LMFDB - Embedded newform 2366.2.a.be.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,2,Mod(1,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, 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("2366.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2366.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:	$18.8926051182$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.6052921.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 11x^{4} + 7x^{3} + 33x^{2} - 9x - 27 $ x^6 - x^5 - 11x^4 + 7x^3 + 33x^2 - 9x - 27
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.96881$ of defining polynomial
Character	$\chi$	$=$	2366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.96881 q^{3} +1.00000 q^{4} -2.90010 q^{5} -1.96881 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.876202 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.96881 q^{3} +1.00000 q^{4} -2.90010 q^{5} -1.96881 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.876202 q^{9} +2.90010 q^{10} +2.70204 q^{11} +1.96881 q^{12} +1.00000 q^{14} -5.70975 q^{15} +1.00000 q^{16} -0.0298061 q^{17} -0.876202 q^{18} -1.70795 q^{19} -2.90010 q^{20} -1.96881 q^{21} -2.70204 q^{22} +7.87955 q^{23} -1.96881 q^{24} +3.41060 q^{25} -4.18135 q^{27} -1.00000 q^{28} -6.57207 q^{29} +5.70975 q^{30} -2.40615 q^{31} -1.00000 q^{32} +5.31980 q^{33} +0.0298061 q^{34} +2.90010 q^{35} +0.876202 q^{36} +3.81023 q^{37} +1.70795 q^{38} +2.90010 q^{40} -9.83800 q^{41} +1.96881 q^{42} -8.36362 q^{43} +2.70204 q^{44} -2.54108 q^{45} -7.87955 q^{46} -4.76407 q^{47} +1.96881 q^{48} +1.00000 q^{49} -3.41060 q^{50} -0.0586824 q^{51} +10.4371 q^{53} +4.18135 q^{54} -7.83620 q^{55} +1.00000 q^{56} -3.36262 q^{57} +6.57207 q^{58} +9.31705 q^{59} -5.70975 q^{60} -5.27261 q^{61} +2.40615 q^{62} -0.876202 q^{63} +1.00000 q^{64} -5.31980 q^{66} -11.9112 q^{67} -0.0298061 q^{68} +15.5133 q^{69} -2.90010 q^{70} +14.8176 q^{71} -0.876202 q^{72} -13.1669 q^{73} -3.81023 q^{74} +6.71482 q^{75} -1.70795 q^{76} -2.70204 q^{77} -9.28611 q^{79} -2.90010 q^{80} -10.8609 q^{81} +9.83800 q^{82} -13.4184 q^{83} -1.96881 q^{84} +0.0864407 q^{85} +8.36362 q^{86} -12.9391 q^{87} -2.70204 q^{88} -0.0106617 q^{89} +2.54108 q^{90} +7.87955 q^{92} -4.73724 q^{93} +4.76407 q^{94} +4.95322 q^{95} -1.96881 q^{96} +5.91535 q^{97} -1.00000 q^{98} +2.36753 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + q^{3} + 6 q^{4} - 4 q^{5} - q^{6} - 6 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + q^3 + 6 * q^4 - 4 * q^5 - q^6 - 6 * q^7 - 6 * q^8 + 5 * q^9	$ 6 q - 6 q^{2} + q^{3} + 6 q^{4} - 4 q^{5} - q^{6} - 6 q^{7} - 6 q^{8} + 5 q^{9} + 4 q^{10} - 6 q^{11} + q^{12} + 6 q^{14} + 5 q^{15} + 6 q^{16} - 9 q^{17} - 5 q^{18} - 10 q^{19} - 4 q^{20} - q^{21} + 6 q^{22} + 21 q^{23} - q^{24} + 8 q^{25} + 7 q^{27} - 6 q^{28} - q^{29} - 5 q^{30} - 20 q^{31} - 6 q^{32} - 9 q^{33} + 9 q^{34} + 4 q^{35} + 5 q^{36} - 16 q^{37} + 10 q^{38} + 4 q^{40} - 2 q^{41} + q^{42} + 2 q^{43} - 6 q^{44} - 17 q^{45} - 21 q^{46} + 5 q^{47} + q^{48} + 6 q^{49} - 8 q^{50} - 15 q^{51} + 28 q^{53} - 7 q^{54} - 29 q^{55} + 6 q^{56} - 22 q^{57} + q^{58} + 12 q^{59} + 5 q^{60} - 27 q^{61} + 20 q^{62} - 5 q^{63} + 6 q^{64} + 9 q^{66} - 16 q^{67} - 9 q^{68} - 15 q^{69} - 4 q^{70} - 5 q^{72} - 38 q^{73} + 16 q^{74} - 7 q^{75} - 10 q^{76} + 6 q^{77} + 6 q^{79} - 4 q^{80} - 26 q^{81} + 2 q^{82} + 6 q^{83} - q^{84} - 9 q^{85} - 2 q^{86} - 39 q^{87} + 6 q^{88} + q^{89} + 17 q^{90} + 21 q^{92} + 7 q^{93} - 5 q^{94} + 3 q^{95} - q^{96} - 16 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 + q^3 + 6 * q^4 - 4 * q^5 - q^6 - 6 * q^7 - 6 * q^8 + 5 * q^9 + 4 * q^10 - 6 * q^11 + q^12 + 6 * q^14 + 5 * q^15 + 6 * q^16 - 9 * q^17 - 5 * q^18 - 10 * q^19 - 4 * q^20 - q^21 + 6 * q^22 + 21 * q^23 - q^24 + 8 * q^25 + 7 * q^27 - 6 * q^28 - q^29 - 5 * q^30 - 20 * q^31 - 6 * q^32 - 9 * q^33 + 9 * q^34 + 4 * q^35 + 5 * q^36 - 16 * q^37 + 10 * q^38 + 4 * q^40 - 2 * q^41 + q^42 + 2 * q^43 - 6 * q^44 - 17 * q^45 - 21 * q^46 + 5 * q^47 + q^48 + 6 * q^49 - 8 * q^50 - 15 * q^51 + 28 * q^53 - 7 * q^54 - 29 * q^55 + 6 * q^56 - 22 * q^57 + q^58 + 12 * q^59 + 5 * q^60 - 27 * q^61 + 20 * q^62 - 5 * q^63 + 6 * q^64 + 9 * q^66 - 16 * q^67 - 9 * q^68 - 15 * q^69 - 4 * q^70 - 5 * q^72 - 38 * q^73 + 16 * q^74 - 7 * q^75 - 10 * q^76 + 6 * q^77 + 6 * q^79 - 4 * q^80 - 26 * q^81 + 2 * q^82 + 6 * q^83 - q^84 - 9 * q^85 - 2 * q^86 - 39 * q^87 + 6 * q^88 + q^89 + 17 * q^90 + 21 * q^92 + 7 * q^93 - 5 * q^94 + 3 * q^95 - q^96 - 16 * q^97 - 6 * q^98 + 4 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.96881	1.13669	0.568346	−	0.822790i	$-0.307584\pi$
$3$	1.96881	1.13669	0.568346	+	0.822790i	$0.307584\pi$
$4$	1.00000	0.500000
$5$	−2.90010	−1.29697	−0.648483	−	0.761229i	$-0.724596\pi$
$5$	−2.90010	−1.29697	−0.648483	+	0.761229i	$0.724596\pi$
$6$	−1.96881	−0.803762
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	0.876202	0.292067
$10$	2.90010	0.917093
$11$	2.70204	0.814696	0.407348	−	0.913273i	$-0.366454\pi$
$11$	2.70204	0.814696	0.407348	+	0.913273i	$0.366454\pi$
$12$	1.96881	0.568346
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	−5.70975	−1.47425
$16$	1.00000	0.250000
$17$	−0.0298061	−0.00722904	−0.00361452	−	0.999993i	$-0.501151\pi$
$17$	−0.0298061	−0.00722904	−0.00361452	+	0.999993i	$0.501151\pi$
$18$	−0.876202	−0.206523
$19$	−1.70795	−0.391830	−0.195915	−	0.980621i	$-0.562768\pi$
$19$	−1.70795	−0.391830	−0.195915	+	0.980621i	$0.562768\pi$
$20$	−2.90010	−0.648483
$21$	−1.96881	−0.429629
$22$	−2.70204	−0.576077
$23$	7.87955	1.64300	0.821500	−	0.570209i	$-0.193138\pi$
$23$	7.87955	1.64300	0.821500	+	0.570209i	$0.193138\pi$
$24$	−1.96881	−0.401881
$25$	3.41060	0.682121
$26$	0	0
$27$	−4.18135	−0.804701
$28$	−1.00000	−0.188982
$29$	−6.57207	−1.22040	−0.610201	−	0.792247i	$-0.708911\pi$
$29$	−6.57207	−1.22040	−0.610201	+	0.792247i	$0.708911\pi$
$30$	5.70975	1.04245
$31$	−2.40615	−0.432156	−0.216078	−	0.976376i	$-0.569327\pi$
$31$	−2.40615	−0.432156	−0.216078	+	0.976376i	$0.569327\pi$
