LMFDB - Embedded newform 289.4.b.e.288.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,4,Mod(288,289)]

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([1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("289.288");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	289.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$17.0515519917$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 34 x^{10} + 124 x^{9} + 671 x^{8} - 1984 x^{7} - 5452 x^{6} + 8264 x^{5} + \cdots + 300356 $ x^12 - 4x^11 - 34x^10 + 124x^9 + 671x^8 - 1984x^7 - 5452x^6 + 8264x^5 + 24252x^4 + 25328x^3 - 31008x^2 - 174688*x + 300356
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			288.3
Root			$3.68604 + 0.765367i$ of defining polynomial
Character	$\chi$	$=$	289.288
Dual form			289.4.b.e.288.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68604 q^{2} -4.33137i q^{3} -0.785167 q^{4} +2.08666i q^{5} +11.6343i q^{6} -24.9985i q^{7} +23.5973 q^{8} +8.23920 q^{9} +O(q^{10})$	\(q-2.68604 q^{2} -4.33137i q^{3} -0.785167 q^{4} +2.08666i q^{5} +11.6343i q^{6} -24.9985i q^{7} +23.5973 q^{8} +8.23920 q^{9} -5.60485i q^{10} +3.82158i q^{11} +3.40085i q^{12} +17.6726 q^{13} +67.1470i q^{14} +9.03809 q^{15} -57.1022 q^{16} -22.1309 q^{18} +160.915 q^{19} -1.63837i q^{20} -108.278 q^{21} -10.2649i q^{22} +99.9676i q^{23} -102.209i q^{24} +120.646 q^{25} -47.4693 q^{26} -152.634i q^{27} +19.6280i q^{28} -200.583i q^{29} -24.2767 q^{30} +76.5382i q^{31} -35.3998 q^{32} +16.5527 q^{33} +52.1632 q^{35} -6.46915 q^{36} -244.759i q^{37} -432.224 q^{38} -76.5465i q^{39} +49.2395i q^{40} +54.1132i q^{41} +290.839 q^{42} -142.087 q^{43} -3.00058i q^{44} +17.1924i q^{45} -268.517i q^{46} -468.451 q^{47} +247.331i q^{48} -281.924 q^{49} -324.060 q^{50} -13.8759 q^{52} +96.5673 q^{53} +409.982i q^{54} -7.97432 q^{55} -589.898i q^{56} -696.981i q^{57} +538.776i q^{58} -364.484 q^{59} -7.09641 q^{60} -707.872i q^{61} -205.585i q^{62} -205.967i q^{63} +551.903 q^{64} +36.8766i q^{65} -44.4612 q^{66} -304.454 q^{67} +432.997 q^{69} -140.113 q^{70} -470.003i q^{71} +194.423 q^{72} -142.056i q^{73} +657.432i q^{74} -522.562i q^{75} -126.345 q^{76} +95.5336 q^{77} +205.607i q^{78} -717.865i q^{79} -119.153i q^{80} -438.657 q^{81} -145.350i q^{82} +367.639 q^{83} +85.0162 q^{84} +381.653 q^{86} -868.802 q^{87} +90.1791i q^{88} +1042.28 q^{89} -46.1795i q^{90} -441.788i q^{91} -78.4913i q^{92} +331.516 q^{93} +1258.28 q^{94} +335.773i q^{95} +153.330i q^{96} +903.534i q^{97} +757.260 q^{98} +31.4867i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{2} + 16 q^{4} + 96 q^{8} + 36 q^{9}+O(q^{10}) $ 12 * q + 8 * q^2 + 16 * q^4 + 96 * q^8 + 36 * q^9	$ 12 q + 8 q^{2} + 16 q^{4} + 96 q^{8} + 36 q^{9} - 8 q^{13} + 192 q^{15} - 184 q^{16} + 352 q^{19} - 256 q^{21} + 492 q^{25} + 784 q^{26} + 744 q^{30} - 24 q^{32} - 1400 q^{33} - 632 q^{35} + 856 q^{36} - 624 q^{38} + 1664 q^{42} + 1200 q^{43} - 1512 q^{47} + 1052 q^{49} - 2856 q^{50} + 792 q^{52} + 2504 q^{53} - 1424 q^{55} + 3408 q^{59} + 2808 q^{60} + 272 q^{64} - 272 q^{66} - 1080 q^{67} - 344 q^{69} - 2600 q^{70} + 248 q^{72} - 896 q^{76} - 848 q^{77} - 2404 q^{81} + 2960 q^{83} + 4768 q^{84} - 1200 q^{86} + 160 q^{87} - 2144 q^{89} - 3800 q^{93} - 5984 q^{94} + 3464 q^{98}+O(q^{100}) $ 12 * q + 8 * q^2 + 16 * q^4 + 96 * q^8 + 36 * q^9 - 8 * q^13 + 192 * q^15 - 184 * q^16 + 352 * q^19 - 256 * q^21 + 492 * q^25 + 784 * q^26 + 744 * q^30 - 24 * q^32 - 1400 * q^33 - 632 * q^35 + 856 * q^36 - 624 * q^38 + 1664 * q^42 + 1200 * q^43 - 1512 * q^47 + 1052 * q^49 - 2856 * q^50 + 792 * q^52 + 2504 * q^53 - 1424 * q^55 + 3408 * q^59 + 2808 * q^60 + 272 * q^64 - 272 * q^66 - 1080 * q^67 - 344 * q^69 - 2600 * q^70 + 248 * q^72 - 896 * q^76 - 848 * q^77 - 2404 * q^81 + 2960 * q^83 + 4768 * q^84 - 1200 * q^86 + 160 * q^87 - 2144 * q^89 - 3800 * q^93 - 5984 * q^94 + 3464 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−2.68604	−0.949660	−0.474830	−	0.880078i	$-0.657490\pi$
$2$	−2.68604	−0.949660	−0.474830	+	0.880078i	$0.657490\pi$
$3$	− 4.33137i	− 0.833573i	−0.909004	−	0.416787i	$-0.863156\pi$
$3$	− 4.33137i	− 0.833573i	0.909004	−	0.416787i	$-0.136844\pi$
$4$	−0.785167	−0.0981459
$5$	2.08666i	0.186636i	0.995636	+	0.0933181i	$0.0297474\pi$
$5$	2.08666i	0.186636i	−0.995636	+	0.0933181i	$0.970253\pi$
$6$	11.6343i	0.791611i
$7$	− 24.9985i	− 1.34979i	−0.737913	−	0.674895i	$-0.764189\pi$
$7$	− 24.9985i	− 1.34979i	0.737913	−	0.674895i	$-0.235811\pi$
$8$	23.5973	1.04287
$9$	8.23920	0.305156
$10$	− 5.60485i	− 0.177241i
$11$	3.82158i	0.104750i	0.998627	+	0.0523749i	$0.0166791\pi$
$11$	3.82158i	0.104750i	−0.998627	+	0.0523749i	$0.983321\pi$
$12$	3.40085i	0.0818118i
$13$	17.6726	0.377038	0.188519	−	0.982070i	$-0.439631\pi$
$13$	17.6726	0.377038	0.188519	+	0.982070i	$0.439631\pi$
$14$	67.1470i	1.28184i
$15$	9.03809	0.155575
$16$	−57.1022	−0.892221
$17$	0	0
$17$	0	0
$18$	−22.1309	−0.289794
$19$	160.915	1.94297	0.971483	−	0.237111i	$-0.0762006\pi$
$19$	160.915	1.94297	0.971483	+	0.237111i	$0.0762006\pi$
$20$	− 1.63837i	− 0.0183176i
$21$	−108.278	−1.12515
$22$	− 10.2649i	− 0.0994768i
$23$	99.9676i	0.906291i	0.891437	+	0.453145i	$0.149698\pi$
$23$	99.9676i	0.906291i	−0.891437	+	0.453145i	$0.850302\pi$
$24$	− 102.209i	− 0.869305i
$25$	120.646	0.965167
$26$	−47.4693	−0.358058
$27$	− 152.634i	− 1.08794i
$28$	19.6280i	0.132476i
$29$	− 200.583i	− 1.28439i	−0.766540	−	0.642197i	$-0.778023\pi$
$29$	− 200.583i	− 1.28439i	0.766540	−	0.642197i	$-0.221977\pi$
$30$	−24.2767	−0.147743
$31$	76.5382i	0.443441i	0.975110	+	0.221720i	$0.0711672\pi$
$31$	76.5382i	0.443441i	−0.975110	+	0.221720i	$0.928833\pi$
$32$	−35.3998	−0.195558
$33$	16.5527	0.0873167
$34$	0	0
$35$	52.1632	0.251920
$36$	−6.46915	−0.0299498
$37$	− 244.759i	− 1.08752i	−0.839242	−	0.543758i	$-0.817001\pi$
$37$	− 244.759i	− 1.08752i	0.839242	−	0.543758i	$-0.182999\pi$
$38$	−432.224	−1.84516
$39$	− 76.5465i	− 0.314289i
$40$	49.2395i	0.194636i
$41$	54.1132i	0.206123i	0.994675	+	0.103062i	$0.0328639\pi$
$41$	54.1132i	0.206123i	−0.994675	+	0.103062i	$0.967136\pi$
$42$	290.839	1.06851
