LMFDB - Embedded newform 7595.2.a.bf.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7595,2,Mod(1,7595)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7595, 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("7595.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7595 = 5 \cdot 7^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7595.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:	$60.6463803352$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 1085)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	7595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00699 q^{2} +1.95367 q^{3} +2.02800 q^{4} +1.00000 q^{5} +3.92099 q^{6} +0.0561989 q^{8} +0.816828 q^{9} +O(q^{10})$	\(q+2.00699 q^{2} +1.95367 q^{3} +2.02800 q^{4} +1.00000 q^{5} +3.92099 q^{6} +0.0561989 q^{8} +0.816828 q^{9} +2.00699 q^{10} -3.58898 q^{11} +3.96205 q^{12} -6.74961 q^{13} +1.95367 q^{15} -3.94321 q^{16} -1.85146 q^{17} +1.63936 q^{18} +4.97079 q^{19} +2.02800 q^{20} -7.20304 q^{22} -7.86622 q^{23} +0.109794 q^{24} +1.00000 q^{25} -13.5464 q^{26} -4.26520 q^{27} -3.79957 q^{29} +3.92099 q^{30} -1.00000 q^{31} -8.02638 q^{32} -7.01168 q^{33} -3.71585 q^{34} +1.65653 q^{36} -1.00360 q^{37} +9.97631 q^{38} -13.1865 q^{39} +0.0561989 q^{40} +6.71782 q^{41} +10.9082 q^{43} -7.27845 q^{44} +0.816828 q^{45} -15.7874 q^{46} -8.89963 q^{47} -7.70374 q^{48} +2.00699 q^{50} -3.61713 q^{51} -13.6882 q^{52} +4.70576 q^{53} -8.56020 q^{54} -3.58898 q^{55} +9.71128 q^{57} -7.62570 q^{58} +4.20645 q^{59} +3.96205 q^{60} -2.79814 q^{61} -2.00699 q^{62} -8.22242 q^{64} -6.74961 q^{65} -14.0724 q^{66} +6.93388 q^{67} -3.75475 q^{68} -15.3680 q^{69} -12.9206 q^{71} +0.0459049 q^{72} +1.74112 q^{73} -2.01421 q^{74} +1.95367 q^{75} +10.0808 q^{76} -26.4652 q^{78} +10.7369 q^{79} -3.94321 q^{80} -10.7833 q^{81} +13.4826 q^{82} -3.57358 q^{83} -1.85146 q^{85} +21.8926 q^{86} -7.42312 q^{87} -0.201697 q^{88} +0.451305 q^{89} +1.63936 q^{90} -15.9527 q^{92} -1.95367 q^{93} -17.8614 q^{94} +4.97079 q^{95} -15.6809 q^{96} -11.6880 q^{97} -2.93158 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) $ 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9	$ 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9} - 4 q^{10} - 4 q^{11} - 21 q^{12} - 24 q^{13} - 5 q^{15} + 20 q^{16} - 18 q^{17} - 16 q^{18} - 17 q^{19} + 22 q^{20} + 9 q^{22} - 19 q^{23} - 21 q^{24} + 21 q^{25} - 16 q^{26} - 17 q^{27} - 4 q^{29} - 6 q^{30} - 21 q^{31} - 18 q^{32} - 27 q^{33} + 2 q^{34} + 52 q^{36} - 19 q^{37} + 10 q^{38} + 21 q^{39} - 12 q^{40} - 5 q^{41} - 15 q^{43} - 11 q^{44} + 20 q^{45} + 6 q^{46} - 4 q^{47} - 19 q^{48} - 4 q^{50} + 35 q^{51} - 66 q^{52} - 19 q^{53} - 11 q^{54} - 4 q^{55} - 27 q^{57} - q^{58} + q^{59} - 21 q^{60} - 60 q^{61} + 4 q^{62} - 10 q^{64} - 24 q^{65} - 64 q^{66} + 2 q^{67} - 11 q^{68} - 18 q^{69} - q^{71} - 37 q^{72} - 51 q^{73} + 11 q^{74} - 5 q^{75} - 13 q^{76} - 40 q^{78} + q^{79} + 20 q^{80} + 21 q^{81} + 2 q^{82} - 38 q^{83} - 18 q^{85} + 26 q^{86} - 32 q^{87} + 5 q^{88} - 2 q^{89} - 16 q^{90} - 86 q^{92} + 5 q^{93} - 67 q^{94} - 17 q^{95} + 56 q^{96} - 42 q^{97} - 35 q^{99}+O(q^{100}) $ 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9 - 4 * q^10 - 4 * q^11 - 21 * q^12 - 24 * q^13 - 5 * q^15 + 20 * q^16 - 18 * q^17 - 16 * q^18 - 17 * q^19 + 22 * q^20 + 9 * q^22 - 19 * q^23 - 21 * q^24 + 21 * q^25 - 16 * q^26 - 17 * q^27 - 4 * q^29 - 6 * q^30 - 21 * q^31 - 18 * q^32 - 27 * q^33 + 2 * q^34 + 52 * q^36 - 19 * q^37 + 10 * q^38 + 21 * q^39 - 12 * q^40 - 5 * q^41 - 15 * q^43 - 11 * q^44 + 20 * q^45 + 6 * q^46 - 4 * q^47 - 19 * q^48 - 4 * q^50 + 35 * q^51 - 66 * q^52 - 19 * q^53 - 11 * q^54 - 4 * q^55 - 27 * q^57 - q^58 + q^59 - 21 * q^60 - 60 * q^61 + 4 * q^62 - 10 * q^64 - 24 * q^65 - 64 * q^66 + 2 * q^67 - 11 * q^68 - 18 * q^69 - q^71 - 37 * q^72 - 51 * q^73 + 11 * q^74 - 5 * q^75 - 13 * q^76 - 40 * q^78 + q^79 + 20 * q^80 + 21 * q^81 + 2 * q^82 - 38 * q^83 - 18 * q^85 + 26 * q^86 - 32 * q^87 + 5 * q^88 - 2 * q^89 - 16 * q^90 - 86 * q^92 + 5 * q^93 - 67 * q^94 - 17 * q^95 + 56 * q^96 - 42 * q^97 - 35 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.00699	1.41915	0.709577	−	0.704627i	$-0.248886\pi$
$2$	2.00699	1.41915	0.709577	+	0.704627i	$0.248886\pi$
$3$	1.95367	1.12795	0.563976	−	0.825791i	$-0.309271\pi$
$3$	1.95367	1.12795	0.563976	+	0.825791i	$0.309271\pi$
$4$	2.02800	1.01400
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.92099	1.60074
$7$	0	0
$7$	0	0
$8$	0.0561989	0.0198693
$9$	0.816828	0.272276
$10$	2.00699	0.634665
$11$	−3.58898	−1.08212	−0.541059	−	0.840985i	$-0.681976\pi$
$11$	−3.58898	−1.08212	−0.541059	+	0.840985i	$0.681976\pi$
$12$	3.96205	1.14374
$13$	−6.74961	−1.87201	−0.936003	−	0.351993i	$-0.885504\pi$
$13$	−6.74961	−1.87201	−0.936003	+	0.351993i	$0.885504\pi$
$14$	0	0
$15$	1.95367	0.504436
$16$	−3.94321	−0.985803
$17$	−1.85146	−0.449044	−0.224522	−	0.974469i	$-0.572082\pi$
$17$	−1.85146	−0.449044	−0.224522	+	0.974469i	$0.572082\pi$
$18$	1.63936	0.386402
$19$	4.97079	1.14038	0.570188	−	0.821514i	$-0.306870\pi$
$19$	4.97079	1.14038	0.570188	+	0.821514i	$0.306870\pi$
$20$	2.02800	0.453475
$21$	0	0
$22$	−7.20304	−1.53569
$23$	−7.86622	−1.64022	−0.820110	−	0.572206i	$-0.806088\pi$
$23$	−7.86622	−1.64022	−0.820110	+	0.572206i	$0.806088\pi$
$24$	0.109794	0.0224116
$25$	1.00000	0.200000
$26$	−13.5464	−2.65667
$27$	−4.26520	−0.820838
$28$	0	0
$29$	−3.79957	−0.705563	−0.352782	−	0.935706i	$-0.614764\pi$
$29$	−3.79957	−0.705563	−0.352782	+	0.935706i	$0.614764\pi$
$30$	3.92099	0.715872
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−8.02638	−1.41888
$33$	−7.01168	−1.22058
$34$	−3.71585	−0.637263
$35$	0	0
$36$	1.65653	0.276088
$37$	−1.00360	−0.164991	−0.0824953	−	0.996591i	$-0.526289\pi$
$37$	−1.00360	−0.164991	−0.0824953	+	0.996591i	$0.526289\pi$
