LMFDB - Embedded newform 483.8.a.h.1.19

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			1.19
Root			$20.5409$ 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)

$f(q)$	$=$	$q+21.5409 q^{2} +27.0000 q^{3} +336.012 q^{4} -418.533 q^{5} +581.605 q^{6} +343.000 q^{7} +4480.78 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+21.5409 q^{2} +27.0000 q^{3} +336.012 q^{4} -418.533 q^{5} +581.605 q^{6} +343.000 q^{7} +4480.78 q^{8} +729.000 q^{9} -9015.59 q^{10} -3903.15 q^{11} +9072.33 q^{12} +7552.72 q^{13} +7388.54 q^{14} -11300.4 q^{15} +53510.7 q^{16} +13197.8 q^{17} +15703.3 q^{18} +9202.42 q^{19} -140632. q^{20} +9261.00 q^{21} -84077.5 q^{22} -12167.0 q^{23} +120981. q^{24} +97044.5 q^{25} +162693. q^{26} +19683.0 q^{27} +115252. q^{28} +143364. q^{29} -243421. q^{30} +106011. q^{31} +579130. q^{32} -105385. q^{33} +284292. q^{34} -143557. q^{35} +244953. q^{36} -280753. q^{37} +198229. q^{38} +203923. q^{39} -1.87535e6 q^{40} +698962. q^{41} +199491. q^{42} +149877. q^{43} -1.31151e6 q^{44} -305110. q^{45} -262089. q^{46} -9245.74 q^{47} +1.44479e6 q^{48} +117649. q^{49} +2.09043e6 q^{50} +356340. q^{51} +2.53781e6 q^{52} +1.19404e6 q^{53} +423990. q^{54} +1.63359e6 q^{55} +1.53691e6 q^{56} +248465. q^{57} +3.08819e6 q^{58} +2.02441e6 q^{59} -3.79707e6 q^{60} -406183. q^{61} +2.28357e6 q^{62} +250047. q^{63} +5.62565e6 q^{64} -3.16106e6 q^{65} -2.27009e6 q^{66} -2.54620e6 q^{67} +4.43461e6 q^{68} -328509. q^{69} -3.09235e6 q^{70} -575192. q^{71} +3.26649e6 q^{72} +2.42709e6 q^{73} -6.04768e6 q^{74} +2.62020e6 q^{75} +3.09212e6 q^{76} -1.33878e6 q^{77} +4.39270e6 q^{78} +3.92493e6 q^{79} -2.23960e7 q^{80} +531441. q^{81} +1.50563e7 q^{82} -9.57535e6 q^{83} +3.11181e6 q^{84} -5.52370e6 q^{85} +3.22848e6 q^{86} +3.87082e6 q^{87} -1.74891e7 q^{88} +8.17428e6 q^{89} -6.57236e6 q^{90} +2.59058e6 q^{91} -4.08826e6 q^{92} +2.86229e6 q^{93} -199162. q^{94} -3.85151e6 q^{95} +1.56365e7 q^{96} -2.56371e6 q^{97} +2.53427e6 q^{98} -2.84539e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	21.5409	1.90397	0.951984	−	0.306147i	$-0.0990399\pi$
$2$	21.5409	1.90397	0.951984	+	0.306147i	$0.0990399\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	336.012	2.62510
$5$	−418.533	−1.49739	−0.748694	−	0.662916i	$-0.769319\pi$
$5$	−418.533	−1.49739	−0.748694	+	0.662916i	$0.769319\pi$
$6$	581.605	1.09926
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	4480.78	3.09413
$9$	729.000	0.333333
$10$	−9015.59	−2.85098
$11$	−3903.15	−0.884180	−0.442090	−	0.896971i	$-0.645763\pi$
$11$	−3903.15	−0.884180	−0.442090	+	0.896971i	$0.645763\pi$
$12$	9072.33	1.51560
$13$	7552.72	0.953458	0.476729	−	0.879050i	$-0.341822\pi$
$13$	7552.72	0.953458	0.476729	+	0.879050i	$0.341822\pi$
$14$	7388.54	0.719632
$15$	−11300.4	−0.864517
$16$	53510.7	3.26603
$17$	13197.8	0.651522	0.325761	−	0.945452i	$-0.394379\pi$
$17$	13197.8	0.651522	0.325761	+	0.945452i	$0.394379\pi$
$18$	15703.3	0.634656
$19$	9202.42	0.307797	0.153898	−	0.988087i	$-0.450817\pi$
$19$	9202.42	0.307797	0.153898	+	0.988087i	$0.450817\pi$
$20$	−140632.	−3.93079
$21$	9261.00	0.218218
$22$	−84077.5	−1.68345
$23$	−12167.0	−0.208514
$23$	−12167.0	−0.208514
$24$	120981.	1.78640
$25$	97044.5	1.24217
$26$	162693.	1.81535
$27$	19683.0	0.192450
$28$	115252.	0.992193
$29$	143364.	1.09156	0.545778	−	0.837930i	$-0.316234\pi$
$29$	143364.	1.09156	0.545778	+	0.837930i	$0.316234\pi$
$30$	−243421.	−1.64601
$31$	106011.	0.639122	0.319561	−	0.947566i	$-0.396465\pi$
$31$	106011.	0.639122	0.319561	+	0.947566i	$0.396465\pi$
$32$	579130.	3.12429
$33$	−105385.	−0.510481
$34$	284292.	1.24048
$35$	−143557.	−0.565959
$36$	244953.	0.875032
$37$	−280753.	−0.911210	−0.455605	−	0.890182i	$-0.650577\pi$
$37$	−280753.	−0.911210	−0.455605	+	0.890182i	$0.650577\pi$
$38$	198229.	0.586036
$39$	203923.	0.550479
$40$	−1.87535e6	−4.63311
$41$	698962.	1.58384	0.791918	−	0.610628i	$-0.209083\pi$
$41$	698962.	1.58384	0.791918	+	0.610628i	$0.209083\pi$
$42$	199491.	0.415480
$43$	149877.	0.287471	0.143736	−	0.989616i	$-0.454089\pi$
$43$	149877.	0.287471	0.143736	+	0.989616i	$0.454089\pi$
$44$	−1.31151e6	−2.32106
$45$	−305110.	−0.499129
$46$	−262089.	−0.397005
$47$	−9245.74	−0.0129897	−0.00649485	−	0.999979i	$-0.502067\pi$
$47$	−9245.74	−0.0129897	−0.00649485	+	0.999979i	$0.502067\pi$
$48$	1.44479e6	1.88564
$49$	117649.	0.142857
$50$	2.09043e6	2.36505
$51$	356340.	0.376157
$52$	2.53781e6	2.50292
$53$	1.19404e6	1.10167	0.550836	−	0.834614i	$-0.314309\pi$
$53$	1.19404e6	1.10167	0.550836	+	0.834614i	$0.314309\pi$
$54$	423990.	0.366419
$55$	1.63359e6	1.32396
$56$	1.53691e6	1.16947
$57$	248465.	0.177707
$58$	3.08819e6	2.07829
$59$	2.02441e6	1.28326	0.641631	−	0.767013i	$-0.278258\pi$
$59$	2.02441e6	1.28326	0.641631	+	0.767013i	$0.278258\pi$
$60$	−3.79707e6	−2.26944
$61$	−406183.	−0.229122	−0.114561	−	0.993416i	$-0.536546\pi$
$61$	−406183.	−0.229122	−0.114561	+	0.993416i	$0.536546\pi$
$62$	2.28357e6	1.21687
$63$	250047.	0.125988
$64$	5.62565e6	2.68252
$65$	−3.16106e6	−1.42770
$66$	−2.27009e6	−0.971940
$67$	−2.54620e6	−1.03426	−0.517132	−	0.855906i	$-0.673000\pi$
$67$	−2.54620e6	−1.03426	−0.517132	+	0.855906i	$0.673000\pi$
$68$	4.43461e6	1.71031
$69$	−328509.	−0.120386
$70$	−3.09235e6	−1.07757
$71$	−575192.	−0.190726	−0.0953628	−	0.995443i	$-0.530401\pi$
$71$	−575192.	−0.190726	−0.0953628	+	0.995443i	$0.530401\pi$
$72$	3.26649e6	1.03138
$73$	2.42709e6	0.730223	0.365112	−	0.930964i	$-0.381031\pi$
$73$	2.42709e6	0.730223	0.365112	+	0.930964i	$0.381031\pi$
$74$	−6.04768e6	−1.73491
$75$	2.62020e6	0.717167
$76$	3.09212e6	0.807996
$77$	−1.33878e6	−0.334188
$78$	4.39270e6	1.04810
$79$	3.92493e6	0.895647	0.447823	−	0.894122i	$-0.352199\pi$
$79$	3.92493e6	0.895647	0.447823	+	0.894122i	$0.352199\pi$
$80$	−2.23960e7	−4.89052
$81$	531441.	0.111111
$82$	1.50563e7	3.01557
