LMFDB - Embedded newform 6223.2.a.k.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6223,2,Mod(1,6223)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6223, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6223.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6223 = 7^{2} \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6223.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:	$49.6909051778$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - 20 x^{14} + 38 x^{13} + 155 x^{12} - 275 x^{11} - 593 x^{10} + 957 x^{9} + 1177 x^{8} + \cdots + 1 $ x^16 - 2x^15 - 20x^14 + 38x^13 + 155x^12 - 275x^11 - 593x^10 + 957x^9 + 1177x^8 - 1655x^7 - 1150x^6 + 1279x^5 + 474x^4 - 280x^3 - 83x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 889)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$-1.72082$ of defining polynomial
Character	$\chi$	$=$	6223.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.72082 q^{2} -1.16137 q^{3} +0.961212 q^{4} +4.11468 q^{5} -1.99850 q^{6} -1.78756 q^{8} -1.65122 q^{9} +O(q^{10})$	\(q+1.72082 q^{2} -1.16137 q^{3} +0.961212 q^{4} +4.11468 q^{5} -1.99850 q^{6} -1.78756 q^{8} -1.65122 q^{9} +7.08062 q^{10} +1.90264 q^{11} -1.11632 q^{12} +0.956847 q^{13} -4.77867 q^{15} -4.99850 q^{16} -0.151705 q^{17} -2.84145 q^{18} +2.06568 q^{19} +3.95508 q^{20} +3.27410 q^{22} -6.66025 q^{23} +2.07602 q^{24} +11.9306 q^{25} +1.64656 q^{26} +5.40179 q^{27} +4.22490 q^{29} -8.22322 q^{30} +2.46514 q^{31} -5.02637 q^{32} -2.20967 q^{33} -0.261057 q^{34} -1.58717 q^{36} +0.302428 q^{37} +3.55465 q^{38} -1.11125 q^{39} -7.35526 q^{40} +6.55602 q^{41} +1.79751 q^{43} +1.82884 q^{44} -6.79426 q^{45} -11.4611 q^{46} +0.645672 q^{47} +5.80510 q^{48} +20.5304 q^{50} +0.176186 q^{51} +0.919732 q^{52} +0.596441 q^{53} +9.29549 q^{54} +7.82878 q^{55} -2.39901 q^{57} +7.27028 q^{58} -8.74718 q^{59} -4.59331 q^{60} +11.3645 q^{61} +4.24205 q^{62} +1.34753 q^{64} +3.93712 q^{65} -3.80244 q^{66} +11.3637 q^{67} -0.145821 q^{68} +7.73501 q^{69} +6.20333 q^{71} +2.95166 q^{72} +2.03377 q^{73} +0.520423 q^{74} -13.8559 q^{75} +1.98555 q^{76} -1.91226 q^{78} +8.04816 q^{79} -20.5672 q^{80} -1.31980 q^{81} +11.2817 q^{82} +9.02002 q^{83} -0.624220 q^{85} +3.09318 q^{86} -4.90667 q^{87} -3.40110 q^{88} -2.23627 q^{89} -11.6917 q^{90} -6.40191 q^{92} -2.86293 q^{93} +1.11108 q^{94} +8.49961 q^{95} +5.83747 q^{96} -2.48387 q^{97} -3.14169 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 4 q^{3} + 12 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 4 * q^3 + 12 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 14 * q^9	$ 16 q - 2 q^{2} + 4 q^{3} + 12 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 14 q^{9} + 2 q^{10} - 22 q^{11} + 10 q^{12} + 4 q^{13} - 14 q^{15} + 12 q^{16} + 18 q^{17} - 5 q^{18} + 15 q^{19} + 40 q^{20} - 11 q^{22} - 5 q^{23} + 26 q^{24} + 15 q^{25} + 24 q^{26} + 10 q^{27} - 12 q^{29} + 3 q^{30} + 32 q^{31} - 9 q^{32} + 10 q^{33} + 14 q^{34} + 10 q^{36} - 2 q^{37} - 3 q^{38} - 41 q^{39} + 14 q^{40} + 45 q^{41} - 3 q^{43} - 54 q^{44} + 22 q^{45} + 49 q^{47} - 10 q^{48} - 6 q^{50} - 12 q^{51} - 38 q^{52} + 16 q^{53} + 67 q^{54} - 7 q^{55} + 8 q^{57} + 16 q^{58} + 35 q^{59} + 56 q^{60} + 11 q^{61} - 17 q^{62} - 2 q^{64} + 14 q^{65} - 86 q^{66} + 17 q^{67} + 71 q^{68} + 17 q^{69} - 81 q^{71} + 13 q^{72} + 15 q^{73} + 13 q^{74} + 48 q^{75} - 14 q^{76} - 10 q^{78} - 34 q^{79} + 33 q^{80} + 40 q^{81} + 14 q^{82} + 39 q^{83} - 17 q^{85} + 36 q^{86} - 7 q^{87} + 61 q^{88} + 32 q^{89} - 79 q^{90} + 37 q^{92} + 27 q^{93} - 13 q^{94} - 33 q^{95} + 55 q^{96} + 4 q^{97} - 73 q^{99}+O(q^{100}) $ 16 * q - 2 * q^2 + 4 * q^3 + 12 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 14 * q^9 + 2 * q^10 - 22 * q^11 + 10 * q^12 + 4 * q^13 - 14 * q^15 + 12 * q^16 + 18 * q^17 - 5 * q^18 + 15 * q^19 + 40 * q^20 - 11 * q^22 - 5 * q^23 + 26 * q^24 + 15 * q^25 + 24 * q^26 + 10 * q^27 - 12 * q^29 + 3 * q^30 + 32 * q^31 - 9 * q^32 + 10 * q^33 + 14 * q^34 + 10 * q^36 - 2 * q^37 - 3 * q^38 - 41 * q^39 + 14 * q^40 + 45 * q^41 - 3 * q^43 - 54 * q^44 + 22 * q^45 + 49 * q^47 - 10 * q^48 - 6 * q^50 - 12 * q^51 - 38 * q^52 + 16 * q^53 + 67 * q^54 - 7 * q^55 + 8 * q^57 + 16 * q^58 + 35 * q^59 + 56 * q^60 + 11 * q^61 - 17 * q^62 - 2 * q^64 + 14 * q^65 - 86 * q^66 + 17 * q^67 + 71 * q^68 + 17 * q^69 - 81 * q^71 + 13 * q^72 + 15 * q^73 + 13 * q^74 + 48 * q^75 - 14 * q^76 - 10 * q^78 - 34 * q^79 + 33 * q^80 + 40 * q^81 + 14 * q^82 + 39 * q^83 - 17 * q^85 + 36 * q^86 - 7 * q^87 + 61 * q^88 + 32 * q^89 - 79 * q^90 + 37 * q^92 + 27 * q^93 - 13 * q^94 - 33 * q^95 + 55 * q^96 + 4 * q^97 - 73 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.72082	1.21680	0.608401	−	0.793630i	$-0.291811\pi$
$2$	1.72082	1.21680	0.608401	+	0.793630i	$0.291811\pi$
$3$	−1.16137	−0.670517	−0.335258	−	0.942126i	$-0.608824\pi$
$3$	−1.16137	−0.670517	−0.335258	+	0.942126i	$0.608824\pi$
$4$	0.961212	0.480606
$5$	4.11468	1.84014	0.920071	−	0.391750i	$-0.128130\pi$
$5$	4.11468	1.84014	0.920071	+	0.391750i	$0.128130\pi$
$6$	−1.99850	−0.815886
$7$	0	0
$7$	0	0
$8$	−1.78756	−0.631999
$9$	−1.65122	−0.550407
$10$	7.08062	2.23909
$11$	1.90264	0.573669	0.286834	−	0.957980i	$-0.407397\pi$
$11$	1.90264	0.573669	0.286834	+	0.957980i	$0.407397\pi$
$12$	−1.11632	−0.322254
$13$	0.956847	0.265381	0.132691	−	0.991157i	$-0.457638\pi$
$13$	0.956847	0.265381	0.132691	+	0.991157i	$0.457638\pi$
$14$	0	0
$15$	−4.77867	−1.23385
$16$	−4.99850	−1.24962
$17$	−0.151705	−0.0367940	−0.0183970	−	0.999831i	$-0.505856\pi$
$17$	−0.151705	−0.0367940	−0.0183970	+	0.999831i	$0.505856\pi$
$18$	−2.84145	−0.669736
$19$	2.06568	0.473899	0.236949	−	0.971522i	$-0.423852\pi$
$19$	2.06568	0.473899	0.236949	+	0.971522i	$0.423852\pi$
$20$	3.95508	0.884384
$21$	0	0
$22$	3.27410	0.698041
$23$	−6.66025	−1.38876	−0.694379	−	0.719609i	$-0.744321\pi$
$23$	−6.66025	−1.38876	−0.694379	+	0.719609i	$0.744321\pi$
