LMFDB - Embedded newform 289.10.a.i.1.16

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			1.16
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)

$f(q)$	$=$	$q-24.0067 q^{2} +194.286 q^{3} +64.3195 q^{4} -2543.89 q^{5} -4664.15 q^{6} +1962.84 q^{7} +10747.3 q^{8} +18063.9 q^{9} +O(q^{10})$	\(q-24.0067 q^{2} +194.286 q^{3} +64.3195 q^{4} -2543.89 q^{5} -4664.15 q^{6} +1962.84 q^{7} +10747.3 q^{8} +18063.9 q^{9} +61070.2 q^{10} -18226.6 q^{11} +12496.4 q^{12} -165432. q^{13} -47121.2 q^{14} -494241. q^{15} -290939. q^{16} -433653. q^{18} +137579. q^{19} -163622. q^{20} +381352. q^{21} +437559. q^{22} -695539. q^{23} +2.08805e6 q^{24} +4.51824e6 q^{25} +3.97148e6 q^{26} -314571. q^{27} +126249. q^{28} -4.23015e6 q^{29} +1.18651e7 q^{30} -3.78840e6 q^{31} +1.48184e6 q^{32} -3.54116e6 q^{33} -4.99325e6 q^{35} +1.16186e6 q^{36} +1.18678e7 q^{37} -3.30282e6 q^{38} -3.21411e7 q^{39} -2.73399e7 q^{40} -9.83530e6 q^{41} -9.15498e6 q^{42} -3.54345e7 q^{43} -1.17233e6 q^{44} -4.59525e7 q^{45} +1.66976e7 q^{46} +5.08554e7 q^{47} -5.65252e7 q^{48} -3.65009e7 q^{49} -1.08468e8 q^{50} -1.06405e7 q^{52} +1.55202e7 q^{53} +7.55180e6 q^{54} +4.63664e7 q^{55} +2.10953e7 q^{56} +2.67297e7 q^{57} +1.01552e8 q^{58} -9.29686e7 q^{59} -3.17893e7 q^{60} -2.04285e8 q^{61} +9.09468e7 q^{62} +3.54565e7 q^{63} +1.13387e8 q^{64} +4.20841e8 q^{65} +8.50115e7 q^{66} +5.35413e7 q^{67} -1.35133e8 q^{69} +1.19871e8 q^{70} -1.33664e8 q^{71} +1.94138e8 q^{72} +4.37702e7 q^{73} -2.84906e8 q^{74} +8.77828e8 q^{75} +8.84904e6 q^{76} -3.57759e7 q^{77} +7.71600e8 q^{78} +1.37020e8 q^{79} +7.40115e8 q^{80} -4.16668e8 q^{81} +2.36113e8 q^{82} -4.10757e8 q^{83} +2.45284e7 q^{84} +8.50664e8 q^{86} -8.21856e8 q^{87} -1.95887e8 q^{88} +2.89162e8 q^{89} +1.10317e9 q^{90} -3.24717e8 q^{91} -4.47367e7 q^{92} -7.36032e8 q^{93} -1.22087e9 q^{94} -3.49986e8 q^{95} +2.87900e8 q^{96} -2.82905e8 q^{97} +8.76264e8 q^{98} -3.29243e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−24.0067	−1.06095	−0.530477	−	0.847699i	$-0.677987\pi$
$2$	−24.0067	−1.06095	−0.530477	+	0.847699i	$0.677987\pi$
$3$	194.286	1.38483	0.692413	−	0.721502i	$-0.256548\pi$
$3$	194.286	1.38483	0.692413	+	0.721502i	$0.256548\pi$
$4$	64.3195	0.125624
$5$	−2543.89	−1.82026	−0.910129	−	0.414326i	$-0.864018\pi$
$5$	−2543.89	−1.82026	−0.910129	+	0.414326i	$0.864018\pi$
$6$	−4664.15	−1.46924
$7$	1962.84	0.308990	0.154495	−	0.987994i	$-0.450625\pi$
$7$	1962.84	0.308990	0.154495	+	0.987994i	$0.450625\pi$
$8$	10747.3	0.927673
$9$	18063.9	0.917740
$10$	61070.2	1.93121
$11$	−18226.6	−0.375352	−0.187676	−	0.982231i	$-0.560095\pi$
$11$	−18226.6	−0.375352	−0.187676	+	0.982231i	$0.560095\pi$
$12$	12496.4	0.173967
$13$	−165432.	−1.60648	−0.803240	−	0.595656i	$-0.796892\pi$
$13$	−165432.	−1.60648	−0.803240	+	0.595656i	$0.796892\pi$
$14$	−47121.2	−0.327824
$15$	−494241.	−2.52074
$16$	−290939.	−1.10984
$17$	0	0
$17$	0	0
$18$	−433653.	−0.973681
$19$	137579.	0.242193	0.121097	−	0.992641i	$-0.461359\pi$
$19$	137579.	0.242193	0.121097	+	0.992641i	$0.461359\pi$
$20$	−163622.	−0.228668
$21$	381352.	0.427897
$22$	437559.	0.398231
$23$	−695539.	−0.518258	−0.259129	−	0.965843i	$-0.583435\pi$
$23$	−695539.	−0.518258	−0.259129	+	0.965843i	$0.583435\pi$
$24$	2.08805e6	1.28466
$25$	4.51824e6	2.31334
$26$	3.97148e6	1.70440
$27$	−314571.	−0.113915
$28$	126249.	0.0388165
$29$	−4.23015e6	−1.11062	−0.555309	−	0.831644i	$-0.687400\pi$
$29$	−4.23015e6	−1.11062	−0.555309	+	0.831644i	$0.687400\pi$
$30$	1.18651e7	2.67439
$31$	−3.78840e6	−0.736764	−0.368382	−	0.929675i	$-0.620088\pi$
$31$	−3.78840e6	−0.736764	−0.368382	+	0.929675i	$0.620088\pi$
$32$	1.48184e6	0.249819
$33$	−3.54116e6	−0.519796
$34$	0	0
$35$	−4.99325e6	−0.562441
$36$	1.16186e6	0.115290
$37$	1.18678e7	1.04103	0.520513	−	0.853854i	$-0.325741\pi$
$37$	1.18678e7	1.04103	0.520513	+	0.853854i	$0.325741\pi$
$38$	−3.30282e6	−0.256956
$39$	−3.21411e7	−2.22469
$40$	−2.73399e7	−1.68860
$41$	−9.83530e6	−0.543576	−0.271788	−	0.962357i	$-0.587615\pi$
$41$	−9.83530e6	−0.543576	−0.271788	+	0.962357i	$0.587615\pi$
$42$	−9.15498e6	−0.453979
$43$	−3.54345e7	−1.58059	−0.790293	−	0.612729i	$-0.790072\pi$
$43$	−3.54345e7	−1.58059	−0.790293	+	0.612729i	$0.790072\pi$
$44$	−1.17233e6	−0.0471532
$45$	−4.59525e7	−1.67052
$46$	1.66976e7	0.549848
$47$	5.08554e7	1.52018	0.760092	−	0.649815i	$-0.225154\pi$
$47$	5.08554e7	1.52018	0.760092	+	0.649815i	$0.225154\pi$
$48$	−5.65252e7	−1.53694
$49$	−3.65009e7	−0.904525
$50$	−1.08468e8	−2.45435
$51$	0	0
$52$	−1.06405e7	−0.201813
$53$	1.55202e7	0.270182	0.135091	−	0.990833i	$-0.456867\pi$
$53$	1.55202e7	0.270182	0.135091	+	0.990833i	$0.456867\pi$
$54$	7.55180e6	0.120859
$55$	4.63664e7	0.683237
$56$	2.10953e7	0.286641
$57$	2.67297e7	0.335395
$58$	1.01552e8	1.17831
$59$	−9.29686e7	−0.998854	−0.499427	−	0.866356i	$-0.666456\pi$
$59$	−9.29686e7	−0.998854	−0.499427	+	0.866356i	$0.666456\pi$
$60$	−3.17893e7	−0.316665
$61$	−2.04285e8	−1.88909	−0.944543	−	0.328387i	$-0.893495\pi$
$61$	−2.04285e8	−1.88909	−0.944543	+	0.328387i	$0.893495\pi$
$62$	9.09468e7	0.781673
$63$	3.54565e7	0.283572
$64$	1.13387e8	0.844796
$65$	4.20841e8	2.92421
$66$	8.50115e7	0.551480
$67$	5.35413e7	0.324603	0.162301	−	0.986741i	$-0.448108\pi$
$67$	5.35413e7	0.324603	0.162301	+	0.986741i	$0.448108\pi$
$68$	0	0
$69$	−1.35133e8	−0.717697
$70$	1.19871e8	0.596724
$71$	−1.33664e8	−0.624242	−0.312121	−	0.950042i	$-0.601039\pi$
$71$	−1.33664e8	−0.624242	−0.312121	+	0.950042i	$0.601039\pi$
$72$	1.94138e8	0.851363
$73$	4.37702e7	0.180395	0.0901977	−	0.995924i	$-0.471250\pi$
$73$	4.37702e7	0.180395	0.0901977	+	0.995924i	$0.471250\pi$
$74$	−2.84906e8	−1.10448
$75$	8.77828e8	3.20357
$76$	8.84904e6	0.0304253
$77$	−3.57759e7	−0.115980
$78$	7.71600e8	2.36030
$79$	1.37020e8	0.395787	0.197893	−	0.980224i	$-0.436590\pi$
$79$	1.37020e8	0.395787	0.197893	+	0.980224i	$0.436590\pi$
