LMFDB - Embedded newform 845.2.a.l.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(1,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("845.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.a (trivial)

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:	yes
Analytic conductor:	$6.74735897080$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.4752.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 3x^{2} + 4x + 1 $ x^4 - 2x^3 - 3x^2 + 4*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.219687$ of defining polynomial
Character	$\chi$	$=$	845.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.219687 q^{2} -1.60020 q^{3} -1.95174 q^{4} +1.00000 q^{5} -0.351542 q^{6} +0.332247 q^{7} -0.868145 q^{8} -0.439374 q^{9} +O(q^{10})$	\(q+0.219687 q^{2} -1.60020 q^{3} -1.95174 q^{4} +1.00000 q^{5} -0.351542 q^{6} +0.332247 q^{7} -0.868145 q^{8} -0.439374 q^{9} +0.219687 q^{10} +5.37182 q^{11} +3.12316 q^{12} +0.0729902 q^{14} -1.60020 q^{15} +3.71276 q^{16} -5.06430 q^{17} -0.0965246 q^{18} -2.26795 q^{19} -1.95174 q^{20} -0.531659 q^{21} +1.18012 q^{22} -2.83918 q^{23} +1.38920 q^{24} +1.00000 q^{25} +5.50367 q^{27} -0.648458 q^{28} -2.90348 q^{29} -0.351542 q^{30} -5.46410 q^{31} +2.55193 q^{32} -8.59596 q^{33} -1.11256 q^{34} +0.332247 q^{35} +0.857542 q^{36} -5.97201 q^{37} -0.498239 q^{38} -0.868145 q^{40} -3.73205 q^{41} -0.116799 q^{42} -5.06430 q^{43} -10.4844 q^{44} -0.439374 q^{45} -0.623730 q^{46} -8.34285 q^{47} -5.94114 q^{48} -6.88961 q^{49} +0.219687 q^{50} +8.10387 q^{51} -1.56063 q^{53} +1.20908 q^{54} +5.37182 q^{55} -0.288438 q^{56} +3.62916 q^{57} -0.637855 q^{58} -2.70732 q^{59} +3.12316 q^{60} +14.1039 q^{61} -1.20039 q^{62} -0.145980 q^{63} -6.86488 q^{64} -1.88842 q^{66} -10.3322 q^{67} +9.88418 q^{68} +4.54324 q^{69} +0.0729902 q^{70} -12.7973 q^{71} +0.381440 q^{72} +9.68922 q^{73} -1.31197 q^{74} -1.60020 q^{75} +4.42644 q^{76} +1.78477 q^{77} +4.51851 q^{79} +3.71276 q^{80} -7.48883 q^{81} -0.819883 q^{82} +4.26371 q^{83} +1.03766 q^{84} -5.06430 q^{85} -1.11256 q^{86} +4.64613 q^{87} -4.66351 q^{88} -3.22584 q^{89} -0.0965246 q^{90} +5.54133 q^{92} +8.74363 q^{93} -1.83281 q^{94} -2.26795 q^{95} -4.08359 q^{96} +2.50791 q^{97} -1.51356 q^{98} -2.36023 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{5} + 4 q^{6} - 10 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 4 * q^5 + 4 * q^6 - 10 * q^7 - 6 * q^8 + 4 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{5} + 4 q^{6} - 10 q^{7} - 6 q^{8} + 4 q^{9} - 2 q^{10} - 10 q^{12} + 2 q^{14} - 2 q^{15} + 2 q^{16} - 2 q^{17} - 20 q^{18} - 16 q^{19} + 2 q^{20} - 4 q^{21} + 12 q^{22} - 10 q^{23} + 24 q^{24} + 4 q^{25} - 2 q^{27} - 8 q^{28} + 8 q^{29} + 4 q^{30} - 8 q^{31} - 4 q^{32} - 18 q^{33} + 4 q^{34} - 10 q^{35} + 20 q^{36} + 2 q^{37} + 8 q^{38} - 6 q^{40} - 8 q^{41} - 4 q^{42} - 2 q^{43} - 12 q^{44} + 4 q^{45} - 16 q^{46} - 8 q^{47} - 28 q^{48} + 12 q^{49} - 2 q^{50} + 4 q^{51} - 12 q^{53} + 16 q^{54} + 12 q^{56} + 14 q^{57} - 22 q^{58} - 12 q^{59} - 10 q^{60} + 28 q^{61} + 4 q^{62} - 4 q^{63} + 4 q^{64} + 6 q^{66} - 30 q^{67} + 14 q^{68} - 16 q^{69} + 2 q^{70} - 4 q^{71} - 12 q^{72} + 8 q^{73} - 10 q^{74} - 2 q^{75} - 20 q^{76} + 18 q^{77} - 8 q^{79} + 2 q^{80} - 8 q^{81} + 4 q^{82} + 12 q^{83} + 28 q^{84} - 2 q^{85} + 4 q^{86} - 22 q^{87} - 18 q^{88} + 12 q^{89} - 20 q^{90} + 22 q^{92} - 8 q^{93} - 32 q^{94} - 16 q^{95} - 4 q^{96} - 2 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 4 * q^5 + 4 * q^6 - 10 * q^7 - 6 * q^8 + 4 * q^9 - 2 * q^10 - 10 * q^12 + 2 * q^14 - 2 * q^15 + 2 * q^16 - 2 * q^17 - 20 * q^18 - 16 * q^19 + 2 * q^20 - 4 * q^21 + 12 * q^22 - 10 * q^23 + 24 * q^24 + 4 * q^25 - 2 * q^27 - 8 * q^28 + 8 * q^29 + 4 * q^30 - 8 * q^31 - 4 * q^32 - 18 * q^33 + 4 * q^34 - 10 * q^35 + 20 * q^36 + 2 * q^37 + 8 * q^38 - 6 * q^40 - 8 * q^41 - 4 * q^42 - 2 * q^43 - 12 * q^44 + 4 * q^45 - 16 * q^46 - 8 * q^47 - 28 * q^48 + 12 * q^49 - 2 * q^50 + 4 * q^51 - 12 * q^53 + 16 * q^54 + 12 * q^56 + 14 * q^57 - 22 * q^58 - 12 * q^59 - 10 * q^60 + 28 * q^61 + 4 * q^62 - 4 * q^63 + 4 * q^64 + 6 * q^66 - 30 * q^67 + 14 * q^68 - 16 * q^69 + 2 * q^70 - 4 * q^71 - 12 * q^72 + 8 * q^73 - 10 * q^74 - 2 * q^75 - 20 * q^76 + 18 * q^77 - 8 * q^79 + 2 * q^80 - 8 * q^81 + 4 * q^82 + 12 * q^83 + 28 * q^84 - 2 * q^85 + 4 * q^86 - 22 * q^87 - 18 * q^88 + 12 * q^89 - 20 * q^90 + 22 * q^92 - 8 * q^93 - 32 * q^94 - 16 * q^95 - 4 * q^96 - 2 * q^97 + 24 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	0.219687	0.155342	0.0776710	−	0.996979i	$-0.475252\pi$
$2$	0.219687	0.155342	0.0776710	+	0.996979i	$0.475252\pi$
$3$	−1.60020	−0.923873	−0.461937	−	0.886913i	$-0.652845\pi$
$3$	−1.60020	−0.923873	−0.461937	+	0.886913i	$0.652845\pi$
$4$	−1.95174	−0.975869
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.351542	−0.143516
$7$	0.332247	0.125577	0.0627887	−	0.998027i	$-0.480001\pi$
$7$	0.332247	0.125577	0.0627887	+	0.998027i	$0.480001\pi$
$8$	−0.868145	−0.306936
$9$	−0.439374	−0.146458
$10$	0.219687	0.0694711
$11$	5.37182	1.61966	0.809832	−	0.586662i	$-0.199558\pi$
$11$	5.37182	1.61966	0.809832	+	0.586662i	$0.199558\pi$
$12$	3.12316	0.901579
$13$	0	0
$13$	0	0
$14$	0.0729902	0.0195074
$15$	−1.60020	−0.413169
$16$	3.71276	0.928189
$17$	−5.06430	−1.22827	−0.614136	−	0.789200i	$-0.710495\pi$
$17$	−5.06430	−1.22827	−0.614136	+	0.789200i	$0.710495\pi$
$18$	−0.0965246	−0.0227511
$19$	−2.26795	−0.520303	−0.260152	−	0.965568i	$-0.583773\pi$
$19$	−2.26795	−0.520303	−0.260152	+	0.965568i	$0.583773\pi$
$20$	−1.95174	−0.436422
$21$	−0.531659	−0.116018
$22$	1.18012	0.251602
$23$	−2.83918	−0.592010	−0.296005	−	0.955186i	$-0.595654\pi$
$23$	−2.83918	−0.592010	−0.296005	+	0.955186i	$0.595654\pi$
$24$	1.38920	0.283570
$25$	1.00000	0.200000
$26$	0	0
$27$	5.50367	1.05918
$28$	−0.648458	−0.122547
$29$	−2.90348	−0.539162	−0.269581	−	0.962978i	$-0.586885\pi$
$29$	−2.90348	−0.539162	−0.269581	+	0.962978i	$0.586885\pi$
$30$	−0.351542	−0.0641825
$31$	−5.46410	−0.981382	−0.490691	−	0.871334i	$-0.663256\pi$
$31$	−5.46410	−0.981382	−0.490691	+	0.871334i	$0.663256\pi$
$32$	2.55193	0.451122
$33$	−8.59596	−1.49636
$34$	−1.11256	−0.190802
$35$	0.332247	0.0561599
$36$	0.857542	0.142924
