LMFDB - Embedded newform 4235.2.a.y.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.173513.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 3x^{2} + 3x - 1 $ x^5 - 2x^4 - 5x^3 + 3x^2 + 3x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.293545$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.40663 q^{2} -0.321225 q^{3} +3.79186 q^{4} -1.00000 q^{5} -0.773069 q^{6} +1.00000 q^{7} +4.31233 q^{8} -2.89681 q^{9} +O(q^{10})$	\(q+2.40663 q^{2} -0.321225 q^{3} +3.79186 q^{4} -1.00000 q^{5} -0.773069 q^{6} +1.00000 q^{7} +4.31233 q^{8} -2.89681 q^{9} -2.40663 q^{10} -1.21804 q^{12} -4.76679 q^{13} +2.40663 q^{14} +0.321225 q^{15} +2.79447 q^{16} +0.284654 q^{17} -6.97155 q^{18} -7.09353 q^{19} -3.79186 q^{20} -0.321225 q^{21} +9.19849 q^{23} -1.38523 q^{24} +1.00000 q^{25} -11.4719 q^{26} +1.89420 q^{27} +3.79186 q^{28} -9.56618 q^{29} +0.773069 q^{30} -6.23683 q^{31} -1.89942 q^{32} +0.685056 q^{34} -1.00000 q^{35} -10.9843 q^{36} +2.86108 q^{37} -17.0715 q^{38} +1.53121 q^{39} -4.31233 q^{40} +3.08304 q^{41} -0.773069 q^{42} +4.95715 q^{43} +2.89681 q^{45} +22.1373 q^{46} -3.41990 q^{47} -0.897653 q^{48} +1.00000 q^{49} +2.40663 q^{50} -0.0914380 q^{51} -18.0750 q^{52} -7.44219 q^{53} +4.55865 q^{54} +4.31233 q^{56} +2.27862 q^{57} -23.0222 q^{58} -8.43413 q^{59} +1.21804 q^{60} -7.83020 q^{61} -15.0097 q^{62} -2.89681 q^{63} -10.1601 q^{64} +4.76679 q^{65} +2.33196 q^{67} +1.07937 q^{68} -2.95478 q^{69} -2.40663 q^{70} -12.7182 q^{71} -12.4920 q^{72} -0.750610 q^{73} +6.88556 q^{74} -0.321225 q^{75} -26.8976 q^{76} +3.68506 q^{78} -7.66727 q^{79} -2.79447 q^{80} +8.08198 q^{81} +7.41973 q^{82} +9.39958 q^{83} -1.21804 q^{84} -0.284654 q^{85} +11.9300 q^{86} +3.07290 q^{87} -14.7733 q^{89} +6.97155 q^{90} -4.76679 q^{91} +34.8793 q^{92} +2.00343 q^{93} -8.23043 q^{94} +7.09353 q^{95} +0.610143 q^{96} +11.9388 q^{97} +2.40663 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} + 5 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 + 5 * q^7 + 6 * q^8 + 3 * q^9	$ 5 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} + 5 q^{7} + 6 q^{8} + 3 q^{9} + 2 q^{10} + 11 q^{12} - 12 q^{13} - 2 q^{14} + 2 q^{15} + 2 q^{16} - 14 q^{17} - 7 q^{18} - 9 q^{19} - 4 q^{20} - 2 q^{21} + 17 q^{23} - 6 q^{24} + 5 q^{25} - 11 q^{26} - 11 q^{27} + 4 q^{28} - 3 q^{29} + 5 q^{30} + 2 q^{31} + 5 q^{32} + 16 q^{34} - 5 q^{35} - 15 q^{36} + 4 q^{37} - 11 q^{38} - 2 q^{39} - 6 q^{40} + 15 q^{41} - 5 q^{42} - 4 q^{43} - 3 q^{45} + 10 q^{46} - 2 q^{47} - 10 q^{48} + 5 q^{49} - 2 q^{50} + 18 q^{51} - 4 q^{52} + 6 q^{53} - 4 q^{54} + 6 q^{56} - 32 q^{58} - 6 q^{59} - 11 q^{60} - 20 q^{61} - 21 q^{62} + 3 q^{63} - 26 q^{64} + 12 q^{65} + 3 q^{67} - 5 q^{68} + 2 q^{70} - 6 q^{71} - 34 q^{72} - 11 q^{73} + 15 q^{74} - 2 q^{75} - 47 q^{76} + 31 q^{78} - 19 q^{79} - 2 q^{80} + 33 q^{81} - 8 q^{83} + 11 q^{84} + 14 q^{85} + 27 q^{86} + 30 q^{87} + q^{89} + 7 q^{90} - 12 q^{91} + 44 q^{92} + 3 q^{93} - 28 q^{94} + 9 q^{95} + 4 q^{96} - 7 q^{97} - 2 q^{98}+O(q^{100}) $ 5 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 + 5 * q^7 + 6 * q^8 + 3 * q^9 + 2 * q^10 + 11 * q^12 - 12 * q^13 - 2 * q^14 + 2 * q^15 + 2 * q^16 - 14 * q^17 - 7 * q^18 - 9 * q^19 - 4 * q^20 - 2 * q^21 + 17 * q^23 - 6 * q^24 + 5 * q^25 - 11 * q^26 - 11 * q^27 + 4 * q^28 - 3 * q^29 + 5 * q^30 + 2 * q^31 + 5 * q^32 + 16 * q^34 - 5 * q^35 - 15 * q^36 + 4 * q^37 - 11 * q^38 - 2 * q^39 - 6 * q^40 + 15 * q^41 - 5 * q^42 - 4 * q^43 - 3 * q^45 + 10 * q^46 - 2 * q^47 - 10 * q^48 + 5 * q^49 - 2 * q^50 + 18 * q^51 - 4 * q^52 + 6 * q^53 - 4 * q^54 + 6 * q^56 - 32 * q^58 - 6 * q^59 - 11 * q^60 - 20 * q^61 - 21 * q^62 + 3 * q^63 - 26 * q^64 + 12 * q^65 + 3 * q^67 - 5 * q^68 + 2 * q^70 - 6 * q^71 - 34 * q^72 - 11 * q^73 + 15 * q^74 - 2 * q^75 - 47 * q^76 + 31 * q^78 - 19 * q^79 - 2 * q^80 + 33 * q^81 - 8 * q^83 + 11 * q^84 + 14 * q^85 + 27 * q^86 + 30 * q^87 + q^89 + 7 * q^90 - 12 * q^91 + 44 * q^92 + 3 * q^93 - 28 * q^94 + 9 * q^95 + 4 * q^96 - 7 * q^97 - 2 * q^98

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 $

$2$	2.40663	1.70174	0.850871	−	0.525374i	$-0.176075\pi$
$2$	2.40663	1.70174	0.850871	+	0.525374i	$0.176075\pi$
$3$	−0.321225	−0.185459	−0.0927297	−	0.995691i	$-0.529559\pi$
$3$	−0.321225	−0.185459	−0.0927297	+	0.995691i	$0.529559\pi$
$4$	3.79186	1.89593
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.773069	−0.315604
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	4.31233	1.52464
$9$	−2.89681	−0.965605
$10$	−2.40663	−0.761043
$11$	0	0
$11$	0	0
$12$	−1.21804	−0.351618
$13$	−4.76679	−1.32207	−0.661035	−	0.750355i	$-0.729882\pi$
$13$	−4.76679	−1.32207	−0.661035	+	0.750355i	$0.729882\pi$
$14$	2.40663	0.643198
$15$	0.321225	0.0829399
$16$	2.79447	0.698617
$17$	0.284654	0.0690387	0.0345194	−	0.999404i	$-0.489010\pi$
$17$	0.284654	0.0690387	0.0345194	+	0.999404i	$0.489010\pi$
$18$	−6.97155	−1.64321
$19$	−7.09353	−1.62737	−0.813683	−	0.581308i	$-0.802541\pi$
$19$	−7.09353	−1.62737	−0.813683	+	0.581308i	$0.802541\pi$
$20$	−3.79186	−0.847885
$21$	−0.321225	−0.0700970
$22$	0	0
$23$	9.19849	1.91802	0.959008	−	0.283378i	$-0.0914550\pi$
$23$	9.19849	1.91802	0.959008	+	0.283378i	$0.0914550\pi$
$24$	−1.38523	−0.282759
$25$	1.00000	0.200000
$26$	−11.4719	−2.24982
$27$	1.89420	0.364540
$28$	3.79186	0.716594
$29$	−9.56618	−1.77639	−0.888197	−	0.459462i	$-0.848042\pi$
$29$	−9.56618	−1.77639	−0.888197	+	0.459462i	$0.848042\pi$
$30$	0.773069	0.141142
$31$	−6.23683	−1.12017	−0.560084	−	0.828436i	$-0.689231\pi$
$31$	−6.23683	−1.12017	−0.560084	+	0.828436i	$0.689231\pi$
$32$	−1.89942	−0.335774
$33$	0	0
$34$	0.685056	0.117486
$35$	−1.00000	−0.169031
$36$	−10.9843	−1.83072
$37$	2.86108	0.470359	0.235179	−	0.971952i	$-0.424432\pi$
$37$	2.86108	0.470359	0.235179	+	0.971952i	$0.424432\pi$
$38$	−17.0715	−2.76936
$39$	1.53121	0.245190
$40$	−4.31233	−0.681840