$83$	−9.57535e6	−1.83815	−0.919076	−	0.394081i	$-0.871063\pi$
$83$	−9.57535e6	−1.83815	−0.919076	+	0.394081i	$0.871063\pi$
$84$	3.11181e6	0.572843
$85$	−5.52370e6	−0.975582
$86$	3.22848e6	0.547336
$87$	3.87082e6	0.630210
$88$	−1.74891e7	−2.73577
$89$	8.17428e6	1.22909	0.614546	−	0.788881i	$-0.289339\pi$
$89$	8.17428e6	1.22909	0.614546	+	0.788881i	$0.289339\pi$
$90$	−6.57236e6	−0.950326
$91$	2.59058e6	0.360373
$92$	−4.08826e6	−0.547370
$93$	2.86229e6	0.368997
$94$	−199162.	−0.0247320
$95$	−3.85151e6	−0.460891
$96$	1.56365e7	1.80381
$97$	−2.56371e6	−0.285212	−0.142606	−	0.989780i	$-0.545548\pi$
$97$	−2.56371e6	−0.285212	−0.142606	+	0.989780i	$0.545548\pi$
$98$	2.53427e6	0.271995
$99$	−2.84539e6	−0.294727
$100$	3.26081e7	3.26081
$101$	−4.04171e6	−0.390338	−0.195169	−	0.980770i	$-0.562525\pi$
$101$	−4.04171e6	−0.390338	−0.195169	+	0.980770i	$0.562525\pi$
$102$	7.67590e6	0.716190
$103$	−3.40659e6	−0.307178	−0.153589	−	0.988135i	$-0.549083\pi$
$103$	−3.40659e6	−0.307178	−0.153589	+	0.988135i	$0.549083\pi$
$104$	3.38421e7	2.95012
$105$	−3.87603e6	−0.326757
$106$	2.57207e7	2.09755
$107$	−438458.	−0.0346007	−0.0173003	−	0.999850i	$-0.505507\pi$
$107$	−438458.	−0.0346007	−0.0173003	+	0.999850i	$0.505507\pi$
$108$	6.61373e6	0.505200
$109$	1.23776e7	0.915472	0.457736	−	0.889088i	$-0.348661\pi$
$109$	1.23776e7	0.915472	0.457736	+	0.889088i	$0.348661\pi$
$110$	3.51892e7	2.52078
$111$	−7.58033e6	−0.526087
$112$	1.83542e7	1.23444
$113$	1.57245e7	1.02518	0.512592	−	0.858633i	$-0.328685\pi$
$113$	1.57245e7	1.02518	0.512592	+	0.858633i	$0.328685\pi$
$114$	5.35218e6	0.338348
$115$	5.09229e6	0.312227
$116$	4.81719e7	2.86544
$117$	5.50593e6	0.317819
$118$	4.36076e7	2.44329
$119$	4.52684e6	0.246252
$120$	−5.06345e7	−2.67493
$121$	−4.25262e6	−0.218227
$122$	−8.74956e6	−0.436241
$123$	1.88720e7	0.914428
$124$	3.56209e7	1.67776
$125$	−7.91843e6	−0.362622
$126$	5.38625e6	0.239877
$127$	−2.66980e7	−1.15656	−0.578278	−	0.815840i	$-0.696275\pi$
$127$	−2.66980e7	−1.15656	−0.578278	+	0.815840i	$0.696275\pi$
$128$	4.70531e7	1.98314
$129$	4.04667e6	0.165972
$130$	−6.80922e7	−2.71829
$131$	3.51154e7	1.36473	0.682367	−	0.731010i	$-0.260951\pi$
$131$	3.51154e7	1.36473	0.682367	+	0.731010i	$0.260951\pi$
$132$	−3.54106e7	−1.34006
$133$	3.15643e6	0.116336
$134$	−5.48476e7	−1.96920
$135$	−8.23798e6	−0.288172
$136$	5.91363e7	2.01590
$137$	8.28271e6	0.275201	0.137601	−	0.990488i	$-0.456061\pi$
$137$	8.28271e6	0.275201	0.137601	+	0.990488i	$0.456061\pi$
$138$	−7.07639e6	−0.229211
$139$	−2.04084e7	−0.644550	−0.322275	−	0.946646i	$-0.604448\pi$
$139$	−2.04084e7	−0.644550	−0.322275	+	0.946646i	$0.604448\pi$
$140$	−4.82368e7	−1.48570
$141$	−249635.	−0.00749961
$142$	−1.23902e7	−0.363135
$143$	−2.94794e7	−0.843028
$144$	3.90093e7	1.08868
$145$	−6.00024e7	−1.63448
$146$	5.22818e7	1.39032
$147$	3.17652e6	0.0824786
$148$	−9.43364e7	−2.39201
$149$	4.61497e7	1.14292	0.571461	−	0.820629i	$-0.306377\pi$
$149$	4.61497e7	1.14292	0.571461	+	0.820629i	$0.306377\pi$
$150$	5.64416e7	1.36546
$151$	−6.89206e7	−1.62903	−0.814516	−	0.580142i	$-0.802997\pi$
$151$	−6.89206e7	−1.62903	−0.814516	+	0.580142i	$0.802997\pi$
$152$	4.12340e7	0.952364
$153$	9.62118e6	0.217174
$154$	−2.88386e7	−0.636284
$155$	−4.43689e7	−0.957013
$156$	6.85208e7	1.44506
$157$	4.65073e7	0.959119	0.479560	−	0.877509i	$-0.340796\pi$
$157$	4.65073e7	0.959119	0.479560	+	0.877509i	$0.340796\pi$
$158$	8.45466e7	1.70528
$159$	3.22390e7	0.636050
$160$	−2.42385e8	−4.67827
$161$	−4.17328e6	−0.0788110
$162$	1.14477e7	0.211552
$163$	−9.06342e7	−1.63921	−0.819607	−	0.572927i	$-0.805808\pi$
$163$	−9.06342e7	−1.63921	−0.819607	+	0.572927i	$0.805808\pi$
$164$	2.34860e8	4.15772
$165$	4.41070e7	0.764388
$166$	−2.06262e8	−3.49978
$167$	5.38365e7	0.894477	0.447238	−	0.894415i	$-0.352408\pi$
$167$	5.38365e7	0.894477	0.447238	+	0.894415i	$0.352408\pi$
$168$	4.14965e7	0.675195
$169$	−5.70495e6	−0.0909177
$170$	−1.18986e8	−1.85748
$171$	6.70856e6	0.102599
$172$	5.03604e7	0.754639
$173$	1.09196e8	1.60341	0.801705	−	0.597720i	$-0.203927\pi$
$173$	1.09196e8	1.60341	0.801705	+	0.597720i	$0.203927\pi$
$174$	8.33811e7	1.19990
$175$	3.32863e7	0.469496
$176$	−2.08860e8	−2.88776
$177$	5.46590e7	0.740892
$178$	1.76082e8	2.34015
$179$	−1.21903e8	−1.58865	−0.794325	−	0.607493i	$-0.792175\pi$
$179$	−1.21903e8	−1.58865	−0.794325	+	0.607493i	$0.792175\pi$
$180$	−1.02521e8	−1.31026
$181$	−1.46259e8	−1.83336	−0.916679	−	0.399624i	$-0.869141\pi$
$181$	−1.46259e8	−1.83336	−0.916679	+	0.399624i	$0.869141\pi$
$182$	5.58036e7	0.686139
$183$	−1.09669e7	−0.132284
$184$	−5.45177e7	−0.645171
$185$	1.17504e8	1.36443
$186$	6.16564e7	0.702559
$187$	−5.15128e7	−0.576063
$188$	−3.10668e6	−0.0340992
$189$	6.75127e6	0.0727393
$190$	−8.29652e7	−0.877523
$191$	−9.74020e7	−1.01147	−0.505733	−	0.862690i	$-0.668778\pi$
$191$	−9.74020e7	−1.01147	−0.505733	+	0.862690i	$0.668778\pi$
$192$	1.51893e8	1.54875
$193$	−1.05597e8	−1.05730	−0.528652	−	0.848838i	$-0.677302\pi$
$193$	−1.05597e8	−1.05730	−0.528652	+	0.848838i	$0.677302\pi$
$194$	−5.52248e7	−0.543036
$195$	−8.53486e7	−0.824281
$196$	3.95315e7	0.375014
$197$	−7.40436e7	−0.690010	−0.345005	−	0.938601i	$-0.612123\pi$
$197$	−7.40436e7	−0.690010	−0.345005	+	0.938601i	$0.612123\pi$
$198$	−6.12925e7	−0.561150
$199$	3.60520e7	0.324297	0.162149	−	0.986766i	$-0.448158\pi$
$199$	3.60520e7	0.324297	0.162149	+	0.986766i	$0.448158\pi$
$200$	4.34835e8	3.84344
$201$	−6.87475e7	−0.597132
$202$	−8.70623e7	−0.743191
$203$	4.91737e7	0.412569
$204$	1.19735e8	0.987447
$205$	−2.92538e8	−2.37162
$206$	−7.33812e7	−0.584857
$207$	−8.86974e6	−0.0695048
$208$	4.04151e8	3.11402
$209$	−3.59184e7	−0.272148
$210$	−8.34933e7	−0.622135
$211$	−1.04489e8	−0.765738	−0.382869	−	0.923803i	$-0.625064\pi$
$211$	−1.04489e8	−0.765738	−0.382869	+	0.923803i	$0.625064\pi$
$212$	4.01211e8	2.89199
$213$	−1.55302e7	−0.110115
