LMFDB - Embedded newform 4235.2.a.y.1.4

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			1.4
Root			$0.859039$ 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)

$f(q)$	$=$	$q+0.164091 q^{2} -3.27813 q^{3} -1.97307 q^{4} -1.00000 q^{5} -0.537912 q^{6} +1.00000 q^{7} -0.651947 q^{8} +7.74611 q^{9} +O(q^{10})$	\(q+0.164091 q^{2} -3.27813 q^{3} -1.97307 q^{4} -1.00000 q^{5} -0.537912 q^{6} +1.00000 q^{7} -0.651947 q^{8} +7.74611 q^{9} -0.164091 q^{10} +6.46799 q^{12} -3.42008 q^{13} +0.164091 q^{14} +3.27813 q^{15} +3.83917 q^{16} -7.07103 q^{17} +1.27107 q^{18} -3.96406 q^{19} +1.97307 q^{20} -3.27813 q^{21} +1.19102 q^{23} +2.13717 q^{24} +1.00000 q^{25} -0.561206 q^{26} -15.5584 q^{27} -1.97307 q^{28} -1.37724 q^{29} +0.537912 q^{30} +6.97897 q^{31} +1.93387 q^{32} -1.16030 q^{34} -1.00000 q^{35} -15.2837 q^{36} +4.23612 q^{37} -0.650467 q^{38} +11.2115 q^{39} +0.651947 q^{40} +10.2573 q^{41} -0.537912 q^{42} -6.46699 q^{43} -7.74611 q^{45} +0.195436 q^{46} -0.387258 q^{47} -12.5853 q^{48} +1.00000 q^{49} +0.164091 q^{50} +23.1797 q^{51} +6.74807 q^{52} +9.52227 q^{53} -2.55299 q^{54} -0.651947 q^{56} +12.9947 q^{57} -0.225994 q^{58} -5.87905 q^{59} -6.46799 q^{60} +3.14306 q^{61} +1.14519 q^{62} +7.74611 q^{63} -7.36101 q^{64} +3.42008 q^{65} +14.1685 q^{67} +13.9517 q^{68} -3.90431 q^{69} -0.164091 q^{70} +0.339839 q^{71} -5.05006 q^{72} -11.7433 q^{73} +0.695111 q^{74} -3.27813 q^{75} +7.82138 q^{76} +1.83970 q^{78} +10.0204 q^{79} -3.83917 q^{80} +27.7639 q^{81} +1.68313 q^{82} +0.194278 q^{83} +6.46799 q^{84} +7.07103 q^{85} -1.06118 q^{86} +4.51478 q^{87} +12.6852 q^{89} -1.27107 q^{90} -3.42008 q^{91} -2.34997 q^{92} -22.8780 q^{93} -0.0635457 q^{94} +3.96406 q^{95} -6.33947 q^{96} -18.4750 q^{97} +0.164091 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.164091	0.116030	0.0580151	−	0.998316i	$-0.481523\pi$
$2$	0.164091	0.116030	0.0580151	+	0.998316i	$0.481523\pi$
$3$	−3.27813	−1.89263	−0.946314	−	0.323250i	$-0.895224\pi$
$3$	−3.27813	−1.89263	−0.946314	+	0.323250i	$0.895224\pi$
$4$	−1.97307	−0.986537
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.537912	−0.219602
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−0.651947	−0.230498
$9$	7.74611	2.58204
$10$	−0.164091	−0.0518903
$11$	0	0
$11$	0	0
$12$	6.46799	1.86715
$13$	−3.42008	−0.948560	−0.474280	−	0.880374i	$-0.657292\pi$
$13$	−3.42008	−0.948560	−0.474280	+	0.880374i	$0.657292\pi$
$14$	0.164091	0.0438553
$15$	3.27813	0.846409
$16$	3.83917	0.959792
$17$	−7.07103	−1.71498	−0.857489	−	0.514502i	$-0.827977\pi$
$17$	−7.07103	−1.71498	−0.857489	+	0.514502i	$0.827977\pi$
$18$	1.27107	0.299594
$19$	−3.96406	−0.909417	−0.454708	−	0.890640i	$-0.650257\pi$
$19$	−3.96406	−0.909417	−0.454708	+	0.890640i	$0.650257\pi$
$20$	1.97307	0.441193
$21$	−3.27813	−0.715346
$22$	0	0
$23$	1.19102	0.248344	0.124172	−	0.992261i	$-0.460372\pi$
$23$	1.19102	0.248344	0.124172	+	0.992261i	$0.460372\pi$
$24$	2.13717	0.436247
$25$	1.00000	0.200000
$26$	−0.561206	−0.110062
$27$	−15.5584	−2.99421
$28$	−1.97307	−0.372876
$29$	−1.37724	−0.255748	−0.127874	−	0.991790i	$-0.540815\pi$
$29$	−1.37724	−0.255748	−0.127874	+	0.991790i	$0.540815\pi$
$30$	0.537912	0.0982089
$31$	6.97897	1.25346	0.626730	−	0.779236i	$-0.284393\pi$
$31$	6.97897	1.25346	0.626730	+	0.779236i	$0.284393\pi$
$32$	1.93387	0.341863
$33$	0	0
$34$	−1.16030	−0.198989
$35$	−1.00000	−0.169031
$36$	−15.2837	−2.54728
$37$	4.23612	0.696414	0.348207	−	0.937418i	$-0.386791\pi$
$37$	4.23612	0.696414	0.348207	+	0.937418i	$0.386791\pi$
$38$	−0.650467	−0.105520
$39$	11.2115	1.79527
$40$	0.651947	0.103082
$41$	10.2573	1.60192	0.800958	−	0.598721i	$-0.204324\pi$
$41$	10.2573	1.60192	0.800958	+	0.598721i	$0.204324\pi$
$42$	−0.537912	−0.0830017
$43$	−6.46699	−0.986207	−0.493103	−	0.869971i	$-0.664138\pi$
$43$	−6.46699	−0.986207	−0.493103	+	0.869971i	$0.664138\pi$
$44$	0	0
$45$	−7.74611	−1.15472
$46$	0.195436	0.0288154
$47$	−0.387258	−0.0564873	−0.0282437	−	0.999601i	$-0.508991\pi$
$47$	−0.387258	−0.0564873	−0.0282437	+	0.999601i	$0.508991\pi$
$48$	−12.5853	−1.81653
$49$	1.00000	0.142857
$50$	0.164091	0.0232060
$51$	23.1797	3.24581
$52$	6.74807	0.935790
$53$	9.52227	1.30798	0.653992	−	0.756501i	$-0.273093\pi$
$53$	9.52227	1.30798	0.653992	+	0.756501i	$0.273093\pi$
$54$	−2.55299	−0.347418
$55$	0	0
$56$	−0.651947	−0.0871201
$57$	12.9947	1.72119
$58$	−0.225994	−0.0296745
$59$	−5.87905	−0.765387	−0.382694	−	0.923875i	$-0.625003\pi$
$59$	−5.87905	−0.765387	−0.382694	+	0.923875i	$0.625003\pi$
$60$	−6.46799	−0.835013
$61$	3.14306	0.402428	0.201214	−	0.979547i	$-0.435511\pi$
$61$	3.14306	0.402428	0.201214	+	0.979547i	$0.435511\pi$
$62$	1.14519	0.145439
$63$	7.74611	0.975918
$64$	−7.36101	−0.920126
$65$	3.42008	0.424209
$66$	0	0
$67$	14.1685	1.73095	0.865476	−	0.500950i	$-0.167016\pi$
$67$	14.1685	1.73095	0.865476	+	0.500950i	$0.167016\pi$
$68$	13.9517	1.69189
$69$	−3.90431	−0.470023
$70$	−0.164091	−0.0196127
$71$	0.339839	0.0403315	0.0201657	−	0.999797i	$-0.493581\pi$
$71$	0.339839	0.0403315	0.0201657	+	0.999797i	$0.493581\pi$
$72$	−5.05006	−0.595155
$73$	−11.7433	−1.37445	−0.687225	−	0.726444i	$-0.741171\pi$
$73$	−11.7433	−1.37445	−0.687225	+	0.726444i	$0.741171\pi$
$74$	0.695111	0.0808050
$75$	−3.27813	−0.378525
$76$	7.82138	0.897173
$77$	0	0
$78$	1.83970	0.208305
$79$	10.0204	1.12739	0.563694	−	0.825984i	$-0.309380\pi$
