LMFDB - Embedded newform 289.4.b.e.288.4

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

$q$-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	$0.136844\pi$
$3$	4.33137i	0.833573i	−0.909004	+	0.416787i	$0.863156\pi$
$4$	−0.785167	−0.0981459
$5$	− 2.08666i	− 0.186636i	−0.995636	−	0.0933181i	$-0.970253\pi$
$5$	− 2.08666i	− 0.186636i	0.995636	−	0.0933181i	$-0.0297474\pi$
$6$	− 11.6343i	− 0.791611i
$7$	24.9985i	1.34979i	0.737913	+	0.674895i	$0.235811\pi$
$7$	24.9985i	1.34979i	−0.737913	+	0.674895i	$0.764189\pi$
$8$	23.5973	1.04287
$9$	8.23920	0.305156
$10$	5.60485i	0.177241i
$11$	− 3.82158i	− 0.104750i	−0.998627	−	0.0523749i	$-0.983321\pi$
$11$	− 3.82158i	− 0.104750i	0.998627	−	0.0523749i	$-0.0166791\pi$
$12$	− 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	$-0.850302\pi$
$23$	− 99.9676i	− 0.906291i	0.891437	−	0.453145i	$-0.149698\pi$
$24$	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	$0.221977\pi$
$29$	200.583i	1.28439i	−0.766540	+	0.642197i	$0.778023\pi$
$30$	−24.2767	−0.147743
$31$	− 76.5382i	− 0.443441i	−0.975110	−	0.221720i	$-0.928833\pi$
$31$	− 76.5382i	− 0.443441i	0.975110	−	0.221720i	$-0.0711672\pi$
$32$	−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	$0.182999\pi$
$37$	244.759i	1.08752i	−0.839242	+	0.543758i	$0.817001\pi$
$38$	−432.224	−1.84516
$39$	76.5465i	0.314289i
$40$	− 49.2395i	− 0.194636i
$41$	− 54.1132i	− 0.206123i	−0.994675	−	0.103062i	$-0.967136\pi$
$41$	− 54.1132i	− 0.206123i	0.994675	−	0.103062i	$-0.0328639\pi$
$42$	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	$0.266550\pi$
$61$	707.872i	1.48580i	−0.669404	+	0.742899i	$0.733450\pi$
$62$	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	$0.128497\pi$
$71$	470.003i	0.785621i	−0.919619	+	0.392810i	$0.871503\pi$
$72$	194.423	0.318236
$73$	142.056i	0.227759i	0.993495	+	0.113880i	$0.0363278\pi$
$73$	142.056i	0.227759i	−0.993495	+	0.113880i	$0.963672\pi$
$74$	− 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	$0.170791\pi$
$79$	717.865i	1.02236i	−0.859475	+	0.511178i	$0.829209\pi$
$80$	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	$-0.843212\pi$
$97$	− 903.534i	− 0.945773i	0.881123	−	0.472887i	$-0.156788\pi$
$98$	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	$-0.686637\pi$
$107$	− 1843.89i	− 1.66594i	0.553315	−	0.832972i	$-0.313363\pi$
$108$	− 119.843i	− 0.106777i
$109$	372.960i	0.327735i	0.986482	+	0.163867i	$0.0523969\pi$
$109$	372.960i	0.327735i	−0.986482	+	0.163867i	$0.947603\pi$
$110$	21.4194	0.0185660
$111$	−1060.14	−0.906524
$112$	− 1427.47i	− 1.20431i
$113$	− 1779.13i	− 1.48112i	−0.671990	−	0.740560i	$-0.734560\pi$
$113$	− 1779.13i	− 1.48112i	0.671990	−	0.740560i	$-0.265440\pi$
$114$	− 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	$0.0603791\pi$
$131$	565.413i	0.377102i	−0.982063	+	0.188551i	$0.939621\pi$
$132$	−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	$0.0971284\pi$
$139$	984.663i	0.600849i	−0.953806	+	0.300425i	$0.902872\pi$
$140$	−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	$-0.866745\pi$
$163$	− 1691.93i	− 0.813022i	0.913646	−	0.406511i	$-0.133255\pi$
$164$	42.4879i	0.0202302i
$165$	− 34.5397i	− 0.0162965i
$166$	−987.495	−0.461714
$167$	1255.82i	0.581907i	0.956737	+	0.290953i	$0.0939725\pi$
$167$	1255.82i	0.581907i	−0.956737	+	0.290953i	$0.906028\pi$
$168$	−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	$-0.971902\pi$
$173$	− 401.192i	− 0.176313i	0.996107	−	0.0881564i	$-0.0280975\pi$
$174$	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	$0.181419\pi$
$181$	2627.89i	1.07917i	−0.841931	+	0.539585i	$0.818581\pi$
