LMFDB - Embedded newform 961.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(1,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("961.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.8.2051578125.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 9x^{6} + 19x^{5} + 14x^{4} - 28x^{3} - 11x^{2} + 6x + 1 $ x^8 - 2x^7 - 9x^6 + 19x^5 + 14x^4 - 28x^3 - 11x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.28064$ of defining polynomial
Character	$\chi$	$=$	961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.69016 q^{2} -1.41916 q^{3} +5.23694 q^{4} +0.608384 q^{5} +3.81777 q^{6} -1.72688 q^{7} -8.70786 q^{8} -0.985973 q^{9} -1.63665 q^{10} +1.33739 q^{11} -7.43207 q^{12} -3.67067 q^{13} +4.64557 q^{14} -0.863396 q^{15} +12.9516 q^{16} +2.76282 q^{17} +2.65242 q^{18} -2.56768 q^{19} +3.18607 q^{20} +2.45072 q^{21} -3.59779 q^{22} +0.539261 q^{23} +12.3579 q^{24} -4.62987 q^{25} +9.87466 q^{26} +5.65675 q^{27} -9.04356 q^{28} +8.13087 q^{29} +2.32267 q^{30} -17.4262 q^{32} -1.89798 q^{33} -7.43241 q^{34} -1.05061 q^{35} -5.16348 q^{36} -7.74498 q^{37} +6.90745 q^{38} +5.20928 q^{39} -5.29772 q^{40} -0.104052 q^{41} -6.59283 q^{42} +3.00470 q^{43} +7.00384 q^{44} -0.599850 q^{45} -1.45070 q^{46} -6.72498 q^{47} -18.3805 q^{48} -4.01789 q^{49} +12.4551 q^{50} -3.92089 q^{51} -19.2230 q^{52} -2.79875 q^{53} -15.2175 q^{54} +0.813648 q^{55} +15.0374 q^{56} +3.64396 q^{57} -21.8733 q^{58} +0.466233 q^{59} -4.52155 q^{60} +5.11468 q^{61} +1.70266 q^{63} +20.9759 q^{64} -2.23317 q^{65} +5.10586 q^{66} +8.29847 q^{67} +14.4687 q^{68} -0.765299 q^{69} +2.82629 q^{70} +4.75871 q^{71} +8.58572 q^{72} -7.50619 q^{73} +20.8352 q^{74} +6.57054 q^{75} -13.4468 q^{76} -2.30951 q^{77} -14.0138 q^{78} +9.69896 q^{79} +7.87956 q^{80} -5.06994 q^{81} +0.279916 q^{82} +16.6846 q^{83} +12.8343 q^{84} +1.68085 q^{85} -8.08312 q^{86} -11.5390 q^{87} -11.6458 q^{88} +15.3163 q^{89} +1.61369 q^{90} +6.33879 q^{91} +2.82407 q^{92} +18.0912 q^{94} -1.56213 q^{95} +24.7306 q^{96} -1.27918 q^{97} +10.8087 q^{98} -1.31863 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 3 q^{3} + 8 q^{4} + 3 q^{5} + 11 q^{6} - 2 q^{7} - 9 q^{8} + 5 q^{9} - 13 q^{10} + 18 q^{11} + 8 q^{13} - 9 q^{14} + 18 q^{15} + 4 q^{16} + 14 q^{17} + 23 q^{18} - 6 q^{19} - 7 q^{20} - q^{21}+ \cdots + 6 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 + 3 * q^3 + 8 * q^4 + 3 * q^5 + 11 * q^6 - 2 * q^7 - 9 * q^8 + 5 * q^9 - 13 * q^10 + 18 * q^11 + 8 * q^13 - 9 * q^14 + 18 * q^15 + 4 * q^16 + 14 * q^17 + 23 * q^18 - 6 * q^19 - 7 * q^20 - q^21 + 4 * q^22 + 22 * q^23 + 30 * q^24 + 13 * q^25 + 9 * q^26 + 18 * q^27 - 5 * q^28 + 12 * q^29 + 11 * q^30 - 21 * q^32 + 6 * q^33 - 7 * q^34 - 12 * q^35 - q^36 - 8 * q^37 + 7 * q^38 + q^39 + 11 * q^40 - 22 * q^41 - 6 * q^42 - 2 * q^43 + 4 * q^44 + 18 * q^46 - 18 * q^47 - q^48 - 2 * q^49 + 27 * q^50 + 2 * q^51 - q^52 + 6 * q^53 - 7 * q^54 + 28 * q^55 + 30 * q^56 - 17 * q^57 - 5 * q^58 - 4 * q^59 - 40 * q^60 + 30 * q^61 - 23 * q^63 + 9 * q^64 + 3 * q^65 + 10 * q^66 - 13 * q^67 + 30 * q^68 + 22 * q^69 - 39 * q^70 - q^71 + 3 * q^72 + 2 * q^73 + 8 * q^74 + 23 * q^75 - 33 * q^76 - 24 * q^77 + 8 * q^79 + 24 * q^80 - 28 * q^81 - 19 * q^82 + 39 * q^83 + 8 * q^84 - 26 * q^85 - 16 * q^86 - 15 * q^87 - 17 * q^88 + 27 * q^89 + 8 * q^90 + 16 * q^91 + 32 * q^92 + 22 * q^94 - 6 * q^95 - 12 * q^96 + 34 * q^97 + 10 * q^98 + 6 * q^99

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 $

$2$	−2.69016	−1.90223	−0.951114	−	0.308841i	$-0.900059\pi$
$2$	−2.69016	−1.90223	−0.951114	+	0.308841i	$0.900059\pi$
$3$	−1.41916	−0.819355	−0.409677	−	0.912230i	$-0.634359\pi$
$3$	−1.41916	−0.819355	−0.409677	+	0.912230i	$0.634359\pi$
$4$	5.23694	2.61847
$5$	0.608384	0.272077	0.136039	−	0.990704i	$-0.456563\pi$
$5$	0.608384	0.272077	0.136039	+	0.990704i	$0.456563\pi$
$6$	3.81777	1.55860
$7$	−1.72688	−0.652699	−0.326349	−	0.945249i	$-0.605819\pi$
$7$	−1.72688	−0.652699	−0.326349	+	0.945249i	$0.605819\pi$
$8$	−8.70786	−3.07869
$9$	−0.985973	−0.328658
$10$	−1.63665	−0.517553
$11$	1.33739	0.403239	0.201619	−	0.979464i	$-0.435380\pi$
$11$	1.33739	0.403239	0.201619	+	0.979464i	$0.435380\pi$
$12$	−7.43207	−2.14545
$13$	−3.67067	−1.01806	−0.509030	−	0.860749i	$-0.669996\pi$
$13$	−3.67067	−1.01806	−0.509030	+	0.860749i	$0.669996\pi$
$14$	4.64557	1.24158
$15$	−0.863396	−0.222928
$16$	12.9516	3.23791
$17$	2.76282	0.670082	0.335041	−	0.942204i	$-0.391250\pi$
$17$	2.76282	0.670082	0.335041	+	0.942204i	$0.391250\pi$
$18$	2.65242	0.625181
$19$	−2.56768	−0.589066	−0.294533	−	0.955641i	$-0.595164\pi$
$19$	−2.56768	−0.589066	−0.294533	+	0.955641i	$0.595164\pi$
$20$	3.18607	0.712426
$21$	2.45072	0.534792
$22$	−3.59779	−0.767052
$23$	0.539261	0.112444	0.0562218	−	0.998418i	$-0.482095\pi$
$23$	0.539261	0.112444	0.0562218	+	0.998418i	$0.482095\pi$
$24$	12.3579	2.52254
$25$	−4.62987	−0.925974
$26$	9.87466	1.93658
$27$	5.65675	1.08864
$28$	−9.04356	−1.70907
$29$	8.13087	1.50986	0.754932	−	0.655803i	$-0.227670\pi$
$29$	8.13087	1.50986	0.754932	+	0.655803i	$0.227670\pi$
$30$	2.32267	0.424060
$31$	0	0
$31$	0	0
$32$	−17.4262	−3.08054
$33$	−1.89798	−0.330396
$34$	−7.43241	−1.27465
$35$	−1.05061	−0.177585
$36$	−5.16348	−0.860580
$37$	−7.74498	−1.27327	−0.636633	−	0.771167i	$-0.719673\pi$
$37$	−7.74498	−1.27327	−0.636633	+	0.771167i	$0.719673\pi$
$38$	6.90745	1.12054
$39$	5.20928	0.834152
$40$	−5.29772	−0.837643
$41$	−0.104052	−0.0162502	−0.00812508	−	0.999967i	$-0.502586\pi$
$41$	−0.104052	−0.0162502	−0.00812508	+	0.999967i	$0.502586\pi$
$42$	−6.59283	−1.01730
$43$	3.00470	0.458213	0.229106	−	0.973401i	$-0.426420\pi$
$43$	3.00470	0.458213	0.229106	+	0.973401i	$0.426420\pi$
$44$	7.00384	1.05587
$45$	−0.599850	−0.0894203
$46$	−1.45070	−0.213893
$47$	−6.72498	−0.980939	−0.490470	−	0.871458i	$-0.663175\pi$
$47$	−6.72498	−0.980939	−0.490470	+	0.871458i	$0.663175\pi$
$48$	−18.3805	−2.65300
$49$	−4.01789	−0.573984
$50$	12.4551	1.76141
$51$	−3.92089	−0.549035
$52$	−19.2230	−2.66576
$53$	−2.79875	−0.384437	−0.192219	−	0.981352i	$-0.561568\pi$
$53$	−2.79875	−0.384437	−0.192219	+	0.981352i	$0.561568\pi$
$54$	−15.2175	−2.07084
