LMFDB - Embedded newform 5239.2.a.v.1.17

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			1.17
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)

$f(q)$	$=$	$q-1.26938 q^{2} +3.36016 q^{3} -0.388685 q^{4} -2.56909 q^{5} -4.26531 q^{6} -0.213862 q^{7} +3.03214 q^{8} +8.29068 q^{9} +O(q^{10})$	\(q-1.26938 q^{2} +3.36016 q^{3} -0.388685 q^{4} -2.56909 q^{5} -4.26531 q^{6} -0.213862 q^{7} +3.03214 q^{8} +8.29068 q^{9} +3.26114 q^{10} +0.706541 q^{11} -1.30604 q^{12} +0.271472 q^{14} -8.63256 q^{15} -3.07155 q^{16} -3.40545 q^{17} -10.5240 q^{18} -4.17871 q^{19} +0.998566 q^{20} -0.718612 q^{21} -0.896866 q^{22} +7.87457 q^{23} +10.1885 q^{24} +1.60022 q^{25} +17.7776 q^{27} +0.0831251 q^{28} -0.277080 q^{29} +10.9580 q^{30} +1.00000 q^{31} -2.16532 q^{32} +2.37409 q^{33} +4.32280 q^{34} +0.549432 q^{35} -3.22246 q^{36} +3.14418 q^{37} +5.30436 q^{38} -7.78984 q^{40} +6.95329 q^{41} +0.912189 q^{42} +8.93248 q^{43} -0.274622 q^{44} -21.2995 q^{45} -9.99579 q^{46} -6.34266 q^{47} -10.3209 q^{48} -6.95426 q^{49} -2.03129 q^{50} -11.4429 q^{51} -4.95904 q^{53} -22.5664 q^{54} -1.81517 q^{55} -0.648461 q^{56} -14.0412 q^{57} +0.351719 q^{58} -9.73850 q^{59} +3.35534 q^{60} +8.84499 q^{61} -1.26938 q^{62} -1.77307 q^{63} +8.89171 q^{64} -3.01362 q^{66} +14.4969 q^{67} +1.32365 q^{68} +26.4598 q^{69} -0.697436 q^{70} +11.4524 q^{71} +25.1385 q^{72} -2.28309 q^{73} -3.99115 q^{74} +5.37701 q^{75} +1.62420 q^{76} -0.151103 q^{77} -7.67017 q^{79} +7.89110 q^{80} +34.8634 q^{81} -8.82633 q^{82} +4.41344 q^{83} +0.279314 q^{84} +8.74891 q^{85} -11.3387 q^{86} -0.931034 q^{87} +2.14233 q^{88} +5.25669 q^{89} +27.0371 q^{90} -3.06073 q^{92} +3.36016 q^{93} +8.05122 q^{94} +10.7355 q^{95} -7.27583 q^{96} -2.29137 q^{97} +8.82757 q^{98} +5.85771 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.26938	−0.897584	−0.448792	−	0.893636i	$-0.648146\pi$
$2$	−1.26938	−0.897584	−0.448792	+	0.893636i	$0.648146\pi$
$3$	3.36016	1.93999	0.969995	−	0.243125i	$-0.0781724\pi$
$3$	3.36016	1.93999	0.969995	+	0.243125i	$0.0781724\pi$
$4$	−0.388685	−0.194342
$5$	−2.56909	−1.14893	−0.574466	−	0.818528i	$-0.694790\pi$
$5$	−2.56909	−1.14893	−0.574466	+	0.818528i	$0.694790\pi$
$6$	−4.26531	−1.74130
$7$	−0.213862	−0.0808324	−0.0404162	−	0.999183i	$-0.512868\pi$
$7$	−0.213862	−0.0808324	−0.0404162	+	0.999183i	$0.512868\pi$
$8$	3.03214	1.07202
$9$	8.29068	2.76356
$10$	3.26114	1.03126
$11$	0.706541	0.213030	0.106515	−	0.994311i	$-0.466031\pi$
$11$	0.706541	0.213030	0.106515	+	0.994311i	$0.466031\pi$
$12$	−1.30604	−0.377022
$13$	0	0
$13$	0	0
$14$	0.271472	0.0725539
$15$	−8.63256	−2.22892
$16$	−3.07155	−0.767889
$17$	−3.40545	−0.825943	−0.412971	−	0.910744i	$-0.635509\pi$
$17$	−3.40545	−0.825943	−0.412971	+	0.910744i	$0.635509\pi$
$18$	−10.5240	−2.48053
$19$	−4.17871	−0.958663	−0.479331	−	0.877634i	$-0.659121\pi$
$19$	−4.17871	−0.958663	−0.479331	+	0.877634i	$0.659121\pi$
$20$	0.998566	0.223286
$21$	−0.718612	−0.156814
$22$	−0.896866	−0.191213
$23$	7.87457	1.64196	0.820981	−	0.570955i	$-0.193427\pi$
$23$	7.87457	1.64196	0.820981	+	0.570955i	$0.193427\pi$
$24$	10.1885	2.07971
$25$	1.60022	0.320045
$26$	0	0
$27$	17.7776	3.42129
$28$	0.0831251	0.0157092
$29$	−0.277080	−0.0514525	−0.0257262	−	0.999669i	$-0.508190\pi$
$29$	−0.277080	−0.0514525	−0.0257262	+	0.999669i	$0.508190\pi$
$30$	10.9580	2.00064
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−2.16532	−0.382778
$33$	2.37409	0.413276
$34$	4.32280	0.741353
$35$	0.549432	0.0928710
$36$	−3.22246	−0.537077
$37$	3.14418	0.516900	0.258450	−	0.966025i	$-0.416788\pi$
$37$	3.14418	0.516900	0.258450	+	0.966025i	$0.416788\pi$
$38$	5.30436	0.860481
$39$	0	0
$40$	−7.78984	−1.23168
$41$	6.95329	1.08592	0.542960	−	0.839758i	$-0.317303\pi$
$41$	6.95329	1.08592	0.542960	+	0.839758i	$0.317303\pi$
$42$	0.912189	0.140754
$43$	8.93248	1.36219	0.681095	−	0.732195i	$-0.261504\pi$
$43$	8.93248	1.36219	0.681095	+	0.732195i	$0.261504\pi$
$44$	−0.274622	−0.0414008
$45$	−21.2995	−3.17514
$46$	−9.99579	−1.47380
$47$	−6.34266	−0.925172	−0.462586	−	0.886574i	$-0.653078\pi$
$47$	−6.34266	−0.925172	−0.462586	+	0.886574i	$0.653078\pi$
$48$	−10.3209	−1.48970
$49$	−6.95426	−0.993466
$50$	−2.03129	−0.287267
$51$	−11.4429	−1.60232
$52$	0	0
$53$	−4.95904	−0.681176	−0.340588	−	0.940213i	$-0.610626\pi$
$53$	−4.95904	−0.681176	−0.340588	+	0.940213i	$0.610626\pi$
$54$	−22.5664	−3.07090
$55$	−1.81517	−0.244757
$56$	−0.648461	−0.0866542
$57$	−14.0412	−1.85980
$58$	0.351719	0.0461829
$59$	−9.73850	−1.26784	−0.633922	−	0.773397i	$-0.718556\pi$
$59$	−9.73850	−1.26784	−0.633922	+	0.773397i	$0.718556\pi$
$60$	3.35534	0.433173
$61$	8.84499	1.13249	0.566243	−	0.824239i	$-0.308397\pi$
$61$	8.84499	1.13249	0.566243	+	0.824239i	$0.308397\pi$
$62$	−1.26938	−0.161211
$63$	−1.77307	−0.223385
$64$	8.89171	1.11146
$65$	0	0
$66$	−3.01362	−0.370950
$67$	14.4969	1.77108	0.885540	−	0.464563i	$-0.153789\pi$
$67$	14.4969	1.77108	0.885540	+	0.464563i	$0.153789\pi$
$68$	1.32365	0.160516
$69$	26.4598	3.18539
$70$	−0.697436	−0.0833595
$71$	11.4524	1.35915	0.679576	−	0.733605i	$-0.262164\pi$
$71$	11.4524	1.35915	0.679576	+	0.733605i	$0.262164\pi$
$72$	25.1385	2.96260
$73$	−2.28309	−0.267215	−0.133608	−	0.991034i	$-0.542656\pi$
$73$	−2.28309	−0.267215	−0.133608	+	0.991034i	$0.542656\pi$
$74$	−3.99115	−0.463962
$75$	5.37701	0.620884
$76$	1.62420	0.186309
$77$	−0.151103	−0.0172197
