LMFDB - Embedded newform 6035.2.a.g.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$0$
Dimension:	$58$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.54425 q^{2} -3.31836 q^{3} +0.384710 q^{4} +1.00000 q^{5} +5.12438 q^{6} +3.26635 q^{7} +2.49441 q^{8} +8.01151 q^{9} +O(q^{10})$	\(q-1.54425 q^{2} -3.31836 q^{3} +0.384710 q^{4} +1.00000 q^{5} +5.12438 q^{6} +3.26635 q^{7} +2.49441 q^{8} +8.01151 q^{9} -1.54425 q^{10} -3.42076 q^{11} -1.27661 q^{12} +6.51202 q^{13} -5.04407 q^{14} -3.31836 q^{15} -4.62142 q^{16} +1.00000 q^{17} -12.3718 q^{18} -3.50455 q^{19} +0.384710 q^{20} -10.8389 q^{21} +5.28251 q^{22} -3.37124 q^{23} -8.27736 q^{24} +1.00000 q^{25} -10.0562 q^{26} -16.6300 q^{27} +1.25660 q^{28} +5.37824 q^{29} +5.12438 q^{30} +9.46196 q^{31} +2.14780 q^{32} +11.3513 q^{33} -1.54425 q^{34} +3.26635 q^{35} +3.08211 q^{36} +5.39032 q^{37} +5.41191 q^{38} -21.6092 q^{39} +2.49441 q^{40} +5.02953 q^{41} +16.7380 q^{42} +12.6059 q^{43} -1.31600 q^{44} +8.01151 q^{45} +5.20603 q^{46} -8.02063 q^{47} +15.3355 q^{48} +3.66906 q^{49} -1.54425 q^{50} -3.31836 q^{51} +2.50524 q^{52} -10.1160 q^{53} +25.6809 q^{54} -3.42076 q^{55} +8.14763 q^{56} +11.6294 q^{57} -8.30535 q^{58} +5.52554 q^{59} -1.27661 q^{60} +8.89566 q^{61} -14.6116 q^{62} +26.1684 q^{63} +5.92609 q^{64} +6.51202 q^{65} -17.5293 q^{66} +10.0921 q^{67} +0.384710 q^{68} +11.1870 q^{69} -5.04407 q^{70} +1.00000 q^{71} +19.9840 q^{72} -6.42130 q^{73} -8.32400 q^{74} -3.31836 q^{75} -1.34824 q^{76} -11.1734 q^{77} +33.3701 q^{78} +4.70849 q^{79} -4.62142 q^{80} +31.1498 q^{81} -7.76685 q^{82} +1.12223 q^{83} -4.16984 q^{84} +1.00000 q^{85} -19.4666 q^{86} -17.8469 q^{87} -8.53279 q^{88} +7.41500 q^{89} -12.3718 q^{90} +21.2705 q^{91} -1.29695 q^{92} -31.3982 q^{93} +12.3859 q^{94} -3.50455 q^{95} -7.12718 q^{96} +4.21981 q^{97} -5.66594 q^{98} -27.4055 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9}+O(q^{10}) $ 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9	\( 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9} + q^{10} + 28 q^{11} + 18 q^{12} + 37 q^{13} + 28 q^{14} + 6 q^{15} + 83 q^{16} + 58 q^{17} - 12 q^{18} + 19 q^{19} + 69 q^{20} + 31 q^{21} + 13 q^{22} + 14 q^{23} + 13 q^{24} + 58 q^{25} + 18 q^{26} + 9 q^{27} + 8 q^{28} + 60 q^{29} + 10 q^{30} + 39 q^{31} - 30 q^{32} + 13 q^{33} + q^{34} + 13 q^{35} + 113 q^{36} + 60 q^{37} - q^{38} + 41 q^{39} - 3 q^{40} + 65 q^{41} - 30 q^{42} + 17 q^{43} + 69 q^{44} + 84 q^{45} + 24 q^{46} + 16 q^{47} + 14 q^{48} + 117 q^{49} + q^{50} + 6 q^{51} + 61 q^{52} + 5 q^{53} + 24 q^{54} + 28 q^{55} + 105 q^{56} + 8 q^{57} - 34 q^{58} + 22 q^{59} + 18 q^{60} + 113 q^{61} - 19 q^{62} + 8 q^{63} + 89 q^{64} + 37 q^{65} - 37 q^{66} + 19 q^{67} + 69 q^{68} + 75 q^{69} + 28 q^{70} + 58 q^{71} - 17 q^{72} + 49 q^{73} + 29 q^{74} + 6 q^{75} - 6 q^{76} + 17 q^{77} - 12 q^{78} + 7 q^{79} + 83 q^{80} + 134 q^{81} + 7 q^{82} - 12 q^{83} - 18 q^{84} + 58 q^{85} + 23 q^{86} - 36 q^{87} - 33 q^{88} + 52 q^{89} - 12 q^{90} + 31 q^{91} + 80 q^{92} - 37 q^{93} + 4 q^{94} + 19 q^{95} - 35 q^{96} + 26 q^{97} - 33 q^{98} + 57 q^{99}+O(q^{100}) \) 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9 + q^10 + 28 * q^11 + 18 * q^12 + 37 * q^13 + 28 * q^14 + 6 * q^15 + 83 * q^16 + 58 * q^17 - 12 * q^18 + 19 * q^19 + 69 * q^20 + 31 * q^21 + 13 * q^22 + 14 * q^23 + 13 * q^24 + 58 * q^25 + 18 * q^26 + 9 * q^27 + 8 * q^28 + 60 * q^29 + 10 * q^30 + 39 * q^31 - 30 * q^32 + 13 * q^33 + q^34 + 13 * q^35 + 113 * q^36 + 60 * q^37 - q^38 + 41 * q^39 - 3 * q^40 + 65 * q^41 - 30 * q^42 + 17 * q^43 + 69 * q^44 + 84 * q^45 + 24 * q^46 + 16 * q^47 + 14 * q^48 + 117 * q^49 + q^50 + 6 * q^51 + 61 * q^52 + 5 * q^53 + 24 * q^54 + 28 * q^55 + 105 * q^56 + 8 * q^57 - 34 * q^58 + 22 * q^59 + 18 * q^60 + 113 * q^61 - 19 * q^62 + 8 * q^63 + 89 * q^64 + 37 * q^65 - 37 * q^66 + 19 * q^67 + 69 * q^68 + 75 * q^69 + 28 * q^70 + 58 * q^71 - 17 * q^72 + 49 * q^73 + 29 * q^74 + 6 * q^75 - 6 * q^76 + 17 * q^77 - 12 * q^78 + 7 * q^79 + 83 * q^80 + 134 * q^81 + 7 * q^82 - 12 * q^83 - 18 * q^84 + 58 * q^85 + 23 * q^86 - 36 * q^87 - 33 * q^88 + 52 * q^89 - 12 * q^90 + 31 * q^91 + 80 * q^92 - 37 * q^93 + 4 * q^94 + 19 * q^95 - 35 * q^96 + 26 * q^97 - 33 * q^98 + 57 * 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 $

$2$	−1.54425	−1.09195	−0.545975	−	0.837801i	$-0.683841\pi$
$2$	−1.54425	−1.09195	−0.545975	+	0.837801i	$0.683841\pi$
$3$	−3.31836	−1.91586	−0.957928	−	0.287009i	$-0.907339\pi$
$3$	−3.31836	−1.91586	−0.957928	+	0.287009i	$0.907339\pi$
$4$	0.384710	0.192355
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	5.12438	2.09202
$7$	3.26635	1.23457	0.617283	−	0.786742i	$-0.288234\pi$
$7$	3.26635	1.23457	0.617283	+	0.786742i	$0.288234\pi$
$8$	2.49441	0.881908
$9$	8.01151	2.67050
$10$	−1.54425	−0.488335
$11$	−3.42076	−1.03140	−0.515699	−	0.856770i	$-0.672468\pi$
$11$	−3.42076	−1.03140	−0.515699	+	0.856770i	$0.672468\pi$
$12$	−1.27661	−0.368524
$13$	6.51202	1.80611	0.903055	−	0.429526i	$-0.141319\pi$
$13$	6.51202	1.80611	0.903055	+	0.429526i	$0.141319\pi$
$14$	−5.04407	−1.34808
$15$	−3.31836	−0.856797
$16$	−4.62142	−1.15535
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−12.3718	−2.91606
$19$	−3.50455	−0.804000	−0.402000	−	0.915640i	$-0.631685\pi$
$19$	−3.50455	−0.804000	−0.402000	+	0.915640i	$0.631685\pi$
$20$	0.384710	0.0860237
$21$	−10.8389	−2.36525
$22$	5.28251	1.12624
$23$	−3.37124	−0.702952	−0.351476	−	0.936197i	$-0.614320\pi$
$23$	−3.37124	−0.702952	−0.351476	+	0.936197i	$0.614320\pi$
$24$	−8.27736	−1.68961
$25$	1.00000	0.200000
$26$	−10.0562	−1.97218
$27$	−16.6300	−3.20044
$28$	1.25660	0.237475
$29$	5.37824	0.998714	0.499357	−	0.866396i	$-0.333570\pi$
$29$	5.37824	0.998714	0.499357	+	0.866396i	$0.333570\pi$
$30$	5.12438	0.935579
$31$	9.46196	1.69942	0.849709	−	0.527252i	$-0.176778\pi$
$31$	9.46196	1.69942	0.849709	+	0.527252i	$0.176778\pi$
$32$	2.14780	0.379681
$33$	11.3513	1.97601
$34$	−1.54425	−0.264837
$35$	3.26635	0.552114
$36$	3.08211	0.513684
$37$	5.39032	0.886162	0.443081	−	0.896481i	$-0.353885\pi$