$41$	3.08304	0.481490	0.240745	−	0.970588i	$-0.422608\pi$
$41$	3.08304	0.481490	0.240745	+	0.970588i	$0.422608\pi$
$42$	−0.773069	−0.119287
$43$	4.95715	0.755958	0.377979	−	0.925814i	$-0.376619\pi$
$43$	4.95715	0.755958	0.377979	+	0.925814i	$0.376619\pi$
$44$	0	0
$45$	2.89681	0.431832
$46$	22.1373	3.26397
$47$	−3.41990	−0.498844	−0.249422	−	0.968395i	$-0.580241\pi$
$47$	−3.41990	−0.498844	−0.249422	+	0.968395i	$0.580241\pi$
$48$	−0.897653	−0.129565
$49$	1.00000	0.142857
$50$	2.40663	0.340349
$51$	−0.0914380	−0.0128039
$52$	−18.0750	−2.50655
$53$	−7.44219	−1.02226	−0.511131	−	0.859503i	$-0.670773\pi$
$53$	−7.44219	−1.02226	−0.511131	+	0.859503i	$0.670773\pi$
$54$	4.55865	0.620353
$55$	0	0
$56$	4.31233	0.576260
$57$	2.27862	0.301810
$58$	−23.0222	−3.02297
$59$	−8.43413	−1.09803	−0.549015	−	0.835812i	$-0.684997\pi$
$59$	−8.43413	−1.09803	−0.549015	+	0.835812i	$0.684997\pi$
$60$	1.21804	0.157248
$61$	−7.83020	−1.00255	−0.501277	−	0.865287i	$-0.667136\pi$
$61$	−7.83020	−1.00255	−0.501277	+	0.865287i	$0.667136\pi$
$62$	−15.0097	−1.90624
$63$	−2.89681	−0.364964
$64$	−10.1601	−1.27002
$65$	4.76679	0.591247
$66$	0	0
$67$	2.33196	0.284894	0.142447	−	0.989802i	$-0.454503\pi$
$67$	2.33196	0.284894	0.142447	+	0.989802i	$0.454503\pi$
$68$	1.07937	0.130893
$69$	−2.95478	−0.355714
$70$	−2.40663	−0.287647
$71$	−12.7182	−1.50937	−0.754686	−	0.656086i	$-0.772211\pi$
$71$	−12.7182	−1.50937	−0.754686	+	0.656086i	$0.772211\pi$
$72$	−12.4920	−1.47220
$73$	−0.750610	−0.0878522	−0.0439261	−	0.999035i	$-0.513987\pi$
$73$	−0.750610	−0.0878522	−0.0439261	+	0.999035i	$0.513987\pi$
$74$	6.88556	0.800430
$75$	−0.321225	−0.0370919
$76$	−26.8976	−3.08537
$77$	0	0
$78$	3.68506	0.417250
$79$	−7.66727	−0.862636	−0.431318	−	0.902200i	$-0.641951\pi$
$79$	−7.66727	−0.862636	−0.431318	+	0.902200i	$0.641951\pi$
$80$	−2.79447	−0.312431
$81$	8.08198	0.897998
$82$	7.41973	0.819372
$83$	9.39958	1.03174	0.515869	−	0.856667i	$-0.327469\pi$
$83$	9.39958	1.03174	0.515869	+	0.856667i	$0.327469\pi$
$84$	−1.21804	−0.132899
$85$	−0.284654	−0.0308751
$86$	11.9300	1.28645
$87$	3.07290	0.329449
$88$	0	0
$89$	−14.7733	−1.56597	−0.782984	−	0.622042i	$-0.786303\pi$
$89$	−14.7733	−1.56597	−0.782984	+	0.622042i	$0.786303\pi$
$90$	6.97155	0.734866
$91$	−4.76679	−0.499695
$92$	34.8793	3.63642
$93$	2.00343	0.207746
$94$	−8.23043	−0.848904
$95$	7.09353	0.727781
$96$	0.610143	0.0622724
$97$	11.9388	1.21220	0.606099	−	0.795389i	$-0.292733\pi$
$97$	11.9388	1.21220	0.606099	+	0.795389i	$0.292733\pi$
$98$	2.40663	0.243106
$99$	0	0
$100$	3.79186	0.379186
$101$	13.7715	1.37032	0.685160	−	0.728393i	$-0.259732\pi$
$101$	13.7715	1.37032	0.685160	+	0.728393i	$0.259732\pi$
$102$	−0.220057	−0.0217889
$103$	10.9843	1.08232	0.541158	−	0.840921i	$-0.317986\pi$
$103$	10.9843	1.08232	0.541158	+	0.840921i	$0.317986\pi$
$104$	−20.5560	−2.01568
$105$	0.321225	0.0313484
$106$	−17.9106	−1.73963
$107$	−10.0331	−0.969940	−0.484970	−	0.874531i	$-0.661170\pi$
$107$	−10.0331	−0.969940	−0.484970	+	0.874531i	$0.661170\pi$
$108$	7.18255	0.691141
$109$	9.15250	0.876651	0.438325	−	0.898816i	$-0.355572\pi$
$109$	9.15250	0.876651	0.438325	+	0.898816i	$0.355572\pi$
$110$	0	0
$111$	−0.919051	−0.0872325
$112$	2.79447	0.264052
$113$	15.4820	1.45643	0.728213	−	0.685351i	$-0.240351\pi$
$113$	15.4820	1.45643	0.728213	+	0.685351i	$0.240351\pi$
$114$	5.48379	0.513604
$115$	−9.19849	−0.857763
$116$	−36.2736	−3.36792
$117$	13.8085	1.27660
$118$	−20.2978	−1.86857
$119$	0.284654	0.0260942
$120$	1.38523	0.126454
$121$	0	0
$122$	−18.8444	−1.70609
$123$	−0.990349	−0.0892968
$124$	−23.6492	−2.12376
$125$	−1.00000	−0.0894427
$126$	−6.97155	−0.621075
$127$	−1.07543	−0.0954293	−0.0477147	−	0.998861i	$-0.515194\pi$
$127$	−1.07543	−0.0954293	−0.0477147	+	0.998861i	$0.515194\pi$
$128$	−20.6528	−1.82547
$129$	−1.59236	−0.140199
$130$	11.4719	1.00615
$131$	7.90703	0.690840	0.345420	−	0.938448i	$-0.387736\pi$
$131$	7.90703	0.690840	0.345420	+	0.938448i	$0.387736\pi$
$132$	0	0
$133$	−7.09353	−0.615087
$134$	5.61216	0.484817
$135$	−1.89420	−0.163027
$136$	1.22752	0.105259
$137$	6.89605	0.589169	0.294585	−	0.955625i	$-0.404819\pi$
$137$	6.89605	0.589169	0.294585	+	0.955625i	$0.404819\pi$
$138$	−7.11106	−0.605334
$139$	−21.2625	−1.80346	−0.901731	−	0.432297i	$-0.857703\pi$
$139$	−21.2625	−1.80346	−0.901731	+	0.432297i	$0.857703\pi$
$140$	−3.79186	−0.320470
$141$	1.09856	0.0925153
$142$	−30.6080	−2.56856
$143$	0	0
$144$	−8.09505	−0.674588
$145$	9.56618	0.794428
$146$	−1.80644	−0.149502
$147$	−0.321225	−0.0264942
$148$	10.8488	0.891767
$149$	11.2308	0.920066	0.460033	−	0.887902i	$-0.347838\pi$
$149$	11.2308	0.920066	0.460033	+	0.887902i	$0.347838\pi$
$150$	−0.773069	−0.0631208
$151$	0.306818	0.0249685	0.0124843	−	0.999922i	$-0.496026\pi$
$151$	0.306818	0.0249685	0.0124843	+	0.999922i	$0.496026\pi$
$152$	−30.5897	−2.48115
$153$	−0.824590	−0.0666641
$154$	0	0
$155$	6.23683	0.500954
$156$	5.80614	0.464863
$157$	−1.95122	−0.155724	−0.0778620	−	0.996964i	$-0.524809\pi$
$157$	−1.95122	−0.155724	−0.0778620	+	0.996964i	$0.524809\pi$
$158$	−18.4523	−1.46798
$159$	2.39062	0.189588
$160$	1.89942	0.150163
$161$	9.19849	0.724942
$162$	19.4503	1.52816
$163$	17.9429	1.40539	0.702697	−	0.711490i	$-0.251979\pi$
$163$	17.9429	1.40539	0.702697	+	0.711490i	$0.251979\pi$
$164$	11.6904	0.912870
$165$	0	0
$166$	22.6213	1.75575
$167$	−15.0799	−1.16692	−0.583460	−	0.812142i	$-0.698302\pi$
$167$	−15.0799	−1.16692	−0.583460	+	0.812142i	$0.698302\pi$
$168$	−1.38523	−0.106873
$169$	9.72227	0.747867
$170$	−0.685056	−0.0525414
$171$	20.5486	1.57139
$172$	18.7968	1.43324
$173$	−24.7045	−1.87825	−0.939125	−	0.343576i	$-0.888362\pi$
$173$	−24.7045	−1.87825	−0.939125	+	0.343576i	$0.888362\pi$
$174$	7.39532	0.560638
$175$	1.00000	0.0755929
$176$	0	0
$177$	2.70925	0.203640
$178$	−35.5539	−2.66487
$179$	−16.4156	−1.22696	−0.613479	−	0.789711i	$-0.710231\pi$
$179$	−16.4156	−1.22696	−0.613479	+	0.789711i	$0.710231\pi$
