LMFDB - Embedded newform 6017.2.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$107$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41316 q^{2} -1.13111 q^{3} +3.82334 q^{4} +3.33661 q^{5} +2.72954 q^{6} -4.21510 q^{7} -4.40000 q^{8} -1.72060 q^{9} +O(q^{10})$	\(q-2.41316 q^{2} -1.13111 q^{3} +3.82334 q^{4} +3.33661 q^{5} +2.72954 q^{6} -4.21510 q^{7} -4.40000 q^{8} -1.72060 q^{9} -8.05177 q^{10} -1.00000 q^{11} -4.32460 q^{12} +4.74360 q^{13} +10.1717 q^{14} -3.77406 q^{15} +2.97123 q^{16} +6.58257 q^{17} +4.15208 q^{18} -3.55656 q^{19} +12.7570 q^{20} +4.76773 q^{21} +2.41316 q^{22} -6.52486 q^{23} +4.97687 q^{24} +6.13295 q^{25} -11.4471 q^{26} +5.33950 q^{27} -16.1158 q^{28} +1.23594 q^{29} +9.10740 q^{30} -5.99394 q^{31} +1.62996 q^{32} +1.13111 q^{33} -15.8848 q^{34} -14.0641 q^{35} -6.57843 q^{36} +5.06983 q^{37} +8.58254 q^{38} -5.36551 q^{39} -14.6811 q^{40} -10.4280 q^{41} -11.5053 q^{42} +4.62349 q^{43} -3.82334 q^{44} -5.74097 q^{45} +15.7455 q^{46} -3.89858 q^{47} -3.36077 q^{48} +10.7671 q^{49} -14.7998 q^{50} -7.44559 q^{51} +18.1364 q^{52} -7.39583 q^{53} -12.8851 q^{54} -3.33661 q^{55} +18.5464 q^{56} +4.02284 q^{57} -2.98252 q^{58} +12.0064 q^{59} -14.4295 q^{60} +14.8730 q^{61} +14.4643 q^{62} +7.25250 q^{63} -9.87580 q^{64} +15.8275 q^{65} -2.72954 q^{66} -2.93758 q^{67} +25.1674 q^{68} +7.38031 q^{69} +33.9390 q^{70} +8.53772 q^{71} +7.57064 q^{72} -11.9826 q^{73} -12.2343 q^{74} -6.93702 q^{75} -13.5979 q^{76} +4.21510 q^{77} +12.9478 q^{78} +10.6453 q^{79} +9.91382 q^{80} -0.877740 q^{81} +25.1644 q^{82} +3.89542 q^{83} +18.2286 q^{84} +21.9635 q^{85} -11.1572 q^{86} -1.39798 q^{87} +4.40000 q^{88} -2.44827 q^{89} +13.8539 q^{90} -19.9948 q^{91} -24.9467 q^{92} +6.77978 q^{93} +9.40789 q^{94} -11.8668 q^{95} -1.84366 q^{96} -11.1462 q^{97} -25.9827 q^{98} +1.72060 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) $ 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9 - 14 * q^10 - 107 * q^11 - 50 * q^12 - 24 * q^13 - 17 * q^14 - 47 * q^15 + 63 * q^16 + 25 * q^17 - 37 * q^18 - 55 * q^19 - 31 * q^20 + 15 * q^21 + 3 * q^22 - 38 * q^23 + 4 * q^24 + 62 * q^25 - 16 * q^26 - 57 * q^27 - 101 * q^28 + 27 * q^29 - 14 * q^30 - 112 * q^31 - 4 * q^32 + 18 * q^33 - 66 * q^34 + 8 * q^35 + 35 * q^36 - 60 * q^37 - 45 * q^38 - 58 * q^39 - 50 * q^40 - 14 * q^41 - 36 * q^42 - 78 * q^43 - 91 * q^44 - 68 * q^45 - 18 * q^46 - 109 * q^47 - 99 * q^48 + 61 * q^49 - 32 * q^50 - 10 * q^51 - 111 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 44 * q^56 + q^57 - 98 * q^58 - 48 * q^59 - 119 * q^60 - 30 * q^61 + 32 * q^62 - 126 * q^63 + 3 * q^64 + 43 * q^65 - 77 * q^67 + 53 * q^68 - 51 * q^69 - 87 * q^70 - 40 * q^71 - 82 * q^72 - 83 * q^73 + 11 * q^74 - 69 * q^75 - 108 * q^76 + 54 * q^77 - 53 * q^78 - 66 * q^79 - 96 * q^80 + 51 * q^81 - 133 * q^82 - 32 * q^83 + 27 * q^84 - 66 * q^85 - 46 * q^86 - 136 * q^87 + 3 * q^88 - 56 * q^89 + 9 * q^90 - 86 * q^91 - 94 * q^92 - 33 * q^93 - 93 * q^94 - 25 * q^95 - 4 * q^96 - 109 * q^97 - 38 * q^98 - 95 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.41316	−1.70636	−0.853181	−	0.521616i	$-0.825329\pi$
$2$	−2.41316	−1.70636	−0.853181	+	0.521616i	$0.825329\pi$
$3$	−1.13111	−0.653044	−0.326522	−	0.945190i	$-0.605877\pi$
$3$	−1.13111	−0.653044	−0.326522	+	0.945190i	$0.605877\pi$
$4$	3.82334	1.91167
$5$	3.33661	1.49218	0.746088	−	0.665847i	$-0.231930\pi$
$5$	3.33661	1.49218	0.746088	+	0.665847i	$0.231930\pi$
$6$	2.72954	1.11433
$7$	−4.21510	−1.59316	−0.796579	−	0.604534i	$-0.793359\pi$
$7$	−4.21510	−1.59316	−0.796579	+	0.604534i	$0.793359\pi$
$8$	−4.40000	−1.55563
$9$	−1.72060	−0.573533
$10$	−8.05177	−2.54619
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.32460	−1.24840
$13$	4.74360	1.31564	0.657819	−	0.753176i	$-0.271479\pi$
$13$	4.74360	1.31564	0.657819	+	0.753176i	$0.271479\pi$
$14$	10.1717	2.71850
$15$	−3.77406	−0.974457
$16$	2.97123	0.742807
$17$	6.58257	1.59651	0.798254	−	0.602321i	$-0.205757\pi$
$17$	6.58257	1.59651	0.798254	+	0.602321i	$0.205757\pi$
$18$	4.15208	0.978655
$19$	−3.55656	−0.815930	−0.407965	−	0.912998i	$-0.633761\pi$
$19$	−3.55656	−0.815930	−0.407965	+	0.912998i	$0.633761\pi$
$20$	12.7570	2.85255
$21$	4.76773	1.04040
$22$	2.41316	0.514487
$23$	−6.52486	−1.36053	−0.680264	−	0.732967i	$-0.738135\pi$
$23$	−6.52486	−1.36053	−0.680264	+	0.732967i	$0.738135\pi$
$24$	4.97687	1.01590
$25$	6.13295	1.22659
$26$	−11.4471	−2.24495
$27$	5.33950	1.02759
$28$	−16.1158	−3.04559
$29$	1.23594	0.229509	0.114754	−	0.993394i	$-0.463392\pi$
$29$	1.23594	0.229509	0.114754	+	0.993394i	$0.463392\pi$
$30$	9.10740	1.66278
$31$	−5.99394	−1.07654	−0.538272	−	0.842771i	$-0.680923\pi$
$31$	−5.99394	−1.07654	−0.538272	+	0.842771i	$0.680923\pi$
$32$	1.62996	0.288139
$33$	1.13111	0.196900
$34$	−15.8848	−2.72422
$35$	−14.0641	−2.37727
$36$	−6.57843	−1.09640
$37$	5.06983	0.833475	0.416738	−	0.909027i	$-0.363173\pi$
$37$	5.06983	0.833475	0.416738	+	0.909027i	$0.363173\pi$
$38$	8.58254	1.39227
$39$	−5.36551	−0.859170
$40$	−14.6811	−2.32128
$41$	−10.4280	−1.62858	−0.814289	−	0.580460i	$-0.802873\pi$
$41$	−10.4280	−1.62858	−0.814289	+	0.580460i	$0.802873\pi$
$42$	−11.5053	−1.77530
$43$	4.62349	0.705076	0.352538	−	0.935798i	$-0.385319\pi$
$43$	4.62349	0.705076	0.352538	+	0.935798i	$0.385319\pi$
$44$	−3.82334	−0.576390
$45$	−5.74097	−0.855813
$46$	15.7455	2.32155
$47$	−3.89858	−0.568666	−0.284333	−	0.958726i	$-0.591772\pi$
$47$	−3.89858	−0.568666	−0.284333	+	0.958726i	$0.591772\pi$
$48$	−3.36077	−0.485086
$49$	10.7671	1.53816
$50$	−14.7998	−2.09301
$51$	−7.44559	−1.04259
$52$	18.1364	2.51506
$53$	−7.39583	−1.01589	−0.507947	−	0.861388i	$-0.669596\pi$
$53$	−7.39583	−1.01589	−0.507947	+	0.861388i	$0.669596\pi$
$54$	−12.8851	−1.75343
