LMFDB - Embedded newform 241.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [241,2,Mod(1,241)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(241, 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("241.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	241.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:	$1.92439468871$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 14 x^{10} + 44 x^{9} + 65 x^{8} - 219 x^{7} - 123 x^{6} + 444 x^{5} + 105 x^{4} + \cdots - 1 $ x^12 - 3x^11 - 14x^10 + 44x^9 + 65x^8 - 219x^7 - 123x^6 + 444x^5 + 105x^4 - 328x^3 - 45x^2 + 18*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.28632$ of defining polynomial
Character	$\chi$	$=$	241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.28632 q^{2} -0.126224 q^{3} -0.345373 q^{4} +0.612768 q^{5} +0.162365 q^{6} +1.03110 q^{7} +3.01691 q^{8} -2.98407 q^{9} +O(q^{10})$	\(q-1.28632 q^{2} -0.126224 q^{3} -0.345373 q^{4} +0.612768 q^{5} +0.162365 q^{6} +1.03110 q^{7} +3.01691 q^{8} -2.98407 q^{9} -0.788217 q^{10} +0.227935 q^{11} +0.0435945 q^{12} +3.38088 q^{13} -1.32633 q^{14} -0.0773462 q^{15} -3.18997 q^{16} +7.12130 q^{17} +3.83847 q^{18} +3.40112 q^{19} -0.211634 q^{20} -0.130150 q^{21} -0.293198 q^{22} +6.91488 q^{23} -0.380807 q^{24} -4.62452 q^{25} -4.34890 q^{26} +0.755335 q^{27} -0.356115 q^{28} +0.569431 q^{29} +0.0994922 q^{30} +4.93697 q^{31} -1.93048 q^{32} -0.0287710 q^{33} -9.16030 q^{34} +0.631826 q^{35} +1.03062 q^{36} -5.37832 q^{37} -4.37494 q^{38} -0.426749 q^{39} +1.84866 q^{40} +10.7559 q^{41} +0.167415 q^{42} -0.910247 q^{43} -0.0787228 q^{44} -1.82854 q^{45} -8.89477 q^{46} -8.50333 q^{47} +0.402652 q^{48} -5.93683 q^{49} +5.94862 q^{50} -0.898882 q^{51} -1.16766 q^{52} -7.76696 q^{53} -0.971605 q^{54} +0.139671 q^{55} +3.11074 q^{56} -0.429304 q^{57} -0.732472 q^{58} +11.2505 q^{59} +0.0267133 q^{60} -3.65450 q^{61} -6.35054 q^{62} -3.07688 q^{63} +8.86317 q^{64} +2.07169 q^{65} +0.0370088 q^{66} -12.0694 q^{67} -2.45951 q^{68} -0.872826 q^{69} -0.812732 q^{70} -9.48630 q^{71} -9.00266 q^{72} -7.10488 q^{73} +6.91825 q^{74} +0.583726 q^{75} -1.17466 q^{76} +0.235024 q^{77} +0.548937 q^{78} +0.366201 q^{79} -1.95471 q^{80} +8.85686 q^{81} -13.8356 q^{82} +17.8030 q^{83} +0.0449504 q^{84} +4.36370 q^{85} +1.17087 q^{86} -0.0718760 q^{87} +0.687660 q^{88} -7.54236 q^{89} +2.35209 q^{90} +3.48603 q^{91} -2.38822 q^{92} -0.623166 q^{93} +10.9380 q^{94} +2.08410 q^{95} +0.243674 q^{96} -7.85505 q^{97} +7.63668 q^{98} -0.680174 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9} - 7 q^{10} + 22 q^{11} - 7 q^{12} - 5 q^{13} + 6 q^{14} + 13 q^{15} + 15 q^{16} - 4 q^{17} - q^{18} - 6 q^{19} + 10 q^{20} - 14 q^{21} - 12 q^{22} + 32 q^{23} - 15 q^{24} + 4 q^{25} + 8 q^{26} - 5 q^{27} - 11 q^{28} + 6 q^{29} - 19 q^{30} + 8 q^{31} + q^{32} - 24 q^{33} - 19 q^{34} + 15 q^{35} - 8 q^{36} - 8 q^{37} - 10 q^{38} + 31 q^{39} - 52 q^{40} - q^{41} - 49 q^{42} - 2 q^{43} + 42 q^{44} - 15 q^{45} - 25 q^{46} + 34 q^{47} - 49 q^{48} - 9 q^{49} - 27 q^{50} - 3 q^{51} - 41 q^{52} + 5 q^{53} - 40 q^{54} - 3 q^{55} + q^{56} - 22 q^{57} - 33 q^{58} + 26 q^{59} - 57 q^{60} - 26 q^{61} - 17 q^{62} - 4 q^{63} + 13 q^{64} - 25 q^{65} - 2 q^{66} + 6 q^{67} - 35 q^{68} - 2 q^{69} - 4 q^{70} + 94 q^{71} + 17 q^{72} - 22 q^{73} + 26 q^{74} - 20 q^{76} - 7 q^{77} + 54 q^{78} + 9 q^{79} + 19 q^{80} + 4 q^{81} + 15 q^{82} - 8 q^{83} + 2 q^{84} + 4 q^{85} + 9 q^{86} + 4 q^{87} + 6 q^{88} - 3 q^{89} + 11 q^{90} - 20 q^{91} + 36 q^{92} + 12 q^{93} + 48 q^{94} + 33 q^{95} - 23 q^{96} - 29 q^{97} + 28 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9 - 7 * q^10 + 22 * q^11 - 7 * q^12 - 5 * q^13 + 6 * q^14 + 13 * q^15 + 15 * q^16 - 4 * q^17 - q^18 - 6 * q^19 + 10 * q^20 - 14 * q^21 - 12 * q^22 + 32 * q^23 - 15 * q^24 + 4 * q^25 + 8 * q^26 - 5 * q^27 - 11 * q^28 + 6 * q^29 - 19 * q^30 + 8 * q^31 + q^32 - 24 * q^33 - 19 * q^34 + 15 * q^35 - 8 * q^36 - 8 * q^37 - 10 * q^38 + 31 * q^39 - 52 * q^40 - q^41 - 49 * q^42 - 2 * q^43 + 42 * q^44 - 15 * q^45 - 25 * q^46 + 34 * q^47 - 49 * q^48 - 9 * q^49 - 27 * q^50 - 3 * q^51 - 41 * q^52 + 5 * q^53 - 40 * q^54 - 3 * q^55 + q^56 - 22 * q^57 - 33 * q^58 + 26 * q^59 - 57 * q^60 - 26 * q^61 - 17 * q^62 - 4 * q^63 + 13 * q^64 - 25 * q^65 - 2 * q^66 + 6 * q^67 - 35 * q^68 - 2 * q^69 - 4 * q^70 + 94 * q^71 + 17 * q^72 - 22 * q^73 + 26 * q^74 - 20 * q^76 - 7 * q^77 + 54 * q^78 + 9 * q^79 + 19 * q^80 + 4 * q^81 + 15 * q^82 - 8 * q^83 + 2 * q^84 + 4 * q^85 + 9 * q^86 + 4 * q^87 + 6 * q^88 - 3 * q^89 + 11 * q^90 - 20 * q^91 + 36 * q^92 + 12 * q^93 + 48 * q^94 + 33 * q^95 - 23 * q^96 - 29 * q^97 + 28 * q^98 + 36 * 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 $

$2$	−1.28632	−0.909568	−0.454784	−	0.890602i	$-0.650283\pi$
$2$	−1.28632	−0.909568	−0.454784	+	0.890602i	$0.650283\pi$
$3$	−0.126224	−0.0728757	−0.0364378	−	0.999336i	$-0.511601\pi$
$3$	−0.126224	−0.0728757	−0.0364378	+	0.999336i	$0.511601\pi$
$4$	−0.345373	−0.172687
$5$	0.612768	0.274038	0.137019	−	0.990568i	$-0.456248\pi$
$5$	0.612768	0.274038	0.137019	+	0.990568i	$0.456248\pi$
$6$	0.162365	0.0662853
$7$	1.03110	0.389720	0.194860	−	0.980831i	$-0.437575\pi$
$7$	1.03110	0.389720	0.194860	+	0.980831i	$0.437575\pi$
$8$	3.01691	1.06664
$9$	−2.98407	−0.994689
$10$	−0.788217	−0.249256
$11$	0.227935	0.0687251	0.0343625	−	0.999409i	$-0.489060\pi$
$11$	0.227935	0.0687251	0.0343625	+	0.999409i	$0.489060\pi$
$12$	0.0435945	0.0125847
$13$	3.38088	0.937686	0.468843	−	0.883281i	$-0.344671\pi$
$13$	3.38088	0.937686	0.468843	+	0.883281i	$0.344671\pi$
$14$	−1.32633	−0.354477
$15$	−0.0773462	−0.0199707
$16$	−3.18997	−0.797493
$17$	7.12130	1.72717	0.863585	−	0.504203i	$-0.168214\pi$
$17$	7.12130	1.72717	0.863585	+	0.504203i	$0.168214\pi$
$18$	3.83847	0.904737
$19$	3.40112	0.780270	0.390135	−	0.920758i	$-0.372428\pi$
$19$	3.40112	0.780270	0.390135	+	0.920758i	$0.372428\pi$
$20$	−0.211634	−0.0473227
$21$	−0.130150	−0.0284011
$22$	−0.293198	−0.0625101
$23$	6.91488	1.44185	0.720926	−	0.693012i	$-0.243717\pi$
$23$	6.91488	1.44185	0.720926	+	0.693012i	$0.243717\pi$
$24$	−0.380807	−0.0777319
$25$	−4.62452	−0.924903
$26$	−4.34890	−0.852889
$27$	0.755335	0.145364
$28$	−0.356115	−0.0672995
$29$	0.569431	0.105741	0.0528703	−	0.998601i	$-0.483163\pi$