$43$	−142.087	−0.503909	−0.251955	−	0.967739i	$-0.581073\pi$
$43$	−142.087	−0.503909	−0.251955	+	0.967739i	$0.581073\pi$
$44$	− 3.00058i	− 0.0102808i
$45$	17.1924i	0.0569531i
$46$	− 268.517i	− 0.860668i
$47$	−468.451	−1.45384	−0.726921	−	0.686721i	$-0.759049\pi$
$47$	−468.451	−1.45384	−0.726921	+	0.686721i	$0.759049\pi$
$48$	247.331i	0.743732i
$49$	−281.924	−0.821935
$50$	−324.060	−0.916580
$51$	0	0
$52$	−13.8759	−0.0370047
$53$	96.5673	0.250274	0.125137	−	0.992139i	$-0.460063\pi$
$53$	96.5673	0.250274	0.125137	+	0.992139i	$0.460063\pi$
$54$	409.982i	1.03318i
$55$	−7.97432	−0.0195501
$56$	− 589.898i	− 1.40765i
$57$	− 696.981i	− 1.61960i
$58$	538.776i	1.21974i
$59$	−364.484	−0.804268	−0.402134	−	0.915581i	$-0.631731\pi$
$59$	−364.484	−0.804268	−0.402134	+	0.915581i	$0.631731\pi$
$60$	−7.09641	−0.0152690
$61$	− 707.872i	− 1.48580i	−0.669404	−	0.742899i	$-0.733450\pi$
$61$	− 707.872i	− 1.48580i	0.669404	−	0.742899i	$-0.266550\pi$
$62$	− 205.585i	− 0.421118i
$63$	− 205.967i	− 0.411896i
$64$	551.903	1.07794
$65$	36.8766i	0.0703689i
$66$	−44.4612	−0.0829212
$67$	−304.454	−0.555150	−0.277575	−	0.960704i	$-0.589531\pi$
$67$	−304.454	−0.555150	−0.277575	+	0.960704i	$0.589531\pi$
$68$	0	0
$69$	432.997	0.755460
$70$	−140.113	−0.239238
$71$	− 470.003i	− 0.785621i	−0.919619	−	0.392810i	$-0.871503\pi$
$71$	− 470.003i	− 0.785621i	0.919619	−	0.392810i	$-0.128497\pi$
$72$	194.423	0.318236
$73$	− 142.056i	− 0.227759i	−0.993495	−	0.113880i	$-0.963672\pi$
$73$	− 142.056i	− 0.227759i	0.993495	−	0.113880i	$-0.0363278\pi$
$74$	657.432i	1.03277i
$75$	− 522.562i	− 0.804537i
$76$	−126.345	−0.190694
$77$	95.5336	0.141390
$78$	205.607i	0.298467i
$79$	− 717.865i	− 1.02236i	−0.859475	−	0.511178i	$-0.829209\pi$
$79$	− 717.865i	− 1.02236i	0.859475	−	0.511178i	$-0.170791\pi$
$80$	− 119.153i	− 0.166521i
$81$	−438.657	−0.601725
$82$	− 145.350i	− 0.195747i
$83$	367.639	0.486188	0.243094	−	0.970003i	$-0.421838\pi$
$83$	367.639	0.486188	0.243094	+	0.970003i	$0.421838\pi$
$84$	85.0162	0.110429
$85$	0	0
$86$	381.653	0.478542
$87$	−868.802	−1.07064
$88$	90.1791i	0.109240i
$89$	1042.28	1.24137	0.620684	−	0.784061i	$-0.286855\pi$
$89$	1042.28	1.24137	0.620684	+	0.784061i	$0.286855\pi$
$90$	− 46.1795i	− 0.0540861i
$91$	− 441.788i	− 0.508922i
$92$	− 78.4913i	− 0.0889488i
$93$	331.516	0.369640
$94$	1258.28	1.38066
$95$	335.773i	0.362628i
$96$	153.330i	0.163012i
$97$	903.534i	0.945773i	0.881123	+	0.472887i	$0.156788\pi$
$97$	903.534i	0.945773i	−0.881123	+	0.472887i	$0.843212\pi$
$98$	757.260	0.780559
$99$	31.4867i	0.0319650i
$100$	−94.7272	−0.0947272
$101$	443.233	0.436667	0.218333	−	0.975874i	$-0.429938\pi$
$101$	443.233	0.436667	0.218333	+	0.975874i	$0.429938\pi$
$102$	0	0
$103$	−1396.36	−1.33580	−0.667901	−	0.744250i	$-0.732807\pi$
$103$	−1396.36	−1.33580	−0.667901	+	0.744250i	$0.732807\pi$
$104$	417.026	0.393200
$105$	− 225.938i	− 0.209994i
$106$	−259.384	−0.237676
$107$	1843.89i	1.66594i	0.553315	+	0.832972i	$0.313363\pi$
$107$	1843.89i	1.66594i	−0.553315	+	0.832972i	$0.686637\pi$
$108$	119.843i	0.106777i
$109$	− 372.960i	− 0.327735i	−0.986482	−	0.163867i	$-0.947603\pi$
$109$	− 372.960i	− 0.327735i	0.986482	−	0.163867i	$-0.0523969\pi$
$110$	21.4194	0.0185660
$111$	−1060.14	−0.906524
$112$	1427.47i	1.20431i
$113$	1779.13i	1.48112i	0.671990	+	0.740560i	$0.265440\pi$
$113$	1779.13i	1.48112i	−0.671990	+	0.740560i	$0.734560\pi$
$114$	1872.12i	1.53807i
$115$	−208.598	−0.169147
$116$	157.492i	0.126058i
$117$	145.608	0.115055
$118$	979.020	0.763781
$119$	0	0
$120$	213.275	0.162244
$121$	1316.40	0.989027
$122$	1901.37i	1.41100i
$123$	234.384	0.171819
$124$	− 60.0953i	− 0.0435219i
$125$	512.578i	0.366771i
$126$	553.238i	0.391161i
$127$	−1735.00	−1.21225	−0.606126	−	0.795368i	$-0.707277\pi$
$127$	−1735.00	−1.21225	−0.606126	+	0.795368i	$0.707277\pi$
$128$	−1199.24	−0.828114
$129$	615.433i	0.420045i
$130$	− 99.0522i	− 0.0668265i
$131$	− 565.413i	− 0.377102i	−0.982063	−	0.188551i	$-0.939621\pi$
$131$	− 565.413i	− 0.377102i	0.982063	−	0.188551i	$-0.0603791\pi$
$132$	−12.9966	−0.00856978
$133$	− 4022.62i	− 2.62260i
$134$	817.778	0.527203
$135$	318.495	0.203050
$136$	0	0
$137$	−1150.24	−0.717314	−0.358657	−	0.933469i	$-0.616765\pi$
$137$	−1150.24	−0.717314	−0.358657	+	0.933469i	$0.616765\pi$
$138$	−1163.05	−0.717430
$139$	− 984.663i	− 0.600849i	−0.953806	−	0.300425i	$-0.902872\pi$
$139$	− 984.663i	− 0.600849i	0.953806	−	0.300425i	$-0.0971284\pi$
$140$	−40.9569	−0.0247249
$141$	2029.04i	1.21188i
$142$	1262.45i	0.746073i
$143$	67.5371i	0.0394947i
$144$	−470.476	−0.272266
$145$	418.549	0.239714
$146$	381.569i	0.216294i
$147$	1221.12i	0.685143i
$148$	192.176i	0.106735i
$149$	1772.18	0.974382	0.487191	−	0.873295i	$-0.338021\pi$
$149$	1772.18	0.974382	0.487191	+	0.873295i	$0.338021\pi$
$150$	1403.63i	0.764037i
$151$	1892.09	1.01971	0.509855	−	0.860260i	$-0.329699\pi$
$151$	1892.09	1.01971	0.509855	+	0.860260i	$0.329699\pi$
$152$	3797.16	2.02625
$153$	0	0
$154$	−256.607	−0.134273
$155$	−159.709	−0.0827621
$156$	60.1019i	0.0308462i
$157$	289.955	0.147395	0.0736973	−	0.997281i	$-0.476520\pi$
$157$	289.955	0.147395	0.0736973	+	0.997281i	$0.476520\pi$
$158$	1928.22i	0.970891i
$159$	− 418.269i	− 0.208622i
$160$	− 73.8673i	− 0.0364982i
$161$	2499.04	1.22330
$162$	1178.25	0.571434
$163$	1691.93i	0.813022i	0.913646	+	0.406511i	$0.133255\pi$
$163$	1691.93i	0.813022i	−0.913646	+	0.406511i	$0.866745\pi$
$164$	− 42.4879i	− 0.0202302i
$165$	34.5397i	0.0162965i
$166$	−987.495	−0.461714
$167$	− 1255.82i	− 0.581907i	−0.956737	−	0.290953i	$-0.906028\pi$
$167$	− 1255.82i	− 0.581907i	0.956737	−	0.290953i	$-0.0939725\pi$
$168$	−2555.07	−1.17338
$169$	−1884.68	−0.857842
$170$	0	0
$171$	1325.81	0.592907
$172$	111.562	0.0494566
$173$	401.192i	0.176313i	0.996107	+	0.0881564i	$0.0280975\pi$
$173$	401.192i	0.176313i	−0.996107	+	0.0881564i	$0.971902\pi$
$174$	2333.64	1.01674
$175$	− 3015.96i	− 1.30277i
$176$	− 218.220i	− 0.0934601i
$177$	1578.72i	0.670416i
$178$	−2799.62	−1.17888
$179$	769.231	0.321201	0.160601	−	0.987019i	$-0.448657\pi$
$179$	769.231	0.321201	0.160601	+	0.987019i	$0.448657\pi$
$180$	− 13.4989i	− 0.00558971i