$180$	10.9843	0.818722
$181$	8.33171	0.619291	0.309646	−	0.950852i	$-0.399790\pi$
$181$	8.33171	0.619291	0.309646	+	0.950852i	$0.399790\pi$
$182$	−11.4719	−0.850353
$183$	2.51526	0.185933
$184$	39.6669	2.92429
$185$	−2.86108	−0.210351
$186$	4.82150	0.353529
$187$	0	0
$188$	−12.9678	−0.945772
$189$	1.89420	0.137783
$190$	17.0715	1.23850
$191$	−5.74610	−0.415773	−0.207887	−	0.978153i	$-0.566658\pi$
$191$	−5.74610	−0.415773	−0.207887	+	0.978153i	$0.566658\pi$
$192$	3.26369	0.235537
$193$	9.93884	0.715414	0.357707	−	0.933834i	$-0.383559\pi$
$193$	9.93884	0.715414	0.357707	+	0.933834i	$0.383559\pi$
$194$	28.7322	2.06285
$195$	−1.53121	−0.109652
$196$	3.79186	0.270847
$197$	3.14958	0.224398	0.112199	−	0.993686i	$-0.464211\pi$
$197$	3.14958	0.224398	0.112199	+	0.993686i	$0.464211\pi$
$198$	0	0
$199$	5.31856	0.377023	0.188511	−	0.982071i	$-0.439634\pi$
$199$	5.31856	0.377023	0.188511	+	0.982071i	$0.439634\pi$
$200$	4.31233	0.304928
$201$	−0.749084	−0.0528363
$202$	33.1430	2.33193
$203$	−9.56618	−0.671414
$204$	−0.346720	−0.0242752
$205$	−3.08304	−0.215329
$206$	26.4351	1.84182
$207$	−26.6463	−1.85205
$208$	−13.3206	−0.923620
$209$	0	0
$210$	0.773069	0.0533468
$211$	1.58756	0.109292	0.0546461	−	0.998506i	$-0.482597\pi$
$211$	1.58756	0.109292	0.0546461	+	0.998506i	$0.482597\pi$
$212$	−28.2197	−1.93814
$213$	4.08540	0.279927
$214$	−24.1460	−1.65059
$215$	−4.95715	−0.338075
$216$	8.16844	0.555792
$217$	−6.23683	−0.423383
$218$	22.0267	1.49183
$219$	0.241115	0.0162930
$220$	0	0
$221$	−1.35689	−0.0912740
$222$	−2.21181	−0.148447
$223$	−8.74931	−0.585897	−0.292948	−	0.956128i	$-0.594636\pi$
$223$	−8.74931	−0.585897	−0.292948	+	0.956128i	$0.594636\pi$
$224$	−1.89942	−0.126911
$225$	−2.89681	−0.193121
$226$	37.2595	2.47846
$227$	−7.32115	−0.485922	−0.242961	−	0.970036i	$-0.578119\pi$
$227$	−7.32115	−0.485922	−0.242961	+	0.970036i	$0.578119\pi$
$228$	8.64020	0.572211
$229$	8.24158	0.544619	0.272309	−	0.962210i	$-0.412213\pi$
$229$	8.24158	0.544619	0.272309	+	0.962210i	$0.412213\pi$
$230$	−22.1373	−1.45969
$231$	0	0
$232$	−41.2526	−2.70836
$233$	−13.4000	−0.877863	−0.438932	−	0.898520i	$-0.644643\pi$
$233$	−13.4000	−0.877863	−0.438932	+	0.898520i	$0.644643\pi$
$234$	33.2319	2.17244
$235$	3.41990	0.223090
$236$	−31.9810	−2.08179
$237$	2.46292	0.159984
$238$	0.685056	0.0444056
$239$	3.20926	0.207589	0.103795	−	0.994599i	$-0.466902\pi$
$239$	3.20926	0.207589	0.103795	+	0.994599i	$0.466902\pi$
$240$	0.897653	0.0579432
$241$	−6.67350	−0.429878	−0.214939	−	0.976627i	$-0.568955\pi$
$241$	−6.67350	−0.429878	−0.214939	+	0.976627i	$0.568955\pi$
$242$	0	0
$243$	−8.27875	−0.531082
$244$	−29.6910	−1.90077
$245$	−1.00000	−0.0638877
$246$	−2.38340	−0.151960
$247$	33.8133	2.15149
$248$	−26.8953	−1.70785
$249$	−3.01938	−0.191345
$250$	−2.40663	−0.152209
$251$	14.4513	0.912159	0.456080	−	0.889939i	$-0.349253\pi$
$251$	14.4513	0.912159	0.456080	+	0.889939i	$0.349253\pi$
$252$	−10.9843	−0.691946
$253$	0	0
$254$	−2.58817	−0.162396
$255$	0.0914380	0.00572607
$256$	−29.3834	−1.83646
$257$	6.68992	0.417306	0.208653	−	0.977990i	$-0.433092\pi$
$257$	6.68992	0.417306	0.208653	+	0.977990i	$0.433092\pi$
$258$	−3.83222	−0.238583
$259$	2.86108	0.177779
$260$	18.0750	1.12096
$261$	27.7114	1.71530
$262$	19.0293	1.17563
$263$	24.5565	1.51422	0.757110	−	0.653287i	$-0.226610\pi$
$263$	24.5565	1.51422	0.757110	+	0.653287i	$0.226610\pi$
$264$	0	0
$265$	7.44219	0.457170
$266$	−17.0715	−1.04672
$267$	4.74556	0.290423
$268$	8.84246	0.540139
$269$	−24.2805	−1.48041	−0.740203	−	0.672384i	$-0.765271\pi$
$269$	−24.2805	−1.48041	−0.740203	+	0.672384i	$0.765271\pi$
$270$	−4.55865	−0.277430
$271$	−11.4013	−0.692580	−0.346290	−	0.938128i	$-0.612559\pi$
$271$	−11.4013	−0.692580	−0.346290	+	0.938128i	$0.612559\pi$
$272$	0.795456	0.0482316
$273$	1.53121	0.0926731
$274$	16.5962	1.00261
$275$	0	0
$276$	−11.2041	−0.674409
$277$	−10.2450	−0.615563	−0.307781	−	0.951457i	$-0.599587\pi$
$277$	−10.2450	−0.615563	−0.307781	+	0.951457i	$0.599587\pi$
$278$	−51.1709	−3.06903
$279$	18.0669	1.08164
$280$	−4.31233	−0.257711
$281$	13.9922	0.834704	0.417352	−	0.908745i	$-0.362958\pi$
$281$	13.9922	0.834704	0.417352	+	0.908745i	$0.362958\pi$
$282$	2.64382	0.157437
$283$	6.35828	0.377961	0.188980	−	0.981981i	$-0.439482\pi$
$283$	6.35828	0.377961	0.188980	+	0.981981i	$0.439482\pi$
$284$	−48.2256	−2.86166
$285$	−2.27862	−0.134974
$286$	0	0
$287$	3.08304	0.181986
$288$	5.50228	0.324225
$289$	−16.9190	−0.995234
$290$	23.0222	1.35191
$291$	−3.83503	−0.224814
$292$	−2.84620	−0.166562
$293$	2.18117	0.127426	0.0637128	−	0.997968i	$-0.479706\pi$
$293$	2.18117	0.127426	0.0637128	+	0.997968i	$0.479706\pi$
$294$	−0.773069	−0.0450863
$295$	8.43413	0.491054
$296$	12.3379	0.717128
$297$	0	0
$298$	27.0285	1.56572
$299$	−43.8472	−2.53575
$300$	−1.21804	−0.0703235
$301$	4.95715	0.285725
$302$	0.738398	0.0424900
$303$	−4.42376	−0.254139
$304$	−19.8226	−1.13691
$305$	7.83020	0.448356
$306$	−1.98448	−0.113445
$307$	−11.9841	−0.683966	−0.341983	−	0.939706i	$-0.611099\pi$
$307$	−11.9841	−0.683966	−0.341983	+	0.939706i	$0.611099\pi$
$308$	0	0
$309$	−3.52843	−0.200726
$310$	15.0097	0.852495
$311$	9.08109	0.514941	0.257471	−	0.966286i	$-0.417111\pi$
$311$	9.08109	0.514941	0.257471	+	0.966286i	$0.417111\pi$
$312$	6.60310	0.373827
$313$	6.96402	0.393630	0.196815	−	0.980441i	$-0.436940\pi$
$313$	6.96402	0.393630	0.196815	+	0.980441i	$0.436940\pi$
$314$	−4.69585	−0.265002
$315$	2.89681	0.163217
$316$	−29.0732	−1.63550
$317$	−22.7634	−1.27852	−0.639259	−	0.768992i	$-0.720759\pi$
$317$	−22.7634	−1.27852	−0.639259	+	0.768992i	$0.720759\pi$
$318$	5.75332	0.322630
$319$	0	0
$320$	10.1601	0.567969
$321$	3.22290	0.179884
$322$	22.1373	1.23367
$323$	−2.01920	−0.112351
$324$	30.6457	1.70254
$325$	−4.76679	−0.264414
$326$	43.1818	2.39162
$327$	−2.94001	−0.162583
$328$	13.2951	0.734099
$329$	−3.41990	−0.188545
$330$	0	0
