LMFDB - Embedded newform 3549.2.a.bg.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.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:	$28.3389076774$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + \cdots + 281 $ x^15 - 2x^14 - 27x^13 + 51x^12 + 290x^11 - 510x^10 - 1575x^9 + 2522x^8 + 4553x^7 - 6393x^6 - 6785x^5 + 7806x^4 + 4632x^3 - 3811x^2 - 1041x + 281
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.415563$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.415563 q^{2} +1.00000 q^{3} -1.82731 q^{4} +4.32224 q^{5} +0.415563 q^{6} +1.00000 q^{7} -1.59049 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.415563 q^{2} +1.00000 q^{3} -1.82731 q^{4} +4.32224 q^{5} +0.415563 q^{6} +1.00000 q^{7} -1.59049 q^{8} +1.00000 q^{9} +1.79616 q^{10} +3.32197 q^{11} -1.82731 q^{12} +0.415563 q^{14} +4.32224 q^{15} +2.99367 q^{16} -5.26423 q^{17} +0.415563 q^{18} +0.118179 q^{19} -7.89805 q^{20} +1.00000 q^{21} +1.38049 q^{22} -7.51837 q^{23} -1.59049 q^{24} +13.6817 q^{25} +1.00000 q^{27} -1.82731 q^{28} -2.46042 q^{29} +1.79616 q^{30} +10.0410 q^{31} +4.42503 q^{32} +3.32197 q^{33} -2.18762 q^{34} +4.32224 q^{35} -1.82731 q^{36} +5.38066 q^{37} +0.0491107 q^{38} -6.87447 q^{40} +11.7059 q^{41} +0.415563 q^{42} -0.378528 q^{43} -6.07025 q^{44} +4.32224 q^{45} -3.12436 q^{46} +3.46970 q^{47} +2.99367 q^{48} +1.00000 q^{49} +5.68562 q^{50} -5.26423 q^{51} +4.33879 q^{53} +0.415563 q^{54} +14.3583 q^{55} -1.59049 q^{56} +0.118179 q^{57} -1.02246 q^{58} +8.88207 q^{59} -7.89805 q^{60} -6.67086 q^{61} +4.17269 q^{62} +1.00000 q^{63} -4.14845 q^{64} +1.38049 q^{66} -3.42565 q^{67} +9.61936 q^{68} -7.51837 q^{69} +1.79616 q^{70} -7.25425 q^{71} -1.59049 q^{72} -13.9967 q^{73} +2.23600 q^{74} +13.6817 q^{75} -0.215949 q^{76} +3.32197 q^{77} -0.278553 q^{79} +12.9393 q^{80} +1.00000 q^{81} +4.86455 q^{82} -14.5998 q^{83} -1.82731 q^{84} -22.7532 q^{85} -0.157302 q^{86} -2.46042 q^{87} -5.28355 q^{88} -7.54564 q^{89} +1.79616 q^{90} +13.7384 q^{92} +10.0410 q^{93} +1.44188 q^{94} +0.510796 q^{95} +4.42503 q^{96} +7.20532 q^{97} +0.415563 q^{98} +3.32197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 2 q^{2} + 15 q^{3} + 28 q^{4} + 9 q^{5} - 2 q^{6} + 15 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) $ 15 * q - 2 * q^2 + 15 * q^3 + 28 * q^4 + 9 * q^5 - 2 * q^6 + 15 * q^7 - 9 * q^8 + 15 * q^9	\( 15 q - 2 q^{2} + 15 q^{3} + 28 q^{4} + 9 q^{5} - 2 q^{6} + 15 q^{7} - 9 q^{8} + 15 q^{9} + 21 q^{10} - 5 q^{11} + 28 q^{12} - 2 q^{14} + 9 q^{15} + 50 q^{16} - q^{17} - 2 q^{18} - 3 q^{19} + 23 q^{20} + 15 q^{21} + 21 q^{22} + 4 q^{23} - 9 q^{24} + 50 q^{25} + 15 q^{27} + 28 q^{28} + 9 q^{29} + 21 q^{30} - 7 q^{31} - 35 q^{32} - 5 q^{33} + 2 q^{34} + 9 q^{35} + 28 q^{36} - 17 q^{37} - 12 q^{38} + 46 q^{40} + 22 q^{41} - 2 q^{42} + 36 q^{43} - 29 q^{44} + 9 q^{45} + q^{46} + 12 q^{47} + 50 q^{48} + 15 q^{49} - 53 q^{50} - q^{51} - 5 q^{53} - 2 q^{54} + 43 q^{55} - 9 q^{56} - 3 q^{57} - 29 q^{58} + 29 q^{59} + 23 q^{60} + 12 q^{61} + 14 q^{62} + 15 q^{63} + 95 q^{64} + 21 q^{66} + 12 q^{67} - 16 q^{68} + 4 q^{69} + 21 q^{70} - 36 q^{71} - 9 q^{72} + 29 q^{73} - 5 q^{74} + 50 q^{75} - 25 q^{76} - 5 q^{77} + 35 q^{79} + 89 q^{80} + 15 q^{81} + 51 q^{82} + 10 q^{83} + 28 q^{84} - 23 q^{85} - 19 q^{86} + 9 q^{87} + 73 q^{88} - 25 q^{89} + 21 q^{90} - 31 q^{92} - 7 q^{93} - 19 q^{94} - 7 q^{95} - 35 q^{96} + 26 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 15 * q - 2 * q^2 + 15 * q^3 + 28 * q^4 + 9 * q^5 - 2 * q^6 + 15 * q^7 - 9 * q^8 + 15 * q^9 + 21 * q^10 - 5 * q^11 + 28 * q^12 - 2 * q^14 + 9 * q^15 + 50 * q^16 - q^17 - 2 * q^18 - 3 * q^19 + 23 * q^20 + 15 * q^21 + 21 * q^22 + 4 * q^23 - 9 * q^24 + 50 * q^25 + 15 * q^27 + 28 * q^28 + 9 * q^29 + 21 * q^30 - 7 * q^31 - 35 * q^32 - 5 * q^33 + 2 * q^34 + 9 * q^35 + 28 * q^36 - 17 * q^37 - 12 * q^38 + 46 * q^40 + 22 * q^41 - 2 * q^42 + 36 * q^43 - 29 * q^44 + 9 * q^45 + q^46 + 12 * q^47 + 50 * q^48 + 15 * q^49 - 53 * q^50 - q^51 - 5 * q^53 - 2 * q^54 + 43 * q^55 - 9 * q^56 - 3 * q^57 - 29 * q^58 + 29 * q^59 + 23 * q^60 + 12 * q^61 + 14 * q^62 + 15 * q^63 + 95 * q^64 + 21 * q^66 + 12 * q^67 - 16 * q^68 + 4 * q^69 + 21 * q^70 - 36 * q^71 - 9 * q^72 + 29 * q^73 - 5 * q^74 + 50 * q^75 - 25 * q^76 - 5 * q^77 + 35 * q^79 + 89 * q^80 + 15 * q^81 + 51 * q^82 + 10 * q^83 + 28 * q^84 - 23 * q^85 - 19 * q^86 + 9 * q^87 + 73 * q^88 - 25 * q^89 + 21 * q^90 - 31 * q^92 - 7 * q^93 - 19 * q^94 - 7 * q^95 - 35 * q^96 + 26 * q^97 - 2 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.415563	0.293848	0.146924	−	0.989148i	$-0.453063\pi$
$2$	0.415563	0.293848	0.146924	+	0.989148i	$0.453063\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.82731	−0.913654
$5$	4.32224	1.93296	0.966481	−	0.256737i	$-0.0826473\pi$
$5$	4.32224	1.93296	0.966481	+	0.256737i	$0.0826473\pi$
$6$	0.415563	0.169653
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.59049	−0.562323
$9$	1.00000	0.333333
$10$	1.79616	0.567997
$11$	3.32197	1.00161	0.500805	−	0.865560i	$-0.333037\pi$
$11$	3.32197	1.00161	0.500805	+	0.865560i	$0.333037\pi$
$12$	−1.82731	−0.527498
$13$	0	0
$13$	0	0
$14$	0.415563	0.111064
$15$	4.32224	1.11600
$16$	2.99367	0.748416
$17$	−5.26423	−1.27676	−0.638381	−	0.769720i	$-0.720396\pi$
$17$	−5.26423	−1.27676	−0.638381	+	0.769720i	$0.720396\pi$
$18$	0.415563	0.0979492
$19$	0.118179	0.0271121	0.0135560	−	0.999908i	$-0.495685\pi$
$19$	0.118179	0.0271121	0.0135560	+	0.999908i	$0.495685\pi$
$20$	−7.89805	−1.76606
$21$	1.00000	0.218218
$22$	1.38049	0.294321
$23$	−7.51837	−1.56769	−0.783844	−	0.620958i	$-0.786744\pi$
$23$	−7.51837	−1.56769	−0.783844	+	0.620958i	$0.786744\pi$
$24$	−1.59049	−0.324657
$25$	13.6817	2.73635
$26$	0	0
$27$	1.00000	0.192450
$28$	−1.82731	−0.345329
$29$	−2.46042	−0.456888	−0.228444	−	0.973557i	$-0.573364\pi$
$29$	−2.46042	−0.456888	−0.228444	+	0.973557i	$0.573364\pi$
$30$	1.79616	0.327933
$31$	10.0410	1.80342	0.901712	−	0.432338i	$-0.142311\pi$
$31$	10.0410	1.80342	0.901712	+	0.432338i	$0.142311\pi$
