LMFDB - Embedded newform 5239.2.a.m.1.5

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:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 4 x^{16} - 19 x^{15} + 90 x^{14} + 116 x^{13} - 776 x^{12} - 146 x^{11} + 3232 x^{10} + \cdots - 1 $ x^17 - 4x^16 - 19x^15 + 90x^14 + 116x^13 - 776x^12 - 146x^11 + 3232x^10 - 995x^9 - 6763x^8 + 3668x^7 + 6782x^6 - 4160x^5 - 2876x^4 + 1449x^3 + 392x^2 + 6x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 403)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.89716$ of defining polynomial
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)

$f(q)$	$=$	$q-1.89716 q^{2} +2.58453 q^{3} +1.59922 q^{4} -2.49083 q^{5} -4.90328 q^{6} +2.96856 q^{7} +0.760339 q^{8} +3.67982 q^{9} +O(q^{10})$	\(q-1.89716 q^{2} +2.58453 q^{3} +1.59922 q^{4} -2.49083 q^{5} -4.90328 q^{6} +2.96856 q^{7} +0.760339 q^{8} +3.67982 q^{9} +4.72551 q^{10} -5.64920 q^{11} +4.13325 q^{12} -5.63183 q^{14} -6.43764 q^{15} -4.64093 q^{16} +3.29349 q^{17} -6.98121 q^{18} -3.56495 q^{19} -3.98339 q^{20} +7.67234 q^{21} +10.7174 q^{22} +2.02348 q^{23} +1.96512 q^{24} +1.20424 q^{25} +1.75701 q^{27} +4.74738 q^{28} -2.06433 q^{29} +12.2132 q^{30} -1.00000 q^{31} +7.28392 q^{32} -14.6005 q^{33} -6.24828 q^{34} -7.39417 q^{35} +5.88484 q^{36} +7.33569 q^{37} +6.76328 q^{38} -1.89388 q^{40} +1.11323 q^{41} -14.5557 q^{42} +9.40292 q^{43} -9.03433 q^{44} -9.16580 q^{45} -3.83887 q^{46} -3.52821 q^{47} -11.9946 q^{48} +1.81233 q^{49} -2.28463 q^{50} +8.51213 q^{51} +4.28934 q^{53} -3.33333 q^{54} +14.0712 q^{55} +2.25711 q^{56} -9.21373 q^{57} +3.91636 q^{58} -2.01779 q^{59} -10.2952 q^{60} -2.63033 q^{61} +1.89716 q^{62} +10.9237 q^{63} -4.53691 q^{64} +27.6996 q^{66} -13.1004 q^{67} +5.26702 q^{68} +5.22975 q^{69} +14.0279 q^{70} -10.4571 q^{71} +2.79791 q^{72} +11.5690 q^{73} -13.9170 q^{74} +3.11239 q^{75} -5.70114 q^{76} -16.7700 q^{77} -11.4827 q^{79} +11.5598 q^{80} -6.49840 q^{81} -2.11197 q^{82} -4.67683 q^{83} +12.2698 q^{84} -8.20351 q^{85} -17.8389 q^{86} -5.33532 q^{87} -4.29531 q^{88} -3.28654 q^{89} +17.3890 q^{90} +3.23599 q^{92} -2.58453 q^{93} +6.69358 q^{94} +8.87968 q^{95} +18.8255 q^{96} +3.32777 q^{97} -3.43828 q^{98} -20.7880 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9}+O(q^{10}) $ 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9	$ 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9} + 6 q^{10} - 13 q^{11} + 4 q^{12} - 4 q^{15} + 34 q^{16} - 6 q^{17} + 12 q^{18} - 4 q^{19} - 28 q^{20} - 18 q^{21} - 34 q^{22} - 8 q^{23} - 40 q^{24} + 8 q^{25} - 3 q^{27} - 21 q^{28} - 6 q^{29} + 19 q^{30} - 17 q^{31} - 6 q^{32} - 7 q^{33} - 24 q^{34} - 9 q^{35} - 14 q^{37} + 11 q^{38} - 10 q^{40} - 43 q^{41} + 33 q^{42} + 18 q^{43} - 28 q^{44} - 26 q^{45} - 7 q^{46} - 6 q^{47} - 95 q^{48} - q^{49} - 44 q^{50} + 26 q^{51} - 5 q^{53} - 27 q^{54} + 39 q^{55} + 39 q^{56} - 46 q^{57} - 8 q^{58} + q^{59} - 21 q^{60} - 19 q^{61} + 4 q^{62} - 5 q^{63} + 42 q^{64} + 26 q^{66} - 10 q^{67} + 34 q^{68} + 32 q^{69} + 24 q^{70} - 35 q^{71} + 26 q^{72} - 11 q^{73} - 68 q^{74} - 62 q^{75} - 2 q^{76} + 21 q^{77} + q^{79} - 49 q^{80} + 37 q^{81} + 35 q^{82} - 24 q^{83} + 34 q^{84} + 13 q^{85} - 76 q^{86} - 22 q^{87} - 37 q^{88} - 42 q^{89} + 15 q^{90} + 15 q^{92} + 42 q^{94} + 34 q^{95} - 33 q^{96} + 38 q^{97} - 8 q^{98} - 17 q^{99}+O(q^{100}) $ 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9 + 6 * q^10 - 13 * q^11 + 4 * q^12 - 4 * q^15 + 34 * q^16 - 6 * q^17 + 12 * q^18 - 4 * q^19 - 28 * q^20 - 18 * q^21 - 34 * q^22 - 8 * q^23 - 40 * q^24 + 8 * q^25 - 3 * q^27 - 21 * q^28 - 6 * q^29 + 19 * q^30 - 17 * q^31 - 6 * q^32 - 7 * q^33 - 24 * q^34 - 9 * q^35 - 14 * q^37 + 11 * q^38 - 10 * q^40 - 43 * q^41 + 33 * q^42 + 18 * q^43 - 28 * q^44 - 26 * q^45 - 7 * q^46 - 6 * q^47 - 95 * q^48 - q^49 - 44 * q^50 + 26 * q^51 - 5 * q^53 - 27 * q^54 + 39 * q^55 + 39 * q^56 - 46 * q^57 - 8 * q^58 + q^59 - 21 * q^60 - 19 * q^61 + 4 * q^62 - 5 * q^63 + 42 * q^64 + 26 * q^66 - 10 * q^67 + 34 * q^68 + 32 * q^69 + 24 * q^70 - 35 * q^71 + 26 * q^72 - 11 * q^73 - 68 * q^74 - 62 * q^75 - 2 * q^76 + 21 * q^77 + q^79 - 49 * q^80 + 37 * q^81 + 35 * q^82 - 24 * q^83 + 34 * q^84 + 13 * q^85 - 76 * q^86 - 22 * q^87 - 37 * q^88 - 42 * q^89 + 15 * q^90 + 15 * q^92 + 42 * q^94 + 34 * q^95 - 33 * q^96 + 38 * q^97 - 8 * q^98 - 17 * 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 $

$2$	−1.89716	−1.34150	−0.670748	−	0.741685i	$-0.734027\pi$
$2$	−1.89716	−1.34150	−0.670748	+	0.741685i	$0.734027\pi$
$3$	2.58453	1.49218	0.746091	−	0.665844i	$-0.231929\pi$
$3$	2.58453	1.49218	0.746091	+	0.665844i	$0.231929\pi$
$4$	1.59922	0.799611
$5$	−2.49083	−1.11393	−0.556967	−	0.830535i	$-0.688035\pi$
$5$	−2.49083	−1.11393	−0.556967	+	0.830535i	$0.688035\pi$
$6$	−4.90328	−2.00176
$7$	2.96856	1.12201	0.561005	−	0.827813i	$-0.310415\pi$
$7$	2.96856	1.12201	0.561005	+	0.827813i	$0.310415\pi$
$8$	0.760339	0.268821
$9$	3.67982	1.22661
$10$	4.72551	1.49434
$11$	−5.64920	−1.70330	−0.851649	−	0.524113i	$-0.824397\pi$
$11$	−5.64920	−1.70330	−0.851649	+	0.524113i	$0.824397\pi$
$12$	4.13325	1.19317
$13$	0	0
$13$	0	0
$14$	−5.63183	−1.50517
$15$	−6.43764	−1.66219
$16$	−4.64093	−1.16023
$17$	3.29349	0.798788	0.399394	−	0.916779i	$-0.369221\pi$
$17$	3.29349	0.798788	0.399394	+	0.916779i	$0.369221\pi$
$18$	−6.98121	−1.64549
$19$	−3.56495	−0.817855	−0.408927	−	0.912567i	$-0.634097\pi$
$19$	−3.56495	−0.817855	−0.408927	+	0.912567i	$0.634097\pi$
$20$	−3.98339	−0.890714
$21$	7.67234	1.67424
$22$	10.7174	2.28497
$23$	2.02348	0.421924	0.210962	−	0.977494i	$-0.432340\pi$
$23$	2.02348	0.421924	0.210962	+	0.977494i	$0.432340\pi$
$24$	1.96512	0.401129
$25$	1.20424	0.240847
$26$	0	0
$27$	1.75701	0.338136
$28$	4.74738	0.897171
$29$	−2.06433	−0.383336	−0.191668	−	0.981460i	$-0.561390\pi$
$29$	−2.06433	−0.383336	−0.191668	+	0.981460i	$0.561390\pi$
$30$	12.2132	2.22982
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	7.28392	1.28763
