LMFDB - Embedded newform 289.10.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$148.845356651$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-41.2664 q^{2} +175.384 q^{3} +1190.92 q^{4} -699.952 q^{5} -7237.48 q^{6} -8848.92 q^{7} -28016.5 q^{8} +11076.6 q^{9} +O(q^{10})$	\(q-41.2664 q^{2} +175.384 q^{3} +1190.92 q^{4} -699.952 q^{5} -7237.48 q^{6} -8848.92 q^{7} -28016.5 q^{8} +11076.6 q^{9} +28884.5 q^{10} -90585.7 q^{11} +208868. q^{12} -26249.8 q^{13} +365163. q^{14} -122760. q^{15} +546392. q^{16} -457091. q^{18} +379311. q^{19} -833585. q^{20} -1.55196e6 q^{21} +3.73815e6 q^{22} +199283. q^{23} -4.91365e6 q^{24} -1.46319e6 q^{25} +1.08324e6 q^{26} -1.50943e6 q^{27} -1.05383e7 q^{28} -1.64726e6 q^{29} +5.06588e6 q^{30} -6.16598e6 q^{31} -8.20319e6 q^{32} -1.58873e7 q^{33} +6.19382e6 q^{35} +1.31913e7 q^{36} -2.00498e7 q^{37} -1.56528e7 q^{38} -4.60380e6 q^{39} +1.96102e7 q^{40} -2.54059e7 q^{41} +6.40439e7 q^{42} -445870. q^{43} -1.07880e8 q^{44} -7.75308e6 q^{45} -8.22371e6 q^{46} +1.95869e7 q^{47} +9.58285e7 q^{48} +3.79498e7 q^{49} +6.03807e7 q^{50} -3.12614e7 q^{52} +5.99655e7 q^{53} +6.22887e7 q^{54} +6.34056e7 q^{55} +2.47916e8 q^{56} +6.65251e7 q^{57} +6.79767e7 q^{58} -1.04158e7 q^{59} -1.46198e8 q^{60} -1.47082e8 q^{61} +2.54448e8 q^{62} -9.80159e7 q^{63} +5.87635e7 q^{64} +1.83736e7 q^{65} +6.55612e8 q^{66} -1.11288e8 q^{67} +3.49511e7 q^{69} -2.55597e8 q^{70} -9.69765e7 q^{71} -3.10328e8 q^{72} -6.26027e6 q^{73} +8.27383e8 q^{74} -2.56621e8 q^{75} +4.51728e8 q^{76} +8.01586e8 q^{77} +1.89982e8 q^{78} -3.35598e8 q^{79} -3.82448e8 q^{80} -4.82750e8 q^{81} +1.04841e9 q^{82} -4.77542e8 q^{83} -1.84826e9 q^{84} +1.83995e7 q^{86} -2.88904e8 q^{87} +2.53790e9 q^{88} -1.92204e8 q^{89} +3.19942e8 q^{90} +2.32283e8 q^{91} +2.37330e8 q^{92} -1.08142e9 q^{93} -8.08282e8 q^{94} -2.65499e8 q^{95} -1.43871e9 q^{96} +2.12176e8 q^{97} -1.56605e9 q^{98} -1.00338e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−41.2664	−1.82374	−0.911868	−	0.410484i	$-0.865360\pi$
$2$	−41.2664	−1.82374	−0.911868	+	0.410484i	$0.865360\pi$
$3$	175.384	1.25010	0.625050	−	0.780585i	$-0.285079\pi$
$3$	175.384	1.25010	0.625050	+	0.780585i	$0.285079\pi$
$4$	1190.92	2.32601
$5$	−699.952	−0.500845	−0.250422	−	0.968137i	$-0.580569\pi$
$5$	−699.952	−0.500845	−0.250422	+	0.968137i	$0.580569\pi$
$6$	−7237.48	−2.27985
$7$	−8848.92	−1.39299	−0.696497	−	0.717560i	$-0.745259\pi$
$7$	−8848.92	−1.39299	−0.696497	+	0.717560i	$0.745259\pi$
$8$	−28016.5	−2.41830
$9$	11076.6	0.562749
$10$	28884.5	0.913408
$11$	−90585.7	−1.86549	−0.932744	−	0.360539i	$-0.882593\pi$
$11$	−90585.7	−1.86549	−0.932744	+	0.360539i	$0.882593\pi$
$12$	208868.	2.90775
$13$	−26249.8	−0.254907	−0.127453	−	0.991845i	$-0.540680\pi$
$13$	−26249.8	−0.254907	−0.127453	+	0.991845i	$0.540680\pi$
$14$	365163.	2.54045
$15$	−122760.	−0.626106
$16$	546392.	2.08432
$17$	0	0
$17$	0	0
$18$	−457091.	−1.02631
$19$	379311.	0.667735	0.333867	−	0.942620i	$-0.391646\pi$
$19$	379311.	0.667735	0.333867	+	0.942620i	$0.391646\pi$
$20$	−833585.	−1.16497
$21$	−1.55196e6	−1.74138
$22$	3.73815e6	3.40216
$23$	199283.	0.148489	0.0742447	−	0.997240i	$-0.476345\pi$
$23$	199283.	0.148489	0.0742447	+	0.997240i	$0.476345\pi$
$24$	−4.91365e6	−3.02311
$25$	−1.46319e6	−0.749155
$26$	1.08324e6	0.464882
$27$	−1.50943e6	−0.546607
$28$	−1.05383e7	−3.24012
$29$	−1.64726e6	−0.432486	−0.216243	−	0.976340i	$-0.569380\pi$
$29$	−1.64726e6	−0.432486	−0.216243	+	0.976340i	$0.569380\pi$
$30$	5.06588e6	1.14185
$31$	−6.16598e6	−1.19915	−0.599577	−	0.800317i	$-0.704664\pi$
$31$	−6.16598e6	−1.19915	−0.599577	+	0.800317i	$0.704664\pi$
$32$	−8.20319e6	−1.38295
$33$	−1.58873e7	−2.33205
$34$	0	0
$35$	6.19382e6	0.697673
$36$	1.31913e7	1.30896
$37$	−2.00498e7	−1.75874	−0.879371	−	0.476138i	$-0.842036\pi$
$37$	−2.00498e7	−1.75874	−0.879371	+	0.476138i	$0.842036\pi$
$38$	−1.56528e7	−1.21777
$39$	−4.60380e6	−0.318659
$40$	1.96102e7	1.21119
$41$	−2.54059e7	−1.40413	−0.702064	−	0.712114i	$-0.747738\pi$
$41$	−2.54059e7	−1.40413	−0.702064	+	0.712114i	$0.747738\pi$
$42$	6.40439e7	3.17582
$43$	−445870.	−0.0198884	−0.00994420	−	0.999951i	$-0.503165\pi$
$43$	−445870.	−0.0198884	−0.00994420	+	0.999951i	$0.503165\pi$
$44$	−1.07880e8	−4.33915
$45$	−7.75308e6	−0.281850
$46$	−8.22371e6	−0.270805
$47$	1.95869e7	0.585498	0.292749	−	0.956189i	$-0.405430\pi$
$47$	1.95869e7	0.585498	0.292749	+	0.956189i	$0.405430\pi$
$48$	9.58285e7	2.60561
$49$	3.79498e7	0.940432
$50$	6.03807e7	1.36626
$51$	0	0
$52$	−3.12614e7	−0.592916
$53$	5.99655e7	1.04390	0.521951	−	0.852975i	$-0.325204\pi$
$53$	5.99655e7	1.04390	0.521951	+	0.852975i	$0.325204\pi$
$54$	6.22887e7	0.996867
$55$	6.34056e7	0.934320
$56$	2.47916e8	3.36867
$57$	6.65251e7	0.834735
$58$	6.79767e7	0.788740
$59$	−1.04158e7	−0.111907	−0.0559535	−	0.998433i	$-0.517820\pi$
$59$	−1.04158e7	−0.111907	−0.0559535	+	0.998433i	$0.517820\pi$
$60$	−1.46198e8	−1.45633
$61$	−1.47082e8	−1.36011	−0.680056	−	0.733160i	$-0.738045\pi$
$61$	−1.47082e8	−1.36011	−0.680056	+	0.733160i	$0.738045\pi$
$62$	2.54448e8	2.18694
$63$	−9.80159e7	−0.783906
$64$	5.87635e7	0.437822
$65$	1.83736e7	0.127669
$66$	6.55612e8	4.25304
$67$	−1.11288e8	−0.674703	−0.337352	−	0.941379i	$-0.609531\pi$
$67$	−1.11288e8	−0.674703	−0.337352	+	0.941379i	$0.609531\pi$
$68$	0	0
$69$	3.49511e7	0.185627
$70$	−2.55597e8	−1.27237
$71$	−9.69765e7	−0.452902	−0.226451	−	0.974023i	$-0.572712\pi$
$71$	−9.69765e7	−0.452902	−0.226451	+	0.974023i	$0.572712\pi$
$72$	−3.10328e8	−1.36089
$73$	−6.26027e6	−0.0258012	−0.0129006	−	0.999917i	$-0.504107\pi$
$73$	−6.26027e6	−0.0258012	−0.0129006	+	0.999917i	$0.504107\pi$
$74$	8.27383e8	3.20748
$75$	−2.56621e8	−0.936518
$76$	4.51728e8	1.55316
$77$	8.01586e8	2.59861
$78$	1.89982e8	0.581149
$79$	−3.35598e8	−0.969388	−0.484694	−	0.874684i	$-0.661069\pi$