$32$	4.42503	0.782243
$33$	3.32197	0.578280
$34$	−2.18762	−0.375174
$35$	4.32224	0.730591
$36$	−1.82731	−0.304551
$37$	5.38066	0.884574	0.442287	−	0.896873i	$-0.354167\pi$
$37$	5.38066	0.884574	0.442287	+	0.896873i	$0.354167\pi$
$38$	0.0491107	0.00796681
$39$	0	0
$40$	−6.87447	−1.08695
$41$	11.7059	1.82816	0.914078	−	0.405538i	$-0.132916\pi$
$41$	11.7059	1.82816	0.914078	+	0.405538i	$0.132916\pi$
$42$	0.415563	0.0641228
$43$	−0.378528	−0.0577249	−0.0288625	−	0.999583i	$-0.509188\pi$
$43$	−0.378528	−0.0577249	−0.0288625	+	0.999583i	$0.509188\pi$
$44$	−6.07025	−0.915125
$45$	4.32224	0.644321
$46$	−3.12436	−0.460662
$47$	3.46970	0.506108	0.253054	−	0.967452i	$-0.418565\pi$
$47$	3.46970	0.506108	0.253054	+	0.967452i	$0.418565\pi$
$48$	2.99367	0.432098
$49$	1.00000	0.142857
$50$	5.68562	0.804068
$51$	−5.26423	−0.737139
$52$	0	0
$53$	4.33879	0.595979	0.297989	−	0.954569i	$-0.403684\pi$
$53$	4.33879	0.595979	0.297989	+	0.954569i	$0.403684\pi$
$54$	0.415563	0.0565510
$55$	14.3583	1.93608
$56$	−1.59049	−0.212538
$57$	0.118179	0.0156532
$58$	−1.02246	−0.134256
$59$	8.88207	1.15635	0.578173	−	0.815914i	$-0.303766\pi$
$59$	8.88207	1.15635	0.578173	+	0.815914i	$0.303766\pi$
$60$	−7.89805	−1.01963
$61$	−6.67086	−0.854116	−0.427058	−	0.904224i	$-0.640450\pi$
$61$	−6.67086	−0.854116	−0.427058	+	0.904224i	$0.640450\pi$
$62$	4.17269	0.529932
$63$	1.00000	0.125988
$64$	−4.14845	−0.518556
$65$	0	0
$66$	1.38049	0.169926
$67$	−3.42565	−0.418509	−0.209255	−	0.977861i	$-0.567104\pi$
$67$	−3.42565	−0.418509	−0.209255	+	0.977861i	$0.567104\pi$
$68$	9.61936	1.16652
$69$	−7.51837	−0.905105
$70$	1.79616	0.214682
$71$	−7.25425	−0.860921	−0.430460	−	0.902609i	$-0.641649\pi$
$71$	−7.25425	−0.860921	−0.430460	+	0.902609i	$0.641649\pi$
$72$	−1.59049	−0.187441
$73$	−13.9967	−1.63819	−0.819093	−	0.573660i	$-0.805523\pi$
$73$	−13.9967	−1.63819	−0.819093	+	0.573660i	$0.805523\pi$
$74$	2.23600	0.259930
$75$	13.6817	1.57983
$76$	−0.215949	−0.0247710
$77$	3.32197	0.378573
$78$	0	0
$79$	−0.278553	−0.0313397	−0.0156698	−	0.999877i	$-0.504988\pi$
$79$	−0.278553	−0.0313397	−0.0156698	+	0.999877i	$0.504988\pi$
$80$	12.9393	1.44666
$81$	1.00000	0.111111
$82$	4.86455	0.537199
$83$	−14.5998	−1.60254	−0.801270	−	0.598302i	$-0.795842\pi$
$83$	−14.5998	−1.60254	−0.801270	+	0.598302i	$0.795842\pi$
$84$	−1.82731	−0.199376
$85$	−22.7532	−2.46793
$86$	−0.157302	−0.0169623
$87$	−2.46042	−0.263785
$88$	−5.28355	−0.563228
$89$	−7.54564	−0.799836	−0.399918	−	0.916551i	$-0.630961\pi$
$89$	−7.54564	−0.799836	−0.399918	+	0.916551i	$0.630961\pi$
$90$	1.79616	0.189332
$91$	0	0
$92$	13.7384	1.43232
$93$	10.0410	1.04121
$94$	1.44188	0.148719
$95$	0.510796	0.0524066
$96$	4.42503	0.451628
$97$	7.20532	0.731590	0.365795	−	0.930696i	$-0.380797\pi$
$97$	7.20532	0.731590	0.365795	+	0.930696i	$0.380797\pi$
$98$	0.415563	0.0419782
$99$	3.32197	0.333870
$100$	−25.0007	−2.50007
$101$	3.90068	0.388132	0.194066	−	0.980988i	$-0.437832\pi$
$101$	3.90068	0.388132	0.194066	+	0.980988i	$0.437832\pi$
$102$	−2.18762	−0.216607
$103$	−0.253309	−0.0249593	−0.0124797	−	0.999922i	$-0.503972\pi$
$103$	−0.253309	−0.0249593	−0.0124797	+	0.999922i	$0.503972\pi$
$104$	0	0
$105$	4.32224	0.421807
$106$	1.80304	0.175127
$107$	1.25329	0.121160	0.0605800	−	0.998163i	$-0.480705\pi$
$107$	1.25329	0.121160	0.0605800	+	0.998163i	$0.480705\pi$
$108$	−1.82731	−0.175833
$109$	−3.26860	−0.313075	−0.156537	−	0.987672i	$-0.550033\pi$
$109$	−3.26860	−0.313075	−0.156537	+	0.987672i	$0.550033\pi$
$110$	5.96679	0.568911
$111$	5.38066	0.510709
$112$	2.99367	0.282875
$113$	−0.0957171	−0.00900431	−0.00450215	−	0.999990i	$-0.501433\pi$
$113$	−0.0957171	−0.00900431	−0.00450215	+	0.999990i	$0.501433\pi$
$114$	0.0491107	0.00459964
$115$	−32.4962	−3.03028
$116$	4.49594	0.417438
$117$	0	0
$118$	3.69106	0.339790
$119$	−5.26423	−0.482571
$120$	−6.87447	−0.627550
$121$	0.0354611	0.00322374
$122$	−2.77217	−0.250980
$123$	11.7059	1.05549
$124$	−18.3481	−1.64770
$125$	37.5245	3.35629
$126$	0.415563	0.0370213
$127$	15.5224	1.37739	0.688696	−	0.725050i	$-0.258183\pi$
$127$	15.5224	1.37739	0.688696	+	0.725050i	$0.258183\pi$
$128$	−10.5740	−0.934619
$129$	−0.378528	−0.0333275
$130$	0	0
$131$	8.00203	0.699141	0.349570	−	0.936910i	$-0.386328\pi$
$131$	8.00203	0.699141	0.349570	+	0.936910i	$0.386328\pi$
$132$	−6.07025	−0.528348
$133$	0.118179	0.0102474
$134$	−1.42357	−0.122978
$135$	4.32224	0.371999
$136$	8.37269	0.717952
$137$	−9.28221	−0.793033	−0.396516	−	0.918028i	$-0.629781\pi$
$137$	−9.28221	−0.793033	−0.396516	+	0.918028i	$0.629781\pi$
$138$	−3.12436	−0.265963
$139$	4.27962	0.362992	0.181496	−	0.983392i	$-0.441906\pi$
$139$	4.27962	0.362992	0.181496	+	0.983392i	$0.441906\pi$
$140$	−7.89805	−0.667507
$141$	3.46970	0.292202
$142$	−3.01460	−0.252980
$143$	0	0
$144$	2.99367	0.249472
$145$	−10.6345	−0.883148
$146$	−5.81650	−0.481377
$147$	1.00000	0.0824786
$148$	−9.83211	−0.808195
$149$	11.0346	0.903988	0.451994	−	0.892021i	$-0.350713\pi$
$149$	11.0346	0.903988	0.451994	+	0.892021i	$0.350713\pi$
$150$	5.68562	0.464229
$151$	7.54592	0.614078	0.307039	−	0.951697i	$-0.400662\pi$
$151$	7.54592	0.614078	0.307039	+	0.951697i	$0.400662\pi$
$152$	−0.187962	−0.0152457
$153$	−5.26423	−0.425588
$154$	1.38049	0.111243
$155$	43.3997	3.48595
$156$	0	0
$157$	−21.5422	−1.71926	−0.859629	−	0.510918i	$-0.829306\pi$
$157$	−21.5422	−1.71926	−0.859629	+	0.510918i	$0.829306\pi$
$158$	−0.115756	−0.00920909
$159$	4.33879	0.344089
$160$	19.1260	1.51205
$161$	−7.51837	−0.592531
$162$	0.415563	0.0326497
$163$	22.3911	1.75381	0.876903	−	0.480667i	$-0.159605\pi$
$163$	22.3911	1.75381	0.876903	+	0.480667i	$0.159605\pi$
$164$	−21.3903	−1.67030
$165$	14.3583	1.11779
$166$	−6.06716	−0.470903
$167$	8.14259	0.630093	0.315046	−	0.949076i	$-0.397980\pi$
$167$	8.14259	0.630093	0.315046	+	0.949076i	$0.397980\pi$
$168$	−1.59049	−0.122709
$169$	0	0
$170$	−9.45541	−0.725197
$171$	0.118179	0.00903735
$172$	0.691686	0.0527406
$173$	−14.3336	−1.08976	−0.544880	−	0.838514i	$-0.683425\pi$
$173$	−14.3336	−1.08976	−0.544880	+	0.838514i	$0.683425\pi$