$214$	−9.44480e6	−0.0658786
$215$	−6.27282e7	−0.430456
$216$	8.81952e7	0.595466
$217$	3.63616e7	0.241565
$218$	2.66626e8	1.74303
$219$	6.55314e7	0.421595
$220$	5.48908e8	3.47552
$221$	9.96791e7	0.621199
$222$	−1.63287e8	−1.00165
$223$	−1.61225e8	−0.973565	−0.486782	−	0.873523i	$-0.661830\pi$
$223$	−1.61225e8	−0.973565	−0.486782	+	0.873523i	$0.661830\pi$
$224$	1.98642e8	1.18087
$225$	7.07455e7	0.414057
$226$	3.38720e8	1.95192
$227$	1.48351e8	0.841780	0.420890	−	0.907112i	$-0.361718\pi$
$227$	1.48351e8	0.841780	0.420890	+	0.907112i	$0.361718\pi$
$228$	8.34874e7	0.466497
$229$	1.46805e8	0.807823	0.403911	−	0.914798i	$-0.367650\pi$
$229$	1.46805e8	0.807823	0.403911	+	0.914798i	$0.367650\pi$
$230$	1.09693e8	0.594470
$231$	−3.61470e7	−0.192944
$232$	6.42381e8	3.37742
$233$	1.69372e8	0.877194	0.438597	−	0.898684i	$-0.355476\pi$
$233$	1.69372e8	0.877194	0.438597	+	0.898684i	$0.355476\pi$
$234$	1.18603e8	0.605118
$235$	3.86964e6	0.0194506
$236$	6.80225e8	3.36869
$237$	1.05973e8	0.517102
$238$	9.75123e7	0.468857
$239$	−1.85923e8	−0.880928	−0.440464	−	0.897770i	$-0.645186\pi$
$239$	−1.85923e8	−0.880928	−0.440464	+	0.897770i	$0.645186\pi$
$240$	−6.04691e8	−2.82354
$241$	−1.76203e7	−0.0810873	−0.0405437	−	0.999178i	$-0.512909\pi$
$241$	−1.76203e7	−0.0810873	−0.0405437	+	0.999178i	$0.512909\pi$
$242$	−9.16054e7	−0.415497
$243$	1.43489e7	0.0641500
$244$	−1.36482e8	−0.601468
$245$	−4.92399e7	−0.213913
$246$	4.06520e8	1.74104
$247$	6.95033e7	0.293471
$248$	4.75010e8	1.97753
$249$	−2.58534e8	−1.06126
$250$	−1.70571e8	−0.690421
$251$	−5.09356e7	−0.203312	−0.101656	−	0.994820i	$-0.532414\pi$
$251$	−5.09356e7	−0.203312	−0.101656	+	0.994820i	$0.532414\pi$
$252$	8.40189e7	0.330731
$253$	4.74896e7	0.184364
$254$	−5.75101e8	−2.20204
$255$	−1.49140e8	−0.563252
$256$	2.93485e8	1.09332
$257$	−3.32947e8	−1.22351	−0.611757	−	0.791046i	$-0.709537\pi$
$257$	−3.32947e8	−1.22351	−0.611757	+	0.791046i	$0.709537\pi$
$258$	8.71690e7	0.316005
$259$	−9.62983e7	−0.344405
$260$	−1.06215e9	−3.74784
$261$	1.04512e8	0.363852
$262$	7.56418e8	2.59841
$263$	−4.99380e8	−1.69272	−0.846361	−	0.532610i	$-0.821211\pi$
$263$	−4.99380e8	−1.69272	−0.846361	+	0.532610i	$0.821211\pi$
$264$	−4.72207e8	−1.57950
$265$	−4.99743e8	−1.64963
$266$	6.79925e7	0.221501
$267$	2.20706e8	0.709617
$268$	−8.55555e8	−2.71504
$269$	3.14705e8	0.985759	0.492879	−	0.870098i	$-0.335944\pi$
$269$	3.14705e8	0.985759	0.492879	+	0.870098i	$0.335944\pi$
$270$	−1.77454e8	−0.548671
$271$	−3.62693e8	−1.10700	−0.553499	−	0.832850i	$-0.686708\pi$
$271$	−3.62693e8	−1.10700	−0.553499	+	0.832850i	$0.686708\pi$
$272$	7.06222e8	2.12789
$273$	6.99457e7	0.208062
$274$	1.78417e8	0.523975
$275$	−3.78779e8	−1.09830
$276$	−1.10383e8	−0.316024
$277$	7.61942e7	0.215398	0.107699	−	0.994184i	$-0.465652\pi$
$277$	7.61942e7	0.215398	0.107699	+	0.994184i	$0.465652\pi$
$278$	−4.39615e8	−1.22720
$279$	7.72818e7	0.213041
$280$	−6.43246e8	−1.75115
$281$	−7.92371e7	−0.213038	−0.106519	−	0.994311i	$-0.533970\pi$
$281$	−7.92371e7	−0.213038	−0.106519	+	0.994311i	$0.533970\pi$
$282$	−5.37737e6	−0.0142790
$283$	−1.90892e8	−0.500651	−0.250326	−	0.968162i	$-0.580538\pi$
$283$	−1.90892e8	−0.500651	−0.250326	+	0.968162i	$0.580538\pi$
$284$	−1.93272e8	−0.500673
$285$	−1.03991e8	−0.266096
$286$	−6.35013e8	−1.60510
$287$	2.39744e8	0.598634
$288$	4.22186e8	1.04143
$289$	−2.36157e8	−0.575518
$290$	−1.29251e9	−3.11200
$291$	−6.92203e7	−0.164668
$292$	8.15532e8	1.91691
$293$	5.98136e8	1.38920	0.694598	−	0.719398i	$-0.255582\pi$
$293$	5.98136e8	1.38920	0.694598	+	0.719398i	$0.255582\pi$
$294$	6.84253e7	0.157037
$295$	−8.47280e8	−1.92154
$296$	−1.25799e9	−2.81940
$297$	−7.68256e7	−0.170160
$298$	9.94108e8	2.17609
$299$	−9.18939e7	−0.198810
$300$	8.80420e8	1.88263
$301$	5.14077e7	0.108654
$302$	−1.48461e9	−3.10162
$303$	−1.09126e8	−0.225362
$304$	4.92427e8	1.00527
$305$	1.70001e8	0.343085
$306$	2.07249e8	0.413493
$307$	6.68156e8	1.31793	0.658966	−	0.752172i	$-0.270994\pi$
$307$	6.68156e8	1.31793	0.658966	+	0.752172i	$0.270994\pi$
$308$	−4.49846e8	−0.877277
$309$	−9.19779e7	−0.177349
$310$	−9.55748e8	−1.82212
$311$	−9.02755e8	−1.70180	−0.850900	−	0.525328i	$-0.823943\pi$
$311$	−9.02755e8	−1.70180	−0.850900	+	0.525328i	$0.823943\pi$
$312$	9.13736e8	1.70326
$313$	3.97062e8	0.731902	0.365951	−	0.930634i	$-0.380744\pi$
$313$	3.97062e8	0.731902	0.365951	+	0.930634i	$0.380744\pi$
$314$	1.00181e9	1.82613
$315$	−1.04653e8	−0.188653
$316$	1.31882e9	2.35116
$317$	4.22150e7	0.0744319	0.0372160	−	0.999307i	$-0.488151\pi$
$317$	4.22150e7	0.0744319	0.0372160	+	0.999307i	$0.488151\pi$
$318$	6.94458e8	1.21102
$319$	−5.59569e8	−0.965132
$320$	−2.35452e9	−4.01677
$321$	−1.18384e7	−0.0199767
$322$	−8.98964e7	−0.150054
$323$	1.21451e8	0.200537
$324$	1.78571e8	0.291677
$325$	7.32950e8	1.18436
$326$	−1.95235e9	−3.12101
$327$	3.34196e8	0.528548
$328$	3.13190e9	4.90060
$329$	−3.17129e6	−0.00490965
$330$	9.50107e8	1.45537
$331$	4.26078e8	0.645790	0.322895	−	0.946435i	$-0.395344\pi$
$331$	4.26078e8	0.645790	0.322895	+	0.946435i	$0.395344\pi$
$332$	−3.21744e9	−4.82532
$333$	−2.04669e8	−0.303737
$334$	1.15969e9	1.70306
$335$	1.06567e9	1.54869
$336$	4.95562e8	0.712707
$337$	−8.46622e7	−0.120499	−0.0602497	−	0.998183i	$-0.519190\pi$
$337$	−8.46622e7	−0.120499	−0.0602497	+	0.998183i	$0.519190\pi$
$338$	−1.22890e8	−0.173104
$339$	4.24561e8	0.591890
$340$	−1.85603e9	−2.56100
$341$	−4.13775e8	−0.565098
$342$	1.44509e8	0.195345
$343$	4.03536e7	0.0539949
$344$	6.71564e8	0.889473
$345$	1.37492e8	0.180264
$346$	2.35218e9	3.05284
$347$	7.88085e8	1.01256	0.506279	−	0.862370i	$-0.331021\pi$
$347$	7.88085e8	1.01256	0.506279	+	0.862370i	$0.331021\pi$
$348$	1.30064e9	1.65436
$349$	−1.35189e9	−1.70236	−0.851180	−	0.524874i	$-0.824113\pi$
$349$	−1.35189e9	−1.70236	−0.851180	+	0.524874i	$0.824113\pi$
$350$	7.17018e8	0.893906
