LMFDB - Embedded newform 289.2.b.d.288.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,2,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, 2, names="a")

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

chi := DirichletCharacter("289.288");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
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:	$2.30767661842$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			288.5
Root			$-1.53209i$ of defining polynomial
Character	$\chi$	$=$	289.288
Dual form			289.2.b.d.288.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.87939 q^{2} -2.53209i q^{3} +1.53209 q^{4} -0.120615i q^{5} -4.75877i q^{6} -1.53209i q^{7} -0.879385 q^{8} -3.41147 q^{9} +O(q^{10})$	\(q+1.87939 q^{2} -2.53209i q^{3} +1.53209 q^{4} -0.120615i q^{5} -4.75877i q^{6} -1.53209i q^{7} -0.879385 q^{8} -3.41147 q^{9} -0.226682i q^{10} +2.69459i q^{11} -3.87939i q^{12} +4.57398 q^{13} -2.87939i q^{14} -0.305407 q^{15} -4.71688 q^{16} -6.41147 q^{18} +1.87939 q^{19} -0.184793i q^{20} -3.87939 q^{21} +5.06418i q^{22} +7.41147i q^{23} +2.22668i q^{24} +4.98545 q^{25} +8.59627 q^{26} +1.04189i q^{27} -2.34730i q^{28} -3.41147i q^{29} -0.573978 q^{30} -3.83750i q^{31} -7.10607 q^{32} +6.82295 q^{33} -0.184793 q^{35} -5.22668 q^{36} +5.24897i q^{37} +3.53209 q^{38} -11.5817i q^{39} +0.106067i q^{40} +6.24897i q^{41} -7.29086 q^{42} -5.49020 q^{43} +4.12836i q^{44} +0.411474i q^{45} +13.9290i q^{46} -7.34730 q^{47} +11.9436i q^{48} +4.65270 q^{49} +9.36959 q^{50} +7.00774 q^{52} -0.822948 q^{53} +1.95811i q^{54} +0.325008 q^{55} +1.34730i q^{56} -4.75877i q^{57} -6.41147i q^{58} +3.14290 q^{59} -0.467911 q^{60} +1.22668i q^{61} -7.21213i q^{62} +5.22668i q^{63} -3.92127 q^{64} -0.551689i q^{65} +12.8229 q^{66} -14.6236 q^{67} +18.7665 q^{69} -0.347296 q^{70} +0.170245i q^{71} +3.00000 q^{72} +11.8007i q^{73} +9.86484i q^{74} -12.6236i q^{75} +2.87939 q^{76} +4.12836 q^{77} -21.7665i q^{78} -4.14796i q^{79} +0.568926i q^{80} -7.59627 q^{81} +11.7442i q^{82} +2.43376 q^{83} -5.94356 q^{84} -10.3182 q^{86} -8.63816 q^{87} -2.36959i q^{88} -15.0915 q^{89} +0.773318i q^{90} -7.00774i q^{91} +11.3550i q^{92} -9.71688 q^{93} -13.8084 q^{94} -0.226682i q^{95} +17.9932i q^{96} -11.1925i q^{97} +8.74422 q^{98} -9.19253i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{8}+O(q^{10}) $ 6 * q + 6 * q^8	$ 6 q + 6 q^{8} + 12 q^{13} - 6 q^{15} - 12 q^{16} - 18 q^{18} - 12 q^{21} - 6 q^{25} + 24 q^{26} + 12 q^{30} - 18 q^{32} + 6 q^{35} - 18 q^{36} + 12 q^{38} - 12 q^{42} - 30 q^{43} - 42 q^{47} + 30 q^{49} + 42 q^{50} - 6 q^{52} + 36 q^{53} + 12 q^{55} + 18 q^{59} - 12 q^{60} - 6 q^{64} + 36 q^{66} - 18 q^{67} + 42 q^{69} + 18 q^{72} + 6 q^{76} - 12 q^{77} - 18 q^{81} - 18 q^{83} - 6 q^{84} + 12 q^{86} - 18 q^{87} - 30 q^{89} - 42 q^{93} - 6 q^{94} - 6 q^{98}+O(q^{100}) $ 6 * q + 6 * q^8 + 12 * q^13 - 6 * q^15 - 12 * q^16 - 18 * q^18 - 12 * q^21 - 6 * q^25 + 24 * q^26 + 12 * q^30 - 18 * q^32 + 6 * q^35 - 18 * q^36 + 12 * q^38 - 12 * q^42 - 30 * q^43 - 42 * q^47 + 30 * q^49 + 42 * q^50 - 6 * q^52 + 36 * q^53 + 12 * q^55 + 18 * q^59 - 12 * q^60 - 6 * q^64 + 36 * q^66 - 18 * q^67 + 42 * q^69 + 18 * q^72 + 6 * q^76 - 12 * q^77 - 18 * q^81 - 18 * q^83 - 6 * q^84 + 12 * q^86 - 18 * q^87 - 30 * q^89 - 42 * q^93 - 6 * q^94 - 6 * 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 $

$2$	1.87939	1.32893	0.664463	−	0.747321i	$-0.268660\pi$
$2$	1.87939	1.32893	0.664463	+	0.747321i	$0.268660\pi$
$3$	− 2.53209i	− 1.46190i	−0.682430	−	0.730951i	$-0.739077\pi$
$3$	− 2.53209i	− 1.46190i	0.682430	−	0.730951i	$-0.260923\pi$
$4$	1.53209	0.766044
$5$	− 0.120615i	− 0.0539406i	−0.999636	−	0.0269703i	$-0.991414\pi$
$5$	− 0.120615i	− 0.0539406i	0.999636	−	0.0269703i	$-0.00858595\pi$
$6$	− 4.75877i	− 1.94276i
$7$	− 1.53209i	− 0.579075i	−0.957167	−	0.289538i	$-0.906498\pi$
$7$	− 1.53209i	− 0.579075i	0.957167	−	0.289538i	$-0.0935015\pi$
$8$	−0.879385	−0.310910
$9$	−3.41147	−1.13716
$10$	− 0.226682i	− 0.0716830i
$11$	2.69459i	0.812450i	0.913773	+	0.406225i	$0.133155\pi$
$11$	2.69459i	0.812450i	−0.913773	+	0.406225i	$0.866845\pi$
$12$	− 3.87939i	− 1.11988i
$13$	4.57398	1.26859	0.634297	−	0.773090i	$-0.281290\pi$
$13$	4.57398	1.26859	0.634297	+	0.773090i	$0.281290\pi$
$14$	− 2.87939i	− 0.769548i
$15$	−0.305407	−0.0788558
$16$	−4.71688	−1.17922
$17$	0	0
$17$	0	0
$18$	−6.41147	−1.51120
$19$	1.87939	0.431161	0.215580	−	0.976486i	$-0.430836\pi$
$19$	1.87939	0.431161	0.215580	+	0.976486i	$0.430836\pi$
$20$	− 0.184793i	− 0.0413209i
$21$	−3.87939	−0.846551
$22$	5.06418i	1.07969i
$23$	7.41147i	1.54540i	0.634772	+	0.772700i	$0.281094\pi$
$23$	7.41147i	1.54540i	−0.634772	+	0.772700i	$0.718906\pi$
$24$	2.22668i	0.454519i
$25$	4.98545	0.997090
$26$	8.59627	1.68587
$27$	1.04189i	0.200512i
$28$	− 2.34730i	− 0.443597i
$29$	− 3.41147i	− 0.633495i	−0.948510	−	0.316747i	$-0.897409\pi$
$29$	− 3.41147i	− 0.633495i	0.948510	−	0.316747i	$-0.102591\pi$
$30$	−0.573978	−0.104794
$31$	− 3.83750i	− 0.689235i	−0.938743	−	0.344617i	$-0.888009\pi$
$31$	− 3.83750i	− 0.689235i	0.938743	−	0.344617i	$-0.111991\pi$
$32$	−7.10607	−1.25619
$33$	6.82295	1.18772
$34$	0	0
$35$	−0.184793	−0.0312356
$36$	−5.22668	−0.871114
$37$	5.24897i	0.862925i	0.902131	+	0.431463i	$0.142002\pi$
$37$	5.24897i	0.862925i	−0.902131	+	0.431463i	$0.857998\pi$
$38$	3.53209	0.572980
$39$	− 11.5817i	− 1.85456i
$40$	0.106067i	0.0167706i
$41$	6.24897i	0.975925i	0.872865	+	0.487963i	$0.162260\pi$
$41$	6.24897i	0.975925i	−0.872865	+	0.487963i	$0.837740\pi$
$42$	−7.29086	−1.12500
$43$	−5.49020	−0.837248	−0.418624	−	0.908160i	$-0.637487\pi$
$43$	−5.49020	−0.837248	−0.418624	+	0.908160i	$0.637487\pi$
$44$	4.12836i	0.622373i
$45$	0.411474i	0.0613389i
$46$	13.9290i	2.05372i
$47$	−7.34730	−1.07171	−0.535857	−	0.844309i	$-0.680011\pi$
$47$	−7.34730	−1.07171	−0.535857	+	0.844309i	$0.680011\pi$
$48$	11.9436i	1.72390i
$49$	4.65270	0.664672
$50$	9.36959	1.32506
$51$	0	0
$52$	7.00774	0.971799
$53$	−0.822948	−0.113041	−0.0565203	−	0.998401i	$-0.518001\pi$
$53$	−0.822948	−0.113041	−0.0565203	+	0.998401i	$0.518001\pi$
$54$	1.95811i	0.266465i