$38$	9.97631	1.61837
$39$	−13.1865	−2.11153
$40$	0.0561989	0.00888583
$41$	6.71782	1.04915	0.524573	−	0.851365i	$-0.324225\pi$
$41$	6.71782	1.04915	0.524573	+	0.851365i	$0.324225\pi$
$42$	0	0
$43$	10.9082	1.66348	0.831742	−	0.555162i	$-0.187344\pi$
$43$	10.9082	1.66348	0.831742	+	0.555162i	$0.187344\pi$
$44$	−7.27845	−1.09727
$45$	0.816828	0.121766
$46$	−15.7874	−2.32773
$47$	−8.89963	−1.29814	−0.649072	−	0.760727i	$-0.724843\pi$
$47$	−8.89963	−1.29814	−0.649072	+	0.760727i	$0.724843\pi$
$48$	−7.70374	−1.11194
$49$	0	0
$50$	2.00699	0.283831
$51$	−3.61713	−0.506500
$52$	−13.6882	−1.89821
$53$	4.70576	0.646386	0.323193	−	0.946333i	$-0.395244\pi$
$53$	4.70576	0.646386	0.323193	+	0.946333i	$0.395244\pi$
$54$	−8.56020	−1.16490
$55$	−3.58898	−0.483938
$56$	0	0
$57$	9.71128	1.28629
$58$	−7.62570	−1.00130
$59$	4.20645	0.547634	0.273817	−	0.961782i	$-0.411714\pi$
$59$	4.20645	0.547634	0.273817	+	0.961782i	$0.411714\pi$
$60$	3.96205	0.511498
$61$	−2.79814	−0.358265	−0.179133	−	0.983825i	$-0.557329\pi$
$61$	−2.79814	−0.358265	−0.179133	+	0.983825i	$0.557329\pi$
$62$	−2.00699	−0.254888
$63$	0	0
$64$	−8.22242	−1.02780
$65$	−6.74961	−0.837186
$66$	−14.0724	−1.73219
$67$	6.93388	0.847108	0.423554	−	0.905871i	$-0.360782\pi$
$67$	6.93388	0.847108	0.423554	+	0.905871i	$0.360782\pi$
$68$	−3.75475	−0.455331
$69$	−15.3680	−1.85009
$70$	0	0
$71$	−12.9206	−1.53339	−0.766697	−	0.642009i	$-0.778101\pi$
$71$	−12.9206	−1.53339	−0.766697	+	0.642009i	$0.778101\pi$
$72$	0.0459049	0.00540994
$73$	1.74112	0.203782	0.101891	−	0.994796i	$-0.467511\pi$
$73$	1.74112	0.203782	0.101891	+	0.994796i	$0.467511\pi$
$74$	−2.01421	−0.234147
$75$	1.95367	0.225590
$76$	10.0808	1.15634
$77$	0	0
$78$	−26.4652	−2.99659
$79$	10.7369	1.20800	0.603999	−	0.796985i	$-0.293573\pi$
$79$	10.7369	1.20800	0.603999	+	0.796985i	$0.293573\pi$
$80$	−3.94321	−0.440865
$81$	−10.7833	−1.19814
$82$	13.4826	1.48890
$83$	−3.57358	−0.392251	−0.196126	−	0.980579i	$-0.562836\pi$
$83$	−3.57358	−0.392251	−0.196126	+	0.980579i	$0.562836\pi$
$84$	0	0
$85$	−1.85146	−0.200819
$86$	21.8926	2.36074
$87$	−7.42312	−0.795842
$88$	−0.201697	−0.0215009
$89$	0.451305	0.0478382	0.0239191	−	0.999714i	$-0.492386\pi$
$89$	0.451305	0.0478382	0.0239191	+	0.999714i	$0.492386\pi$
$90$	1.63936	0.172804
$91$	0	0
$92$	−15.9527	−1.66318
$93$	−1.95367	−0.202586
$94$	−17.8614	−1.84227
$95$	4.97079	0.509992
$96$	−15.6809	−1.60043
$97$	−11.6880	−1.18674	−0.593368	−	0.804932i	$-0.702202\pi$
$97$	−11.6880	−1.18674	−0.593368	+	0.804932i	$0.702202\pi$
$98$	0	0
$99$	−2.93158	−0.294635
$100$	2.02800	0.202800
$101$	5.92406	0.589466	0.294733	−	0.955580i	$-0.404769\pi$
$101$	5.92406	0.589466	0.294733	+	0.955580i	$0.404769\pi$
$102$	−7.25954	−0.718802
$103$	−8.45220	−0.832820	−0.416410	−	0.909177i	$-0.636712\pi$
$103$	−8.45220	−0.832820	−0.416410	+	0.909177i	$0.636712\pi$
$104$	−0.379321	−0.0371955
$105$	0	0
$106$	9.44441	0.917322
$107$	−6.93719	−0.670644	−0.335322	−	0.942104i	$-0.608845\pi$
$107$	−6.93719	−0.670644	−0.335322	+	0.942104i	$0.608845\pi$
$108$	−8.64983	−0.832330
$109$	−15.6963	−1.50343	−0.751715	−	0.659488i	$-0.770773\pi$
$109$	−15.6963	−1.50343	−0.751715	+	0.659488i	$0.770773\pi$
$110$	−7.20304	−0.686783
$111$	−1.96070	−0.186102
$112$	0	0
$113$	15.9111	1.49679	0.748396	−	0.663252i	$-0.230824\pi$
$113$	15.9111	1.49679	0.748396	+	0.663252i	$0.230824\pi$
$114$	19.4904	1.82545
$115$	−7.86622	−0.733528
$116$	−7.70554	−0.715442
$117$	−5.51327	−0.509702
$118$	8.44230	0.777177
$119$	0	0
$120$	0.109794	0.0100228
$121$	1.88077	0.170979
$122$	−5.61584	−0.508434
$123$	13.1244	1.18339
$124$	−2.02800	−0.182120
$125$	1.00000	0.0894427
$126$	0	0
$127$	−6.16328	−0.546903	−0.273451	−	0.961886i	$-0.588165\pi$
$127$	−6.16328	−0.546903	−0.273451	+	0.961886i	$0.588165\pi$
$128$	−0.449547	−0.0397347
$129$	21.3110	1.87633
$130$	−13.5464	−1.18810
$131$	11.7215	1.02411	0.512055	−	0.858953i	$-0.328885\pi$
$131$	11.7215	1.02411	0.512055	+	0.858953i	$0.328885\pi$
$132$	−14.2197	−1.23767
$133$	0	0
$134$	13.9162	1.20218
$135$	−4.26520	−0.367090
$136$	−0.104050	−0.00892220
$137$	−0.873841	−0.0746573	−0.0373286	−	0.999303i	$-0.511885\pi$
$137$	−0.873841	−0.0746573	−0.0373286	+	0.999303i	$0.511885\pi$
$138$	−30.8434	−2.62556
$139$	−7.82763	−0.663931	−0.331966	−	0.943291i	$-0.607712\pi$
$139$	−7.82763	−0.663931	−0.331966	+	0.943291i	$0.607712\pi$
$140$	0	0
$141$	−17.3869	−1.46424
$142$	−25.9315	−2.17612
$143$	24.2242	2.02573
$144$	−3.22093	−0.268411
$145$	−3.79957	−0.315537
$146$	3.49440	0.289199
$147$	0	0
$148$	−2.03530	−0.167301
$149$	18.1427	1.48631	0.743155	−	0.669119i	$-0.233329\pi$
$149$	18.1427	1.48631	0.743155	+	0.669119i	$0.233329\pi$
$150$	3.92099	0.320148
$151$	16.8607	1.37211	0.686053	−	0.727552i	$-0.259342\pi$
$151$	16.8607	1.37211	0.686053	+	0.727552i	$0.259342\pi$
$152$	0.279353	0.0226585
$153$	−1.51232	−0.122264
$154$	0	0
$155$	−1.00000	−0.0803219
$156$	−26.7423	−2.14110
$157$	−23.7357	−1.89432	−0.947158	−	0.320767i	$-0.896059\pi$
$157$	−23.7357	−1.89432	−0.947158	+	0.320767i	$0.896059\pi$
$158$	21.5489	1.71434
$159$	9.19351	0.729093
$160$	−8.02638	−0.634541
$161$	0	0
$162$	−21.6419	−1.70035
$163$	−8.58534	−0.672456	−0.336228	−	0.941781i	$-0.609151\pi$
$163$	−8.58534	−0.672456	−0.336228	+	0.941781i	$0.609151\pi$
$164$	13.6237	1.06384
$165$	−7.01168	−0.545859
$166$	−7.17213	−0.556665
$167$	2.07823	0.160818	0.0804092	−	0.996762i	$-0.474377\pi$
$167$	2.07823	0.160818	0.0804092	+	0.996762i	$0.474377\pi$
$168$	0	0
$169$	32.5573	2.50440
$170$	−3.71585	−0.284993
$171$	4.06028	0.310497
$172$	22.1218	1.68677
$173$	−5.84960	−0.444737	−0.222369	−	0.974963i	$-0.571379\pi$
$173$	−5.84960	−0.444737	−0.222369	+	0.974963i	$0.571379\pi$
$174$	−14.8981	−1.12942
$175$	0	0
$176$	14.1521	1.06676
$177$	8.21803	0.617705
$178$	0.905763	0.0678898
