LMFDB - Embedded newform 5239.2.a.v.1.8

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			1.8
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)

$f(q)$	$=$	$q-2.22015 q^{2} -3.28822 q^{3} +2.92906 q^{4} +0.803718 q^{5} +7.30033 q^{6} +3.80869 q^{7} -2.06266 q^{8} +7.81236 q^{9} +O(q^{10})$	\(q-2.22015 q^{2} -3.28822 q^{3} +2.92906 q^{4} +0.803718 q^{5} +7.30033 q^{6} +3.80869 q^{7} -2.06266 q^{8} +7.81236 q^{9} -1.78438 q^{10} +4.96444 q^{11} -9.63139 q^{12} -8.45587 q^{14} -2.64280 q^{15} -1.27871 q^{16} -6.52186 q^{17} -17.3446 q^{18} +5.38414 q^{19} +2.35414 q^{20} -12.5238 q^{21} -11.0218 q^{22} +4.96718 q^{23} +6.78248 q^{24} -4.35404 q^{25} -15.8241 q^{27} +11.1559 q^{28} +2.47983 q^{29} +5.86741 q^{30} +1.00000 q^{31} +6.96425 q^{32} -16.3241 q^{33} +14.4795 q^{34} +3.06112 q^{35} +22.8829 q^{36} -4.54677 q^{37} -11.9536 q^{38} -1.65780 q^{40} -8.61906 q^{41} +27.8047 q^{42} +0.759397 q^{43} +14.5412 q^{44} +6.27894 q^{45} -11.0279 q^{46} +9.57226 q^{47} +4.20468 q^{48} +7.50614 q^{49} +9.66661 q^{50} +21.4453 q^{51} +1.98302 q^{53} +35.1318 q^{54} +3.99001 q^{55} -7.85605 q^{56} -17.7042 q^{57} -5.50559 q^{58} +13.3406 q^{59} -7.74093 q^{60} +0.241031 q^{61} -2.22015 q^{62} +29.7549 q^{63} -12.9043 q^{64} +36.2420 q^{66} -3.80020 q^{67} -19.1029 q^{68} -16.3332 q^{69} -6.79614 q^{70} +1.36505 q^{71} -16.1143 q^{72} +8.33905 q^{73} +10.0945 q^{74} +14.3170 q^{75} +15.7705 q^{76} +18.9080 q^{77} +3.79475 q^{79} -1.02772 q^{80} +28.5959 q^{81} +19.1356 q^{82} -9.21004 q^{83} -36.6830 q^{84} -5.24174 q^{85} -1.68597 q^{86} -8.15420 q^{87} -10.2400 q^{88} +5.43029 q^{89} -13.9402 q^{90} +14.5492 q^{92} -3.28822 q^{93} -21.2518 q^{94} +4.32733 q^{95} -22.9000 q^{96} -6.10461 q^{97} -16.6648 q^{98} +38.7840 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.22015	−1.56988	−0.784941	−	0.619570i	$-0.787307\pi$
$2$	−2.22015	−1.56988	−0.784941	+	0.619570i	$0.787307\pi$
$3$	−3.28822	−1.89845	−0.949226	−	0.314595i	$-0.898131\pi$
$3$	−3.28822	−1.89845	−0.949226	+	0.314595i	$0.898131\pi$
$4$	2.92906	1.46453
$5$	0.803718	0.359434	0.179717	−	0.983718i	$-0.442482\pi$
$5$	0.803718	0.359434	0.179717	+	0.983718i	$0.442482\pi$
$6$	7.30033	2.98035
$7$	3.80869	1.43955	0.719775	−	0.694207i	$-0.244245\pi$
$7$	3.80869	1.43955	0.719775	+	0.694207i	$0.244245\pi$
$8$	−2.06266	−0.729261
$9$	7.81236	2.60412
$10$	−1.78438	−0.564269
$11$	4.96444	1.49683	0.748417	−	0.663228i	$-0.230814\pi$
$11$	4.96444	1.49683	0.748417	+	0.663228i	$0.230814\pi$
$12$	−9.63139	−2.78034
$13$	0	0
$13$	0	0
$14$	−8.45587	−2.25993
$15$	−2.64280	−0.682368
$16$	−1.27871	−0.319678
$17$	−6.52186	−1.58178	−0.790891	−	0.611957i	$-0.790383\pi$
$17$	−6.52186	−1.58178	−0.790891	+	0.611957i	$0.790383\pi$
$18$	−17.3446	−4.08816
$19$	5.38414	1.23521	0.617603	−	0.786490i	$-0.288104\pi$
$19$	5.38414	1.23521	0.617603	+	0.786490i	$0.288104\pi$
$20$	2.35414	0.526402
$21$	−12.5238	−2.73292
$22$	−11.0218	−2.34985
$23$	4.96718	1.03573	0.517864	−	0.855463i	$-0.326727\pi$
$23$	4.96718	1.03573	0.517864	+	0.855463i	$0.326727\pi$
$24$	6.78248	1.38447
$25$	−4.35404	−0.870807
$26$	0	0
$27$	−15.8241	−3.04534
$28$	11.1559	2.10827
$29$	2.47983	0.460492	0.230246	−	0.973132i	$-0.426047\pi$
$29$	2.47983	0.460492	0.230246	+	0.973132i	$0.426047\pi$
$30$	5.86741	1.07124
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	6.96425	1.23112
$33$	−16.3241	−2.84167
$34$	14.4795	2.48321
$35$	3.06112	0.517423
$36$	22.8829	3.81382
$37$	−4.54677	−0.747484	−0.373742	−	0.927533i	$-0.621925\pi$
$37$	−4.54677	−0.747484	−0.373742	+	0.927533i	$0.621925\pi$
$38$	−11.9536	−1.93913
$39$	0	0
$40$	−1.65780	−0.262121
$41$	−8.61906	−1.34607	−0.673035	−	0.739610i	$-0.735010\pi$
$41$	−8.61906	−1.34607	−0.673035	+	0.739610i	$0.735010\pi$
$42$	27.8047	4.29036
$43$	0.759397	0.115807	0.0579034	−	0.998322i	$-0.481558\pi$
$43$	0.759397	0.115807	0.0579034	+	0.998322i	$0.481558\pi$
$44$	14.5412	2.19216
$45$	6.27894	0.936009
$46$	−11.0279	−1.62597
$47$	9.57226	1.39626	0.698129	−	0.715972i	$-0.254016\pi$
$47$	9.57226	1.39626	0.698129	+	0.715972i	$0.254016\pi$
$48$	4.20468	0.606893
$49$	7.50614	1.07231
$50$	9.66661	1.36707
$51$	21.4453	3.00294
$52$	0	0
$53$	1.98302	0.272388	0.136194	−	0.990682i	$-0.456513\pi$
$53$	1.98302	0.272388	0.136194	+	0.990682i	$0.456513\pi$
$54$	35.1318	4.78083
$55$	3.99001	0.538013
$56$	−7.85605	−1.04981
$57$	−17.7042	−2.34498
$58$	−5.50559	−0.722919
$59$	13.3406	1.73679	0.868397	−	0.495870i	$-0.165151\pi$
$59$	13.3406	1.73679	0.868397	+	0.495870i	$0.165151\pi$
$60$	−7.74093	−0.999350
$61$	0.241031	0.0308609	0.0154304	−	0.999881i	$-0.495088\pi$
$61$	0.241031	0.0308609	0.0154304	+	0.999881i	$0.495088\pi$
$62$	−2.22015	−0.281959
$63$	29.7549	3.74876
$64$	−12.9043	−1.61303
$65$	0	0
$66$	36.2420	4.46108
$67$	−3.80020	−0.464269	−0.232134	−	0.972684i	$-0.574571\pi$
$67$	−3.80020	−0.464269	−0.232134	+	0.972684i	$0.574571\pi$
$68$	−19.1029	−2.31657
$69$	−16.3332	−1.96628
$70$	−6.79614	−0.812294
$71$	1.36505	0.162001	0.0810007	−	0.996714i	$-0.474188\pi$
$71$	1.36505	0.162001	0.0810007	+	0.996714i	$0.474188\pi$
$72$	−16.1143	−1.89908
$73$	8.33905	0.976011	0.488006	−	0.872840i	$-0.337725\pi$
$73$	8.33905	0.976011	0.488006	+	0.872840i	$0.337725\pi$
$74$	10.0945	1.17346
$75$	14.3170	1.65319
$76$	15.7705	1.80900
$77$	18.9080	2.15477
$78$	0	0
$79$	3.79475	0.426943	0.213471	−	0.976949i	$-0.431523\pi$
