LMFDB - Embedded newform 5915.2.a.n.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5915,2,Mod(1,5915)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5915, 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("5915.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5915 = 5 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5915.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:	$47.2315127956$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.12197.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + 3x + 1 $ x^4 - x^3 - 5x^2 + 3x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 455)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.819751$ of defining polynomial
Character	$\chi$	$=$	5915.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.819751 q^{2} +1.40013 q^{3} -1.32801 q^{4} +1.00000 q^{5} +1.14776 q^{6} +1.00000 q^{7} -2.72814 q^{8} -1.03963 q^{9} +O(q^{10})$	\(q+0.819751 q^{2} +1.40013 q^{3} -1.32801 q^{4} +1.00000 q^{5} +1.14776 q^{6} +1.00000 q^{7} -2.72814 q^{8} -1.03963 q^{9} +0.819751 q^{10} -4.43976 q^{11} -1.85938 q^{12} +0.819751 q^{14} +1.40013 q^{15} +0.419620 q^{16} +6.69565 q^{17} -0.852241 q^{18} -1.96037 q^{19} -1.32801 q^{20} +1.40013 q^{21} -3.63950 q^{22} +5.09578 q^{23} -3.81975 q^{24} +1.00000 q^{25} -5.65602 q^{27} -1.32801 q^{28} -3.03963 q^{29} +1.14776 q^{30} -7.03963 q^{31} +5.80026 q^{32} -6.21625 q^{33} +5.48877 q^{34} +1.00000 q^{35} +1.38064 q^{36} -4.67914 q^{37} -1.60701 q^{38} -2.72814 q^{40} +1.20039 q^{41} +1.14776 q^{42} +1.63950 q^{43} +5.89604 q^{44} -1.03963 q^{45} +4.17727 q^{46} +8.65602 q^{47} +0.587523 q^{48} +1.00000 q^{49} +0.819751 q^{50} +9.37479 q^{51} -11.7518 q^{53} -4.63653 q^{54} -4.43976 q^{55} -2.72814 q^{56} -2.74477 q^{57} -2.49174 q^{58} -4.96037 q^{59} -1.85938 q^{60} -0.216251 q^{61} -5.77075 q^{62} -1.03963 q^{63} +3.91553 q^{64} -5.09578 q^{66} -10.2169 q^{67} -8.89187 q^{68} +7.13476 q^{69} +0.819751 q^{70} -11.3913 q^{71} +2.83626 q^{72} -6.83924 q^{73} -3.83573 q^{74} +1.40013 q^{75} +2.60338 q^{76} -4.43976 q^{77} +1.59987 q^{79} +0.419620 q^{80} -4.80026 q^{81} +0.984023 q^{82} +6.15127 q^{83} -1.85938 q^{84} +6.69565 q^{85} +1.34398 q^{86} -4.25588 q^{87} +12.1123 q^{88} -13.2169 q^{89} -0.852241 q^{90} -6.76724 q^{92} -9.85641 q^{93} +7.09578 q^{94} -1.96037 q^{95} +8.12113 q^{96} +13.8311 q^{97} +0.819751 q^{98} +4.61573 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 3 q^{4} + 4 q^{5} - 6 q^{6} + 4 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q + q^2 + 3 * q^4 + 4 * q^5 - 6 * q^6 + 4 * q^7 + 3 * q^8 + 6 * q^9	$ 4 q + q^{2} + 3 q^{4} + 4 q^{5} - 6 q^{6} + 4 q^{7} + 3 q^{8} + 6 q^{9} + q^{10} - 2 q^{11} + 5 q^{12} + q^{14} + 5 q^{16} - 14 q^{18} - 18 q^{19} + 3 q^{20} - 10 q^{22} - 12 q^{23} - 13 q^{24} + 4 q^{25} - 6 q^{27} + 3 q^{28} - 2 q^{29} - 6 q^{30} - 18 q^{31} + 12 q^{32} - 24 q^{33} + 7 q^{34} + 4 q^{35} - 9 q^{36} - 4 q^{37} + 11 q^{38} + 3 q^{40} - 12 q^{41} - 6 q^{42} + 2 q^{43} - 20 q^{44} + 6 q^{45} - 2 q^{46} + 18 q^{47} - 24 q^{48} + 4 q^{49} + q^{50} - 4 q^{51} + 2 q^{53} + 7 q^{54} - 2 q^{55} + 3 q^{56} + 6 q^{57} - 16 q^{58} - 30 q^{59} + 5 q^{60} - 20 q^{62} + 6 q^{63} - 19 q^{64} + 12 q^{66} - 12 q^{67} - 36 q^{68} + 14 q^{69} + q^{70} + 8 q^{71} - 3 q^{72} - 34 q^{73} - 38 q^{74} - 2 q^{77} + 12 q^{79} + 5 q^{80} - 8 q^{81} - 21 q^{82} - 2 q^{83} + 5 q^{84} + 22 q^{86} - 6 q^{87} + 4 q^{88} - 24 q^{89} - 14 q^{90} - 40 q^{92} - 6 q^{93} - 4 q^{94} - 18 q^{95} + 36 q^{96} - 14 q^{97} + q^{98} + 40 q^{99}+O(q^{100}) $ 4 * q + q^2 + 3 * q^4 + 4 * q^5 - 6 * q^6 + 4 * q^7 + 3 * q^8 + 6 * q^9 + q^10 - 2 * q^11 + 5 * q^12 + q^14 + 5 * q^16 - 14 * q^18 - 18 * q^19 + 3 * q^20 - 10 * q^22 - 12 * q^23 - 13 * q^24 + 4 * q^25 - 6 * q^27 + 3 * q^28 - 2 * q^29 - 6 * q^30 - 18 * q^31 + 12 * q^32 - 24 * q^33 + 7 * q^34 + 4 * q^35 - 9 * q^36 - 4 * q^37 + 11 * q^38 + 3 * q^40 - 12 * q^41 - 6 * q^42 + 2 * q^43 - 20 * q^44 + 6 * q^45 - 2 * q^46 + 18 * q^47 - 24 * q^48 + 4 * q^49 + q^50 - 4 * q^51 + 2 * q^53 + 7 * q^54 - 2 * q^55 + 3 * q^56 + 6 * q^57 - 16 * q^58 - 30 * q^59 + 5 * q^60 - 20 * q^62 + 6 * q^63 - 19 * q^64 + 12 * q^66 - 12 * q^67 - 36 * q^68 + 14 * q^69 + q^70 + 8 * q^71 - 3 * q^72 - 34 * q^73 - 38 * q^74 - 2 * q^77 + 12 * q^79 + 5 * q^80 - 8 * q^81 - 21 * q^82 - 2 * q^83 + 5 * q^84 + 22 * q^86 - 6 * q^87 + 4 * q^88 - 24 * q^89 - 14 * q^90 - 40 * q^92 - 6 * q^93 - 4 * q^94 - 18 * q^95 + 36 * q^96 - 14 * q^97 + q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.819751	0.579652	0.289826	−	0.957079i	$-0.406403\pi$
$2$	0.819751	0.579652	0.289826	+	0.957079i	$0.406403\pi$
$3$	1.40013	0.808366	0.404183	−	0.914678i	$-0.367556\pi$
$3$	1.40013	0.808366	0.404183	+	0.914678i	$0.367556\pi$
$4$	−1.32801	−0.664004
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.14776	0.468571
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.72814	−0.964543
$9$	−1.03963	−0.346544
$10$	0.819751	0.259228
$11$	−4.43976	−1.33864	−0.669320	−	0.742975i	$-0.733414\pi$
$11$	−4.43976	−1.33864	−0.669320	+	0.742975i	$0.733414\pi$
$12$	−1.85938	−0.536758
$13$	0	0
$13$	0	0
$14$	0.819751	0.219088
$15$	1.40013	0.361512
$16$	0.419620	0.104905
$17$	6.69565	1.62393	0.811967	−	0.583704i	$-0.198397\pi$
$17$	6.69565	1.62393	0.811967	+	0.583704i	$0.198397\pi$
$18$	−0.852241	−0.200875
$19$	−1.96037	−0.449739	−0.224869	−	0.974389i	$-0.572196\pi$
$19$	−1.96037	−0.449739	−0.224869	+	0.974389i	$0.572196\pi$
$20$	−1.32801	−0.296952
$21$	1.40013	0.305534
$22$	−3.63950	−0.775945
$23$	5.09578	1.06254	0.531272	−	0.847201i	$-0.321714\pi$
$23$	5.09578	1.06254	0.531272	+	0.847201i	$0.321714\pi$
$24$	−3.81975	−0.779703
$25$	1.00000	0.200000
$26$	0	0
$27$	−5.65602	−1.08850
$28$	−1.32801	−0.250970
$29$	−3.03963	−0.564446	−0.282223	−	0.959349i	$-0.591072\pi$
$29$	−3.03963	−0.564446	−0.282223	+	0.959349i	$0.591072\pi$
$30$	1.14776	0.209551
$31$	−7.03963	−1.26436	−0.632178	−	0.774823i	$-0.717839\pi$
$31$	−7.03963	−1.26436	−0.632178	+	0.774823i	$0.717839\pi$
