LMFDB - Embedded newform 289.4.b.b.288.5

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:	$6$
Coefficient field:	6.0.27793984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{3} + 49x^{2} - 14x + 2 $ x^6 - 2x^3 + 49x^2 - 14*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			288.5
Root			$1.79483 + 1.79483i$ of defining polynomial
Character	$\chi$	$=$	289.288
Dual form			289.4.b.b.288.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.03251 q^{2} -8.47535i q^{3} +17.3261 q^{4} -0.885690i q^{5} -42.6523i q^{6} +3.81828i q^{7} +46.9339 q^{8} -44.8316 q^{9} +O(q^{10})$	\(q+5.03251 q^{2} -8.47535i q^{3} +17.3261 q^{4} -0.885690i q^{5} -42.6523i q^{6} +3.81828i q^{7} +46.9339 q^{8} -44.8316 q^{9} -4.45724i q^{10} -52.3720i q^{11} -146.845i q^{12} -8.06025 q^{13} +19.2156i q^{14} -7.50653 q^{15} +97.5862 q^{16} -225.616 q^{18} +66.5154 q^{19} -15.3456i q^{20} +32.3613 q^{21} -263.563i q^{22} +180.226i q^{23} -397.782i q^{24} +124.216 q^{25} -40.5633 q^{26} +151.129i q^{27} +66.1562i q^{28} +41.2800i q^{29} -37.7767 q^{30} +34.9114i q^{31} +115.632 q^{32} -443.871 q^{33} +3.38182 q^{35} -776.759 q^{36} -130.368i q^{37} +334.739 q^{38} +68.3134i q^{39} -41.5689i q^{40} -17.9081i q^{41} +162.859 q^{42} -277.620 q^{43} -907.405i q^{44} +39.7069i q^{45} +906.987i q^{46} +463.789 q^{47} -827.078i q^{48} +328.421 q^{49} +625.116 q^{50} -139.653 q^{52} +329.944 q^{53} +760.560i q^{54} -46.3853 q^{55} +179.207i q^{56} -563.741i q^{57} +207.742i q^{58} -678.656 q^{59} -130.059 q^{60} +340.280i q^{61} +175.692i q^{62} -171.180i q^{63} -198.770 q^{64} +7.13888i q^{65} -2233.79 q^{66} +15.3925 q^{67} +1527.48 q^{69} +17.0190 q^{70} +670.203i q^{71} -2104.12 q^{72} -193.480i q^{73} -656.080i q^{74} -1052.77i q^{75} +1152.46 q^{76} +199.971 q^{77} +343.788i q^{78} +1080.15i q^{79} -86.4311i q^{80} +70.4207 q^{81} -90.1229i q^{82} +865.668 q^{83} +560.697 q^{84} -1397.13 q^{86} +349.863 q^{87} -2458.02i q^{88} +1129.46 q^{89} +199.825i q^{90} -30.7763i q^{91} +3122.61i q^{92} +295.886 q^{93} +2334.02 q^{94} -58.9120i q^{95} -980.023i q^{96} +379.412i q^{97} +1652.78 q^{98} +2347.92i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} + 50 q^{4} + 78 q^{8} - 118 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 + 50 * q^4 + 78 * q^8 - 118 * q^9	$ 6 q - 2 q^{2} + 50 q^{4} + 78 q^{8} - 118 q^{9} + 60 q^{13} - 216 q^{15} + 274 q^{16} - 206 q^{18} - 160 q^{19} - 384 q^{21} + 446 q^{25} - 52 q^{26} + 800 q^{30} + 142 q^{32} - 664 q^{33} - 664 q^{35} - 2626 q^{36} + 1448 q^{38} + 2256 q^{42} - 1112 q^{43} + 1280 q^{47} + 538 q^{49} + 1094 q^{50} - 1548 q^{52} - 604 q^{53} + 152 q^{55} - 1272 q^{59} - 2656 q^{60} - 1838 q^{64} - 4936 q^{66} + 2016 q^{67} + 1152 q^{69} + 3008 q^{70} - 1854 q^{72} + 1816 q^{76} + 1008 q^{77} - 1010 q^{81} + 4792 q^{83} - 4080 q^{84} - 2528 q^{86} - 2856 q^{87} - 340 q^{89} - 1264 q^{93} + 4032 q^{94} + 5714 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 + 50 * q^4 + 78 * q^8 - 118 * q^9 + 60 * q^13 - 216 * q^15 + 274 * q^16 - 206 * q^18 - 160 * q^19 - 384 * q^21 + 446 * q^25 - 52 * q^26 + 800 * q^30 + 142 * q^32 - 664 * q^33 - 664 * q^35 - 2626 * q^36 + 1448 * q^38 + 2256 * q^42 - 1112 * q^43 + 1280 * q^47 + 538 * q^49 + 1094 * q^50 - 1548 * q^52 - 604 * q^53 + 152 * q^55 - 1272 * q^59 - 2656 * q^60 - 1838 * q^64 - 4936 * q^66 + 2016 * q^67 + 1152 * q^69 + 3008 * q^70 - 1854 * q^72 + 1816 * q^76 + 1008 * q^77 - 1010 * q^81 + 4792 * q^83 - 4080 * q^84 - 2528 * q^86 - 2856 * q^87 - 340 * q^89 - 1264 * q^93 + 4032 * q^94 + 5714 * 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 $

$2$	5.03251	1.77926	0.889630	−	0.456681i	$-0.150962\pi$
$2$	5.03251	1.77926	0.889630	+	0.456681i	$0.150962\pi$
$3$	− 8.47535i	− 1.63108i	−0.578699	−	0.815541i	$-0.696439\pi$
$3$	− 8.47535i	− 1.63108i	0.578699	−	0.815541i	$-0.303561\pi$
$4$	17.3261	2.16577
$5$	− 0.885690i	− 0.0792185i	−0.999215	−	0.0396092i	$-0.987389\pi$
$5$	− 0.885690i	− 0.0792185i	0.999215	−	0.0396092i	$-0.0126113\pi$
$6$	− 42.6523i	− 2.90212i
$7$	3.81828i	0.206168i	0.994673	+	0.103084i	$0.0328711\pi$
$7$	3.81828i	0.206168i	−0.994673	+	0.103084i	$0.967129\pi$
$8$	46.9339	2.07421
$9$	−44.8316	−1.66043
$10$	− 4.45724i	− 0.140950i
$11$	− 52.3720i	− 1.43552i	−0.696289	−	0.717761i	$-0.745167\pi$
$11$	− 52.3720i	− 1.43552i	0.696289	−	0.717761i	$-0.254833\pi$
$12$	− 146.845i	− 3.53255i
$13$	−8.06025	−0.171962	−0.0859811	−	0.996297i	$-0.527402\pi$
$13$	−8.06025	−0.171962	−0.0859811	+	0.996297i	$0.527402\pi$
$14$	19.2156i	0.366827i
$15$	−7.50653	−0.129212
$16$	97.5862	1.52478
$17$	0	0
$17$	0	0
$18$	−225.616	−2.95434
$19$	66.5154	0.803141	0.401570	−	0.915828i	$-0.368465\pi$
$19$	66.5154	0.803141	0.401570	+	0.915828i	$0.368465\pi$
$20$	− 15.3456i	− 0.171569i
$21$	32.3613	0.336277
$22$	− 263.563i	− 2.55417i
$23$	180.226i	1.63390i	0.576711	+	0.816948i	$0.304336\pi$
$23$	180.226i	1.63390i	−0.576711	+	0.816948i	$0.695664\pi$
$24$	− 397.782i	− 3.38320i
$25$	124.216	0.993724
$26$	−40.5633	−0.305966
$27$	151.129i	1.07722i
$28$	66.1562i	0.446512i
$29$	41.2800i	0.264328i	0.991228	+	0.132164i	$0.0421925\pi$
$29$	41.2800i	0.264328i	−0.991228	+	0.132164i	$0.957807\pi$
$30$	−37.7767	−0.229902
$31$	34.9114i	0.202267i	0.994873	+	0.101133i	$0.0322469\pi$
$31$	34.9114i	0.202267i	−0.994873	+	0.101133i	$0.967753\pi$
$32$	115.632	0.638783
$33$	−443.871	−2.34146
$34$	0	0
$35$	3.38182	0.0163323
$36$	−776.759	−3.59611
$37$	− 130.368i	− 0.579255i	−0.957139	−	0.289627i	$-0.906469\pi$
$37$	− 130.368i	− 0.579255i	0.957139	−	0.289627i	$-0.0935314\pi$
$38$	334.739	1.42900
$39$	68.3134i	0.280485i
$40$	− 41.5689i	− 0.164315i
$41$	− 17.9081i	− 0.0682142i	−0.999418	−	0.0341071i	$-0.989141\pi$
$41$	− 17.9081i	− 0.0682142i	0.999418	−	0.0341071i	$-0.0108587\pi$
$42$	162.859	0.598325
$43$	−277.620	−0.984573	−0.492287	−	0.870433i	$-0.663839\pi$
$43$	−277.620	−0.984573	−0.492287	+	0.870433i	$0.663839\pi$
$44$	− 907.405i	− 3.10901i
$45$	39.7069i	0.131537i
$46$	906.987i	2.90713i
$47$	463.789	1.43937	0.719687	−	0.694299i	$-0.244285\pi$
$47$	463.789	1.43937	0.719687	+	0.694299i	$0.244285\pi$
