LMFDB - Embedded newform 578.2.b.f.577.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [578,2,Mod(577,578)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("578.577"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(578, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 578 = 2 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	578.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,6,0,6,0,0,0,6,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$4.61535323683$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.419904.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 6x^{4} + 9x^{2} + 1 $ x^6 + 6x^4 + 9x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			577.6
Root			$1.87939i$ of defining polynomial
Character	$\chi$	$=$	578.577
Dual form			578.2.b.f.577.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +3.22668i q^{3} +1.00000 q^{4} +1.18479i q^{5} +3.22668i q^{6} -1.12061i q^{7} +1.00000 q^{8} -7.41147 q^{9} +1.18479i q^{10} +3.41147i q^{11} +3.22668i q^{12} +0.347296 q^{13} -1.12061i q^{14} -3.82295 q^{15} +1.00000 q^{16} -7.41147 q^{18} -0.347296 q^{19} +1.18479i q^{20} +3.61587 q^{21} +3.41147i q^{22} +0.411474i q^{23} +3.22668i q^{24} +3.59627 q^{25} +0.347296 q^{26} -14.2344i q^{27} -1.12061i q^{28} -8.78106i q^{29} -3.82295 q^{30} +8.71688i q^{31} +1.00000 q^{32} -11.0077 q^{33} +1.32770 q^{35} -7.41147 q^{36} -0.475652i q^{37} -0.347296 q^{38} +1.12061i q^{39} +1.18479i q^{40} -2.63816i q^{41} +3.61587 q^{42} +9.33275 q^{43} +3.41147i q^{44} -8.78106i q^{45} +0.411474i q^{46} -7.86484 q^{47} +3.22668i q^{48} +5.74422 q^{49} +3.59627 q^{50} +0.347296 q^{52} -8.41921 q^{53} -14.2344i q^{54} -4.04189 q^{55} -1.12061i q^{56} -1.12061i q^{57} -8.78106i q^{58} +6.41147 q^{59} -3.82295 q^{60} +5.70233i q^{61} +8.71688i q^{62} +8.30541i q^{63} +1.00000 q^{64} +0.411474i q^{65} -11.0077 q^{66} +7.31315 q^{67} -1.32770 q^{69} +1.32770 q^{70} +7.59627i q^{71} -7.41147 q^{72} +9.04189i q^{73} -0.475652i q^{74} +11.6040i q^{75} -0.347296 q^{76} +3.82295 q^{77} +1.12061i q^{78} -13.2763i q^{79} +1.18479i q^{80} +23.6955 q^{81} -2.63816i q^{82} +7.73917 q^{83} +3.61587 q^{84} +9.33275 q^{86} +28.3337 q^{87} +3.41147i q^{88} +7.18479 q^{89} -8.78106i q^{90} -0.389185i q^{91} +0.411474i q^{92} -28.1266 q^{93} -7.86484 q^{94} -0.411474i q^{95} +3.22668i q^{96} +0.221629i q^{97} +5.74422 q^{98} -25.2841i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} + 6 q^{8} - 24 q^{9} + 18 q^{15} + 6 q^{16} - 24 q^{18} - 6 q^{25} + 18 q^{30} + 6 q^{32} - 18 q^{33} - 24 q^{36} + 18 q^{43} - 24 q^{49} - 6 q^{50} + 18 q^{53} - 18 q^{55} + 18 q^{59}+ \cdots - 24 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 + 6 * q^8 - 24 * q^9 + 18 * q^15 + 6 * q^16 - 24 * q^18 - 6 * q^25 + 18 * q^30 + 6 * q^32 - 18 * q^33 - 24 * q^36 + 18 * q^43 - 24 * q^49 - 6 * q^50 + 18 * q^53 - 18 * q^55 + 18 * q^59 + 18 * q^60 + 6 * q^64 - 18 * q^66 - 24 * q^72 - 18 * q^77 + 6 * q^81 + 18 * q^83 + 18 * q^86 + 36 * q^89 - 18 * q^93 - 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/578\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	3.22668i	1.86293i	0.363837	+	0.931463i	$0.381467\pi$
$3$	3.22668i	1.86293i	−0.363837	+	0.931463i	$0.618533\pi$
$4$	1.00000	0.500000
$5$	1.18479i	0.529855i	0.964268	+	0.264928i	$0.0853481\pi$
$5$	1.18479i	0.529855i	−0.964268	+	0.264928i	$0.914652\pi$
$6$	3.22668i	1.31729i
$7$	− 1.12061i	− 0.423553i	−0.977318	−	0.211776i	$-0.932075\pi$
$7$	− 1.12061i	− 0.423553i	0.977318	−	0.211776i	$-0.0679248\pi$
$8$	1.00000	0.353553
$9$	−7.41147	−2.47049
$10$	1.18479i	0.374664i
$11$	3.41147i	1.02860i	0.857611	+	0.514299i	$0.171948\pi$
$11$	3.41147i	1.02860i	−0.857611	+	0.514299i	$0.828052\pi$
$12$	3.22668i	0.931463i
$13$	0.347296	0.0963227	0.0481613	−	0.998840i	$-0.484664\pi$
$13$	0.347296	0.0963227	0.0481613	+	0.998840i	$0.484664\pi$
$14$	− 1.12061i	− 0.299497i
$15$	−3.82295	−0.987081
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	−7.41147	−1.74690
$19$	−0.347296	−0.0796752	−0.0398376	−	0.999206i	$-0.512684\pi$
$19$	−0.347296	−0.0796752	−0.0398376	+	0.999206i	$0.512684\pi$
$20$	1.18479i	0.264928i
$21$	3.61587	0.789047
$22$	3.41147i	0.727329i
$23$	0.411474i	0.0857983i	0.999079	+	0.0428991i	$0.0136594\pi$
$23$	0.411474i	0.0857983i	−0.999079	+	0.0428991i	$0.986341\pi$
$24$	3.22668i	0.658644i
$25$	3.59627	0.719253
$26$	0.347296	0.0681104
$27$	− 14.2344i	− 2.73942i
$28$	− 1.12061i	− 0.211776i
$29$	− 8.78106i	− 1.63060i	−0.579038	−	0.815301i	$-0.696572\pi$
$29$	− 8.78106i	− 1.63060i	0.579038	−	0.815301i	$-0.303428\pi$
$30$	−3.82295	−0.697972
$31$	8.71688i	1.56560i	0.622275	+	0.782799i	$0.286209\pi$
$31$	8.71688i	1.56560i	−0.622275	+	0.782799i	$0.713791\pi$
$32$	1.00000	0.176777
$33$	−11.0077	−1.91620
$34$	0	0
$35$	1.32770	0.224422
$36$	−7.41147	−1.23525
$37$	− 0.475652i	− 0.0781967i	−0.999235	−	0.0390983i	$-0.987551\pi$
$37$	− 0.475652i	− 0.0781967i	0.999235	−	0.0390983i	$-0.0124486\pi$
$38$	−0.347296	−0.0563389
$39$	1.12061i	0.179442i
$40$	1.18479i	0.187332i
$41$	− 2.63816i	− 0.412011i	−0.978551	−	0.206005i	$-0.933954\pi$
$41$	− 2.63816i	− 0.412011i	0.978551	−	0.206005i	$-0.0660464\pi$
$42$	3.61587	0.557940
$43$	9.33275	1.42323	0.711615	−	0.702569i	$-0.247964\pi$
$43$	9.33275	1.42323	0.711615	+	0.702569i	$0.247964\pi$
$44$	3.41147i	0.514299i
$45$	− 8.78106i	− 1.30900i
$46$	0.411474i	0.0606686i
$47$	−7.86484	−1.14720	−0.573602	−	0.819134i	$-0.694454\pi$
$47$	−7.86484	−1.14720	−0.573602	+	0.819134i	$0.694454\pi$
$48$	3.22668i	0.465731i
$49$	5.74422	0.820603
$50$	3.59627	0.508589
$51$	0	0
$52$	0.347296	0.0481613
$53$	−8.41921	−1.15647	−0.578234	−	0.815871i	$-0.696258\pi$
$53$	−8.41921	−1.15647	−0.578234	+	0.815871i	$0.696258\pi$
$54$	− 14.2344i	− 1.93706i
$55$	−4.04189	−0.545008
$56$	− 1.12061i	− 0.149748i
$57$	− 1.12061i	− 0.148429i
$58$	− 8.78106i	− 1.15301i
$59$	6.41147	0.834703	0.417351	−	0.908745i	$-0.362958\pi$
$59$	6.41147	0.834703	0.417351	+	0.908745i	$0.362958\pi$
$60$	−3.82295	−0.493540
