LMFDB - Embedded newform 289.10.a.i.1.26

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:	$52$
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.26
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)

$f(q)$	$=$	$q-3.16073 q^{2} +48.7228 q^{3} -502.010 q^{4} +693.070 q^{5} -154.000 q^{6} -1403.76 q^{7} +3205.01 q^{8} -17309.1 q^{9} +O(q^{10})$	\(q-3.16073 q^{2} +48.7228 q^{3} -502.010 q^{4} +693.070 q^{5} -154.000 q^{6} -1403.76 q^{7} +3205.01 q^{8} -17309.1 q^{9} -2190.61 q^{10} -70859.5 q^{11} -24459.3 q^{12} -180297. q^{13} +4436.90 q^{14} +33768.3 q^{15} +246899. q^{16} +54709.3 q^{18} -848219. q^{19} -347928. q^{20} -68395.0 q^{21} +223968. q^{22} -1.57720e6 q^{23} +156157. q^{24} -1.47278e6 q^{25} +569869. q^{26} -1.80236e6 q^{27} +704700. q^{28} +3.09944e6 q^{29} -106733. q^{30} -3.35981e6 q^{31} -2.42135e6 q^{32} -3.45248e6 q^{33} -972902. q^{35} +8.68933e6 q^{36} +1.90025e7 q^{37} +2.68099e6 q^{38} -8.78456e6 q^{39} +2.22130e6 q^{40} +8.64702e6 q^{41} +216178. q^{42} -1.02839e7 q^{43} +3.55722e7 q^{44} -1.19964e7 q^{45} +4.98510e6 q^{46} +5.71205e6 q^{47} +1.20296e7 q^{48} -3.83831e7 q^{49} +4.65506e6 q^{50} +9.05107e7 q^{52} -7.52705e7 q^{53} +5.69677e6 q^{54} -4.91106e7 q^{55} -4.49906e6 q^{56} -4.13277e7 q^{57} -9.79650e6 q^{58} -1.41700e8 q^{59} -1.69520e7 q^{60} -105485. q^{61} +1.06195e7 q^{62} +2.42977e7 q^{63} -1.18759e8 q^{64} -1.24958e8 q^{65} +1.09123e7 q^{66} +1.57737e6 q^{67} -7.68456e7 q^{69} +3.07508e6 q^{70} +3.25699e8 q^{71} -5.54758e7 q^{72} -1.83933e7 q^{73} -6.00617e7 q^{74} -7.17580e7 q^{75} +4.25814e8 q^{76} +9.94695e7 q^{77} +2.77656e7 q^{78} +1.47125e8 q^{79} +1.71118e8 q^{80} +2.52879e8 q^{81} -2.73309e7 q^{82} -3.70887e8 q^{83} +3.43350e7 q^{84} +3.25045e7 q^{86} +1.51014e8 q^{87} -2.27106e8 q^{88} -3.54830e8 q^{89} +3.79174e7 q^{90} +2.53093e8 q^{91} +7.91769e8 q^{92} -1.63700e8 q^{93} -1.80542e7 q^{94} -5.87875e8 q^{95} -1.17975e8 q^{96} -1.53915e9 q^{97} +1.21319e8 q^{98} +1.22651e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) $ 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9	$ 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9} + 156200 q^{13} + 1207872 q^{15} + 3407880 q^{16} + 2193336 q^{18} + 1185568 q^{19} + 5198336 q^{21} + 13827692 q^{25} + 3618944 q^{26} - 9167544 q^{30} + 61884888 q^{32} + 1635208 q^{33} + 46992776 q^{35} + 156027320 q^{36} + 84813952 q^{38} - 4635776 q^{42} + 125448912 q^{43} + 164193176 q^{47} + 270850284 q^{49} - 226223888 q^{50} + 103553016 q^{52} + 426167208 q^{53} + 677761520 q^{55} + 375214512 q^{59} + 336918024 q^{60} + 190014416 q^{64} + 1377178928 q^{66} + 311910088 q^{67} + 533688136 q^{69} + 1477690280 q^{70} + 2757942680 q^{72} + 4047975520 q^{76} + 3440336432 q^{77} + 3266558756 q^{81} + 2072890608 q^{83} + 2630025952 q^{84} + 1538547296 q^{86} - 1010436256 q^{87} + 1873849184 q^{89} - 1998451624 q^{93} - 6880776704 q^{94} - 4667454128 q^{98}+O(q^{100}) $ 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9 + 156200 * q^13 + 1207872 * q^15 + 3407880 * q^16 + 2193336 * q^18 + 1185568 * q^19 + 5198336 * q^21 + 13827692 * q^25 + 3618944 * q^26 - 9167544 * q^30 + 61884888 * q^32 + 1635208 * q^33 + 46992776 * q^35 + 156027320 * q^36 + 84813952 * q^38 - 4635776 * q^42 + 125448912 * q^43 + 164193176 * q^47 + 270850284 * q^49 - 226223888 * q^50 + 103553016 * q^52 + 426167208 * q^53 + 677761520 * q^55 + 375214512 * q^59 + 336918024 * q^60 + 190014416 * q^64 + 1377178928 * q^66 + 311910088 * q^67 + 533688136 * q^69 + 1477690280 * q^70 + 2757942680 * q^72 + 4047975520 * q^76 + 3440336432 * q^77 + 3266558756 * q^81 + 2072890608 * q^83 + 2630025952 * q^84 + 1538547296 * q^86 - 1010436256 * q^87 + 1873849184 * q^89 - 1998451624 * q^93 - 6880776704 * q^94 - 4667454128 * q^98

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 $

$2$	−3.16073	−0.139686	−0.0698429	−	0.997558i	$-0.522250\pi$
$2$	−3.16073	−0.139686	−0.0698429	+	0.997558i	$0.522250\pi$
$3$	48.7228	0.347286	0.173643	−	0.984809i	$-0.444446\pi$
$3$	48.7228	0.347286	0.173643	+	0.984809i	$0.444446\pi$
$4$	−502.010	−0.980488
$5$	693.070	0.495920	0.247960	−	0.968770i	$-0.420240\pi$
$5$	693.070	0.495920	0.247960	+	0.968770i	$0.420240\pi$
$6$	−154.000	−0.0485109
$7$	−1403.76	−0.220979	−0.110489	−	0.993877i	$-0.535242\pi$
$7$	−1403.76	−0.220979	−0.110489	+	0.993877i	$0.535242\pi$
$8$	3205.01	0.276646
$9$	−17309.1	−0.879393
$10$	−2190.61	−0.0692731
$11$	−70859.5	−1.45925	−0.729627	−	0.683845i	$-0.760306\pi$
$11$	−70859.5	−1.45925	−0.729627	+	0.683845i	$0.760306\pi$
$12$	−24459.3	−0.340509
$13$	−180297.	−1.75082	−0.875412	−	0.483378i	$-0.839410\pi$
$13$	−180297.	−1.75082	−0.875412	+	0.483378i	$0.839410\pi$
$14$	4436.90	0.0308676
$15$	33768.3	0.172226
$16$	246899.	0.941844
$17$	0	0
$17$	0	0
$18$	54709.3	0.122839
$19$	−848219.	−1.49320	−0.746598	−	0.665275i	$-0.768314\pi$
$19$	−848219.	−1.49320	−0.746598	+	0.665275i	$0.768314\pi$
$20$	−347928.	−0.486244
$21$	−68395.0	−0.0767428
$22$	223968.	0.203837
$23$	−1.57720e6	−1.17520	−0.587599	−	0.809152i	$-0.699927\pi$
$23$	−1.57720e6	−1.17520	−0.587599	+	0.809152i	$0.699927\pi$
$24$	156157.	0.0960752
$25$	−1.47278e6	−0.754063
$26$	569869.	0.244565
$27$	−1.80236e6	−0.652686
$28$	704700.	0.216667
$29$	3.09944e6	0.813753	0.406876	−	0.913483i	$-0.366618\pi$
$29$	3.09944e6	0.813753	0.406876	+	0.913483i	$0.366618\pi$
$30$	−106733.	−0.0240575
$31$	−3.35981e6	−0.653412	−0.326706	−	0.945126i	$-0.605939\pi$
$31$	−3.35981e6	−0.653412	−0.326706	+	0.945126i	$0.605939\pi$
$32$	−2.42135e6	−0.408208
$33$	−3.45248e6	−0.506778
$34$	0	0
$35$	−972902.	−0.109588
$36$	8.68933e6	0.862234
$37$	1.90025e7	1.66687	0.833437	−	0.552614i	$-0.186370\pi$
$37$	1.90025e7	1.66687	0.833437	+	0.552614i	$0.186370\pi$
$38$	2.68099e6	0.208578
$39$	−8.78456e6	−0.608036
$40$	2.22130e6	0.137194
$41$	8.64702e6	0.477902	0.238951	−	0.971032i	$-0.423196\pi$
$41$	8.64702e6	0.477902	0.238951	+	0.971032i	$0.423196\pi$
$42$	216178.	0.0107199
$43$	−1.02839e7	−0.458720	−0.229360	−	0.973342i	$-0.573663\pi$
$43$	−1.02839e7	−0.458720	−0.229360	+	0.973342i	$0.573663\pi$
$44$	3.55722e7	1.43078
$45$	−1.19964e7	−0.436109
$46$	4.98510e6	0.164159
$47$	5.71205e6	0.170746	0.0853732	−	0.996349i	$-0.472792\pi$
$47$	5.71205e6	0.170746	0.0853732	+	0.996349i	$0.472792\pi$
$48$	1.20296e7	0.327089
$49$	−3.83831e7	−0.951168