$55$	0.813648	0.109712
$56$	15.0374	2.00946
$57$	3.64396	0.482654
$58$	−21.8733	−2.87210
$59$	0.466233	0.0606983	0.0303492	−	0.999539i	$-0.490338\pi$
$59$	0.466233	0.0606983	0.0303492	+	0.999539i	$0.490338\pi$
$60$	−4.52155	−0.583730
$61$	5.11468	0.654867	0.327434	−	0.944874i	$-0.393816\pi$
$61$	5.11468	0.654867	0.327434	+	0.944874i	$0.393816\pi$
$62$	0	0
$63$	1.70266	0.214514
$64$	20.9759	2.62198
$65$	−2.23317	−0.276991
$66$	5.10586	0.628488
$67$	8.29847	1.01382	0.506910	−	0.861999i	$-0.330788\pi$
$67$	8.29847	1.01382	0.506910	+	0.861999i	$0.330788\pi$
$68$	14.4687	1.75459
$69$	−0.765299	−0.0921312
$70$	2.82629	0.337806
$71$	4.75871	0.564755	0.282377	−	0.959303i	$-0.408877\pi$
$71$	4.75871	0.564755	0.282377	+	0.959303i	$0.408877\pi$
$72$	8.58572	1.01184
$73$	−7.50619	−0.878533	−0.439267	−	0.898357i	$-0.644762\pi$
$73$	−7.50619	−0.878533	−0.439267	+	0.898357i	$0.644762\pi$
$74$	20.8352	2.42204
$75$	6.57054	0.758701
$76$	−13.4468	−1.54245
$77$	−2.30951	−0.263194
$78$	−14.0138	−1.58675
$79$	9.69896	1.09122	0.545609	−	0.838040i	$-0.316298\pi$
$79$	9.69896	1.09122	0.545609	+	0.838040i	$0.316298\pi$
$80$	7.87956	0.880962
$81$	−5.06994	−0.563327
$82$	0.279916	0.0309115
$83$	16.6846	1.83137	0.915686	−	0.401895i	$-0.131648\pi$
$83$	16.6846	1.83137	0.915686	+	0.401895i	$0.131648\pi$
$84$	12.8343	1.40034
$85$	1.68085	0.182314
$86$	−8.08312	−0.871625
$87$	−11.5390	−1.23711
$88$	−11.6458	−1.24145
$89$	15.3163	1.62352	0.811761	−	0.583990i	$-0.198509\pi$
$89$	15.3163	1.62352	0.811761	+	0.583990i	$0.198509\pi$
$90$	1.61369	0.170098
$91$	6.33879	0.664486
$92$	2.82407	0.294430
$93$	0	0
$94$	18.0912	1.86597
$95$	−1.56213	−0.160271
$96$	24.7306	2.52406
$97$	−1.27918	−0.129881	−0.0649404	−	0.997889i	$-0.520686\pi$
$97$	−1.27918	−0.129881	−0.0649404	+	0.997889i	$0.520686\pi$
$98$	10.8087	1.09185
$99$	−1.31863	−0.132528
$100$	−24.2463	−2.42463
$101$	8.12024	0.807994	0.403997	−	0.914760i	$-0.367621\pi$
$101$	8.12024	0.807994	0.403997	+	0.914760i	$0.367621\pi$
$102$	10.5478	1.04439
$103$	15.1525	1.49302	0.746511	−	0.665374i	$-0.231728\pi$
$103$	15.1525	1.49302	0.746511	+	0.665374i	$0.231728\pi$
$104$	31.9636	3.13429
$105$	1.49098	0.145505
$106$	7.52906	0.731287
$107$	−12.3756	−1.19640	−0.598198	−	0.801348i	$-0.704116\pi$
$107$	−12.3756	−1.19640	−0.598198	+	0.801348i	$0.704116\pi$
$108$	29.6240	2.85057
$109$	7.20958	0.690553	0.345276	−	0.938501i	$-0.387785\pi$
$109$	7.20958	0.690553	0.345276	+	0.938501i	$0.387785\pi$
$110$	−2.18884	−0.208698
$111$	10.9914	1.04326
$112$	−22.3659	−2.11338
$113$	16.6718	1.56835	0.784176	−	0.620539i	$-0.213086\pi$
$113$	16.6718	1.56835	0.784176	+	0.620539i	$0.213086\pi$
$114$	−9.80281	−0.918117
$115$	0.328077	0.0305934
$116$	42.5808	3.95353
$117$	3.61918	0.334593
$118$	−1.25424	−0.115462
$119$	−4.77105	−0.437362
$120$	7.51834	0.686327
$121$	−9.21138	−0.837398
$122$	−13.7593	−1.24571
$123$	0.147667	0.0133147
$124$	0	0
$125$	−5.85866	−0.524014
$126$	−4.58041	−0.408055
$127$	12.9094	1.14553	0.572764	−	0.819721i	$-0.305871\pi$
$127$	12.9094	1.14553	0.572764	+	0.819721i	$0.305871\pi$
$128$	−21.5760	−1.90707
$129$	−4.26417	−0.375439
$130$	6.00758	0.526900
$131$	−2.43778	−0.212990	−0.106495	−	0.994313i	$-0.533963\pi$
$131$	−2.43778	−0.212990	−0.106495	+	0.994313i	$0.533963\pi$
$132$	−9.93960	−0.865131
$133$	4.43407	0.384482
$134$	−22.3242	−1.92851
$135$	3.44147	0.296195
$136$	−24.0583	−2.06298
$137$	−8.14382	−0.695774	−0.347887	−	0.937536i	$-0.613101\pi$
$137$	−8.14382	−0.695774	−0.347887	+	0.937536i	$0.613101\pi$
$138$	2.05877	0.175255
$139$	1.35336	0.114791	0.0573954	−	0.998352i	$-0.481720\pi$
$139$	1.35336	0.114791	0.0573954	+	0.998352i	$0.481720\pi$
$140$	−5.50195	−0.465000
$141$	9.54385	0.803737
$142$	−12.8017	−1.07429
$143$	−4.90912	−0.410521
$144$	−12.7700	−1.06416
$145$	4.94669	0.410800
$146$	20.1928	1.67117
$147$	5.70204	0.470297
$148$	−40.5600	−3.33401
$149$	−9.00385	−0.737624	−0.368812	−	0.929504i	$-0.620235\pi$
$149$	−9.00385	−0.737624	−0.368812	+	0.929504i	$0.620235\pi$
$150$	−17.6758	−1.44322
$151$	3.20841	0.261097	0.130548	−	0.991442i	$-0.458326\pi$
$151$	3.20841	0.261097	0.130548	+	0.991442i	$0.458326\pi$
$152$	22.3590	1.81355
$153$	−2.72407	−0.220228
$154$	6.21295	0.500654
$155$	0	0
$156$	27.2807	2.18420
$157$	−3.32677	−0.265505	−0.132753	−	0.991149i	$-0.542382\pi$
$157$	−3.32677	−0.265505	−0.132753	+	0.991149i	$0.542382\pi$
$158$	−26.0917	−2.07574
$159$	3.97188	0.314991
$160$	−10.6018	−0.838146
$161$	−0.931238	−0.0733918
$162$	13.6389	1.07158
$163$	1.74035	0.136314	0.0681572	−	0.997675i	$-0.478288\pi$
$163$	1.74035	0.136314	0.0681572	+	0.997675i	$0.478288\pi$
$164$	−0.544913	−0.0425506
$165$	−1.15470	−0.0898933
$166$	−44.8841	−3.48368
$167$	14.0165	1.08463	0.542314	−	0.840176i	$-0.317548\pi$
$167$	14.0165	1.08463	0.542314	+	0.840176i	$0.317548\pi$
$168$	−21.3406	−1.64646
$169$	0.473782	0.0364447
$170$	−4.52176	−0.346803
$171$	2.53166	0.193601
$172$	15.7354	1.19982
$173$	−0.0119809	−0.000910890 0	−0.000455445	−	1.00000i	$-0.500145\pi$
$173$	−0.0119809	−0.000910890 0	−0.000455445		1.00000i	$0.500145\pi$
$174$	31.0418	2.35327
$175$	7.99522	0.604382
$176$	17.3214	1.30565
$177$	−0.661661	−0.0497335
$178$	−41.2032	−3.08831
$179$	9.97800	0.745791	0.372896	−	0.927873i	$-0.378365\pi$
$179$	9.97800	0.745791	0.372896	+	0.927873i	$0.378365\pi$
$180$	−3.14138	−0.234144
$181$	18.6032	1.38276	0.691381	−	0.722490i	$-0.257003\pi$
$181$	18.6032	1.38276	0.691381	+	0.722490i	$0.257003\pi$
$182$	−17.0523	−1.26400
$183$	−7.25857	−0.536569
$184$	−4.69581	−0.346180
$185$	−4.71192	−0.346427
$186$	0	0
$187$	3.69497	0.270203
$188$	−35.2183	−2.56856
$189$	−9.76852	−0.710556
$190$	4.20238	0.304873
$191$	1.19812	0.0866928	0.0433464	−	0.999060i	$-0.486198\pi$
$191$	1.19812	0.0866928	0.0433464	+	0.999060i	$0.486198\pi$
$192$	−29.7682	−2.14834
$193$	12.7266	0.916078	0.458039	−	0.888932i	$-0.348552\pi$
$193$	12.7266	0.916078	0.458039	+	0.888932i	$0.348552\pi$
$194$	3.44118	0.247063
$195$	3.16924	0.226954
$196$	−21.0414	−1.50296
$197$	2.96860	0.211504	0.105752	−	0.994393i	$-0.466275\pi$
$197$	2.96860	0.211504	0.105752	+	0.994393i	$0.466275\pi$
$198$	3.54733	0.252098