$80$	7.40115e8	2.02020
$81$	−4.16668e8	−1.07549
$82$	2.36113e8	0.576709
$83$	−4.10757e8	−0.950023	−0.475011	−	0.879980i	$-0.657556\pi$
$83$	−4.10757e8	−0.950023	−0.475011	+	0.879980i	$0.657556\pi$
$84$	2.45284e7	0.0537541
$85$	0	0
$86$	8.50664e8	1.67693
$87$	−8.21856e8	−1.53801
$88$	−1.95887e8	−0.348204
$89$	2.89162e8	0.488524	0.244262	−	0.969709i	$-0.421454\pi$
$89$	2.89162e8	0.488524	0.244262	+	0.969709i	$0.421454\pi$
$90$	1.10317e9	1.77235
$91$	−3.24717e8	−0.496385
$92$	−4.47367e7	−0.0651057
$93$	−7.36032e8	−1.02029
$94$	−1.22087e9	−1.61285
$95$	−3.49986e8	−0.440854
$96$	2.87900e8	0.345956
$97$	−2.82905e8	−0.324465	−0.162233	−	0.986753i	$-0.551869\pi$
$97$	−2.82905e8	−0.324465	−0.162233	+	0.986753i	$0.551869\pi$
$98$	8.76264e8	0.959660
$99$	−3.29243e8	−0.344475
$100$	2.90611e8	0.290611
$101$	2.20849e8	0.211179	0.105589	−	0.994410i	$-0.466327\pi$
$101$	2.20849e8	0.211179	0.105589	+	0.994410i	$0.466327\pi$
$102$	0	0
$103$	−1.05360e8	−0.0922372	−0.0461186	−	0.998936i	$-0.514685\pi$
$103$	−1.05360e8	−0.0922372	−0.0461186	+	0.998936i	$0.514685\pi$
$104$	−1.77795e9	−1.49029
$105$	−9.70116e8	−0.778882
$106$	−3.72588e8	−0.286651
$107$	4.96752e8	0.366364	0.183182	−	0.983079i	$-0.441360\pi$
$107$	4.96752e8	0.366364	0.183182	+	0.983079i	$0.441360\pi$
$108$	−2.02331e7	−0.0143105
$109$	6.36599e8	0.431963	0.215982	−	0.976397i	$-0.430705\pi$
$109$	6.36599e8	0.431963	0.215982	+	0.976397i	$0.430705\pi$
$110$	−1.11310e9	−0.724883
$111$	2.30574e9	1.44164
$112$	−5.71066e8	−0.342930
$113$	9.53685e8	0.550240	0.275120	−	0.961410i	$-0.411282\pi$
$113$	9.53685e8	0.550240	0.275120	+	0.961410i	$0.411282\pi$
$114$	−6.41690e8	−0.355839
$115$	1.76937e9	0.943363
$116$	−2.72081e8	−0.139520
$117$	−2.98835e9	−1.47433
$118$	2.23186e9	1.05974
$119$	0	0
$120$	−5.31176e9	−2.33842
$121$	−2.02574e9	−0.859111
$122$	4.90419e9	2.00423
$123$	−1.91086e9	−0.752757
$124$	−2.43668e8	−0.0925553
$125$	−6.52536e9	−2.39061
$126$	−8.51193e8	−0.300857
$127$	5.40081e9	1.84222	0.921111	−	0.389299i	$-0.127283\pi$
$127$	5.40081e9	1.84222	0.921111	+	0.389299i	$0.127283\pi$
$128$	−3.48073e9	−1.14611
$129$	−6.88441e9	−2.18884
$130$	−1.01030e10	−3.10245
$131$	2.76594e9	0.820582	0.410291	−	0.911955i	$-0.365427\pi$
$131$	2.76594e9	0.820582	0.410291	+	0.911955i	$0.365427\pi$
$132$	−2.27766e8	−0.0652989
$133$	2.70046e8	0.0748352
$134$	−1.28535e9	−0.344389
$135$	8.00233e8	0.207355
$136$	0	0
$137$	−3.06041e9	−0.742228	−0.371114	−	0.928587i	$-0.621024\pi$
$137$	−3.06041e9	−0.742228	−0.371114	+	0.928587i	$0.621024\pi$
$138$	3.24409e9	0.761443
$139$	−3.55042e9	−0.806702	−0.403351	−	0.915045i	$-0.632155\pi$
$139$	−3.55042e9	−0.806702	−0.403351	+	0.915045i	$0.632155\pi$
$140$	−3.21163e8	−0.0706561
$141$	9.88046e9	2.10519
$142$	3.20883e9	0.662292
$143$	3.01527e9	0.602995
$144$	−5.25548e9	−1.01855
$145$	1.07610e10	2.02161
$146$	−1.05078e9	−0.191391
$147$	−7.09159e9	−1.25261
$148$	7.63330e8	0.130778
$149$	−3.88137e9	−0.645130	−0.322565	−	0.946547i	$-0.604545\pi$
$149$	−3.88137e9	−0.645130	−0.322565	+	0.946547i	$0.604545\pi$
$150$	−2.10737e10	−3.39884
$151$	8.28467e9	1.29682	0.648409	−	0.761292i	$-0.275435\pi$
$151$	8.28467e9	1.29682	0.648409	+	0.761292i	$0.275435\pi$
$152$	1.47861e9	0.224676
$153$	0	0
$154$	8.58860e8	0.123049
$155$	9.63727e9	1.34110
$156$	−2.06730e9	−0.279475
$157$	−1.15724e10	−1.52011	−0.760053	−	0.649861i	$-0.774827\pi$
$157$	−1.15724e10	−1.52011	−0.760053	+	0.649861i	$0.774827\pi$
$158$	−3.28939e9	−0.419912
$159$	3.01535e9	0.374155
$160$	−3.76963e9	−0.454736
$161$	−1.36523e9	−0.160136
$162$	1.00028e10	1.14105
$163$	−7.06563e9	−0.783983	−0.391991	−	0.919969i	$-0.628214\pi$
$163$	−7.06563e9	−0.783983	−0.391991	+	0.919969i	$0.628214\pi$
$164$	−6.32602e8	−0.0682862
$165$	9.00832e9	0.946163
$166$	9.86091e9	1.00793
$167$	9.51502e9	0.946642	0.473321	−	0.880890i	$-0.343055\pi$
$167$	9.51502e9	0.946642	0.473321	+	0.880890i	$0.343055\pi$
$168$	4.09850e9	0.396948
$169$	1.67633e10	1.58078
$170$	0	0
$171$	2.48522e9	0.222270
$172$	−2.27913e9	−0.198560
$173$	1.34873e10	1.14477	0.572385	−	0.819985i	$-0.306018\pi$
$173$	1.34873e10	1.14477	0.572385	+	0.819985i	$0.306018\pi$
$174$	1.97300e10	1.63176
$175$	8.86858e9	0.714797
$176$	5.30282e9	0.416581
$177$	−1.80625e10	−1.38324
$178$	−6.94181e9	−0.518302
$179$	−2.32156e10	−1.69021	−0.845107	−	0.534597i	$-0.820463\pi$
$179$	−2.32156e10	−1.69021	−0.845107	+	0.534597i	$0.820463\pi$
$180$	−2.95564e9	−0.209858
$181$	1.04604e10	0.724425	0.362212	−	0.932096i	$-0.382022\pi$
$181$	1.04604e10	0.724425	0.362212	+	0.932096i	$0.382022\pi$
$182$	7.79537e9	0.526642
$183$	−3.96896e10	−2.61605
$184$	−7.47517e9	−0.480774
$185$	−3.01903e10	−1.89493
$186$	1.76697e10	1.08248
$187$	0	0
$188$	3.27099e9	0.190972
$189$	−6.17453e8	−0.0351986
$190$	8.40200e9	0.467726
$191$	2.86896e10	1.55982	0.779909	−	0.625893i	$-0.215265\pi$
$191$	2.86896e10	1.55982	0.779909	+	0.625893i	$0.215265\pi$
$192$	2.20294e10	1.16989
$193$	1.05634e9	0.0548022	0.0274011	−	0.999625i	$-0.491277\pi$
$193$	1.05634e9	0.0548022	0.0274011	+	0.999625i	$0.491277\pi$
$194$	6.79161e9	0.344243
$195$	8.17633e10	4.04951
$196$	−2.34772e9	−0.113630
$197$	−1.48923e9	−0.0704474	−0.0352237	−	0.999379i	$-0.511214\pi$
$197$	−1.48923e9	−0.0704474	−0.0352237	+	0.999379i	$0.511214\pi$
$198$	7.90402e9	0.365473
$199$	1.25548e10	0.567504	0.283752	−	0.958898i	$-0.408421\pi$
$199$	1.25548e10	0.567504	0.283752	+	0.958898i	$0.408421\pi$
$200$	4.85589e10	2.14602
$201$	1.04023e10	0.449518
$202$	−5.30186e9	−0.224051
$203$	−8.30310e9	−0.343169
$204$	0	0
$205$	2.50199e10	0.989448
$206$	2.52933e9	0.0978595
$207$	−1.25641e10	−0.475626
$208$	4.81306e10	1.78294
$209$	−2.50760e9	−0.0909076
$210$	2.32892e10	0.826358
$211$	−3.03540e10	−1.05425	−0.527127	−	0.849787i	$-0.676731\pi$
$211$	−3.03540e10	−1.05425	−0.527127	+	0.849787i	$0.676731\pi$
$212$	9.98253e8	0.0339414