$55$	−3.33661	−0.449908
$56$	18.5464	2.47837
$57$	4.02284	0.532838
$58$	−2.98252	−0.391624
$59$	12.0064	1.56311	0.781553	−	0.623839i	$-0.214428\pi$
$59$	12.0064	1.56311	0.781553	+	0.623839i	$0.214428\pi$
$60$	−14.4295	−1.86284
$61$	14.8730	1.90430	0.952149	−	0.305633i	$-0.0988682\pi$
$61$	14.8730	1.90430	0.952149	+	0.305633i	$0.0988682\pi$
$62$	14.4643	1.83697
$63$	7.25250	0.913729
$64$	−9.87580	−1.23448
$65$	15.8275	1.96316
$66$	−2.72954	−0.335983
$67$	−2.93758	−0.358883	−0.179442	−	0.983769i	$-0.557429\pi$
$67$	−2.93758	−0.358883	−0.179442	+	0.983769i	$0.557429\pi$
$68$	25.1674	3.05199
$69$	7.38031	0.888485
$70$	33.9390	4.05649
$71$	8.53772	1.01324	0.506621	−	0.862169i	$-0.330894\pi$
$71$	8.53772	1.01324	0.506621	+	0.862169i	$0.330894\pi$
$72$	7.57064	0.892208
$73$	−11.9826	−1.40245	−0.701227	−	0.712938i	$-0.747364\pi$
$73$	−11.9826	−1.40245	−0.701227	+	0.712938i	$0.747364\pi$
$74$	−12.2343	−1.42221
$75$	−6.93702	−0.801018
$76$	−13.5979	−1.55979
$77$	4.21510	0.480355
$78$	12.9478	1.46605
$79$	10.6453	1.19769	0.598844	−	0.800866i	$-0.295627\pi$
$79$	10.6453	1.19769	0.598844	+	0.800866i	$0.295627\pi$
$80$	9.91382	1.10840
$81$	−0.877740	−0.0975266
$82$	25.1644	2.77894
$83$	3.89542	0.427577	0.213789	−	0.976880i	$-0.431420\pi$
$83$	3.89542	0.427577	0.213789	+	0.976880i	$0.431420\pi$
$84$	18.2286	1.98891
$85$	21.9635	2.38227
$86$	−11.1572	−1.20311
$87$	−1.39798	−0.149879
$88$	4.40000	0.469042
$89$	−2.44827	−0.259517	−0.129758	−	0.991546i	$-0.541420\pi$
$89$	−2.44827	−0.259517	−0.129758	+	0.991546i	$0.541420\pi$
$90$	13.8539	1.46033
$91$	−19.9948	−2.09602
$92$	−24.9467	−2.60088
$93$	6.77978	0.703030
$94$	9.40789	0.970350
$95$	−11.8668	−1.21751
$96$	−1.84366	−0.188167
$97$	−11.1462	−1.13172	−0.565860	−	0.824501i	$-0.691456\pi$
$97$	−11.1462	−1.13172	−0.565860	+	0.824501i	$0.691456\pi$
$98$	−25.9827	−2.62465
$99$	1.72060	0.172927
$100$	23.4483	2.34483
$101$	−7.92012	−0.788082	−0.394041	−	0.919093i	$-0.628923\pi$
$101$	−7.92012	−0.788082	−0.394041	+	0.919093i	$0.628923\pi$
$102$	17.9674	1.77904
$103$	−4.12333	−0.406284	−0.203142	−	0.979149i	$-0.565115\pi$
$103$	−4.12333	−0.406284	−0.203142	+	0.979149i	$0.565115\pi$
$104$	−20.8718	−2.04665
$105$	15.9080	1.55247
$106$	17.8473	1.73348
$107$	−9.63303	−0.931261	−0.465630	−	0.884979i	$-0.654172\pi$
$107$	−9.63303	−0.931261	−0.465630	+	0.884979i	$0.654172\pi$
$108$	20.4147	1.96440
$109$	4.48597	0.429678	0.214839	−	0.976649i	$-0.431077\pi$
$109$	4.48597	0.429678	0.214839	+	0.976649i	$0.431077\pi$
$110$	8.05177	0.767706
$111$	−5.73452	−0.544296
$112$	−12.5240	−1.18341
$113$	−17.2562	−1.62333	−0.811665	−	0.584123i	$-0.801439\pi$
$113$	−17.2562	−1.62333	−0.811665	+	0.584123i	$0.801439\pi$
$114$	−9.70776	−0.909215
$115$	−21.7709	−2.03015
$116$	4.72542	0.438744
$117$	−8.16183	−0.754562
$118$	−28.9735	−2.66722
$119$	−27.7462	−2.54349
$120$	16.6058	1.51590
$121$	1.00000	0.0909091
$122$	−35.8910	−3.24942
$123$	11.7952	1.06353
$124$	−22.9168	−2.05799
$125$	3.78022	0.338113
$126$	−17.5014	−1.55915
$127$	9.01769	0.800190	0.400095	−	0.916474i	$-0.368977\pi$
$127$	9.01769	0.800190	0.400095	+	0.916474i	$0.368977\pi$
$128$	20.5720	1.81832
$129$	−5.22966	−0.460446
$130$	−38.1943	−3.34987
$131$	0.761029	0.0664914	0.0332457	−	0.999447i	$-0.489416\pi$
$131$	0.761029	0.0664914	0.0332457	+	0.999447i	$0.489416\pi$
$132$	4.32460	0.376408
$133$	14.9912	1.29991
$134$	7.08886	0.612384
$135$	17.8158	1.53334
$136$	−28.9633	−2.48358
$137$	5.86737	0.501283	0.250642	−	0.968080i	$-0.419358\pi$
$137$	5.86737	0.501283	0.250642	+	0.968080i	$0.419358\pi$
$138$	−17.8099	−1.51608
$139$	−21.3452	−1.81048	−0.905240	−	0.424900i	$-0.860309\pi$
$139$	−21.3452	−1.81048	−0.905240	+	0.424900i	$0.860309\pi$
$140$	−53.7719	−4.54456
$141$	4.40971	0.371364
$142$	−20.6029	−1.72896
$143$	−4.74360	−0.396680
$144$	−5.11229	−0.426024
$145$	4.12385	0.342467
$146$	28.9158	2.39309
$147$	−12.1787	−1.00448
$148$	19.3837	1.59333
$149$	15.2863	1.25230	0.626152	−	0.779701i	$-0.284629\pi$
$149$	15.2863	1.25230	0.626152	+	0.779701i	$0.284629\pi$
$150$	16.7401	1.36683
$151$	20.6089	1.67713	0.838565	−	0.544801i	$-0.183395\pi$
$151$	20.6089	1.67713	0.838565	+	0.544801i	$0.183395\pi$
$152$	15.6488	1.26929
$153$	−11.3260	−0.915651
$154$	−10.1717	−0.819660
$155$	−19.9994	−1.60639
$156$	−20.5142	−1.64245
$157$	−13.9106	−1.11019	−0.555094	−	0.831787i	$-0.687318\pi$
$157$	−13.9106	−1.11019	−0.555094	+	0.831787i	$0.687318\pi$
$158$	−25.6888	−2.04369
$159$	8.36546	0.663424
$160$	5.43853	0.429954
$161$	27.5030	2.16754
$162$	2.11813	0.166416
$163$	5.12912	0.401744	0.200872	−	0.979618i	$-0.435623\pi$
$163$	5.12912	0.401744	0.200872	+	0.979618i	$0.435623\pi$
$164$	−39.8697	−3.11330
$165$	3.77406	0.293810
$166$	−9.40026	−0.729602
$167$	0.301297	0.0233150	0.0116575	−	0.999932i	$-0.496289\pi$
$167$	0.301297	0.0233150	0.0116575	+	0.999932i	$0.496289\pi$
$168$	−20.9780	−1.61849
$169$	9.50174	0.730903
$170$	−53.0013	−4.06502
$171$	6.11941	0.467963
$172$	17.6772	1.34787
$173$	−13.2392	−1.00656	−0.503279	−	0.864124i	$-0.667873\pi$
$173$	−13.2392	−1.00656	−0.503279	+	0.864124i	$0.667873\pi$
$174$	3.37355	0.255748
$175$	−25.8510	−1.95415
$176$	−2.97123	−0.223965
$177$	−13.5806	−1.02078
$178$	5.90808	0.442829
$179$	22.3052	1.66717	0.833585	−	0.552391i	$-0.186284\pi$
$179$	22.3052	1.66717	0.833585	+	0.552391i	$0.186284\pi$
$180$	−21.9496	−1.63603
$181$	14.6724	1.09059	0.545297	−	0.838243i	$-0.316417\pi$
$181$	14.6724	1.09059	0.545297	+	0.838243i	$0.316417\pi$
$182$	48.2505	3.57657
$183$	−16.8230	−1.24359
$184$	28.7094	2.11648
$185$	16.9160	1.24369
$186$	−16.3607	−1.19962
$187$	−6.58257	−0.481365
$188$	−14.9056	−1.08710
$189$	−22.5065	−1.63711
$190$	28.6366	2.07751
$191$	−13.5308	−0.979053	−0.489527	−	0.871988i	$-0.662830\pi$