$79$	−3.35598e8	−0.969388	−0.484694	+	0.874684i	$0.661069\pi$
$80$	−3.82448e8	−1.04392
$81$	−4.82750e8	−1.24606
$82$	1.04841e9	2.56076
$83$	−4.77542e8	−1.10449	−0.552243	−	0.833683i	$-0.686228\pi$
$83$	−4.77542e8	−1.10449	−0.552243	+	0.833683i	$0.686228\pi$
$84$	−1.84826e9	−4.05047
$85$	0	0
$86$	1.83995e7	0.0362712
$87$	−2.88904e8	−0.540651
$88$	2.53790e9	4.51130
$89$	−1.92204e8	−0.324719	−0.162359	−	0.986732i	$-0.551910\pi$
$89$	−1.92204e8	−0.324719	−0.162359	+	0.986732i	$0.551910\pi$
$90$	3.19942e8	0.514020
$91$	2.32283e8	0.355083
$92$	2.37330e8	0.345388
$93$	−1.08142e9	−1.49906
$94$	−8.08282e8	−1.06779
$95$	−2.65499e8	−0.334431
$96$	−1.43871e9	−1.72883
$97$	2.12176e8	0.243345	0.121673	−	0.992570i	$-0.461174\pi$
$97$	2.12176e8	0.243345	0.121673	+	0.992570i	$0.461174\pi$
$98$	−1.56605e9	−1.71510
$99$	−1.00338e9	−1.04980
$100$	−1.74254e9	−1.74254
$101$	1.38707e9	1.32633	0.663164	−	0.748474i	$-0.269213\pi$
$101$	1.38707e9	1.32633	0.663164	+	0.748474i	$0.269213\pi$
$102$	0	0
$103$	7.73415e6	0.00677088	0.00338544	−	0.999994i	$-0.498922\pi$
$103$	7.73415e6	0.00677088	0.00338544	+	0.999994i	$0.498922\pi$
$104$	7.35429e8	0.616440
$105$	1.08630e9	0.872161
$106$	−2.47456e9	−1.90380
$107$	5.67291e8	0.418388	0.209194	−	0.977874i	$-0.432916\pi$
$107$	5.67291e8	0.418388	0.209194	+	0.977874i	$0.432916\pi$
$108$	−1.79761e9	−1.27142
$109$	6.09841e8	0.413807	0.206903	−	0.978361i	$-0.433661\pi$
$109$	6.09841e8	0.413807	0.206903	+	0.978361i	$0.433661\pi$
$110$	−2.61652e9	−1.70395
$111$	−3.51641e9	−2.19860
$112$	−4.83498e9	−2.90345
$113$	−3.03208e9	−1.74940	−0.874698	−	0.484667i	$-0.838941\pi$
$113$	−3.03208e9	−1.74940	−0.874698	+	0.484667i	$0.838941\pi$
$114$	−2.74525e9	−1.52234
$115$	−1.39489e8	−0.0743701
$116$	−1.96176e9	−1.00597
$117$	−2.90758e8	−0.143448
$118$	4.29822e8	0.204089
$119$	0	0
$120$	3.43932e9	1.51411
$121$	5.84782e9	2.48005
$122$	6.06954e9	2.48049
$123$	−4.45578e9	−1.75530
$124$	−7.34318e9	−2.78925
$125$	2.39126e9	0.876055
$126$	4.04476e9	1.42964
$127$	−2.97440e9	−1.01457	−0.507286	−	0.861778i	$-0.669351\pi$
$127$	−2.97440e9	−1.01457	−0.507286	+	0.861778i	$0.669351\pi$
$128$	1.77507e9	0.584482
$129$	−7.81985e7	−0.0248625
$130$	−7.58213e8	−0.232834
$131$	1.96884e9	0.584103	0.292051	−	0.956403i	$-0.405662\pi$
$131$	1.96884e9	0.584103	0.292051	+	0.956403i	$0.405662\pi$
$132$	−1.89205e10	−5.42437
$133$	−3.35649e9	−0.930151
$134$	4.59247e9	1.23048
$135$	1.05653e9	0.273765
$136$	0	0
$137$	3.63646e9	0.881935	0.440968	−	0.897523i	$-0.354635\pi$
$137$	3.63646e9	0.881935	0.440968	+	0.897523i	$0.354635\pi$
$138$	−1.44231e9	−0.338534
$139$	−2.98093e9	−0.677307	−0.338653	−	0.940911i	$-0.609971\pi$
$139$	−2.98093e9	−0.677307	−0.338653	+	0.940911i	$0.609971\pi$
$140$	7.37633e9	1.62280
$141$	3.43523e9	0.731931
$142$	4.00187e9	0.825973
$143$	2.37786e9	0.475526
$144$	6.05216e9	1.17295
$145$	1.15300e9	0.216608
$146$	2.58339e8	0.0470546
$147$	6.65579e9	1.17563
$148$	−2.38777e10	−4.09085
$149$	3.23876e9	0.538319	0.269160	−	0.963096i	$-0.413254\pi$
$149$	3.23876e9	0.538319	0.269160	+	0.963096i	$0.413254\pi$
$150$	1.05898e10	1.70796
$151$	−1.17467e9	−0.183874	−0.0919368	−	0.995765i	$-0.529306\pi$
$151$	−1.17467e9	−0.183874	−0.0919368	+	0.995765i	$0.529306\pi$
$152$	−1.06270e10	−1.61478
$153$	0	0
$154$	−3.30786e10	−4.73919
$155$	4.31589e9	0.600590
$156$	−5.48275e9	−0.741204
$157$	−3.41677e9	−0.448815	−0.224407	−	0.974495i	$-0.572045\pi$
$157$	−3.41677e9	−0.448815	−0.224407	+	0.974495i	$0.572045\pi$
$158$	1.38489e10	1.76791
$159$	1.05170e10	1.30498
$160$	5.74183e9	0.692645
$161$	−1.76344e9	−0.206845
$162$	1.99214e10	2.27249
$163$	1.00303e10	1.11293	0.556465	−	0.830871i	$-0.312157\pi$
$163$	1.00303e10	1.11293	0.556465	+	0.830871i	$0.312157\pi$
$164$	−3.02563e10	−3.26602
$165$	1.11203e10	1.16799
$166$	1.97065e10	2.01429
$167$	6.74539e9	0.671094	0.335547	−	0.942024i	$-0.391079\pi$
$167$	6.74539e9	0.671094	0.335547	+	0.942024i	$0.391079\pi$
$168$	4.34805e10	4.21117
$169$	−9.91545e9	−0.935023
$170$	0	0
$171$	4.20147e9	0.375767
$172$	−5.30995e8	−0.0462607
$173$	−6.83966e9	−0.580533	−0.290267	−	0.956946i	$-0.593744\pi$
$173$	−6.83966e9	−0.580533	−0.290267	+	0.956946i	$0.593744\pi$
$174$	1.19220e10	0.986004
$175$	1.29477e10	1.04357
$176$	−4.94953e10	−3.88828
$177$	−1.82676e9	−0.139895
$178$	7.93157e9	0.592201
$179$	8.27428e9	0.602409	0.301205	−	0.953559i	$-0.402611\pi$
$179$	8.27428e9	0.602409	0.301205	+	0.953559i	$0.402611\pi$
$180$	−9.23328e9	−0.655586
$181$	6.86242e9	0.475252	0.237626	−	0.971357i	$-0.423631\pi$
$181$	6.86242e9	0.475252	0.237626	+	0.971357i	$0.423631\pi$
$182$	−9.58547e9	−0.647578
$183$	−2.57958e10	−1.70028
$184$	−5.58322e9	−0.359091
$185$	1.40339e10	0.880856
$186$	4.46262e10	2.73389
$187$	0	0
$188$	2.33264e10	1.36188
$189$	1.33568e10	0.761421
$190$	1.09562e10	0.609915
$191$	3.87326e9	0.210585	0.105292	−	0.994441i	$-0.466422\pi$
$191$	3.87326e9	0.210585	0.105292	+	0.994441i	$0.466422\pi$
$192$	1.03062e10	0.547321
$193$	2.20422e10	1.14353	0.571765	−	0.820417i	$-0.306259\pi$
$193$	2.20422e10	1.14353	0.571765	+	0.820417i	$0.306259\pi$
$194$	−8.75573e9	−0.443797
$195$	3.22244e9	0.159599
$196$	4.51951e10	2.18746
$197$	−1.88786e10	−0.893043	−0.446521	−	0.894773i	$-0.647337\pi$
$197$	−1.88786e10	−0.893043	−0.446521	+	0.894773i	$0.647337\pi$
$198$	4.14059e10	1.91456
$199$	−1.72935e10	−0.781709	−0.390854	−	0.920453i	$-0.627820\pi$
$199$	−1.72935e10	−0.781709	−0.390854	+	0.920453i	$0.627820\pi$
$200$	4.09936e10	1.81168
$201$	−1.95182e10	−0.843446
$202$	−5.72392e10	−2.41887
$203$	1.45765e10	0.602450
$204$	0	0
$205$	1.77829e10	0.703250
$206$	−3.19161e8	−0.0123483
$207$	2.20738e9	0.0835622
$208$	−1.43427e10	−0.531307
$209$	−3.43601e10	−1.24565
$210$	−4.48276e10	−1.59059
$211$	4.22364e9	0.146695	0.0733476	−	0.997306i	$-0.476632\pi$
$211$	4.22364e9	0.146695	0.0733476	+	0.997306i	$0.476632\pi$