$48$	− 827.078i	− 2.48705i
$49$	328.421	0.957495
$50$	625.116	1.76809
$51$	0	0
$52$	−139.653	−0.372431
$53$	329.944	0.855118	0.427559	−	0.903987i	$-0.359374\pi$
$53$	329.944	0.855118	0.427559	+	0.903987i	$0.359374\pi$
$54$	760.560i	1.91665i
$55$	−46.3853	−0.113720
$56$	179.207i	0.427635i
$57$	− 563.741i	− 1.30999i
$58$	207.742i	0.470308i
$59$	−678.656	−1.49752	−0.748759	−	0.662843i	$-0.769350\pi$
$59$	−678.656	−1.49752	−0.748759	+	0.662843i	$0.769350\pi$
$60$	−130.059	−0.279843
$61$	340.280i	0.714237i	0.934059	+	0.357118i	$0.116241\pi$
$61$	340.280i	0.714237i	−0.934059	+	0.357118i	$0.883759\pi$
$62$	175.692i	0.359885i
$63$	− 171.180i	− 0.342328i
$64$	−198.770	−0.388223
$65$	7.13888i	0.0136226i
$66$	−2233.79	−4.16606
$67$	15.3925	0.0280671	0.0140336	−	0.999902i	$-0.495533\pi$
$67$	15.3925	0.0280671	0.0140336	+	0.999902i	$0.495533\pi$
$68$	0	0
$69$	1527.48	2.66502
$70$	17.0190	0.0290595
$71$	670.203i	1.12026i	0.828405	+	0.560130i	$0.189249\pi$
$71$	670.203i	1.12026i	−0.828405	+	0.560130i	$0.810751\pi$
$72$	−2104.12	−3.44408
$73$	− 193.480i	− 0.310207i	−0.987898	−	0.155103i	$-0.950429\pi$
$73$	− 193.480i	− 0.310207i	0.987898	−	0.155103i	$-0.0495711\pi$
$74$	− 656.080i	− 1.03065i
$75$	− 1052.77i	− 1.62085i
$76$	1152.46	1.73942
$77$	199.971	0.295959
$78$	343.788i	0.499055i
$79$	1080.15i	1.53831i	0.639061	+	0.769156i	$0.279323\pi$
$79$	1080.15i	1.53831i	−0.639061	+	0.769156i	$0.720677\pi$
$80$	− 86.4311i	− 0.120791i
$81$	70.4207	0.0965990
$82$	− 90.1229i	− 0.121371i
$83$	865.668	1.14481	0.572406	−	0.819970i	$-0.306010\pi$
$83$	865.668	1.14481	0.572406	+	0.819970i	$0.306010\pi$
$84$	560.697	0.728298
$85$	0	0
$86$	−1397.13	−1.75181
$87$	349.863	0.431141
$88$	− 2458.02i	− 2.97757i
$89$	1129.46	1.34520	0.672599	−	0.740008i	$-0.265178\pi$
$89$	1129.46	1.34520	0.672599	+	0.740008i	$0.265178\pi$
$90$	199.825i	0.234038i
$91$	− 30.7763i	− 0.0354531i
$92$	3122.61i	3.53864i
$93$	295.886	0.329914
$94$	2334.02	2.56102
$95$	− 58.9120i	− 0.0636236i
$96$	− 980.023i	− 1.04191i
$97$	379.412i	0.397149i	0.980086	+	0.198574i	$0.0636311\pi$
$97$	379.412i	0.397149i	−0.980086	+	0.198574i	$0.936369\pi$
$98$	1652.78	1.70363
$99$	2347.92i	2.38359i
$100$	2152.18	2.15218
$101$	131.732	0.129780	0.0648902	−	0.997892i	$-0.479330\pi$
$101$	131.732	0.129780	0.0648902	+	0.997892i	$0.479330\pi$
$102$	0	0
$103$	195.988	0.187488	0.0937442	−	0.995596i	$-0.470116\pi$
$103$	195.988	0.187488	0.0937442	+	0.995596i	$0.470116\pi$
$104$	−378.299	−0.356685
$105$	− 28.6621i	− 0.0266394i
$106$	1660.45	1.52148
$107$	485.147i	0.438326i	0.975688	+	0.219163i	$0.0703327\pi$
$107$	485.147i	0.438326i	−0.975688	+	0.219163i	$0.929667\pi$
$108$	2618.49i	2.33300i
$109$	− 1255.12i	− 1.10292i	−0.834201	−	0.551460i	$-0.814071\pi$
$109$	− 1255.12i	− 1.10292i	0.834201	−	0.551460i	$-0.185929\pi$
$110$	−233.435	−0.202337
$111$	−1104.92	−0.944812
$112$	372.612i	0.314362i
$113$	− 1013.35i	− 0.843612i	−0.906686	−	0.421806i	$-0.861396\pi$
$113$	− 1013.35i	− 0.843612i	0.906686	−	0.421806i	$-0.138604\pi$
$114$	− 2837.03i	− 2.33081i
$115$	159.624	0.129435
$116$	715.224i	0.572473i
$117$	361.354	0.285531
$118$	−3415.34	−2.66447
$119$	0	0
$120$	−352.311	−0.268012
$121$	−1411.83	−1.06073
$122$	1712.46i	1.27081i
$123$	−151.778	−0.111263
$124$	604.880i	0.438063i
$125$	− 220.728i	− 0.157940i
$126$	− 861.464i	− 0.609090i
$127$	−1927.72	−1.34691	−0.673456	−	0.739227i	$-0.735191\pi$
$127$	−1927.72	−1.34691	−0.673456	+	0.739227i	$0.735191\pi$
$128$	−1925.37	−1.32953
$129$	2352.93i	1.60592i
$130$	35.9265i	0.0242381i
$131$	406.738i	0.271274i	0.990759	+	0.135637i	$0.0433081\pi$
$131$	406.738i	0.271274i	−0.990759	+	0.135637i	$0.956692\pi$
$132$	−7690.58	−5.07105
$133$	253.975i	0.165582i
$134$	77.4631	0.0499387
$135$	133.854	0.0853355
$136$	0	0
$137$	−130.552	−0.0814149	−0.0407074	−	0.999171i	$-0.512961\pi$
$137$	−130.552	−0.0814149	−0.0407074	+	0.999171i	$0.512961\pi$
$138$	7687.03	4.74177
$139$	− 2073.54i	− 1.26529i	−0.774443	−	0.632644i	$-0.781970\pi$
$139$	− 2073.54i	− 1.26529i	0.774443	−	0.632644i	$-0.218030\pi$
$140$	58.5938	0.0353720
$141$	− 3930.78i	− 2.34774i
$142$	3372.80i	1.99323i
$143$	422.131i	0.246856i
$144$	−4374.95	−2.53180
$145$	36.5613	0.0209397
$146$	− 973.689i	− 0.551939i
$147$	− 2783.48i	− 1.56175i
$148$	− 2258.78i	− 1.25453i
$149$	−1852.73	−1.01867	−0.509334	−	0.860569i	$-0.670108\pi$
$149$	−1852.73	−1.01867	−0.509334	+	0.860569i	$0.670108\pi$
$150$	− 5298.08i	− 2.88391i
$151$	−2050.86	−1.10527	−0.552637	−	0.833422i	$-0.686378\pi$
$151$	−2050.86	−1.10527	−0.552637	+	0.833422i	$0.686378\pi$
$152$	3121.83	1.66588
$153$	0	0
$154$	1006.36	0.526588
$155$	30.9207	0.0160233
$156$	1183.61i	0.607465i
$157$	−262.991	−0.133688	−0.0668438	−	0.997763i	$-0.521293\pi$
$157$	−262.991	−0.133688	−0.0668438	+	0.997763i	$0.521293\pi$
$158$	5435.88i	2.73706i
$159$	− 2796.39i	− 1.39477i
$160$	− 102.414i	− 0.0506035i
$161$	−688.152	−0.336857
$162$	354.393	0.171875
$163$	− 1444.98i	− 0.694354i	−0.937800	−	0.347177i	$-0.887140\pi$
$163$	− 1444.98i	− 0.694354i	0.937800	−	0.347177i	$-0.112860\pi$
$164$	− 310.279i	− 0.147736i
$165$	393.132i	0.185487i
$166$	4356.48	2.03692
$167$	501.565i	0.232409i	0.993225	+	0.116204i	$0.0370728\pi$
$167$	501.565i	0.232409i	−0.993225	+	0.116204i	$0.962927\pi$
$168$	1518.84	0.697508
$169$	−2132.03	−0.970429
$170$	0	0
$171$	−2981.99	−1.33356
$172$	−4810.08	−2.13236
$173$	2590.14i	1.13829i	0.822237	+	0.569146i	$0.192726\pi$
$173$	2590.14i	1.13829i	−0.822237	+	0.569146i	$0.807274\pi$
$174$	1760.69	0.767112
$175$	474.290i	0.204874i
$176$	− 5110.79i	− 2.18886i
$177$	5751.85i	2.44257i
$178$	5684.02	2.39346
$179$	−2165.65	−0.904294	−0.452147	−	0.891943i	$-0.649342\pi$
$179$	−2165.65	−0.904294	−0.452147	+	0.891943i	$0.649342\pi$
$180$	687.968i	0.284878i
$181$	− 1925.56i	− 0.790750i	−0.918520	−	0.395375i	$-0.870615\pi$
$181$	− 1925.56i	− 0.790750i	0.918520	−	0.395375i	$-0.129385\pi$
$182$	− 154.882i	− 0.0630803i
$183$	2884.00	1.16498
$184$	8458.69i	3.38904i
$185$	−115.466	−0.0458877
$186$	1489.05	0.587003
$187$	0	0
$188$	8035.68	3.11735
$189$	−577.055	−0.222088
$190$	− 296.475i	− 0.113203i