$33$	−14.6005	−2.54163
$34$	−6.24828	−1.07157
$35$	−7.39417	−1.24984
$36$	5.88484	0.980807
$37$	7.33569	1.20598	0.602990	−	0.797748i	$-0.293976\pi$
$37$	7.33569	1.20598	0.602990	+	0.797748i	$0.293976\pi$
$38$	6.76328	1.09715
$39$	0	0
$40$	−1.89388	−0.299448
$41$	1.11323	0.173857	0.0869285	−	0.996215i	$-0.472295\pi$
$41$	1.11323	0.173857	0.0869285	+	0.996215i	$0.472295\pi$
$42$	−14.5557	−2.24599
$43$	9.40292	1.43393	0.716966	−	0.697108i	$-0.245530\pi$
$43$	9.40292	1.43393	0.716966	+	0.697108i	$0.245530\pi$
$44$	−9.03433	−1.36198
$45$	−9.16580	−1.36636
$46$	−3.83887	−0.566010
$47$	−3.52821	−0.514642	−0.257321	−	0.966326i	$-0.582840\pi$
$47$	−3.52821	−0.514642	−0.257321	+	0.966326i	$0.582840\pi$
$48$	−11.9946	−1.73128
$49$	1.81233	0.258904
$50$	−2.28463	−0.323095
$51$	8.51213	1.19194
$52$	0	0
$53$	4.28934	0.589186	0.294593	−	0.955623i	$-0.404816\pi$
$53$	4.28934	0.589186	0.294593	+	0.955623i	$0.404816\pi$
$54$	−3.33333	−0.453608
$55$	14.0712	1.89736
$56$	2.25711	0.301619
$57$	−9.21373	−1.22039
$58$	3.91636	0.514243
$59$	−2.01779	−0.262694	−0.131347	−	0.991336i	$-0.541930\pi$
$59$	−2.01779	−0.262694	−0.131347	+	0.991336i	$0.541930\pi$
$60$	−10.2952	−1.32911
$61$	−2.63033	−0.336780	−0.168390	−	0.985720i	$-0.553857\pi$
$61$	−2.63033	−0.336780	−0.168390	+	0.985720i	$0.553857\pi$
$62$	1.89716	0.240940
$63$	10.9237	1.37626
$64$	−4.53691	−0.567114
$65$	0	0
$66$	27.6996	3.40959
$67$	−13.1004	−1.60047	−0.800233	−	0.599690i	$-0.795291\pi$
$67$	−13.1004	−1.60047	−0.800233	+	0.599690i	$0.795291\pi$
$68$	5.26702	0.638720
$69$	5.22975	0.629588
$70$	14.0279	1.67666
$71$	−10.4571	−1.24103	−0.620517	−	0.784193i	$-0.713077\pi$
$71$	−10.4571	−1.24103	−0.620517	+	0.784193i	$0.713077\pi$
$72$	2.79791	0.329737
$73$	11.5690	1.35405	0.677024	−	0.735961i	$-0.263269\pi$
$73$	11.5690	1.35405	0.677024	+	0.735961i	$0.263269\pi$
$74$	−13.9170	−1.61782
$75$	3.11239	0.359388
$76$	−5.70114	−0.653966
$77$	−16.7700	−1.91112
$78$	0	0
$79$	−11.4827	−1.29190	−0.645951	−	0.763379i	$-0.723539\pi$
$79$	−11.4827	−1.29190	−0.645951	+	0.763379i	$0.723539\pi$
$80$	11.5598	1.29242
$81$	−6.49840	−0.722045
$82$	−2.11197	−0.233229
$83$	−4.67683	−0.513348	−0.256674	−	0.966498i	$-0.582627\pi$
$83$	−4.67683	−0.513348	−0.256674	+	0.966498i	$0.582627\pi$
$84$	12.2698	1.33874
$85$	−8.20351	−0.889796
$86$	−17.8389	−1.92361
$87$	−5.33532	−0.572007
$88$	−4.29531	−0.457881
$89$	−3.28654	−0.348372	−0.174186	−	0.984713i	$-0.555729\pi$
$89$	−3.28654	−0.348372	−0.174186	+	0.984713i	$0.555729\pi$
$90$	17.3890	1.83296
$91$	0	0
$92$	3.23599	0.337376
$93$	−2.58453	−0.268004
$94$	6.69358	0.690390
$95$	8.87968	0.911036
$96$	18.8255	1.92137
$97$	3.32777	0.337884	0.168942	−	0.985626i	$-0.445965\pi$
$97$	3.32777	0.337884	0.168942	+	0.985626i	$0.445965\pi$
$98$	−3.43828	−0.347319
$99$	−20.7880	−2.08927
$100$	1.92584	0.192584
$101$	−12.6743	−1.26114	−0.630569	−	0.776134i	$-0.717178\pi$
$101$	−12.6743	−1.26114	−0.630569	+	0.776134i	$0.717178\pi$
$102$	−16.1489	−1.59898
$103$	−16.6149	−1.63712	−0.818559	−	0.574423i	$-0.805227\pi$
$103$	−16.6149	−1.63712	−0.818559	+	0.574423i	$0.805227\pi$
$104$	0	0
$105$	−19.1105	−1.86499
$106$	−8.13756	−0.790390
$107$	−7.63559	−0.738160	−0.369080	−	0.929398i	$-0.620327\pi$
$107$	−7.63559	−0.738160	−0.369080	+	0.929398i	$0.620327\pi$
$108$	2.80985	0.270378
$109$	11.7915	1.12942	0.564710	−	0.825290i	$-0.308988\pi$
$109$	11.7915	1.12942	0.564710	+	0.825290i	$0.308988\pi$
$110$	−26.6953	−2.54530
$111$	18.9594	1.79954
$112$	−13.7769	−1.30179
$113$	−19.7258	−1.85565	−0.927823	−	0.373021i	$-0.878322\pi$
$113$	−19.7258	−1.85565	−0.927823	+	0.373021i	$0.878322\pi$
$114$	17.4799	1.63715
$115$	−5.04014	−0.469996
$116$	−3.30132	−0.306520
$117$	0	0
$118$	3.82807	0.352403
$119$	9.77690	0.896247
$120$	−4.89479	−0.446831
$121$	20.9135	1.90122
$122$	4.99017	0.451788
$123$	2.87718	0.259426
$124$	−1.59922	−0.143614
$125$	9.45461	0.845646
$126$	−20.7241	−1.84625
$127$	−4.57534	−0.405996	−0.202998	−	0.979179i	$-0.565069\pi$
$127$	−4.57534	−0.405996	−0.202998	+	0.979179i	$0.565069\pi$
$128$	−5.96059	−0.526846
$129$	24.3022	2.13969
$130$	0	0
$131$	20.3900	1.78148	0.890740	−	0.454513i	$-0.150187\pi$
$131$	20.3900	1.78148	0.890740	+	0.454513i	$0.150187\pi$
$132$	−23.3495	−2.03232
$133$	−10.5827	−0.917641
$134$	24.8535	2.14702
$135$	−4.37641	−0.376661
$136$	2.50417	0.214731
$137$	−20.5549	−1.75612	−0.878061	−	0.478549i	$-0.841163\pi$
$137$	−20.5549	−1.75612	−0.878061	+	0.478549i	$0.841163\pi$
$138$	−9.92168	−0.844590
$139$	11.7116	0.993363	0.496682	−	0.867933i	$-0.334552\pi$
$139$	11.7116	0.993363	0.496682	+	0.867933i	$0.334552\pi$
$140$	−11.8249	−0.999389
$141$	−9.11877	−0.767939
$142$	19.8389	1.66484
$143$	0	0
$144$	−17.0778	−1.42315
$145$	5.14189	0.427011
$146$	−21.9482	−1.81645
$147$	4.68403	0.386332
$148$	11.7314	0.964316
$149$	−15.1676	−1.24258	−0.621290	−	0.783581i	$-0.713391\pi$
$149$	−15.1676	−1.24258	−0.621290	+	0.783581i	$0.713391\pi$
$150$	−5.90470	−0.482117
$151$	−7.05570	−0.574184	−0.287092	−	0.957903i	$-0.592689\pi$
$151$	−7.05570	−0.574184	−0.287092	+	0.957903i	$0.592689\pi$
$152$	−2.71057	−0.219856
$153$	12.1194	0.979797
$154$	31.8153	2.56375
$155$	2.49083	0.200068
$156$	0	0
$157$	12.6395	1.00874	0.504372	−	0.863487i	$-0.331724\pi$
$157$	12.6395	1.00874	0.504372	+	0.863487i	$0.331724\pi$
$158$	21.7845	1.73308
$159$	11.0859	0.879172
$160$	−18.1430	−1.43433
$161$	6.00681	0.473403
$162$	12.3285	0.968620
$163$	24.0991	1.88759	0.943793	−	0.330536i	$-0.107230\pi$
$163$	24.0991	1.88759	0.943793	+	0.330536i	$0.107230\pi$
$164$	1.78030	0.139018
$165$	36.3675	2.83120
$166$	8.87270	0.688655
$167$	5.52508	0.427544	0.213772	−	0.976884i	$-0.431425\pi$
$167$	5.52508	0.427544	0.213772	+	0.976884i	$0.431425\pi$
$168$	5.83358	0.450070
$169$	0	0
$170$	15.5634	1.19366
$171$	−13.1183	−1.00319
$172$	15.0374	1.14659
$173$	−15.7460	−1.19715	−0.598575	−	0.801067i	$-0.704266\pi$
$173$	−15.7460	−1.19715	−0.598575	+	0.801067i	$0.704266\pi$