$174$	−1.02246	−0.0775125
$175$	13.6817	1.03424
$176$	9.94486	0.749622
$177$	8.88207	0.667617
$178$	−3.13569	−0.235030
$179$	12.7843	0.955546	0.477773	−	0.878483i	$-0.341444\pi$
$179$	12.7843	0.955546	0.477773	+	0.878483i	$0.341444\pi$
$180$	−7.89805	−0.588686
$181$	20.9807	1.55948	0.779741	−	0.626102i	$-0.215351\pi$
$181$	20.9807	1.55948	0.779741	+	0.626102i	$0.215351\pi$
$182$	0	0
$183$	−6.67086	−0.493124
$184$	11.9579	0.881547
$185$	23.2565	1.70985
$186$	4.17269	0.305956
$187$	−17.4876	−1.27882
$188$	−6.34021	−0.462407
$189$	1.00000	0.0727393
$190$	0.212268	0.0153996
$191$	−5.41589	−0.391880	−0.195940	−	0.980616i	$-0.562776\pi$
$191$	−5.41589	−0.391880	−0.195940	+	0.980616i	$0.562776\pi$
$192$	−4.14845	−0.299389
$193$	−11.2327	−0.808546	−0.404273	−	0.914638i	$-0.632475\pi$
$193$	−11.2327	−0.808546	−0.404273	+	0.914638i	$0.632475\pi$
$194$	2.99427	0.214976
$195$	0	0
$196$	−1.82731	−0.130522
$197$	−0.705420	−0.0502591	−0.0251295	−	0.999684i	$-0.508000\pi$
$197$	−0.705420	−0.0502591	−0.0251295	+	0.999684i	$0.508000\pi$
$198$	1.38049	0.0981070
$199$	11.6826	0.828156	0.414078	−	0.910241i	$-0.364104\pi$
$199$	11.6826	0.828156	0.414078	+	0.910241i	$0.364104\pi$
$200$	−21.7606	−1.53871
$201$	−3.42565	−0.241626
$202$	1.62098	0.114052
$203$	−2.46042	−0.172688
$204$	9.61936	0.673490
$205$	50.5957	3.53376
$206$	−0.105266	−0.00733423
$207$	−7.51837	−0.522563
$208$	0	0
$209$	0.392586	0.0271557
$210$	1.79616	0.123947
$211$	4.38529	0.301896	0.150948	−	0.988542i	$-0.451767\pi$
$211$	4.38529	0.301896	0.150948	+	0.988542i	$0.451767\pi$
$212$	−7.92831	−0.544518
$213$	−7.25425	−0.497053
$214$	0.520821	0.0356026
$215$	−1.63609	−0.111580
$216$	−1.59049	−0.108219
$217$	10.0410	0.681630
$218$	−1.35831	−0.0919963
$219$	−13.9967	−0.945807
$220$	−26.2371	−1.76890
$221$	0	0
$222$	2.23600	0.150071
$223$	−14.8375	−0.993594	−0.496797	−	0.867867i	$-0.665491\pi$
$223$	−14.8375	−0.993594	−0.496797	+	0.867867i	$0.665491\pi$
$224$	4.42503	0.295660
$225$	13.6817	0.912115
$226$	−0.0397765	−0.00264589
$227$	0.0625704	0.00415294	0.00207647	−	0.999998i	$-0.499339\pi$
$227$	0.0625704	0.00415294	0.00207647	+	0.999998i	$0.499339\pi$
$228$	−0.215949	−0.0143016
$229$	−0.184720	−0.0122066	−0.00610331	−	0.999981i	$-0.501943\pi$
$229$	−0.184720	−0.0122066	−0.00610331	+	0.999981i	$0.501943\pi$
$230$	−13.5042	−0.890442
$231$	3.32197	0.218569
$232$	3.91327	0.256919
$233$	0.190546	0.0124831	0.00624154	−	0.999981i	$-0.498013\pi$
$233$	0.190546	0.0124831	0.00624154	+	0.999981i	$0.498013\pi$
$234$	0	0
$235$	14.9969	0.978288
$236$	−16.2303	−1.05650
$237$	−0.278553	−0.0180940
$238$	−2.18762	−0.141802
$239$	−17.7380	−1.14737	−0.573687	−	0.819075i	$-0.694487\pi$
$239$	−17.7380	−1.14737	−0.573687	+	0.819075i	$0.694487\pi$
$240$	12.9393	0.835230
$241$	4.72194	0.304167	0.152084	−	0.988368i	$-0.451402\pi$
$241$	4.72194	0.304167	0.152084	+	0.988368i	$0.451402\pi$
$242$	0.0147363	0.000947288 0
$243$	1.00000	0.0641500
$244$	12.1897	0.780366
$245$	4.32224	0.276138
$246$	4.86455	0.310152
$247$	0	0
$248$	−15.9702	−1.01411
$249$	−14.5998	−0.925227
$250$	15.5938	0.986238
$251$	−13.2188	−0.834362	−0.417181	−	0.908823i	$-0.636982\pi$
$251$	−13.2188	−0.834362	−0.417181	+	0.908823i	$0.636982\pi$
$252$	−1.82731	−0.115110
$253$	−24.9758	−1.57021
$254$	6.45055	0.404744
$255$	−22.7532	−1.42486
$256$	3.90273	0.243921
$257$	−17.4150	−1.08632	−0.543160	−	0.839629i	$-0.682772\pi$
$257$	−17.4150	−1.08632	−0.543160	+	0.839629i	$0.682772\pi$
$258$	−0.157302	−0.00979321
$259$	5.38066	0.334338
$260$	0	0
$261$	−2.46042	−0.152296
$262$	3.32535	0.205441
$263$	−25.2510	−1.55704	−0.778522	−	0.627618i	$-0.784030\pi$
$263$	−25.2510	−1.55704	−0.778522	+	0.627618i	$0.784030\pi$
$264$	−5.28355	−0.325180
$265$	18.7533	1.15201
$266$	0.0491107	0.00301117
$267$	−7.54564	−0.461785
$268$	6.25971	0.382372
$269$	−15.7373	−0.959519	−0.479759	−	0.877400i	$-0.659276\pi$
$269$	−15.7373	−0.959519	−0.479759	+	0.877400i	$0.659276\pi$
$270$	1.79616	0.109311
$271$	−10.7178	−0.651059	−0.325530	−	0.945532i	$-0.605543\pi$
$271$	−10.7178	−0.651059	−0.325530	+	0.945532i	$0.605543\pi$
$272$	−15.7593	−0.955550
$273$	0	0
$274$	−3.85735	−0.233031
$275$	45.4502	2.74075
$276$	13.7384	0.826953
$277$	−19.1268	−1.14922	−0.574608	−	0.818429i	$-0.694845\pi$
$277$	−19.1268	−1.14922	−0.574608	+	0.818429i	$0.694845\pi$
$278$	1.77845	0.106664
$279$	10.0410	0.601141
$280$	−6.87447	−0.410828
$281$	8.87426	0.529394	0.264697	−	0.964332i	$-0.414728\pi$
$281$	8.87426	0.529394	0.264697	+	0.964332i	$0.414728\pi$
$282$	1.44188	0.0858627
$283$	−20.4319	−1.21455	−0.607274	−	0.794492i	$-0.707737\pi$
$283$	−20.4319	−1.21455	−0.607274	+	0.794492i	$0.707737\pi$
$284$	13.2557	0.786583
$285$	0.510796	0.0302570
$286$	0	0
$287$	11.7059	0.690978
$288$	4.42503	0.260748
$289$	10.7121	0.630123
$290$	−4.41931	−0.259511
$291$	7.20532	0.422384
$292$	25.5762	1.49673
$293$	−16.0750	−0.939114	−0.469557	−	0.882902i	$-0.655586\pi$
$293$	−16.0750	−0.939114	−0.469557	+	0.882902i	$0.655586\pi$
$294$	0.415563	0.0242361
$295$	38.3904	2.23517
$296$	−8.55787	−0.497416
$297$	3.32197	0.192760
$298$	4.58557	0.265635
$299$	0	0
$300$	−25.0007	−1.44342
$301$	−0.378528	−0.0218180
$302$	3.13581	0.180445
$303$	3.90068	0.224088
$304$	0.353788	0.0202911
$305$	−28.8330	−1.65098
$306$	−2.18762	−0.125058
$307$	−6.03807	−0.344611	−0.172305	−	0.985044i	$-0.555122\pi$
$307$	−6.03807	−0.344611	−0.172305	+	0.985044i	$0.555122\pi$
$308$	−6.07025	−0.345885
$309$	−0.253309	−0.0144103
$310$	18.0353	1.02434
$311$	−12.2263	−0.693289	−0.346645	−	0.937997i	$-0.612679\pi$
$311$	−12.2263	−0.693289	−0.346645	+	0.937997i	$0.612679\pi$
$312$	0	0
$313$	−6.55638	−0.370589	−0.185294	−	0.982683i	$-0.559324\pi$
$313$	−6.55638	−0.370589	−0.185294	+	0.982683i	$0.559324\pi$
$314$	−8.95217	−0.505200
$315$	4.32224	0.243530
$316$	0.509002	0.0286336
$317$	6.92785	0.389107	0.194553	−	0.980892i	$-0.437674\pi$
$317$	6.92785	0.389107	0.194553	+	0.980892i	$0.437674\pi$
$318$	1.80304	0.101110
$319$	−8.17343	−0.457624
$320$	−17.9306	−1.00235
$321$	1.25329	0.0699517
