LMFDB - Embedded newform 7935.2.a.bl.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, 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("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{10} + 92x^{8} - 4x^{7} - 234x^{6} + 32x^{5} + 252x^{4} - 68x^{3} - 76x^{2} + 32x - 2 $ x^12 - 16x^10 + 92x^8 - 4x^7 - 234x^6 + 32x^5 + 252x^4 - 68x^3 - 76x^2 + 32*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.64536$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.64536 q^{2} +1.00000 q^{3} +0.707219 q^{4} -1.00000 q^{5} -1.64536 q^{6} -0.989641 q^{7} +2.12709 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.64536 q^{2} +1.00000 q^{3} +0.707219 q^{4} -1.00000 q^{5} -1.64536 q^{6} -0.989641 q^{7} +2.12709 q^{8} +1.00000 q^{9} +1.64536 q^{10} +1.34525 q^{11} +0.707219 q^{12} -2.26203 q^{13} +1.62832 q^{14} -1.00000 q^{15} -4.91428 q^{16} -3.15546 q^{17} -1.64536 q^{18} +3.44375 q^{19} -0.707219 q^{20} -0.989641 q^{21} -2.21342 q^{22} +2.12709 q^{24} +1.00000 q^{25} +3.72186 q^{26} +1.00000 q^{27} -0.699893 q^{28} +4.14367 q^{29} +1.64536 q^{30} -1.63544 q^{31} +3.83159 q^{32} +1.34525 q^{33} +5.19187 q^{34} +0.989641 q^{35} +0.707219 q^{36} +7.10804 q^{37} -5.66621 q^{38} -2.26203 q^{39} -2.12709 q^{40} +1.58787 q^{41} +1.62832 q^{42} +5.99652 q^{43} +0.951387 q^{44} -1.00000 q^{45} -4.40732 q^{47} -4.91428 q^{48} -6.02061 q^{49} -1.64536 q^{50} -3.15546 q^{51} -1.59975 q^{52} -3.12338 q^{53} -1.64536 q^{54} -1.34525 q^{55} -2.10506 q^{56} +3.44375 q^{57} -6.81785 q^{58} -1.32147 q^{59} -0.707219 q^{60} -8.72696 q^{61} +2.69089 q^{62} -0.989641 q^{63} +3.52421 q^{64} +2.26203 q^{65} -2.21342 q^{66} +6.20230 q^{67} -2.23160 q^{68} -1.62832 q^{70} -13.1896 q^{71} +2.12709 q^{72} +6.78962 q^{73} -11.6953 q^{74} +1.00000 q^{75} +2.43548 q^{76} -1.33131 q^{77} +3.72186 q^{78} -16.4459 q^{79} +4.91428 q^{80} +1.00000 q^{81} -2.61262 q^{82} +4.32576 q^{83} -0.699893 q^{84} +3.15546 q^{85} -9.86645 q^{86} +4.14367 q^{87} +2.86147 q^{88} +11.4638 q^{89} +1.64536 q^{90} +2.23859 q^{91} -1.63544 q^{93} +7.25163 q^{94} -3.44375 q^{95} +3.83159 q^{96} -0.241541 q^{97} +9.90609 q^{98} +1.34525 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9	$ 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9} + 24 q^{11} + 8 q^{12} - 8 q^{13} + 16 q^{14} - 12 q^{15} + 28 q^{17} + 16 q^{19} - 8 q^{20} + 4 q^{21} + 12 q^{25} - 36 q^{26} + 12 q^{27} + 8 q^{28} - 16 q^{29} + 20 q^{32} + 24 q^{33} + 16 q^{34} - 4 q^{35} + 8 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{39} - 4 q^{41} + 16 q^{42} - 12 q^{43} + 16 q^{44} - 12 q^{45} + 4 q^{47} + 24 q^{49} + 28 q^{51} - 36 q^{52} + 28 q^{53} - 24 q^{55} + 56 q^{56} + 16 q^{57} + 20 q^{59} - 8 q^{60} + 32 q^{61} + 12 q^{62} + 4 q^{63} - 4 q^{64} + 8 q^{65} - 4 q^{67} + 64 q^{68} - 16 q^{70} - 8 q^{71} + 4 q^{73} - 36 q^{74} + 12 q^{75} + 8 q^{76} - 28 q^{77} - 36 q^{78} + 40 q^{79} + 12 q^{81} - 28 q^{82} + 100 q^{83} + 8 q^{84} - 28 q^{85} - 20 q^{86} - 16 q^{87} + 80 q^{89} - 24 q^{91} + 44 q^{94} - 16 q^{95} + 20 q^{96} - 8 q^{97} + 28 q^{98} + 24 q^{99}+O(q^{100}) $ 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9 + 24 * q^11 + 8 * q^12 - 8 * q^13 + 16 * q^14 - 12 * q^15 + 28 * q^17 + 16 * q^19 - 8 * q^20 + 4 * q^21 + 12 * q^25 - 36 * q^26 + 12 * q^27 + 8 * q^28 - 16 * q^29 + 20 * q^32 + 24 * q^33 + 16 * q^34 - 4 * q^35 + 8 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^39 - 4 * q^41 + 16 * q^42 - 12 * q^43 + 16 * q^44 - 12 * q^45 + 4 * q^47 + 24 * q^49 + 28 * q^51 - 36 * q^52 + 28 * q^53 - 24 * q^55 + 56 * q^56 + 16 * q^57 + 20 * q^59 - 8 * q^60 + 32 * q^61 + 12 * q^62 + 4 * q^63 - 4 * q^64 + 8 * q^65 - 4 * q^67 + 64 * q^68 - 16 * q^70 - 8 * q^71 + 4 * q^73 - 36 * q^74 + 12 * q^75 + 8 * q^76 - 28 * q^77 - 36 * q^78 + 40 * q^79 + 12 * q^81 - 28 * q^82 + 100 * q^83 + 8 * q^84 - 28 * q^85 - 20 * q^86 - 16 * q^87 + 80 * q^89 - 24 * q^91 + 44 * q^94 - 16 * q^95 + 20 * q^96 - 8 * q^97 + 28 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.64536	−1.16345	−0.581724	−	0.813387i	$-0.697621\pi$
$2$	−1.64536	−1.16345	−0.581724	+	0.813387i	$0.697621\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.707219	0.353610
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.64536	−0.671717
$7$	−0.989641	−0.374049	−0.187024	−	0.982355i	$-0.559884\pi$
$7$	−0.989641	−0.374049	−0.187024	+	0.982355i	$0.559884\pi$
$8$	2.12709	0.752041
$9$	1.00000	0.333333
$10$	1.64536	0.520309
$11$	1.34525	0.405608	0.202804	−	0.979219i	$-0.434995\pi$
$11$	1.34525	0.405608	0.202804	+	0.979219i	$0.434995\pi$
$12$	0.707219	0.204157
$13$	−2.26203	−0.627374	−0.313687	−	0.949526i	$-0.601564\pi$
$13$	−2.26203	−0.627374	−0.313687	+	0.949526i	$0.601564\pi$
$14$	1.62832	0.435186
$15$	−1.00000	−0.258199
$16$	−4.91428	−1.22857
$17$	−3.15546	−0.765311	−0.382655	−	0.923891i	$-0.624990\pi$
$17$	−3.15546	−0.765311	−0.382655	+	0.923891i	$0.624990\pi$
$18$	−1.64536	−0.387816
$19$	3.44375	0.790050	0.395025	−	0.918670i	$-0.370736\pi$
$19$	3.44375	0.790050	0.395025	+	0.918670i	$0.370736\pi$
$20$	−0.707219	−0.158139
$21$	−0.989641	−0.215957
$22$	−2.21342	−0.471904
$23$	0	0
$23$	0	0
$24$	2.12709	0.434191
$25$	1.00000	0.200000
$26$	3.72186	0.729916
$27$	1.00000	0.192450
$28$	−0.699893	−0.132267
$29$	4.14367	0.769461	0.384730	−	0.923029i	$-0.374294\pi$
$29$	4.14367	0.769461	0.384730	+	0.923029i	$0.374294\pi$
$30$	1.64536	0.300401
$31$	−1.63544	−0.293734	−0.146867	−	0.989156i	$-0.546919\pi$
$31$	−1.63544	−0.293734	−0.146867	+	0.989156i	$0.546919\pi$
$32$	3.83159	0.677335
$33$	1.34525	0.234178
$34$	5.19187	0.890399
$35$	0.989641	0.167280
$36$	0.707219	0.117870
$37$	7.10804	1.16856	0.584278	−	0.811554i	$-0.301378\pi$
$37$	7.10804	1.16856	0.584278	+	0.811554i	$0.301378\pi$
$38$	−5.66621	−0.919181
$39$	−2.26203	−0.362214
$40$	−2.12709	−0.336323
$41$	1.58787	0.247983	0.123992	−	0.992283i	$-0.460430\pi$
$41$	1.58787	0.247983	0.123992	+	0.992283i	$0.460430\pi$
$42$	1.62832	0.251255
