LMFDB - Embedded newform 1511.2.a.b.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1511,2,Mod(1,1511)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1511, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1511.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1511 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1511.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:	$12.0653957454$
Analytic rank:	$0$
Dimension:	$87$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	1511.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48500 q^{2} -2.64034 q^{3} +4.17524 q^{4} -4.22842 q^{5} +6.56126 q^{6} +2.88857 q^{7} -5.40548 q^{8} +3.97140 q^{9} +O(q^{10})$	\(q-2.48500 q^{2} -2.64034 q^{3} +4.17524 q^{4} -4.22842 q^{5} +6.56126 q^{6} +2.88857 q^{7} -5.40548 q^{8} +3.97140 q^{9} +10.5076 q^{10} +1.59138 q^{11} -11.0241 q^{12} -6.02570 q^{13} -7.17811 q^{14} +11.1645 q^{15} +5.08215 q^{16} +5.67096 q^{17} -9.86895 q^{18} +5.97967 q^{19} -17.6547 q^{20} -7.62681 q^{21} -3.95459 q^{22} -5.09149 q^{23} +14.2723 q^{24} +12.8795 q^{25} +14.9739 q^{26} -2.56484 q^{27} +12.0605 q^{28} -2.66200 q^{29} -27.7437 q^{30} +5.66587 q^{31} -1.81820 q^{32} -4.20179 q^{33} -14.0923 q^{34} -12.2141 q^{35} +16.5816 q^{36} -11.2611 q^{37} -14.8595 q^{38} +15.9099 q^{39} +22.8566 q^{40} -10.7330 q^{41} +18.9527 q^{42} -0.102427 q^{43} +6.64441 q^{44} -16.7927 q^{45} +12.6524 q^{46} -9.71941 q^{47} -13.4186 q^{48} +1.34384 q^{49} -32.0056 q^{50} -14.9733 q^{51} -25.1588 q^{52} -0.219549 q^{53} +6.37364 q^{54} -6.72903 q^{55} -15.6141 q^{56} -15.7884 q^{57} +6.61509 q^{58} +1.31817 q^{59} +46.6143 q^{60} -0.500960 q^{61} -14.0797 q^{62} +11.4717 q^{63} -5.64606 q^{64} +25.4792 q^{65} +10.4415 q^{66} +1.78769 q^{67} +23.6776 q^{68} +13.4433 q^{69} +30.3520 q^{70} +4.17022 q^{71} -21.4673 q^{72} -6.83316 q^{73} +27.9839 q^{74} -34.0063 q^{75} +24.9666 q^{76} +4.59682 q^{77} -39.5362 q^{78} +10.6082 q^{79} -21.4894 q^{80} -5.14216 q^{81} +26.6716 q^{82} +10.6460 q^{83} -31.8438 q^{84} -23.9792 q^{85} +0.254531 q^{86} +7.02860 q^{87} -8.60219 q^{88} -9.20307 q^{89} +41.7300 q^{90} -17.4057 q^{91} -21.2582 q^{92} -14.9598 q^{93} +24.1528 q^{94} -25.2845 q^{95} +4.80068 q^{96} -7.02174 q^{97} -3.33944 q^{98} +6.32002 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9}+O(q^{10}) $ 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9	\( 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9} + 25 q^{10} + 17 q^{11} + 34 q^{13} + 12 q^{14} + 16 q^{15} + 152 q^{16} + 32 q^{17} + 14 q^{18} + 56 q^{19} + 3 q^{20} + 38 q^{21} + 32 q^{22} + 8 q^{23} + 8 q^{24} + 179 q^{25} + 11 q^{26} - 2 q^{27} + 45 q^{28} + 40 q^{29} + 24 q^{30} + 31 q^{31} + 26 q^{32} + 31 q^{33} + 31 q^{34} + 22 q^{35} + 180 q^{36} + 35 q^{37} - 15 q^{38} + 59 q^{39} + 42 q^{40} + 45 q^{41} - 30 q^{42} + 82 q^{43} + 25 q^{44} + 20 q^{45} + 69 q^{46} - 7 q^{47} - 39 q^{48} + 222 q^{49} + 17 q^{50} + 53 q^{51} + 54 q^{52} + 16 q^{53} - 7 q^{54} + 49 q^{55} + 12 q^{56} + 52 q^{57} + 17 q^{58} - 7 q^{59} - 6 q^{60} + 131 q^{61} - 8 q^{62} + 19 q^{63} + 213 q^{64} + 57 q^{65} + 17 q^{66} + 38 q^{67} + 13 q^{68} + 45 q^{69} - 5 q^{71} + 4 q^{72} + 91 q^{73} + q^{74} - 44 q^{75} + 150 q^{76} + 5 q^{77} - 87 q^{78} + 120 q^{79} - 41 q^{80} + 247 q^{81} + 20 q^{82} - 33 q^{83} - 16 q^{84} + 110 q^{85} - 22 q^{86} - 13 q^{87} + 78 q^{88} + 53 q^{89} - 33 q^{90} + 32 q^{91} - 31 q^{92} + 13 q^{93} + 79 q^{94} - 25 q^{95} - 51 q^{96} + 92 q^{97} - 36 q^{98} + 35 q^{99}+O(q^{100}) \) 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9 + 25 * q^10 + 17 * q^11 + 34 * q^13 + 12 * q^14 + 16 * q^15 + 152 * q^16 + 32 * q^17 + 14 * q^18 + 56 * q^19 + 3 * q^20 + 38 * q^21 + 32 * q^22 + 8 * q^23 + 8 * q^24 + 179 * q^25 + 11 * q^26 - 2 * q^27 + 45 * q^28 + 40 * q^29 + 24 * q^30 + 31 * q^31 + 26 * q^32 + 31 * q^33 + 31 * q^34 + 22 * q^35 + 180 * q^36 + 35 * q^37 - 15 * q^38 + 59 * q^39 + 42 * q^40 + 45 * q^41 - 30 * q^42 + 82 * q^43 + 25 * q^44 + 20 * q^45 + 69 * q^46 - 7 * q^47 - 39 * q^48 + 222 * q^49 + 17 * q^50 + 53 * q^51 + 54 * q^52 + 16 * q^53 - 7 * q^54 + 49 * q^55 + 12 * q^56 + 52 * q^57 + 17 * q^58 - 7 * q^59 - 6 * q^60 + 131 * q^61 - 8 * q^62 + 19 * q^63 + 213 * q^64 + 57 * q^65 + 17 * q^66 + 38 * q^67 + 13 * q^68 + 45 * q^69 - 5 * q^71 + 4 * q^72 + 91 * q^73 + q^74 - 44 * q^75 + 150 * q^76 + 5 * q^77 - 87 * q^78 + 120 * q^79 - 41 * q^80 + 247 * q^81 + 20 * q^82 - 33 * q^83 - 16 * q^84 + 110 * q^85 - 22 * q^86 - 13 * q^87 + 78 * q^88 + 53 * q^89 - 33 * q^90 + 32 * q^91 - 31 * q^92 + 13 * q^93 + 79 * q^94 - 25 * q^95 - 51 * q^96 + 92 * q^97 - 36 * q^98 + 35 * 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 $

$2$	−2.48500	−1.75716	−0.878581	−	0.477593i	$-0.841509\pi$
$2$	−2.48500	−1.75716	−0.878581	+	0.477593i	$0.841509\pi$
$3$	−2.64034	−1.52440	−0.762201	−	0.647340i	$-0.775881\pi$
$3$	−2.64034	−1.52440	−0.762201	+	0.647340i	$0.775881\pi$
$4$	4.17524	2.08762
$5$	−4.22842	−1.89100	−0.945502	−	0.325615i	$-0.894429\pi$
$5$	−4.22842	−1.89100	−0.945502	+	0.325615i	$0.894429\pi$
$6$	6.56126	2.67862
$7$	2.88857	1.09178	0.545888	−	0.837858i	$-0.316192\pi$
$7$	2.88857	1.09178	0.545888	+	0.837858i	$0.316192\pi$
$8$	−5.40548	−1.91113
$9$	3.97140	1.32380
$10$	10.5076	3.32280
$11$	1.59138	0.479820	0.239910	−	0.970795i	$-0.422882\pi$
$11$	1.59138	0.479820	0.239910	+	0.970795i	$0.422882\pi$
$12$	−11.0241	−3.18237
$13$	−6.02570	−1.67123	−0.835614	−	0.549316i	$-0.814888\pi$
$13$	−6.02570	−1.67123	−0.835614	+	0.549316i	$0.814888\pi$
$14$	−7.17811	−1.91843
$15$	11.1645	2.88265
$16$	5.08215	1.27054
$17$	5.67096	1.37541	0.687704	−	0.725991i	$-0.258619\pi$
$17$	5.67096	1.37541	0.687704	+	0.725991i	$0.258619\pi$
$18$	−9.86895	−2.32613
$19$	5.97967	1.37183	0.685915	−	0.727681i	$-0.259402\pi$
$19$	5.97967	1.37183	0.685915	+	0.727681i	$0.259402\pi$
$20$	−17.6547	−3.94770
$21$	−7.62681	−1.66431
$22$	−3.95459	−0.843122
$23$	−5.09149	−1.06165	−0.530824	−	0.847482i	$-0.678118\pi$
$23$	−5.09149	−1.06165	−0.530824	+	0.847482i	$0.678118\pi$
$24$	14.2723	2.91332
$25$	12.8795	2.57590
$26$	14.9739	2.93662
$27$	−2.56484	−0.493604