$322$	−3.12436	−0.174114
$323$	−0.622120	−0.0346157
$324$	−1.82731	−0.101517
$325$	0	0
$326$	9.30492	0.515352
$327$	−3.26860	−0.180754
$328$	−18.6181	−1.02801
$329$	3.46970	0.191291
$330$	5.96679	0.328461
$331$	15.4100	0.847012	0.423506	−	0.905893i	$-0.360799\pi$
$331$	15.4100	0.847012	0.423506	+	0.905893i	$0.360799\pi$
$332$	26.6784	1.46417
$333$	5.38066	0.294858
$334$	3.38376	0.185151
$335$	−14.8065	−0.808963
$336$	2.99367	0.163318
$337$	23.1479	1.26095	0.630473	−	0.776211i	$-0.282861\pi$
$337$	23.1479	1.26095	0.630473	+	0.776211i	$0.282861\pi$
$338$	0	0
$339$	−0.0957171	−0.00519864
$340$	41.5771	2.25484
$341$	33.3560	1.80633
$342$	0.0491107	0.00265560
$343$	1.00000	0.0539949
$344$	0.602044	0.0324600
$345$	−32.4962	−1.74953
$346$	−5.95650	−0.320224
$347$	26.9284	1.44559	0.722795	−	0.691062i	$-0.242857\pi$
$347$	26.9284	1.44559	0.722795	+	0.691062i	$0.242857\pi$
$348$	4.49594	0.241008
$349$	30.6502	1.64067	0.820334	−	0.571884i	$-0.193787\pi$
$349$	30.6502	1.64067	0.820334	+	0.571884i	$0.193787\pi$
$350$	5.68562	0.303909
$351$	0	0
$352$	14.6998	0.783503
$353$	16.2989	0.867505	0.433752	−	0.901032i	$-0.357189\pi$
$353$	16.2989	0.867505	0.433752	+	0.901032i	$0.357189\pi$
$354$	3.69106	0.196178
$355$	−31.3546	−1.66413
$356$	13.7882	0.730773
$357$	−5.26423	−0.278612
$358$	5.31270	0.280785
$359$	13.6562	0.720744	0.360372	−	0.932809i	$-0.382650\pi$
$359$	13.6562	0.720744	0.360372	+	0.932809i	$0.382650\pi$
$360$	−6.87447	−0.362316
$361$	−18.9860	−0.999265
$362$	8.71881	0.458250
$363$	0.0354611	0.00186123
$364$	0	0
$365$	−60.4969	−3.16655
$366$	−2.77217	−0.144903
$367$	−20.9628	−1.09425	−0.547124	−	0.837051i	$-0.684277\pi$
$367$	−20.9628	−1.09425	−0.547124	+	0.837051i	$0.684277\pi$
$368$	−22.5075	−1.17328
$369$	11.7059	0.609385
$370$	9.66453	0.502435
$371$	4.33879	0.225259
$372$	−18.3481	−0.951303
$373$	4.45107	0.230467	0.115234	−	0.993338i	$-0.463238\pi$
$373$	4.45107	0.230467	0.115234	+	0.993338i	$0.463238\pi$
$374$	−7.26720	−0.375778
$375$	37.5245	1.93776
$376$	−5.51852	−0.284596
$377$	0	0
$378$	0.415563	0.0213743
$379$	1.61744	0.0830826	0.0415413	−	0.999137i	$-0.486773\pi$
$379$	1.61744	0.0830826	0.0415413	+	0.999137i	$0.486773\pi$
$380$	−0.933382	−0.0478815
$381$	15.5224	0.795238
$382$	−2.25065	−0.115153
$383$	−16.3959	−0.837791	−0.418895	−	0.908035i	$-0.637583\pi$
$383$	−16.3959	−0.837791	−0.418895	+	0.908035i	$0.637583\pi$
$384$	−10.5740	−0.539603
$385$	14.3583	0.731768
$386$	−4.66789	−0.237589
$387$	−0.378528	−0.0192416
$388$	−13.1663	−0.668420
$389$	15.1735	0.769326	0.384663	−	0.923057i	$-0.374318\pi$
$389$	15.1735	0.769326	0.384663	+	0.923057i	$0.374318\pi$
$390$	0	0
$391$	39.5784	2.00157
$392$	−1.59049	−0.0803318
$393$	8.00203	0.403649
$394$	−0.293147	−0.0147685
$395$	−1.20397	−0.0605784
$396$	−6.07025	−0.305042
$397$	6.54905	0.328688	0.164344	−	0.986403i	$-0.447449\pi$
$397$	6.54905	0.328688	0.164344	+	0.986403i	$0.447449\pi$
$398$	4.85485	0.243352
$399$	0.118179	0.00591634
$400$	40.9585	2.04793
$401$	29.4546	1.47089	0.735447	−	0.677582i	$-0.236972\pi$
$401$	29.4546	1.47089	0.735447	+	0.677582i	$0.236972\pi$
$402$	−1.42357	−0.0710014
$403$	0	0
$404$	−7.12774	−0.354618
$405$	4.32224	0.214774
$406$	−1.02246	−0.0507438
$407$	17.8744	0.885999
$408$	8.37269	0.414510
$409$	−4.76580	−0.235654	−0.117827	−	0.993034i	$-0.537593\pi$
$409$	−4.76580	−0.235654	−0.117827	+	0.993034i	$0.537593\pi$
$410$	21.0257	1.03839
$411$	−9.28221	−0.457858
$412$	0.462874	0.0228042
$413$	8.88207	0.437058
$414$	−3.12436	−0.153554
$415$	−63.1040	−3.09765
$416$	0	0
$417$	4.27962	0.209574
$418$	0.163144	0.00797964
$419$	21.2897	1.04007	0.520036	−	0.854144i	$-0.325919\pi$
$419$	21.2897	1.04007	0.520036	+	0.854144i	$0.325919\pi$
$420$	−7.89805	−0.385386
$421$	−37.3246	−1.81909	−0.909544	−	0.415608i	$-0.863569\pi$
$421$	−37.3246	−1.81909	−0.909544	+	0.415608i	$0.863569\pi$
$422$	1.82237	0.0887114
$423$	3.46970	0.168703
$424$	−6.90080	−0.335132
$425$	−72.0237	−3.49366
$426$	−3.01460	−0.146058
$427$	−6.67086	−0.322826
$428$	−2.29014	−0.110698
$429$	0	0
$430$	−0.679897	−0.0327876
$431$	0.534607	0.0257511	0.0128756	−	0.999917i	$-0.495901\pi$
$431$	0.534607	0.0257511	0.0128756	+	0.999917i	$0.495901\pi$
$432$	2.99367	0.144033
$433$	13.1324	0.631102	0.315551	−	0.948909i	$-0.397811\pi$
$433$	13.1324	0.631102	0.315551	+	0.948909i	$0.397811\pi$
$434$	4.17269	0.200295
$435$	−10.6345	−0.509886
$436$	5.97273	0.286042
$437$	−0.888511	−0.0425033
$438$	−5.81650	−0.277923
$439$	−37.2212	−1.77647	−0.888236	−	0.459387i	$-0.848069\pi$
$439$	−37.2212	−1.77647	−0.888236	+	0.459387i	$0.848069\pi$
$440$	−22.8367	−1.08870
$441$	1.00000	0.0476190
$442$	0	0
$443$	−4.01164	−0.190599	−0.0952994	−	0.995449i	$-0.530381\pi$
$443$	−4.01164	−0.190599	−0.0952994	+	0.995449i	$0.530381\pi$
$444$	−9.83211	−0.466611
$445$	−32.6140	−1.54605
$446$	−6.16593	−0.291965
$447$	11.0346	0.521918
$448$	−4.14845	−0.195996
$449$	−6.94095	−0.327564	−0.163782	−	0.986497i	$-0.552369\pi$
$449$	−6.94095	−0.327564	−0.163782	+	0.986497i	$0.552369\pi$
$450$	5.68562	0.268023
$451$	38.8866	1.83110
$452$	0.174905	0.00822682
$453$	7.54592	0.354538
$454$	0.0260020	0.00122033
$455$	0	0
$456$	−0.187962	−0.00880212
$457$	−36.0079	−1.68438	−0.842189	−	0.539182i	$-0.818734\pi$
$457$	−36.0079	−1.68438	−0.842189	+	0.539182i	$0.818734\pi$
$458$	−0.0767628	−0.00358689
$459$	−5.26423	−0.245713
$460$	59.3805	2.76863
$461$	−12.5958	−0.586646	−0.293323	−	0.956013i	$-0.594761\pi$
$461$	−12.5958	−0.586646	−0.293323	+	0.956013i	$0.594761\pi$
$462$	1.38049	0.0642261
$463$	−20.9880	−0.975395	−0.487697	−	0.873013i	$-0.662163\pi$
$463$	−20.9880	−0.975395	−0.487697	+	0.873013i	$0.662163\pi$
$464$	−7.36567	−0.341943
$465$	43.3997	2.01261
$466$	0.0791839	0.00366812
$467$	12.8360	0.593980	0.296990	−	0.954881i	$-0.404017\pi$
$467$	12.8360	0.593980	0.296990	+	0.954881i	$0.404017\pi$
$468$	0	0
$469$	−3.42565	−0.158182
$470$	6.23215	0.287468
$471$	−21.5422	−0.992614
$472$	−14.1268	−0.650240
$473$	−1.25746	−0.0578179
$474$	−0.115756	−0.00531687
$475$	1.61689	0.0741879
$476$	9.61936	0.440903