$29$	0.569431	0.105741	0.0528703	+	0.998601i	$0.483163\pi$
$30$	0.0994922	0.0181647
$31$	4.93697	0.886706	0.443353	−	0.896347i	$-0.353789\pi$
$31$	4.93697	0.886706	0.443353	+	0.896347i	$0.353789\pi$
$32$	−1.93048	−0.341264
$33$	−0.0287710	−0.00500838
$34$	−9.16030	−1.57098
$35$	0.631826	0.106798
$36$	1.03062	0.171770
$37$	−5.37832	−0.884190	−0.442095	−	0.896968i	$-0.645765\pi$
$37$	−5.37832	−0.884190	−0.442095	+	0.896968i	$0.645765\pi$
$38$	−4.37494	−0.709709
$39$	−0.426749	−0.0683345
$40$	1.84866	0.292299
$41$	10.7559	1.67979	0.839897	−	0.542747i	$-0.182616\pi$
$41$	10.7559	1.67979	0.839897	+	0.542747i	$0.182616\pi$
$42$	0.167415	0.0258327
$43$	−0.910247	−0.138811	−0.0694057	−	0.997589i	$-0.522110\pi$
$43$	−0.910247	−0.138811	−0.0694057	+	0.997589i	$0.522110\pi$
$44$	−0.0787228	−0.0118679
$45$	−1.82854	−0.272583
$46$	−8.89477	−1.31146
$47$	−8.50333	−1.24034	−0.620169	−	0.784468i	$-0.712936\pi$
$47$	−8.50333	−1.24034	−0.620169	+	0.784468i	$0.712936\pi$
$48$	0.402652	0.0581178
$49$	−5.93683	−0.848118
$50$	5.94862	0.841262
$51$	−0.898882	−0.125869
$52$	−1.16766	−0.161926
$53$	−7.76696	−1.06687	−0.533437	−	0.845840i	$-0.679100\pi$
$53$	−7.76696	−1.06687	−0.533437	+	0.845840i	$0.679100\pi$
$54$	−0.971605	−0.132219
$55$	0.139671	0.0188333
$56$	3.11074	0.415690
$57$	−0.429304	−0.0568627
$58$	−0.732472	−0.0961783
$59$	11.2505	1.46468	0.732342	−	0.680937i	$-0.238427\pi$
$59$	11.2505	1.46468	0.732342	+	0.680937i	$0.238427\pi$
$60$	0.0267133	0.00344867
$61$	−3.65450	−0.467910	−0.233955	−	0.972247i	$-0.575167\pi$
$61$	−3.65450	−0.467910	−0.233955	+	0.972247i	$0.575167\pi$
$62$	−6.35054	−0.806519
$63$	−3.07688	−0.387650
$64$	8.86317	1.10790
$65$	2.07169	0.256962
$66$	0.0370088	0.00455546
$67$	−12.0694	−1.47451	−0.737257	−	0.675613i	$-0.763879\pi$
$67$	−12.0694	−1.47451	−0.737257	+	0.675613i	$0.763879\pi$
$68$	−2.45951	−0.298259
$69$	−0.872826	−0.105076
$70$	−0.812732	−0.0971401
$71$	−9.48630	−1.12582	−0.562908	−	0.826519i	$-0.690318\pi$
$71$	−9.48630	−1.12582	−0.562908	+	0.826519i	$0.690318\pi$
$72$	−9.00266	−1.06097
$73$	−7.10488	−0.831563	−0.415782	−	0.909464i	$-0.636492\pi$
$73$	−7.10488	−0.831563	−0.415782	+	0.909464i	$0.636492\pi$
$74$	6.91825	0.804231
$75$	0.583726	0.0674029
$76$	−1.17466	−0.134742
$77$	0.235024	0.0267835
$78$	0.548937	0.0621548
$79$	0.366201	0.0412008	0.0206004	−	0.999788i	$-0.493442\pi$
$79$	0.366201	0.0412008	0.0206004	+	0.999788i	$0.493442\pi$
$80$	−1.95471	−0.218543
$81$	8.85686	0.984096
$82$	−13.8356	−1.52789
$83$	17.8030	1.95413	0.977067	−	0.212932i	$-0.0683014\pi$
$83$	17.8030	1.95413	0.977067	+	0.212932i	$0.0683014\pi$
$84$	0.0449504	0.00490449
$85$	4.36370	0.473310
$86$	1.17087	0.126258
$87$	−0.0718760	−0.00770592
$88$	0.687660	0.0733048
$89$	−7.54236	−0.799489	−0.399744	−	0.916627i	$-0.630901\pi$
$89$	−7.54236	−0.799489	−0.399744	+	0.916627i	$0.630901\pi$
$90$	2.35209	0.247932
$91$	3.48603	0.365435
$92$	−2.38822	−0.248989
$93$	−0.623166	−0.0646193
$94$	10.9380	1.12817
$95$	2.08410	0.213824
$96$	0.243674	0.0248699
$97$	−7.85505	−0.797560	−0.398780	−	0.917047i	$-0.630566\pi$
$97$	−7.85505	−0.797560	−0.398780	+	0.917047i	$0.630566\pi$
$98$	7.63668	0.771421
$99$	−0.680174	−0.0683601
$100$	1.59718	0.159718
$101$	17.4801	1.73933	0.869666	−	0.493640i	$-0.164334\pi$
$101$	17.4801	1.73933	0.869666	+	0.493640i	$0.164334\pi$
$102$	1.15625	0.114486
$103$	6.10361	0.601407	0.300703	−	0.953718i	$-0.402779\pi$
$103$	6.10361	0.601407	0.300703	+	0.953718i	$0.402779\pi$
$104$	10.1998	1.00017
$105$	−0.0797518	−0.00778298
$106$	9.99081	0.970394
$107$	7.86203	0.760051	0.380026	−	0.924976i	$-0.375915\pi$
$107$	7.86203	0.760051	0.380026	+	0.924976i	$0.375915\pi$
$108$	−0.260873	−0.0251025
$109$	−4.17241	−0.399644	−0.199822	−	0.979832i	$-0.564036\pi$
$109$	−4.17241	−0.399644	−0.199822	+	0.979832i	$0.564036\pi$
$110$	−0.179662	−0.0171301
$111$	0.678875	0.0644359
$112$	−3.28919	−0.310799
$113$	3.62203	0.340732	0.170366	−	0.985381i	$-0.445505\pi$
$113$	3.62203	0.340732	0.170366	+	0.985381i	$0.445505\pi$
$114$	0.552224	0.0517205
$115$	4.23721	0.395122
$116$	−0.196666	−0.0182600
$117$	−10.0888	−0.932706
$118$	−14.4717	−1.33223
$119$	7.34279	0.673113
$120$	−0.233346	−0.0213015
$121$	−10.9480	−0.995277
$122$	4.70086	0.425596
$123$	−1.35766	−0.122416
$124$	−1.70510	−0.153122
$125$	−5.89759	−0.527497
$126$	3.95786	0.352594
$127$	13.5446	1.20189	0.600943	−	0.799292i	$-0.294792\pi$
$127$	13.5446	1.20189	0.600943	+	0.799292i	$0.294792\pi$
$128$	−7.53993	−0.666442
$129$	0.114895	0.0101160
$130$	−2.66486	−0.233724
$131$	1.03003	0.0899942	0.0449971	−	0.998987i	$-0.485672\pi$
$131$	1.03003	0.0899942	0.0449971	+	0.998987i	$0.485672\pi$
$132$	0.00993673	0.000864881 0
$133$	3.50690	0.304087
$134$	15.5252	1.34117
$135$	0.462845	0.0398353
$136$	21.4843	1.84226
$137$	−11.5780	−0.989180	−0.494590	−	0.869127i	$-0.664682\pi$
$137$	−11.5780	−0.989180	−0.494590	+	0.869127i	$0.664682\pi$
$138$	1.12274	0.0955736
$139$	0.110960	0.00941151	0.00470575	−	0.999989i	$-0.498502\pi$
$139$	0.110960	0.00941151	0.00470575	+	0.999989i	$0.498502\pi$
$140$	−0.218216	−0.0184426
$141$	1.07333	0.0903904
$142$	12.2024	1.02401
$143$	0.770621	0.0644425
$144$	9.51909	0.793257
$145$	0.348929	0.0289769
$146$	9.13917	0.756363
$147$	0.749372	0.0618072
$148$	1.85753	0.152688
$149$	−19.5413	−1.60089	−0.800443	−	0.599409i	$-0.795402\pi$
$149$	−19.5413	−1.60089	−0.800443	+	0.599409i	$0.795402\pi$
$150$	−0.750861	−0.0613075
$151$	17.7745	1.44647	0.723233	−	0.690604i	$-0.242655\pi$
$151$	17.7745	1.44647	0.723233	+	0.690604i	$0.242655\pi$
$152$	10.2609	0.832266
$153$	−21.2505	−1.71800
$154$	−0.302317	−0.0243614
$155$	3.02522	0.242991
$156$	0.147388	0.0118005
$157$	6.98884	0.557770	0.278885	−	0.960325i	$-0.410035\pi$
$157$	6.98884	0.557770	0.278885	+	0.960325i	$0.410035\pi$
$158$	−0.471053	−0.0374749
$159$	0.980379	0.0777491
$160$	−1.18294	−0.0935194
$161$	7.12995	0.561918
$162$	−11.3928	−0.895102
$163$	−8.87693	−0.695295	−0.347647	−	0.937625i	$-0.613019\pi$
$163$	−8.87693	−0.695295	−0.347647	+	0.937625i	$0.613019\pi$
$164$	−3.71481	−0.290078
$165$	−0.0176299	−0.00137249
$166$	−22.9004	−1.77742
$167$	4.85435	0.375641	0.187820	−	0.982203i	$-0.439858\pi$
$167$	4.85435	0.375641	0.187820	+	0.982203i	$0.439858\pi$
