LMFDB - Embedded newform 169.10.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,10,Mod(1,169)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("169.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	169.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:	$87.0410563117$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 1602x^{2} + 1544x + 342272 $ x^4 - x^3 - 1602x^2 + 1544x + 342272
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 13)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-15.3567$ of defining polynomial
Character	$\chi$	$=$	169.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.35673 q^{2} +42.6243 q^{3} -457.879 q^{4} +1236.25 q^{5} -313.575 q^{6} -892.010 q^{7} +7135.13 q^{8} -17866.2 q^{9} +O(q^{10})$	\(q-7.35673 q^{2} +42.6243 q^{3} -457.879 q^{4} +1236.25 q^{5} -313.575 q^{6} -892.010 q^{7} +7135.13 q^{8} -17866.2 q^{9} -9094.74 q^{10} +27149.8 q^{11} -19516.8 q^{12} +6562.27 q^{14} +52694.2 q^{15} +181943. q^{16} -34643.4 q^{17} +131437. q^{18} -428885. q^{19} -566052. q^{20} -38021.3 q^{21} -199734. q^{22} +2.03704e6 q^{23} +304130. q^{24} -424814. q^{25} -1.60051e6 q^{27} +408432. q^{28} -5.26400e6 q^{29} -387657. q^{30} +4.15910e6 q^{31} -4.99169e6 q^{32} +1.15724e6 q^{33} +254862. q^{34} -1.10275e6 q^{35} +8.18054e6 q^{36} +7.58854e6 q^{37} +3.15519e6 q^{38} +8.82080e6 q^{40} +4.92536e6 q^{41} +279712. q^{42} +1.71882e7 q^{43} -1.24313e7 q^{44} -2.20870e7 q^{45} -1.49859e7 q^{46} +2.95568e7 q^{47} +7.75518e6 q^{48} -3.95579e7 q^{49} +3.12524e6 q^{50} -1.47665e6 q^{51} -2.72331e7 q^{53} +1.17745e7 q^{54} +3.35640e7 q^{55} -6.36461e6 q^{56} -1.82809e7 q^{57} +3.87258e7 q^{58} +1.13602e8 q^{59} -2.41276e7 q^{60} -3.76868e7 q^{61} -3.05973e7 q^{62} +1.59368e7 q^{63} -5.64321e7 q^{64} -8.51352e6 q^{66} -1.90094e8 q^{67} +1.58625e7 q^{68} +8.68273e7 q^{69} +8.11260e6 q^{70} -6.87130e7 q^{71} -1.27477e8 q^{72} -3.61495e8 q^{73} -5.58268e7 q^{74} -1.81074e7 q^{75} +1.96377e8 q^{76} -2.42179e7 q^{77} -1.42229e8 q^{79} +2.24926e8 q^{80} +2.83439e8 q^{81} -3.62346e7 q^{82} +5.80240e7 q^{83} +1.74091e7 q^{84} -4.28279e7 q^{85} -1.26449e8 q^{86} -2.24374e8 q^{87} +1.93718e8 q^{88} +8.59928e8 q^{89} +1.62488e8 q^{90} -9.32716e8 q^{92} +1.77279e8 q^{93} -2.17442e8 q^{94} -5.30208e8 q^{95} -2.12767e8 q^{96} -1.46970e9 q^{97} +2.91017e8 q^{98} -4.85064e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 33 q^{2} - 163 q^{3} + 1429 q^{4} - 471 q^{5} + 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9}+O(q^{10}) $ 4 * q + 33 * q^2 - 163 * q^3 + 1429 * q^4 - 471 * q^5 + 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9	\( 4 q + 33 q^{2} - 163 q^{3} + 1429 q^{4} - 471 q^{5} + 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9} - 67831 q^{10} + 40140 q^{11} - 155479 q^{12} - 277653 q^{14} - 83307 q^{15} + 726609 q^{16} + 78717 q^{17} - 1691026 q^{18} - 209664 q^{19} - 870843 q^{20} - 1138431 q^{21} + 1364090 q^{22} - 4257444 q^{23} - 3561573 q^{24} - 2900157 q^{25} - 2077801 q^{27} - 4035181 q^{28} - 1647936 q^{29} - 744143 q^{30} + 11366002 q^{31} + 29458959 q^{32} + 14413222 q^{33} - 26257659 q^{34} - 13789797 q^{35} - 11587714 q^{36} - 4636891 q^{37} + 25172466 q^{38} + 22536791 q^{40} - 13859538 q^{41} + 75564923 q^{42} - 33368081 q^{43} - 66489222 q^{44} + 17423928 q^{45} - 71369332 q^{46} + 3943005 q^{47} - 620787 q^{48} + 23294923 q^{49} + 4217748 q^{50} - 19664471 q^{51} - 171019326 q^{53} + 64946915 q^{54} - 121160538 q^{55} - 281552967 q^{56} + 47829030 q^{57} - 79964734 q^{58} + 63389388 q^{59} - 37708135 q^{60} + 77050190 q^{61} - 95878740 q^{62} + 155695476 q^{63} + 768962465 q^{64} - 42396374 q^{66} + 41174072 q^{67} - 717615423 q^{68} + 546642556 q^{69} - 409056389 q^{70} - 252460989 q^{71} - 562579254 q^{72} - 594415068 q^{73} - 957058539 q^{74} + 533318748 q^{75} + 326897170 q^{76} + 561950454 q^{77} + 115998984 q^{79} + 509107233 q^{80} + 437803700 q^{81} - 875148240 q^{82} + 79577862 q^{83} - 108899441 q^{84} - 549463469 q^{85} + 589924887 q^{86} - 1087526510 q^{87} - 2327564370 q^{88} + 1152240276 q^{89} + 877550038 q^{90} - 4213481460 q^{92} - 1618266556 q^{93} + 1859909503 q^{94} - 1273705170 q^{95} - 3171454029 q^{96} - 1049098084 q^{97} - 420532254 q^{98} - 2132181050 q^{99}+O(q^{100}) \) 4 * q + 33 * q^2 - 163 * q^3 + 1429 * q^4 - 471 * q^5 + 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9 - 67831 * q^10 + 40140 * q^11 - 155479 * q^12 - 277653 * q^14 - 83307 * q^15 + 726609 * q^16 + 78717 * q^17 - 1691026 * q^18 - 209664 * q^19 - 870843 * q^20 - 1138431 * q^21 + 1364090 * q^22 - 4257444 * q^23 - 3561573 * q^24 - 2900157 * q^25 - 2077801 * q^27 - 4035181 * q^28 - 1647936 * q^29 - 744143 * q^30 + 11366002 * q^31 + 29458959 * q^32 + 14413222 * q^33 - 26257659 * q^34 - 13789797 * q^35 - 11587714 * q^36 - 4636891 * q^37 + 25172466 * q^38 + 22536791 * q^40 - 13859538 * q^41 + 75564923 * q^42 - 33368081 * q^43 - 66489222 * q^44 + 17423928 * q^45 - 71369332 * q^46 + 3943005 * q^47 - 620787 * q^48 + 23294923 * q^49 + 4217748 * q^50 - 19664471 * q^51 - 171019326 * q^53 + 64946915 * q^54 - 121160538 * q^55 - 281552967 * q^56 + 47829030 * q^57 - 79964734 * q^58 + 63389388 * q^59 - 37708135 * q^60 + 77050190 * q^61 - 95878740 * q^62 + 155695476 * q^63 + 768962465 * q^64 - 42396374 * q^66 + 41174072 * q^67 - 717615423 * q^68 + 546642556 * q^69 - 409056389 * q^70 - 252460989 * q^71 - 562579254 * q^72 - 594415068 * q^73 - 957058539 * q^74 + 533318748 * q^75 + 326897170 * q^76 + 561950454 * q^77 + 115998984 * q^79 + 509107233 * q^80 + 437803700 * q^81 - 875148240 * q^82 + 79577862 * q^83 - 108899441 * q^84 - 549463469 * q^85 + 589924887 * q^86 - 1087526510 * q^87 - 2327564370 * q^88 + 1152240276 * q^89 + 877550038 * q^90 - 4213481460 * q^92 - 1618266556 * q^93 + 1859909503 * q^94 - 1273705170 * q^95 - 3171454029 * q^96 - 1049098084 * q^97 - 420532254 * q^98 - 2132181050 * 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 $

$2$	−7.35673	−0.325124	−0.162562	−	0.986698i	$-0.551976\pi$
$2$	−7.35673	−0.325124	−0.162562	+	0.986698i	$0.551976\pi$
$3$	42.6243	0.303817	0.151908	−	0.988395i	$-0.451458\pi$
$3$	42.6243	0.303817	0.151908	+	0.988395i	$0.451458\pi$
$4$	−457.879	−0.894294
$5$	1236.25	0.884588	0.442294	−	0.896870i	$-0.354165\pi$
$5$	1236.25	0.884588	0.442294	+	0.896870i	$0.354165\pi$
$6$	−313.575	−0.0987782
$7$	−892.010	−0.140420	−0.0702099	−	0.997532i	$-0.522367\pi$
$7$	−892.010	−0.140420	−0.0702099	+	0.997532i	$0.522367\pi$
$8$	7135.13	0.615881
$9$	−17866.2	−0.907695
$10$	−9094.74	−0.287601
$11$	27149.8	0.559114	0.279557	−	0.960129i	$-0.409812\pi$
$11$	27149.8	0.559114	0.279557	+	0.960129i	$0.409812\pi$
$12$	−19516.8	−0.271702
$13$	0	0
$13$	0	0
$14$	6562.27	0.0456539
$15$	52694.2	0.268753