$199$	13.1841	0.934593	0.467296	−	0.884101i	$-0.345228\pi$
$199$	13.1841	0.934593	0.467296	+	0.884101i	$0.345228\pi$
$200$	40.3163	2.85079
$201$	−11.7769	−0.830678
$202$	−21.8447	−1.53699
$203$	−14.0410	−0.985487
$204$	−20.5335	−1.43763
$205$	−0.0633035	−0.00442131
$206$	−40.7626	−2.84007
$207$	−0.531696	−0.0369555
$208$	−47.5411	−3.29638
$209$	−3.43399	−0.237534
$210$	−4.01097	−0.276783
$211$	18.3323	1.26205	0.631023	−	0.775764i	$-0.282635\pi$
$211$	18.3323	1.26205	0.631023	+	0.775764i	$0.282635\pi$
$212$	−14.6569	−1.00664
$213$	−6.75339	−0.462735
$214$	33.2923	2.27582
$215$	1.82801	0.124669
$216$	−49.2582	−3.35160
$217$	0	0
$218$	−19.3949	−1.31359
$219$	10.6525	0.719830
$220$	4.26102	0.287278
$221$	−10.1414	−0.682183
$222$	−29.5686	−1.98451
$223$	−9.39601	−0.629203	−0.314602	−	0.949224i	$-0.601871\pi$
$223$	−9.39601	−0.629203	−0.314602	+	0.949224i	$0.601871\pi$
$224$	30.0929	2.01067
$225$	4.56493	0.304328
$226$	−44.8497	−2.98336
$227$	8.45942	0.561472	0.280736	−	0.959785i	$-0.409422\pi$
$227$	8.45942	0.561472	0.280736	+	0.959785i	$0.409422\pi$
$228$	19.0832	1.26381
$229$	−22.8434	−1.50954	−0.754768	−	0.655991i	$-0.772251\pi$
$229$	−22.8434	−1.50954	−0.754768	+	0.655991i	$0.772251\pi$
$230$	−0.882579	−0.0581956
$231$	3.27758	0.215649
$232$	−70.8025	−4.64841
$233$	16.2535	1.06480	0.532400	−	0.846493i	$-0.321290\pi$
$233$	16.2535	1.06480	0.532400	+	0.846493i	$0.321290\pi$
$234$	−9.73615	−0.636472
$235$	−4.09137	−0.266891
$236$	2.44163	0.158937
$237$	−13.7644	−0.894095
$238$	12.8349	0.831962
$239$	−18.2730	−1.18198	−0.590991	−	0.806678i	$-0.701263\pi$
$239$	−18.2730	−1.18198	−0.590991	+	0.806678i	$0.701263\pi$
$240$	−11.1824	−0.721820
$241$	18.1715	1.17053	0.585266	−	0.810841i	$-0.300990\pi$
$241$	18.1715	1.17053	0.585266	+	0.810841i	$0.300990\pi$
$242$	24.7800	1.59292
$243$	−9.77517	−0.627078
$244$	26.7852	1.71475
$245$	−2.44442	−0.156168
$246$	−0.397246	−0.0253275
$247$	9.42508	0.599704
$248$	0	0
$249$	−23.6782	−1.50054
$250$	15.7607	0.996794
$251$	22.9302	1.44734	0.723671	−	0.690145i	$-0.242453\pi$
$251$	22.9302	1.44734	0.723671	+	0.690145i	$0.242453\pi$
$252$	8.91670	0.561699
$253$	0.721203	0.0453417
$254$	−34.7284	−2.17905
$255$	−2.38541	−0.149380
$256$	16.0910	1.00569
$257$	0.106193	0.00662414	0.00331207	−	0.999995i	$-0.498946\pi$
$257$	0.106193	0.00662414	0.00331207	+	0.999995i	$0.498946\pi$
$258$	11.4713	0.714170
$259$	13.3746	0.831060
$260$	−11.6950	−0.725292
$261$	−8.01681	−0.496228
$262$	6.55802	0.405156
$263$	7.29731	0.449971	0.224986	−	0.974362i	$-0.427766\pi$
$263$	7.29731	0.449971	0.224986	+	0.974362i	$0.427766\pi$
$264$	16.5273	1.01719
$265$	−1.70271	−0.104597
$266$	−11.9283	−0.731373
$267$	−21.7363	−1.33024
$268$	43.4586	2.65465
$269$	−16.2194	−0.988912	−0.494456	−	0.869203i	$-0.664633\pi$
$269$	−16.2194	−0.988912	−0.494456	+	0.869203i	$0.664633\pi$
$270$	−9.25810	−0.563430
$271$	5.14564	0.312575	0.156288	−	0.987712i	$-0.450047\pi$
$271$	5.14564	0.312575	0.156288	+	0.987712i	$0.450047\pi$
$272$	35.7830	2.16966
$273$	−8.99579	−0.544450
$274$	21.9082	1.32352
$275$	−6.19195	−0.373389
$276$	−4.00782	−0.241243
$277$	16.9228	1.01679	0.508397	−	0.861123i	$-0.330238\pi$
$277$	16.9228	1.01679	0.508397	+	0.861123i	$0.330238\pi$
$278$	−3.64076	−0.218358
$279$	0	0
$280$	9.14853	0.546729
$281$	1.90667	0.113742	0.0568711	−	0.998382i	$-0.481888\pi$
$281$	1.90667	0.113742	0.0568711	+	0.998382i	$0.481888\pi$
$282$	−25.6744	−1.52889
$283$	−15.3098	−0.910074	−0.455037	−	0.890473i	$-0.650374\pi$
$283$	−15.3098	−0.910074	−0.455037	+	0.890473i	$0.650374\pi$
$284$	24.9211	1.47879
$285$	2.21692	0.131319
$286$	13.2063	0.780905
$287$	0.179685	0.0106065
$288$	17.1817	1.01244
$289$	−9.36683	−0.550990
$290$	−13.3074	−0.781435
$291$	1.81536	0.106418
$292$	−39.3094	−2.30041
$293$	26.7937	1.56530	0.782651	−	0.622460i	$-0.213867\pi$
$293$	26.7937	1.56530	0.782651	+	0.622460i	$0.213867\pi$
$294$	−15.3394	−0.894611
$295$	0.283648	0.0165146
$296$	67.4422	3.92000
$297$	7.56529	0.438983
$298$	24.2218	1.40313
$299$	−1.97945	−0.114474
$300$	34.4095	1.98663
$301$	−5.18876	−0.299075
$302$	−8.63112	−0.496665
$303$	−11.5240	−0.662034
$304$	−33.2556	−1.90734
$305$	3.11169	0.178175
$306$	7.32816	0.418923
$307$	8.95126	0.510875	0.255438	−	0.966826i	$-0.417780\pi$
$307$	8.95126	0.510875	0.255438	+	0.966826i	$0.417780\pi$
$308$	−12.0948	−0.689164
$309$	−21.5039	−1.22331
$310$	0	0
$311$	20.6556	1.17127	0.585637	−	0.810574i	$-0.300844\pi$
$311$	20.6556	1.17127	0.585637	+	0.810574i	$0.300844\pi$
$312$	−45.3617	−2.56810
$313$	−0.451321	−0.0255102	−0.0127551	−	0.999919i	$-0.504060\pi$
$313$	−0.451321	−0.0255102	−0.0127551	+	0.999919i	$0.504060\pi$
$314$	8.94953	0.505051
$315$	1.03587	0.0583646
$316$	50.7928	2.85732
$317$	−5.58084	−0.313451	−0.156726	−	0.987642i	$-0.550094\pi$
$317$	−5.58084	−0.313451	−0.156726	+	0.987642i	$0.550094\pi$
$318$	−10.6850	−0.599184
$319$	10.8742	0.608836
$320$	12.7614	0.713383
$321$	17.5630	0.980273
$322$	2.50517	0.139608
$323$	−7.09403	−0.394722
$324$	−26.5509	−1.47505
$325$	16.9947	0.942696
$326$	−4.68180	−0.259301
$327$	−10.2316	−0.565808
$328$	0.906069	0.0500293
$329$	11.6132	0.640258
$330$	3.10632	0.170997
$331$	−24.2055	−1.33045	−0.665226	−	0.746642i	$-0.731665\pi$
$331$	−24.2055	−1.33045	−0.665226	+	0.746642i	$0.731665\pi$
$332$	87.3761	4.79539
$333$	7.63634	0.418469
$334$	−37.7065	−2.06321
$335$	5.04865	0.275837
$336$	31.7409	1.73161
$337$	−11.0360	−0.601168	−0.300584	−	0.953755i	$-0.597182\pi$
$337$	−11.0360	−0.601168	−0.300584	+	0.953755i	$0.597182\pi$
$338$	−1.27455	−0.0693262
$339$	−23.6600	−1.28504
$340$	8.80253	0.477384
$341$	0	0
$342$	−6.81056	−0.368273
$343$	19.0266	1.02734
$344$	−26.1645	−1.41070
$345$	−0.465596	−0.0250668
$346$	0.0322304	0.00173272
$347$	18.5674	0.996749	0.498375	−	0.866962i	$-0.333930\pi$
$347$	18.5674	0.996749	0.498375	+	0.866962i	$0.333930\pi$
$348$	−60.4292	−3.23935
$349$	−32.1746	−1.72227	−0.861134	−	0.508378i	$-0.830245\pi$
$349$	−32.1746	−1.72227	−0.861134	+	0.508378i	$0.830245\pi$
$350$	−21.5084	−1.14967
$351$	−20.7640	−1.10830
$352$	−23.3056	−1.24219
$353$	−32.2134	−1.71455	−0.857273	−	0.514863i	$-0.827843\pi$
$353$	−32.2134	−1.71455	−0.857273	+	0.514863i	$0.827843\pi$