$168$	−0.392651	−0.0302937
$169$	−1.56968	−0.120745
$170$	−5.61313	−0.430508
$171$	−10.1492	−0.776126
$172$	0.314375	0.0239709
$173$	−13.5277	−1.02849	−0.514247	−	0.857642i	$-0.671928\pi$
$173$	−13.5277	−1.02849	−0.514247	+	0.857642i	$0.671928\pi$
$174$	0.0924558	0.00700905
$175$	−4.76835	−0.360453
$176$	−0.727107	−0.0548077
$177$	−1.42008	−0.106740
$178$	9.70191	0.727189
$179$	−10.4800	−0.783310	−0.391655	−	0.920112i	$-0.628097\pi$
$179$	−10.4800	−0.783310	−0.391655	+	0.920112i	$0.628097\pi$
$180$	0.631529	0.0470714
$181$	−8.82686	−0.656095	−0.328048	−	0.944661i	$-0.606391\pi$
$181$	−8.82686	−0.656095	−0.328048	+	0.944661i	$0.606391\pi$
$182$	−4.48416	−0.332388
$183$	0.461286	0.0340993
$184$	20.8616	1.53793
$185$	−3.29566	−0.242302
$186$	0.801593	0.0587756
$187$	1.62320	0.118700
$188$	2.93682	0.214190
$189$	0.778827	0.0566514
$190$	−2.68082	−0.194487
$191$	−3.25920	−0.235827	−0.117914	−	0.993024i	$-0.537621\pi$
$191$	−3.25920	−0.235827	−0.117914	+	0.993024i	$0.537621\pi$
$192$	−1.11875	−0.0807386
$193$	16.9658	1.22123	0.610613	−	0.791929i	$-0.290923\pi$
$193$	16.9658	1.22123	0.610613	+	0.791929i	$0.290923\pi$
$194$	10.1041	0.725434
$195$	−0.261498	−0.0187262
$196$	2.05042	0.146459
$197$	−18.5572	−1.32214	−0.661072	−	0.750322i	$-0.729898\pi$
$197$	−18.5572	−1.32214	−0.661072	+	0.750322i	$0.729898\pi$
$198$	0.874924	0.0621781
$199$	−19.6484	−1.39284	−0.696420	−	0.717634i	$-0.745225\pi$
$199$	−19.6484	−1.39284	−0.696420	+	0.717634i	$0.745225\pi$
$200$	−13.9517	−0.986537
$201$	1.52345	0.107456
$202$	−22.4850	−1.58204
$203$	0.587141	0.0412092
$204$	0.310450	0.0217358
$205$	6.59088	0.460327
$206$	−7.85121	−0.547020
$207$	−20.6345	−1.43419
$208$	−10.7849	−0.747798
$209$	0.775235	0.0536241
$210$	0.102587	0.00707915
$211$	−8.18657	−0.563587	−0.281794	−	0.959475i	$-0.590929\pi$
$211$	−8.18657	−0.563587	−0.281794	+	0.959475i	$0.590929\pi$
$212$	2.68250	0.184235
$213$	1.19740	0.0820446
$214$	−10.1131	−0.691318
$215$	−0.557770	−0.0380396
$216$	2.27878	0.155051
$217$	5.09052	0.345567
$218$	5.36706	0.363503
$219$	0.896809	0.0606007
$220$	−0.0482388	−0.00325226
$221$	24.0762	1.61954
$222$	−0.873252	−0.0586088
$223$	15.5070	1.03843	0.519213	−	0.854645i	$-0.326225\pi$
$223$	15.5070	1.03843	0.519213	+	0.854645i	$0.326225\pi$
$224$	−1.99053	−0.132998
$225$	13.7999	0.919991
$226$	−4.65910	−0.309919
$227$	−27.1128	−1.79954	−0.899769	−	0.436366i	$-0.856265\pi$
$227$	−27.1128	−1.79954	−0.899769	+	0.436366i	$0.856265\pi$
$228$	0.148270	0.00981944
$229$	8.10947	0.535889	0.267944	−	0.963434i	$-0.413656\pi$
$229$	8.10947	0.535889	0.267944	+	0.963434i	$0.413656\pi$
$230$	−5.45042	−0.359390
$231$	−0.0296658	−0.00195187
$232$	1.71792	0.112787
$233$	−4.34697	−0.284780	−0.142390	−	0.989811i	$-0.545479\pi$
$233$	−4.34697	−0.284780	−0.142390	+	0.989811i	$0.545479\pi$
$234$	12.9774	0.848359
$235$	−5.21056	−0.339900
$236$	−3.88561	−0.252932
$237$	−0.0462235	−0.00300254
$238$	−9.44520	−0.612241
$239$	18.3619	1.18773	0.593867	−	0.804563i	$-0.297601\pi$
$239$	18.3619	1.18773	0.593867	+	0.804563i	$0.297601\pi$
$240$	0.246732	0.0159265
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	14.0827	0.905272
$243$	−3.38396	−0.217081
$244$	1.26217	0.0808019
$245$	−3.63790	−0.232417
$246$	1.74639	0.111346
$247$	11.4988	0.731649
$248$	14.8944	0.945795
$249$	−2.24717	−0.142409
$250$	7.58621	0.479794
$251$	12.3629	0.780337	0.390169	−	0.920743i	$-0.372417\pi$
$251$	12.3629	0.780337	0.390169	+	0.920743i	$0.372417\pi$
$252$	1.06267	0.0669420
$253$	1.57614	0.0990914
$254$	−17.4227	−1.09320
$255$	−0.550806	−0.0344928
$256$	−8.02755	−0.501722
$257$	−12.1589	−0.758452	−0.379226	−	0.925304i	$-0.623810\pi$
$257$	−12.1589	−0.758452	−0.379226	+	0.925304i	$0.623810\pi$
$258$	−0.147793	−0.00920116
$259$	−5.54560	−0.344587
$260$	−0.715507	−0.0443739
$261$	−1.69922	−0.105179
$262$	−1.32495	−0.0818558
$263$	−5.76048	−0.355207	−0.177603	−	0.984102i	$-0.556834\pi$
$263$	−5.76048	−0.355207	−0.177603	+	0.984102i	$0.556834\pi$
$264$	−0.0867994	−0.00534213
$265$	−4.75934	−0.292364
$266$	−4.51101	−0.276588
$267$	0.952030	0.0582633
$268$	4.16846	0.254629
$269$	14.4585	0.881551	0.440776	−	0.897617i	$-0.354703\pi$
$269$	14.4585	0.881551	0.440776	+	0.897617i	$0.354703\pi$
$270$	−0.595368	−0.0362329
$271$	6.81638	0.414065	0.207033	−	0.978334i	$-0.433619\pi$
$271$	6.81638	0.414065	0.207033	+	0.978334i	$0.433619\pi$
$272$	−22.7167	−1.37741
$273$	−0.440022	−0.0266313
$274$	14.8931	0.899726
$275$	−1.05409	−0.0635640
$276$	0.301451	0.0181452
$277$	−25.1323	−1.51005	−0.755027	−	0.655693i	$-0.772376\pi$
$277$	−25.1323	−1.51005	−0.755027	+	0.655693i	$0.772376\pi$
$278$	−0.142730	−0.00856040
$279$	−14.7323	−0.881997
$280$	1.90616	0.113915
$281$	−6.03331	−0.359917	−0.179959	−	0.983674i	$-0.557596\pi$
$281$	−6.03331	−0.359917	−0.179959	+	0.983674i	$0.557596\pi$
$282$	−1.38064	−0.0822162
$283$	−3.47423	−0.206521	−0.103261	−	0.994654i	$-0.532928\pi$
$283$	−3.47423	−0.206521	−0.103261	+	0.994654i	$0.532928\pi$
$284$	3.27631	0.194414
$285$	−0.263064	−0.0155825
$286$	−0.991267	−0.0586148
$287$	11.0905	0.654649
$288$	5.76069	0.339452
$289$	33.7130	1.98312
$290$	−0.448835	−0.0263565
$291$	0.991499	0.0581227
$292$	2.45384	0.143600
$293$	−19.7300	−1.15264	−0.576321	−	0.817224i	$-0.695512\pi$
$293$	−19.7300	−1.15264	−0.576321	+	0.817224i	$0.695512\pi$
$294$	−0.963935	−0.0562178
$295$	6.89391	0.401379
$296$	−16.2259	−0.943111
$297$	0.172167	0.00999017
$298$	25.1364	1.45611
$299$	23.3783	1.35200
$300$	−0.201604	−0.0116396
$301$	−0.938558	−0.0540976
$302$	−22.8637	−1.31566
$303$	−2.20641	−0.126755
$304$	−10.8495	−0.622260
$305$	−2.23936	−0.128225
$306$	27.3349	1.56263
$307$	−0.0265060	−0.00151278	−0.000756388	−	1.00000i	$-0.500241\pi$
$307$	−0.0265060	−0.00151278	−0.000756388		1.00000i	$0.500241\pi$
$308$	−0.0811712	−0.00462516
$309$	−0.770424	−0.0438279
$310$	−3.89140	−0.221017
$311$	21.2822	1.20680	0.603400	−	0.797439i	$-0.293812\pi$
$311$	21.2822	1.20680	0.603400	+	0.797439i	$0.293812\pi$
$312$	−1.28746	−0.0728882
$313$	10.6916	0.604323	0.302161	−	0.953257i	$-0.402292\pi$
$313$	10.6916	0.604323	0.302161	+	0.953257i	$0.402292\pi$
$314$	−8.98990	−0.507329
$315$	−1.88541	−0.106231
$316$	−0.126476	−0.00711484
$317$	−2.07826	−0.116727	−0.0583633	−	0.998295i	$-0.518588\pi$
