LMFDB - Embedded newform 289.4.b.b.288.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("289.288");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.0515519917$
Analytic rank:	$0$
Dimension:	$6$
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			288.4
Root			$-1.93854 + 1.93854i$ of defining polynomial
Character	$\chi$	$=$	289.288
Dual form			289.4.b.b.288.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.36122 q^{2} +3.15463i q^{3} -6.14708 q^{4} +3.03171i q^{5} -4.29415i q^{6} +7.94049i q^{7} +19.2573 q^{8} +17.0483 q^{9} +O(q^{10})$	\(q-1.36122 q^{2} +3.15463i q^{3} -6.14708 q^{4} +3.03171i q^{5} -4.29415i q^{6} +7.94049i q^{7} +19.2573 q^{8} +17.0483 q^{9} -4.12682i q^{10} -27.6161i q^{11} -19.3918i q^{12} +58.1117 q^{13} -10.8088i q^{14} -9.56391 q^{15} +22.9632 q^{16} -23.2065 q^{18} -89.1688 q^{19} -18.6361i q^{20} -25.0493 q^{21} +37.5916i q^{22} +115.269i q^{23} +60.7497i q^{24} +115.809 q^{25} -79.1029 q^{26} +138.956i q^{27} -48.8108i q^{28} -128.558i q^{29} +13.0186 q^{30} +273.460i q^{31} -185.316 q^{32} +87.1187 q^{33} -24.0732 q^{35} -104.797 q^{36} -132.351i q^{37} +121.379 q^{38} +183.321i q^{39} +58.3825i q^{40} +470.559i q^{41} +34.0977 q^{42} -352.642 q^{43} +169.758i q^{44} +51.6854i q^{45} -156.907i q^{46} +152.598 q^{47} +72.4403i q^{48} +279.949 q^{49} -157.641 q^{50} -357.217 q^{52} -527.614 q^{53} -189.150i q^{54} +83.7239 q^{55} +152.912i q^{56} -281.295i q^{57} +174.995i q^{58} +292.020 q^{59} +58.7901 q^{60} +53.8962i q^{61} -372.239i q^{62} +135.372i q^{63} +68.5514 q^{64} +176.178i q^{65} -118.588 q^{66} +52.9572 q^{67} -363.632 q^{69} +32.7690 q^{70} +788.400i q^{71} +328.304 q^{72} +295.780i q^{73} +180.159i q^{74} +365.334i q^{75} +548.127 q^{76} +219.285 q^{77} -249.541i q^{78} +720.325i q^{79} +69.6175i q^{80} +21.9487 q^{81} -640.535i q^{82} +116.051 q^{83} +153.980 q^{84} +480.024 q^{86} +405.552 q^{87} -531.812i q^{88} -813.329 q^{89} -70.3553i q^{90} +461.435i q^{91} -708.569i q^{92} -862.664 q^{93} -207.720 q^{94} -270.334i q^{95} -584.605i q^{96} +794.693i q^{97} -381.072 q^{98} -470.808i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.36122	−0.481264	−0.240632	−	0.970616i	$-0.577355\pi$
$2$	−1.36122	−0.481264	−0.240632	+	0.970616i	$0.577355\pi$
$3$	3.15463i	0.607109i	0.952814	+	0.303555i	$0.0981735\pi$
$3$	3.15463i	0.607109i	−0.952814	+	0.303555i	$0.901827\pi$
$4$	−6.14708	−0.768385
$5$	3.03171i	0.271164i	0.990766	+	0.135582i	$0.0432904\pi$
$5$	3.03171i	0.271164i	−0.990766	+	0.135582i	$0.956710\pi$
$6$	− 4.29415i	− 0.292180i
$7$	7.94049i	0.428746i	0.976752	+	0.214373i	$0.0687708\pi$
$7$	7.94049i	0.428746i	−0.976752	+	0.214373i	$0.931229\pi$
$8$	19.2573	0.851061
$9$	17.0483	0.631419
$10$	− 4.12682i	− 0.130502i
$11$	− 27.6161i	− 0.756961i	−0.925609	−	0.378481i	$-0.876447\pi$
$11$	− 27.6161i	− 0.756961i	0.925609	−	0.378481i	$-0.123553\pi$
$12$	− 19.3918i	− 0.466493i
$13$	58.1117	1.23979	0.619896	−	0.784684i	$-0.287175\pi$
$13$	58.1117	1.23979	0.619896	+	0.784684i	$0.287175\pi$
$14$	− 10.8088i	− 0.206340i
$15$	−9.56391	−0.164626
$16$	22.9632	0.358799
$17$	0	0
$17$	0	0
$18$	−23.2065	−0.303879
$19$	−89.1688	−1.07667	−0.538335	−	0.842731i	$-0.680946\pi$
$19$	−89.1688	−1.07667	−0.538335	+	0.842731i	$0.680946\pi$
$20$	− 18.6361i	− 0.208358i
$21$	−25.0493	−0.260296
$22$	37.5916i	0.364298i
$23$	115.269i	1.04501i	0.852635	+	0.522507i	$0.175003\pi$
$23$	115.269i	1.04501i	−0.852635	+	0.522507i	$0.824997\pi$
$24$	60.7497i	0.516687i
$25$	115.809	0.926470
$26$	−79.1029	−0.596668
$27$	138.956i	0.990449i
$28$	− 48.8108i	− 0.329442i
$29$	− 128.558i	− 0.823191i	−0.911367	−	0.411596i	$-0.864972\pi$
$29$	− 128.558i	− 0.823191i	0.911367	−	0.411596i	$-0.135028\pi$
$30$	13.0186	0.0792287
$31$	273.460i	1.58435i	0.610295	+	0.792174i	$0.291051\pi$
$31$	273.460i	1.58435i	−0.610295	+	0.792174i	$0.708949\pi$
$32$	−185.316	−1.02374
$33$	87.1187	0.459558
$34$	0	0
$35$	−24.0732	−0.116260
$36$	−104.797	−0.485172
$37$	− 132.351i	− 0.588063i	−0.955796	−	0.294031i	$-0.905003\pi$
$37$	− 132.351i	− 0.588063i	0.955796	−	0.294031i	$-0.0949970\pi$
$38$	121.379	0.518163
$39$	183.321i	0.752689i
$40$	58.3825i	0.230777i
$41$	470.559i	1.79241i	0.443636	+	0.896207i	$0.353688\pi$
$41$	470.559i	1.79241i	−0.443636	+	0.896207i	$0.646312\pi$
$42$	34.0977	0.125271
$43$	−352.642	−1.25064	−0.625318	−	0.780370i	$-0.715031\pi$
$43$	−352.642	−1.25064	−0.625318	+	0.780370i	$0.715031\pi$
$44$	169.758i	0.581637i
$45$	51.6854i	0.171218i
$46$	− 156.907i	− 0.502928i
$47$	152.598	0.473589	0.236795	−	0.971560i	$-0.423903\pi$
$47$	152.598	0.473589	0.236795	+	0.971560i	$0.423903\pi$
$48$	72.4403i	0.217830i
$49$	279.949	0.816177
$50$	−157.641	−0.445877
$51$	0	0
$52$	−357.217	−0.952637
$53$	−527.614	−1.36742	−0.683711	−	0.729753i	$-0.739635\pi$
$53$	−527.614	−1.36742	−0.683711	+	0.729753i	$0.739635\pi$
$54$	− 189.150i	− 0.476668i
$55$	83.7239	0.205261
$56$	152.912i	0.364889i
$57$	− 281.295i	− 0.653656i
$58$	174.995i	0.396173i
$59$	292.020	0.644368	0.322184	−	0.946677i	$-0.395583\pi$
$59$	292.020	0.644368	0.322184	+	0.946677i	$0.395583\pi$
$60$	58.7901	0.126496
$61$	53.8962i	0.113126i	0.998399	+	0.0565632i	$0.0180142\pi$
$61$	53.8962i	0.113126i	−0.998399	+	0.0565632i	$0.981986\pi$
$62$	− 372.239i	− 0.762490i
$63$	135.372i	0.270718i
$64$	68.5514	0.133889
$65$	176.178i	0.336187i
$66$	−118.588	−0.221169
$67$	52.9572	0.0965635	0.0482817	−	0.998834i	$-0.484625\pi$
$67$	52.9572	0.0965635	0.0482817	+	0.998834i	$0.484625\pi$
$68$	0	0
$69$	−363.632	−0.634437
$70$	32.7690	0.0559520
$71$	788.400i	1.31783i	0.752218	+	0.658915i	$0.228984\pi$
$71$	788.400i	1.31783i	−0.752218	+	0.658915i	$0.771016\pi$
$72$	328.304	0.537375
$73$	295.780i	0.474224i	0.971482	+	0.237112i	$0.0762009\pi$
$73$	295.780i	0.474224i	−0.971482	+	0.237112i	$0.923799\pi$