$477$	4.33879	0.198660
$478$	−7.37124	−0.337153
$479$	−11.1856	−0.511085	−0.255542	−	0.966798i	$-0.582254\pi$
$479$	−11.1856	−0.511085	−0.255542	+	0.966798i	$0.582254\pi$
$480$	19.1260	0.872980
$481$	0	0
$482$	1.96227	0.0893788
$483$	−7.51837	−0.342098
$484$	−0.0647984	−0.00294538
$485$	31.1431	1.41414
$486$	0.415563	0.0188503
$487$	29.7826	1.34958	0.674789	−	0.738011i	$-0.264235\pi$
$487$	29.7826	1.34958	0.674789	+	0.738011i	$0.264235\pi$
$488$	10.6099	0.480289
$489$	22.3911	1.01256
$490$	1.79616	0.0811424
$491$	−10.7199	−0.483781	−0.241891	−	0.970304i	$-0.577768\pi$
$491$	−10.7199	−0.483781	−0.241891	+	0.970304i	$0.577768\pi$
$492$	−21.3903	−0.964349
$493$	12.9522	0.583338
$494$	0	0
$495$	14.3583	0.645359
$496$	30.0595	1.34971
$497$	−7.25425	−0.325397
$498$	−6.06716	−0.271876
$499$	−10.9031	−0.488088	−0.244044	−	0.969764i	$-0.578474\pi$
$499$	−10.9031	−0.488088	−0.244044	+	0.969764i	$0.578474\pi$
$500$	−68.5687	−3.06649
$501$	8.14259	0.363784
$502$	−5.49324	−0.245175
$503$	8.98933	0.400814	0.200407	−	0.979713i	$-0.435774\pi$
$503$	8.98933	0.400814	0.200407	+	0.979713i	$0.435774\pi$
$504$	−1.59049	−0.0708460
$505$	16.8597	0.750245
$506$	−10.3790	−0.461403
$507$	0	0
$508$	−28.3642	−1.25846
$509$	2.53243	0.112248	0.0561239	−	0.998424i	$-0.482126\pi$
$509$	2.53243	0.112248	0.0561239	+	0.998424i	$0.482126\pi$
$510$	−9.45541	−0.418693
$511$	−13.9967	−0.619176
$512$	22.7699	1.00629
$513$	0.118179	0.00521772
$514$	−7.23705	−0.319212
$515$	−1.09486	−0.0482454
$516$	0.691686	0.0304498
$517$	11.5262	0.506923
$518$	2.23600	0.0982443
$519$	−14.3336	−0.629174
$520$	0	0
$521$	−12.2815	−0.538062	−0.269031	−	0.963132i	$-0.586703\pi$
$521$	−12.2815	−0.538062	−0.269031	+	0.963132i	$0.586703\pi$
$522$	−1.02246	−0.0447518
$523$	−41.1027	−1.79729	−0.898647	−	0.438673i	$-0.855449\pi$
$523$	−41.1027	−1.79729	−0.898647	+	0.438673i	$0.855449\pi$
$524$	−14.6222	−0.638772
$525$	13.6817	0.597119
$526$	−10.4934	−0.457534
$527$	−52.8583	−2.30254
$528$	9.94486	0.432794
$529$	33.5259	1.45765
$530$	7.79318	0.338514
$531$	8.88207	0.385449
$532$	−0.215949	−0.00936257
$533$	0	0
$534$	−3.13569	−0.135695
$535$	5.41701	0.234198
$536$	5.44845	0.235337
$537$	12.7843	0.551685
$538$	−6.53983	−0.281952
$539$	3.32197	0.143087
$540$	−7.89805	−0.339878
$541$	−39.2640	−1.68809	−0.844046	−	0.536270i	$-0.819833\pi$
$541$	−39.2640	−1.68809	−0.844046	+	0.536270i	$0.819833\pi$
$542$	−4.45392	−0.191312
$543$	20.9807	0.900368
$544$	−23.2944	−0.998739
$545$	−14.1276	−0.605162
$546$	0	0
$547$	13.8409	0.591793	0.295897	−	0.955220i	$-0.404382\pi$
$547$	13.8409	0.591793	0.295897	+	0.955220i	$0.404382\pi$
$548$	16.9615	0.724557
$549$	−6.67086	−0.284705
$550$	18.8874	0.805363
$551$	−0.290769	−0.0123872
$552$	11.9579	0.508961
$553$	−0.278553	−0.0118453
$554$	−7.94838	−0.337694
$555$	23.2565	0.987182
$556$	−7.82017	−0.331649
$557$	−32.7700	−1.38851	−0.694255	−	0.719729i	$-0.744266\pi$
$557$	−32.7700	−1.38851	−0.694255	+	0.719729i	$0.744266\pi$
$558$	4.17269	0.176644
$559$	0	0
$560$	12.9393	0.546787
$561$	−17.4876	−0.738326
$562$	3.68782	0.155561
$563$	−35.6426	−1.50216	−0.751079	−	0.660212i	$-0.770466\pi$
$563$	−35.6426	−1.50216	−0.751079	+	0.660212i	$0.770466\pi$
$564$	−6.34021	−0.266971
$565$	−0.413712	−0.0174050
$566$	−8.49074	−0.356892
$567$	1.00000	0.0419961
$568$	11.5378	0.484115
$569$	−37.4955	−1.57189	−0.785946	−	0.618296i	$-0.787823\pi$
$569$	−37.4955	−1.57189	−0.785946	+	0.618296i	$0.787823\pi$
$570$	0.212268	0.00889094
$571$	−20.8001	−0.870458	−0.435229	−	0.900320i	$-0.643333\pi$
$571$	−20.8001	−0.870458	−0.435229	+	0.900320i	$0.643333\pi$
$572$	0	0
$573$	−5.41589	−0.226252
$574$	4.86455	0.203042
$575$	−102.864	−4.28974
$576$	−4.14845	−0.172852
$577$	−25.9570	−1.08061	−0.540303	−	0.841471i	$-0.681690\pi$
$577$	−25.9570	−1.08061	−0.540303	+	0.841471i	$0.681690\pi$
$578$	4.45155	0.185160
$579$	−11.2327	−0.466814
$580$	19.4325	0.806891
$581$	−14.5998	−0.605703
$582$	2.99427	0.124116
$583$	14.4133	0.596939
$584$	22.2615	0.921189
$585$	0	0
$586$	−6.68020	−0.275957
$587$	−38.3127	−1.58133	−0.790667	−	0.612246i	$-0.790266\pi$
$587$	−38.3127	−1.58133	−0.790667	+	0.612246i	$0.790266\pi$
$588$	−1.82731	−0.0753569
$589$	1.18664	0.0488945
$590$	15.9536	0.656801
$591$	−0.705420	−0.0290171
$592$	16.1079	0.662030
$593$	20.6171	0.846642	0.423321	−	0.905980i	$-0.360864\pi$
$593$	20.6171	0.846642	0.423321	+	0.905980i	$0.360864\pi$
$594$	1.38049	0.0566421
$595$	−22.7532	−0.932792
$596$	−20.1636	−0.825932
$597$	11.6826	0.478136
$598$	0	0
$599$	12.5620	0.513268	0.256634	−	0.966509i	$-0.417386\pi$
$599$	12.5620	0.513268	0.256634	+	0.966509i	$0.417386\pi$
$600$	−21.7606	−0.888374
$601$	45.2688	1.84655	0.923277	−	0.384134i	$-0.125500\pi$
$601$	45.2688	1.84655	0.923277	+	0.384134i	$0.125500\pi$
$602$	−0.157302	−0.00641116
$603$	−3.42565	−0.139503
$604$	−13.7887	−0.561055
$605$	0.153271	0.00623137
$606$	1.62098	0.0658478
$607$	1.11155	0.0451165	0.0225582	−	0.999746i	$-0.492819\pi$
$607$	1.11155	0.0451165	0.0225582	+	0.999746i	$0.492819\pi$
$608$	0.522945	0.0212082
$609$	−2.46042	−0.0997012
$610$	−11.9820	−0.485135
$611$	0	0
$612$	9.61936	0.388840
$613$	−16.9221	−0.683479	−0.341739	−	0.939795i	$-0.611016\pi$
$613$	−16.9221	−0.683479	−0.341739	+	0.939795i	$0.611016\pi$
$614$	−2.50920	−0.101263
$615$	50.5957	2.04022
$616$	−5.28355	−0.212880
$617$	−29.2034	−1.17569	−0.587843	−	0.808975i	$-0.700023\pi$
$617$	−29.2034	−1.17569	−0.587843	+	0.808975i	$0.700023\pi$
$618$	−0.105266	−0.00423442
$619$	10.3246	0.414983	0.207491	−	0.978237i	$-0.433470\pi$
$619$	10.3246	0.414983	0.207491	+	0.978237i	$0.433470\pi$
$620$	−79.3046	−3.18495
$621$	−7.51837	−0.301702
$622$	−5.08080	−0.203721
$623$	−7.54564	−0.302310
$624$	0	0
$625$	93.7810	3.75124
$626$	−2.72459	−0.108897
$627$	0.392586	0.0156784
$628$	39.3643	1.57081
$629$	−28.3250	−1.12939
$630$	1.79616	0.0715608
$631$	39.6457	1.57827	0.789135	−	0.614220i	$-0.210529\pi$
$631$	39.6457	1.57827	0.789135	+	0.614220i	$0.210529\pi$
$632$	0.443036	0.0176230
$633$	4.38529	0.174300
$634$	2.87896	0.114338
$635$	67.0916	2.66245
