LMFDB - Embedded newform 7007.2.a.bi.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7007,2,Mod(1,7007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7007, 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("7007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7007 = 7^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7007.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:	$55.9511766963$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 1001)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	7007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.02090 q^{2} +1.38596 q^{3} -0.957757 q^{4} -3.23836 q^{5} +1.41493 q^{6} -3.01958 q^{8} -1.07912 q^{9} +O(q^{10})$	\(q+1.02090 q^{2} +1.38596 q^{3} -0.957757 q^{4} -3.23836 q^{5} +1.41493 q^{6} -3.01958 q^{8} -1.07912 q^{9} -3.30606 q^{10} +1.00000 q^{11} -1.32741 q^{12} +1.00000 q^{13} -4.48824 q^{15} -1.16719 q^{16} -4.79402 q^{17} -1.10168 q^{18} -8.20454 q^{19} +3.10157 q^{20} +1.02090 q^{22} +6.06375 q^{23} -4.18502 q^{24} +5.48701 q^{25} +1.02090 q^{26} -5.65349 q^{27} -7.24736 q^{29} -4.58206 q^{30} +6.08184 q^{31} +4.84758 q^{32} +1.38596 q^{33} -4.89423 q^{34} +1.03353 q^{36} +1.71737 q^{37} -8.37604 q^{38} +1.38596 q^{39} +9.77851 q^{40} -4.92464 q^{41} -7.44999 q^{43} -0.957757 q^{44} +3.49458 q^{45} +6.19050 q^{46} +9.27427 q^{47} -1.61768 q^{48} +5.60170 q^{50} -6.64431 q^{51} -0.957757 q^{52} +4.16269 q^{53} -5.77167 q^{54} -3.23836 q^{55} -11.3712 q^{57} -7.39886 q^{58} +1.60379 q^{59} +4.29864 q^{60} +11.9262 q^{61} +6.20897 q^{62} +7.28329 q^{64} -3.23836 q^{65} +1.41493 q^{66} -12.6271 q^{67} +4.59150 q^{68} +8.40410 q^{69} +3.44987 q^{71} +3.25849 q^{72} +8.57996 q^{73} +1.75327 q^{74} +7.60476 q^{75} +7.85796 q^{76} +1.41493 q^{78} +9.46470 q^{79} +3.77978 q^{80} -4.59814 q^{81} -5.02758 q^{82} -5.15030 q^{83} +15.5248 q^{85} -7.60572 q^{86} -10.0445 q^{87} -3.01958 q^{88} -15.5328 q^{89} +3.56763 q^{90} -5.80760 q^{92} +8.42918 q^{93} +9.46813 q^{94} +26.5693 q^{95} +6.71854 q^{96} -11.7633 q^{97} -1.07912 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} + 2 q^{3} + 30 q^{4} + q^{5} - 2 q^{6} + 21 q^{8} + 37 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 + 2 * q^3 + 30 * q^4 + q^5 - 2 * q^6 + 21 * q^8 + 37 * q^9	$ 25 q + 6 q^{2} + 2 q^{3} + 30 q^{4} + q^{5} - 2 q^{6} + 21 q^{8} + 37 q^{9} + 3 q^{10} + 25 q^{11} - 9 q^{12} + 25 q^{13} + 32 q^{16} + q^{17} + 44 q^{18} - 5 q^{19} - 4 q^{20} + 6 q^{22} + 15 q^{23} + 4 q^{24} + 50 q^{25} + 6 q^{26} + 17 q^{27} + 24 q^{29} + q^{30} + 12 q^{31} + 48 q^{32} + 2 q^{33} + 8 q^{34} + 30 q^{36} + 33 q^{37} - 16 q^{38} + 2 q^{39} + 21 q^{40} - 12 q^{41} + 38 q^{43} + 30 q^{44} + 22 q^{45} + 39 q^{46} - 4 q^{47} - 82 q^{48} + 16 q^{50} + 51 q^{51} + 30 q^{52} + 2 q^{53} - 10 q^{54} + q^{55} + 38 q^{57} + 17 q^{58} + 4 q^{59} - 33 q^{60} + 22 q^{61} - 42 q^{62} + 41 q^{64} + q^{65} - 2 q^{66} + 24 q^{67} - 14 q^{68} + 30 q^{69} + 9 q^{71} + 102 q^{72} - 11 q^{73} + 39 q^{74} + 16 q^{75} - 58 q^{76} - 2 q^{78} + 19 q^{79} + 33 q^{80} + 73 q^{81} + 32 q^{82} - 16 q^{83} + 14 q^{85} + 27 q^{86} + 11 q^{87} + 21 q^{88} - 13 q^{89} - 40 q^{90} + 17 q^{93} + 56 q^{94} + 15 q^{95} - 55 q^{96} - 34 q^{97} + 37 q^{99}+O(q^{100}) $ 25 * q + 6 * q^2 + 2 * q^3 + 30 * q^4 + q^5 - 2 * q^6 + 21 * q^8 + 37 * q^9 + 3 * q^10 + 25 * q^11 - 9 * q^12 + 25 * q^13 + 32 * q^16 + q^17 + 44 * q^18 - 5 * q^19 - 4 * q^20 + 6 * q^22 + 15 * q^23 + 4 * q^24 + 50 * q^25 + 6 * q^26 + 17 * q^27 + 24 * q^29 + q^30 + 12 * q^31 + 48 * q^32 + 2 * q^33 + 8 * q^34 + 30 * q^36 + 33 * q^37 - 16 * q^38 + 2 * q^39 + 21 * q^40 - 12 * q^41 + 38 * q^43 + 30 * q^44 + 22 * q^45 + 39 * q^46 - 4 * q^47 - 82 * q^48 + 16 * q^50 + 51 * q^51 + 30 * q^52 + 2 * q^53 - 10 * q^54 + q^55 + 38 * q^57 + 17 * q^58 + 4 * q^59 - 33 * q^60 + 22 * q^61 - 42 * q^62 + 41 * q^64 + q^65 - 2 * q^66 + 24 * q^67 - 14 * q^68 + 30 * q^69 + 9 * q^71 + 102 * q^72 - 11 * q^73 + 39 * q^74 + 16 * q^75 - 58 * q^76 - 2 * q^78 + 19 * q^79 + 33 * q^80 + 73 * q^81 + 32 * q^82 - 16 * q^83 + 14 * q^85 + 27 * q^86 + 11 * q^87 + 21 * q^88 - 13 * q^89 - 40 * q^90 + 17 * q^93 + 56 * q^94 + 15 * q^95 - 55 * q^96 - 34 * q^97 + 37 * 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 $

$2$	1.02090	0.721888	0.360944	−	0.932588i	$-0.382455\pi$
$2$	1.02090	0.721888	0.360944	+	0.932588i	$0.382455\pi$
$3$	1.38596	0.800183	0.400092	−	0.916475i	$-0.368978\pi$
$3$	1.38596	0.800183	0.400092	+	0.916475i	$0.368978\pi$
$4$	−0.957757	−0.478878
$5$	−3.23836	−1.44824	−0.724120	−	0.689674i	$-0.757754\pi$
$5$	−3.23836	−1.44824	−0.724120	+	0.689674i	$0.757754\pi$
$6$	1.41493	0.577642
$7$	0	0
$7$	0	0
$8$	−3.01958	−1.06758
$9$	−1.07912	−0.359707
$10$	−3.30606	−1.04547
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.32741	−0.383190
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	−4.48824	−1.15886
$16$	−1.16719	−0.291797
$17$	−4.79402	−1.16272	−0.581360	−	0.813646i	$-0.697479\pi$
$17$	−4.79402	−1.16272	−0.581360	+	0.813646i	$0.697479\pi$
$18$	−1.10168	−0.259668
$19$	−8.20454	−1.88225	−0.941126	−	0.338057i	$-0.890230\pi$
$19$	−8.20454	−1.88225	−0.941126	+	0.338057i	$0.890230\pi$
$20$	3.10157	0.693531
$21$	0	0
$22$	1.02090	0.217657
$23$	6.06375	1.26438	0.632190	−	0.774814i	$-0.282156\pi$
$23$	6.06375	1.26438	0.632190	+	0.774814i	$0.282156\pi$
$24$	−4.18502	−0.854263
$25$	5.48701	1.09740
$26$	1.02090	0.200216
$27$	−5.65349	−1.08801
$28$	0	0
$29$	−7.24736	−1.34580	−0.672901	−	0.739733i	$-0.734952\pi$
$29$	−7.24736	−1.34580	−0.672901	+	0.739733i	$0.734952\pi$
$30$	−4.58206	−0.836565
$31$	6.08184	1.09233	0.546165	−	0.837677i	$-0.316087\pi$
$31$	6.08184	1.09233	0.546165	+	0.837677i	$0.316087\pi$
$32$	4.84758	0.856939
$33$	1.38596	0.241264
$34$	−4.89423	−0.839353
$35$	0	0
$36$	1.03353	0.172256