$212$	7.14140e10	2.42813
$213$	−1.70081e10	−0.566172
$214$	−2.34101e10	−0.763029
$215$	3.12087e8	0.00996100
$216$	4.22889e10	1.32186
$217$	5.45623e10	1.67041
$218$	−2.51660e10	−0.754674
$219$	−1.09795e9	−0.0322541
$220$	7.55109e10	2.17324
$221$	0	0
$222$	1.45110e11	4.00967
$223$	−3.32949e10	−0.901584	−0.450792	−	0.892629i	$-0.648858\pi$
$223$	−3.32949e10	−0.901584	−0.450792	+	0.892629i	$0.648858\pi$
$224$	7.25894e10	1.92645
$225$	−1.62072e10	−0.421586
$226$	1.25123e11	3.19044
$227$	−5.61856e10	−1.40446	−0.702229	−	0.711951i	$-0.747812\pi$
$227$	−5.61856e10	−1.40446	−0.702229	+	0.711951i	$0.747812\pi$
$228$	7.92259e10	1.94160
$229$	−5.10412e10	−1.22648	−0.613241	−	0.789896i	$-0.710135\pi$
$229$	−5.10412e10	−1.22648	−0.613241	+	0.789896i	$0.710135\pi$
$230$	5.75620e9	0.135631
$231$	1.40585e11	3.24853
$232$	4.61506e10	1.04588
$233$	5.13207e10	1.14075	0.570376	−	0.821384i	$-0.306797\pi$
$233$	5.13207e10	1.14075	0.570376	+	0.821384i	$0.306797\pi$
$234$	1.19986e10	0.261612
$235$	−1.37099e10	−0.293244
$236$	−1.24043e10	−0.260297
$237$	−5.88586e10	−1.21183
$238$	0	0
$239$	−7.40848e9	−0.146872	−0.0734360	−	0.997300i	$-0.523396\pi$
$239$	−7.40848e9	−0.146872	−0.0734360	+	0.997300i	$0.523396\pi$
$240$	−6.70753e10	−1.30500
$241$	9.23211e9	0.176289	0.0881443	−	0.996108i	$-0.471906\pi$
$241$	9.23211e9	0.176289	0.0881443	+	0.996108i	$0.471906\pi$
$242$	−2.41319e11	−4.52295
$243$	−5.49566e10	−1.01109
$244$	−1.75163e11	−3.16364
$245$	−2.65630e10	−0.471010
$246$	1.83874e11	3.20120
$247$	−9.95684e9	−0.170210
$248$	1.72749e11	2.89991
$249$	−8.37534e10	−1.38072
$250$	−9.86786e10	−1.59769
$251$	6.79026e10	1.07983	0.539914	−	0.841720i	$-0.318457\pi$
$251$	6.79026e10	1.07983	0.539914	+	0.841720i	$0.318457\pi$
$252$	−1.16729e11	−1.82337
$253$	−1.80522e10	−0.277005
$254$	1.22743e11	1.85031
$255$	0	0
$256$	−1.03338e11	−1.50376
$257$	−4.71754e10	−0.674553	−0.337276	−	0.941406i	$-0.609506\pi$
$257$	−4.71754e10	−0.674553	−0.337276	+	0.941406i	$0.609506\pi$
$258$	3.22697e9	0.0453426
$259$	1.77419e11	2.44992
$260$	2.18815e10	0.296959
$261$	−1.82461e10	−0.243381
$262$	−8.12469e10	−1.06525
$263$	−1.02251e11	−1.31786	−0.658929	−	0.752206i	$-0.728990\pi$
$263$	−1.02251e11	−1.31786	−0.658929	+	0.752206i	$0.728990\pi$
$264$	4.45107e11	5.63958
$265$	−4.19729e10	−0.522833
$266$	1.38510e11	1.69635
$267$	−3.37095e10	−0.405931
$268$	−1.32535e11	−1.56937
$269$	1.29503e11	1.50798	0.753990	−	0.656886i	$-0.228127\pi$
$269$	1.29503e11	1.50798	0.753990	+	0.656886i	$0.228127\pi$
$270$	−4.35991e10	−0.499276
$271$	−1.37457e9	−0.0154813	−0.00774064	−	0.999970i	$-0.502464\pi$
$271$	−1.37457e9	−0.0154813	−0.00774064	+	0.999970i	$0.502464\pi$
$272$	0	0
$273$	4.07387e10	0.443890
$274$	−1.50064e11	−1.60842
$275$	1.32544e11	1.39754
$276$	4.16239e10	0.431770
$277$	1.09412e11	1.11662	0.558310	−	0.829633i	$-0.311450\pi$
$277$	1.09412e11	1.11662	0.558310	+	0.829633i	$0.311450\pi$
$278$	1.23012e11	1.23523
$279$	−6.82981e10	−0.674822
$280$	−1.73529e11	−1.68718
$281$	−5.78233e10	−0.553254	−0.276627	−	0.960977i	$-0.589217\pi$
$281$	−5.78233e10	−0.553254	−0.276627	+	0.960977i	$0.589217\pi$
$282$	−1.41760e11	−1.33485
$283$	7.68143e10	0.711874	0.355937	−	0.934510i	$-0.384162\pi$
$283$	7.68143e10	0.711874	0.355937	+	0.934510i	$0.384162\pi$
$284$	−1.15491e11	−1.05345
$285$	−4.65644e10	−0.418073
$286$	−9.81257e10	−0.867233
$287$	2.24814e11	1.95594
$288$	−9.08633e10	−0.778256
$289$	0	0
$290$	−4.75804e10	−0.395036
$291$	3.72122e10	0.304206
$292$	−7.45546e9	−0.0600139
$293$	1.53859e11	1.21960	0.609802	−	0.792554i	$-0.291249\pi$
$293$	1.53859e11	1.21960	0.609802	+	0.792554i	$0.291249\pi$
$294$	−2.74661e11	−2.14404
$295$	7.29054e9	0.0560480
$296$	5.61725e11	4.25316
$297$	1.36733e11	1.01969
$298$	−1.33652e11	−0.981752
$299$	−5.23115e9	−0.0378509
$300$	−3.05614e11	−2.17835
$301$	3.94547e9	0.0277044
$302$	4.84744e10	0.335337
$303$	2.43269e11	1.65804
$304$	2.07252e11	1.39177
$305$	1.02950e11	0.681205
$306$	0	0
$307$	7.97146e10	0.512171	0.256086	−	0.966654i	$-0.417567\pi$
$307$	7.97146e10	0.512171	0.256086	+	0.966654i	$0.417567\pi$
$308$	9.54623e11	6.04441
$309$	1.35645e9	0.00846428
$310$	−1.78101e11	−1.09532
$311$	2.53546e10	0.153687	0.0768433	−	0.997043i	$-0.475516\pi$
$311$	2.53546e10	0.153687	0.0768433	+	0.997043i	$0.475516\pi$
$312$	1.28983e11	0.770611
$313$	−1.21031e10	−0.0712763	−0.0356382	−	0.999365i	$-0.511346\pi$
$313$	−1.21031e10	−0.0712763	−0.0356382	+	0.999365i	$0.511346\pi$
$314$	1.40998e11	0.818520
$315$	6.86064e10	0.392615
$316$	−3.99670e11	−2.25481
$317$	−2.26225e11	−1.25827	−0.629135	−	0.777296i	$-0.716591\pi$
$317$	−2.26225e11	−1.25827	−0.629135	+	0.777296i	$0.716591\pi$
$318$	−4.33999e11	−2.37994
$319$	1.49219e11	0.806798
$320$	−4.11316e10	−0.219281
$321$	9.94939e10	0.523026
$322$	7.27709e10	0.377230
$323$	0	0
$324$	−5.74916e11	−2.89836
$325$	3.84085e10	0.190965
$326$	−4.13913e11	−2.02969
$327$	1.06956e11	0.517300
$328$	7.11784e11	3.39560
$329$	−1.73323e11	−0.815595
$330$	−4.58897e11	−2.13011
$331$	−7.16543e10	−0.328107	−0.164054	−	0.986451i	$-0.552457\pi$
$331$	−7.16543e10	−0.328107	−0.164054	+	0.986451i	$0.552457\pi$
$332$	−5.68714e11	−2.56905
$333$	−2.22083e11	−0.989730
$334$	−2.78358e11	−1.22390
$335$	7.78964e10	0.337922
$336$	−8.47979e11	−3.62960
$337$	1.03196e11	0.435843	0.217922	−	0.975966i	$-0.430072\pi$
$337$	1.03196e11	0.435843	0.217922	+	0.975966i	$0.430072\pi$
$338$	4.09175e11	1.70523
$339$	−5.31780e11	−2.18692
$340$	0	0
$341$	5.58550e11	2.23701
$342$	−1.73380e11	−0.685300
$343$	2.12710e10	0.0829782
$344$	1.24917e10	0.0480961
$345$	−2.44641e10	−0.0929700
$346$	2.82248e11	1.05874
$347$	−1.44300e10	−0.0534297	−0.0267149	−	0.999643i	$-0.508505\pi$
$347$	−1.44300e10	−0.0534297	−0.0267149	+	0.999643i	$0.508505\pi$
$348$	−3.44061e11	−1.25756
$349$	−5.24580e11	−1.89277	−0.946384	−	0.323045i	$-0.895293\pi$