$32$	5.80026	1.02535
$33$	−6.21625	−1.08211
$34$	5.48877	0.941316
$35$	1.00000	0.169031
$36$	1.38064	0.230107
$37$	−4.67914	−0.769245	−0.384623	−	0.923074i	$-0.625668\pi$
$37$	−4.67914	−0.769245	−0.384623	+	0.923074i	$0.625668\pi$
$38$	−1.60701	−0.260692
$39$	0	0
$40$	−2.72814	−0.431357
$41$	1.20039	0.187470	0.0937349	−	0.995597i	$-0.470119\pi$
$41$	1.20039	0.187470	0.0937349	+	0.995597i	$0.470119\pi$
$42$	1.14776	0.177103
$43$	1.63950	0.250022	0.125011	−	0.992155i	$-0.460103\pi$
$43$	1.63950	0.250022	0.125011	+	0.992155i	$0.460103\pi$
$44$	5.89604	0.888862
$45$	−1.03963	−0.154979
$46$	4.17727	0.615905
$47$	8.65602	1.26261	0.631305	−	0.775535i	$-0.282520\pi$
$47$	8.65602	1.26261	0.631305	+	0.775535i	$0.282520\pi$
$48$	0.587523	0.0848017
$49$	1.00000	0.142857
$50$	0.819751	0.115930
$51$	9.37479	1.31273
$52$	0	0
$53$	−11.7518	−1.61423	−0.807117	−	0.590392i	$-0.798973\pi$
$53$	−11.7518	−1.61423	−0.807117	+	0.590392i	$0.798973\pi$
$54$	−4.63653	−0.630951
$55$	−4.43976	−0.598658
$56$	−2.72814	−0.364563
$57$	−2.74477	−0.363554
$58$	−2.49174	−0.327182
$59$	−4.96037	−0.645785	−0.322892	−	0.946436i	$-0.604655\pi$
$59$	−4.96037	−0.645785	−0.322892	+	0.946436i	$0.604655\pi$
$60$	−1.85938	−0.240046
$61$	−0.216251	−0.0276881	−0.0138441	−	0.999904i	$-0.504407\pi$
$61$	−0.216251	−0.0276881	−0.0138441	+	0.999904i	$0.504407\pi$
$62$	−5.77075	−0.732886
$63$	−1.03963	−0.130982
$64$	3.91553	0.489441
$65$	0	0
$66$	−5.09578	−0.627247
$67$	−10.2169	−1.24819	−0.624097	−	0.781347i	$-0.714533\pi$
$67$	−10.2169	−1.24819	−0.624097	+	0.781347i	$0.714533\pi$
$68$	−8.89187	−1.07830
$69$	7.13476	0.858924
$70$	0.819751	0.0979790
$71$	−11.3913	−1.35190	−0.675949	−	0.736948i	$-0.736266\pi$
$71$	−11.3913	−1.35190	−0.675949	+	0.736948i	$0.736266\pi$
$72$	2.83626	0.334257
$73$	−6.83924	−0.800473	−0.400236	−	0.916412i	$-0.631072\pi$
$73$	−6.83924	−0.800473	−0.400236	+	0.916412i	$0.631072\pi$
$74$	−3.83573	−0.445894
$75$	1.40013	0.161673
$76$	2.60338	0.298628
$77$	−4.43976	−0.505958
$78$	0	0
$79$	1.59987	0.179999	0.0899997	−	0.995942i	$-0.471313\pi$
$79$	1.59987	0.179999	0.0899997	+	0.995942i	$0.471313\pi$
$80$	0.419620	0.0469150
$81$	−4.80026	−0.533362
$82$	0.984023	0.108667
$83$	6.15127	0.675190	0.337595	−	0.941291i	$-0.390387\pi$
$83$	6.15127	0.675190	0.337595	+	0.941291i	$0.390387\pi$
$84$	−1.85938	−0.202876
$85$	6.69565	0.726245
$86$	1.34398	0.144926
$87$	−4.25588	−0.456279
$88$	12.1123	1.29117
$89$	−13.2169	−1.40099	−0.700495	−	0.713658i	$-0.747037\pi$
$89$	−13.2169	−1.40099	−0.700495	+	0.713658i	$0.747037\pi$
$90$	−0.852241	−0.0898341
$91$	0	0
$92$	−6.76724	−0.705533
$93$	−9.85641	−1.02206
$94$	7.09578	0.731874
$95$	−1.96037	−0.201129
$96$	8.12113	0.828859
$97$	13.8311	1.40433	0.702166	−	0.712013i	$-0.252217\pi$
$97$	13.8311	1.40433	0.702166	+	0.712013i	$0.252217\pi$
$98$	0.819751	0.0828074
$99$	4.61573	0.463898
$100$	−1.32801	−0.132801
$101$	−11.0958	−1.10407	−0.552036	−	0.833820i	$-0.686149\pi$
$101$	−11.0958	−1.10407	−0.552036	+	0.833820i	$0.686149\pi$
$102$	7.68499	0.760928
$103$	−13.2147	−1.30208	−0.651041	−	0.759043i	$-0.725667\pi$
$103$	−13.2147	−1.30208	−0.651041	+	0.759043i	$0.725667\pi$
$104$	0	0
$105$	1.40013	0.136639
$106$	−9.63355	−0.935693
$107$	−16.3358	−1.57924	−0.789621	−	0.613595i	$-0.789723\pi$
$107$	−16.3358	−1.57924	−0.789621	+	0.613595i	$0.789723\pi$
$108$	7.51123	0.722769
$109$	−5.81677	−0.557146	−0.278573	−	0.960415i	$-0.589861\pi$
$109$	−5.81677	−0.557146	−0.278573	+	0.960415i	$0.589861\pi$
$110$	−3.63950	−0.347013
$111$	−6.55140	−0.621832
$112$	0.419620	0.0396504
$113$	−12.6170	−1.18691	−0.593455	−	0.804867i	$-0.702237\pi$
$113$	−12.6170	−1.18691	−0.593455	+	0.804867i	$0.702237\pi$
$114$	−2.25003	−0.210734
$115$	5.09578	0.475184
$116$	4.03666	0.374794
$117$	0	0
$118$	−4.06627	−0.374330
$119$	6.69565	0.613789
$120$	−3.81975	−0.348694
$121$	8.71151	0.791955
$122$	−0.177272	−0.0160495
$123$	1.68071	0.151544
$124$	9.34869	0.839537
$125$	1.00000	0.0894427
$126$	−0.852241	−0.0759237
$127$	−16.8145	−1.49205	−0.746025	−	0.665918i	$-0.768040\pi$
$127$	−16.8145	−1.49205	−0.746025	+	0.665918i	$0.768040\pi$
$128$	−8.39076	−0.741646
$129$	2.29552	0.202109
$130$	0	0
$131$	4.50474	0.393581	0.196791	−	0.980446i	$-0.436948\pi$
$131$	4.50474	0.393581	0.196791	+	0.980446i	$0.436948\pi$
$132$	8.25523	0.718526
$133$	−1.96037	−0.169985
$134$	−8.37532	−0.723518
$135$	−5.65602	−0.486792
$136$	−18.2667	−1.56635
$137$	−0.278351	−0.0237811	−0.0118906	−	0.999929i	$-0.503785\pi$
$137$	−0.278351	−0.0237811	−0.0118906	+	0.999929i	$0.503785\pi$
$138$	5.84873	0.497877
$139$	20.0473	1.70039	0.850195	−	0.526467i	$-0.176484\pi$
$139$	20.0473	1.70039	0.850195	+	0.526467i	$0.176484\pi$
$140$	−1.32801	−0.112237
$141$	12.1196	1.02065
$142$	−9.33803	−0.783630
$143$	0	0
$144$	−0.436251	−0.0363543
$145$	−3.03963	−0.252428
$146$	−5.60648	−0.463995
$147$	1.40013	0.115481
$148$	6.21393	0.510782
$149$	4.37479	0.358396	0.179198	−	0.983813i	$-0.442650\pi$
$149$	4.37479	0.358396	0.179198	+	0.983813i	$0.442650\pi$
$150$	1.14776	0.0937141
$151$	11.9610	0.973374	0.486687	−	0.873576i	$-0.338205\pi$
$151$	11.9610	0.973374	0.486687	+	0.873576i	$0.338205\pi$
$152$	5.34815	0.433792
$153$	−6.96102	−0.562765
$154$	−3.63950	−0.293279
$155$	−7.03963	−0.565437
$156$	0	0
$157$	12.6472	1.00936	0.504678	−	0.863308i	$-0.331611\pi$
$157$	12.6472	1.00936	0.504678	+	0.863308i	$0.331611\pi$
$158$	1.31149	0.104337
$159$	−16.4541	−1.30489
$160$	5.80026	0.458551
$161$	5.09578	0.401604
$162$	−3.93502	−0.309164
$163$	−3.57740	−0.280204	−0.140102	−	0.990137i	$-0.544743\pi$
$163$	−3.57740	−0.280204	−0.140102	+	0.990137i	$0.544743\pi$
$164$	−1.59413	−0.124481
$165$	−6.21625	−0.483935
$166$	5.04251	0.391375
$167$	−10.2305	−0.791663	−0.395831	−	0.918323i	$-0.629544\pi$
$167$	−10.2305	−0.791663	−0.395831	+	0.918323i	$0.629544\pi$
$168$	−3.81975	−0.294700
$169$	0	0
$170$	5.48877	0.420969
$171$	2.03806	0.155855
$172$	−2.17727	−0.166015
$173$	−4.77714	−0.363199	−0.181600	−	0.983373i	$-0.558127\pi$