$43$	5.99652	0.914461	0.457230	−	0.889348i	$-0.348842\pi$
$43$	5.99652	0.914461	0.457230	+	0.889348i	$0.348842\pi$
$44$	0.951387	0.143427
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−4.40732	−0.642873	−0.321437	−	0.946931i	$-0.604166\pi$
$47$	−4.40732	−0.642873	−0.321437	+	0.946931i	$0.604166\pi$
$48$	−4.91428	−0.709315
$49$	−6.02061	−0.860087
$50$	−1.64536	−0.232689
$51$	−3.15546	−0.441852
$52$	−1.59975	−0.221845
$53$	−3.12338	−0.429029	−0.214515	−	0.976721i	$-0.568817\pi$
$53$	−3.12338	−0.429029	−0.214515	+	0.976721i	$0.568817\pi$
$54$	−1.64536	−0.223906
$55$	−1.34525	−0.181394
$56$	−2.10506	−0.281300
$57$	3.44375	0.456135
$58$	−6.81785	−0.895227
$59$	−1.32147	−0.172041	−0.0860204	−	0.996293i	$-0.527415\pi$
$59$	−1.32147	−0.172041	−0.0860204	+	0.996293i	$0.527415\pi$
$60$	−0.707219	−0.0913016
$61$	−8.72696	−1.11737	−0.558686	−	0.829379i	$-0.688694\pi$
$61$	−8.72696	−1.11737	−0.558686	+	0.829379i	$0.688694\pi$
$62$	2.69089	0.341744
$63$	−0.989641	−0.124683
$64$	3.52421	0.440526
$65$	2.26203	0.280570
$66$	−2.21342	−0.272454
$67$	6.20230	0.757732	0.378866	−	0.925452i	$-0.376314\pi$
$67$	6.20230	0.757732	0.378866	+	0.925452i	$0.376314\pi$
$68$	−2.23160	−0.270621
$69$	0	0
$70$	−1.62832	−0.194621
$71$	−13.1896	−1.56532	−0.782660	−	0.622450i	$-0.786138\pi$
$71$	−13.1896	−1.56532	−0.782660	+	0.622450i	$0.786138\pi$
$72$	2.12709	0.250680
$73$	6.78962	0.794665	0.397332	−	0.917675i	$-0.369936\pi$
$73$	6.78962	0.794665	0.397332	+	0.917675i	$0.369936\pi$
$74$	−11.6953	−1.35955
$75$	1.00000	0.115470
$76$	2.43548	0.279369
$77$	−1.33131	−0.151717
$78$	3.72186	0.421417
$79$	−16.4459	−1.85031	−0.925156	−	0.379587i	$-0.876066\pi$
$79$	−16.4459	−1.85031	−0.925156	+	0.379587i	$0.876066\pi$
$80$	4.91428	0.549433
$81$	1.00000	0.111111
$82$	−2.61262	−0.288515
$83$	4.32576	0.474814	0.237407	−	0.971410i	$-0.423703\pi$
$83$	4.32576	0.474814	0.237407	+	0.971410i	$0.423703\pi$
$84$	−0.699893	−0.0763646
$85$	3.15546	0.342257
$86$	−9.86645	−1.06393
$87$	4.14367	0.444248
$88$	2.86147	0.305034
$89$	11.4638	1.21516	0.607581	−	0.794257i	$-0.292140\pi$
$89$	11.4638	1.21516	0.607581	+	0.794257i	$0.292140\pi$
$90$	1.64536	0.173436
$91$	2.23859	0.234668
$92$	0	0
$93$	−1.63544	−0.169587
$94$	7.25163	0.747949
$95$	−3.44375	−0.353321
$96$	3.83159	0.391060
$97$	−0.241541	−0.0245247	−0.0122624	−	0.999925i	$-0.503903\pi$
$97$	−0.241541	−0.0245247	−0.0122624	+	0.999925i	$0.503903\pi$
$98$	9.90609	1.00067
$99$	1.34525	0.135203
$100$	0.707219	0.0707219
$101$	−4.26291	−0.424176	−0.212088	−	0.977251i	$-0.568026\pi$
$101$	−4.26291	−0.424176	−0.212088	+	0.977251i	$0.568026\pi$
$102$	5.19187	0.514072
$103$	1.83946	0.181247	0.0906235	−	0.995885i	$-0.471114\pi$
$103$	1.83946	0.181247	0.0906235	+	0.995885i	$0.471114\pi$
$104$	−4.81155	−0.471811
$105$	0.989641	0.0965790
$106$	5.13910	0.499153
$107$	1.80235	0.174239	0.0871197	−	0.996198i	$-0.472234\pi$
$107$	1.80235	0.174239	0.0871197	+	0.996198i	$0.472234\pi$
$108$	0.707219	0.0680522
$109$	2.92323	0.279995	0.139998	−	0.990152i	$-0.455291\pi$
$109$	2.92323	0.279995	0.139998	+	0.990152i	$0.455291\pi$
$110$	2.21342	0.211042
$111$	7.10804	0.674666
$112$	4.86337	0.459545
$113$	10.5134	0.989022	0.494511	−	0.869171i	$-0.335347\pi$
$113$	10.5134	0.989022	0.494511	+	0.869171i	$0.335347\pi$
$114$	−5.66621	−0.530689
$115$	0	0
$116$	2.93048	0.272089
$117$	−2.26203	−0.209125
$118$	2.17430	0.200160
$119$	3.12277	0.286264
$120$	−2.12709	−0.194176
$121$	−9.19030	−0.835482
$122$	14.3590	1.30000
$123$	1.58787	0.143173
$124$	−1.15661	−0.103867
$125$	−1.00000	−0.0894427
$126$	1.62832	0.145062
$127$	5.75709	0.510860	0.255430	−	0.966828i	$-0.417783\pi$
$127$	5.75709	0.510860	0.255430	+	0.966828i	$0.417783\pi$
$128$	−13.4618	−1.18986
$129$	5.99652	0.527964
$130$	−3.72186	−0.326428
$131$	14.2902	1.24854	0.624268	−	0.781210i	$-0.285397\pi$
$131$	14.2902	1.24854	0.624268	+	0.781210i	$0.285397\pi$
$132$	0.951387	0.0828076
$133$	−3.40807	−0.295517
$134$	−10.2050	−0.881581
$135$	−1.00000	−0.0860663
$136$	−6.71195	−0.575545
$137$	9.83155	0.839966	0.419983	−	0.907532i	$-0.362036\pi$
$137$	9.83155	0.839966	0.419983	+	0.907532i	$0.362036\pi$
$138$	0	0
$139$	12.3806	1.05010	0.525052	−	0.851070i	$-0.324046\pi$
$139$	12.3806	1.05010	0.525052	+	0.851070i	$0.324046\pi$
$140$	0.699893	0.0591517
$141$	−4.40732	−0.371163
$142$	21.7017	1.82117
$143$	−3.04299	−0.254468
$144$	−4.91428	−0.409523
$145$	−4.14367	−0.344113
$146$	−11.1714	−0.924550
$147$	−6.02061	−0.496572
$148$	5.02694	0.413212
$149$	22.7817	1.86635	0.933177	−	0.359418i	$-0.117025\pi$
$149$	22.7817	1.86635	0.933177	+	0.359418i	$0.117025\pi$
$150$	−1.64536	−0.134343
$151$	−14.2114	−1.15651	−0.578255	−	0.815856i	$-0.696266\pi$
$151$	−14.2114	−1.15651	−0.578255	+	0.815856i	$0.696266\pi$
$152$	7.32517	0.594150
$153$	−3.15546	−0.255104
$154$	2.19049	0.176515
$155$	1.63544	0.131362
$156$	−1.59975	−0.128082
$157$	10.7430	0.857388	0.428694	−	0.903450i	$-0.358974\pi$
$157$	10.7430	0.857388	0.428694	+	0.903450i	$0.358974\pi$
$158$	27.0595	2.15274
$159$	−3.12338	−0.247700
$160$	−3.83159	−0.302913
$161$	0	0
$162$	−1.64536	−0.129272
$163$	−10.2792	−0.805130	−0.402565	−	0.915391i	$-0.631881\pi$
$163$	−10.2792	−0.805130	−0.402565	+	0.915391i	$0.631881\pi$
$164$	1.12297	0.0876892
$165$	−1.34525	−0.104728
$166$	−7.11745	−0.552421
$167$	11.7815	0.911680	0.455840	−	0.890062i	$-0.349339\pi$
$167$	11.7815	0.911680	0.455840	+	0.890062i	$0.349339\pi$
$168$	−2.10506	−0.162409
$169$	−7.88323	−0.606402
$170$	−5.19187	−0.398198
$171$	3.44375	0.263350
$172$	4.24085	0.323362
$173$	−8.71562	−0.662636	−0.331318	−	0.943519i	$-0.607493\pi$
$173$	−8.71562	−0.662636	−0.331318	+	0.943519i	$0.607493\pi$
$174$	−6.81785	−0.516860
$175$	−0.989641	−0.0748098
$176$	−6.61094	−0.498318
$177$	−1.32147	−0.0993278
$178$	−18.8621	−1.41378
$179$	8.28847	0.619509	0.309755	−	0.950816i	$-0.399753\pi$
$179$	8.28847	0.619509	0.309755	+	0.950816i	$0.399753\pi$
$180$	−0.707219	−0.0527130