$349$	−5.24580e11	−1.89277	−0.946384	+	0.323045i	$0.895293\pi$
$350$	−5.34304e11	−1.90319
$351$	3.96222e10	0.139334
$352$	7.43091e11	2.57988
$353$	−3.33276e11	−1.14240	−0.571200	−	0.820811i	$-0.693522\pi$
$353$	−3.33276e11	−1.14240	−0.571200	+	0.820811i	$0.693522\pi$
$354$	7.53839e10	0.255131
$355$	6.78788e10	0.226833
$356$	−2.28899e11	−0.755300
$357$	0	0
$358$	−3.41450e11	−1.09864
$359$	−1.56163e11	−0.496195	−0.248098	−	0.968735i	$-0.579805\pi$
$359$	−1.56163e11	−0.496195	−0.248098	+	0.968735i	$0.579805\pi$
$360$	2.17214e11	0.681596
$361$	−1.78811e11	−0.554130
$362$	−2.83188e11	−0.866734
$363$	1.02562e12	3.10031
$364$	2.76630e11	0.825928
$365$	4.38188e9	0.0129224
$366$	1.06450e12	3.10086
$367$	5.01847e11	1.44402	0.722012	−	0.691881i	$-0.243218\pi$
$367$	5.01847e11	1.44402	0.722012	+	0.691881i	$0.243218\pi$
$368$	1.08887e11	0.309499
$369$	−2.81410e11	−0.790171
$370$	−5.79128e11	−1.60645
$371$	−5.30630e11	−1.45415
$372$	−1.28788e12	−3.48683
$373$	−4.29931e11	−1.15003	−0.575015	−	0.818143i	$-0.695004\pi$
$373$	−4.29931e11	−1.15003	−0.575015	+	0.818143i	$0.695004\pi$
$374$	0	0
$375$	4.19389e11	1.09516
$376$	−5.48757e11	−1.41591
$377$	4.32404e10	0.110244
$378$	−5.51188e11	−1.38863
$379$	−5.20247e11	−1.29519	−0.647595	−	0.761985i	$-0.724225\pi$
$379$	−5.20247e11	−1.29519	−0.647595	+	0.761985i	$0.724225\pi$
$380$	−3.16188e11	−0.777892
$381$	−5.21663e11	−1.26832
$382$	−1.59836e11	−0.384051
$383$	5.98804e10	0.142197	0.0710985	−	0.997469i	$-0.477350\pi$
$383$	5.98804e10	0.142197	0.0710985	+	0.997469i	$0.477350\pi$
$384$	3.11320e11	0.730661
$385$	−5.61071e11	−1.30150
$386$	−9.09604e11	−2.08550
$387$	−4.93872e9	−0.0111922
$388$	2.52684e11	0.566024
$389$	5.55917e10	0.123094	0.0615470	−	0.998104i	$-0.480397\pi$
$389$	5.55917e10	0.123094	0.0615470	+	0.998104i	$0.480397\pi$
$390$	−1.32979e11	−0.291066
$391$	0	0
$392$	−1.06322e12	−2.27424
$393$	3.45303e11	0.730186
$394$	7.79053e11	1.62867
$395$	2.34902e11	0.485513
$396$	−1.19494e12	−2.44185
$397$	−2.15249e11	−0.434894	−0.217447	−	0.976072i	$-0.569773\pi$
$397$	−2.15249e11	−0.434894	−0.217447	+	0.976072i	$0.569773\pi$
$398$	7.13643e11	1.42563
$399$	−5.88675e11	−1.16278
$400$	−7.99477e11	−1.56148
$401$	2.85995e11	0.552344	0.276172	−	0.961108i	$-0.410934\pi$
$401$	2.85995e11	0.552344	0.276172	+	0.961108i	$0.410934\pi$
$402$	8.05446e11	1.53822
$403$	1.61856e11	0.305672
$404$	1.65188e12	3.08505
$405$	3.37902e11	0.624084
$406$	−6.01520e11	−1.09871
$407$	1.81622e12	3.28091
$408$	0	0
$409$	2.43866e11	0.430919	0.215460	−	0.976513i	$-0.430875\pi$
$409$	2.43866e11	0.430919	0.215460	+	0.976513i	$0.430875\pi$
$410$	−7.33836e11	−1.28254
$411$	6.37778e11	1.10251
$412$	9.21074e9	0.0157492
$413$	9.21683e10	0.155886
$414$	−9.10906e10	−0.152395
$415$	3.34257e11	0.553176
$416$	2.15332e11	0.352524
$417$	−5.22808e11	−0.846701
$418$	1.41792e12	2.27174
$419$	1.03402e12	1.63894	0.819472	−	0.573119i	$-0.194267\pi$
$419$	1.03402e12	1.63894	0.819472	+	0.573119i	$0.194267\pi$
$420$	1.29369e12	2.02866
$421$	1.12377e12	1.74344	0.871720	−	0.490004i	$-0.163005\pi$
$421$	1.12377e12	1.74344	0.871720	+	0.490004i	$0.163005\pi$
$422$	−1.74294e11	−0.267533
$423$	2.16956e11	0.329488
$424$	−1.68002e12	−2.52446
$425$	0	0
$426$	7.01865e11	1.03255
$427$	1.30152e12	1.89463
$428$	6.75597e11	0.973175
$429$	4.17039e11	0.594454
$430$	−1.28787e10	−0.0181662
$431$	2.79192e11	0.389722	0.194861	−	0.980831i	$-0.437574\pi$
$431$	2.79192e11	0.389722	0.194861	+	0.980831i	$0.437574\pi$
$432$	−8.24740e11	−1.13930
$433$	−5.92406e11	−0.809886	−0.404943	−	0.914342i	$-0.632709\pi$
$433$	−5.92406e11	−0.809886	−0.404943	+	0.914342i	$0.632709\pi$
$434$	−2.25159e12	−3.04639
$435$	2.02219e11	0.270782
$436$	7.26271e11	0.962520
$437$	7.55903e10	0.0991515
$438$	4.53085e10	0.0588229
$439$	1.19622e12	1.53716	0.768580	−	0.639754i	$-0.220964\pi$
$439$	1.19622e12	1.53716	0.768580	+	0.639754i	$0.220964\pi$
$440$	−1.77641e12	−2.25946
$441$	4.20354e11	0.529227
$442$	0	0
$443$	6.14827e11	0.758466	0.379233	−	0.925301i	$-0.376188\pi$
$443$	6.14827e11	0.758466	0.379233	+	0.925301i	$0.376188\pi$
$444$	−4.18776e12	−5.11397
$445$	1.34534e11	0.162634
$446$	1.37396e12	1.64425
$447$	5.68026e11	0.672953
$448$	−5.19993e11	−0.609883
$449$	−1.57287e12	−1.82636	−0.913178	−	0.407562i	$-0.866379\pi$
$449$	−1.57287e12	−1.82636	−0.913178	+	0.407562i	$0.866379\pi$
$450$	6.68812e11	0.768861
$451$	2.30141e12	2.61938
$452$	−3.61097e12	−4.06912
$453$	−2.06018e11	−0.229860
$454$	2.31858e12	2.56136
$455$	−1.62587e11	−0.177842
$456$	−1.86380e12	−2.01864
$457$	−1.08480e12	−1.16340	−0.581699	−	0.813404i	$-0.697612\pi$
$457$	−1.08480e12	−1.16340	−0.581699	+	0.813404i	$0.697612\pi$
$458$	2.10629e12	2.23678
$459$	0	0
$460$	−1.66120e11	−0.172986
$461$	1.24066e12	1.27938	0.639691	−	0.768633i	$-0.279062\pi$
$461$	1.24066e12	1.27938	0.639691	+	0.768633i	$0.279062\pi$
$462$	−5.80146e12	−5.92445
$463$	−1.73183e12	−1.75142	−0.875710	−	0.482837i	$-0.839607\pi$
$463$	−1.73183e12	−1.75142	−0.875710	+	0.482837i	$0.839607\pi$
$464$	−9.00052e11	−0.901439
$465$	7.56939e11	0.750797
$466$	−2.11782e12	−2.08043
$467$	−1.47573e12	−1.43575	−0.717877	−	0.696170i	$-0.754886\pi$
$467$	−1.47573e12	−1.43575	−0.717877	+	0.696170i	$0.754886\pi$
$468$	−3.46269e11	−0.333663
$469$	9.84781e11	0.939857
$470$	5.65758e11	0.534799
$471$	−5.99247e11	−0.561063
$472$	2.91814e11	0.270624
$473$	4.03894e10	0.0371016
$474$	2.42888e12	2.21006
$475$	−5.55005e11	−0.500237
$476$	0	0
$477$	6.64213e11	0.587455
$478$	3.05722e11	0.267856
$479$	−1.07230e12	−0.930691	−0.465345	−	0.885129i	$-0.654070\pi$
$479$	−1.07230e12	−0.930691	−0.465345	+	0.885129i	$0.654070\pi$
$480$	1.00703e12	0.865875
$481$	5.26303e11	0.448315
$482$	−3.80976e11	−0.321504
$483$	−3.09280e11	−0.258577
$484$	6.96428e12	5.76862
$485$	−1.48513e11	−0.121878
$486$	2.26786e12	1.84397