$79$	10.0204	1.12739	0.563694	+	0.825984i	$0.309380\pi$
$80$	−3.83917	−0.429232
$81$	27.7639	3.08488
$82$	1.68313	0.185870
$83$	0.194278	0.0213248	0.0106624	−	0.999943i	$-0.496606\pi$
$83$	0.194278	0.0213248	0.0106624	+	0.999943i	$0.496606\pi$
$84$	6.46799	0.705715
$85$	7.07103	0.766961
$86$	−1.06118	−0.114430
$87$	4.51478	0.484035
$88$	0	0
$89$	12.6852	1.34463	0.672314	−	0.740266i	$-0.265300\pi$
$89$	12.6852	1.34463	0.672314	+	0.740266i	$0.265300\pi$
$90$	−1.27107	−0.133983
$91$	−3.42008	−0.358522
$92$	−2.34997	−0.245001
$93$	−22.8780	−2.37233
$94$	−0.0635457	−0.00655423
$95$	3.96406	0.406704
$96$	−6.33947	−0.647019
$97$	−18.4750	−1.87585	−0.937926	−	0.346836i	$-0.887256\pi$
$97$	−18.4750	−1.87585	−0.937926	+	0.346836i	$0.887256\pi$
$98$	0.164091	0.0165757
$99$	0	0
$100$	−1.97307	−0.197307
$101$	1.83395	0.182484	0.0912422	−	0.995829i	$-0.470916\pi$
$101$	1.83395	0.182484	0.0912422	+	0.995829i	$0.470916\pi$
$102$	3.80360	0.376612
$103$	15.2837	1.50594	0.752972	−	0.658053i	$-0.228620\pi$
$103$	15.2837	1.50594	0.752972	+	0.658053i	$0.228620\pi$
$104$	2.22971	0.218641
$105$	3.27813	0.319912
$106$	1.56252	0.151766
$107$	1.17954	0.114031	0.0570154	−	0.998373i	$-0.481842\pi$
$107$	1.17954	0.114031	0.0570154	+	0.998373i	$0.481842\pi$
$108$	30.6978	2.95390
$109$	−3.75666	−0.359823	−0.179911	−	0.983683i	$-0.557581\pi$
$109$	−3.75666	−0.359823	−0.179911	+	0.983683i	$0.557581\pi$
$110$	0	0
$111$	−13.8865	−1.31805
$112$	3.83917	0.362767
$113$	10.3037	0.969289	0.484645	−	0.874711i	$-0.338949\pi$
$113$	10.3037	0.969289	0.484645	+	0.874711i	$0.338949\pi$
$114$	2.13231	0.199710
$115$	−1.19102	−0.111063
$116$	2.71741	0.252305
$117$	−26.4923	−2.44922
$118$	−0.964701	−0.0888080
$119$	−7.07103	−0.648201
$120$	−2.13717	−0.195096
$121$	0	0
$122$	0.515750	0.0466938
$123$	−33.6246	−3.03183
$124$	−13.7700	−1.23659
$125$	−1.00000	−0.0894427
$126$	1.27107	0.113236
$127$	7.15239	0.634672	0.317336	−	0.948313i	$-0.397212\pi$
$127$	7.15239	0.634672	0.317336	+	0.948313i	$0.397212\pi$
$128$	−5.07562	−0.448625
$129$	21.1996	1.86652
$130$	0.561206	0.0492210
$131$	19.4758	1.70161	0.850803	−	0.525484i	$-0.176116\pi$
$131$	19.4758	1.70161	0.850803	+	0.525484i	$0.176116\pi$
$132$	0	0
$133$	−3.96406	−0.343727
$134$	2.32492	0.200843
$135$	15.5584	1.33905
$136$	4.60994	0.395299
$137$	−9.59810	−0.820021	−0.410010	−	0.912081i	$-0.634475\pi$
$137$	−9.59810	−0.820021	−0.410010	+	0.912081i	$0.634475\pi$
$138$	−0.640663	−0.0545368
$139$	−14.3907	−1.22060	−0.610300	−	0.792170i	$-0.708951\pi$
$139$	−14.3907	−1.22060	−0.610300	+	0.792170i	$0.708951\pi$
$140$	1.97307	0.166755
$141$	1.26948	0.106909
$142$	0.0557646	0.00467966
$143$	0	0
$144$	29.7386	2.47822
$145$	1.37724	0.114374
$146$	−1.92698	−0.159478
$147$	−3.27813	−0.270375
$148$	−8.35818	−0.687038
$149$	−21.4554	−1.75770	−0.878849	−	0.477100i	$-0.841688\pi$
$149$	−21.4554	−1.75770	−0.878849	+	0.477100i	$0.841688\pi$
$150$	−0.537912	−0.0439204
$151$	0.0822054	0.00668978	0.00334489	−	0.999994i	$-0.498935\pi$
$151$	0.0822054	0.00668978	0.00334489	+	0.999994i	$0.498935\pi$
$152$	2.58436	0.209619
$153$	−54.7730	−4.42814
$154$	0	0
$155$	−6.97897	−0.560565
$156$	−22.1210	−1.77110
$157$	20.0790	1.60248	0.801239	−	0.598345i	$-0.204175\pi$
$157$	20.0790	1.60248	0.801239	+	0.598345i	$0.204175\pi$
$158$	1.64427	0.130811
$159$	−31.2152	−2.47553
$160$	−1.93387	−0.152886
$161$	1.19102	0.0938653
$162$	4.55582	0.357939
$163$	−17.7257	−1.38838	−0.694191	−	0.719791i	$-0.744238\pi$
$163$	−17.7257	−1.38838	−0.694191	+	0.719791i	$0.744238\pi$
$164$	−20.2383	−1.58035
$165$	0	0
$166$	0.0318793	0.00247432
$167$	22.9221	1.77376	0.886881	−	0.461998i	$-0.152867\pi$
$167$	22.9221	1.77376	0.886881	+	0.461998i	$0.152867\pi$
$168$	2.13717	0.164886
$169$	−1.30304	−0.100234
$170$	1.16030	0.0889906
$171$	−30.7060	−2.34815
$172$	12.7599	0.972930
$173$	−19.6082	−1.49078	−0.745392	−	0.666626i	$-0.767738\pi$
$173$	−19.6082	−1.49078	−0.745392	+	0.666626i	$0.767738\pi$
$174$	0.740837	0.0561627
$175$	1.00000	0.0755929
$176$	0	0
$177$	19.2723	1.44859
$178$	2.08153	0.156017
$179$	7.83308	0.585472	0.292736	−	0.956193i	$-0.405434\pi$
$179$	7.83308	0.585472	0.292736	+	0.956193i	$0.405434\pi$
$180$	15.2837	1.13918
$181$	0.984920	0.0732085	0.0366043	−	0.999330i	$-0.488346\pi$
$181$	0.984920	0.0732085	0.0366043	+	0.999330i	$0.488346\pi$
$182$	−0.561206	−0.0415994
$183$	−10.3034	−0.761646
$184$	−0.776480	−0.0572429
$185$	−4.23612	−0.311446
$186$	−3.75408	−0.275262
$187$	0	0
$188$	0.764088	0.0557269
$189$	−15.5584	−1.13170
$190$	0.650467	0.0471899
$191$	−0.106330	−0.00769380	−0.00384690	−	0.999993i	$-0.501225\pi$
$191$	−0.106330	−0.00769380	−0.00384690	+	0.999993i	$0.501225\pi$
$192$	24.1303	1.74146
$193$	−3.99558	−0.287608	−0.143804	−	0.989606i	$-0.545934\pi$
$193$	−3.99558	−0.287608	−0.143804	+	0.989606i	$0.545934\pi$
$194$	−3.03159	−0.217655
$195$	−11.2115	−0.802869
$196$	−1.97307	−0.140934
$197$	−5.82520	−0.415028	−0.207514	−	0.978232i	$-0.566537\pi$
$197$	−5.82520	−0.415028	−0.207514	+	0.978232i	$0.566537\pi$
$198$	0	0
$199$	−7.39859	−0.524472	−0.262236	−	0.965004i	$-0.584460\pi$
$199$	−7.39859	−0.524472	−0.262236	+	0.965004i	$0.584460\pi$
$200$	−0.651947	−0.0460996
$201$	−46.4460	−3.27605
$202$	0.300935	0.0211737
$203$	−1.37724	−0.0966636
$204$	−45.7354	−3.20212
$205$	−10.2573	−0.716398
$206$	2.50792	0.174735
$207$	9.22575	0.641234
$208$	−13.1303	−0.910421
$209$	0	0
$210$	0.537912	0.0371195