$37$	5.39032	0.886162	0.443081	+	0.896481i	$0.353885\pi$
$38$	5.41191	0.877927
$39$	−21.6092	−3.46025
$40$	2.49441	0.394401
$41$	5.02953	0.785480	0.392740	−	0.919650i	$-0.371527\pi$
$41$	5.02953	0.785480	0.392740	+	0.919650i	$0.371527\pi$
$42$	16.7380	2.58273
$43$	12.6059	1.92238	0.961188	−	0.275895i	$-0.0889741\pi$
$43$	12.6059	1.92238	0.961188	+	0.275895i	$0.0889741\pi$
$44$	−1.31600	−0.198395
$45$	8.01151	1.19429
$46$	5.20603	0.767588
$47$	−8.02063	−1.16993	−0.584965	−	0.811059i	$-0.698892\pi$
$47$	−8.02063	−1.16993	−0.584965	+	0.811059i	$0.698892\pi$
$48$	15.3355	2.21349
$49$	3.66906	0.524151
$50$	−1.54425	−0.218390
$51$	−3.31836	−0.464663
$52$	2.50524	0.347414
$53$	−10.1160	−1.38954	−0.694772	−	0.719230i	$-0.744495\pi$
$53$	−10.1160	−1.38954	−0.694772	+	0.719230i	$0.744495\pi$
$54$	25.6809	3.49473
$55$	−3.42076	−0.461256
$56$	8.14763	1.08877
$57$	11.6294	1.54035
$58$	−8.30535	−1.09055
$59$	5.52554	0.719364	0.359682	−	0.933075i	$-0.382885\pi$
$59$	5.52554	0.719364	0.359682	+	0.933075i	$0.382885\pi$
$60$	−1.27661	−0.164809
$61$	8.89566	1.13897	0.569486	−	0.822001i	$-0.307142\pi$
$61$	8.89566	1.13897	0.569486	+	0.822001i	$0.307142\pi$
$62$	−14.6116	−1.85568
$63$	26.1684	3.29691
$64$	5.92609	0.740762
$65$	6.51202	0.807717
$66$	−17.5293	−2.15771
$67$	10.0921	1.23294	0.616471	−	0.787377i	$-0.288562\pi$
$67$	10.0921	1.23294	0.616471	+	0.787377i	$0.288562\pi$
$68$	0.384710	0.0466529
$69$	11.1870	1.34675
$70$	−5.04407	−0.602881
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	19.9840	2.35514
$73$	−6.42130	−0.751556	−0.375778	−	0.926710i	$-0.622625\pi$
$73$	−6.42130	−0.751556	−0.375778	+	0.926710i	$0.622625\pi$
$74$	−8.32400	−0.967645
$75$	−3.31836	−0.383171
$76$	−1.34824	−0.154653
$77$	−11.1734	−1.27333
$78$	33.3701	3.77841
$79$	4.70849	0.529747	0.264873	−	0.964283i	$-0.414670\pi$
$79$	4.70849	0.529747	0.264873	+	0.964283i	$0.414670\pi$
$80$	−4.62142	−0.516690
$81$	31.1498	3.46109
$82$	−7.76685	−0.857705
$83$	1.12223	0.123180	0.0615902	−	0.998102i	$-0.480383\pi$
$83$	1.12223	0.123180	0.0615902	+	0.998102i	$0.480383\pi$
$84$	−4.16984	−0.454967
$85$	1.00000	0.108465
$86$	−19.4666	−2.09914
$87$	−17.8469	−1.91339
$88$	−8.53279	−0.909599
$89$	7.41500	0.785988	0.392994	−	0.919541i	$-0.371439\pi$
$89$	7.41500	0.785988	0.392994	+	0.919541i	$0.371439\pi$
$90$	−12.3718	−1.30410
$91$	21.2705	2.22976
$92$	−1.29695	−0.135216
$93$	−31.3982	−3.25584
$94$	12.3859	1.27750
$95$	−3.50455	−0.359560
$96$	−7.12718	−0.727415
$97$	4.21981	0.428456	0.214228	−	0.976784i	$-0.431276\pi$
$97$	4.21981	0.428456	0.214228	+	0.976784i	$0.431276\pi$
$98$	−5.66594	−0.572347
$99$	−27.4055	−2.75435
$100$	0.384710	0.0384710
$101$	12.0196	1.19599	0.597995	−	0.801500i	$-0.295964\pi$
$101$	12.0196	1.19599	0.597995	+	0.801500i	$0.295964\pi$
$102$	5.12438	0.507389
$103$	−16.3569	−1.61169	−0.805844	−	0.592127i	$-0.798288\pi$
$103$	−16.3569	−1.61169	−0.805844	+	0.592127i	$0.798288\pi$
$104$	16.2437	1.59282
$105$	−10.8389	−1.05777
$106$	15.6217	1.51731
$107$	10.3167	0.997358	0.498679	−	0.866787i	$-0.333819\pi$
$107$	10.3167	0.997358	0.498679	+	0.866787i	$0.333819\pi$
$108$	−6.39772	−0.615621
$109$	−2.73406	−0.261876	−0.130938	−	0.991391i	$-0.541799\pi$
$109$	−2.73406	−0.261876	−0.130938	+	0.991391i	$0.541799\pi$
$110$	5.28251	0.503668
$111$	−17.8870	−1.69776
$112$	−15.0952	−1.42636
$113$	17.1733	1.61553	0.807765	−	0.589504i	$-0.200677\pi$
$113$	17.1733	1.61553	0.807765	+	0.589504i	$0.200677\pi$
$114$	−17.9587	−1.68198
$115$	−3.37124	−0.314369
$116$	2.06906	0.192108
$117$	52.1711	4.82322
$118$	−8.53282	−0.785510
$119$	3.26635	0.299426
$120$	−8.27736	−0.755616
$121$	0.701616	0.0637832
$122$	−13.7371	−1.24370
$123$	−16.6898	−1.50487
$124$	3.64011	0.326891
$125$	1.00000	0.0894427
$126$	−40.4106	−3.60006
$127$	6.46119	0.573338	0.286669	−	0.958030i	$-0.407452\pi$
$127$	6.46119	0.573338	0.286669	+	0.958030i	$0.407452\pi$
$128$	−13.4470	−1.18856
$129$	−41.8308	−3.68299
$130$	−10.0562	−0.881986
$131$	−2.38860	−0.208693	−0.104347	−	0.994541i	$-0.533275\pi$
$131$	−2.38860	−0.208693	−0.104347	+	0.994541i	$0.533275\pi$
$132$	4.36696	0.380095
$133$	−11.4471	−0.992590
$134$	−15.5847	−1.34631
$135$	−16.6300	−1.43128
$136$	2.49441	0.213894
$137$	−20.5307	−1.75405	−0.877027	−	0.480442i	$-0.840476\pi$
$137$	−20.5307	−1.75405	−0.877027	+	0.480442i	$0.840476\pi$
$138$	−17.2755	−1.47059
$139$	−11.4416	−0.970465	−0.485232	−	0.874385i	$-0.661265\pi$
$139$	−11.4416	−0.970465	−0.485232	+	0.874385i	$0.661265\pi$
$140$	1.25660	0.106202
$141$	26.6153	2.24142
$142$	−1.54425	−0.129591
$143$	−22.2761	−1.86282
$144$	−37.0245	−3.08538
$145$	5.37824	0.446638
$146$	9.91610	0.820662
$147$	−12.1752	−1.00420
$148$	2.07371	0.170458
$149$	−9.52949	−0.780686	−0.390343	−	0.920669i	$-0.627644\pi$
$149$	−9.52949	−0.780686	−0.390343	+	0.920669i	$0.627644\pi$
$150$	5.12438	0.418404
$151$	−3.68368	−0.299774	−0.149887	−	0.988703i	$-0.547891\pi$
$151$	−3.68368	−0.299774	−0.149887	+	0.988703i	$0.547891\pi$
$152$	−8.74180	−0.709054
$153$	8.01151	0.647692
$154$	17.2546	1.39041
$155$	9.46196	0.760003
$156$	−8.31328	−0.665595
$157$	22.7547	1.81602	0.908012	−	0.418944i	$-0.137600\pi$
$157$	22.7547	1.81602	0.908012	+	0.418944i	$0.137600\pi$
$158$	−7.27109	−0.578457
$159$	33.5686	2.66217
$160$	2.14780	0.169799
$161$	−11.0116	−0.867839
$162$	−48.1031	−3.77933
$163$	−23.3962	−1.83253	−0.916265	−	0.400573i	$-0.868811\pi$
$163$	−23.3962	−1.83253	−0.916265	+	0.400573i	$0.868811\pi$
$164$	1.93491	0.151091
$165$	11.3513	0.883699
$166$	−1.73300	−0.134507
$167$	−11.7441	−0.908785	−0.454392	−	0.890802i	$-0.650144\pi$
$167$	−11.7441	−0.908785	−0.454392	+	0.890802i	$0.650144\pi$
$168$	−27.0368	−2.08593
$169$	29.4064	2.26203
$170$	−1.54425	−0.118439
$171$	−28.0768	−2.14708
$172$	4.84960	0.369778
$173$	−0.385370	−0.0292992	−0.0146496	−	0.999893i	$-0.504663\pi$
$173$	−0.385370	−0.0292992	−0.0146496	+	0.999893i	$0.504663\pi$
$174$	27.5601	2.08933
$175$	3.26635	0.246913
$176$	15.8088	1.19163
$177$	−18.3357	−1.37820
$178$	−11.4506	−0.858260
$179$	4.05912	0.303393	0.151697	−	0.988427i	$-0.451526\pi$