$79$	3.79475	0.426943	0.213471	+	0.976949i	$0.431523\pi$
$80$	−1.02772	−0.114903
$81$	28.5959	3.17732
$82$	19.1356	2.11317
$83$	−9.21004	−1.01093	−0.505467	−	0.862846i	$-0.668680\pi$
$83$	−9.21004	−1.01093	−0.505467	+	0.862846i	$0.668680\pi$
$84$	−36.6830	−4.00245
$85$	−5.24174	−0.568546
$86$	−1.68597	−0.181803
$87$	−8.15420	−0.874222
$88$	−10.2400	−1.09158
$89$	5.43029	0.575609	0.287805	−	0.957689i	$-0.407075\pi$
$89$	5.43029	0.575609	0.287805	+	0.957689i	$0.407075\pi$
$90$	−13.9402	−1.46942
$91$	0	0
$92$	14.5492	1.51686
$93$	−3.28822	−0.340972
$94$	−21.2518	−2.19196
$95$	4.32733	0.443975
$96$	−22.9000	−2.33722
$97$	−6.10461	−0.619829	−0.309915	−	0.950764i	$-0.600300\pi$
$97$	−6.10461	−0.619829	−0.309915	+	0.950764i	$0.600300\pi$
$98$	−16.6648	−1.68339
$99$	38.7840	3.89793
$100$	−12.7533	−1.27533
$101$	9.68611	0.963804	0.481902	−	0.876225i	$-0.339946\pi$
$101$	9.68611	0.963804	0.481902	+	0.876225i	$0.339946\pi$
$102$	−47.6117	−4.71426
$103$	−11.8124	−1.16391	−0.581956	−	0.813220i	$-0.697713\pi$
$103$	−11.8124	−1.16391	−0.581956	+	0.813220i	$0.697713\pi$
$104$	0	0
$105$	−10.0656	−0.982303
$106$	−4.40260	−0.427618
$107$	−6.80329	−0.657699	−0.328849	−	0.944382i	$-0.606661\pi$
$107$	−6.80329	−0.657699	−0.328849	+	0.944382i	$0.606661\pi$
$108$	−46.3497	−4.46000
$109$	3.67032	0.351553	0.175776	−	0.984430i	$-0.443756\pi$
$109$	3.67032	0.351553	0.175776	+	0.984430i	$0.443756\pi$
$110$	−8.85842	−0.844617
$111$	14.9507	1.41906
$112$	−4.87022	−0.460192
$113$	14.8353	1.39559	0.697794	−	0.716299i	$-0.254165\pi$
$113$	14.8353	1.39559	0.697794	+	0.716299i	$0.254165\pi$
$114$	39.3060	3.68134
$115$	3.99221	0.372276
$116$	7.26357	0.674406
$117$	0	0
$118$	−29.6180	−2.72656
$119$	−24.8397	−2.27706
$120$	5.45120	0.497624
$121$	13.6456	1.24051
$122$	−0.535125	−0.0484479
$123$	28.3413	2.55545
$124$	2.92906	0.263038
$125$	−7.51801	−0.672431
$126$	−66.0603	−5.88512
$127$	1.83049	0.162430	0.0812148	−	0.996697i	$-0.474120\pi$
$127$	1.83049	0.162430	0.0812148	+	0.996697i	$0.474120\pi$
$128$	14.7209	1.30115
$129$	−2.49706	−0.219854
$130$	0	0
$131$	3.70843	0.324007	0.162004	−	0.986790i	$-0.448204\pi$
$131$	3.70843	0.324007	0.162004	+	0.986790i	$0.448204\pi$
$132$	−47.8144	−4.16171
$133$	20.5065	1.77814
$134$	8.43702	0.728848
$135$	−12.7181	−1.09460
$136$	13.4524	1.15353
$137$	18.8613	1.61143	0.805714	−	0.592304i	$-0.201782\pi$
$137$	18.8613	1.61143	0.805714	+	0.592304i	$0.201782\pi$
$138$	36.2620	3.08683
$139$	1.16169	0.0985330	0.0492665	−	0.998786i	$-0.484312\pi$
$139$	1.16169	0.0985330	0.0492665	+	0.998786i	$0.484312\pi$
$140$	8.96621	0.757783
$141$	−31.4756	−2.65073
$142$	−3.03061	−0.254323
$143$	0	0
$144$	−9.98974	−0.832479
$145$	1.99308	0.165517
$146$	−18.5139	−1.53222
$147$	−24.6818	−2.03572
$148$	−13.3178	−1.09471
$149$	−1.01295	−0.0829837	−0.0414919	−	0.999139i	$-0.513211\pi$
$149$	−1.01295	−0.0829837	−0.0414919	+	0.999139i	$0.513211\pi$
$150$	−31.7859	−2.59531
$151$	−6.98227	−0.568209	−0.284105	−	0.958793i	$-0.591696\pi$
$151$	−6.98227	−0.568209	−0.284105	+	0.958793i	$0.591696\pi$
$152$	−11.1057	−0.900788
$153$	−50.9511	−4.11915
$154$	−41.9786	−3.38273
$155$	0.803718	0.0645562
$156$	0	0
$157$	−2.61863	−0.208989	−0.104495	−	0.994525i	$-0.533322\pi$
$157$	−2.61863	−0.208989	−0.104495	+	0.994525i	$0.533322\pi$
$158$	−8.42492	−0.670250
$159$	−6.52059	−0.517116
$160$	5.59730	0.442505
$161$	18.9185	1.49098
$162$	−63.4871	−4.98802
$163$	0.485874	0.0380566	0.0190283	−	0.999819i	$-0.493943\pi$
$163$	0.485874	0.0380566	0.0190283	+	0.999819i	$0.493943\pi$
$164$	−25.2458	−1.97136
$165$	−13.1200	−1.02139
$166$	20.4477	1.58705
$167$	−15.8595	−1.22725	−0.613624	−	0.789598i	$-0.710289\pi$
$167$	−15.8595	−1.22725	−0.613624	+	0.789598i	$0.710289\pi$
$168$	25.8324	1.99301
$169$	0	0
$170$	11.6374	0.892551
$171$	42.0628	3.21663
$172$	2.22432	0.169603
$173$	2.36148	0.179540	0.0897700	−	0.995963i	$-0.471387\pi$
$173$	2.36148	0.179540	0.0897700	+	0.995963i	$0.471387\pi$
$174$	18.1036	1.37243
$175$	−16.5832	−1.25357
$176$	−6.34808	−0.478504
$177$	−43.8666	−3.29722
$178$	−12.0561	−0.903639
$179$	4.90477	0.366600	0.183300	−	0.983057i	$-0.441322\pi$
$179$	4.90477	0.366600	0.183300	+	0.983057i	$0.441322\pi$
$180$	18.3914	1.37081
$181$	5.80785	0.431694	0.215847	−	0.976427i	$-0.430749\pi$
$181$	5.80785	0.431694	0.215847	+	0.976427i	$0.430749\pi$
$182$	0	0
$183$	−0.792562	−0.0585879
$184$	−10.2456	−0.755316
$185$	−3.65432	−0.268671
$186$	7.30033	0.535286
$187$	−32.3773	−2.36767
$188$	28.0378	2.04486
$189$	−60.2690	−4.38393
$190$	−9.60733	−0.696989
$191$	−10.6522	−0.770768	−0.385384	−	0.922756i	$-0.625931\pi$
$191$	−10.6522	−0.770768	−0.385384	+	0.922756i	$0.625931\pi$
$192$	42.4320	3.06227
$193$	9.59960	0.690994	0.345497	−	0.938420i	$-0.387710\pi$
$193$	9.59960	0.690994	0.345497	+	0.938420i	$0.387710\pi$
$194$	13.5531	0.973059
$195$	0	0
$196$	21.9860	1.57043
$197$	−6.04630	−0.430781	−0.215390	−	0.976528i	$-0.569102\pi$
$197$	−6.04630	−0.430781	−0.215390	+	0.976528i	$0.569102\pi$
$198$	−86.1062	−6.11930
$199$	18.6494	1.32202	0.661010	−	0.750377i	$-0.270128\pi$
$199$	18.6494	1.32202	0.661010	+	0.750377i	$0.270128\pi$
$200$	8.98091	0.635046
$201$	12.4959	0.881392
$202$	−21.5046	−1.51306
$203$	9.44490	0.662902
$204$	62.8146	4.39790
$205$	−6.92729	−0.483823
$206$	26.2254	1.82721
$207$	38.8054	2.69716
$208$	0	0
$209$	26.7292	1.84890