$191$	−2783.52	−1.05449	−0.527247	−	0.849712i	$-0.676776\pi$
$191$	−2783.52	−1.05449	−0.527247	+	0.849712i	$0.676776\pi$
$192$	1684.65i	0.633223i
$193$	2258.27i	0.842246i	0.907004	+	0.421123i	$0.138364\pi$
$193$	2258.27i	0.842246i	−0.907004	+	0.421123i	$0.861636\pi$
$194$	1909.39i	0.706631i
$195$	60.5045	0.0222196
$196$	5690.27	2.07371
$197$	− 1270.70i	− 0.459560i	−0.973243	−	0.229780i	$-0.926199\pi$
$197$	− 1270.70i	− 0.459560i	0.973243	−	0.229780i	$-0.0738007\pi$
$198$	11815.9i	4.24102i
$199$	4794.36i	1.70786i	0.520392	+	0.853928i	$0.325786\pi$
$199$	4794.36i	1.70786i	−0.520392	+	0.853928i	$0.674214\pi$
$200$	5829.92	2.06119
$201$	− 130.457i	− 0.0457798i
$202$	662.942	0.230913
$203$	−157.619	−0.0544960
$204$	0	0
$205$	−15.8611	−0.00540383
$206$	986.313	0.333591
$207$	− 8079.80i	− 2.71297i
$208$	−786.569	−0.262205
$209$	− 3483.54i	− 1.15293i
$210$	− 144.242i	− 0.0473984i
$211$	− 2807.00i	− 0.915837i	−0.888994	−	0.457918i	$-0.848595\pi$
$211$	− 2807.00i	− 0.915837i	0.888994	−	0.457918i	$-0.151405\pi$
$212$	5716.66	1.85199
$213$	5680.21	1.82724
$214$	2441.50i	0.779896i
$215$	245.885i	0.0779964i
$216$	7093.09i	2.23437i
$217$	−133.302	−0.0417009
$218$	− 6316.38i	− 1.96238i
$219$	−1639.81	−0.505973
$220$	−803.679	−0.246291
$221$	0	0
$222$	−5560.51	−1.68107
$223$	−4684.30	−1.40665	−0.703327	−	0.710866i	$-0.748303\pi$
$223$	−4684.30	−1.40665	−0.703327	+	0.710866i	$0.748303\pi$
$224$	441.516i	0.131697i
$225$	−5568.79	−1.65001
$226$	− 5099.70i	− 1.50101i
$227$	− 1395.72i	− 0.408095i	−0.978961	−	0.204047i	$-0.934590\pi$
$227$	− 1395.72i	− 0.408095i	0.978961	−	0.204047i	$-0.0654096\pi$
$228$	− 9767.47i	− 2.83713i
$229$	−894.638	−0.258163	−0.129082	−	0.991634i	$-0.541203\pi$
$229$	−894.638	−0.258163	−0.129082	+	0.991634i	$0.541203\pi$
$230$	803.309	0.230298
$231$	− 1694.83i	− 0.482733i
$232$	1937.43i	0.548270i
$233$	− 1196.13i	− 0.336313i	−0.985760	−	0.168156i	$-0.946219\pi$
$233$	− 1196.13i	− 0.336313i	0.985760	−	0.168156i	$-0.0537814\pi$
$234$	1818.52	0.508035
$235$	− 410.773i	− 0.114025i
$236$	−11758.5	−3.24328
$237$	9154.67	2.50911
$238$	0	0
$239$	4948.82	1.33938	0.669691	−	0.742639i	$-0.266426\pi$
$239$	4948.82	1.33938	0.669691	+	0.742639i	$0.266426\pi$
$240$	−732.534	−0.197020
$241$	6702.73i	1.79154i	0.444518	+	0.895770i	$0.353375\pi$
$241$	6702.73i	1.79154i	−0.444518	+	0.895770i	$0.646625\pi$
$242$	−7105.03	−1.88731
$243$	3483.65i	0.919656i
$244$	5895.75i	1.54687i
$245$	− 290.879i	− 0.0758513i
$246$	−763.824	−0.197966
$247$	−536.130	−0.138110
$248$	1638.53i	0.419543i
$249$	− 7336.85i	− 1.86728i
$250$	− 1110.81i	− 0.281016i
$251$	−4756.08	−1.19602	−0.598010	−	0.801489i	$-0.704042\pi$
$251$	−4756.08	−1.19602	−0.598010	+	0.801489i	$0.704042\pi$
$252$	− 2965.89i	− 0.741402i
$253$	9438.77	2.34550
$254$	−9701.29	−2.39651
$255$	0	0
$256$	−8099.28	−1.97736
$257$	−2892.84	−0.702143	−0.351071	−	0.936349i	$-0.614183\pi$
$257$	−2892.84	−0.702143	−0.351071	+	0.936349i	$0.614183\pi$
$258$	11841.1i	2.85735i
$259$	497.784	0.119424
$260$	123.689i	0.0295034i
$261$	− 1850.65i	− 0.438898i
$262$	2046.92i	0.482667i
$263$	−5415.48	−1.26971	−0.634853	−	0.772633i	$-0.718939\pi$
$263$	−5415.48	−1.26971	−0.634853	+	0.772633i	$0.718939\pi$
$264$	−20832.6	−4.85666
$265$	− 292.228i	− 0.0677412i
$266$	1278.13i	0.294613i
$267$	− 9572.58i	− 2.19413i
$268$	266.693	0.0607869
$269$	− 5787.00i	− 1.31167i	−0.754904	−	0.655835i	$-0.772317\pi$
$269$	− 5787.00i	− 1.31167i	0.754904	−	0.655835i	$-0.227683\pi$
$270$	673.620	0.151834
$271$	5465.13	1.22503	0.612515	−	0.790459i	$-0.290158\pi$
$271$	5465.13	1.22503	0.612515	+	0.790459i	$0.290158\pi$
$272$	0	0
$273$	−260.840	−0.0578270
$274$	−657.006	−0.144858
$275$	− 6505.42i	− 1.42651i
$276$	26465.3	5.77182
$277$	1207.65i	0.261952i	0.991386	+	0.130976i	$0.0418111\pi$
$277$	1207.65i	0.261952i	−0.991386	+	0.130976i	$0.958189\pi$
$278$	− 10435.1i	− 2.25128i
$279$	− 1565.13i	− 0.335850i
$280$	158.722	0.0338766
$281$	1197.18	0.254155	0.127077	−	0.991893i	$-0.459440\pi$
$281$	1197.18	0.254155	0.127077	+	0.991893i	$0.459440\pi$
$282$	− 19781.7i	− 4.17724i
$283$	3164.73i	0.664748i	0.943148	+	0.332374i	$0.107850\pi$
$283$	3164.73i	0.664748i	−0.943148	+	0.332374i	$0.892150\pi$
$284$	11612.0i	2.42622i
$285$	−499.300	−0.103775
$286$	2124.38i	0.439221i
$287$	68.3784	0.0140636
$288$	−5183.98	−1.06066
$289$	0	0
$290$	183.995	0.0372571
$291$	3215.65	0.647782
$292$	− 3352.26i	− 0.671836i
$293$	7456.21	1.48668	0.743339	−	0.668915i	$-0.233241\pi$
$293$	7456.21	1.48668	0.743339	+	0.668915i	$0.233241\pi$
$294$	− 14007.9i	− 2.77877i
$295$	601.079i	0.118631i
$296$	− 6118.70i	− 1.20149i
$297$	7914.94	1.54637
$298$	−9323.89	−1.81248
$299$	− 1452.66i	− 0.280969i
$300$	− 18240.5i	− 3.51038i
$301$	− 1060.03i	− 0.202988i
$302$	−10321.0	−1.96657
$303$	− 1116.47i	− 0.211683i
$304$	6490.98	1.22462
$305$	301.383	0.0565808
$306$	0	0
$307$	−6535.48	−1.21498	−0.607491	−	0.794327i	$-0.707824\pi$
$307$	−6535.48	−1.21498	−0.607491	+	0.794327i	$0.707824\pi$
$308$	3464.73	0.640978
$309$	− 1661.07i	− 0.305809i
$310$	155.608	0.0285096
$311$	8935.89i	1.62928i	0.579963	+	0.814642i	$0.303067\pi$
$311$	8935.89i	1.62928i	−0.579963	+	0.814642i	$0.696933\pi$
$312$	3206.22i	0.581783i
$313$	− 2628.71i	− 0.474707i	−0.971423	−	0.237353i	$-0.923720\pi$
$313$	− 2628.71i	− 0.474707i	0.971423	−	0.237353i	$-0.0762799\pi$
$314$	−1323.50	−0.237865
$315$	−151.612	−0.0271187
$316$	18714.9i	3.33163i
$317$	4268.54i	0.756293i	0.925746	+	0.378147i	$0.123438\pi$
$317$	4268.54i	0.756293i	−0.925746	+	0.378147i	$0.876562\pi$
$318$	− 14072.9i	− 2.48166i
$319$	2161.92	0.379449
$320$	176.048i	0.0307544i
$321$	4111.79	0.714946
$322$	−3463.13	−0.599357
$323$	0	0
$324$	1220.12	0.209211
$325$	−1001.21	−0.170883
$326$	− 7271.89i	− 1.23544i
$327$	−10637.5	−1.79895
$328$	− 840.500i	− 0.141490i
$329$	1770.88i	0.296753i
$330$	1978.44i	0.330029i
$331$	−992.298	−0.164778	−0.0823892	−	0.996600i	$-0.526255\pi$
$331$	−992.298	−0.164778	−0.0823892	+	0.996600i	$0.526255\pi$
$332$	14998.7	2.47940
$333$	5844.63i	0.961812i
$334$	2524.13i	0.413516i
$335$	− 13.6330i	− 0.00222344i
$336$	3158.02	0.512750
$337$	− 8042.26i	− 1.29997i	−0.759947	−	0.649985i	$-0.774775\pi$