$191$	−13.5308	−0.979053	−0.489527	+	0.871988i	$0.662830\pi$
$192$	11.1706	0.806167
$193$	0.736105	0.0529860	0.0264930	−	0.999649i	$-0.491566\pi$
$193$	0.736105	0.0529860	0.0264930	+	0.999649i	$0.491566\pi$
$194$	26.8974	1.93112
$195$	−17.9026	−1.28203
$196$	41.1662	2.94044
$197$	14.9276	1.06355	0.531775	−	0.846886i	$-0.321525\pi$
$197$	14.9276	1.06355	0.531775	+	0.846886i	$0.321525\pi$
$198$	−4.15208	−0.295075
$199$	−4.21924	−0.299094	−0.149547	−	0.988755i	$-0.547782\pi$
$199$	−4.21924	−0.299094	−0.149547	+	0.988755i	$0.547782\pi$
$200$	−26.9850	−1.90813
$201$	3.32272	0.234367
$202$	19.1125	1.34475
$203$	−5.20962	−0.365644
$204$	−28.4670	−1.99309
$205$	−34.7941	−2.43013
$206$	9.95025	0.693267
$207$	11.2267	0.780308
$208$	14.0943	0.977264
$209$	3.55656	0.246012
$210$	−38.3886	−2.64907
$211$	−12.5050	−0.860883	−0.430442	−	0.902618i	$-0.641642\pi$
$211$	−12.5050	−0.860883	−0.430442	+	0.902618i	$0.641642\pi$
$212$	−28.2767	−1.94205
$213$	−9.65707	−0.661691
$214$	23.2460	1.58907
$215$	15.4268	1.05210
$216$	−23.4938	−1.59855
$217$	25.2651	1.71510
$218$	−10.8254	−0.733186
$219$	13.5536	0.915864
$220$	−12.7570	−0.860075
$221$	31.2251	2.10043
$222$	13.8383	0.928766
$223$	−25.4236	−1.70249	−0.851244	−	0.524769i	$-0.824152\pi$
$223$	−25.4236	−1.70249	−0.851244	+	0.524769i	$0.824152\pi$
$224$	−6.87044	−0.459051
$225$	−10.5524	−0.703490
$226$	41.6421	2.76999
$227$	−14.6195	−0.970329	−0.485165	−	0.874423i	$-0.661240\pi$
$227$	−14.6195	−0.970329	−0.485165	+	0.874423i	$0.661240\pi$
$228$	15.3807	1.01861
$229$	10.2381	0.676551	0.338275	−	0.941047i	$-0.390156\pi$
$229$	10.2381	0.676551	0.338275	+	0.941047i	$0.390156\pi$
$230$	52.5367	3.46416
$231$	−4.76773	−0.313693
$232$	−5.43814	−0.357031
$233$	18.5370	1.21440	0.607200	−	0.794549i	$-0.292293\pi$
$233$	18.5370	1.21440	0.607200	+	0.794549i	$0.292293\pi$
$234$	19.6958	1.28755
$235$	−13.0080	−0.848550
$236$	45.9047	2.98814
$237$	−12.0409	−0.782143
$238$	66.9560	4.34012
$239$	−10.0752	−0.651711	−0.325856	−	0.945420i	$-0.605652\pi$
$239$	−10.0752	−0.651711	−0.325856	+	0.945420i	$0.605652\pi$
$240$	−11.2136	−0.723833
$241$	−24.6150	−1.58559	−0.792795	−	0.609489i	$-0.791375\pi$
$241$	−24.6150	−1.58559	−0.792795	+	0.609489i	$0.791375\pi$
$242$	−2.41316	−0.155124
$243$	−15.0257	−0.963898
$244$	56.8647	3.64039
$245$	35.9255	2.29520
$246$	−28.4636	−1.81477
$247$	−16.8709	−1.07347
$248$	26.3733	1.67471
$249$	−4.40613	−0.279227
$250$	−9.12227	−0.576943
$251$	−16.7040	−1.05435	−0.527174	−	0.849757i	$-0.676749\pi$
$251$	−16.7040	−1.05435	−0.527174	+	0.849757i	$0.676749\pi$
$252$	27.7288	1.74675
$253$	6.52486	0.410215
$254$	−21.7611	−1.36541
$255$	−24.8430	−1.55573
$256$	−29.8918	−1.86824
$257$	−14.7107	−0.917629	−0.458814	−	0.888532i	$-0.651726\pi$
$257$	−14.7107	−0.917629	−0.458814	+	0.888532i	$0.651726\pi$
$258$	12.6200	0.785686
$259$	−21.3699	−1.32786
$260$	60.5140	3.75292
$261$	−2.12656	−0.131631
$262$	−1.83648	−0.113458
$263$	10.2542	0.632302	0.316151	−	0.948709i	$-0.397609\pi$
$263$	10.2542	0.632302	0.316151	+	0.948709i	$0.397609\pi$
$264$	−4.97687	−0.306305
$265$	−24.6770	−1.51589
$266$	−36.1763	−2.21811
$267$	2.76926	0.169476
$268$	−11.2314	−0.686065
$269$	4.98381	0.303868	0.151934	−	0.988391i	$-0.451450\pi$
$269$	4.98381	0.303868	0.151934	+	0.988391i	$0.451450\pi$
$270$	−42.9924	−2.61643
$271$	27.9899	1.70027	0.850133	−	0.526567i	$-0.176521\pi$
$271$	27.9899	1.70027	0.850133	+	0.526567i	$0.176521\pi$
$272$	19.5583	1.18590
$273$	22.6162	1.36879
$274$	−14.1589	−0.855370
$275$	−6.13295	−0.369831
$276$	28.2174	1.69849
$277$	22.2283	1.33557	0.667784	−	0.744355i	$-0.267243\pi$
$277$	22.2283	1.33557	0.667784	+	0.744355i	$0.267243\pi$
$278$	51.5095	3.08933
$279$	10.3132	0.617433
$280$	61.8822	3.69817
$281$	−4.91298	−0.293084	−0.146542	−	0.989204i	$-0.546814\pi$
$281$	−4.91298	−0.293084	−0.146542	+	0.989204i	$0.546814\pi$
$282$	−10.6413	−0.633681
$283$	−13.2769	−0.789231	−0.394616	−	0.918846i	$-0.629122\pi$
$283$	−13.2769	−0.789231	−0.394616	+	0.918846i	$0.629122\pi$
$284$	32.6426	1.93698
$285$	13.4226	0.795089
$286$	11.4471	0.676879
$287$	43.9550	2.59458
$288$	−2.80450	−0.165257
$289$	26.3303	1.54884
$290$	−9.95151	−0.584373
$291$	12.6075	0.739064
$292$	−45.8134	−2.68103
$293$	10.6043	0.619507	0.309754	−	0.950817i	$-0.399753\pi$
$293$	10.6043	0.619507	0.309754	+	0.950817i	$0.399753\pi$
$294$	29.3892	1.71401
$295$	40.0608	2.33243
$296$	−22.3073	−1.29658
$297$	−5.33950	−0.309829
$298$	−36.8883	−2.13688
$299$	−30.9513	−1.78996
$300$	−26.5226	−1.53128
$301$	−19.4885	−1.12330
$302$	−49.7326	−2.86179
$303$	8.95850	0.514652
$304$	−10.5673	−0.606078
$305$	49.6255	2.84155
$306$	27.3314	1.56243
$307$	−15.2294	−0.869187	−0.434594	−	0.900627i	$-0.643108\pi$
$307$	−15.2294	−0.869187	−0.434594	+	0.900627i	$0.643108\pi$
$308$	16.1158	0.918280
$309$	4.66392	0.265321
$310$	48.2618	2.74109
$311$	−1.39838	−0.0792949	−0.0396475	−	0.999214i	$-0.512623\pi$
$311$	−1.39838	−0.0792949	−0.0396475	+	0.999214i	$0.512623\pi$
$312$	23.6083	1.33655
$313$	−28.9052	−1.63382	−0.816908	−	0.576768i	$-0.804314\pi$
$313$	−28.9052	−1.63382	−0.816908	+	0.576768i	$0.804314\pi$
$314$	33.5685	1.89438
$315$	24.1988	1.36345
$316$	40.7005	2.28958
$317$	−31.7875	−1.78536	−0.892681	−	0.450689i	$-0.851178\pi$
$317$	−31.7875	−1.78536	−0.892681	+	0.450689i	$0.851178\pi$
$318$	−20.1872	−1.13204
$319$	−1.23594	−0.0691994
$320$	−32.9517	−1.84205
$321$	10.8960	0.608154
$322$	−66.3690	−3.69860
$323$	−23.4113	−1.30264
$324$	−3.35589	−0.186439
$325$	29.0923	1.61375
$326$	−12.3774	−0.685520
$327$	−5.07411	−0.280599
$328$	45.8831	2.53347
$329$	16.4329	0.905975
$330$	−9.10740	−0.501346
$331$	12.3656	0.679676	0.339838	−	0.940484i	$-0.389628\pi$
$331$	12.3656	0.679676	0.339838	+	0.940484i	$0.389628\pi$
$332$	14.8935	0.817386
