LMFDB - Embedded newform 4019.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4019,2,Mod(1,4019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4019, 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("4019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4019.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:	$32.0918765724$
Analytic rank:	$0$
Dimension:	$186$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	4019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55030 q^{2} +3.02512 q^{3} +4.50404 q^{4} -1.05624 q^{5} -7.71496 q^{6} +5.05580 q^{7} -6.38607 q^{8} +6.15132 q^{9} +O(q^{10})$	\(q-2.55030 q^{2} +3.02512 q^{3} +4.50404 q^{4} -1.05624 q^{5} -7.71496 q^{6} +5.05580 q^{7} -6.38607 q^{8} +6.15132 q^{9} +2.69374 q^{10} -0.831588 q^{11} +13.6253 q^{12} +4.92701 q^{13} -12.8938 q^{14} -3.19526 q^{15} +7.27832 q^{16} +2.01746 q^{17} -15.6877 q^{18} +1.20792 q^{19} -4.75737 q^{20} +15.2944 q^{21} +2.12080 q^{22} -1.13685 q^{23} -19.3186 q^{24} -3.88435 q^{25} -12.5654 q^{26} +9.53312 q^{27} +22.7715 q^{28} +0.739150 q^{29} +8.14889 q^{30} +6.03259 q^{31} -5.78979 q^{32} -2.51565 q^{33} -5.14513 q^{34} -5.34016 q^{35} +27.7058 q^{36} -4.84051 q^{37} -3.08057 q^{38} +14.9048 q^{39} +6.74525 q^{40} -8.88368 q^{41} -39.0053 q^{42} +0.443812 q^{43} -3.74551 q^{44} -6.49730 q^{45} +2.89932 q^{46} +5.43952 q^{47} +22.0178 q^{48} +18.5611 q^{49} +9.90626 q^{50} +6.10304 q^{51} +22.1915 q^{52} +2.61411 q^{53} -24.3123 q^{54} +0.878361 q^{55} -32.2867 q^{56} +3.65410 q^{57} -1.88506 q^{58} +9.90028 q^{59} -14.3916 q^{60} -3.30195 q^{61} -15.3849 q^{62} +31.0999 q^{63} +0.209065 q^{64} -5.20413 q^{65} +6.41567 q^{66} +8.70028 q^{67} +9.08672 q^{68} -3.43911 q^{69} +13.6190 q^{70} -8.26681 q^{71} -39.2828 q^{72} -6.47664 q^{73} +12.3448 q^{74} -11.7506 q^{75} +5.44053 q^{76} -4.20434 q^{77} -38.0117 q^{78} -6.44420 q^{79} -7.68769 q^{80} +10.3848 q^{81} +22.6561 q^{82} -0.268665 q^{83} +68.8866 q^{84} -2.13093 q^{85} -1.13185 q^{86} +2.23602 q^{87} +5.31058 q^{88} -3.30186 q^{89} +16.5701 q^{90} +24.9100 q^{91} -5.12043 q^{92} +18.2493 q^{93} -13.8724 q^{94} -1.27586 q^{95} -17.5148 q^{96} +6.16415 q^{97} -47.3365 q^{98} -5.11537 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) $ 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9} + 50 q^{10} + 25 q^{11} + 17 q^{12} + 113 q^{13} + 12 q^{14} + 12 q^{15} + 252 q^{16} + 35 q^{17} + 13 q^{18} + 97 q^{19} + 55 q^{20} + 115 q^{21} + 14 q^{22} + 27 q^{23} + 122 q^{24} + 244 q^{25} + 39 q^{26} + 34 q^{27} + 66 q^{28} + 91 q^{29} + 4 q^{30} + 135 q^{31} + 21 q^{32} + 32 q^{33} + 58 q^{34} + 17 q^{35} + 273 q^{36} + 133 q^{37} - 3 q^{38} + 55 q^{39} + 142 q^{40} + 97 q^{41} - 8 q^{42} + 67 q^{43} + 44 q^{44} + 154 q^{45} + 101 q^{46} + 20 q^{47} - 7 q^{48} + 312 q^{49} + 21 q^{50} + 23 q^{51} + 193 q^{52} + 22 q^{53} + 141 q^{54} + 88 q^{55} + 28 q^{56} + 65 q^{57} + 62 q^{58} + 41 q^{59} + q^{60} + 377 q^{61} + 29 q^{62} + 39 q^{63} + 311 q^{64} + 21 q^{65} + 35 q^{66} + 42 q^{67} + 24 q^{68} + 137 q^{69} + 35 q^{70} + 17 q^{71} - 8 q^{72} + 213 q^{73} - 9 q^{74} + 2 q^{75} + 242 q^{76} + 60 q^{77} + 103 q^{79} + 80 q^{80} + 270 q^{81} + 84 q^{82} + 42 q^{83} + 137 q^{84} + 294 q^{85} - 9 q^{86} + 22 q^{87} - 13 q^{88} + 78 q^{89} + 69 q^{90} + 118 q^{91} + 49 q^{92} + 51 q^{93} + 93 q^{94} + 10 q^{95} + 260 q^{96} + 142 q^{97} - 31 q^{98} + 78 q^{99}+O(q^{100}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9 + 50 * q^10 + 25 * q^11 + 17 * q^12 + 113 * q^13 + 12 * q^14 + 12 * q^15 + 252 * q^16 + 35 * q^17 + 13 * q^18 + 97 * q^19 + 55 * q^20 + 115 * q^21 + 14 * q^22 + 27 * q^23 + 122 * q^24 + 244 * q^25 + 39 * q^26 + 34 * q^27 + 66 * q^28 + 91 * q^29 + 4 * q^30 + 135 * q^31 + 21 * q^32 + 32 * q^33 + 58 * q^34 + 17 * q^35 + 273 * q^36 + 133 * q^37 - 3 * q^38 + 55 * q^39 + 142 * q^40 + 97 * q^41 - 8 * q^42 + 67 * q^43 + 44 * q^44 + 154 * q^45 + 101 * q^46 + 20 * q^47 - 7 * q^48 + 312 * q^49 + 21 * q^50 + 23 * q^51 + 193 * q^52 + 22 * q^53 + 141 * q^54 + 88 * q^55 + 28 * q^56 + 65 * q^57 + 62 * q^58 + 41 * q^59 + q^60 + 377 * q^61 + 29 * q^62 + 39 * q^63 + 311 * q^64 + 21 * q^65 + 35 * q^66 + 42 * q^67 + 24 * q^68 + 137 * q^69 + 35 * q^70 + 17 * q^71 - 8 * q^72 + 213 * q^73 - 9 * q^74 + 2 * q^75 + 242 * q^76 + 60 * q^77 + 103 * q^79 + 80 * q^80 + 270 * q^81 + 84 * q^82 + 42 * q^83 + 137 * q^84 + 294 * q^85 - 9 * q^86 + 22 * q^87 - 13 * q^88 + 78 * q^89 + 69 * q^90 + 118 * q^91 + 49 * q^92 + 51 * q^93 + 93 * q^94 + 10 * q^95 + 260 * q^96 + 142 * q^97 - 31 * q^98 + 78 * 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 $

$2$	−2.55030	−1.80334	−0.901668	−	0.432429i	$-0.857657\pi$
$2$	−2.55030	−1.80334	−0.901668	+	0.432429i	$0.857657\pi$
$3$	3.02512	1.74655	0.873276	−	0.487227i	$-0.161991\pi$
$3$	3.02512	1.74655	0.873276	+	0.487227i	$0.161991\pi$
$4$	4.50404	2.25202
$5$	−1.05624	−0.472367	−0.236184	−	0.971708i	$-0.575897\pi$
$5$	−1.05624	−0.472367	−0.236184	+	0.971708i	$0.575897\pi$
$6$	−7.71496	−3.14962
$7$	5.05580	1.91091	0.955456	−	0.295132i	$-0.0953636\pi$
$7$	5.05580	1.91091	0.955456	+	0.295132i	$0.0953636\pi$
$8$	−6.38607	−2.25782
$9$	6.15132	2.05044
$10$	2.69374	0.851837
$11$	−0.831588	−0.250733	−0.125367	−	0.992110i	$-0.540011\pi$
$11$	−0.831588	−0.250733	−0.125367	+	0.992110i	$0.540011\pi$
$12$	13.6253	3.93327
$13$	4.92701	1.36651	0.683253	−	0.730182i	$-0.260565\pi$
$13$	4.92701	1.36651	0.683253	+	0.730182i	$0.260565\pi$
$14$	−12.8938	−3.44602
$15$	−3.19526	−0.825013
$16$	7.27832	1.81958
$17$	2.01746	0.489305	0.244653	−	0.969611i	$-0.421326\pi$
$17$	2.01746	0.489305	0.244653	+	0.969611i	$0.421326\pi$
$18$	−15.6877	−3.69763
$19$	1.20792	0.277116	0.138558	−	0.990354i	$-0.455753\pi$
$19$	1.20792	0.277116	0.138558	+	0.990354i	$0.455753\pi$
$20$	−4.75737	−1.06378
$21$	15.2944	3.33751
$22$	2.12080	0.452156
$23$	−1.13685	−0.237050	−0.118525	−	0.992951i	$-0.537817\pi$