$179$	4.05912	0.303393	0.151697	+	0.988427i	$0.451526\pi$
$180$	3.08211	0.229727
$181$	−6.34903	−0.471919	−0.235960	−	0.971763i	$-0.575823\pi$
$181$	−6.34903	−0.471919	−0.235960	+	0.971763i	$0.575823\pi$
$182$	−32.8471	−2.43479
$183$	−29.5190	−2.18211
$184$	−8.40926	−0.619939
$185$	5.39032	0.396304
$186$	48.4866	3.55521
$187$	−3.42076	−0.250151
$188$	−3.08562	−0.225042
$189$	−54.3194	−3.95116
$190$	5.41191	0.392621
$191$	−10.6445	−0.770206	−0.385103	−	0.922874i	$-0.625834\pi$
$191$	−10.6445	−0.770206	−0.385103	+	0.922874i	$0.625834\pi$
$192$	−19.6649	−1.41919
$193$	−11.1890	−0.805404	−0.402702	−	0.915331i	$-0.631929\pi$
$193$	−11.1890	−0.805404	−0.402702	+	0.915331i	$0.631929\pi$
$194$	−6.51644	−0.467853
$195$	−21.6092	−1.54747
$196$	1.41152	0.100823
$197$	4.32951	0.308465	0.154233	−	0.988035i	$-0.450710\pi$
$197$	4.32951	0.308465	0.154233	+	0.988035i	$0.450710\pi$
$198$	42.3209	3.00762
$199$	14.9922	1.06277	0.531386	−	0.847130i	$-0.321671\pi$
$199$	14.9922	1.06277	0.531386	+	0.847130i	$0.321671\pi$
$200$	2.49441	0.176382
$201$	−33.4891	−2.36214
$202$	−18.5612	−1.30596
$203$	17.5672	1.23298
$204$	−1.27661	−0.0893803
$205$	5.02953	0.351277
$206$	25.2591	1.75988
$207$	−27.0087	−1.87723
$208$	−30.0948	−2.08670
$209$	11.9882	0.829244
$210$	16.7380	1.15503
$211$	20.1606	1.38792	0.693958	−	0.720016i	$-0.255865\pi$
$211$	20.1606	1.38792	0.693958	+	0.720016i	$0.255865\pi$
$212$	−3.89174	−0.267286
$213$	−3.31836	−0.227370
$214$	−15.9316	−1.08906
$215$	12.6059	0.859713
$216$	−41.4821	−2.82250
$217$	30.9061	2.09804
$218$	4.22208	0.285955
$219$	21.3082	1.43987
$220$	−1.31600	−0.0887247
$221$	6.51202	0.438046
$222$	27.6220	1.85387
$223$	11.3611	0.760796	0.380398	−	0.924823i	$-0.375787\pi$
$223$	11.3611	0.760796	0.380398	+	0.924823i	$0.375787\pi$
$224$	7.01548	0.468741
$225$	8.01151	0.534101
$226$	−26.5199	−1.76408
$227$	−9.02900	−0.599276	−0.299638	−	0.954053i	$-0.596866\pi$
$227$	−9.02900	−0.599276	−0.299638	+	0.954053i	$0.596866\pi$
$228$	4.47393	0.296293
$229$	21.1973	1.40076	0.700378	−	0.713772i	$-0.253015\pi$
$229$	21.1973	1.40076	0.700378	+	0.713772i	$0.253015\pi$
$230$	5.20603	0.343276
$231$	37.0774	2.43951
$232$	13.4156	0.880774
$233$	−17.3296	−1.13530	−0.567650	−	0.823270i	$-0.692147\pi$
$233$	−17.3296	−1.13530	−0.567650	+	0.823270i	$0.692147\pi$
$234$	−80.5653	−5.26672
$235$	−8.02063	−0.523208
$236$	2.12573	0.138373
$237$	−15.6245	−1.01492
$238$	−5.04407	−0.326958
$239$	2.80198	0.181245	0.0906224	−	0.995885i	$-0.471114\pi$
$239$	2.80198	0.181245	0.0906224	+	0.995885i	$0.471114\pi$
$240$	15.3355	0.989904
$241$	4.24195	0.273248	0.136624	−	0.990623i	$-0.456375\pi$
$241$	4.24195	0.273248	0.136624	+	0.990623i	$0.456375\pi$
$242$	−1.08347	−0.0696481
$243$	−53.4762	−3.43050
$244$	3.42225	0.219087
$245$	3.66906	0.234407
$246$	25.7732	1.64324
$247$	−22.8217	−1.45211
$248$	23.6020	1.49873
$249$	−3.72395	−0.235996
$250$	−1.54425	−0.0976670
$251$	−3.81644	−0.240891	−0.120446	−	0.992720i	$-0.538432\pi$
$251$	−3.81644	−0.240891	−0.120446	+	0.992720i	$0.538432\pi$
$252$	10.0672	0.634177
$253$	11.5322	0.725023
$254$	−9.97769	−0.626056
$255$	−3.31836	−0.207804
$256$	8.91331	0.557082
$257$	−13.3544	−0.833027	−0.416513	−	0.909130i	$-0.636748\pi$
$257$	−13.3544	−0.833027	−0.416513	+	0.909130i	$0.636748\pi$
$258$	64.5972	4.02165
$259$	17.6067	1.09403
$260$	2.50524	0.155368
$261$	43.0878	2.66707
$262$	3.68860	0.227883
$263$	9.11662	0.562155	0.281077	−	0.959685i	$-0.409308\pi$
$263$	9.11662	0.562155	0.281077	+	0.959685i	$0.409308\pi$
$264$	28.3149	1.74266
$265$	−10.1160	−0.621423
$266$	17.6772	1.08386
$267$	−24.6056	−1.50584
$268$	3.88252	0.237163
$269$	22.8431	1.39277	0.696383	−	0.717671i	$-0.254792\pi$
$269$	22.8431	1.39277	0.696383	+	0.717671i	$0.254792\pi$
$270$	25.6809	1.56289
$271$	−23.8855	−1.45094	−0.725472	−	0.688252i	$-0.758378\pi$
$271$	−23.8855	−1.45094	−0.725472	+	0.688252i	$0.758378\pi$
$272$	−4.62142	−0.280215
$273$	−70.5833	−4.27190
$274$	31.7045	1.91534
$275$	−3.42076	−0.206280
$276$	4.30374	0.259055
$277$	−3.54895	−0.213235	−0.106618	−	0.994300i	$-0.534002\pi$
$277$	−3.54895	−0.213235	−0.106618	+	0.994300i	$0.534002\pi$
$278$	17.6687	1.05970
$279$	75.8046	4.53830
$280$	8.14763	0.486914
$281$	11.5966	0.691795	0.345898	−	0.938272i	$-0.387574\pi$
$281$	11.5966	0.691795	0.345898	+	0.938272i	$0.387574\pi$
$282$	−41.1008	−2.44751
$283$	29.0387	1.72617	0.863086	−	0.505057i	$-0.168529\pi$
$283$	29.0387	1.72617	0.863086	+	0.505057i	$0.168529\pi$
$284$	0.384710	0.0228283
$285$	11.6294	0.688864
$286$	34.3998	2.03410
$287$	16.4282	0.969726
$288$	17.2071	1.01394
$289$	1.00000	0.0588235
$290$	−8.30535	−0.487707
$291$	−14.0028	−0.820861
$292$	−2.47034	−0.144566
$293$	2.65448	0.155076	0.0775381	−	0.996989i	$-0.475294\pi$
$293$	2.65448	0.155076	0.0775381	+	0.996989i	$0.475294\pi$
$294$	18.8016	1.09653
$295$	5.52554	0.321710
$296$	13.4457	0.781514
$297$	56.8873	3.30093
$298$	14.7159	0.852471
$299$	−21.9536	−1.26961
$300$	−1.27661	−0.0737048
$301$	41.1752	2.37330
$302$	5.68853	0.327338
$303$	−39.8852	−2.29135
$304$	16.1960	0.928904
$305$	8.89566	0.509364
$306$	−12.3718	−0.707248
$307$	−33.1405	−1.89143	−0.945714	−	0.324999i	$-0.894636\pi$
$307$	−33.1405	−1.89143	−0.945714	+	0.324999i	$0.894636\pi$
$308$	−4.29852	−0.244931
$309$	54.2779	3.08776
$310$	−14.6116	−0.829885
$311$	−4.98972	−0.282941	−0.141471	−	0.989942i	$-0.545183\pi$
$311$	−4.98972	−0.282941	−0.141471	+	0.989942i	$0.545183\pi$
$312$	−53.9023	−3.05162
$313$	−13.1010	−0.740513	−0.370257	−	0.928930i	$-0.620730\pi$
$313$	−13.1010	−0.740513	−0.370257	+	0.928930i	$0.620730\pi$
$314$	−35.1390	−1.98301
$315$	26.1684	1.47442
$316$	1.81140	0.101899
$317$	28.2830	1.58853	0.794265	−	0.607572i	$-0.207856\pi$
$317$	28.2830	1.58853	0.794265	+	0.607572i	$0.207856\pi$
$318$	−51.8384	−2.90695
$319$	−18.3977	−1.03007
$320$	5.92609	0.331279
$321$	−34.2347	−1.91079
$322$	17.0047	0.947637
$323$	−3.50455	−0.194999
$324$	11.9836	0.665757
$325$	6.51202	0.361222
$326$	36.1296	2.00103
$327$	9.07260	0.501716
$328$	12.5457	0.692721
$329$	−26.1982	−1.44435
