LMFDB - Embedded newform 289.10.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, 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("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.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:	$148.845356651$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-43.7427 q^{2} +83.5916 q^{3} +1401.42 q^{4} -712.522 q^{5} -3656.52 q^{6} +5542.36 q^{7} -38905.7 q^{8} -12695.4 q^{9} +O(q^{10})$	\(q-43.7427 q^{2} +83.5916 q^{3} +1401.42 q^{4} -712.522 q^{5} -3656.52 q^{6} +5542.36 q^{7} -38905.7 q^{8} -12695.4 q^{9} +31167.6 q^{10} +36089.6 q^{11} +117147. q^{12} -175561. q^{13} -242438. q^{14} -59560.8 q^{15} +984313. q^{16} +555333. q^{18} -512948. q^{19} -998544. q^{20} +463295. q^{21} -1.57866e6 q^{22} -1.41122e6 q^{23} -3.25219e6 q^{24} -1.44544e6 q^{25} +7.67951e6 q^{26} -2.70657e6 q^{27} +7.76719e6 q^{28} -6.23829e6 q^{29} +2.60535e6 q^{30} -100038. q^{31} -2.31367e7 q^{32} +3.01679e6 q^{33} -3.94906e6 q^{35} -1.77917e7 q^{36} -1.77417e7 q^{37} +2.24377e7 q^{38} -1.46754e7 q^{39} +2.77212e7 q^{40} +2.70173e7 q^{41} -2.02658e7 q^{42} +778967. q^{43} +5.05768e7 q^{44} +9.04578e6 q^{45} +6.17308e7 q^{46} +1.03172e7 q^{47} +8.22803e7 q^{48} -9.63580e6 q^{49} +6.32273e7 q^{50} -2.46035e8 q^{52} +3.35090e7 q^{53} +1.18392e8 q^{54} -2.57146e7 q^{55} -2.15630e8 q^{56} -4.28782e7 q^{57} +2.72880e8 q^{58} +1.32523e8 q^{59} -8.34699e7 q^{60} -4.00552e7 q^{61} +4.37595e6 q^{62} -7.03628e7 q^{63} +5.08095e8 q^{64} +1.25091e8 q^{65} -1.31962e8 q^{66} +2.73645e8 q^{67} -1.17967e8 q^{69} +1.72742e8 q^{70} +1.50488e8 q^{71} +4.93925e8 q^{72} +1.55653e7 q^{73} +7.76071e8 q^{74} -1.20826e8 q^{75} -7.18857e8 q^{76} +2.00022e8 q^{77} +6.41943e8 q^{78} -4.95165e7 q^{79} -7.01344e8 q^{80} +2.36382e7 q^{81} -1.18181e9 q^{82} -2.23284e8 q^{83} +6.49272e8 q^{84} -3.40741e7 q^{86} -5.21469e8 q^{87} -1.40409e9 q^{88} +3.53228e7 q^{89} -3.95687e8 q^{90} -9.73023e8 q^{91} -1.97772e9 q^{92} -8.36237e6 q^{93} -4.51304e8 q^{94} +3.65487e8 q^{95} -1.93404e9 q^{96} -1.41983e9 q^{97} +4.21496e8 q^{98} -4.58174e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) $ 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9} + 60000 q^{10} + 76902 q^{11} + 373248 q^{12} + 54216 q^{13} + 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} + 6439479 q^{20} - 138102 q^{21} + 267324 q^{22} + 4041462 q^{23} + 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} + 13281612 q^{27} + 18614784 q^{28} + 4005936 q^{29} + 22471686 q^{30} + 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} + 22076682 q^{37} - 27401376 q^{38} + 62736162 q^{39} - 12231630 q^{40} + 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} - 49578936 q^{44} + 129308238 q^{45} + 140524827 q^{46} - 118557912 q^{47} + 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} + 209848575 q^{54} - 365439924 q^{55} + 203095059 q^{56} - 4614108 q^{57} - 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} + 175597116 q^{61} + 720602571 q^{62} + 587415936 q^{63} + 853082511 q^{64} + 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} + 1308709542 q^{71} - 275337849 q^{72} + 494841342 q^{73} + 1545361890 q^{74} + 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} + 2270624538 q^{78} + 1980107868 q^{79} + 2897000199 q^{80} + 1598298840 q^{81} + 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} - 2705904618 q^{88} + 148394658 q^{89} + 117916215 q^{90} + 636340896 q^{91} - 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} + 4878626298 q^{95} - 8390096634 q^{96} - 891786822 q^{97} + 4285627647 q^{98} - 1476187998 q^{99}+O(q^{100}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9 + 60000 * q^10 + 76902 * q^11 + 373248 * q^12 + 54216 * q^13 + 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 + 6439479 * q^20 - 138102 * q^21 + 267324 * q^22 + 4041462 * q^23 + 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 + 13281612 * q^27 + 18614784 * q^28 + 4005936 * q^29 + 22471686 * q^30 + 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 + 22076682 * q^37 - 27401376 * q^38 + 62736162 * q^39 - 12231630 * q^40 + 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 - 49578936 * q^44 + 129308238 * q^45 + 140524827 * q^46 - 118557912 * q^47 + 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 + 209848575 * q^54 - 365439924 * q^55 + 203095059 * q^56 - 4614108 * q^57 - 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 + 175597116 * q^61 + 720602571 * q^62 + 587415936 * q^63 + 853082511 * q^64 + 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 + 1308709542 * q^71 - 275337849 * q^72 + 494841342 * q^73 + 1545361890 * q^74 + 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 + 2270624538 * q^78 + 1980107868 * q^79 + 2897000199 * q^80 + 1598298840 * q^81 + 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 - 2705904618 * q^88 + 148394658 * q^89 + 117916215 * q^90 + 636340896 * q^91 - 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 + 4878626298 * q^95 - 8390096634 * q^96 - 891786822 * q^97 + 4285627647 * q^98 - 1476187998 * 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 $

$2$	−43.7427	−1.93317	−0.966586	−	0.256343i	$-0.917482\pi$
$2$	−43.7427	−1.93317	−0.966586	+	0.256343i	$0.917482\pi$
$3$	83.5916	0.595823	0.297911	−	0.954594i	$-0.403710\pi$
$3$	83.5916	0.595823	0.297911	+	0.954594i	$0.403710\pi$
$4$	1401.42	2.73715
$5$	−712.522	−0.509839	−0.254920	−	0.966962i	$-0.582049\pi$
$5$	−712.522	−0.509839	−0.254920	+	0.966962i	$0.582049\pi$
$6$	−3656.52	−1.15183
$7$	5542.36	0.872477	0.436238	−	0.899831i	$-0.356310\pi$
$7$	5542.36	0.872477	0.436238	+	0.899831i	$0.356310\pi$
$8$	−38905.7	−3.35822
$9$	−12695.4	−0.644995
$10$	31167.6	0.985607
$11$	36089.6	0.743216	0.371608	−	0.928390i	$-0.378807\pi$
$11$	36089.6	0.743216	0.371608	+	0.928390i	$0.378807\pi$
$12$	117147.	1.63086
$13$	−175561.	−1.70484	−0.852419	−	0.522859i	$-0.824865\pi$
$13$	−175561.	−1.70484	−0.852419	+	0.522859i	$0.824865\pi$
$14$	−242438.	−1.68665
$15$	−59560.8	−0.303774
$16$	984313.	3.75486
$17$	0	0
$17$	0	0
$18$	555333.	1.24689
$19$	−512948.	−0.902988	−0.451494	−	0.892274i	$-0.649109\pi$
$19$	−512948.	−0.902988	−0.451494	+	0.892274i	$0.649109\pi$
$20$	−998544.	−1.39551
$21$	463295.	0.519841
$22$	−1.57866e6	−1.43676
$23$	−1.41122e6	−1.05153	−0.525764	−	0.850630i	$-0.676221\pi$
$23$	−1.41122e6	−1.05153	−0.525764	+	0.850630i	$0.676221\pi$
$24$	−3.25219e6	−2.00090
$25$	−1.44544e6	−0.740064
$26$	7.67951e6	3.29574
$27$	−2.70657e6	−0.980126
$28$	7.76719e6	2.38810