$181$	6.87424	0.510958	0.255479	−	0.966815i	$-0.417767\pi$
$181$	6.87424	0.510958	0.255479	+	0.966815i	$0.417767\pi$
$182$	−3.68330	−0.273024
$183$	−8.72696	−0.645115
$184$	0	0
$185$	−7.10804	−0.522594
$186$	2.69089	0.197306
$187$	−4.24488	−0.310416
$188$	−3.11694	−0.227326
$189$	−0.989641	−0.0719858
$190$	5.66621	0.411070
$191$	23.0453	1.66750	0.833750	−	0.552141i	$-0.186189\pi$
$191$	23.0453	1.66750	0.833750	+	0.552141i	$0.186189\pi$
$192$	3.52421	0.254338
$193$	−23.7942	−1.71274	−0.856372	−	0.516359i	$-0.827287\pi$
$193$	−23.7942	−1.71274	−0.856372	+	0.516359i	$0.827287\pi$
$194$	0.397422	0.0285333
$195$	2.26203	0.161987
$196$	−4.25789	−0.304135
$197$	−21.0439	−1.49932	−0.749660	−	0.661824i	$-0.769783\pi$
$197$	−21.0439	−1.49932	−0.749660	+	0.661824i	$0.769783\pi$
$198$	−2.21342	−0.157301
$199$	−22.7884	−1.61543	−0.807715	−	0.589573i	$-0.799296\pi$
$199$	−22.7884	−1.61543	−0.807715	+	0.589573i	$0.799296\pi$
$200$	2.12709	0.150408
$201$	6.20230	0.437477
$202$	7.01404	0.493506
$203$	−4.10075	−0.287816
$204$	−2.23160	−0.156243
$205$	−1.58787	−0.110901
$206$	−3.02657	−0.210871
$207$	0	0
$208$	11.1162	0.770772
$209$	4.63270	0.320451
$210$	−1.62832	−0.112365
$211$	26.0453	1.79303	0.896517	−	0.443010i	$-0.146089\pi$
$211$	26.0453	1.79303	0.896517	+	0.443010i	$0.146089\pi$
$212$	−2.20891	−0.151709
$213$	−13.1896	−0.903738
$214$	−2.96551	−0.202718
$215$	−5.99652	−0.408959
$216$	2.12709	0.144730
$217$	1.61850	0.109871
$218$	−4.80978	−0.325759
$219$	6.78962	0.458800
$220$	−0.951387	−0.0641425
$221$	7.13773	0.480136
$222$	−11.6953	−0.784938
$223$	−4.38399	−0.293574	−0.146787	−	0.989168i	$-0.546893\pi$
$223$	−4.38399	−0.293574	−0.146787	+	0.989168i	$0.546893\pi$
$224$	−3.79189	−0.253356
$225$	1.00000	0.0666667
$226$	−17.2984	−1.15067
$227$	−20.8311	−1.38261	−0.691305	−	0.722563i	$-0.742964\pi$
$227$	−20.8311	−1.38261	−0.691305	+	0.722563i	$0.742964\pi$
$228$	2.43548	0.161294
$229$	−12.7324	−0.841383	−0.420691	−	0.907204i	$-0.638212\pi$
$229$	−12.7324	−0.841383	−0.420691	+	0.907204i	$0.638212\pi$
$230$	0	0
$231$	−1.33131	−0.0875940
$232$	8.81398	0.578666
$233$	7.60430	0.498174	0.249087	−	0.968481i	$-0.419869\pi$
$233$	7.60430	0.498174	0.249087	+	0.968481i	$0.419869\pi$
$234$	3.72186	0.243305
$235$	4.40732	0.287502
$236$	−0.934569	−0.0608353
$237$	−16.4459	−1.06828
$238$	−5.13809	−0.333053
$239$	−0.697596	−0.0451238	−0.0225619	−	0.999745i	$-0.507182\pi$
$239$	−0.697596	−0.0451238	−0.0225619	+	0.999745i	$0.507182\pi$
$240$	4.91428	0.317215
$241$	−2.89220	−0.186303	−0.0931515	−	0.995652i	$-0.529694\pi$
$241$	−2.89220	−0.186303	−0.0931515	+	0.995652i	$0.529694\pi$
$242$	15.1214	0.972039
$243$	1.00000	0.0641500
$244$	−6.17187	−0.395114
$245$	6.02061	0.384643
$246$	−2.61262	−0.166574
$247$	−7.78985	−0.495656
$248$	−3.47873	−0.220900
$249$	4.32576	0.274134
$250$	1.64536	0.104062
$251$	4.55691	0.287630	0.143815	−	0.989605i	$-0.454063\pi$
$251$	4.55691	0.287630	0.143815	+	0.989605i	$0.454063\pi$
$252$	−0.699893	−0.0440891
$253$	0	0
$254$	−9.47251	−0.594358
$255$	3.15546	0.197602
$256$	15.1011	0.943818
$257$	29.1217	1.81656	0.908280	−	0.418364i	$-0.137396\pi$
$257$	29.1217	1.81656	0.908280	+	0.418364i	$0.137396\pi$
$258$	−9.86645	−0.614258
$259$	−7.03441	−0.437097
$260$	1.59975	0.0992122
$261$	4.14367	0.256487
$262$	−23.5125	−1.45261
$263$	−10.1797	−0.627706	−0.313853	−	0.949472i	$-0.601620\pi$
$263$	−10.1797	−0.627706	−0.313853	+	0.949472i	$0.601620\pi$
$264$	2.86147	0.176112
$265$	3.12338	0.191868
$266$	5.60751	0.343819
$267$	11.4638	0.701574
$268$	4.38639	0.267941
$269$	−4.54977	−0.277405	−0.138702	−	0.990334i	$-0.544293\pi$
$269$	−4.54977	−0.277405	−0.138702	+	0.990334i	$0.544293\pi$
$270$	1.64536	0.100134
$271$	−19.3328	−1.17438	−0.587192	−	0.809448i	$-0.699767\pi$
$271$	−19.3328	−1.17438	−0.587192	+	0.809448i	$0.699767\pi$
$272$	15.5068	0.940238
$273$	2.23859	0.135486
$274$	−16.1765	−0.977256
$275$	1.34525	0.0811216
$276$	0	0
$277$	16.1627	0.971123	0.485562	−	0.874202i	$-0.338615\pi$
$277$	16.1627	0.971123	0.485562	+	0.874202i	$0.338615\pi$
$278$	−20.3705	−1.22174
$279$	−1.63544	−0.0979112
$280$	2.10506	0.125801
$281$	−7.12401	−0.424983	−0.212491	−	0.977163i	$-0.568158\pi$
$281$	−7.12401	−0.424983	−0.212491	+	0.977163i	$0.568158\pi$
$282$	7.25163	0.431829
$283$	5.37170	0.319314	0.159657	−	0.987173i	$-0.448961\pi$
$283$	5.37170	0.319314	0.159657	+	0.987173i	$0.448961\pi$
$284$	−9.32795	−0.553512
$285$	−3.44375	−0.203990
$286$	5.00683	0.296060
$287$	−1.57142	−0.0927579
$288$	3.83159	0.225778
$289$	−7.04309	−0.414299
$290$	6.81785	0.400358
$291$	−0.241541	−0.0141594
$292$	4.80175	0.281001
$293$	16.3004	0.952277	0.476139	−	0.879370i	$-0.342036\pi$
$293$	16.3004	0.952277	0.476139	+	0.879370i	$0.342036\pi$
$294$	9.90609	0.577735
$295$	1.32147	0.0769390
$296$	15.1195	0.878802
$297$	1.34525	0.0780593
$298$	−37.4842	−2.17140
$299$	0	0
$300$	0.707219	0.0408313
$301$	−5.93440	−0.342053
$302$	23.3830	1.34554
$303$	−4.26291	−0.244898
$304$	−16.9235	−0.970631
$305$	8.72696	0.499704
$306$	5.19187	0.296800
$307$	24.0919	1.37500	0.687499	−	0.726185i	$-0.258709\pi$
$307$	24.0919	1.37500	0.687499	+	0.726185i	$0.258709\pi$
$308$	−0.941531	−0.0536487
$309$	1.83946	0.104643
$310$	−2.69089	−0.152832
$311$	15.5490	0.881704	0.440852	−	0.897580i	$-0.354676\pi$
$311$	15.5490	0.881704	0.440852	+	0.897580i	$0.354676\pi$
$312$	−4.81155	−0.272400
$313$	−3.04559	−0.172147	−0.0860734	−	0.996289i	$-0.527432\pi$
$313$	−3.04559	−0.172147	−0.0860734	+	0.996289i	$0.527432\pi$
$314$	−17.6762	−0.997526
$315$	0.989641	0.0557599
$316$	−11.6309	−0.654288
$317$	−5.56657	−0.312650	−0.156325	−	0.987706i	$-0.549965\pi$
$317$	−5.56657	−0.312650	−0.156325	+	0.987706i	$0.549965\pi$
$318$	5.13910	0.288186
$319$	5.57428	0.312100
$320$	−3.52421	−0.197009
$321$	1.80235	0.100597
$322$	0	0
$323$	−10.8666	−0.604634
$324$	0.707219	0.0392900
$325$	−2.26203	−0.125475
$326$	16.9130	0.936726
$327$	2.92323	0.161655
$328$	3.37754	0.186494
$329$	4.36166	0.240466