$330$	−17.5293	−0.964955
$331$	−18.6972	−1.02769	−0.513847	−	0.857882i	$-0.671780\pi$
$331$	−18.6972	−1.02769	−0.513847	+	0.857882i	$0.671780\pi$
$332$	0.431731	0.0236943
$333$	43.1846	2.36650
$334$	18.1358	0.992348
$335$	10.0921	0.551389
$336$	50.0912	2.73270
$337$	−15.3191	−0.834483	−0.417241	−	0.908796i	$-0.637003\pi$
$337$	−15.3191	−0.834483	−0.417241	+	0.908796i	$0.637003\pi$
$338$	−45.4108	−2.47002
$339$	−56.9873	−3.09512
$340$	0.384710	0.0208638
$341$	−32.3671	−1.75278
$342$	43.3576	2.34451
$343$	−10.8800	−0.587467
$344$	31.4442	1.69536
$345$	11.1870	0.602287
$346$	0.595108	0.0319932
$347$	26.4135	1.41795	0.708974	−	0.705234i	$-0.249158\pi$
$347$	26.4135	1.41795	0.708974	+	0.705234i	$0.249158\pi$
$348$	−6.86589	−0.368050
$349$	5.89159	0.315369	0.157685	−	0.987490i	$-0.449597\pi$
$349$	5.89159	0.315369	0.157685	+	0.987490i	$0.449597\pi$
$350$	−5.04407	−0.269617
$351$	−108.295	−5.78035
$352$	−7.34712	−0.391603
$353$	−23.6001	−1.25611	−0.628053	−	0.778171i	$-0.716148\pi$
$353$	−23.6001	−1.25611	−0.628053	+	0.778171i	$0.716148\pi$
$354$	28.3150	1.50492
$355$	1.00000	0.0530745
$356$	2.85262	0.151189
$357$	−10.8389	−0.573657
$358$	−6.26830	−0.331290
$359$	19.1327	1.00978	0.504892	−	0.863183i	$-0.331532\pi$
$359$	19.1327	1.00978	0.504892	+	0.863183i	$0.331532\pi$
$360$	19.9840	1.05325
$361$	−6.71811	−0.353585
$362$	9.80449	0.515312
$363$	−2.32821	−0.122199
$364$	8.18299	0.428905
$365$	−6.42130	−0.336106
$366$	45.5847	2.38275
$367$	−4.20362	−0.219427	−0.109714	−	0.993963i	$-0.534993\pi$
$367$	−4.20362	−0.219427	−0.109714	+	0.993963i	$0.534993\pi$
$368$	15.5799	0.812158
$369$	40.2941	2.09763
$370$	−8.32400	−0.432744
$371$	−33.0425	−1.71548
$372$	−12.0792	−0.626277
$373$	−5.74882	−0.297663	−0.148831	−	0.988863i	$-0.547551\pi$
$373$	−5.74882	−0.297663	−0.148831	+	0.988863i	$0.547551\pi$
$374$	5.28251	0.273152
$375$	−3.31836	−0.171359
$376$	−20.0068	−1.03177
$377$	35.0232	1.80379
$378$	83.8828	4.31447
$379$	−21.0490	−1.08122	−0.540608	−	0.841275i	$-0.681806\pi$
$379$	−21.0490	−1.08122	−0.540608	+	0.841275i	$0.681806\pi$
$380$	−1.34824	−0.0691630
$381$	−21.4405	−1.09843
$382$	16.4377	0.841027
$383$	−13.9953	−0.715126	−0.357563	−	0.933889i	$-0.616392\pi$
$383$	−13.9953	−0.715126	−0.357563	+	0.933889i	$0.616392\pi$
$384$	44.6219	2.27710
$385$	−11.1734	−0.569450
$386$	17.2787	0.879461
$387$	100.992	5.13371
$388$	1.62340	0.0824157
$389$	−4.86456	−0.246643	−0.123322	−	0.992367i	$-0.539355\pi$
$389$	−4.86456	−0.246643	−0.123322	+	0.992367i	$0.539355\pi$
$390$	33.3701	1.68976
$391$	−3.37124	−0.170491
$392$	9.15214	0.462253
$393$	7.92624	0.399826
$394$	−6.68585	−0.336828
$395$	4.70849	0.236910
$396$	−10.5432	−0.529813
$397$	−26.9700	−1.35358	−0.676792	−	0.736174i	$-0.736630\pi$
$397$	−26.9700	−1.35358	−0.676792	+	0.736174i	$0.736630\pi$
$398$	−23.1518	−1.16049
$399$	37.9856	1.90166
$400$	−4.62142	−0.231071
$401$	−3.94337	−0.196923	−0.0984613	−	0.995141i	$-0.531392\pi$
$401$	−3.94337	−0.196923	−0.0984613	+	0.995141i	$0.531392\pi$
$402$	51.7156	2.57934
$403$	61.6164	3.06933
$404$	4.62404	0.230055
$405$	31.1498	1.54785
$406$	−27.1282	−1.34635
$407$	−18.4390	−0.913987
$408$	−8.27736	−0.409790
$409$	−3.63362	−0.179671	−0.0898354	−	0.995957i	$-0.528634\pi$
$409$	−3.63362	−0.179671	−0.0898354	+	0.995957i	$0.528634\pi$
$410$	−7.76685	−0.383577
$411$	68.1282	3.36051
$412$	−6.29264	−0.310016
$413$	18.0484	0.888102
$414$	41.7082	2.04985
$415$	1.12223	0.0550879
$416$	13.9865	0.685746
$417$	37.9674	1.85927
$418$	−18.5128	−0.905493
$419$	−18.4019	−0.898994	−0.449497	−	0.893282i	$-0.648397\pi$
$419$	−18.4019	−0.898994	−0.449497	+	0.893282i	$0.648397\pi$
$420$	−4.16984	−0.203467
$421$	6.46463	0.315067	0.157533	−	0.987514i	$-0.449646\pi$
$421$	6.46463	0.315067	0.157533	+	0.987514i	$0.449646\pi$
$422$	−31.1331	−1.51553
$423$	−64.2574	−3.12430
$424$	−25.2336	−1.22545
$425$	1.00000	0.0485071
$426$	5.12438	0.248277
$427$	29.0563	1.40613
$428$	3.96895	0.191847
$429$	73.9200	3.56889
$430$	−19.4666	−0.938763
$431$	−30.4452	−1.46650	−0.733248	−	0.679961i	$-0.761996\pi$
$431$	−30.4452	−1.46650	−0.733248	+	0.679961i	$0.761996\pi$
$432$	76.8542	3.69765
$433$	−6.39954	−0.307542	−0.153771	−	0.988106i	$-0.549142\pi$
$433$	−6.39954	−0.307542	−0.153771	+	0.988106i	$0.549142\pi$
$434$	−47.7267	−2.29096
$435$	−17.8469	−0.855695
$436$	−1.05182	−0.0503731
$437$	11.8147	0.565173
$438$	−32.9052	−1.57227
$439$	23.5806	1.12544	0.562720	−	0.826648i	$-0.309755\pi$
$439$	23.5806	1.12544	0.562720	+	0.826648i	$0.309755\pi$
$440$	−8.53279	−0.406785
$441$	29.3947	1.39975
$442$	−10.0562	−0.478324
$443$	−14.0156	−0.665899	−0.332950	−	0.942945i	$-0.608044\pi$
$443$	−14.0156	−0.665899	−0.332950	+	0.942945i	$0.608044\pi$
$444$	−6.88131	−0.326572
$445$	7.41500	0.351505
$446$	−17.5444	−0.830752
$447$	31.6223	1.49568
$448$	19.3567	0.914518
$449$	0.269512	0.0127191	0.00635954	−	0.999980i	$-0.497976\pi$
$449$	0.269512	0.0127191	0.00635954	+	0.999980i	$0.497976\pi$
$450$	−12.3718	−0.583211
$451$	−17.2048	−0.810143
$452$	6.60675	0.310755
$453$	12.2238	0.574323
$454$	13.9430	0.654379
$455$	21.2705	0.997179
$456$	29.0084	1.35844
$457$	−29.8005	−1.39401	−0.697005	−	0.717066i	$-0.745484\pi$
$457$	−29.8005	−1.39401	−0.697005	+	0.717066i	$0.745484\pi$
$458$	−32.7339	−1.52956
$459$	−16.6300	−0.776222
$460$	−1.29695	−0.0604705
$461$	−6.27694	−0.292346	−0.146173	−	0.989259i	$-0.546696\pi$
$461$	−6.27694	−0.292346	−0.146173	+	0.989259i	$0.546696\pi$
$462$	−57.2568	−2.66383
$463$	−17.2870	−0.803394	−0.401697	−	0.915773i	$-0.631580\pi$
$463$	−17.2870	−0.803394	−0.401697	+	0.915773i	$0.631580\pi$
$464$	−24.8551	−1.15387
$465$	−31.3982	−1.45606
$466$	26.7613	1.23969
$467$	−26.1636	−1.21071	−0.605353	−	0.795957i	$-0.706968\pi$
$467$	−26.1636	−1.21071	−0.605353	+	0.795957i	$0.706968\pi$
$468$	20.0707	0.927770
$469$	32.9643	1.52215
$470$	12.3859	0.571317
$471$	−75.5083	−3.47924
$472$	13.7830	0.634413
$473$	−43.1217	−1.98274
$474$	24.1281	1.10824
$475$	−3.50455	−0.160800
$476$	1.25660	0.0575961
$477$	−81.0447	−3.71078
$478$	−4.32695	−0.197910
$479$	30.3901	1.38856	0.694280	−	0.719705i	$-0.255723\pi$