$50$	4.65506e6	0.105332
$51$	0	0
$52$	9.05107e7	1.71666
$53$	−7.52705e7	−1.31034	−0.655169	−	0.755482i	$-0.727403\pi$
$53$	−7.52705e7	−1.31034	−0.655169	+	0.755482i	$0.727403\pi$
$54$	5.69677e6	0.0911710
$55$	−4.91106e7	−0.723674
$56$	−4.49906e6	−0.0611329
$57$	−4.13277e7	−0.518566
$58$	−9.79650e6	−0.113670
$59$	−1.41700e8	−1.52243	−0.761213	−	0.648502i	$-0.775396\pi$
$59$	−1.41700e8	−1.52243	−0.761213	+	0.648502i	$0.775396\pi$
$60$	−1.69520e7	−0.168866
$61$	−105485.	−0.000975457 0	−0.000487729	−	1.00000i	$-0.500155\pi$
$61$	−105485.	−0.000975457 0	−0.000487729		1.00000i	$0.500155\pi$
$62$	1.06195e7	0.0912724
$63$	2.42977e7	0.194327
$64$	−1.18759e8	−0.884823
$65$	−1.24958e8	−0.868269
$66$	1.09123e7	0.0707897
$67$	1.57737e6	0.00956308	0.00478154	−	0.999989i	$-0.498478\pi$
$67$	1.57737e6	0.00956308	0.00478154	+	0.999989i	$0.498478\pi$
$68$	0	0
$69$	−7.68456e7	−0.408130
$70$	3.07508e6	0.0153079
$71$	3.25699e8	1.52109	0.760543	−	0.649288i	$-0.224933\pi$
$71$	3.25699e8	1.52109	0.760543	+	0.649288i	$0.224933\pi$
$72$	−5.54758e7	−0.243281
$73$	−1.83933e7	−0.0758067	−0.0379033	−	0.999281i	$-0.512068\pi$
$73$	−1.83933e7	−0.0758067	−0.0379033	+	0.999281i	$0.512068\pi$
$74$	−6.00617e7	−0.232839
$75$	−7.17580e7	−0.261875
$76$	4.25814e8	1.46406
$77$	9.94695e7	0.322464
$78$	2.77656e7	0.0849340
$79$	1.47125e8	0.424977	0.212488	−	0.977164i	$-0.431843\pi$
$79$	1.47125e8	0.424977	0.212488	+	0.977164i	$0.431843\pi$
$80$	1.71118e8	0.467080
$81$	2.52879e8	0.652724
$82$	−2.73309e7	−0.0667562
$83$	−3.70887e8	−0.857809	−0.428905	−	0.903350i	$-0.641100\pi$
$83$	−3.70887e8	−0.857809	−0.428905	+	0.903350i	$0.641100\pi$
$84$	3.43350e7	0.0752454
$85$	0	0
$86$	3.25045e7	0.0640767
$87$	1.51014e8	0.282605
$88$	−2.27106e8	−0.403697
$89$	−3.54830e8	−0.599467	−0.299733	−	0.954023i	$-0.596898\pi$
$89$	−3.54830e8	−0.599467	−0.299733	+	0.954023i	$0.596898\pi$
$90$	3.79174e7	0.0609182
$91$	2.53093e8	0.386895
$92$	7.91769e8	1.15227
$93$	−1.63700e8	−0.226921
$94$	−1.80542e7	−0.0238508
$95$	−5.87875e8	−0.740507
$96$	−1.17975e8	−0.141765
$97$	−1.53915e9	−1.76525	−0.882627	−	0.470074i	$-0.844227\pi$
$97$	−1.53915e9	−1.76525	−0.882627	+	0.470074i	$0.844227\pi$
$98$	1.21319e8	0.132865
$99$	1.22651e9	1.28326
$100$	7.39350e8	0.739350
$101$	−469843.	−0.000449269 0	−0.000224635	−	1.00000i	$-0.500072\pi$
$101$	−469843.	−0.000449269 0	−0.000224635		1.00000i	$0.500072\pi$
$102$	0	0
$103$	4.96841e7	0.0434961	0.0217480	−	0.999763i	$-0.493077\pi$
$103$	4.96841e7	0.0434961	0.0217480	+	0.999763i	$0.493077\pi$
$104$	−5.77853e8	−0.484359
$105$	−4.74025e7	−0.0380583
$106$	2.37910e8	0.183036
$107$	1.07290e9	0.791282	0.395641	−	0.918405i	$-0.370522\pi$
$107$	1.07290e9	0.791282	0.395641	+	0.918405i	$0.370522\pi$
$108$	9.04802e8	0.639951
$109$	−2.18593e9	−1.48326	−0.741630	−	0.670810i	$-0.765947\pi$
$109$	−2.18593e9	−1.48326	−0.741630	+	0.670810i	$0.765947\pi$
$110$	1.55225e8	0.101087
$111$	9.25855e8	0.578881
$112$	−3.46586e8	−0.208128
$113$	−9.94007e8	−0.573504	−0.286752	−	0.958005i	$-0.592576\pi$
$113$	−9.94007e8	−0.573504	−0.286752	+	0.958005i	$0.592576\pi$
$114$	1.30626e8	0.0724363
$115$	−1.09311e9	−0.582805
$116$	−1.55595e9	−0.797875
$117$	3.12077e9	1.53966
$118$	4.47876e8	0.212661
$119$	0	0
$120$	1.08228e8	0.0476457
$121$	2.66312e9	1.12942
$122$	333411.	0.000136258 0
$123$	4.21307e8	0.165969
$124$	1.68666e9	0.640663
$125$	−2.37439e9	−0.869876
$126$	−7.67986e7	−0.0271448
$127$	2.52436e9	0.861062	0.430531	−	0.902576i	$-0.358326\pi$
$127$	2.52436e9	0.861062	0.430531	+	0.902576i	$0.358326\pi$
$128$	1.61509e9	0.531806
$129$	−5.01058e8	−0.159307
$130$	3.94959e8	0.121285
$131$	2.82581e9	0.838344	0.419172	−	0.907907i	$-0.362320\pi$
$131$	2.82581e9	0.838344	0.419172	+	0.907907i	$0.362320\pi$
$132$	1.73318e9	0.496890
$133$	1.19069e9	0.329965
$134$	−4.98565e6	−0.00133583
$135$	−1.24916e9	−0.323680
$136$	0	0
$137$	−8.41682e8	−0.204129	−0.102065	−	0.994778i	$-0.532545\pi$
$137$	−8.41682e8	−0.204129	−0.102065	+	0.994778i	$0.532545\pi$
$138$	2.42888e8	0.0570099
$139$	1.92994e9	0.438507	0.219254	−	0.975668i	$-0.429638\pi$
$139$	1.92994e9	0.438507	0.219254	+	0.975668i	$0.429638\pi$
$140$	4.88406e8	0.107450
$141$	2.78307e8	0.0592978
$142$	−1.02945e9	−0.212474
$143$	1.27757e10	2.55490
$144$	−4.27359e9	−0.828251
$145$	2.14813e9	0.403557
$146$	5.81363e7	0.0105891
$147$	−1.87013e9	−0.330327
$148$	−9.53944e9	−1.63435
$149$	−8.74761e9	−1.45396	−0.726978	−	0.686661i	$-0.759076\pi$
$149$	−8.74761e9	−1.45396	−0.726978	+	0.686661i	$0.759076\pi$
$150$	2.26808e8	0.0365803
$151$	−5.65562e8	−0.0885287	−0.0442644	−	0.999020i	$-0.514094\pi$
$151$	−5.65562e8	−0.0885287	−0.0442644	+	0.999020i	$0.514094\pi$
$152$	−2.71855e9	−0.413087
$153$	0	0
$154$	−3.14396e8	−0.0450437
$155$	−2.32858e9	−0.324041
$156$	4.40994e9	0.596172
$157$	−5.95073e9	−0.781667	−0.390834	−	0.920461i	$-0.627813\pi$
$157$	−5.95073e9	−0.781667	−0.390834	+	0.920461i	$0.627813\pi$
$158$	−4.65023e8	−0.0593632
$159$	−3.66739e9	−0.455062
$160$	−1.67816e9	−0.202439
$161$	2.21400e9	0.259694
$162$	−7.99281e8	−0.0911763
$163$	6.13248e9	0.680443	0.340221	−	0.940345i	$-0.389498\pi$
$163$	6.13248e9	0.680443	0.340221	+	0.940345i	$0.389498\pi$
$164$	−4.34089e9	−0.468577
$165$	−2.39281e9	−0.251322
$166$	1.17227e9	0.119824
$167$	−1.05371e10	−1.04833	−0.524165	−	0.851617i	$-0.675622\pi$
$167$	−1.05371e10	−1.04833	−0.524165	+	0.851617i	$0.675622\pi$
$168$	−2.19207e8	−0.0212306
$169$	2.19024e10	2.06538
$170$	0	0
$171$	1.46819e10	1.31311
$172$	5.16259e9	0.449769
$173$	1.27909e10	1.08566	0.542828	−	0.839844i	$-0.317354\pi$
$173$	1.27909e10	1.08566	0.542828	+	0.839844i	$0.317354\pi$
$174$	−4.77313e8	−0.0394759
$175$	2.06742e9	0.166632
$176$	−1.74951e10	−1.37439
$177$	−6.90403e9	−0.528717
$178$	1.12152e9	0.0837370
$179$	2.46986e10	1.79818	0.899090	−	0.437765i	$-0.144230\pi$
$179$	2.46986e10	1.79818	0.899090	+	0.437765i	$0.144230\pi$
$180$	6.02231e9	0.427599
$181$	9.00010e8	0.0623295	0.0311647	−	0.999514i	$-0.490078\pi$
$181$	9.00010e8	0.0623295	0.0311647	+	0.999514i	$0.490078\pi$
$182$	−7.99957e8	−0.0540438
$183$	−5.13955e6	−0.000338762 0
$184$	−5.05494e9	−0.325114
$185$	1.31701e10	0.826637
$186$	5.17410e8	0.0316976
$187$	0	0
$188$	−2.86750e9	−0.167415
$189$	2.53007e9	0.144230
$190$	1.85811e9	0.103438
$191$	−6.14045e9	−0.333849	−0.166924	−	0.985970i	$-0.553384\pi$