$330$	2.21342	0.121845
$331$	−12.5975	−0.692419	−0.346210	−	0.938157i	$-0.612531\pi$
$331$	−12.5975	−0.692419	−0.346210	+	0.938157i	$0.612531\pi$
$332$	3.05926	0.167899
$333$	7.10804	0.389518
$334$	−19.3849	−1.06069
$335$	−6.20230	−0.338868
$336$	4.86337	0.265319
$337$	12.1856	0.663794	0.331897	−	0.943316i	$-0.392311\pi$
$337$	12.1856	0.663794	0.331897	+	0.943316i	$0.392311\pi$
$338$	12.9708	0.705517
$339$	10.5134	0.571012
$340$	2.23160	0.121026
$341$	−2.20008	−0.119141
$342$	−5.66621	−0.306394
$343$	12.8857	0.695764
$344$	12.7552	0.687712
$345$	0	0
$346$	14.3404	0.770942
$347$	3.31951	0.178200	0.0891002	−	0.996023i	$-0.471601\pi$
$347$	3.31951	0.178200	0.0891002	+	0.996023i	$0.471601\pi$
$348$	2.93048	0.157090
$349$	5.19204	0.277924	0.138962	−	0.990298i	$-0.455623\pi$
$349$	5.19204	0.277924	0.138962	+	0.990298i	$0.455623\pi$
$350$	1.62832	0.0870372
$351$	−2.26203	−0.120738
$352$	5.15444	0.274733
$353$	26.7146	1.42187	0.710937	−	0.703256i	$-0.248271\pi$
$353$	26.7146	1.42187	0.710937	+	0.703256i	$0.248271\pi$
$354$	2.17430	0.115563
$355$	13.1896	0.700032
$356$	8.10743	0.429693
$357$	3.12277	0.165274
$358$	−13.6375	−0.720767
$359$	18.6180	0.982621	0.491310	−	0.870985i	$-0.336518\pi$
$359$	18.6180	0.982621	0.491310	+	0.870985i	$0.336518\pi$
$360$	−2.12709	−0.112108
$361$	−7.14061	−0.375822
$362$	−11.3106	−0.594473
$363$	−9.19030	−0.482366
$364$	1.58318	0.0829810
$365$	−6.78962	−0.355385
$366$	14.3590	0.750558
$367$	−15.5436	−0.811372	−0.405686	−	0.914013i	$-0.632967\pi$
$367$	−15.5436	−0.811372	−0.405686	+	0.914013i	$0.632967\pi$
$368$	0	0
$369$	1.58787	0.0826611
$370$	11.6953	0.608010
$371$	3.09102	0.160478
$372$	−1.15661	−0.0599677
$373$	−15.6204	−0.808793	−0.404397	−	0.914584i	$-0.632518\pi$
$373$	−15.6204	−0.808793	−0.404397	+	0.914584i	$0.632518\pi$
$374$	6.98437	0.361153
$375$	−1.00000	−0.0516398
$376$	−9.37477	−0.483467
$377$	−9.37310	−0.482739
$378$	1.62832	0.0837516
$379$	36.0540	1.85197	0.925985	−	0.377561i	$-0.123237\pi$
$379$	36.0540	1.85197	0.925985	+	0.377561i	$0.123237\pi$
$380$	−2.43548	−0.124938
$381$	5.75709	0.294945
$382$	−37.9179	−1.94005
$383$	28.1943	1.44066	0.720331	−	0.693631i	$-0.243990\pi$
$383$	28.1943	1.44066	0.720331	+	0.693631i	$0.243990\pi$
$384$	−13.4618	−0.686968
$385$	1.33131	0.0678501
$386$	39.1501	1.99269
$387$	5.99652	0.304820
$388$	−0.170822	−0.00867219
$389$	26.2545	1.33115	0.665577	−	0.746329i	$-0.268185\pi$
$389$	26.2545	1.33115	0.665577	+	0.746329i	$0.268185\pi$
$390$	−3.72186	−0.188464
$391$	0	0
$392$	−12.8064	−0.646821
$393$	14.2902	0.720843
$394$	34.6249	1.74438
$395$	16.4459	0.827485
$396$	0.951387	0.0478090
$397$	30.3076	1.52109	0.760547	−	0.649282i	$-0.224931\pi$
$397$	30.3076	1.52109	0.760547	+	0.649282i	$0.224931\pi$
$398$	37.4953	1.87947
$399$	−3.40807	−0.170617
$400$	−4.91428	−0.245714
$401$	−10.4083	−0.519767	−0.259884	−	0.965640i	$-0.583684\pi$
$401$	−10.4083	−0.519767	−0.259884	+	0.965640i	$0.583684\pi$
$402$	−10.2050	−0.508981
$403$	3.69941	0.184281
$404$	−3.01481	−0.149993
$405$	−1.00000	−0.0496904
$406$	6.74722	0.334859
$407$	9.56210	0.473976
$408$	−6.71195	−0.332291
$409$	−18.2185	−0.900847	−0.450423	−	0.892815i	$-0.648727\pi$
$409$	−18.2185	−0.900847	−0.450423	+	0.892815i	$0.648727\pi$
$410$	2.61262	0.129028
$411$	9.83155	0.484955
$412$	1.30090	0.0640907
$413$	1.30778	0.0643517
$414$	0	0
$415$	−4.32576	−0.212343
$416$	−8.66715	−0.424942
$417$	12.3806	0.606278
$418$	−7.62247	−0.372827
$419$	24.7228	1.20779	0.603894	−	0.797065i	$-0.293615\pi$
$419$	24.7228	1.20779	0.603894	+	0.797065i	$0.293615\pi$
$420$	0.699893	0.0341513
$421$	−9.59686	−0.467723	−0.233861	−	0.972270i	$-0.575136\pi$
$421$	−9.59686	−0.467723	−0.233861	+	0.972270i	$0.575136\pi$
$422$	−42.8540	−2.08610
$423$	−4.40732	−0.214291
$424$	−6.64372	−0.322648
$425$	−3.15546	−0.153062
$426$	21.7017	1.05145
$427$	8.63655	0.417952
$428$	1.27465	0.0616127
$429$	−3.04299	−0.146917
$430$	9.86645	0.475803
$431$	16.0359	0.772421	0.386211	−	0.922411i	$-0.373784\pi$
$431$	16.0359	0.772421	0.386211	+	0.922411i	$0.373784\pi$
$432$	−4.91428	−0.236438
$433$	1.54467	0.0742322	0.0371161	−	0.999311i	$-0.488183\pi$
$433$	1.54467	0.0742322	0.0371161	+	0.999311i	$0.488183\pi$
$434$	−2.66302	−0.127829
$435$	−4.14367	−0.198674
$436$	2.06737	0.0990089
$437$	0	0
$438$	−11.1714	−0.533789
$439$	16.3901	0.782259	0.391129	−	0.920336i	$-0.372084\pi$
$439$	16.3901	0.782259	0.391129	+	0.920336i	$0.372084\pi$
$440$	−2.86147	−0.136415
$441$	−6.02061	−0.286696
$442$	−11.7442	−0.558613
$443$	24.9878	1.18720	0.593602	−	0.804759i	$-0.297705\pi$
$443$	24.9878	1.18720	0.593602	+	0.804759i	$0.297705\pi$
$444$	5.02694	0.238568
$445$	−11.4638	−0.543437
$446$	7.21326	0.341558
$447$	22.7817	1.07754
$448$	−3.48770	−0.164778
$449$	−38.0303	−1.79476	−0.897382	−	0.441255i	$-0.854533\pi$
$449$	−38.0303	−1.79476	−0.897382	+	0.441255i	$0.854533\pi$
$450$	−1.64536	−0.0775632
$451$	2.13608	0.100584
$452$	7.43531	0.349728
$453$	−14.2114	−0.667711
$454$	34.2748	1.60859
$455$	−2.23859	−0.104947
$456$	7.32517	0.343033
$457$	−10.4477	−0.488723	−0.244362	−	0.969684i	$-0.578578\pi$
$457$	−10.4477	−0.488723	−0.244362	+	0.969684i	$0.578578\pi$
$458$	20.9495	0.978905
$459$	−3.15546	−0.147284
$460$	0	0
$461$	−31.1122	−1.44904	−0.724520	−	0.689253i	$-0.757939\pi$
$461$	−31.1122	−1.44904	−0.724520	+	0.689253i	$0.757939\pi$
$462$	2.19049	0.101911
$463$	−13.9931	−0.650314	−0.325157	−	0.945660i	$-0.605417\pi$
$463$	−13.9931	−0.650314	−0.325157	+	0.945660i	$0.605417\pi$
$464$	−20.3632	−0.945336
$465$	1.63544	0.0758417
$466$	−12.5118	−0.579599
$467$	37.6348	1.74153	0.870766	−	0.491698i	$-0.163624\pi$
$467$	37.6348	1.74153	0.870766	+	0.491698i	$0.163624\pi$
$468$	−1.59975	−0.0739484
$469$	−6.13805	−0.283429
$470$	−7.25163	−0.334493
$471$	10.7430	0.495013
$472$	−2.81089	−0.129382
$473$	8.06682	0.370913
$474$	27.0595	1.24289
$475$	3.44375	0.158010
$476$	2.20848	0.101226
$477$	−3.12338	−0.143010
$478$	1.14780	0.0524991
