LMFDB - Embedded newform 241.2.a.b.1.6

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			1.6
Root			$0.0822506$ 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)

$f(q)$	$=$	$q+0.0822506 q^{2} +1.81824 q^{3} -1.99323 q^{4} +4.31963 q^{5} +0.149552 q^{6} +0.690569 q^{7} -0.328446 q^{8} +0.306010 q^{9} +O(q^{10})$	\(q+0.0822506 q^{2} +1.81824 q^{3} -1.99323 q^{4} +4.31963 q^{5} +0.149552 q^{6} +0.690569 q^{7} -0.328446 q^{8} +0.306010 q^{9} +0.355292 q^{10} -2.95833 q^{11} -3.62419 q^{12} -1.93470 q^{13} +0.0567997 q^{14} +7.85414 q^{15} +3.95945 q^{16} -2.07477 q^{17} +0.0251695 q^{18} +3.74689 q^{19} -8.61004 q^{20} +1.25562 q^{21} -0.243324 q^{22} +4.34832 q^{23} -0.597195 q^{24} +13.6592 q^{25} -0.159131 q^{26} -4.89833 q^{27} -1.37647 q^{28} -8.10772 q^{29} +0.646008 q^{30} -2.80197 q^{31} +0.982559 q^{32} -5.37896 q^{33} -0.170651 q^{34} +2.98300 q^{35} -0.609951 q^{36} -9.72312 q^{37} +0.308183 q^{38} -3.51777 q^{39} -1.41876 q^{40} -4.09401 q^{41} +0.103276 q^{42} +3.02779 q^{43} +5.89665 q^{44} +1.32185 q^{45} +0.357652 q^{46} +6.71240 q^{47} +7.19925 q^{48} -6.52312 q^{49} +1.12348 q^{50} -3.77244 q^{51} +3.85632 q^{52} -0.0484656 q^{53} -0.402890 q^{54} -12.7789 q^{55} -0.226814 q^{56} +6.81275 q^{57} -0.666864 q^{58} +4.50676 q^{59} -15.6551 q^{60} -9.62232 q^{61} -0.230464 q^{62} +0.211321 q^{63} -7.83809 q^{64} -8.35721 q^{65} -0.442423 q^{66} -0.964160 q^{67} +4.13551 q^{68} +7.90631 q^{69} +0.245353 q^{70} +7.76289 q^{71} -0.100508 q^{72} +16.4250 q^{73} -0.799732 q^{74} +24.8358 q^{75} -7.46842 q^{76} -2.04293 q^{77} -0.289338 q^{78} -6.83310 q^{79} +17.1034 q^{80} -9.82439 q^{81} -0.336735 q^{82} -9.15477 q^{83} -2.50275 q^{84} -8.96225 q^{85} +0.249037 q^{86} -14.7418 q^{87} +0.971651 q^{88} -2.36597 q^{89} +0.108723 q^{90} -1.33605 q^{91} -8.66723 q^{92} -5.09467 q^{93} +0.552099 q^{94} +16.1852 q^{95} +1.78653 q^{96} -5.25335 q^{97} -0.536530 q^{98} -0.905280 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.0822506	0.0581599	0.0290800	−	0.999577i	$-0.490742\pi$
$2$	0.0822506	0.0581599	0.0290800	+	0.999577i	$0.490742\pi$
$3$	1.81824	1.04976	0.524882	−	0.851175i	$-0.324110\pi$
$3$	1.81824	1.04976	0.524882	+	0.851175i	$0.324110\pi$
$4$	−1.99323	−0.996617
$5$	4.31963	1.93180	0.965899	−	0.258920i	$-0.0833667\pi$
$5$	4.31963	1.93180	0.965899	+	0.258920i	$0.0833667\pi$
$6$	0.149552	0.0610542
$7$	0.690569	0.261010	0.130505	−	0.991448i	$-0.458340\pi$
$7$	0.690569	0.261010	0.130505	+	0.991448i	$0.458340\pi$
$8$	−0.328446	−0.116123
$9$	0.306010	0.102003
$10$	0.355292	0.112353
$11$	−2.95833	−0.891970	−0.445985	−	0.895040i	$-0.647147\pi$
$11$	−2.95833	−0.891970	−0.445985	+	0.895040i	$0.647147\pi$
$12$	−3.62419	−1.04621
$13$	−1.93470	−0.536591	−0.268295	−	0.963337i	$-0.586460\pi$
$13$	−1.93470	−0.536591	−0.268295	+	0.963337i	$0.586460\pi$
$14$	0.0567997	0.0151803
$15$	7.85414	2.02793
$16$	3.95945	0.989864
$17$	−2.07477	−0.503206	−0.251603	−	0.967830i	$-0.580958\pi$
$17$	−2.07477	−0.503206	−0.251603	+	0.967830i	$0.580958\pi$
$18$	0.0251695	0.00593251
$19$	3.74689	0.859595	0.429797	−	0.902925i	$-0.358585\pi$
$19$	3.74689	0.859595	0.429797	+	0.902925i	$0.358585\pi$
$20$	−8.61004	−1.92526
$21$	1.25562	0.273999
$22$	−0.243324	−0.0518769
$23$	4.34832	0.906688	0.453344	−	0.891336i	$-0.350231\pi$
$23$	4.34832	0.906688	0.453344	+	0.891336i	$0.350231\pi$
$24$	−0.597195	−0.121902
$25$	13.6592	2.73184
$26$	−0.159131	−0.0312081
$27$	−4.89833	−0.942684
$28$	−1.37647	−0.260127
$29$	−8.10772	−1.50557	−0.752783	−	0.658269i	$-0.771289\pi$
$29$	−8.10772	−1.50557	−0.752783	+	0.658269i	$0.771289\pi$
$30$	0.646008	0.117944
$31$	−2.80197	−0.503249	−0.251624	−	0.967825i	$-0.580965\pi$
$31$	−2.80197	−0.503249	−0.251624	+	0.967825i	$0.580965\pi$
$32$	0.982559	0.173694
$33$	−5.37896	−0.936358
$34$	−0.170651	−0.0292664
$35$	2.98300	0.504219
$36$	−0.609951	−0.101658
$37$	−9.72312	−1.59847	−0.799236	−	0.601018i	$-0.794762\pi$
$37$	−9.72312	−1.59847	−0.799236	+	0.601018i	$0.794762\pi$
$38$	0.308183	0.0499940
$39$	−3.51777	−0.563293
$40$	−1.41876	−0.224326
$41$	−4.09401	−0.639378	−0.319689	−	0.947523i	$-0.603578\pi$
$41$	−4.09401	−0.639378	−0.319689	+	0.947523i	$0.603578\pi$
$42$	0.103276	0.0159358
$43$	3.02779	0.461733	0.230867	−	0.972985i	$-0.425844\pi$
$43$	3.02779	0.461733	0.230867	+	0.972985i	$0.425844\pi$
$44$	5.89665	0.888953
$45$	1.32185	0.197050
$46$	0.357652	0.0527329
$47$	6.71240	0.979104	0.489552	−	0.871974i	$-0.337160\pi$
$47$	6.71240	0.979104	0.489552	+	0.871974i	$0.337160\pi$
$48$	7.19925	1.03912
$49$	−6.52312	−0.931874
$50$	1.12348	0.158884
$51$	−3.77244	−0.528248
$52$	3.85632	0.534776
$53$	−0.0484656	−0.00665726	−0.00332863	−	0.999994i	$-0.501060\pi$
$53$	−0.0484656	−0.00665726	−0.00332863	+	0.999994i	$0.501060\pi$
$54$	−0.402890	−0.0548264
$55$	−12.7789	−1.72311
$56$	−0.226814	−0.0303093
$57$	6.81275	0.902371
$58$	−0.666864	−0.0875636
$59$	4.50676	0.586730	0.293365	−	0.956000i	$-0.405225\pi$
$59$	4.50676	0.586730	0.293365	+	0.956000i	$0.405225\pi$
$60$	−15.6551	−2.02107
$61$	−9.62232	−1.23201	−0.616006	−	0.787742i	$-0.711250\pi$
$61$	−9.62232	−1.23201	−0.616006	+	0.787742i	$0.711250\pi$
$62$	−0.230464	−0.0292689
$63$	0.211321	0.0266240
$64$	−7.83809	−0.979762
$65$	−8.35721	−1.03658
$66$	−0.442423	−0.0544585
$67$	−0.964160	−0.117791	−0.0588954	−	0.998264i	$-0.518758\pi$
$67$	−0.964160	−0.117791	−0.0588954	+	0.998264i	$0.518758\pi$
$68$	4.13551	0.501504
$69$	7.90631	0.951808
$70$	0.245353	0.0293254
$71$	7.76289	0.921286	0.460643	−	0.887586i	$-0.347619\pi$
$71$	7.76289	0.921286	0.460643	+	0.887586i	$0.347619\pi$
$72$	−0.100508	−0.0118450
$73$	16.4250	1.92241	0.961203	−	0.275841i	$-0.0889563\pi$