$16$	181943.	0.694056
$17$	−34643.4	−0.100601	−0.0503003	−	0.998734i	$-0.516018\pi$
$17$	−34643.4	−0.100601	−0.0503003	+	0.998734i	$0.516018\pi$
$18$	131437.	0.295114
$19$	−428885.	−0.755004	−0.377502	−	0.926009i	$-0.623217\pi$
$19$	−428885.	−0.755004	−0.377502	+	0.926009i	$0.623217\pi$
$20$	−566052.	−0.791081
$21$	−38021.3	−0.0426619
$22$	−199734.	−0.181782
$23$	2.03704e6	1.51783	0.758916	−	0.651188i	$-0.225729\pi$
$23$	2.03704e6	1.51783	0.758916	+	0.651188i	$0.225729\pi$
$24$	304130.	0.187115
$25$	−424814.	−0.217505
$26$	0	0
$27$	−1.60051e6	−0.579590
$28$	408432.	0.125577
$29$	−5.26400e6	−1.38205	−0.691026	−	0.722830i	$-0.742841\pi$
$29$	−5.26400e6	−1.38205	−0.691026	+	0.722830i	$0.742841\pi$
$30$	−387657.	−0.0873780
$31$	4.15910e6	0.808856	0.404428	−	0.914570i	$-0.367471\pi$
$31$	4.15910e6	0.808856	0.404428	+	0.914570i	$0.367471\pi$
$32$	−4.99169e6	−0.841536
$33$	1.15724e6	0.169868
$34$	254862.	0.0327077
$35$	−1.10275e6	−0.124214
$36$	8.18054e6	0.811747
$37$	7.58854e6	0.665657	0.332829	−	0.942987i	$-0.391997\pi$
$37$	7.58854e6	0.665657	0.332829	+	0.942987i	$0.391997\pi$
$38$	3.15519e6	0.245470
$39$	0	0
$40$	8.82080e6	0.544801
$41$	4.92536e6	0.272214	0.136107	−	0.990694i	$-0.456541\pi$
$41$	4.92536e6	0.272214	0.136107	+	0.990694i	$0.456541\pi$
$42$	279712.	0.0138704
$43$	1.71882e7	0.766696	0.383348	−	0.923604i	$-0.374771\pi$
$43$	1.71882e7	0.766696	0.383348	+	0.923604i	$0.374771\pi$
$44$	−1.24313e7	−0.500012
$45$	−2.20870e7	−0.802936
$46$	−1.49859e7	−0.493484
$47$	2.95568e7	0.883522	0.441761	−	0.897133i	$-0.354354\pi$
$47$	2.95568e7	0.883522	0.441761	+	0.897133i	$0.354354\pi$
$48$	7.75518e6	0.210866
$49$	−3.95579e7	−0.980282
$50$	3.12524e6	0.0707161
$51$	−1.47665e6	−0.0305642
$52$	0	0
$53$	−2.72331e7	−0.474084	−0.237042	−	0.971499i	$-0.576178\pi$
$53$	−2.72331e7	−0.474084	−0.237042	+	0.971499i	$0.576178\pi$
$54$	1.17745e7	0.188439
$55$	3.35640e7	0.494585
$56$	−6.36461e6	−0.0864819
$57$	−1.82809e7	−0.229383
$58$	3.87258e7	0.449339
$59$	1.13602e8	1.22054	0.610272	−	0.792192i	$-0.291060\pi$
$59$	1.13602e8	1.22054	0.610272	+	0.792192i	$0.291060\pi$
$60$	−2.41276e7	−0.240344
$61$	−3.76868e7	−0.348502	−0.174251	−	0.984701i	$-0.555750\pi$
$61$	−3.76868e7	−0.348502	−0.174251	+	0.984701i	$0.555750\pi$
$62$	−3.05973e7	−0.262979
$63$	1.59368e7	0.127458
$64$	−5.64321e7	−0.420452
$65$	0	0
$66$	−8.51352e6	−0.0552283
$67$	−1.90094e8	−1.15247	−0.576237	−	0.817283i	$-0.695479\pi$
$67$	−1.90094e8	−1.15247	−0.576237	+	0.817283i	$0.695479\pi$
$68$	1.58625e7	0.0899666
$69$	8.68273e7	0.461143
$70$	8.11260e6	0.0403849
$71$	−6.87130e7	−0.320905	−0.160453	−	0.987044i	$-0.551295\pi$
$71$	−6.87130e7	−0.320905	−0.160453	+	0.987044i	$0.551295\pi$
$72$	−1.27477e8	−0.559033
$73$	−3.61495e8	−1.48987	−0.744937	−	0.667135i	$-0.767520\pi$
$73$	−3.61495e8	−1.48987	−0.744937	+	0.667135i	$0.767520\pi$
$74$	−5.58268e7	−0.216421
$75$	−1.81074e7	−0.0660816
$76$	1.96377e8	0.675196
$77$	−2.42179e7	−0.0785107
$78$	0	0
$79$	−1.42229e8	−0.410834	−0.205417	−	0.978675i	$-0.565855\pi$
$79$	−1.42229e8	−0.410834	−0.205417	+	0.978675i	$0.565855\pi$
$80$	2.24926e8	0.613953
$81$	2.83439e8	0.731606
$82$	−3.62346e7	−0.0885035
$83$	5.80240e7	0.134201	0.0671006	−	0.997746i	$-0.478625\pi$
$83$	5.80240e7	0.134201	0.0671006	+	0.997746i	$0.478625\pi$
$84$	1.74091e7	0.0381523
$85$	−4.28279e7	−0.0889901
$86$	−1.26449e8	−0.249272
$87$	−2.24374e8	−0.419891
$88$	1.93718e8	0.344348
$89$	8.59928e8	1.45280	0.726402	−	0.687270i	$-0.241191\pi$
$89$	8.59928e8	1.45280	0.726402	+	0.687270i	$0.241191\pi$
$90$	1.62488e8	0.261054
$91$	0	0
$92$	−9.32716e8	−1.35739
$93$	1.77279e8	0.245744
$94$	−2.17442e8	−0.287255
$95$	−5.30208e8	−0.667867
$96$	−2.12767e8	−0.255673
$97$	−1.46970e9	−1.68560	−0.842802	−	0.538223i	$-0.819096\pi$
$97$	−1.46970e9	−1.68560	−0.842802	+	0.538223i	$0.819096\pi$
$98$	2.91017e8	0.318714
$99$	−4.85064e8	−0.507505
$100$	1.94513e8	0.194513
$101$	−4.15100e8	−0.396923	−0.198462	−	0.980109i	$-0.563595\pi$
$101$	−4.15100e8	−0.396923	−0.198462	+	0.980109i	$0.563595\pi$
$102$	1.08633e7	0.00993716
$103$	1.86377e9	1.63164	0.815821	−	0.578305i	$-0.196286\pi$
$103$	1.86377e9	1.63164	0.815821	+	0.578305i	$0.196286\pi$
$104$	0	0
$105$	−4.70038e7	−0.0377382
$106$	2.00346e8	0.154136
$107$	−7.50777e8	−0.553712	−0.276856	−	0.960911i	$-0.589293\pi$
$107$	−7.50777e8	−0.553712	−0.276856	+	0.960911i	$0.589293\pi$
$108$	7.32838e8	0.518324
$109$	−2.07010e9	−1.40467	−0.702333	−	0.711849i	$-0.747858\pi$
$109$	−2.07010e9	−1.40467	−0.702333	+	0.711849i	$0.747858\pi$
$110$	−2.46921e8	−0.160802
$111$	3.23456e8	0.202238
$112$	−1.62295e8	−0.0974592
$113$	−2.10155e9	−1.21251	−0.606257	−	0.795268i	$-0.707330\pi$
$113$	−2.10155e9	−1.21251	−0.606257	+	0.795268i	$0.707330\pi$
$114$	1.34488e8	0.0745780
$115$	2.51829e9	1.34266
$116$	2.41027e9	1.23596
$117$	0	0
$118$	−8.35741e8	−0.396828
$119$	3.09023e7	0.0141263
$120$	3.75980e8	0.165520
$121$	−1.62083e9	−0.687392
$122$	2.77251e8	0.113306
$123$	2.09940e8	0.0827033
$124$	−1.90436e9	−0.723356
$125$	−2.93972e9	−1.07699
$126$	−1.17243e8	−0.0414398
$127$	−4.77696e9	−1.62943	−0.814713	−	0.579865i	$-0.803105\pi$
$127$	−4.77696e9	−1.62943	−0.814713	+	0.579865i	$0.803105\pi$
$128$	2.97090e9	0.978235
$129$	7.32636e8	0.232935
$130$	0	0
$131$	−4.62884e9	−1.37326	−0.686628	−	0.727009i	$-0.740910\pi$
$131$	−4.62884e9	−1.37326	−0.686628	+	0.727009i	$0.740910\pi$
$132$	−5.29877e8	−0.151912
$133$	3.82569e8	0.106018
$134$	1.39847e9	0.374697
$135$	−1.97863e9	−0.512698
$136$	−2.47186e8	−0.0619581
$137$	−3.85972e9	−0.936080	−0.468040	−	0.883707i	$-0.655040\pi$
$137$	−3.85972e9	−0.936080	−0.468040	+	0.883707i	$0.655040\pi$
$138$	−6.38765e8	−0.149929
$139$	−8.38068e9	−1.90420	−0.952100	−	0.305786i	$-0.901081\pi$
$139$	−8.38068e9	−1.90420	−0.952100	+	0.305786i	$0.901081\pi$
$140$	5.04924e8	0.111084
$141$	1.25984e9	0.268429
$142$	5.05503e8	0.104334
$143$	0	0
$144$	−3.25062e9	−0.629991
$145$	−6.50761e9	−1.22255
$146$	2.65942e9	0.484394
$147$	−1.68613e9	−0.297826
$148$	−3.47463e9	−0.595293
$149$	−3.96089e9	−0.658347	−0.329174	−	0.944269i	$-0.606770\pi$
$149$	−3.96089e9	−0.658347	−0.329174	+	0.944269i	$0.606770\pi$
$150$	1.33211e8	0.0214847
$151$	−1.11419e10	−1.74407	−0.872036	−	0.489442i	$-0.837201\pi$
$151$	−1.11419e10	−1.74407	−0.872036	+	0.489442i	$0.837201\pi$
$152$	−3.06015e9	−0.464993
$153$	6.18946e8	0.0913148
$154$	1.78165e8	0.0255257
$155$	5.14168e9	0.715504
$156$	0	0
$157$	−7.39104e9	−0.970861	−0.485430	−	0.874275i	$-0.661337\pi$
$157$	−7.39104e9	−0.970861	−0.485430	+	0.874275i	$0.661337\pi$
$158$	1.04634e9	0.133572
$159$	−1.16079e9	−0.144035
$160$	−6.17097e9	−0.744412
$161$	−1.81706e9	−0.213134
$162$	−2.08519e9	−0.237863
$163$	7.32911e8	0.0813218	0.0406609	−	0.999173i	$-0.487054\pi$
$163$	7.32911e8	0.0813218	0.0406609	+	0.999173i	$0.487054\pi$