$37$	−5.97201	−0.981793	−0.490896	−	0.871218i	$-0.663331\pi$
$37$	−5.97201	−0.981793	−0.490896	+	0.871218i	$0.663331\pi$
$38$	−0.498239	−0.0808250
$39$	0	0
$40$	−0.868145	−0.137266
$41$	−3.73205	−0.582848	−0.291424	−	0.956594i	$-0.594129\pi$
$41$	−3.73205	−0.582848	−0.291424	+	0.956594i	$0.594129\pi$
$42$	−0.116799	−0.0180224
$43$	−5.06430	−0.772298	−0.386149	−	0.922436i	$-0.626195\pi$
$43$	−5.06430	−0.772298	−0.386149	+	0.922436i	$0.626195\pi$
$44$	−10.4844	−1.58058
$45$	−0.439374	−0.0654980
$46$	−0.623730	−0.0919640
$47$	−8.34285	−1.21693	−0.608465	−	0.793581i	$-0.708214\pi$
$47$	−8.34285	−1.21693	−0.608465	+	0.793581i	$0.708214\pi$
$48$	−5.94114	−0.857529
$49$	−6.88961	−0.984230
$50$	0.219687	0.0310684
$51$	8.10387	1.13477
$52$	0	0
$53$	−1.56063	−0.214369	−0.107184	−	0.994239i	$-0.534183\pi$
$53$	−1.56063	−0.214369	−0.107184	+	0.994239i	$0.534183\pi$
$54$	1.20908	0.164536
$55$	5.37182	0.724336
$56$	−0.288438	−0.0385442
$57$	3.62916	0.480694
$58$	−0.637855	−0.0837545
$59$	−2.70732	−0.352463	−0.176232	−	0.984349i	$-0.556391\pi$
$59$	−2.70732	−0.352463	−0.176232	+	0.984349i	$0.556391\pi$
$60$	3.12316	0.403199
$61$	14.1039	1.80582	0.902908	−	0.429835i	$-0.141428\pi$
$61$	14.1039	1.80582	0.902908	+	0.429835i	$0.141428\pi$
$62$	−1.20039	−0.152450
$63$	−0.145980	−0.0183918
$64$	−6.86488	−0.858111
$65$	0	0
$66$	−1.88842	−0.232448
$67$	−10.3322	−1.26228	−0.631142	−	0.775667i	$-0.717414\pi$
$67$	−10.3322	−1.26228	−0.631142	+	0.775667i	$0.717414\pi$
$68$	9.88418	1.19863
$69$	4.54324	0.546942
$70$	0.0729902	0.00872400
$71$	−12.7973	−1.51876	−0.759382	−	0.650645i	$-0.774498\pi$
$71$	−12.7973	−1.51876	−0.759382	+	0.650645i	$0.774498\pi$
$72$	0.381440	0.0449531
$73$	9.68922	1.13404	0.567019	−	0.823705i	$-0.308097\pi$
$73$	9.68922	1.13404	0.567019	+	0.823705i	$0.308097\pi$
$74$	−1.31197	−0.152514
$75$	−1.60020	−0.184775
$76$	4.42644	0.507748
$77$	1.78477	0.203393
$78$	0	0
$79$	4.51851	0.508372	0.254186	−	0.967155i	$-0.418192\pi$
$79$	4.51851	0.508372	0.254186	+	0.967155i	$0.418192\pi$
$80$	3.71276	0.415099
$81$	−7.48883	−0.832092
$82$	−0.819883	−0.0905409
$83$	4.26371	0.468003	0.234001	−	0.972236i	$-0.424818\pi$
$83$	4.26371	0.468003	0.234001	+	0.972236i	$0.424818\pi$
$84$	1.03766	0.113218
$85$	−5.06430	−0.549300
$86$	−1.11256	−0.119970
$87$	4.64613	0.498117
$88$	−4.66351	−0.497132
$89$	−3.22584	−0.341938	−0.170969	−	0.985276i	$-0.554690\pi$
$89$	−3.22584	−0.341938	−0.170969	+	0.985276i	$0.554690\pi$
$90$	−0.0965246	−0.0101746
$91$	0	0
$92$	5.54133	0.577724
$93$	8.74363	0.906672
$94$	−1.83281	−0.189040
$95$	−2.26795	−0.232687
$96$	−4.08359	−0.416780
$97$	2.50791	0.254640	0.127320	−	0.991862i	$-0.459363\pi$
$97$	2.50791	0.254640	0.127320	+	0.991862i	$0.459363\pi$
$98$	−1.51356	−0.152892
$99$	−2.36023	−0.237213
$100$	−1.95174	−0.195174
$101$	12.4467	1.23849	0.619247	−	0.785196i	$-0.287438\pi$
$101$	12.4467	1.23849	0.619247	+	0.785196i	$0.287438\pi$
$102$	1.78031	0.176277
$103$	−15.0247	−1.48043	−0.740215	−	0.672370i	$-0.765276\pi$
$103$	−15.0247	−1.48043	−0.740215	+	0.672370i	$0.765276\pi$
$104$	0	0
$105$	−0.531659	−0.0518846
$106$	−0.342849	−0.0333004
$107$	−13.0643	−1.26297	−0.631487	−	0.775387i	$-0.717555\pi$
$107$	−13.0643	−1.26297	−0.631487	+	0.775387i	$0.717555\pi$
$108$	−10.7417	−1.03362
$109$	11.2325	1.07587	0.537937	−	0.842985i	$-0.319204\pi$
$109$	11.2325	1.07587	0.537937	+	0.842985i	$0.319204\pi$
$110$	1.18012	0.112520
$111$	9.55639	0.907052
$112$	1.23355	0.116560
$113$	−18.3438	−1.72564	−0.862821	−	0.505509i	$-0.831305\pi$
$113$	−18.3438	−1.72564	−0.862821	+	0.505509i	$0.831305\pi$
$114$	0.797279	0.0746721
$115$	−2.83918	−0.264755
$116$	5.66682	0.526151
$117$	0	0
$118$	−0.594763	−0.0547524
$119$	−1.68260	−0.154243
$120$	1.38920	0.126816
$121$	17.8564	1.62331
$122$	3.09843	0.280519
$123$	5.97201	0.538478
$124$	10.6645	0.957700
$125$	1.00000	0.0894427
$126$	−0.0320700	−0.00285702
$127$	3.23996	0.287500	0.143750	−	0.989614i	$-0.454084\pi$
$127$	3.23996	0.287500	0.143750	+	0.989614i	$0.454084\pi$
$128$	−6.61199	−0.584423
$129$	8.10387	0.713506
$130$	0	0
$131$	0.175664	0.0153478	0.00767390	−	0.999971i	$-0.497557\pi$
$131$	0.175664	0.0153478	0.00767390	+	0.999971i	$0.497557\pi$
$132$	16.7771	1.46025
$133$	−0.753518	−0.0653383
$134$	−2.26986	−0.196086
$135$	5.50367	0.473681
$136$	4.39654	0.377001
$137$	17.9829	1.53638	0.768190	−	0.640221i	$-0.221157\pi$
$137$	17.9829	1.53638	0.768190	+	0.640221i	$0.221157\pi$
$138$	0.998090	0.0849631
$139$	11.9861	1.01665	0.508325	−	0.861165i	$-0.330265\pi$
$139$	11.9861	1.01665	0.508325	+	0.861165i	$0.330265\pi$
$140$	−0.648458	−0.0548047
$141$	13.3502	1.12429
$142$	−2.81140	−0.235928
$143$	0	0
$144$	−1.63129	−0.135941
$145$	−2.90348	−0.241121
$146$	2.12859	0.176164
$147$	11.0247	0.909304
$148$	11.6558	0.958101
$149$	3.41041	0.279391	0.139696	−	0.990194i	$-0.455388\pi$
$149$	3.41041	0.279391	0.139696	+	0.990194i	$0.455388\pi$
$150$	−0.351542	−0.0287033
$151$	−7.96141	−0.647890	−0.323945	−	0.946076i	$-0.605009\pi$
$151$	−7.96141	−0.647890	−0.323945	+	0.946076i	$0.605009\pi$
$152$	1.96891	0.159700
$153$	2.22512	0.179890
$154$	0.392090	0.0315955
$155$	−5.46410	−0.438887
$156$	0	0
$157$	−16.4329	−1.31148	−0.655742	−	0.754985i	$-0.727644\pi$
$157$	−16.4329	−1.31148	−0.655742	+	0.754985i	$0.727644\pi$
$158$	0.992658	0.0789716
$159$	2.49731	0.198049
$160$	2.55193	0.201748
$161$	−0.943307	−0.0743430
$162$	−1.64520	−0.129259
$163$	−17.8072	−1.39477	−0.697384	−	0.716697i	$-0.745653\pi$
$163$	−17.8072	−1.39477	−0.697384	+	0.716697i	$0.745653\pi$
$164$	7.28398	0.568784
$165$	−8.59596	−0.669194
$166$	0.936681	0.0727006
$167$	6.29366	0.487018	0.243509	−	0.969899i	$-0.421702\pi$
$167$	6.29366	0.487018	0.243509	+	0.969899i	$0.421702\pi$
$168$	0.461557	0.0356099
$169$	0	0
$170$	−1.11256	−0.0853294
$171$	0.996477	0.0762025
$172$	9.88418	0.753662
$173$	15.9751	1.21457	0.607283	−	0.794486i	$-0.292260\pi$
$173$	15.9751	1.21457	0.607283	+	0.794486i	$0.292260\pi$
$174$	1.02069	0.0773786
$175$	0.332247	0.0251155
$176$	19.9442	1.50335
$177$	4.33225	0.325632
$178$	−0.708674	−0.0531173
$179$	23.6174	1.76525	0.882625	−	0.470079i	$-0.155774\pi$
$179$	23.6174	1.76525	0.882625	+	0.470079i	$0.155774\pi$
$180$	0.857542	0.0639174