$73$	16.4250	1.92241	0.961203	+	0.275841i	$0.0889563\pi$
$74$	−0.799732	−0.0929670
$75$	24.8358	2.86779
$76$	−7.46842	−0.856687
$77$	−2.04293	−0.232813
$78$	−0.289338	−0.0327611
$79$	−6.83310	−0.768783	−0.384392	−	0.923170i	$-0.625589\pi$
$79$	−6.83310	−0.768783	−0.384392	+	0.923170i	$0.625589\pi$
$80$	17.1034	1.91222
$81$	−9.82439	−1.09160
$82$	−0.336735	−0.0371862
$83$	−9.15477	−1.00487	−0.502433	−	0.864616i	$-0.667562\pi$
$83$	−9.15477	−1.00487	−0.502433	+	0.864616i	$0.667562\pi$
$84$	−2.50275	−0.273072
$85$	−8.96225	−0.972092
$86$	0.249037	0.0268544
$87$	−14.7418	−1.58049
$88$	0.971651	0.103578
$89$	−2.36597	−0.250793	−0.125396	−	0.992107i	$-0.540020\pi$
$89$	−2.36597	−0.250793	−0.125396	+	0.992107i	$0.540020\pi$
$90$	0.108723	0.0114604
$91$	−1.33605	−0.140056
$92$	−8.66723	−0.903621
$93$	−5.09467	−0.528292
$94$	0.552099	0.0569447
$95$	16.1852	1.66056
$96$	1.78653	0.182337
$97$	−5.25335	−0.533396	−0.266698	−	0.963780i	$-0.585933\pi$
$97$	−5.25335	−0.533396	−0.266698	+	0.963780i	$0.585933\pi$
$98$	−0.536530	−0.0541977
$99$	−0.905280	−0.0909840
$100$	−27.2260	−2.72260
$101$	9.93584	0.988653	0.494327	−	0.869276i	$-0.335415\pi$
$101$	9.93584	0.988653	0.494327	+	0.869276i	$0.335415\pi$
$102$	−0.310285	−0.0307228
$103$	19.2644	1.89818	0.949090	−	0.315005i	$-0.102006\pi$
$103$	19.2644	1.89818	0.949090	+	0.315005i	$0.102006\pi$
$104$	0.635446	0.0623106
$105$	5.42382	0.529311
$106$	−0.00398632	−0.000387186 0
$107$	−7.88030	−0.761817	−0.380909	−	0.924613i	$-0.624389\pi$
$107$	−7.88030	−0.761817	−0.380909	+	0.924613i	$0.624389\pi$
$108$	9.76352	0.939495
$109$	−1.72728	−0.165443	−0.0827215	−	0.996573i	$-0.526361\pi$
$109$	−1.72728	−0.165443	−0.0827215	+	0.996573i	$0.526361\pi$
$110$	−1.05107	−0.100216
$111$	−17.6790	−1.67802
$112$	2.73427	0.258365
$113$	14.0431	1.32107	0.660533	−	0.750797i	$-0.270330\pi$
$113$	14.0431	1.32107	0.660533	+	0.750797i	$0.270330\pi$
$114$	0.560353	0.0524818
$115$	18.7831	1.75154
$116$	16.1606	1.50047
$117$	−0.592040	−0.0547341
$118$	0.370684	0.0341242
$119$	−1.43277	−0.131342
$120$	−2.57966	−0.235490
$121$	−2.24829	−0.204390
$122$	−0.791441	−0.0716537
$123$	−7.44392	−0.671195
$124$	5.58499	0.501547
$125$	37.4046	3.34557
$126$	0.0173813	0.00154845
$127$	−1.65498	−0.146856	−0.0734278	−	0.997301i	$-0.523394\pi$
$127$	−1.65498	−0.146856	−0.0734278	+	0.997301i	$0.523394\pi$
$128$	−2.60981	−0.230676
$129$	5.50525	0.484711
$130$	−0.687385	−0.0602877
$131$	17.1541	1.49876	0.749381	−	0.662139i	$-0.230351\pi$
$131$	17.1541	1.49876	0.749381	+	0.662139i	$0.230351\pi$
$132$	10.7215	0.933190
$133$	2.58748	0.224363
$134$	−0.0793027	−0.00685071
$135$	−21.1590	−1.82107
$136$	0.681450	0.0584339
$137$	14.7651	1.26147	0.630733	−	0.776000i	$-0.282755\pi$
$137$	14.7651	1.26147	0.630733	+	0.776000i	$0.282755\pi$
$138$	0.650298	0.0553571
$139$	20.3570	1.72666	0.863329	−	0.504641i	$-0.168375\pi$
$139$	20.3570	1.72666	0.863329	+	0.504641i	$0.168375\pi$
$140$	−5.94582	−0.502514
$141$	12.2048	1.02783
$142$	0.638502	0.0535819
$143$	5.72349	0.478623
$144$	1.21163	0.100970
$145$	−35.0223	−2.90845
$146$	1.35097	0.111807
$147$	−11.8606	−0.978247
$148$	19.3805	1.59306
$149$	8.37820	0.686369	0.343185	−	0.939268i	$-0.388494\pi$
$149$	8.37820	0.686369	0.343185	+	0.939268i	$0.388494\pi$
$150$	2.04276	0.166790
$151$	−22.0074	−1.79093	−0.895467	−	0.445128i	$-0.853158\pi$
$151$	−22.0074	−1.79093	−0.895467	+	0.445128i	$0.853158\pi$
$152$	−1.23065	−0.0998188
$153$	−0.634902	−0.0513288
$154$	−0.168032	−0.0135404
$155$	−12.1035	−0.972175
$156$	7.01173	0.561388
$157$	−0.208187	−0.0166151	−0.00830757	−	0.999965i	$-0.502644\pi$
$157$	−0.208187	−0.0166151	−0.00830757	+	0.999965i	$0.502644\pi$
$158$	−0.562026	−0.0447124
$159$	−0.0881222	−0.00698855
$160$	4.24429	0.335541
$161$	3.00281	0.236655
$162$	−0.808062	−0.0634873
$163$	7.85060	0.614906	0.307453	−	0.951563i	$-0.400523\pi$
$163$	7.85060	0.614906	0.307453	+	0.951563i	$0.400523\pi$
$164$	8.16033	0.637215
$165$	−23.2351	−1.80885
$166$	−0.752985	−0.0584430
$167$	−13.8766	−1.07380	−0.536900	−	0.843646i	$-0.680405\pi$
$167$	−13.8766	−1.07380	−0.536900	+	0.843646i	$0.680405\pi$
$168$	−0.412404	−0.0318176
$169$	−9.25692	−0.712071
$170$	−0.737150	−0.0565368
$171$	1.14659	0.0876816
$172$	−6.03509	−0.460171
$173$	19.3500	1.47115	0.735577	−	0.677441i	$-0.236911\pi$
$173$	19.3500	1.47115	0.735577	+	0.677441i	$0.236911\pi$
$174$	−1.21252	−0.0919211
$175$	9.43262	0.713039
$176$	−11.7134	−0.882929
$177$	8.19439	0.615928
$178$	−0.194603	−0.0145861
$179$	−7.02479	−0.525057	−0.262529	−	0.964924i	$-0.584556\pi$
$179$	−7.02479	−0.525057	−0.262529	+	0.964924i	$0.584556\pi$
$180$	−2.63476	−0.196383
$181$	7.22067	0.536708	0.268354	−	0.963320i	$-0.413520\pi$
$181$	7.22067	0.536708	0.268354	+	0.963320i	$0.413520\pi$
$182$	−0.109891	−0.00814563
$183$	−17.4957	−1.29332
$184$	−1.42819	−0.105287
$185$	−42.0003	−3.08792
$186$	−0.419039	−0.0307254
$187$	6.13786	0.448845
$188$	−13.3794	−0.975793
$189$	−3.38263	−0.246050
$190$	1.33124	0.0965782
$191$	20.7694	1.50282	0.751412	−	0.659834i	$-0.229373\pi$
$191$	20.7694	1.50282	0.751412	+	0.659834i	$0.229373\pi$
$192$	−14.2516	−1.02852
$193$	−19.7206	−1.41952	−0.709762	−	0.704442i	$-0.751197\pi$
$193$	−19.7206	−1.41952	−0.709762	+	0.704442i	$0.751197\pi$
$194$	−0.432091	−0.0310223
$195$	−15.1954	−1.08817
$196$	13.0021	0.928721
$197$	−16.2977	−1.16116	−0.580582	−	0.814201i	$-0.697175\pi$
$197$	−16.2977	−1.16116	−0.580582	+	0.814201i	$0.697175\pi$
$198$	−0.0744598	−0.00529162
$199$	4.79014	0.339564	0.169782	−	0.985482i	$-0.445694\pi$
$199$	4.79014	0.339564	0.169782	+	0.985482i	$0.445694\pi$
$200$	−4.48631	−0.317230