$28$	12.0605	2.27922
$29$	−2.66200	−0.494322	−0.247161	−	0.968974i	$-0.579498\pi$
$29$	−2.66200	−0.494322	−0.247161	+	0.968974i	$0.579498\pi$
$30$	−27.7437	−5.06529
$31$	5.66587	1.01762	0.508810	−	0.860879i	$-0.330086\pi$
$31$	5.66587	1.01762	0.508810	+	0.860879i	$0.330086\pi$
$32$	−1.81820	−0.321416
$33$	−4.20179	−0.731438
$34$	−14.0923	−2.41682
$35$	−12.2141	−2.06456
$36$	16.5816	2.76360
$37$	−11.2611	−1.85132	−0.925658	−	0.378360i	$-0.876488\pi$
$37$	−11.2611	−1.85132	−0.925658	+	0.378360i	$0.876488\pi$
$38$	−14.8595	−2.41053
$39$	15.9099	2.54762
$40$	22.8566	3.61395
$41$	−10.7330	−1.67621	−0.838107	−	0.545506i	$-0.816338\pi$
$41$	−10.7330	−1.67621	−0.838107	+	0.545506i	$0.816338\pi$
$42$	18.9527	2.92446
$43$	−0.102427	−0.0156199	−0.00780997	−	0.999970i	$-0.502486\pi$
$43$	−0.102427	−0.0156199	−0.00780997	+	0.999970i	$0.502486\pi$
$44$	6.64441	1.00168
$45$	−16.7927	−2.50332
$46$	12.6524	1.86549
$47$	−9.71941	−1.41772	−0.708861	−	0.705348i	$-0.750791\pi$
$47$	−9.71941	−1.41772	−0.708861	+	0.705348i	$0.750791\pi$
$48$	−13.4186	−1.93681
$49$	1.34384	0.191977
$50$	−32.0056	−4.52627
$51$	−14.9733	−2.09668
$52$	−25.1588	−3.48889
$53$	−0.219549	−0.0301574	−0.0150787	−	0.999886i	$-0.504800\pi$
$53$	−0.219549	−0.0301574	−0.0150787	+	0.999886i	$0.504800\pi$
$54$	6.37364	0.867342
$55$	−6.72903	−0.907342
$56$	−15.6141	−2.08652
$57$	−15.7884	−2.09122
$58$	6.61509	0.868604
$59$	1.31817	0.171611	0.0858055	−	0.996312i	$-0.472654\pi$
$59$	1.31817	0.171611	0.0858055	+	0.996312i	$0.472654\pi$
$60$	46.6143	6.01788
$61$	−0.500960	−0.0641414	−0.0320707	−	0.999486i	$-0.510210\pi$
$61$	−0.500960	−0.0641414	−0.0320707	+	0.999486i	$0.510210\pi$
$62$	−14.0797	−1.78812
$63$	11.4717	1.44530
$64$	−5.64606	−0.705757
$65$	25.4792	3.16030
$66$	10.4415	1.28526
$67$	1.78769	0.218401	0.109201	−	0.994020i	$-0.465171\pi$
$67$	1.78769	0.218401	0.109201	+	0.994020i	$0.465171\pi$
$68$	23.6776	2.87133
$69$	13.4433	1.61838
$70$	30.3520	3.62776
$71$	4.17022	0.494914	0.247457	−	0.968899i	$-0.420405\pi$
$71$	4.17022	0.494914	0.247457	+	0.968899i	$0.420405\pi$
$72$	−21.4673	−2.52995
$73$	−6.83316	−0.799761	−0.399881	−	0.916567i	$-0.630948\pi$
$73$	−6.83316	−0.799761	−0.399881	+	0.916567i	$0.630948\pi$
$74$	27.9839	3.25306
$75$	−34.0063	−3.92671
$76$	24.9666	2.86386
$77$	4.59682	0.523856
$78$	−39.5362	−4.47659
$79$	10.6082	1.19351	0.596755	−	0.802423i	$-0.296456\pi$
$79$	10.6082	1.19351	0.596755	+	0.802423i	$0.296456\pi$
$80$	−21.4894	−2.40259
$81$	−5.14216	−0.571351
$82$	26.6716	2.94538
$83$	10.6460	1.16856	0.584278	−	0.811554i	$-0.301378\pi$
$83$	10.6460	1.16856	0.584278	+	0.811554i	$0.301378\pi$
$84$	−31.8438	−3.47444
$85$	−23.9792	−2.60090
$86$	0.254531	0.0274468
$87$	7.02860	0.753545
$88$	−8.60219	−0.916996
$89$	−9.20307	−0.975523	−0.487762	−	0.872977i	$-0.662186\pi$
$89$	−9.20307	−0.975523	−0.487762	+	0.872977i	$0.662186\pi$
$90$	41.7300	4.39873
$91$	−17.4057	−1.82461
$92$	−21.2582	−2.21632
$93$	−14.9598	−1.55126
$94$	24.1528	2.49117
$95$	−25.2845	−2.59414
$96$	4.80068	0.489968
$97$	−7.02174	−0.712950	−0.356475	−	0.934305i	$-0.616021\pi$
$97$	−7.02174	−0.712950	−0.356475	+	0.934305i	$0.616021\pi$
$98$	−3.33944	−0.337334
$99$	6.32002	0.635186
$100$	53.7750	5.37750
$101$	−3.99479	−0.397496	−0.198748	−	0.980051i	$-0.563688\pi$
$101$	−3.99479	−0.397496	−0.198748	+	0.980051i	$0.563688\pi$
$102$	37.2086	3.68420
$103$	11.5120	1.13431	0.567155	−	0.823611i	$-0.308044\pi$
$103$	11.5120	1.13431	0.567155	+	0.823611i	$0.308044\pi$
$104$	32.5718	3.19393
$105$	32.2493	3.14721
$106$	0.545581	0.0529915
$107$	−9.67180	−0.935008	−0.467504	−	0.883991i	$-0.654847\pi$
$107$	−9.67180	−0.935008	−0.467504	+	0.883991i	$0.654847\pi$
$108$	−10.7088	−1.03046
$109$	4.06714	0.389561	0.194780	−	0.980847i	$-0.437601\pi$
$109$	4.06714	0.389561	0.194780	+	0.980847i	$0.437601\pi$
$110$	16.7217	1.59435
$111$	29.7332	2.82215
$112$	14.6802	1.38714
$113$	13.8775	1.30549	0.652743	−	0.757579i	$-0.273618\pi$
$113$	13.8775	1.30549	0.652743	+	0.757579i	$0.273618\pi$
$114$	39.2342	3.67462
$115$	21.5289	2.00758
$116$	−11.1145	−1.03196
$117$	−23.9305	−2.21238
$118$	−3.27565	−0.301548
$119$	16.3810	1.50164
$120$	−60.3493	−5.50911
$121$	−8.46750	−0.769773
$122$	1.24489	0.112707
$123$	28.3388	2.55522
$124$	23.6564	2.12440
$125$	−33.3178	−2.98003
$126$	−28.5072	−2.53962
$127$	0.801792	0.0711475	0.0355738	−	0.999367i	$-0.488674\pi$
$127$	0.801792	0.0711475	0.0355738	+	0.999367i	$0.488674\pi$
$128$	17.6669	1.56155
$129$	0.270442	0.0238111
$130$	−63.3158	−5.55316
$131$	−8.01172	−0.699988	−0.349994	−	0.936752i	$-0.613816\pi$
$131$	−8.01172	−0.699988	−0.349994	+	0.936752i	$0.613816\pi$
$132$	−17.5435	−1.52697
$133$	17.2727	1.49773
$134$	−4.44242	−0.383767
$135$	10.8452	0.933407
$136$	−30.6542	−2.62858
$137$	21.9998	1.87957	0.939785	−	0.341766i	$-0.111025\pi$
$137$	21.9998	1.87957	0.939785	+	0.341766i	$0.111025\pi$
$138$	−33.4066	−2.84376
$139$	8.20860	0.696244	0.348122	−	0.937449i	$-0.386819\pi$
$139$	8.20860	0.696244	0.348122	+	0.937449i	$0.386819\pi$
$140$	−50.9967	−4.31001
$141$	25.6626	2.16118
$142$	−10.3630	−0.869643
$143$	−9.58920	−0.801889
$144$	20.1833	1.68194
$145$	11.2561	0.934765
$146$	16.9804	1.40531
$147$	−3.54819	−0.292650
$148$	−47.0179	−3.86485
$149$	15.3978	1.26143	0.630717	−	0.776013i	$-0.282761\pi$
$149$	15.3978	1.26143	0.630717	+	0.776013i	$0.282761\pi$
$150$	84.5057	6.89986
$151$	8.99696	0.732162	0.366081	−	0.930583i	$-0.380699\pi$
$151$	8.99696	0.732162	0.366081	+	0.930583i	$0.380699\pi$
$152$	−32.3230	−2.62174
$153$	22.5217	1.82077
$154$	−11.4231	−0.920501
$155$	−23.9576	−1.92432
$156$	66.4277	5.31847
$157$	−14.2118	−1.13423	−0.567114	−	0.823639i	$-0.691940\pi$
$157$	−14.2118	−1.13423	−0.567114	+	0.823639i	$0.691940\pi$
$158$	−26.3613	−2.09719
$159$	0.579685	0.0459720
$160$	7.68813	0.607800
$161$	−14.7071	−1.15908
$162$	12.7783	1.00396
$163$	11.3089	0.885780	0.442890	−	0.896576i	$-0.353953\pi$
$163$	11.3089	0.885780	0.442890	+	0.896576i	$0.353953\pi$
$164$	−44.8129	−3.49930
$165$	17.7669	1.38315
$166$	−26.4554	−2.05334
$167$	−11.2444	−0.870121	−0.435060	−	0.900401i	$-0.643273\pi$