$164$	−2.25522e9	−0.243440
$165$	1.43064e9	0.150263
$166$	−4.26867e8	−0.0436321
$167$	1.23516e10	1.22885	0.614427	−	0.788974i	$-0.289387\pi$
$167$	1.23516e10	1.22885	0.614427	+	0.788974i	$0.289387\pi$
$168$	−2.71287e8	−0.0262747
$169$	0	0
$170$	3.15073e8	0.0289329
$171$	7.66252e9	0.685314
$172$	−7.87012e9	−0.685651
$173$	1.12727e10	0.956794	0.478397	−	0.878144i	$-0.341218\pi$
$173$	1.12727e10	0.956794	0.478397	+	0.878144i	$0.341218\pi$
$174$	1.65066e9	0.136517
$175$	3.78938e8	0.0305420
$176$	4.93971e9	0.388056
$177$	4.84222e9	0.370822
$178$	−6.32626e9	−0.472342
$179$	−3.32764e9	−0.242269	−0.121134	−	0.992636i	$-0.538653\pi$
$179$	−3.32764e9	−0.242269	−0.121134	+	0.992636i	$0.538653\pi$
$180$	1.01132e10	0.718061
$181$	1.56098e10	1.08104	0.540521	−	0.841330i	$-0.318227\pi$
$181$	1.56098e10	1.08104	0.540521	+	0.841330i	$0.318227\pi$
$182$	0	0
$183$	−1.60637e9	−0.105881
$184$	1.45345e10	0.934805
$185$	9.38133e9	0.588832
$186$	−1.30419e9	−0.0798974
$187$	−9.40564e8	−0.0562472
$188$	−1.35334e10	−0.790129
$189$	1.42767e9	0.0813859
$190$	3.90060e9	0.217140
$191$	2.64757e10	1.43945	0.719725	−	0.694259i	$-0.244268\pi$
$191$	2.64757e10	1.43945	0.719725	+	0.694259i	$0.244268\pi$
$192$	−2.40538e9	−0.127740
$193$	2.67204e9	0.138623	0.0693114	−	0.997595i	$-0.477920\pi$
$193$	2.67204e9	0.138623	0.0693114	+	0.997595i	$0.477920\pi$
$194$	1.08122e10	0.548031
$195$	0	0
$196$	1.81127e10	0.876661
$197$	−1.38233e10	−0.653903	−0.326951	−	0.945041i	$-0.606021\pi$
$197$	−1.38233e10	−0.653903	−0.326951	+	0.945041i	$0.606021\pi$
$198$	3.56848e9	0.165002
$199$	−1.21811e10	−0.550616	−0.275308	−	0.961356i	$-0.588780\pi$
$199$	−1.21811e10	−0.550616	−0.275308	+	0.961356i	$0.588780\pi$
$200$	−3.03110e9	−0.133957
$201$	−8.10261e9	−0.350141
$202$	3.05378e9	0.129049
$203$	4.69554e9	0.194068
$204$	6.76128e8	0.0273334
$205$	6.08897e9	0.240797
$206$	−1.37112e10	−0.530486
$207$	−3.63941e10	−1.37773
$208$	0	0
$209$	−1.16441e10	−0.422133
$210$	3.45794e8	0.0122696
$211$	−3.16880e9	−0.110058	−0.0550292	−	0.998485i	$-0.517525\pi$
$211$	−3.16880e9	−0.110058	−0.0550292	+	0.998485i	$0.517525\pi$
$212$	1.24695e10	0.423971
$213$	−2.92885e9	−0.0974963
$214$	5.52326e9	0.180025
$215$	2.12489e10	0.678210
$216$	−1.14198e10	−0.356959
$217$	−3.70996e9	−0.113579
$218$	1.52292e10	0.456691
$219$	−1.54085e10	−0.452648
$220$	−1.53682e10	−0.442305
$221$	0	0
$222$	−2.37958e9	−0.0657524
$223$	1.00184e10	0.271285	0.135642	−	0.990758i	$-0.456690\pi$
$223$	1.00184e10	0.271285	0.135642	+	0.990758i	$0.456690\pi$
$224$	4.45264e9	0.118168
$225$	7.58980e9	0.197428
$226$	1.54605e10	0.394218
$227$	5.23965e10	1.30974	0.654871	−	0.755741i	$-0.272723\pi$
$227$	5.23965e10	1.30974	0.654871	+	0.755741i	$0.272723\pi$
$228$	8.37044e9	0.205136
$229$	2.94853e10	0.708510	0.354255	−	0.935149i	$-0.384734\pi$
$229$	2.94853e10	0.708510	0.354255	+	0.935149i	$0.384734\pi$
$230$	−1.85263e10	−0.436530
$231$	−1.03227e9	−0.0238529
$232$	−3.75593e10	−0.851180
$233$	−6.67468e10	−1.48364	−0.741820	−	0.670599i	$-0.766037\pi$
$233$	−6.67468e10	−1.48364	−0.741820	+	0.670599i	$0.766037\pi$
$234$	0	0
$235$	3.65396e10	0.781553
$236$	−5.20161e10	−1.09152
$237$	−6.06241e9	−0.124818
$238$	−2.27340e8	−0.00459281
$239$	7.42940e10	1.47286	0.736432	−	0.676511i	$-0.236509\pi$
$239$	7.42940e10	1.47286	0.736432	+	0.676511i	$0.236509\pi$
$240$	9.58733e9	0.186529
$241$	−9.01496e10	−1.72142	−0.860711	−	0.509095i	$-0.829980\pi$
$241$	−9.01496e10	−1.72142	−0.860711	+	0.509095i	$0.829980\pi$
$242$	1.19240e10	0.223488
$243$	4.35842e10	0.801864
$244$	1.72560e10	0.311663
$245$	−4.89034e10	−0.867146
$246$	−1.54447e9	−0.0268889
$247$	0	0
$248$	2.96757e10	0.498160
$249$	2.47323e9	0.0407726
$250$	2.16267e10	0.350156
$251$	3.62007e10	0.575685	0.287843	−	0.957678i	$-0.407062\pi$
$251$	3.62007e10	0.575685	0.287843	+	0.957678i	$0.407062\pi$
$252$	−7.29712e9	−0.113985
$253$	5.53053e10	0.848641
$254$	3.51428e10	0.529766
$255$	−1.82551e9	−0.0270367
$256$	7.03715e9	0.102404
$257$	−1.97638e10	−0.282600	−0.141300	−	0.989967i	$-0.545128\pi$
$257$	−1.97638e10	−0.282600	−0.141300	+	0.989967i	$0.545128\pi$
$258$	−5.38980e9	−0.0757329
$259$	−6.76905e9	−0.0934714
$260$	0	0
$261$	9.40474e10	1.25448
$262$	3.40531e10	0.446479
$263$	−1.70457e10	−0.219692	−0.109846	−	0.993949i	$-0.535036\pi$
$263$	−1.70457e10	−0.219692	−0.109846	+	0.993949i	$0.535036\pi$
$264$	8.25708e9	0.104619
$265$	−3.36669e10	−0.419369
$266$	−2.81446e9	−0.0344689
$267$	3.66539e10	0.441386
$268$	8.70398e10	1.03065
$269$	6.56819e10	0.764822	0.382411	−	0.923992i	$-0.375094\pi$
$269$	6.56819e10	0.764822	0.382411	+	0.923992i	$0.375094\pi$
$270$	1.45562e10	0.166691
$271$	−1.52442e11	−1.71689	−0.858447	−	0.512902i	$-0.828570\pi$
$271$	−1.52442e11	−1.71689	−0.858447	+	0.512902i	$0.828570\pi$
$272$	−6.30312e9	−0.0698225
$273$	0	0
$274$	2.83949e10	0.304343
$275$	−1.15336e10	−0.121610
$276$	−3.97564e10	−0.412397
$277$	−1.21612e11	−1.24113	−0.620566	−	0.784154i	$-0.713097\pi$
$277$	−1.21612e11	−1.24113	−0.620566	+	0.784154i	$0.713097\pi$
$278$	6.16544e10	0.619102
$279$	−7.43071e10	−0.734195
$280$	−7.86824e9	−0.0765008
$281$	2.03083e11	1.94310	0.971548	−	0.236842i	$-0.0761124\pi$
$281$	2.03083e11	1.94310	0.971548	+	0.236842i	$0.0761124\pi$
$282$	−9.26829e9	−0.0872728
$283$	3.09567e10	0.286891	0.143445	−	0.989658i	$-0.454182\pi$
$283$	3.09567e10	0.286891	0.143445	+	0.989658i	$0.454182\pi$
$284$	3.14622e10	0.286984
$285$	−2.25998e10	−0.202909
$286$	0	0
$287$	−4.39347e9	−0.0382243
$288$	8.91824e10	0.763858
$289$	−1.17388e11	−0.989880
$290$	4.78747e10	0.397480
$291$	−6.26449e10	−0.512115
$292$	1.65521e11	1.33238
$293$	7.81733e10	0.619661	0.309831	−	0.950792i	$-0.399728\pi$
$293$	7.81733e10	0.619661	0.309831	+	0.950792i	$0.399728\pi$
$294$	1.24044e10	0.0968306
$295$	1.40441e11	1.07968
$296$	5.41452e10	0.409966
$297$	−4.34535e10	−0.324057
$298$	2.91392e10	0.214045
$299$	0	0
$300$	8.29099e9	0.0590964
$301$	−1.53321e10	−0.107659
$302$	8.19682e10	0.567040
$303$	−1.76933e10	−0.120592
$304$	−7.80324e10	−0.524015
$305$	−4.65902e10	−0.308280
$306$	−4.55341e9	−0.0296887
$307$	−1.19962e11	−0.770766	−0.385383	−	0.922757i	$-0.625931\pi$
$307$	−1.19962e11	−0.770766	−0.385383	+	0.922757i	$0.625931\pi$
$308$	1.10889e10	0.0702116
$309$	7.94419e10	0.495720
$310$	−3.78259e10	−0.232628
$311$	1.16227e11	0.704504	0.352252	−	0.935905i	$-0.385416\pi$
$311$	1.16227e11	0.704504	0.352252	+	0.935905i	$0.385416\pi$
$312$	0	0
$313$	9.92344e10	0.584403	0.292202	−	0.956357i	$-0.405612\pi$
$313$	9.92344e10	0.584403	0.292202	+	0.956357i	$0.405612\pi$
$314$	5.43738e10	0.315651
$315$	1.97018e10	0.112748
$316$	6.51236e10	0.367406
$317$	2.98194e11	1.65856	0.829281	−	0.558832i	$-0.188750\pi$
$317$	2.98194e11	1.65856	0.829281	+	0.558832i	$0.188750\pi$
$318$	8.53963e9	0.0468292