$351$	1.48660e8	0.183493
$352$	−2.26043e9	−2.76243
$353$	1.16294e9	1.40717	0.703584	−	0.710612i	$-0.251582\pi$
$353$	1.16294e9	1.40717	0.703584	+	0.710612i	$0.251582\pi$
$354$	1.17741e9	1.41064
$355$	2.40737e8	0.285590
$356$	2.74666e9	3.22649
$357$	1.22225e8	0.142174
$358$	−2.62590e9	−3.02474
$359$	3.20965e8	0.366123	0.183062	−	0.983101i	$-0.441399\pi$
$359$	3.20965e8	0.366123	0.183062	+	0.983101i	$0.441399\pi$
$360$	−1.36713e9	−1.54437
$361$	−8.09187e8	−0.905261
$362$	−3.15056e9	−3.49066
$363$	−1.14821e8	−0.125993
$364$	8.70468e8	0.946014
$365$	−1.01582e9	−1.09343
$366$	−2.36238e8	−0.251864
$367$	1.47063e9	1.55301	0.776503	−	0.630113i	$-0.216992\pi$
$367$	1.47063e9	1.55301	0.776503	+	0.630113i	$0.216992\pi$
$368$	−6.51064e8	−0.681015
$369$	5.09543e8	0.527945
$370$	2.53115e9	2.59784
$371$	4.09554e8	0.416393
$372$	9.61764e8	0.968653
$373$	1.80310e9	1.79903	0.899517	−	0.436885i	$-0.143918\pi$
$373$	1.80310e9	1.79903	0.899517	+	0.436885i	$0.143918\pi$
$374$	−1.10964e9	−1.09681
$375$	−2.13798e8	−0.209360
$376$	−4.14281e7	−0.0401918
$377$	1.08279e9	1.04075
$378$	1.45429e8	0.138493
$379$	−1.75872e9	−1.65943	−0.829715	−	0.558187i	$-0.811497\pi$
$379$	−1.75872e9	−1.65943	−0.829715	+	0.558187i	$0.811497\pi$
$380$	−1.29415e9	−1.20988
$381$	−7.20847e8	−0.667737
$382$	−2.09813e9	−1.92580
$383$	−1.98546e9	−1.80578	−0.902892	−	0.429867i	$-0.858560\pi$
$383$	−1.98546e9	−1.80578	−0.902892	+	0.429867i	$0.858560\pi$
$384$	1.27043e9	1.14497
$385$	5.60323e8	0.500410
$386$	−2.27465e9	−2.01307
$387$	1.09260e8	0.0958237
$388$	−8.61439e8	−0.748710
$389$	2.22288e9	1.91466	0.957332	−	0.288989i	$-0.0933191\pi$
$389$	2.22288e9	1.91466	0.957332	+	0.288989i	$0.0933191\pi$
$390$	−1.83849e9	−1.56940
$391$	−1.60577e8	−0.135852
$392$	5.27159e8	0.442019
$393$	9.48115e8	0.787929
$394$	−1.59497e9	−1.31376
$395$	−1.64271e9	−1.34113
$396$	−9.56087e8	−0.773685
$397$	2.60848e7	0.0209229	0.0104614	−	0.999945i	$-0.496670\pi$
$397$	2.60848e7	0.0209229	0.0104614	+	0.999945i	$0.496670\pi$
$398$	7.76594e8	0.617452
$399$	8.52236e7	0.0671668
$400$	5.19292e9	4.05697
$401$	−4.03978e8	−0.312862	−0.156431	−	0.987689i	$-0.549999\pi$
$401$	−4.03978e8	−0.312862	−0.156431	+	0.987689i	$0.549999\pi$
$402$	−1.48089e9	−1.13692
$403$	8.00669e8	0.609376
$404$	−1.35806e9	−1.02467
$405$	−2.22425e8	−0.166376
$406$	1.05925e9	0.785519
$407$	1.09582e9	0.805673
$408$	1.59668e9	1.16388
$409$	1.09692e9	0.792759	0.396380	−	0.918087i	$-0.370266\pi$
$409$	1.09692e9	0.792759	0.396380	+	0.918087i	$0.370266\pi$
$410$	−6.30155e9	−4.51548
$411$	2.23633e8	0.158888
$412$	−1.14466e9	−0.806371
$413$	6.94371e8	0.485028
$414$	−1.91063e8	−0.132335
$415$	4.00760e9	2.75243
$416$	4.37401e9	2.97888
$417$	−5.51026e8	−0.372131
$418$	−7.73716e8	−0.518161
$419$	1.03725e9	0.688865	0.344432	−	0.938811i	$-0.388071\pi$
$419$	1.03725e9	0.688865	0.344432	+	0.938811i	$0.388071\pi$
$420$	−1.30239e9	−0.857768
$421$	−1.19528e9	−0.780698	−0.390349	−	0.920667i	$-0.627646\pi$
$421$	−1.19528e9	−0.780698	−0.390349	+	0.920667i	$0.627646\pi$
$422$	−2.25078e9	−1.45794
$423$	−6.74015e6	−0.00432990
$424$	5.35021e9	3.40871
$425$	1.28077e9	0.809302
$426$	−3.34535e8	−0.209656
$427$	−1.39321e8	−0.0866000
$428$	−1.47327e8	−0.0908302
$429$	−7.95943e8	−0.486723
$430$	−1.35123e9	−0.819574
$431$	3.69920e8	0.222555	0.111277	−	0.993789i	$-0.464506\pi$
$431$	3.69920e8	0.222555	0.111277	+	0.993789i	$0.464506\pi$
$432$	1.05325e9	0.628548
$433$	−2.84469e9	−1.68394	−0.841972	−	0.539522i	$-0.818605\pi$
$433$	−2.84469e9	−1.68394	−0.841972	+	0.539522i	$0.818605\pi$
$434$	7.83264e8	0.459933
$435$	−1.62006e9	−0.943669
$436$	4.15904e9	2.40320
$437$	−1.11966e8	−0.0641801
$438$	1.41161e9	0.802703
$439$	−3.24948e9	−1.83311	−0.916553	−	0.399914i	$-0.869040\pi$
$439$	−3.24948e9	−1.83311	−0.916553	+	0.399914i	$0.869040\pi$
$440$	7.31978e9	4.09650
$441$	8.57661e7	0.0476190
$442$	2.14718e9	1.18274
$443$	1.61325e9	0.881633	0.440816	−	0.897597i	$-0.354689\pi$
$443$	1.61325e9	0.881633	0.440816	+	0.897597i	$0.354689\pi$
$444$	−2.54708e9	−1.38103
$445$	−3.42120e9	−1.84043
$446$	−3.47293e9	−1.85364
$447$	1.24604e9	0.659867
$448$	1.92960e9	1.01390
$449$	1.99351e9	1.03934	0.519669	−	0.854368i	$-0.326055\pi$
$449$	1.99351e9	1.03934	0.519669	+	0.854368i	$0.326055\pi$
$450$	1.52392e9	0.788351
$451$	−2.72815e9	−1.40040
$452$	5.28362e9	2.69120
$453$	−1.86085e9	−0.940522
$454$	3.19561e9	1.60272
$455$	−1.08424e9	−0.539619
$456$	1.11332e9	0.549848
$457$	−1.65890e9	−0.813044	−0.406522	−	0.913641i	$-0.633259\pi$
$457$	−1.65890e9	−0.813044	−0.406522	+	0.913641i	$0.633259\pi$
$458$	3.16231e9	1.53807
$459$	2.59772e8	0.125386
$460$	1.71107e9	0.819626
$461$	−5.24014e8	−0.249109	−0.124555	−	0.992213i	$-0.539750\pi$
$461$	−5.24014e8	−0.249109	−0.124555	+	0.992213i	$0.539750\pi$
$462$	−7.78641e8	−0.367359
$463$	3.78082e9	1.77032	0.885161	−	0.465285i	$-0.154048\pi$
$463$	3.78082e9	1.77032	0.885161	+	0.465285i	$0.154048\pi$
$464$	7.67148e9	3.56506
$465$	−1.19796e9	−0.552532
$466$	3.64843e9	1.67015
$467$	−3.02034e9	−1.37229	−0.686146	−	0.727464i	$-0.740699\pi$
$467$	−3.02034e9	−1.37229	−0.686146	+	0.727464i	$0.740699\pi$
$468$	1.85006e9	0.834306
$469$	−8.73347e8	−0.390915
$470$	8.33558e7	0.0370334
$471$	1.25570e9	0.553748
$472$	9.07092e9	3.97058
$473$	−5.84990e8	−0.254176
$474$	2.28276e9	0.984546
$475$	8.93044e8	0.382336
$476$	1.52107e9	0.646436
$477$	8.70452e8	0.367224
$478$	−4.00496e9	−1.67726
$479$	−9.77237e8	−0.406280	−0.203140	−	0.979150i	$-0.565115\pi$
$479$	−9.77237e8	−0.406280	−0.203140	+	0.979150i	$0.565115\pi$
$480$	−6.54439e9	−2.70100
$481$	−2.12045e9	−0.868800
$482$	−3.79557e8	−0.154388
$483$	−1.12679e8	−0.0455016
$484$	−1.42893e9	−0.572866
$485$	1.07300e9	0.427074
$486$	3.09089e8	0.122140
$487$	4.59114e7	0.0180123	0.00900615	−	0.999959i	$-0.497133\pi$
$487$	4.59114e7	0.0180123	0.00900615	+	0.999959i	$0.497133\pi$