$181$	−2.62590	−0.195182	−0.0975909	−	0.995227i	$-0.531114\pi$
$181$	−2.62590	−0.195182	−0.0975909	+	0.995227i	$0.531114\pi$
$182$	0	0
$183$	−22.5689	−1.66834
$184$	2.46482	0.181709
$185$	−5.97201	−0.439071
$186$	1.92086	0.140844
$187$	−27.2045	−1.98939
$188$	16.2831	1.18756
$189$	1.82858	0.133009
$190$	−0.498239	−0.0361460
$191$	−2.01582	−0.145860	−0.0729298	−	0.997337i	$-0.523235\pi$
$191$	−2.01582	−0.145860	−0.0729298	+	0.997337i	$0.523235\pi$
$192$	10.9852	0.792786
$193$	−22.8211	−1.64270	−0.821348	−	0.570427i	$-0.806778\pi$
$193$	−22.8211	−1.64270	−0.821348	+	0.570427i	$0.806778\pi$
$194$	0.550955	0.0395563
$195$	0	0
$196$	13.4467	0.960480
$197$	0.643026	0.0458137	0.0229068	−	0.999738i	$-0.492708\pi$
$197$	0.643026	0.0458137	0.0229068	+	0.999738i	$0.492708\pi$
$198$	−0.518513	−0.0368491
$199$	3.06684	0.217403	0.108701	−	0.994074i	$-0.465331\pi$
$199$	3.06684	0.217403	0.108701	+	0.994074i	$0.465331\pi$
$200$	−0.868145	−0.0613871
$201$	16.5336	1.16619
$202$	2.73438	0.192390
$203$	−0.964670	−0.0677065
$204$	−15.8166	−1.10739
$205$	−3.73205	−0.260658
$206$	−3.30074	−0.229973
$207$	1.24746	0.0867045
$208$	0	0
$209$	−12.1830	−0.842716
$210$	−0.116799	−0.00805987
$211$	−8.20039	−0.564538	−0.282269	−	0.959335i	$-0.591087\pi$
$211$	−8.20039	−0.564538	−0.282269	+	0.959335i	$0.591087\pi$
$212$	3.04593	0.209196
$213$	20.4782	1.40314
$214$	−2.87005	−0.196193
$215$	−5.06430	−0.345382
$216$	−4.77798	−0.325101
$217$	−1.81543	−0.123239
$218$	2.46762	0.167129
$219$	−15.5046	−1.04771
$220$	−10.4844	−0.706856
$221$	0	0
$222$	2.09941	0.140903
$223$	−10.2442	−0.686002	−0.343001	−	0.939335i	$-0.611443\pi$
$223$	−10.2442	−0.686002	−0.343001	+	0.939335i	$0.611443\pi$
$224$	0.847871	0.0566508
$225$	−0.439374	−0.0292916
$226$	−4.02990	−0.268065
$227$	−7.04381	−0.467514	−0.233757	−	0.972295i	$-0.575102\pi$
$227$	−7.04381	−0.467514	−0.233757	+	0.972295i	$0.575102\pi$
$228$	−7.08317	−0.469095
$229$	−1.32899	−0.0878219	−0.0439109	−	0.999035i	$-0.513982\pi$
$229$	−1.32899	−0.0878219	−0.0439109	+	0.999035i	$0.513982\pi$
$230$	−0.623730	−0.0411275
$231$	−2.85598	−0.187909
$232$	2.52064	0.165488
$233$	−1.24746	−0.0817238	−0.0408619	−	0.999165i	$-0.513010\pi$
$233$	−1.24746	−0.0817238	−0.0408619	+	0.999165i	$0.513010\pi$
$234$	0	0
$235$	−8.34285	−0.544227
$236$	5.28398	0.343958
$237$	−7.23050	−0.469672
$238$	−0.369644	−0.0239605
$239$	9.94207	0.643099	0.321549	−	0.946893i	$-0.395796\pi$
$239$	9.94207	0.643099	0.321549	+	0.946893i	$0.395796\pi$
$240$	−5.94114	−0.383499
$241$	22.5869	1.45495	0.727475	−	0.686134i	$-0.240694\pi$
$241$	22.5869	1.45495	0.727475	+	0.686134i	$0.240694\pi$
$242$	3.92282	0.252168
$243$	−4.52742	−0.290434
$244$	−27.5270	−1.76224
$245$	−6.88961	−0.440161
$246$	1.31197	0.0836483
$247$	0	0
$248$	4.74363	0.301221
$249$	−6.82277	−0.432376
$250$	0.219687	0.0138942
$251$	−6.76836	−0.427215	−0.213608	−	0.976920i	$-0.568521\pi$
$251$	−6.76836	−0.427215	−0.213608	+	0.976920i	$0.568521\pi$
$252$	0.284915	0.0179480
$253$	−15.2515	−0.958856
$254$	0.711777	0.0446609
$255$	8.10387	0.507484
$256$	12.2772	0.767325
$257$	−10.2538	−0.639616	−0.319808	−	0.947482i	$-0.603618\pi$
$257$	−10.2538	−0.639616	−0.319808	+	0.947482i	$0.603618\pi$
$258$	1.78031	0.110837
$259$	−1.98418	−0.123291
$260$	0	0
$261$	1.27571	0.0789645
$262$	0.0385910	0.00238416
$263$	18.6570	1.15044	0.575220	−	0.817999i	$-0.304917\pi$
$263$	18.6570	1.15044	0.575220	+	0.817999i	$0.304917\pi$
$264$	7.46254	0.459287
$265$	−1.56063	−0.0958685
$266$	−0.165538	−0.0101498
$267$	5.16197	0.315907
$268$	20.1658	1.23182
$269$	17.9579	1.09491	0.547456	−	0.836835i	$-0.315596\pi$
$269$	17.9579	1.09491	0.547456	+	0.836835i	$0.315596\pi$
$270$	1.20908	0.0735825
$271$	−30.8977	−1.87690	−0.938450	−	0.345415i	$-0.887738\pi$
$271$	−30.8977	−1.87690	−0.938450	+	0.345415i	$0.887738\pi$
$272$	−18.8025	−1.14007
$273$	0	0
$274$	3.95060	0.238665
$275$	5.37182	0.323933
$276$	−8.86721	−0.533744
$277$	26.5045	1.59250	0.796250	−	0.604967i	$-0.206814\pi$
$277$	26.5045	1.59250	0.796250	+	0.604967i	$0.206814\pi$
$278$	2.63320	0.157929
$279$	2.40078	0.143731
$280$	−0.288438	−0.0172375
$281$	−4.97766	−0.296942	−0.148471	−	0.988917i	$-0.547435\pi$
$281$	−4.97766	−0.296942	−0.148471	+	0.988917i	$0.547435\pi$
$282$	2.93286	0.174649
$283$	−12.5863	−0.748180	−0.374090	−	0.927392i	$-0.622045\pi$
$283$	−12.5863	−0.748180	−0.374090	+	0.927392i	$0.622045\pi$
$284$	24.9770	1.48211
$285$	3.62916	0.214973
$286$	0	0
$287$	−1.23996	−0.0731926
$288$	−1.12125	−0.0660704
$289$	8.64711	0.508653
$290$	−0.637855	−0.0374562
$291$	−4.01315	−0.235255
$292$	−18.9108	−1.10667
$293$	−16.9176	−0.988337	−0.494168	−	0.869366i	$-0.664527\pi$
$293$	−16.9176	−0.988337	−0.494168	+	0.869366i	$0.664527\pi$
$294$	2.42199	0.141253
$295$	−2.70732	−0.157626
$296$	5.18457	0.301347
$297$	29.5647	1.71552
$298$	0.749222	0.0434012
$299$	0	0
$300$	3.12316	0.180316
$301$	−1.68260	−0.0969832
$302$	−1.74902	−0.100645
$303$	−19.9172	−1.14421
$304$	−8.42034	−0.482940
$305$	14.1039	0.807585
$306$	0.488829	0.0279445
$307$	4.30426	0.245657	0.122828	−	0.992428i	$-0.460803\pi$
$307$	4.30426	0.245657	0.122828	+	0.992428i	$0.460803\pi$
$308$	−3.48340	−0.198485
$309$	24.0425	1.36773
$310$	−1.20039	−0.0681776
$311$	−2.22512	−0.126175	−0.0630875	−	0.998008i	$-0.520095\pi$
$311$	−2.22512	−0.126175	−0.0630875	+	0.998008i	$0.520095\pi$
$312$	0	0
$313$	7.20887	0.407469	0.203735	−	0.979026i	$-0.434692\pi$
$313$	7.20887	0.407469	0.203735	+	0.979026i	$0.434692\pi$
$314$	−3.61008	−0.203729
$315$	−0.145980	−0.00822506
$316$	−8.81895	−0.496105
$317$	0.321644	0.0180653	0.00903266	−	0.999959i	$-0.497125\pi$
$317$	0.321644	0.0180653	0.00903266	+	0.999959i	$0.497125\pi$
$318$	0.548626	0.0307654
$319$	−15.5969	−0.873261
$320$	−6.86488	−0.383759
$321$	20.9054	1.16683
$322$	−0.207232	−0.0115486
$323$	11.4856	0.639074
$324$	14.6162	0.812013
$325$	0	0
$326$	−3.91201	−0.216666
$327$	−17.9741	−0.993972
$328$	3.23996	0.178897
$329$	−2.77188	−0.152819
$330$	−1.88842	−0.103954
$331$	−16.6320	−0.914178	−0.457089	−	0.889421i	$-0.651108\pi$
$331$	−16.6320	−0.914178	−0.457089	+	0.889421i	$0.651108\pi$
$332$	−8.32164	−0.456710
$333$	2.62395	0.143791
$334$	1.38263	0.0756543
$335$	−10.3322	−0.564511
$336$	−1.97392	−0.107686
