LMFDB - Embedded newform 289.10.a.f.1.7

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:	$1$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-17.1503 q^{2} -137.714 q^{3} -217.866 q^{4} +1247.89 q^{5} +2361.84 q^{6} +10551.1 q^{7} +12517.4 q^{8} -717.820 q^{9} +O(q^{10})$	\(q-17.1503 q^{2} -137.714 q^{3} -217.866 q^{4} +1247.89 q^{5} +2361.84 q^{6} +10551.1 q^{7} +12517.4 q^{8} -717.820 q^{9} -21401.7 q^{10} +49404.8 q^{11} +30003.2 q^{12} +54354.1 q^{13} -180956. q^{14} -171852. q^{15} -103131. q^{16} +12310.9 q^{18} +716600. q^{19} -271872. q^{20} -1.45304e6 q^{21} -847310. q^{22} -203029. q^{23} -1.72383e6 q^{24} -395901. q^{25} -932191. q^{26} +2.80948e6 q^{27} -2.29873e6 q^{28} -6.48924e6 q^{29} +2.94732e6 q^{30} -3.52103e6 q^{31} -4.64020e6 q^{32} -6.80374e6 q^{33} +1.31666e7 q^{35} +156388. q^{36} -1.86422e7 q^{37} -1.22899e7 q^{38} -7.48532e6 q^{39} +1.56204e7 q^{40} -1.92239e7 q^{41} +2.49202e7 q^{42} -1.47802e7 q^{43} -1.07636e7 q^{44} -895759. q^{45} +3.48203e6 q^{46} -7.91732e6 q^{47} +1.42026e7 q^{48} +7.09730e7 q^{49} +6.78985e6 q^{50} -1.18419e7 q^{52} +1.83584e7 q^{53} -4.81836e7 q^{54} +6.16517e7 q^{55} +1.32073e8 q^{56} -9.86859e7 q^{57} +1.11293e8 q^{58} -8.19772e7 q^{59} +3.74406e7 q^{60} +2.69459e7 q^{61} +6.03869e7 q^{62} -7.57382e6 q^{63} +1.32384e8 q^{64} +6.78278e7 q^{65} +1.16686e8 q^{66} -5.75938e7 q^{67} +2.79600e7 q^{69} -2.25812e8 q^{70} +2.86560e7 q^{71} -8.98528e6 q^{72} +3.69579e8 q^{73} +3.19720e8 q^{74} +5.45212e7 q^{75} -1.56123e8 q^{76} +5.21277e8 q^{77} +1.28376e8 q^{78} +5.25163e7 q^{79} -1.28696e8 q^{80} -3.72776e8 q^{81} +3.29696e8 q^{82} -1.13599e8 q^{83} +3.16568e8 q^{84} +2.53486e8 q^{86} +8.93659e8 q^{87} +6.18422e8 q^{88} -6.81819e8 q^{89} +1.53626e7 q^{90} +5.73497e8 q^{91} +4.42332e7 q^{92} +4.84896e8 q^{93} +1.35785e8 q^{94} +8.94236e8 q^{95} +6.39020e8 q^{96} -1.61987e9 q^{97} -1.21721e9 q^{98} -3.54638e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 5124 q^{4} + 108368 q^{9}+O(q^{10}) $ 24 * q + 5124 * q^4 + 108368 * q^9	$ 24 q + 5124 q^{4} + 108368 q^{9} - 244832 q^{13} - 127332 q^{15} - 279932 q^{16} + 888764 q^{18} - 2280212 q^{19} + 775748 q^{21} - 2762628 q^{25} - 3334452 q^{26} - 39084792 q^{30} + 2010240 q^{32} - 30349992 q^{33} - 25532364 q^{35} + 31177320 q^{36} - 13171392 q^{38} - 86527192 q^{42} + 61046960 q^{43} - 153365328 q^{47} + 169445876 q^{49} - 236105676 q^{50} - 209898380 q^{52} + 85777812 q^{53} - 255767540 q^{55} - 767709024 q^{59} + 429639656 q^{60} - 1006108924 q^{64} + 346830788 q^{66} - 26076868 q^{67} - 751973532 q^{69} - 319504544 q^{70} - 1171736028 q^{72} - 1640047616 q^{76} - 174401076 q^{77} - 347156560 q^{81} - 1649346672 q^{83} - 935672904 q^{84} + 690159588 q^{86} - 257027500 q^{87} + 191594460 q^{89} + 1842509012 q^{93} + 2877218432 q^{94} + 4413444720 q^{98}+O(q^{100}) $ 24 * q + 5124 * q^4 + 108368 * q^9 - 244832 * q^13 - 127332 * q^15 - 279932 * q^16 + 888764 * q^18 - 2280212 * q^19 + 775748 * q^21 - 2762628 * q^25 - 3334452 * q^26 - 39084792 * q^30 + 2010240 * q^32 - 30349992 * q^33 - 25532364 * q^35 + 31177320 * q^36 - 13171392 * q^38 - 86527192 * q^42 + 61046960 * q^43 - 153365328 * q^47 + 169445876 * q^49 - 236105676 * q^50 - 209898380 * q^52 + 85777812 * q^53 - 255767540 * q^55 - 767709024 * q^59 + 429639656 * q^60 - 1006108924 * q^64 + 346830788 * q^66 - 26076868 * q^67 - 751973532 * q^69 - 319504544 * q^70 - 1171736028 * q^72 - 1640047616 * q^76 - 174401076 * q^77 - 347156560 * q^81 - 1649346672 * q^83 - 935672904 * q^84 + 690159588 * q^86 - 257027500 * q^87 + 191594460 * q^89 + 1842509012 * q^93 + 2877218432 * q^94 + 4413444720 * 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 $

$2$	−17.1503	−0.757945	−0.378973	−	0.925408i	$-0.623723\pi$
$2$	−17.1503	−0.757945	−0.378973	+	0.925408i	$0.623723\pi$
$3$	−137.714	−0.981596	−0.490798	−	0.871273i	$-0.663295\pi$
$3$	−137.714	−0.981596	−0.490798	+	0.871273i	$0.663295\pi$
$4$	−217.866	−0.425519
$5$	1247.89	0.892916	0.446458	−	0.894805i	$-0.352685\pi$
$5$	1247.89	0.892916	0.446458	+	0.894805i	$0.352685\pi$
$6$	2361.84	0.743996
$7$	10551.1	1.66096	0.830478	−	0.557051i	$-0.188067\pi$
$7$	10551.1	1.66096	0.830478	+	0.557051i	$0.188067\pi$
$8$	12517.4	1.08047
$9$	−717.820	−0.0364690
$10$	−21401.7	−0.676781
$11$	49404.8	1.01742	0.508712	−	0.860937i	$-0.330122\pi$
$11$	49404.8	1.01742	0.508712	+	0.860937i	$0.330122\pi$
$12$	30003.2	0.417688
$13$	54354.1	0.527821	0.263911	−	0.964547i	$-0.414988\pi$
$13$	54354.1	0.527821	0.263911	+	0.964547i	$0.414988\pi$
$14$	−180956.	−1.25891
$15$	−171852.	−0.876483
$16$	−103131.	−0.393415
$17$	0	0
$17$	0	0
$18$	12310.9	0.0276415
$19$	716600.	1.26149	0.630747	−	0.775988i	$-0.282748\pi$
$19$	716600.	1.26149	0.630747	+	0.775988i	$0.282748\pi$
$20$	−271872.	−0.379953
$21$	−1.45304e6	−1.63039
$22$	−847310.	−0.771152
$23$	−203029.	−0.151281	−0.0756404	−	0.997135i	$-0.524100\pi$
$23$	−203029.	−0.151281	−0.0756404	+	0.997135i	$0.524100\pi$
$24$	−1.72383e6	−1.06058
$25$	−395901.	−0.202702
$26$	−932191.	−0.400060
$27$	2.80948e6	1.01739
$28$	−2.29873e6	−0.706768
$29$	−6.48924e6	−1.70374	−0.851869	−	0.523756i	$-0.824531\pi$
$29$	−6.48924e6	−1.70374	−0.851869	+	0.523756i	$0.824531\pi$
$30$	2.94732e6	0.664326
$31$	−3.52103e6	−0.684766	−0.342383	−	0.939560i	$-0.611234\pi$
$31$	−3.52103e6	−0.684766	−0.342383	+	0.939560i	$0.611234\pi$
$32$	−4.64020e6	−0.782279
$33$	−6.80374e6	−0.998700
$34$	0	0
$35$	1.31666e7	1.48309
$36$	156388.	0.0155183
$37$	−1.86422e7	−1.63527	−0.817634	−	0.575739i	$-0.804714\pi$
$37$	−1.86422e7	−1.63527	−0.817634	+	0.575739i	$0.804714\pi$
$38$	−1.22899e7	−0.956144
$39$	−7.48532e6	−0.518107
$40$	1.56204e7	0.964764
$41$	−1.92239e7	−1.06246	−0.531231	−	0.847227i	$-0.678271\pi$
$41$	−1.92239e7	−1.06246	−0.531231	+	0.847227i	$0.678271\pi$
$42$	2.49202e7	1.23575
$43$	−1.47802e7	−0.659285	−0.329642	−	0.944106i	$-0.606928\pi$
$43$	−1.47802e7	−0.659285	−0.329642	+	0.944106i	$0.606928\pi$
$44$	−1.07636e7	−0.432933
$45$	−895759.	−0.0325638
$46$	3.48203e6	0.114663
$47$	−7.91732e6	−0.236667	−0.118334	−	0.992974i	$-0.537755\pi$
$47$	−7.91732e6	−0.236667	−0.118334	+	0.992974i	$0.537755\pi$
$48$	1.42026e7	0.386174
$49$	7.09730e7	1.75878
$50$	6.78985e6	0.153637
$51$	0	0
$52$	−1.18419e7	−0.224598