$319$	−1.42917e11	−0.772725
$320$	−6.97642e10	−0.371927
$321$	−3.20014e10	−0.168227
$322$	1.33676e10	0.0692950
$323$	1.48580e10	0.0759539
$324$	−1.29781e11	−0.654271
$325$	0	0
$326$	−5.39183e9	−0.0264397
$327$	−8.82367e10	−0.426761
$328$	3.51431e10	0.167652
$329$	−2.63650e10	−0.124064
$330$	−1.05248e10	−0.0488542
$331$	−6.87707e10	−0.314904	−0.157452	−	0.987527i	$-0.550328\pi$
$331$	−6.87707e10	−0.314904	−0.157452	+	0.987527i	$0.550328\pi$
$332$	−2.65680e10	−0.120015
$333$	−1.35578e11	−0.604214
$334$	−9.08675e10	−0.399530
$335$	−2.35003e11	−1.01946
$336$	−6.91769e9	−0.0296097
$337$	−1.56091e11	−0.659239	−0.329619	−	0.944114i	$-0.606920\pi$
$337$	−1.56091e11	−0.659239	−0.329619	+	0.944114i	$0.606920\pi$
$338$	0	0
$339$	−8.95772e10	−0.368382
$340$	1.96100e10	0.0795833
$341$	1.12919e11	0.452243
$342$	−5.63711e10	−0.222812
$343$	7.12819e10	0.278071
$344$	1.22640e11	0.472194
$345$	1.07340e11	0.407921
$346$	−8.29298e10	−0.311077
$347$	−1.65467e11	−0.612673	−0.306337	−	0.951923i	$-0.599103\pi$
$347$	−1.65467e11	−0.612673	−0.306337	+	0.951923i	$0.599103\pi$
$348$	1.02736e11	0.375506
$349$	4.02009e11	1.45051	0.725257	−	0.688478i	$-0.241721\pi$
$349$	4.02009e11	1.45051	0.725257	+	0.688478i	$0.241721\pi$
$350$	−2.78775e9	−0.00992995
$351$	0	0
$352$	−1.35524e11	−0.470514
$353$	−2.74001e11	−0.939217	−0.469609	−	0.882875i	$-0.655605\pi$
$353$	−2.74001e11	−0.939217	−0.469609	+	0.882875i	$0.655605\pi$
$354$	−3.56229e10	−0.120563
$355$	−8.49464e10	−0.283869
$356$	−3.93743e11	−1.29923
$357$	1.31719e9	0.00429182
$358$	2.44805e10	0.0787675
$359$	−8.26405e10	−0.262584	−0.131292	−	0.991344i	$-0.541913\pi$
$359$	−8.26405e10	−0.262584	−0.131292	+	0.991344i	$0.541913\pi$
$360$	−1.57594e11	−0.494513
$361$	−1.38746e11	−0.429969
$362$	−1.14837e11	−0.351473
$363$	−6.90869e10	−0.208841
$364$	0	0
$365$	−4.46898e11	−1.31792
$366$	1.18176e10	0.0344244
$367$	4.83059e10	0.138996	0.0694980	−	0.997582i	$-0.477860\pi$
$367$	4.83059e10	0.138996	0.0694980	+	0.997582i	$0.477860\pi$
$368$	3.70624e11	1.05346
$369$	−8.79974e10	−0.247088
$370$	−6.90158e10	−0.191444
$371$	2.42922e10	0.0665708
$372$	−8.11721e10	−0.219768
$373$	8.53749e10	0.228371	0.114185	−	0.993459i	$-0.463574\pi$
$373$	8.53749e10	0.228371	0.114185	+	0.993459i	$0.463574\pi$
$374$	6.91947e9	0.0182873
$375$	−1.25304e11	−0.327207
$376$	2.10892e11	0.544145
$377$	0	0
$378$	−1.05030e10	−0.0264605
$379$	2.25085e11	0.560365	0.280182	−	0.959947i	$-0.409605\pi$
$379$	2.25085e11	0.560365	0.280182	+	0.959947i	$0.409605\pi$
$380$	2.42771e11	0.597270
$381$	−2.03614e11	−0.495047
$382$	−1.94774e11	−0.468001
$383$	−6.84152e11	−1.62464	−0.812322	−	0.583210i	$-0.801797\pi$
$383$	−6.84152e11	−1.62464	−0.812322	+	0.583210i	$0.801797\pi$
$384$	1.26633e11	0.297204
$385$	−2.99394e10	−0.0694495
$386$	−1.96574e10	−0.0450696
$387$	−3.07088e11	−0.695926
$388$	6.72944e11	1.50743
$389$	7.47317e11	1.65475	0.827374	−	0.561652i	$-0.189834\pi$
$389$	7.47317e11	1.65475	0.827374	+	0.561652i	$0.189834\pi$
$390$	0	0
$391$	−7.05700e10	−0.152695
$392$	−2.82251e11	−0.603738
$393$	−1.97301e11	−0.417218
$394$	1.01694e11	0.212600
$395$	−1.75830e11	−0.363419
$396$	2.22100e11	0.453859
$397$	−1.63235e11	−0.329804	−0.164902	−	0.986310i	$-0.552731\pi$
$397$	−1.63235e11	−0.329804	−0.164902	+	0.986310i	$0.552731\pi$
$398$	8.96133e10	0.179019
$399$	1.63067e10	0.0322099
$400$	−7.72918e10	−0.150961
$401$	7.33836e11	1.41726	0.708629	−	0.705581i	$-0.249314\pi$
$401$	7.33836e11	1.41726	0.708629	+	0.705581i	$0.249314\pi$
$402$	5.96087e10	0.113839
$403$	0	0
$404$	1.90065e11	0.354966
$405$	3.50401e11	0.647170
$406$	−3.45438e10	−0.0630961
$407$	2.06028e11	0.372178
$408$	−1.05361e10	−0.0188239
$409$	−7.45800e11	−1.31785	−0.658927	−	0.752207i	$-0.728990\pi$
$409$	−7.45800e11	−1.31785	−0.658927	+	0.752207i	$0.728990\pi$
$410$	−4.47949e10	−0.0782891
$411$	−1.64518e11	−0.284397
$412$	−8.53380e11	−1.45917
$413$	−1.01334e11	−0.171388
$414$	2.67741e11	0.447934
$415$	7.17321e10	0.118713
$416$	0	0
$417$	−3.57221e11	−0.578528
$418$	8.56628e10	0.137246
$419$	−5.46254e11	−0.865828	−0.432914	−	0.901435i	$-0.642515\pi$
$419$	−5.46254e11	−0.865828	−0.432914	+	0.901435i	$0.642515\pi$
$420$	2.15220e10	0.0337490
$421$	2.95449e11	0.458366	0.229183	−	0.973383i	$-0.426394\pi$
$421$	2.95449e11	0.458366	0.229183	+	0.973383i	$0.426394\pi$
$422$	2.33120e10	0.0357827
$423$	−5.28067e11	−0.801969
$424$	−1.94312e11	−0.291980
$425$	1.47170e10	0.0218811
$426$	2.15467e10	0.0316984
$427$	3.36170e10	0.0489365
$428$	3.43765e11	0.495182
$429$	0	0
$430$	−1.56323e11	−0.220502
$431$	5.49479e11	0.767014	0.383507	−	0.923538i	$-0.374716\pi$
$431$	5.49479e11	0.767014	0.383507	+	0.923538i	$0.374716\pi$
$432$	−2.91201e11	−0.402268
$433$	−7.54093e11	−1.03093	−0.515465	−	0.856910i	$-0.672381\pi$
$433$	−7.54093e11	−1.03093	−0.515465	+	0.856910i	$0.672381\pi$
$434$	2.72931e10	0.0369275
$435$	−2.77382e11	−0.371430
$436$	9.47856e11	1.25618
$437$	−8.73654e11	−1.14597
$438$	1.13356e11	0.147167
$439$	9.98220e10	0.128273	0.0641366	−	0.997941i	$-0.479571\pi$
$439$	9.98220e10	0.128273	0.0641366	+	0.997941i	$0.479571\pi$
$440$	2.39483e11	0.304606
$441$	7.06749e11	0.889798
$442$	0	0
$443$	−1.08040e12	−1.33281	−0.666404	−	0.745591i	$-0.732168\pi$
$443$	−1.08040e12	−1.33281	−0.666404	+	0.745591i	$0.732168\pi$
$444$	−1.48104e11	−0.180860
$445$	1.06309e12	1.28513
$446$	−7.37024e10	−0.0882013
$447$	−1.68830e11	−0.200017
$448$	5.03380e10	0.0590398
$449$	−1.02947e12	−1.19538	−0.597688	−	0.801729i	$-0.703914\pi$
$449$	−1.02947e12	−1.19538	−0.597688	+	0.801729i	$0.703914\pi$
$450$	−5.58361e10	−0.0641887
$451$	1.33723e11	0.152199
$452$	9.62256e11	1.08435
$453$	−4.74917e11	−0.529878
$454$	−3.85466e11	−0.425829
$455$	0	0
$456$	−1.30437e11	−0.141273
$457$	−1.06106e12	−1.13793	−0.568966	−	0.822361i	$-0.692657\pi$
$457$	−1.06106e12	−1.13793	−0.568966	+	0.822361i	$0.692657\pi$
$458$	−2.16915e11	−0.230354
$459$	5.54471e10	0.0583071
$460$	−1.15307e12	−1.20073
$461$	7.20760e11	0.743253	0.371626	−	0.928382i	$-0.378800\pi$
$461$	7.20760e11	0.743253	0.371626	+	0.928382i	$0.378800\pi$
$462$	7.59414e9	0.00775514
$463$	−1.41179e11	−0.142776	−0.0713880	−	0.997449i	$-0.522743\pi$
$463$	−1.41179e11	−0.142776	−0.0713880	+	0.997449i	$0.522743\pi$
$464$	−9.57745e11	−0.959222
$465$	2.19161e11	0.217382
$466$	4.91038e11	0.482368
$467$	−5.23104e11	−0.508935	−0.254467	−	0.967081i	$-0.581900\pi$
$467$	−5.23104e11	−0.508935	−0.254467	+	0.967081i	$0.581900\pi$
$468$	0	0
$469$	1.69565e11	0.161830
$470$	−2.68812e11	−0.254102
$471$	−3.15038e11	−0.294964
$472$	8.10568e11	0.751710
$473$	4.66658e11	0.428670
$474$	4.45995e10	0.0405814
$475$	1.82196e11	0.164217
$476$	−1.41495e10	−0.0126331
$477$	4.86551e11	0.430324
$478$	−5.46560e11	−0.478864
$479$	−1.22387e12	−1.06224	−0.531122	−	0.847295i	$-0.678230\pi$