$24$	2.07602	0.423766
$25$	11.9306	2.38613
$26$	1.64656	0.322917
$27$	5.40179	1.03957
$28$	0	0
$29$	4.22490	0.784544	0.392272	−	0.919849i	$-0.371689\pi$
$29$	4.22490	0.784544	0.392272	+	0.919849i	$0.371689\pi$
$30$	−8.22322	−1.50135
$31$	2.46514	0.442751	0.221376	−	0.975189i	$-0.428945\pi$
$31$	2.46514	0.442751	0.221376	+	0.975189i	$0.428945\pi$
$32$	−5.02637	−0.888545
$33$	−2.20967	−0.384655
$34$	−0.261057	−0.0447710
$35$	0	0
$36$	−1.58717	−0.264529
$37$	0.302428	0.0497188	0.0248594	−	0.999691i	$-0.492086\pi$
$37$	0.302428	0.0497188	0.0248594	+	0.999691i	$0.492086\pi$
$38$	3.55465	0.576641
$39$	−1.11125	−0.177943
$40$	−7.35526	−1.16297
$41$	6.55602	1.02388	0.511939	−	0.859022i	$-0.328927\pi$
$41$	6.55602	1.02388	0.511939	+	0.859022i	$0.328927\pi$
$42$	0	0
$43$	1.79751	0.274118	0.137059	−	0.990563i	$-0.456235\pi$
$43$	1.79751	0.274118	0.137059	+	0.990563i	$0.456235\pi$
$44$	1.82884	0.275709
$45$	−6.79426	−1.01283
$46$	−11.4611	−1.68984
$47$	0.645672	0.0941809	0.0470905	−	0.998891i	$-0.485005\pi$
$47$	0.645672	0.0941809	0.0470905	+	0.998891i	$0.485005\pi$
$48$	5.80510	0.837894
$49$	0	0
$50$	20.5304	2.90344
$51$	0.176186	0.0246710
$52$	0.919732	0.127544
$53$	0.596441	0.0819274	0.0409637	−	0.999161i	$-0.486957\pi$
$53$	0.596441	0.0819274	0.0409637	+	0.999161i	$0.486957\pi$
$54$	9.29549	1.26496
$55$	7.82878	1.05563
$56$	0	0
$57$	−2.39901	−0.317757
$58$	7.27028	0.954634
$59$	−8.74718	−1.13879	−0.569393	−	0.822065i	$-0.692822\pi$
$59$	−8.74718	−1.13879	−0.569393	+	0.822065i	$0.692822\pi$
$60$	−4.59331	−0.592994
$61$	11.3645	1.45508	0.727540	−	0.686065i	$-0.240663\pi$
$61$	11.3645	1.45508	0.727540	+	0.686065i	$0.240663\pi$
$62$	4.24205	0.538741
$63$	0	0
$64$	1.34753	0.168441
$65$	3.93712	0.488340
$66$	−3.80244	−0.468048
$67$	11.3637	1.38830	0.694151	−	0.719830i	$-0.255780\pi$
$67$	11.3637	1.38830	0.694151	+	0.719830i	$0.255780\pi$
$68$	−0.145821	−0.0176834
$69$	7.73501	0.931186
$70$	0	0
$71$	6.20333	0.736200	0.368100	−	0.929786i	$-0.380008\pi$
$71$	6.20333	0.736200	0.368100	+	0.929786i	$0.380008\pi$
$72$	2.95166	0.347857
$73$	2.03377	0.238035	0.119017	−	0.992892i	$-0.462026\pi$
$73$	2.03377	0.238035	0.119017	+	0.992892i	$0.462026\pi$
$74$	0.520423	0.0604979
$75$	−13.8559	−1.59994
$76$	1.98555	0.227759
$77$	0	0
$78$	−1.91226	−0.216521
$79$	8.04816	0.905489	0.452744	−	0.891640i	$-0.350445\pi$
$79$	8.04816	0.905489	0.452744	+	0.891640i	$0.350445\pi$
$80$	−20.5672	−2.29949
$81$	−1.31980	−0.146645
$82$	11.2817	1.24586
$83$	9.02002	0.990076	0.495038	−	0.868871i	$-0.335154\pi$
$83$	9.02002	0.990076	0.495038	+	0.868871i	$0.335154\pi$
$84$	0	0
$85$	−0.624220	−0.0677062
$86$	3.09318	0.333547
$87$	−4.90667	−0.526050
$88$	−3.40110	−0.362558
$89$	−2.23627	−0.237044	−0.118522	−	0.992951i	$-0.537816\pi$
$89$	−2.23627	−0.237044	−0.118522	+	0.992951i	$0.537816\pi$
$90$	−11.6917	−1.23241
$91$	0	0
$92$	−6.40191	−0.667446
$93$	−2.86293	−0.296872
$94$	1.11108	0.114600
$95$	8.49961	0.872041
$96$	5.83747	0.595784
$97$	−2.48387	−0.252199	−0.126099	−	0.992018i	$-0.540246\pi$
$97$	−2.48387	−0.252199	−0.126099	+	0.992018i	$0.540246\pi$
$98$	0	0
$99$	−3.14169	−0.315751
$100$	11.4679	1.14679
$101$	17.1534	1.70682	0.853411	−	0.521238i	$-0.174530\pi$
$101$	17.1534	1.70682	0.853411	+	0.521238i	$0.174530\pi$
$102$	0.303184	0.0300197
$103$	−9.27419	−0.913813	−0.456907	−	0.889515i	$-0.651043\pi$
$103$	−9.27419	−0.913813	−0.456907	+	0.889515i	$0.651043\pi$
$104$	−1.71042	−0.167721
$105$	0	0
$106$	1.02637	0.0996894
$107$	−16.1726	−1.56346	−0.781730	−	0.623617i	$-0.785663\pi$
$107$	−16.1726	−1.56346	−0.781730	+	0.623617i	$0.785663\pi$
$108$	5.19226	0.499626
$109$	−10.4597	−1.00186	−0.500928	−	0.865489i	$-0.667008\pi$
$109$	−10.4597	−1.00186	−0.500928	+	0.865489i	$0.667008\pi$
$110$	13.4719	1.28450
$111$	−0.351230	−0.0333373
$112$	0	0
$113$	15.1643	1.42654	0.713269	−	0.700891i	$-0.247214\pi$
$113$	15.1643	1.42654	0.713269	+	0.700891i	$0.247214\pi$
$114$	−4.12826	−0.386647
$115$	−27.4048	−2.55551
$116$	4.06102	0.377056
$117$	−1.57997	−0.146068
$118$	−15.0523	−1.38568
$119$	0	0
$120$	8.54218	0.779791
$121$	−7.37995	−0.670904
$122$	19.5563	1.77054
$123$	−7.61397	−0.686528
$124$	2.36952	0.212789
$125$	28.5174	2.55067
$126$	0	0
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	12.3716	1.09350
$129$	−2.08757	−0.183800
$130$	6.77507	0.594213
$131$	12.5063	1.09268	0.546341	−	0.837563i	$-0.316020\pi$
$131$	12.5063	1.09268	0.546341	+	0.837563i	$0.316020\pi$
$132$	−2.12396	−0.184867
$133$	0	0
$134$	19.5549	1.68929
$135$	22.2266	1.91297
$136$	0.271183	0.0232538
$137$	−12.8382	−1.09684	−0.548422	−	0.836202i	$-0.684771\pi$
$137$	−12.8382	−1.09684	−0.548422	+	0.836202i	$0.684771\pi$
$138$	13.3105	1.13307
$139$	−15.6034	−1.32346	−0.661730	−	0.749742i	$-0.730177\pi$
$139$	−15.6034	−1.32346	−0.661730	+	0.749742i	$0.730177\pi$
$140$	0	0
$141$	−0.749864	−0.0631499
$142$	10.6748	0.895809
$143$	1.82054	0.152241
$144$	8.25362	0.687802
$145$	17.3841	1.44367
$146$	3.49974	0.289641
$147$	0	0
$148$	0.290697	0.0238952
$149$	−2.15071	−0.176193	−0.0880966	−	0.996112i	$-0.528078\pi$
$149$	−2.15071	−0.176193	−0.0880966	+	0.996112i	$0.528078\pi$
$150$	−23.8434	−1.94681
$151$	−1.26618	−0.103041	−0.0515203	−	0.998672i	$-0.516407\pi$
$151$	−1.26618	−0.103041	−0.0515203	+	0.998672i	$0.516407\pi$
$152$	−3.69253	−0.299504
$153$	0.250499	0.0202517
$154$	0	0
$155$	10.1433	0.814726
$156$	−1.06815	−0.0855204
$157$	2.86075	0.228312	0.114156	−	0.993463i	$-0.463584\pi$
$157$	2.86075	0.228312	0.114156	+	0.993463i	$0.463584\pi$
$158$	13.8494	1.10180
$159$	−0.692688	−0.0549337
$160$	−20.6819	−1.63505
$161$	0	0
$162$	−2.27114	−0.178438
$163$	12.6597	0.991584	0.495792	−	0.868441i	$-0.334878\pi$
$163$	12.6597	0.991584	0.495792	+	0.868441i	$0.334878\pi$
$164$	6.30173	0.492082
$165$	−9.09211	−0.707819
$166$	15.5218	1.20473
$167$	17.0641	1.32046	0.660228	−	0.751065i	$-0.270460\pi$