$53$	1.83584e7	0.319590	0.159795	−	0.987150i	$-0.448917\pi$
$53$	1.83584e7	0.319590	0.159795	+	0.987150i	$0.448917\pi$
$54$	−4.81836e7	−0.771129
$55$	6.16517e7	0.908474
$56$	1.32073e8	1.79461
$57$	−9.86859e7	−1.23828
$58$	1.11293e8	1.29134
$59$	−8.19772e7	−0.880763	−0.440382	−	0.897811i	$-0.645157\pi$
$59$	−8.19772e7	−0.880763	−0.440382	+	0.897811i	$0.645157\pi$
$60$	3.74406e7	0.372960
$61$	2.69459e7	0.249178	0.124589	−	0.992208i	$-0.460239\pi$
$61$	2.69459e7	0.249178	0.124589	+	0.992208i	$0.460239\pi$
$62$	6.03869e7	0.519015
$63$	−7.57382e6	−0.0605735
$64$	1.32384e8	0.986339
$65$	6.78278e7	0.471300
$66$	1.16686e8	0.756960
$67$	−5.75938e7	−0.349172	−0.174586	−	0.984642i	$-0.555859\pi$
$67$	−5.75938e7	−0.349172	−0.174586	+	0.984642i	$0.555859\pi$
$68$	0	0
$69$	2.79600e7	0.148497
$70$	−2.25812e8	−1.12410
$71$	2.86560e7	0.133830	0.0669149	−	0.997759i	$-0.478684\pi$
$71$	2.86560e7	0.133830	0.0669149	+	0.997759i	$0.478684\pi$
$72$	−8.98528e6	−0.0394035
$73$	3.69579e8	1.52319	0.761596	−	0.648052i	$-0.224416\pi$
$73$	3.69579e8	1.52319	0.761596	+	0.648052i	$0.224416\pi$
$74$	3.19720e8	1.23944
$75$	5.45212e7	0.198971
$76$	−1.56123e8	−0.536790
$77$	5.21277e8	1.68990
$78$	1.28376e8	0.392697
$79$	5.25163e7	0.151695	0.0758476	−	0.997119i	$-0.475834\pi$
$79$	5.25163e7	0.151695	0.0758476	+	0.997119i	$0.475834\pi$
$80$	−1.28696e8	−0.351286
$81$	−3.72776e8	−0.962201
$82$	3.29696e8	0.805289
$83$	−1.13599e8	−0.262739	−0.131369	−	0.991333i	$-0.541937\pi$
$83$	−1.13599e8	−0.262739	−0.131369	+	0.991333i	$0.541937\pi$
$84$	3.16568e8	0.693761
$85$	0	0
$86$	2.53486e8	0.499702
$87$	8.93659e8	1.67238
$88$	6.18422e8	1.09929
$89$	−6.81819e8	−1.15190	−0.575949	−	0.817485i	$-0.695367\pi$
$89$	−6.81819e8	−1.15190	−0.575949	+	0.817485i	$0.695367\pi$
$90$	1.53626e7	0.0246816
$91$	5.73497e8	0.876688
$92$	4.42332e7	0.0643728
$93$	4.84896e8	0.672164
$94$	1.35785e8	0.179381
$95$	8.94236e8	1.12641
$96$	6.39020e8	0.767882
$97$	−1.61987e9	−1.85784	−0.928918	−	0.370286i	$-0.879260\pi$
$97$	−1.61987e9	−1.85784	−0.928918	+	0.370286i	$0.879260\pi$
$98$	−1.21721e9	−1.33306
$99$	−3.54638e7	−0.0371045
$100$	8.62533e7	0.0862533
$101$	−1.17936e9	−1.12772	−0.563858	−	0.825872i	$-0.690683\pi$
$101$	−1.17936e9	−1.12772	−0.563858	+	0.825872i	$0.690683\pi$
$102$	0	0
$103$	−2.87825e8	−0.251977	−0.125988	−	0.992032i	$-0.540210\pi$
$103$	−2.87825e8	−0.251977	−0.125988	+	0.992032i	$0.540210\pi$
$104$	6.80374e8	0.570293
$105$	−1.81323e9	−1.45580
$106$	−3.14852e8	−0.242231
$107$	−6.86881e7	−0.0506587	−0.0253294	−	0.999679i	$-0.508063\pi$
$107$	−6.86881e7	−0.0506587	−0.0253294	+	0.999679i	$0.508063\pi$
$108$	−6.12090e8	−0.432920
$109$	−2.40193e9	−1.62982	−0.814912	−	0.579584i	$-0.803215\pi$
$109$	−2.40193e9	−1.62982	−0.814912	+	0.579584i	$0.803215\pi$
$110$	−1.05735e9	−0.688574
$111$	2.56729e9	1.60517
$112$	−1.08815e9	−0.653445
$113$	−2.79285e9	−1.61137	−0.805685	−	0.592345i	$-0.798202\pi$
$113$	−2.79285e9	−1.61137	−0.805685	+	0.592345i	$0.798202\pi$
$114$	1.69250e9	0.938547
$115$	−2.53358e8	−0.135081
$116$	1.41378e9	0.724972
$117$	−3.90164e7	−0.0192491
$118$	1.40594e9	0.667570
$119$	0	0
$120$	−2.15115e9	−0.947009
$121$	8.28881e7	0.0351526
$122$	−4.62132e8	−0.188863
$123$	2.64740e9	1.04291
$124$	7.67112e8	0.291381
$125$	−2.93132e9	−1.07391
$126$	1.29894e8	0.0459114
$127$	4.35945e9	1.48701	0.743507	−	0.668728i	$-0.233161\pi$
$127$	4.35945e9	1.48701	0.743507	+	0.668728i	$0.233161\pi$
$128$	1.05346e8	0.0346875
$129$	2.03545e9	0.647151
$130$	−1.16327e9	−0.357220
$131$	5.93689e8	0.176132	0.0880660	−	0.996115i	$-0.471931\pi$
$131$	5.93689e8	0.176132	0.0880660	+	0.996115i	$0.471931\pi$
$132$	1.48230e9	0.424966
$133$	7.56095e9	2.09529
$134$	9.87753e8	0.264653
$135$	3.50592e9	0.908447
$136$	0	0
$137$	−2.51782e9	−0.610636	−0.305318	−	0.952250i	$-0.598763\pi$
$137$	−2.51782e9	−0.610636	−0.305318	+	0.952250i	$0.598763\pi$
$138$	−4.79524e8	−0.112552
$139$	1.27183e9	0.288978	0.144489	−	0.989506i	$-0.453846\pi$
$139$	1.27183e9	0.288978	0.144489	+	0.989506i	$0.453846\pi$
$140$	−2.86856e9	−0.631085
$141$	1.09033e9	0.232312
$142$	−4.91460e8	−0.101436
$143$	2.68535e9	0.537018
$144$	7.40297e7	0.0143475
$145$	−8.09784e9	−1.52129
$146$	−6.33841e9	−1.15450
$147$	−9.77398e9	−1.72641
$148$	4.06149e9	0.695837
$149$	−1.57163e9	−0.261223	−0.130612	−	0.991434i	$-0.541694\pi$
$149$	−1.57163e9	−0.261223	−0.130612	+	0.991434i	$0.541694\pi$
$150$	−9.35058e8	−0.150809
$151$	−8.34738e9	−1.30663	−0.653317	−	0.757084i	$-0.726623\pi$
$151$	−8.34738e9	−1.30663	−0.653317	+	0.757084i	$0.726623\pi$
$152$	8.97000e9	1.36300
$153$	0	0
$154$	−8.94008e9	−1.28085
$155$	−4.39385e9	−0.611439
$156$	1.63080e9	0.220465
$157$	−1.34348e9	−0.176474	−0.0882372	−	0.996099i	$-0.528123\pi$
$157$	−1.34348e9	−0.176474	−0.0882372	+	0.996099i	$0.528123\pi$
$158$	−9.00672e8	−0.114977
$159$	−2.52821e9	−0.313708
$160$	−5.79044e9	−0.698509
$161$	−2.14219e9	−0.251271
$162$	6.39324e9	0.729296
$163$	−4.86448e9	−0.539749	−0.269875	−	0.962895i	$-0.586982\pi$
$163$	−4.86448e9	−0.539749	−0.269875	+	0.962895i	$0.586982\pi$
$164$	4.18822e9	0.452098
$165$	−8.49030e9	−0.891755
$166$	1.94827e9	0.199142
$167$	8.13796e9	0.809639	0.404819	−	0.914397i	$-0.367334\pi$
$167$	8.13796e9	0.809639	0.404819	+	0.914397i	$0.367334\pi$
$168$	−1.81884e10	−1.76158
$169$	−7.65013e9	−0.721405
$170$	0	0
$171$	−5.14390e8	−0.0460055
$172$	3.22010e9	0.280538
$173$	−6.18512e9	−0.524977	−0.262489	−	0.964935i	$-0.584543\pi$
$173$	−6.18512e9	−0.524977	−0.262489	+	0.964935i	$0.584543\pi$
$174$	−1.53266e10	−1.26757
$175$	−4.17721e9	−0.336678
$176$	−5.09518e9	−0.400270
$177$	1.12894e10	0.864554
$178$	1.16934e10	0.873076
$179$	2.59694e10	1.89071	0.945353	−	0.326049i	$-0.105718\pi$
$179$	2.59694e10	1.89071	0.945353	+	0.326049i	$0.105718\pi$
$180$	1.95155e8	0.0138565
$181$	−1.14180e10	−0.790744	−0.395372	−	0.918521i	$-0.629384\pi$
$181$	−1.14180e10	−0.790744	−0.395372	+	0.918521i	$0.629384\pi$
$182$	−9.83568e9	−0.664482
$183$	−3.71084e9	−0.244592
$184$	−2.54141e9	−0.163454
$185$	−2.32633e10	−1.46016
$186$	−8.31613e9	−0.509463
$187$	0	0
$188$	1.72491e9	0.100706
$189$	2.96432e10	1.68985
$190$	−1.53365e10	−0.853756
$191$	8.71201e9	0.473661	0.236831	−	0.971551i	$-0.423891\pi$
$191$	8.71201e9	0.473661	0.236831	+	0.971551i	$0.423891\pi$
$192$	−1.82312e10	−0.968187