$201$	−1.75308	−0.123653
$202$	0.817229	0.0575000
$203$	−5.59893	−0.392968
$204$	7.51936	0.526461
$205$	−17.6846	−1.23515
$206$	1.58451	0.110398
$207$	1.33063	0.0924853
$208$	−7.66038	−0.531152
$209$	−11.0845	−0.766733
$210$	0.446112	0.0307847
$211$	−4.30473	−0.296350	−0.148175	−	0.988961i	$-0.547340\pi$
$211$	−4.30473	−0.296350	−0.148175	+	0.988961i	$0.547340\pi$
$212$	0.0966033	0.00663474
$213$	14.1148	0.967132
$214$	−0.648159	−0.0443072
$215$	13.0789	0.891975
$216$	1.60884	0.109467
$217$	−1.93495	−0.131353
$218$	−0.142069	−0.00962215
$219$	29.8647	2.01807
$220$	25.4713	1.71728
$221$	4.01407	0.270016
$222$	−1.45411	−0.0975933
$223$	14.8068	0.991540	0.495770	−	0.868454i	$-0.334886\pi$
$223$	14.8068	0.991540	0.495770	+	0.868454i	$0.334886\pi$
$224$	0.678524	0.0453358
$225$	4.17986	0.278657
$226$	1.15505	0.0768331
$227$	−11.9026	−0.790000	−0.395000	−	0.918681i	$-0.629255\pi$
$227$	−11.9026	−0.790000	−0.395000	+	0.918681i	$0.629255\pi$
$228$	−13.5794	−0.899319
$229$	−5.11465	−0.337985	−0.168993	−	0.985617i	$-0.554051\pi$
$229$	−5.11465	−0.337985	−0.168993	+	0.985617i	$0.554051\pi$
$230$	1.54492	0.101869
$231$	−3.71454	−0.244399
$232$	2.66295	0.174831
$233$	−14.9300	−0.978097	−0.489048	−	0.872257i	$-0.662656\pi$
$233$	−14.9300	−0.978097	−0.489048	+	0.872257i	$0.662656\pi$
$234$	−0.0486956	−0.00318333
$235$	28.9951	1.89143
$236$	−8.98303	−0.584746
$237$	−12.4242	−0.807041
$238$	−0.117846	−0.00763884
$239$	29.8624	1.93164	0.965820	−	0.259215i	$-0.0834638\pi$
$239$	29.8624	1.93164	0.965820	+	0.259215i	$0.0834638\pi$
$240$	31.0981	2.00737
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−0.184923	−0.0118873
$243$	−3.16814	−0.203237
$244$	19.1795	1.22784
$245$	−28.1774	−1.80019
$246$	−0.612266	−0.0390367
$247$	−7.24912	−0.461250
$248$	0.920296	0.0584388
$249$	−16.6456	−1.05487
$250$	3.07655	0.194578
$251$	13.0620	0.824464	0.412232	−	0.911079i	$-0.364749\pi$
$251$	13.0620	0.824464	0.412232	+	0.911079i	$0.364749\pi$
$252$	−0.421213	−0.0265339
$253$	−12.8638	−0.808738
$254$	−0.136123	−0.00854111
$255$	−16.2956	−1.02047
$256$	15.4615	0.966346
$257$	6.35830	0.396620	0.198310	−	0.980139i	$-0.436455\pi$
$257$	6.35830	0.396620	0.198310	+	0.980139i	$0.436455\pi$
$258$	0.452810	0.0281907
$259$	−6.71448	−0.417218
$260$	16.6579	1.03308
$261$	−2.48105	−0.153573
$262$	1.41094	0.0871679
$263$	4.66189	0.287465	0.143732	−	0.989617i	$-0.454090\pi$
$263$	4.66189	0.287465	0.143732	+	0.989617i	$0.454090\pi$
$264$	1.76670	0.108733
$265$	−0.209353	−0.0128605
$266$	0.212822	0.0130489
$267$	−4.30192	−0.263273
$268$	1.92180	0.117392
$269$	−10.5251	−0.641728	−0.320864	−	0.947125i	$-0.603973\pi$
$269$	−10.5251	−0.641728	−0.320864	+	0.947125i	$0.603973\pi$
$270$	−1.74034	−0.105914
$271$	10.3212	0.626968	0.313484	−	0.949593i	$-0.398504\pi$
$271$	10.3212	0.626968	0.313484	+	0.949593i	$0.398504\pi$
$272$	−8.21497	−0.498106
$273$	−2.42926	−0.147025
$274$	1.21444	0.0733667
$275$	−40.4084	−2.43672
$276$	−15.7591	−0.948588
$277$	22.1023	1.32800	0.663999	−	0.747734i	$-0.268858\pi$
$277$	22.1023	1.32800	0.663999	+	0.747734i	$0.268858\pi$
$278$	1.67437	0.100422
$279$	−0.857432	−0.0513331
$280$	−0.979754	−0.0585515
$281$	4.22803	0.252223	0.126111	−	0.992016i	$-0.459750\pi$
$281$	4.22803	0.252223	0.126111	+	0.992016i	$0.459750\pi$
$282$	1.00385	0.0597784
$283$	−3.06769	−0.182355	−0.0911776	−	0.995835i	$-0.529063\pi$
$283$	−3.06769	−0.182355	−0.0911776	+	0.995835i	$0.529063\pi$
$284$	−15.4733	−0.918169
$285$	29.4286	1.74320
$286$	0.470761	0.0278367
$287$	−2.82720	−0.166884
$288$	0.300673	0.0177173
$289$	−12.6953	−0.746783
$290$	−2.88061	−0.169155
$291$	−9.55186	−0.559940
$292$	−32.7390	−1.91590
$293$	−15.4694	−0.903735	−0.451867	−	0.892085i	$-0.649242\pi$
$293$	−15.4694	−0.903735	−0.451867	+	0.892085i	$0.649242\pi$
$294$	−0.975542	−0.0568948
$295$	19.4675	1.13344
$296$	3.19352	0.185619
$297$	14.4909	0.840846
$298$	0.689112	0.0399192
$299$	−8.41272	−0.486520
$300$	−49.5035	−2.85809
$301$	2.09089	0.120517
$302$	−1.81012	−0.104161
$303$	18.0658	1.03785
$304$	14.8356	0.850881
$305$	−41.5648	−2.38000
$306$	−0.0522210	−0.00298528
$307$	−20.2412	−1.15523	−0.577614	−	0.816310i	$-0.696016\pi$
$307$	−20.2412	−1.15523	−0.577614	+	0.816310i	$0.696016\pi$
$308$	4.07204	0.232026
$309$	35.0274	1.99264
$310$	−0.995518	−0.0565416
$311$	1.49434	0.0847363	0.0423681	−	0.999102i	$-0.486510\pi$
$311$	1.49434	0.0847363	0.0423681	+	0.999102i	$0.486510\pi$
$312$	1.15540	0.0654114
$313$	−21.6470	−1.22356	−0.611780	−	0.791028i	$-0.709546\pi$
$313$	−21.6470	−1.22356	−0.611780	+	0.791028i	$0.709546\pi$
$314$	−0.0171235	−0.000966335 0
$315$	0.912829	0.0514321
$316$	13.6200	0.766183
$317$	28.9329	1.62504	0.812518	−	0.582936i	$-0.198096\pi$
$317$	28.9329	1.62504	0.812518	+	0.582936i	$0.198096\pi$
$318$	−0.00724810	−0.000406453 0
$319$	23.9853	1.34292
$320$	−33.8577	−1.89270
$321$	−14.3283	−0.799728
$322$	0.246983	0.0137638
$323$	−7.77394	−0.432553
$324$	19.5823	1.08791
$325$	−26.4265	−1.46588
$326$	0.645716	0.0357629
$327$	−3.14061	−0.173676
$328$	1.34466	0.0742465
$329$	4.63537	0.255556
$330$	−1.91110	−0.105203
$331$	−27.5701	−1.51539	−0.757695	−	0.652609i	$-0.773675\pi$
$331$	−27.5701	−1.51539	−0.757695	+	0.652609i	$0.773675\pi$
$332$	18.2476	1.00147
$333$	−2.97538	−0.163050
$334$	−1.14135	−0.0624521
$335$	−4.16481	−0.227548
$336$	4.97158	0.271222
$337$	−8.25450	−0.449651	−0.224826	−	0.974399i	$-0.572181\pi$
$337$	−8.25450	−0.449651	−0.224826	+	0.974399i	$0.572181\pi$
$338$	−0.761387	−0.0414140
$339$	25.5338	1.38681
$340$	17.8639	0.968804
$341$	8.28915	0.448883
$342$	0.0943074	0.00509956
$343$	−9.33864	−0.504239
$344$	−0.994464	−0.0536179