$213$	−2.59691e10	−0.864466
$214$	−1.19253e10	−0.388695
$215$	9.01413e10	2.87707
$216$	−3.38079e9	−0.105676
$217$	−7.43603e9	−0.227652
$218$	−1.52826e10	−0.458293
$219$	8.50392e9	0.249816
$220$	2.98226e9	0.0858310
$221$	0	0
$222$	−5.53530e10	−1.52951
$223$	2.73787e10	0.741380	0.370690	−	0.928757i	$-0.379121\pi$
$223$	2.73787e10	0.741380	0.370690	+	0.928757i	$0.379121\pi$
$224$	2.90862e9	0.0771916
$225$	8.16169e10	2.12304
$226$	−2.28948e10	−0.583779
$227$	3.41868e10	0.854560	0.427280	−	0.904119i	$-0.359472\pi$
$227$	3.41868e10	0.854560	0.427280	+	0.904119i	$0.359472\pi$
$228$	1.71924e9	0.0421337
$229$	3.42397e9	0.0822753	0.0411377	−	0.999153i	$-0.486902\pi$
$229$	3.42397e9	0.0822753	0.0411377	+	0.999153i	$0.486902\pi$
$230$	−4.24767e10	−1.00087
$231$	−6.95074e9	−0.160612
$232$	−4.54627e10	−1.03029
$233$	3.46809e10	0.770882	0.385441	−	0.922732i	$-0.374049\pi$
$233$	3.46809e10	0.770882	0.385441	+	0.922732i	$0.374049\pi$
$234$	7.17403e10	1.56420
$235$	−1.29370e11	−2.76713
$236$	−5.97970e9	−0.125480
$237$	2.66210e10	0.548096
$238$	0	0
$239$	6.84083e10	1.35618	0.678092	−	0.734977i	$-0.262807\pi$
$239$	6.84083e10	1.35618	0.678092	+	0.734977i	$0.262807\pi$
$240$	1.43794e11	2.79762
$241$	−2.87585e10	−0.549148	−0.274574	−	0.961566i	$-0.588537\pi$
$241$	−2.87585e10	−0.549148	−0.274574	+	0.961566i	$0.588537\pi$
$242$	4.86312e10	0.911478
$243$	−7.47609e10	−1.37545
$244$	−1.31395e10	−0.237315
$245$	9.28541e10	1.64647
$246$	4.58733e10	0.798641
$247$	−2.27601e10	−0.389078
$248$	−4.07151e10	−0.683476
$249$	−7.98042e10	−1.31562
$250$	1.56652e11	2.53633
$251$	5.08079e10	0.807978	0.403989	−	0.914764i	$-0.367623\pi$
$251$	5.08079e10	0.807978	0.403989	+	0.914764i	$0.367623\pi$
$252$	2.28055e9	0.0356235
$253$	1.26773e10	0.194529
$254$	−1.29655e11	−1.95451
$255$	0	0
$256$	2.55069e10	0.371174
$257$	4.43960e10	0.634811	0.317406	−	0.948290i	$-0.397188\pi$
$257$	4.43960e10	0.634811	0.317406	+	0.948290i	$0.397188\pi$
$258$	1.65272e11	2.32225
$259$	2.32945e10	0.321666
$260$	2.70683e10	0.367351
$261$	−7.64129e10	−1.01926
$262$	−6.64010e10	−0.870600
$263$	4.45406e10	0.574057	0.287028	−	0.957922i	$-0.407333\pi$
$263$	4.45406e10	0.574057	0.287028	+	0.957922i	$0.407333\pi$
$264$	−3.80580e10	−0.482201
$265$	−3.94817e10	−0.491801
$266$	−6.48291e9	−0.0793967
$267$	5.61800e10	0.676520
$268$	3.44375e9	0.0407779
$269$	7.75647e10	0.903189	0.451594	−	0.892223i	$-0.350855\pi$
$269$	7.75647e10	0.903189	0.451594	+	0.892223i	$0.350855\pi$
$270$	−1.92109e10	−0.219994
$271$	2.04736e10	0.230586	0.115293	−	0.993332i	$-0.463219\pi$
$271$	2.04736e10	0.230586	0.115293	+	0.993332i	$0.463219\pi$
$272$	0	0
$273$	−6.30879e10	−0.687407
$274$	7.34703e10	0.787470
$275$	−8.23521e10	−0.868315
$276$	−8.69170e9	−0.0901600
$277$	9.13323e10	0.932106	0.466053	−	0.884757i	$-0.345676\pi$
$277$	9.13323e10	0.932106	0.466053	+	0.884757i	$0.345676\pi$
$278$	8.52337e10	0.855874
$279$	−6.84332e10	−0.676158
$280$	−5.36640e10	−0.521761
$281$	1.59049e11	1.52179	0.760893	−	0.648877i	$-0.224761\pi$
$281$	1.59049e11	1.52179	0.760893	+	0.648877i	$0.224761\pi$
$282$	−2.37197e11	−2.23351
$283$	4.93813e10	0.457639	0.228820	−	0.973469i	$-0.426513\pi$
$283$	4.93813e10	0.457639	0.228820	+	0.973469i	$0.426513\pi$
$284$	−8.59723e9	−0.0784198
$285$	−6.79973e10	−0.610506
$286$	−7.23865e10	−0.639750
$287$	−1.93051e10	−0.167959
$288$	2.67678e10	0.229269
$289$	0	0
$290$	−2.58336e11	−2.14484
$291$	−5.49644e10	−0.449328
$292$	2.81528e9	0.0226620
$293$	9.46411e10	0.750197	0.375099	−	0.926985i	$-0.377609\pi$
$293$	9.46411e10	0.750197	0.375099	+	0.926985i	$0.377609\pi$
$294$	1.70245e11	1.32896
$295$	2.36502e11	1.81817
$296$	1.27547e11	0.965731
$297$	5.73356e9	0.0427583
$298$	9.31787e10	0.684453
$299$	1.15065e11	0.832571
$300$	5.64615e10	0.402445
$301$	−6.95523e10	−0.488385
$302$	−1.98887e11	−1.37586
$303$	4.29079e10	0.292446
$304$	−4.00271e10	−0.268796
$305$	5.19677e11	3.43862
$306$	0	0
$307$	1.91043e11	1.22746	0.613731	−	0.789515i	$-0.289668\pi$
$307$	1.91043e11	1.22746	0.613731	+	0.789515i	$0.289668\pi$
$308$	−2.30109e9	−0.0145699
$309$	−2.04698e10	−0.127732
$310$	−2.31359e11	−1.42285
$311$	1.82343e11	1.10526	0.552632	−	0.833425i	$-0.313623\pi$
$311$	1.82343e11	1.10526	0.552632	+	0.833425i	$0.313623\pi$
$312$	−3.45430e11	−2.06379
$313$	−2.16835e11	−1.27697	−0.638483	−	0.769636i	$-0.720438\pi$
$313$	−2.16835e11	−1.27697	−0.638483	+	0.769636i	$0.720438\pi$
$314$	2.77814e11	1.61276
$315$	−9.01974e10	−0.516174
$316$	8.81305e9	0.0497204
$317$	−2.39301e11	−1.33100	−0.665499	−	0.746399i	$-0.731781\pi$
$317$	−2.39301e11	−1.33100	−0.665499	+	0.746399i	$0.731781\pi$
$318$	−7.23885e10	−0.396961
$319$	7.71011e10	0.416872
$320$	−2.88443e11	−1.53775
$321$	9.65117e10	0.507350
$322$	3.27747e10	0.169897
$323$	0	0
$324$	−2.67999e10	−0.135108
$325$	−7.47462e11	−3.71633
$326$	1.69622e11	0.831770
$327$	1.23682e11	0.598194
$328$	−1.05703e11	−0.504260
$329$	9.98210e10	0.469721
$330$	−2.16260e11	−1.00384
$331$	−2.69499e11	−1.23404	−0.617022	−	0.786946i	$-0.711661\pi$
$331$	−2.69499e11	−1.23404	−0.617022	+	0.786946i	$0.711661\pi$
$332$	−2.64197e10	−0.119346
$333$	2.14378e11	0.955391
$334$	−2.28424e11	−1.00434
$335$	−1.36203e11	−0.590860
$336$	−1.10950e11	−0.474898
$337$	−1.88865e11	−0.797657	−0.398828	−	0.917026i	$-0.630583\pi$
$337$	−1.88865e11	−0.797657	−0.398828	+	0.917026i	$0.630583\pi$
$338$	−4.02432e11	−1.67713
$339$	1.85287e11	0.761985
$340$	0	0
$341$	6.90496e10	0.276546
$342$	−5.96617e10	−0.235819
$343$	−1.50853e11	−0.588479
$344$	−3.80825e11	−1.46627
$345$	3.43763e11	1.30639
$346$	−3.23786e11	−1.21455
$347$	1.69621e11	0.628054	0.314027	−	0.949414i	$-0.398322\pi$
$347$	1.69621e11	0.628054	0.314027	+	0.949414i	$0.398322\pi$
$348$	−5.28614e10	−0.193211
$349$	−3.05069e11	−1.10074	−0.550369	−	0.834922i	$-0.685513\pi$
$349$	−3.05069e11	−1.10074	−0.550369	+	0.834922i	$0.685513\pi$