$337$	24.2186	1.31927	0.659636	−	0.751586i	$-0.270711\pi$
$337$	24.2186	1.31927	0.659636	+	0.751586i	$0.270711\pi$
$338$	0	0
$339$	29.3537	1.59427
$340$	9.88418	0.536045
$341$	−29.3521	−1.58951
$342$	0.218913	0.0118375
$343$	−4.61478	−0.249174
$344$	4.39654	0.237046
$345$	4.54324	0.244600
$346$	3.50952	0.188673
$347$	−6.27360	−0.336784	−0.168392	−	0.985720i	$-0.553857\pi$
$347$	−6.27360	−0.336784	−0.168392	+	0.985720i	$0.553857\pi$
$348$	−9.06802	−0.486097
$349$	−7.06994	−0.378445	−0.189223	−	0.981934i	$-0.560597\pi$
$349$	−7.06994	−0.378445	−0.189223	+	0.981934i	$0.560597\pi$
$350$	0.0729902	0.00390149
$351$	0	0
$352$	13.7085	0.730666
$353$	21.7898	1.15976	0.579878	−	0.814704i	$-0.303100\pi$
$353$	21.7898	1.15976	0.579878	+	0.814704i	$0.303100\pi$
$354$	0.951738	0.0505843
$355$	−12.7973	−0.679212
$356$	6.29598	0.333687
$357$	2.69248	0.142501
$358$	5.18844	0.274217
$359$	−23.9737	−1.26528	−0.632642	−	0.774444i	$-0.718029\pi$
$359$	−23.9737	−1.26528	−0.632642	+	0.774444i	$0.718029\pi$
$360$	0.381440	0.0201037
$361$	−13.8564	−0.729285
$362$	−0.576876	−0.0303199
$363$	−28.5737	−1.49973
$364$	0	0
$365$	9.68922	0.507157
$366$	−4.95810	−0.259164
$367$	6.39133	0.333625	0.166812	−	0.985989i	$-0.446653\pi$
$367$	6.39133	0.333625	0.166812	+	0.985989i	$0.446653\pi$
$368$	−10.5412	−0.549497
$369$	1.63977	0.0853628
$370$	−1.31197	−0.0682062
$371$	−0.518513	−0.0269198
$372$	−17.0653	−0.884793
$373$	−20.0801	−1.03971	−0.519855	−	0.854255i	$-0.674014\pi$
$373$	−20.0801	−1.03971	−0.519855	+	0.854255i	$0.674014\pi$
$374$	−5.97647	−0.309036
$375$	−1.60020	−0.0826338
$376$	7.24280	0.373519
$377$	0	0
$378$	0.401714	0.0206619
$379$	5.46182	0.280555	0.140277	−	0.990112i	$-0.455201\pi$
$379$	5.46182	0.280555	0.140277	+	0.990112i	$0.455201\pi$
$380$	4.42644	0.227072
$381$	−5.18457	−0.265614
$382$	−0.442849	−0.0226581
$383$	5.66775	0.289609	0.144804	−	0.989460i	$-0.453745\pi$
$383$	5.66775	0.289609	0.144804	+	0.989460i	$0.453745\pi$
$384$	10.5805	0.539933
$385$	1.78477	0.0909602
$386$	−5.01349	−0.255180
$387$	2.22512	0.113109
$388$	−4.89478	−0.248495
$389$	10.6174	0.538325	0.269162	−	0.963095i	$-0.413253\pi$
$389$	10.6174	0.538325	0.269162	+	0.963095i	$0.413253\pi$
$390$	0	0
$391$	14.3784	0.727149
$392$	5.98118	0.302095
$393$	−0.281096	−0.0141794
$394$	0.141264	0.00711679
$395$	4.51851	0.227351
$396$	4.60656	0.231488
$397$	−28.0338	−1.40697	−0.703487	−	0.710708i	$-0.748375\pi$
$397$	−28.0338	−1.40697	−0.703487	+	0.710708i	$0.748375\pi$
$398$	0.673745	0.0337718
$399$	1.20578	0.0603643
$400$	3.71276	0.185638
$401$	22.5143	1.12431	0.562155	−	0.827032i	$-0.309973\pi$
$401$	22.5143	1.12431	0.562155	+	0.827032i	$0.309973\pi$
$402$	3.63222	0.181159
$403$	0	0
$404$	−24.2927	−1.20861
$405$	−7.48883	−0.372123
$406$	−0.211925	−0.0105177
$407$	−32.0805	−1.59017
$408$	−7.03533	−0.348301
$409$	−4.28772	−0.212014	−0.106007	−	0.994365i	$-0.533807\pi$
$409$	−4.28772	−0.212014	−0.106007	+	0.994365i	$0.533807\pi$
$410$	−0.819883	−0.0404911
$411$	−28.7761	−1.41942
$412$	29.3243	1.44471
$413$	−0.899499	−0.0442614
$414$	0.274051	0.0134689
$415$	4.26371	0.209297
$416$	0	0
$417$	−19.1802	−0.939257
$418$	−2.67645	−0.130909
$419$	17.7116	0.865266	0.432633	−	0.901570i	$-0.357585\pi$
$419$	17.7116	0.865266	0.432633	+	0.901570i	$0.357585\pi$
$420$	1.03766	0.0506326
$421$	−12.8787	−0.627672	−0.313836	−	0.949477i	$-0.601614\pi$
$421$	−12.8787	−0.627672	−0.313836	+	0.949477i	$0.601614\pi$
$422$	−1.80152	−0.0876965
$423$	3.66563	0.178229
$424$	1.35485	0.0657973
$425$	−5.06430	−0.245655
$426$	4.49880	0.217967
$427$	4.68596	0.226770
$428$	25.4981	1.23250
$429$	0	0
$430$	−1.11256	−0.0536524
$431$	−9.49845	−0.457524	−0.228762	−	0.973482i	$-0.573468\pi$
$431$	−9.49845	−0.457524	−0.228762	+	0.973482i	$0.573468\pi$
$432$	20.4338	0.983121
$433$	−1.39628	−0.0671010	−0.0335505	−	0.999437i	$-0.510681\pi$
$433$	−1.39628	−0.0671010	−0.0335505	+	0.999437i	$0.510681\pi$
$434$	−0.398826	−0.0191443
$435$	4.64613	0.222765
$436$	−21.9228	−1.04991
$437$	6.43911	0.308024
$438$	−3.40617	−0.162753
$439$	4.16180	0.198632	0.0993159	−	0.995056i	$-0.468335\pi$
$439$	4.16180	0.198632	0.0993159	+	0.995056i	$0.468335\pi$
$440$	−4.66351	−0.222324
$441$	3.02711	0.144148
$442$	0	0
$443$	9.54563	0.453526	0.226763	−	0.973950i	$-0.427186\pi$
$443$	9.54563	0.453526	0.226763	+	0.973950i	$0.427186\pi$
$444$	−18.6516	−0.885164
$445$	−3.22584	−0.152919
$446$	−2.25052	−0.106565
$447$	−5.45732	−0.258122
$448$	−2.28083	−0.107759
$449$	−21.7171	−1.02489	−0.512446	−	0.858720i	$-0.671260\pi$
$449$	−21.7171	−1.02489	−0.512446	+	0.858720i	$0.671260\pi$
$450$	−0.0965246	−0.00455022
$451$	−20.0479	−0.944018
$452$	35.8023	1.68400
$453$	12.7398	0.598569
$454$	−1.54743	−0.0726246
$455$	0	0
$456$	−3.15064	−0.147542
$457$	−4.72259	−0.220914	−0.110457	−	0.993881i	$-0.535231\pi$
$457$	−4.72259	−0.220914	−0.110457	+	0.993881i	$0.535231\pi$
$458$	−0.291961	−0.0136424
$459$	−27.8722	−1.30096
$460$	5.54133	0.258366
$461$	1.78151	0.0829730	0.0414865	−	0.999139i	$-0.486791\pi$
$461$	1.78151	0.0829730	0.0414865	+	0.999139i	$0.486791\pi$
$462$	−0.627421	−0.0291902
$463$	−6.80200	−0.316116	−0.158058	−	0.987430i	$-0.550523\pi$
$463$	−6.80200	−0.316116	−0.158058	+	0.987430i	$0.550523\pi$
$464$	−10.7799	−0.500444
$465$	8.74363	0.405476
$466$	−0.274051	−0.0126952
$467$	18.2374	0.843927	0.421963	−	0.906613i	$-0.361341\pi$
$467$	18.2374	0.843927	0.421963	+	0.906613i	$0.361341\pi$
$468$	0	0
$469$	−3.43285	−0.158514
$470$	−1.83281	−0.0845414
$471$	26.2958	1.21165
$472$	2.35035	0.108184
$473$	−27.2045	−1.25086
$474$	−1.58845	−0.0729598
$475$	−2.26795	−0.104061
$476$	3.28398	0.150521
$477$	0.685698	0.0313960
$478$	2.18414	0.0999003
$479$	35.1807	1.60745	0.803724	−	0.595002i	$-0.202849\pi$
$479$	35.1807	1.60745	0.803724	+	0.595002i	$0.202849\pi$
$480$	−4.08359	−0.186390
$481$	0	0
$482$	4.96204	0.226015
$483$	1.50948	0.0686835
$484$	−34.8510	−1.58414
$485$	2.50791	0.113878
$486$	−0.994615	−0.0451166
$487$	10.3040	0.466919	0.233459	−	0.972367i	$-0.424995\pi$
$487$	10.3040	0.466919	0.233459	+	0.972367i	$0.424995\pi$
$488$	−12.2442	−0.554269
$489$	28.4950	1.28859
$490$	−1.51356	−0.0683756
$491$	9.33198	0.421147	0.210573	−	0.977578i	$-0.432467\pi$
$491$	9.33198	0.421147	0.210573	+	0.977578i	$0.432467\pi$