$636$	−7.92831	−0.314378
$637$	0	0
$638$	−3.39658	−0.134472
$639$	−7.25425	−0.286974
$640$	−45.7034	−1.80658
$641$	−27.3047	−1.07847	−0.539236	−	0.842155i	$-0.681287\pi$
$641$	−27.3047	−1.07847	−0.539236	+	0.842155i	$0.681287\pi$
$642$	0.520821	0.0205552
$643$	2.71488	0.107064	0.0535322	−	0.998566i	$-0.482952\pi$
$643$	2.71488	0.107064	0.0535322	+	0.998566i	$0.482952\pi$
$644$	13.7384	0.541368
$645$	−1.63609	−0.0644208
$646$	−0.258530	−0.0101717
$647$	−10.5518	−0.414834	−0.207417	−	0.978253i	$-0.566506\pi$
$647$	−10.5518	−0.414834	−0.207417	+	0.978253i	$0.566506\pi$
$648$	−1.59049	−0.0624803
$649$	29.5059	1.15821
$650$	0	0
$651$	10.0410	0.393539
$652$	−40.9154	−1.60237
$653$	−8.55364	−0.334730	−0.167365	−	0.985895i	$-0.553526\pi$
$653$	−8.55364	−0.334730	−0.167365	+	0.985895i	$0.553526\pi$
$654$	−1.35831	−0.0531141
$655$	34.5867	1.35141
$656$	35.0436	1.36822
$657$	−13.9967	−0.546062
$658$	1.44188	0.0562104
$659$	−26.2916	−1.02418	−0.512088	−	0.858933i	$-0.671128\pi$
$659$	−26.2916	−1.02418	−0.512088	+	0.858933i	$0.671128\pi$
$660$	−26.2371	−1.02128
$661$	−3.08987	−0.120182	−0.0600909	−	0.998193i	$-0.519139\pi$
$661$	−3.08987	−0.120182	−0.0600909	+	0.998193i	$0.519139\pi$
$662$	6.40385	0.248893
$663$	0	0
$664$	23.2209	0.901145
$665$	0.510796	0.0198078
$666$	2.23600	0.0866434
$667$	18.4983	0.716259
$668$	−14.8790	−0.575686
$669$	−14.8375	−0.573652
$670$	−6.15302	−0.237712
$671$	−22.1604	−0.855492
$672$	4.42503	0.170699
$673$	−2.93113	−0.112987	−0.0564933	−	0.998403i	$-0.517992\pi$
$673$	−2.93113	−0.112987	−0.0564933	+	0.998403i	$0.517992\pi$
$674$	9.61941	0.370526
$675$	13.6817	0.526610
$676$	0	0
$677$	31.4703	1.20950	0.604750	−	0.796415i	$-0.293273\pi$
$677$	31.4703	1.20950	0.604750	+	0.796415i	$0.293273\pi$
$678$	−0.0397765	−0.00152761
$679$	7.20532	0.276515
$680$	36.1888	1.38778
$681$	0.0625704	0.00239770
$682$	13.8615	0.530785
$683$	−1.39640	−0.0534318	−0.0267159	−	0.999643i	$-0.508505\pi$
$683$	−1.39640	−0.0534318	−0.0267159	+	0.999643i	$0.508505\pi$
$684$	−0.215949	−0.00825701
$685$	−40.1199	−1.53290
$686$	0.415563	0.0158663
$687$	−0.184720	−0.00704750
$688$	−1.13319	−0.0432023
$689$	0	0
$690$	−13.5042	−0.514097
$691$	−30.1321	−1.14628	−0.573140	−	0.819458i	$-0.694275\pi$
$691$	−30.1321	−1.14628	−0.573140	+	0.819458i	$0.694275\pi$
$692$	26.1918	0.995664
$693$	3.32197	0.126191
$694$	11.1904	0.424783
$695$	18.4975	0.701651
$696$	3.91327	0.148332
$697$	−61.6226	−2.33412
$698$	12.7371	0.482107
$699$	0.190546	0.00720711
$700$	−25.0007	−0.944938
$701$	−30.3056	−1.14463	−0.572313	−	0.820035i	$-0.693954\pi$
$701$	−30.3056	−1.14463	−0.572313	+	0.820035i	$0.693954\pi$
$702$	0	0
$703$	0.635879	0.0239826
$704$	−13.7810	−0.519391
$705$	14.9969	0.564815
$706$	6.77324	0.254914
$707$	3.90068	0.146700
$708$	−16.2303	−0.609971
$709$	44.2264	1.66096	0.830479	−	0.557050i	$-0.188067\pi$
$709$	44.2264	1.66096	0.830479	+	0.557050i	$0.188067\pi$
$710$	−13.0298	−0.489000
$711$	−0.278553	−0.0104466
$712$	12.0012	0.449766
$713$	−75.4922	−2.82721
$714$	−2.18762	−0.0818696
$715$	0	0
$716$	−23.3609	−0.873038
$717$	−17.7380	−0.662436
$718$	5.67500	0.211789
$719$	38.6174	1.44019	0.720093	−	0.693878i	$-0.244099\pi$
$719$	38.6174	1.44019	0.720093	+	0.693878i	$0.244099\pi$
$720$	12.9393	0.482220
$721$	−0.253309	−0.00943373
$722$	−7.88990	−0.293632
$723$	4.72194	0.175611
$724$	−38.3382	−1.42483
$725$	−33.6628	−1.25020
$726$	0.0147363	0.000546917 0
$727$	3.77723	0.140090	0.0700448	−	0.997544i	$-0.477686\pi$
$727$	3.77723	0.140090	0.0700448	+	0.997544i	$0.477686\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−25.1403	−0.930484
$731$	1.99266	0.0737010
$732$	12.1897	0.450545
$733$	15.0366	0.555391	0.277695	−	0.960669i	$-0.410429\pi$
$733$	15.0366	0.555391	0.277695	+	0.960669i	$0.410429\pi$
$734$	−8.71136	−0.321542
$735$	4.32224	0.159428
$736$	−33.2690	−1.22631
$737$	−11.3799	−0.419183
$738$	4.86455	0.179066
$739$	8.27720	0.304482	0.152241	−	0.988343i	$-0.451351\pi$
$739$	8.27720	0.304482	0.152241	+	0.988343i	$0.451351\pi$
$740$	−42.4967	−1.56221
$741$	0	0
$742$	1.80304	0.0661918
$743$	38.8141	1.42395	0.711976	−	0.702204i	$-0.247801\pi$
$743$	38.8141	1.42395	0.711976	+	0.702204i	$0.247801\pi$
$744$	−15.9702	−0.585494
$745$	47.6941	1.74738
$746$	1.84970	0.0677223
$747$	−14.5998	−0.534180
$748$	31.9552	1.16840
$749$	1.25329	0.0457942
$750$	15.5938	0.569405
$751$	45.7595	1.66979	0.834894	−	0.550411i	$-0.185529\pi$
$751$	45.7595	1.66979	0.834894	+	0.550411i	$0.185529\pi$
$752$	10.3871	0.378780
$753$	−13.2188	−0.481719
$754$	0	0
$755$	32.6152	1.18699
$756$	−1.82731	−0.0664585
$757$	−35.1055	−1.27593	−0.637965	−	0.770065i	$-0.720224\pi$
$757$	−35.1055	−1.27593	−0.637965	+	0.770065i	$0.720224\pi$
$758$	0.672151	0.0244136
$759$	−24.9758	−0.906563
$760$	−0.812416	−0.0294694
$761$	4.99677	0.181133	0.0905665	−	0.995890i	$-0.471132\pi$
$761$	4.99677	0.181133	0.0905665	+	0.995890i	$0.471132\pi$
$762$	6.45055	0.233679
$763$	−3.26860	−0.118331
$764$	9.89650	0.358043
$765$	−22.7532	−0.822645
$766$	−6.81353	−0.246183
$767$	0	0
$768$	3.90273	0.140828
$769$	−10.8083	−0.389756	−0.194878	−	0.980827i	$-0.562431\pi$
$769$	−10.8083	−0.389756	−0.194878	+	0.980827i	$0.562431\pi$
$770$	5.96679	0.215028
$771$	−17.4150	−0.627187
$772$	20.5255	0.738731
$773$	5.52880	0.198857	0.0994285	−	0.995045i	$-0.468299\pi$
$773$	5.52880	0.198857	0.0994285	+	0.995045i	$0.468299\pi$
$774$	−0.157302	−0.00565411
$775$	137.379	4.93479
$776$	−11.4600	−0.411389
$777$	5.38066	0.193030
$778$	6.30554	0.226065
$779$	1.38339	0.0495651
$780$	0	0
$781$	−24.0984	−0.862307
$782$	16.4473	0.588155
$783$	−2.46042	−0.0879282
$784$	2.99367	0.106917
$785$	−93.1107	−3.32326
$786$	3.32535	0.118611
$787$	−6.79072	−0.242063	−0.121031	−	0.992649i	$-0.538620\pi$
$787$	−6.79072	−0.242063	−0.121031	+	0.992649i	$0.538620\pi$
$788$	1.28902	0.0459194
$789$	−25.2510	−0.898960
$790$	−0.500327	−0.0178008
$791$	−0.0957171	−0.00340331
$792$	−5.28355	−0.187743
$793$	0	0
$794$	2.72155	0.0965840
$795$	18.7533	0.665110
$796$	−21.3477	−0.756648