$55$	0.325008	0.0438240
$56$	1.34730i	0.180040i
$57$	− 4.75877i	− 0.630315i
$58$	− 6.41147i	− 0.841868i
$59$	3.14290	0.409171	0.204586	−	0.978849i	$-0.434415\pi$
$59$	3.14290	0.409171	0.204586	+	0.978849i	$0.434415\pi$
$60$	−0.467911	−0.0604071
$61$	1.22668i	0.157060i	0.996912	+	0.0785302i	$0.0250227\pi$
$61$	1.22668i	0.157060i	−0.996912	+	0.0785302i	$0.974977\pi$
$62$	− 7.21213i	− 0.915942i
$63$	5.22668i	0.658500i
$64$	−3.92127	−0.490159
$65$	− 0.551689i	− 0.0684286i
$66$	12.8229	1.57840
$67$	−14.6236	−1.78656	−0.893279	−	0.449503i	$-0.851601\pi$
$67$	−14.6236	−1.78656	−0.893279	+	0.449503i	$0.851601\pi$
$68$	0	0
$69$	18.7665	2.25922
$70$	−0.347296	−0.0415099
$71$	0.170245i	0.0202043i	0.999949	+	0.0101022i	$0.00321567\pi$
$71$	0.170245i	0.0202043i	−0.999949	+	0.0101022i	$0.996784\pi$
$72$	3.00000	0.353553
$73$	11.8007i	1.38116i	0.723255	+	0.690581i	$0.242645\pi$
$73$	11.8007i	1.38116i	−0.723255	+	0.690581i	$0.757355\pi$
$74$	9.86484i	1.14676i
$75$	− 12.6236i	− 1.45765i
$76$	2.87939	0.330288
$77$	4.12836	0.470470
$78$	− 21.7665i	− 2.46457i
$79$	− 4.14796i	− 0.466682i	−0.972395	−	0.233341i	$-0.925034\pi$
$79$	− 4.14796i	− 0.466682i	0.972395	−	0.233341i	$-0.0749658\pi$
$80$	0.568926i	0.0636078i
$81$	−7.59627	−0.844030
$82$	11.7442i	1.29693i
$83$	2.43376	0.267140	0.133570	−	0.991039i	$-0.457356\pi$
$83$	2.43376	0.267140	0.133570	+	0.991039i	$0.457356\pi$
$84$	−5.94356	−0.648496
$85$	0	0
$86$	−10.3182	−1.11264
$87$	−8.63816	−0.926108
$88$	− 2.36959i	− 0.252599i
$89$	−15.0915	−1.59970	−0.799849	−	0.600201i	$-0.795087\pi$
$89$	−15.0915	−1.59970	−0.799849	+	0.600201i	$0.795087\pi$
$90$	0.773318i	0.0815149i
$91$	− 7.00774i	− 0.734611i
$92$	11.3550i	1.18384i
$93$	−9.71688	−1.00759
$94$	−13.8084	−1.42423
$95$	− 0.226682i	− 0.0232570i
$96$	17.9932i	1.83642i
$97$	− 11.1925i	− 1.13643i	−0.822880	−	0.568215i	$-0.807634\pi$
$97$	− 11.1925i	− 1.13643i	0.822880	−	0.568215i	$-0.192366\pi$
$98$	8.74422	0.883300
$99$	− 9.19253i	− 0.923884i
$100$	7.63816	0.763816
$101$	7.78106	0.774244	0.387122	−	0.922028i	$-0.373469\pi$
$101$	7.78106	0.774244	0.387122	+	0.922028i	$0.373469\pi$
$102$	0	0
$103$	−10.8598	−1.07005	−0.535023	−	0.844837i	$-0.679697\pi$
$103$	−10.8598	−1.07005	−0.535023	+	0.844837i	$0.679697\pi$
$104$	−4.02229	−0.394418
$105$	0.467911i	0.0456634i
$106$	−1.54664	−0.150223
$107$	− 12.0419i	− 1.16413i	−0.813141	−	0.582067i	$-0.802244\pi$
$107$	− 12.0419i	− 1.16413i	0.813141	−	0.582067i	$-0.197756\pi$
$108$	1.59627i	0.153601i
$109$	− 6.61081i	− 0.633201i	−0.948559	−	0.316601i	$-0.897459\pi$
$109$	− 6.61081i	− 0.633201i	0.948559	−	0.316601i	$-0.102541\pi$
$110$	0.610815	0.0582389
$111$	13.2909	1.26151
$112$	7.22668i	0.682857i
$113$	− 5.08647i	− 0.478495i	−0.970959	−	0.239247i	$-0.923099\pi$
$113$	− 5.08647i	− 0.478495i	0.970959	−	0.239247i	$-0.0769007\pi$
$114$	− 8.94356i	− 0.837641i
$115$	0.893933	0.0833597
$116$	− 5.22668i	− 0.485285i
$117$	−15.6040	−1.44259
$118$	5.90673	0.543758
$119$	0	0
$120$	0.268571	0.0245170
$121$	3.73917	0.339925
$122$	2.30541i	0.208722i
$123$	15.8229	1.42671
$124$	− 5.87939i	− 0.527984i
$125$	− 1.20439i	− 0.107724i
$126$	9.82295i	0.875098i
$127$	2.20439	0.195608	0.0978041	−	0.995206i	$-0.468818\pi$
$127$	2.20439	0.195608	0.0978041	+	0.995206i	$0.468818\pi$
$128$	6.84255	0.604802
$129$	13.9017i	1.22397i
$130$	− 1.03684i	− 0.0909366i
$131$	1.99319i	0.174146i	0.996202	+	0.0870730i	$0.0277514\pi$
$131$	1.99319i	0.174146i	−0.996202	+	0.0870730i	$0.972249\pi$
$132$	10.4534	0.909848
$133$	− 2.87939i	− 0.249674i
$134$	−27.4834	−2.37420
$135$	0.125667	0.0108157
$136$	0	0
$137$	−12.6236	−1.07851	−0.539254	−	0.842143i	$-0.681294\pi$
$137$	−12.6236	−1.07851	−0.539254	+	0.842143i	$0.681294\pi$
$138$	35.2695	3.00234
$139$	− 5.23442i	− 0.443978i	−0.975049	−	0.221989i	$-0.928745\pi$
$139$	− 5.23442i	− 0.443978i	0.975049	−	0.221989i	$-0.0712549\pi$
$140$	−0.283119	−0.0239279
$141$	18.6040i	1.56674i
$142$	0.319955i	0.0268500i
$143$	12.3250i	1.03067i
$144$	16.0915	1.34096
$145$	−0.411474	−0.0341711
$146$	22.1780i	1.83546i
$147$	− 11.7811i	− 0.971685i
$148$	8.04189i	0.661039i
$149$	9.65270	0.790780	0.395390	−	0.918513i	$-0.370609\pi$
$149$	9.65270	0.790780	0.395390	+	0.918513i	$0.370609\pi$
$150$	− 23.7246i	− 1.93711i
$151$	−1.20708	−0.0982309	−0.0491154	−	0.998793i	$-0.515640\pi$
$151$	−1.20708	−0.0982309	−0.0491154	+	0.998793i	$0.515640\pi$
$152$	−1.65270	−0.134052
$153$	0	0
$154$	7.75877	0.625220
$155$	−0.462859	−0.0371777
$156$	− 17.7442i	− 1.42067i
$157$	15.0942	1.20465	0.602324	−	0.798251i	$-0.294241\pi$
$157$	15.0942	1.20465	0.602324	+	0.798251i	$0.294241\pi$
$158$	− 7.79561i	− 0.620185i
$159$	2.08378i	0.165254i
$160$	0.857097i	0.0677594i
$161$	11.3550	0.894902
$162$	−14.2763	−1.12165
$163$	− 6.55438i	− 0.513378i	−0.966494	−	0.256689i	$-0.917368\pi$
$163$	− 6.55438i	− 0.513378i	0.966494	−	0.256689i	$-0.0826317\pi$
$164$	9.57398i	0.747602i
$165$	− 0.822948i	− 0.0640664i
$166$	4.57398	0.355010
$167$	3.94356i	0.305162i	0.988291	+	0.152581i	$0.0487585\pi$
$167$	3.94356i	0.305162i	−0.988291	+	0.152581i	$0.951241\pi$
$168$	3.41147	0.263201
$169$	7.92127	0.609329
$170$	0	0
$171$	−6.41147	−0.490298
$172$	−8.41147	−0.641369
$173$	18.9341i	1.43953i	0.694218	+	0.719765i	$0.255751\pi$
$173$	18.9341i	1.43953i	−0.694218	+	0.719765i	$0.744249\pi$
$174$	−16.2344	−1.23073
$175$	− 7.63816i	− 0.577390i
$176$	− 12.7101i	− 0.958058i
$177$	− 7.95811i	− 0.598168i
$178$	−28.3628	−2.12588
$179$	−7.25402	−0.542191	−0.271096	−	0.962552i	$-0.587386\pi$
$179$	−7.25402	−0.542191	−0.271096	+	0.962552i	$0.587386\pi$
$180$	0.630415i	0.0469884i
$181$	25.0993i	1.86561i	0.360377	+	0.932807i	$0.382648\pi$
$181$	25.0993i	1.86561i	−0.360377	+	0.932807i	$0.617352\pi$
$182$	− 13.1702i	− 0.976243i
$183$	3.10607	0.229607
$184$	− 6.51754i	− 0.480479i
$185$	0.633103	0.0465467
$186$	−18.2618	−1.33902
$187$	0	0
$188$	−11.2567	−0.820980
$189$	1.59627	0.116111
$190$	− 0.426022i	− 0.0309069i
$191$	14.1557	1.02427	0.512135	−	0.858905i	$-0.328855\pi$
$191$	14.1557	1.02427	0.512135	+	0.858905i	$0.328855\pi$
$192$	9.92902i	0.716565i
$193$	− 16.4311i	− 1.18273i	−0.806402	−	0.591367i	$-0.798588\pi$