$337$	− 8042.26i	− 1.29997i	0.759947	−	0.649985i	$-0.225225\pi$
$338$	−10729.5	−1.72665
$339$	−8588.52	−1.37600
$340$	0	0
$341$	1828.38	0.290359
$342$	−15006.9	−2.37275
$343$	2563.68i	0.403573i
$344$	−13029.8	−2.04221
$345$	− 1352.87i	− 0.211119i
$346$	13034.9i	2.02532i
$347$	− 7414.16i	− 1.14701i	−0.819202	−	0.573506i	$-0.805583\pi$
$347$	− 7414.16i	− 1.14701i	0.819202	−	0.573506i	$-0.194417\pi$
$348$	6061.78	0.933751
$349$	859.194	0.131781	0.0658905	−	0.997827i	$-0.479011\pi$
$349$	859.194	0.131781	0.0658905	+	0.997827i	$0.479011\pi$
$350$	2386.87i	0.364525i
$351$	− 1218.14i	− 0.185241i
$352$	− 6055.89i	− 0.916988i
$353$	569.084	0.0858053	0.0429027	−	0.999079i	$-0.486339\pi$
$353$	569.084	0.0858053	0.0429027	+	0.999079i	$0.486339\pi$
$354$	28946.3i	4.34598i
$355$	593.592	0.0887453
$356$	19569.2	2.91339
$357$	0	0
$358$	−10898.7	−1.60897
$359$	5005.21	0.735835	0.367918	−	0.929858i	$-0.380071\pi$
$359$	5005.21	0.735835	0.367918	+	0.929858i	$0.380071\pi$
$360$	1863.60i	0.272834i
$361$	−2434.71	−0.354965
$362$	− 9690.40i	− 1.40695i
$363$	11965.7i	1.73013i
$364$	− 533.235i	− 0.0767833i
$365$	−171.363	−0.0245741
$366$	14513.7	2.07280
$367$	− 10975.3i	− 1.56105i	−0.625127	−	0.780523i	$-0.714953\pi$
$367$	− 10975.3i	− 1.56105i	0.625127	−	0.780523i	$-0.285047\pi$
$368$	17587.5i	2.49134i
$369$	802.851i	0.113265i
$370$	−581.083	−0.0816462
$371$	1259.82i	0.176298i
$372$	5126.57	0.714517
$373$	−3211.72	−0.445835	−0.222918	−	0.974837i	$-0.571558\pi$
$373$	−3211.72	−0.445835	−0.222918	+	0.974837i	$0.571558\pi$
$374$	0	0
$375$	−1870.74	−0.257613
$376$	21767.4	2.98556
$377$	− 332.727i	− 0.0454544i
$378$	−2904.03	−0.395152
$379$	− 8051.48i	− 1.09123i	−0.838035	−	0.545616i	$-0.816296\pi$
$379$	− 8051.48i	− 1.09123i	0.838035	−	0.545616i	$-0.183704\pi$
$380$	− 1020.72i	− 0.137794i
$381$	16338.1i	2.19692i
$382$	−14008.1	−1.87622
$383$	2584.16	0.344763	0.172382	−	0.985030i	$-0.444854\pi$
$383$	2584.16	0.344763	0.172382	+	0.985030i	$0.444854\pi$
$384$	16318.2i	2.16858i
$385$	− 177.112i	− 0.0234454i
$386$	11364.7i	1.49858i
$387$	12446.2	1.63482
$388$	6573.74i	0.860132i
$389$	5174.31	0.674417	0.337208	−	0.941430i	$-0.390517\pi$
$389$	5174.31	0.674417	0.337208	+	0.941430i	$0.390517\pi$
$390$	304.489	0.0395344
$391$	0	0
$392$	15414.1	1.98604
$393$	3447.25	0.442470
$394$	− 6394.79i	− 0.817677i
$395$	956.680	0.121863
$396$	40680.4i	5.16230i
$397$	− 5149.36i	− 0.650980i	−0.945545	−	0.325490i	$-0.894471\pi$
$397$	− 5149.36i	− 0.650980i	0.945545	−	0.325490i	$-0.105529\pi$
$398$	24127.7i	3.03872i
$399$	2152.53	0.270078
$400$	12121.7	1.51522
$401$	8700.49i	1.08350i	0.840541	+	0.541748i	$0.182237\pi$
$401$	8700.49i	1.08350i	−0.840541	+	0.541748i	$0.817763\pi$
$402$	− 656.527i	− 0.0814542i
$403$	− 281.394i	− 0.0347823i
$404$	2282.41	0.281074
$405$	− 62.3709i	− 0.00765243i
$406$	−793.219	−0.0969625
$407$	−6827.65	−0.831533
$408$	0	0
$409$	12346.0	1.49260	0.746299	−	0.665611i	$-0.231829\pi$
$409$	12346.0	1.49260	0.746299	+	0.665611i	$0.231829\pi$
$410$	−79.8209	−0.00961482
$411$	1106.48i	0.132794i
$412$	3395.72	0.406056
$413$	− 2591.30i	− 0.308740i
$414$	− 40661.7i	− 4.82708i
$415$	− 766.713i	− 0.0906903i
$416$	−932.023	−0.109847
$417$	−17574.0	−2.06379
$418$	− 17531.0i	− 2.05136i
$419$	− 5763.33i	− 0.671974i	−0.941867	−	0.335987i	$-0.890930\pi$
$419$	− 5763.33i	− 0.671974i	0.941867	−	0.335987i	$-0.109070\pi$
$420$	− 496.604i	− 0.0576947i
$421$	−1876.12	−0.217188	−0.108594	−	0.994086i	$-0.534635\pi$
$421$	−1876.12	−0.217188	−0.108594	+	0.994086i	$0.534635\pi$
$422$	− 14126.2i	− 1.62951i
$423$	−20792.4	−2.38998
$424$	15485.6	1.77369
$425$	0	0
$426$	28585.7	3.25113
$427$	−1299.29	−0.147253
$428$	8405.72i	0.949313i
$429$	3577.71	0.402642
$430$	1237.42i	0.138776i
$431$	83.9299i	0.00937996i	0.999989	+	0.00468998i	$0.00149287\pi$
$431$	83.9299i	0.00937996i	−0.999989	+	0.00468998i	$0.998507\pi$
$432$	14748.1i	1.64252i
$433$	15345.0	1.70308	0.851539	−	0.524291i	$-0.175669\pi$
$433$	15345.0	1.70308	0.851539	+	0.524291i	$0.175669\pi$
$434$	−670.842	−0.0741968
$435$	− 309.870i	− 0.0341543i
$436$	− 21746.3i	− 2.38867i
$437$	11987.8i	1.31225i
$438$	−8252.36	−0.900258
$439$	− 3064.74i	− 0.333194i	−0.986025	−	0.166597i	$-0.946722\pi$
$439$	− 3064.74i	− 0.333194i	0.986025	−	0.166597i	$-0.0532778\pi$
$440$	−2177.05	−0.235879
$441$	−14723.6	−1.58985
$442$	0	0
$443$	−1792.97	−0.192295	−0.0961474	−	0.995367i	$-0.530652\pi$
$443$	−1792.97	−0.192295	−0.0961474	+	0.995367i	$0.530652\pi$
$444$	−19144.0	−2.04624
$445$	− 1000.35i	− 0.106564i
$446$	−23573.8	−2.50281
$447$	15702.6i	1.66153i
$448$	− 758.960i	− 0.0800391i
$449$	2499.19i	0.262681i	0.991337	+	0.131341i	$0.0419282\pi$
$449$	2499.19i	0.262681i	−0.991337	+	0.131341i	$0.958072\pi$
$450$	−28025.0	−2.93580
$451$	−937.885	−0.0979231
$452$	− 17557.5i	− 1.82707i
$453$	17381.7i	1.80279i
$454$	− 7024.00i	− 0.726107i
$455$	−27.2583	−0.00280854
$456$	− 26458.6i	− 2.71719i
$457$	−14784.4	−1.51331	−0.756656	−	0.653813i	$-0.773168\pi$
$457$	−14784.4	−1.51331	−0.756656	+	0.653813i	$0.773168\pi$
$458$	−4502.28	−0.459340
$459$	0	0
$460$	2765.67	0.280326
$461$	17746.9	1.79297	0.896483	−	0.443078i	$-0.146113\pi$
$461$	17746.9	1.79297	0.896483	+	0.443078i	$0.146113\pi$
$462$	− 8529.23i	− 0.858909i
$463$	18486.4	1.85559	0.927793	−	0.373096i	$-0.121704\pi$
$463$	18486.4	1.85559	0.927793	+	0.373096i	$0.121704\pi$
$464$	4028.36i	0.403043i
$465$	− 262.064i	− 0.0261353i
$466$	− 6019.52i	− 0.598388i
$467$	−7406.57	−0.733908	−0.366954	−	0.930239i	$-0.619599\pi$
$467$	−7406.57	−0.733908	−0.366954	+	0.930239i	$0.619599\pi$
$468$	6260.87	0.618395
$469$	58.7731i	0.00578655i
$470$	− 2067.22i	− 0.202880i
$471$	2228.94i	0.218055i
$472$	−31852.0	−3.10616
$473$	14539.5i	1.41338i
$474$	46071.0	4.46437
$475$	8262.24	0.798101
$476$	0	0
$477$	−14791.9	−1.41986
$478$	24905.0	2.38311
$479$	18550.9i	1.76955i	0.466019	+	0.884775i	$0.345688\pi$
$479$	18550.9i	1.76955i	−0.466019	+	0.884775i	$0.654312\pi$
$480$	−867.997	−0.0825384
$481$	1050.80i	0.0996100i
$482$	33731.6i	3.18762i
$483$	5832.34i	0.549442i
$484$	−24461.5	−2.29729
$485$	336.041	0.0314615