$317$	−2.07826	−0.116727	−0.0583633	+	0.998295i	$0.518588\pi$
$318$	−1.26108	−0.0707181
$319$	0.129793	0.00726703
$320$	5.43106	0.303605
$321$	−0.992380	−0.0553892
$322$	−9.17141	−0.511103
$323$	24.2204	1.34766
$324$	−3.05892	−0.169940
$325$	−15.6349	−0.867269
$326$	11.4186	0.632418
$327$	0.526659	0.0291243
$328$	32.4496	1.79173
$329$	−8.76780	−0.483384
$330$	0.0226778	0.00124837
$331$	−28.1272	−1.54601	−0.773006	−	0.634399i	$-0.781248\pi$
$331$	−28.1272	−1.54601	−0.773006	+	0.634399i	$0.781248\pi$
$332$	−6.14869	−0.337453
$333$	16.0493	0.879494
$334$	−6.24426	−0.341671
$335$	−7.39575	−0.404073
$336$	0.415175	0.0226497
$337$	23.5835	1.28468	0.642338	−	0.766422i	$-0.277965\pi$
$337$	23.5835	1.28468	0.642338	+	0.766422i	$0.277965\pi$
$338$	2.01911	0.109825
$339$	−0.457188	−0.0248311
$340$	−1.50711	−0.0817344
$341$	1.12531	0.0609389
$342$	13.0551	0.705940
$343$	−13.3392	−0.720249
$344$	−2.74613	−0.148061
$345$	−0.534839	−0.0287948
$346$	17.4010	0.935484
$347$	−21.8697	−1.17403	−0.587013	−	0.809578i	$-0.699696\pi$
$347$	−21.8697	−1.17403	−0.587013	+	0.809578i	$0.699696\pi$
$348$	0.0248241	0.00133071
$349$	18.8525	1.00915	0.504575	−	0.863368i	$-0.331649\pi$
$349$	18.8525	1.00915	0.504575	+	0.863368i	$0.331649\pi$
$350$	6.13364	0.327857
$351$	2.55369	0.136306
$352$	−0.440025	−0.0234534
$353$	−11.3768	−0.605526	−0.302763	−	0.953066i	$-0.597909\pi$
$353$	−11.3768	−0.605526	−0.302763	+	0.953066i	$0.597909\pi$
$354$	1.82668	0.0970871
$355$	−5.81289	−0.308516
$356$	2.60493	0.138061
$357$	−0.926839	−0.0490535
$358$	13.4806	0.712473
$359$	−0.146567	−0.00773548	−0.00386774	−	0.999993i	$-0.501231\pi$
$359$	−0.146567	−0.00773548	−0.00386774	+	0.999993i	$0.501231\pi$
$360$	−5.51653	−0.290747
$361$	−7.43238	−0.391178
$362$	11.3542	0.596763
$363$	1.38191	0.0725315
$364$	−1.20398	−0.0631058
$365$	−4.35364	−0.227880
$366$	−0.593363	−0.0310156
$367$	32.6647	1.70508	0.852541	−	0.522660i	$-0.175060\pi$
$367$	32.6647	1.70508	0.852541	+	0.522660i	$0.175060\pi$
$368$	−22.0583	−1.14987
$369$	−32.0964	−1.67087
$370$	4.23928	0.220390
$371$	−8.00852	−0.415782
$372$	0.215225	0.0111589
$373$	−17.7530	−0.919218	−0.459609	−	0.888121i	$-0.652010\pi$
$373$	−17.7530	−0.919218	−0.459609	+	0.888121i	$0.652010\pi$
$374$	−2.08795	−0.107966
$375$	0.744420	0.0384417
$376$	−25.6538	−1.32299
$377$	1.92517	0.0991515
$378$	−1.00182	−0.0515282
$379$	−4.82435	−0.247810	−0.123905	−	0.992294i	$-0.539542\pi$
$379$	−4.82435	−0.247810	−0.123905	+	0.992294i	$0.539542\pi$
$380$	−0.719791	−0.0369245
$381$	−1.70965	−0.0875882
$382$	4.19238	0.214501
$383$	14.7127	0.751783	0.375892	−	0.926664i	$-0.377336\pi$
$383$	14.7127	0.751783	0.375892	+	0.926664i	$0.377336\pi$
$384$	0.951722	0.0485674
$385$	0.144015	0.00733970
$386$	−21.8235	−1.11079
$387$	2.71624	0.138074
$388$	2.71293	0.137728
$389$	4.90322	0.248603	0.124301	−	0.992244i	$-0.460331\pi$
$389$	4.90322	0.248603	0.124301	+	0.992244i	$0.460331\pi$
$390$	0.336371	0.0170328
$391$	49.2430	2.49032
$392$	−17.9109	−0.904635
$393$	−0.130015	−0.00655839
$394$	23.8705	1.20258
$395$	0.224396	0.0112906
$396$	0.234914	0.0118049
$397$	−14.8959	−0.747606	−0.373803	−	0.927508i	$-0.621946\pi$
$397$	−14.8959	−0.747606	−0.373803	+	0.927508i	$0.621946\pi$
$398$	25.2742	1.26688
$399$	−0.442656	−0.0221605
$400$	14.7521	0.737603
$401$	6.72128	0.335645	0.167822	−	0.985817i	$-0.446327\pi$
$401$	6.72128	0.335645	0.167822	+	0.985817i	$0.446327\pi$
$402$	−1.95965	−0.0977386
$403$	16.6913	0.831452
$404$	−6.03715	−0.300360
$405$	5.42720	0.269680
$406$	−0.755253	−0.0374826
$407$	−1.22591	−0.0607660
$408$	−2.71184	−0.134256
$409$	−2.59935	−0.128529	−0.0642647	−	0.997933i	$-0.520470\pi$
$409$	−2.59935	−0.128529	−0.0642647	+	0.997933i	$0.520470\pi$
$410$	−8.47800	−0.418699
$411$	1.46143	0.0720871
$412$	−2.10803	−0.103855
$413$	11.6004	0.570817
$414$	26.5426	1.30450
$415$	10.9091	0.535507
$416$	−6.52672	−0.319999
$417$	−0.0140059	−0.000685870 0
$418$	−0.997203	−0.0487748
$419$	−13.1622	−0.643018	−0.321509	−	0.946907i	$-0.604190\pi$
$419$	−13.1622	−0.643018	−0.321509	+	0.946907i	$0.604190\pi$
$420$	0.0275442	0.00134402
$421$	−6.53715	−0.318601	−0.159301	−	0.987230i	$-0.550924\pi$
$421$	−6.53715	−0.318601	−0.159301	+	0.987230i	$0.550924\pi$
$422$	10.5306	0.512620
$423$	25.3745	1.23375
$424$	−23.4322	−1.13797
$425$	−32.9326	−1.59746
$426$	−1.54025	−0.0746251
$427$	−3.76816	−0.182354
$428$	−2.71534	−0.131251
$429$	−0.0972711	−0.00469629
$430$	0.717472	0.0345996
$431$	10.8319	0.521755	0.260878	−	0.965372i	$-0.415988\pi$
$431$	10.8319	0.521755	0.260878	+	0.965372i	$0.415988\pi$
$432$	−2.40950	−0.115927
$433$	−25.6037	−1.23044	−0.615218	−	0.788357i	$-0.710932\pi$
$433$	−25.6037	−1.23044	−0.615218	+	0.788357i	$0.710932\pi$
$434$	−6.54805	−0.314317
$435$	−0.0440433	−0.00211171
$436$	1.44104	0.0690132
$437$	23.5183	1.12503
$438$	−1.15359	−0.0551205
$439$	14.6842	0.700839	0.350419	−	0.936593i	$-0.386039\pi$
$439$	14.6842	0.700839	0.350419	+	0.936593i	$0.386039\pi$
$440$	0.421375	0.0200883
$441$	17.7159	0.843614
$442$	−30.9698	−1.47308
$443$	−15.2687	−0.725436	−0.362718	−	0.931899i	$-0.618151\pi$
$443$	−15.2687	−0.725436	−0.362718	+	0.931899i	$0.618151\pi$
$444$	−0.234465	−0.0111272
$445$	−4.62171	−0.219090
$446$	−19.9470	−0.944518
$447$	2.46659	0.116666
$448$	9.13883	0.431769
$449$	31.2160	1.47317	0.736587	−	0.676343i	$-0.236436\pi$
$449$	31.2160	1.47317	0.736587	+	0.676343i	$0.236436\pi$
$450$	−17.7511	−0.836794
$451$	2.45165	0.115444
$452$	−1.25095	−0.0588399
$453$	−2.24357	−0.105412
$454$	34.8758	1.63680
$455$	2.13612	0.100143
$456$	−1.29517	−0.0606519
$457$	9.43632	0.441412	0.220706	−	0.975340i	$-0.429164\pi$
$457$	9.43632	0.441412	0.220706	+	0.975340i	$0.429164\pi$
$458$	−10.4314	−0.487427
$459$	5.37897	0.251069
$460$	−1.46342	−0.0682324
$461$	8.65525	0.403115	0.201557	−	0.979477i	$-0.435400\pi$
$461$	8.65525	0.403115	0.201557	+	0.979477i	$0.435400\pi$
$462$	0.0381598	0.00177536
$463$	−12.5415	−0.582853	−0.291426	−	0.956593i	$-0.594130\pi$
$463$	−12.5415	−0.582853	−0.291426	+	0.956593i	$0.594130\pi$
$464$	−1.81647	−0.0843274
$465$	−0.381856	−0.0177081
$466$	5.59161	0.259026
$467$	−5.28477	−0.244550	−0.122275	−	0.992496i	$-0.539019\pi$
$467$	−5.28477	−0.244550	−0.122275	+	0.992496i	$0.539019\pi$
$468$	3.48439	0.161066
$469$	−12.4448	−0.574647