$179$	5.65417	0.422613	0.211306	−	0.977420i	$-0.432228\pi$
$179$	5.65417	0.422613	0.211306	+	0.977420i	$0.432228\pi$
$180$	1.65653	0.123470
$181$	4.54081	0.337516	0.168758	−	0.985658i	$-0.446024\pi$
$181$	4.54081	0.337516	0.168758	+	0.985658i	$0.446024\pi$
$182$	0	0
$183$	−5.46665	−0.404106
$184$	−0.442073	−0.0325900
$185$	−1.00360	−0.0737861
$186$	−3.92099	−0.287501
$187$	6.64483	0.485918
$188$	−18.0485	−1.31632
$189$	0	0
$190$	9.97631	0.723758
$191$	10.0235	0.725278	0.362639	−	0.931930i	$-0.381876\pi$
$191$	10.0235	0.725278	0.362639	+	0.931930i	$0.381876\pi$
$192$	−16.0639	−1.15931
$193$	11.5066	0.828266	0.414133	−	0.910216i	$-0.364085\pi$
$193$	11.5066	0.828266	0.414133	+	0.910216i	$0.364085\pi$
$194$	−23.4577	−1.68416
$195$	−13.1865	−0.944306
$196$	0	0
$197$	5.91009	0.421077	0.210538	−	0.977586i	$-0.432478\pi$
$197$	5.91009	0.421077	0.210538	+	0.977586i	$0.432478\pi$
$198$	−5.88365	−0.418132
$199$	−10.4636	−0.741748	−0.370874	−	0.928683i	$-0.620942\pi$
$199$	−10.4636	−0.741748	−0.370874	+	0.928683i	$0.620942\pi$
$200$	0.0561989	0.00397386
$201$	13.5465	0.955497
$202$	11.8895	0.836544
$203$	0	0
$204$	−7.33555	−0.513591
$205$	6.71782	0.469193
$206$	−16.9635	−1.18190
$207$	−6.42535	−0.446593
$208$	26.6152	1.84543
$209$	−17.8400	−1.23402
$210$	0	0
$211$	14.3008	0.984504	0.492252	−	0.870453i	$-0.336174\pi$
$211$	14.3008	0.984504	0.492252	+	0.870453i	$0.336174\pi$
$212$	9.54329	0.655436
$213$	−25.2426	−1.72960
$214$	−13.9229	−0.951747
$215$	10.9082	0.743933
$216$	−0.239700	−0.0163095
$217$	0	0
$218$	−31.5022	−2.13360
$219$	3.40157	0.229857
$220$	−7.27845	−0.490713
$221$	12.4966	0.840613
$222$	−3.93510	−0.264107
$223$	−15.4588	−1.03520	−0.517601	−	0.855622i	$-0.673175\pi$
$223$	−15.4588	−1.03520	−0.517601	+	0.855622i	$0.673175\pi$
$224$	0	0
$225$	0.816828	0.0544552
$226$	31.9334	2.12418
$227$	15.2743	1.01379	0.506895	−	0.862008i	$-0.330793\pi$
$227$	15.2743	1.01379	0.506895	+	0.862008i	$0.330793\pi$
$228$	19.6945	1.30430
$229$	−23.0859	−1.52556	−0.762779	−	0.646660i	$-0.776165\pi$
$229$	−23.0859	−1.52556	−0.762779	+	0.646660i	$0.776165\pi$
$230$	−15.7874	−1.04099
$231$	0	0
$232$	−0.213532	−0.0140191
$233$	8.88444	0.582039	0.291020	−	0.956717i	$-0.406005\pi$
$233$	8.88444	0.582039	0.291020	+	0.956717i	$0.406005\pi$
$234$	−11.0651	−0.723347
$235$	−8.89963	−0.580548
$236$	8.53070	0.555301
$237$	20.9764	1.36256
$238$	0	0
$239$	−10.5757	−0.684084	−0.342042	−	0.939685i	$-0.611119\pi$
$239$	−10.5757	−0.684084	−0.342042	+	0.939685i	$0.611119\pi$
$240$	−7.70374	−0.497274
$241$	−2.21764	−0.142851	−0.0714255	−	0.997446i	$-0.522755\pi$
$241$	−2.21764	−0.142851	−0.0714255	+	0.997446i	$0.522755\pi$
$242$	3.77468	0.242646
$243$	−8.27137	−0.530609
$244$	−5.67464	−0.363281
$245$	0	0
$246$	26.3405	1.67941
$247$	−33.5509	−2.13479
$248$	−0.0561989	−0.00356864
$249$	−6.98159	−0.442440
$250$	2.00699	0.126933
$251$	1.07213	0.0676720	0.0338360	−	0.999427i	$-0.489228\pi$
$251$	1.07213	0.0676720	0.0338360	+	0.999427i	$0.489228\pi$
$252$	0	0
$253$	28.2317	1.77491
$254$	−12.3696	−0.776140
$255$	−3.61713	−0.226514
$256$	15.5426	0.971413
$257$	−12.8765	−0.803213	−0.401607	−	0.915812i	$-0.631548\pi$
$257$	−12.8765	−0.803213	−0.401607	+	0.915812i	$0.631548\pi$
$258$	42.7710	2.66280
$259$	0	0
$260$	−13.6882	−0.848908
$261$	−3.10360	−0.192108
$262$	23.5248	1.45337
$263$	−12.6570	−0.780463	−0.390231	−	0.920717i	$-0.627605\pi$
$263$	−12.6570	−0.780463	−0.390231	+	0.920717i	$0.627605\pi$
$264$	−0.394049	−0.0242520
$265$	4.70576	0.289073
$266$	0	0
$267$	0.881701	0.0539592
$268$	14.0619	0.858968
$269$	−8.35036	−0.509130	−0.254565	−	0.967056i	$-0.581932\pi$
$269$	−8.35036	−0.509130	−0.254565	+	0.967056i	$0.581932\pi$
$270$	−8.56020	−0.520957
$271$	3.27623	0.199017	0.0995083	−	0.995037i	$-0.468273\pi$
$271$	3.27623	0.199017	0.0995083	+	0.995037i	$0.468273\pi$
$272$	7.30068	0.442669
$273$	0	0
$274$	−1.75379	−0.105950
$275$	−3.58898	−0.216424
$276$	−31.1663	−1.87599
$277$	−27.1030	−1.62846	−0.814231	−	0.580541i	$-0.802841\pi$
$277$	−27.1030	−1.62846	−0.814231	+	0.580541i	$0.802841\pi$
$278$	−15.7100	−0.942221
$279$	−0.816828	−0.0489022
$280$	0	0
$281$	17.9519	1.07092	0.535459	−	0.844561i	$-0.320139\pi$
$281$	17.9519	1.07092	0.535459	+	0.844561i	$0.320139\pi$
$282$	−34.8954	−2.07799
$283$	−25.6435	−1.52435	−0.762175	−	0.647371i	$-0.775868\pi$
$283$	−25.6435	−1.52435	−0.762175	+	0.647371i	$0.775868\pi$
$284$	−26.2030	−1.55486
$285$	9.71128	0.575247
$286$	48.6177	2.87483
$287$	0	0
$288$	−6.55617	−0.386326
$289$	−13.5721	−0.798360
$290$	−7.62570	−0.447797
$291$	−22.8345	−1.33858
$292$	3.53099	0.206636
$293$	−31.9576	−1.86698	−0.933491	−	0.358602i	$-0.883253\pi$
$293$	−31.9576	−1.86698	−0.933491	+	0.358602i	$0.883253\pi$
$294$	0	0
$295$	4.20645	0.244909
$296$	−0.0564012	−0.00327825
$297$	15.3077	0.888243
$298$	36.4122	2.10930
$299$	53.0939	3.07050
$300$	3.96205	0.228749
$301$	0	0
$302$	33.8393	1.94723
$303$	11.5737	0.664890
$304$	−19.6009	−1.12419
$305$	−2.79814	−0.160221
$306$	−3.03521	−0.173511
$307$	29.9118	1.70716	0.853578	−	0.520965i	$-0.174428\pi$
$307$	29.9118	1.70716	0.853578	+	0.520965i	$0.174428\pi$
$308$	0	0
$309$	−16.5128	−0.939382
$310$	−2.00699	−0.113989
$311$	−13.8169	−0.783483	−0.391742	−	0.920075i	$-0.628127\pi$
$311$	−13.8169	−0.783483	−0.391742	+	0.920075i	$0.628127\pi$
$312$	−0.741068	−0.0419547
$313$	−30.7130	−1.73600	−0.868002	−	0.496561i	$-0.834596\pi$
$313$	−30.7130	−1.73600	−0.868002	+	0.496561i	$0.834596\pi$
$314$	−47.6373	−2.68833
$315$	0	0
$316$	21.7745	1.22491
$317$	10.8864	0.611441	0.305720	−	0.952121i	$-0.401103\pi$
$317$	10.8864	0.611441	0.305720	+	0.952121i	$0.401103\pi$
$318$	18.4513	1.03470
$319$	13.6366	0.763503
$320$	−8.22242	−0.459647
$321$	−13.5530	−0.756454
$322$	0	0
$323$	−9.20319	−0.512079
$324$	−21.8685	−1.21492
$325$	−6.74961	−0.374401