$78$	0	0
$79$	−7.67017	−0.862961	−0.431481	−	0.902122i	$-0.642009\pi$
$79$	−7.67017	−0.862961	−0.431481	+	0.902122i	$0.642009\pi$
$80$	7.89110	0.882252
$81$	34.8634	3.87371
$82$	−8.82633	−0.974706
$83$	4.41344	0.484438	0.242219	−	0.970222i	$-0.422125\pi$
$83$	4.41344	0.484438	0.242219	+	0.970222i	$0.422125\pi$
$84$	0.279314	0.0304756
$85$	8.74891	0.948952
$86$	−11.3387	−1.22268
$87$	−0.931034	−0.0998173
$88$	2.14233	0.228373
$89$	5.25669	0.557208	0.278604	−	0.960406i	$-0.410128\pi$
$89$	5.25669	0.557208	0.278604	+	0.960406i	$0.410128\pi$
$90$	27.0371	2.84996
$91$	0	0
$92$	−3.06073	−0.319103
$93$	3.36016	0.348433
$94$	8.05122	0.830420
$95$	10.7355	1.10144
$96$	−7.27583	−0.742586
$97$	−2.29137	−0.232653	−0.116327	−	0.993211i	$-0.537112\pi$
$97$	−2.29137	−0.232653	−0.116327	+	0.993211i	$0.537112\pi$
$98$	8.82757	0.891720
$99$	5.85771	0.588722
$100$	−0.621983	−0.0621983
$101$	−14.1720	−1.41017	−0.705085	−	0.709123i	$-0.749091\pi$
$101$	−14.1720	−1.41017	−0.705085	+	0.709123i	$0.749091\pi$
$102$	14.5253	1.43822
$103$	14.9248	1.47058	0.735291	−	0.677751i	$-0.237045\pi$
$103$	14.9248	1.47058	0.735291	+	0.677751i	$0.237045\pi$
$104$	0	0
$105$	1.84618	0.180169
$106$	6.29488	0.611413
$107$	10.5773	1.02255	0.511273	−	0.859418i	$-0.329174\pi$
$107$	10.5773	1.02255	0.511273	+	0.859418i	$0.329174\pi$
$108$	−6.90986	−0.664902
$109$	−8.98462	−0.860571	−0.430285	−	0.902693i	$-0.641587\pi$
$109$	−8.98462	−0.860571	−0.430285	+	0.902693i	$0.641587\pi$
$110$	2.30413	0.219690
$111$	10.5650	1.00278
$112$	0.656890	0.0620703
$113$	−5.30132	−0.498707	−0.249353	−	0.968413i	$-0.580218\pi$
$113$	−5.30132	−0.498707	−0.249353	+	0.968413i	$0.580218\pi$
$114$	17.8235	1.66932
$115$	−20.2305	−1.88650
$116$	0.107697	0.00999940
$117$	0	0
$118$	12.3618	1.13800
$119$	0.728298	0.0667630
$120$	−26.1751	−2.38945
$121$	−10.5008	−0.954618
$122$	−11.2276	−1.01650
$123$	23.3642	2.10668
$124$	−0.388685	−0.0349049
$125$	8.73433	0.781222
$126$	2.25069	0.200507
$127$	1.30938	0.116188	0.0580942	−	0.998311i	$-0.481498\pi$
$127$	1.30938	0.116188	0.0580942	+	0.998311i	$0.481498\pi$
$128$	−6.95629	−0.614855
$129$	30.0146	2.64264
$130$	0	0
$131$	14.4904	1.26604	0.633018	−	0.774137i	$-0.281816\pi$
$131$	14.4904	1.26604	0.633018	+	0.774137i	$0.281816\pi$
$132$	−0.922773	−0.0803171
$133$	0.893670	0.0774910
$134$	−18.4020	−1.58969
$135$	−45.6721	−3.93083
$136$	−10.3258	−0.885430
$137$	10.6754	0.912058	0.456029	−	0.889965i	$-0.349271\pi$
$137$	10.6754	0.912058	0.456029	+	0.889965i	$0.349271\pi$
$138$	−33.5875	−2.85916
$139$	17.6789	1.49950	0.749751	−	0.661720i	$-0.230173\pi$
$139$	17.6789	1.49950	0.749751	+	0.661720i	$0.230173\pi$
$140$	−0.213556	−0.0180488
$141$	−21.3124	−1.79483
$142$	−14.5374	−1.21995
$143$	0	0
$144$	−25.4653	−2.12211
$145$	0.711844	0.0591154
$146$	2.89810	0.239848
$147$	−23.3674	−1.92731
$148$	−1.22210	−0.100456
$149$	−7.97452	−0.653298	−0.326649	−	0.945146i	$-0.605920\pi$
$149$	−7.97452	−0.653298	−0.326649	+	0.945146i	$0.605920\pi$
$150$	−6.82545	−0.557296
$151$	14.6873	1.19524	0.597618	−	0.801781i	$-0.296114\pi$
$151$	14.6873	1.19524	0.597618	+	0.801781i	$0.296114\pi$
$152$	−12.6704	−1.02771
$153$	−28.2335	−2.28254
$154$	0.191806	0.0154562
$155$	−2.56909	−0.206354
$156$	0	0
$157$	−9.83478	−0.784901	−0.392450	−	0.919773i	$-0.628373\pi$
$157$	−9.83478	−0.784901	−0.392450	+	0.919773i	$0.628373\pi$
$158$	9.73632	0.774580
$159$	−16.6632	−1.32147
$160$	5.56290	0.439786
$161$	−1.68408	−0.132724
$162$	−44.2548	−3.47698
$163$	18.0922	1.41709	0.708545	−	0.705666i	$-0.249352\pi$
$163$	18.0922	1.41709	0.708545	+	0.705666i	$0.249352\pi$
$164$	−2.70264	−0.211040
$165$	−6.09926	−0.474826
$166$	−5.60231	−0.434824
$167$	−13.6230	−1.05418	−0.527088	−	0.849811i	$-0.676716\pi$
$167$	−13.6230	−1.05418	−0.527088	+	0.849811i	$0.676716\pi$
$168$	−2.17893	−0.168108
$169$	0	0
$170$	−11.1057	−0.851765
$171$	−34.6444	−2.64932
$172$	−3.47192	−0.264731
$173$	20.7218	1.57545	0.787727	−	0.616025i	$-0.211258\pi$
$173$	20.7218	1.57545	0.787727	+	0.616025i	$0.211258\pi$
$174$	1.18183	0.0895944
$175$	−0.342228	−0.0258700
$176$	−2.17018	−0.163583
$177$	−32.7229	−2.45961
$178$	−6.67272	−0.500141
$179$	−14.2402	−1.06437	−0.532183	−	0.846630i	$-0.678628\pi$
$179$	−14.2402	−1.06437	−0.532183	+	0.846630i	$0.678628\pi$
$180$	8.27880	0.617065
$181$	−23.7662	−1.76653	−0.883266	−	0.468873i	$-0.844660\pi$
$181$	−23.7662	−1.76653	−0.883266	+	0.468873i	$0.844660\pi$
$182$	0	0
$183$	29.7206	2.19701
$184$	23.8768	1.76022
$185$	−8.07769	−0.593883
$186$	−4.26531	−0.312748
$187$	−2.40609	−0.175951
$188$	2.46530	0.179800
$189$	−3.80195	−0.276551
$190$	−13.6274	−0.988634
$191$	−7.30052	−0.528247	−0.264124	−	0.964489i	$-0.585083\pi$
$191$	−7.30052	−0.528247	−0.264124	+	0.964489i	$0.585083\pi$
$192$	29.8776	2.15623
$193$	14.8736	1.07063	0.535313	−	0.844654i	$-0.320194\pi$
$193$	14.8736	1.07063	0.535313	+	0.844654i	$0.320194\pi$
$194$	2.90861	0.208826
$195$	0	0
$196$	2.70302	0.193073
$197$	22.7449	1.62050	0.810252	−	0.586082i	$-0.199330\pi$
$197$	22.7449	1.62050	0.810252	+	0.586082i	$0.199330\pi$
$198$	−7.43563	−0.528428
$199$	−8.93722	−0.633543	−0.316771	−	0.948502i	$-0.602599\pi$
$199$	−8.93722	−0.633543	−0.316771	+	0.948502i	$0.602599\pi$
$200$	4.85210	0.343096
$201$	48.7120	3.43588
$202$	17.9896	1.26575
$203$	0.0592570	0.00415903
$204$	4.44767	0.311399
$205$	−17.8636	−1.24765
$206$	−18.9452	−1.31997
$207$	65.2856	4.53766