$492$	−11.6558	−0.525484
$493$	14.7041	0.662238
$494$	0	0
$495$	−2.36023	−0.106085
$496$	−20.2869	−0.910907
$497$	−4.25187	−0.190722
$498$	−1.49887	−0.0671661
$499$	−23.9421	−1.07179	−0.535897	−	0.844283i	$-0.680026\pi$
$499$	−23.9421	−1.07179	−0.535897	+	0.844283i	$0.680026\pi$
$500$	−1.95174	−0.0872844
$501$	−10.0711	−0.449943
$502$	−1.48692	−0.0663645
$503$	42.1443	1.87912	0.939560	−	0.342385i	$-0.111235\pi$
$503$	42.1443	1.87912	0.939560	+	0.342385i	$0.111235\pi$
$504$	0.126732	0.00564510
$505$	12.4467	0.553872
$506$	−3.35056	−0.148951
$507$	0	0
$508$	−6.32355	−0.280562
$509$	33.5602	1.48753	0.743765	−	0.668441i	$-0.233038\pi$
$509$	33.5602	1.48753	0.743765	+	0.668441i	$0.233038\pi$
$510$	1.78031	0.0788336
$511$	3.21921	0.142409
$512$	15.9211	0.703621
$513$	−12.4820	−0.551096
$514$	−2.25263	−0.0993593
$515$	−15.0247	−0.662069
$516$	−15.8166	−0.696288
$517$	−44.8162	−1.97102
$518$	−0.435898	−0.0191523
$519$	−25.5633	−1.12210
$520$	0	0
$521$	12.4649	0.546098	0.273049	−	0.962000i	$-0.411968\pi$
$521$	12.4649	0.546098	0.273049	+	0.962000i	$0.411968\pi$
$522$	0.280257	0.0122665
$523$	−5.65956	−0.247475	−0.123738	−	0.992315i	$-0.539488\pi$
$523$	−5.65956	−0.247475	−0.123738	+	0.992315i	$0.539488\pi$
$524$	−0.342849	−0.0149774
$525$	−0.531659	−0.0232035
$526$	4.09870	0.178712
$527$	27.6718	1.20540
$528$	−31.9147	−1.38891
$529$	−14.9391	−0.649525
$530$	−0.342849	−0.0148924
$531$	1.18953	0.0516211
$532$	1.47067	0.0637616
$533$	0	0
$534$	1.13402	0.0490737
$535$	−13.0643	−0.564819
$536$	8.96989	0.387440
$537$	−37.7925	−1.63087
$538$	3.94511	0.170086
$539$	−37.0097	−1.59412
$540$	−10.7417	−0.462250
$541$	15.4750	0.665321	0.332660	−	0.943047i	$-0.392054\pi$
$541$	15.4750	0.665321	0.332660	+	0.943047i	$0.392054\pi$
$542$	−6.78781	−0.291562
$543$	4.20196	0.180323
$544$	−12.9237	−0.554101
$545$	11.2325	0.481146
$546$	0	0
$547$	25.1765	1.07647	0.538234	−	0.842795i	$-0.319092\pi$
$547$	25.1765	1.07647	0.538234	+	0.842795i	$0.319092\pi$
$548$	−35.0979	−1.49931
$549$	−6.19687	−0.264476
$550$	1.18012	0.0503204
$551$	6.58493	0.280528
$552$	−3.94419	−0.167876
$553$	1.50126	0.0638401
$554$	5.82269	0.247382
$555$	9.55639	0.405646
$556$	−23.3938	−0.992118
$557$	−42.3489	−1.79438	−0.897190	−	0.441645i	$-0.854395\pi$
$557$	−42.3489	−1.79438	−0.897190	+	0.441645i	$0.854395\pi$
$558$	0.527420	0.0223275
$559$	0	0
$560$	1.23355	0.0521270
$561$	43.5325	1.83794
$562$	−1.09353	−0.0461276
$563$	23.7905	1.00265	0.501326	−	0.865259i	$-0.332846\pi$
$563$	23.7905	1.00265	0.501326	+	0.865259i	$0.332846\pi$
$564$	−26.0561	−1.09716
$565$	−18.3438	−0.771731
$566$	−2.76505	−0.116224
$567$	−2.48814	−0.104492
$568$	11.1099	0.466162
$569$	−26.7421	−1.12109	−0.560543	−	0.828125i	$-0.689407\pi$
$569$	−26.7421	−1.12109	−0.560543	+	0.828125i	$0.689407\pi$
$570$	0.797279	0.0333944
$571$	−16.7159	−0.699539	−0.349769	−	0.936836i	$-0.613740\pi$
$571$	−16.7159	−0.699539	−0.349769	+	0.936836i	$0.613740\pi$
$572$	0	0
$573$	3.22571	0.134756
$574$	−0.272403	−0.0113699
$575$	−2.83918	−0.118402
$576$	3.01625	0.125677
$577$	20.6768	0.860786	0.430393	−	0.902642i	$-0.358375\pi$
$577$	20.6768	0.860786	0.430393	+	0.902642i	$0.358375\pi$
$578$	1.89966	0.0790153
$579$	36.5182	1.51764
$580$	5.66682	0.235302
$581$	1.41660	0.0587706
$582$	−0.881636	−0.0365450
$583$	−8.38340	−0.347205
$584$	−8.41165	−0.348076
$585$	0	0
$586$	−3.71657	−0.153530
$587$	−20.7972	−0.858391	−0.429196	−	0.903212i	$-0.641203\pi$
$587$	−20.7972	−0.858391	−0.429196	+	0.903212i	$0.641203\pi$
$588$	−21.5174	−0.887362
$589$	12.3923	0.510616
$590$	−0.594763	−0.0244860
$591$	−1.02897	−0.0423260
$592$	−22.1726	−0.911289
$593$	21.8475	0.897169	0.448585	−	0.893740i	$-0.351928\pi$
$593$	21.8475	0.897169	0.448585	+	0.893740i	$0.351928\pi$
$594$	6.49498	0.266492
$595$	−1.68260	−0.0689797
$596$	−6.65622	−0.272649
$597$	−4.90755	−0.200853
$598$	0	0
$599$	−3.58040	−0.146291	−0.0731456	−	0.997321i	$-0.523304\pi$
$599$	−3.58040	−0.146291	−0.0731456	+	0.997321i	$0.523304\pi$
$600$	1.38920	0.0567139
$601$	21.3486	0.870829	0.435414	−	0.900230i	$-0.356602\pi$
$601$	21.3486	0.870829	0.435414	+	0.900230i	$0.356602\pi$
$602$	−0.369644	−0.0150656
$603$	4.53972	0.184872
$604$	15.5386	0.632256
$605$	17.8564	0.725966
$606$	−4.37554	−0.177744
$607$	−3.29976	−0.133933	−0.0669665	−	0.997755i	$-0.521332\pi$
$607$	−3.29976	−0.133933	−0.0669665	+	0.997755i	$0.521332\pi$
$608$	−5.78766	−0.234720
$609$	1.54366	0.0625523
$610$	3.09843	0.125452
$611$	0	0
$612$	−4.34285	−0.175549
$613$	−9.88635	−0.399306	−0.199653	−	0.979867i	$-0.563981\pi$
$613$	−9.88635	−0.399306	−0.199653	+	0.979867i	$0.563981\pi$
$614$	0.945589	0.0381609
$615$	5.97201	0.240815
$616$	−1.54944	−0.0624286
$617$	45.7169	1.84049	0.920246	−	0.391339i	$-0.127988\pi$
$617$	45.7169	1.84049	0.920246	+	0.391339i	$0.127988\pi$
$618$	5.28182	0.212466
$619$	−19.9143	−0.800425	−0.400212	−	0.916422i	$-0.631064\pi$
$619$	−19.9143	−0.800425	−0.400212	+	0.916422i	$0.631064\pi$
$620$	10.6645	0.428296
$621$	−15.6259	−0.627046
$622$	−0.488829	−0.0196003
$623$	−1.07177	−0.0429397
$624$	0	0
$625$	1.00000	0.0400000
$626$	1.58369	0.0632971
$627$	19.4952	0.778563
$628$	32.0726	1.27984
$629$	30.2440	1.20591
$630$	−0.0320700	−0.00127770
$631$	−14.5958	−0.581050	−0.290525	−	0.956867i	$-0.593830\pi$
$631$	−14.5958	−0.581050	−0.290525	+	0.956867i	$0.593830\pi$
$632$	−3.92272	−0.156038
$633$	13.1222	0.521562
$634$	0.0706609	0.00280630
$635$	3.23996	0.128574
$636$	−4.87409	−0.193270
$637$	0	0
$638$	−3.42644	−0.135654
$639$	5.62281	0.222435
$640$	−6.61199	−0.261362
$641$	−14.1637	−0.559431	−0.279716	−	0.960083i	$-0.590240\pi$
$641$	−14.1637	−0.559431	−0.279716	+	0.960083i	$0.590240\pi$
$642$	4.59265	0.181257
$643$	−16.7716	−0.661408	−0.330704	−	0.943735i	$-0.607286\pi$
$643$	−16.7716	−0.661408	−0.330704	+	0.943735i	$0.607286\pi$
$644$	1.84109	0.0725490
$645$	8.10387	0.319089
$646$	2.52323	0.0992751
$647$	−2.99168	−0.117615	−0.0588075	−	0.998269i	$-0.518730\pi$
$647$	−2.99168	−0.117615	−0.0588075	+	0.998269i	$0.518730\pi$
$648$	6.50139	0.255399
$649$	−14.5432	−0.570872
$650$	0	0
$651$	2.90504	0.113858
$652$	34.7550	1.36111
$653$	−11.6643	−0.456461	−0.228230	−	0.973607i	$-0.573294\pi$