$487$	−2.21909e12	−1.78770	−0.893848	−	0.448370i	$-0.852005\pi$
$487$	−2.21909e12	−1.78770	−0.893848	+	0.448370i	$0.852005\pi$
$488$	4.12072e12	3.28916
$489$	1.75915e12	1.39127
$490$	1.09616e12	0.858998
$491$	1.84461e12	1.43231	0.716155	−	0.697941i	$-0.245900\pi$
$491$	1.84461e12	1.43231	0.716155	+	0.697941i	$0.245900\pi$
$492$	−5.30647e12	−4.08285
$493$	0	0
$494$	4.10883e11	0.310418
$495$	7.02318e11	0.525788
$496$	−3.36904e12	−2.49942
$497$	8.58137e11	0.630889
$498$	3.45620e12	2.51807
$499$	8.68109e11	0.626790	0.313395	−	0.949623i	$-0.398534\pi$
$499$	8.68109e11	0.626790	0.313395	+	0.949623i	$0.398534\pi$
$500$	2.84779e12	2.03771
$501$	1.18303e12	0.838934
$502$	−2.80210e12	−1.96932
$503$	9.49807e11	0.661575	0.330788	−	0.943705i	$-0.392686\pi$
$503$	9.49807e11	0.661575	0.330788	+	0.943705i	$0.392686\pi$
$504$	2.74606e12	1.89572
$505$	−9.70879e11	−0.664284
$506$	7.44950e11	0.505184
$507$	−1.73901e12	−1.16887
$508$	−3.54227e12	−2.35991
$509$	1.21433e12	0.801872	0.400936	−	0.916106i	$-0.368685\pi$
$509$	1.21433e12	0.801872	0.400936	+	0.916106i	$0.368685\pi$
$510$	0	0
$511$	5.53966e10	0.0359409
$512$	3.35555e12	2.15798
$513$	−5.72542e11	−0.364989
$514$	1.94676e12	1.23021
$515$	−5.41353e9	−0.00339116
$516$	−9.31280e10	−0.0578305
$517$	−1.77429e12	−1.09224
$518$	−7.32145e12	−4.46800
$519$	−1.19957e12	−0.725724
$520$	−5.14765e11	−0.308741
$521$	3.04153e12	1.80852	0.904258	−	0.426985i	$-0.140424\pi$
$521$	3.04153e12	1.80852	0.904258	+	0.426985i	$0.140424\pi$
$522$	7.52950e11	0.443863
$523$	2.35988e12	1.37922	0.689608	−	0.724183i	$-0.257783\pi$
$523$	2.35988e12	1.37922	0.689608	+	0.724183i	$0.257783\pi$
$524$	2.34472e12	1.35863
$525$	2.27082e12	1.30456
$526$	4.21955e12	2.40342
$527$	0	0
$528$	−8.68069e12	−4.86073
$529$	−1.76144e12	−0.977951
$530$	1.73207e12	0.953509
$531$	−1.15371e11	−0.0629756
$532$	−3.99731e12	−2.16354
$533$	6.66899e11	0.357921
$534$	1.39107e12	0.740311
$535$	−3.97076e11	−0.209547
$536$	3.11791e12	1.63163
$537$	1.45118e12	0.753072
$538$	−5.34414e12	−2.75016
$539$	−3.43771e12	−1.75436
$540$	1.25824e12	0.636782
$541$	8.17432e10	0.0410264	0.0205132	−	0.999790i	$-0.493470\pi$
$541$	8.17432e10	0.0410264	0.0205132	+	0.999790i	$0.493470\pi$
$542$	5.67238e10	0.0282337
$543$	1.20356e12	0.594112
$544$	0	0
$545$	−4.26860e11	−0.207253
$546$	−1.68114e12	−0.809537
$547$	−2.18248e12	−1.04233	−0.521167	−	0.853454i	$-0.674503\pi$
$547$	−2.18248e12	−1.04233	−0.521167	+	0.853454i	$0.674503\pi$
$548$	4.33073e12	2.05139
$549$	−1.62917e12	−0.765402
$550$	−5.46963e12	−2.54874
$551$	−6.24825e11	−0.288786
$552$	−9.79209e11	−0.448900
$553$	2.96968e12	1.35035
$554$	−4.51503e12	−2.03642
$555$	2.46132e12	1.10116
$556$	−3.55005e12	−1.57542
$557$	−3.53439e11	−0.155584	−0.0777921	−	0.996970i	$-0.524787\pi$
$557$	−3.53439e11	−0.155584	−0.0777921	+	0.996970i	$0.524787\pi$
$558$	2.81842e12	1.23070
$559$	1.17040e10	0.00506969
$560$	3.38425e12	1.45418
$561$	0	0
$562$	2.38616e12	1.00899
$563$	1.08142e10	0.00453634	0.00226817	−	0.999997i	$-0.499278\pi$
$563$	1.08142e10	0.00453634	0.00226817	+	0.999997i	$0.499278\pi$
$564$	4.09108e12	1.70248
$565$	2.12231e12	0.876176
$566$	−3.16985e12	−1.29827
$567$	4.27182e12	1.73576
$568$	2.71694e12	1.09525
$569$	3.31804e12	1.32702	0.663508	−	0.748169i	$-0.269067\pi$
$569$	3.31804e12	1.32702	0.663508	+	0.748169i	$0.269067\pi$
$570$	1.92154e12	0.762454
$571$	1.02415e12	0.403184	0.201592	−	0.979470i	$-0.435389\pi$
$571$	1.02415e12	0.403184	0.201592	+	0.979470i	$0.435389\pi$
$572$	2.83183e12	1.10608
$573$	6.79309e11	0.263252
$574$	−9.27729e12	−3.56712
$575$	−2.91590e11	−0.111242
$576$	6.50898e11	0.246384
$577$	−2.29132e12	−0.860585	−0.430293	−	0.902689i	$-0.641590\pi$
$577$	−2.29132e12	−0.860585	−0.430293	+	0.902689i	$0.641590\pi$
$578$	0	0
$579$	3.86586e12	1.42953
$580$	1.37313e12	0.503833
$581$	4.22574e12	1.53854
$582$	−1.53562e12	−0.554791
$583$	−5.43201e12	−1.94739
$584$	1.75391e11	0.0623949
$585$	2.03517e11	0.0718454
$586$	−6.34921e12	−2.22423
$587$	−2.59032e12	−0.900495	−0.450247	−	0.892904i	$-0.648664\pi$
$587$	−2.59032e12	−0.900495	−0.450247	+	0.892904i	$0.648664\pi$
$588$	7.92651e12	2.73454
$589$	−2.33882e12	−0.800717
$590$	−3.00854e11	−0.102217
$591$	−3.31101e12	−1.11639
$592$	−1.09550e13	−3.66578
$593$	1.13589e12	0.377216	0.188608	−	0.982052i	$-0.439602\pi$
$593$	1.13589e12	0.377216	0.188608	+	0.982052i	$0.439602\pi$
$594$	−5.64247e12	−1.85964
$595$	0	0
$596$	3.85709e12	1.25214
$597$	−3.03301e12	−0.977214
$598$	2.15871e11	0.0690301
$599$	−1.61658e12	−0.513071	−0.256535	−	0.966535i	$-0.582581\pi$
$599$	−1.61658e12	−0.513071	−0.256535	+	0.966535i	$0.582581\pi$
$600$	7.18962e12	2.26478
$601$	−3.21649e12	−1.00565	−0.502825	−	0.864388i	$-0.667706\pi$
$601$	−3.21649e12	−1.00565	−0.502825	+	0.864388i	$0.667706\pi$
$602$	−1.62815e11	−0.0505256
$603$	−1.23269e12	−0.379689
$604$	−1.39894e12	−0.427692
$605$	−4.09319e12	−1.24212
$606$	−1.00389e13	−3.02383
$607$	−3.09505e11	−0.0925377	−0.0462688	−	0.998929i	$-0.514733\pi$
$607$	−3.09505e11	−0.0925377	−0.0462688	+	0.998929i	$0.514733\pi$
$608$	−3.11156e12	−0.923446
$609$	2.55649e12	0.753123
$610$	−4.24839e12	−1.24234
$611$	−5.14153e11	−0.149247
$612$	0	0
$613$	−9.05807e11	−0.259098	−0.129549	−	0.991573i	$-0.541353\pi$
$613$	−9.05807e11	−0.259098	−0.129549	+	0.991573i	$0.541353\pi$
$614$	−3.28954e12	−0.934065
$615$	3.11883e12	0.879132
$616$	−2.24577e13	−6.28422
$617$	−3.56373e12	−0.989968	−0.494984	−	0.868902i	$-0.664826\pi$
$617$	−3.56373e12	−0.989968	−0.494984	+	0.868902i	$0.664826\pi$
$618$	−5.59758e10	−0.0154366
$619$	−5.84557e12	−1.60036	−0.800182	−	0.599757i	$-0.795264\pi$
$619$	−5.84557e12	−1.60036	−0.800182	+	0.599757i	$0.795264\pi$
$620$	5.13987e12	1.39698
$621$	−3.00804e11	−0.0811654
$622$	−1.04630e12	−0.280284
$623$	1.70080e12	0.452331
$624$	−2.51548e12	−0.664187
$625$	1.18403e12	0.310387
$626$	4.99450e11	0.129989