$173$	−4.77714	−0.363199	−0.181600	+	0.983373i	$0.558127\pi$
$174$	−3.48877	−0.264483
$175$	1.00000	0.0755929
$176$	−1.86302	−0.140430
$177$	−6.94516	−0.522030
$178$	−10.8346	−0.812086
$179$	−10.9119	−0.815594	−0.407797	−	0.913073i	$-0.633703\pi$
$179$	−10.9119	−0.815594	−0.407797	+	0.913073i	$0.633703\pi$
$180$	1.38064	0.102907
$181$	4.07927	0.303210	0.151605	−	0.988441i	$-0.451556\pi$
$181$	4.07927	0.303210	0.151605	+	0.988441i	$0.451556\pi$
$182$	0	0
$183$	−0.302780	−0.0223821
$184$	−13.9020	−1.02487
$185$	−4.67914	−0.344017
$186$	−8.07980	−0.592440
$187$	−29.7271	−2.17386
$188$	−11.4953	−0.838378
$189$	−5.65602	−0.411415
$190$	−1.60701	−0.116585
$191$	−18.5752	−1.34405	−0.672026	−	0.740527i	$-0.734576\pi$
$191$	−18.5752	−1.34405	−0.672026	+	0.740527i	$0.734576\pi$
$192$	5.48226	0.395648
$193$	−16.6567	−1.19897	−0.599487	−	0.800385i	$-0.704629\pi$
$193$	−16.6567	−1.19897	−0.599487	+	0.800385i	$0.704629\pi$
$194$	11.3380	0.814023
$195$	0	0
$196$	−1.32801	−0.0948577
$197$	−6.75840	−0.481516	−0.240758	−	0.970585i	$-0.577396\pi$
$197$	−6.75840	−0.481516	−0.240758	+	0.970585i	$0.577396\pi$
$198$	3.78375	0.268899
$199$	21.3263	1.51178	0.755891	−	0.654697i	$-0.227204\pi$
$199$	21.3263	1.51178	0.755891	+	0.654697i	$0.227204\pi$
$200$	−2.72814	−0.192909
$201$	−14.3050	−1.00900
$202$	−9.09578	−0.639977
$203$	−3.03963	−0.213340
$204$	−12.4498	−0.871660
$205$	1.20039	0.0838391
$206$	−10.8328	−0.754754
$207$	−5.29774	−0.368219
$208$	0	0
$209$	8.70357	0.602038
$210$	1.14776	0.0792029
$211$	−14.9912	−1.03203	−0.516017	−	0.856578i	$-0.672586\pi$
$211$	−14.9912	−1.03203	−0.516017	+	0.856578i	$0.672586\pi$
$212$	15.6065	1.07186
$213$	−15.9493	−1.09283
$214$	−13.3913	−0.915410
$215$	1.63950	0.111813
$216$	15.4304	1.04991
$217$	−7.03963	−0.477881
$218$	−4.76831	−0.322951
$219$	−9.57583	−0.647075
$220$	5.89604	0.397511
$221$	0	0
$222$	−5.37052	−0.360446
$223$	12.1526	0.813797	0.406899	−	0.913473i	$-0.366610\pi$
$223$	12.1526	0.813797	0.406899	+	0.913473i	$0.366610\pi$
$224$	5.80026	0.387546
$225$	−1.03963	−0.0693089
$226$	−10.3428	−0.687995
$227$	8.99777	0.597203	0.298602	−	0.954378i	$-0.403480\pi$
$227$	8.99777	0.597203	0.298602	+	0.954378i	$0.403480\pi$
$228$	3.64508	0.241401
$229$	−7.08810	−0.468395	−0.234197	−	0.972189i	$-0.575246\pi$
$229$	−7.08810	−0.468395	−0.234197	+	0.972189i	$0.575246\pi$
$230$	4.17727	0.275441
$231$	−6.21625	−0.408999
$232$	8.29254	0.544432
$233$	−14.4728	−0.948144	−0.474072	−	0.880486i	$-0.657216\pi$
$233$	−14.4728	−0.948144	−0.474072	+	0.880486i	$0.657216\pi$
$234$	0	0
$235$	8.65602	0.564656
$236$	6.58741	0.428804
$237$	2.24003	0.145505
$238$	5.48877	0.355784
$239$	17.2010	1.11264	0.556322	−	0.830967i	$-0.312212\pi$
$239$	17.2010	1.11264	0.556322	+	0.830967i	$0.312212\pi$
$240$	0.587523	0.0379245
$241$	−7.59987	−0.489551	−0.244775	−	0.969580i	$-0.578714\pi$
$241$	−7.59987	−0.489551	−0.244775	+	0.969580i	$0.578714\pi$
$242$	7.14127	0.459058
$243$	10.2471	0.657349
$244$	0.287183	0.0183850
$245$	1.00000	0.0638877
$246$	1.37776	0.0878429
$247$	0	0
$248$	19.2051	1.21952
$249$	8.61259	0.545800
$250$	0.819751	0.0518456
$251$	28.8938	1.82376	0.911881	−	0.410455i	$-0.134630\pi$
$251$	28.8938	1.82376	0.911881	+	0.410455i	$0.134630\pi$
$252$	1.38064	0.0869722
$253$	−22.6241	−1.42236
$254$	−13.7837	−0.864869
$255$	9.37479	0.587072
$256$	−14.7094	−0.919338
$257$	29.5036	1.84038	0.920192	−	0.391468i	$-0.128033\pi$
$257$	29.5036	1.84038	0.920192	+	0.391468i	$0.128033\pi$
$258$	1.88175	0.117153
$259$	−4.67914	−0.290747
$260$	0	0
$261$	3.16010	0.195606
$262$	3.69277	0.228140
$263$	−5.89473	−0.363485	−0.181742	−	0.983346i	$-0.558174\pi$
$263$	−5.89473	−0.363485	−0.181742	+	0.983346i	$0.558174\pi$
$264$	16.9588	1.04374
$265$	−11.7518	−0.721907
$266$	−1.60701	−0.0985323
$267$	−18.5054	−1.13251
$268$	13.5681	0.828805
$269$	−11.7188	−0.714506	−0.357253	−	0.934008i	$-0.616287\pi$
$269$	−11.7188	−0.714506	−0.357253	+	0.934008i	$0.616287\pi$
$270$	−4.63653	−0.282170
$271$	10.9905	0.667626	0.333813	−	0.942639i	$-0.391665\pi$
$271$	10.9905	0.667626	0.333813	+	0.942639i	$0.391665\pi$
$272$	2.80963	0.170359
$273$	0	0
$274$	−0.228178	−0.0137848
$275$	−4.43976	−0.267728
$276$	−9.47502	−0.570329
$277$	7.27901	0.437353	0.218677	−	0.975797i	$-0.429826\pi$
$277$	7.27901	0.437353	0.218677	+	0.975797i	$0.429826\pi$
$278$	16.4338	0.985635
$279$	7.31864	0.438155
$280$	−2.72814	−0.163037
$281$	−30.0473	−1.79247	−0.896236	−	0.443577i	$-0.853709\pi$
$281$	−30.0473	−1.79247	−0.896236	+	0.443577i	$0.853709\pi$
$282$	9.93502	0.591622
$283$	11.2477	0.668607	0.334303	−	0.942466i	$-0.391499\pi$
$283$	11.2477	0.668607	0.334303	+	0.942466i	$0.391499\pi$
$284$	15.1277	0.897666
$285$	−2.74477	−0.162586
$286$	0	0
$287$	1.20039	0.0708569
$288$	−6.03015	−0.355330
$289$	27.8317	1.63716
$290$	−2.49174	−0.146320
$291$	19.3653	1.13521
$292$	9.08257	0.531517
$293$	11.4233	0.667353	0.333677	−	0.942688i	$-0.391711\pi$
$293$	11.4233	0.667353	0.333677	+	0.942688i	$0.391711\pi$
$294$	1.14776	0.0669387
$295$	−4.96037	−0.288804
$296$	12.7653	0.741970
$297$	25.1114	1.45711
$298$	3.58624	0.207745
$299$	0	0
$300$	−1.85938	−0.107352
$301$	1.63950	0.0944994
$302$	9.80506	0.564218
$303$	−15.5355	−0.892494
$304$	−0.822610	−0.0471799
$305$	−0.216251	−0.0123825
$306$	−5.70631	−0.326208
$307$	17.4576	0.996357	0.498179	−	0.867074i	$-0.334002\pi$
$307$	17.4576	0.996357	0.498179	+	0.867074i	$0.334002\pi$
$308$	5.89604	0.335958
$309$	−18.5023	−1.05256
$310$	−5.77075	−0.327756
$311$	−9.39130	−0.532532	−0.266266	−	0.963900i	$-0.585790\pi$
$311$	−9.39130	−0.532532	−0.266266	+	0.963900i	$0.585790\pi$
$312$	0	0
$313$	2.31161	0.130660	0.0653300	−	0.997864i	$-0.479190\pi$
$313$	2.31161	0.130660	0.0653300	+	0.997864i	$0.479190\pi$
$314$	10.3675	0.585074
$315$	−1.03963	−0.0585767
$316$	−2.12464	−0.119520
$317$	30.0286	1.68657	0.843286	−	0.537464i	$-0.180618\pi$
$317$	30.0286	1.68657	0.843286	+	0.537464i	$0.180618\pi$
$318$	−13.4882	−0.756382
$319$	13.4953	0.755589
$320$	3.91553	0.218885
$321$	−22.8723	−1.27661
$322$	4.17727	0.232790
