LMFDB - Embedded newform 2695.2.a.w.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2695,2,Mod(1,2695)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2695, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2695.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2695 = 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2695.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:	$21.5196833447$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 56x^{6} - 92x^{5} - 86x^{4} + 116x^{3} + 31x^{2} - 22x + 1 $ x^10 - 2x^9 - 13x^8 + 24x^7 + 56x^6 - 92x^5 - 86x^4 + 116x^3 + 31x^2 - 22*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$2.48590$ of defining polynomial
Character	$\chi$	$=$	2695.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.48590 q^{2} -0.309874 q^{3} +4.17970 q^{4} -1.00000 q^{5} -0.770315 q^{6} +5.41853 q^{8} -2.90398 q^{9} +O(q^{10})$	\(q+2.48590 q^{2} -0.309874 q^{3} +4.17970 q^{4} -1.00000 q^{5} -0.770315 q^{6} +5.41853 q^{8} -2.90398 q^{9} -2.48590 q^{10} -1.00000 q^{11} -1.29518 q^{12} -6.09371 q^{13} +0.309874 q^{15} +5.11052 q^{16} -6.51173 q^{17} -7.21900 q^{18} -1.99131 q^{19} -4.17970 q^{20} -2.48590 q^{22} -3.32487 q^{23} -1.67906 q^{24} +1.00000 q^{25} -15.1484 q^{26} +1.82949 q^{27} +2.43341 q^{29} +0.770315 q^{30} +0.329434 q^{31} +1.86719 q^{32} +0.309874 q^{33} -16.1875 q^{34} -12.1378 q^{36} +3.90467 q^{37} -4.95021 q^{38} +1.88828 q^{39} -5.41853 q^{40} +4.32437 q^{41} -8.06725 q^{43} -4.17970 q^{44} +2.90398 q^{45} -8.26531 q^{46} +8.07885 q^{47} -1.58362 q^{48} +2.48590 q^{50} +2.01781 q^{51} -25.4699 q^{52} +12.2063 q^{53} +4.54792 q^{54} +1.00000 q^{55} +0.617055 q^{57} +6.04922 q^{58} -2.37942 q^{59} +1.29518 q^{60} -9.18757 q^{61} +0.818941 q^{62} -5.57939 q^{64} +6.09371 q^{65} +0.770315 q^{66} +7.66921 q^{67} -27.2171 q^{68} +1.03029 q^{69} +4.72654 q^{71} -15.7353 q^{72} +5.41329 q^{73} +9.70664 q^{74} -0.309874 q^{75} -8.32310 q^{76} +4.69407 q^{78} -15.8557 q^{79} -5.11052 q^{80} +8.14503 q^{81} +10.7500 q^{82} +13.3346 q^{83} +6.51173 q^{85} -20.0544 q^{86} -0.754050 q^{87} -5.41853 q^{88} -13.6059 q^{89} +7.21900 q^{90} -13.8970 q^{92} -0.102083 q^{93} +20.0832 q^{94} +1.99131 q^{95} -0.578594 q^{96} +17.8793 q^{97} +2.90398 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 10 q^{4} - 10 q^{5} - 4 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 10 * q^4 - 10 * q^5 - 4 * q^6 + 6 * q^8 + 10 * q^9	$ 10 q + 2 q^{2} + 10 q^{4} - 10 q^{5} - 4 q^{6} + 6 q^{8} + 10 q^{9} - 2 q^{10} - 10 q^{11} - 4 q^{12} - 8 q^{13} + 6 q^{16} - 28 q^{17} - 10 q^{18} - 8 q^{19} - 10 q^{20} - 2 q^{22} - 8 q^{23} - 32 q^{24} + 10 q^{25} - 12 q^{26} - 8 q^{29} + 4 q^{30} + 4 q^{31} + 14 q^{32} - 20 q^{34} - 22 q^{36} + 28 q^{37} - 24 q^{38} - 24 q^{39} - 6 q^{40} - 44 q^{41} + 20 q^{43} - 10 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} - 16 q^{48} + 2 q^{50} - 4 q^{51} - 36 q^{52} + 8 q^{54} + 10 q^{55} + 12 q^{57} - 8 q^{58} - 16 q^{59} + 4 q^{60} - 16 q^{61} - 36 q^{62} - 34 q^{64} + 8 q^{65} + 4 q^{66} + 20 q^{67} - 8 q^{68} - 4 q^{69} - 4 q^{71} + 10 q^{72} - 20 q^{73} - 16 q^{74} - 4 q^{76} + 52 q^{78} - 20 q^{79} - 6 q^{80} + 10 q^{81} + 32 q^{82} - 16 q^{83} + 28 q^{85} - 20 q^{86} - 20 q^{87} - 6 q^{88} - 44 q^{89} + 10 q^{90} - 24 q^{92} + 16 q^{93} - 24 q^{94} + 8 q^{95} + 4 q^{97} - 10 q^{99}+O(q^{100}) $ 10 * q + 2 * q^2 + 10 * q^4 - 10 * q^5 - 4 * q^6 + 6 * q^8 + 10 * q^9 - 2 * q^10 - 10 * q^11 - 4 * q^12 - 8 * q^13 + 6 * q^16 - 28 * q^17 - 10 * q^18 - 8 * q^19 - 10 * q^20 - 2 * q^22 - 8 * q^23 - 32 * q^24 + 10 * q^25 - 12 * q^26 - 8 * q^29 + 4 * q^30 + 4 * q^31 + 14 * q^32 - 20 * q^34 - 22 * q^36 + 28 * q^37 - 24 * q^38 - 24 * q^39 - 6 * q^40 - 44 * q^41 + 20 * q^43 - 10 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 - 16 * q^48 + 2 * q^50 - 4 * q^51 - 36 * q^52 + 8 * q^54 + 10 * q^55 + 12 * q^57 - 8 * q^58 - 16 * q^59 + 4 * q^60 - 16 * q^61 - 36 * q^62 - 34 * q^64 + 8 * q^65 + 4 * q^66 + 20 * q^67 - 8 * q^68 - 4 * q^69 - 4 * q^71 + 10 * q^72 - 20 * q^73 - 16 * q^74 - 4 * q^76 + 52 * q^78 - 20 * q^79 - 6 * q^80 + 10 * q^81 + 32 * q^82 - 16 * q^83 + 28 * q^85 - 20 * q^86 - 20 * q^87 - 6 * q^88 - 44 * q^89 + 10 * q^90 - 24 * q^92 + 16 * q^93 - 24 * q^94 + 8 * q^95 + 4 * q^97 - 10 * 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 $

$2$	2.48590	1.75780	0.878899	−	0.477008i	$-0.158279\pi$
$2$	2.48590	1.75780	0.878899	+	0.477008i	$0.158279\pi$
$3$	−0.309874	−0.178906	−0.0894528	−	0.995991i	$-0.528512\pi$
$3$	−0.309874	−0.178906	−0.0894528	+	0.995991i	$0.528512\pi$
$4$	4.17970	2.08985
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.770315	−0.314480
$7$	0	0
$7$	0	0
$8$	5.41853	1.91574
$9$	−2.90398	−0.967993
$10$	−2.48590	−0.786111
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.29518	−0.373886
$13$	−6.09371	−1.69009	−0.845045	−	0.534695i	$-0.820427\pi$
$13$	−6.09371	−1.69009	−0.845045	+	0.534695i	$0.820427\pi$
$14$	0	0
$15$	0.309874	0.0800090
$16$	5.11052	1.27763
$17$	−6.51173	−1.57933	−0.789663	−	0.613540i	$-0.789745\pi$
$17$	−6.51173	−1.57933	−0.789663	+	0.613540i	$0.789745\pi$
$18$	−7.21900	−1.70154
$19$	−1.99131	−0.456838	−0.228419	−	0.973563i	$-0.573356\pi$
$19$	−1.99131	−0.456838	−0.228419	+	0.973563i	$0.573356\pi$
$20$	−4.17970	−0.934610
$21$	0	0
$22$	−2.48590	−0.529996
$23$	−3.32487	−0.693284	−0.346642	−	0.937997i	$-0.612678\pi$
$23$	−3.32487	−0.693284	−0.346642	+	0.937997i	$0.612678\pi$
$24$	−1.67906	−0.342737
$25$	1.00000	0.200000
$26$	−15.1484	−2.97084
$27$	1.82949	0.352085
$28$	0	0
$29$	2.43341	0.451873	0.225937	−	0.974142i	$-0.427456\pi$
$29$	2.43341	0.451873	0.225937	+	0.974142i	$0.427456\pi$
$30$	0.770315	0.140640
$31$	0.329434	0.0591681	0.0295841	−	0.999562i	$-0.490582\pi$
$31$	0.329434	0.0591681	0.0295841	+	0.999562i	$0.490582\pi$