$23$	−1.13685	−0.237050	−0.118525	+	0.992951i	$0.537817\pi$
$24$	−19.3186	−3.94339
$25$	−3.88435	−0.776869
$26$	−12.5654	−2.46427
$27$	9.53312	1.83465
$28$	22.7715	4.30342
$29$	0.739150	0.137257	0.0686284	−	0.997642i	$-0.478138\pi$
$29$	0.739150	0.137257	0.0686284	+	0.997642i	$0.478138\pi$
$30$	8.14889	1.48778
$31$	6.03259	1.08349	0.541743	−	0.840544i	$-0.317765\pi$
$31$	6.03259	1.08349	0.541743	+	0.840544i	$0.317765\pi$
$32$	−5.78979	−1.02350
$33$	−2.51565	−0.437918
$34$	−5.14513	−0.882382
$35$	−5.34016	−0.902652
$36$	27.7058	4.61764
$37$	−4.84051	−0.795775	−0.397887	−	0.917434i	$-0.630256\pi$
$37$	−4.84051	−0.795775	−0.397887	+	0.917434i	$0.630256\pi$
$38$	−3.08057	−0.499734
$39$	14.9048	2.38667
$40$	6.74525	1.06652
$41$	−8.88368	−1.38740	−0.693699	−	0.720265i	$-0.744020\pi$
$41$	−8.88368	−1.38740	−0.693699	+	0.720265i	$0.744020\pi$
$42$	−39.0053	−6.01865
$43$	0.443812	0.0676807	0.0338403	−	0.999427i	$-0.489226\pi$
$43$	0.443812	0.0676807	0.0338403	+	0.999427i	$0.489226\pi$
$44$	−3.74551	−0.564657
$45$	−6.49730	−0.968561
$46$	2.89932	0.427481
$47$	5.43952	0.793435	0.396718	−	0.917941i	$-0.370149\pi$
$47$	5.43952	0.793435	0.396718	+	0.917941i	$0.370149\pi$
$48$	22.0178	3.17799
$49$	18.5611	2.65159
$50$	9.90626	1.40096
$51$	6.10304	0.854597
$52$	22.1915	3.07740
$53$	2.61411	0.359076	0.179538	−	0.983751i	$-0.442540\pi$
$53$	2.61411	0.359076	0.179538	+	0.983751i	$0.442540\pi$
$54$	−24.3123	−3.30849
$55$	0.878361	0.118438
$56$	−32.2867	−4.31449
$57$	3.65410	0.483998
$58$	−1.88506	−0.247520
$59$	9.90028	1.28891	0.644453	−	0.764644i	$-0.277085\pi$
$59$	9.90028	1.28891	0.644453	+	0.764644i	$0.277085\pi$
$60$	−14.3916	−1.85795
$61$	−3.30195	−0.422771	−0.211385	−	0.977403i	$-0.567798\pi$
$61$	−3.30195	−0.422771	−0.211385	+	0.977403i	$0.567798\pi$
$62$	−15.3849	−1.95389
$63$	31.0999	3.91821
$64$	0.209065	0.0261331
$65$	−5.20413	−0.645493
$66$	6.41567	0.789714
$67$	8.70028	1.06291	0.531454	−	0.847087i	$-0.321646\pi$
$67$	8.70028	1.06291	0.531454	+	0.847087i	$0.321646\pi$
$68$	9.08672	1.10193
$69$	−3.43911	−0.414020
$70$	13.6190	1.62779
$71$	−8.26681	−0.981090	−0.490545	−	0.871416i	$-0.663202\pi$
$71$	−8.26681	−0.981090	−0.490545	+	0.871416i	$0.663202\pi$
$72$	−39.2828	−4.62952
$73$	−6.47664	−0.758034	−0.379017	−	0.925390i	$-0.623738\pi$
$73$	−6.47664	−0.758034	−0.379017	+	0.925390i	$0.623738\pi$
$74$	12.3448	1.43505
$75$	−11.7506	−1.35684
$76$	5.44053	0.624072
$77$	−4.20434	−0.479129
$78$	−38.0117	−4.30397
$79$	−6.44420	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$79$	−6.44420	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$80$	−7.68769	−0.859510
$81$	10.3848	1.15387
$82$	22.6561	2.50194
$83$	−0.268665	−0.0294898	−0.0147449	−	0.999891i	$-0.504694\pi$
$83$	−0.268665	−0.0294898	−0.0147449	+	0.999891i	$0.504694\pi$
$84$	68.8866	7.51614
$85$	−2.13093	−0.231132
$86$	−1.13185	−0.122051
$87$	2.23602	0.239726
$88$	5.31058	0.566110
$89$	−3.30186	−0.349997	−0.174998	−	0.984569i	$-0.555992\pi$
$89$	−3.30186	−0.349997	−0.174998	+	0.984569i	$0.555992\pi$
$90$	16.5701	1.74664
$91$	24.9100	2.61127
$92$	−5.12043	−0.533842
$93$	18.2493	1.89236
$94$	−13.8724	−1.43083
$95$	−1.27586	−0.130901
$96$	−17.5148	−1.78759
$97$	6.16415	0.625874	0.312937	−	0.949774i	$-0.398687\pi$
$97$	6.16415	0.625874	0.312937	+	0.949774i	$0.398687\pi$
$98$	−47.3365	−4.78171
$99$	−5.11537	−0.514114
$100$	−17.4953	−1.74953
$101$	−7.76806	−0.772951	−0.386475	−	0.922300i	$-0.626308\pi$
$101$	−7.76806	−0.772951	−0.386475	+	0.922300i	$0.626308\pi$
$102$	−15.5646	−1.54113
$103$	−13.5708	−1.33717	−0.668587	−	0.743634i	$-0.733101\pi$
$103$	−13.5708	−1.33717	−0.668587	+	0.743634i	$0.733101\pi$
$104$	−31.4642	−3.08532
$105$	−16.1546	−1.57653
$106$	−6.66677	−0.647534
$107$	−10.6971	−1.03413	−0.517066	−	0.855946i	$-0.672976\pi$
$107$	−10.6971	−1.03413	−0.517066	+	0.855946i	$0.672976\pi$
$108$	42.9376	4.13167
$109$	−16.3758	−1.56852	−0.784260	−	0.620433i	$-0.786957\pi$
$109$	−16.3758	−1.56852	−0.784260	+	0.620433i	$0.786957\pi$
$110$	−2.24009	−0.213584
$111$	−14.6431	−1.38986
$112$	36.7978	3.47706
$113$	15.0452	1.41534	0.707668	−	0.706545i	$-0.249747\pi$
$113$	15.0452	1.41534	0.707668	+	0.706545i	$0.249747\pi$
$114$	−9.31907	−0.872810
$115$	1.20079	0.111975
$116$	3.32917	0.309105
$117$	30.3076	2.80194
$118$	−25.2487	−2.32433
$119$	10.1999	0.935020
$120$	20.4052	1.86273
$121$	−10.3085	−0.937133
$122$	8.42096	0.762398
$123$	−26.8741	−2.42316
$124$	27.1711	2.44003
$125$	9.38405	0.839335
$126$	−79.3141	−7.06586
$127$	20.7453	1.84085	0.920426	−	0.390917i	$-0.127842\pi$
$127$	20.7453	1.84085	0.920426	+	0.390917i	$0.127842\pi$
$128$	11.0464	0.976373
$129$	1.34258	0.118208
$130$	13.2721	1.16404
$131$	1.65756	0.144821	0.0724107	−	0.997375i	$-0.476931\pi$
$131$	1.65756	0.144821	0.0724107	+	0.997375i	$0.476931\pi$
$132$	−11.3306	−0.986202
$133$	6.10701	0.529545
$134$	−22.1883	−1.91678
$135$	−10.0693	−0.866628
$136$	−12.8836	−1.10476
$137$	7.25442	0.619787	0.309893	−	0.950771i	$-0.399707\pi$
$137$	7.25442	0.619787	0.309893	+	0.950771i	$0.399707\pi$
$138$	8.77076	0.746617
$139$	11.3032	0.958726	0.479363	−	0.877617i	$-0.340868\pi$
$139$	11.3032	0.958726	0.479363	+	0.877617i	$0.340868\pi$
$140$	−24.0523	−2.03279
$141$	16.4552	1.38578
$142$	21.0829	1.76924
$143$	−4.09724	−0.342629
$144$	44.7713	3.73094
$145$	−0.780724	−0.0648356
$146$	16.5174	1.36699
$147$	56.1495	4.63113
$148$	−21.8019	−1.79210
$149$	−9.28543	−0.760692	−0.380346	−	0.924844i	$-0.624195\pi$
$149$	−9.28543	−0.760692	−0.380346	+	0.924844i	$0.624195\pi$
$150$	29.9676	2.44684
$151$	14.6454	1.19182	0.595912	−	0.803050i	$-0.296791\pi$
$151$	14.6454	1.19182	0.595912	+	0.803050i	$0.296791\pi$
$152$	−7.71387	−0.625678
$153$	12.4100	1.00329
$154$	10.7223	0.864032
$155$	−6.37189	−0.511803
$156$	67.1317	5.37484
$157$	−21.1198	−1.68554	−0.842770	−	0.538274i	$-0.819077\pi$
$157$	−21.1198	−1.68554	−0.842770	+	0.538274i	$0.819077\pi$