$61$	5.70233i	0.730109i	0.930986	+	0.365054i	$0.118950\pi$
$61$	5.70233i	0.730109i	−0.930986	+	0.365054i	$0.881050\pi$
$62$	8.71688i	1.10705i
$63$	8.30541i	1.04638i
$64$	1.00000	0.125000
$65$	0.411474i	0.0510371i
$66$	−11.0077	−1.35496
$67$	7.31315	0.893443	0.446722	−	0.894673i	$-0.352591\pi$
$67$	7.31315	0.893443	0.446722	+	0.894673i	$0.352591\pi$
$68$	0	0
$69$	−1.32770	−0.159836
$70$	1.32770	0.158690
$71$	7.59627i	0.901511i	0.892647	+	0.450755i	$0.148845\pi$
$71$	7.59627i	0.901511i	−0.892647	+	0.450755i	$0.851155\pi$
$72$	−7.41147	−0.873451
$73$	9.04189i	1.05827i	0.848537	+	0.529137i	$0.177484\pi$
$73$	9.04189i	1.05827i	−0.848537	+	0.529137i	$0.822516\pi$
$74$	− 0.475652i	− 0.0552934i
$75$	11.6040i	1.33992i
$76$	−0.347296	−0.0398376
$77$	3.82295	0.435665
$78$	1.12061i	0.126885i
$79$	− 13.2763i	− 1.49370i	−0.664992	−	0.746851i	$-0.731565\pi$
$79$	− 13.2763i	− 1.49370i	0.664992	−	0.746851i	$-0.268435\pi$
$80$	1.18479i	0.132464i
$81$	23.6955	2.63284
$82$	− 2.63816i	− 0.291336i
$83$	7.73917	0.849484	0.424742	−	0.905314i	$-0.360365\pi$
$83$	7.73917	0.849484	0.424742	+	0.905314i	$0.360365\pi$
$84$	3.61587	0.394523
$85$	0	0
$86$	9.33275	1.00638
$87$	28.3337	3.03769
$88$	3.41147i	0.363664i
$89$	7.18479	0.761586	0.380793	−	0.924660i	$-0.375651\pi$
$89$	7.18479	0.761586	0.380793	+	0.924660i	$0.375651\pi$
$90$	− 8.78106i	− 0.925605i
$91$	− 0.389185i	− 0.0407977i
$92$	0.411474i	0.0428991i
$93$	−28.1266	−2.91659
$94$	−7.86484	−0.811196
$95$	− 0.411474i	− 0.0422164i
$96$	3.22668i	0.329322i
$97$	0.221629i	0.0225030i	0.999937	+	0.0112515i	$0.00358154\pi$
$97$	0.221629i	0.0225030i	−0.999937	+	0.0112515i	$0.996418\pi$
$98$	5.74422	0.580254
$99$	− 25.2841i	− 2.54114i
$100$	3.59627	0.359627
$101$	−4.86484	−0.484069	−0.242035	−	0.970268i	$-0.577815\pi$
$101$	−4.86484	−0.484069	−0.242035	+	0.970268i	$0.577815\pi$
$102$	0	0
$103$	12.3969	1.22151	0.610753	−	0.791821i	$-0.290867\pi$
$103$	12.3969	1.22151	0.610753	+	0.791821i	$0.290867\pi$
$104$	0.347296	0.0340552
$105$	4.28405i	0.418081i
$106$	−8.41921	−0.817746
$107$	− 8.85710i	− 0.856248i	−0.903720	−	0.428124i	$-0.859175\pi$
$107$	− 8.85710i	− 0.856248i	0.903720	−	0.428124i	$-0.140825\pi$
$108$	− 14.2344i	− 1.36971i
$109$	− 11.8726i	− 1.13719i	−0.822619	−	0.568593i	$-0.807488\pi$
$109$	− 11.8726i	− 1.13719i	0.822619	−	0.568593i	$-0.192512\pi$
$110$	−4.04189	−0.385379
$111$	1.53478	0.145675
$112$	− 1.12061i	− 0.105888i
$113$	10.8648i	1.02208i	0.859558	+	0.511039i	$0.170739\pi$
$113$	10.8648i	1.02208i	−0.859558	+	0.511039i	$0.829261\pi$
$114$	− 1.12061i	− 0.104955i
$115$	−0.487511	−0.0454607
$116$	− 8.78106i	− 0.815301i
$117$	−2.57398	−0.237964
$118$	6.41147	0.590224
$119$	0	0
$120$	−3.82295	−0.348986
$121$	−0.638156	−0.0580142
$122$	5.70233i	0.516265i
$123$	8.51249	0.767545
$124$	8.71688i	0.782799i
$125$	10.1848i	0.910956i
$126$	8.30541i	0.739904i
$127$	6.55169	0.581368	0.290684	−	0.956819i	$-0.406117\pi$
$127$	6.55169	0.581368	0.290684	+	0.956819i	$0.406117\pi$
$128$	1.00000	0.0883883
$129$	30.1138i	2.65137i
$130$	0.411474i	0.0360887i
$131$	0.0496299i	0.00433618i	0.999998	+	0.00216809i	$0.000690125\pi$
$131$	0.0496299i	0.00433618i	−0.999998	+	0.00216809i	$0.999310\pi$
$132$	−11.0077	−0.958101
$133$	0.389185i	0.0337467i
$134$	7.31315	0.631760
$135$	16.8648	1.45149
$136$	0	0
$137$	−8.13341	−0.694884	−0.347442	−	0.937701i	$-0.612950\pi$
$137$	−8.13341	−0.694884	−0.347442	+	0.937701i	$0.612950\pi$
$138$	−1.32770	−0.113021
$139$	− 15.3824i	− 1.30472i	−0.757911	−	0.652358i	$-0.773780\pi$
$139$	− 15.3824i	− 1.30472i	0.757911	−	0.652358i	$-0.226220\pi$
$140$	1.32770	0.112211
$141$	− 25.3773i	− 2.13716i
$142$	7.59627i	0.637465i
$143$	1.18479i	0.0990773i
$144$	−7.41147	−0.617623
$145$	10.4037	0.863983
$146$	9.04189i	0.748312i
$147$	18.5348i	1.52872i
$148$	− 0.475652i	− 0.0390983i
$149$	−16.1088	−1.31968	−0.659840	−	0.751406i	$-0.729376\pi$
$149$	−16.1088	−1.31968	−0.659840	+	0.751406i	$0.729376\pi$
$150$	11.6040i	0.947463i
$151$	2.70233	0.219913	0.109956	−	0.993936i	$-0.464929\pi$
$151$	2.70233	0.219913	0.109956	+	0.993936i	$0.464929\pi$
$152$	−0.347296	−0.0281695
$153$	0	0
$154$	3.82295	0.308062
$155$	−10.3277	−0.829541
$156$	1.12061i	0.0897210i
$157$	−23.5594	−1.88025	−0.940124	−	0.340834i	$-0.889291\pi$
$157$	−23.5594	−1.88025	−0.940124	+	0.340834i	$0.889291\pi$
$158$	− 13.2763i	− 1.05621i
$159$	− 27.1661i	− 2.15441i
$160$	1.18479i	0.0936661i
$161$	0.461104	0.0363401
$162$	23.6955	1.86170
$163$	− 1.87433i	− 0.146809i	−0.997302	−	0.0734045i	$-0.976614\pi$
$163$	− 1.87433i	− 0.146809i	0.997302	−	0.0734045i	$-0.0233864\pi$
$164$	− 2.63816i	− 0.206005i
$165$	− 13.0419i	− 1.01531i
$166$	7.73917	0.600676
$167$	8.85710i	0.685383i	0.939448	+	0.342691i	$0.111339\pi$
$167$	8.85710i	0.685383i	−0.939448	+	0.342691i	$0.888661\pi$
$168$	3.61587	0.278970
$169$	−12.8794	−0.990722
$170$	0	0
$171$	2.57398	0.196837
$172$	9.33275	0.711615
$173$	− 6.41147i	− 0.487455i	−0.969844	−	0.243728i	$-0.921630\pi$
$173$	− 6.41147i	− 0.487455i	0.969844	−	0.243728i	$-0.0783703\pi$
$174$	28.3337	2.14797
$175$	− 4.03003i	− 0.304642i
$176$	3.41147i	0.257150i
$177$	20.6878i	1.55499i
$178$	7.18479	0.538523
$179$	1.26083	0.0942388	0.0471194	−	0.998889i	$-0.484996\pi$
$179$	1.26083	0.0942388	0.0471194	+	0.998889i	$0.484996\pi$
$180$	− 8.78106i	− 0.654502i
$181$	− 15.3209i	− 1.13879i	−0.822063	−	0.569396i	$-0.807177\pi$
$181$	− 15.3209i	− 1.13879i	0.822063	−	0.569396i	$-0.192823\pi$
$182$	− 0.389185i	− 0.0288483i
$183$	−18.3996	−1.36014
$184$	0.411474i	0.0303343i
$185$	0.563549	0.0414329
$186$	−28.1266	−2.06234
$187$	0	0
$188$	−7.86484	−0.573602
$189$	−15.9513	−1.16029
$190$	− 0.411474i	− 0.0298515i
$191$	10.3601	0.749630	0.374815	−	0.927100i	$-0.377706\pi$
$191$	10.3601	0.749630	0.374815	+	0.927100i	$0.377706\pi$
$192$	3.22668i	0.232866i
$193$	− 15.2540i	− 1.09801i	−0.835820	−	0.549004i	$-0.815007\pi$
$193$	− 15.2540i	− 1.09801i	0.835820	−	0.549004i	$-0.184993\pi$
$194$	0.221629i	0.0159120i
$195$	−1.32770	−0.0950783
$196$	5.74422	0.410302