$211$	−12.9364	−0.890581	−0.445290	−	0.895386i	$-0.646900\pi$
$211$	−12.9364	−0.890581	−0.445290	+	0.895386i	$0.646900\pi$
$212$	−18.7881	−1.29038
$213$	−1.11403	−0.0763324
$214$	0.193553	0.0132310
$215$	6.46699	0.441045
$216$	10.1432	0.690159
$217$	6.97897	0.473764
$218$	−0.616436	−0.0417503
$219$	38.4961	2.60132
$220$	0	0
$221$	24.1835	1.62676
$222$	−2.27866	−0.152934
$223$	−19.6080	−1.31305	−0.656523	−	0.754306i	$-0.727973\pi$
$223$	−19.6080	−1.31305	−0.656523	+	0.754306i	$0.727973\pi$
$224$	1.93387	0.129212
$225$	7.74611	0.516407
$226$	1.69075	0.112467
$227$	6.20128	0.411594	0.205797	−	0.978595i	$-0.434021\pi$
$227$	6.20128	0.411594	0.205797	+	0.978595i	$0.434021\pi$
$228$	−25.6395	−1.69801
$229$	−15.5651	−1.02857	−0.514286	−	0.857619i	$-0.671943\pi$
$229$	−15.5651	−1.02857	−0.514286	+	0.857619i	$0.671943\pi$
$230$	−0.195436	−0.0128866
$231$	0	0
$232$	0.897891	0.0589494
$233$	−26.0819	−1.70869	−0.854343	−	0.519710i	$-0.826040\pi$
$233$	−26.0819	−1.70869	−0.854343	+	0.519710i	$0.826040\pi$
$234$	−4.34716	−0.284183
$235$	0.387258	0.0252619
$236$	11.5998	0.755083
$237$	−32.8483	−2.13372
$238$	−1.16030	−0.0752108
$239$	−1.21063	−0.0783091	−0.0391545	−	0.999233i	$-0.512466\pi$
$239$	−1.21063	−0.0783091	−0.0391545	+	0.999233i	$0.512466\pi$
$240$	12.5853	0.812376
$241$	18.7671	1.20889	0.604447	−	0.796645i	$-0.293394\pi$
$241$	18.7671	1.20889	0.604447	+	0.796645i	$0.293394\pi$
$242$	0	0
$243$	−44.3386	−2.84432
$244$	−6.20150	−0.397010
$245$	−1.00000	−0.0638877
$246$	−5.51751	−0.351783
$247$	13.5574	0.862636
$248$	−4.54992	−0.288920
$249$	−0.636867	−0.0403598
$250$	−0.164091	−0.0103781
$251$	−21.8153	−1.37697	−0.688485	−	0.725250i	$-0.741724\pi$
$251$	−21.8153	−1.37697	−0.688485	+	0.725250i	$0.741724\pi$
$252$	−15.2837	−0.962780
$253$	0	0
$254$	1.17364	0.0736410
$255$	−23.1797	−1.45157
$256$	13.8891	0.868072
$257$	−11.9068	−0.742725	−0.371362	−	0.928488i	$-0.621109\pi$
$257$	−11.9068	−0.742725	−0.371362	+	0.928488i	$0.621109\pi$
$258$	3.47867	0.216573
$259$	4.23612	0.263220
$260$	−6.74807	−0.418498
$261$	−10.6683	−0.660351
$262$	3.19581	0.197438
$263$	10.2101	0.629583	0.314792	−	0.949161i	$-0.398065\pi$
$263$	10.2101	0.629583	0.314792	+	0.949161i	$0.398065\pi$
$264$	0	0
$265$	−9.52227	−0.584948
$266$	−0.650467	−0.0398827
$267$	−41.5837	−2.54488
$268$	−27.9554	−1.70765
$269$	10.4517	0.637253	0.318626	−	0.947880i	$-0.396778\pi$
$269$	10.4517	0.637253	0.318626	+	0.947880i	$0.396778\pi$
$270$	2.55299	0.155370
$271$	−24.2173	−1.47110	−0.735548	−	0.677472i	$-0.763075\pi$
$271$	−24.2173	−1.47110	−0.735548	+	0.677472i	$0.763075\pi$
$272$	−27.1469	−1.64602
$273$	11.2115	0.678548
$274$	−1.57496	−0.0951471
$275$	0	0
$276$	7.70348	0.463695
$277$	−7.96360	−0.478486	−0.239243	−	0.970960i	$-0.576899\pi$
$277$	−7.96360	−0.478486	−0.239243	+	0.970960i	$0.576899\pi$
$278$	−2.36138	−0.141626
$279$	54.0599	3.23648
$280$	0.651947	0.0389613
$281$	1.17820	0.0702857	0.0351429	−	0.999382i	$-0.488811\pi$
$281$	1.17820	0.0702857	0.0351429	+	0.999382i	$0.488811\pi$
$282$	0.208311	0.0124047
$283$	11.5877	0.688818	0.344409	−	0.938820i	$-0.388079\pi$
$283$	11.5877	0.688818	0.344409	+	0.938820i	$0.388079\pi$
$284$	−0.670527	−0.0397885
$285$	−12.9947	−0.769738
$286$	0	0
$287$	10.2573	0.605467
$288$	14.9800	0.882703
$289$	32.9995	1.94115
$290$	0.225994	0.0132708
$291$	60.5634	3.55029
$292$	23.1704	1.35595
$293$	2.54149	0.148476	0.0742378	−	0.997241i	$-0.476348\pi$
$293$	2.54149	0.148476	0.0742378	+	0.997241i	$0.476348\pi$
$294$	−0.537912	−0.0313717
$295$	5.87905	0.342291
$296$	−2.76173	−0.160522
$297$	0	0
$298$	−3.52065	−0.203946
$299$	−4.07338	−0.235569
$300$	6.46799	0.373429
$301$	−6.46699	−0.372751
$302$	0.0134892	0.000776216 0
$303$	−6.01191	−0.345375
$304$	−15.2187	−0.872851
$305$	−3.14306	−0.179971
$306$	−8.98778	−0.513797
$307$	2.89989	0.165505	0.0827526	−	0.996570i	$-0.473629\pi$
$307$	2.89989	0.165505	0.0827526	+	0.996570i	$0.473629\pi$
$308$	0	0
$309$	−50.1017	−2.85019
$310$	−1.14519	−0.0650424
$311$	−17.3344	−0.982942	−0.491471	−	0.870894i	$-0.663541\pi$
$311$	−17.3344	−0.982942	−0.491471	+	0.870894i	$0.663541\pi$
$312$	−7.30928	−0.413807
$313$	−0.201307	−0.0113785	−0.00568927	−	0.999984i	$-0.501811\pi$
$313$	−0.201307	−0.0113785	−0.00568927	+	0.999984i	$0.501811\pi$
$314$	3.29479	0.185936
$315$	−7.74611	−0.436444
$316$	−19.7711	−1.11221
$317$	0.108622	0.00610082	0.00305041	−	0.999995i	$-0.499029\pi$
$317$	0.108622	0.00610082	0.00305041	+	0.999995i	$0.499029\pi$
$318$	−5.12215	−0.287236
$319$	0	0
$320$	7.36101	0.411493
$321$	−3.86669	−0.215818
$322$	0.195436	0.0108912
$323$	28.0300	1.55963
$324$	−54.7803	−3.04335
$325$	−3.42008	−0.189712
$326$	−2.90863	−0.161094
$327$	12.3148	0.681010
$328$	−6.68719	−0.369238
$329$	−0.387258	−0.0213502
$330$	0	0
$331$	2.63909	0.145057	0.0725287	−	0.997366i	$-0.476893\pi$
$331$	2.63909	0.145057	0.0725287	+	0.997366i	$0.476893\pi$
$332$	−0.383325	−0.0210377
$333$	32.8135	1.79817
$334$	3.76131	0.205810
$335$	−14.1685	−0.774106
$336$	−12.5853	−0.686583
$337$	−12.5232	−0.682184	−0.341092	−	0.940030i	$-0.610797\pi$
$337$	−12.5232	−0.682184	−0.341092	+	0.940030i	$0.610797\pi$
$338$	−0.213818	−0.0116301
$339$	−33.7768	−1.83450
$340$	−13.9517	−0.756636
$341$	0	0
$342$	−5.03859	−0.272456
$343$	1.00000	0.0539949
$344$	4.21614	0.227319
$345$	3.90431	0.210201
$346$	−3.21754	−0.172976
$347$	−27.1671	−1.45841	−0.729203	−	0.684297i	$-0.760109\pi$