$191$	−6.14045e9	−0.333849	−0.166924	+	0.985970i	$0.553384\pi$
$192$	−5.78627e9	−0.307286
$193$	−9.55369e9	−0.495637	−0.247818	−	0.968807i	$-0.579714\pi$
$193$	−9.55369e9	−0.495637	−0.247818	+	0.968807i	$0.579714\pi$
$194$	4.86483e9	0.246581
$195$	−6.08832e9	−0.301538
$196$	1.92687e10	0.932609
$197$	−1.04669e10	−0.495132	−0.247566	−	0.968871i	$-0.579631\pi$
$197$	−1.04669e10	−0.495132	−0.247566	+	0.968871i	$0.579631\pi$
$198$	−3.87668e9	−0.179253
$199$	−3.53275e10	−1.59689	−0.798443	−	0.602070i	$-0.794343\pi$
$199$	−3.53275e10	−1.59689	−0.798443	+	0.602070i	$0.794343\pi$
$200$	−4.72027e9	−0.208609
$201$	7.68541e7	0.00332112
$202$	1.48505e6	6.27566e−5 0
$203$	−4.35086e9	−0.179822
$204$	0	0
$205$	5.99299e9	0.237001
$206$	−1.57038e8	−0.00607579
$207$	2.72999e10	1.03346
$208$	−4.45150e10	−1.64900
$209$	6.01044e10	2.17895
$210$	1.49827e8	0.00531621
$211$	4.50442e10	1.56447	0.782236	−	0.622982i	$-0.214079\pi$
$211$	4.50442e10	1.56447	0.782236	+	0.622982i	$0.214079\pi$
$212$	3.77865e10	1.28477
$213$	1.58690e10	0.528251
$214$	−3.39114e9	−0.110531
$215$	−7.12743e9	−0.227489
$216$	−5.77658e9	−0.180563
$217$	4.71636e9	0.144390
$218$	6.90913e9	0.207190
$219$	−8.96175e8	−0.0263266
$220$	2.46540e10	0.709554
$221$	0	0
$222$	−2.92638e9	−0.0808615
$223$	−7.88599e9	−0.213542	−0.106771	−	0.994284i	$-0.534051\pi$
$223$	−7.88599e9	−0.213542	−0.106771	+	0.994284i	$0.534051\pi$
$224$	3.39898e9	0.0902054
$225$	2.54925e10	0.663117
$226$	3.14179e9	0.0801104
$227$	−4.14267e10	−1.03553	−0.517767	−	0.855522i	$-0.673237\pi$
$227$	−4.14267e10	−1.03553	−0.517767	+	0.855522i	$0.673237\pi$
$228$	2.07469e10	0.508447
$229$	5.69986e10	1.36963	0.684817	−	0.728715i	$-0.259882\pi$
$229$	5.69986e10	1.36963	0.684817	+	0.728715i	$0.259882\pi$
$230$	3.45502e9	0.0814096
$231$	4.84644e9	0.111987
$232$	9.93375e9	0.225122
$233$	−3.29248e10	−0.731849	−0.365924	−	0.930645i	$-0.619247\pi$
$233$	−3.29248e10	−0.731849	−0.365924	+	0.930645i	$0.619247\pi$
$234$	−9.86391e9	−0.215069
$235$	3.95885e9	0.0846766
$236$	7.11349e10	1.49272
$237$	7.16836e9	0.147588
$238$	0	0
$239$	2.59786e10	0.515022	0.257511	−	0.966275i	$-0.417098\pi$
$239$	2.59786e10	0.515022	0.257511	+	0.966275i	$0.417098\pi$
$240$	8.33736e9	0.162210
$241$	4.10474e10	0.783806	0.391903	−	0.920007i	$-0.371817\pi$
$241$	4.10474e10	0.783806	0.391903	+	0.920007i	$0.371817\pi$
$242$	−8.41741e9	−0.157765
$243$	4.77968e10	0.879368
$244$	5.29547e7	0.000956424 0
$245$	−2.66022e10	−0.471704
$246$	−1.33164e9	−0.0231835
$247$	1.52931e11	2.61432
$248$	−1.07682e10	−0.180764
$249$	−1.80707e10	−0.297905
$250$	7.50481e9	0.121509
$251$	1.09883e10	0.174742	0.0873709	−	0.996176i	$-0.472153\pi$
$251$	1.09883e10	0.174742	0.0873709	+	0.996176i	$0.472153\pi$
$252$	−1.21977e10	−0.190535
$253$	1.11760e11	1.71491
$254$	−7.97881e9	−0.120278
$255$	0	0
$256$	5.56997e10	0.810538
$257$	6.43551e10	0.920204	0.460102	−	0.887866i	$-0.347813\pi$
$257$	6.43551e10	0.920204	0.460102	+	0.887866i	$0.347813\pi$
$258$	1.58371e9	0.0222529
$259$	−2.66749e10	−0.368344
$260$	6.27302e10	0.851328
$261$	−5.36485e10	−0.715608
$262$	−8.93163e9	−0.117105
$263$	−5.72295e10	−0.737597	−0.368798	−	0.929509i	$-0.620231\pi$
$263$	−5.72295e10	−0.737597	−0.368798	+	0.929509i	$0.620231\pi$
$264$	−1.10652e10	−0.140198
$265$	−5.21677e10	−0.649823
$266$	−3.76346e9	−0.0460914
$267$	−1.72883e10	−0.208186
$268$	−7.91857e8	−0.00937649
$269$	1.58670e10	0.184761	0.0923804	−	0.995724i	$-0.470552\pi$
$269$	1.58670e10	0.184761	0.0923804	+	0.995724i	$0.470552\pi$
$270$	3.94826e9	0.0452136
$271$	5.18158e10	0.583580	0.291790	−	0.956482i	$-0.405749\pi$
$271$	5.18158e10	0.583580	0.291790	+	0.956482i	$0.405749\pi$
$272$	0	0
$273$	1.23314e10	0.134363
$274$	2.66033e9	0.0285140
$275$	1.04360e11	1.10037
$276$	3.85772e10	0.400166
$277$	2.66855e10	0.272343	0.136172	−	0.990685i	$-0.456520\pi$
$277$	2.66855e10	0.272343	0.136172	+	0.990685i	$0.456520\pi$
$278$	−6.10001e9	−0.0612532
$279$	5.81553e10	0.574606
$280$	−3.11816e9	−0.0303171
$281$	2.04044e10	0.195229	0.0976147	−	0.995224i	$-0.468879\pi$
$281$	2.04044e10	0.195229	0.0976147	+	0.995224i	$0.468879\pi$
$282$	−8.79653e8	−0.00828306
$283$	−7.84801e10	−0.727311	−0.363656	−	0.931533i	$-0.618472\pi$
$283$	−7.84801e10	−0.727311	−0.363656	+	0.931533i	$0.618472\pi$
$284$	−1.63504e11	−1.49141
$285$	−2.86430e10	−0.257167
$286$	−4.03806e10	−0.356883
$287$	−1.21383e10	−0.105606
$288$	4.19113e10	0.358975
$289$	0	0
$290$	−6.78966e9	−0.0563712
$291$	−7.49916e10	−0.613047
$292$	9.23363e9	0.0743275
$293$	−1.21258e11	−0.961180	−0.480590	−	0.876945i	$-0.659578\pi$
$293$	−1.21258e11	−0.961180	−0.480590	+	0.876945i	$0.659578\pi$
$294$	5.91098e9	0.0461420
$295$	−9.82081e10	−0.755002
$296$	6.09032e10	0.461134
$297$	1.27714e11	0.952435
$298$	2.76488e10	0.203097
$299$	2.84364e11	2.05757
$300$	3.60232e10	0.256765
$301$	1.44360e10	0.101367
$302$	1.78759e9	0.0123662
$303$	−2.28921e7	−0.000156025 0
$304$	−2.09424e11	−1.40636
$305$	−7.31088e7	−0.000483749 0
$306$	0	0
$307$	−4.04188e10	−0.259693	−0.129847	−	0.991534i	$-0.541448\pi$
$307$	−4.04188e10	−0.259693	−0.129847	+	0.991534i	$0.541448\pi$
$308$	−4.99347e10	−0.316172
$309$	2.42075e9	0.0151056
$310$	7.36002e9	0.0452639
$311$	−1.95903e11	−1.18746	−0.593732	−	0.804663i	$-0.702346\pi$
$311$	−1.95903e11	−1.18746	−0.593732	+	0.804663i	$0.702346\pi$
$312$	−2.81546e10	−0.168211
$313$	1.86102e11	1.09598	0.547989	−	0.836486i	$-0.315394\pi$
$313$	1.86102e11	1.09598	0.547989	+	0.836486i	$0.315394\pi$
$314$	1.88087e10	0.109188
$315$	1.68400e10	0.0963708
$316$	−7.38583e10	−0.416685
$317$	−8.28806e10	−0.460984	−0.230492	−	0.973074i	$-0.574034\pi$
$317$	−8.28806e10	−0.460984	−0.230492	+	0.973074i	$0.574034\pi$
$318$	1.15916e10	0.0635657
$319$	−2.19625e11	−1.18747
$320$	−8.23083e10	−0.438802
$321$	5.22746e10	0.274801
$322$	−6.99787e9	−0.0362756
$323$	0	0
$324$	−1.26948e11	−0.639988
$325$	2.65537e11	1.32023
$326$	−1.93831e10	−0.0950482
$327$	−1.06505e11	−0.515115
$328$	2.77138e10	0.132210
$329$	−8.01833e9	−0.0377313
$330$	7.56302e9	0.0351061
$331$	−2.09793e11	−0.960648	−0.480324	−	0.877091i	$-0.659481\pi$
$331$	−2.09793e11	−0.960648	−0.480324	+	0.877091i	$0.659481\pi$
$332$	1.86189e11	0.841071
$333$	−3.28916e11	−1.46584
$334$	3.33050e10	0.146437
$335$	1.09323e9	0.00474253
$336$	−1.68866e10	−0.0722798
$337$	−1.83928e11	−0.776805	−0.388403	−	0.921490i	$-0.626973\pi$
