LMFDB - Embedded newform 1849.2.a.q.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 27 x^{18} + 300 x^{16} - 1775 x^{14} + 6037 x^{12} - 11859 x^{10} + 12809 x^{8} - 6823 x^{6} + \cdots + 1 $ x^20 - 27x^18 + 300x^16 - 1775x^14 + 6037x^12 - 11859x^10 + 12809x^8 - 6823x^6 + 1500x^4 - 75*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$1.88727$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.88727 q^{2} -0.805985 q^{3} +1.56178 q^{4} -0.126968 q^{5} -1.52111 q^{6} -1.51778 q^{7} -0.827047 q^{8} -2.35039 q^{9} +O(q^{10})$	\(q+1.88727 q^{2} -0.805985 q^{3} +1.56178 q^{4} -0.126968 q^{5} -1.52111 q^{6} -1.51778 q^{7} -0.827047 q^{8} -2.35039 q^{9} -0.239623 q^{10} +4.20742 q^{11} -1.25877 q^{12} +2.33450 q^{13} -2.86445 q^{14} +0.102334 q^{15} -4.68441 q^{16} -5.59036 q^{17} -4.43581 q^{18} +4.97337 q^{19} -0.198296 q^{20} +1.22331 q^{21} +7.94052 q^{22} -8.06526 q^{23} +0.666587 q^{24} -4.98388 q^{25} +4.40583 q^{26} +4.31233 q^{27} -2.37043 q^{28} -2.64659 q^{29} +0.193132 q^{30} -1.48706 q^{31} -7.18663 q^{32} -3.39112 q^{33} -10.5505 q^{34} +0.192709 q^{35} -3.67078 q^{36} -5.37156 q^{37} +9.38608 q^{38} -1.88157 q^{39} +0.105009 q^{40} -4.56519 q^{41} +2.30871 q^{42} +6.57104 q^{44} +0.298424 q^{45} -15.2213 q^{46} +5.99224 q^{47} +3.77556 q^{48} -4.69635 q^{49} -9.40591 q^{50} +4.50575 q^{51} +3.64597 q^{52} -4.41545 q^{53} +8.13852 q^{54} -0.534208 q^{55} +1.25527 q^{56} -4.00846 q^{57} -4.99483 q^{58} -13.8133 q^{59} +0.159823 q^{60} -9.98483 q^{61} -2.80647 q^{62} +3.56737 q^{63} -4.19428 q^{64} -0.296407 q^{65} -6.39994 q^{66} -2.10668 q^{67} -8.73088 q^{68} +6.50048 q^{69} +0.363694 q^{70} -4.55021 q^{71} +1.94388 q^{72} +15.1051 q^{73} -10.1376 q^{74} +4.01693 q^{75} +7.76729 q^{76} -6.38593 q^{77} -3.55103 q^{78} +14.9751 q^{79} +0.594770 q^{80} +3.57549 q^{81} -8.61572 q^{82} -2.09355 q^{83} +1.91053 q^{84} +0.709797 q^{85} +2.13312 q^{87} -3.47973 q^{88} +14.1765 q^{89} +0.563206 q^{90} -3.54326 q^{91} -12.5961 q^{92} +1.19855 q^{93} +11.3089 q^{94} -0.631459 q^{95} +5.79232 q^{96} +5.55966 q^{97} -8.86326 q^{98} -9.88907 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9}+O(q^{10}) $ 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9	$ 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9} + 12 q^{10} - 20 q^{11} + 6 q^{13} - 34 q^{14} - 34 q^{15} + 14 q^{16} - 8 q^{17} + 12 q^{21} - 46 q^{23} + 2 q^{24} + 20 q^{25} - 38 q^{31} - 76 q^{35} - 46 q^{36} - 68 q^{38} - 64 q^{40} - 56 q^{41} - 58 q^{44} - 24 q^{47} - 20 q^{49} - 20 q^{52} - 42 q^{53} + 66 q^{54} - 46 q^{56} + 2 q^{57} + 12 q^{58} - 90 q^{59} + 18 q^{60} - 28 q^{64} + 76 q^{66} - 62 q^{67} - 54 q^{68} + 24 q^{74} - 36 q^{78} - 10 q^{79} - 48 q^{81} - 68 q^{83} + 70 q^{84} - 12 q^{87} + 58 q^{90} - 8 q^{92} - 42 q^{95} - 22 q^{96} - 44 q^{97} - 38 q^{99}+O(q^{100}) $ 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9 + 12 * q^10 - 20 * q^11 + 6 * q^13 - 34 * q^14 - 34 * q^15 + 14 * q^16 - 8 * q^17 + 12 * q^21 - 46 * q^23 + 2 * q^24 + 20 * q^25 - 38 * q^31 - 76 * q^35 - 46 * q^36 - 68 * q^38 - 64 * q^40 - 56 * q^41 - 58 * q^44 - 24 * q^47 - 20 * q^49 - 20 * q^52 - 42 * q^53 + 66 * q^54 - 46 * q^56 + 2 * q^57 + 12 * q^58 - 90 * q^59 + 18 * q^60 - 28 * q^64 + 76 * q^66 - 62 * q^67 - 54 * q^68 + 24 * q^74 - 36 * q^78 - 10 * q^79 - 48 * q^81 - 68 * q^83 + 70 * q^84 - 12 * q^87 + 58 * q^90 - 8 * q^92 - 42 * q^95 - 22 * q^96 - 44 * q^97 - 38 * 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 $

$2$	1.88727	1.33450	0.667250	−	0.744834i	$-0.267471\pi$
$2$	1.88727	1.33450	0.667250	+	0.744834i	$0.267471\pi$
$3$	−0.805985	−0.465336	−0.232668	−	0.972556i	$-0.574745\pi$
$3$	−0.805985	−0.465336	−0.232668	+	0.972556i	$0.574745\pi$
$4$	1.56178	0.780888
$5$	−0.126968	−0.0567818	−0.0283909	−	0.999597i	$-0.509038\pi$
$5$	−0.126968	−0.0567818	−0.0283909	+	0.999597i	$0.509038\pi$
$6$	−1.52111	−0.620990
$7$	−1.51778	−0.573666	−0.286833	−	0.957981i	$-0.592603\pi$
$7$	−1.51778	−0.573666	−0.286833	+	0.957981i	$0.592603\pi$
$8$	−0.827047	−0.292405
$9$	−2.35039	−0.783463
$10$	−0.239623	−0.0757753
$11$	4.20742	1.26858	0.634292	−	0.773093i	$-0.281292\pi$
$11$	4.20742	1.26858	0.634292	+	0.773093i	$0.281292\pi$
$12$	−1.25877	−0.363375
$13$	2.33450	0.647474	0.323737	−	0.946147i	$-0.395061\pi$
$13$	2.33450	0.647474	0.323737	+	0.946147i	$0.395061\pi$
$14$	−2.86445	−0.765557
$15$	0.102334	0.0264226
$16$	−4.68441	−1.17110
$17$	−5.59036	−1.35586	−0.677931	−	0.735126i	$-0.737123\pi$
$17$	−5.59036	−1.35586	−0.677931	+	0.735126i	$0.737123\pi$
$18$	−4.43581	−1.04553
$19$	4.97337	1.14097	0.570485	−	0.821308i	$-0.306755\pi$
$19$	4.97337	1.14097	0.570485	+	0.821308i	$0.306755\pi$
$20$	−0.198296	−0.0443402
$21$	1.22331	0.266947
$22$	7.94052	1.69292
$23$	−8.06526	−1.68172	−0.840861	−	0.541251i	$-0.817951\pi$
$23$	−8.06526	−1.68172	−0.840861	+	0.541251i	$0.817951\pi$
$24$	0.666587	0.136067
$25$	−4.98388	−0.996776
$26$	4.40583	0.864054
$27$	4.31233	0.829909
$28$	−2.37043	−0.447969
$29$	−2.64659	−0.491460	−0.245730	−	0.969338i	$-0.579028\pi$
$29$	−2.64659	−0.491460	−0.245730	+	0.969338i	$0.579028\pi$
$30$	0.193132	0.0352610
$31$	−1.48706	−0.267083	−0.133542	−	0.991043i	$-0.542635\pi$
$31$	−1.48706	−0.267083	−0.133542	+	0.991043i	$0.542635\pi$
$32$	−7.18663	−1.27043
$33$	−3.39112	−0.590318
$34$	−10.5505	−1.80940
$35$	0.192709	0.0325738
$36$	−3.67078	−0.611796
$37$	−5.37156	−0.883078	−0.441539	−	0.897242i	$-0.645567\pi$
$37$	−5.37156	−0.883078	−0.441539	+	0.897242i	$0.645567\pi$
$38$	9.38608	1.52262
$39$	−1.88157	−0.301293
$40$	0.105009	0.0166033
$41$	−4.56519	−0.712962	−0.356481	−	0.934303i	$-0.616024\pi$
$41$	−4.56519	−0.712962	−0.356481	+	0.934303i	$0.616024\pi$
$42$	2.30871	0.356241
$43$	0	0
$43$	0	0
$44$	6.57104	0.990622
$45$	0.298424	0.0444865
$46$	−15.2213	−2.24426
$47$	5.99224	0.874057	0.437029	−	0.899448i	$-0.356031\pi$