$653$	−11.6643	−0.456461	−0.228230	+	0.973607i	$0.573294\pi$
$654$	−3.94868	−0.154406
$655$	0.175664	0.00686374
$656$	−13.8562	−0.540993
$657$	−4.25719	−0.166089
$658$	−0.608946	−0.0237392
$659$	−1.81047	−0.0705260	−0.0352630	−	0.999378i	$-0.511227\pi$
$659$	−1.81047	−0.0705260	−0.0352630	+	0.999378i	$0.511227\pi$
$660$	16.7771	0.653046
$661$	12.3406	0.479992	0.239996	−	0.970774i	$-0.422854\pi$
$661$	12.3406	0.479992	0.239996	+	0.970774i	$0.422854\pi$
$662$	−3.65383	−0.142010
$663$	0	0
$664$	−3.70152	−0.143647
$665$	−0.753518	−0.0292202
$666$	0.576446	0.0223368
$667$	8.24348	0.319189
$668$	−12.2836	−0.475265
$669$	16.3927	0.633779
$670$	−2.26986	−0.0876923
$671$	75.7634	2.92481
$672$	−1.35676	−0.0523381
$673$	9.26625	0.357188	0.178594	−	0.983923i	$-0.442845\pi$
$673$	9.26625	0.357188	0.178594	+	0.983923i	$0.442845\pi$
$674$	5.32051	0.204938
$675$	5.50367	0.211836
$676$	0	0
$677$	13.8984	0.534158	0.267079	−	0.963675i	$-0.413941\pi$
$677$	13.8984	0.534158	0.267079	+	0.963675i	$0.413941\pi$
$678$	6.44863	0.247658
$679$	0.833244	0.0319770
$680$	4.39654	0.168600
$681$	11.2715	0.431924
$682$	−6.44828	−0.246917
$683$	37.7512	1.44451	0.722255	−	0.691626i	$-0.243105\pi$
$683$	37.7512	1.44451	0.722255	+	0.691626i	$0.243105\pi$
$684$	−1.94486	−0.0743637
$685$	17.9829	0.687090
$686$	−1.01381	−0.0387073
$687$	2.12664	0.0811363
$688$	−18.8025	−0.716838
$689$	0	0
$690$	0.998090	0.0379966
$691$	1.65291	0.0628797	0.0314399	−	0.999506i	$-0.489991\pi$
$691$	1.65291	0.0628797	0.0314399	+	0.999506i	$0.489991\pi$
$692$	−31.1792	−1.18526
$693$	−0.784180	−0.0297885
$694$	−1.37823	−0.0523168
$695$	11.9861	0.454660
$696$	−4.03351	−0.152890
$697$	18.9002	0.715897
$698$	−1.55317	−0.0587885
$699$	1.99618	0.0755025
$700$	−0.648458	−0.0245094
$701$	20.4819	0.773590	0.386795	−	0.922166i	$-0.373582\pi$
$701$	20.4819	0.773590	0.386795	+	0.922166i	$0.373582\pi$
$702$	0	0
$703$	13.5442	0.510830
$704$	−36.8769	−1.38985
$705$	13.3502	0.502797
$706$	4.78694	0.180159
$707$	4.13538	0.155527
$708$	−8.45541	−0.317774
$709$	−21.9417	−0.824039	−0.412020	−	0.911175i	$-0.635177\pi$
$709$	−21.9417	−0.824039	−0.412020	+	0.911175i	$0.635177\pi$
$710$	−2.81140	−0.105510
$711$	−1.98532	−0.0744552
$712$	2.80049	0.104953
$713$	15.5136	0.580987
$714$	0.591503	0.0221364
$715$	0	0
$716$	−46.0950	−1.72265
$717$	−15.9093	−0.594142
$718$	−5.26671	−0.196552
$719$	38.8475	1.44877	0.724384	−	0.689397i	$-0.242124\pi$
$719$	38.8475	1.44877	0.724384	+	0.689397i	$0.242124\pi$
$720$	−1.63129	−0.0607945
$721$	−4.99191	−0.185909
$722$	−3.04407	−0.113289
$723$	−36.1434	−1.34419
$724$	5.12507	0.190472
$725$	−2.90348	−0.107832
$726$	−6.27728	−0.232972
$727$	−30.6598	−1.13711	−0.568555	−	0.822645i	$-0.692497\pi$
$727$	−30.6598	−1.13711	−0.568555	+	0.822645i	$0.692497\pi$
$728$	0	0
$729$	29.7112	1.10042
$730$	2.12859	0.0787828
$731$	25.6471	0.948593
$732$	44.0487	1.62809
$733$	−24.3858	−0.900709	−0.450355	−	0.892850i	$-0.648702\pi$
$733$	−24.3858	−0.900709	−0.450355	+	0.892850i	$0.648702\pi$
$734$	1.40409	0.0518259
$735$	11.0247	0.406653
$736$	−7.24539	−0.267069
$737$	−55.5029	−2.04448
$738$	0.360235	0.0132604
$739$	−38.2788	−1.40811	−0.704054	−	0.710146i	$-0.748629\pi$
$739$	−38.2788	−1.40811	−0.704054	+	0.710146i	$0.748629\pi$
$740$	11.6558	0.428476
$741$	0	0
$742$	−0.113910	−0.00418178
$743$	40.0079	1.46775	0.733874	−	0.679286i	$-0.237710\pi$
$743$	40.0079	1.46775	0.733874	+	0.679286i	$0.237710\pi$
$744$	−7.59074	−0.278290
$745$	3.41041	0.124948
$746$	−4.41134	−0.161511
$747$	−1.87336	−0.0685427
$748$	53.0960	1.94138
$749$	−4.34057	−0.158601
$750$	−0.351542	−0.0128365
$751$	25.6020	0.934230	0.467115	−	0.884197i	$-0.345293\pi$
$751$	25.6020	0.934230	0.467115	+	0.884197i	$0.345293\pi$
$752$	−30.9750	−1.12954
$753$	10.8307	0.394693
$754$	0	0
$755$	−7.96141	−0.289745
$756$	−3.56890	−0.129800
$757$	−1.84848	−0.0671840	−0.0335920	−	0.999436i	$-0.510695\pi$
$757$	−1.84848	−0.0671840	−0.0335920	+	0.999436i	$0.510695\pi$
$758$	1.19989	0.0435820
$759$	24.4055	0.885862
$760$	1.96891	0.0714198
$761$	−26.2124	−0.950199	−0.475099	−	0.879932i	$-0.657588\pi$
$761$	−26.2124	−0.950199	−0.475099	+	0.879932i	$0.657588\pi$
$762$	−1.13898	−0.0412610
$763$	3.73195	0.135106
$764$	3.93435	0.142340
$765$	2.22512	0.0804494
$766$	1.24513	0.0449884
$767$	0	0
$768$	−19.6459	−0.708911
$769$	44.3495	1.59928	0.799641	−	0.600478i	$-0.205023\pi$
$769$	44.3495	1.59928	0.799641	+	0.600478i	$0.205023\pi$
$770$	0.392090	0.0141299
$771$	16.4081	0.590924
$772$	44.5408	1.60306
$773$	23.2638	0.836742	0.418371	−	0.908276i	$-0.362601\pi$
$773$	23.2638	0.836742	0.418371	+	0.908276i	$0.362601\pi$
$774$	0.488829	0.0175706
$775$	−5.46410	−0.196276
$776$	−2.17723	−0.0781580
$777$	3.17508	0.113905
$778$	2.33251	0.0836245
$779$	8.46410	0.303258
$780$	0	0
$781$	−68.7449	−2.45989
$782$	3.15875	0.112957
$783$	−15.9798	−0.571071
$784$	−25.5794	−0.913552
$785$	−16.4329	−0.586514
$786$	−0.0617531	−0.00220266
$787$	47.9133	1.70793	0.853963	−	0.520334i	$-0.174192\pi$
$787$	47.9133	1.70793	0.853963	+	0.520334i	$0.174192\pi$
$788$	−1.25502	−0.0447081
$789$	−29.8548	−1.06286
$790$	0.992658	0.0353172
$791$	−6.09467	−0.216702
$792$	2.04903	0.0728090
$793$	0	0
$794$	−6.15865	−0.218562
$795$	2.49731	0.0885704
$796$	−5.98567	−0.212156
$797$	−20.6952	−0.733060	−0.366530	−	0.930406i	$-0.619454\pi$
$797$	−20.6952	−0.733060	−0.366530	+	0.930406i	$0.619454\pi$
$798$	0.264893	0.00937712
$799$	42.2507	1.49472
$800$	2.55193	0.0902245
$801$	1.41735	0.0500795
$802$	4.94609	0.174653
$803$	52.0487	1.83676
$804$	−32.2693	−1.13805
$805$	−0.943307	−0.0332472
$806$	0	0
$807$	−28.7361	−1.01156
$808$	−10.8056	−0.380138
$809$	15.8915	0.558714	0.279357	−	0.960187i	$-0.409879\pi$
$809$	15.8915	0.558714	0.279357	+	0.960187i	$0.409879\pi$
$810$	−1.64520	−0.0578063
$811$	23.8796	0.838525	0.419263	−	0.907865i	$-0.362289\pi$
$811$	23.8796	0.838525	0.419263	+	0.907865i	$0.362289\pi$
$812$	1.88278	0.0660727
$813$	49.4423	1.73402
$814$	−7.04768	−0.247021
$815$	−17.8072	−0.623759
$816$	30.0877	1.05328
$817$	11.4856	0.401829
$818$	−0.941956	−0.0329347
$819$	0	0
$820$	7.28398	0.254368
$821$	−15.9097	−0.555251	−0.277626	−	0.960689i	$-0.589547\pi$
$821$	−15.9097	−0.555251	−0.277626	+	0.960689i	$0.589547\pi$
$822$	−6.32174	−0.220496