$167$	−11.2444	−0.870121	−0.435060	+	0.900401i	$0.643273\pi$
$168$	41.2266	3.18070
$169$	23.3091	1.79301
$170$	59.5883	4.57021
$171$	23.7477	1.81603
$172$	−0.427656	−0.0326085
$173$	2.67782	0.203591	0.101796	−	0.994805i	$-0.467541\pi$
$173$	2.67782	0.203591	0.101796	+	0.994805i	$0.467541\pi$
$174$	−17.4661	−1.32410
$175$	37.2033	2.81231
$176$	8.08765	0.609629
$177$	−3.48042	−0.261604
$178$	22.8697	1.71415
$179$	−9.80805	−0.733088	−0.366544	−	0.930401i	$-0.619459\pi$
$179$	−9.80805	−0.733088	−0.366544	+	0.930401i	$0.619459\pi$
$180$	−70.1138	−5.22597
$181$	2.72410	0.202481	0.101240	−	0.994862i	$-0.467719\pi$
$181$	2.72410	0.202481	0.101240	+	0.994862i	$0.467719\pi$
$182$	43.2531	3.20613
$183$	1.32271	0.0977772
$184$	27.5219	2.02894
$185$	47.6167	3.50085
$186$	37.1752	2.72582
$187$	9.02466	0.659949
$188$	−40.5809	−2.95966
$189$	−7.40872	−0.538905
$190$	62.8321	4.55832
$191$	7.47097	0.540581	0.270290	−	0.962779i	$-0.412880\pi$
$191$	7.47097	0.540581	0.270290	+	0.962779i	$0.412880\pi$
$192$	14.9075	1.07586
$193$	−15.9999	−1.15170	−0.575848	−	0.817557i	$-0.695328\pi$
$193$	−15.9999	−1.15170	−0.575848	+	0.817557i	$0.695328\pi$
$194$	17.4490	1.25277
$195$	−67.2737	−4.81757
$196$	5.61084	0.400774
$197$	3.21006	0.228708	0.114354	−	0.993440i	$-0.463520\pi$
$197$	3.21006	0.228708	0.114354	+	0.993440i	$0.463520\pi$
$198$	−15.7053	−1.11613
$199$	−7.00887	−0.496846	−0.248423	−	0.968652i	$-0.579912\pi$
$199$	−7.00887	−0.496846	−0.248423	+	0.968652i	$0.579912\pi$
$200$	−69.6198	−4.92287
$201$	−4.72012	−0.332931
$202$	9.92706	0.698465
$203$	−7.68938	−0.539689
$204$	−62.5170	−4.37706
$205$	45.3836	3.16973
$206$	−28.6073	−1.99317
$207$	−20.2204	−1.40541
$208$	−30.6235	−2.12336
$209$	9.51594	0.658232
$210$	−80.1397	−5.53016
$211$	16.6407	1.14559	0.572797	−	0.819697i	$-0.305858\pi$
$211$	16.6407	1.14559	0.572797	+	0.819697i	$0.305858\pi$
$212$	−0.916672	−0.0629573
$213$	−11.0108	−0.754447
$214$	24.0345	1.64296
$215$	0.433103	0.0295374
$216$	13.8642	0.943339
$217$	16.3663	1.11101
$218$	−10.1068	−0.684522
$219$	18.0419	1.21916
$220$	−28.0953	−1.89419
$221$	−34.1715	−2.29862
$222$	−73.8871	−4.95898
$223$	−18.6540	−1.24917	−0.624584	−	0.780958i	$-0.714731\pi$
$223$	−18.6540	−1.24917	−0.624584	+	0.780958i	$0.714731\pi$
$224$	−5.25201	−0.350915
$225$	51.1497	3.40998
$226$	−34.4857	−2.29395
$227$	−11.1076	−0.737239	−0.368619	−	0.929580i	$-0.620169\pi$
$227$	−11.1076	−0.737239	−0.368619	+	0.929580i	$0.620169\pi$
$228$	−65.9203	−4.36568
$229$	0.595508	0.0393523	0.0196761	−	0.999806i	$-0.493736\pi$
$229$	0.595508	0.0393523	0.0196761	+	0.999806i	$0.493736\pi$
$230$	−53.4995	−3.52765
$231$	−12.1372	−0.798568
$232$	14.3894	0.944711
$233$	26.4680	1.73397	0.866987	−	0.498331i	$-0.166054\pi$
$233$	26.4680	1.73397	0.866987	+	0.498331i	$0.166054\pi$
$234$	59.4674	3.88750
$235$	41.0977	2.68092
$236$	5.50367	0.358258
$237$	−28.0092	−1.81939
$238$	−40.7067	−2.63862
$239$	12.7811	0.826740	0.413370	−	0.910563i	$-0.364352\pi$
$239$	12.7811	0.826740	0.413370	+	0.910563i	$0.364352\pi$
$240$	56.7395	3.66252
$241$	−9.63913	−0.620911	−0.310455	−	0.950588i	$-0.600482\pi$
$241$	−9.63913	−0.620911	−0.310455	+	0.950588i	$0.600482\pi$
$242$	21.0418	1.35262
$243$	21.2716	1.36457
$244$	−2.09163	−0.133903
$245$	−5.68230	−0.363029
$246$	−70.4220	−4.48994
$247$	−36.0317	−2.29264
$248$	−30.6267	−1.94480
$249$	−28.1092	−1.78135
$250$	82.7948	5.23640
$251$	7.07503	0.446572	0.223286	−	0.974753i	$-0.428322\pi$
$251$	7.07503	0.446572	0.223286	+	0.974753i	$0.428322\pi$
$252$	47.8970	3.01723
$253$	−8.10251	−0.509400
$254$	−1.99246	−0.125018
$255$	63.3132	3.96482
$256$	−32.6101	−2.03813
$257$	10.0795	0.628741	0.314371	−	0.949300i	$-0.398207\pi$
$257$	10.0795	0.628741	0.314371	+	0.949300i	$0.398207\pi$
$258$	−0.672048	−0.0418399
$259$	−32.5285	−2.02122
$260$	106.382	6.59751
$261$	−10.5719	−0.654384
$262$	19.9092	1.22999
$263$	14.1876	0.874843	0.437421	−	0.899257i	$-0.355892\pi$
$263$	14.1876	0.874843	0.437421	+	0.899257i	$0.355892\pi$
$264$	22.7127	1.39787
$265$	0.928346	0.0570278
$266$	−42.9227	−2.63176
$267$	24.2992	1.48709
$268$	7.46404	0.455939
$269$	−12.0118	−0.732375	−0.366187	−	0.930541i	$-0.619337\pi$
$269$	−12.0118	−0.732375	−0.366187	+	0.930541i	$0.619337\pi$
$270$	−26.9504	−1.64015
$271$	−6.41236	−0.389523	−0.194762	−	0.980851i	$-0.562393\pi$
$271$	−6.41236	−0.389523	−0.194762	+	0.980851i	$0.562393\pi$
$272$	28.8207	1.74751
$273$	45.9569	2.78144
$274$	−54.6696	−3.30271
$275$	20.4962	1.23597
$276$	56.1289	3.37856
$277$	−0.730948	−0.0439184	−0.0219592	−	0.999759i	$-0.506990\pi$
$277$	−0.730948	−0.0439184	−0.0219592	+	0.999759i	$0.506990\pi$
$278$	−20.3984	−1.22341
$279$	22.5014	1.34713
$280$	66.0229	3.94562
$281$	28.5003	1.70018	0.850092	−	0.526634i	$-0.176546\pi$
$281$	28.5003	1.70018	0.850092	+	0.526634i	$0.176546\pi$
$282$	−63.7716	−3.79754
$283$	−22.6576	−1.34686	−0.673428	−	0.739253i	$-0.735179\pi$
$283$	−22.6576	−1.34686	−0.673428	+	0.739253i	$0.735179\pi$
$284$	17.4117	1.03319
$285$	66.7598	3.95451
$286$	23.8292	1.40905
$287$	−31.0030	−1.83005
$288$	−7.22083	−0.425491
$289$	15.1597	0.891750
$290$	−27.9713	−1.64253
$291$	18.5398	1.08682
$292$	−28.5301	−1.66960
$293$	3.63495	0.212356	0.106178	−	0.994347i	$-0.466139\pi$
$293$	3.63495	0.212356	0.106178	+	0.994347i	$0.466139\pi$
$294$	8.81726	0.514233
$295$	−5.57376	−0.324517
$296$	60.8718	3.53810
$297$	−4.08164	−0.236841
$298$	−38.2635	−2.21654
$299$	30.6798	1.77426
$300$	−141.984	−8.19747
$301$	−0.295867	−0.0170535
$302$	−22.3575	−1.28653
$303$	10.5476	0.605944
$304$	30.3896	1.74296
$305$	2.11827	0.121292
$306$	−55.9664	−3.19939
$307$	−27.1991	−1.55233	−0.776167	−	0.630528i	$-0.782838\pi$
$307$	−27.1991	−1.55233	−0.776167	+	0.630528i	$0.782838\pi$
$308$	19.1928	1.09361
$309$	−30.3956	−1.72914
$310$	59.5348	3.38135
$311$	18.8474	1.06874	0.534370	−	0.845251i	$-0.320549\pi$
$311$	18.8474	1.06874	0.534370	+	0.845251i	$0.320549\pi$
$312$	−86.0007	−4.86883
$313$	7.79240	0.440453	0.220226	−	0.975449i	$-0.429320\pi$
$313$	7.79240	0.440453	0.220226	+	0.975449i	$0.429320\pi$
$314$	35.3165	1.99302
$315$	−48.5070	−2.73306
$316$	44.2916	2.49160
$317$	−17.7039	−0.994352	−0.497176	−	0.867650i	$-0.665630\pi$