$337$	−1.83928e11	−0.776805	−0.388403	+	0.921490i	$0.626973\pi$
$338$	−6.92275e10	−0.288505
$339$	−4.84308e10	−0.199170
$340$	0	0
$341$	2.38075e11	0.953495
$342$	−4.64055e10	−0.183422
$343$	1.10527e11	0.431167
$344$	−3.29599e10	−0.126903
$345$	−5.32594e10	−0.202400
$346$	−4.04284e10	−0.151651
$347$	−3.67210e11	−1.35967	−0.679833	−	0.733367i	$-0.737948\pi$
$347$	−3.67210e11	−1.35967	−0.679833	+	0.733367i	$0.737948\pi$
$348$	−7.58103e10	−0.277091
$349$	−3.32580e11	−1.20000	−0.600001	−	0.799999i	$-0.704833\pi$
$349$	−3.32580e11	−1.20000	−0.600001	+	0.799999i	$0.704833\pi$
$350$	−6.53457e9	−0.0232761
$351$	3.24959e11	1.14274
$352$	1.71575e11	0.595680
$353$	1.82460e11	0.625436	0.312718	−	0.949846i	$-0.398761\pi$
$353$	1.82460e11	0.625436	0.312718	+	0.949846i	$0.398761\pi$
$354$	2.18218e10	0.0738542
$355$	2.25732e11	0.754337
$356$	1.78128e11	0.587770
$357$	0	0
$358$	−7.80655e10	−0.251180
$359$	−2.39037e11	−0.759523	−0.379761	−	0.925084i	$-0.623994\pi$
$359$	−2.39037e11	−0.759523	−0.379761	+	0.925084i	$0.623994\pi$
$360$	−3.84486e10	−0.120648
$361$	3.96788e11	1.22964
$362$	−2.84469e9	−0.00870655
$363$	1.29755e11	0.392233
$364$	−1.27055e11	−0.379346
$365$	−1.27479e10	−0.0375941
$366$	1.62447e7	4.73203e−5 0
$367$	4.60251e11	1.32433	0.662167	−	0.749356i	$-0.269637\pi$
$367$	4.60251e11	1.32433	0.662167	+	0.749356i	$0.269637\pi$
$368$	−3.89409e11	−1.10685
$369$	−1.49672e11	−0.420264
$370$	−4.16270e10	−0.115469
$371$	1.05661e11	0.289557
$372$	8.21788e10	0.222493
$373$	−5.13638e10	−0.137394	−0.0686970	−	0.997638i	$-0.521884\pi$
$373$	−5.13638e10	−0.137394	−0.0686970	+	0.997638i	$0.521884\pi$
$374$	0	0
$375$	−1.15687e11	−0.302095
$376$	1.83072e10	0.0472363
$377$	−5.58819e11	−1.42474
$378$	−7.99688e9	−0.0201469
$379$	2.87645e11	0.716112	0.358056	−	0.933700i	$-0.383440\pi$
$379$	2.87645e11	0.716112	0.358056	+	0.933700i	$0.383440\pi$
$380$	2.95119e11	0.726058
$381$	1.22994e11	0.299034
$382$	1.94083e10	0.0466339
$383$	−4.55170e11	−1.08088	−0.540442	−	0.841381i	$-0.681743\pi$
$383$	−4.55170e11	−1.08088	−0.540442	+	0.841381i	$0.681743\pi$
$384$	7.86920e10	0.184688
$385$	6.89393e10	0.159917
$386$	3.01966e10	0.0692334
$387$	1.78004e11	0.403395
$388$	7.72667e11	1.73081
$389$	−3.73375e11	−0.826746	−0.413373	−	0.910562i	$-0.635649\pi$
$389$	−3.73375e11	−0.826746	−0.413373	+	0.910562i	$0.635649\pi$
$390$	1.92435e10	0.0421205
$391$	0	0
$392$	−1.23018e11	−0.263137
$393$	1.37682e11	0.291145
$394$	3.30831e10	0.0691630
$395$	1.01968e11	0.210755
$396$	−6.15722e11	−1.25822
$397$	6.40761e11	1.29461	0.647305	−	0.762231i	$-0.275896\pi$
$397$	6.40761e11	1.29461	0.647305	+	0.762231i	$0.275896\pi$
$398$	1.11661e11	0.223062
$399$	5.80140e10	0.114592
$400$	−3.63627e11	−0.710210
$401$	−7.66581e11	−1.48050	−0.740250	−	0.672331i	$-0.765293\pi$
$401$	−7.66581e11	−1.48050	−0.740250	+	0.672331i	$0.765293\pi$
$402$	−2.42915e8	−0.000463914 0
$403$	6.05763e11	1.14401
$404$	2.35866e8	0.000440503 0
$405$	1.75263e11	0.323699
$406$	1.37519e10	0.0251186
$407$	−1.34651e12	−2.43239
$408$	0	0
$409$	1.19521e11	0.211199	0.105599	−	0.994409i	$-0.466324\pi$
$409$	1.19521e11	0.211199	0.105599	+	0.994409i	$0.466324\pi$
$410$	−1.89422e10	−0.0331057
$411$	−4.10091e10	−0.0708912
$412$	−2.49419e10	−0.0426474
$413$	1.98913e11	0.336424
$414$	−8.62875e10	−0.144360
$415$	−2.57051e11	−0.425405
$416$	4.36560e11	0.714701
$417$	9.40320e10	0.152287
$418$	−1.89974e11	−0.304369
$419$	−2.93517e10	−0.0465232	−0.0232616	−	0.999729i	$-0.507405\pi$
$419$	−2.93517e10	−0.0465232	−0.0232616	+	0.999729i	$0.507405\pi$
$420$	2.37965e10	0.0373157
$421$	5.90937e11	0.916794	0.458397	−	0.888747i	$-0.348424\pi$
$421$	5.90937e11	0.916794	0.458397	+	0.888747i	$0.348424\pi$
$422$	−1.42373e11	−0.218535
$423$	−9.88703e10	−0.150153
$424$	−2.41243e11	−0.362500
$425$	0	0
$426$	−5.01575e10	−0.0737892
$427$	1.48076e8	0.000215555 0
$428$	−5.38605e11	−0.775842
$429$	6.22470e11	0.887280
$430$	2.25279e10	0.0317769
$431$	4.80166e11	0.670261	0.335130	−	0.942172i	$-0.391220\pi$
$431$	4.80166e11	0.670261	0.335130	+	0.942172i	$0.391220\pi$
$432$	−4.45000e11	−0.614729
$433$	−8.08383e11	−1.10515	−0.552576	−	0.833463i	$-0.686355\pi$
$433$	−8.08383e11	−1.10515	−0.552576	+	0.833463i	$0.686355\pi$
$434$	−1.49071e10	−0.0201693
$435$	1.04663e11	0.140149
$436$	1.09736e12	1.45432
$437$	1.33781e12	1.75480
$438$	2.83257e9	0.00367745
$439$	−6.77593e11	−0.870720	−0.435360	−	0.900257i	$-0.643379\pi$
$439$	−6.77593e11	−0.870720	−0.435360	+	0.900257i	$0.643379\pi$
$440$	−1.57400e11	−0.200202
$441$	6.64376e11	0.836450
$442$	0	0
$443$	−1.48947e12	−1.83744	−0.918722	−	0.394905i	$-0.870778\pi$
$443$	−1.48947e12	−1.83744	−0.918722	+	0.394905i	$0.870778\pi$
$444$	−4.64788e11	−0.567586
$445$	−2.45922e11	−0.297288
$446$	2.49255e10	0.0298288
$447$	−4.26208e11	−0.504938
$448$	1.66709e11	0.195527
$449$	−1.36840e12	−1.58893	−0.794466	−	0.607309i	$-0.792249\pi$
$449$	−1.36840e12	−1.58893	−0.794466	+	0.607309i	$0.792249\pi$
$450$	−8.05748e10	−0.0926281
$451$	−6.12724e11	−0.697381
$452$	4.99001e11	0.562314
$453$	−2.75558e10	−0.0307448
$454$	1.30939e11	0.144649
$455$	1.75411e11	0.191869
$456$	−1.32456e11	−0.143459
$457$	−7.79766e11	−0.836260	−0.418130	−	0.908387i	$-0.637314\pi$
$457$	−7.79766e11	−0.836260	−0.418130	+	0.908387i	$0.637314\pi$
$458$	−1.80157e11	−0.191318
$459$	0	0
$460$	5.48751e11	0.571433
$461$	−7.40627e11	−0.763740	−0.381870	−	0.924216i	$-0.624720\pi$
$461$	−7.40627e11	−0.763740	−0.381870	+	0.924216i	$0.624720\pi$
$462$	−1.53183e10	−0.0156430
$463$	−3.53227e9	−0.00357223	−0.00178611	−	0.999998i	$-0.500569\pi$
$463$	−3.53227e9	−0.00357223	−0.00178611	+	0.999998i	$0.500569\pi$
$464$	7.65249e11	0.766429
$465$	−1.13455e11	−0.112535
$466$	1.04066e11	0.102229
$467$	5.27254e11	0.512972	0.256486	−	0.966548i	$-0.417435\pi$
$467$	5.27254e11	0.512972	0.256486	+	0.966548i	$0.417435\pi$
$468$	−1.56666e12	−1.50962
$469$	−2.21425e9	−0.00211324
$470$	−1.25128e10	−0.0118281
$471$	−2.89936e11	−0.271462
$472$	−4.54150e11	−0.421173
$473$	7.28709e11	0.669389
$474$	−2.26572e10	−0.0206160
$475$	1.24924e12	1.12596
$476$	0	0
$477$	1.30286e12	1.15230
$478$	−8.21115e10	−0.0719413
$479$	−1.22669e12	−1.06470	−0.532348	−	0.846526i	$-0.678690\pi$
$479$	−1.22669e12	−1.06470	−0.532348	+	0.846526i	$0.678690\pi$
$480$	−8.17648e10	−0.0703041
$481$	−3.42608e12	−2.91840
$482$	−1.29740e11	−0.109487