$158$	16.4347	1.30747
$159$	7.90798	0.627144
$160$	6.11543	0.483468
$161$	−5.74769	−0.452982
$162$	−26.4844	−2.08081
$163$	−0.0323757	−0.00253586	−0.00126793	−	0.999999i	$-0.500404\pi$
$163$	−0.0323757	−0.00253586	−0.00126793	+	0.999999i	$0.500404\pi$
$164$	−40.0125	−3.12445
$165$	2.65714	0.206858
$166$	0.685176	0.0531800
$167$	5.42944	0.420143	0.210071	−	0.977686i	$-0.432630\pi$
$167$	5.42944	0.420143	0.210071	+	0.977686i	$0.432630\pi$
$168$	−97.6710	−7.53548
$169$	11.2754	0.867339
$170$	5.43452	0.416808
$171$	7.43031	0.568210
$172$	1.99895	0.152418
$173$	2.26187	0.171967	0.0859836	−	0.996297i	$-0.472597\pi$
$173$	2.26187	0.171967	0.0859836	+	0.996297i	$0.472597\pi$
$174$	−5.70252	−0.432307
$175$	−19.6385	−1.48453
$176$	−6.05257	−0.456229
$177$	29.9495	2.25114
$178$	8.42076	0.631162
$179$	−13.2548	−0.990713	−0.495357	−	0.868690i	$-0.664963\pi$
$179$	−13.2548	−0.990713	−0.495357	+	0.868690i	$0.664963\pi$
$180$	−29.2641	−2.18122
$181$	−6.79274	−0.504900	−0.252450	−	0.967610i	$-0.581236\pi$
$181$	−6.79274	−0.504900	−0.252450	+	0.967610i	$0.581236\pi$
$182$	−63.5280	−4.70901
$183$	−9.98877	−0.738391
$184$	7.26001	0.535215
$185$	5.11276	0.375898
$186$	−46.5412	−3.41257
$187$	−1.67769	−0.122685
$188$	24.4998	1.78683
$189$	48.1975	3.50585
$190$	3.25383	0.236058
$191$	1.50280	0.108739	0.0543693	−	0.998521i	$-0.482685\pi$
$191$	1.50280	0.108739	0.0543693	+	0.998521i	$0.482685\pi$
$192$	0.632446	0.0456428
$193$	−17.5018	−1.25981	−0.629903	−	0.776674i	$-0.716905\pi$
$193$	−17.5018	−1.25981	−0.629903	+	0.776674i	$0.716905\pi$
$194$	−15.7204	−1.12866
$195$	−15.7431	−1.12739
$196$	83.6001	5.97144
$197$	15.9733	1.13805	0.569027	−	0.822319i	$-0.307320\pi$
$197$	15.9733	1.13805	0.569027	+	0.822319i	$0.307320\pi$
$198$	13.0457	0.927120
$199$	−21.6866	−1.53732	−0.768660	−	0.639658i	$-0.779076\pi$
$199$	−21.6866	−1.53732	−0.768660	+	0.639658i	$0.779076\pi$
$200$	24.8057	1.75403
$201$	26.3193	1.85642
$202$	19.8109	1.39389
$203$	3.73700	0.262286
$204$	27.4884	1.92457
$205$	9.38334	0.655361
$206$	34.6097	2.41137
$207$	−6.99314	−0.486057
$208$	35.8604	2.48647
$209$	−1.00449	−0.0694822
$210$	41.1991	2.84301
$211$	18.1257	1.24783	0.623914	−	0.781493i	$-0.285542\pi$
$211$	18.1257	1.24783	0.623914	+	0.781493i	$0.285542\pi$
$212$	11.7741	0.808646
$213$	−25.0081	−1.71352
$214$	27.2810	1.86489
$215$	−0.468774	−0.0319701
$216$	−60.8791	−4.14230
$217$	30.4996	2.07045
$218$	41.7633	2.82857
$219$	−19.5926	−1.32394
$220$	3.95618	0.266725
$221$	9.94003	0.668639
$222$	37.3443	2.50639
$223$	1.80127	0.120622	0.0603109	−	0.998180i	$-0.480791\pi$
$223$	1.80127	0.120622	0.0603109	+	0.998180i	$0.480791\pi$
$224$	−29.2720	−1.95582
$225$	−23.8939	−1.59292
$226$	−38.3699	−2.55233
$227$	−19.4560	−1.29134	−0.645668	−	0.763618i	$-0.723421\pi$
$227$	−19.4560	−1.29134	−0.645668	+	0.763618i	$0.723421\pi$
$228$	16.4582	1.08997
$229$	0.781120	0.0516179	0.0258089	−	0.999667i	$-0.491784\pi$
$229$	0.781120	0.0516179	0.0258089	+	0.999667i	$0.491784\pi$
$230$	−3.06239	−0.201928
$231$	−12.7186	−0.836824
$232$	−4.72027	−0.309901
$233$	−21.8208	−1.42953	−0.714765	−	0.699365i	$-0.753466\pi$
$233$	−21.8208	−1.42953	−0.714765	+	0.699365i	$0.753466\pi$
$234$	−77.2936	−5.05284
$235$	−5.74547	−0.374793
$236$	44.5913	2.90264
$237$	−19.4945	−1.26630
$238$	−26.0127	−1.68616
$239$	−14.6206	−0.945725	−0.472863	−	0.881136i	$-0.656779\pi$
$239$	−14.6206	−0.945725	−0.472863	+	0.881136i	$0.656779\pi$
$240$	−23.2562	−1.50118
$241$	13.0234	0.838914	0.419457	−	0.907775i	$-0.362221\pi$
$241$	13.0234	0.838914	0.419457	+	0.907775i	$0.362221\pi$
$242$	26.2897	1.68997
$243$	2.81589	0.180639
$244$	−14.8721	−0.952089
$245$	−19.6051	−1.25252
$246$	68.5372	4.36977
$247$	5.95144	0.378681
$248$	−38.5246	−2.44631
$249$	−0.812742	−0.0515054
$250$	−23.9322	−1.51360
$251$	8.00408	0.505213	0.252607	−	0.967569i	$-0.418712\pi$
$251$	8.00408	0.505213	0.252607	+	0.967569i	$0.418712\pi$
$252$	140.075	8.82390
$253$	0.945392	0.0594363
$254$	−52.9069	−3.31967
$255$	−6.44631	−0.403683
$256$	−28.5898	−1.78686
$257$	1.01470	0.0632952	0.0316476	−	0.999499i	$-0.489925\pi$
$257$	1.01470	0.0632952	0.0316476	+	0.999499i	$0.489925\pi$
$258$	−3.42399	−0.213168
$259$	−24.4726	−1.52066
$260$	−23.4396	−1.45366
$261$	4.54675	0.281437
$262$	−4.22727	−0.261162
$263$	4.09619	0.252582	0.126291	−	0.991993i	$-0.459693\pi$
$263$	4.09619	0.252582	0.126291	+	0.991993i	$0.459693\pi$
$264$	16.0651	0.988740
$265$	−2.76114	−0.169616
$266$	−15.5747	−0.954948
$267$	−9.98852	−0.611288
$268$	39.1864	2.39369
$269$	−5.41150	−0.329945	−0.164973	−	0.986298i	$-0.552754\pi$
$269$	−5.41150	−0.329945	−0.164973	+	0.986298i	$0.552754\pi$
$270$	25.6798	1.56282
$271$	−9.60792	−0.583640	−0.291820	−	0.956473i	$-0.594261\pi$
$271$	−9.60792	−0.583640	−0.291820	+	0.956473i	$0.594261\pi$
$272$	14.6837	0.890331
$273$	75.3555	4.56072
$274$	−18.5010	−1.11768
$275$	3.23018	0.194787
$276$	−15.4899	−0.932382
$277$	2.34209	0.140723	0.0703613	−	0.997522i	$-0.477585\pi$
$277$	2.34209	0.140723	0.0703613	+	0.997522i	$0.477585\pi$
$278$	−28.8266	−1.72891
$279$	37.1084	2.22162
$280$	34.1027	2.03802
$281$	−26.7765	−1.59735	−0.798675	−	0.601762i	$-0.794465\pi$
$281$	−26.7765	−1.59735	−0.798675	+	0.601762i	$0.794465\pi$
$282$	−41.9657	−2.49902
$283$	13.5206	0.803715	0.401857	−	0.915702i	$-0.368365\pi$
$283$	13.5206	0.803715	0.401857	+	0.915702i	$0.368365\pi$
$284$	−37.2341	−2.20944
$285$	−3.85963	−0.228625
$286$	10.4492	0.617875
$287$	−44.9141	−2.65120
$288$	−35.6149	−2.09863
$289$	−12.9299	−0.760580
$290$	1.99108	0.116920
$291$	18.6473	1.09312
$292$	−29.1711	−1.70711
$293$	23.7477	1.38736	0.693679	−	0.720284i	$-0.255989\pi$
$293$	23.7477	1.38736	0.693679	+	0.720284i	$0.255989\pi$
$294$	−143.198	−8.35149
$295$	−10.4571	−0.608837
$296$	30.9118	1.79671
$297$	−7.92763	−0.460008
$298$	23.6807	1.37178
$299$	−5.60128	−0.323930
$300$	−52.9252	−3.05564
$301$	2.24382	0.129332