$470$	6.70247	0.309162
$471$	−0.882161	−0.0406479
$472$	33.9416	1.56229
$473$	−0.207477	−0.00953982
$474$	0.0594583	0.00273101
$475$	−15.7285	−0.721675
$476$	−2.53601	−0.116238
$477$	23.1771	1.06121
$478$	−23.6194	−1.08032
$479$	−29.0596	−1.32777	−0.663884	−	0.747835i	$-0.731093\pi$
$479$	−29.0596	−1.32777	−0.663884	+	0.747835i	$0.731093\pi$
$480$	0.149315	0.00681529
$481$	−18.1834	−0.829093
$482$	−1.28632	−0.0585904
$483$	−0.899973	−0.0409502
$484$	3.78116	0.171871
$485$	−4.81332	−0.218562
$486$	4.35286	0.197450
$487$	−36.2854	−1.64425	−0.822124	−	0.569309i	$-0.807211\pi$
$487$	−36.2854	−1.64425	−0.822124	+	0.569309i	$0.807211\pi$
$488$	−11.0253	−0.499091
$489$	1.12048	0.0506701
$490$	4.67951	0.211399
$491$	−3.99282	−0.180193	−0.0900967	−	0.995933i	$-0.528718\pi$
$491$	−3.99282	−0.180193	−0.0900967	+	0.995933i	$0.528718\pi$
$492$	0.468899	0.0211396
$493$	4.05509	0.182632
$494$	−14.7911	−0.665484
$495$	−0.416789	−0.0187333
$496$	−15.7488	−0.707142
$497$	−9.78134	−0.438753
$498$	2.89059	0.129530
$499$	9.25262	0.414204	0.207102	−	0.978319i	$-0.433597\pi$
$499$	9.25262	0.414204	0.207102	+	0.978319i	$0.433597\pi$
$500$	2.03687	0.0910916
$501$	−0.612737	−0.0273751
$502$	−15.9026	−0.709769
$503$	30.0225	1.33864	0.669319	−	0.742975i	$-0.266586\pi$
$503$	30.0225	1.33864	0.669319	+	0.742975i	$0.266586\pi$
$504$	−9.28266	−0.413482
$505$	10.7112	0.476643
$506$	−2.02743	−0.0901303
$507$	0.198132	0.00879934
$508$	−4.67793	−0.207550
$509$	8.01192	0.355122	0.177561	−	0.984110i	$-0.443179\pi$
$509$	8.01192	0.355122	0.177561	+	0.984110i	$0.443179\pi$
$510$	0.708514	0.0313735
$511$	−7.32586	−0.324077
$512$	25.4059	1.12279
$513$	2.56898	0.113423
$514$	15.6403	0.689864
$515$	3.74009	0.164808
$516$	−0.0396818	−0.00174689
$517$	−1.93821	−0.0852423
$518$	7.13343	0.313425
$519$	1.70753	0.0749521
$520$	6.25010	0.274085
$521$	−10.1940	−0.446608	−0.223304	−	0.974749i	$-0.571684\pi$
$521$	−10.1940	−0.446608	−0.223304	+	0.974749i	$0.571684\pi$
$522$	2.18575	0.0956675
$523$	−41.0217	−1.79375	−0.896877	−	0.442281i	$-0.854170\pi$
$523$	−41.0217	−1.79375	−0.896877	+	0.442281i	$0.854170\pi$
$524$	−0.355745	−0.0155408
$525$	0.601882	0.0262683
$526$	7.40984	0.323084
$527$	35.1577	1.53149
$528$	0.0917786	0.00399415
$529$	24.8156	1.07894
$530$	6.12205	0.265925
$531$	−33.5721	−1.45691
$532$	−1.21119	−0.0525118
$533$	36.3644	1.57512
$534$	−1.22462	−0.0529944
$535$	4.81760	0.208283
$536$	−36.4123	−1.57277
$537$	1.32283	0.0570842
$538$	−18.5983	−0.801831
$539$	−1.35321	−0.0582870
$540$	−0.159854	−0.00687903
$541$	−25.9044	−1.11372	−0.556858	−	0.830608i	$-0.687993\pi$
$541$	−25.9044	−1.11372	−0.556858	+	0.830608i	$0.687993\pi$
$542$	−8.76806	−0.376620
$543$	1.11416	0.0478134
$544$	−13.7476	−0.589422
$545$	−2.55671	−0.109518
$546$	0.566010	0.0242230
$547$	−43.6488	−1.86629	−0.933145	−	0.359501i	$-0.882947\pi$
$547$	−43.6488	−1.86629	−0.933145	+	0.359501i	$0.882947\pi$
$548$	3.99875	0.170818
$549$	10.9053	0.465425
$550$	1.35590	0.0578158
$551$	1.93670	0.0825063
$552$	−2.63324	−0.112078
$553$	0.377591	0.0160568
$554$	32.3283	1.37350
$555$	0.415992	0.0176579
$556$	−0.0383227	−0.00162524
$557$	22.1122	0.936925	0.468463	−	0.883483i	$-0.344808\pi$
$557$	22.1122	0.936925	0.468463	+	0.883483i	$0.344808\pi$
$558$	18.9504	0.802236
$559$	−3.07743	−0.130162
$560$	−2.01551	−0.0851707
$561$	−0.204887	−0.00865033
$562$	7.76078	0.327369
$563$	19.0461	0.802697	0.401348	−	0.915925i	$-0.368542\pi$
$563$	19.0461	0.802697	0.401348	+	0.915925i	$0.368542\pi$
$564$	−0.370699	−0.0156092
$565$	2.21946	0.0933735
$566$	4.46898	0.187845
$567$	9.13233	0.383522
$568$	−28.6193	−1.20084
$569$	−24.1421	−1.01209	−0.506045	−	0.862507i	$-0.668893\pi$
$569$	−24.1421	−1.01209	−0.506045	+	0.862507i	$0.668893\pi$
$570$	0.338385	0.0141734
$571$	−37.2649	−1.55949	−0.779745	−	0.626098i	$-0.784651\pi$
$571$	−37.2649	−1.55949	−0.779745	+	0.626098i	$0.784651\pi$
$572$	−0.266152	−0.0111284
$573$	0.411390	0.0171861
$574$	−14.2659	−0.595447
$575$	−31.9780	−1.33357
$576$	−26.4483	−1.10201
$577$	−6.94471	−0.289112	−0.144556	−	0.989497i	$-0.546175\pi$
$577$	−6.94471	−0.289112	−0.144556	+	0.989497i	$0.546175\pi$
$578$	−43.3658	−1.80378
$579$	−2.14150	−0.0889977
$580$	−0.120511	−0.00500393
$581$	18.3567	0.761565
$582$	−1.27539	−0.0528665
$583$	−1.77036	−0.0733209
$584$	−21.4348	−0.886977
$585$	−6.18206	−0.255597
$586$	25.3792	1.04841
$587$	−33.6812	−1.39017	−0.695085	−	0.718927i	$-0.744633\pi$
$587$	−33.6812	−1.39017	−0.695085	+	0.718927i	$0.744633\pi$
$588$	−0.258813	−0.0106733
$589$	16.7912	0.691871
$590$	−8.86780	−0.365081
$591$	2.34237	0.0963522
$592$	17.1567	0.705135
$593$	−25.1034	−1.03087	−0.515437	−	0.856927i	$-0.672370\pi$
$593$	−25.1034	−1.03087	−0.515437	+	0.856927i	$0.672370\pi$
$594$	−0.221463	−0.00908673
$595$	4.49942	0.184458
$596$	6.74905	0.276452
$597$	2.48011	0.101504
$598$	−30.0721	−1.22974
$599$	−5.93752	−0.242601	−0.121300	−	0.992616i	$-0.538706\pi$
$599$	−5.93752	−0.242601	−0.121300	+	0.992616i	$0.538706\pi$
$600$	1.76105	0.0718945
$601$	−29.7235	−1.21245	−0.606223	−	0.795294i	$-0.707316\pi$
$601$	−29.7235	−1.21245	−0.606223	+	0.795294i	$0.707316\pi$
$602$	1.20729	0.0492054
$603$	36.0159	1.46668
$604$	−6.13883	−0.249785
$605$	−6.70861	−0.272744
$606$	2.83816	0.115292
$607$	16.5792	0.672929	0.336464	−	0.941696i	$-0.390769\pi$
$607$	16.5792	0.672929	0.336464	+	0.941696i	$0.390769\pi$
$608$	−6.56580	−0.266279
$609$	−0.0741115	−0.00300315
$610$	2.88054	0.116629
$611$	−28.7487	−1.16305
$612$	7.33934	0.296675
$613$	39.4836	1.59473	0.797364	−	0.603499i	$-0.206227\pi$
$613$	39.4836	1.59473	0.797364	+	0.603499i	$0.206227\pi$
$614$	0.0340952	0.00137597
$615$	−0.831930	−0.0335466
$616$	0.709047	0.0285683
$617$	38.4323	1.54723	0.773613	−	0.633658i	$-0.218447\pi$
$617$	38.4323	1.54723	0.773613	+	0.633658i	$0.218447\pi$
$618$	0.991014	0.0398644
$619$	14.9244	0.599861	0.299931	−	0.953961i	$-0.403036\pi$
$619$	14.9244	0.599861	0.299931	+	0.953961i	$0.403036\pi$
$620$	−1.04483	−0.0419614
$621$	5.22305	0.209594
$622$	−27.3757	−1.09767
$623$	−7.77695	−0.311577
$624$	1.36132	0.0544963
$625$	19.5087	0.780349
$626$	−13.7528	−0.549672
$627$	−0.0978535	−0.00390789
$628$	−2.41376	−0.0963195
$629$	−38.3006	−1.52715
$630$	2.42525	0.0966242
$631$	30.8867	1.22958	0.614791	−	0.788690i	$-0.289241\pi$