$331$	26.5867	1.46134	0.730669	−	0.682732i	$-0.239208\pi$
$331$	26.5867	1.46134	0.730669	+	0.682732i	$0.239208\pi$
$332$	35.6419	1.95610
$333$	−8.28802	−0.454181
$334$	−36.2918	−1.98580
$335$	−2.33196	−0.127409
$336$	−0.897653	−0.0489710
$337$	22.3595	1.21800	0.608999	−	0.793171i	$-0.291571\pi$
$337$	22.3595	1.21800	0.608999	+	0.793171i	$0.291571\pi$
$338$	23.3979	1.27268
$339$	−4.97321	−0.270108
$340$	−1.07937	−0.0585369
$341$	0	0
$342$	49.4529	2.67411
$343$	1.00000	0.0539949
$344$	21.3769	1.15256
$345$	2.95478	0.159080
$346$	−59.4546	−3.19630
$347$	−17.7009	−0.950234	−0.475117	−	0.879923i	$-0.657594\pi$
$347$	−17.7009	−0.950234	−0.475117	+	0.879923i	$0.657594\pi$
$348$	11.6520	0.624612
$349$	−2.85200	−0.152664	−0.0763320	−	0.997082i	$-0.524321\pi$
$349$	−2.85200	−0.152664	−0.0763320	+	0.997082i	$0.524321\pi$
$350$	2.40663	0.128640
$351$	−9.02927	−0.481947
$352$	0	0
$353$	0.548804	0.0292099	0.0146049	−	0.999893i	$-0.495351\pi$
$353$	0.548804	0.0292099	0.0146049	+	0.999893i	$0.495351\pi$
$354$	6.52017	0.346543
$355$	12.7182	0.675012
$356$	−56.0183	−2.96896
$357$	−0.0914380	−0.00483941
$358$	−39.5062	−2.08797
$359$	−23.7324	−1.25255	−0.626274	−	0.779603i	$-0.715421\pi$
$359$	−23.7324	−1.25255	−0.626274	+	0.779603i	$0.715421\pi$
$360$	12.4920	0.658388
$361$	31.3181	1.64832
$362$	20.0513	1.05387
$363$	0	0
$364$	−18.0750	−0.947386
$365$	0.750610	0.0392887
$366$	6.05329	0.316410
$367$	21.5679	1.12584	0.562918	−	0.826513i	$-0.309679\pi$
$367$	21.5679	1.12584	0.562918	+	0.826513i	$0.309679\pi$
$368$	25.7049	1.33996
$369$	−8.93099	−0.464929
$370$	−6.88556	−0.357963
$371$	−7.44219	−0.386379
$372$	7.59670	0.393871
$373$	−9.65009	−0.499663	−0.249831	−	0.968289i	$-0.580375\pi$
$373$	−9.65009	−0.499663	−0.249831	+	0.968289i	$0.580375\pi$
$374$	0	0
$375$	0.321225	0.0165880
$376$	−14.7478	−0.760557
$377$	45.5999	2.34852
$378$	4.55865	0.234471
$379$	1.91750	0.0984955	0.0492477	−	0.998787i	$-0.484318\pi$
$379$	1.91750	0.0984955	0.0492477	+	0.998787i	$0.484318\pi$
$380$	26.8976	1.37982
$381$	0.345456	0.0176983
$382$	−13.8287	−0.707539
$383$	−5.38688	−0.275257	−0.137628	−	0.990484i	$-0.543948\pi$
$383$	−5.38688	−0.275257	−0.137628	+	0.990484i	$0.543948\pi$
$384$	6.63421	0.338550
$385$	0	0
$386$	23.9191	1.21745
$387$	−14.3599	−0.729957
$388$	45.2701	2.29824
$389$	8.31392	0.421532	0.210766	−	0.977537i	$-0.432404\pi$
$389$	8.31392	0.421532	0.210766	+	0.977537i	$0.432404\pi$
$390$	−3.68506	−0.186600
$391$	2.61839	0.132417
$392$	4.31233	0.217806
$393$	−2.53994	−0.128123
$394$	7.57987	0.381868
$395$	7.66727	0.385782
$396$	0	0
$397$	−15.8950	−0.797746	−0.398873	−	0.917006i	$-0.630599\pi$
$397$	−15.8950	−0.797746	−0.398873	+	0.917006i	$0.630599\pi$
$398$	12.7998	0.641596
$399$	2.27862	0.114074
$400$	2.79447	0.139723
$401$	34.2863	1.71218	0.856089	−	0.516829i	$-0.172888\pi$
$401$	34.2863	1.71218	0.856089	+	0.516829i	$0.172888\pi$
$402$	−1.80277	−0.0899138
$403$	29.7296	1.48094
$404$	52.2197	2.59803
$405$	−8.08198	−0.401597
$406$	−23.0222	−1.14257
$407$	0	0
$408$	−0.394311	−0.0195213
$409$	−29.1522	−1.44148	−0.720742	−	0.693203i	$-0.756199\pi$
$409$	−29.1522	−1.44148	−0.720742	+	0.693203i	$0.756199\pi$
$410$	−7.41973	−0.366434
$411$	−2.21518	−0.109267
$412$	41.6509	2.05199
$413$	−8.43413	−0.415017
$414$	−64.1277	−3.15171
$415$	−9.39958	−0.461407
$416$	9.05415	0.443916
$417$	6.83005	0.334469
$418$	0	0
$419$	−19.8745	−0.970935	−0.485467	−	0.874255i	$-0.661351\pi$
$419$	−19.8745	−0.970935	−0.485467	+	0.874255i	$0.661351\pi$
$420$	1.21804	0.0594342
$421$	−9.13157	−0.445046	−0.222523	−	0.974927i	$-0.571429\pi$
$421$	−9.13157	−0.445046	−0.222523	+	0.974927i	$0.571429\pi$
$422$	3.82067	0.185987
$423$	9.90682	0.481686
$424$	−32.0932	−1.55858
$425$	0.284654	0.0138077
$426$	9.83204	0.476364
$427$	−7.83020	−0.378930
$428$	−38.0442	−1.83894
$429$	0	0
$430$	−11.9300	−0.575316
$431$	−6.14835	−0.296155	−0.148078	−	0.988976i	$-0.547309\pi$
$431$	−6.14835	−0.296155	−0.148078	+	0.988976i	$0.547309\pi$
$432$	5.29329	0.254674
$433$	−21.4207	−1.02941	−0.514707	−	0.857366i	$-0.672099\pi$
$433$	−21.4207	−1.02941	−0.514707	+	0.857366i	$0.672099\pi$
$434$	−15.0097	−0.720490
$435$	−3.07290	−0.147334
$436$	34.7050	1.66207
$437$	−65.2497	−3.12132
$438$	0.580273	0.0277265
$439$	23.6732	1.12986	0.564931	−	0.825138i	$-0.308903\pi$
$439$	23.6732	1.12986	0.564931	+	0.825138i	$0.308903\pi$
$440$	0	0
$441$	−2.89681	−0.137944
$442$	−3.26552	−0.155325
$443$	36.5672	1.73736	0.868680	−	0.495374i	$-0.164969\pi$
$443$	36.5672	1.73736	0.868680	+	0.495374i	$0.164969\pi$
$444$	−3.48491	−0.165387
$445$	14.7733	0.700322
$446$	−21.0563	−0.997046
$447$	−3.60763	−0.170635
$448$	−10.1601	−0.480022
$449$	31.3388	1.47897	0.739485	−	0.673173i	$-0.235069\pi$
$449$	31.3388	1.47897	0.739485	+	0.673173i	$0.235069\pi$
$450$	−6.97155	−0.328642
$451$	0	0
$452$	58.7056	2.76128
$453$	−0.0985578	−0.00463065
$454$	−17.6193	−0.826914
$455$	4.76679	0.223470
$456$	9.82616	0.460152
$457$	−15.7455	−0.736541	−0.368271	−	0.929719i	$-0.620050\pi$
$457$	−15.7455	−0.736541	−0.368271	+	0.929719i	$0.620050\pi$
$458$	19.8344	0.926801
$459$	0.539193	0.0251674
$460$	−34.8793	−1.62626
$461$	14.5224	0.676374	0.338187	−	0.941079i	$-0.390186\pi$
$461$	14.5224	0.676374	0.338187	+	0.941079i	$0.390186\pi$
$462$	0	0
$463$	−19.0465	−0.885167	−0.442583	−	0.896727i	$-0.645938\pi$
$463$	−19.0465	−0.885167	−0.442583	+	0.896727i	$0.645938\pi$
$464$	−26.7324	−1.24102
$465$	−2.00343	−0.0929066
$466$	−32.2488	−1.49390
$467$	−24.8958	−1.15204	−0.576020	−	0.817435i	$-0.695395\pi$
$467$	−24.8958	−1.15204	−0.576020	+	0.817435i	$0.695395\pi$
$468$	52.3599	2.42034
$469$	2.33196	0.107680
$470$	8.23043	0.379641
$471$	0.626780	0.0288805
$472$	−36.3708	−1.67410
$473$	0	0
$474$	5.92733	0.272251
$475$	−7.09353	−0.325473
$476$	1.07937	0.0494727
$477$	21.5586	0.987102
$478$	7.72348	0.353264
$479$	−29.1610	−1.33240	−0.666199	−	0.745774i	$-0.732080\pi$