$193$	− 16.4311i	− 1.18273i	0.806402	−	0.591367i	$-0.201412\pi$
$194$	− 21.0351i	− 1.51023i
$195$	−1.39693	−0.100036
$196$	7.12836	0.509168
$197$	− 20.2395i	− 1.44200i	−0.692934	−	0.721001i	$-0.743682\pi$
$197$	− 20.2395i	− 1.44200i	0.692934	−	0.721001i	$-0.256318\pi$
$198$	− 17.2763i	− 1.22777i
$199$	− 22.1753i	− 1.57197i	−0.618249	−	0.785983i	$-0.712158\pi$
$199$	− 22.1753i	− 1.57197i	0.618249	−	0.785983i	$-0.287842\pi$
$200$	−4.38413	−0.310005
$201$	37.0283i	2.61177i
$202$	14.6236	1.02891
$203$	−5.22668	−0.366841
$204$	0	0
$205$	0.753718	0.0526420
$206$	−20.4097	−1.42201
$207$	− 25.2841i	− 1.75736i
$208$	−21.5749	−1.49595
$209$	5.06418i	0.350297i
$210$	0.879385i	0.0606833i
$211$	7.18748i	0.494807i	0.968913	+	0.247403i	$0.0795773\pi$
$211$	7.18748i	0.494807i	−0.968913	+	0.247403i	$0.920423\pi$
$212$	−1.26083	−0.0865942
$213$	0.431074	0.0295367
$214$	− 22.6313i	− 1.54705i
$215$	0.662199i	0.0451616i
$216$	− 0.916222i	− 0.0623410i
$217$	−5.87939	−0.399119
$218$	− 12.4243i	− 0.841478i
$219$	29.8803	2.01912
$220$	0.497941	0.0335711
$221$	0	0
$222$	24.9786	1.67646
$223$	6.01960	0.403102	0.201551	−	0.979478i	$-0.435402\pi$
$223$	6.01960	0.403102	0.201551	+	0.979478i	$0.435402\pi$
$224$	10.8871i	0.727427i
$225$	−17.0077	−1.13385
$226$	− 9.55943i	− 0.635884i
$227$	22.0351i	1.46252i	0.682099	+	0.731260i	$0.261067\pi$
$227$	22.0351i	1.46252i	−0.682099	+	0.731260i	$0.738933\pi$
$228$	− 7.29086i	− 0.482849i
$229$	−3.69965	−0.244479	−0.122240	−	0.992501i	$-0.539008\pi$
$229$	−3.69965	−0.244479	−0.122240	+	0.992501i	$0.539008\pi$
$230$	1.68004	0.110779
$231$	− 10.4534i	− 0.687781i
$232$	3.00000i	0.196960i
$233$	29.1506i	1.90972i	0.297053	+	0.954861i	$0.403996\pi$
$233$	29.1506i	1.90972i	−0.297053	+	0.954861i	$0.596004\pi$
$234$	−29.3259	−1.91710
$235$	0.886192i	0.0578088i
$236$	4.81521	0.313443
$237$	−10.5030	−0.682243
$238$	0	0
$239$	12.4834	0.807484	0.403742	−	0.914873i	$-0.367709\pi$
$239$	12.4834	0.807484	0.403742	+	0.914873i	$0.367709\pi$
$240$	1.44057	0.0929884
$241$	− 16.2172i	− 1.04464i	−0.852749	−	0.522320i	$-0.825067\pi$
$241$	− 16.2172i	− 1.04464i	0.852749	−	0.522320i	$-0.174933\pi$
$242$	7.02734	0.451735
$243$	22.3601i	1.43440i
$244$	1.87939i	0.120315i
$245$	− 0.561185i	− 0.0358528i
$246$	29.7374	1.89599
$247$	8.59627	0.546967
$248$	3.37464i	0.214290i
$249$	− 6.16250i	− 0.390533i
$250$	− 2.26352i	− 0.143157i
$251$	15.9959	1.00965	0.504826	−	0.863221i	$-0.331557\pi$
$251$	15.9959	1.00965	0.504826	+	0.863221i	$0.331557\pi$
$252$	8.00774i	0.504440i
$253$	−19.9709	−1.25556
$254$	4.14290	0.259949
$255$	0	0
$256$	20.7023	1.29390
$257$	9.66044	0.602602	0.301301	−	0.953529i	$-0.402579\pi$
$257$	9.66044	0.602602	0.301301	+	0.953529i	$0.402579\pi$
$258$	26.1266i	1.62657i
$259$	8.04189	0.499699
$260$	− 0.845237i	− 0.0524194i
$261$	11.6382i	0.720384i
$262$	3.74598i	0.231427i
$263$	−27.9813	−1.72540	−0.862701	−	0.505714i	$-0.831229\pi$
$263$	−27.9813	−1.72540	−0.862701	+	0.505714i	$0.831229\pi$
$264$	−6.00000	−0.369274
$265$	0.0992597i	0.00609748i
$266$	− 5.41147i	− 0.331799i
$267$	38.2131i	2.33860i
$268$	−22.4047	−1.36858
$269$	6.64590i	0.405207i	0.979261	+	0.202604i	$0.0649403\pi$
$269$	6.64590i	0.405207i	−0.979261	+	0.202604i	$0.935060\pi$
$270$	0.236177	0.0143733
$271$	17.0000	1.03268	0.516338	−	0.856385i	$-0.327295\pi$
$271$	17.0000	1.03268	0.516338	+	0.856385i	$0.327295\pi$
$272$	0	0
$273$	−17.7442	−1.07393
$274$	−23.7246	−1.43326
$275$	13.4338i	0.810086i
$276$	28.7520	1.73066
$277$	− 20.1489i	− 1.21063i	−0.795986	−	0.605315i	$-0.793047\pi$
$277$	− 20.1489i	− 1.21063i	0.795986	−	0.605315i	$-0.206953\pi$
$278$	− 9.83750i	− 0.590014i
$279$	13.0915i	0.783769i
$280$	0.162504	0.00971146
$281$	−16.4730	−0.982695	−0.491347	−	0.870964i	$-0.663495\pi$
$281$	−16.4730	−0.982695	−0.491347	+	0.870964i	$0.663495\pi$
$282$	34.9641i	2.08208i
$283$	− 18.4456i	− 1.09648i	−0.836322	−	0.548239i	$-0.815298\pi$
$283$	− 18.4456i	− 1.09648i	0.836322	−	0.548239i	$-0.184702\pi$
$284$	0.260830i	0.0154774i
$285$	−0.573978	−0.0339995
$286$	23.1634i	1.36968i
$287$	9.57398	0.565134
$288$	24.2422	1.42848
$289$	0	0
$290$	−0.773318	−0.0454108
$291$	−28.3405	−1.66135
$292$	18.0797i	1.05803i
$293$	−10.9513	−0.639782	−0.319891	−	0.947454i	$-0.603646\pi$
$293$	−10.9513	−0.639782	−0.319891	+	0.947454i	$0.603646\pi$
$294$	− 22.1411i	− 1.29130i
$295$	− 0.379081i	− 0.0220709i
$296$	− 4.61587i	− 0.268292i
$297$	−2.80747	−0.162906
$298$	18.1411	1.05089
$299$	33.8999i	1.96048i
$300$	− 19.3405i	− 1.11662i
$301$	8.41147i	0.484829i
$302$	−2.26857	−0.130542
$303$	− 19.7023i	− 1.13187i
$304$	−8.86484	−0.508433
$305$	0.147956	0.00847193
$306$	0	0
$307$	−5.78106	−0.329942	−0.164971	−	0.986298i	$-0.552753\pi$
$307$	−5.78106	−0.329942	−0.164971	+	0.986298i	$0.552753\pi$
$308$	6.32501	0.360401
$309$	27.4979i	1.56430i
$310$	−0.869890	−0.0494064
$311$	− 0.120615i	− 0.00683944i	−0.999994	−	0.00341972i	$-0.998911\pi$
$311$	− 0.120615i	− 0.00683944i	0.999994	−	0.00341972i	$-0.00108853\pi$
$312$	10.1848i	0.576600i
$313$	10.3892i	0.587231i	0.955924	+	0.293616i	$0.0948586\pi$
$313$	10.3892i	0.587231i	−0.955924	+	0.293616i	$0.905141\pi$
$314$	28.3678	1.60089
$315$	0.630415	0.0355199
$316$	− 6.35504i	− 0.357499i
$317$	27.8016i	1.56149i	0.624848	+	0.780747i	$0.285161\pi$
$317$	27.8016i	1.56149i	−0.624848	+	0.780747i	$0.714839\pi$
$318$	3.91622i	0.219611i
$319$	9.19253	0.514683
$320$	0.472964i	0.0264395i
$321$	−30.4911	−1.70185
$322$	21.3405	1.18926
$323$	0	0
$324$	−11.6382	−0.646564
$325$	22.8033	1.26490
$326$	− 12.3182i	− 0.682242i
$327$	−16.7392	−0.925678
$328$	− 5.49525i	− 0.303425i
$329$	11.2567i	0.620603i
$330$	− 1.54664i	− 0.0851396i
$331$	−8.77837	−0.482503	−0.241251	−	0.970463i	$-0.577558\pi$
$331$	−8.77837	−0.482503	−0.241251	+	0.970463i	$0.577558\pi$
$332$	3.72874	0.204641
$333$	− 17.9067i	− 0.981283i
$334$	7.41147i	0.405538i
$335$	1.76382i	0.0963679i
$336$	18.2986	0.998270
$337$	− 1.46110i	− 0.0795914i	−0.999208	−	0.0397957i	$-0.987329\pi$
$337$	− 1.46110i	− 0.0795914i	0.999208	−	0.0397957i	$-0.0126707\pi$
$338$	14.8871	0.809753
$339$	−12.8794	−0.699512
$340$	0	0
$341$	10.3405	0.559969
$342$	−12.0496	−0.651569
$343$	− 17.8530i	− 0.963970i