$210$	22.3472	1.54210
$211$	1.45180	0.0999458	0.0499729	−	0.998751i	$-0.484086\pi$
$211$	1.45180	0.0999458	0.0499729	+	0.998751i	$0.484086\pi$
$212$	5.80839	0.398922
$213$	−4.48857	−0.307552
$214$	15.1043	1.03251
$215$	0.610341	0.0416249
$216$	32.6397	2.22085
$217$	3.80869	0.258551
$218$	−8.14866	−0.551897
$219$	−27.4206	−1.85291
$220$	11.6870	0.787937
$221$	0	0
$222$	−33.1929	−2.22776
$223$	−23.0796	−1.54553	−0.772764	−	0.634694i	$-0.781126\pi$
$223$	−23.0796	−1.54553	−0.772764	+	0.634694i	$0.781126\pi$
$224$	26.5247	1.77226
$225$	−34.0153	−2.26769
$226$	−32.9366	−2.19091
$227$	10.8839	0.722389	0.361195	−	0.932490i	$-0.382369\pi$
$227$	10.8839	0.722389	0.361195	+	0.932490i	$0.382369\pi$
$228$	−51.8568	−3.43430
$229$	−18.8793	−1.24758	−0.623790	−	0.781592i	$-0.714408\pi$
$229$	−18.8793	−1.24758	−0.623790	+	0.781592i	$0.714408\pi$
$230$	−8.86331	−0.584429
$231$	−62.1736	−4.09072
$232$	−5.11504	−0.335819
$233$	14.0612	0.921183	0.460591	−	0.887612i	$-0.347637\pi$
$233$	14.0612	0.921183	0.460591	+	0.887612i	$0.347637\pi$
$234$	0	0
$235$	7.69340	0.501862
$236$	39.0754	2.54359
$237$	−12.4780	−0.810530
$238$	55.1480	3.57471
$239$	26.2508	1.69803	0.849013	−	0.528372i	$-0.177197\pi$
$239$	26.2508	1.69803	0.849013	+	0.528372i	$0.177197\pi$
$240$	3.37937	0.218138
$241$	−10.6495	−0.685997	−0.342999	−	0.939336i	$-0.611443\pi$
$241$	−10.6495	−0.685997	−0.342999	+	0.939336i	$0.611443\pi$
$242$	−30.2953	−1.94746
$243$	−46.5572	−2.98664
$244$	0.705995	0.0451967
$245$	6.03282	0.385423
$246$	−62.9219	−4.01176
$247$	0	0
$248$	−2.06266	−0.130979
$249$	30.2846	1.91921
$250$	16.6911	1.05564
$251$	19.0519	1.20254	0.601272	−	0.799045i	$-0.294661\pi$
$251$	19.0519	1.20254	0.601272	+	0.799045i	$0.294661\pi$
$252$	87.1539	5.49018
$253$	24.6592	1.55031
$254$	−4.06396	−0.254995
$255$	17.2360	1.07936
$256$	−6.87405	−0.429628
$257$	−26.3488	−1.64360	−0.821798	−	0.569779i	$-0.807029\pi$
$257$	−26.3488	−1.64360	−0.821798	+	0.569779i	$0.807029\pi$
$258$	5.54385	0.345145
$259$	−17.3172	−1.07604
$260$	0	0
$261$	19.3733	1.19918
$262$	−8.23328	−0.508653
$263$	30.2000	1.86221	0.931107	−	0.364747i	$-0.118844\pi$
$263$	30.2000	1.86221	0.931107	+	0.364747i	$0.118844\pi$
$264$	33.6712	2.07232
$265$	1.59379	0.0979056
$266$	−45.5276	−2.79147
$267$	−17.8560	−1.09277
$268$	−11.1310	−0.679937
$269$	−28.4079	−1.73206	−0.866029	−	0.499994i	$-0.833336\pi$
$269$	−28.4079	−1.73206	−0.866029	+	0.499994i	$0.833336\pi$
$270$	28.2361	1.71839
$271$	5.14445	0.312503	0.156251	−	0.987717i	$-0.450059\pi$
$271$	5.14445	0.312503	0.156251	+	0.987717i	$0.450059\pi$
$272$	8.33957	0.505661
$273$	0	0
$274$	−41.8749	−2.52975
$275$	−21.6153	−1.30345
$276$	−47.8409	−2.87968
$277$	−10.7222	−0.644234	−0.322117	−	0.946700i	$-0.604394\pi$
$277$	−10.7222	−0.644234	−0.322117	+	0.946700i	$0.604394\pi$
$278$	−2.57912	−0.154685
$279$	7.81236	0.467714
$280$	−6.31405	−0.377337
$281$	18.8429	1.12407	0.562036	−	0.827113i	$-0.310018\pi$
$281$	18.8429	1.12407	0.562036	+	0.827113i	$0.310018\pi$
$282$	69.8806	4.16133
$283$	−10.6294	−0.631851	−0.315925	−	0.948784i	$-0.602315\pi$
$283$	−10.6294	−0.631851	−0.315925	+	0.948784i	$0.602315\pi$
$284$	3.99831	0.237256
$285$	−14.2292	−0.842865
$286$	0	0
$287$	−32.8273	−1.93774
$288$	54.4072	3.20598
$289$	25.5346	1.50204
$290$	−4.42494	−0.259842
$291$	20.0733	1.17672
$292$	24.4256	1.42940
$293$	32.4964	1.89846	0.949229	−	0.314585i	$-0.101865\pi$
$293$	32.4964	1.89846	0.949229	+	0.314585i	$0.101865\pi$
$294$	54.7973	3.19584
$295$	10.7221	0.624262
$296$	9.37844	0.545111
$297$	−78.5576	−4.55837
$298$	2.24889	0.130275
$299$	0	0
$300$	41.9354	2.42114
$301$	2.89231	0.166710
$302$	15.5017	0.892022
$303$	−31.8500	−1.82974
$304$	−6.88476	−0.394868
$305$	0.193721	0.0110924
$306$	113.119	6.46658
$307$	12.5500	0.716264	0.358132	−	0.933671i	$-0.383414\pi$
$307$	12.5500	0.716264	0.358132	+	0.933671i	$0.383414\pi$
$308$	55.3828	3.15573
$309$	38.8418	2.20963
$310$	−1.78438	−0.101346
$311$	25.4224	1.44157	0.720786	−	0.693158i	$-0.243781\pi$
$311$	25.4224	1.44157	0.720786	+	0.693158i	$0.243781\pi$
$312$	0	0
$313$	1.23850	0.0700041	0.0350021	−	0.999387i	$-0.488856\pi$
$313$	1.23850	0.0700041	0.0350021	+	0.999387i	$0.488856\pi$
$314$	5.81374	0.328089
$315$	23.9145	1.34743
$316$	11.1151	0.625272
$317$	14.2715	0.801566	0.400783	−	0.916173i	$-0.368738\pi$
$317$	14.2715	0.801566	0.400783	+	0.916173i	$0.368738\pi$
$318$	14.4767	0.811812
$319$	12.3109	0.689281
$320$	−10.3714	−0.579778
$321$	22.3707	1.24861
$322$	−42.0018	−2.34067
$323$	−35.1146	−1.95383
$324$	83.7591	4.65329
$325$	0	0
$326$	−1.07871	−0.0597443
$327$	−12.0688	−0.667406
$328$	17.7782	0.981637
$329$	36.4578	2.00998
$330$	29.1284	1.60346
$331$	−11.2145	−0.616404	−0.308202	−	0.951321i	$-0.599727\pi$
$331$	−11.2145	−0.616404	−0.308202	+	0.951321i	$0.599727\pi$
$332$	−26.9768	−1.48054
$333$	−35.5210	−1.94654
$334$	35.2105	1.92664
$335$	−3.05429	−0.166874
$336$	16.0143	0.873652
$337$	22.9280	1.24897	0.624485	−	0.781037i	$-0.285309\pi$
$337$	22.9280	1.24897	0.624485	+	0.781037i	$0.285309\pi$
$338$	0	0
$339$	−48.7817	−2.64946
$340$	−15.3534	−0.832654
$341$	4.96444	0.268839
$342$	−93.3858	−5.04973
$343$	1.92773	0.104087
$344$	−1.56638	−0.0844535
$345$	−13.1273	−0.706748
$346$	−5.24284	−0.281857
$347$	−25.4328	−1.36530	−0.682651	−	0.730744i	$-0.739173\pi$
$347$	−25.4328	−1.36530	−0.682651	+	0.730744i	$0.739173\pi$