$32$	−1.00000	−0.176777
$33$	5.31980	0.926058
$34$	0.0298061	0.00511170
$35$	2.90010	0.490207
$36$	0.876202	0.146034
$37$	3.81023	0.626398	0.313199	−	0.949688i	$-0.398599\pi$
$37$	3.81023	0.626398	0.313199	+	0.949688i	$0.398599\pi$
$38$	1.70795	0.277065
$39$	0	0
$40$	2.90010	0.458547
$41$	−9.83800	−1.53644	−0.768219	−	0.640187i	$-0.778857\pi$
$41$	−9.83800	−1.53644	−0.768219	+	0.640187i	$0.778857\pi$
$42$	1.96881	0.303794
$43$	−8.36362	−1.27544	−0.637720	−	0.770268i	$-0.720122\pi$
$43$	−8.36362	−1.27544	−0.637720	+	0.770268i	$0.720122\pi$
$44$	2.70204	0.407348
$45$	−2.54108	−0.378801
$46$	−7.87955	−1.16178
$47$	−4.76407	−0.694911	−0.347456	−	0.937696i	$-0.612954\pi$
$47$	−4.76407	−0.694911	−0.347456	+	0.937696i	$0.612954\pi$
$48$	1.96881	0.284173
$49$	1.00000	0.142857
$50$	−3.41060	−0.482332
$51$	−0.0586824	−0.00821718
$52$	0	0
$53$	10.4371	1.43365	0.716825	−	0.697253i	$-0.245594\pi$
$53$	10.4371	1.43365	0.716825	+	0.697253i	$0.245594\pi$
$54$	4.18135	0.569010
$55$	−7.83620	−1.05663
$56$	1.00000	0.133631
$57$	−3.36262	−0.445389
$58$	6.57207	0.862954
$59$	9.31705	1.21298	0.606488	−	0.795092i	$-0.292578\pi$
$59$	9.31705	1.21298	0.606488	+	0.795092i	$0.292578\pi$
$60$	−5.70975	−0.737125
$61$	−5.27261	−0.675089	−0.337544	−	0.941310i	$-0.609596\pi$
$61$	−5.27261	−0.675089	−0.337544	+	0.941310i	$0.609596\pi$
$62$	2.40615	0.305581
$63$	−0.876202	−0.110391
$64$	1.00000	0.125000
$65$	0	0
$66$	−5.31980	−0.654822
$67$	−11.9112	−1.45518	−0.727591	−	0.686011i	$-0.759360\pi$
$67$	−11.9112	−1.45518	−0.727591	+	0.686011i	$0.759360\pi$
$68$	−0.0298061	−0.00361452
$69$	15.5133	1.86758
$70$	−2.90010	−0.346629
$71$	14.8176	1.75852	0.879261	−	0.476340i	$-0.158037\pi$
$71$	14.8176	1.75852	0.879261	+	0.476340i	$0.158037\pi$
$72$	−0.876202	−0.103261
$73$	−13.1669	−1.54106	−0.770532	−	0.637402i	$-0.780009\pi$
$73$	−13.1669	−1.54106	−0.770532	+	0.637402i	$0.780009\pi$
$74$	−3.81023	−0.442930
$75$	6.71482	0.775361
$76$	−1.70795	−0.195915
$77$	−2.70204	−0.307926
$78$	0	0
$79$	−9.28611	−1.04477	−0.522384	−	0.852710i	$-0.674957\pi$
$79$	−9.28611	−1.04477	−0.522384	+	0.852710i	$0.674957\pi$
$80$	−2.90010	−0.324242
$81$	−10.8609	−1.20676
$82$	9.83800	1.08643
$83$	−13.4184	−1.47286	−0.736429	−	0.676515i	$-0.763490\pi$
$83$	−13.4184	−1.47286	−0.736429	+	0.676515i	$0.763490\pi$
$84$	−1.96881	−0.214814
$85$	0.0864407	0.00937581
$86$	8.36362	0.901872
$87$	−12.9391	−1.38722
$88$	−2.70204	−0.288039
$89$	−0.0106617	−0.00113014	−0.000565068	−	1.00000i	$-0.500180\pi$
$89$	−0.0106617	−0.00113014	−0.000565068		1.00000i	$0.500180\pi$
$90$	2.54108	0.267853
$91$	0	0
$92$	7.87955	0.821500
$93$	−4.73724	−0.491228
$94$	4.76407	0.491376
$95$	4.95322	0.508190
$96$	−1.96881	−0.200941
$97$	5.91535	0.600613	0.300307	−	0.953843i	$-0.402911\pi$
$97$	5.91535	0.600613	0.300307	+	0.953843i	$0.402911\pi$
$98$	−1.00000	−0.101015
$99$	2.36753	0.237946
$100$	3.41060	0.341060
$101$	−16.0682	−1.59885	−0.799425	−	0.600766i	$-0.794862\pi$
$101$	−16.0682	−1.59885	−0.799425	+	0.600766i	$0.794862\pi$
$102$	0.0586824	0.00581043
$103$	−13.0405	−1.28492	−0.642459	−	0.766320i	$-0.722086\pi$
$103$	−13.0405	−1.28492	−0.642459	+	0.766320i	$0.722086\pi$
$104$	0	0
$105$	5.70975	0.557214
$106$	−10.4371	−1.01374
$107$	−14.4061	−1.39269	−0.696343	−	0.717709i	$-0.745191\pi$
$107$	−14.4061	−1.39269	−0.696343	+	0.717709i	$0.745191\pi$
$108$	−4.18135	−0.402351
$109$	5.08453	0.487009	0.243505	−	0.969900i	$-0.421703\pi$
$109$	5.08453	0.487009	0.243505	+	0.969900i	$0.421703\pi$
$110$	7.83620	0.747153
$111$	7.50161	0.712021
$112$	−1.00000	−0.0944911
$113$	−19.3761	−1.82275	−0.911376	−	0.411575i	$-0.864979\pi$
$113$	−19.3761	−1.82275	−0.911376	+	0.411575i	$0.864979\pi$
$114$	3.36262	0.314938
$115$	−22.8515	−2.13091
$116$	−6.57207	−0.610201
$117$	0	0
$118$	−9.31705	−0.857704
$119$	0.0298061	0.00273232
$120$	5.70975	0.521226
$121$	−3.69897	−0.336270
$122$	5.27261	0.477360
$123$	−19.3691	−1.74646
$124$	−2.40615	−0.216078
$125$	4.60941	0.412278
$126$	0.876202	0.0780582
$127$	−5.30416	−0.470668	−0.235334	−	0.971915i	$-0.575618\pi$
$127$	−5.30416	−0.470668	−0.235334	+	0.971915i	$0.575618\pi$
$128$	−1.00000	−0.0883883
$129$	−16.4663	−1.44978
$130$	0	0
$131$	−2.72894	−0.238428	−0.119214	−	0.992869i	$-0.538038\pi$
$131$	−2.72894	−0.238428	−0.119214	+	0.992869i	$0.538038\pi$
$132$	5.31980	0.463029
$133$	1.70795	0.148098
$134$	11.9112	1.02897
$135$	12.1263	1.04367
$136$	0.0298061	0.00255585
$137$	18.6021	1.58928	0.794640	−	0.607080i	$-0.207659\pi$
$137$	18.6021	1.58928	0.794640	+	0.607080i	$0.207659\pi$
$138$	−15.5133	−1.32058
$139$	13.9773	1.18554	0.592771	−	0.805371i	$-0.298034\pi$
$139$	13.9773	1.18554	0.592771	+	0.805371i	$0.298034\pi$
$140$	2.90010	0.245104
$141$	−9.37954	−0.789900
$142$	−14.8176	−1.24346
$143$	0	0
$144$	0.876202	0.0730168
$145$	19.0597	1.58282
$146$	13.1669	1.08970
$147$	1.96881	0.162384
$148$	3.81023	0.313199
$149$	0.159237	0.0130452	0.00652259	−	0.999979i	$-0.497924\pi$
$149$	0.159237	0.0130452	0.00652259	+	0.999979i	$0.497924\pi$
$150$	−6.71482	−0.548263
$151$	−9.81702	−0.798898	−0.399449	−	0.916755i	$-0.630799\pi$
$151$	−9.81702	−0.798898	−0.399449	+	0.916755i	$0.630799\pi$
$152$	1.70795	0.138533
$153$	−0.0261161	−0.00211136
$154$	2.70204	0.217737
$155$	6.97807	0.560492
$156$	0	0
$157$	4.94712	0.394823	0.197412	−	0.980321i	$-0.436746\pi$
$157$	4.94712	0.394823	0.197412	+	0.980321i	$0.436746\pi$
$158$	9.28611	0.738763
$159$	20.5487	1.62962
$160$	2.90010	0.229273
$161$	−7.87955	−0.620995
$162$	10.8609	0.853311
$163$	−2.82200	−0.221036	−0.110518	−	0.993874i	$-0.535251\pi$
$163$	−2.82200	−0.221036	−0.110518	+	0.993874i	$0.535251\pi$
$164$	−9.83800	−0.768219
$165$	−15.4280	−1.20107
$166$	13.4184	1.04147
$167$	−2.22107	−0.171872	−0.0859359	−	0.996301i	$-0.527388\pi$
$167$	−2.22107	−0.171872	−0.0859359	+	0.996301i	$0.527388\pi$
$168$	1.96881	0.151897
$169$	0	0
$170$	−0.0864407	−0.00662970
$171$	−1.49650	−0.114441
$172$	−8.36362	−0.637720
$173$	21.2060	1.61226	0.806130	−	0.591738i	$-0.201558\pi$