$326$	−17.2307	−0.954319
$327$	−30.6653	−1.69580
$328$	0.377534	0.0208458
$329$	0	0
$330$	−14.0724	−0.774658
$331$	−20.0297	−1.10093	−0.550465	−	0.834858i	$-0.685549\pi$
$331$	−20.0297	−1.10093	−0.550465	+	0.834858i	$0.685549\pi$
$332$	−7.24722	−0.397743
$333$	−0.819768	−0.0449230
$334$	4.17098	0.228226
$335$	6.93388	0.378838
$336$	0	0
$337$	−7.98280	−0.434851	−0.217425	−	0.976077i	$-0.569766\pi$
$337$	−7.98280	−0.434851	−0.217425	+	0.976077i	$0.569766\pi$
$338$	65.3420	3.55414
$339$	31.0851	1.68831
$340$	−3.75475	−0.203630
$341$	3.58898	0.194354
$342$	8.14893	0.440644
$343$	0	0
$344$	0.613029	0.0330523
$345$	−15.3680	−0.827385
$346$	−11.7401	−0.631151
$347$	4.63318	0.248722	0.124361	−	0.992237i	$-0.460312\pi$
$347$	4.63318	0.248722	0.124361	+	0.992237i	$0.460312\pi$
$348$	−15.0541	−0.806984
$349$	7.20821	0.385847	0.192923	−	0.981214i	$-0.438203\pi$
$349$	7.20821	0.385847	0.192923	+	0.981214i	$0.438203\pi$
$350$	0	0
$351$	28.7884	1.53661
$352$	28.8065	1.53539
$353$	−14.0917	−0.750025	−0.375012	−	0.927020i	$-0.622362\pi$
$353$	−14.0917	−0.750025	−0.375012	+	0.927020i	$0.622362\pi$
$354$	16.4935	0.876619
$355$	−12.9206	−0.685755
$356$	0.915247	0.0485080
$357$	0	0
$358$	11.3479	0.599753
$359$	12.4355	0.656320	0.328160	−	0.944622i	$-0.393571\pi$
$359$	12.4355	0.656320	0.328160	+	0.944622i	$0.393571\pi$
$360$	0.0459049	0.00241940
$361$	5.70872	0.300459
$362$	9.11335	0.478987
$363$	3.67440	0.192856
$364$	0	0
$365$	1.74112	0.0911343
$366$	−10.9715	−0.573489
$367$	−16.3841	−0.855246	−0.427623	−	0.903957i	$-0.640649\pi$
$367$	−16.3841	−0.855246	−0.427623	+	0.903957i	$0.640649\pi$
$368$	31.0182	1.61693
$369$	5.48730	0.285658
$370$	−2.01421	−0.104714
$371$	0	0
$372$	−3.96205	−0.205423
$373$	31.4752	1.62973	0.814863	−	0.579654i	$-0.196812\pi$
$373$	31.4752	1.62973	0.814863	+	0.579654i	$0.196812\pi$
$374$	13.3361	0.689593
$375$	1.95367	0.100887
$376$	−0.500149	−0.0257932
$377$	25.6457	1.32082
$378$	0	0
$379$	−15.9605	−0.819834	−0.409917	−	0.912123i	$-0.634442\pi$
$379$	−15.9605	−0.819834	−0.409917	+	0.912123i	$0.634442\pi$
$380$	10.0808	0.517132
$381$	−12.0410	−0.616880
$382$	20.1171	1.02928
$383$	15.4041	0.787113	0.393556	−	0.919300i	$-0.371245\pi$
$383$	15.4041	0.787113	0.393556	+	0.919300i	$0.371245\pi$
$384$	−0.878267	−0.0448189
$385$	0	0
$386$	23.0937	1.17544
$387$	8.91012	0.452927
$388$	−23.7033	−1.20335
$389$	−7.93663	−0.402403	−0.201201	−	0.979550i	$-0.564485\pi$
$389$	−7.93663	−0.402403	−0.201201	+	0.979550i	$0.564485\pi$
$390$	−26.4652	−1.34012
$391$	14.5639	0.736530
$392$	0	0
$393$	22.8999	1.15515
$394$	11.8615	0.597573
$395$	10.7369	0.540233
$396$	−5.94525	−0.298760
$397$	7.25728	0.364232	0.182116	−	0.983277i	$-0.441705\pi$
$397$	7.25728	0.364232	0.182116	+	0.983277i	$0.441705\pi$
$398$	−21.0004	−1.05265
$399$	0	0
$400$	−3.94321	−0.197161
$401$	33.6142	1.67861	0.839307	−	0.543658i	$-0.182961\pi$
$401$	33.6142	1.67861	0.839307	+	0.543658i	$0.182961\pi$
$402$	27.1877	1.35600
$403$	6.74961	0.336222
$404$	12.0140	0.597719
$405$	−10.7833	−0.535825
$406$	0	0
$407$	3.60190	0.178539
$408$	−0.203279	−0.0100638
$409$	8.05649	0.398368	0.199184	−	0.979962i	$-0.436171\pi$
$409$	8.05649	0.398368	0.199184	+	0.979962i	$0.436171\pi$
$410$	13.4826	0.665857
$411$	−1.70720	−0.0842099
$412$	−17.1411	−0.844481
$413$	0	0
$414$	−12.8956	−0.633784
$415$	−3.57358	−0.175420
$416$	54.1749	2.65614
$417$	−15.2926	−0.748883
$418$	−35.8048	−1.75127
$419$	32.4393	1.58477	0.792383	−	0.610024i	$-0.208840\pi$
$419$	32.4393	1.58477	0.792383	+	0.610024i	$0.208840\pi$
$420$	0	0
$421$	−16.3297	−0.795862	−0.397931	−	0.917415i	$-0.630272\pi$
$421$	−16.3297	−0.795862	−0.397931	+	0.917415i	$0.630272\pi$
$422$	28.7014	1.39716
$423$	−7.26947	−0.353454
$424$	0.264459	0.0128433
$425$	−1.85146	−0.0898088
$426$	−50.6616	−2.45456
$427$	0	0
$428$	−14.0686	−0.680033
$429$	47.3261	2.28493
$430$	21.8926	1.05576
$431$	−36.6086	−1.76337	−0.881686	−	0.471837i	$-0.843591\pi$
$431$	−36.6086	−1.76337	−0.881686	+	0.471837i	$0.843591\pi$
$432$	16.8186	0.809184
$433$	5.67273	0.272614	0.136307	−	0.990667i	$-0.456477\pi$
$433$	5.67273	0.272614	0.136307	+	0.990667i	$0.456477\pi$
$434$	0	0
$435$	−7.42312	−0.355911
$436$	−31.8321	−1.52448
$437$	−39.1013	−1.87047
$438$	6.82691	0.326202
$439$	−19.3714	−0.924547	−0.462274	−	0.886737i	$-0.652966\pi$
$439$	−19.3714	−0.924547	−0.462274	+	0.886737i	$0.652966\pi$
$440$	−0.201697	−0.00961552
$441$	0	0
$442$	25.0805	1.19296
$443$	8.36655	0.397507	0.198753	−	0.980050i	$-0.436311\pi$
$443$	8.36655	0.397507	0.198753	+	0.980050i	$0.436311\pi$
$444$	−3.97631	−0.188707
$445$	0.451305	0.0213939
$446$	−31.0257	−1.46911
$447$	35.4449	1.67649
$448$	0	0
$449$	22.6280	1.06788	0.533941	−	0.845522i	$-0.320711\pi$
$449$	22.6280	1.06788	0.533941	+	0.845522i	$0.320711\pi$
$450$	1.63936	0.0772804
$451$	−24.1101	−1.13530
$452$	32.2678	1.51775
$453$	32.9403	1.54767
$454$	30.6553	1.43872
$455$	0	0
$456$	0.545763	0.0255577
$457$	30.0956	1.40781	0.703907	−	0.710292i	$-0.251437\pi$
$457$	30.0956	1.40781	0.703907	+	0.710292i	$0.251437\pi$
$458$	−46.3331	−2.16500
$459$	7.89682	0.368592
$460$	−15.9527	−0.743798
$461$	6.50418	0.302930	0.151465	−	0.988463i	$-0.451601\pi$
$461$	6.50418	0.302930	0.151465	+	0.988463i	$0.451601\pi$
$462$	0	0
$463$	−31.7998	−1.47786	−0.738931	−	0.673781i	$-0.764669\pi$
$463$	−31.7998	−1.47786	−0.738931	+	0.673781i	$0.764669\pi$
$464$	14.9825	0.695547
$465$	−1.95367	−0.0905993
$466$	17.8310	0.826004
$467$	9.81383	0.454130	0.227065	−	0.973880i	$-0.427087\pi$
$467$	9.81383	0.454130	0.227065	+	0.973880i	$0.427087\pi$
$468$	−11.1809	−0.516839
$469$	0	0
$470$	−17.8614	−0.823887
$471$	−46.3718	−2.13670
$472$	0.236398	0.0108811
$473$	−39.1493	−1.80009
$474$	42.0994	1.93369
$475$	4.97079	0.228075
$476$	0	0
$477$	3.84380	0.175996
$478$	−21.2253	−0.970821