$193$	−8.81349e9	−0.457236	−0.228618	−	0.973516i	$-0.573421\pi$
$193$	−8.81349e9	−0.457236	−0.228618	+	0.973516i	$0.573421\pi$
$194$	2.77813e10	1.40814
$195$	−9.34084e9	−0.462626
$196$	−1.54626e10	−0.748392
$197$	−5.68585e9	−0.268966	−0.134483	−	0.990916i	$-0.542937\pi$
$197$	−5.68585e9	−0.268966	−0.134483	+	0.990916i	$0.542937\pi$
$198$	6.08216e8	0.0281232
$199$	3.90377e10	1.76460	0.882299	−	0.470690i	$-0.155995\pi$
$199$	3.90377e10	1.76460	0.882299	+	0.470690i	$0.155995\pi$
$200$	−4.95568e9	−0.219012
$201$	7.93148e9	0.342746
$202$	2.02264e10	0.854746
$203$	−6.84688e10	−2.82983
$204$	0	0
$205$	−2.39892e10	−0.948690
$206$	4.93629e9	0.190985
$207$	1.45739e8	0.00551707
$208$	−5.60561e9	−0.207653
$209$	3.54035e10	1.28348
$210$	3.10976e10	1.10342
$211$	3.82325e10	1.32789	0.663945	−	0.747781i	$-0.268881\pi$
$211$	3.82325e10	1.32789	0.663945	+	0.747781i	$0.268881\pi$
$212$	−3.99966e9	−0.135991
$213$	−3.94633e9	−0.131367
$214$	1.17802e9	0.0383966
$215$	−1.84441e10	−0.588686
$216$	3.51675e10	1.09926
$217$	−3.71509e10	−1.13737
$218$	4.11939e10	1.23532
$219$	−5.08963e10	−1.49516
$220$	−1.34318e10	−0.386573
$221$	0	0
$222$	−4.40299e10	−1.21663
$223$	−6.60414e10	−1.78832	−0.894158	−	0.447752i	$-0.852225\pi$
$223$	−6.60414e10	−1.78832	−0.894158	+	0.447752i	$0.852225\pi$
$224$	−4.89594e10	−1.29933
$225$	2.84186e8	0.00739233
$226$	4.78984e10	1.22133
$227$	3.77697e10	0.944119	0.472060	−	0.881567i	$-0.343511\pi$
$227$	3.77697e10	0.944119	0.472060	+	0.881567i	$0.343511\pi$
$228$	2.15003e10	0.526911
$229$	−2.64797e10	−0.636288	−0.318144	−	0.948042i	$-0.603060\pi$
$229$	−2.64797e10	−0.636288	−0.318144	+	0.948042i	$0.603060\pi$
$230$	4.34518e9	0.102384
$231$	−7.17872e10	−1.65880
$232$	−8.12287e10	−1.84083
$233$	−4.55178e10	−1.01176	−0.505882	−	0.862603i	$-0.668833\pi$
$233$	−4.55178e10	−1.01176	−0.505882	+	0.862603i	$0.668833\pi$
$234$	6.69146e8	0.0145898
$235$	−9.87993e9	−0.211324
$236$	1.78600e10	0.374781
$237$	−7.23223e9	−0.148903
$238$	0	0
$239$	3.15730e10	0.625929	0.312964	−	0.949765i	$-0.398678\pi$
$239$	3.15730e10	0.625929	0.312964	+	0.949765i	$0.398678\pi$
$240$	1.77233e10	0.344821
$241$	−7.10036e9	−0.135583	−0.0677913	−	0.997700i	$-0.521595\pi$
$241$	−7.10036e9	−0.135583	−0.0677913	+	0.997700i	$0.521595\pi$
$242$	−1.42156e9	−0.0266438
$243$	−3.96245e9	−0.0729013
$244$	−5.87059e9	−0.106030
$245$	8.85663e10	1.57044
$246$	−4.54038e10	−0.790468
$247$	3.89501e10	0.665844
$248$	−4.40743e10	−0.739866
$249$	1.56442e10	0.257903
$250$	5.02732e10	0.813966
$251$	5.74029e10	0.912855	0.456428	−	0.889761i	$-0.349129\pi$
$251$	5.74029e10	0.912855	0.456428	+	0.889761i	$0.349129\pi$
$252$	1.65008e9	0.0257752
$253$	−1.00306e10	−0.153917
$254$	−7.47661e10	−1.12708
$255$	0	0
$256$	−6.95874e10	−1.01263
$257$	−3.44724e10	−0.492915	−0.246457	−	0.969154i	$-0.579267\pi$
$257$	−3.44724e10	−0.492915	−0.246457	+	0.969154i	$0.579267\pi$
$258$	−3.49086e10	−0.490505
$259$	−1.96696e11	−2.71611
$260$	−1.47773e10	−0.200547
$261$	4.65810e9	0.0621337
$262$	−1.01820e10	−0.133498
$263$	−1.19112e11	−1.53516	−0.767581	−	0.640952i	$-0.778540\pi$
$263$	−1.19112e11	−1.53516	−0.767581	+	0.640952i	$0.778540\pi$
$264$	−8.51655e10	−1.07906
$265$	2.29092e10	0.285367
$266$	−1.29673e11	−1.58811
$267$	9.38962e10	1.13070
$268$	1.25477e10	0.148579
$269$	1.18649e11	1.38159	0.690793	−	0.723052i	$-0.257261\pi$
$269$	1.18649e11	1.38159	0.690793	+	0.723052i	$0.257261\pi$
$270$	−6.01277e10	−0.688553
$271$	4.58480e9	0.0516367	0.0258184	−	0.999667i	$-0.491781\pi$
$271$	4.58480e9	0.0516367	0.0258184	+	0.999667i	$0.491781\pi$
$272$	0	0
$273$	−7.89787e10	−0.860554
$274$	4.31815e10	0.462829
$275$	−1.95594e10	−0.206234
$276$	−6.09153e9	−0.0631881
$277$	−1.37135e11	−1.39955	−0.699775	−	0.714364i	$-0.746716\pi$
$277$	−1.37135e11	−1.39955	−0.699775	+	0.714364i	$0.746716\pi$
$278$	−2.18124e10	−0.219029
$279$	2.52747e9	0.0249728
$280$	1.64813e11	1.60243
$281$	1.43100e11	1.36918	0.684590	−	0.728928i	$-0.259981\pi$
$281$	1.43100e11	1.36918	0.684590	+	0.728928i	$0.259981\pi$
$282$	−1.86995e10	−0.176080
$283$	1.67247e11	1.54995	0.774977	−	0.631989i	$-0.217761\pi$
$283$	1.67247e11	1.54995	0.774977	+	0.631989i	$0.217761\pi$
$284$	−6.24315e9	−0.0569471
$285$	−1.23149e11	−1.10568
$286$	−4.60547e10	−0.407031
$287$	−2.02834e11	−1.76470
$288$	3.33083e9	0.0285289
$289$	0	0
$290$	1.38881e11	1.15306
$291$	2.23079e11	1.82364
$292$	−8.05187e10	−0.648147
$293$	6.00192e10	0.475758	0.237879	−	0.971295i	$-0.423548\pi$
$293$	6.00192e10	0.475758	0.237879	+	0.971295i	$0.423548\pi$
$294$	1.67627e11	1.30852
$295$	−1.02298e11	−0.786447
$296$	−2.33352e11	−1.76685
$297$	1.38802e11	1.03512
$298$	2.69540e10	0.197993
$299$	−1.10355e10	−0.0798492
$300$	−1.18783e10	−0.0846659
$301$	−1.55948e11	−1.09504
$302$	1.43161e11	0.990358
$303$	1.62414e11	1.10696
$304$	−7.39039e10	−0.496291
$305$	3.36255e10	0.222495
$306$	0	0
$307$	−2.28024e11	−1.46507	−0.732535	−	0.680729i	$-0.761663\pi$
$307$	−2.28024e11	−1.46507	−0.732535	+	0.680729i	$0.761663\pi$
$308$	−1.13568e11	−0.719083
$309$	3.96375e10	0.247339
$310$	7.53561e10	0.463437
$311$	3.53354e10	0.214185	0.107092	−	0.994249i	$-0.465846\pi$
$311$	3.53354e10	0.214185	0.107092	+	0.994249i	$0.465846\pi$
$312$	−9.36971e10	−0.559797
$313$	2.02146e11	1.19046	0.595232	−	0.803554i	$-0.297060\pi$
$313$	2.02146e11	1.19046	0.595232	+	0.803554i	$0.297060\pi$
$314$	2.30411e10	0.133758
$315$	−9.45128e9	−0.0540870
$316$	−1.14415e10	−0.0645492
$317$	−3.07825e11	−1.71213	−0.856065	−	0.516869i	$-0.827097\pi$
$317$	−3.07825e11	−1.71213	−0.856065	+	0.516869i	$0.827097\pi$
$318$	4.33596e10	0.237773
$319$	−3.20600e11	−1.73342
$320$	1.65201e11	0.880718
$321$	9.45932e9	0.0497264
$322$	3.67393e10	0.190450
$323$	0	0
$324$	8.12152e10	0.409435
$325$	−2.15189e10	−0.106990
$326$	8.34275e10	0.409100
$327$	3.30780e11	1.59983
$328$	−2.40634e11	−1.14795
$329$	−8.35368e10	−0.393094
$330$	1.45612e11	0.675901
$331$	1.74695e11	0.799934	0.399967	−	0.916530i	$-0.369022\pi$
$331$	1.74695e11	0.799934	0.399967	+	0.916530i	$0.369022\pi$
$332$	2.47494e10	0.111800
$333$	1.33817e10	0.0596366
$334$	−1.39569e11	−0.613662
$335$	−7.18706e10	−0.311781
$336$	1.49854e11	0.641419
$337$	−2.00363e11	−0.846221	−0.423111	−	0.906078i	$-0.639062\pi$
$337$	−2.00363e11	−0.846221	−0.423111	+	0.906078i	$0.639062\pi$