$333$	−8.72315	−0.478026
$334$	−0.727077	−0.0397839
$335$	−9.80157	−0.535517
$336$	14.1660	0.772818
$337$	15.6678	0.853477	0.426738	−	0.904375i	$-0.359663\pi$
$337$	15.6678	0.853477	0.426738	+	0.904375i	$0.359663\pi$
$338$	−22.9292	−1.24718
$339$	19.5186	1.06011
$340$	83.9737	4.55411
$341$	5.99394	0.324590
$342$	−14.7671	−0.798514
$343$	−15.8786	−0.857366
$344$	−20.3434	−1.09684
$345$	24.6252	1.32578
$346$	31.9483	1.71755
$347$	26.9714	1.44790	0.723951	−	0.689852i	$-0.242324\pi$
$347$	26.9714	1.44790	0.723951	+	0.689852i	$0.242324\pi$
$348$	−5.34495	−0.286519
$349$	−28.0169	−1.49971	−0.749855	−	0.661603i	$-0.769877\pi$
$349$	−28.0169	−1.49971	−0.749855	+	0.661603i	$0.769877\pi$
$350$	62.3826	3.33449
$351$	25.3284	1.35193
$352$	−1.62996	−0.0868771
$353$	28.6318	1.52391	0.761957	−	0.647627i	$-0.224239\pi$
$353$	28.6318	1.52391	0.761957	+	0.647627i	$0.224239\pi$
$354$	32.7720	1.74181
$355$	28.4870	1.51193
$356$	−9.36058	−0.496110
$357$	31.3839	1.66101
$358$	−53.8260	−2.84479
$359$	−16.6486	−0.878678	−0.439339	−	0.898321i	$-0.644787\pi$
$359$	−16.6486	−0.878678	−0.439339	+	0.898321i	$0.644787\pi$
$360$	25.2602	1.33133
$361$	−6.35091	−0.334258
$362$	−35.4069	−1.86095
$363$	−1.13111	−0.0593677
$364$	−76.4467	−4.00689
$365$	−39.9811	−2.09271
$366$	40.5966	2.12202
$367$	−17.8235	−0.930379	−0.465190	−	0.885211i	$-0.654014\pi$
$367$	−17.8235	−0.930379	−0.465190	+	0.885211i	$0.654014\pi$
$368$	−19.3868	−1.01061
$369$	17.9424	0.934043
$370$	−40.8211	−2.12219
$371$	31.1742	1.61848
$372$	25.9214	1.34396
$373$	24.4153	1.26418	0.632088	−	0.774897i	$-0.282198\pi$
$373$	24.4153	1.26418	0.632088	+	0.774897i	$0.282198\pi$
$374$	15.8848	0.821383
$375$	−4.27583	−0.220803
$376$	17.1537	0.884637
$377$	5.86281	0.301950
$378$	54.3118	2.79350
$379$	−33.1562	−1.70312	−0.851560	−	0.524257i	$-0.824343\pi$
$379$	−33.1562	−1.70312	−0.851560	+	0.524257i	$0.824343\pi$
$380$	−45.3709	−2.32748
$381$	−10.2000	−0.522560
$382$	32.6519	1.67062
$383$	−27.1189	−1.38571	−0.692856	−	0.721076i	$-0.743648\pi$
$383$	−27.1189	−1.38571	−0.692856	+	0.721076i	$0.743648\pi$
$384$	−23.2691	−1.18744
$385$	14.0641	0.716775
$386$	−1.77634	−0.0904132
$387$	−7.95517	−0.404384
$388$	−42.6155	−2.16347
$389$	34.4664	1.74752	0.873758	−	0.486361i	$-0.161676\pi$
$389$	34.4664	1.74752	0.873758	+	0.486361i	$0.161676\pi$
$390$	43.2019	2.18761
$391$	−42.9504	−2.17209
$392$	−47.3752	−2.39281
$393$	−0.860804	−0.0434218
$394$	−36.0228	−1.81480
$395$	35.5191	1.78716
$396$	6.57843	0.330579
$397$	19.7090	0.989167	0.494584	−	0.869130i	$-0.335321\pi$
$397$	19.7090	0.989167	0.494584	+	0.869130i	$0.335321\pi$
$398$	10.1817	0.510363
$399$	−16.9567	−0.848896
$400$	18.2224	0.911119
$401$	2.06893	0.103318	0.0516588	−	0.998665i	$-0.483549\pi$
$401$	2.06893	0.103318	0.0516588	+	0.998665i	$0.483549\pi$
$402$	−8.01825	−0.399914
$403$	−28.4328	−1.41634
$404$	−30.2813	−1.50655
$405$	−2.92867	−0.145527
$406$	12.5716	0.623920
$407$	−5.06983	−0.251302
$408$	32.7606	1.62189
$409$	−10.7772	−0.532899	−0.266450	−	0.963849i	$-0.585851\pi$
$409$	−10.7772	−0.532899	−0.266450	+	0.963849i	$0.585851\pi$
$410$	83.9637	4.14667
$411$	−6.63661	−0.327360
$412$	−15.7649	−0.776680
$413$	−50.6084	−2.49028
$414$	−27.0918	−1.33149
$415$	12.9975	0.638021
$416$	7.73187	0.379086
$417$	24.1437	1.18232
$418$	−8.58254	−0.419786
$419$	1.15367	0.0563606	0.0281803	−	0.999603i	$-0.491029\pi$
$419$	1.15367	0.0563606	0.0281803	+	0.999603i	$0.491029\pi$
$420$	60.8218	2.96780
$421$	−23.0868	−1.12518	−0.562591	−	0.826735i	$-0.690195\pi$
$421$	−23.0868	−1.12518	−0.562591	+	0.826735i	$0.690195\pi$
$422$	30.1767	1.46898
$423$	6.70789	0.326149
$424$	32.5416	1.58036
$425$	40.3706	1.95826
$426$	23.3040	1.12908
$427$	−62.6914	−3.03385
$428$	−36.8303	−1.78026
$429$	5.36551	0.259049
$430$	−37.2273	−1.79526
$431$	15.7499	0.758644	0.379322	−	0.925265i	$-0.376157\pi$
$431$	15.7499	0.758644	0.379322	+	0.925265i	$0.376157\pi$
$432$	15.8649	0.763298
$433$	7.47773	0.359357	0.179678	−	0.983725i	$-0.442494\pi$
$433$	7.47773	0.359357	0.179678	+	0.983725i	$0.442494\pi$
$434$	−60.9686	−2.92659
$435$	−4.66451	−0.223646
$436$	17.1514	0.821402
$437$	23.2060	1.11010
$438$	−32.7069	−1.56280
$439$	−24.9878	−1.19260	−0.596301	−	0.802761i	$-0.703364\pi$
$439$	−24.9878	−1.19260	−0.596301	+	0.802761i	$0.703364\pi$
$440$	14.6811	0.699893
$441$	−18.5258	−0.882183
$442$	−75.3511	−3.58409
$443$	−24.2548	−1.15238	−0.576190	−	0.817316i	$-0.695461\pi$
$443$	−24.2548	−1.15238	−0.576190	+	0.817316i	$0.695461\pi$
$444$	−21.9250	−1.04051
$445$	−8.16893	−0.387245
$446$	61.3511	2.90506
$447$	−17.2905	−0.817810
$448$	41.6275	1.96671
$449$	4.45579	0.210282	0.105141	−	0.994457i	$-0.466471\pi$
$449$	4.45579	0.210282	0.105141	+	0.994457i	$0.466471\pi$
$450$	25.4645	1.20041
$451$	10.4280	0.491035
$452$	−65.9764	−3.10327
$453$	−23.3109	−1.09524
$454$	35.2791	1.65573
$455$	−66.7147	−3.12763
$456$	−17.7005	−0.828902
$457$	−22.2568	−1.04113	−0.520564	−	0.853822i	$-0.674278\pi$
$457$	−22.2568	−1.04113	−0.520564	+	0.853822i	$0.674278\pi$
$458$	−24.7061	−1.15444
$459$	35.1476	1.64055
$460$	−83.2375	−3.88097
$461$	−4.89209	−0.227847	−0.113924	−	0.993490i	$-0.536342\pi$
$461$	−4.89209	−0.227847	−0.113924	+	0.993490i	$0.536342\pi$
$462$	11.5053	0.535274
$463$	−23.5821	−1.09595	−0.547977	−	0.836494i	$-0.684602\pi$
$463$	−23.5821	−1.09595	−0.547977	+	0.836494i	$0.684602\pi$
$464$	3.67226	0.170480
$465$	22.6215	1.04905
$466$	−44.7328	−2.07221
$467$	18.9279	0.875880	0.437940	−	0.899004i	$-0.355708\pi$
$467$	18.9279	0.875880	0.437940	+	0.899004i	$0.355708\pi$
$468$	−31.2054	−1.44247
$469$	12.3822	0.571758
$470$	31.3904	1.44793
$471$	15.7344	0.725002
$472$	−52.8283	−2.43162
$473$	−4.62349	−0.212588
$474$	29.0567	1.33462
$475$	−21.8122	−1.00081
$476$	−106.083	−4.86231