$483$	1.07873e11	0.0901880
$484$	−1.33691e12	−1.10739
$485$	−1.06674e12	−0.875426
$486$	−1.51073e11	−0.122835
$487$	−5.60939e11	−0.451893	−0.225946	−	0.974140i	$-0.572547\pi$
$487$	−5.60939e11	−0.451893	−0.225946	+	0.974140i	$0.572547\pi$
$488$	−3.38082e8	−0.000269856 0
$489$	2.98792e11	0.236308
$490$	8.40822e10	0.0658903
$491$	−1.52981e12	−1.18788	−0.593939	−	0.804510i	$-0.702428\pi$
$491$	−1.52981e12	−1.18788	−0.593939	+	0.804510i	$0.702428\pi$
$492$	−2.11500e11	−0.162730
$493$	0	0
$494$	−4.83374e11	−0.365184
$495$	8.50060e11	0.636394
$496$	−8.29534e11	−0.615413
$497$	−4.57202e11	−0.336128
$498$	5.71165e10	0.0416131
$499$	1.70905e12	1.23397	0.616983	−	0.786977i	$-0.288355\pi$
$499$	1.70905e12	1.23397	0.616983	+	0.786977i	$0.288355\pi$
$500$	1.19197e12	0.852903
$501$	−5.13398e11	−0.364070
$502$	−3.47309e10	−0.0244090
$503$	1.33924e12	0.932829	0.466415	−	0.884566i	$-0.345545\pi$
$503$	1.33924e12	0.932829	0.466415	+	0.884566i	$0.345545\pi$
$504$	7.78745e10	0.0537599
$505$	−3.25634e8	−0.000222802 0
$506$	−3.53242e11	−0.239549
$507$	1.06715e12	0.717279
$508$	−1.26725e12	−0.844261
$509$	−1.86732e12	−1.23307	−0.616536	−	0.787327i	$-0.711465\pi$
$509$	−1.86732e12	−1.23307	−0.616536	+	0.787327i	$0.711465\pi$
$510$	0	0
$511$	2.58198e10	0.0167517
$512$	−1.00298e12	−0.645026
$513$	1.52880e12	0.974589
$514$	−2.03409e11	−0.128539
$515$	3.44346e10	0.0215706
$516$	2.51536e11	0.156198
$517$	−4.04753e11	−0.249162
$518$	8.43121e10	0.0514524
$519$	6.23207e11	0.377033
$520$	−4.00492e11	−0.240203
$521$	1.66544e12	0.990280	0.495140	−	0.868813i	$-0.335117\pi$
$521$	1.66544e12	0.990280	0.495140	+	0.868813i	$0.335117\pi$
$522$	1.69568e11	0.0999604
$523$	1.76906e12	1.03392	0.516959	−	0.856010i	$-0.327064\pi$
$523$	1.76906e12	1.03392	0.516959	+	0.856010i	$0.327064\pi$
$524$	−1.41858e12	−0.821986
$525$	1.00731e11	0.0578689
$526$	1.80887e11	0.103032
$527$	0	0
$528$	−8.52412e11	−0.477306
$529$	6.86403e11	0.381091
$530$	1.64888e11	0.0907711
$531$	2.45270e12	1.33881
$532$	−5.97740e11	−0.323527
$533$	−1.55903e12	−0.836723
$534$	5.46437e10	0.0290807
$535$	7.43593e11	0.392413
$536$	5.05550e9	0.00264559
$537$	1.20338e12	0.624482
$538$	−5.01513e10	−0.0258085
$539$	2.71981e12	1.38800
$540$	6.27091e11	0.317365
$541$	−2.63385e12	−1.32191	−0.660957	−	0.750424i	$-0.729849\pi$
$541$	−2.63385e12	−1.32191	−0.660957	+	0.750424i	$0.729849\pi$
$542$	−1.63776e11	−0.0815178
$543$	4.38510e10	0.0216461
$544$	0	0
$545$	−1.51500e12	−0.735579
$546$	−3.89762e10	−0.0187686
$547$	−1.41089e12	−0.673828	−0.336914	−	0.941535i	$-0.609383\pi$
$547$	−1.41089e12	−0.673828	−0.336914	+	0.941535i	$0.609383\pi$
$548$	4.22533e11	0.200146
$549$	1.82586e9	0.000857810 0
$550$	−3.29855e11	−0.153706
$551$	−2.62901e12	−1.21509
$552$	−2.46291e11	−0.112907
$553$	−2.06528e11	−0.0939109
$554$	−8.43457e10	−0.0380425
$555$	6.41682e11	0.287079
$556$	−9.68848e11	−0.429951
$557$	−3.98910e12	−1.75601	−0.878003	−	0.478655i	$-0.841125\pi$
$557$	−3.98910e12	−1.75601	−0.878003	+	0.478655i	$0.841125\pi$
$558$	−1.83813e11	−0.0802643
$559$	1.85414e12	0.803138
$560$	−2.40208e11	−0.103215
$561$	0	0
$562$	−6.44928e10	−0.0272708
$563$	1.73158e12	0.726364	0.363182	−	0.931718i	$-0.381690\pi$
$563$	1.73158e12	0.726364	0.363182	+	0.931718i	$0.381690\pi$
$564$	−1.39713e11	−0.0581407
$565$	−6.88917e11	−0.284412
$566$	2.48054e11	0.101595
$567$	−3.54980e11	−0.144238
$568$	1.04387e12	0.420802
$569$	−1.12143e12	−0.448503	−0.224252	−	0.974531i	$-0.571994\pi$
$569$	−1.12143e12	−0.448503	−0.224252	+	0.974531i	$0.571994\pi$
$570$	9.05326e10	0.0359226
$571$	−4.36285e12	−1.71754	−0.858771	−	0.512360i	$-0.828771\pi$
$571$	−4.36285e12	−1.71754	−0.858771	+	0.512360i	$0.828771\pi$
$572$	−6.41354e12	−2.50505
$573$	−2.99180e11	−0.115941
$574$	3.83659e10	0.0147517
$575$	2.32287e12	0.886173
$576$	2.05561e12	0.778107
$577$	1.07137e12	0.402390	0.201195	−	0.979551i	$-0.435517\pi$
$577$	1.07137e12	0.402390	0.201195	+	0.979551i	$0.435517\pi$
$578$	0	0
$579$	−4.65483e11	−0.172127
$580$	−1.07838e12	−0.395683
$581$	5.20636e11	0.189558
$582$	2.37028e11	0.0856340
$583$	5.33363e12	1.91212
$584$	−5.89508e10	−0.0209716
$585$	2.16291e12	0.763550
$586$	3.83263e11	0.134263
$587$	1.81524e12	0.631049	0.315524	−	0.948918i	$-0.397820\pi$
$587$	1.81524e12	0.631049	0.315524	+	0.948918i	$0.397820\pi$
$588$	9.38825e11	0.323882
$589$	2.84986e12	0.975673
$590$	3.10409e11	0.105463
$591$	−5.09978e11	−0.171952
$592$	4.69169e12	1.56994
$593$	2.22713e12	0.739603	0.369801	−	0.929111i	$-0.379426\pi$
$593$	2.22713e12	0.739603	0.369801	+	0.929111i	$0.379426\pi$
$594$	−4.03670e11	−0.133042
$595$	0	0
$596$	4.39139e12	1.42559
$597$	−1.72126e12	−0.554576
$598$	−8.98796e11	−0.287413
$599$	−2.65815e12	−0.843644	−0.421822	−	0.906679i	$-0.638609\pi$
$599$	−2.65815e12	−0.843644	−0.421822	+	0.906679i	$0.638609\pi$
$600$	−2.29985e11	−0.0724468
$601$	2.62762e11	0.0821538	0.0410769	−	0.999156i	$-0.486921\pi$
$601$	2.62762e11	0.0821538	0.0410769	+	0.999156i	$0.486921\pi$
$602$	−4.56284e10	−0.0141596
$603$	−2.73029e10	−0.00840971
$604$	2.83918e11	0.0868013
$605$	1.84573e12	0.560105
$606$	7.23557e7	2.17945e−5 0
$607$	−3.95484e12	−1.18244	−0.591221	−	0.806509i	$-0.701354\pi$
$607$	−3.95484e12	−1.18244	−0.591221	+	0.806509i	$0.701354\pi$
$608$	2.05383e12	0.609535
$609$	−2.11986e11	−0.0624497
$610$	2.31077e8	6.75729e−5 0
$611$	−1.02986e12	−0.298947
$612$	0	0
$613$	−1.76259e12	−0.504171	−0.252086	−	0.967705i	$-0.581116\pi$
$613$	−1.76259e12	−0.504171	−0.252086	+	0.967705i	$0.581116\pi$
$614$	1.27753e11	0.0362754
$615$	2.91995e11	0.0823072
$616$	3.18801e11	0.0892085
$617$	1.91721e11	0.0532582	0.0266291	−	0.999645i	$-0.491523\pi$
$617$	1.91721e11	0.0532582	0.0266291	+	0.999645i	$0.491523\pi$
$618$	−7.65134e9	−0.00211003
$619$	1.97924e12	0.541864	0.270932	−	0.962599i	$-0.412668\pi$
$619$	1.97924e12	0.541864	0.270932	+	0.962599i	$0.412668\pi$
$620$	1.16897e12	0.317718
$621$	2.84268e12	0.767036
$622$	6.19198e11	0.165872
$623$	4.98095e11	0.132469
$624$	−2.16890e12	−0.572675
$625$	1.23090e12	0.322674
$626$	−5.88218e11	−0.153092
$627$	2.92846e12	0.756720
$628$	2.98733e12	0.766415
$629$	0	0
$630$	−5.32268e10	−0.0134616
$631$	5.02119e12	1.26088	0.630441	−	0.776238i	$-0.282874\pi$
$631$	5.02119e12	1.26088	0.630441	+	0.776238i	$0.282874\pi$
$632$	4.71538e11	0.117568
$633$	2.19468e12	0.543319
$634$	2.61963e11	0.0643929