$173$	21.2060	1.61226	0.806130	+	0.591738i	$0.201558\pi$
$174$	12.9391	0.980913
$175$	−3.41060	−0.257817
$176$	2.70204	0.203674
$177$	18.3435	1.37878
$178$	0.0106617	0.000799126 0
$179$	2.42346	0.181138	0.0905688	−	0.995890i	$-0.471131\pi$
$179$	2.42346	0.181138	0.0905688	+	0.995890i	$0.471131\pi$
$180$	−2.54108	−0.189401
$181$	−1.17008	−0.0869712	−0.0434856	−	0.999054i	$-0.513846\pi$
$181$	−1.17008	−0.0869712	−0.0434856	+	0.999054i	$0.513846\pi$
$182$	0	0
$183$	−10.3808	−0.767368
$184$	−7.87955	−0.580888
$185$	−11.0501	−0.812417
$186$	4.73724	0.347351
$187$	−0.0805373	−0.00588947
$188$	−4.76407	−0.347456
$189$	4.18135	0.304148
$190$	−4.95322	−0.359344
$191$	17.2963	1.25151	0.625757	−	0.780018i	$-0.284790\pi$
$191$	17.2963	1.25151	0.625757	+	0.780018i	$0.284790\pi$
$192$	1.96881	0.142086
$193$	4.45829	0.320915	0.160457	−	0.987043i	$-0.448703\pi$
$193$	4.45829	0.320915	0.160457	+	0.987043i	$0.448703\pi$
$194$	−5.91535	−0.424698
$195$	0	0
$196$	1.00000	0.0714286
$197$	−7.12787	−0.507840	−0.253920	−	0.967225i	$-0.581720\pi$
$197$	−7.12787	−0.507840	−0.253920	+	0.967225i	$0.581720\pi$
$198$	−2.36753	−0.168253
$199$	−26.5203	−1.87997	−0.939986	−	0.341213i	$-0.889162\pi$
$199$	−26.5203	−1.87997	−0.939986	+	0.341213i	$0.889162\pi$
$200$	−3.41060	−0.241166
$201$	−23.4508	−1.65409
$202$	16.0682	1.13056
$203$	6.57207	0.461269
$204$	−0.0586824	−0.00410859
$205$	28.5312	1.99271
$206$	13.0405	0.908574
$207$	6.90407	0.479866
$208$	0	0
$209$	−4.61494	−0.319222
$210$	−5.70975	−0.394010
$211$	10.2856	0.708092	0.354046	−	0.935228i	$-0.384806\pi$
$211$	10.2856	0.708092	0.354046	+	0.935228i	$0.384806\pi$
$212$	10.4371	0.716825
$213$	29.1730	1.99890
$214$	14.4061	0.984778
$215$	24.2554	1.65420
$216$	4.18135	0.284505
$217$	2.40615	0.163340
$218$	−5.08453	−0.344368
$219$	−25.9230	−1.75171
$220$	−7.83620	−0.528317
$221$	0	0
$222$	−7.50161	−0.503475
$223$	−5.49090	−0.367698	−0.183849	−	0.982955i	$-0.558856\pi$
$223$	−5.49090	−0.367698	−0.183849	+	0.982955i	$0.558856\pi$
$224$	1.00000	0.0668153
$225$	2.98838	0.199225
$226$	19.3761	1.28888
$227$	−24.8093	−1.64665	−0.823326	−	0.567568i	$-0.807884\pi$
$227$	−24.8093	−1.64665	−0.823326	+	0.567568i	$0.807884\pi$
$228$	−3.36262	−0.222695
$229$	17.6756	1.16803	0.584017	−	0.811741i	$-0.301480\pi$
$229$	17.6756	1.16803	0.584017	+	0.811741i	$0.301480\pi$
$230$	22.8515	1.50678
$231$	−5.31980	−0.350017
$232$	6.57207	0.431477
$233$	2.42722	0.159013	0.0795063	−	0.996834i	$-0.474666\pi$
$233$	2.42722	0.159013	0.0795063	+	0.996834i	$0.474666\pi$
$234$	0	0
$235$	13.8163	0.901276
$236$	9.31705	0.606488
$237$	−18.2826	−1.18758
$238$	−0.0298061	−0.00193204
$239$	11.8577	0.767013	0.383507	−	0.923538i	$-0.374716\pi$
$239$	11.8577	0.767013	0.383507	+	0.923538i	$0.374716\pi$
$240$	−5.70975	−0.368563
$241$	−25.9502	−1.67160	−0.835800	−	0.549035i	$-0.814995\pi$
$241$	−25.9502	−1.67160	−0.835800	+	0.549035i	$0.814995\pi$
$242$	3.69897	0.237779
$243$	−8.83892	−0.567017
$244$	−5.27261	−0.337544
$245$	−2.90010	−0.185281
$246$	19.3691	1.23493
$247$	0	0
$248$	2.40615	0.152790
$249$	−26.4182	−1.67419
$250$	−4.60941	−0.291525
$251$	−2.65757	−0.167745	−0.0838723	−	0.996477i	$-0.526729\pi$
$251$	−2.65757	−0.167745	−0.0838723	+	0.996477i	$0.526729\pi$
$252$	−0.876202	−0.0551955
$253$	21.2909	1.33855
$254$	5.30416	0.332813
$255$	0.170185	0.0106574
$256$	1.00000	0.0625000
$257$	9.30522	0.580444	0.290222	−	0.956959i	$-0.406271\pi$
$257$	9.30522	0.580444	0.290222	+	0.956959i	$0.406271\pi$
$258$	16.4663	1.02515
$259$	−3.81023	−0.236756
$260$	0	0
$261$	−5.75845	−0.356439
$262$	2.72894	0.168594
$263$	27.1636	1.67498	0.837489	−	0.546454i	$-0.184023\pi$
$263$	27.1636	1.67498	0.837489	+	0.546454i	$0.184023\pi$
$264$	−5.31980	−0.327411
$265$	−30.2688	−1.85940
$266$	−1.70795	−0.104721
$267$	−0.0209908	−0.00128461
$268$	−11.9112	−0.727591
$269$	19.4389	1.18521	0.592604	−	0.805494i	$-0.298100\pi$
$269$	19.4389	1.18521	0.592604	+	0.805494i	$0.298100\pi$
$270$	−12.1263	−0.737986
$271$	0.327549	0.0198972	0.00994858	−	0.999951i	$-0.496833\pi$
$271$	0.327549	0.0198972	0.00994858	+	0.999951i	$0.496833\pi$
$272$	−0.0298061	−0.00180726
$273$	0	0
$274$	−18.6021	−1.12379
$275$	9.21560	0.555721
$276$	15.5133	0.933792
$277$	−8.08634	−0.485861	−0.242930	−	0.970044i	$-0.578109\pi$
$277$	−8.08634	−0.485861	−0.242930	+	0.970044i	$0.578109\pi$
$278$	−13.9773	−0.838305
$279$	−2.10827	−0.126219
$280$	−2.90010	−0.173314
$281$	1.17570	0.0701366	0.0350683	−	0.999385i	$-0.488835\pi$
$281$	1.17570	0.0701366	0.0350683	+	0.999385i	$0.488835\pi$
$282$	9.37954	0.558543
$283$	6.25986	0.372110	0.186055	−	0.982539i	$-0.440430\pi$
$283$	6.25986	0.372110	0.186055	+	0.982539i	$0.440430\pi$
$284$	14.8176	0.879261
$285$	9.75193	0.577655
$286$	0	0
$287$	9.83800	0.580719
$288$	−0.876202	−0.0516307
$289$	−16.9991	−0.999948
$290$	−19.0597	−1.11922
$291$	11.6462	0.682712
$292$	−13.1669	−0.770532
$293$	19.0166	1.11096	0.555482	−	0.831529i	$-0.312534\pi$
$293$	19.0166	1.11096	0.555482	+	0.831529i	$0.312534\pi$
$294$	−1.96881	−0.114823
$295$	−27.0204	−1.57319
$296$	−3.81023	−0.221465
$297$	−11.2982	−0.655587
$298$	−0.159237	−0.00922433
$299$	0	0
$300$	6.71482	0.387680
$301$	8.36362	0.482071
$302$	9.81702	0.564906
$303$	−31.6353	−1.81740
$304$	−1.70795	−0.0979574
$305$	15.2911	0.875567
$306$	0.0261161	0.00149296
$307$	−7.99210	−0.456133	−0.228067	−	0.973646i	$-0.573240\pi$
$307$	−7.99210	−0.456133	−0.228067	+	0.973646i	$0.573240\pi$
$308$	−2.70204	−0.153963
$309$	−25.6742	−1.46056
$310$	−6.97807	−0.396328
$311$	−31.9778	−1.81329	−0.906647	−	0.421891i	$-0.861367\pi$
$311$	−31.9778	−1.81329	−0.906647	+	0.421891i	$0.861367\pi$
$312$	0	0
$313$	−7.64078	−0.431882	−0.215941	−	0.976406i	$-0.569282\pi$
$313$	−7.64078	−0.431882	−0.215941	+	0.976406i	$0.569282\pi$
$314$	−4.94712	−0.279182
$315$	2.54108	0.143173
$316$	−9.28611	−0.522384
$317$	−7.99006	−0.448766	−0.224383	−	0.974501i	$-0.572037\pi$
$317$	−7.99006	−0.448766	−0.224383	+	0.974501i	$0.572037\pi$
$318$	−20.5487	−1.15231
$319$	−17.7580	−0.994257