$317$	−17.7039	−0.994352	−0.497176	+	0.867650i	$0.665630\pi$
$318$	−1.44052	−0.0807804
$319$	−4.23627	−0.237185
$320$	23.8739	1.33459
$321$	25.5369	1.42533
$322$	36.5472	2.03670
$323$	33.9105	1.88683
$324$	−21.4697	−1.19276
$325$	−77.6080	−4.30492
$326$	−28.1026	−1.55646
$327$	−10.7386	−0.593848
$328$	58.0171	3.20346
$329$	−28.0752	−1.54784
$330$	−44.1509	−2.43043
$331$	−11.7235	−0.644382	−0.322191	−	0.946675i	$-0.604419\pi$
$331$	−11.7235	−0.644382	−0.322191	+	0.946675i	$0.604419\pi$
$332$	44.4498	2.43950
$333$	−44.7225	−2.45078
$334$	27.9425	1.52894
$335$	−7.55910	−0.412998
$336$	−38.7606	−2.11457
$337$	−7.64650	−0.416532	−0.208266	−	0.978072i	$-0.566782\pi$
$337$	−7.64650	−0.416532	−0.208266	+	0.978072i	$0.566782\pi$
$338$	−57.9231	−3.15060
$339$	−36.6414	−1.99009
$340$	−100.119	−5.42970
$341$	9.01656	0.488274
$342$	−59.0131	−3.19106
$343$	−16.3382	−0.882181
$344$	0.553666	0.0298517
$345$	−56.8437	−3.06036
$346$	−6.65439	−0.357742
$347$	5.09403	0.273462	0.136731	−	0.990608i	$-0.456340\pi$
$347$	5.09403	0.273462	0.136731	+	0.990608i	$0.456340\pi$
$348$	29.3461	1.57312
$349$	21.5777	1.15503	0.577513	−	0.816382i	$-0.304023\pi$
$349$	21.5777	1.15503	0.577513	+	0.816382i	$0.304023\pi$
$350$	−92.4504	−4.94168
$351$	15.4550	0.824925
$352$	−2.89346	−0.154222
$353$	23.2910	1.23966	0.619828	−	0.784738i	$-0.287202\pi$
$353$	23.2910	1.23966	0.619828	+	0.784738i	$0.287202\pi$
$354$	8.64884	0.459681
$355$	−17.6334	−0.935884
$356$	−38.4250	−2.03652
$357$	−43.2513	−2.28910
$358$	24.3730	1.28815
$359$	−21.0452	−1.11073	−0.555363	−	0.831608i	$-0.687421\pi$
$359$	−21.0452	−1.11073	−0.555363	+	0.831608i	$0.687421\pi$
$360$	90.7729	4.78415
$361$	16.7565	0.881919
$362$	−6.76940	−0.355792
$363$	22.3571	1.17344
$364$	−72.6728	−3.80909
$365$	28.8934	1.51235
$366$	−3.28693	−0.171811
$367$	10.5653	0.551502	0.275751	−	0.961229i	$-0.411073\pi$
$367$	10.5653	0.551502	0.275751	+	0.961229i	$0.411073\pi$
$368$	−25.8757	−1.34887
$369$	−42.6251	−2.21898
$370$	−118.328	−6.15156
$371$	−0.634184	−0.0329252
$372$	−62.4609	−3.23844
$373$	−23.8634	−1.23560	−0.617801	−	0.786335i	$-0.711976\pi$
$373$	−23.8634	−1.23560	−0.617801	+	0.786335i	$0.711976\pi$
$374$	−22.4263	−1.15964
$375$	87.9703	4.54277
$376$	52.5381	2.70944
$377$	16.0404	0.826125
$378$	18.4107	0.946944
$379$	6.64950	0.341562	0.170781	−	0.985309i	$-0.445371\pi$
$379$	6.64950	0.341562	0.170781	+	0.985309i	$0.445371\pi$
$380$	−105.569	−5.41558
$381$	−2.11700	−0.108457
$382$	−18.5654	−0.949888
$383$	−15.8530	−0.810052	−0.405026	−	0.914305i	$-0.632738\pi$
$383$	−15.8530	−0.810052	−0.405026	+	0.914305i	$0.632738\pi$
$384$	−46.6466	−2.38043
$385$	−19.4373	−0.990615
$386$	39.7598	2.02372
$387$	−0.406778	−0.0206777
$388$	−29.3175	−1.48837
$389$	32.6350	1.65466	0.827329	−	0.561717i	$-0.189859\pi$
$389$	32.6350	1.65466	0.827329	+	0.561717i	$0.189859\pi$
$390$	167.175	8.46525
$391$	−28.8736	−1.46020
$392$	−7.26408	−0.366892
$393$	21.1537	1.06706
$394$	−7.97702	−0.401876
$395$	−44.8557	−2.25693
$396$	26.3876	1.32603
$397$	15.4557	0.775699	0.387849	−	0.921723i	$-0.373218\pi$
$397$	15.4557	0.775699	0.387849	+	0.921723i	$0.373218\pi$
$398$	17.4171	0.873039
$399$	−45.6058	−2.28315
$400$	65.4556	3.27278
$401$	1.56811	0.0783074	0.0391537	−	0.999233i	$-0.487534\pi$
$401$	1.56811	0.0783074	0.0391537	+	0.999233i	$0.487534\pi$
$402$	11.7295	0.585015
$403$	−34.1408	−1.70068
$404$	−16.6792	−0.829821
$405$	21.7432	1.08043
$406$	19.1081	0.948321
$407$	−17.9208	−0.888299
$408$	80.9377	4.00701
$409$	24.8916	1.23081	0.615405	−	0.788211i	$-0.288993\pi$
$409$	24.8916	1.23081	0.615405	+	0.788211i	$0.288993\pi$
$410$	−112.778	−5.56973
$411$	−58.0870	−2.86522
$412$	48.0653	2.36801
$413$	3.80762	0.187361
$414$	50.2477	2.46954
$415$	−45.0159	−2.20974
$416$	10.9560	0.537160
$417$	−21.6735	−1.06136
$418$	−23.6472	−1.15662
$419$	39.4424	1.92689	0.963443	−	0.267915i	$-0.0863346\pi$
$419$	39.4424	1.92689	0.963443	+	0.267915i	$0.0863346\pi$
$420$	134.649	6.57018
$421$	4.73545	0.230792	0.115396	−	0.993320i	$-0.463186\pi$
$421$	4.73545	0.230792	0.115396	+	0.993320i	$0.463186\pi$
$422$	−41.3522	−2.01299
$423$	−38.5997	−1.87678
$424$	1.18677	0.0576346
$425$	73.0391	3.54291
$426$	27.3619	1.32569
$427$	−1.44706	−0.0700281
$428$	−40.3821	−1.95194
$429$	25.3188	1.22240
$430$	−1.07626	−0.0519020
$431$	17.7928	0.857050	0.428525	−	0.903530i	$-0.359033\pi$
$431$	17.7928	0.857050	0.428525	+	0.903530i	$0.359033\pi$
$432$	−13.0349	−0.627142
$433$	−8.38349	−0.402885	−0.201442	−	0.979500i	$-0.564563\pi$
$433$	−8.38349	−0.402885	−0.201442	+	0.979500i	$0.564563\pi$
$434$	−40.6702	−1.95223
$435$	−29.7198	−1.42496
$436$	16.9813	0.813255
$437$	−30.4454	−1.45640
$438$	−44.8341	−2.14226
$439$	−15.8528	−0.756613	−0.378306	−	0.925680i	$-0.623493\pi$
$439$	−15.8528	−0.756613	−0.378306	+	0.925680i	$0.623493\pi$
$440$	36.3736	1.73404
$441$	5.33692	0.254139
$442$	84.9163	4.03905
$443$	3.91930	0.186211	0.0931057	−	0.995656i	$-0.470321\pi$
$443$	3.91930	0.186211	0.0931057	+	0.995656i	$0.470321\pi$
$444$	124.143	5.89158
$445$	38.9144	1.84472
$446$	46.3554	2.19499
$447$	−40.6554	−1.92293
$448$	−16.3090	−0.770530
$449$	4.48970	0.211882	0.105941	−	0.994372i	$-0.466215\pi$
$449$	4.48970	0.211882	0.105941	+	0.994372i	$0.466215\pi$
$450$	−127.107	−5.99189
$451$	−17.0803	−0.804281
$452$	57.9420	2.72536
$453$	−23.7551	−1.11611
$454$	27.6025	1.29545
$455$	73.5984	3.45034
$456$	85.3437	3.99659
$457$	33.8973	1.58565	0.792825	−	0.609449i	$-0.208609\pi$
$457$	33.8973	1.58565	0.792825	+	0.609449i	$0.208609\pi$
$458$	−1.47984	−0.0691484
$459$	−14.5451	−0.678907
$460$	89.8885	4.19107
$461$	−23.2475	−1.08274	−0.541372	−	0.840783i	$-0.682095\pi$
$461$	−23.2475	−1.08274	−0.541372	+	0.840783i	$0.682095\pi$
$462$	30.1609	1.40321
$463$	12.3245	0.572769	0.286385	−	0.958115i	$-0.407546\pi$
$463$	12.3245	0.572769	0.286385	+	0.958115i	$0.407546\pi$
$464$	−13.5287	−0.628055
$465$	63.2563	2.93344
$466$	−65.7730	−3.04687
$467$	20.9835	0.971001	0.485500	−	0.874236i	$-0.338637\pi$
$467$	20.9835	0.971001	0.485500	+	0.874236i	$0.338637\pi$
$468$	−99.9156	−4.61860
$469$	5.16387	0.238445
$470$	−102.128	−4.71081