$197$	− 21.2422i	− 1.51344i	−0.653738	−	0.756721i	$-0.726800\pi$
$197$	− 21.2422i	− 1.51344i	0.653738	−	0.756721i	$-0.273200\pi$
$198$	− 25.2841i	− 1.79686i
$199$	13.0838i	0.927484i	0.885970	+	0.463742i	$0.153494\pi$
$199$	13.0838i	0.927484i	−0.885970	+	0.463742i	$0.846506\pi$
$200$	3.59627	0.254294
$201$	23.5972i	1.66442i
$202$	−4.86484	−0.342289
$203$	−9.84018	−0.690646
$204$	0	0
$205$	3.12567	0.218306
$206$	12.3969	0.863735
$207$	− 3.04963i	− 0.211964i
$208$	0.347296	0.0240807
$209$	− 1.18479i	− 0.0819538i
$210$	4.28405i	0.295628i
$211$	− 9.95130i	− 0.685076i	−0.939504	−	0.342538i	$-0.888713\pi$
$211$	− 9.95130i	− 0.685076i	0.939504	−	0.342538i	$-0.111287\pi$
$212$	−8.41921	−0.578234
$213$	−24.5107	−1.67945
$214$	− 8.85710i	− 0.605459i
$215$	11.0574i	0.754106i
$216$	− 14.2344i	− 0.968530i
$217$	9.76827	0.663113
$218$	− 11.8726i	− 0.804112i
$219$	−29.1753	−1.97148
$220$	−4.04189	−0.272504
$221$	0	0
$222$	1.53478	0.103008
$223$	−19.7638	−1.32348	−0.661742	−	0.749732i	$-0.730182\pi$
$223$	−19.7638	−1.32348	−0.661742	+	0.749732i	$0.730182\pi$
$224$	− 1.12061i	− 0.0748742i
$225$	−26.6536	−1.77691
$226$	10.8648i	0.722718i
$227$	− 3.55438i	− 0.235912i	−0.993019	−	0.117956i	$-0.962366\pi$
$227$	− 3.55438i	− 0.235912i	0.993019	−	0.117956i	$-0.0376342\pi$
$228$	− 1.12061i	− 0.0742145i
$229$	2.04189	0.134932	0.0674659	−	0.997722i	$-0.478509\pi$
$229$	2.04189	0.134932	0.0674659	+	0.997722i	$0.478509\pi$
$230$	−0.487511	−0.0321456
$231$	12.3354i	0.811612i
$232$	− 8.78106i	− 0.576505i
$233$	− 3.91622i	− 0.256560i	−0.991738	−	0.128280i	$-0.959054\pi$
$233$	− 3.91622i	− 0.256560i	0.991738	−	0.128280i	$-0.0409457\pi$
$234$	−2.57398	−0.168266
$235$	− 9.31820i	− 0.607852i
$236$	6.41147	0.417351
$237$	42.8384	2.78266
$238$	0	0
$239$	−21.5544	−1.39424	−0.697118	−	0.716956i	$-0.745535\pi$
$239$	−21.5544	−1.39424	−0.697118	+	0.716956i	$0.745535\pi$
$240$	−3.82295	−0.246770
$241$	− 25.1925i	− 1.62279i	−0.584496	−	0.811397i	$-0.698708\pi$
$241$	− 25.1925i	− 1.62279i	0.584496	−	0.811397i	$-0.301292\pi$
$242$	−0.638156	−0.0410222
$243$	33.7547i	2.16536i
$244$	5.70233i	0.365054i
$245$	6.80571i	0.434801i
$246$	8.51249	0.542736
$247$	−0.120615	−0.00767453
$248$	8.71688i	0.553523i
$249$	24.9718i	1.58253i
$250$	10.1848i	0.644143i
$251$	3.07604	0.194158	0.0970789	−	0.995277i	$-0.469050\pi$
$251$	3.07604	0.194158	0.0970789	+	0.995277i	$0.469050\pi$
$252$	8.30541i	0.523191i
$253$	−1.40373	−0.0882520
$254$	6.55169	0.411090
$255$	0	0
$256$	1.00000	0.0625000
$257$	24.9394	1.55568	0.777840	−	0.628462i	$-0.216315\pi$
$257$	24.9394	1.55568	0.777840	+	0.628462i	$0.216315\pi$
$258$	30.1138i	1.87480i
$259$	−0.533023	−0.0331204
$260$	0.411474i	0.0255185i
$261$	65.0806i	4.02839i
$262$	0.0496299i	0.00306614i
$263$	15.2422	0.939872	0.469936	−	0.882700i	$-0.344277\pi$
$263$	15.2422	0.939872	0.469936	+	0.882700i	$0.344277\pi$
$264$	−11.0077	−0.677480
$265$	− 9.97502i	− 0.612761i
$266$	0.389185i	0.0238625i
$267$	23.1830i	1.41878i
$268$	7.31315	0.446722
$269$	− 3.77332i	− 0.230063i	−0.993362	−	0.115032i	$-0.963303\pi$
$269$	− 3.77332i	− 0.230063i	0.993362	−	0.115032i	$-0.0366969\pi$
$270$	16.8648	1.02636
$271$	4.72462	0.287000	0.143500	−	0.989650i	$-0.454164\pi$
$271$	4.72462	0.287000	0.143500	+	0.989650i	$0.454164\pi$
$272$	0	0
$273$	1.25578	0.0760031
$274$	−8.13341	−0.491357
$275$	12.2686i	0.739823i
$276$	−1.32770	−0.0799179
$277$	18.2276i	1.09519i	0.836743	+	0.547596i	$0.184457\pi$
$277$	18.2276i	1.09519i	−0.836743	+	0.547596i	$0.815543\pi$
$278$	− 15.3824i	− 0.922574i
$279$	− 64.6049i	− 3.86780i
$280$	1.32770	0.0793450
$281$	−25.3773	−1.51388	−0.756942	−	0.653482i	$-0.773308\pi$
$281$	−25.3773	−1.51388	−0.756942	+	0.653482i	$0.773308\pi$
$282$	− 25.3773i	− 1.51120i
$283$	− 13.0446i	− 0.775420i	−0.921781	−	0.387710i	$-0.873266\pi$
$283$	− 13.0446i	− 0.775420i	0.921781	−	0.387710i	$-0.126734\pi$
$284$	7.59627i	0.450755i
$285$	1.32770	0.0786459
$286$	1.18479i	0.0700583i
$287$	−2.95636	−0.174508
$288$	−7.41147	−0.436725
$289$	0	0
$290$	10.4037	0.610928
$291$	−0.715127	−0.0419215
$292$	9.04189i	0.529137i
$293$	3.80571	0.222332	0.111166	−	0.993802i	$-0.464541\pi$
$293$	3.80571	0.222332	0.111166	+	0.993802i	$0.464541\pi$
$294$	18.5348i	1.08097i
$295$	7.59627i	0.442272i
$296$	− 0.475652i	− 0.0276467i
$297$	48.5604	2.81776
$298$	−16.1088	−0.933155
$299$	0.142903i	0.00826432i
$300$	11.6040i	0.669958i
$301$	− 10.4584i	− 0.602813i
$302$	2.70233	0.155502
$303$	− 15.6973i	− 0.901785i
$304$	−0.347296	−0.0199188
$305$	−6.75608	−0.386852
$306$	0	0
$307$	13.1070	0.748056	0.374028	−	0.927417i	$-0.377976\pi$
$307$	13.1070	0.748056	0.374028	+	0.927417i	$0.377976\pi$
$308$	3.82295	0.217833
$309$	40.0009i	2.27557i
$310$	−10.3277	−0.586574
$311$	10.3277i	0.585630i	0.956169	+	0.292815i	$0.0945920\pi$
$311$	10.3277i	0.585630i	−0.956169	+	0.292815i	$0.905408\pi$
$312$	1.12061i	0.0634423i
$313$	21.7178i	1.22756i	0.789476	+	0.613782i	$0.210353\pi$
$313$	21.7178i	1.22756i	−0.789476	+	0.613782i	$0.789647\pi$
$314$	−23.5594	−1.32954
$315$	−9.84018	−0.554432
$316$	− 13.2763i	− 0.746851i
$317$	− 11.1830i	− 0.628102i	−0.949406	−	0.314051i	$-0.898314\pi$
$317$	− 11.1830i	− 0.628102i	0.949406	−	0.314051i	$-0.101686\pi$
$318$	− 27.1661i	− 1.52340i
$319$	29.9564	1.67723
$320$	1.18479i	0.0662319i
$321$	28.5790	1.59513
$322$	0.461104	0.0256963
$323$	0	0
$324$	23.6955	1.31642
$325$	1.24897	0.0692804
$326$	− 1.87433i	− 0.103810i
$327$	38.3090	2.11849
$328$	− 2.63816i	− 0.145668i
$329$	8.81345i	0.485901i
$330$	− 13.0419i	− 0.717932i
$331$	−18.0847	−0.994026	−0.497013	−	0.867743i	$-0.665570\pi$
$331$	−18.0847	−0.994026	−0.497013	+	0.867743i	$0.665570\pi$
$332$	7.73917	0.424742
$333$	3.52528i	0.193184i
$334$	8.85710i	0.484639i
$335$	8.66456i	0.473396i
$336$	3.61587	0.197262
$337$	− 1.68004i	− 0.0915179i	−0.998953	−	0.0457589i	$-0.985429\pi$
$337$	− 1.68004i	− 0.0915179i	0.998953	−	0.0457589i	$-0.0145706\pi$
$338$	−12.8794	−0.700546
$339$	−35.0574	−1.90406
$340$	0	0
$341$	−29.7374	−1.61037
$342$	2.57398	0.139185
$343$	− 14.2814i	− 0.771121i