$29$	−6.23829e6	−1.63785	−0.818926	−	0.573899i	$-0.805430\pi$
$29$	−6.23829e6	−1.63785	−0.818926	+	0.573899i	$0.805430\pi$
$30$	2.60535e6	0.587247
$31$	−100038.	−0.0194553	−0.00972767	−	0.999953i	$-0.503096\pi$
$31$	−100038.	−0.0194553	−0.00972767	+	0.999953i	$0.503096\pi$
$32$	−2.31367e7	−3.90056
$33$	3.01679e6	0.442825
$34$	0	0
$35$	−3.94906e6	−0.444823
$36$	−1.77917e7	−1.76545
$37$	−1.77417e7	−1.55628	−0.778141	−	0.628090i	$-0.783837\pi$
$37$	−1.77417e7	−1.55628	−0.778141	+	0.628090i	$0.783837\pi$
$38$	2.24377e7	1.74563
$39$	−1.46754e7	−1.01578
$40$	2.77212e7	1.71215
$41$	2.70173e7	1.49319	0.746594	−	0.665280i	$-0.231688\pi$
$41$	2.70173e7	1.49319	0.746594	+	0.665280i	$0.231688\pi$
$42$	−2.02658e7	−1.00494
$43$	778967.	0.0347465	0.0173733	−	0.999849i	$-0.494470\pi$
$43$	778967.	0.0347465	0.0173733	+	0.999849i	$0.494470\pi$
$44$	5.05768e7	2.03430
$45$	9.04578e6	0.328844
$46$	6.17308e7	2.03278
$47$	1.03172e7	0.308406	0.154203	−	0.988039i	$-0.450719\pi$
$47$	1.03172e7	0.308406	0.154203	+	0.988039i	$0.450719\pi$
$48$	8.22803e7	2.23723
$49$	−9.63580e6	−0.238784
$50$	6.32273e7	1.43067
$51$	0	0
$52$	−2.46035e8	−4.66640
$53$	3.35090e7	0.583338	0.291669	−	0.956519i	$-0.405789\pi$
$53$	3.35090e7	0.583338	0.291669	+	0.956519i	$0.405789\pi$
$54$	1.18392e8	1.89475
$55$	−2.57146e7	−0.378921
$56$	−2.15630e8	−2.92997
$57$	−4.28782e7	−0.538021
$58$	2.72880e8	3.16625
$59$	1.32523e8	1.42383	0.711915	−	0.702265i	$-0.247828\pi$
$59$	1.32523e8	1.42383	0.711915	+	0.702265i	$0.247828\pi$
$60$	−8.34699e7	−0.831475
$61$	−4.00552e7	−0.370403	−0.185202	−	0.982701i	$-0.559294\pi$
$61$	−4.00552e7	−0.370403	−0.185202	+	0.982701i	$0.559294\pi$
$62$	4.37595e6	0.0376105
$63$	−7.03628e7	−0.562744
$64$	5.08095e8	3.78561
$65$	1.25091e8	0.869193
$66$	−1.31962e8	−0.856057
$67$	2.73645e8	1.65902	0.829509	−	0.558494i	$-0.188621\pi$
$67$	2.73645e8	1.65902	0.829509	+	0.558494i	$0.188621\pi$
$68$	0	0
$69$	−1.17967e8	−0.626524
$70$	1.72742e8	0.859919
$71$	1.50488e8	0.702813	0.351406	−	0.936223i	$-0.385704\pi$
$71$	1.50488e8	0.702813	0.351406	+	0.936223i	$0.385704\pi$
$72$	4.93925e8	2.16603
$73$	1.55653e7	0.0641511	0.0320755	−	0.999485i	$-0.489788\pi$
$73$	1.55653e7	0.0641511	0.0320755	+	0.999485i	$0.489788\pi$
$74$	7.76071e8	3.00856
$75$	−1.20826e8	−0.440947
$76$	−7.18857e8	−2.47162
$77$	2.00022e8	0.648439
$78$	6.41943e8	1.96368
$79$	−4.95165e7	−0.143030	−0.0715152	−	0.997440i	$-0.522783\pi$
$79$	−4.95165e7	−0.143030	−0.0715152	+	0.997440i	$0.522783\pi$
$80$	−7.01344e8	−1.91437
$81$	2.36382e7	0.0610143
$82$	−1.18181e9	−2.88659
$83$	−2.23284e8	−0.516423	−0.258211	−	0.966088i	$-0.583133\pi$
$83$	−2.23284e8	−0.516423	−0.258211	+	0.966088i	$0.583133\pi$
$84$	6.49272e8	1.42289
$85$	0	0
$86$	−3.40741e7	−0.0671710
$87$	−5.21469e8	−0.975869
$88$	−1.40409e9	−2.49588
$89$	3.53228e7	0.0596761	0.0298380	−	0.999555i	$-0.490501\pi$
$89$	3.53228e7	0.0596761	0.0298380	+	0.999555i	$0.490501\pi$
$90$	−3.95687e8	−0.635712
$91$	−9.73023e8	−1.48743
$92$	−1.97772e9	−2.87819
$93$	−8.36237e6	−0.0115919
$94$	−4.51304e8	−0.596203
$95$	3.65487e8	0.460379
$96$	−1.93404e9	−2.32404
$97$	−1.41983e9	−1.62841	−0.814207	−	0.580575i	$-0.802828\pi$
$97$	−1.41983e9	−1.62841	−0.814207	+	0.580575i	$0.802828\pi$
$98$	4.21496e8	0.461611
$99$	−4.58174e8	−0.479371
$100$	−2.02567e9	−2.02567
$101$	−6.69672e8	−0.640348	−0.320174	−	0.947359i	$-0.603741\pi$
$101$	−6.69672e8	−0.640348	−0.320174	+	0.947359i	$0.603741\pi$
$102$	0	0
$103$	8.49559e8	0.743748	0.371874	−	0.928283i	$-0.378715\pi$
$103$	8.49559e8	0.743748	0.371874	+	0.928283i	$0.378715\pi$
$104$	6.83033e9	5.72521
$105$	−3.30108e8	−0.265036
$106$	−1.46577e9	−1.12769
$107$	1.20391e9	0.887905	0.443952	−	0.896050i	$-0.353576\pi$
$107$	1.20391e9	0.887905	0.443952	+	0.896050i	$0.353576\pi$
$108$	−3.79304e9	−2.68275
$109$	1.20826e9	0.819861	0.409930	−	0.912117i	$-0.365553\pi$
$109$	1.20826e9	0.819861	0.409930	+	0.912117i	$0.365553\pi$
$110$	1.12483e9	0.732519
$111$	−1.48306e9	−0.927268
$112$	5.45542e9	3.27602
$113$	−2.90740e9	−1.67746	−0.838729	−	0.544549i	$-0.816701\pi$
$113$	−2.90740e9	−1.67746	−0.838729	+	0.544549i	$0.816701\pi$
$114$	1.87561e9	1.04009
$115$	1.00553e9	0.536110
$116$	−8.74248e9	−4.48305
$117$	2.22883e9	1.09961
$118$	−5.79693e9	−2.75251
$119$	0	0
$120$	2.31726e9	1.02014
$121$	−1.05549e9	−0.447630
$122$	1.75212e9	0.716053
$123$	2.25842e9	0.889675
$124$	−1.40196e8	−0.0532523
$125$	2.42155e9	0.887153
$126$	3.07786e9	1.08788
$127$	−1.75281e8	−0.0597884	−0.0298942	−	0.999553i	$-0.509517\pi$
$127$	−1.75281e8	−0.0597884	−0.0298942	+	0.999553i	$0.509517\pi$
$128$	−1.03794e10	−3.41766
$129$	6.51151e7	0.0207028
$130$	−5.47182e9	−1.68030
$131$	4.29446e9	1.27405	0.637027	−	0.770841i	$-0.280164\pi$
$131$	4.29446e9	1.27405	0.637027	+	0.770841i	$0.280164\pi$
$132$	4.22779e9	1.21208
$133$	−2.84295e9	−0.787837
$134$	−1.19700e10	−3.20717
$135$	1.92849e9	0.499706
$136$	0	0
$137$	−1.83424e9	−0.444850	−0.222425	−	0.974950i	$-0.571397\pi$
$137$	−1.83424e9	−0.444850	−0.222425	+	0.974950i	$0.571397\pi$
$138$	5.16017e9	1.21118
$139$	3.09950e9	0.704247	0.352123	−	0.935954i	$-0.385460\pi$
$139$	3.09950e9	0.704247	0.352123	+	0.935954i	$0.385460\pi$
$140$	−5.53430e9	−1.21755
$141$	8.62435e8	0.183756
$142$	−6.58275e9	−1.35866
$143$	−6.33593e9	−1.26706
$144$	−1.24963e10	−2.42186
$145$	4.44492e9	0.835041
$146$	−6.80867e8	−0.124015
$147$	−8.05472e8	−0.142273
$148$	−2.48637e10	−4.25978
$149$	2.53473e9	0.421302	0.210651	−	0.977561i	$-0.432442\pi$
$149$	2.53473e9	0.421302	0.210651	+	0.977561i	$0.432442\pi$
$150$	5.28527e9	0.852426
$151$	−1.10620e9	−0.173156	−0.0865780	−	0.996245i	$-0.527593\pi$
$151$	−1.10620e9	−0.173156	−0.0865780	+	0.996245i	$0.527593\pi$
$152$	1.99566e10	3.03243
$153$	0	0
$154$	−8.74949e9	−1.25354
$155$	7.12795e7	0.00991909
$156$	−2.05665e10	−2.78035
$157$	−1.70941e9	−0.224542	−0.112271	−	0.993678i	$-0.535813\pi$
$157$	−1.70941e9	−0.224542	−0.112271	+	0.993678i	$0.535813\pi$
$158$	2.16599e9	0.276502
$159$	2.80107e9	0.347566
$160$	1.64854e10	1.98866
$161$	−7.82152e9	−0.917434
$162$	−1.03400e9	−0.117951
$163$	−4.74641e9	−0.526649	−0.263324	−	0.964707i	$-0.584819\pi$
$163$	−4.74641e9	−0.526649	−0.263324	+	0.964707i	$0.584819\pi$
$164$	3.78626e10	4.08708
$165$	−2.14953e9	−0.225769
$166$	9.76703e9	0.998334
$167$	2.19497e8	0.0218376	0.0109188	−	0.999940i	$-0.496524\pi$
$167$	2.19497e8	0.0218376	0.0109188	+	0.999940i	$0.496524\pi$
$168$	−1.80248e10	−1.74574
$169$	2.02172e10	1.90647
$170$	0	0
$171$	6.51210e9	0.582423
$172$	1.09166e9	0.0951065
$173$	1.63408e10	1.38697	0.693485	−	0.720471i	$-0.256074\pi$