$174$	10.1220	0.767345
$175$	3.57484	0.270233
$176$	26.2176	1.97622
$177$	−5.21505	−0.391987
$178$	6.23509	0.467340
$179$	−0.742250	−0.0554784	−0.0277392	−	0.999615i	$-0.508831\pi$
$179$	−0.742250	−0.0554784	−0.0277392	+	0.999615i	$0.508831\pi$
$180$	−14.6581	−1.09255
$181$	−24.5507	−1.82484	−0.912418	−	0.409259i	$-0.865787\pi$
$181$	−24.5507	−1.82484	−0.912418	+	0.409259i	$0.865787\pi$
$182$	0	0
$183$	−6.79818	−0.502536
$184$	1.53853	0.113422
$185$	−18.2720	−1.34338
$186$	4.90328	0.359526
$187$	−18.6056	−1.36057
$188$	−5.64239	−0.411513
$189$	5.21578	0.379392
$190$	−16.8462	−1.22215
$191$	−7.77573	−0.562632	−0.281316	−	0.959615i	$-0.590771\pi$
$191$	−7.77573	−0.562632	−0.281316	+	0.959615i	$0.590771\pi$
$192$	−11.7258	−0.846237
$193$	13.2181	0.951457	0.475729	−	0.879592i	$-0.342184\pi$
$193$	13.2181	0.951457	0.475729	+	0.879592i	$0.342184\pi$
$194$	−6.31331	−0.453269
$195$	0	0
$196$	2.89832	0.207023
$197$	−8.15090	−0.580728	−0.290364	−	0.956916i	$-0.593776\pi$
$197$	−8.15090	−0.580728	−0.290364	+	0.956916i	$0.593776\pi$
$198$	39.4382	2.80275
$199$	−2.50990	−0.177922	−0.0889611	−	0.996035i	$-0.528355\pi$
$199$	−2.50990	−0.177922	−0.0889611	+	0.996035i	$0.528355\pi$
$200$	0.915628	0.0647446
$201$	−33.8584	−2.38818
$202$	24.0451	1.69181
$203$	−6.12807	−0.430106
$204$	13.6128	0.953086
$205$	−2.77286	−0.193665
$206$	31.5212	2.19619
$207$	7.44603	0.517535
$208$	0	0
$209$	20.1391	1.39305
$210$	36.2557	2.50188
$211$	16.2553	1.11906	0.559530	−	0.828810i	$-0.310982\pi$
$211$	16.2553	1.11906	0.559530	+	0.828810i	$0.310982\pi$
$212$	6.85960	0.471120
$213$	−27.0268	−1.85185
$214$	14.4859	0.990239
$215$	−23.4211	−1.59730
$216$	1.33592	0.0908980
$217$	−2.96856	−0.201519
$218$	−22.3704	−1.51511
$219$	29.9005	2.02049
$220$	22.5030	1.51715
$221$	0	0
$222$	−35.9690	−2.41408
$223$	1.89893	0.127161	0.0635807	−	0.997977i	$-0.479748\pi$
$223$	1.89893	0.127161	0.0635807	+	0.997977i	$0.479748\pi$
$224$	21.6227	1.44473
$225$	4.43136	0.295424
$226$	37.4230	2.48934
$227$	−3.18302	−0.211264	−0.105632	−	0.994405i	$-0.533687\pi$
$227$	−3.18302	−0.211264	−0.105632	+	0.994405i	$0.533687\pi$
$228$	−14.7348	−0.975836
$229$	6.15048	0.406435	0.203217	−	0.979134i	$-0.434860\pi$
$229$	6.15048	0.406435	0.203217	+	0.979134i	$0.434860\pi$
$230$	9.56196	0.630497
$231$	−43.3426	−2.85173
$232$	−1.56959	−0.103049
$233$	−24.6570	−1.61533	−0.807667	−	0.589638i	$-0.799270\pi$
$233$	−24.6570	−1.61533	−0.807667	+	0.589638i	$0.799270\pi$
$234$	0	0
$235$	8.78816	0.573276
$236$	−3.22690	−0.210053
$237$	−29.6774	−1.92775
$238$	−18.5484	−1.20231
$239$	1.51703	0.0981285	0.0490643	−	0.998796i	$-0.484376\pi$
$239$	1.51703	0.0981285	0.0490643	+	0.998796i	$0.484376\pi$
$240$	29.8766	1.92853
$241$	−29.0937	−1.87409	−0.937044	−	0.349212i	$-0.886449\pi$
$241$	−29.0937	−1.87409	−0.937044	+	0.349212i	$0.886449\pi$
$242$	−39.6762	−2.55048
$243$	−22.0664	−1.41556
$244$	−4.20649	−0.269293
$245$	−4.51421	−0.288402
$246$	−5.45847	−0.348019
$247$	0	0
$248$	−0.760339	−0.0482816
$249$	−12.0874	−0.766009
$250$	−17.9369	−1.13443
$251$	−11.3407	−0.715816	−0.357908	−	0.933757i	$-0.616510\pi$
$251$	−11.3407	−0.715816	−0.357908	+	0.933757i	$0.616510\pi$
$252$	17.4695	1.10047
$253$	−11.4310	−0.718663
$254$	8.68017	0.544642
$255$	−21.2023	−1.32774
$256$	20.3820	1.27388
$257$	−27.4128	−1.70996	−0.854982	−	0.518658i	$-0.826432\pi$
$257$	−27.4128	−1.70996	−0.854982	+	0.518658i	$0.826432\pi$
$258$	−46.1051	−2.87038
$259$	21.7764	1.35312
$260$	0	0
$261$	−7.59634	−0.470202
$262$	−38.6831	−2.38985
$263$	−6.21216	−0.383058	−0.191529	−	0.981487i	$-0.561345\pi$
$263$	−6.21216	−0.383058	−0.191529	+	0.981487i	$0.561345\pi$
$264$	−11.1014	−0.683242
$265$	−10.6840	−0.656313
$266$	20.0772	1.23101
$267$	−8.49417	−0.519835
$268$	−20.9504	−1.27975
$269$	17.2578	1.05223	0.526115	−	0.850414i	$-0.323648\pi$
$269$	17.2578	1.05223	0.526115	+	0.850414i	$0.323648\pi$
$270$	8.30275	0.505289
$271$	−16.6258	−1.00994	−0.504972	−	0.863136i	$-0.668497\pi$
$271$	−16.6258	−1.00994	−0.504972	+	0.863136i	$0.668497\pi$
$272$	−15.2848	−0.926780
$273$	0	0
$274$	38.9959	2.35583
$275$	−6.80297	−0.410234
$276$	8.36353	0.503426
$277$	21.4015	1.28589	0.642946	−	0.765911i	$-0.277712\pi$
$277$	21.4015	1.28589	0.642946	+	0.765911i	$0.277712\pi$
$278$	−22.2188	−1.33259
$279$	−3.67982	−0.220305
$280$	−5.62208	−0.335984
$281$	11.7116	0.698658	0.349329	−	0.937000i	$-0.386410\pi$
$281$	11.7116	0.698658	0.349329	+	0.937000i	$0.386410\pi$
$282$	17.2998	1.03019
$283$	−12.5342	−0.745082	−0.372541	−	0.928016i	$-0.621513\pi$
$283$	−12.5342	−0.745082	−0.372541	+	0.928016i	$0.621513\pi$
$284$	−16.7233	−0.992345
$285$	22.9498	1.35943
$286$	0	0
$287$	3.30468	0.195069
$288$	26.8035	1.57941
$289$	−6.15295	−0.361938
$290$	−9.75499	−0.572833
$291$	8.60073	0.504184
$292$	18.5014	1.08271
$293$	2.82177	0.164850	0.0824249	−	0.996597i	$-0.473734\pi$
$293$	2.82177	0.164850	0.0824249	+	0.996597i	$0.473734\pi$
$294$	−8.88636	−0.518263
$295$	5.02597	0.292623
$296$	5.57762	0.324192
$297$	−9.92568	−0.575947
$298$	28.7754	1.66692
$299$	0	0
$300$	4.97740	0.287370
$301$	27.9131	1.60888
$302$	13.3858	0.770266
$303$	−32.7571	−1.88185
$304$	16.5447	0.948902
$305$	6.55171	0.375150
$306$	−22.9925	−1.31439
$307$	20.2127	1.15360	0.576800	−	0.816886i	$-0.304301\pi$
$307$	20.2127	1.15360	0.576800	+	0.816886i	$0.304301\pi$
$308$	−26.8189	−1.52815
$309$	−42.9418	−2.44288
$310$	−4.72551	−0.268391
$311$	−13.1691	−0.746750	−0.373375	−	0.927681i	$-0.621800\pi$
$311$	−13.1691	−0.746750	−0.373375	+	0.927681i	$0.621800\pi$
$312$	0	0
$313$	−16.2123	−0.916375	−0.458187	−	0.888856i	$-0.651501\pi$
$313$	−16.2123	−0.916375	−0.458187	+	0.888856i	$0.651501\pi$
$314$	−23.9792	−1.35323
$315$	−27.2092	−1.53306
$316$	−18.3634	−1.03302
$317$	−1.95796	−0.109970	−0.0549849	−	0.998487i	$-0.517511\pi$
$317$	−1.95796	−0.109970	−0.0549849	+	0.998487i	$0.517511\pi$
$318$	−21.0318	−1.17941
$319$	11.6618	0.652935
$320$	11.3007	0.631727