$344$	9.33275	0.503188
$345$	− 1.57304i	− 0.0846899i
$346$	− 6.41147i	− 0.344683i
$347$	22.4766i	1.20661i	0.797512	+	0.603303i	$0.206149\pi$
$347$	22.4766i	1.20661i	−0.797512	+	0.603303i	$0.793851\pi$
$348$	28.3337	1.51884
$349$	21.1070	1.12983	0.564916	−	0.825148i	$-0.308909\pi$
$349$	21.1070	1.12983	0.564916	+	0.825148i	$0.308909\pi$
$350$	− 4.03003i	− 0.215414i
$351$	− 4.94356i	− 0.263868i
$352$	3.41147i	0.181832i
$353$	3.86659	0.205798	0.102899	−	0.994692i	$-0.467188\pi$
$353$	3.86659	0.205798	0.102899	+	0.994692i	$0.467188\pi$
$354$	20.6878i	1.09954i
$355$	−9.00000	−0.477670
$356$	7.18479	0.380793
$357$	0	0
$358$	1.26083	0.0666369
$359$	−36.4347	−1.92295	−0.961475	−	0.274893i	$-0.911358\pi$
$359$	−36.4347	−1.92295	−0.961475	+	0.274893i	$0.911358\pi$
$360$	− 8.78106i	− 0.462802i
$361$	−18.8794	−0.993652
$362$	− 15.3209i	− 0.805248i
$363$	− 2.05913i	− 0.108076i
$364$	− 0.389185i	− 0.0203989i
$365$	−10.7128	−0.560732
$366$	−18.3996	−0.961763
$367$	− 13.7570i	− 0.718110i	−0.933316	−	0.359055i	$-0.883099\pi$
$367$	− 13.7570i	− 0.718110i	0.933316	−	0.359055i	$-0.116901\pi$
$368$	0.411474i	0.0214496i
$369$	19.5526i	1.01787i
$370$	0.563549	0.0292975
$371$	9.43470i	0.489825i
$372$	−28.1266	−1.45830
$373$	22.7638	1.17867	0.589333	−	0.807890i	$-0.299391\pi$
$373$	22.7638	1.17867	0.589333	+	0.807890i	$0.299391\pi$
$374$	0	0
$375$	−32.8631	−1.69704
$376$	−7.86484	−0.405598
$377$	− 3.04963i	− 0.157064i
$378$	−15.9513	−0.820447
$379$	8.91859i	0.458117i	0.973413	+	0.229058i	$0.0735647\pi$
$379$	8.91859i	0.458117i	−0.973413	+	0.229058i	$0.926435\pi$
$380$	− 0.411474i	− 0.0211082i
$381$	21.1402i	1.08305i
$382$	10.3601	0.530068
$383$	−19.4097	−0.991790	−0.495895	−	0.868382i	$-0.665160\pi$
$383$	−19.4097	−0.991790	−0.495895	+	0.868382i	$0.665160\pi$
$384$	3.22668i	0.164661i
$385$	4.52940i	0.230840i
$386$	− 15.2540i	− 0.776409i
$387$	−69.1694	−3.51608
$388$	0.221629i	0.0112515i
$389$	−35.6614	−1.80810	−0.904052	−	0.427423i	$-0.859422\pi$
$389$	−35.6614	−1.80810	−0.904052	+	0.427423i	$0.859422\pi$
$390$	−1.32770	−0.0672305
$391$	0	0
$392$	5.74422	0.290127
$393$	−0.160140	−0.00807798
$394$	− 21.2422i	− 1.07016i
$395$	15.7297	0.791446
$396$	− 25.2841i	− 1.27057i
$397$	− 7.44562i	− 0.373685i	−0.982390	−	0.186843i	$-0.940175\pi$
$397$	− 7.44562i	− 0.373685i	0.982390	−	0.186843i	$-0.0598254\pi$
$398$	13.0838i	0.655831i
$399$	−1.25578	−0.0628675
$400$	3.59627	0.179813
$401$	− 2.36959i	− 0.118331i	−0.998248	−	0.0591657i	$-0.981156\pi$
$401$	− 2.36959i	− 0.118331i	0.998248	−	0.0591657i	$-0.0188440\pi$
$402$	23.5972i	1.17692i
$403$	3.02734i	0.150803i
$404$	−4.86484	−0.242035
$405$	28.0743i	1.39502i
$406$	−9.84018	−0.488360
$407$	1.62267	0.0804330
$408$	0	0
$409$	−28.8357	−1.42584	−0.712918	−	0.701248i	$-0.752627\pi$
$409$	−28.8357	−1.42584	−0.712918	+	0.701248i	$0.752627\pi$
$410$	3.12567	0.154366
$411$	− 26.2439i	− 1.29452i
$412$	12.3969	0.610753
$413$	− 7.18479i	− 0.353541i
$414$	− 3.04963i	− 0.149881i
$415$	9.16931i	0.450104i
$416$	0.347296	0.0170276
$417$	49.6340	2.43059
$418$	− 1.18479i	− 0.0579501i
$419$	− 30.6800i	− 1.49882i	−0.662107	−	0.749409i	$-0.730338\pi$
$419$	− 30.6800i	− 1.49882i	0.662107	−	0.749409i	$-0.269662\pi$
$420$	4.28405i	0.209040i
$421$	−6.20708	−0.302515	−0.151257	−	0.988494i	$-0.548332\pi$
$421$	−6.20708	−0.302515	−0.151257	+	0.988494i	$0.548332\pi$
$422$	− 9.95130i	− 0.484422i
$423$	58.2900	2.83416
$424$	−8.41921	−0.408873
$425$	0	0
$426$	−24.5107	−1.18755
$427$	6.39012	0.309240
$428$	− 8.85710i	− 0.428124i
$429$	−3.82295	−0.184574
$430$	11.0574i	0.533234i
$431$	− 8.73143i	− 0.420578i	−0.977639	−	0.210289i	$-0.932559\pi$
$431$	− 8.73143i	− 0.420578i	0.977639	−	0.210289i	$-0.0674405\pi$
$432$	− 14.2344i	− 0.684854i
$433$	−20.9855	−1.00850	−0.504248	−	0.863559i	$-0.668230\pi$
$433$	−20.9855	−1.00850	−0.504248	+	0.863559i	$0.668230\pi$
$434$	9.76827	0.468892
$435$	33.5695i	1.60954i
$436$	− 11.8726i	− 0.568593i
$437$	− 0.142903i	− 0.00683600i
$438$	−29.1753	−1.39405
$439$	− 8.46616i	− 0.404068i	−0.979379	−	0.202034i	$-0.935245\pi$
$439$	− 8.46616i	− 0.404068i	0.979379	−	0.202034i	$-0.0647551\pi$
$440$	−4.04189	−0.192690
$441$	−42.5732	−2.02729
$442$	0	0
$443$	23.9564	1.13820	0.569100	−	0.822268i	$-0.307292\pi$
$443$	23.9564	1.13820	0.569100	+	0.822268i	$0.307292\pi$
$444$	1.53478	0.0728373
$445$	8.51249i	0.403531i
$446$	−19.7638	−0.935844
$447$	− 51.9778i	− 2.45847i
$448$	− 1.12061i	− 0.0529441i
$449$	− 6.12567i	− 0.289088i	−0.989498	−	0.144544i	$-0.953828\pi$
$449$	− 6.12567i	− 0.289088i	0.989498	−	0.144544i	$-0.0461715\pi$
$450$	−26.6536	−1.25646
$451$	9.00000	0.423793
$452$	10.8648i	0.511039i
$453$	8.71957i	0.409681i
$454$	− 3.55438i	− 0.166815i
$455$	0.461104	0.0216169
$456$	− 1.12061i	− 0.0524776i
$457$	−1.01691	−0.0475691	−0.0237846	−	0.999717i	$-0.507572\pi$
$457$	−1.01691	−0.0475691	−0.0237846	+	0.999717i	$0.507572\pi$
$458$	2.04189	0.0954112
$459$	0	0
$460$	−0.487511	−0.0227303
$461$	23.0838	1.07512	0.537559	−	0.843226i	$-0.319346\pi$
$461$	23.0838	1.07512	0.537559	+	0.843226i	$0.319346\pi$
$462$	12.3354i	0.573896i
$463$	19.3628	0.899865	0.449932	−	0.893063i	$-0.351448\pi$
$463$	19.3628	0.899865	0.449932	+	0.893063i	$0.351448\pi$
$464$	− 8.78106i	− 0.407650i
$465$	− 33.3242i	− 1.54537i
$466$	− 3.91622i	− 0.181415i
$467$	10.6895	0.494653	0.247326	−	0.968932i	$-0.420448\pi$
$467$	10.6895	0.494653	0.247326	+	0.968932i	$0.420448\pi$
$468$	−2.57398	−0.118982
$469$	− 8.19522i	− 0.378420i
$470$	− 9.31820i	− 0.429817i
$471$	− 76.0188i	− 3.50276i
$472$	6.41147	0.295112
$473$	31.8384i	1.46393i
$474$	42.8384	1.96763
$475$	−1.24897	−0.0573067
$476$	0	0
$477$	62.3988	2.85704
$478$	−21.5544	−0.985874
$479$	19.0155i	0.868840i	0.900711	+	0.434420i	$0.143047\pi$
$479$	19.0155i	0.868840i	−0.900711	+	0.434420i	$0.856953\pi$
$480$	−3.82295	−0.174493
$481$	− 0.165192i	− 0.00753211i
$482$	− 25.1925i	− 1.14749i
$483$	1.48784i	0.0676989i
$484$	−0.638156	−0.0290071
$485$	−0.262585	−0.0119234
$486$	33.7547i	1.53114i