$74$	180.159i	0.283014i
$75$	365.334i	0.562468i
$76$	548.127	0.827296
$77$	219.285	0.324544
$78$	− 249.541i	− 0.362242i
$79$	720.325i	1.02586i	0.858430	+	0.512930i	$0.171440\pi$
$79$	720.325i	1.02586i	−0.858430	+	0.512930i	$0.828560\pi$
$80$	69.6175i	0.0972934i
$81$	21.9487	0.0301079
$82$	− 640.535i	− 0.862625i
$83$	116.051	0.153473	0.0767363	−	0.997051i	$-0.475550\pi$
$83$	116.051	0.153473	0.0767363	+	0.997051i	$0.475550\pi$
$84$	153.980	0.200007
$85$	0	0
$86$	480.024	0.601887
$87$	405.552	0.499767
$88$	− 531.812i	− 0.644220i
$89$	−813.329	−0.968682	−0.484341	−	0.874879i	$-0.660941\pi$
$89$	−813.329	−0.968682	−0.484341	+	0.874879i	$0.660941\pi$
$90$	− 70.3553i	− 0.0824011i
$91$	461.435i	0.531556i
$92$	− 708.569i	− 0.802972i
$93$	−862.664	−0.961872
$94$	−207.720	−0.227922
$95$	− 270.334i	− 0.291954i
$96$	− 584.605i	− 0.621521i
$97$	794.693i	0.831844i	0.909400	+	0.415922i	$0.136541\pi$
$97$	794.693i	0.831844i	−0.909400	+	0.415922i	$0.863459\pi$
$98$	−381.072	−0.392797
$99$	− 470.808i	− 0.477959i
$100$	−711.885	−0.711885
$101$	265.513	0.261579	0.130790	−	0.991410i	$-0.458249\pi$
$101$	265.513	0.261579	0.130790	+	0.991410i	$0.458249\pi$
$102$	0	0
$103$	523.107	0.500420	0.250210	−	0.968192i	$-0.419500\pi$
$103$	523.107	0.500420	0.250210	+	0.968192i	$0.419500\pi$
$104$	1119.07	1.05514
$105$	− 75.9421i	− 0.0705828i
$106$	718.199	0.658091
$107$	− 986.039i	− 0.890878i	−0.895312	−	0.445439i	$-0.853048\pi$
$107$	− 986.039i	− 0.890878i	0.895312	−	0.445439i	$-0.146952\pi$
$108$	− 854.174i	− 0.761046i
$109$	− 1814.39i	− 1.59438i	−0.603732	−	0.797188i	$-0.706320\pi$
$109$	− 1814.39i	− 1.59438i	0.603732	−	0.797188i	$-0.293680\pi$
$110$	−113.967	−0.0987846
$111$	417.518	0.357018
$112$	182.339i	0.153834i
$113$	707.339i	0.588857i	0.955673	+	0.294429i	$0.0951293\pi$
$113$	707.339i	0.588857i	−0.955673	+	0.294429i	$0.904871\pi$
$114$	382.904i	0.314581i
$115$	−349.463	−0.283370
$116$	790.253i	0.632527i
$117$	990.706	0.782827
$118$	−397.503	−0.310112
$119$	0	0
$120$	−184.175	−0.140107
$121$	568.350	0.427010
$122$	− 73.3647i	− 0.0544437i
$123$	−1484.44	−1.08819
$124$	− 1680.98i	− 1.21739i
$125$	730.061i	0.522389i
$126$	− 184.271i	− 0.130287i
$127$	−2648.18	−1.85030	−0.925151	−	0.379600i	$-0.876062\pi$
$127$	−2648.18	−1.85030	−0.925151	+	0.379600i	$0.876062\pi$
$128$	1389.22	0.959302
$129$	− 1112.46i	− 0.759273i
$130$	− 239.817i	− 0.161795i
$131$	− 1979.08i	− 1.31995i	−0.751289	−	0.659974i	$-0.770567\pi$
$131$	− 1979.08i	− 1.31995i	0.751289	−	0.659974i	$-0.229433\pi$
$132$	−535.525	−0.353117
$133$	− 708.044i	− 0.461618i
$134$	−72.0865	−0.0464726
$135$	−421.274	−0.268574
$136$	0	0
$137$	3141.92	1.95936	0.979679	−	0.200570i	$-0.0642794\pi$
$137$	3141.92	1.95936	0.979679	+	0.200570i	$0.0642794\pi$
$138$	494.984	0.305332
$139$	1468.07i	0.895830i	0.894076	+	0.447915i	$0.147833\pi$
$139$	1468.07i	0.895830i	−0.894076	+	0.447915i	$0.852167\pi$
$140$	147.980	0.0893327
$141$	481.390i	0.287520i
$142$	− 1073.19i	− 0.634224i
$143$	− 1604.82i	− 0.938474i
$144$	391.483	0.226553
$145$	389.749	0.223220
$146$	− 402.621i	− 0.228227i
$147$	883.135i	0.495508i
$148$	813.570i	0.451858i
$149$	−286.027	−0.157263	−0.0786316	−	0.996904i	$-0.525055\pi$
$149$	−286.027	−0.157263	−0.0786316	+	0.996904i	$0.525055\pi$
$150$	− 497.300i	− 0.270696i
$151$	669.626	0.360883	0.180442	−	0.983586i	$-0.442247\pi$
$151$	669.626	0.360883	0.180442	+	0.983586i	$0.442247\pi$
$152$	−1717.15	−0.916311
$153$	0	0
$154$	−298.496	−0.156191
$155$	−829.049	−0.429618
$156$	− 1126.89i	− 0.578354i
$157$	720.809	0.366413	0.183206	−	0.983074i	$-0.441352\pi$
$157$	720.809	0.366413	0.183206	+	0.983074i	$0.441352\pi$
$158$	− 980.522i	− 0.493710i
$159$	− 1664.43i	− 0.830174i
$160$	− 561.825i	− 0.277601i
$161$	−915.294	−0.448045
$162$	−29.8770	−0.0144899
$163$	676.599i	0.325125i	0.986698	+	0.162562i	$0.0519759\pi$
$163$	676.599i	0.325125i	−0.986698	+	0.162562i	$0.948024\pi$
$164$	− 2892.56i	− 1.37726i
$165$	264.118i	0.124616i
$166$	−157.971	−0.0738609
$167$	− 2835.67i	− 1.31396i	−0.753909	−	0.656979i	$-0.771834\pi$
$167$	− 2835.67i	− 1.31396i	0.753909	−	0.656979i	$-0.228166\pi$
$168$	−482.382	−0.221527
$169$	1179.97	0.537083
$170$	0	0
$171$	−1520.18	−0.679829
$172$	2167.72	0.960970
$173$	− 177.314i	− 0.0779243i	−0.999241	−	0.0389621i	$-0.987595\pi$
$173$	− 177.314i	− 0.0779243i	0.999241	−	0.0389621i	$-0.0124052\pi$
$174$	−552.046	−0.240520
$175$	919.578i	0.397220i
$176$	− 634.153i	− 0.271597i
$177$	921.214i	0.391202i
$178$	1107.12	0.466192
$179$	1023.76	0.427483	0.213741	−	0.976890i	$-0.431435\pi$
$179$	1023.76	0.427483	0.213741	+	0.976890i	$0.431435\pi$
$180$	− 317.714i	− 0.131561i
$181$	3450.21i	1.41686i	0.705779	+	0.708432i	$0.250597\pi$
$181$	3450.21i	1.41686i	−0.705779	+	0.708432i	$0.749403\pi$
$182$	− 628.116i	− 0.255819i
$183$	−170.023	−0.0686800
$184$	2219.78i	0.889370i
$185$	401.248	0.159461
$186$	1174.28	0.462915
$187$	0	0
$188$	−938.031	−0.363899
$189$	−1103.38	−0.424651
$190$	367.984i	0.140507i
$191$	−490.894	−0.185968	−0.0929839	−	0.995668i	$-0.529640\pi$
$191$	−490.894	−0.185968	−0.0929839	+	0.995668i	$0.529640\pi$
$192$	216.254i	0.0812855i
$193$	3548.80i	1.32357i	0.749696	+	0.661783i	$0.230200\pi$
$193$	3548.80i	1.32357i	−0.749696	+	0.661783i	$0.769800\pi$
$194$	− 1081.75i	− 0.400337i
$195$	−555.775	−0.204102
$196$	−1720.87	−0.627138
$197$	− 1363.15i	− 0.492996i	−0.969143	−	0.246498i	$-0.920720\pi$
$197$	− 1363.15i	− 0.492996i	0.969143	−	0.246498i	$-0.0792799\pi$
$198$	640.874i	0.230025i
$199$	3737.46i	1.33137i	0.746235	+	0.665683i	$0.231860\pi$
$199$	3737.46i	1.33137i	−0.746235	+	0.665683i	$0.768140\pi$
$200$	2230.16	0.788482
$201$	167.060i	0.0586246i
$202$	−361.422	−0.125889
$203$	1020.81	0.352940
$204$	0	0
$205$	−1426.60	−0.486038
$206$	−712.064	−0.240834
$207$	1965.15i	0.659841i
$208$	1334.43	0.444836
