LMFDB - Embedded newform 5239.2.a.v.1.44

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5239,2,Mod(1,5239)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5239, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5239.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5239 = 13^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5239.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:	$41.8336256189$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.44
Character	$\chi$	$=$	5239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.12031 q^{2} -3.21196 q^{3} +2.49571 q^{4} +1.10938 q^{5} -6.81034 q^{6} -3.09903 q^{7} +1.05106 q^{8} +7.31667 q^{9} +O(q^{10})$	\(q+2.12031 q^{2} -3.21196 q^{3} +2.49571 q^{4} +1.10938 q^{5} -6.81034 q^{6} -3.09903 q^{7} +1.05106 q^{8} +7.31667 q^{9} +2.35222 q^{10} +3.71202 q^{11} -8.01612 q^{12} -6.57090 q^{14} -3.56327 q^{15} -2.76284 q^{16} +2.35444 q^{17} +15.5136 q^{18} +8.07407 q^{19} +2.76869 q^{20} +9.95394 q^{21} +7.87063 q^{22} -6.81650 q^{23} -3.37597 q^{24} -3.76928 q^{25} -13.8650 q^{27} -7.73428 q^{28} +2.35340 q^{29} -7.55525 q^{30} +1.00000 q^{31} -7.96021 q^{32} -11.9229 q^{33} +4.99215 q^{34} -3.43799 q^{35} +18.2603 q^{36} +5.91652 q^{37} +17.1195 q^{38} +1.16603 q^{40} -4.45809 q^{41} +21.1054 q^{42} -7.80402 q^{43} +9.26414 q^{44} +8.11695 q^{45} -14.4531 q^{46} -4.86732 q^{47} +8.87414 q^{48} +2.60397 q^{49} -7.99204 q^{50} -7.56237 q^{51} +3.61596 q^{53} -29.3980 q^{54} +4.11803 q^{55} -3.25728 q^{56} -25.9336 q^{57} +4.98994 q^{58} +3.22596 q^{59} -8.89291 q^{60} +1.59654 q^{61} +2.12031 q^{62} -22.6746 q^{63} -11.3524 q^{64} -25.2801 q^{66} +12.6119 q^{67} +5.87601 q^{68} +21.8943 q^{69} -7.28961 q^{70} +11.1918 q^{71} +7.69029 q^{72} -10.5849 q^{73} +12.5449 q^{74} +12.1068 q^{75} +20.1506 q^{76} -11.5037 q^{77} +11.6075 q^{79} -3.06504 q^{80} +22.5837 q^{81} -9.45252 q^{82} +2.18227 q^{83} +24.8422 q^{84} +2.61197 q^{85} -16.5469 q^{86} -7.55902 q^{87} +3.90157 q^{88} +6.95843 q^{89} +17.2105 q^{90} -17.0120 q^{92} -3.21196 q^{93} -10.3202 q^{94} +8.95720 q^{95} +25.5679 q^{96} +18.6112 q^{97} +5.52122 q^{98} +27.1596 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 2 q^{2} + 7 q^{3} + 64 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 6 q^{8} + 95 q^{9}+O(q^{10}) $ 54 * q + 2 * q^2 + 7 * q^3 + 64 * q^4 + 5 * q^5 - 3 * q^6 + 5 * q^7 + 6 * q^8 + 95 * q^9	\( 54 q + 2 q^{2} + 7 q^{3} + 64 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 6 q^{8} + 95 q^{9} - 6 q^{10} - 7 q^{11} + 5 q^{12} + 38 q^{14} + 4 q^{15} + 76 q^{16} + 62 q^{17} - 9 q^{18} + 8 q^{19} + 16 q^{20} - 6 q^{21} + 15 q^{22} + 38 q^{23} - 99 q^{24} + 87 q^{25} + 25 q^{27} + 19 q^{28} + 95 q^{29} + 41 q^{30} + 54 q^{31} + 9 q^{32} + 12 q^{33} + 7 q^{34} + 53 q^{35} + 97 q^{36} - 24 q^{37} - 16 q^{38} - 28 q^{40} + 22 q^{41} + 11 q^{42} + 11 q^{43} - 24 q^{44} + 8 q^{45} + 9 q^{46} + 45 q^{47} + 2 q^{48} + 105 q^{49} + 6 q^{50} + 58 q^{51} + 56 q^{53} + 50 q^{54} + q^{55} + 91 q^{56} - 51 q^{57} + 25 q^{58} + 36 q^{59} + 100 q^{60} + 48 q^{61} + 2 q^{62} - 56 q^{63} + 90 q^{64} - 24 q^{66} + 26 q^{67} + 140 q^{68} + 47 q^{69} - 24 q^{70} + 40 q^{71} + 7 q^{72} + 9 q^{73} + 114 q^{74} + 18 q^{75} - 67 q^{76} + 65 q^{77} + 33 q^{79} + 53 q^{80} + 210 q^{81} - 6 q^{82} - 41 q^{83} - 37 q^{84} + 37 q^{85} - 42 q^{86} - 16 q^{87} - 22 q^{88} - 24 q^{89} - 40 q^{90} + 87 q^{92} + 7 q^{93} - 4 q^{94} + 61 q^{95} - 200 q^{96} + 28 q^{97} + 68 q^{98} + 39 q^{99}+O(q^{100}) \) 54 * q + 2 * q^2 + 7 * q^3 + 64 * q^4 + 5 * q^5 - 3 * q^6 + 5 * q^7 + 6 * q^8 + 95 * q^9 - 6 * q^10 - 7 * q^11 + 5 * q^12 + 38 * q^14 + 4 * q^15 + 76 * q^16 + 62 * q^17 - 9 * q^18 + 8 * q^19 + 16 * q^20 - 6 * q^21 + 15 * q^22 + 38 * q^23 - 99 * q^24 + 87 * q^25 + 25 * q^27 + 19 * q^28 + 95 * q^29 + 41 * q^30 + 54 * q^31 + 9 * q^32 + 12 * q^33 + 7 * q^34 + 53 * q^35 + 97 * q^36 - 24 * q^37 - 16 * q^38 - 28 * q^40 + 22 * q^41 + 11 * q^42 + 11 * q^43 - 24 * q^44 + 8 * q^45 + 9 * q^46 + 45 * q^47 + 2 * q^48 + 105 * q^49 + 6 * q^50 + 58 * q^51 + 56 * q^53 + 50 * q^54 + q^55 + 91 * q^56 - 51 * q^57 + 25 * q^58 + 36 * q^59 + 100 * q^60 + 48 * q^61 + 2 * q^62 - 56 * q^63 + 90 * q^64 - 24 * q^66 + 26 * q^67 + 140 * q^68 + 47 * q^69 - 24 * q^70 + 40 * q^71 + 7 * q^72 + 9 * q^73 + 114 * q^74 + 18 * q^75 - 67 * q^76 + 65 * q^77 + 33 * q^79 + 53 * q^80 + 210 * q^81 - 6 * q^82 - 41 * q^83 - 37 * q^84 + 37 * q^85 - 42 * q^86 - 16 * q^87 - 22 * q^88 - 24 * q^89 - 40 * q^90 + 87 * q^92 + 7 * q^93 - 4 * q^94 + 61 * q^95 - 200 * q^96 + 28 * q^97 + 68 * q^98 + 39 * 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 $

$2$	2.12031	1.49929	0.749643	−	0.661843i	$-0.230225\pi$
$2$	2.12031	1.49929	0.749643	+	0.661843i	$0.230225\pi$
$3$	−3.21196	−1.85442	−0.927212	−	0.374536i	$-0.877802\pi$
$3$	−3.21196	−1.85442	−0.927212	+	0.374536i	$0.877802\pi$
$4$	2.49571	1.24786
$5$	1.10938	0.496129	0.248064	−	0.968744i	$-0.420206\pi$
$5$	1.10938	0.496129	0.248064	+	0.968744i	$0.420206\pi$
$6$	−6.81034	−2.78031
$7$	−3.09903	−1.17132	−0.585661	−	0.810556i	$-0.699165\pi$
$7$	−3.09903	−1.17132	−0.585661	+	0.810556i	$0.699165\pi$
$8$	1.05106	0.371607
$9$	7.31667	2.43889
$10$	2.35222	0.743839
$11$	3.71202	1.11922	0.559608	−	0.828757i	$-0.310952\pi$
$11$	3.71202	1.11922	0.559608	+	0.828757i	$0.310952\pi$
$12$	−8.01612	−2.31406
$13$	0	0
$13$	0	0
$14$	−6.57090	−1.75615
$15$	−3.56327	−0.920034
$16$	−2.76284	−0.690711
$17$	2.35444	0.571036	0.285518	−	0.958373i	$-0.407834\pi$
$17$	2.35444	0.571036	0.285518	+	0.958373i	$0.407834\pi$
$18$	15.5136	3.65659
$19$	8.07407	1.85232	0.926160	−	0.377131i	$-0.123089\pi$
$19$	8.07407	1.85232	0.926160	+	0.377131i	$0.123089\pi$
$20$	2.76869	0.619098
$21$	9.95394	2.17213
$22$	7.87063	1.67802
$23$	−6.81650	−1.42134	−0.710669	−	0.703526i	$-0.751608\pi$
$23$	−6.81650	−1.42134	−0.710669	+	0.703526i	$0.751608\pi$
$24$	−3.37597	−0.689117
$25$	−3.76928	−0.753856
$26$	0	0
$27$	−13.8650	−2.66831