$477$	12.7253	0.582649
$478$	24.3131	1.11205
$479$	26.4588	1.20893	0.604466	−	0.796631i	$-0.293387\pi$
$479$	26.4588	1.20893	0.604466	+	0.796631i	$0.293387\pi$
$480$	−6.15155	−0.280779
$481$	24.0493	1.09655
$482$	59.3998	2.70559
$483$	−31.1088	−1.41550
$484$	3.82334	0.173788
$485$	−37.1904	−1.68873
$486$	36.2593	1.64476
$487$	−9.89850	−0.448544	−0.224272	−	0.974527i	$-0.572000\pi$
$487$	−9.89850	−0.448544	−0.224272	+	0.974527i	$0.572000\pi$
$488$	−65.4414	−2.96239
$489$	−5.80158	−0.262356
$490$	−86.6940	−3.91644
$491$	18.6242	0.840501	0.420250	−	0.907408i	$-0.361942\pi$
$491$	18.6242	0.840501	0.420250	+	0.907408i	$0.361942\pi$
$492$	45.0968	2.03312
$493$	8.13568	0.366412
$494$	40.7121	1.83172
$495$	5.74097	0.258037
$496$	−17.8093	−0.799663
$497$	−35.9874	−1.61425
$498$	10.6327	0.476462
$499$	4.78003	0.213984	0.106992	−	0.994260i	$-0.465878\pi$
$499$	4.78003	0.213984	0.106992	+	0.994260i	$0.465878\pi$
$500$	14.4530	0.646360
$501$	−0.340799	−0.0152258
$502$	40.3095	1.79910
$503$	20.0896	0.895752	0.447876	−	0.894096i	$-0.352181\pi$
$503$	20.0896	0.895752	0.447876	+	0.894096i	$0.352181\pi$
$504$	−31.9110	−1.42143
$505$	−26.4263	−1.17596
$506$	−15.7455	−0.699974
$507$	−10.7475	−0.477312
$508$	34.4776	1.52970
$509$	−34.3235	−1.52136	−0.760681	−	0.649126i	$-0.775135\pi$
$509$	−34.3235	−1.52136	−0.760681	+	0.649126i	$0.775135\pi$
$510$	59.9501	2.65464
$511$	50.5077	2.23433
$512$	30.9898	1.36957
$513$	−18.9902	−0.838439
$514$	35.4993	1.56581
$515$	−13.7579	−0.606247
$516$	−19.9947	−0.880219
$517$	3.89858	0.171459
$518$	51.5689	2.26581
$519$	14.9749	0.657327
$520$	−69.6411	−3.05397
$521$	−2.07514	−0.0909133	−0.0454567	−	0.998966i	$-0.514474\pi$
$521$	−2.07514	−0.0909133	−0.0454567	+	0.998966i	$0.514474\pi$
$522$	5.13173	0.224610
$523$	0.953347	0.0416869	0.0208435	−	0.999783i	$-0.493365\pi$
$523$	0.953347	0.0416869	0.0208435	+	0.999783i	$0.493365\pi$
$524$	2.90967	0.127110
$525$	29.2402	1.27615
$526$	−24.7450	−1.07893
$527$	−39.4555	−1.71871
$528$	3.36077	0.146259
$529$	19.5738	0.851036
$530$	59.5495	2.58666
$531$	−20.6583	−0.896493
$532$	57.3166	2.48499
$533$	−49.4662	−2.14262
$534$	−6.68266	−0.289187
$535$	−32.1417	−1.38961
$536$	12.9254	0.558291
$537$	−25.2296	−1.08874
$538$	−12.0267	−0.518509
$539$	−10.7671	−0.463771
$540$	68.1158	2.93124
$541$	−1.97276	−0.0848154	−0.0424077	−	0.999100i	$-0.513503\pi$
$541$	−1.97276	−0.0848154	−0.0424077	+	0.999100i	$0.513503\pi$
$542$	−67.5441	−2.90127
$543$	−16.5961	−0.712206
$544$	10.7293	0.460016
$545$	14.9679	0.641155
$546$	−54.5765	−2.33566
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	22.4329	0.958287
$549$	−25.5906	−1.09218
$550$	14.7998	0.631065
$551$	−4.39569	−0.187263
$552$	−32.4734	−1.38216
$553$	−44.8710	−1.90811
$554$	−53.6404	−2.27896
$555$	−19.1338	−0.812186
$556$	−81.6101	−3.46104
$557$	−18.7261	−0.793450	−0.396725	−	0.917938i	$-0.629853\pi$
$557$	−18.7261	−0.793450	−0.396725	+	0.917938i	$0.629853\pi$
$558$	−24.8873	−1.05356
$559$	21.9320	0.927624
$560$	−41.7878	−1.76585
$561$	7.44559	0.314353
$562$	11.8558	0.500106
$563$	20.9604	0.883378	0.441689	−	0.897168i	$-0.354380\pi$
$563$	20.9604	0.883378	0.441689	+	0.897168i	$0.354380\pi$
$564$	16.8598	0.709925
$565$	−57.5773	−2.42230
$566$	32.0393	1.34671
$567$	3.69976	0.155375
$568$	−37.5660	−1.57623
$569$	6.27275	0.262967	0.131484	−	0.991318i	$-0.458026\pi$
$569$	6.27275	0.262967	0.131484	+	0.991318i	$0.458026\pi$
$570$	−32.3910	−1.35671
$571$	−29.0605	−1.21614	−0.608071	−	0.793883i	$-0.708056\pi$
$571$	−29.0605	−1.21614	−0.608071	+	0.793883i	$0.708056\pi$
$572$	−18.1364	−0.758320
$573$	15.3048	0.639365
$574$	−106.070	−4.42730
$575$	−40.0167	−1.66881
$576$	16.9923	0.708012
$577$	−43.5624	−1.81353	−0.906763	−	0.421640i	$-0.861455\pi$
$577$	−43.5624	−1.81353	−0.906763	+	0.421640i	$0.861455\pi$
$578$	−63.5391	−2.64288
$579$	−0.832612	−0.0346022
$580$	15.7669	0.654684
$581$	−16.4196	−0.681199
$582$	−30.4239	−1.26111
$583$	7.39583	0.306304
$584$	52.7233	2.18171
$585$	−27.2328	−1.12594
$586$	−25.5897	−1.05710
$587$	−23.4126	−0.966340	−0.483170	−	0.875526i	$-0.660515\pi$
$587$	−23.4126	−0.966340	−0.483170	+	0.875526i	$0.660515\pi$
$588$	−46.5633	−1.92024
$589$	21.3178	0.878384
$590$	−96.6731	−3.97997
$591$	−16.8847	−0.694546
$592$	15.0636	0.619111
$593$	4.46720	0.183446	0.0917230	−	0.995785i	$-0.470763\pi$
$593$	4.46720	0.183446	0.0917230	+	0.995785i	$0.470763\pi$
$594$	12.8851	0.528680
$595$	−92.5783	−3.79534
$596$	58.4448	2.39399
$597$	4.77241	0.195322
$598$	74.6905	3.05432
$599$	0.807312	0.0329859	0.0164929	−	0.999864i	$-0.494750\pi$
$599$	0.807312	0.0329859	0.0164929	+	0.999864i	$0.494750\pi$
$600$	30.5229	1.24609
$601$	27.0302	1.10259	0.551293	−	0.834312i	$-0.314135\pi$
$601$	27.0302	1.10259	0.551293	+	0.834312i	$0.314135\pi$
$602$	47.0288	1.91675
$603$	5.05441	0.205831
$604$	78.7949	3.20612
$605$	3.33661	0.135652
$606$	−21.6183	−0.878182
$607$	6.94026	0.281696	0.140848	−	0.990031i	$-0.455017\pi$
$607$	6.94026	0.281696	0.140848	+	0.990031i	$0.455017\pi$
$608$	−5.79704	−0.235101
$609$	5.89263	0.238781
$610$	−119.754	−4.84871
$611$	−18.4933	−0.748159
$612$	−43.3030	−1.75042
$613$	7.29051	0.294461	0.147231	−	0.989102i	$-0.452964\pi$
$613$	7.29051	0.294461	0.147231	+	0.989102i	$0.452964\pi$
$614$	36.7510	1.48315
$615$	39.3558	1.58698
$616$	−18.5464	−0.747258
$617$	−21.8986	−0.881606	−0.440803	−	0.897604i	$-0.645306\pi$
$617$	−21.8986	−0.881606	−0.440803	+	0.897604i	$0.645306\pi$
$618$	−11.2548	−0.452734
$619$	32.9984	1.32632	0.663159	−	0.748479i	$-0.269215\pi$
$619$	32.9984	1.32632	0.663159	+	0.748479i	$0.269215\pi$
$620$	−76.4645	−3.07089
$621$	−34.8395	−1.39806
$622$	3.37452	0.135306
$623$	10.3197	0.413451
$624$	−15.9422	−0.638197
$625$	−18.0517	−0.722066
$626$	69.7527	2.78788