$47$	5.99224	0.874057	0.437029	+	0.899448i	$0.356031\pi$
$48$	3.77556	0.544956
$49$	−4.69635	−0.670907
$50$	−9.40591	−1.33020
$51$	4.50575	0.630931
$52$	3.64597	0.505605
$53$	−4.41545	−0.606509	−0.303254	−	0.952910i	$-0.598073\pi$
$53$	−4.41545	−0.606509	−0.303254	+	0.952910i	$0.598073\pi$
$54$	8.13852	1.10751
$55$	−0.534208	−0.0720326
$56$	1.25527	0.167743
$57$	−4.00846	−0.530934
$58$	−4.99483	−0.655853
$59$	−13.8133	−1.79834	−0.899171	−	0.437598i	$-0.855829\pi$
$59$	−13.8133	−1.79834	−0.899171	+	0.437598i	$0.855829\pi$
$60$	0.159823	0.0206331
$61$	−9.98483	−1.27843	−0.639213	−	0.769030i	$-0.720740\pi$
$61$	−9.98483	−1.27843	−0.639213	+	0.769030i	$0.720740\pi$
$62$	−2.80647	−0.356422
$63$	3.56737	0.449446
$64$	−4.19428	−0.524285
$65$	−0.296407	−0.0367648
$66$	−6.39994	−0.787778
$67$	−2.10668	−0.257371	−0.128686	−	0.991685i	$-0.541076\pi$
$67$	−2.10668	−0.257371	−0.128686	+	0.991685i	$0.541076\pi$
$68$	−8.73088	−1.05878
$69$	6.50048	0.782565
$70$	0.363694	0.0434698
$71$	−4.55021	−0.540010	−0.270005	−	0.962859i	$-0.587025\pi$
$71$	−4.55021	−0.540010	−0.270005	+	0.962859i	$0.587025\pi$
$72$	1.94388	0.229089
$73$	15.1051	1.76791	0.883957	−	0.467568i	$-0.154870\pi$
$73$	15.1051	1.76791	0.883957	+	0.467568i	$0.154870\pi$
$74$	−10.1376	−1.17847
$75$	4.01693	0.463835
$76$	7.76729	0.890969
$77$	−6.38593	−0.727744
$78$	−3.55103	−0.402075
$79$	14.9751	1.68483	0.842414	−	0.538831i	$-0.181134\pi$
$79$	14.9751	1.68483	0.842414	+	0.538831i	$0.181134\pi$
$80$	0.594770	0.0664973
$81$	3.57549	0.397277
$82$	−8.61572	−0.951447
$83$	−2.09355	−0.229797	−0.114898	−	0.993377i	$-0.536654\pi$
$83$	−2.09355	−0.229797	−0.114898	+	0.993377i	$0.536654\pi$
$84$	1.91053	0.208456
$85$	0.709797	0.0769883
$86$	0	0
$87$	2.13312	0.228694
$88$	−3.47973	−0.370941
$89$	14.1765	1.50270	0.751351	−	0.659903i	$-0.229402\pi$
$89$	14.1765	1.50270	0.751351	+	0.659903i	$0.229402\pi$
$90$	0.563206	0.0593671
$91$	−3.54326	−0.371434
$92$	−12.5961	−1.31324
$93$	1.19855	0.124283
$94$	11.3089	1.16643
$95$	−0.631459	−0.0647864
$96$	5.79232	0.591176
$97$	5.55966	0.564498	0.282249	−	0.959341i	$-0.408920\pi$
$97$	5.55966	0.564498	0.282249	+	0.959341i	$0.408920\pi$
$98$	−8.86326	−0.895325
$99$	−9.88907	−0.993889
$100$	−7.78370	−0.778370
$101$	−11.2689	−1.12130	−0.560650	−	0.828053i	$-0.689449\pi$
$101$	−11.2689	−1.12130	−0.560650	+	0.828053i	$0.689449\pi$
$102$	8.50354	0.841976
$103$	−2.13212	−0.210084	−0.105042	−	0.994468i	$-0.533498\pi$
$103$	−2.13212	−0.210084	−0.105042	+	0.994468i	$0.533498\pi$
$104$	−1.93074	−0.189325
$105$	−0.155321	−0.0151578
$106$	−8.33313	−0.809385
$107$	−1.42861	−0.138109	−0.0690543	−	0.997613i	$-0.521998\pi$
$107$	−1.42861	−0.138109	−0.0690543	+	0.997613i	$0.521998\pi$
$108$	6.73489	0.648066
$109$	5.67601	0.543663	0.271832	−	0.962345i	$-0.412371\pi$
$109$	5.67601	0.543663	0.271832	+	0.962345i	$0.412371\pi$
$110$	−1.00819	−0.0961274
$111$	4.32939	0.410928
$112$	7.10990	0.671822
$113$	−13.0542	−1.22803	−0.614016	−	0.789293i	$-0.710447\pi$
$113$	−13.0542	−1.22803	−0.614016	+	0.789293i	$0.710447\pi$
$114$	−7.56504	−0.708531
$115$	1.02403	0.0954913
$116$	−4.13339	−0.383775
$117$	−5.48699	−0.507272
$118$	−26.0694	−2.39989
$119$	8.48493	0.777812
$120$	−0.0846353	−0.00772611
$121$	6.70238	0.609307
$122$	−18.8440	−1.70606
$123$	3.67947	0.331767
$124$	−2.32245	−0.208562
$125$	1.26763	0.113381
$126$	6.73258	0.599786
$127$	10.5480	0.935981	0.467991	−	0.883733i	$-0.344978\pi$
$127$	10.5480	0.935981	0.467991	+	0.883733i	$0.344978\pi$
$128$	6.45755	0.570772
$129$	0	0
$130$	−0.559399	−0.0490626
$131$	3.32904	0.290860	0.145430	−	0.989369i	$-0.453543\pi$
$131$	3.32904	0.290860	0.145430	+	0.989369i	$0.453543\pi$
$132$	−5.29616	−0.460972
$133$	−7.54848	−0.654536
$134$	−3.97586	−0.343462
$135$	−0.547529	−0.0471238
$136$	4.62349	0.396461
$137$	11.8040	1.00848	0.504242	−	0.863562i	$-0.331772\pi$
$137$	11.8040	1.00848	0.504242	+	0.863562i	$0.331772\pi$
$138$	12.2681	1.04433
$139$	−3.72683	−0.316106	−0.158053	−	0.987431i	$-0.550522\pi$
$139$	−3.72683	−0.316106	−0.158053	+	0.987431i	$0.550522\pi$
$140$	0.300969	0.0254365
$141$	−4.82965	−0.406730
$142$	−8.58745	−0.720643
$143$	9.82223	0.821376
$144$	11.0102	0.917515
$145$	0.336033	0.0279060
$146$	28.5073	2.35928
$147$	3.78519	0.312197
$148$	−8.38916	−0.689585
$149$	9.25643	0.758316	0.379158	−	0.925332i	$-0.376214\pi$
$149$	9.25643	0.758316	0.379158	+	0.925332i	$0.376214\pi$
$150$	7.58102	0.618988
$151$	−16.4755	−1.34076	−0.670378	−	0.742020i	$-0.733868\pi$
$151$	−16.4755	−1.34076	−0.670378	+	0.742020i	$0.733868\pi$
$152$	−4.11321	−0.333626
$153$	13.1395	1.06227
$154$	−12.0520	−0.971174
$155$	0.188809	0.0151655
$156$	−2.93859	−0.235276
$157$	23.3387	1.86263	0.931315	−	0.364216i	$-0.118663\pi$
$157$	23.3387	1.86263	0.931315	+	0.364216i	$0.118663\pi$
$158$	28.2620	2.24840
$159$	3.55879	0.282230
$160$	0.912473	0.0721373
$161$	12.2413	0.964748
$162$	6.74790	0.530165
$163$	17.7009	1.38644	0.693220	−	0.720726i	$-0.256192\pi$
$163$	17.7009	1.38644	0.693220	+	0.720726i	$0.256192\pi$
$164$	−7.12979	−0.556743
$165$	0.430564	0.0335193
$166$	−3.95108	−0.306664
$167$	−7.17863	−0.555499	−0.277749	−	0.960654i	$-0.589589\pi$
$167$	−7.17863	−0.555499	−0.277749	+	0.960654i	$0.589589\pi$
$168$	−1.01173	−0.0780568
$169$	−7.55010	−0.580777
$170$	1.33958	0.102741
$171$	−11.6894	−0.893907
$172$	0	0
$173$	−4.63680	−0.352529	−0.176265	−	0.984343i	$-0.556401\pi$
$173$	−4.63680	−0.352529	−0.176265	+	0.984343i	$0.556401\pi$
$174$	4.02576	0.305192
$175$	7.56443	0.571817
$176$	−19.7093	−1.48564
$177$	11.1333	0.836833
$178$	26.7548	2.00535
$179$	5.73214	0.428440	0.214220	−	0.976785i	$-0.431279\pi$
$179$	5.73214	0.428440	0.214220	+	0.976785i	$0.431279\pi$
$180$	0.466072	0.0347389
$181$	0.971446	0.0722070	0.0361035	−	0.999348i	$-0.488505\pi$
$181$	0.971446	0.0722070	0.0361035	+	0.999348i	$0.488505\pi$
$182$	−6.68707	−0.495679
$183$	8.04762	0.594897
