LMFDB - Embedded newform 289.4.b.e.288.9

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			288.9
Root			$-2.49971 + 0.765367i$ of defining polynomial
Character	$\chi$	$=$	289.288
Dual form			289.4.b.e.288.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.49971 q^{2} -2.82539i q^{3} +4.24796 q^{4} -8.71933i q^{5} -9.88806i q^{6} +6.85501i q^{7} -13.1311 q^{8} +19.0171 q^{9} +O(q^{10})$	\(q+3.49971 q^{2} -2.82539i q^{3} +4.24796 q^{4} -8.71933i q^{5} -9.88806i q^{6} +6.85501i q^{7} -13.1311 q^{8} +19.0171 q^{9} -30.5151i q^{10} -61.7928i q^{11} -12.0022i q^{12} -5.37363 q^{13} +23.9905i q^{14} -24.6355 q^{15} -79.9385 q^{16} +66.5545 q^{18} -96.7877 q^{19} -37.0393i q^{20} +19.3681 q^{21} -216.257i q^{22} -116.525i q^{23} +37.1004i q^{24} +48.9733 q^{25} -18.8061 q^{26} -130.017i q^{27} +29.1198i q^{28} -197.375i q^{29} -86.2172 q^{30} +138.070i q^{31} -174.713 q^{32} -174.589 q^{33} +59.7710 q^{35} +80.7840 q^{36} +111.428i q^{37} -338.729 q^{38} +15.1826i q^{39} +114.494i q^{40} +166.487i q^{41} +67.7827 q^{42} -165.887 q^{43} -262.493i q^{44} -165.817i q^{45} -407.804i q^{46} -130.994 q^{47} +225.858i q^{48} +296.009 q^{49} +171.392 q^{50} -22.8269 q^{52} +714.232 q^{53} -455.020i q^{54} -538.792 q^{55} -90.0135i q^{56} +273.463i q^{57} -690.754i q^{58} +846.216 q^{59} -104.651 q^{60} +4.99209i q^{61} +483.205i q^{62} +130.363i q^{63} +28.0634 q^{64} +46.8544i q^{65} -611.011 q^{66} -314.069 q^{67} -329.230 q^{69} +209.181 q^{70} -118.468i q^{71} -249.715 q^{72} +650.548i q^{73} +389.965i q^{74} -138.369i q^{75} -411.150 q^{76} +423.590 q^{77} +53.1347i q^{78} -208.405i q^{79} +697.010i q^{80} +146.115 q^{81} +582.655i q^{82} +742.430 q^{83} +82.2749 q^{84} -580.555 q^{86} -557.662 q^{87} +811.405i q^{88} +215.527 q^{89} -580.310i q^{90} -36.8362i q^{91} -494.994i q^{92} +390.102 q^{93} -458.441 q^{94} +843.923i q^{95} +493.633i q^{96} -705.690i q^{97} +1035.94 q^{98} -1175.12i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.49971	1.23733	0.618667	−	0.785653i	$-0.287673\pi$
$2$	3.49971	1.23733	0.618667	+	0.785653i	$0.287673\pi$
$3$	− 2.82539i	− 0.543747i	−0.962333	−	0.271874i	$-0.912357\pi$
$3$	− 2.82539i	− 0.543747i	0.962333	−	0.271874i	$-0.0876433\pi$
$4$	4.24796	0.530995
$5$	− 8.71933i	− 0.779880i	−0.920840	−	0.389940i	$-0.872496\pi$
$5$	− 8.71933i	− 0.779880i	0.920840	−	0.389940i	$-0.127504\pi$
$6$	− 9.88806i	− 0.672797i
$7$	6.85501i	0.370136i	0.982726	+	0.185068i	$0.0592505\pi$
$7$	6.85501i	0.370136i	−0.982726	+	0.185068i	$0.940750\pi$
$8$	−13.1311	−0.580316
$9$	19.0171	0.704339
$10$	− 30.5151i	− 0.964972i
$11$	− 61.7928i	− 1.69375i	−0.531793	−	0.846875i	$-0.678481\pi$
$11$	− 61.7928i	− 1.69375i	0.531793	−	0.846875i	$-0.321519\pi$
$12$	− 12.0022i	− 0.288727i
$13$	−5.37363	−0.114644	−0.0573221	−	0.998356i	$-0.518256\pi$
$13$	−5.37363	−0.114644	−0.0573221	+	0.998356i	$0.518256\pi$
$14$	23.9905i	0.457981i
$15$	−24.6355	−0.424058
$16$	−79.9385	−1.24904
$17$	0	0
$17$	0	0
$18$	66.5545	0.871502
$19$	−96.7877	−1.16866	−0.584332	−	0.811515i	$-0.698643\pi$
$19$	−96.7877	−1.16866	−0.584332	+	0.811515i	$0.698643\pi$
$20$	− 37.0393i	− 0.414112i
$21$	19.3681	0.201260
$22$	− 216.257i	− 2.09573i
$23$	− 116.525i	− 1.05640i	−0.849120	−	0.528200i	$-0.822867\pi$
$23$	− 116.525i	− 1.05640i	0.849120	−	0.528200i	$-0.177133\pi$
$24$	37.1004i	0.315545i
$25$	48.9733	0.391787
$26$	−18.8061	−0.141853
$27$	− 130.017i	− 0.926730i
$28$	29.1198i	0.196540i
$29$	− 197.375i	− 1.26385i	−0.775031	−	0.631924i	$-0.782266\pi$
$29$	− 197.375i	− 1.26385i	0.775031	−	0.631924i	$-0.217734\pi$
$30$	−86.2172	−0.524701
$31$	138.070i	0.799939i	0.916528	+	0.399970i	$0.130979\pi$
$31$	138.070i	0.799939i	−0.916528	+	0.399970i	$0.869021\pi$
$32$	−174.713	−0.965162
$33$	−174.589	−0.920972
$34$	0	0
$35$	59.7710	0.288661
$36$	80.7840	0.374000
$37$	111.428i	0.495098i	0.968875	+	0.247549i	$0.0796251\pi$
$37$	111.428i	0.495098i	−0.968875	+	0.247549i	$0.920375\pi$
$38$	−338.729	−1.44603
$39$	15.1826i	0.0623375i
$40$	114.494i	0.452577i
$41$	166.487i	0.634167i	0.948398	+	0.317084i	$0.102704\pi$
$41$	166.487i	0.634167i	−0.948398	+	0.317084i	$0.897296\pi$
$42$	67.7827	0.249026
$43$	−165.887	−0.588314	−0.294157	−	0.955757i	$-0.595039\pi$
$43$	−165.887	−0.588314	−0.294157	+	0.955757i	$0.595039\pi$
$44$	− 262.493i	− 0.899372i
$45$	− 165.817i	− 0.549300i
$46$	− 407.804i	− 1.30712i
$47$	−130.994	−0.406541	−0.203271	−	0.979123i	$-0.565157\pi$
$47$	−130.994	−0.406541	−0.203271	+	0.979123i	$0.565157\pi$
$48$	225.858i	0.679162i
$49$	296.009	0.863000
$50$	171.392	0.484771
$51$	0	0
$52$	−22.8269	−0.0608755
$53$	714.232	1.85108	0.925541	−	0.378648i	$-0.123611\pi$
$53$	714.232	1.85108	0.925541	+	0.378648i	$0.123611\pi$
$54$	− 455.020i	− 1.14667i
$55$	−538.792	−1.32092
$56$	− 90.0135i	− 0.214796i
$57$	273.463i	0.635458i
$58$	− 690.754i	− 1.56380i
$59$	846.216	1.86725	0.933627	−	0.358247i	$-0.116625\pi$
$59$	846.216	1.86725	0.933627	+	0.358247i	$0.116625\pi$
$60$	−104.651	−0.225172
$61$	4.99209i	0.0104782i	0.999986	+	0.00523911i	$0.00166767\pi$
$61$	4.99209i	0.0104782i	−0.999986	+	0.00523911i	$0.998332\pi$
$62$	483.205i	0.989792i
$63$	130.363i	0.260701i
$64$	28.0634	0.0548113
$65$	46.8544i	0.0894088i
$66$	−611.011	−1.13955
$67$	−314.069	−0.572681	−0.286341	−	0.958128i	$-0.592439\pi$
$67$	−314.069	−0.572681	−0.286341	+	0.958128i	$0.592439\pi$
$68$	0	0
$69$	−329.230	−0.574415
$70$	209.181	0.357171
$71$	− 118.468i	− 0.198022i	−0.995086	−	0.0990108i	$-0.968432\pi$
$71$	− 118.468i	− 0.198022i	0.995086	−	0.0990108i	$-0.0315678\pi$
$72$	−249.715	−0.408739
$73$	650.548i	1.04303i	0.853243	+	0.521513i	$0.174632\pi$
$73$	650.548i	1.04303i	−0.853243	+	0.521513i	$0.825368\pi$
$74$	389.965i	0.612601i
$75$	− 138.369i	− 0.213033i