$173$	1.63408e10	1.38697	0.693485	+	0.720471i	$0.256074\pi$
$174$	2.28104e10	1.88652
$175$	−8.01114e9	−0.645689
$176$	3.55235e10	2.79067
$177$	1.10778e10	0.848351
$178$	−1.54512e9	−0.115364
$179$	8.32078e9	0.605795	0.302897	−	0.953023i	$-0.402046\pi$
$179$	8.32078e9	0.605795	0.302897	+	0.953023i	$0.402046\pi$
$180$	1.26770e10	0.900096
$181$	−5.65108e9	−0.391361	−0.195681	−	0.980668i	$-0.562692\pi$
$181$	−5.65108e9	−0.391361	−0.195681	+	0.980668i	$0.562692\pi$
$182$	4.25627e10	2.87546
$183$	−3.34828e9	−0.220695
$184$	5.49047e10	3.53126
$185$	1.26414e10	0.793453
$186$	3.65792e8	0.0224092
$187$	0	0
$188$	1.44588e10	0.844156
$189$	−1.50008e10	−0.855137
$190$	−1.59874e10	−0.889991
$191$	−4.52797e9	−0.246180	−0.123090	−	0.992395i	$-0.539280\pi$
$191$	−4.52797e9	−0.246180	−0.123090	+	0.992395i	$0.539280\pi$
$192$	4.24725e10	2.25555
$193$	−2.74959e10	−1.42646	−0.713230	−	0.700931i	$-0.752768\pi$
$193$	−2.74959e10	−1.42646	−0.713230	+	0.700931i	$0.752768\pi$
$194$	6.21073e10	3.14800
$195$	1.04566e10	0.517885
$196$	−1.35038e10	−0.653589
$197$	1.50301e10	0.710991	0.355495	−	0.934678i	$-0.384312\pi$
$197$	1.50301e10	0.710991	0.355495	+	0.934678i	$0.384312\pi$
$198$	2.00417e10	0.926706
$199$	−5.79615e9	−0.262000	−0.131000	−	0.991382i	$-0.541819\pi$
$199$	−5.79615e9	−0.262000	−0.131000	+	0.991382i	$0.541819\pi$
$200$	5.62358e10	2.48529
$201$	2.28744e10	0.988480
$202$	2.92932e10	1.23790
$203$	−3.45749e10	−1.42899
$204$	0	0
$205$	−1.92504e10	−0.761286
$206$	−3.71620e10	−1.43779
$207$	1.79161e10	0.678231
$208$	−1.72807e11	−6.40142
$209$	−1.85121e10	−0.671115
$210$	1.44398e10	0.512359
$211$	−3.03732e10	−1.05492	−0.527460	−	0.849580i	$-0.676856\pi$
$211$	−3.03732e10	−1.05492	−0.527460	+	0.849580i	$0.676856\pi$
$212$	4.69603e10	1.59669
$213$	1.25795e10	0.418752
$214$	−5.26622e10	−1.71647
$215$	−5.55031e8	−0.0177151
$216$	1.05301e11	3.29147
$217$	−5.54449e8	−0.0169743
$218$	−5.28524e10	−1.58493
$219$	1.30113e9	0.0382227
$220$	−3.60371e10	−1.03716
$221$	0	0
$222$	6.48730e10	1.79257
$223$	4.61309e10	1.24916	0.624582	−	0.780959i	$-0.285269\pi$
$223$	4.61309e10	1.24916	0.624582	+	0.780959i	$0.285269\pi$
$224$	−1.28232e11	−3.40315
$225$	1.83505e10	0.477338
$226$	1.27177e11	3.24282
$227$	−1.32854e9	−0.0332092	−0.0166046	−	0.999862i	$-0.505286\pi$
$227$	−1.32854e9	−0.0332092	−0.0166046	+	0.999862i	$0.505286\pi$
$228$	−6.00904e10	−1.47265
$229$	1.58431e10	0.380699	0.190349	−	0.981716i	$-0.439038\pi$
$229$	1.58431e10	0.380699	0.190349	+	0.981716i	$0.439038\pi$
$230$	−4.39845e10	−1.03639
$231$	1.67201e10	0.386355
$232$	2.42705e11	5.50026
$233$	−4.53578e8	−0.0100821	−0.00504104	−	0.999987i	$-0.501605\pi$
$233$	−4.53578e8	−0.0100821	−0.00504104	+	0.999987i	$0.501605\pi$
$234$	−9.74948e10	−2.12574
$235$	−7.35126e9	−0.157238
$236$	1.85721e11	3.89724
$237$	−4.13917e9	−0.0852208
$238$	0	0
$239$	6.02131e10	1.19371	0.596857	−	0.802348i	$-0.296416\pi$
$239$	6.02131e10	1.19371	0.596857	+	0.802348i	$0.296416\pi$
$240$	−5.86265e10	−1.14063
$241$	−1.95681e10	−0.373656	−0.186828	−	0.982393i	$-0.559821\pi$
$241$	−1.95681e10	−0.373656	−0.186828	+	0.982393i	$0.559821\pi$
$242$	4.61699e10	0.865346
$243$	5.52493e10	1.01648
$244$	−5.61343e10	−1.01385
$245$	6.86572e9	0.121741
$246$	−9.87893e10	−1.71989
$247$	9.00537e10	1.53945
$248$	3.89206e9	0.0653352
$249$	−1.86646e10	−0.307696
$250$	−1.05925e11	−1.71502
$251$	−1.06749e11	−1.69759	−0.848794	−	0.528724i	$-0.822671\pi$
$251$	−1.06749e11	−1.69759	−0.848794	+	0.528724i	$0.822671\pi$
$252$	−9.86080e10	−1.54032
$253$	−5.09305e10	−0.781513
$254$	7.66724e9	0.115581
$255$	0	0
$256$	1.93880e11	2.82132
$257$	−1.35700e10	−0.194035	−0.0970176	−	0.995283i	$-0.530930\pi$
$257$	−1.35700e10	−0.194035	−0.0970176	+	0.995283i	$0.530930\pi$
$258$	−2.84831e9	−0.0400220
$259$	−9.83311e10	−1.35782
$260$	1.75305e11	2.37911
$261$	7.91979e10	1.05641
$262$	−1.87851e11	−2.46297
$263$	−4.47087e10	−0.576224	−0.288112	−	0.957597i	$-0.593027\pi$
$263$	−4.47087e10	−0.576224	−0.288112	+	0.957597i	$0.593027\pi$
$264$	−1.17370e11	−1.48710
$265$	−2.38759e10	−0.297409
$266$	1.24358e11	1.52302
$267$	2.95269e9	0.0355564
$268$	3.83492e11	4.54098
$269$	9.73705e10	1.13381	0.566907	−	0.823782i	$-0.308140\pi$
$269$	9.73705e10	1.13381	0.566907	+	0.823782i	$0.308140\pi$
$270$	−8.43572e10	−0.966018
$271$	−8.62013e10	−0.970850	−0.485425	−	0.874278i	$-0.661335\pi$
$271$	−8.62013e10	−0.970850	−0.485425	+	0.874278i	$0.661335\pi$
$272$	0	0
$273$	−8.13366e10	−0.886245
$274$	8.02346e10	0.859971
$275$	−5.21653e10	−0.550027
$276$	−1.65321e11	−1.71489
$277$	−1.81712e10	−0.185449	−0.0927243	−	0.995692i	$-0.529558\pi$
$277$	−1.81712e10	−0.185449	−0.0927243	+	0.995692i	$0.529558\pi$
$278$	−1.35580e11	−1.36143
$279$	1.27003e9	0.0125486
$280$	1.53641e11	1.49381
$281$	−3.90556e10	−0.373684	−0.186842	−	0.982390i	$-0.559825\pi$
$281$	−3.90556e10	−0.373684	−0.186842	+	0.982390i	$0.559825\pi$
$282$	−3.77252e10	−0.355231
$283$	−1.56085e11	−1.44651	−0.723255	−	0.690581i	$-0.757355\pi$
$283$	−1.56085e11	−1.44651	−0.723255	+	0.690581i	$0.757355\pi$
$284$	2.10897e11	1.92371
$285$	3.05516e10	0.274304
$286$	2.77151e11	2.44945
$287$	1.49740e11	1.30277
$288$	2.93731e11	2.51585
$289$	0	0
$290$	−1.94433e11	−1.61428
$291$	−1.18686e11	−0.970246
$292$	2.18135e10	0.175591
$293$	1.99350e11	1.58020	0.790099	−	0.612980i	$-0.210029\pi$
$293$	1.99350e11	1.58020	0.790099	+	0.612980i	$0.210029\pi$
$294$	3.52335e10	0.275038
$295$	−9.44258e10	−0.725925
$296$	6.90255e11	5.22633
$297$	−9.76789e10	−0.728445
$298$	−1.10876e11	−0.814449
$299$	2.47756e11	1.79269
$300$	−1.69329e11	−1.20694
$301$	4.31732e9	0.0303155
$302$	4.83882e10	0.334740
$303$	−5.59789e10	−0.381534
$304$	−5.04901e11	−3.39059
$305$	2.85402e10	0.188846
$306$	0	0
$307$	−1.45882e11	−0.937298	−0.468649	−	0.883384i	$-0.655259\pi$
$307$	−1.45882e11	−0.937298	−0.468649	+	0.883384i	$0.655259\pi$
$308$	2.80315e11	1.77488
$309$	7.10160e10	0.443142
$310$	−3.11796e9	−0.0191753
$311$	−5.10899e10	−0.309680	−0.154840	−	0.987940i	$-0.549486\pi$
$311$	−5.10899e10	−0.309680	−0.154840	+	0.987940i	$0.549486\pi$
$312$	5.70958e11	3.41121
$313$	2.60411e11	1.53359	0.766797	−	0.641890i	$-0.221849\pi$
$313$	2.60411e11	1.53359	0.766797	+	0.641890i	$0.221849\pi$
$314$	7.47742e10	0.434079
$315$	5.01350e10	0.286909
$316$	−6.93936e10	−0.391496
$317$	6.41873e8	0.00357012	0.00178506	−	0.999998i	$-0.499432\pi$
$317$	6.41873e8	0.00357012	0.00178506	+	0.999998i	$0.499432\pi$
$318$	−1.22526e11	−0.671905
$319$	−2.25137e11	−1.21728
$320$	−3.62029e11	−1.93005
$321$	1.00637e11	0.529034
$322$	3.42134e11	1.77356
$323$	0	0
$324$	3.31271e10	0.167006