$479$	30.3901	1.38856	0.694280	+	0.719705i	$0.255723\pi$
$480$	−7.12718	−0.325310
$481$	35.1018	1.60051
$482$	−6.55063	−0.298373
$483$	36.5406	1.66266
$484$	0.269918	0.0122690
$485$	4.21981	0.191611
$486$	82.5806	3.74593
$487$	30.8042	1.39587	0.697936	−	0.716160i	$-0.254102\pi$
$487$	30.8042	1.39587	0.697936	+	0.716160i	$0.254102\pi$
$488$	22.1894	1.00447
$489$	77.6369	3.51086
$490$	−5.66594	−0.255961
$491$	6.67804	0.301376	0.150688	−	0.988581i	$-0.451851\pi$
$491$	6.67804	0.301376	0.150688	+	0.988581i	$0.451851\pi$
$492$	−6.42072	−0.289468
$493$	5.37824	0.242224
$494$	35.2424	1.58563
$495$	−27.4055	−1.23178
$496$	−43.7277	−1.96343
$497$	3.26635	0.146516
$498$	5.75071	0.257696
$499$	40.7530	1.82435	0.912177	−	0.409795i	$-0.134400\pi$
$499$	40.7530	1.82435	0.912177	+	0.409795i	$0.134400\pi$
$500$	0.384710	0.0172047
$501$	38.9711	1.74110
$502$	5.89354	0.263041
$503$	36.3871	1.62242	0.811209	−	0.584756i	$-0.198810\pi$
$503$	36.3871	1.62242	0.811209	+	0.584756i	$0.198810\pi$
$504$	65.2748	2.90757
$505$	12.0196	0.534863
$506$	−17.8086	−0.791689
$507$	−97.5810	−4.33372
$508$	2.48568	0.110284
$509$	−32.1243	−1.42388	−0.711941	−	0.702239i	$-0.752184\pi$
$509$	−32.1243	−1.42388	−0.711941	+	0.702239i	$0.752184\pi$
$510$	5.12438	0.226911
$511$	−20.9742	−0.927845
$512$	13.1296	0.580250
$513$	58.2807	2.57316
$514$	20.6226	0.909623
$515$	−16.3569	−0.720769
$516$	−16.0927	−0.708442
$517$	27.4367	1.20666
$518$	−27.1891	−1.19462
$519$	1.27880	0.0561330
$520$	16.2437	0.712332
$521$	5.58368	0.244626	0.122313	−	0.992492i	$-0.460969\pi$
$521$	5.58368	0.244626	0.122313	+	0.992492i	$0.460969\pi$
$522$	−66.5384	−2.91231
$523$	−20.6588	−0.903347	−0.451673	−	0.892183i	$-0.649173\pi$
$523$	−20.6588	−0.903347	−0.451673	+	0.892183i	$0.649173\pi$
$524$	−0.918919	−0.0401432
$525$	−10.8389	−0.473050
$526$	−14.0783	−0.613845
$527$	9.46196	0.412169
$528$	−52.4592	−2.28299
$529$	−11.6348	−0.505859
$530$	15.6217	0.678563
$531$	44.2679	1.92107
$532$	−4.40381	−0.190929
$533$	32.7524	1.41866
$534$	37.9973	1.64430
$535$	10.3167	0.446032
$536$	25.1738	1.08734
$537$	−13.4696	−0.581258
$538$	−35.2754	−1.52083
$539$	−12.5510	−0.540608
$540$	−6.39772	−0.275314
$541$	16.8329	0.723703	0.361851	−	0.932236i	$-0.382145\pi$
$541$	16.8329	0.723703	0.361851	+	0.932236i	$0.382145\pi$
$542$	36.8853	1.58436
$543$	21.0684	0.904130
$544$	2.14780	0.0920862
$545$	−2.73406	−0.117114
$546$	108.998	4.66470
$547$	18.4265	0.787861	0.393931	−	0.919140i	$-0.371115\pi$
$547$	18.4265	0.787861	0.393931	+	0.919140i	$0.371115\pi$
$548$	−7.89835	−0.337401
$549$	71.2676	3.04163
$550$	5.28251	0.225247
$551$	−18.8483	−0.802966
$552$	27.9049	1.18771
$553$	15.3796	0.654007
$554$	5.48046	0.232842
$555$	−17.8870	−0.759261
$556$	−4.40170	−0.186674
$557$	−0.856868	−0.0363067	−0.0181533	−	0.999835i	$-0.505779\pi$
$557$	−0.856868	−0.0363067	−0.0181533	+	0.999835i	$0.505779\pi$
$558$	−117.061	−4.95560
$559$	82.0896	3.47202
$560$	−15.0952	−0.637888
$561$	11.3513	0.479253
$562$	−17.9081	−0.755406
$563$	−20.3650	−0.858284	−0.429142	−	0.903237i	$-0.641184\pi$
$563$	−20.3650	−0.858284	−0.429142	+	0.903237i	$0.641184\pi$
$564$	10.2392	0.431147
$565$	17.1733	0.722487
$566$	−44.8430	−1.88489
$567$	101.746	4.27294
$568$	2.49441	0.104663
$569$	5.17237	0.216837	0.108418	−	0.994105i	$-0.465421\pi$
$569$	5.17237	0.216837	0.108418	+	0.994105i	$0.465421\pi$
$570$	−17.9587	−0.752205
$571$	−18.6385	−0.779998	−0.389999	−	0.920815i	$-0.627525\pi$
$571$	−18.6385	−0.779998	−0.389999	+	0.920815i	$0.627525\pi$
$572$	−8.56982	−0.358322
$573$	35.3222	1.47560
$574$	−25.3693	−1.05889
$575$	−3.37124	−0.140590
$576$	47.4770	1.97821
$577$	−23.4529	−0.976359	−0.488179	−	0.872743i	$-0.662339\pi$
$577$	−23.4529	−0.976359	−0.488179	+	0.872743i	$0.662339\pi$
$578$	−1.54425	−0.0642324
$579$	37.1292	1.54304
$580$	2.06906	0.0859131
$581$	3.66559	0.152074
$582$	21.6239	0.896339
$583$	34.6046	1.43317
$584$	−16.0174	−0.662804
$585$	52.1711	2.15701
$586$	−4.09918	−0.169335
$587$	27.8125	1.14794	0.573972	−	0.818875i	$-0.305402\pi$
$587$	27.8125	1.14794	0.573972	+	0.818875i	$0.305402\pi$
$588$	−4.68394	−0.193162
$589$	−33.1599	−1.36633
$590$	−8.53282	−0.351291
$591$	−14.3669	−0.590975
$592$	−24.9109	−1.02383
$593$	12.7234	0.522486	0.261243	−	0.965273i	$-0.415868\pi$
$593$	12.7234	0.522486	0.261243	+	0.965273i	$0.415868\pi$
$594$	−87.8482	−3.60446
$595$	3.26635	0.133907
$596$	−3.66609	−0.150169
$597$	−49.7497	−2.03612
$598$	33.9018	1.38635
$599$	−24.5620	−1.00357	−0.501787	−	0.864991i	$-0.667324\pi$
$599$	−24.5620	−1.00357	−0.501787	+	0.864991i	$0.667324\pi$
$600$	−8.27736	−0.337922
$601$	31.0287	1.26569	0.632843	−	0.774280i	$-0.281888\pi$
$601$	31.0287	1.26569	0.632843	+	0.774280i	$0.281888\pi$
$602$	−63.5848	−2.59152
$603$	80.8527	3.29258
$604$	−1.41715	−0.0576629
$605$	0.701616	0.0285247
$606$	61.5928	2.50203
$607$	42.2859	1.71633	0.858166	−	0.513373i	$-0.171604\pi$
$607$	42.2859	1.71633	0.858166	+	0.513373i	$0.171604\pi$
$608$	−7.52708	−0.305264
$609$	−58.2944	−2.36221
$610$	−13.7371	−0.556200
$611$	−52.2305	−2.11302
$612$	3.08211	0.124587
$613$	−2.62975	−0.106215	−0.0531073	−	0.998589i	$-0.516913\pi$
$613$	−2.62975	−0.106215	−0.0531073	+	0.998589i	$0.516913\pi$
$614$	51.1772	2.06535
$615$	−16.6898	−0.672997
$616$	−27.8711	−1.12296
$617$	−38.5997	−1.55397	−0.776983	−	0.629522i	$-0.783251\pi$
$617$	−38.5997	−1.55397	−0.776983	+	0.629522i	$0.783251\pi$
$618$	−83.8187	−3.37168
$619$	16.3318	0.656430	0.328215	−	0.944603i	$-0.393553\pi$
$619$	16.3318	0.656430	0.328215	+	0.944603i	$0.393553\pi$
$620$	3.64011	0.146190
$621$	56.0637	2.24976
$622$	7.70538	0.308958
$623$	24.2200	0.970353
$624$	99.8653	3.99781
$625$	1.00000	0.0400000
$626$	20.2313	0.808604
$627$	−39.7813	−1.58871
$628$	8.75396	0.349321
$629$	5.39032	0.214926
$630$	−40.4106	−1.61000
$631$	46.5146	1.85172	0.925858	−	0.377871i	$-0.123344\pi$
$631$	46.5146	1.85172	0.925858	+	0.377871i	$0.123344\pi$
$632$	11.7449	0.467188
$633$	−66.9002	−2.65905
$634$	−43.6760	−1.73459
$635$	6.46119	0.256404
$636$	12.9142	0.512081
$637$	23.8930	0.946674