$479$	−2.74411	−0.125382	−0.0626908	−	0.998033i	$-0.519968\pi$
$479$	−2.74411	−0.125382	−0.0626908	+	0.998033i	$0.519968\pi$
$480$	−15.6809	−0.715732
$481$	6.77390	0.308863
$482$	−4.45078	−0.202728
$483$	0	0
$484$	3.81420	0.173373
$485$	−11.6880	−0.530724
$486$	−16.6006	−0.753016
$487$	−32.1646	−1.45752	−0.728758	−	0.684772i	$-0.759902\pi$
$487$	−32.1646	−1.45752	−0.728758	+	0.684772i	$0.759902\pi$
$488$	−0.157253	−0.00711849
$489$	−16.7729	−0.758498
$490$	0	0
$491$	12.5712	0.567331	0.283665	−	0.958923i	$-0.408450\pi$
$491$	12.5712	0.567331	0.283665	+	0.958923i	$0.408450\pi$
$492$	26.6163	1.19996
$493$	7.03474	0.316829
$494$	−67.3362	−3.02960
$495$	−2.93158	−0.131765
$496$	3.94321	0.177055
$497$	0	0
$498$	−14.0120	−0.627891
$499$	−16.4840	−0.737925	−0.368963	−	0.929444i	$-0.620287\pi$
$499$	−16.4840	−0.737925	−0.368963	+	0.929444i	$0.620287\pi$
$500$	2.02800	0.0906950
$501$	4.06018	0.181395
$502$	2.15174	0.0960370
$503$	13.4405	0.599281	0.299640	−	0.954052i	$-0.403133\pi$
$503$	13.4405	0.599281	0.299640	+	0.954052i	$0.403133\pi$
$504$	0	0
$505$	5.92406	0.263617
$506$	56.6607	2.51887
$507$	63.6061	2.82485
$508$	−12.4991	−0.554560
$509$	27.6259	1.22450	0.612249	−	0.790665i	$-0.290265\pi$
$509$	27.6259	1.22450	0.612249	+	0.790665i	$0.290265\pi$
$510$	−7.25954	−0.321458
$511$	0	0
$512$	32.0929	1.41832
$513$	−21.2014	−0.936064
$514$	−25.8430	−1.13988
$515$	−8.45220	−0.372449
$516$	43.2188	1.90260
$517$	31.9406	1.40474
$518$	0	0
$519$	−11.4282	−0.501642
$520$	−0.379321	−0.0166343
$521$	20.5073	0.898442	0.449221	−	0.893421i	$-0.351702\pi$
$521$	20.5073	0.898442	0.449221	+	0.893421i	$0.351702\pi$
$522$	−6.22889	−0.272631
$523$	23.0631	1.00848	0.504239	−	0.863564i	$-0.331773\pi$
$523$	23.0631	1.00848	0.504239	+	0.863564i	$0.331773\pi$
$524$	23.7711	1.03845
$525$	0	0
$526$	−25.4024	−1.10760
$527$	1.85146	0.0806507
$528$	27.6486	1.20325
$529$	38.8774	1.69032
$530$	9.44441	0.410239
$531$	3.43595	0.149108
$532$	0	0
$533$	−45.3427	−1.96401
$534$	1.76956	0.0765765
$535$	−6.93719	−0.299921
$536$	0.389676	0.0168315
$537$	11.0464	0.476687
$538$	−16.7591	−0.722535
$539$	0	0
$540$	−8.64983	−0.372229
$541$	32.5579	1.39977	0.699887	−	0.714254i	$-0.253234\pi$
$541$	32.5579	1.39977	0.699887	+	0.714254i	$0.253234\pi$
$542$	6.57535	0.282435
$543$	8.87124	0.380702
$544$	14.8605	0.637138
$545$	−15.6963	−0.672354
$546$	0	0
$547$	27.4435	1.17340	0.586700	−	0.809805i	$-0.300427\pi$
$547$	27.4435	1.17340	0.586700	+	0.809805i	$0.300427\pi$
$548$	−1.77215	−0.0757026
$549$	−2.28560	−0.0975471
$550$	−7.20304	−0.307139
$551$	−18.8869	−0.804608
$552$	−0.863665	−0.0367600
$553$	0	0
$554$	−54.3954	−2.31104
$555$	−1.96070	−0.0832271
$556$	−15.8745	−0.673227
$557$	3.85223	0.163224	0.0816121	−	0.996664i	$-0.473993\pi$
$557$	3.85223	0.163224	0.0816121	+	0.996664i	$0.473993\pi$
$558$	−1.63936	−0.0693998
$559$	−73.6261	−3.11405
$560$	0	0
$561$	12.9818	0.548093
$562$	36.0292	1.51980
$563$	−35.1770	−1.48253	−0.741266	−	0.671212i	$-0.765774\pi$
$563$	−35.1770	−1.48253	−0.741266	+	0.671212i	$0.765774\pi$
$564$	−35.2607	−1.48474
$565$	15.9111	0.669386
$566$	−51.4663	−2.16329
$567$	0	0
$568$	−0.726125	−0.0304675
$569$	−36.1553	−1.51571	−0.757854	−	0.652424i	$-0.773752\pi$
$569$	−36.1553	−1.51571	−0.757854	+	0.652424i	$0.773752\pi$
$570$	19.4904	0.816364
$571$	−25.7296	−1.07675	−0.538375	−	0.842705i	$-0.680962\pi$
$571$	−25.7296	−1.07675	−0.538375	+	0.842705i	$0.680962\pi$
$572$	49.1267	2.05409
$573$	19.5827	0.818079
$574$	0	0
$575$	−7.86622	−0.328044
$576$	−6.71631	−0.279846
$577$	15.4194	0.641916	0.320958	−	0.947093i	$-0.395995\pi$
$577$	15.4194	0.641916	0.320958	+	0.947093i	$0.395995\pi$
$578$	−27.2391	−1.13300
$579$	22.4802	0.934244
$580$	−7.70554	−0.319955
$581$	0	0
$582$	−45.8285	−1.89965
$583$	−16.8889	−0.699466
$584$	0.0978490	0.00404902
$585$	−5.51327	−0.227946
$586$	−64.1385	−2.64954
$587$	−0.863658	−0.0356470	−0.0178235	−	0.999841i	$-0.505674\pi$
$587$	−0.863658	−0.0356470	−0.0178235	+	0.999841i	$0.505674\pi$
$588$	0	0
$589$	−4.97079	−0.204818
$590$	8.44230	0.347564
$591$	11.5464	0.474954
$592$	3.95740	0.162648
$593$	−36.0774	−1.48152	−0.740761	−	0.671769i	$-0.765535\pi$
$593$	−36.0774	−1.48152	−0.740761	+	0.671769i	$0.765535\pi$
$594$	30.7224	1.26055
$595$	0	0
$596$	36.7935	1.50712
$597$	−20.4425	−0.836656
$598$	106.559	4.35751
$599$	−7.56864	−0.309246	−0.154623	−	0.987974i	$-0.549416\pi$
$599$	−7.56864	−0.309246	−0.154623	+	0.987974i	$0.549416\pi$
$600$	0.109794	0.00448233
$601$	36.5210	1.48972	0.744862	−	0.667219i	$-0.232515\pi$
$601$	36.5210	1.48972	0.744862	+	0.667219i	$0.232515\pi$
$602$	0	0
$603$	5.66379	0.230647
$604$	34.1936	1.39132
$605$	1.88077	0.0764641
$606$	23.2282	0.943581
$607$	3.54521	0.143895	0.0719477	−	0.997408i	$-0.477079\pi$
$607$	3.54521	0.143895	0.0719477	+	0.997408i	$0.477079\pi$
$608$	−39.8974	−1.61805
$609$	0	0
$610$	−5.61584	−0.227379
$611$	60.0690	2.43013
$612$	−3.06699	−0.123976
$613$	−36.9256	−1.49141	−0.745706	−	0.666275i	$-0.767888\pi$
$613$	−36.9256	−1.49141	−0.745706	+	0.666275i	$0.767888\pi$
$614$	60.0326	2.42272
$615$	13.1244	0.529227
$616$	0	0
$617$	−42.1447	−1.69668	−0.848341	−	0.529450i	$-0.822398\pi$
$617$	−42.1447	−1.69668	−0.848341	+	0.529450i	$0.822398\pi$
$618$	−33.1410	−1.33313
$619$	−30.8449	−1.23976	−0.619881	−	0.784696i	$-0.712819\pi$
$619$	−30.8449	−1.23976	−0.619881	+	0.784696i	$0.712819\pi$
$620$	−2.02800	−0.0814465
$621$	33.5510	1.34635
$622$	−27.7303	−1.11188
$623$	0	0
$624$	51.9972	2.08156
$625$	1.00000	0.0400000
$626$	−61.6407	−2.46366
$627$	−34.8536	−1.39192
$628$	−48.1361	−1.92084
$629$	1.85812	0.0740880
$630$	0	0
$631$	−35.4904	−1.41285	−0.706425	−	0.707788i	$-0.749693\pi$
$631$	−35.4904	−1.41285	−0.706425	+	0.707788i	$0.749693\pi$
$632$	0.603403	0.0240021
$633$	27.9390	1.11047
$634$	21.8489	0.867729
$635$	−6.16328	−0.244582