$209$	2462.50i	0.814997i
$210$	103.374i	0.0339690i
$211$	5266.12i	1.71817i	0.511829	+	0.859087i	$0.328968\pi$
$211$	5266.12i	1.71817i	−0.511829	+	0.859087i	$0.671032\pi$
$212$	3243.28	1.05071
$213$	−2487.11	−0.800066
$214$	1342.22i	0.428748i
$215$	− 1069.11i	− 0.339128i
$216$	2675.92i	0.842932i
$217$	−2171.40	−0.679283
$218$	2469.78i	0.767316i
$219$	−933.075	−0.287906
$220$	−514.657	−0.157719
$221$	0	0
$222$	−568.334	−0.171820
$223$	−704.546	−0.211569	−0.105785	−	0.994389i	$-0.533735\pi$
$223$	−704.546	−0.211569	−0.105785	+	0.994389i	$0.533735\pi$
$224$	− 1471.50i	− 0.438923i
$225$	1974.34	0.584990
$226$	− 962.845i	− 0.283396i
$227$	2151.26i	0.629006i	0.949256	+	0.314503i	$0.101838\pi$
$227$	2151.26i	0.629006i	−0.949256	+	0.314503i	$0.898162\pi$
$228$	1729.14i	0.502259i
$229$	3916.94	1.13030	0.565149	−	0.824989i	$-0.308819\pi$
$229$	3916.94	1.13030	0.565149	+	0.824989i	$0.308819\pi$
$230$	475.696	0.136376
$231$	691.764i	0.197034i
$232$	− 2475.67i	− 0.700586i
$233$	− 5192.74i	− 1.46003i	−0.683429	−	0.730017i	$-0.739512\pi$
$233$	− 5192.74i	− 1.46003i	0.683429	−	0.730017i	$-0.260488\pi$
$234$	−1348.57	−0.376747
$235$	462.632i	0.128420i
$236$	−1795.07	−0.495123
$237$	−2272.36	−0.622809
$238$	0	0
$239$	334.305	0.0904786	0.0452393	−	0.998976i	$-0.485595\pi$
$239$	334.305	0.0904786	0.0452393	+	0.998976i	$0.485595\pi$
$240$	−219.618	−0.0590677
$241$	− 1918.45i	− 0.512773i	−0.966574	−	0.256386i	$-0.917468\pi$
$241$	− 1918.45i	− 0.512773i	0.966574	−	0.256386i	$-0.0825320\pi$
$242$	−773.651	−0.205505
$243$	3821.06i	1.00873i
$244$	− 331.304i	− 0.0869245i
$245$	848.722i	0.221318i
$246$	2020.65	0.523708
$247$	−5181.75	−1.33485
$248$	5266.09i	1.34838i
$249$	366.097i	0.0931746i
$250$	− 993.775i	− 0.251407i
$251$	7695.71	1.93525	0.967627	−	0.252385i	$-0.0812148\pi$
$251$	7695.71	1.93525	0.967627	+	0.252385i	$0.0812148\pi$
$252$	− 832.141i	− 0.208016i
$253$	3183.29	0.791035
$254$	3604.76	0.890484
$255$	0	0
$256$	−2439.44	−0.595567
$257$	−5335.10	−1.29492	−0.647460	−	0.762099i	$-0.724169\pi$
$257$	−5335.10	−1.29492	−0.647460	+	0.762099i	$0.724169\pi$
$258$	1514.30i	0.365411i
$259$	1050.93	0.252130
$260$	− 1082.98i	− 0.258321i
$261$	− 2191.69i	− 0.519778i
$262$	2693.97i	0.635244i
$263$	−3934.15	−0.922396	−0.461198	−	0.887297i	$-0.652580\pi$
$263$	−3934.15	−0.922396	−0.461198	+	0.887297i	$0.652580\pi$
$264$	1677.67	0.391112
$265$	− 1599.57i	− 0.370795i
$266$	963.804i	0.222160i
$267$	− 2565.75i	− 0.588095i
$268$	−325.532	−0.0741979
$269$	3424.04i	0.776088i	0.921641	+	0.388044i	$0.126849\pi$
$269$	3424.04i	0.776088i	−0.921641	+	0.388044i	$0.873151\pi$
$270$	573.447	0.129255
$271$	549.034	0.123068	0.0615340	−	0.998105i	$-0.480401\pi$
$271$	549.034	0.123068	0.0615340	+	0.998105i	$0.480401\pi$
$272$	0	0
$273$	−1455.66	−0.322712
$274$	−4276.85	−0.942970
$275$	− 3198.19i	− 0.701302i
$276$	2235.27	0.487492
$277$	5203.65i	1.12873i	0.825527	+	0.564363i	$0.190878\pi$
$277$	5203.65i	1.12873i	−0.825527	+	0.564363i	$0.809122\pi$
$278$	− 1998.37i	− 0.431131i
$279$	4662.02i	1.00039i
$280$	−463.585	−0.0989447
$281$	1986.73	0.421774	0.210887	−	0.977510i	$-0.432365\pi$
$281$	1986.73	0.421774	0.210887	+	0.977510i	$0.432365\pi$
$282$	− 655.279i	− 0.138373i
$283$	− 753.696i	− 0.158313i	−0.996862	−	0.0791565i	$-0.974777\pi$
$283$	− 753.696i	− 0.158313i	0.996862	−	0.0791565i	$-0.0252227\pi$
$284$	− 4846.36i	− 1.01260i
$285$	852.803	0.177248
$286$	2184.51i	0.451654i
$287$	−3736.47	−0.768490
$288$	−3159.33	−0.646407
$289$	0	0
$290$	−530.534	−0.107428
$291$	−2506.96	−0.505020
$292$	− 1818.18i	− 0.364387i
$293$	−7202.22	−1.43603	−0.718017	−	0.696025i	$-0.754950\pi$
$293$	−7202.22	−1.43603	−0.718017	+	0.696025i	$0.754950\pi$
$294$	− 1202.14i	− 0.238471i
$295$	885.318i	0.174729i
$296$	− 2548.72i	− 0.500477i
$297$	3837.43	0.749731
$298$	389.345	0.0756852
$299$	6698.50i	1.29560i
$300$	− 2245.74i	− 0.432192i
$301$	− 2800.15i	− 0.536205i
$302$	−911.509	−0.173680
$303$	837.595i	0.158807i
$304$	−2047.60	−0.386308
$305$	−163.398	−0.0306758
$306$	0	0
$307$	2425.71	0.450953	0.225477	−	0.974249i	$-0.427606\pi$
$307$	2425.71	0.450953	0.225477	+	0.974249i	$0.427606\pi$
$308$	−1347.96	−0.249375
$309$	1650.21i	0.303809i
$310$	1128.52	0.206760
$311$	− 9544.94i	− 1.74033i	−0.492757	−	0.870167i	$-0.664011\pi$
$311$	− 9544.94i	− 1.74033i	0.492757	−	0.870167i	$-0.335989\pi$
$312$	3530.27i	0.640584i
$313$	− 588.379i	− 0.106253i	−0.998588	−	0.0531264i	$-0.983081\pi$
$313$	− 588.379i	− 0.106253i	0.998588	−	0.0531264i	$-0.0169186\pi$
$314$	−981.180	−0.176341
$315$	−410.407	−0.0734090
$316$	− 4427.89i	− 0.788255i
$317$	− 7653.31i	− 1.35600i	−0.735061	−	0.678001i	$-0.762846\pi$
$317$	− 7653.31i	− 1.35600i	0.735061	−	0.678001i	$-0.237154\pi$
$318$	2265.65i	0.399533i
$319$	−3550.26	−0.623124
$320$	207.828i	0.0363060i
$321$	3110.59	0.540860
$322$	1245.92	0.215628
$323$	0	0
$324$	−134.920	−0.0231345
$325$	6729.85	1.14863
$326$	− 921.001i	− 0.156471i
$327$	5723.73	0.967960
$328$	9061.70i	1.52545i
$329$	1211.70i	0.203050i
$330$	− 359.523i	− 0.0599730i
$331$	−752.266	−0.124919	−0.0624597	−	0.998047i	$-0.519894\pi$
$331$	−752.266	−0.124919	−0.0624597	+	0.998047i	$0.519894\pi$
$332$	−713.373	−0.117926
$333$	− 2256.36i	− 0.371314i
$334$	3859.98i	0.632361i
$335$	160.551i	0.0261845i
$336$	−575.211	−0.0933939
$337$	− 1968.57i	− 0.318204i	−0.987262	−	0.159102i	$-0.949140\pi$
$337$	− 1968.57i	− 0.318204i	0.987262	−	0.159102i	$-0.0508598\pi$
$338$	−1606.20	−0.258479
$339$	−2231.39	−0.357501
$340$	0	0
$341$	7551.89	1.19929
$342$	2069.30	0.327178
$343$	4946.52i	0.778678i
$344$	−6790.93	−1.06437
$345$	− 1102.43i	− 0.172037i
$346$	241.363i	0.0375022i
$347$	− 3983.10i	− 0.616207i	−0.951353	−	0.308104i	$-0.900306\pi$
$347$	− 3983.10i	− 0.616207i	0.951353	−	0.308104i	$-0.0996944\pi$
$348$	−2492.96	−0.384013