$350$	−2.12905e11	−0.758367
$351$	5.20402e10	0.183002
$352$	−2.70089e10	−0.0937702
$353$	−1.48766e10	−0.0509938	−0.0254969	−	0.999675i	$-0.508117\pi$
$353$	−1.48766e10	−0.0509938	−0.0254969	+	0.999675i	$0.508117\pi$
$354$	4.33619e11	1.46755
$355$	3.40027e11	1.13628
$356$	1.85988e10	0.0613704
$357$	0	0
$358$	5.57329e11	1.79324
$359$	−8.13885e10	−0.258606	−0.129303	−	0.991605i	$-0.541274\pi$
$359$	−8.13885e10	−0.258606	−0.129303	+	0.991605i	$0.541274\pi$
$360$	−4.93866e11	−1.54970
$361$	−3.03760e11	−0.941342
$362$	−2.51118e11	−0.768582
$363$	−3.93572e11	−1.18972
$364$	−2.08857e10	−0.0623580
$365$	−1.11346e11	−0.328366
$366$	9.52814e11	2.77551
$367$	2.76299e11	0.795028	0.397514	−	0.917596i	$-0.369873\pi$
$367$	2.76299e11	0.795028	0.397514	+	0.917596i	$0.369873\pi$
$368$	2.02359e11	0.575185
$369$	−1.77664e11	−0.498861
$370$	7.24767e11	2.01044
$371$	3.04637e10	0.0834834
$372$	−4.73412e10	−0.128173
$373$	6.75562e10	0.180707	0.0903536	−	0.995910i	$-0.471200\pi$
$373$	6.75562e10	0.180707	0.0903536	+	0.995910i	$0.471200\pi$
$374$	0	0
$375$	−1.26778e12	−3.31058
$376$	5.46558e11	1.41023
$377$	6.99803e11	1.78418
$378$	1.48230e10	0.0373441
$379$	−2.28533e10	−0.0568948	−0.0284474	−	0.999595i	$-0.509056\pi$
$379$	−2.28533e10	−0.0568948	−0.0284474	+	0.999595i	$0.509056\pi$
$380$	−2.25110e10	−0.0553819
$381$	1.04930e12	2.55116
$382$	−6.88741e11	−1.65490
$383$	5.41458e11	1.28579	0.642896	−	0.765954i	$-0.277733\pi$
$383$	5.41458e11	1.28579	0.642896	+	0.765954i	$0.277733\pi$
$384$	−6.76256e11	−1.58716
$385$	9.10098e10	0.211113
$386$	−2.53593e10	−0.0581426
$387$	−6.40084e11	−1.45057
$388$	−1.81963e10	−0.0407607
$389$	−2.43923e11	−0.540107	−0.270054	−	0.962845i	$-0.587041\pi$
$389$	−2.43923e11	−0.540107	−0.270054	+	0.962845i	$0.587041\pi$
$390$	−1.96286e12	−4.29635
$391$	0	0
$392$	−3.92286e11	−0.839104
$393$	5.37382e11	1.13636
$394$	3.57515e10	0.0747415
$395$	−3.48563e11	−0.720434
$396$	−2.11768e10	−0.0432744
$397$	6.74857e11	1.36350	0.681749	−	0.731586i	$-0.261220\pi$
$397$	6.74857e11	1.36350	0.681749	+	0.731586i	$0.261220\pi$
$398$	−3.01398e11	−0.602096
$399$	5.24661e10	0.103634
$400$	−1.31453e12	−2.56744
$401$	3.75361e11	0.724937	0.362468	−	0.931996i	$-0.381934\pi$
$401$	3.75361e11	0.724937	0.362468	+	0.931996i	$0.381934\pi$
$402$	−2.49724e11	−0.476918
$403$	6.26724e11	1.18360
$404$	1.42049e10	0.0265291
$405$	1.05996e12	1.95767
$406$	1.99330e11	0.364087
$407$	−2.16309e11	−0.390751
$408$	0	0
$409$	6.31772e11	1.11636	0.558182	−	0.829719i	$-0.311499\pi$
$409$	6.31772e11	1.11636	0.558182	+	0.829719i	$0.311499\pi$
$410$	−6.00644e11	−1.04976
$411$	−5.94594e11	−1.02786
$412$	−6.77668e9	−0.0115872
$413$	−1.82482e11	−0.308636
$414$	3.01623e11	0.504618
$415$	1.04492e12	1.72929
$416$	−2.45144e11	−0.401330
$417$	−6.89795e11	−1.11714
$418$	6.01991e10	0.0964488
$419$	−5.81662e11	−0.921951	−0.460975	−	0.887413i	$-0.652500\pi$
$419$	−5.81662e11	−0.921951	−0.460975	+	0.887413i	$0.652500\pi$
$420$	−6.23974e10	−0.0978463
$421$	3.73500e11	0.579457	0.289729	−	0.957109i	$-0.406435\pi$
$421$	3.73500e11	0.579457	0.289729	+	0.957109i	$0.406435\pi$
$422$	7.28698e11	1.11851
$423$	9.18645e11	1.39513
$424$	1.66801e11	0.250640
$425$	0	0
$426$	6.23430e11	0.917159
$427$	−4.00979e11	−0.583708
$428$	3.19508e10	0.0460241
$429$	5.85823e11	0.835042
$430$	−2.16399e12	−3.05244
$431$	−1.32118e12	−1.84423	−0.922113	−	0.386920i	$-0.873539\pi$
$431$	−1.32118e12	−1.84423	−0.922113	+	0.386920i	$0.873539\pi$
$432$	9.15208e10	0.126428
$433$	4.56730e11	0.624401	0.312201	−	0.950016i	$-0.398934\pi$
$433$	4.56730e11	0.624401	0.312201	+	0.950016i	$0.398934\pi$
$434$	1.78514e11	0.241529
$435$	2.09071e12	2.79958
$436$	4.09458e10	0.0542650
$437$	−9.56917e10	−0.125519
$438$	−2.04151e11	−0.265043
$439$	−2.27163e11	−0.291909	−0.145954	−	0.989291i	$-0.546625\pi$
$439$	−2.27163e11	−0.291909	−0.145954	+	0.989291i	$0.546625\pi$
$440$	4.98314e11	0.633820
$441$	−6.59347e11	−0.830119
$442$	0	0
$443$	1.03387e12	1.27541	0.637706	−	0.770280i	$-0.279883\pi$
$443$	1.03387e12	1.27541	0.637706	+	0.770280i	$0.279883\pi$
$444$	1.48304e11	0.181105
$445$	−7.35595e11	−0.889239
$446$	−6.57271e11	−0.786571
$447$	−7.54094e11	−0.893392
$448$	2.22560e11	0.261033
$449$	−1.06299e12	−1.23430	−0.617150	−	0.786845i	$-0.711713\pi$
$449$	−1.06299e12	−1.23430	−0.617150	+	0.786845i	$0.711713\pi$
$450$	−1.95935e12	−2.25245
$451$	1.79264e11	0.204032
$452$	6.13406e10	0.0691233
$453$	1.60959e12	1.79587
$454$	−8.20712e11	−0.906649
$455$	8.26044e11	0.903549
$456$	2.87272e11	0.311137
$457$	−8.26432e10	−0.0886307	−0.0443154	−	0.999018i	$-0.514111\pi$
$457$	−8.26432e10	−0.0886307	−0.0443154	+	0.999018i	$0.514111\pi$
$458$	−8.21980e10	−0.0872904
$459$	0	0
$460$	1.13805e11	0.118509
$461$	1.90976e11	0.196936	0.0984680	−	0.995140i	$-0.468606\pi$
$461$	1.90976e11	0.196936	0.0984680	+	0.995140i	$0.468606\pi$
$462$	1.66864e11	0.170402
$463$	9.16066e11	0.926429	0.463214	−	0.886246i	$-0.346696\pi$
$463$	9.16066e11	0.926429	0.463214	+	0.886246i	$0.346696\pi$
$464$	1.23071e12	1.23261
$465$	1.87238e12	1.85719
$466$	−8.32571e11	−0.817871
$467$	1.75288e12	1.70540	0.852701	−	0.522400i	$-0.174963\pi$
$467$	1.75288e12	1.70540	0.852701	+	0.522400i	$0.174963\pi$
$468$	−1.92209e11	−0.185211
$469$	1.05093e11	0.100299
$470$	3.10575e12	2.93580
$471$	−2.24834e12	−2.10508
$472$	−9.99162e11	−0.926610
$473$	6.45850e11	0.593276
$474$	−6.39081e11	−0.581505
$475$	6.21616e11	0.560275
$476$	0	0
$477$	2.80355e11	0.247957
$478$	−1.64225e12	−1.43885
$479$	−8.05193e11	−0.698860	−0.349430	−	0.936963i	$-0.613625\pi$
$479$	−8.05193e11	−0.698860	−0.349430	+	0.936963i	$0.613625\pi$
$480$	−7.32385e11	−0.629730
$481$	−1.96331e12	−1.67239
$482$	6.90395e11	0.582620
$483$	−2.65245e11	−0.221761
$484$	−1.30295e11	−0.107925
$485$	7.19679e11	0.590610
$486$	1.79476e12	1.45929
$487$	−2.02412e11	−0.163063	−0.0815315	−	0.996671i	$-0.525981\pi$