$638$	28.4106	1.12479
$639$	8.01151	0.316931
$640$	−13.4470	−0.531538
$641$	−11.5799	−0.457380	−0.228690	−	0.973499i	$-0.573444\pi$
$641$	−11.5799	−0.457380	−0.228690	+	0.973499i	$0.573444\pi$
$642$	52.8669	2.08649
$643$	−11.3292	−0.446778	−0.223389	−	0.974729i	$-0.571712\pi$
$643$	−11.3292	−0.446778	−0.223389	+	0.974729i	$0.571712\pi$
$644$	−4.23629	−0.166933
$645$	−41.8308	−1.64709
$646$	5.41191	0.212929
$647$	−18.6603	−0.733613	−0.366806	−	0.930297i	$-0.619549\pi$
$647$	−18.6603	−0.733613	−0.366806	+	0.930297i	$0.619549\pi$
$648$	77.7004	3.05236
$649$	−18.9016	−0.741951
$650$	−10.0562	−0.394436
$651$	−102.557	−4.01955
$652$	−9.00074	−0.352496
$653$	48.0477	1.88025	0.940126	−	0.340828i	$-0.110708\pi$
$653$	48.0477	1.88025	0.940126	+	0.340828i	$0.110708\pi$
$654$	−14.0104	−0.547849
$655$	−2.38860	−0.0933304
$656$	−23.2435	−0.907508
$657$	−51.4443	−2.00703
$658$	40.4566	1.57716
$659$	8.64355	0.336705	0.168352	−	0.985727i	$-0.446155\pi$
$659$	8.64355	0.336705	0.168352	+	0.985727i	$0.446155\pi$
$660$	4.36696	0.169984
$661$	2.63917	0.102652	0.0513260	−	0.998682i	$-0.483655\pi$
$661$	2.63917	0.102652	0.0513260	+	0.998682i	$0.483655\pi$
$662$	28.8732	1.12219
$663$	−21.6092	−0.839233
$664$	2.79930	0.108634
$665$	−11.4471	−0.443900
$666$	−66.6878	−2.58410
$667$	−18.1313	−0.702048
$668$	−4.51807	−0.174809
$669$	−37.7003	−1.45758
$670$	−15.5847	−0.602089
$671$	−30.4299	−1.17473
$672$	−23.2799	−0.898041
$673$	−48.0874	−1.85363	−0.926816	−	0.375515i	$-0.877466\pi$
$673$	−48.0874	−1.85363	−0.926816	+	0.375515i	$0.877466\pi$
$674$	23.6565	0.911213
$675$	−16.6300	−0.640089
$676$	11.3129	0.435113
$677$	35.4812	1.36365	0.681827	−	0.731514i	$-0.261186\pi$
$677$	35.4812	1.36365	0.681827	+	0.731514i	$0.261186\pi$
$678$	88.0026	3.37972
$679$	13.7834	0.528957
$680$	2.49441	0.0956564
$681$	29.9615	1.14813
$682$	49.9829	1.91394
$683$	15.8927	0.608118	0.304059	−	0.952653i	$-0.401658\pi$
$683$	15.8927	0.608118	0.304059	+	0.952653i	$0.401658\pi$
$684$	−10.8014	−0.413002
$685$	−20.5307	−0.784437
$686$	16.8015	0.641484
$687$	−70.3402	−2.68365
$688$	−58.2569	−2.22103
$689$	−65.8758	−2.50967
$690$	−17.2755	−0.657667
$691$	−15.2598	−0.580510	−0.290255	−	0.956949i	$-0.593740\pi$
$691$	−15.2598	−0.580510	−0.290255	+	0.956949i	$0.593740\pi$
$692$	−0.148256	−0.00563584
$693$	−89.5159	−3.40043
$694$	−40.7890	−1.54833
$695$	−11.4416	−0.434005
$696$	−44.5176	−1.68744
$697$	5.02953	0.190507
$698$	−9.09809	−0.344368
$699$	57.5059	2.17507
$700$	1.25660	0.0474949
$701$	−26.5178	−1.00157	−0.500783	−	0.865573i	$-0.666954\pi$
$701$	−26.5178	−1.00157	−0.500783	+	0.865573i	$0.666954\pi$
$702$	167.234	6.31186
$703$	−18.8906	−0.712474
$704$	−20.2718	−0.764020
$705$	26.6153	1.00239
$706$	36.4444	1.37160
$707$	39.2601	1.47653
$708$	−7.05394	−0.265103
$709$	−43.4182	−1.63060	−0.815302	−	0.579036i	$-0.803429\pi$
$709$	−43.4182	−1.63060	−0.815302	+	0.579036i	$0.803429\pi$
$710$	−1.54425	−0.0579547
$711$	37.7221	1.41469
$712$	18.4961	0.693169
$713$	−31.8985	−1.19461
$714$	16.7380	0.626405
$715$	−22.2761	−0.833078
$716$	1.56158	0.0583592
$717$	−9.29796	−0.347239
$718$	−29.5456	−1.10263
$719$	−1.40987	−0.0525791	−0.0262896	−	0.999654i	$-0.508369\pi$
$719$	−1.40987	−0.0525791	−0.0262896	+	0.999654i	$0.508369\pi$
$720$	−37.0245	−1.37982
$721$	−53.4272	−1.98973
$722$	10.3744	0.386097
$723$	−14.0763	−0.523504
$724$	−2.44253	−0.0907760
$725$	5.37824	0.199743
$726$	3.59534	0.133436
$727$	13.2521	0.491491	0.245746	−	0.969334i	$-0.420967\pi$
$727$	13.2521	0.491491	0.245746	+	0.969334i	$0.420967\pi$
$728$	53.0575	1.96644
$729$	84.0039	3.11126
$730$	9.91610	0.367011
$731$	12.6059	0.466245
$732$	−11.3562	−0.419739
$733$	−5.54865	−0.204944	−0.102472	−	0.994736i	$-0.532675\pi$
$733$	−5.54865	−0.204944	−0.102472	+	0.994736i	$0.532675\pi$
$734$	6.49144	0.239603
$735$	−12.1752	−0.449091
$736$	−7.24075	−0.266898
$737$	−34.5226	−1.27166
$738$	−62.2242	−2.29050
$739$	47.0954	1.73243	0.866217	−	0.499668i	$-0.166545\pi$
$739$	47.0954	1.73243	0.866217	+	0.499668i	$0.166545\pi$
$740$	2.07371	0.0762310
$741$	75.7307	2.78204
$742$	51.0260	1.87322
$743$	−31.7264	−1.16393	−0.581964	−	0.813215i	$-0.697715\pi$
$743$	−31.7264	−1.16393	−0.581964	+	0.813215i	$0.697715\pi$
$744$	−78.3200	−2.87135
$745$	−9.52949	−0.349134
$746$	8.87762	0.325033
$747$	8.99073	0.328954
$748$	−1.31600	−0.0481178
$749$	33.6981	1.23130
$750$	5.12438	0.187116
$751$	−6.78596	−0.247623	−0.123812	−	0.992306i	$-0.539512\pi$
$751$	−6.78596	−0.247623	−0.123812	+	0.992306i	$0.539512\pi$
$752$	37.0667	1.35168
$753$	12.6643	0.461513
$754$	−54.0846	−1.96964
$755$	−3.68368	−0.134063
$756$	−20.8972	−0.760024
$757$	−36.3601	−1.32153	−0.660764	−	0.750593i	$-0.729768\pi$
$757$	−36.3601	−1.32153	−0.660764	+	0.750593i	$0.729768\pi$
$758$	32.5050	1.18063
$759$	−38.2680	−1.38904
$760$	−8.74180	−0.317098
$761$	20.5254	0.744045	0.372022	−	0.928224i	$-0.378664\pi$
$761$	20.5254	0.744045	0.372022	+	0.928224i	$0.378664\pi$
$762$	33.1096	1.19943
$763$	−8.93041	−0.323303
$764$	−4.09503	−0.148153
$765$	8.01151	0.289657
$766$	21.6122	0.780882
$767$	35.9824	1.29925
$768$	−29.5776	−1.06729
$769$	−20.8889	−0.753274	−0.376637	−	0.926361i	$-0.622920\pi$
$769$	−20.8889	−0.753274	−0.376637	+	0.926361i	$0.622920\pi$
$770$	17.2546	0.621811
$771$	44.3148	1.59596
$772$	−4.30453	−0.154923
$773$	−21.2415	−0.764002	−0.382001	−	0.924162i	$-0.624765\pi$
$773$	−21.2415	−0.764002	−0.382001	+	0.924162i	$0.624765\pi$
$774$	−155.957	−5.60576
$775$	9.46196	0.339883
$776$	10.5259	0.377859
$777$	−58.4253	−2.09599
$778$	7.51211	0.269322
$779$	−17.6262	−0.631525
$780$	−8.31328	−0.297663
$781$	−3.42076	−0.122405
$782$	5.20603	0.186167
$783$	−89.4401	−3.19633
$784$	−16.9562	−0.605580
$785$	22.7547	0.812151
$786$	−12.2401	−0.436590
$787$	−17.5895	−0.626996	−0.313498	−	0.949589i	$-0.601501\pi$
$787$	−17.5895	−0.626996	−0.313498	+	0.949589i	$0.601501\pi$
$788$	1.66561	0.0593348
$789$	−30.2522	−1.07701
$790$	−7.27109	−0.258694
$791$	56.0941	1.99448
$792$	−68.3606	−2.42909
$793$	57.9287	2.05711
$794$	41.6484	1.47805
$795$	33.5686	1.19056
$796$	5.76766	0.204429