$167$	17.0641	1.32046	0.660228	+	0.751065i	$0.270460\pi$
$168$	0	0
$169$	−12.0844	−0.929573
$170$	−1.07417	−0.0823850
$171$	−3.41089	−0.260837
$172$	1.72779	0.131743
$173$	19.1596	1.45667	0.728337	−	0.685219i	$-0.240294\pi$
$173$	19.1596	1.45667	0.728337	+	0.685219i	$0.240294\pi$
$174$	−8.44347	−0.640098
$175$	0	0
$176$	−9.51036	−0.716870
$177$	10.1587	0.763575
$178$	−3.84821	−0.288436
$179$	−13.6433	−1.01975	−0.509873	−	0.860250i	$-0.670308\pi$
$179$	−13.6433	−1.01975	−0.509873	+	0.860250i	$0.670308\pi$
$180$	−6.53072	−0.486771
$181$	14.3725	1.06830	0.534151	−	0.845389i	$-0.320632\pi$
$181$	14.3725	1.06830	0.534151	+	0.845389i	$0.320632\pi$
$182$	0	0
$183$	−13.1984	−0.975656
$184$	11.9056	0.877695
$185$	1.24439	0.0914897
$186$	−4.92658	−0.361235
$187$	−0.288642	−0.0211076
$188$	0.620628	0.0452639
$189$	0	0
$190$	14.6263	1.06110
$191$	−24.2155	−1.75218	−0.876088	−	0.482152i	$-0.839855\pi$
$191$	−24.2155	−1.75218	−0.876088	+	0.482152i	$0.839855\pi$
$192$	−1.56498	−0.112943
$193$	5.45506	0.392664	0.196332	−	0.980537i	$-0.437097\pi$
$193$	5.45506	0.392664	0.196332	+	0.980537i	$0.437097\pi$
$194$	−4.27428	−0.306876
$195$	−4.57245	−0.327440
$196$	0	0
$197$	−5.48164	−0.390551	−0.195275	−	0.980748i	$-0.562560\pi$
$197$	−5.48164	−0.390551	−0.195275	+	0.980748i	$0.562560\pi$
$198$	−5.40627	−0.384207
$199$	8.82801	0.625801	0.312901	−	0.949786i	$-0.398699\pi$
$199$	8.82801	0.625801	0.312901	+	0.949786i	$0.398699\pi$
$200$	−21.3268	−1.50803
$201$	−13.1975	−0.930880
$202$	29.5178	2.07686
$203$	0	0
$204$	0.169352	0.0118570
$205$	26.9760	1.88408
$206$	−15.9592	−1.11193
$207$	10.9976	0.764383
$208$	−4.78279	−0.331627
$209$	3.93025	0.271861
$210$	0	0
$211$	−4.96059	−0.341501	−0.170751	−	0.985314i	$-0.554619\pi$
$211$	−4.96059	−0.341501	−0.170751	+	0.985314i	$0.554619\pi$
$212$	0.573306	0.0393748
$213$	−7.20436	−0.493634
$214$	−27.8300	−1.90242
$215$	7.39618	0.504415
$216$	−9.65604	−0.657010
$217$	0	0
$218$	−17.9992	−1.21906
$219$	−2.36196	−0.159606
$220$	7.52512	0.507343
$221$	−0.145159	−0.00976444
$222$	−0.604403	−0.0405649
$223$	28.2073	1.88890	0.944449	−	0.328659i	$-0.106597\pi$
$223$	28.2073	1.88890	0.944449	+	0.328659i	$0.106597\pi$
$224$	0	0
$225$	−19.7001	−1.31334
$226$	26.0950	1.73581
$227$	13.3743	0.887684	0.443842	−	0.896105i	$-0.353615\pi$
$227$	13.3743	0.887684	0.443842	+	0.896105i	$0.353615\pi$
$228$	−2.30596	−0.152716
$229$	−25.7395	−1.70091	−0.850456	−	0.526046i	$-0.823674\pi$
$229$	−25.7395	−1.70091	−0.850456	+	0.526046i	$0.823674\pi$
$230$	−47.1587	−3.10955
$231$	0	0
$232$	−7.55227	−0.495831
$233$	9.69883	0.635391	0.317696	−	0.948193i	$-0.397091\pi$
$233$	9.69883	0.635391	0.317696	+	0.948193i	$0.397091\pi$
$234$	−2.71883	−0.177736
$235$	2.65674	0.173306
$236$	−8.40790	−0.547307
$237$	−9.34688	−0.607145
$238$	0	0
$239$	−2.10529	−0.136180	−0.0680899	−	0.997679i	$-0.521690\pi$
$239$	−2.10529	−0.136180	−0.0680899	+	0.997679i	$0.521690\pi$
$240$	23.8862	1.54184
$241$	11.2452	0.724367	0.362183	−	0.932107i	$-0.382031\pi$
$241$	11.2452	0.724367	0.362183	+	0.932107i	$0.382031\pi$
$242$	−12.6995	−0.816357
$243$	−14.6726	−0.941246
$244$	10.9237	0.699321
$245$	0	0
$246$	−13.1022	−0.835368
$247$	1.97654	0.125764
$248$	−4.40659	−0.279819
$249$	−10.4756	−0.663862
$250$	49.0732	3.10366
$251$	5.06128	0.319465	0.159733	−	0.987160i	$-0.448937\pi$
$251$	5.06128	0.319465	0.159733	+	0.987160i	$0.448937\pi$
$252$	0	0
$253$	−12.6721	−0.796687
$254$	−1.72082	−0.107974
$255$	0.724950	0.0453981
$256$	18.5942	1.16214
$257$	−26.7217	−1.66685	−0.833426	−	0.552631i	$-0.813624\pi$
$257$	−26.7217	−1.66685	−0.833426	+	0.552631i	$0.813624\pi$
$258$	−3.59233	−0.223649
$259$	0	0
$260$	3.78441	0.234699
$261$	−6.97624	−0.431818
$262$	21.5211	1.32958
$263$	−4.86117	−0.299753	−0.149876	−	0.988705i	$-0.547888\pi$
$263$	−4.86117	−0.299753	−0.149876	+	0.988705i	$0.547888\pi$
$264$	3.94993	0.243101
$265$	2.45417	0.150758
$266$	0	0
$267$	2.59714	0.158942
$268$	10.9230	0.667226
$269$	−13.3191	−0.812082	−0.406041	−	0.913855i	$-0.633091\pi$
$269$	−13.3191	−0.812082	−0.406041	+	0.913855i	$0.633091\pi$
$270$	38.2480	2.32770
$271$	−32.4393	−1.97055	−0.985275	−	0.170978i	$-0.945307\pi$
$271$	−32.4393	−1.97055	−0.985275	+	0.170978i	$0.945307\pi$
$272$	0.758299	0.0459786
$273$	0	0
$274$	−22.0922	−1.33464
$275$	22.6997	1.36885
$276$	7.43499	0.447534
$277$	12.9208	0.776337	0.388168	−	0.921588i	$-0.373108\pi$
$277$	12.9208	0.776337	0.388168	+	0.921588i	$0.373108\pi$
$278$	−26.8505	−1.61039
$279$	−4.07048	−0.243694
$280$	0	0
$281$	17.3588	1.03554	0.517769	−	0.855521i	$-0.326763\pi$
$281$	17.3588	1.03554	0.517769	+	0.855521i	$0.326763\pi$
$282$	−1.29038	−0.0768409
$283$	−22.3800	−1.33035	−0.665177	−	0.746685i	$-0.731644\pi$
$283$	−22.3800	−1.33035	−0.665177	+	0.746685i	$0.731644\pi$
$284$	5.96272	0.353822
$285$	−9.87118	−0.584718
$286$	3.13281	0.185247
$287$	0	0
$288$	8.29965	0.489061
$289$	−16.9770	−0.998646
$290$	29.9149	1.75666
$291$	2.88469	0.169103
$292$	1.95488	0.114401
$293$	−10.4775	−0.612102	−0.306051	−	0.952015i	$-0.599008\pi$
$293$	−10.4775	−0.612102	−0.306051	+	0.952015i	$0.599008\pi$
$294$	0	0
$295$	−35.9919	−2.09553
$296$	−0.540609	−0.0314222
$297$	10.2777	0.596371
$298$	−3.70098	−0.214392
$299$	−6.37284	−0.368551
$300$	−13.3184	−0.768940
$301$	0	0
$302$	−2.17887	−0.125380
$303$	−19.9214	−1.14445
$304$	−10.3253	−0.592195
$305$	46.7615	2.67756
$306$	0.431064	0.0246423
$307$	−9.32113	−0.531985	−0.265993	−	0.963975i	$-0.585700\pi$
$307$	−9.32113	−0.531985	−0.265993	+	0.963975i	$0.585700\pi$
$308$	0	0
$309$	10.7708	0.612727
$310$	17.4547	0.991360
$311$	2.77055	0.157104	0.0785518	−	0.996910i	$-0.474970\pi$
$311$	2.77055	0.157104	0.0785518	+	0.996910i	$0.474970\pi$
$312$	1.98643	0.112460
$313$	−2.44798	−0.138368	−0.0691840	−	0.997604i	$-0.522040\pi$
$313$	−2.44798	−0.138368	−0.0691840	+	0.997604i	$0.522040\pi$
$314$	4.92282	0.277811
$315$	0	0
$316$	7.73599	0.435183
