$	5.93360e9	0.485821
$763$	3.45544e9	0.281623
$764$	−1.55048e10	−1.25788
$765$	6.79825e9	0.549013
$766$	5.52990e9	0.444546
$767$	2.82575e10	2.26126
$768$	−5.79104e9	−0.461310
$769$	1.06606e10	0.845359	0.422680	−	0.906279i	$-0.361090\pi$
$769$	1.06606e10	0.845359	0.422680	+	0.906279i	$0.361090\pi$
$770$	5.82629e9	0.459912
$771$	−4.96810e9	−0.390391
$772$	3.26092e9	0.255082
$773$	1.54329e10	1.20177	0.600883	−	0.799337i	$-0.294816\pi$
$773$	1.54329e10	1.20177	0.600883	+	0.799337i	$0.294816\pi$
$774$	−2.05706e9	−0.159460
$775$	9.12743e9	0.704356
$776$	5.55308e9	0.426597
$777$	9.14148e8	0.0699106
$778$	4.98242e9	0.379325
$779$	−1.46805e9	−0.111265
$780$	1.63686e10	1.23504
$781$	3.98235e9	0.299131
$782$	−1.56579e9	−0.117087
$783$	2.50645e9	0.186592
$784$	4.17608e8	0.0309502
$785$	2.35150e10	1.73501
$786$	4.21302e9	0.309467
$787$	−1.28866e10	−0.942380	−0.471190	−	0.882032i	$-0.656175\pi$
$787$	−1.28866e10	−0.942380	−0.471190	+	0.882032i	$0.656175\pi$
$788$	1.34655e10	0.980347
$789$	−8.32090e9	−0.603116
$790$	−6.57972e9	−0.474802
$791$	2.27875e9	0.163711
$792$	−6.15412e9	−0.440178
$793$	−3.05583e10	−2.17607
$794$	6.51568e9	0.461943
$795$	7.00508e9	0.494456
$796$	3.48694e9	0.245047
$797$	2.06840e10	1.44721	0.723605	−	0.690215i	$-0.242484\pi$
$797$	2.06840e10	1.44721	0.723605	+	0.690215i	$0.242484\pi$
$798$	−7.89534e8	−0.0549998
$799$	1.71599e10	1.19015
$800$	2.22967e10	1.53966
$801$	5.19579e9	0.357222
$802$	−1.18307e10	−0.809840
$803$	7.23288e9	0.492955
$804$	2.98191e9	0.202348
$805$	−1.83912e9	−0.124258
$806$	−7.22765e9	−0.486211
$807$	−1.58613e10	−1.06238
$808$	1.42223e10	0.948487
$809$	2.04638e10	1.35883	0.679417	−	0.733752i	$-0.262233\pi$
$809$	2.04638e10	1.35883	0.679417	+	0.733752i	$0.262233\pi$
$810$	1.42430e9	0.0941681
$811$	1.09335e10	0.719759	0.359879	−	0.932999i	$-0.382818\pi$
$811$	1.09335e10	0.719759	0.359879	+	0.932999i	$0.382818\pi$
$812$	−3.97534e9	−0.260572
$813$	7.34133e9	0.479135
$814$	3.80473e9	0.247251
$815$	1.86255e10	1.20519
$816$	2.02806e9	0.130667
$817$	6.50436e9	0.417280
$818$	−1.35640e10	−0.866467
$819$	−3.77940e9	−0.240397
$820$	−4.20035e9	−0.266034
$821$	2.73530e10	1.72506	0.862530	−	0.506007i	$-0.168879\pi$
$821$	2.73530e10	1.72506	0.862530	+	0.506007i	$0.168879\pi$
$822$	8.41163e9	0.528237
$823$	−1.74267e10	−1.08972	−0.544860	−	0.838527i	$-0.683417\pi$
$823$	−1.74267e10	−1.08972	−0.544860	+	0.838527i	$0.683417\pi$
$824$	8.16349e9	0.508313
$825$	1.98647e10	1.23167
$826$	−3.89978e9	−0.240774
$827$	1.98497e10	1.22035	0.610175	−	0.792267i	$-0.291099\pi$
$827$	1.98497e10	1.22035	0.610175	+	0.792267i	$0.291099\pi$
$828$	8.07279e8	0.0494216
$829$	9.04996e9	0.551704	0.275852	−	0.961200i	$-0.411040\pi$
$829$	9.04996e9	0.551704	0.275852	+	0.961200i	$0.411040\pi$
$830$	1.48410e10	0.900925
$831$	1.41481e10	0.855253
$832$	−1.07885e10	−0.649424
$833$	2.48957e9	0.149234
$834$	3.26235e9	0.194737
$835$	1.34470e10	0.799326
$836$	8.08655e9	0.478676
$837$	1.54765e9	0.0912293