$184$	6.67035	0.491744
$185$	0.682016	0.0501428
$186$	2.26197	0.165856
$187$	−23.5210	−1.72002
$188$	9.35853	0.682541
$189$	−6.54517	−0.476091
$190$	−1.19173	−0.0864573
$191$	1.17671	0.0851436	0.0425718	−	0.999093i	$-0.486445\pi$
$191$	1.17671	0.0851436	0.0425718	+	0.999093i	$0.486445\pi$
$192$	3.38052	0.243968
$193$	3.87170	0.278691	0.139345	−	0.990244i	$-0.455500\pi$
$193$	3.87170	0.278691	0.139345	+	0.990244i	$0.455500\pi$
$194$	10.4926	0.753321
$195$	0.238900	0.0171080
$196$	−7.33464	−0.523903
$197$	18.1072	1.29008	0.645042	−	0.764147i	$-0.276840\pi$
$197$	18.1072	1.29008	0.645042	+	0.764147i	$0.276840\pi$
$198$	−18.6633	−1.32634
$199$	−17.8987	−1.26881	−0.634403	−	0.773003i	$-0.718754\pi$
$199$	−17.8987	−1.26881	−0.634403	+	0.773003i	$0.718754\pi$
$200$	4.12190	0.291462
$201$	1.69795	0.119764
$202$	−21.2675	−1.49637
$203$	4.01695	0.281934
$204$	7.03696	0.492686
$205$	0.579633	0.0404833
$206$	−4.02388	−0.280357
$207$	18.9565	1.31757
$208$	−10.9358	−0.758258
$209$	20.9251	1.44742
$210$	−0.293132	−0.0202280
$211$	−23.1719	−1.59522	−0.797609	−	0.603175i	$-0.793902\pi$
$211$	−23.1719	−1.59522	−0.797609	+	0.603175i	$0.793902\pi$
$212$	−6.89594	−0.473615
$213$	3.66740	0.251286
$214$	−2.69616	−0.184306
$215$	0	0
$216$	−3.56650	−0.242670
$217$	2.25702	0.153217
$218$	10.7121	0.725518
$219$	−12.1745	−0.822674
$220$	−0.834313	−0.0562494
$221$	−13.0507	−0.877885
$222$	8.17072	0.548383
$223$	−5.07688	−0.339973	−0.169986	−	0.985446i	$-0.554372\pi$
$223$	−5.07688	−0.339973	−0.169986	+	0.985446i	$0.554372\pi$
$224$	10.9077	0.728803
$225$	11.7141	0.780937
$226$	−24.6367	−1.63881
$227$	8.59401	0.570404	0.285202	−	0.958467i	$-0.407939\pi$
$227$	8.59401	0.570404	0.285202	+	0.958467i	$0.407939\pi$
$228$	−6.26032	−0.414600
$229$	−19.1845	−1.26775	−0.633873	−	0.773437i	$-0.718536\pi$
$229$	−19.1845	−1.26775	−0.633873	+	0.773437i	$0.718536\pi$
$230$	1.93262	0.127433
$231$	5.14696	0.338645
$232$	2.18886	0.143706
$233$	22.8579	1.49747	0.748736	−	0.662869i	$-0.230661\pi$
$233$	22.8579	1.49747	0.748736	+	0.662869i	$0.230661\pi$
$234$	−10.3554	−0.676954
$235$	−0.760823	−0.0496306
$236$	−21.5733	−1.40430
$237$	−12.0697	−0.784011
$238$	16.0133	1.03799
$239$	−11.0421	−0.714253	−0.357127	−	0.934056i	$-0.616244\pi$
$239$	−11.0421	−0.714253	−0.357127	+	0.934056i	$0.616244\pi$
$240$	−0.479376	−0.0309436
$241$	−12.6547	−0.815158	−0.407579	−	0.913170i	$-0.633627\pi$
$241$	−12.6547	−0.815158	−0.407579	+	0.913170i	$0.633627\pi$
$242$	12.6492	0.813119
$243$	−15.8188	−1.01478
$244$	−15.5941	−0.998307
$245$	0.596286	0.0380953
$246$	6.94414	0.442742
$247$	11.6103	0.738749
$248$	1.22987	0.0780965
$249$	1.68737	0.106933
$250$	2.39236	0.151306
$251$	−11.4052	−0.719888	−0.359944	−	0.932974i	$-0.617204\pi$
$251$	−11.4052	−0.719888	−0.359944	+	0.932974i	$0.617204\pi$
$252$	5.57143	0.350967
$253$	−33.9339	−2.13341
$254$	19.9068	1.24907
$255$	−0.572086	−0.0358254
$256$	20.5757	1.28598
$257$	−17.0581	−1.06406	−0.532028	−	0.846726i	$-0.678570\pi$
$257$	−17.0581	−1.06406	−0.532028	+	0.846726i	$0.678570\pi$
$258$	0	0
$259$	8.15283	0.506592
$260$	−0.462921	−0.0287092
$261$	6.22053	0.385041
$262$	6.28279	0.388152
$263$	−6.77841	−0.417974	−0.208987	−	0.977918i	$-0.567017\pi$
$263$	−6.77841	−0.417974	−0.208987	+	0.977918i	$0.567017\pi$
$264$	2.80461	0.172612
$265$	0.560621	0.0344387
$266$	−14.2460	−0.873478
$267$	−11.4260	−0.699261
$268$	−3.29015	−0.200978
$269$	−19.1767	−1.16922	−0.584611	−	0.811314i	$-0.698753\pi$
$269$	−19.1767	−1.16922	−0.584611	+	0.811314i	$0.698753\pi$
$270$	−1.03333	−0.0628866
$271$	−6.35388	−0.385971	−0.192985	−	0.981202i	$-0.561817\pi$
$271$	−6.35388	−0.385971	−0.192985	+	0.981202i	$0.561817\pi$
$272$	26.1875	1.58785
$273$	2.85581	0.172842
$274$	22.2773	1.34582
$275$	−20.9693	−1.26449
$276$	10.1523	0.611096
$277$	18.6255	1.11910	0.559548	−	0.828798i	$-0.310975\pi$
$277$	18.6255	1.11910	0.559548	+	0.828798i	$0.310975\pi$
$278$	−7.03353	−0.421843
$279$	3.49516	0.209250
$280$	−0.159380	−0.00952476
$281$	−6.78540	−0.404783	−0.202391	−	0.979305i	$-0.564871\pi$
$281$	−6.78540	−0.404783	−0.202391	+	0.979305i	$0.564871\pi$
$282$	−9.11484	−0.542781
$283$	−7.23759	−0.430230	−0.215115	−	0.976589i	$-0.569013\pi$
$283$	−7.23759	−0.430230	−0.215115	+	0.976589i	$0.569013\pi$
$284$	−7.10640	−0.421687
$285$	0.508947	0.0301474
$286$	18.5372	1.09613
$287$	6.92894	0.409002
$288$	16.8914	0.995334
$289$	14.2521	0.838360
$290$	0.634184	0.0372406
$291$	−4.48100	−0.262681
$292$	23.5907	1.38054
$293$	8.89839	0.519850	0.259925	−	0.965629i	$-0.416302\pi$
$293$	8.89839	0.519850	0.259925	+	0.965629i	$0.416302\pi$
$294$	7.14365	0.416626
$295$	1.75385	0.102113
$296$	4.44253	0.258217
$297$	18.1438	1.05281
$298$	17.4694	1.01197
$299$	−18.8284	−1.08887
$300$	6.27354	0.362203
$301$	0	0
$302$	−31.0936	−1.78924
$303$	9.08259	0.521781
$304$	−23.2973	−1.33619
$305$	1.26775	0.0725914
$306$	24.7978	1.41759
$307$	15.0380	0.858263	0.429131	−	0.903242i	$-0.358820\pi$
$307$	15.0380	0.858263	0.429131	+	0.903242i	$0.358820\pi$
$308$	−9.97339	−0.568287
$309$	1.71846	0.0977595
$310$	0.356332	0.0202383
$311$	−20.3119	−1.15178	−0.575891	−	0.817526i	$-0.695345\pi$
$311$	−20.3119	−1.15178	−0.575891	+	0.817526i	$0.695345\pi$
$312$	1.55615	0.0880996
$313$	2.25316	0.127356	0.0636781	−	0.997970i	$-0.479717\pi$
$313$	2.25316	0.127356	0.0636781	+	0.997970i	$0.479717\pi$
$314$	44.0463	2.48568
$315$	−0.452942	−0.0255204
$316$	23.3877	1.31566
$317$	−8.07220	−0.453380	−0.226690	−	0.973967i	$-0.572790\pi$
$317$	−8.07220	−0.453380	−0.226690	+	0.973967i	$0.572790\pi$
$318$	6.71638	0.376636
$319$	−11.1353	−0.623459
$320$	0.532539	0.0297699
$321$	1.15143	0.0642668
$322$	23.1026	1.28745
$323$	−27.8029	−1.54700
$324$	5.58411	0.310228
$325$	−11.6349	−0.645387
$326$	33.4063	1.85020
$327$	−4.57478	−0.252986
$328$	3.77562	0.208474
$329$	−9.09489	−0.501417
$330$	0.812588	0.0447315
$331$	3.99703	0.219697	0.109848	−	0.993948i	$-0.464964\pi$