$635$	1.74956e12	0.427018
$636$	1.84107e12	0.446182
$637$	6.92034e12	1.66533
$638$	6.94175e11	0.165873
$639$	−5.63755e12	−1.33763
$640$	1.11937e12	0.263733
$641$	−4.09009e12	−0.956911	−0.478455	−	0.878112i	$-0.658803\pi$
$641$	−4.09009e12	−0.956911	−0.478455	+	0.878112i	$0.658803\pi$
$642$	−1.65226e11	−0.0383858
$643$	−6.25243e12	−1.44245	−0.721223	−	0.692703i	$-0.756420\pi$
$643$	−6.25243e12	−1.44245	−0.721223	+	0.692703i	$0.756420\pi$
$644$	−1.11145e12	−0.254627
$645$	−3.47268e11	−0.0790036
$646$	0	0
$647$	4.16798e12	0.935096	0.467548	−	0.883968i	$-0.345137\pi$
$647$	4.16798e12	0.935096	0.467548	+	0.883968i	$0.345137\pi$
$648$	8.10479e11	0.180574
$649$	1.00408e13	2.22161
$650$	−8.39291e11	−0.184418
$651$	2.29794e11	0.0501447
$652$	−3.07856e12	−0.667166
$653$	−3.50131e12	−0.753565	−0.376783	−	0.926302i	$-0.622970\pi$
$653$	−3.50131e12	−0.753565	−0.376783	+	0.926302i	$0.622970\pi$
$654$	3.36633e11	0.0719542
$655$	1.95848e12	0.415752
$656$	2.13494e12	0.450109
$657$	3.18372e11	0.0666638
$658$	2.53438e10	0.00527053
$659$	4.29957e12	0.888056	0.444028	−	0.896013i	$-0.353549\pi$
$659$	4.29957e12	0.888056	0.444028	+	0.896013i	$0.353549\pi$
$660$	1.20121e12	0.246418
$661$	7.54567e11	0.153742	0.0768708	−	0.997041i	$-0.475507\pi$
$661$	7.54567e11	0.153742	0.0768708	+	0.997041i	$0.475507\pi$
$662$	6.63097e11	0.134189
$663$	0	0
$664$	−1.18870e12	−0.237310
$665$	8.25234e11	0.163636
$666$	1.03961e12	0.204757
$667$	−4.88844e12	−0.956321
$668$	5.28974e12	1.02787
$669$	−3.84228e11	−0.0741602
$670$	−3.45541e9	−0.000662464 0
$671$	7.47465e9	0.00142344
$672$	1.65608e11	0.0313271
$673$	1.30783e12	0.245745	0.122872	−	0.992422i	$-0.460789\pi$
$673$	1.30783e12	0.245745	0.122872	+	0.992422i	$0.460789\pi$
$674$	5.81345e11	0.108509
$675$	2.65448e12	0.492166
$676$	−1.09952e13	−2.02508
$677$	−1.07226e12	−0.196178	−0.0980890	−	0.995178i	$-0.531273\pi$
$677$	−1.07226e12	−0.196178	−0.0980890	+	0.995178i	$0.531273\pi$
$678$	1.53077e11	0.0278212
$679$	2.16059e12	0.390084
$680$	0	0
$681$	−2.01843e12	−0.359626
$682$	−7.52489e11	−0.133190
$683$	3.99462e12	0.702397	0.351198	−	0.936301i	$-0.385774\pi$
$683$	3.99462e12	0.702397	0.351198	+	0.936301i	$0.385774\pi$
$684$	−7.37046e12	−1.28748
$685$	−5.83345e11	−0.101232
$686$	−3.49346e11	−0.0602279
$687$	2.77713e12	0.475654
$688$	−2.53907e12	−0.432043
$689$	1.35710e13	2.29417
$690$	1.68338e11	0.0282724
$691$	−8.15611e12	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$691$	−8.15611e12	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$692$	−6.42113e12	−1.06447
$693$	−1.72173e12	−0.283573
$694$	1.16065e12	0.189926
$695$	1.33758e12	0.217465
$696$	4.84000e11	0.0781815
$697$	0	0
$698$	1.05120e12	0.167623
$699$	−1.60419e12	−0.254161
$700$	−1.03787e12	−0.163381
$701$	−3.16374e12	−0.494846	−0.247423	−	0.968908i	$-0.579584\pi$
$701$	−3.16374e12	−0.494846	−0.247423	+	0.968908i	$0.579584\pi$
$702$	−1.02711e12	−0.159624
$703$	−1.61183e13	−2.48897
$704$	8.41520e12	1.29118
$705$	1.92886e11	0.0294070
$706$	−5.76708e11	−0.0873645
$707$	6.59546e8	9.92790e−5 0
$708$	3.46589e12	0.518400
$709$	−1.24882e12	−0.185606	−0.0928032	−	0.995684i	$-0.529583\pi$
$709$	−1.24882e12	−0.185606	−0.0928032	+	0.995684i	$0.529583\pi$
$710$	−7.13478e11	−0.105370
$711$	−2.54660e12	−0.373721
$712$	−1.13723e12	−0.165840
$713$	5.29909e12	0.767889
$714$	0	0
$715$	8.85448e12	1.26703
$716$	−1.23989e13	−1.76309
$717$	1.26575e12	0.178860
$718$	7.55533e11	0.106095
$719$	3.11496e12	0.434683	0.217342	−	0.976096i	$-0.430261\pi$
$719$	3.11496e12	0.434683	0.217342	+	0.976096i	$0.430261\pi$
$720$	−2.96190e12	−0.410747
$721$	−6.97444e10	−0.00961172
$722$	−1.25414e12	−0.171763
$723$	1.99994e12	0.272205
$724$	−4.51814e11	−0.0611133
$725$	−4.56479e12	−0.613621
$726$	−4.10120e11	−0.0547894
$727$	1.86046e12	0.247010	0.123505	−	0.992344i	$-0.460586\pi$
$727$	1.86046e12	0.247010	0.123505	+	0.992344i	$0.460586\pi$
$728$	8.11165e11	0.107033
$729$	−2.64862e12	−0.347332
$730$	4.02925e10	0.00525136
$731$	0	0
$732$	2.58010e9	0.000332152 0
$733$	2.39194e12	0.306043	0.153022	−	0.988223i	$-0.451100\pi$
$733$	2.39194e12	0.306043	0.153022	+	0.988223i	$0.451100\pi$
$734$	−1.45473e12	−0.184991
$735$	−1.29613e12	−0.163816
$736$	3.81894e12	0.479726
$737$	−1.11772e11	−0.0139550
$738$	4.73073e11	0.0587049
$739$	−2.40469e12	−0.296592	−0.148296	−	0.988943i	$-0.547379\pi$
$739$	−2.40469e12	−0.296592	−0.148296	+	0.988943i	$0.547379\pi$
$740$	−6.61150e12	−0.810507
$741$	7.45124e12	0.907917
$742$	−3.33967e11	−0.0404470
$743$	−1.49917e12	−0.180468	−0.0902341	−	0.995921i	$-0.528762\pi$
$743$	−1.49917e12	−0.180468	−0.0902341	+	0.995921i	$0.528762\pi$
$744$	−5.24659e11	−0.0627767
$745$	−6.06270e12	−0.721046
$746$	1.62347e11	0.0191920
$747$	6.41972e12	0.754351
$748$	0	0
$749$	−1.50609e12	−0.174857
$750$	3.65655e11	0.0421984
$751$	1.21712e13	1.39622	0.698109	−	0.715991i	$-0.254025\pi$
$751$	1.21712e13	1.39622	0.698109	+	0.715991i	$0.254025\pi$
$752$	1.41030e12	0.160816
$753$	5.35379e11	0.0606853
$754$	1.76628e12	0.199016
$755$	−3.91974e11	−0.0439032
$756$	−1.27012e12	−0.141416
$757$	8.17858e12	0.905204	0.452602	−	0.891713i	$-0.350496\pi$
$757$	8.17858e12	0.905204	0.452602	+	0.891713i	$0.350496\pi$
$758$	−9.09170e11	−0.100031
$759$	5.44524e12	0.595565
$760$	−1.88415e12	−0.204858
$761$	1.48106e12	0.160082	0.0800410	−	0.996792i	$-0.474495\pi$
$761$	1.48106e12	0.160082	0.0800410	+	0.996792i	$0.474495\pi$
$762$	−3.88750e11	−0.0417709
$763$	3.06851e12	0.327769
$764$	3.08256e12	0.327335
$765$	0	0
$766$	1.43867e12	0.150984
$767$	2.55481e13	2.66550
$768$	2.71385e12	0.281488
$769$	1.09709e13	1.13129	0.565644	−	0.824650i	$-0.308628\pi$
$769$	1.09709e13	1.13129	0.565644	+	0.824650i	$0.308628\pi$
$770$	−2.17899e11	−0.0223381
$771$	3.13556e12	0.319574
$772$	4.79605e12	0.485966
$773$	9.16618e12	0.923381	0.461690	−	0.887041i	$-0.347243\pi$
$773$	9.16618e12	0.923381	0.461690	+	0.887041i	$0.347243\pi$
$774$	−5.62623e11	−0.0563486
$775$	4.94826e12	0.492714
$776$	−4.93298e12	−0.488351
$777$	−1.29968e12	−0.127921
$778$	1.18014e12	0.115485
$779$	−7.33457e12	−0.713602
$780$	3.05639e12	0.295654
$781$	−2.30789e13	−2.21965
$782$	0	0
$783$	−5.58631e12	−0.531125
$784$	−9.47674e12	−0.895853
$785$	−4.12427e12	−0.387645
$786$	−4.35174e11	−0.0406688
$787$	−1.19335e13	−1.10887	−0.554435	−	0.832227i	$-0.687066\pi$