$487$	3.13104i	0.141881i	0.997481	+	0.0709406i	$0.0226001\pi$
$487$	3.13104i	0.141881i	−0.997481	+	0.0709406i	$0.977400\pi$
$488$	5.70233i	0.258133i
$489$	6.04788	0.273494
$490$	6.80571i	0.307451i
$491$	−33.3851	−1.50665	−0.753323	−	0.657650i	$-0.771551\pi$
$491$	−33.3851	−1.50665	−0.753323	+	0.657650i	$0.771551\pi$
$492$	8.51249	0.383773
$493$	0	0
$494$	−0.120615	−0.00542671
$495$	29.9564	1.34644
$496$	8.71688i	0.391400i
$497$	8.51249	0.381837
$498$	24.9718i	1.11901i
$499$	3.93077i	0.175965i	0.996122	+	0.0879827i	$0.0280420\pi$
$499$	3.93077i	0.175965i	−0.996122	+	0.0879827i	$0.971958\pi$
$500$	10.1848i	0.455478i
$501$	−28.5790	−1.27682
$502$	3.07604	0.137290
$503$	− 4.47977i	− 0.199743i	−0.995000	−	0.0998716i	$-0.968157\pi$
$503$	− 4.47977i	− 0.199743i	0.995000	−	0.0998716i	$-0.0318432\pi$
$504$	8.30541i	0.369952i
$505$	− 5.76382i	− 0.256487i
$506$	−1.40373	−0.0624036
$507$	− 41.5577i	− 1.84564i
$508$	6.55169	0.290684
$509$	−2.58853	−0.114734	−0.0573672	−	0.998353i	$-0.518271\pi$
$509$	−2.58853	−0.114734	−0.0573672	+	0.998353i	$0.518271\pi$
$510$	0	0
$511$	10.1325	0.448234
$512$	1.00000	0.0441942
$513$	4.94356i	0.218264i
$514$	24.9394	1.10003
$515$	14.6878i	0.647221i
$516$	30.1138i	1.32569i
$517$	− 26.8307i	− 1.18001i
$518$	−0.533023	−0.0234197
$519$	20.6878	0.908093
$520$	0.411474i	0.0180443i
$521$	38.4020i	1.68242i	0.540708	+	0.841211i	$0.318157\pi$
$521$	38.4020i	1.68242i	−0.540708	+	0.841211i	$0.681843\pi$
$522$	65.0806i	2.84850i
$523$	31.6614	1.38446	0.692228	−	0.721679i	$-0.256629\pi$
$523$	31.6614	1.38446	0.692228	+	0.721679i	$0.256629\pi$
$524$	0.0496299i	0.00216809i
$525$	13.0036	0.567525
$526$	15.2422	0.664590
$527$	0	0
$528$	−11.0077	−0.479050
$529$	22.8307	0.992639
$530$	− 9.97502i	− 0.433287i
$531$	−47.5185	−2.06213
$532$	0.389185i	0.0168733i
$533$	− 0.916222i	− 0.0396860i
$534$	23.1830i	1.00323i
$535$	10.4938	0.453687
$536$	7.31315	0.315880
$537$	4.06830i	0.175560i
$538$	− 3.77332i	− 0.162679i
$539$	19.5963i	0.844071i
$540$	16.8648	0.725747
$541$	− 37.9394i	− 1.63114i	−0.578656	−	0.815572i	$-0.696422\pi$
$541$	− 37.9394i	− 1.63114i	0.578656	−	0.815572i	$-0.303578\pi$
$542$	4.72462	0.202940
$543$	49.4356	2.12149
$544$	0	0
$545$	14.0665	0.602544
$546$	1.25578	0.0537423
$547$	1.48845i	0.0636413i	0.999494	+	0.0318207i	$0.0101305\pi$
$547$	1.48845i	0.0636413i	−0.999494	+	0.0318207i	$0.989869\pi$
$548$	−8.13341	−0.347442
$549$	− 42.2627i	− 1.80373i
$550$	12.2686i	0.523134i
$551$	3.04963i	0.129919i
$552$	−1.32770	−0.0565105
$553$	−14.8776	−0.632661
$554$	18.2276i	0.774417i
$555$	1.81839i	0.0771865i
$556$	− 15.3824i	− 0.652358i
$557$	23.3259	0.988352	0.494176	−	0.869362i	$-0.335470\pi$
$557$	23.3259	0.988352	0.494176	+	0.869362i	$0.335470\pi$
$558$	− 64.6049i	− 2.73495i
$559$	3.24123	0.137089
$560$	1.32770	0.0561054
$561$	0	0
$562$	−25.3773	−1.07048
$563$	4.37733	0.184482	0.0922411	−	0.995737i	$-0.470597\pi$
$563$	4.37733	0.184482	0.0922411	+	0.995737i	$0.470597\pi$
$564$	− 25.3773i	− 1.06858i
$565$	−12.8726	−0.541553
$566$	− 13.0446i	− 0.548304i
$567$	− 26.5536i	− 1.11514i
$568$	7.59627i	0.318732i
$569$	−4.69553	−0.196847	−0.0984234	−	0.995145i	$-0.531380\pi$
$569$	−4.69553	−0.196847	−0.0984234	+	0.995145i	$0.531380\pi$
$570$	1.32770	0.0556111
$571$	13.4679i	0.563615i	0.959471	+	0.281807i	$0.0909339\pi$
$571$	13.4679i	0.563615i	−0.959471	+	0.281807i	$0.909066\pi$
$572$	1.18479i	0.0495387i
$573$	33.4287i	1.39650i
$574$	−2.95636	−0.123396
$575$	1.47977i	0.0617107i
$576$	−7.41147	−0.308811
$577$	22.8066	0.949453	0.474727	−	0.880133i	$-0.342547\pi$
$577$	22.8066	0.949453	0.474727	+	0.880133i	$0.342547\pi$
$578$	0	0
$579$	49.2199	2.04551
$580$	10.4037	0.431992
$581$	− 8.67263i	− 0.359801i
$582$	−0.715127	−0.0296430
$583$	− 28.7219i	− 1.18954i
$584$	9.04189i	0.374156i
$585$	− 3.04963i	− 0.126087i
$586$	3.80571	0.157213
$587$	−38.5945	−1.59297	−0.796483	−	0.604661i	$-0.793309\pi$
$587$	−38.5945	−1.59297	−0.796483	+	0.604661i	$0.793309\pi$
$588$	18.5348i	0.764361i
$589$	− 3.02734i	− 0.124739i
$590$	7.59627i	0.312733i
$591$	68.5417	2.81943
$592$	− 0.475652i	− 0.0195492i
$593$	−2.30272	−0.0945613	−0.0472807	−	0.998882i	$-0.515056\pi$
$593$	−2.30272	−0.0945613	−0.0472807	+	0.998882i	$0.515056\pi$
$594$	48.5604	1.99246
$595$	0	0
$596$	−16.1088	−0.659840
$597$	−42.2172	−1.72783
$598$	0.142903i	0.00584376i
$599$	−29.1830	−1.19239	−0.596193	−	0.802841i	$-0.703321\pi$
$599$	−29.1830	−1.19239	−0.596193	+	0.802841i	$0.703321\pi$
$600$	11.6040i	0.473732i
$601$	− 14.0428i	− 0.572819i	−0.958107	−	0.286409i	$-0.907538\pi$
$601$	− 14.0428i	− 0.572819i	0.958107	−	0.286409i	$-0.0924617\pi$
$602$	− 10.4584i	− 0.426253i
$603$	−54.2012	−2.20724
$604$	2.70233	0.109956
$605$	− 0.756082i	− 0.0307391i
$606$	− 15.6973i	− 0.637658i
$607$	10.2635i	0.416583i	0.978067	+	0.208292i	$0.0667903\pi$
$607$	10.2635i	0.416583i	−0.978067	+	0.208292i	$0.933210\pi$
$608$	−0.347296	−0.0140847
$609$	− 31.7511i	− 1.28662i
$610$	−6.75608	−0.273546
$611$	−2.73143	−0.110502
$612$	0	0
$613$	2.66725	0.107729	0.0538646	−	0.998548i	$-0.482846\pi$
$613$	2.66725	0.107729	0.0538646	+	0.998548i	$0.482846\pi$
$614$	13.1070	0.528955
$615$	10.0855i	0.406688i
$616$	3.82295	0.154031
$617$	39.5544i	1.59240i	0.605034	+	0.796200i	$0.293160\pi$
$617$	39.5544i	1.59240i	−0.605034	+	0.796200i	$0.706840\pi$
$618$	40.0009i	1.60907i
$619$	22.3851i	0.899732i	0.893096	+	0.449866i	$0.148528\pi$
$619$	22.3851i	0.899732i	−0.893096	+	0.449866i	$0.851472\pi$
$620$	−10.3277	−0.414770
$621$	5.85710	0.235037
$622$	10.3277i	0.414103i
$623$	− 8.05138i	− 0.322572i
$624$	1.12061i	0.0448605i
$625$	5.91447	0.236579
$626$	21.7178i	0.868018i
$627$	3.82295	0.152674
$628$	−23.5594	−0.940124
$629$	0	0
$630$	−9.84018	−0.392042
$631$	13.9727	0.556243	0.278121	−	0.960546i	$-0.410288\pi$
$631$	13.9727	0.556243	0.278121	+	0.960546i	$0.410288\pi$
$632$	− 13.2763i	− 0.528103i
$633$	32.1097	1.27625
$634$	− 11.1830i	− 0.444135i
$635$	7.76239i	0.308041i
$636$	− 27.1661i	− 1.07721i
$637$	1.99495	0.0790427
$638$	29.9564	1.18598
$639$	− 56.2995i	− 2.22718i