$338$	1.31202e11	0.546785
$339$	3.84615e11	1.58171
$340$	0	0
$341$	−1.73956e11	−0.696698
$342$	8.82196e9	0.0348697
$343$	3.23069e11	1.26029
$344$	−1.85011e11	−0.712334
$345$	3.48910e10	0.132595
$346$	1.06077e11	0.397904
$347$	−6.15863e10	−0.228035	−0.114017	−	0.993479i	$-0.536372\pi$
$347$	−6.15863e10	−0.228035	−0.114017	+	0.993479i	$0.536372\pi$
$348$	−1.94698e11	−0.711630
$349$	4.21517e10	0.152090	0.0760450	−	0.997104i	$-0.475771\pi$
$349$	4.21517e10	0.152090	0.0760450	+	0.997104i	$0.475771\pi$
$350$	7.16406e10	0.255184
$351$	1.52707e11	0.537002
$352$	−2.29248e11	−0.795909
$353$	−1.90620e11	−0.653405	−0.326702	−	0.945127i	$-0.605937\pi$
$353$	−1.90620e11	−0.653405	−0.326702	+	0.945127i	$0.605937\pi$
$354$	−1.93617e11	−0.655284
$355$	3.57594e10	0.119499
$356$	1.48545e11	0.490155
$357$	0	0
$358$	−4.45385e11	−1.43305
$359$	−3.44172e10	−0.109358	−0.0546790	−	0.998504i	$-0.517414\pi$
$359$	−3.44172e10	−0.109358	−0.0546790	+	0.998504i	$0.517414\pi$
$360$	−1.12126e10	−0.0351840
$361$	1.90828e11	0.591370
$362$	1.95822e11	0.599341
$363$	−1.14149e10	−0.0345057
$364$	−1.24945e11	−0.373047
$365$	4.61193e11	1.36008
$366$	6.36421e10	0.185387
$367$	3.99011e11	1.14812	0.574060	−	0.818813i	$-0.305368\pi$
$367$	3.99011e11	1.14812	0.574060	+	0.818813i	$0.305368\pi$
$368$	2.09387e10	0.0595161
$369$	1.37993e10	0.0387470
$370$	3.98974e11	1.10672
$371$	1.93702e11	0.530824
$372$	−1.05642e11	−0.286018
$373$	1.16645e11	0.312016	0.156008	−	0.987756i	$-0.450137\pi$
$373$	1.16645e11	0.312016	0.156008	+	0.987756i	$0.450137\pi$
$374$	0	0
$375$	4.03684e11	1.05415
$376$	−9.91047e10	−0.255711
$377$	−3.52716e11	−0.899269
$378$	−5.08392e11	−1.28081
$379$	2.86797e11	0.714001	0.357000	−	0.934104i	$-0.383799\pi$
$379$	2.86797e11	0.714001	0.357000	+	0.934104i	$0.383799\pi$
$380$	−1.94823e11	−0.479308
$381$	−6.00358e11	−1.45965
$382$	−1.49414e11	−0.359010
$383$	−2.62825e11	−0.624125	−0.312063	−	0.950062i	$-0.601020\pi$
$383$	−2.62825e11	−0.624125	−0.312063	+	0.950062i	$0.601020\pi$
$384$	−1.45076e10	−0.0340491
$385$	6.50495e11	1.50894
$386$	1.51154e11	0.346560
$387$	1.06095e10	0.0240435
$388$	3.52914e11	0.790544
$389$	4.43883e11	0.982867	0.491434	−	0.870915i	$-0.336473\pi$
$389$	4.43883e11	0.982867	0.491434	+	0.870915i	$0.336473\pi$
$390$	1.60199e11	0.350645
$391$	0	0
$392$	8.88400e11	1.90030
$393$	−8.17594e10	−0.172890
$394$	9.75142e10	0.203861
$395$	6.55344e10	0.135451
$396$	7.72634e9	0.0157887
$397$	7.16568e11	1.44777	0.723886	−	0.689919i	$-0.242354\pi$
$397$	7.16568e11	1.44777	0.723886	+	0.689919i	$0.242354\pi$
$398$	−6.69510e11	−1.33747
$399$	−1.04125e12	−2.05673
$400$	4.08298e10	0.0797458
$401$	5.94351e9	0.0114787	0.00573936	−	0.999984i	$-0.498173\pi$
$401$	5.94351e9	0.0114787	0.00573936	+	0.999984i	$0.498173\pi$
$402$	−1.36028e11	−0.259782
$403$	−1.91382e11	−0.361434
$404$	2.56942e11	0.479864
$405$	−4.65183e11	−0.859164
$406$	1.17426e12	2.14486
$407$	−9.21013e11	−1.66376
$408$	0	0
$409$	8.83784e11	1.56168	0.780839	−	0.624732i	$-0.214792\pi$
$409$	8.83784e11	1.56168	0.780839	+	0.624732i	$0.214792\pi$
$410$	4.11424e11	0.719055
$411$	3.46740e11	0.599398
$412$	6.27071e10	0.107221
$413$	−8.64953e11	−1.46291
$414$	−2.49947e9	−0.00418163
$415$	−1.41759e11	−0.234604
$416$	−2.52214e11	−0.412903
$417$	−1.75150e11	−0.283659
$418$	−6.07182e11	−0.972805
$419$	7.55644e11	1.19772	0.598858	−	0.800855i	$-0.295621\pi$
$419$	7.55644e11	1.19772	0.598858	+	0.800855i	$0.295621\pi$
$420$	3.95041e11	0.619470
$421$	−8.69830e11	−1.34948	−0.674738	−	0.738057i	$-0.735743\pi$
$421$	−8.69830e11	−1.34948	−0.674738	+	0.738057i	$0.735743\pi$
$422$	−6.55701e11	−1.00647
$423$	5.68322e9	0.00863103
$424$	2.29800e11	0.345305
$425$	0	0
$426$	6.76810e10	0.0995688
$427$	2.84310e11	0.413873
$428$	1.49648e10	0.0215563
$429$	−3.69811e11	−0.527135
$430$	3.16322e11	0.446191
$431$	−8.39478e11	−1.17182	−0.585911	−	0.810376i	$-0.699263\pi$
$431$	−8.39478e11	−1.17182	−0.585911	+	0.810376i	$0.699263\pi$
$432$	−2.89745e11	−0.400258
$433$	7.65233e11	1.04616	0.523080	−	0.852283i	$-0.324783\pi$
$433$	7.65233e11	1.04616	0.523080	+	0.852283i	$0.324783\pi$
$434$	6.37151e11	0.862062
$435$	1.11519e12	1.49330
$436$	5.23298e11	0.693521
$437$	−1.45491e11	−0.190840
$438$	8.72889e11	1.13325
$439$	−5.25589e11	−0.675392	−0.337696	−	0.941255i	$-0.609648\pi$
$439$	−5.25589e11	−0.675392	−0.337696	+	0.941255i	$0.609648\pi$
$440$	7.71721e11	0.981575
$441$	−5.09458e10	−0.0641409
$442$	0	0
$443$	3.31208e10	0.0408587	0.0204294	−	0.999791i	$-0.493497\pi$
$443$	3.31208e10	0.0408587	0.0204294	+	0.999791i	$0.493497\pi$
$444$	−5.59324e11	−0.683031
$445$	−8.50834e11	−1.02855
$446$	1.13263e12	1.35545
$447$	2.16435e11	0.256416
$448$	1.39680e12	1.63827
$449$	1.02545e12	1.19071	0.595354	−	0.803464i	$-0.297012\pi$
$449$	1.02545e12	1.19071	0.595354	+	0.803464i	$0.297012\pi$
$450$	−4.87389e9	−0.00560298
$451$	−9.49752e11	−1.08098
$452$	6.08467e11	0.685668
$453$	1.14955e12	1.28259
$454$	−6.47763e11	−0.715591
$455$	7.15660e11	0.782809
$456$	−1.23530e12	−1.33792
$457$	7.69863e11	0.825640	0.412820	−	0.910813i	$-0.364544\pi$
$457$	7.69863e11	0.825640	0.412820	+	0.910813i	$0.364544\pi$
$458$	4.54136e11	0.482272
$459$	0	0
$460$	5.51980e10	0.0574795
$461$	−1.11125e12	−1.14593	−0.572963	−	0.819581i	$-0.694206\pi$
$461$	−1.11125e12	−1.14593	−0.572963	+	0.819581i	$0.694206\pi$
$462$	1.23118e12	1.25728
$463$	4.08973e11	0.413600	0.206800	−	0.978383i	$-0.433695\pi$
$463$	4.08973e11	0.413600	0.206800	+	0.978383i	$0.433695\pi$
$464$	6.69243e11	0.670275
$465$	6.05095e11	0.600186
$466$	7.80646e11	0.766862
$467$	−6.23914e11	−0.607014	−0.303507	−	0.952829i	$-0.598158\pi$
$467$	−6.23914e11	−0.607014	−0.303507	+	0.952829i	$0.598158\pi$
$468$	8.50035e9	0.00819087
$469$	−6.07680e11	−0.579959
$470$	1.69444e11	0.160172
$471$	1.85016e11	0.173227
$472$	−1.02615e12	−0.951634
$473$	−7.30214e11	−0.670772
$474$	1.24035e11	0.112861
$475$	−2.83703e11	−0.255707
$476$	0	0
$477$	−1.31780e10	−0.0116551
$478$	−5.41487e11	−0.474420
$479$	9.44440e11	0.819718	0.409859	−	0.912149i	$-0.365578\pi$
$479$	9.44440e11	0.819718	0.409859	+	0.912149i	$0.365578\pi$
$480$	7.97426e11	0.685654
$481$	−1.01328e12	−0.863129
$482$	1.21774e11	0.102764
$483$	2.95010e11	0.246646
$484$	−1.80585e10	−0.0149581
$485$	−2.02142e12	−1.65889