$321$	−19.7344	−1.10147
$322$	−11.3959	−0.635068
$323$	−11.7411	−0.653292
$324$	−10.3924	−0.577355
$325$	0	0
$326$	−45.7199	−2.53219
$327$	30.4755	1.68530
$328$	0.846431	0.0467364
$329$	−10.4737	−0.577433
$330$	−68.9950	−3.79805
$331$	24.5182	1.34764	0.673822	−	0.738894i	$-0.264652\pi$
$331$	24.5182	1.34764	0.673822	+	0.738894i	$0.264652\pi$
$332$	−7.47929	−0.410479
$333$	26.9940	1.47926
$334$	−10.4820	−0.573548
$335$	32.6308	1.78281
$336$	−35.6068	−1.94251
$337$	27.7039	1.50913	0.754564	−	0.656226i	$-0.227848\pi$
$337$	27.7039	1.50913	0.754564	+	0.656226i	$0.227848\pi$
$338$	0	0
$339$	−50.9820	−2.76896
$340$	−13.1192	−0.711491
$341$	5.64920	0.305921
$342$	24.8876	1.34577
$343$	−15.3999	−0.831516
$344$	7.14941	0.385470
$345$	−13.0264	−0.701319
$346$	29.8728	1.60597
$347$	15.7190	0.843841	0.421921	−	0.906633i	$-0.361356\pi$
$347$	15.7190	0.843841	0.421921	+	0.906633i	$0.361356\pi$
$348$	−8.53237	−0.457383
$349$	−24.5815	−1.31582	−0.657908	−	0.753099i	$-0.728558\pi$
$349$	−24.5815	−1.31582	−0.657908	+	0.753099i	$0.728558\pi$
$350$	−6.78205	−0.362516
$351$	0	0
$352$	−41.1483	−2.19321
$353$	−22.7901	−1.21299	−0.606497	−	0.795086i	$-0.707426\pi$
$353$	−22.7901	−1.21299	−0.606497	+	0.795086i	$0.707426\pi$
$354$	9.89379	0.525849
$355$	26.0470	1.38243
$356$	−5.25590	−0.278562
$357$	25.2687	1.33736
$358$	1.40817	0.0744241
$359$	33.7165	1.77949	0.889744	−	0.456461i	$-0.150883\pi$
$359$	33.7165	1.77949	0.889744	+	0.456461i	$0.150883\pi$
$360$	−6.96912	−0.367305
$361$	−6.29115	−0.331113
$362$	46.5766	2.44801
$363$	54.0515	2.83697
$364$	0	0
$365$	−28.8164	−1.50832
$366$	12.8973	0.674150
$367$	11.8133	0.616650	0.308325	−	0.951281i	$-0.400231\pi$
$367$	11.8133	0.616650	0.308325	+	0.951281i	$0.400231\pi$
$368$	−9.39083	−0.489531
$369$	4.09648	0.213254
$370$	34.6649	1.80214
$371$	12.7331	0.661072
$372$	−4.13325	−0.214299
$373$	−25.7463	−1.33309	−0.666547	−	0.745463i	$-0.732228\pi$
$373$	−25.7463	−1.33309	−0.666547	+	0.745463i	$0.732228\pi$
$374$	35.2978	1.82520
$375$	24.4357	1.26186
$376$	−2.68263	−0.138346
$377$	0	0
$378$	−9.89517	−0.508953
$379$	−21.1902	−1.08847	−0.544233	−	0.838934i	$-0.683179\pi$
$379$	−21.1902	−1.08847	−0.544233	+	0.838934i	$0.683179\pi$
$380$	14.2006	0.728475
$381$	−11.8251	−0.605820
$382$	14.7518	0.754768
$383$	18.2126	0.930622	0.465311	−	0.885147i	$-0.345942\pi$
$383$	18.2126	0.930622	0.465311	+	0.885147i	$0.345942\pi$
$384$	−15.4053	−0.786151
$385$	41.7711	2.12885
$386$	−25.0768	−1.27638
$387$	34.6010	1.75887
$388$	5.32184	0.270176
$389$	−21.7952	−1.10506	−0.552531	−	0.833492i	$-0.686338\pi$
$389$	−21.7952	−1.10506	−0.552531	+	0.833492i	$0.686338\pi$
$390$	0	0
$391$	6.66430	0.337028
$392$	1.37799	0.0695988
$393$	52.6986	2.65829
$394$	15.4636	0.779044
$395$	28.6014	1.43909
$396$	−33.2447	−1.67061
$397$	2.11326	0.106062	0.0530308	−	0.998593i	$-0.483112\pi$
$397$	2.11326	0.106062	0.0530308	+	0.998593i	$0.483112\pi$
$398$	4.76169	0.238682
$399$	−27.3515	−1.36929
$400$	−5.58877	−0.279439
$401$	−24.7652	−1.23671	−0.618357	−	0.785897i	$-0.712202\pi$
$401$	−24.7652	−1.23671	−0.618357	+	0.785897i	$0.712202\pi$
$402$	64.2348	3.20374
$403$	0	0
$404$	−20.2690	−1.00842
$405$	16.1864	0.804310
$406$	11.6259	0.576986
$407$	−41.4408	−2.05414
$408$	6.47210	0.320417
$409$	−21.0882	−1.04274	−0.521371	−	0.853330i	$-0.674579\pi$
$409$	−21.0882	−1.04274	−0.521371	+	0.853330i	$0.674579\pi$
$410$	5.26057	0.259801
$411$	−53.1248	−2.62045
$412$	−26.5710	−1.30906
$413$	−5.98992	−0.294745
$414$	−14.1263	−0.694271
$415$	11.6492	0.571836
$416$	0	0
$417$	30.2690	1.48228
$418$	−38.2071	−1.86877
$419$	−7.48712	−0.365770	−0.182885	−	0.983134i	$-0.558544\pi$
$419$	−7.48712	−0.365770	−0.182885	+	0.983134i	$0.558544\pi$
$420$	−30.5619	−1.49127
$421$	−3.24144	−0.157978	−0.0789891	−	0.996875i	$-0.525169\pi$
$421$	−3.24144	−0.157978	−0.0789891	+	0.996875i	$0.525169\pi$
$422$	−30.8389	−1.50121
$423$	−12.9831	−0.631262
$424$	3.26135	0.158385
$425$	3.96613	0.192386
$426$	51.2743	2.48425
$427$	−7.80829	−0.377870
$428$	−12.2110	−0.590241
$429$	0	0
$430$	44.4336	2.14278
$431$	8.39397	0.404323	0.202162	−	0.979352i	$-0.435203\pi$
$431$	8.39397	0.404323	0.202162	+	0.979352i	$0.435203\pi$
$432$	−8.15415	−0.392317
$433$	16.2712	0.781942	0.390971	−	0.920403i	$-0.372139\pi$
$433$	16.2712	0.781942	0.390971	+	0.920403i	$0.372139\pi$
$434$	5.63183	0.270337
$435$	13.2894	0.637177
$436$	18.8572	0.903097
$437$	−7.21359	−0.345073
$438$	−56.7260	−2.71047
$439$	18.7417	0.894494	0.447247	−	0.894410i	$-0.352404\pi$
$439$	18.7417	0.894494	0.447247	+	0.894410i	$0.352404\pi$
$440$	10.6989	0.510049
$441$	6.66904	0.317573
$442$	0	0
$443$	−12.7569	−0.606099	−0.303049	−	0.952975i	$-0.598005\pi$
$443$	−12.7569	−0.606099	−0.303049	+	0.952975i	$0.598005\pi$
$444$	30.3202	1.43893
$445$	8.18621	0.388063
$446$	−3.60257	−0.170587
$447$	−39.2012	−1.85415
$448$	−13.4681	−0.636307
$449$	12.7377	0.601130	0.300565	−	0.953761i	$-0.402825\pi$
$449$	12.7377	0.601130	0.300565	+	0.953761i	$0.402825\pi$
$450$	−8.40701	−0.396310
$451$	−6.28885	−0.296130
$452$	−31.5459	−1.48380
$453$	−18.2357	−0.856787
$454$	6.03870	0.283410
$455$	0	0
$456$	−7.00556	−0.328065
$457$	−4.53298	−0.212044	−0.106022	−	0.994364i	$-0.533811\pi$
$457$	−4.53298	−0.212044	−0.106022	+	0.994364i	$0.533811\pi$
$458$	−11.6685	−0.545231
$459$	5.78668	0.270099
$460$	−8.06031	−0.375814
$461$	28.0085	1.30449	0.652243	−	0.758010i	$-0.273828\pi$
$461$	28.0085	1.30449	0.652243	+	0.758010i	$0.273828\pi$
$462$	82.2278	3.82559
$463$	−21.1680	−0.983759	−0.491880	−	0.870663i	$-0.663690\pi$
$463$	−21.1680	−0.983759	−0.491880	+	0.870663i	$0.663690\pi$
$464$	9.58040	0.444759
$465$	6.43764	0.298538
$466$	46.7784	2.16697
$467$	−16.9473	−0.784228	−0.392114	−	0.919917i	$-0.628256\pi$
$467$	−16.9473	−0.784228	−0.392114	+	0.919917i	$0.628256\pi$
$468$	0	0
$469$	−38.8892	−1.79574
$470$	−16.6726	−0.769048
$471$	32.6673	1.50523
$472$	−1.53421	−0.0706175
$473$	−53.1190	−2.44241
$474$	56.3028	2.58607