$317$	13.7948	0.774794	0.387397	−	0.921913i	$-0.373374\pi$
$317$	13.7948	0.774794	0.387397	+	0.921913i	$0.373374\pi$
$318$	−1.19199	−0.0668434
$319$	8.03847	0.450068
$320$	5.54466	0.309956
$321$	18.7823	1.04833
$322$	0	0
$323$	−0.313374	−0.0174366
$324$	−1.26861	−0.0704784
$325$	11.4158	0.633234
$326$	21.7850	1.20656
$327$	12.1476	0.671762
$328$	−11.7193	−0.647091
$329$	0	0
$330$	−15.6459	−0.861276
$331$	12.9957	0.714308	0.357154	−	0.934046i	$-0.383747\pi$
$331$	12.9957	0.714308	0.357154	+	0.934046i	$0.383747\pi$
$332$	8.67015	0.475836
$333$	−0.499375	−0.0273656
$334$	29.3641	1.60673
$335$	46.7582	2.55467
$336$	0	0
$337$	10.1574	0.553308	0.276654	−	0.960970i	$-0.410774\pi$
$337$	10.1574	0.553308	0.276654	+	0.960970i	$0.410774\pi$
$338$	−20.7951	−1.13111
$339$	−17.6113	−0.956517
$340$	−0.600008	−0.0325400
$341$	4.69028	0.253993
$342$	−5.86952	−0.317387
$343$	0	0
$344$	−3.21316	−0.173242
$345$	31.8271	1.71352
$346$	32.9701	1.77248
$347$	7.43989	0.399394	0.199697	−	0.979858i	$-0.436004\pi$
$347$	7.43989	0.399394	0.199697	+	0.979858i	$0.436004\pi$
$348$	−4.71635	−0.252823
$349$	16.7754	0.897965	0.448982	−	0.893541i	$-0.351787\pi$
$349$	16.7754	0.897965	0.448982	+	0.893541i	$0.351787\pi$
$350$	0	0
$351$	5.16868	0.275884
$352$	−9.56339	−0.509730
$353$	10.5724	0.562712	0.281356	−	0.959603i	$-0.409216\pi$
$353$	10.5724	0.562712	0.281356	+	0.959603i	$0.409216\pi$
$354$	17.4813	0.929120
$355$	25.5248	1.35471
$356$	−2.14953	−0.113925
$357$	0	0
$358$	−23.4776	−1.24083
$359$	−20.3552	−1.07431	−0.537154	−	0.843484i	$-0.680501\pi$
$359$	−20.3552	−1.07431	−0.537154	+	0.843484i	$0.680501\pi$
$360$	12.1452	0.640107
$361$	−14.7330	−0.775420
$362$	24.7325	1.29991
$363$	8.57084	0.449853
$364$	0	0
$365$	8.36831	0.438018
$366$	−22.7121	−1.18718
$367$	−30.4336	−1.58862	−0.794311	−	0.607511i	$-0.792168\pi$
$367$	−30.4336	−1.58862	−0.794311	+	0.607511i	$0.792168\pi$
$368$	33.2912	1.73543
$369$	−10.8254	−0.563550
$370$	2.14138	0.111325
$371$	0	0
$372$	−2.75189	−0.142679
$373$	22.5148	1.16577	0.582887	−	0.812553i	$-0.301923\pi$
$373$	22.5148	1.16577	0.582887	+	0.812553i	$0.301923\pi$
$374$	−0.496699	−0.0256837
$375$	−33.1192	−1.71027
$376$	−1.15418	−0.0595223
$377$	4.04258	0.208203
$378$	0	0
$379$	−32.0316	−1.64535	−0.822676	−	0.568511i	$-0.807520\pi$
$379$	−32.0316	−1.64535	−0.822676	+	0.568511i	$0.807520\pi$
$380$	8.16993	0.419108
$381$	1.16137	0.0594988
$382$	−41.6705	−2.13205
$383$	17.1166	0.874620	0.437310	−	0.899311i	$-0.355931\pi$
$383$	17.1166	0.874620	0.437310	+	0.899311i	$0.355931\pi$
$384$	−14.3680	−0.733213
$385$	0	0
$386$	9.38717	0.477794
$387$	−2.96808	−0.150876
$388$	−2.38752	−0.121208
$389$	31.4659	1.59539	0.797693	−	0.603063i	$-0.206053\pi$
$389$	31.4659	1.59539	0.797693	+	0.603063i	$0.206053\pi$
$390$	−7.86835	−0.398430
$391$	1.01040	0.0510980
$392$	0	0
$393$	−14.5245	−0.732662
$394$	−9.43290	−0.475222
$395$	33.1156	1.66623
$396$	−3.01983	−0.151752
$397$	29.3356	1.47231	0.736155	−	0.676812i	$-0.236639\pi$
$397$	29.3356	1.47231	0.736155	+	0.676812i	$0.236639\pi$
$398$	15.1914	0.761476
$399$	0	0
$400$	−59.6352	−2.98176
$401$	−3.02453	−0.151038	−0.0755188	−	0.997144i	$-0.524061\pi$
$401$	−3.02453	−0.151038	−0.0755188	+	0.997144i	$0.524061\pi$
$402$	−22.7105	−1.13270
$403$	2.35876	0.117498
$404$	16.4880	0.820309
$405$	−5.43058	−0.269847
$406$	0	0
$407$	0.575412	0.0285221
$408$	−0.314944	−0.0155920
$409$	8.58154	0.424330	0.212165	−	0.977234i	$-0.431949\pi$
$409$	8.58154	0.424330	0.212165	+	0.977234i	$0.431949\pi$
$410$	46.4207	2.29256
$411$	14.9099	0.735452
$412$	−8.91446	−0.439184
$413$	0	0
$414$	18.9248	0.930102
$415$	37.1145	1.82188
$416$	−4.80946	−0.235803
$417$	18.1213	0.887402
$418$	6.76324	0.330801
$419$	−19.1800	−0.937003	−0.468501	−	0.883463i	$-0.655206\pi$
$419$	−19.1800	−0.937003	−0.468501	+	0.883463i	$0.655206\pi$
$420$	0	0
$421$	32.4549	1.58175	0.790876	−	0.611976i	$-0.209625\pi$
$421$	32.4549	1.58175	0.790876	+	0.611976i	$0.209625\pi$
$422$	−8.53628	−0.415539
$423$	−1.06615	−0.0518379
$424$	−1.06618	−0.0517781
$425$	−1.80994	−0.0877951
$426$	−12.3974	−0.600655
$427$	0	0
$428$	−15.5453	−0.751408
$429$	−2.11432	−0.102080
$430$	12.7275	0.613773
$431$	−19.4248	−0.935662	−0.467831	−	0.883818i	$-0.654964\pi$
$431$	−19.4248	−0.935662	−0.467831	+	0.883818i	$0.654964\pi$
$432$	−27.0008	−1.29908
$433$	−16.3673	−0.786561	−0.393280	−	0.919419i	$-0.628660\pi$
$433$	−16.3673	−0.786561	−0.393280	+	0.919419i	$0.628660\pi$
$434$	0	0
$435$	−20.1894	−0.968007
$436$	−10.0540	−0.481498
$437$	−13.7579	−0.658131
$438$	−4.06449	−0.194209
$439$	−15.8233	−0.755205	−0.377602	−	0.925968i	$-0.623251\pi$
$439$	−15.8233	−0.755205	−0.377602	+	0.925968i	$0.623251\pi$
$440$	−13.9944	−0.667159
$441$	0	0
$442$	−0.249792	−0.0118814
$443$	19.2944	0.916706	0.458353	−	0.888770i	$-0.348439\pi$
$443$	19.2944	0.916706	0.458353	+	0.888770i	$0.348439\pi$
$444$	−0.337607	−0.0160221
$445$	−9.20155	−0.436195
$446$	48.5395	2.29841
$447$	2.49777	0.118140
$448$	0	0
$449$	3.84275	0.181351	0.0906753	−	0.995881i	$-0.471097\pi$
$449$	3.84275	0.181351	0.0906753	+	0.995881i	$0.471097\pi$
$450$	−33.9003	−1.59808
$451$	12.4738	0.587367
$452$	14.5761	0.685602
$453$	1.47051	0.0690905
$454$	23.0147	1.08014
$455$	0	0
$456$	4.28839	0.200822
$457$	14.7578	0.690342	0.345171	−	0.938540i	$-0.387821\pi$
$457$	14.7578	0.690342	0.345171	+	0.938540i	$0.387821\pi$
$458$	−44.2929	−2.06967
$459$	−0.819480	−0.0382501
$460$	−26.3419	−1.22820
$461$	22.2373	1.03569	0.517847	−	0.855473i	$-0.326733\pi$
$461$	22.2373	1.03569	0.517847	+	0.855473i	$0.326733\pi$
$462$	0	0
$463$	−23.1151	−1.07425	−0.537124	−	0.843503i	$-0.680489\pi$
$463$	−23.1151	−1.07425	−0.537124	+	0.843503i	$0.680489\pi$
$464$	−21.1181	−0.980384
$465$	−11.7801	−0.546287
$466$	16.6899	0.773145
$467$	−27.9366	−1.29275	−0.646376	−	0.763019i	$-0.723716\pi$
$467$	−27.9366	−1.29275	−0.646376	+	0.763019i	$0.723716\pi$
$468$	−1.51868	−0.0702011
$469$	0	0
$470$	4.57176	0.210880