$345$	34.1523	1.83870
$346$	1.59155	0.0855622
$347$	21.2018	1.13817	0.569085	−	0.822278i	$-0.307297\pi$
$347$	21.2018	1.13817	0.569085	+	0.822278i	$0.307297\pi$
$348$	29.3839	1.57514
$349$	21.3257	1.14154	0.570770	−	0.821110i	$-0.306645\pi$
$349$	21.3257	1.14154	0.570770	+	0.821110i	$0.306645\pi$
$350$	0.775838	0.0414703
$351$	9.47682	0.505835
$352$	−2.90673	−0.154929
$353$	2.80184	0.149127	0.0745635	−	0.997216i	$-0.476244\pi$
$353$	2.80184	0.149127	0.0745635	+	0.997216i	$0.476244\pi$
$354$	0.673993	0.0358223
$355$	33.5328	1.77974
$356$	4.71594	0.249944
$357$	−2.60513	−0.137878
$358$	−0.577793	−0.0305373
$359$	4.62788	0.244250	0.122125	−	0.992515i	$-0.461029\pi$
$359$	4.62788	0.244250	0.122125	+	0.992515i	$0.461029\pi$
$360$	−0.434157	−0.0228821
$361$	−4.96085	−0.261097
$362$	0.593904	0.0312149
$363$	−4.08793	−0.214561
$364$	2.66305	0.139582
$365$	70.9501	3.71370
$366$	−1.43903	−0.0752194
$367$	−0.106183	−0.00554270	−0.00277135	−	0.999996i	$-0.500882\pi$
$367$	−0.106183	−0.00554270	−0.00277135	+	0.999996i	$0.500882\pi$
$368$	17.2170	0.897497
$369$	−1.25281	−0.0652187
$370$	−3.45455	−0.179593
$371$	−0.0334688	−0.00173761
$372$	10.1549	0.526505
$373$	−16.6703	−0.863157	−0.431579	−	0.902075i	$-0.642043\pi$
$373$	−16.6703	−0.863157	−0.431579	+	0.902075i	$0.642043\pi$
$374$	0.504843	0.0261048
$375$	68.0106	3.51205
$376$	−2.20466	−0.113697
$377$	15.6860	0.807872
$378$	−0.278223	−0.0143103
$379$	−16.5660	−0.850939	−0.425469	−	0.904973i	$-0.639891\pi$
$379$	−16.5660	−0.850939	−0.425469	+	0.904973i	$0.639891\pi$
$380$	−32.2608	−1.65495
$381$	−3.00915	−0.154164
$382$	1.70830	0.0874041
$383$	−25.0198	−1.27845	−0.639226	−	0.769019i	$-0.720745\pi$
$383$	−25.0198	−1.27845	−0.639226	+	0.769019i	$0.720745\pi$
$384$	−4.74526	−0.242156
$385$	−8.82470	−0.449748
$386$	−1.62203	−0.0825594
$387$	0.926534	0.0470984
$388$	10.4712	0.531592
$389$	−32.6696	−1.65641	−0.828207	−	0.560423i	$-0.810639\pi$
$389$	−32.6696	−1.65641	−0.828207	+	0.560423i	$0.810639\pi$
$390$	−1.24983	−0.0632878
$391$	−9.02178	−0.456251
$392$	2.14249	0.108212
$393$	31.1904	1.57335
$394$	−1.34050	−0.0675333
$395$	−29.5165	−1.48513
$396$	1.80443	0.0906763
$397$	−21.9103	−1.09964	−0.549822	−	0.835282i	$-0.685305\pi$
$397$	−21.9103	−1.09964	−0.549822	+	0.835282i	$0.685305\pi$
$398$	0.393992	0.0197490
$399$	4.70467	0.235528
$400$	54.0830	2.70415
$401$	10.2229	0.510508	0.255254	−	0.966874i	$-0.417841\pi$
$401$	10.2229	0.510508	0.255254	+	0.966874i	$0.417841\pi$
$402$	−0.144192	−0.00719162
$403$	5.42099	0.270039
$404$	−19.8045	−0.985309
$405$	−42.4377	−2.10875
$406$	−0.460516	−0.0228550
$407$	28.7642	1.42579
$408$	1.23904	0.0613418
$409$	−16.7739	−0.829417	−0.414709	−	0.909954i	$-0.636117\pi$
$409$	−16.7739	−0.829417	−0.414709	+	0.909954i	$0.636117\pi$
$410$	−1.45457	−0.0718361
$411$	26.8465	1.32424
$412$	−38.3985	−1.89176
$413$	3.11223	0.153143
$414$	0.109445	0.00537894
$415$	−39.5452	−1.94120
$416$	−1.90096	−0.0932023
$417$	37.0140	1.81258
$418$	−0.911708	−0.0445931
$419$	32.5790	1.59159	0.795793	−	0.605569i	$-0.207054\pi$
$419$	32.5790	1.59159	0.795793	+	0.605569i	$0.207054\pi$
$420$	−10.8110	−0.527520
$421$	11.5346	0.562163	0.281082	−	0.959684i	$-0.409307\pi$
$421$	11.5346	0.562163	0.281082	+	0.959684i	$0.409307\pi$
$422$	−0.354066	−0.0172357
$423$	2.05406	0.0998721
$424$	0.0159183	0.000773062 0
$425$	−28.3397	−1.37468
$426$	1.16095	0.0562483
$427$	−6.64487	−0.321568
$428$	15.7073	0.759240
$429$	10.4067	0.502441
$430$	1.07575	0.0518772
$431$	15.2713	0.735590	0.367795	−	0.929907i	$-0.380113\pi$
$431$	15.2713	0.735590	0.367795	+	0.929907i	$0.380113\pi$
$432$	−19.3947	−0.933129
$433$	8.69941	0.418067	0.209034	−	0.977908i	$-0.432968\pi$
$433$	8.69941	0.418067	0.209034	+	0.977908i	$0.432968\pi$
$434$	−0.159151	−0.00763949
$435$	−63.6792	−3.05318
$436$	3.44287	0.164883
$437$	16.2927	0.779384
$438$	2.45639	0.117371
$439$	29.4040	1.40338	0.701689	−	0.712484i	$-0.252430\pi$
$439$	29.4040	1.40338	0.701689	+	0.712484i	$0.252430\pi$
$440$	4.19717	0.200092
$441$	−1.99614	−0.0950543
$442$	0.330160	0.0157041
$443$	−35.7878	−1.70033	−0.850164	−	0.526518i	$-0.823497\pi$
$443$	−35.7878	−1.70033	−0.850164	+	0.526518i	$0.823497\pi$
$444$	35.2384	1.67234
$445$	−10.2201	−0.484481
$446$	1.21787	0.0576679
$447$	15.2336	0.720525
$448$	−5.41274	−0.255728
$449$	−7.50777	−0.354314	−0.177157	−	0.984183i	$-0.556690\pi$
$449$	−7.50777	−0.354314	−0.177157	+	0.984183i	$0.556690\pi$
$450$	0.343796	0.0162067
$451$	12.1114	0.570306
$452$	−27.9912	−1.31660
$453$	−40.0147	−1.88006
$454$	−0.978992	−0.0459464
$455$	−5.77123	−0.270559
$456$	−2.23762	−0.104786
$457$	−31.7902	−1.48708	−0.743540	−	0.668691i	$-0.766855\pi$
$457$	−31.7902	−1.48708	−0.743540	+	0.668691i	$0.766855\pi$
$458$	−0.420683	−0.0196572
$459$	10.1629	0.474364
$460$	−37.4392	−1.74561
$461$	−12.8715	−0.599487	−0.299743	−	0.954020i	$-0.596901\pi$
$461$	−12.8715	−0.599487	−0.299743	+	0.954020i	$0.596901\pi$
$462$	−0.305523	−0.0142142
$463$	−11.8687	−0.551587	−0.275794	−	0.961217i	$-0.588941\pi$
$463$	−11.8687	−0.551587	−0.275794	+	0.961217i	$0.588941\pi$
$464$	−32.1021	−1.49030
$465$	−22.0071	−1.02055
$466$	−1.22800	−0.0568860
$467$	−18.9191	−0.875473	−0.437736	−	0.899103i	$-0.644220\pi$
$467$	−18.9191	−0.875473	−0.437736	+	0.899103i	$0.644220\pi$
$468$	1.18007	0.0545490
$469$	−0.665818	−0.0307446
$470$	2.38486	0.110006
$471$	−0.378535	−0.0174420
$472$	−1.48023	−0.0681329
$473$	−8.95719	−0.411852
$474$	−1.02190	−0.0469374
$475$	51.1795	2.34828
$476$	2.85585	0.130898
$477$	−0.0148310	−0.000679063 0
$478$	2.45620	0.112344
$479$	23.7911	1.08704	0.543522	−	0.839395i	$-0.317091\pi$
$479$	23.7911	1.08704	0.543522	+	0.839395i	$0.317091\pi$