$348$	−23.8842	−1.28033
$349$	10.2682	0.549645	0.274823	−	0.961495i	$-0.411381\pi$
$349$	10.2682	0.549645	0.274823	+	0.961495i	$0.411381\pi$
$350$	36.8172	1.96796
$351$	0	0
$352$	34.5736	1.84278
$353$	0.883294	0.0470130	0.0235065	−	0.999724i	$-0.492517\pi$
$353$	0.883294	0.0470130	0.0235065	+	0.999724i	$0.492517\pi$
$354$	97.3905	5.17625
$355$	1.09711	0.0582288
$356$	15.9057	0.842998
$357$	81.6784	4.32288
$358$	−10.8893	−0.575519
$359$	−22.5089	−1.18797	−0.593987	−	0.804475i	$-0.702447\pi$
$359$	−22.5089	−1.18797	−0.593987	+	0.804475i	$0.702447\pi$
$360$	−12.9513	−0.682595
$361$	9.98897	0.525735
$362$	−12.8943	−0.677709
$363$	−44.8698	−2.35505
$364$	0	0
$365$	6.70224	0.350811
$366$	1.75961	0.0919761
$367$	−21.5390	−1.12433	−0.562163	−	0.827026i	$-0.690031\pi$
$367$	−21.5390	−1.12433	−0.562163	+	0.827026i	$0.690031\pi$
$368$	−6.35158	−0.331099
$369$	−67.3352	−3.50533
$370$	8.11314	0.421782
$371$	7.55270	0.392117
$372$	−9.63139	−0.499365
$373$	−8.91261	−0.461478	−0.230739	−	0.973016i	$-0.574114\pi$
$373$	−8.91261	−0.461478	−0.230739	+	0.973016i	$0.574114\pi$
$374$	71.8826	3.71696
$375$	24.7208	1.27658
$376$	−19.7443	−1.01824
$377$	0	0
$378$	133.806	6.88225
$379$	33.9030	1.74148	0.870741	−	0.491742i	$-0.163640\pi$
$379$	33.9030	1.74148	0.870741	+	0.491742i	$0.163640\pi$
$380$	12.6750	0.650216
$381$	−6.01904	−0.308365
$382$	23.6495	1.21001
$383$	6.01938	0.307576	0.153788	−	0.988104i	$-0.450853\pi$
$383$	6.01938	0.307576	0.153788	+	0.988104i	$0.450853\pi$
$384$	−48.4054	−2.47018
$385$	15.1967	0.774496
$386$	−21.3125	−1.08478
$387$	5.93268	0.301575
$388$	−17.8808	−0.907760
$389$	−6.01178	−0.304810	−0.152405	−	0.988318i	$-0.548702\pi$
$389$	−6.01178	−0.304810	−0.152405	+	0.988318i	$0.548702\pi$
$390$	0	0
$391$	−32.3952	−1.63830
$392$	−15.4826	−0.781991
$393$	−12.1941	−0.615112
$394$	13.4237	0.676275
$395$	3.04991	0.153458
$396$	113.601	5.70865
$397$	34.1037	1.71162	0.855808	−	0.517294i	$-0.173060\pi$
$397$	34.1037	1.71162	0.855808	+	0.517294i	$0.173060\pi$
$398$	−41.4044	−2.07542
$399$	−67.4299	−3.37572
$400$	5.56755	0.278378
$401$	−12.9840	−0.648392	−0.324196	−	0.945990i	$-0.605094\pi$
$401$	−12.9840	−0.648392	−0.324196	+	0.945990i	$0.605094\pi$
$402$	−27.7427	−1.38368
$403$	0	0
$404$	28.3713	1.41152
$405$	22.9830	1.14204
$406$	−20.9691	−1.04068
$407$	−22.5721	−1.11886
$408$	−44.2343	−2.18993
$409$	−3.04192	−0.150413	−0.0752067	−	0.997168i	$-0.523962\pi$
$409$	−3.04192	−0.150413	−0.0752067	+	0.997168i	$0.523962\pi$
$410$	15.3796	0.759546
$411$	−62.0200	−3.05922
$412$	−34.5994	−1.70459
$413$	50.8101	2.50020
$414$	−86.1537	−4.23423
$415$	−7.40228	−0.363364
$416$	0	0
$417$	−3.81988	−0.187060
$418$	−59.3429	−2.90256
$419$	−5.24844	−0.256403	−0.128202	−	0.991748i	$-0.540920\pi$
$419$	−5.24844	−0.256403	−0.128202	+	0.991748i	$0.540920\pi$
$420$	−29.4828	−1.43861
$421$	9.25690	0.451153	0.225577	−	0.974225i	$-0.427573\pi$
$421$	9.25690	0.451153	0.225577	+	0.974225i	$0.427573\pi$
$422$	−3.22321	−0.156903
$423$	74.7819	3.63602
$424$	−4.09030	−0.198642
$425$	28.3964	1.37743
$426$	9.96530	0.482820
$427$	0.918013	0.0444258
$428$	−19.9273	−0.963221
$429$	0	0
$430$	−1.35505	−0.0653462
$431$	−23.9122	−1.15181	−0.575904	−	0.817517i	$-0.695350\pi$
$431$	−23.9122	−1.15181	−0.575904	+	0.817517i	$0.695350\pi$
$432$	20.2344	0.973528
$433$	−38.2800	−1.83962	−0.919809	−	0.392367i	$-0.871656\pi$
$433$	−38.2800	−1.83962	−0.919809	+	0.392367i	$0.871656\pi$
$434$	−8.45587	−0.405895
$435$	−6.55368	−0.314225
$436$	10.7506	0.514860
$437$	26.7440	1.27934
$438$	60.8778	2.90885
$439$	7.59672	0.362572	0.181286	−	0.983430i	$-0.441974\pi$
$439$	7.59672	0.362572	0.181286	+	0.983430i	$0.441974\pi$
$440$	−8.23004	−0.392352
$441$	58.6406	2.79241
$442$	0	0
$443$	−3.59209	−0.170665	−0.0853326	−	0.996353i	$-0.527195\pi$
$443$	−3.59209	−0.170665	−0.0853326	+	0.996353i	$0.527195\pi$
$444$	43.7917	2.07826
$445$	4.36442	0.206893
$446$	51.2403	2.42630
$447$	3.33078	0.157541
$448$	−49.1484	−2.32204
$449$	−36.5626	−1.72549	−0.862747	−	0.505636i	$-0.831258\pi$
$449$	−36.5626	−1.72549	−0.862747	+	0.505636i	$0.831258\pi$
$450$	75.5190	3.56000
$451$	−42.7888	−2.01484
$452$	43.4535	2.04388
$453$	22.9592	1.07872
$454$	−24.1639	−1.13407
$455$	0	0
$456$	36.5178	1.71010
$457$	7.00568	0.327712	0.163856	−	0.986484i	$-0.447607\pi$
$457$	7.00568	0.327712	0.163856	+	0.986484i	$0.447607\pi$
$458$	41.9149	1.95855
$459$	103.202	4.81707
$460$	11.6934	0.545210
$461$	−1.65186	−0.0769348	−0.0384674	−	0.999260i	$-0.512248\pi$
$461$	−1.65186	−0.0769348	−0.0384674	+	0.999260i	$0.512248\pi$
$462$	138.035	6.42196
$463$	−8.88153	−0.412760	−0.206380	−	0.978472i	$-0.566168\pi$
$463$	−8.88153	−0.412760	−0.206380	+	0.978472i	$0.566168\pi$
$464$	−3.17098	−0.147209
$465$	−2.64280	−0.122557
$466$	−31.2181	−1.44615
$467$	−20.0346	−0.927089	−0.463545	−	0.886074i	$-0.653423\pi$
$467$	−20.0346	−0.927089	−0.463545	+	0.886074i	$0.653423\pi$
$468$	0	0
$469$	−14.4738	−0.668338
$470$	−17.0805	−0.787865
$471$	8.61061	0.396756
$472$	−27.5171	−1.26658
$473$	3.76998	0.173344
$474$	27.7029	1.27244
$475$	−23.4427	−1.07563
$476$	−72.7572	−3.33482
$477$	15.4920	0.709332
$478$	−58.2808	−2.66570
$479$	17.3704	0.793673	0.396837	−	0.917889i	$-0.370108\pi$
$479$	17.3704	0.793673	0.396837	+	0.917889i	$0.370108\pi$
$480$	−18.4051	−0.840075
$481$	0	0
$482$	23.6436	1.07694
$483$	−62.2079	−2.83056