$32$	1.86719	0.330076
$33$	0.309874	0.0539421
$34$	−16.1875	−2.77614
$35$	0	0
$36$	−12.1378	−2.02296
$37$	3.90467	0.641925	0.320962	−	0.947092i	$-0.395994\pi$
$37$	3.90467	0.641925	0.320962	+	0.947092i	$0.395994\pi$
$38$	−4.95021	−0.803030
$39$	1.88828	0.302367
$40$	−5.41853	−0.856745
$41$	4.32437	0.675354	0.337677	−	0.941262i	$-0.390359\pi$
$41$	4.32437	0.675354	0.337677	+	0.941262i	$0.390359\pi$
$42$	0	0
$43$	−8.06725	−1.23024	−0.615122	−	0.788432i	$-0.710893\pi$
$43$	−8.06725	−1.23024	−0.615122	+	0.788432i	$0.710893\pi$
$44$	−4.17970	−0.630114
$45$	2.90398	0.432900
$46$	−8.26531	−1.21865
$47$	8.07885	1.17842	0.589211	−	0.807979i	$-0.299439\pi$
$47$	8.07885	1.17842	0.589211	+	0.807979i	$0.299439\pi$
$48$	−1.58362	−0.228575
$49$	0	0
$50$	2.48590	0.351560
$51$	2.01781	0.282550
$52$	−25.4699	−3.53204
$53$	12.2063	1.67666	0.838329	−	0.545165i	$-0.183533\pi$
$53$	12.2063	1.67666	0.838329	+	0.545165i	$0.183533\pi$
$54$	4.54792	0.618894
$55$	1.00000	0.134840
$56$	0	0
$57$	0.617055	0.0817310
$58$	6.04922	0.794301
$59$	−2.37942	−0.309774	−0.154887	−	0.987932i	$-0.549501\pi$
$59$	−2.37942	−0.309774	−0.154887	+	0.987932i	$0.549501\pi$
$60$	1.29518	0.167207
$61$	−9.18757	−1.17635	−0.588174	−	0.808735i	$-0.700153\pi$
$61$	−9.18757	−1.17635	−0.588174	+	0.808735i	$0.700153\pi$
$62$	0.818941	0.104006
$63$	0	0
$64$	−5.57939	−0.697424
$65$	6.09371	0.755831
$66$	0.770315	0.0948192
$67$	7.66921	0.936943	0.468472	−	0.883479i	$-0.344805\pi$
$67$	7.66921	0.936943	0.468472	+	0.883479i	$0.344805\pi$
$68$	−27.2171	−3.30056
$69$	1.03029	0.124032
$70$	0	0
$71$	4.72654	0.560937	0.280468	−	0.959863i	$-0.409510\pi$
$71$	4.72654	0.560937	0.280468	+	0.959863i	$0.409510\pi$
$72$	−15.7353	−1.85442
$73$	5.41329	0.633578	0.316789	−	0.948496i	$-0.397395\pi$
$73$	5.41329	0.633578	0.316789	+	0.948496i	$0.397395\pi$
$74$	9.70664	1.12837
$75$	−0.309874	−0.0357811
$76$	−8.32310	−0.954725
$77$	0	0
$78$	4.69407	0.531499
$79$	−15.8557	−1.78390	−0.891952	−	0.452131i	$-0.850664\pi$
$79$	−15.8557	−1.78390	−0.891952	+	0.452131i	$0.850664\pi$
$80$	−5.11052	−0.571374
$81$	8.14503	0.905003
$82$	10.7500	1.18714
$83$	13.3346	1.46366	0.731831	−	0.681486i	$-0.238666\pi$
$83$	13.3346	1.46366	0.731831	+	0.681486i	$0.238666\pi$
$84$	0	0
$85$	6.51173	0.706296
$86$	−20.0544	−2.16252
$87$	−0.754050	−0.0808426
$88$	−5.41853	−0.577617
$89$	−13.6059	−1.44222	−0.721110	−	0.692820i	$-0.756368\pi$
$89$	−13.6059	−1.44222	−0.721110	+	0.692820i	$0.756368\pi$
$90$	7.21900	0.760950
$91$	0	0
$92$	−13.8970	−1.44886
$93$	−0.102083	−0.0105855
$94$	20.0832	2.07143
$95$	1.99131	0.204304
$96$	−0.578594	−0.0590525
$97$	17.8793	1.81537	0.907683	−	0.419658i	$-0.137850\pi$
$97$	17.8793	1.81537	0.907683	+	0.419658i	$0.137850\pi$
$98$	0	0
$99$	2.90398	0.291861
$100$	4.17970	0.417970
$101$	−5.54488	−0.551736	−0.275868	−	0.961196i	$-0.588965\pi$
$101$	−5.54488	−0.551736	−0.275868	+	0.961196i	$0.588965\pi$
$102$	5.01609	0.496666
$103$	−2.21707	−0.218455	−0.109227	−	0.994017i	$-0.534838\pi$
$103$	−2.21707	−0.218455	−0.109227	+	0.994017i	$0.534838\pi$
$104$	−33.0189	−3.23777
$105$	0	0
$106$	30.3435	2.94722
$107$	−10.8420	−1.04813	−0.524066	−	0.851678i	$-0.675585\pi$
$107$	−10.8420	−1.04813	−0.524066	+	0.851678i	$0.675585\pi$
$108$	7.64672	0.735806
$109$	−1.43563	−0.137509	−0.0687544	−	0.997634i	$-0.521902\pi$
$109$	−1.43563	−0.137509	−0.0687544	+	0.997634i	$0.521902\pi$
$110$	2.48590	0.237021
$111$	−1.20996	−0.114844
$112$	0	0
$113$	−14.9055	−1.40219	−0.701096	−	0.713067i	$-0.747305\pi$
$113$	−14.9055	−1.40219	−0.701096	+	0.713067i	$0.747305\pi$
$114$	1.53394	0.143666
$115$	3.32487	0.310046
$116$	10.1709	0.944348
$117$	17.6960	1.63600
$118$	−5.91500	−0.544520
$119$	0	0
$120$	1.67906	0.153276
$121$	1.00000	0.0909091
$122$	−22.8394	−2.06778
$123$	−1.34001	−0.120825
$124$	1.37694	0.123653
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	7.27246	0.645327	0.322663	−	0.946514i	$-0.395422\pi$
$127$	7.27246	0.645327	0.322663	+	0.946514i	$0.395422\pi$
$128$	−17.6042	−1.55601
$129$	2.49983	0.220098
$130$	15.1484	1.32860
$131$	1.97094	0.172202	0.0861010	−	0.996286i	$-0.472559\pi$
$131$	1.97094	0.172202	0.0861010	+	0.996286i	$0.472559\pi$
$132$	1.29518	0.112731
$133$	0	0
$134$	19.0649	1.64696
$135$	−1.82949	−0.157457
$136$	−35.2840	−3.02558
$137$	−1.89795	−0.162153	−0.0810763	−	0.996708i	$-0.525836\pi$
$137$	−1.89795	−0.162153	−0.0810763	+	0.996708i	$0.525836\pi$
$138$	2.56120	0.218024
$139$	−7.31010	−0.620035	−0.310017	−	0.950731i	$-0.600335\pi$
$139$	−7.31010	−0.620035	−0.310017	+	0.950731i	$0.600335\pi$
$140$	0	0
$141$	−2.50342	−0.210826
$142$	11.7497	0.986014
$143$	6.09371	0.509581
$144$	−14.8408	−1.23674
$145$	−2.43341	−0.202084
$146$	13.4569	1.11370
$147$	0	0
$148$	16.3204	1.34153
$149$	−12.4345	−1.01867	−0.509337	−	0.860567i	$-0.670109\pi$
$149$	−12.4345	−1.01867	−0.509337	+	0.860567i	$0.670109\pi$
$150$	−0.770315	−0.0628960
$151$	−22.9307	−1.86608	−0.933039	−	0.359775i	$-0.882853\pi$
$151$	−22.9307	−1.86608	−0.933039	+	0.359775i	$0.882853\pi$
$152$	−10.7900	−0.875184
$153$	18.9099	1.52878
$154$	0	0
$155$	−0.329434	−0.0264608
$156$	7.89245	0.631902
$157$	4.13796	0.330245	0.165122	−	0.986273i	$-0.447198\pi$
$157$	4.13796	0.330245	0.165122	+	0.986273i	$0.447198\pi$
$158$	−39.4157	−3.13574
$159$	−3.78239	−0.299963
$160$	−1.86719	−0.147615
$161$	0	0
$162$	20.2477	1.59081
$163$	−21.3842	−1.67494	−0.837469	−	0.546485i	$-0.815965\pi$
$163$	−21.3842	−1.67494	−0.837469	+	0.546485i	$0.815965\pi$
$164$	18.0746	1.41139
$165$	−0.309874	−0.0241236
$166$	33.1485	2.57282
$167$	−10.7161	−0.829238	−0.414619	−	0.909995i	$-0.636085\pi$
$167$	−10.7161	−0.829238	−0.414619	+	0.909995i	$0.636085\pi$
$168$	0	0
$169$	24.1333	1.85641
$170$	16.1875	1.24153
$171$	5.78273	0.442216
$172$	−33.7187	−2.57103
$173$	−2.95240	−0.224467	−0.112233	−	0.993682i	$-0.535800\pi$