$480$	7.71716	0.352238
$481$	18.8114	0.857725
$482$	0.0822506	0.00374641
$483$	5.45985	0.248432
$484$	4.48136	0.203698
$485$	−22.6925	−1.03041
$486$	−0.260582	−0.0118202
$487$	1.59589	0.0723165	0.0361583	−	0.999346i	$-0.488488\pi$
$487$	1.59589	0.0723165	0.0361583	+	0.999346i	$0.488488\pi$
$488$	3.16041	0.143065
$489$	14.2743	0.645506
$490$	−2.31761	−0.104699
$491$	−31.8604	−1.43784	−0.718920	−	0.695093i	$-0.755363\pi$
$491$	−31.8604	−1.43784	−0.718920	+	0.695093i	$0.755363\pi$
$492$	14.8375	0.668925
$493$	16.8217	0.757610
$494$	−0.596244	−0.0268263
$495$	−3.91047	−0.175763
$496$	−11.0943	−0.498148
$497$	5.36081	0.240465
$498$	−1.36911	−0.0613513
$499$	17.3389	0.776194	0.388097	−	0.921619i	$-0.373133\pi$
$499$	17.3389	0.776194	0.388097	+	0.921619i	$0.373133\pi$
$500$	−74.5561	−3.33425
$501$	−25.2310	−1.12724
$502$	1.07435	0.0479508
$503$	−13.8066	−0.615607	−0.307803	−	0.951450i	$-0.599594\pi$
$503$	−13.8066	−0.615607	−0.307803	+	0.951450i	$0.599594\pi$
$504$	−0.0694076	−0.00309166
$505$	42.9192	1.90988
$506$	−1.05805	−0.0470362
$507$	−16.8313	−0.747506
$508$	3.29876	0.146359
$509$	37.2876	1.65274	0.826372	−	0.563124i	$-0.190401\pi$
$509$	37.2876	1.65274	0.826372	+	0.563124i	$0.190401\pi$
$510$	−1.34032	−0.0593503
$511$	11.3426	0.501768
$512$	6.49133	0.286879
$513$	−18.3535	−0.810326
$514$	0.522974	0.0230674
$515$	83.2152	3.66690
$516$	−10.9733	−0.483071
$517$	−19.8575	−0.873332
$518$	−0.552270	−0.0242653
$519$	35.1830	1.54436
$520$	2.74489	0.120371
$521$	35.4359	1.55248	0.776238	−	0.630439i	$-0.217125\pi$
$521$	35.4359	1.55248	0.776238	+	0.630439i	$0.217125\pi$
$522$	−0.204067	−0.00893179
$523$	−22.2983	−0.975036	−0.487518	−	0.873113i	$-0.662098\pi$
$523$	−22.2983	−0.975036	−0.487518	+	0.873113i	$0.662098\pi$
$524$	−34.1922	−1.49369
$525$	17.1508	0.748522
$526$	0.383443	0.0167189
$527$	5.81345	0.253238
$528$	−21.2978	−0.926866
$529$	−4.09210	−0.177917
$530$	−0.0172194	−0.000747964 0
$531$	1.37912	0.0598485
$532$	−5.15746	−0.223604
$533$	7.92071	0.343084
$534$	−0.353835	−0.0153119
$535$	−34.0400	−1.47168
$536$	0.316674	0.0136782
$537$	−12.7728	−0.551186
$538$	−0.865698	−0.0373229
$539$	19.2975	0.831203
$540$	42.1748	1.81491
$541$	−28.0367	−1.20539	−0.602697	−	0.797970i	$-0.705907\pi$
$541$	−28.0367	−1.20539	−0.602697	+	0.797970i	$0.705907\pi$
$542$	0.848925	0.0364644
$543$	13.1289	0.563416
$544$	−2.03859	−0.0874037
$545$	−7.46119	−0.319602
$546$	−0.199808	−0.00855099
$547$	−13.1556	−0.562491	−0.281245	−	0.959636i	$-0.590747\pi$
$547$	−13.1556	−0.562491	−0.281245	+	0.959636i	$0.590747\pi$
$548$	−29.4303	−1.25720
$549$	−2.94453	−0.125669
$550$	−3.32362	−0.141719
$551$	−30.3787	−1.29418
$552$	−2.59679	−0.110527
$553$	−4.71872	−0.200660
$554$	1.81793	0.0772363
$555$	−76.3668	−3.24159
$556$	−40.5763	−1.72082
$557$	−20.1003	−0.851678	−0.425839	−	0.904799i	$-0.640021\pi$
$557$	−20.1003	−0.851678	−0.425839	+	0.904799i	$0.640021\pi$
$558$	−0.0705243	−0.00298553
$559$	−5.85787	−0.247762
$560$	11.8111	0.499108
$561$	11.1601	0.471181
$562$	0.347757	0.0146693
$563$	−1.97240	−0.0831268	−0.0415634	−	0.999136i	$-0.513234\pi$
$563$	−1.97240	−0.0831268	−0.0415634	+	0.999136i	$0.513234\pi$
$564$	−24.3270	−1.02435
$565$	60.6611	2.55203
$566$	−0.252319	−0.0106058
$567$	−6.78441	−0.284919
$568$	−2.54969	−0.106983
$569$	19.0863	0.800139	0.400070	−	0.916485i	$-0.368986\pi$
$569$	19.0863	0.800139	0.400070	+	0.916485i	$0.368986\pi$
$570$	2.42052	0.101384
$571$	10.1484	0.424697	0.212348	−	0.977194i	$-0.431889\pi$
$571$	10.1484	0.424697	0.212348	+	0.977194i	$0.431889\pi$
$572$	−11.4083	−0.477004
$573$	37.7639	1.57761
$574$	−0.232539	−0.00970597
$575$	59.3946	2.47693
$576$	−2.39854	−0.0999391
$577$	11.2993	0.470395	0.235198	−	0.971948i	$-0.424426\pi$
$577$	11.2993	0.470395	0.235198	+	0.971948i	$0.424426\pi$
$578$	−1.04420	−0.0434329
$579$	−35.8569	−1.49016
$580$	69.8078	2.89861
$581$	−6.32200	−0.262281
$582$	−0.785646	−0.0325661
$583$	0.143377	0.00593807
$584$	−5.39474	−0.223236
$585$	−2.55739	−0.105735
$586$	−1.27237	−0.0525611
$587$	36.1850	1.49352	0.746758	−	0.665095i	$-0.231609\pi$
$587$	36.1850	1.49352	0.746758	+	0.665095i	$0.231609\pi$
$588$	23.6410	0.974938
$589$	−10.4987	−0.432590
$590$	1.60122	0.0659210
$591$	−29.6332	−1.21895
$592$	−38.4983	−1.58227
$593$	−28.2897	−1.16172	−0.580858	−	0.814005i	$-0.697283\pi$
$593$	−28.2897	−1.16172	−0.580858	+	0.814005i	$0.697283\pi$
$594$	1.19188	0.0489035
$595$	−6.18905	−0.253726
$596$	−16.6997	−0.684047
$597$	8.70965	0.356462
$598$	−0.691951	−0.0282960
$599$	−10.9989	−0.449404	−0.224702	−	0.974427i	$-0.572141\pi$
$599$	−10.9989	−0.449404	−0.224702	+	0.974427i	$0.572141\pi$
$600$	−8.15720	−0.333016
$601$	−10.3224	−0.421058	−0.210529	−	0.977588i	$-0.567519\pi$
$601$	−10.3224	−0.421058	−0.210529	+	0.977588i	$0.567519\pi$
$602$	0.171977	0.00700927
$603$	−0.295043	−0.0120151
$604$	43.8658	1.78488
$605$	−9.71176	−0.394839
$606$	1.48592	0.0603614
$607$	−26.4559	−1.07381	−0.536906	−	0.843642i	$-0.680407\pi$
$607$	−26.4559	−1.07381	−0.536906	+	0.843642i	$0.680407\pi$
$608$	3.68154	0.149306
$609$	−10.1802	−0.412524
$610$	−3.41873	−0.138420
$611$	−12.9865	−0.525378
$612$	1.26551	0.0511552
$613$	33.8484	1.36712	0.683561	−	0.729893i	$-0.260430\pi$
$613$	33.8484	1.36712	0.683561	+	0.729893i	$0.260430\pi$
$614$	−1.66485	−0.0671879
$615$	−32.1550	−1.29661
$616$	0.670992	0.0270350
$617$	−0.659865	−0.0265651	−0.0132826	−	0.999912i	$-0.504228\pi$
$617$	−0.659865	−0.0265651	−0.0132826	+	0.999912i	$0.504228\pi$
$618$	2.88103	0.115892
$619$	−34.8866	−1.40221	−0.701106	−	0.713057i	$-0.747310\pi$
$619$	−34.8866	−1.40221	−0.701106	+	0.713057i	$0.747310\pi$