$631$	30.8867	1.22958	0.614791	+	0.788690i	$0.289241\pi$
$632$	1.10479	0.0439464
$633$	1.03334	0.0410718
$634$	2.67331	0.106171
$635$	8.29967	0.329362
$636$	−0.338597	−0.0134262
$637$	−20.0717	−0.795269
$638$	−0.166956	−0.00660986
$639$	28.3077	1.11984
$640$	−4.62022	−0.182630
$641$	31.6649	1.25069	0.625344	−	0.780349i	$-0.284959\pi$
$641$	31.6649	1.25069	0.625344	+	0.780349i	$0.284959\pi$
$642$	1.27652	0.0503803
$643$	−17.2630	−0.680786	−0.340393	−	0.940283i	$-0.610560\pi$
$643$	−17.2630	−0.680786	−0.340393	+	0.940283i	$0.610560\pi$
$644$	−2.46249	−0.0970359
$645$	0.0704041	0.00277216
$646$	−31.1553	−1.22579
$647$	35.2693	1.38658	0.693289	−	0.720659i	$-0.256161\pi$
$647$	35.2693	1.38658	0.693289	+	0.720659i	$0.256161\pi$
$648$	26.7203	1.04967
$649$	2.56437	0.100661
$650$	20.1115	0.788840
$651$	−0.642548	−0.0251834
$652$	3.06586	0.120068
$653$	−38.0371	−1.48851	−0.744253	−	0.667898i	$-0.767194\pi$
$653$	−38.0371	−1.48851	−0.744253	+	0.667898i	$0.767194\pi$
$654$	−0.677454	−0.0264905
$655$	0.631169	0.0246618
$656$	−34.3111	−1.33962
$657$	21.2014	0.827147
$658$	11.2782	0.439671
$659$	−7.14619	−0.278376	−0.139188	−	0.990266i	$-0.544449\pi$
$659$	−7.14619	−0.278376	−0.139188	+	0.990266i	$0.544449\pi$
$660$	0.00608891	0.000237010 0
$661$	33.6588	1.30917	0.654587	−	0.755986i	$-0.272842\pi$
$661$	33.6588	1.30917	0.654587	+	0.755986i	$0.272842\pi$
$662$	36.1807	1.40620
$663$	−3.03901	−0.118025
$664$	53.7100	2.08435
$665$	2.14892	0.0833314
$666$	−20.6445	−0.799960
$667$	3.93754	0.152462
$668$	−1.67656	−0.0648682
$669$	−1.95736	−0.0756759
$670$	9.51332	0.367531
$671$	−0.832989	−0.0321572
$672$	0.251253	0.00969229
$673$	−4.10894	−0.158388	−0.0791939	−	0.996859i	$-0.525235\pi$
$673$	−4.10894	−0.158388	−0.0791939	+	0.996859i	$0.525235\pi$
$674$	−30.3360	−1.16850
$675$	−3.49306	−0.134448
$676$	0.542126	0.0208510
$677$	−26.3822	−1.01395	−0.506976	−	0.861960i	$-0.669237\pi$
$677$	−26.3822	−1.01395	−0.506976	+	0.861960i	$0.669237\pi$
$678$	0.588092	0.0225855
$679$	−8.09936	−0.310825
$680$	13.1649	0.504850
$681$	3.42229	0.131143
$682$	−1.44751	−0.0554281
$683$	−18.1548	−0.694676	−0.347338	−	0.937740i	$-0.612914\pi$
$683$	−18.1548	−0.694676	−0.347338	+	0.937740i	$0.612914\pi$
$684$	3.50525	0.134027
$685$	−7.09465	−0.271073
$686$	17.1585	0.655115
$687$	−1.02361	−0.0390532
$688$	2.90366	0.110701
$689$	−26.2591	−1.00039
$690$	0.687976	0.0261908
$691$	28.1899	1.07239	0.536196	−	0.844093i	$-0.319861\pi$
$691$	28.1899	1.07239	0.536196	+	0.844093i	$0.319861\pi$
$692$	4.67212	0.177607
$693$	−0.701329	−0.0266413
$694$	28.1315	1.06786
$695$	0.0679927	0.00257911
$696$	−0.216843	−0.00821942
$697$	76.5962	2.90129
$698$	−24.2504	−0.917890
$699$	0.548694	0.0207535
$700$	1.64686	0.0622455
$701$	39.3669	1.48687	0.743434	−	0.668809i	$-0.233196\pi$
$701$	39.3669	1.48687	0.743434	+	0.668809i	$0.233196\pi$
$702$	−3.28487	−0.123980
$703$	−18.2923	−0.689907
$704$	2.02023	0.0761402
$705$	0.657700	0.0247704
$706$	14.6342	0.550766
$707$	18.0237	0.677853
$708$	0.490458	0.0184326
$709$	48.4112	1.81812	0.909060	−	0.416664i	$-0.136801\pi$
$709$	48.4112	1.81812	0.909060	+	0.416664i	$0.136801\pi$
$710$	7.47726	0.280617
$711$	−1.09277	−0.0409820
$712$	−22.7546	−0.852765
$713$	34.1386	1.27850
$714$	1.19221	0.0446175
$715$	0.472211	0.0176597
$716$	3.61950	0.135267
$717$	−2.31772	−0.0865569
$718$	0.188532	0.00703595
$719$	−10.8564	−0.404877	−0.202438	−	0.979295i	$-0.564887\pi$
$719$	−10.8564	−0.404877	−0.202438	+	0.979295i	$0.564887\pi$
$720$	5.83299	0.217383
$721$	6.29345	0.234380
$722$	9.56045	0.355803
$723$	−0.126224	−0.00469433
$724$	3.04856	0.113299
$725$	−2.63334	−0.0977999
$726$	−1.77758	−0.0659723
$727$	−37.5110	−1.39121	−0.695604	−	0.718426i	$-0.744863\pi$
$727$	−37.5110	−1.39121	−0.695604	+	0.718426i	$0.744863\pi$
$728$	10.5170	0.389787
$729$	−26.1434	−0.968276
$730$	5.60019	0.207272
$731$	−6.48215	−0.239751
$732$	−0.159316	−0.00588849
$733$	−1.31177	−0.0484512	−0.0242256	−	0.999707i	$-0.507712\pi$
$733$	−1.31177	−0.0484512	−0.0242256	+	0.999707i	$0.507712\pi$
$734$	−42.0173	−1.55089
$735$	0.459191	0.0169375
$736$	−13.3491	−0.492053
$737$	−2.75105	−0.101336
$738$	41.2863	1.51977
$739$	52.6696	1.93748	0.968742	−	0.248072i	$-0.0797969\pi$
$739$	52.6696	1.93748	0.968742	+	0.248072i	$0.0797969\pi$
$740$	1.13823	0.0418423
$741$	−1.45142	−0.0533194
$742$	10.3015	0.378182
$743$	44.6512	1.63809	0.819046	−	0.573728i	$-0.194503\pi$
$743$	44.6512	1.63809	0.819046	+	0.573728i	$0.194503\pi$
$744$	−1.88003	−0.0689254
$745$	−11.9743	−0.438704
$746$	22.8362	0.836091
$747$	−53.1254	−1.94376
$748$	−0.560609	−0.0204979
$749$	8.10656	0.296207
$750$	−0.957564	−0.0349653
$751$	−30.0001	−1.09472	−0.547360	−	0.836897i	$-0.684367\pi$
$751$	−30.0001	−1.09472	−0.547360	+	0.836897i	$0.684367\pi$
$752$	27.1254	0.989160
$753$	−1.56049	−0.0568676
$754$	−2.47640	−0.0901850
$755$	10.8916	0.396386
$756$	−0.268986	−0.00978294
$757$	10.8998	0.396160	0.198080	−	0.980186i	$-0.436529\pi$
$757$	10.8998	0.396160	0.198080	+	0.980186i	$0.436529\pi$
$758$	6.20568	0.225400
$759$	−0.198948	−0.00722135
$760$	6.28752	0.228072
$761$	54.3944	1.97180	0.985898	−	0.167348i	$-0.0535203\pi$
$761$	54.3944	1.97180	0.985898	+	0.167348i	$0.0535203\pi$
$762$	2.19917	0.0796674
$763$	−4.30218	−0.155749
$764$	1.12564	0.0407242
$765$	−13.0216	−0.470796
$766$	−18.9253	−0.683798
$767$	38.0364	1.37341
$768$	1.01327	0.0365633
$769$	−16.9359	−0.610723	−0.305361	−	0.952237i	$-0.598777\pi$
$769$	−16.9359	−0.610723	−0.305361	+	0.952237i	$0.598777\pi$
$770$	−0.185250	−0.00667596
$771$	1.53475	0.0552727
$772$	−5.85954	−0.210890
$773$	−29.5026	−1.06113	−0.530567	−	0.847643i	$-0.678021\pi$
$773$	−29.5026	−1.06113	−0.530567	+	0.847643i	$0.678021\pi$
$774$	−3.49396	−0.125588
$775$	−22.8311	−0.820117
$776$	−23.6980	−0.850707
$777$	0.699989	0.0251120
$778$	−6.30712	−0.226121
$779$	36.5822	1.31069
$780$	0.0903144	0.00323377
$781$	−2.16226	−0.0773718
$782$	−63.3423	−2.26512
$783$	0.430111	0.0153709
$784$	18.9383	0.676368
$785$	4.28253	0.152850
$786$	0.167241	0.00596530
$787$	−5.96992	−0.212805	−0.106402	−	0.994323i	$-0.533933\pi$
$787$	−5.96992	−0.212805	−0.106402	+	0.994323i	$0.533933\pi$
$788$	6.40916	0.228317
$789$	0.727113	0.0258859
$790$	−0.288646	−0.0102696
$791$	3.73468	0.132790
$792$	−2.05202	−0.0729154