$347$	−27.1671	−1.45841	−0.729203	+	0.684297i	$0.760109\pi$
$348$	−8.90800	−0.477519
$349$	14.0130	0.750100	0.375050	−	0.927005i	$-0.377626\pi$
$349$	14.0130	0.750100	0.375050	+	0.927005i	$0.377626\pi$
$350$	0.164091	0.00877105
$351$	53.2108	2.84018
$352$	0	0
$353$	15.7525	0.838423	0.419212	−	0.907889i	$-0.362307\pi$
$353$	15.7525	0.838423	0.419212	+	0.907889i	$0.362307\pi$
$354$	3.16241	0.168080
$355$	−0.339839	−0.0180368
$356$	−25.0288	−1.32653
$357$	23.1797	1.22680
$358$	1.28534	0.0679324
$359$	27.9672	1.47605	0.738027	−	0.674772i	$-0.235758\pi$
$359$	27.9672	1.47605	0.738027	+	0.674772i	$0.235758\pi$
$360$	5.05006	0.266161
$361$	−3.28626	−0.172961
$362$	0.161617	0.00849440
$363$	0	0
$364$	6.74807	0.353695
$365$	11.7433	0.614673
$366$	−1.69069	−0.0883739
$367$	3.15007	0.164433	0.0822163	−	0.996615i	$-0.473800\pi$
$367$	3.15007	0.164433	0.0822163	+	0.996615i	$0.473800\pi$
$368$	4.57252	0.238359
$369$	79.4539	4.13620
$370$	−0.695111	−0.0361371
$371$	9.52227	0.494372
$372$	45.1399	2.34039
$373$	−25.6739	−1.32935	−0.664673	−	0.747135i	$-0.731429\pi$
$373$	−25.6739	−1.32935	−0.664673	+	0.747135i	$0.731429\pi$
$374$	0	0
$375$	3.27813	0.169282
$376$	0.252472	0.0130202
$377$	4.71029	0.242592
$378$	−2.55299	−0.131312
$379$	−4.43236	−0.227675	−0.113838	−	0.993499i	$-0.536314\pi$
$379$	−4.43236	−0.227675	−0.113838	+	0.993499i	$0.536314\pi$
$380$	−7.82138	−0.401228
$381$	−23.4464	−1.20120
$382$	−0.0174479	−0.000892713 0
$383$	7.49597	0.383026	0.191513	−	0.981490i	$-0.438661\pi$
$383$	7.49597	0.383026	0.191513	+	0.981490i	$0.438661\pi$
$384$	16.6385	0.849080
$385$	0	0
$386$	−0.655641	−0.0333712
$387$	−50.0940	−2.54642
$388$	36.4525	1.85060
$389$	−22.4902	−1.14030	−0.570148	−	0.821542i	$-0.693114\pi$
$389$	−22.4902	−1.14030	−0.570148	+	0.821542i	$0.693114\pi$
$390$	−1.83970	−0.0931570
$391$	−8.42172	−0.425905
$392$	−0.651947	−0.0329283
$393$	−63.8441	−3.22051
$394$	−0.955865	−0.0481558
$395$	−10.0204	−0.504183
$396$	0	0
$397$	−4.29363	−0.215491	−0.107746	−	0.994179i	$-0.534363\pi$
$397$	−4.29363	−0.215491	−0.107746	+	0.994179i	$0.534363\pi$
$398$	−1.21405	−0.0608546
$399$	12.9947	0.650547
$400$	3.83917	0.191958
$401$	25.1851	1.25768	0.628842	−	0.777533i	$-0.283529\pi$
$401$	25.1851	1.25768	0.628842	+	0.777533i	$0.283529\pi$
$402$	−7.62139	−0.380120
$403$	−23.8687	−1.18898
$404$	−3.61851	−0.180028
$405$	−27.7639	−1.37960
$406$	−0.225994	−0.0112159
$407$	0	0
$408$	−15.1120	−0.748154
$409$	−2.35178	−0.116288	−0.0581440	−	0.998308i	$-0.518518\pi$
$409$	−2.35178	−0.116288	−0.0581440	+	0.998308i	$0.518518\pi$
$410$	−1.68313	−0.0831238
$411$	31.4638	1.55199
$412$	−30.1558	−1.48567
$413$	−5.87905	−0.289289
$414$	1.51387	0.0744025
$415$	−0.194278	−0.00953673
$416$	−6.61399	−0.324278
$417$	47.1744	2.31014
$418$	0	0
$419$	9.08678	0.443918	0.221959	−	0.975056i	$-0.428755\pi$
$419$	9.08678	0.443918	0.221959	+	0.975056i	$0.428755\pi$
$420$	−6.46799	−0.315605
$421$	20.7124	1.00946	0.504731	−	0.863277i	$-0.331592\pi$
$421$	20.7124	1.00946	0.504731	+	0.863277i	$0.331592\pi$
$422$	−2.12276	−0.103334
$423$	−2.99974	−0.145852
$424$	−6.20802	−0.301488
$425$	−7.07103	−0.342996
$426$	−0.182804	−0.00885686
$427$	3.14306	0.152104
$428$	−2.32733	−0.112496
$429$	0	0
$430$	1.06118	0.0511745
$431$	−6.97733	−0.336086	−0.168043	−	0.985780i	$-0.553745\pi$
$431$	−6.97733	−0.336086	−0.168043	+	0.985780i	$0.553745\pi$
$432$	−59.7312	−2.87382
$433$	5.68801	0.273348	0.136674	−	0.990616i	$-0.456359\pi$
$433$	5.68801	0.273348	0.136674	+	0.990616i	$0.456359\pi$
$434$	1.14519	0.0549708
$435$	−4.51478	−0.216467
$436$	7.41217	0.354979
$437$	−4.72126	−0.225848
$438$	6.31687	0.301832
$439$	38.3629	1.83096	0.915482	−	0.402360i	$-0.131810\pi$
$439$	38.3629	1.83096	0.915482	+	0.402360i	$0.131810\pi$
$440$	0	0
$441$	7.74611	0.368862
$442$	3.96831	0.188753
$443$	14.6210	0.694667	0.347333	−	0.937742i	$-0.387087\pi$
$443$	14.6210	0.694667	0.347333	+	0.937742i	$0.387087\pi$
$444$	27.3992	1.30031
$445$	−12.6852	−0.601336
$446$	−3.21750	−0.152353
$447$	70.3336	3.32667
$448$	−7.36101	−0.347775
$449$	−30.4767	−1.43829	−0.719143	−	0.694862i	$-0.755466\pi$
$449$	−30.4767	−1.43829	−0.719143	+	0.694862i	$0.755466\pi$
$450$	1.27107	0.0599188
$451$	0	0
$452$	−20.3299	−0.956240
$453$	−0.269480	−0.0126613
$454$	1.01758	0.0477573
$455$	3.42008	0.160336
$456$	−8.47184	−0.396730
$457$	1.90600	0.0891590	0.0445795	−	0.999006i	$-0.485805\pi$
$457$	1.90600	0.0891590	0.0445795	+	0.999006i	$0.485805\pi$
$458$	−2.55410	−0.119345
$459$	110.014	5.13500
$460$	2.34997	0.109568
$461$	18.6043	0.866490	0.433245	−	0.901276i	$-0.357368\pi$
$461$	18.6043	0.866490	0.433245	+	0.901276i	$0.357368\pi$
$462$	0	0
$463$	6.73166	0.312847	0.156423	−	0.987690i	$-0.450004\pi$
$463$	6.73166	0.312847	0.156423	+	0.987690i	$0.450004\pi$
$464$	−5.28747	−0.245465
$465$	22.8780	1.06094
$466$	−4.27982	−0.198259
$467$	10.7816	0.498915	0.249457	−	0.968386i	$-0.419748\pi$
$467$	10.7816	0.498915	0.249457	+	0.968386i	$0.419748\pi$
$468$	52.2713	2.41624
$469$	14.1685	0.654239
$470$	0.0635457	0.00293114
$471$	−65.8214	−3.03289
$472$	3.83283	0.176420
$473$	0	0
$474$	−5.39012	−0.247576
$475$	−3.96406	−0.181883
$476$	13.9517	0.639474
$477$	73.7606	3.37726
$478$	−0.198654	−0.00908621
$479$	22.6770	1.03614	0.518069	−	0.855339i	$-0.326651\pi$
$479$	22.6770	1.03614	0.518069	+	0.855339i	$0.326651\pi$
$480$	6.33947	0.289356
$481$	−14.4879	−0.660590