$182$	− 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	$0.325610\pi$
$193$	4577.63i	1.70728i	−0.520864	+	0.853640i	$0.674390\pi$
$194$	2426.93i	0.898163i
$195$	159.726	0.0586576
$196$	221.357	0.0806696
$197$	2640.99i	0.955140i	0.878594	+	0.477570i	$0.158482\pi$
$197$	2640.99i	0.955140i	−0.878594	+	0.477570i	$0.841518\pi$
$198$	84.5748i	0.0303559i
$199$	− 1650.96i	− 0.588106i	−0.955789	−	0.294053i	$-0.904996\pi$
$199$	− 1650.96i	− 0.588106i	0.955789	−	0.294053i	$-0.0950043\pi$
$200$	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	$-0.942328\pi$
$211$	− 1104.55i	− 0.360381i	0.983632	−	0.180191i	$-0.0576715\pi$
$212$	−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	$-0.875601\pi$
$227$	− 2605.70i	− 0.761879i	0.924600	−	0.380940i	$-0.124399\pi$
$228$	− 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	$0.207530\pi$
$233$	4315.97i	1.21351i	−0.794888	+	0.606756i	$0.792470\pi$
$234$	−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	$0.160877\pi$
$241$	3622.86i	0.968335i	−0.874975	+	0.484167i	$0.839123\pi$
$242$	−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	$-0.708913\pi$
$269$	− 6990.63i	− 1.58449i	0.610206	−	0.792243i	$-0.291087\pi$
$270$	−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	$-0.716158\pi$
$277$	− 7174.85i	− 1.55630i	0.628078	−	0.778150i	$-0.283842\pi$
$278$	− 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	$0.0780327\pi$
$283$	2310.88i	0.485398i	−0.970102	+	0.242699i	$0.921967\pi$
$284$	− 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	$-0.962366\pi$
$311$	− 1293.87i	− 0.235912i	0.993019	−	0.117956i	$-0.0376341\pi$
$312$	1806.30i	0.327761i
$313$	− 385.448i	− 0.0696064i	−0.999394	−	0.0348032i	$-0.988920\pi$
$313$	− 385.448i	− 0.0696064i	0.999394	−	0.0348032i	$-0.0110804\pi$
$314$	−778.833	−0.139975
$315$	429.783	0.0768747
$316$	− 563.644i	− 0.100340i
$317$	− 649.047i	− 0.114997i	−0.998346	−	0.0574986i	$-0.981688\pi$
$317$	− 649.047i	− 0.114997i	0.998346	−	0.0574986i	$-0.0183125\pi$
$318$	− 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	$0.0145497\pi$
$337$	565.364i	0.0913867i	−0.998956	+	0.0456934i	$0.985450\pi$
$338$	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	$0.0946761\pi$
$347$	3788.72i	0.586135i	−0.956092	+	0.293068i	$0.905324\pi$
$348$	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	$0.0225999\pi$
$367$	997.517i	0.141880i	−0.997481	+	0.0709400i	$0.977400\pi$
$368$	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	$0.262429\pi$
$379$	10833.9i	1.46834i	−0.678965	+	0.734170i	$0.737571\pi$
$380$	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	$0.108143\pi$
$397$	5272.03i	0.666487i	−0.942841	+	0.333244i	$0.891857\pi$
$398$	4434.54i	0.558501i
$399$	−17423.5	−2.18613
$400$	−6889.14	−0.861143
$401$	− 3600.34i	− 0.448360i	−0.974548	−	0.224180i	$-0.928030\pi$
$401$	− 3600.34i	− 0.448360i	0.974548	−	0.224180i	$-0.0719704\pi$
$402$	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	$-0.880081\pi$
$419$	− 6310.52i	− 0.735774i	0.929871	−	0.367887i	$-0.119919\pi$
$420$	− 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	$0.0159676\pi$
$431$	897.334i	0.100286i	−0.998742	+	0.0501428i	$0.984032\pi$
$432$	− 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	$0.0243174\pi$
$439$	1404.01i	0.152642i	−0.997083	+	0.0763210i	$0.975683\pi$
$440$	−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	$-0.925567\pi$
$449$	− 4409.11i	− 0.463427i	0.972784	−	0.231714i	$-0.0744333\pi$
$450$	−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	$-0.863851\pi$