$354$	1.77997	0.0946043
$355$	2.89512	0.153657
$356$	80.2104	4.25114
$357$	6.77091	0.358355
$358$	−26.8424	−1.41866
$359$	21.1623	1.11690	0.558451	−	0.829538i	$-0.311396\pi$
$359$	21.1623	1.11690	0.558451	+	0.829538i	$0.311396\pi$
$360$	5.22341	0.275298
$361$	−12.4070	−0.653002
$362$	−50.0454	−2.63033
$363$	13.0725	0.686126
$364$	33.1959	1.73994
$365$	−4.56664	−0.239029
$366$	19.5267	1.02068
$367$	−12.9964	−0.678408	−0.339204	−	0.940713i	$-0.610158\pi$
$367$	−12.9964	−0.678408	−0.339204	+	0.940713i	$0.610158\pi$
$368$	6.98431	0.364082
$369$	0.102592	0.00534074
$370$	12.6758	0.658983
$371$	4.83309	0.250922
$372$	0	0
$373$	−4.42592	−0.229166	−0.114583	−	0.993414i	$-0.536553\pi$
$373$	−4.42592	−0.229166	−0.114583	+	0.993414i	$0.536553\pi$
$374$	−9.94005	−0.513988
$375$	8.31439	0.429354
$376$	58.5602	3.02001
$377$	−29.8457	−1.53713
$378$	26.2788	1.35164
$379$	−14.9557	−0.768225	−0.384112	−	0.923286i	$-0.625492\pi$
$379$	−14.9557	−0.768225	−0.384112	+	0.923286i	$0.625492\pi$
$380$	−8.18079	−0.419666
$381$	−18.3206	−0.938593
$382$	−3.22312	−0.164909
$383$	11.6503	0.595305	0.297652	−	0.954674i	$-0.403796\pi$
$383$	11.6503	0.595305	0.297652	+	0.954674i	$0.403796\pi$
$384$	30.6199	1.56256
$385$	−1.40507	−0.0716091
$386$	−34.2364	−1.74259
$387$	−2.96256	−0.150595
$388$	−6.69897	−0.340089
$389$	−14.4019	−0.730207	−0.365103	−	0.930967i	$-0.618966\pi$
$389$	−14.4019	−0.730207	−0.365103	+	0.930967i	$0.618966\pi$
$390$	−8.52575	−0.431718
$391$	1.48988	0.0753465
$392$	34.9872	1.76712
$393$	3.45962	0.174515
$394$	−7.98598	−0.402328
$395$	5.90069	0.296896
$396$	−6.90560	−0.347019
$397$	15.7901	0.792484	0.396242	−	0.918146i	$-0.370314\pi$
$397$	15.7901	0.792484	0.396242	+	0.918146i	$0.370314\pi$
$398$	−35.4672	−1.77781
$399$	−6.29267	−0.315028
$400$	−59.9644	−2.99822
$401$	−31.0232	−1.54923	−0.774613	−	0.632436i	$-0.782055\pi$
$401$	−31.0232	−1.54923	−0.774613	+	0.632436i	$0.782055\pi$
$402$	31.6817	1.58014
$403$	0	0
$404$	42.5252	2.11571
$405$	−3.08447	−0.153268
$406$	37.7725	1.87462
$407$	−10.3581	−0.513431
$408$	34.1426	1.69031
$409$	−6.58582	−0.325648	−0.162824	−	0.986655i	$-0.552060\pi$
$409$	−6.58582	−0.325648	−0.162824	+	0.986655i	$0.552060\pi$
$410$	0.170296	0.00841033
$411$	11.5574	0.570086
$412$	79.3527	3.90943
$413$	−0.805127	−0.0396177
$414$	1.43035	0.0702977
$415$	10.1506	0.498275
$416$	63.9657	3.13618
$417$	−1.92064	−0.0940544
$418$	9.23797	0.451844
$419$	−14.6720	−0.716773	−0.358387	−	0.933573i	$-0.616673\pi$
$419$	−14.6720	−0.716773	−0.358387	+	0.933573i	$0.616673\pi$
$420$	7.80817	0.381000
$421$	−26.7159	−1.30205	−0.651026	−	0.759056i	$-0.725661\pi$
$421$	−26.7159	−1.30205	−0.651026	+	0.759056i	$0.725661\pi$
$422$	−49.3167	−2.40070
$423$	6.63065	0.322393
$424$	24.3711	1.18356
$425$	−12.7915	−0.620479
$426$	18.1677	0.880226
$427$	−8.83243	−0.427431
$428$	−64.8103	−3.13272
$429$	6.96685	0.336363
$430$	−4.91764	−0.237150
$431$	3.98801	0.192096	0.0960478	−	0.995377i	$-0.469380\pi$
$431$	3.98801	0.192096	0.0960478	+	0.995377i	$0.469380\pi$
$432$	73.2642	3.52492
$433$	−18.0766	−0.868704	−0.434352	−	0.900743i	$-0.643023\pi$
$433$	−18.0766	−0.868704	−0.434352	+	0.900743i	$0.643023\pi$
$434$	0	0
$435$	−7.02016	−0.336591
$436$	37.7561	1.80819
$437$	−1.38465	−0.0662367
$438$	−28.6569	−1.36928
$439$	22.9086	1.09337	0.546684	−	0.837339i	$-0.315890\pi$
$439$	22.9086	1.09337	0.546684	+	0.837339i	$0.315890\pi$
$440$	−7.08513	−0.337771
$441$	3.96153	0.188644
$442$	27.2819	1.29767
$443$	−21.4913	−1.02108	−0.510542	−	0.859853i	$-0.670555\pi$
$443$	−21.4913	−1.02108	−0.510542	+	0.859853i	$0.670555\pi$
$444$	57.5612	2.73174
$445$	9.31817	0.441724
$446$	25.2767	1.19689
$447$	12.7779	0.604376
$448$	−36.2228	−1.71137
$449$	−18.7996	−0.887209	−0.443604	−	0.896223i	$-0.646300\pi$
$449$	−18.7996	−0.887209	−0.443604	+	0.896223i	$0.646300\pi$
$450$	−12.2804	−0.578902
$451$	−0.139158	−0.00655270
$452$	87.3092	4.10668
$453$	−4.55326	−0.213931
$454$	−22.7572	−1.06805
$455$	3.85642	0.180792
$456$	−31.7311	−1.48594
$457$	−4.10599	−0.192070	−0.0960351	−	0.995378i	$-0.530616\pi$
$457$	−4.10599	−0.192070	−0.0960351	+	0.995378i	$0.530616\pi$
$458$	61.4524	2.87148
$459$	15.6286	0.729480
$460$	1.71812	0.0801078
$461$	22.8750	1.06540	0.532698	−	0.846305i	$-0.321178\pi$
$461$	22.8750	1.06540	0.532698	+	0.846305i	$0.321178\pi$
$462$	−8.81720	−0.410213
$463$	16.5670	0.769932	0.384966	−	0.922931i	$-0.374213\pi$
$463$	16.5670	0.769932	0.384966	+	0.922931i	$0.374213\pi$
$464$	105.308	4.88880
$465$	0	0
$466$	−43.7244	−2.02549
$467$	38.1462	1.76520	0.882599	−	0.470127i	$-0.155792\pi$
$467$	38.1462	1.76520	0.882599	+	0.470127i	$0.155792\pi$
$468$	18.9534	0.876121
$469$	−14.3305	−0.661719
$470$	11.0064	0.507688
$471$	4.72123	0.217543
$472$	−4.05989	−0.186872
$473$	4.01847	0.184769
$474$	37.0284	1.70077
$475$	11.8880	0.545459
$476$	−24.9857	−1.14522
$477$	2.75949	0.126348
$478$	49.1572	2.24840
$479$	−33.6848	−1.53910	−0.769548	−	0.638589i	$-0.779518\pi$
$479$	−33.6848	−1.53910	−0.769548	+	0.638589i	$0.779518\pi$
$480$	15.0457	0.686739
$481$	28.4292	1.29626
$482$	−48.8843	−2.22662
$483$	1.32158	0.0601340
$484$	−48.2394	−2.19270
$485$	−0.778230	−0.0353376
$486$	26.2967	1.19284
$487$	20.6767	0.936950	0.468475	−	0.883477i	$-0.344804\pi$
$487$	20.6767	0.936950	0.468475	+	0.883477i	$0.344804\pi$
$488$	−44.5379	−2.01614
$489$	−2.46984	−0.111690
$490$	6.57587	0.297067
$491$	−24.7327	−1.11617	−0.558087	−	0.829783i	$-0.688464\pi$
$491$	−24.7327	−1.11617	−0.558087	+	0.829783i	$0.688464\pi$
$492$	0.773321	0.0348640
$493$	22.4641	1.01173
$494$	−25.3549	−1.14077
$495$	−0.802235	−0.0360578
$496$	0	0
$497$	−8.21771	−0.368615
$498$	63.6980	2.85437
$499$	24.5602	1.09946	0.549732	−	0.835341i	$-0.314730\pi$
$499$	24.5602	1.09946	0.549732	+	0.835341i	$0.314730\pi$
$500$	−30.6814	−1.37211
$501$	−19.8917	−0.888695
$502$	−61.6858	−2.75317
$503$	14.7391	0.657185	0.328593	−	0.944472i	$-0.393426\pi$
$503$	14.7391	0.657185	0.328593	+	0.944472i	$0.393426\pi$
$504$	−14.8265	−0.660425
$505$	4.94022	0.219837
$506$	−1.94015	−0.0862501
$507$	−0.672374	−0.0298612
$508$	67.6059	2.99953
$509$	−15.5063	−0.687304	−0.343652	−	0.939097i	$-0.611664\pi$