$475$	−4.29304	−0.196978
$476$	15.6354	0.716649
$477$	15.7840	0.722698
$478$	−2.87805	−0.131639
$479$	5.34040	0.244009	0.122005	−	0.992530i	$-0.461068\pi$
$479$	5.34040	0.244009	0.122005	+	0.992530i	$0.461068\pi$
$480$	−46.8912	−2.14028
$481$	0	0
$482$	55.1954	2.51408
$483$	15.5248	0.706403
$484$	33.4453	1.52024
$485$	−8.28890	−0.376380
$486$	41.8635	1.89897
$487$	2.71605	0.123076	0.0615381	−	0.998105i	$-0.480399\pi$
$487$	2.71605	0.123076	0.0615381	+	0.998105i	$0.480399\pi$
$488$	−1.99995	−0.0905333
$489$	62.2849	2.81662
$490$	8.56418	0.386890
$491$	−9.14955	−0.412913	−0.206457	−	0.978456i	$-0.566193\pi$
$491$	−9.14955	−0.412913	−0.206457	+	0.978456i	$0.566193\pi$
$492$	4.60125	0.207440
$493$	−6.79883	−0.306204
$494$	0	0
$495$	51.7794	2.32731
$496$	4.64093	0.208384
$497$	−31.0426	−1.39245
$498$	22.9318	1.02760
$499$	38.5417	1.72536	0.862681	−	0.505748i	$-0.168783\pi$
$499$	38.5417	1.72536	0.862681	+	0.505748i	$0.168783\pi$
$500$	15.1200	0.676188
$501$	14.2798	0.637973
$502$	21.5151	0.960264
$503$	−7.00868	−0.312502	−0.156251	−	0.987717i	$-0.549941\pi$
$503$	−7.00868	−0.312502	−0.156251	+	0.987717i	$0.549941\pi$
$504$	8.30575	0.369968
$505$	31.5695	1.40482
$506$	21.6865	0.964083
$507$	0	0
$508$	−7.31699	−0.324639
$509$	0.0356217	0.00157890	0.000789452	−	1.00000i	$-0.499749\pi$
$509$	0.0356217	0.00157890	0.000789452		1.00000i	$0.499749\pi$
$510$	40.2241	1.78115
$511$	34.3432	1.51925
$512$	−26.7468	−1.18205
$513$	−6.26364	−0.276546
$514$	52.0065	2.29391
$515$	41.3850	1.82364
$516$	38.8646	1.71092
$517$	19.9315	0.876588
$518$	−41.3134	−1.81521
$519$	−40.6962	−1.78636
$520$	0	0
$521$	2.60597	0.114170	0.0570849	−	0.998369i	$-0.481819\pi$
$521$	2.60597	0.114170	0.0570849	+	0.998369i	$0.481819\pi$
$522$	14.4115	0.630774
$523$	9.35387	0.409016	0.204508	−	0.978865i	$-0.434440\pi$
$523$	9.35387	0.409016	0.204508	+	0.978865i	$0.434440\pi$
$524$	32.6081	1.42449
$525$	9.23930	0.403236
$526$	11.7855	0.513871
$527$	−3.29349	−0.143466
$528$	67.7602	2.94888
$529$	−18.9055	−0.821980
$530$	20.2693	0.880442
$531$	−7.42510	−0.322222
$532$	−16.9242	−0.733756
$533$	0	0
$534$	16.1148	0.697356
$535$	19.0190	0.822261
$536$	−9.96073	−0.430238
$537$	−1.91837	−0.0827838
$538$	−32.7409	−1.41156
$539$	−10.2382	−0.440991
$540$	−6.99885	−0.301182
$541$	−30.2246	−1.29946	−0.649728	−	0.760167i	$-0.725117\pi$
$541$	−30.2246	−1.29946	−0.649728	+	0.760167i	$0.725117\pi$
$542$	31.5418	1.35484
$543$	−63.4520	−2.72299
$544$	23.9895	1.02854
$545$	−29.3706	−1.25810
$546$	0	0
$547$	−1.42924	−0.0611098	−0.0305549	−	0.999533i	$-0.509727\pi$
$547$	−1.42924	−0.0611098	−0.0305549	+	0.999533i	$0.509727\pi$
$548$	−32.8718	−1.40422
$549$	−9.67914	−0.413096
$550$	12.9063	0.550328
$551$	7.35922	0.313513
$552$	3.97638	0.169246
$553$	−34.0870	−1.44953
$554$	−40.6021	−1.72502
$555$	−47.2245	−2.00457
$556$	18.7294	0.794304
$557$	26.1605	1.10846	0.554229	−	0.832364i	$-0.313013\pi$
$557$	26.1605	1.10846	0.554229	+	0.832364i	$0.313013\pi$
$558$	6.98121	0.295538
$559$	0	0
$560$	34.3158	1.45011
$561$	−48.0867	−2.03022
$562$	−22.2189	−0.937247
$563$	4.79779	0.202203	0.101101	−	0.994876i	$-0.467763\pi$
$563$	4.79779	0.202203	0.101101	+	0.994876i	$0.467763\pi$
$564$	−14.5829	−0.614052
$565$	49.1336	2.06707
$566$	23.7794	0.999525
$567$	−19.2909	−0.810141
$568$	−7.95097	−0.333615
$569$	21.6349	0.906984	0.453492	−	0.891260i	$-0.350178\pi$
$569$	21.6349	0.906984	0.453492	+	0.891260i	$0.350178\pi$
$570$	−43.5395	−1.82367
$571$	9.72235	0.406868	0.203434	−	0.979089i	$-0.434790\pi$
$571$	9.72235	0.406868	0.203434	+	0.979089i	$0.434790\pi$
$572$	0	0
$573$	−20.0966	−0.839549
$574$	−6.26952	−0.261685
$575$	2.43674	0.101619
$576$	−16.6950	−0.695625
$577$	7.52972	0.313466	0.156733	−	0.987641i	$-0.449904\pi$
$577$	7.52972	0.313466	0.156733	+	0.987641i	$0.449904\pi$
$578$	11.6731	0.485539
$579$	34.1625	1.41975
$580$	8.22302	0.341442
$581$	−13.8834	−0.575982
$582$	−16.3170	−0.676360
$583$	−24.2313	−1.00356
$584$	8.79636	0.363996
$585$	0	0
$586$	−5.35336	−0.221145
$587$	−14.3688	−0.593063	−0.296531	−	0.955023i	$-0.595830\pi$
$587$	−14.3688	−0.593063	−0.296531	+	0.955023i	$0.595830\pi$
$588$	7.49080	0.308916
$589$	3.56495	0.146891
$590$	−9.53508	−0.392553
$591$	−21.0663	−0.866551
$592$	−34.0445	−1.39922
$593$	−12.6386	−0.519007	−0.259503	−	0.965742i	$-0.583559\pi$
$593$	−12.6386	−0.519007	−0.259503	+	0.965742i	$0.583559\pi$
$594$	18.8306	0.772630
$595$	−24.3526	−0.998359
$596$	−24.2564	−0.993581
$597$	−6.48692	−0.265492
$598$	0	0
$599$	42.3639	1.73094	0.865470	−	0.500960i	$-0.167020\pi$
$599$	42.3639	1.73094	0.865470	+	0.500960i	$0.167020\pi$
$600$	2.36647	0.0966108
$601$	−5.90724	−0.240961	−0.120481	−	0.992716i	$-0.538444\pi$
$601$	−5.90724	−0.240961	−0.120481	+	0.992716i	$0.538444\pi$
$602$	−52.9557	−2.15831
$603$	−48.2070	−1.96314
$604$	−11.2836	−0.459124
$605$	−52.0919	−2.11784
$606$	62.1455	2.52449
$607$	−38.3346	−1.55595	−0.777976	−	0.628294i	$-0.783754\pi$
$607$	−38.3346	−1.55595	−0.777976	+	0.628294i	$0.783754\pi$
$608$	−25.9668	−1.05309
$609$	−15.8382	−0.641797
$610$	−12.4297	−0.503262
$611$	0	0
$612$	19.3817	0.783457
$613$	−32.4136	−1.30917	−0.654586	−	0.755987i	$-0.727157\pi$
$613$	−32.4136	−1.30917	−0.654586	+	0.755987i	$0.727157\pi$
$614$	−38.3468	−1.54755
$615$	−7.16656	−0.288984
$616$	−12.7509	−0.513747
$617$	0.312394	0.0125765	0.00628825	−	0.999980i	$-0.497998\pi$
$617$	0.312394	0.0125765	0.00628825	+	0.999980i	$0.497998\pi$
$618$	81.4676	3.27711
$619$	15.6259	0.628059	0.314029	−	0.949413i	$-0.398321\pi$
$619$	15.6259	0.628059	0.314029	+	0.949413i	$0.398321\pi$
$620$	3.98339	0.159977
$621$	3.55527	0.142668
$622$	24.9839	1.00176
$623$	−9.75627	−0.390877
$624$	0	0
$625$	−29.5710	−1.18284
$626$	30.7574	1.22931
$627$	52.0502	2.07868
$628$	20.2134	0.806603
$629$	24.1600	0.963323
$630$	51.6202	2.05660
$631$	−8.07335	−0.321395	−0.160697	−	0.987004i	$-0.551374\pi$
$631$	−8.07335	−0.321395	−0.160697	+	0.987004i	$0.551374\pi$
$632$	−8.73073	−0.347290