$479$	−35.0032	−1.59934	−0.799669	−	0.600441i	$-0.794992\pi$
$479$	−35.0032	−1.59934	−0.799669	+	0.600441i	$0.794992\pi$
$480$	−3.83159	−0.174887
$481$	−16.0786	−0.733121
$482$	4.75872	0.216754
$483$	0	0
$484$	−6.49956	−0.295434
$485$	0.241541	0.0109678
$486$	−1.64536	−0.0746352
$487$	35.0124	1.58656	0.793281	−	0.608856i	$-0.208371\pi$
$487$	35.0124	1.58656	0.793281	+	0.608856i	$0.208371\pi$
$488$	−18.5631	−0.840310
$489$	−10.2792	−0.464842
$490$	−9.90609	−0.447512
$491$	26.7207	1.20589	0.602943	−	0.797784i	$-0.293995\pi$
$491$	26.7207	1.20589	0.602943	+	0.797784i	$0.293995\pi$
$492$	1.12297	0.0506274
$493$	−13.0752	−0.588877
$494$	12.8171	0.576670
$495$	−1.34525	−0.0604645
$496$	8.03701	0.360872
$497$	13.0530	0.585506
$498$	−7.11745	−0.318940
$499$	−19.1112	−0.855533	−0.427766	−	0.903889i	$-0.640699\pi$
$499$	−19.1112	−0.855533	−0.427766	+	0.903889i	$0.640699\pi$
$500$	−0.707219	−0.0316278
$501$	11.7815	0.526359
$502$	−7.49777	−0.334642
$503$	21.7875	0.971455	0.485727	−	0.874110i	$-0.338555\pi$
$503$	21.7875	0.971455	0.485727	+	0.874110i	$0.338555\pi$
$504$	−2.10506	−0.0937667
$505$	4.26291	0.189697
$506$	0	0
$507$	−7.88323	−0.350107
$508$	4.07153	0.180645
$509$	7.82241	0.346722	0.173361	−	0.984858i	$-0.444537\pi$
$509$	7.82241	0.346722	0.173361	+	0.984858i	$0.444537\pi$
$510$	−5.19187	−0.229900
$511$	−6.71928	−0.297243
$512$	2.07678	0.0917817
$513$	3.44375	0.152045
$514$	−47.9157	−2.11347
$515$	−1.83946	−0.0810562
$516$	4.24085	0.186693
$517$	−5.92894	−0.260755
$518$	11.5742	0.508539
$519$	−8.71562	−0.382573
$520$	4.81155	0.211000
$521$	−7.63681	−0.334575	−0.167287	−	0.985908i	$-0.553501\pi$
$521$	−7.63681	−0.334575	−0.167287	+	0.985908i	$0.553501\pi$
$522$	−6.81785	−0.298409
$523$	−15.1694	−0.663312	−0.331656	−	0.943400i	$-0.607607\pi$
$523$	−15.1694	−0.663312	−0.331656	+	0.943400i	$0.607607\pi$
$524$	10.1063	0.441495
$525$	−0.989641	−0.0431915
$526$	16.7493	0.730303
$527$	5.16056	0.224798
$528$	−6.61094	−0.287704
$529$	0	0
$530$	−5.13910	−0.223228
$531$	−1.32147	−0.0573469
$532$	−2.41025	−0.104498
$533$	−3.59180	−0.155578
$534$	−18.8621	−0.816245
$535$	−1.80235	−0.0779223
$536$	13.1929	0.569845
$537$	8.28847	0.357674
$538$	7.48603	0.322746
$539$	−8.09923	−0.348858
$540$	−0.707219	−0.0304339
$541$	19.0191	0.817693	0.408847	−	0.912603i	$-0.365931\pi$
$541$	19.0191	0.817693	0.408847	+	0.912603i	$0.365931\pi$
$542$	31.8095	1.36633
$543$	6.87424	0.295002
$544$	−12.0904	−0.518372
$545$	−2.92323	−0.125218
$546$	−3.68330	−0.157631
$547$	42.4961	1.81700	0.908500	−	0.417885i	$-0.137228\pi$
$547$	42.4961	1.81700	0.908500	+	0.417885i	$0.137228\pi$
$548$	6.95306	0.297020
$549$	−8.72696	−0.372457
$550$	−2.21342	−0.0943808
$551$	14.2698	0.607912
$552$	0	0
$553$	16.2756	0.692107
$554$	−26.5935	−1.12985
$555$	−7.10804	−0.301720
$556$	8.75576	0.371327
$557$	38.9143	1.64885	0.824426	−	0.565969i	$-0.191498\pi$
$557$	38.9143	1.64885	0.824426	+	0.565969i	$0.191498\pi$
$558$	2.69089	0.113915
$559$	−13.5643	−0.573709
$560$	−4.86337	−0.205515
$561$	−4.24488	−0.179219
$562$	11.7216	0.494445
$563$	6.48891	0.273475	0.136738	−	0.990607i	$-0.456338\pi$
$563$	6.48891	0.273475	0.136738	+	0.990607i	$0.456338\pi$
$564$	−3.11694	−0.131247
$565$	−10.5134	−0.442304
$566$	−8.83839	−0.371505
$567$	−0.989641	−0.0415610
$568$	−28.0556	−1.17718
$569$	44.7520	1.87610	0.938052	−	0.346496i	$-0.112629\pi$
$569$	44.7520	1.87610	0.938052	+	0.346496i	$0.112629\pi$
$570$	5.66621	0.237332
$571$	−7.96133	−0.333171	−0.166586	−	0.986027i	$-0.553274\pi$
$571$	−7.96133	−0.333171	−0.166586	+	0.986027i	$0.553274\pi$
$572$	−2.15206	−0.0899823
$573$	23.0453	0.962732
$574$	2.58555	0.107919
$575$	0	0
$576$	3.52421	0.146842
$577$	41.0817	1.71025	0.855126	−	0.518420i	$-0.173480\pi$
$577$	41.0817	1.71025	0.855126	+	0.518420i	$0.173480\pi$
$578$	11.5884	0.482015
$579$	−23.7942	−0.988854
$580$	−2.93048	−0.121682
$581$	−4.28095	−0.177604
$582$	0.397422	0.0164737
$583$	−4.20173	−0.174018
$584$	14.4422	0.597621
$585$	2.26203	0.0935233
$586$	−26.8200	−1.10792
$587$	−9.10815	−0.375934	−0.187967	−	0.982175i	$-0.560190\pi$
$587$	−9.10815	−0.375934	−0.187967	+	0.982175i	$0.560190\pi$
$588$	−4.25789	−0.175592
$589$	−5.63204	−0.232064
$590$	−2.17430	−0.0895144
$591$	−21.0439	−0.865632
$592$	−34.9309	−1.43565
$593$	−24.2845	−0.997245	−0.498623	−	0.866819i	$-0.666161\pi$
$593$	−24.2845	−0.997245	−0.498623	+	0.866819i	$0.666161\pi$
$594$	−2.21342	−0.0908179
$595$	−3.12277	−0.128021
$596$	16.1117	0.659960
$597$	−22.7884	−0.932669
$598$	0	0
$599$	−20.6417	−0.843399	−0.421699	−	0.906736i	$-0.638566\pi$
$599$	−20.6417	−0.843399	−0.421699	+	0.906736i	$0.638566\pi$
$600$	2.12709	0.0868382
$601$	12.4038	0.505960	0.252980	−	0.967472i	$-0.418589\pi$
$601$	12.4038	0.505960	0.252980	+	0.967472i	$0.418589\pi$
$602$	9.76424	0.397961
$603$	6.20230	0.252577
$604$	−10.0506	−0.408953
$605$	9.19030	0.373639
$606$	7.01404	0.284926
$607$	−31.0040	−1.25841	−0.629206	−	0.777239i	$-0.716620\pi$
$607$	−31.0040	−1.25841	−0.629206	+	0.777239i	$0.716620\pi$
$608$	13.1950	0.535128
$609$	−4.10075	−0.166171
$610$	−14.3590	−0.581379
$611$	9.96947	0.403322
$612$	−2.23160	−0.0902071
$613$	37.5346	1.51601	0.758004	−	0.652250i	$-0.226175\pi$
$613$	37.5346	1.51601	0.758004	+	0.652250i	$0.226175\pi$
$614$	−39.6399	−1.59974
$615$	−1.58787	−0.0640290
$616$	−2.83183	−0.114098
$617$	5.95563	0.239765	0.119882	−	0.992788i	$-0.461748\pi$
$617$	5.95563	0.239765	0.119882	+	0.992788i	$0.461748\pi$
$618$	−3.02657	−0.121747
$619$	−0.524997	−0.0211014	−0.0105507	−	0.999944i	$-0.503358\pi$
$619$	−0.524997	−0.0211014	−0.0105507	+	0.999944i	$0.503358\pi$
$620$	1.15661	0.0464508
$621$	0	0
$622$	−25.5838	−1.02582
$623$	−11.3451	−0.454530
$624$	11.1162	0.445006
$625$	1.00000	0.0400000
$626$	5.01110	0.200284
$627$	4.63270	0.185012
$628$	7.59768	0.303181
$629$	−22.4291	−0.894308
$630$	−1.62832	−0.0648737
$631$	18.8256	0.749436	0.374718	−	0.927139i	$-0.377740\pi$
$631$	18.8256	0.749436	0.374718	+	0.927139i	$0.377740\pi$