$37$	1.71737	0.282334	0.141167	−	0.989986i	$-0.454915\pi$
$37$	1.71737	0.282334	0.141167	+	0.989986i	$0.454915\pi$
$38$	−8.37604	−1.35877
$39$	1.38596	0.221931
$40$	9.77851	1.54612
$41$	−4.92464	−0.769099	−0.384550	−	0.923104i	$-0.625643\pi$
$41$	−4.92464	−0.769099	−0.384550	+	0.923104i	$0.625643\pi$
$42$	0	0
$43$	−7.44999	−1.13611	−0.568057	−	0.822990i	$-0.692305\pi$
$43$	−7.44999	−1.13611	−0.568057	+	0.822990i	$0.692305\pi$
$44$	−0.957757	−0.144387
$45$	3.49458	0.520942
$46$	6.19050	0.912740
$47$	9.27427	1.35279	0.676396	−	0.736539i	$-0.263541\pi$
$47$	9.27427	1.35279	0.676396	+	0.736539i	$0.263541\pi$
$48$	−1.61768	−0.233491
$49$	0	0
$50$	5.60170	0.792201
$51$	−6.64431	−0.930389
$52$	−0.957757	−0.132817
$53$	4.16269	0.571789	0.285894	−	0.958261i	$-0.407709\pi$
$53$	4.16269	0.571789	0.285894	+	0.958261i	$0.407709\pi$
$54$	−5.77167	−0.785424
$55$	−3.23836	−0.436661
$56$	0	0
$57$	−11.3712	−1.50615
$58$	−7.39886	−0.971517
$59$	1.60379	0.208796	0.104398	−	0.994536i	$-0.466708\pi$
$59$	1.60379	0.208796	0.104398	+	0.994536i	$0.466708\pi$
$60$	4.29864	0.554952
$61$	11.9262	1.52699	0.763496	−	0.645812i	$-0.223481\pi$
$61$	11.9262	1.52699	0.763496	+	0.645812i	$0.223481\pi$
$62$	6.20897	0.788540
$63$	0	0
$64$	7.28329	0.910411
$65$	−3.23836	−0.401670
$66$	1.41493	0.174166
$67$	−12.6271	−1.54264	−0.771322	−	0.636445i	$-0.780404\pi$
$67$	−12.6271	−1.54264	−0.771322	+	0.636445i	$0.780404\pi$
$68$	4.59150	0.556801
$69$	8.40410	1.01174
$70$	0	0
$71$	3.44987	0.409424	0.204712	−	0.978822i	$-0.434374\pi$
$71$	3.44987	0.409424	0.204712	+	0.978822i	$0.434374\pi$
$72$	3.25849	0.384017
$73$	8.57996	1.00421	0.502104	−	0.864807i	$-0.332559\pi$
$73$	8.57996	1.00421	0.502104	+	0.864807i	$0.332559\pi$
$74$	1.75327	0.203813
$75$	7.60476	0.878122
$76$	7.85796	0.901369
$77$	0	0
$78$	1.41493	0.160209
$79$	9.46470	1.06486	0.532431	−	0.846474i	$-0.321279\pi$
$79$	9.46470	1.06486	0.532431	+	0.846474i	$0.321279\pi$
$80$	3.77978	0.422593
$81$	−4.59814	−0.510905
$82$	−5.02758	−0.555203
$83$	−5.15030	−0.565319	−0.282659	−	0.959220i	$-0.591217\pi$
$83$	−5.15030	−0.565319	−0.282659	+	0.959220i	$0.591217\pi$
$84$	0	0
$85$	15.5248	1.68390
$86$	−7.60572	−0.820146
$87$	−10.0445	−1.07689
$88$	−3.01958	−0.321889
$89$	−15.5328	−1.64647	−0.823237	−	0.567698i	$-0.807834\pi$
$89$	−15.5328	−1.64647	−0.823237	+	0.567698i	$0.807834\pi$
$90$	3.56763	0.376061
$91$	0	0
$92$	−5.80760	−0.605484
$93$	8.42918	0.874065
$94$	9.46813	0.976563
$95$	26.5693	2.72595
$96$	6.71854	0.685708
$97$	−11.7633	−1.19438	−0.597191	−	0.802099i	$-0.703716\pi$
$97$	−11.7633	−1.19438	−0.597191	+	0.802099i	$0.703716\pi$
$98$	0	0
$99$	−1.07912	−0.108456
$100$	−5.25522	−0.525522
$101$	1.21038	0.120437	0.0602184	−	0.998185i	$-0.480820\pi$
$101$	1.21038	0.120437	0.0602184	+	0.998185i	$0.480820\pi$
$102$	−6.78319	−0.671636
$103$	−2.72275	−0.268281	−0.134141	−	0.990962i	$-0.542827\pi$
$103$	−2.72275	−0.268281	−0.134141	+	0.990962i	$0.542827\pi$
$104$	−3.01958	−0.296094
$105$	0	0
$106$	4.24970	0.412767
$107$	15.1491	1.46452	0.732260	−	0.681025i	$-0.238466\pi$
$107$	15.1491	1.46452	0.732260	+	0.681025i	$0.238466\pi$
$108$	5.41467	0.521027
$109$	3.66109	0.350669	0.175334	−	0.984509i	$-0.443899\pi$
$109$	3.66109	0.350669	0.175334	+	0.984509i	$0.443899\pi$
$110$	−3.30606	−0.315220
$111$	2.38020	0.225919
$112$	0	0
$113$	12.8965	1.21320	0.606600	−	0.795007i	$-0.292533\pi$
$113$	12.8965	1.21320	0.606600	+	0.795007i	$0.292533\pi$
$114$	−11.6088	−1.08727
$115$	−19.6366	−1.83113
$116$	6.94121	0.644475
$117$	−1.07912	−0.0997646
$118$	1.63731	0.150727
$119$	0	0
$120$	13.5526	1.23718
$121$	1.00000	0.0909091
$122$	12.1755	1.10232
$123$	−6.82534	−0.615421
$124$	−5.82492	−0.523093
$125$	−1.57711	−0.141061
$126$	0	0
$127$	18.2556	1.61992	0.809959	−	0.586486i	$-0.199489\pi$
$127$	18.2556	1.61992	0.809959	+	0.586486i	$0.199489\pi$
$128$	−2.25963	−0.199725
$129$	−10.3254	−0.909099
$130$	−3.30606	−0.289960
$131$	−6.48044	−0.566199	−0.283100	−	0.959091i	$-0.591363\pi$
$131$	−6.48044	−0.566199	−0.283100	+	0.959091i	$0.591363\pi$
$132$	−1.32741	−0.115536
$133$	0	0
$134$	−12.8910	−1.11362
$135$	18.3081	1.57571
$136$	14.4759	1.24130
$137$	1.05495	0.0901307	0.0450653	−	0.998984i	$-0.485650\pi$
$137$	1.05495	0.0901307	0.0450653	+	0.998984i	$0.485650\pi$
$138$	8.57978	0.730359
$139$	9.17581	0.778282	0.389141	−	0.921178i	$-0.372772\pi$
$139$	9.17581	0.778282	0.389141	+	0.921178i	$0.372772\pi$
$140$	0	0
$141$	12.8538	1.08248
$142$	3.52198	0.295558
$143$	1.00000	0.0836242
$144$	1.25954	0.104961
$145$	23.4696	1.94904
$146$	8.75931	0.724926
$147$	0	0
$148$	−1.64482	−0.135203
$149$	6.88613	0.564134	0.282067	−	0.959395i	$-0.408980\pi$
$149$	6.88613	0.564134	0.282067	+	0.959395i	$0.408980\pi$
$150$	7.76373	0.633906
$151$	16.8115	1.36810	0.684051	−	0.729434i	$-0.260216\pi$
$151$	16.8115	1.36810	0.684051	+	0.729434i	$0.260216\pi$
$152$	24.7743	2.00946
$153$	5.17332	0.418238
$154$	0	0
$155$	−19.6952	−1.58196
$156$	−1.32741	−0.106278
$157$	4.00084	0.319302	0.159651	−	0.987174i	$-0.448963\pi$
$157$	4.00084	0.319302	0.159651	+	0.987174i	$0.448963\pi$
$158$	9.66254	0.768710
$159$	5.76931	0.457536
$160$	−15.6982	−1.24105
$161$	0	0
$162$	−4.69426	−0.368816
$163$	2.79832	0.219181	0.109591	−	0.993977i	$-0.465046\pi$
$163$	2.79832	0.219181	0.109591	+	0.993977i	$0.465046\pi$
$164$	4.71661	0.368305
$165$	−4.48824	−0.349409
$166$	−5.25796	−0.408097
$167$	−15.3965	−1.19142	−0.595710	−	0.803200i	$-0.703129\pi$
$167$	−15.3965	−1.19142	−0.595710	+	0.803200i	$0.703129\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	15.8493	1.21559
$171$	8.85368	0.677058
$172$	7.13528	0.544060
$173$	8.26949	0.628718	0.314359	−	0.949304i	$-0.398210\pi$
$173$	8.26949	0.628718	0.314359	+	0.949304i	$0.398210\pi$
$174$	−10.2545	−0.777392
$175$	0	0
$176$	−1.16719	−0.0879802
$177$	2.22279	0.167075