$627$	−6.02622e12	−1.55719
$628$	−4.06909e12	−1.04395
$629$	0	0
$630$	−2.83114e12	−0.716026
$631$	6.52192e12	1.63773	0.818866	−	0.573984i	$-0.194603\pi$
$631$	6.52192e12	1.63773	0.818866	+	0.573984i	$0.194603\pi$
$632$	9.40229e12	2.34427
$633$	7.40759e11	0.183384
$634$	9.33550e12	2.29475
$635$	2.08194e12	0.508143
$636$	1.25249e13	3.03540
$637$	−9.96176e11	−0.239722
$638$	−6.15771e12	−1.47139
$639$	−1.07417e12	−0.254870
$640$	−1.24247e12	−0.292735
$641$	−4.50098e12	−1.05304	−0.526521	−	0.850162i	$-0.676504\pi$
$641$	−4.50098e12	−1.05304	−0.526521	+	0.850162i	$0.676504\pi$
$642$	−4.10576e12	−0.953862
$643$	−6.50124e12	−1.49985	−0.749923	−	0.661525i	$-0.769909\pi$
$643$	−6.50124e12	−1.49985	−0.749923	+	0.661525i	$0.769909\pi$
$644$	−2.10011e12	−0.481123
$645$	5.47352e10	0.0124522
$646$	0	0
$647$	−4.54317e11	−0.101927	−0.0509635	−	0.998701i	$-0.516229\pi$
$647$	−4.54317e11	−0.101927	−0.0509635	+	0.998701i	$0.516229\pi$
$648$	1.35250e13	3.01335
$649$	9.43520e11	0.208761
$650$	−1.58498e12	−0.348269
$651$	9.56936e12	2.08818
$652$	1.19452e13	2.58869
$653$	6.21441e12	1.33749	0.668745	−	0.743492i	$-0.266832\pi$
$653$	6.21441e12	1.33749	0.668745	+	0.743492i	$0.266832\pi$
$654$	−4.41371e12	−0.943418
$655$	−1.37809e12	−0.292545
$656$	−1.38816e13	−2.92665
$657$	−6.93424e10	−0.0145196
$658$	7.15242e12	1.48743
$659$	3.63356e12	0.750494	0.375247	−	0.926925i	$-0.377558\pi$
$659$	3.63356e12	0.750494	0.375247	+	0.926925i	$0.377558\pi$
$660$	1.32434e13	2.71677
$661$	3.58304e12	0.730038	0.365019	−	0.931000i	$-0.381063\pi$
$661$	3.58304e12	0.730038	0.365019	+	0.931000i	$0.381063\pi$
$662$	2.95692e12	0.598381
$663$	0	0
$664$	1.33791e13	2.67098
$665$	2.34938e12	0.465861
$666$	9.16458e12	1.80501
$667$	−3.28272e11	−0.0642196
$668$	8.03321e12	1.56097
$669$	−5.83940e12	−1.12707
$670$	−3.21451e12	−0.616280
$671$	1.33235e13	2.53728
$672$	1.27310e13	2.40825
$673$	−2.38054e12	−0.447308	−0.223654	−	0.974669i	$-0.571799\pi$
$673$	−2.38054e12	−0.447308	−0.223654	+	0.974669i	$0.571799\pi$
$674$	−4.25855e12	−0.794863
$675$	2.20858e12	0.409493
$676$	−1.18085e13	−2.17487
$677$	7.75240e12	1.41836	0.709181	−	0.705027i	$-0.249065\pi$
$677$	7.75240e12	1.41836	0.709181	+	0.705027i	$0.249065\pi$
$678$	2.19446e13	3.98836
$679$	−1.87753e12	−0.338978
$680$	0	0
$681$	−9.85407e12	−1.75571
$682$	−2.30494e13	−4.07971
$683$	−5.35319e12	−0.941282	−0.470641	−	0.882325i	$-0.655977\pi$
$683$	−5.35319e12	−0.941282	−0.470641	+	0.882325i	$0.655977\pi$
$684$	5.00361e12	0.874039
$685$	−2.54535e12	−0.441713
$686$	−8.77777e11	−0.151330
$687$	−8.95181e12	−1.53322
$688$	−2.43620e11	−0.0414538
$689$	−1.57408e12	−0.266098
$690$	1.00955e12	0.169553
$691$	−1.40491e12	−0.234422	−0.117211	−	0.993107i	$-0.537395\pi$
$691$	−1.40491e12	−0.234422	−0.117211	+	0.993107i	$0.537395\pi$
$692$	−8.14547e12	−1.35033
$693$	8.87884e12	1.46237
$694$	5.95474e11	0.0974417
$695$	2.08651e12	0.339226
$696$	8.09408e12	1.30745
$697$	0	0
$698$	2.16475e13	3.45191
$699$	9.00084e12	1.42605
$700$	1.54196e13	2.42735
$701$	6.06553e12	0.948720	0.474360	−	0.880331i	$-0.342680\pi$
$701$	6.06553e12	0.948720	0.474360	+	0.880331i	$0.342680\pi$
$702$	−1.63507e12	−0.254108
$703$	−7.60510e12	−1.17437
$704$	−5.32313e12	−0.816752
$705$	−2.40450e12	−0.366584
$706$	1.37531e13	2.08344
$707$	−1.22740e13	−1.84757
$708$	−2.17552e12	−0.325397
$709$	−4.47055e12	−0.664436	−0.332218	−	0.943203i	$-0.607797\pi$
$709$	−4.47055e12	−0.664436	−0.332218	+	0.943203i	$0.607797\pi$
$710$	−2.80112e12	−0.413684
$711$	−3.71728e12	−0.545522
$712$	5.38489e12	0.785266
$713$	−1.22878e12	−0.178062
$714$	0	0
$715$	−1.66439e12	−0.238164
$716$	9.85400e12	1.40121
$717$	−1.29933e12	−0.183604
$718$	6.44428e12	0.904929
$719$	−1.09463e13	−1.52752	−0.763760	−	0.645500i	$-0.776649\pi$
$719$	−1.09463e13	−1.52752	−0.763760	+	0.645500i	$0.776649\pi$
$720$	−4.23622e12	−0.587465
$721$	−6.84389e10	−0.00943180
$722$	7.37889e12	1.01059
$723$	1.61916e12	0.220378
$724$	8.17258e12	1.10544
$725$	2.41026e12	0.323999
$726$	−4.23235e13	−5.65414
$727$	4.35490e12	0.578194	0.289097	−	0.957300i	$-0.406645\pi$
$727$	4.35490e12	0.578194	0.289097	+	0.957300i	$0.406645\pi$
$728$	−6.50775e12	−0.858697
$729$	−1.36549e11	−0.0179067
$730$	−1.80825e11	−0.0235670
$731$	0	0
$732$	−3.07207e13	−3.95486
$733$	−2.30603e12	−0.295051	−0.147525	−	0.989058i	$-0.547131\pi$
$733$	−2.30603e12	−0.295051	−0.147525	+	0.989058i	$0.547131\pi$
$734$	−2.07094e13	−2.63352
$735$	−4.65873e12	−0.588810
$736$	−1.63476e12	−0.205354
$737$	1.00811e13	1.25865
$738$	1.16128e13	1.44106
$739$	−1.13265e13	−1.39700	−0.698498	−	0.715612i	$-0.746148\pi$
$739$	−1.13265e13	−1.39700	−0.698498	+	0.715612i	$0.746148\pi$
$740$	1.67132e13	2.04888
$741$	−1.74627e12	−0.212780
$742$	2.18972e13	2.65198
$743$	1.47703e13	1.77803	0.889016	−	0.457877i	$-0.151390\pi$
$743$	1.47703e13	1.77803	0.889016	+	0.457877i	$0.151390\pi$
$744$	3.02975e13	3.62517
$745$	−2.26697e12	−0.269614
$746$	1.77417e13	2.09735
$747$	−5.28954e12	−0.621549
$748$	0	0
$749$	−5.01992e12	−0.582812
$750$	−1.73067e13	−1.99727
$751$	4.97306e12	0.570485	0.285243	−	0.958455i	$-0.407926\pi$
$751$	4.97306e12	0.570485	0.285243	+	0.958455i	$0.407926\pi$
$752$	1.07021e13	1.22037
$753$	1.19090e13	1.34989
$754$	−1.78438e12	−0.201055
$755$	8.22212e11	0.0920921
$756$	1.59069e13	1.77107
$757$	−4.59977e12	−0.509102	−0.254551	−	0.967059i	$-0.581928\pi$
$757$	−4.59977e12	−0.509102	−0.254551	+	0.967059i	$0.581928\pi$
$758$	2.14687e13	2.36208
$759$	−3.16607e12	−0.346284
$760$	7.43837e12	0.808754
$761$	−1.36003e13	−1.47000	−0.734999	−	0.678068i	$-0.762817\pi$
$761$	−1.36003e13	−1.47000	−0.734999	+	0.678068i	$0.762817\pi$
$762$	2.15272e13	2.31307
$763$	−5.39644e12	−0.576430
$764$	4.61274e12	0.489823
$765$	0	0
$766$	−2.47105e12	−0.259330
$767$	2.73412e11	0.0285258
$768$	−1.81238e13	−1.87985
$769$	−3.92919e12	−0.405168	−0.202584	−	0.979265i	$-0.564934\pi$