$632$	−34.9820	−1.39151
$633$	26.0453	1.03521
$634$	9.15902	0.363751
$635$	−5.75709	−0.228463
$636$	−2.20891	−0.0875892
$637$	13.6188	0.539596
$638$	−9.17171	−0.363111
$639$	−13.1896	−0.521773
$640$	13.4618	0.532123
$641$	29.5539	1.16731	0.583655	−	0.812002i	$-0.301622\pi$
$641$	29.5539	1.16731	0.583655	+	0.812002i	$0.301622\pi$
$642$	−2.96551	−0.117040
$643$	9.21364	0.363351	0.181675	−	0.983359i	$-0.441848\pi$
$643$	9.21364	0.363351	0.181675	+	0.983359i	$0.441848\pi$
$644$	0	0
$645$	−5.99652	−0.236113
$646$	17.8795	0.703459
$647$	23.2912	0.915671	0.457835	−	0.889037i	$-0.348625\pi$
$647$	23.2912	0.915671	0.457835	+	0.889037i	$0.348625\pi$
$648$	2.12709	0.0835601
$649$	−1.77771	−0.0697811
$650$	3.72186	0.145983
$651$	1.61850	0.0634339
$652$	−7.26966	−0.284702
$653$	22.7334	0.889627	0.444814	−	0.895623i	$-0.353270\pi$
$653$	22.7334	0.889627	0.444814	+	0.895623i	$0.353270\pi$
$654$	−4.80978	−0.188077
$655$	−14.2902	−0.558363
$656$	−7.80322	−0.304665
$657$	6.78962	0.264888
$658$	−7.17651	−0.279770
$659$	−8.79047	−0.342428	−0.171214	−	0.985234i	$-0.554769\pi$
$659$	−8.79047	−0.342428	−0.171214	+	0.985234i	$0.554769\pi$
$660$	−0.951387	−0.0370327
$661$	32.6564	1.27019	0.635093	−	0.772436i	$-0.280962\pi$
$661$	32.6564	1.27019	0.635093	+	0.772436i	$0.280962\pi$
$662$	20.7274	0.805593
$663$	7.13773	0.277207
$664$	9.20130	0.357080
$665$	3.40807	0.132159
$666$	−11.6953	−0.453184
$667$	0	0
$668$	8.33211	0.322379
$669$	−4.38399	−0.169495
$670$	10.2050	0.394255
$671$	−11.7399	−0.453215
$672$	−3.79189	−0.146275
$673$	−46.9386	−1.80935	−0.904674	−	0.426104i	$-0.859886\pi$
$673$	−46.9386	−1.80935	−0.904674	+	0.426104i	$0.859886\pi$
$674$	−20.0498	−0.772289
$675$	1.00000	0.0384900
$676$	−5.57517	−0.214430
$677$	32.0735	1.23268	0.616341	−	0.787479i	$-0.288614\pi$
$677$	32.0735	1.23268	0.616341	+	0.787479i	$0.288614\pi$
$678$	−17.2984	−0.664342
$679$	0.239039	0.00917346
$680$	6.71195	0.257392
$681$	−20.8311	−0.798251
$682$	3.61992	0.138614
$683$	−25.4638	−0.974347	−0.487173	−	0.873305i	$-0.661972\pi$
$683$	−25.4638	−0.974347	−0.487173	+	0.873305i	$0.661972\pi$
$684$	2.43548	0.0931230
$685$	−9.83155	−0.375644
$686$	−21.2017	−0.809484
$687$	−12.7324	−0.485773
$688$	−29.4686	−1.12348
$689$	7.06518	0.269162
$690$	0	0
$691$	26.2106	0.997097	0.498548	−	0.866862i	$-0.333867\pi$
$691$	26.2106	0.997097	0.498548	+	0.866862i	$0.333867\pi$
$692$	−6.16385	−0.234314
$693$	−1.33131	−0.0505724
$694$	−5.46179	−0.207327
$695$	−12.3806	−0.469621
$696$	8.81398	0.334093
$697$	−5.01045	−0.189784
$698$	−8.54279	−0.323349
$699$	7.60430	0.287621
$700$	−0.699893	−0.0264535
$701$	−3.98663	−0.150573	−0.0752865	−	0.997162i	$-0.523987\pi$
$701$	−3.98663	−0.150573	−0.0752865	+	0.997162i	$0.523987\pi$
$702$	3.72186	0.140472
$703$	24.4783	0.923217
$704$	4.74094	0.178681
$705$	4.40732	0.165989
$706$	−43.9552	−1.65428
$707$	4.21875	0.158663
$708$	−0.934569	−0.0351233
$709$	−6.77432	−0.254415	−0.127207	−	0.991876i	$-0.540601\pi$
$709$	−6.77432	−0.254415	−0.127207	+	0.991876i	$0.540601\pi$
$710$	−21.7017	−0.814451
$711$	−16.4459	−0.616771
$712$	24.3846	0.913852
$713$	0	0
$714$	−5.13809	−0.192288
$715$	3.04299	0.113802
$716$	5.86177	0.219064
$717$	−0.697596	−0.0260522
$718$	−30.6334	−1.14323
$719$	7.84728	0.292654	0.146327	−	0.989236i	$-0.453255\pi$
$719$	7.84728	0.292654	0.146327	+	0.989236i	$0.453255\pi$
$720$	4.91428	0.183144
$721$	−1.82040	−0.0677953
$722$	11.7489	0.437249
$723$	−2.89220	−0.107562
$724$	4.86159	0.180680
$725$	4.14367	0.153892
$726$	15.1214	0.561207
$727$	−16.7048	−0.619545	−0.309773	−	0.950811i	$-0.600253\pi$
$727$	−16.7048	−0.619545	−0.309773	+	0.950811i	$0.600253\pi$
$728$	4.76170	0.176480
$729$	1.00000	0.0370370
$730$	11.1714	0.413472
$731$	−18.9218	−0.699847
$732$	−6.17187	−0.228119
$733$	42.0067	1.55155	0.775776	−	0.631009i	$-0.217359\pi$
$733$	42.0067	1.55155	0.775776	+	0.631009i	$0.217359\pi$
$734$	25.5749	0.943988
$735$	6.02061	0.222074
$736$	0	0
$737$	8.34365	0.307342
$738$	−2.61262	−0.0961718
$739$	4.00485	0.147321	0.0736604	−	0.997283i	$-0.476532\pi$
$739$	4.00485	0.147321	0.0736604	+	0.997283i	$0.476532\pi$
$740$	−5.02694	−0.184794
$741$	−7.78985	−0.286167
$742$	−5.08586	−0.186708
$743$	5.14116	0.188611	0.0943054	−	0.995543i	$-0.469937\pi$
$743$	5.14116	0.188611	0.0943054	+	0.995543i	$0.469937\pi$
$744$	−3.47873	−0.127537
$745$	−22.7817	−0.834659
$746$	25.7012	0.940988
$747$	4.32576	0.158271
$748$	−3.00206	−0.109766
$749$	−1.78368	−0.0651741
$750$	1.64536	0.0600802
$751$	23.3228	0.851062	0.425531	−	0.904944i	$-0.360087\pi$
$751$	23.3228	0.851062	0.425531	+	0.904944i	$0.360087\pi$
$752$	21.6588	0.789815
$753$	4.55691	0.166063
$754$	15.4222	0.561642
$755$	14.2114	0.517207
$756$	−0.699893	−0.0254549
$757$	−47.9903	−1.74424	−0.872119	−	0.489294i	$-0.837254\pi$
$757$	−47.9903	−1.74424	−0.872119	+	0.489294i	$0.837254\pi$
$758$	−59.3219	−2.15467
$759$	0	0
$760$	−7.32517	−0.265712
$761$	5.99208	0.217213	0.108606	−	0.994085i	$-0.465361\pi$
$761$	5.99208	0.217213	0.108606	+	0.994085i	$0.465361\pi$
$762$	−9.47251	−0.343153
$763$	−2.89295	−0.104732
$764$	16.2981	0.589644
$765$	3.15546	0.114086
$766$	−46.3899	−1.67613
$767$	2.98920	0.107934
$768$	15.1011	0.544914
$769$	−32.0685	−1.15642	−0.578210	−	0.815888i	$-0.696249\pi$
$769$	−32.0685	−1.15642	−0.578210	+	0.815888i	$0.696249\pi$
$770$	−2.19049	−0.0789400
$771$	29.1217	1.04879
$772$	−16.8277	−0.605643
$773$	−13.1081	−0.471466	−0.235733	−	0.971818i	$-0.575749\pi$
$773$	−13.1081	−0.471466	−0.235733	+	0.971818i	$0.575749\pi$
$774$	−9.86645	−0.354642
$775$	−1.63544	−0.0587467
$776$	−0.513780	−0.0184436
$777$	−7.03441	−0.252358
$778$	−43.1981	−1.54873
$779$	5.46821	0.195919
$780$	1.59975	0.0572802
$781$	−17.7433	−0.634907
$782$	0	0
$783$	4.14367	0.148083
$784$	29.5870	1.05668
$785$	−10.7430	−0.383436
$786$	−23.5125	−0.838663
$787$	16.6961	0.595152	0.297576	−	0.954698i	$-0.403822\pi$
$787$	16.6961	0.595152	0.297576	+	0.954698i	$0.403822\pi$