$349$	−1495.61	−0.229393	−0.114697	−	0.993401i	$-0.536590\pi$
$349$	−1495.61	−0.229393	−0.114697	+	0.993401i	$0.536590\pi$
$350$	− 1251.75i	− 0.191168i
$351$	8074.98i	1.22795i
$352$	5117.72i	0.774930i
$353$	6482.49	0.977417	0.488708	−	0.872447i	$-0.337468\pi$
$353$	6482.49	0.977417	0.488708	+	0.872447i	$0.337468\pi$
$354$	− 1253.98i	− 0.188272i
$355$	−2390.20	−0.357348
$356$	4999.59	0.744320
$357$	0	0
$358$	−1393.56	−0.205732
$359$	4943.42	0.726751	0.363376	−	0.931643i	$-0.381624\pi$
$359$	4943.42	0.726751	0.363376	+	0.931643i	$0.381624\pi$
$360$	995.322i	0.145717i
$361$	1092.08	0.159218
$362$	− 4696.50i	− 0.681886i
$363$	1792.94i	0.259242i
$364$	− 2836.48i	− 0.408439i
$365$	−896.717	−0.128593
$366$	231.439	0.0330533
$367$	14.8871i	0.00211743i	0.999999	+	0.00105872i	$0.000337000\pi$
$367$	14.8871i	0.00211743i	−0.999999	+	0.00105872i	$0.999663\pi$
$368$	2646.95i	0.374950i
$369$	8022.23i	1.13176i
$370$	−546.188	−0.0767431
$371$	− 4189.51i	− 0.586276i
$372$	5302.86	0.739088
$373$	1923.18	0.266966	0.133483	−	0.991051i	$-0.457384\pi$
$373$	1923.18	0.266966	0.133483	+	0.991051i	$0.457384\pi$
$374$	0	0
$375$	−2303.07	−0.317147
$376$	2938.63	0.403053
$377$	− 7470.70i	− 1.02059i
$378$	1501.94	0.204369
$379$	− 9592.87i	− 1.30014i	−0.759875	−	0.650069i	$-0.774740\pi$
$379$	− 9592.87i	− 1.30014i	0.759875	−	0.650069i	$-0.225260\pi$
$380$	1661.76i	0.224333i
$381$	− 8354.04i	− 1.12333i
$382$	668.215	0.0894996
$383$	9083.77	1.21190	0.605951	−	0.795502i	$-0.292793\pi$
$383$	9083.77	1.21190	0.605951	+	0.795502i	$0.292793\pi$
$384$	4382.47i	0.582401i
$385$	664.809i	0.0880046i
$386$	− 4830.70i	− 0.636985i
$387$	−6011.95	−0.789675
$388$	− 4885.04i	− 0.639176i
$389$	1143.78	0.149079	0.0745396	−	0.997218i	$-0.476251\pi$
$389$	1143.78	0.149079	0.0745396	+	0.997218i	$0.476251\pi$
$390$	756.533	0.0982271
$391$	0	0
$392$	5391.06	0.694616
$393$	6243.27	0.801352
$394$	1855.55i	0.237262i
$395$	−2183.81	−0.278176
$396$	2894.09i	0.367256i
$397$	− 10604.5i	− 1.34061i	−0.742084	−	0.670307i	$-0.766162\pi$
$397$	− 10604.5i	− 1.34061i	0.742084	−	0.670307i	$-0.233838\pi$
$398$	− 5087.51i	− 0.640739i
$399$	2233.62	0.280252
$400$	2659.33	0.332417
$401$	− 13785.4i	− 1.71674i	−0.513035	−	0.858368i	$-0.671479\pi$
$401$	− 13785.4i	− 1.71674i	0.513035	−	0.858368i	$-0.328521\pi$
$402$	− 227.406i	− 0.0282139i
$403$	15891.2i	1.96426i
$404$	−1632.13	−0.200993
$405$	66.5420i	0.00816419i
$406$	−1389.55	−0.169857
$407$	−3655.01	−0.445141
$408$	0	0
$409$	−9505.94	−1.14924	−0.574619	−	0.818421i	$-0.694850\pi$
$409$	−9505.94	−1.14924	−0.574619	+	0.818421i	$0.694850\pi$
$410$	1941.91	0.233913
$411$	9911.59i	1.18954i
$412$	−3215.58	−0.384515
$413$	2318.78i	0.276270i
$414$	− 2675.00i	− 0.317558i
$415$	351.832i	0.0416162i
$416$	−10769.1	−1.26922
$417$	−4631.23	−0.543866
$418$	− 3352.00i	− 0.392229i
$419$	− 9680.86i	− 1.12874i	−0.825523	−	0.564369i	$-0.809120\pi$
$419$	− 9680.86i	− 1.12874i	0.825523	−	0.564369i	$-0.190880\pi$
$420$	466.822i	0.0542347i
$421$	−12360.3	−1.43089	−0.715444	−	0.698671i	$-0.753775\pi$
$421$	−12360.3	−1.43089	−0.715444	+	0.698671i	$0.753775\pi$
$422$	− 7168.36i	− 0.826897i
$423$	2601.54	0.299033
$424$	−10160.4	−1.16376
$425$	0	0
$426$	3385.51	0.385043
$427$	−427.962	−0.0485025
$428$	6061.25i	0.684537i
$429$	5062.61	0.569756
$430$	1455.29i	0.163210i
$431$	− 2970.58i	− 0.331990i	−0.986127	−	0.165995i	$-0.946916\pi$
$431$	− 2970.58i	− 0.331990i	0.986127	−	0.165995i	$-0.0530835\pi$
$432$	3190.87i	0.355372i
$433$	−6131.50	−0.680510	−0.340255	−	0.940333i	$-0.610513\pi$
$433$	−6131.50	−0.680510	−0.340255	+	0.940333i	$0.610513\pi$
$434$	2955.76	0.326915
$435$	1229.51i	0.135519i
$436$	11153.2i	1.22509i
$437$	− 10278.4i	− 1.12513i
$438$	1270.12	0.138559
$439$	− 2544.91i	− 0.276679i	−0.990385	−	0.138339i	$-0.955824\pi$
$439$	− 2544.91i	− 0.276679i	0.990385	−	0.138339i	$-0.0441765\pi$
$440$	1612.30	0.174689
$441$	4772.65	0.515349
$442$	0	0
$443$	8529.82	0.914817	0.457408	−	0.889257i	$-0.348778\pi$
$443$	8529.82	0.914817	0.457408	+	0.889257i	$0.348778\pi$
$444$	−2566.51	−0.274327
$445$	− 2465.77i	− 0.262672i
$446$	959.043	0.101821
$447$	− 902.308i	− 0.0954759i
$448$	544.331i	0.0574046i
$449$	− 8855.74i	− 0.930798i	−0.885101	−	0.465399i	$-0.845911\pi$
$449$	− 8855.74i	− 0.930798i	0.885101	−	0.465399i	$-0.154089\pi$
$450$	−2687.52	−0.281535
$451$	12995.0	1.35679
$452$	− 4348.07i	− 0.452469i
$453$	2112.42i	0.219095i
$454$	− 2928.35i	− 0.302718i
$455$	−1398.94	−0.144139
$456$	− 5416.98i	− 0.556301i
$457$	7154.78	0.732356	0.366178	−	0.930545i	$-0.380666\pi$
$457$	7154.78	0.732356	0.366178	+	0.930545i	$0.380666\pi$
$458$	−5331.82	−0.543973
$459$	0	0
$460$	2148.17	0.217737
$461$	7263.06	0.733784	0.366892	−	0.930264i	$-0.380422\pi$
$461$	7263.06	0.733784	0.366892	+	0.930264i	$0.380422\pi$
$462$	− 941.645i	− 0.0948253i
$463$	352.898	0.0354224	0.0177112	−	0.999843i	$-0.494362\pi$
$463$	352.898	0.0354224	0.0177112	+	0.999843i	$0.494362\pi$
$464$	− 2952.09i	− 0.295360i
$465$	− 2615.34i	− 0.260825i
$466$	7068.47i	0.702662i
$467$	−1483.02	−0.146951	−0.0734753	−	0.997297i	$-0.523409\pi$
$467$	−1483.02	−0.146951	−0.0734753	+	0.997297i	$0.523409\pi$
$468$	−6089.94	−0.601512
$469$	420.506i	0.0414012i
$470$	− 629.745i	− 0.0618042i
$471$	2273.89i	0.222452i
$472$	5623.51	0.548396
$473$	9738.60i	0.946683i
$474$	3093.19	0.299736
$475$	−10326.5	−0.997502
$476$	0	0
$477$	−8994.92	−0.863415
$478$	−455.063	−0.0435441
$479$	− 9990.10i	− 0.952942i	−0.879190	−	0.476471i	$-0.841916\pi$
$479$	− 9990.10i	− 0.952942i	0.879190	−	0.476471i	$-0.158084\pi$
$480$	1772.35	0.168534
$481$	− 7691.13i	− 0.729075i
$482$	2611.44i	0.246779i
$483$	− 2887.42i	− 0.272012i
$484$	−3493.69	−0.328108
$485$	−2409.27	−0.225566
$486$	− 5201.30i	− 0.485465i
$487$	1129.88i	0.105133i	0.998617	+	0.0525663i	$0.0167401\pi$