$769$	−3.92919e12	−0.405168	−0.202584	+	0.979265i	$0.564934\pi$
$770$	2.31534e13	2.37360
$771$	−8.27381e12	−0.843258
$772$	2.62505e13	2.65986
$773$	1.26776e11	0.0127711	0.00638557	−	0.999980i	$-0.497967\pi$
$773$	1.26776e11	0.0127711	0.00638557	+	0.999980i	$0.497967\pi$
$774$	2.03803e11	0.0204116
$775$	9.02202e12	0.898351
$776$	−5.94443e12	−0.588481
$777$	3.11165e13	3.06264
$778$	−2.29407e12	−0.224491
$779$	−9.63672e12	−0.937585
$780$	3.83766e12	0.371228
$781$	8.78468e12	0.844883
$782$	0	0
$783$	2.48643e12	0.236400
$784$	2.07355e13	1.96016
$785$	2.39157e12	0.224787
$786$	−1.42494e13	−1.33167
$787$	5.21193e12	0.484298	0.242149	−	0.970239i	$-0.422148\pi$
$787$	5.21193e12	0.484298	0.242149	+	0.970239i	$0.422148\pi$
$788$	−2.24829e13	−2.07723
$789$	−1.79333e13	−1.64745
$790$	−9.69359e12	−0.885447
$791$	2.68307e13	2.43690
$792$	2.81112e13	2.53873
$793$	3.86087e12	0.346702
$794$	8.88255e12	0.793132
$795$	−7.36138e12	−0.653593
$796$	−2.05952e13	−1.81826
$797$	−2.04646e13	−1.79656	−0.898280	−	0.439424i	$-0.855183\pi$
$797$	−2.04646e13	−1.79656	−0.898280	+	0.439424i	$0.855183\pi$
$798$	2.42925e13	2.12060
$799$	0	0
$800$	1.20028e13	1.03605
$801$	−2.12896e12	−0.182735
$802$	−1.18020e13	−1.00733
$803$	5.67091e11	0.0481318
$804$	−2.32446e13	−1.96187
$805$	1.23432e12	0.103597
$806$	−6.67922e12	−0.557465
$807$	2.27128e13	1.88512
$808$	−3.88608e13	−3.20745
$809$	2.47572e12	0.203204	0.101602	−	0.994825i	$-0.467603\pi$
$809$	2.47572e12	0.203204	0.101602	+	0.994825i	$0.467603\pi$
$810$	−1.39440e13	−1.13816
$811$	−3.77855e12	−0.306713	−0.153356	−	0.988171i	$-0.549008\pi$
$811$	−3.77855e12	−0.306713	−0.153356	+	0.988171i	$0.549008\pi$
$812$	1.73594e13	1.40131
$813$	−2.41079e11	−0.0193531
$814$	−7.49491e13	−5.98352
$815$	−7.02070e12	−0.557405
$816$	0	0
$817$	−1.69123e11	−0.0132802
$818$	−1.00635e13	−0.785883
$819$	2.57290e12	0.199823
$820$	2.11779e13	1.63577
$821$	−8.59353e12	−0.660127	−0.330063	−	0.943959i	$-0.607070\pi$
$821$	−8.59353e12	−0.660127	−0.330063	+	0.943959i	$0.607070\pi$
$822$	−2.63188e13	−2.01068
$823$	8.64495e12	0.656846	0.328423	−	0.944531i	$-0.393483\pi$
$823$	8.64495e12	0.656846	0.328423	+	0.944531i	$0.393483\pi$
$824$	−2.16684e11	−0.0163740
$825$	2.32462e13	1.74706
$826$	−3.80346e12	−0.284294
$827$	1.08552e13	0.806979	0.403490	−	0.914984i	$-0.367797\pi$
$827$	1.08552e13	0.806979	0.403490	+	0.914984i	$0.367797\pi$
$828$	2.62881e12	0.194367
$829$	−1.09679e13	−0.806547	−0.403274	−	0.915079i	$-0.632128\pi$
$829$	−1.09679e13	−0.806547	−0.403274	+	0.915079i	$0.632128\pi$
$830$	−1.37936e13	−1.00885
$831$	1.91891e13	1.39589
$832$	−1.54253e12	−0.111604
$833$	0	0
$834$	2.15744e13	1.54416
$835$	−4.72145e12	−0.336114
$836$	−4.09201e13	−2.89740
$837$	9.30711e12	0.655466
$838$	−4.26702e13	−2.98900
$839$	7.29579e12	0.508327	0.254164	−	0.967161i	$-0.418200\pi$
$839$	7.29579e12	0.508327	0.254164	+	0.967161i	$0.418200\pi$
$840$	−3.04343e13	−2.10914
$841$	−1.17937e13	−0.812956
$842$	−4.63739e13	−3.17957
$843$	−1.01413e13	−0.691622
$844$	5.03001e12	0.341215
$845$	6.94033e12	0.468301
$846$	−8.95300e12	−0.600900
$847$	−5.17469e13	−3.45469
$848$	3.27646e13	2.17583
$849$	1.34720e13	0.889913
$850$	0	0
$851$	−3.99558e12	−0.261154
$852$	−2.02553e13	−1.31692
$853$	2.42665e13	1.56941	0.784704	−	0.619871i	$-0.212815\pi$
$853$	2.42665e13	1.56941	0.784704	+	0.619871i	$0.212815\pi$
$854$	−5.37089e13	−3.45530
$855$	−2.94083e12	−0.188201
$856$	−1.58935e13	−1.01179
$857$	6.43774e12	0.407680	0.203840	−	0.979004i	$-0.434658\pi$
$857$	6.43774e12	0.407680	0.203840	+	0.979004i	$0.434658\pi$
$858$	−1.72097e13	−1.08413
$859$	−1.05863e13	−0.663399	−0.331699	−	0.943385i	$-0.607622\pi$
$859$	−1.05863e13	−0.663399	−0.331699	+	0.943385i	$0.607622\pi$
$860$	3.71671e11	0.0231694
$861$	3.94289e13	2.44512
$862$	−1.15212e13	−0.710750
$863$	−5.29030e11	−0.0324662	−0.0162331	−	0.999868i	$-0.505167\pi$
$863$	−5.29030e11	−0.0324662	−0.0162331	+	0.999868i	$0.505167\pi$
$864$	1.23821e13	0.755933
$865$	4.78743e12	0.290757
$866$	2.44465e13	1.47702
$867$	0	0
$868$	6.49793e13	3.88540
$869$	3.04004e13	1.80838
$870$	−8.34484e12	−0.493835
$871$	2.92130e12	0.171986
$872$	−1.70856e13	−1.00071
$873$	2.35018e12	0.136942
$874$	−3.11934e12	−0.180826
$875$	−2.11600e13	−1.22034
$876$	−1.30757e12	−0.0750233
$877$	−8.95643e12	−0.511254	−0.255627	−	0.966775i	$-0.582282\pi$
$877$	−8.95643e12	−0.511254	−0.255627	+	0.966775i	$0.582282\pi$
$878$	−4.93635e13	−2.80337
$879$	2.69844e13	1.52463
$880$	3.46443e13	1.94742
$881$	−9.86603e12	−0.551761	−0.275880	−	0.961192i	$-0.588969\pi$
$881$	−9.86603e12	−0.551761	−0.275880	+	0.961192i	$0.588969\pi$
$882$	−1.73465e13	−0.965170
$883$	−2.95451e13	−1.63555	−0.817773	−	0.575541i	$-0.804791\pi$
$883$	−2.95451e13	−1.63555	−0.817773	+	0.575541i	$0.804791\pi$
$884$	0	0
$885$	1.27864e12	0.0700656
$886$	−2.53717e13	−1.38324
$887$	−1.21200e13	−0.657425	−0.328712	−	0.944430i	$-0.606615\pi$
$887$	−1.21200e13	−0.657425	−0.328712	+	0.944430i	$0.606615\pi$
$888$	9.85177e13	5.31687
$889$	2.63202e13	1.41329
$890$	−5.55172e12	−0.296601
$891$	4.37303e13	2.32452
$892$	−3.96515e13	−2.09710
$893$	7.42953e12	0.390958
$894$	−2.34404e13	−1.22729
$895$	−5.79160e12	−0.301714
$896$	−1.57075e13	−0.814180
$897$	−9.17460e11	−0.0473174
$898$	6.49069e13	3.33079
$899$	1.01570e13	0.518617
$900$	−1.93014e13	−0.980614
$901$	0	0
$902$	−9.49709e13	−4.77706
$903$	6.91972e11	0.0346333
$904$	8.49485e13	4.23056
$905$	−4.80336e12	−0.238027
$906$	8.50164e12	0.419205
$907$	−3.13056e13	−1.53599	−0.767997	−	0.640453i	$-0.778746\pi$
$907$	−3.13056e13	−1.53599	−0.767997	+	0.640453i	$0.778746\pi$
$908$	−6.69125e13	−3.26679
$909$	1.53639e13	0.746389
$910$	6.70937e12	0.324336
$911$	2.59379e13	1.24768	0.623838	−	0.781554i	$-0.285573\pi$
$911$	2.59379e13	1.24768	0.623838	+	0.781554i	$0.285573\pi$
$912$	3.63488e13	1.73986