$76$	−411.150	−0.620554
$77$	423.590	0.626917
$78$	53.1347i	0.0771323i
$79$	− 208.405i	− 0.296803i	−0.988927	−	0.148402i	$-0.952587\pi$
$79$	− 208.405i	− 0.296803i	0.988927	−	0.148402i	$-0.0474128\pi$
$80$	697.010i	0.974101i
$81$	146.115	0.200432
$82$	582.655i	0.784677i
$83$	742.430	0.981834	0.490917	−	0.871206i	$-0.336662\pi$
$83$	742.430	0.981834	0.490917	+	0.871206i	$0.336662\pi$
$84$	82.2749	0.106868
$85$	0	0
$86$	−580.555	−0.727940
$87$	−557.662	−0.687214
$88$	811.405i	0.982910i
$89$	215.527	0.256695	0.128348	−	0.991729i	$-0.459033\pi$
$89$	215.527	0.256695	0.128348	+	0.991729i	$0.459033\pi$
$90$	− 580.310i	− 0.679667i
$91$	− 36.8362i	− 0.0424339i
$92$	− 494.994i	− 0.560943i
$93$	390.102	0.434965
$94$	−458.441	−0.503027
$95$	843.923i	0.911418i
$96$	493.633i	0.524805i
$97$	− 705.690i	− 0.738680i	−0.929294	−	0.369340i	$-0.879584\pi$
$97$	− 705.690i	− 0.738680i	0.929294	−	0.369340i	$-0.120416\pi$
$98$	1035.94	1.06782
$99$	− 1175.12i	− 1.19297i
$100$	208.037	0.208037
$101$	−546.988	−0.538884	−0.269442	−	0.963017i	$-0.586839\pi$
$101$	−546.988	−0.538884	−0.269442	+	0.963017i	$0.586839\pi$
$102$	0	0
$103$	1550.96	1.48369	0.741846	−	0.670570i	$-0.233950\pi$
$103$	1550.96	1.48369	0.741846	+	0.670570i	$0.233950\pi$
$104$	70.5614	0.0665299
$105$	− 168.877i	− 0.156959i
$106$	2499.60	2.29041
$107$	245.779i	0.222059i	0.993817	+	0.111029i	$0.0354148\pi$
$107$	245.779i	0.222059i	−0.993817	+	0.111029i	$0.964585\pi$
$108$	− 552.305i	− 0.492089i
$109$	1993.39i	1.75167i	0.482612	+	0.875834i	$0.339688\pi$
$109$	1993.39i	1.75167i	−0.482612	+	0.875834i	$0.660312\pi$
$110$	−1885.61	−1.63442
$111$	314.827	0.269208
$112$	− 547.979i	− 0.462314i
$113$	− 1082.75i	− 0.901387i	−0.892679	−	0.450693i	$-0.851177\pi$
$113$	− 1082.75i	− 0.901387i	0.892679	−	0.450693i	$-0.148823\pi$
$114$	957.042i	0.786273i
$115$	−1016.02	−0.823865
$116$	− 838.440i	− 0.671096i
$117$	−102.191	−0.0807484
$118$	2961.51	2.31042
$119$	0	0
$120$	323.491	0.246088
$121$	−2487.35	−1.86879
$122$	17.4708i	0.0129651i
$123$	470.391	0.344827
$124$	586.516i	0.424764i
$125$	− 1516.93i	− 1.08543i
$126$	456.231i	0.322574i
$127$	−1016.07	−0.709932	−0.354966	−	0.934879i	$-0.615508\pi$
$127$	−1016.07	−0.709932	−0.354966	+	0.934879i	$0.615508\pi$
$128$	1495.92	1.03298
$129$	468.695i	0.319894i
$130$	163.977i	0.110629i
$131$	1108.85i	0.739550i	0.929121	+	0.369775i	$0.120565\pi$
$131$	1108.85i	0.739550i	−0.929121	+	0.369775i	$0.879435\pi$
$132$	−741.647	−0.489031
$133$	− 663.480i	− 0.432564i
$134$	−1099.15	−0.708598
$135$	−1133.66	−0.722738
$136$	0	0
$137$	−1975.27	−1.23182	−0.615909	−	0.787818i	$-0.711211\pi$
$137$	−1975.27	−1.23182	−0.615909	+	0.787818i	$0.711211\pi$
$138$	−1152.21	−0.710743
$139$	1038.50i	0.633702i	0.948475	+	0.316851i	$0.102626\pi$
$139$	1038.50i	0.633702i	−0.948475	+	0.316851i	$0.897374\pi$
$140$	253.905	0.153278
$141$	370.110i	0.221056i
$142$	− 414.603i	− 0.245019i
$143$	332.052i	0.194179i
$144$	−1520.20	−0.879747
$145$	−1720.97	−0.985650
$146$	2276.73i	1.29057i
$147$	− 836.342i	− 0.469254i
$148$	473.340i	0.262894i
$149$	119.562	0.0657377	0.0328689	−	0.999460i	$-0.489536\pi$
$149$	119.562	0.0657377	0.0328689	+	0.999460i	$0.489536\pi$
$150$	− 484.251i	− 0.263593i
$151$	1567.85	0.844966	0.422483	−	0.906371i	$-0.361159\pi$
$151$	1567.85	0.844966	0.422483	+	0.906371i	$0.361159\pi$
$152$	1270.92	0.678194
$153$	0	0
$154$	1482.44	0.775705
$155$	1203.88	0.623857
$156$	64.4951i	0.0331009i
$157$	2121.62	1.07850	0.539248	−	0.842147i	$-0.318709\pi$
$157$	2121.62	1.07850	0.539248	+	0.842147i	$0.318709\pi$
$158$	− 729.358i	− 0.367245i
$159$	− 2017.99i	− 1.00652i
$160$	1523.38i	0.752711i
$161$	798.782	0.391011
$162$	511.359	0.248001
$163$	443.287i	0.213012i	0.994312	+	0.106506i	$0.0339663\pi$
$163$	443.287i	0.213012i	−0.994312	+	0.106506i	$0.966034\pi$
$164$	707.229i	0.336740i
$165$	1522.30i	0.718248i
$166$	2598.29	1.21486
$167$	− 2352.44i	− 1.09005i	−0.838421	−	0.545023i	$-0.816521\pi$
$167$	− 2352.44i	− 1.09005i	0.838421	−	0.545023i	$-0.183479\pi$
$168$	−254.324	−0.116795
$169$	−2168.12	−0.986857
$170$	0	0
$171$	−1840.63	−0.823135
$172$	−704.680	−0.312391
$173$	− 1900.27i	− 0.835116i	−0.908650	−	0.417558i	$-0.862886\pi$
$173$	− 1900.27i	− 0.835116i	0.908650	−	0.417558i	$-0.137114\pi$
$174$	−1951.65	−0.850313
$175$	335.713i	0.145014i
$176$	4939.63i	2.11556i
$177$	− 2390.89i	− 1.01531i
$178$	754.283	0.317617
$179$	−99.7302	−0.0416435	−0.0208217	−	0.999783i	$-0.506628\pi$
$179$	−99.7302	−0.0416435	−0.0208217	+	0.999783i	$0.506628\pi$
$180$	− 704.382i	− 0.291675i
$181$	3878.82i	1.59287i	0.604721	+	0.796437i	$0.293285\pi$
$181$	3878.82i	1.59287i	−0.604721	+	0.796437i	$0.706715\pi$
$182$	− 128.916i	− 0.0525049i
$183$	14.1046	0.00569750
$184$	1530.10i	0.613046i
$185$	971.575	0.386117
$186$	1365.24	0.538197
$187$	0	0
$188$	−556.457	−0.215871
$189$	891.265	0.343016
$190$	2953.48i	1.12773i
$191$	−2326.90	−0.881511	−0.440756	−	0.897627i	$-0.645289\pi$
$191$	−2326.90	−0.881511	−0.440756	+	0.897627i	$0.645289\pi$
$192$	− 79.2901i	− 0.0298035i
$193$	1396.48i	0.520835i	0.965496	+	0.260418i	$0.0838602\pi$
$193$	1396.48i	0.520835i	−0.965496	+	0.260418i	$0.916140\pi$
$194$	− 2469.71i	− 0.913994i
$195$	132.382	0.0486158
$196$	1257.43	0.458248
$197$	− 2023.83i	− 0.731939i	−0.930627	−	0.365969i	$-0.880738\pi$
$197$	− 2023.83i	− 0.731939i	0.930627	−	0.365969i	$-0.119262\pi$
$198$	− 4112.59i	− 1.47611i
$199$	− 4143.34i	− 1.47595i	−0.674830	−	0.737973i	$-0.735783\pi$
$199$	− 4143.34i	− 1.47595i	0.674830	−	0.737973i	$-0.264217\pi$
$200$	−643.072	−0.227360
$201$	887.369i	0.311394i
$202$	−1914.30	−0.666780
$203$	1353.01	0.467795
$204$	0	0
$205$	1451.65	0.494575
$206$	5427.90	1.83582
$207$	− 2215.98i	− 0.744063i
$208$	429.560	0.143195