$486$	17531.5i	1.63631i
$487$	10203.4i	0.949406i	0.880146	+	0.474703i	$0.157444\pi$
$487$	10203.4i	0.949406i	−0.880146	+	0.474703i	$0.842556\pi$
$488$	15970.7i	1.48147i
$489$	−12246.7	−1.13255
$490$	− 1463.85i	− 0.134959i
$491$	1247.46	0.114658	0.0573290	−	0.998355i	$-0.481742\pi$
$491$	1247.46	0.114658	0.0573290	+	0.998355i	$0.481742\pi$
$492$	−2629.73	−0.240970
$493$	0	0
$494$	−2698.08	−0.245734
$495$	2079.53	0.188824
$496$	3406.87i	0.308413i
$497$	−2559.03	−0.230962
$498$	− 36922.7i	− 3.32238i
$499$	70.0303i	0.00628254i	0.999995	+	0.00314127i	$0.000999898\pi$
$499$	70.0303i	0.00628254i	−0.999995	+	0.00314127i	$0.999000\pi$
$500$	− 3824.36i	− 0.342061i
$501$	4250.94	0.379078
$502$	−23935.0	−2.12803
$503$	1444.29i	0.128028i	0.997949	+	0.0640138i	$0.0203902\pi$
$503$	1444.29i	0.128028i	−0.997949	+	0.0640138i	$0.979610\pi$
$504$	− 8034.15i	− 0.710058i
$505$	− 116.674i	− 0.0102810i
$506$	47500.7	4.17325
$507$	18069.7i	1.58285i
$508$	−33400.0	−2.91710
$509$	14272.8	1.24289	0.621445	−	0.783458i	$-0.286546\pi$
$509$	14272.8	1.24289	0.621445	+	0.783458i	$0.286546\pi$
$510$	0	0
$511$	738.761	0.0639547
$512$	−25356.7	−2.18871
$513$	10052.4i	0.865157i
$514$	−14558.3	−1.24929
$515$	− 173.585i	− 0.0148525i
$516$	40767.2i	3.47805i
$517$	− 24289.6i	− 2.06625i
$518$	2505.10	0.212486
$519$	21952.3	1.85665
$520$	335.055i	0.0282561i
$521$	14874.0i	1.25075i	0.780324	+	0.625376i	$0.215054\pi$
$521$	14874.0i	1.25075i	−0.780324	+	0.625376i	$0.784946\pi$
$522$	− 9313.42i	− 0.780914i
$523$	−8142.90	−0.680811	−0.340406	−	0.940279i	$-0.610564\pi$
$523$	−8142.90	−0.680811	−0.340406	+	0.940279i	$0.610564\pi$
$524$	7047.21i	0.587517i
$525$	4019.78	0.334167
$526$	−27253.4	−2.25914
$527$	0	0
$528$	−43315.7	−3.57022
$529$	−20314.2	−1.66962
$530$	− 1470.64i	− 0.120529i
$531$	30425.3	2.48652
$532$	4400.40i	0.358612i
$533$	144.344i	0.0117303i
$534$	− 48174.1i	− 3.90393i
$535$	429.689	0.0347235
$536$	722.432	0.0582170
$537$	18354.7i	1.47498i
$538$	− 29123.1i	− 2.33380i
$539$	− 17200.0i	− 1.37451i
$540$	2319.17	0.184817
$541$	− 3179.67i	− 0.252689i	−0.991986	−	0.126344i	$-0.959676\pi$
$541$	− 3179.67i	− 0.252689i	0.991986	−	0.126344i	$-0.0403244\pi$
$542$	27503.3	2.17965
$543$	−16319.8	−1.28978
$544$	0	0
$545$	−1111.64	−0.0873716
$546$	−1312.68	−0.102889
$547$	− 2107.07i	− 0.164702i	−0.996603	−	0.0823509i	$-0.973757\pi$
$547$	− 2107.07i	− 0.164702i	0.996603	−	0.0823509i	$-0.0262428\pi$
$548$	−2261.97	−0.176326
$549$	− 15255.3i	− 1.18594i
$550$	− 32738.6i	− 2.53814i
$551$	2745.76i	0.212292i
$552$	71690.4	5.52780
$553$	−4124.33	−0.317151
$554$	6077.51i	0.466081i
$555$	978.614i	0.0748466i
$556$	− 35926.4i	− 2.74032i
$557$	467.382	0.0355540	0.0177770	−	0.999842i	$-0.494341\pi$
$557$	467.382	0.0355540	0.0177770	+	0.999842i	$0.494341\pi$
$558$	− 7876.55i	− 0.597565i
$559$	2237.69	0.169309
$560$	330.019	0.0249033
$561$	0	0
$562$	6024.80	0.452208
$563$	−14612.6	−1.09387	−0.546935	−	0.837175i	$-0.684206\pi$
$563$	−14612.6	−1.09387	−0.546935	+	0.837175i	$0.684206\pi$
$564$	− 68105.2i	− 5.08466i
$565$	−897.515	−0.0668297
$566$	15926.5i	1.18276i
$567$	268.886i	0.0199156i
$568$	31455.3i	2.32365i
$569$	−11602.3	−0.854821	−0.427410	−	0.904058i	$-0.640574\pi$
$569$	−11602.3	−0.854821	−0.427410	+	0.904058i	$0.640574\pi$
$570$	−2512.73	−0.184643
$571$	− 10534.9i	− 0.772104i	−0.922477	−	0.386052i	$-0.873839\pi$
$571$	− 10534.9i	− 0.772104i	0.922477	−	0.386052i	$-0.126161\pi$
$572$	7313.91i	0.534633i
$573$	23591.3i	1.71997i
$574$	344.115	0.0250228
$575$	22386.8i	1.62364i
$576$	8911.18	0.644617
$577$	14404.7	1.03930	0.519650	−	0.854379i	$-0.326062\pi$
$577$	14404.7	1.03930	0.519650	+	0.854379i	$0.326062\pi$
$578$	0	0
$579$	19139.6	1.37377
$580$	633.466	0.0453504
$581$	3305.37i	0.236024i
$582$	16182.8	1.15257
$583$	− 17279.8i	− 1.22754i
$584$	− 9080.77i	− 0.643433i
$585$	− 320.047i	− 0.0226194i
$586$	37523.5	2.64519
$587$	11004.9	0.773799	0.386900	−	0.922122i	$-0.373546\pi$
$587$	11004.9	0.773799	0.386900	+	0.922122i	$0.373546\pi$
$588$	− 48227.0i	− 3.38240i
$589$	2322.14i	0.162449i
$590$	3024.94i	0.211076i
$591$	−10769.6	−0.749581
$592$	− 12722.2i	− 0.883239i
$593$	−1853.59	−0.128361	−0.0641804	−	0.997938i	$-0.520443\pi$
$593$	−1853.59	−0.128361	−0.0641804	+	0.997938i	$0.520443\pi$
$594$	39832.0	2.75139
$595$	0	0
$596$	−32100.7	−2.20620
$597$	40633.9	2.78565
$598$	− 7310.53i	− 0.499916i
$599$	19074.7	1.30112	0.650559	−	0.759456i	$-0.274535\pi$
$599$	19074.7	1.30112	0.650559	+	0.759456i	$0.274535\pi$
$600$	− 49410.7i	− 3.36197i
$601$	− 27776.0i	− 1.88520i	−0.333923	−	0.942600i	$-0.608373\pi$
$601$	− 27776.0i	− 1.88520i	0.333923	−	0.942600i	$-0.391627\pi$
$602$	− 5334.62i	− 0.361168i
$603$	−690.073	−0.0466035
$604$	−35533.4	−2.39377
$605$	1250.44i	0.0840291i
$606$	− 5618.67i	− 0.376638i
$607$	− 18728.3i	− 1.25232i	−0.779695	−	0.626159i	$-0.784626\pi$
$607$	− 18728.3i	− 1.25232i	0.779695	−	0.626159i	$-0.215374\pi$
$608$	7691.32	0.513033
$609$	1335.88i	0.0888874i
$610$	1516.71	0.100672
$611$	−3738.25	−0.247518
$612$	0	0
$613$	−24405.3	−1.60802	−0.804012	−	0.594613i	$-0.797305\pi$
$613$	−24405.3	−1.60802	−0.804012	+	0.594613i	$0.797305\pi$
$614$	−32889.8	−2.16177
$615$	134.428i	0.00881409i
$616$	9385.43	0.613880
$617$	22516.4i	1.46917i	0.678518	+	0.734584i	$0.262623\pi$
$617$	22516.4i	1.46917i	−0.678518	+	0.734584i	$0.737377\pi$
$618$	− 8359.35i	− 0.544114i
$619$	− 5146.53i	− 0.334179i	−0.985942	−	0.167089i	$-0.946563\pi$
$619$	− 5146.53i	− 0.334179i	0.985942	−	0.167089i	$-0.0534369\pi$
$620$	535.736	0.0347027
$621$	−27237.4	−1.76006
$622$	44969.9i	2.89892i
$623$	4312.60i	0.277337i
$624$	6666.45i	0.427679i
$625$	15331.4	0.981213
$626$	− 13229.0i	− 0.844627i
$627$	−29524.3	−1.88052
$628$	−4556.62	−0.289536
$629$	0	0
$630$	−762.990	−0.0482512
$631$	3858.77	0.243447	0.121724	−	0.992564i	$-0.461158\pi$
$631$	3858.77	0.243447	0.121724	+	0.992564i	$0.461158\pi$
$632$	50695.8i	3.19078i
$633$	−23790.3	−1.49381
$634$	21481.5i	1.34564i
$635$	1707.36i	0.106700i
$636$	− 48450.7i	− 3.02075i
$637$	−2647.15	−0.164653
$638$	10879.9	0.675138
$639$	− 30046.3i	− 1.86011i
$640$	1705.28i	0.105324i