$486$	6.79573e10	0.0552552
$487$	−1.15316e12	−0.928988	−0.464494	−	0.885576i	$-0.653764\pi$
$487$	−1.15316e12	−0.928988	−0.464494	+	0.885576i	$0.653764\pi$
$488$	3.37294e11	0.269228
$489$	6.69907e11	0.529816
$490$	−1.51894e12	−1.19031
$491$	−9.77635e11	−0.759119	−0.379560	−	0.925167i	$-0.623924\pi$
$491$	−9.77635e11	−0.759119	−0.379560	+	0.925167i	$0.623924\pi$
$492$	−5.76778e11	−0.443778
$493$	0	0
$494$	−6.68008e11	−0.504673
$495$	−4.42548e10	−0.0331312
$496$	3.63129e11	0.269397
$497$	3.02353e11	0.222285
$498$	−2.68304e11	−0.195477
$499$	−9.46788e11	−0.683598	−0.341799	−	0.939773i	$-0.611036\pi$
$499$	−9.46788e11	−0.683598	−0.341799	+	0.939773i	$0.611036\pi$
$500$	6.38634e11	0.456969
$501$	−1.12071e12	−0.794738
$502$	−9.84479e11	−0.691894
$503$	7.38032e11	0.514066	0.257033	−	0.966403i	$-0.417255\pi$
$503$	7.38032e11	0.514066	0.257033	+	0.966403i	$0.417255\pi$
$504$	−9.48049e10	−0.0654476
$505$	−1.47171e12	−1.00695
$506$	1.72029e11	0.116661
$507$	1.05353e12	0.708128
$508$	−9.49775e11	−0.632753
$509$	−2.67500e11	−0.176642	−0.0883209	−	0.996092i	$-0.528150\pi$
$509$	−2.67500e11	−0.176642	−0.0883209	+	0.996092i	$0.528150\pi$
$510$	0	0
$511$	3.89948e12	2.52996
$512$	1.13951e12	0.732831
$513$	2.01327e12	1.28344
$514$	5.91213e11	0.373602
$515$	−3.59173e11	−0.224994
$516$	−4.43454e11	−0.275375
$517$	−3.91154e11	−0.240791
$518$	3.37341e12	2.05866
$519$	8.51778e11	0.515316
$520$	8.49031e11	0.509223
$521$	2.53884e12	1.50961	0.754807	−	0.655947i	$-0.227730\pi$
$521$	2.53884e12	1.50961	0.754807	+	0.655947i	$0.227730\pi$
$522$	−7.98881e10	−0.0470939
$523$	2.26847e12	1.32579	0.662895	−	0.748712i	$-0.269328\pi$
$523$	2.26847e12	1.32579	0.662895	+	0.748712i	$0.269328\pi$
$524$	−1.29344e11	−0.0749475
$525$	5.75261e11	0.330482
$526$	2.04281e12	1.16357
$527$	0	0
$528$	7.01679e11	0.392903
$529$	−1.75993e12	−0.977114
$530$	−3.92900e11	−0.216292
$531$	5.88449e10	0.0321206
$532$	−1.64727e12	−0.891585
$533$	−1.04490e12	−0.560791
$534$	−1.61035e12	−0.857008
$535$	−8.57150e10	−0.0452340
$536$	−7.20927e11	−0.377268
$537$	−3.57636e12	−1.85591
$538$	−2.03487e12	−1.04717
$539$	3.50641e12	1.78942
$540$	−7.63819e11	−0.386561
$541$	−8.45533e11	−0.424368	−0.212184	−	0.977230i	$-0.568058\pi$
$541$	−8.45533e11	−0.424368	−0.212184	+	0.977230i	$0.568058\pi$
$542$	−7.86310e10	−0.0391378
$543$	1.57242e12	0.776191
$544$	0	0
$545$	−2.99734e12	−1.45530
$546$	1.35451e12	0.652253
$547$	−3.23511e12	−1.54506	−0.772531	−	0.634977i	$-0.781010\pi$
$547$	−3.23511e12	−1.54506	−0.772531	+	0.634977i	$0.781010\pi$
$548$	5.48547e11	0.259837
$549$	−1.93423e10	−0.00908727
$550$	3.35451e11	0.156314
$551$	−4.65019e12	−2.14926
$552$	3.49988e11	0.160445
$553$	5.54107e11	0.251959
$554$	2.35191e12	1.06078
$555$	3.20369e12	1.43328
$556$	−2.77089e11	−0.122965
$557$	−2.60766e12	−1.14790	−0.573948	−	0.818892i	$-0.694589\pi$
$557$	−2.60766e12	−1.14790	−0.573948	+	0.818892i	$0.694589\pi$
$558$	−4.33469e10	−0.0189280
$559$	−8.03365e11	−0.347985
$560$	−1.35789e12	−0.583471
$561$	0	0
$562$	−2.45421e12	−1.03776
$563$	1.28685e12	0.539809	0.269905	−	0.962887i	$-0.413008\pi$
$563$	1.28685e12	0.539809	0.269905	+	0.962887i	$0.413008\pi$
$564$	−2.37545e11	−0.0988530
$565$	−3.48517e12	−1.43882
$566$	−2.86834e12	−1.17478
$567$	−3.93322e12	−1.59817
$568$	3.58700e11	0.144598
$569$	−1.78057e12	−0.712120	−0.356060	−	0.934463i	$-0.615880\pi$
$569$	−1.78057e12	−0.712120	−0.356060	+	0.934463i	$0.615880\pi$
$570$	2.11205e12	0.838044
$571$	−3.30918e12	−1.30274	−0.651371	−	0.758759i	$-0.725806\pi$
$571$	−3.30918e12	−1.30274	−0.651371	+	0.758759i	$0.725806\pi$
$572$	−5.85046e11	−0.228511
$573$	−1.19977e12	−0.464944
$574$	3.47867e12	1.33755
$575$	8.03797e10	0.0306649
$576$	−9.50280e10	−0.0359708
$577$	2.72309e12	1.02275	0.511377	−	0.859357i	$-0.329136\pi$
$577$	2.72309e12	1.02275	0.511377	+	0.859357i	$0.329136\pi$
$578$	0	0
$579$	1.21374e12	0.448821
$580$	1.76424e12	0.647339
$581$	−1.19860e12	−0.436398
$582$	−3.82588e12	−1.38222
$583$	9.06992e11	0.325158
$584$	4.62619e12	1.64576
$585$	−4.86881e10	−0.0171879
$586$	−1.02935e12	−0.360599
$587$	−2.10387e12	−0.731388	−0.365694	−	0.930735i	$-0.619168\pi$
$587$	−2.10387e12	−0.731388	−0.365694	+	0.930735i	$0.619168\pi$
$588$	2.12941e12	0.734619
$589$	−2.52317e12	−0.863829
$590$	1.75445e12	0.596084
$591$	7.83021e11	0.264016
$592$	1.92259e12	0.643338
$593$	2.56437e12	0.851599	0.425799	−	0.904818i	$-0.359993\pi$
$593$	2.56437e12	0.851599	0.425799	+	0.904818i	$0.359993\pi$
$594$	−2.38050e12	−0.784566
$595$	0	0
$596$	3.42404e11	0.111155
$597$	−5.37605e12	−1.73212
$598$	1.89262e11	0.0605214
$599$	1.25542e12	0.398446	0.199223	−	0.979954i	$-0.436158\pi$
$599$	1.25542e12	0.398446	0.199223	+	0.979954i	$0.436158\pi$
$600$	6.82467e11	0.214981
$601$	−3.06302e12	−0.957666	−0.478833	−	0.877906i	$-0.658940\pi$
$601$	−3.06302e12	−0.957666	−0.478833	+	0.877906i	$0.658940\pi$
$602$	2.67457e12	0.829983
$603$	4.13420e10	0.0127340
$604$	1.81861e12	0.555998
$605$	1.03435e11	0.0313883
$606$	−2.78546e12	−0.839016
$607$	−4.32257e12	−1.29239	−0.646193	−	0.763174i	$-0.723640\pi$
$607$	−4.32257e12	−1.29239	−0.646193	+	0.763174i	$0.723640\pi$
$608$	−3.32516e12	−0.986840
$609$	9.42913e12	2.77775
$610$	−5.76689e11	−0.168639
$611$	−4.30339e11	−0.124918
$612$	0	0
$613$	−2.94392e12	−0.842082	−0.421041	−	0.907042i	$-0.638335\pi$
$613$	−2.94392e12	−0.842082	−0.421041	+	0.907042i	$0.638335\pi$
$614$	3.91070e12	1.11044
$615$	3.30366e12	0.931230
$616$	6.52506e12	1.82588
$617$	4.71135e12	1.30877	0.654383	−	0.756163i	$-0.272928\pi$
$617$	4.71135e12	1.30877	0.654383	+	0.756163i	$0.272928\pi$
$618$	−6.79797e11	−0.187470
$619$	1.54237e12	0.422261	0.211131	−	0.977458i	$-0.432285\pi$
$619$	1.54237e12	0.422261	0.211131	+	0.977458i	$0.432285\pi$
$620$	9.57270e11	0.260179
$621$	−5.70407e11	−0.153912
$622$	−6.06015e11	−0.162340
$623$	−7.19397e12	−1.91325
$624$	7.71971e11	0.203831
$625$	−2.88471e12	−0.756211
$626$	−3.46688e12	−0.902307
$627$	−4.87556e12	−1.25985
$628$	2.92697e11	0.0750932
$629$	0	0
$630$	1.62093e11	0.0409950
$631$	−8.86330e11	−0.222568	−0.111284	−	0.993789i	$-0.535496\pi$
$631$	−8.86330e11	−0.222568	−0.111284	+	0.993789i	$0.535496\pi$
$632$	6.57370e11	0.163901
$633$	−5.26516e12	−1.30345
$634$	5.27930e12	1.29770
$635$	5.44011e12	1.32778
$636$	5.50809e11	0.133489