$181$	− 2627.89i	− 1.07917i	−0.841931	−	0.539585i	$-0.818581\pi$
$181$	− 2627.89i	− 1.07917i	0.841931	−	0.539585i	$-0.181419\pi$
$182$	1186.66i	0.483303i
$183$	−3066.06	−1.23852
$184$	2358.97i	0.945139i
$185$	510.727	0.202970
$186$	−890.465	−0.351033
$187$	0	0
$188$	367.812	0.142689
$189$	−3815.62	−1.46850
$190$	− 901.902i	− 0.344373i
$191$	207.856	0.0787430	0.0393715	−	0.999225i	$-0.487464\pi$
$191$	207.856	0.0787430	0.0393715	+	0.999225i	$0.487464\pi$
$192$	− 2390.50i	− 0.898538i
$193$	− 4577.63i	− 1.70728i	−0.520864	−	0.853640i	$-0.674390\pi$
$193$	− 4577.63i	− 1.70728i	0.520864	−	0.853640i	$-0.325610\pi$
$194$	− 2426.93i	− 0.898163i
$195$	159.726	0.0586576
$196$	221.357	0.0806696
$197$	− 2640.99i	− 0.955140i	−0.878594	−	0.477570i	$-0.841518\pi$
$197$	− 2640.99i	− 0.955140i	0.878594	−	0.477570i	$-0.158482\pi$
$198$	− 84.5748i	− 0.0303559i
$199$	1650.96i	0.588106i	0.955789	+	0.294053i	$0.0950043\pi$
$199$	1650.96i	0.588106i	−0.955789	+	0.294053i	$0.904996\pi$
$200$	2846.92	1.00654
$201$	1318.71i	0.462758i
$202$	−1190.54	−0.414685
$203$	−5014.28	−1.73366
$204$	0	0
$205$	−112.916	−0.0384701
$206$	3750.69	1.26856
$207$	823.653i	0.276560i
$208$	−1009.14	−0.336401
$209$	614.947i	0.203525i
$210$	606.881i	0.199423i
$211$	1104.55i	0.360381i	0.983632	+	0.180191i	$0.0576715\pi$
$211$	1104.55i	0.360381i	−0.983632	+	0.180191i	$0.942328\pi$
$212$	−75.8215	−0.0245634
$213$	−2035.76	−0.654873
$214$	− 4952.78i	− 1.58208i
$215$	− 296.487i	− 0.0940477i
$216$	− 3601.76i	− 1.13458i
$217$	1913.34	0.598552
$218$	1001.79i	0.311237i
$219$	−615.299	−0.189854
$220$	6.26117	0.00191876
$221$	0	0
$222$	2847.59	0.860889
$223$	−2164.79	−0.650067	−0.325033	−	0.945703i	$-0.605376\pi$
$223$	−2164.79	−0.650067	−0.325033	+	0.945703i	$0.605376\pi$
$224$	884.942i	0.263963i
$225$	994.025	0.294526
$226$	− 4778.83i	− 1.40656i
$227$	2605.70i	0.761879i	0.924600	+	0.380940i	$0.124399\pi$
$227$	2605.70i	0.761879i	−0.924600	+	0.380940i	$0.875601\pi$
$228$	547.247i	0.158958i
$229$	1128.94	0.325774	0.162887	−	0.986645i	$-0.447919\pi$
$229$	1128.94	0.325774	0.162887	+	0.986645i	$0.447919\pi$
$230$	560.304	0.160632
$231$	− 413.792i	− 0.117859i
$232$	− 4733.24i	− 1.33945i
$233$	− 4315.97i	− 1.21351i	−0.794888	−	0.606756i	$-0.792470\pi$
$233$	− 4315.97i	− 1.21351i	0.794888	−	0.606756i	$-0.207530\pi$
$234$	−391.109	−0.109263
$235$	− 977.496i	− 0.271340i
$236$	286.181	0.0789356
$237$	−3109.34	−0.852209
$238$	0	0
$239$	788.197	0.213323	0.106662	−	0.994295i	$-0.465984\pi$
$239$	788.197	0.213323	0.106662	+	0.994295i	$0.465984\pi$
$240$	−516.094	−0.138807
$241$	− 3622.86i	− 0.968335i	−0.874975	−	0.484167i	$-0.839123\pi$
$241$	− 3622.86i	− 0.968335i	0.874975	−	0.484167i	$-0.160877\pi$
$242$	−3535.90	−0.939240
$243$	− 2221.13i	− 0.586361i
$244$	555.798i	0.145825i
$245$	− 588.278i	− 0.153403i
$246$	−629.567	−0.163170
$247$	2843.78	0.732571
$248$	1806.10i	0.462449i
$249$	− 1592.38i	− 0.405274i
$250$	− 1376.81i	− 0.348308i
$251$	−5974.99	−1.50254	−0.751271	−	0.659994i	$-0.770559\pi$
$251$	−5974.99	−1.50254	−0.751271	+	0.659994i	$0.770559\pi$
$252$	161.719i	0.0404259i
$253$	−382.034	−0.0949339
$254$	4660.28	1.15123
$255$	0	0
$256$	−1194.02	−0.291509
$257$	3750.91	0.910411	0.455205	−	0.890386i	$-0.349566\pi$
$257$	3750.91	0.910411	0.455205	+	0.890386i	$0.349566\pi$
$258$	− 1653.08i	− 0.398900i
$259$	−6118.59	−1.46792
$260$	− 28.9543i	− 0.00690642i
$261$	− 1652.65i	− 0.391940i
$262$	1518.73i	0.358119i
$263$	7566.43	1.77401	0.887007	−	0.461755i	$-0.152780\pi$
$263$	7566.43	1.77401	0.887007	+	0.461755i	$0.152780\pi$
$264$	390.599	0.0910596
$265$	201.503i	0.0467103i
$266$	10804.9i	2.49057i
$267$	− 4514.52i	− 1.03477i
$268$	239.048	0.0544857
$269$	6990.63i	1.58449i	0.610206	+	0.792243i	$0.291087\pi$
$269$	6990.63i	1.58449i	−0.610206	+	0.792243i	$0.708913\pi$
$270$	−855.492	−0.192828
$271$	−1356.64	−0.304097	−0.152049	−	0.988373i	$-0.548587\pi$
$271$	−1356.64	−0.304097	−0.152049	+	0.988373i	$0.548587\pi$
$272$	0	0
$273$	−1913.55	−0.424224
$274$	3089.61	0.681204
$275$	461.057i	0.101101i
$276$	−339.975	−0.0741453
$277$	7174.85i	1.55630i	0.628078	+	0.778150i	$0.283842\pi$
$277$	7174.85i	1.55630i	−0.628078	+	0.778150i	$0.716158\pi$
$278$	2644.85i	0.570603i
$279$	630.613i	0.135318i
$280$	1230.91	0.262718
$281$	−6611.42	−1.40357	−0.701787	−	0.712387i	$-0.747614\pi$
$281$	−6611.42	−1.40357	−0.701787	+	0.712387i	$0.747614\pi$
$282$	− 5450.08i	− 1.15088i
$283$	− 2310.88i	− 0.485398i	−0.970102	−	0.242699i	$-0.921967\pi$
$283$	− 2310.88i	− 0.485398i	0.970102	−	0.242699i	$-0.0780327\pi$
$284$	369.031i	0.0771055i
$285$	1454.36	0.302277
$286$	− 181.408i	− 0.0375065i
$287$	1352.75	0.278223
$288$	−291.666	−0.0596757
$289$	0	0
$290$	−1124.24	−0.227647
$291$	3913.55	0.788371
$292$	111.538i	0.0223537i
$293$	−6445.85	−1.28522	−0.642612	−	0.766192i	$-0.722149\pi$
$293$	−6445.85	−1.28522	−0.642612	+	0.766192i	$0.722149\pi$
$294$	− 3279.98i	− 0.650653i
$295$	− 760.553i	− 0.150105i
$296$	− 5775.65i	− 1.13413i
$297$	583.303	0.113962
$298$	−4760.16	−0.925332
$299$	1766.69i	0.341706i
$300$	410.299i	0.0789621i
$301$	3551.96i	0.680172i
$302$	−5082.24	−0.968378
$303$	− 1919.81i	− 0.363994i
$304$	−9188.57	−1.73356
$305$	1477.08	0.277304
$306$	0	0
$307$	221.421	0.0411634	0.0205817	−	0.999788i	$-0.493448\pi$
$307$	221.421	0.0411634	0.0205817	+	0.999788i	$0.493448\pi$
$308$	−75.0099	−0.0138769
$309$	6048.17i	1.11349i
$310$	428.985	0.0785959
$311$	1293.87i	0.235912i	0.993019	+	0.117956i	$0.0376341\pi$
$311$	1293.87i	0.235912i	−0.993019	+	0.117956i	$0.962366\pi$
$312$	− 1806.30i	− 0.327761i
$313$	385.448i	0.0696064i	0.999394	+	0.0348032i	$0.0110804\pi$
$313$	385.448i	0.0696064i	−0.999394	+	0.0348032i	$0.988920\pi$
$314$	−778.833	−0.139975
$315$	429.783	0.0768747
$316$	563.644i	0.100340i
$317$	649.047i	0.114997i	0.998346	+	0.0574986i	$0.0183125\pi$
$317$	649.047i	0.114997i	−0.998346	+	0.0574986i	$0.981688\pi$
$318$	1123.49i	0.198120i
$319$	766.545	0.134540
$320$	1151.63i	0.201182i
$321$	7986.60	1.38869
$322$	−6712.53	−1.16172
$323$	0	0
$324$	344.419	0.0590568
$325$	2132.12	0.363904
$326$	− 4544.61i	− 0.772094i
$327$	−1615.43	−0.273191
$328$	1276.93i	0.214959i