$641$	− 18689.3i	− 1.15161i	−0.817587	−	0.575805i	$-0.804689\pi$
$641$	− 18689.3i	− 1.15161i	0.817587	−	0.575805i	$-0.195311\pi$
$642$	20692.6	1.27208
$643$	− 26473.5i	− 1.62366i	−0.583893	−	0.811831i	$-0.698471\pi$
$643$	− 26473.5i	− 1.62366i	0.583893	−	0.811831i	$-0.301529\pi$
$644$	−11923.0	−0.729555
$645$	2083.96	0.127219
$646$	0	0
$647$	14397.7	0.874855	0.437427	−	0.899254i	$-0.355890\pi$
$647$	14397.7	0.874855	0.437427	+	0.899254i	$0.355890\pi$
$648$	3305.12	0.200366
$649$	35542.6i	2.14972i
$650$	−5038.59	−0.304046
$651$	1129.78i	0.0680177i
$652$	− 25036.0i	− 1.50381i
$653$	20939.5i	1.25486i	0.778672	+	0.627431i	$0.215893\pi$
$653$	20939.5i	1.25486i	−0.778672	+	0.627431i	$0.784107\pi$
$654$	−53533.6	−3.20081
$655$	360.244	0.0214899
$656$	− 1747.59i	− 0.104012i
$657$	8674.02i	0.515077i
$658$	8911.96i	0.528001i
$659$	4031.76	0.238323	0.119162	−	0.992875i	$-0.461979\pi$
$659$	4031.76	0.238323	0.119162	+	0.992875i	$0.461979\pi$
$660$	6811.47i	0.401721i
$661$	−6691.52	−0.393752	−0.196876	−	0.980428i	$-0.563080\pi$
$661$	−6691.52	−0.393752	−0.196876	+	0.980428i	$0.563080\pi$
$662$	−4993.75	−0.293184
$663$	0	0
$664$	40629.2	2.37458
$665$	224.943	0.0131171
$666$	29413.1i	1.71131i
$667$	−7439.71	−0.431884
$668$	8690.19i	0.503344i
$669$	39701.1i	2.29437i
$670$	− 68.6083i	− 0.00395607i
$671$	17821.2	1.02530
$672$	3742.01	0.214808
$673$	10319.2i	0.591048i	0.955335	+	0.295524i	$0.0954942\pi$
$673$	10319.2i	0.591048i	−0.955335	+	0.295524i	$0.904506\pi$
$674$	− 40472.7i	− 2.31298i
$675$	18772.6i	1.07046i
$676$	−36939.9	−2.10172
$677$	19813.3i	1.12480i	0.826866	+	0.562398i	$0.190121\pi$
$677$	19813.3i	1.12480i	−0.826866	+	0.562398i	$0.809879\pi$
$678$	−43221.8	−2.44826
$679$	−1448.70	−0.0818793
$680$	0	0
$681$	−11829.3	−0.665636
$682$	9201.33	0.516624
$683$	− 5924.61i	− 0.331916i	−0.986133	−	0.165958i	$-0.946928\pi$
$683$	− 5924.61i	− 0.331916i	0.986133	−	0.165958i	$-0.0530717\pi$
$684$	−51666.4	−2.88818
$685$	115.629i	0.00644957i
$686$	12901.7i	0.718061i
$687$	7582.38i	0.421085i
$688$	−27091.9	−1.50126
$689$	−2659.43	−0.147048
$690$	− 6808.33i	− 0.375636i
$691$	1973.16i	0.108629i	0.998524	+	0.0543143i	$0.0172973\pi$
$691$	1973.16i	0.108629i	−0.998524	+	0.0543143i	$0.982703\pi$
$692$	44877.1i	2.46528i
$693$	−8965.03	−0.491419
$694$	− 37311.8i	− 2.04083i
$695$	−1836.51	−0.100234
$696$	16420.4	0.894274
$697$	0	0
$698$	4323.90	0.234473
$699$	−10137.6	−0.548554
$700$	8217.63i	0.443710i
$701$	−12840.1	−0.691815	−0.345907	−	0.938269i	$-0.612429\pi$
$701$	−12840.1	−0.691815	−0.345907	+	0.938269i	$0.612429\pi$
$702$	− 6130.30i	− 0.329591i
$703$	− 8671.50i	− 0.465223i
$704$	10410.0i	0.557302i
$705$	−3481.45	−0.185984
$706$	2863.92	0.152670
$707$	502.990i	0.0267566i
$708$	99657.5i	5.29005i
$709$	27749.7i	1.46990i	0.678119	+	0.734952i	$0.262796\pi$
$709$	27749.7i	1.46990i	−0.678119	+	0.734952i	$0.737204\pi$
$710$	2987.26	0.157901
$711$	− 48425.0i	− 2.55426i
$712$	53010.0	2.79022
$713$	−6291.92	−0.330483
$714$	0	0
$715$	373.877	0.0195555
$716$	−37522.4	−1.95849
$717$	− 41943.0i	− 2.18464i
$718$	25188.8	1.30924
$719$	− 16888.3i	− 0.875979i	−0.898980	−	0.437989i	$-0.855691\pi$
$719$	− 16888.3i	− 0.875979i	0.898980	−	0.437989i	$-0.144309\pi$
$720$	3874.85i	0.200565i
$721$	748.339i	0.0386541i
$722$	−12252.7	−0.631575
$723$	56808.0	2.92215
$724$	− 33362.6i	− 1.71258i
$725$	5127.62i	0.262669i
$726$	60217.6i	3.07835i
$727$	2135.25	0.108930	0.0544649	−	0.998516i	$-0.482655\pi$
$727$	2135.25	0.108930	0.0544649	+	0.998516i	$0.482655\pi$
$728$	− 1444.45i	− 0.0735371i
$729$	31426.5	1.59663
$730$	−862.386	−0.0437238
$731$	0	0
$732$	49968.6	2.52308
$733$	−4795.27	−0.241633	−0.120817	−	0.992675i	$-0.538551\pi$
$733$	−4795.27	−0.241633	−0.120817	+	0.992675i	$0.538551\pi$
$734$	− 55233.1i	− 2.77751i
$735$	−2465.30	−0.123720
$736$	20839.9i	1.04371i
$737$	− 806.138i	− 0.0402910i
$738$	4040.36i	0.201528i
$739$	32747.6	1.63010	0.815048	−	0.579393i	$-0.196710\pi$
$739$	32747.6	1.63010	0.815048	+	0.579393i	$0.196710\pi$
$740$	−2000.58	−0.0993821
$741$	4543.89i	0.225269i
$742$	6340.05i	0.313680i
$743$	− 12299.4i	− 0.607298i	−0.952784	−	0.303649i	$-0.901795\pi$
$743$	− 12299.4i	− 0.607298i	0.952784	−	0.303649i	$-0.0982050\pi$
$744$	13887.1	0.684309
$745$	1640.94i	0.0806974i
$746$	−16163.0	−0.793257
$747$	−38809.3	−1.90088
$748$	0	0
$749$	−1852.43	−0.0903688
$750$	−9414.54	−0.458361
$751$	− 30102.6i	− 1.46266i	−0.682021	−	0.731332i	$-0.738899\pi$
$751$	− 30102.6i	− 1.46266i	0.682021	−	0.731332i	$-0.261101\pi$
$752$	45259.4	2.19474
$753$	40309.4i	1.95081i
$754$	− 1674.45i	− 0.0808753i
$755$	1816.42i	0.0875581i
$756$	−9998.14	−0.480990
$757$	−38826.3	−1.86416	−0.932078	−	0.362257i	$-0.882006\pi$
$757$	−38826.3	−1.86416	−0.932078	+	0.362257i	$0.882006\pi$
$758$	− 40519.2i	− 1.94159i
$759$	− 79996.9i	− 3.82570i
$760$	− 2764.97i	− 0.131968i
$761$	19981.6	0.951815	0.475907	−	0.879495i	$-0.342120\pi$
$761$	19981.6	0.951815	0.475907	+	0.879495i	$0.342120\pi$
$762$	82221.8i	3.90890i
$763$	4792.39	0.227387
$764$	−48227.7	−2.28379
$765$	0	0
$766$	13004.8	0.613424
$767$	5470.14	0.257517
$768$	68644.2i	3.22524i
$769$	−22407.7	−1.05077	−0.525384	−	0.850865i	$-0.676078\pi$
$769$	−22407.7	−1.05077	−0.525384	+	0.850865i	$0.676078\pi$
$770$	− 891.320i	− 0.0417155i
$771$	24517.9i	1.14525i
$772$	39127.0i	1.82411i
$773$	6902.77	0.321184	0.160592	−	0.987021i	$-0.448660\pi$
$773$	6902.77	0.321184	0.160592	+	0.987021i	$0.448660\pi$
$774$	62635.4	2.90876
$775$	4336.54i	0.200997i
$776$	17807.3i	0.823768i
$777$	− 4218.89i	− 0.194790i
$778$	26039.8	1.19996
$779$	− 1191.17i	− 0.0547856i
$780$	1048.31	0.0481225
$781$	35099.9	1.60816
$782$	0	0
$783$	−6238.62	−0.284738
$784$	32049.3	1.45997
$785$	232.928i	0.0105905i
$786$	17348.3	0.787270
$787$	22185.9i	1.00488i	0.864611	+	0.502442i	$0.167565\pi$
$787$	22185.9i	1.00488i	−0.864611	+	0.502442i	$0.832435\pi$
$788$	− 22016.3i	− 0.995301i
$789$	45898.1i	2.07099i
$790$	4814.50	0.216826
$791$	3869.27	0.173926
$792$	110197.i	4.94405i
$793$	− 2742.74i	− 0.122822i
$794$	− 25914.2i	− 1.15826i
$795$	−2476.73	−0.110491
$796$	83067.8i	3.69882i