$173$	−2.95240	−0.224467	−0.112233	+	0.993682i	$0.535800\pi$
$174$	−1.87449	−0.142105
$175$	0	0
$176$	−5.11052	−0.385220
$177$	0.737319	0.0554203
$178$	−33.8229	−2.53513
$179$	22.7948	1.70376	0.851882	−	0.523734i	$-0.175462\pi$
$179$	22.7948	1.70376	0.851882	+	0.523734i	$0.175462\pi$
$180$	12.1378	0.904696
$181$	0.396824	0.0294957	0.0147478	−	0.999891i	$-0.495305\pi$
$181$	0.396824	0.0294957	0.0147478	+	0.999891i	$0.495305\pi$
$182$	0	0
$183$	2.84698	0.210455
$184$	−18.0159	−1.32815
$185$	−3.90467	−0.287077
$186$	−0.253768	−0.0186072
$187$	6.51173	0.476185
$188$	33.7672	2.46273
$189$	0	0
$190$	4.95021	0.359126
$191$	−18.7890	−1.35952	−0.679761	−	0.733434i	$-0.737916\pi$
$191$	−18.7890	−1.35952	−0.679761	+	0.733434i	$0.737916\pi$
$192$	1.72890	0.124773
$193$	−12.7181	−0.915466	−0.457733	−	0.889090i	$-0.651338\pi$
$193$	−12.7181	−0.915466	−0.457733	+	0.889090i	$0.651338\pi$
$194$	44.4461	3.19104
$195$	−1.88828	−0.135222
$196$	0	0
$197$	−5.48363	−0.390692	−0.195346	−	0.980734i	$-0.562583\pi$
$197$	−5.48363	−0.390692	−0.195346	+	0.980734i	$0.562583\pi$
$198$	7.21900	0.513032
$199$	11.5896	0.821562	0.410781	−	0.911734i	$-0.365256\pi$
$199$	11.5896	0.821562	0.410781	+	0.911734i	$0.365256\pi$
$200$	5.41853	0.383148
$201$	−2.37649	−0.167624
$202$	−13.7840	−0.969840
$203$	0	0
$204$	8.43387	0.590489
$205$	−4.32437	−0.302027
$206$	−5.51142	−0.383999
$207$	9.65536	0.671094
$208$	−31.1420	−2.15931
$209$	1.99131	0.137742
$210$	0	0
$211$	−9.96758	−0.686197	−0.343098	−	0.939299i	$-0.611476\pi$
$211$	−9.96758	−0.686197	−0.343098	+	0.939299i	$0.611476\pi$
$212$	51.0185	3.50397
$213$	−1.46463	−0.100355
$214$	−26.9520	−1.84240
$215$	8.06725	0.550182
$216$	9.91313	0.674503
$217$	0	0
$218$	−3.56885	−0.241713
$219$	−1.67744	−0.113351
$220$	4.17970	0.281796
$221$	39.6806	2.66921
$222$	−3.00783	−0.201872
$223$	−5.60903	−0.375609	−0.187804	−	0.982206i	$-0.560137\pi$
$223$	−5.60903	−0.375609	−0.187804	+	0.982206i	$0.560137\pi$
$224$	0	0
$225$	−2.90398	−0.193599
$226$	−37.0536	−2.46477
$227$	−22.5666	−1.49780	−0.748899	−	0.662684i	$-0.769417\pi$
$227$	−22.5666	−1.49780	−0.748899	+	0.662684i	$0.769417\pi$
$228$	2.57911	0.170806
$229$	1.39968	0.0924936	0.0462468	−	0.998930i	$-0.485274\pi$
$229$	1.39968	0.0924936	0.0462468	+	0.998930i	$0.485274\pi$
$230$	8.26531	0.544998
$231$	0	0
$232$	13.1855	0.865671
$233$	−21.1444	−1.38522	−0.692609	−	0.721313i	$-0.743539\pi$
$233$	−21.1444	−1.38522	−0.692609	+	0.721313i	$0.743539\pi$
$234$	43.9905	2.87575
$235$	−8.07885	−0.527006
$236$	−9.94527	−0.647382
$237$	4.91326	0.319150
$238$	0	0
$239$	0.855172	0.0553165	0.0276582	−	0.999617i	$-0.491195\pi$
$239$	0.855172	0.0553165	0.0276582	+	0.999617i	$0.491195\pi$
$240$	1.58362	0.102222
$241$	23.9172	1.54064	0.770322	−	0.637655i	$-0.220095\pi$
$241$	23.9172	1.54064	0.770322	+	0.637655i	$0.220095\pi$
$242$	2.48590	0.159800
$243$	−8.01239	−0.513995
$244$	−38.4013	−2.45839
$245$	0	0
$246$	−3.33113	−0.212385
$247$	12.1345	0.772098
$248$	1.78505	0.113351
$249$	−4.13204	−0.261857
$250$	−2.48590	−0.157222
$251$	−7.85038	−0.495512	−0.247756	−	0.968823i	$-0.579693\pi$
$251$	−7.85038	−0.495512	−0.247756	+	0.968823i	$0.579693\pi$
$252$	0	0
$253$	3.32487	0.209033
$254$	18.0786	1.13435
$255$	−2.01781	−0.126360
$256$	−32.6035	−2.03772
$257$	−0.521882	−0.0325541	−0.0162771	−	0.999868i	$-0.505181\pi$
$257$	−0.521882	−0.0325541	−0.0162771	+	0.999868i	$0.505181\pi$
$258$	6.21432	0.386887
$259$	0	0
$260$	25.4699	1.57958
$261$	−7.06657	−0.437410
$262$	4.89957	0.302696
$263$	−3.29635	−0.203262	−0.101631	−	0.994822i	$-0.532406\pi$
$263$	−3.29635	−0.203262	−0.101631	+	0.994822i	$0.532406\pi$
$264$	1.67906	0.103339
$265$	−12.2063	−0.749824
$266$	0	0
$267$	4.21610	0.258021
$268$	32.0550	1.95807
$269$	−8.74090	−0.532942	−0.266471	−	0.963843i	$-0.585858\pi$
$269$	−8.74090	−0.532942	−0.266471	+	0.963843i	$0.585858\pi$
$270$	−4.54792	−0.276778
$271$	8.44805	0.513183	0.256591	−	0.966520i	$-0.417401\pi$
$271$	8.44805	0.513183	0.256591	+	0.966520i	$0.417401\pi$
$272$	−33.2784	−2.01780
$273$	0	0
$274$	−4.71811	−0.285032
$275$	−1.00000	−0.0603023
$276$	4.30631	0.259209
$277$	16.3588	0.982903	0.491452	−	0.870905i	$-0.336466\pi$
$277$	16.3588	0.982903	0.491452	+	0.870905i	$0.336466\pi$
$278$	−18.1722	−1.08990
$279$	−0.956670	−0.0572743
$280$	0	0
$281$	−4.44573	−0.265210	−0.132605	−	0.991169i	$-0.542334\pi$
$281$	−4.44573	−0.265210	−0.132605	+	0.991169i	$0.542334\pi$
$282$	−6.22326	−0.370590
$283$	−22.7706	−1.35357	−0.676785	−	0.736181i	$-0.736627\pi$
$283$	−22.7706	−1.35357	−0.676785	+	0.736181i	$0.736627\pi$
$284$	19.7555	1.17228
$285$	−0.617055	−0.0365512
$286$	15.1484	0.895741
$287$	0	0
$288$	−5.42229	−0.319511
$289$	25.4026	1.49427
$290$	−6.04922	−0.355222
$291$	−5.54031	−0.324779
$292$	22.6260	1.32408
$293$	−3.65128	−0.213310	−0.106655	−	0.994296i	$-0.534014\pi$
$293$	−3.65128	−0.213310	−0.106655	+	0.994296i	$0.534014\pi$
$294$	0	0
$295$	2.37942	0.138535
$296$	21.1576	1.22976
$297$	−1.82949	−0.106158
$298$	−30.9110	−1.79062
$299$	20.2608	1.17171
$300$	−1.29518	−0.0747773
$301$	0	0
$302$	−57.0036	−3.28019
$303$	1.71821	0.0987086
$304$	−10.1766	−0.583671
$305$	9.18757	0.526079
$306$	47.0082	2.68728
$307$	33.4220	1.90750	0.953748	−	0.300607i	$-0.0971892\pi$
$307$	33.4220	1.90750	0.953748	+	0.300607i	$0.0971892\pi$
$308$	0	0
$309$	0.687012	0.0390827
$310$	−0.818941	−0.0465127
$311$	−6.75025	−0.382772	−0.191386	−	0.981515i	$-0.561298\pi$
$311$	−6.75025	−0.382772	−0.191386	+	0.981515i	$0.561298\pi$
$312$	10.2317	0.579256
$313$	5.19374	0.293567	0.146784	−	0.989169i	$-0.453108\pi$
$313$	5.19374	0.293567	0.146784	+	0.989169i	$0.453108\pi$
$314$	10.2866	0.580504
$315$	0	0
$316$	−66.2721	−3.72809
$317$	18.3036	1.02803	0.514016	−	0.857780i	$-0.328157\pi$
$317$	18.3036	1.02803	0.514016	+	0.857780i	$0.328157\pi$