$344$	4.82800	0.260308
$345$	− 2.26352i	− 0.121864i
$346$	35.5844i	1.91303i
$347$	31.3560i	1.68328i	0.540042	+	0.841638i	$0.318409\pi$
$347$	31.3560i	1.68328i	−0.540042	+	0.841638i	$0.681591\pi$
$348$	−13.2344	−0.709440
$349$	29.7743	1.59378	0.796890	−	0.604125i	$-0.206477\pi$
$349$	29.7743	1.59378	0.796890	+	0.604125i	$0.206477\pi$
$350$	− 14.3550i	− 0.767309i
$351$	4.76558i	0.254368i
$352$	− 19.1480i	− 1.02059i
$353$	−28.3141	−1.50701	−0.753503	−	0.657444i	$-0.771638\pi$
$353$	−28.3141	−1.50701	−0.753503	+	0.657444i	$0.771638\pi$
$354$	− 14.9564i	− 0.794921i
$355$	0.0205340	0.00108983
$356$	−23.1215	−1.22544
$357$	0	0
$358$	−13.6331	−0.720532
$359$	2.81790	0.148723	0.0743614	−	0.997231i	$-0.476308\pi$
$359$	2.81790	0.148723	0.0743614	+	0.997231i	$0.476308\pi$
$360$	− 0.361844i	− 0.0190709i
$361$	−15.4679	−0.814101
$362$	47.1712i	2.47926i
$363$	− 9.46791i	− 0.496936i
$364$	− 10.7365i	− 0.562745i
$365$	1.42333	0.0745007
$366$	5.83750	0.305131
$367$	− 8.31820i	− 0.434207i	−0.976149	−	0.217103i	$-0.930339\pi$
$367$	− 8.31820i	− 0.434207i	0.976149	−	0.217103i	$-0.0696608\pi$
$368$	− 34.9590i	− 1.82237i
$369$	− 21.3182i	− 1.10978i
$370$	1.18984	0.0618571
$371$	1.26083i	0.0654590i
$372$	−14.8871	−0.771862
$373$	−9.21894	−0.477339	−0.238669	−	0.971101i	$-0.576711\pi$
$373$	−9.21894	−0.477339	−0.238669	+	0.971101i	$0.576711\pi$
$374$	0	0
$375$	−3.04963	−0.157482
$376$	6.46110	0.333206
$377$	− 15.6040i	− 0.803647i
$378$	3.00000	0.154303
$379$	10.3628i	0.532300i	0.963932	+	0.266150i	$0.0857517\pi$
$379$	10.3628i	0.532300i	−0.963932	+	0.266150i	$0.914248\pi$
$380$	− 0.347296i	− 0.0178159i
$381$	− 5.58172i	− 0.285960i
$382$	26.6040	1.36118
$383$	−13.2713	−0.678130	−0.339065	−	0.940763i	$-0.610111\pi$
$383$	−13.2713	−0.678130	−0.339065	+	0.940763i	$0.610111\pi$
$384$	− 17.3259i	− 0.884161i
$385$	− 0.497941i	− 0.0253774i
$386$	− 30.8803i	− 1.57177i
$387$	18.7297	0.952083
$388$	− 17.1480i	− 0.870556i
$389$	26.2763	1.33226	0.666131	−	0.745835i	$-0.267949\pi$
$389$	26.2763	1.33226	0.666131	+	0.745835i	$0.267949\pi$
$390$	−2.62536	−0.132940
$391$	0	0
$392$	−4.09152	−0.206653
$393$	5.04694	0.254585
$394$	− 38.0378i	− 1.91632i
$395$	−0.500305	−0.0251731
$396$	− 14.0838i	− 0.707736i
$397$	− 25.4766i	− 1.27863i	−0.768944	−	0.639317i	$-0.779217\pi$
$397$	− 25.4766i	− 1.27863i	0.768944	−	0.639317i	$-0.220783\pi$
$398$	− 41.6759i	− 2.08903i
$399$	−7.29086	−0.365000
$400$	−23.5158	−1.17579
$401$	0.900740i	0.0449808i	0.999747	+	0.0224904i	$0.00715952\pi$
$401$	0.900740i	0.0449808i	−0.999747	+	0.0224904i	$0.992840\pi$
$402$	69.5904i	3.47085i
$403$	− 17.5526i	− 0.874358i
$404$	11.9213	0.593106
$405$	0.916222i	0.0455274i
$406$	−9.82295	−0.487505
$407$	−14.1438	−0.701084
$408$	0	0
$409$	−15.3259	−0.757819	−0.378910	−	0.925434i	$-0.623701\pi$
$409$	−15.3259	−0.757819	−0.378910	+	0.925434i	$0.623701\pi$
$410$	1.41653	0.0699573
$411$	31.9641i	1.57667i
$412$	−16.6382	−0.819703
$413$	− 4.81521i	− 0.236941i
$414$	− 47.5185i	− 2.33541i
$415$	− 0.293548i	− 0.0144097i
$416$	−32.5030	−1.59359
$417$	−13.2540	−0.649052
$418$	9.51754i	0.465518i
$419$	− 2.38413i	− 0.116473i	−0.998303	−	0.0582363i	$-0.981452\pi$
$419$	− 2.38413i	− 0.116473i	0.998303	−	0.0582363i	$-0.0185477\pi$
$420$	0.716881i	0.0349802i
$421$	−8.28581	−0.403826	−0.201913	−	0.979404i	$-0.564716\pi$
$421$	−8.28581	−0.403826	−0.201913	+	0.979404i	$0.564716\pi$
$422$	13.5080i	0.657561i
$423$	25.0651	1.21871
$424$	0.723689	0.0351454
$425$	0	0
$426$	0.810155	0.0392521
$427$	1.87939	0.0909498
$428$	− 18.4492i	− 0.891778i
$429$	31.2080	1.50674
$430$	1.24453i	0.0600164i
$431$	− 32.3191i	− 1.55676i	−0.627795	−	0.778379i	$-0.716042\pi$
$431$	− 32.3191i	− 1.55676i	0.627795	−	0.778379i	$-0.283958\pi$
$432$	− 4.91447i	− 0.236447i
$433$	15.0642	0.723938	0.361969	−	0.932190i	$-0.382105\pi$
$433$	15.0642	0.723938	0.361969	+	0.932190i	$0.382105\pi$
$434$	−11.0496	−0.530399
$435$	1.04189i	0.0499548i
$436$	− 10.1284i	− 0.485060i
$437$	13.9290i	0.666315i
$438$	56.1566	2.68327
$439$	− 2.57304i	− 0.122805i	−0.998113	−	0.0614024i	$-0.980443\pi$
$439$	− 2.57304i	− 0.122805i	0.998113	−	0.0614024i	$-0.0195573\pi$
$440$	−0.285807	−0.0136253
$441$	−15.8726	−0.755837
$442$	0	0
$443$	23.4662	1.11491	0.557455	−	0.830207i	$-0.311778\pi$
$443$	23.4662	1.11491	0.557455	+	0.830207i	$0.311778\pi$
$444$	20.3628	0.966375
$445$	1.82026i	0.0862886i
$446$	11.3131	0.535693
$447$	− 24.4415i	− 1.15604i
$448$	6.00774i	0.283839i
$449$	− 18.8580i	− 0.889965i	−0.895539	−	0.444983i	$-0.853210\pi$
$449$	− 18.8580i	− 0.889965i	0.895539	−	0.444983i	$-0.146790\pi$
$450$	−31.9641	−1.50680
$451$	−16.8384	−0.792891
$452$	− 7.79292i	− 0.366548i
$453$	3.05644i	0.143604i
$454$	41.4124i	1.94358i
$455$	−0.845237	−0.0396253
$456$	4.18479i	0.195971i
$457$	2.10782	0.0985997	0.0492999	−	0.998784i	$-0.484301\pi$
$457$	2.10782	0.0985997	0.0492999	+	0.998784i	$0.484301\pi$
$458$	−6.95306	−0.324895
$459$	0	0
$460$	1.36959	0.0638572
$461$	21.9077	1.02034	0.510171	−	0.860073i	$-0.329582\pi$
$461$	21.9077	1.02034	0.510171	+	0.860073i	$0.329582\pi$
$462$	− 19.6459i	− 0.914010i
$463$	14.1557	0.657871	0.328936	−	0.944352i	$-0.393310\pi$
$463$	14.1557	0.657871	0.328936	+	0.944352i	$0.393310\pi$
$464$	16.0915i	0.747030i
$465$	1.17200i	0.0543502i
$466$	54.7853i	2.53788i
$467$	29.6878	1.37379	0.686893	−	0.726758i	$-0.258974\pi$
$467$	29.6878	1.37379	0.686893	+	0.726758i	$0.258974\pi$
$468$	−23.9067	−1.10509
$469$	22.4047i	1.03455i
$470$	1.66550i	0.0768236i
$471$	− 38.2199i	− 1.76108i
$472$	−2.76382	−0.127215
$473$	− 14.7939i	− 0.680222i
$474$	−19.7392	−0.906650
$475$	9.36959	0.429906
$476$	0	0
$477$	2.80747	0.128545
$478$	23.4611	1.07309
$479$	− 38.2959i	− 1.74978i	−0.484317	−	0.874892i	$-0.660932\pi$
$479$	− 38.2959i	− 1.74978i	0.484317	−	0.874892i	$-0.339068\pi$
$480$	2.17024	0.0990577
$481$	24.0087i	1.09470i
$482$	− 30.4783i	− 1.38825i
$483$	− 28.7520i	− 1.30826i
$484$	5.72874	0.260397
$485$	−1.34998	−0.0612996
$486$	42.0232i	1.90621i
$487$	− 23.3509i	− 1.05813i	−0.848581	−	0.529066i	$-0.822543\pi$
$487$	− 23.3509i	− 1.05813i	0.848581	−	0.529066i	$-0.177457\pi$
$488$	− 1.07873i	− 0.0488316i