$323$	−13.1259	−0.730346
$324$	6.37479	0.354155
$325$	0	0
$326$	−2.93258	−0.162421
$327$	−8.14425	−0.450378
$328$	−3.27484	−0.180823
$329$	8.65602	0.477222
$330$	−5.09578	−0.280513
$331$	23.2543	1.27817	0.639086	−	0.769135i	$-0.279313\pi$
$331$	23.2543	1.27817	0.639086	+	0.769135i	$0.279313\pi$
$332$	−8.16894	−0.448329
$333$	4.86459	0.266578
$334$	−8.38650	−0.458889
$335$	−10.2169	−0.558209
$336$	0.587523	0.0320520
$337$	−14.3831	−0.783498	−0.391749	−	0.920072i	$-0.628130\pi$
$337$	−14.3831	−0.783498	−0.391749	+	0.920072i	$0.628130\pi$
$338$	0	0
$339$	−17.6655	−0.959458
$340$	−8.89187	−0.482230
$341$	31.2543	1.69252
$342$	1.67070	0.0903414
$343$	1.00000	0.0539949
$344$	−4.47279	−0.241157
$345$	7.13476	0.384123
$346$	−3.91607	−0.210529
$347$	25.6941	1.37933	0.689665	−	0.724128i	$-0.257758\pi$
$347$	25.6941	1.37933	0.689665	+	0.724128i	$0.257758\pi$
$348$	5.65185	0.302971
$349$	−22.4629	−1.20241	−0.601205	−	0.799095i	$-0.705313\pi$
$349$	−22.4629	−1.20241	−0.601205	+	0.799095i	$0.705313\pi$
$350$	0.819751	0.0438175
$351$	0	0
$352$	−25.7518	−1.37258
$353$	5.04251	0.268386	0.134193	−	0.990955i	$-0.457156\pi$
$353$	5.04251	0.268386	0.134193	+	0.990955i	$0.457156\pi$
$354$	−5.69331	−0.302596
$355$	−11.3913	−0.604587
$356$	17.5522	0.930262
$357$	9.37479	0.496166
$358$	−8.94504	−0.472760
$359$	35.6881	1.88355	0.941774	−	0.336248i	$-0.109158\pi$
$359$	35.6881	1.88355	0.941774	+	0.336248i	$0.109158\pi$
$360$	2.83626	0.149484
$361$	−15.1570	−0.797735
$362$	3.34398	0.175756
$363$	12.1973	0.640190
$364$	0	0
$365$	−6.83924	−0.357982
$366$	−0.248204	−0.0129738
$367$	−3.56750	−0.186222	−0.0931109	−	0.995656i	$-0.529681\pi$
$367$	−3.56750	−0.186222	−0.0931109	+	0.995656i	$0.529681\pi$
$368$	2.13829	0.111466
$369$	−1.24797	−0.0649666
$370$	−3.83573	−0.199410
$371$	−11.7518	−0.610123
$372$	13.0894	0.678653
$373$	−12.7023	−0.657698	−0.328849	−	0.944383i	$-0.606661\pi$
$373$	−12.7023	−0.657698	−0.328849	+	0.944383i	$0.606661\pi$
$374$	−24.3688	−1.26008
$375$	1.40013	0.0723024
$376$	−23.6148	−1.21784
$377$	0	0
$378$	−4.63653	−0.238477
$379$	29.6335	1.52217	0.761087	−	0.648650i	$-0.224666\pi$
$379$	29.6335	1.52217	0.761087	+	0.648650i	$0.224666\pi$
$380$	2.60338	0.133551
$381$	−23.5426	−1.20612
$382$	−15.2270	−0.779082
$383$	26.4008	1.34902	0.674509	−	0.738267i	$-0.264356\pi$
$383$	26.4008	1.34902	0.674509	+	0.738267i	$0.264356\pi$
$384$	−11.7482	−0.599521
$385$	−4.43976	−0.226271
$386$	−13.6543	−0.694987
$387$	−1.70448	−0.0866437
$388$	−18.3678	−0.932482
$389$	−18.5184	−0.938919	−0.469459	−	0.882954i	$-0.655551\pi$
$389$	−18.5184	−0.938919	−0.469459	+	0.882954i	$0.655551\pi$
$390$	0	0
$391$	34.1196	1.72550
$392$	−2.72814	−0.137792
$393$	6.30723	0.318158
$394$	−5.54021	−0.279112
$395$	1.59987	0.0804982
$396$	−6.12972	−0.308030
$397$	−35.6551	−1.78948	−0.894739	−	0.446589i	$-0.852639\pi$
$397$	−35.6551	−1.78948	−0.894739	+	0.446589i	$0.852639\pi$
$398$	17.4823	0.876307
$399$	−2.74477	−0.137410
$400$	0.419620	0.0209810
$401$	24.6053	1.22873	0.614366	−	0.789021i	$-0.289412\pi$
$401$	24.6053	1.22873	0.614366	+	0.789021i	$0.289412\pi$
$402$	−11.7265	−0.584867
$403$	0	0
$404$	14.7353	0.733108
$405$	−4.80026	−0.238527
$406$	−2.49174	−0.123663
$407$	20.7743	1.02974
$408$	−25.5757	−1.26619
$409$	19.9031	0.984143	0.492072	−	0.870555i	$-0.336240\pi$
$409$	19.9031	0.984143	0.492072	+	0.870555i	$0.336240\pi$
$410$	0.984023	0.0485975
$411$	−0.389727	−0.0192238
$412$	17.5492	0.864587
$413$	−4.96037	−0.244084
$414$	−4.34283	−0.213439
$415$	6.15127	0.301954
$416$	0	0
$417$	28.0689	1.37454
$418$	7.13476	0.348972
$419$	−11.9940	−0.585948	−0.292974	−	0.956120i	$-0.594645\pi$
$419$	−11.9940	−0.585948	−0.292974	+	0.956120i	$0.594645\pi$
$420$	−1.85938	−0.0907287
$421$	−9.47502	−0.461784	−0.230892	−	0.972979i	$-0.574164\pi$
$421$	−9.47502	−0.461784	−0.230892	+	0.972979i	$0.574164\pi$
$422$	−12.2890	−0.598221
$423$	−8.99908	−0.437550
$424$	32.0605	1.55700
$425$	6.69565	0.324787
$426$	−13.0745	−0.633460
$427$	−0.216251	−0.0104651
$428$	21.6941	1.04862
$429$	0	0
$430$	1.34398	0.0648127
$431$	−31.4849	−1.51657	−0.758286	−	0.651922i	$-0.773963\pi$
$431$	−31.4849	−1.51657	−0.758286	+	0.651922i	$0.773963\pi$
$432$	−2.37338	−0.114189
$433$	−0.741890	−0.0356530	−0.0178265	−	0.999841i	$-0.505675\pi$
$433$	−0.741890	−0.0356530	−0.0178265	+	0.999841i	$0.505675\pi$
$434$	−5.77075	−0.277005
$435$	−4.25588	−0.204054
$436$	7.72472	0.369947
$437$	−9.98960	−0.477867
$438$	−7.84980	−0.375078
$439$	29.1574	1.39161	0.695803	−	0.718233i	$-0.255049\pi$
$439$	29.1574	1.39161	0.695803	+	0.718233i	$0.255049\pi$
$440$	12.1123	0.577431
$441$	−1.03963	−0.0495064
$442$	0	0
$443$	−39.1893	−1.86194	−0.930971	−	0.365094i	$-0.881037\pi$
$443$	−39.1893	−1.86194	−0.930971	+	0.365094i	$0.881037\pi$
$444$	8.70031	0.412899
$445$	−13.2169	−0.626541
$446$	9.96209	0.471719
$447$	6.12527	0.289715
$448$	3.91553	0.184991
$449$	−21.7331	−1.02565	−0.512823	−	0.858494i	$-0.671400\pi$
$449$	−21.7331	−1.02565	−0.512823	+	0.858494i	$0.671400\pi$
$450$	−0.852241	−0.0401750
$451$	−5.32946	−0.250955
$452$	16.7555	0.788114
$453$	16.7470	0.786842
$454$	7.37594	0.346170
$455$	0	0
$456$	7.48811	0.350663
$457$	−21.1579	−0.989724	−0.494862	−	0.868972i	$-0.664781\pi$
$457$	−21.1579	−0.989724	−0.494862	+	0.868972i	$0.664781\pi$
$458$	−5.81048	−0.271506
$459$	−37.8707	−1.76765
$460$	−6.76724	−0.315524
$461$	−16.4122	−0.764392	−0.382196	−	0.924081i	$-0.624832\pi$
$461$	−16.4122	−0.764392	−0.382196	+	0.924081i	$0.624832\pi$
$462$	−5.09578	−0.237077
$463$	−7.09643	−0.329799	−0.164900	−	0.986310i	$-0.552730\pi$
$463$	−7.09643	−0.329799	−0.164900	+	0.986310i	$0.552730\pi$
$464$	−1.27549	−0.0592132
$465$	−9.85641	−0.457080
$466$	−11.8641	−0.549593
$467$	−6.86590	−0.317716	−0.158858	−	0.987301i	$-0.550781\pi$
$467$	−6.86590	−0.317716	−0.158858	+	0.987301i	$0.550781\pi$
$468$	0	0
$469$	−10.2169	−0.471773
$470$	7.09578	0.327304
$471$	17.7077	0.815928
$472$	13.5326	0.622887
$473$	−7.27901	−0.334689
$474$	1.83626	0.0843424
$475$	−1.96037	−0.0899478