$484$	39.9689	1.81677
$485$	−4.90639	−0.222788
$486$	103.364	4.68868
$487$	−2.03419	−0.0921777	−0.0460889	−	0.998937i	$-0.514676\pi$
$487$	−2.03419	−0.0921777	−0.0460889	+	0.998937i	$0.514676\pi$
$488$	−0.497166	−0.0225056
$489$	−1.59766	−0.0722485
$490$	−13.3938	−0.605069
$491$	−31.4241	−1.41815	−0.709074	−	0.705134i	$-0.750887\pi$
$491$	−31.4241	−1.41815	−0.709074	+	0.705134i	$0.750887\pi$
$492$	83.0135	3.74254
$493$	−16.1731	−0.728399
$494$	0	0
$495$	31.1714	1.40105
$496$	−1.27871	−0.0574158
$497$	5.19905	0.233209
$498$	−67.2363	−3.01293
$499$	8.66080	0.387710	0.193855	−	0.981030i	$-0.437901\pi$
$499$	8.66080	0.387710	0.193855	+	0.981030i	$0.437901\pi$
$500$	−22.0207	−0.984797
$501$	52.1496	2.32987
$502$	−42.2980	−1.88785
$503$	44.2429	1.97269	0.986347	−	0.164680i	$-0.0526591\pi$
$503$	44.2429	1.97269	0.986347	+	0.164680i	$0.0526591\pi$
$504$	−61.3742	−2.73383
$505$	7.78491	0.346424
$506$	−54.7472	−2.43381
$507$	0	0
$508$	5.36162	0.237883
$509$	−12.3572	−0.547722	−0.273861	−	0.961769i	$-0.588301\pi$
$509$	−12.3572	−0.547722	−0.273861	+	0.961769i	$0.588301\pi$
$510$	−38.2664	−1.69446
$511$	31.7609	1.40502
$512$	−14.1804	−0.626689
$513$	−85.1990	−3.76163
$514$	58.4984	2.58025
$515$	−9.49386	−0.418350
$516$	−7.31405	−0.321983
$517$	47.5209	2.08997
$518$	38.4469	1.68926
$519$	−7.76505	−0.340848
$520$	0	0
$521$	15.4715	0.677818	0.338909	−	0.940819i	$-0.389942\pi$
$521$	15.4715	0.677818	0.338909	+	0.940819i	$0.389942\pi$
$522$	−43.0116	−1.88257
$523$	−19.7145	−0.862054	−0.431027	−	0.902339i	$-0.641849\pi$
$523$	−19.7145	−0.862054	−0.431027	+	0.902339i	$0.641849\pi$
$524$	10.8622	0.474519
$525$	54.5291	2.37984
$526$	−67.0486	−2.92346
$527$	−6.52186	−0.284097
$528$	20.8738	0.908417
$529$	1.67286	0.0727331
$530$	−3.53845	−0.153700
$531$	104.221	4.52282
$532$	60.0650	2.60415
$533$	0	0
$534$	39.6429	1.71552
$535$	−5.46793	−0.236399
$536$	7.83854	0.338573
$537$	−16.1279	−0.695972
$538$	63.0697	2.71913
$539$	37.2638	1.60506
$540$	−37.2521	−1.60308
$541$	−13.4184	−0.576903	−0.288451	−	0.957495i	$-0.593140\pi$
$541$	−13.4184	−0.576903	−0.288451	+	0.957495i	$0.593140\pi$
$542$	−11.4214	−0.490593
$543$	−19.0975	−0.819550
$544$	−45.4199	−1.94736
$545$	2.94990	0.126360
$546$	0	0
$547$	1.93988	0.0829433	0.0414717	−	0.999140i	$-0.486795\pi$
$547$	1.93988	0.0829433	0.0414717	+	0.999140i	$0.486795\pi$
$548$	55.2459	2.35999
$549$	1.88302	0.0803654
$550$	47.9893	2.04627
$551$	13.3517	0.568803
$552$	33.6898	1.43393
$553$	14.4530	0.614606
$554$	23.8049	1.01137
$555$	12.0162	0.510059
$556$	3.40266	0.144305
$557$	2.87733	0.121916	0.0609581	−	0.998140i	$-0.480584\pi$
$557$	2.87733	0.121916	0.0609581	+	0.998140i	$0.480584\pi$
$558$	−17.3446	−0.734256
$559$	0	0
$560$	−3.91428	−0.165409
$561$	106.464	4.49490
$562$	−41.8340	−1.76466
$563$	−44.1714	−1.86160	−0.930801	−	0.365526i	$-0.880889\pi$
$563$	−44.1714	−1.86160	−0.930801	+	0.365526i	$0.880889\pi$
$564$	−92.1942	−3.88208
$565$	11.9234	0.501621
$566$	23.5988	0.991932
$567$	108.913	4.57391
$568$	−2.81563	−0.118141
$569$	21.7365	0.911242	0.455621	−	0.890174i	$-0.349417\pi$
$569$	21.7365	0.911242	0.455621	+	0.890174i	$0.349417\pi$
$570$	31.5910	1.32320
$571$	−39.6357	−1.65870	−0.829350	−	0.558729i	$-0.811289\pi$
$571$	−39.6357	−1.65870	−0.829350	+	0.558729i	$0.811289\pi$
$572$	0	0
$573$	35.0268	1.46327
$574$	72.8816	3.04202
$575$	−21.6273	−0.901920
$576$	−100.813	−4.20053
$577$	9.07586	0.377833	0.188917	−	0.981993i	$-0.439502\pi$
$577$	9.07586	0.377833	0.188917	+	0.981993i	$0.439502\pi$
$578$	−56.6907	−2.35802
$579$	−31.5655	−1.31182
$580$	5.83787	0.242404
$581$	−35.0782	−1.45529
$582$	−44.5657	−1.84731
$583$	9.84457	0.407720
$584$	−17.2006	−0.711767
$585$	0	0
$586$	−72.1468	−2.98036
$587$	−4.46693	−0.184370	−0.0921849	−	0.995742i	$-0.529385\pi$
$587$	−4.46693	−0.184370	−0.0921849	+	0.995742i	$0.529385\pi$
$588$	−72.2946	−2.98138
$589$	5.38414	0.221850
$590$	−23.8046	−0.980019
$591$	19.8815	0.817816
$592$	5.81400	0.238954
$593$	20.5063	0.842094	0.421047	−	0.907039i	$-0.361663\pi$
$593$	20.5063	0.842094	0.421047	+	0.907039i	$0.361663\pi$
$594$	174.410	7.15611
$595$	−19.9642	−0.818451
$596$	−2.96698	−0.121532
$597$	−61.3232	−2.50979
$598$	0	0
$599$	29.9875	1.22526	0.612629	−	0.790371i	$-0.290112\pi$
$599$	29.9875	1.22526	0.612629	+	0.790371i	$0.290112\pi$
$600$	−29.5312	−1.20560
$601$	−10.8766	−0.443664	−0.221832	−	0.975085i	$-0.571204\pi$
$601$	−10.8766	−0.443664	−0.221832	+	0.975085i	$0.571204\pi$
$602$	−6.42136	−0.261715
$603$	−29.6886	−1.20901
$604$	−20.4515	−0.832161
$605$	10.9672	0.445882
$606$	70.7118	2.87247
$607$	−22.1239	−0.897980	−0.448990	−	0.893537i	$-0.648216\pi$
$607$	−22.1239	−0.897980	−0.448990	+	0.893537i	$0.648216\pi$
$608$	37.4965	1.52068
$609$	−31.0569	−1.25849
$610$	−0.430090	−0.0174138
$611$	0	0
$612$	−149.239	−6.03263
$613$	34.3790	1.38855	0.694277	−	0.719708i	$-0.255724\pi$
$613$	34.3790	1.38855	0.694277	+	0.719708i	$0.255724\pi$
$614$	−27.8628	−1.12445
$615$	22.7784	0.918515
$616$	−39.0008	−1.57139
$617$	34.0803	1.37202	0.686011	−	0.727591i	$-0.259360\pi$
$617$	34.0803	1.37202	0.686011	+	0.727591i	$0.259360\pi$
$618$	−86.2346	−3.46886
$619$	10.6558	0.428292	0.214146	−	0.976802i	$-0.431303\pi$
$619$	10.6558	0.428292	0.214146	+	0.976802i	$0.431303\pi$
$620$	2.35414	0.0945447
$621$	−78.6010	−3.15415
$622$	−56.4415	−2.26310
$623$	20.6823	0.828619
$624$	0	0