$488$	−1.82002e9	−0.708934
$489$	−2.44712e9	−0.946400
$490$	−1.06067e9	−0.407283
$491$	−8.20935e8	−0.312985	−0.156492	−	0.987679i	$-0.550019\pi$
$491$	−8.20935e8	−0.312985	−0.156492	+	0.987679i	$0.550019\pi$
$492$	6.34122e9	2.40046
$493$	1.89208e9	0.711173
$494$	1.49717e9	0.558760
$495$	1.19089e9	0.441320
$496$	5.67270e9	2.08739
$497$	−1.97291e8	−0.0720875
$498$	−5.56908e9	−2.02060
$499$	−1.47734e7	−0.00532264	−0.00266132	−	0.999996i	$-0.500847\pi$
$499$	−1.47734e7	−0.00532264	−0.00266132	+	0.999996i	$0.500847\pi$
$500$	−2.66069e9	−0.951918
$501$	1.45358e9	0.516426
$502$	−1.09720e9	−0.387100
$503$	−1.57681e9	−0.552447	−0.276223	−	0.961093i	$-0.589083\pi$
$503$	−1.57681e9	−0.552447	−0.276223	+	0.961093i	$0.589083\pi$
$504$	1.12041e9	0.389824
$505$	1.69159e9	0.584487
$506$	1.02297e9	0.351024
$507$	−1.54034e8	−0.0524913
$508$	−8.97087e9	−3.03607
$509$	2.04783e9	0.688305	0.344153	−	0.938914i	$-0.388166\pi$
$509$	2.04783e9	0.688305	0.344153	+	0.938914i	$0.388166\pi$
$510$	−3.21261e9	−1.07241
$511$	8.32491e8	0.275998
$512$	2.99154e8	0.0985030
$513$	1.81131e8	0.0592355
$514$	−7.17198e9	−2.32953
$515$	1.42577e9	0.459964
$516$	1.35973e9	0.435691
$517$	3.60875e7	0.0114852
$518$	−2.07436e9	−0.655736
$519$	2.94829e9	0.925729
$520$	−1.41640e10	−4.41748
$521$	−2.89271e9	−0.896135	−0.448068	−	0.894000i	$-0.647888\pi$
$521$	−2.89271e9	−0.896135	−0.448068	+	0.894000i	$0.647888\pi$
$522$	2.25129e9	0.692763
$523$	2.85654e8	0.0873141	0.0436571	−	0.999047i	$-0.486099\pi$
$523$	2.85654e8	0.0873141	0.0436571	+	0.999047i	$0.486099\pi$
$524$	1.17992e10	3.58256
$525$	8.98729e8	0.271064
$526$	−1.07571e10	−3.22289
$527$	1.39910e9	0.416402
$528$	−5.63922e9	−1.66725
$529$	1.48036e8	0.0434783
$530$	−1.07649e10	−3.14084
$531$	1.47579e9	0.427754
$532$	1.06060e9	0.305394
$533$	5.27906e9	1.51012
$534$	4.75421e9	1.35109
$535$	1.83509e8	0.0518107
$536$	−1.14090e10	−3.20015
$537$	−3.29138e9	−0.917208
$538$	6.77904e9	1.87685
$539$	−4.59201e8	−0.126311
$540$	−2.76806e9	−0.756480
$541$	6.21403e9	1.68726	0.843631	−	0.536923i	$-0.180413\pi$
$541$	6.21403e9	1.68726	0.843631	+	0.536923i	$0.180413\pi$
$542$	−7.81275e9	−2.10769
$543$	−3.94899e9	−1.05849
$544$	7.64323e9	2.03555
$545$	−5.18044e9	−1.37082
$546$	1.50670e9	0.396143
$547$	3.06386e8	0.0800410	0.0400205	−	0.999199i	$-0.487258\pi$
$547$	3.06386e8	0.0800410	0.0400205	+	0.999199i	$0.487258\pi$
$548$	2.78309e9	0.722430
$549$	−2.96107e8	−0.0763741
$550$	−8.15926e9	−2.09113
$551$	1.31929e9	0.335978
$552$	−1.47198e9	−0.372490
$553$	1.34625e9	0.338523
$554$	1.64129e9	0.410112
$555$	3.17261e9	0.787756
$556$	−6.85746e9	−1.69200
$557$	−4.68801e9	−1.14946	−0.574732	−	0.818341i	$-0.694894\pi$
$557$	−4.68801e9	−1.14946	−0.574732	+	0.818341i	$0.694894\pi$
$558$	1.66472e9	0.405622
$559$	1.13198e9	0.274092
$560$	−7.68181e9	−1.84844
$561$	−1.39085e9	−0.332590
$562$	−1.70684e9	−0.405617
$563$	1.37644e9	0.325072	0.162536	−	0.986703i	$-0.448033\pi$
$563$	1.37644e9	0.325072	0.162536	+	0.986703i	$0.448033\pi$
$564$	−8.38804e7	−0.0196872
$565$	−6.58120e9	−1.53510
$566$	−4.11199e9	−0.953224
$567$	1.82284e8	0.0419961
$568$	−2.57731e9	−0.590130
$569$	−6.27506e9	−1.42799	−0.713994	−	0.700152i	$-0.753116\pi$
$569$	−6.27506e9	−1.42799	−0.713994	+	0.700152i	$0.753116\pi$
$570$	−2.24006e9	−0.506638
$571$	−2.69591e9	−0.606010	−0.303005	−	0.952989i	$-0.597990\pi$
$571$	−2.69591e9	−0.606010	−0.303005	+	0.952989i	$0.597990\pi$
$572$	−9.90543e9	−2.21303
$573$	−2.62985e9	−0.583970
$574$	5.16431e9	1.13978
$575$	−1.18074e9	−0.259010
$576$	4.10110e9	0.894173
$577$	−2.81001e8	−0.0608964	−0.0304482	−	0.999536i	$-0.509693\pi$
$577$	−2.81001e8	−0.0608964	−0.0304482	+	0.999536i	$0.509693\pi$
$578$	−5.08706e9	−1.09577
$579$	−2.85111e9	−0.610435
$580$	−2.01615e10	−4.29067
$581$	−3.28435e9	−0.694756
$582$	−1.49107e9	−0.313522
$583$	−4.66050e9	−0.974075
$584$	1.08753e10	2.25941
$585$	−2.30441e9	−0.475899
$586$	1.28844e10	2.64499
$587$	−1.72279e9	−0.351560	−0.175780	−	0.984430i	$-0.556245\pi$
$587$	−1.72279e9	−0.351560	−0.175780	+	0.984430i	$0.556245\pi$
$588$	1.06735e9	0.216514
$589$	9.75554e8	0.196720
$590$	−1.82512e10	−3.65856
$591$	−1.99918e9	−0.398378
$592$	−1.50233e10	−2.97604
$593$	−7.98450e9	−1.57238	−0.786188	−	0.617988i	$-0.787948\pi$
$593$	−7.98450e9	−1.57238	−0.786188	+	0.617988i	$0.787948\pi$
$594$	−1.65490e9	−0.323980
$595$	−1.89463e9	−0.368735
$596$	1.55069e10	3.00028
$597$	9.73403e8	0.187233
$598$	−1.97948e9	−0.378527
$599$	−2.96312e9	−0.563321	−0.281660	−	0.959514i	$-0.590885\pi$
$599$	−2.96312e9	−0.563321	−0.281660	+	0.959514i	$0.590885\pi$
$600$	1.17405e10	2.21901
$601$	6.66065e9	1.25157	0.625786	−	0.779995i	$-0.284778\pi$
$601$	6.66065e9	1.25157	0.625786	+	0.779995i	$0.284778\pi$
$602$	1.10737e9	0.206874
$603$	−1.85618e9	−0.344754
$604$	−2.31581e10	−4.27636
$605$	1.77986e9	0.326770
$606$	−2.35068e9	−0.429081
$607$	−4.76711e9	−0.865157	−0.432579	−	0.901596i	$-0.642396\pi$
$607$	−4.76711e9	−0.865157	−0.432579	+	0.901596i	$0.642396\pi$
$608$	5.32940e9	0.961647
$609$	1.32769e9	0.238197
$610$	3.66198e9	0.653223
$611$	−6.98305e7	−0.0123851
$612$	3.23283e9	0.570103
$613$	6.14428e9	1.07736	0.538678	−	0.842512i	$-0.318924\pi$
$613$	6.14428e9	1.07736	0.538678	+	0.842512i	$0.318924\pi$
$614$	1.43927e10	2.50930
$615$	−7.89854e9	−1.36925
$616$	−5.99878e9	−1.03402
$617$	−6.85201e8	−0.117441	−0.0587205	−	0.998274i	$-0.518702\pi$
$617$	−6.85201e8	−0.117441	−0.0587205	+	0.998274i	$0.518702\pi$
$618$	−1.98129e9	−0.337667
$619$	9.10086e9	1.54229	0.771143	−	0.636662i	$-0.219685\pi$
$619$	9.10086e9	1.54229	0.771143	+	0.636662i	$0.219685\pi$
$620$	−1.49085e10	−2.51225
$621$	−2.39483e8	−0.0401286
$622$	−1.94462e10	−3.24017
$623$	2.80378e9	0.464553
$624$	1.09121e10	1.79788
$625$	−4.26748e9	−0.699184
$626$	8.55309e9	1.39352
$627$	−9.69796e8	−0.157125
$628$	1.56270e10	2.51778
$629$	−3.70531e9	−0.593673