$302$	−37.3501	−2.14926
$303$	−23.4993	−1.35000
$304$	8.79164	0.504235
$305$	3.48766	0.199703
$306$	−31.6493	−1.80927
$307$	13.1993	0.753322	0.376661	−	0.926351i	$-0.377072\pi$
$307$	13.1993	0.753322	0.376661	+	0.926351i	$0.377072\pi$
$308$	−18.9365	−1.07901
$309$	−41.0533	−2.33544
$310$	16.2503	0.922953
$311$	−10.3552	−0.587188	−0.293594	−	0.955930i	$-0.594851\pi$
$311$	−10.3552	−0.587188	−0.293594	+	0.955930i	$0.594851\pi$
$312$	−95.1829	−5.38867
$313$	−17.1686	−0.970429	−0.485214	−	0.874395i	$-0.661258\pi$
$313$	−17.1686	−0.970429	−0.485214	+	0.874395i	$0.661258\pi$
$314$	53.8618	3.03960
$315$	−32.8491	−1.85084
$316$	−29.0250	−1.63278
$317$	−6.95538	−0.390653	−0.195327	−	0.980738i	$-0.562577\pi$
$317$	−6.95538	−0.390653	−0.195327	+	0.980738i	$0.562577\pi$
$318$	−20.1678	−1.13095
$319$	−0.614669	−0.0344148
$320$	−0.220824	−0.0123444
$321$	−32.3601	−1.80616
$322$	14.6584	0.816878
$323$	2.43693	0.135594
$324$	46.7736	2.59853
$325$	−19.1382	−1.06160
$326$	0.0825679	0.00457301
$327$	−49.5388	−2.73950
$328$	56.7318	3.13249
$329$	27.5011	1.51619
$330$	−6.77652	−0.373035
$331$	−32.6708	−1.79575	−0.897876	−	0.440249i	$-0.854890\pi$
$331$	−32.6708	−1.79575	−0.897876	+	0.440249i	$0.854890\pi$
$332$	−1.21008	−0.0664116
$333$	−29.7755	−1.63169
$334$	−13.8467	−0.757659
$335$	−9.18963	−0.502083
$336$	111.317	6.07286
$337$	24.3683	1.32743	0.663714	−	0.747986i	$-0.268979\pi$
$337$	24.3683	1.32743	0.663714	+	0.747986i	$0.268979\pi$
$338$	−28.7557	−1.56410
$339$	45.5136	2.47196
$340$	−9.59780	−0.520514
$341$	−5.01663	−0.271666
$342$	−18.9496	−1.02467
$343$	58.4507	3.15604
$344$	−2.83421	−0.152810
$345$	3.63254	0.195569
$346$	−5.76846	−0.310115
$347$	29.3887	1.57767	0.788834	−	0.614607i	$-0.210685\pi$
$347$	29.3887	1.57767	0.788834	+	0.614607i	$0.210685\pi$
$348$	10.0711	0.539868
$349$	6.76226	0.361976	0.180988	−	0.983485i	$-0.442071\pi$
$349$	6.76226	0.361976	0.180988	+	0.983485i	$0.442071\pi$
$350$	50.0841	2.67711
$351$	46.9697	2.50706
$352$	4.81472	0.256625
$353$	23.5015	1.25086	0.625429	−	0.780281i	$-0.284924\pi$
$353$	23.5015	1.25086	0.625429	+	0.780281i	$0.284924\pi$
$354$	−76.3802	−4.05956
$355$	8.73178	0.463435
$356$	−14.8717	−0.788201
$357$	30.8558	1.63306
$358$	33.8039	1.78659
$359$	−9.69587	−0.511728	−0.255864	−	0.966713i	$-0.582360\pi$
$359$	−9.69587	−0.511728	−0.255864	+	0.966713i	$0.582360\pi$
$360$	41.4922	2.18683
$361$	−17.5409	−0.923207
$362$	17.3235	0.910505
$363$	−31.1843	−1.63675
$364$	112.196	5.88065
$365$	6.84092	0.358070
$366$	25.4744	1.33157
$367$	−32.2254	−1.68215	−0.841075	−	0.540918i	$-0.818077\pi$
$367$	−32.2254	−1.68215	−0.841075	+	0.540918i	$0.818077\pi$
$368$	−8.27437	−0.431331
$369$	−54.6464	−2.84478
$370$	−13.0391	−0.677870
$371$	13.2164	0.686162
$372$	82.1956	4.26164
$373$	−9.86625	−0.510855	−0.255428	−	0.966828i	$-0.582216\pi$
$373$	−9.86625	−0.510855	−0.255428	+	0.966828i	$0.582216\pi$
$374$	4.27863	0.221243
$375$	28.3878	1.46594
$376$	−34.7372	−1.79143
$377$	3.64180	0.187562
$378$	−122.918	−6.32223
$379$	−24.0192	−1.23378	−0.616892	−	0.787048i	$-0.711608\pi$
$379$	−24.0192	−1.23378	−0.616892	+	0.787048i	$0.711608\pi$
$380$	−5.74653	−0.294791
$381$	62.7571	3.21514
$382$	−3.83259	−0.196092
$383$	−5.06507	−0.258813	−0.129406	−	0.991592i	$-0.541307\pi$
$383$	−5.06507	−0.258813	−0.129406	+	0.991592i	$0.541307\pi$
$384$	33.4166	1.70528
$385$	4.44082	0.226325
$386$	44.6349	2.27185
$387$	2.73003	0.138775
$388$	27.7636	1.40948
$389$	−26.4390	−1.34051	−0.670255	−	0.742131i	$-0.733815\pi$
$389$	−26.4390	−1.34051	−0.670255	+	0.742131i	$0.733815\pi$
$390$	40.1496	2.03306
$391$	−2.29355	−0.115990
$392$	−118.533	−5.98680
$393$	5.01430	0.252938
$394$	−40.7368	−2.05229
$395$	6.80666	0.342480
$396$	−23.0398	−1.15780
$397$	13.9593	0.700597	0.350299	−	0.936638i	$-0.386080\pi$
$397$	13.9593	0.700597	0.350299	+	0.936638i	$0.386080\pi$
$398$	55.3073	2.77230
$399$	18.4744	0.924877
$400$	−28.2715	−1.41358
$401$	7.25195	0.362145	0.181073	−	0.983470i	$-0.442043\pi$
$401$	7.25195	0.362145	0.181073	+	0.983470i	$0.442043\pi$
$402$	−67.1223	−3.34776
$403$	29.7226	1.48059
$404$	−34.9877	−1.74070
$405$	−10.9689	−0.545049
$406$	−9.53047	−0.472989
$407$	4.02531	0.199527
$408$	−38.9745	−1.92952
$409$	36.2281	1.79136	0.895682	−	0.444695i	$-0.146688\pi$
$409$	36.2281	1.79136	0.895682	+	0.444695i	$0.146688\pi$
$410$	−23.9304	−1.18184
$411$	21.9455	1.08249
$412$	−61.1236	−3.01135
$413$	50.0538	2.46299
$414$	17.8346	0.876524
$415$	0.283776	0.0139300
$416$	−28.5263	−1.39862
$417$	34.1935	1.67446
$418$	2.56176	0.125300
$419$	−29.9845	−1.46484	−0.732420	−	0.680853i	$-0.761609\pi$
$419$	−29.9845	−1.46484	−0.732420	+	0.680853i	$0.761609\pi$
$420$	−72.7611	−3.55038
$421$	36.9650	1.80156	0.900782	−	0.434272i	$-0.142994\pi$
$421$	36.9650	1.80156	0.900782	+	0.434272i	$0.142994\pi$
$422$	−46.2261	−2.25025
$423$	33.4602	1.62689
$424$	−16.6939	−0.810727
$425$	−7.83650	−0.380126
$426$	63.7781	3.09006
$427$	−16.6940	−0.807878
$428$	−48.1804	−2.32889
$429$	−12.3946	−0.598418
$430$	1.19552	0.0576529
$431$	8.86994	0.427250	0.213625	−	0.976916i	$-0.431473\pi$
$431$	8.86994	0.427250	0.213625	+	0.976916i	$0.431473\pi$
$432$	69.3851	3.33829
$433$	−37.2294	−1.78913	−0.894566	−	0.446936i	$-0.852515\pi$
$433$	−37.2294	−1.78913	−0.894566	+	0.446936i	$0.852515\pi$
$434$	−77.7832	−3.73371
$435$	−2.36178	−0.113239
$436$	−73.7574	−3.53234
$437$	−1.37323	−0.0656904
$438$	49.9670	2.38752
$439$	7.36865	0.351687	0.175843	−	0.984418i	$-0.443735\pi$
$439$	7.36865	0.351687	0.175843	+	0.984418i	$0.443735\pi$
$440$	−5.60927	−0.267412
$441$	114.175	5.43693
$442$	−25.3501	−1.20578
$443$	28.4203	1.35029	0.675144	−	0.737686i	$-0.264081\pi$
$443$	28.4203	1.35029	0.675144	+	0.737686i	$0.264081\pi$
$444$	−65.9531	−3.13000
$445$	3.48758	0.165327
$446$	−4.59378	−0.217522
$447$	−28.0895	−1.32859
$448$	1.05699	0.0499381
$449$	35.3313	1.66739	0.833693	−	0.552228i	$-0.186222\pi$