$471$	−3.32238	−0.153087
$472$	15.6362	0.719712
$473$	3.42002	0.157253
$474$	−16.0843	−0.738775
$475$	24.6448	1.13078
$476$	0	0
$477$	−0.984856	−0.0450934
$478$	−3.62282	−0.165704
$479$	−0.489744	−0.0223770	−0.0111885	−	0.999937i	$-0.503561\pi$
$479$	−0.489744	−0.0223770	−0.0111885	+	0.999937i	$0.503561\pi$
$480$	24.0193	1.09633
$481$	0.289377	0.0131944
$482$	19.3509	0.881410
$483$	0	0
$484$	−7.09369	−0.322441
$485$	−10.2203	−0.464082
$486$	−25.2488	−1.14531
$487$	−20.6762	−0.936928	−0.468464	−	0.883483i	$-0.655192\pi$
$487$	−20.6762	−0.936928	−0.468464	+	0.883483i	$0.655192\pi$
$488$	−20.3149	−0.919610
$489$	−14.7026	−0.664874
$490$	0	0
$491$	34.3912	1.55205	0.776026	−	0.630701i	$-0.217233\pi$
$491$	34.3912	1.55205	0.776026	+	0.630701i	$0.217233\pi$
$492$	−7.31863	−0.329950
$493$	−0.640940	−0.0288665
$494$	3.40126	0.153030
$495$	−12.9271	−0.581028
$496$	−12.3220	−0.553273
$497$	0	0
$498$	−18.0265	−0.807789
$499$	6.72669	0.301128	0.150564	−	0.988600i	$-0.451891\pi$
$499$	6.72669	0.301128	0.150564	+	0.988600i	$0.451891\pi$
$500$	27.4112	1.22587
$501$	−19.8177	−0.885388
$502$	8.70954	0.388726
$503$	17.0515	0.760290	0.380145	−	0.924927i	$-0.375874\pi$
$503$	17.0515	0.760290	0.380145	+	0.924927i	$0.375874\pi$
$504$	0	0
$505$	70.5806	3.14080
$506$	−21.8064	−0.969411
$507$	14.0345	0.623294
$508$	−0.961212	−0.0426469
$509$	2.99210	0.132623	0.0663113	−	0.997799i	$-0.478877\pi$
$509$	2.99210	0.132623	0.0663113	+	0.997799i	$0.478877\pi$
$510$	1.24751	0.0552405
$511$	0	0
$512$	7.25402	0.320585
$513$	11.1583	0.492653
$514$	−45.9831	−2.02823
$515$	−38.1604	−1.68155
$516$	−2.00660	−0.0883356
$517$	1.22848	0.0540287
$518$	0	0
$519$	−22.2513	−0.976724
$520$	−7.03786	−0.308631
$521$	25.3004	1.10843	0.554216	−	0.832373i	$-0.313018\pi$
$521$	25.3004	1.10843	0.554216	+	0.832373i	$0.313018\pi$
$522$	−12.0048	−0.525437
$523$	10.6453	0.465485	0.232743	−	0.972538i	$-0.425230\pi$
$523$	10.6453	0.465485	0.232743	+	0.972538i	$0.425230\pi$
$524$	12.0212	0.525150
$525$	0	0
$526$	−8.36519	−0.364740
$527$	−0.373975	−0.0162906
$528$	11.0450	0.480674
$529$	21.3590	0.928651
$530$	4.22317	0.183443
$531$	14.4435	0.626796
$532$	0	0
$533$	6.27311	0.271719
$534$	4.46920	0.193401
$535$	−66.5450	−2.87699
$536$	−20.3134	−0.877406
$537$	15.8449	0.683757
$538$	−22.9198	−0.988142
$539$	0	0
$540$	21.3645	0.919382
$541$	−41.9713	−1.80449	−0.902244	−	0.431225i	$-0.858082\pi$
$541$	−41.9713	−1.80449	−0.902244	+	0.431225i	$0.858082\pi$
$542$	−55.8222	−2.39777
$543$	−16.6918	−0.716314
$544$	0.762528	0.0326931
$545$	−43.0383	−1.84356
$546$	0	0
$547$	−3.21658	−0.137531	−0.0687656	−	0.997633i	$-0.521906\pi$
$547$	−3.21658	−0.137531	−0.0687656	+	0.997633i	$0.521906\pi$
$548$	−12.3403	−0.527150
$549$	−18.7654	−0.800887
$550$	39.0621	1.66561
$551$	8.72727	0.371794
$552$	−13.8268	−0.588509
$553$	0	0
$554$	22.2344	0.944648
$555$	−1.44520	−0.0613454
$556$	−14.9981	−0.636063
$557$	−39.5930	−1.67761	−0.838804	−	0.544434i	$-0.816745\pi$
$557$	−39.5930	−1.67761	−0.838804	+	0.544434i	$0.816745\pi$
$558$	−7.00456	−0.296527
$559$	1.71994	0.0727457
$560$	0	0
$561$	0.335219	0.0141530
$562$	29.8713	1.26004
$563$	−25.3819	−1.06972	−0.534860	−	0.844941i	$-0.679636\pi$
$563$	−25.3819	−1.06972	−0.534860	+	0.844941i	$0.679636\pi$
$564$	−0.720778	−0.0303502
$565$	62.3963	2.62503
$566$	−38.5119	−1.61878
$567$	0	0
$568$	−11.0889	−0.465278
$569$	−40.5881	−1.70154	−0.850771	−	0.525537i	$-0.823864\pi$
$569$	−40.5881	−1.70154	−0.850771	+	0.525537i	$0.823864\pi$
$570$	−16.9865	−0.711486
$571$	43.8798	1.83631	0.918156	−	0.396220i	$-0.129678\pi$
$571$	43.8798	1.83631	0.918156	+	0.396220i	$0.129678\pi$
$572$	1.74992	0.0731680
$573$	28.1232	1.17486
$574$	0	0
$575$	−79.4610	−3.31375
$576$	−2.22507	−0.0927112
$577$	25.8864	1.07767	0.538833	−	0.842413i	$-0.318865\pi$
$577$	25.8864	1.07767	0.538833	+	0.842413i	$0.318865\pi$
$578$	−29.2143	−1.21515
$579$	−6.33534	−0.263288
$580$	16.7098	0.693838
$581$	0	0
$582$	4.96402	0.205765
$583$	1.13481	0.0469992
$584$	−3.63549	−0.150438
$585$	−6.50106	−0.268786
$586$	−18.0299	−0.744807
$587$	24.9754	1.03085	0.515423	−	0.856936i	$-0.327635\pi$
$587$	24.9754	1.03085	0.515423	+	0.856936i	$0.327635\pi$
$588$	0	0
$589$	5.09217	0.209819
$590$	−61.9355	−2.54984
$591$	6.36621	0.261871
$592$	−1.51168	−0.0621298
$593$	31.7171	1.30246	0.651232	−	0.758878i	$-0.274252\pi$
$593$	31.7171	1.30246	0.651232	+	0.758878i	$0.274252\pi$
$594$	17.6860	0.725665
$595$	0	0
$596$	−2.06729	−0.0846795
$597$	−10.2526	−0.419610
$598$	−10.9665	−0.448453
$599$	7.33960	0.299888	0.149944	−	0.988694i	$-0.452091\pi$
$599$	7.33960	0.299888	0.149944	+	0.988694i	$0.452091\pi$
$600$	24.7683	1.01116
$601$	−41.9979	−1.71313	−0.856565	−	0.516039i	$-0.827406\pi$
$601$	−41.9979	−1.71313	−0.856565	+	0.516039i	$0.827406\pi$
$602$	0	0
$603$	−18.7641	−0.764131
$604$	−1.21707	−0.0495219
$605$	−30.3662	−1.23456
$606$	−34.2810	−1.39257
$607$	19.8014	0.803716	0.401858	−	0.915702i	$-0.368365\pi$
$607$	19.8014	0.803716	0.401858	+	0.915702i	$0.368365\pi$
$608$	−10.3829	−0.421080
$609$	0	0
$610$	80.4680	3.25806
$611$	0.617809	0.0249939
$612$	0.240783	0.00973308
$613$	21.9400	0.886150	0.443075	−	0.896485i	$-0.353888\pi$
$613$	21.9400	0.886150	0.443075	+	0.896485i	$0.353888\pi$
$614$	−16.0400	−0.647320
$615$	−31.3291	−1.26331
$616$	0	0
$617$	−32.2483	−1.29827	−0.649133	−	0.760675i	$-0.724868\pi$
$617$	−32.2483	−1.29827	−0.649133	+	0.760675i	$0.724868\pi$
$618$	18.5345	0.745567
$619$	−28.0029	−1.12553	−0.562765	−	0.826617i	$-0.690263\pi$
$619$	−28.0029	−1.12553	−0.562765	+	0.826617i	$0.690263\pi$
$620$	9.74982	0.391562
$621$	−35.9773	−1.44372
$622$	4.76761	0.191164
$623$	0	0
$624$	5.55459	0.222362
$625$	57.6868	2.30747
$626$	−4.21253	−0.168366
$627$	−4.56447	−0.182287
$628$	2.74978	0.109728
$629$	−0.0458799	−0.00182935
$630$	0	0
$631$	−4.65983	−0.185505	−0.0927524	−	0.995689i	$-0.529567\pi$
$631$	−4.65983	−0.185505	−0.0927524	+	0.995689i	$0.529567\pi$