$627$	−4.02284	−0.160657
$628$	−53.1850	−2.12231
$629$	33.3725	1.33065
$630$	−58.3954	−2.32653
$631$	−17.9982	−0.716498	−0.358249	−	0.933626i	$-0.616626\pi$
$631$	−17.9982	−0.716498	−0.358249	+	0.933626i	$0.616626\pi$
$632$	−46.8392	−1.86317
$633$	14.1445	0.562195
$634$	76.7082	3.04647
$635$	30.0885	1.19402
$636$	31.9840	1.26825
$637$	51.0747	2.02365
$638$	2.98252	0.118079
$639$	−14.6900	−0.581127
$640$	68.6406	2.71326
$641$	30.8182	1.21724	0.608622	−	0.793460i	$-0.291723\pi$
$641$	30.8182	1.21724	0.608622	+	0.793460i	$0.291723\pi$
$642$	−26.2937	−1.03773
$643$	−32.6371	−1.28708	−0.643541	−	0.765412i	$-0.722535\pi$
$643$	−32.6371	−1.28708	−0.643541	+	0.765412i	$0.722535\pi$
$644$	105.153	4.14361
$645$	−17.4493	−0.687066
$646$	56.4952	2.22277
$647$	−18.7076	−0.735471	−0.367736	−	0.929930i	$-0.619867\pi$
$647$	−18.7076	−0.735471	−0.367736	+	0.929930i	$0.619867\pi$
$648$	3.86205	0.151716
$649$	−12.0064	−0.471294
$650$	−70.2043	−2.75364
$651$	−28.5775	−1.12004
$652$	19.6103	0.768000
$653$	21.7988	0.853051	0.426526	−	0.904475i	$-0.359737\pi$
$653$	21.7988	0.853051	0.426526	+	0.904475i	$0.359737\pi$
$654$	12.2446	0.478803
$655$	2.53926	0.0992169
$656$	−30.9839	−1.20972
$657$	20.6172	0.804354
$658$	−39.6552	−1.54592
$659$	−18.9404	−0.737813	−0.368906	−	0.929467i	$-0.620268\pi$
$659$	−18.9404	−0.737813	−0.368906	+	0.929467i	$0.620268\pi$
$660$	14.4295	0.561667
$661$	7.93805	0.308754	0.154377	−	0.988012i	$-0.450663\pi$
$661$	7.93805	0.308754	0.154377	+	0.988012i	$0.450663\pi$
$662$	−29.8402	−1.15977
$663$	−35.3189	−1.37167
$664$	−17.1398	−0.665154
$665$	50.0199	1.93969
$666$	21.0503	0.815684
$667$	−8.06435	−0.312253
$668$	1.15196	0.0445706
$669$	28.7568	1.11180
$670$	23.6527	0.913785
$671$	−14.8730	−0.574168
$672$	7.77119	0.299780
$673$	15.7882	0.608591	0.304295	−	0.952578i	$-0.401579\pi$
$673$	15.7882	0.608591	0.304295	+	0.952578i	$0.401579\pi$
$674$	−37.8088	−1.45634
$675$	32.7469	1.26043
$676$	36.3283	1.39724
$677$	−42.6760	−1.64017	−0.820086	−	0.572241i	$-0.806074\pi$
$677$	−42.6760	−1.64017	−0.820086	+	0.572241i	$0.806074\pi$
$678$	−47.1016	−1.80892
$679$	46.9822	1.80301
$680$	−96.6393	−3.70595
$681$	16.5362	0.633668
$682$	−14.4643	−0.553868
$683$	33.3480	1.27603	0.638013	−	0.770026i	$-0.279757\pi$
$683$	33.3480	1.27603	0.638013	+	0.770026i	$0.279757\pi$
$684$	23.3966	0.894590
$685$	19.5771	0.748003
$686$	38.3177	1.46298
$687$	−11.5803	−0.441818
$688$	13.7374	0.523735
$689$	−35.0828	−1.33655
$690$	−59.4245	−2.26225
$691$	−27.9718	−1.06410	−0.532049	−	0.846713i	$-0.678578\pi$
$691$	−27.9718	−1.06410	−0.532049	+	0.846713i	$0.678578\pi$
$692$	−50.6179	−1.92420
$693$	−7.25250	−0.275500
$694$	−65.0863	−2.47064
$695$	−71.2207	−2.70156
$696$	6.15111	0.233157
$697$	−68.6430	−2.60004
$698$	67.6092	2.55905
$699$	−20.9673	−0.793057
$700$	−98.8371	−3.73569
$701$	−33.2417	−1.25552	−0.627762	−	0.778406i	$-0.716029\pi$
$701$	−33.2417	−1.25552	−0.627762	+	0.778406i	$0.716029\pi$
$702$	−61.1215	−2.30688
$703$	−18.0311	−0.680058
$704$	9.87580	0.372208
$705$	14.7135	0.554141
$706$	−69.0930	−2.60035
$707$	33.3841	1.25554
$708$	−51.9230	−1.95139
$709$	−25.5257	−0.958639	−0.479320	−	0.877640i	$-0.659117\pi$
$709$	−25.5257	−0.958639	−0.479320	+	0.877640i	$0.659117\pi$
$710$	−68.7437	−2.57991
$711$	−18.3163	−0.686914
$712$	10.7724	0.403713
$713$	39.1096	1.46467
$714$	−75.7344	−2.83429
$715$	−15.8275	−0.591916
$716$	85.2803	3.18708
$717$	11.3961	0.425596
$718$	40.1757	1.49934
$719$	51.8594	1.93403	0.967015	−	0.254720i	$-0.0819832\pi$
$719$	51.8594	1.93403	0.967015	+	0.254720i	$0.0819832\pi$
$720$	−17.0577	−0.635703
$721$	17.3803	0.647275
$722$	15.3258	0.570365
$723$	27.8421	1.03546
$724$	56.0977	2.08485
$725$	7.57997	0.281513
$726$	2.72954	0.101303
$727$	−47.0949	−1.74665	−0.873327	−	0.487134i	$-0.838042\pi$
$727$	−47.0949	−1.74665	−0.873327	+	0.487134i	$0.838042\pi$
$728$	87.9769	3.26064
$729$	19.6289	0.726994
$730$	96.4808	3.57092
$731$	30.4345	1.12566
$732$	−64.3199	−2.37733
$733$	−24.7292	−0.913393	−0.456696	−	0.889623i	$-0.650967\pi$
$733$	−24.7292	−0.913393	−0.456696	+	0.889623i	$0.650967\pi$
$734$	43.0109	1.58756
$735$	−40.6356	−1.49887
$736$	−10.6353	−0.392021
$737$	2.93758	0.108207
$738$	−43.2978	−1.59381
$739$	−12.3813	−0.455453	−0.227726	−	0.973725i	$-0.573129\pi$
$739$	−12.3813	−0.455453	−0.227726	+	0.973725i	$0.573129\pi$
$740$	64.6757	2.37753
$741$	19.0827	0.701022
$742$	−75.2282	−2.76171
$743$	−30.9678	−1.13610	−0.568048	−	0.822995i	$-0.692301\pi$
$743$	−30.9678	−1.13610	−0.568048	+	0.822995i	$0.692301\pi$
$744$	−29.8310	−1.09366
$745$	51.0045	1.86866
$746$	−58.9180	−2.15714
$747$	−6.70245	−0.245230
$748$	−25.1674	−0.920211
$749$	40.6042	1.48365
$750$	10.3183	0.376769
$751$	−25.9618	−0.947360	−0.473680	−	0.880697i	$-0.657075\pi$
$751$	−25.9618	−0.947360	−0.473680	+	0.880697i	$0.657075\pi$
$752$	−11.5836	−0.422409
$753$	18.8940	0.688537
$754$	−14.1479	−0.515236
$755$	68.7639	2.50258
$756$	−86.0500	−3.12961
$757$	−49.1595	−1.78673	−0.893367	−	0.449328i	$-0.851663\pi$
$757$	−49.1595	−1.78673	−0.893367	+	0.449328i	$0.851663\pi$
$758$	80.0112	2.90614
$759$	−7.38031	−0.267888
$760$	52.2141	1.89400
$761$	−9.22055	−0.334245	−0.167122	−	0.985936i	$-0.553448\pi$
$761$	−9.22055	−0.334245	−0.167122	+	0.985936i	$0.553448\pi$
$762$	24.6141	0.891675
$763$	−18.9088	−0.684545
$764$	−51.7327	−1.87162
$765$	−37.7903	−1.36631
$766$	65.4423	2.36453
$767$	56.9538	2.05648
$768$	33.8108	1.22004
$769$	−43.8057	−1.57967	−0.789836	−	0.613318i	$-0.789835\pi$
$769$	−43.8057	−1.57967	−0.789836	+	0.613318i	$0.789835\pi$
$770$	−33.9390	−1.22308
$771$	16.6394	0.599252
$772$	2.81438	0.101292
$773$	−28.1554	−1.01268	−0.506340	−	0.862334i	$-0.669002\pi$
$773$	−28.1554	−1.01268	−0.506340	+	0.862334i	$0.669002\pi$
$774$	19.1971	0.690025