$633$	42.0123	1.66984
$634$	3.71456	0.147524
$635$	11.3964	0.452253
$636$	17.7289	0.702996
$637$	0	0
$638$	−22.1243	−0.875910
$639$	−38.4803	−1.52226
$640$	14.8468	0.586872
$641$	−28.1761	−1.11289	−0.556444	−	0.830885i	$-0.687835\pi$
$641$	−28.1761	−1.11289	−0.556444	+	0.830885i	$0.687835\pi$
$642$	37.4394	1.47762
$643$	−29.0335	−1.14497	−0.572486	−	0.819915i	$-0.694021\pi$
$643$	−29.0335	−1.14497	−0.572486	+	0.819915i	$0.694021\pi$
$644$	9.60623	0.378538
$645$	−60.5326	−2.38347
$646$	22.2748	0.876389
$647$	−21.5412	−0.846873	−0.423436	−	0.905926i	$-0.639176\pi$
$647$	−21.5412	−0.846873	−0.423436	+	0.905926i	$0.639176\pi$
$648$	−4.94099	−0.194100
$649$	11.3989	0.447446
$650$	0	0
$651$	−7.67234	−0.300703
$652$	38.5398	1.50934
$653$	−4.99122	−0.195322	−0.0976608	−	0.995220i	$-0.531136\pi$
$653$	−4.99122	−0.195322	−0.0976608	+	0.995220i	$0.531136\pi$
$654$	−57.8170	−2.26082
$655$	−50.7880	−1.98445
$656$	−5.16642	−0.201715
$657$	42.5718	1.66088
$658$	19.8703	0.774623
$659$	1.89776	0.0739263	0.0369631	−	0.999317i	$-0.488232\pi$
$659$	1.89776	0.0739263	0.0369631	+	0.999317i	$0.488232\pi$
$660$	58.1597	2.26386
$661$	9.28896	0.361299	0.180649	−	0.983548i	$-0.442180\pi$
$661$	9.28896	0.361299	0.180649	+	0.983548i	$0.442180\pi$
$662$	−46.5150	−1.80786
$663$	0	0
$664$	−3.55598	−0.137999
$665$	26.3598	1.02219
$666$	−51.2120	−1.98442
$667$	−4.17712	−0.161739
$668$	8.83584	0.341869
$669$	4.90784	0.189748
$670$	−61.9059	−2.39163
$671$	14.8593	0.573636
$672$	55.8847	2.15580
$673$	46.9927	1.81144	0.905719	−	0.423879i	$-0.139332\pi$
$673$	46.9927	1.81144	0.905719	+	0.423879i	$0.139332\pi$
$674$	−52.5588	−2.02449
$675$	2.11585	0.0814391
$676$	0	0
$677$	−15.4889	−0.595288	−0.297644	−	0.954677i	$-0.596201\pi$
$677$	−15.4889	−0.595288	−0.297644	+	0.954677i	$0.596201\pi$
$678$	96.7210	3.71455
$679$	9.87867	0.379108
$680$	−6.23745	−0.239195
$681$	−8.22661	−0.315244
$682$	−10.7174	−0.410392
$683$	−42.4836	−1.62559	−0.812794	−	0.582551i	$-0.802055\pi$
$683$	−42.4836	−1.62559	−0.812794	+	0.582551i	$0.802055\pi$
$684$	−20.9792	−0.802158
$685$	51.1987	1.95620
$686$	29.2161	1.11548
$687$	15.8961	0.606475
$688$	−43.6383	−1.66369
$689$	0	0
$690$	24.7132	0.940816
$691$	−31.4191	−1.19524	−0.597620	−	0.801779i	$-0.703887\pi$
$691$	−31.4191	−1.19524	−0.597620	+	0.801779i	$0.703887\pi$
$692$	−25.1814	−0.957254
$693$	−61.7104	−2.34418
$694$	−29.8215	−1.13201
$695$	−29.1716	−1.10654
$696$	−4.05666	−0.153767
$697$	3.66640	0.138875
$698$	46.6350	1.76516
$699$	−63.7269	−2.41037
$700$	5.71697	0.216081
$701$	23.9020	0.902764	0.451382	−	0.892331i	$-0.350931\pi$
$701$	23.9020	0.902764	0.451382	+	0.892331i	$0.350931\pi$
$702$	0	0
$703$	−26.1514	−0.986317
$704$	25.6299	0.965964
$705$	22.7133	0.855432
$706$	43.2365	1.62723
$707$	−37.6243	−1.41501
$708$	−8.34002	−0.313437
$709$	−24.2089	−0.909184	−0.454592	−	0.890700i	$-0.650215\pi$
$709$	−24.2089	−0.909184	−0.454592	+	0.890700i	$0.650215\pi$
$710$	−49.4153	−1.85452
$711$	−42.2542	−1.58465
$712$	−2.49888	−0.0936496
$713$	−2.02348	−0.0757799
$714$	−47.9389	−1.79407
$715$	0	0
$716$	−1.18702	−0.0443612
$717$	3.92082	0.146426
$718$	−63.9656	−2.38717
$719$	12.7873	0.476886	0.238443	−	0.971156i	$-0.423363\pi$
$719$	12.7873	0.476886	0.238443	+	0.971156i	$0.423363\pi$
$720$	42.5378	1.58529
$721$	−49.3224	−1.83686
$722$	11.9353	0.444187
$723$	−75.1936	−2.79648
$724$	−39.2620	−1.45916
$725$	−2.48594	−0.0923253
$726$	−102.544	−3.80578
$727$	−3.06971	−0.113849	−0.0569246	−	0.998378i	$-0.518129\pi$
$727$	−3.06971	−0.113849	−0.0569246	+	0.998378i	$0.518129\pi$
$728$	0	0
$729$	−37.5361	−1.39022
$730$	54.6694	2.02340
$731$	30.9684	1.14541
$732$	−10.8718	−0.401834
$733$	7.47513	0.276100	0.138050	−	0.990425i	$-0.455917\pi$
$733$	7.47513	0.276100	0.138050	+	0.990425i	$0.455917\pi$
$734$	−22.4118	−0.827234
$735$	−11.6671	−0.430348
$736$	14.7389	0.543282
$737$	74.0066	2.72607
$738$	−7.77168	−0.286079
$739$	20.7795	0.764386	0.382193	−	0.924083i	$-0.375169\pi$
$739$	20.7795	0.764386	0.382193	+	0.924083i	$0.375169\pi$
$740$	−29.2209	−1.07418
$741$	0	0
$742$	−24.1568	−0.886825
$743$	36.8035	1.35019	0.675094	−	0.737731i	$-0.264103\pi$
$743$	36.8035	1.35019	0.675094	+	0.737731i	$0.264103\pi$
$744$	−1.96512	−0.0720449
$745$	37.7800	1.38415
$746$	48.8449	1.78834
$747$	−17.2099	−0.629676
$748$	−29.7544	−1.08793
$749$	−22.6667	−0.828223
$750$	−46.3586	−1.69278
$751$	−1.91775	−0.0699798	−0.0349899	−	0.999388i	$-0.511140\pi$
$751$	−1.91775	−0.0699798	−0.0349899	+	0.999388i	$0.511140\pi$
$752$	16.3742	0.597104
$753$	−29.3103	−1.06813
$754$	0	0
$755$	17.5745	0.639603
$756$	8.34119	0.303366
$757$	42.5623	1.54695	0.773477	−	0.633824i	$-0.218516\pi$
$757$	42.5623	1.54695	0.773477	+	0.633824i	$0.218516\pi$
$758$	40.2012	1.46017
$759$	−29.5439	−1.07238
$760$	6.75157	0.244905
$761$	11.4005	0.413269	0.206634	−	0.978418i	$-0.433749\pi$
$761$	11.4005	0.413269	0.206634	+	0.978418i	$0.433749\pi$
$762$	22.4342	0.812705
$763$	35.0037	1.26722
$764$	−12.4351	−0.449887
$765$	−30.1874	−1.09143
$766$	−34.5523	−1.24843
$767$	0	0
$768$	52.6780	1.90085
$769$	−33.6010	−1.21168	−0.605842	−	0.795585i	$-0.707164\pi$
$769$	−33.6010	−1.21168	−0.605842	+	0.795585i	$0.707164\pi$
$770$	−79.2466	−2.85585
$771$	−70.8493	−2.55158
$772$	21.1386	0.760796
$773$	14.3584	0.516437	0.258219	−	0.966087i	$-0.416865\pi$
$773$	14.3584	0.516437	0.258219	+	0.966087i	$0.416865\pi$
$774$	−65.6437	−2.35951
$775$	−1.20424	−0.0432574
$776$	2.53023	0.0908301
$777$	56.2819	2.01910
$778$	41.3491	1.48244
$779$	−3.96860	−0.142190
$780$	0	0
$781$	59.0744	2.11385
$782$	−12.6433	−0.452122
$783$	−3.62704	−0.129620
$784$	−8.41090	−0.300389
$785$	−31.4829	−1.12367
$786$	−99.9777	−3.56609
$787$	3.04903	0.108686	0.0543431	−	0.998522i	$-0.482694\pi$
$787$	3.04903	0.108686	0.0543431	+	0.998522i	$0.482694\pi$
$788$	−13.0351	−0.464356
$789$	−16.0556	−0.571593
$790$	−54.2615	−1.93054
$791$	−58.5571	−2.08205
$792$	−15.8059	−0.561640
$793$	0	0
$794$	−4.00920	−0.142281