$793$	−12.3554	−0.438753
$794$	19.1610	0.679998
$795$	0.600744	0.0213062
$796$	6.78605	0.240525
$797$	19.1226	0.677357	0.338679	−	0.940902i	$-0.390020\pi$
$797$	19.1226	0.677357	0.338679	+	0.940902i	$0.390020\pi$
$798$	0.569399	0.0201565
$799$	−60.5548	−2.14227
$800$	8.92755	0.315637
$801$	22.5069	0.795243
$802$	−8.64573	−0.305291
$803$	−1.61945	−0.0571492
$804$	−0.526161	−0.0185563
$805$	4.36900	0.153987
$806$	−21.4704	−0.756262
$807$	−1.82502	−0.0642436
$808$	52.7358	1.85524
$809$	34.3768	1.20862	0.604312	−	0.796748i	$-0.293448\pi$
$809$	34.3768	1.20862	0.604312	+	0.796748i	$0.293448\pi$
$810$	−6.98113	−0.245292
$811$	18.2250	0.639967	0.319984	−	0.947423i	$-0.396323\pi$
$811$	18.2250	0.639967	0.319984	+	0.947423i	$0.396323\pi$
$812$	−0.202783	−0.00711629
$813$	−0.860393	−0.0301753
$814$	1.57691	0.0552708
$815$	−5.43949	−0.190537
$816$	2.86741	0.100379
$817$	−3.09586	−0.108310
$818$	3.34360	0.116906
$819$	−10.4025	−0.363494
$820$	−2.27632	−0.0794924
$821$	36.2130	1.26384	0.631920	−	0.775033i	$-0.282267\pi$
$821$	36.2130	1.26384	0.631920	+	0.775033i	$0.282267\pi$
$822$	−1.87987	−0.0655681
$823$	−42.2212	−1.47174	−0.735869	−	0.677124i	$-0.763226\pi$
$823$	−42.2212	−1.47174	−0.735869	+	0.677124i	$0.763226\pi$
$824$	18.4140	0.641483
$825$	0.133052	0.00463227
$826$	−14.9218	−0.519196
$827$	15.1566	0.527048	0.263524	−	0.964653i	$-0.415115\pi$
$827$	15.1566	0.527048	0.263524	+	0.964653i	$0.415115\pi$
$828$	7.12660	0.247666
$829$	−3.49294	−0.121315	−0.0606575	−	0.998159i	$-0.519320\pi$
$829$	−3.49294	−0.121315	−0.0606575	+	0.998159i	$0.519320\pi$
$830$	−14.0326	−0.487080
$831$	3.17231	0.110046
$832$	29.9653	1.03886
$833$	−42.2780	−1.46484
$834$	0.0180161	0.000623845 0
$835$	2.97459	0.102940
$836$	−0.267746	−0.00926017
$837$	3.72907	0.128895
$838$	16.9309	0.584868
$839$	−28.5020	−0.983999	−0.491999	−	0.870596i	$-0.663734\pi$
$839$	−28.5020	−0.983999	−0.491999	+	0.870596i	$0.663734\pi$
$840$	−0.240604	−0.00830162
$841$	−28.6757	−0.988819
$842$	8.40889	0.289789
$843$	0.761550	0.0262292
$844$	2.82743	0.0973240
$845$	−0.961849	−0.0330886
$846$	−32.6398	−1.12218
$847$	−11.2886	−0.387879
$848$	24.7764	0.850824
$849$	0.438532	0.0150504
$850$	42.3619	1.45300
$851$	−37.1904	−1.27487
$852$	−0.413551	−0.0141680
$853$	5.52236	0.189082	0.0945410	−	0.995521i	$-0.469862\pi$
$853$	5.52236	0.189082	0.0945410	+	0.995521i	$0.469862\pi$
$854$	4.84707	0.165863
$855$	−6.21908	−0.212688
$856$	23.7190	0.810700
$857$	−17.0172	−0.581298	−0.290649	−	0.956830i	$-0.593871\pi$
$857$	−17.0172	−0.581298	−0.290649	+	0.956830i	$0.593871\pi$
$858$	0.125122	0.00427160
$859$	−1.16642	−0.0397979	−0.0198989	−	0.999802i	$-0.506334\pi$
$859$	−1.16642	−0.0397979	−0.0198989	+	0.999802i	$0.506334\pi$
$860$	0.192639	0.00656893
$861$	−1.39989	−0.0477080
$862$	−13.9333	−0.474572
$863$	−8.50057	−0.289363	−0.144681	−	0.989478i	$-0.546216\pi$
$863$	−8.50057	−0.289363	−0.144681	+	0.989478i	$0.546216\pi$
$864$	−1.45816	−0.0496077
$865$	−8.28935	−0.281846
$866$	32.9346	1.11916
$867$	−4.25540	−0.144521
$868$	−1.75813	−0.0596749
$869$	0.0834701	0.00283153
$870$	0.0566539	0.00192075
$871$	−40.8052	−1.38263
$872$	−12.5878	−0.426275
$873$	23.4400	0.793324
$874$	−30.2522	−1.02329
$875$	−6.08102	−0.205576
$876$	−0.309734	−0.0104649
$877$	7.37310	0.248972	0.124486	−	0.992221i	$-0.460272\pi$
$877$	7.37310	0.248972	0.124486	+	0.992221i	$0.460272\pi$
$878$	−18.8886	−0.637460
$879$	2.49041	0.0839995
$880$	−0.445547	−0.0150194
$881$	−48.8726	−1.64656	−0.823279	−	0.567637i	$-0.807858\pi$
$881$	−48.8726	−1.64656	−0.823279	+	0.567637i	$0.807858\pi$
$882$	−22.7884	−0.767324
$883$	−26.8006	−0.901911	−0.450956	−	0.892546i	$-0.648917\pi$
$883$	−26.8006	−0.901911	−0.450956	+	0.892546i	$0.648917\pi$
$884$	−8.31529	−0.279674
$885$	−0.870180	−0.0292508
$886$	19.6404	0.659833
$887$	−3.15346	−0.105883	−0.0529414	−	0.998598i	$-0.516860\pi$
$887$	−3.15346	−0.105883	−0.0529414	+	0.998598i	$0.516860\pi$
$888$	2.04810	0.0687298
$889$	13.9658	0.468399
$890$	5.94502	0.199277
$891$	2.01879	0.0676320
$892$	−5.35571	−0.179322
$893$	−28.9208	−0.967799
$894$	−3.17283	−0.106115
$895$	−6.42179	−0.214657
$896$	−7.77443	−0.259726
$897$	−2.95092	−0.0985282
$898$	−40.1538	−1.33995
$899$	2.81126	0.0937609
$900$	−4.76611	−0.158870
$901$	−55.3109	−1.84267
$902$	−3.15362	−0.105004
$903$	0.118469	0.00394240
$904$	10.9273	0.363438
$905$	−5.40881	−0.179795
$906$	2.88596	0.0958795
$907$	−25.7319	−0.854414	−0.427207	−	0.904154i	$-0.640502\pi$
$907$	−25.7319	−0.854414	−0.427207	+	0.904154i	$0.640502\pi$
$908$	9.36404	0.310756
$909$	−52.1617	−1.73010
$910$	−2.74775	−0.0910869
$911$	10.3710	0.343606	0.171803	−	0.985131i	$-0.445041\pi$
$911$	10.3710	0.343606	0.171803	+	0.985131i	$0.445041\pi$
$912$	1.36947	0.0453476
$913$	4.05793	0.134298
$914$	−12.1381	−0.401494
$915$	0.282661	0.00934450
$916$	−2.80079	−0.0925409
$917$	1.06207	0.0350725
$918$	−6.91909	−0.228364
$919$	−33.5553	−1.10689	−0.553444	−	0.832887i	$-0.686687\pi$
$919$	−33.5553	−1.10689	−0.553444	+	0.832887i	$0.686687\pi$
$920$	12.7833	0.421452
$921$	0.00334570	0.000110244 0
$922$	−11.1334	−0.366660
$923$	−32.0720	−1.05566
$924$	0.0102458	0.000337062 0
$925$	24.8721	0.817790
$926$	16.1324	0.530144
$927$	−18.2136	−0.598213
$928$	−1.09928	−0.0360855
$929$	11.6222	0.381314	0.190657	−	0.981657i	$-0.438938\pi$
$929$	11.6222	0.381314	0.190657	+	0.981657i	$0.438938\pi$
$930$	0.491190	0.0161068
$931$	−20.1919	−0.661762
$932$	1.50133	0.0491777
$933$	−2.68633	−0.0879464
$934$	6.79792	0.222435
$935$	0.994642	0.0325283
$936$	−30.4369	−0.994860
$937$	46.3339	1.51366	0.756831	−	0.653611i	$-0.226747\pi$
$937$	46.3339	1.51366	0.756831	+	0.653611i	$0.226747\pi$
$938$	16.0080	0.522681
$939$	−1.34954	−0.0440404
$940$	1.79959	0.0586961
$941$	−7.22995	−0.235690	−0.117845	−	0.993032i	$-0.537599\pi$
$941$	−7.22995	−0.235690	−0.117845	+	0.993032i	$0.537599\pi$
$942$	1.13474	0.0369720
$943$	74.3759	2.42201
$944$	−35.8886	−1.16807
$945$	0.477240	0.0155246
$946$	0.266883	0.00867711
$947$	30.3453	0.986091	0.493045	−	0.870004i	$-0.335884\pi$
$947$	30.3453	0.986091	0.493045	+	0.870004i	$0.335884\pi$
$948$	0.0159644	0.000518498 0
$949$	−24.0207	−0.779745
$950$	20.2320	0.656412
$951$	0.262327	0.00850653
$952$	22.1525	0.717967
$953$	4.89634	0.158608	0.0793040	−	0.996850i	$-0.474730\pi$