$838$	−5.30945e9	−0.311670
$839$	−1.57847e9	−0.0922719	−0.0461359	−	0.998935i	$-0.514691\pi$
$839$	−1.57847e9	−0.0922719	−0.0461359	+	0.998935i	$0.514691\pi$
$840$	−5.43598e9	−0.316447
$841$	−1.03416e9	−0.0599518
$842$	4.12928e9	0.238387
$843$	1.57824e10	0.907353
$844$	1.40411e9	0.0803899
$845$	7.30258e10	4.16368
$846$	3.59517e9	0.204138
$847$	7.09424e9	0.401156
$848$	2.08976e9	0.117682
$849$	8.91369e9	0.499897
$850$	1.49388e10	0.834354
$851$	−1.20100e9	−0.0668019
$852$	−1.54406e9	−0.0855315
$853$	1.29045e8	0.00711900	0.00355950	−	0.999994i	$-0.498867\pi$
$853$	1.29045e8	0.00711900	0.00355950	+	0.999994i	$0.498867\pi$
$854$	4.21730e9	0.231703
$855$	−4.50360e9	−0.246422
$856$	2.33530e10	1.27258
$857$	−2.90635e10	−1.57730	−0.788651	−	0.614841i	$-0.789220\pi$
$857$	−2.90635e10	−1.57730	−0.788651	+	0.614841i	$0.789220\pi$
$858$	−1.57301e10	−0.850207
$859$	7.65884e9	0.412275	0.206137	−	0.978523i	$-0.433911\pi$
$859$	7.65884e9	0.412275	0.206137	+	0.978523i	$0.433911\pi$
$860$	1.86102e10	0.997714
$861$	9.69835e8	0.0517830
$862$	−7.12185e9	−0.378719
$863$	−2.57939e10	−1.36609	−0.683045	−	0.730376i	$-0.739345\pi$
$863$	−2.57939e10	−1.36609	−0.683045	+	0.730376i	$0.739345\pi$
$864$	3.78064e9	0.199419
$865$	−4.69859e10	−2.46838
$866$	−5.91376e9	−0.309422
$867$	1.01117e9	0.0526936
$868$	−2.45464e9	−0.127400
$869$	−1.55601e10	−0.804347
$870$	9.21464e9	0.474418
$871$	1.83409e10	0.940494
$872$	−1.34183e10	−0.685313
$873$	−3.03930e9	−0.154605
$874$	1.03728e9	0.0525541
$875$	5.73751e9	0.289531
$876$	−2.80437e9	−0.140952
$877$	−1.92870e10	−0.965529	−0.482764	−	0.875750i	$-0.660367\pi$
$877$	−1.92870e10	−0.965529	−0.482764	+	0.875750i	$0.660367\pi$
$878$	−6.69861e9	−0.334006
$879$	−1.38238e10	−0.686541
$880$	9.91437e9	0.490428
$881$	−2.12165e10	−1.04534	−0.522670	−	0.852535i	$-0.675064\pi$
$881$	−2.12165e10	−1.04534	−0.522670	+	0.852535i	$0.675064\pi$
$882$	5.21590e8	0.0255970
$883$	2.25175e10	1.10067	0.550337	−	0.834943i	$-0.314499\pi$
$883$	2.25175e10	1.10067	0.550337	+	0.834943i	$0.314499\pi$
$884$	2.91106e10	1.41732
$885$	−2.22448e10	−1.07877
$886$	−1.42567e10	−0.688654
$887$	5.06010e9	0.243459	0.121730	−	0.992563i	$-0.461156\pi$
$887$	5.06010e9	0.243459	0.121730	+	0.992563i	$0.461156\pi$
$888$	−3.54985e9	−0.170123
$889$	1.23947e10	0.591669
$890$	1.91016e10	0.908251
$891$	3.36827e9	0.159527
$892$	−1.61237e10	−0.760657
$893$	−1.13679e10	−0.534193
$894$	−1.36777e9	−0.0640225
$895$	−1.75713e10	−0.819261
$896$	−6.94402e9	−0.322502
$897$	4.96534e9	0.229708
$898$	−1.55278e10	−0.715553
$899$	1.00127e10	0.459612
$900$	−7.70205e9	−0.352174
$901$	1.24581e10	0.567435
$902$	4.03650e9	0.183140
$903$	−4.29698e9	−0.194203
$904$	−8.84890e9	−0.398382
$905$	6.55172e10	2.93823
$906$	−4.55951e9	−0.203690
$907$	3.63505e10	1.61765	0.808826	−	0.588048i	$-0.200103\pi$
$907$	3.63505e10	1.61765	0.808826	+	0.588048i	$0.200103\pi$
$908$	−6.08947e9	−0.269947
$909$	−7.78415e9	−0.343746
$910$	−1.38945e10	−0.611220