$318$	−9.40266	−0.527275
$319$	−2.43341	−0.136245
$320$	5.57939	0.311897
$321$	3.35964	0.187517
$322$	0	0
$323$	12.9669	0.721497
$324$	34.0438	1.89132
$325$	−6.09371	−0.338018
$326$	−53.1589	−2.94420
$327$	0.444865	0.0246011
$328$	23.4318	1.29380
$329$	0	0
$330$	−0.770315	−0.0424045
$331$	−0.328367	−0.0180487	−0.00902435	−	0.999959i	$-0.502873\pi$
$331$	−0.328367	−0.0180487	−0.00902435	+	0.999959i	$0.502873\pi$
$332$	55.7347	3.05884
$333$	−11.3391	−0.621378
$334$	−26.6392	−1.45763
$335$	−7.66921	−0.419014
$336$	0	0
$337$	27.4829	1.49709	0.748543	−	0.663086i	$-0.230754\pi$
$337$	27.4829	1.49709	0.748543	+	0.663086i	$0.230754\pi$
$338$	59.9929	3.26318
$339$	4.61882	0.250860
$340$	27.2171	1.47606
$341$	−0.329434	−0.0178399
$342$	14.3753	0.777327
$343$	0	0
$344$	−43.7126	−2.35683
$345$	−1.03029	−0.0554690
$346$	−7.33938	−0.394567
$347$	30.2668	1.62481	0.812403	−	0.583096i	$-0.198159\pi$
$347$	30.2668	1.62481	0.812403	+	0.583096i	$0.198159\pi$
$348$	−3.15171	−0.168949
$349$	−35.5537	−1.90315	−0.951573	−	0.307423i	$-0.900533\pi$
$349$	−35.5537	−1.90315	−0.951573	+	0.307423i	$0.900533\pi$
$350$	0	0
$351$	−11.1484	−0.595055
$352$	−1.86719	−0.0995217
$353$	32.9914	1.75596	0.877978	−	0.478701i	$-0.158892\pi$
$353$	32.9914	1.75596	0.877978	+	0.478701i	$0.158892\pi$
$354$	1.83290	0.0974177
$355$	−4.72654	−0.250859
$356$	−56.8686	−3.01403
$357$	0	0
$358$	56.6656	2.99487
$359$	0.619992	0.0327219	0.0163610	−	0.999866i	$-0.494792\pi$
$359$	0.619992	0.0327219	0.0163610	+	0.999866i	$0.494792\pi$
$360$	15.7353	0.829323
$361$	−15.0347	−0.791299
$362$	0.986464	0.0518474
$363$	−0.309874	−0.0162641
$364$	0	0
$365$	−5.41329	−0.283345
$366$	7.07732	0.369938
$367$	−12.0625	−0.629656	−0.314828	−	0.949149i	$-0.601947\pi$
$367$	−12.0625	−0.629656	−0.314828	+	0.949149i	$0.601947\pi$
$368$	−16.9918	−0.885761
$369$	−12.5579	−0.653738
$370$	−9.70664	−0.504624
$371$	0	0
$372$	−0.426677	−0.0221222
$373$	27.7369	1.43616	0.718081	−	0.695960i	$-0.245021\pi$
$373$	27.7369	1.43616	0.718081	+	0.695960i	$0.245021\pi$
$374$	16.1875	0.837037
$375$	0.309874	0.0160018
$376$	43.7755	2.25755
$377$	−14.8285	−0.763706
$378$	0	0
$379$	10.7808	0.553774	0.276887	−	0.960902i	$-0.410697\pi$
$379$	10.7808	0.553774	0.276887	+	0.960902i	$0.410697\pi$
$380$	8.32310	0.426966
$381$	−2.25354	−0.115453
$382$	−46.7075	−2.38976
$383$	−21.7195	−1.10982	−0.554908	−	0.831912i	$-0.687246\pi$
$383$	−21.7195	−1.10982	−0.554908	+	0.831912i	$0.687246\pi$
$384$	5.45507	0.278378
$385$	0	0
$386$	−31.6158	−1.60920
$387$	23.4271	1.19087
$388$	74.7301	3.79385
$389$	7.57871	0.384256	0.192128	−	0.981370i	$-0.438461\pi$
$389$	7.57871	0.384256	0.192128	+	0.981370i	$0.438461\pi$
$390$	−4.69407	−0.237694
$391$	21.6507	1.09492
$392$	0	0
$393$	−0.610743	−0.0308079
$394$	−13.6318	−0.686758
$395$	15.8557	0.797786
$396$	12.1378	0.609946
$397$	6.05681	0.303982	0.151991	−	0.988382i	$-0.451431\pi$
$397$	6.05681	0.303982	0.151991	+	0.988382i	$0.451431\pi$
$398$	28.8105	1.44414
$399$	0	0
$400$	5.11052	0.255526
$401$	−1.97385	−0.0985694	−0.0492847	−	0.998785i	$-0.515694\pi$
$401$	−1.97385	−0.0985694	−0.0492847	+	0.998785i	$0.515694\pi$
$402$	−5.90771	−0.294650
$403$	−2.00748	−0.0999995
$404$	−23.1759	−1.15305
$405$	−8.14503	−0.404730
$406$	0	0
$407$	−3.90467	−0.193548
$408$	10.9336	0.541293
$409$	−5.79110	−0.286351	−0.143176	−	0.989697i	$-0.545731\pi$
$409$	−5.79110	−0.286351	−0.143176	+	0.989697i	$0.545731\pi$
$410$	−10.7500	−0.530903
$411$	0.588124	0.0290100
$412$	−9.26670	−0.456538
$413$	0	0
$414$	24.0023	1.17965
$415$	−13.3346	−0.654570
$416$	−11.3781	−0.557859
$417$	2.26521	0.110928
$418$	4.95021	0.242123
$419$	32.6665	1.59587	0.797933	−	0.602747i	$-0.205927\pi$
$419$	32.6665	1.59587	0.797933	+	0.602747i	$0.205927\pi$
$420$	0	0
$421$	−32.1963	−1.56915	−0.784575	−	0.620034i	$-0.787119\pi$
$421$	−32.1963	−1.56915	−0.784575	+	0.620034i	$0.787119\pi$
$422$	−24.7784	−1.20620
$423$	−23.4608	−1.14070
$424$	66.1399	3.21204
$425$	−6.51173	−0.315865
$426$	−3.64092	−0.176403
$427$	0	0
$428$	−45.3162	−2.19044
$429$	−1.88828	−0.0911670
$430$	20.0544	0.967108
$431$	−27.8452	−1.34126	−0.670629	−	0.741793i	$-0.733976\pi$
$431$	−27.8452	−1.34126	−0.670629	+	0.741793i	$0.733976\pi$
$432$	9.34963	0.449834
$433$	13.2034	0.634516	0.317258	−	0.948339i	$-0.397238\pi$
$433$	13.2034	0.634516	0.317258	+	0.948339i	$0.397238\pi$
$434$	0	0
$435$	0.754050	0.0361539
$436$	−6.00053	−0.287373
$437$	6.62086	0.316719
$438$	−4.16994	−0.199247
$439$	23.5101	1.12208	0.561038	−	0.827790i	$-0.310402\pi$
$439$	23.5101	1.12208	0.561038	+	0.827790i	$0.310402\pi$
$440$	5.41853	0.258318
$441$	0	0
$442$	98.6420	4.69192
$443$	−21.5372	−1.02327	−0.511633	−	0.859204i	$-0.670959\pi$
$443$	−21.5372	−1.02327	−0.511633	+	0.859204i	$0.670959\pi$
$444$	−5.05726	−0.240007
$445$	13.6059	0.644981
$446$	−13.9435	−0.660244
$447$	3.85313	0.182247
$448$	0	0
$449$	−3.20153	−0.151090	−0.0755448	−	0.997142i	$-0.524070\pi$
$449$	−3.20153	−0.151090	−0.0755448	+	0.997142i	$0.524070\pi$
$450$	−7.21900	−0.340307
$451$	−4.32437	−0.203627
$452$	−62.3006	−2.93037
$453$	7.10563	0.333852
$454$	−56.0983	−2.63283
$455$	0	0
$456$	3.34353	0.156575
$457$	−32.0299	−1.49829	−0.749147	−	0.662404i	$-0.769536\pi$
$457$	−32.0299	−1.49829	−0.749147	+	0.662404i	$0.769536\pi$
$458$	3.47947	0.162585
$459$	−11.9131	−0.556057
$460$	13.8970	0.647951
$461$	−9.68419	−0.451038	−0.225519	−	0.974239i	$-0.572408\pi$
$461$	−9.68419	−0.451038	−0.225519	+	0.974239i	$0.572408\pi$
$462$	0	0
$463$	12.9357	0.601172	0.300586	−	0.953755i	$-0.402818\pi$
$463$	12.9357	0.601172	0.300586	+	0.953755i	$0.402818\pi$
$464$	12.4360	0.577327
$465$	0.102083	0.00473399
$466$	−52.5630	−2.43493
$467$	−33.7014	−1.55951	−0.779757	−	0.626082i	$-0.784658\pi$
$467$	−33.7014	−1.55951	−0.779757	+	0.626082i	$0.784658\pi$