$28$	−7.73428	−1.46164
$29$	2.35340	0.437015	0.218508	−	0.975835i	$-0.429881\pi$
$29$	2.35340	0.437015	0.218508	+	0.975835i	$0.429881\pi$
$30$	−7.55525	−1.37939
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−7.96021	−1.40718
$33$	−11.9229	−2.07550
$34$	4.99215	0.856146
$35$	−3.43799	−0.581127
$36$	18.2603	3.04338
$37$	5.91652	0.972671	0.486335	−	0.873772i	$-0.338333\pi$
$37$	5.91652	0.972671	0.486335	+	0.873772i	$0.338333\pi$
$38$	17.1195	2.77716
$39$	0	0
$40$	1.16603	0.184365
$41$	−4.45809	−0.696236	−0.348118	−	0.937451i	$-0.613179\pi$
$41$	−4.45809	−0.696236	−0.348118	+	0.937451i	$0.613179\pi$
$42$	21.1054	3.25664
$43$	−7.80402	−1.19010	−0.595051	−	0.803688i	$-0.702868\pi$
$43$	−7.80402	−1.19010	−0.595051	+	0.803688i	$0.702868\pi$
$44$	9.26414	1.39662
$45$	8.11695	1.21000
$46$	−14.4531	−2.13099
$47$	−4.86732	−0.709972	−0.354986	−	0.934872i	$-0.615514\pi$
$47$	−4.86732	−0.709972	−0.354986	+	0.934872i	$0.615514\pi$
$48$	8.87414	1.28087
$49$	2.60397	0.371996
$50$	−7.99204	−1.13025
$51$	−7.56237	−1.05894
$52$	0	0
$53$	3.61596	0.496690	0.248345	−	0.968672i	$-0.420113\pi$
$53$	3.61596	0.496690	0.248345	+	0.968672i	$0.420113\pi$
$54$	−29.3980	−4.00056
$55$	4.11803	0.555276
$56$	−3.25728	−0.435272
$57$	−25.9336	−3.43499
$58$	4.98994	0.655211
$59$	3.22596	0.419984	0.209992	−	0.977703i	$-0.432656\pi$
$59$	3.22596	0.419984	0.209992	+	0.977703i	$0.432656\pi$
$60$	−8.89291	−1.14807
$61$	1.59654	0.204416	0.102208	−	0.994763i	$-0.467409\pi$
$61$	1.59654	0.204416	0.102208	+	0.994763i	$0.467409\pi$
$62$	2.12031	0.269280
$63$	−22.6746	−2.85673
$64$	−11.3524	−1.41905
$65$	0	0
$66$	−25.2801	−3.11177
$67$	12.6119	1.54079	0.770397	−	0.637564i	$-0.220058\pi$
$67$	12.6119	1.54079	0.770397	+	0.637564i	$0.220058\pi$
$68$	5.87601	0.712571
$69$	21.8943	2.63577
$70$	−7.28961	−0.871275
$71$	11.1918	1.32822	0.664111	−	0.747634i	$-0.268810\pi$
$71$	11.1918	1.32822	0.664111	+	0.747634i	$0.268810\pi$
$72$	7.69029	0.906309
$73$	−10.5849	−1.23887	−0.619435	−	0.785048i	$-0.712638\pi$
$73$	−10.5849	−1.23887	−0.619435	+	0.785048i	$0.712638\pi$
$74$	12.5449	1.45831
$75$	12.1068	1.39797
$76$	20.1506	2.31143
$77$	−11.5037	−1.31096
$78$	0	0
$79$	11.6075	1.30594	0.652972	−	0.757382i	$-0.273522\pi$
$79$	11.6075	1.30594	0.652972	+	0.757382i	$0.273522\pi$
$80$	−3.06504	−0.342682
$81$	22.5837	2.50930
$82$	−9.45252	−1.04386
$83$	2.18227	0.239535	0.119768	−	0.992802i	$-0.461785\pi$
$83$	2.18227	0.239535	0.119768	+	0.992802i	$0.461785\pi$
$84$	24.8422	2.71050
$85$	2.61197	0.283308
$86$	−16.5469	−1.78430
$87$	−7.55902	−0.810412
$88$	3.90157	0.415909
$89$	6.95843	0.737592	0.368796	−	0.929510i	$-0.379770\pi$
$89$	6.95843	0.737592	0.368796	+	0.929510i	$0.379770\pi$
$90$	17.2105	1.81414
$91$	0	0
$92$	−17.0120	−1.77363
$93$	−3.21196	−0.333064
$94$	−10.3202	−1.06445
$95$	8.95720	0.918989
$96$	25.5679	2.60951
$97$	18.6112	1.88968	0.944839	−	0.327536i	$-0.106218\pi$
$97$	18.6112	1.88968	0.944839	+	0.327536i	$0.106218\pi$
$98$	5.52122	0.557728
$99$	27.1596	2.72965
$100$	−9.40704	−0.940704
$101$	11.5033	1.14462	0.572311	−	0.820037i	$-0.306047\pi$
$101$	11.5033	1.14462	0.572311	+	0.820037i	$0.306047\pi$
$102$	−16.0346	−1.58766
$103$	−16.8834	−1.66357	−0.831784	−	0.555100i	$-0.812680\pi$
$103$	−16.8834	−1.66357	−0.831784	+	0.555100i	$0.812680\pi$
$104$	0	0
$105$	11.0427	1.07766
$106$	7.66694	0.744679
$107$	13.1492	1.27118	0.635590	−	0.772027i	$-0.280757\pi$
$107$	13.1492	1.27118	0.635590	+	0.772027i	$0.280757\pi$
$108$	−34.6030	−3.32967
$109$	9.81054	0.939680	0.469840	−	0.882752i	$-0.344312\pi$
$109$	9.81054	0.939680	0.469840	+	0.882752i	$0.344312\pi$
$110$	8.73151	0.832517
$111$	−19.0036	−1.80374
$112$	8.56213	0.809045
$113$	15.7270	1.47947	0.739735	−	0.672898i	$-0.234951\pi$
$113$	15.7270	1.47947	0.739735	+	0.672898i	$0.234951\pi$
$114$	−54.9872	−5.15003
$115$	−7.56208	−0.705167
$116$	5.87341	0.545332
$117$	0	0
$118$	6.84004	0.629676
$119$	−7.29648	−0.668868
$120$	−3.74523	−0.341891
$121$	2.77910	0.252646
$122$	3.38515	0.306477
$123$	14.3192	1.29112
$124$	2.49571	0.224122
$125$	−9.72845	−0.870139
$126$	−48.0771	−4.28305
$127$	−6.87747	−0.610277	−0.305138	−	0.952308i	$-0.598703\pi$
$127$	−6.87747	−0.610277	−0.305138	+	0.952308i	$0.598703\pi$
$128$	−8.15023	−0.720385
$129$	25.0662	2.20695
$130$	0	0
$131$	−12.4782	−1.09022	−0.545111	−	0.838364i	$-0.683512\pi$
$131$	−12.4782	−1.09022	−0.545111	+	0.838364i	$0.683512\pi$
$132$	−29.7560	−2.58993
$133$	−25.0218	−2.16966
$134$	26.7412	2.31009
$135$	−15.3815	−1.32383
$136$	2.47467	0.212201
$137$	6.31298	0.539354	0.269677	−	0.962951i	$-0.413083\pi$
$137$	6.31298	0.539354	0.269677	+	0.962951i	$0.413083\pi$
$138$	46.4227	3.95176
$139$	3.42188	0.290240	0.145120	−	0.989414i	$-0.453643\pi$
$139$	3.42188	0.290240	0.145120	+	0.989414i	$0.453643\pi$
$140$	−8.58024	−0.725163
$141$	15.6336	1.31659
$142$	23.7301	1.99138
$143$	0	0
$144$	−20.2148	−1.68457
$145$	2.61081	0.216816
$146$	−22.4433	−1.85742
$147$	−8.36384	−0.689838
$148$	14.7659	1.21375
$149$	11.1433	0.912894	0.456447	−	0.889751i	$-0.349122\pi$
$149$	11.1433	0.912894	0.456447	+	0.889751i	$0.349122\pi$
$150$	25.6701	2.09595
$151$	−6.63537	−0.539979	−0.269989	−	0.962863i	$-0.587020\pi$
$151$	−6.63537	−0.539979	−0.269989	+	0.962863i	$0.587020\pi$
$152$	8.48637	0.688335
$153$	17.2267	1.39270
$154$	−24.3913	−1.96551
$155$	1.10938	0.0891074
$156$	0	0
$157$	9.01468	0.719450	0.359725	−	0.933058i	$-0.382871\pi$
$157$	9.01468	0.719450	0.359725	+	0.933058i	$0.382871\pi$
$158$	24.6115	1.95798
$159$	−11.6143	−0.921073
$160$	−8.83088	−0.698143
$161$	21.1245	1.66485
$162$	47.8844	3.76215
$163$	7.15112	0.560119	0.280060	−	0.959983i	$-0.409646\pi$
$163$	7.15112	0.560119	0.280060	+	0.959983i	$0.409646\pi$
$164$	−11.1261	−0.868802
$165$	−13.2270	−1.02972
$166$	4.62708	0.359131
$167$	−0.0888303	−0.00687389	−0.00343695	−	0.999994i	$-0.501094\pi$
$167$	−0.0888303	−0.00687389	−0.00343695	+	0.999994i	$0.501094\pi$
$168$	10.4622	0.807179
$169$	0	0
$170$	5.53818	0.424759
$171$	59.0754	4.51761