$640$	1.18479i	0.0468330i
$641$	− 24.5868i	− 0.971119i	−0.874204	−	0.485560i	$-0.838616\pi$
$641$	− 24.5868i	− 0.971119i	0.874204	−	0.485560i	$-0.161384\pi$
$642$	28.5790	1.12792
$643$	29.6996i	1.17124i	0.810586	+	0.585620i	$0.199149\pi$
$643$	29.6996i	1.17124i	−0.810586	+	0.585620i	$0.800851\pi$
$644$	0.461104	0.0181700
$645$	−35.6786	−1.40484
$646$	0	0
$647$	16.3946	0.644537	0.322268	−	0.946648i	$-0.395555\pi$
$647$	16.3946	0.644537	0.322268	+	0.946648i	$0.395555\pi$
$648$	23.6955	0.930848
$649$	21.8726i	0.858574i
$650$	1.24897	0.0489886
$651$	31.5191i	1.23533i
$652$	− 1.87433i	− 0.0734045i
$653$	− 35.8307i	− 1.40216i	−0.713081	−	0.701082i	$-0.752701\pi$
$653$	− 35.8307i	− 1.40216i	0.713081	−	0.701082i	$-0.247299\pi$
$654$	38.3090	1.49800
$655$	−0.0588011	−0.00229755
$656$	− 2.63816i	− 0.103003i
$657$	− 67.0137i	− 2.61445i
$658$	8.81345i	0.343584i
$659$	−28.5354	−1.11158	−0.555790	−	0.831322i	$-0.687584\pi$
$659$	−28.5354	−1.11158	−0.555790	+	0.831322i	$0.687584\pi$
$660$	− 13.0419i	− 0.507655i
$661$	45.1462	1.75598	0.877992	−	0.478676i	$-0.158883\pi$
$661$	45.1462	1.75598	0.877992	+	0.478676i	$0.158883\pi$
$662$	−18.0847	−0.702882
$663$	0	0
$664$	7.73917	0.300338
$665$	−0.461104	−0.0178808
$666$	3.52528i	0.136602i
$667$	3.61318	0.139903
$668$	8.85710i	0.342691i
$669$	− 63.7716i	− 2.46555i
$670$	8.66456i	0.334741i
$671$	−19.4534	−0.750989
$672$	3.61587	0.139485
$673$	4.91178i	0.189335i	0.995509	+	0.0946676i	$0.0301788\pi$
$673$	4.91178i	0.189335i	−0.995509	+	0.0946676i	$0.969821\pi$
$674$	− 1.68004i	− 0.0647129i
$675$	− 51.1908i	− 1.97033i
$676$	−12.8794	−0.495361
$677$	− 18.7885i	− 0.722100i	−0.932547	−	0.361050i	$-0.882418\pi$
$677$	− 18.7885i	− 0.722100i	0.932547	−	0.361050i	$-0.117582\pi$
$678$	−35.0574	−1.34637
$679$	0.248361	0.00953122
$680$	0	0
$681$	11.4688	0.439487
$682$	−29.7374	−1.13870
$683$	25.5699i	0.978403i	0.872171	+	0.489202i	$0.162712\pi$
$683$	25.5699i	0.978403i	−0.872171	+	0.489202i	$0.837288\pi$
$684$	2.57398	0.0984185
$685$	− 9.63640i	− 0.368188i
$686$	− 14.2814i	− 0.545265i
$687$	6.58853i	0.251368i
$688$	9.33275	0.355808
$689$	−2.92396	−0.111394
$690$	− 1.57304i	− 0.0598848i
$691$	41.6091i	1.58288i	0.611245	+	0.791442i	$0.290669\pi$
$691$	41.6091i	1.58288i	−0.611245	+	0.791442i	$0.709331\pi$
$692$	− 6.41147i	− 0.243728i
$693$	−28.3337	−1.07631
$694$	22.4766i	0.853200i
$695$	18.2249	0.691311
$696$	28.3337	1.07399
$697$	0	0
$698$	21.1070	0.798912
$699$	12.6364	0.477953
$700$	− 4.03003i	− 0.152321i
$701$	−0.746911	−0.0282104	−0.0141052	−	0.999901i	$-0.504490\pi$
$701$	−0.746911	−0.0282104	−0.0141052	+	0.999901i	$0.504490\pi$
$702$	− 4.94356i	− 0.186583i
$703$	0.165192i	0.00623034i
$704$	3.41147i	0.128575i
$705$	30.0669	1.13238
$706$	3.86659	0.145521
$707$	5.45161i	0.205029i
$708$	20.6878i	0.777495i
$709$	− 21.1310i	− 0.793593i	−0.917907	−	0.396797i	$-0.870122\pi$
$709$	− 21.1310i	− 0.793593i	0.917907	−	0.396797i	$-0.129878\pi$
$710$	−9.00000	−0.337764
$711$	98.3970i	3.69018i
$712$	7.18479	0.269261
$713$	−3.58677	−0.134326
$714$	0	0
$715$	−1.40373	−0.0524967
$716$	1.26083	0.0471194
$717$	− 69.5491i	− 2.59736i
$718$	−36.4347	−1.35973
$719$	3.46110i	0.129077i	0.997915	+	0.0645387i	$0.0205576\pi$
$719$	3.46110i	0.129077i	−0.997915	+	0.0645387i	$0.979442\pi$
$720$	− 8.78106i	− 0.327251i
$721$	− 13.8922i	− 0.517372i
$722$	−18.8794	−0.702618
$723$	81.2883	3.02314
$724$	− 15.3209i	− 0.569396i
$725$	− 31.5790i	− 1.17282i
$726$	− 2.05913i	− 0.0764213i
$727$	−36.3327	−1.34751	−0.673754	−	0.738956i	$-0.735319\pi$
$727$	−36.3327	−1.34751	−0.673754	+	0.738956i	$0.735319\pi$
$728$	− 0.389185i	− 0.0144242i
$729$	−37.8289	−1.40107
$730$	−10.7128	−0.396497
$731$	0	0
$732$	−18.3996	−0.680069
$733$	−6.90167	−0.254919	−0.127460	−	0.991844i	$-0.540682\pi$
$733$	−6.90167	−0.254919	−0.127460	+	0.991844i	$0.540682\pi$
$734$	− 13.7570i	− 0.507781i
$735$	−21.9599	−0.810002
$736$	0.411474i	0.0151671i
$737$	24.9486i	0.918994i
$738$	19.5526i	0.719742i
$739$	36.3651	1.33771	0.668857	−	0.743391i	$-0.266784\pi$
$739$	36.3651	1.33771	0.668857	+	0.743391i	$0.266784\pi$
$740$	0.563549	0.0207165
$741$	− 0.389185i	− 0.0142971i
$742$	9.43470i	0.346359i
$743$	48.3150i	1.77251i	0.463201	+	0.886253i	$0.346701\pi$
$743$	48.3150i	1.77251i	−0.463201	+	0.886253i	$0.653299\pi$
$744$	−28.1266	−1.03117
$745$	− 19.0855i	− 0.699240i
$746$	22.7638	0.833443
$747$	−57.3587	−2.09864
$748$	0	0
$749$	−9.92539	−0.362666
$750$	−32.8631	−1.19999
$751$	10.9436i	0.399336i	0.979864	+	0.199668i	$0.0639864\pi$
$751$	10.9436i	0.399336i	−0.979864	+	0.199668i	$0.936014\pi$
$752$	−7.86484	−0.286801
$753$	9.92539i	0.361701i
$754$	− 3.04963i	− 0.111061i
$755$	3.20170i	0.116522i
$756$	−15.9513	−0.580143
$757$	−20.0601	−0.729095	−0.364548	−	0.931185i	$-0.618776\pi$
$757$	−20.0601	−0.729095	−0.364548	+	0.931185i	$0.618776\pi$
$758$	8.91859i	0.323938i
$759$	− 4.52940i	− 0.164407i
$760$	− 0.411474i	− 0.0149257i
$761$	−36.4671	−1.32193	−0.660965	−	0.750416i	$-0.729853\pi$
$761$	−36.4671	−1.32193	−0.660965	+	0.750416i	$0.729853\pi$
$762$	21.1402i	0.765829i
$763$	−13.3046	−0.481658
$764$	10.3601	0.374815
$765$	0	0
$766$	−19.4097	−0.701302
$767$	2.22668	0.0804008
$768$	3.22668i	0.116433i
$769$	45.8120	1.65202	0.826012	−	0.563653i	$-0.190604\pi$
$769$	45.8120	1.65202	0.826012	+	0.563653i	$0.190604\pi$
$770$	4.52940i	0.163228i
$771$	80.4716i	2.89812i
$772$	− 15.2540i	− 0.549004i
$773$	42.1549	1.51621	0.758103	−	0.652135i	$-0.226127\pi$
$773$	42.1549	1.51621	0.758103	+	0.652135i	$0.226127\pi$
$774$	−69.1694	−2.48624
$775$	31.3482i	1.12606i
$776$	0.221629i	0.00795602i
$777$	− 1.71989i	− 0.0617009i
$778$	−35.6614	−1.27852
$779$	0.916222i	0.0328271i
$780$	−1.32770	−0.0475391
$781$	−25.9145	−0.927293
$782$	0	0
$783$	−124.993	−4.46690
$784$	5.74422	0.205151
$785$	− 27.9130i	− 0.996259i
$786$	−0.160140	−0.00571200
$787$	− 22.2145i	− 0.791861i	−0.918280	−	0.395931i	$-0.870422\pi$
$787$	− 22.2145i	− 0.791861i	0.918280	−	0.395931i	$-0.129578\pi$
$788$	− 21.2422i	− 0.756721i