$489$	−16.5963	−0.750509
$490$	− 1.05468i	− 0.0476457i
$491$	−31.3928	−1.41674	−0.708369	−	0.705843i	$-0.750569\pi$
$491$	−31.3928	−1.41674	−0.708369	+	0.705843i	$0.750569\pi$
$492$	24.2422	1.09292
$493$	0	0
$494$	16.1557	0.726879
$495$	−1.10876	−0.0498348
$496$	18.1010i	0.812760i
$497$	0.260830	0.0116998
$498$	− 11.5817i	− 0.518989i
$499$	16.1310i	0.722125i	0.932542	+	0.361062i	$0.117586\pi$
$499$	16.1310i	0.722125i	−0.932542	+	0.361062i	$0.882414\pi$
$500$	− 1.84524i	− 0.0825215i
$501$	9.98545	0.446117
$502$	30.0624	1.34175
$503$	− 34.3637i	− 1.53220i	−0.642720	−	0.766101i	$-0.722194\pi$
$503$	− 34.3637i	− 1.53220i	0.642720	−	0.766101i	$-0.277806\pi$
$504$	− 4.59627i	− 0.204734i
$505$	− 0.938511i	− 0.0417632i
$506$	−37.5330	−1.66855
$507$	− 20.0574i	− 0.890779i
$508$	3.37733	0.149845
$509$	20.0283	0.887738	0.443869	−	0.896092i	$-0.353606\pi$
$509$	20.0283	0.887738	0.443869	+	0.896092i	$0.353606\pi$
$510$	0	0
$511$	18.0797	0.799797
$512$	25.2226	1.11469
$513$	1.95811i	0.0864527i
$514$	18.1557	0.800813
$515$	1.30985i	0.0577189i
$516$	21.2986i	0.937619i
$517$	− 19.7980i	− 0.870714i
$518$	15.1138	0.664063
$519$	47.9427	2.10445
$520$	0.485147i	0.0212751i
$521$	− 5.58584i	− 0.244720i	−0.992486	−	0.122360i	$-0.960954\pi$
$521$	− 5.58584i	− 0.244720i	0.992486	−	0.122360i	$-0.0390462\pi$
$522$	21.8726i	0.957337i
$523$	5.51249	0.241044	0.120522	−	0.992711i	$-0.461543\pi$
$523$	5.51249	0.241044	0.120522	+	0.992711i	$0.461543\pi$
$524$	3.05375i	0.133404i
$525$	−19.3405	−0.844088
$526$	−52.5877	−2.29293
$527$	0	0
$528$	−32.1830	−1.40059
$529$	−31.9299	−1.38826
$530$	0.186547i	0.00810309i
$531$	−10.7219	−0.465292
$532$	− 4.41147i	− 0.191262i
$533$	28.5827i	1.23805i
$534$	71.8171i	3.10783i
$535$	−1.45243	−0.0627940
$536$	12.8598	0.555458
$537$	18.3678i	0.792630i
$538$	12.4902i	0.538491i
$539$	12.5371i	0.540013i
$540$	0.192533	0.00828531
$541$	− 13.9949i	− 0.601690i	−0.953673	−	0.300845i	$-0.902731\pi$
$541$	− 13.9949i	− 0.601690i	0.953673	−	0.300845i	$-0.0972686\pi$
$542$	31.9495	1.37235
$543$	63.5536	2.72734
$544$	0	0
$545$	−0.797362	−0.0341552
$546$	−33.3482	−1.42717
$547$	29.4175i	1.25780i	0.777486	+	0.628900i	$0.216494\pi$
$547$	29.4175i	1.25780i	−0.777486	+	0.628900i	$0.783506\pi$
$548$	−19.3405	−0.826185
$549$	− 4.18479i	− 0.178603i
$550$	25.2472i	1.07654i
$551$	− 6.41147i	− 0.273138i
$552$	−16.5030	−0.702414
$553$	−6.35504	−0.270244
$554$	− 37.8675i	− 1.60884i
$555$	− 1.60307i	− 0.0680467i
$556$	− 8.01960i	− 0.340107i
$557$	32.0574	1.35831	0.679157	−	0.733993i	$-0.262345\pi$
$557$	32.0574	1.35831	0.679157	+	0.733993i	$0.262345\pi$
$558$	24.6040i	1.04157i
$559$	−25.1121	−1.06213
$560$	0.871644	0.0368337
$561$	0	0
$562$	−30.9590	−1.30593
$563$	−18.6483	−0.785930	−0.392965	−	0.919553i	$-0.628551\pi$
$563$	−18.6483	−0.785930	−0.392965	+	0.919553i	$0.628551\pi$
$564$	28.5030i	1.20019i
$565$	−0.613503	−0.0258103
$566$	− 34.6664i	− 1.45714i
$567$	11.6382i	0.488757i
$568$	− 0.149711i	− 0.00628172i
$569$	−27.6554	−1.15937	−0.579687	−	0.814839i	$-0.696825\pi$
$569$	−27.6554	−1.15937	−0.579687	+	0.814839i	$0.696825\pi$
$570$	−1.07873	−0.0451828
$571$	33.1762i	1.38838i	0.719791	+	0.694191i	$0.244238\pi$
$571$	33.1762i	1.38838i	−0.719791	+	0.694191i	$0.755762\pi$
$572$	18.8830i	0.789538i
$573$	− 35.8435i	− 1.49738i
$574$	17.9932	0.751021
$575$	36.9495i	1.54090i
$576$	13.3773	0.557389
$577$	2.70233	0.112500	0.0562498	−	0.998417i	$-0.482086\pi$
$577$	2.70233	0.112500	0.0562498	+	0.998417i	$0.482086\pi$
$578$	0	0
$579$	−41.6049	−1.72904
$580$	−0.630415	−0.0261766
$581$	− 3.72874i	− 0.154694i
$582$	−53.2627	−2.20781
$583$	− 2.21751i	− 0.0918399i
$584$	− 10.3773i	− 0.429417i
$585$	1.88207i	0.0778142i
$586$	−20.5817	−0.850223
$587$	−6.31551	−0.260669	−0.130335	−	0.991470i	$-0.541605\pi$
$587$	−6.31551	−0.260669	−0.130335	+	0.991470i	$0.541605\pi$
$588$	− 18.0496i	− 0.744354i
$589$	− 7.21213i	− 0.297171i
$590$	− 0.712438i	− 0.0293306i
$591$	−51.2481	−2.10807
$592$	− 24.7588i	− 1.01758i
$593$	10.2148	0.419472	0.209736	−	0.977758i	$-0.432739\pi$
$593$	10.2148	0.419472	0.209736	+	0.977758i	$0.432739\pi$
$594$	−5.27631	−0.216490
$595$	0	0
$596$	14.7888	0.605773
$597$	−56.1498	−2.29806
$598$	63.7110i	2.60534i
$599$	−21.4347	−0.875798	−0.437899	−	0.899024i	$-0.644277\pi$
$599$	−21.4347	−0.875798	−0.437899	+	0.899024i	$0.644277\pi$
$600$	11.1010i	0.453197i
$601$	17.4557i	0.712034i	0.934479	+	0.356017i	$0.115865\pi$
$601$	17.4557i	0.712034i	−0.934479	+	0.356017i	$0.884135\pi$
$602$	15.8084i	0.644302i
$603$	49.8881	2.03160
$604$	−1.84936	−0.0752492
$605$	− 0.450999i	− 0.0183357i
$606$	− 37.0283i	− 1.50417i
$607$	8.50980i	0.345402i	0.984974	+	0.172701i	$0.0552495\pi$
$607$	8.50980i	0.345402i	−0.984974	+	0.172701i	$0.944751\pi$
$608$	−13.3550	−0.541618
$609$	13.2344i	0.536286i
$610$	0.278066	0.0112586
$611$	−33.6064	−1.35957
$612$	0	0
$613$	9.78106	0.395053	0.197527	−	0.980298i	$-0.436709\pi$
$613$	9.78106	0.395053	0.197527	+	0.980298i	$0.436709\pi$
$614$	−10.8648	−0.438469
$615$	− 1.90848i	− 0.0769574i
$616$	−3.63041	−0.146274
$617$	− 22.8512i	− 0.919956i	−0.887930	−	0.459978i	$-0.847857\pi$
$617$	− 22.8512i	− 0.919956i	0.887930	−	0.459978i	$-0.152143\pi$
$618$	51.6792i	2.07884i
$619$	− 41.2627i	− 1.65849i	−0.558887	−	0.829244i	$-0.688771\pi$
$619$	− 41.2627i	− 1.65849i	0.558887	−	0.829244i	$-0.311229\pi$
$620$	−0.709141	−0.0284798
$621$	−7.72193	−0.309871
$622$	− 0.226682i	− 0.00908910i
$623$	23.1215i	0.926345i
$624$	54.6296i	2.18693i
$625$	24.7820	0.991280
$626$	19.5253i	0.780387i
$627$	12.8229	0.512099
$628$	23.1257	0.922815
$629$	0	0
$630$	1.18479	0.0472033
$631$	−9.54252	−0.379882	−0.189941	−	0.981796i	$-0.560830\pi$
$631$	−9.54252	−0.379882	−0.189941	+	0.981796i	$0.560830\pi$
$632$	3.64765i	0.145096i
$633$	18.1993	0.723359
$634$	52.2499i	2.07511i
$635$	− 0.265882i	− 0.0105512i
$636$	3.19253i	0.126592i
$637$	21.2814	0.843198
$638$	17.2763	0.683976
$639$	− 0.580785i	− 0.0229755i
$640$	− 0.825312i	− 0.0326233i
$641$	− 9.42871i	− 0.372412i	−0.982511	−	0.186206i	$-0.940381\pi$
$641$	− 9.42871i	− 0.372412i	0.982511	−	0.186206i	$-0.0596191\pi$
$642$	−57.3046	−2.26163