$449$	35.3313	1.66739	0.833693	+	0.552228i	$0.186222\pi$
$450$	60.9366	2.87258
$451$	7.38756	0.347867
$452$	67.7644	3.18737
$453$	44.3039	2.08158
$454$	49.6186	2.32871
$455$	−26.3110	−1.23348
$456$	−23.3353	−1.09278
$457$	−29.8255	−1.39518	−0.697589	−	0.716498i	$-0.745744\pi$
$457$	−29.8255	−1.39518	−0.697589	+	0.716498i	$0.745744\pi$
$458$	−1.99209	−0.0930844
$459$	19.2327	0.897704
$460$	5.40843	0.252169
$461$	9.39211	0.437434	0.218717	−	0.975788i	$-0.429813\pi$
$461$	9.39211	0.437434	0.218717	+	0.975788i	$0.429813\pi$
$462$	32.4363	1.50908
$463$	26.1182	1.21382	0.606908	−	0.794772i	$-0.292409\pi$
$463$	26.1182	1.21382	0.606908	+	0.794772i	$0.292409\pi$
$464$	5.37978	0.249750
$465$	−19.2757	−0.893890
$466$	55.6497	2.57792
$467$	16.5982	0.768073	0.384036	−	0.923318i	$-0.374534\pi$
$467$	16.5982	0.768073	0.384036	+	0.923318i	$0.374534\pi$
$468$	136.507	6.31003
$469$	43.9869	2.03113
$470$	14.6527	0.675878
$471$	−63.8897	−2.94388
$472$	−63.2238	−2.91011
$473$	−0.369069	−0.0169698
$474$	49.7168	2.28357
$475$	−4.69199	−0.215283
$476$	45.9406	2.10569
$477$	16.0802	0.736263
$478$	37.2868	1.70546
$479$	28.9355	1.32210	0.661049	−	0.750343i	$-0.270112\pi$
$479$	28.9355	1.32210	0.661049	+	0.750343i	$0.270112\pi$
$480$	18.4999	0.844401
$481$	−23.8492	−1.08743
$482$	−33.2137	−1.51284
$483$	−17.3874	−0.791156
$484$	−46.4298	−2.11044
$485$	−6.51085	−0.295642
$486$	−7.18137	−0.325754
$487$	41.1160	1.86314	0.931571	−	0.363558i	$-0.118438\pi$
$487$	41.1160	1.86314	0.931571	+	0.363558i	$0.118438\pi$
$488$	21.0865	0.954539
$489$	−0.0979403	−0.00442901
$490$	49.9989	2.25872
$491$	2.08265	0.0939886	0.0469943	−	0.998895i	$-0.485036\pi$
$491$	2.08265	0.0939886	0.0469943	+	0.998895i	$0.485036\pi$
$492$	−121.042	−5.45701
$493$	1.49120	0.0671605
$494$	−15.1780	−0.682889
$495$	5.40308	0.242850
$496$	43.9072	1.97149
$497$	−41.7954	−1.87478
$498$	2.07274	0.0928816
$499$	−25.7710	−1.15367	−0.576835	−	0.816861i	$-0.695712\pi$
$499$	−25.7710	−1.15367	−0.576835	+	0.816861i	$0.695712\pi$
$500$	42.2662	1.89020
$501$	16.4247	0.733801
$502$	−20.4128	−0.911070
$503$	41.7507	1.86157	0.930787	−	0.365563i	$-0.119124\pi$
$503$	41.7507	1.86157	0.930787	+	0.365563i	$0.119124\pi$
$504$	−198.606	−8.84661
$505$	8.20497	0.365117
$506$	−2.41104	−0.107184
$507$	34.1094	1.51485
$508$	93.4379	4.14564
$509$	−2.88878	−0.128043	−0.0640215	−	0.997949i	$-0.520393\pi$
$509$	−2.88878	−0.128043	−0.0640215	+	0.997949i	$0.520393\pi$
$510$	16.4400	0.727977
$511$	−32.7446	−1.44854
$512$	50.8198	2.24594
$513$	11.5153	0.508411
$514$	−2.58779	−0.114143
$515$	14.3341	0.631637
$516$	6.04705	0.266206
$517$	−4.52344	−0.198941
$518$	62.4126	2.74225
$519$	6.84243	0.300349
$520$	33.2339	1.45740
$521$	27.2437	1.19357	0.596785	−	0.802401i	$-0.296445\pi$
$521$	27.2437	1.19357	0.596785	+	0.802401i	$0.296445\pi$
$522$	−11.5956	−0.507525
$523$	31.5756	1.38070	0.690352	−	0.723474i	$-0.257456\pi$
$523$	31.5756	1.38070	0.690352	+	0.723474i	$0.257456\pi$
$524$	7.46570	0.326141
$525$	−59.4087	−2.59281
$526$	−10.4465	−0.455491
$527$	12.1705	0.530155
$528$	−18.3097	−0.796828
$529$	−21.7076	−0.943807
$530$	7.04174	0.305874
$531$	60.8998	2.64283
$532$	27.5062	1.19255
$533$	−43.7699	−1.89589
$534$	25.4738	1.10236
$535$	11.2988	0.488490
$536$	−55.5606	−2.39985
$537$	−40.0974	−1.73033
$538$	13.8010	0.595002
$539$	−15.4352	−0.664841
$540$	−45.3526	−1.95166
$541$	−24.7602	−1.06452	−0.532262	−	0.846580i	$-0.678658\pi$
$541$	−24.7602	−1.06452	−0.532262	+	0.846580i	$0.678658\pi$
$542$	24.5031	1.05250
$543$	−20.5488	−0.881834
$544$	−11.6807	−0.500804
$545$	17.2969	0.740917
$546$	−192.179	−8.22452
$547$	−7.69428	−0.328984	−0.164492	−	0.986378i	$-0.552598\pi$
$547$	−7.69428	−0.328984	−0.164492	+	0.986378i	$0.552598\pi$
$548$	32.6742	1.39577
$549$	−20.3113	−0.866867
$550$	−8.23793	−0.351266
$551$	0.892836	0.0380361
$552$	21.9624	0.934781
$553$	−32.5806	−1.38547
$554$	−5.97304	−0.253770
$555$	15.4667	0.656525
$556$	50.9102	2.15907
$557$	5.65253	0.239505	0.119753	−	0.992804i	$-0.461790\pi$
$557$	5.65253	0.239505	0.119753	+	0.992804i	$0.461790\pi$
$558$	−94.6377	−4.00633
$559$	2.18666	0.0924860
$560$	−38.8674	−1.64245
$561$	−5.07522	−0.214276
$562$	68.2881	2.88056
$563$	−15.6464	−0.659417	−0.329708	−	0.944083i	$-0.606950\pi$
$563$	−15.6464	−0.659417	−0.329708	+	0.944083i	$0.606950\pi$
$564$	74.1148	3.12080
$565$	−15.8915	−0.668558
$566$	−34.4816	−1.44937
$567$	52.5035	2.20494
$568$	52.7924	2.21512
$569$	−29.6485	−1.24293	−0.621464	−	0.783443i	$-0.713462\pi$
$569$	−29.6485	−1.24293	−0.621464	+	0.783443i	$0.713462\pi$
$570$	9.84322	0.412287
$571$	−8.03446	−0.336232	−0.168116	−	0.985767i	$-0.553768\pi$
$571$	−8.03446	−0.336232	−0.168116	+	0.985767i	$0.553768\pi$
$572$	−18.4542	−0.771607
$573$	4.54613	0.189917
$574$	114.545	4.78100
$575$	4.41592	0.184157
$576$	1.28603	0.0535844
$577$	−15.7770	−0.656806	−0.328403	−	0.944538i	$-0.606510\pi$
$577$	−15.7770	−0.656806	−0.328403	+	0.944538i	$0.606510\pi$
$578$	32.9751	1.37158
$579$	−52.9449	−2.20032
$580$	−3.51641	−0.146011
$581$	−1.35832	−0.0563524
$582$	−47.5561	−1.97127
$583$	−2.17386	−0.0900322
$584$	41.3603	1.71150
$585$	−32.0123	−1.32354
$586$	−60.5639	−2.50187
$587$	34.2653	1.41428	0.707140	−	0.707073i	$-0.249985\pi$
$587$	34.2653	1.41428	0.707140	+	0.707073i	$0.249985\pi$
$588$	252.900	10.4294
$589$	7.28690	0.300251
$590$	26.6688	1.09794
$591$	48.3212	1.98767
$592$	−35.2308	−1.44798
$593$	35.5934	1.46165	0.730823	−	0.682567i	$-0.239137\pi$
$593$	35.5934	1.46165	0.730823	+	0.682567i	$0.239137\pi$
$594$	20.2178	0.829548
$595$	−10.7736	−0.441673
$596$	−41.8220	−1.71309
$597$	−65.6044	−2.68501
$598$	14.2850	0.584155
$599$	20.3031	0.829562	0.414781	−	0.909921i	$-0.363858\pi$
$599$	20.3031	0.829562	0.414781	+	0.909921i	$0.363858\pi$
$600$	75.0401	3.06350
$601$	40.5653	1.65469	0.827347	−	0.561691i	$-0.189849\pi$
$601$	40.5653	1.65469	0.827347	+	0.561691i	$0.189849\pi$
$602$	−5.72243	−0.233229
$603$	53.5182	2.17943