$471$	37.5241	1.72902
$472$	−7.12533	−0.327970
$473$	−0.163000	−0.00749476
$474$	69.6028	3.19696
$475$	77.0151	3.53370
$476$	68.3944	3.13485
$477$	−0.871920	−0.0399225
$478$	−31.7610	−1.45272
$479$	−17.5830	−0.803387	−0.401693	−	0.915774i	$-0.631578\pi$
$479$	−17.5830	−0.803387	−0.401693	+	0.915774i	$0.631578\pi$
$480$	−20.2993	−0.926531
$481$	67.8562	3.09397
$482$	23.9533	1.09104
$483$	38.8318	1.76691
$484$	−35.3539	−1.60699
$485$	29.6908	1.34819
$486$	−52.8599	−2.39778
$487$	24.2894	1.10066	0.550328	−	0.834949i	$-0.314503\pi$
$487$	24.2894	1.10066	0.550328	+	0.834949i	$0.314503\pi$
$488$	2.70793	0.122582
$489$	−29.8593	−1.35028
$490$	14.1205	0.637901
$491$	−7.07150	−0.319133	−0.159566	−	0.987187i	$-0.551010\pi$
$491$	−7.07150	−0.319133	−0.159566	+	0.987187i	$0.551010\pi$
$492$	118.321	5.33434
$493$	−15.0961	−0.679894
$494$	89.5389	4.02855
$495$	−26.7237	−1.20114
$496$	28.7948	1.29292
$497$	12.0460	0.540335
$498$	69.8514	3.13012
$499$	−12.9564	−0.580010	−0.290005	−	0.957025i	$-0.593657\pi$
$499$	−12.9564	−0.580010	−0.290005	+	0.957025i	$0.593657\pi$
$500$	−139.110	−6.22118
$501$	29.6892	1.32641
$502$	−17.5815	−0.784700
$503$	−13.3566	−0.595543	−0.297771	−	0.954637i	$-0.596243\pi$
$503$	−13.3566	−0.595543	−0.297771	+	0.954637i	$0.596243\pi$
$504$	−62.0099	−2.76214
$505$	16.8916	0.751667
$506$	20.1348	0.895099
$507$	−61.5439	−2.73326
$508$	3.34767	0.148529
$509$	−1.13040	−0.0501041	−0.0250520	−	0.999686i	$-0.507975\pi$
$509$	−1.13040	−0.0501041	−0.0250520	+	0.999686i	$0.507975\pi$
$510$	−157.333	−6.96684
$511$	−19.7381	−0.873161
$512$	45.7025	2.01979
$513$	−15.3369	−0.677141
$514$	−25.0476	−1.10480
$515$	−48.6775	−2.14498
$516$	1.12916	0.0497085
$517$	−15.4673	−0.680251
$518$	80.8335	3.55162
$519$	−7.07036	−0.310355
$520$	−137.727	−6.03973
$521$	16.7298	0.732948	0.366474	−	0.930428i	$-0.380565\pi$
$521$	16.7298	0.732948	0.366474	+	0.930428i	$0.380565\pi$
$522$	26.2712	1.14986
$523$	14.9766	0.654881	0.327440	−	0.944872i	$-0.393814\pi$
$523$	14.9766	0.654881	0.327440	+	0.944872i	$0.393814\pi$
$524$	−33.4509	−1.46131
$525$	−98.2295	−4.28709
$526$	−35.2561	−1.53724
$527$	32.1309	1.39964
$528$	−21.3542	−0.929320
$529$	2.92326	0.127098
$530$	−2.30694	−0.100207
$531$	5.23498	0.227179
$532$	72.1177	3.12670
$533$	64.6739	2.80134
$534$	−60.3837	−2.61306
$535$	40.8964	1.76811
$536$	−9.66333	−0.417392
$537$	25.8966	1.11752
$538$	29.8495	1.28690
$539$	2.13856	0.0921142
$540$	45.2814	1.94860
$541$	−5.45639	−0.234589	−0.117294	−	0.993097i	$-0.537422\pi$
$541$	−5.45639	−0.234589	−0.117294	+	0.993097i	$0.537422\pi$
$542$	15.9347	0.684455
$543$	−7.19256	−0.308662
$544$	−10.3110	−0.442079
$545$	−17.1975	−0.736662
$546$	−114.203	−4.88744
$547$	−7.20899	−0.308234	−0.154117	−	0.988053i	$-0.549253\pi$
$547$	−7.20899	−0.308234	−0.154117	+	0.988053i	$0.549253\pi$
$548$	91.8545	3.92383
$549$	−1.98952	−0.0849105
$550$	−50.9331	−2.17180
$551$	−15.9179	−0.678126
$552$	−72.6673	−3.09293
$553$	30.6424	1.30305
$554$	1.81641	0.0771718
$555$	−125.724	−5.33670
$556$	34.2729	1.45349
$557$	−30.5338	−1.29376	−0.646878	−	0.762593i	$-0.723926\pi$
$557$	−30.5338	−1.29376	−0.646878	+	0.762593i	$0.723926\pi$
$558$	−55.9162	−2.36712
$559$	0.617193	0.0261045
$560$	−62.0738	−2.62310
$561$	−23.8282	−1.00603
$562$	−70.8233	−2.98750
$563$	31.4630	1.32601	0.663003	−	0.748617i	$-0.269282\pi$
$563$	31.4630	1.32601	0.663003	+	0.748617i	$0.269282\pi$
$564$	107.147	4.51172
$565$	−58.6799	−2.46868
$566$	56.3043	2.36665
$567$	−14.8535	−0.623788
$568$	−22.5420	−0.945842
$569$	46.3965	1.94504	0.972521	−	0.232813i	$-0.0747931\pi$
$569$	46.3965	1.94504	0.972521	+	0.232813i	$0.0747931\pi$
$570$	−165.898	−6.94872
$571$	12.7791	0.534787	0.267394	−	0.963587i	$-0.413838\pi$
$571$	12.7791	0.534787	0.267394	+	0.963587i	$0.413838\pi$
$572$	−40.0372	−1.67404
$573$	−19.7259	−0.824062
$574$	77.0427	3.21570
$575$	−65.5758	−2.73470
$576$	−22.4228	−0.934283
$577$	11.3574	0.472815	0.236407	−	0.971654i	$-0.424030\pi$
$577$	11.3574	0.472815	0.236407	+	0.971654i	$0.424030\pi$
$578$	−37.6720	−1.56695
$579$	42.2452	1.75565
$580$	46.9967	1.95143
$581$	30.7518	1.27580
$582$	−46.0715	−1.90972
$583$	−0.349387	−0.0144701
$584$	36.9365	1.52844
$585$	101.188	4.18361
$586$	−9.03287	−0.373144
$587$	28.3368	1.16958	0.584792	−	0.811183i	$-0.301176\pi$
$587$	28.3368	1.16958	0.584792	+	0.811183i	$0.301176\pi$
$588$	−14.8145	−0.610941
$589$	33.8800	1.39600
$590$	13.8508	0.570229
$591$	−8.47566	−0.348642
$592$	−57.2307	−2.35217
$593$	8.34191	0.342561	0.171281	−	0.985222i	$-0.445210\pi$
$593$	8.34191	0.342561	0.171281	+	0.985222i	$0.445210\pi$
$594$	10.1429	0.416168
$595$	−69.2655	−2.83961
$596$	64.2894	2.63339
$597$	18.5058	0.757393
$598$	−76.2394	−3.11766
$599$	−22.3859	−0.914664	−0.457332	−	0.889296i	$-0.651195\pi$
$599$	−22.3859	−0.914664	−0.457332	+	0.889296i	$0.651195\pi$
$600$	183.820	7.50443
$601$	−48.6800	−1.98570	−0.992849	−	0.119374i	$-0.961911\pi$
$601$	−48.6800	−1.98570	−0.992849	+	0.119374i	$0.961911\pi$
$602$	0.735230	0.0299657
$603$	7.09965	0.289120
$604$	37.5645	1.52848
$605$	35.8041	1.45564
$606$	−26.2108	−1.06474
$607$	29.7178	1.20621	0.603104	−	0.797663i	$-0.293930\pi$
$607$	29.7178	1.20621	0.603104	+	0.797663i	$0.293930\pi$
$608$	−10.8723	−0.440929
$609$	20.3026	0.822703
$610$	−5.26390	−0.213129
$611$	58.5663	2.36934
$612$	94.0334	3.80107
$613$	39.0523	1.57731	0.788655	−	0.614837i	$-0.210778\pi$
$613$	39.0523	1.57731	0.788655	+	0.614837i	$0.210778\pi$
$614$	67.5898	2.72770
$615$	−119.828	−4.83194
$616$	−24.8480	−1.00116
$617$	4.71204	0.189699	0.0948497	−	0.995492i	$-0.469763\pi$
$617$	4.71204	0.189699	0.0948497	+	0.995492i	$0.469763\pi$
$618$	75.5331	3.03839
$619$	23.8468	0.958483	0.479241	−	0.877683i	$-0.340912\pi$
$619$	23.8468	0.958483	0.479241	+	0.877683i	$0.340912\pi$
$620$	−100.029	−4.01726
$621$	13.0589	0.524034
$622$	−46.8359	−1.87795
$623$	−26.5837	−1.06505
$624$	80.8566	3.23685
$625$	76.4839	3.05936
$626$	−19.3641	−0.773947
$627$	−25.1253	−1.00341
$628$	−59.3378	−2.36784
$629$	−63.8613	−2.54632
$630$	120.540	4.80243
$631$	29.6409	1.17999	0.589993	−	0.807408i	$-0.299130\pi$