$487$	1129.88i	0.105133i	−0.998617	+	0.0525663i	$0.983260\pi$
$488$	1037.90i	0.0962774i
$489$	−2134.42	−0.197386
$490$	− 1155.30i	− 0.106512i
$491$	−18774.9	−1.72566	−0.862832	−	0.505491i	$-0.831311\pi$
$491$	−18774.9	−1.72566	−0.862832	+	0.505491i	$0.831311\pi$
$492$	9124.97	0.836149
$493$	0	0
$494$	7053.51	0.642414
$495$	1427.35	0.129605
$496$	6279.49i	0.568463i
$497$	−6260.28	−0.565014
$498$	− 498.339i	− 0.0448416i
$499$	− 17329.1i	− 1.55462i	−0.629118	−	0.777310i	$-0.716584\pi$
$499$	− 17329.1i	− 1.55462i	0.629118	−	0.777310i	$-0.283416\pi$
$500$	− 4487.74i	− 0.401396i
$501$	8945.50	0.797716
$502$	−10475.6	−0.931369
$503$	20837.0i	1.84707i	0.383518	+	0.923533i	$0.374712\pi$
$503$	20837.0i	1.84707i	−0.383518	+	0.923533i	$0.625288\pi$
$504$	2606.90i	0.230398i
$505$	804.957i	0.0709309i
$506$	−4333.16	−0.380697
$507$	3722.37i	0.326068i
$508$	16278.6	1.42174
$509$	11835.0	1.03060	0.515301	−	0.857009i	$-0.327680\pi$
$509$	11835.0	1.03060	0.515301	+	0.857009i	$0.327680\pi$
$510$	0	0
$511$	−2348.63	−0.203322
$512$	−7793.12	−0.672676
$513$	− 12390.6i	− 1.06639i
$514$	7262.26	0.623199
$515$	1585.91i	0.135696i
$516$	6838.35i	0.583414i
$517$	− 4214.16i	− 0.358489i
$518$	−1430.55	−0.121341
$519$	559.359	0.0473086
$520$	3392.71i	0.286115i
$521$	− 7686.37i	− 0.646346i	−0.946340	−	0.323173i	$-0.895250\pi$
$521$	− 7686.37i	− 0.646346i	0.946340	−	0.323173i	$-0.104750\pi$
$522$	2983.37i	0.250151i
$523$	11476.4	0.959518	0.479759	−	0.877400i	$-0.340724\pi$
$523$	11476.4	0.959518	0.479759	+	0.877400i	$0.340724\pi$
$524$	12165.6i	1.01423i
$525$	−2900.93	−0.241156
$526$	5355.25	0.443916
$527$	0	0
$528$	2000.52	0.164889
$529$	−1120.01	−0.0920535
$530$	2177.37i	0.178451i
$531$	4978.44	0.406866
$532$	4352.40i	0.354700i
$533$	27345.0i	2.22222i
$534$	3492.56i	0.283029i
$535$	2989.38	0.241574
$536$	1019.81	0.0821814
$537$	3229.59i	0.259529i
$538$	− 4660.88i	− 0.373504i
$539$	− 7731.09i	− 0.617814i
$540$	2589.60	0.206368
$541$	− 546.481i	− 0.0434289i	−0.999764	−	0.0217145i	$-0.993088\pi$
$541$	− 546.481i	− 0.0434289i	0.999764	−	0.0217145i	$-0.00691247\pi$
$542$	−747.357	−0.0592283
$543$	−10884.1	−0.860191
$544$	0	0
$545$	5500.69	0.432337
$546$	1981.47	0.155310
$547$	8397.33i	0.656388i	0.944610	+	0.328194i	$0.106440\pi$
$547$	8397.33i	0.656388i	−0.944610	+	0.328194i	$0.893560\pi$
$548$	−19313.6	−1.50554
$549$	918.839i	0.0714301i
$550$	4353.44i	0.337512i
$551$	11463.3i	0.886305i
$552$	−7002.58	−0.539945
$553$	−5719.73	−0.439833
$554$	− 7083.32i	− 0.543215i
$555$	1265.79i	0.0968105i
$556$	− 9024.36i	− 0.688342i
$557$	−4881.65	−0.371350	−0.185675	−	0.982611i	$-0.559447\pi$
$557$	−4881.65	−0.371350	−0.185675	+	0.982611i	$0.559447\pi$
$558$	− 6346.04i	− 0.481451i
$559$	−20492.6	−1.55053
$560$	−552.797	−0.0417142
$561$	0	0
$562$	−2704.38	−0.202985
$563$	−7198.57	−0.538870	−0.269435	−	0.963019i	$-0.586837\pi$
$563$	−7198.57	−0.538870	−0.269435	+	0.963019i	$0.586837\pi$
$564$	− 2959.14i	− 0.220926i
$565$	−2144.44	−0.159677
$566$	1025.95i	0.0761904i
$567$	174.283i	0.0129087i
$568$	15182.5i	1.12155i
$569$	23946.9	1.76433	0.882167	−	0.470937i	$-0.156084\pi$
$569$	23946.9	1.76433	0.882167	+	0.470937i	$0.156084\pi$
$570$	−1160.85	−0.0853032
$571$	− 1593.15i	− 0.116763i	−0.998294	−	0.0583813i	$-0.981406\pi$
$571$	− 1593.15i	− 0.116763i	0.998294	−	0.0583813i	$-0.0185939\pi$
$572$	9864.95i	0.721109i
$573$	− 1548.59i	− 0.112903i
$574$	5086.16	0.369847
$575$	13349.2i	0.968174i
$576$	1168.69	0.0845403
$577$	12937.4	0.933435	0.466717	−	0.884406i	$-0.345436\pi$
$577$	12937.4	0.933435	0.466717	+	0.884406i	$0.345436\pi$
$578$	0	0
$579$	−11195.2	−0.803549
$580$	−2395.82	−0.171519
$581$	921.499i	0.0658007i
$582$	3412.53	0.243048
$583$	14570.6i	1.03508i
$584$	5695.92i	0.403594i
$585$	3003.53i	0.212275i
$586$	9803.82	0.691112
$587$	12899.2	0.906998	0.453499	−	0.891257i	$-0.350176\pi$
$587$	12899.2	0.906998	0.453499	+	0.891257i	$0.350176\pi$
$588$	− 5428.70i	− 0.380741i
$589$	− 24384.1i	− 1.70582i
$590$	− 1205.11i	− 0.0840911i
$591$	4300.23	0.299302
$592$	− 3039.19i	− 0.210997i
$593$	−4357.13	−0.301730	−0.150865	−	0.988554i	$-0.548206\pi$
$593$	−4357.13	−0.301730	−0.150865	+	0.988554i	$0.548206\pi$
$594$	−5223.59	−0.360819
$595$	0	0
$596$	1758.23	0.120839
$597$	−11790.3	−0.808284
$598$	− 9118.14i	− 0.623526i
$599$	13726.8	0.936328	0.468164	−	0.883642i	$-0.344916\pi$
$599$	13726.8	0.936328	0.468164	+	0.883642i	$0.344916\pi$
$600$	7035.35i	0.478695i
$601$	− 2531.41i	− 0.171811i	−0.996303	−	0.0859056i	$-0.972622\pi$
$601$	− 2531.41i	− 0.171811i	0.996303	−	0.0859056i	$-0.0273783\pi$
$602$	3811.62i	0.258057i
$603$	902.830	0.0609720
$604$	−4116.24	−0.277297
$605$	1723.07i	0.115790i
$606$	− 1140.15i	− 0.0764283i
$607$	185.004i	0.0123708i	0.999981	+	0.00618540i	$0.00196889\pi$
$607$	185.004i	0.0123708i	−0.999981	+	0.00618540i	$0.998031\pi$
$608$	16524.4	1.10223
$609$	3220.28i	0.214273i
$610$	222.420	0.0147632
$611$	8867.73	0.587152
$612$	0	0
$613$	−17706.9	−1.16668	−0.583339	−	0.812228i	$-0.698254\pi$
$613$	−17706.9	−1.16668	−0.583339	+	0.812228i	$0.698254\pi$
$614$	−3301.93	−0.217028
$615$	− 4500.39i	− 0.295078i
$616$	4222.84	0.276207
$617$	− 6183.89i	− 0.403491i	−0.979438	−	0.201746i	$-0.935339\pi$
$617$	− 6183.89i	− 0.403491i	0.979438	−	0.201746i	$-0.0646614\pi$
$618$	− 2246.30i	− 0.146213i
$619$	1247.51i	0.0810046i	0.999179	+	0.0405023i	$0.0128958\pi$
$619$	1247.51i	0.0810046i	−0.999179	+	0.0405023i	$0.987104\pi$
$620$	5096.23	0.330112
$621$	−16017.4	−1.03503
$622$	12992.8i	0.837561i
$623$	− 6458.23i	− 0.415318i
$624$	4209.63i	0.270064i
$625$	12262.8	0.784817
$626$	800.914i	0.0511357i
$627$	−7768.27	−0.494792
$628$	−4430.87	−0.281546
$629$	0	0
$630$	558.655	0.0353292
$631$	−24053.3	−1.51750	−0.758752	−	0.651379i	$-0.774191\pi$
$631$	−24053.3	−1.51750	−0.758752	+	0.651379i	$0.774191\pi$
$632$	13871.5i	0.873069i