$625$	15.7278	0.629113
$626$	−2.74965	−0.109898
$627$	−87.8914	−3.51005
$628$	−7.67013	−0.306071
$629$	29.6534	1.18236
$630$	−53.0939	−2.11531
$631$	−22.6174	−0.900383	−0.450192	−	0.892932i	$-0.648644\pi$
$631$	−22.6174	−0.900383	−0.450192	+	0.892932i	$0.648644\pi$
$632$	−7.82729	−0.311353
$633$	−4.77382	−0.189742
$634$	−31.6848	−1.25837
$635$	1.47120	0.0583827
$636$	−19.0992	−0.757333
$637$	0	0
$638$	−27.3321	−1.08209
$639$	10.6642	0.421871
$640$	11.8314	0.467679
$641$	39.8292	1.57316	0.786579	−	0.617490i	$-0.211850\pi$
$641$	39.8292	1.57316	0.786579	+	0.617490i	$0.211850\pi$
$642$	−49.6663	−1.96017
$643$	29.5173	1.16405	0.582025	−	0.813171i	$-0.302261\pi$
$643$	29.5173	1.16405	0.582025	+	0.813171i	$0.302261\pi$
$644$	55.4134	2.18359
$645$	−2.00693	−0.0790229
$646$	77.9597	3.06728
$647$	−7.45918	−0.293251	−0.146625	−	0.989192i	$-0.546841\pi$
$647$	−7.45918	−0.293251	−0.146625	+	0.989192i	$0.546841\pi$
$648$	−58.9836	−2.31710
$649$	66.2284	2.59969
$650$	0	0
$651$	−12.5238	−0.490846
$652$	1.42316	0.0557351
$653$	−28.8716	−1.12983	−0.564917	−	0.825148i	$-0.691092\pi$
$653$	−28.8716	−1.12983	−0.564917	+	0.825148i	$0.691092\pi$
$654$	26.7945	1.04775
$655$	2.98054	0.116459
$656$	11.0213	0.430309
$657$	65.1476	2.54165
$658$	−80.9417	−3.15544
$659$	23.5392	0.916958	0.458479	−	0.888705i	$-0.348394\pi$
$659$	23.5392	0.916958	0.458479	+	0.888705i	$0.348394\pi$
$660$	−38.4294	−1.49586
$661$	−24.7855	−0.964045	−0.482022	−	0.876159i	$-0.660098\pi$
$661$	−24.7855	−0.964045	−0.482022	+	0.876159i	$0.660098\pi$
$662$	24.8978	0.967682
$663$	0	0
$664$	18.9972	0.737234
$665$	16.4815	0.639124
$666$	78.8619	3.05584
$667$	12.3177	0.476945
$668$	−46.4536	−1.79734
$669$	75.8908	2.93411
$670$	6.78099	0.261972
$671$	1.19658	0.0461936
$672$	−87.2189	−3.36454
$673$	−44.0821	−1.69924	−0.849620	−	0.527396i	$-0.823169\pi$
$673$	−44.0821	−1.69924	−0.849620	+	0.527396i	$0.823169\pi$
$674$	−50.9037	−1.96074
$675$	68.8986	2.65191
$676$	0	0
$677$	23.5179	0.903867	0.451933	−	0.892052i	$-0.350734\pi$
$677$	23.5179	0.903867	0.451933	+	0.892052i	$0.350734\pi$
$678$	108.303	4.15933
$679$	−23.2506	−0.892275
$680$	10.8119	0.414619
$681$	−35.7886	−1.37142
$682$	−11.0218	−0.422046
$683$	29.3110	1.12156	0.560778	−	0.827966i	$-0.310502\pi$
$683$	29.3110	1.12156	0.560778	+	0.827966i	$0.310502\pi$
$684$	123.205	4.71085
$685$	15.1592	0.579202
$686$	−4.27984	−0.163405
$687$	62.0792	2.36847
$688$	−0.971048	−0.0370209
$689$	0	0
$690$	29.1445	1.10951
$691$	30.0473	1.14305	0.571527	−	0.820583i	$-0.306351\pi$
$691$	30.0473	1.14305	0.571527	+	0.820583i	$0.306351\pi$
$692$	6.91692	0.262942
$693$	147.716	5.61127
$694$	56.4646	2.14337
$695$	0.933669	0.0354161
$696$	16.8194	0.637536
$697$	56.2123	2.12919
$698$	−22.7970	−0.862879
$699$	−46.2364	−1.74882
$700$	−48.5732	−1.83590
$701$	22.7426	0.858978	0.429489	−	0.903072i	$-0.358694\pi$
$701$	22.7426	0.858978	0.429489	+	0.903072i	$0.358694\pi$
$702$	0	0
$703$	−24.4804	−0.923297
$704$	−64.0624	−2.41444
$705$	−25.2976	−0.952761
$706$	−1.96104	−0.0738049
$707$	36.8914	1.38744
$708$	−128.488	−4.82888
$709$	−41.7170	−1.56672	−0.783358	−	0.621571i	$-0.786495\pi$
$709$	−41.7170	−1.56672	−0.783358	+	0.621571i	$0.786495\pi$
$710$	−2.43576	−0.0914123
$711$	29.6460	1.11181
$712$	−11.2008	−0.419770
$713$	4.96718	0.186022
$714$	−181.338	−6.78642
$715$	0	0
$716$	14.3664	0.536897
$717$	−86.3184	−3.22362
$718$	49.9731	1.86498
$719$	−9.71176	−0.362187	−0.181094	−	0.983466i	$-0.557964\pi$
$719$	−9.71176	−0.362187	−0.181094	+	0.983466i	$0.557964\pi$
$720$	−8.02894	−0.299221
$721$	−44.9899	−1.67551
$722$	−22.1770	−0.825343
$723$	35.0180	1.30233
$724$	17.0116	0.632230
$725$	−10.7973	−0.401000
$726$	99.6176	3.69716
$727$	35.0160	1.29867	0.649335	−	0.760503i	$-0.275047\pi$
$727$	35.0160	1.29867	0.649335	+	0.760503i	$0.275047\pi$
$728$	0	0
$729$	67.3023	2.49268
$730$	−14.8800	−0.550733
$731$	−4.95268	−0.183181
$732$	−2.32146	−0.0858038
$733$	−40.3336	−1.48976	−0.744878	−	0.667201i	$-0.767492\pi$
$733$	−40.3336	−1.48976	−0.744878	+	0.667201i	$0.767492\pi$
$734$	47.8198	1.76506
$735$	−19.8372	−0.731707
$736$	34.5927	1.27510
$737$	−18.8659	−0.694933
$738$	149.494	5.50295
$739$	−15.7613	−0.579790	−0.289895	−	0.957058i	$-0.593620\pi$
$739$	−15.7613	−0.579790	−0.289895	+	0.957058i	$0.593620\pi$
$740$	−10.7037	−0.393477
$741$	0	0
$742$	−16.7681	−0.615578
$743$	−14.8995	−0.546608	−0.273304	−	0.961928i	$-0.588117\pi$
$743$	−14.8995	−0.546608	−0.273304	+	0.961928i	$0.588117\pi$
$744$	6.78248	0.248658
$745$	−0.814123	−0.0298271
$746$	19.7873	0.724466
$747$	−71.9521	−2.63259
$748$	−94.8353	−3.46752
$749$	−25.9116	−0.946791
$750$	−54.8840	−2.00408
$751$	23.5447	0.859158	0.429579	−	0.903029i	$-0.358662\pi$
$751$	23.5447	0.859158	0.429579	+	0.903029i	$0.358662\pi$
$752$	−12.2401	−0.446352
$753$	−62.6466	−2.28297
$754$	0	0
$755$	−5.61178	−0.204234
$756$	−176.532	−6.42040
$757$	23.5868	0.857277	0.428638	−	0.903476i	$-0.358993\pi$
$757$	23.5868	0.857277	0.428638	+	0.903476i	$0.358993\pi$
$758$	−75.2698	−2.73392
$759$	−81.0849	−2.94320
$760$	−8.92583	−0.323774
$761$	32.2553	1.16926	0.584628	−	0.811302i	$-0.301241\pi$
$761$	32.2553	1.16926	0.584628	+	0.811302i	$0.301241\pi$
$762$	13.3632	0.484097
$763$	13.9791	0.506078
$764$	−31.2010	−1.12881
$765$	−40.9503	−1.48056
$766$	−13.3639	−0.482858
$767$	0	0
$768$	22.6033	0.815628
$769$	−35.9722	−1.29719	−0.648595	−	0.761134i	$-0.724643\pi$