$620$	24.1251	0.968886
$621$	−21.2995	−0.854720
$622$	0.122910	0.00492826
$623$	−1.63387	−0.0654595
$624$	−13.9284	−0.557584
$625$	93.2779	3.73111
$626$	−1.78048	−0.0711622
$627$	−20.1544	−0.804888
$628$	0.414966	0.0165589
$629$	20.1733	0.804361
$630$	0.0750807	0.00299129
$631$	−6.39474	−0.254571	−0.127285	−	0.991866i	$-0.540626\pi$
$631$	−6.39474	−0.254571	−0.127285	+	0.991866i	$0.540626\pi$
$632$	2.24430	0.0892735
$633$	−7.82705	−0.311097
$634$	2.37975	0.0945120
$635$	−7.14890	−0.283695
$636$	0.175648	0.00696491
$637$	12.6203	0.500035
$638$	1.97280	0.0781041
$639$	2.37553	0.0939743
$640$	−11.2734	−0.445620
$641$	16.9466	0.669352	0.334676	−	0.942333i	$-0.391373\pi$
$641$	16.9466	0.669352	0.334676	+	0.942333i	$0.391373\pi$
$642$	−1.17851	−0.0465121
$643$	14.3993	0.567852	0.283926	−	0.958846i	$-0.408363\pi$
$643$	14.3993	0.567852	0.283926	+	0.958846i	$0.408363\pi$
$644$	−5.98531	−0.235854
$645$	23.7807	0.936363
$646$	−0.639411	−0.0251573
$647$	4.38744	0.172488	0.0862441	−	0.996274i	$-0.472514\pi$
$647$	4.38744	0.172488	0.0862441	+	0.996274i	$0.472514\pi$
$648$	3.22678	0.126760
$649$	−13.3325	−0.523346
$650$	−2.17360	−0.0852555
$651$	−3.51822	−0.137890
$652$	−15.6481	−0.612826
$653$	−4.56970	−0.178826	−0.0894132	−	0.995995i	$-0.528499\pi$
$653$	−4.56970	−0.178826	−0.0894132	+	0.995995i	$0.528499\pi$
$654$	−0.258317	−0.0101010
$655$	74.0994	2.89530
$656$	−16.2101	−0.632897
$657$	5.02624	0.196092
$658$	0.381262	0.0148631
$659$	−13.6506	−0.531751	−0.265875	−	0.964007i	$-0.585661\pi$
$659$	−13.6506	−0.531751	−0.265875	+	0.964007i	$0.585661\pi$
$660$	46.3131	1.80273
$661$	32.4151	1.26080	0.630401	−	0.776270i	$-0.282891\pi$
$661$	32.4151	1.26080	0.630401	+	0.776270i	$0.282891\pi$
$662$	−2.26766	−0.0881350
$663$	7.29856	0.283453
$664$	3.00685	0.116688
$665$	11.1770	0.433424
$666$	−0.244726	−0.00948295
$667$	−35.2550	−1.36508
$668$	27.6592	1.07017
$669$	26.9225	1.04088
$670$	−0.342558	−0.0132342
$671$	28.4660	1.09892
$672$	1.23372	0.0475919
$673$	0.237992	0.00917391	0.00458696	−	0.999989i	$-0.498540\pi$
$673$	0.237992	0.00917391	0.00458696	+	0.999989i	$0.498540\pi$
$674$	−0.678938	−0.0261517
$675$	−66.9073	−2.57526
$676$	18.4512	0.709662
$677$	−30.9534	−1.18964	−0.594818	−	0.803860i	$-0.702776\pi$
$677$	−30.9534	−1.18964	−0.594818	+	0.803860i	$0.702776\pi$
$678$	2.10017	0.0806566
$679$	−3.62780	−0.139222
$680$	2.94361	0.112882
$681$	−21.6417	−0.829313
$682$	0.681788	0.0261070
$683$	−28.5801	−1.09359	−0.546794	−	0.837267i	$-0.684152\pi$
$683$	−28.5801	−1.09359	−0.546794	+	0.837267i	$0.684152\pi$
$684$	−2.28542	−0.0873850
$685$	63.7796	2.43689
$686$	−0.768108	−0.0293265
$687$	−9.29968	−0.354805
$688$	11.9884	0.457053
$689$	0.0937666	0.00357222
$690$	2.80905	0.106939
$691$	−6.89241	−0.262200	−0.131100	−	0.991369i	$-0.541851\pi$
$691$	−6.89241	−0.262200	−0.131100	+	0.991369i	$0.541851\pi$
$692$	−38.5691	−1.46618
$693$	−0.625158	−0.0237478
$694$	1.74386	0.0661959
$695$	87.9347	3.33555
$696$	4.84189	0.183531
$697$	8.49415	0.321739
$698$	1.75405	0.0663919
$699$	−27.1464	−1.02677
$700$	−18.8014	−0.710627
$701$	−29.3972	−1.11032	−0.555158	−	0.831745i	$-0.687342\pi$
$701$	−29.3972	−1.11032	−0.555158	+	0.831745i	$0.687342\pi$
$702$	0.779474	0.0294194
$703$	−36.4314	−1.37404
$704$	23.1877	0.873918
$705$	52.7202	1.98556
$706$	0.230453	0.00867321
$707$	6.86138	0.258049
$708$	−16.3333	−0.613845
$709$	−10.8690	−0.408195	−0.204098	−	0.978951i	$-0.565426\pi$
$709$	−10.8690	−0.408195	−0.204098	+	0.978951i	$0.565426\pi$
$710$	2.75809	0.103509
$711$	−2.09100	−0.0784186
$712$	0.777094	0.0291228
$713$	−12.1839	−0.456290
$714$	−0.214273	−0.00801898
$715$	24.7234	0.924602
$716$	14.0021	0.523281
$717$	54.2972	2.02776
$718$	0.380646	0.0142056
$719$	−30.8283	−1.14970	−0.574850	−	0.818259i	$-0.694940\pi$
$719$	−30.8283	−1.14970	−0.574850	+	0.818259i	$0.694940\pi$
$720$	5.23381	0.195053
$721$	13.3034	0.495445
$722$	−0.408032	−0.0151854
$723$	1.81824	0.0676212
$724$	−14.3925	−0.534892
$725$	−110.745	−4.11297
$726$	−0.336235	−0.0124788
$727$	28.0322	1.03966	0.519828	−	0.854271i	$-0.325996\pi$
$727$	28.0322	1.03966	0.519828	+	0.854271i	$0.325996\pi$
$728$	0.438819	0.0162637
$729$	23.7127	0.878248
$730$	5.83569	0.215989
$731$	−6.28197	−0.232347
$732$	34.8731	1.28895
$733$	25.8442	0.954578	0.477289	−	0.878746i	$-0.341619\pi$
$733$	25.8442	0.954578	0.477289	+	0.878746i	$0.341619\pi$
$734$	−0.00873360	−0.000322363 0
$735$	−51.2335	−1.88977
$736$	4.27248	0.157486
$737$	2.85230	0.105066
$738$	−0.103044	−0.00379312
$739$	−43.0752	−1.58455	−0.792273	−	0.610166i	$-0.791103\pi$
$739$	−43.0752	−1.58455	−0.792273	+	0.610166i	$0.791103\pi$
$740$	83.7164	3.07748
$741$	−13.1807	−0.484204
$742$	−0.00275283	−0.000101059 0
$743$	13.1212	0.481372	0.240686	−	0.970603i	$-0.422628\pi$
$743$	13.1212	0.481372	0.240686	+	0.970603i	$0.422628\pi$
$744$	1.67332	0.0613470
$745$	36.1907	1.32593
$746$	−1.37114	−0.0502012
$747$	−2.80146	−0.102500
$748$	−12.2342	−0.447327
$749$	−5.44189	−0.198842
$750$	5.59391	0.204261
$751$	33.6870	1.22926	0.614629	−	0.788817i	$-0.289306\pi$
$751$	33.6870	1.22926	0.614629	+	0.788817i	$0.289306\pi$
$752$	26.5775	0.969180
$753$	23.7498	0.865492
$754$	1.29019	0.0469858
$755$	−95.0637	−3.45972
$756$	6.74238	0.245218
$757$	−46.0911	−1.67521	−0.837604	−	0.546278i	$-0.816044\pi$
$757$	−46.0911	−1.67521	−0.837604	+	0.546278i	$0.816044\pi$
$758$	−1.36256	−0.0494905
$759$	−23.3895	−0.848984
$760$	−5.31595	−0.192830
$761$	14.2727	0.517387	0.258693	−	0.965960i	$-0.416708\pi$
$761$	14.2727	0.517387	0.258693	+	0.965960i	$0.416708\pi$
$762$	−0.247505	−0.00896615
$763$	−1.19280	−0.0431823
$764$	−41.3983	−1.49774