$797$	16291.1	0.724040	0.362020	−	0.932170i	$-0.382087\pi$
$797$	16291.1	0.724040	0.362020	+	0.932170i	$0.382087\pi$
$798$	10832.6	0.480539
$799$	0	0
$800$	14363.3	0.634775
$801$	−50635.5	−2.23361
$802$	43785.3i	1.92782i
$803$	−10132.9	−0.445309
$804$	− 2260.32i	− 0.0991485i
$805$	609.489i	0.0266853i
$806$	− 1416.12i	− 0.0618867i
$807$	−49046.8	−2.13944
$808$	6182.70	0.269191
$809$	17696.8i	0.769082i	0.923108	+	0.384541i	$0.125640\pi$
$809$	17696.8i	0.769082i	−0.923108	+	0.384541i	$0.874360\pi$
$810$	− 313.882i	− 0.0136157i
$811$	3095.34i	0.134022i	0.997752	+	0.0670111i	$0.0213463\pi$
$811$	3095.34i	0.134022i	−0.997752	+	0.0670111i	$0.978654\pi$
$812$	−2730.93	−0.118026
$813$	− 46318.9i	− 1.99812i
$814$	−34360.2	−1.47951
$815$	−1279.81	−0.0550057
$816$	0	0
$817$	−18466.0	−0.790751
$818$	62131.5	2.65572
$819$	1379.75i	0.0588674i
$820$	−274.811	−0.0117034
$821$	− 12323.5i	− 0.523864i	−0.965086	−	0.261932i	$-0.915640\pi$
$821$	− 12323.5i	− 0.523864i	0.965086	−	0.261932i	$-0.0843597\pi$
$822$	5568.36i	0.236276i
$823$	− 34436.5i	− 1.45854i	−0.684225	−	0.729271i	$-0.739860\pi$
$823$	− 34436.5i	− 1.45854i	0.684225	−	0.729271i	$-0.260140\pi$
$824$	9198.50	0.388889
$825$	−55135.7	−2.32676
$826$	− 13040.8i	− 0.549329i
$827$	18761.6i	0.788880i	0.918922	+	0.394440i	$0.129061\pi$
$827$	18761.6i	0.788880i	−0.918922	+	0.394440i	$0.870939\pi$
$828$	− 139992.i	− 5.87567i
$829$	22423.8	0.939457	0.469728	−	0.882811i	$-0.344352\pi$
$829$	22423.8	0.939457	0.469728	+	0.882811i	$0.344352\pi$
$830$	− 3858.49i	− 0.161362i
$831$	10235.3	0.427265
$832$	1602.13	0.0667596
$833$	0	0
$834$	−88441.1	−3.67202
$835$	444.231	0.0184111
$836$	− 60356.4i	− 2.49697i
$837$	−5276.13	−0.217885
$838$	− 29004.0i	− 1.19562i
$839$	9128.63i	0.375632i	0.982204	+	0.187816i	$0.0601409\pi$
$839$	9128.63i	0.375632i	−0.982204	+	0.187816i	$0.939859\pi$
$840$	− 1345.22i	− 0.0552555i
$841$	22685.0	0.930131
$842$	−9441.58	−0.386435
$843$	− 10146.5i	− 0.414547i
$844$	− 48634.4i	− 1.98349i
$845$	1888.32i	0.0768759i
$846$	−104638.	−4.25240
$847$	− 5390.75i	− 0.218688i
$848$	32198.0	1.30387
$849$	26822.2	1.08426
$850$	0	0
$851$	23495.7	0.946442
$852$	98416.1	3.95737
$853$	− 27204.8i	− 1.09200i	−0.837786	−	0.545999i	$-0.816150\pi$
$853$	− 27204.8i	− 1.09200i	0.837786	−	0.545999i	$-0.183850\pi$
$854$	−6538.68	−0.262001
$855$	2641.12i	0.105643i
$856$	22769.8i	0.909179i
$857$	− 38060.0i	− 1.51704i	−0.651649	−	0.758520i	$-0.725923\pi$
$857$	− 38060.0i	− 1.51704i	0.651649	−	0.758520i	$-0.274077\pi$
$858$	18004.9	0.716405
$859$	33326.2	1.32372	0.661860	−	0.749627i	$-0.269767\pi$
$859$	33326.2	1.32372	0.661860	+	0.749627i	$0.269767\pi$
$860$	4260.24i	0.168922i
$861$	− 579.531i	− 0.0229389i
$862$	422.378i	0.0166894i
$863$	−41724.2	−1.64578	−0.822890	−	0.568201i	$-0.807640\pi$
$863$	−41724.2	−1.64578	−0.822890	+	0.568201i	$0.807640\pi$
$864$	17475.4i	0.688108i
$865$	2294.06	0.0901737
$866$	77223.8	3.03022
$867$	0	0
$868$	−2309.60	−0.0903146
$869$	56569.7	2.20828
$870$	− 1559.42i	− 0.0607694i
$871$	−124.068	−0.00482649
$872$	− 58907.5i	− 2.28768i
$873$	− 17009.6i	− 0.659438i
$874$	60328.6i	2.33483i
$875$	842.801	0.0325621
$876$	−28411.6	−1.09582
$877$	− 49337.3i	− 1.89966i	−0.312767	−	0.949830i	$-0.601256\pi$
$877$	− 49337.3i	− 1.89966i	0.312767	−	0.949830i	$-0.398744\pi$
$878$	− 15423.3i	− 0.592838i
$879$	− 63194.0i	− 2.42489i
$880$	−4526.57	−0.173398
$881$	− 8845.46i	− 0.338265i	−0.985593	−	0.169132i	$-0.945903\pi$
$881$	− 8845.46i	− 0.338265i	0.985593	−	0.169132i	$-0.0540965\pi$
$882$	−74096.8	−2.82876
$883$	14724.2	0.561165	0.280582	−	0.959830i	$-0.409472\pi$
$883$	14724.2	0.561165	0.280582	+	0.959830i	$0.409472\pi$
$884$	0	0
$885$	5094.36	0.193497
$886$	−9023.14	−0.342143
$887$	− 3864.38i	− 0.146283i	−0.997322	−	0.0731415i	$-0.976698\pi$
$887$	− 3864.38i	− 0.146283i	0.997322	−	0.0731415i	$-0.0233025\pi$
$888$	−51858.1	−1.95974
$889$	− 7360.60i	− 0.277690i
$890$	− 5034.28i	− 0.189606i
$891$	− 3688.07i	− 0.138670i
$892$	−81160.9	−3.04649
$893$	30849.1	1.15602
$894$	79023.2i	2.95630i
$895$	1918.10i	0.0716368i
$896$	− 7351.61i	− 0.274107i
$897$	−12311.8	−0.458283
$898$	12577.2i	0.467379i
$899$	−1441.14	−0.0534648
$900$	−96485.6	−3.57354
$901$	0	0
$902$	−4719.92	−0.174231
$903$	−8984.15	−0.331089
$904$	− 47560.6i	− 1.74982i
$905$	−1705.45	−0.0626421
$906$	87473.7i	3.20764i
$907$	− 743.409i	− 0.0272155i	−0.999907	−	0.0136078i	$-0.995668\pi$
$907$	− 743.409i	− 0.0272155i	0.999907	−	0.0136078i	$-0.00433162\pi$
$908$	− 24182.5i	− 0.883839i
$909$	−5905.76	−0.215491
$910$	−137.177	−0.00499713
$911$	16291.0i	0.592475i	0.955114	+	0.296238i	$0.0957320\pi$
$911$	16291.0i	0.592475i	−0.955114	+	0.296238i	$0.904268\pi$
$912$	− 55013.4i	− 1.99745i
$913$	− 45336.8i	− 1.64340i
$914$	−74402.5	−2.69258
$915$	− 2554.33i	− 0.0922879i
$916$	−15500.6	−0.559122
$917$	−1553.04	−0.0559280
$918$	0	0
$919$	−6188.99	−0.222150	−0.111075	−	0.993812i	$-0.535429\pi$
$919$	−6188.99	−0.222150	−0.111075	+	0.993812i	$0.535429\pi$
$920$	7491.78	0.268474
$921$	55390.5i	1.98174i
$922$	89311.6	3.19015
$923$	− 5402.00i	− 0.192643i
$924$	− 29364.8i	− 1.04549i
$925$	− 16193.8i	− 0.575620i
$926$	93033.0	3.30157
$927$	−8786.47	−0.311311
$928$	4773.30i	0.168848i
$929$	− 31661.7i	− 1.11818i	−0.829108	−	0.559089i	$-0.811151\pi$
$929$	− 31661.7i	− 1.11818i	0.829108	−	0.559089i	$-0.188849\pi$
$930$	− 1318.84i	− 0.0465015i
$931$	21845.0	0.769003
$932$	− 20724.3i	− 0.728376i
$933$	75734.8	2.65750
$934$	−37273.6	−1.30581
$935$	0	0
$936$	16959.8	0.592251
$937$	−35010.5	−1.22064	−0.610322	−	0.792153i	$-0.708960\pi$
$937$	−35010.5	−1.22064	−0.610322	+	0.792153i	$0.708960\pi$
$938$	295.776i	0.0102958i
$939$	−22279.2	−0.774286
$940$	− 7117.12i	− 0.246952i
$941$	− 45625.8i	− 1.58061i	−0.612711	−	0.790307i	$-0.709921\pi$
$941$	− 45625.8i	− 1.58061i	0.612711	−	0.790307i	$-0.290079\pi$
$942$	11217.2i	0.387977i
$943$	3227.51	0.111455
$944$	−66227.5	−2.28339
$945$	511.092i	0.0175934i
$946$	73170.2i	2.51477i
$947$	21508.4i	0.738044i	0.929421	+	0.369022i	$0.120307\pi$
$947$	21508.4i	0.738044i	−0.929421	+	0.369022i	$0.879693\pi$
$948$	158615.	5.43416
$949$	1559.50i	0.0533439i
$950$	41579.8	1.42003