$172$	−19.4766	−1.48508
$173$	−3.54547	−0.269557	−0.134778	−	0.990876i	$-0.543032\pi$
$173$	−3.54547	−0.269557	−0.134778	+	0.990876i	$0.543032\pi$
$174$	−16.0275	−1.21504
$175$	11.6811	0.883008
$176$	−10.2557	−0.773055
$177$	−10.3617	−0.778829
$178$	14.7540	1.10586
$179$	3.12388	0.233490	0.116745	−	0.993162i	$-0.462754\pi$
$179$	3.12388	0.233490	0.116745	+	0.993162i	$0.462754\pi$
$180$	20.2576	1.50991
$181$	21.8808	1.62638	0.813192	−	0.581996i	$-0.197728\pi$
$181$	21.8808	1.62638	0.813192	+	0.581996i	$0.197728\pi$
$182$	0	0
$183$	−5.12801	−0.379073
$184$	−7.16458	−0.528180
$185$	6.56366	0.482570
$186$	−6.81034	−0.499359
$187$	8.73974	0.639113
$188$	−12.1474	−0.885943
$189$	42.9679	3.12546
$190$	18.9920	1.37783
$191$	19.0805	1.38062	0.690309	−	0.723514i	$-0.257474\pi$
$191$	19.0805	1.38062	0.690309	+	0.723514i	$0.257474\pi$
$192$	36.4635	2.63153
$193$	18.7874	1.35235	0.676173	−	0.736743i	$-0.263637\pi$
$193$	18.7874	1.35235	0.676173	+	0.736743i	$0.263637\pi$
$194$	39.4614	2.83317
$195$	0	0
$196$	6.49876	0.464197
$197$	6.63782	0.472925	0.236462	−	0.971641i	$-0.424012\pi$
$197$	6.63782	0.472925	0.236462	+	0.971641i	$0.424012\pi$
$198$	57.5869	4.09252
$199$	−11.1886	−0.793138	−0.396569	−	0.918005i	$-0.629799\pi$
$199$	−11.1886	−0.793138	−0.396569	+	0.918005i	$0.629799\pi$
$200$	−3.96175	−0.280138
$201$	−40.5090	−2.85729
$202$	24.3906	1.71612
$203$	−7.29325	−0.511886
$204$	−18.8735	−1.32141
$205$	−4.94570	−0.345423
$206$	−35.7980	−2.49416
$207$	−49.8741	−3.46649
$208$	0	0
$209$	29.9711	2.07315
$210$	23.4139	1.61571
$211$	0.452910	0.0311796	0.0155898	−	0.999878i	$-0.495037\pi$
$211$	0.452910	0.0311796	0.0155898	+	0.999878i	$0.495037\pi$
$212$	9.02438	0.619797
$213$	−35.9476	−2.46309
$214$	27.8804	1.90586
$215$	−8.65761	−0.590444
$216$	−14.5730	−0.991565
$217$	−3.09903	−0.210376
$218$	20.8014	1.40885
$219$	33.9983	2.29739
$220$	10.2774	0.692904
$221$	0	0
$222$	−40.2936	−2.70433
$223$	−14.1873	−0.950051	−0.475025	−	0.879972i	$-0.657561\pi$
$223$	−14.1873	−0.950051	−0.475025	+	0.879972i	$0.657561\pi$
$224$	24.6689	1.64826
$225$	−27.5786	−1.83857
$226$	33.3461	2.21815
$227$	9.91652	0.658182	0.329091	−	0.944298i	$-0.393258\pi$
$227$	9.91652	0.658182	0.329091	+	0.944298i	$0.393258\pi$
$228$	−64.7228	−4.28637
$229$	10.2456	0.677046	0.338523	−	0.940958i	$-0.390073\pi$
$229$	10.2456	0.677046	0.338523	+	0.940958i	$0.390073\pi$
$230$	−16.0339	−1.05725
$231$	36.9493	2.43108
$232$	2.47357	0.162398
$233$	−9.84726	−0.645116	−0.322558	−	0.946550i	$-0.604543\pi$
$233$	−9.84726	−0.645116	−0.322558	+	0.946550i	$0.604543\pi$
$234$	0	0
$235$	−5.39970	−0.352238
$236$	8.05107	0.524080
$237$	−37.2827	−2.42177
$238$	−15.4708	−1.00282
$239$	−24.8407	−1.60681	−0.803404	−	0.595434i	$-0.796980\pi$
$239$	−24.8407	−1.60681	−0.803404	+	0.595434i	$0.796980\pi$
$240$	9.84477	0.635477
$241$	5.67897	0.365815	0.182907	−	0.983130i	$-0.441449\pi$
$241$	5.67897	0.365815	0.182907	+	0.983130i	$0.441449\pi$
$242$	5.89256	0.378788
$243$	−30.9429	−1.98499
$244$	3.98450	0.255081
$245$	2.88879	0.184558
$246$	30.3611	1.93575
$247$	0	0
$248$	1.05106	0.0667426
$249$	−7.00935	−0.444200
$250$	−20.6273	−1.30459
$251$	11.8999	0.751117	0.375558	−	0.926799i	$-0.377451\pi$
$251$	11.8999	0.751117	0.375558	+	0.926799i	$0.377451\pi$
$252$	−56.5892	−3.56478
$253$	−25.3030	−1.59079
$254$	−14.5824	−0.914979
$255$	−8.38953	−0.525373
$256$	5.42384	0.338990
$257$	7.36901	0.459666	0.229833	−	0.973230i	$-0.426182\pi$
$257$	7.36901	0.459666	0.229833	+	0.973230i	$0.426182\pi$
$258$	53.1481	3.30885
$259$	−18.3355	−1.13931
$260$	0	0
$261$	17.2191	1.06583
$262$	−26.4575	−1.63455
$263$	−26.7859	−1.65169	−0.825845	−	0.563898i	$-0.809301\pi$
$263$	−26.7859	−1.65169	−0.825845	+	0.563898i	$0.809301\pi$
$264$	−12.5317	−0.771272
$265$	4.01146	0.246422
$266$	−53.0539	−3.25294
$267$	−22.3502	−1.36781
$268$	31.4758	1.92269
$269$	3.15062	0.192097	0.0960484	−	0.995377i	$-0.469380\pi$
$269$	3.15062	0.192097	0.0960484	+	0.995377i	$0.469380\pi$
$270$	−32.6135	−1.98480
$271$	−22.4603	−1.36437	−0.682183	−	0.731182i	$-0.738969\pi$
$271$	−22.4603	−1.36437	−0.682183	+	0.731182i	$0.738969\pi$
$272$	−6.50496	−0.394421
$273$	0	0
$274$	13.3855	0.808645
$275$	−13.9917	−0.843728
$276$	54.6419	3.28906
$277$	8.12853	0.488396	0.244198	−	0.969725i	$-0.421475\pi$
$277$	8.12853	0.488396	0.244198	+	0.969725i	$0.421475\pi$
$278$	7.25544	0.435152
$279$	7.31667	0.438038
$280$	−3.61355	−0.215951
$281$	−2.24245	−0.133774	−0.0668868	−	0.997761i	$-0.521307\pi$
$281$	−2.24245	−0.133774	−0.0668868	+	0.997761i	$0.521307\pi$
$282$	33.1482	1.97394
$283$	−19.1061	−1.13574	−0.567870	−	0.823118i	$-0.692232\pi$
$283$	−19.1061	−1.13574	−0.567870	+	0.823118i	$0.692232\pi$
$284$	27.9315	1.65743
$285$	−28.7701	−1.70420
$286$	0	0
$287$	13.8157	0.815517
$288$	−58.2423	−3.43196
$289$	−11.4566	−0.673917
$290$	5.53572	0.325069
$291$	−59.7783	−3.50426
$292$	−26.4169	−1.54593
$293$	24.6913	1.44248	0.721239	−	0.692686i	$-0.243573\pi$
$293$	24.6913	1.44248	0.721239	+	0.692686i	$0.243573\pi$
$294$	−17.7339	−1.03426
$295$	3.57881	0.208366
$296$	6.21864	0.361451
$297$	−51.4671	−2.98642
$298$	23.6272	1.36869
$299$	0	0
$300$	30.2150	1.74446
$301$	24.1849	1.39399
$302$	−14.0690	−0.809582
$303$	−36.9481	−2.12262
$304$	−22.3074	−1.27942
$305$	1.77116	0.101416
$306$	36.5259	2.08805
$307$	20.6082	1.17617	0.588086	−	0.808798i	$-0.299881\pi$
$307$	20.6082	1.17617	0.588086	+	0.808798i	$0.299881\pi$
$308$	−28.7098	−1.63589
$309$	54.2287	3.08496
$310$	2.35222	0.133597
$311$	−19.4692	−1.10400	−0.552000	−	0.833844i	$-0.686135\pi$
$311$	−19.4692	−1.10400	−0.552000	+	0.833844i	$0.686135\pi$
$312$	0	0
$313$	−31.9205	−1.80425	−0.902127	−	0.431470i	$-0.857995\pi$
$313$	−31.9205	−1.80425	−0.902127	+	0.431470i	$0.857995\pi$
$314$	19.1139	1.07866
$315$	−25.1547	−1.41730
$316$	28.9689	1.62963
$317$	13.5755	0.762475	0.381237	−	0.924477i	$-0.375498\pi$
$317$	13.5755	0.762475	0.381237	+	0.924477i	$0.375498\pi$
$318$	−24.6259	−1.38095
$319$	8.73587	0.489115