$632$	−14.3866	−0.572268
$633$	5.76108	0.228982
$634$	23.7383	0.942770
$635$	−4.11468	−0.163286
$636$	−0.665820	−0.0264015
$637$	0	0
$638$	13.8327	0.547644
$639$	−10.2431	−0.405210
$640$	50.9052	2.01220
$641$	−20.5992	−0.813619	−0.406809	−	0.913513i	$-0.633359\pi$
$641$	−20.5992	−0.813619	−0.406809	+	0.913513i	$0.633359\pi$
$642$	32.3209	1.27561
$643$	40.0660	1.58005	0.790025	−	0.613074i	$-0.210067\pi$
$643$	40.0660	1.58005	0.790025	+	0.613074i	$0.210067\pi$
$644$	0	0
$645$	−8.58970	−0.338219
$646$	−0.539260	−0.0212169
$647$	−16.4147	−0.645328	−0.322664	−	0.946514i	$-0.604578\pi$
$647$	−16.4147	−0.645328	−0.322664	+	0.946514i	$0.604578\pi$
$648$	2.35923	0.0926795
$649$	−16.6428	−0.653286
$650$	19.6445	0.770520
$651$	0	0
$652$	12.1687	0.476561
$653$	8.93179	0.349528	0.174764	−	0.984610i	$-0.444084\pi$
$653$	8.93179	0.349528	0.174764	+	0.984610i	$0.444084\pi$
$654$	20.9037	0.817401
$655$	51.4596	2.01069
$656$	−32.7703	−1.27946
$657$	−3.35820	−0.131016
$658$	0	0
$659$	26.5807	1.03544	0.517718	−	0.855552i	$-0.326782\pi$
$659$	26.5807	1.03544	0.517718	+	0.855552i	$0.326782\pi$
$660$	−8.73944	−0.340182
$661$	−44.3578	−1.72532	−0.862660	−	0.505785i	$-0.831203\pi$
$661$	−44.3578	−1.72532	−0.862660	+	0.505785i	$0.831203\pi$
$662$	22.3632	0.869171
$663$	0.168583	0.00654722
$664$	−16.1239	−0.625727
$665$	0	0
$666$	−0.859333	−0.0332985
$667$	−28.1389	−1.08954
$668$	16.4022	0.634619
$669$	−32.7590	−1.26654
$670$	80.4623	3.10853
$671$	21.6227	0.834734
$672$	0	0
$673$	−37.6652	−1.45189	−0.725943	−	0.687755i	$-0.758596\pi$
$673$	−37.6652	−1.45189	−0.725943	+	0.687755i	$0.758596\pi$
$674$	17.4790	0.673266
$675$	64.4467	2.48056
$676$	−11.6157	−0.446758
$677$	8.65007	0.332449	0.166225	−	0.986088i	$-0.446842\pi$
$677$	8.65007	0.332449	0.166225	+	0.986088i	$0.446842\pi$
$678$	−30.3059	−1.16389
$679$	0	0
$680$	1.11583	0.0427903
$681$	−15.5325	−0.595207
$682$	8.07111	0.309059
$683$	−10.7169	−0.410071	−0.205035	−	0.978755i	$-0.565731\pi$
$683$	−10.7169	−0.410071	−0.205035	+	0.978755i	$0.565731\pi$
$684$	−3.27859	−0.125360
$685$	−52.8252	−2.01835
$686$	0	0
$687$	29.8930	1.14049
$688$	−8.98484	−0.342544
$689$	0.570702	0.0217420
$690$	54.7687	2.08501
$691$	16.7214	0.636110	0.318055	−	0.948072i	$-0.396970\pi$
$691$	16.7214	0.636110	0.318055	+	0.948072i	$0.396970\pi$
$692$	18.4164	0.700086
$693$	0	0
$694$	12.8027	0.485983
$695$	−64.2029	−2.43535
$696$	8.77098	0.332463
$697$	−0.994585	−0.0376726
$698$	28.8673	1.09264
$699$	−11.2639	−0.426041
$700$	0	0
$701$	−26.9332	−1.01725	−0.508627	−	0.860987i	$-0.669847\pi$
$701$	−26.9332	−1.01725	−0.508627	+	0.860987i	$0.669847\pi$
$702$	8.89435	0.335696
$703$	0.624718	0.0235617
$704$	2.56387	0.0966294
$705$	−3.08545	−0.116205
$706$	18.1932	0.684709
$707$	0	0
$708$	9.76467	0.366979
$709$	3.60561	0.135411	0.0677057	−	0.997705i	$-0.478432\pi$
$709$	3.60561	0.135411	0.0677057	+	0.997705i	$0.478432\pi$
$710$	43.9234	1.64842
$711$	−13.2893	−0.498387
$712$	3.99748	0.149812
$713$	−16.4184	−0.614875
$714$	0	0
$715$	7.49094	0.280145
$716$	−13.1141	−0.490096
$717$	2.44502	0.0913109
$718$	−35.0276	−1.30722
$719$	−48.7999	−1.81993	−0.909964	−	0.414686i	$-0.863891\pi$
$719$	−48.7999	−1.81993	−0.909964	+	0.414686i	$0.863891\pi$
$720$	33.9611	1.26565
$721$	0	0
$722$	−25.3528	−0.943532
$723$	−13.0598	−0.485700
$724$	13.8150	0.513432
$725$	50.4057	1.87202
$726$	14.7489	0.547381
$727$	−36.5934	−1.35717	−0.678587	−	0.734520i	$-0.737407\pi$
$727$	−36.5934	−1.35717	−0.678587	+	0.734520i	$0.737407\pi$
$728$	0	0
$729$	20.9997	0.777766
$730$	14.4003	0.532981
$731$	−0.272692	−0.0100859
$732$	−12.6865	−0.468906
$733$	23.0187	0.850214	0.425107	−	0.905143i	$-0.360236\pi$
$733$	23.0187	0.850214	0.425107	+	0.905143i	$0.360236\pi$
$734$	−52.3707	−1.93304
$735$	0	0
$736$	33.4769	1.23397
$737$	21.6212	0.796425
$738$	−18.6286	−0.685729
$739$	−41.9045	−1.54148	−0.770740	−	0.637149i	$-0.780113\pi$
$739$	−41.9045	−1.54148	−0.770740	+	0.637149i	$0.780113\pi$
$740$	1.19613	0.0439705
$741$	−2.29549	−0.0843268
$742$	0	0
$743$	8.99203	0.329886	0.164943	−	0.986303i	$-0.447256\pi$
$743$	8.99203	0.329886	0.164943	+	0.986303i	$0.447256\pi$
$744$	5.11768	0.187623
$745$	−8.84950	−0.324221
$746$	38.7439	1.41852
$747$	−14.8940	−0.544945
$748$	−0.277446	−0.0101444
$749$	0	0
$750$	−56.9921	−2.08106
$751$	−36.1068	−1.31756	−0.658778	−	0.752338i	$-0.728926\pi$
$751$	−36.1068	−1.31756	−0.658778	+	0.752338i	$0.728926\pi$
$752$	−3.22739	−0.117691
$753$	−5.87801	−0.214207
$754$	6.95654	0.253342
$755$	−5.20995	−0.189609
$756$	0	0
$757$	39.8948	1.45000	0.725001	−	0.688748i	$-0.241839\pi$
$757$	39.8948	1.45000	0.725001	+	0.688748i	$0.241839\pi$
$758$	−55.1205	−2.00207
$759$	14.7170	0.534192
$760$	−15.1936	−0.551130
$761$	12.5087	0.453440	0.226720	−	0.973960i	$-0.427200\pi$
$761$	12.5087	0.453440	0.226720	+	0.973960i	$0.427200\pi$
$762$	1.99850	0.0723982
$763$	0	0
$764$	−23.2763	−0.842106
$765$	1.03073	0.0372660
$766$	29.4546	1.06424
$767$	−8.36971	−0.302213
$768$	−21.5947	−0.779232
$769$	−28.6812	−1.03427	−0.517136	−	0.855904i	$-0.673002\pi$
$769$	−28.6812	−1.03427	−0.517136	+	0.855904i	$0.673002\pi$
$770$	0	0
$771$	31.0337	1.11765
$772$	5.24347	0.188717
$773$	−31.2783	−1.12500	−0.562501	−	0.826797i	$-0.690161\pi$
$773$	−31.2783	−1.12500	−0.562501	+	0.826797i	$0.690161\pi$
$774$	−5.10753	−0.183586
$775$	29.4106	1.05646
$776$	4.44007	0.159389
$777$	0	0
$778$	54.1471	1.94127
$779$	13.5426	0.485215
$780$	−4.39510	−0.157370
$781$	11.8027	0.422335
$782$	1.73871	0.0621761
$783$	22.8220	0.815591
$784$	0	0
$785$	11.7711	0.420128
$786$	−24.9939	−0.891504
$787$	−12.1523	−0.433184	−0.216592	−	0.976262i	$-0.569494\pi$
$787$	−12.1523	−0.433184	−0.216592	+	0.976262i	$0.569494\pi$
$788$	−5.26902	−0.187701
$789$	5.64562	0.200989
$790$	56.9860	2.02747
$791$	0	0
$792$	5.61597	0.199555
$793$	10.8741	0.386152
$794$	50.4812	1.79151
$795$	−2.85019	−0.101086