$633$	−16612.7	−1.04312
$634$	10417.8i	0.652596i
$635$	− 8028.51i	− 0.501735i
$636$	10231.4i	0.637893i
$637$	16268.3	1.01189
$638$	4832.69	0.299887
$639$	13440.9i	0.832102i
$640$	4211.70i	0.260128i
$641$	− 21286.8i	− 1.31167i	−0.754905	−	0.655834i	$-0.772317\pi$
$641$	− 21286.8i	− 1.31167i	0.754905	−	0.655834i	$-0.227683\pi$
$642$	−4234.20	−0.260297
$643$	− 1789.41i	− 0.109747i	−0.998493	−	0.0548736i	$-0.982524\pi$
$643$	− 1789.41i	− 0.109747i	0.998493	−	0.0548736i	$-0.0174756\pi$
$644$	5626.38	0.344271
$645$	3372.64	0.205888
$646$	0	0
$647$	−4378.61	−0.266060	−0.133030	−	0.991112i	$-0.542471\pi$
$647$	−4378.61	−0.266060	−0.133030	+	0.991112i	$0.542471\pi$
$648$	422.672	0.0256237
$649$	− 8064.45i	− 0.487762i
$650$	−9160.81	−0.552795
$651$	− 6849.97i	− 0.412399i
$652$	− 4159.11i	− 0.249821i
$653$	7665.15i	0.459358i	0.973266	+	0.229679i	$0.0737676\pi$
$653$	7665.15i	0.459358i	−0.973266	+	0.229679i	$0.926232\pi$
$654$	−7791.26	−0.465845
$655$	5999.99	0.357922
$656$	10805.5i	0.643117i
$657$	5042.54i	0.299434i
$658$	− 1649.39i	− 0.0977205i
$659$	−4710.22	−0.278428	−0.139214	−	0.990262i	$-0.544458\pi$
$659$	−4710.22	−0.278428	−0.139214	+	0.990262i	$0.544458\pi$
$660$	− 1623.55i	− 0.0957527i
$661$	31266.6	1.83983	0.919916	−	0.392116i	$-0.128257\pi$
$661$	31266.6	1.83983	0.919916	+	0.392116i	$0.128257\pi$
$662$	1024.00	0.0601192
$663$	0	0
$664$	2234.82	0.130614
$665$	2146.58	0.125174
$666$	3071.40i	0.178700i
$667$	14818.7	0.860246
$668$	17431.1i	1.00962i
$669$	− 2222.58i	− 0.128446i
$670$	− 218.545i	− 0.0126017i
$671$	1488.40	0.0856322
$672$	4642.05	0.266474
$673$	− 11723.0i	− 0.671454i	−0.941959	−	0.335727i	$-0.891018\pi$
$673$	− 11723.0i	− 0.671454i	0.941959	−	0.335727i	$-0.108982\pi$
$674$	2679.65i	0.153140i
$675$	16092.3i	0.917621i
$676$	−7253.37	−0.412686
$677$	− 289.531i	− 0.0164366i	−0.999966	−	0.00821829i	$-0.997384\pi$
$677$	− 289.531i	− 0.0164366i	0.999966	−	0.00821829i	$-0.00261599\pi$
$678$	3037.42	0.172052
$679$	−6310.25	−0.356650
$680$	0	0
$681$	−6786.45	−0.381875
$682$	−10279.8	−0.577175
$683$	1720.10i	0.0963660i	0.998839	+	0.0481830i	$0.0153431\pi$
$683$	1720.10i	0.0963660i	−0.998839	+	0.0481830i	$0.984657\pi$
$684$	9344.64	0.522370
$685$	9525.37i	0.531308i
$686$	− 6733.30i	− 0.374750i
$687$	12356.5i	0.686215i
$688$	−8097.77	−0.448728
$689$	−30660.5	−1.69532
$690$	1500.65i	0.0827951i
$691$	16777.7i	0.923665i	0.886967	+	0.461832i	$0.152808\pi$
$691$	16777.7i	0.923665i	−0.886967	+	0.461832i	$0.847192\pi$
$692$	1089.96i	0.0598758i
$693$	3738.44	0.204923
$694$	5421.88i	0.296559i
$695$	−4450.77	−0.242917
$696$	7809.84	0.425332
$697$	0	0
$698$	2035.86	0.110399
$699$	16381.2	0.886400
$700$	− 5652.71i	− 0.305218i
$701$	23981.1	1.29209	0.646043	−	0.763301i	$-0.276423\pi$
$701$	23981.1	1.29209	0.646043	+	0.763301i	$0.276423\pi$
$702$	− 10991.8i	− 0.590969i
$703$	11801.6i	0.633150i
$704$	− 1893.12i	− 0.101349i
$705$	−1459.43	−0.0779652
$706$	−8824.10	−0.470396
$707$	2108.30i	0.112151i
$708$	− 5662.78i	− 0.300593i
$709$	− 7709.28i	− 0.408361i	−0.978933	−	0.204181i	$-0.934547\pi$
$709$	− 7709.28i	− 0.408361i	0.978933	−	0.204181i	$-0.0654530\pi$
$710$	3253.59	0.171979
$711$	12280.3i	0.647747i
$712$	−15662.5	−0.824407
$713$	−31521.5	−1.65567
$714$	0	0
$715$	4865.34	0.254480
$716$	−6293.13	−0.328471
$717$	1054.61i	0.0549304i
$718$	−6729.09	−0.349760
$719$	− 11976.5i	− 0.621209i	−0.950539	−	0.310605i	$-0.899468\pi$
$719$	− 11976.5i	− 0.621209i	0.950539	−	0.310605i	$-0.100532\pi$
$720$	1186.86i	0.0614329i
$721$	4153.72i	0.214553i
$722$	−1486.56	−0.0766260
$723$	6052.00	0.311309
$724$	− 21208.7i	− 1.08870i
$725$	− 14888.1i	− 0.762662i
$726$	− 2440.58i	− 0.124764i
$727$	−18597.3	−0.948745	−0.474372	−	0.880324i	$-0.657325\pi$
$727$	−18597.3	−0.948745	−0.474372	+	0.880324i	$0.657325\pi$
$728$	8886.00i	0.452386i
$729$	−11461.4	−0.582300
$730$	1220.63	0.0618870
$731$	0	0
$732$	1045.14	0.0527727
$733$	23569.5	1.18767	0.593833	−	0.804588i	$-0.297614\pi$
$733$	23569.5	1.18767	0.593833	+	0.804588i	$0.297614\pi$
$734$	− 20.2646i	− 0.00101905i
$735$	−2677.41	−0.134364
$736$	− 21361.3i	− 1.06982i
$737$	− 1462.47i	− 0.0730948i
$738$	− 10920.0i	− 0.544678i
$739$	−10149.1	−0.505199	−0.252599	−	0.967571i	$-0.581285\pi$
$739$	−10149.1	−0.505199	−0.252599	+	0.967571i	$0.581285\pi$
$740$	−2466.50	−0.122528
$741$	− 16346.5i	− 0.810397i
$742$	5702.85i	0.282154i
$743$	27758.0i	1.37058i	0.728269	+	0.685291i	$0.240325\pi$
$743$	27758.0i	1.37058i	−0.728269	+	0.685291i	$0.759675\pi$
$744$	−16612.6	−0.818611
$745$	− 867.148i	− 0.0426441i
$746$	−2617.87	−0.128481
$747$	1978.47	0.0969054
$748$	0	0
$749$	7829.63	0.381960
$750$	3134.99	0.152632
$751$	− 815.225i	− 0.0396112i	−0.999804	−	0.0198056i	$-0.993695\pi$
$751$	− 815.225i	− 0.0396112i	0.999804	−	0.0198056i	$-0.00630473\pi$
$752$	3504.13	0.169924
$753$	24277.1i	1.17491i
$754$	10169.3i	0.491172i
$755$	2030.11i	0.0978585i
$756$	6782.56	0.326295
$757$	13239.4	0.635659	0.317829	−	0.948148i	$-0.397046\pi$
$757$	13239.4	0.635659	0.317829	+	0.948148i	$0.397046\pi$
$758$	13058.0i	0.625710i
$759$	10042.1i	0.480244i
$760$	− 5205.90i	− 0.248471i
$761$	−11028.2	−0.525324	−0.262662	−	0.964888i	$-0.584600\pi$
$761$	−11028.2	−0.525324	−0.262662	+	0.964888i	$0.584600\pi$
$762$	11371.7i	0.540621i
$763$	14407.1	0.683582
$764$	3017.56	0.142895
$765$	0	0
$766$	−12365.0	−0.583246
$767$	16969.8	0.798882
$768$	− 7695.55i	− 0.361574i
$769$	−18921.2	−0.887277	−0.443639	−	0.896206i	$-0.646313\pi$
$769$	−18921.2	−0.887277	−0.443639	+	0.896206i	$0.646313\pi$
$770$	− 904.952i	− 0.0423535i
$771$	− 16830.3i	− 0.786158i
$772$	− 21814.7i	− 1.01701i
$773$	−38728.6	−1.80203	−0.901016	−	0.433786i	$-0.857177\pi$
$773$	−38728.6	−1.80203	−0.901016	+	0.433786i	$0.857177\pi$
$774$	8183.59	0.380043
$775$	31669.0i	1.46785i
$776$	15303.6i	0.707949i