$329$	11710.6i	1.96238i
$330$	− 92.7753i	− 0.0154761i
$331$	−1429.71	−0.237415	−0.118707	−	0.992929i	$-0.537875\pi$
$331$	−1429.71	−0.237415	−0.118707	+	0.992929i	$0.537875\pi$
$332$	−288.658	−0.0477174
$333$	− 2016.61i	− 0.331861i
$334$	3373.19i	0.552614i
$335$	− 635.292i	− 0.103611i
$336$	6182.89	1.00388
$337$	− 565.364i	− 0.0913867i	−0.998956	−	0.0456934i	$-0.985450\pi$
$337$	− 565.364i	− 0.0913867i	0.998956	−	0.0456934i	$-0.0145497\pi$
$338$	5062.33	0.814659
$339$	7706.08	1.23462
$340$	0	0
$341$	−292.497	−0.0464504
$342$	−3561.18	−0.563060
$343$	− 1526.81i	− 0.240350i
$344$	−3352.88	−0.525509
$345$	903.516i	0.140996i
$346$	− 1077.62i	− 0.167437i
$347$	− 3788.72i	− 0.586135i	−0.956092	−	0.293068i	$-0.905324\pi$
$347$	− 3788.72i	− 0.586135i	0.956092	−	0.293068i	$-0.0946761\pi$
$348$	682.155	0.105079
$349$	6387.30	0.979669	0.489834	−	0.871816i	$-0.337057\pi$
$349$	6387.30	0.979669	0.489834	+	0.871816i	$0.337057\pi$
$350$	8101.01i	1.23719i
$351$	− 2697.44i	− 0.410196i
$352$	− 135.283i	− 0.0204847i
$353$	6291.34	0.948595	0.474298	−	0.880365i	$-0.342702\pi$
$353$	6291.34	0.948595	0.474298	+	0.880365i	$0.342702\pi$
$354$	− 4240.50i	− 0.636667i
$355$	980.735	0.146625
$356$	−818.367	−0.121835
$357$	0	0
$358$	−2066.19	−0.305032
$359$	3369.51	0.495364	0.247682	−	0.968841i	$-0.420331\pi$
$359$	3369.51	0.495364	0.247682	+	0.968841i	$0.420331\pi$
$360$	405.694i	0.0593944i
$361$	19034.5	2.77511
$362$	7058.63i	1.02484i
$363$	− 5701.80i	− 0.824427i
$364$	346.877i	0.0499486i
$365$	296.423	0.0425081
$366$	8235.56	1.17617
$367$	− 997.517i	− 0.141880i	−0.997481	−	0.0709400i	$-0.977400\pi$
$367$	− 997.517i	− 0.141880i	0.997481	−	0.0709400i	$-0.0225999\pi$
$368$	− 5708.37i	− 0.808612i
$369$	445.849i	0.0628997i
$370$	−1371.84	−0.192752
$371$	− 2414.04i	− 0.337818i
$372$	−260.295	−0.0362787
$373$	3180.59	0.441514	0.220757	−	0.975329i	$-0.429147\pi$
$373$	3180.59	0.441514	0.220757	+	0.975329i	$0.429147\pi$
$374$	0	0
$375$	2220.17	0.305731
$376$	−11054.2	−1.51616
$377$	− 3544.83i	− 0.484265i
$378$	10248.9	1.39457
$379$	− 10833.9i	− 1.46834i	−0.678965	−	0.734170i	$-0.737571\pi$
$379$	− 10833.9i	− 1.46834i	0.678965	−	0.734170i	$-0.262429\pi$
$380$	− 263.638i	− 0.0355904i
$381$	7514.92i	1.01050i
$382$	−558.310	−0.0747791
$383$	7567.93	1.00967	0.504834	−	0.863216i	$-0.331554\pi$
$383$	7567.93	1.00967	0.504834	+	0.863216i	$0.331554\pi$
$384$	5194.34i	0.690294i
$385$	199.346i	0.0263886i
$386$	12295.7i	1.62134i
$387$	−1170.69	−0.153771
$388$	− 709.426i	− 0.0928238i
$389$	−9599.36	−1.25117	−0.625587	−	0.780154i	$-0.715141\pi$
$389$	−9599.36	−1.25117	−0.625587	+	0.780154i	$0.715141\pi$
$390$	−429.032	−0.0557048
$391$	0	0
$392$	−6652.65	−0.857168
$393$	−2449.02	−0.314342
$394$	7093.81i	0.907058i
$395$	1497.94	0.190809
$396$	− 24.7224i	− 0.00313724i
$397$	− 5272.03i	− 0.666487i	−0.942841	−	0.333244i	$-0.891857\pi$
$397$	− 5272.03i	− 0.666487i	0.942841	−	0.333244i	$-0.108143\pi$
$398$	− 4434.54i	− 0.558501i
$399$	−17423.5	−2.18613
$400$	−6889.14	−0.861143
$401$	3600.34i	0.448360i	0.974548	+	0.224180i	$0.0719704\pi$
$401$	3600.34i	0.448360i	−0.974548	+	0.224180i	$0.928030\pi$
$402$	− 3542.10i	− 0.439463i
$403$	1352.63i	0.167194i
$404$	−348.012	−0.0428571
$405$	− 915.327i	− 0.112304i
$406$	13468.6	1.64639
$407$	935.364	0.113917
$408$	0	0
$409$	9516.13	1.15047	0.575235	−	0.817988i	$-0.304911\pi$
$409$	9516.13	1.15047	0.575235	+	0.817988i	$0.304911\pi$
$410$	303.296	0.0365335
$411$	4982.14i	0.597933i
$412$	1096.38	0.131104
$413$	9111.55i	1.08559i
$414$	− 2212.37i	− 0.262638i
$415$	767.137i	0.0907404i
$416$	−625.606	−0.0737329
$417$	−4264.95	−0.500852
$418$	− 1651.78i	− 0.193280i
$419$	6310.52i	0.735774i	0.929871	+	0.367887i	$0.119919\pi$
$419$	6310.52i	0.735774i	−0.929871	+	0.367887i	$0.880081\pi$
$420$	177.400i	0.0206100i
$421$	−1544.81	−0.178835	−0.0894177	−	0.995994i	$-0.528501\pi$
$421$	−1544.81	−0.178835	−0.0894177	+	0.995994i	$0.528501\pi$
$422$	− 2966.88i	− 0.342240i
$423$	−3859.66	−0.443648
$424$	2278.73	0.261002
$425$	0	0
$426$	5468.14	0.621906
$427$	−17695.7	−2.00552
$428$	− 1447.77i	− 0.163506i
$429$	292.528	0.0329217
$430$	796.378i	0.0893134i
$431$	− 897.334i	− 0.100286i	−0.998742	−	0.0501428i	$-0.984032\pi$
$431$	− 897.334i	− 0.100286i	0.998742	−	0.0501428i	$-0.0159676\pi$
$432$	8715.74i	0.970686i
$433$	−4896.47	−0.543440	−0.271720	−	0.962376i	$-0.587592\pi$
$433$	−4896.47	−0.543440	−0.271720	+	0.962376i	$0.587592\pi$
$434$	−5139.31	−0.568421
$435$	− 1812.89i	− 0.199819i
$436$	292.836i	0.0321659i
$437$	16086.2i	1.76089i
$438$	1652.72	0.180297
$439$	− 1404.01i	− 0.152642i	−0.997083	−	0.0763210i	$-0.975683\pi$
$439$	− 1404.01i	− 0.152642i	0.997083	−	0.0763210i	$-0.0243174\pi$
$440$	−188.173	−0.0203881
$441$	−2322.83	−0.250818
$442$	0	0
$443$	−6453.57	−0.692141	−0.346070	−	0.938209i	$-0.612484\pi$
$443$	−6453.57	−0.692141	−0.346070	+	0.938209i	$0.612484\pi$
$444$	832.388	0.0889716
$445$	2174.89i	0.231684i
$446$	5814.71	0.617342
$447$	− 7675.99i	− 0.812219i
$448$	− 13796.7i	− 1.45499i
$449$	4409.11i	0.463427i	0.972784	+	0.231714i	$0.0744333\pi$
$449$	4409.11i	0.463427i	−0.972784	+	0.231714i	$0.925567\pi$
$450$	−2670.00	−0.279700
$451$	−206.798	−0.0215914
$452$	− 1396.92i	− 0.145366i
$453$	− 8195.36i	− 0.850003i
$454$	− 6999.03i	− 0.723526i
$455$	921.859	0.0949833
$456$	− 16446.9i	− 1.68903i
$457$	−12571.6	−1.28681	−0.643406	−	0.765525i	$-0.722479\pi$
$457$	−12571.6	−1.28681	−0.643406	+	0.765525i	$0.722479\pi$
$458$	−3032.37	−0.309374
$459$	0	0
$460$	163.784	0.0166011
$461$	5115.00	0.516767	0.258383	−	0.966042i	$-0.416810\pi$
$461$	5115.00	0.516767	0.258383	+	0.966042i	$0.416810\pi$
$462$	1111.46i	0.111926i
$463$	5280.96	0.530080	0.265040	−	0.964237i	$-0.414615\pi$
$463$	5280.96	0.530080	0.265040	+	0.964237i	$0.414615\pi$
$464$	11453.8i	1.14596i
$465$	691.759i	0.0689883i
$466$	11592.9i	1.15242i
$467$	4430.45	0.439008	0.219504	−	0.975612i	$-0.429556\pi$
$467$	4430.45	0.439008	0.219504	+	0.975612i	$0.429556\pi$
$468$	−114.327	−0.0112922
$469$	7610.90i	0.749336i
$470$	2625.60i	0.257680i
$471$	− 1255.91i	− 0.122864i
$472$	−8600.86	−0.838743
$473$	− 542.997i	− 0.0527844i