$476$	−8.89187	−0.407558
$477$	12.2176	0.559404
$478$	14.1006	0.644946
$479$	16.8304	0.769001	0.384500	−	0.923125i	$-0.374374\pi$
$479$	16.8304	0.769001	0.384500	+	0.923125i	$0.374374\pi$
$480$	8.12113	0.370677
$481$	0	0
$482$	−6.23000	−0.283769
$483$	7.13476	0.324643
$484$	−11.5690	−0.525861
$485$	13.8311	0.628036
$486$	8.40003	0.381033
$487$	−7.97243	−0.361265	−0.180633	−	0.983551i	$-0.557815\pi$
$487$	−7.97243	−0.361265	−0.180633	+	0.983551i	$0.557815\pi$
$488$	0.589963	0.0267064
$489$	−5.00883	−0.226507
$490$	0.819751	0.0370326
$491$	13.8370	0.624456	0.312228	−	0.950007i	$-0.398925\pi$
$491$	13.8370	0.624456	0.312228	+	0.950007i	$0.398925\pi$
$492$	−2.23199	−0.100626
$493$	−20.3523	−0.916622
$494$	0	0
$495$	4.61573	0.207462
$496$	−2.95397	−0.132637
$497$	−11.3913	−0.510970
$498$	7.06018	0.316374
$499$	35.5428	1.59111	0.795557	−	0.605878i	$-0.207178\pi$
$499$	35.5428	1.59111	0.795557	+	0.605878i	$0.207178\pi$
$500$	−1.32801	−0.0593903
$501$	−14.3241	−0.639953
$502$	23.6857	1.05715
$503$	−22.1136	−0.985997	−0.492998	−	0.870030i	$-0.664099\pi$
$503$	−22.1136	−0.985997	−0.492998	+	0.870030i	$0.664099\pi$
$504$	2.83626	0.126337
$505$	−11.0958	−0.493756
$506$	−18.5461	−0.824475
$507$	0	0
$508$	22.3299	0.990727
$509$	27.5505	1.22115	0.610577	−	0.791957i	$-0.290938\pi$
$509$	27.5505	1.22115	0.610577	+	0.791957i	$0.290938\pi$
$510$	7.68499	0.340297
$511$	−6.83924	−0.302550
$512$	4.72347	0.208750
$513$	11.0879	0.489541
$514$	24.1856	1.06678
$515$	−13.2147	−0.582308
$516$	−3.04847	−0.134201
$517$	−38.4307	−1.69018
$518$	−3.83573	−0.168532
$519$	−6.68862	−0.293598
$520$	0	0
$521$	37.7804	1.65519	0.827594	−	0.561327i	$-0.189709\pi$
$521$	37.7804	1.65519	0.827594	+	0.561327i	$0.189709\pi$
$522$	2.59050	0.113383
$523$	−40.5417	−1.77276	−0.886381	−	0.462956i	$-0.846789\pi$
$523$	−40.5417	−1.77276	−0.886381	+	0.462956i	$0.846789\pi$
$524$	−5.98233	−0.261340
$525$	1.40013	0.0611067
$526$	−4.83221	−0.210695
$527$	−47.1349	−2.05323
$528$	−2.60847	−0.113519
$529$	2.96697	0.128999
$530$	−9.63355	−0.418455
$531$	5.15696	0.223793
$532$	2.60338	0.112871
$533$	0	0
$534$	−15.1698	−0.656462
$535$	−16.3358	−0.706258
$536$	27.8731	1.20394
$537$	−15.2781	−0.659298
$538$	−9.60648	−0.414165
$539$	−4.43976	−0.191234
$540$	7.51123	0.323232
$541$	−26.6243	−1.14467	−0.572334	−	0.820021i	$-0.693962\pi$
$541$	−26.6243	−1.14467	−0.572334	+	0.820021i	$0.693962\pi$
$542$	9.00949	0.386991
$543$	5.71151	0.245104
$544$	38.8365	1.66510
$545$	−5.81677	−0.249163
$546$	0	0
$547$	−8.55801	−0.365914	−0.182957	−	0.983121i	$-0.558567\pi$
$547$	−8.55801	−0.365914	−0.182957	+	0.983121i	$0.558567\pi$
$548$	0.369652	0.0157907
$549$	0.224822	0.00959517
$550$	−3.63950	−0.155189
$551$	5.95880	0.253853
$552$	−19.4646	−0.828469
$553$	1.59987	0.0680334
$554$	5.96697	0.253512
$555$	−6.55140	−0.278092
$556$	−26.6230	−1.12907
$557$	35.1640	1.48995	0.744973	−	0.667095i	$-0.232462\pi$
$557$	35.1640	1.48995	0.744973	+	0.667095i	$0.232462\pi$
$558$	5.99946	0.253978
$559$	0	0
$560$	0.419620	0.0177322
$561$	−41.6218	−1.75728
$562$	−24.6313	−1.03901
$563$	3.58689	0.151169	0.0755847	−	0.997139i	$-0.475918\pi$
$563$	3.58689	0.151169	0.0755847	+	0.997139i	$0.475918\pi$
$564$	−16.0949	−0.677716
$565$	−12.6170	−0.530803
$566$	9.22032	0.387559
$567$	−4.80026	−0.201592
$568$	31.0770	1.30396
$569$	34.9903	1.46687	0.733434	−	0.679761i	$-0.237916\pi$
$569$	34.9903	1.46687	0.733434	+	0.679761i	$0.237916\pi$
$570$	−2.25003	−0.0942433
$571$	−34.4915	−1.44342	−0.721711	−	0.692194i	$-0.756644\pi$
$571$	−34.4915	−1.44342	−0.721711	+	0.692194i	$0.756644\pi$
$572$	0	0
$573$	−26.0077	−1.08649
$574$	0.984023	0.0410723
$575$	5.09578	0.212509
$576$	−4.07072	−0.169613
$577$	−5.16076	−0.214845	−0.107423	−	0.994213i	$-0.534260\pi$
$577$	−5.16076	−0.214845	−0.107423	+	0.994213i	$0.534260\pi$
$578$	22.8151	0.948982
$579$	−23.3215	−0.969209
$580$	4.03666	0.167613
$581$	6.15127	0.255198
$582$	15.8747	0.658029
$583$	52.1752	2.16088
$584$	18.6584	0.772090
$585$	0	0
$586$	9.36423	0.386833
$587$	4.02600	0.166171	0.0830854	−	0.996542i	$-0.473523\pi$
$587$	4.02600	0.166171	0.0830854	+	0.996542i	$0.473523\pi$
$588$	−1.85938	−0.0766797
$589$	13.8003	0.568630
$590$	−4.06627	−0.167406
$591$	−9.46265	−0.389241
$592$	−1.96346	−0.0806977
$593$	−0.190487	−0.00782236	−0.00391118	−	0.999992i	$-0.501245\pi$
$593$	−0.190487	−0.00782236	−0.00391118	+	0.999992i	$0.501245\pi$
$594$	20.5851	0.844616
$595$	6.69565	0.274495
$596$	−5.80975	−0.237977
$597$	29.8596	1.22207
$598$	0	0
$599$	18.0330	0.736809	0.368405	−	0.929666i	$-0.379904\pi$
$599$	18.0330	0.736809	0.368405	+	0.929666i	$0.379904\pi$
$600$	−3.81975	−0.155941
$601$	10.1196	0.412785	0.206393	−	0.978469i	$-0.433828\pi$
$601$	10.1196	0.412785	0.206393	+	0.978469i	$0.433828\pi$
$602$	1.34398	0.0547767
$603$	10.6218	0.432555
$604$	−15.8843	−0.646324
$605$	8.71151	0.354173
$606$	−12.7353	−0.517335
$607$	−18.9830	−0.770496	−0.385248	−	0.922813i	$-0.625884\pi$
$607$	−18.9830	−0.770496	−0.385248	+	0.922813i	$0.625884\pi$
$608$	−11.3706	−0.461140
$609$	−4.25588	−0.172457
$610$	−0.177272	−0.00717754
$611$	0	0
$612$	9.24429	0.373678
$613$	−18.6690	−0.754034	−0.377017	−	0.926206i	$-0.623050\pi$
$613$	−18.6690	−0.754034	−0.377017	+	0.926206i	$0.623050\pi$
$614$	14.3109	0.577540
$615$	1.68071	0.0677726
$616$	12.1123	0.488018
$617$	−26.3505	−1.06083	−0.530416	−	0.847738i	$-0.677964\pi$
$617$	−26.3505	−1.06083	−0.530416	+	0.847738i	$0.677964\pi$
$618$	−15.1673	−0.610117
$619$	15.8412	0.636712	0.318356	−	0.947971i	$-0.396869\pi$
$619$	15.8412	0.636712	0.318356	+	0.947971i	$0.396869\pi$
$620$	9.34869	0.375452
$621$	−28.8218	−1.15658
$622$	−7.69853	−0.308683
$623$	−13.2169	−0.529524
$624$	0	0
$625$	1.00000	0.0400000
$626$	1.89495	0.0757373
$627$	12.1861	0.486667
$628$	−16.7956	−0.670216
$629$	−31.3299	−1.24920
$630$	−0.852241	−0.0339541
$631$	25.6406	1.02074	0.510368	−	0.859956i	$-0.329509\pi$
$631$	25.6406	1.02074	0.510368	+	0.859956i	$0.329509\pi$
$632$	−4.36466	−0.173617
$633$	−20.9896	−0.834262
$634$	24.6160	0.977625