$468$	73.9640	3.41899
$469$	0	0
$470$	−20.0832	−0.926370
$471$	−1.28224	−0.0590827
$472$	−12.8930	−0.593446
$473$	8.06725	0.370933
$474$	12.2139	0.561002
$475$	−1.99131	−0.0913677
$476$	0	0
$477$	−35.4467	−1.62299
$478$	2.12587	0.0972351
$479$	−27.3011	−1.24742	−0.623710	−	0.781656i	$-0.714375\pi$
$479$	−27.3011	−1.24742	−0.623710	+	0.781656i	$0.714375\pi$
$480$	0.578594	0.0264091
$481$	−23.7939	−1.08491
$482$	59.4559	2.70814
$483$	0	0
$484$	4.17970	0.189987
$485$	−17.8793	−0.811856
$486$	−19.9180	−0.903499
$487$	30.6494	1.38886	0.694429	−	0.719562i	$-0.255657\pi$
$487$	30.6494	1.38886	0.694429	+	0.719562i	$0.255657\pi$
$488$	−49.7831	−2.25358
$489$	6.62639	0.299656
$490$	0	0
$491$	27.1061	1.22328	0.611640	−	0.791136i	$-0.290510\pi$
$491$	27.1061	1.22328	0.611640	+	0.791136i	$0.290510\pi$
$492$	−5.60084	−0.252506
$493$	−15.8457	−0.713655
$494$	30.1651	1.35719
$495$	−2.90398	−0.130524
$496$	1.68358	0.0755950
$497$	0	0
$498$	−10.2718	−0.460292
$499$	18.1558	0.812765	0.406382	−	0.913703i	$-0.366790\pi$
$499$	18.1558	0.812765	0.406382	+	0.913703i	$0.366790\pi$
$500$	−4.17970	−0.186922
$501$	3.32064	0.148355
$502$	−19.5153	−0.871009
$503$	0.451977	0.0201527	0.0100763	−	0.999949i	$-0.496793\pi$
$503$	0.451977	0.0201527	0.0100763	+	0.999949i	$0.496793\pi$
$504$	0	0
$505$	5.54488	0.246744
$506$	8.26531	0.367438
$507$	−7.47826	−0.332121
$508$	30.3967	1.34864
$509$	−2.04251	−0.0905326	−0.0452663	−	0.998975i	$-0.514414\pi$
$509$	−2.04251	−0.0905326	−0.0452663	+	0.998975i	$0.514414\pi$
$510$	−5.01609	−0.222116
$511$	0	0
$512$	−45.8407	−2.02589
$513$	−3.64308	−0.160846
$514$	−1.29735	−0.0572236
$515$	2.21707	0.0976958
$516$	10.4485	0.459971
$517$	−8.07885	−0.355308
$518$	0	0
$519$	0.914871	0.0401584
$520$	33.0189	1.44798
$521$	−12.8633	−0.563551	−0.281775	−	0.959480i	$-0.590923\pi$
$521$	−12.8633	−0.563551	−0.281775	+	0.959480i	$0.590923\pi$
$522$	−17.5668	−0.768878
$523$	28.8748	1.26261	0.631304	−	0.775536i	$-0.282520\pi$
$523$	28.8748	1.26261	0.631304	+	0.775536i	$0.282520\pi$
$524$	8.23796	0.359877
$525$	0	0
$526$	−8.19440	−0.357293
$527$	−2.14519	−0.0934458
$528$	1.58362	0.0689180
$529$	−11.9452	−0.519357
$530$	−30.3435	−1.31804
$531$	6.90978	0.299859
$532$	0	0
$533$	−26.3515	−1.14141
$534$	10.4808	0.453549
$535$	10.8420	0.468739
$536$	41.5559	1.79494
$537$	−7.06351	−0.304813
$538$	−21.7290	−0.936805
$539$	0	0
$540$	−7.64672	−0.329062
$541$	−44.1207	−1.89690	−0.948448	−	0.316932i	$-0.897347\pi$
$541$	−44.1207	−1.89690	−0.948448	+	0.316932i	$0.897347\pi$
$542$	21.0010	0.902071
$543$	−0.122965	−0.00527694
$544$	−12.1587	−0.521298
$545$	1.43563	0.0614958
$546$	0	0
$547$	18.3638	0.785179	0.392590	−	0.919714i	$-0.371579\pi$
$547$	18.3638	0.785179	0.392590	+	0.919714i	$0.371579\pi$
$548$	−7.93287	−0.338875
$549$	26.6805	1.13870
$550$	−2.48590	−0.105999
$551$	−4.84568	−0.206433
$552$	5.58266	0.237614
$553$	0	0
$554$	40.6663	1.72775
$555$	1.20996	0.0513598
$556$	−30.5541	−1.29578
$557$	27.1334	1.14968	0.574840	−	0.818266i	$-0.305064\pi$
$557$	27.1334	1.14968	0.574840	+	0.818266i	$0.305064\pi$
$558$	−2.37819	−0.100677
$559$	49.1595	2.07922
$560$	0	0
$561$	−2.01781	−0.0851922
$562$	−11.0516	−0.466185
$563$	−2.71725	−0.114519	−0.0572593	−	0.998359i	$-0.518236\pi$
$563$	−2.71725	−0.114519	−0.0572593	+	0.998359i	$0.518236\pi$
$564$	−10.4636	−0.440596
$565$	14.9055	0.627079
$566$	−56.6054	−2.37930
$567$	0	0
$568$	25.6109	1.07461
$569$	26.8179	1.12427	0.562133	−	0.827047i	$-0.309981\pi$
$569$	26.8179	1.12427	0.562133	+	0.827047i	$0.309981\pi$
$570$	−1.53394	−0.0642496
$571$	30.7681	1.28760	0.643802	−	0.765192i	$-0.277356\pi$
$571$	30.7681	1.28760	0.643802	+	0.765192i	$0.277356\pi$
$572$	25.4699	1.06495
$573$	5.82220	0.243226
$574$	0	0
$575$	−3.32487	−0.138657
$576$	16.2024	0.675101
$577$	−13.1398	−0.547017	−0.273508	−	0.961870i	$-0.588184\pi$
$577$	−13.1398	−0.547017	−0.273508	+	0.961870i	$0.588184\pi$
$578$	63.1485	2.62663
$579$	3.94099	0.163782
$580$	−10.1709	−0.422325
$581$	0	0
$582$	−13.7727	−0.570896
$583$	−12.2063	−0.505531
$584$	29.3321	1.21377
$585$	−17.6960	−0.731639
$586$	−9.07672	−0.374956
$587$	−38.9016	−1.60564	−0.802821	−	0.596220i	$-0.796669\pi$
$587$	−38.9016	−1.60564	−0.802821	+	0.596220i	$0.796669\pi$
$588$	0	0
$589$	−0.656007	−0.0270303
$590$	5.91500	0.243517
$591$	1.69923	0.0698970
$592$	19.9549	0.820143
$593$	8.93188	0.366788	0.183394	−	0.983039i	$-0.441292\pi$
$593$	8.93188	0.366788	0.183394	+	0.983039i	$0.441292\pi$
$594$	−4.54792	−0.186604
$595$	0	0
$596$	−51.9726	−2.12888
$597$	−3.59130	−0.146982
$598$	50.3664	2.05963
$599$	38.6495	1.57917	0.789587	−	0.613639i	$-0.210295\pi$
$599$	38.6495	1.57917	0.789587	+	0.613639i	$0.210295\pi$
$600$	−1.67906	−0.0685473
$601$	−0.858268	−0.0350095	−0.0175047	−	0.999847i	$-0.505572\pi$
$601$	−0.858268	−0.0350095	−0.0175047	+	0.999847i	$0.505572\pi$
$602$	0	0
$603$	−22.2712	−0.906954
$604$	−95.8438	−3.89983
$605$	−1.00000	−0.0406558
$606$	4.27130	0.173510
$607$	−35.8541	−1.45527	−0.727637	−	0.685962i	$-0.759382\pi$
$607$	−35.8541	−1.45527	−0.727637	+	0.685962i	$0.759382\pi$
$608$	−3.71816	−0.150792
$609$	0	0
$610$	22.8394	0.924740
$611$	−49.2302	−1.99164
$612$	79.0379	3.19492
$613$	18.2029	0.735207	0.367604	−	0.929983i	$-0.380178\pi$
$613$	18.2029	0.735207	0.367604	+	0.929983i	$0.380178\pi$
$614$	83.0839	3.35299
$615$	1.34001	0.0540344
$616$	0	0
$617$	−42.3234	−1.70388	−0.851939	−	0.523641i	$-0.824573\pi$
$617$	−42.3234	−1.70388	−0.851939	+	0.523641i	$0.824573\pi$
$618$	1.70784	0.0686995
$619$	−43.5478	−1.75033	−0.875166	−	0.483822i	$-0.839248\pi$
$619$	−43.5478	−1.75033	−0.875166	+	0.483822i	$0.839248\pi$
$620$	−1.37694	−0.0552992
$621$	−6.08281	−0.244095
$622$	−16.7805	−0.672835
$623$	0	0
$624$	9.65009	0.386313
$625$	1.00000	0.0400000
$626$	12.9111	0.516032
$627$	−0.617055	−0.0246428