$178$	−15.8575	−1.18857
$179$	−9.13763	−0.682978	−0.341489	−	0.939886i	$-0.610931\pi$
$179$	−9.13763	−0.682978	−0.341489	+	0.939886i	$0.610931\pi$
$180$	−3.34696	−0.249468
$181$	−19.2760	−1.43277	−0.716387	−	0.697703i	$-0.754205\pi$
$181$	−19.2760	−1.43277	−0.716387	+	0.697703i	$0.754205\pi$
$182$	0	0
$183$	16.5292	1.22187
$184$	−18.3100	−1.34983
$185$	−5.56147	−0.408887
$186$	8.60537	0.630977
$187$	−4.79402	−0.350573
$188$	−8.88249	−0.647822
$189$	0	0
$190$	27.1247	1.96783
$191$	2.22059	0.160677	0.0803383	−	0.996768i	$-0.474400\pi$
$191$	2.22059	0.160677	0.0803383	+	0.996768i	$0.474400\pi$
$192$	10.0943	0.728496
$193$	15.9291	1.14660	0.573299	−	0.819346i	$-0.305663\pi$
$193$	15.9291	1.14660	0.573299	+	0.819346i	$0.305663\pi$
$194$	−12.0092	−0.862209
$195$	−4.48824	−0.321409
$196$	0	0
$197$	−9.02193	−0.642786	−0.321393	−	0.946946i	$-0.604151\pi$
$197$	−9.02193	−0.642786	−0.321393	+	0.946946i	$0.604151\pi$
$198$	−1.10168	−0.0782927
$199$	−12.0591	−0.854848	−0.427424	−	0.904051i	$-0.640579\pi$
$199$	−12.0591	−0.854848	−0.427424	+	0.904051i	$0.640579\pi$
$200$	−16.5685	−1.17157
$201$	−17.5006	−1.23440
$202$	1.23568	0.0869419
$203$	0	0
$204$	6.36363	0.445543
$205$	15.9478	1.11384
$206$	−2.77967	−0.193669
$207$	−6.54351	−0.454805
$208$	−1.16719	−0.0809300
$209$	−8.20454	−0.567520
$210$	0	0
$211$	−19.6827	−1.35501	−0.677505	−	0.735518i	$-0.736939\pi$
$211$	−19.6827	−1.35501	−0.677505	+	0.735518i	$0.736939\pi$
$212$	−3.98684	−0.273817
$213$	4.78138	0.327615
$214$	15.4658	1.05722
$215$	24.1258	1.64537
$216$	17.0712	1.16155
$217$	0	0
$218$	3.73762	0.253144
$219$	11.8915	0.803551
$220$	3.10157	0.209108
$221$	−4.79402	−0.322480
$222$	2.42995	0.163088
$223$	27.5664	1.84598	0.922992	−	0.384819i	$-0.125736\pi$
$223$	27.5664	1.84598	0.922992	+	0.384819i	$0.125736\pi$
$224$	0	0
$225$	−5.92114	−0.394742
$226$	13.1661	0.875794
$227$	15.3274	1.01732	0.508659	−	0.860968i	$-0.330141\pi$
$227$	15.3274	1.01732	0.508659	+	0.860968i	$0.330141\pi$
$228$	10.8908	0.721261
$229$	−21.6422	−1.43016	−0.715078	−	0.699044i	$-0.753609\pi$
$229$	−21.6422	−1.43016	−0.715078	+	0.699044i	$0.753609\pi$
$230$	−20.0471	−1.32187
$231$	0	0
$232$	21.8840	1.43676
$233$	11.3880	0.746054	0.373027	−	0.927820i	$-0.378320\pi$
$233$	11.3880	0.746054	0.373027	+	0.927820i	$0.378320\pi$
$234$	−1.10168	−0.0720189
$235$	−30.0335	−1.95917
$236$	−1.53604	−0.0999878
$237$	13.1177	0.852085
$238$	0	0
$239$	19.9330	1.28936	0.644680	−	0.764453i	$-0.276991\pi$
$239$	19.9330	1.28936	0.644680	+	0.764453i	$0.276991\pi$
$240$	5.23862	0.338152
$241$	17.0291	1.09694	0.548470	−	0.836170i	$-0.315210\pi$
$241$	17.0291	1.09694	0.548470	+	0.836170i	$0.315210\pi$
$242$	1.02090	0.0656261
$243$	10.5876	0.679197
$244$	−11.4224	−0.731244
$245$	0	0
$246$	−6.96802	−0.444264
$247$	−8.20454	−0.522043
$248$	−18.3646	−1.16615
$249$	−7.13810	−0.452359
$250$	−1.61008	−0.101830
$251$	9.48244	0.598526	0.299263	−	0.954171i	$-0.403259\pi$
$251$	9.48244	0.598526	0.299263	+	0.954171i	$0.403259\pi$
$252$	0	0
$253$	6.06375	0.381225
$254$	18.6372	1.16940
$255$	21.5167	1.34743
$256$	−16.8734	−1.05459
$257$	−4.54349	−0.283415	−0.141707	−	0.989909i	$-0.545259\pi$
$257$	−4.54349	−0.283415	−0.141707	+	0.989909i	$0.545259\pi$
$258$	−10.5412	−0.656267
$259$	0	0
$260$	3.10157	0.192351
$261$	7.82077	0.484094
$262$	−6.61591	−0.408732
$263$	−17.9279	−1.10548	−0.552741	−	0.833353i	$-0.686418\pi$
$263$	−17.9279	−1.10548	−0.552741	+	0.833353i	$0.686418\pi$
$264$	−4.18502	−0.257570
$265$	−13.4803	−0.828088
$266$	0	0
$267$	−21.5278	−1.31748
$268$	12.0937	0.738739
$269$	−13.0715	−0.796981	−0.398491	−	0.917172i	$-0.630466\pi$
$269$	−13.0715	−0.796981	−0.398491	+	0.917172i	$0.630466\pi$
$270$	18.6908	1.13748
$271$	7.74544	0.470502	0.235251	−	0.971935i	$-0.424409\pi$
$271$	7.74544	0.470502	0.235251	+	0.971935i	$0.424409\pi$
$272$	5.59552	0.339278
$273$	0	0
$274$	1.07700	0.0650642
$275$	5.48701	0.330879
$276$	−8.04909	−0.484498
$277$	17.4861	1.05064	0.525320	−	0.850905i	$-0.323946\pi$
$277$	17.4861	1.05064	0.525320	+	0.850905i	$0.323946\pi$
$278$	9.36762	0.561832
$279$	−6.56303	−0.392918
$280$	0	0
$281$	22.7675	1.35820	0.679098	−	0.734048i	$-0.262371\pi$
$281$	22.7675	1.35820	0.679098	+	0.734048i	$0.262371\pi$
$282$	13.1224	0.781430
$283$	6.08471	0.361699	0.180849	−	0.983511i	$-0.442115\pi$
$283$	6.08471	0.361699	0.180849	+	0.983511i	$0.442115\pi$
$284$	−3.30414	−0.196064
$285$	36.8240	2.18126
$286$	1.02090	0.0603673
$287$	0	0
$288$	−5.23112	−0.308247
$289$	5.98260	0.351918
$290$	23.9602	1.40699
$291$	−16.3034	−0.955724
$292$	−8.21751	−0.480894
$293$	−32.3607	−1.89053	−0.945265	−	0.326302i	$-0.894197\pi$
$293$	−32.3607	−1.89053	−0.945265	+	0.326302i	$0.894197\pi$
$294$	0	0
$295$	−5.19366	−0.302387
$296$	−5.18574	−0.301415
$297$	−5.65349	−0.328049
$298$	7.03007	0.407241
$299$	6.06375	0.350676
$300$	−7.28351	−0.420514
$301$	0	0
$302$	17.1629	0.987616
$303$	1.67753	0.0963716
$304$	9.57625	0.549236
$305$	−38.6214	−2.21145
$306$	5.28146	0.301921
$307$	−19.5270	−1.11447	−0.557233	−	0.830356i	$-0.688137\pi$
$307$	−19.5270	−1.11447	−0.557233	+	0.830356i	$0.688137\pi$
$308$	0	0
$309$	−3.77362	−0.214674
$310$	−20.1069	−1.14200
$311$	−3.36505	−0.190815	−0.0954074	−	0.995438i	$-0.530415\pi$
$311$	−3.36505	−0.190815	−0.0954074	+	0.995438i	$0.530415\pi$
$312$	−4.18502	−0.236930
$313$	−1.22858	−0.0694433	−0.0347216	−	0.999397i	$-0.511054\pi$
$313$	−1.22858	−0.0694433	−0.0347216	+	0.999397i	$0.511054\pi$
$314$	4.08447	0.230500
$315$	0	0
$316$	−9.06488	−0.509939
$317$	0.820320	0.0460738	0.0230369	−	0.999735i	$-0.492666\pi$
$317$	0.820320	0.0460738	0.0230369	+	0.999735i	$0.492666\pi$
$318$	5.88991	0.330290
$319$	−7.24736	−0.405774
$320$	−23.5859	−1.31849
$321$	20.9960	1.17188
$322$	0	0
$323$	39.3327	2.18853
$324$	4.40390	0.244661
$325$	5.48701	0.304364