$635$	−16.8145	−0.667265
$636$	21.8511	0.866453
$637$	0	0
$638$	11.0628	0.437979
$639$	11.8428	0.468493
$640$	−8.39076	−0.331674
$641$	−37.1850	−1.46872	−0.734359	−	0.678762i	$-0.762517\pi$
$641$	−37.1850	−1.46872	−0.734359	+	0.678762i	$0.762517\pi$
$642$	−18.7496	−0.739987
$643$	6.52498	0.257320	0.128660	−	0.991689i	$-0.458932\pi$
$643$	6.52498	0.257320	0.128660	+	0.991689i	$0.458932\pi$
$644$	−6.76724	−0.266666
$645$	2.29552	0.0903859
$646$	−10.7600	−0.423346
$647$	−14.2334	−0.559573	−0.279787	−	0.960062i	$-0.590264\pi$
$647$	−14.2334	−0.559573	−0.279787	+	0.960062i	$0.590264\pi$
$648$	13.0958	0.514451
$649$	22.0229	0.864473
$650$	0	0
$651$	−9.85641	−0.386303
$652$	4.75082	0.186056
$653$	−6.86079	−0.268483	−0.134242	−	0.990949i	$-0.542860\pi$
$653$	−6.86079	−0.268483	−0.134242	+	0.990949i	$0.542860\pi$
$654$	−6.67626	−0.261062
$655$	4.50474	0.176015
$656$	0.503709	0.0196665
$657$	7.11030	0.277399
$658$	7.09578	0.276622
$659$	−36.0953	−1.40607	−0.703036	−	0.711154i	$-0.748173\pi$
$659$	−36.0953	−1.40607	−0.703036	+	0.711154i	$0.748173\pi$
$660$	8.25523	0.321334
$661$	−28.3869	−1.10412	−0.552062	−	0.833803i	$-0.686159\pi$
$661$	−28.3869	−1.10412	−0.552062	+	0.833803i	$0.686159\pi$
$662$	19.0628	0.740895
$663$	0	0
$664$	−16.7815	−0.651249
$665$	−1.96037	−0.0760198
$666$	3.98775	0.154522
$667$	−15.4893	−0.599748
$668$	13.5862	0.525667
$669$	17.0152	0.657846
$670$	−8.37532	−0.323567
$671$	0.960105	0.0370644
$672$	8.12113	0.313279
$673$	39.7993	1.53415	0.767076	−	0.641556i	$-0.221711\pi$
$673$	39.7993	1.53415	0.767076	+	0.641556i	$0.221711\pi$
$674$	−11.7906	−0.454156
$675$	−5.65602	−0.217700
$676$	0	0
$677$	−43.2626	−1.66272	−0.831359	−	0.555735i	$-0.812437\pi$
$677$	−43.2626	−1.66272	−0.831359	+	0.555735i	$0.812437\pi$
$678$	−14.4813	−0.556152
$679$	13.8311	0.530787
$680$	−18.2667	−0.700494
$681$	12.5981	0.482759
$682$	25.6208	0.981070
$683$	2.29617	0.0878606	0.0439303	−	0.999035i	$-0.486012\pi$
$683$	2.29617	0.0878606	0.0439303	+	0.999035i	$0.486012\pi$
$684$	−2.70656	−0.103488
$685$	−0.278351	−0.0106352
$686$	0.819751	0.0312982
$687$	−9.92427	−0.378634
$688$	0.687969	0.0262286
$689$	0	0
$690$	5.84873	0.222657
$691$	−5.63512	−0.214370	−0.107185	−	0.994239i	$-0.534184\pi$
$691$	−5.63512	−0.214370	−0.107185	+	0.994239i	$0.534184\pi$
$692$	6.34408	0.241166
$693$	4.61573	0.175337
$694$	21.0628	0.799531
$695$	20.0473	0.760438
$696$	11.6106	0.440100
$697$	8.03741	0.304439
$698$	−18.4140	−0.696979
$699$	−20.2638	−0.766447
$700$	−1.32801	−0.0501940
$701$	11.8018	0.445749	0.222875	−	0.974847i	$-0.428456\pi$
$701$	11.8018	0.445749	0.222875	+	0.974847i	$0.428456\pi$
$702$	0	0
$703$	9.17282	0.345960
$704$	−17.3840	−0.655186
$705$	12.1196	0.456449
$706$	4.13361	0.155570
$707$	−11.0958	−0.417300
$708$	9.22323	0.346630
$709$	33.2626	1.24920	0.624602	−	0.780943i	$-0.285261\pi$
$709$	33.2626	1.24920	0.624602	+	0.780943i	$0.285261\pi$
$710$	−9.33803	−0.350450
$711$	−1.66328	−0.0623778
$712$	36.0576	1.35131
$713$	−35.8724	−1.34343
$714$	7.68499	0.287604
$715$	0	0
$716$	14.4911	0.541557
$717$	24.0837	0.899423
$718$	29.2554	1.09180
$719$	21.8685	0.815559	0.407779	−	0.913080i	$-0.366303\pi$
$719$	21.8685	0.815559	0.407779	+	0.913080i	$0.366303\pi$
$720$	−0.436251	−0.0162581
$721$	−13.2147	−0.492140
$722$	−12.4249	−0.462408
$723$	−10.6408	−0.395736
$724$	−5.41730	−0.201332
$725$	−3.03963	−0.112889
$726$	9.99871	0.371087
$727$	31.9405	1.18461	0.592303	−	0.805715i	$-0.298219\pi$
$727$	31.9405	1.18461	0.592303	+	0.805715i	$0.298219\pi$
$728$	0	0
$729$	28.7480	1.06474
$730$	−5.60648	−0.207505
$731$	10.9775	0.406019
$732$	0.402094	0.0148618
$733$	28.1669	1.04037	0.520184	−	0.854055i	$-0.325864\pi$
$733$	28.1669	1.04037	0.520184	+	0.854055i	$0.325864\pi$
$734$	−2.92446	−0.107944
$735$	1.40013	0.0516446
$736$	29.5569	1.08948
$737$	45.3607	1.67088
$738$	−1.02302	−0.0376580
$739$	−5.01544	−0.184496	−0.0922480	−	0.995736i	$-0.529405\pi$
$739$	−5.01544	−0.184496	−0.0922480	+	0.995736i	$0.529405\pi$
$740$	6.21393	0.228429
$741$	0	0
$742$	−9.63355	−0.353659
$743$	−48.6331	−1.78417	−0.892087	−	0.451864i	$-0.850759\pi$
$743$	−48.6331	−1.78417	−0.892087	+	0.451864i	$0.850759\pi$
$744$	26.8896	0.985822
$745$	4.37479	0.160280
$746$	−10.4127	−0.381236
$747$	−6.39507	−0.233983
$748$	39.4778	1.44345
$749$	−16.3358	−0.596897
$750$	1.14776	0.0419102
$751$	−38.3990	−1.40120	−0.700599	−	0.713555i	$-0.747084\pi$
$751$	−38.3990	−1.40120	−0.700599	+	0.713555i	$0.747084\pi$
$752$	3.63224	0.132454
$753$	40.4551	1.47427
$754$	0	0
$755$	11.9610	0.435306
$756$	7.51123	0.273181
$757$	−13.3770	−0.486196	−0.243098	−	0.970002i	$-0.578164\pi$
$757$	−13.3770	−0.486196	−0.243098	+	0.970002i	$0.578164\pi$
$758$	24.2921	0.882330
$759$	−31.6766	−1.14979
$760$	5.34815	0.193998
$761$	16.3197	0.591589	0.295795	−	0.955252i	$-0.404416\pi$
$761$	16.3197	0.591589	0.295795	+	0.955252i	$0.404416\pi$
$762$	−19.2991	−0.699131
$763$	−5.81677	−0.210581
$764$	24.6680	0.892456
$765$	−6.96102	−0.251676
$766$	21.6421	0.781960
$767$	0	0
$768$	−20.5951	−0.743161
$769$	−46.7377	−1.68540	−0.842702	−	0.538381i	$-0.819036\pi$
$769$	−46.7377	−1.68540	−0.842702	+	0.538381i	$0.819036\pi$
$770$	−3.63950	−0.131159
$771$	41.3089	1.48770
$772$	22.1202	0.796123
$773$	19.6078	0.705243	0.352622	−	0.935766i	$-0.385290\pi$
$773$	19.6078	0.705243	0.352622	+	0.935766i	$0.385290\pi$
$774$	−1.39725	−0.0502232
$775$	−7.03963	−0.252871
$776$	−37.7331	−1.35454
$777$	−6.55140	−0.235030
$778$	−15.1805	−0.544246
$779$	−2.35321	−0.0843125
$780$	0	0
$781$	50.5747	1.80970
$782$	27.9695	1.00019
$783$	17.1922	0.614400
$784$	0.419620	0.0149864
$785$	12.6472	0.451397
$786$	5.17036	0.184421
$787$	6.03303	0.215054	0.107527	−	0.994202i	$-0.465707\pi$
$787$	6.03303	0.215054	0.107527	+	0.994202i	$0.465707\pi$
$788$	8.97521	0.319729
$789$	−8.25340	−0.293829
$790$	1.31149	0.0466609
$791$	−12.6170	−0.448610
$792$	−12.5923	−0.447450
$793$	0	0
$794$	−29.2283	−1.03727
$795$	−16.4541	−0.583565
$796$	−28.3215	−1.00383
$797$	20.3732	0.721656	0.360828	−	0.932632i	$-0.382494\pi$