$604$	65.9634	2.68401
$605$	10.8883	0.442671
$606$	59.9303	2.43450
$607$	−2.13219	−0.0865430	−0.0432715	−	0.999063i	$-0.513778\pi$
$607$	−2.13219	−0.0865430	−0.0432715	+	0.999063i	$0.513778\pi$
$608$	−6.99361	−0.283628
$609$	11.3048	0.458096
$610$	−8.89460	−0.360132
$611$	26.8006	1.08423
$612$	55.8953	2.25944
$613$	−25.8368	−1.04354	−0.521770	−	0.853086i	$-0.674728\pi$
$613$	−25.8368	−1.04354	−0.521770	+	0.853086i	$0.674728\pi$
$614$	−33.6621	−1.35849
$615$	28.3857	1.14462
$616$	26.8492	1.08179
$617$	4.94025	0.198887	0.0994435	−	0.995043i	$-0.468294\pi$
$617$	4.94025	0.198887	0.0994435	+	0.995043i	$0.468294\pi$
$618$	104.698	4.21159
$619$	16.7361	0.672681	0.336341	−	0.941740i	$-0.390811\pi$
$619$	16.7361	0.672681	0.336341	+	0.941740i	$0.390811\pi$
$620$	−28.6993	−1.15259
$621$	−10.8377	−0.434903
$622$	26.4088	1.05890
$623$	−16.6936	−0.668814
$624$	108.482	4.34274
$625$	9.50988	0.380395
$626$	43.7852	1.75001
$627$	−3.03871	−0.121354
$628$	−95.1243	−3.79587
$629$	−9.76552	−0.389377
$630$	83.7751	3.33768
$631$	22.9817	0.914887	0.457443	−	0.889239i	$-0.348765\pi$
$631$	22.9817	0.914887	0.457443	+	0.889239i	$0.348765\pi$
$632$	41.1531	1.63698
$633$	54.8325	2.17939
$634$	17.7383	0.704479
$635$	−21.9122	−0.869558
$636$	35.6179	1.41234
$637$	91.4508	3.62341
$638$	1.56759	0.0620615
$639$	−50.8518	−2.01167
$640$	−11.6677	−0.461206
$641$	−27.2333	−1.07565	−0.537825	−	0.843057i	$-0.680754\pi$
$641$	−27.2333	−1.07565	−0.537825	+	0.843057i	$0.680754\pi$
$642$	82.5280	3.25712
$643$	6.11953	0.241331	0.120665	−	0.992693i	$-0.461497\pi$
$643$	6.11953	0.241331	0.120665	+	0.992693i	$0.461497\pi$
$644$	−25.8879	−1.02012
$645$	−1.41810	−0.0558374
$646$	−6.21491	−0.244522
$647$	36.6537	1.44100	0.720502	−	0.693453i	$-0.243911\pi$
$647$	36.6537	1.44100	0.720502	+	0.693453i	$0.243911\pi$
$648$	−66.3181	−2.60522
$649$	−8.23295	−0.323172
$650$	48.8082	1.91442
$651$	92.2647	3.61614
$652$	−0.145822	−0.00571082
$653$	−38.9767	−1.52528	−0.762638	−	0.646825i	$-0.776096\pi$
$653$	−38.9767	−1.52528	−0.762638	+	0.646825i	$0.776096\pi$
$654$	126.339	4.94024
$655$	−1.75079	−0.0684088
$656$	−64.6583	−2.52448
$657$	−39.8399	−1.55430
$658$	−70.1362	−2.73419
$659$	20.2941	0.790547	0.395273	−	0.918564i	$-0.370650\pi$
$659$	20.2941	0.790547	0.395273	+	0.918564i	$0.370650\pi$
$660$	11.9679	0.465849
$661$	5.45987	0.212364	0.106182	−	0.994347i	$-0.466137\pi$
$661$	5.45987	0.212364	0.106182	+	0.994347i	$0.466137\pi$
$662$	83.3205	3.23834
$663$	30.0697	1.16781
$664$	1.71571	0.0665825
$665$	−6.45050	−0.250140
$666$	75.9366	2.94248
$667$	−0.840304	−0.0325367
$668$	24.4545	0.946171
$669$	5.44904	0.210672
$670$	23.4363	0.905424
$671$	2.74586	0.106003
$672$	−88.5512	−3.41594
$673$	−34.4977	−1.32979	−0.664894	−	0.746938i	$-0.731523\pi$
$673$	−34.4977	−1.32979	−0.664894	+	0.746938i	$0.731523\pi$
$674$	−62.1467	−2.39380
$675$	−37.0299	−1.42528
$676$	50.7849	1.95327
$677$	−26.7164	−1.02679	−0.513397	−	0.858151i	$-0.671613\pi$
$677$	−26.7164	−1.02679	−0.513397	+	0.858151i	$0.671613\pi$
$678$	−116.073	−4.45777
$679$	31.1647	1.19599
$680$	13.6083	0.521853
$681$	−58.8565	−2.25539
$682$	12.7939	0.489905
$683$	1.97540	0.0755867	0.0377933	−	0.999286i	$-0.487967\pi$
$683$	1.97540	0.0755867	0.0377933	+	0.999286i	$0.487967\pi$
$684$	33.4665	1.27962
$685$	−7.66245	−0.292767
$686$	−149.067	−5.69140
$687$	2.36298	0.0901532
$688$	3.23021	0.123150
$689$	12.8797	0.490679
$690$	−9.26407	−0.352677
$691$	8.19996	0.311941	0.155971	−	0.987762i	$-0.450149\pi$
$691$	8.19996	0.311941	0.155971	+	0.987762i	$0.450149\pi$
$692$	10.1876	0.387274
$693$	−25.8623	−0.982427
$694$	−74.9500	−2.84506
$695$	−11.9390	−0.452871
$696$	−14.2793	−0.541257
$697$	−17.9224	−0.678861
$698$	−17.2458	−0.652764
$699$	−66.0105	−2.49675
$700$	−88.4526	−3.34319
$701$	4.35411	0.164452	0.0822262	−	0.996614i	$-0.473797\pi$
$701$	4.35411	0.164452	0.0822262	+	0.996614i	$0.473797\pi$
$702$	−119.787	−4.52107
$703$	−5.84695	−0.220522
$704$	−0.173856	−0.00655244
$705$	−17.3807	−0.654595
$706$	−59.9359	−2.25572
$707$	−39.2738	−1.47704
$708$	134.894	5.06962
$709$	48.9389	1.83794	0.918969	−	0.394329i	$-0.129023\pi$
$709$	48.9389	1.83794	0.918969	+	0.394329i	$0.129023\pi$
$710$	−22.2687	−0.835729
$711$	−39.6404	−1.48663
$712$	21.0859	0.790229
$713$	−6.85816	−0.256840
$714$	−78.6915	−2.94496
$715$	4.32769	0.161846
$716$	−59.7004	−2.23111
$717$	−44.2289	−1.65176
$718$	24.7274	0.922818
$719$	−28.0566	−1.04634	−0.523168	−	0.852230i	$-0.675250\pi$
$719$	−28.0566	−1.04634	−0.523168	+	0.852230i	$0.675250\pi$
$720$	−47.2895	−1.76237
$721$	−68.6114	−2.55522
$722$	44.7347	1.66485
$723$	39.3974	1.46521
$724$	−30.5948	−1.13705
$725$	−2.87112	−0.106631
$726$	79.5294	2.95161
$727$	7.17863	0.266241	0.133120	−	0.991100i	$-0.457500\pi$
$727$	7.17863	0.266241	0.133120	+	0.991100i	$0.457500\pi$
$728$	−159.077	−5.89578
$729$	−22.6360	−0.838371
$730$	−17.4464	−0.645721
$731$	0.895371	0.0331165
$732$	−44.9899	−1.66287
$733$	−28.3097	−1.04564	−0.522821	−	0.852442i	$-0.675121\pi$
$733$	−28.3097	−1.04564	−0.522821	+	0.852442i	$0.675121\pi$
$734$	82.1844	3.03348
$735$	−59.3077	−2.18760
$736$	6.58213	0.242620
$737$	−7.23505	−0.266506
$738$	139.365	5.13009
$739$	1.04107	0.0382963	0.0191482	−	0.999817i	$-0.493905\pi$
$739$	1.04107	0.0382963	0.0191482	+	0.999817i	$0.493905\pi$
$740$	23.0281	0.846530
$741$	18.0038	0.661386
$742$	−33.7059	−1.23738
$743$	−32.4274	−1.18964	−0.594822	−	0.803857i	$-0.702778\pi$
$743$	−32.4274	−1.18964	−0.594822	+	0.803857i	$0.702778\pi$
$744$	−116.541	−4.27261
$745$	9.80769	0.359326
$746$	25.1619	0.921244
$747$	−1.65264	−0.0604671
$748$	−7.55641	−0.276290
$749$	−54.0826	−1.97614
$750$	−72.3975	−2.64358
$751$	28.6356	1.04493	0.522463	−	0.852662i	$-0.325013\pi$
$751$	28.6356	1.04493	0.522463	+	0.852662i	$0.325013\pi$
$752$	39.5906	1.44372
$753$	24.2133	0.882381
$754$	−9.28769	−0.338238
$755$	−15.4691	−0.562978
$756$	217.084	7.89526