$631$	29.6409	1.17999	0.589993	+	0.807408i	$0.299130\pi$
$632$	−57.3422	−2.28095
$633$	−43.9372	−1.74635
$634$	43.9943	1.74724
$635$	−3.39031	−0.134540
$636$	2.42033	0.0959722
$637$	−8.09756	−0.320837
$638$	10.5271	0.416773
$639$	16.5616	0.655167
$640$	−74.7029	−2.95289
$641$	−27.3311	−1.07951	−0.539756	−	0.841822i	$-0.681483\pi$
$641$	−27.3311	−1.07951	−0.539756	+	0.841822i	$0.681483\pi$
$642$	−63.4592	−2.50453
$643$	−23.7046	−0.934817	−0.467408	−	0.884042i	$-0.654812\pi$
$643$	−23.7046	−0.934817	−0.467408	+	0.884042i	$0.654812\pi$
$644$	−61.4058	−2.41973
$645$	−1.14354	−0.0450268
$646$	−84.2676	−3.31546
$647$	24.6270	0.968187	0.484093	−	0.875016i	$-0.339149\pi$
$647$	24.6270	0.968187	0.484093	+	0.875016i	$0.339149\pi$
$648$	27.7958	1.09192
$649$	2.09771	0.0823423
$650$	192.856	7.56444
$651$	−43.2125	−1.69363
$652$	47.2173	1.84917
$653$	18.1327	0.709586	0.354793	−	0.934945i	$-0.384551\pi$
$653$	18.1327	0.709586	0.354793	+	0.934945i	$0.384551\pi$
$654$	26.6855	1.04349
$655$	33.8769	1.32368
$656$	−54.5468	−2.12969
$657$	−27.1373	−1.05873
$658$	69.7669	2.71980
$659$	−47.9336	−1.86723	−0.933614	−	0.358281i	$-0.883363\pi$
$659$	−47.9336	−1.86723	−0.933614	+	0.358281i	$0.883363\pi$
$660$	74.1812	2.88750
$661$	−7.62351	−0.296520	−0.148260	−	0.988948i	$-0.547367\pi$
$661$	−7.62351	−0.296520	−0.148260	+	0.988948i	$0.547367\pi$
$662$	29.1329	1.13228
$663$	90.2244	3.50403
$664$	−57.5470	−2.23326
$665$	−73.0361	−2.83222
$666$	111.135	4.30641
$667$	13.5536	0.524796
$668$	−46.9482	−1.81648
$669$	49.2531	1.90423
$670$	18.7844	0.725704
$671$	−0.797219	−0.0307763
$672$	13.8671	0.534935
$673$	21.3674	0.823652	0.411826	−	0.911263i	$-0.364891\pi$
$673$	21.3674	0.823652	0.411826	+	0.911263i	$0.364891\pi$
$674$	19.0016	0.731914
$675$	−33.0339	−1.27147
$676$	97.3210	3.74312
$677$	23.1229	0.888684	0.444342	−	0.895857i	$-0.353438\pi$
$677$	23.1229	0.888684	0.444342	+	0.895857i	$0.353438\pi$
$678$	91.0539	3.49691
$679$	−20.2828	−0.778382
$680$	129.619	4.97066
$681$	29.3279	1.12385
$682$	−22.4062	−0.857977
$683$	31.0025	1.18628	0.593139	−	0.805100i	$-0.297888\pi$
$683$	31.0025	1.18628	0.593139	+	0.805100i	$0.297888\pi$
$684$	99.1523	3.79118
$685$	−93.0243	−3.55428
$686$	40.6005	1.55014
$687$	−1.57235	−0.0599887
$688$	−0.520548	−0.0198457
$689$	1.32294	0.0504000
$690$	141.257	5.37756
$691$	18.2830	0.695518	0.347759	−	0.937584i	$-0.386943\pi$
$691$	18.2830	0.695518	0.347759	+	0.937584i	$0.386943\pi$
$692$	11.1805	0.425021
$693$	18.2558	0.693482
$694$	−12.6587	−0.480517
$695$	−34.7094	−1.31660
$696$	−37.9930	−1.44012
$697$	−60.8664	−2.30548
$698$	−53.6206	−2.02957
$699$	−69.8845	−2.64327
$700$	155.333	5.87103
$701$	8.29022	0.313117	0.156559	−	0.987669i	$-0.449960\pi$
$701$	8.29022	0.313117	0.156559	+	0.987669i	$0.449960\pi$
$702$	−38.4056	−1.44953
$703$	−67.3378	−2.53969
$704$	−8.98504	−0.338636
$705$	−108.512	−4.08680
$706$	−57.8782	−2.17828
$707$	−11.5392	−0.433977
$708$	−14.5316	−0.546130
$709$	14.4999	0.544553	0.272277	−	0.962219i	$-0.412223\pi$
$709$	14.4999	0.544553	0.272277	+	0.962219i	$0.412223\pi$
$710$	43.8191	1.64450
$711$	42.1293	1.57997
$712$	49.7470	1.86435
$713$	−28.8477	−1.08035
$714$	107.480	4.02233
$715$	40.5471	1.51638
$716$	−40.9510	−1.53041
$717$	−33.7464	−1.26028
$718$	52.2975	1.95173
$719$	23.1166	0.862104	0.431052	−	0.902327i	$-0.358142\pi$
$719$	23.1166	0.862104	0.431052	+	0.902327i	$0.358142\pi$
$720$	−85.3433	−3.18056
$721$	33.2532	1.23841
$722$	−41.6399	−1.54968
$723$	25.4506	0.946518
$724$	11.3738	0.422703
$725$	−34.2853	−1.27332
$726$	−55.5575	−2.06193
$727$	9.59284	0.355779	0.177889	−	0.984051i	$-0.443073\pi$
$727$	9.59284	0.355779	0.177889	+	0.984051i	$0.443073\pi$
$728$	94.0859	3.48706
$729$	−40.7378	−1.50881
$730$	−71.8003	−2.65745
$731$	−0.580858	−0.0214838
$732$	5.52262	0.204122
$733$	6.27148	0.231643	0.115821	−	0.993270i	$-0.463050\pi$
$733$	6.27148	0.231643	0.115821	+	0.993270i	$0.463050\pi$
$734$	−26.2547	−0.969079
$735$	15.0032	0.553402
$736$	9.25737	0.341231
$737$	2.84490	0.104793
$738$	105.924	3.89910
$739$	−3.90609	−0.143688	−0.0718440	−	0.997416i	$-0.522888\pi$
$739$	−3.90609	−0.143688	−0.0718440	+	0.997416i	$0.522888\pi$
$740$	198.811	7.30844
$741$	95.1360	3.49491
$742$	1.57595	0.0578549
$743$	−4.93960	−0.181216	−0.0906081	−	0.995887i	$-0.528881\pi$
$743$	−4.93960	−0.181216	−0.0906081	+	0.995887i	$0.528881\pi$
$744$	80.8650	2.96466
$745$	−65.1081	−2.38538
$746$	59.3007	2.17115
$747$	42.2797	1.54694
$748$	37.6801	1.37772
$749$	−27.9377	−1.02082
$750$	−218.607	−7.98238
$751$	19.5886	0.714797	0.357398	−	0.933952i	$-0.383664\pi$
$751$	19.5886	0.714797	0.357398	+	0.933952i	$0.383664\pi$
$752$	−49.3955	−1.80127
$753$	−18.6805	−0.680756
$754$	−39.8605	−1.45164
$755$	−38.0429	−1.38452
$756$	−30.9332	−1.12503
$757$	37.6005	1.36661	0.683307	−	0.730131i	$-0.260541\pi$
$757$	37.6005	1.36661	0.683307	+	0.730131i	$0.260541\pi$
$758$	−16.5240	−0.600180
$759$	21.3934	0.776531
$760$	136.675	4.95772
$761$	−37.8358	−1.37155	−0.685773	−	0.727816i	$-0.740536\pi$
$761$	−37.8358	−1.37155	−0.685773	+	0.727816i	$0.740536\pi$
$762$	5.26076	0.190577
$763$	11.7482	0.425314
$764$	31.1931	1.12853
$765$	−95.2309	−3.44308
$766$	39.3948	1.42339
$767$	−7.94289	−0.286801
$768$	86.1019	3.10694
$769$	12.8899	0.464820	0.232410	−	0.972618i	$-0.425339\pi$
$769$	12.8899	0.464820	0.232410	+	0.972618i	$0.425339\pi$
$770$	48.3017	1.74067
$771$	−26.6133	−0.958454
$772$	−66.8034	−2.40431
$773$	51.1965	1.84141	0.920704	−	0.390261i	$-0.127615\pi$
$773$	51.1965	1.84141	0.920704	+	0.390261i	$0.127615\pi$
$774$	1.01084	0.0363341
$775$	72.9735	2.62129
$776$	37.9559	1.36254
$777$	85.8865	3.08116
$778$	−81.0980	−2.90750
$779$	−64.1799	−2.29948
$780$	−280.884	−10.0573
$781$	6.63641	0.237469
$782$	71.7510	2.56581
$783$	6.82762	0.243999
$784$	6.82958	0.243914
$785$	60.0935	2.14483
$786$	−52.5670	−1.87500
$787$	−6.14865	−0.219176	−0.109588	−	0.993977i	$-0.534953\pi$
$787$	−6.14865	−0.219176	−0.109588	+	0.993977i	$0.534953\pi$
$788$	13.4028	0.477454
$789$	−37.4600	−1.33361
$790$	111.467	3.96580
$791$	40.0862	1.42530
$792$	−34.1628	−1.21392
$793$	3.01864	0.107195
$794$	−38.4074	−1.36303
$795$	−2.45115	−0.0869334