$482$	3.07952	0.140268
$483$	−3.90431	−0.177652
$484$	0	0
$485$	18.4750	0.838906
$486$	−7.27558	−0.330027
$487$	−21.6859	−0.982683	−0.491341	−	0.870967i	$-0.663493\pi$
$487$	−21.6859	−0.982683	−0.491341	+	0.870967i	$0.663493\pi$
$488$	−2.04911	−0.0927589
$489$	58.1070	2.62769
$490$	−0.164091	−0.00741289
$491$	−2.54893	−0.115031	−0.0575157	−	0.998345i	$-0.518318\pi$
$491$	−2.54893	−0.115031	−0.0575157	+	0.998345i	$0.518318\pi$
$492$	66.3438	2.99101
$493$	9.73854	0.438602
$494$	2.22465	0.100092
$495$	0	0
$496$	26.7935	1.20306
$497$	0.339839	0.0152439
$498$	−0.104504	−0.00468296
$499$	24.1867	1.08274	0.541372	−	0.840783i	$-0.317905\pi$
$499$	24.1867	1.08274	0.541372	+	0.840783i	$0.317905\pi$
$500$	1.97307	0.0882386
$501$	−75.1414	−3.35707
$502$	−3.57971	−0.159770
$503$	39.3976	1.75665	0.878327	−	0.478060i	$-0.158660\pi$
$503$	39.3976	1.75665	0.878327	+	0.478060i	$0.158660\pi$
$504$	−5.05006	−0.224947
$505$	−1.83395	−0.0816095
$506$	0	0
$507$	4.27153	0.189705
$508$	−14.1122	−0.626127
$509$	−16.1856	−0.717415	−0.358707	−	0.933450i	$-0.616782\pi$
$509$	−16.1856	−0.717415	−0.358707	+	0.933450i	$0.616782\pi$
$510$	−3.80360	−0.168426
$511$	−11.7433	−0.519494
$512$	12.4303	0.549348
$513$	61.6742	2.72298
$514$	−1.95380	−0.0861784
$515$	−15.2837	−0.673478
$516$	−41.8284	−1.84139
$517$	0	0
$518$	0.695111	0.0305414
$519$	64.2782	2.82150
$520$	−2.22971	−0.0977794
$521$	−44.2132	−1.93701	−0.968507	−	0.248986i	$-0.919903\pi$
$521$	−44.2132	−1.93701	−0.968507	+	0.248986i	$0.919903\pi$
$522$	−1.75057	−0.0766206
$523$	−26.7584	−1.17006	−0.585031	−	0.811011i	$-0.698918\pi$
$523$	−26.7584	−1.17006	−0.585031	+	0.811011i	$0.698918\pi$
$524$	−38.4272	−1.67870
$525$	−3.27813	−0.143069
$526$	1.67539	0.0730506
$527$	−49.3486	−2.14966
$528$	0	0
$529$	−21.5815	−0.938325
$530$	−1.56252	−0.0678716
$531$	−45.5398	−1.97626
$532$	7.82138	0.339100
$533$	−35.0807	−1.51951
$534$	−6.82353	−0.295283
$535$	−1.17954	−0.0509961
$536$	−9.23709	−0.398981
$537$	−25.6778	−1.10808
$538$	1.71504	0.0739405
$539$	0	0
$540$	−30.6978	−1.32102
$541$	34.7014	1.49193	0.745964	−	0.665986i	$-0.231989\pi$
$541$	34.7014	1.49193	0.745964	+	0.665986i	$0.231989\pi$
$542$	−3.97385	−0.170692
$543$	−3.22869	−0.138556
$544$	−13.6745	−0.586287
$545$	3.75666	0.160918
$546$	1.83970	0.0787321
$547$	−28.9159	−1.23635	−0.618176	−	0.786039i	$-0.712128\pi$
$547$	−28.9159	−1.23635	−0.618176	+	0.786039i	$0.712128\pi$
$548$	18.9378	0.808981
$549$	24.3465	1.03908
$550$	0	0
$551$	5.45947	0.232581
$552$	2.54540	0.108339
$553$	10.0204	0.426113
$554$	−1.30676	−0.0555188
$555$	13.8865	0.589451
$556$	28.3938	1.20417
$557$	−11.3349	−0.480275	−0.240138	−	0.970739i	$-0.577193\pi$
$557$	−11.3349	−0.480275	−0.240138	+	0.970739i	$0.577193\pi$
$558$	8.87076	0.375529
$559$	22.1176	0.935476
$560$	−3.83917	−0.162235
$561$	0	0
$562$	0.193333	0.00815526
$563$	−28.6998	−1.20955	−0.604776	−	0.796396i	$-0.706737\pi$
$563$	−28.6998	−1.20955	−0.604776	+	0.796396i	$0.706737\pi$
$564$	−2.50478	−0.105470
$565$	−10.3037	−0.433479
$566$	1.90144	0.0799236
$567$	27.7639	1.16597
$568$	−0.221557	−0.00929633
$569$	−7.31957	−0.306853	−0.153426	−	0.988160i	$-0.549031\pi$
$569$	−7.31957	−0.306853	−0.153426	+	0.988160i	$0.549031\pi$
$570$	−2.13231	−0.0893128
$571$	−32.3161	−1.35239	−0.676193	−	0.736724i	$-0.736372\pi$
$571$	−32.3161	−1.35239	−0.676193	+	0.736724i	$0.736372\pi$
$572$	0	0
$573$	0.348565	0.0145615
$574$	1.68313	0.0702524
$575$	1.19102	0.0496689
$576$	−57.0192	−2.37580
$577$	−28.4485	−1.18433	−0.592163	−	0.805818i	$-0.701726\pi$
$577$	−28.4485	−1.18433	−0.592163	+	0.805818i	$0.701726\pi$
$578$	5.41494	0.225232
$579$	13.0980	0.544335
$580$	−2.71741	−0.112834
$581$	0.194278	0.00806000
$582$	9.93793	0.411940
$583$	0	0
$584$	7.65602	0.316808
$585$	26.4923	1.09532
$586$	0.417037	0.0172276
$587$	−25.0706	−1.03477	−0.517387	−	0.855752i	$-0.673095\pi$
$587$	−25.0706	−1.03477	−0.517387	+	0.855752i	$0.673095\pi$
$588$	6.46799	0.266735
$589$	−27.6650	−1.13992
$590$	0.964701	0.0397161
$591$	19.0957	0.785493
$592$	16.2632	0.668413
$593$	−39.6026	−1.62629	−0.813143	−	0.582064i	$-0.802245\pi$
$593$	−39.6026	−1.62629	−0.813143	+	0.582064i	$0.802245\pi$
$594$	0	0
$595$	7.07103	0.289884
$596$	42.3332	1.73403
$597$	24.2535	0.992631
$598$	−0.668406	−0.0273332
$599$	5.99181	0.244819	0.122409	−	0.992480i	$-0.460938\pi$
$599$	5.99181	0.244819	0.122409	+	0.992480i	$0.460938\pi$
$600$	2.13717	0.0872494
$601$	−45.3928	−1.85161	−0.925806	−	0.378000i	$-0.876612\pi$
$601$	−45.3928	−1.85161	−0.925806	+	0.378000i	$0.876612\pi$
$602$	−1.06118	−0.0432504
$603$	109.750	4.46939
$604$	−0.162197	−0.00659972
$605$	0	0
$606$	−0.986502	−0.0400739
$607$	22.3454	0.906973	0.453487	−	0.891263i	$-0.350180\pi$
$607$	22.3454	0.906973	0.453487	+	0.891263i	$0.350180\pi$
$608$	−7.66596	−0.310896
$609$	4.51478	0.182948
$610$	−0.515750	−0.0208821
$611$	1.32445	0.0535816
$612$	108.071	4.36852
$613$	27.4246	1.10767	0.553835	−	0.832627i	$-0.313164\pi$
$613$	27.4246	1.10767	0.553835	+	0.832627i	$0.313164\pi$
$614$	0.475847	0.0192036
$615$	33.6246	1.35587
$616$	0	0
$617$	1.53475	0.0617866	0.0308933	−	0.999523i	$-0.490165\pi$
$617$	1.53475	0.0617866	0.0308933	+	0.999523i	$0.490165\pi$
$618$	−8.22126	−0.330708
$619$	−8.61965	−0.346453	−0.173226	−	0.984882i	$-0.555419\pi$
$619$	−8.61965	−0.346453	−0.173226	+	0.984882i	$0.555419\pi$
$620$	13.7700	0.553018
$621$	−18.5303	−0.743594
$622$	−2.84442	−0.114051