$208$	0	0
$209$	−2.95243	−0.204224
$210$	−2.34350	−0.161717
$211$	−10.0580	−0.692422	−0.346211	−	0.938157i	$-0.612532\pi$
$211$	−10.0580	−0.692422	−0.346211	+	0.938157i	$0.612532\pi$
$212$	1.92750	0.132381
$213$	38.4820	2.63674
$214$	−13.4266	−0.917822
$215$	−22.9484	−1.56506
$216$	53.9040	3.66770
$217$	−0.213862	−0.0145179
$218$	11.4049	0.772435
$219$	−7.67155	−0.518395
$220$	0.705528	0.0475667
$221$	0	0
$222$	−13.4109	−0.900081
$223$	−21.0132	−1.40715	−0.703573	−	0.710623i	$-0.748413\pi$
$223$	−21.0132	−1.40715	−0.703573	+	0.710623i	$0.748413\pi$
$224$	0.463081	0.0309409
$225$	13.2670	0.884464
$226$	6.72937	0.447631
$227$	13.8256	0.917638	0.458819	−	0.888530i	$-0.348273\pi$
$227$	13.8256	0.917638	0.458819	+	0.888530i	$0.348273\pi$
$228$	5.45758	0.361437
$229$	2.87367	0.189898	0.0949489	−	0.995482i	$-0.469731\pi$
$229$	2.87367	0.189898	0.0949489	+	0.995482i	$0.469731\pi$
$230$	25.6801	1.69330
$231$	−0.507729	−0.0334061
$232$	−0.840145	−0.0551582
$233$	22.7768	1.49216	0.746078	−	0.665859i	$-0.231935\pi$
$233$	22.7768	1.49216	0.746078	+	0.665859i	$0.231935\pi$
$234$	0	0
$235$	16.2949	1.06296
$236$	3.78521	0.246396
$237$	−25.7730	−1.67414
$238$	−0.924484	−0.0599254
$239$	22.1496	1.43274	0.716371	−	0.697720i	$-0.245802\pi$
$239$	22.1496	1.43274	0.716371	+	0.697720i	$0.245802\pi$
$240$	26.5154	1.71156
$241$	26.2959	1.69387	0.846935	−	0.531696i	$-0.178445\pi$
$241$	26.2959	1.69387	0.846935	+	0.531696i	$0.178445\pi$
$242$	13.3295	0.856850
$243$	63.8140	4.09367
$244$	−3.43791	−0.220090
$245$	17.8661	1.14143
$246$	−29.6579	−1.89092
$247$	0	0
$248$	3.03214	0.192541
$249$	14.8299	0.939805
$250$	−11.0871	−0.701213
$251$	22.9597	1.44920	0.724602	−	0.689168i	$-0.242024\pi$
$251$	22.9597	1.44920	0.724602	+	0.689168i	$0.242024\pi$
$252$	0.689164	0.0434132
$253$	5.56371	0.349787
$254$	−1.66209	−0.104289
$255$	29.3977	1.84096
$256$	−8.95329	−0.559580
$257$	−10.6242	−0.662720	−0.331360	−	0.943504i	$-0.607507\pi$
$257$	−10.6242	−0.662720	−0.331360	+	0.943504i	$0.607507\pi$
$258$	−38.0998	−2.37199
$259$	−0.672422	−0.0417823
$260$	0	0
$261$	−2.29718	−0.142192
$262$	−18.3938	−1.13637
$263$	9.66393	0.595903	0.297952	−	0.954581i	$-0.403697\pi$
$263$	9.66393	0.595903	0.297952	+	0.954581i	$0.403697\pi$
$264$	7.19858	0.443042
$265$	12.7402	0.782625
$266$	−1.13440	−0.0695547
$267$	17.6633	1.08098
$268$	−5.63473	−0.344196
$269$	−10.2029	−0.622082	−0.311041	−	0.950397i	$-0.600678\pi$
$269$	−10.2029	−0.622082	−0.311041	+	0.950397i	$0.600678\pi$
$270$	57.9751	3.52825
$271$	−3.44899	−0.209511	−0.104756	−	0.994498i	$-0.533406\pi$
$271$	−3.44899	−0.209511	−0.104756	+	0.994498i	$0.533406\pi$
$272$	10.4600	0.634232
$273$	0	0
$274$	−13.5510	−0.818649
$275$	1.13062	0.0681792
$276$	−10.2845	−0.619056
$277$	6.85642	0.411963	0.205981	−	0.978556i	$-0.433961\pi$
$277$	6.85642	0.411963	0.205981	+	0.978556i	$0.433961\pi$
$278$	−22.4411	−1.34593
$279$	8.29068	0.496350
$280$	1.66595	0.0995598
$281$	2.64138	0.157572	0.0787858	−	0.996892i	$-0.474896\pi$
$281$	2.64138	0.157572	0.0787858	+	0.996892i	$0.474896\pi$
$282$	27.0534	1.61101
$283$	14.0880	0.837445	0.418722	−	0.908114i	$-0.362478\pi$
$283$	14.0880	0.837445	0.418722	+	0.908114i	$0.362478\pi$
$284$	−4.45138	−0.264141
$285$	36.0730	2.13678
$286$	0	0
$287$	−1.48705	−0.0877776
$288$	−17.9520	−1.05783
$289$	−5.40291	−0.317818
$290$	−0.903597	−0.0530610
$291$	−7.69937	−0.451345
$292$	0.887402	0.0519313
$293$	−24.5450	−1.43393	−0.716967	−	0.697107i	$-0.754470\pi$
$293$	−24.5450	−1.43393	−0.716967	+	0.697107i	$0.754470\pi$
$294$	29.6621	1.72993
$295$	25.0191	1.45667
$296$	9.53360	0.554129
$297$	12.5606	0.728838
$298$	10.1227	0.586390
$299$	0	0
$300$	−2.08996	−0.120664
$301$	−1.91032	−0.110109
$302$	−18.6437	−1.07283
$303$	−47.6203	−2.73572
$304$	12.8351	0.736146
$305$	−22.7236	−1.30115
$306$	35.8389	2.04878
$307$	−25.5180	−1.45639	−0.728194	−	0.685371i	$-0.759640\pi$
$307$	−25.5180	−1.45639	−0.728194	+	0.685371i	$0.759640\pi$
$308$	0.0587313	0.00334653
$309$	50.1497	2.85291
$310$	3.26114	0.185220
$311$	6.87663	0.389938	0.194969	−	0.980809i	$-0.437539\pi$
$311$	6.87663	0.389938	0.194969	+	0.980809i	$0.437539\pi$
$312$	0	0
$313$	−22.9053	−1.29468	−0.647341	−	0.762200i	$-0.724119\pi$
$313$	−22.9053	−1.29468	−0.647341	+	0.762200i	$0.724119\pi$
$314$	12.4840	0.704514
$315$	4.55517	0.256655
$316$	2.98128	0.167710
$317$	1.45819	0.0819003	0.0409502	−	0.999161i	$-0.486962\pi$
$317$	1.45819	0.0819003	0.0409502	+	0.999161i	$0.486962\pi$
$318$	21.1518	1.18613
$319$	−0.195768	−0.0109609
$320$	−22.8436	−1.27700
$321$	35.5415	1.98373
$322$	2.13773	0.119131
$323$	14.2304	0.791801
$324$	−13.5509	−0.752826
$325$	0	0
$326$	−22.9658	−1.27196
$327$	−30.1898	−1.66950
$328$	21.0833	1.16413
$329$	1.35646	0.0747839
$330$	7.74225	0.426197
$331$	12.7129	0.698762	0.349381	−	0.936981i	$-0.386392\pi$
$331$	12.7129	0.698762	0.349381	+	0.936981i	$0.386392\pi$
$332$	−1.71544	−0.0941468
$333$	26.0674	1.42849
$334$	17.2927	0.946212
$335$	−37.2439	−2.03485
$336$	2.20726	0.120416
$337$	−17.7660	−0.967774	−0.483887	−	0.875130i	$-0.660775\pi$
$337$	−17.7660	−0.967774	−0.483887	+	0.875130i	$0.660775\pi$
$338$	0	0
$339$	−17.8133	−0.967486
$340$	−3.40057	−0.184422
$341$	0.706541	0.0382613
$342$	43.9768	2.37799
$343$	2.98429	0.161137
$344$	27.0845	1.46030
$345$	−67.9777	−3.65980
$346$	−26.3038	−1.41410
$347$	24.8273	1.33280	0.666401	−	0.745594i	$-0.267834\pi$