$479$	−29.1610	−1.33240	−0.666199	+	0.745774i	$0.732080\pi$
$480$	−0.610143	−0.0278491
$481$	−13.6382	−0.621847
$482$	−16.0606	−0.731542
$483$	−2.95478	−0.134447
$484$	0	0
$485$	−11.9388	−0.542112
$486$	−19.9239	−0.903765
$487$	21.2981	0.965111	0.482556	−	0.875865i	$-0.339709\pi$
$487$	21.2981	0.965111	0.482556	+	0.875865i	$0.339709\pi$
$488$	−33.7664	−1.52853
$489$	−5.76370	−0.260643
$490$	−2.40663	−0.108720
$491$	−21.1562	−0.954765	−0.477382	−	0.878696i	$-0.658414\pi$
$491$	−21.1562	−0.954765	−0.477382	+	0.878696i	$0.658414\pi$
$492$	−3.75526	−0.169300
$493$	−2.72305	−0.122640
$494$	81.3761	3.66129
$495$	0	0
$496$	−17.4286	−0.782568
$497$	−12.7182	−0.570489
$498$	−7.26653	−0.325621
$499$	−42.2019	−1.88922	−0.944608	−	0.328201i	$-0.893558\pi$
$499$	−42.2019	−1.88922	−0.944608	+	0.328201i	$0.893558\pi$
$500$	−3.79186	−0.169577
$501$	4.84405	0.216416
$502$	34.7789	1.55226
$503$	1.88539	0.0840655	0.0420327	−	0.999116i	$-0.486617\pi$
$503$	1.88539	0.0840655	0.0420327	+	0.999116i	$0.486617\pi$
$504$	−12.4920	−0.556439
$505$	−13.7715	−0.612825
$506$	0	0
$507$	−3.12304	−0.138699
$508$	−4.07789	−0.180927
$509$	36.1928	1.60422	0.802109	−	0.597178i	$-0.203711\pi$
$509$	36.1928	1.60422	0.802109	+	0.597178i	$0.203711\pi$
$510$	0.220057	0.00974430
$511$	−0.750610	−0.0332050
$512$	−29.4092	−1.29972
$513$	−13.4366	−0.593240
$514$	16.1002	0.710147
$515$	−10.9843	−0.484026
$516$	−6.03800	−0.265808
$517$	0	0
$518$	6.88556	0.302534
$519$	7.93571	0.348339
$520$	20.5560	0.901439
$521$	24.8823	1.09012	0.545058	−	0.838399i	$-0.316508\pi$
$521$	24.8823	1.09012	0.545058	+	0.838399i	$0.316508\pi$
$522$	66.6911	2.91899
$523$	−2.06176	−0.0901546	−0.0450773	−	0.998984i	$-0.514353\pi$
$523$	−2.06176	−0.0901546	−0.0450773	+	0.998984i	$0.514353\pi$
$524$	29.9823	1.30978
$525$	−0.321225	−0.0140194
$526$	59.0984	2.57681
$527$	−1.77534	−0.0773349
$528$	0	0
$529$	61.6121	2.67879
$530$	17.9106	0.777986
$531$	24.4321	1.06026
$532$	−26.8976	−1.16616
$533$	−14.6962	−0.636563
$534$	11.4208	0.494226
$535$	10.0331	0.433770
$536$	10.0562	0.434361
$537$	5.27310	0.227551
$538$	−58.4340	−2.51927
$539$	0	0
$540$	−7.18255	−0.309088
$541$	−21.7379	−0.934586	−0.467293	−	0.884103i	$-0.654771\pi$
$541$	−21.7379	−0.934586	−0.467293	+	0.884103i	$0.654771\pi$
$542$	−27.4387	−1.17859
$543$	−2.67636	−0.114853
$544$	−0.540679	−0.0231814
$545$	−9.15250	−0.392050
$546$	3.68506	0.157706
$547$	13.2751	0.567603	0.283802	−	0.958883i	$-0.408404\pi$
$547$	13.2751	0.567603	0.283802	+	0.958883i	$0.408404\pi$
$548$	26.1488	1.11702
$549$	22.6826	0.968071
$550$	0	0
$551$	67.8580	2.89085
$552$	−12.7420	−0.542336
$553$	−7.66727	−0.326046
$554$	−24.6559	−1.04753
$555$	0.919051	0.0390115
$556$	−80.6244	−3.41924
$557$	12.1905	0.516528	0.258264	−	0.966074i	$-0.416850\pi$
$557$	12.1905	0.516528	0.258264	+	0.966074i	$0.416850\pi$
$558$	43.4804	1.84067
$559$	−23.6297	−0.999429
$560$	−2.79447	−0.118088
$561$	0	0
$562$	33.6740	1.42045
$563$	19.6678	0.828899	0.414450	−	0.910072i	$-0.363974\pi$
$563$	19.6678	0.828899	0.414450	+	0.910072i	$0.363974\pi$
$564$	4.16557	0.175402
$565$	−15.4820	−0.651334
$566$	15.3020	0.643192
$567$	8.08198	0.339411
$568$	−54.8451	−2.30125
$569$	6.46635	0.271084	0.135542	−	0.990772i	$-0.456722\pi$
$569$	6.46635	0.271084	0.135542	+	0.990772i	$0.456722\pi$
$570$	−5.48379	−0.229691
$571$	34.9789	1.46382	0.731910	−	0.681402i	$-0.238629\pi$
$571$	34.9789	1.46382	0.731910	+	0.681402i	$0.238629\pi$
$572$	0	0
$573$	1.84579	0.0771090
$574$	7.41973	0.309693
$575$	9.19849	0.383603
$576$	29.4320	1.22634
$577$	8.74822	0.364193	0.182097	−	0.983281i	$-0.441712\pi$
$577$	8.74822	0.364193	0.182097	+	0.983281i	$0.441712\pi$
$578$	−40.7177	−1.69363
$579$	−3.19261	−0.132680
$580$	36.2736	1.50618
$581$	9.39958	0.389960
$582$	−9.22950	−0.382575
$583$	0	0
$584$	−3.23688	−0.133943
$585$	−13.8085	−0.570911
$586$	5.24927	0.216845
$587$	25.8465	1.06680	0.533400	−	0.845863i	$-0.320914\pi$
$587$	25.8465	1.06680	0.533400	+	0.845863i	$0.320914\pi$
$588$	−1.21804	−0.0502311
$589$	44.2411	1.82292
$590$	20.2978	0.835648
$591$	−1.01172	−0.0416168
$592$	7.99520	0.328601
$593$	27.7338	1.13889	0.569445	−	0.822029i	$-0.307158\pi$
$593$	27.7338	1.13889	0.569445	+	0.822029i	$0.307158\pi$
$594$	0	0
$595$	−0.284654	−0.0116697
$596$	42.5857	1.74438
$597$	−1.70845	−0.0699224
$598$	−105.524	−4.31520
$599$	9.62585	0.393302	0.196651	−	0.980474i	$-0.436993\pi$
$599$	9.62585	0.393302	0.196651	+	0.980474i	$0.436993\pi$
$600$	−1.38523	−0.0565518
$601$	−39.4592	−1.60957	−0.804787	−	0.593564i	$-0.797720\pi$
$601$	−39.4592	−1.60957	−0.804787	+	0.593564i	$0.797720\pi$
$602$	11.9300	0.486231
$603$	−6.75526	−0.275095
$604$	1.16341	0.0473386
$605$	0	0
$606$	−10.6463	−0.432478
$607$	28.3346	1.15007	0.575033	−	0.818130i	$-0.304989\pi$
$607$	28.3346	1.15007	0.575033	+	0.818130i	$0.304989\pi$
$608$	13.4736	0.546427
$609$	3.07290	0.124520
$610$	18.8444	0.762987
$611$	16.3019	0.659506
$612$	−3.12673	−0.126390
$613$	−25.3797	−1.02508	−0.512538	−	0.858665i	$-0.671295\pi$
$613$	−25.3797	−1.02508	−0.512538	+	0.858665i	$0.671295\pi$
$614$	−28.8412	−1.16394
$615$	0.990349	0.0399347
$616$	0	0
$617$	27.3188	1.09981	0.549907	−	0.835226i	$-0.314663\pi$
$617$	27.3188	1.09981	0.549907	+	0.835226i	$0.314663\pi$
$618$	−8.49163	−0.341583
$619$	40.8391	1.64146	0.820731	−	0.571315i	$-0.193567\pi$
$619$	40.8391	1.64146	0.820731	+	0.571315i	$0.193567\pi$
$620$	23.6492	0.949773
$621$	17.4238	0.699193
$622$	21.8548	0.876297
$623$	−14.7733	−0.591880
$624$	4.27892	0.171294
$625$	1.00000	0.0400000
$626$	16.7598	0.669857
$627$	0	0
$628$	−7.39874	−0.295242
$629$	0.814419	0.0324730
$630$	6.97155	0.277753
$631$	−15.7081	−0.625330	−0.312665	−	0.949863i	$-0.601222\pi$
$631$	−15.7081	−0.625330	−0.312665	+	0.949863i	$0.601222\pi$
$632$	−33.0638	−1.31521
$633$	−0.509964	−0.0202692
$634$	−54.7829	−2.17571
$635$	1.07543	0.0426773
$636$	9.06488	0.359446
$637$	−4.76679	−0.188867
$638$	0	0