$796$	8.48559	0.300764
$797$	−40.0647	−1.41916	−0.709582	−	0.704623i	$-0.751116\pi$
$797$	−40.0647	−1.41916	−0.709582	+	0.704623i	$0.751116\pi$
$798$	0	0
$799$	−0.0979520	−0.00346529
$800$	−59.9677	−2.12018
$801$	3.69258	0.130471
$802$	−5.20466	−0.183783
$803$	3.86954	0.136553
$804$	−12.6856	−0.447386
$805$	0	0
$806$	4.05899	0.142972
$807$	15.4684	0.544515
$808$	−30.6627	−1.07871
$809$	−17.2428	−0.606226	−0.303113	−	0.952955i	$-0.598026\pi$
$809$	−17.2428	−0.606226	−0.303113	+	0.952955i	$0.598026\pi$
$810$	−9.34503	−0.328351
$811$	11.7905	0.414019	0.207010	−	0.978339i	$-0.433627\pi$
$811$	11.7905	0.414019	0.207010	+	0.978339i	$0.433627\pi$
$812$	0	0
$813$	37.6741	1.32129
$814$	0.990179	0.0347058
$815$	52.0907	1.82466
$816$	−0.880665	−0.0308295
$817$	3.71307	0.129904
$818$	14.7673	0.516325
$819$	0	0
$820$	25.9296	0.905502
$821$	22.4832	0.784670	0.392335	−	0.919822i	$-0.371667\pi$
$821$	22.4832	0.784670	0.392335	+	0.919822i	$0.371667\pi$
$822$	25.6572	0.894899
$823$	15.2298	0.530878	0.265439	−	0.964128i	$-0.414483\pi$
$823$	15.2298	0.530878	0.265439	+	0.964128i	$0.414483\pi$
$824$	16.5782	0.577529
$825$	−26.3628	−0.917834
$826$	0	0
$827$	−30.0385	−1.04454	−0.522271	−	0.852780i	$-0.674915\pi$
$827$	−30.0385	−1.04454	−0.522271	+	0.852780i	$0.674915\pi$
$828$	10.5710	0.367367
$829$	−16.9736	−0.589517	−0.294758	−	0.955572i	$-0.595239\pi$
$829$	−16.9736	−0.589517	−0.294758	+	0.955572i	$0.595239\pi$
$830$	63.8673	2.21687
$831$	−15.0058	−0.520547
$832$	1.28938	0.0447012
$833$	0	0
$834$	31.1834	1.07979
$835$	70.2132	2.42983
$836$	3.77780	0.130658
$837$	13.3161	0.460273
$838$	−33.0052	−1.14015
$839$	24.8666	0.858490	0.429245	−	0.903188i	$-0.358780\pi$
$839$	24.8666	0.858490	0.429245	+	0.903188i	$0.358780\pi$
$840$	0	0
$841$	−11.1502	−0.384491
$842$	55.8489	1.92468
$843$	−20.1599	−0.694345
$844$	−4.76818	−0.164128
$845$	−49.7237	−1.71055
$846$	−1.83464	−0.0630764
$847$	0	0
$848$	−2.98131	−0.102378
$849$	25.9915	0.892025
$850$	−3.11458	−0.106829
$851$	−2.01424	−0.0690474
$852$	−6.92492	−0.237244
$853$	3.82276	0.130889	0.0654443	−	0.997856i	$-0.479154\pi$
$853$	3.82276	0.130889	0.0654443	+	0.997856i	$0.479154\pi$
$854$	0	0
$855$	−14.0347	−0.479978
$856$	28.9095	0.988106
$857$	11.5675	0.395137	0.197569	−	0.980289i	$-0.436696\pi$
$857$	11.5675	0.395137	0.197569	+	0.980289i	$0.436696\pi$
$858$	−3.63835	−0.124211
$859$	−21.9356	−0.748434	−0.374217	−	0.927341i	$-0.622088\pi$
$859$	−21.9356	−0.748434	−0.374217	+	0.927341i	$0.622088\pi$
$860$	7.10930	0.242425
$861$	0	0
$862$	−33.4266	−1.13851
$863$	−37.0986	−1.26285	−0.631426	−	0.775436i	$-0.717530\pi$
$863$	−37.0986	−1.26285	−0.631426	+	0.775436i	$0.717530\pi$
$864$	−27.1514	−0.923708
$865$	78.8355	2.68049
$866$	−28.1651	−0.957089
$867$	19.7165	0.669609
$868$	0	0
$869$	15.3128	0.519451
$870$	−34.7422	−1.17787
$871$	10.8734	0.368430
$872$	18.6974	0.633173
$873$	4.10142	0.138812
$874$	−23.6749	−0.800815
$875$	0	0
$876$	−2.27034	−0.0767077
$877$	44.2268	1.49343	0.746716	−	0.665143i	$-0.231629\pi$
$877$	44.2268	1.49343	0.746716	+	0.665143i	$0.231629\pi$
$878$	−27.2290	−0.918934
$879$	12.1683	0.410425
$880$	−39.1321	−1.31914
$881$	−42.8685	−1.44427	−0.722137	−	0.691750i	$-0.756840\pi$
$881$	−42.8685	−1.44427	−0.722137	+	0.691750i	$0.756840\pi$
$882$	0	0
$883$	−19.5065	−0.656447	−0.328223	−	0.944600i	$-0.606450\pi$
$883$	−19.5065	−0.656447	−0.328223	+	0.944600i	$0.606450\pi$
$884$	−0.139528	−0.00469285
$885$	41.7999	1.40509
$886$	33.2022	1.11545
$887$	30.7871	1.03373	0.516864	−	0.856067i	$-0.327099\pi$
$887$	30.7871	1.03373	0.516864	+	0.856067i	$0.327099\pi$
$888$	0.627846	0.0210691
$889$	0	0
$890$	−15.8342	−0.530763
$891$	−2.51112	−0.0841256
$892$	27.1132	0.907815
$893$	1.33375	0.0446322
$894$	4.29821	0.143754
$895$	−56.1378	−1.87648
$896$	0	0
$897$	7.40122	0.247120
$898$	6.61267	0.220668
$899$	10.4149	0.347358
$900$	−18.9360	−0.631200
$901$	−0.0904833	−0.00301444
$902$	21.4651	0.714710
$903$	0	0
$904$	−27.1072	−0.901571
$905$	59.1384	1.96583
$906$	2.53048	0.0840694
$907$	58.4950	1.94229	0.971147	−	0.238483i	$-0.0766500\pi$
$907$	58.4950	1.94229	0.971147	+	0.238483i	$0.0766500\pi$
$908$	12.8555	0.426626
$909$	−28.3240	−0.939447
$910$	0	0
$911$	−17.4513	−0.578188	−0.289094	−	0.957301i	$-0.593354\pi$
$911$	−17.4513	−0.578188	−0.289094	+	0.957301i	$0.593354\pi$
$912$	11.9915	0.397077
$913$	17.1619	0.567975
$914$	25.3955	0.840009
$915$	−54.3074	−1.79535
$916$	−24.7411	−0.817469
$917$	0	0
$918$	−1.41018	−0.0465427
$919$	11.1696	0.368452	0.184226	−	0.982884i	$-0.441022\pi$
$919$	11.1696	0.368452	0.184226	+	0.982884i	$0.441022\pi$
$920$	48.9879	1.61508
$921$	10.8253	0.356705
$922$	38.2664	1.26024
$923$	5.93564	0.195374
$924$	0	0
$925$	3.60815	0.118635
$926$	−39.7768	−1.30715
$927$	15.3137	0.502969
$928$	−21.2359	−0.697102
$929$	−31.6788	−1.03935	−0.519673	−	0.854365i	$-0.673946\pi$
$929$	−31.6788	−1.03935	−0.519673	+	0.854365i	$0.673946\pi$
$930$	−20.2713	−0.664723
$931$	0	0
$932$	9.32263	0.305373
$933$	−3.21763	−0.105341
$934$	−48.0738	−1.57302
$935$	−1.18767	−0.0388409
$936$	2.82429	0.0923148
$937$	−9.99759	−0.326607	−0.163304	−	0.986576i	$-0.552215\pi$
$937$	−9.99759	−0.326607	−0.163304	+	0.986576i	$0.552215\pi$
$938$	0	0
$939$	2.84301	0.0927781
$940$	2.55369	0.0832921
$941$	−40.8696	−1.33231	−0.666155	−	0.745813i	$-0.732061\pi$
$941$	−40.8696	−1.33231	−0.666155	+	0.745813i	$0.732061\pi$
$942$	−5.71721	−0.186277
$943$	−43.6648	−1.42192
$944$	43.7228	1.42305
$945$	0	0
$946$	5.88523	0.191345
$947$	−20.8268	−0.676781	−0.338391	−	0.941006i	$-0.609883\pi$
$947$	−20.8268	−0.676781	−0.338391	+	0.941006i	$0.609883\pi$
$948$	−8.98434	−0.291798
$949$	1.94600	0.0631700
$950$	42.4092	1.37594
$951$	−16.0209	−0.519512
$952$	0	0
$953$	21.2199	0.687381	0.343690	−	0.939083i	$-0.388323\pi$
$953$	21.2199	0.687381	0.343690	+	0.939083i	$0.388323\pi$
$954$	−1.69476	−0.0548698
$955$	−99.6393	−3.22425
$956$	−2.02363	−0.0654489