$509$	−15.5063	−0.687304	−0.343652	+	0.939097i	$0.611664\pi$
$510$	6.41712	0.284155
$511$	12.9623	0.573418
$512$	−0.135395	−0.00598366
$513$	−14.5247	−0.641282
$514$	−0.285676	−0.0126006
$515$	9.21854	0.406217
$516$	−22.3312	−0.983075
$517$	−8.99394	−0.395553
$518$	−35.9799	−1.58086
$519$	0.0170028	0.000746342 0
$520$	19.4462	0.852771
$521$	29.4146	1.28867	0.644337	−	0.764741i	$-0.277133\pi$
$521$	29.4146	1.28867	0.644337	+	0.764741i	$0.277133\pi$
$522$	21.5665	0.943939
$523$	−45.0260	−1.96885	−0.984424	−	0.175810i	$-0.943746\pi$
$523$	−45.0260	−1.96885	−0.984424	+	0.175810i	$0.943746\pi$
$524$	−12.7665	−0.557708
$525$	−11.3465	−0.495203
$526$	−19.6309	−0.855947
$527$	0	0
$528$	−24.5819	−1.06979
$529$	−22.7092	−0.987356
$530$	4.58056	0.198967
$531$	−0.459693	−0.0199490
$532$	23.2209	1.00676
$533$	0.381940	0.0165436
$534$	58.4741	2.53042
$535$	−7.52912	−0.325512
$536$	−72.2619	−3.12124
$537$	−14.1604	−0.611068
$538$	43.6326	1.88114
$539$	−5.37349	−0.231453
$540$	18.0228	0.775577
$541$	37.7787	1.62423	0.812117	−	0.583495i	$-0.198315\pi$
$541$	37.7787	1.62423	0.812117	+	0.583495i	$0.198315\pi$
$542$	−13.8426	−0.594589
$543$	−26.4009	−1.13297
$544$	−48.1454	−2.06422
$545$	4.38619	0.187884
$546$	24.2001	1.03567
$547$	−18.2088	−0.778550	−0.389275	−	0.921122i	$-0.627274\pi$
$547$	−18.2088	−0.778550	−0.389275	+	0.921122i	$0.627274\pi$
$548$	−42.6487	−1.82186
$549$	−5.04293	−0.215227
$550$	16.6573	0.710270
$551$	−20.8774	−0.889409
$552$	6.66412	0.283644
$553$	−16.7489	−0.712237
$554$	−45.5250	−1.93417
$555$	6.68699	0.283847
$556$	7.08748	0.300576
$557$	9.19760	0.389715	0.194857	−	0.980832i	$-0.437576\pi$
$557$	9.19760	0.389715	0.194857	+	0.980832i	$0.437576\pi$
$558$	0	0
$559$	−11.0293	−0.466488
$560$	−13.6071	−0.575003
$561$	−5.24377	−0.221392
$562$	−5.12923	−0.216364
$563$	−36.1618	−1.52404	−0.762019	−	0.647555i	$-0.775792\pi$
$563$	−36.1618	−1.52404	−0.762019	+	0.647555i	$0.775792\pi$
$564$	49.9805	2.10456
$565$	10.1429	0.426713
$566$	41.1858	1.73117
$567$	8.75517	0.367683
$568$	−41.4382	−1.73871
$569$	−41.4998	−1.73976	−0.869880	−	0.493263i	$-0.835804\pi$
$569$	−41.4998	−1.73976	−0.869880	+	0.493263i	$0.835804\pi$
$570$	−5.96387	−0.249799
$571$	32.3931	1.35561	0.677805	−	0.735242i	$-0.262931\pi$
$571$	32.3931	1.35561	0.677805	+	0.735242i	$0.262931\pi$
$572$	−25.7087	−1.07494
$573$	−1.70033	−0.0710322
$574$	−0.483381	−0.0201759
$575$	−2.49671	−0.104120
$576$	−20.6816	−0.861735
$577$	40.9825	1.70613	0.853063	−	0.521809i	$-0.174743\pi$
$577$	40.9825	1.70613	0.853063	+	0.521809i	$0.174743\pi$
$578$	25.1982	1.04811
$579$	−18.0611	−0.750593
$580$	25.9055	1.07567
$581$	−28.8123	−1.19533
$582$	−4.88361	−0.202432
$583$	−3.74302	−0.155020
$584$	65.3629	2.70474
$585$	2.20185	0.0910352
$586$	−72.0791	−2.97756
$587$	−25.5314	−1.05379	−0.526897	−	0.849929i	$-0.676644\pi$
$587$	−25.5314	−1.05379	−0.526897	+	0.849929i	$0.676644\pi$
$588$	29.8612	1.23146
$589$	0	0
$590$	−0.763058	−0.0314146
$591$	−4.21292	−0.173297
$592$	−100.310	−4.12272
$593$	44.5318	1.82870	0.914350	−	0.404925i	$-0.132702\pi$
$593$	44.5318	1.82870	0.914350	+	0.404925i	$0.132702\pi$
$594$	−20.3518	−0.835045
$595$	−2.90263	−0.118996
$596$	−47.1526	−1.93145
$597$	−18.7103	−0.765763
$598$	5.32502	0.217756
$599$	18.9800	0.775500	0.387750	−	0.921765i	$-0.373252\pi$
$599$	18.9800	0.775500	0.387750	+	0.921765i	$0.373252\pi$
$600$	−57.2154	−2.33581
$601$	12.8398	0.523747	0.261873	−	0.965102i	$-0.415660\pi$
$601$	12.8398	0.523747	0.261873	+	0.965102i	$0.415660\pi$
$602$	13.9586	0.568909
$603$	−8.18206	−0.333199
$604$	16.8022	0.683673
$605$	−5.60405	−0.227837
$606$	31.0012	1.25934
$607$	−38.1393	−1.54803	−0.774013	−	0.633170i	$-0.781754\pi$
$607$	−38.1393	−1.54803	−0.774013	+	0.633170i	$0.781754\pi$
$608$	44.7448	1.81464
$609$	19.9265	0.807463
$610$	−8.37092	−0.338929
$611$	24.6852	0.998654
$612$	−14.2658	−0.576659
$613$	18.5424	0.748920	0.374460	−	0.927243i	$-0.377828\pi$
$613$	18.5424	0.748920	0.374460	+	0.927243i	$0.377828\pi$
$614$	−24.0803	−0.971801
$615$	0.0898380	0.00362262
$616$	20.1109	0.810293
$617$	8.13555	0.327525	0.163762	−	0.986500i	$-0.447637\pi$
$617$	8.13555	0.327525	0.163762	+	0.986500i	$0.447637\pi$
$618$	57.8488	2.32702
$619$	5.36063	0.215462	0.107731	−	0.994180i	$-0.465641\pi$
$619$	5.36063	0.215462	0.107731	+	0.994180i	$0.465641\pi$
$620$	0	0
$621$	3.05046	0.122411
$622$	−55.5669	−2.22803
$623$	−26.4494	−1.05967
$624$	67.4686	2.70091
$625$	19.5850	0.783401
$626$	1.21412	0.0485261
$627$	4.87340	0.194625
$628$	−17.4221	−0.695217
$629$	−21.3980	−0.853193
$630$	−2.78665	−0.111023
$631$	−29.0470	−1.15634	−0.578172	−	0.815915i	$-0.696234\pi$
$631$	−29.0470	−1.15634	−0.578172	+	0.815915i	$0.696234\pi$
$632$	−84.4572	−3.35953
$633$	−26.0165	−1.03406
$634$	15.0133	0.596256
$635$	7.85389	0.311672
$636$	20.8005	0.824793
$637$	14.7483	0.584350
$638$	−29.2532	−1.15814
$639$	−4.69196	−0.185611
$640$	−13.1265	−0.518870
$641$	27.6055	1.09035	0.545177	−	0.838321i	$-0.316463\pi$
$641$	27.6055	1.09035	0.545177	+	0.838321i	$0.316463\pi$
$642$	−47.2473	−1.86470
$643$	4.22904	0.166777	0.0833885	−	0.996517i	$-0.473426\pi$
$643$	4.22904	0.166777	0.0833885	+	0.996517i	$0.473426\pi$
$644$	−4.87683	−0.192174
$645$	−2.59425	−0.102148
$646$	19.0840	0.750852
$647$	26.2809	1.03321	0.516604	−	0.856225i	$-0.327196\pi$
$647$	26.2809	1.03321	0.516604	+	0.856225i	$0.327196\pi$
$648$	44.1483	1.73431
$649$	0.623536	0.0244759
$650$	−45.7184	−1.79322
$651$	0	0
$652$	9.11408	0.356935
$653$	−13.3517	−0.522494	−0.261247	−	0.965272i	$-0.584134\pi$
$653$	−13.3517	−0.522494	−0.261247	+	0.965272i	$0.584134\pi$
$654$	27.5245	1.07629
$655$	−1.48311	−0.0579498
$656$	−1.34764	−0.0526166
$657$	7.40090	0.288737
$658$	−31.2414	−1.21792
$659$	−15.4158	−0.600515	−0.300258	−	0.953858i	$-0.597073\pi$
$659$	−15.4158	−0.600515	−0.300258	+	0.953858i	$0.597073\pi$
$660$	−6.04709	−0.235383
$661$	−4.72306	−0.183706	−0.0918530	−	0.995773i	$-0.529279\pi$
$661$	−4.72306	−0.183706	−0.0918530	+	0.995773i	$0.529279\pi$
$662$	65.1164	2.53082
$663$	14.3923	0.558950
$664$	−145.287	−5.63823
$665$	2.69762	0.104609
$666$	−20.5429	−0.796023