$347$	24.8273	1.33280	0.666401	+	0.745594i	$0.267834\pi$
$348$	0.361879	0.0193987
$349$	7.90061	0.422910	0.211455	−	0.977388i	$-0.432180\pi$
$349$	7.90061	0.422910	0.211455	+	0.977388i	$0.432180\pi$
$350$	0.434416	0.0232205
$351$	0	0
$352$	−1.52989	−0.0815433
$353$	26.3026	1.39994	0.699972	−	0.714170i	$-0.253196\pi$
$353$	26.3026	1.39994	0.699972	+	0.714170i	$0.253196\pi$
$354$	41.5377	2.20770
$355$	−29.4223	−1.56157
$356$	−2.04320	−0.108289
$357$	2.44720	0.129519
$358$	18.0762	0.955358
$359$	29.8489	1.57537	0.787683	−	0.616081i	$-0.211281\pi$
$359$	29.8489	1.57537	0.787683	+	0.616081i	$0.211281\pi$
$360$	−64.5831	−3.40383
$361$	−1.53835	−0.0809655
$362$	30.1683	1.58561
$363$	−35.2844	−1.85195
$364$	0	0
$365$	5.86546	0.307012
$366$	−37.7266	−1.97200
$367$	−4.11323	−0.214709	−0.107354	−	0.994221i	$-0.534238\pi$
$367$	−4.11323	−0.214709	−0.107354	+	0.994221i	$0.534238\pi$
$368$	−24.1872	−1.26084
$369$	57.6475	3.00101
$370$	10.2536	0.533060
$371$	1.06055	0.0550611
$372$	−1.30604	−0.0677152
$373$	6.31093	0.326767	0.163384	−	0.986563i	$-0.447759\pi$
$373$	6.31093	0.326767	0.163384	+	0.986563i	$0.447759\pi$
$374$	3.05423	0.157931
$375$	29.3488	1.51556
$376$	−19.2318	−0.991806
$377$	0	0
$378$	4.82611	0.248228
$379$	11.8348	0.607911	0.303955	−	0.952686i	$-0.401693\pi$
$379$	11.8348	0.607911	0.303955	+	0.952686i	$0.401693\pi$
$380$	−4.17272	−0.214056
$381$	4.39972	0.225404
$382$	9.26711	0.474146
$383$	32.3273	1.65185	0.825924	−	0.563782i	$-0.190654\pi$
$383$	32.3273	1.65185	0.825924	+	0.563782i	$0.190654\pi$
$384$	−23.3742	−1.19281
$385$	0.388196	0.0197843
$386$	−18.8802	−0.960976
$387$	74.0564	3.76450
$388$	0.890620	0.0452144
$389$	12.8445	0.651241	0.325620	−	0.945501i	$-0.394427\pi$
$389$	12.8445	0.651241	0.325620	+	0.945501i	$0.394427\pi$
$390$	0	0
$391$	−26.8165	−1.35617
$392$	−21.0863	−1.06502
$393$	48.6902	2.45610
$394$	−28.8718	−1.45454
$395$	19.7053	0.991484
$396$	−2.27680	−0.114414
$397$	−9.77191	−0.490438	−0.245219	−	0.969468i	$-0.578860\pi$
$397$	−9.77191	−0.490438	−0.245219	+	0.969468i	$0.578860\pi$
$398$	11.3447	0.568658
$399$	3.00288	0.150332
$400$	−4.91518	−0.245759
$401$	−5.95818	−0.297537	−0.148769	−	0.988872i	$-0.547531\pi$
$401$	−5.95818	−0.297537	−0.148769	+	0.988872i	$0.547531\pi$
$402$	−61.8338	−3.08399
$403$	0	0
$404$	5.50846	0.274056
$405$	−89.5672	−4.45063
$406$	−0.0752194	−0.00373308
$407$	2.22149	0.110115
$408$	−34.6963	−1.71772
$409$	−12.0221	−0.594455	−0.297227	−	0.954807i	$-0.596062\pi$
$409$	−12.0221	−0.594455	−0.297227	+	0.954807i	$0.596062\pi$
$410$	22.6756	1.11987
$411$	35.8709	1.76938
$412$	−5.80103	−0.285796
$413$	2.08270	0.102483
$414$	−82.8720	−4.07294
$415$	−11.3385	−0.556586
$416$	0	0
$417$	59.4039	2.90902
$418$	3.74775	0.183308
$419$	29.6381	1.44792	0.723959	−	0.689843i	$-0.242321\pi$
$419$	29.6381	1.44792	0.723959	+	0.689843i	$0.242321\pi$
$420$	−0.717582	−0.0350144
$421$	−27.3798	−1.33441	−0.667204	−	0.744875i	$-0.732509\pi$
$421$	−27.3798	−1.33441	−0.667204	+	0.744875i	$0.732509\pi$
$422$	12.7674	0.621507
$423$	−52.5850	−2.55677
$424$	−15.0365	−0.730236
$425$	−5.44948	−0.264339
$426$	−48.8481	−2.36670
$427$	−1.89161	−0.0915415
$428$	−4.11124	−0.198724
$429$	0	0
$430$	29.1301	1.40478
$431$	4.70165	0.226471	0.113235	−	0.993568i	$-0.463879\pi$
$431$	4.70165	0.226471	0.113235	+	0.993568i	$0.463879\pi$
$432$	−54.6047	−2.62717
$433$	19.9488	0.958679	0.479340	−	0.877630i	$-0.340876\pi$
$433$	19.9488	0.958679	0.479340	+	0.877630i	$0.340876\pi$
$434$	0.271472	0.0130311
$435$	2.39191	0.114683
$436$	3.49219	0.167245
$437$	−32.9056	−1.57409
$438$	9.73807	0.465303
$439$	−28.9630	−1.38233	−0.691163	−	0.722699i	$-0.742901\pi$
$439$	−28.9630	−1.38233	−0.691163	+	0.722699i	$0.742901\pi$
$440$	−5.50384	−0.262385
$441$	−57.6556	−2.74550
$442$	0	0
$443$	14.3920	0.683786	0.341893	−	0.939739i	$-0.388932\pi$
$443$	14.3920	0.683786	0.341893	+	0.939739i	$0.388932\pi$
$444$	−4.10644	−0.194883
$445$	−13.5049	−0.640194
$446$	26.6736	1.26303
$447$	−26.7957	−1.26739
$448$	−1.90160	−0.0898424
$449$	21.3928	1.00959	0.504794	−	0.863240i	$-0.331568\pi$
$449$	21.3928	1.00959	0.504794	+	0.863240i	$0.331568\pi$
$450$	−16.8408	−0.793881
$451$	4.91278	0.231334
$452$	2.06054	0.0969198
$453$	49.3517	2.31875
$454$	−17.5499	−0.823658
$455$	0	0
$456$	−42.5747	−1.99374
$457$	−21.7558	−1.01769	−0.508846	−	0.860857i	$-0.669928\pi$
$457$	−21.7558	−1.01769	−0.508846	+	0.860857i	$0.669928\pi$
$458$	−3.64777	−0.170449
$459$	−60.5406	−2.82579
$460$	7.86328	0.366627
$461$	6.86069	0.319534	0.159767	−	0.987155i	$-0.448926\pi$
$461$	6.86069	0.319534	0.159767	+	0.987155i	$0.448926\pi$
$462$	0.644499	0.0299848
$463$	−2.89548	−0.134564	−0.0672822	−	0.997734i	$-0.521433\pi$
$463$	−2.89548	−0.134564	−0.0672822	+	0.997734i	$0.521433\pi$
$464$	0.851066	0.0395098
$465$	−8.63256	−0.400325
$466$	−28.9123	−1.33934
$467$	13.6876	0.633387	0.316693	−	0.948528i	$-0.397427\pi$
$467$	13.6876	0.633387	0.316693	+	0.948528i	$0.397427\pi$
$468$	0	0
$469$	−3.10035	−0.143161
$470$	−20.6843	−0.954096
$471$	−33.0464	−1.52270
$472$	−29.5285	−1.35916
$473$	6.31117	0.290188
$474$	32.7156	1.50268
$475$	−6.68688	−0.306815
$476$	−0.283078	−0.0129749
$477$	−41.1138	−1.88247
$478$	−28.1162	−1.28601
$479$	−6.85519	−0.313222	−0.156611	−	0.987660i	$-0.550057\pi$
$479$	−6.85519	−0.313222	−0.156611	+	0.987660i	$0.550057\pi$
$480$	18.6923	0.853181
$481$	0	0
$482$	−33.3794	−1.52039