$911$	−8.71735e9	−0.382006	−0.191003	−	0.981589i	$-0.561174\pi$
$911$	−8.71735e9	−0.382006	−0.191003	+	0.981589i	$0.561174\pi$
$912$	−1.34352e9	−0.0586492
$913$	3.50968e10	1.52623
$914$	−9.44453e9	−0.409137
$915$	2.40560e10	1.03813
$916$	1.76309e10	0.757951
$917$	8.80057e9	0.376893
$918$	2.53304e9	0.108067
$919$	−3.56010e10	−1.51307	−0.756534	−	0.653955i	$-0.773109\pi$
$919$	−3.56010e10	−1.51307	−0.756534	+	0.653955i	$0.773109\pi$
$920$	7.14173e9	0.302375
$921$	−8.40187e9	−0.354378
$922$	−2.13471e10	−0.896978
$923$	−9.49708e9	−0.397543
$924$	−5.34222e9	−0.222777
$925$	1.14584e10	0.476024
$926$	−2.11286e10	−0.874443
$927$	−4.46803e9	−0.184220
$928$	2.44592e10	1.00467
$929$	1.93216e10	0.790657	0.395328	−	0.918540i	$-0.370631\pi$
$929$	1.93216e10	0.790657	0.395328	+	0.918540i	$0.370631\pi$
$930$	5.68974e9	0.231954
$931$	−1.64926e9	−0.0669829
$932$	6.52191e9	0.263888
$933$	8.54338e8	0.0344385
$934$	−1.27156e9	−0.0510651
$935$	5.91046e10	2.36472
$936$	1.46763e10	0.584993
$937$	1.08212e10	0.429720	0.214860	−	0.976645i	$-0.431070\pi$
$937$	1.08212e10	0.429720	0.214860	+	0.976645i	$0.431070\pi$
$938$	−2.53119e9	−0.100142
$939$	5.88517e9	0.231969
$940$	−3.25255e10	−1.27725
$941$	−3.27237e10	−1.28026	−0.640130	−	0.768267i	$-0.721119\pi$
$941$	−3.27237e10	−1.28026	−0.640130	+	0.768267i	$0.721119\pi$
$942$	8.76172e9	0.341516
$943$	−1.27416e9	−0.0494803
$944$	−6.63610e9	−0.256750
$945$	2.97521e9	0.114685
$946$	−1.78842e10	−0.686833
$947$	2.39497e9	0.0916379	0.0458190	−	0.998950i	$-0.485410\pi$
$947$	2.39497e9	0.0916379	0.0458190	+	0.998950i	$0.485410\pi$
$948$	6.03306e9	0.229990
$949$	−1.72489e10	−0.655134
$950$	−9.89645e9	−0.374496
$951$	2.08139e10	0.784731
$952$	−9.66759e9	−0.363152
$953$	−2.32590e10	−0.870493	−0.435246	−	0.900311i	$-0.643339\pi$
$953$	−2.32590e10	−0.870493	−0.435246	+	0.900311i	$0.643339\pi$
$954$	2.61010e9	0.0973281
$955$	7.50736e10	2.78917
$956$	1.78627e10	0.661218
$957$	2.17913e10	0.803695
$958$	5.99226e9	0.220197
$959$	1.75710e10	0.643327
$960$	8.49288e9	0.309817
$961$	−2.13301e10	−0.775285
$962$	−9.07348e9	−0.328595
$963$	−1.27816e10	−0.461203
$964$	−1.00803e10	−0.362413
$965$	−1.57892e10	−0.565608
$966$	−6.85259e8	−0.0244588
$967$	−4.66488e10	−1.65900	−0.829502	−	0.558503i	$-0.811376\pi$
$967$	−4.66488e10	−1.65900	−0.829502	+	0.558503i	$0.811376\pi$
$968$	−2.75486e10	−0.976191
$969$	−8.00941e9	−0.282792
$970$	−1.11736e10	−0.393090
$971$	2.40942e10	0.844588	0.422294	−	0.906459i	$-0.361225\pi$
$971$	2.40942e10	0.844588	0.422294	+	0.906459i	$0.361225\pi$
$972$	−1.30596e9	−0.0456141
$973$	6.81470e9	0.237166
$974$	−2.68005e10	−0.929364
$975$	−4.73731e10	−1.63688
$976$	7.17642e9	0.247078
$977$	−3.70025e10	−1.26940	−0.634702	−	0.772757i	$-0.718877\pi$
$977$	−3.70025e10	−1.26940	−0.634702	+	0.772757i	$0.718877\pi$
$978$	6.93988e9	0.237228
$979$	4.51727e10	1.53864
$980$	−4.71882e9	−0.160156
$981$	7.34407e9	0.248368
$982$	1.32853e10	0.447692
$983$	−2.17942e9	−0.0731820	−0.0365910	−	0.999330i	$-0.511650\pi$