$479$	−1.22387e12	−1.06224	−0.531122	+	0.847295i	$0.678230\pi$
$480$	−2.63033e11	−0.226165
$481$	0	0
$482$	6.63206e11	0.559676
$483$	−7.74508e10	−0.0647536
$484$	7.42145e11	0.614730
$485$	−1.81691e12	−1.49107
$486$	−3.20637e11	−0.260706
$487$	3.77344e11	0.303988	0.151994	−	0.988381i	$-0.451431\pi$
$487$	3.77344e11	0.303988	0.151994	+	0.988381i	$0.451431\pi$
$488$	−2.68900e11	−0.214636
$489$	3.12398e10	0.0247069
$490$	3.59769e11	0.281930
$491$	−2.35736e12	−1.83046	−0.915229	−	0.402934i	$-0.867990\pi$
$491$	−2.35736e12	−1.83046	−0.915229	+	0.402934i	$0.867990\pi$
$492$	−9.61271e10	−0.0739610
$493$	1.82363e11	0.139035
$494$	0	0
$495$	−5.99659e11	−0.448933
$496$	7.56717e11	0.561392
$497$	6.12927e10	0.0450614
$498$	−1.81949e10	−0.0132562
$499$	2.64345e12	1.90862	0.954309	−	0.298822i	$-0.0965938\pi$
$499$	2.64345e12	1.90862	0.954309	+	0.298822i	$0.0965938\pi$
$500$	1.34604e12	0.963145
$501$	5.26480e11	0.373346
$502$	−2.66319e11	−0.187169
$503$	1.53328e11	0.106799	0.0533994	−	0.998573i	$-0.482994\pi$
$503$	1.53328e11	0.106799	0.0533994	+	0.998573i	$0.482994\pi$
$504$	1.13711e11	0.0784993
$505$	−5.13167e11	−0.351113
$506$	−4.06866e11	−0.275914
$507$	0	0
$508$	2.18727e12	1.45719
$509$	6.36840e11	0.420533	0.210267	−	0.977644i	$-0.432567\pi$
$509$	6.36840e11	0.420533	0.210267	+	0.977644i	$0.432567\pi$
$510$	1.34298e10	0.00879029
$511$	3.22457e11	0.209208
$512$	−1.57287e12	−1.01153
$513$	6.86433e11	0.437593
$514$	1.45397e11	0.0918801
$515$	2.30408e12	1.44333
$516$	−3.35458e11	−0.208312
$517$	8.02463e11	0.493989
$518$	4.97981e10	0.0303899
$519$	4.80489e11	0.290690
$520$	0	0
$521$	1.84033e12	1.09427	0.547137	−	0.837043i	$-0.315718\pi$
$521$	1.84033e12	1.09427	0.547137	+	0.837043i	$0.315718\pi$
$522$	−6.91881e11	−0.407863
$523$	−1.13176e10	−0.00661447	−0.00330724	−	0.999995i	$-0.501053\pi$
$523$	−1.13176e10	−0.00661447	−0.00330724	+	0.999995i	$0.501053\pi$
$524$	2.11945e12	1.22809
$525$	1.61520e10	0.00927917
$526$	1.25401e11	0.0714272
$527$	−1.44085e11	−0.0813715
$528$	2.10552e11	0.117898
$529$	2.34837e12	1.30382
$530$	2.47678e11	0.136347
$531$	−2.02964e12	−1.10788
$532$	−1.75170e11	−0.0948108
$533$	0	0
$534$	−2.69652e11	−0.143506
$535$	−9.28148e11	−0.489807
$536$	−1.35634e12	−0.709787
$537$	−1.41838e11	−0.0736053
$538$	−4.83203e11	−0.248662
$539$	−1.07399e12	−0.548089
$540$	9.05970e11	0.458503
$541$	2.25189e12	1.13021	0.565107	−	0.825018i	$-0.308835\pi$
$541$	2.25189e12	1.13021	0.565107	+	0.825018i	$0.308835\pi$
$542$	1.12148e12	0.558204
$543$	6.65356e11	0.328439
$544$	1.72929e11	0.0846591
$545$	−2.55916e12	−1.24255
$546$	0	0
$547$	1.92777e11	0.0920686	0.0460343	−	0.998940i	$-0.485342\pi$
$547$	1.92777e11	0.0920686	0.0460343	+	0.998940i	$0.485342\pi$
$548$	1.76728e12	0.837131
$549$	6.73318e11	0.316333
$550$	8.48498e10	0.0395384
$551$	2.25765e12	1.04346
$552$	6.19524e11	0.284009
$553$	1.26870e11	0.0576892
$554$	8.94667e11	0.403522
$555$	3.99873e11	0.178897
$556$	3.83733e12	1.70292
$557$	−3.00574e12	−1.32313	−0.661566	−	0.749887i	$-0.730108\pi$
$557$	−3.00574e12	−1.32313	−0.661566	+	0.749887i	$0.730108\pi$
$558$	5.46657e11	0.238705
$559$	0	0
$560$	−2.00636e11	−0.0862112
$561$	−4.00909e10	−0.0170888
$562$	−1.49402e12	−0.631748
$563$	−1.64962e11	−0.0691984	−0.0345992	−	0.999401i	$-0.511015\pi$
$563$	−1.64962e11	−0.0691984	−0.0345992	+	0.999401i	$0.511015\pi$
$564$	−5.76854e11	−0.240054
$565$	−2.59804e12	−1.07258
$566$	−2.27740e11	−0.0932751
$567$	−2.52831e11	−0.102732
$568$	−4.90277e11	−0.197639
$569$	−2.35127e11	−0.0940368	−0.0470184	−	0.998894i	$-0.514972\pi$
$569$	−2.35127e11	−0.0940368	−0.0470184	+	0.998894i	$0.514972\pi$
$570$	1.66260e11	0.0659707
$571$	−2.71697e12	−1.06960	−0.534801	−	0.844978i	$-0.679613\pi$
$571$	−2.71697e12	−1.06960	−0.534801	+	0.844978i	$0.679613\pi$
$572$	0	0
$573$	1.12851e12	0.437329
$574$	3.23216e10	0.0124276
$575$	−8.65362e11	−0.330136
$576$	1.00823e12	0.381643
$577$	3.01507e12	1.13242	0.566209	−	0.824262i	$-0.308410\pi$
$577$	3.01507e12	1.13242	0.566209	+	0.824262i	$0.308410\pi$
$578$	8.63589e11	0.321834
$579$	1.13894e11	0.0421159
$580$	2.97969e12	1.09332
$581$	−5.17580e10	−0.0188445
$582$	4.60862e11	0.166501
$583$	−7.39374e11	−0.265067
$584$	−2.57931e12	−0.917585
$585$	0	0
$586$	−5.75100e11	−0.201467
$587$	9.84708e11	0.342323	0.171161	−	0.985243i	$-0.445248\pi$
$587$	9.84708e11	0.342323	0.171161	+	0.985243i	$0.445248\pi$
$588$	7.72042e11	0.266344
$589$	−1.78377e12	−0.610690
$590$	−1.03318e12	−0.351030
$591$	−5.89208e11	−0.198667
$592$	1.38068e12	0.462003
$593$	−1.01065e12	−0.335625	−0.167812	−	0.985819i	$-0.553670\pi$
$593$	−1.01065e12	−0.335625	−0.167812	+	0.985819i	$0.553670\pi$
$594$	3.19676e11	0.105359
$595$	3.82029e10	0.0124960
$596$	1.81361e12	0.588756
$597$	−5.19213e11	−0.167286
$598$	0	0
$599$	5.47507e12	1.73768	0.868839	−	0.495095i	$-0.164867\pi$
$599$	5.47507e12	1.73768	0.868839	+	0.495095i	$0.164867\pi$
$600$	−1.29199e11	−0.0406984
$601$	9.94557e11	0.310953	0.155476	−	0.987840i	$-0.450309\pi$
$601$	9.94557e11	0.310953	0.155476	+	0.987840i	$0.450309\pi$
$602$	1.12794e11	0.0350027
$603$	3.39624e12	1.04609
$604$	5.10165e12	1.55971
$605$	−2.00375e12	−0.608058
$606$	1.30165e11	0.0392074
$607$	4.57629e12	1.36825	0.684124	−	0.729366i	$-0.260185\pi$
$607$	4.57629e12	1.36825	0.684124	+	0.729366i	$0.260185\pi$
$608$	2.14086e12	0.635363
$609$	2.00144e11	0.0589610
$610$	3.42752e11	0.100229
$611$	0	0
$612$	−2.83402e11	−0.0816623
$613$	−2.27107e12	−0.649617	−0.324809	−	0.945780i	$-0.605300\pi$
$613$	−2.27107e12	−0.649617	−0.324809	+	0.945780i	$0.605300\pi$
$614$	8.82531e11	0.250595
$615$	2.59538e11	0.0731583
$616$	−1.72798e11	−0.0483532
$617$	−3.53862e12	−0.982994	−0.491497	−	0.870879i	$-0.663550\pi$
$617$	−3.53862e12	−0.982994	−0.491497	+	0.870879i	$0.663550\pi$
$618$	−5.84432e11	−0.161171
$619$	−1.97957e12	−0.541956	−0.270978	−	0.962586i	$-0.587347\pi$
$619$	−1.97957e12	−0.541956	−0.270978	+	0.962586i	$0.587347\pi$
$620$	−2.35426e12	−0.639871
$621$	−3.26029e12	−0.879720
$622$	−8.55047e11	−0.229052
$623$	−7.67065e11	−0.204003
$624$	0	0
$625$	−2.80452e12	−0.735187
$626$	−7.30040e11	−0.190004
$627$	−4.96324e11	−0.128251
$628$	3.38420e12	0.868235
$629$	−2.62893e11	−0.0669656
$630$	−1.44941e11	−0.0366572
$631$	−3.71649e11	−0.0933256	−0.0466628	−	0.998911i	$-0.514859\pi$
$631$	−3.71649e11	−0.0933256	−0.0466628	+	0.998911i	$0.514859\pi$
$632$	−1.01482e12	−0.253025
$633$	−1.35068e11	−0.0334376
$634$	−2.19373e12	−0.539239
$635$	−5.90551e12	−1.44137
$636$	5.31502e11	0.128809
$637$	0	0
$638$	1.05140e12	0.251232
$639$	1.22764e12	0.291284
$640$	3.67277e12	0.865335
$641$	1.07772e12	0.252143	0.126071	−	0.992021i	$-0.459763\pi$
$641$	1.07772e12	0.252143	0.126071	+	0.992021i	$0.459763\pi$
$642$	2.35425e11	0.0546947
$643$	6.69209e12	1.54388	0.771938	−	0.635698i	$-0.219288\pi$