$795$	−27.6132	−0.979339
$796$	−4.01389	−0.142269
$797$	14.8095	0.524578	0.262289	−	0.964989i	$-0.415523\pi$
$797$	14.8095	0.524578	0.262289	+	0.964989i	$0.415523\pi$
$798$	51.8902	1.83689
$799$	−11.6201	−0.411089
$800$	8.77155	0.310121
$801$	−12.0938	−0.427315
$802$	46.9836	1.65905
$803$	−65.3555	−2.30635
$804$	−54.1471	−1.90962
$805$	−14.9619	−0.527339
$806$	0	0
$807$	44.6035	1.57012
$808$	−9.63675	−0.339020
$809$	12.8500	0.451783	0.225892	−	0.974152i	$-0.427470\pi$
$809$	12.8500	0.451783	0.225892	+	0.974152i	$0.427470\pi$
$810$	−30.7083	−1.07898
$811$	10.5053	0.368892	0.184446	−	0.982843i	$-0.440951\pi$
$811$	10.5053	0.368892	0.184446	+	0.982843i	$0.440951\pi$
$812$	−9.80015	−0.343918
$813$	−42.9699	−1.50702
$814$	78.6199	2.75563
$815$	−60.0267	−2.10265
$816$	−39.5042	−1.38292
$817$	−33.5209	−1.17275
$818$	40.0076	1.39883
$819$	0	0
$820$	−4.43443	−0.154857
$821$	24.8265	0.866450	0.433225	−	0.901286i	$-0.357376\pi$
$821$	24.8265	0.866450	0.433225	+	0.901286i	$0.357376\pi$
$822$	100.786	3.51533
$823$	20.7853	0.724531	0.362265	−	0.932075i	$-0.382003\pi$
$823$	20.7853	0.724531	0.362265	+	0.932075i	$0.382003\pi$
$824$	−12.6330	−0.440091
$825$	−17.5825	−0.612144
$826$	11.3639	0.395399
$827$	−53.5015	−1.86043	−0.930214	−	0.367017i	$-0.880379\pi$
$827$	−53.5015	−1.86043	−0.930214	+	0.367017i	$0.880379\pi$
$828$	11.9079	0.413827
$829$	18.5703	0.644972	0.322486	−	0.946574i	$-0.395481\pi$
$829$	18.5703	0.644972	0.322486	+	0.946574i	$0.395481\pi$
$830$	−22.1004	−0.767115
$831$	55.3129	1.91878
$832$	0	0
$833$	5.96888	0.206810
$834$	−57.4251	−1.98847
$835$	−13.7620	−0.476255
$836$	32.2069	1.11390
$837$	−1.75701	−0.0607310
$838$	14.2043	0.490679
$839$	24.9469	0.861263	0.430631	−	0.902528i	$-0.358291\pi$
$839$	24.9469	0.861263	0.430631	+	0.902528i	$0.358291\pi$
$840$	−14.5305	−0.501348
$841$	−24.7386	−0.853054
$842$	6.14954	0.211927
$843$	30.2691	1.04252
$844$	25.9958	0.894812
$845$	0	0
$846$	24.6311	0.846836
$847$	62.0828	2.13319
$848$	−19.9065	−0.683593
$849$	−32.3951	−1.11180
$850$	−7.52439	−0.258085
$851$	14.8436	0.508833
$852$	−43.2219	−1.48076
$853$	−1.47222	−0.0504078	−0.0252039	−	0.999682i	$-0.508024\pi$
$853$	−1.47222	−0.0504078	−0.0252039	+	0.999682i	$0.508024\pi$
$854$	14.8136	0.506911
$855$	32.6756	1.11748
$856$	−5.80564	−0.198433
$857$	19.4301	0.663719	0.331859	−	0.943329i	$-0.392324\pi$
$857$	19.4301	0.663719	0.331859	+	0.943329i	$0.392324\pi$
$858$	0	0
$859$	−39.0912	−1.33377	−0.666887	−	0.745159i	$-0.732374\pi$
$859$	−39.0912	−1.33377	−0.666887	+	0.745159i	$0.732374\pi$
$860$	−37.4555	−1.27722
$861$	8.54106	0.291079
$862$	−15.9247	−0.542398
$863$	14.7349	0.501583	0.250791	−	0.968041i	$-0.419309\pi$
$863$	14.7349	0.501583	0.250791	+	0.968041i	$0.419309\pi$
$864$	12.7979	0.435393
$865$	39.2207	1.33354
$866$	−30.8690	−1.04897
$867$	−15.9025	−0.540078
$868$	−4.74738	−0.161137
$869$	64.8680	2.20049
$870$	−25.2121	−0.854771
$871$	0	0
$872$	8.96553	0.303611
$873$	12.2456	0.414450
$874$	13.6854	0.462914
$875$	28.0665	0.948822
$876$	47.8175	1.61560
$877$	−52.8086	−1.78322	−0.891610	−	0.452804i	$-0.850424\pi$
$877$	−52.8086	−1.78322	−0.891610	+	0.452804i	$0.850424\pi$
$878$	−35.5561	−1.19996
$879$	7.29297	0.245986
$880$	−65.3035	−2.20138
$881$	33.9636	1.14426	0.572131	−	0.820162i	$-0.306117\pi$
$881$	33.9636	1.14426	0.572131	+	0.820162i	$0.306117\pi$
$882$	−12.6522	−0.426023
$883$	−31.5787	−1.06271	−0.531354	−	0.847150i	$-0.678317\pi$
$883$	−31.5787	−1.06271	−0.531354	+	0.847150i	$0.678317\pi$
$884$	0	0
$885$	12.9898	0.436647
$886$	24.2019	0.813079
$887$	14.0622	0.472161	0.236081	−	0.971733i	$-0.424137\pi$
$887$	14.0622	0.472161	0.236081	+	0.971733i	$0.424137\pi$
$888$	14.4155	0.483754
$889$	−13.5822	−0.455531
$890$	−15.5306	−0.520585
$891$	36.7108	1.22986
$892$	3.03680	0.101680
$893$	12.5779	0.420902
$894$	74.3711	2.48734
$895$	1.84882	0.0617992
$896$	−17.6943	−0.591127
$897$	0	0
$898$	−24.1655	−0.806413
$899$	2.06433	0.0688492
$900$	7.08674	0.236225
$901$	14.1269	0.470634
$902$	11.9310	0.397258
$903$	72.1423	2.40075
$904$	−14.9983	−0.498836
$905$	61.1515	2.03275
$906$	34.5960	1.14938
$907$	−44.4078	−1.47454	−0.737269	−	0.675599i	$-0.763885\pi$
$907$	−44.4078	−1.47454	−0.737269	+	0.675599i	$0.763885\pi$
$908$	−5.09035	−0.168929
$909$	−46.6390	−1.54692
$910$	0	0
$911$	4.30189	0.142528	0.0712640	−	0.997457i	$-0.477297\pi$
$911$	4.30189	0.142528	0.0712640	+	0.997457i	$0.477297\pi$
$912$	42.7603	1.41593
$913$	26.4203	0.874385
$914$	8.59979	0.284456
$915$	16.9331	0.559792
$916$	9.83598	0.324990
$917$	60.5288	1.99884
$918$	−10.9783	−0.362337
$919$	12.8183	0.422837	0.211419	−	0.977396i	$-0.432192\pi$
$919$	12.8183	0.422837	0.211419	+	0.977396i	$0.432192\pi$
$920$	−3.83222	−0.126345
$921$	52.2404	1.72138
$922$	−53.1367	−1.74996
$923$	0	0
$924$	−69.3144	−2.28028
$925$	8.83390	0.290457
$926$	40.1591	1.31971
$927$	−61.1399	−2.00810
$928$	−15.0364	−0.493594
$929$	−45.5295	−1.49377	−0.746887	−	0.664951i	$-0.768453\pi$
$929$	−45.5295	−1.49377	−0.746887	+	0.664951i	$0.768453\pi$
$930$	−12.2132	−0.400488
$931$	−6.46086	−0.211746
$932$	−39.4321	−1.29164
$933$	−34.0359	−1.11429
$934$	32.1518	1.05204
$935$	46.3433	1.51559
$936$	0	0
$937$	9.57857	0.312918	0.156459	−	0.987684i	$-0.449992\pi$
$937$	9.57857	0.312918	0.156459	+	0.987684i	$0.449992\pi$
$938$	73.7791	2.40897
$939$	−41.9013	−1.36740
$940$	14.0542	0.458398
$941$	25.6281	0.835451	0.417725	−	0.908573i	$-0.362827\pi$
$941$	25.6281	0.835451	0.417725	+	0.908573i	$0.362827\pi$
$942$	−61.9751	−2.01926
$943$	2.25259	0.0733546
$944$	9.36443	0.304786
$945$	−12.9916	−0.422617
$946$	100.775	3.27649
$947$	0.408779	0.0132835	0.00664177	−	0.999978i	$-0.497886\pi$
$947$	0.408779	0.0132835	0.00664177	+	0.999978i	$0.497886\pi$
$948$	−47.4607	−1.54145
$949$	0	0
$950$	8.14458	0.264245
$951$	−5.06040	−0.164095
$952$	7.43376	0.240930
$953$	−32.5461	−1.05427	−0.527136	−	0.849781i	$-0.676734\pi$
$953$	−32.5461	−1.05427	−0.527136	+	0.849781i	$0.676734\pi$