$637$	3.85767e12	0.928320
$638$	5.49839e12	1.31384
$639$	−2.05698e10	−0.00488064
$640$	1.31460e11	0.0309730
$641$	6.76463e11	0.158264	0.0791321	−	0.996864i	$-0.474785\pi$
$641$	6.76463e11	0.158264	0.0791321	+	0.996864i	$0.474785\pi$
$642$	−1.62231e11	−0.0376899
$643$	2.40010e12	0.553706	0.276853	−	0.960912i	$-0.410708\pi$
$643$	2.40010e12	0.553706	0.276853	+	0.960912i	$0.410708\pi$
$644$	4.66710e11	0.106920
$645$	2.54001e12	0.577851
$646$	0	0
$647$	−3.20876e12	−0.719893	−0.359947	−	0.932973i	$-0.617205\pi$
$647$	−3.20876e12	−0.719893	−0.359947	+	0.932973i	$0.617205\pi$
$648$	−4.66621e12	−1.03962
$649$	−4.05007e12	−0.896110
$650$	3.69056e11	0.0810927
$651$	5.11620e12	1.11643
$652$	1.05980e12	0.229673
$653$	3.25917e12	0.701452	0.350726	−	0.936478i	$-0.385935\pi$
$653$	3.25917e12	0.701452	0.350726	+	0.936478i	$0.385935\pi$
$654$	−5.67298e12	−1.21258
$655$	7.40857e11	0.157271
$656$	1.98258e12	0.417989
$657$	−2.65291e11	−0.0555494
$658$	1.43269e12	0.297944
$659$	−7.89910e12	−1.63152	−0.815762	−	0.578388i	$-0.803682\pi$
$659$	−7.89910e12	−1.63152	−0.815762	+	0.578388i	$0.803682\pi$
$660$	1.84975e12	0.379459
$661$	2.00399e12	0.408309	0.204154	−	0.978939i	$-0.434556\pi$
$661$	2.00399e12	0.408309	0.204154	+	0.978939i	$0.434556\pi$
$662$	−2.99608e12	−0.606306
$663$	0	0
$664$	−1.42197e12	−0.283880
$665$	9.43521e12	1.87092
$666$	−2.29501e11	−0.0452013
$667$	1.31751e12	0.257743
$668$	−1.77298e12	−0.344517
$669$	9.09483e12	1.75540
$670$	1.23261e12	0.236313
$671$	1.33126e12	0.253519
$672$	6.74240e12	1.27542
$673$	4.26205e12	0.800849	0.400425	−	0.916330i	$-0.368863\pi$
$673$	4.26205e12	0.800849	0.400425	+	0.916330i	$0.368863\pi$
$674$	3.43630e12	0.641389
$675$	−1.11228e12	−0.206227
$676$	1.66670e12	0.306971
$677$	3.93790e12	0.720469	0.360235	−	0.932862i	$-0.382697\pi$
$677$	3.93790e12	0.720469	0.360235	+	0.932862i	$0.382697\pi$
$678$	−6.59629e12	−1.19885
$679$	−1.70915e13	−3.08578
$680$	0	0
$681$	−5.20142e12	−0.926744
$682$	2.98340e12	0.528059
$683$	−7.18518e12	−1.26341	−0.631706	−	0.775208i	$-0.717645\pi$
$683$	−7.18518e12	−1.26341	−0.631706	+	0.775208i	$0.717645\pi$
$684$	1.12068e11	0.0195762
$685$	−3.14196e12	−0.545247
$686$	−5.54075e12	−0.955234
$687$	3.64663e12	0.624578
$688$	1.52430e12	0.259372
$689$	9.97852e11	0.168686
$690$	−5.98392e11	−0.100500
$691$	−1.16786e12	−0.194867	−0.0974337	−	0.995242i	$-0.531063\pi$
$691$	−1.16786e12	−0.194867	−0.0974337	+	0.995242i	$0.531063\pi$
$692$	1.34752e12	0.223388
$693$	−3.74183e11	−0.0616290
$694$	1.05623e12	0.172838
$695$	1.58711e12	0.258033
$696$	1.11863e13	1.80695
$697$	0	0
$698$	−7.22916e11	−0.115276
$699$	6.26844e12	0.993144
$700$	9.10071e11	0.143263
$701$	−6.97976e12	−1.09172	−0.545858	−	0.837878i	$-0.683796\pi$
$701$	−6.97976e12	−1.09172	−0.545858	+	0.837878i	$0.683796\pi$
$702$	−2.61897e12	−0.407018
$703$	−1.33590e13	−2.06288
$704$	6.54042e12	1.00353
$705$	1.36061e12	0.207435
$706$	3.26920e12	0.495245
$707$	−1.24436e13	−1.87309
$708$	−2.45958e12	−0.367884
$709$	−9.30606e12	−1.38311	−0.691557	−	0.722322i	$-0.743075\pi$
$709$	−9.30606e12	−1.38311	−0.691557	+	0.722322i	$0.743075\pi$
$710$	−6.13287e11	−0.0905735
$711$	−3.76972e10	−0.00553218
$712$	−8.53464e12	−1.24459
$713$	7.14873e11	0.103592
$714$	0	0
$715$	3.35102e12	0.479512
$716$	−5.65785e12	−0.804531
$717$	−4.34805e12	−0.614409
$718$	5.90267e11	0.0828874
$719$	6.74044e12	0.940607	0.470304	−	0.882505i	$-0.344144\pi$
$719$	6.74044e12	0.940607	0.470304	+	0.882505i	$0.344144\pi$
$720$	9.23808e10	0.0128111
$721$	−3.03688e12	−0.418522
$722$	−3.27276e12	−0.448226
$723$	9.77820e11	0.133087
$724$	2.48759e12	0.336477
$725$	2.56910e12	0.345350
$726$	1.95769e11	0.0261534
$727$	1.09765e12	0.145733	0.0728667	−	0.997342i	$-0.476785\pi$
$727$	1.09765e12	0.145733	0.0728667	+	0.997342i	$0.476785\pi$
$728$	7.17872e12	0.947231
$729$	7.88304e12	1.03376
$730$	−7.90963e12	−1.03087
$731$	0	0
$732$	8.08464e11	0.104078
$733$	5.10680e12	0.653403	0.326701	−	0.945128i	$-0.394063\pi$
$733$	5.10680e12	0.653403	0.326701	+	0.945128i	$0.394063\pi$
$734$	−6.84317e12	−0.870212
$735$	−1.21968e13	−1.54154
$736$	9.42096e11	0.118344
$737$	−2.84541e12	−0.355256
$738$	−2.36663e11	−0.0293681
$739$	4.59083e12	0.566228	0.283114	−	0.959086i	$-0.408633\pi$
$739$	4.59083e12	0.566228	0.283114	+	0.959086i	$0.408633\pi$
$740$	5.06828e12	0.621324
$741$	−5.36398e12	−0.653590
$742$	−3.32205e12	−0.402336
$743$	1.88392e12	0.226784	0.113392	−	0.993550i	$-0.463828\pi$
$743$	1.88392e12	0.226784	0.113392	+	0.993550i	$0.463828\pi$
$744$	6.06966e12	0.726250
$745$	−1.96122e12	−0.233250
$746$	−2.00051e12	−0.236491
$747$	8.15439e10	0.00958183
$748$	0	0
$749$	−7.24738e11	−0.0841420
$750$	−6.92332e12	−0.798986
$751$	3.33952e12	0.383093	0.191547	−	0.981484i	$-0.438650\pi$
$751$	3.33952e12	0.383093	0.191547	+	0.981484i	$0.438650\pi$
$752$	8.16524e11	0.0931084
$753$	−7.90519e12	−0.896055
$754$	6.04921e12	0.681597
$755$	−1.04166e13	−1.16671
$756$	−6.45824e12	−0.719062
$757$	−9.95427e12	−1.10174	−0.550869	−	0.834592i	$-0.685703\pi$
$757$	−9.95427e12	−1.10174	−0.550869	+	0.834592i	$0.685703\pi$
$758$	−4.91867e12	−0.541174
$759$	1.38136e12	0.151084
$760$	1.11936e13	1.21705
$761$	9.18933e12	0.993237	0.496618	−	0.867969i	$-0.334575\pi$
$761$	9.18933e12	0.993237	0.496618	+	0.867969i	$0.334575\pi$
$762$	1.02963e13	1.10633
$763$	−2.53431e13	−2.70707
$764$	−1.89805e12	−0.201552
$765$	0	0
$766$	4.50753e12	0.473053
$767$	−4.45580e12	−0.464886
$768$	9.58317e12	0.993994
$769$	7.03483e11	0.0725412	0.0362706	−	0.999342i	$-0.488452\pi$
$769$	7.03483e11	0.0725412	0.0362706	+	0.999342i	$0.488452\pi$
$770$	−1.11562e13	−1.14369
$771$	4.74733e12	0.483843
$772$	1.92016e12	0.194562
$773$	7.75675e12	0.781398	0.390699	−	0.920518i	$-0.372233\pi$
$773$	7.75675e12	0.781398	0.390699	+	0.920518i	$0.372233\pi$
$774$	−1.81957e11	−0.0182236
$775$	1.39398e12	0.138803
$776$	−2.02766e13	−2.00733
$777$	2.70878e13	2.66612
$778$	−7.61274e12	−0.744960
$779$	−1.37758e13	−1.34029
$780$	2.03505e12	0.196856
$781$	1.41574e12	0.136162
$782$	0	0
$783$	−1.82314e13	−1.73337
$784$	−7.31953e12	−0.691928
$785$	−1.67651e12	−0.157577
$786$	1.40220e12	0.131042
$787$	1.18912e13	1.10494	0.552470	−	0.833533i	$-0.313686\pi$
$787$	1.18912e13	1.10494	0.552470	+	0.833533i	$0.313686\pi$
$788$	1.23875e12	0.114450
$789$	1.64034e13	1.50691