$765$	−2.74254	−0.0991568
$766$	−2.05789	−0.0743547
$767$	−8.71925	−0.314834
$768$	28.1128	1.01443
$769$	13.0154	0.469349	0.234674	−	0.972074i	$-0.424598\pi$
$769$	13.0154	0.469349	0.234674	+	0.972074i	$0.424598\pi$
$770$	−0.725837	−0.0261573
$771$	11.5609	0.416357
$772$	39.3079	1.41472
$773$	−29.9438	−1.07700	−0.538502	−	0.842624i	$-0.681010\pi$
$773$	−29.9438	−1.07700	−0.538502	+	0.842624i	$0.681010\pi$
$774$	0.0762080	0.00273924
$775$	−38.2727	−1.37480
$776$	1.72544	0.0619397
$777$	−12.2086	−0.437980
$778$	−2.68709	−0.0963369
$779$	−15.3398	−0.549606
$780$	30.2881	1.08449
$781$	−22.9652	−0.821759
$782$	−0.742046	−0.0265355
$783$	39.7143	1.41927
$784$	−25.8280	−0.922428
$785$	−0.899291	−0.0320971
$786$	2.56542	0.0915057
$787$	13.7932	0.491676	0.245838	−	0.969311i	$-0.420937\pi$
$787$	13.7932	0.491676	0.245838	+	0.969311i	$0.420937\pi$
$788$	32.4852	1.15724
$789$	8.47646	0.301770
$790$	−2.42774	−0.0863753
$791$	9.69774	0.344812
$792$	0.297335	0.0105654
$793$	18.6163	0.661086
$794$	−1.80213	−0.0639553
$795$	−0.380655	−0.0135005
$796$	−9.54788	−0.338416
$797$	18.4152	0.652300	0.326150	−	0.945318i	$-0.394249\pi$
$797$	18.4152	0.652300	0.326150	+	0.945318i	$0.394249\pi$
$798$	0.386962	0.0136983
$799$	−13.9267	−0.492691
$800$	13.4210	0.474503
$801$	−0.724013	−0.0255817
$802$	0.840841	0.0296911
$803$	−48.5907	−1.71473
$804$	3.49429	0.123234
$805$	12.9710	0.457169
$806$	0.445879	0.0157054
$807$	−19.1372	−0.673663
$808$	−3.26339	−0.114806
$809$	−14.7007	−0.516849	−0.258425	−	0.966031i	$-0.583203\pi$
$809$	−14.7007	−0.516849	−0.258425	+	0.966031i	$0.583203\pi$
$810$	−3.49053	−0.122645
$811$	−46.3555	−1.62776	−0.813882	−	0.581031i	$-0.802650\pi$
$811$	−46.3555	−1.62776	−0.813882	+	0.581031i	$0.802650\pi$
$812$	11.1600	0.391639
$813$	18.7665	0.658168
$814$	2.36587	0.0829238
$815$	33.9117	1.18787
$816$	−14.9368	−0.522893
$817$	11.3448	0.396903
$818$	−1.37967	−0.0482389
$819$	−0.408844	−0.0142862
$820$	35.2496	1.23097
$821$	39.2626	1.37027	0.685137	−	0.728414i	$-0.259742\pi$
$821$	39.2626	1.37027	0.685137	+	0.728414i	$0.259742\pi$
$822$	2.20814	0.0770177
$823$	−29.0804	−1.01368	−0.506839	−	0.862041i	$-0.669186\pi$
$823$	−29.0804	−1.01368	−0.506839	+	0.862041i	$0.669186\pi$
$824$	−6.32732	−0.220423
$825$	−73.4724	−2.55798
$826$	0.255982	0.00890677
$827$	30.7270	1.06848	0.534242	−	0.845332i	$-0.320597\pi$
$827$	30.7270	1.06848	0.534242	+	0.845332i	$0.320597\pi$
$828$	−2.65226	−0.0921725
$829$	−16.4599	−0.571675	−0.285837	−	0.958278i	$-0.592272\pi$
$829$	−16.4599	−0.571675	−0.285837	+	0.958278i	$0.592272\pi$
$830$	−3.25262	−0.112900
$831$	40.1873	1.39408
$832$	15.1644	0.525731
$833$	13.5340	0.468925
$834$	3.04442	0.105420
$835$	−59.9416	−2.07436
$836$	22.0941	0.764139
$837$	13.7250	0.474405
$838$	2.67964	0.0925665
$839$	43.2285	1.49241	0.746206	−	0.665715i	$-0.231873\pi$
$839$	43.2285	1.49241	0.746206	+	0.665715i	$0.231873\pi$
$840$	−1.78143	−0.0614652
$841$	36.7351	1.26673
$842$	0.948729	0.0326954
$843$	7.68758	0.264774
$844$	8.58034	0.295347
$845$	−39.9865	−1.37558
$846$	0.168948	0.00580855
$847$	−1.55260	−0.0533478
$848$	−0.191897	−0.00658978
$849$	−5.57781	−0.191430
$850$	−2.33096	−0.0799513
$851$	−42.2793	−1.44931
$852$	−28.1342	−0.963861
$853$	8.36996	0.286582	0.143291	−	0.989681i	$-0.454232\pi$
$853$	8.36996	0.286582	0.143291	+	0.989681i	$0.454232\pi$
$854$	−0.546544	−0.0187024
$855$	4.95283	0.169383
$856$	2.58825	0.0884646
$857$	18.3641	0.627305	0.313653	−	0.949538i	$-0.398447\pi$
$857$	18.3641	0.627305	0.313653	+	0.949538i	$0.398447\pi$
$858$	0.855958	0.0292219
$859$	2.47499	0.0844457	0.0422228	−	0.999108i	$-0.486556\pi$
$859$	2.47499	0.0844457	0.0422228	+	0.999108i	$0.486556\pi$
$860$	−26.0694	−0.888958
$861$	−5.14053	−0.175189
$862$	1.25607	0.0427819
$863$	−10.0917	−0.343525	−0.171762	−	0.985138i	$-0.554946\pi$
$863$	−10.0917	−0.343525	−0.171762	+	0.985138i	$0.554946\pi$
$864$	−4.81290	−0.163738
$865$	83.5849	2.84197
$866$	0.715532	0.0243148
$867$	−23.0832	−0.783946
$868$	3.85682	0.130909
$869$	20.2146	0.685732
$870$	−5.23765	−0.177573
$871$	1.86536	0.0632055
$872$	0.567316	0.0192118
$873$	−1.60758	−0.0544083
$874$	1.34008	0.0453289
$875$	25.8304	0.873227
$876$	−59.5274	−2.01125
$877$	53.6453	1.81147	0.905736	−	0.423843i	$-0.139319\pi$
$877$	53.6453	1.81147	0.905736	+	0.423843i	$0.139319\pi$
$878$	2.41850	0.0816203
$879$	−28.1272	−0.948708
$880$	−50.5974	−1.70564
$881$	30.6985	1.03426	0.517130	−	0.855907i	$-0.327001\pi$
$881$	30.6985	1.03426	0.517130	+	0.855907i	$0.327001\pi$
$882$	−0.164184	−0.00552835
$883$	−21.8831	−0.736424	−0.368212	−	0.929742i	$-0.620030\pi$
$883$	−21.8831	−0.736424	−0.368212	+	0.929742i	$0.620030\pi$
$884$	−8.00099	−0.269102
$885$	35.3967	1.18985
$886$	−2.94356	−0.0988910
$887$	−23.3921	−0.785431	−0.392715	−	0.919660i	$-0.628464\pi$
$887$	−23.3921	−0.785431	−0.392715	+	0.919660i	$0.628464\pi$
$888$	5.80660	0.194857
$889$	−1.14288	−0.0383308
$890$	−0.840612	−0.0281774
$891$	29.0638	0.973673
$892$	−29.5135	−0.988186
$893$	25.1506	0.841633
$894$	1.25297	0.0419057
$895$	−30.3445	−1.01430
$896$	−1.80225	−0.0602089
$897$	−15.2964	−0.510731
$898$	−0.617518	−0.0206069
$899$	22.7176	0.757674
$900$	−8.33144	−0.277715
$901$	0.100555	0.00334997
$902$	0.996173	0.0331689
$903$	3.80175	0.126514
$904$	−4.61240	−0.153406
$905$	31.1906	1.03681
$906$	−3.29124	−0.109344
$907$	−2.98723	−0.0991893	−0.0495947	−	0.998769i	$-0.515793\pi$
$907$	−2.98723	−0.0991893	−0.0495947	+	0.998769i	$0.515793\pi$
$908$	23.7246	0.787328
$909$	3.04047	0.100846
$910$	−0.474687	−0.0157357
$911$	42.1883	1.39776	0.698880	−	0.715239i	$-0.253682\pi$
$911$	42.1883	1.39776	0.698880	+	0.715239i	$0.253682\pi$