$797$	20.3732	0.721656	0.360828	+	0.932632i	$0.382494\pi$
$798$	−2.25003	−0.0796501
$799$	57.9576	2.05039
$800$	5.80026	0.205070
$801$	13.7407	0.485505
$802$	20.1702	0.712236
$803$	30.3646	1.07154
$804$	18.9972	0.669978
$805$	5.09578	0.179603
$806$	0	0
$807$	−16.4078	−0.577582
$808$	30.2708	1.06492
$809$	24.9984	0.878898	0.439449	−	0.898268i	$-0.355174\pi$
$809$	24.9984	0.878898	0.439449	+	0.898268i	$0.355174\pi$
$810$	−3.93502	−0.138263
$811$	−33.1041	−1.16244	−0.581221	−	0.813746i	$-0.697425\pi$
$811$	−33.1041	−1.16244	−0.581221	+	0.813746i	$0.697425\pi$
$812$	4.03666	0.141659
$813$	15.3882	0.539686
$814$	17.0297	0.596892
$815$	−3.57740	−0.125311
$816$	3.93385	0.137712
$817$	−3.21403	−0.112445
$818$	16.3156	0.570460
$819$	0	0
$820$	−1.59413	−0.0556695
$821$	−34.5476	−1.20572	−0.602860	−	0.797847i	$-0.705972\pi$
$821$	−34.5476	−1.20572	−0.602860	+	0.797847i	$0.705972\pi$
$822$	−0.319480	−0.0111431
$823$	−49.6364	−1.73021	−0.865107	−	0.501587i	$-0.832750\pi$
$823$	−49.6364	−1.73021	−0.865107	+	0.501587i	$0.832750\pi$
$824$	36.0515	1.25591
$825$	−6.21625	−0.216422
$826$	−4.06627	−0.141484
$827$	5.03806	0.175191	0.0875953	−	0.996156i	$-0.472082\pi$
$827$	5.03806	0.175191	0.0875953	+	0.996156i	$0.472082\pi$
$828$	7.03544	0.244499
$829$	9.75906	0.338946	0.169473	−	0.985535i	$-0.445793\pi$
$829$	9.75906	0.338946	0.169473	+	0.985535i	$0.445793\pi$
$830$	5.04251	0.175028
$831$	10.1916	0.353541
$832$	0	0
$833$	6.69565	0.231990
$834$	23.0095	0.796753
$835$	−10.2305	−0.354042
$836$	−11.5584	−0.399756
$837$	39.8163	1.37625
$838$	−9.83214	−0.339645
$839$	36.9742	1.27649	0.638245	−	0.769833i	$-0.279661\pi$
$839$	36.9742	1.27649	0.638245	+	0.769833i	$0.279661\pi$
$840$	−3.81975	−0.131794
$841$	−19.7606	−0.681401
$842$	−7.76716	−0.267674
$843$	−42.0702	−1.44897
$844$	19.9084	0.685275
$845$	0	0
$846$	−7.37701	−0.253627
$847$	8.71151	0.299331
$848$	−4.93129	−0.169341
$849$	15.7483	0.540479
$850$	5.48877	0.188263
$851$	−23.8438	−0.817357
$852$	21.1808	0.725642
$853$	−41.6491	−1.42604	−0.713020	−	0.701144i	$-0.752673\pi$
$853$	−41.6491	−1.42604	−0.713020	+	0.701144i	$0.752673\pi$
$854$	−0.177272	−0.00606613
$855$	2.03806	0.0697003
$856$	44.5663	1.52325
$857$	−38.9629	−1.33095	−0.665474	−	0.746421i	$-0.731771\pi$
$857$	−38.9629	−1.33095	−0.665474	+	0.746421i	$0.731771\pi$
$858$	0	0
$859$	12.0345	0.410613	0.205306	−	0.978698i	$-0.434181\pi$
$859$	12.0345	0.410613	0.205306	+	0.978698i	$0.434181\pi$
$860$	−2.17727	−0.0742444
$861$	1.68071	0.0572783
$862$	−25.8097	−0.879084
$863$	26.0209	0.885762	0.442881	−	0.896581i	$-0.353956\pi$
$863$	26.0209	0.885762	0.442881	+	0.896581i	$0.353956\pi$
$864$	−32.8064	−1.11610
$865$	−4.77714	−0.162428
$866$	−0.608165	−0.0206663
$867$	38.9680	1.32342
$868$	9.34869	0.317315
$869$	−7.10304	−0.240954
$870$	−3.48877	−0.118280
$871$	0	0
$872$	15.8690	0.537391
$873$	−14.3792	−0.486663
$874$	−8.18898	−0.276997
$875$	1.00000	0.0338062
$876$	12.7168	0.429660
$877$	44.6567	1.50795	0.753974	−	0.656904i	$-0.228134\pi$
$877$	44.6567	1.50795	0.753974	+	0.656904i	$0.228134\pi$
$878$	23.9018	0.806647
$879$	15.9940	0.539466
$880$	−1.86302	−0.0628022
$881$	−12.6417	−0.425911	−0.212955	−	0.977062i	$-0.568309\pi$
$881$	−12.6417	−0.425911	−0.212955	+	0.977062i	$0.568309\pi$
$882$	−0.852241	−0.0286964
$883$	−19.0498	−0.641076	−0.320538	−	0.947236i	$-0.603864\pi$
$883$	−19.0498	−0.641076	−0.320538	+	0.947236i	$0.603864\pi$
$884$	0	0
$885$	−6.94516	−0.233459
$886$	−32.1255	−1.07928
$887$	47.4477	1.59314	0.796569	−	0.604548i	$-0.206646\pi$
$887$	47.4477	1.59314	0.796569	+	0.604548i	$0.206646\pi$
$888$	17.8731	0.599783
$889$	−16.8145	−0.563942
$890$	−10.8346	−0.363176
$891$	21.3120	0.713980
$892$	−16.1387	−0.540364
$893$	−16.9690	−0.567845
$894$	5.02120	0.167934
$895$	−10.9119	−0.364745
$896$	−8.39076	−0.280316
$897$	0	0
$898$	−17.8157	−0.594518
$899$	21.3979	0.713660
$900$	1.38064	0.0460214
$901$	−78.6859	−2.62141
$902$	−4.36883	−0.145466
$903$	2.29552	0.0763901
$904$	34.4210	1.14483
$905$	4.07927	0.135599
$906$	13.7284	0.456095
$907$	5.18545	0.172180	0.0860900	−	0.996287i	$-0.472563\pi$
$907$	5.18545	0.172180	0.0860900	+	0.996287i	$0.472563\pi$
$908$	−11.9491	−0.396545
$909$	11.5355	0.382610
$910$	0	0
$911$	37.9817	1.25839	0.629195	−	0.777248i	$-0.283385\pi$
$911$	37.9817	1.25839	0.629195	+	0.777248i	$0.283385\pi$
$912$	−1.15176	−0.0381386
$913$	−27.3102	−0.903836
$914$	−17.3442	−0.573695
$915$	−0.302780	−0.0100096
$916$	9.41305	0.311016
$917$	4.50474	0.148760
$918$	−31.0446	−1.02462
$919$	21.7705	0.718141	0.359071	−	0.933310i	$-0.383094\pi$
$919$	21.7705	0.718141	0.359071	+	0.933310i	$0.383094\pi$
$920$	−13.9020	−0.458335
$921$	24.4429	0.805421
$922$	−13.4539	−0.443081
$923$	0	0
$924$	8.25523	0.271577
$925$	−4.67914	−0.153849
$926$	−5.81731	−0.191169
$927$	13.7384	0.451229
$928$	−17.6307	−0.578755
$929$	22.9297	0.752300	0.376150	−	0.926559i	$-0.377248\pi$
$929$	22.9297	0.752300	0.376150	+	0.926559i	$0.377248\pi$
$930$	−8.07980	−0.264947
$931$	−1.96037	−0.0642484
$932$	19.2200	0.629571
$933$	−13.1490	−0.430480
$934$	−5.62833	−0.184164
$935$	−29.7271	−0.972180
$936$	0	0
$937$	−39.3660	−1.28603	−0.643015	−	0.765854i	$-0.722317\pi$
$937$	−39.3660	−1.28603	−0.643015	+	0.765854i	$0.722317\pi$
$938$	−8.37532	−0.273464
$939$	3.23656	0.105621
$940$	−11.4953	−0.374934
$941$	−2.85161	−0.0929598	−0.0464799	−	0.998919i	$-0.514800\pi$
$941$	−2.85161	−0.0929598	−0.0464799	+	0.998919i	$0.514800\pi$
$942$	14.5159	0.472954
$943$	6.11694	0.199195
$944$	−2.08147	−0.0677461
$945$	−5.65602	−0.183990
$946$	−5.96697	−0.194003
$947$	10.5054	0.341380	0.170690	−	0.985325i	$-0.445400\pi$
$947$	10.5054	0.341380	0.170690	+	0.985325i	$0.445400\pi$
$948$	−2.97477	−0.0966161
$949$	0	0
$950$	−1.60701	−0.0521384
$951$	42.0439	1.36337
$952$	−18.2667	−0.592026
$953$	−17.3607	−0.562367	−0.281183	−	0.959654i	$-0.590727\pi$
$953$	−17.3607	−0.562367	−0.281183	+	0.959654i	$0.590727\pi$
$954$	10.0154	0.324259
$955$	−18.5752	−0.601079
$956$	−22.8431	−0.738799
$957$	18.8951	0.610793