$757$	−43.4264	−1.57836	−0.789180	−	0.614162i	$-0.789494\pi$
$757$	−43.4264	−1.57836	−0.789180	+	0.614162i	$0.789494\pi$
$758$	61.2563	2.22493
$759$	2.85992	0.103809
$760$	8.14774	0.295549
$761$	8.48133	0.307448	0.153724	−	0.988114i	$-0.450873\pi$
$761$	8.48133	0.307448	0.153724	+	0.988114i	$0.450873\pi$
$762$	−160.049	−5.79798
$763$	−82.7929	−2.99730
$764$	6.76866	0.244882
$765$	−13.1080	−0.473922
$766$	12.9175	0.466727
$767$	48.7787	1.76130
$768$	−86.4874	−3.12085
$769$	33.2714	1.19980	0.599899	−	0.800076i	$-0.295207\pi$
$769$	33.2714	1.19980	0.599899	+	0.800076i	$0.295207\pi$
$770$	−11.3254	−0.408140
$771$	3.06958	0.110548
$772$	−78.8288	−2.83711
$773$	−32.8369	−1.18106	−0.590530	−	0.807016i	$-0.701081\pi$
$773$	−32.8369	−1.18106	−0.590530	+	0.807016i	$0.701081\pi$
$774$	−6.96240	−0.250258
$775$	−23.4327	−0.841727
$776$	−39.3647	−1.41311
$777$	−74.0326	−2.65590
$778$	67.4274	2.41739
$779$	−10.7308	−0.384470
$780$	−70.9076	−2.53890
$781$	6.87458	0.245992
$782$	5.84925	0.209169
$783$	7.04641	0.251818
$784$	135.094	4.82478
$785$	22.3076	0.796194
$786$	−12.7880	−0.456132
$787$	−52.1213	−1.85792	−0.928962	−	0.370175i	$-0.879298\pi$
$787$	−52.1213	−1.85792	−0.928962	+	0.370175i	$0.879298\pi$
$788$	71.9446	2.56292
$789$	12.3915	0.441148
$790$	−17.3590	−0.617607
$791$	76.0657	2.70459
$792$	32.6671	1.16077
$793$	−16.2687	−0.577719
$794$	−35.6005	−1.26341
$795$	−8.35277	−0.296242
$796$	−97.6772	−3.46208
$797$	21.9823	0.778653	0.389327	−	0.921100i	$-0.372708\pi$
$797$	21.9823	0.778653	0.389327	+	0.921100i	$0.372708\pi$
$798$	−47.1153	−1.66786
$799$	10.9740	0.388232
$800$	22.4895	0.795125
$801$	−20.3108	−0.717648
$802$	−18.4947	−0.653070
$803$	5.38590	0.190064
$804$	118.543	4.18071
$805$	6.07097	0.213974
$806$	−75.8017	−2.67000
$807$	−16.3704	−0.576266
$808$	49.6074	1.74518
$809$	−3.84048	−0.135024	−0.0675120	−	0.997718i	$-0.521506\pi$
$809$	−3.84048	−0.135024	−0.0675120	+	0.997718i	$0.521506\pi$
$810$	27.9740	0.982907
$811$	−6.03522	−0.211925	−0.105963	−	0.994370i	$-0.533792\pi$
$811$	−6.03522	−0.211925	−0.105963	+	0.994370i	$0.533792\pi$
$812$	16.8316	0.590673
$813$	−29.0651	−1.01936
$814$	−10.2658	−0.359815
$815$	0.0341967	0.00119786
$816$	44.4199	1.55501
$817$	0.536090	0.0187554
$818$	−92.3926	−3.23043
$819$	153.229	5.35426
$820$	42.2630	1.47589
$821$	49.9607	1.74364	0.871820	−	0.489827i	$-0.162940\pi$
$821$	49.9607	1.74364	0.871820	+	0.489827i	$0.162940\pi$
$822$	−55.9676	−1.95209
$823$	24.7304	0.862047	0.431024	−	0.902341i	$-0.358153\pi$
$823$	24.7304	0.862047	0.431024	+	0.902341i	$0.358153\pi$
$824$	86.6643	3.01909
$825$	9.77166	0.340205
$826$	−127.652	−4.44159
$827$	24.4754	0.851093	0.425546	−	0.904937i	$-0.360082\pi$
$827$	24.4754	0.851093	0.425546	+	0.904937i	$0.360082\pi$
$828$	−31.4974	−1.09461
$829$	−19.9422	−0.692623	−0.346311	−	0.938120i	$-0.612566\pi$
$829$	−19.9422	−0.692623	−0.346311	+	0.938120i	$0.612566\pi$
$830$	−0.723714	−0.0251205
$831$	7.08509	0.245779
$832$	1.03007	0.0357111
$833$	37.4463	1.29744
$834$	−87.2038	−3.01962
$835$	−5.73482	−0.198462
$836$	−4.52428	−0.156476
$837$	57.5094	1.98782
$838$	76.4697	2.64160
$839$	41.1323	1.42004	0.710022	−	0.704180i	$-0.248685\pi$
$839$	41.1323	1.42004	0.710022	+	0.704180i	$0.248685\pi$
$840$	103.164	3.55951
$841$	−28.4537	−0.981161
$842$	−94.2719	−3.24882
$843$	−81.0019	−2.78985
$844$	81.6391	2.81013
$845$	−11.9096	−0.409703
$846$	−85.3337	−2.93383
$847$	−52.1175	−1.79078
$848$	19.0263	0.653367
$849$	40.9013	1.40373
$850$	19.9855	0.685496
$851$	5.50294	0.188638
$852$	−112.637	−3.85889
$853$	−7.31763	−0.250551	−0.125275	−	0.992122i	$-0.539981\pi$
$853$	−7.31763	−0.250551	−0.125275	+	0.992122i	$0.539981\pi$
$854$	42.5747	1.45688
$855$	−7.84823	−0.268404
$856$	68.3127	2.33488
$857$	−31.4283	−1.07357	−0.536786	−	0.843719i	$-0.680362\pi$
$857$	−31.4283	−1.07357	−0.536786	+	0.843719i	$0.680362\pi$
$858$	31.6101	1.07915
$859$	42.4709	1.44909	0.724544	−	0.689229i	$-0.242051\pi$
$859$	42.4709	1.44909	0.724544	+	0.689229i	$0.242051\pi$
$860$	−2.11138	−0.0719974
$861$	−135.870	−4.63045
$862$	−22.6210	−0.770476
$863$	−42.6371	−1.45138	−0.725691	−	0.688021i	$-0.758480\pi$
$863$	−42.6371	−1.45138	−0.725691	+	0.688021i	$0.758480\pi$
$864$	−55.1947	−1.87776
$865$	−2.38909	−0.0812316
$866$	94.9463	3.22641
$867$	−39.1143	−1.32839
$868$	137.371	4.66269
$869$	5.35892	0.181789
$870$	6.02325	0.204207
$871$	42.8663	1.45247
$872$	104.577	3.54143
$873$	37.9177	1.28332
$874$	3.50214	0.118462
$875$	47.4439	1.60390
$876$	−88.2459	−2.98155
$877$	17.7564	0.599590	0.299795	−	0.954004i	$-0.403082\pi$
$877$	17.7564	0.599590	0.299795	+	0.954004i	$0.403082\pi$
$878$	−18.7923	−0.634209
$879$	71.8397	2.42309
$880$	6.39299	0.215508
$881$	−27.2594	−0.918394	−0.459197	−	0.888334i	$-0.651863\pi$
$881$	−27.2594	−0.918394	−0.459197	+	0.888334i	$0.651863\pi$
$882$	−291.182	−9.80461
$883$	32.9514	1.10890	0.554451	−	0.832216i	$-0.312928\pi$
$883$	32.9514	1.10890	0.554451	+	0.832216i	$0.312928\pi$
$884$	44.7703	1.50579
$885$	−31.6340	−1.06336
$886$	−72.4803	−2.43502
$887$	−44.6601	−1.49954	−0.749770	−	0.661698i	$-0.769836\pi$
$887$	−44.6601	−1.49954	−0.749770	+	0.661698i	$0.769836\pi$
$888$	93.5118	3.13805
$889$	104.884	3.51771
$890$	−8.89438	−0.298140
$891$	−8.63588	−0.289313
$892$	8.11299	0.271643
$893$	6.57051	0.219874
$894$	71.6367	2.39589
$895$	14.0004	0.467980
$896$	55.8484	1.86576
$897$	−16.9445	−0.565761
$898$	−90.1054	−3.00686
$899$	4.45899	0.148716
$900$	−107.619	−3.58730
$901$	5.27386	0.175698
$902$	−18.8405	−0.627320
$903$	6.78782	0.225885
$904$	−96.0799	−3.19557
$905$	7.17479	0.238498
$906$	−112.988	−3.75379
$907$	0.178068	0.00591264	0.00295632	−	0.999996i	$-0.499059\pi$
$907$	0.178068	0.00591264	0.00295632	+	0.999996i	$0.499059\pi$
$908$	−87.6305	−2.90812
$909$	−47.7838	−1.58489
$910$	67.1011	2.22438
$911$	24.6164	0.815577	0.407788	−	0.913076i	$-0.366300\pi$
$911$	24.6164	0.815577	0.407788	+	0.913076i	$0.366300\pi$