$320$	−12.5941	−0.704033
$321$	−42.2346	−2.35731
$322$	44.7905	2.49608
$323$	19.0100	1.05774
$324$	56.3624	3.13124
$325$	0	0
$326$	15.1626	0.839778
$327$	−31.5111	−1.74257
$328$	−4.68573	−0.258726
$329$	15.0840	0.831606
$330$	−28.0452	−1.54384
$331$	−24.3611	−1.33901	−0.669503	−	0.742809i	$-0.733493\pi$
$331$	−24.3611	−1.33901	−0.669503	+	0.742809i	$0.733493\pi$
$332$	5.44631	0.298905
$333$	43.2893	2.37224
$334$	−0.188348	−0.0103059
$335$	13.9914	0.764433
$336$	−27.5012	−1.50031
$337$	26.1422	1.42406	0.712028	−	0.702151i	$-0.247777\pi$
$337$	26.1422	1.42406	0.712028	+	0.702151i	$0.247777\pi$
$338$	0	0
$339$	−50.5144	−2.74357
$340$	6.51872	0.353527
$341$	3.71202	0.201017
$342$	125.258	6.77318
$343$	13.6234	0.735595
$344$	−8.20252	−0.442250
$345$	24.2891	1.30768
$346$	−7.51749	−0.404143
$347$	−4.93577	−0.264966	−0.132483	−	0.991185i	$-0.542295\pi$
$347$	−4.93577	−0.264966	−0.132483	+	0.991185i	$0.542295\pi$
$348$	−18.8651	−1.01128
$349$	28.2850	1.51406	0.757030	−	0.653380i	$-0.226650\pi$
$349$	28.2850	1.51406	0.757030	+	0.653380i	$0.226650\pi$
$350$	24.7676	1.32388
$351$	0	0
$352$	−29.5485	−1.57494
$353$	−10.6616	−0.567458	−0.283729	−	0.958905i	$-0.591572\pi$
$353$	−10.6616	−0.567458	−0.283729	+	0.958905i	$0.591572\pi$
$354$	−21.9699	−1.16769
$355$	12.4159	0.658970
$356$	17.3662	0.920409
$357$	23.4360	1.24036
$358$	6.62360	0.350068
$359$	18.6701	0.985368	0.492684	−	0.870208i	$-0.336016\pi$
$359$	18.6701	0.985368	0.492684	+	0.870208i	$0.336016\pi$
$360$	8.53144	0.449646
$361$	46.1907	2.43109
$362$	46.3940	2.43841
$363$	−8.92636	−0.468512
$364$	0	0
$365$	−11.7427	−0.614639
$366$	−10.8730	−0.568339
$367$	23.3624	1.21951	0.609754	−	0.792591i	$-0.291268\pi$
$367$	23.3624	1.21951	0.609754	+	0.792591i	$0.291268\pi$
$368$	18.8329	0.981734
$369$	−32.6183	−1.69804
$370$	13.9170	0.723510
$371$	−11.2059	−0.581784
$372$	−8.01612	−0.415617
$373$	25.0054	1.29473	0.647365	−	0.762180i	$-0.275871\pi$
$373$	25.0054	1.29473	0.647365	+	0.762180i	$0.275871\pi$
$374$	18.5310	0.958213
$375$	31.2474	1.61361
$376$	−5.11587	−0.263831
$377$	0	0
$378$	91.1053	4.68595
$379$	−5.36261	−0.275459	−0.137729	−	0.990470i	$-0.543980\pi$
$379$	−5.36261	−0.275459	−0.137729	+	0.990470i	$0.543980\pi$
$380$	22.3546	1.14677
$381$	22.0901	1.13171
$382$	40.4566	2.06994
$383$	−12.7471	−0.651347	−0.325674	−	0.945482i	$-0.605591\pi$
$383$	−12.7471	−0.651347	−0.325674	+	0.945482i	$0.605591\pi$
$384$	26.1782	1.33590
$385$	−12.7619	−0.650407
$386$	39.8351	2.02755
$387$	−57.0995	−2.90253
$388$	46.4481	2.35805
$389$	12.4086	0.629140	0.314570	−	0.949234i	$-0.398140\pi$
$389$	12.4086	0.629140	0.314570	+	0.949234i	$0.398140\pi$
$390$	0	0
$391$	−16.0491	−0.811636
$392$	2.73694	0.138236
$393$	40.0793	2.02173
$394$	14.0742	0.709049
$395$	12.8771	0.647916
$396$	67.7827	3.40621
$397$	14.6540	0.735463	0.367731	−	0.929932i	$-0.380135\pi$
$397$	14.6540	0.735463	0.367731	+	0.929932i	$0.380135\pi$
$398$	−23.7233	−1.18914
$399$	80.3689	4.02348
$400$	10.4139	0.520697
$401$	−28.7626	−1.43634	−0.718169	−	0.695869i	$-0.755019\pi$
$401$	−28.7626	−1.43634	−0.718169	+	0.695869i	$0.755019\pi$
$402$	−85.8917	−4.28389
$403$	0	0
$404$	28.7090	1.42832
$405$	25.0538	1.24493
$406$	−15.4639	−0.767463
$407$	21.9623	1.08863
$408$	−7.94854	−0.393511
$409$	−7.67728	−0.379617	−0.189809	−	0.981821i	$-0.560787\pi$
$409$	−7.67728	−0.379617	−0.189809	+	0.981821i	$0.560787\pi$
$410$	−10.4864	−0.517887
$411$	−20.2770	−1.00019
$412$	−42.1360	−2.07589
$413$	−9.99734	−0.491937
$414$	−105.749	−5.19726
$415$	2.42096	0.118840
$416$	0	0
$417$	−10.9909	−0.538228
$418$	63.5481	3.10824
$419$	9.23550	0.451184	0.225592	−	0.974222i	$-0.427568\pi$
$419$	9.23550	0.451184	0.225592	+	0.974222i	$0.427568\pi$
$420$	27.5594	1.34476
$421$	−0.378402	−0.0184422	−0.00922108	−	0.999957i	$-0.502935\pi$
$421$	−0.378402	−0.0184422	−0.00922108	+	0.999957i	$0.502935\pi$
$422$	0.960309	0.0467471
$423$	−35.6126	−1.73154
$424$	3.80060	0.184573
$425$	−8.87456	−0.430479
$426$	−76.2200	−3.69287
$427$	−4.94771	−0.239436
$428$	32.8166	1.58625
$429$	0	0
$430$	−18.3568	−0.885244
$431$	−26.8387	−1.29278	−0.646388	−	0.763009i	$-0.723721\pi$
$431$	−26.8387	−1.29278	−0.646388	+	0.763009i	$0.723721\pi$
$432$	38.3068	1.84303
$433$	−2.48155	−0.119256	−0.0596279	−	0.998221i	$-0.518991\pi$
$433$	−2.48155	−0.119256	−0.0596279	+	0.998221i	$0.518991\pi$
$434$	−6.57090	−0.315413
$435$	−8.38581	−0.402069
$436$	24.4843	1.17259
$437$	−55.0369	−2.63277
$438$	72.0868	3.44444
$439$	3.12910	0.149344	0.0746719	−	0.997208i	$-0.476209\pi$
$439$	3.12910	0.149344	0.0746719	+	0.997208i	$0.476209\pi$
$440$	4.32832	0.206344
$441$	19.0524	0.907257
$442$	0	0
$443$	14.8597	0.706006	0.353003	−	0.935622i	$-0.385161\pi$
$443$	14.8597	0.706006	0.353003	+	0.935622i	$0.385161\pi$
$444$	−47.4276	−2.25081
$445$	7.71953	0.365941
$446$	−30.0814	−1.42440
$447$	−35.7918	−1.69289
$448$	35.1815	1.66217
$449$	24.3769	1.15042	0.575208	−	0.818007i	$-0.304921\pi$
$449$	24.3769	1.15042	0.575208	+	0.818007i	$0.304921\pi$
$450$	−58.4751	−2.75654
$451$	−16.5485	−0.779239
$452$	39.2500	1.84617
$453$	21.3125	1.00135
$454$	21.0261	0.986803
$455$	0	0
$456$	−27.2579	−1.27647
$457$	31.4937	1.47321	0.736606	−	0.676322i	$-0.236427\pi$
$457$	31.4937	1.47321	0.736606	+	0.676322i	$0.236427\pi$
$458$	21.7238	1.01508
$459$	−32.6443	−1.52370
$460$	−18.8728	−0.879947
$461$	−21.2345	−0.988989	−0.494494	−	0.869181i	$-0.664647\pi$
$461$	−21.2345	−0.988989	−0.494494	+	0.869181i	$0.664647\pi$
$462$	78.3439	3.64489
$463$	−20.5089	−0.953128	−0.476564	−	0.879140i	$-0.658118\pi$
$463$	−20.5089	−0.953128	−0.476564	+	0.879140i	$0.658118\pi$
$464$	−6.50208	−0.301851
$465$	−3.56327	−0.165243
$466$	−20.8792	−0.967212
$467$	−35.9757	−1.66476	−0.832379	−	0.554207i	$-0.813021\pi$
$467$	−35.9757	−1.66476	−0.832379	+	0.554207i	$0.813021\pi$
$468$	0	0
$469$	−39.0848	−1.80477
$470$	−11.4490	−0.528105
$471$	−28.9548	−1.33417
$472$	3.39069	0.156069
$473$	−28.9687	−1.33198
$474$	−79.0510	−3.63093
$475$	−30.4335	−1.39638