$957$	−9.33564	−0.301778
$958$	−0.842759	−0.0272283
$959$	0	0
$960$	−6.43939	−0.207831
$961$	−24.9231	−0.803971
$962$	0.497965	0.0160550
$963$	26.7045	0.860540
$964$	10.8090	0.348135
$965$	22.4459	0.722558
$966$	0	0
$967$	−30.7468	−0.988751	−0.494375	−	0.869249i	$-0.664603\pi$
$967$	−30.7468	−0.988751	−0.494375	+	0.869249i	$0.664603\pi$
$968$	13.1921	0.424011
$969$	0.363943	0.0116915
$970$	−17.5873	−0.564695
$971$	42.4586	1.36256	0.681280	−	0.732022i	$-0.261423\pi$
$971$	42.4586	1.36256	0.681280	+	0.732022i	$0.261423\pi$
$972$	−14.1035	−0.452369
$973$	0	0
$974$	−35.5799	−1.14005
$975$	−13.2579	−0.424594
$976$	−56.8056	−1.81830
$977$	−46.3699	−1.48351	−0.741753	−	0.670673i	$-0.766005\pi$
$977$	−46.3699	−1.48351	−0.741753	+	0.670673i	$0.766005\pi$
$978$	−25.3005	−0.809020
$979$	−4.25483	−0.135985
$980$	0	0
$981$	17.2713	0.551429
$982$	59.1809	1.88854
$983$	−38.3831	−1.22423	−0.612115	−	0.790769i	$-0.709681\pi$
$983$	−38.3831	−1.22423	−0.612115	+	0.790769i	$0.709681\pi$
$984$	13.6105	0.433885
$985$	−22.5552	−0.718669
$986$	−1.10294	−0.0351248
$987$	0	0
$988$	1.89987	0.0604429
$989$	−11.9719	−0.380683
$990$	−22.2451	−0.706995
$991$	−46.2877	−1.47038	−0.735188	−	0.677863i	$-0.762906\pi$
$991$	−46.2877	−1.47038	−0.735188	+	0.677863i	$0.762906\pi$
$992$	−12.3907	−0.393404
$993$	−15.0928	−0.478955
$994$	0	0
$995$	36.3245	1.15156
$996$	−10.0692	−0.319056
$997$	−5.68852	−0.180157	−0.0900786	−	0.995935i	$-0.528712\pi$
$997$	−5.68852	−0.180157	−0.0900786	+	0.995935i	$0.528712\pi$
$998$	11.5754	0.366413
$999$	1.63365	0.0516864

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6223.2.a.k.1.14		16
7.6	odd	2		889.2.a.c.1.14	✓	16
21.20	even	2		8001.2.a.t.1.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
889.2.a.c.1.14	✓	16	7.6	odd	2
6223.2.a.k.1.14		16	1.1	even	1	trivial
8001.2.a.t.1.3		16	21.20	even	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:	\( N \)	\(=\)	\( 6223 = 7^{2} \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6223.a (trivial)

\(f(q)\)	\(=\)	\(q+1.72082 q^{2} -1.16137 q^{3} +0.961212 q^{4} +4.11468 q^{5} -1.99850 q^{6} -1.78756 q^{8} -1.65122 q^{9} +O(q^{10})\)	\(q+1.72082 q^{2} -1.16137 q^{3} +0.961212 q^{4} +4.11468 q^{5} -1.99850 q^{6} -1.78756 q^{8} -1.65122 q^{9} +7.08062 q^{10} +1.90264 q^{11} -1.11632 q^{12} +0.956847 q^{13} -4.77867 q^{15} -4.99850 q^{16} -0.151705 q^{17} -2.84145 q^{18} +2.06568 q^{19} +3.95508 q^{20} +3.27410 q^{22} -6.66025 q^{23} +2.07602 q^{24} +11.9306 q^{25} +1.64656 q^{26} +5.40179 q^{27} +4.22490 q^{29} -8.22322 q^{30} +2.46514 q^{31} -5.02637 q^{32} -2.20967 q^{33} -0.261057 q^{34} -1.58717 q^{36} +0.302428 q^{37} +3.55465 q^{38} -1.11125 q^{39} -7.35526 q^{40} +6.55602 q^{41} +1.79751 q^{43} +1.82884 q^{44} -6.79426 q^{45} -11.4611 q^{46} +0.645672 q^{47} +5.80510 q^{48} +20.5304 q^{50} +0.176186 q^{51} +0.919732 q^{52} +0.596441 q^{53} +9.29549 q^{54} +7.82878 q^{55} -2.39901 q^{57} +7.27028 q^{58} -8.74718 q^{59} -4.59331 q^{60} +11.3645 q^{61} +4.24205 q^{62} +1.34753 q^{64} +3.93712 q^{65} -3.80244 q^{66} +11.3637 q^{67} -0.145821 q^{68} +7.73501 q^{69} +6.20333 q^{71} +2.95166 q^{72} +2.03377 q^{73} +0.520423 q^{74} -13.8559 q^{75} +1.98555 q^{76} -1.91226 q^{78} +8.04816 q^{79} -20.5672 q^{80} -1.31980 q^{81} +11.2817 q^{82} +9.02002 q^{83} -0.624220 q^{85} +3.09318 q^{86} -4.90667 q^{87} -3.40110 q^{88} -2.23627 q^{89} -11.6917 q^{90} -6.40191 q^{92} -2.86293 q^{93} +1.11108 q^{94} +8.49961 q^{95} +5.83747 q^{96} -2.48387 q^{97} -3.14169 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 4 q^{3} + 12 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 4 * q^3 + 12 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 14 * q^9	\( 16 q - 2 q^{2} + 4 q^{3} + 12 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 14 q^{9} + 2 q^{10} - 22 q^{11} + 10 q^{12} + 4 q^{13} - 14 q^{15} + 12 q^{16} + 18 q^{17} - 5 q^{18} + 15 q^{19} + 40 q^{20} - 11 q^{22} - 5 q^{23} + 26 q^{24} + 15 q^{25} + 24 q^{26} + 10 q^{27} - 12 q^{29} + 3 q^{30} + 32 q^{31} - 9 q^{32} + 10 q^{33} + 14 q^{34} + 10 q^{36} - 2 q^{37} - 3 q^{38} - 41 q^{39} + 14 q^{40} + 45 q^{41} - 3 q^{43} - 54 q^{44} + 22 q^{45} + 49 q^{47} - 10 q^{48} - 6 q^{50} - 12 q^{51} - 38 q^{52} + 16 q^{53} + 67 q^{54} - 7 q^{55} + 8 q^{57} + 16 q^{58} + 35 q^{59} + 56 q^{60} + 11 q^{61} - 17 q^{62} - 2 q^{64} + 14 q^{65} - 86 q^{66} + 17 q^{67} + 71 q^{68} + 17 q^{69} - 81 q^{71} + 13 q^{72} + 15 q^{73} + 13 q^{74} + 48 q^{75} - 14 q^{76} - 10 q^{78} - 34 q^{79} + 33 q^{80} + 40 q^{81} + 14 q^{82} + 39 q^{83} - 17 q^{85} + 36 q^{86} - 7 q^{87} + 61 q^{88} + 32 q^{89} - 79 q^{90} + 37 q^{92} + 27 q^{93} - 13 q^{94} - 33 q^{95} + 55 q^{96} + 4 q^{97} - 73 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 4 * q^3 + 12 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 14 * q^9 + 2 * q^10 - 22 * q^11 + 10 * q^12 + 4 * q^13 - 14 * q^15 + 12 * q^16 + 18 * q^17 - 5 * q^18 + 15 * q^19 + 40 * q^20 - 11 * q^22 - 5 * q^23 + 26 * q^24 + 15 * q^25 + 24 * q^26 + 10 * q^27 - 12 * q^29 + 3 * q^30 + 32 * q^31 - 9 * q^32 + 10 * q^33 + 14 * q^34 + 10 * q^36 - 2 * q^37 - 3 * q^38 - 41 * q^39 + 14 * q^40 + 45 * q^41 - 3 * q^43 - 54 * q^44 + 22 * q^45 + 49 * q^47 - 10 * q^48 - 6 * q^50 - 12 * q^51 - 38 * q^52 + 16 * q^53 + 67 * q^54 - 7 * q^55 + 8 * q^57 + 16 * q^58 + 35 * q^59 + 56 * q^60 + 11 * q^61 - 17 * q^62 - 2 * q^64 + 14 * q^65 - 86 * q^66 + 17 * q^67 + 71 * q^68 + 17 * q^69 - 81 * q^71 + 13 * q^72 + 15 * q^73 + 13 * q^74 + 48 * q^75 - 14 * q^76 - 10 * q^78 - 34 * q^79 + 33 * q^80 + 40 * q^81 + 14 * q^82 + 39 * q^83 - 17 * q^85 + 36 * q^86 - 7 * q^87 + 61 * q^88 + 32 * q^89 - 79 * q^90 + 37 * q^92 + 27 * q^93 - 13 * q^94 - 33 * q^95 + 55 * q^96 + 4 * q^97 - 73 * q^99

Introduction

L-functions

Modular forms

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Database

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