$474$	8351.83	0.809308
$475$	19413.7	1.87529
$476$	0	0
$477$	795.637	0.0763726
$478$	−2117.13	−0.202584
$479$	8697.09i	0.829604i	0.909912	+	0.414802i	$0.136149\pi$
$479$	8697.09i	0.829604i	−0.909912	+	0.414802i	$0.863851\pi$
$480$	−319.947	−0.0304240
$481$	− 4325.52i	− 0.410034i
$482$	9731.15i	0.919589i
$483$	− 10824.3i	− 1.01971i
$484$	−1033.59	−0.0970690
$485$	−1885.37	−0.176516
$486$	5966.06i	0.556844i
$487$	13031.1i	1.21252i	0.795268	+	0.606258i	$0.207330\pi$
$487$	13031.1i	1.21252i	−0.795268	+	0.606258i	$0.792670\pi$
$488$	− 16703.9i	− 1.54949i
$489$	7328.40	0.677713
$490$	1580.14i	0.145681i
$491$	11760.3	1.08093	0.540464	−	0.841367i	$-0.318249\pi$
$491$	11760.3	1.08093	0.540464	+	0.841367i	$0.318249\pi$
$492$	−184.031	−0.0168633
$493$	0	0
$494$	−7638.51	−0.695694
$495$	−65.7020	−0.00596583
$496$	− 4370.50i	− 0.395647i
$497$	−11749.4	−1.06042
$498$	4277.21i	0.384872i
$499$	10724.6i	0.962118i	0.876688	+	0.481059i	$0.159748\pi$
$499$	10724.6i	0.962118i	−0.876688	+	0.481059i	$0.840252\pi$
$500$	− 402.460i	− 0.0359971i
$501$	−5439.43	−0.485062
$502$	16049.1	1.42690
$503$	3904.96i	0.346150i	0.984909	+	0.173075i	$0.0553703\pi$
$503$	3904.96i	0.346150i	−0.984909	+	0.173075i	$0.944630\pi$
$504$	− 4860.29i	− 0.429552i
$505$	924.875i	0.0814978i
$506$	1026.16	0.0901549
$507$	8163.25i	0.715075i
$508$	1362.26	0.118978
$509$	15132.3	1.31774	0.658870	−	0.752257i	$-0.271035\pi$
$509$	15132.3	1.31774	0.658870	+	0.752257i	$0.271035\pi$
$510$	0	0
$511$	−3551.19	−0.307427
$512$	12801.1	1.10495
$513$	− 24561.1i	− 2.11383i
$514$	−10075.1	−0.864581
$515$	− 2913.73i	− 0.249309i
$516$	− 483.218i	− 0.0412257i
$517$	− 1790.22i	− 0.152290i
$518$	16434.8	1.39402
$519$	1737.71	0.146970
$520$	870.190i	0.0733853i
$521$	16534.9i	1.39041i	0.718810	+	0.695207i	$0.244687\pi$
$521$	16534.9i	1.39041i	−0.718810	+	0.695207i	$0.755313\pi$
$522$	4439.08i	0.372210i
$523$	−8724.36	−0.729426	−0.364713	−	0.931120i	$-0.618833\pi$
$523$	−8724.36	−0.729426	−0.364713	+	0.931120i	$0.618833\pi$
$524$	443.944i	0.0370111i
$525$	−13063.3	−1.08596
$526$	−20323.8	−1.68471
$527$	0	0
$528$	−945.194	−0.0779058
$529$	2173.47	0.178637
$530$	− 541.245i	− 0.0443589i
$531$	−3003.06	−0.245427
$532$	3158.43i	0.257397i
$533$	956.319i	0.0777163i
$534$	12126.2i	0.982681i
$535$	−3847.57	−0.310925
$536$	−7184.32	−0.578946
$537$	− 3331.83i	− 0.267745i
$538$	− 18777.2i	− 1.50472i
$539$	− 1077.39i	− 0.0860976i
$540$	−250.072	−0.0199285
$541$	8246.12i	0.655320i	0.944796	+	0.327660i	$0.106260\pi$
$541$	8246.12i	0.655320i	−0.944796	+	0.327660i	$0.893740\pi$
$542$	3644.01	0.288789
$543$	−11382.4	−0.899567
$544$	0	0
$545$	778.240	0.0611672
$546$	5139.87	0.402868
$547$	23842.2i	1.86366i	0.362898	+	0.931829i	$0.381787\pi$
$547$	23842.2i	1.86366i	−0.362898	+	0.931829i	$0.618213\pi$
$548$	903.134	0.0704014
$549$	− 5832.30i	− 0.453399i
$550$	− 1238.42i	− 0.0960117i
$551$	− 32276.8i	− 2.49553i
$552$	10217.6	0.787843
$553$	−17945.5	−1.37997
$554$	− 19272.0i	− 1.47796i
$555$	− 2212.15i	− 0.169190i
$556$	773.126i	0.0589709i
$557$	19341.5	1.47132	0.735661	−	0.677350i	$-0.236872\pi$
$557$	19341.5	1.47132	0.735661	+	0.677350i	$0.236872\pi$
$558$	− 1693.86i	− 0.128506i
$559$	−2511.05	−0.189993
$560$	−2978.63	−0.224768
$561$	0	0
$562$	17758.6	1.33292
$563$	14210.3	1.06376	0.531878	−	0.846821i	$-0.321487\pi$
$563$	14210.3	1.06376	0.531878	+	0.846821i	$0.321487\pi$
$564$	− 1593.13i	− 0.118942i
$565$	−3712.44	−0.276431
$566$	6207.12i	0.460963i
$567$	10965.8i	0.812202i
$568$	− 11090.8i	− 0.819297i
$569$	9576.15	0.705542	0.352771	−	0.935710i	$-0.385239\pi$
$569$	9576.15	0.705542	0.352771	+	0.935710i	$0.385239\pi$
$570$	−3906.48	−0.287060
$571$	− 14785.0i	− 1.08359i	−0.840510	−	0.541796i	$-0.817745\pi$
$571$	− 14785.0i	− 1.08359i	0.840510	−	0.541796i	$-0.182255\pi$
$572$	− 53.0279i	− 0.00387624i
$573$	− 900.301i	− 0.0656381i
$574$	−3633.54	−0.264218
$575$	12060.7i	0.874722i
$576$	4547.24	0.328938
$577$	−11438.5	−0.825284	−0.412642	−	0.910893i	$-0.635394\pi$
$577$	−11438.5	−0.825284	−0.412642	+	0.910893i	$0.635394\pi$
$578$	0	0
$579$	−19827.4	−1.42314
$580$	−328.631	−0.0235270
$581$	− 9190.42i	− 0.656253i
$582$	−10512.0	−0.748685
$583$	369.039i	0.0262162i
$584$	− 3352.15i	− 0.237522i
$585$	303.834i	0.0214735i
$586$	17313.8	1.22053
$587$	7892.09	0.554925	0.277463	−	0.960736i	$-0.410507\pi$
$587$	7892.09	0.554925	0.277463	+	0.960736i	$0.410507\pi$
$588$	− 958.782i	− 0.0672440i
$589$	12316.1i	0.861590i
$590$	2042.88i	0.142549i
$591$	−11439.1	−0.796179
$592$	13976.2i	0.970304i
$593$	−7829.44	−0.542186	−0.271093	−	0.962553i	$-0.587385\pi$
$593$	−7829.44	−0.542186	−0.271093	+	0.962553i	$0.587385\pi$
$594$	−1566.78	−0.108225
$595$	0	0
$596$	−1391.46	−0.0956317
$597$	7150.91	0.490230
$598$	− 4745.40i	− 0.324504i
$599$	−18939.7	−1.29191	−0.645956	−	0.763375i	$-0.723541\pi$
$599$	−18939.7	−1.29191	−0.645956	+	0.763375i	$0.723541\pi$
$600$	− 12331.1i	− 0.839024i
$601$	17777.4i	1.20658i	0.797522	+	0.603290i	$0.206144\pi$
$601$	17777.4i	1.20658i	−0.797522	+	0.603290i	$0.793856\pi$
$602$	− 9540.73i	− 0.645932i
$603$	−2508.46	−0.169407
$604$	−1485.61	−0.100080
$605$	2746.86i	0.184588i
$606$	5156.69i	0.345670i
$607$	− 17713.3i	− 1.18445i	−0.805774	−	0.592223i	$-0.798250\pi$
$607$	− 17713.3i	− 1.18445i	0.805774	−	0.592223i	$-0.201750\pi$
$608$	−5696.35	−0.379963
$609$	21718.7i	1.44513i
$610$	−3967.51	−0.263344
$611$	−8278.74	−0.548154
$612$	0	0
$613$	25427.3	1.67537	0.837683	−	0.546156i	$-0.183910\pi$
$613$	25427.3	1.67537	0.837683	+	0.546156i	$0.183910\pi$
$614$	−594.746	−0.0390912
$615$	489.080i	0.0320676i
$616$	2254.34	0.147451
$617$	− 10028.4i	− 0.654343i	−0.944965	−	0.327172i	$-0.893904\pi$
$617$	− 10028.4i	− 0.654343i	0.944965	−	0.327172i	$-0.106096\pi$
$618$	− 16245.6i	− 1.05744i
$619$	4460.94i	0.289661i	0.989456	+	0.144831i	$0.0462638\pi$
$619$	4460.94i	0.289661i	−0.989456	+	0.144831i	$0.953736\pi$
$620$	125.398	0.00812276
$621$	15258.5	0.985993
$622$	− 3475.39i	− 0.224036i
$623$	− 26055.5i	− 1.67559i
$624$	4370.97i	0.280415i
$625$	14011.2	0.896714
$626$	− 1035.33i	− 0.0661024i
$627$	2663.57	0.169653
$628$	−227.664	−0.0144662
$629$	0	0
$630$	−1154.42	−0.0730049