$209$	5980.78i	1.97942i
$210$	− 591.019i	− 0.194211i
$211$	− 2350.55i	− 0.766912i	−0.923559	−	0.383456i	$-0.874734\pi$
$211$	− 2350.55i	− 0.766912i	0.923559	−	0.383456i	$-0.125266\pi$
$212$	3034.03	0.982914
$213$	−334.718	−0.107674
$214$	860.153i	0.274761i
$215$	1446.42i	0.458814i
$216$	1707.25i	0.537796i
$217$	−946.471	−0.296086
$218$	6976.27i	2.16740i
$219$	1838.05	0.567143
$220$	−2288.77	−0.701402
$221$	0	0
$222$	1101.80	0.333100
$223$	−412.388	−0.123837	−0.0619183	−	0.998081i	$-0.519722\pi$
$223$	−412.388	−0.123837	−0.0619183	+	0.998081i	$0.519722\pi$
$224$	− 1197.66i	− 0.357241i
$225$	931.333	0.275951
$226$	− 3789.31i	− 1.11532i
$227$	1915.89i	0.560186i	0.959973	+	0.280093i	$0.0903654\pi$
$227$	1915.89i	0.560186i	−0.959973	+	0.280093i	$0.909635\pi$
$228$	1161.66i	0.337425i
$229$	4863.54	1.40346	0.701729	−	0.712444i	$-0.252412\pi$
$229$	4863.54	1.40346	0.701729	+	0.712444i	$0.252412\pi$
$230$	−3555.78	−1.01940
$231$	− 1196.81i	− 0.340884i
$232$	2591.74i	0.733431i
$233$	− 555.672i	− 0.156237i	−0.996944	−	0.0781186i	$-0.975109\pi$
$233$	− 555.672i	− 0.156237i	0.996944	−	0.0781186i	$-0.0248913\pi$
$234$	−357.639	−0.0999127
$235$	1142.18i	0.317053i
$236$	3594.69	0.991502
$237$	−588.828	−0.161386
$238$	0	0
$239$	−3205.56	−0.867575	−0.433787	−	0.901015i	$-0.642823\pi$
$239$	−3205.56	−0.867575	−0.433787	+	0.901015i	$0.642823\pi$
$240$	1969.33	0.529665
$241$	− 893.396i	− 0.238791i	−0.992847	−	0.119396i	$-0.961904\pi$
$241$	− 893.396i	− 0.238791i	0.992847	−	0.119396i	$-0.0380957\pi$
$242$	−8705.02	−2.31231
$243$	− 3923.28i	− 1.03571i
$244$	21.2062i	0.00556388i
$245$	− 2581.00i	− 0.673036i
$246$	1646.23	0.426666
$247$	520.101	0.133981
$248$	− 1813.01i	− 0.464218i
$249$	− 2097.66i	− 0.533870i
$250$	− 5308.81i	− 1.34304i
$251$	−2431.39	−0.611427	−0.305713	−	0.952124i	$-0.598895\pi$
$251$	−2431.39	−0.611427	−0.305713	+	0.952124i	$0.598895\pi$
$252$	553.775i	0.138431i
$253$	−7200.43	−1.78928
$254$	−3555.94	−0.878422
$255$	0	0
$256$	5010.77	1.22333
$257$	3215.44	0.780442	0.390221	−	0.920721i	$-0.372399\pi$
$257$	3215.44	0.780442	0.390221	+	0.920721i	$0.372399\pi$
$258$	1640.30i	0.395816i
$259$	−763.838	−0.183253
$260$	199.035i	0.0474756i
$261$	− 3753.50i	− 0.890177i
$262$	3880.67i	0.915070i
$263$	−2659.16	−0.623464	−0.311732	−	0.950170i	$-0.600909\pi$
$263$	−2659.16	−0.623464	−0.311732	+	0.950170i	$0.600909\pi$
$264$	2292.54	0.534455
$265$	− 6227.62i	− 1.44362i
$266$	− 2321.99i	− 0.535226i
$267$	− 608.950i	− 0.139577i
$268$	−1334.15	−0.304091
$269$	− 5712.40i	− 1.29476i	−0.762166	−	0.647381i	$-0.775864\pi$
$269$	− 5712.40i	− 1.29476i	0.762166	−	0.647381i	$-0.224136\pi$
$270$	−3967.47	−0.894268
$271$	−250.885	−0.0562369	−0.0281185	−	0.999605i	$-0.508952\pi$
$271$	−250.885	−0.0562369	−0.0281185	+	0.999605i	$0.508952\pi$
$272$	0	0
$273$	−104.077	−0.0230733
$274$	−6912.88	−1.52417
$275$	− 3026.20i	− 0.663589i
$276$	−1398.55	−0.305011
$277$	− 3688.27i	− 0.800024i	−0.916510	−	0.400012i	$-0.869006\pi$
$277$	− 3688.27i	− 0.800024i	0.916510	−	0.400012i	$-0.130994\pi$
$278$	3634.46i	0.784101i
$279$	2625.70i	0.563428i
$280$	−784.857	−0.167515
$281$	−3532.00	−0.749827	−0.374914	−	0.927060i	$-0.622328\pi$
$281$	−3532.00	−0.749827	−0.374914	+	0.927060i	$0.622328\pi$
$282$	1295.28i	0.273520i
$283$	− 788.220i	− 0.165565i	−0.996568	−	0.0827824i	$-0.973619\pi$
$283$	− 788.220i	− 0.165565i	0.996568	−	0.0827824i	$-0.0263806\pi$
$284$	− 503.246i	− 0.105148i
$285$	2384.42	0.495581
$286$	1162.08i	0.240264i
$287$	−1141.27	−0.234728
$288$	−3322.54	−0.679801
$289$	0	0
$290$	−6022.91	−1.21958
$291$	−1993.85	−0.401656
$292$	2763.50i	0.553841i
$293$	−1413.82	−0.281899	−0.140949	−	0.990017i	$-0.545015\pi$
$293$	−1413.82	−0.281899	−0.140949	+	0.990017i	$0.545015\pi$
$294$	− 2926.95i	− 0.580624i
$295$	− 7378.44i	− 1.45623i
$296$	− 1463.16i	− 0.287313i
$297$	−8034.09	−1.56965
$298$	418.433	0.0813395
$299$	626.163i	0.121110i
$300$	− 587.786i	− 0.113119i
$301$	− 1137.15i	− 0.217756i
$302$	5487.02	1.04551
$303$	1545.46i	0.293017i
$304$	7737.06	1.45971
$305$	43.5276	0.00817175
$306$	0	0
$307$	4499.58	0.836498	0.418249	−	0.908333i	$-0.362644\pi$
$307$	4499.58	0.836498	0.418249	+	0.908333i	$0.362644\pi$
$308$	1799.39	0.332890
$309$	− 4382.06i	− 0.806754i
$310$	4213.22	0.771919
$311$	− 4716.79i	− 0.860014i	−0.902825	−	0.430007i	$-0.858511\pi$
$311$	− 4716.79i	− 0.860014i	0.902825	−	0.430007i	$-0.141489\pi$
$312$	− 199.364i	− 0.0361755i
$313$	6171.31i	1.11445i	0.830361	+	0.557225i	$0.188134\pi$
$313$	6171.31i	1.11445i	−0.830361	+	0.557225i	$0.811866\pi$
$314$	7425.05	1.33446
$315$	1136.67	0.203315
$316$	− 885.298i	− 0.157601i
$317$	1186.87i	0.210287i	0.994457	+	0.105144i	$0.0335302\pi$
$317$	1186.87i	0.210287i	−0.994457	+	0.105144i	$0.966470\pi$
$318$	− 7062.37i	− 1.24540i
$319$	−12196.3	−2.14064
$320$	− 244.694i	− 0.0427462i
$321$	694.421	0.120744
$322$	2795.50	0.483811
$323$	0	0
$324$	620.690	0.106428
$325$	−263.164	−0.0449161
$326$	1551.37i	0.263567i
$327$	5632.10	0.952465
$328$	− 2186.15i	− 0.368018i
$329$	− 897.965i	− 0.150475i
$330$	5327.60i	0.888712i
$331$	−3070.09	−0.509811	−0.254905	−	0.966966i	$-0.582044\pi$
$331$	−3070.09	−0.509811	−0.254905	+	0.966966i	$0.582044\pi$
$332$	3153.81	0.521349
$333$	2119.04i	0.348716i
$334$	− 8232.87i	− 1.34875i
$335$	2738.47i	0.446623i
$336$	−1548.26	−0.251382
$337$	4437.46i	0.717281i	0.933476	+	0.358640i	$0.116760\pi$
$337$	4437.46i	0.717281i	−0.933476	+	0.358640i	$0.883240\pi$
$338$	−7587.80	−1.22107
$339$	−3059.20	−0.490127
$340$	0	0
$341$	8531.74	1.35490
$342$	−6441.65	−1.01849
$343$	4380.41i	0.689563i
$344$	2178.27	0.341408
$345$	2870.66i	0.447975i
$346$	− 6650.40i	− 1.03332i
$347$	− 8714.21i	− 1.34814i	−0.738669	−	0.674068i	$-0.764545\pi$