$789$	49.1816i	1.75091i
$790$	15.7297	0.559637
$791$	12.1753	0.432904
$792$	− 25.2841i	− 0.898430i
$793$	1.98040i	0.0703261i
$794$	− 7.44562i	− 0.264235i
$795$	32.1862	1.14153
$796$	13.0838i	0.463742i
$797$	−5.68180	−0.201260	−0.100630	−	0.994924i	$-0.532086\pi$
$797$	−5.68180	−0.201260	−0.100630	+	0.994924i	$0.532086\pi$
$798$	−1.25578	−0.0444540
$799$	0	0
$800$	3.59627	0.127147
$801$	−53.2499	−1.88149
$802$	− 2.36959i	− 0.0836730i
$803$	−30.8462	−1.08854
$804$	23.5972i	0.832209i
$805$	0.546313i	0.0192550i
$806$	3.02734i	0.106634i
$807$	12.1753	0.428591
$808$	−4.86484	−0.171144
$809$	− 17.8631i	− 0.628033i	−0.949418	−	0.314016i	$-0.898325\pi$
$809$	− 17.8631i	− 0.628033i	0.949418	−	0.314016i	$-0.101675\pi$
$810$	28.0743i	0.986430i
$811$	2.49794i	0.0877146i	0.999038	+	0.0438573i	$0.0139647\pi$
$811$	2.49794i	0.0877146i	−0.999038	+	0.0438573i	$0.986035\pi$
$812$	−9.84018	−0.345323
$813$	15.2449i	0.534660i
$814$	1.62267	0.0568747
$815$	2.22070	0.0777876
$816$	0	0
$817$	−3.24123	−0.113396
$818$	−28.8357	−1.00822
$819$	2.88444i	0.100790i
$820$	3.12567	0.109153
$821$	25.7128i	0.897382i	0.893687	+	0.448691i	$0.148110\pi$
$821$	25.7128i	0.897382i	−0.893687	+	0.448691i	$0.851890\pi$
$822$	− 26.2439i	− 0.915362i
$823$	− 13.3304i	− 0.464668i	−0.972636	−	0.232334i	$-0.925364\pi$
$823$	− 13.3304i	− 0.464668i	0.972636	−	0.232334i	$-0.0746362\pi$
$824$	12.3969	0.431867
$825$	−39.5868	−1.37823
$826$	− 7.18479i	− 0.249991i
$827$	11.2855i	0.392435i	0.980560	+	0.196217i	$0.0628658\pi$
$827$	11.2855i	0.392435i	−0.980560	+	0.196217i	$0.937134\pi$
$828$	− 3.04963i	− 0.105982i
$829$	−25.9786	−0.902276	−0.451138	−	0.892454i	$-0.648982\pi$
$829$	−25.9786	−0.902276	−0.451138	+	0.892454i	$0.648982\pi$
$830$	9.16931i	0.318271i
$831$	−58.8147	−2.04026
$832$	0.347296	0.0120403
$833$	0	0
$834$	49.6340	1.71869
$835$	−10.4938	−0.363154
$836$	− 1.18479i	− 0.0409769i
$837$	124.080	4.28882
$838$	− 30.6800i	− 1.05982i
$839$	20.9736i	0.724089i	0.932161	+	0.362044i	$0.117921\pi$
$839$	20.9736i	0.724089i	−0.932161	+	0.362044i	$0.882079\pi$
$840$	4.28405i	0.147814i
$841$	−48.1070	−1.65886
$842$	−6.20708	−0.213910
$843$	− 81.8846i	− 2.82025i
$844$	− 9.95130i	− 0.342538i
$845$	− 15.2594i	− 0.524939i
$846$	58.2900	2.00405
$847$	0.715127i	0.0245720i
$848$	−8.41921	−0.289117
$849$	42.0907	1.44455
$850$	0	0
$851$	0.195718	0.00670914
$852$	−24.5107	−0.839724
$853$	50.9650i	1.74501i	0.488606	+	0.872505i	$0.337506\pi$
$853$	50.9650i	1.74501i	−0.488606	+	0.872505i	$0.662494\pi$
$854$	6.39012	0.218665
$855$	3.04963i	0.104295i
$856$	− 8.85710i	− 0.302729i
$857$	− 39.0060i	− 1.33242i	−0.745765	−	0.666210i	$-0.767916\pi$
$857$	− 39.0060i	− 1.33242i	0.745765	−	0.666210i	$-0.232084\pi$
$858$	−3.82295	−0.130513
$859$	12.6742	0.432437	0.216219	−	0.976345i	$-0.430628\pi$
$859$	12.6742	0.432437	0.216219	+	0.976345i	$0.430628\pi$
$860$	11.0574i	0.377053i
$861$	− 9.53922i	− 0.325096i
$862$	− 8.73143i	− 0.297394i
$863$	31.9905	1.08897	0.544485	−	0.838771i	$-0.316725\pi$
$863$	31.9905	1.08897	0.544485	+	0.838771i	$0.316725\pi$
$864$	− 14.2344i	− 0.484265i
$865$	7.59627	0.258281
$866$	−20.9855	−0.713115
$867$	0	0
$868$	9.76827	0.331557
$869$	45.2918	1.53642
$870$	33.5695i	1.13811i
$871$	2.53983	0.0860588
$872$	− 11.8726i	− 0.402056i
$873$	− 1.64260i	− 0.0555935i
$874$	− 0.142903i	− 0.00483378i
$875$	11.4132	0.385838
$876$	−29.1753	−0.985742
$877$	28.6212i	0.966471i	0.875490	+	0.483235i	$0.160538\pi$
$877$	28.6212i	0.966471i	−0.875490	+	0.483235i	$0.839462\pi$
$878$	− 8.46616i	− 0.285719i
$879$	12.2798i	0.414188i
$880$	−4.04189	−0.136252
$881$	− 18.2594i	− 0.615175i	−0.951520	−	0.307587i	$-0.900478\pi$
$881$	− 18.2594i	− 0.615175i	0.951520	−	0.307587i	$-0.0995216\pi$
$882$	−42.5732	−1.43351
$883$	−18.4688	−0.621526	−0.310763	−	0.950487i	$-0.600585\pi$
$883$	−18.4688	−0.621526	−0.310763	+	0.950487i	$0.600585\pi$
$884$	0	0
$885$	−24.5107	−0.823919
$886$	23.9564	0.804830
$887$	43.4858i	1.46011i	0.683389	+	0.730054i	$0.260505\pi$
$887$	43.4858i	1.46011i	−0.683389	+	0.730054i	$0.739495\pi$
$888$	1.53478	0.0515038
$889$	− 7.34192i	− 0.246240i
$890$	8.51249i	0.285339i
$891$	80.8367i	2.70813i
$892$	−19.7638	−0.661742
$893$	2.73143	0.0914038
$894$	− 51.9778i	− 1.73840i
$895$	1.49382i	0.0499330i
$896$	− 1.12061i	− 0.0374371i
$897$	−0.461104	−0.0153958
$898$	− 6.12567i	− 0.204416i
$899$	76.5435	2.55287
$900$	−26.6536	−0.888455
$901$	0	0
$902$	9.00000	0.299667
$903$	33.7460	1.12300
$904$	10.8648i	0.361359i
$905$	18.1521	0.603395
$906$	8.71957i	0.289688i
$907$	26.3993i	0.876574i	0.898835	+	0.438287i	$0.144415\pi$
$907$	26.3993i	0.876574i	−0.898835	+	0.438287i	$0.855585\pi$
$908$	− 3.55438i	− 0.117956i
$909$	36.0556	1.19589
$910$	0.461104	0.0152854
$911$	2.66138i	0.0881754i	0.999028	+	0.0440877i	$0.0140381\pi$
$911$	2.66138i	0.0881754i	−0.999028	+	0.0440877i	$0.985962\pi$
$912$	− 1.12061i	− 0.0371073i
$913$	26.4020i	0.873778i
$914$	−1.01691	−0.0336365
$915$	− 21.7997i	− 0.720677i
$916$	2.04189	0.0674659
$917$	0.0556159	0.00183660
$918$	0	0
$919$	15.1088	0.498392	0.249196	−	0.968453i	$-0.419834\pi$
$919$	15.1088	0.498392	0.249196	+	0.968453i	$0.419834\pi$
$920$	−0.487511	−0.0160728
$921$	42.2921i	1.39357i
$922$	23.0838	0.760224
$923$	2.63816i	0.0868360i
$924$	12.3354i	0.405806i
$925$	− 1.71057i	− 0.0562432i
$926$	19.3628	0.636300
$927$	−91.8795	−3.01772
$928$	− 8.78106i	− 0.288252i
$929$	− 4.94087i	− 0.162105i	−0.996710	−	0.0810524i	$-0.974172\pi$
$929$	− 4.94087i	− 0.162105i	0.996710	−	0.0810524i	$-0.0258281\pi$
$930$	− 33.3242i	− 1.09274i
$931$	−1.99495	−0.0653818
$932$	− 3.91622i	− 0.128280i
$933$	−33.3242	−1.09098
$934$	10.6895	0.349772
$935$	0	0
$936$	−2.57398	−0.0841331
$937$	−3.41416	−0.111536	−0.0557679	−	0.998444i	$-0.517761\pi$
$937$	−3.41416	−0.111536	−0.0557679	+	0.998444i	$0.517761\pi$
$938$	− 8.19522i	− 0.267583i
$939$	−70.0765	−2.28686
$940$	− 9.31820i	− 0.303926i
$941$	28.2608i	0.921277i	0.887588	+	0.460638i	$0.152379\pi$
$941$	28.2608i	0.921277i	−0.887588	+	0.460638i	$0.847621\pi$
$942$	− 76.0188i	− 2.47683i