$643$	− 11.0060i	− 0.434034i	−0.976168	−	0.217017i	$-0.930367\pi$
$643$	− 11.0060i	− 0.434034i	0.976168	−	0.217017i	$-0.0696327\pi$
$644$	17.3969	0.685535
$645$	1.67675	0.0660219
$646$	0	0
$647$	28.9840	1.13948	0.569740	−	0.821825i	$-0.307044\pi$
$647$	28.9840	1.13948	0.569740	+	0.821825i	$0.307044\pi$
$648$	6.68004	0.262417
$649$	8.46884i	0.332431i
$650$	42.8563	1.68096
$651$	14.8871i	0.583472i
$652$	− 10.0419i	− 0.393271i
$653$	− 14.7178i	− 0.575953i	−0.957638	−	0.287976i	$-0.907018\pi$
$653$	− 14.7178i	− 0.575953i	0.957638	−	0.287976i	$-0.0929824\pi$
$654$	−31.4593	−1.23016
$655$	0.240408	0.00939354
$656$	− 29.4757i	− 1.15083i
$657$	− 40.2576i	− 1.57060i
$658$	21.1557i	0.824735i
$659$	2.19759	0.0856058	0.0428029	−	0.999084i	$-0.486371\pi$
$659$	2.19759	0.0856058	0.0428029	+	0.999084i	$0.486371\pi$
$660$	− 1.26083i	− 0.0490777i
$661$	26.6023	1.03471	0.517354	−	0.855772i	$-0.326917\pi$
$661$	26.6023	1.03471	0.517354	+	0.855772i	$0.326917\pi$
$662$	−16.4979	−0.641211
$663$	0	0
$664$	−2.14022	−0.0830565
$665$	−0.347296	−0.0134676
$666$	− 33.6536i	− 1.30405i
$667$	25.2841	0.979002
$668$	6.04189i	0.233768i
$669$	− 15.2422i	− 0.589296i
$670$	3.31490i	0.128066i
$671$	−3.30541	−0.127604
$672$	27.5672	1.06343
$673$	7.24392i	0.279233i	0.990206	+	0.139616i	$0.0445869\pi$
$673$	7.24392i	0.279233i	−0.990206	+	0.139616i	$0.955413\pi$
$674$	− 2.74598i	− 0.105771i
$675$	5.19429i	0.199928i
$676$	12.1361	0.466773
$677$	− 22.9273i	− 0.881166i	−0.897712	−	0.440583i	$-0.854772\pi$
$677$	− 22.9273i	− 0.881166i	0.897712	−	0.440583i	$-0.145228\pi$
$678$	−24.2053	−0.929600
$679$	−17.1480	−0.658078
$680$	0	0
$681$	55.7948	2.13806
$682$	19.4338	0.744157
$683$	− 4.29591i	− 0.164378i	−0.996617	−	0.0821892i	$-0.973809\pi$
$683$	− 4.29591i	− 0.164378i	0.996617	−	0.0821892i	$-0.0261912\pi$
$684$	−9.82295	−0.375590
$685$	1.52259i	0.0581753i
$686$	− 33.5526i	− 1.28105i
$687$	9.36783i	0.357405i
$688$	25.8966	0.987299
$689$	−3.76415	−0.143403
$690$	− 4.25402i	− 0.161948i
$691$	20.6331i	0.784920i	0.919769	+	0.392460i	$0.128376\pi$
$691$	20.6331i	0.784920i	−0.919769	+	0.392460i	$0.871624\pi$
$692$	29.0087i	1.10274i
$693$	−14.0838	−0.534998
$694$	58.9299i	2.23695i
$695$	−0.631349	−0.0239484
$696$	7.59627	0.287936
$697$	0	0
$698$	55.9573	2.11801
$699$	73.8120	2.79183
$700$	− 11.7023i	− 0.442307i
$701$	−28.2772	−1.06802	−0.534008	−	0.845479i	$-0.679315\pi$
$701$	−28.2772	−1.06802	−0.534008	+	0.845479i	$0.679315\pi$
$702$	8.95636i	0.338036i
$703$	9.86484i	0.372059i
$704$	− 10.5662i	− 0.398230i
$705$	2.24392	0.0845108
$706$	−53.2131	−2.00270
$707$	− 11.9213i	− 0.448346i
$708$	− 12.1925i	− 0.458223i
$709$	27.1002i	1.01777i	0.860835	+	0.508885i	$0.169942\pi$
$709$	27.1002i	1.01777i	−0.860835	+	0.508885i	$0.830058\pi$
$710$	0.0385913	0.00144831
$711$	14.1506i	0.530691i
$712$	13.2713	0.497361
$713$	28.4415	1.06514
$714$	0	0
$715$	1.48658	0.0555949
$716$	−11.1138	−0.415342
$717$	− 31.6091i	− 1.18046i
$718$	5.29591	0.197642
$719$	− 25.8402i	− 0.963676i	−0.876260	−	0.481838i	$-0.839969\pi$
$719$	− 25.8402i	− 0.963676i	0.876260	−	0.481838i	$-0.160031\pi$
$720$	− 1.94087i	− 0.0723321i
$721$	16.6382i	0.619637i
$722$	−29.0702	−1.08188
$723$	−41.0634	−1.52716
$724$	38.4543i	1.42914i
$725$	− 17.0077i	− 0.631652i
$726$	− 17.7939i	− 0.660392i
$727$	−31.6290	−1.17305	−0.586527	−	0.809930i	$-0.699505\pi$
$727$	−31.6290	−1.17305	−0.586527	+	0.809930i	$0.699505\pi$
$728$	6.16250i	0.228398i
$729$	33.8289	1.25292
$730$	2.67499	0.0990059
$731$	0	0
$732$	4.75877	0.175889
$733$	−25.6040	−0.945706	−0.472853	−	0.881141i	$-0.656776\pi$
$733$	−25.6040	−0.945706	−0.472853	+	0.881141i	$0.656776\pi$
$734$	− 15.6331i	− 0.577028i
$735$	−1.42097	−0.0524133
$736$	− 52.6664i	− 1.94131i
$737$	− 39.4047i	− 1.45149i
$738$	− 40.0651i	− 1.47482i
$739$	−21.6382	−0.795972	−0.397986	−	0.917391i	$-0.630291\pi$
$739$	−21.6382	−0.795972	−0.397986	+	0.917391i	$0.630291\pi$
$740$	0.969971	0.0356568
$741$	− 21.7665i	− 0.799613i
$742$	2.36959i	0.0869902i
$743$	− 26.7547i	− 0.981533i	−0.871291	−	0.490766i	$-0.836717\pi$
$743$	− 26.7547i	− 0.981533i	0.871291	−	0.490766i	$-0.163283\pi$
$744$	8.54488	0.313271
$745$	− 1.16426i	− 0.0426551i
$746$	−17.3259	−0.634348
$747$	−8.30272	−0.303781
$748$	0	0
$749$	−18.4492	−0.674121
$750$	−5.73143	−0.209282
$751$	41.9513i	1.53082i	0.643540	+	0.765412i	$0.277465\pi$
$751$	41.9513i	1.53082i	−0.643540	+	0.765412i	$0.722535\pi$
$752$	34.6563	1.26379
$753$	− 40.5030i	− 1.47601i
$754$	− 29.3259i	− 1.06799i
$755$	0.145592i	0.00529863i
$756$	2.44562	0.0889464
$757$	4.99319	0.181481	0.0907403	−	0.995875i	$-0.471077\pi$
$757$	4.99319	0.181481	0.0907403	+	0.995875i	$0.471077\pi$
$758$	19.4757i	0.707388i
$759$	50.5681i	1.83551i
$760$	0.199340i	0.00723084i
$761$	13.2935	0.481891	0.240945	−	0.970539i	$-0.422543\pi$
$761$	13.2935	0.481891	0.240945	+	0.970539i	$0.422543\pi$
$762$	− 10.4902i	− 0.380020i
$763$	−10.1284	−0.366671
$764$	21.6878	0.784637
$765$	0	0
$766$	−24.9418	−0.901184
$767$	14.3756	0.519072
$768$	− 52.4201i	− 1.89155i
$769$	8.25166	0.297562	0.148781	−	0.988870i	$-0.452465\pi$
$769$	8.25166	0.297562	0.148781	+	0.988870i	$0.452465\pi$
$770$	− 0.935822i	− 0.0337247i
$771$	− 24.4611i	− 0.880945i
$772$	− 25.1739i	− 0.906027i
$773$	−26.1043	−0.938907	−0.469453	−	0.882957i	$-0.655549\pi$
$773$	−26.1043	−0.938907	−0.469453	+	0.882957i	$0.655549\pi$
$774$	35.2003	1.26525
$775$	− 19.1317i	− 0.687229i
$776$	9.84255i	0.353327i
$777$	− 20.3628i	− 0.730511i
$778$	49.3833	1.77048
$779$	11.7442i	0.420780i
$780$	−2.14022	−0.0766320
$781$	−0.458740	−0.0164150
$782$	0	0
$783$	3.55438	0.127023
$784$	−21.9463	−0.783795
$785$	− 1.82058i	− 0.0649794i
$786$	9.48515	0.338324
$787$	26.8634i	0.957577i	0.877930	+	0.478789i	$0.158924\pi$
$787$	26.8634i	0.957577i	−0.877930	+	0.478789i	$0.841076\pi$
$788$	− 31.0087i	− 1.10464i
$789$	70.8512i	2.52237i
$790$	−0.940265	−0.0334531
$791$	−7.79292	−0.277084
$792$	8.08378i	0.287245i
$793$	5.61081i	0.199246i
$794$	− 47.8803i	− 1.69921i
$795$	0.251334	0.00891391
$796$	− 33.9745i	− 1.20420i
$797$	18.8212	0.666681	0.333340	−	0.942807i	$-0.391824\pi$
$797$	18.8212	0.666681	0.333340	+	0.942807i	$0.391824\pi$