$628$	17.2954	0.690163
$629$	−25.4262	−1.01381
$630$	0	0
$631$	7.79085	0.310149	0.155074	−	0.987903i	$-0.450438\pi$
$631$	7.79085	0.310149	0.155074	+	0.987903i	$0.450438\pi$
$632$	−85.9145	−3.41749
$633$	3.08869	0.122764
$634$	45.5010	1.80707
$635$	−7.27246	−0.288599
$636$	−15.8093	−0.626879
$637$	0	0
$638$	−6.04922	−0.239491
$639$	−13.7258	−0.542983
$640$	17.6042	0.695867
$641$	−46.7504	−1.84653	−0.923265	−	0.384163i	$-0.874490\pi$
$641$	−46.7504	−1.84653	−0.923265	+	0.384163i	$0.874490\pi$
$642$	8.35172	0.329616
$643$	41.8374	1.64990	0.824952	−	0.565202i	$-0.191202\pi$
$643$	41.8374	1.64990	0.824952	+	0.565202i	$0.191202\pi$
$644$	0	0
$645$	−2.49983	−0.0984306
$646$	32.2344	1.26825
$647$	26.7640	1.05220	0.526100	−	0.850423i	$-0.323654\pi$
$647$	26.7640	1.05220	0.526100	+	0.850423i	$0.323654\pi$
$648$	44.1341	1.73375
$649$	2.37942	0.0934004
$650$	−15.1484	−0.594167
$651$	0	0
$652$	−89.3795	−3.50037
$653$	−1.26534	−0.0495164	−0.0247582	−	0.999693i	$-0.507882\pi$
$653$	−1.26534	−0.0495164	−0.0247582	+	0.999693i	$0.507882\pi$
$654$	1.10589	0.0432438
$655$	−1.97094	−0.0770111
$656$	22.0998	0.862853
$657$	−15.7201	−0.613299
$658$	0	0
$659$	−35.9967	−1.40223	−0.701116	−	0.713047i	$-0.747315\pi$
$659$	−35.9967	−1.40223	−0.701116	+	0.713047i	$0.747315\pi$
$660$	−1.29518	−0.0504148
$661$	10.8905	0.423590	0.211795	−	0.977314i	$-0.432069\pi$
$661$	10.8905	0.423590	0.211795	+	0.977314i	$0.432069\pi$
$662$	−0.816289	−0.0317260
$663$	−12.2960	−0.477536
$664$	72.2539	2.80400
$665$	0	0
$666$	−28.1879	−1.09226
$667$	−8.09078	−0.313276
$668$	−44.7902	−1.73298
$669$	1.73809	0.0671985
$670$	−19.0649	−0.736541
$671$	9.18757	0.354682
$672$	0	0
$673$	27.4766	1.05915	0.529573	−	0.848264i	$-0.322352\pi$
$673$	27.4766	1.05915	0.529573	+	0.848264i	$0.322352\pi$
$674$	68.3197	2.63158
$675$	1.82949	0.0704170
$676$	100.870	3.87961
$677$	51.2277	1.96884	0.984420	−	0.175832i	$-0.0562617\pi$
$677$	51.2277	1.96884	0.984420	+	0.175832i	$0.0562617\pi$
$678$	11.4819	0.440961
$679$	0	0
$680$	35.2840	1.35308
$681$	6.99279	0.267964
$682$	−0.818941	−0.0313589
$683$	−13.3292	−0.510029	−0.255015	−	0.966937i	$-0.582080\pi$
$683$	−13.3292	−0.510029	−0.255015	+	0.966937i	$0.582080\pi$
$684$	24.1701	0.924167
$685$	1.89795	0.0725169
$686$	0	0
$687$	−0.433725	−0.0165476
$688$	−41.2279	−1.57180
$689$	−74.3813	−2.83370
$690$	−2.56120	−0.0975032
$691$	35.5777	1.35344	0.676721	−	0.736240i	$-0.263401\pi$
$691$	35.5777	1.35344	0.676721	+	0.736240i	$0.263401\pi$
$692$	−12.3402	−0.469103
$693$	0	0
$694$	75.2403	2.85608
$695$	7.31010	0.277288
$696$	−4.08584	−0.154873
$697$	−28.1592	−1.06660
$698$	−88.3830	−3.34534
$699$	6.55211	0.247823
$700$	0	0
$701$	21.6278	0.816871	0.408435	−	0.912787i	$-0.366075\pi$
$701$	21.6278	0.816871	0.408435	+	0.912787i	$0.366075\pi$
$702$	−27.7137	−1.04599
$703$	−7.77543	−0.293256
$704$	5.57939	0.210281
$705$	2.50342	0.0942844
$706$	82.0134	3.08661
$707$	0	0
$708$	3.08178	0.115820
$709$	−24.2213	−0.909651	−0.454826	−	0.890581i	$-0.650298\pi$
$709$	−24.2213	−0.909651	−0.454826	+	0.890581i	$0.650298\pi$
$710$	−11.7497	−0.440959
$711$	46.0445	1.72681
$712$	−73.7239	−2.76292
$713$	−1.09533	−0.0410203
$714$	0	0
$715$	−6.09371	−0.227892
$716$	95.2755	3.56061
$717$	−0.264995	−0.00989642
$718$	1.54124	0.0575185
$719$	29.3678	1.09523	0.547617	−	0.836729i	$-0.315535\pi$
$719$	29.3678	1.09523	0.547617	+	0.836729i	$0.315535\pi$
$720$	14.8408	0.553086
$721$	0	0
$722$	−37.3747	−1.39094
$723$	−7.41132	−0.275630
$724$	1.65861	0.0616416
$725$	2.43341	0.0903746
$726$	−0.770315	−0.0285891
$727$	51.5250	1.91096	0.955478	−	0.295062i	$-0.0953403\pi$
$727$	51.5250	1.91096	0.955478	+	0.295062i	$0.0953403\pi$
$728$	0	0
$729$	−21.9522	−0.813046
$730$	−13.4569	−0.498062
$731$	52.5318	1.94296
$732$	11.8996	0.439820
$733$	−31.8109	−1.17496	−0.587480	−	0.809238i	$-0.699880\pi$
$733$	−31.8109	−1.17496	−0.587480	+	0.809238i	$0.699880\pi$
$734$	−29.9861	−1.10681
$735$	0	0
$736$	−6.20818	−0.228837
$737$	−7.66921	−0.282499
$738$	−31.2177	−1.14914
$739$	11.4682	0.421863	0.210932	−	0.977501i	$-0.432350\pi$
$739$	11.4682	0.421863	0.210932	+	0.977501i	$0.432350\pi$
$740$	−16.3204	−0.599949
$741$	−3.76015	−0.138133
$742$	0	0
$743$	4.45832	0.163560	0.0817799	−	0.996650i	$-0.473940\pi$
$743$	4.45832	0.163560	0.0817799	+	0.996650i	$0.473940\pi$
$744$	−0.553140	−0.0202791
$745$	12.4345	0.455565
$746$	68.9511	2.52448
$747$	−38.7234	−1.41681
$748$	27.2171	0.995156
$749$	0	0
$750$	0.770315	0.0281279
$751$	4.72577	0.172446	0.0862229	−	0.996276i	$-0.472520\pi$
$751$	4.72577	0.172446	0.0862229	+	0.996276i	$0.472520\pi$
$752$	41.2872	1.50559
$753$	2.43263	0.0886498
$754$	−36.8622	−1.34244
$755$	22.9307	0.834535
$756$	0	0
$757$	7.00746	0.254690	0.127345	−	0.991858i	$-0.459354\pi$
$757$	7.00746	0.254690	0.127345	+	0.991858i	$0.459354\pi$
$758$	26.8001	0.973423
$759$	−1.03029	−0.0373972
$760$	10.7900	0.391394
$761$	−38.7541	−1.40484	−0.702418	−	0.711765i	$-0.747896\pi$
$761$	−38.7541	−1.40484	−0.702418	+	0.711765i	$0.747896\pi$
$762$	−5.60209	−0.202942
$763$	0	0
$764$	−78.5323	−2.84120
$765$	−18.9099	−0.683690
$766$	−53.9926	−1.95083
$767$	14.4995	0.523546
$768$	10.1030	0.364559
$769$	−3.23226	−0.116558	−0.0582792	−	0.998300i	$-0.518561\pi$
$769$	−3.23226	−0.116558	−0.0582792	+	0.998300i	$0.518561\pi$
$770$	0	0
$771$	0.161718	0.00582412
$772$	−53.1577	−1.91319
$773$	−17.5297	−0.630499	−0.315250	−	0.949009i	$-0.602088\pi$
$773$	−17.5297	−0.630499	−0.315250	+	0.949009i	$0.602088\pi$
$774$	58.2375	2.09330
$775$	0.329434	0.0118336
$776$	96.8794	3.47777
$777$	0	0
$778$	18.8399	0.675444
$779$	−8.61118	−0.308528
$780$	−7.89245	−0.282595
$781$	−4.72654	−0.169129
$782$	53.8215	1.92465
$783$	4.45189	0.159098
$784$	0	0
$785$	−4.13796	−0.147690
$786$	−1.51825	−0.0541541
$787$	11.6524	0.415363	0.207681	−	0.978197i	$-0.433408\pi$