$943$	1.08553	0.0353498
$944$	6.41147	0.208676
$945$	− 18.8990i	− 0.614784i
$946$	31.8384i	1.03516i
$947$	− 6.08410i	− 0.197707i	−0.995102	−	0.0988534i	$-0.968483\pi$
$947$	− 6.08410i	− 0.197707i	0.995102	−	0.0988534i	$-0.0315175\pi$
$948$	42.8384	1.39133
$949$	3.14022i	0.101936i
$950$	−1.24897	−0.0405219
$951$	36.0841	1.17011
$952$	0	0
$953$	26.7110	0.865254	0.432627	−	0.901573i	$-0.357587\pi$
$953$	26.7110	0.865254	0.432627	+	0.901573i	$0.357587\pi$
$954$	62.3988	2.02024
$955$	12.2746i	0.397195i
$956$	−21.5544	−0.697118
$957$	96.6596i	3.12456i
$958$	19.0155i	0.614362i
$959$	9.11442i	0.294320i
$960$	−3.82295	−0.123385
$961$	−44.9840	−1.45110
$962$	− 0.165192i	− 0.00532601i
$963$	65.6441i	2.11535i
$964$	− 25.1925i	− 0.811397i
$965$	18.0729	0.581786
$966$	1.48784i	0.0478703i
$967$	27.1070	0.871702	0.435851	−	0.900019i	$-0.356447\pi$
$967$	27.1070	0.871702	0.435851	+	0.900019i	$0.356447\pi$
$968$	−0.638156	−0.0205111
$969$	0	0
$970$	−0.262585	−0.00843108
$971$	−50.0725	−1.60690	−0.803452	−	0.595370i	$-0.797006\pi$
$971$	−50.0725	−1.60690	−0.803452	+	0.595370i	$0.797006\pi$
$972$	33.7547i	1.08268i
$973$	−17.2377	−0.552616
$974$	3.13104i	0.100325i
$975$	4.03003i	0.129064i
$976$	5.70233i	0.182527i
$977$	−2.25309	−0.0720827	−0.0360414	−	0.999350i	$-0.511475\pi$
$977$	−2.25309	−0.0720827	−0.0360414	+	0.999350i	$0.511475\pi$
$978$	6.04788	0.193390
$979$	24.5107i	0.783366i
$980$	6.80571i	0.217400i
$981$	87.9933i	2.80941i
$982$	−33.3851	−1.06536
$983$	34.7047i	1.10691i	0.832880	+	0.553454i	$0.186691\pi$
$983$	34.7047i	1.10691i	−0.832880	+	0.553454i	$0.813309\pi$
$984$	8.51249	0.271368
$985$	25.1676	0.801905
$986$	0	0
$987$	−28.4382	−0.905198
$988$	−0.120615	−0.00383727
$989$	3.84018i	0.122111i
$990$	29.9564	0.952075
$991$	− 15.3200i	− 0.486654i	−0.969944	−	0.243327i	$-0.921761\pi$
$991$	− 15.3200i	− 0.486654i	0.969944	−	0.243327i	$-0.0782389\pi$
$992$	8.71688i	0.276761i
$993$	− 58.3536i	− 1.85180i
$994$	8.51249	0.270000
$995$	−15.5016	−0.491433
$996$	24.9718i	0.791263i
$997$	52.6076i	1.66610i	0.553197	+	0.833050i	$0.313408\pi$
$997$	52.6076i	1.66610i	−0.553197	+	0.833050i	$0.686592\pi$
$998$	3.93077i	0.124426i
$999$	−6.77063	−0.214213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	578.2.b.f.577.6		6
17.2	even	8		578.2.c.g.251.6		12
17.3	odd	16		578.2.d.h.399.1		24
17.4	even	4		578.2.a.f.1.3	yes	3
17.5	odd	16		578.2.d.h.179.1		24
17.6	odd	16		578.2.d.h.423.6		24
17.7	odd	16		578.2.d.h.155.6		24
17.8	even	8		578.2.c.g.327.6		12
17.9	even	8		578.2.c.g.327.1		12
17.10	odd	16		578.2.d.h.155.1		24
17.11	odd	16		578.2.d.h.423.1		24
17.12	odd	16		578.2.d.h.179.6		24
17.13	even	4		578.2.a.e.1.1	✓	3
17.14	odd	16		578.2.d.h.399.6		24
17.15	even	8		578.2.c.g.251.1		12
17.16	even	2	inner	578.2.b.f.577.1		6
51.38	odd	4		5202.2.a.bo.1.2		3
51.47	odd	4		5202.2.a.bn.1.2		3
68.47	odd	4		4624.2.a.bj.1.3		3
68.55	odd	4		4624.2.a.ba.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
578.2.a.e.1.1	✓	3	17.13	even	4
578.2.a.f.1.3	yes	3	17.4	even	4
578.2.b.f.577.1		6	17.16	even	2	inner
578.2.b.f.577.6		6	1.1	even	1	trivial
578.2.c.g.251.1		12	17.15	even	8
578.2.c.g.251.6		12	17.2	even	8
578.2.c.g.327.1		12	17.9	even	8
578.2.c.g.327.6		12	17.8	even	8
578.2.d.h.155.1		24	17.10	odd	16
578.2.d.h.155.6		24	17.7	odd	16
578.2.d.h.179.1		24	17.5	odd	16
578.2.d.h.179.6		24	17.12	odd	16
578.2.d.h.399.1		24	17.3	odd	16
578.2.d.h.399.6		24	17.14	odd	16
578.2.d.h.423.1		24	17.11	odd	16
578.2.d.h.423.6		24	17.6	odd	16
4624.2.a.ba.1.1		3	68.55	odd	4
4624.2.a.bj.1.3		3	68.47	odd	4
5202.2.a.bn.1.2		3	51.47	odd	4
5202.2.a.bo.1.2		3	51.38	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 578 = 2 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	578.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.22668i q^{3} +1.00000 q^{4} +1.18479i q^{5} +3.22668i q^{6} -1.12061i q^{7} +1.00000 q^{8} -7.41147 q^{9} +1.18479i q^{10} +3.41147i q^{11} +3.22668i q^{12} +0.347296 q^{13} -1.12061i q^{14} -3.82295 q^{15} +1.00000 q^{16} -7.41147 q^{18} -0.347296 q^{19} +1.18479i q^{20} +3.61587 q^{21} +3.41147i q^{22} +0.411474i q^{23} +3.22668i q^{24} +3.59627 q^{25} +0.347296 q^{26} -14.2344i q^{27} -1.12061i q^{28} -8.78106i q^{29} -3.82295 q^{30} +8.71688i q^{31} +1.00000 q^{32} -11.0077 q^{33} +1.32770 q^{35} -7.41147 q^{36} -0.475652i q^{37} -0.347296 q^{38} +1.12061i q^{39} +1.18479i q^{40} -2.63816i q^{41} +3.61587 q^{42} +9.33275 q^{43} +3.41147i q^{44} -8.78106i q^{45} +0.411474i q^{46} -7.86484 q^{47} +3.22668i q^{48} +5.74422 q^{49} +3.59627 q^{50} +0.347296 q^{52} -8.41921 q^{53} -14.2344i q^{54} -4.04189 q^{55} -1.12061i q^{56} -1.12061i q^{57} -8.78106i q^{58} +6.41147 q^{59} -3.82295 q^{60} +5.70233i q^{61} +8.71688i q^{62} +8.30541i q^{63} +1.00000 q^{64} +0.411474i q^{65} -11.0077 q^{66} +7.31315 q^{67} -1.32770 q^{69} +1.32770 q^{70} +7.59627i q^{71} -7.41147 q^{72} +9.04189i q^{73} -0.475652i q^{74} +11.6040i q^{75} -0.347296 q^{76} +3.82295 q^{77} +1.12061i q^{78} -13.2763i q^{79} +1.18479i q^{80} +23.6955 q^{81} -2.63816i q^{82} +7.73917 q^{83} +3.61587 q^{84} +9.33275 q^{86} +28.3337 q^{87} +3.41147i q^{88} +7.18479 q^{89} -8.78106i q^{90} -0.389185i q^{91} +0.411474i q^{92} -28.1266 q^{93} -7.86484 q^{94} -0.411474i q^{95} +3.22668i q^{96} +0.221629i q^{97} +5.74422 q^{98} -25.2841i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} + 6 q^{8} - 24 q^{9} + 18 q^{15} + 6 q^{16} - 24 q^{18} - 6 q^{25} + 18 q^{30} + 6 q^{32} - 18 q^{33} - 24 q^{36} + 18 q^{43} - 24 q^{49} - 6 q^{50} + 18 q^{53} - 18 q^{55} + 18 q^{59}+ \cdots - 24 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 + 6 * q^8 - 24 * q^9 + 18 * q^15 + 6 * q^16 - 24 * q^18 - 6 * q^25 + 18 * q^30 + 6 * q^32 - 18 * q^33 - 24 * q^36 + 18 * q^43 - 24 * q^49 - 6 * q^50 + 18 * q^53 - 18 * q^55 + 18 * q^59 + 18 * q^60 + 6 * q^64 - 18 * q^66 - 24 * q^72 - 18 * q^77 + 6 * q^81 + 18 * q^83 + 18 * q^86 + 36 * q^89 - 18 * q^93 - 24 * q^98

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