$798$	−13.7023	−0.485057
$799$	0	0
$800$	−35.4270	−1.25253
$801$	51.4843	1.81911
$802$	1.69284i	0.0597762i
$803$	−31.7980	−1.12213
$804$	56.7306i	2.00073i
$805$	− 1.36959i	− 0.0482715i
$806$	− 32.9881i	− 1.16196i
$807$	16.8280	0.592374
$808$	−6.84255	−0.240720
$809$	− 25.7573i	− 0.905580i	−0.891617	−	0.452790i	$-0.850429\pi$
$809$	− 25.7573i	− 0.905580i	0.891617	−	0.452790i	$-0.149571\pi$
$810$	1.72193i	0.0605026i
$811$	26.4483i	0.928726i	0.885645	+	0.464363i	$0.153717\pi$
$811$	26.4483i	0.928726i	−0.885645	+	0.464363i	$0.846283\pi$
$812$	−8.00774	−0.281017
$813$	− 43.0455i	− 1.50967i
$814$	−26.5817	−0.931689
$815$	−0.790555	−0.0276919
$816$	0	0
$817$	−10.3182	−0.360988
$818$	−28.8033	−1.00709
$819$	23.9067i	0.835369i
$820$	1.15476	0.0403261
$821$	31.5030i	1.09946i	0.835342	+	0.549731i	$0.185270\pi$
$821$	31.5030i	1.09946i	−0.835342	+	0.549731i	$0.814730\pi$
$822$	60.0729i	2.09528i
$823$	− 11.6895i	− 0.407472i	−0.979026	−	0.203736i	$-0.934692\pi$
$823$	− 11.6895i	− 0.407472i	0.979026	−	0.203736i	$-0.0653084\pi$
$824$	9.54993	0.332688
$825$	34.0155	1.18427
$826$	− 9.04963i	− 0.314877i
$827$	− 3.32264i	− 0.115540i	−0.998330	−	0.0577698i	$-0.981601\pi$
$827$	− 3.32264i	− 0.115540i	0.998330	−	0.0577698i	$-0.0183989\pi$
$828$	− 38.7374i	− 1.34622i
$829$	6.01186	0.208801	0.104400	−	0.994535i	$-0.466708\pi$
$829$	6.01186	0.208801	0.104400	+	0.994535i	$0.466708\pi$
$830$	− 0.551689i	− 0.0191494i
$831$	−51.0188	−1.76982
$832$	−17.9358	−0.621813
$833$	0	0
$834$	−24.9094	−0.862542
$835$	0.475652	0.0164606
$836$	7.75877i	0.268343i
$837$	3.99825	0.138200
$838$	− 4.48070i	− 0.154783i
$839$	41.4115i	1.42968i	0.699287	+	0.714841i	$0.253501\pi$
$839$	41.4115i	1.42968i	−0.699287	+	0.714841i	$0.746499\pi$
$840$	− 0.411474i	− 0.0141972i
$841$	17.3618	0.598684
$842$	−15.5722	−0.536654
$843$	41.7110i	1.43660i
$844$	11.0119i	0.379044i
$845$	− 0.955423i	− 0.0328675i
$846$	47.1070	1.61957
$847$	− 5.72874i	− 0.196842i
$848$	3.88175	0.133300
$849$	−46.7060	−1.60294
$850$	0	0
$851$	−38.9026	−1.33356
$852$	0.660444	0.0226265
$853$	− 23.9982i	− 0.821684i	−0.911706	−	0.410842i	$-0.865235\pi$
$853$	− 23.9982i	− 0.821684i	0.911706	−	0.410842i	$-0.134765\pi$
$854$	3.53209	0.120866
$855$	0.773318i	0.0264469i
$856$	10.5895i	0.361940i
$857$	31.8553i	1.08816i	0.839034	+	0.544079i	$0.183121\pi$
$857$	31.8553i	1.08816i	−0.839034	+	0.544079i	$0.816879\pi$
$858$	58.6519	2.00234
$859$	−24.0806	−0.821619	−0.410810	−	0.911721i	$-0.634754\pi$
$859$	−24.0806	−0.821619	−0.410810	+	0.911721i	$0.634754\pi$
$860$	1.01455i	0.0345958i
$861$	− 24.2422i	− 0.826171i
$862$	− 60.7401i	− 2.06882i
$863$	−20.8590	−0.710047	−0.355024	−	0.934857i	$-0.615527\pi$
$863$	−20.8590	−0.710047	−0.355024	+	0.934857i	$0.615527\pi$
$864$	− 7.40373i	− 0.251880i
$865$	2.28373	0.0776491
$866$	28.3114	0.962060
$867$	0	0
$868$	−9.00774	−0.305743
$869$	11.1771	0.379156
$870$	1.95811i	0.0663862i
$871$	−66.8881	−2.26642
$872$	5.81345i	0.196868i
$873$	38.1830i	1.29230i
$874$	26.1780i	0.885484i
$875$	−1.84524	−0.0623804
$876$	45.7793	1.54674
$877$	22.3669i	0.755276i	0.925953	+	0.377638i	$0.123264\pi$
$877$	22.3669i	0.755276i	−0.925953	+	0.377638i	$0.876736\pi$
$878$	− 4.83574i	− 0.163198i
$879$	27.7297i	0.935299i
$880$	−1.53302	−0.0516782
$881$	− 56.4279i	− 1.90110i	−0.310566	−	0.950552i	$-0.600518\pi$
$881$	− 56.4279i	− 1.90110i	0.310566	−	0.950552i	$-0.399482\pi$
$882$	−29.8307	−1.00445
$883$	−45.4219	−1.52857	−0.764284	−	0.644879i	$-0.776908\pi$
$883$	−45.4219	−1.52857	−0.764284	+	0.644879i	$0.776908\pi$
$884$	0	0
$885$	−0.959866	−0.0322655
$886$	44.1019	1.48163
$887$	− 17.4816i	− 0.586976i	−0.955963	−	0.293488i	$-0.905184\pi$
$887$	− 17.4816i	− 0.586976i	0.955963	−	0.293488i	$-0.0948161\pi$
$888$	−11.6878	−0.392216
$889$	− 3.37733i	− 0.113272i
$890$	3.42097i	0.114671i
$891$	− 20.4688i	− 0.685732i
$892$	9.22256	0.308794
$893$	−13.8084	−0.462080
$894$	− 45.9350i	− 1.53630i
$895$	0.874942i	0.0292461i
$896$	− 10.4834i	− 0.350226i
$897$	85.8376	2.86603
$898$	− 35.4415i	− 1.18270i
$899$	−13.0915	−0.436627
$900$	−26.0574	−0.868579
$901$	0	0
$902$	−31.6459	−1.05369
$903$	21.2986	0.708773
$904$	4.47296i	0.148769i
$905$	3.02734	0.100632
$906$	5.74422i	0.190839i
$907$	− 10.4138i	− 0.345786i	−0.984941	−	0.172893i	$-0.944689\pi$
$907$	− 10.4138i	− 0.345786i	0.984941	−	0.172893i	$-0.0553115\pi$
$908$	33.7597i	1.12036i
$909$	−26.5449	−0.880438
$910$	−1.58853	−0.0526591
$911$	44.2722i	1.46680i	0.679796	+	0.733402i	$0.262068\pi$
$911$	44.2722i	1.46680i	−0.679796	+	0.733402i	$0.737932\pi$
$912$	22.4466i	0.743280i
$913$	6.55800i	0.217038i
$914$	3.96141	0.131032
$915$	− 0.374638i	− 0.0123851i
$916$	−5.66819	−0.187282
$917$	3.05375	0.100844
$918$	0	0
$919$	−31.0615	−1.02462	−0.512312	−	0.858799i	$-0.671211\pi$
$919$	−31.0615	−1.02462	−0.512312	+	0.858799i	$0.671211\pi$
$920$	−0.786112	−0.0259173
$921$	14.6382i	0.482344i
$922$	41.1729	1.35596
$923$	0.778695i	0.0256311i
$924$	− 16.0155i	− 0.526871i
$925$	26.1685i	0.860415i
$926$	26.6040	0.874262
$927$	37.0479	1.21681
$928$	24.2422i	0.795788i
$929$	22.3969i	0.734819i	0.930059	+	0.367410i	$0.119755\pi$
$929$	22.3969i	0.734819i	−0.930059	+	0.367410i	$0.880245\pi$
$930$	2.20264i	0.0722274i
$931$	8.74422	0.286580
$932$	44.6614i	1.46293i
$933$	−0.305407	−0.00999859
$934$	55.7948	1.82566
$935$	0	0
$936$	13.7219	0.448515
$937$	−58.1661	−1.90020	−0.950102	−	0.311939i	$-0.899022\pi$
$937$	−58.1661	−1.90020	−0.950102	+	0.311939i	$0.899022\pi$
$938$	42.1070i	1.37484i
$939$	26.3063	0.858475
$940$	1.35773i	0.0442841i
$941$	10.4397i	0.340326i	0.985416	+	0.170163i	$0.0544294\pi$
$941$	10.4397i	0.340326i	−0.985416	+	0.170163i	$0.945571\pi$
$942$	− 71.8299i	− 2.34034i
$943$	−46.3141	−1.50819
$944$	−14.8247	−0.482503
$945$	− 0.192533i	− 0.00626311i
$946$	− 27.8033i	− 0.903965i
$947$	4.04364i	0.131401i	0.997839	+	0.0657004i	$0.0209282\pi$
$947$	4.04364i	0.131401i	−0.997839	+	0.0657004i	$0.979072\pi$
$948$	−16.0915	−0.522628
$949$	53.9760i	1.75213i
$950$	17.6091	0.571313
$951$	70.3961	2.28275
$952$	0	0
$953$	4.37639	0.141765	0.0708826	−	0.997485i	$-0.477418\pi$
$953$	4.37639	0.141765	0.0708826	+	0.997485i	$0.477418\pi$