$347$	− 8714.21i	− 1.34814i	0.738669	−	0.674068i	$-0.235455\pi$
$348$	−2368.92	−0.364907
$349$	100.929	0.0154803	0.00774014	−	0.999970i	$-0.497536\pi$
$349$	100.929	0.0154803	0.00774014	+	0.999970i	$0.497536\pi$
$350$	1174.90i	0.179431i
$351$	698.660i	0.106244i
$352$	10796.0i	1.63474i
$353$	8688.88	1.31009	0.655046	−	0.755589i	$-0.272649\pi$
$353$	8688.88	1.31009	0.655046	+	0.755589i	$0.272649\pi$
$354$	− 8367.43i	− 1.25628i
$355$	−1032.96	−0.154433
$356$	915.551	0.136304
$357$	0	0
$358$	−349.026	−0.0515269
$359$	−2411.52	−0.354526	−0.177263	−	0.984163i	$-0.556724\pi$
$359$	−2411.52	−0.354526	−0.177263	+	0.984163i	$0.556724\pi$
$360$	2177.35i	0.318768i
$361$	2508.85	0.365775
$362$	13574.7i	1.97092i
$363$	7027.76i	1.01615i
$364$	− 156.479i	− 0.0225322i
$365$	5672.34	0.813435
$366$	49.3620	0.00704971
$367$	− 2274.20i	− 0.323467i	−0.986834	−	0.161734i	$-0.948291\pi$
$367$	− 2274.20i	− 0.323467i	0.986834	−	0.161734i	$-0.0517085\pi$
$368$	9314.86i	1.31948i
$369$	3166.10i	0.446669i
$370$	3400.23	0.477755
$371$	4896.07i	0.685151i
$372$	1657.14	0.230964
$373$	9493.93	1.31790	0.658951	−	0.752186i	$-0.271001\pi$
$373$	9493.93	1.31790	0.658951	+	0.752186i	$0.271001\pi$
$374$	0	0
$375$	−4285.93	−0.590198
$376$	1720.09	0.235922
$377$	1060.62i	0.144893i
$378$	3119.17	0.424425
$379$	5337.70i	0.723428i	0.932289	+	0.361714i	$0.117808\pi$
$379$	5337.70i	0.723428i	−0.932289	+	0.361714i	$0.882192\pi$
$380$	3584.95i	0.483958i
$381$	2870.79i	0.386024i
$382$	−8143.47	−1.09072
$383$	779.426	0.103986	0.0519932	−	0.998647i	$-0.483443\pi$
$383$	779.426	0.103986	0.0519932	+	0.998647i	$0.483443\pi$
$384$	− 4226.56i	− 0.561681i
$385$	− 3693.42i	− 0.488920i
$386$	4887.29i	0.644447i
$387$	−3154.69	−0.414372
$388$	− 2997.74i	− 0.392235i
$389$	10826.1	1.41106	0.705532	−	0.708679i	$-0.250708\pi$
$389$	10826.1	1.41106	0.705532	+	0.708679i	$0.250708\pi$
$390$	463.299	0.0601540
$391$	0	0
$392$	−3886.91	−0.500813
$393$	3132.95	0.402128
$394$	− 7082.81i	− 0.905652i
$395$	−1817.16	−0.231471
$396$	− 4991.88i	− 0.633463i
$397$	6106.87i	0.772027i	0.922493	+	0.386014i	$0.126148\pi$
$397$	6106.87i	0.772027i	−0.922493	+	0.386014i	$0.873852\pi$
$398$	− 14500.5i	− 1.82624i
$399$	−1874.59	−0.235206
$400$	−3914.86	−0.489357
$401$	11451.6i	1.42609i	0.701116	+	0.713047i	$0.252686\pi$
$401$	11451.6i	1.42609i	−0.701116	+	0.713047i	$0.747314\pi$
$402$	3105.53i	0.385298i
$403$	− 741.937i	− 0.0917085i
$404$	−2323.58	−0.286145
$405$	− 1274.02i	− 0.156313i
$406$	4735.12	0.578818
$407$	6885.44	0.838571
$408$	0	0
$409$	−7597.11	−0.918466	−0.459233	−	0.888316i	$-0.651876\pi$
$409$	−7597.11	−0.918466	−0.459233	+	0.888316i	$0.651876\pi$
$410$	5080.36	0.611954
$411$	5580.93i	0.669798i
$412$	6588.40	0.787833
$413$	5800.82i	0.691137i
$414$	− 7755.28i	− 0.920655i
$415$	− 6473.49i	− 0.765713i
$416$	938.843	0.110650
$417$	2934.18	0.344574
$418$	20931.0i	2.44921i
$419$	6887.55i	0.803052i	0.915848	+	0.401526i	$0.131520\pi$
$419$	6887.55i	0.803052i	−0.915848	+	0.401526i	$0.868480\pi$
$420$	− 717.381i	− 0.0833444i
$421$	13586.7	1.57286	0.786431	−	0.617678i	$-0.211927\pi$
$421$	13586.7	1.57286	0.786431	+	0.617678i	$0.211927\pi$
$422$	− 8226.24i	− 0.948926i
$423$	−2491.13	−0.286343
$424$	−9378.62	−1.07421
$425$	0	0
$426$	−1171.42	−0.133228
$427$	−34.2208	−0.00387836
$428$	1044.06i	0.117912i
$429$	938.177	0.105584
$430$	5062.05i	0.567706i
$431$	16814.5i	1.87917i	0.342311	+	0.939587i	$0.388790\pi$
$431$	16814.5i	1.87917i	−0.342311	+	0.939587i	$0.611210\pi$
$432$	10393.3i	1.15752i
$433$	248.824	0.0276159	0.0138080	−	0.999905i	$-0.495605\pi$
$433$	248.824	0.0276159	0.0138080	+	0.999905i	$0.495605\pi$
$434$	−3312.37	−0.366357
$435$	4862.43i	0.535944i
$436$	8467.82i	0.930127i
$437$	11278.2i	1.23458i
$438$	6432.66	0.701745
$439$	− 9870.05i	− 1.07306i	−0.843882	−	0.536528i	$-0.819735\pi$
$439$	− 9870.05i	− 1.07306i	0.843882	−	0.536528i	$-0.180265\pi$
$440$	7074.91	0.766552
$441$	5629.24	0.607844
$442$	0	0
$443$	−10000.3	−1.07253	−0.536264	−	0.844051i	$-0.680165\pi$
$443$	−10000.3	−1.07253	−0.536264	+	0.844051i	$0.680165\pi$
$444$	1337.37	0.142948
$445$	− 1879.25i	− 0.200191i
$446$	−1443.24	−0.153227
$447$	− 337.810i	− 0.0357447i
$448$	192.375i	0.0202876i
$449$	8580.38i	0.901856i	0.892560	+	0.450928i	$0.148907\pi$
$449$	8580.38i	0.901856i	−0.892560	+	0.450928i	$0.851093\pi$
$450$	3259.39	0.341443
$451$	10287.7	1.07412
$452$	− 4599.48i	− 0.478632i
$453$	− 4429.80i	− 0.459448i
$454$	6705.07i	0.693137i
$455$	−321.187	−0.0330934
$456$	− 3590.86i	− 0.368766i
$457$	−8345.86	−0.854273	−0.427137	−	0.904187i	$-0.640478\pi$
$457$	−8345.86	−0.854273	−0.427137	+	0.904187i	$0.640478\pi$
$458$	17021.0	1.73655
$459$	0	0
$460$	−4316.02	−0.437468
$461$	8600.87	0.868942	0.434471	−	0.900686i	$-0.356935\pi$
$461$	8600.87	0.868942	0.434471	+	0.900686i	$0.356935\pi$
$462$	− 4188.48i	− 0.421788i
$463$	−15888.5	−1.59482	−0.797408	−	0.603440i	$-0.793796\pi$
$463$	−15888.5	−1.59482	−0.797408	+	0.603440i	$0.793796\pi$
$464$	15777.8i	1.57860i
$465$	− 3401.43i	− 0.339221i
$466$	− 1944.69i	− 0.193318i
$467$	5941.71	0.588757	0.294378	−	0.955689i	$-0.404887\pi$
$467$	5941.71	0.588757	0.294378	+	0.955689i	$0.404887\pi$
$468$	−434.103	−0.0428770
$469$	− 2152.95i	− 0.211970i
$470$	3997.29i	0.392301i
$471$	− 5994.41i	− 0.586429i
$472$	−11111.7	−1.08360
$473$	10250.6i	0.996456i
$474$	−2060.72	−0.199688
$475$	−4740.02	−0.457867
$476$	0	0
$477$	13582.7	1.30379
$478$	−11218.5	−1.07348
$479$	14915.1i	1.42273i	0.702822	+	0.711366i	$0.251923\pi$
$479$	14915.1i	1.42273i	−0.702822	+	0.711366i	$0.748077\pi$
$480$	4304.15	0.409285
$481$	− 598.771i	− 0.0567601i
$482$	− 3126.63i	− 0.295465i
$483$	− 2256.87i	− 0.212611i
$484$	−10566.2	−0.992316
$485$	−6153.15	−0.576082
$486$	− 13730.3i	− 1.28152i