$326$	2.85681	0.158224
$327$	5.07412	0.280600
$328$	14.8704	0.821078
$329$	0	0
$330$	−4.58206	−0.252234
$331$	7.73617	0.425219	0.212609	−	0.977137i	$-0.431804\pi$
$331$	7.73617	0.425219	0.212609	+	0.977137i	$0.431804\pi$
$332$	4.93273	0.270719
$333$	−1.85325	−0.101557
$334$	−15.7184	−0.860071
$335$	40.8911	2.23412
$336$	0	0
$337$	4.64723	0.253151	0.126575	−	0.991957i	$-0.459601\pi$
$337$	4.64723	0.253151	0.126575	+	0.991957i	$0.459601\pi$
$338$	1.02090	0.0555298
$339$	17.8740	0.970782
$340$	−14.8690	−0.806382
$341$	6.08184	0.329350
$342$	9.03875	0.488760
$343$	0	0
$344$	22.4959	1.21290
$345$	−27.2156	−1.46524
$346$	8.44235	0.453864
$347$	−8.85597	−0.475414	−0.237707	−	0.971337i	$-0.576396\pi$
$347$	−8.85597	−0.475414	−0.237707	+	0.971337i	$0.576396\pi$
$348$	9.62023	0.515698
$349$	18.7943	1.00604	0.503019	−	0.864275i	$-0.332223\pi$
$349$	18.7943	1.00604	0.503019	+	0.864275i	$0.332223\pi$
$350$	0	0
$351$	−5.65349	−0.301761
$352$	4.84758	0.258377
$353$	−18.7399	−0.997423	−0.498712	−	0.866768i	$-0.666193\pi$
$353$	−18.7399	−0.997423	−0.498712	+	0.866768i	$0.666193\pi$
$354$	2.26925	0.120609
$355$	−11.1719	−0.592945
$356$	14.8766	0.788461
$357$	0	0
$358$	−9.32863	−0.493034
$359$	35.1043	1.85273	0.926367	−	0.376622i	$-0.122914\pi$
$359$	35.1043	1.85273	0.926367	+	0.376622i	$0.122914\pi$
$360$	−10.5522	−0.556149
$361$	48.3145	2.54287
$362$	−19.6789	−1.03430
$363$	1.38596	0.0727439
$364$	0	0
$365$	−27.7850	−1.45434
$366$	16.8747	0.882056
$367$	−3.46929	−0.181096	−0.0905479	−	0.995892i	$-0.528862\pi$
$367$	−3.46929	−0.181096	−0.0905479	+	0.995892i	$0.528862\pi$
$368$	−7.07754	−0.368942
$369$	5.31427	0.276650
$370$	−5.67772	−0.295171
$371$	0	0
$372$	−8.07310	−0.418571
$373$	−17.3676	−0.899262	−0.449631	−	0.893214i	$-0.648444\pi$
$373$	−17.3676	−0.899262	−0.449631	+	0.893214i	$0.648444\pi$
$374$	−4.89423	−0.253074
$375$	−2.18581	−0.112875
$376$	−28.0044	−1.44422
$377$	−7.24736	−0.373258
$378$	0	0
$379$	2.41786	0.124197	0.0620985	−	0.998070i	$-0.480221\pi$
$379$	2.41786	0.124197	0.0620985	+	0.998070i	$0.480221\pi$
$380$	−25.4469	−1.30540
$381$	25.3014	1.29623
$382$	2.26701	0.115990
$383$	−1.16308	−0.0594306	−0.0297153	−	0.999558i	$-0.509460\pi$
$383$	−1.16308	−0.0594306	−0.0297153	+	0.999558i	$0.509460\pi$
$384$	−3.13175	−0.159816
$385$	0	0
$386$	16.2620	0.827715
$387$	8.03943	0.408667
$388$	11.2664	0.571963
$389$	21.4137	1.08572	0.542860	−	0.839823i	$-0.317342\pi$
$389$	21.4137	1.08572	0.542860	+	0.839823i	$0.317342\pi$
$390$	−4.58206	−0.232021
$391$	−29.0697	−1.47012
$392$	0	0
$393$	−8.98163	−0.453063
$394$	−9.21052	−0.464019
$395$	−30.6501	−1.54218
$396$	1.03353	0.0519370
$397$	−7.32256	−0.367509	−0.183754	−	0.982972i	$-0.558825\pi$
$397$	−7.32256	−0.367509	−0.183754	+	0.982972i	$0.558825\pi$
$398$	−12.3112	−0.617104
$399$	0	0
$400$	−6.40437	−0.320219
$401$	18.7995	0.938800	0.469400	−	0.882986i	$-0.344470\pi$
$401$	18.7995	0.938800	0.469400	+	0.882986i	$0.344470\pi$
$402$	−17.8664	−0.891097
$403$	6.08184	0.302958
$404$	−1.15925	−0.0576746
$405$	14.8905	0.739913
$406$	0	0
$407$	1.71737	0.0851268
$408$	20.0630	0.993268
$409$	−8.78415	−0.434348	−0.217174	−	0.976133i	$-0.569684\pi$
$409$	−8.78415	−0.434348	−0.217174	+	0.976133i	$0.569684\pi$
$410$	16.2811	0.804068
$411$	1.46212	0.0721211
$412$	2.60774	0.128474
$413$	0	0
$414$	−6.68029	−0.328318
$415$	16.6785	0.818718
$416$	4.84758	0.237672
$417$	12.7173	0.622768
$418$	−8.37604	−0.409686
$419$	−38.2464	−1.86846	−0.934229	−	0.356673i	$-0.883911\pi$
$419$	−38.2464	−1.86846	−0.934229	+	0.356673i	$0.883911\pi$
$420$	0	0
$421$	−7.24846	−0.353268	−0.176634	−	0.984277i	$-0.556521\pi$
$421$	−7.24846	−0.353268	−0.176634	+	0.984277i	$0.556521\pi$
$422$	−20.0941	−0.978165
$423$	−10.0080	−0.486608
$424$	−12.5696	−0.610433
$425$	−26.3048	−1.27597
$426$	4.88132	0.236501
$427$	0	0
$428$	−14.5092	−0.701327
$429$	1.38596	0.0669147
$430$	24.6301	1.18777
$431$	4.37311	0.210646	0.105323	−	0.994438i	$-0.466412\pi$
$431$	4.37311	0.210646	0.105323	+	0.994438i	$0.466412\pi$
$432$	6.59869	0.317480
$433$	−4.82105	−0.231685	−0.115842	−	0.993268i	$-0.536957\pi$
$433$	−4.82105	−0.231685	−0.115842	+	0.993268i	$0.536957\pi$
$434$	0	0
$435$	32.5279	1.55959
$436$	−3.50644	−0.167928
$437$	−49.7503	−2.37988
$438$	12.1400	0.580073
$439$	38.0413	1.81561	0.907805	−	0.419392i	$-0.137757\pi$
$439$	38.0413	1.81561	0.907805	+	0.419392i	$0.137757\pi$
$440$	9.77851	0.466172
$441$	0	0
$442$	−4.89423	−0.232795
$443$	11.7925	0.560278	0.280139	−	0.959959i	$-0.409619\pi$
$443$	11.7925	0.560278	0.280139	+	0.959959i	$0.409619\pi$
$444$	−2.27965	−0.108188
$445$	50.3009	2.38449
$446$	28.1426	1.33259
$447$	9.54389	0.451411
$448$	0	0
$449$	−26.1941	−1.23617	−0.618087	−	0.786109i	$-0.712092\pi$
$449$	−26.1941	−1.23617	−0.618087	+	0.786109i	$0.712092\pi$
$450$	−6.04491	−0.284960
$451$	−4.92464	−0.231892
$452$	−12.3517	−0.580975
$453$	23.3001	1.09473
$454$	15.6478	0.734389
$455$	0	0
$456$	34.3362	1.60794
$457$	−33.3662	−1.56080	−0.780402	−	0.625278i	$-0.784985\pi$
$457$	−33.3662	−1.56080	−0.780402	+	0.625278i	$0.784985\pi$
$458$	−22.0946	−1.03241
$459$	27.1029	1.26506
$460$	18.8071	0.876886
$461$	34.1948	1.59261	0.796304	−	0.604896i	$-0.206785\pi$
$461$	34.1948	1.59261	0.796304	+	0.604896i	$0.206785\pi$
$462$	0	0
$463$	9.03569	0.419924	0.209962	−	0.977710i	$-0.432666\pi$
$463$	9.03569	0.419924	0.209962	+	0.977710i	$0.432666\pi$
$464$	8.45904	0.392701
$465$	−27.2967	−1.26586
$466$	11.6261	0.538567
$467$	24.8643	1.15058	0.575291	−	0.817949i	$-0.304889\pi$
$467$	24.8643	1.15058	0.575291	+	0.817949i	$0.304889\pi$
$468$	1.03353	0.0477751
$469$	0	0
$470$	−30.6613	−1.41430
$471$	5.54500	0.255500
$472$	−4.84278	−0.222907
$473$	−7.44999	−0.342551
$474$	13.3919	0.615109
$475$	−45.0184	−2.06559
$476$	0	0
$477$	−4.49204	−0.205676
$478$	20.3497	0.930773