$483$	−5.65877	−0.257483
$484$	4.08150	0.185523
$485$	5.88673	0.267303
$486$	−81.0039	−3.67441
$487$	−13.5973	−0.616152	−0.308076	−	0.951362i	$-0.599685\pi$
$487$	−13.5973	−0.616152	−0.308076	+	0.951362i	$0.599685\pi$
$488$	26.8192	1.21405
$489$	60.7927	2.74914
$490$	−22.6788	−1.02453
$491$	−15.1744	−0.684810	−0.342405	−	0.939552i	$-0.611242\pi$
$491$	−15.1744	−0.684810	−0.342405	+	0.939552i	$0.611242\pi$
$492$	−9.08129	−0.409416
$493$	0.943582	0.0424968
$494$	0	0
$495$	−15.0490	−0.676402
$496$	−3.07155	−0.137917
$497$	−2.44924	−0.109864
$498$	−18.8247	−0.843554
$499$	−41.6511	−1.86456	−0.932280	−	0.361737i	$-0.882184\pi$
$499$	−41.6511	−1.86456	−0.932280	+	0.361737i	$0.882184\pi$
$500$	−3.39490	−0.151825
$501$	−45.7754	−2.04509
$502$	−29.1445	−1.30078
$503$	−5.68865	−0.253645	−0.126822	−	0.991925i	$-0.540478\pi$
$503$	−5.68865	−0.253645	−0.126822	+	0.991925i	$0.540478\pi$
$504$	−5.37618	−0.239474
$505$	36.4092	1.62019
$506$	−7.06244	−0.313964
$507$	0	0
$508$	−0.508935	−0.0225803
$509$	7.02046	0.311177	0.155588	−	0.987822i	$-0.450273\pi$
$509$	7.02046	0.311177	0.155588	+	0.987822i	$0.450273\pi$
$510$	−37.3168	−1.65241
$511$	0.488267	0.0215997
$512$	25.2777	1.11713
$513$	−74.2873	−3.27987
$514$	13.4861	0.594847
$515$	−38.3431	−1.68960
$516$	−11.6662	−0.513576
$517$	−4.48135	−0.197090
$518$	0.853557	0.0375031
$519$	69.6288	3.05636
$520$	0	0
$521$	−16.0647	−0.703807	−0.351903	−	0.936036i	$-0.614465\pi$
$521$	−16.0647	−0.703807	−0.351903	+	0.936036i	$0.614465\pi$
$522$	2.91599	0.127629
$523$	36.4359	1.59323	0.796616	−	0.604486i	$-0.206621\pi$
$523$	36.4359	1.59323	0.796616	+	0.604486i	$0.206621\pi$
$524$	−5.63221	−0.246044
$525$	−1.14994	−0.0501876
$526$	−12.2672	−0.534874
$527$	−3.40545	−0.148344
$528$	−7.29215	−0.317350
$529$	39.0089	1.69604
$530$	−16.1721	−0.702472
$531$	−80.7388	−3.50377
$532$	−0.347356	−0.0150598
$533$	0	0
$534$	−22.4214	−0.970269
$535$	−27.1741	−1.17484
$536$	43.9567	1.89864
$537$	−47.8495	−2.06486
$538$	12.9513	0.558371
$539$	−4.91347	−0.211638
$540$	17.7521	0.763927
$541$	16.5765	0.712677	0.356339	−	0.934357i	$-0.384025\pi$
$541$	16.5765	0.712677	0.356339	+	0.934357i	$0.384025\pi$
$542$	4.37807	0.188054
$543$	−79.8584	−3.42705
$544$	7.37389	0.316153
$545$	23.0823	0.988737
$546$	0	0
$547$	−35.6084	−1.52250	−0.761252	−	0.648456i	$-0.775415\pi$
$547$	−35.6084	−1.52250	−0.761252	+	0.648456i	$0.775415\pi$
$548$	−4.14935	−0.177251
$549$	73.3310	3.12969
$550$	−1.43519	−0.0611966
$551$	1.15784	0.0493256
$552$	80.2299	3.41481
$553$	1.64036	0.0697552
$554$	−8.70338	−0.369771
$555$	−27.1423	−1.15213
$556$	−6.87151	−0.291417
$557$	9.08753	0.385051	0.192526	−	0.981292i	$-0.438332\pi$
$557$	9.08753	0.385051	0.192526	+	0.981292i	$0.438332\pi$
$558$	−10.5240	−0.445516
$559$	0	0
$560$	−1.68761	−0.0713146
$561$	−8.08485	−0.341343
$562$	−3.35291	−0.141434
$563$	−11.5082	−0.485012	−0.242506	−	0.970150i	$-0.577969\pi$
$563$	−11.5082	−0.485012	−0.242506	+	0.970150i	$0.577969\pi$
$564$	8.28379	0.348811
$565$	13.6196	0.572980
$566$	−17.8830	−0.751677
$567$	−7.45597	−0.313121
$568$	34.7253	1.45704
$569$	36.2216	1.51849	0.759243	−	0.650807i	$-0.225569\pi$
$569$	36.2216	1.51849	0.759243	+	0.650807i	$0.225569\pi$
$570$	−45.7902	−1.91794
$571$	3.69446	0.154609	0.0773043	−	0.997008i	$-0.475369\pi$
$571$	3.69446	0.154609	0.0773043	+	0.997008i	$0.475369\pi$
$572$	0	0
$573$	−24.5309	−1.02479
$574$	1.88762	0.0787878
$575$	12.6011	0.525502
$576$	73.7184	3.07160
$577$	−0.547978	−0.0228126	−0.0114063	−	0.999935i	$-0.503631\pi$
$577$	−0.547978	−0.0228126	−0.0114063	+	0.999935i	$0.503631\pi$
$578$	6.85833	0.285269
$579$	49.9777	2.07700
$580$	−0.276683	−0.0114886
$581$	−0.943869	−0.0391583
$582$	9.77339	0.405120
$583$	−3.50376	−0.145111
$584$	−6.92264	−0.286461
$585$	0	0
$586$	31.1568	1.28708
$587$	5.60542	0.231360	0.115680	−	0.993287i	$-0.463095\pi$
$587$	5.60542	0.231360	0.115680	+	0.993287i	$0.463095\pi$
$588$	9.08257	0.374559
$589$	−4.17871	−0.172181
$590$	−31.7586	−1.30748
$591$	76.4264	3.14376
$592$	−9.65752	−0.396922
$593$	−23.8496	−0.979385	−0.489693	−	0.871895i	$-0.662891\pi$
$593$	−23.8496	−0.979385	−0.489693	+	0.871895i	$0.662891\pi$
$594$	−15.9441	−0.654194
$595$	−1.87106	−0.0767061
$596$	3.09958	0.126964
$597$	−30.0305	−1.22907
$598$	0	0
$599$	−29.5177	−1.20606	−0.603031	−	0.797718i	$-0.706041\pi$
$599$	−29.5177	−1.20606	−0.603031	+	0.797718i	$0.706041\pi$
$600$	16.3039	0.665602
$601$	6.75608	0.275586	0.137793	−	0.990461i	$-0.455999\pi$
$601$	6.75608	0.275586	0.137793	+	0.990461i	$0.455999\pi$
$602$	2.42492	0.0988323
$603$	120.189	4.89449
$604$	−5.70873	−0.232285
$605$	26.9775	1.09679
$606$	60.4481	2.45554
$607$	28.5491	1.15877	0.579387	−	0.815053i	$-0.303292\pi$
$607$	28.5491	1.15877	0.579387	+	0.815053i	$0.303292\pi$
$608$	9.04826	0.366955
$609$	0.199113	0.00806847
$610$	28.8448	1.16789
$611$	0	0
$612$	10.9739	0.443595
$613$	18.2072	0.735382	0.367691	−	0.929948i	$-0.380148\pi$
$613$	18.2072	0.735382	0.367691	+	0.929948i	$0.380148\pi$
$614$	32.3919	1.30723
$615$	−60.0246	−2.42043
$616$	−0.458164	−0.0184600
$617$	−14.2625	−0.574187	−0.287094	−	0.957903i	$-0.592689\pi$
$617$	−14.2625	−0.574187	−0.287094	+	0.957903i	$0.592689\pi$
$618$	−63.6588	−2.56073
$619$	−22.0101	−0.884662	−0.442331	−	0.896852i	$-0.645848\pi$
$619$	−22.0101	−0.884662	−0.442331	+	0.896852i	$0.645848\pi$
$620$	0.998566	0.0401034
$621$	139.991	5.61763
$622$	−8.72902	−0.350002