$951$	36177.4	1.23358
$952$	0	0
$953$	35686.7	1.21302	0.606509	−	0.795076i	$-0.292569\pi$
$953$	35686.7	1.21302	0.606509	+	0.795076i	$0.292569\pi$
$954$	−74440.5	−2.52631
$955$	2465.34i	0.0835355i
$956$	85744.0	2.90079
$957$	− 18323.0i	− 0.618912i
$958$	93357.8i	3.14849i
$959$	− 498.486i	− 0.0167851i
$960$	1492.07	0.0501630
$961$	28572.2	0.959088
$962$	5288.17i	0.177232i
$963$	− 21749.9i	− 0.727810i
$964$	116133.i	3.88006i
$965$	2000.12	0.0667215
$966$	29351.3i	0.977600i
$967$	3731.33	0.124086	0.0620432	−	0.998073i	$-0.480238\pi$
$967$	3731.33	0.124086	0.0620432	+	0.998073i	$0.480238\pi$
$968$	−66262.5	−2.20016
$969$	0	0
$970$	1691.13	0.0559782
$971$	−17645.1	−0.583171	−0.291585	−	0.956545i	$-0.594183\pi$
$971$	−17645.1	−0.583171	−0.291585	+	0.956545i	$0.594183\pi$
$972$	60358.3i	1.99176i
$973$	7917.35	0.260862
$974$	51348.7i	1.68924i
$975$	8485.59i	0.278725i
$976$	33206.7i	1.08906i
$977$	−24941.2	−0.816723	−0.408362	−	0.912820i	$-0.633900\pi$
$977$	−24941.2	−0.816723	−0.408362	+	0.912820i	$0.633900\pi$
$978$	−61631.8	−2.01510
$979$	− 59152.1i	− 1.93106i
$980$	− 5039.81i	− 0.164276i
$981$	56268.9i	1.83132i
$982$	6277.85	0.204006
$983$	22506.2i	0.730252i	0.930958	+	0.365126i	$0.118974\pi$
$983$	22506.2i	0.730252i	−0.930958	+	0.365126i	$0.881026\pi$
$984$	−7123.53	−0.230782
$985$	−1125.44	−0.0364057
$986$	0	0
$987$	15008.8	0.484029
$988$	−9289.07	−0.299114
$989$	− 50034.2i	− 1.60869i
$990$	10465.3	0.335967
$991$	− 32694.1i	− 1.04799i	−0.851720	−	0.523997i	$-0.824440\pi$
$991$	− 32694.1i	− 1.04799i	0.851720	−	0.523997i	$-0.175560\pi$
$992$	4036.88i	0.129205i
$993$	8410.08i	0.268767i
$994$	−12878.3	−0.410941
$995$	4246.32	0.135294
$996$	− 127119.i	− 4.04410i
$997$	18248.8i	0.579686i	0.957074	+	0.289843i	$0.0936030\pi$
$997$	18248.8i	0.579686i	−0.957074	+	0.289843i	$0.906397\pi$
$998$	352.428i	0.0111783i
$999$	19702.5	0.623983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.b.b.288.5		6
17.4	even	4		289.4.a.b.1.1		3
17.13	even	4		17.4.a.b.1.1	✓	3
17.16	even	2	inner	289.4.b.b.288.6		6
51.47	odd	4		153.4.a.g.1.3		3
68.47	odd	4		272.4.a.h.1.1		3
85.13	odd	4		425.4.b.f.324.6		6
85.47	odd	4		425.4.b.f.324.1		6
85.64	even	4		425.4.a.g.1.3		3
119.13	odd	4		833.4.a.d.1.1		3
136.13	even	4		1088.4.a.v.1.1		3
136.115	odd	4		1088.4.a.x.1.3		3
187.98	odd	4		2057.4.a.e.1.3		3
204.47	even	4		2448.4.a.bi.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.a.b.1.1	✓	3	17.13	even	4
153.4.a.g.1.3		3	51.47	odd	4
272.4.a.h.1.1		3	68.47	odd	4
289.4.a.b.1.1		3	17.4	even	4
289.4.b.b.288.5		6	1.1	even	1	trivial
289.4.b.b.288.6		6	17.16	even	2	inner
425.4.a.g.1.3		3	85.64	even	4
425.4.b.f.324.1		6	85.47	odd	4
425.4.b.f.324.6		6	85.13	odd	4
833.4.a.d.1.1		3	119.13	odd	4
1088.4.a.v.1.1		3	136.13	even	4
1088.4.a.x.1.3		3	136.115	odd	4
2057.4.a.e.1.3		3	187.98	odd	4
2448.4.a.bi.1.2		3	204.47	even	4

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)

\(f(q)\)	\(=\)	\(q+5.03251 q^{2} -8.47535i q^{3} +17.3261 q^{4} -0.885690i q^{5} -42.6523i q^{6} +3.81828i q^{7} +46.9339 q^{8} -44.8316 q^{9} +O(q^{10})\)	\(q+5.03251 q^{2} -8.47535i q^{3} +17.3261 q^{4} -0.885690i q^{5} -42.6523i q^{6} +3.81828i q^{7} +46.9339 q^{8} -44.8316 q^{9} -4.45724i q^{10} -52.3720i q^{11} -146.845i q^{12} -8.06025 q^{13} +19.2156i q^{14} -7.50653 q^{15} +97.5862 q^{16} -225.616 q^{18} +66.5154 q^{19} -15.3456i q^{20} +32.3613 q^{21} -263.563i q^{22} +180.226i q^{23} -397.782i q^{24} +124.216 q^{25} -40.5633 q^{26} +151.129i q^{27} +66.1562i q^{28} +41.2800i q^{29} -37.7767 q^{30} +34.9114i q^{31} +115.632 q^{32} -443.871 q^{33} +3.38182 q^{35} -776.759 q^{36} -130.368i q^{37} +334.739 q^{38} +68.3134i q^{39} -41.5689i q^{40} -17.9081i q^{41} +162.859 q^{42} -277.620 q^{43} -907.405i q^{44} +39.7069i q^{45} +906.987i q^{46} +463.789 q^{47} -827.078i q^{48} +328.421 q^{49} +625.116 q^{50} -139.653 q^{52} +329.944 q^{53} +760.560i q^{54} -46.3853 q^{55} +179.207i q^{56} -563.741i q^{57} +207.742i q^{58} -678.656 q^{59} -130.059 q^{60} +340.280i q^{61} +175.692i q^{62} -171.180i q^{63} -198.770 q^{64} +7.13888i q^{65} -2233.79 q^{66} +15.3925 q^{67} +1527.48 q^{69} +17.0190 q^{70} +670.203i q^{71} -2104.12 q^{72} -193.480i q^{73} -656.080i q^{74} -1052.77i q^{75} +1152.46 q^{76} +199.971 q^{77} +343.788i q^{78} +1080.15i q^{79} -86.4311i q^{80} +70.4207 q^{81} -90.1229i q^{82} +865.668 q^{83} +560.697 q^{84} -1397.13 q^{86} +349.863 q^{87} -2458.02i q^{88} +1129.46 q^{89} +199.825i q^{90} -30.7763i q^{91} +3122.61i q^{92} +295.886 q^{93} +2334.02 q^{94} -58.9120i q^{95} -980.023i q^{96} +379.412i q^{97} +1652.78 q^{98} +2347.92i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} + 50 q^{4} + 78 q^{8} - 118 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 + 50 * q^4 + 78 * q^8 - 118 * q^9	\( 6 q - 2 q^{2} + 50 q^{4} + 78 q^{8} - 118 q^{9} + 60 q^{13} - 216 q^{15} + 274 q^{16} - 206 q^{18} - 160 q^{19} - 384 q^{21} + 446 q^{25} - 52 q^{26} + 800 q^{30} + 142 q^{32} - 664 q^{33} - 664 q^{35} - 2626 q^{36} + 1448 q^{38} + 2256 q^{42} - 1112 q^{43} + 1280 q^{47} + 538 q^{49} + 1094 q^{50} - 1548 q^{52} - 604 q^{53} + 152 q^{55} - 1272 q^{59} - 2656 q^{60} - 1838 q^{64} - 4936 q^{66} + 2016 q^{67} + 1152 q^{69} + 3008 q^{70} - 1854 q^{72} + 1816 q^{76} + 1008 q^{77} - 1010 q^{81} + 4792 q^{83} - 4080 q^{84} - 2528 q^{86} - 2856 q^{87} - 340 q^{89} - 1264 q^{93} + 4032 q^{94} + 5714 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 + 50 * q^4 + 78 * q^8 - 118 * q^9 + 60 * q^13 - 216 * q^15 + 274 * q^16 - 206 * q^18 - 160 * q^19 - 384 * q^21 + 446 * q^25 - 52 * q^26 + 800 * q^30 + 142 * q^32 - 664 * q^33 - 664 * q^35 - 2626 * q^36 + 1448 * q^38 + 2256 * q^42 - 1112 * q^43 + 1280 * q^47 + 538 * q^49 + 1094 * q^50 - 1548 * q^52 - 604 * q^53 + 152 * q^55 - 1272 * q^59 - 2656 * q^60 - 1838 * q^64 - 4936 * q^66 + 2016 * q^67 + 1152 * q^69 + 3008 * q^70 - 1854 * q^72 + 1816 * q^76 + 1008 * q^77 - 1010 * q^81 + 4792 * q^83 - 4080 * q^84 - 2528 * q^86 - 2856 * q^87 - 340 * q^89 - 1264 * q^93 + 4032 * q^94 + 5714 * q^98

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