$476$	−18.2099	−0.834651
$477$	26.4568	1.21137
$478$	−52.6699	−2.40906
$479$	−28.4775	−1.30117	−0.650585	−	0.759433i	$-0.725476\pi$
$479$	−28.4775	−1.30117	−0.650585	+	0.759433i	$0.725476\pi$
$480$	28.3644	1.29465
$481$	0	0
$482$	12.0412	0.548460
$483$	−67.8511	−3.08733
$484$	6.93584	0.315266
$485$	20.6468	0.937524
$486$	−65.6085	−2.97606
$487$	37.6400	1.70563	0.852815	−	0.522214i	$-0.174894\pi$
$487$	37.6400	1.70563	0.852815	+	0.522214i	$0.174894\pi$
$488$	1.67806	0.0759623
$489$	−22.9691	−1.03870
$490$	6.12512	0.276705
$491$	28.7846	1.29903	0.649515	−	0.760349i	$-0.274972\pi$
$491$	28.7846	1.29903	0.649515	+	0.760349i	$0.274972\pi$
$492$	35.7366	1.61113
$493$	5.54095	0.249552
$494$	0	0
$495$	30.1303	1.35426
$496$	−2.76284	−0.124055
$497$	−34.6837	−1.55578
$498$	−14.8620	−0.665982
$499$	36.6241	1.63952	0.819760	−	0.572707i	$-0.194107\pi$
$499$	36.6241	1.63952	0.819760	+	0.572707i	$0.194107\pi$
$500$	−24.2794	−1.08581
$501$	0.285319	0.0127471
$502$	25.2315	1.12614
$503$	10.7569	0.479628	0.239814	−	0.970819i	$-0.422914\pi$
$503$	10.7569	0.479628	0.239814	+	0.970819i	$0.422914\pi$
$504$	−23.8324	−1.06158
$505$	12.7615	0.567880
$506$	−53.6502	−2.38504
$507$	0	0
$508$	−17.1642	−0.761538
$509$	25.2388	1.11869	0.559345	−	0.828935i	$-0.311053\pi$
$509$	25.2388	1.11869	0.559345	+	0.828935i	$0.311053\pi$
$510$	−17.7884	−0.787684
$511$	32.8029	1.45111
$512$	27.8007	1.22863
$513$	−111.947	−4.94257
$514$	15.6246	0.689171
$515$	−18.7300	−0.825344
$516$	62.5580	2.75396
$517$	−18.0676	−0.794613
$518$	−38.8769	−1.70815
$519$	11.3879	0.499873
$520$	0	0
$521$	−44.4940	−1.94932	−0.974659	−	0.223697i	$-0.928187\pi$
$521$	−44.4940	−1.94932	−0.974659	+	0.223697i	$0.928187\pi$
$522$	36.5097	1.59799
$523$	8.39941	0.367280	0.183640	−	0.982994i	$-0.441212\pi$
$523$	8.39941	0.367280	0.183640	+	0.982994i	$0.441212\pi$
$524$	−31.1419	−1.36044
$525$	−37.5192	−1.63747
$526$	−56.7944	−2.47635
$527$	2.35444	0.102561
$528$	32.9410	1.43357
$529$	23.4647	1.02020
$530$	8.50554	0.369457
$531$	23.6033	1.02430
$532$	−62.4472	−2.70743
$533$	0	0
$534$	−47.3893	−2.05074
$535$	14.5874	0.630669
$536$	13.2560	0.572570
$537$	−10.0338	−0.432990
$538$	6.68029	0.288008
$539$	9.66599	0.416344
$540$	−38.3878	−1.65195
$541$	−9.03959	−0.388642	−0.194321	−	0.980938i	$-0.562250\pi$
$541$	−9.03959	−0.388642	−0.194321	+	0.980938i	$0.562250\pi$
$542$	−47.6228	−2.04557
$543$	−70.2800	−3.01601
$544$	−18.7419	−0.803551
$545$	10.8836	0.466202
$546$	0	0
$547$	15.3025	0.654287	0.327144	−	0.944975i	$-0.393914\pi$
$547$	15.3025	0.654287	0.327144	+	0.944975i	$0.393914\pi$
$548$	15.7554	0.673036
$549$	11.6813	0.498547
$550$	−29.6666	−1.26499
$551$	19.0015	0.809492
$552$	23.0123	0.979469
$553$	−35.9719	−1.52968
$554$	17.2350	0.732245
$555$	−21.0822	−0.894890
$556$	8.54002	0.362177
$557$	−8.13377	−0.344639	−0.172319	−	0.985041i	$-0.555126\pi$
$557$	−8.13377	−0.344639	−0.172319	+	0.985041i	$0.555126\pi$
$558$	15.5136	0.656743
$559$	0	0
$560$	9.49864	0.401391
$561$	−28.0717	−1.18519
$562$	−4.75470	−0.200565
$563$	0.257576	0.0108555	0.00542776	−	0.999985i	$-0.498272\pi$
$563$	0.257576	0.0108555	0.00542776	+	0.999985i	$0.498272\pi$
$564$	39.0171	1.64291
$565$	17.4472	0.734008
$566$	−40.5108	−1.70280
$567$	−69.9874	−2.93920
$568$	11.7633	0.493577
$569$	−46.2437	−1.93864	−0.969318	−	0.245810i	$-0.920946\pi$
$569$	−46.2437	−1.93864	−0.969318	+	0.245810i	$0.920946\pi$
$570$	−61.0016	−2.55508
$571$	29.6599	1.24123	0.620614	−	0.784116i	$-0.286883\pi$
$571$	29.6599	1.24123	0.620614	+	0.784116i	$0.286883\pi$
$572$	0	0
$573$	−61.2859	−2.56025
$574$	29.2936	1.22269
$575$	25.6933	1.07148
$576$	−83.0620	−3.46092
$577$	−8.29571	−0.345355	−0.172677	−	0.984978i	$-0.555242\pi$
$577$	−8.29571	−0.345355	−0.172677	+	0.984978i	$0.555242\pi$
$578$	−24.2915	−1.01039
$579$	−60.3443	−2.50782
$580$	6.51583	0.270555
$581$	−6.76291	−0.280573
$582$	−126.748	−5.25389
$583$	13.4225	0.555903
$584$	−11.1254	−0.460373
$585$	0	0
$586$	52.3531	2.16269
$587$	2.68210	0.110702	0.0553511	−	0.998467i	$-0.482372\pi$
$587$	2.68210	0.110702	0.0553511	+	0.998467i	$0.482372\pi$
$588$	−20.8737	−0.860819
$589$	8.07407	0.332686
$590$	7.58819	0.312401
$591$	−21.3204	−0.877004
$592$	−16.3464	−0.671834
$593$	29.2574	1.20146	0.600729	−	0.799453i	$-0.294877\pi$
$593$	29.2574	1.20146	0.600729	+	0.799453i	$0.294877\pi$
$594$	−109.126	−4.47750
$595$	−8.09456	−0.331845
$596$	27.8105	1.13916
$597$	35.9373	1.47081
$598$	0	0
$599$	5.53259	0.226056	0.113028	−	0.993592i	$-0.463945\pi$
$599$	5.53259	0.226056	0.113028	+	0.993592i	$0.463945\pi$
$600$	12.7250	0.519495
$601$	16.9879	0.692950	0.346475	−	0.938059i	$-0.387379\pi$
$601$	16.9879	0.692950	0.346475	+	0.938059i	$0.387379\pi$
$602$	51.2794	2.08999
$603$	92.2775	3.75783
$604$	−16.5600	−0.673816
$605$	3.08308	0.125345
$606$	−78.3415	−3.18241
$607$	−25.8976	−1.05115	−0.525576	−	0.850746i	$-0.676150\pi$
$607$	−25.8976	−1.05115	−0.525576	+	0.850746i	$0.676150\pi$
$608$	−64.2714	−2.60655
$609$	23.4256	0.949254
$610$	3.75541	0.152052
$611$	0	0
$612$	42.9929	1.73788
$613$	−8.56133	−0.345789	−0.172894	−	0.984940i	$-0.555312\pi$
$613$	−8.56133	−0.345789	−0.172894	+	0.984940i	$0.555312\pi$
$614$	43.6958	1.76342
$615$	15.8854	0.640561
$616$	−12.0911	−0.487163
$617$	−26.2823	−1.05809	−0.529043	−	0.848595i	$-0.677449\pi$
$617$	−26.2823	−1.05809	−0.529043	+	0.848595i	$0.677449\pi$
$618$	114.982	4.62524
$619$	16.9375	0.680776	0.340388	−	0.940285i	$-0.389442\pi$
$619$	16.9375	0.680776	0.340388	+	0.940285i	$0.389442\pi$
$620$	2.76869	0.111193
$621$	94.5106	3.79258
$622$	−41.2808	−1.65521
$623$	−21.5644	−0.863958
$624$	0	0
$625$	8.05388	0.322155
$626$	−67.6814	−2.70509
$627$	−96.2660	−3.84449
$628$	22.4980	0.897770
$629$	13.9301	0.555430
$630$	−53.3357	−2.12494
$631$	−31.5316	−1.25525	−0.627627	−	0.778514i	$-0.715974\pi$
$631$	−31.5316	−1.25525	−0.627627	+	0.778514i	$0.715974\pi$
$632$	12.2002	0.485298
$633$	−1.45473	−0.0578202
$634$	28.7842	1.14317
$635$	−7.62971	−0.302776
$636$	−28.9859	−1.14937