$623$	−1.12421	−0.0450405
$624$	0	0
$625$	−30.4404	−1.21762
$626$	29.0754	1.16209
$627$	−9.92065	−0.396193
$628$	3.82263	0.152539
$629$	−10.7074	−0.426930
$630$	−5.78222	−0.230369
$631$	−4.19804	−0.167122	−0.0835608	−	0.996503i	$-0.526629\pi$
$631$	−4.19804	−0.167122	−0.0835608	+	0.996503i	$0.526629\pi$
$632$	−23.2570	−0.925114
$633$	−33.7965	−1.34329
$634$	−1.85100	−0.0735124
$635$	−3.36391	−0.133493
$636$	6.47672	0.256819
$637$	0	0
$638$	0.248504	0.00983836
$639$	94.9484	3.75610
$640$	17.8713	0.706426
$641$	11.5344	0.455581	0.227790	−	0.973710i	$-0.426850\pi$
$641$	11.5344	0.455581	0.227790	+	0.973710i	$0.426850\pi$
$642$	−45.1155	−1.78057
$643$	19.1879	0.756697	0.378349	−	0.925663i	$-0.376492\pi$
$643$	19.1879	0.756697	0.378349	+	0.925663i	$0.376492\pi$
$644$	0.654575	0.0257939
$645$	−77.1102	−3.03621
$646$	−18.0637	−0.710708
$647$	−27.0205	−1.06229	−0.531143	−	0.847282i	$-0.678237\pi$
$647$	−27.0205	−1.06229	−0.531143	+	0.847282i	$0.678237\pi$
$648$	105.711	4.15271
$649$	−6.88065	−0.270089
$650$	0	0
$651$	−0.718612	−0.0281646
$652$	−7.03216	−0.275401
$653$	−43.5733	−1.70516	−0.852578	−	0.522600i	$-0.824962\pi$
$653$	−43.5733	−1.70516	−0.852578	+	0.522600i	$0.824962\pi$
$654$	38.3222	1.49852
$655$	−37.2272	−1.45459
$656$	−21.3574	−0.833866
$657$	−18.9284	−0.738466
$658$	−1.72185	−0.0671249
$659$	−31.3973	−1.22306	−0.611532	−	0.791219i	$-0.709447\pi$
$659$	−31.3973	−1.22306	−0.611532	+	0.791219i	$0.709447\pi$
$660$	2.37069	0.0922789
$661$	0.0876791	0.00341032	0.00170516	−	0.999999i	$-0.499457\pi$
$661$	0.0876791	0.00341032	0.00170516	+	0.999999i	$0.499457\pi$
$662$	−16.1374	−0.627198
$663$	0	0
$664$	13.3822	0.519329
$665$	−2.29592	−0.0890319
$666$	−33.0894	−1.28219
$667$	−2.18189	−0.0844830
$668$	5.29504	0.204871
$669$	−70.6077	−2.72985
$670$	47.2765	1.82645
$671$	6.24935	0.241253
$672$	1.55603	0.0600250
$673$	−6.40770	−0.246999	−0.123499	−	0.992345i	$-0.539412\pi$
$673$	−6.40770	−0.246999	−0.123499	+	0.992345i	$0.539412\pi$
$674$	22.5517	0.868659
$675$	28.4481	1.09497
$676$	0	0
$677$	16.8182	0.646377	0.323188	−	0.946335i	$-0.395245\pi$
$677$	16.8182	0.646377	0.323188	+	0.946335i	$0.395245\pi$
$678$	22.6118	0.868400
$679$	0.490038	0.0188059
$680$	26.5279	1.01730
$681$	46.4563	1.78021
$682$	−0.896866	−0.0343428
$683$	−9.85866	−0.377231	−0.188616	−	0.982051i	$-0.560400\pi$
$683$	−9.85866	−0.377231	−0.188616	+	0.982051i	$0.560400\pi$
$684$	13.4658	0.514876
$685$	−27.4260	−1.04789
$686$	−3.78819	−0.144634
$687$	9.65601	0.368400
$688$	−27.4366	−1.04601
$689$	0	0
$690$	86.2893	3.28498
$691$	1.04309	0.0396809	0.0198404	−	0.999803i	$-0.493684\pi$
$691$	1.04309	0.0396809	0.0198404	+	0.999803i	$0.493684\pi$
$692$	−8.05427	−0.306177
$693$	−1.25274	−0.0475878
$694$	−31.5152	−1.19630
$695$	−45.4186	−1.72283
$696$	−2.82302	−0.107006
$697$	−23.6791	−0.896908
$698$	−10.0288	−0.379597
$699$	76.5336	2.89477
$700$	0.133019	0.00502764
$701$	−2.63555	−0.0995434	−0.0497717	−	0.998761i	$-0.515849\pi$
$701$	−2.63555	−0.0995434	−0.0497717	+	0.998761i	$0.515849\pi$
$702$	0	0
$703$	−13.1386	−0.495533
$704$	6.28236	0.236775
$705$	54.7534	2.06213
$706$	−33.3878	−1.25657
$707$	3.03087	0.113987
$708$	12.7189	0.478006
$709$	−15.3752	−0.577429	−0.288715	−	0.957415i	$-0.593228\pi$
$709$	−15.3752	−0.577429	−0.288715	+	0.957415i	$0.593228\pi$
$710$	37.3480	1.40164
$711$	−63.5909	−2.38485
$712$	15.9390	0.597340
$713$	7.87457	0.294905
$714$	−3.10641	−0.116255
$715$	0	0
$716$	5.53496	0.206851
$717$	74.4264	2.77950
$718$	−37.8895	−1.41402
$719$	−0.131512	−0.00490457	−0.00245228	−	0.999997i	$-0.500781\pi$
$719$	−0.131512	−0.00490457	−0.00245228	+	0.999997i	$0.500781\pi$
$720$	65.4226	2.43816
$721$	−3.19185	−0.118871
$722$	1.95274	0.0726734
$723$	88.3586	3.28609
$724$	9.23758	0.343312
$725$	−0.443390	−0.0164671
$726$	44.7891	1.66228
$727$	−14.4705	−0.536681	−0.268341	−	0.963324i	$-0.586475\pi$
$727$	−14.4705	−0.536681	−0.268341	+	0.963324i	$0.586475\pi$
$728$	0	0
$729$	109.835	4.06797
$730$	−7.44547	−0.275569
$731$	−30.4191	−1.12509
$732$	−11.5519	−0.426972
$733$	0.761565	0.0281291	0.0140645	−	0.999901i	$-0.495523\pi$
$733$	0.761565	0.0281291	0.0140645	+	0.999901i	$0.495523\pi$
$734$	5.22124	0.192719
$735$	60.0331	2.21435
$736$	−17.0510	−0.628507
$737$	10.2427	0.377293
$738$	−73.1763	−2.69366
$739$	−30.0279	−1.10459	−0.552297	−	0.833647i	$-0.686249\pi$
$739$	−30.0279	−1.10459	−0.552297	+	0.833647i	$0.686249\pi$
$740$	3.13967	0.115417
$741$	0	0
$742$	−1.34624	−0.0494220
$743$	8.34190	0.306035	0.153017	−	0.988223i	$-0.451101\pi$
$743$	8.34190	0.306035	0.153017	+	0.988223i	$0.451101\pi$
$744$	10.1885	0.373528
$745$	20.4873	0.750595
$746$	−8.01094	−0.293301
$747$	36.5904	1.33877
$748$	0.935211	0.0341947
$749$	−2.26209	−0.0826549
$750$	−37.2546	−1.36035
$751$	−11.6837	−0.426345	−0.213172	−	0.977015i	$-0.568380\pi$
$751$	−11.6837	−0.426345	−0.213172	+	0.977015i	$0.568380\pi$
$752$	19.4818	0.710429
$753$	77.1483	2.81144
$754$	0	0
$755$	−37.7330	−1.37325
$756$	1.47776	0.0537456
$757$	8.74941	0.318003	0.159001	−	0.987278i	$-0.449173\pi$
$757$	8.74941	0.318003	0.159001	+	0.987278i	$0.449173\pi$
$758$	−15.0228	−0.545651
$759$	18.6950	0.678584
$760$	32.5515	1.18077
$761$	−3.60347	−0.130626	−0.0653128	−	0.997865i	$-0.520805\pi$
$761$	−3.60347	−0.130626	−0.0653128	+	0.997865i	$0.520805\pi$
$762$	−5.58489	−0.202319
$763$	1.92147	0.0695620
$764$	2.83760	0.102661