$630$	−2.25432e9	−0.359190
$631$	−2.00906e8	−0.0318339	−0.0159169	−	0.999873i	$-0.505067\pi$
$631$	−2.00906e8	−0.0318339	−0.0159169	+	0.999873i	$0.505067\pi$
$632$	1.75867e10	2.77125
$633$	−2.82119e9	−0.442099
$634$	9.09351e8	0.141716
$635$	1.11740e10	1.73181
$636$	1.08327e10	1.66969
$637$	8.88570e8	0.136208
$638$	−1.20537e10	−1.83758
$639$	−4.19315e8	−0.0635752
$640$	−1.96933e10	−2.96953
$641$	−7.21469e8	−0.108197	−0.0540984	−	0.998536i	$-0.517228\pi$
$641$	−7.21469e8	−0.108197	−0.0540984	+	0.998536i	$0.517228\pi$
$642$	−2.55010e8	−0.0380351
$643$	9.89409e9	1.46770	0.733850	−	0.679312i	$-0.237722\pi$
$643$	9.89409e9	1.46770	0.733850	+	0.679312i	$0.237722\pi$
$644$	−1.40227e9	−0.206887
$645$	−1.69366e9	−0.248524
$646$	2.61618e9	0.381815
$647$	4.31982e9	0.627047	0.313524	−	0.949580i	$-0.398491\pi$
$647$	4.31982e9	0.627047	0.313524	+	0.949580i	$0.398491\pi$
$648$	2.38127e9	0.343792
$649$	−7.90155e9	−1.13463
$650$	1.57884e10	2.25498
$651$	9.81765e8	0.139468
$652$	−3.04542e10	−4.30309
$653$	−9.75503e9	−1.37098	−0.685492	−	0.728080i	$-0.740413\pi$
$653$	−9.75503e9	−1.37098	−0.685492	+	0.728080i	$0.740413\pi$
$654$	7.19890e9	1.00634
$655$	−1.46969e10	−2.04353
$656$	3.74019e10	5.17286
$657$	1.76935e9	0.243408
$658$	−6.83126e7	−0.00934781
$659$	−9.57926e9	−1.30387	−0.651933	−	0.758277i	$-0.726042\pi$
$659$	−9.57926e9	−1.30387	−0.651933	+	0.758277i	$0.726042\pi$
$660$	1.48205e10	2.00659
$661$	1.87353e9	0.252322	0.126161	−	0.992010i	$-0.459734\pi$
$661$	1.87353e9	0.252322	0.126161	+	0.992010i	$0.459734\pi$
$662$	9.17812e9	1.22956
$663$	2.69133e9	0.358650
$664$	−4.29050e10	−5.68748
$665$	−1.32107e9	−0.174201
$666$	−4.40876e9	−0.578305
$667$	−1.74431e9	−0.227605
$668$	1.80897e10	2.34809
$669$	−4.35307e9	−0.562088
$670$	2.29555e10	2.94866
$671$	1.58539e9	0.202585
$672$	5.36333e9	0.681776
$673$	−5.79857e9	−0.733277	−0.366639	−	0.930363i	$-0.619491\pi$
$673$	−5.79857e9	−0.733277	−0.366639	+	0.930363i	$0.619491\pi$
$674$	−1.82370e9	−0.229427
$675$	1.91013e9	0.239056
$676$	−1.91693e9	−0.238668
$677$	−1.58471e10	−1.96286	−0.981428	−	0.191832i	$-0.938557\pi$
$677$	−1.58471e10	−1.96286	−0.981428	+	0.191832i	$0.938557\pi$
$678$	9.14544e9	1.12694
$679$	−8.79354e8	−0.107800
$680$	−2.47505e10	−3.01858
$681$	4.00547e9	0.486002
$682$	−8.91311e9	−1.07593
$683$	1.15963e10	1.39267	0.696334	−	0.717717i	$-0.254813\pi$
$683$	1.15963e10	1.39267	0.696334	+	0.717717i	$0.254813\pi$
$684$	2.25416e9	0.269332
$685$	−3.46658e9	−0.412083
$686$	8.69255e8	0.102805
$687$	3.96373e9	0.466397
$688$	8.02000e9	0.938890
$689$	9.01822e9	1.05040
$690$	2.96170e9	0.343218
$691$	−5.81006e9	−0.669896	−0.334948	−	0.942237i	$-0.608719\pi$
$691$	−5.81006e9	−0.669896	−0.334948	+	0.942237i	$0.608719\pi$
$692$	3.66911e10	4.20910
$693$	−9.75970e8	−0.111396
$694$	1.69761e10	1.92788
$695$	8.54156e9	0.965141
$696$	1.73443e10	1.94995
$697$	9.22474e9	1.03190
$698$	−2.91209e10	−3.24124
$699$	4.57304e9	0.506448
$700$	1.11846e10	1.23247
$701$	−1.53112e10	−1.67879	−0.839393	−	0.543525i	$-0.817089\pi$
$701$	−1.53112e10	−1.67879	−0.839393	+	0.543525i	$0.817089\pi$
$702$	3.20228e9	0.349365
$703$	−2.58361e9	−0.280468
$704$	−2.19577e10	−2.37183
$705$	1.04480e8	0.0112298
$706$	2.50508e10	2.67920
$707$	−1.38631e9	−0.147534
$708$	1.83661e10	1.94491
$709$	1.11355e10	1.17340	0.586702	−	0.809803i	$-0.300426\pi$
$709$	1.11355e10	1.17340	0.586702	+	0.809803i	$0.300426\pi$
$710$	5.18570e9	0.543755
$711$	2.86127e9	0.298549
$712$	3.66272e10	3.80297
$713$	−1.28983e9	−0.133266
$714$	2.63283e9	0.270695
$715$	1.23381e10	1.26234
$716$	−4.09609e10	−4.17036
$717$	−5.01992e9	−0.508604
$718$	6.91389e9	0.697087
$719$	7.37267e9	0.739731	0.369865	−	0.929085i	$-0.379404\pi$
$719$	7.37267e9	0.739731	0.369865	+	0.929085i	$0.379404\pi$
$720$	−1.63267e10	−1.63017
$721$	−1.16846e9	−0.116102
$722$	−1.74307e10	−1.72359
$723$	−4.75747e8	−0.0468158
$724$	−4.91448e10	−4.81274
$725$	1.39127e10	1.35590
$726$	−2.47335e9	−0.239887
$727$	5.76449e9	0.556404	0.278202	−	0.960523i	$-0.410261\pi$
$727$	5.76449e9	0.556404	0.278202	+	0.960523i	$0.410261\pi$
$728$	1.16078e10	1.11504
$729$	3.87420e8	0.0370370
$730$	−2.18816e10	−2.08185
$731$	1.97804e9	0.187294
$732$	−3.68503e9	−0.347258
$733$	−1.70502e9	−0.159906	−0.0799532	−	0.996799i	$-0.525477\pi$
$733$	−1.70502e9	−0.159906	−0.0799532	+	0.996799i	$0.525477\pi$
$734$	3.16788e10	2.95688
$735$	−1.32948e9	−0.123502
$736$	−7.04628e9	−0.651460
$737$	9.93820e9	0.914474
$738$	1.09760e10	1.00519
$739$	1.93445e10	1.76320	0.881601	−	0.471996i	$-0.156466\pi$
$739$	1.93445e10	1.76320	0.881601	+	0.471996i	$0.156466\pi$
$740$	3.94829e10	3.58177
$741$	1.87659e9	0.169436
$742$	8.82219e9	0.792798
$743$	4.53412e8	0.0405539	0.0202769	−	0.999794i	$-0.493545\pi$
$743$	4.53412e8	0.0405539	0.0202769	+	0.999794i	$0.493545\pi$
$744$	1.28253e10	1.14173
$745$	−1.93151e10	−1.71140
$746$	3.88405e10	3.42531
$747$	−6.98043e9	−0.612717
$748$	−1.73089e10	−1.51222
$749$	−1.50391e8	−0.0130778
$750$	−4.60540e9	−0.398615
$751$	8.96446e9	0.772297	0.386149	−	0.922437i	$-0.373805\pi$
$751$	8.96446e9	0.772297	0.386149	+	0.922437i	$0.373805\pi$
$752$	−4.94746e8	−0.0424248
$753$	−1.37526e9	−0.117382
$754$	2.33242e10	1.98156
$755$	2.88455e10	2.43929
$756$	2.26851e9	0.190948
$757$	−2.34274e10	−1.96286	−0.981429	−	0.191825i	$-0.938559\pi$
$757$	−2.34274e10	−1.96286	−0.981429	+	0.191825i	$0.938559\pi$
$758$	−3.78845e10	−3.15950
$759$	1.28222e9	0.106443
$760$	−1.72578e10	−1.42606
$761$	1.40396e10	1.15481	0.577404	−	0.816458i	$-0.304066\pi$
$761$	1.40396e10	1.15481	0.577404	+	0.816458i	$0.304066\pi$
$762$	−1.55277e10	−1.27135
$763$	4.24553e9	0.346016
$764$	−3.27282e10	−2.65519
$765$	−4.02678e9	−0.325194
$766$	−4.27687e10	−3.43816
$767$	1.52898e10	1.22354
$768$	7.92411e9	0.631228
$769$	−1.32323e10	−1.04928	−0.524641	−	0.851324i	$-0.675800\pi$