$487$	− 8222.85i	− 0.765119i	−0.923931	−	0.382559i	$-0.875043\pi$
$487$	− 8222.85i	− 0.765119i	0.923931	−	0.382559i	$-0.124957\pi$
$488$	− 65.5514i	− 0.00608068i
$489$	1252.46	0.115825
$490$	− 9032.74i	− 0.832771i
$491$	2635.62	0.242248	0.121124	−	0.992637i	$-0.461350\pi$
$491$	2635.62	0.242248	0.121124	+	0.992637i	$0.461350\pi$
$492$	1998.20	0.183101
$493$	0	0
$494$	1820.20	0.165779
$495$	−10246.3	−0.930376
$496$	− 11037.1i	− 0.999156i
$497$	812.097	0.0732949
$498$	− 7341.19i	− 0.660575i
$499$	− 12763.9i	− 1.14507i	−0.819879	−	0.572537i	$-0.805959\pi$
$499$	− 12763.9i	− 1.14507i	0.819879	−	0.572537i	$-0.194041\pi$
$500$	− 6443.86i	− 0.576356i
$501$	−6646.58	−0.592709
$502$	−8509.16	−0.756539
$503$	6403.16i	0.567600i	0.958884	+	0.283800i	$0.0915951\pi$
$503$	6403.16i	0.567600i	−0.958884	+	0.283800i	$0.908405\pi$
$504$	− 1711.80i	− 0.151289i
$505$	4769.36i	0.420265i
$506$	−25199.4	−2.21393
$507$	6125.81i	0.536601i
$508$	−4316.21	−0.376970
$509$	−7892.36	−0.687274	−0.343637	−	0.939103i	$-0.611659\pi$
$509$	−7892.36	−0.687274	−0.343637	+	0.939103i	$0.611659\pi$
$510$	0	0
$511$	−4459.51	−0.386061
$512$	5568.89	0.480688
$513$	12584.0i	1.08304i
$514$	11253.1	0.965667
$515$	− 13523.3i	− 1.15710i
$516$	1991.00i	0.169862i
$517$	8094.49i	0.688579i
$518$	−2673.21	−0.226745
$519$	−5369.02	−0.454092
$520$	− 615.248i	− 0.0518854i
$521$	8506.79i	0.715335i	0.933849	+	0.357667i	$0.116428\pi$
$521$	8506.79i	0.715335i	−0.933849	+	0.357667i	$0.883572\pi$
$522$	− 13136.2i	− 1.10145i
$523$	18757.8	1.56830	0.784150	−	0.620571i	$-0.213099\pi$
$523$	18757.8	1.56830	0.784150	+	0.620571i	$0.213099\pi$
$524$	4710.37i	0.392697i
$525$	948.521	0.0788511
$526$	−9306.30	−0.771433
$527$	0	0
$528$	13956.4	1.15033
$529$	−1411.14	−0.115981
$530$	− 21794.9i	− 1.78624i
$531$	16092.6	1.31518
$532$	− 2818.44i	− 0.229689i
$533$	− 894.638i	− 0.0727037i
$534$	− 2131.15i	− 0.172704i
$535$	2143.02	0.173179
$536$	4124.06	0.332336
$537$	281.777i	0.0226435i
$538$	− 19991.7i	− 1.60205i
$539$	− 18291.2i	− 1.46170i
$540$	−4815.73	−0.383770
$541$	13399.5i	1.06486i	0.846475	+	0.532429i	$0.178721\pi$
$541$	13399.5i	1.06486i	−0.846475	+	0.532429i	$0.821279\pi$
$542$	−878.026	−0.0695838
$543$	10959.2	0.866121
$544$	0	0
$545$	17381.0	1.36609
$546$	−364.239	−0.0285494
$547$	7133.73i	0.557616i	0.960347	+	0.278808i	$0.0899394\pi$
$547$	7133.73i	0.557616i	−0.960347	+	0.278808i	$0.910061\pi$
$548$	−8390.88	−0.654089
$549$	94.9352i	0.00738021i
$550$	− 10590.8i	− 0.821080i
$551$	19103.4i	1.47701i
$552$	4323.13	0.333342
$553$	1428.62	0.109857
$554$	− 12907.9i	− 0.989897i
$555$	− 2745.08i	− 0.209950i
$556$	4411.52i	0.336493i
$557$	5175.60	0.393712	0.196856	−	0.980432i	$-0.436927\pi$
$557$	5175.60	0.393712	0.196856	+	0.980432i	$0.436927\pi$
$558$	9189.18i	0.697149i
$559$	891.413	0.0674468
$560$	−4778.01	−0.360550
$561$	0	0
$562$	−12361.0	−0.927787
$563$	−5569.32	−0.416907	−0.208454	−	0.978032i	$-0.566843\pi$
$563$	−5569.32	−0.416907	−0.208454	+	0.978032i	$0.566843\pi$
$564$	1572.21i	0.117379i
$565$	−9440.87	−0.702974
$566$	− 2758.54i	− 0.204859i
$567$	1001.62i	0.0741870i
$568$	1555.61i	0.114915i
$569$	15330.1	1.12948	0.564738	−	0.825270i	$-0.308977\pi$
$569$	15330.1	1.12948	0.564738	+	0.825270i	$0.308977\pi$
$570$	8344.76	0.613199
$571$	− 22285.0i	− 1.63327i	−0.577153	−	0.816636i	$-0.695836\pi$
$571$	− 22285.0i	− 1.63327i	0.577153	−	0.816636i	$-0.304164\pi$
$572$	1410.54i	0.103108i
$573$	6574.41i	0.479319i
$574$	−3994.11	−0.290437
$575$	− 5706.63i	− 0.413883i
$576$	533.686	0.0386057
$577$	−19321.1	−1.39401	−0.697007	−	0.717064i	$-0.745485\pi$
$577$	−19321.1	−1.39401	−0.697007	+	0.717064i	$0.745485\pi$
$578$	0	0
$579$	3945.62	0.283203
$580$	−7310.63	−0.523375
$581$	5089.36i	0.363412i
$582$	−6977.91	−0.496982
$583$	− 44134.4i	− 3.13527i
$584$	− 8542.38i	− 0.605285i
$585$	891.037i	0.0629741i
$586$	−4947.96	−0.348803
$587$	23571.2	1.65739	0.828696	−	0.559699i	$-0.189083\pi$
$587$	23571.2	1.65739	0.828696	+	0.559699i	$0.189083\pi$
$588$	− 3552.74i	− 0.249171i
$589$	− 13363.5i	− 0.934860i
$590$	− 25822.4i	− 1.80185i
$591$	−5718.12	−0.397990
$592$	− 8907.37i	− 0.618396i
$593$	−27338.0	−1.89315	−0.946576	−	0.322481i	$-0.895483\pi$
$593$	−27338.0	−1.89315	−0.946576	+	0.322481i	$0.895483\pi$
$594$	−28117.0	−1.94218
$595$	0	0
$596$	507.895	0.0349064
$597$	−11706.6	−0.802542
$598$	2191.39i	0.149854i
$599$	−3930.83	−0.268129	−0.134064	−	0.990973i	$-0.542803\pi$
$599$	−3930.83	−0.268129	−0.134064	+	0.990973i	$0.542803\pi$
$600$	1816.93i	0.123626i
$601$	22459.9i	1.52439i	0.647347	+	0.762196i	$0.275879\pi$
$601$	22459.9i	1.52439i	−0.647347	+	0.762196i	$0.724121\pi$
$602$	− 3979.71i	− 0.269437i
$603$	−5972.70	−0.403362
$604$	6660.16	0.448673
$605$	21688.1i	1.45743i
$606$	5408.64i	0.362560i
$607$	− 2227.26i	− 0.148932i	−0.997224	−	0.0744660i	$-0.976275\pi$
$607$	− 2227.26i	− 0.148932i	0.997224	−	0.0744660i	$-0.0237252\pi$
$608$	16910.1	1.12795
$609$	− 3822.77i	− 0.254362i
$610$	152.334	0.0101112
$611$	703.913	0.0466076
$612$	0	0
$613$	721.642	0.0475479	0.0237739	−	0.999717i	$-0.492432\pi$
$613$	721.642	0.0475479	0.0237739	+	0.999717i	$0.492432\pi$
$614$	15747.2	1.03503
$615$	− 4101.49i	− 0.268924i
$616$	−5562.19	−0.363810
$617$	6831.58i	0.445752i	0.974847	+	0.222876i	$0.0715445\pi$
$617$	6831.58i	0.445752i	−0.974847	+	0.222876i	$0.928455\pi$
$618$	− 15335.9i	− 0.998224i
$619$	− 16094.9i	− 1.04509i	−0.852612	−	0.522544i	$-0.824983\pi$
$619$	− 16094.9i	− 1.04509i	0.852612	−	0.522544i	$-0.175017\pi$
$620$	5114.02	0.331265
$621$	−15150.2	−0.978997
$622$	− 16507.4i	− 1.06412i
$623$	1477.44i	0.0950120i
$624$	− 1213.68i	− 0.0778620i
$625$	−7104.94	−0.454716
$626$	21597.8i	1.37895i
$627$	16898.1	1.07631
$628$	9012.55	0.572675
$629$	0	0