$667$	4.38466	0.169775
$668$	73.4034	2.84006
$669$	13.3345	0.515541
$670$	−13.5817	−0.524705
$671$	6.84033	0.264068
$672$	−42.7068	−1.64745
$673$	31.0730	1.19778	0.598888	−	0.800833i	$-0.295609\pi$
$673$	31.0730	1.19778	0.598888	+	0.800833i	$0.295609\pi$
$674$	29.6885	1.14356
$675$	−26.1900	−1.00805
$676$	2.48116	0.0954294
$677$	9.03995	0.347434	0.173717	−	0.984796i	$-0.444422\pi$
$677$	9.03995	0.347434	0.173717	+	0.984796i	$0.444422\pi$
$678$	63.6491	2.44443
$679$	2.20898	0.0847730
$680$	−14.6367	−0.561290
$681$	−12.0053	−0.460044
$682$	0	0
$683$	7.13535	0.273027	0.136513	−	0.990638i	$-0.456410\pi$
$683$	7.13535	0.273027	0.136513	+	0.990638i	$0.456410\pi$
$684$	13.2581	0.506938
$685$	−4.95457	−0.189304
$686$	−51.1844	−1.95423
$687$	32.4186	1.23685
$688$	38.9158	1.48365
$689$	10.2733	0.391380
$690$	1.25252	0.0476828
$691$	36.4754	1.38759	0.693795	−	0.720172i	$-0.255937\pi$
$691$	36.4754	1.38759	0.693795	+	0.720172i	$0.255937\pi$
$692$	−0.0627431	−0.00238514
$693$	2.27712	0.0865006
$694$	−49.9491	−1.89604
$695$	0.823364	0.0312320
$696$	100.480	3.80870
$697$	−0.287476	−0.0108889
$698$	86.5547	3.27615
$699$	−23.0664	−0.872450
$700$	41.8705	1.58256
$701$	−1.61444	−0.0609766	−0.0304883	−	0.999535i	$-0.509706\pi$
$701$	−1.61444	−0.0609766	−0.0304883	+	0.999535i	$0.509706\pi$
$702$	55.8585	2.10824
$703$	19.8866	0.750037
$704$	28.0530	1.05729
$705$	5.80632	0.218679
$706$	86.6590	3.26145
$707$	−14.0227	−0.527377
$708$	−3.46507	−0.130225
$709$	−11.4880	−0.431439	−0.215720	−	0.976455i	$-0.569210\pi$
$709$	−11.4880	−0.431439	−0.215720	+	0.976455i	$0.569210\pi$
$710$	−7.78833	−0.292291
$711$	−9.56291	−0.358637
$712$	−133.372	−4.99833
$713$	0	0
$714$	−18.2148	−0.681672
$715$	−2.98663	−0.111694
$716$	52.2542	1.95283
$717$	25.9324	0.968462
$718$	−56.9298	−2.12460
$719$	14.1710	0.528489	0.264244	−	0.964456i	$-0.414877\pi$
$719$	14.1710	0.528489	0.264244	+	0.964456i	$0.414877\pi$
$720$	−7.76904	−0.289535
$721$	−26.1666	−0.974493
$722$	33.3768	1.24216
$723$	−25.7884	−0.959081
$724$	97.4236	3.62072
$725$	−37.6449	−1.39809
$726$	−35.1670	−1.30517
$727$	−26.9477	−0.999436	−0.499718	−	0.866188i	$-0.666563\pi$
$727$	−26.9477	−0.999436	−0.499718	+	0.866188i	$0.666563\pi$
$728$	−55.1974	−2.04575
$729$	29.0824	1.07713
$730$	12.2850	0.454688
$731$	8.30145	0.307040
$732$	−38.0127	−1.40499
$733$	−28.4235	−1.04985	−0.524924	−	0.851149i	$-0.675906\pi$
$733$	−28.4235	−1.04985	−0.524924	+	0.851149i	$0.675906\pi$
$734$	34.9624	1.29049
$735$	3.46903	0.127957
$736$	−9.39725	−0.346387
$737$	11.0983	0.408811
$738$	−0.275989	−0.0101593
$739$	0.697306	0.0256508	0.0128254	−	0.999918i	$-0.495917\pi$
$739$	0.697306	0.0256508	0.0128254	+	0.999918i	$0.495917\pi$
$740$	−24.6760	−0.907108
$741$	−13.3757	−0.491370
$742$	−13.0018	−0.477310
$743$	18.1815	0.667015	0.333508	−	0.942747i	$-0.391768\pi$
$743$	18.1815	0.667015	0.333508	+	0.942747i	$0.391768\pi$
$744$	0	0
$745$	−5.47779	−0.200691
$746$	11.9064	0.435925
$747$	−16.4506	−0.601894
$748$	19.3503	0.707519
$749$	21.3712	0.780886
$750$	−22.3670	−0.816728
$751$	−37.0660	−1.35256	−0.676279	−	0.736646i	$-0.736408\pi$
$751$	−37.0660	−1.35256	−0.676279	+	0.736646i	$0.736408\pi$
$752$	−87.0995	−3.17619
$753$	−32.5417	−1.18589
$754$	80.2895	2.92397
$755$	1.95194	0.0710385
$756$	−51.1571	−1.86057
$757$	−6.40201	−0.232685	−0.116342	−	0.993209i	$-0.537117\pi$
$757$	−6.40201	−0.232685	−0.116342	+	0.993209i	$0.537117\pi$
$758$	40.2333	1.46134
$759$	−1.02351	−0.0371509
$760$	13.6028	0.493427
$761$	21.3388	0.773532	0.386766	−	0.922178i	$-0.373592\pi$
$761$	21.3388	0.773532	0.386766	+	0.922178i	$0.373592\pi$
$762$	49.2853	1.78542
$763$	−12.4501	−0.450723
$764$	6.27447	0.227002
$765$	−1.65728	−0.0599190
$766$	−31.3412	−1.13241
$767$	−1.71138	−0.0617945
$768$	−22.8358	−0.824017
$769$	−12.2566	−0.441983	−0.220991	−	0.975276i	$-0.570929\pi$
$769$	−12.2566	−0.441983	−0.220991	+	0.975276i	$0.570929\pi$
$770$	3.77986	0.136217
$771$	−0.150705	−0.00542752
$772$	66.6482	2.39872
$773$	34.7035	1.24820	0.624098	−	0.781346i	$-0.285466\pi$
$773$	34.7035	1.24820	0.624098	+	0.781346i	$0.285466\pi$
$774$	7.96974	0.286466
$775$	0	0
$776$	11.1389	0.399863
$777$	−18.9808	−0.680933
$778$	38.7434	1.38902
$779$	0.267172	0.00957242
$780$	16.5971	0.594272
$781$	6.36426	0.227731
$782$	−4.00801	−0.143326
$783$	45.9943	1.64370
$784$	−52.0382	−1.85851
$785$	−2.02395	−0.0722380
$786$	−9.30691	−0.331966
$787$	20.1182	0.717136	0.358568	−	0.933504i	$-0.383265\pi$
$787$	20.1182	0.717136	0.358568	+	0.933504i	$0.383265\pi$
$788$	15.5463	0.553816
$789$	−10.3561	−0.368686
$790$	−15.8738	−0.564763
$791$	−28.7902	−1.02366
$792$	11.4825	0.408012
$793$	−18.7743	−0.666694
$794$	−42.4779	−1.50748
$795$	2.41643	0.0857018
$796$	69.0441	2.44720
$797$	−26.2019	−0.928121	−0.464060	−	0.885804i	$-0.653608\pi$
$797$	−26.2019	−0.928121	−0.464060	+	0.885804i	$0.653608\pi$
$798$	16.9283	0.599254
$799$	−18.5799	−0.657310
$800$	80.6809	2.85250
$801$	−15.1014	−0.533583
$802$	83.4573	2.94698
$803$	−10.0387	−0.354259
$804$	−61.6748	−2.17510
$805$	−0.566550	−0.0199683
$806$	0	0
$807$	23.0179	0.810270
$808$	−70.7099	−2.48757
$809$	−36.4501	−1.28152	−0.640759	−	0.767742i	$-0.721380\pi$
$809$	−36.4501	−1.28152	−0.640759	+	0.767742i	$0.721380\pi$
$810$	8.29770	0.291551
$811$	−19.1064	−0.670918	−0.335459	−	0.942055i	$-0.608891\pi$
$811$	−19.1064	−0.670918	−0.335459	+	0.942055i	$0.608891\pi$
$812$	−73.5320	−2.58047
$813$	−7.30251	−0.256110
$814$	27.8648	0.976662
$815$	1.05880	0.0370881
$816$	−50.7820	−1.77773
$817$	−7.71511	−0.269917
$818$	17.7169	0.619456
$819$	−6.24988	−0.218388
$820$	−0.331516	−0.0115770
$821$	−39.4598	−1.37716	−0.688578	−	0.725162i	$-0.741765\pi$
$821$	−39.4598	−1.37716	−0.688578	+	0.725162i	$0.741765\pi$
$822$	−31.0913	−1.08443
$823$	31.5880	1.10109	0.550544	−	0.834806i	$-0.314420\pi$
$823$	31.5880	1.10109	0.550544	+	0.834806i	$0.314420\pi$
$824$	−131.946	−4.59656
$825$	8.78740	0.305938
$826$	2.16592	0.0753619
$827$	−19.8298	−0.689551	−0.344776	−	0.938685i	$-0.612045\pi$
$827$	−19.8298	−0.689551	−0.344776	+	0.938685i	$0.612045\pi$
$828$	−2.78446	−0.0967667
$829$	−8.99987	−0.312578	−0.156289	−	0.987711i	$-0.549953\pi$