$320$	−2.90010	−0.162121
$321$	−28.3627	−1.58305
$322$	7.87955	0.439110
$323$	0.0509072	0.00283255
$324$	−10.8609	−0.603382
$325$	0	0
$326$	2.82200	0.156296
$327$	10.0105	0.553579
$328$	9.83800	0.543213
$329$	4.76407	0.262652
$330$	15.4280	0.849282
$331$	−28.6843	−1.57663	−0.788317	−	0.615270i	$-0.789047\pi$
$331$	−28.6843	−1.57663	−0.788317	+	0.615270i	$0.789047\pi$
$332$	−13.4184	−0.736429
$333$	3.33853	0.182950
$334$	2.22107	0.121532
$335$	34.5437	1.88732
$336$	−1.96881	−0.107407
$337$	24.8904	1.35587	0.677934	−	0.735123i	$-0.262876\pi$
$337$	24.8904	1.35587	0.677934	+	0.735123i	$0.262876\pi$
$338$	0	0
$339$	−38.1478	−2.07191
$340$	0.0864407	0.00468791
$341$	−6.50150	−0.352076
$342$	1.49650	0.0809217
$343$	−1.00000	−0.0539949
$344$	8.36362	0.450936
$345$	−44.9902	−2.42219
$346$	−21.2060	−1.14004
$347$	6.92508	0.371758	0.185879	−	0.982573i	$-0.440487\pi$
$347$	6.92508	0.371758	0.185879	+	0.982573i	$0.440487\pi$
$348$	−12.9391	−0.693610
$349$	3.63622	0.194642	0.0973211	−	0.995253i	$-0.468973\pi$
$349$	3.63622	0.194642	0.0973211	+	0.995253i	$0.468973\pi$
$350$	3.41060	0.182304
$351$	0	0
$352$	−2.70204	−0.144019
$353$	15.4309	0.821305	0.410653	−	0.911792i	$-0.365301\pi$
$353$	15.4309	0.821305	0.410653	+	0.911792i	$0.365301\pi$
$354$	−18.3435	−0.974945
$355$	−42.9725	−2.28074
$356$	−0.0106617	−0.000565068 0
$357$	0.0586824	0.00310580
$358$	−2.42346	−0.128084
$359$	−1.58732	−0.0837754	−0.0418877	−	0.999122i	$-0.513337\pi$
$359$	−1.58732	−0.0837754	−0.0418877	+	0.999122i	$0.513337\pi$
$360$	2.54108	0.133926
$361$	−16.0829	−0.846470
$362$	1.17008	0.0614979
$363$	−7.28256	−0.382235
$364$	0	0
$365$	38.1852	1.99871
$366$	10.3808	0.542611
$367$	−2.97145	−0.155109	−0.0775543	−	0.996988i	$-0.524711\pi$
$367$	−2.97145	−0.155109	−0.0775543	+	0.996988i	$0.524711\pi$
$368$	7.87955	0.410750
$369$	−8.62007	−0.448743
$370$	11.0501	0.574465
$371$	−10.4371	−0.541869
$372$	−4.73724	−0.245614
$373$	17.6510	0.913932	0.456966	−	0.889484i	$-0.348936\pi$
$373$	17.6510	0.913932	0.456966	+	0.889484i	$0.348936\pi$
$374$	0.0805373	0.00416448
$375$	9.07504	0.468633
$376$	4.76407	0.245688
$377$	0	0
$378$	−4.18135	−0.215065
$379$	9.90111	0.508586	0.254293	−	0.967127i	$-0.418157\pi$
$379$	9.90111	0.508586	0.254293	+	0.967127i	$0.418157\pi$
$380$	4.95322	0.254095
$381$	−10.4429	−0.535005
$382$	−17.2963	−0.884954
$383$	−6.30154	−0.321994	−0.160997	−	0.986955i	$-0.551471\pi$
$383$	−6.30154	−0.321994	−0.160997	+	0.986955i	$0.551471\pi$
$384$	−1.96881	−0.100470
$385$	7.83620	0.399370
$386$	−4.45829	−0.226921
$387$	−7.32821	−0.372514
$388$	5.91535	0.300307
$389$	−3.71450	−0.188333	−0.0941664	−	0.995556i	$-0.530019\pi$
$389$	−3.71450	−0.188333	−0.0941664	+	0.995556i	$0.530019\pi$
$390$	0	0
$391$	−0.234858	−0.0118773
$392$	−1.00000	−0.0505076
$393$	−5.37275	−0.271020
$394$	7.12787	0.359097
$395$	26.9307	1.35503
$396$	2.36753	0.118973
$397$	13.6290	0.684019	0.342010	−	0.939696i	$-0.388892\pi$
$397$	13.6290	0.684019	0.342010	+	0.939696i	$0.388892\pi$
$398$	26.5203	1.32934
$399$	3.36262	0.168341
$400$	3.41060	0.170530
$401$	27.5298	1.37477	0.687387	−	0.726291i	$-0.258758\pi$
$401$	27.5298	1.37477	0.687387	+	0.726291i	$0.258758\pi$
$402$	23.4508	1.16962
$403$	0	0
$404$	−16.0682	−0.799425
$405$	31.4977	1.56513
$406$	−6.57207	−0.326166
$407$	10.2954	0.510324
$408$	0.0586824	0.00290521
$409$	29.8834	1.47764	0.738818	−	0.673905i	$-0.235384\pi$
$409$	29.8834	1.47764	0.738818	+	0.673905i	$0.235384\pi$
$410$	−28.5312	−1.40906
$411$	36.6239	1.80652
$412$	−13.0405	−0.642459
$413$	−9.31705	−0.458462
$414$	−6.90407	−0.339317
$415$	38.9147	1.91025
$416$	0	0
$417$	27.5187	1.34760
$418$	4.61494	0.225724
$419$	−13.0400	−0.637044	−0.318522	−	0.947916i	$-0.603186\pi$
$419$	−13.0400	−0.637044	−0.318522	+	0.947916i	$0.603186\pi$
$420$	5.70975	0.278607
$421$	−34.2491	−1.66920	−0.834599	−	0.550859i	$-0.814300\pi$
$421$	−34.2491	−1.66920	−0.834599	+	0.550859i	$0.814300\pi$
$422$	−10.2856	−0.500697
$423$	−4.17429	−0.202961
$424$	−10.4371	−0.506872
$425$	−0.101657	−0.00493108
$426$	−29.1730	−1.41343
$427$	5.27261	0.255160
$428$	−14.4061	−0.696343
$429$	0	0
$430$	−24.2554	−1.16970
$431$	−8.96721	−0.431935	−0.215968	−	0.976400i	$-0.569291\pi$
$431$	−8.96721	−0.431935	−0.215968	+	0.976400i	$0.569291\pi$
$432$	−4.18135	−0.201175
$433$	−10.3823	−0.498942	−0.249471	−	0.968382i	$-0.580257\pi$
$433$	−10.3823	−0.498942	−0.249471	+	0.968382i	$0.580257\pi$
$434$	−2.40615	−0.115499
$435$	37.5248	1.79918
$436$	5.08453	0.243505
$437$	−13.4578	−0.643776
$438$	25.9230	1.23865
$439$	11.3125	0.539917	0.269959	−	0.962872i	$-0.412990\pi$
$439$	11.3125	0.539917	0.269959	+	0.962872i	$0.412990\pi$
$440$	7.83620	0.373576
$441$	0.876202	0.0417239
$442$	0	0
$443$	14.8783	0.706889	0.353445	−	0.935455i	$-0.385010\pi$
$443$	14.8783	0.706889	0.353445	+	0.935455i	$0.385010\pi$
$444$	7.50161	0.356010
$445$	0.0309200	0.00146575
$446$	5.49090	0.260002
$447$	0.313506	0.0148283
$448$	−1.00000	−0.0472456
$449$	−22.4689	−1.06038	−0.530188	−	0.847880i	$-0.677879\pi$
$449$	−22.4689	−1.06038	−0.530188	+	0.847880i	$0.677879\pi$
$450$	−2.98838	−0.140873
$451$	−26.5827	−1.25173
$452$	−19.3761	−0.911376
$453$	−19.3278	−0.908101
$454$	24.8093	1.16436
$455$	0	0
$456$	3.36262	0.157469
$457$	24.9437	1.16682	0.583409	−	0.812179i	$-0.301719\pi$
$457$	24.9437	1.16682	0.583409	+	0.812179i	$0.301719\pi$
$458$	−17.6756	−0.825925
$459$	0.124630	0.00581721
$460$	−22.8515	−1.06546
$461$	7.95426	0.370467	0.185233	−	0.982695i	$-0.440696\pi$
$461$	7.95426	0.370467	0.185233	+	0.982695i	$0.440696\pi$
$462$	5.31980	0.247499
$463$	−8.57505	−0.398516	−0.199258	−	0.979947i	$-0.563853\pi$
$463$	−8.57505	−0.398516	−0.199258	+	0.979947i	$0.563853\pi$
$464$	−6.57207	−0.305100
$465$	13.7385	0.637107
$466$	−2.42722	−0.112439
$467$	12.1706	0.563187	0.281594	−	0.959534i	$-0.409137\pi$
$467$	12.1706	0.563187	0.281594	+	0.959534i	$0.409137\pi$
$468$	0	0
$469$	11.9112	0.550007
$470$	−13.8163	−0.637299
$471$	9.73993	0.448792
$472$	−9.31705	−0.428852
$473$	−22.5988	−1.03910
$474$	18.2826	0.839746