$913$	4.32585e13	2.06041
$914$	4.47659e13	2.12173
$915$	1.80558e13	0.851574
$916$	−6.07859e13	−2.85281
$917$	−1.74221e13	−0.813651
$918$	0	0
$919$	−2.19375e13	−1.01454	−0.507268	−	0.861788i	$-0.669345\pi$
$919$	−2.19375e13	−1.01454	−0.507268	+	0.861788i	$0.669345\pi$
$920$	3.90799e12	0.179849
$921$	1.39807e13	0.640265
$922$	−5.11978e13	−2.33325
$923$	2.54561e12	0.115448
$924$	1.67426e14	7.55611
$925$	2.93367e13	1.31757
$926$	7.14664e13	3.19413
$927$	8.56680e10	0.00381031
$928$	1.35128e13	0.598108
$929$	−1.67080e12	−0.0735960	−0.0367980	−	0.999323i	$-0.511716\pi$
$929$	−1.67080e12	−0.0735960	−0.0367980	+	0.999323i	$0.511716\pi$
$930$	−3.12362e13	−1.36926
$931$	1.43948e13	0.627959
$932$	6.11188e13	2.65340
$933$	4.44680e12	0.192123
$934$	6.08980e13	2.61844
$935$	0	0
$936$	8.14604e12	0.346901
$937$	4.07852e13	1.72852	0.864260	−	0.503046i	$-0.167787\pi$
$937$	4.07852e13	1.72852	0.864260	+	0.503046i	$0.167787\pi$
$938$	−4.06384e13	−1.71405
$939$	−2.12268e12	−0.0891025
$940$	−1.63274e13	−0.682088
$941$	−1.37791e13	−0.572884	−0.286442	−	0.958098i	$-0.592473\pi$
$941$	−1.37791e13	−0.572884	−0.286442	+	0.958098i	$0.592473\pi$
$942$	2.47288e13	1.02323
$943$	−5.06296e12	−0.208498
$944$	−5.69109e12	−0.233250
$945$	−9.34912e12	−0.381353
$946$	−1.66673e12	−0.0676635
$947$	−1.07895e13	−0.435939	−0.217969	−	0.975956i	$-0.569943\pi$
$947$	−1.07895e13	−0.435939	−0.217969	+	0.975956i	$0.569943\pi$
$948$	−7.00958e13	−2.81873
$949$	1.64331e11	0.00657690
$950$	2.29031e13	0.912300
$951$	−3.96763e13	−1.57296
$952$	0	0
$953$	−3.87488e13	−1.52174	−0.760870	−	0.648905i	$-0.775227\pi$
$953$	−3.87488e13	−1.52174	−0.760870	+	0.648905i	$0.775227\pi$
$954$	−2.74097e13	−1.07136
$955$	−2.71110e12	−0.105470
$956$	−8.82290e12	−0.341626
$957$	2.61706e13	1.00858
$958$	4.42499e13	1.69733
$959$	−3.21788e13	−1.22853
$960$	−7.21383e12	−0.274123
$961$	1.15797e13	0.437969
$962$	−2.17187e13	−0.817608
$963$	6.28365e12	0.235447
$964$	1.09947e13	0.410049
$965$	−1.54285e13	−0.572731
$966$	1.27629e13	0.471575
$967$	3.06413e13	1.12691	0.563454	−	0.826148i	$-0.309472\pi$
$967$	3.06413e13	1.12691	0.563454	+	0.826148i	$0.309472\pi$
$968$	−1.63836e14	−5.99749
$969$	0	0
$970$	6.12859e12	0.222274
$971$	−4.68780e13	−1.69232	−0.846160	−	0.532929i	$-0.821091\pi$
$971$	−4.68780e13	−1.69232	−0.846160	+	0.532929i	$0.821091\pi$
$972$	−6.54489e13	−2.35182
$973$	2.63780e13	0.943484
$974$	9.15737e13	3.26029
$975$	6.73625e12	0.238725
$976$	−8.03644e13	−2.83491
$977$	1.42867e13	0.501656	0.250828	−	0.968032i	$-0.419297\pi$
$977$	1.42867e13	0.501656	0.250828	+	0.968032i	$0.419297\pi$
$978$	−7.25937e13	−2.53731
$979$	1.74109e13	0.605759
$980$	−3.16344e13	−1.09558
$981$	6.75496e12	0.232869
$982$	−7.61203e13	−2.61215
$983$	7.35838e12	0.251357	0.125679	−	0.992071i	$-0.459889\pi$
$983$	7.35838e12	0.251357	0.125679	+	0.992071i	$0.459889\pi$
$984$	1.24836e14	4.24483
$985$	1.32141e13	0.447276
$986$	0	0
$987$	−3.03981e13	−1.01958
$988$	−1.18578e13	−0.395911
$989$	−8.88544e10	−0.00295322
$990$	−2.89821e13	−0.958898
$991$	−3.30115e13	−1.08726	−0.543630	−	0.839325i	$-0.682951\pi$
$991$	−3.30115e13	−1.08726	−0.543630	+	0.839325i	$0.682951\pi$
$992$	5.05807e13	1.65837
$993$	−1.25670e13	−0.410167
$994$	−3.54123e13	−1.15057
$995$	1.21046e13	0.391515
$996$	−9.97434e13	−3.21157
$997$	−2.85504e13	−0.915132	−0.457566	−	0.889176i	$-0.651279\pi$
$997$	−2.85504e13	−0.915132	−0.457566	+	0.889176i	$0.651279\pi$
$998$	−3.58238e13	−1.14310
$999$	3.02637e13	0.961341

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.i.1.2		52
17.11	odd	16		17.10.d.a.2.1	✓	52
17.14	odd	16		17.10.d.a.9.1	yes	52
17.16	even	2	inner	289.10.a.i.1.1		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.d.a.2.1	✓	52	17.11	odd	16
17.10.d.a.9.1	yes	52	17.14	odd	16
289.10.a.i.1.1		52	17.16	even	2	inner
289.10.a.i.1.2		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)

\(f(q)\)	\(=\)	\(q-41.2664 q^{2} +175.384 q^{3} +1190.92 q^{4} -699.952 q^{5} -7237.48 q^{6} -8848.92 q^{7} -28016.5 q^{8} +11076.6 q^{9} +O(q^{10})\)	\(q-41.2664 q^{2} +175.384 q^{3} +1190.92 q^{4} -699.952 q^{5} -7237.48 q^{6} -8848.92 q^{7} -28016.5 q^{8} +11076.6 q^{9} +28884.5 q^{10} -90585.7 q^{11} +208868. q^{12} -26249.8 q^{13} +365163. q^{14} -122760. q^{15} +546392. q^{16} -457091. q^{18} +379311. q^{19} -833585. q^{20} -1.55196e6 q^{21} +3.73815e6 q^{22} +199283. q^{23} -4.91365e6 q^{24} -1.46319e6 q^{25} +1.08324e6 q^{26} -1.50943e6 q^{27} -1.05383e7 q^{28} -1.64726e6 q^{29} +5.06588e6 q^{30} -6.16598e6 q^{31} -8.20319e6 q^{32} -1.58873e7 q^{33} +6.19382e6 q^{35} +1.31913e7 q^{36} -2.00498e7 q^{37} -1.56528e7 q^{38} -4.60380e6 q^{39} +1.96102e7 q^{40} -2.54059e7 q^{41} +6.40439e7 q^{42} -445870. q^{43} -1.07880e8 q^{44} -7.75308e6 q^{45} -8.22371e6 q^{46} +1.95869e7 q^{47} +9.58285e7 q^{48} +3.79498e7 q^{49} +6.03807e7 q^{50} -3.12614e7 q^{52} +5.99655e7 q^{53} +6.22887e7 q^{54} +6.34056e7 q^{55} +2.47916e8 q^{56} +6.65251e7 q^{57} +6.79767e7 q^{58} -1.04158e7 q^{59} -1.46198e8 q^{60} -1.47082e8 q^{61} +2.54448e8 q^{62} -9.80159e7 q^{63} +5.87635e7 q^{64} +1.83736e7 q^{65} +6.55612e8 q^{66} -1.11288e8 q^{67} +3.49511e7 q^{69} -2.55597e8 q^{70} -9.69765e7 q^{71} -3.10328e8 q^{72} -6.26027e6 q^{73} +8.27383e8 q^{74} -2.56621e8 q^{75} +4.51728e8 q^{76} +8.01586e8 q^{77} +1.89982e8 q^{78} -3.35598e8 q^{79} -3.82448e8 q^{80} -4.82750e8 q^{81} +1.04841e9 q^{82} -4.77542e8 q^{83} -1.84826e9 q^{84} +1.83995e7 q^{86} -2.88904e8 q^{87} +2.53790e9 q^{88} -1.92204e8 q^{89} +3.19942e8 q^{90} +2.32283e8 q^{91} +2.37330e8 q^{92} -1.08142e9 q^{93} -8.08282e8 q^{94} -2.65499e8 q^{95} -1.43871e9 q^{96} +2.12176e8 q^{97} -1.56605e9 q^{98} -1.00338e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) \) 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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