$983$	−2.17942e9	−0.0731820	−0.0365910	+	0.999330i	$0.511650\pi$
$984$	−3.76609e9	−0.126011
$985$	−6.51992e10	−2.17378
$986$	1.63877e10	0.544439
$987$	7.50994e9	0.248615
$988$	−1.92847e10	−0.636157
$989$	5.64532e9	0.185567
$990$	1.23830e10	0.405604
$991$	−2.17322e10	−0.709326	−0.354663	−	0.934994i	$-0.615404\pi$
$991$	−2.17322e10	−0.709326	−0.354663	+	0.934994i	$0.615404\pi$
$992$	1.51027e10	0.491208
$993$	1.75328e10	0.568236
$994$	1.31068e9	0.0423296
$995$	−1.68836e10	−0.543356
$996$	−1.36079e10	−0.436399
$997$	3.35378e10	1.07177	0.535884	−	0.844291i	$-0.319978\pi$
$997$	3.35378e10	1.07177	0.535884	+	0.844291i	$0.319978\pi$
$998$	−1.17135e10	−0.373019
$999$	1.94290e9	0.0616553

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.8.a.h.1.12	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.8.a.h.1.12	✓	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)

\(f(q)\)	\(=\)	\(q+6.08154 q^{2} +27.0000 q^{3} -91.0149 q^{4} +440.690 q^{5} +164.202 q^{6} +343.000 q^{7} -1331.95 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+6.08154 q^{2} +27.0000 q^{3} -91.0149 q^{4} +440.690 q^{5} +164.202 q^{6} +343.000 q^{7} -1331.95 q^{8} +729.000 q^{9} +2680.07 q^{10} +6337.99 q^{11} -2457.40 q^{12} -15114.8 q^{13} +2085.97 q^{14} +11898.6 q^{15} +3549.61 q^{16} +21161.0 q^{17} +4433.44 q^{18} -14018.4 q^{19} -40109.3 q^{20} +9261.00 q^{21} +38544.7 q^{22} -12167.0 q^{23} -35962.6 q^{24} +116082. q^{25} -91921.1 q^{26} +19683.0 q^{27} -31218.1 q^{28} +127341. q^{29} +72361.9 q^{30} +78628.9 q^{31} +192076. q^{32} +171126. q^{33} +128692. q^{34} +151157. q^{35} -66349.8 q^{36} +98709.4 q^{37} -85253.7 q^{38} -408099. q^{39} -586976. q^{40} +104723. q^{41} +56321.1 q^{42} -463986. q^{43} -576851. q^{44} +321263. q^{45} -73994.1 q^{46} +810921. q^{47} +95839.5 q^{48} +117649. q^{49} +705960. q^{50} +571348. q^{51} +1.37567e6 q^{52} +588730. q^{53} +119703. q^{54} +2.79309e6 q^{55} -456858. q^{56} -378498. q^{57} +774429. q^{58} -1.86953e6 q^{59} -1.08295e6 q^{60} +2.02175e6 q^{61} +478185. q^{62} +250047. q^{63} +713770. q^{64} -6.66093e6 q^{65} +1.04071e6 q^{66} -1.21344e6 q^{67} -1.92597e6 q^{68} -328509. q^{69} +919265. q^{70} +628331. q^{71} -970990. q^{72} +1.14120e6 q^{73} +600305. q^{74} +3.13422e6 q^{75} +1.27589e6 q^{76} +2.17393e6 q^{77} -2.48187e6 q^{78} -2.45505e6 q^{79} +1.56428e6 q^{80} +531441. q^{81} +636874. q^{82} +5.53752e6 q^{83} -842889. q^{84} +9.32545e6 q^{85} -2.82175e6 q^{86} +3.43821e6 q^{87} -8.44187e6 q^{88} +7.12729e6 q^{89} +1.95377e6 q^{90} -5.18437e6 q^{91} +1.10738e6 q^{92} +2.12298e6 q^{93} +4.93165e6 q^{94} -6.17778e6 q^{95} +5.18606e6 q^{96} -4.16914e6 q^{97} +715487. q^{98} +4.62039e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 24 q^{2} + 540 q^{3} + 1486 q^{4} + 1069 q^{5} + 648 q^{6} + 6860 q^{7} + 2127 q^{8} + 14580 q^{9}+O(q^{10}) \) 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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