$630$	3978.03	0.251569
$631$	27131.0	1.71168	0.855838	−	0.517245i	$-0.173042\pi$
$631$	27131.0	1.71168	0.855838	+	0.517245i	$0.173042\pi$
$632$	2736.58i	0.172240i
$633$	−6641.23	−0.417007
$634$	4153.69i	0.260196i
$635$	8859.42i	0.553662i
$636$	− 8572.32i	− 0.534457i
$637$	−1590.64	−0.0989380
$638$	−42683.7	−2.64869
$639$	− 2252.92i	− 0.139474i
$640$	− 13043.4i	− 0.805603i
$641$	13901.7i	0.856606i	0.903635	+	0.428303i	$0.140888\pi$
$641$	13901.7i	0.856606i	−0.903635	+	0.428303i	$0.859112\pi$
$642$	2430.27	0.149401
$643$	8827.31i	0.541392i	0.962665	+	0.270696i	$0.0872539\pi$
$643$	8827.31i	0.541392i	−0.962665	+	0.270696i	$0.912746\pi$
$644$	3393.19	0.207625
$645$	4086.71	0.249479
$646$	0	0
$647$	−14695.4	−0.892946	−0.446473	−	0.894797i	$-0.647320\pi$
$647$	−14695.4	−0.892946	−0.446473	+	0.894797i	$0.647320\pi$
$648$	−1918.64	−0.116314
$649$	− 52290.1i	− 3.16266i
$650$	−920.999	−0.0555762
$651$	2674.15i	0.160996i
$652$	1883.06i	0.113108i
$653$	− 6942.30i	− 0.416039i	−0.978125	−	0.208019i	$-0.933298\pi$
$653$	− 6942.30i	− 0.416039i	0.978125	−	0.208019i	$-0.0667017\pi$
$654$	19710.7	1.17852
$655$	9668.47	0.576761
$656$	− 13308.7i	− 0.792100i
$657$	12371.6i	0.734644i
$658$	− 3142.61i	− 0.186188i
$659$	−11804.8	−0.697800	−0.348900	−	0.937160i	$-0.613445\pi$
$659$	−11804.8	−0.697800	−0.348900	+	0.937160i	$0.613445\pi$
$660$	6466.66i	0.381386i
$661$	−3863.35	−0.227333	−0.113666	−	0.993519i	$-0.536259\pi$
$661$	−3863.35	−0.227333	−0.113666	+	0.993519i	$0.536259\pi$
$662$	−10744.4	−0.630806
$663$	0	0
$664$	−9748.88	−0.569774
$665$	−5785.10	−0.337348
$666$	7416.01i	0.431479i
$667$	−22999.1	−1.33513
$668$	− 9993.08i	− 0.578808i
$669$	1165.16i	0.0673358i
$670$	9583.85i	0.552622i
$671$	308.475	0.0177475
$672$	−3383.86	−0.194249
$673$	876.547i	0.0502057i	0.999685	+	0.0251028i	$0.00799132\pi$
$673$	876.547i	0.0502057i	−0.999685	+	0.0251028i	$0.992009\pi$
$674$	15529.8i	0.887516i
$675$	− 6367.35i	− 0.363080i
$676$	−9210.10	−0.524016
$677$	20341.1i	1.15476i	0.816477	+	0.577378i	$0.195924\pi$
$677$	20341.1i	1.15476i	−0.816477	+	0.577378i	$0.804076\pi$
$678$	−10706.3	−0.606450
$679$	4837.51	0.273412
$680$	0	0
$681$	5413.15	0.304600
$682$	29858.6	1.67646
$683$	30034.8i	1.68265i	0.540531	+	0.841324i	$0.318223\pi$
$683$	30034.8i	1.68265i	−0.540531	+	0.841324i	$0.681777\pi$
$684$	−7818.90	−0.437080
$685$	17223.1i	0.960670i
$686$	15330.2i	0.853219i
$687$	− 13741.4i	− 0.763126i
$688$	13260.7	0.734827
$689$	−3838.02	−0.212216
$690$	10046.5i	0.554294i
$691$	10797.7i	0.594450i	0.954807	+	0.297225i	$0.0960612\pi$
$691$	10797.7i	0.594450i	−0.954807	+	0.297225i	$0.903939\pi$
$692$	− 8072.28i	− 0.443442i
$693$	8055.48	0.441562
$694$	− 30497.2i	− 1.66810i
$695$	9055.04	0.494212
$696$	7322.68	0.398801
$697$	0	0
$698$	353.223	0.0191543
$699$	−1569.99	−0.0849536
$700$	1426.09i	0.0770018i
$701$	−328.897	−0.0177208	−0.00886039	−	0.999961i	$-0.502820\pi$
$701$	−328.897	−0.0177208	−0.00886039	+	0.999961i	$0.502820\pi$
$702$	2445.11i	0.131460i
$703$	− 10784.8i	− 0.578603i
$704$	− 1734.12i	− 0.0928366i
$705$	3227.11	0.172397
$706$	30408.6	1.62102
$707$	− 3749.60i	− 0.199460i
$708$	− 10156.4i	− 0.539127i
$709$	− 4850.17i	− 0.256914i	−0.991715	−	0.128457i	$-0.958998\pi$
$709$	− 4850.17i	− 0.256914i	0.991715	−	0.128457i	$-0.0410024\pi$
$710$	−3615.06	−0.191085
$711$	− 3963.28i	− 0.209050i
$712$	−2830.10	−0.148964
$713$	16088.7	0.845056
$714$	0	0
$715$	2895.27	0.151436
$716$	−423.650	−0.0221125
$717$	9056.97i	0.471741i
$718$	−8439.60	−0.438667
$719$	32883.0i	1.70560i	0.522236	+	0.852801i	$0.325098\pi$
$719$	32883.0i	1.70560i	−0.522236	+	0.852801i	$0.674902\pi$
$720$	13255.1i	0.686097i
$721$	10631.8i	0.549167i
$722$	8780.24	0.452586
$723$	−2524.20	−0.129842
$724$	16477.1i	0.845808i
$725$	− 9666.10i	− 0.495159i
$726$	24595.1i	1.25731i
$727$	−16213.2	−0.827116	−0.413558	−	0.910478i	$-0.635714\pi$
$727$	−16213.2	−0.827116	−0.413558	+	0.910478i	$0.635714\pi$
$728$	483.699i	0.0246251i
$729$	−7139.71	−0.362735
$730$	19851.5	1.00649
$731$	0	0
$732$	59.9158	0.00302534
$733$	24861.1	1.25275	0.626374	−	0.779523i	$-0.284538\pi$
$733$	24861.1	1.25275	0.626374	+	0.779523i	$0.284538\pi$
$734$	− 7959.05i	− 0.400237i
$735$	−7292.34	−0.365962
$736$	20358.5i	1.01960i
$737$	19407.2i	0.969979i
$738$	11080.4i	0.552678i
$739$	−1024.01	−0.0509727	−0.0254863	−	0.999675i	$-0.508113\pi$
$739$	−1024.01	−0.0509727	−0.0254863	+	0.999675i	$0.508113\pi$
$740$	4127.21	0.205026
$741$	− 1469.49i	− 0.0728516i
$742$	17134.8i	0.847761i
$743$	− 6870.67i	− 0.339247i	−0.985509	−	0.169623i	$-0.945745\pi$
$743$	− 6870.67i	− 0.339247i	0.985509	−	0.169623i	$-0.0542551\pi$
$744$	−5122.45	−0.252417
$745$	− 1042.50i	− 0.0512676i
$746$	33226.0	1.63068
$747$	14118.9	0.691544
$748$	0	0
$749$	−1684.81	−0.0821919
$750$	−14999.5	−0.730272
$751$	12169.0i	0.591284i	0.955299	+	0.295642i	$0.0955335\pi$
$751$	12169.0i	0.591284i	−0.955299	+	0.295642i	$0.904466\pi$
$752$	10471.5	0.507786
$753$	6869.64i	0.332462i
$754$	3711.85i	0.179281i
$755$	− 13670.6i	− 0.658972i
$756$	3786.05	0.182140
$757$	−28243.4	−1.35604	−0.678021	−	0.735043i	$-0.737162\pi$
$757$	−28243.4	−1.35604	−0.678021	+	0.735043i	$0.737162\pi$
$758$	18680.4i	0.895121i
$759$	20344.0i	0.972914i
$760$	− 11081.6i	− 0.528910i
$761$	30505.2	1.45310	0.726552	−	0.687112i	$-0.241122\pi$
$761$	30505.2	1.45310	0.726552	+	0.687112i	$0.241122\pi$
$762$	10046.9i	0.477640i
$763$	−13664.7	−0.648355
$764$	−9884.58	−0.468078
$765$	0	0
$766$	2727.76	0.128666
$767$	−4547.25	−0.214070
$768$	− 14157.4i	− 0.665184i
$769$	20404.5	0.956834	0.478417	−	0.878133i	$-0.341211\pi$
$769$	20404.5	0.956834	0.478417	+	0.878133i	$0.341211\pi$
$770$	− 12925.9i	− 0.604957i
$771$	− 9084.89i	− 0.424363i
$772$	5932.21i	0.276561i