$643$	6.69209e12	1.54388	0.771938	+	0.635698i	$0.219288\pi$
$644$	8.31992e11	0.190604
$645$	9.05721e11	0.206051
$646$	−1.09307e11	−0.0246945
$647$	1.58975e12	0.356664	0.178332	−	0.983970i	$-0.442930\pi$
$647$	1.58975e12	0.356664	0.178332	+	0.983970i	$0.442930\pi$
$648$	2.02238e12	0.450583
$649$	3.08429e12	0.682423
$650$	0	0
$651$	−1.58134e11	−0.0345073
$652$	−3.35584e11	−0.0727256
$653$	−1.96565e12	−0.423055	−0.211527	−	0.977372i	$-0.567844\pi$
$653$	−1.96565e12	−0.423055	−0.211527	+	0.977372i	$0.567844\pi$
$654$	6.49133e11	0.138750
$655$	−5.72240e12	−1.21476
$656$	8.96134e11	0.188932
$657$	6.45853e12	1.35235
$658$	1.93960e11	0.0403362
$659$	1.09426e11	0.0226014	0.0113007	−	0.999936i	$-0.496403\pi$
$659$	1.09426e11	0.0226014	0.0113007	+	0.999936i	$0.496403\pi$
$660$	−6.55060e11	−0.134380
$661$	2.69590e12	0.549285	0.274643	−	0.961546i	$-0.411440\pi$
$661$	2.69590e12	0.549285	0.274643	+	0.961546i	$0.411440\pi$
$662$	5.05927e11	0.102383
$663$	0	0
$664$	4.14009e11	0.0826520
$665$	4.72951e11	0.0937818
$666$	9.97411e11	0.196445
$667$	−1.07230e13	−2.09772
$668$	−5.65555e12	−1.09896
$669$	4.27026e11	0.0824208
$670$	1.72885e12	0.331452
$671$	−1.02319e12	−0.194852
$672$	1.89790e11	0.0359015
$673$	−6.37187e12	−1.19729	−0.598644	−	0.801015i	$-0.704294\pi$
$673$	−6.37187e12	−1.19729	−0.598644	+	0.801015i	$0.704294\pi$
$674$	1.14832e12	0.214335
$675$	6.79918e11	0.126064
$676$	0	0
$677$	−6.61270e12	−1.20985	−0.604923	−	0.796284i	$-0.706796\pi$
$677$	−6.61270e12	−1.20985	−0.604923	+	0.796284i	$0.706796\pi$
$678$	6.58995e11	0.119770
$679$	1.31099e12	0.236692
$680$	−3.05583e11	−0.0548073
$681$	2.23336e12	0.397921
$682$	−8.30713e11	−0.147035
$683$	−3.52480e12	−0.619785	−0.309893	−	0.950772i	$-0.600293\pi$
$683$	−3.52480e12	−0.619785	−0.309893	+	0.950772i	$0.600293\pi$
$684$	−3.50851e12	−0.612872
$685$	−4.77157e12	−0.828045
$686$	−5.24401e11	−0.0904076
$687$	1.25679e12	0.215257
$688$	3.12727e12	0.532130
$689$	0	0
$690$	−7.89672e11	−0.132625
$691$	−1.21020e12	−0.201932	−0.100966	−	0.994890i	$-0.532193\pi$
$691$	−1.21020e12	−0.201932	−0.100966	+	0.994890i	$0.532193\pi$
$692$	−5.16151e12	−0.855656
$693$	4.32681e11	0.0712638
$694$	1.21730e12	0.199195
$695$	−1.03606e13	−1.68443
$696$	−1.60094e12	−0.258603
$697$	−1.70632e11	−0.0273849
$698$	−2.95747e12	−0.471597
$699$	−2.84503e12	−0.450755
$700$	−1.73508e11	−0.0273135
$701$	3.34752e12	0.523591	0.261796	−	0.965123i	$-0.415685\pi$
$701$	3.34752e12	0.523591	0.261796	+	0.965123i	$0.415685\pi$
$702$	0	0
$703$	−3.25461e12	−0.502574
$704$	−1.53212e12	−0.235081
$705$	1.55748e12	0.237449
$706$	2.01575e12	0.305362
$707$	3.70273e11	0.0557359
$708$	−2.21715e12	−0.331624
$709$	−1.09345e13	−1.62514	−0.812568	−	0.582866i	$-0.801931\pi$
$709$	−1.09345e13	−1.62514	−0.812568	+	0.582866i	$0.801931\pi$
$710$	6.24928e11	0.0922926
$711$	2.54109e12	0.372912
$712$	6.13570e12	0.894755
$713$	8.47224e12	1.22771
$714$	−9.69020e9	−0.00139537
$715$	0	0
$716$	1.52365e12	0.216660
$717$	3.16673e12	0.447481
$718$	6.07964e11	0.0853724
$719$	4.73071e12	0.660156	0.330078	−	0.943954i	$-0.392925\pi$
$719$	4.73071e12	0.660156	0.330078	+	0.943954i	$0.392925\pi$
$720$	−4.01857e12	−0.557283
$721$	−1.66250e12	−0.229115
$722$	1.02071e12	0.139793
$723$	−3.84256e12	−0.522997
$724$	−7.14738e12	−0.966770
$725$	2.23622e12	0.300603
$726$	5.08254e11	0.0678994
$727$	1.40402e13	1.86410	0.932049	−	0.362333i	$-0.118020\pi$
$727$	1.40402e13	1.86410	0.932049	+	0.362333i	$0.118020\pi$
$728$	0	0
$729$	−3.72119e12	−0.487987
$730$	3.28770e12	0.428489
$731$	−5.95459e11	−0.0771301
$732$	7.35524e11	0.0946884
$733$	1.78493e12	0.228377	0.114188	−	0.993459i	$-0.463573\pi$
$733$	1.78493e12	0.228377	0.114188	+	0.993459i	$0.463573\pi$
$734$	−3.55373e11	−0.0451910
$735$	−2.08448e12	−0.263453
$736$	−1.01683e13	−1.27731
$737$	−5.16101e12	−0.644364
$738$	6.47373e11	0.0803342
$739$	1.24956e13	1.54119	0.770595	−	0.637325i	$-0.219959\pi$
$739$	1.24956e13	1.54119	0.770595	+	0.637325i	$0.219959\pi$
$740$	−4.29551e12	−0.526589
$741$	0	0
$742$	−1.78711e11	−0.0216438
$743$	−4.21591e12	−0.507506	−0.253753	−	0.967269i	$-0.581665\pi$
$743$	−4.21591e12	−0.507506	−0.253753	+	0.967269i	$0.581665\pi$
$744$	1.26491e12	0.151349
$745$	−4.89665e12	−0.582366
$746$	−6.28080e11	−0.0742489
$747$	−1.03667e12	−0.121814
$748$	4.30664e11	0.0503016
$749$	6.69701e11	0.0777522
$750$	9.21825e11	0.106383
$751$	9.94988e12	1.14140	0.570701	−	0.821158i	$-0.306672\pi$
$751$	9.94988e12	1.14140	0.570701	+	0.821158i	$0.306672\pi$
$752$	5.37765e12	0.613214
$753$	1.54303e12	0.174903
$754$	0	0
$755$	−1.37742e13	−1.54278
$756$	−6.53699e11	−0.0727829
$757$	−1.61992e13	−1.79293	−0.896465	−	0.443115i	$-0.853873\pi$
$757$	−1.61992e13	−1.79293	−0.896465	+	0.443115i	$0.853873\pi$
$758$	−1.65589e12	−0.182188
$759$	2.35735e12	0.257831
$760$	−3.78310e12	−0.411327
$761$	−4.79250e12	−0.518001	−0.259001	−	0.965877i	$-0.583393\pi$
$761$	−4.79250e12	−0.518001	−0.259001	+	0.965877i	$0.583393\pi$
$762$	1.49794e12	0.160952
$763$	1.84655e12	0.197243
$764$	−1.21226e13	−1.28729
$765$	7.65171e11	0.0807759
$766$	5.03312e12	0.528211
$767$	0	0
$768$	2.99954e11	0.0311121
$769$	8.41625e11	0.0867861	0.0433930	−	0.999058i	$-0.486183\pi$
$769$	8.41625e11	0.0867861	0.0433930	+	0.999058i	$0.486183\pi$
$770$	2.20256e11	0.0225797
$771$	−8.42419e11	−0.0858585
$772$	−1.22347e12	−0.123970
$773$	−3.90333e12	−0.393213	−0.196607	−	0.980482i	$-0.562992\pi$
$773$	−3.90333e12	−0.393213	−0.196607	+	0.980482i	$0.562992\pi$
$774$	2.25916e12	0.226263
$775$	−1.76684e12	−0.175930
$776$	−1.04865e13	−1.03813
$777$	−2.88526e11	−0.0283982
$778$	−5.49781e12	−0.537999
$779$	−2.11241e12	−0.205523
$780$	0	0
$781$	−1.86555e12	−0.179422
$782$	5.19164e11	0.0496449
$783$	8.42507e12	0.801024
$784$	−7.19727e12	−0.680371
$785$	−9.13716e12	−0.858812
$786$	1.45149e12	0.135648
$787$	1.42677e13	1.32577	0.662884	−	0.748723i	$-0.269332\pi$
$787$	1.42677e13	1.32577	0.662884	+	0.748723i	$0.269332\pi$
$788$	6.32939e12	0.584782
$789$	−7.26562e11	−0.0667461
$790$	1.29354e12	0.118156
$791$	1.87460e12	0.170261
$792$	−3.46099e12	−0.312563
$793$	0	0
$794$	1.20087e12	0.107227
$795$	−1.43503e12	−0.127411
$796$	5.57748e12	0.492413
$797$	1.77300e13	1.55649	0.778245	−	0.627960i	$-0.216110\pi$
$797$	1.77300e13	1.55649	0.778245	+	0.627960i	$0.216110\pi$
$798$	−1.19964e11	−0.0104722
$799$	−1.02395e12	−0.0888829
$800$	2.12054e12	0.183038
$801$	−1.53636e13	−1.31870
$802$	−5.39863e12	−0.460785
$803$	−9.81453e12	−0.833009
$804$	3.71001e12	0.313129
$805$	−2.24634e12	−0.188535
$806$	0	0
$807$	2.79964e12	0.232366
$808$	−2.96179e12	−0.244458
$809$	6.57374e12	0.539565	0.269783	−	0.962921i	$-0.413048\pi$
$809$	6.57374e12	0.539565	0.269783	+	0.962921i	$0.413048\pi$
$810$	−2.57781e12	−0.210411
$811$	−1.30848e13	−1.06212	−0.531060	−	0.847334i	$-0.678206\pi$