$777$	3315.29i	0.153070i
$778$	−1556.93	−0.0717465
$779$	− 41959.2i	− 1.92984i
$780$	3416.39	0.156829
$781$	21772.5	0.997545
$782$	0	0
$783$	17863.9	0.815329
$784$	6428.50	0.292844
$785$	2185.28i	0.0993579i
$786$	−8498.47	−0.385662
$787$	− 20587.3i	− 0.932477i	−0.884659	−	0.466239i	$-0.845609\pi$
$787$	− 20587.3i	− 0.932477i	0.884659	−	0.466239i	$-0.154391\pi$
$788$	8379.37i	0.378811i
$789$	− 12410.8i	− 0.559995i
$790$	2972.66	0.133876
$791$	−5616.62	−0.252470
$792$	− 9066.49i	− 0.406772i
$793$	3132.00i	0.140253i
$794$	14435.0i	0.645190i
$795$	5046.05	0.225113
$796$	− 22974.5i	− 1.02300i
$797$	15871.4	0.705385	0.352693	−	0.935739i	$-0.385266\pi$
$797$	15871.4	0.705385	0.352693	+	0.935739i	$0.385266\pi$
$798$	−3040.45	−0.134876
$799$	0	0
$800$	−21461.3	−0.948463
$801$	−13865.9	−0.611644
$802$	18765.0i	0.826204i
$803$	8168.28	0.358969
$804$	− 1026.93i	− 0.0450462i
$805$	− 2774.90i	− 0.121494i
$806$	− 21631.4i	− 0.945329i
$807$	−10801.6	−0.471170
$808$	5113.06	0.222620
$809$	− 39667.1i	− 1.72388i	−0.507007	−	0.861942i	$-0.669248\pi$
$809$	− 39667.1i	− 1.72388i	0.507007	−	0.861942i	$-0.330752\pi$
$810$	− 90.5783i	− 0.00392913i
$811$	8003.87i	0.346552i	0.984873	+	0.173276i	$0.0554353\pi$
$811$	8003.87i	0.346552i	−0.984873	+	0.173276i	$0.944565\pi$
$812$	−6275.00	−0.271194
$813$	1732.00i	0.0747157i
$814$	4975.28	0.214230
$815$	−2051.25	−0.0881621
$816$	0	0
$817$	31444.7	1.34652
$818$	12939.7	0.553088
$819$	7866.69i	0.335634i
$820$	8769.40	0.373464
$821$	− 13279.1i	− 0.564489i	−0.959343	−	0.282244i	$-0.908921\pi$
$821$	− 13279.1i	− 0.564489i	0.959343	−	0.282244i	$-0.0910789\pi$
$822$	− 13491.9i	− 0.572486i
$823$	− 28934.0i	− 1.22549i	−0.790281	−	0.612745i	$-0.790065\pi$
$823$	− 28934.0i	− 1.22549i	0.790281	−	0.612745i	$-0.209935\pi$
$824$	10073.6	0.425887
$825$	10089.1	0.425767
$826$	− 3156.37i	− 0.132959i
$827$	13679.6i	0.575193i	0.957752	+	0.287597i	$0.0928563\pi$
$827$	13679.6i	0.575193i	−0.957752	+	0.287597i	$0.907144\pi$
$828$	− 12079.9i	− 0.507012i
$829$	16514.5	0.691886	0.345943	−	0.938256i	$-0.387559\pi$
$829$	16514.5	0.691886	0.345943	+	0.938256i	$0.387559\pi$
$830$	− 478.921i	− 0.0200284i
$831$	−16415.6	−0.685260
$832$	3983.64	0.165995
$833$	0	0
$834$	6304.13	0.261744
$835$	8596.93	0.356298
$836$	− 15137.1i	− 0.626231i
$837$	−37998.9	−1.56922
$838$	13177.8i	0.543221i
$839$	87.9839i	0.00362043i	0.999998	+	0.00181022i	$0.000576210\pi$
$839$	87.9839i	0.00362043i	−0.999998	+	0.00181022i	$0.999424\pi$
$840$	− 1462.44i	− 0.0600702i
$841$	7861.94	0.322356
$842$	16825.1	0.688635
$843$	6267.41i	0.256063i
$844$	− 32371.3i	− 1.32022i
$845$	3577.33i	0.145638i
$846$	−3541.27	−0.143914
$847$	4512.98i	0.183079i
$848$	−12115.7	−0.490630
$849$	2377.63	0.0961133
$850$	0	0
$851$	15256.0	0.614534
$852$	15288.5	0.614758
$853$	8162.96i	0.327660i	0.986489	+	0.163830i	$0.0523849\pi$
$853$	8162.96i	0.327660i	−0.986489	+	0.163830i	$0.947615\pi$
$854$	582.551	0.0233425
$855$	− 4608.73i	− 0.184345i
$856$	− 18988.4i	− 0.758191i
$857$	− 18724.9i	− 0.746361i	−0.927759	−	0.373181i	$-0.878267\pi$
$857$	− 18724.9i	− 0.746361i	0.927759	−	0.373181i	$-0.121733\pi$
$858$	−6891.34	−0.274203
$859$	46422.5	1.84391	0.921953	−	0.387301i	$-0.126593\pi$
$859$	46422.5	1.84391	0.921953	+	0.387301i	$0.126593\pi$
$860$	6571.88i	0.260580i
$861$	− 11787.2i	− 0.466557i
$862$	4043.61i	0.159775i
$863$	29112.3	1.14831	0.574157	−	0.818746i	$-0.305330\pi$
$863$	29112.3	1.14831	0.574157	+	0.818746i	$0.305330\pi$
$864$	− 25750.8i	− 1.01396i
$865$	537.563	0.0211303
$866$	8346.33	0.327505
$867$	0	0
$868$	13347.8	0.521950
$869$	19892.6	0.776536
$870$	− 1673.64i	− 0.0652204i
$871$	3077.43	0.119719
$872$	− 34940.2i	− 1.35691i
$873$	13548.2i	0.525241i
$874$	13991.2i	0.541487i
$875$	−5797.04	−0.223972
$876$	5735.69	0.221222
$877$	− 39163.0i	− 1.50791i	−0.656924	−	0.753957i	$-0.728143\pi$
$877$	− 39163.0i	− 1.50791i	0.656924	−	0.753957i	$-0.271857\pi$
$878$	3464.19i	0.133156i
$879$	− 22720.3i	− 0.871830i
$880$	1922.57	0.0736473
$881$	− 35073.2i	− 1.34125i	−0.741795	−	0.670627i	$-0.766025\pi$
$881$	− 35073.2i	− 1.34125i	0.741795	−	0.670627i	$-0.233975\pi$
$882$	−6496.63	−0.248019
$883$	−48775.7	−1.85893	−0.929463	−	0.368915i	$-0.879729\pi$
$883$	−48775.7	−1.85893	−0.929463	+	0.368915i	$0.879729\pi$
$884$	0	0
$885$	−2792.85	−0.106080
$886$	−11611.0	−0.440269
$887$	13296.0i	0.503309i	0.967817	+	0.251654i	$0.0809746\pi$
$887$	13296.0i	0.503309i	−0.967817	+	0.251654i	$0.919025\pi$
$888$	8040.27	0.303844
$889$	− 21027.9i	− 0.793309i
$890$	3356.46i	0.126415i
$891$	− 606.137i	− 0.0227905i
$892$	4330.90	0.162566
$893$	−13607.0	−0.509899
$894$	1228.24i	0.0459492i
$895$	3103.74i	0.115918i
$896$	11031.1i	0.411297i
$897$	−21131.3	−0.786570
$898$	12054.6i	0.447960i
$899$	35155.3	1.30422
$900$	−12136.4	−0.449498
$901$	0	0
$902$	−17689.1	−0.652974
$903$	8833.44	0.325535
$904$	13621.4i	0.501153i
$905$	−10460.0	−0.384202
$906$	− 2875.47i	− 0.105443i
$907$	11675.0i	0.427410i	0.976898	+	0.213705i	$0.0685532\pi$
$907$	11675.0i	0.427410i	−0.976898	+	0.213705i	$0.931447\pi$
$908$	− 13224.0i	− 0.483319i
$909$	4526.54	0.165166
$910$	1904.26	0.0693689
$911$	− 18552.9i	− 0.674738i	−0.941372	−	0.337369i	$-0.890463\pi$
$911$	− 18552.9i	− 0.674738i	0.941372	−	0.337369i	$-0.109537\pi$
$912$	− 6459.41i	− 0.234531i
$913$	− 3204.87i	− 0.116173i
$914$	−9739.24	−0.352457
$915$	− 515.459i	− 0.0186235i
$916$	−24077.7	−0.868504
$917$	15714.9	0.565922
$918$	0	0
$919$	33956.8	1.21886	0.609429	−	0.792841i	$-0.291399\pi$
$919$	33956.8	1.21886	0.609429	+	0.792841i	$0.291399\pi$
$920$	−6729.71	−0.241165
$921$	7652.23i	0.273778i
$922$	−9886.63	−0.353144
$923$	45815.3i	1.63383i
$924$	− 4252.33i	− 0.151398i
$925$	− 15327.4i	− 0.544823i
$926$	−480.372	−0.0170475
$927$	8918.08	0.315974
$928$	23823.8i	0.842732i