$487$	−2.02412e11	−0.163063	−0.0815315	+	0.996671i	$0.525981\pi$
$488$	−2.19551e12	−1.75245
$489$	−1.37275e12	−1.08568
$490$	−2.22912e12	−1.74683
$491$	−1.40366e12	−1.08992	−0.544960	−	0.838462i	$-0.683455\pi$
$491$	−1.40366e12	−1.08992	−0.544960	+	0.838462i	$0.683455\pi$
$492$	−1.22905e11	−0.0945645
$493$	0	0
$494$	5.46393e11	0.412794
$495$	8.37557e11	0.627034
$496$	1.10219e12	0.817692
$497$	−2.62362e11	−0.192884
$498$	1.91583e12	1.39581
$499$	−1.34731e12	−0.972784	−0.486392	−	0.873741i	$-0.661687\pi$
$499$	−1.34731e12	−0.972784	−0.486392	+	0.873741i	$0.661687\pi$
$500$	−4.19708e11	−0.300319
$501$	1.84863e12	1.31093
$502$	−1.21973e12	−0.857228
$503$	−9.70190e11	−0.675773	−0.337887	−	0.941187i	$-0.609712\pi$
$503$	−9.70190e11	−0.675773	−0.337887	+	0.941187i	$0.609712\pi$
$504$	3.81062e11	0.263062
$505$	−5.61816e11	−0.384400
$506$	−3.04340e11	−0.206386
$507$	3.25687e12	2.18910
$508$	3.47378e11	0.231428
$509$	−4.58129e11	−0.302523	−0.151261	−	0.988494i	$-0.548334\pi$
$509$	−4.58129e11	−0.302523	−0.151261	+	0.988494i	$0.548334\pi$
$510$	0	0
$511$	8.59139e10	0.0557403
$512$	1.16980e12	0.752311
$513$	−4.32785e10	−0.0275895
$514$	−1.06580e12	−0.673506
$515$	2.68023e11	0.167896
$516$	−4.42802e11	−0.274970
$517$	−9.26920e11	−0.570604
$518$	−5.59224e11	−0.341273
$519$	2.62039e12	1.58531
$520$	4.52291e12	2.71271
$521$	−9.79258e11	−0.582274	−0.291137	−	0.956681i	$-0.594034\pi$
$521$	−9.79258e11	−0.582274	−0.291137	+	0.956681i	$0.594034\pi$
$522$	1.83442e12	1.08139
$523$	−1.82449e12	−1.06631	−0.533157	−	0.846016i	$-0.678994\pi$
$523$	−1.82449e12	−1.06631	−0.533157	+	0.846016i	$0.678994\pi$
$524$	1.77904e11	0.103085
$525$	1.72304e12	0.989869
$526$	−1.06927e12	−0.609048
$527$	0	0
$528$	1.03026e12	0.576892
$529$	−1.31738e12	−0.731409
$530$	9.47823e11	0.521778
$531$	−1.67937e12	−0.916689
$532$	1.73693e10	0.00940110
$533$	1.62708e12	0.873243
$534$	−1.34869e12	−0.717757
$535$	−1.26368e12	−0.666876
$536$	5.75425e11	0.301125
$537$	−4.51046e12	−2.34065
$538$	−1.86207e12	−0.958242
$539$	6.65286e11	0.339515
$540$	5.14706e10	0.0260488
$541$	−2.54541e12	−1.27753	−0.638763	−	0.769403i	$-0.720554\pi$
$541$	−2.54541e12	−1.27753	−0.638763	+	0.769403i	$0.720554\pi$
$542$	−4.91502e11	−0.244641
$543$	2.03230e12	1.00320
$544$	0	0
$545$	−1.61944e12	−0.786285
$546$	1.51453e12	0.729307
$547$	−7.76701e11	−0.370946	−0.185473	−	0.982649i	$-0.559382\pi$
$547$	−7.76701e11	−0.370946	−0.185473	+	0.982649i	$0.559382\pi$
$548$	−1.96844e11	−0.0932417
$549$	−3.69018e12	−1.73369
$550$	1.97700e12	0.921243
$551$	−5.81981e11	−0.268984
$552$	−1.45232e12	−0.665788
$553$	2.68948e11	0.122294
$554$	−2.19258e12	−0.988922
$555$	−5.86553e12	−2.62415
$556$	−2.28361e11	−0.101341
$557$	1.13490e12	0.499586	0.249793	−	0.968299i	$-0.419637\pi$
$557$	1.13490e12	0.499586	0.249793	+	0.968299i	$0.419637\pi$
$558$	1.64285e12	0.717373
$559$	5.86201e12	2.53918
$560$	1.45273e12	0.624221
$561$	0	0
$562$	−3.81824e12	−1.61455
$563$	6.84519e11	0.287143	0.143571	−	0.989640i	$-0.454141\pi$
$563$	6.84519e11	0.287143	0.143571	+	0.989640i	$0.454141\pi$
$564$	6.35507e11	0.264463
$565$	−2.42607e12	−1.00158
$566$	−1.18548e12	−0.485534
$567$	−8.17853e11	−0.332316
$568$	−1.43653e12	−0.579092
$569$	4.27388e11	0.170930	0.0854648	−	0.996341i	$-0.472762\pi$
$569$	4.27388e11	0.170930	0.0854648	+	0.996341i	$0.472762\pi$
$570$	1.63239e12	0.647719
$571$	−3.34538e12	−1.31699	−0.658496	−	0.752584i	$-0.728807\pi$
$571$	−3.34538e12	−1.31699	−0.658496	+	0.752584i	$0.728807\pi$
$572$	1.93941e11	0.0757507
$573$	5.57397e12	2.16008
$574$	4.63451e11	0.178197
$575$	−3.14261e12	−1.19891
$576$	2.04820e12	0.775303
$577$	−6.11445e10	−0.0229650	−0.0114825	−	0.999934i	$-0.503655\pi$
$577$	−6.11445e10	−0.0229650	−0.0114825	+	0.999934i	$0.503655\pi$
$578$	0	0
$579$	2.05233e11	0.0758914
$580$	6.92143e11	0.253963
$581$	−8.06251e11	−0.293547
$582$	1.31951e12	0.476716
$583$	−2.82881e11	−0.101413
$584$	4.70412e11	0.167348
$585$	7.60202e12	2.68366
$586$	−2.27202e12	−0.795925
$587$	−1.97678e12	−0.687206	−0.343603	−	0.939115i	$-0.611648\pi$
$587$	−1.97678e12	−0.687206	−0.343603	+	0.939115i	$0.611648\pi$
$588$	−4.56128e11	−0.157358
$589$	−5.21206e11	−0.178439
$590$	−5.67761e12	−1.92900
$591$	−2.89337e11	−0.0975573
$592$	−3.45279e12	−1.15537
$593$	−2.58955e12	−0.859959	−0.429980	−	0.902839i	$-0.641479\pi$
$593$	−2.58955e12	−0.859959	−0.429980	+	0.902839i	$0.641479\pi$
$594$	−1.37644e11	−0.0453646
$595$	0	0
$596$	−2.49648e11	−0.0810438
$597$	2.43921e12	0.785894
$598$	−2.76232e12	−0.883320
$599$	2.28277e12	0.724507	0.362253	−	0.932080i	$-0.382008\pi$
$599$	2.28277e12	0.724507	0.362253	+	0.932080i	$0.382008\pi$
$600$	9.43429e12	2.97186
$601$	−3.16197e12	−0.988603	−0.494302	−	0.869290i	$-0.664576\pi$
$601$	−3.16197e12	−0.988603	−0.494302	+	0.869290i	$0.664576\pi$
$602$	1.66972e12	0.518154
$603$	9.67163e11	0.297901
$604$	5.32866e11	0.162912
$605$	5.15325e12	1.56380
$606$	−1.03007e12	−0.310271
$607$	−2.56502e12	−0.766906	−0.383453	−	0.923560i	$-0.625265\pi$
$607$	−2.56502e12	−0.766906	−0.383453	+	0.923560i	$0.625265\pi$
$608$	2.03870e11	0.0605046
$609$	−1.61317e12	−0.475229
$610$	−1.24757e13	−3.64822
$611$	−8.41312e12	−2.44215
$612$	0	0
$613$	−1.33870e12	−0.382923	−0.191461	−	0.981500i	$-0.561323\pi$
$613$	−1.33870e12	−0.382923	−0.191461	+	0.981500i	$0.561323\pi$
$614$	−4.58630e12	−1.30228
$615$	4.86100e12	1.37021
$616$	−3.84495e11	−0.107591
$617$	−3.94532e11	−0.109597	−0.0547985	−	0.998497i	$-0.517452\pi$
$617$	−3.94532e11	−0.109597	−0.0547985	+	0.998497i	$0.517452\pi$
$618$	4.91412e11	0.135518
$619$	−4.29120e12	−1.17482	−0.587410	−	0.809290i	$-0.699852\pi$
$619$	−4.29120e12	−1.17482	−0.587410	+	0.809290i	$0.699852\pi$
$620$	6.19864e11	0.168474
$621$	2.18796e11	0.0590375
$622$	−4.37743e12	−1.17264
$623$	5.67579e11	0.150949
$624$	9.35109e12	2.46906
$625$	7.77509e12	2.03819