$479$	− 8697.09i	− 0.829604i	0.909912	−	0.414802i	$-0.136149\pi$
$480$	−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	$-0.792670\pi$
$487$	− 13031.1i	− 1.21252i	0.795268	−	0.606258i	$-0.207330\pi$
$488$	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	$-0.840252\pi$
$499$	− 10724.6i	− 0.962118i	0.876688	−	0.481059i	$-0.159748\pi$
$500$	402.460i	0.0359971i
$501$	−5439.43	−0.485062
$502$	16049.1	1.42690
$503$	− 3904.96i	− 0.346150i	−0.984909	−	0.173075i	$-0.944630\pi$
$503$	− 3904.96i	− 0.346150i	0.984909	−	0.173075i	$-0.0553703\pi$
$504$	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	$-0.755313\pi$
$521$	− 16534.9i	− 1.39041i	0.718810	−	0.695207i	$-0.244687\pi$
$522$	− 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	$-0.893740\pi$
$541$	− 8246.12i	− 0.655320i	0.944796	−	0.327660i	$-0.106260\pi$
$542$	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	$-0.618213\pi$
$547$	− 23842.2i	− 1.86366i	0.362898	−	0.931829i	$-0.381787\pi$
$548$	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	$0.182255\pi$
$571$	14785.0i	1.08359i	−0.840510	+	0.541796i	$0.817745\pi$
$572$	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	$-0.793856\pi$
$601$	− 17777.4i	− 1.20658i	0.797522	−	0.603290i	$-0.206144\pi$
$602$	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	$0.201750\pi$
$607$	17713.3i	1.18445i	−0.805774	+	0.592223i	$0.798250\pi$
$608$	−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	$0.106096\pi$
$617$	10028.4i	0.654343i	−0.944965	+	0.327172i	$0.893904\pi$
$618$	16245.6i	1.05744i
$619$	− 4460.94i	− 0.289661i	−0.989456	−	0.144831i	$-0.953736\pi$
$619$	− 4460.94i	− 0.289661i	0.989456	−	0.144831i	$-0.0462638\pi$
$620$	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	$0.0104283\pi$
$641$	1063.17i	0.0655115i	−0.999463	+	0.0327557i	$0.989572\pi$
$642$	−21452.4	−1.31878
$643$	6571.26i	0.403025i	0.979486	+	0.201513i	$0.0645857\pi$
$643$	6571.26i	0.403025i	−0.979486	+	0.201513i	$0.935414\pi$
$644$	−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	$-0.717030\pi$
$653$	− 25912.0i	− 1.55285i	0.630208	−	0.776427i	$-0.282970\pi$
$654$	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	$-0.961283\pi$
$673$	− 4236.79i	− 0.242669i	0.992612	−	0.121335i	$-0.0387174\pi$
$674$	− 1518.59i	− 0.0867863i
$675$	18414.7i	1.05005i
$676$	1479.79	0.0841938
$677$	23130.5i	1.31311i	0.754278	+	0.656555i	$0.227987\pi$
$677$	23130.5i	1.31311i	−0.754278	+	0.656555i	$0.772013\pi$
$678$	−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	$-0.895840\pi$
$683$	− 11474.5i	− 0.642839i	0.946937	−	0.321419i	$-0.104160\pi$
$684$	−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	$-0.862381\pi$
$691$	− 15221.6i	− 0.837997i	0.907987	−	0.418999i	$-0.137619\pi$
$692$	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	$-0.798395\pi$
$709$	− 22346.8i	− 1.18371i	0.806044	−	0.591856i	$-0.201605\pi$
$710$	−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	$0.318648\pi$
$719$	32468.2i	1.68409i	−0.539408	+	0.842045i	$0.681352\pi$
$720$	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	$0.0594420\pi$
$743$	7520.20i	0.371318i	−0.982614	+	0.185659i	$0.940558\pi$
$744$	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	$-0.914515\pi$
$751$	− 10921.9i	− 0.530685i	0.964154	−	0.265342i	$-0.0854850\pi$
$752$	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	$-0.787158\pi$
$787$	− 27374.1i	− 1.23987i	0.784651	−	0.619937i	$-0.212842\pi$
$788$	− 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	$-0.731600\pi$
$809$	− 34367.2i	− 1.49355i	0.665074	−	0.746777i	$-0.268400\pi$
$810$	− 2458.61i	− 0.106650i