$929$	23695.3i	0.836832i	0.908256	+	0.418416i	$0.137415\pi$
$929$	23695.3i	0.836832i	−0.908256	+	0.418416i	$0.862585\pi$
$930$	3560.06i	0.125526i
$931$	−24962.7	−0.878753
$932$	31920.2i	1.12187i
$933$	30110.8	1.05657
$934$	2018.72	0.0707221
$935$	0	0
$936$	19078.3	0.666234
$937$	−7990.62	−0.278593	−0.139297	−	0.990251i	$-0.544484\pi$
$937$	−7990.62	−0.278593	−0.139297	+	0.990251i	$0.544484\pi$
$938$	− 572.402i	− 0.0199249i
$939$	1856.12	0.0645071
$940$	− 2843.83i	− 0.0986762i
$941$	− 24385.9i	− 0.844799i	−0.906410	−	0.422400i	$-0.861188\pi$
$941$	− 24385.9i	− 0.844799i	0.906410	−	0.422400i	$-0.138812\pi$
$942$	− 3095.26i	− 0.107058i
$943$	−54241.0	−1.87310
$944$	6705.69	0.231199
$945$	− 3345.12i	− 0.115150i
$946$	− 13256.4i	− 0.455605i
$947$	− 1174.62i	− 0.0403064i	−0.999797	−	0.0201532i	$-0.993585\pi$
$947$	− 1174.62i	− 0.0403064i	0.999797	−	0.0201532i	$-0.00641539\pi$
$948$	13968.4	0.478557
$949$	17188.3i	0.587939i
$950$	14056.7	0.480063
$951$	24143.4	0.823241
$952$	0	0
$953$	−33546.9	−1.14029	−0.570143	−	0.821546i	$-0.693112\pi$
$953$	−33546.9	−1.14029	−0.570143	+	0.821546i	$0.693112\pi$
$954$	12244.1	0.415531
$955$	− 1488.25i	− 0.0504277i
$956$	−2055.00	−0.0695224
$957$	− 11199.8i	− 0.378304i
$958$	13598.7i	0.458617i
$959$	24948.4i	0.840067i
$960$	−655.620	−0.0220417
$961$	−44989.1	−1.51016
$962$	10469.3i	0.350878i
$963$	− 16810.3i	− 0.562517i
$964$	11792.9i	0.394007i
$965$	−10758.9	−0.358903
$966$	3930.41i	0.130910i
$967$	−24766.8	−0.823625	−0.411813	−	0.911269i	$-0.635104\pi$
$967$	−24766.8	−0.823625	−0.411813	+	0.911269i	$0.635104\pi$
$968$	10944.9	0.363411
$969$	0	0
$970$	3279.56	0.108557
$971$	−42324.3	−1.39882	−0.699409	−	0.714721i	$-0.746553\pi$
$971$	−42324.3	−1.39882	−0.699409	+	0.714721i	$0.746553\pi$
$972$	− 23488.3i	− 0.775091i
$973$	−11657.2	−0.384083
$974$	− 1538.01i	− 0.0505966i
$975$	21230.2i	0.697344i
$976$	1237.63i	0.0405896i
$977$	11320.4	0.370698	0.185349	−	0.982673i	$-0.440658\pi$
$977$	11320.4	0.370698	0.185349	+	0.982673i	$0.440658\pi$
$978$	2905.42	0.0949949
$979$	22461.0i	0.733254i
$980$	− 5217.16i	− 0.170057i
$981$	− 30932.2i	− 1.00672i
$982$	25556.8	0.830500
$983$	− 11311.9i	− 0.367032i	−0.983017	−	0.183516i	$-0.941252\pi$
$983$	− 11311.9i	− 0.367032i	0.983017	−	0.183516i	$-0.0587478\pi$
$984$	−28586.3	−0.926116
$985$	4132.66	0.133683
$986$	0	0
$987$	−3822.47	−0.123273
$988$	31852.6	1.02568
$989$	− 40648.8i	− 1.30693i
$990$	−1942.94	−0.0623744
$991$	− 29405.5i	− 0.942580i	−0.881978	−	0.471290i	$-0.843788\pi$
$991$	− 29405.5i	− 0.942580i	0.881978	−	0.471290i	$-0.156212\pi$
$992$	− 50676.5i	− 1.62196i
$993$	− 2373.12i	− 0.0758397i
$994$	8521.63	0.271921
$995$	−11330.9	−0.361018
$996$	− 2250.43i	− 0.0715939i
$997$	54905.9i	1.74412i	0.489398	+	0.872060i	$0.337216\pi$
$997$	54905.9i	1.74412i	−0.489398	+	0.872060i	$0.662784\pi$
$998$	23588.7i	0.748183i
$999$	18390.9	0.582446

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.b.b.288.4		6
17.4	even	4		17.4.a.b.1.2	✓	3
17.13	even	4		289.4.a.b.1.2		3
17.16	even	2	inner	289.4.b.b.288.3		6
51.38	odd	4		153.4.a.g.1.2		3
68.55	odd	4		272.4.a.h.1.2		3
85.4	even	4		425.4.a.g.1.2		3
85.38	odd	4		425.4.b.f.324.3		6
85.72	odd	4		425.4.b.f.324.4		6
119.55	odd	4		833.4.a.d.1.2		3
136.21	even	4		1088.4.a.v.1.2		3
136.123	odd	4		1088.4.a.x.1.2		3
187.21	odd	4		2057.4.a.e.1.2		3
204.191	even	4		2448.4.a.bi.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.a.b.1.2	✓	3	17.4	even	4
153.4.a.g.1.2		3	51.38	odd	4
272.4.a.h.1.2		3	68.55	odd	4
289.4.a.b.1.2		3	17.13	even	4
289.4.b.b.288.3		6	17.16	even	2	inner
289.4.b.b.288.4		6	1.1	even	1	trivial
425.4.a.g.1.2		3	85.4	even	4
425.4.b.f.324.3		6	85.38	odd	4
425.4.b.f.324.4		6	85.72	odd	4
833.4.a.d.1.2		3	119.55	odd	4
1088.4.a.v.1.2		3	136.21	even	4
1088.4.a.x.1.2		3	136.123	odd	4
2057.4.a.e.1.2		3	187.21	odd	4
2448.4.a.bi.1.1		3	204.191	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)

\(f(q)\)	\(=\)	\(q-1.36122 q^{2} +3.15463i q^{3} -6.14708 q^{4} +3.03171i q^{5} -4.29415i q^{6} +7.94049i q^{7} +19.2573 q^{8} +17.0483 q^{9} +O(q^{10})\)	\(q-1.36122 q^{2} +3.15463i q^{3} -6.14708 q^{4} +3.03171i q^{5} -4.29415i q^{6} +7.94049i q^{7} +19.2573 q^{8} +17.0483 q^{9} -4.12682i q^{10} -27.6161i q^{11} -19.3918i q^{12} +58.1117 q^{13} -10.8088i q^{14} -9.56391 q^{15} +22.9632 q^{16} -23.2065 q^{18} -89.1688 q^{19} -18.6361i q^{20} -25.0493 q^{21} +37.5916i q^{22} +115.269i q^{23} +60.7497i q^{24} +115.809 q^{25} -79.1029 q^{26} +138.956i q^{27} -48.8108i q^{28} -128.558i q^{29} +13.0186 q^{30} +273.460i q^{31} -185.316 q^{32} +87.1187 q^{33} -24.0732 q^{35} -104.797 q^{36} -132.351i q^{37} +121.379 q^{38} +183.321i q^{39} +58.3825i q^{40} +470.559i q^{41} +34.0977 q^{42} -352.642 q^{43} +169.758i q^{44} +51.6854i q^{45} -156.907i q^{46} +152.598 q^{47} +72.4403i q^{48} +279.949 q^{49} -157.641 q^{50} -357.217 q^{52} -527.614 q^{53} -189.150i q^{54} +83.7239 q^{55} +152.912i q^{56} -281.295i q^{57} +174.995i q^{58} +292.020 q^{59} +58.7901 q^{60} +53.8962i q^{61} -372.239i q^{62} +135.372i q^{63} +68.5514 q^{64} +176.178i q^{65} -118.588 q^{66} +52.9572 q^{67} -363.632 q^{69} +32.7690 q^{70} +788.400i q^{71} +328.304 q^{72} +295.780i q^{73} +180.159i q^{74} +365.334i q^{75} +548.127 q^{76} +219.285 q^{77} -249.541i q^{78} +720.325i q^{79} +69.6175i q^{80} +21.9487 q^{81} -640.535i q^{82} +116.051 q^{83} +153.980 q^{84} +480.024 q^{86} +405.552 q^{87} -531.812i q^{88} -813.329 q^{89} -70.3553i q^{90} +461.435i q^{91} -708.569i q^{92} -862.664 q^{93} -207.720 q^{94} -270.334i q^{95} -584.605i q^{96} +794.693i q^{97} -381.072 q^{98} -470.808i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} + 50 q^{4} + 78 q^{8} - 118 q^{9}+O(q^{10}) \) 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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