$631$	1098.49	0.0693032	0.0346516	−	0.999399i	$-0.488968\pi$
$631$	1098.49	0.0693032	0.0346516	+	0.999399i	$0.488968\pi$
$632$	− 16939.7i	− 1.06618i
$633$	4784.23	0.300404
$634$	− 1743.37i	− 0.109208i
$635$	− 3620.34i	− 0.226250i
$636$	328.411i	0.0204754i
$637$	−4982.32	−0.309901
$638$	−2058.97	−0.127767
$639$	− 3872.45i	− 0.239737i
$640$	− 2502.39i	− 0.154556i
$641$	− 1063.17i	− 0.0655115i	−0.999463	−	0.0327557i	$-0.989572\pi$
$641$	− 1063.17i	− 0.0655115i	0.999463	−	0.0327557i	$-0.0104283\pi$
$642$	−21452.4	−1.31878
$643$	− 6571.26i	− 0.403025i	−0.979486	−	0.201513i	$-0.935414\pi$
$643$	− 6571.26i	− 0.403025i	0.979486	−	0.201513i	$-0.0645857\pi$
$644$	−1962.16	−0.120062
$645$	−1284.20	−0.0783957
$646$	0	0
$647$	−14783.1	−0.898273	−0.449137	−	0.893463i	$-0.648268\pi$
$647$	−14783.1	−0.898273	−0.449137	+	0.893463i	$0.648268\pi$
$648$	−10351.1	−0.627518
$649$	− 1392.90i	− 0.0842469i
$650$	−5726.98	−0.345585
$651$	− 8287.38i	− 0.498937i
$652$	− 1328.45i	− 0.0797948i
$653$	25912.0i	1.55285i	0.630208	+	0.776427i	$0.282970\pi$
$653$	25912.0i	1.55285i	−0.630208	+	0.776427i	$0.717030\pi$
$654$	4339.12	0.259439
$655$	1179.82	0.0703809
$656$	− 3089.98i	− 0.183908i
$657$	− 1170.43i	− 0.0695020i
$658$	− 31455.1i	− 1.86360i
$659$	4302.30	0.254315	0.127158	−	0.991883i	$-0.459415\pi$
$659$	4302.30	0.254315	0.127158	+	0.991883i	$0.459415\pi$
$660$	− 27.1195i	− 0.00159943i
$661$	7467.66	0.439423	0.219711	−	0.975565i	$-0.429488\pi$
$661$	7467.66	0.439423	0.219711	+	0.975565i	$0.429488\pi$
$662$	3840.28	0.225463
$663$	0	0
$664$	8675.31	0.507029
$665$	8393.82	0.489471
$666$	5416.72i	0.315155i
$667$	20051.9	1.16403
$668$	986.031i	0.0571118i
$669$	9376.50i	0.541878i
$670$	1706.42i	0.0983953i
$671$	2705.19	0.155637
$672$	3833.01	0.220032
$673$	4236.79i	0.242669i	0.992612	+	0.121335i	$0.0387174\pi$
$673$	4236.79i	0.242669i	−0.992612	+	0.121335i	$0.961283\pi$
$674$	1518.59i	0.0867863i
$675$	− 18414.7i	− 1.05005i
$676$	1479.79	0.0841938
$677$	− 23130.5i	− 1.31311i	−0.754278	−	0.656555i	$-0.772013\pi$
$677$	− 23130.5i	− 1.31311i	0.754278	−	0.656555i	$-0.227987\pi$
$678$	−20698.9	−1.17247
$679$	22587.0	1.27660
$680$	0	0
$681$	11286.3	0.635082
$682$	785.659	0.0441121
$683$	11474.5i	0.642839i	0.946937	+	0.321419i	$0.104160\pi$
$683$	11474.5i	0.642839i	−0.946937	+	0.321419i	$0.895840\pi$
$684$	−1040.98	−0.0581914
$685$	− 2400.16i	− 0.133877i
$686$	4101.08i	0.228251i
$687$	− 4889.84i	− 0.271556i
$688$	8113.49	0.449599
$689$	1706.59	0.0943629
$690$	− 2426.88i	− 0.133898i
$691$	15221.6i	0.837997i	0.907987	+	0.418999i	$0.137619\pi$
$691$	15221.6i	0.837997i	−0.907987	+	0.418999i	$0.862381\pi$
$692$	− 315.003i	− 0.0173044i
$693$	787.120	0.0431461
$694$	10176.7i	0.556629i
$695$	2054.65	0.112140
$696$	−20501.4	−1.11653
$697$	0	0
$698$	−17156.6	−0.930352
$699$	−18694.1	−1.01155
$700$	2368.04i	0.127862i
$701$	−23996.1	−1.29289	−0.646447	−	0.762959i	$-0.723746\pi$
$701$	−23996.1	−1.29289	−0.646447	+	0.762959i	$0.723746\pi$
$702$	7245.44i	0.389546i
$703$	− 39385.2i	− 2.11300i
$704$	2109.14i	0.112914i
$705$	−4233.90	−0.226181
$706$	−16898.8	−0.900843
$707$	− 11080.2i	− 0.589409i
$708$	− 1239.56i	− 0.0657986i
$709$	22346.8i	1.18371i	0.806044	+	0.591856i	$0.201605\pi$
$709$	22346.8i	1.18371i	−0.806044	+	0.591856i	$0.798395\pi$
$710$	−2634.30	−0.139244
$711$	− 5914.63i	− 0.311978i
$712$	24595.1	1.29458
$713$	−7651.34	−0.401886
$714$	0	0
$715$	−140.927	−0.00737113
$716$	−603.975	−0.0315246
$717$	− 3413.98i	− 0.177820i
$718$	−9050.64	−0.470427
$719$	− 32468.2i	− 1.68409i	−0.539408	−	0.842045i	$-0.681352\pi$
$719$	− 32468.2i	− 1.68409i	0.539408	−	0.842045i	$-0.318648\pi$
$720$	− 981.722i	− 0.0508148i
$721$	34906.9i	1.80305i
$722$	−51127.5	−2.63541
$723$	−15691.9	−0.807178
$724$	2063.34i	0.105916i
$725$	− 24199.6i	− 1.23965i
$726$	15315.3i	0.782925i
$727$	−2899.33	−0.147909	−0.0739547	−	0.997262i	$-0.523562\pi$
$727$	−2899.33	−0.147909	−0.0739547	+	0.997262i	$0.523562\pi$
$728$	− 10425.0i	− 0.530737i
$729$	−21464.3	−1.09050
$730$	−796.204	−0.0403683
$731$	0	0
$732$	2407.37	0.121556
$733$	−16399.9	−0.826390	−0.413195	−	0.910643i	$-0.635587\pi$
$733$	−16399.9	−0.826390	−0.413195	+	0.910643i	$0.635587\pi$
$734$	2679.37i	0.134738i
$735$	−2548.05	−0.127873
$736$	− 3538.84i	− 0.177233i
$737$	− 1163.50i	− 0.0581519i
$738$	− 1197.57i	− 0.0597333i
$739$	−6470.65	−0.322093	−0.161047	−	0.986947i	$-0.551487\pi$
$739$	−6470.65	−0.322093	−0.161047	+	0.986947i	$0.551487\pi$
$740$	−401.006	−0.0199207
$741$	− 12317.5i	− 0.610652i
$742$	6484.21i	0.320812i
$743$	− 7520.20i	− 0.371318i	−0.982614	−	0.185659i	$-0.940558\pi$
$743$	− 7520.20i	− 0.371318i	0.982614	−	0.185659i	$-0.0594420\pi$
$744$	7822.89	0.385485
$745$	3697.94i	0.181855i
$746$	−8543.20	−0.419288
$747$	3029.05	0.148363
$748$	0	0
$749$	46094.6	2.24868
$750$	−5963.47	−0.290340
$751$	10921.9i	0.530685i	0.964154	+	0.265342i	$0.0854850\pi$
$751$	10921.9i	0.530685i	−0.964154	+	0.265342i	$0.914515\pi$
$752$	26749.6	1.29715
$753$	25879.9i	1.25248i
$754$	9521.56i	0.459887i
$755$	3948.14i	0.190315i
$756$	2995.90	0.144127
$757$	−17112.9	−0.821636	−0.410818	−	0.911717i	$-0.634757\pi$
$757$	−17112.9	−0.821636	−0.410818	+	0.911717i	$0.634757\pi$
$758$	29100.4i	1.39442i
$759$	1654.73i	0.0791343i
$760$	7923.36i	0.378172i
$761$	−35934.3	−1.71172	−0.855860	−	0.517207i	$-0.826972\pi$
$761$	−35934.3	−1.71172	−0.855860	+	0.517207i	$0.826972\pi$
$762$	− 20185.4i	− 0.959633i
$763$	−9323.44	−0.442374
$764$	−163.202	−0.00772831
$765$	0	0
$766$	−20327.8	−0.958842
$767$	−6441.37	−0.303239
$768$	5171.75i	0.242994i
$769$	29085.3	1.36390	0.681952	−	0.731397i	$-0.261131\pi$
$769$	29085.3	1.36390	0.681952	+	0.731397i	$0.261131\pi$
$770$	− 535.451i	− 0.0250602i
$771$	− 16246.6i	− 0.758894i
$772$	3594.21i	0.167563i
$773$	16502.8	0.767873	0.383936	−	0.923360i	$-0.374568\pi$
$773$	16502.8	0.767873	0.383936	+	0.923360i	$0.374568\pi$
$774$	3144.51	0.146030
$775$	9234.02i	0.427994i
$776$	21321.0i	0.986314i
$777$	26501.9i	1.22362i
$778$	25784.3	1.18819
$779$	8707.60i	0.400491i
$780$	−125.412	−0.00575701
$781$	1796.15	0.0822937
$782$	0	0
$783$	−30615.9	−1.39735