$639$	36.8423	1.45746
$640$	20.6528	0.816375
$641$	−30.9780	−1.22356	−0.611779	−	0.791029i	$-0.709546\pi$
$641$	−30.9780	−1.22356	−0.611779	+	0.791029i	$0.709546\pi$
$642$	7.75631	0.306117
$643$	−21.4712	−0.846743	−0.423372	−	0.905956i	$-0.639154\pi$
$643$	−21.4712	−0.846743	−0.423372	+	0.905956i	$0.639154\pi$
$644$	34.8793	1.37444
$645$	1.59236	0.0626991
$646$	−4.85947	−0.191193
$647$	−15.5854	−0.612726	−0.306363	−	0.951915i	$-0.599112\pi$
$647$	−15.5854	−0.612726	−0.306363	+	0.951915i	$0.599112\pi$
$648$	34.8522	1.36912
$649$	0	0
$650$	−11.4719	−0.449964
$651$	2.00343	0.0785204
$652$	68.0368	2.66453
$653$	−15.7529	−0.616459	−0.308229	−	0.951312i	$-0.599736\pi$
$653$	−15.7529	−0.616459	−0.308229	+	0.951312i	$0.599736\pi$
$654$	−7.07552	−0.276675
$655$	−7.90703	−0.308953
$656$	8.61545	0.336377
$657$	2.17438	0.0848305
$658$	−8.23043	−0.320856
$659$	−9.73277	−0.379135	−0.189568	−	0.981868i	$-0.560709\pi$
$659$	−9.73277	−0.379135	−0.189568	+	0.981868i	$0.560709\pi$
$660$	0	0
$661$	−30.5789	−1.18938	−0.594690	−	0.803955i	$-0.702725\pi$
$661$	−30.5789	−1.18938	−0.594690	+	0.803955i	$0.702725\pi$
$662$	63.9843	2.48682
$663$	0.435866	0.0169276
$664$	40.5341	1.57303
$665$	7.09353	0.275075
$666$	−19.9462	−0.772899
$667$	−87.9943	−3.40715
$668$	−57.1810	−2.21240
$669$	2.81050	0.108660
$670$	−5.61216	−0.216817
$671$	0	0
$672$	0.610143	0.0235368
$673$	−49.9855	−1.92680	−0.963400	−	0.268068i	$-0.913615\pi$
$673$	−49.9855	−1.92680	−0.963400	+	0.268068i	$0.913615\pi$
$674$	53.8109	2.07272
$675$	1.89420	0.0729080
$676$	36.8654	1.41790
$677$	33.4873	1.28702	0.643511	−	0.765437i	$-0.277477\pi$
$677$	33.4873	1.28702	0.643511	+	0.765437i	$0.277477\pi$
$678$	−11.9687	−0.459654
$679$	11.9388	0.458168
$680$	−1.22752	−0.0470734
$681$	2.35174	0.0901188
$682$	0	0
$683$	−27.2746	−1.04364	−0.521818	−	0.853057i	$-0.674746\pi$
$683$	−27.2746	−1.04364	−0.521818	+	0.853057i	$0.674746\pi$
$684$	77.9175	2.97925
$685$	−6.89605	−0.263484
$686$	2.40663	0.0918855
$687$	−2.64740	−0.101005
$688$	13.8526	0.528125
$689$	35.4753	1.35150
$690$	7.11106	0.270714
$691$	−44.5342	−1.69416	−0.847080	−	0.531465i	$-0.821642\pi$
$691$	−44.5342	−1.69416	−0.847080	+	0.531465i	$0.821642\pi$
$692$	−93.6760	−3.56103
$693$	0	0
$694$	−42.5995	−1.61705
$695$	21.2625	0.806533
$696$	13.2514	0.502291
$697$	0.877599	0.0332414
$698$	−6.86370	−0.259795
$699$	4.30442	0.162808
$700$	3.79186	0.143319
$701$	−36.4241	−1.37572	−0.687860	−	0.725844i	$-0.741450\pi$
$701$	−36.4241	−1.37572	−0.687860	+	0.725844i	$0.741450\pi$
$702$	−21.7301	−0.820150
$703$	−20.2952	−0.765447
$704$	0	0
$705$	−1.09856	−0.0413741
$706$	1.32077	0.0497077
$707$	13.7715	0.517932
$708$	10.2731	0.386087
$709$	3.00071	0.112694	0.0563471	−	0.998411i	$-0.482055\pi$
$709$	3.00071	0.112694	0.0563471	+	0.998411i	$0.482055\pi$
$710$	30.6080	1.14870
$711$	22.2107	0.832965
$712$	−63.7074	−2.38754
$713$	−57.3694	−2.14850
$714$	−0.220057	−0.00823544
$715$	0	0
$716$	−62.2456	−2.32623
$717$	−1.03089	−0.0384994
$718$	−57.1151	−2.13151
$719$	42.3787	1.58046	0.790230	−	0.612811i	$-0.209961\pi$
$719$	42.3787	1.58046	0.790230	+	0.612811i	$0.209961\pi$
$720$	8.09505	0.301685
$721$	10.9843	0.409077
$722$	75.3711	2.80502
$723$	2.14369	0.0797249
$724$	31.5927	1.17413
$725$	−9.56618	−0.355279
$726$	0	0
$727$	−1.27333	−0.0472253	−0.0236126	−	0.999721i	$-0.507517\pi$
$727$	−1.27333	−0.0472253	−0.0236126	+	0.999721i	$0.507517\pi$
$728$	−20.5560	−0.761855
$729$	−21.5866	−0.799503
$730$	1.80644	0.0668593
$731$	1.41107	0.0521904
$732$	9.53749	0.352516
$733$	37.1466	1.37204	0.686020	−	0.727583i	$-0.259356\pi$
$733$	37.1466	1.37204	0.686020	+	0.727583i	$0.259356\pi$
$734$	51.9059	1.91588
$735$	0.321225	0.0118486
$736$	−17.4718	−0.644020
$737$	0	0
$738$	−21.4936	−0.791189
$739$	20.4448	0.752074	0.376037	−	0.926605i	$-0.377287\pi$
$739$	20.4448	0.752074	0.376037	+	0.926605i	$0.377287\pi$
$740$	−10.8488	−0.398810
$741$	−10.8617	−0.399014
$742$	−17.9106	−0.657518
$743$	−40.5600	−1.48800	−0.744000	−	0.668179i	$-0.767074\pi$
$743$	−40.5600	−1.48800	−0.744000	+	0.668179i	$0.767074\pi$
$744$	8.63944	0.316737
$745$	−11.2308	−0.411466
$746$	−23.2242	−0.850297
$747$	−27.2288	−0.996251
$748$	0	0
$749$	−10.0331	−0.366603
$750$	0.773069	0.0282285
$751$	−20.4219	−0.745205	−0.372602	−	0.927991i	$-0.621534\pi$
$751$	−20.4219	−0.745205	−0.372602	+	0.927991i	$0.621534\pi$
$752$	−9.55680	−0.348501
$753$	−4.64212	−0.169168
$754$	109.742	3.99657
$755$	−0.306818	−0.0111663
$756$	7.18255	0.261227
$757$	42.3910	1.54073	0.770364	−	0.637604i	$-0.220074\pi$
$757$	42.3910	1.54073	0.770364	+	0.637604i	$0.220074\pi$
$758$	4.61471	0.167614
$759$	0	0
$760$	30.5897	1.10960
$761$	4.05235	0.146898	0.0734488	−	0.997299i	$-0.476599\pi$
$761$	4.05235	0.146898	0.0734488	+	0.997299i	$0.476599\pi$
$762$	0.831385	0.0301179
$763$	9.15250	0.331343
$764$	−21.7884	−0.788276
$765$	0.824590	0.0298131
$766$	−12.9642	−0.468416
$767$	40.2037	1.45167
$768$	9.43868	0.340589
$769$	−43.8660	−1.58185	−0.790924	−	0.611914i	$-0.790400\pi$
$769$	−43.8660	−1.58185	−0.790924	+	0.611914i	$0.790400\pi$
$770$	0	0
$771$	−2.14897	−0.0773933
$772$	37.6867	1.35637
$773$	24.8656	0.894355	0.447177	−	0.894445i	$-0.352429\pi$
$773$	24.8656	0.894355	0.447177	+	0.894445i	$0.352429\pi$
$774$	−34.5590	−1.24220
$775$	−6.23683	−0.224033
$776$	51.4840	1.84817
$777$	−0.919051	−0.0329708
$778$	20.0085	0.717339
$779$	−21.8696	−0.783561
$780$	−5.80614	−0.207893
$781$	0	0
$782$	6.30148	0.225340
$783$	−18.1203	−0.647567
$784$	2.79447	0.0998024
$785$	1.95122	0.0696419
$786$	−6.11268	−0.218032
$787$	47.0782	1.67816	0.839079	−	0.544009i	$-0.183094\pi$
$787$	47.0782	1.67816	0.839079	+	0.544009i	$0.183094\pi$
$788$	11.9428	0.425443
$789$	−7.88817	−0.280826
$790$	18.4523	0.656502
$791$	15.4820	0.550478
$792$	0	0
$793$	37.3249	1.32545
$794$	−38.2533	−1.35756
$795$	−2.39062	−0.0847864
$796$	20.1672	0.714808