$811$	−1.30848e13	−1.06212	−0.531060	+	0.847334i	$0.678206\pi$
$812$	−2.14999e12	−0.173553
$813$	−6.49774e12	−0.521621
$814$	−1.51569e12	−0.121004
$815$	9.06060e11	0.0719363
$816$	−2.68666e11	−0.0212132
$817$	−7.37177e12	−0.578858
$818$	5.48665e12	0.428467
$819$	0	0
$820$	−2.78801e12	−0.215344
$821$	−4.25638e12	−0.326961	−0.163480	−	0.986547i	$-0.552272\pi$
$821$	−4.25638e12	−0.326961	−0.163480	+	0.986547i	$0.552272\pi$
$822$	1.21031e12	0.0924644
$823$	−4.41691e12	−0.335598	−0.167799	−	0.985821i	$-0.553666\pi$
$823$	−4.41691e12	−0.335598	−0.167799	+	0.985821i	$0.553666\pi$
$824$	1.32982e13	1.00490
$825$	−4.91613e11	−0.0369471
$826$	7.45489e11	0.0557226
$827$	1.65971e13	1.23384	0.616919	−	0.787026i	$-0.288380\pi$
$827$	1.65971e13	1.23384	0.616919	+	0.787026i	$0.288380\pi$
$828$	1.66641e13	1.23210
$829$	−1.79742e13	−1.32176	−0.660882	−	0.750490i	$-0.729817\pi$
$829$	−1.79742e13	−1.32176	−0.660882	+	0.750490i	$0.729817\pi$
$830$	−5.27714e11	−0.0385964
$831$	−5.18363e12	−0.377077
$832$	0	0
$833$	1.37042e12	0.0986171
$834$	2.62798e12	0.188094
$835$	1.52697e13	1.08703
$836$	5.33161e12	0.377511
$837$	−6.65667e12	−0.468805
$838$	4.01864e12	0.281502
$839$	−3.10688e12	−0.216469	−0.108234	−	0.994125i	$-0.534520\pi$
$839$	−3.10688e12	−0.216469	−0.108234	+	0.994125i	$0.534520\pi$
$840$	−3.35378e11	−0.0232422
$841$	1.32025e13	0.910070
$842$	−2.17354e12	−0.149026
$843$	8.65626e12	0.590345
$844$	1.45092e12	0.0984246
$845$	0	0
$846$	3.88485e12	0.260740
$847$	1.44580e12	0.0965234
$848$	−4.95486e12	−0.329041
$849$	1.31951e12	0.0871622
$850$	−1.08269e11	−0.00711409
$851$	1.54581e13	1.01036
$852$	1.34106e12	0.0871904
$853$	−1.20700e13	−0.780613	−0.390306	−	0.920685i	$-0.627631\pi$
$853$	−1.20700e13	−0.780613	−0.390306	+	0.920685i	$0.627631\pi$
$854$	−2.47311e11	−0.0159105
$855$	9.47279e12	0.606220
$856$	−5.35690e12	−0.341021
$857$	−6.31368e12	−0.399824	−0.199912	−	0.979814i	$-0.564066\pi$
$857$	−6.31368e12	−0.399824	−0.199912	+	0.979814i	$0.564066\pi$
$858$	0	0
$859$	1.86663e13	1.16974	0.584870	−	0.811127i	$-0.301146\pi$
$859$	1.86663e13	1.16974	0.584870	+	0.811127i	$0.301146\pi$
$860$	−9.72943e12	−0.606519
$861$	−1.87269e11	−0.0116132
$862$	−4.04237e12	−0.249375
$863$	1.78712e13	1.09675	0.548373	−	0.836234i	$-0.315247\pi$
$863$	1.78712e13	1.09675	0.548373	+	0.836234i	$0.315247\pi$
$864$	7.98924e12	0.487746
$865$	1.39358e13	0.846368
$866$	5.54766e12	0.335181
$867$	−5.00357e12	−0.300742
$868$	1.69871e12	0.101573
$869$	−3.86149e12	−0.229703
$870$	2.04063e12	0.120761
$871$	0	0
$872$	−1.47705e13	−0.865107
$873$	2.62579e13	1.53002
$874$	6.42723e12	0.372583
$875$	2.62226e12	0.151231
$876$	7.05521e12	0.404801
$877$	3.76100e12	0.214687	0.107343	−	0.994222i	$-0.465766\pi$
$877$	3.76100e12	0.214687	0.107343	+	0.994222i	$0.465766\pi$
$878$	−7.34363e11	−0.0417047
$879$	3.33208e12	0.188263
$880$	6.10671e12	0.343270
$881$	2.05824e13	1.15108	0.575539	−	0.817775i	$-0.304792\pi$
$881$	2.05824e13	1.15108	0.575539	+	0.817775i	$0.304792\pi$
$882$	−5.19936e12	−0.289295
$883$	−3.01536e13	−1.66923	−0.834616	−	0.550833i	$-0.814310\pi$
$883$	−3.01536e13	−1.66923	−0.834616	+	0.550833i	$0.814310\pi$
$884$	0	0
$885$	5.98619e12	0.328024
$886$	7.94821e12	0.433329
$887$	−3.34317e13	−1.81343	−0.906717	−	0.421739i	$-0.861420\pi$
$887$	−3.34317e13	−1.81343	−0.906717	+	0.421739i	$0.861420\pi$
$888$	2.30790e12	0.124554
$889$	4.26109e12	0.228804
$890$	−7.82083e12	−0.417828
$891$	7.69533e12	0.409051
$892$	−4.58720e12	−0.242608
$893$	−1.26765e13	−0.667063
$894$	1.24204e12	0.0650304
$895$	−4.11379e12	−0.214308
$896$	−2.65007e12	−0.137364
$897$	0	0
$898$	7.57351e12	0.388646
$899$	−2.18935e13	−1.11788
$900$	−3.47521e12	−0.176559
$901$	9.43448e11	0.0476932
$902$	−9.83762e11	−0.0494835
$903$	−6.53519e11	−0.0327087
$904$	−1.49948e13	−0.746765
$905$	1.92976e13	0.956277
$906$	3.49384e12	0.172276
$907$	2.03004e13	0.996030	0.498015	−	0.867169i	$-0.334063\pi$
$907$	2.03004e13	0.996030	0.498015	+	0.867169i	$0.334063\pi$
$908$	−2.39912e13	−1.17129
$909$	7.41625e12	0.360285
$910$	0	0
$911$	1.74407e13	0.838940	0.419470	−	0.907769i	$-0.362216\pi$
$911$	1.74407e13	0.838940	0.419470	+	0.907769i	$0.362216\pi$
$912$	−3.32608e12	−0.159205
$913$	1.57534e12	0.0750337
$914$	7.80592e12	0.369970
$915$	−1.98588e12	−0.0936607
$916$	−1.35007e13	−0.633617
$917$	4.12897e12	0.192832
$918$	−4.07909e11	−0.0189571
$919$	1.69619e13	0.784430	0.392215	−	0.919874i	$-0.371709\pi$
$919$	1.69619e13	0.784430	0.392215	+	0.919874i	$0.371709\pi$
$920$	1.79683e13	0.826917
$921$	−5.11332e12	−0.234172
$922$	−5.30243e12	−0.241650
$923$	0	0
$924$	4.72655e11	0.0213315
$925$	−3.22372e12	−0.144784
$926$	1.03861e12	0.0464200
$927$	−3.32984e13	−1.48103
$928$	2.62762e13	1.16305
$929$	−4.90922e12	−0.216243	−0.108121	−	0.994138i	$-0.534484\pi$
$929$	−4.90922e12	−0.216243	−0.108121	+	0.994138i	$0.534484\pi$
$930$	−1.61230e12	−0.0706763
$931$	1.69658e13	0.740117
$932$	3.05619e13	1.32681
$933$	4.95408e12	0.214040
$934$	3.84833e12	0.165467
$935$	−1.16277e12	−0.0497556
$936$	0	0
$937$	1.13139e13	0.479497	0.239749	−	0.970835i	$-0.422935\pi$
$937$	1.13139e13	0.479497	0.239749	+	0.970835i	$0.422935\pi$
$938$	−1.24745e12	−0.0526149
$939$	4.22980e12	0.177552
$940$	−1.67307e13	−0.698938
$941$	−7.23052e11	−0.0300619	−0.0150310	−	0.999887i	$-0.504785\pi$
$941$	−7.23052e11	−0.0300619	−0.0150310	+	0.999887i	$0.504785\pi$
$942$	2.31765e12	0.0958999
$943$	1.00332e13	0.413176
$944$	2.06691e13	0.847126
$945$	1.76495e12	0.0719930
$946$	−3.43307e12	−0.139371
$947$	−4.04364e13	−1.63380	−0.816898	−	0.576782i	$-0.804308\pi$
$947$	−4.04364e13	−1.63380	−0.816898	+	0.576782i	$0.804308\pi$
$948$	2.77585e12	0.111624
$949$	0	0
$950$	−1.34037e12	−0.0533910
$951$	1.27103e13	0.503899
$952$	2.20492e11	0.00870014
$953$	4.03093e13	1.58302	0.791511	−	0.611155i	$-0.209295\pi$
$953$	4.03093e13	1.58302	0.791511	+	0.611155i	$0.209295\pi$
$954$	−3.57942e12	−0.139909
$955$	3.27305e13	1.27332
$956$	−3.40176e13	−1.31717
$957$	−6.09172e12	−0.234767
$958$	9.00366e12	0.345362
$959$	3.44291e12	0.131444
$960$	−2.97365e12	−0.112998
$961$	−9.14153e12	−0.345751
$962$	0	0
$963$	1.34135e13	0.502602
$964$	4.12776e13	1.53946
$965$	3.30330e12	0.122624
$966$	5.69784e11	0.0210530
$967$	−1.74415e13	−0.641451	−0.320726	−	0.947172i	$-0.603927\pi$
$967$	−1.74415e13	−0.641451	−0.320726	+	0.947172i	$0.603927\pi$
$968$	−1.15649e13	−0.423352
$969$	6.33314e11	0.0230761
$970$	1.33665e13	0.484782
$971$	−5.09597e13	−1.83967	−0.919836	−	0.392303i	$-0.871678\pi$
$971$	−5.09597e13	−1.83967	−0.919836	+	0.392303i	$0.871678\pi$
$972$	−1.99563e13	−0.717102
$973$	7.47565e12	0.267388
$974$	−2.77601e12	−0.0988340
$975$	0	0
$976$	−6.85683e12	−0.241880
$977$	−3.19652e13	−1.12241	−0.561205	−	0.827677i	$-0.689662\pi$