$787$	11.6524	0.415363	0.207681	+	0.978197i	$0.433408\pi$
$788$	−22.9199	−0.816489
$789$	1.02145	0.0363646
$790$	39.4157	1.40235
$791$	0	0
$792$	15.7353	0.559129
$793$	55.9864	1.98813
$794$	15.0566	0.534339
$795$	3.78239	0.134148
$796$	48.4409	1.71694
$797$	−49.0584	−1.73774	−0.868869	−	0.495042i	$-0.835153\pi$
$797$	−49.0584	−1.73774	−0.868869	+	0.495042i	$0.835153\pi$
$798$	0	0
$799$	−52.6073	−1.86111
$800$	1.86719	0.0660152
$801$	39.5112	1.39606
$802$	−4.90680	−0.173265
$803$	−5.41329	−0.191031
$804$	−9.93301	−0.350310
$805$	0	0
$806$	−4.99039	−0.175779
$807$	2.70858	0.0953464
$808$	−30.0451	−1.05698
$809$	9.17809	0.322684	0.161342	−	0.986899i	$-0.448418\pi$
$809$	9.17809	0.322684	0.161342	+	0.986899i	$0.448418\pi$
$810$	−20.2477	−0.711433
$811$	−14.4728	−0.508209	−0.254104	−	0.967177i	$-0.581781\pi$
$811$	−14.4728	−0.508209	−0.254104	+	0.967177i	$0.581781\pi$
$812$	0	0
$813$	−2.61783	−0.0918112
$814$	−9.70664	−0.340217
$815$	21.3842	0.749055
$816$	10.3121	0.360995
$817$	16.0644	0.562023
$818$	−14.3961	−0.503348
$819$	0	0
$820$	−18.0746	−0.631193
$821$	4.51828	0.157689	0.0788445	−	0.996887i	$-0.474877\pi$
$821$	4.51828	0.157689	0.0788445	+	0.996887i	$0.474877\pi$
$822$	1.46202	0.0509938
$823$	19.0502	0.664049	0.332025	−	0.943271i	$-0.392268\pi$
$823$	19.0502	0.664049	0.332025	+	0.943271i	$0.392268\pi$
$824$	−12.0133	−0.418502
$825$	0.309874	0.0107884
$826$	0	0
$827$	39.9612	1.38959	0.694794	−	0.719209i	$-0.255496\pi$
$827$	39.9612	1.38959	0.694794	+	0.719209i	$0.255496\pi$
$828$	40.3566	1.40249
$829$	6.35105	0.220581	0.110290	−	0.993899i	$-0.464822\pi$
$829$	6.35105	0.220581	0.110290	+	0.993899i	$0.464822\pi$
$830$	−33.1485	−1.15060
$831$	−5.06915	−0.175847
$832$	33.9992	1.17871
$833$	0	0
$834$	5.63108	0.194988
$835$	10.7161	0.370846
$836$	8.32310	0.287860
$837$	0.602696	0.0208322
$838$	81.2058	2.80521
$839$	−38.9846	−1.34590	−0.672949	−	0.739689i	$-0.734973\pi$
$839$	−38.9846	−1.34590	−0.672949	+	0.739689i	$0.734973\pi$
$840$	0	0
$841$	−23.0785	−0.795811
$842$	−80.0367	−2.75825
$843$	1.37761	0.0474475
$844$	−41.6616	−1.43405
$845$	−24.1333	−0.830210
$846$	−58.3213	−2.00513
$847$	0	0
$848$	62.3803	2.14215
$849$	7.05600	0.242161
$850$	−16.1875	−0.555227
$851$	−12.9826	−0.445036
$852$	−6.12172	−0.209727
$853$	−31.2311	−1.06933	−0.534666	−	0.845063i	$-0.679563\pi$
$853$	−31.2311	−1.06933	−0.534666	+	0.845063i	$0.679563\pi$
$854$	0	0
$855$	−5.78273	−0.197765
$856$	−58.7475	−2.00795
$857$	−22.4229	−0.765952	−0.382976	−	0.923758i	$-0.625101\pi$
$857$	−22.4229	−0.765952	−0.382976	+	0.923758i	$0.625101\pi$
$858$	−4.69407	−0.160253
$859$	−42.1822	−1.43924	−0.719619	−	0.694369i	$-0.755683\pi$
$859$	−42.1822	−1.43924	−0.719619	+	0.694369i	$0.755683\pi$
$860$	33.7187	1.14980
$861$	0	0
$862$	−69.2205	−2.35766
$863$	8.38842	0.285545	0.142772	−	0.989756i	$-0.454398\pi$
$863$	8.38842	0.285545	0.142772	+	0.989756i	$0.454398\pi$
$864$	3.41601	0.116215
$865$	2.95240	0.100385
$866$	32.8224	1.11535
$867$	−7.87161	−0.267334
$868$	0	0
$869$	15.8557	0.537867
$870$	1.87449	0.0635513
$871$	−46.7339	−1.58352
$872$	−7.77903	−0.263431
$873$	−51.9210	−1.75726
$874$	16.4588	0.556728
$875$	0	0
$876$	−7.01119	−0.236886
$877$	16.8319	0.568374	0.284187	−	0.958769i	$-0.408276\pi$
$877$	16.8319	0.568374	0.284187	+	0.958769i	$0.408276\pi$
$878$	58.4438	1.97238
$879$	1.13143	0.0381623
$880$	5.11052	0.172276
$881$	−26.8542	−0.904742	−0.452371	−	0.891830i	$-0.649422\pi$
$881$	−26.8542	−0.904742	−0.452371	+	0.891830i	$0.649422\pi$
$882$	0	0
$883$	23.1208	0.778076	0.389038	−	0.921222i	$-0.372808\pi$
$883$	23.1208	0.778076	0.389038	+	0.921222i	$0.372808\pi$
$884$	165.853	5.57824
$885$	−0.737319	−0.0247847
$886$	−53.5395	−1.79869
$887$	−21.4717	−0.720948	−0.360474	−	0.932769i	$-0.617385\pi$
$887$	−21.4717	−0.720948	−0.360474	+	0.932769i	$0.617385\pi$
$888$	−6.55618	−0.220011
$889$	0	0
$890$	33.8229	1.13375
$891$	−8.14503	−0.272869
$892$	−23.4441	−0.784966
$893$	−16.0875	−0.538348
$894$	9.57849	0.320353
$895$	−22.7948	−0.761946
$896$	0	0
$897$	−6.27829	−0.209626
$898$	−7.95869	−0.265585
$899$	0.801649	0.0267365
$900$	−12.1378	−0.404592
$901$	−79.4838	−2.64799
$902$	−10.7500	−0.357935
$903$	0	0
$904$	−80.7659	−2.68623
$905$	−0.396824	−0.0131909
$906$	17.6639	0.586844
$907$	−14.0397	−0.466180	−0.233090	−	0.972455i	$-0.574884\pi$
$907$	−14.0397	−0.466180	−0.233090	+	0.972455i	$0.574884\pi$
$908$	−94.3217	−3.13018
$909$	16.1022	0.534076
$910$	0	0
$911$	53.8144	1.78295	0.891476	−	0.453068i	$-0.149671\pi$
$911$	53.8144	1.78295	0.891476	+	0.453068i	$0.149671\pi$
$912$	3.15347	0.104422
$913$	−13.3346	−0.441311
$914$	−79.6231	−2.63370
$915$	−2.84698	−0.0941184
$916$	5.85026	0.193298
$917$	0	0
$918$	−29.6149	−0.977436
$919$	40.0450	1.32096	0.660481	−	0.750843i	$-0.270353\pi$
$919$	40.0450	1.32096	0.660481	+	0.750843i	$0.270353\pi$
$920$	18.0159	0.593968
$921$	−10.3566	−0.341262
$922$	−24.0739	−0.792833
$923$	−28.8021	−0.948034
$924$	0	0
$925$	3.90467	0.128385
$926$	32.1568	1.05674
$927$	6.43833	0.211462
$928$	4.54365	0.149153
$929$	−15.2957	−0.501836	−0.250918	−	0.968008i	$-0.580733\pi$
$929$	−15.2957	−0.501836	−0.250918	+	0.968008i	$0.580733\pi$
$930$	0.253768	0.00832139
$931$	0	0
$932$	−88.3776	−2.89490
$933$	2.09173	0.0684800
$934$	−83.7783	−2.74131
$935$	−6.51173	−0.212956
$936$	95.8863	3.13414
$937$	−57.6091	−1.88201	−0.941004	−	0.338394i	$-0.890116\pi$
$937$	−57.6091	−1.88201	−0.941004	+	0.338394i	$0.890116\pi$
$938$	0	0
$939$	−1.60940	−0.0525208
$940$	−33.7672	−1.10137
$941$	13.0800	0.426396	0.213198	−	0.977009i	$-0.431612\pi$
$941$	13.0800	0.426396	0.213198	+	0.977009i	$0.431612\pi$
$942$	−3.18753	−0.103855
$943$	−14.3780	−0.468212
$944$	−12.1601	−0.395777
$945$	0	0
$946$	20.0544	0.652024
$947$	5.81886	0.189088	0.0945438	−	0.995521i	$-0.469861\pi$