$829$	−8.99987	−0.312578	−0.156289	+	0.987711i	$0.549953\pi$
$830$	−27.3068	−0.947832
$831$	−24.0163	−0.833115
$832$	−76.9954	−2.66933
$833$	−11.1007	−0.384617
$834$	5.16683	0.178913
$835$	8.52740	0.295103
$836$	−17.9836	−0.621976
$837$	0	0
$838$	39.4699	1.36347
$839$	−31.8452	−1.09942	−0.549709	−	0.835356i	$-0.685261\pi$
$839$	−31.8452	−1.09942	−0.549709	+	0.835356i	$0.685261\pi$
$840$	−12.9833	−0.447965
$841$	37.1110	1.27969
$842$	71.8698	2.47680
$843$	−2.70587	−0.0931953
$844$	96.0050	3.30463
$845$	0.288241	0.00991579
$846$	−17.8375	−0.613265
$847$	15.9069	0.546569
$848$	−36.2483	−1.24477
$849$	21.7271	0.745673
$850$	34.4111	1.18029
$851$	−4.17656	−0.143171
$852$	−35.3671	−1.21166
$853$	−49.0917	−1.68087	−0.840434	−	0.541914i	$-0.817700\pi$
$853$	−49.0917	−1.68087	−0.840434	+	0.541914i	$0.817700\pi$
$854$	23.7606	0.813071
$855$	1.54022	0.0526744
$856$	107.765	3.68334
$857$	19.2405	0.657242	0.328621	−	0.944462i	$-0.393416\pi$
$857$	19.2405	0.657242	0.328621	+	0.944462i	$0.393416\pi$
$858$	−18.7419	−0.639838
$859$	−4.64215	−0.158388	−0.0791940	−	0.996859i	$-0.525235\pi$
$859$	−4.64215	−0.158388	−0.0791940	+	0.996859i	$0.525235\pi$
$860$	9.57319	0.326443
$861$	−0.255002	−0.00869046
$862$	−10.7284	−0.365410
$863$	38.5304	1.31159	0.655795	−	0.754939i	$-0.272333\pi$
$863$	38.5304	1.31159	0.655795	+	0.754939i	$0.272333\pi$
$864$	−98.5755	−3.35361
$865$	−0.00728897	−0.000247833 0
$866$	48.6287	1.65247
$867$	13.2931	0.451456
$868$	0	0
$869$	12.9713	0.440022
$870$	18.8853	0.640273
$871$	−30.4609	−1.03213
$872$	−62.7800	−2.12600
$873$	1.26123	0.0426863
$874$	3.72492	0.125997
$875$	10.1172	0.342023
$876$	55.7866	1.88485
$877$	−9.25834	−0.312632	−0.156316	−	0.987707i	$-0.549962\pi$
$877$	−9.25834	−0.312632	−0.156316	+	0.987707i	$0.549962\pi$
$878$	−61.6277	−2.07983
$879$	−38.0246	−1.28254
$880$	10.5381	0.355238
$881$	17.8791	0.602361	0.301181	−	0.953567i	$-0.402619\pi$
$881$	17.8791	0.602361	0.301181	+	0.953567i	$0.402619\pi$
$882$	−10.6571	−0.358844
$883$	48.3156	1.62595	0.812975	−	0.582299i	$-0.197847\pi$
$883$	48.3156	1.62595	0.812975	+	0.582299i	$0.197847\pi$
$884$	−53.1098	−1.78628
$885$	−0.402544	−0.0135314
$886$	57.8150	1.94233
$887$	23.5122	0.789463	0.394732	−	0.918797i	$-0.370838\pi$
$887$	23.5122	0.789463	0.394732	+	0.918797i	$0.370838\pi$
$888$	−95.7116	−3.21187
$889$	−22.2930	−0.747684
$890$	−25.0673	−0.840259
$891$	−6.78050	−0.227155
$892$	−49.2063	−1.64755
$893$	17.2676	0.577838
$894$	−34.3746	−1.14966
$895$	6.07046	0.202913
$896$	37.2591	1.24474
$897$	2.80916	0.0937951
$898$	50.5739	1.68767
$899$	0	0
$900$	23.9062	0.796874
$901$	−7.73243	−0.257605
$902$	0.374357	0.0124647
$903$	7.36370	0.245049
$904$	−145.176	−4.82847
$905$	11.3179	0.376219
$906$	12.2490	0.406945
$907$	−12.5821	−0.417783	−0.208892	−	0.977939i	$-0.566986\pi$
$907$	−12.5821	−0.417783	−0.208892	+	0.977939i	$0.566986\pi$
$908$	44.3015	1.47020
$909$	−8.00634	−0.265553
$910$	−10.3744	−0.343907
$911$	47.2845	1.56660	0.783302	−	0.621641i	$-0.213534\pi$
$911$	47.2845	1.56660	0.783302	+	0.621641i	$0.213534\pi$
$912$	47.1952	1.56279
$913$	22.3138	0.738480
$914$	11.0458	0.365361
$915$	−4.41599	−0.145988
$916$	−119.630	−3.95267
$917$	4.20976	0.139018
$918$	−42.0433	−1.38764
$919$	−23.1319	−0.763050	−0.381525	−	0.924359i	$-0.624601\pi$
$919$	−23.1319	−0.763050	−0.381525	+	0.924359i	$0.624601\pi$
$920$	−2.85685	−0.0941877
$921$	−12.7033	−0.418588
$922$	−61.5374	−2.02663
$923$	−17.4676	−0.574954
$924$	17.1645	0.564670
$925$	35.8582	1.17901
$926$	−44.5677	−1.46459
$927$	−14.9400	−0.490693
$928$	−141.690	−4.65120
$929$	−1.68694	−0.0553468	−0.0276734	−	0.999617i	$-0.508810\pi$
$929$	−1.68694	−0.0553468	−0.0276734	+	0.999617i	$0.508810\pi$
$930$	0	0
$931$	10.3166	0.338114
$932$	85.1184	2.78815
$933$	−29.3137	−0.959689
$934$	−102.619	−3.35781
$935$	2.24796	0.0735162
$936$	−31.5153	−1.03011
$937$	19.7267	0.644442	0.322221	−	0.946665i	$-0.395571\pi$
$937$	19.7267	0.644442	0.322221	+	0.946665i	$0.395571\pi$
$938$	38.5511	1.25874
$939$	0.640498	0.0209019
$940$	−21.4262	−0.698847
$941$	8.82326	0.287630	0.143815	−	0.989605i	$-0.454063\pi$
$941$	8.82326	0.287630	0.143815	+	0.989605i	$0.454063\pi$
$942$	−12.7009	−0.413816
$943$	−0.0561111	−0.00182723
$944$	6.03847	0.196536
$945$	−5.94301	−0.193326
$946$	−10.8103	−0.351473
$947$	−15.5612	−0.505670	−0.252835	−	0.967509i	$-0.581363\pi$
$947$	−15.5612	−0.505670	−0.252835	+	0.967509i	$0.581363\pi$
$948$	−72.0834	−2.34116
$949$	27.5527	0.894399
$950$	−31.9806	−1.03759
$951$	7.92013	0.256828
$952$	41.5457	1.34650
$953$	−9.65172	−0.312650	−0.156325	−	0.987706i	$-0.549965\pi$
$953$	−9.65172	−0.312650	−0.156325	+	0.987706i	$0.549965\pi$
$954$	−7.42345	−0.240343
$955$	0.728916	0.0235872
$956$	−95.6945	−3.09498
$957$	−15.4322	−0.498853
$958$	90.6172	2.92771
$959$	14.0634	0.454131
$960$	−18.1105	−0.584514
$961$	0	0
$962$	−76.4790	−2.46578
$963$	12.2020	0.393205
$964$	95.1632	3.06500
$965$	7.74263	0.249244
$966$	−3.55525	−0.114388
$967$	−28.3976	−0.913204	−0.456602	−	0.889671i	$-0.650934\pi$
$967$	−28.3976	−0.913204	−0.456602	+	0.889671i	$0.650934\pi$
$968$	80.2114	2.57809
$969$	10.0676	0.323418
$970$	2.09356	0.0672202
$971$	−22.1271	−0.710092	−0.355046	−	0.934849i	$-0.615535\pi$
$971$	−22.1271	−0.710092	−0.355046	+	0.934849i	$0.615535\pi$
$972$	−51.1920	−1.64198
$973$	−2.33709	−0.0749238
$974$	−55.6235	−1.78229
$975$	−24.1183	−0.772403
$976$	66.2434	2.12040
$977$	−19.9123	−0.637051	−0.318525	−	0.947914i	$-0.603188\pi$
$977$	−19.9123	−0.637051	−0.318525	+	0.947914i	$0.603188\pi$
$978$	6.64424	0.212460
$979$	20.4839	0.654667
$980$	−12.8013	−0.408921
$981$	−7.10845	−0.226955
$982$	66.5349	2.12322
$983$	24.9304	0.795156	0.397578	−	0.917568i	$-0.369851\pi$
$983$	24.9304	0.795156	0.397578	+	0.917568i	$0.369851\pi$
$984$	−1.28586	−0.0409918
$985$	1.80605	0.0575454
$986$	−60.4320	−1.92455
$987$	−16.4811	−0.524598
$988$	49.3586	1.57031
$989$	1.62032	0.0515231
$990$	2.15814	0.0685901
$991$	42.0512	1.33580	0.667900	−	0.744251i	$-0.267193\pi$
$991$	42.0512	1.33580	0.667900	+	0.744251i	$0.267193\pi$
$992$	0	0
$993$	34.3515	1.09011
$994$	22.1069	0.701189
$995$	8.02096	0.254282
$996$	−124.001	−3.92912