$953$	4.89634	0.158608	0.0793040	+	0.996850i	$0.474730\pi$
$954$	−29.8133	−0.965240
$955$	−1.99713	−0.0646256
$956$	−6.34172	−0.205106
$957$	−0.0163831	−0.000529590 0
$958$	37.3801	1.20770
$959$	−11.9382	−0.385503
$960$	−0.685532	−0.0221254
$961$	−6.62631	−0.213752
$962$	23.3898	0.754116
$963$	−23.4608	−0.756015
$964$	−0.345373	−0.0111237
$965$	10.3961	0.334662
$966$	1.15766	0.0372470
$967$	25.6038	0.823363	0.411681	−	0.911328i	$-0.364942\pi$
$967$	25.6038	0.823363	0.411681	+	0.911328i	$0.364942\pi$
$968$	−33.0292	−1.06160
$969$	−3.05720	−0.0982116
$970$	6.19148	0.198797
$971$	19.2440	0.617570	0.308785	−	0.951132i	$-0.400078\pi$
$971$	19.2440	0.617570	0.308785	+	0.951132i	$0.400078\pi$
$972$	1.16873	0.0374870
$973$	0.114411	0.00366785
$974$	46.6747	1.49555
$975$	1.97351	0.0632028
$976$	11.6577	0.373155
$977$	14.0956	0.450957	0.225479	−	0.974248i	$-0.427605\pi$
$977$	14.0956	0.450957	0.225479	+	0.974248i	$0.427605\pi$
$978$	−1.44131	−0.0460879
$979$	−1.71917	−0.0549449
$980$	1.25643	0.0401353
$981$	12.4507	0.397521
$982$	5.13606	0.163898
$983$	−50.6189	−1.61449	−0.807246	−	0.590216i	$-0.799043\pi$
$983$	−50.6189	−1.61449	−0.807246	+	0.590216i	$0.799043\pi$
$984$	−4.09593	−0.130574
$985$	−11.3712	−0.362318
$986$	−5.21615	−0.166116
$987$	1.10671	0.0352270
$988$	−3.97137	−0.126346
$989$	−6.29425	−0.200145
$990$	0.536125	0.0170392
$991$	15.7226	0.499444	0.249722	−	0.968318i	$-0.419661\pi$
$991$	15.7226	0.499444	0.249722	+	0.968318i	$0.419661\pi$
$992$	−9.53074	−0.302601
$993$	3.55034	0.112667
$994$	12.5820	0.399076
$995$	−12.0399	−0.381691
$996$	0.776114	0.0245921
$997$	−9.08507	−0.287727	−0.143864	−	0.989598i	$-0.545953\pi$
$997$	−9.08507	−0.287727	−0.143864	+	0.989598i	$0.545953\pi$
$998$	−11.9019	−0.376747
$999$	−4.06243	−0.128530

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	241.2.a.b.1.4	✓	12
3.2	odd	2		2169.2.a.h.1.9		12
4.3	odd	2		3856.2.a.n.1.7		12
5.4	even	2		6025.2.a.h.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.b.1.4	✓	12	1.1	even	1	trivial
2169.2.a.h.1.9		12	3.2	odd	2
3856.2.a.n.1.7		12	4.3	odd	2
6025.2.a.h.1.9		12	5.4	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:	\( N \)	\(=\)	\( 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	241.a (trivial)

\(f(q)\)	\(=\)	\(q-1.28632 q^{2} -0.126224 q^{3} -0.345373 q^{4} +0.612768 q^{5} +0.162365 q^{6} +1.03110 q^{7} +3.01691 q^{8} -2.98407 q^{9} +O(q^{10})\)	\(q-1.28632 q^{2} -0.126224 q^{3} -0.345373 q^{4} +0.612768 q^{5} +0.162365 q^{6} +1.03110 q^{7} +3.01691 q^{8} -2.98407 q^{9} -0.788217 q^{10} +0.227935 q^{11} +0.0435945 q^{12} +3.38088 q^{13} -1.32633 q^{14} -0.0773462 q^{15} -3.18997 q^{16} +7.12130 q^{17} +3.83847 q^{18} +3.40112 q^{19} -0.211634 q^{20} -0.130150 q^{21} -0.293198 q^{22} +6.91488 q^{23} -0.380807 q^{24} -4.62452 q^{25} -4.34890 q^{26} +0.755335 q^{27} -0.356115 q^{28} +0.569431 q^{29} +0.0994922 q^{30} +4.93697 q^{31} -1.93048 q^{32} -0.0287710 q^{33} -9.16030 q^{34} +0.631826 q^{35} +1.03062 q^{36} -5.37832 q^{37} -4.37494 q^{38} -0.426749 q^{39} +1.84866 q^{40} +10.7559 q^{41} +0.167415 q^{42} -0.910247 q^{43} -0.0787228 q^{44} -1.82854 q^{45} -8.89477 q^{46} -8.50333 q^{47} +0.402652 q^{48} -5.93683 q^{49} +5.94862 q^{50} -0.898882 q^{51} -1.16766 q^{52} -7.76696 q^{53} -0.971605 q^{54} +0.139671 q^{55} +3.11074 q^{56} -0.429304 q^{57} -0.732472 q^{58} +11.2505 q^{59} +0.0267133 q^{60} -3.65450 q^{61} -6.35054 q^{62} -3.07688 q^{63} +8.86317 q^{64} +2.07169 q^{65} +0.0370088 q^{66} -12.0694 q^{67} -2.45951 q^{68} -0.872826 q^{69} -0.812732 q^{70} -9.48630 q^{71} -9.00266 q^{72} -7.10488 q^{73} +6.91825 q^{74} +0.583726 q^{75} -1.17466 q^{76} +0.235024 q^{77} +0.548937 q^{78} +0.366201 q^{79} -1.95471 q^{80} +8.85686 q^{81} -13.8356 q^{82} +17.8030 q^{83} +0.0449504 q^{84} +4.36370 q^{85} +1.17087 q^{86} -0.0718760 q^{87} +0.687660 q^{88} -7.54236 q^{89} +2.35209 q^{90} +3.48603 q^{91} -2.38822 q^{92} -0.623166 q^{93} +10.9380 q^{94} +2.08410 q^{95} +0.243674 q^{96} -7.85505 q^{97} +7.63668 q^{98} -0.680174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9} - 7 q^{10} + 22 q^{11} - 7 q^{12} - 5 q^{13} + 6 q^{14} + 13 q^{15} + 15 q^{16} - 4 q^{17} - q^{18} - 6 q^{19} + 10 q^{20} - 14 q^{21} - 12 q^{22} + 32 q^{23} - 15 q^{24} + 4 q^{25} + 8 q^{26} - 5 q^{27} - 11 q^{28} + 6 q^{29} - 19 q^{30} + 8 q^{31} + q^{32} - 24 q^{33} - 19 q^{34} + 15 q^{35} - 8 q^{36} - 8 q^{37} - 10 q^{38} + 31 q^{39} - 52 q^{40} - q^{41} - 49 q^{42} - 2 q^{43} + 42 q^{44} - 15 q^{45} - 25 q^{46} + 34 q^{47} - 49 q^{48} - 9 q^{49} - 27 q^{50} - 3 q^{51} - 41 q^{52} + 5 q^{53} - 40 q^{54} - 3 q^{55} + q^{56} - 22 q^{57} - 33 q^{58} + 26 q^{59} - 57 q^{60} - 26 q^{61} - 17 q^{62} - 4 q^{63} + 13 q^{64} - 25 q^{65} - 2 q^{66} + 6 q^{67} - 35 q^{68} - 2 q^{69} - 4 q^{70} + 94 q^{71} + 17 q^{72} - 22 q^{73} + 26 q^{74} - 20 q^{76} - 7 q^{77} + 54 q^{78} + 9 q^{79} + 19 q^{80} + 4 q^{81} + 15 q^{82} - 8 q^{83} + 2 q^{84} + 4 q^{85} + 9 q^{86} + 4 q^{87} + 6 q^{88} - 3 q^{89} + 11 q^{90} - 20 q^{91} + 36 q^{92} + 12 q^{93} + 48 q^{94} + 33 q^{95} - 23 q^{96} - 29 q^{97} + 28 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9 - 7 * q^10 + 22 * q^11 - 7 * q^12 - 5 * q^13 + 6 * q^14 + 13 * q^15 + 15 * q^16 - 4 * q^17 - q^18 - 6 * q^19 + 10 * q^20 - 14 * q^21 - 12 * q^22 + 32 * q^23 - 15 * q^24 + 4 * q^25 + 8 * q^26 - 5 * q^27 - 11 * q^28 + 6 * q^29 - 19 * q^30 + 8 * q^31 + q^32 - 24 * q^33 - 19 * q^34 + 15 * q^35 - 8 * q^36 - 8 * q^37 - 10 * q^38 + 31 * q^39 - 52 * q^40 - q^41 - 49 * q^42 - 2 * q^43 + 42 * q^44 - 15 * q^45 - 25 * q^46 + 34 * q^47 - 49 * q^48 - 9 * q^49 - 27 * q^50 - 3 * q^51 - 41 * q^52 + 5 * q^53 - 40 * q^54 - 3 * q^55 + q^56 - 22 * q^57 - 33 * q^58 + 26 * q^59 - 57 * q^60 - 26 * q^61 - 17 * q^62 - 4 * q^63 + 13 * q^64 - 25 * q^65 - 2 * q^66 + 6 * q^67 - 35 * q^68 - 2 * q^69 - 4 * q^70 + 94 * q^71 + 17 * q^72 - 22 * q^73 + 26 * q^74 - 20 * q^76 - 7 * q^77 + 54 * q^78 + 9 * q^79 + 19 * q^80 + 4 * q^81 + 15 * q^82 - 8 * q^83 + 2 * q^84 + 4 * q^85 + 9 * q^86 + 4 * q^87 + 6 * q^88 - 3 * q^89 + 11 * q^90 - 20 * q^91 + 36 * q^92 + 12 * q^93 + 48 * q^94 + 33 * q^95 - 23 * q^96 - 29 * q^97 + 28 * q^98 + 36 * q^99

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