$475$	−5.82513	−0.267275
$476$	0.0298061	0.00136616
$477$	9.14503	0.418722
$478$	−11.8577	−0.542360
$479$	12.9470	0.591564	0.295782	−	0.955255i	$-0.404420\pi$
$479$	12.9470	0.591564	0.295782	+	0.955255i	$0.404420\pi$
$480$	5.70975	0.260613
$481$	0	0
$482$	25.9502	1.18200
$483$	−15.5133	−0.705880
$484$	−3.69897	−0.168135
$485$	−17.1551	−0.778975
$486$	8.83892	0.400942
$487$	5.25820	0.238272	0.119136	−	0.992878i	$-0.461988\pi$
$487$	5.25820	0.238272	0.119136	+	0.992878i	$0.461988\pi$
$488$	5.27261	0.238680
$489$	−5.55598	−0.251250
$490$	2.90010	0.131013
$491$	−18.2501	−0.823613	−0.411807	−	0.911271i	$-0.635102\pi$
$491$	−18.2501	−0.823613	−0.411807	+	0.911271i	$0.635102\pi$
$492$	−19.3691	−0.873228
$493$	0.195888	0.00882233
$494$	0	0
$495$	−6.86609	−0.308608
$496$	−2.40615	−0.108039
$497$	−14.8176	−0.664659
$498$	26.4182	1.18383
$499$	−21.8922	−0.980029	−0.490014	−	0.871714i	$-0.663009\pi$
$499$	−21.8922	−0.980029	−0.490014	+	0.871714i	$0.663009\pi$
$500$	4.60941	0.206139
$501$	−4.37286	−0.195365
$502$	2.65757	0.118613
$503$	34.0744	1.51930	0.759651	−	0.650331i	$-0.225370\pi$
$503$	34.0744	1.51930	0.759651	+	0.650331i	$0.225370\pi$
$504$	0.876202	0.0390291
$505$	46.5996	2.07365
$506$	−21.2909	−0.946495
$507$	0	0
$508$	−5.30416	−0.235334
$509$	34.5426	1.53107	0.765537	−	0.643392i	$-0.222474\pi$
$509$	34.5426	1.53107	0.765537	+	0.643392i	$0.222474\pi$
$510$	−0.170185	−0.00753592
$511$	13.1669	0.582467
$512$	−1.00000	−0.0441942
$513$	7.14152	0.315306
$514$	−9.30522	−0.410436
$515$	37.8188	1.66650
$516$	−16.4663	−0.724891
$517$	−12.8727	−0.566142
$518$	3.81023	0.167412
$519$	41.7505	1.83264
$520$	0	0
$521$	−23.1604	−1.01468	−0.507338	−	0.861747i	$-0.669370\pi$
$521$	−23.1604	−1.01468	−0.507338	+	0.861747i	$0.669370\pi$
$522$	5.75845	0.252041
$523$	26.4452	1.15637	0.578184	−	0.815906i	$-0.303762\pi$
$523$	26.4452	1.15637	0.578184	+	0.815906i	$0.303762\pi$
$524$	−2.72894	−0.119214
$525$	−6.71482	−0.293059
$526$	−27.1636	−1.18439
$527$	0.0717178	0.00312407
$528$	5.31980	0.231515
$529$	39.0873	1.69945
$530$	30.2688	1.31479
$531$	8.16361	0.354271
$532$	1.70795	0.0740488
$533$	0	0
$534$	0.0209908	0.000908360 0
$535$	41.7791	1.80627
$536$	11.9112	0.514485
$537$	4.77132	0.205898
$538$	−19.4389	−0.838069
$539$	2.70204	0.116385
$540$	12.1263	0.521835
$541$	−13.1221	−0.564164	−0.282082	−	0.959390i	$-0.591025\pi$
$541$	−13.1221	−0.564164	−0.282082	+	0.959390i	$0.591025\pi$
$542$	−0.327549	−0.0140694
$543$	−2.30366	−0.0988594
$544$	0.0298061	0.00127793
$545$	−14.7457	−0.631635
$546$	0	0
$547$	23.4815	1.00400	0.501998	−	0.864869i	$-0.332599\pi$
$547$	23.4815	1.00400	0.501998	+	0.864869i	$0.332599\pi$
$548$	18.6021	0.794640
$549$	−4.61987	−0.197171
$550$	−9.21560	−0.392954
$551$	11.2247	0.478190
$552$	−15.5133	−0.660290
$553$	9.28611	0.394885
$554$	8.08634	0.343556
$555$	−21.7554	−0.923467
$556$	13.9773	0.592771
$557$	−16.7928	−0.711534	−0.355767	−	0.934575i	$-0.615780\pi$
$557$	−16.7928	−0.711534	−0.355767	+	0.934575i	$0.615780\pi$
$558$	2.10827	0.0892501
$559$	0	0
$560$	2.90010	0.122552
$561$	−0.158562	−0.00669451
$562$	−1.17570	−0.0495941
$563$	−21.3582	−0.900141	−0.450071	−	0.892993i	$-0.648601\pi$
$563$	−21.3582	−0.900141	−0.450071	+	0.892993i	$0.648601\pi$
$564$	−9.37954	−0.394950
$565$	56.1928	2.36405
$566$	−6.25986	−0.263121
$567$	10.8609	0.456114
$568$	−14.8176	−0.621732
$569$	−9.25253	−0.387886	−0.193943	−	0.981013i	$-0.562128\pi$
$569$	−9.25253	−0.387886	−0.193943	+	0.981013i	$0.562128\pi$
$570$	−9.75193	−0.408464
$571$	9.08279	0.380103	0.190051	−	0.981774i	$-0.439135\pi$
$571$	9.08279	0.380103	0.190051	+	0.981774i	$0.439135\pi$
$572$	0	0
$573$	34.0530	1.42259
$574$	−9.83800	−0.410630
$575$	26.8740	1.12072
$576$	0.876202	0.0365084
$577$	20.0697	0.835513	0.417756	−	0.908559i	$-0.362817\pi$
$577$	20.0697	0.835513	0.417756	+	0.908559i	$0.362817\pi$
$578$	16.9991	0.707070
$579$	8.77751	0.364781
$580$	19.0597	0.791410
$581$	13.4184	0.556688
$582$	−11.6462	−0.482750
$583$	28.2016	1.16799
$584$	13.1669	0.544848
$585$	0	0
$586$	−19.0166	−0.785570
$587$	−21.7954	−0.899593	−0.449796	−	0.893131i	$-0.648503\pi$
$587$	−21.7954	−0.899593	−0.449796	+	0.893131i	$0.648503\pi$
$588$	1.96881	0.0811922
$589$	4.10956	0.169332
$590$	27.0204	1.11241
$591$	−14.0334	−0.577257
$592$	3.81023	0.156599
$593$	−13.7999	−0.566695	−0.283347	−	0.959017i	$-0.591445\pi$
$593$	−13.7999	−0.566695	−0.283347	+	0.959017i	$0.591445\pi$
$594$	11.2982	0.463570
$595$	−0.0864407	−0.00354372
$596$	0.159237	0.00652259
$597$	−52.2133	−2.13695
$598$	0	0
$599$	−22.6224	−0.924325	−0.462163	−	0.886795i	$-0.652926\pi$
$599$	−22.6224	−0.924325	−0.462163	+	0.886795i	$0.652926\pi$
$600$	−6.71482	−0.274131
$601$	11.9334	0.486775	0.243387	−	0.969929i	$-0.421741\pi$
$601$	11.9334	0.486775	0.243387	+	0.969929i	$0.421741\pi$
$602$	−8.36362	−0.340876
$603$	−10.4366	−0.425011
$604$	−9.81702	−0.399449
$605$	10.7274	0.436131
$606$	31.6353	1.28509
$607$	18.2994	0.742751	0.371376	−	0.928483i	$-0.378886\pi$
$607$	18.2994	0.742751	0.371376	+	0.928483i	$0.378886\pi$
$608$	1.70795	0.0692663
$609$	12.9391	0.524320
$610$	−15.2911	−0.619119
$611$	0	0
$612$	−0.0261161	−0.00105568
$613$	−35.2787	−1.42489	−0.712446	−	0.701727i	$-0.752413\pi$
$613$	−35.2787	−1.42489	−0.712446	+	0.701727i	$0.752413\pi$
$614$	7.99210	0.322535
$615$	56.1725	2.26509
$616$	2.70204	0.108868
$617$	−31.5356	−1.26958	−0.634789	−	0.772686i	$-0.718913\pi$
$617$	−31.5356	−1.26958	−0.634789	+	0.772686i	$0.718913\pi$
$618$	25.6742	1.03277
$619$	22.0013	0.884307	0.442153	−	0.896939i	$-0.354215\pi$
$619$	22.0013	0.884307	0.442153	+	0.896939i	$0.354215\pi$
$620$	6.97807	0.280246
$621$	−32.9471	−1.32212
$622$	31.9778	1.28219
$623$	0.0106617	0.000427151 0
$624$	0	0
$625$	−30.4208	−1.21683
$626$	7.64078	0.305387
$627$	−9.08593	−0.362857
$628$	4.94712	0.197412
$629$	−0.113568	−0.00452825
$630$	−2.54108	−0.101239
$631$	14.3075	0.569573	0.284786	−	0.958591i	$-0.408077\pi$
$631$	14.3075	0.569573	0.284786	+	0.958591i	$0.408077\pi$
$632$	9.28611	0.369382