$790$	−1.12394e12	−0.102664
$791$	−2.94678e13	−2.67641
$792$	−4.43916e11	−0.0400901
$793$	1.46462e12	0.131521
$794$	−1.22894e13	−1.09733
$795$	−3.15492e12	−0.280115
$796$	−8.50498e12	−0.750870
$797$	−1.21193e13	−1.06394	−0.531968	−	0.846765i	$-0.678547\pi$
$797$	−1.21193e13	−1.06394	−0.531968	+	0.846765i	$0.678547\pi$
$798$	1.78578e13	1.55889
$799$	0	0
$800$	1.83706e12	0.158569
$801$	4.89424e11	0.0420086
$802$	−1.01933e11	−0.00870024
$803$	1.82590e13	1.54973
$804$	−1.72800e12	−0.145845
$805$	−2.67322e12	−0.224364
$806$	3.28227e12	0.273947
$807$	−1.63396e13	−1.35616
$808$	−1.47626e13	−1.21846
$809$	−9.13191e12	−0.749537	−0.374769	−	0.927118i	$-0.622278\pi$
$809$	−9.13191e12	−0.749537	−0.374769	+	0.927118i	$0.622278\pi$
$810$	7.97805e12	0.651200
$811$	−4.07495e12	−0.330771	−0.165386	−	0.986229i	$-0.552887\pi$
$811$	−4.07495e12	−0.330771	−0.165386	+	0.986229i	$0.552887\pi$
$812$	1.49170e13	1.20415
$813$	−6.31392e11	−0.0506864
$814$	1.57957e13	1.26104
$815$	−6.07032e12	−0.481950
$816$	0	0
$817$	−1.05915e13	−0.831684
$818$	−1.51572e13	−1.18367
$819$	−4.11668e11	−0.0319720
$820$	5.22643e12	0.403685
$821$	−6.29838e12	−0.483821	−0.241910	−	0.970299i	$-0.577774\pi$
$821$	−6.29838e12	−0.483821	−0.241910	+	0.970299i	$0.577774\pi$
$822$	−5.94671e12	−0.454311
$823$	1.64856e13	1.25258	0.626291	−	0.779590i	$-0.284572\pi$
$823$	1.64856e13	1.25258	0.626291	+	0.779590i	$0.284572\pi$
$824$	−3.60283e12	−0.272252
$825$	2.69361e12	0.202438
$826$	1.48342e13	1.10881
$827$	−1.72010e13	−1.27873	−0.639364	−	0.768904i	$-0.720802\pi$
$827$	−1.72010e13	−1.27873	−0.639364	+	0.768904i	$0.720802\pi$
$828$	−3.17515e10	−0.00234762
$829$	−2.13805e11	−0.0157225	−0.00786126	−	0.999969i	$-0.502502\pi$
$829$	−2.13805e11	−0.0157225	−0.00786126	+	0.999969i	$0.502502\pi$
$830$	2.43122e12	0.177817
$831$	1.88854e13	1.37379
$832$	7.19562e12	0.520611
$833$	0	0
$834$	3.00388e12	0.214998
$835$	1.01553e13	0.722939
$836$	−7.71320e12	−0.546143
$837$	−9.89227e12	−0.696677
$838$	−1.29595e13	−0.907803
$839$	−3.76284e12	−0.262172	−0.131086	−	0.991371i	$-0.541846\pi$
$839$	−3.76284e12	−0.262172	−0.131086	+	0.991371i	$0.541846\pi$
$840$	−2.26970e13	−1.57294
$841$	2.76030e13	1.90272
$842$	1.49179e13	1.02283
$843$	−1.97069e13	−1.34398
$844$	−8.32956e12	−0.565042
$845$	−9.54651e12	−0.644153
$846$	−9.74691e10	−0.00654185
$847$	8.74564e11	0.0583870
$848$	−1.89332e12	−0.125731
$849$	−2.30322e13	−1.52143
$850$	0	0
$851$	3.78491e12	0.247385
$852$	8.59771e11	0.0558990
$853$	2.62940e13	1.70054	0.850268	−	0.526349i	$-0.176440\pi$
$853$	2.62940e13	1.70054	0.850268	+	0.526349i	$0.176440\pi$
$854$	−4.87602e12	−0.313693
$855$	−6.41901e11	−0.0410790
$856$	−8.59800e11	−0.0547350
$857$	−5.69782e12	−0.360823	−0.180412	−	0.983591i	$-0.557743\pi$
$857$	−5.69782e12	−0.360823	−0.180412	+	0.983591i	$0.557743\pi$
$858$	6.34239e12	0.399540
$859$	1.45341e13	0.910794	0.455397	−	0.890288i	$-0.349497\pi$
$859$	1.45341e13	0.910794	0.455397	+	0.890288i	$0.349497\pi$
$860$	4.01833e12	0.250497
$861$	2.79331e13	1.73223
$862$	1.43973e13	0.888176
$863$	−1.96660e13	−1.20689	−0.603445	−	0.797404i	$-0.706206\pi$
$863$	−1.96660e13	−1.20689	−0.603445	+	0.797404i	$0.706206\pi$
$864$	−1.30365e13	−0.795885
$865$	−7.71833e12	−0.468760
$866$	−1.31240e13	−0.792932
$867$	0	0
$868$	8.09391e12	0.483971
$869$	2.59456e12	0.154338
$870$	−1.91258e13	−1.13184
$871$	−3.13046e12	−0.184300
$872$	−3.00660e13	−1.76097
$873$	1.16278e12	0.0677535
$874$	2.49522e12	0.144646
$875$	−3.09288e13	−1.78372
$876$	1.10886e13	0.636219
$877$	1.83939e13	1.04997	0.524985	−	0.851112i	$-0.324071\pi$
$877$	1.83939e13	1.04997	0.524985	+	0.851112i	$0.324071\pi$
$878$	9.01404e12	0.511910
$879$	−8.26550e12	−0.467002
$880$	−6.35822e12	−0.357407
$881$	−1.41078e13	−0.788982	−0.394491	−	0.918900i	$-0.629079\pi$
$881$	−1.41078e13	−0.788982	−0.394491	+	0.918900i	$0.629079\pi$
$882$	8.73738e11	0.0486153
$883$	6.63294e12	0.367183	0.183592	−	0.983003i	$-0.441228\pi$
$883$	6.63294e12	0.367183	0.183592	+	0.983003i	$0.441228\pi$
$884$	0	0
$885$	1.40879e13	0.771974
$886$	−5.68034e11	−0.0309687
$887$	2.52778e13	1.37115	0.685573	−	0.728004i	$-0.259552\pi$
$887$	2.52778e13	1.37115	0.685573	+	0.728004i	$0.259552\pi$
$888$	3.21359e13	1.73433
$889$	4.59972e13	2.46987
$890$	1.45921e13	0.779584
$891$	−1.84169e13	−0.978967
$892$	1.43881e13	0.760962
$893$	−5.67355e12	−0.298555
$894$	−3.71194e12	−0.194349
$895$	3.24069e13	1.68824
$896$	1.11152e12	0.0576144
$897$	1.51974e12	0.0783797
$898$	−1.75868e13	−0.902491
$899$	2.28488e13	1.16666
$900$	−6.19144e10	−0.00314558
$901$	0	0
$902$	1.62886e13	0.819320
$903$	2.14763e13	1.07489
$904$	−3.49594e13	−1.74103
$905$	−1.42484e13	−0.706068
$906$	−1.97152e13	−0.972131
$907$	−3.76033e12	−0.184499	−0.0922493	−	0.995736i	$-0.529406\pi$
$907$	−3.76033e12	−0.184499	−0.0922493	+	0.995736i	$0.529406\pi$
$908$	−8.22871e12	−0.401741
$909$	8.46567e11	0.0411267
$910$	−1.22738e13	−0.593326
$911$	5.70301e11	0.0274329	0.0137164	−	0.999906i	$-0.495634\pi$
$911$	5.70301e11	0.0274329	0.0137164	+	0.999906i	$0.495634\pi$
$912$	1.01776e13	0.487157
$913$	−5.61235e12	−0.267317
$914$	−1.32034e13	−0.625790
$915$	−4.63071e12	−0.218400
$916$	5.76902e12	0.270753
$917$	6.26410e12	0.292547
$918$	0	0
$919$	2.65353e13	1.22717	0.613585	−	0.789629i	$-0.289727\pi$
$919$	2.65353e13	1.22717	0.613585	+	0.789629i	$0.289727\pi$
$920$	−3.17140e12	−0.145950
$921$	3.14022e13	1.43811
$922$	1.90583e13	0.868549
$923$	1.55757e12	0.0706382
$924$	1.56400e13	0.705850
$925$	7.38046e12	0.331471
$926$	−7.01404e12	−0.313486
$927$	2.06606e11	0.00918935
$928$	3.01113e13	1.33280
$929$	1.55680e13	0.685742	0.342871	−	0.939382i	$-0.388601\pi$
$929$	1.55680e13	0.685742	0.342871	+	0.939382i	$0.388601\pi$
$930$	−1.03776e13	−0.454908
$931$	5.08592e13	2.21869
$932$	9.91676e12	0.430525
$933$	−4.86619e12	−0.210243
$934$	1.07003e13	0.460083
$935$	0	0
$936$	−4.88386e11	−0.0207980
$937$	1.83498e13	0.777683	0.388841	−	0.921305i	$-0.372875\pi$
$937$	1.83498e13	0.777683	0.388841	+	0.921305i	$0.372875\pi$
$938$	1.04219e13	0.439577
$939$	−2.78384e13	−1.16856
$940$	2.15250e12	0.0899223
$941$	1.16741e13	0.485369	0.242684	−	0.970105i	$-0.421972\pi$
$941$	1.16741e13	0.485369	0.242684	+	0.970105i	$0.421972\pi$
$942$	−3.17308e12	−0.131296
$943$	3.90301e12	0.160730