$788$	−14.8827	−0.530174
$789$	−10.1797	−0.362406
$790$	−27.0595	−0.962735
$791$	−10.4045	−0.369943
$792$	2.86147	0.101678
$793$	19.7406	0.701010
$794$	−49.8670	−1.76971
$795$	3.12338	0.110775
$796$	−16.1164	−0.571231
$797$	21.6220	0.765892	0.382946	−	0.923771i	$-0.374910\pi$
$797$	21.6220	0.765892	0.382946	+	0.923771i	$0.374910\pi$
$798$	5.60751	0.198504
$799$	13.9071	0.491998
$800$	3.83159	0.135467
$801$	11.4638	0.405054
$802$	17.1255	0.604722
$803$	9.13373	0.322322
$804$	4.38639	0.154696
$805$	0	0
$806$	−6.08687	−0.214401
$807$	−4.54977	−0.160160
$808$	−9.06762	−0.318998
$809$	−36.2162	−1.27329	−0.636646	−	0.771156i	$-0.719679\pi$
$809$	−36.2162	−1.27329	−0.636646	+	0.771156i	$0.719679\pi$
$810$	1.64536	0.0578122
$811$	−4.51591	−0.158575	−0.0792875	−	0.996852i	$-0.525265\pi$
$811$	−4.51591	−0.158575	−0.0792875	+	0.996852i	$0.525265\pi$
$812$	−2.90013	−0.101774
$813$	−19.3328	−0.678031
$814$	−15.7331	−0.551446
$815$	10.2792	0.360065
$816$	15.5068	0.542847
$817$	20.6505	0.722469
$818$	29.9760	1.04809
$819$	2.23859	0.0782228
$820$	−1.12297	−0.0392158
$821$	−15.3721	−0.536490	−0.268245	−	0.963351i	$-0.586444\pi$
$821$	−15.3721	−0.536490	−0.268245	+	0.963351i	$0.586444\pi$
$822$	−16.1765	−0.564219
$823$	−38.8120	−1.35290	−0.676451	−	0.736488i	$-0.736483\pi$
$823$	−38.8120	−1.35290	−0.676451	+	0.736488i	$0.736483\pi$
$824$	3.91270	0.136305
$825$	1.34525	0.0468356
$826$	−2.15177	−0.0748698
$827$	20.1046	0.699107	0.349554	−	0.936916i	$-0.386333\pi$
$827$	20.1046	0.699107	0.349554	+	0.936916i	$0.386333\pi$
$828$	0	0
$829$	38.9271	1.35199	0.675997	−	0.736904i	$-0.263713\pi$
$829$	38.9271	1.35199	0.675997	+	0.736904i	$0.263713\pi$
$830$	7.11745	0.247050
$831$	16.1627	0.560678
$832$	−7.97186	−0.276375
$833$	18.9978	0.658234
$834$	−20.3705	−0.705373
$835$	−11.7815	−0.407716
$836$	3.27633	0.113314
$837$	−1.63544	−0.0565291
$838$	−40.6780	−1.40520
$839$	12.0557	0.416209	0.208104	−	0.978107i	$-0.433271\pi$
$839$	12.0557	0.416209	0.208104	+	0.978107i	$0.433271\pi$
$840$	2.10506	0.0726314
$841$	−11.8300	−0.407930
$842$	15.7903	0.544171
$843$	−7.12401	−0.245364
$844$	18.4197	0.634034
$845$	7.88323	0.271191
$846$	7.25163	0.249316
$847$	9.09510	0.312511
$848$	15.3492	0.527093
$849$	5.37170	0.184356
$850$	5.19187	0.178080
$851$	0	0
$852$	−9.32795	−0.319570
$853$	−2.24930	−0.0770145	−0.0385072	−	0.999258i	$-0.512260\pi$
$853$	−2.24930	−0.0770145	−0.0385072	+	0.999258i	$0.512260\pi$
$854$	−14.2103	−0.486265
$855$	−3.44375	−0.117774
$856$	3.83376	0.131035
$857$	29.7866	1.01749	0.508746	−	0.860917i	$-0.330109\pi$
$857$	29.7866	1.01749	0.508746	+	0.860917i	$0.330109\pi$
$858$	5.00683	0.170930
$859$	8.72738	0.297774	0.148887	−	0.988854i	$-0.452431\pi$
$859$	8.72738	0.297774	0.148887	+	0.988854i	$0.452431\pi$
$860$	−4.24085	−0.144612
$861$	−1.57142	−0.0535538
$862$	−26.3849	−0.898672
$863$	21.1276	0.719194	0.359597	−	0.933108i	$-0.382914\pi$
$863$	21.1276	0.719194	0.359597	+	0.933108i	$0.382914\pi$
$864$	3.83159	0.130353
$865$	8.71562	0.296340
$866$	−2.54155	−0.0863653
$867$	−7.04309	−0.239196
$868$	1.14463	0.0388514
$869$	−22.1239	−0.750502
$870$	6.81785	0.231147
$871$	−14.0298	−0.475381
$872$	6.21799	0.210568
$873$	−0.241541	−0.00817492
$874$	0	0
$875$	0.989641	0.0334560
$876$	4.80175	0.162236
$877$	−20.2337	−0.683243	−0.341622	−	0.939838i	$-0.610976\pi$
$877$	−20.2337	−0.683243	−0.341622	+	0.939838i	$0.610976\pi$
$878$	−26.9677	−0.910117
$879$	16.3004	0.549798
$880$	6.61094	0.222855
$881$	56.0904	1.88973	0.944867	−	0.327455i	$-0.106191\pi$
$881$	56.0904	1.88973	0.944867	+	0.327455i	$0.106191\pi$
$882$	9.90609	0.333555
$883$	−12.7453	−0.428912	−0.214456	−	0.976734i	$-0.568798\pi$
$883$	−12.7453	−0.428912	−0.214456	+	0.976734i	$0.568798\pi$
$884$	5.04794	0.169781
$885$	1.32147	0.0444207
$886$	−41.1139	−1.38125
$887$	52.9544	1.77803	0.889017	−	0.457875i	$-0.151389\pi$
$887$	52.9544	1.77803	0.889017	+	0.457875i	$0.151389\pi$
$888$	15.1195	0.507376
$889$	−5.69745	−0.191086
$890$	18.8621	0.632261
$891$	1.34525	0.0450676
$892$	−3.10044	−0.103810
$893$	−15.1777	−0.507902
$894$	−37.4842	−1.25366
$895$	−8.28847	−0.277053
$896$	13.3223	0.445067
$897$	0	0
$898$	62.5737	2.08811
$899$	−6.77673	−0.226017
$900$	0.707219	0.0235740
$901$	9.85570	0.328341
$902$	−3.51463	−0.117024
$903$	−5.93440	−0.197484
$904$	22.3631	0.743785
$905$	−6.87424	−0.228507
$906$	23.3830	0.776847
$907$	21.5279	0.714823	0.357412	−	0.933947i	$-0.383659\pi$
$907$	21.5279	0.714823	0.357412	+	0.933947i	$0.383659\pi$
$908$	−14.7322	−0.488904
$909$	−4.26291	−0.141392
$910$	3.68330	0.122100
$911$	−18.0084	−0.596646	−0.298323	−	0.954465i	$-0.596427\pi$
$911$	−18.0084	−0.596646	−0.298323	+	0.954465i	$0.596427\pi$
$912$	−16.9235	−0.560394
$913$	5.81923	0.192588
$914$	17.1903	0.568604
$915$	8.72696	0.288504
$916$	−9.00462	−0.297521
$917$	−14.1421	−0.467014
$918$	5.19187	0.171357
$919$	37.1127	1.22424	0.612118	−	0.790767i	$-0.290318\pi$
$919$	37.1127	1.22424	0.612118	+	0.790767i	$0.290318\pi$
$920$	0	0
$921$	24.0919	0.793856
$922$	51.1909	1.68588
$923$	29.8353	0.982040
$924$	−0.941531	−0.0309741
$925$	7.10804	0.233711
$926$	23.0237	0.756606
$927$	1.83946	0.0604157
$928$	15.8768	0.521183
$929$	−12.7476	−0.418236	−0.209118	−	0.977890i	$-0.567059\pi$
$929$	−12.7476	−0.418236	−0.209118	+	0.977890i	$0.567059\pi$
$930$	−2.69089	−0.0882378
$931$	−20.7335	−0.679512
$932$	5.37790	0.176159
$933$	15.5490	0.509052
$934$	−61.9229	−2.02618
$935$	4.24488	0.138822
$936$	−4.81155	−0.157270
$937$	4.44200	0.145114	0.0725569	−	0.997364i	$-0.476884\pi$
$937$	4.44200	0.145114	0.0725569	+	0.997364i	$0.476884\pi$
$938$	10.0993	0.329754
$939$	−3.04559	−0.0993891
$940$	3.11694	0.101663
$941$	0.865175	0.0282039	0.0141020	−	0.999901i	$-0.495511\pi$
$941$	0.865175	0.0282039	0.0141020	+	0.999901i	$0.495511\pi$
$942$	−17.6762	−0.575922
$943$	0	0
$944$	6.49407	0.211364
$945$	0.989641	0.0321930
$946$	−13.2728	−0.431537
$947$	13.5878	0.441545	0.220773	−	0.975325i	$-0.429142\pi$