$626$	5.20548e12	1.35480
$627$	−4.87191e11	−0.125891
$628$	−7.44330e11	−0.190962
$629$	0	0
$630$	2.16534e12	0.547638
$631$	−2.10436e12	−0.528431	−0.264215	−	0.964464i	$-0.585113\pi$
$631$	−2.10436e12	−0.528431	−0.264215	+	0.964464i	$0.585113\pi$
$632$	1.47259e12	0.367161
$633$	−5.89735e12	−1.45996
$634$	5.74481e12	1.41213
$635$	−1.37391e13	−3.35332
$636$	1.93946e11	0.0470028
$637$	6.03842e12	1.45310
$638$	−1.85094e12	−0.442282
$639$	−2.41450e12	−0.572892
$640$	8.85459e12	2.08621
$641$	4.70391e12	1.10052	0.550260	−	0.834993i	$-0.314528\pi$
$641$	4.70391e12	1.10052	0.550260	+	0.834993i	$0.314528\pi$
$642$	−2.31692e12	−0.538275
$643$	2.97950e12	0.687376	0.343688	−	0.939084i	$-0.388324\pi$
$643$	2.97950e12	0.687376	0.343688	+	0.939084i	$0.388324\pi$
$644$	−8.78111e10	−0.0201170
$645$	1.75132e13	3.98424
$646$	0	0
$647$	−6.15794e11	−0.138155	−0.0690774	−	0.997611i	$-0.522006\pi$
$647$	−6.15794e11	−0.138155	−0.0690774	+	0.997611i	$0.522006\pi$
$648$	−4.47806e12	−0.997706
$649$	1.69450e12	0.374922
$650$	1.79441e13	3.94285
$651$	−1.44471e12	−0.315259
$652$	−4.54458e11	−0.0984871
$653$	6.22513e12	1.33980	0.669899	−	0.742453i	$-0.266338\pi$
$653$	6.22513e12	1.33980	0.669899	+	0.742453i	$0.266338\pi$
$654$	−2.96919e12	−0.634656
$655$	−7.03624e12	−1.49367
$656$	2.86147e12	0.603284
$657$	7.90660e11	0.165556
$658$	−2.39637e12	−0.498353
$659$	5.49448e12	1.13486	0.567430	−	0.823421i	$-0.307938\pi$
$659$	5.49448e12	1.13486	0.567430	+	0.823421i	$0.307938\pi$
$660$	5.79411e11	0.118861
$661$	−2.29988e11	−0.0468596	−0.0234298	−	0.999725i	$-0.507459\pi$
$661$	−2.29988e11	−0.0468596	−0.0234298	+	0.999725i	$0.507459\pi$
$662$	6.46976e12	1.30926
$663$	0	0
$664$	−4.41454e12	−0.881310
$665$	−6.86967e11	−0.136219
$666$	−5.14650e12	−1.01363
$667$	2.94223e12	0.575586
$668$	6.12002e11	0.118921
$669$	5.31929e12	1.02668
$670$	3.26978e12	0.626876
$671$	3.72342e12	0.709072
$672$	5.65102e11	0.106897
$673$	9.70100e11	0.182284	0.0911420	−	0.995838i	$-0.470948\pi$
$673$	9.70100e11	0.182284	0.0911420	+	0.995838i	$0.470948\pi$
$674$	4.53401e12	0.846277
$675$	−1.42131e12	−0.263524
$676$	1.07821e12	0.198584
$677$	−5.03955e12	−0.922026	−0.461013	−	0.887393i	$-0.652514\pi$
$677$	−5.03955e12	−0.922026	−0.461013	+	0.887393i	$0.652514\pi$
$678$	−4.44813e12	−0.808432
$679$	−5.55298e11	−0.100256
$680$	0	0
$681$	6.64201e12	1.18342
$682$	−1.65765e12	−0.293402
$683$	−5.01528e12	−0.881864	−0.440932	−	0.897540i	$-0.645352\pi$
$683$	−5.01528e12	−0.881864	−0.440932	+	0.897540i	$0.645352\pi$
$684$	1.59848e11	0.0279225
$685$	7.78534e12	1.35105
$686$	3.62148e12	0.624349
$687$	6.65227e11	0.113937
$688$	1.03093e13	1.75420
$689$	−2.56754e12	−0.434042
$690$	−8.25261e12	−1.38602
$691$	−2.82622e12	−0.471580	−0.235790	−	0.971804i	$-0.575768\pi$
$691$	−2.82622e12	−0.471580	−0.235790	+	0.971804i	$0.575768\pi$
$692$	8.67498e11	0.143811
$693$	−6.46252e11	−0.106439
$694$	−4.07203e12	−0.666336
$695$	9.03187e12	1.46841
$696$	−8.83275e12	−1.42677
$697$	0	0
$698$	7.32369e12	1.16783
$699$	6.73799e12	1.06754
$700$	5.70423e11	0.0897958
$701$	2.11841e12	0.331343	0.165672	−	0.986181i	$-0.447021\pi$
$701$	2.11841e12	0.331343	0.165672	+	0.986181i	$0.447021\pi$
$702$	−1.24931e12	−0.194157
$703$	1.63276e12	0.252129
$704$	−2.06665e12	−0.317095
$705$	−2.51348e13	−3.83199
$706$	3.57137e11	0.0541021
$707$	4.33492e11	0.0652520
$708$	−1.16177e12	−0.173768
$709$	1.08197e13	1.60808	0.804039	−	0.594576i	$-0.202680\pi$
$709$	1.08197e13	1.60808	0.804039	+	0.594576i	$0.202680\pi$
$710$	−8.16291e12	−1.20554
$711$	2.47511e12	0.363230
$712$	3.10771e12	0.453190
$713$	2.63498e12	0.381834
$714$	0	0
$715$	−7.67050e12	−1.09761
$716$	−1.49322e12	−0.212332
$717$	1.32907e13	1.87808
$718$	1.95387e12	0.274369
$719$	−2.57986e12	−0.360011	−0.180006	−	0.983666i	$-0.557612\pi$
$719$	−2.57986e12	−0.360011	−0.180006	+	0.983666i	$0.557612\pi$
$720$	1.33694e13	1.85402
$721$	−2.06804e11	−0.0285004
$722$	7.29225e12	0.998721
$723$	−5.58736e12	−0.760473
$724$	6.72806e11	0.0910052
$725$	−1.91128e13	−2.56923
$726$	9.44834e12	1.26224
$727$	−4.66836e11	−0.0619811	−0.0309905	−	0.999520i	$-0.509866\pi$
$727$	−4.66836e11	−0.0619811	−0.0309905	+	0.999520i	$0.509866\pi$
$728$	−3.48984e12	−0.460483
$729$	−6.32368e12	−0.829271
$730$	2.67306e12	0.348381
$731$	0	0
$732$	−2.55282e12	−0.328639
$733$	−8.68081e12	−1.11069	−0.555344	−	0.831621i	$-0.687414\pi$
$733$	−8.68081e12	−1.11069	−0.555344	+	0.831621i	$0.687414\pi$
$734$	−6.63302e12	−0.843488
$735$	1.80402e13	2.28007
$736$	−1.03068e12	−0.129471
$737$	−9.75875e11	−0.121840
$738$	4.26511e12	0.529269
$739$	1.36517e13	1.68379	0.841894	−	0.539643i	$-0.181441\pi$
$739$	1.36517e13	1.68379	0.841894	+	0.539643i	$0.181441\pi$
$740$	−1.94182e12	−0.238049
$741$	−4.42195e12	−0.538805
$742$	−7.31332e11	−0.0885721
$743$	5.41571e12	0.651937	0.325968	−	0.945381i	$-0.394310\pi$
$743$	5.41571e12	0.651937	0.325968	+	0.945381i	$0.394310\pi$
$744$	−7.91036e12	−0.946495
$745$	9.87377e12	1.17430
$746$	−1.62180e12	−0.191722
$747$	−7.41987e12	−0.871874
$748$	0	0
$749$	9.75045e11	0.113203
$750$	3.04352e13	3.51237
$751$	−4.96526e12	−0.569590	−0.284795	−	0.958588i	$-0.591926\pi$
$751$	−4.96526e12	−0.569590	−0.284795	+	0.958588i	$0.591926\pi$
$752$	−1.47958e13	−1.68717
$753$	9.87125e12	1.11891
$754$	−1.67999e13	−1.89294
$755$	−2.10753e13	−2.36054
$756$	−3.97143e10	−0.00442179
$757$	1.38118e13	1.52869	0.764343	−	0.644810i	$-0.223064\pi$
$757$	1.38118e13	1.52869	0.764343	+	0.644810i	$0.223064\pi$
$758$	5.48631e11	0.0603627
$759$	2.46302e12	0.269389
$760$	−3.76141e12	−0.408968
$761$	1.56510e13	1.69166	0.845828	−	0.533455i	$-0.179107\pi$
$761$	1.56510e13	1.69166	0.845828	+	0.533455i	$0.179107\pi$
$762$	−2.51902e13	−2.70666
$763$	1.24954e12	0.133472
$764$	1.84530e12	0.195951
$765$	0	0
$766$	−1.29986e13	−1.36417
$767$	1.53800e13	1.60464
$768$	4.95562e12	0.514011
$769$	−4.07932e11	−0.0420648	−0.0210324	−	0.999779i	$-0.506695\pi$