$773$	−30606.6	−1.42412	−0.712059	−	0.702119i	$-0.752237\pi$
$773$	−30606.6	−1.42412	−0.712059	+	0.702119i	$0.752237\pi$
$774$	−11040.5	−0.512716
$775$	6761.75i	0.313406i
$776$	9266.46i	0.428668i
$777$	2158.14i	0.0996435i
$778$	37888.1	1.74596
$779$	− 16113.9i	− 0.741129i
$780$	562.354	0.0258147
$781$	−7320.46	−0.335399
$782$	0	0
$783$	−25662.0	−1.17124
$784$	−23662.5	−1.07792
$785$	− 18499.1i	− 0.841097i
$786$	10964.4	0.497567
$787$	− 36091.5i	− 1.63472i	−0.576127	−	0.817360i	$-0.695437\pi$
$787$	− 36091.5i	− 1.63472i	0.576127	−	0.817360i	$-0.304563\pi$
$788$	− 8597.14i	− 0.388656i
$789$	7513.19i	0.339007i
$790$	−6359.51	−0.286407
$791$	7422.27	0.333635
$792$	15430.6i	0.692302i
$793$	− 26.8256i	− 0.00120127i
$794$	21372.3i	0.955255i
$795$	−17595.5	−0.784966
$796$	− 17600.7i	− 0.783720i
$797$	21357.2	0.949199	0.474599	−	0.880202i	$-0.342593\pi$
$797$	21357.2	0.949199	0.474599	+	0.880202i	$0.342593\pi$
$798$	−6560.53	−0.291028
$799$	0	0
$800$	−8556.28	−0.378138
$801$	4098.72	0.180800
$802$	40077.1i	1.76455i
$803$	40199.2	1.76662
$804$	3769.51i	0.165349i
$805$	− 6964.84i	− 0.304942i
$806$	− 2596.56i	− 0.113474i
$807$	−16139.8	−0.704024
$808$	7182.52	0.312723
$809$	− 26168.9i	− 1.13727i	−0.822591	−	0.568633i	$-0.807473\pi$
$809$	− 26168.9i	− 1.13727i	0.822591	−	0.568633i	$-0.192527\pi$
$810$	− 4458.71i	− 0.193411i
$811$	20028.2i	0.867185i	0.901109	+	0.433592i	$0.142754\pi$
$811$	20028.2i	0.867185i	−0.901109	+	0.433592i	$0.857246\pi$
$812$	5747.51	0.248397
$813$	708.850i	0.0305787i
$814$	24097.0	1.03759
$815$	3865.16	0.166124
$816$	0	0
$817$	16055.8	0.687541
$818$	−26587.7	−1.13645
$819$	− 700.520i	− 0.0298879i
$820$	6166.56	0.262617
$821$	2162.08i	0.0919087i	0.998944	+	0.0459544i	$0.0146329\pi$
$821$	2162.08i	0.0919087i	−0.998944	+	0.0459544i	$0.985367\pi$
$822$	19531.6i	0.828763i
$823$	− 39375.6i	− 1.66773i	−0.551965	−	0.833867i	$-0.686122\pi$
$823$	− 39375.6i	− 1.66773i	0.551965	−	0.833867i	$-0.313878\pi$
$824$	−20365.7	−0.861011
$825$	−8550.21	−0.360825
$826$	20301.2i	0.855167i
$827$	− 22589.8i	− 0.949849i	−0.880026	−	0.474925i	$-0.842475\pi$
$827$	− 22589.8i	− 0.949849i	0.880026	−	0.474925i	$-0.157525\pi$
$828$	− 9413.38i	− 0.395094i
$829$	−10977.3	−0.459898	−0.229949	−	0.973203i	$-0.573856\pi$
$829$	−10977.3	−0.459898	−0.229949	+	0.973203i	$0.573856\pi$
$830$	− 22655.3i	− 0.947443i
$831$	−10420.8	−0.435011
$832$	−150.802	−0.00628380
$833$	0	0
$834$	10268.8	0.426353
$835$	−20511.7	−0.850105
$836$	25406.1i	1.05106i
$837$	17951.4	0.741327
$838$	24104.4i	0.993643i
$839$	− 44593.9i	− 1.83499i	−0.397752	−	0.917493i	$-0.630210\pi$
$839$	− 44593.9i	− 1.83499i	0.397752	−	0.917493i	$-0.369790\pi$
$840$	2217.53i	0.0910858i
$841$	−14567.8	−0.597310
$842$	47549.4	1.94615
$843$	9979.30i	0.407717i
$844$	− 9985.03i	− 0.407226i
$845$	18904.6i	0.769630i
$846$	−8718.23	−0.354301
$847$	− 17050.8i	− 0.691704i
$848$	−57094.6	−2.31207
$849$	−2227.03	−0.0900254
$850$	0	0
$851$	12984.1	0.523021
$852$	−1421.87	−0.0571742
$853$	− 37075.9i	− 1.48822i	−0.668055	−	0.744112i	$-0.732873\pi$
$853$	− 37075.9i	− 1.48822i	0.668055	−	0.744112i	$-0.267127\pi$
$854$	−119.763	−0.00479883
$855$	16049.0i	0.641947i
$856$	− 3227.33i	− 0.128864i
$857$	45571.5i	1.81645i	0.418487	+	0.908223i	$0.362560\pi$
$857$	45571.5i	1.81645i	−0.418487	+	0.908223i	$0.637440\pi$
$858$	3283.34	0.130643
$859$	−68.5340	−0.00272218	−0.00136109	−	0.999999i	$-0.500433\pi$
$859$	−68.5340	−0.00272218	−0.00136109	+	0.999999i	$0.500433\pi$
$860$	6144.33i	0.243628i
$861$	3224.53i	0.127633i
$862$	58845.7i	2.32516i
$863$	−5064.23	−0.199755	−0.0998774	−	0.995000i	$-0.531845\pi$
$863$	−5064.23	−0.199755	−0.0998774	+	0.995000i	$0.531845\pi$
$864$	22715.6i	0.894445i
$865$	−16569.1	−0.651291
$866$	870.810	0.0341701
$867$	0	0
$868$	−4020.57	−0.157220
$869$	−12878.0	−0.502710
$870$	17017.1i	0.663142i
$871$	1687.69	0.0656546
$872$	− 26175.3i	− 1.01652i
$873$	− 13420.2i	− 0.520281i
$874$	39470.4i	1.52758i
$875$	10398.6	0.401755
$876$	7807.98	0.301150
$877$	− 3826.86i	− 0.147348i	−0.997282	−	0.0736738i	$-0.976528\pi$
$877$	− 3826.86i	− 0.147348i	0.997282	−	0.0736738i	$-0.0234724\pi$
$878$	− 34542.3i	− 1.32773i
$879$	3994.60i	0.153282i
$880$	43070.2	1.64988
$881$	− 41015.0i	− 1.56848i	−0.620457	−	0.784240i	$-0.713053\pi$
$881$	− 41015.0i	− 1.56848i	0.620457	−	0.784240i	$-0.286947\pi$
$882$	19700.7	0.752106
$883$	7085.32	0.270034	0.135017	−	0.990843i	$-0.456891\pi$
$883$	7085.32	0.270034	0.135017	+	0.990843i	$0.456891\pi$
$884$	0	0
$885$	−20847.0	−0.791824
$886$	−34998.2	−1.32707
$887$	− 17254.1i	− 0.653141i	−0.945173	−	0.326570i	$-0.894107\pi$
$887$	− 17254.1i	− 0.653141i	0.945173	−	0.326570i	$-0.105893\pi$
$888$	−4134.01	−0.156226
$889$	− 6965.14i	− 0.262771i
$890$	− 6576.84i	− 0.247704i
$891$	− 9028.85i	− 0.339481i
$892$	−1751.81	−0.0657566
$893$	12678.6	0.475110
$894$	− 1182.24i	− 0.0442281i
$895$	869.580i	0.0324769i
$896$	10254.5i	0.382344i
$897$	1769.16	0.0658534
$898$	30028.8i	1.11590i
$899$	27251.5	1.01100
$900$	3956.26	0.146528
$901$	0	0
$902$	36003.9	1.32905
$903$	−3212.91	−0.118404
$904$	14217.7i	0.523089i
$905$	33820.7	1.24225
$906$	− 15503.0i	− 0.568491i
$907$	− 18106.5i	− 0.662861i	−0.943480	−	0.331431i	$-0.892469\pi$
$907$	− 18106.5i	− 0.662861i	0.943480	−	0.331431i	$-0.107531\pi$
$908$	8138.63i	0.297456i
$909$	−10402.1	−0.379557
$910$	−1124.06	−0.0409476
$911$	− 19160.7i	− 0.696840i	−0.937339	−	0.348420i	$-0.886718\pi$
$911$	− 19160.7i	− 0.696840i	0.937339	−	0.348420i	$-0.113282\pi$
$912$	− 21860.2i	− 0.793712i
$913$	− 45876.8i	− 1.66298i
$914$	−29208.1	−1.05702
$915$	− 122.983i	− 0.00444337i
$916$	20660.1	0.745229
$917$	−7601.21	−0.273734
$918$	0	0
$919$	−13214.6	−0.474329	−0.237165	−	0.971469i	$-0.576218\pi$