$325$	2.53763e11	1.26169
$326$	2.07621e11	1.01810
$327$	1.01000e11	0.488492
$328$	−1.05113e12	−5.01445
$329$	5.71819e10	0.269077
$330$	9.40261e10	0.436451
$331$	−2.52438e11	−1.15592	−0.577962	−	0.816063i	$-0.696152\pi$
$331$	−2.52438e11	−1.15592	−0.577962	+	0.816063i	$0.696152\pi$
$332$	−3.12915e11	−1.41353
$333$	2.25239e11	1.00379
$334$	−9.60139e9	−0.0422158
$335$	−1.94978e11	−0.845832
$336$	4.56027e11	1.95193
$337$	2.71455e11	1.14647	0.573235	−	0.819391i	$-0.305688\pi$
$337$	2.71455e11	1.14647	0.573235	+	0.819391i	$0.305688\pi$
$338$	−8.84354e11	−3.68554
$339$	−2.43034e11	−0.999468
$340$	0	0
$341$	−3.61034e9	−0.0144595
$342$	−2.84857e11	−1.12592
$343$	−2.77060e11	−1.08081
$344$	−3.03063e10	−0.116686
$345$	8.40537e10	0.319427
$346$	−7.14792e11	−2.68125
$347$	−1.21278e11	−0.449053	−0.224527	−	0.974468i	$-0.572084\pi$
$347$	−1.21278e11	−0.449053	−0.224527	+	0.974468i	$0.572084\pi$
$348$	−7.30798e11	−2.67110
$349$	4.94486e11	1.78418	0.892092	−	0.451854i	$-0.149237\pi$
$349$	4.94486e11	1.78418	0.892092	+	0.451854i	$0.149237\pi$
$350$	3.50429e11	1.24823
$351$	4.75168e11	1.67096
$352$	−8.34996e11	−2.89896
$353$	2.59580e11	0.889785	0.444893	−	0.895584i	$-0.353242\pi$
$353$	2.59580e11	0.889785	0.444893	+	0.895584i	$0.353242\pi$
$354$	−4.84574e11	−1.64001
$355$	−1.07226e11	−0.358321
$356$	4.95022e10	0.163343
$357$	0	0
$358$	−3.63973e11	−1.17111
$359$	5.64703e11	1.79430	0.897150	−	0.441725i	$-0.145633\pi$
$359$	5.64703e11	1.79430	0.897150	+	0.441725i	$0.145633\pi$
$360$	−3.51933e11	−1.10433
$361$	−5.95720e10	−0.184612
$362$	2.47193e11	0.756569
$363$	−8.82299e10	−0.266708
$364$	−1.36362e12	−4.07133
$365$	−1.10906e10	−0.0327067
$366$	1.46463e11	0.426641
$367$	5.01887e10	0.144414	0.0722069	−	0.997390i	$-0.476996\pi$
$367$	5.01887e10	0.144414	0.0722069	+	0.997390i	$0.476996\pi$
$368$	−1.38909e12	−3.94834
$369$	−3.42996e11	−0.963099
$370$	−5.52967e11	−1.53388
$371$	1.85719e11	0.508949
$372$	−1.17192e10	−0.0317289
$373$	2.42202e11	0.647870	0.323935	−	0.946079i	$-0.394994\pi$
$373$	2.42202e11	0.647870	0.323935	+	0.946079i	$0.394994\pi$
$374$	0	0
$375$	2.02421e11	0.528586
$376$	−4.01400e11	−1.03570
$377$	1.09520e12	2.79227
$378$	6.56174e11	1.65313
$379$	6.36704e11	1.58512	0.792559	−	0.609796i	$-0.208749\pi$
$379$	6.36704e11	1.58512	0.792559	+	0.609796i	$0.208749\pi$
$380$	5.12201e11	1.26013
$381$	−1.46520e10	−0.0356233
$382$	1.98066e11	0.475909
$383$	4.29691e10	0.102038	0.0510190	−	0.998698i	$-0.483753\pi$
$383$	4.29691e10	0.102038	0.0510190	+	0.998698i	$0.483753\pi$
$384$	−8.67634e11	−2.03632
$385$	−1.42520e11	−0.330599
$386$	1.20274e12	2.75759
$387$	−9.88934e9	−0.0224113
$388$	−1.98979e12	−4.45722
$389$	5.97037e11	1.32199	0.660995	−	0.750391i	$-0.270135\pi$
$389$	5.97037e11	1.32199	0.660995	+	0.750391i	$0.270135\pi$
$390$	−4.57398e11	−1.00116
$391$	0	0
$392$	3.74888e11	0.801889
$393$	3.58981e11	0.759110
$394$	−6.57457e11	−1.37447
$395$	3.52816e10	0.0729225
$396$	−6.42095e11	−1.31211
$397$	−4.91474e11	−0.992986	−0.496493	−	0.868041i	$-0.665379\pi$
$397$	−4.91474e11	−0.992986	−0.496493	+	0.868041i	$0.665379\pi$
$398$	2.53539e11	0.506491
$399$	−2.37646e11	−0.469411
$400$	−1.42276e12	−2.77883
$401$	2.34902e11	0.453668	0.226834	−	0.973933i	$-0.427163\pi$
$401$	2.34902e11	0.453668	0.226834	+	0.973933i	$0.427163\pi$
$402$	−1.00059e12	−1.91090
$403$	1.75628e10	0.0331682
$404$	−9.38493e11	−1.75273
$405$	−1.68427e10	−0.0311075
$406$	1.51240e12	2.76248
$407$	−6.40292e11	−1.15665
$408$	0	0
$409$	1.31401e11	0.232191	0.116095	−	0.993238i	$-0.462962\pi$
$409$	1.31401e11	0.232191	0.116095	+	0.993238i	$0.462962\pi$
$410$	8.42065e11	1.47170
$411$	−1.53327e11	−0.265052
$412$	1.19059e12	2.03575
$413$	7.34493e11	1.24226
$414$	−7.83699e11	−1.31114
$415$	1.59094e11	0.263293
$416$	4.06191e12	6.64983
$417$	2.59092e11	0.419606
$418$	8.09769e11	1.29738
$419$	−6.01297e11	−0.953072	−0.476536	−	0.879155i	$-0.658108\pi$
$419$	−6.01297e11	−0.953072	−0.476536	+	0.879155i	$0.658108\pi$
$420$	−4.62621e11	−0.725443
$421$	1.16288e11	0.180412	0.0902062	−	0.995923i	$-0.471247\pi$
$421$	1.16288e11	0.180412	0.0902062	+	0.995923i	$0.471247\pi$
$422$	1.32861e12	2.03934
$423$	−1.30982e11	−0.198921
$424$	−1.30369e12	−1.95898
$425$	0	0
$426$	−5.50263e11	−0.809519
$427$	−2.22001e11	−0.323168
$428$	1.68718e12	2.43033
$429$	−5.29630e11	−0.754945
$430$	2.42786e10	0.0342464
$431$	−9.23955e11	−1.28974	−0.644871	−	0.764291i	$-0.723089\pi$
$431$	−9.23955e11	−1.28974	−0.644871	+	0.764291i	$0.723089\pi$
$432$	−2.66411e12	−3.68023
$433$	−3.64410e11	−0.498189	−0.249095	−	0.968479i	$-0.580133\pi$
$433$	−3.64410e11	−0.498189	−0.249095	+	0.968479i	$0.580133\pi$
$434$	2.42531e10	0.0328143
$435$	3.71558e11	0.497536
$436$	1.69328e12	2.24408
$437$	7.23885e11	0.949518
$438$	−5.69148e10	−0.0738910
$439$	6.78960e11	0.872476	0.436238	−	0.899831i	$-0.356311\pi$
$439$	6.78960e11	0.872476	0.436238	+	0.899831i	$0.356311\pi$
$440$	1.00045e12	1.27250
$441$	1.22331e11	0.154015
$442$	0	0
$443$	−5.20909e11	−0.642607	−0.321303	−	0.946976i	$-0.604121\pi$
$443$	−5.20909e11	−0.642607	−0.321303	+	0.946976i	$0.604121\pi$
$444$	−2.07839e12	−2.53807
$445$	−2.51683e10	−0.0304252
$446$	−2.01789e12	−2.41485
$447$	2.11882e11	0.251021
$448$	2.81605e12	3.30285
$449$	8.95134e11	1.03939	0.519696	−	0.854351i	$-0.326045\pi$
$449$	8.95134e11	1.03939	0.519696	+	0.854351i	$0.326045\pi$
$450$	−8.02699e11	−0.922776
$451$	9.75043e11	1.10976
$452$	−4.07450e12	−4.59146
$453$	−9.24690e10	−0.103170
$454$	5.81139e10	0.0641991
$455$	6.93300e11	0.758351
$456$	1.66821e12	1.80679
$457$	1.95511e11	0.209675	0.104838	−	0.994489i	$-0.466568\pi$
$457$	1.95511e11	0.209675	0.104838	+	0.994489i	$0.466568\pi$
$458$	−6.93021e11	−0.735956
$459$	0	0
$460$	1.40917e12	1.46742
$461$	−6.94628e11	−0.716305	−0.358153	−	0.933663i	$-0.616593\pi$
$461$	−6.94628e11	−0.716305	−0.358153	+	0.933663i	$0.616593\pi$
$462$	−7.31384e11	−0.746890
$463$	1.44310e12	1.45943	0.729713	−	0.683753i	$-0.239654\pi$
$463$	1.44310e12	1.45943	0.729713	+	0.683753i	$0.239654\pi$
$464$	−6.14043e12	−6.14990
$465$	5.95837e9	0.00591002
$466$	1.98407e10	0.0194904
$467$	−1.73333e12	−1.68637	−0.843187	−	0.537620i	$-0.819324\pi$
$467$	−1.73333e12	−1.68637	−0.843187	+	0.537620i	$0.819324\pi$
$468$	3.12353e12	3.00981
$469$	1.51664e12	1.44745
$470$	3.21564e11	0.303967
$471$	−1.42892e11	−0.133787
$472$	−5.15592e12	−4.78153
$473$	2.81126e10	0.0258242
$474$	1.81058e11	0.164746
$475$	7.41434e11	0.668269
$476$	0	0
$477$	−4.25412e11	−0.376250
$478$	−2.63388e12	−2.30765
$479$	4.61090e11	0.400199	0.200100	−	0.979776i	$-0.435873\pi$