$637$	0	0
$638$	18.5227	0.733323
$639$	81.8868	3.23939
$640$	−9.04169	−0.357404
$641$	−19.7000	−0.778101	−0.389051	−	0.921216i	$-0.627197\pi$
$641$	−19.7000	−0.778101	−0.389051	+	0.921216i	$0.627197\pi$
$642$	−89.5505	−3.53428
$643$	−24.8436	−0.979735	−0.489868	−	0.871797i	$-0.662955\pi$
$643$	−24.8436	−0.979735	−0.489868	+	0.871797i	$0.662955\pi$
$644$	52.7207	2.07749
$645$	27.8079	1.09493
$646$	40.3070	1.58586
$647$	−4.05703	−0.159498	−0.0797492	−	0.996815i	$-0.525412\pi$
$647$	−4.05703	−0.159498	−0.0797492	+	0.996815i	$0.525412\pi$
$648$	23.7369	0.932473
$649$	11.9748	0.470054
$650$	0	0
$651$	9.95394	0.390126
$652$	17.8471	0.698948
$653$	12.2860	0.480788	0.240394	−	0.970675i	$-0.422723\pi$
$653$	12.2860	0.480788	0.240394	+	0.970675i	$0.422723\pi$
$654$	−66.8132	−2.61260
$655$	−13.8430	−0.540890
$656$	12.3170	0.480898
$657$	−77.4463	−3.02147
$658$	31.9827	1.24681
$659$	−37.4736	−1.45976	−0.729882	−	0.683573i	$-0.760425\pi$
$659$	−37.4736	−1.45976	−0.729882	+	0.683573i	$0.760425\pi$
$660$	−33.0107	−1.28494
$661$	−28.1667	−1.09556	−0.547779	−	0.836623i	$-0.684527\pi$
$661$	−28.1667	−1.09556	−0.547779	+	0.836623i	$0.684527\pi$
$662$	−51.6530	−2.00755
$663$	0	0
$664$	2.29370	0.0890129
$665$	−27.7586	−1.07643
$666$	91.7866	3.55666
$667$	−16.0420	−0.621147
$668$	−0.221695	−0.00857763
$669$	45.5689	1.76180
$670$	29.6661	1.14610
$671$	5.92638	0.228785
$672$	−79.2355	−3.05658
$673$	−1.64713	−0.0634921	−0.0317461	−	0.999496i	$-0.510107\pi$
$673$	−1.64713	−0.0634921	−0.0317461	+	0.999496i	$0.510107\pi$
$674$	55.4296	2.13507
$675$	52.2610	2.01153
$676$	0	0
$677$	−14.8798	−0.571877	−0.285938	−	0.958248i	$-0.592305\pi$
$677$	−14.8798	−0.571877	−0.285938	+	0.958248i	$0.592305\pi$
$678$	−107.106	−4.11339
$679$	−57.6765	−2.21342
$680$	2.74534	0.105279
$681$	−31.8514	−1.22055
$682$	7.87063	0.301382
$683$	18.4845	0.707290	0.353645	−	0.935380i	$-0.384942\pi$
$683$	18.4845	0.707290	0.353645	+	0.935380i	$0.384942\pi$
$684$	147.435	5.63732
$685$	7.00348	0.267589
$686$	28.8859	1.10287
$687$	−32.9083	−1.25553
$688$	21.5613	0.822017
$689$	0	0
$690$	51.5003	1.96058
$691$	28.4193	1.08112	0.540561	−	0.841305i	$-0.318212\pi$
$691$	28.4193	1.08112	0.540561	+	0.841305i	$0.318212\pi$
$692$	−8.84846	−0.336368
$693$	−84.1685	−3.19730
$694$	−10.4654	−0.397260
$695$	3.79615	0.143996
$696$	−7.94501	−0.301155
$697$	−10.4963	−0.397576
$698$	59.9729	2.27001
$699$	31.6290	1.19632
$700$	29.1527	1.10187
$701$	37.2934	1.40855	0.704276	−	0.709926i	$-0.251272\pi$
$701$	37.2934	1.40855	0.704276	+	0.709926i	$0.251272\pi$
$702$	0	0
$703$	47.7705	1.80170
$704$	−42.1404	−1.58823
$705$	17.3436	0.653198
$706$	−22.6058	−0.850781
$707$	−35.6491	−1.34072
$708$	−25.8597	−0.971867
$709$	−43.0647	−1.61733	−0.808665	−	0.588270i	$-0.799809\pi$
$709$	−43.0647	−1.61733	−0.808665	+	0.588270i	$0.799809\pi$
$710$	26.3256	0.987983
$711$	84.9281	3.18505
$712$	7.31376	0.274095
$713$	−6.81650	−0.255280
$714$	49.6916	1.85966
$715$	0	0
$716$	7.79631	0.291362
$717$	79.7871	2.97970
$718$	39.5863	1.47735
$719$	11.0582	0.412402	0.206201	−	0.978510i	$-0.433890\pi$
$719$	11.0582	0.412402	0.206201	+	0.978510i	$0.433890\pi$
$720$	−22.4259	−0.835763
$721$	52.3220	1.94857
$722$	97.9385	3.64490
$723$	−18.2406	−0.678376
$724$	54.6081	2.02949
$725$	−8.87062	−0.329447
$726$	−18.9266	−0.702434
$727$	26.0637	0.966647	0.483324	−	0.875442i	$-0.339429\pi$
$727$	26.0637	0.966647	0.483324	+	0.875442i	$0.339429\pi$
$728$	0	0
$729$	31.6363	1.17171
$730$	−24.8981	−0.921519
$731$	−18.3741	−0.679591
$732$	−12.7980	−0.473029
$733$	−8.85392	−0.327027	−0.163514	−	0.986541i	$-0.552283\pi$
$733$	−8.85392	−0.327027	−0.163514	+	0.986541i	$0.552283\pi$
$734$	49.5355	1.82839
$735$	−9.27866	−0.342249
$736$	54.2608	2.00008
$737$	46.8158	1.72448
$738$	−69.1610	−2.54585
$739$	−18.9624	−0.697544	−0.348772	−	0.937208i	$-0.613401\pi$
$739$	−18.9624	−0.697544	−0.348772	+	0.937208i	$0.613401\pi$
$740$	16.3810	0.602178
$741$	0	0
$742$	−23.7601	−0.872260
$743$	45.4648	1.66794	0.833971	−	0.551808i	$-0.186062\pi$
$743$	45.4648	1.66794	0.833971	+	0.551808i	$0.186062\pi$
$744$	−3.37597	−0.123769
$745$	12.3621	0.452913
$746$	53.0192	1.94117
$747$	15.9669	0.584200
$748$	21.8119	0.797522
$749$	−40.7497	−1.48896
$750$	66.2541	2.41926
$751$	−4.01277	−0.146428	−0.0732140	−	0.997316i	$-0.523326\pi$
$751$	−4.01277	−0.146428	−0.0732140	+	0.997316i	$0.523326\pi$
$752$	13.4477	0.490386
$753$	−38.2221	−1.39289
$754$	0	0
$755$	−7.36113	−0.267899
$756$	107.236	3.90012
$757$	−43.6640	−1.58699	−0.793497	−	0.608574i	$-0.791742\pi$
$757$	−43.6640	−1.58699	−0.793497	+	0.608574i	$0.791742\pi$
$758$	−11.3704	−0.412991
$759$	81.2722	2.94999
$760$	9.41459	0.341503
$761$	−18.1096	−0.656472	−0.328236	−	0.944596i	$-0.606454\pi$
$761$	−18.1096	−0.656472	−0.328236	+	0.944596i	$0.606454\pi$
$762$	46.8379	1.69676
$763$	−30.4031	−1.10067
$764$	47.6195	1.72281
$765$	19.1109	0.690956
$766$	−27.0278	−0.976555
$767$	0	0
$768$	−17.4211	−0.628631
$769$	−43.7464	−1.57753	−0.788767	−	0.614692i	$-0.789280\pi$
$769$	−43.7464	−1.57753	−0.788767	+	0.614692i	$0.789280\pi$
$770$	−27.0592	−0.975145
$771$	−23.6690	−0.852417
$772$	46.8879	1.68753
$773$	−29.7795	−1.07109	−0.535546	−	0.844506i	$-0.679894\pi$
$773$	−29.7795	−1.07109	−0.535546	+	0.844506i	$0.679894\pi$
$774$	−121.069	−4.35172
$775$	−3.76928	−0.135397
$776$	19.5615	0.702218
$777$	58.8927	2.11277
$778$	26.3101	0.943261
$779$	−35.9949	−1.28965
$780$	0	0
$781$	41.5442	1.48657
$782$	−34.0290	−1.21687
$783$	−32.6298	−1.16609
$784$	−7.19436	−0.256942
$785$	10.0007	0.356940
$786$	84.9805	3.03115
$787$	24.7197	0.881162	0.440581	−	0.897713i	$-0.354773\pi$
$787$	24.7197	0.881162	0.440581	+	0.897713i	$0.354773\pi$
$788$	16.5661	0.590142
$789$	86.0352	3.06293
$790$	27.3034	0.971412
$791$	−48.7383	−1.73294
$792$	28.5465	1.01436
$793$	0	0
$794$	31.0710	1.10267
$795$	−12.8846	−0.456971
$796$	−27.9235	−0.989722
$797$	−38.8733	−1.37696	−0.688481	−	0.725255i	$-0.741722\pi$
$797$	−38.8733	−1.37696	−0.688481	+	0.725255i	$0.741722\pi$