$769$	−1.32323e10	−1.04928	−0.524641	+	0.851324i	$0.675800\pi$
$770$	1.20699e10	0.952764
$771$	−8.98956e9	−0.706396
$772$	−3.54818e10	−2.77553
$773$	7.54548e9	0.587569	0.293784	−	0.955872i	$-0.405085\pi$
$773$	7.54548e9	0.587569	0.293784	+	0.955872i	$0.405085\pi$
$774$	2.35356e9	0.182445
$775$	1.02878e10	0.793898
$776$	−1.14874e10	−0.882485
$777$	−2.60005e9	−0.198842
$778$	4.78830e10	3.64546
$779$	6.43214e9	0.487500
$780$	−2.86782e10	−2.16382
$781$	2.24506e9	0.168636
$782$	−3.45899e9	−0.258658
$783$	2.82183e9	0.210070
$784$	6.29548e9	0.466576
$785$	−1.94648e10	−1.43617
$786$	2.04233e10	1.50019
$787$	−4.56457e9	−0.333801	−0.166901	−	0.985974i	$-0.553376\pi$
$787$	−4.56457e9	−0.333801	−0.166901	+	0.985974i	$0.553376\pi$
$788$	−2.48796e10	−1.81134
$789$	−1.34832e10	−0.977293
$790$	−3.53855e10	−2.55347
$791$	5.39349e9	0.387483
$792$	−1.27496e10	−0.911922
$793$	−3.06778e9	−0.218458
$794$	5.61892e8	0.0398365
$795$	−1.34931e10	−0.952414
$796$	1.21139e10	0.851311
$797$	−2.72172e10	−1.90432	−0.952160	−	0.305600i	$-0.901143\pi$
$797$	−2.72172e10	−1.90432	−0.952160	+	0.305600i	$0.901143\pi$
$798$	1.83580e9	0.127883
$799$	−1.22023e8	−0.00846308
$800$	5.62014e10	3.88090
$801$	5.95905e9	0.409698
$802$	−8.70208e9	−0.595679
$803$	−9.47328e9	−0.645648
$804$	−2.31000e10	−1.56753
$805$	1.74665e9	0.118011
$806$	1.72472e10	1.16023
$807$	8.49703e9	0.569128
$808$	−1.81100e10	−1.20776
$809$	1.69801e10	1.12751	0.563755	−	0.825942i	$-0.309356\pi$
$809$	1.69801e10	1.12751	0.563755	+	0.825942i	$0.309356\pi$
$810$	−4.79125e9	−0.316775
$811$	−4.01062e9	−0.264021	−0.132011	−	0.991248i	$-0.542143\pi$
$811$	−4.01062e9	−0.264021	−0.132011	+	0.991248i	$0.542143\pi$
$812$	1.65230e10	1.08303
$813$	−9.79271e9	−0.639125
$814$	2.36050e10	1.53398
$815$	3.79334e10	2.45454
$816$	1.90680e10	1.22854
$817$	1.37923e9	0.0884827
$818$	2.36286e10	1.50939
$819$	1.88853e9	0.120124
$820$	−9.82965e10	−6.22572
$821$	2.33765e10	1.47428	0.737139	−	0.675741i	$-0.236176\pi$
$821$	2.33765e10	1.47428	0.737139	+	0.675741i	$0.236176\pi$
$822$	4.81727e9	0.302517
$823$	−1.61275e10	−1.00848	−0.504239	−	0.863564i	$-0.668227\pi$
$823$	−1.61275e10	−1.00848	−0.504239	+	0.863564i	$0.668227\pi$
$824$	−1.52642e10	−0.950448
$825$	−1.02270e10	−0.634104
$826$	1.49574e10	0.923478
$827$	−2.72119e10	−1.67298	−0.836489	−	0.547984i	$-0.815396\pi$
$827$	−2.72119e10	−1.67298	−0.836489	+	0.547984i	$0.815396\pi$
$828$	−2.98034e9	−0.182457
$829$	2.95831e10	1.80345	0.901724	−	0.432313i	$-0.142303\pi$
$829$	2.95831e10	1.80345	0.901724	+	0.432313i	$0.142303\pi$
$830$	8.63274e10	5.24053
$831$	2.05724e9	0.124360
$832$	4.24890e10	2.55767
$833$	1.55270e9	0.0930746
$834$	−1.18696e10	−0.708525
$835$	−2.25323e10	−1.33938
$836$	−1.20690e10	−0.714414
$837$	2.08661e9	0.122999
$838$	2.23433e10	1.31158
$839$	9.93375e9	0.580693	0.290346	−	0.956922i	$-0.406230\pi$
$839$	9.93375e9	0.580693	0.290346	+	0.956922i	$0.406230\pi$
$840$	−1.73676e10	−1.01103
$841$	3.30326e9	0.191495
$842$	−2.57475e10	−1.48642
$843$	−2.13940e9	−0.122997
$844$	−3.51094e10	−2.01014
$845$	2.38771e9	0.136139
$846$	−1.45189e8	−0.00824400
$847$	−1.45865e9	−0.0824819
$848$	6.38937e10	3.59809
$849$	−5.15409e9	−0.289051
$850$	2.75890e10	1.54088
$851$	3.41592e9	0.190000
$852$	−5.21834e9	−0.289064
$853$	8.90903e9	0.491483	0.245742	−	0.969335i	$-0.420969\pi$
$853$	8.90903e9	0.491483	0.245742	+	0.969335i	$0.420969\pi$
$854$	−3.00110e9	−0.164884
$855$	−2.80775e9	−0.153630
$856$	−1.96463e9	−0.107059
$857$	−1.89059e10	−1.02604	−0.513020	−	0.858377i	$-0.671473\pi$
$857$	−1.89059e10	−1.02604	−0.513020	+	0.858377i	$0.671473\pi$
$858$	−1.71454e10	−0.926704
$859$	−1.31077e10	−0.705587	−0.352794	−	0.935701i	$-0.614768\pi$
$859$	−1.31077e10	−0.705587	−0.352794	+	0.935701i	$0.614768\pi$
$860$	−2.10775e10	−1.12999
$861$	6.47309e9	0.345621
$862$	7.96842e9	0.423737
$863$	−3.65452e9	−0.193550	−0.0967749	−	0.995306i	$-0.530853\pi$
$863$	−3.65452e9	−0.193550	−0.0967749	+	0.995306i	$0.530853\pi$
$864$	1.13990e10	0.601270
$865$	−4.57020e10	−2.40093
$866$	−6.12773e10	−3.20617
$867$	−6.37625e9	−0.332276
$868$	1.22180e10	0.634132
$869$	−1.53196e10	−0.791913
$870$	−3.48977e10	−1.79672
$871$	−1.92308e10	−0.986127
$872$	5.54615e10	2.83259
$873$	−1.86895e9	−0.0950708
$874$	−2.41185e9	−0.122197
$875$	−2.71602e9	−0.137058
$876$	2.20194e10	1.10673
$877$	−2.34609e10	−1.17448	−0.587241	−	0.809412i	$-0.699786\pi$
$877$	−2.34609e10	−1.17448	−0.587241	+	0.809412i	$0.699786\pi$
$878$	−6.99968e10	−3.49017
$879$	1.61497e10	0.802053
$880$	8.74147e10	4.32409
$881$	3.38000e9	0.166533	0.0832666	−	0.996527i	$-0.473465\pi$
$881$	3.38000e9	0.166533	0.0832666	+	0.996527i	$0.473465\pi$
$882$	1.84748e9	0.0906652
$883$	2.85739e10	1.39671	0.698356	−	0.715751i	$-0.253915\pi$
$883$	2.85739e10	1.39671	0.698356	+	0.715751i	$0.253915\pi$
$884$	3.34934e10	1.63071
$885$	−2.28766e10	−1.10940
$886$	3.47509e10	1.67860
$887$	−3.97516e9	−0.191259	−0.0956295	−	0.995417i	$-0.530486\pi$
$887$	−3.97516e9	−0.191259	−0.0956295	+	0.995417i	$0.530486\pi$
$888$	−3.39658e10	−1.62778
$889$	−9.15743e9	−0.437137
$890$	−7.36960e10	−3.50412
$891$	−2.07429e9	−0.0982422
$892$	−5.41735e10	−2.55570
$893$	−8.50832e7	−0.00399819
$894$	2.68409e10	1.25637
$895$	5.10203e10	2.37883
$896$	1.61392e10	0.749557
$897$	−2.48114e9	−0.114783
$898$	4.29422e10	1.97887
$899$	1.51981e10	0.697637
$900$	2.37713e10	1.08694
$901$	1.57586e10	0.717763
$902$	−5.87670e10	−2.66631
$903$	1.38801e9	0.0627313
$904$	7.04579e10	3.17205
$905$	6.12141e10	2.74525
$906$	−4.00846e10	−1.79072
$907$	3.86398e10	1.71953	0.859765	−	0.510690i	$-0.170610\pi$
$907$	3.86398e10	1.71953	0.859765	+	0.510690i	$0.170610\pi$
$908$	4.98476e10	2.20975
$909$	−2.94641e9	−0.130113
$910$	−2.33556e10	−1.02742
$911$	1.76735e10	0.774476	0.387238	−	0.921980i	$-0.373429\pi$
$911$	1.76735e10	0.774476	0.387238	+	0.921980i	$0.373429\pi$
$912$	1.32955e10	0.580396