$797$	53.9242	1.91009	0.955047	−	0.296454i	$-0.0958043\pi$
$797$	53.9242	1.91009	0.955047	+	0.296454i	$0.0958043\pi$
$798$	−58.6593	−2.07652
$799$	−8.02063	−0.283750
$800$	2.14780	0.0759362
$801$	59.4053	2.09898
$802$	6.08955	0.215030
$803$	21.9657	0.775154
$804$	−12.8836	−0.454369
$805$	−11.0116	−0.388110
$806$	−95.1512	−3.35156
$807$	−75.8015	−2.66834
$808$	29.9817	1.05475
$809$	51.0838	1.79601	0.898005	−	0.439984i	$-0.145016\pi$
$809$	51.0838	1.79601	0.898005	+	0.439984i	$0.145016\pi$
$810$	−48.1031	−1.69017
$811$	23.5571	0.827202	0.413601	−	0.910458i	$-0.364271\pi$
$811$	23.5571	0.827202	0.413601	+	0.910458i	$0.364271\pi$
$812$	6.75828	0.237169
$813$	79.2608	2.77980
$814$	28.4744	0.998028
$815$	−23.3962	−0.819532
$816$	15.3355	0.536851
$817$	−44.1779	−1.54559
$818$	5.61121	0.196191
$819$	170.409	5.95458
$820$	1.93491	0.0675699
$821$	10.5852	0.369427	0.184713	−	0.982792i	$-0.440864\pi$
$821$	10.5852	0.369427	0.184713	+	0.982792i	$0.440864\pi$
$822$	−105.207	−3.66951
$823$	−0.372454	−0.0129829	−0.00649147	−	0.999979i	$-0.502066\pi$
$823$	−0.372454	−0.0129829	−0.00649147	+	0.999979i	$0.502066\pi$
$824$	−40.8007	−1.42136
$825$	11.3513	0.395202
$826$	−27.8712	−0.969763
$827$	−9.92426	−0.345100	−0.172550	−	0.985001i	$-0.555201\pi$
$827$	−9.92426	−0.345100	−0.172550	+	0.985001i	$0.555201\pi$
$828$	−10.3905	−0.361095
$829$	8.27087	0.287259	0.143630	−	0.989632i	$-0.454123\pi$
$829$	8.27087	0.287259	0.143630	+	0.989632i	$0.454123\pi$
$830$	−1.73300	−0.0601533
$831$	11.7767	0.408528
$832$	38.5908	1.33790
$833$	3.66906	0.127125
$834$	−58.6312	−2.03023
$835$	−11.7441	−0.406421
$836$	4.61199	0.159509
$837$	−157.352	−5.43889
$838$	28.4172	0.981656
$839$	−21.8343	−0.753804	−0.376902	−	0.926253i	$-0.623011\pi$
$839$	−21.8343	−0.753804	−0.376902	+	0.926253i	$0.623011\pi$
$840$	−27.0368	−0.932857
$841$	−0.0745381	−0.00257028
$842$	−9.98301	−0.344037
$843$	−38.4817	−1.32538
$844$	7.75599	0.266972
$845$	29.4064	1.01161
$846$	99.2295	3.41158
$847$	2.29172	0.0787446
$848$	46.7504	1.60542
$849$	−96.3609	−3.30710
$850$	−1.54425	−0.0529674
$851$	−18.1720	−0.622929
$852$	−1.27661	−0.0437358
$853$	−49.1983	−1.68452	−0.842259	−	0.539073i	$-0.818775\pi$
$853$	−49.1983	−1.68452	−0.842259	+	0.539073i	$0.818775\pi$
$854$	−44.8703	−1.53543
$855$	−28.0768	−0.960205
$856$	25.7342	0.879578
$857$	−4.18751	−0.143043	−0.0715214	−	0.997439i	$-0.522785\pi$
$857$	−4.18751	−0.143043	−0.0715214	+	0.997439i	$0.522785\pi$
$858$	−114.151	−3.89705
$859$	52.1778	1.78028	0.890141	−	0.455685i	$-0.150606\pi$
$859$	52.1778	1.78028	0.890141	+	0.455685i	$0.150606\pi$
$860$	4.84960	0.165370
$861$	−54.5147	−1.85786
$862$	47.0151	1.60134
$863$	46.4148	1.57998	0.789989	−	0.613121i	$-0.210086\pi$
$863$	46.4148	1.57998	0.789989	+	0.613121i	$0.210086\pi$
$864$	−35.7179	−1.21515
$865$	−0.385370	−0.0131030
$866$	9.88250	0.335821
$867$	−3.31836	−0.112697
$868$	11.8899	0.403569
$869$	−16.1066	−0.546380
$870$	27.5601	0.934376
$871$	65.7198	2.22683
$872$	−6.81988	−0.230950
$873$	33.8070	1.14419
$874$	−18.2448	−0.617140
$875$	3.26635	0.110423
$876$	8.19747	0.276967
$877$	32.0089	1.08086	0.540431	−	0.841388i	$-0.318261\pi$
$877$	32.0089	1.08086	0.540431	+	0.841388i	$0.318261\pi$
$878$	−36.4143	−1.22892
$879$	−8.80851	−0.297104
$880$	15.8088	0.532914
$881$	−14.2548	−0.480257	−0.240128	−	0.970741i	$-0.577190\pi$
$881$	−14.2548	−0.480257	−0.240128	+	0.970741i	$0.577190\pi$
$882$	−45.3928	−1.52845
$883$	29.1547	0.981134	0.490567	−	0.871403i	$-0.336790\pi$
$883$	29.1547	0.981134	0.490567	+	0.871403i	$0.336790\pi$
$884$	2.50524	0.0842603
$885$	−18.3357	−0.616349
$886$	21.6435	0.727129
$887$	−10.3820	−0.348592	−0.174296	−	0.984693i	$-0.555765\pi$
$887$	−10.3820	−0.348592	−0.174296	+	0.984693i	$0.555765\pi$
$888$	−44.6176	−1.49727
$889$	21.1045	0.707823
$890$	−11.4506	−0.383825
$891$	−106.556	−3.56976
$892$	4.37073	0.146343
$893$	28.1087	0.940623
$894$	−48.8327	−1.63321
$895$	4.05912	0.135682
$896$	−43.9226	−1.46735
$897$	72.8498	2.43238
$898$	−0.416195	−0.0138886
$899$	50.8887	1.69723
$900$	3.08211	0.102737
$901$	−10.1160	−0.337014
$902$	26.5685	0.884636
$903$	−136.634	−4.54690
$904$	42.8374	1.42475
$905$	−6.34903	−0.211049
$906$	−18.8766	−0.627132
$907$	47.5245	1.57803	0.789013	−	0.614377i	$-0.210593\pi$
$907$	47.5245	1.57803	0.789013	+	0.614377i	$0.210593\pi$
$908$	−3.47354	−0.115274
$909$	96.2948	3.19390
$910$	−32.8471	−1.08887
$911$	29.4415	0.975441	0.487721	−	0.873000i	$-0.337828\pi$
$911$	29.4415	0.975441	0.487721	+	0.873000i	$0.337828\pi$
$912$	−53.7442	−1.77965
$913$	−3.83887	−0.127048
$914$	46.0195	1.52219
$915$	−29.5190	−0.975868
$916$	8.15480	0.269442
$917$	−7.80202	−0.257645
$918$	25.6809	0.847596
$919$	−33.7561	−1.11351	−0.556755	−	0.830676i	$-0.687954\pi$
$919$	−33.7561	−1.11351	−0.556755	+	0.830676i	$0.687954\pi$
$920$	−8.40926	−0.277245
$921$	109.972	3.62370
$922$	9.69317	0.319227
$923$	6.51202	0.214346
$924$	14.2640	0.469253
$925$	5.39032	0.177232
$926$	26.6954	0.877267
$927$	−131.043	−4.30402
$928$	11.5514	0.379193
$929$	−6.44706	−0.211521	−0.105761	−	0.994392i	$-0.533728\pi$
$929$	−6.44706	−0.211521	−0.105761	+	0.994392i	$0.533728\pi$
$930$	48.4866	1.58994
$931$	−12.8584	−0.421417
$932$	−6.66687	−0.218381
$933$	16.5577	0.542074
$934$	40.4031	1.32203
$935$	−3.42076	−0.111871
$936$	130.136	4.25364
$937$	47.8220	1.56228	0.781138	−	0.624358i	$-0.214639\pi$
$937$	47.8220	1.56228	0.781138	+	0.624358i	$0.214639\pi$
$938$	−50.9051	−1.66211
$939$	43.4739	1.41872
$940$	−3.08562	−0.100642
$941$	−10.4410	−0.340366	−0.170183	−	0.985412i	$-0.554436\pi$
$941$	−10.4410	−0.340366	−0.170183	+	0.985412i	$0.554436\pi$
$942$	116.604	3.79916
$943$	−16.9557	−0.552154
$944$	−25.5358	−0.831121
$945$	−54.3194	−1.76701
$946$	66.5906	2.16505
$947$	25.1441	0.817074	0.408537	−	0.912742i	$-0.366039\pi$
$947$	25.1441	0.817074	0.408537	+	0.912742i	$0.366039\pi$
$948$	−6.01089	−0.195224
$949$	−41.8156	−1.35739
$950$	5.41191	0.175585
$951$	−93.8531	−3.04339
$952$	8.14763	0.264066
$953$	9.75606	0.316030	0.158015	−	0.987437i	$-0.449491\pi$