$798$	170.407	6.03234
$799$	−11.4598	−0.405420
$800$	30.0043	1.06081
$801$	50.9126	1.79891
$802$	−60.9857	−2.15348
$803$	−39.2914	−1.38656
$804$	−101.099	−3.56548
$805$	23.4351	0.825978
$806$	0	0
$807$	−10.1197	−0.356229
$808$	12.0907	0.425350
$809$	25.1942	0.885779	0.442890	−	0.896576i	$-0.353953\pi$
$809$	25.1942	0.885779	0.442890	+	0.896576i	$0.353953\pi$
$810$	53.1219	1.86651
$811$	9.76638	0.342944	0.171472	−	0.985189i	$-0.445148\pi$
$811$	9.76638	0.342944	0.171472	+	0.985189i	$0.445148\pi$
$812$	−18.2019	−0.638760
$813$	72.1415	2.53011
$814$	46.5668	1.63217
$815$	7.93330	0.277891
$816$	20.8937	0.731424
$817$	−63.0102	−2.20445
$818$	−16.2782	−0.569154
$819$	0	0
$820$	−12.3430	−0.431038
$821$	11.6020	0.404913	0.202457	−	0.979291i	$-0.435107\pi$
$821$	11.6020	0.404913	0.202457	+	0.979291i	$0.435107\pi$
$822$	−42.9935	−1.49957
$823$	14.3048	0.498636	0.249318	−	0.968422i	$-0.419794\pi$
$823$	14.3048	0.498636	0.249318	+	0.968422i	$0.419794\pi$
$824$	−17.7455	−0.618193
$825$	44.9406	1.56463
$826$	−21.1975	−0.737554
$827$	3.02945	0.105344	0.0526722	−	0.998612i	$-0.483226\pi$
$827$	3.02945	0.105344	0.0526722	+	0.998612i	$0.483226\pi$
$828$	−124.471	−4.32568
$829$	12.1126	0.420687	0.210343	−	0.977628i	$-0.432542\pi$
$829$	12.1126	0.420687	0.210343	+	0.977628i	$0.432542\pi$
$830$	5.13318	0.178175
$831$	−26.1085	−0.905693
$832$	0	0
$833$	6.13090	0.212423
$834$	−23.3042	−0.806957
$835$	−0.0985464	−0.00341034
$836$	74.7993	2.58699
$837$	−13.8650	−0.479243
$838$	19.5821	0.676453
$839$	−28.1969	−0.973467	−0.486733	−	0.873551i	$-0.661812\pi$
$839$	−28.1969	−0.973467	−0.486733	+	0.873551i	$0.661812\pi$
$840$	11.6066	0.400465
$841$	−23.4615	−0.809018
$842$	−0.802328	−0.0276501
$843$	7.20267	0.248073
$844$	1.13033	0.0389077
$845$	0	0
$846$	−75.5098	−2.59608
$847$	−8.61252	−0.295930
$848$	−9.99032	−0.343069
$849$	61.3680	2.10614
$850$	−18.8168	−0.645411
$851$	−40.3300	−1.38249
$852$	−89.7149	−3.07358
$853$	−35.1191	−1.20245	−0.601227	−	0.799078i	$-0.705321\pi$
$853$	−35.1191	−1.20245	−0.601227	+	0.799078i	$0.705321\pi$
$854$	−10.4907	−0.358984
$855$	65.5369	2.24131
$856$	13.8206	0.472380
$857$	−35.1871	−1.20197	−0.600984	−	0.799261i	$-0.705224\pi$
$857$	−35.1871	−1.20197	−0.600984	+	0.799261i	$0.705224\pi$
$858$	0	0
$859$	−9.39640	−0.320601	−0.160301	−	0.987068i	$-0.551246\pi$
$859$	−9.39640	−0.320601	−0.160301	+	0.987068i	$0.551246\pi$
$860$	−21.6069	−0.736789
$861$	−44.3755	−1.51231
$862$	−56.9064	−1.93824
$863$	−6.64602	−0.226233	−0.113117	−	0.993582i	$-0.536083\pi$
$863$	−6.64602	−0.226233	−0.113117	+	0.993582i	$0.536083\pi$
$864$	110.368	3.75480
$865$	−3.93326	−0.133735
$866$	−5.26166	−0.178798
$867$	36.7981	1.24973
$868$	−7.73428	−0.262519
$869$	43.0872	1.46163
$870$	−17.7805	−0.602816
$871$	0	0
$872$	10.3115	0.349192
$873$	136.172	4.60872
$874$	−116.695	−3.94728
$875$	30.1487	1.01921
$876$	84.8499	2.86681
$877$	−8.56354	−0.289170	−0.144585	−	0.989492i	$-0.546185\pi$
$877$	−8.56354	−0.289170	−0.144585	+	0.989492i	$0.546185\pi$
$878$	6.63466	0.223909
$879$	−79.3073	−2.67497
$880$	−11.3775	−0.383535
$881$	8.00869	0.269819	0.134910	−	0.990858i	$-0.456926\pi$
$881$	8.00869	0.269819	0.134910	+	0.990858i	$0.456926\pi$
$882$	40.3970	1.36024
$883$	33.6301	1.13174	0.565871	−	0.824494i	$-0.308540\pi$
$883$	33.6301	1.13174	0.565871	+	0.824494i	$0.308540\pi$
$884$	0	0
$885$	−11.4950	−0.386400
$886$	31.5072	1.05850
$887$	18.6158	0.625058	0.312529	−	0.949908i	$-0.398824\pi$
$887$	18.6158	0.625058	0.312529	+	0.949908i	$0.398824\pi$
$888$	−19.9740	−0.670284
$889$	21.3135	0.714831
$890$	16.3678	0.548650
$891$	83.8311	2.80845
$892$	−35.4074	−1.18553
$893$	−39.2991	−1.31510
$894$	−75.8897	−2.53813
$895$	3.46557	0.115841
$896$	25.2578	0.843803
$897$	0	0
$898$	51.6865	1.72480
$899$	2.35340	0.0784903
$900$	−68.8282	−2.29427
$901$	8.51356	0.283628
$902$	−35.0880	−1.16830
$903$	−77.6808	−2.58505
$904$	16.5301	0.549782
$905$	24.2740	0.806896
$906$	45.1891	1.50131
$907$	56.0061	1.85965	0.929825	−	0.368001i	$-0.119958\pi$
$907$	56.0061	1.85965	0.929825	+	0.368001i	$0.119958\pi$
$908$	24.7488	0.821317
$909$	84.1660	2.79161
$910$	0	0
$911$	21.0231	0.696527	0.348264	−	0.937397i	$-0.386771\pi$
$911$	21.0231	0.696527	0.348264	+	0.937397i	$0.386771\pi$
$912$	71.6505	2.37258
$913$	8.10063	0.268092
$914$	66.7763	2.20876
$915$	−5.68890	−0.188069
$916$	25.5700	0.844856
$917$	38.6701	1.27700
$918$	−69.2160	−2.28447
$919$	−6.62723	−0.218612	−0.109306	−	0.994008i	$-0.534863\pi$
$919$	−6.62723	−0.218612	−0.109306	+	0.994008i	$0.534863\pi$
$920$	−7.94822	−0.262045
$921$	−66.1927	−2.18112
$922$	−45.0237	−1.48278
$923$	0	0
$924$	92.2147	3.03364
$925$	−22.3010	−0.733254
$926$	−43.4851	−1.42901
$927$	−123.530	−4.05726
$928$	−18.7336	−0.614959
$929$	−7.34274	−0.240908	−0.120454	−	0.992719i	$-0.538435\pi$
$929$	−7.34274	−0.240908	−0.120454	+	0.992719i	$0.538435\pi$
$930$	−7.55525	−0.247746
$931$	21.0246	0.689055
$932$	−24.5759	−0.805012
$933$	62.5344	2.04728
$934$	−76.2796	−2.49595
$935$	9.69568	0.317083
$936$	0	0
$937$	23.5797	0.770315	0.385158	−	0.922851i	$-0.374147\pi$
$937$	23.5797	0.770315	0.385158	+	0.922851i	$0.374147\pi$
$938$	−82.8718	−2.70586
$939$	102.527	3.34585
$940$	−13.4761	−0.439542
$941$	−39.1800	−1.27723	−0.638616	−	0.769525i	$-0.720493\pi$
$941$	−39.1800	−1.27723	−0.638616	+	0.769525i	$0.720493\pi$
$942$	−61.3931	−2.00029
$943$	30.3885	0.989587
$944$	−8.91283	−0.290088
$945$	47.6677	1.55063
$946$	−61.4226	−1.99702
$947$	1.60414	0.0521276	0.0260638	−	0.999660i	$-0.491703\pi$
$947$	1.60414	0.0521276	0.0260638	+	0.999660i	$0.491703\pi$
$948$	−93.0470	−3.02203
$949$	0	0
$950$	−64.5283	−2.09358
$951$	−43.6038	−1.41395
$952$	−7.66907	−0.248556
$953$	26.0100	0.842545	0.421272	−	0.906934i	$-0.361584\pi$
$953$	26.0100	0.842545	0.421272	+	0.906934i	$0.361584\pi$
$954$	56.0965	1.81619
$955$	21.1675	0.684965
$956$	−61.9951	−2.00507
$957$	−28.0592	−0.907027
$958$	−60.3811	−1.95083
$959$	−19.5641	−0.631757
$960$	40.4518	1.30558