$797$	−20.3187	−0.719725	−0.359863	−	0.933005i	$-0.617176\pi$
$797$	−20.3187	−0.719725	−0.359863	+	0.933005i	$0.617176\pi$
$798$	5.48379	0.194124
$799$	−0.973489	−0.0344396
$800$	−1.89942	−0.0671548
$801$	42.7955	1.51211
$802$	82.5144	2.91369
$803$	0	0
$804$	−2.84042	−0.100174
$805$	−9.19849	−0.324204
$806$	71.5482	2.52018
$807$	7.79949	0.274555
$808$	59.3875	2.08924
$809$	−17.6907	−0.621970	−0.310985	−	0.950415i	$-0.600659\pi$
$809$	−17.6907	−0.621970	−0.310985	+	0.950415i	$0.600659\pi$
$810$	−19.4503	−0.683414
$811$	−25.5677	−0.897804	−0.448902	−	0.893581i	$-0.648185\pi$
$811$	−25.5677	−0.897804	−0.448902	+	0.893581i	$0.648185\pi$
$812$	−36.2736	−1.27295
$813$	3.66238	0.128445
$814$	0	0
$815$	−17.9429	−0.628511
$816$	−0.255521	−0.00894501
$817$	−35.1637	−1.23022
$818$	−70.1585	−2.45304
$819$	13.8085	0.482508
$820$	−11.6904	−0.408248
$821$	−1.94318	−0.0678175	−0.0339087	−	0.999425i	$-0.510796\pi$
$821$	−1.94318	−0.0678175	−0.0339087	+	0.999425i	$0.510796\pi$
$822$	−5.33112	−0.185944
$823$	2.38290	0.0830627	0.0415313	−	0.999137i	$-0.486776\pi$
$823$	2.38290	0.0830627	0.0415313	+	0.999137i	$0.486776\pi$
$824$	47.3680	1.65014
$825$	0	0
$826$	−20.2978	−0.706251
$827$	−25.6827	−0.893076	−0.446538	−	0.894765i	$-0.647343\pi$
$827$	−25.6827	−0.893076	−0.446538	+	0.894765i	$0.647343\pi$
$828$	−101.039	−3.51135
$829$	−45.3942	−1.57661	−0.788303	−	0.615288i	$-0.789040\pi$
$829$	−45.3942	−1.57661	−0.788303	+	0.615288i	$0.789040\pi$
$830$	−22.6213	−0.785196
$831$	3.29095	0.114162
$832$	48.4312	1.67905
$833$	0.284654	0.00986268
$834$	16.4374	0.569180
$835$	15.0799	0.521863
$836$	0	0
$837$	−11.8138	−0.408346
$838$	−47.8306	−1.65228
$839$	−33.1060	−1.14295	−0.571474	−	0.820620i	$-0.693628\pi$
$839$	−33.1060	−1.14295	−0.571474	+	0.820620i	$0.693628\pi$
$840$	1.38523	0.0477950
$841$	62.5118	2.15558
$842$	−21.9763	−0.757353
$843$	−4.49464	−0.154804
$844$	6.01980	0.207210
$845$	−9.72227	−0.334456
$846$	23.8420	0.819706
$847$	0	0
$848$	−20.7969	−0.714170
$849$	−2.04244	−0.0700963
$850$	0.685056	0.0234972
$851$	26.3176	0.902156
$852$	15.4913	0.530722
$853$	−18.5516	−0.635195	−0.317597	−	0.948226i	$-0.602876\pi$
$853$	−18.5516	−0.635195	−0.317597	+	0.948226i	$0.602876\pi$
$854$	−18.8444	−0.644841
$855$	−20.5486	−0.702748
$856$	−43.2662	−1.47881
$857$	−34.2369	−1.16951	−0.584755	−	0.811210i	$-0.698809\pi$
$857$	−34.2369	−1.16951	−0.584755	+	0.811210i	$0.698809\pi$
$858$	0	0
$859$	−21.4685	−0.732494	−0.366247	−	0.930518i	$-0.619358\pi$
$859$	−21.4685	−0.732494	−0.366247	+	0.930518i	$0.619358\pi$
$860$	−18.7968	−0.640965
$861$	−0.990349	−0.0337510
$862$	−14.7968	−0.503980
$863$	1.59188	0.0541881	0.0270940	−	0.999633i	$-0.491375\pi$
$863$	1.59188	0.0541881	0.0270940	+	0.999633i	$0.491375\pi$
$864$	−3.59790	−0.122403
$865$	24.7045	0.839979
$866$	−51.5517	−1.75180
$867$	5.43480	0.184575
$868$	−23.6492	−0.802705
$869$	0	0
$870$	−7.39532	−0.250725
$871$	−11.1160	−0.376650
$872$	39.4686	1.33658
$873$	−34.5844	−1.17050
$874$	−157.032	−5.31168
$875$	−1.00000	−0.0338062
$876$	0.914272	0.0308904
$877$	−23.2074	−0.783657	−0.391828	−	0.920038i	$-0.628157\pi$
$877$	−23.2074	−0.783657	−0.391828	+	0.920038i	$0.628157\pi$
$878$	56.9727	1.92273
$879$	−0.700647	−0.0236323
$880$	0	0
$881$	−30.9648	−1.04323	−0.521615	−	0.853181i	$-0.674670\pi$
$881$	−30.9648	−1.04323	−0.521615	+	0.853181i	$0.674670\pi$
$882$	−6.97155	−0.234744
$883$	−53.5660	−1.80264	−0.901319	−	0.433156i	$-0.857400\pi$
$883$	−53.5660	−1.80264	−0.901319	+	0.433156i	$0.857400\pi$
$884$	−5.14512	−0.173049
$885$	−2.70925	−0.0910706
$886$	88.0036	2.95654
$887$	43.8144	1.47114	0.735571	−	0.677447i	$-0.236914\pi$
$887$	43.8144	1.47114	0.735571	+	0.677447i	$0.236914\pi$
$888$	−3.96326	−0.132998
$889$	−1.07543	−0.0360689
$890$	35.5539	1.19177
$891$	0	0
$892$	−33.1761	−1.11082
$893$	24.2592	0.811802
$894$	−8.68222	−0.290377
$895$	16.4156	0.548712
$896$	−20.6528	−0.689963
$897$	14.0848	0.470279
$898$	75.4209	2.51683
$899$	59.6626	1.98986
$900$	−10.9843	−0.366144
$901$	−2.11845	−0.0705758
$902$	0	0
$903$	−1.59236	−0.0529904
$904$	66.7637	2.22053
$905$	−8.33171	−0.276956
$906$	−0.237192	−0.00788017
$907$	27.8887	0.926031	0.463015	−	0.886350i	$-0.346767\pi$
$907$	27.8887	0.926031	0.463015	+	0.886350i	$0.346767\pi$
$908$	−27.7608	−0.921273
$909$	−39.8936	−1.32319
$910$	11.4719	0.380289
$911$	−31.8145	−1.05406	−0.527031	−	0.849846i	$-0.676695\pi$
$911$	−31.8145	−1.05406	−0.527031	+	0.849846i	$0.676695\pi$
$912$	6.36753	0.210850
$913$	0	0
$914$	−37.8934	−1.25340
$915$	−2.51526	−0.0831518
$916$	31.2509	1.03256
$917$	7.90703	0.261113
$918$	1.29764	0.0428284
$919$	0.532639	0.0175701	0.00878507	−	0.999961i	$-0.497204\pi$
$919$	0.532639	0.0175701	0.00878507	+	0.999961i	$0.497204\pi$
$920$	−39.6669	−1.30778
$921$	3.84958	0.126848
$922$	34.9499	1.15102
$923$	60.6249	1.99549
$924$	0	0
$925$	2.86108	0.0940718
$926$	−45.8379	−1.50633
$927$	−31.8195	−1.04509
$928$	18.1702	0.596467
$929$	14.1414	0.463964	0.231982	−	0.972720i	$-0.425479\pi$
$929$	14.1414	0.463964	0.231982	+	0.972720i	$0.425479\pi$
$930$	−4.82150	−0.158103
$931$	−7.09353	−0.232481
$932$	−50.8109	−1.66437
$933$	−2.91707	−0.0955007
$934$	−59.9149	−1.96048
$935$	0	0
$936$	59.5469	1.94635
$937$	22.6170	0.738865	0.369432	−	0.929258i	$-0.379552\pi$
$937$	22.6170	0.738865	0.369432	+	0.929258i	$0.379552\pi$
$938$	5.61216	0.183244
$939$	−2.23702	−0.0730023
$940$	12.9678	0.422962
$941$	9.76728	0.318404	0.159202	−	0.987246i	$-0.449108\pi$
$941$	9.76728	0.318404	0.159202	+	0.987246i	$0.449108\pi$
$942$	1.50843	0.0491472
$943$	28.3593	0.923505
$944$	−23.5689	−0.767103
$945$	−1.89420	−0.0616185
$946$	0	0
$947$	−2.25459	−0.0732642	−0.0366321	−	0.999329i	$-0.511663\pi$
$947$	−2.25459	−0.0732642	−0.0366321	+	0.999329i	$0.511663\pi$
$948$	9.33904	0.303318
$949$	3.57800	0.116147
$950$	−17.0715	−0.553872
$951$	7.31216	0.237113
$952$	1.22752	0.0397843
$953$	−34.8012	−1.12732	−0.563661	−	0.826006i	$-0.690608\pi$