$811$	1316.99i	0.0570232i	0.999593	+	0.0285116i	$0.00907676\pi$
$811$	1316.99i	0.0570232i	−0.999593	+	0.0285116i	$0.990923\pi$
$812$	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	$-0.747956\pi$
$821$	− 33481.1i	− 1.42326i	0.702552	−	0.711632i	$-0.252044\pi$
$822$	13382.2i	0.567833i
$823$	11746.8i	0.497529i	0.968564	+	0.248765i	$0.0800246\pi$
$823$	11746.8i	0.497529i	−0.968564	+	0.248765i	$0.919975\pi$
$824$	−32950.5	−1.39306
$825$	1997.01	0.0842752
$826$	24474.0i	1.03094i
$827$	− 4367.84i	− 0.183658i	−0.995775	−	0.0918288i	$-0.970729\pi$
$827$	− 4367.84i	− 0.183658i	0.995775	−	0.0918288i	$-0.0292713\pi$
$828$	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	$-0.822871\pi$
$839$	− 25672.1i	− 1.05638i	0.849127	−	0.528189i	$-0.177129\pi$
$840$	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	$0.100723\pi$
$853$	15504.6i	0.622355i	−0.950352	+	0.311178i	$0.899277\pi$
$854$	47531.5	1.90456
$855$	− 2766.50i	− 0.110658i
$856$	− 43511.0i	− 1.73736i
$857$	− 35915.1i	− 1.43155i	−0.698332	−	0.715774i	$-0.746074\pi$
$857$	− 35915.1i	− 1.43155i	0.698332	−	0.715774i	$-0.253926\pi$
$858$	−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	$-0.851080\pi$
$877$	− 23424.6i	− 0.901932i	0.892541	−	0.450966i	$-0.148920\pi$
$878$	− 3771.24i	− 0.144958i
$879$	− 27919.4i	− 1.07133i
$880$	455.351	0.0174430
$881$	− 2452.52i	− 0.0937882i	−0.998900	−	0.0468941i	$-0.985068\pi$
$881$	− 2452.52i	− 0.0937882i	0.998900	−	0.0468941i	$-0.0149323\pi$
$882$	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	$-0.918786\pi$
$887$	− 13334.4i	− 0.504762i	0.967628	−	0.252381i	$-0.0812137\pi$
$888$	−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	$-0.914897\pi$
$907$	− 14432.7i	− 0.528368i	0.964472	−	0.264184i	$-0.0851026\pi$
$908$	2045.91i	0.0747753i
$909$	3651.89	0.133251
$910$	−2476.15	−0.0902018
$911$	50465.5i	1.83534i	0.397343	+	0.917670i	$0.369932\pi$
$911$	50465.5i	1.83534i	−0.397343	+	0.917670i	$0.630068\pi$
$912$	− 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	$0.0842095\pi$
$929$	14807.7i	0.522954i	−0.965210	+	0.261477i	$0.915790\pi$
$930$	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	$0.235778\pi$
$941$	38958.4i	1.34964i	−0.737984	+	0.674819i	$0.764222\pi$
$942$	− 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	$0.0782914\pi$
$947$	14191.6i	0.486974i	−0.969904	+	0.243487i	$0.921709\pi$
$948$	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	$0.0772813\pi$
$983$	14818.7i	0.480816i	−0.970672	+	0.240408i	$0.922719\pi$
$984$	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	$-0.995467\pi$
$991$	− 888.414i	− 0.0284777i	0.999899	−	0.0142389i	$-0.00453252\pi$
$992$	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	$-0.974102\pi$
$997$	− 5116.97i	− 0.162544i	0.996692	−	0.0812718i	$-0.0258982\pi$
$998$	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.288.4		12
17.3	odd	16		17.4.d.a.8.1	✓	12
17.4	even	4		289.4.a.g.1.10		12
17.11	odd	16		17.4.d.a.15.1	yes	12
17.13	even	4		289.4.a.g.1.9		12
17.16	even	2	inner	289.4.b.e.288.3		12
51.11	even	16		153.4.l.a.100.3		12
51.20	even	16		153.4.l.a.127.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.d.a.8.1	✓	12	17.3	odd	16
17.4.d.a.15.1	yes	12	17.11	odd	16
153.4.l.a.100.3		12	51.11	even	16
153.4.l.a.127.3		12	51.20	even	16
289.4.a.g.1.9		12	17.13	even	4
289.4.a.g.1.10		12	17.4	even	4
289.4.b.e.288.3		12	17.16	even	2	inner
289.4.b.e.288.4		12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
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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