$796$	−29.2637	−1.03723
$797$	48.6662	1.72385	0.861923	−	0.507039i	$-0.169260\pi$
$797$	48.6662	1.72385	0.861923	+	0.507039i	$0.169260\pi$
$798$	113.331	4.01186
$799$	−55.1183	−1.94995
$800$	−23.4176	−0.827936
$801$	−36.5491	−1.29140
$802$	−3.89675	−0.137599
$803$	−10.8742	−0.383741
$804$	−19.7076	−0.695034
$805$	62.1878	2.19183
$806$	84.8400	2.98836
$807$	31.7154	1.11643
$808$	21.5937	0.759665
$809$	−37.5735	−1.32101	−0.660507	−	0.750820i	$-0.729659\pi$
$809$	−37.5735	−1.32101	−0.660507	+	0.750820i	$0.729659\pi$
$810$	−54.0319	−1.89849
$811$	−28.5725	−1.00332	−0.501659	−	0.865066i	$-0.667277\pi$
$811$	−28.5725	−1.00332	−0.501659	+	0.865066i	$0.667277\pi$
$812$	−32.1050	−1.12667
$813$	16.9308	0.593790
$814$	44.5331	1.56089
$815$	−47.8186	−1.67501
$816$	−76.0964	−2.66391
$817$	−0.612478	−0.0214279
$818$	−61.8557	−2.16273
$819$	−69.1249	−2.41542
$820$	189.488	6.61719
$821$	3.93881	0.137465	0.0687327	−	0.997635i	$-0.478104\pi$
$821$	3.93881	0.137465	0.0687327	+	0.997635i	$0.478104\pi$
$822$	144.346	5.03466
$823$	−23.3684	−0.814570	−0.407285	−	0.913301i	$-0.633525\pi$
$823$	−23.3684	−0.814570	−0.407285	+	0.913301i	$0.633525\pi$
$824$	−62.2278	−2.16781
$825$	−54.1170	−1.88411
$826$	−9.46195	−0.329223
$827$	13.5431	0.470938	0.235469	−	0.971882i	$-0.424337\pi$
$827$	13.5431	0.470938	0.235469	+	0.971882i	$0.424337\pi$
$828$	−84.4249	−2.93397
$829$	−40.8041	−1.41719	−0.708593	−	0.705617i	$-0.750670\pi$
$829$	−40.8041	−1.41719	−0.708593	+	0.705617i	$0.750670\pi$
$830$	111.865	3.88288
$831$	1.92995	0.0669493
$832$	34.0215	1.17948
$833$	7.62084	0.264046
$834$	53.8587	1.86498
$835$	47.5462	1.64540
$836$	39.7314	1.37414
$837$	−14.5320	−0.502301
$838$	−98.0144	−3.38585
$839$	26.4331	0.912572	0.456286	−	0.889833i	$-0.349179\pi$
$839$	26.4331	0.912572	0.456286	+	0.889833i	$0.349179\pi$
$840$	−174.323	−6.01472
$841$	−21.9137	−0.755646
$842$	−11.7676	−0.405538
$843$	−75.2505	−2.59176
$844$	69.4790	2.39156
$845$	−98.5604	−3.39058
$846$	95.9204	3.29781
$847$	−24.4590	−0.840420
$848$	−1.11578	−0.0383162
$849$	59.8239	2.05315
$850$	−181.502	−6.22548
$851$	57.3359	1.96545
$852$	−45.9727	−1.57500
$853$	12.9406	0.443079	0.221539	−	0.975151i	$-0.428892\pi$
$853$	12.9406	0.443079	0.221539	+	0.975151i	$0.428892\pi$
$854$	3.59594	0.123051
$855$	−100.415	−3.43412
$856$	52.2807	1.78692
$857$	15.9147	0.543635	0.271817	−	0.962349i	$-0.412375\pi$
$857$	15.9147	0.543635	0.271817	+	0.962349i	$0.412375\pi$
$858$	−62.9172	−2.14796
$859$	39.9630	1.36352	0.681760	−	0.731576i	$-0.261215\pi$
$859$	39.9630	1.36352	0.681760	+	0.731576i	$0.261215\pi$
$860$	1.80831	0.0616628
$861$	81.8586	2.78973
$862$	−44.2152	−1.50598
$863$	−55.9172	−1.90344	−0.951721	−	0.306963i	$-0.900687\pi$
$863$	−55.9172	−1.90344	−0.951721	+	0.306963i	$0.900687\pi$
$864$	4.66341	0.158652
$865$	−11.3229	−0.384992
$866$	20.8330	0.707934
$867$	−40.0269	−1.35938
$868$	68.3330	2.31937
$869$	16.8816	0.572670
$870$	73.8539	2.50388
$871$	−10.7721	−0.364999
$872$	−21.9848	−0.744500
$873$	−27.8862	−0.943804
$874$	75.6570	2.55914
$875$	−96.2407	−3.25353
$876$	75.3292	2.54514
$877$	0.338378	0.0114262	0.00571310	−	0.999984i	$-0.498181\pi$
$877$	0.338378	0.0114262	0.00571310	+	0.999984i	$0.498181\pi$
$878$	39.3942	1.32949
$879$	−9.59752	−0.323716
$880$	−34.1979	−1.15281
$881$	−39.1744	−1.31982	−0.659910	−	0.751345i	$-0.729405\pi$
$881$	−39.1744	−1.31982	−0.659910	+	0.751345i	$0.729405\pi$
$882$	−13.2623	−0.446564
$883$	30.7903	1.03618	0.518088	−	0.855328i	$-0.326644\pi$
$883$	30.7903	1.03618	0.518088	+	0.855328i	$0.326644\pi$
$884$	−142.674	−4.79865
$885$	14.7166	0.494694
$886$	−9.73946	−0.327204
$887$	36.5978	1.22883	0.614416	−	0.788982i	$-0.289392\pi$
$887$	36.5978	1.22883	0.614416	+	0.788982i	$0.289392\pi$
$888$	−160.722	−5.39349
$889$	2.31603	0.0776772
$890$	−96.7024	−3.24147
$891$	−8.18314	−0.274146
$892$	−77.8851	−2.60779
$893$	−58.1189	−1.94487
$894$	101.029	3.37890
$895$	41.4725	1.38627
$896$	51.0320	1.70486
$897$	−81.0051	−2.70468
$898$	−11.1569	−0.372311
$899$	−15.0826	−0.503031
$900$	213.562	7.11874
$901$	−1.24506	−0.0414788
$902$	42.4447	1.41325
$903$	0.781190	0.0259964
$904$	−75.0146	−2.49495
$905$	−11.5186	−0.382892
$906$	59.0314	1.96119
$907$	24.7141	0.820617	0.410308	−	0.911947i	$-0.365421\pi$
$907$	24.7141	0.820617	0.410308	+	0.911947i	$0.365421\pi$
$908$	−46.3770	−1.53907
$909$	−15.8649	−0.526206
$910$	−182.892	−6.06282
$911$	−18.0196	−0.597015	−0.298507	−	0.954407i	$-0.596489\pi$
$911$	−18.0196	−0.597015	−0.298507	+	0.954407i	$0.596489\pi$
$912$	−80.2389	−2.65698
$913$	16.9419	0.560696
$914$	−84.2350	−2.78625
$915$	−5.59295	−0.184897
$916$	2.48639	0.0821526
$917$	−23.1424	−0.764230
$918$	36.1446	1.19295
$919$	−35.8457	−1.18244	−0.591221	−	0.806510i	$-0.701354\pi$
$919$	−35.8457	−1.18244	−0.591221	+	0.806510i	$0.701354\pi$
$920$	−116.374	−3.83674
$921$	71.8149	2.36638
$922$	57.7701	1.90256
$923$	−25.1285	−0.827114
$924$	−50.6756	−1.66711
$925$	−145.038	−4.76881
$926$	−30.6265	−1.00645
$927$	45.7188	1.50160
$928$	4.84007	0.158883
$929$	−57.5413	−1.88787	−0.943934	−	0.330133i	$-0.892906\pi$
$929$	−57.5413	−1.88787	−0.943934	+	0.330133i	$0.892906\pi$
$930$	−157.192	−5.15454
$931$	8.03570	0.263359
$932$	110.510	3.61988
$933$	−49.7637	−1.62919
$934$	−52.1441	−1.70621
$935$	−38.1600	−1.24797
$936$	129.356	4.22813
$937$	34.4702	1.12609	0.563046	−	0.826425i	$-0.309629\pi$
$937$	34.4702	1.12609	0.563046	+	0.826425i	$0.309629\pi$
$938$	−12.8322	−0.418987
$939$	−20.5746	−0.671427
$940$	171.593	5.59674
$941$	−14.6841	−0.478687	−0.239344	−	0.970935i	$-0.576932\pi$
$941$	−14.6841	−0.478687	−0.239344	+	0.970935i	$0.576932\pi$
$942$	−93.2475	−3.03817
$943$	54.6470	1.77955
$944$	6.69913	0.218038
$945$	31.3272	1.01907
$946$	0.405056	0.0131695
$947$	54.4608	1.76974	0.884869	−	0.465840i	$-0.154248\pi$
$947$	54.4608	1.76974	0.884869	+	0.465840i	$0.154248\pi$
$948$	−116.945	−3.79820
$949$	41.1746	1.33658
$950$	−191.383	−6.20928
$951$	46.7444	1.51579
$952$	−88.5469	−2.86982
$953$	5.55961	0.180093	0.0900467	−	0.995938i	$-0.471298\pi$
$953$	5.55961	0.180093	0.0900467	+	0.995938i	$0.471298\pi$
$954$	2.16672	0.0701502