$787$	−1.19335e13	−1.10887	−0.554435	+	0.832227i	$0.687066\pi$
$788$	5.25450e12	0.485471
$789$	−2.78838e12	−0.256157
$790$	−3.22293e11	−0.0294394
$791$	1.39534e12	0.126732
$792$	3.93099e12	0.355008
$793$	1.90187e10	0.00170785
$794$	−2.02527e12	−0.180839
$795$	−2.54176e12	−0.225674
$796$	1.77347e13	1.56573
$797$	1.29174e13	1.13400	0.566998	−	0.823719i	$-0.308105\pi$
$797$	1.29174e13	1.13400	0.566998	+	0.823719i	$0.308105\pi$
$798$	−1.83366e11	−0.0160069
$799$	0	0
$800$	3.56611e12	0.307815
$801$	6.14178e12	0.527166
$802$	2.42296e12	0.206805
$803$	1.30334e12	0.110621
$804$	−3.85815e10	−0.00325632
$805$	1.53446e12	0.128788
$806$	−1.91465e12	−0.159802
$807$	7.73086e11	0.0641648
$808$	−1.50585e9	−0.000124289 0
$809$	−1.87403e13	−1.53818	−0.769090	−	0.639141i	$-0.779290\pi$
$809$	−1.87403e13	−1.53818	−0.769090	+	0.639141i	$0.779290\pi$
$810$	−5.53958e11	−0.0452162
$811$	1.44351e13	1.17173	0.585863	−	0.810410i	$-0.300755\pi$
$811$	1.44351e13	1.17173	0.585863	+	0.810410i	$0.300755\pi$
$812$	2.18418e12	0.176313
$813$	2.52461e12	0.202669
$814$	4.25595e12	0.339771
$815$	4.25023e12	0.337446
$816$	0	0
$817$	8.72296e12	0.684959
$818$	−3.77775e11	−0.0295014
$819$	−4.38080e12	−0.340233
$820$	−3.00854e12	−0.232377
$821$	1.36625e13	1.04951	0.524753	−	0.851254i	$-0.324158\pi$
$821$	1.36625e13	1.04951	0.524753	+	0.851254i	$0.324158\pi$
$822$	1.29619e11	0.00990250
$823$	3.29063e12	0.250023	0.125011	−	0.992155i	$-0.460103\pi$
$823$	3.29063e12	0.250023	0.125011	+	0.992155i	$0.460103\pi$
$824$	1.59238e11	0.0120330
$825$	5.08474e12	0.382143
$826$	−6.28709e11	−0.0469937
$827$	2.02901e13	1.50838	0.754189	−	0.656657i	$-0.228030\pi$
$827$	2.02901e13	1.50838	0.754189	+	0.656657i	$0.228030\pi$
$828$	−1.37048e13	−1.01330
$829$	5.53609e12	0.407106	0.203553	−	0.979064i	$-0.434751\pi$
$829$	5.53609e12	0.407106	0.203553	+	0.979064i	$0.434751\pi$
$830$	8.12468e11	0.0594231
$831$	1.30019e12	0.0945809
$832$	2.14118e13	1.54917
$833$	0	0
$834$	−2.97210e11	−0.0212724
$835$	−7.30296e12	−0.519888
$836$	−3.01730e13	−2.13644
$837$	6.05559e12	0.426473
$838$	9.27727e10	0.00649863
$839$	−1.88526e13	−1.31354	−0.656770	−	0.754091i	$-0.728078\pi$
$839$	−1.88526e13	−1.31354	−0.656770	+	0.754091i	$0.728078\pi$
$840$	−1.51926e11	−0.0105287
$841$	−4.90060e12	−0.337806
$842$	−1.86779e12	−0.128063
$843$	9.94160e11	0.0678004
$844$	−2.26126e13	−1.53395
$845$	1.51799e13	1.02427
$846$	3.12502e11	0.0209743
$847$	−3.73838e12	−0.249579
$848$	−1.85842e13	−1.23413
$849$	−3.82377e12	−0.252585
$850$	0	0
$851$	−2.99707e13	−1.95891
$852$	−7.96638e12	−0.517944
$853$	−2.52027e13	−1.62995	−0.814977	−	0.579493i	$-0.803251\pi$
$853$	−2.52027e13	−1.62995	−0.814977	+	0.579493i	$0.803251\pi$
$854$	−4.68028e8	−3.01100e−5 0
$855$	1.01756e13	0.651196
$856$	3.43865e12	0.218905
$857$	−1.17200e13	−0.742187	−0.371093	−	0.928596i	$-0.621017\pi$
$857$	−1.17200e13	−0.742187	−0.371093	+	0.928596i	$0.621017\pi$
$858$	−1.96746e12	−0.123940
$859$	−2.50929e13	−1.57247	−0.786234	−	0.617929i	$-0.787972\pi$
$859$	−2.50929e13	−1.57247	−0.786234	+	0.617929i	$0.787972\pi$
$860$	3.57804e12	0.223050
$861$	−5.91413e11	−0.0366755
$862$	−1.51767e12	−0.0936259
$863$	−3.41067e12	−0.209311	−0.104655	−	0.994509i	$-0.533374\pi$
$863$	−3.41067e12	−0.209311	−0.104655	+	0.994509i	$0.533374\pi$
$864$	4.36413e12	0.266432
$865$	8.86496e12	0.538399
$866$	2.55508e12	0.154374
$867$	0	0
$868$	−2.36766e12	−0.141573
$869$	−1.04252e13	−0.620149
$870$	−3.30811e11	−0.0195769
$871$	−2.84395e11	−0.0167433
$872$	−7.00593e12	−0.410338
$873$	2.66412e13	1.55235
$874$	−4.22846e12	−0.245121
$875$	3.33307e12	0.192224
$876$	4.49889e11	0.0258129
$877$	−1.30928e13	−0.747369	−0.373685	−	0.927556i	$-0.621906\pi$
$877$	−1.30928e13	−0.747369	−0.373685	+	0.927556i	$0.621906\pi$
$878$	2.14169e12	0.121627
$879$	−5.90802e12	−0.333804
$880$	−1.21254e13	−0.681589
$881$	−1.14786e13	−0.641943	−0.320971	−	0.947089i	$-0.604009\pi$
$881$	−1.14786e13	−0.641943	−0.320971	+	0.947089i	$0.604009\pi$
$882$	−2.09991e12	−0.116840
$883$	−2.06011e13	−1.14042	−0.570212	−	0.821497i	$-0.693139\pi$
$883$	−2.06011e13	−1.14042	−0.570212	+	0.821497i	$0.693139\pi$
$884$	0	0
$885$	−4.78498e12	−0.262201
$886$	4.70780e12	0.256665
$887$	3.14157e13	1.70408	0.852042	−	0.523474i	$-0.175364\pi$
$887$	3.14157e13	1.70408	0.852042	+	0.523474i	$0.175364\pi$
$888$	2.96738e12	0.160145
$889$	−3.54359e12	−0.190276
$890$	7.77292e11	0.0415269
$891$	−1.79189e13	−0.952491
$892$	3.95884e12	0.209376
$893$	−4.84507e12	−0.254958
$894$	1.34713e12	0.0705327
$895$	1.71178e13	0.891754
$896$	−2.26720e12	−0.117518
$897$	1.38550e13	0.714563
$898$	4.32515e12	0.221951
$899$	−1.04135e13	−0.531716
$900$	−1.27975e13	−0.650179
$901$	0	0
$902$	1.93665e12	0.0974142
$903$	7.03364e11	0.0352035
$904$	−3.18580e12	−0.158658
$905$	6.23770e11	0.0309105
$906$	8.70964e10	0.00429461
$907$	2.60421e13	1.27774	0.638870	−	0.769315i	$-0.279402\pi$
$907$	2.60421e13	1.27774	0.638870	+	0.769315i	$0.279402\pi$
$908$	2.07966e13	1.01533
$909$	8.13256e9	0.000395084 0
$910$	−5.54426e11	−0.0268014
$911$	1.36730e13	0.657705	0.328853	−	0.944381i	$-0.393338\pi$
$911$	1.36730e13	0.657705	0.328853	+	0.944381i	$0.393338\pi$
$912$	−1.02037e13	−0.488408
$913$	2.62809e13	1.25176
$914$	2.46463e12	0.116814
$915$	−3.56207e9	−0.000167999 0
$916$	−2.86138e13	−1.34291
$917$	−3.96675e12	−0.185256
$918$	0	0
$919$	−5.85920e12	−0.270968	−0.135484	−	0.990780i	$-0.543259\pi$
$919$	−5.85920e12	−0.270968	−0.135484	+	0.990780i	$0.543259\pi$
$920$	−3.50343e12	−0.161231
$921$	−1.96932e12	−0.0901877
$922$	2.34092e12	0.106684
$923$	−5.87224e13	−2.66315
$924$	−2.43296e12	−0.109802
$925$	−2.79865e13	−1.25693
$926$	1.11645e10	0.000498990 0
$927$	−8.59987e11	−0.0382501
$928$	−7.50482e12	−0.332181
$929$	3.04808e13	1.34263	0.671313	−	0.741174i	$-0.265731\pi$
$929$	3.04808e13	1.34263	0.671313	+	0.741174i	$0.265731\pi$
$930$	3.58601e11	0.0157195
$931$	3.25573e13	1.42028
$932$	1.65286e13	0.717569
$933$	−9.54497e12	−0.412389
$934$	−1.66651e12	−0.0716550
$935$	0	0
$936$	1.00021e13	0.425941
$937$	3.39079e13	1.43705	0.718526	−	0.695500i	$-0.244817\pi$
$937$	3.39079e13	1.43705	0.718526	+	0.695500i	$0.244817\pi$
$938$	6.99864e9	0.000295190 0
$939$	9.06742e12	0.380617
$940$	−1.98738e12	−0.0830244
$941$	−7.87407e11	−0.0327375	−0.0163688	−	0.999866i	$-0.505211\pi$
$941$	−7.87407e11	−0.0327375	−0.0163688	+	0.999866i	$0.505211\pi$