$944$	8.45442e12	0.346505
$945$	3.69914e13	1.50889
$946$	1.25234e13	0.508409
$947$	−3.52620e13	−1.42473	−0.712365	−	0.701809i	$-0.752376\pi$
$947$	−3.52620e13	−1.42473	−0.712365	+	0.701809i	$0.752376\pi$
$948$	1.57566e12	0.0633612
$949$	2.00881e13	0.803974
$950$	4.86560e12	0.193812
$951$	4.23918e13	1.68062
$952$	0	0
$953$	1.56668e12	0.0615266	0.0307633	−	0.999527i	$-0.490206\pi$
$953$	1.56668e12	0.0615266	0.0307633	+	0.999527i	$0.490206\pi$
$954$	2.26007e11	0.00883395
$955$	1.08716e13	0.422940
$956$	−6.87867e12	−0.266345
$957$	4.41511e13	1.70152
$958$	−1.61975e13	−0.621302
$959$	−2.65659e13	−1.01424
$960$	−2.27505e13	−0.864509
$961$	−1.40420e13	−0.531095
$962$	1.73781e13	0.654205
$963$	4.93057e10	0.00184748
$964$	1.54692e12	0.0576929
$965$	−1.09982e13	−0.408273
$966$	−5.05953e12	−0.186945
$967$	5.21004e13	1.91612	0.958058	−	0.286573i	$-0.0925160\pi$
$967$	5.21004e13	1.91612	0.958058	+	0.286573i	$0.0925160\pi$
$968$	1.03755e12	0.0379812
$969$	0	0
$970$	3.46680e13	1.25735
$971$	−4.84504e13	−1.74909	−0.874543	−	0.484948i	$-0.838838\pi$
$971$	−4.84504e13	−1.74909	−0.874543	+	0.484948i	$0.838838\pi$
$972$	8.63281e11	0.0310209
$973$	1.34193e13	0.479979
$974$	1.97771e13	0.704122
$975$	2.96345e12	0.105021
$976$	−2.77897e12	−0.0980301
$977$	−1.73873e12	−0.0610530	−0.0305265	−	0.999534i	$-0.509718\pi$
$977$	−1.73873e12	−0.0610530	−0.0305265	+	0.999534i	$0.509718\pi$
$978$	−1.14891e13	−0.401571
$979$	−3.36852e13	−1.17197
$980$	−1.92956e13	−0.668251
$981$	1.72415e12	0.0594381
$982$	1.67668e13	0.575371
$983$	−8.20211e12	−0.280178	−0.140089	−	0.990139i	$-0.544739\pi$
$983$	−8.20211e12	−0.280178	−0.140089	+	0.990139i	$0.544739\pi$
$984$	3.31387e13	1.12683
$985$	−7.09530e12	−0.240164
$986$	0	0
$987$	1.15042e13	0.385859
$988$	−8.48589e12	−0.283329
$989$	3.00082e12	0.0997371
$990$	7.58985e11	0.0251116
$991$	−1.65692e12	−0.0545719	−0.0272860	−	0.999628i	$-0.508686\pi$
$991$	−1.65692e12	−0.0545719	−0.0272860	+	0.999628i	$0.508686\pi$
$992$	1.63383e13	0.535678
$993$	−2.40579e13	−0.785212
$994$	−5.18546e12	−0.168480
$995$	4.87147e13	1.57564
$996$	−3.40834e12	−0.109743
$997$	3.74947e13	1.20183	0.600913	−	0.799314i	$-0.294804\pi$
$997$	3.74947e13	1.20183	0.600913	+	0.799314i	$0.294804\pi$
$998$	1.62377e13	0.518130
$999$	−5.23748e13	−1.66371

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.f.1.7		24
17.8	even	8		17.10.c.a.13.9	yes	24
17.15	even	8		17.10.c.a.4.4	✓	24
17.16	even	2	inner	289.10.a.f.1.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.4	✓	24	17.15	even	8
17.10.c.a.13.9	yes	24	17.8	even	8
289.10.a.f.1.7		24	1.1	even	1	trivial
289.10.a.f.1.8		24	17.16	even	2	inner

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)

\(f(q)\)	\(=\)	\(q-17.1503 q^{2} -137.714 q^{3} -217.866 q^{4} +1247.89 q^{5} +2361.84 q^{6} +10551.1 q^{7} +12517.4 q^{8} -717.820 q^{9} +O(q^{10})\)	\(q-17.1503 q^{2} -137.714 q^{3} -217.866 q^{4} +1247.89 q^{5} +2361.84 q^{6} +10551.1 q^{7} +12517.4 q^{8} -717.820 q^{9} -21401.7 q^{10} +49404.8 q^{11} +30003.2 q^{12} +54354.1 q^{13} -180956. q^{14} -171852. q^{15} -103131. q^{16} +12310.9 q^{18} +716600. q^{19} -271872. q^{20} -1.45304e6 q^{21} -847310. q^{22} -203029. q^{23} -1.72383e6 q^{24} -395901. q^{25} -932191. q^{26} +2.80948e6 q^{27} -2.29873e6 q^{28} -6.48924e6 q^{29} +2.94732e6 q^{30} -3.52103e6 q^{31} -4.64020e6 q^{32} -6.80374e6 q^{33} +1.31666e7 q^{35} +156388. q^{36} -1.86422e7 q^{37} -1.22899e7 q^{38} -7.48532e6 q^{39} +1.56204e7 q^{40} -1.92239e7 q^{41} +2.49202e7 q^{42} -1.47802e7 q^{43} -1.07636e7 q^{44} -895759. q^{45} +3.48203e6 q^{46} -7.91732e6 q^{47} +1.42026e7 q^{48} +7.09730e7 q^{49} +6.78985e6 q^{50} -1.18419e7 q^{52} +1.83584e7 q^{53} -4.81836e7 q^{54} +6.16517e7 q^{55} +1.32073e8 q^{56} -9.86859e7 q^{57} +1.11293e8 q^{58} -8.19772e7 q^{59} +3.74406e7 q^{60} +2.69459e7 q^{61} +6.03869e7 q^{62} -7.57382e6 q^{63} +1.32384e8 q^{64} +6.78278e7 q^{65} +1.16686e8 q^{66} -5.75938e7 q^{67} +2.79600e7 q^{69} -2.25812e8 q^{70} +2.86560e7 q^{71} -8.98528e6 q^{72} +3.69579e8 q^{73} +3.19720e8 q^{74} +5.45212e7 q^{75} -1.56123e8 q^{76} +5.21277e8 q^{77} +1.28376e8 q^{78} +5.25163e7 q^{79} -1.28696e8 q^{80} -3.72776e8 q^{81} +3.29696e8 q^{82} -1.13599e8 q^{83} +3.16568e8 q^{84} +2.53486e8 q^{86} +8.93659e8 q^{87} +6.18422e8 q^{88} -6.81819e8 q^{89} +1.53626e7 q^{90} +5.73497e8 q^{91} +4.42332e7 q^{92} +4.84896e8 q^{93} +1.35785e8 q^{94} +8.94236e8 q^{95} +6.39020e8 q^{96} -1.61987e9 q^{97} -1.21721e9 q^{98} -3.54638e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 5124 q^{4} + 108368 q^{9}+O(q^{10}) \) 24 * q + 5124 * q^4 + 108368 * q^9	\( 24 q + 5124 q^{4} + 108368 q^{9} - 244832 q^{13} - 127332 q^{15} - 279932 q^{16} + 888764 q^{18} - 2280212 q^{19} + 775748 q^{21} - 2762628 q^{25} - 3334452 q^{26} - 39084792 q^{30} + 2010240 q^{32} - 30349992 q^{33} - 25532364 q^{35} + 31177320 q^{36} - 13171392 q^{38} - 86527192 q^{42} + 61046960 q^{43} - 153365328 q^{47} + 169445876 q^{49} - 236105676 q^{50} - 209898380 q^{52} + 85777812 q^{53} - 255767540 q^{55} - 767709024 q^{59} + 429639656 q^{60} - 1006108924 q^{64} + 346830788 q^{66} - 26076868 q^{67} - 751973532 q^{69} - 319504544 q^{70} - 1171736028 q^{72} - 1640047616 q^{76} - 174401076 q^{77} - 347156560 q^{81} - 1649346672 q^{83} - 935672904 q^{84} + 690159588 q^{86} - 257027500 q^{87} + 191594460 q^{89} + 1842509012 q^{93} + 2877218432 q^{94} + 4413444720 q^{98}+O(q^{100}) \) 24 * q + 5124 * q^4 + 108368 * q^9 - 244832 * q^13 - 127332 * q^15 - 279932 * q^16 + 888764 * q^18 - 2280212 * q^19 + 775748 * q^21 - 2762628 * q^25 - 3334452 * q^26 - 39084792 * q^30 + 2010240 * q^32 - 30349992 * q^33 - 25532364 * q^35 + 31177320 * q^36 - 13171392 * q^38 - 86527192 * q^42 + 61046960 * q^43 - 153365328 * q^47 + 169445876 * q^49 - 236105676 * q^50 - 209898380 * q^52 + 85777812 * q^53 - 255767540 * q^55 - 767709024 * q^59 + 429639656 * q^60 - 1006108924 * q^64 + 346830788 * q^66 - 26076868 * q^67 - 751973532 * q^69 - 319504544 * q^70 - 1171736028 * q^72 - 1640047616 * q^76 - 174401076 * q^77 - 347156560 * q^81 - 1649346672 * q^83 - 935672904 * q^84 + 690159588 * q^86 - 257027500 * q^87 + 191594460 * q^89 + 1842509012 * q^93 + 2877218432 * q^94 + 4413444720 * q^98

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