$954$	5.27631	0.170827
$955$	− 1.70739i	− 0.0552497i
$956$	19.1257	0.618568
$957$	− 23.2763i	− 0.752416i
$958$	− 71.9728i	− 2.32533i
$959$	19.3405i	0.624537i
$960$	1.19759	0.0386519
$961$	16.2736	0.524956
$962$	45.1215i	1.45478i
$963$	41.0806i	1.32380i
$964$	− 24.8462i	− 0.800241i
$965$	−1.98183	−0.0637974
$966$	− 54.0360i	− 1.73858i
$967$	−24.4371	−0.785843	−0.392921	−	0.919572i	$-0.628536\pi$
$967$	−24.4371	−0.785843	−0.392921	+	0.919572i	$0.628536\pi$
$968$	−3.28817	−0.105686
$969$	0	0
$970$	−2.53714	−0.0814627
$971$	−20.5253	−0.658688	−0.329344	−	0.944210i	$-0.606828\pi$
$971$	−20.5253	−0.658688	−0.329344	+	0.944210i	$0.606828\pi$
$972$	34.2576i	1.09881i
$973$	−8.01960	−0.257097
$974$	− 43.8854i	− 1.40618i
$975$	− 57.7401i	− 1.84916i
$976$	− 5.78611i	− 0.185209i
$977$	−28.3073	−0.905630	−0.452815	−	0.891605i	$-0.649580\pi$
$977$	−28.3073	−0.905630	−0.452815	+	0.891605i	$0.649580\pi$
$978$	−31.1908	−0.997371
$979$	− 40.6655i	− 1.29967i
$980$	− 0.859785i	− 0.0274648i
$981$	22.5526i	0.720050i
$982$	−58.9992	−1.88274
$983$	26.6742i	0.850774i	0.905012	+	0.425387i	$0.139862\pi$
$983$	26.6742i	0.850774i	−0.905012	+	0.425387i	$0.860138\pi$
$984$	−13.9145	−0.443577
$985$	−2.44118	−0.0777824
$986$	0	0
$987$	28.5030	0.907260
$988$	13.1702	0.419001
$989$	− 40.6905i	− 1.29388i
$990$	−2.08378	−0.0662268
$991$	− 34.8857i	− 1.10818i	−0.832457	−	0.554090i	$-0.813066\pi$
$991$	− 34.8857i	− 1.10818i	0.832457	−	0.554090i	$-0.186934\pi$
$992$	27.2695i	0.865808i
$993$	22.2276i	0.705372i
$994$	0.490200	0.0155482
$995$	−2.67467	−0.0847927
$996$	− 9.44150i	− 0.299165i
$997$	− 45.3164i	− 1.43519i	−0.696463	−	0.717593i	$-0.745244\pi$
$997$	− 45.3164i	− 1.43519i	0.696463	−	0.717593i	$-0.254756\pi$
$998$	30.3164i	0.959650i
$999$	−5.46884	−0.173027

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.b.d.288.5		6
17.2	even	8		289.2.c.d.251.5		12
17.3	odd	16		289.2.d.f.110.6		24
17.4	even	4		289.2.a.d.1.1	✓	3
17.5	odd	16		289.2.d.f.179.2		24
17.6	odd	16		289.2.d.f.134.5		24
17.7	odd	16		289.2.d.f.155.1		24
17.8	even	8		289.2.c.d.38.1		12
17.9	even	8		289.2.c.d.38.2		12
17.10	odd	16		289.2.d.f.155.2		24
17.11	odd	16		289.2.d.f.134.6		24
17.12	odd	16		289.2.d.f.179.1		24
17.13	even	4		289.2.a.e.1.1	yes	3
17.14	odd	16		289.2.d.f.110.5		24
17.15	even	8		289.2.c.d.251.6		12
17.16	even	2	inner	289.2.b.d.288.6		6
51.38	odd	4		2601.2.a.x.1.3		3
51.47	odd	4		2601.2.a.w.1.3		3
68.47	odd	4		4624.2.a.bd.1.1		3
68.55	odd	4		4624.2.a.bg.1.3		3
85.4	even	4		7225.2.a.t.1.3		3
85.64	even	4		7225.2.a.s.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.a.d.1.1	✓	3	17.4	even	4
289.2.a.e.1.1	yes	3	17.13	even	4
289.2.b.d.288.5		6	1.1	even	1	trivial
289.2.b.d.288.6		6	17.16	even	2	inner
289.2.c.d.38.1		12	17.8	even	8
289.2.c.d.38.2		12	17.9	even	8
289.2.c.d.251.5		12	17.2	even	8
289.2.c.d.251.6		12	17.15	even	8
289.2.d.f.110.5		24	17.14	odd	16
289.2.d.f.110.6		24	17.3	odd	16
289.2.d.f.134.5		24	17.6	odd	16
289.2.d.f.134.6		24	17.11	odd	16
289.2.d.f.155.1		24	17.7	odd	16
289.2.d.f.155.2		24	17.10	odd	16
289.2.d.f.179.1		24	17.12	odd	16
289.2.d.f.179.2		24	17.5	odd	16
2601.2.a.w.1.3		3	51.47	odd	4
2601.2.a.x.1.3		3	51.38	odd	4
4624.2.a.bd.1.1		3	68.47	odd	4
4624.2.a.bg.1.3		3	68.55	odd	4
7225.2.a.s.1.3		3	85.64	even	4
7225.2.a.t.1.3		3	85.4	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.87939 q^{2} -2.53209i q^{3} +1.53209 q^{4} -0.120615i q^{5} -4.75877i q^{6} -1.53209i q^{7} -0.879385 q^{8} -3.41147 q^{9} +O(q^{10})\)	\(q+1.87939 q^{2} -2.53209i q^{3} +1.53209 q^{4} -0.120615i q^{5} -4.75877i q^{6} -1.53209i q^{7} -0.879385 q^{8} -3.41147 q^{9} -0.226682i q^{10} +2.69459i q^{11} -3.87939i q^{12} +4.57398 q^{13} -2.87939i q^{14} -0.305407 q^{15} -4.71688 q^{16} -6.41147 q^{18} +1.87939 q^{19} -0.184793i q^{20} -3.87939 q^{21} +5.06418i q^{22} +7.41147i q^{23} +2.22668i q^{24} +4.98545 q^{25} +8.59627 q^{26} +1.04189i q^{27} -2.34730i q^{28} -3.41147i q^{29} -0.573978 q^{30} -3.83750i q^{31} -7.10607 q^{32} +6.82295 q^{33} -0.184793 q^{35} -5.22668 q^{36} +5.24897i q^{37} +3.53209 q^{38} -11.5817i q^{39} +0.106067i q^{40} +6.24897i q^{41} -7.29086 q^{42} -5.49020 q^{43} +4.12836i q^{44} +0.411474i q^{45} +13.9290i q^{46} -7.34730 q^{47} +11.9436i q^{48} +4.65270 q^{49} +9.36959 q^{50} +7.00774 q^{52} -0.822948 q^{53} +1.95811i q^{54} +0.325008 q^{55} +1.34730i q^{56} -4.75877i q^{57} -6.41147i q^{58} +3.14290 q^{59} -0.467911 q^{60} +1.22668i q^{61} -7.21213i q^{62} +5.22668i q^{63} -3.92127 q^{64} -0.551689i q^{65} +12.8229 q^{66} -14.6236 q^{67} +18.7665 q^{69} -0.347296 q^{70} +0.170245i q^{71} +3.00000 q^{72} +11.8007i q^{73} +9.86484i q^{74} -12.6236i q^{75} +2.87939 q^{76} +4.12836 q^{77} -21.7665i q^{78} -4.14796i q^{79} +0.568926i q^{80} -7.59627 q^{81} +11.7442i q^{82} +2.43376 q^{83} -5.94356 q^{84} -10.3182 q^{86} -8.63816 q^{87} -2.36959i q^{88} -15.0915 q^{89} +0.773318i q^{90} -7.00774i q^{91} +11.3550i q^{92} -9.71688 q^{93} -13.8084 q^{94} -0.226682i q^{95} +17.9932i q^{96} -11.1925i q^{97} +8.74422 q^{98} -9.19253i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{8}+O(q^{10}) \) 6 * q + 6 * q^8	\( 6 q + 6 q^{8} + 12 q^{13} - 6 q^{15} - 12 q^{16} - 18 q^{18} - 12 q^{21} - 6 q^{25} + 24 q^{26} + 12 q^{30} - 18 q^{32} + 6 q^{35} - 18 q^{36} + 12 q^{38} - 12 q^{42} - 30 q^{43} - 42 q^{47} + 30 q^{49} + 42 q^{50} - 6 q^{52} + 36 q^{53} + 12 q^{55} + 18 q^{59} - 12 q^{60} - 6 q^{64} + 36 q^{66} - 18 q^{67} + 42 q^{69} + 18 q^{72} + 6 q^{76} - 12 q^{77} - 18 q^{81} - 18 q^{83} - 6 q^{84} + 12 q^{86} - 18 q^{87} - 30 q^{89} - 42 q^{93} - 6 q^{94} - 6 q^{98}+O(q^{100}) \) 6 * q + 6 * q^8 + 12 * q^13 - 6 * q^15 - 12 * q^16 - 18 * q^18 - 12 * q^21 - 6 * q^25 + 24 * q^26 + 12 * q^30 - 18 * q^32 + 6 * q^35 - 18 * q^36 + 12 * q^38 - 12 * q^42 - 30 * q^43 - 42 * q^47 + 30 * q^49 + 42 * q^50 - 6 * q^52 + 36 * q^53 + 12 * q^55 + 18 * q^59 - 12 * q^60 - 6 * q^64 + 36 * q^66 - 18 * q^67 + 42 * q^69 + 18 * q^72 + 6 * q^76 - 12 * q^77 - 18 * q^81 - 18 * q^83 - 6 * q^84 + 12 * q^86 - 18 * q^87 - 30 * q^89 - 42 * q^93 - 6 * q^94 - 6 * q^98

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