$797$	−10.3512	−0.366657	−0.183328	−	0.983052i	$-0.558687\pi$
$797$	−10.3512	−0.366657	−0.183328	+	0.983052i	$0.558687\pi$
$798$	0.0491107	0.00173850
$799$	−18.2653	−0.646180
$800$	60.5421	2.14049
$801$	−7.54564	−0.266612
$802$	12.2403	0.432219
$803$	−46.4965	−1.64082
$804$	6.25971	0.220763
$805$	−32.4962	−1.14534
$806$	0	0
$807$	−15.7373	−0.553978
$808$	−6.20399	−0.218255
$809$	4.16152	0.146311	0.0731556	−	0.997321i	$-0.476693\pi$
$809$	4.16152	0.146311	0.0731556	+	0.997321i	$0.476693\pi$
$810$	1.79616	0.0631107
$811$	28.3669	0.996096	0.498048	−	0.867150i	$-0.334050\pi$
$811$	28.3669	0.996096	0.498048	+	0.867150i	$0.334050\pi$
$812$	4.49594	0.157777
$813$	−10.7178	−0.375889
$814$	7.42793	0.260349
$815$	96.7796	3.39004
$816$	−15.7593	−0.551687
$817$	−0.0447339	−0.00156504
$818$	−1.98049	−0.0692463
$819$	0	0
$820$	−92.4539	−3.22863
$821$	−43.0173	−1.50132	−0.750658	−	0.660691i	$-0.770263\pi$
$821$	−43.0173	−1.50132	−0.750658	+	0.660691i	$0.770263\pi$
$822$	−3.85735	−0.134540
$823$	22.0229	0.767669	0.383834	−	0.923402i	$-0.374603\pi$
$823$	22.0229	0.767669	0.383834	+	0.923402i	$0.374603\pi$
$824$	0.402885	0.0140352
$825$	45.4502	1.58237
$826$	3.69106	0.128428
$827$	−30.0713	−1.04568	−0.522841	−	0.852430i	$-0.675128\pi$
$827$	−30.0713	−1.04568	−0.522841	+	0.852430i	$0.675128\pi$
$828$	13.7384	0.477441
$829$	−50.5308	−1.75501	−0.877504	−	0.479570i	$-0.840793\pi$
$829$	−50.5308	−1.75501	−0.877504	+	0.479570i	$0.840793\pi$
$830$	−26.2237	−0.910238
$831$	−19.1268	−0.663500
$832$	0	0
$833$	−5.26423	−0.182395
$834$	1.77845	0.0615827
$835$	35.1942	1.21795
$836$	−0.717375	−0.0248109
$837$	10.0410	0.347069
$838$	8.84723	0.305623
$839$	46.9147	1.61967	0.809837	−	0.586655i	$-0.199555\pi$
$839$	46.9147	1.61967	0.809837	+	0.586655i	$0.199555\pi$
$840$	−6.87447	−0.237192
$841$	−22.9463	−0.791253
$842$	−15.5107	−0.534535
$843$	8.87426	0.305646
$844$	−8.01328	−0.275828
$845$	0	0
$846$	1.44188	0.0495729
$847$	0.0354611	0.00121846
$848$	12.9889	0.446040
$849$	−20.4319	−0.701220
$850$	−29.9304	−1.02660
$851$	−40.4538	−1.38674
$852$	13.2557	0.454134
$853$	28.9771	0.992157	0.496078	−	0.868278i	$-0.334773\pi$
$853$	28.9771	0.992157	0.496078	+	0.868278i	$0.334773\pi$
$854$	−2.77217	−0.0948615
$855$	0.510796	0.0174689
$856$	−1.99334	−0.0681310
$857$	5.56795	0.190198	0.0950988	−	0.995468i	$-0.469683\pi$
$857$	5.56795	0.190198	0.0950988	+	0.995468i	$0.469683\pi$
$858$	0	0
$859$	19.0380	0.649567	0.324784	−	0.945788i	$-0.394709\pi$
$859$	19.0380	0.649567	0.324784	+	0.945788i	$0.394709\pi$
$860$	2.98963	0.101946
$861$	11.7059	0.398936
$862$	0.222163	0.00756691
$863$	34.0312	1.15843	0.579217	−	0.815173i	$-0.303358\pi$
$863$	34.0312	1.15843	0.579217	+	0.815173i	$0.303358\pi$
$864$	4.42503	0.150543
$865$	−61.9530	−2.10647
$866$	5.45734	0.185448
$867$	10.7121	0.363802
$868$	−18.3481	−0.622774
$869$	−0.925344	−0.0313902
$870$	−4.41931	−0.149829
$871$	0	0
$872$	5.19866	0.176049
$873$	7.20532	0.243863
$874$	−0.369233	−0.0124895
$875$	37.5245	1.26856
$876$	25.5762	0.864140
$877$	−42.5065	−1.43534	−0.717671	−	0.696383i	$-0.754792\pi$
$877$	−42.5065	−1.43534	−0.717671	+	0.696383i	$0.754792\pi$
$878$	−15.4678	−0.522012
$879$	−16.0750	−0.542198
$880$	42.9840	1.44899
$881$	−40.9431	−1.37941	−0.689704	−	0.724091i	$-0.742259\pi$
$881$	−40.9431	−1.37941	−0.689704	+	0.724091i	$0.742259\pi$
$882$	0.415563	0.0139927
$883$	17.7038	0.595779	0.297890	−	0.954600i	$-0.403717\pi$
$883$	17.7038	0.595779	0.297890	+	0.954600i	$0.403717\pi$
$884$	0	0
$885$	38.3904	1.29048
$886$	−1.66709	−0.0560070
$887$	14.0736	0.472546	0.236273	−	0.971687i	$-0.424074\pi$
$887$	14.0736	0.472546	0.236273	+	0.971687i	$0.424074\pi$
$888$	−8.55787	−0.287183
$889$	15.5224	0.520605
$890$	−13.5532	−0.454304
$891$	3.32197	0.111290
$892$	27.1127	0.907801
$893$	0.410045	0.0137216
$894$	4.58557	0.153364
$895$	55.2569	1.84703
$896$	−10.5740	−0.353253
$897$	0	0
$898$	−2.88440	−0.0962538
$899$	−24.7052	−0.823963
$900$	−25.0007	−0.833357
$901$	−22.8404	−0.760924
$902$	16.1599	0.538064
$903$	−0.378528	−0.0125966
$904$	0.152237	0.00506332
$905$	90.6835	3.01442
$906$	3.13581	0.104180
$907$	46.3181	1.53797	0.768984	−	0.639269i	$-0.220763\pi$
$907$	46.3181	1.53797	0.768984	+	0.639269i	$0.220763\pi$
$908$	−0.114335	−0.00379435
$909$	3.90068	0.129377
$910$	0	0
$911$	−45.4712	−1.50653	−0.753263	−	0.657719i	$-0.771521\pi$
$911$	−45.4712	−1.50653	−0.753263	+	0.657719i	$0.771521\pi$
$912$	0.353788	0.0117151
$913$	−48.5002	−1.60512
$914$	−14.9636	−0.494951
$915$	−28.8330	−0.953191
$916$	0.337540	0.0111526
$917$	8.00203	0.264250
$918$	−2.18762	−0.0722022
$919$	8.52183	0.281109	0.140555	−	0.990073i	$-0.455111\pi$
$919$	8.52183	0.281109	0.140555	+	0.990073i	$0.455111\pi$
$920$	51.6848	1.70400
$921$	−6.03807	−0.198961
$922$	−5.23436	−0.172384
$923$	0	0
$924$	−6.07025	−0.199697
$925$	73.6167	2.42050
$926$	−8.72184	−0.286617
$927$	−0.253309	−0.00831977
$928$	−10.8874	−0.357398
$929$	−56.0590	−1.83924	−0.919618	−	0.392814i	$-0.871502\pi$
$929$	−56.0590	−1.83924	−0.919618	+	0.392814i	$0.871502\pi$
$930$	18.0353	0.591402
$931$	0.118179	0.00387315
$932$	−0.348186	−0.0114052
$933$	−12.2263	−0.400271
$934$	5.33418	0.174540
$935$	−75.5855	−2.47191
$936$	0	0
$937$	−50.0468	−1.63496	−0.817479	−	0.575958i	$-0.804629\pi$
$937$	−50.0468	−1.63496	−0.817479	+	0.575958i	$0.804629\pi$
$938$	−1.42357	−0.0464813
$939$	−6.55638	−0.213959
$940$	−27.4039	−0.893816
$941$	30.1842	0.983978	0.491989	−	0.870601i	$-0.336270\pi$
$941$	30.1842	0.983978	0.491989	+	0.870601i	$0.336270\pi$
$942$	−8.95217	−0.291677
$943$	−88.0094	−2.86598
$944$	26.5899	0.865429
$945$	4.32224	0.140602
$946$	−0.522553	−0.0169897
$947$	−26.1774	−0.850653	−0.425326	−	0.905040i	$-0.639841\pi$
$947$	−26.1774	−0.850653	−0.425326	+	0.905040i	$0.639841\pi$
$948$	0.509002	0.0165316
$949$	0	0
$950$	0.671920	0.0218000
$951$	6.92785	0.224651
$952$	8.37269	0.271361
$953$	−17.2735	−0.559542	−0.279771	−	0.960067i	$-0.590259\pi$
$953$	−17.2735	−0.559542	−0.279771	+	0.960067i	$0.590259\pi$
$954$	1.80304	0.0583757
$955$	−23.4088	−0.757490
$956$	32.4127	1.04830