$823$	−14.8115	−0.516295	−0.258147	−	0.966106i	$-0.583112\pi$
$823$	−14.8115	−0.516295	−0.258147	+	0.966106i	$0.583112\pi$
$824$	13.0436	0.454397
$825$	−8.59596	−0.299273
$826$	−0.197608	−0.00687566
$827$	−33.9498	−1.18055	−0.590275	−	0.807202i	$-0.700981\pi$
$827$	−33.9498	−1.18055	−0.590275	+	0.807202i	$0.700981\pi$
$828$	−2.43472	−0.0846122
$829$	23.3146	0.809749	0.404875	−	0.914372i	$-0.367315\pi$
$829$	23.3146	0.809749	0.404875	+	0.914372i	$0.367315\pi$
$830$	0.936681	0.0325127
$831$	−42.4124	−1.47127
$832$	0	0
$833$	34.8910	1.20890
$834$	−4.21363	−0.145906
$835$	6.29366	0.217801
$836$	23.7780	0.822380
$837$	−30.0726	−1.03946
$838$	3.89100	0.134412
$839$	14.7930	0.510710	0.255355	−	0.966847i	$-0.417808\pi$
$839$	14.7930	0.510710	0.255355	+	0.966847i	$0.417808\pi$
$840$	0.461557	0.0159252
$841$	−20.5698	−0.709305
$842$	−2.82929	−0.0975038
$843$	7.96523	0.274337
$844$	16.0050	0.550915
$845$	0	0
$846$	0.805291	0.0276865
$847$	5.93273	0.203851
$848$	−5.79422	−0.198974
$849$	20.1406	0.691223
$850$	−1.11256	−0.0381605
$851$	16.9556	0.581231
$852$	−39.9681	−1.36929
$853$	16.3452	0.559650	0.279825	−	0.960051i	$-0.409724\pi$
$853$	16.3452	0.559650	0.279825	+	0.960051i	$0.409724\pi$
$854$	1.02944	0.0352268
$855$	0.996477	0.0340788
$856$	11.3417	0.387651
$857$	−34.1418	−1.16626	−0.583132	−	0.812378i	$-0.698173\pi$
$857$	−34.1418	−1.16626	−0.583132	+	0.812378i	$0.698173\pi$
$858$	0	0
$859$	−45.1996	−1.54219	−0.771096	−	0.636719i	$-0.780291\pi$
$859$	−45.1996	−1.54219	−0.771096	+	0.636719i	$0.780291\pi$
$860$	9.88418	0.337048
$861$	1.98418	0.0676207
$862$	−2.08669	−0.0710728
$863$	−4.75058	−0.161712	−0.0808559	−	0.996726i	$-0.525765\pi$
$863$	−4.75058	−0.161712	−0.0808559	+	0.996726i	$0.525765\pi$
$864$	14.0450	0.477821
$865$	15.9751	0.543170
$866$	−0.306745	−0.0104236
$867$	−13.8371	−0.469931
$868$	3.54324	0.120265
$869$	24.2726	0.823392
$870$	1.02069	0.0346048
$871$	0	0
$872$	−9.75140	−0.330224
$873$	−1.10191	−0.0372940
$874$	1.41459	0.0478492
$875$	0.332247	0.0112320
$876$	30.2610	1.02242
$877$	−2.25506	−0.0761481	−0.0380741	−	0.999275i	$-0.512122\pi$
$877$	−2.25506	−0.0761481	−0.0380741	+	0.999275i	$0.512122\pi$
$878$	0.914293	0.0308559
$879$	27.0715	0.913098
$880$	19.9442	0.672320
$881$	−2.98304	−0.100501	−0.0502507	−	0.998737i	$-0.516002\pi$
$881$	−2.98304	−0.100501	−0.0502507	+	0.998737i	$0.516002\pi$
$882$	0.665017	0.0223923
$883$	28.2874	0.951947	0.475973	−	0.879460i	$-0.342096\pi$
$883$	28.2874	0.951947	0.475973	+	0.879460i	$0.342096\pi$
$884$	0	0
$885$	4.33225	0.145627
$886$	2.09705	0.0704517
$887$	−27.9816	−0.939531	−0.469766	−	0.882791i	$-0.655662\pi$
$887$	−27.9816	−0.939531	−0.469766	+	0.882791i	$0.655662\pi$
$888$	−8.29633	−0.278407
$889$	1.07647	0.0361035
$890$	−0.708674	−0.0237548
$891$	−40.2286	−1.34771
$892$	19.9940	0.669448
$893$	18.9212	0.633172
$894$	−1.19890	−0.0400973
$895$	23.6174	0.789443
$896$	−2.19681	−0.0733903
$897$	0	0
$898$	−4.77095	−0.159209
$899$	15.8649	0.529124
$900$	0.857542	0.0285847
$901$	7.90348	0.263303
$902$	−4.40426	−0.146646
$903$	2.69248	0.0896002
$904$	15.9251	0.529661
$905$	−2.62590	−0.0872879
$906$	2.79877	0.0929829
$907$	16.5520	0.549600	0.274800	−	0.961501i	$-0.411388\pi$
$907$	16.5520	0.549600	0.274800	+	0.961501i	$0.411388\pi$
$908$	13.7477	0.456232
$909$	−5.46876	−0.181387
$910$	0	0
$911$	7.04863	0.233532	0.116766	−	0.993159i	$-0.462747\pi$
$911$	7.04863	0.233532	0.116766	+	0.993159i	$0.462747\pi$
$912$	13.4742	0.446175
$913$	22.9039	0.758007
$914$	−1.03749	−0.0343172
$915$	−22.5689	−0.746106
$916$	2.59383	0.0857026
$917$	0.0583636	0.00192734
$918$	−6.12316	−0.202094
$919$	16.5438	0.545728	0.272864	−	0.962053i	$-0.412029\pi$
$919$	16.5438	0.545728	0.272864	+	0.962053i	$0.412029\pi$
$920$	2.46482	0.0812626
$921$	−6.88766	−0.226956
$922$	0.391374	0.0128892
$923$	0	0
$924$	5.57412	0.183375
$925$	−5.97201	−0.196359
$926$	−1.49431	−0.0491060
$927$	6.60147	0.216821
$928$	−7.40948	−0.243228
$929$	−33.8367	−1.11015	−0.555074	−	0.831801i	$-0.687310\pi$
$929$	−33.8367	−1.11015	−0.555074	+	0.831801i	$0.687310\pi$
$930$	1.92086	0.0629875
$931$	15.6253	0.512098
$932$	2.43472	0.0797517
$933$	3.56063	0.116570
$934$	4.00652	0.131097
$935$	−27.2045	−0.889681
$936$	0	0
$937$	−30.4606	−0.995104	−0.497552	−	0.867434i	$-0.665768\pi$
$937$	−30.4606	−0.995104	−0.497552	+	0.867434i	$0.665768\pi$
$938$	−0.754153	−0.0246240
$939$	−11.5356	−0.376450
$940$	16.2831	0.531095
$941$	38.2101	1.24561	0.622807	−	0.782375i	$-0.285992\pi$
$941$	38.2101	1.24561	0.622807	+	0.782375i	$0.285992\pi$
$942$	5.77684	0.188220
$943$	10.5960	0.345052
$944$	−10.0516	−0.327153
$945$	1.82858	0.0594836
$946$	−5.97647	−0.194312
$947$	−52.4482	−1.70434	−0.852169	−	0.523266i	$-0.824713\pi$
$947$	−52.4482	−1.70434	−0.852169	+	0.523266i	$0.824713\pi$
$948$	14.1120	0.458338
$949$	0	0
$950$	−0.498239	−0.0161650
$951$	−0.514693	−0.0166901
$952$	1.46074	0.0473427
$953$	39.7500	1.28763	0.643814	−	0.765182i	$-0.277351\pi$
$953$	39.7500	1.28763	0.643814	+	0.765182i	$0.277351\pi$
$954$	0.150639	0.00487711
$955$	−2.01582	−0.0652304
$956$	−19.4043	−0.627580
$957$	24.9581	0.806782
$958$	7.72874	0.249704
$959$	5.97475	0.192935
$960$	10.9852	0.354544
$961$	−1.14359	−0.0368901
$962$	0	0
$963$	5.74011	0.184972
$964$	−44.0837	−1.41984
$965$	−22.8211	−0.734636
$966$	0.331612	0.0106694
$967$	−25.7857	−0.829214	−0.414607	−	0.910001i	$-0.636081\pi$
$967$	−25.7857	−0.829214	−0.414607	+	0.910001i	$0.636081\pi$
$968$	−15.5019	−0.498251
$969$	−18.3792	−0.590424
$970$	0.550955	0.0176901
$971$	−55.5252	−1.78189	−0.890945	−	0.454111i	$-0.849957\pi$
$971$	−55.5252	−1.78189	−0.890945	+	0.454111i	$0.849957\pi$
$972$	8.83634	0.283426
$973$	3.98235	0.127668
$974$	2.26365	0.0725321
$975$	0	0
$976$	52.3642	1.67614
$977$	40.5161	1.29622	0.648112	−	0.761545i	$-0.275559\pi$
$977$	40.5161	1.29622	0.648112	+	0.761545i	$0.275559\pi$
$978$	6.25998	0.200172
$979$	−17.3286	−0.553824
$980$	13.4467	0.429540
$981$	−4.93525	−0.157570
$982$	2.05011	0.0654218
$983$	−34.8059	−1.11014	−0.555068	−	0.831805i	$-0.687308\pi$
$983$	−34.8059	−1.11014	−0.555068	+	0.831805i	$0.687308\pi$
$984$	−5.18457	−0.165278
$985$	0.643026	0.0204885
$986$	3.23029	0.102873
$987$	4.43555	0.141185
$988$	0	0