$479$	−5.07645	−0.231949	−0.115974	−	0.993252i	$-0.536999\pi$
$479$	−5.07645	−0.231949	−0.115974	+	0.993252i	$0.536999\pi$
$480$	−21.7571	−0.993071
$481$	1.71737	0.0783053
$482$	17.3851	0.791867
$483$	0	0
$484$	−0.957757	−0.0435344
$485$	38.0938	1.72975
$486$	10.8090	0.490304
$487$	10.8725	0.492681	0.246340	−	0.969183i	$-0.420772\pi$
$487$	10.8725	0.492681	0.246340	+	0.969183i	$0.420772\pi$
$488$	−36.0121	−1.63019
$489$	3.87835	0.175385
$490$	0	0
$491$	−10.2761	−0.463753	−0.231876	−	0.972745i	$-0.574487\pi$
$491$	−10.2761	−0.463753	−0.231876	+	0.972745i	$0.574487\pi$
$492$	6.53702	0.294712
$493$	34.7440	1.56479
$494$	−8.37604	−0.376856
$495$	3.49458	0.157070
$496$	−7.09866	−0.318739
$497$	0	0
$498$	−7.28731	−0.326552
$499$	−16.3118	−0.730215	−0.365108	−	0.930965i	$-0.618968\pi$
$499$	−16.3118	−0.730215	−0.365108	+	0.930965i	$0.618968\pi$
$500$	1.51049	0.0675510
$501$	−21.3389	−0.953354
$502$	9.68065	0.432069
$503$	−20.6109	−0.918994	−0.459497	−	0.888179i	$-0.651970\pi$
$503$	−20.6109	−0.918994	−0.459497	+	0.888179i	$0.651970\pi$
$504$	0	0
$505$	−3.91964	−0.174422
$506$	6.19050	0.275201
$507$	1.38596	0.0615526
$508$	−17.4844	−0.775744
$509$	−13.7475	−0.609349	−0.304675	−	0.952457i	$-0.598548\pi$
$509$	−13.7475	−0.609349	−0.304675	+	0.952457i	$0.598548\pi$
$510$	21.9665	0.972691
$511$	0	0
$512$	−12.7069	−0.561570
$513$	46.3843	2.04792
$514$	−4.63846	−0.204594
$515$	8.81727	0.388536
$516$	9.88920	0.435348
$517$	9.27427	0.407882
$518$	0	0
$519$	11.4612	0.503089
$520$	9.77851	0.428816
$521$	5.37509	0.235487	0.117744	−	0.993044i	$-0.462434\pi$
$521$	5.37509	0.235487	0.117744	+	0.993044i	$0.462434\pi$
$522$	7.98425	0.349461
$523$	31.7443	1.38808	0.694040	−	0.719936i	$-0.255829\pi$
$523$	31.7443	1.38808	0.694040	+	0.719936i	$0.255829\pi$
$524$	6.20669	0.271140
$525$	0	0
$526$	−18.3027	−0.798034
$527$	−29.1564	−1.27007
$528$	−1.61768	−0.0704003
$529$	13.7691	0.598654
$530$	−13.7621	−0.597787
$531$	−1.73068	−0.0751052
$532$	0	0
$533$	−4.92464	−0.213310
$534$	−21.9778	−0.951073
$535$	−49.0583	−2.12098
$536$	38.1286	1.64690
$537$	−12.6644	−0.546508
$538$	−13.3447	−0.575331
$539$	0	0
$540$	−17.5347	−0.754572
$541$	19.9565	0.857995	0.428997	−	0.903306i	$-0.358867\pi$
$541$	19.9565	0.857995	0.428997	+	0.903306i	$0.358867\pi$
$542$	7.90734	0.339650
$543$	−26.7157	−1.14648
$544$	−23.2394	−0.996380
$545$	−11.8560	−0.507853
$546$	0	0
$547$	−11.4257	−0.488528	−0.244264	−	0.969709i	$-0.578546\pi$
$547$	−11.4257	−0.488528	−0.244264	+	0.969709i	$0.578546\pi$
$548$	−1.01039	−0.0431616
$549$	−12.8698	−0.549269
$550$	5.60170	0.238857
$551$	59.4613	2.53314
$552$	−25.3769	−1.08011
$553$	0	0
$554$	17.8516	0.758444
$555$	−7.70796	−0.327185
$556$	−8.78819	−0.372702
$557$	−10.9049	−0.462058	−0.231029	−	0.972947i	$-0.574209\pi$
$557$	−10.9049	−0.462058	−0.231029	+	0.972947i	$0.574209\pi$
$558$	−6.70022	−0.283643
$559$	−7.44999	−0.315101
$560$	0	0
$561$	−6.64431	−0.280523
$562$	23.2434	0.980465
$563$	24.0189	1.01228	0.506138	−	0.862453i	$-0.331073\pi$
$563$	24.0189	1.01228	0.506138	+	0.862453i	$0.331073\pi$
$564$	−12.3108	−0.518377
$565$	−41.7635	−1.75701
$566$	6.21190	0.261106
$567$	0	0
$568$	−10.4172	−0.437095
$569$	−7.39163	−0.309873	−0.154937	−	0.987924i	$-0.549517\pi$
$569$	−7.39163	−0.309873	−0.154937	+	0.987924i	$0.549517\pi$
$570$	37.5937	1.57463
$571$	18.5036	0.774353	0.387176	−	0.922006i	$-0.373450\pi$
$571$	18.5036	0.774353	0.387176	+	0.922006i	$0.373450\pi$
$572$	−0.957757	−0.0400458
$573$	3.07765	0.128571
$574$	0	0
$575$	33.2718	1.38753
$576$	−7.85954	−0.327481
$577$	6.49857	0.270539	0.135270	−	0.990809i	$-0.456810\pi$
$577$	6.49857	0.270539	0.135270	+	0.990809i	$0.456810\pi$
$578$	6.10765	0.254045
$579$	22.0770	0.917489
$580$	−22.4782	−0.933355
$581$	0	0
$582$	−16.6442	−0.689925
$583$	4.16269	0.172401
$584$	−25.9079	−1.07208
$585$	3.49458	0.144483
$586$	−33.0371	−1.36475
$587$	−34.8019	−1.43643	−0.718215	−	0.695821i	$-0.755041\pi$
$587$	−34.8019	−1.43643	−0.718215	+	0.695821i	$0.755041\pi$
$588$	0	0
$589$	−49.8987	−2.05604
$590$	−5.30222	−0.218289
$591$	−12.5040	−0.514347
$592$	−2.00449	−0.0823842
$593$	−20.6215	−0.846822	−0.423411	−	0.905938i	$-0.639167\pi$
$593$	−20.6215	−0.846822	−0.423411	+	0.905938i	$0.639167\pi$
$594$	−5.77167	−0.236814
$595$	0	0
$596$	−6.59524	−0.270152
$597$	−16.7134	−0.684036
$598$	6.19050	0.253148
$599$	−19.6409	−0.802507	−0.401253	−	0.915967i	$-0.631425\pi$
$599$	−19.6409	−0.802507	−0.401253	+	0.915967i	$0.631425\pi$
$600$	−22.9632	−0.937469
$601$	−3.17432	−0.129483	−0.0647417	−	0.997902i	$-0.520622\pi$
$601$	−3.17432	−0.129483	−0.0647417	+	0.997902i	$0.520622\pi$
$602$	0	0
$603$	13.6261	0.554899
$604$	−16.1014	−0.655155
$605$	−3.23836	−0.131658
$606$	1.71260	0.0695694
$607$	36.7844	1.49303	0.746516	−	0.665367i	$-0.231725\pi$
$607$	36.7844	1.49303	0.746516	+	0.665367i	$0.231725\pi$
$608$	−39.7722	−1.61297
$609$	0	0
$610$	−39.4287	−1.59642
$611$	9.27427	0.375197
$612$	−4.95478	−0.200285
$613$	−9.24389	−0.373357	−0.186679	−	0.982421i	$-0.559772\pi$
$613$	−9.24389	−0.373357	−0.186679	+	0.982421i	$0.559772\pi$
$614$	−19.9352	−0.804520
$615$	22.1030	0.891277
$616$	0	0
$617$	−43.4223	−1.74812	−0.874058	−	0.485822i	$-0.838520\pi$
$617$	−43.4223	−1.74812	−0.874058	+	0.485822i	$0.838520\pi$
$618$	−3.85251	−0.154970
$619$	38.4526	1.54554	0.772770	−	0.634686i	$-0.218871\pi$
$619$	38.4526	1.54554	0.772770	+	0.634686i	$0.218871\pi$
$620$	18.8632	0.757565
$621$	−34.2813	−1.37566
$622$	−3.43539	−0.137747
$623$	0	0
$624$	−1.61768	−0.0647588
$625$	−22.3278	−0.893111
$626$	−1.25426	−0.0501302
$627$	−11.3712	−0.454120
$628$	−3.83183	−0.152907
$629$	−8.23309	−0.328275
$630$	0	0
$631$	−24.8342	−0.988633	−0.494317	−	0.869282i	$-0.664582\pi$
$631$	−24.8342	−0.988633	−0.494317	+	0.869282i	$0.664582\pi$
$632$	−28.5794	−1.13683
$633$	−27.2794	−1.08426