$947$	13.5878	0.441545	0.220773	+	0.975325i	$0.429142\pi$
$948$	−11.6309	−0.377753
$949$	−15.3583	−0.498552
$950$	−5.66621	−0.183836
$951$	−5.56657	−0.180508
$952$	6.64242	0.215282
$953$	8.92675	0.289166	0.144583	−	0.989493i	$-0.453816\pi$
$953$	8.92675	0.289166	0.144583	+	0.989493i	$0.453816\pi$
$954$	5.13910	0.166384
$955$	−23.0453	−0.745729
$956$	−0.493354	−0.0159562
$957$	5.57428	0.180191
$958$	57.5930	1.86075
$959$	−9.72970	−0.314189
$960$	−3.52421	−0.113743
$961$	−28.3253	−0.913720
$962$	26.4551	0.852947
$963$	1.80235	0.0580798
$964$	−2.04542	−0.0658785
$965$	23.7942	0.765963
$966$	0	0
$967$	−0.908241	−0.0292070	−0.0146035	−	0.999893i	$-0.504649\pi$
$967$	−0.908241	−0.0292070	−0.0146035	+	0.999893i	$0.504649\pi$
$968$	−19.5486	−0.628317
$969$	−10.8666	−0.349085
$970$	−0.397422	−0.0127605
$971$	32.5637	1.04502	0.522509	−	0.852634i	$-0.324996\pi$
$971$	32.5637	1.04502	0.522509	+	0.852634i	$0.324996\pi$
$972$	0.707219	0.0226841
$973$	−12.2523	−0.392791
$974$	−57.6081	−1.84588
$975$	−2.26203	−0.0724429
$976$	42.8867	1.37277
$977$	−49.5453	−1.58509	−0.792547	−	0.609811i	$-0.791245\pi$
$977$	−49.5453	−1.58509	−0.792547	+	0.609811i	$0.791245\pi$
$978$	16.9130	0.540819
$979$	15.4217	0.492880
$980$	4.25789	0.136013
$981$	2.92323	0.0933317
$982$	−43.9652	−1.40299
$983$	11.2376	0.358422	0.179211	−	0.983811i	$-0.442645\pi$
$983$	11.2376	0.358422	0.179211	+	0.983811i	$0.442645\pi$
$984$	3.37754	0.107672
$985$	21.0439	0.670516
$986$	21.5134	0.685127
$987$	4.36166	0.138833
$988$	−5.50913	−0.175269
$989$	0	0
$990$	2.21342	0.0703473
$991$	−53.3591	−1.69501	−0.847504	−	0.530788i	$-0.821896\pi$
$991$	−53.3591	−1.69501	−0.847504	+	0.530788i	$0.821896\pi$
$992$	−6.26633	−0.198956
$993$	−12.5975	−0.399768
$994$	−21.4769	−0.681206
$995$	22.7884	0.722442
$996$	3.05926	0.0969364
$997$	20.8347	0.659841	0.329921	−	0.944009i	$-0.392978\pi$
$997$	20.8347	0.659841	0.329921	+	0.944009i	$0.392978\pi$
$998$	31.4448	0.995367
$999$	7.10804	0.224889

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bl.1.4	✓	12
23.22	odd	2		7935.2.a.bm.1.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bl.1.4	✓	12	1.1	even	1	trivial
7935.2.a.bm.1.4	yes	12	23.22	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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q-1.64536 q^{2} +1.00000 q^{3} +0.707219 q^{4} -1.00000 q^{5} -1.64536 q^{6} -0.989641 q^{7} +2.12709 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.64536 q^{2} +1.00000 q^{3} +0.707219 q^{4} -1.00000 q^{5} -1.64536 q^{6} -0.989641 q^{7} +2.12709 q^{8} +1.00000 q^{9} +1.64536 q^{10} +1.34525 q^{11} +0.707219 q^{12} -2.26203 q^{13} +1.62832 q^{14} -1.00000 q^{15} -4.91428 q^{16} -3.15546 q^{17} -1.64536 q^{18} +3.44375 q^{19} -0.707219 q^{20} -0.989641 q^{21} -2.21342 q^{22} +2.12709 q^{24} +1.00000 q^{25} +3.72186 q^{26} +1.00000 q^{27} -0.699893 q^{28} +4.14367 q^{29} +1.64536 q^{30} -1.63544 q^{31} +3.83159 q^{32} +1.34525 q^{33} +5.19187 q^{34} +0.989641 q^{35} +0.707219 q^{36} +7.10804 q^{37} -5.66621 q^{38} -2.26203 q^{39} -2.12709 q^{40} +1.58787 q^{41} +1.62832 q^{42} +5.99652 q^{43} +0.951387 q^{44} -1.00000 q^{45} -4.40732 q^{47} -4.91428 q^{48} -6.02061 q^{49} -1.64536 q^{50} -3.15546 q^{51} -1.59975 q^{52} -3.12338 q^{53} -1.64536 q^{54} -1.34525 q^{55} -2.10506 q^{56} +3.44375 q^{57} -6.81785 q^{58} -1.32147 q^{59} -0.707219 q^{60} -8.72696 q^{61} +2.69089 q^{62} -0.989641 q^{63} +3.52421 q^{64} +2.26203 q^{65} -2.21342 q^{66} +6.20230 q^{67} -2.23160 q^{68} -1.62832 q^{70} -13.1896 q^{71} +2.12709 q^{72} +6.78962 q^{73} -11.6953 q^{74} +1.00000 q^{75} +2.43548 q^{76} -1.33131 q^{77} +3.72186 q^{78} -16.4459 q^{79} +4.91428 q^{80} +1.00000 q^{81} -2.61262 q^{82} +4.32576 q^{83} -0.699893 q^{84} +3.15546 q^{85} -9.86645 q^{86} +4.14367 q^{87} +2.86147 q^{88} +11.4638 q^{89} +1.64536 q^{90} +2.23859 q^{91} -1.63544 q^{93} +7.25163 q^{94} -3.44375 q^{95} +3.83159 q^{96} -0.241541 q^{97} +9.90609 q^{98} +1.34525 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9	\( 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9} + 24 q^{11} + 8 q^{12} - 8 q^{13} + 16 q^{14} - 12 q^{15} + 28 q^{17} + 16 q^{19} - 8 q^{20} + 4 q^{21} + 12 q^{25} - 36 q^{26} + 12 q^{27} + 8 q^{28} - 16 q^{29} + 20 q^{32} + 24 q^{33} + 16 q^{34} - 4 q^{35} + 8 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{39} - 4 q^{41} + 16 q^{42} - 12 q^{43} + 16 q^{44} - 12 q^{45} + 4 q^{47} + 24 q^{49} + 28 q^{51} - 36 q^{52} + 28 q^{53} - 24 q^{55} + 56 q^{56} + 16 q^{57} + 20 q^{59} - 8 q^{60} + 32 q^{61} + 12 q^{62} + 4 q^{63} - 4 q^{64} + 8 q^{65} - 4 q^{67} + 64 q^{68} - 16 q^{70} - 8 q^{71} + 4 q^{73} - 36 q^{74} + 12 q^{75} + 8 q^{76} - 28 q^{77} - 36 q^{78} + 40 q^{79} + 12 q^{81} - 28 q^{82} + 100 q^{83} + 8 q^{84} - 28 q^{85} - 20 q^{86} - 16 q^{87} + 80 q^{89} - 24 q^{91} + 44 q^{94} - 16 q^{95} + 20 q^{96} - 8 q^{97} + 28 q^{98} + 24 q^{99}+O(q^{100}) \) 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9 + 24 * q^11 + 8 * q^12 - 8 * q^13 + 16 * q^14 - 12 * q^15 + 28 * q^17 + 16 * q^19 - 8 * q^20 + 4 * q^21 + 12 * q^25 - 36 * q^26 + 12 * q^27 + 8 * q^28 - 16 * q^29 + 20 * q^32 + 24 * q^33 + 16 * q^34 - 4 * q^35 + 8 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^39 - 4 * q^41 + 16 * q^42 - 12 * q^43 + 16 * q^44 - 12 * q^45 + 4 * q^47 + 24 * q^49 + 28 * q^51 - 36 * q^52 + 28 * q^53 - 24 * q^55 + 56 * q^56 + 16 * q^57 + 20 * q^59 - 8 * q^60 + 32 * q^61 + 12 * q^62 + 4 * q^63 - 4 * q^64 + 8 * q^65 - 4 * q^67 + 64 * q^68 - 16 * q^70 - 8 * q^71 + 4 * q^73 - 36 * q^74 + 12 * q^75 + 8 * q^76 - 28 * q^77 - 36 * q^78 + 40 * q^79 + 12 * q^81 - 28 * q^82 + 100 * q^83 + 8 * q^84 - 28 * q^85 - 20 * q^86 - 16 * q^87 + 80 * q^89 - 24 * q^91 + 44 * q^94 - 16 * q^95 + 20 * q^96 - 8 * q^97 + 28 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

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Database

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