$947$	5.81886	0.189088	0.0945438	+	0.995521i	$0.469861\pi$
$948$	20.5360	0.666977
$949$	−32.9870	−1.07080
$950$	−4.95021	−0.160606
$951$	−5.67180	−0.183921
$952$	0	0
$953$	−1.20161	−0.0389238	−0.0194619	−	0.999811i	$-0.506195\pi$
$953$	−1.20161	−0.0389238	−0.0194619	+	0.999811i	$0.506195\pi$
$954$	−88.1170	−2.85289
$955$	18.7890	0.607996
$956$	3.57436	0.115603
$957$	0.754050	0.0243750
$958$	−67.8679	−2.19271
$959$	0	0
$960$	−1.72890	−0.0558002
$961$	−30.8915	−0.996499
$962$	−59.1494	−1.90705
$963$	31.4848	1.01458
$964$	99.9669	3.21972
$965$	12.7181	0.409409
$966$	0	0
$967$	−20.1908	−0.649291	−0.324646	−	0.945836i	$-0.605245\pi$
$967$	−20.1908	−0.649291	−0.324646	+	0.945836i	$0.605245\pi$
$968$	5.41853	0.174158
$969$	−4.01810	−0.129080
$970$	−44.4461	−1.42708
$971$	−46.7509	−1.50031	−0.750154	−	0.661263i	$-0.770021\pi$
$971$	−46.7509	−1.50031	−0.750154	+	0.661263i	$0.770021\pi$
$972$	−33.4894	−1.07417
$973$	0	0
$974$	76.1914	2.44133
$975$	1.88828	0.0604733
$976$	−46.9533	−1.50294
$977$	−44.2569	−1.41590	−0.707952	−	0.706260i	$-0.750381\pi$
$977$	−44.2569	−1.41590	−0.707952	+	0.706260i	$0.750381\pi$
$978$	16.4725	0.526734
$979$	13.6059	0.434846
$980$	0	0
$981$	4.16905	0.133108
$982$	67.3830	2.15028
$983$	27.1964	0.867429	0.433715	−	0.901050i	$-0.357203\pi$
$983$	27.1964	0.867429	0.433715	+	0.901050i	$0.357203\pi$
$984$	−7.26088	−0.231468
$985$	5.48363	0.174723
$986$	−39.3909	−1.25446
$987$	0	0
$988$	50.7185	1.61357
$989$	26.8226	0.852909
$990$	−7.21900	−0.229435
$991$	−32.6150	−1.03605	−0.518025	−	0.855365i	$-0.673333\pi$
$991$	−32.6150	−1.03605	−0.518025	+	0.855365i	$0.673333\pi$
$992$	0.615117	0.0195300
$993$	0.101752	0.00322901
$994$	0	0
$995$	−11.5896	−0.367414
$996$	−17.2707	−0.547243
$997$	14.8030	0.468816	0.234408	−	0.972138i	$-0.424685\pi$
$997$	14.8030	0.468816	0.234408	+	0.972138i	$0.424685\pi$
$998$	45.1335	1.42868
$999$	7.14355	0.226012

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.w.1.9	✓	10
7.6	odd	2		2695.2.a.x.1.9	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2695.2.a.w.1.9	✓	10	1.1	even	1	trivial
2695.2.a.x.1.9	yes	10	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2695.a (trivial)

\(f(q)\)	\(=\)	\(q+2.48590 q^{2} -0.309874 q^{3} +4.17970 q^{4} -1.00000 q^{5} -0.770315 q^{6} +5.41853 q^{8} -2.90398 q^{9} +O(q^{10})\)	\(q+2.48590 q^{2} -0.309874 q^{3} +4.17970 q^{4} -1.00000 q^{5} -0.770315 q^{6} +5.41853 q^{8} -2.90398 q^{9} -2.48590 q^{10} -1.00000 q^{11} -1.29518 q^{12} -6.09371 q^{13} +0.309874 q^{15} +5.11052 q^{16} -6.51173 q^{17} -7.21900 q^{18} -1.99131 q^{19} -4.17970 q^{20} -2.48590 q^{22} -3.32487 q^{23} -1.67906 q^{24} +1.00000 q^{25} -15.1484 q^{26} +1.82949 q^{27} +2.43341 q^{29} +0.770315 q^{30} +0.329434 q^{31} +1.86719 q^{32} +0.309874 q^{33} -16.1875 q^{34} -12.1378 q^{36} +3.90467 q^{37} -4.95021 q^{38} +1.88828 q^{39} -5.41853 q^{40} +4.32437 q^{41} -8.06725 q^{43} -4.17970 q^{44} +2.90398 q^{45} -8.26531 q^{46} +8.07885 q^{47} -1.58362 q^{48} +2.48590 q^{50} +2.01781 q^{51} -25.4699 q^{52} +12.2063 q^{53} +4.54792 q^{54} +1.00000 q^{55} +0.617055 q^{57} +6.04922 q^{58} -2.37942 q^{59} +1.29518 q^{60} -9.18757 q^{61} +0.818941 q^{62} -5.57939 q^{64} +6.09371 q^{65} +0.770315 q^{66} +7.66921 q^{67} -27.2171 q^{68} +1.03029 q^{69} +4.72654 q^{71} -15.7353 q^{72} +5.41329 q^{73} +9.70664 q^{74} -0.309874 q^{75} -8.32310 q^{76} +4.69407 q^{78} -15.8557 q^{79} -5.11052 q^{80} +8.14503 q^{81} +10.7500 q^{82} +13.3346 q^{83} +6.51173 q^{85} -20.0544 q^{86} -0.754050 q^{87} -5.41853 q^{88} -13.6059 q^{89} +7.21900 q^{90} -13.8970 q^{92} -0.102083 q^{93} +20.0832 q^{94} +1.99131 q^{95} -0.578594 q^{96} +17.8793 q^{97} +2.90398 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 10 q^{4} - 10 q^{5} - 4 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 10 * q^4 - 10 * q^5 - 4 * q^6 + 6 * q^8 + 10 * q^9	\( 10 q + 2 q^{2} + 10 q^{4} - 10 q^{5} - 4 q^{6} + 6 q^{8} + 10 q^{9} - 2 q^{10} - 10 q^{11} - 4 q^{12} - 8 q^{13} + 6 q^{16} - 28 q^{17} - 10 q^{18} - 8 q^{19} - 10 q^{20} - 2 q^{22} - 8 q^{23} - 32 q^{24} + 10 q^{25} - 12 q^{26} - 8 q^{29} + 4 q^{30} + 4 q^{31} + 14 q^{32} - 20 q^{34} - 22 q^{36} + 28 q^{37} - 24 q^{38} - 24 q^{39} - 6 q^{40} - 44 q^{41} + 20 q^{43} - 10 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} - 16 q^{48} + 2 q^{50} - 4 q^{51} - 36 q^{52} + 8 q^{54} + 10 q^{55} + 12 q^{57} - 8 q^{58} - 16 q^{59} + 4 q^{60} - 16 q^{61} - 36 q^{62} - 34 q^{64} + 8 q^{65} + 4 q^{66} + 20 q^{67} - 8 q^{68} - 4 q^{69} - 4 q^{71} + 10 q^{72} - 20 q^{73} - 16 q^{74} - 4 q^{76} + 52 q^{78} - 20 q^{79} - 6 q^{80} + 10 q^{81} + 32 q^{82} - 16 q^{83} + 28 q^{85} - 20 q^{86} - 20 q^{87} - 6 q^{88} - 44 q^{89} + 10 q^{90} - 24 q^{92} + 16 q^{93} - 24 q^{94} + 8 q^{95} + 4 q^{97} - 10 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 10 * q^4 - 10 * q^5 - 4 * q^6 + 6 * q^8 + 10 * q^9 - 2 * q^10 - 10 * q^11 - 4 * q^12 - 8 * q^13 + 6 * q^16 - 28 * q^17 - 10 * q^18 - 8 * q^19 - 10 * q^20 - 2 * q^22 - 8 * q^23 - 32 * q^24 + 10 * q^25 - 12 * q^26 - 8 * q^29 + 4 * q^30 + 4 * q^31 + 14 * q^32 - 20 * q^34 - 22 * q^36 + 28 * q^37 - 24 * q^38 - 24 * q^39 - 6 * q^40 - 44 * q^41 + 20 * q^43 - 10 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 - 16 * q^48 + 2 * q^50 - 4 * q^51 - 36 * q^52 + 8 * q^54 + 10 * q^55 + 12 * q^57 - 8 * q^58 - 16 * q^59 + 4 * q^60 - 16 * q^61 - 36 * q^62 - 34 * q^64 + 8 * q^65 + 4 * q^66 + 20 * q^67 - 8 * q^68 - 4 * q^69 - 4 * q^71 + 10 * q^72 - 20 * q^73 - 16 * q^74 - 4 * q^76 + 52 * q^78 - 20 * q^79 - 6 * q^80 + 10 * q^81 + 32 * q^82 - 16 * q^83 + 28 * q^85 - 20 * q^86 - 20 * q^87 - 6 * q^88 - 44 * q^89 + 10 * q^90 - 24 * q^92 + 16 * q^93 - 24 * q^94 + 8 * q^95 + 4 * q^97 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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