$634$	0.837467	0.0332601
$635$	−59.1181	−2.34603
$636$	−5.52559	−0.219104
$637$	0	0
$638$	−7.39886	−0.292924
$639$	−3.72282	−0.147273
$640$	7.31750	0.289250
$641$	−9.42965	−0.372449	−0.186224	−	0.982507i	$-0.559625\pi$
$641$	−9.42965	−0.372449	−0.186224	+	0.982507i	$0.559625\pi$
$642$	21.4349	0.845969
$643$	−26.8222	−1.05776	−0.528882	−	0.848695i	$-0.677389\pi$
$643$	−26.8222	−1.05776	−0.528882	+	0.848695i	$0.677389\pi$
$644$	0	0
$645$	33.4373	1.31659
$646$	40.1549	1.57987
$647$	28.3192	1.11334	0.556671	−	0.830733i	$-0.312078\pi$
$647$	28.3192	1.11334	0.556671	+	0.830733i	$0.312078\pi$
$648$	13.8845	0.545434
$649$	1.60379	0.0629543
$650$	5.60170	0.219717
$651$	0	0
$652$	−2.68011	−0.104961
$653$	−7.73168	−0.302564	−0.151282	−	0.988491i	$-0.548340\pi$
$653$	−7.73168	−0.302564	−0.151282	+	0.988491i	$0.548340\pi$
$654$	5.18019	0.202561
$655$	20.9860	0.819993
$656$	5.74798	0.224421
$657$	−9.25880	−0.361220
$658$	0	0
$659$	−8.34168	−0.324946	−0.162473	−	0.986713i	$-0.551947\pi$
$659$	−8.34168	−0.324946	−0.162473	+	0.986713i	$0.551947\pi$
$660$	4.29864	0.167324
$661$	15.5180	0.603581	0.301790	−	0.953374i	$-0.402416\pi$
$661$	15.5180	0.603581	0.301790	+	0.953374i	$0.402416\pi$
$662$	7.89788	0.306960
$663$	−6.64431	−0.258044
$664$	15.5518	0.603525
$665$	0	0
$666$	−1.89198	−0.0733129
$667$	−43.9462	−1.70160
$668$	14.7461	0.570545
$669$	38.2059	1.47713
$670$	41.7459	1.61278
$671$	11.9262	0.460406
$672$	0	0
$673$	29.8481	1.15056	0.575280	−	0.817957i	$-0.304893\pi$
$673$	29.8481	1.15056	0.575280	+	0.817957i	$0.304893\pi$
$674$	4.74437	0.182746
$675$	−31.0207	−1.19399
$676$	−0.957757	−0.0368368
$677$	6.17346	0.237265	0.118633	−	0.992938i	$-0.462149\pi$
$677$	6.17346	0.237265	0.118633	+	0.992938i	$0.462149\pi$
$678$	18.2476	0.700796
$679$	0	0
$680$	−46.8784	−1.79770
$681$	21.2432	0.814041
$682$	6.20897	0.237754
$683$	−3.22259	−0.123309	−0.0616545	−	0.998098i	$-0.519638\pi$
$683$	−3.22259	−0.123309	−0.0616545	+	0.998098i	$0.519638\pi$
$684$	−8.47967	−0.324228
$685$	−3.41632	−0.130531
$686$	0	0
$687$	−29.9952	−1.14439
$688$	8.69555	0.331515
$689$	4.16269	0.158586
$690$	−27.7844	−1.05774
$691$	6.42695	0.244493	0.122246	−	0.992500i	$-0.460990\pi$
$691$	6.42695	0.244493	0.122246	+	0.992500i	$0.460990\pi$
$692$	−7.92016	−0.301079
$693$	0	0
$694$	−9.04109	−0.343195
$695$	−29.7146	−1.12714
$696$	30.3303	1.14967
$697$	23.6088	0.894247
$698$	19.1872	0.726247
$699$	15.7833	0.596980
$700$	0	0
$701$	36.5622	1.38093	0.690467	−	0.723364i	$-0.257405\pi$
$701$	36.5622	1.38093	0.690467	+	0.723364i	$0.257405\pi$
$702$	−5.77167	−0.217837
$703$	−14.0902	−0.531423
$704$	7.28329	0.274499
$705$	−41.6251	−1.56769
$706$	−19.1316	−0.720028
$707$	0	0
$708$	−2.12889	−0.0800085
$709$	−48.3499	−1.81582	−0.907910	−	0.419166i	$-0.862323\pi$
$709$	−48.3499	−1.81582	−0.907910	+	0.419166i	$0.862323\pi$
$710$	−11.4055	−0.428040
$711$	−10.2135	−0.383038
$712$	46.9026	1.75775
$713$	36.8787	1.38112
$714$	0	0
$715$	−3.23836	−0.121108
$716$	8.75162	0.327064
$717$	27.6263	1.03172
$718$	35.8381	1.33747
$719$	−15.5599	−0.580287	−0.290143	−	0.956983i	$-0.593703\pi$
$719$	−15.5599	−0.580287	−0.290143	+	0.956983i	$0.593703\pi$
$720$	−4.07884	−0.152009
$721$	0	0
$722$	49.3245	1.83567
$723$	23.6016	0.877753
$724$	18.4617	0.686124
$725$	−39.7663	−1.47688
$726$	1.41493	0.0525129
$727$	21.7131	0.805294	0.402647	−	0.915355i	$-0.368090\pi$
$727$	21.7131	0.805294	0.402647	+	0.915355i	$0.368090\pi$
$728$	0	0
$729$	28.4684	1.05439
$730$	−28.3658	−1.04987
$731$	35.7154	1.32098
$732$	−15.8310	−0.585129
$733$	−8.62552	−0.318591	−0.159295	−	0.987231i	$-0.550922\pi$
$733$	−8.62552	−0.318591	−0.159295	+	0.987231i	$0.550922\pi$
$734$	−3.54181	−0.130731
$735$	0	0
$736$	29.3945	1.08350
$737$	−12.6271	−0.465125
$738$	5.42536	0.199710
$739$	−7.07880	−0.260398	−0.130199	−	0.991488i	$-0.541562\pi$
$739$	−7.07880	−0.260398	−0.130199	+	0.991488i	$0.541562\pi$
$740$	5.32653	0.195807
$741$	−11.3712	−0.417730
$742$	0	0
$743$	−29.4927	−1.08198	−0.540991	−	0.841028i	$-0.681951\pi$
$743$	−29.4927	−1.08198	−0.540991	+	0.841028i	$0.681951\pi$
$744$	−25.4526	−0.933138
$745$	−22.2998	−0.817002
$746$	−17.7307	−0.649166
$747$	5.55779	0.203349
$748$	4.59150	0.167882
$749$	0	0
$750$	−2.23150	−0.0814827
$751$	−31.3753	−1.14490	−0.572451	−	0.819939i	$-0.694007\pi$
$751$	−31.3753	−1.14490	−0.572451	+	0.819939i	$0.694007\pi$
$752$	−10.8248	−0.394741
$753$	13.1423	0.478931
$754$	−7.39886	−0.269450
$755$	−54.4419	−1.98134
$756$	0	0
$757$	−5.32246	−0.193448	−0.0967240	−	0.995311i	$-0.530836\pi$
$757$	−5.32246	−0.193448	−0.0967240	+	0.995311i	$0.530836\pi$
$758$	2.46840	0.0896562
$759$	8.40410	0.305050
$760$	−80.2282	−2.91018
$761$	−39.2070	−1.42125	−0.710626	−	0.703570i	$-0.751588\pi$
$761$	−39.2070	−1.42125	−0.710626	+	0.703570i	$0.751588\pi$
$762$	25.8303	0.935734
$763$	0	0
$764$	−2.12679	−0.0769445
$765$	−16.7531	−0.605709
$766$	−1.18739	−0.0429022
$767$	1.60379	0.0579095
$768$	−23.3859	−0.843865
$769$	−5.94544	−0.214398	−0.107199	−	0.994238i	$-0.534188\pi$
$769$	−5.94544	−0.214398	−0.107199	+	0.994238i	$0.534188\pi$
$770$	0	0
$771$	−6.29708	−0.226784
$772$	−15.2562	−0.549081
$773$	−54.9968	−1.97810	−0.989050	−	0.147584i	$-0.952850\pi$
$773$	−54.9968	−1.97810	−0.989050	+	0.147584i	$0.952850\pi$
$774$	8.20748	0.295012
$775$	33.3711	1.19873
$776$	35.5202	1.27510
$777$	0	0
$778$	21.8613	0.783767
$779$	40.4044	1.44764
$780$	4.29864	0.153916
$781$	3.44987	0.123446
$782$	−29.6774	−1.06126
$783$	40.9729	1.46425
$784$	0	0
$785$	−12.9562	−0.462426
$786$	−9.16937	−0.327061
$787$	44.6916	1.59308	0.796542	−	0.604583i	$-0.206660\pi$
$787$	44.6916	1.59308	0.796542	+	0.604583i	$0.206660\pi$
$788$	8.64081	0.307816
$789$	−24.8473	−0.884588
$790$	−31.2908	−1.11328
$791$	0	0
$792$	3.25849	0.115785
$793$	11.9262	0.423512
$794$	−7.47563	−0.265300