$331$	3.99703	0.219697	0.109848	+	0.993948i	$0.464964\pi$
$332$	−3.26965	−0.179445
$333$	12.6252	0.691859
$334$	−13.5480	−0.741313
$335$	0.267481	0.0146140
$336$	−5.73047	−0.312623
$337$	30.5333	1.66325	0.831627	−	0.555334i	$-0.187410\pi$
$337$	30.5333	1.66325	0.831627	+	0.555334i	$0.187410\pi$
$338$	−14.2491	−0.775046
$339$	10.5215	0.571447
$340$	1.10854	0.0601192
$341$	−6.25667	−0.338818
$342$	−22.0609	−1.19292
$343$	17.7525	0.958543
$344$	0	0
$345$	−0.825353	−0.0444355
$346$	−8.75087	−0.470450
$347$	13.3094	0.714484	0.357242	−	0.934012i	$-0.383717\pi$
$347$	13.3094	0.714484	0.357242	+	0.934012i	$0.383717\pi$
$348$	3.33145	0.178584
$349$	−26.7370	−1.43120	−0.715598	−	0.698512i	$-0.753846\pi$
$349$	−26.7370	−1.43120	−0.715598	+	0.698512i	$0.753846\pi$
$350$	14.2761	0.763089
$351$	10.0671	0.537345
$352$	−30.2372	−1.61165
$353$	−0.146688	−0.00780744	−0.00390372	−	0.999992i	$-0.501243\pi$
$353$	−0.146688	−0.00780744	−0.00390372	+	0.999992i	$0.501243\pi$
$354$	21.0116	1.11675
$355$	0.577731	0.0306628
$356$	22.1405	1.17344
$357$	−6.83872	−0.361944
$358$	10.8181	0.571753
$359$	25.9280	1.36843	0.684214	−	0.729281i	$-0.260145\pi$
$359$	25.9280	1.36843	0.684214	+	0.729281i	$0.260145\pi$
$360$	−0.246811	−0.0130081
$361$	5.73443	0.301812
$362$	1.83338	0.0963602
$363$	−5.40201	−0.283532
$364$	−5.53377	−0.290048
$365$	−1.91786	−0.100385
$366$	15.1880	0.793890
$367$	20.4684	1.06844	0.534221	−	0.845345i	$-0.320605\pi$
$367$	20.4684	1.06844	0.534221	+	0.845345i	$0.320605\pi$
$368$	37.7810	1.96947
$369$	10.7300	0.558579
$370$	1.28715	0.0669155
$371$	6.70167	0.347934
$372$	1.87186	0.0970513
$373$	−34.1590	−1.76869	−0.884344	−	0.466835i	$-0.845394\pi$
$373$	−34.1590	−1.76869	−0.884344	+	0.466835i	$0.845394\pi$
$374$	−44.3904	−2.29537
$375$	−1.02169	−0.0527600
$376$	−4.95586	−0.255579
$377$	−6.17848	−0.318208
$378$	−12.3525	−0.635343
$379$	−21.8917	−1.12450	−0.562250	−	0.826968i	$-0.690064\pi$
$379$	−21.8917	−1.12450	−0.562250	+	0.826968i	$0.690064\pi$
$380$	−0.986198	−0.0505909
$381$	−8.50151	−0.435545
$382$	2.22076	0.113624
$383$	18.3858	0.939471	0.469735	−	0.882807i	$-0.344349\pi$
$383$	18.3858	0.939471	0.469735	+	0.882807i	$0.344349\pi$
$384$	−5.20469	−0.265601
$385$	0.810809	0.0413227
$386$	7.30693	0.371913
$387$	0	0
$388$	8.68293	0.440809
$389$	−8.37856	−0.424810	−0.212405	−	0.977182i	$-0.568130\pi$
$389$	−8.37856	−0.424810	−0.212405	+	0.977182i	$0.568130\pi$
$390$	0.450868	0.0228306
$391$	45.0877	2.28018
$392$	3.88410	0.196177
$393$	−2.68316	−0.135347
$394$	34.1731	1.72162
$395$	−1.90136	−0.0956677
$396$	−15.4445	−0.776115
$397$	16.8086	0.843598	0.421799	−	0.906689i	$-0.361399\pi$
$397$	16.8086	0.843598	0.421799	+	0.906689i	$0.361399\pi$
$398$	−33.7796	−1.69322
$399$	6.08396	0.304579
$400$	23.3465	1.16733
$401$	5.69004	0.284147	0.142074	−	0.989856i	$-0.454623\pi$
$401$	5.69004	0.284147	0.142074	+	0.989856i	$0.454623\pi$
$402$	3.20448	0.159825
$403$	−3.47154	−0.172929
$404$	−17.5995	−0.875610
$405$	−0.453973	−0.0225581
$406$	7.58105	0.376241
$407$	−22.6004	−1.12026
$408$	−3.72646	−0.184487
$409$	35.6595	1.76325	0.881624	−	0.471952i	$-0.156451\pi$
$409$	35.6595	1.76325	0.881624	+	0.471952i	$0.156451\pi$
$410$	1.09392	0.0540249
$411$	−9.51386	−0.469284
$412$	−3.32989	−0.164052
$413$	20.9656	1.03165
$414$	35.7759	1.75829
$415$	0.265814	0.0130483
$416$	−16.7772	−0.822570
$417$	3.00377	0.147095
$418$	39.4912	1.93158
$419$	16.1497	0.788965	0.394482	−	0.918903i	$-0.370924\pi$
$419$	16.1497	0.788965	0.394482	+	0.918903i	$0.370924\pi$
$420$	−0.242576	−0.0118365
$421$	13.5145	0.658658	0.329329	−	0.944215i	$-0.393177\pi$
$421$	13.5145	0.658658	0.329329	+	0.944215i	$0.393177\pi$
$422$	−43.7315	−2.12882
$423$	−14.0841	−0.684791
$424$	3.65178	0.177346
$425$	27.8617	1.35149
$426$	6.92136	0.335341
$427$	15.1548	0.733390
$428$	−2.23116	−0.107847
$429$	−7.91657	−0.382215
$430$	0	0
$431$	17.6669	0.850987	0.425493	−	0.904962i	$-0.360101\pi$
$431$	17.6669	0.850987	0.425493	+	0.904962i	$0.360101\pi$
$432$	−20.2007	−0.971908
$433$	−8.76277	−0.421112	−0.210556	−	0.977582i	$-0.567527\pi$
$433$	−8.76277	−0.421112	−0.210556	+	0.977582i	$0.567527\pi$
$434$	4.25960	0.204467
$435$	−0.270838	−0.0129857
$436$	8.86465	0.424540
$437$	−40.1115	−1.91879
$438$	−22.9764	−1.09786
$439$	−31.0062	−1.47984	−0.739921	−	0.672693i	$-0.765137\pi$
$439$	−31.0062	−1.47984	−0.739921	+	0.672693i	$0.765137\pi$
$440$	0.441815	0.0210627
$441$	11.0382	0.525631
$442$	−24.6302	−1.17154
$443$	−13.5160	−0.642164	−0.321082	−	0.947051i	$-0.604046\pi$
$443$	−13.5160	−0.642164	−0.321082	+	0.947051i	$0.604046\pi$
$444$	6.76154	0.320888
$445$	−1.79996	−0.0853262
$446$	−9.58142	−0.453693
$447$	−7.46054	−0.352872
$448$	6.36599	0.300765
$449$	−9.20057	−0.434202	−0.217101	−	0.976149i	$-0.569660\pi$
$449$	−9.20057	−0.434202	−0.217101	+	0.976149i	$0.569660\pi$
$450$	22.1075	1.04216
$451$	−19.2076	−0.904453
$452$	−20.3877	−0.958955
$453$	13.2790	0.623902
$454$	16.2192	0.761204
$455$	0.449880	0.0210907
$456$	3.31519	0.155248
$457$	1.72720	0.0807950	0.0403975	−	0.999184i	$-0.487138\pi$
$457$	1.72720	0.0807950	0.0403975	+	0.999184i	$0.487138\pi$
$458$	−36.2062	−1.69181
$459$	−24.1075	−1.12524
$460$	1.59931	0.0745680
$461$	−15.9037	−0.740709	−0.370354	−	0.928891i	$-0.620764\pi$
$461$	−15.9037	−0.740709	−0.370354	+	0.928891i	$0.620764\pi$
$462$	9.71369	0.451922
$463$	−37.0012	−1.71959	−0.859795	−	0.510639i	$-0.829409\pi$
$463$	−37.0012	−1.71959	−0.859795	+	0.510639i	$0.829409\pi$
$464$	12.3977	0.575550
$465$	−0.152177	−0.00705704
$466$	43.1390	1.99837
$467$	−24.9002	−1.15225	−0.576123	−	0.817363i	$-0.695435\pi$
$467$	−24.9002	−1.15225	−0.576123	+	0.817363i	$0.695435\pi$
$468$	−8.56944	−0.396122
$469$	3.19747	0.147645
$470$	−1.43588	−0.0662320
$471$	−18.8106	−0.866748
$472$	11.4243	0.525845
$473$	0	0
$474$	−22.7787	−1.04626
$475$	−24.7867	−1.13729
$476$	13.2516	0.607384