$961$	1.00000	0.0322581
$962$	0	0
$963$	96.2083	3.10027
$964$	14.1731	0.456484
$965$	20.8423	0.670937
$966$	−143.865	−4.62879
$967$	1.43627	0.0461872	0.0230936	−	0.999733i	$-0.492648\pi$
$967$	1.43627	0.0461872	0.0230936	+	0.999733i	$0.492648\pi$
$968$	2.92101	0.0938850
$969$	−61.0592	−1.96150
$970$	43.7776	1.40562
$971$	21.0937	0.676929	0.338465	−	0.940979i	$-0.390092\pi$
$971$	21.0937	0.676929	0.338465	+	0.940979i	$0.390092\pi$
$972$	−77.2246	−2.47698
$973$	−10.6045	−0.339964
$974$	79.8084	2.55722
$975$	0	0
$976$	−4.41098	−0.141192
$977$	−49.6302	−1.58781	−0.793905	−	0.608042i	$-0.791955\pi$
$977$	−49.6302	−1.58781	−0.793905	+	0.608042i	$0.791955\pi$
$978$	−48.7016	−1.55731
$979$	25.8298	0.825526
$980$	7.20958	0.230302
$981$	71.7805	2.29178
$982$	61.0322	1.94762
$983$	−38.0572	−1.21384	−0.606918	−	0.794764i	$-0.707595\pi$
$983$	−38.0572	−1.21384	−0.606918	+	0.794764i	$0.707595\pi$
$984$	15.0504	0.479788
$985$	7.36385	0.234632
$986$	11.7485	0.374149
$987$	−48.4491	−1.54215
$988$	0	0
$989$	53.1961	1.69154
$990$	63.8856	2.03042
$991$	−26.7317	−0.849160	−0.424580	−	0.905390i	$-0.639578\pi$
$991$	−26.7317	−0.849160	−0.424580	+	0.905390i	$0.639578\pi$
$992$	−7.96021	−0.252737
$993$	78.2468	2.48309
$994$	−73.5402	−2.33255
$995$	−12.4124	−0.393499
$996$	−17.4933	−0.554297
$997$	−47.3736	−1.50034	−0.750168	−	0.661247i	$-0.770028\pi$
$997$	−47.3736	−1.50034	−0.750168	+	0.661247i	$0.770028\pi$
$998$	77.6545	2.45811
$999$	−82.0324	−2.59539

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.v.1.44	yes	54
13.12	even	2		5239.2.a.u.1.11	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5239.2.a.u.1.11	✓	54	13.12	even	2
5239.2.a.v.1.44	yes	54	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5239 = 13^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5239.a (trivial)

\(f(q)\)	\(=\)	\(q+2.12031 q^{2} -3.21196 q^{3} +2.49571 q^{4} +1.10938 q^{5} -6.81034 q^{6} -3.09903 q^{7} +1.05106 q^{8} +7.31667 q^{9} +O(q^{10})\)	\(q+2.12031 q^{2} -3.21196 q^{3} +2.49571 q^{4} +1.10938 q^{5} -6.81034 q^{6} -3.09903 q^{7} +1.05106 q^{8} +7.31667 q^{9} +2.35222 q^{10} +3.71202 q^{11} -8.01612 q^{12} -6.57090 q^{14} -3.56327 q^{15} -2.76284 q^{16} +2.35444 q^{17} +15.5136 q^{18} +8.07407 q^{19} +2.76869 q^{20} +9.95394 q^{21} +7.87063 q^{22} -6.81650 q^{23} -3.37597 q^{24} -3.76928 q^{25} -13.8650 q^{27} -7.73428 q^{28} +2.35340 q^{29} -7.55525 q^{30} +1.00000 q^{31} -7.96021 q^{32} -11.9229 q^{33} +4.99215 q^{34} -3.43799 q^{35} +18.2603 q^{36} +5.91652 q^{37} +17.1195 q^{38} +1.16603 q^{40} -4.45809 q^{41} +21.1054 q^{42} -7.80402 q^{43} +9.26414 q^{44} +8.11695 q^{45} -14.4531 q^{46} -4.86732 q^{47} +8.87414 q^{48} +2.60397 q^{49} -7.99204 q^{50} -7.56237 q^{51} +3.61596 q^{53} -29.3980 q^{54} +4.11803 q^{55} -3.25728 q^{56} -25.9336 q^{57} +4.98994 q^{58} +3.22596 q^{59} -8.89291 q^{60} +1.59654 q^{61} +2.12031 q^{62} -22.6746 q^{63} -11.3524 q^{64} -25.2801 q^{66} +12.6119 q^{67} +5.87601 q^{68} +21.8943 q^{69} -7.28961 q^{70} +11.1918 q^{71} +7.69029 q^{72} -10.5849 q^{73} +12.5449 q^{74} +12.1068 q^{75} +20.1506 q^{76} -11.5037 q^{77} +11.6075 q^{79} -3.06504 q^{80} +22.5837 q^{81} -9.45252 q^{82} +2.18227 q^{83} +24.8422 q^{84} +2.61197 q^{85} -16.5469 q^{86} -7.55902 q^{87} +3.90157 q^{88} +6.95843 q^{89} +17.2105 q^{90} -17.0120 q^{92} -3.21196 q^{93} -10.3202 q^{94} +8.95720 q^{95} +25.5679 q^{96} +18.6112 q^{97} +5.52122 q^{98} +27.1596 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 2 q^{2} + 7 q^{3} + 64 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 6 q^{8} + 95 q^{9}+O(q^{10}) \) 54 * q + 2 * q^2 + 7 * q^3 + 64 * q^4 + 5 * q^5 - 3 * q^6 + 5 * q^7 + 6 * q^8 + 95 * q^9	\( 54 q + 2 q^{2} + 7 q^{3} + 64 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 6 q^{8} + 95 q^{9} - 6 q^{10} - 7 q^{11} + 5 q^{12} + 38 q^{14} + 4 q^{15} + 76 q^{16} + 62 q^{17} - 9 q^{18} + 8 q^{19} + 16 q^{20} - 6 q^{21} + 15 q^{22} + 38 q^{23} - 99 q^{24} + 87 q^{25} + 25 q^{27} + 19 q^{28} + 95 q^{29} + 41 q^{30} + 54 q^{31} + 9 q^{32} + 12 q^{33} + 7 q^{34} + 53 q^{35} + 97 q^{36} - 24 q^{37} - 16 q^{38} - 28 q^{40} + 22 q^{41} + 11 q^{42} + 11 q^{43} - 24 q^{44} + 8 q^{45} + 9 q^{46} + 45 q^{47} + 2 q^{48} + 105 q^{49} + 6 q^{50} + 58 q^{51} + 56 q^{53} + 50 q^{54} + q^{55} + 91 q^{56} - 51 q^{57} + 25 q^{58} + 36 q^{59} + 100 q^{60} + 48 q^{61} + 2 q^{62} - 56 q^{63} + 90 q^{64} - 24 q^{66} + 26 q^{67} + 140 q^{68} + 47 q^{69} - 24 q^{70} + 40 q^{71} + 7 q^{72} + 9 q^{73} + 114 q^{74} + 18 q^{75} - 67 q^{76} + 65 q^{77} + 33 q^{79} + 53 q^{80} + 210 q^{81} - 6 q^{82} - 41 q^{83} - 37 q^{84} + 37 q^{85} - 42 q^{86} - 16 q^{87} - 22 q^{88} - 24 q^{89} - 40 q^{90} + 87 q^{92} + 7 q^{93} - 4 q^{94} + 61 q^{95} - 200 q^{96} + 28 q^{97} + 68 q^{98} + 39 q^{99}+O(q^{100}) \) 54 * q + 2 * q^2 + 7 * q^3 + 64 * q^4 + 5 * q^5 - 3 * q^6 + 5 * q^7 + 6 * q^8 + 95 * q^9 - 6 * q^10 - 7 * q^11 + 5 * q^12 + 38 * q^14 + 4 * q^15 + 76 * q^16 + 62 * q^17 - 9 * q^18 + 8 * q^19 + 16 * q^20 - 6 * q^21 + 15 * q^22 + 38 * q^23 - 99 * q^24 + 87 * q^25 + 25 * q^27 + 19 * q^28 + 95 * q^29 + 41 * q^30 + 54 * q^31 + 9 * q^32 + 12 * q^33 + 7 * q^34 + 53 * q^35 + 97 * q^36 - 24 * q^37 - 16 * q^38 - 28 * q^40 + 22 * q^41 + 11 * q^42 + 11 * q^43 - 24 * q^44 + 8 * q^45 + 9 * q^46 + 45 * q^47 + 2 * q^48 + 105 * q^49 + 6 * q^50 + 58 * q^51 + 56 * q^53 + 50 * q^54 + q^55 + 91 * q^56 - 51 * q^57 + 25 * q^58 + 36 * q^59 + 100 * q^60 + 48 * q^61 + 2 * q^62 - 56 * q^63 + 90 * q^64 - 24 * q^66 + 26 * q^67 + 140 * q^68 + 47 * q^69 - 24 * q^70 + 40 * q^71 + 7 * q^72 + 9 * q^73 + 114 * q^74 + 18 * q^75 - 67 * q^76 + 65 * q^77 + 33 * q^79 + 53 * q^80 + 210 * q^81 - 6 * q^82 - 41 * q^83 - 37 * q^84 + 37 * q^85 - 42 * q^86 - 16 * q^87 - 22 * q^88 - 24 * q^89 - 40 * q^90 + 87 * q^92 + 7 * q^93 - 4 * q^94 + 61 * q^95 - 200 * q^96 + 28 * q^97 + 68 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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