$775$	−36.7605	−1.32048
$776$	49.0431	1.76054
$777$	24.1716	0.867151
$778$	−83.1729	−2.98189
$779$	37.0877	1.32881
$780$	−68.4477	−2.45082
$781$	−8.53772	−0.305504
$782$	103.646	3.70638
$783$	6.59931	0.235840
$784$	31.9914	1.14255
$785$	−46.4143	−1.65660
$786$	2.07726	0.0740933
$787$	−37.4531	−1.33506	−0.667529	−	0.744584i	$-0.732648\pi$
$787$	−37.4531	−1.33506	−0.667529	+	0.744584i	$0.732648\pi$
$788$	57.0734	2.03316
$789$	−11.5986	−0.412921
$790$	−85.7133	−3.04954
$791$	72.7368	2.58622
$792$	−7.57064	−0.269011
$793$	70.5518	2.50537
$794$	−47.5610	−1.68788
$795$	27.9123	0.989946
$796$	−16.1316	−0.571769
$797$	−41.7800	−1.47993	−0.739963	−	0.672648i	$-0.765157\pi$
$797$	−41.7800	−1.47993	−0.739963	+	0.672648i	$0.765157\pi$
$798$	40.9192	1.44852
$799$	−25.6627	−0.907880
$800$	9.99646	0.353428
$801$	4.21250	0.148841
$802$	−4.99267	−0.176297
$803$	11.9826	0.422856
$804$	12.7039	0.448031
$805$	91.7666	3.23435
$806$	68.6130	2.41679
$807$	−5.63722	−0.198439
$808$	34.8485	1.22597
$809$	−54.8373	−1.92798	−0.963989	−	0.265943i	$-0.914317\pi$
$809$	−54.8373	−1.92798	−0.963989	+	0.265943i	$0.914317\pi$
$810$	7.06735	0.248321
$811$	35.4944	1.24638	0.623188	−	0.782072i	$-0.285837\pi$
$811$	35.4944	1.24638	0.623188	+	0.782072i	$0.285837\pi$
$812$	−19.9181	−0.698989
$813$	−31.6596	−1.11035
$814$	12.2343	0.428812
$815$	17.1139	0.599472
$816$	−22.1225	−0.774443
$817$	−16.4437	−0.575292
$818$	26.0072	0.909319
$819$	34.4030	1.20214
$820$	−133.030	−4.64559
$821$	9.81078	0.342399	0.171199	−	0.985236i	$-0.445236\pi$
$821$	9.81078	0.342399	0.171199	+	0.985236i	$0.445236\pi$
$822$	16.0152	0.558594
$823$	−18.7151	−0.652368	−0.326184	−	0.945306i	$-0.605763\pi$
$823$	−18.7151	−0.652368	−0.326184	+	0.945306i	$0.605763\pi$
$824$	18.1427	0.632029
$825$	6.93702	0.241516
$826$	122.126	4.24931
$827$	−1.35024	−0.0469524	−0.0234762	−	0.999724i	$-0.507473\pi$
$827$	−1.35024	−0.0469524	−0.0234762	+	0.999724i	$0.507473\pi$
$828$	42.9233	1.49169
$829$	17.4377	0.605638	0.302819	−	0.953048i	$-0.402072\pi$
$829$	17.4377	0.605638	0.302819	+	0.953048i	$0.402072\pi$
$830$	−31.3650	−1.08869
$831$	−25.1426	−0.872186
$832$	−46.8468	−1.62412
$833$	70.8751	2.45568
$834$	−58.2627	−2.01747
$835$	1.00531	0.0347902
$836$	13.5979	0.470294
$837$	−32.0046	−1.10624
$838$	−2.78400	−0.0961715
$839$	13.5088	0.466375	0.233187	−	0.972432i	$-0.425084\pi$
$839$	13.5088	0.466375	0.233187	+	0.972432i	$0.425084\pi$
$840$	−69.9953	−2.41507
$841$	−27.4724	−0.947326
$842$	55.7121	1.91997
$843$	5.55710	0.191397
$844$	−47.8110	−1.64572
$845$	31.7036	1.09064
$846$	−16.1872	−0.556528
$847$	−4.21510	−0.144833
$848$	−21.9747	−0.754613
$849$	15.0176	0.515403
$850$	−97.4207	−3.34150
$851$	−33.0800	−1.13397
$852$	−36.9222	−1.26493
$853$	−19.5871	−0.670649	−0.335325	−	0.942103i	$-0.608846\pi$
$853$	−19.5871	−0.670649	−0.335325	+	0.942103i	$0.608846\pi$
$854$	151.284	5.17684
$855$	20.4181	0.698283
$856$	42.3853	1.44870
$857$	−8.20188	−0.280171	−0.140086	−	0.990139i	$-0.544738\pi$
$857$	−8.20188	−0.280171	−0.140086	+	0.990139i	$0.544738\pi$
$858$	−12.9478	−0.442032
$859$	−38.7419	−1.32186	−0.660928	−	0.750449i	$-0.729837\pi$
$859$	−38.7419	−1.32186	−0.660928	+	0.750449i	$0.729837\pi$
$860$	58.9817	2.01126
$861$	−49.7178	−1.69438
$862$	−38.0069	−1.29452
$863$	5.44661	0.185405	0.0927024	−	0.995694i	$-0.470449\pi$
$863$	5.44661	0.185405	0.0927024	+	0.995694i	$0.470449\pi$
$864$	8.70316	0.296087
$865$	−44.1740	−1.50196
$866$	−18.0450	−0.613193
$867$	−29.7823	−1.01146
$868$	96.5968	3.27871
$869$	−10.6453	−0.361117
$870$	11.2562	0.381621
$871$	−13.9347	−0.472160
$872$	−19.7383	−0.668422
$873$	19.1781	0.649079
$874$	−55.9999	−1.89422
$875$	−15.9340	−0.538668
$876$	51.8198	1.75083
$877$	−29.1740	−0.985137	−0.492568	−	0.870274i	$-0.663942\pi$
$877$	−29.1740	−0.985137	−0.492568	+	0.870274i	$0.663942\pi$
$878$	60.2995	2.03501
$879$	−11.9945	−0.404566
$880$	−9.91382	−0.334195
$881$	−5.53843	−0.186595	−0.0932973	−	0.995638i	$-0.529741\pi$
$881$	−5.53843	−0.186595	−0.0932973	+	0.995638i	$0.529741\pi$
$882$	44.7058	1.50532
$883$	14.7749	0.497215	0.248608	−	0.968604i	$-0.420027\pi$
$883$	14.7749	0.497215	0.248608	+	0.968604i	$0.420027\pi$
$884$	119.384	4.01532
$885$	−45.3130	−1.52318
$886$	58.5307	1.96638
$887$	11.7260	0.393722	0.196861	−	0.980431i	$-0.436925\pi$
$887$	11.7260	0.393722	0.196861	+	0.980431i	$0.436925\pi$
$888$	25.2319	0.846726
$889$	−38.0105	−1.27483
$890$	19.7129	0.660779
$891$	0.877740	0.0294054
$892$	−97.2029	−3.25459
$893$	13.8655	0.463992
$894$	41.7246	1.39548
$895$	74.4238	2.48771
$896$	−86.7129	−2.89687
$897$	35.0092	1.16892
$898$	−10.7525	−0.358817
$899$	−7.40816	−0.247076
$900$	−40.3452	−1.34484
$901$	−48.6836	−1.62189
$902$	−25.1644	−0.837882
$903$	22.0435	0.733563
$904$	75.9275	2.52531
$905$	48.9562	1.62736
$906$	56.2529	1.86888
$907$	4.23519	0.140627	0.0703135	−	0.997525i	$-0.477600\pi$
$907$	4.23519	0.140627	0.0703135	+	0.997525i	$0.477600\pi$
$908$	−55.8952	−1.85495
$909$	13.6274	0.451991
$910$	160.993	5.33687
$911$	56.9174	1.88576	0.942879	−	0.333134i	$-0.108106\pi$
$911$	56.9174	1.88576	0.942879	+	0.333134i	$0.108106\pi$
$912$	11.9528	0.395796
$913$	−3.89542	−0.128919
$914$	53.7092	1.77654
$915$	−56.1317	−1.85566
$916$	39.1436	1.29334
$917$	−3.20781	−0.105931
$918$	−84.8168	−2.79937
$919$	3.11629	0.102797	0.0513984	−	0.998678i	$-0.483632\pi$
$919$	3.11629	0.102797	0.0513984	+	0.998678i	$0.483632\pi$
$920$	95.7920	3.15817
$921$	17.2261	0.567618
$922$	11.8054	0.388790
$923$	40.4995	1.33306
$924$	−18.2286	−0.599678
$925$	31.0930	1.02233
$926$	56.9074	1.87009
$927$	7.09460	0.233017
$928$	2.01453	0.0661303
$929$	−19.3265	−0.634081	−0.317041	−	0.948412i	$-0.602689\pi$
$929$	−19.3265	−0.634081	−0.317041	+	0.948412i	$0.602689\pi$
$930$	−54.5892	−1.79005