$477$	10.3780	0.475177
$478$	−20.8394	−0.953170
$479$	−24.2938	−1.11001	−0.555007	−	0.831846i	$-0.687284\pi$
$479$	−24.2938	−1.11001	−0.555007	+	0.831846i	$0.687284\pi$
$480$	−0.735440	−0.0335681
$481$	−12.5399	−0.571771
$482$	−23.8827	−1.08783
$483$	−9.86628	−0.448931
$484$	10.4676	0.475800
$485$	−0.705899	−0.0320532
$486$	−29.8543	−1.35422
$487$	−2.21295	−0.100278	−0.0501392	−	0.998742i	$-0.515966\pi$
$487$	−2.21295	−0.100278	−0.0501392	+	0.998742i	$0.515966\pi$
$488$	8.25792	0.373818
$489$	−14.2666	−0.645160
$490$	1.12535	0.0508382
$491$	17.2974	0.780621	0.390311	−	0.920683i	$-0.372368\pi$
$491$	17.2974	0.780621	0.390311	+	0.920683i	$0.372368\pi$
$492$	5.74651	0.259073
$493$	14.7954	0.666352
$494$	21.9118	0.985859
$495$	1.25560	0.0564348
$496$	6.96598	0.312782
$497$	6.90621	0.309786
$498$	3.18451	0.142701
$499$	−0.427045	−0.0191171	−0.00955857	−	0.999954i	$-0.503043\pi$
$499$	−0.427045	−0.0191171	−0.00955857	+	0.999954i	$0.503043\pi$
$500$	1.97976	0.0885375
$501$	5.78587	0.258493
$502$	−21.5246	−0.960690
$503$	9.00341	0.401442	0.200721	−	0.979648i	$-0.435672\pi$
$503$	9.00341	0.401442	0.200721	+	0.979648i	$0.435672\pi$
$504$	−2.95038	−0.131420
$505$	1.43079	0.0636695
$506$	−64.0424	−2.84703
$507$	6.08527	0.270256
$508$	16.4736	0.730896
$509$	25.3091	1.12180	0.560902	−	0.827882i	$-0.310454\pi$
$509$	25.3091	1.12180	0.560902	+	0.827882i	$0.310454\pi$
$510$	−1.07968	−0.0478090
$511$	−22.9262	−1.01419
$512$	25.9167	1.14537
$513$	21.4468	0.946901
$514$	−32.1932	−1.41998
$515$	0.270711	0.0119290
$516$	0	0
$517$	25.2118	1.10882
$518$	15.3866	0.676047
$519$	3.73719	0.164044
$520$	0.245143	0.0107502
$521$	−11.2777	−0.494086	−0.247043	−	0.969004i	$-0.579459\pi$
$521$	−11.2777	−0.494086	−0.247043	+	0.969004i	$0.579459\pi$
$522$	11.7398	0.513837
$523$	−10.7109	−0.468354	−0.234177	−	0.972194i	$-0.575239\pi$
$523$	−10.7109	−0.468354	−0.234177	+	0.972194i	$0.575239\pi$
$524$	5.19922	0.227129
$525$	−6.09681	−0.266087
$526$	−12.7927	−0.557787
$527$	8.31318	0.362128
$528$	15.8854	0.691322
$529$	42.0484	1.82819
$530$	1.05804	0.0459584
$531$	32.4667	1.40893
$532$	−11.7890	−0.511119
$533$	−10.6574	−0.461625
$534$	−21.5639	−0.933163
$535$	0.181387	0.00784206
$536$	1.74232	0.0752567
$537$	−4.62002	−0.199369
$538$	−36.1915	−1.56032
$539$	−19.7595	−0.851102
$540$	−0.855117	−0.0367984
$541$	−3.71797	−0.159848	−0.0799240	−	0.996801i	$-0.525468\pi$
$541$	−3.71797	−0.159848	−0.0799240	+	0.996801i	$0.525468\pi$
$542$	−11.9915	−0.515077
$543$	−0.782971	−0.0336005
$544$	40.1759	1.72253
$545$	−0.720672	−0.0308702
$546$	5.38968	0.230657
$547$	4.46329	0.190837	0.0954183	−	0.995437i	$-0.469581\pi$
$547$	4.46329	0.190837	0.0954183	+	0.995437i	$0.469581\pi$
$548$	18.4352	0.787513
$549$	23.4682	1.00160
$550$	−39.5746	−1.68747
$551$	−13.1625	−0.560741
$552$	−5.37620	−0.228826
$553$	−22.7289	−0.966529
$554$	35.1512	1.49343
$555$	−0.549695	−0.0233332
$556$	−5.82048	−0.246843
$557$	20.6313	0.874174	0.437087	−	0.899419i	$-0.356010\pi$
$557$	20.6313	0.874174	0.437087	+	0.899419i	$0.356010\pi$
$558$	6.59630	0.279244
$559$	0	0
$560$	−0.902730	−0.0381473
$561$	18.9576	0.800389
$562$	−12.8059	−0.540182
$563$	18.4481	0.777493	0.388747	−	0.921345i	$-0.372908\pi$
$563$	18.4481	0.777493	0.388747	+	0.921345i	$0.372908\pi$
$564$	−7.54283	−0.317610
$565$	1.65746	0.0697300
$566$	−13.6593	−0.574142
$567$	−5.42680	−0.227904
$568$	3.76323	0.157902
$569$	28.0115	1.17430	0.587151	−	0.809477i	$-0.300249\pi$
$569$	28.0115	1.17430	0.587151	+	0.809477i	$0.300249\pi$
$570$	0.960518	0.0402317
$571$	−10.8537	−0.454214	−0.227107	−	0.973870i	$-0.572927\pi$
$571$	−10.8537	−0.454214	−0.227107	+	0.973870i	$0.572927\pi$
$572$	15.3401	0.641402
$573$	−0.948409	−0.0396204
$574$	13.0768	0.545813
$575$	40.1963	1.67630
$576$	9.85818	0.410758
$577$	9.95115	0.414272	0.207136	−	0.978312i	$-0.433586\pi$
$577$	9.95115	0.414272	0.207136	+	0.978312i	$0.433586\pi$
$578$	26.8975	1.11879
$579$	−3.12053	−0.129685
$580$	0.524808	0.0217915
$581$	3.17754	0.131827
$582$	−8.45684	−0.350547
$583$	−18.5776	−0.769407
$584$	−12.4926	−0.516947
$585$	0.696672	0.0288038
$586$	16.7936	0.693739
$587$	−21.0785	−0.870002	−0.435001	−	0.900430i	$-0.643252\pi$
$587$	−21.0785	−0.870002	−0.435001	+	0.900430i	$0.643252\pi$
$588$	5.91161	0.243791
$589$	−7.39568	−0.304734
$590$	3.30999	0.136270
$591$	−14.5941	−0.600322
$592$	25.1626	1.03417
$593$	−20.2135	−0.830071	−0.415035	−	0.909805i	$-0.636231\pi$
$593$	−20.2135	−0.830071	−0.415035	+	0.909805i	$0.636231\pi$
$594$	34.2422	1.40497
$595$	−1.07731	−0.0441656
$596$	14.4565	0.592160
$597$	14.4261	0.590420
$598$	−35.5341	−1.45310
$599$	−38.6386	−1.57873	−0.789366	−	0.613923i	$-0.789590\pi$
$599$	−38.6386	−1.57873	−0.789366	+	0.613923i	$0.789590\pi$
$600$	−3.32219	−0.135628
$601$	−33.5518	−1.36861	−0.684304	−	0.729197i	$-0.739894\pi$
$601$	−33.5518	−1.36861	−0.684304	+	0.729197i	$0.739894\pi$
$602$	0	0
$603$	4.95151	0.201641
$604$	−25.7310	−1.04698
$605$	−0.850988	−0.0345976
$606$	17.1413	0.696316
$607$	20.5281	0.833208	0.416604	−	0.909088i	$-0.363220\pi$
$607$	20.5281	0.833208	0.416604	+	0.909088i	$0.363220\pi$
$608$	−35.7418	−1.44952
$609$	−3.23760	−0.131194
$610$	2.39259	0.0968731
$611$	13.9889	0.565930
$612$	20.5210	0.829511
$613$	−8.09532	−0.326967	−0.163484	−	0.986546i	$-0.552273\pi$
$613$	−8.09532	−0.326967	−0.163484	+	0.986546i	$0.552273\pi$
$614$	28.3807	1.14535
$615$	−0.467175	−0.0188383
$616$	5.28146	0.212796
$617$	−3.35191	−0.134943	−0.0674715	−	0.997721i	$-0.521493\pi$
$617$	−3.35191	−0.134943	−0.0674715	+	0.997721i	$0.521493\pi$
$618$	3.24318	0.130460
$619$	8.03530	0.322966	0.161483	−	0.986876i	$-0.448372\pi$
$619$	8.03530	0.322966	0.161483	+	0.986876i	$0.448372\pi$
$620$	0.294877	0.0118425
$621$	−34.7801	−1.39568
$622$	−38.3340	−1.53705
$623$	−21.5167	−0.862050
$624$	8.81406	0.352845
$625$	24.7584	0.990338
$626$	4.25231	0.169957