$989$	14.3784	0.457208
$990$	−0.518513	−0.0164794
$991$	43.8855	1.39407	0.697034	−	0.717038i	$-0.254503\pi$
$991$	43.8855	1.39407	0.697034	+	0.717038i	$0.254503\pi$
$992$	−13.9440	−0.442723
$993$	26.6145	0.844584
$994$	−0.934079	−0.0296272
$995$	3.06684	0.0972254
$996$	13.3163	0.421942
$997$	−5.49137	−0.173914	−0.0869568	−	0.996212i	$-0.527714\pi$
$997$	−5.49137	−0.173914	−0.0869568	+	0.996212i	$0.527714\pi$
$998$	−5.25976	−0.166495
$999$	−32.8680	−1.03990

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.a.l.1.3		4
3.2	odd	2		7605.2.a.cj.1.2		4
5.4	even	2		4225.2.a.bl.1.2		4
13.2	odd	12		845.2.m.g.316.3		8
13.3	even	3		845.2.e.n.191.2		8
13.4	even	6		845.2.e.m.146.3		8
13.5	odd	4		845.2.c.g.506.4		8
13.6	odd	12		65.2.m.a.36.2	✓	8
13.7	odd	12		845.2.m.g.361.3		8
13.8	odd	4		845.2.c.g.506.5		8
13.9	even	3		845.2.e.n.146.2		8
13.10	even	6		845.2.e.m.191.3		8
13.11	odd	12		65.2.m.a.56.2	yes	8
13.12	even	2		845.2.a.m.1.2		4
39.11	even	12		585.2.bu.c.316.3		8
39.32	even	12		585.2.bu.c.361.3		8
39.38	odd	2		7605.2.a.cf.1.3		4
52.11	even	12		1040.2.da.b.641.2		8
52.19	even	12		1040.2.da.b.881.2		8
65.19	odd	12		325.2.n.d.101.3		8
65.24	odd	12		325.2.n.d.251.3		8
65.32	even	12		325.2.m.c.49.2		8
65.37	even	12		325.2.m.b.199.3		8
65.58	even	12		325.2.m.b.49.3		8
65.63	even	12		325.2.m.c.199.2		8
65.64	even	2		4225.2.a.bi.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.2	✓	8	13.6	odd	12
65.2.m.a.56.2	yes	8	13.11	odd	12
325.2.m.b.49.3		8	65.58	even	12
325.2.m.b.199.3		8	65.37	even	12
325.2.m.c.49.2		8	65.32	even	12
325.2.m.c.199.2		8	65.63	even	12
325.2.n.d.101.3		8	65.19	odd	12
325.2.n.d.251.3		8	65.24	odd	12
585.2.bu.c.316.3		8	39.11	even	12
585.2.bu.c.361.3		8	39.32	even	12
845.2.a.l.1.3		4	1.1	even	1	trivial
845.2.a.m.1.2		4	13.12	even	2
845.2.c.g.506.4		8	13.5	odd	4
845.2.c.g.506.5		8	13.8	odd	4
845.2.e.m.146.3		8	13.4	even	6
845.2.e.m.191.3		8	13.10	even	6
845.2.e.n.146.2		8	13.9	even	3
845.2.e.n.191.2		8	13.3	even	3
845.2.m.g.316.3		8	13.2	odd	12
845.2.m.g.361.3		8	13.7	odd	12
1040.2.da.b.641.2		8	52.11	even	12
1040.2.da.b.881.2		8	52.19	even	12
4225.2.a.bi.1.3		4	65.64	even	2
4225.2.a.bl.1.2		4	5.4	even	2
7605.2.a.cf.1.3		4	39.38	odd	2
7605.2.a.cj.1.2		4	3.2	odd	2

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.a (trivial)

\(f(q)\)	\(=\)	\(q+0.219687 q^{2} -1.60020 q^{3} -1.95174 q^{4} +1.00000 q^{5} -0.351542 q^{6} +0.332247 q^{7} -0.868145 q^{8} -0.439374 q^{9} +O(q^{10})\)	\(q+0.219687 q^{2} -1.60020 q^{3} -1.95174 q^{4} +1.00000 q^{5} -0.351542 q^{6} +0.332247 q^{7} -0.868145 q^{8} -0.439374 q^{9} +0.219687 q^{10} +5.37182 q^{11} +3.12316 q^{12} +0.0729902 q^{14} -1.60020 q^{15} +3.71276 q^{16} -5.06430 q^{17} -0.0965246 q^{18} -2.26795 q^{19} -1.95174 q^{20} -0.531659 q^{21} +1.18012 q^{22} -2.83918 q^{23} +1.38920 q^{24} +1.00000 q^{25} +5.50367 q^{27} -0.648458 q^{28} -2.90348 q^{29} -0.351542 q^{30} -5.46410 q^{31} +2.55193 q^{32} -8.59596 q^{33} -1.11256 q^{34} +0.332247 q^{35} +0.857542 q^{36} -5.97201 q^{37} -0.498239 q^{38} -0.868145 q^{40} -3.73205 q^{41} -0.116799 q^{42} -5.06430 q^{43} -10.4844 q^{44} -0.439374 q^{45} -0.623730 q^{46} -8.34285 q^{47} -5.94114 q^{48} -6.88961 q^{49} +0.219687 q^{50} +8.10387 q^{51} -1.56063 q^{53} +1.20908 q^{54} +5.37182 q^{55} -0.288438 q^{56} +3.62916 q^{57} -0.637855 q^{58} -2.70732 q^{59} +3.12316 q^{60} +14.1039 q^{61} -1.20039 q^{62} -0.145980 q^{63} -6.86488 q^{64} -1.88842 q^{66} -10.3322 q^{67} +9.88418 q^{68} +4.54324 q^{69} +0.0729902 q^{70} -12.7973 q^{71} +0.381440 q^{72} +9.68922 q^{73} -1.31197 q^{74} -1.60020 q^{75} +4.42644 q^{76} +1.78477 q^{77} +4.51851 q^{79} +3.71276 q^{80} -7.48883 q^{81} -0.819883 q^{82} +4.26371 q^{83} +1.03766 q^{84} -5.06430 q^{85} -1.11256 q^{86} +4.64613 q^{87} -4.66351 q^{88} -3.22584 q^{89} -0.0965246 q^{90} +5.54133 q^{92} +8.74363 q^{93} -1.83281 q^{94} -2.26795 q^{95} -4.08359 q^{96} +2.50791 q^{97} -1.51356 q^{98} -2.36023 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{5} + 4 q^{6} - 10 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 4 * q^5 + 4 * q^6 - 10 * q^7 - 6 * q^8 + 4 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{5} + 4 q^{6} - 10 q^{7} - 6 q^{8} + 4 q^{9} - 2 q^{10} - 10 q^{12} + 2 q^{14} - 2 q^{15} + 2 q^{16} - 2 q^{17} - 20 q^{18} - 16 q^{19} + 2 q^{20} - 4 q^{21} + 12 q^{22} - 10 q^{23} + 24 q^{24} + 4 q^{25} - 2 q^{27} - 8 q^{28} + 8 q^{29} + 4 q^{30} - 8 q^{31} - 4 q^{32} - 18 q^{33} + 4 q^{34} - 10 q^{35} + 20 q^{36} + 2 q^{37} + 8 q^{38} - 6 q^{40} - 8 q^{41} - 4 q^{42} - 2 q^{43} - 12 q^{44} + 4 q^{45} - 16 q^{46} - 8 q^{47} - 28 q^{48} + 12 q^{49} - 2 q^{50} + 4 q^{51} - 12 q^{53} + 16 q^{54} + 12 q^{56} + 14 q^{57} - 22 q^{58} - 12 q^{59} - 10 q^{60} + 28 q^{61} + 4 q^{62} - 4 q^{63} + 4 q^{64} + 6 q^{66} - 30 q^{67} + 14 q^{68} - 16 q^{69} + 2 q^{70} - 4 q^{71} - 12 q^{72} + 8 q^{73} - 10 q^{74} - 2 q^{75} - 20 q^{76} + 18 q^{77} - 8 q^{79} + 2 q^{80} - 8 q^{81} + 4 q^{82} + 12 q^{83} + 28 q^{84} - 2 q^{85} + 4 q^{86} - 22 q^{87} - 18 q^{88} + 12 q^{89} - 20 q^{90} + 22 q^{92} - 8 q^{93} - 32 q^{94} - 16 q^{95} - 4 q^{96} - 2 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 4 * q^5 + 4 * q^6 - 10 * q^7 - 6 * q^8 + 4 * q^9 - 2 * q^10 - 10 * q^12 + 2 * q^14 - 2 * q^15 + 2 * q^16 - 2 * q^17 - 20 * q^18 - 16 * q^19 + 2 * q^20 - 4 * q^21 + 12 * q^22 - 10 * q^23 + 24 * q^24 + 4 * q^25 - 2 * q^27 - 8 * q^28 + 8 * q^29 + 4 * q^30 - 8 * q^31 - 4 * q^32 - 18 * q^33 + 4 * q^34 - 10 * q^35 + 20 * q^36 + 2 * q^37 + 8 * q^38 - 6 * q^40 - 8 * q^41 - 4 * q^42 - 2 * q^43 - 12 * q^44 + 4 * q^45 - 16 * q^46 - 8 * q^47 - 28 * q^48 + 12 * q^49 - 2 * q^50 + 4 * q^51 - 12 * q^53 + 16 * q^54 + 12 * q^56 + 14 * q^57 - 22 * q^58 - 12 * q^59 - 10 * q^60 + 28 * q^61 + 4 * q^62 - 4 * q^63 + 4 * q^64 + 6 * q^66 - 30 * q^67 + 14 * q^68 - 16 * q^69 + 2 * q^70 - 4 * q^71 - 12 * q^72 + 8 * q^73 - 10 * q^74 - 2 * q^75 - 20 * q^76 + 18 * q^77 - 8 * q^79 + 2 * q^80 - 8 * q^81 + 4 * q^82 + 12 * q^83 + 28 * q^84 - 2 * q^85 + 4 * q^86 - 22 * q^87 - 18 * q^88 + 12 * q^89 - 20 * q^90 + 22 * q^92 - 8 * q^93 - 32 * q^94 - 16 * q^95 - 4 * q^96 - 2 * q^97 + 24 * q^98 - 24 * q^99

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