$623$	12.6852	0.508222
$624$	43.0427	1.72309
$625$	1.00000	0.0400000
$626$	−0.0330328	−0.00132025
$627$	0	0
$628$	−39.6173	−1.58090
$629$	−29.9538	−1.19433
$630$	−1.27107	−0.0506407
$631$	11.5656	0.460420	0.230210	−	0.973141i	$-0.426059\pi$
$631$	11.5656	0.460420	0.230210	+	0.973141i	$0.426059\pi$
$632$	−6.53280	−0.259861
$633$	42.4073	1.68554
$634$	0.0178239	0.000707879 0
$635$	−7.15239	−0.283834
$636$	61.5899	2.44220
$637$	−3.42008	−0.135509
$638$	0	0
$639$	2.63243	0.104137
$640$	5.07562	0.200631
$641$	12.2408	0.483484	0.241742	−	0.970341i	$-0.422281\pi$
$641$	12.2408	0.483484	0.241742	+	0.970341i	$0.422281\pi$
$642$	−0.634491	−0.0250414
$643$	−23.5116	−0.927206	−0.463603	−	0.886043i	$-0.653444\pi$
$643$	−23.5116	−0.927206	−0.463603	+	0.886043i	$0.653444\pi$
$644$	−2.34997	−0.0926016
$645$	−21.1996	−0.834734
$646$	4.59948	0.180964
$647$	27.9447	1.09862	0.549310	−	0.835619i	$-0.314891\pi$
$647$	27.9447	1.09862	0.549310	+	0.835619i	$0.314891\pi$
$648$	−18.1006	−0.711059
$649$	0	0
$650$	−0.561206	−0.0220123
$651$	−22.8780	−0.896658
$652$	34.9741	1.36969
$653$	2.10740	0.0824688	0.0412344	−	0.999150i	$-0.486871\pi$
$653$	2.10740	0.0824688	0.0412344	+	0.999150i	$0.486871\pi$
$654$	2.02075	0.0790177
$655$	−19.4758	−0.760982
$656$	39.3794	1.53751
$657$	−90.9650	−3.54888
$658$	−0.0635457	−0.00247727
$659$	18.8837	0.735606	0.367803	−	0.929904i	$-0.380110\pi$
$659$	18.8837	0.735606	0.367803	+	0.929904i	$0.380110\pi$
$660$	0	0
$661$	27.9541	1.08729	0.543644	−	0.839316i	$-0.317044\pi$
$661$	27.9541	1.08729	0.543644	+	0.839316i	$0.317044\pi$
$662$	0.433052	0.0168310
$663$	−79.2766	−3.07885
$664$	−0.126659	−0.00491532
$665$	3.96406	0.153719
$666$	5.38441	0.208642
$667$	−1.64032	−0.0635135
$668$	−45.2269	−1.74988
$669$	64.2773	2.48511
$670$	−2.32492	−0.0898196
$671$	0	0
$672$	−6.33947	−0.244550
$673$	−4.43986	−0.171144	−0.0855720	−	0.996332i	$-0.527272\pi$
$673$	−4.43986	−0.171144	−0.0855720	+	0.996332i	$0.527272\pi$
$674$	−2.05496	−0.0791539
$675$	−15.5584	−0.598841
$676$	2.57099	0.0988844
$677$	44.2511	1.70071	0.850354	−	0.526210i	$-0.176388\pi$
$677$	44.2511	1.70071	0.850354	+	0.526210i	$0.176388\pi$
$678$	−5.54248	−0.212858
$679$	−18.4750	−0.709005
$680$	−4.60994	−0.176783
$681$	−20.3286	−0.778993
$682$	0	0
$683$	−0.738650	−0.0282637	−0.0141318	−	0.999900i	$-0.504498\pi$
$683$	−0.738650	−0.0282637	−0.0141318	+	0.999900i	$0.504498\pi$
$684$	60.5852	2.31653
$685$	9.59810	0.366724
$686$	0.164091	0.00626504
$687$	51.0244	1.94670
$688$	−24.8279	−0.946554
$689$	−32.5669	−1.24070
$690$	0.640663	0.0243896
$691$	−27.6402	−1.05148	−0.525742	−	0.850644i	$-0.676212\pi$
$691$	−27.6402	−1.05148	−0.525742	+	0.850644i	$0.676212\pi$
$692$	38.6884	1.47071
$693$	0	0
$694$	−4.45789	−0.169219
$695$	14.3907	0.545869
$696$	−2.94340	−0.111569
$697$	−72.5295	−2.74725
$698$	2.29942	0.0870341
$699$	85.4999	3.23390
$700$	−1.97307	−0.0745752
$701$	−21.9762	−0.830030	−0.415015	−	0.909814i	$-0.636224\pi$
$701$	−21.9762	−0.830030	−0.415015	+	0.909814i	$0.636224\pi$
$702$	8.73144	0.329547
$703$	−16.7922	−0.633330
$704$	0	0
$705$	−1.26948	−0.0478114
$706$	2.58486	0.0972824
$707$	1.83395	0.0689726
$708$	−38.0256	−1.42909
$709$	−14.9149	−0.560141	−0.280071	−	0.959979i	$-0.590358\pi$
$709$	−14.9149	−0.560141	−0.280071	+	0.959979i	$0.590358\pi$
$710$	−0.0557646	−0.00209281
$711$	77.6195	2.91096
$712$	−8.27008	−0.309934
$713$	8.31208	0.311290
$714$	3.80360	0.142346
$715$	0	0
$716$	−15.4552	−0.577590
$717$	3.96859	0.148210
$718$	4.58918	0.171267
$719$	1.21369	0.0452628	0.0226314	−	0.999744i	$-0.492796\pi$
$719$	1.21369	0.0452628	0.0226314	+	0.999744i	$0.492796\pi$
$720$	−29.7386	−1.10829
$721$	15.2837	0.569193
$722$	−0.539248	−0.0200687
$723$	−61.5209	−2.28799
$724$	−1.94332	−0.0722229
$725$	−1.37724	−0.0511496
$726$	0	0
$727$	−6.85349	−0.254182	−0.127091	−	0.991891i	$-0.540564\pi$
$727$	−6.85349	−0.254182	−0.127091	+	0.991891i	$0.540564\pi$
$728$	2.22971	0.0826387
$729$	62.0557	2.29836
$730$	1.92698	0.0713206
$731$	45.7283	1.69132
$732$	20.3293	0.751392
$733$	−39.3168	−1.45220	−0.726100	−	0.687589i	$-0.758669\pi$
$733$	−39.3168	−1.45220	−0.726100	+	0.687589i	$0.758669\pi$
$734$	0.516900	0.0190791
$735$	3.27813	0.120916
$736$	2.30327	0.0848997
$737$	0	0
$738$	13.0377	0.479924
$739$	10.2900	0.378523	0.189261	−	0.981927i	$-0.439391\pi$
$739$	10.2900	0.378523	0.189261	+	0.981927i	$0.439391\pi$
$740$	8.35818	0.307253
$741$	−44.4429	−1.63265
$742$	1.56252	0.0573620
$743$	−41.1973	−1.51138	−0.755691	−	0.654928i	$-0.772699\pi$
$743$	−41.1973	−1.51138	−0.755691	+	0.654928i	$0.772699\pi$
$744$	14.9152	0.546818
$745$	21.4554	0.786067
$746$	−4.21287	−0.154244
$747$	1.50490	0.0550613
$748$	0	0
$749$	1.17954	0.0430996
$750$	0.537912	0.0196418
$751$	20.0630	0.732110	0.366055	−	0.930593i	$-0.380708\pi$
$751$	20.0630	0.732110	0.366055	+	0.930593i	$0.380708\pi$
$752$	−1.48675	−0.0542161
$753$	71.5134	2.60609
$754$	0.772918	0.0281480
$755$	−0.0822054	−0.00299176
$756$	30.6978	1.11647
$757$	−15.7342	−0.571869	−0.285934	−	0.958249i	$-0.592304\pi$
$757$	−15.7342	−0.571869	−0.285934	+	0.958249i	$0.592304\pi$
$758$	−0.727312	−0.0264172
$759$	0	0
$760$	−2.58436	−0.0937444
$761$	34.1599	1.23829	0.619147	−	0.785275i	$-0.287479\pi$
$761$	34.1599	1.23829	0.619147	+	0.785275i	$0.287479\pi$
$762$	−3.84736	−0.139375
$763$	−3.75666	−0.136000
$764$	0.209798	0.00759022
$765$	54.7730	1.98032
$766$	1.23002	0.0444426