$919$	−13214.6	−0.474329	−0.237165	+	0.971469i	$0.576218\pi$
$920$	13341.4	0.478102
$921$	− 12713.1i	− 0.454843i
$922$	30100.5	1.07517
$923$	636.601i	0.0227020i
$924$	− 5084.00i	− 0.181008i
$925$	5456.99i	0.193973i
$926$	−55605.0	−1.97332
$927$	29494.8	1.04502
$928$	34483.9i	1.21982i
$929$	− 8124.36i	− 0.286923i	−0.989656	−	0.143462i	$-0.954177\pi$
$929$	− 8124.36i	− 0.286923i	0.989656	−	0.143462i	$-0.0458233\pi$
$930$	− 11904.0i	− 0.419729i
$931$	−28650.0	−1.00856
$932$	− 2360.47i	− 0.0829612i
$933$	−13326.8	−0.467631
$934$	20794.2	0.728489
$935$	0	0
$936$	1341.88	0.0468596
$937$	11617.7	0.405053	0.202526	−	0.979277i	$-0.435085\pi$
$937$	11617.7	0.405053	0.202526	+	0.979277i	$0.435085\pi$
$938$	− 7534.68i	− 0.262277i
$939$	17436.4	0.605980
$940$	4851.93i	0.168354i
$941$	− 12810.7i	− 0.443801i	−0.975069	−	0.221901i	$-0.928774\pi$
$941$	− 12810.7i	− 0.443801i	0.975069	−	0.221901i	$-0.0712260\pi$
$942$	− 20978.7i	− 0.725608i
$943$	19399.9	0.669934
$944$	−67645.3	−2.33227
$945$	− 7771.23i	− 0.267511i
$946$	35874.1i	1.23295i
$947$	− 21469.3i	− 0.736703i	−0.929687	−	0.368351i	$-0.879922\pi$
$947$	− 21469.3i	− 0.736703i	0.929687	−	0.368351i	$-0.120078\pi$
$948$	−2501.31	−0.0856951
$949$	− 3495.80i	− 0.119577i
$950$	−16588.7	−0.566534
$951$	3353.37	0.114343
$952$	0	0
$953$	15897.5	0.540369	0.270184	−	0.962809i	$-0.412915\pi$
$953$	15897.5	0.540369	0.270184	+	0.962809i	$0.412915\pi$
$954$	47535.3	1.61322
$955$	20289.0i	0.687473i
$956$	−13617.1	−0.460678
$957$	34459.5i	1.16397i
$958$	52198.5i	1.76039i
$959$	− 13540.5i	− 0.455940i
$960$	−691.356	−0.0232432
$961$	10727.7	0.360097
$962$	− 2095.52i	− 0.0702312i
$963$	4674.01i	0.156405i
$964$	− 3795.11i	− 0.126797i
$965$	12176.4	0.406189
$966$	− 7898.40i	− 0.263071i
$967$	33191.2	1.10378	0.551891	−	0.833916i	$-0.313906\pi$
$967$	33191.2	1.10378	0.551891	+	0.833916i	$0.313906\pi$
$968$	32661.6	1.08449
$969$	0	0
$970$	−21534.2	−0.712806
$971$	−31834.5	−1.05213	−0.526065	−	0.850445i	$-0.676333\pi$
$971$	−31834.5	−1.05213	−0.526065	+	0.850445i	$0.676333\pi$
$972$	− 16665.9i	− 0.549959i
$973$	−7118.94	−0.234556
$974$	− 28777.6i	− 0.946708i
$975$	743.543i	0.0244230i
$976$	− 399.060i	− 0.0130877i
$977$	14447.7	0.473105	0.236552	−	0.971619i	$-0.423982\pi$
$977$	14447.7	0.473105	0.236552	+	0.971619i	$0.423982\pi$
$978$	4383.24	0.143314
$979$	− 13318.0i	− 0.434777i
$980$	− 10964.0i	− 0.357379i
$981$	37908.5i	1.23377i
$982$	9223.90	0.299742
$983$	− 7830.90i	− 0.254086i	−0.991897	−	0.127043i	$-0.959451\pi$
$983$	− 7830.90i	− 0.254086i	0.991897	−	0.127043i	$-0.0405487\pi$
$984$	−6176.73	−0.200109
$985$	−17646.4	−0.570824
$986$	0	0
$987$	−2537.10	−0.0818206
$988$	2209.37	0.0711430
$989$	19330.0i	0.621494i
$990$	−35859.0	−1.15119
$991$	14647.7i	0.469526i	0.972053	+	0.234763i	$0.0754315\pi$
$991$	14647.7i	0.469526i	−0.972053	+	0.234763i	$0.924569\pi$
$992$	− 24122.6i	− 0.772071i
$993$	8674.21i	0.277208i
$994$	2842.10	0.0906902
$995$	−36127.1	−1.15106
$996$	− 8910.76i	− 0.283482i
$997$	49174.6i	1.56206i	0.624492	+	0.781031i	$0.285306\pi$
$997$	49174.6i	1.56206i	−0.624492	+	0.781031i	$0.714694\pi$
$998$	− 44670.1i	− 1.41684i
$999$	14487.5	0.458822

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.b.e.288.9		12
17.4	even	4		289.4.a.g.1.3		12
17.6	odd	16		17.4.d.a.15.3	yes	12
17.13	even	4		289.4.a.g.1.4		12
17.14	odd	16		17.4.d.a.8.3	✓	12
17.16	even	2	inner	289.4.b.e.288.10		12
51.14	even	16		153.4.l.a.127.1		12
51.23	even	16		153.4.l.a.100.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.d.a.8.3	✓	12	17.14	odd	16
17.4.d.a.15.3	yes	12	17.6	odd	16
153.4.l.a.100.1		12	51.23	even	16
153.4.l.a.127.1		12	51.14	even	16
289.4.a.g.1.3		12	17.4	even	4
289.4.a.g.1.4		12	17.13	even	4
289.4.b.e.288.9		12	1.1	even	1	trivial
289.4.b.e.288.10		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)

\(f(q)\)	\(=\)	\(q+3.49971 q^{2} -2.82539i q^{3} +4.24796 q^{4} -8.71933i q^{5} -9.88806i q^{6} +6.85501i q^{7} -13.1311 q^{8} +19.0171 q^{9} +O(q^{10})\)	\(q+3.49971 q^{2} -2.82539i q^{3} +4.24796 q^{4} -8.71933i q^{5} -9.88806i q^{6} +6.85501i q^{7} -13.1311 q^{8} +19.0171 q^{9} -30.5151i q^{10} -61.7928i q^{11} -12.0022i q^{12} -5.37363 q^{13} +23.9905i q^{14} -24.6355 q^{15} -79.9385 q^{16} +66.5545 q^{18} -96.7877 q^{19} -37.0393i q^{20} +19.3681 q^{21} -216.257i q^{22} -116.525i q^{23} +37.1004i q^{24} +48.9733 q^{25} -18.8061 q^{26} -130.017i q^{27} +29.1198i q^{28} -197.375i q^{29} -86.2172 q^{30} +138.070i q^{31} -174.713 q^{32} -174.589 q^{33} +59.7710 q^{35} +80.7840 q^{36} +111.428i q^{37} -338.729 q^{38} +15.1826i q^{39} +114.494i q^{40} +166.487i q^{41} +67.7827 q^{42} -165.887 q^{43} -262.493i q^{44} -165.817i q^{45} -407.804i q^{46} -130.994 q^{47} +225.858i q^{48} +296.009 q^{49} +171.392 q^{50} -22.8269 q^{52} +714.232 q^{53} -455.020i q^{54} -538.792 q^{55} -90.0135i q^{56} +273.463i q^{57} -690.754i q^{58} +846.216 q^{59} -104.651 q^{60} +4.99209i q^{61} +483.205i q^{62} +130.363i q^{63} +28.0634 q^{64} +46.8544i q^{65} -611.011 q^{66} -314.069 q^{67} -329.230 q^{69} +209.181 q^{70} -118.468i q^{71} -249.715 q^{72} +650.548i q^{73} +389.965i q^{74} -138.369i q^{75} -411.150 q^{76} +423.590 q^{77} +53.1347i q^{78} -208.405i q^{79} +697.010i q^{80} +146.115 q^{81} +582.655i q^{82} +742.430 q^{83} +82.2749 q^{84} -580.555 q^{86} -557.662 q^{87} +811.405i q^{88} +215.527 q^{89} -580.310i q^{90} -36.8362i q^{91} -494.994i q^{92} +390.102 q^{93} -458.441 q^{94} +843.923i q^{95} +493.633i q^{96} -705.690i q^{97} +1035.94 q^{98} -1175.12i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{2} + 16 q^{4} + 96 q^{8} + 36 q^{9}+O(q^{10}) \) 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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