$977$	−3.19652e13	−1.12241	−0.561205	+	0.827677i	$0.689662\pi$
$978$	−2.29823e11	−0.00803283
$979$	2.33469e13	0.812283
$980$	2.23918e13	0.775483
$981$	3.69848e13	1.27501
$982$	1.73425e13	0.595127
$983$	5.12376e13	1.75024	0.875121	−	0.483904i	$-0.160782\pi$
$983$	5.12376e13	1.75024	0.875121	+	0.483904i	$0.160782\pi$
$984$	1.49795e12	0.0509354
$985$	−1.70890e13	−0.578434
$986$	−1.34159e12	−0.0452038
$987$	−1.12379e12	−0.0376927
$988$	0	0
$989$	3.50131e13	1.16372
$990$	4.41153e12	0.145959
$991$	−1.90444e13	−0.627243	−0.313622	−	0.949548i	$-0.601542\pi$
$991$	−1.90444e13	−0.627243	−0.313622	+	0.949548i	$0.601542\pi$
$992$	−2.07609e13	−0.680682
$993$	−2.93130e12	−0.0956730
$994$	−4.50914e11	−0.0146506
$995$	−1.50589e13	−0.487068
$996$	−1.13244e12	−0.0364627
$997$	4.27709e13	1.37095	0.685473	−	0.728098i	$-0.259595\pi$
$997$	4.27709e13	1.37095	0.685473	+	0.728098i	$0.259595\pi$
$998$	−1.94471e13	−0.620538
$999$	−1.21455e13	−0.385808

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.10.a.a.1.2		4
13.12	even	2		13.10.a.a.1.3	✓	4
39.38	odd	2		117.10.a.c.1.2		4
52.51	odd	2		208.10.a.g.1.2		4
65.64	even	2		325.10.a.a.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.a.1.3	✓	4	13.12	even	2
117.10.a.c.1.2		4	39.38	odd	2
169.10.a.a.1.2		4	1.1	even	1	trivial
208.10.a.g.1.2		4	52.51	odd	2
325.10.a.a.1.2		4	65.64	even	2

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	169.a (trivial)

\(f(q)\)	\(=\)	\(q-7.35673 q^{2} +42.6243 q^{3} -457.879 q^{4} +1236.25 q^{5} -313.575 q^{6} -892.010 q^{7} +7135.13 q^{8} -17866.2 q^{9} +O(q^{10})\)	\(q-7.35673 q^{2} +42.6243 q^{3} -457.879 q^{4} +1236.25 q^{5} -313.575 q^{6} -892.010 q^{7} +7135.13 q^{8} -17866.2 q^{9} -9094.74 q^{10} +27149.8 q^{11} -19516.8 q^{12} +6562.27 q^{14} +52694.2 q^{15} +181943. q^{16} -34643.4 q^{17} +131437. q^{18} -428885. q^{19} -566052. q^{20} -38021.3 q^{21} -199734. q^{22} +2.03704e6 q^{23} +304130. q^{24} -424814. q^{25} -1.60051e6 q^{27} +408432. q^{28} -5.26400e6 q^{29} -387657. q^{30} +4.15910e6 q^{31} -4.99169e6 q^{32} +1.15724e6 q^{33} +254862. q^{34} -1.10275e6 q^{35} +8.18054e6 q^{36} +7.58854e6 q^{37} +3.15519e6 q^{38} +8.82080e6 q^{40} +4.92536e6 q^{41} +279712. q^{42} +1.71882e7 q^{43} -1.24313e7 q^{44} -2.20870e7 q^{45} -1.49859e7 q^{46} +2.95568e7 q^{47} +7.75518e6 q^{48} -3.95579e7 q^{49} +3.12524e6 q^{50} -1.47665e6 q^{51} -2.72331e7 q^{53} +1.17745e7 q^{54} +3.35640e7 q^{55} -6.36461e6 q^{56} -1.82809e7 q^{57} +3.87258e7 q^{58} +1.13602e8 q^{59} -2.41276e7 q^{60} -3.76868e7 q^{61} -3.05973e7 q^{62} +1.59368e7 q^{63} -5.64321e7 q^{64} -8.51352e6 q^{66} -1.90094e8 q^{67} +1.58625e7 q^{68} +8.68273e7 q^{69} +8.11260e6 q^{70} -6.87130e7 q^{71} -1.27477e8 q^{72} -3.61495e8 q^{73} -5.58268e7 q^{74} -1.81074e7 q^{75} +1.96377e8 q^{76} -2.42179e7 q^{77} -1.42229e8 q^{79} +2.24926e8 q^{80} +2.83439e8 q^{81} -3.62346e7 q^{82} +5.80240e7 q^{83} +1.74091e7 q^{84} -4.28279e7 q^{85} -1.26449e8 q^{86} -2.24374e8 q^{87} +1.93718e8 q^{88} +8.59928e8 q^{89} +1.62488e8 q^{90} -9.32716e8 q^{92} +1.77279e8 q^{93} -2.17442e8 q^{94} -5.30208e8 q^{95} -2.12767e8 q^{96} -1.46970e9 q^{97} +2.91017e8 q^{98} -4.85064e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 33 q^{2} - 163 q^{3} + 1429 q^{4} - 471 q^{5} + 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9}+O(q^{10}) \) 4 * q + 33 * q^2 - 163 * q^3 + 1429 * q^4 - 471 * q^5 + 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9	\( 4 q + 33 q^{2} - 163 q^{3} + 1429 q^{4} - 471 q^{5} + 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9} - 67831 q^{10} + 40140 q^{11} - 155479 q^{12} - 277653 q^{14} - 83307 q^{15} + 726609 q^{16} + 78717 q^{17} - 1691026 q^{18} - 209664 q^{19} - 870843 q^{20} - 1138431 q^{21} + 1364090 q^{22} - 4257444 q^{23} - 3561573 q^{24} - 2900157 q^{25} - 2077801 q^{27} - 4035181 q^{28} - 1647936 q^{29} - 744143 q^{30} + 11366002 q^{31} + 29458959 q^{32} + 14413222 q^{33} - 26257659 q^{34} - 13789797 q^{35} - 11587714 q^{36} - 4636891 q^{37} + 25172466 q^{38} + 22536791 q^{40} - 13859538 q^{41} + 75564923 q^{42} - 33368081 q^{43} - 66489222 q^{44} + 17423928 q^{45} - 71369332 q^{46} + 3943005 q^{47} - 620787 q^{48} + 23294923 q^{49} + 4217748 q^{50} - 19664471 q^{51} - 171019326 q^{53} + 64946915 q^{54} - 121160538 q^{55} - 281552967 q^{56} + 47829030 q^{57} - 79964734 q^{58} + 63389388 q^{59} - 37708135 q^{60} + 77050190 q^{61} - 95878740 q^{62} + 155695476 q^{63} + 768962465 q^{64} - 42396374 q^{66} + 41174072 q^{67} - 717615423 q^{68} + 546642556 q^{69} - 409056389 q^{70} - 252460989 q^{71} - 562579254 q^{72} - 594415068 q^{73} - 957058539 q^{74} + 533318748 q^{75} + 326897170 q^{76} + 561950454 q^{77} + 115998984 q^{79} + 509107233 q^{80} + 437803700 q^{81} - 875148240 q^{82} + 79577862 q^{83} - 108899441 q^{84} - 549463469 q^{85} + 589924887 q^{86} - 1087526510 q^{87} - 2327564370 q^{88} + 1152240276 q^{89} + 877550038 q^{90} - 4213481460 q^{92} - 1618266556 q^{93} + 1859909503 q^{94} - 1273705170 q^{95} - 3171454029 q^{96} - 1049098084 q^{97} - 420532254 q^{98} - 2132181050 q^{99}+O(q^{100}) \) 4 * q + 33 * q^2 - 163 * q^3 + 1429 * q^4 - 471 * q^5 + 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9 - 67831 * q^10 + 40140 * q^11 - 155479 * q^12 - 277653 * q^14 - 83307 * q^15 + 726609 * q^16 + 78717 * q^17 - 1691026 * q^18 - 209664 * q^19 - 870843 * q^20 - 1138431 * q^21 + 1364090 * q^22 - 4257444 * q^23 - 3561573 * q^24 - 2900157 * q^25 - 2077801 * q^27 - 4035181 * q^28 - 1647936 * q^29 - 744143 * q^30 + 11366002 * q^31 + 29458959 * q^32 + 14413222 * q^33 - 26257659 * q^34 - 13789797 * q^35 - 11587714 * q^36 - 4636891 * q^37 + 25172466 * q^38 + 22536791 * q^40 - 13859538 * q^41 + 75564923 * q^42 - 33368081 * q^43 - 66489222 * q^44 + 17423928 * q^45 - 71369332 * q^46 + 3943005 * q^47 - 620787 * q^48 + 23294923 * q^49 + 4217748 * q^50 - 19664471 * q^51 - 171019326 * q^53 + 64946915 * q^54 - 121160538 * q^55 - 281552967 * q^56 + 47829030 * q^57 - 79964734 * q^58 + 63389388 * q^59 - 37708135 * q^60 + 77050190 * q^61 - 95878740 * q^62 + 155695476 * q^63 + 768962465 * q^64 - 42396374 * q^66 + 41174072 * q^67 - 717615423 * q^68 + 546642556 * q^69 - 409056389 * q^70 - 252460989 * q^71 - 562579254 * q^72 - 594415068 * q^73 - 957058539 * q^74 + 533318748 * q^75 + 326897170 * q^76 + 561950454 * q^77 + 115998984 * q^79 + 509107233 * q^80 + 437803700 * q^81 - 875148240 * q^82 + 79577862 * q^83 - 108899441 * q^84 - 549463469 * q^85 + 589924887 * q^86 - 1087526510 * q^87 - 2327564370 * q^88 + 1152240276 * q^89 + 877550038 * q^90 - 4213481460 * q^92 - 1618266556 * q^93 + 1859909503 * q^94 - 1273705170 * q^95 - 3171454029 * q^96 - 1049098084 * q^97 - 420532254 * q^98 - 2132181050 * q^99

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