$942$	9.16411e11	0.0379194
$943$	−1.36381e13	−0.561630
$944$	−3.49856e13	−1.43389
$945$	1.75352e12	0.0715265
$946$	−2.30325e12	−0.0935042
$947$	3.22201e13	1.30182	0.650911	−	0.759154i	$-0.274387\pi$
$947$	3.22201e13	1.30182	0.650911	+	0.759154i	$0.274387\pi$
$948$	−3.59859e12	−0.144709
$949$	3.31625e12	0.132724
$950$	−3.94851e12	−0.157281
$951$	−4.03818e12	−0.160093
$952$	0	0
$953$	2.73548e13	1.07427	0.537137	−	0.843495i	$-0.319506\pi$
$953$	2.73548e13	1.07427	0.537137	+	0.843495i	$0.319506\pi$
$954$	−4.11800e12	−0.160960
$955$	−4.25576e12	−0.165562
$956$	−1.30415e13	−0.504973
$957$	−1.07008e13	−0.412392
$958$	3.87724e12	0.148723
$959$	1.18152e12	0.0451083
$960$	−4.01029e12	−0.152390
$961$	−1.51513e13	−0.573052
$962$	1.08289e13	0.407660
$963$	−1.85709e13	−0.695848
$964$	−2.06062e13	−0.768512
$965$	−6.62138e12	−0.245796
$966$	−3.40956e11	−0.0125980
$967$	−1.95420e13	−0.718703	−0.359351	−	0.933202i	$-0.617002\pi$
$967$	−1.95420e13	−0.718703	−0.359351	+	0.933202i	$0.617002\pi$
$968$	8.53534e12	0.312451
$969$	0	0
$970$	3.37167e12	0.122285
$971$	−1.61450e13	−0.582844	−0.291422	−	0.956595i	$-0.594128\pi$
$971$	−1.61450e13	−0.582844	−0.291422	+	0.956595i	$0.594128\pi$
$972$	−2.39945e13	−0.862210
$973$	−2.70916e12	−0.0969008
$974$	1.77298e12	0.0631230
$975$	1.29377e13	0.458497
$976$	−2.60442e10	−0.000918729 0
$977$	−3.98851e13	−1.40051	−0.700254	−	0.713894i	$-0.746930\pi$
$977$	−3.98851e13	−1.40051	−0.700254	+	0.713894i	$0.746930\pi$
$978$	−9.44399e11	−0.0330089
$979$	2.51431e13	0.874774
$980$	1.33545e13	0.462500
$981$	3.78364e13	1.30437
$982$	4.83532e12	0.165930
$983$	−1.43855e13	−0.491399	−0.245699	−	0.969346i	$-0.579018\pi$
$983$	−1.43855e13	−0.491399	−0.245699	+	0.969346i	$0.579018\pi$
$984$	1.35029e12	0.0459146
$985$	−7.25431e12	−0.245546
$986$	0	0
$987$	−3.90675e11	−0.0131036
$988$	−7.67729e13	−2.56331
$989$	1.62197e13	0.539087
$990$	−2.68681e12	−0.0888952
$991$	1.39476e13	0.459376	0.229688	−	0.973264i	$-0.426229\pi$
$991$	1.39476e13	0.459376	0.229688	+	0.973264i	$0.426229\pi$
$992$	8.13527e12	0.266728
$993$	−1.02217e13	−0.333619
$994$	1.44509e12	0.0469523
$995$	−2.44844e13	−0.791928
$996$	9.07166e12	0.292092
$997$	−3.99911e12	−0.128185	−0.0640923	−	0.997944i	$-0.520415\pi$
$997$	−3.99911e12	−0.128185	−0.0640923	+	0.997944i	$0.520415\pi$
$998$	−5.40185e12	−0.172367
$999$	−3.42493e13	−1.08795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.i.1.26		52
17.11	odd	16		17.10.d.a.2.7	✓	52
17.14	odd	16		17.10.d.a.9.7	yes	52
17.16	even	2	inner	289.10.a.i.1.25		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.d.a.2.7	✓	52	17.11	odd	16
17.10.d.a.9.7	yes	52	17.14	odd	16
289.10.a.i.1.25		52	17.16	even	2	inner
289.10.a.i.1.26		52	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)

\(f(q)\)	\(=\)	\(q-3.16073 q^{2} +48.7228 q^{3} -502.010 q^{4} +693.070 q^{5} -154.000 q^{6} -1403.76 q^{7} +3205.01 q^{8} -17309.1 q^{9} +O(q^{10})\)	\(q-3.16073 q^{2} +48.7228 q^{3} -502.010 q^{4} +693.070 q^{5} -154.000 q^{6} -1403.76 q^{7} +3205.01 q^{8} -17309.1 q^{9} -2190.61 q^{10} -70859.5 q^{11} -24459.3 q^{12} -180297. q^{13} +4436.90 q^{14} +33768.3 q^{15} +246899. q^{16} +54709.3 q^{18} -848219. q^{19} -347928. q^{20} -68395.0 q^{21} +223968. q^{22} -1.57720e6 q^{23} +156157. q^{24} -1.47278e6 q^{25} +569869. q^{26} -1.80236e6 q^{27} +704700. q^{28} +3.09944e6 q^{29} -106733. q^{30} -3.35981e6 q^{31} -2.42135e6 q^{32} -3.45248e6 q^{33} -972902. q^{35} +8.68933e6 q^{36} +1.90025e7 q^{37} +2.68099e6 q^{38} -8.78456e6 q^{39} +2.22130e6 q^{40} +8.64702e6 q^{41} +216178. q^{42} -1.02839e7 q^{43} +3.55722e7 q^{44} -1.19964e7 q^{45} +4.98510e6 q^{46} +5.71205e6 q^{47} +1.20296e7 q^{48} -3.83831e7 q^{49} +4.65506e6 q^{50} +9.05107e7 q^{52} -7.52705e7 q^{53} +5.69677e6 q^{54} -4.91106e7 q^{55} -4.49906e6 q^{56} -4.13277e7 q^{57} -9.79650e6 q^{58} -1.41700e8 q^{59} -1.69520e7 q^{60} -105485. q^{61} +1.06195e7 q^{62} +2.42977e7 q^{63} -1.18759e8 q^{64} -1.24958e8 q^{65} +1.09123e7 q^{66} +1.57737e6 q^{67} -7.68456e7 q^{69} +3.07508e6 q^{70} +3.25699e8 q^{71} -5.54758e7 q^{72} -1.83933e7 q^{73} -6.00617e7 q^{74} -7.17580e7 q^{75} +4.25814e8 q^{76} +9.94695e7 q^{77} +2.77656e7 q^{78} +1.47125e8 q^{79} +1.71118e8 q^{80} +2.52879e8 q^{81} -2.73309e7 q^{82} -3.70887e8 q^{83} +3.43350e7 q^{84} +3.25045e7 q^{86} +1.51014e8 q^{87} -2.27106e8 q^{88} -3.54830e8 q^{89} +3.79174e7 q^{90} +2.53093e8 q^{91} +7.91769e8 q^{92} -1.63700e8 q^{93} -1.80542e7 q^{94} -5.87875e8 q^{95} -1.17975e8 q^{96} -1.53915e9 q^{97} +1.21319e8 q^{98} +1.22651e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) \) 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9} + 156200 q^{13} + 1207872 q^{15} + 3407880 q^{16} + 2193336 q^{18} + 1185568 q^{19} + 5198336 q^{21} + 13827692 q^{25} + 3618944 q^{26} - 9167544 q^{30} + 61884888 q^{32} + 1635208 q^{33} + 46992776 q^{35} + 156027320 q^{36} + 84813952 q^{38} - 4635776 q^{42} + 125448912 q^{43} + 164193176 q^{47} + 270850284 q^{49} - 226223888 q^{50} + 103553016 q^{52} + 426167208 q^{53} + 677761520 q^{55} + 375214512 q^{59} + 336918024 q^{60} + 190014416 q^{64} + 1377178928 q^{66} + 311910088 q^{67} + 533688136 q^{69} + 1477690280 q^{70} + 2757942680 q^{72} + 4047975520 q^{76} + 3440336432 q^{77} + 3266558756 q^{81} + 2072890608 q^{83} + 2630025952 q^{84} + 1538547296 q^{86} - 1010436256 q^{87} + 1873849184 q^{89} - 1998451624 q^{93} - 6880776704 q^{94} - 4667454128 q^{98}+O(q^{100}) \) 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9 + 156200 * q^13 + 1207872 * q^15 + 3407880 * q^16 + 2193336 * q^18 + 1185568 * q^19 + 5198336 * q^21 + 13827692 * q^25 + 3618944 * q^26 - 9167544 * q^30 + 61884888 * q^32 + 1635208 * q^33 + 46992776 * q^35 + 156027320 * q^36 + 84813952 * q^38 - 4635776 * q^42 + 125448912 * q^43 + 164193176 * q^47 + 270850284 * q^49 - 226223888 * q^50 + 103553016 * q^52 + 426167208 * q^53 + 677761520 * q^55 + 375214512 * q^59 + 336918024 * q^60 + 190014416 * q^64 + 1377178928 * q^66 + 311910088 * q^67 + 533688136 * q^69 + 1477690280 * q^70 + 2757942680 * q^72 + 4047975520 * q^76 + 3440336432 * q^77 + 3266558756 * q^81 + 2072890608 * q^83 + 2630025952 * q^84 + 1538547296 * q^86 - 1010436256 * q^87 + 1873849184 * q^89 - 1998451624 * q^93 - 6880776704 * q^94 - 4667454128 * q^98

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