$997$	14.4647	0.458100	0.229050	−	0.973415i	$-0.426438\pi$
$997$	14.4647	0.458100	0.229050	+	0.973415i	$0.426438\pi$
$998$	−66.0707	−2.09143
$999$	−43.8114	−1.38613

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.a.j.1.1		8
3.2	odd	2		8649.2.a.be.1.8		8
31.2	even	5		961.2.d.n.531.1		16
31.3	odd	30		961.2.g.k.846.1		16
31.4	even	5		961.2.d.q.388.4		16
31.5	even	3		961.2.c.i.521.1		16
31.6	odd	6		961.2.c.j.439.1		16
31.7	even	15		961.2.g.m.235.2		16
31.8	even	5		961.2.d.q.374.4		16
31.9	even	15		961.2.g.m.732.2		16
31.10	even	15		961.2.g.j.844.1		16
31.11	odd	30		961.2.g.t.338.2		16
31.12	odd	30		31.2.g.a.20.1	yes	16
31.13	odd	30		31.2.g.a.14.1	✓	16
31.14	even	15		961.2.g.n.816.2		16
31.15	odd	10		961.2.d.o.628.1		16
31.16	even	5		961.2.d.n.628.1		16
31.17	odd	30		961.2.g.t.816.2		16
31.18	even	15		961.2.g.l.448.1		16
31.19	even	15		961.2.g.l.547.1		16
31.20	even	15		961.2.g.n.338.2		16
31.21	odd	30		961.2.g.k.844.1		16
31.22	odd	30		961.2.g.s.732.2		16
31.23	odd	10		961.2.d.p.374.4		16
31.24	odd	30		961.2.g.s.235.2		16
31.25	even	3		961.2.c.i.439.1		16
31.26	odd	6		961.2.c.j.521.1		16
31.27	odd	10		961.2.d.p.388.4		16
31.28	even	15		961.2.g.j.846.1		16
31.29	odd	10		961.2.d.o.531.1		16
31.30	odd	2		961.2.a.i.1.1		8
93.44	even	30		279.2.y.c.262.2		16
93.74	even	30		279.2.y.c.82.2		16
93.92	even	2		8649.2.a.bf.1.8		8
124.43	even	30		496.2.bg.c.113.1		16
124.75	even	30		496.2.bg.c.417.1		16
155.12	even	60		775.2.ck.a.299.4		32
155.13	even	60		775.2.ck.a.324.4		32
155.43	even	60		775.2.ck.a.299.1		32
155.44	odd	30		775.2.bl.a.76.2		16
155.74	odd	30		775.2.bl.a.51.2		16
155.137	even	60		775.2.ck.a.324.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.14.1	✓	16	31.13	odd	30
31.2.g.a.20.1	yes	16	31.12	odd	30
279.2.y.c.82.2		16	93.74	even	30
279.2.y.c.262.2		16	93.44	even	30
496.2.bg.c.113.1		16	124.43	even	30
496.2.bg.c.417.1		16	124.75	even	30
775.2.bl.a.51.2		16	155.74	odd	30
775.2.bl.a.76.2		16	155.44	odd	30
775.2.ck.a.299.1		32	155.43	even	60
775.2.ck.a.299.4		32	155.12	even	60
775.2.ck.a.324.1		32	155.137	even	60
775.2.ck.a.324.4		32	155.13	even	60
961.2.a.i.1.1		8	31.30	odd	2
961.2.a.j.1.1		8	1.1	even	1	trivial
961.2.c.i.439.1		16	31.25	even	3
961.2.c.i.521.1		16	31.5	even	3
961.2.c.j.439.1		16	31.6	odd	6
961.2.c.j.521.1		16	31.26	odd	6
961.2.d.n.531.1		16	31.2	even	5
961.2.d.n.628.1		16	31.16	even	5
961.2.d.o.531.1		16	31.29	odd	10
961.2.d.o.628.1		16	31.15	odd	10
961.2.d.p.374.4		16	31.23	odd	10
961.2.d.p.388.4		16	31.27	odd	10
961.2.d.q.374.4		16	31.8	even	5
961.2.d.q.388.4		16	31.4	even	5
961.2.g.j.844.1		16	31.10	even	15
961.2.g.j.846.1		16	31.28	even	15
961.2.g.k.844.1		16	31.21	odd	30
961.2.g.k.846.1		16	31.3	odd	30
961.2.g.l.448.1		16	31.18	even	15
961.2.g.l.547.1		16	31.19	even	15
961.2.g.m.235.2		16	31.7	even	15
961.2.g.m.732.2		16	31.9	even	15
961.2.g.n.338.2		16	31.20	even	15
961.2.g.n.816.2		16	31.14	even	15
961.2.g.s.235.2		16	31.24	odd	30
961.2.g.s.732.2		16	31.22	odd	30
961.2.g.t.338.2		16	31.11	odd	30
961.2.g.t.816.2		16	31.17	odd	30
8649.2.a.be.1.8		8	3.2	odd	2
8649.2.a.bf.1.8		8	93.92	even	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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69016 q^{2} -1.41916 q^{3} +5.23694 q^{4} +0.608384 q^{5} +3.81777 q^{6} -1.72688 q^{7} -8.70786 q^{8} -0.985973 q^{9} -1.63665 q^{10} +1.33739 q^{11} -7.43207 q^{12} -3.67067 q^{13} +4.64557 q^{14} -0.863396 q^{15} +12.9516 q^{16} +2.76282 q^{17} +2.65242 q^{18} -2.56768 q^{19} +3.18607 q^{20} +2.45072 q^{21} -3.59779 q^{22} +0.539261 q^{23} +12.3579 q^{24} -4.62987 q^{25} +9.87466 q^{26} +5.65675 q^{27} -9.04356 q^{28} +8.13087 q^{29} +2.32267 q^{30} -17.4262 q^{32} -1.89798 q^{33} -7.43241 q^{34} -1.05061 q^{35} -5.16348 q^{36} -7.74498 q^{37} +6.90745 q^{38} +5.20928 q^{39} -5.29772 q^{40} -0.104052 q^{41} -6.59283 q^{42} +3.00470 q^{43} +7.00384 q^{44} -0.599850 q^{45} -1.45070 q^{46} -6.72498 q^{47} -18.3805 q^{48} -4.01789 q^{49} +12.4551 q^{50} -3.92089 q^{51} -19.2230 q^{52} -2.79875 q^{53} -15.2175 q^{54} +0.813648 q^{55} +15.0374 q^{56} +3.64396 q^{57} -21.8733 q^{58} +0.466233 q^{59} -4.52155 q^{60} +5.11468 q^{61} +1.70266 q^{63} +20.9759 q^{64} -2.23317 q^{65} +5.10586 q^{66} +8.29847 q^{67} +14.4687 q^{68} -0.765299 q^{69} +2.82629 q^{70} +4.75871 q^{71} +8.58572 q^{72} -7.50619 q^{73} +20.8352 q^{74} +6.57054 q^{75} -13.4468 q^{76} -2.30951 q^{77} -14.0138 q^{78} +9.69896 q^{79} +7.87956 q^{80} -5.06994 q^{81} +0.279916 q^{82} +16.6846 q^{83} +12.8343 q^{84} +1.68085 q^{85} -8.08312 q^{86} -11.5390 q^{87} -11.6458 q^{88} +15.3163 q^{89} +1.61369 q^{90} +6.33879 q^{91} +2.82407 q^{92} +18.0912 q^{94} -1.56213 q^{95} +24.7306 q^{96} -1.27918 q^{97} +10.8087 q^{98} -1.31863 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 3 q^{3} + 8 q^{4} + 3 q^{5} + 11 q^{6} - 2 q^{7} - 9 q^{8} + 5 q^{9} - 13 q^{10} + 18 q^{11} + 8 q^{13} - 9 q^{14} + 18 q^{15} + 4 q^{16} + 14 q^{17} + 23 q^{18} - 6 q^{19} - 7 q^{20} - q^{21}+ \cdots + 6 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 3 * q^3 + 8 * q^4 + 3 * q^5 + 11 * q^6 - 2 * q^7 - 9 * q^8 + 5 * q^9 - 13 * q^10 + 18 * q^11 + 8 * q^13 - 9 * q^14 + 18 * q^15 + 4 * q^16 + 14 * q^17 + 23 * q^18 - 6 * q^19 - 7 * q^20 - q^21 + 4 * q^22 + 22 * q^23 + 30 * q^24 + 13 * q^25 + 9 * q^26 + 18 * q^27 - 5 * q^28 + 12 * q^29 + 11 * q^30 - 21 * q^32 + 6 * q^33 - 7 * q^34 - 12 * q^35 - q^36 - 8 * q^37 + 7 * q^38 + q^39 + 11 * q^40 - 22 * q^41 - 6 * q^42 - 2 * q^43 + 4 * q^44 + 18 * q^46 - 18 * q^47 - q^48 - 2 * q^49 + 27 * q^50 + 2 * q^51 - q^52 + 6 * q^53 - 7 * q^54 + 28 * q^55 + 30 * q^56 - 17 * q^57 - 5 * q^58 - 4 * q^59 - 40 * q^60 + 30 * q^61 - 23 * q^63 + 9 * q^64 + 3 * q^65 + 10 * q^66 - 13 * q^67 + 30 * q^68 + 22 * q^69 - 39 * q^70 - q^71 + 3 * q^72 + 2 * q^73 + 8 * q^74 + 23 * q^75 - 33 * q^76 - 24 * q^77 + 8 * q^79 + 24 * q^80 - 28 * q^81 - 19 * q^82 + 39 * q^83 + 8 * q^84 - 26 * q^85 - 16 * q^86 - 15 * q^87 - 17 * q^88 + 27 * q^89 + 8 * q^90 + 16 * q^91 + 32 * q^92 + 22 * q^94 - 6 * q^95 - 12 * q^96 + 34 * q^97 + 10 * q^98 + 6 * q^99

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