$769$	−4.07932e11	−0.0420648	−0.0210324	+	0.999779i	$0.506695\pi$
$770$	−2.18484e12	−0.223981
$771$	8.62550e12	0.879102
$772$	6.79436e10	0.00688447
$773$	2.25431e11	0.0227094	0.0113547	−	0.999936i	$-0.496386\pi$
$773$	2.25431e11	0.0227094	0.0113547	+	0.999936i	$0.496386\pi$
$774$	1.53663e13	1.53899
$775$	−1.71169e13	−1.70438
$776$	−3.04047e12	−0.300998
$777$	4.52579e12	0.445451
$778$	5.85578e12	0.573029
$779$	−1.35313e12	−0.131650
$780$	5.25898e12	0.508716
$781$	2.43625e12	0.234310
$782$	0	0
$783$	1.33068e12	0.126516
$784$	1.06195e13	1.00388
$785$	2.94388e13	2.76698
$786$	−1.29008e13	−1.20563
$787$	−1.53299e13	−1.42446	−0.712232	−	0.701944i	$-0.752316\pi$
$787$	−1.53299e13	−1.42446	−0.712232	+	0.701944i	$0.752316\pi$
$788$	−9.57868e10	−0.00884989
$789$	8.65359e12	0.794968
$790$	8.36783e12	0.764348
$791$	1.87193e12	0.170018
$792$	−3.53848e12	−0.319560
$793$	3.37953e13	3.03478
$794$	−1.62011e13	−1.44661
$795$	−7.67072e12	−0.681058
$796$	8.07516e11	0.0712922
$797$	−5.72337e12	−0.502446	−0.251223	−	0.967929i	$-0.580833\pi$
$797$	−5.72337e12	−0.502446	−0.251223	+	0.967929i	$0.580833\pi$
$798$	−1.25954e12	−0.109951
$799$	0	0
$800$	6.69530e12	0.577917
$801$	5.22338e12	0.448338
$802$	−9.01117e12	−0.769125
$803$	−7.97781e11	−0.0677117
$804$	6.69071e11	0.0564703
$805$	3.47300e12	0.291489
$806$	−1.50455e13	−1.25574
$807$	1.50697e13	1.25076
$808$	2.37354e12	0.195905
$809$	−3.52847e12	−0.289613	−0.144807	−	0.989460i	$-0.546256\pi$
$809$	−3.52847e12	−0.289613	−0.144807	+	0.989460i	$0.546256\pi$
$810$	−2.54460e13	−2.07700
$811$	−1.52284e13	−1.23612	−0.618058	−	0.786133i	$-0.712080\pi$
$811$	−1.52284e13	−1.23612	−0.618058	+	0.786133i	$0.712080\pi$
$812$	−5.34052e11	−0.0431103
$813$	3.97772e12	0.319321
$814$	5.19286e12	0.414569
$815$	1.79742e13	1.42705
$816$	0	0
$817$	−4.87505e12	−0.382807
$818$	−1.51667e13	−1.18441
$819$	−5.86565e12	−0.455553
$820$	1.60927e12	0.124298
$821$	−2.18898e13	−1.68150	−0.840752	−	0.541420i	$-0.817887\pi$
$821$	−2.18898e13	−1.68150	−0.840752	+	0.541420i	$0.817887\pi$
$822$	1.42742e13	1.09051
$823$	−1.41049e13	−1.07169	−0.535846	−	0.844316i	$-0.680007\pi$
$823$	−1.41049e13	−1.07169	−0.535846	+	0.844316i	$0.680007\pi$
$824$	−1.13233e12	−0.0855660
$825$	−1.59998e13	−1.20246
$826$	4.38079e12	0.327448
$827$	−1.50447e12	−0.111843	−0.0559216	−	0.998435i	$-0.517810\pi$
$827$	−1.50447e12	−0.111843	−0.0559216	+	0.998435i	$0.517810\pi$
$828$	−8.08119e11	−0.0597501
$829$	1.36965e13	1.00720	0.503600	−	0.863937i	$-0.332009\pi$
$829$	1.36965e13	1.00720	0.503600	+	0.863937i	$0.332009\pi$
$830$	−2.50850e13	−1.83469
$831$	1.77445e13	1.29080
$832$	−1.87578e13	−1.35715
$833$	0	0
$834$	1.65597e13	1.18524
$835$	−2.42051e13	−1.72313
$836$	−1.61288e11	−0.0114202
$837$	1.19172e12	0.0839286
$838$	1.39638e13	0.978148
$839$	1.29771e12	0.0904170	0.0452085	−	0.998978i	$-0.485605\pi$
$839$	1.29771e12	0.0904170	0.0452085	+	0.998978i	$0.485605\pi$
$840$	−1.04261e13	−0.722548
$841$	3.38699e12	0.233470
$842$	−8.96649e12	−0.614778
$843$	3.09010e13	2.10741
$844$	−1.95236e12	−0.132440
$845$	−4.26440e13	−2.87742
$846$	−2.20536e13	−1.48017
$847$	−3.97620e12	−0.265456
$848$	−4.51543e12	−0.299859
$849$	9.59407e12	0.633750
$850$	0	0
$851$	−8.25450e12	−0.539520
$852$	−1.67032e12	−0.108598
$853$	−8.68335e12	−0.561587	−0.280793	−	0.959768i	$-0.590598\pi$
$853$	−8.68335e12	−0.561587	−0.280793	+	0.959768i	$0.590598\pi$
$854$	9.62615e12	0.619288
$855$	−6.32211e12	−0.404589
$856$	5.33875e12	0.339866
$857$	−1.27598e13	−0.808034	−0.404017	−	0.914751i	$-0.632386\pi$
$857$	−1.27598e13	−0.808034	−0.404017	+	0.914751i	$0.632386\pi$
$858$	−1.40636e13	−0.885942
$859$	2.56569e12	0.160781	0.0803905	−	0.996763i	$-0.474383\pi$
$859$	2.56569e12	0.160781	0.0803905	+	0.996763i	$0.474383\pi$
$860$	5.79785e12	0.361430
$861$	−3.75071e12	−0.232594
$862$	3.17171e13	1.95664
$863$	−2.29743e13	−1.40992	−0.704960	−	0.709247i	$-0.749035\pi$
$863$	−2.29743e13	−1.40992	−0.704960	+	0.709247i	$0.749035\pi$
$864$	−4.66144e11	−0.0284582
$865$	−3.43102e13	−2.08378
$866$	−1.09646e13	−0.662461
$867$	0	0
$868$	−4.78282e11	−0.0285986
$869$	−2.49740e12	−0.148559
$870$	−5.01910e13	−2.97022
$871$	−8.85745e12	−0.521467
$872$	6.84173e12	0.400721
$873$	−5.11037e12	−0.297775
$874$	2.29724e12	0.133169
$875$	−1.28082e13	−0.738674
$876$	5.46968e11	0.0313829
$877$	2.71354e13	1.54895	0.774475	−	0.632604i	$-0.218014\pi$
$877$	2.71354e13	1.54895	0.774475	+	0.632604i	$0.218014\pi$
$878$	5.45342e12	0.309702
$879$	1.83874e13	1.03889
$880$	−1.34898e13	−0.758285
$881$	8.69256e12	0.486134	0.243067	−	0.970009i	$-0.421846\pi$
$881$	8.69256e12	0.486134	0.243067	+	0.970009i	$0.421846\pi$
$882$	1.58287e13	0.880719
$883$	1.44572e13	0.800318	0.400159	−	0.916446i	$-0.368955\pi$
$883$	1.44572e13	0.800318	0.400159	+	0.916446i	$0.368955\pi$
$884$	0	0
$885$	4.59488e13	2.51785
$886$	−2.48199e13	−1.35315
$887$	2.51921e13	1.36649	0.683246	−	0.730188i	$-0.260567\pi$
$887$	2.51921e13	1.36649	0.683246	+	0.730188i	$0.260567\pi$
$888$	2.47805e13	1.33737
$889$	1.06009e13	0.569228
$890$	1.76592e13	0.943442
$891$	7.59444e12	0.403688
$892$	1.76099e12	0.0931352
$893$	6.99664e12	0.368178
$894$	1.81033e13	0.947848
$895$	5.90579e13	3.07662
$896$	−6.83213e12	−0.354136
$897$	2.23554e13	1.15296
$898$	2.55188e13	1.30954
$899$	1.60255e13	0.818263
$900$	5.24956e12	0.266705
$901$	0	0
$902$	−4.30353e12	−0.216469
$903$	−1.35130e13	−0.676327
$904$	1.02495e13	0.510442
$905$	−2.66100e13	−1.31864
$906$	−3.86409e13	−1.90533
$907$	−3.05227e13	−1.49758	−0.748790	−	0.662807i	$-0.769365\pi$
$907$	−3.05227e13	−1.49758	−0.748790	+	0.662807i	$0.769365\pi$
$908$	2.19888e12	0.107353
$909$	3.98940e12	0.193807
$910$	−1.98306e13	−0.958625
$911$	−3.56835e13	−1.71646	−0.858231	−	0.513264i	$-0.828436\pi$
$911$	−3.56835e13	−1.71646	−0.858231	+	0.513264i	$0.828436\pi$
$912$	−7.77669e12	−0.372236