$953$	−34.8012	−1.12732	−0.563661	+	0.826006i	$0.690608\pi$
$954$	51.8836	1.67979
$955$	5.74610	0.185939
$956$	12.1690	0.393575
$957$	0	0
$958$	−70.1796	−2.26740
$959$	6.89605	0.222685
$960$	−3.26369	−0.105335
$961$	7.89802	0.254775
$962$	−32.8220	−1.05822
$963$	29.0641	0.936579
$964$	−25.3050	−0.815018
$965$	−9.93884	−0.319943
$966$	−7.11106	−0.228795
$967$	−15.6979	−0.504812	−0.252406	−	0.967621i	$-0.581222\pi$
$967$	−15.6979	−0.504812	−0.252406	+	0.967621i	$0.581222\pi$
$968$	0	0
$969$	0.648618	0.0208366
$970$	−28.7322	−0.922535
$971$	−40.7043	−1.30626	−0.653132	−	0.757244i	$-0.726545\pi$
$971$	−40.7043	−1.30626	−0.653132	+	0.757244i	$0.726545\pi$
$972$	−31.3918	−1.00689
$973$	−21.2625	−0.681645
$974$	51.2567	1.64237
$975$	1.53121	0.0490380
$976$	−21.8812	−0.700401
$977$	27.2222	0.870916	0.435458	−	0.900209i	$-0.356586\pi$
$977$	27.2222	0.870916	0.435458	+	0.900209i	$0.356586\pi$
$978$	−13.8711	−0.443548
$979$	0	0
$980$	−3.79186	−0.121126
$981$	−26.5131	−0.846498
$982$	−50.9150	−1.62476
$983$	40.3619	1.28734	0.643672	−	0.765301i	$-0.277410\pi$
$983$	40.3619	1.28734	0.643672	+	0.765301i	$0.277410\pi$
$984$	−4.27072	−0.136145
$985$	−3.14958	−0.100354
$986$	−6.55337	−0.208702
$987$	1.09856	0.0349675
$988$	128.215	4.07907
$989$	45.5982	1.44994
$990$	0	0
$991$	−13.5653	−0.430916	−0.215458	−	0.976513i	$-0.569124\pi$
$991$	−13.5653	−0.430916	−0.215458	+	0.976513i	$0.569124\pi$
$992$	11.8464	0.376123
$993$	−8.54031	−0.271019
$994$	−30.6080	−0.970826
$995$	−5.31856	−0.168610
$996$	−11.4491	−0.362777
$997$	−61.8983	−1.96034	−0.980170	−	0.198158i	$-0.936504\pi$
$997$	−61.8983	−1.96034	−0.980170	+	0.198158i	$0.936504\pi$
$998$	−101.564	−3.21496
$999$	5.41947	0.171465

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.y.1.5	✓	5
11.10	odd	2		4235.2.a.be.1.1	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.y.1.5	✓	5	1.1	even	1	trivial
4235.2.a.be.1.1	yes	5	11.10	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:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+2.40663 q^{2} -0.321225 q^{3} +3.79186 q^{4} -1.00000 q^{5} -0.773069 q^{6} +1.00000 q^{7} +4.31233 q^{8} -2.89681 q^{9} +O(q^{10})\)	\(q+2.40663 q^{2} -0.321225 q^{3} +3.79186 q^{4} -1.00000 q^{5} -0.773069 q^{6} +1.00000 q^{7} +4.31233 q^{8} -2.89681 q^{9} -2.40663 q^{10} -1.21804 q^{12} -4.76679 q^{13} +2.40663 q^{14} +0.321225 q^{15} +2.79447 q^{16} +0.284654 q^{17} -6.97155 q^{18} -7.09353 q^{19} -3.79186 q^{20} -0.321225 q^{21} +9.19849 q^{23} -1.38523 q^{24} +1.00000 q^{25} -11.4719 q^{26} +1.89420 q^{27} +3.79186 q^{28} -9.56618 q^{29} +0.773069 q^{30} -6.23683 q^{31} -1.89942 q^{32} +0.685056 q^{34} -1.00000 q^{35} -10.9843 q^{36} +2.86108 q^{37} -17.0715 q^{38} +1.53121 q^{39} -4.31233 q^{40} +3.08304 q^{41} -0.773069 q^{42} +4.95715 q^{43} +2.89681 q^{45} +22.1373 q^{46} -3.41990 q^{47} -0.897653 q^{48} +1.00000 q^{49} +2.40663 q^{50} -0.0914380 q^{51} -18.0750 q^{52} -7.44219 q^{53} +4.55865 q^{54} +4.31233 q^{56} +2.27862 q^{57} -23.0222 q^{58} -8.43413 q^{59} +1.21804 q^{60} -7.83020 q^{61} -15.0097 q^{62} -2.89681 q^{63} -10.1601 q^{64} +4.76679 q^{65} +2.33196 q^{67} +1.07937 q^{68} -2.95478 q^{69} -2.40663 q^{70} -12.7182 q^{71} -12.4920 q^{72} -0.750610 q^{73} +6.88556 q^{74} -0.321225 q^{75} -26.8976 q^{76} +3.68506 q^{78} -7.66727 q^{79} -2.79447 q^{80} +8.08198 q^{81} +7.41973 q^{82} +9.39958 q^{83} -1.21804 q^{84} -0.284654 q^{85} +11.9300 q^{86} +3.07290 q^{87} -14.7733 q^{89} +6.97155 q^{90} -4.76679 q^{91} +34.8793 q^{92} +2.00343 q^{93} -8.23043 q^{94} +7.09353 q^{95} +0.610143 q^{96} +11.9388 q^{97} +2.40663 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} + 5 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 + 5 * q^7 + 6 * q^8 + 3 * q^9	\( 5 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} + 5 q^{7} + 6 q^{8} + 3 q^{9} + 2 q^{10} + 11 q^{12} - 12 q^{13} - 2 q^{14} + 2 q^{15} + 2 q^{16} - 14 q^{17} - 7 q^{18} - 9 q^{19} - 4 q^{20} - 2 q^{21} + 17 q^{23} - 6 q^{24} + 5 q^{25} - 11 q^{26} - 11 q^{27} + 4 q^{28} - 3 q^{29} + 5 q^{30} + 2 q^{31} + 5 q^{32} + 16 q^{34} - 5 q^{35} - 15 q^{36} + 4 q^{37} - 11 q^{38} - 2 q^{39} - 6 q^{40} + 15 q^{41} - 5 q^{42} - 4 q^{43} - 3 q^{45} + 10 q^{46} - 2 q^{47} - 10 q^{48} + 5 q^{49} - 2 q^{50} + 18 q^{51} - 4 q^{52} + 6 q^{53} - 4 q^{54} + 6 q^{56} - 32 q^{58} - 6 q^{59} - 11 q^{60} - 20 q^{61} - 21 q^{62} + 3 q^{63} - 26 q^{64} + 12 q^{65} + 3 q^{67} - 5 q^{68} + 2 q^{70} - 6 q^{71} - 34 q^{72} - 11 q^{73} + 15 q^{74} - 2 q^{75} - 47 q^{76} + 31 q^{78} - 19 q^{79} - 2 q^{80} + 33 q^{81} - 8 q^{83} + 11 q^{84} + 14 q^{85} + 27 q^{86} + 30 q^{87} + q^{89} + 7 q^{90} - 12 q^{91} + 44 q^{92} + 3 q^{93} - 28 q^{94} + 9 q^{95} + 4 q^{96} - 7 q^{97} - 2 q^{98}+O(q^{100}) \) 5 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 + 5 * q^7 + 6 * q^8 + 3 * q^9 + 2 * q^10 + 11 * q^12 - 12 * q^13 - 2 * q^14 + 2 * q^15 + 2 * q^16 - 14 * q^17 - 7 * q^18 - 9 * q^19 - 4 * q^20 - 2 * q^21 + 17 * q^23 - 6 * q^24 + 5 * q^25 - 11 * q^26 - 11 * q^27 + 4 * q^28 - 3 * q^29 + 5 * q^30 + 2 * q^31 + 5 * q^32 + 16 * q^34 - 5 * q^35 - 15 * q^36 + 4 * q^37 - 11 * q^38 - 2 * q^39 - 6 * q^40 + 15 * q^41 - 5 * q^42 - 4 * q^43 - 3 * q^45 + 10 * q^46 - 2 * q^47 - 10 * q^48 + 5 * q^49 - 2 * q^50 + 18 * q^51 - 4 * q^52 + 6 * q^53 - 4 * q^54 + 6 * q^56 - 32 * q^58 - 6 * q^59 - 11 * q^60 - 20 * q^61 - 21 * q^62 + 3 * q^63 - 26 * q^64 + 12 * q^65 + 3 * q^67 - 5 * q^68 + 2 * q^70 - 6 * q^71 - 34 * q^72 - 11 * q^73 + 15 * q^74 - 2 * q^75 - 47 * q^76 + 31 * q^78 - 19 * q^79 - 2 * q^80 + 33 * q^81 - 8 * q^83 + 11 * q^84 + 14 * q^85 + 27 * q^86 + 30 * q^87 + q^89 + 7 * q^90 - 12 * q^91 + 44 * q^92 + 3 * q^93 - 28 * q^94 + 9 * q^95 + 4 * q^96 - 7 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

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Database

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