$912$	26.9748	0.893224
$913$	27.0828	0.896311
$914$	−2.61476	−0.0864885
$915$	−75.5750	−2.49843
$916$	10.1947	0.336842
$917$	11.8461	0.391192
$918$	0.835906	0.0275890
$919$	−53.2428	−1.75632	−0.878160	−	0.478367i	$-0.841229\pi$
$919$	−53.2428	−1.75632	−0.878160	+	0.478367i	$0.841229\pi$
$920$	−6.16924	−0.203394
$921$	−36.8035	−1.21272
$922$	−1.05869	−0.0348661
$923$	−15.0189	−0.494353
$924$	7.40396	0.243572
$925$	−132.810	−4.36677
$926$	−0.976211	−0.0320803
$927$	5.89511	0.193621
$928$	−7.96631	−0.261507
$929$	−27.2213	−0.893103	−0.446552	−	0.894758i	$-0.647348\pi$
$929$	−27.2213	−0.893103	−0.446552	+	0.894758i	$0.647348\pi$
$930$	−1.81009	−0.0593553
$931$	−24.4414	−0.801033
$932$	29.7590	0.974788
$933$	2.71708	0.0889531
$934$	−1.55611	−0.0509174
$935$	26.5133	0.867077
$936$	0.194453	0.00635590
$937$	7.54293	0.246417	0.123208	−	0.992381i	$-0.460682\pi$
$937$	7.54293	0.246417	0.123208	+	0.992381i	$0.460682\pi$
$938$	−0.0547639	−0.00178811
$939$	−39.3595	−1.28445
$940$	−57.7940	−1.88503
$941$	35.4553	1.15581	0.577905	−	0.816104i	$-0.303870\pi$
$941$	35.4553	1.15581	0.577905	+	0.816104i	$0.303870\pi$
$942$	−0.0311347	−0.00101442
$943$	−17.8021	−0.579716
$944$	17.8443	0.580783
$945$	−14.6117	−0.475319
$946$	−0.736734	−0.0239533
$947$	33.0630	1.07440	0.537202	−	0.843454i	$-0.319481\pi$
$947$	33.0630	1.07440	0.537202	+	0.843454i	$0.319481\pi$
$948$	24.7644	0.804311
$949$	−31.7776	−1.03155
$950$	4.20954	0.136576
$951$	52.6071	1.70590
$952$	0.470588	0.0152518
$953$	−5.14501	−0.166663	−0.0833316	−	0.996522i	$-0.526556\pi$
$953$	−5.14501	−0.166663	−0.0833316	+	0.996522i	$0.526556\pi$
$954$	−0.00121986	−3.94943e−5 0
$955$	89.7162	2.90315
$956$	−59.5228	−1.92511
$957$	43.6111	1.40975
$958$	1.95683	0.0632223
$959$	10.1963	0.329255
$960$	−61.5615	−1.98689
$961$	−23.1490	−0.746741
$962$	1.54725	0.0498852
$963$	−2.41145	−0.0777080
$964$	−1.99323	−0.0641978
$965$	−85.1859	−2.74223
$966$	0.449076	0.0144488
$967$	2.82789	0.0909390	0.0454695	−	0.998966i	$-0.485522\pi$
$967$	2.82789	0.0909390	0.0454695	+	0.998966i	$0.485522\pi$
$968$	0.738440	0.0237344
$969$	−14.1349	−0.454079
$970$	−1.86647	−0.0599288
$971$	−43.0152	−1.38042	−0.690211	−	0.723608i	$-0.742482\pi$
$971$	−43.0152	−1.38042	−0.690211	+	0.723608i	$0.742482\pi$
$972$	6.31486	0.202549
$973$	14.0579	0.450676
$974$	0.131263	0.00420592
$975$	−48.0499	−1.53883
$976$	−38.0991	−1.21952
$977$	−5.45876	−0.174641	−0.0873207	−	0.996180i	$-0.527830\pi$
$977$	−5.45876	−0.174641	−0.0873207	+	0.996180i	$0.527830\pi$
$978$	1.17407	0.0375426
$979$	6.99933	0.223700
$980$	56.1643	1.79410
$981$	−0.528564	−0.0168758
$982$	−2.62054	−0.0836246
$983$	16.8518	0.537489	0.268745	−	0.963211i	$-0.413391\pi$
$983$	16.8518	0.537489	0.268745	+	0.963211i	$0.413391\pi$
$984$	2.44492	0.0779413
$985$	−70.4002	−2.24314
$986$	1.38359	0.0440625
$987$	8.42824	0.268274
$988$	14.4492	0.459690
$989$	13.1658	0.418648
$990$	−0.321639	−0.0102223
$991$	57.3144	1.82065	0.910326	−	0.413892i	$-0.135831\pi$
$991$	57.3144	1.82065	0.910326	+	0.413892i	$0.135831\pi$
$992$	−2.75310	−0.0874111
$993$	−50.1292	−1.59080
$994$	0.440929	0.0139854
$995$	20.6916	0.655969
$996$	33.1786	1.05130
$997$	−39.3642	−1.24668	−0.623339	−	0.781952i	$-0.714224\pi$
$997$	−39.3642	−1.24668	−0.623339	+	0.781952i	$0.714224\pi$
$998$	1.42613	0.0451434
$999$	47.6271	1.50685

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	241.2.a.b.1.6	✓	12
3.2	odd	2		2169.2.a.h.1.7		12
4.3	odd	2		3856.2.a.n.1.4		12
5.4	even	2		6025.2.a.h.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.b.1.6	✓	12	1.1	even	1	trivial
2169.2.a.h.1.7		12	3.2	odd	2
3856.2.a.n.1.4		12	4.3	odd	2
6025.2.a.h.1.7		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)

\(f(q)\)	\(=\)	\(q+0.0822506 q^{2} +1.81824 q^{3} -1.99323 q^{4} +4.31963 q^{5} +0.149552 q^{6} +0.690569 q^{7} -0.328446 q^{8} +0.306010 q^{9} +O(q^{10})\)	\(q+0.0822506 q^{2} +1.81824 q^{3} -1.99323 q^{4} +4.31963 q^{5} +0.149552 q^{6} +0.690569 q^{7} -0.328446 q^{8} +0.306010 q^{9} +0.355292 q^{10} -2.95833 q^{11} -3.62419 q^{12} -1.93470 q^{13} +0.0567997 q^{14} +7.85414 q^{15} +3.95945 q^{16} -2.07477 q^{17} +0.0251695 q^{18} +3.74689 q^{19} -8.61004 q^{20} +1.25562 q^{21} -0.243324 q^{22} +4.34832 q^{23} -0.597195 q^{24} +13.6592 q^{25} -0.159131 q^{26} -4.89833 q^{27} -1.37647 q^{28} -8.10772 q^{29} +0.646008 q^{30} -2.80197 q^{31} +0.982559 q^{32} -5.37896 q^{33} -0.170651 q^{34} +2.98300 q^{35} -0.609951 q^{36} -9.72312 q^{37} +0.308183 q^{38} -3.51777 q^{39} -1.41876 q^{40} -4.09401 q^{41} +0.103276 q^{42} +3.02779 q^{43} +5.89665 q^{44} +1.32185 q^{45} +0.357652 q^{46} +6.71240 q^{47} +7.19925 q^{48} -6.52312 q^{49} +1.12348 q^{50} -3.77244 q^{51} +3.85632 q^{52} -0.0484656 q^{53} -0.402890 q^{54} -12.7789 q^{55} -0.226814 q^{56} +6.81275 q^{57} -0.666864 q^{58} +4.50676 q^{59} -15.6551 q^{60} -9.62232 q^{61} -0.230464 q^{62} +0.211321 q^{63} -7.83809 q^{64} -8.35721 q^{65} -0.442423 q^{66} -0.964160 q^{67} +4.13551 q^{68} +7.90631 q^{69} +0.245353 q^{70} +7.76289 q^{71} -0.100508 q^{72} +16.4250 q^{73} -0.799732 q^{74} +24.8358 q^{75} -7.46842 q^{76} -2.04293 q^{77} -0.289338 q^{78} -6.83310 q^{79} +17.1034 q^{80} -9.82439 q^{81} -0.336735 q^{82} -9.15477 q^{83} -2.50275 q^{84} -8.96225 q^{85} +0.249037 q^{86} -14.7418 q^{87} +0.971651 q^{88} -2.36597 q^{89} +0.108723 q^{90} -1.33605 q^{91} -8.66723 q^{92} -5.09467 q^{93} +0.552099 q^{94} +16.1852 q^{95} +1.78653 q^{96} -5.25335 q^{97} -0.536530 q^{98} -0.905280 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) \) 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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