$479$	4.61090e11	0.400199	0.200100	+	0.979776i	$0.435873\pi$
$480$	1.37804e12	1.18489
$481$	3.11476e12	2.65321
$482$	8.55961e11	0.722341
$483$	−6.53814e11	−0.546628
$484$	−1.47918e12	−1.22523
$485$	1.01166e12	0.830229
$486$	−2.41675e12	−1.96503
$487$	1.31130e12	1.05638	0.528191	−	0.849126i	$-0.322871\pi$
$487$	1.31130e12	1.05638	0.528191	+	0.849126i	$0.322871\pi$
$488$	1.55838e12	1.24389
$489$	−3.96760e11	−0.313789
$490$	−3.00325e11	−0.235347
$491$	−2.42631e11	−0.188399	−0.0941997	−	0.995553i	$-0.530029\pi$
$491$	−2.42631e11	−0.188399	−0.0941997	+	0.995553i	$0.530029\pi$
$492$	3.16500e12	2.43518
$493$	0	0
$494$	−3.93919e12	−2.97602
$495$	3.26459e11	0.244402
$496$	−9.84690e10	−0.0730520
$497$	8.34060e11	0.613188
$498$	8.16441e11	0.594830
$499$	1.85899e12	1.34223	0.671113	−	0.741355i	$-0.265816\pi$
$499$	1.85899e12	1.34223	0.671113	+	0.741355i	$0.265816\pi$
$500$	3.39361e12	2.42827
$501$	1.83481e10	0.0130113
$502$	4.66949e12	3.28173
$503$	1.96267e12	1.36707	0.683537	−	0.729916i	$-0.260441\pi$
$503$	1.96267e12	1.36707	0.683537	+	0.729916i	$0.260441\pi$
$504$	2.73752e12	1.88981
$505$	4.77156e11	0.326474
$506$	2.22784e12	1.51080
$507$	1.68999e12	1.13592
$508$	−2.45642e11	−0.163650
$509$	−1.96893e12	−1.30017	−0.650085	−	0.759861i	$-0.725267\pi$
$509$	−1.96893e12	−1.30017	−0.650085	+	0.759861i	$0.725267\pi$
$510$	0	0
$511$	8.62684e10	0.0559703
$512$	−3.16655e12	−2.03644
$513$	1.38833e12	0.885042
$514$	5.93588e11	0.375103
$515$	−6.05329e11	−0.379192
$516$	9.12538e10	0.0566666
$517$	3.72345e11	0.229213
$518$	4.30127e12	2.62490
$519$	1.36596e12	0.826388
$520$	−4.86676e12	−2.91894
$521$	7.98293e11	0.474671	0.237335	−	0.971428i	$-0.423726\pi$
$521$	7.98293e11	0.474671	0.237335	+	0.971428i	$0.423726\pi$
$522$	−3.46433e12	−2.04222
$523$	−1.48202e12	−0.866158	−0.433079	−	0.901356i	$-0.642573\pi$
$523$	−1.48202e12	−0.866158	−0.433079	+	0.901356i	$0.642573\pi$
$524$	6.01835e12	3.48728
$525$	−6.69664e11	−0.384716
$526$	1.95568e12	1.11394
$527$	0	0
$528$	2.96946e12	1.66274
$529$	1.90403e11	0.105712
$530$	1.04440e12	0.574942
$531$	−1.68244e12	−0.918364
$532$	−3.98417e12	−2.15643
$533$	−4.74318e12	−2.54564
$534$	−1.29159e11	−0.0687366
$535$	−8.57811e11	−0.452689
$536$	−1.06464e13	−5.57134
$537$	6.95547e11	0.360946
$538$	−4.25925e12	−2.19186
$539$	−3.47752e11	−0.177468
$540$	2.70263e12	1.36777
$541$	−1.28357e12	−0.644219	−0.322109	−	0.946702i	$-0.604392\pi$
$541$	−1.28357e12	−0.644219	−0.322109	+	0.946702i	$0.604392\pi$
$542$	3.77068e12	1.87682
$543$	−4.72383e11	−0.233182
$544$	0	0
$545$	−8.60909e11	−0.417997
$546$	3.55788e12	1.71326
$547$	2.44820e12	1.16924	0.584619	−	0.811308i	$-0.301244\pi$
$547$	2.44820e12	1.16924	0.584619	+	0.811308i	$0.301244\pi$
$548$	−2.57054e12	−1.21762
$549$	5.08519e11	0.238908
$550$	2.28185e12	1.06330
$551$	3.19992e12	1.47896
$552$	4.58957e12	2.10400
$553$	−2.74439e11	−0.124791
$554$	7.94855e11	0.358504
$555$	1.05671e12	0.472757
$556$	4.34371e12	1.92763
$557$	−2.37115e11	−0.104378	−0.0521892	−	0.998637i	$-0.516620\pi$
$557$	−2.37115e11	−0.104378	−0.0521892	+	0.998637i	$0.516620\pi$
$558$	−5.55546e10	−0.0242586
$559$	−1.36756e11	−0.0592372
$560$	−3.88711e12	−1.67025
$561$	0	0
$562$	1.70840e12	0.722396
$563$	−1.25277e12	−0.525512	−0.262756	−	0.964862i	$-0.584631\pi$
$563$	−1.25277e12	−0.525512	−0.262756	+	0.964862i	$0.584631\pi$
$564$	1.20864e12	0.502967
$565$	2.07159e12	0.855234
$566$	6.82756e12	2.79635
$567$	1.31012e11	0.0532336
$568$	−5.85485e12	−2.36020
$569$	9.49810e11	0.379867	0.189933	−	0.981797i	$-0.439173\pi$
$569$	9.49810e11	0.379867	0.189933	+	0.981797i	$0.439173\pi$
$570$	−1.33641e12	−0.530277
$571$	4.03177e12	1.58721	0.793604	−	0.608435i	$-0.208202\pi$
$571$	4.03177e12	1.58721	0.793604	+	0.608435i	$0.208202\pi$
$572$	−8.87931e12	−3.46815
$573$	−3.78500e11	−0.146680
$574$	−6.55002e12	−2.51848
$575$	2.03984e12	0.778198
$576$	−6.45050e12	−2.44170
$577$	−2.32183e12	−0.872045	−0.436023	−	0.899936i	$-0.643613\pi$
$577$	−2.32183e12	−0.872045	−0.436023	+	0.899936i	$0.643613\pi$
$578$	0	0
$579$	−2.29842e12	−0.849917
$580$	6.22921e12	2.28564
$581$	−1.23752e12	−0.450567
$582$	5.19165e12	1.87565
$583$	1.20933e12	0.433546
$584$	−6.05578e11	−0.215433
$585$	−1.58809e12	−0.560625
$586$	−8.72009e12	−3.05479
$587$	−3.45750e12	−1.20196	−0.600982	−	0.799263i	$-0.705224\pi$
$587$	−3.45750e12	−1.20196	−0.600982	+	0.799263i	$0.705224\pi$
$588$	−1.12881e12	−0.389423
$589$	5.13145e10	0.0175679
$590$	4.13044e12	1.40334
$591$	1.25639e12	0.423624
$592$	−1.74634e13	−5.84361
$593$	4.64446e12	1.54237	0.771186	−	0.636610i	$-0.219664\pi$
$593$	4.64446e12	1.54237	0.771186	+	0.636610i	$0.219664\pi$
$594$	4.27274e12	1.40821
$595$	0	0
$596$	3.55223e12	1.15317
$597$	−4.84510e11	−0.156105
$598$	−1.08375e13	−3.46557
$599$	−2.82740e10	−0.00897358	−0.00448679	−	0.999990i	$-0.501428\pi$
$599$	−2.82740e10	−0.00897358	−0.00448679	+	0.999990i	$0.501428\pi$
$600$	4.70084e12	1.48080
$601$	−4.13809e12	−1.29379	−0.646896	−	0.762578i	$-0.723933\pi$
$601$	−4.13809e12	−1.29379	−0.646896	+	0.762578i	$0.723933\pi$
$602$	−1.88851e11	−0.0586051
$603$	−3.47404e12	−1.07006
$604$	−1.55025e12	−0.473954
$605$	7.52058e11	0.228219
$606$	2.44867e12	0.737570
$607$	−4.30595e12	−1.28742	−0.643709	−	0.765270i	$-0.722605\pi$
$607$	−4.30595e12	−1.28742	−0.643709	+	0.765270i	$0.722605\pi$
$608$	1.18680e13	3.52216
$609$	−2.89017e12	−0.851423
$610$	−1.24843e12	−0.365072
$611$	−1.81131e12	−0.525783
$612$	0	0
$613$	6.41377e12	1.83460	0.917300	−	0.398197i	$-0.130364\pi$
$613$	6.41377e12	1.83460	0.917300	+	0.398197i	$0.130364\pi$
$614$	6.38125e12	1.81196
$615$	−1.60917e12	−0.453591
$616$	−7.78199e12	−2.17760
$617$	−5.16320e12	−1.43429	−0.717143	−	0.696926i	$-0.754551\pi$
$617$	−5.16320e12	−1.43429	−0.717143	+	0.696926i	$0.754551\pi$
$618$	−3.10643e12	−0.856670
$619$	−6.94645e12	−1.90176	−0.950878	−	0.309566i	$-0.899816\pi$
$619$	−6.94645e12	−1.90176	−0.950878	+	0.309566i	$0.899816\pi$
$620$	9.98927e10	0.0271501
$621$	3.81957e12	1.03063
$622$	2.23481e12	0.598665
$623$	1.95772e11	0.0520660
$624$	−1.44452e13	−3.81411
$625$	1.09771e12	0.287759
$626$	−1.13911e13	−2.96470
$627$	−1.54746e12	−0.399866
$628$	−2.39561e12	−0.614607
$629$	0	0
$630$	−2.19304e12	−0.554644
$631$	2.70305e12	0.678770	0.339385	−	0.940648i	$-0.389781\pi$
$631$	2.70305e12	0.678770	0.339385	+	0.940648i	$0.389781\pi$
$632$	1.92648e12	0.480327
$633$	−2.53895e12	−0.628545
$634$	−2.80772e10	−0.00690165
$635$	1.24891e11	0.0304825
$636$	3.92549e12	0.951342
$637$	1.69167e12	0.407088
$638$	9.84812e12	2.35321
$639$	−1.91051e12	−0.453311
$640$	7.39558e12	1.74246