$636$	18.6445	0.739301
$637$	0	0
$638$	27.3685	1.08353
$639$	−10.5539	−0.417507
$640$	−0.449547	−0.0177699
$641$	−21.0832	−0.832735	−0.416367	−	0.909196i	$-0.636697\pi$
$641$	−21.0832	−0.832735	−0.416367	+	0.909196i	$0.636697\pi$
$642$	−27.2007	−1.07353
$643$	−32.1940	−1.26961	−0.634803	−	0.772674i	$-0.718919\pi$
$643$	−32.1940	−1.26961	−0.634803	+	0.772674i	$0.718919\pi$
$644$	0	0
$645$	21.3110	0.839120
$646$	−18.4707	−0.726720
$647$	−38.1185	−1.49859	−0.749297	−	0.662234i	$-0.769608\pi$
$647$	−38.1185	−1.49859	−0.749297	+	0.662234i	$0.769608\pi$
$648$	−0.606009	−0.0238063
$649$	−15.0969	−0.592604
$650$	−13.5464	−0.531333
$651$	0	0
$652$	−17.4111	−0.681871
$653$	−2.30345	−0.0901412	−0.0450706	−	0.998984i	$-0.514351\pi$
$653$	−2.30345	−0.0901412	−0.0450706	+	0.998984i	$0.514351\pi$
$654$	−61.5450	−2.40660
$655$	11.7215	0.457996
$656$	−26.4898	−1.03425
$657$	1.42219	0.0554851
$658$	0	0
$659$	−42.6572	−1.66169	−0.830845	−	0.556504i	$-0.812142\pi$
$659$	−42.6572	−1.66169	−0.830845	+	0.556504i	$0.812142\pi$
$660$	−14.2197	−0.553501
$661$	−25.8627	−1.00594	−0.502970	−	0.864304i	$-0.667760\pi$
$661$	−25.8627	−1.00594	−0.502970	+	0.864304i	$0.667760\pi$
$662$	−40.1993	−1.56239
$663$	24.4142	0.948171
$664$	−0.200831	−0.00779376
$665$	0	0
$666$	−1.64526	−0.0637527
$667$	29.8883	1.15728
$668$	4.21466	0.163070
$669$	−30.2015	−1.16766
$670$	13.9162	0.537630
$671$	10.0425	0.387685
$672$	0	0
$673$	−37.0900	−1.42971	−0.714856	−	0.699271i	$-0.753508\pi$
$673$	−37.0900	−1.42971	−0.714856	+	0.699271i	$0.753508\pi$
$674$	−16.0214	−0.617121
$675$	−4.26520	−0.164168
$676$	66.0262	2.53947
$677$	26.4089	1.01497	0.507487	−	0.861659i	$-0.330574\pi$
$677$	26.4089	1.01497	0.507487	+	0.861659i	$0.330574\pi$
$678$	62.3874	2.39597
$679$	0	0
$680$	−0.104050	−0.00399013
$681$	29.8409	1.14351
$682$	7.20304	0.275819
$683$	9.46361	0.362115	0.181057	−	0.983473i	$-0.442048\pi$
$683$	9.46361	0.362115	0.181057	+	0.983473i	$0.442048\pi$
$684$	8.23425	0.314845
$685$	−0.873841	−0.0333878
$686$	0	0
$687$	−45.1022	−1.72076
$688$	−43.0133	−1.63987
$689$	−31.7621	−1.21004
$690$	−30.8434	−1.17419
$691$	−21.9179	−0.833796	−0.416898	−	0.908953i	$-0.636883\pi$
$691$	−21.9179	−0.833796	−0.416898	+	0.908953i	$0.636883\pi$
$692$	−11.8630	−0.450964
$693$	0	0
$694$	9.29874	0.352975
$695$	−7.82763	−0.296919
$696$	−0.417171	−0.0158128
$697$	−12.4377	−0.471113
$698$	14.4668	0.547576
$699$	17.3573	0.656513
$700$	0	0
$701$	8.37682	0.316388	0.158194	−	0.987408i	$-0.449433\pi$
$701$	8.37682	0.316388	0.158194	+	0.987408i	$0.449433\pi$
$702$	57.7780	2.18069
$703$	−4.98868	−0.188151
$704$	29.5101	1.11220
$705$	−17.3869	−0.654830
$706$	−28.2818	−1.06440
$707$	0	0
$708$	16.6662	0.626353
$709$	34.9299	1.31182	0.655910	−	0.754839i	$-0.272285\pi$
$709$	34.9299	1.31182	0.655910	+	0.754839i	$0.272285\pi$
$710$	−25.9315	−0.973192
$711$	8.77022	0.328909
$712$	0.0253628	0.000950513 0
$713$	7.86622	0.294592
$714$	0	0
$715$	24.2242	0.905934
$716$	11.4667	0.428530
$717$	−20.6614	−0.771614
$718$	24.9579	0.931420
$719$	19.6170	0.731589	0.365794	−	0.930696i	$-0.380797\pi$
$719$	19.6170	0.731589	0.365794	+	0.930696i	$0.380797\pi$
$720$	−3.22093	−0.120037
$721$	0	0
$722$	11.4573	0.426398
$723$	−4.33254	−0.161129
$724$	9.20877	0.342241
$725$	−3.79957	−0.141113
$726$	7.37448	0.273693
$727$	52.3114	1.94012	0.970062	−	0.242858i	$-0.0780850\pi$
$727$	52.3114	1.94012	0.970062	+	0.242858i	$0.0780850\pi$
$728$	0	0
$729$	16.1903	0.599640
$730$	3.49440	0.129334
$731$	−20.1960	−0.746977
$732$	−11.0864	−0.409764
$733$	−5.38237	−0.198802	−0.0994011	−	0.995047i	$-0.531693\pi$
$733$	−5.38237	−0.198802	−0.0994011	+	0.995047i	$0.531693\pi$
$734$	−32.8828	−1.21373
$735$	0	0
$736$	63.1372	2.32727
$737$	−24.8855	−0.916671
$738$	11.0130	0.405392
$739$	−13.9886	−0.514579	−0.257289	−	0.966334i	$-0.582829\pi$
$739$	−13.9886	−0.514579	−0.257289	+	0.966334i	$0.582829\pi$
$740$	−2.03530	−0.0748191
$741$	−65.5474	−2.40794
$742$	0	0
$743$	−31.9990	−1.17393	−0.586965	−	0.809612i	$-0.699677\pi$
$743$	−31.9990	−1.17393	−0.586965	+	0.809612i	$0.699677\pi$
$744$	−0.109794	−0.00402525
$745$	18.1427	0.664698
$746$	63.1704	2.31283
$747$	−2.91900	−0.106801
$748$	13.4757	0.492722
$749$	0	0
$750$	3.92099	0.143174
$751$	−25.1103	−0.916287	−0.458143	−	0.888878i	$-0.651485\pi$
$751$	−25.1103	−0.916287	−0.458143	+	0.888878i	$0.651485\pi$
$752$	35.0931	1.27971
$753$	2.09458	0.0763308
$754$	51.4705	1.87445
$755$	16.8607	0.613624
$756$	0	0
$757$	33.0628	1.20169	0.600844	−	0.799366i	$-0.294831\pi$
$757$	33.0628	1.20169	0.600844	+	0.799366i	$0.294831\pi$
$758$	−32.0325	−1.16347
$759$	55.1554	2.00201
$760$	0.279353	0.0101332
$761$	8.42431	0.305381	0.152691	−	0.988274i	$-0.451206\pi$
$761$	8.42431	0.305381	0.152691	+	0.988274i	$0.451206\pi$
$762$	−24.1662	−0.875448
$763$	0	0
$764$	20.3278	0.735432
$765$	−1.51232	−0.0546781
$766$	30.9159	1.11704
$767$	−28.3919	−1.02517
$768$	30.3651	1.09571
$769$	−38.3579	−1.38322	−0.691611	−	0.722270i	$-0.743099\pi$
$769$	−38.3579	−1.38322	−0.691611	+	0.722270i	$0.743099\pi$
$770$	0	0
$771$	−25.1564	−0.905986
$772$	23.3355	0.839862
$773$	−5.35926	−0.192759	−0.0963797	−	0.995345i	$-0.530726\pi$
$773$	−5.35926	−0.192759	−0.0963797	+	0.995345i	$0.530726\pi$
$774$	17.8825	0.642774
$775$	−1.00000	−0.0359211
$776$	−0.656852	−0.0235796
$777$	0	0
$778$	−15.9287	−0.571072
$779$	33.3928	1.19642
$780$	−26.7423	−0.957527
$781$	46.3718	1.65931
$782$	29.2297	1.04525
$783$	16.2059	0.579153
$784$	0	0
$785$	−23.7357	−0.847164
$786$	45.9598	1.63933
$787$	−14.7474	−0.525689	−0.262844	−	0.964838i	$-0.584661\pi$
$787$	−14.7474	−0.525689	−0.262844	+	0.964838i	$0.584661\pi$
$788$	11.9857	0.426972
$789$	−24.7276	−0.880325
$790$	21.5489	0.766674
$791$	0	0
$792$	−0.164752	−0.00585419
$793$	18.8864	0.670675
$794$	14.5653	0.516902
$795$	9.19351	0.326060