$769$	−35.9722	−1.29719	−0.648595	+	0.761134i	$0.724643\pi$
$770$	−33.7390	−1.21587
$771$	86.6407	3.12029
$772$	28.1178	1.01198
$773$	9.05643	0.325737	0.162869	−	0.986648i	$-0.447925\pi$
$773$	9.05643	0.325737	0.162869	+	0.986648i	$0.447925\pi$
$774$	−13.1714	−0.473437
$775$	−4.35404	−0.156402
$776$	12.5917	0.452017
$777$	56.9428	2.04281
$778$	13.3471	0.478515
$779$	−46.4062	−1.66267
$780$	0	0
$781$	6.77669	0.242489
$782$	71.9223	2.57193
$783$	−39.2410	−1.40236
$784$	−9.59818	−0.342792
$785$	−2.10464	−0.0751178
$786$	27.0728	0.965654
$787$	−23.7503	−0.846606	−0.423303	−	0.905988i	$-0.639129\pi$
$787$	−23.7503	−0.846606	−0.423303	+	0.905988i	$0.639129\pi$
$788$	−17.7100	−0.630892
$789$	−99.3042	−3.53532
$790$	−6.77126	−0.240911
$791$	56.5031	2.00902
$792$	−79.9982	−2.84261
$793$	0	0
$794$	−75.7153	−2.68704
$795$	−5.24072	−0.185869
$796$	54.6252	1.93614
$797$	17.8837	0.633474	0.316737	−	0.948513i	$-0.397413\pi$
$797$	17.8837	0.633474	0.316737	+	0.948513i	$0.397413\pi$
$798$	149.704	5.29948
$799$	−62.4289	−2.20858
$800$	−30.3226	−1.07207
$801$	42.4234	1.49896
$802$	28.8265	1.01790
$803$	41.3987	1.46093
$804$	36.6013	1.29083
$805$	15.2051	0.535910
$806$	0	0
$807$	93.4112	3.28823
$808$	−19.9792	−0.702865
$809$	21.7884	0.766038	0.383019	−	0.923741i	$-0.374884\pi$
$809$	21.7884	0.766038	0.383019	+	0.923741i	$0.374884\pi$
$810$	−51.0258	−1.79286
$811$	40.4121	1.41906	0.709531	−	0.704674i	$-0.248907\pi$
$811$	40.4121	1.41906	0.709531	+	0.704674i	$0.248907\pi$
$812$	27.6647	0.970841
$813$	−16.9161	−0.593272
$814$	50.1135	1.75648
$815$	0.390506	0.0136788
$816$	−27.4223	−0.959972
$817$	4.08870	0.143045
$818$	6.75352	0.236131
$819$	0	0
$820$	−20.2905	−0.708575
$821$	−19.2951	−0.673403	−0.336702	−	0.941611i	$-0.609311\pi$
$821$	−19.2951	−0.673403	−0.336702	+	0.941611i	$0.609311\pi$
$822$	137.694	4.80262
$823$	43.6597	1.52188	0.760941	−	0.648822i	$-0.224738\pi$
$823$	43.6597	1.52188	0.760941	+	0.648822i	$0.224738\pi$
$824$	24.3650	0.848796
$825$	71.0759	2.47454
$826$	−112.806	−3.92502
$827$	−32.1301	−1.11727	−0.558636	−	0.829413i	$-0.688675\pi$
$827$	−32.1301	−1.11727	−0.558636	+	0.829413i	$0.688675\pi$
$828$	113.663	3.95008
$829$	1.13210	0.0393196	0.0196598	−	0.999807i	$-0.493742\pi$
$829$	1.13210	0.0393196	0.0196598	+	0.999807i	$0.493742\pi$
$830$	16.4342	0.570438
$831$	35.2569	1.22305
$832$	0	0
$833$	−48.9540	−1.69615
$834$	8.48070	0.293663
$835$	−12.7466	−0.441114
$836$	78.2916	2.70777
$837$	−15.8241	−0.546960
$838$	11.6523	0.402523
$839$	−35.0636	−1.21053	−0.605265	−	0.796024i	$-0.706933\pi$
$839$	−35.0636	−1.21053	−0.605265	+	0.796024i	$0.706933\pi$
$840$	20.7619	0.716355
$841$	−22.8505	−0.787947
$842$	−20.5517	−0.708258
$843$	−61.9594	−2.13399
$844$	4.25241	0.146374
$845$	0	0
$846$	−166.027	−5.70813
$847$	51.9720	1.78578
$848$	−2.53571	−0.0870765
$849$	34.9517	1.19954
$850$	−63.0443	−2.16240
$851$	−22.5846	−0.774190
$852$	−13.1473	−0.450419
$853$	−44.6440	−1.52858	−0.764291	−	0.644871i	$-0.776911\pi$
$853$	−44.6440	−1.52858	−0.764291	+	0.644871i	$0.776911\pi$
$854$	−2.03813	−0.0697432
$855$	33.8067	1.15616
$856$	14.0329	0.479634
$857$	7.46741	0.255082	0.127541	−	0.991833i	$-0.459292\pi$
$857$	7.46741	0.255082	0.127541	+	0.991833i	$0.459292\pi$
$858$	0	0
$859$	−25.8243	−0.881113	−0.440557	−	0.897725i	$-0.645219\pi$
$859$	−25.8243	−0.881113	−0.440557	+	0.897725i	$0.645219\pi$
$860$	1.78773	0.0609610
$861$	107.943	3.67870
$862$	53.0886	1.80821
$863$	26.9240	0.916504	0.458252	−	0.888822i	$-0.348476\pi$
$863$	26.9240	0.916504	0.458252	+	0.888822i	$0.348476\pi$
$864$	−110.203	−3.74918
$865$	1.89796	0.0645327
$866$	84.9873	2.88798
$867$	−83.9633	−2.85154
$868$	11.1559	0.378656
$869$	18.8388	0.639063
$870$	14.5502	0.493297
$871$	0	0
$872$	−7.57063	−0.256374
$873$	−47.6914	−1.61411
$874$	−59.3757	−2.00841
$875$	−28.6338	−0.967999
$876$	−80.3166	−2.71365
$877$	−6.73326	−0.227366	−0.113683	−	0.993517i	$-0.536265\pi$
$877$	−6.73326	−0.227366	−0.113683	+	0.993517i	$0.536265\pi$
$878$	−16.8659	−0.569195
$879$	−106.855	−3.60413
$880$	−5.10207	−0.171991
$881$	47.6456	1.60522	0.802611	−	0.596503i	$-0.203444\pi$
$881$	47.6456	1.60522	0.802611	+	0.596503i	$0.203444\pi$
$882$	−130.191	−4.38376
$883$	−2.72370	−0.0916599	−0.0458300	−	0.998949i	$-0.514593\pi$
$883$	−2.72370	−0.0916599	−0.0458300	+	0.998949i	$0.514593\pi$
$884$	0	0
$885$	−35.2564	−1.18513
$886$	7.97497	0.267924
$887$	31.3731	1.05341	0.526703	−	0.850049i	$-0.323428\pi$
$887$	31.3731	1.05341	0.526703	+	0.850049i	$0.323428\pi$
$888$	−30.8383	−1.03487
$889$	6.97177	0.233826
$890$	−9.68967	−0.324799
$891$	141.962	4.75592
$892$	−67.6018	−2.26347
$893$	51.5384	1.72467
$894$	−7.39483	−0.247320
$895$	3.94205	0.131768
$896$	56.0673	1.87308
$897$	0	0
$898$	81.1744	2.70882
$899$	2.47983	0.0827069
$900$	−99.6330	−3.32110
$901$	−12.9330	−0.430859
$902$	94.9974	3.16307
$903$	−9.51053	−0.316491
$904$	−30.6002	−1.01775
$905$	4.66787	0.155165
$906$	−50.9729	−1.69346
$907$	−12.3208	−0.409106	−0.204553	−	0.978856i	$-0.565574\pi$
$907$	−12.3208	−0.409106	−0.204553	+	0.978856i	$0.565574\pi$
$908$	31.8796	1.05796
$909$	75.6714	2.50986
$910$	0	0
$911$	8.20482	0.271838	0.135919	−	0.990720i	$-0.456601\pi$
$911$	8.20482	0.271838	0.135919	+	0.990720i	$0.456601\pi$
$912$	22.6386	0.749638
$913$	−45.7227	−1.51320
$914$	−15.5537	−0.514470
$915$	−0.636997	−0.0210585