$913$	3.73740e10	1.62526
$914$	−3.57343e10	−1.54801
$915$	4.59002e9	0.198080
$916$	4.93282e10	2.12061
$917$	1.20446e10	0.515821
$918$	5.59573e9	0.238730
$919$	1.68021e10	0.714099	0.357049	−	0.934086i	$-0.383783\pi$
$919$	1.68021e10	0.714099	0.357049	+	0.934086i	$0.383783\pi$
$920$	2.28174e10	0.966071
$921$	1.80402e10	0.760909
$922$	−1.12878e10	−0.474296
$923$	−4.34427e9	−0.181849
$924$	−1.21458e10	−0.506496
$925$	−2.72455e10	−1.13188
$926$	8.14424e10	3.37064
$927$	−2.48340e9	−0.102393
$928$	8.30263e10	3.41034
$929$	3.83436e9	0.156906	0.0784528	−	0.996918i	$-0.475002\pi$
$929$	3.83436e9	0.156906	0.0784528	+	0.996918i	$0.475002\pi$
$930$	−2.58052e10	−1.05200
$931$	1.08266e9	0.0439710
$932$	5.69110e10	2.30272
$933$	−2.43744e10	−0.982535
$934$	−6.50610e10	−2.61280
$935$	2.15598e10	0.862589
$936$	2.46709e10	0.983375
$937$	−2.10506e10	−0.835941	−0.417971	−	0.908461i	$-0.637258\pi$
$937$	−2.10506e10	−0.835941	−0.417971	+	0.908461i	$0.637258\pi$
$938$	−1.88127e10	−0.744289
$939$	1.07207e10	0.422564
$940$	1.30025e9	0.0510597
$941$	−8.44859e9	−0.330537	−0.165269	−	0.986249i	$-0.552849\pi$
$941$	−8.44859e9	−0.330537	−0.165269	+	0.986249i	$0.552849\pi$
$942$	2.70489e10	1.05432
$943$	−8.50427e9	−0.330253
$944$	1.08327e11	4.19118
$945$	−2.82563e9	−0.108919
$946$	−1.26012e10	−0.483943
$947$	−3.67679e10	−1.40684	−0.703419	−	0.710775i	$-0.748344\pi$
$947$	−3.67679e10	−1.40684	−0.703419	+	0.710775i	$0.748344\pi$
$948$	3.56082e10	1.35744
$949$	1.83311e10	0.696237
$950$	1.92370e10	0.727956
$951$	1.13980e9	0.0429733
$952$	2.02838e10	0.761937
$953$	3.47305e10	1.29983	0.649914	−	0.760008i	$-0.274805\pi$
$953$	3.47305e10	1.29983	0.649914	+	0.760008i	$0.274805\pi$
$954$	1.87504e10	0.699182
$955$	4.07659e10	1.51456
$956$	−6.24724e10	−2.31252
$957$	−1.51084e10	−0.557219
$958$	−2.10506e10	−0.773544
$959$	2.84097e9	0.104016
$960$	−6.35720e10	−2.31908
$961$	−1.62744e10	−0.591524
$962$	−4.56765e10	−1.65417
$963$	−3.19636e8	−0.0115336
$964$	−5.92063e9	−0.212862
$965$	4.41957e10	1.58319
$966$	−2.42720e9	−0.0866336
$967$	−6.92286e8	−0.0246203	−0.0123101	−	0.999924i	$-0.503919\pi$
$967$	−6.92286e8	−0.0246203	−0.0123101	+	0.999924i	$0.503919\pi$
$968$	−1.90551e10	−0.675222
$969$	3.27919e9	0.115780
$970$	2.31134e10	0.813135
$971$	−6.62316e9	−0.232166	−0.116083	−	0.993240i	$-0.537034\pi$
$971$	−6.62316e9	−0.232166	−0.116083	+	0.993240i	$0.537034\pi$
$972$	4.82141e9	0.168400
$973$	−7.00007e9	−0.243617
$974$	9.88975e8	0.0342949
$975$	1.97896e10	0.683789
$976$	−2.17351e10	−0.748320
$977$	−1.43404e10	−0.491961	−0.245981	−	0.969275i	$-0.579110\pi$
$977$	−1.43404e10	−0.491961	−0.245981	+	0.969275i	$0.579110\pi$
$978$	−5.27133e10	−1.80192
$979$	−3.19054e10	−1.08674
$980$	−1.65452e10	−0.561541
$981$	9.02330e9	0.305157
$982$	−1.76837e10	−0.595913
$983$	2.83526e10	0.952041	0.476021	−	0.879434i	$-0.342079\pi$
$983$	2.83526e10	0.952041	0.476021	+	0.879434i	$0.342079\pi$
$984$	8.45612e10	2.82936
$985$	3.09897e10	1.03321
$986$	4.07572e10	1.35405
$987$	−8.56248e7	−0.00283459
$988$	2.33540e10	0.770391
$989$	−1.82355e9	−0.0599419
$990$	2.56529e10	0.840259
$991$	−4.34070e10	−1.41678	−0.708390	−	0.705821i	$-0.750578\pi$
$991$	−4.34070e10	−1.41678	−0.708390	+	0.705821i	$0.750578\pi$
$992$	6.13940e10	1.99680
$993$	1.15041e10	0.372847
$994$	−4.24983e9	−0.137252
$995$	−1.50889e10	−0.485599
$996$	−8.68707e10	−2.78590
$997$	2.71957e10	0.869095	0.434548	−	0.900649i	$-0.356908\pi$
$997$	2.71957e10	0.869095	0.434548	+	0.900649i	$0.356908\pi$
$998$	−3.18232e8	−0.0101341
$999$	−5.52606e9	−0.175362

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.8.a.h.1.19	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.8.a.h.1.19	✓	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)

\(f(q)\)	\(=\)	\(q+21.5409 q^{2} +27.0000 q^{3} +336.012 q^{4} -418.533 q^{5} +581.605 q^{6} +343.000 q^{7} +4480.78 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+21.5409 q^{2} +27.0000 q^{3} +336.012 q^{4} -418.533 q^{5} +581.605 q^{6} +343.000 q^{7} +4480.78 q^{8} +729.000 q^{9} -9015.59 q^{10} -3903.15 q^{11} +9072.33 q^{12} +7552.72 q^{13} +7388.54 q^{14} -11300.4 q^{15} +53510.7 q^{16} +13197.8 q^{17} +15703.3 q^{18} +9202.42 q^{19} -140632. q^{20} +9261.00 q^{21} -84077.5 q^{22} -12167.0 q^{23} +120981. q^{24} +97044.5 q^{25} +162693. q^{26} +19683.0 q^{27} +115252. q^{28} +143364. q^{29} -243421. q^{30} +106011. q^{31} +579130. q^{32} -105385. q^{33} +284292. q^{34} -143557. q^{35} +244953. q^{36} -280753. q^{37} +198229. q^{38} +203923. q^{39} -1.87535e6 q^{40} +698962. q^{41} +199491. q^{42} +149877. q^{43} -1.31151e6 q^{44} -305110. q^{45} -262089. q^{46} -9245.74 q^{47} +1.44479e6 q^{48} +117649. q^{49} +2.09043e6 q^{50} +356340. q^{51} +2.53781e6 q^{52} +1.19404e6 q^{53} +423990. q^{54} +1.63359e6 q^{55} +1.53691e6 q^{56} +248465. q^{57} +3.08819e6 q^{58} +2.02441e6 q^{59} -3.79707e6 q^{60} -406183. q^{61} +2.28357e6 q^{62} +250047. q^{63} +5.62565e6 q^{64} -3.16106e6 q^{65} -2.27009e6 q^{66} -2.54620e6 q^{67} +4.43461e6 q^{68} -328509. q^{69} -3.09235e6 q^{70} -575192. q^{71} +3.26649e6 q^{72} +2.42709e6 q^{73} -6.04768e6 q^{74} +2.62020e6 q^{75} +3.09212e6 q^{76} -1.33878e6 q^{77} +4.39270e6 q^{78} +3.92493e6 q^{79} -2.23960e7 q^{80} +531441. q^{81} +1.50563e7 q^{82} -9.57535e6 q^{83} +3.11181e6 q^{84} -5.52370e6 q^{85} +3.22848e6 q^{86} +3.87082e6 q^{87} -1.74891e7 q^{88} +8.17428e6 q^{89} -6.57236e6 q^{90} +2.59058e6 q^{91} -4.08826e6 q^{92} +2.86229e6 q^{93} -199162. q^{94} -3.85151e6 q^{95} +1.56365e7 q^{96} -2.56371e6 q^{97} +2.53427e6 q^{98} -2.84539e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 24 q^{2} + 540 q^{3} + 1486 q^{4} + 1069 q^{5} + 648 q^{6} + 6860 q^{7} + 2127 q^{8} + 14580 q^{9}+O(q^{10}) \) 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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