$633$	20.2504	0.804883
$634$	7.99006	0.317326
$635$	15.3826	0.610441
$636$	20.5487	0.814809
$637$	0	0
$638$	17.7580	0.703046
$639$	12.9832	0.513607
$640$	2.90010	0.114637
$641$	8.02319	0.316897	0.158448	−	0.987367i	$-0.449351\pi$
$641$	8.02319	0.316897	0.158448	+	0.987367i	$0.449351\pi$
$642$	28.3627	1.11939
$643$	−14.5085	−0.572158	−0.286079	−	0.958206i	$-0.592352\pi$
$643$	−14.5085	−0.572158	−0.286079	+	0.958206i	$0.592352\pi$
$644$	−7.87955	−0.310498
$645$	47.7541	1.88032
$646$	−0.0509072	−0.00200292
$647$	−2.92119	−0.114844	−0.0574219	−	0.998350i	$-0.518288\pi$
$647$	−2.92119	−0.114844	−0.0574219	+	0.998350i	$0.518288\pi$
$648$	10.8609	0.426655
$649$	25.1751	0.988208
$650$	0	0
$651$	4.73724	0.185667
$652$	−2.82200	−0.110518
$653$	47.4979	1.85873	0.929367	−	0.369156i	$-0.120353\pi$
$653$	47.4979	1.85873	0.929367	+	0.369156i	$0.120353\pi$
$654$	−10.0105	−0.391440
$655$	7.91421	0.309234
$656$	−9.83800	−0.384110
$657$	−11.5368	−0.450094
$658$	−4.76407	−0.185723
$659$	30.2013	1.17647	0.588237	−	0.808688i	$-0.299822\pi$
$659$	30.2013	1.17647	0.588237	+	0.808688i	$0.299822\pi$
$660$	−15.4280	−0.600533
$661$	−29.1655	−1.13441	−0.567203	−	0.823578i	$-0.691974\pi$
$661$	−29.1655	−1.13441	−0.567203	+	0.823578i	$0.691974\pi$
$662$	28.6843	1.11485
$663$	0	0
$664$	13.4184	0.520734
$665$	−4.95322	−0.192078
$666$	−3.33853	−0.129365
$667$	−51.7849	−2.00512
$668$	−2.22107	−0.0859359
$669$	−10.8105	−0.417959
$670$	−34.5437	−1.33454
$671$	−14.2468	−0.549992
$672$	1.96881	0.0759484
$673$	−19.0440	−0.734093	−0.367047	−	0.930203i	$-0.619631\pi$
$673$	−19.0440	−0.734093	−0.367047	+	0.930203i	$0.619631\pi$
$674$	−24.8904	−0.958743
$675$	−14.2609	−0.548903
$676$	0	0
$677$	−32.3703	−1.24409	−0.622046	−	0.782980i	$-0.713698\pi$
$677$	−32.3703	−1.24409	−0.622046	+	0.782980i	$0.713698\pi$
$678$	38.1478	1.46506
$679$	−5.91535	−0.227010
$680$	−0.0864407	−0.00331485
$681$	−48.8448	−1.87174
$682$	6.50150	0.248955
$683$	44.7164	1.71103	0.855513	−	0.517782i	$-0.173242\pi$
$683$	44.7164	1.71103	0.855513	+	0.517782i	$0.173242\pi$
$684$	−1.49650	−0.0572203
$685$	−53.9479	−2.06124
$686$	1.00000	0.0381802
$687$	34.7998	1.32770
$688$	−8.36362	−0.318860
$689$	0	0
$690$	44.9902	1.71275
$691$	−8.37875	−0.318743	−0.159371	−	0.987219i	$-0.550947\pi$
$691$	−8.37875	−0.318743	−0.159371	+	0.987219i	$0.550947\pi$
$692$	21.2060	0.806130
$693$	−2.36753	−0.0899352
$694$	−6.92508	−0.262872
$695$	−40.5357	−1.53761
$696$	12.9391	0.490456
$697$	0.293232	0.0111070
$698$	−3.63622	−0.137633
$699$	4.77873	0.180748
$700$	−3.41060	−0.128909
$701$	−18.9265	−0.714846	−0.357423	−	0.933943i	$-0.616344\pi$
$701$	−18.9265	−0.714846	−0.357423	+	0.933943i	$0.616344\pi$
$702$	0	0
$703$	−6.50766	−0.245441
$704$	2.70204	0.101837
$705$	27.2016	1.02447
$706$	−15.4309	−0.580751
$707$	16.0682	0.604308
$708$	18.3435	0.689390
$709$	3.34119	0.125481	0.0627405	−	0.998030i	$-0.480016\pi$
$709$	3.34119	0.125481	0.0627405	+	0.998030i	$0.480016\pi$
$710$	42.9725	1.61273
$711$	−8.13650	−0.305143
$712$	0.0106617	0.000399563 0
$713$	−18.9593	−0.710033
$714$	−0.0586824	−0.00219613
$715$	0	0
$716$	2.42346	0.0905688
$717$	23.3456	0.871857
$718$	1.58732	0.0592382
$719$	27.6030	1.02942	0.514708	−	0.857365i	$-0.327900\pi$
$719$	27.6030	1.02942	0.514708	+	0.857365i	$0.327900\pi$
$720$	−2.54108	−0.0947003
$721$	13.0405	0.485653
$722$	16.0829	0.598544
$723$	−51.0909	−1.90009
$724$	−1.17008	−0.0434856
$725$	−22.4147	−0.832462
$726$	7.28256	0.270281
$727$	46.7351	1.73331	0.866655	−	0.498908i	$-0.166265\pi$
$727$	46.7351	1.73331	0.866655	+	0.498908i	$0.166265\pi$
$728$	0	0
$729$	15.1805	0.562241
$730$	−38.1852	−1.41330
$731$	0.249287	0.00922020
$732$	−10.3808	−0.383684
$733$	20.0110	0.739125	0.369562	−	0.929206i	$-0.379508\pi$
$733$	20.0110	0.739125	0.369562	+	0.929206i	$0.379508\pi$
$734$	2.97145	0.109678
$735$	−5.70975	−0.210607
$736$	−7.87955	−0.290444
$737$	−32.1845	−1.18553
$738$	8.62007	0.317309
$739$	−2.33524	−0.0859033	−0.0429516	−	0.999077i	$-0.513676\pi$
$739$	−2.33524	−0.0859033	−0.0429516	+	0.999077i	$0.513676\pi$
$740$	−11.0501	−0.406208
$741$	0	0
$742$	10.4371	0.383159
$743$	−5.56374	−0.204114	−0.102057	−	0.994779i	$-0.532542\pi$
$743$	−5.56374	−0.204114	−0.102057	+	0.994779i	$0.532542\pi$
$744$	4.73724	0.173675
$745$	−0.461803	−0.0169192
$746$	−17.6510	−0.646247
$747$	−11.7572	−0.430174
$748$	−0.0805373	−0.00294473
$749$	14.4061	0.526386
$750$	−9.07504	−0.331374
$751$	−6.59254	−0.240565	−0.120283	−	0.992740i	$-0.538380\pi$
$751$	−6.59254	−0.240565	−0.120283	+	0.992740i	$0.538380\pi$
$752$	−4.76407	−0.173728
$753$	−5.23225	−0.190674
$754$	0	0
$755$	28.4704	1.03614
$756$	4.18135	0.152074
$757$	−16.8369	−0.611946	−0.305973	−	0.952040i	$-0.598982\pi$
$757$	−16.8369	−0.611946	−0.305973	+	0.952040i	$0.598982\pi$
$758$	−9.90111	−0.359625
$759$	41.9176	1.52151
$760$	−4.95322	−0.179672
$761$	30.7703	1.11542	0.557712	−	0.830034i	$-0.311679\pi$
$761$	30.7703	1.11542	0.557712	+	0.830034i	$0.311679\pi$
$762$	10.4429	0.378305
$763$	−5.08453	−0.184072
$764$	17.2963	0.625757
$765$	0.0757395	0.00273837
$766$	6.30154	0.227684
$767$	0	0
$768$	1.96881	0.0710432
$769$	−48.1106	−1.73491	−0.867456	−	0.497514i	$-0.834246\pi$
$769$	−48.1106	−1.73491	−0.867456	+	0.497514i	$0.834246\pi$
$770$	−7.83620	−0.282397
$771$	18.3202	0.659786
$772$	4.45829	0.160457
$773$	−35.9782	−1.29405	−0.647023	−	0.762470i	$-0.723986\pi$
$773$	−35.9782	−1.29405	−0.647023	+	0.762470i	$0.723986\pi$
$774$	7.32821	0.263407
$775$	−8.20641	−0.294783
$776$	−5.91535	−0.212349
$777$	−7.50161	−0.269119
$778$	3.71450	0.133171
$779$	16.8028	0.602022
$780$	0	0
$781$	40.0377	1.43266
$782$	0.234858	0.00839852
$783$	27.4801	0.982059
$784$	1.00000	0.0357143
$785$	−14.3472	−0.512072
$786$	5.37275	0.191640
$787$	12.8730	0.458874	0.229437	−	0.973323i	$-0.426311\pi$
$787$	12.8730	0.458874	0.229437	+	0.973323i	$0.426311\pi$
$788$	−7.12787	−0.253920
$789$	53.4798	1.90393
$790$	−26.9307	−0.958151
$791$	19.3761	0.688935
$792$	−2.36753	−0.0841266
$793$	0	0
$794$	−13.6290	−0.483675