$627$	−16.8653	−0.673535
$628$	36.4498	1.45450
$629$	30.0289	1.19733
$630$	−0.854822	−0.0340569
$631$	−3.99405	−0.159001	−0.0795004	−	0.996835i	$-0.525332\pi$
$631$	−3.99405	−0.159001	−0.0795004	+	0.996835i	$0.525332\pi$
$632$	−12.3851	−0.492653
$633$	18.6762	0.742312
$634$	−15.2344	−0.605035
$635$	−1.33926	−0.0531467
$636$	5.55802	0.220390
$637$	−10.9636	−0.434395
$638$	−21.0153	−0.832005
$639$	10.6947	0.423078
$640$	−0.819902	−0.0324095
$641$	6.96404	0.275063	0.137531	−	0.990497i	$-0.456083\pi$
$641$	6.96404	0.275063	0.137531	+	0.990497i	$0.456083\pi$
$642$	2.17306	0.0857640
$643$	2.90942	0.114736	0.0573681	−	0.998353i	$-0.481729\pi$
$643$	2.90942	0.114736	0.0573681	+	0.998353i	$0.481729\pi$
$644$	19.1181	0.753360
$645$	0	0
$646$	−52.4715	−2.06447
$647$	5.91505	0.232545	0.116272	−	0.993217i	$-0.462905\pi$
$647$	5.91505	0.232545	0.116272	+	0.993217i	$0.462905\pi$
$648$	−2.95710	−0.116166
$649$	−58.1185	−2.28135
$650$	−21.9581	−0.861268
$651$	−1.81913	−0.0712972
$652$	27.6448	1.08265
$653$	−40.6003	−1.58881	−0.794406	−	0.607386i	$-0.792218\pi$
$653$	−40.6003	−1.58881	−0.794406	+	0.607386i	$0.792218\pi$
$654$	−8.63383	−0.337609
$655$	−0.422682	−0.0165156
$656$	21.3852	0.834952
$657$	−35.5028	−1.38510
$658$	−17.1645	−0.669141
$659$	−37.7627	−1.47102	−0.735512	−	0.677511i	$-0.763058\pi$
$659$	−37.7627	−1.47102	−0.735512	+	0.677511i	$0.763058\pi$
$660$	0.672444	0.0261748
$661$	−16.6857	−0.648998	−0.324499	−	0.945886i	$-0.605196\pi$
$661$	−16.6857	−0.648998	−0.324499	+	0.945886i	$0.605196\pi$
$662$	7.54346	0.293185
$663$	10.5187	0.408511
$664$	1.73146	0.0671938
$665$	0.958416	0.0371658
$666$	23.8272	0.923285
$667$	21.3455	0.826500
$668$	−11.2114	−0.433782
$669$	4.09189	0.158201
$670$	0.504807	0.0195024
$671$	−42.0103	−1.62179
$672$	−8.79146	−0.339138
$673$	−18.0195	−0.694599	−0.347300	−	0.937754i	$-0.612901\pi$
$673$	−18.0195	−0.694599	−0.347300	+	0.937754i	$0.612901\pi$
$674$	57.6245	2.21961
$675$	−21.4921	−0.827233
$676$	−11.7916	−0.453522
$677$	−11.6551	−0.447940	−0.223970	−	0.974596i	$-0.571902\pi$
$677$	−11.6551	−0.447940	−0.223970	+	0.974596i	$0.571902\pi$
$678$	19.8568	0.762596
$679$	−8.43833	−0.323833
$680$	−0.587035	−0.0225118
$681$	−6.92664	−0.265429
$682$	−11.8080	−0.452152
$683$	−40.1996	−1.53820	−0.769098	−	0.639131i	$-0.779294\pi$
$683$	−40.1996	−1.53820	−0.769098	+	0.639131i	$0.779294\pi$
$684$	−18.2561	−0.698041
$685$	−1.49873	−0.0572636
$686$	33.5036	1.27917
$687$	15.4624	0.589928
$688$	0	0
$689$	−10.3079	−0.392699
$690$	−1.55766	−0.0592991
$691$	−32.2000	−1.22495	−0.612474	−	0.790491i	$-0.709825\pi$
$691$	−32.2000	−1.22495	−0.612474	+	0.790491i	$0.709825\pi$
$692$	−7.24163	−0.275286
$693$	15.0094	0.570161
$694$	25.1183	0.953478
$695$	0.473189	0.0179491
$696$	−1.76419	−0.0668713
$697$	25.5210	0.966678
$698$	−50.4598	−1.90993
$699$	−18.4231	−0.696827
$700$	11.8139	0.446525
$701$	4.57474	0.172786	0.0863928	−	0.996261i	$-0.472466\pi$
$701$	4.57474	0.172786	0.0863928	+	0.996261i	$0.472466\pi$
$702$	18.9994	0.717086
$703$	−26.7147	−1.00757
$704$	−17.6471	−0.665099
$705$	0.613212	0.0230949
$706$	−0.276840	−0.0104190
$707$	17.1037	0.643252
$708$	17.3878	0.653472
$709$	24.4283	0.917425	0.458713	−	0.888585i	$-0.348311\pi$
$709$	24.4283	0.917425	0.458713	+	0.888585i	$0.348311\pi$
$710$	1.09033	0.0409194
$711$	−35.1973	−1.32000
$712$	−11.7246	−0.439398
$713$	11.9935	0.449160
$714$	−12.9065	−0.483013
$715$	−1.24711	−0.0466392
$716$	8.95232	0.334564
$717$	8.89975	0.332367
$718$	48.9331	1.82617
$719$	−38.7132	−1.44376	−0.721879	−	0.692019i	$-0.756721\pi$
$719$	−38.7132	−1.44376	−0.721879	+	0.692019i	$0.756721\pi$
$720$	−1.39794	−0.0520982
$721$	3.23608	0.120518
$722$	10.8224	0.402768
$723$	10.1995	0.379322
$724$	1.51718	0.0563856
$725$	13.1903	0.489876
$726$	−10.1950	−0.378373
$727$	−24.9476	−0.925256	−0.462628	−	0.886553i	$-0.653093\pi$
$727$	−24.9476	−0.925256	−0.462628	+	0.886553i	$0.653093\pi$
$728$	2.93044	0.108609
$729$	2.02324	0.0749347
$730$	−3.61952	−0.133964
$731$	0	0
$732$	12.5686	0.464548
$733$	42.6308	1.57460	0.787302	−	0.616568i	$-0.211477\pi$
$733$	42.6308	1.57460	0.787302	+	0.616568i	$0.211477\pi$
$734$	38.6293	1.42583
$735$	−0.480598	−0.0177271
$736$	57.9621	2.13651
$737$	−8.86367	−0.326497
$738$	20.2503	0.745424
$739$	35.3259	1.29948	0.649741	−	0.760155i	$-0.274877\pi$
$739$	35.3259	1.29948	0.649741	+	0.760155i	$0.274877\pi$
$740$	1.06516	0.0391559
$741$	−9.35776	−0.343766
$742$	12.6478	0.464317
$743$	1.09759	0.0402668	0.0201334	−	0.999797i	$-0.493591\pi$
$743$	1.09759	0.0402668	0.0201334	+	0.999797i	$0.493591\pi$
$744$	−0.991253	−0.0363411
$745$	−1.17527	−0.0430586
$746$	−64.4672	−2.36031
$747$	4.92065	0.180037
$748$	−36.7345	−1.34315
$749$	2.16831	0.0792282
$750$	−1.92821	−0.0704082
$751$	0.238664	0.00870899	0.00435449	−	0.999991i	$-0.498614\pi$
$751$	0.238664	0.00870899	0.00435449	+	0.999991i	$0.498614\pi$
$752$	−28.0701	−1.02361
$753$	9.19240	0.334990
$754$	−11.6604	−0.424648
$755$	2.09186	0.0761306
$756$	−10.2221	−0.371773
$757$	−11.4593	−0.416494	−0.208247	−	0.978076i	$-0.566776\pi$
$757$	−11.4593	−0.416494	−0.208247	+	0.978076i	$0.566776\pi$
$758$	−41.3154	−1.50064
$759$	27.3502	0.992750
$760$	0.522247	0.0189439
$761$	2.43813	0.0883821	0.0441910	−	0.999023i	$-0.485929\pi$
$761$	2.43813	0.0883821	0.0441910	+	0.999023i	$0.485929\pi$
$762$	−16.0446	−0.581235
$763$	−8.61493	−0.311881
$764$	1.83775	0.0664876
$765$	−1.66830	−0.0603175
$766$	34.6989	1.25372
$767$	−32.2472	−1.16438
$768$	−16.5837	−0.598412
$769$	−20.4390	−0.737048	−0.368524	−	0.929618i	$-0.620137\pi$
$769$	−20.4390	−0.737048	−0.368524	+	0.929618i	$0.620137\pi$
$770$	1.53021	0.0551451
$771$	13.7486	0.495144
$772$	6.04672	0.217626
$773$	−37.8123	−1.36002	−0.680008	−	0.733205i	$-0.738024\pi$
$773$	−37.8123	−1.36002	−0.680008	+	0.733205i	$0.738024\pi$
$774$	0	0
$775$	7.41131	0.266222
$776$	−4.59810	−0.165062
$777$	−6.57106	−0.235736