$954$	−29.9447	−0.969497
$955$	19.3680	0.626734
$956$	2.42607	0.0784647
$957$	30.1403	0.974298
$958$	−10.1316	−0.327337
$959$	−61.0183	−1.97038
$960$	29.2070	0.942651
$961$	1.00000	0.0322581
$962$	0	0
$963$	−28.0976	−0.905431
$964$	−46.5272	−1.49854
$965$	−32.9240	−1.05986
$966$	−29.4531	−0.947637
$967$	−33.5445	−1.07872	−0.539359	−	0.842076i	$-0.681333\pi$
$967$	−33.5445	−1.07872	−0.539359	+	0.842076i	$0.681333\pi$
$968$	15.9013	0.511088
$969$	−30.3453	−0.974831
$970$	15.7254	0.504912
$971$	9.16999	0.294279	0.147139	−	0.989116i	$-0.452993\pi$
$971$	9.16999	0.294279	0.147139	+	0.989116i	$0.452993\pi$
$972$	−35.2890	−1.13190
$973$	34.7665	1.11456
$974$	−5.15280	−0.165106
$975$	0	0
$976$	12.2072	0.390743
$977$	−0.364370	−0.0116572	−0.00582861	−	0.999983i	$-0.501855\pi$
$977$	−0.364370	−0.0116572	−0.00582861	+	0.999983i	$0.501855\pi$
$978$	−118.165	−3.77849
$979$	18.5663	0.593382
$980$	−7.21922	−0.230610
$981$	43.3905	1.38535
$982$	17.3582	0.553921
$983$	56.7921	1.81139	0.905694	−	0.423933i	$-0.139351\pi$
$983$	56.7921	1.81139	0.905694	+	0.423933i	$0.139351\pi$
$984$	2.18763	0.0697391
$985$	20.3025	0.646892
$986$	12.8985	0.410771
$987$	−27.0696	−0.861634
$988$	0	0
$989$	19.0266	0.605011
$990$	−98.2339	−3.12208
$991$	−0.354507	−0.0112613	−0.00563065	−	0.999984i	$-0.501792\pi$
$991$	−0.354507	−0.0112613	−0.00563065	+	0.999984i	$0.501792\pi$
$992$	−7.28392	−0.231265
$993$	63.3682	2.01093
$994$	58.8928	1.86797
$995$	6.25174	0.198193
$996$	−19.3305	−0.612509
$997$	42.2819	1.33908	0.669541	−	0.742775i	$-0.266491\pi$
$997$	42.2819	1.33908	0.669541	+	0.742775i	$0.266491\pi$
$998$	−73.1198	−2.31457
$999$	12.8889	0.407786

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.m.1.5		17
13.3	even	3		403.2.f.b.373.13	yes	34
13.9	even	3		403.2.f.b.94.13	✓	34
13.12	even	2		5239.2.a.n.1.13		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.b.94.13	✓	34	13.9	even	3
403.2.f.b.373.13	yes	34	13.3	even	3
5239.2.a.m.1.5		17	1.1	even	1	trivial
5239.2.a.n.1.13		17	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.89716 q^{2} +2.58453 q^{3} +1.59922 q^{4} -2.49083 q^{5} -4.90328 q^{6} +2.96856 q^{7} +0.760339 q^{8} +3.67982 q^{9} +O(q^{10})\)	\(q-1.89716 q^{2} +2.58453 q^{3} +1.59922 q^{4} -2.49083 q^{5} -4.90328 q^{6} +2.96856 q^{7} +0.760339 q^{8} +3.67982 q^{9} +4.72551 q^{10} -5.64920 q^{11} +4.13325 q^{12} -5.63183 q^{14} -6.43764 q^{15} -4.64093 q^{16} +3.29349 q^{17} -6.98121 q^{18} -3.56495 q^{19} -3.98339 q^{20} +7.67234 q^{21} +10.7174 q^{22} +2.02348 q^{23} +1.96512 q^{24} +1.20424 q^{25} +1.75701 q^{27} +4.74738 q^{28} -2.06433 q^{29} +12.2132 q^{30} -1.00000 q^{31} +7.28392 q^{32} -14.6005 q^{33} -6.24828 q^{34} -7.39417 q^{35} +5.88484 q^{36} +7.33569 q^{37} +6.76328 q^{38} -1.89388 q^{40} +1.11323 q^{41} -14.5557 q^{42} +9.40292 q^{43} -9.03433 q^{44} -9.16580 q^{45} -3.83887 q^{46} -3.52821 q^{47} -11.9946 q^{48} +1.81233 q^{49} -2.28463 q^{50} +8.51213 q^{51} +4.28934 q^{53} -3.33333 q^{54} +14.0712 q^{55} +2.25711 q^{56} -9.21373 q^{57} +3.91636 q^{58} -2.01779 q^{59} -10.2952 q^{60} -2.63033 q^{61} +1.89716 q^{62} +10.9237 q^{63} -4.53691 q^{64} +27.6996 q^{66} -13.1004 q^{67} +5.26702 q^{68} +5.22975 q^{69} +14.0279 q^{70} -10.4571 q^{71} +2.79791 q^{72} +11.5690 q^{73} -13.9170 q^{74} +3.11239 q^{75} -5.70114 q^{76} -16.7700 q^{77} -11.4827 q^{79} +11.5598 q^{80} -6.49840 q^{81} -2.11197 q^{82} -4.67683 q^{83} +12.2698 q^{84} -8.20351 q^{85} -17.8389 q^{86} -5.33532 q^{87} -4.29531 q^{88} -3.28654 q^{89} +17.3890 q^{90} +3.23599 q^{92} -2.58453 q^{93} +6.69358 q^{94} +8.87968 q^{95} +18.8255 q^{96} +3.32777 q^{97} -3.43828 q^{98} -20.7880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9}+O(q^{10}) \) 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9	\( 17 q - 4 q^{2} + 20 q^{4} - 7 q^{5} - 6 q^{6} - 6 q^{7} - 6 q^{8} + 17 q^{9} + 6 q^{10} - 13 q^{11} + 4 q^{12} - 4 q^{15} + 34 q^{16} - 6 q^{17} + 12 q^{18} - 4 q^{19} - 28 q^{20} - 18 q^{21} - 34 q^{22} - 8 q^{23} - 40 q^{24} + 8 q^{25} - 3 q^{27} - 21 q^{28} - 6 q^{29} + 19 q^{30} - 17 q^{31} - 6 q^{32} - 7 q^{33} - 24 q^{34} - 9 q^{35} - 14 q^{37} + 11 q^{38} - 10 q^{40} - 43 q^{41} + 33 q^{42} + 18 q^{43} - 28 q^{44} - 26 q^{45} - 7 q^{46} - 6 q^{47} - 95 q^{48} - q^{49} - 44 q^{50} + 26 q^{51} - 5 q^{53} - 27 q^{54} + 39 q^{55} + 39 q^{56} - 46 q^{57} - 8 q^{58} + q^{59} - 21 q^{60} - 19 q^{61} + 4 q^{62} - 5 q^{63} + 42 q^{64} + 26 q^{66} - 10 q^{67} + 34 q^{68} + 32 q^{69} + 24 q^{70} - 35 q^{71} + 26 q^{72} - 11 q^{73} - 68 q^{74} - 62 q^{75} - 2 q^{76} + 21 q^{77} + q^{79} - 49 q^{80} + 37 q^{81} + 35 q^{82} - 24 q^{83} + 34 q^{84} + 13 q^{85} - 76 q^{86} - 22 q^{87} - 37 q^{88} - 42 q^{89} + 15 q^{90} + 15 q^{92} + 42 q^{94} + 34 q^{95} - 33 q^{96} + 38 q^{97} - 8 q^{98} - 17 q^{99}+O(q^{100}) \) 17 * q - 4 * q^2 + 20 * q^4 - 7 * q^5 - 6 * q^6 - 6 * q^7 - 6 * q^8 + 17 * q^9 + 6 * q^10 - 13 * q^11 + 4 * q^12 - 4 * q^15 + 34 * q^16 - 6 * q^17 + 12 * q^18 - 4 * q^19 - 28 * q^20 - 18 * q^21 - 34 * q^22 - 8 * q^23 - 40 * q^24 + 8 * q^25 - 3 * q^27 - 21 * q^28 - 6 * q^29 + 19 * q^30 - 17 * q^31 - 6 * q^32 - 7 * q^33 - 24 * q^34 - 9 * q^35 - 14 * q^37 + 11 * q^38 - 10 * q^40 - 43 * q^41 + 33 * q^42 + 18 * q^43 - 28 * q^44 - 26 * q^45 - 7 * q^46 - 6 * q^47 - 95 * q^48 - q^49 - 44 * q^50 + 26 * q^51 - 5 * q^53 - 27 * q^54 + 39 * q^55 + 39 * q^56 - 46 * q^57 - 8 * q^58 + q^59 - 21 * q^60 - 19 * q^61 + 4 * q^62 - 5 * q^63 + 42 * q^64 + 26 * q^66 - 10 * q^67 + 34 * q^68 + 32 * q^69 + 24 * q^70 - 35 * q^71 + 26 * q^72 - 11 * q^73 - 68 * q^74 - 62 * q^75 - 2 * q^76 + 21 * q^77 + q^79 - 49 * q^80 + 37 * q^81 + 35 * q^82 - 24 * q^83 + 34 * q^84 + 13 * q^85 - 76 * q^86 - 22 * q^87 - 37 * q^88 - 42 * q^89 + 15 * q^90 + 15 * q^92 + 42 * q^94 + 34 * q^95 - 33 * q^96 + 38 * q^97 - 8 * q^98 - 17 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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