$767$	20.1068	0.726016
$768$	−45.5304	−1.64294
$769$	−50.2610	−1.81246	−0.906229	−	0.422786i	$-0.861052\pi$
$769$	−50.2610	−1.81246	−0.906229	+	0.422786i	$0.861052\pi$
$770$	0	0
$771$	39.0319	1.40570
$772$	7.88358	0.283736
$773$	−41.0757	−1.47739	−0.738696	−	0.674039i	$-0.764558\pi$
$773$	−41.0757	−1.47739	−0.738696	+	0.674039i	$0.764558\pi$
$774$	−8.22000	−0.295462
$775$	6.97897	0.250692
$776$	12.0447	0.432380
$777$	−13.8865	−0.498177
$778$	−3.69044	−0.132309
$779$	−40.6604	−1.45681
$780$	22.1210	0.792060
$781$	0	0
$782$	−1.38193	−0.0494178
$783$	21.4277	0.765762
$784$	3.83917	0.137113
$785$	−20.0790	−0.716650
$786$	−10.4763	−0.373676
$787$	2.28478	0.0814435	0.0407217	−	0.999171i	$-0.487034\pi$
$787$	2.28478	0.0814435	0.0407217	+	0.999171i	$0.487034\pi$
$788$	11.4935	0.409441
$789$	−33.4701	−1.19157
$790$	−1.64427	−0.0585004
$791$	10.3037	0.366357
$792$	0	0
$793$	−10.7495	−0.381727
$794$	−0.704547	−0.0250034
$795$	31.2152	1.10709
$796$	14.5980	0.517411
$797$	−40.5602	−1.43672	−0.718358	−	0.695673i	$-0.755106\pi$
$797$	−40.5602	−1.43672	−0.718358	+	0.695673i	$0.755106\pi$
$798$	2.13231	0.0754831
$799$	2.73831	0.0968745
$800$	1.93387	0.0683726
$801$	98.2610	3.47188
$802$	4.13266	0.145929
$803$	0	0
$804$	91.6414	3.23194
$805$	−1.19102	−0.0419778
$806$	−3.91664	−0.137958
$807$	−34.2621	−1.20608
$808$	−1.19564	−0.0420623
$809$	−3.69566	−0.129932	−0.0649662	−	0.997887i	$-0.520694\pi$
$809$	−3.69566	−0.129932	−0.0649662	+	0.997887i	$0.520694\pi$
$810$	−4.55582	−0.160075
$811$	−36.6961	−1.28858	−0.644288	−	0.764783i	$-0.722846\pi$
$811$	−36.6961	−1.28858	−0.644288	+	0.764783i	$0.722846\pi$
$812$	2.71741	0.0953622
$813$	79.3874	2.78424
$814$	0	0
$815$	17.7257	0.620904
$816$	88.9910	3.11531
$817$	25.6355	0.896873
$818$	−0.385907	−0.0134929
$819$	−26.4923	−0.925717
$820$	20.2383	0.706753
$821$	−1.93727	−0.0676112	−0.0338056	−	0.999428i	$-0.510763\pi$
$821$	−1.93727	−0.0676112	−0.0338056	+	0.999428i	$0.510763\pi$
$822$	5.16293	0.180078
$823$	5.94215	0.207130	0.103565	−	0.994623i	$-0.466975\pi$
$823$	5.94215	0.207130	0.103565	+	0.994623i	$0.466975\pi$
$824$	−9.96414	−0.347117
$825$	0	0
$826$	−0.964701	−0.0335663
$827$	47.7378	1.66001	0.830004	−	0.557758i	$-0.188338\pi$
$827$	47.7378	1.66001	0.830004	+	0.557758i	$0.188338\pi$
$828$	−18.2031	−0.632601
$829$	26.5410	0.921807	0.460903	−	0.887450i	$-0.347525\pi$
$829$	26.5410	0.921807	0.460903	+	0.887450i	$0.347525\pi$
$830$	−0.0318793	−0.00110655
$831$	26.1057	0.905596
$832$	25.1752	0.872795
$833$	−7.07103	−0.244997
$834$	7.74091	0.268046
$835$	−22.9221	−0.793251
$836$	0	0
$837$	−108.581	−3.75312
$838$	1.49106	0.0515079
$839$	8.91496	0.307779	0.153889	−	0.988088i	$-0.450820\pi$
$839$	8.91496	0.307779	0.153889	+	0.988088i	$0.450820\pi$
$840$	−2.13717	−0.0737392
$841$	−27.1032	−0.934593
$842$	3.39873	0.117128
$843$	−3.86230	−0.133025
$844$	25.5245	0.878591
$845$	1.30304	0.0448259
$846$	−0.492232	−0.0169233
$847$	0	0
$848$	36.5576	1.25539
$849$	−37.9860	−1.30368
$850$	−1.16030	−0.0397978
$851$	5.04529	0.172950
$852$	2.19807	0.0753048
$853$	−11.0187	−0.377274	−0.188637	−	0.982047i	$-0.560407\pi$
$853$	−11.0187	−0.377274	−0.188637	+	0.982047i	$0.560407\pi$
$854$	0.515750	0.0176486
$855$	30.7060	1.05012
$856$	−0.769000	−0.0262839
$857$	−20.1527	−0.688402	−0.344201	−	0.938896i	$-0.611850\pi$
$857$	−20.1527	−0.688402	−0.344201	+	0.938896i	$0.611850\pi$
$858$	0	0
$859$	−28.8976	−0.985975	−0.492987	−	0.870037i	$-0.664095\pi$
$859$	−28.8976	−0.985975	−0.492987	+	0.870037i	$0.664095\pi$
$860$	−12.7599	−0.435107
$861$	−33.6246	−1.14592
$862$	−1.14492	−0.0389961
$863$	8.28391	0.281987	0.140994	−	0.990010i	$-0.454970\pi$
$863$	8.28391	0.281987	0.140994	+	0.990010i	$0.454970\pi$
$864$	−30.0878	−1.02361
$865$	19.6082	0.666699
$866$	0.933353	0.0317166
$867$	−108.177	−3.67387
$868$	−13.7700	−0.467385
$869$	0	0
$870$	−0.740837	−0.0251167
$871$	−48.4573	−1.64191
$872$	2.44914	0.0829385
$873$	−143.109	−4.84352
$874$	−0.774718	−0.0262052
$875$	−1.00000	−0.0338062
$876$	−75.9556	−2.56630
$877$	30.9005	1.04344	0.521718	−	0.853118i	$-0.325291\pi$
$877$	30.9005	1.04344	0.521718	+	0.853118i	$0.325291\pi$
$878$	6.29503	0.212447
$879$	−8.33133	−0.281009
$880$	0	0
$881$	−42.5576	−1.43380	−0.716901	−	0.697175i	$-0.754440\pi$
$881$	−42.5576	−1.43380	−0.716901	+	0.697175i	$0.754440\pi$
$882$	1.27107	0.0427992
$883$	23.4043	0.787616	0.393808	−	0.919193i	$-0.371157\pi$
$883$	23.4043	0.787616	0.393808	+	0.919193i	$0.371157\pi$
$884$	−47.7159	−1.60486
$885$	−19.2723	−0.647830
$886$	2.39919	0.0806023
$887$	−34.6100	−1.16209	−0.581044	−	0.813872i	$-0.697356\pi$
$887$	−34.6100	−1.16209	−0.581044	+	0.813872i	$0.697356\pi$
$888$	9.05329	0.303809
$889$	7.15239	0.239883
$890$	−2.08153	−0.0697731
$891$	0	0
$892$	38.6879	1.29537
$893$	1.53511	0.0513705
$894$	11.5411	0.385994
$895$	−7.83308	−0.261831
$896$	−5.07562	−0.169564
$897$	13.3530	0.445845
$898$	−5.00097	−0.166885
$899$	−9.61175	−0.320570
$900$	−15.2837	−0.509455
$901$	−67.3323	−2.24316
$902$	0	0
$903$	21.1996	0.705479
$904$	−6.71746	−0.223419
$905$	−0.984920	−0.0327399
$906$	−0.0442193	−0.00146909
$907$	−46.2557	−1.53589	−0.767947	−	0.640513i	$-0.778722\pi$
$907$	−46.2557	−1.53589	−0.767947	+	0.640513i	$0.778722\pi$
$908$	−12.2356	−0.406052
$909$	14.2060	0.471182
$910$	0.561206	0.0186038
$911$	36.1685	1.19832	0.599158	−	0.800631i	$-0.295502\pi$
$911$	36.1685	1.19832	0.599158	+	0.800631i	$0.295502\pi$