$765$	72.5344	2.62249
$766$	−41.0355	−1.48267
$767$	0	0
$768$	−30.0845	−1.08558
$769$	22.5016	0.811427	0.405714	−	0.914000i	$-0.367023\pi$
$769$	22.5016	0.811427	0.405714	+	0.914000i	$0.367023\pi$
$770$	−0.492767	−0.0177581
$771$	−35.6991	−1.28567
$772$	−5.78114	−0.208068
$773$	−17.9089	−0.644138	−0.322069	−	0.946716i	$-0.604378\pi$
$773$	−17.9089	−0.644138	−0.322069	+	0.946716i	$0.604378\pi$
$774$	−94.0054	−3.37895
$775$	1.60022	0.0574818
$776$	−6.94775	−0.249410
$777$	−2.25945	−0.0810572
$778$	−16.3045	−0.584543
$779$	−29.0558	−1.04103
$780$	0	0
$781$	8.09161	0.289540
$782$	34.0402	1.21727
$783$	−4.92581	−0.176034
$784$	21.3604	0.762871
$785$	25.2664	0.901798
$786$	−61.8062	−2.20455
$787$	−50.7772	−1.81001	−0.905006	−	0.425400i	$-0.860133\pi$
$787$	−50.7772	−1.81001	−0.905006	+	0.425400i	$0.860133\pi$
$788$	−8.84058	−0.314933
$789$	32.4724	1.15605
$790$	−25.0135	−0.889940
$791$	1.13375	0.0403117
$792$	17.7614	0.631123
$793$	0	0
$794$	12.4042	0.440210
$795$	42.8092	1.51828
$796$	3.47376	0.123124
$797$	4.74937	0.168231	0.0841156	−	0.996456i	$-0.473193\pi$
$797$	4.74937	0.168231	0.0841156	+	0.996456i	$0.473193\pi$
$798$	−3.81178	−0.134936
$799$	21.5996	0.764139
$800$	−3.46500	−0.122506
$801$	43.5816	1.53988
$802$	7.56317	0.267065
$803$	−1.61310	−0.0569249
$804$	−18.9336	−0.667737
$805$	4.32654	0.152491
$806$	0	0
$807$	−34.2834	−1.20683
$808$	−42.9716	−1.51174
$809$	−0.592564	−0.0208334	−0.0104167	−	0.999946i	$-0.503316\pi$
$809$	−0.592564	−0.0208334	−0.0104167	+	0.999946i	$0.503316\pi$
$810$	113.694	3.99482
$811$	23.8218	0.836495	0.418248	−	0.908333i	$-0.362644\pi$
$811$	23.8218	0.836495	0.418248	+	0.908333i	$0.362644\pi$
$812$	−0.0230323	−0.000808275 0
$813$	−11.5892	−0.406450
$814$	−2.81991	−0.0988378
$815$	−46.4805	−1.62814
$816$	35.1474	1.23040
$817$	−37.3263	−1.30588
$818$	15.2606	0.533573
$819$	0	0
$820$	6.94332	0.242471
$821$	−1.44381	−0.0503893	−0.0251947	−	0.999683i	$-0.508021\pi$
$821$	−1.44381	−0.0503893	−0.0251947	+	0.999683i	$0.508021\pi$
$822$	−45.5337	−1.58817
$823$	27.7542	0.967450	0.483725	−	0.875220i	$-0.339284\pi$
$823$	27.7542	0.967450	0.483725	+	0.875220i	$0.339284\pi$
$824$	45.2540	1.57650
$825$	3.79908	0.132267
$826$	−2.64373	−0.0919871
$827$	13.1204	0.456242	0.228121	−	0.973633i	$-0.426742\pi$
$827$	13.1204	0.456242	0.228121	+	0.973633i	$0.426742\pi$
$828$	−25.3755	−0.881860
$829$	−52.9010	−1.83733	−0.918663	−	0.395041i	$-0.870730\pi$
$829$	−52.9010	−1.83733	−0.918663	+	0.395041i	$0.870730\pi$
$830$	14.3929	0.499583
$831$	23.0387	0.799203
$832$	0	0
$833$	23.6824	0.820546
$834$	−75.4058	−2.61109
$835$	34.9986	1.21118
$836$	1.14757	0.0396894
$837$	17.7776	0.614482
$838$	−37.6219	−1.29963
$839$	−19.9277	−0.687980	−0.343990	−	0.938973i	$-0.611779\pi$
$839$	−19.9277	−0.687980	−0.343990	+	0.938973i	$0.611779\pi$
$840$	5.59788	0.193145
$841$	−28.9232	−0.997353
$842$	34.7552	1.19774
$843$	8.87547	0.305687
$844$	3.90940	0.134567
$845$	0	0
$846$	66.7501	2.29492
$847$	2.24573	0.0771641
$848$	15.2319	0.523067
$849$	47.3380	1.62463
$850$	6.91744	0.237266
$851$	24.7591	0.848731
$852$	−14.9574	−0.512431
$853$	−35.9732	−1.23170	−0.615850	−	0.787863i	$-0.711187\pi$
$853$	−35.9732	−1.23170	−0.615850	+	0.787863i	$0.711187\pi$
$854$	2.40117	0.0821662
$855$	89.0046	3.04389
$856$	32.0719	1.09619
$857$	12.5639	0.429175	0.214587	−	0.976705i	$-0.431159\pi$
$857$	12.5639	0.429175	0.214587	+	0.976705i	$0.431159\pi$
$858$	0	0
$859$	5.13700	0.175272	0.0876361	−	0.996153i	$-0.472069\pi$
$859$	5.13700	0.175272	0.0876361	+	0.996153i	$0.472069\pi$
$860$	8.91968	0.304158
$861$	−4.99672	−0.170288
$862$	−5.96817	−0.203277
$863$	−52.1083	−1.77379	−0.886894	−	0.461973i	$-0.847142\pi$
$863$	−52.1083	−1.77379	−0.886894	+	0.461973i	$0.847142\pi$
$864$	−38.4941	−1.30960
$865$	−53.2363	−1.81009
$866$	−25.3225	−0.860495
$867$	−18.1547	−0.616565
$868$	0.0831251	0.00282145
$869$	−5.41929	−0.183837
$870$	−3.03623	−0.102938
$871$	0	0
$872$	−27.2426	−0.922551
$873$	−18.9970	−0.642951
$874$	41.7696	1.41288
$875$	−1.86795	−0.0631481
$876$	2.98181	0.100746
$877$	−46.0713	−1.55572	−0.777859	−	0.628439i	$-0.783694\pi$
$877$	−46.0713	−1.55572	−0.777859	+	0.628439i	$0.783694\pi$
$878$	36.7649	1.24075
$879$	−82.4752	−2.78182
$880$	5.57539	0.187946
$881$	−1.97636	−0.0665852	−0.0332926	−	0.999446i	$-0.510599\pi$
$881$	−1.97636	−0.0665852	−0.0332926	+	0.999446i	$0.510599\pi$
$882$	73.1866	2.46432
$883$	31.8195	1.07081	0.535406	−	0.844595i	$-0.320159\pi$
$883$	31.8195	1.07081	0.535406	+	0.844595i	$0.320159\pi$
$884$	0	0
$885$	84.0681	2.82592
$886$	−18.2689	−0.613755
$887$	27.3804	0.919343	0.459671	−	0.888089i	$-0.347967\pi$
$887$	27.3804	0.919343	0.459671	+	0.888089i	$0.347967\pi$
$888$	32.0344	1.07500
$889$	−0.280026	−0.00939179
$890$	17.1428	0.574628
$891$	24.6324	0.825217
$892$	8.16750	0.273468
$893$	26.5042	0.886928
$894$	34.0138	1.13759
$895$	36.5845	1.22288
$896$	1.48769	0.0497002
$897$	0	0
$898$	−27.1555	−0.906191
$899$	−0.277080	−0.00924114
$900$	−5.15667	−0.171889
$901$	16.8877	0.562612
$902$	−6.23617	−0.207642
$903$	−6.41899	−0.213611
$904$	−16.0744	−0.534625
$905$	61.0576	2.02962
$906$	−62.6459	−2.08127
$907$	53.9160	1.79025	0.895126	−	0.445813i	$-0.147085\pi$
$907$	53.9160	1.79025	0.895126	+	0.445813i	$0.147085\pi$
$908$	−5.37381	−0.178336
$909$	−117.496	−3.89709
$910$	0	0
$911$	−49.8766	−1.65249	−0.826243	−	0.563314i	$-0.809526\pi$