$795$	−18.6831	−0.662622
$796$	11.5497	0.409368
$797$	−2.57155	−0.0910891	−0.0455446	−	0.998962i	$-0.514502\pi$
$797$	−2.57155	−0.0910891	−0.0455446	+	0.998962i	$0.514502\pi$
$798$	0	0
$799$	−44.4610	−1.57292
$800$	26.5987	0.940406
$801$	16.7618	0.592248
$802$	19.1924	0.677708
$803$	8.57996	0.302780
$804$	16.7613	0.591127
$805$	0	0
$806$	6.20897	0.218702
$807$	−18.1165	−0.637731
$808$	−3.65483	−0.128576
$809$	39.6919	1.39549	0.697747	−	0.716344i	$-0.254186\pi$
$809$	39.6919	1.39549	0.697747	+	0.716344i	$0.254186\pi$
$810$	15.2017	0.534134
$811$	−33.8232	−1.18769	−0.593846	−	0.804579i	$-0.702391\pi$
$811$	−33.8232	−1.18769	−0.593846	+	0.804579i	$0.702391\pi$
$812$	0	0
$813$	10.7349	0.376488
$814$	1.75327	0.0614520
$815$	−9.06197	−0.317427
$816$	7.75516	0.271485
$817$	61.1238	2.13845
$818$	−8.96777	−0.313551
$819$	0	0
$820$	−15.2741	−0.533394
$821$	5.95304	0.207763	0.103881	−	0.994590i	$-0.466874\pi$
$821$	5.95304	0.207763	0.103881	+	0.994590i	$0.466874\pi$
$822$	1.49268	0.0520633
$823$	28.0447	0.977578	0.488789	−	0.872402i	$-0.337439\pi$
$823$	28.0447	0.977578	0.488789	+	0.872402i	$0.337439\pi$
$824$	8.22158	0.286412
$825$	7.60476	0.264764
$826$	0	0
$827$	13.1813	0.458357	0.229179	−	0.973384i	$-0.426396\pi$
$827$	13.1813	0.458357	0.229179	+	0.973384i	$0.426396\pi$
$828$	6.26709	0.217796
$829$	34.0351	1.18209	0.591044	−	0.806639i	$-0.298716\pi$
$829$	34.0351	1.18209	0.591044	+	0.806639i	$0.298716\pi$
$830$	17.0272	0.591022
$831$	24.2350	0.840704
$832$	7.28329	0.252503
$833$	0	0
$834$	12.9831	0.449569
$835$	49.8596	1.72546
$836$	7.85796	0.271773
$837$	−34.3836	−1.18847
$838$	−39.0459	−1.34882
$839$	−21.0786	−0.727714	−0.363857	−	0.931455i	$-0.618540\pi$
$839$	−21.0786	−0.727714	−0.363857	+	0.931455i	$0.618540\pi$
$840$	0	0
$841$	23.5243	0.811182
$842$	−7.39997	−0.255020
$843$	31.5548	1.08681
$844$	18.8512	0.648885
$845$	−3.23836	−0.111403
$846$	−10.2172	−0.351276
$847$	0	0
$848$	−4.85864	−0.166846
$849$	8.43316	0.289425
$850$	−26.8547	−0.921107
$851$	10.4137	0.356977
$852$	−4.57940	−0.156888
$853$	6.34612	0.217287	0.108643	−	0.994081i	$-0.465349\pi$
$853$	6.34612	0.217287	0.108643	+	0.994081i	$0.465349\pi$
$854$	0	0
$855$	−28.6715	−0.980543
$856$	−45.7440	−1.56350
$857$	−33.2470	−1.13570	−0.567848	−	0.823134i	$-0.692224\pi$
$857$	−33.2470	−1.13570	−0.567848	+	0.823134i	$0.692224\pi$
$858$	1.41493	0.0483049
$859$	−30.0443	−1.02510	−0.512550	−	0.858658i	$-0.671299\pi$
$859$	−30.0443	−1.02510	−0.512550	+	0.858658i	$0.671299\pi$
$860$	−23.1066	−0.787930
$861$	0	0
$862$	4.46453	0.152062
$863$	−4.37115	−0.148796	−0.0743979	−	0.997229i	$-0.523703\pi$
$863$	−4.37115	−0.148796	−0.0743979	+	0.997229i	$0.523703\pi$
$864$	−27.4057	−0.932362
$865$	−26.7796	−0.910535
$866$	−4.92182	−0.167250
$867$	8.29163	0.281599
$868$	0	0
$869$	9.46470	0.321068
$870$	33.2078	1.12585
$871$	−12.6271	−0.427853
$872$	−11.0550	−0.374369
$873$	12.6940	0.429627
$874$	−50.7902	−1.71801
$875$	0	0
$876$	−11.3891	−0.384803
$877$	1.23302	0.0416362	0.0208181	−	0.999783i	$-0.493373\pi$
$877$	1.23302	0.0416362	0.0208181	+	0.999783i	$0.493373\pi$
$878$	38.8364	1.31067
$879$	−44.8505	−1.51277
$880$	3.77978	0.127416
$881$	−31.0801	−1.04711	−0.523557	−	0.851991i	$-0.675395\pi$
$881$	−31.0801	−1.04711	−0.523557	+	0.851991i	$0.675395\pi$
$882$	0	0
$883$	31.3597	1.05534	0.527670	−	0.849450i	$-0.323066\pi$
$883$	31.3597	1.05534	0.527670	+	0.849450i	$0.323066\pi$
$884$	4.59150	0.154429
$885$	−7.19820	−0.241965
$886$	12.0390	0.404458
$887$	54.3189	1.82385	0.911925	−	0.410357i	$-0.134596\pi$
$887$	54.3189	1.82385	0.911925	+	0.410357i	$0.134596\pi$
$888$	−7.18721	−0.241187
$889$	0	0
$890$	51.3523	1.72133
$891$	−4.59814	−0.154044
$892$	−26.4019	−0.884002
$893$	−76.0911	−2.54629
$894$	9.74339	0.325868
$895$	29.5910	0.989117
$896$	0	0
$897$	8.40410	0.280605
$898$	−26.7416	−0.892379
$899$	−44.0773	−1.47006
$900$	5.67101	0.189034
$901$	−19.9560	−0.664830
$902$	−5.02758	−0.167400
$903$	0	0
$904$	−38.9420	−1.29519
$905$	62.4227	2.07500
$906$	23.7871	0.790274
$907$	30.8707	1.02505	0.512523	−	0.858674i	$-0.328711\pi$
$907$	30.8707	1.02505	0.512523	+	0.858674i	$0.328711\pi$
$908$	−14.6800	−0.487172
$909$	−1.30614	−0.0433219
$910$	0	0
$911$	8.81171	0.291945	0.145972	−	0.989289i	$-0.453369\pi$
$911$	8.81171	0.291945	0.145972	+	0.989289i	$0.453369\pi$
$912$	13.2723	0.439489
$913$	−5.15030	−0.170450
$914$	−34.0636	−1.12672
$915$	−53.5276	−1.76957
$916$	20.7280	0.684871
$917$	0	0
$918$	27.6695	0.913228
$919$	55.7030	1.83747	0.918736	−	0.394872i	$-0.129211\pi$
$919$	55.7030	1.83747	0.918736	+	0.394872i	$0.129211\pi$
$920$	59.2944	1.95488
$921$	−27.0637	−0.891778
$922$	34.9095	1.14968
$923$	3.44987	0.113554
$924$	0	0
$925$	9.42321	0.309833
$926$	9.22456	0.303138
$927$	2.93818	0.0965024
$928$	−35.1322	−1.15327
$929$	7.80514	0.256078	0.128039	−	0.991769i	$-0.459132\pi$
$929$	7.80514	0.256078	0.128039	+	0.991769i	$0.459132\pi$
$930$	−27.8673	−0.913806
$931$	0	0
$932$	−10.9070	−0.357269
$933$	−4.66382	−0.152687
$934$	25.3840	0.830591
$935$	15.5248	0.507714
$936$	3.25849	0.106507
$937$	0.225318	0.00736081	0.00368041	−	0.999993i	$-0.498828\pi$
$937$	0.225318	0.00736081	0.00368041	+	0.999993i	$0.498828\pi$
$938$	0	0
$939$	−1.70276	−0.0555673
$940$	28.7648	0.938203
$941$	15.7892	0.514714	0.257357	−	0.966316i	$-0.417148\pi$
$941$	15.7892	0.514714	0.257357	+	0.966316i	$0.417148\pi$
$942$	5.66091	0.184442
$943$	−29.8618	−0.972433
$944$	−1.87193	−0.0609260
$945$	0	0
$946$	−7.60572	−0.247283
$947$	−48.3440	−1.57097	−0.785484	−	0.618882i	$-0.787586\pi$
$947$	−48.3440	−1.57097	−0.785484	+	0.618882i	$0.787586\pi$
$948$	−12.5635	−0.408045
$949$	8.57996	0.278517
$950$	−45.9594	−1.49112
$951$	1.13693	0.0368675
$952$	0	0
$953$	31.2361	1.01184	0.505919	−	0.862581i	$-0.331154\pi$
$953$	31.2361	1.01184	0.505919	+	0.862581i	$0.331154\pi$