$795$	−59.5934	−2.11356
$796$	−26.5203	−0.939986
$797$	29.7168	1.05262	0.526312	−	0.850292i	$-0.323575\pi$
$797$	29.7168	1.05262	0.526312	+	0.850292i	$0.323575\pi$
$798$	−3.36262	−0.119035
$799$	0.141998	0.00502354
$800$	−3.41060	−0.120583
$801$	−0.00934177	−0.000330075 0
$802$	−27.5298	−0.972112
$803$	−35.5774	−1.25550
$804$	−23.4508	−0.827047
$805$	22.8515	0.805410
$806$	0	0
$807$	38.2714	1.34722
$808$	16.0682	0.565279
$809$	9.31145	0.327373	0.163687	−	0.986512i	$-0.447661\pi$
$809$	9.31145	0.327373	0.163687	+	0.986512i	$0.447661\pi$
$810$	−31.4977	−1.10672
$811$	29.7647	1.04518	0.522590	−	0.852584i	$-0.324966\pi$
$811$	29.7647	1.04518	0.522590	+	0.852584i	$0.324966\pi$
$812$	6.57207	0.230634
$813$	0.644880	0.0226169
$814$	−10.2954	−0.360854
$815$	8.18410	0.286677
$816$	−0.0586824	−0.00205430
$817$	14.2846	0.499755
$818$	−29.8834	−1.04485
$819$	0	0
$820$	28.5312	0.996354
$821$	16.1742	0.564483	0.282241	−	0.959343i	$-0.408922\pi$
$821$	16.1742	0.564483	0.282241	+	0.959343i	$0.408922\pi$
$822$	−36.6239	−1.27740
$823$	48.2688	1.68255	0.841273	−	0.540611i	$-0.181807\pi$
$823$	48.2688	1.68255	0.841273	+	0.540611i	$0.181807\pi$
$824$	13.0405	0.454287
$825$	18.1437	0.631684
$826$	9.31705	0.324182
$827$	7.66479	0.266531	0.133265	−	0.991080i	$-0.457454\pi$
$827$	7.66479	0.266531	0.133265	+	0.991080i	$0.457454\pi$
$828$	6.90407	0.239933
$829$	13.6080	0.472624	0.236312	−	0.971677i	$-0.424061\pi$
$829$	13.6080	0.472624	0.236312	+	0.971677i	$0.424061\pi$
$830$	−38.9147	−1.35075
$831$	−15.9204	−0.552274
$832$	0	0
$833$	−0.0298061	−0.00103272
$834$	−27.5187	−0.952894
$835$	6.44134	0.222912
$836$	−4.61494	−0.159611
$837$	10.0609	0.347757
$838$	13.0400	0.450458
$839$	−12.0760	−0.416909	−0.208454	−	0.978032i	$-0.566843\pi$
$839$	−12.0760	−0.416909	−0.208454	+	0.978032i	$0.566843\pi$
$840$	−5.70975	−0.197005
$841$	14.1920	0.489381
$842$	34.2491	1.18030
$843$	2.31473	0.0797236
$844$	10.2856	0.354046
$845$	0	0
$846$	4.17429	0.143515
$847$	3.69897	0.127098
$848$	10.4371	0.358413
$849$	12.3244	0.422974
$850$	0.101657	0.00348680
$851$	30.0229	1.02917
$852$	29.1730	0.999449
$853$	−32.7838	−1.12249	−0.561247	−	0.827648i	$-0.689678\pi$
$853$	−32.7838	−1.12249	−0.561247	+	0.827648i	$0.689678\pi$
$854$	−5.27261	−0.180425
$855$	4.34002	0.148426
$856$	14.4061	0.492389
$857$	−44.7608	−1.52900	−0.764500	−	0.644624i	$-0.777014\pi$
$857$	−44.7608	−1.52900	−0.764500	+	0.644624i	$0.777014\pi$
$858$	0	0
$859$	−16.0074	−0.546166	−0.273083	−	0.961991i	$-0.588043\pi$
$859$	−16.0074	−0.546166	−0.273083	+	0.961991i	$0.588043\pi$
$860$	24.2554	0.827101
$861$	19.3691	0.660098
$862$	8.96721	0.305425
$863$	52.5352	1.78832	0.894159	−	0.447749i	$-0.147774\pi$
$863$	52.5352	1.78832	0.894159	+	0.447749i	$0.147774\pi$
$864$	4.18135	0.142252
$865$	−61.4995	−2.09105
$866$	10.3823	0.352805
$867$	−33.4680	−1.13663
$868$	2.40615	0.0816699
$869$	−25.0915	−0.851169
$870$	−37.5248	−1.27221
$871$	0	0
$872$	−5.08453	−0.172184
$873$	5.18304	0.175419
$874$	13.4578	0.455218
$875$	−4.60941	−0.155827
$876$	−25.9230	−0.875857
$877$	−17.5224	−0.591690	−0.295845	−	0.955236i	$-0.595601\pi$
$877$	−17.5224	−0.591690	−0.295845	+	0.955236i	$0.595601\pi$
$878$	−11.3125	−0.381779
$879$	37.4401	1.26282
$880$	−7.83620	−0.264158
$881$	−15.7495	−0.530616	−0.265308	−	0.964164i	$-0.585474\pi$
$881$	−15.7495	−0.530616	−0.265308	+	0.964164i	$0.585474\pi$
$882$	−0.876202	−0.0295032
$883$	50.7482	1.70781	0.853906	−	0.520428i	$-0.174227\pi$
$883$	50.7482	1.70781	0.853906	+	0.520428i	$0.174227\pi$
$884$	0	0
$885$	−53.1980	−1.78823
$886$	−14.8783	−0.499846
$887$	−37.8542	−1.27102	−0.635510	−	0.772092i	$-0.719210\pi$
$887$	−37.8542	−1.27102	−0.635510	+	0.772092i	$0.719210\pi$
$888$	−7.50161	−0.251737
$889$	5.30416	0.177896
$890$	−0.0309200	−0.00103644
$891$	−29.3465	−0.983146
$892$	−5.49090	−0.183849
$893$	8.13677	0.272287
$894$	−0.313506	−0.0104852
$895$	−7.02827	−0.234929
$896$	1.00000	0.0334077
$897$	0	0
$898$	22.4689	0.749799
$899$	15.8133	0.527405
$900$	2.98838	0.0996126
$901$	−0.311090	−0.0103639
$902$	26.5827	0.885107
$903$	16.4663	0.547966
$904$	19.3761	0.644440
$905$	3.39335	0.112799
$906$	19.3278	0.642124
$907$	44.0060	1.46120	0.730598	−	0.682808i	$-0.239242\pi$
$907$	44.0060	1.46120	0.730598	+	0.682808i	$0.239242\pi$
$908$	−24.8093	−0.823326
$909$	−14.0790	−0.466971
$910$	0	0
$911$	−37.7409	−1.25041	−0.625205	−	0.780460i	$-0.714985\pi$
$911$	−37.7409	−1.25041	−0.625205	+	0.780460i	$0.714985\pi$
$912$	−3.36262	−0.111347
$913$	−36.2570	−1.19993
$914$	−24.9437	−0.825065
$915$	30.1053	0.995250
$916$	17.6756	0.584017
$917$	2.72894	0.0901175
$918$	−0.124630	−0.00411339
$919$	51.0076	1.68259	0.841294	−	0.540579i	$-0.181795\pi$
$919$	51.0076	1.68259	0.841294	+	0.540579i	$0.181795\pi$
$920$	22.8515	0.753392
$921$	−15.7349	−0.518483
$922$	−7.95426	−0.261959
$923$	0	0
$924$	−5.31980	−0.175009
$925$	12.9952	0.427279
$926$	8.57505	0.281794
$927$	−11.4261	−0.375282
$928$	6.57207	0.215739
$929$	41.1327	1.34952	0.674761	−	0.738037i	$-0.264247\pi$
$929$	41.1327	1.34952	0.674761	+	0.738037i	$0.264247\pi$
$930$	−13.7385	−0.450502
$931$	−1.70795	−0.0559757
$932$	2.42722	0.0795063
$933$	−62.9581	−2.06115
$934$	−12.1706	−0.398233
$935$	0.233567	0.00763844
$936$	0	0
$937$	−52.8736	−1.72731	−0.863653	−	0.504087i	$-0.831829\pi$
$937$	−52.8736	−1.72731	−0.863653	+	0.504087i	$0.831829\pi$
$938$	−11.9112	−0.388914
$939$	−15.0432	−0.490917
$940$	13.8163	0.450638
$941$	60.2283	1.96339	0.981693	−	0.190470i	$-0.0610010\pi$
$941$	60.2283	1.96339	0.981693	+	0.190470i	$0.0610010\pi$
$942$	−9.73993	−0.317344
$943$	−77.5190	−2.52437
$944$	9.31705	0.303244
$945$	−12.1263	−0.394470
$946$	22.5988	0.734752
$947$	11.4381	0.371690	0.185845	−	0.982579i	$-0.440498\pi$
$947$	11.4381	0.371690	0.185845	+	0.982579i	$0.440498\pi$
$948$	−18.2826	−0.593790
$949$	0	0
$950$	5.82513	0.188992
$951$	−15.7309	−0.510109
$952$	−0.0298061	−0.000966021 0
$953$	−24.5383	−0.794872	−0.397436	−	0.917630i	$-0.630100\pi$
$953$	−24.5383	−0.794872	−0.397436	+	0.917630i	$0.630100\pi$