$778$	−15.8126	−0.566908
$779$	−22.7044	−0.813468
$780$	0.373108	0.0133594
$781$	−19.1446	−0.685048
$782$	85.0925	3.04290
$783$	−11.4130	−0.407867
$784$	21.9996	0.785700
$785$	−2.96327	−0.105764
$786$	−5.06384	−0.180621
$787$	−44.4684	−1.58513	−0.792564	−	0.609789i	$-0.791254\pi$
$787$	−44.4684	−1.58513	−0.792564	+	0.609789i	$0.791254\pi$
$788$	28.2794	1.00741
$789$	5.46329	0.194498
$790$	−3.58837	−0.127668
$791$	19.8133	0.704481
$792$	8.17872	0.290618
$793$	−23.3096	−0.827748
$794$	31.7223	1.12578
$795$	−0.451852	−0.0160255
$796$	−27.9538	−0.990794
$797$	49.3365	1.74759	0.873794	−	0.486296i	$-0.161652\pi$
$797$	49.3365	1.74759	0.873794	+	0.486296i	$0.161652\pi$
$798$	11.4821	0.406460
$799$	−33.4987	−1.18510
$800$	35.8173	1.26633
$801$	−33.3202	−1.17731
$802$	10.7386	0.379194
$803$	63.5534	2.24275
$804$	2.65181	0.0935223
$805$	−1.55425	−0.0547802
$806$	−6.55171	−0.230774
$807$	15.4561	0.544080
$808$	9.31993	0.327874
$809$	−8.20188	−0.288363	−0.144181	−	0.989551i	$-0.546055\pi$
$809$	−8.20188	−0.288363	−0.144181	+	0.989551i	$0.546055\pi$
$810$	−0.856768	−0.0301038
$811$	41.7992	1.46777	0.733884	−	0.679275i	$-0.237705\pi$
$811$	41.7992	1.46777	0.733884	+	0.679275i	$0.237705\pi$
$812$	6.27357	0.220159
$813$	5.12113	0.179606
$814$	−42.6530	−1.49499
$815$	−2.24745	−0.0787246
$816$	−21.1068	−0.738884
$817$	0	0
$818$	67.2990	2.35305
$819$	8.32803	0.291005
$820$	0.905256	0.0316129
$821$	−21.6404	−0.755255	−0.377627	−	0.925958i	$-0.623260\pi$
$821$	−21.6404	−0.755255	−0.377627	+	0.925958i	$0.623260\pi$
$822$	−17.9552	−0.626259
$823$	7.82315	0.272698	0.136349	−	0.990661i	$-0.456463\pi$
$823$	7.82315	0.272698	0.136349	+	0.990661i	$0.456463\pi$
$824$	1.76336	0.0614296
$825$	16.9009	0.588414
$826$	39.5676	1.37673
$827$	2.98386	0.103759	0.0518794	−	0.998653i	$-0.483479\pi$
$827$	2.98386	0.103759	0.0518794	+	0.998653i	$0.483479\pi$
$828$	29.6058	1.02887
$829$	−2.03260	−0.0705950	−0.0352975	−	0.999377i	$-0.511238\pi$
$829$	−2.03260	−0.0705950	−0.0352975	+	0.999377i	$0.511238\pi$
$830$	0.501661	0.0174129
$831$	−15.0118	−0.520755
$832$	−9.79155	−0.339461
$833$	26.2543	0.909657
$834$	5.66892	0.196299
$835$	0.911457	0.0315423
$836$	32.6802	1.13027
$837$	−6.41268	−0.221655
$838$	30.4788	1.05287
$839$	3.18181	0.109848	0.0549242	−	0.998491i	$-0.482508\pi$
$839$	3.18181	0.109848	0.0549242	+	0.998491i	$0.482508\pi$
$840$	0.128458	0.00443221
$841$	−21.9955	−0.758467
$842$	25.5055	0.878979
$843$	5.46893	0.188360
$844$	−36.1893	−1.24569
$845$	0.958622	0.0329776
$846$	−26.5804	−0.913853
$847$	−10.1727	−0.349539
$848$	20.6838	0.710284
$849$	5.83339	0.200201
$850$	52.5824	1.80356
$851$	43.3230	1.48509
$852$	5.72765	0.196226
$853$	−56.3145	−1.92817	−0.964085	−	0.265592i	$-0.914433\pi$
$853$	−56.3145	−1.92817	−0.964085	+	0.265592i	$0.914433\pi$
$854$	28.6011	0.978708
$855$	1.48417	0.0507577
$856$	1.18152	0.0403836
$857$	−0.562224	−0.0192052	−0.00960260	−	0.999954i	$-0.503057\pi$
$857$	−0.562224	−0.0192052	−0.00960260	+	0.999954i	$0.503057\pi$
$858$	−14.9407	−0.510066
$859$	44.0608	1.50334	0.751668	−	0.659542i	$-0.229250\pi$
$859$	44.0608	1.50334	0.751668	+	0.659542i	$0.229250\pi$
$860$	0	0
$861$	−5.58462	−0.190323
$862$	33.3422	1.13564
$863$	−18.2385	−0.620845	−0.310422	−	0.950599i	$-0.600471\pi$
$863$	−18.2385	−0.620845	−0.310422	+	0.950599i	$0.600471\pi$
$864$	−30.9912	−1.05434
$865$	0.588725	0.0200173
$866$	−16.5377	−0.561973
$867$	−11.4870	−0.390119
$868$	3.52496	0.119645
$869$	63.0064	2.13735
$870$	−0.511143	−0.0173294
$871$	−4.91804	−0.166641
$872$	−4.69433	−0.158970
$873$	−13.0674	−0.442263
$874$	−75.7011	−2.56063
$875$	−1.92399	−0.0650427
$876$	−19.0138	−0.642416
$877$	39.1775	1.32293	0.661465	−	0.749976i	$-0.269935\pi$
$877$	39.1775	1.32293	0.661465	+	0.749976i	$0.269935\pi$
$878$	−58.5169	−1.97485
$879$	−7.17197	−0.241905
$880$	2.50245	0.0843575
$881$	−55.5131	−1.87028	−0.935142	−	0.354273i	$-0.884729\pi$
$881$	−55.5131	−1.87028	−0.935142	+	0.354273i	$0.884729\pi$
$882$	20.8321	0.701453
$883$	−10.7984	−0.363395	−0.181698	−	0.983354i	$-0.558159\pi$
$883$	−10.7984	−0.363395	−0.181698	+	0.983354i	$0.558159\pi$
$884$	−20.3823	−0.685530
$885$	−1.41358	−0.0475169
$886$	−25.5083	−0.856967
$887$	−44.6297	−1.49852	−0.749259	−	0.662277i	$-0.769590\pi$
$887$	−44.6297	−1.49852	−0.749259	+	0.662277i	$0.769590\pi$
$888$	−3.58061	−0.120157
$889$	−16.0095	−0.536941
$890$	−3.39700	−0.113868
$891$	15.0436	0.503979
$892$	−7.92894	−0.265481
$893$	29.8016	0.997273
$894$	−14.0800	−0.470907
$895$	−0.727799	−0.0243276
$896$	−9.80113	−0.327433
$897$	15.1754	0.506691
$898$	−17.3639	−0.579442
$899$	3.93564	0.131261
$900$	18.2947	0.609824
$901$	24.6839	0.822341
$902$	−36.2500	−1.20699
$903$	0	0
$904$	10.7964	0.359083
$905$	−0.123343	−0.00410005
$906$	25.0610	0.832596
$907$	34.9966	1.16204	0.581021	−	0.813888i	$-0.302653\pi$
$907$	34.9966	1.16204	0.581021	+	0.813888i	$0.302653\pi$
$908$	13.4219	0.445422
$909$	26.4864	0.878497
$910$	0.849044	0.0281455
$911$	27.3418	0.905873	0.452936	−	0.891543i	$-0.350376\pi$
$911$	27.3418	0.905873	0.452936	+	0.891543i	$0.350376\pi$
$912$	18.7773	0.621778
$913$	−8.80843	−0.291517
$914$	3.25969	0.107821
$915$	−1.02179	−0.0337794
$916$	−29.9619	−0.989967
$917$	−5.05275	−0.166857
$918$	−45.4973	−1.50163
$919$	42.0714	1.38781	0.693904	−	0.720068i	$-0.255889\pi$
$919$	42.0714	1.38781	0.693904	+	0.720068i	$0.255889\pi$
$920$	−0.846921	−0.0279222
$921$	−12.1204	−0.399380
$922$	−30.0145	−0.988475
$923$	−10.6225	−0.349643
$924$	8.03840	0.264444
$925$	26.7712	0.880231
$926$	−69.8311	−2.29479
$927$	5.01131	0.164593
$928$	19.0201	0.624366
$929$	37.2406	1.22183	0.610913	−	0.791698i	$-0.290803\pi$
$929$	37.2406	1.22183	0.610913	+	0.791698i	$0.290803\pi$
$930$	−0.287198	−0.00941761
$931$	−23.3567	−0.765484
$932$	35.6989	1.16936
$933$	16.3711	0.535966
$934$	−46.9934	−1.53767
$935$	2.98641	0.0976662
$936$	4.53799	0.148329