$641$	2.11271e10	0.00494286	0.00247143	−	0.999997i	$-0.499213\pi$
$641$	2.11271e10	0.00494286	0.00247143	+	0.999997i	$0.499213\pi$
$642$	−4.40212e12	−1.02271
$643$	6.38463e12	1.47294	0.736472	−	0.676468i	$-0.236490\pi$
$643$	6.38463e12	1.47294	0.736472	+	0.676468i	$0.236490\pi$
$644$	−1.09613e13	−2.51116
$645$	−4.63960e10	−0.0105551
$646$	0	0
$647$	−6.90284e12	−1.54867	−0.774334	−	0.632777i	$-0.781915\pi$
$647$	−6.90284e12	−1.54867	−0.774334	+	0.632777i	$0.781915\pi$
$648$	−9.19662e11	−0.204899
$649$	4.78271e12	1.05821
$650$	−1.11003e13	−2.43906
$651$	−4.63473e10	−0.0101137
$652$	−6.65172e12	−1.44152
$653$	−6.56358e11	−0.141264	−0.0706319	−	0.997502i	$-0.522502\pi$
$653$	−6.56358e11	−0.141264	−0.0706319	+	0.997502i	$0.522502\pi$
$654$	−4.41802e12	−0.944338
$655$	−3.05990e12	−0.649563
$656$	2.65935e13	5.60670
$657$	−1.97608e11	−0.0413771
$658$	−2.50129e12	−0.520173
$659$	−4.39856e12	−0.908503	−0.454251	−	0.890874i	$-0.650093\pi$
$659$	−4.39856e12	−0.908503	−0.454251	+	0.890874i	$0.650093\pi$
$660$	−3.01240e12	−0.617966
$661$	−8.91098e12	−1.81559	−0.907797	−	0.419410i	$-0.862237\pi$
$661$	−8.91098e12	−1.81559	−0.907797	+	0.419410i	$0.862237\pi$
$662$	1.10423e13	2.23460
$663$	0	0
$664$	8.68701e12	1.73426
$665$	2.02566e12	0.401670
$666$	−9.85256e12	−1.94051
$667$	8.80363e12	1.72225
$668$	3.07608e11	0.0597728
$669$	3.85615e12	0.744281
$670$	8.52886e12	1.63514
$671$	−1.44558e12	−0.275290
$672$	−1.07191e13	−2.02768
$673$	1.29085e11	0.0242554	0.0121277	−	0.999926i	$-0.496140\pi$
$673$	1.29085e11	0.0242554	0.0121277	+	0.999926i	$0.496140\pi$
$674$	−1.18742e13	−2.21632
$675$	3.91217e12	0.725356
$676$	2.83328e13	5.21831
$677$	2.61666e12	0.478738	0.239369	−	0.970929i	$-0.423059\pi$
$677$	2.61666e12	0.478738	0.239369	+	0.970929i	$0.423059\pi$
$678$	1.06310e13	1.93214
$679$	−7.86924e12	−1.42075
$680$	0	0
$681$	−1.11055e11	−0.0197868
$682$	1.57926e11	0.0279527
$683$	5.88812e12	1.03534	0.517671	−	0.855580i	$-0.326799\pi$
$683$	5.88812e12	1.03534	0.517671	+	0.855580i	$0.326799\pi$
$684$	9.12621e12	1.59418
$685$	1.30694e12	0.226802
$686$	1.21193e13	2.08939
$687$	1.32435e12	0.226829
$688$	7.66748e11	0.130468
$689$	−5.88288e12	−0.994497
$690$	−3.67674e12	−0.617507
$691$	−1.46603e12	−0.244620	−0.122310	−	0.992492i	$-0.539030\pi$
$691$	−1.46603e12	−0.244620	−0.122310	+	0.992492i	$0.539030\pi$
$692$	2.29004e13	3.79635
$693$	−2.53936e12	−0.418240
$694$	5.30500e12	0.868097
$695$	−2.20846e12	−0.359053
$696$	2.02881e13	3.27718
$697$	0	0
$698$	−2.16302e13	−3.44913
$699$	−3.79153e10	−0.00600713
$700$	−1.12270e13	−1.76735
$701$	6.32038e12	0.988580	0.494290	−	0.869297i	$-0.335428\pi$
$701$	6.32038e12	0.988580	0.494290	+	0.869297i	$0.335428\pi$
$702$	−2.07851e13	−3.23024
$703$	9.10058e12	1.40530
$704$	1.83370e13	2.81352
$705$	−6.14504e11	−0.0936858
$706$	−1.13547e13	−1.72011
$707$	−3.71156e12	−0.558688
$708$	1.55247e13	2.32207
$709$	−3.78053e12	−0.561882	−0.280941	−	0.959725i	$-0.590646\pi$
$709$	−3.78053e12	−0.561882	−0.280941	+	0.959725i	$0.590646\pi$
$710$	4.69036e12	0.692697
$711$	6.28634e11	0.0922539
$712$	−1.37426e12	−0.200405
$713$	1.41177e11	0.0204578
$714$	0	0
$715$	4.51449e12	0.645998
$716$	1.16609e13	1.65815
$717$	5.03331e12	0.711242
$718$	−2.47016e13	−3.46869
$719$	9.62888e12	1.34368	0.671840	−	0.740696i	$-0.265504\pi$
$719$	9.62888e12	1.34368	0.671840	+	0.740696i	$0.265504\pi$
$720$	8.90388e12	1.23476
$721$	4.70857e12	0.648903
$722$	2.60584e12	0.356886
$723$	−1.63573e12	−0.222633
$724$	−7.91955e12	−1.07122
$725$	9.01706e12	1.21212
$726$	3.85941e12	0.515593
$727$	9.26284e12	1.22981	0.614907	−	0.788600i	$-0.289194\pi$
$727$	9.26284e12	1.22981	0.614907	+	0.788600i	$0.289194\pi$
$728$	3.78562e13	4.99512
$729$	4.15311e12	0.544627
$730$	4.85133e11	0.0632277
$731$	0	0
$732$	−4.69236e12	−0.604075
$733$	−3.26111e12	−0.417251	−0.208625	−	0.977996i	$-0.566899\pi$
$733$	−3.26111e12	−0.417251	−0.208625	+	0.977996i	$0.566899\pi$
$734$	−2.19539e12	−0.279177
$735$	5.73916e11	0.0725363
$736$	3.26512e13	4.10155
$737$	9.87574e12	1.23301
$738$	1.50036e13	1.86184
$739$	1.43463e13	1.76946	0.884731	−	0.466101i	$-0.154342\pi$
$739$	1.43463e13	1.76946	0.884731	+	0.466101i	$0.154342\pi$
$740$	1.77159e13	2.17180
$741$	7.52773e12	0.917239
$742$	−8.12386e12	−0.983886
$743$	−5.86395e12	−0.705896	−0.352948	−	0.935643i	$-0.614821\pi$
$743$	−5.86395e12	−0.705896	−0.352948	+	0.935643i	$0.614821\pi$
$744$	3.25344e11	0.0389282
$745$	−1.80605e12	−0.214796
$746$	−1.05946e13	−1.25244
$747$	2.83468e12	0.333090
$748$	0	0
$749$	6.67250e12	0.774676
$750$	−8.85445e12	−1.02185
$751$	−7.70810e12	−0.884234	−0.442117	−	0.896957i	$-0.645772\pi$
$751$	−7.70810e12	−0.884234	−0.442117	+	0.896957i	$0.645772\pi$
$752$	1.01554e13	1.15802
$753$	−8.92332e12	−1.01146
$754$	−4.79070e13	−5.39794
$755$	7.88192e11	0.0882817
$756$	−2.10224e13	−2.34064
$757$	9.90551e12	1.09634	0.548170	−	0.836367i	$-0.315325\pi$
$757$	9.90551e12	1.09634	0.548170	+	0.836367i	$0.315325\pi$
$758$	−2.78512e13	−3.06430
$759$	−4.25737e12	−0.465643
$760$	−1.42195e13	−1.54605
$761$	2.67093e12	0.288690	0.144345	−	0.989527i	$-0.453893\pi$
$761$	2.67093e12	0.288690	0.144345	+	0.989527i	$0.453893\pi$
$762$	6.40917e11	0.0688659
$763$	6.69660e12	0.715309
$764$	−6.34560e12	−0.673834
$765$	0	0
$766$	−1.87959e12	−0.197257
$767$	−2.32659e13	−2.42740
$768$	1.62067e13	1.68101
$769$	2.81525e12	0.290301	0.145151	−	0.989410i	$-0.453633\pi$
$769$	2.81525e12	0.290301	0.145151	+	0.989410i	$0.453633\pi$
$770$	6.23420e12	0.639106
$771$	−1.13434e12	−0.115611
$772$	−3.85333e13	−3.90444
$773$	1.90214e12	0.191617	0.0958085	−	0.995400i	$-0.469456\pi$
$773$	1.90214e12	0.191617	0.0958085	+	0.995400i	$0.469456\pi$
$774$	4.32586e11	0.0433250
$775$	1.44599e11	0.0143982
$776$	5.52397e13	5.46856
$777$	−8.21966e12	−0.809020
$778$	−2.61160e13	−2.55563
$779$	−1.38585e13	−1.34833
$780$	1.46541e13	1.41753
$781$	5.43106e12	0.522342
$782$	0	0
$783$	1.68843e13	1.60530
$784$	−9.48464e12	−0.896600
$785$	1.21799e12	0.114480
$786$	−1.57028e13	−1.46749
$787$	−1.30989e13	−1.21716	−0.608580	−	0.793493i	$-0.708260\pi$
$787$	−1.30989e13	−1.21716	−0.608580	+	0.793493i	$0.708260\pi$
$788$	2.10635e13	1.94609
$789$	−3.73727e12	−0.343327
$790$	−1.54331e12	−0.140972
$791$	−1.61139e13	−1.46354
$792$	1.78256e13	1.60983
$793$	7.03214e12	0.631478
$794$	2.14984e13	1.91961
$795$	−1.99583e12	−0.177203
$796$	−8.12286e12	−0.717134
$797$	−9.57855e12	−0.840886	−0.420443	−	0.907319i	$-0.638125\pi$
$797$	−9.57855e12	−0.840886	−0.420443	+	0.907319i	$0.638125\pi$
$798$	1.03953e13	0.907452
$799$	0	0
$800$	3.34427e13	2.88667
$801$	−4.48439e11	−0.0384908