$954$	−4.58593	−0.148475
$955$	−7.19110	−0.232698
$956$	−19.0910	−0.617446
$957$	−10.0445	−0.324694
$958$	−5.18256	−0.167441
$959$	0	0
$960$	−32.6891	−1.05504
$961$	5.98877	0.193186
$962$	1.75327	0.0565276
$963$	−16.3477	−0.526797
$964$	−16.3097	−0.525301
$965$	−51.5841	−1.66055
$966$	0	0
$967$	17.1528	0.551598	0.275799	−	0.961215i	$-0.411058\pi$
$967$	17.1528	0.551598	0.275799	+	0.961215i	$0.411058\pi$
$968$	−3.01958	−0.0970531
$969$	54.5135	1.75123
$970$	38.8901	1.24869
$971$	1.65550	0.0531277	0.0265638	−	0.999647i	$-0.491543\pi$
$971$	1.65550	0.0531277	0.0265638	+	0.999647i	$0.491543\pi$
$972$	−10.1404	−0.325253
$973$	0	0
$974$	11.0998	0.355660
$975$	7.60476	0.243547
$976$	−13.9201	−0.445572
$977$	8.97073	0.286999	0.143500	−	0.989650i	$-0.454164\pi$
$977$	8.97073	0.286999	0.143500	+	0.989650i	$0.454164\pi$
$978$	3.95942	0.126608
$979$	−15.5328	−0.496431
$980$	0	0
$981$	−3.95076	−0.126138
$982$	−10.4909	−0.334777
$983$	−10.4236	−0.332462	−0.166231	−	0.986087i	$-0.553160\pi$
$983$	−10.4236	−0.332462	−0.166231	+	0.986087i	$0.553160\pi$
$984$	20.6097	0.657013
$985$	29.2163	0.930909
$986$	35.4702	1.12960
$987$	0	0
$988$	7.85796	0.249995
$989$	−45.1749	−1.43648
$990$	3.56763	0.113387
$991$	−7.20692	−0.228935	−0.114468	−	0.993427i	$-0.536516\pi$
$991$	−7.20692	−0.228935	−0.114468	+	0.993427i	$0.536516\pi$
$992$	29.4822	0.936061
$993$	10.7220	0.340253
$994$	0	0
$995$	39.0518	1.23803
$996$	6.83656	0.216625
$997$	−33.8291	−1.07138	−0.535689	−	0.844415i	$-0.679948\pi$
$997$	−33.8291	−1.07138	−0.535689	+	0.844415i	$0.679948\pi$
$998$	−16.6527	−0.527133
$999$	−9.70912	−0.307183

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7007.2.a.bi.1.15		25
7.3	odd	6		1001.2.i.d.716.11	yes	50
7.5	odd	6		1001.2.i.d.144.11	✓	50
7.6	odd	2		7007.2.a.bh.1.15		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.i.d.144.11	✓	50	7.5	odd	6
1001.2.i.d.716.11	yes	50	7.3	odd	6
7007.2.a.bh.1.15		25	7.6	odd	2
7007.2.a.bi.1.15		25	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 7007 = 7^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7007.a (trivial)

\(f(q)\)	\(=\)	\(q+1.02090 q^{2} +1.38596 q^{3} -0.957757 q^{4} -3.23836 q^{5} +1.41493 q^{6} -3.01958 q^{8} -1.07912 q^{9} +O(q^{10})\)	\(q+1.02090 q^{2} +1.38596 q^{3} -0.957757 q^{4} -3.23836 q^{5} +1.41493 q^{6} -3.01958 q^{8} -1.07912 q^{9} -3.30606 q^{10} +1.00000 q^{11} -1.32741 q^{12} +1.00000 q^{13} -4.48824 q^{15} -1.16719 q^{16} -4.79402 q^{17} -1.10168 q^{18} -8.20454 q^{19} +3.10157 q^{20} +1.02090 q^{22} +6.06375 q^{23} -4.18502 q^{24} +5.48701 q^{25} +1.02090 q^{26} -5.65349 q^{27} -7.24736 q^{29} -4.58206 q^{30} +6.08184 q^{31} +4.84758 q^{32} +1.38596 q^{33} -4.89423 q^{34} +1.03353 q^{36} +1.71737 q^{37} -8.37604 q^{38} +1.38596 q^{39} +9.77851 q^{40} -4.92464 q^{41} -7.44999 q^{43} -0.957757 q^{44} +3.49458 q^{45} +6.19050 q^{46} +9.27427 q^{47} -1.61768 q^{48} +5.60170 q^{50} -6.64431 q^{51} -0.957757 q^{52} +4.16269 q^{53} -5.77167 q^{54} -3.23836 q^{55} -11.3712 q^{57} -7.39886 q^{58} +1.60379 q^{59} +4.29864 q^{60} +11.9262 q^{61} +6.20897 q^{62} +7.28329 q^{64} -3.23836 q^{65} +1.41493 q^{66} -12.6271 q^{67} +4.59150 q^{68} +8.40410 q^{69} +3.44987 q^{71} +3.25849 q^{72} +8.57996 q^{73} +1.75327 q^{74} +7.60476 q^{75} +7.85796 q^{76} +1.41493 q^{78} +9.46470 q^{79} +3.77978 q^{80} -4.59814 q^{81} -5.02758 q^{82} -5.15030 q^{83} +15.5248 q^{85} -7.60572 q^{86} -10.0445 q^{87} -3.01958 q^{88} -15.5328 q^{89} +3.56763 q^{90} -5.80760 q^{92} +8.42918 q^{93} +9.46813 q^{94} +26.5693 q^{95} +6.71854 q^{96} -11.7633 q^{97} -1.07912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 2 q^{3} + 30 q^{4} + q^{5} - 2 q^{6} + 21 q^{8} + 37 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 + 2 * q^3 + 30 * q^4 + q^5 - 2 * q^6 + 21 * q^8 + 37 * q^9	\( 25 q + 6 q^{2} + 2 q^{3} + 30 q^{4} + q^{5} - 2 q^{6} + 21 q^{8} + 37 q^{9} + 3 q^{10} + 25 q^{11} - 9 q^{12} + 25 q^{13} + 32 q^{16} + q^{17} + 44 q^{18} - 5 q^{19} - 4 q^{20} + 6 q^{22} + 15 q^{23} + 4 q^{24} + 50 q^{25} + 6 q^{26} + 17 q^{27} + 24 q^{29} + q^{30} + 12 q^{31} + 48 q^{32} + 2 q^{33} + 8 q^{34} + 30 q^{36} + 33 q^{37} - 16 q^{38} + 2 q^{39} + 21 q^{40} - 12 q^{41} + 38 q^{43} + 30 q^{44} + 22 q^{45} + 39 q^{46} - 4 q^{47} - 82 q^{48} + 16 q^{50} + 51 q^{51} + 30 q^{52} + 2 q^{53} - 10 q^{54} + q^{55} + 38 q^{57} + 17 q^{58} + 4 q^{59} - 33 q^{60} + 22 q^{61} - 42 q^{62} + 41 q^{64} + q^{65} - 2 q^{66} + 24 q^{67} - 14 q^{68} + 30 q^{69} + 9 q^{71} + 102 q^{72} - 11 q^{73} + 39 q^{74} + 16 q^{75} - 58 q^{76} - 2 q^{78} + 19 q^{79} + 33 q^{80} + 73 q^{81} + 32 q^{82} - 16 q^{83} + 14 q^{85} + 27 q^{86} + 11 q^{87} + 21 q^{88} - 13 q^{89} - 40 q^{90} + 17 q^{93} + 56 q^{94} + 15 q^{95} - 55 q^{96} - 34 q^{97} + 37 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 2 * q^3 + 30 * q^4 + q^5 - 2 * q^6 + 21 * q^8 + 37 * q^9 + 3 * q^10 + 25 * q^11 - 9 * q^12 + 25 * q^13 + 32 * q^16 + q^17 + 44 * q^18 - 5 * q^19 - 4 * q^20 + 6 * q^22 + 15 * q^23 + 4 * q^24 + 50 * q^25 + 6 * q^26 + 17 * q^27 + 24 * q^29 + q^30 + 12 * q^31 + 48 * q^32 + 2 * q^33 + 8 * q^34 + 30 * q^36 + 33 * q^37 - 16 * q^38 + 2 * q^39 + 21 * q^40 - 12 * q^41 + 38 * q^43 + 30 * q^44 + 22 * q^45 + 39 * q^46 - 4 * q^47 - 82 * q^48 + 16 * q^50 + 51 * q^51 + 30 * q^52 + 2 * q^53 - 10 * q^54 + q^55 + 38 * q^57 + 17 * q^58 + 4 * q^59 - 33 * q^60 + 22 * q^61 - 42 * q^62 + 41 * q^64 + q^65 - 2 * q^66 + 24 * q^67 - 14 * q^68 + 30 * q^69 + 9 * q^71 + 102 * q^72 - 11 * q^73 + 39 * q^74 + 16 * q^75 - 58 * q^76 - 2 * q^78 + 19 * q^79 + 33 * q^80 + 73 * q^81 + 32 * q^82 - 16 * q^83 + 14 * q^85 + 27 * q^86 + 11 * q^87 + 21 * q^88 - 13 * q^89 - 40 * q^90 + 17 * q^93 + 56 * q^94 + 15 * q^95 - 55 * q^96 - 34 * q^97 + 37 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more