$955$	−31.5904	−1.02224
$956$	53.3641	1.72592
$957$	11.1852	0.361566
$958$	43.6938	1.41168
$959$	63.5480	2.05207
$960$	−63.0352	−2.03445
$961$	1.10204	0.0355496
$962$	−168.623	−5.43662
$963$	−38.4106	−1.23777
$964$	−40.2457	−1.29623
$965$	67.6541	2.17786
$966$	−96.4972	−3.10475
$967$	−23.7702	−0.764398	−0.382199	−	0.924080i	$-0.624833\pi$
$967$	−23.7702	−0.764398	−0.382199	+	0.924080i	$0.624833\pi$
$968$	45.7709	1.47113
$969$	−89.5352	−2.87628
$970$	−73.7818	−2.36899
$971$	4.22297	0.135521	0.0677607	−	0.997702i	$-0.478415\pi$
$971$	4.22297	0.135521	0.0677607	+	0.997702i	$0.478415\pi$
$972$	88.8140	2.84871
$973$	23.7111	0.760143
$974$	−60.3591	−1.93403
$975$	204.912	6.56242
$976$	−2.54596	−0.0814941
$977$	−24.1884	−0.773857	−0.386928	−	0.922110i	$-0.626464\pi$
$977$	−24.1884	−0.773857	−0.386928	+	0.922110i	$0.626464\pi$
$978$	74.2005	2.37267
$979$	−14.6456	−0.468075
$980$	−23.7250	−0.757866
$981$	16.1522	0.515701
$982$	17.5727	0.560768
$983$	10.6126	0.338491	0.169245	−	0.985574i	$-0.445867\pi$
$983$	10.6126	0.338491	0.169245	+	0.985574i	$0.445867\pi$
$984$	−153.185	−4.88335
$985$	−13.5735	−0.432487
$986$	37.5139	1.19469
$987$	74.1281	2.35952
$988$	−150.441	−4.78617
$989$	0.521505	0.0165829
$990$	66.4085	2.11060
$991$	15.2960	0.485893	0.242947	−	0.970040i	$-0.421886\pi$
$991$	15.2960	0.485893	0.242947	+	0.970040i	$0.421886\pi$
$992$	−10.3017	−0.327079
$993$	30.9541	0.982298
$994$	−29.9342	−0.949457
$995$	29.6364	0.939538
$996$	−117.363	−3.71878
$997$	26.0307	0.824399	0.412200	−	0.911094i	$-0.364761\pi$
$997$	26.0307	0.824399	0.412200	+	0.911094i	$0.364761\pi$
$998$	32.1968	1.01917
$999$	28.8830	0.913817

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1511.2.a.b.1.8	✓	87

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1511.2.a.b.1.8	✓	87	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:	\( N \)	\(=\)	\( 1511 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1511.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48500 q^{2} -2.64034 q^{3} +4.17524 q^{4} -4.22842 q^{5} +6.56126 q^{6} +2.88857 q^{7} -5.40548 q^{8} +3.97140 q^{9} +O(q^{10})\)	\(q-2.48500 q^{2} -2.64034 q^{3} +4.17524 q^{4} -4.22842 q^{5} +6.56126 q^{6} +2.88857 q^{7} -5.40548 q^{8} +3.97140 q^{9} +10.5076 q^{10} +1.59138 q^{11} -11.0241 q^{12} -6.02570 q^{13} -7.17811 q^{14} +11.1645 q^{15} +5.08215 q^{16} +5.67096 q^{17} -9.86895 q^{18} +5.97967 q^{19} -17.6547 q^{20} -7.62681 q^{21} -3.95459 q^{22} -5.09149 q^{23} +14.2723 q^{24} +12.8795 q^{25} +14.9739 q^{26} -2.56484 q^{27} +12.0605 q^{28} -2.66200 q^{29} -27.7437 q^{30} +5.66587 q^{31} -1.81820 q^{32} -4.20179 q^{33} -14.0923 q^{34} -12.2141 q^{35} +16.5816 q^{36} -11.2611 q^{37} -14.8595 q^{38} +15.9099 q^{39} +22.8566 q^{40} -10.7330 q^{41} +18.9527 q^{42} -0.102427 q^{43} +6.64441 q^{44} -16.7927 q^{45} +12.6524 q^{46} -9.71941 q^{47} -13.4186 q^{48} +1.34384 q^{49} -32.0056 q^{50} -14.9733 q^{51} -25.1588 q^{52} -0.219549 q^{53} +6.37364 q^{54} -6.72903 q^{55} -15.6141 q^{56} -15.7884 q^{57} +6.61509 q^{58} +1.31817 q^{59} +46.6143 q^{60} -0.500960 q^{61} -14.0797 q^{62} +11.4717 q^{63} -5.64606 q^{64} +25.4792 q^{65} +10.4415 q^{66} +1.78769 q^{67} +23.6776 q^{68} +13.4433 q^{69} +30.3520 q^{70} +4.17022 q^{71} -21.4673 q^{72} -6.83316 q^{73} +27.9839 q^{74} -34.0063 q^{75} +24.9666 q^{76} +4.59682 q^{77} -39.5362 q^{78} +10.6082 q^{79} -21.4894 q^{80} -5.14216 q^{81} +26.6716 q^{82} +10.6460 q^{83} -31.8438 q^{84} -23.9792 q^{85} +0.254531 q^{86} +7.02860 q^{87} -8.60219 q^{88} -9.20307 q^{89} +41.7300 q^{90} -17.4057 q^{91} -21.2582 q^{92} -14.9598 q^{93} +24.1528 q^{94} -25.2845 q^{95} +4.80068 q^{96} -7.02174 q^{97} -3.33944 q^{98} +6.32002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9}+O(q^{10}) \) 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9	\( 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9} + 25 q^{10} + 17 q^{11} + 34 q^{13} + 12 q^{14} + 16 q^{15} + 152 q^{16} + 32 q^{17} + 14 q^{18} + 56 q^{19} + 3 q^{20} + 38 q^{21} + 32 q^{22} + 8 q^{23} + 8 q^{24} + 179 q^{25} + 11 q^{26} - 2 q^{27} + 45 q^{28} + 40 q^{29} + 24 q^{30} + 31 q^{31} + 26 q^{32} + 31 q^{33} + 31 q^{34} + 22 q^{35} + 180 q^{36} + 35 q^{37} - 15 q^{38} + 59 q^{39} + 42 q^{40} + 45 q^{41} - 30 q^{42} + 82 q^{43} + 25 q^{44} + 20 q^{45} + 69 q^{46} - 7 q^{47} - 39 q^{48} + 222 q^{49} + 17 q^{50} + 53 q^{51} + 54 q^{52} + 16 q^{53} - 7 q^{54} + 49 q^{55} + 12 q^{56} + 52 q^{57} + 17 q^{58} - 7 q^{59} - 6 q^{60} + 131 q^{61} - 8 q^{62} + 19 q^{63} + 213 q^{64} + 57 q^{65} + 17 q^{66} + 38 q^{67} + 13 q^{68} + 45 q^{69} - 5 q^{71} + 4 q^{72} + 91 q^{73} + q^{74} - 44 q^{75} + 150 q^{76} + 5 q^{77} - 87 q^{78} + 120 q^{79} - 41 q^{80} + 247 q^{81} + 20 q^{82} - 33 q^{83} - 16 q^{84} + 110 q^{85} - 22 q^{86} - 13 q^{87} + 78 q^{88} + 53 q^{89} - 33 q^{90} + 32 q^{91} - 31 q^{92} + 13 q^{93} + 79 q^{94} - 25 q^{95} - 51 q^{96} + 92 q^{97} - 36 q^{98} + 35 q^{99}+O(q^{100}) \) 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9 + 25 * q^10 + 17 * q^11 + 34 * q^13 + 12 * q^14 + 16 * q^15 + 152 * q^16 + 32 * q^17 + 14 * q^18 + 56 * q^19 + 3 * q^20 + 38 * q^21 + 32 * q^22 + 8 * q^23 + 8 * q^24 + 179 * q^25 + 11 * q^26 - 2 * q^27 + 45 * q^28 + 40 * q^29 + 24 * q^30 + 31 * q^31 + 26 * q^32 + 31 * q^33 + 31 * q^34 + 22 * q^35 + 180 * q^36 + 35 * q^37 - 15 * q^38 + 59 * q^39 + 42 * q^40 + 45 * q^41 - 30 * q^42 + 82 * q^43 + 25 * q^44 + 20 * q^45 + 69 * q^46 - 7 * q^47 - 39 * q^48 + 222 * q^49 + 17 * q^50 + 53 * q^51 + 54 * q^52 + 16 * q^53 - 7 * q^54 + 49 * q^55 + 12 * q^56 + 52 * q^57 + 17 * q^58 - 7 * q^59 - 6 * q^60 + 131 * q^61 - 8 * q^62 + 19 * q^63 + 213 * q^64 + 57 * q^65 + 17 * q^66 + 38 * q^67 + 13 * q^68 + 45 * q^69 - 5 * q^71 + 4 * q^72 + 91 * q^73 + q^74 - 44 * q^75 + 150 * q^76 + 5 * q^77 - 87 * q^78 + 120 * q^79 - 41 * q^80 + 247 * q^81 + 20 * q^82 - 33 * q^83 - 16 * q^84 + 110 * q^85 - 22 * q^86 - 13 * q^87 + 78 * q^88 + 53 * q^89 - 33 * q^90 + 32 * q^91 - 31 * q^92 + 13 * q^93 + 79 * q^94 - 25 * q^95 - 51 * q^96 + 92 * q^97 - 36 * q^98 + 35 * q^99

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