$802$	−1.02753e13	−0.877017
$803$	5.61745e11	0.0476781
$804$	3.20567e13	2.70562
$805$	5.57301e12	0.467744
$806$	−7.68246e11	−0.0641198
$807$	8.13935e12	0.675552
$808$	2.60541e13	2.15043
$809$	−2.70995e12	−0.222430	−0.111215	−	0.993796i	$-0.535474\pi$
$809$	−2.70995e12	−0.222430	−0.111215	+	0.993796i	$0.535474\pi$
$810$	7.36747e11	0.0601361
$811$	8.05231e11	0.0653622	0.0326811	−	0.999466i	$-0.489595\pi$
$811$	8.05231e11	0.0653622	0.0326811	+	0.999466i	$0.489595\pi$
$812$	−4.84540e13	−3.91136
$813$	−7.20571e12	−0.578455
$814$	2.80081e13	2.23601
$815$	3.38192e12	0.268506
$816$	0	0
$817$	−3.99570e11	−0.0313757
$818$	−5.74785e12	−0.448865
$819$	1.23530e13	0.959386
$820$	−2.69780e13	−2.08376
$821$	−3.07077e12	−0.235886	−0.117943	−	0.993020i	$-0.537630\pi$
$821$	−3.07077e12	−0.235886	−0.117943	+	0.993020i	$0.537630\pi$
$822$	6.70694e12	0.512390
$823$	−1.09157e13	−0.829375	−0.414688	−	0.909964i	$-0.636109\pi$
$823$	−1.09157e13	−0.829375	−0.414688	+	0.909964i	$0.636109\pi$
$824$	−3.30527e13	−2.49767
$825$	−4.36058e12	−0.327719
$826$	−3.21287e13	−2.40150
$827$	−4.38102e12	−0.325687	−0.162844	−	0.986652i	$-0.552067\pi$
$827$	−4.38102e12	−0.325687	−0.162844	+	0.986652i	$0.552067\pi$
$828$	2.51081e13	1.85642
$829$	−9.43248e11	−0.0693634	−0.0346817	−	0.999398i	$-0.511042\pi$
$829$	−9.43248e11	−0.0693634	−0.0346817	+	0.999398i	$0.511042\pi$
$830$	−6.95922e12	−0.508990
$831$	−1.51896e12	−0.110494
$832$	−8.92018e13	−6.45384
$833$	0	0
$834$	−1.13334e13	−0.811171
$835$	−1.56396e11	−0.0111336
$836$	−2.59433e13	−1.83695
$837$	2.70760e11	0.0190687
$838$	2.63023e13	1.84245
$839$	−1.06739e13	−0.743695	−0.371847	−	0.928294i	$-0.621276\pi$
$839$	−1.06739e13	−0.743695	−0.371847	+	0.928294i	$0.621276\pi$
$840$	1.28431e13	0.890047
$841$	2.44091e13	1.68256
$842$	−5.08676e12	−0.348768
$843$	−3.26472e12	−0.222650
$844$	−4.25657e13	−2.88748
$845$	−1.44052e13	−0.971994
$846$	5.72950e12	0.384548
$847$	−5.84990e12	−0.390547
$848$	3.29834e13	2.19035
$849$	−1.30474e13	−0.861863
$850$	0	0
$851$	2.50376e13	1.63647
$852$	1.76293e13	1.14619
$853$	1.66067e11	0.0107402	0.00537012	−	0.999986i	$-0.498291\pi$
$853$	1.66067e11	0.0107402	0.00537012	+	0.999986i	$0.498291\pi$
$854$	9.71091e12	0.624740
$855$	−4.64002e12	−0.296942
$856$	−4.68389e13	−2.98178
$857$	1.03151e13	0.653223	0.326611	−	0.945159i	$-0.394093\pi$
$857$	1.03151e13	0.653223	0.326611	+	0.945159i	$0.394093\pi$
$858$	2.31675e13	1.45944
$859$	1.10331e12	0.0691398	0.0345699	−	0.999402i	$-0.488994\pi$
$859$	1.10331e12	0.0691398	0.0345699	+	0.999402i	$0.488994\pi$
$860$	−7.77833e11	−0.0484890
$861$	1.25170e13	0.776221
$862$	4.04163e13	2.49329
$863$	1.58469e13	0.972514	0.486257	−	0.873816i	$-0.338362\pi$
$863$	1.58469e13	0.972514	0.486257	+	0.873816i	$0.338362\pi$
$864$	6.26211e13	3.82304
$865$	−1.16432e13	−0.707131
$866$	1.59403e13	0.963086
$867$	0	0
$868$	−7.77017e11	−0.0464614
$869$	−1.78703e12	−0.106302
$870$	−1.62529e13	−0.961823
$871$	−4.80414e13	−2.82836
$872$	−4.70081e13	−2.75327
$873$	1.80254e13	1.05032
$874$	−3.16647e13	−1.83558
$875$	1.34211e13	0.774020
$876$	1.82343e12	0.104621
$877$	−3.07621e13	−1.75597	−0.877987	−	0.478684i	$-0.841114\pi$
$877$	−3.07621e13	−1.75597	−0.877987	+	0.478684i	$0.841114\pi$
$878$	−2.96995e13	−1.68665
$879$	1.66640e13	0.941517
$880$	−2.53112e13	−1.42279
$881$	−7.14002e10	−0.00399308	−0.00199654	−	0.999998i	$-0.500636\pi$
$881$	−7.14002e10	−0.00399308	−0.00199654	+	0.999998i	$0.500636\pi$
$882$	−5.35108e12	−0.297737
$883$	−2.91216e13	−1.61210	−0.806050	−	0.591847i	$-0.798399\pi$
$883$	−2.91216e13	−1.61210	−0.806050	+	0.591847i	$0.798399\pi$
$884$	0	0
$885$	−7.89320e12	−0.432522
$886$	2.27860e13	1.24227
$887$	5.81157e12	0.315237	0.157618	−	0.987500i	$-0.449618\pi$
$887$	5.81157e12	0.315237	0.157618	+	0.987500i	$0.449618\pi$
$888$	5.76995e13	3.11397
$889$	−9.71469e11	−0.0521640
$890$	1.10093e12	0.0588171
$891$	8.53094e11	0.0453468
$892$	6.46488e13	3.41916
$893$	−5.29221e12	−0.278487
$894$	−9.26829e12	−0.485267
$895$	−5.92874e12	−0.308858
$896$	−5.75267e13	−2.98183
$897$	2.07103e13	1.06812
$898$	−3.91555e13	−2.00932
$899$	6.24068e11	0.0318650
$900$	2.57168e13	1.30655
$901$	0	0
$902$	−4.26510e13	−2.14536
$903$	3.60892e11	0.0180627
$904$	1.13115e14	5.63327
$905$	4.02652e12	0.199531
$906$	4.04484e12	0.199446
$907$	2.77171e13	1.35993	0.679963	−	0.733246i	$-0.261996\pi$
$907$	2.77171e13	1.35993	0.679963	+	0.733246i	$0.261996\pi$
$908$	−1.86185e12	−0.0908987
$909$	8.50178e12	0.413021
$910$	−3.03268e13	−1.46602
$911$	2.12590e13	1.02261	0.511305	−	0.859399i	$-0.329162\pi$
$911$	2.12590e13	1.02261	0.511305	+	0.859399i	$0.329162\pi$
$912$	−4.22055e13	−2.02019
$913$	−8.05822e12	−0.383814
$914$	−8.55216e12	−0.405339
$915$	2.38572e12	0.112519
$916$	2.22029e13	1.04203
$917$	2.38015e13	1.11158
$918$	0	0
$919$	3.16408e13	1.46328	0.731641	−	0.681690i	$-0.238755\pi$
$919$	3.16408e13	1.46328	0.731641	+	0.681690i	$0.238755\pi$
$920$	−3.91208e13	−1.80037
$921$	−1.21945e13	−0.558464
$922$	3.03849e13	1.38474
$923$	−2.64198e13	−1.19818
$924$	2.34320e13	1.05751
$925$	2.56446e13	1.15175
$926$	−6.31251e13	−2.82132
$927$	−1.07855e13	−0.479714
$928$	1.44334e14	6.38855
$929$	2.81954e13	1.24196	0.620980	−	0.783827i	$-0.286735\pi$
$929$	2.81954e13	1.24196	0.620980	+	0.783827i	$0.286735\pi$
$930$	−2.60635e11	−0.0114251
$931$	4.94267e12	0.215619
$932$	−6.35654e11	−0.0275962
$933$	−4.27069e12	−0.184515
$934$	7.58203e13	3.26005
$935$	0	0
$936$	−8.67141e13	−3.69274
$937$	−1.91653e13	−0.812244	−0.406122	−	0.913819i	$-0.633119\pi$
$937$	−1.91653e13	−0.812244	−0.406122	+	0.913819i	$0.633119\pi$
$938$	−6.63419e13	−2.79818
$939$	2.17682e13	0.913750
$940$	−1.03022e13	−0.430384
$941$	5.92110e11	0.0246178	0.0123089	−	0.999924i	$-0.496082\pi$
$941$	5.92110e11	0.0246178	0.0123089	+	0.999924i	$0.496082\pi$
$942$	6.25050e12	0.258634
$943$	−3.81275e13	−1.57013
$944$	1.30444e14	5.34628
$945$	1.06884e13	0.435982
$946$	−1.22972e12	−0.0499226
$947$	−2.32692e13	−0.940171	−0.470085	−	0.882621i	$-0.655777\pi$
$947$	−2.32692e13	−0.940171	−0.470085	+	0.882621i	$0.655777\pi$
$948$	−5.80072e12	−0.233262
$949$	−2.73266e12	−0.109367
$950$	−3.24323e13	−1.29188
$951$	5.36552e10	0.00212716
$952$	0	0
$953$	3.58962e13	1.40971	0.704856	−	0.709351i	$-0.251012\pi$
$953$	3.58962e13	1.40971	0.704856	+	0.709351i	$0.251012\pi$
$954$	1.86087e13	0.727357
$955$	3.22628e12	0.125512
$956$	8.43840e13	3.26738
$957$	−1.88196e13	−0.725282
$958$	−2.01693e13	−0.773654
$959$	−1.01660e13	−0.388121
$960$	−3.02626e13	−1.14997
$961$	−2.64296e13	−0.999621
$962$	−1.36248e14	−5.12911
$963$	−1.52841e13	−0.572694