$916$	−55.2987	−1.82712
$917$	14.1243	0.466425
$918$	−229.125	−7.56224
$919$	47.8108	1.57713	0.788566	−	0.614951i	$-0.210824\pi$
$919$	47.8108	1.57713	0.788566	+	0.614951i	$0.210824\pi$
$920$	−8.23459	−0.271486
$921$	−41.2669	−1.35979
$922$	3.66738	0.120779
$923$	0	0
$924$	−182.111	−5.99100
$925$	19.7968	0.650914
$926$	19.7183	0.647985
$927$	−92.2829	−3.03097
$928$	17.2701	0.566920
$929$	−19.4076	−0.636743	−0.318372	−	0.947966i	$-0.603136\pi$
$929$	−19.4076	−0.636743	−0.318372	+	0.947966i	$0.603136\pi$
$930$	5.86741	0.192400
$931$	40.4141	1.32452
$932$	41.1863	1.34910
$933$	−83.5943	−2.73675
$934$	44.4797	1.45542
$935$	−26.0223	−0.851019
$936$	0	0
$937$	−4.34866	−0.142065	−0.0710323	−	0.997474i	$-0.522629\pi$
$937$	−4.34866	−0.142065	−0.0710323	+	0.997474i	$0.522629\pi$
$938$	32.1340	1.04921
$939$	−4.07245	−0.132900
$940$	22.5345	0.734993
$941$	−48.9033	−1.59420	−0.797101	−	0.603846i	$-0.793634\pi$
$941$	−48.9033	−1.59420	−0.797101	+	0.603846i	$0.793634\pi$
$942$	−19.1168	−0.622860
$943$	−42.8124	−1.39416
$944$	−17.0587	−0.555214
$945$	−48.4393	−1.57573
$946$	−8.36991	−0.272129
$947$	6.38803	0.207583	0.103791	−	0.994599i	$-0.466903\pi$
$947$	6.38803	0.207583	0.103791	+	0.994599i	$0.466903\pi$
$948$	−36.5487	−1.18705
$949$	0	0
$950$	52.0464	1.68861
$951$	−46.9277	−1.52173
$952$	51.2360	1.66057
$953$	−5.66767	−0.183594	−0.0917969	−	0.995778i	$-0.529261\pi$
$953$	−5.66767	−0.183594	−0.0917969	+	0.995778i	$0.529261\pi$
$954$	−34.3947	−1.11357
$955$	−8.56139	−0.277040
$956$	76.8904	2.48681
$957$	−40.4810	−1.30857
$958$	−38.5648	−1.24597
$959$	71.8369	2.31973
$960$	34.1034	1.10068
$961$	1.00000	0.0322581
$962$	0	0
$963$	−53.1498	−1.71273
$964$	−31.1932	−1.00466
$965$	7.71538	0.248367
$966$	138.111	4.44365
$967$	51.4858	1.65567	0.827835	−	0.560971i	$-0.189572\pi$
$967$	51.4858	1.65567	0.827835	+	0.560971i	$0.189572\pi$
$968$	−28.1463	−0.904657
$969$	115.464	3.70925
$970$	10.8929	0.349750
$971$	60.0649	1.92758	0.963788	−	0.266670i	$-0.0859233\pi$
$971$	60.0649	1.92758	0.963788	+	0.266670i	$0.0859233\pi$
$972$	−136.369	−4.37404
$973$	4.42451	0.141843
$974$	4.51620	0.144708
$975$	0	0
$976$	−0.308209	−0.00986553
$977$	19.4817	0.623276	0.311638	−	0.950201i	$-0.399122\pi$
$977$	19.4817	0.623276	0.311638	+	0.950201i	$0.399122\pi$
$978$	3.54704	0.113422
$979$	26.9583	0.861592
$980$	17.6705	0.564464
$981$	28.6738	0.915485
$982$	69.7661	2.22633
$983$	−33.8727	−1.08037	−0.540186	−	0.841545i	$-0.681646\pi$
$983$	−33.8727	−1.08037	−0.540186	+	0.841545i	$0.681646\pi$
$984$	−58.4585	−1.86359
$985$	−4.85952	−0.154837
$986$	35.9067	1.14350
$987$	−119.881	−3.81586
$988$	0	0
$989$	3.77206	0.119944
$990$	−69.2051	−2.19948
$991$	0.0296479	0.000941796 0	0.000470898	−	1.00000i	$-0.499850\pi$
$991$	0.0296479	0.000941796 0	0.000470898		1.00000i	$0.499850\pi$
$992$	6.96425	0.221115
$993$	36.8756	1.17021
$994$	−11.5427	−0.366111
$995$	14.9888	0.475178
$996$	88.7055	2.81074
$997$	−8.21542	−0.260185	−0.130092	−	0.991502i	$-0.541527\pi$
$997$	−8.21542	−0.260185	−0.130092	+	0.991502i	$0.541527\pi$
$998$	−19.2283	−0.608660
$999$	71.9483	2.27634

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.v.1.8	yes	54
13.12	even	2		5239.2.a.u.1.47	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5239.2.a.u.1.47	✓	54	13.12	even	2
5239.2.a.v.1.8	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)

\(f(q)\)	\(=\)	\(q-2.22015 q^{2} -3.28822 q^{3} +2.92906 q^{4} +0.803718 q^{5} +7.30033 q^{6} +3.80869 q^{7} -2.06266 q^{8} +7.81236 q^{9} +O(q^{10})\)	\(q-2.22015 q^{2} -3.28822 q^{3} +2.92906 q^{4} +0.803718 q^{5} +7.30033 q^{6} +3.80869 q^{7} -2.06266 q^{8} +7.81236 q^{9} -1.78438 q^{10} +4.96444 q^{11} -9.63139 q^{12} -8.45587 q^{14} -2.64280 q^{15} -1.27871 q^{16} -6.52186 q^{17} -17.3446 q^{18} +5.38414 q^{19} +2.35414 q^{20} -12.5238 q^{21} -11.0218 q^{22} +4.96718 q^{23} +6.78248 q^{24} -4.35404 q^{25} -15.8241 q^{27} +11.1559 q^{28} +2.47983 q^{29} +5.86741 q^{30} +1.00000 q^{31} +6.96425 q^{32} -16.3241 q^{33} +14.4795 q^{34} +3.06112 q^{35} +22.8829 q^{36} -4.54677 q^{37} -11.9536 q^{38} -1.65780 q^{40} -8.61906 q^{41} +27.8047 q^{42} +0.759397 q^{43} +14.5412 q^{44} +6.27894 q^{45} -11.0279 q^{46} +9.57226 q^{47} +4.20468 q^{48} +7.50614 q^{49} +9.66661 q^{50} +21.4453 q^{51} +1.98302 q^{53} +35.1318 q^{54} +3.99001 q^{55} -7.85605 q^{56} -17.7042 q^{57} -5.50559 q^{58} +13.3406 q^{59} -7.74093 q^{60} +0.241031 q^{61} -2.22015 q^{62} +29.7549 q^{63} -12.9043 q^{64} +36.2420 q^{66} -3.80020 q^{67} -19.1029 q^{68} -16.3332 q^{69} -6.79614 q^{70} +1.36505 q^{71} -16.1143 q^{72} +8.33905 q^{73} +10.0945 q^{74} +14.3170 q^{75} +15.7705 q^{76} +18.9080 q^{77} +3.79475 q^{79} -1.02772 q^{80} +28.5959 q^{81} +19.1356 q^{82} -9.21004 q^{83} -36.6830 q^{84} -5.24174 q^{85} -1.68597 q^{86} -8.15420 q^{87} -10.2400 q^{88} +5.43029 q^{89} -13.9402 q^{90} +14.5492 q^{92} -3.28822 q^{93} -21.2518 q^{94} +4.32733 q^{95} -22.9000 q^{96} -6.10461 q^{97} -16.6648 q^{98} +38.7840 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 2 q^{2} + 7 q^{3} + 64 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 6 q^{8} + 95 q^{9}+O(q^{10}) \) 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

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Representations

Groups

Database

Properties

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