$937$	−1.17331	−0.0383302	−0.0191651	−	0.999816i	$-0.506101\pi$
$937$	−1.17331	−0.0383302	−0.0191651	+	0.999816i	$0.506101\pi$
$938$	6.03447	0.197033
$939$	−1.81601	−0.0592633
$940$	−1.18823	−0.0387559
$941$	44.7514	1.45886	0.729428	−	0.684058i	$-0.239786\pi$
$941$	44.7514	1.45886	0.729428	+	0.684058i	$0.239786\pi$
$942$	−35.5007	−1.15667
$943$	36.8194	1.19900
$944$	64.7073	2.10604
$945$	0.831027	0.0270333
$946$	0	0
$947$	−31.6885	−1.02974	−0.514868	−	0.857269i	$-0.672159\pi$
$947$	−31.6885	−1.02974	−0.514868	+	0.857269i	$0.672159\pi$
$948$	−18.8501	−0.612224
$949$	35.2628	1.14468
$950$	−46.7791	−1.51771
$951$	6.50607	0.210974
$952$	−7.01743	−0.227436
$953$	22.2967	0.722261	0.361131	−	0.932515i	$-0.382391\pi$
$953$	22.2967	0.722261	0.361131	+	0.932515i	$0.382391\pi$
$954$	19.5861	0.634123
$955$	−0.149404	−0.00483461
$956$	−17.2453	−0.557751
$957$	8.97491	0.290118
$958$	−45.8489	−1.48131
$959$	−17.9159	−0.578534
$960$	−0.429219	−0.0138530
$961$	−28.7887	−0.928667
$962$	−23.6661	−0.763027
$963$	3.35778	0.108203
$964$	−19.7637	−0.636547
$965$	−0.491582	−0.0158246
$966$	−18.6203	−0.599099
$967$	−6.29057	−0.202291	−0.101146	−	0.994872i	$-0.532251\pi$
$967$	−6.29057	−0.202291	−0.101146	+	0.994872i	$0.532251\pi$
$968$	−5.54318	−0.178165
$969$	22.4087	0.719873
$970$	−1.33222	−0.0427750
$971$	−25.9204	−0.831825	−0.415913	−	0.909405i	$-0.636538\pi$
$971$	−25.9204	−0.831825	−0.415913	+	0.909405i	$0.636538\pi$
$972$	−24.7054	−0.792426
$973$	5.65651	0.181339
$974$	−4.17643	−0.133821
$975$	9.37753	0.300321
$976$	46.7730	1.49717
$977$	−17.6307	−0.564056	−0.282028	−	0.959406i	$-0.591007\pi$
$977$	−17.6307	−0.564056	−0.282028	+	0.959406i	$0.591007\pi$
$978$	−26.9250	−0.860965
$979$	59.6463	1.90630
$980$	0.931265	0.0297482
$981$	−13.3408	−0.425940
$982$	32.6448	1.04174
$983$	−45.8216	−1.46148	−0.730741	−	0.682655i	$-0.760825\pi$
$983$	−45.8216	−1.46148	−0.730741	+	0.682655i	$0.760825\pi$
$984$	−3.04309	−0.0970103
$985$	−2.29904	−0.0732534
$986$	27.9229	0.889246
$987$	7.33034	0.233327
$988$	18.1327	0.576880
$989$	0	0
$990$	2.36964	0.0753122
$991$	−39.0259	−1.23970	−0.619850	−	0.784721i	$-0.712806\pi$
$991$	−39.0259	−1.23970	−0.619850	+	0.784721i	$0.712806\pi$
$992$	10.6869	0.339310
$993$	−3.22154	−0.102233
$994$	13.0339	0.413409
$995$	2.27256	0.0720451
$996$	2.63529	0.0835024
$997$	6.51911	0.206462	0.103231	−	0.994657i	$-0.467082\pi$
$997$	6.51911	0.206462	0.103231	+	0.994657i	$0.467082\pi$
$998$	−0.805947	−0.0255118
$999$	−23.1639	−0.732875

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.q.1.17	yes	20
43.42	odd	2	inner	1849.2.a.q.1.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.2.a.q.1.4	✓	20	43.42	odd	2	inner
1849.2.a.q.1.17	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+1.88727 q^{2} -0.805985 q^{3} +1.56178 q^{4} -0.126968 q^{5} -1.52111 q^{6} -1.51778 q^{7} -0.827047 q^{8} -2.35039 q^{9} +O(q^{10})\)	\(q+1.88727 q^{2} -0.805985 q^{3} +1.56178 q^{4} -0.126968 q^{5} -1.52111 q^{6} -1.51778 q^{7} -0.827047 q^{8} -2.35039 q^{9} -0.239623 q^{10} +4.20742 q^{11} -1.25877 q^{12} +2.33450 q^{13} -2.86445 q^{14} +0.102334 q^{15} -4.68441 q^{16} -5.59036 q^{17} -4.43581 q^{18} +4.97337 q^{19} -0.198296 q^{20} +1.22331 q^{21} +7.94052 q^{22} -8.06526 q^{23} +0.666587 q^{24} -4.98388 q^{25} +4.40583 q^{26} +4.31233 q^{27} -2.37043 q^{28} -2.64659 q^{29} +0.193132 q^{30} -1.48706 q^{31} -7.18663 q^{32} -3.39112 q^{33} -10.5505 q^{34} +0.192709 q^{35} -3.67078 q^{36} -5.37156 q^{37} +9.38608 q^{38} -1.88157 q^{39} +0.105009 q^{40} -4.56519 q^{41} +2.30871 q^{42} +6.57104 q^{44} +0.298424 q^{45} -15.2213 q^{46} +5.99224 q^{47} +3.77556 q^{48} -4.69635 q^{49} -9.40591 q^{50} +4.50575 q^{51} +3.64597 q^{52} -4.41545 q^{53} +8.13852 q^{54} -0.534208 q^{55} +1.25527 q^{56} -4.00846 q^{57} -4.99483 q^{58} -13.8133 q^{59} +0.159823 q^{60} -9.98483 q^{61} -2.80647 q^{62} +3.56737 q^{63} -4.19428 q^{64} -0.296407 q^{65} -6.39994 q^{66} -2.10668 q^{67} -8.73088 q^{68} +6.50048 q^{69} +0.363694 q^{70} -4.55021 q^{71} +1.94388 q^{72} +15.1051 q^{73} -10.1376 q^{74} +4.01693 q^{75} +7.76729 q^{76} -6.38593 q^{77} -3.55103 q^{78} +14.9751 q^{79} +0.594770 q^{80} +3.57549 q^{81} -8.61572 q^{82} -2.09355 q^{83} +1.91053 q^{84} +0.709797 q^{85} +2.13312 q^{87} -3.47973 q^{88} +14.1765 q^{89} +0.563206 q^{90} -3.54326 q^{91} -12.5961 q^{92} +1.19855 q^{93} +11.3089 q^{94} -0.631459 q^{95} +5.79232 q^{96} +5.55966 q^{97} -8.86326 q^{98} -9.88907 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9}+O(q^{10}) \) 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9	\( 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9} + 12 q^{10} - 20 q^{11} + 6 q^{13} - 34 q^{14} - 34 q^{15} + 14 q^{16} - 8 q^{17} + 12 q^{21} - 46 q^{23} + 2 q^{24} + 20 q^{25} - 38 q^{31} - 76 q^{35} - 46 q^{36} - 68 q^{38} - 64 q^{40} - 56 q^{41} - 58 q^{44} - 24 q^{47} - 20 q^{49} - 20 q^{52} - 42 q^{53} + 66 q^{54} - 46 q^{56} + 2 q^{57} + 12 q^{58} - 90 q^{59} + 18 q^{60} - 28 q^{64} + 76 q^{66} - 62 q^{67} - 54 q^{68} + 24 q^{74} - 36 q^{78} - 10 q^{79} - 48 q^{81} - 68 q^{83} + 70 q^{84} - 12 q^{87} + 58 q^{90} - 8 q^{92} - 42 q^{95} - 22 q^{96} - 44 q^{97} - 38 q^{99}+O(q^{100}) \) 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9 + 12 * q^10 - 20 * q^11 + 6 * q^13 - 34 * q^14 - 34 * q^15 + 14 * q^16 - 8 * q^17 + 12 * q^21 - 46 * q^23 + 2 * q^24 + 20 * q^25 - 38 * q^31 - 76 * q^35 - 46 * q^36 - 68 * q^38 - 64 * q^40 - 56 * q^41 - 58 * q^44 - 24 * q^47 - 20 * q^49 - 20 * q^52 - 42 * q^53 + 66 * q^54 - 46 * q^56 + 2 * q^57 + 12 * q^58 - 90 * q^59 + 18 * q^60 - 28 * q^64 + 76 * q^66 - 62 * q^67 - 54 * q^68 + 24 * q^74 - 36 * q^78 - 10 * q^79 - 48 * q^81 - 68 * q^83 + 70 * q^84 - 12 * q^87 + 58 * q^90 - 8 * q^92 - 42 * q^95 - 22 * q^96 - 44 * q^97 - 38 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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