$912$	49.8888	1.65198
$913$	0	0
$914$	0.312758	0.0103451
$915$	10.3034	0.340619
$916$	30.7111	1.01472
$917$	19.4758	0.643147
$918$	18.0523	0.595815
$919$	50.5931	1.66891	0.834457	−	0.551074i	$-0.185782\pi$
$919$	50.5931	1.66891	0.834457	+	0.551074i	$0.185782\pi$
$920$	0.776480	0.0255998
$921$	−9.50620	−0.313240
$922$	3.05281	0.100539
$923$	−1.16228	−0.0382568
$924$	0	0
$925$	4.23612	0.139283
$926$	1.10461	0.0362996
$927$	118.389	3.88840
$928$	−2.66341	−0.0874307
$929$	−27.2117	−0.892787	−0.446394	−	0.894837i	$-0.647292\pi$
$929$	−27.2117	−0.892787	−0.446394	+	0.894837i	$0.647292\pi$
$930$	3.75408	0.123101
$931$	−3.96406	−0.129917
$932$	51.4616	1.68568
$933$	56.8243	1.86034
$934$	1.76917	0.0578891
$935$	0	0
$936$	17.2716	0.564540
$937$	7.87042	0.257115	0.128558	−	0.991702i	$-0.458965\pi$
$937$	7.87042	0.257115	0.128558	+	0.991702i	$0.458965\pi$
$938$	2.32492	0.0759114
$939$	0.659910	0.0215354
$940$	−0.764088	−0.0249218
$941$	−14.5219	−0.473401	−0.236700	−	0.971583i	$-0.576066\pi$
$941$	−14.5219	−0.473401	−0.236700	+	0.971583i	$0.576066\pi$
$942$	−10.8007	−0.351907
$943$	12.2166	0.397826
$944$	−22.5707	−0.734613
$945$	15.5584	0.506113
$946$	0	0
$947$	49.1404	1.59685	0.798424	−	0.602095i	$-0.205667\pi$
$947$	49.1404	1.59685	0.798424	+	0.602095i	$0.205667\pi$
$948$	64.8121	2.10500
$949$	40.1631	1.30375
$950$	−0.650467	−0.0211039
$951$	−0.356077	−0.0115466
$952$	4.60994	0.149409
$953$	17.4892	0.566532	0.283266	−	0.959041i	$-0.408582\pi$
$953$	17.4892	0.566532	0.283266	+	0.959041i	$0.408582\pi$
$954$	12.1035	0.391864
$955$	0.106330	0.00344077
$956$	2.38866	0.0772548
$957$	0	0
$958$	3.72110	0.120223
$959$	−9.59810	−0.309939
$960$	−24.1303	−0.778802
$961$	17.7061	0.571163
$962$	−2.37734	−0.0766484
$963$	9.13687	0.294432
$964$	−37.0289	−1.19262
$965$	3.99558	0.128622
$966$	−0.640663	−0.0206130
$967$	−12.9466	−0.416334	−0.208167	−	0.978093i	$-0.566750\pi$
$967$	−12.9466	−0.416334	−0.208167	+	0.978093i	$0.566750\pi$
$968$	0	0
$969$	−91.8858	−2.95180
$970$	3.03159	0.0973384
$971$	13.5026	0.433318	0.216659	−	0.976247i	$-0.430484\pi$
$971$	13.5026	0.433318	0.216659	+	0.976247i	$0.430484\pi$
$972$	87.4833	2.80603
$973$	−14.3907	−0.461343
$974$	−3.55847	−0.114021
$975$	11.2115	0.359054
$976$	12.0668	0.386247
$977$	−45.9006	−1.46849	−0.734245	−	0.678884i	$-0.762464\pi$
$977$	−45.9006	−1.46849	−0.734245	+	0.678884i	$0.762464\pi$
$978$	9.53486	0.304891
$979$	0	0
$980$	1.97307	0.0630275
$981$	−29.0995	−0.929076
$982$	−0.418257	−0.0133471
$983$	31.0288	0.989666	0.494833	−	0.868988i	$-0.335229\pi$
$983$	31.0288	0.989666	0.494833	+	0.868988i	$0.335229\pi$
$984$	21.9215	0.698831
$985$	5.82520	0.185606
$986$	1.59801	0.0508910
$987$	1.26948	0.0404080
$988$	−26.7497	−0.851023
$989$	−7.70230	−0.244919
$990$	0	0
$991$	−20.5880	−0.654000	−0.327000	−	0.945024i	$-0.606038\pi$
$991$	−20.5880	−0.654000	−0.327000	+	0.945024i	$0.606038\pi$
$992$	13.4964	0.428512
$993$	−8.65126	−0.274540
$994$	0.0557646	0.00176875
$995$	7.39859	0.234551
$996$	1.25659	0.0398165
$997$	−43.6146	−1.38129	−0.690644	−	0.723195i	$-0.742673\pi$
$997$	−43.6146	−1.38129	−0.690644	+	0.723195i	$0.742673\pi$
$998$	3.96883	0.125631
$999$	−65.9071	−2.08521

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.y.1.4	✓	5
11.10	odd	2		4235.2.a.be.1.2	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.y.1.4	✓	5	1.1	even	1	trivial
4235.2.a.be.1.2	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)

\(f(q)\)	\(=\)	\(q+0.164091 q^{2} -3.27813 q^{3} -1.97307 q^{4} -1.00000 q^{5} -0.537912 q^{6} +1.00000 q^{7} -0.651947 q^{8} +7.74611 q^{9} +O(q^{10})\)	\(q+0.164091 q^{2} -3.27813 q^{3} -1.97307 q^{4} -1.00000 q^{5} -0.537912 q^{6} +1.00000 q^{7} -0.651947 q^{8} +7.74611 q^{9} -0.164091 q^{10} +6.46799 q^{12} -3.42008 q^{13} +0.164091 q^{14} +3.27813 q^{15} +3.83917 q^{16} -7.07103 q^{17} +1.27107 q^{18} -3.96406 q^{19} +1.97307 q^{20} -3.27813 q^{21} +1.19102 q^{23} +2.13717 q^{24} +1.00000 q^{25} -0.561206 q^{26} -15.5584 q^{27} -1.97307 q^{28} -1.37724 q^{29} +0.537912 q^{30} +6.97897 q^{31} +1.93387 q^{32} -1.16030 q^{34} -1.00000 q^{35} -15.2837 q^{36} +4.23612 q^{37} -0.650467 q^{38} +11.2115 q^{39} +0.651947 q^{40} +10.2573 q^{41} -0.537912 q^{42} -6.46699 q^{43} -7.74611 q^{45} +0.195436 q^{46} -0.387258 q^{47} -12.5853 q^{48} +1.00000 q^{49} +0.164091 q^{50} +23.1797 q^{51} +6.74807 q^{52} +9.52227 q^{53} -2.55299 q^{54} -0.651947 q^{56} +12.9947 q^{57} -0.225994 q^{58} -5.87905 q^{59} -6.46799 q^{60} +3.14306 q^{61} +1.14519 q^{62} +7.74611 q^{63} -7.36101 q^{64} +3.42008 q^{65} +14.1685 q^{67} +13.9517 q^{68} -3.90431 q^{69} -0.164091 q^{70} +0.339839 q^{71} -5.05006 q^{72} -11.7433 q^{73} +0.695111 q^{74} -3.27813 q^{75} +7.82138 q^{76} +1.83970 q^{78} +10.0204 q^{79} -3.83917 q^{80} +27.7639 q^{81} +1.68313 q^{82} +0.194278 q^{83} +6.46799 q^{84} +7.07103 q^{85} -1.06118 q^{86} +4.51478 q^{87} +12.6852 q^{89} -1.27107 q^{90} -3.42008 q^{91} -2.34997 q^{92} -22.8780 q^{93} -0.0635457 q^{94} +3.96406 q^{95} -6.33947 q^{96} -18.4750 q^{97} +0.164091 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} + 5 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 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

Varieties

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Representations

Groups

Database

Properties

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