$784$	16098.5	0.733348
$785$	605.037i	0.0275092i
$786$	6578.17	0.298518
$787$	27374.1i	1.23987i	0.784651	+	0.619937i	$0.212842\pi$
$787$	27374.1i	1.23987i	−0.784651	+	0.619937i	$0.787158\pi$
$788$	2073.62i	0.0937431i
$789$	− 32773.0i	− 1.47877i
$790$	−4023.53	−0.181203
$791$	44475.6	1.99920
$792$	743.003i	0.0333352i
$793$	− 12509.9i	− 0.560202i
$794$	14160.9i	0.632936i
$795$	872.784	0.0389364
$796$	− 1296.28i	− 0.0577202i
$797$	31776.1	1.41226	0.706128	−	0.708084i	$-0.250440\pi$
$797$	31776.1	1.41226	0.706128	+	0.708084i	$0.250440\pi$
$798$	46800.2	2.07608
$799$	0	0
$800$	−4270.84	−0.188746
$801$	8587.58	0.378810
$802$	− 9670.68i	− 0.425790i
$803$	542.879	0.0238578
$804$	− 1035.41i	− 0.0454178i
$805$	5214.63i	0.228313i
$806$	− 3633.22i	− 0.158777i
$807$	30279.0	1.32078
$808$	10459.1	0.455385
$809$	34367.2i	1.49355i	0.665074	+	0.746777i	$0.268400\pi$
$809$	34367.2i	1.49355i	−0.665074	+	0.746777i	$0.731600\pi$
$810$	2458.61i	0.106650i
$811$	− 1316.99i	− 0.0570232i	−0.999593	−	0.0285116i	$-0.990923\pi$
$811$	− 1316.99i	− 0.0570232i	0.999593	−	0.0285116i	$-0.00907676\pi$
$812$	3937.05	0.170152
$813$	5876.14i	0.253487i
$814$	−2512.43	−0.108182
$815$	−3530.49	−0.151739
$816$	0	0
$817$	−22863.9	−0.979078
$818$	−25560.7	−1.09256
$819$	− 3639.98i	− 0.155300i
$820$	88.6577	0.00377568
$821$	33481.1i	1.42326i	0.702552	+	0.711632i	$0.252044\pi$
$821$	33481.1i	1.42326i	−0.702552	+	0.711632i	$0.747956\pi$
$822$	− 13382.2i	− 0.567833i
$823$	− 11746.8i	− 0.497529i	−0.968564	−	0.248765i	$-0.919975\pi$
$823$	− 11746.8i	− 0.497529i	0.968564	−	0.248765i	$-0.0800246\pi$
$824$	−32950.5	−1.39306
$825$	1997.01	0.0842752
$826$	− 24474.0i	− 1.03094i
$827$	4367.84i	0.183658i	0.995775	+	0.0918288i	$0.0292713\pi$
$827$	4367.84i	0.183658i	−0.995775	+	0.0918288i	$0.970729\pi$
$828$	− 646.706i	− 0.0271432i
$829$	19994.7	0.837689	0.418844	−	0.908058i	$-0.362435\pi$
$829$	19994.7	0.837689	0.418844	+	0.908058i	$0.362435\pi$
$830$	− 2060.56i	− 0.0861725i
$831$	31077.0	1.29729
$832$	9753.55	0.406422
$833$	0	0
$834$	11455.8	0.475639
$835$	2620.47	0.108605
$836$	− 482.837i	− 0.0199752i
$837$	11682.3	0.482438
$838$	− 16950.3i	− 0.698735i
$839$	25672.1i	1.05638i	0.849127	+	0.528189i	$0.177129\pi$
$839$	25672.1i	1.05638i	−0.849127	+	0.528189i	$0.822871\pi$
$840$	− 5331.55i	− 0.218995i
$841$	−15844.7	−0.649667
$842$	4149.44	0.169833
$843$	28636.5i	1.16998i
$844$	− 867.258i	− 0.0353700i
$845$	− 3932.68i	− 0.160104i
$846$	10367.2	0.421315
$847$	− 32907.9i	− 1.33498i
$848$	−5514.20	−0.223300
$849$	−10009.3	−0.404614
$850$	0	0
$851$	24467.9	0.985605
$852$	1598.41	0.0642731
$853$	− 15504.6i	− 0.622355i	−0.950352	−	0.311178i	$-0.899277\pi$
$853$	− 15504.6i	− 0.622355i	0.950352	−	0.311178i	$-0.100723\pi$
$854$	47531.5	1.90456
$855$	2766.50i	0.110658i
$856$	43511.0i	1.73736i
$857$	35915.1i	1.43155i	0.698332	+	0.715774i	$0.253926\pi$
$857$	35915.1i	1.43155i	−0.698332	+	0.715774i	$0.746074\pi$
$858$	−785.744	−0.0312644
$859$	36575.0	1.45276	0.726382	−	0.687292i	$-0.241201\pi$
$859$	36575.0	1.45276	0.726382	+	0.687292i	$0.241201\pi$
$860$	232.792i	0.00923040i
$861$	− 5859.25i	− 0.231920i
$862$	2410.28i	0.0952372i
$863$	11402.6	0.449768	0.224884	−	0.974386i	$-0.427800\pi$
$863$	11402.6	0.449768	0.224884	+	0.974386i	$0.427800\pi$
$864$	5403.22i	0.212756i
$865$	−837.151	−0.0329063
$866$	13152.1	0.516083
$867$	0	0
$868$	−1502.29	−0.0587455
$869$	2743.38	0.107092
$870$	4869.51i	0.189761i
$871$	−5380.50	−0.209312
$872$	− 8800.87i	− 0.341783i
$873$	7444.40i	0.288608i
$874$	− 43208.4i	− 1.67225i
$875$	12813.7	0.495065
$876$	483.113	0.0186334
$877$	23424.6i	0.901932i	0.892541	+	0.450966i	$0.148920\pi$
$877$	23424.6i	0.901932i	−0.892541	+	0.450966i	$0.851080\pi$
$878$	3771.24i	0.144958i
$879$	27919.4i	1.07133i
$880$	455.351	0.0174430
$881$	2452.52i	0.0937882i	0.998900	+	0.0468941i	$0.0149323\pi$
$881$	2452.52i	0.0937882i	−0.998900	+	0.0468941i	$0.985068\pi$
$882$	6239.21	0.238192
$883$	3832.99	0.146082	0.0730409	−	0.997329i	$-0.476730\pi$
$883$	3832.99	0.146082	0.0730409	+	0.997329i	$0.476730\pi$
$884$	0	0
$885$	−3294.24	−0.125124
$886$	17334.6	0.657298
$887$	13334.4i	0.504762i	0.967628	+	0.252381i	$0.0812137\pi$
$887$	13334.4i	0.504762i	−0.967628	+	0.252381i	$0.918786\pi$
$888$	−25016.5	−0.945382
$889$	43372.3i	1.63629i
$890$	− 5841.84i	− 0.220021i
$891$	− 1676.36i	− 0.0630306i
$892$	1699.72	0.0638014
$893$	−75380.6	−2.82477
$894$	20618.1i	0.771332i
$895$	1605.12i	0.0599478i
$896$	29979.1i	1.11778i
$897$	7652.18	0.284837
$898$	− 11843.1i	− 0.440098i
$899$	15352.3	0.569553
$900$	−780.476	−0.0289065
$901$	0	0
$902$	555.468	0.0205045
$903$	15384.9	0.566973
$904$	41982.8i	1.54461i
$905$	5483.51	0.201412
$906$	22013.1i	0.807214i
$907$	14432.7i	0.528368i	0.964472	+	0.264184i	$0.0851026\pi$
$907$	14432.7i	0.528368i	−0.964472	+	0.264184i	$0.914897\pi$
$908$	− 2045.91i	− 0.0747753i
$909$	3651.89	0.133251
$910$	−2476.15	−0.0902018
$911$	− 50465.5i	− 1.83534i	−0.397343	−	0.917670i	$-0.630068\pi$
$911$	− 50465.5i	− 1.83534i	0.397343	−	0.917670i	$-0.369932\pi$
$912$	39799.1i	1.44505i
$913$	1404.96i	0.0509282i
$914$	33767.8	1.22203
$915$	− 6397.81i	− 0.231153i
$916$	−886.404	−0.0319734
$917$	−14134.5	−0.509009
$918$	0	0
$919$	−33955.2	−1.21880	−0.609401	−	0.792862i	$-0.708590\pi$
$919$	−33955.2	−1.21880	−0.609401	+	0.792862i	$0.708590\pi$
$920$	−4922.36	−0.176397
$921$	− 959.057i	− 0.0343127i
$922$	−13739.1	−0.490753
$923$	− 8306.16i	− 0.296209i
$924$	324.896i	0.0115674i
$925$	− 29529.1i	− 1.04963i
$926$	−14184.9	−0.503396
$927$	−11504.9	−0.407628
$928$	7100.62i	0.251174i
$929$	− 14807.7i	− 0.522954i	−0.965210	−	0.261477i	$-0.915790\pi$
$929$	− 14807.7i	− 0.522954i	0.965210	−	0.261477i	$-0.0842095\pi$
$930$	− 1858.09i	− 0.0655154i
$931$	−45365.6	−1.59699
$932$	3388.76i	0.119101i
$933$	5604.23	0.196650
$934$	−11900.4	−0.416908
$935$	0	0
$936$	3435.96	0.119987
$937$	5141.33	0.179253	0.0896265	−	0.995975i	$-0.471433\pi$
$937$	5141.33	0.179253	0.0896265	+	0.995975i	$0.471433\pi$
$938$	− 20443.2i	− 0.711614i
$939$	1669.52	0.0580220
$940$	767.498i	0.0266309i
$941$	− 38958.4i	− 1.34964i	−0.737984	−	0.674819i	$-0.764222\pi$