$954$	−9.14503	−0.296081
$955$	−50.1610	−1.62317
$956$	11.8577	0.383507
$957$	−34.9621	−1.13016
$958$	−12.9470	−0.418299
$959$	−18.6021	−0.600692
$960$	−5.70975	−0.184281
$961$	−25.2105	−0.813241
$962$	0	0
$963$	−12.6226	−0.406758
$964$	−25.9502	−0.835800
$965$	−12.9295	−0.416215
$966$	15.5133	0.499133
$967$	−47.5644	−1.52957	−0.764784	−	0.644287i	$-0.777154\pi$
$967$	−47.5644	−1.52957	−0.764784	+	0.644287i	$0.777154\pi$
$968$	3.69897	0.118889
$969$	0.100226	0.00321974
$970$	17.1551	0.550818
$971$	−23.9266	−0.767840	−0.383920	−	0.923366i	$-0.625426\pi$
$971$	−23.9266	−0.767840	−0.383920	+	0.923366i	$0.625426\pi$
$972$	−8.83892	−0.283509
$973$	−13.9773	−0.448093
$974$	−5.25820	−0.168484
$975$	0	0
$976$	−5.27261	−0.168772
$977$	54.4782	1.74291	0.871456	−	0.490474i	$-0.163176\pi$
$977$	54.4782	1.74291	0.871456	+	0.490474i	$0.163176\pi$
$978$	5.55598	0.177661
$979$	−0.0288083	−0.000920717 0
$980$	−2.90010	−0.0926404
$981$	4.45507	0.142239
$982$	18.2501	0.582383
$983$	−28.2938	−0.902431	−0.451215	−	0.892415i	$-0.649009\pi$
$983$	−28.2938	−0.902431	−0.451215	+	0.892415i	$0.649009\pi$
$984$	19.3691	0.617465
$985$	20.6716	0.658651
$986$	−0.195888	−0.00623833
$987$	9.37954	0.298554
$988$	0	0
$989$	−65.9015	−2.09555
$990$	6.86609	0.218219
$991$	−23.6471	−0.751174	−0.375587	−	0.926787i	$-0.622559\pi$
$991$	−23.6471	−0.751174	−0.375587	+	0.926787i	$0.622559\pi$
$992$	2.40615	0.0763952
$993$	−56.4739	−1.79215
$994$	14.8176	0.469985
$995$	76.9116	2.43826
$996$	−26.4182	−0.837093
$997$	35.1608	1.11355	0.556777	−	0.830662i	$-0.312038\pi$
$997$	35.1608	1.11355	0.556777	+	0.830662i	$0.312038\pi$
$998$	21.8922	0.692985
$999$	−15.9319	−0.504063

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.a.be.1.5	✓	6
13.5	odd	4		2366.2.d.q.337.11		12
13.8	odd	4		2366.2.d.q.337.5		12
13.12	even	2		2366.2.a.bg.1.5	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2366.2.a.be.1.5	✓	6	1.1	even	1	trivial
2366.2.a.bg.1.5	yes	6	13.12	even	2
2366.2.d.q.337.5		12	13.8	odd	4
2366.2.d.q.337.11		12	13.5	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.96881 q^{3} +1.00000 q^{4} -2.90010 q^{5} -1.96881 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.876202 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.96881 q^{3} +1.00000 q^{4} -2.90010 q^{5} -1.96881 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.876202 q^{9} +2.90010 q^{10} +2.70204 q^{11} +1.96881 q^{12} +1.00000 q^{14} -5.70975 q^{15} +1.00000 q^{16} -0.0298061 q^{17} -0.876202 q^{18} -1.70795 q^{19} -2.90010 q^{20} -1.96881 q^{21} -2.70204 q^{22} +7.87955 q^{23} -1.96881 q^{24} +3.41060 q^{25} -4.18135 q^{27} -1.00000 q^{28} -6.57207 q^{29} +5.70975 q^{30} -2.40615 q^{31} -1.00000 q^{32} +5.31980 q^{33} +0.0298061 q^{34} +2.90010 q^{35} +0.876202 q^{36} +3.81023 q^{37} +1.70795 q^{38} +2.90010 q^{40} -9.83800 q^{41} +1.96881 q^{42} -8.36362 q^{43} +2.70204 q^{44} -2.54108 q^{45} -7.87955 q^{46} -4.76407 q^{47} +1.96881 q^{48} +1.00000 q^{49} -3.41060 q^{50} -0.0586824 q^{51} +10.4371 q^{53} +4.18135 q^{54} -7.83620 q^{55} +1.00000 q^{56} -3.36262 q^{57} +6.57207 q^{58} +9.31705 q^{59} -5.70975 q^{60} -5.27261 q^{61} +2.40615 q^{62} -0.876202 q^{63} +1.00000 q^{64} -5.31980 q^{66} -11.9112 q^{67} -0.0298061 q^{68} +15.5133 q^{69} -2.90010 q^{70} +14.8176 q^{71} -0.876202 q^{72} -13.1669 q^{73} -3.81023 q^{74} +6.71482 q^{75} -1.70795 q^{76} -2.70204 q^{77} -9.28611 q^{79} -2.90010 q^{80} -10.8609 q^{81} +9.83800 q^{82} -13.4184 q^{83} -1.96881 q^{84} +0.0864407 q^{85} +8.36362 q^{86} -12.9391 q^{87} -2.70204 q^{88} -0.0106617 q^{89} +2.54108 q^{90} +7.87955 q^{92} -4.73724 q^{93} +4.76407 q^{94} +4.95322 q^{95} -1.96881 q^{96} +5.91535 q^{97} -1.00000 q^{98} +2.36753 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + q^{3} + 6 q^{4} - 4 q^{5} - q^{6} - 6 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + q^3 + 6 * q^4 - 4 * q^5 - q^6 - 6 * q^7 - 6 * q^8 + 5 * q^9	\( 6 q - 6 q^{2} + q^{3} + 6 q^{4} - 4 q^{5} - q^{6} - 6 q^{7} - 6 q^{8} + 5 q^{9} + 4 q^{10} - 6 q^{11} + q^{12} + 6 q^{14} + 5 q^{15} + 6 q^{16} - 9 q^{17} - 5 q^{18} - 10 q^{19} - 4 q^{20} - q^{21} + 6 q^{22} + 21 q^{23} - q^{24} + 8 q^{25} + 7 q^{27} - 6 q^{28} - q^{29} - 5 q^{30} - 20 q^{31} - 6 q^{32} - 9 q^{33} + 9 q^{34} + 4 q^{35} + 5 q^{36} - 16 q^{37} + 10 q^{38} + 4 q^{40} - 2 q^{41} + q^{42} + 2 q^{43} - 6 q^{44} - 17 q^{45} - 21 q^{46} + 5 q^{47} + q^{48} + 6 q^{49} - 8 q^{50} - 15 q^{51} + 28 q^{53} - 7 q^{54} - 29 q^{55} + 6 q^{56} - 22 q^{57} + q^{58} + 12 q^{59} + 5 q^{60} - 27 q^{61} + 20 q^{62} - 5 q^{63} + 6 q^{64} + 9 q^{66} - 16 q^{67} - 9 q^{68} - 15 q^{69} - 4 q^{70} - 5 q^{72} - 38 q^{73} + 16 q^{74} - 7 q^{75} - 10 q^{76} + 6 q^{77} + 6 q^{79} - 4 q^{80} - 26 q^{81} + 2 q^{82} + 6 q^{83} - q^{84} - 9 q^{85} - 2 q^{86} - 39 q^{87} + 6 q^{88} + q^{89} + 17 q^{90} + 21 q^{92} + 7 q^{93} - 5 q^{94} + 3 q^{95} - q^{96} - 16 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + q^3 + 6 * q^4 - 4 * q^5 - q^6 - 6 * q^7 - 6 * q^8 + 5 * q^9 + 4 * q^10 - 6 * q^11 + q^12 + 6 * q^14 + 5 * q^15 + 6 * q^16 - 9 * q^17 - 5 * q^18 - 10 * q^19 - 4 * q^20 - q^21 + 6 * q^22 + 21 * q^23 - q^24 + 8 * q^25 + 7 * q^27 - 6 * q^28 - q^29 - 5 * q^30 - 20 * q^31 - 6 * q^32 - 9 * q^33 + 9 * q^34 + 4 * q^35 + 5 * q^36 - 16 * q^37 + 10 * q^38 + 4 * q^40 - 2 * q^41 + q^42 + 2 * q^43 - 6 * q^44 - 17 * q^45 - 21 * q^46 + 5 * q^47 + q^48 + 6 * q^49 - 8 * q^50 - 15 * q^51 + 28 * q^53 - 7 * q^54 - 29 * q^55 + 6 * q^56 - 22 * q^57 + q^58 + 12 * q^59 + 5 * q^60 - 27 * q^61 + 20 * q^62 - 5 * q^63 + 6 * q^64 + 9 * q^66 - 16 * q^67 - 9 * q^68 - 15 * q^69 - 4 * q^70 - 5 * q^72 - 38 * q^73 + 16 * q^74 - 7 * q^75 - 10 * q^76 + 6 * q^77 + 6 * q^79 - 4 * q^80 - 26 * q^81 + 2 * q^82 + 6 * q^83 - q^84 - 9 * q^85 - 2 * q^86 - 39 * q^87 + 6 * q^88 + q^89 + 17 * q^90 + 21 * q^92 + 7 * q^93 - 5 * q^94 + 3 * q^95 - q^96 - 16 * q^97 - 6 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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