$911$	−49.8766	−1.65249	−0.826243	+	0.563314i	$0.809526\pi$
$912$	43.1282	1.42812
$913$	3.11828	0.103200
$914$	27.6163	0.913465
$915$	−76.3549	−2.52422
$916$	−1.11695	−0.0369052
$917$	−3.09896	−0.102337
$918$	76.8487	2.53639
$919$	52.4549	1.73033	0.865164	−	0.501489i	$-0.167214\pi$
$919$	52.4549	1.73033	0.865164	+	0.501489i	$0.167214\pi$
$920$	−61.3417	−2.02237
$921$	−85.7445	−2.82538
$922$	−8.70880	−0.286809
$923$	0	0
$924$	0.197347	0.00649223
$925$	5.03140	0.165431
$926$	3.67545	0.120783
$927$	123.737	4.06404
$928$	0.599967	0.0196949
$929$	−41.6621	−1.36689	−0.683445	−	0.730002i	$-0.739519\pi$
$929$	−41.6621	−1.36689	−0.683445	+	0.730002i	$0.739519\pi$
$930$	10.9580	0.359326
$931$	29.0599	0.952399
$932$	−8.85299	−0.289989
$933$	23.1066	0.756475
$934$	−17.3747	−0.568518
$935$	6.18146	0.202155
$936$	0	0
$937$	−20.8784	−0.682068	−0.341034	−	0.940051i	$-0.610777\pi$
$937$	−20.8784	−0.682068	−0.341034	+	0.940051i	$0.610777\pi$
$938$	3.93550	0.128499
$939$	−76.9654	−2.51167
$940$	−6.33357	−0.206578
$941$	−47.4653	−1.54732	−0.773662	−	0.633599i	$-0.781577\pi$
$941$	−47.4653	−1.54732	−0.773662	+	0.633599i	$0.781577\pi$
$942$	41.9484	1.36675
$943$	54.7542	1.78304
$944$	29.9123	0.973563
$945$	9.76756	0.317739
$946$	−8.01124	−0.260468
$947$	50.5937	1.64408	0.822038	−	0.569433i	$-0.192837\pi$
$947$	50.5937	1.64408	0.822038	+	0.569433i	$0.192837\pi$
$948$	10.0176	0.325356
$949$	0	0
$950$	8.48817	0.275393
$951$	4.89977	0.158886
$952$	2.20830	0.0715714
$953$	−18.5538	−0.601015	−0.300508	−	0.953779i	$-0.597156\pi$
$953$	−18.5538	−0.601015	−0.300508	+	0.953779i	$0.597156\pi$
$954$	52.1889	1.68968
$955$	18.7557	0.606920
$956$	−8.60923	−0.278442
$957$	−0.657813	−0.0212641
$958$	8.70182	0.281143
$959$	−2.28306	−0.0737238
$960$	−76.7582	−2.47736
$961$	1.00000	0.0322581
$962$	0	0
$963$	87.6931	2.82587
$964$	−10.2208	−0.329191
$965$	−38.2116	−1.23008
$966$	7.18310	0.231113
$967$	3.63328	0.116838	0.0584192	−	0.998292i	$-0.481394\pi$
$967$	3.63328	0.116838	0.0584192	+	0.998292i	$0.481394\pi$
$968$	−31.8399	−1.02337
$969$	47.8164	1.53609
$970$	−7.47247	−0.239927
$971$	14.5964	0.468421	0.234210	−	0.972186i	$-0.424750\pi$
$971$	14.5964	0.468421	0.234210	+	0.972186i	$0.424750\pi$
$972$	−24.8035	−0.795573
$973$	−3.78085	−0.121208
$974$	17.2601	0.553048
$975$	0	0
$976$	−27.1679	−0.869623
$977$	22.0589	0.705728	0.352864	−	0.935675i	$-0.385208\pi$
$977$	22.0589	0.705728	0.352864	+	0.935675i	$0.385208\pi$
$978$	−77.1687	−2.46758
$979$	3.71407	0.118702
$980$	−6.94429	−0.221827
$981$	−74.4887	−2.37824
$982$	19.2620	0.614675
$983$	36.3399	1.15906	0.579532	−	0.814949i	$-0.303235\pi$
$983$	36.3399	1.15906	0.579532	+	0.814949i	$0.303235\pi$
$984$	70.8434	2.25840
$985$	−58.4336	−1.86185
$986$	−1.19776	−0.0381445
$987$	4.55792	0.145080
$988$	0	0
$989$	70.3395	2.23667
$990$	19.1028	0.607127
$991$	−26.5711	−0.844060	−0.422030	−	0.906582i	$-0.638682\pi$
$991$	−26.5711	−0.844060	−0.422030	+	0.906582i	$0.638682\pi$
$992$	−2.16532	−0.0687490
$993$	42.7173	1.35559
$994$	3.10901	0.0986118
$995$	22.9605	0.727898
$996$	−5.76415	−0.182644
$997$	−16.3952	−0.519243	−0.259621	−	0.965710i	$-0.583598\pi$
$997$	−16.3952	−0.519243	−0.259621	+	0.965710i	$0.583598\pi$
$998$	52.8709	1.67360
$999$	55.8959	1.76847

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.v.1.17	yes	54
13.12	even	2		5239.2.a.u.1.38	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5239.2.a.u.1.38	✓	54	13.12	even	2
5239.2.a.v.1.17	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)

\(f(q)\)	\(=\)	\(q-1.26938 q^{2} +3.36016 q^{3} -0.388685 q^{4} -2.56909 q^{5} -4.26531 q^{6} -0.213862 q^{7} +3.03214 q^{8} +8.29068 q^{9} +O(q^{10})\)	\(q-1.26938 q^{2} +3.36016 q^{3} -0.388685 q^{4} -2.56909 q^{5} -4.26531 q^{6} -0.213862 q^{7} +3.03214 q^{8} +8.29068 q^{9} +3.26114 q^{10} +0.706541 q^{11} -1.30604 q^{12} +0.271472 q^{14} -8.63256 q^{15} -3.07155 q^{16} -3.40545 q^{17} -10.5240 q^{18} -4.17871 q^{19} +0.998566 q^{20} -0.718612 q^{21} -0.896866 q^{22} +7.87457 q^{23} +10.1885 q^{24} +1.60022 q^{25} +17.7776 q^{27} +0.0831251 q^{28} -0.277080 q^{29} +10.9580 q^{30} +1.00000 q^{31} -2.16532 q^{32} +2.37409 q^{33} +4.32280 q^{34} +0.549432 q^{35} -3.22246 q^{36} +3.14418 q^{37} +5.30436 q^{38} -7.78984 q^{40} +6.95329 q^{41} +0.912189 q^{42} +8.93248 q^{43} -0.274622 q^{44} -21.2995 q^{45} -9.99579 q^{46} -6.34266 q^{47} -10.3209 q^{48} -6.95426 q^{49} -2.03129 q^{50} -11.4429 q^{51} -4.95904 q^{53} -22.5664 q^{54} -1.81517 q^{55} -0.648461 q^{56} -14.0412 q^{57} +0.351719 q^{58} -9.73850 q^{59} +3.35534 q^{60} +8.84499 q^{61} -1.26938 q^{62} -1.77307 q^{63} +8.89171 q^{64} -3.01362 q^{66} +14.4969 q^{67} +1.32365 q^{68} +26.4598 q^{69} -0.697436 q^{70} +11.4524 q^{71} +25.1385 q^{72} -2.28309 q^{73} -3.99115 q^{74} +5.37701 q^{75} +1.62420 q^{76} -0.151103 q^{77} -7.67017 q^{79} +7.89110 q^{80} +34.8634 q^{81} -8.82633 q^{82} +4.41344 q^{83} +0.279314 q^{84} +8.74891 q^{85} -11.3387 q^{86} -0.931034 q^{87} +2.14233 q^{88} +5.25669 q^{89} +27.0371 q^{90} -3.06073 q^{92} +3.36016 q^{93} +8.05122 q^{94} +10.7355 q^{95} -7.27583 q^{96} -2.29137 q^{97} +8.82757 q^{98} +5.85771 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 2 q^{2} + 7 q^{3} + 64 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 6 q^{8} + 95 q^{9}+O(q^{10}) \) 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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