$931$	−38.2937	−1.25503
$932$	70.8732	2.32153
$933$	1.58172	0.0517831
$934$	−45.6761	−1.49457
$935$	−21.9635	−0.718282
$936$	35.9121	1.17382
$937$	−9.84758	−0.321707	−0.160853	−	0.986978i	$-0.551425\pi$
$937$	−9.84758	−0.321707	−0.160853	+	0.986978i	$0.551425\pi$
$938$	−29.8803	−0.975625
$939$	32.6948	1.06695
$940$	−49.7341	−1.62215
$941$	−43.1593	−1.40695	−0.703476	−	0.710719i	$-0.748370\pi$
$941$	−43.1593	−1.40695	−0.703476	+	0.710719i	$0.748370\pi$
$942$	−37.9696	−1.23712
$943$	68.0412	2.21573
$944$	35.6739	1.16109
$945$	−75.0955	−2.44286
$946$	11.1572	0.362752
$947$	43.9391	1.42783	0.713914	−	0.700234i	$-0.246921\pi$
$947$	43.9391	1.42783	0.713914	+	0.700234i	$0.246921\pi$
$948$	−46.0366	−1.49520
$949$	−56.8405	−1.84512
$950$	52.6363	1.70775
$951$	35.9550	1.16592
$952$	122.083	3.95674
$953$	−3.59804	−0.116552	−0.0582759	−	0.998301i	$-0.518560\pi$
$953$	−3.59804	−0.116552	−0.0582759	+	0.998301i	$0.518560\pi$
$954$	−30.7081	−0.994210
$955$	−45.1469	−1.46092
$956$	−38.5209	−1.24586
$957$	1.39798	0.0451903
$958$	−63.8492	−2.06287
$959$	−24.7316	−0.798624
$960$	37.2718	1.20294
$961$	4.92730	0.158945
$962$	−58.0347	−1.87111
$963$	16.5746	0.534109
$964$	−94.1113	−3.03112
$965$	2.45609	0.0790644
$966$	75.0704	2.41535
$967$	−46.6394	−1.49982	−0.749911	−	0.661539i	$-0.769904\pi$
$967$	−46.6394	−1.49982	−0.749911	+	0.661539i	$0.769904\pi$
$968$	−4.40000	−0.141421
$969$	26.4807	0.850681
$970$	89.7462	2.88158
$971$	−14.9924	−0.481130	−0.240565	−	0.970633i	$-0.577333\pi$
$971$	−14.9924	−0.481130	−0.240565	+	0.970633i	$0.577333\pi$
$972$	−57.4482	−1.84265
$973$	89.9724	2.88438
$974$	23.8867	0.765378
$975$	−32.9064	−1.05385
$976$	44.1912	1.41453
$977$	−59.3106	−1.89752	−0.948758	−	0.316004i	$-0.897659\pi$
$977$	−59.3106	−1.89752	−0.948758	+	0.316004i	$0.897659\pi$
$978$	14.0001	0.447675
$979$	2.44827	0.0782472
$980$	137.355	4.38766
$981$	−7.71856	−0.246435
$982$	−44.9433	−1.43420
$983$	−45.6721	−1.45671	−0.728356	−	0.685199i	$-0.759715\pi$
$983$	−45.6721	−1.45671	−0.728356	+	0.685199i	$0.759715\pi$
$984$	−51.8987	−1.65447
$985$	49.8077	1.58700
$986$	−19.6327	−0.625232
$987$	−18.5874	−0.591642
$988$	−64.5030	−2.05211
$989$	−30.1676	−0.959275
$990$	−13.8539	−0.440305
$991$	−0.0374493	−0.00118962	−0.000594809	−	1.00000i	$-0.500189\pi$
$991$	−0.0374493	−0.00118962	−0.000594809		1.00000i	$0.500189\pi$
$992$	−9.76987	−0.310194
$993$	−13.9868	−0.443858
$994$	86.8432	2.75450
$995$	−14.0780	−0.446302
$996$	−16.8461	−0.533789
$997$	−45.0415	−1.42648	−0.713240	−	0.700920i	$-0.752773\pi$
$997$	−45.0415	−1.42648	−0.713240	+	0.700920i	$0.752773\pi$
$998$	−11.5350	−0.365133
$999$	27.0704	0.856468

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.d.1.8	✓	107

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.d.1.8	✓	107	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41316 q^{2} -1.13111 q^{3} +3.82334 q^{4} +3.33661 q^{5} +2.72954 q^{6} -4.21510 q^{7} -4.40000 q^{8} -1.72060 q^{9} +O(q^{10})\)	\(q-2.41316 q^{2} -1.13111 q^{3} +3.82334 q^{4} +3.33661 q^{5} +2.72954 q^{6} -4.21510 q^{7} -4.40000 q^{8} -1.72060 q^{9} -8.05177 q^{10} -1.00000 q^{11} -4.32460 q^{12} +4.74360 q^{13} +10.1717 q^{14} -3.77406 q^{15} +2.97123 q^{16} +6.58257 q^{17} +4.15208 q^{18} -3.55656 q^{19} +12.7570 q^{20} +4.76773 q^{21} +2.41316 q^{22} -6.52486 q^{23} +4.97687 q^{24} +6.13295 q^{25} -11.4471 q^{26} +5.33950 q^{27} -16.1158 q^{28} +1.23594 q^{29} +9.10740 q^{30} -5.99394 q^{31} +1.62996 q^{32} +1.13111 q^{33} -15.8848 q^{34} -14.0641 q^{35} -6.57843 q^{36} +5.06983 q^{37} +8.58254 q^{38} -5.36551 q^{39} -14.6811 q^{40} -10.4280 q^{41} -11.5053 q^{42} +4.62349 q^{43} -3.82334 q^{44} -5.74097 q^{45} +15.7455 q^{46} -3.89858 q^{47} -3.36077 q^{48} +10.7671 q^{49} -14.7998 q^{50} -7.44559 q^{51} +18.1364 q^{52} -7.39583 q^{53} -12.8851 q^{54} -3.33661 q^{55} +18.5464 q^{56} +4.02284 q^{57} -2.98252 q^{58} +12.0064 q^{59} -14.4295 q^{60} +14.8730 q^{61} +14.4643 q^{62} +7.25250 q^{63} -9.87580 q^{64} +15.8275 q^{65} -2.72954 q^{66} -2.93758 q^{67} +25.1674 q^{68} +7.38031 q^{69} +33.9390 q^{70} +8.53772 q^{71} +7.57064 q^{72} -11.9826 q^{73} -12.2343 q^{74} -6.93702 q^{75} -13.5979 q^{76} +4.21510 q^{77} +12.9478 q^{78} +10.6453 q^{79} +9.91382 q^{80} -0.877740 q^{81} +25.1644 q^{82} +3.89542 q^{83} +18.2286 q^{84} +21.9635 q^{85} -11.1572 q^{86} -1.39798 q^{87} +4.40000 q^{88} -2.44827 q^{89} +13.8539 q^{90} -19.9948 q^{91} -24.9467 q^{92} +6.77978 q^{93} +9.40789 q^{94} -11.8668 q^{95} -1.84366 q^{96} -11.1462 q^{97} -25.9827 q^{98} +1.72060 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9 - 14 * q^10 - 107 * q^11 - 50 * q^12 - 24 * q^13 - 17 * q^14 - 47 * q^15 + 63 * q^16 + 25 * q^17 - 37 * q^18 - 55 * q^19 - 31 * q^20 + 15 * q^21 + 3 * q^22 - 38 * q^23 + 4 * q^24 + 62 * q^25 - 16 * q^26 - 57 * q^27 - 101 * q^28 + 27 * q^29 - 14 * q^30 - 112 * q^31 - 4 * q^32 + 18 * q^33 - 66 * q^34 + 8 * q^35 + 35 * q^36 - 60 * q^37 - 45 * q^38 - 58 * q^39 - 50 * q^40 - 14 * q^41 - 36 * q^42 - 78 * q^43 - 91 * q^44 - 68 * q^45 - 18 * q^46 - 109 * q^47 - 99 * q^48 + 61 * q^49 - 32 * q^50 - 10 * q^51 - 111 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 44 * q^56 + q^57 - 98 * q^58 - 48 * q^59 - 119 * q^60 - 30 * q^61 + 32 * q^62 - 126 * q^63 + 3 * q^64 + 43 * q^65 - 77 * q^67 + 53 * q^68 - 51 * q^69 - 87 * q^70 - 40 * q^71 - 82 * q^72 - 83 * q^73 + 11 * q^74 - 69 * q^75 - 108 * q^76 + 54 * q^77 - 53 * q^78 - 66 * q^79 - 96 * q^80 + 51 * q^81 - 133 * q^82 - 32 * q^83 + 27 * q^84 - 66 * q^85 - 46 * q^86 - 136 * q^87 + 3 * q^88 - 56 * q^89 + 9 * q^90 - 86 * q^91 - 94 * q^92 - 33 * q^93 - 93 * q^94 - 25 * q^95 - 4 * q^96 - 109 * q^97 - 38 * q^98 - 95 * q^99

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