$957$	−8.17343	−0.264209
$958$	−4.64834	−0.150181
$959$	−9.28221	−0.299738
$960$	−17.9306	−0.578707
$961$	69.8224	2.25234
$962$	0	0
$963$	1.25329	0.0403867
$964$	−8.62844	−0.277903
$965$	−48.5503	−1.56289
$966$	−3.12436	−0.100525
$967$	52.2470	1.68015	0.840075	−	0.542470i	$-0.182511\pi$
$967$	52.2470	1.68015	0.840075	+	0.542470i	$0.182511\pi$
$968$	−0.0564005	−0.00181278
$969$	−0.622120	−0.0199854
$970$	12.9419	0.415540
$971$	−18.0460	−0.579125	−0.289562	−	0.957159i	$-0.593510\pi$
$971$	−18.0460	−0.579125	−0.289562	+	0.957159i	$0.593510\pi$
$972$	−1.82731	−0.0586109
$973$	4.27962	0.137198
$974$	12.3766	0.396570
$975$	0	0
$976$	−19.9703	−0.639235
$977$	−8.28532	−0.265071	−0.132535	−	0.991178i	$-0.542312\pi$
$977$	−8.28532	−0.265071	−0.132535	+	0.991178i	$0.542312\pi$
$978$	9.30492	0.297539
$979$	−25.0664	−0.801124
$980$	−7.89805	−0.252294
$981$	−3.26860	−0.104358
$982$	−4.45479	−0.142158
$983$	29.0487	0.926509	0.463255	−	0.886225i	$-0.346682\pi$
$983$	29.0487	0.926509	0.463255	+	0.886225i	$0.346682\pi$
$984$	−18.6181	−0.593524
$985$	−3.04899	−0.0971489
$986$	5.38246	0.171412
$987$	3.46970	0.110442
$988$	0	0
$989$	2.84591	0.0904947
$990$	5.96679	0.189637
$991$	8.19764	0.260407	0.130203	−	0.991487i	$-0.458437\pi$
$991$	8.19764	0.260407	0.130203	+	0.991487i	$0.458437\pi$
$992$	44.4319	1.41072
$993$	15.4100	0.489023
$994$	−3.01460	−0.0956173
$995$	50.4949	1.60079
$996$	26.6784	0.845337
$997$	33.4493	1.05935	0.529675	−	0.848201i	$-0.322314\pi$
$997$	33.4493	1.05935	0.529675	+	0.848201i	$0.322314\pi$
$998$	−4.53091	−0.143423
$999$	5.38066	0.170236

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bg.1.9	✓	15
13.12	even	2		3549.2.a.bh.1.7	yes	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.bg.1.9	✓	15	1.1	even	1	trivial
3549.2.a.bh.1.7	yes	15	13.12	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:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q+0.415563 q^{2} +1.00000 q^{3} -1.82731 q^{4} +4.32224 q^{5} +0.415563 q^{6} +1.00000 q^{7} -1.59049 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.415563 q^{2} +1.00000 q^{3} -1.82731 q^{4} +4.32224 q^{5} +0.415563 q^{6} +1.00000 q^{7} -1.59049 q^{8} +1.00000 q^{9} +1.79616 q^{10} +3.32197 q^{11} -1.82731 q^{12} +0.415563 q^{14} +4.32224 q^{15} +2.99367 q^{16} -5.26423 q^{17} +0.415563 q^{18} +0.118179 q^{19} -7.89805 q^{20} +1.00000 q^{21} +1.38049 q^{22} -7.51837 q^{23} -1.59049 q^{24} +13.6817 q^{25} +1.00000 q^{27} -1.82731 q^{28} -2.46042 q^{29} +1.79616 q^{30} +10.0410 q^{31} +4.42503 q^{32} +3.32197 q^{33} -2.18762 q^{34} +4.32224 q^{35} -1.82731 q^{36} +5.38066 q^{37} +0.0491107 q^{38} -6.87447 q^{40} +11.7059 q^{41} +0.415563 q^{42} -0.378528 q^{43} -6.07025 q^{44} +4.32224 q^{45} -3.12436 q^{46} +3.46970 q^{47} +2.99367 q^{48} +1.00000 q^{49} +5.68562 q^{50} -5.26423 q^{51} +4.33879 q^{53} +0.415563 q^{54} +14.3583 q^{55} -1.59049 q^{56} +0.118179 q^{57} -1.02246 q^{58} +8.88207 q^{59} -7.89805 q^{60} -6.67086 q^{61} +4.17269 q^{62} +1.00000 q^{63} -4.14845 q^{64} +1.38049 q^{66} -3.42565 q^{67} +9.61936 q^{68} -7.51837 q^{69} +1.79616 q^{70} -7.25425 q^{71} -1.59049 q^{72} -13.9967 q^{73} +2.23600 q^{74} +13.6817 q^{75} -0.215949 q^{76} +3.32197 q^{77} -0.278553 q^{79} +12.9393 q^{80} +1.00000 q^{81} +4.86455 q^{82} -14.5998 q^{83} -1.82731 q^{84} -22.7532 q^{85} -0.157302 q^{86} -2.46042 q^{87} -5.28355 q^{88} -7.54564 q^{89} +1.79616 q^{90} +13.7384 q^{92} +10.0410 q^{93} +1.44188 q^{94} +0.510796 q^{95} +4.42503 q^{96} +7.20532 q^{97} +0.415563 q^{98} +3.32197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 2 q^{2} + 15 q^{3} + 28 q^{4} + 9 q^{5} - 2 q^{6} + 15 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) \) 15 * q - 2 * q^2 + 15 * q^3 + 28 * q^4 + 9 * q^5 - 2 * q^6 + 15 * q^7 - 9 * q^8 + 15 * q^9	\( 15 q - 2 q^{2} + 15 q^{3} + 28 q^{4} + 9 q^{5} - 2 q^{6} + 15 q^{7} - 9 q^{8} + 15 q^{9} + 21 q^{10} - 5 q^{11} + 28 q^{12} - 2 q^{14} + 9 q^{15} + 50 q^{16} - q^{17} - 2 q^{18} - 3 q^{19} + 23 q^{20} + 15 q^{21} + 21 q^{22} + 4 q^{23} - 9 q^{24} + 50 q^{25} + 15 q^{27} + 28 q^{28} + 9 q^{29} + 21 q^{30} - 7 q^{31} - 35 q^{32} - 5 q^{33} + 2 q^{34} + 9 q^{35} + 28 q^{36} - 17 q^{37} - 12 q^{38} + 46 q^{40} + 22 q^{41} - 2 q^{42} + 36 q^{43} - 29 q^{44} + 9 q^{45} + q^{46} + 12 q^{47} + 50 q^{48} + 15 q^{49} - 53 q^{50} - q^{51} - 5 q^{53} - 2 q^{54} + 43 q^{55} - 9 q^{56} - 3 q^{57} - 29 q^{58} + 29 q^{59} + 23 q^{60} + 12 q^{61} + 14 q^{62} + 15 q^{63} + 95 q^{64} + 21 q^{66} + 12 q^{67} - 16 q^{68} + 4 q^{69} + 21 q^{70} - 36 q^{71} - 9 q^{72} + 29 q^{73} - 5 q^{74} + 50 q^{75} - 25 q^{76} - 5 q^{77} + 35 q^{79} + 89 q^{80} + 15 q^{81} + 51 q^{82} + 10 q^{83} + 28 q^{84} - 23 q^{85} - 19 q^{86} + 9 q^{87} + 73 q^{88} - 25 q^{89} + 21 q^{90} - 31 q^{92} - 7 q^{93} - 19 q^{94} - 7 q^{95} - 35 q^{96} + 26 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 15 * q - 2 * q^2 + 15 * q^3 + 28 * q^4 + 9 * q^5 - 2 * q^6 + 15 * q^7 - 9 * q^8 + 15 * q^9 + 21 * q^10 - 5 * q^11 + 28 * q^12 - 2 * q^14 + 9 * q^15 + 50 * q^16 - q^17 - 2 * q^18 - 3 * q^19 + 23 * q^20 + 15 * q^21 + 21 * q^22 + 4 * q^23 - 9 * q^24 + 50 * q^25 + 15 * q^27 + 28 * q^28 + 9 * q^29 + 21 * q^30 - 7 * q^31 - 35 * q^32 - 5 * q^33 + 2 * q^34 + 9 * q^35 + 28 * q^36 - 17 * q^37 - 12 * q^38 + 46 * q^40 + 22 * q^41 - 2 * q^42 + 36 * q^43 - 29 * q^44 + 9 * q^45 + q^46 + 12 * q^47 + 50 * q^48 + 15 * q^49 - 53 * q^50 - q^51 - 5 * q^53 - 2 * q^54 + 43 * q^55 - 9 * q^56 - 3 * q^57 - 29 * q^58 + 29 * q^59 + 23 * q^60 + 12 * q^61 + 14 * q^62 + 15 * q^63 + 95 * q^64 + 21 * q^66 + 12 * q^67 - 16 * q^68 + 4 * q^69 + 21 * q^70 - 36 * q^71 - 9 * q^72 + 29 * q^73 - 5 * q^74 + 50 * q^75 - 25 * q^76 - 5 * q^77 + 35 * q^79 + 89 * q^80 + 15 * q^81 + 51 * q^82 + 10 * q^83 + 28 * q^84 - 23 * q^85 - 19 * q^86 + 9 * q^87 + 73 * q^88 - 25 * q^89 + 21 * q^90 - 31 * q^92 - 7 * q^93 - 19 * q^94 - 7 * q^95 - 35 * q^96 + 26 * q^97 - 2 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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