$958$	13.7967	0.445753
$959$	−0.278351	−0.00898841
$960$	5.48226	0.176939
$961$	18.5564	0.598595
$962$	0	0
$963$	16.9833	0.547278
$964$	10.0927	0.325064
$965$	−16.6567	−0.536197
$966$	5.84873	0.188180
$967$	−26.9167	−0.865583	−0.432791	−	0.901494i	$-0.642471\pi$
$967$	−26.9167	−0.865583	−0.432791	+	0.901494i	$0.642471\pi$
$968$	−23.7662	−0.763875
$969$	−18.3780	−0.590387
$970$	11.3380	0.364042
$971$	−0.964749	−0.0309603	−0.0154801	−	0.999880i	$-0.504928\pi$
$971$	−0.964749	−0.0309603	−0.0154801	+	0.999880i	$0.504928\pi$
$972$	−13.6082	−0.436482
$973$	20.0473	0.642687
$974$	−6.53541	−0.209408
$975$	0	0
$976$	−0.0907434	−0.00290463
$977$	42.0765	1.34615	0.673074	−	0.739575i	$-0.264974\pi$
$977$	42.0765	1.34615	0.673074	+	0.739575i	$0.264974\pi$
$978$	−4.10600	−0.131295
$979$	58.6799	1.87542
$980$	−1.32801	−0.0424217
$981$	6.04731	0.193076
$982$	11.3429	0.361967
$983$	3.60779	0.115070	0.0575352	−	0.998343i	$-0.481676\pi$
$983$	3.60779	0.115070	0.0575352	+	0.998343i	$0.481676\pi$
$984$	−4.58520	−0.146171
$985$	−6.75840	−0.215341
$986$	−16.6838	−0.531322
$987$	12.1196	0.385770
$988$	0	0
$989$	8.35454	0.265659
$990$	3.78375	0.120255
$991$	24.3045	0.772058	0.386029	−	0.922487i	$-0.373846\pi$
$991$	24.3045	0.772058	0.386029	+	0.922487i	$0.373846\pi$
$992$	−40.8317	−1.29641
$993$	32.5591	1.03323
$994$	−9.33803	−0.296184
$995$	21.3263	0.676090
$996$	−11.4376	−0.362414
$997$	26.4098	0.836406	0.418203	−	0.908354i	$-0.362660\pi$
$997$	26.4098	0.836406	0.418203	+	0.908354i	$0.362660\pi$
$998$	29.1363	0.922292
$999$	26.4653	0.837324

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5915.2.a.n.1.3		4
13.12	even	2		455.2.a.c.1.2	✓	4
39.38	odd	2		4095.2.a.bf.1.3		4
52.51	odd	2		7280.2.a.bw.1.2		4
65.64	even	2		2275.2.a.p.1.3		4
91.90	odd	2		3185.2.a.l.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
455.2.a.c.1.2	✓	4	13.12	even	2
2275.2.a.p.1.3		4	65.64	even	2
3185.2.a.l.1.2		4	91.90	odd	2
4095.2.a.bf.1.3		4	39.38	odd	2
5915.2.a.n.1.3		4	1.1	even	1	trivial
7280.2.a.bw.1.2		4	52.51	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:	\( N \)	\(=\)	\( 5915 = 5 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5915.a (trivial)

\(f(q)\)	\(=\)	\(q+0.819751 q^{2} +1.40013 q^{3} -1.32801 q^{4} +1.00000 q^{5} +1.14776 q^{6} +1.00000 q^{7} -2.72814 q^{8} -1.03963 q^{9} +O(q^{10})\)	\(q+0.819751 q^{2} +1.40013 q^{3} -1.32801 q^{4} +1.00000 q^{5} +1.14776 q^{6} +1.00000 q^{7} -2.72814 q^{8} -1.03963 q^{9} +0.819751 q^{10} -4.43976 q^{11} -1.85938 q^{12} +0.819751 q^{14} +1.40013 q^{15} +0.419620 q^{16} +6.69565 q^{17} -0.852241 q^{18} -1.96037 q^{19} -1.32801 q^{20} +1.40013 q^{21} -3.63950 q^{22} +5.09578 q^{23} -3.81975 q^{24} +1.00000 q^{25} -5.65602 q^{27} -1.32801 q^{28} -3.03963 q^{29} +1.14776 q^{30} -7.03963 q^{31} +5.80026 q^{32} -6.21625 q^{33} +5.48877 q^{34} +1.00000 q^{35} +1.38064 q^{36} -4.67914 q^{37} -1.60701 q^{38} -2.72814 q^{40} +1.20039 q^{41} +1.14776 q^{42} +1.63950 q^{43} +5.89604 q^{44} -1.03963 q^{45} +4.17727 q^{46} +8.65602 q^{47} +0.587523 q^{48} +1.00000 q^{49} +0.819751 q^{50} +9.37479 q^{51} -11.7518 q^{53} -4.63653 q^{54} -4.43976 q^{55} -2.72814 q^{56} -2.74477 q^{57} -2.49174 q^{58} -4.96037 q^{59} -1.85938 q^{60} -0.216251 q^{61} -5.77075 q^{62} -1.03963 q^{63} +3.91553 q^{64} -5.09578 q^{66} -10.2169 q^{67} -8.89187 q^{68} +7.13476 q^{69} +0.819751 q^{70} -11.3913 q^{71} +2.83626 q^{72} -6.83924 q^{73} -3.83573 q^{74} +1.40013 q^{75} +2.60338 q^{76} -4.43976 q^{77} +1.59987 q^{79} +0.419620 q^{80} -4.80026 q^{81} +0.984023 q^{82} +6.15127 q^{83} -1.85938 q^{84} +6.69565 q^{85} +1.34398 q^{86} -4.25588 q^{87} +12.1123 q^{88} -13.2169 q^{89} -0.852241 q^{90} -6.76724 q^{92} -9.85641 q^{93} +7.09578 q^{94} -1.96037 q^{95} +8.12113 q^{96} +13.8311 q^{97} +0.819751 q^{98} +4.61573 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 3 q^{4} + 4 q^{5} - 6 q^{6} + 4 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q + q^2 + 3 * q^4 + 4 * q^5 - 6 * q^6 + 4 * q^7 + 3 * q^8 + 6 * q^9	\( 4 q + q^{2} + 3 q^{4} + 4 q^{5} - 6 q^{6} + 4 q^{7} + 3 q^{8} + 6 q^{9} + q^{10} - 2 q^{11} + 5 q^{12} + q^{14} + 5 q^{16} - 14 q^{18} - 18 q^{19} + 3 q^{20} - 10 q^{22} - 12 q^{23} - 13 q^{24} + 4 q^{25} - 6 q^{27} + 3 q^{28} - 2 q^{29} - 6 q^{30} - 18 q^{31} + 12 q^{32} - 24 q^{33} + 7 q^{34} + 4 q^{35} - 9 q^{36} - 4 q^{37} + 11 q^{38} + 3 q^{40} - 12 q^{41} - 6 q^{42} + 2 q^{43} - 20 q^{44} + 6 q^{45} - 2 q^{46} + 18 q^{47} - 24 q^{48} + 4 q^{49} + q^{50} - 4 q^{51} + 2 q^{53} + 7 q^{54} - 2 q^{55} + 3 q^{56} + 6 q^{57} - 16 q^{58} - 30 q^{59} + 5 q^{60} - 20 q^{62} + 6 q^{63} - 19 q^{64} + 12 q^{66} - 12 q^{67} - 36 q^{68} + 14 q^{69} + q^{70} + 8 q^{71} - 3 q^{72} - 34 q^{73} - 38 q^{74} - 2 q^{77} + 12 q^{79} + 5 q^{80} - 8 q^{81} - 21 q^{82} - 2 q^{83} + 5 q^{84} + 22 q^{86} - 6 q^{87} + 4 q^{88} - 24 q^{89} - 14 q^{90} - 40 q^{92} - 6 q^{93} - 4 q^{94} - 18 q^{95} + 36 q^{96} - 14 q^{97} + q^{98} + 40 q^{99}+O(q^{100}) \) 4 * q + q^2 + 3 * q^4 + 4 * q^5 - 6 * q^6 + 4 * q^7 + 3 * q^8 + 6 * q^9 + q^10 - 2 * q^11 + 5 * q^12 + q^14 + 5 * q^16 - 14 * q^18 - 18 * q^19 + 3 * q^20 - 10 * q^22 - 12 * q^23 - 13 * q^24 + 4 * q^25 - 6 * q^27 + 3 * q^28 - 2 * q^29 - 6 * q^30 - 18 * q^31 + 12 * q^32 - 24 * q^33 + 7 * q^34 + 4 * q^35 - 9 * q^36 - 4 * q^37 + 11 * q^38 + 3 * q^40 - 12 * q^41 - 6 * q^42 + 2 * q^43 - 20 * q^44 + 6 * q^45 - 2 * q^46 + 18 * q^47 - 24 * q^48 + 4 * q^49 + q^50 - 4 * q^51 + 2 * q^53 + 7 * q^54 - 2 * q^55 + 3 * q^56 + 6 * q^57 - 16 * q^58 - 30 * q^59 + 5 * q^60 - 20 * q^62 + 6 * q^63 - 19 * q^64 + 12 * q^66 - 12 * q^67 - 36 * q^68 + 14 * q^69 + q^70 + 8 * q^71 - 3 * q^72 - 34 * q^73 - 38 * q^74 - 2 * q^77 + 12 * q^79 + 5 * q^80 - 8 * q^81 - 21 * q^82 - 2 * q^83 + 5 * q^84 + 22 * q^86 - 6 * q^87 + 4 * q^88 - 24 * q^89 - 14 * q^90 - 40 * q^92 - 6 * q^93 - 4 * q^94 - 18 * q^95 + 36 * q^96 - 14 * q^97 + q^98 + 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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