$796$	−21.2203	−0.752133
$797$	−34.9653	−1.23853	−0.619266	−	0.785181i	$-0.712570\pi$
$797$	−34.9653	−1.23853	−0.619266	+	0.785181i	$0.712570\pi$
$798$	0	0
$799$	16.4773	0.582924
$800$	−8.02638	−0.283775
$801$	0.368638	0.0130252
$802$	67.4633	2.38221
$803$	−6.24884	−0.220517
$804$	27.4723	0.968875
$805$	0	0
$806$	13.5464	0.477151
$807$	−16.3139	−0.574275
$808$	0.332926	0.0117123
$809$	5.47140	0.192364	0.0961821	−	0.995364i	$-0.469337\pi$
$809$	5.47140	0.192364	0.0961821	+	0.995364i	$0.469337\pi$
$810$	−21.6419	−0.760419
$811$	15.4752	0.543409	0.271704	−	0.962381i	$-0.412413\pi$
$811$	15.4752	0.543409	0.271704	+	0.962381i	$0.412413\pi$
$812$	0	0
$813$	6.40067	0.224481
$814$	7.22896	0.253375
$815$	−8.58534	−0.300731
$816$	14.2631	0.499309
$817$	54.2223	1.89700
$818$	16.1693	0.565346
$819$	0	0
$820$	13.6237	0.475762
$821$	38.2525	1.33502	0.667511	−	0.744600i	$-0.267360\pi$
$821$	38.2525	1.33502	0.667511	+	0.744600i	$0.267360\pi$
$822$	−3.42633	−0.119507
$823$	48.6193	1.69476	0.847382	−	0.530984i	$-0.178178\pi$
$823$	48.6193	1.69476	0.847382	+	0.530984i	$0.178178\pi$
$824$	−0.475005	−0.0165476
$825$	−7.01168	−0.244115
$826$	0	0
$827$	−15.2593	−0.530617	−0.265309	−	0.964164i	$-0.585474\pi$
$827$	−15.2593	−0.530617	−0.265309	+	0.964164i	$0.585474\pi$
$828$	−13.0306	−0.452845
$829$	1.74771	0.0607004	0.0303502	−	0.999539i	$-0.490338\pi$
$829$	1.74771	0.0607004	0.0303502	+	0.999539i	$0.490338\pi$
$830$	−7.17213	−0.248948
$831$	−52.9503	−1.83683
$832$	55.4982	1.92405
$833$	0	0
$834$	−30.6921	−1.06278
$835$	2.07823	0.0719201
$836$	−36.1796	−1.25130
$837$	4.26520	0.147427
$838$	65.1054	2.24903
$839$	26.2464	0.906127	0.453064	−	0.891478i	$-0.350331\pi$
$839$	26.2464	0.906127	0.453064	+	0.891478i	$0.350331\pi$
$840$	0	0
$841$	−14.5632	−0.502180
$842$	−32.7735	−1.12945
$843$	35.0720	1.20794
$844$	29.0019	0.998288
$845$	32.5573	1.12000
$846$	−14.5897	−0.501605
$847$	0	0
$848$	−18.5558	−0.637210
$849$	−50.0990	−1.71939
$850$	−3.71585	−0.127453
$851$	7.89453	0.270621
$852$	−51.1921	−1.75381
$853$	−18.9400	−0.648492	−0.324246	−	0.945973i	$-0.605111\pi$
$853$	−18.9400	−0.648492	−0.324246	+	0.945973i	$0.605111\pi$
$854$	0	0
$855$	4.06028	0.138859
$856$	−0.389863	−0.0133252
$857$	−1.88493	−0.0643880	−0.0321940	−	0.999482i	$-0.510249\pi$
$857$	−1.88493	−0.0643880	−0.0321940	+	0.999482i	$0.510249\pi$
$858$	94.9830	3.24267
$859$	36.8502	1.25731	0.628656	−	0.777684i	$-0.283605\pi$
$859$	36.8502	1.25731	0.628656	+	0.777684i	$0.283605\pi$
$860$	22.1218	0.754348
$861$	0	0
$862$	−73.4729	−2.50250
$863$	−25.0122	−0.851425	−0.425712	−	0.904859i	$-0.639976\pi$
$863$	−25.0122	−0.851425	−0.425712	+	0.904859i	$0.639976\pi$
$864$	34.2341	1.16467
$865$	−5.84960	−0.198892
$866$	11.3851	0.386882
$867$	−26.5154	−0.900511
$868$	0	0
$869$	−38.5346	−1.30720
$870$	−14.8981	−0.505093
$871$	−46.8010	−1.58579
$872$	−0.882114	−0.0298721
$873$	−9.54708	−0.323120
$874$	−78.4758	−2.65448
$875$	0	0
$876$	6.89839	0.233075
$877$	−29.9176	−1.01025	−0.505123	−	0.863047i	$-0.668553\pi$
$877$	−29.9176	−1.01025	−0.505123	+	0.863047i	$0.668553\pi$
$878$	−38.8782	−1.31208
$879$	−62.4346	−2.10587
$880$	14.1521	0.477067
$881$	43.8293	1.47665	0.738323	−	0.674447i	$-0.235618\pi$
$881$	43.8293	1.47665	0.738323	+	0.674447i	$0.235618\pi$
$882$	0	0
$883$	34.9147	1.17497	0.587487	−	0.809234i	$-0.300117\pi$
$883$	34.9147	1.17497	0.587487	+	0.809234i	$0.300117\pi$
$884$	25.3431	0.852382
$885$	8.21803	0.276246
$886$	16.7916	0.564124
$887$	13.2508	0.444919	0.222460	−	0.974942i	$-0.428591\pi$
$887$	13.2508	0.444919	0.222460	+	0.974942i	$0.428591\pi$
$888$	−0.110189	−0.00369771
$889$	0	0
$890$	0.905763	0.0303612
$891$	38.7009	1.29653
$892$	−31.3506	−1.04969
$893$	−44.2381	−1.48037
$894$	71.1375	2.37919
$895$	5.65417	0.188998
$896$	0	0
$897$	103.728	3.46338
$898$	45.4141	1.51549
$899$	3.79957	0.126723
$900$	1.65653	0.0552176
$901$	−8.71251	−0.290256
$902$	−48.3887	−1.61117
$903$	0	0
$904$	0.894188	0.0297403
$905$	4.54081	0.150942
$906$	66.1108	2.19638
$907$	0.398975	0.0132477	0.00662387	−	0.999978i	$-0.497892\pi$
$907$	0.398975	0.0132477	0.00662387	+	0.999978i	$0.497892\pi$
$908$	30.9763	1.02798
$909$	4.83894	0.160498
$910$	0	0
$911$	51.2988	1.69961	0.849803	−	0.527100i	$-0.176721\pi$
$911$	51.2988	1.69961	0.849803	+	0.527100i	$0.176721\pi$
$912$	−38.2936	−1.26803
$913$	12.8255	0.424462
$914$	60.4016	1.99791
$915$	−5.46665	−0.180722
$916$	−46.8182	−1.54692
$917$	0	0
$918$	15.8488	0.523089
$919$	−40.9302	−1.35016	−0.675082	−	0.737743i	$-0.735892\pi$
$919$	−40.9302	−1.35016	−0.675082	+	0.737743i	$0.735892\pi$
$920$	−0.442073	−0.0145747
$921$	58.4378	1.92559
$922$	13.0538	0.429905
$923$	87.2091	2.87052
$924$	0	0
$925$	−1.00360	−0.0329981
$926$	−63.8218	−2.09732
$927$	−6.90400	−0.226757
$928$	30.4968	1.00111
$929$	−50.4698	−1.65586	−0.827930	−	0.560831i	$-0.810482\pi$
$929$	−50.4698	−1.65586	−0.827930	+	0.560831i	$0.810482\pi$
$930$	−3.92099	−0.128574
$931$	0	0
$932$	18.0177	0.590188
$933$	−26.9936	−0.883732
$934$	19.6962	0.644480
$935$	6.64483	0.217309
$936$	−0.309840	−0.0101274
$937$	−21.3054	−0.696016	−0.348008	−	0.937492i	$-0.613142\pi$
$937$	−21.3054	−0.696016	−0.348008	+	0.937492i	$0.613142\pi$
$938$	0	0
$939$	−60.0031	−1.95813
$940$	−18.0485	−0.588676
$941$	−14.5809	−0.475323	−0.237661	−	0.971348i	$-0.576381\pi$
$941$	−14.5809	−0.475323	−0.237661	+	0.971348i	$0.576381\pi$
$942$	−93.0676	−3.03231
$943$	−52.8438	−1.72083
$944$	−16.5869	−0.539859
$945$	0	0
$946$	−78.5721	−2.55460
$947$	2.41489	0.0784733	0.0392367	−	0.999230i	$-0.487507\pi$
$947$	2.41489	0.0784733	0.0392367	+	0.999230i	$0.487507\pi$
$948$	42.5402	1.38164
$949$	−11.7519	−0.381482
$950$	9.97631	0.323674
$951$	21.2684	0.689676
$952$	0	0
$953$	−3.80014	−0.123099	−0.0615493	−	0.998104i	$-0.519604\pi$
$953$	−3.80014	−0.123099	−0.0615493	+	0.998104i	$0.519604\pi$