$941$	− 38958.4i	− 1.34964i	0.737984	−	0.674819i	$-0.235778\pi$
$942$	3373.42i	0.116679i
$943$	−5409.57	−0.186808
$944$	20812.8	0.717585
$945$	− 7961.89i	− 0.274074i
$946$	1458.51i	0.0501273i
$947$	− 14191.6i	− 0.486974i	−0.969904	−	0.243487i	$-0.921709\pi$
$947$	− 14191.6i	− 0.486974i	0.969904	−	0.243487i	$-0.0782914\pi$
$948$	2441.35	0.0836408
$949$	− 2510.50i	− 0.0858739i
$950$	−52146.0	−1.78088
$951$	2811.27	0.0958586
$952$	0	0
$953$	−32646.8	−1.10969	−0.554844	−	0.831955i	$-0.687222\pi$
$953$	−32646.8	−1.10969	−0.554844	+	0.831955i	$0.687222\pi$
$954$	−2137.12	−0.0725280
$955$	433.724i	0.0146963i
$956$	−618.867	−0.0209368
$957$	− 3320.19i	− 0.112149i
$958$	− 23360.8i	− 0.787842i
$959$	28754.3i	0.968223i
$960$	4988.15	0.167700
$961$	23932.9	0.803360
$962$	11618.5i	0.389393i
$963$	15192.2i	0.508372i
$964$	2844.55i	0.0950381i
$965$	9551.94	0.318640
$966$	29074.5i	0.968381i
$967$	16183.8	0.538196	0.269098	−	0.963113i	$-0.413274\pi$
$967$	16183.8	0.538196	0.269098	+	0.963113i	$0.413274\pi$
$968$	31063.4	1.03142
$969$	0	0
$970$	5064.18	0.167630
$971$	−28807.7	−0.952095	−0.476048	−	0.879420i	$-0.657931\pi$
$971$	−28807.7	−0.952095	−0.476048	+	0.879420i	$0.657931\pi$
$972$	1743.96i	0.0575490i
$973$	−24615.1	−0.811021
$974$	− 35002.1i	− 1.15148i
$975$	− 9235.02i	− 0.303341i
$976$	40421.0i	1.32566i
$977$	−3155.66	−0.103335	−0.0516675	−	0.998664i	$-0.516454\pi$
$977$	−3155.66	−0.103335	−0.0516675	+	0.998664i	$0.516454\pi$
$978$	−19684.4	−0.643597
$979$	3983.16i	0.130033i
$980$	461.897i	0.0150559i
$981$	− 3072.89i	− 0.100010i
$982$	−31588.8	−1.02651
$983$	− 14818.7i	− 0.480816i	−0.970672	−	0.240408i	$-0.922719\pi$
$983$	− 14818.7i	− 0.480816i	0.970672	−	0.240408i	$-0.0772813\pi$
$984$	5530.85	0.179184
$985$	5510.83	0.178264
$986$	0	0
$987$	50722.8	1.63579
$988$	−2232.84	−0.0718989
$989$	− 14204.1i	− 0.456688i
$990$	176.478	0.00566551
$991$	888.414i	0.0284777i	0.999899	+	0.0142389i	$0.00453252\pi$
$991$	888.414i	0.0284777i	−0.999899	+	0.0142389i	$0.995467\pi$
$992$	− 2709.44i	− 0.0867185i
$993$	6192.63i	0.197902i
$994$	31559.3	1.00704
$995$	−3444.98	−0.109762
$996$	1250.29i	0.0397760i
$997$	5116.97i	0.162544i	0.996692	+	0.0812718i	$0.0258982\pi$
$997$	5116.97i	0.162544i	−0.996692	+	0.0812718i	$0.974102\pi$
$998$	− 28806.6i	− 0.913685i
$999$	−37358.5	−1.18315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.b.e.288.3		12
17.4	even	4		289.4.a.g.1.9		12
17.6	odd	16		17.4.d.a.15.1	yes	12
17.13	even	4		289.4.a.g.1.10		12
17.14	odd	16		17.4.d.a.8.1	✓	12
17.16	even	2	inner	289.4.b.e.288.4		12
51.14	even	16		153.4.l.a.127.3		12
51.23	even	16		153.4.l.a.100.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.d.a.8.1	✓	12	17.14	odd	16
17.4.d.a.15.1	yes	12	17.6	odd	16
153.4.l.a.100.3		12	51.23	even	16
153.4.l.a.127.3		12	51.14	even	16
289.4.a.g.1.9		12	17.4	even	4
289.4.a.g.1.10		12	17.13	even	4
289.4.b.e.288.3		12	1.1	even	1	trivial
289.4.b.e.288.4		12	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	289.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.68604 q^{2} -4.33137i q^{3} -0.785167 q^{4} +2.08666i q^{5} +11.6343i q^{6} -24.9985i q^{7} +23.5973 q^{8} +8.23920 q^{9} +O(q^{10})\)	\(q-2.68604 q^{2} -4.33137i q^{3} -0.785167 q^{4} +2.08666i q^{5} +11.6343i q^{6} -24.9985i q^{7} +23.5973 q^{8} +8.23920 q^{9} -5.60485i q^{10} +3.82158i q^{11} +3.40085i q^{12} +17.6726 q^{13} +67.1470i q^{14} +9.03809 q^{15} -57.1022 q^{16} -22.1309 q^{18} +160.915 q^{19} -1.63837i q^{20} -108.278 q^{21} -10.2649i q^{22} +99.9676i q^{23} -102.209i q^{24} +120.646 q^{25} -47.4693 q^{26} -152.634i q^{27} +19.6280i q^{28} -200.583i q^{29} -24.2767 q^{30} +76.5382i q^{31} -35.3998 q^{32} +16.5527 q^{33} +52.1632 q^{35} -6.46915 q^{36} -244.759i q^{37} -432.224 q^{38} -76.5465i q^{39} +49.2395i q^{40} +54.1132i q^{41} +290.839 q^{42} -142.087 q^{43} -3.00058i q^{44} +17.1924i q^{45} -268.517i q^{46} -468.451 q^{47} +247.331i q^{48} -281.924 q^{49} -324.060 q^{50} -13.8759 q^{52} +96.5673 q^{53} +409.982i q^{54} -7.97432 q^{55} -589.898i q^{56} -696.981i q^{57} +538.776i q^{58} -364.484 q^{59} -7.09641 q^{60} -707.872i q^{61} -205.585i q^{62} -205.967i q^{63} +551.903 q^{64} +36.8766i q^{65} -44.4612 q^{66} -304.454 q^{67} +432.997 q^{69} -140.113 q^{70} -470.003i q^{71} +194.423 q^{72} -142.056i q^{73} +657.432i q^{74} -522.562i q^{75} -126.345 q^{76} +95.5336 q^{77} +205.607i q^{78} -717.865i q^{79} -119.153i q^{80} -438.657 q^{81} -145.350i q^{82} +367.639 q^{83} +85.0162 q^{84} +381.653 q^{86} -868.802 q^{87} +90.1791i q^{88} +1042.28 q^{89} -46.1795i q^{90} -441.788i q^{91} -78.4913i q^{92} +331.516 q^{93} +1258.28 q^{94} +335.773i q^{95} +153.330i q^{96} +903.534i q^{97} +757.260 q^{98} +31.4867i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{2} + 16 q^{4} + 96 q^{8} + 36 q^{9}+O(q^{10}) \) 12 * q + 8 * q^2 + 16 * q^4 + 96 * q^8 + 36 * q^9	\( 12 q + 8 q^{2} + 16 q^{4} + 96 q^{8} + 36 q^{9} - 8 q^{13} + 192 q^{15} - 184 q^{16} + 352 q^{19} - 256 q^{21} + 492 q^{25} + 784 q^{26} + 744 q^{30} - 24 q^{32} - 1400 q^{33} - 632 q^{35} + 856 q^{36} - 624 q^{38} + 1664 q^{42} + 1200 q^{43} - 1512 q^{47} + 1052 q^{49} - 2856 q^{50} + 792 q^{52} + 2504 q^{53} - 1424 q^{55} + 3408 q^{59} + 2808 q^{60} + 272 q^{64} - 272 q^{66} - 1080 q^{67} - 344 q^{69} - 2600 q^{70} + 248 q^{72} - 896 q^{76} - 848 q^{77} - 2404 q^{81} + 2960 q^{83} + 4768 q^{84} - 1200 q^{86} + 160 q^{87} - 2144 q^{89} - 3800 q^{93} - 5984 q^{94} + 3464 q^{98}+O(q^{100}) \) 12 * q + 8 * q^2 + 16 * q^4 + 96 * q^8 + 36 * q^9 - 8 * q^13 + 192 * q^15 - 184 * q^16 + 352 * q^19 - 256 * q^21 + 492 * q^25 + 784 * q^26 + 744 * q^30 - 24 * q^32 - 1400 * q^33 - 632 * q^35 + 856 * q^36 - 624 * q^38 + 1664 * q^42 + 1200 * q^43 - 1512 * q^47 + 1052 * q^49 - 2856 * q^50 + 792 * q^52 + 2504 * q^53 - 1424 * q^55 + 3408 * q^59 + 2808 * q^60 + 272 * q^64 - 272 * q^66 - 1080 * q^67 - 344 * q^69 - 2600 * q^70 + 248 * q^72 - 896 * q^76 - 848 * q^77 - 2404 * q^81 + 2960 * q^83 + 4768 * q^84 - 1200 * q^86 + 160 * q^87 - 2144 * q^89 - 3800 * q^93 - 5984 * q^94 + 3464 * q^98

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