$913$	7.48671e12	0.356593
$914$	1.98399e12	0.0940331
$915$	1.00966e14	4.76189
$916$	2.20228e11	0.0103358
$917$	5.42910e12	0.253551
$918$	0	0
$919$	−2.57192e13	−1.18943	−0.594713	−	0.803938i	$-0.702734\pi$
$919$	−2.57192e13	−1.18943	−0.594713	+	0.803938i	$0.702734\pi$
$920$	1.90160e13	0.875132
$921$	3.71169e13	1.69982
$922$	−4.58470e12	−0.208940
$923$	2.21124e13	1.00283
$924$	−4.47068e11	−0.0201767
$925$	5.36214e13	2.40824
$926$	−2.19917e13	−0.982899
$927$	−1.90320e12	−0.0846498
$928$	−6.26840e12	−0.277454
$929$	4.15886e12	0.183191	0.0915953	−	0.995796i	$-0.470803\pi$
$929$	4.15886e12	0.183191	0.0915953	+	0.995796i	$0.470803\pi$
$930$	−4.49496e13	−1.97039
$931$	−5.02176e12	−0.219070
$932$	2.23066e12	0.0968414
$933$	3.54265e13	1.53060
$934$	−4.20808e13	−1.80935
$935$	0	0
$936$	−3.21167e13	−1.36770
$937$	9.33151e12	0.395479	0.197740	−	0.980255i	$-0.436640\pi$
$937$	9.33151e12	0.395479	0.197740	+	0.980255i	$0.436640\pi$
$938$	−2.52293e12	−0.106412
$939$	−4.21279e13	−1.76838
$940$	−8.32104e12	−0.347618
$941$	2.25028e13	0.935585	0.467792	−	0.883838i	$-0.345050\pi$
$941$	2.25028e13	0.935585	0.467792	+	0.883838i	$0.345050\pi$
$942$	5.39752e13	2.23339
$943$	6.84083e12	0.281713
$944$	2.70481e13	1.10857
$945$	1.57073e12	0.0640706
$946$	−1.55047e13	−0.629438
$947$	7.23383e11	0.0292276	0.0146138	−	0.999893i	$-0.495348\pi$
$947$	7.23383e11	0.0292276	0.0146138	+	0.999893i	$0.495348\pi$
$948$	1.71225e12	0.0688540
$949$	−7.24100e12	−0.289802
$950$	−1.49229e13	−0.594426
$951$	−4.64927e13	−1.84320
$952$	0	0
$953$	4.77982e13	1.87713	0.938563	−	0.345107i	$-0.112157\pi$
$953$	4.77982e13	1.87713	0.938563	+	0.345107i	$0.112157\pi$
$954$	−6.73039e12	−0.263071
$955$	−7.29830e13	−2.83927
$956$	4.39999e12	0.170369
$957$	1.49796e13	0.577295
$958$	1.93300e13	0.741458
$959$	−6.00710e12	−0.229341
$960$	−5.60402e13	−2.12951
$961$	−1.20876e13	−0.457179
$962$	4.71326e13	1.77433
$963$	8.97327e12	0.336227
$964$	−1.84973e12	−0.0689862
$965$	−2.68722e12	−0.0997541
$966$	6.36764e12	0.235278
$967$	−3.15015e13	−1.15854	−0.579272	−	0.815134i	$-0.696663\pi$
$967$	−3.15015e13	−1.15854	−0.579272	+	0.815134i	$0.696663\pi$
$968$	−2.17712e13	−0.796974
$969$	0	0
$970$	−1.72771e13	−0.626611
$971$	6.67606e12	0.241009	0.120505	−	0.992713i	$-0.461549\pi$
$971$	6.67606e12	0.241009	0.120505	+	0.992713i	$0.461549\pi$
$972$	−4.80859e12	−0.172790
$973$	−6.96891e12	−0.249263
$974$	4.85923e12	0.173002
$975$	−1.45221e14	−5.14646
$976$	5.94343e13	2.09659
$977$	−4.15163e13	−1.45778	−0.728891	−	0.684630i	$-0.759964\pi$
$977$	−4.15163e13	−1.45778	−0.728891	+	0.684630i	$0.759964\pi$
$978$	3.29551e13	1.15186
$979$	−5.27043e12	−0.183368
$980$	5.97233e12	0.206836
$981$	1.14995e13	0.396430
$982$	3.36971e13	1.15635
$983$	9.03604e12	0.308665	0.154333	−	0.988019i	$-0.450677\pi$
$983$	9.03604e12	0.308665	0.154333	+	0.988019i	$0.450677\pi$
$984$	−2.05366e13	−0.698313
$985$	3.78844e12	0.128232
$986$	0	0
$987$	1.93938e13	0.650482
$988$	−1.46392e12	−0.0488776
$989$	2.46461e13	0.819151
$990$	−2.01069e13	−0.665254
$991$	−3.19314e13	−1.05169	−0.525844	−	0.850581i	$-0.676251\pi$
$991$	−3.19314e13	−1.05169	−0.525844	+	0.850581i	$0.676251\pi$
$992$	−5.61380e12	−0.184058
$993$	−5.23597e13	−1.70894
$994$	6.29843e12	0.204641
$995$	−3.19379e13	−1.03300
$996$	−5.13297e12	−0.165273
$997$	−3.11747e13	−0.999248	−0.499624	−	0.866242i	$-0.666529\pi$
$997$	−3.11747e13	−0.999248	−0.499624	+	0.866242i	$0.666529\pi$
$998$	3.23445e13	1.03208
$999$	−3.73326e12	−0.118589

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.i.1.16		52
17.10	odd	16		17.10.d.a.15.10	yes	52
17.12	odd	16		17.10.d.a.8.10	✓	52
17.16	even	2	inner	289.10.a.i.1.15		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.d.a.8.10	✓	52	17.12	odd	16
17.10.d.a.15.10	yes	52	17.10	odd	16
289.10.a.i.1.15		52	17.16	even	2	inner
289.10.a.i.1.16		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)

\(f(q)\)	\(=\)	\(q-24.0067 q^{2} +194.286 q^{3} +64.3195 q^{4} -2543.89 q^{5} -4664.15 q^{6} +1962.84 q^{7} +10747.3 q^{8} +18063.9 q^{9} +O(q^{10})\)	\(q-24.0067 q^{2} +194.286 q^{3} +64.3195 q^{4} -2543.89 q^{5} -4664.15 q^{6} +1962.84 q^{7} +10747.3 q^{8} +18063.9 q^{9} +61070.2 q^{10} -18226.6 q^{11} +12496.4 q^{12} -165432. q^{13} -47121.2 q^{14} -494241. q^{15} -290939. q^{16} -433653. q^{18} +137579. q^{19} -163622. q^{20} +381352. q^{21} +437559. q^{22} -695539. q^{23} +2.08805e6 q^{24} +4.51824e6 q^{25} +3.97148e6 q^{26} -314571. q^{27} +126249. q^{28} -4.23015e6 q^{29} +1.18651e7 q^{30} -3.78840e6 q^{31} +1.48184e6 q^{32} -3.54116e6 q^{33} -4.99325e6 q^{35} +1.16186e6 q^{36} +1.18678e7 q^{37} -3.30282e6 q^{38} -3.21411e7 q^{39} -2.73399e7 q^{40} -9.83530e6 q^{41} -9.15498e6 q^{42} -3.54345e7 q^{43} -1.17233e6 q^{44} -4.59525e7 q^{45} +1.66976e7 q^{46} +5.08554e7 q^{47} -5.65252e7 q^{48} -3.65009e7 q^{49} -1.08468e8 q^{50} -1.06405e7 q^{52} +1.55202e7 q^{53} +7.55180e6 q^{54} +4.63664e7 q^{55} +2.10953e7 q^{56} +2.67297e7 q^{57} +1.01552e8 q^{58} -9.29686e7 q^{59} -3.17893e7 q^{60} -2.04285e8 q^{61} +9.09468e7 q^{62} +3.54565e7 q^{63} +1.13387e8 q^{64} +4.20841e8 q^{65} +8.50115e7 q^{66} +5.35413e7 q^{67} -1.35133e8 q^{69} +1.19871e8 q^{70} -1.33664e8 q^{71} +1.94138e8 q^{72} +4.37702e7 q^{73} -2.84906e8 q^{74} +8.77828e8 q^{75} +8.84904e6 q^{76} -3.57759e7 q^{77} +7.71600e8 q^{78} +1.37020e8 q^{79} +7.40115e8 q^{80} -4.16668e8 q^{81} +2.36113e8 q^{82} -4.10757e8 q^{83} +2.45284e7 q^{84} +8.50664e8 q^{86} -8.21856e8 q^{87} -1.95887e8 q^{88} +2.89162e8 q^{89} +1.10317e9 q^{90} -3.24717e8 q^{91} -4.47367e7 q^{92} -7.36032e8 q^{93} -1.22087e9 q^{94} -3.49986e8 q^{95} +2.87900e8 q^{96} -2.82905e8 q^{97} +8.76264e8 q^{98} -3.29243e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) \) 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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