$954$	7.71446	0.249765
$955$	10.0235	0.324354
$956$	−21.4475	−0.693662
$957$	26.6414	0.861194
$958$	−5.50739	−0.177936
$959$	0	0
$960$	−16.0639	−0.518460
$961$	1.00000	0.0322581
$962$	13.5951	0.438325
$963$	−5.66649	−0.182600
$964$	−4.49738	−0.144851
$965$	11.5066	0.370412
$966$	0	0
$967$	−3.45883	−0.111228	−0.0556142	−	0.998452i	$-0.517712\pi$
$967$	−3.45883	−0.111228	−0.0556142	+	0.998452i	$0.517712\pi$
$968$	0.105697	0.00339723
$969$	−17.9800	−0.577601
$970$	−23.4577	−0.753180
$971$	−22.2515	−0.714086	−0.357043	−	0.934088i	$-0.616215\pi$
$971$	−22.2515	−0.714086	−0.357043	+	0.934088i	$0.616215\pi$
$972$	−16.7744	−0.538038
$973$	0	0
$974$	−64.5539	−2.06844
$975$	−13.1865	−0.422307
$976$	11.0337	0.353179
$977$	25.3320	0.810444	0.405222	−	0.914218i	$-0.367194\pi$
$977$	25.3320	0.810444	0.405222	+	0.914218i	$0.367194\pi$
$978$	−33.6631	−1.07643
$979$	−1.61972	−0.0517666
$980$	0	0
$981$	−12.8212	−0.409348
$982$	25.2303	0.805130
$983$	−9.60221	−0.306263	−0.153132	−	0.988206i	$-0.548936\pi$
$983$	−9.60221	−0.306263	−0.153132	+	0.988206i	$0.548936\pi$
$984$	0.737577	0.0235131
$985$	5.91009	0.188311
$986$	14.1186	0.449629
$987$	0	0
$988$	−68.0412	−2.16468
$989$	−85.8062	−2.72848
$990$	−5.88365	−0.186995
$991$	−16.4794	−0.523485	−0.261742	−	0.965138i	$-0.584297\pi$
$991$	−16.4794	−0.523485	−0.261742	+	0.965138i	$0.584297\pi$
$992$	8.02638	0.254838
$993$	−39.1313	−1.24180
$994$	0	0
$995$	−10.4636	−0.331720
$996$	−14.1587	−0.448635
$997$	17.7470	0.562052	0.281026	−	0.959700i	$-0.409325\pi$
$997$	17.7470	0.562052	0.281026	+	0.959700i	$0.409325\pi$
$998$	−33.0832	−1.04723
$999$	4.28055	0.135431

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7595.2.a.bf.1.18		21
7.3	odd	6		1085.2.j.d.156.4	✓	42
7.5	odd	6		1085.2.j.d.466.4	yes	42
7.6	odd	2		7595.2.a.bg.1.18		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1085.2.j.d.156.4	✓	42	7.3	odd	6
1085.2.j.d.466.4	yes	42	7.5	odd	6
7595.2.a.bf.1.18		21	1.1	even	1	trivial
7595.2.a.bg.1.18		21	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7595 = 5 \cdot 7^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7595.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00699 q^{2} +1.95367 q^{3} +2.02800 q^{4} +1.00000 q^{5} +3.92099 q^{6} +0.0561989 q^{8} +0.816828 q^{9} +O(q^{10})\)	\(q+2.00699 q^{2} +1.95367 q^{3} +2.02800 q^{4} +1.00000 q^{5} +3.92099 q^{6} +0.0561989 q^{8} +0.816828 q^{9} +2.00699 q^{10} -3.58898 q^{11} +3.96205 q^{12} -6.74961 q^{13} +1.95367 q^{15} -3.94321 q^{16} -1.85146 q^{17} +1.63936 q^{18} +4.97079 q^{19} +2.02800 q^{20} -7.20304 q^{22} -7.86622 q^{23} +0.109794 q^{24} +1.00000 q^{25} -13.5464 q^{26} -4.26520 q^{27} -3.79957 q^{29} +3.92099 q^{30} -1.00000 q^{31} -8.02638 q^{32} -7.01168 q^{33} -3.71585 q^{34} +1.65653 q^{36} -1.00360 q^{37} +9.97631 q^{38} -13.1865 q^{39} +0.0561989 q^{40} +6.71782 q^{41} +10.9082 q^{43} -7.27845 q^{44} +0.816828 q^{45} -15.7874 q^{46} -8.89963 q^{47} -7.70374 q^{48} +2.00699 q^{50} -3.61713 q^{51} -13.6882 q^{52} +4.70576 q^{53} -8.56020 q^{54} -3.58898 q^{55} +9.71128 q^{57} -7.62570 q^{58} +4.20645 q^{59} +3.96205 q^{60} -2.79814 q^{61} -2.00699 q^{62} -8.22242 q^{64} -6.74961 q^{65} -14.0724 q^{66} +6.93388 q^{67} -3.75475 q^{68} -15.3680 q^{69} -12.9206 q^{71} +0.0459049 q^{72} +1.74112 q^{73} -2.01421 q^{74} +1.95367 q^{75} +10.0808 q^{76} -26.4652 q^{78} +10.7369 q^{79} -3.94321 q^{80} -10.7833 q^{81} +13.4826 q^{82} -3.57358 q^{83} -1.85146 q^{85} +21.8926 q^{86} -7.42312 q^{87} -0.201697 q^{88} +0.451305 q^{89} +1.63936 q^{90} -15.9527 q^{92} -1.95367 q^{93} -17.8614 q^{94} +4.97079 q^{95} -15.6809 q^{96} -11.6880 q^{97} -2.93158 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) \) 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9	\( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9} - 4 q^{10} - 4 q^{11} - 21 q^{12} - 24 q^{13} - 5 q^{15} + 20 q^{16} - 18 q^{17} - 16 q^{18} - 17 q^{19} + 22 q^{20} + 9 q^{22} - 19 q^{23} - 21 q^{24} + 21 q^{25} - 16 q^{26} - 17 q^{27} - 4 q^{29} - 6 q^{30} - 21 q^{31} - 18 q^{32} - 27 q^{33} + 2 q^{34} + 52 q^{36} - 19 q^{37} + 10 q^{38} + 21 q^{39} - 12 q^{40} - 5 q^{41} - 15 q^{43} - 11 q^{44} + 20 q^{45} + 6 q^{46} - 4 q^{47} - 19 q^{48} - 4 q^{50} + 35 q^{51} - 66 q^{52} - 19 q^{53} - 11 q^{54} - 4 q^{55} - 27 q^{57} - q^{58} + q^{59} - 21 q^{60} - 60 q^{61} + 4 q^{62} - 10 q^{64} - 24 q^{65} - 64 q^{66} + 2 q^{67} - 11 q^{68} - 18 q^{69} - q^{71} - 37 q^{72} - 51 q^{73} + 11 q^{74} - 5 q^{75} - 13 q^{76} - 40 q^{78} + q^{79} + 20 q^{80} + 21 q^{81} + 2 q^{82} - 38 q^{83} - 18 q^{85} + 26 q^{86} - 32 q^{87} + 5 q^{88} - 2 q^{89} - 16 q^{90} - 86 q^{92} + 5 q^{93} - 67 q^{94} - 17 q^{95} + 56 q^{96} - 42 q^{97} - 35 q^{99}+O(q^{100}) \) 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9 - 4 * q^10 - 4 * q^11 - 21 * q^12 - 24 * q^13 - 5 * q^15 + 20 * q^16 - 18 * q^17 - 16 * q^18 - 17 * q^19 + 22 * q^20 + 9 * q^22 - 19 * q^23 - 21 * q^24 + 21 * q^25 - 16 * q^26 - 17 * q^27 - 4 * q^29 - 6 * q^30 - 21 * q^31 - 18 * q^32 - 27 * q^33 + 2 * q^34 + 52 * q^36 - 19 * q^37 + 10 * q^38 + 21 * q^39 - 12 * q^40 - 5 * q^41 - 15 * q^43 - 11 * q^44 + 20 * q^45 + 6 * q^46 - 4 * q^47 - 19 * q^48 - 4 * q^50 + 35 * q^51 - 66 * q^52 - 19 * q^53 - 11 * q^54 - 4 * q^55 - 27 * q^57 - q^58 + q^59 - 21 * q^60 - 60 * q^61 + 4 * q^62 - 10 * q^64 - 24 * q^65 - 64 * q^66 + 2 * q^67 - 11 * q^68 - 18 * q^69 - q^71 - 37 * q^72 - 51 * q^73 + 11 * q^74 - 5 * q^75 - 13 * q^76 - 40 * q^78 + q^79 + 20 * q^80 + 21 * q^81 + 2 * q^82 - 38 * q^83 - 18 * q^85 + 26 * q^86 - 32 * q^87 + 5 * q^88 - 2 * q^89 - 16 * q^90 - 86 * q^92 + 5 * q^93 - 67 * q^94 - 17 * q^95 + 56 * q^96 - 42 * q^97 - 35 * q^99

Introduction

L-functions

Modular forms

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