$953$	9.75606	0.316030	0.158015	+	0.987437i	$0.449491\pi$
$954$	125.153	4.05199
$955$	−10.6445	−0.344447
$956$	1.07795	0.0348633
$957$	61.0501	1.97347
$958$	−46.9300	−1.51624
$959$	−67.0604	−2.16549
$960$	−19.6649	−0.634682
$961$	58.5286	1.88802
$962$	−54.2060	−1.74767
$963$	82.6528	2.66345
$964$	1.63192	0.0525606
$965$	−11.1890	−0.360188
$966$	−56.4279	−1.81554
$967$	6.18767	0.198982	0.0994911	−	0.995038i	$-0.468279\pi$
$967$	6.18767	0.198982	0.0994911	+	0.995038i	$0.468279\pi$
$968$	1.75012	0.0562510
$969$	11.6294	0.373589
$970$	−6.51644	−0.209230
$971$	−28.4694	−0.913625	−0.456813	−	0.889563i	$-0.651009\pi$
$971$	−28.4694	−0.913625	−0.456813	+	0.889563i	$0.651009\pi$
$972$	−20.5728	−0.659873
$973$	−37.3723	−1.19810
$974$	−47.5694	−1.52422
$975$	−21.6092	−0.692049
$976$	−41.1105	−1.31592
$977$	30.8827	0.988026	0.494013	−	0.869455i	$-0.335530\pi$
$977$	30.8827	0.988026	0.494013	+	0.869455i	$0.335530\pi$
$978$	−119.891	−3.83369
$979$	−25.3649	−0.810667
$980$	1.41152	0.0450894
$981$	−21.9040	−0.699340
$982$	−10.3126	−0.329087
$983$	−54.1575	−1.72735	−0.863677	−	0.504045i	$-0.831844\pi$
$983$	−54.1575	−1.72735	−0.863677	+	0.504045i	$0.831844\pi$
$984$	−41.6312	−1.32715
$985$	4.32951	0.137950
$986$	−8.30535	−0.264496
$987$	86.9351	2.76717
$988$	−8.77974	−0.279321
$989$	−42.4973	−1.35134
$990$	42.3209	1.34505
$991$	−43.3161	−1.37598	−0.687990	−	0.725720i	$-0.741507\pi$
$991$	−43.3161	−1.37598	−0.687990	+	0.725720i	$0.741507\pi$
$992$	20.3224	0.645237
$993$	62.0442	1.96891
$994$	−5.04407	−0.159988
$995$	14.9922	0.475286
$996$	−1.43264	−0.0453949
$997$	11.4444	0.362447	0.181223	−	0.983442i	$-0.441994\pi$
$997$	11.4444	0.362447	0.181223	+	0.983442i	$0.441994\pi$
$998$	−62.9328	−1.99210
$999$	−89.6409	−2.83611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.g.1.16	✓	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.g.1.16	✓	58	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-1.54425 q^{2} -3.31836 q^{3} +0.384710 q^{4} +1.00000 q^{5} +5.12438 q^{6} +3.26635 q^{7} +2.49441 q^{8} +8.01151 q^{9} +O(q^{10})\)	\(q-1.54425 q^{2} -3.31836 q^{3} +0.384710 q^{4} +1.00000 q^{5} +5.12438 q^{6} +3.26635 q^{7} +2.49441 q^{8} +8.01151 q^{9} -1.54425 q^{10} -3.42076 q^{11} -1.27661 q^{12} +6.51202 q^{13} -5.04407 q^{14} -3.31836 q^{15} -4.62142 q^{16} +1.00000 q^{17} -12.3718 q^{18} -3.50455 q^{19} +0.384710 q^{20} -10.8389 q^{21} +5.28251 q^{22} -3.37124 q^{23} -8.27736 q^{24} +1.00000 q^{25} -10.0562 q^{26} -16.6300 q^{27} +1.25660 q^{28} +5.37824 q^{29} +5.12438 q^{30} +9.46196 q^{31} +2.14780 q^{32} +11.3513 q^{33} -1.54425 q^{34} +3.26635 q^{35} +3.08211 q^{36} +5.39032 q^{37} +5.41191 q^{38} -21.6092 q^{39} +2.49441 q^{40} +5.02953 q^{41} +16.7380 q^{42} +12.6059 q^{43} -1.31600 q^{44} +8.01151 q^{45} +5.20603 q^{46} -8.02063 q^{47} +15.3355 q^{48} +3.66906 q^{49} -1.54425 q^{50} -3.31836 q^{51} +2.50524 q^{52} -10.1160 q^{53} +25.6809 q^{54} -3.42076 q^{55} +8.14763 q^{56} +11.6294 q^{57} -8.30535 q^{58} +5.52554 q^{59} -1.27661 q^{60} +8.89566 q^{61} -14.6116 q^{62} +26.1684 q^{63} +5.92609 q^{64} +6.51202 q^{65} -17.5293 q^{66} +10.0921 q^{67} +0.384710 q^{68} +11.1870 q^{69} -5.04407 q^{70} +1.00000 q^{71} +19.9840 q^{72} -6.42130 q^{73} -8.32400 q^{74} -3.31836 q^{75} -1.34824 q^{76} -11.1734 q^{77} +33.3701 q^{78} +4.70849 q^{79} -4.62142 q^{80} +31.1498 q^{81} -7.76685 q^{82} +1.12223 q^{83} -4.16984 q^{84} +1.00000 q^{85} -19.4666 q^{86} -17.8469 q^{87} -8.53279 q^{88} +7.41500 q^{89} -12.3718 q^{90} +21.2705 q^{91} -1.29695 q^{92} -31.3982 q^{93} +12.3859 q^{94} -3.50455 q^{95} -7.12718 q^{96} +4.21981 q^{97} -5.66594 q^{98} -27.4055 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9}+O(q^{10}) \) 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9	\( 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9} + q^{10} + 28 q^{11} + 18 q^{12} + 37 q^{13} + 28 q^{14} + 6 q^{15} + 83 q^{16} + 58 q^{17} - 12 q^{18} + 19 q^{19} + 69 q^{20} + 31 q^{21} + 13 q^{22} + 14 q^{23} + 13 q^{24} + 58 q^{25} + 18 q^{26} + 9 q^{27} + 8 q^{28} + 60 q^{29} + 10 q^{30} + 39 q^{31} - 30 q^{32} + 13 q^{33} + q^{34} + 13 q^{35} + 113 q^{36} + 60 q^{37} - q^{38} + 41 q^{39} - 3 q^{40} + 65 q^{41} - 30 q^{42} + 17 q^{43} + 69 q^{44} + 84 q^{45} + 24 q^{46} + 16 q^{47} + 14 q^{48} + 117 q^{49} + q^{50} + 6 q^{51} + 61 q^{52} + 5 q^{53} + 24 q^{54} + 28 q^{55} + 105 q^{56} + 8 q^{57} - 34 q^{58} + 22 q^{59} + 18 q^{60} + 113 q^{61} - 19 q^{62} + 8 q^{63} + 89 q^{64} + 37 q^{65} - 37 q^{66} + 19 q^{67} + 69 q^{68} + 75 q^{69} + 28 q^{70} + 58 q^{71} - 17 q^{72} + 49 q^{73} + 29 q^{74} + 6 q^{75} - 6 q^{76} + 17 q^{77} - 12 q^{78} + 7 q^{79} + 83 q^{80} + 134 q^{81} + 7 q^{82} - 12 q^{83} - 18 q^{84} + 58 q^{85} + 23 q^{86} - 36 q^{87} - 33 q^{88} + 52 q^{89} - 12 q^{90} + 31 q^{91} + 80 q^{92} - 37 q^{93} + 4 q^{94} + 19 q^{95} - 35 q^{96} + 26 q^{97} - 33 q^{98} + 57 q^{99}+O(q^{100}) \) 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9 + q^10 + 28 * q^11 + 18 * q^12 + 37 * q^13 + 28 * q^14 + 6 * q^15 + 83 * q^16 + 58 * q^17 - 12 * q^18 + 19 * q^19 + 69 * q^20 + 31 * q^21 + 13 * q^22 + 14 * q^23 + 13 * q^24 + 58 * q^25 + 18 * q^26 + 9 * q^27 + 8 * q^28 + 60 * q^29 + 10 * q^30 + 39 * q^31 - 30 * q^32 + 13 * q^33 + q^34 + 13 * q^35 + 113 * q^36 + 60 * q^37 - q^38 + 41 * q^39 - 3 * q^40 + 65 * q^41 - 30 * q^42 + 17 * q^43 + 69 * q^44 + 84 * q^45 + 24 * q^46 + 16 * q^47 + 14 * q^48 + 117 * q^49 + q^50 + 6 * q^51 + 61 * q^52 + 5 * q^53 + 24 * q^54 + 28 * q^55 + 105 * q^56 + 8 * q^57 - 34 * q^58 + 22 * q^59 + 18 * q^60 + 113 * q^61 - 19 * q^62 + 8 * q^63 + 89 * q^64 + 37 * q^65 - 37 * q^66 + 19 * q^67 + 69 * q^68 + 75 * q^69 + 28 * q^70 + 58 * q^71 - 17 * q^72 + 49 * q^73 + 29 * q^74 + 6 * q^75 - 6 * q^76 + 17 * q^77 - 12 * q^78 + 7 * q^79 + 83 * q^80 + 134 * q^81 + 7 * q^82 - 12 * q^83 - 18 * q^84 + 58 * q^85 + 23 * q^86 - 36 * q^87 - 33 * q^88 + 52 * q^89 - 12 * q^90 + 31 * q^91 + 80 * q^92 - 37 * q^93 + 4 * q^94 + 19 * q^95 - 35 * q^96 + 26 * q^97 - 33 * q^98 + 57 * q^99

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