$964$	−2.74232e13	−1.02275
$965$	1.95914e13	0.727265
$966$	2.85996e13	1.05673
$967$	−2.74118e13	−1.00813	−0.504067	−	0.863664i	$-0.668164\pi$
$967$	−2.74118e13	−1.00813	−0.504067	+	0.863664i	$0.668164\pi$
$968$	4.10645e13	1.50324
$969$	0	0
$970$	−4.42528e13	−1.60497
$971$	−4.52819e13	−1.63470	−0.817350	−	0.576141i	$-0.804558\pi$
$971$	−4.52819e13	−1.63470	−0.817350	+	0.576141i	$0.804558\pi$
$972$	7.74276e13	2.78226
$973$	1.71786e13	0.614439
$974$	−5.73596e13	−2.04217
$975$	2.12124e13	0.751743
$976$	−3.94269e13	−1.39081
$977$	9.97230e12	0.350163	0.175081	−	0.984554i	$-0.443981\pi$
$977$	9.97230e12	0.350163	0.175081	+	0.984554i	$0.443981\pi$
$978$	1.73553e13	0.606608
$979$	1.27479e12	0.0443522
$980$	9.62177e12	0.333225
$981$	−1.53394e13	−0.528806
$982$	1.06133e13	0.364208
$983$	−1.25146e13	−0.427491	−0.213745	−	0.976889i	$-0.568566\pi$
$983$	−1.25146e13	−0.427491	−0.213745	+	0.976889i	$0.568566\pi$
$984$	−8.78654e13	−2.98772
$985$	−1.07093e13	−0.362491
$986$	0	0
$987$	4.77993e12	0.160322
$988$	1.26203e14	4.21371
$989$	−1.09930e12	−0.0365369
$990$	−1.42802e13	−0.472471
$991$	−2.64145e12	−0.0869982	−0.0434991	−	0.999053i	$-0.513851\pi$
$991$	−2.64145e12	−0.0869982	−0.0434991	+	0.999053i	$0.513851\pi$
$992$	2.31456e12	0.0758868
$993$	−2.11017e13	−0.688726
$994$	−3.64840e13	−1.18540
$995$	4.12989e12	0.133578
$996$	−2.61570e13	−0.842212
$997$	−1.22459e13	−0.392520	−0.196260	−	0.980552i	$-0.562880\pi$
$997$	−1.22459e13	−0.392520	−0.196260	+	0.980552i	$0.562880\pi$
$998$	−8.13174e13	−2.59475
$999$	4.80192e13	1.52535

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.h.1.2	yes	36
17.16	even	2		289.10.a.g.1.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.2	✓	36	17.16	even	2
289.10.a.h.1.2	yes	36	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-43.7427 q^{2} +83.5916 q^{3} +1401.42 q^{4} -712.522 q^{5} -3656.52 q^{6} +5542.36 q^{7} -38905.7 q^{8} -12695.4 q^{9} +O(q^{10})\)	\(q-43.7427 q^{2} +83.5916 q^{3} +1401.42 q^{4} -712.522 q^{5} -3656.52 q^{6} +5542.36 q^{7} -38905.7 q^{8} -12695.4 q^{9} +31167.6 q^{10} +36089.6 q^{11} +117147. q^{12} -175561. q^{13} -242438. q^{14} -59560.8 q^{15} +984313. q^{16} +555333. q^{18} -512948. q^{19} -998544. q^{20} +463295. q^{21} -1.57866e6 q^{22} -1.41122e6 q^{23} -3.25219e6 q^{24} -1.44544e6 q^{25} +7.67951e6 q^{26} -2.70657e6 q^{27} +7.76719e6 q^{28} -6.23829e6 q^{29} +2.60535e6 q^{30} -100038. q^{31} -2.31367e7 q^{32} +3.01679e6 q^{33} -3.94906e6 q^{35} -1.77917e7 q^{36} -1.77417e7 q^{37} +2.24377e7 q^{38} -1.46754e7 q^{39} +2.77212e7 q^{40} +2.70173e7 q^{41} -2.02658e7 q^{42} +778967. q^{43} +5.05768e7 q^{44} +9.04578e6 q^{45} +6.17308e7 q^{46} +1.03172e7 q^{47} +8.22803e7 q^{48} -9.63580e6 q^{49} +6.32273e7 q^{50} -2.46035e8 q^{52} +3.35090e7 q^{53} +1.18392e8 q^{54} -2.57146e7 q^{55} -2.15630e8 q^{56} -4.28782e7 q^{57} +2.72880e8 q^{58} +1.32523e8 q^{59} -8.34699e7 q^{60} -4.00552e7 q^{61} +4.37595e6 q^{62} -7.03628e7 q^{63} +5.08095e8 q^{64} +1.25091e8 q^{65} -1.31962e8 q^{66} +2.73645e8 q^{67} -1.17967e8 q^{69} +1.72742e8 q^{70} +1.50488e8 q^{71} +4.93925e8 q^{72} +1.55653e7 q^{73} +7.76071e8 q^{74} -1.20826e8 q^{75} -7.18857e8 q^{76} +2.00022e8 q^{77} +6.41943e8 q^{78} -4.95165e7 q^{79} -7.01344e8 q^{80} +2.36382e7 q^{81} -1.18181e9 q^{82} -2.23284e8 q^{83} +6.49272e8 q^{84} -3.40741e7 q^{86} -5.21469e8 q^{87} -1.40409e9 q^{88} +3.53228e7 q^{89} -3.95687e8 q^{90} -9.73023e8 q^{91} -1.97772e9 q^{92} -8.36237e6 q^{93} -4.51304e8 q^{94} +3.65487e8 q^{95} -1.93404e9 q^{96} -1.41983e9 q^{97} +4.21496e8 q^{98} -4.58174e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9} + 60000 q^{10} + 76902 q^{11} + 373248 q^{12} + 54216 q^{13} + 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} + 6439479 q^{20} - 138102 q^{21} + 267324 q^{22} + 4041462 q^{23} + 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} + 13281612 q^{27} + 18614784 q^{28} + 4005936 q^{29} + 22471686 q^{30} + 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} + 22076682 q^{37} - 27401376 q^{38} + 62736162 q^{39} - 12231630 q^{40} + 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} - 49578936 q^{44} + 129308238 q^{45} + 140524827 q^{46} - 118557912 q^{47} + 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} + 209848575 q^{54} - 365439924 q^{55} + 203095059 q^{56} - 4614108 q^{57} - 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} + 175597116 q^{61} + 720602571 q^{62} + 587415936 q^{63} + 853082511 q^{64} + 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} + 1308709542 q^{71} - 275337849 q^{72} + 494841342 q^{73} + 1545361890 q^{74} + 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} + 2270624538 q^{78} + 1980107868 q^{79} + 2897000199 q^{80} + 1598298840 q^{81} + 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} - 2705904618 q^{88} + 148394658 q^{89} + 117916215 q^{90} + 636340896 q^{91} - 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} + 4878626298 q^{95} - 8390096634 q^{96} - 891786822 q^{97} + 4285627647 q^{98} - 1476187998 q^{99}+O(q^{100}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9 + 60000 * q^10 + 76902 * q^11 + 373248 * q^12 + 54216 * q^13 + 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 + 6439479 * q^20 - 138102 * q^21 + 267324 * q^22 + 4041462 * q^23 + 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 + 13281612 * q^27 + 18614784 * q^28 + 4005936 * q^29 + 22471686 * q^30 + 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 + 22076682 * q^37 - 27401376 * q^38 + 62736162 * q^39 - 12231630 * q^40 + 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 - 49578936 * q^44 + 129308238 * q^45 + 140524827 * q^46 - 118557912 * q^47 + 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 + 209848575 * q^54 - 365439924 * q^55 + 203095059 * q^56 - 4614108 * q^57 - 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 + 175597116 * q^61 + 720602571 * q^62 + 587415936 * q^63 + 853082511 * q^64 + 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 + 1308709542 * q^71 - 275337849 * q^72 + 494841342 * q^73 + 1545361890 * q^74 + 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 + 2270624538 * q^78 + 1980107868 * q^79 + 2897000199 * q^80 + 1598298840 * q^81 + 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 - 2705904618 * q^88 + 148394658 * q^89 + 117916215 * q^90 + 636340896 * q^91 - 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 + 4878626298 * q^95 - 8390096634 * q^96 - 891786822 * q^97 + 4285627647 * q^98 - 1476187998 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more