$912$	26.5957	0.880673
$913$	0.223418	0.00739407
$914$	76.0641	2.51598
$915$	10.5506	0.348792
$916$	3.51820	0.116245
$917$	8.38027	0.276741
$918$	−49.0491	−1.61886
$919$	49.6531	1.63790	0.818952	−	0.573862i	$-0.194556\pi$
$919$	49.6531	1.63790	0.818952	+	0.573862i	$0.194556\pi$
$920$	−7.66835	−0.252818
$921$	39.9293	1.31572
$922$	−23.9527	−0.788841
$923$	−40.7307	−1.34067
$924$	−57.2852	−1.88455
$925$	18.8022	0.618213
$926$	−66.6094	−2.18892
$927$	−83.4786	−2.74180
$928$	−4.27952	−0.140482
$929$	−42.7766	−1.40345	−0.701727	−	0.712446i	$-0.747587\pi$
$929$	−42.7766	−1.40345	−0.701727	+	0.712446i	$0.747587\pi$
$930$	49.1589	1.61198
$931$	22.4204	0.734798
$932$	−98.2820	−3.21933
$933$	−31.3256	−1.02555
$934$	−42.3304	−1.38509
$935$	1.77206	0.0579524
$936$	−193.547	−6.32627
$937$	−22.9731	−0.750498	−0.375249	−	0.926924i	$-0.622443\pi$
$937$	−22.9731	−0.750498	−0.375249	+	0.926924i	$0.622443\pi$
$938$	−112.180	−3.66280
$939$	−51.9371	−1.69490
$940$	−25.8778	−0.844042
$941$	−15.9610	−0.520313	−0.260156	−	0.965566i	$-0.583774\pi$
$941$	−15.9610	−0.520313	−0.260156	+	0.965566i	$0.583774\pi$
$942$	162.938	5.30881
$943$	10.0994	0.328882
$944$	72.0574	2.34527
$945$	−50.9084	−1.65605
$946$	0.941237	0.0306022
$947$	−26.8821	−0.873550	−0.436775	−	0.899571i	$-0.643879\pi$
$947$	−26.8821	−0.873550	−0.436775	+	0.899571i	$0.643879\pi$
$948$	−87.8039	−2.85174
$949$	−31.9105	−1.03586
$950$	11.9660	0.388228
$951$	−21.0408	−0.682296
$952$	−65.1370	−2.11110
$953$	46.0112	1.49045	0.745225	−	0.666813i	$-0.232342\pi$
$953$	46.0112	1.49045	0.745225	+	0.666813i	$0.232342\pi$
$954$	−41.0095	−1.32773
$955$	−1.58732	−0.0513645
$956$	−65.8516	−2.12979
$957$	−1.85944	−0.0601073
$958$	−73.7943	−2.38419
$959$	36.6769	1.18436
$960$	−0.668018	−0.0215602
$961$	5.39216	0.173941
$962$	60.8227	1.96100
$963$	−65.8016	−2.12043
$964$	58.6582	1.88925
$965$	18.4862	0.595091
$966$	44.3432	1.42672
$967$	39.4790	1.26956	0.634780	−	0.772693i	$-0.281091\pi$
$967$	39.4790	1.26956	0.634780	+	0.772693i	$0.281091\pi$
$968$	65.8306	2.11587
$969$	7.37200	0.236823
$970$	16.6046	0.533143
$971$	−35.2173	−1.13018	−0.565088	−	0.825031i	$-0.691158\pi$
$971$	−35.2173	−1.13018	−0.565088	+	0.825031i	$0.691158\pi$
$972$	12.6829	0.406804
$973$	57.1468	1.83204
$974$	−104.858	−3.35987
$975$	−57.8953	−1.85413
$976$	−24.0326	−0.769266
$977$	−30.2323	−0.967218	−0.483609	−	0.875284i	$-0.660674\pi$
$977$	−30.2323	−0.967218	−0.483609	+	0.875284i	$0.660674\pi$
$978$	0.249777	0.00798700
$979$	2.74579	0.0877559
$980$	−88.3022	−2.82071
$981$	−100.733	−3.21616
$982$	−5.31138	−0.169493
$983$	−29.8130	−0.950886	−0.475443	−	0.879746i	$-0.657712\pi$
$983$	−29.8130	−0.950886	−0.475443	+	0.879746i	$0.657712\pi$
$984$	171.620	5.47105
$985$	−16.8718	−0.537579
$986$	−3.80302	−0.121113
$987$	83.1941	2.64810
$988$	26.8055	0.852798
$989$	−0.504548	−0.0160437
$990$	−13.7795	−0.437941
$991$	29.9722	0.952098	0.476049	−	0.879419i	$-0.342069\pi$
$991$	29.9722	0.952098	0.476049	+	0.879419i	$0.342069\pi$
$992$	−34.9274	−1.10895
$993$	−98.8330	−3.13637
$994$	106.591	3.38086
$995$	22.9063	0.726179
$996$	−3.66062	−0.115991
$997$	−33.3667	−1.05673	−0.528367	−	0.849016i	$-0.677195\pi$
$997$	−33.3667	−1.05673	−0.528367	+	0.849016i	$0.677195\pi$
$998$	65.7239	2.08045
$999$	−46.1451	−1.45997

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.b.1.14	✓	186

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.b.1.14	✓	186	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:	\( N \)	\(=\)	\( 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55030 q^{2} +3.02512 q^{3} +4.50404 q^{4} -1.05624 q^{5} -7.71496 q^{6} +5.05580 q^{7} -6.38607 q^{8} +6.15132 q^{9} +O(q^{10})\)	\(q-2.55030 q^{2} +3.02512 q^{3} +4.50404 q^{4} -1.05624 q^{5} -7.71496 q^{6} +5.05580 q^{7} -6.38607 q^{8} +6.15132 q^{9} +2.69374 q^{10} -0.831588 q^{11} +13.6253 q^{12} +4.92701 q^{13} -12.8938 q^{14} -3.19526 q^{15} +7.27832 q^{16} +2.01746 q^{17} -15.6877 q^{18} +1.20792 q^{19} -4.75737 q^{20} +15.2944 q^{21} +2.12080 q^{22} -1.13685 q^{23} -19.3186 q^{24} -3.88435 q^{25} -12.5654 q^{26} +9.53312 q^{27} +22.7715 q^{28} +0.739150 q^{29} +8.14889 q^{30} +6.03259 q^{31} -5.78979 q^{32} -2.51565 q^{33} -5.14513 q^{34} -5.34016 q^{35} +27.7058 q^{36} -4.84051 q^{37} -3.08057 q^{38} +14.9048 q^{39} +6.74525 q^{40} -8.88368 q^{41} -39.0053 q^{42} +0.443812 q^{43} -3.74551 q^{44} -6.49730 q^{45} +2.89932 q^{46} +5.43952 q^{47} +22.0178 q^{48} +18.5611 q^{49} +9.90626 q^{50} +6.10304 q^{51} +22.1915 q^{52} +2.61411 q^{53} -24.3123 q^{54} +0.878361 q^{55} -32.2867 q^{56} +3.65410 q^{57} -1.88506 q^{58} +9.90028 q^{59} -14.3916 q^{60} -3.30195 q^{61} -15.3849 q^{62} +31.0999 q^{63} +0.209065 q^{64} -5.20413 q^{65} +6.41567 q^{66} +8.70028 q^{67} +9.08672 q^{68} -3.43911 q^{69} +13.6190 q^{70} -8.26681 q^{71} -39.2828 q^{72} -6.47664 q^{73} +12.3448 q^{74} -11.7506 q^{75} +5.44053 q^{76} -4.20434 q^{77} -38.0117 q^{78} -6.44420 q^{79} -7.68769 q^{80} +10.3848 q^{81} +22.6561 q^{82} -0.268665 q^{83} +68.8866 q^{84} -2.13093 q^{85} -1.13185 q^{86} +2.23602 q^{87} +5.31058 q^{88} -3.30186 q^{89} +16.5701 q^{90} +24.9100 q^{91} -5.12043 q^{92} +18.2493 q^{93} -13.8724 q^{94} -1.27586 q^{95} -17.5148 q^{96} +6.16415 q^{97} -47.3365 q^{98} -5.11537 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9} + 50 q^{10} + 25 q^{11} + 17 q^{12} + 113 q^{13} + 12 q^{14} + 12 q^{15} + 252 q^{16} + 35 q^{17} + 13 q^{18} + 97 q^{19} + 55 q^{20} + 115 q^{21} + 14 q^{22} + 27 q^{23} + 122 q^{24} + 244 q^{25} + 39 q^{26} + 34 q^{27} + 66 q^{28} + 91 q^{29} + 4 q^{30} + 135 q^{31} + 21 q^{32} + 32 q^{33} + 58 q^{34} + 17 q^{35} + 273 q^{36} + 133 q^{37} - 3 q^{38} + 55 q^{39} + 142 q^{40} + 97 q^{41} - 8 q^{42} + 67 q^{43} + 44 q^{44} + 154 q^{45} + 101 q^{46} + 20 q^{47} - 7 q^{48} + 312 q^{49} + 21 q^{50} + 23 q^{51} + 193 q^{52} + 22 q^{53} + 141 q^{54} + 88 q^{55} + 28 q^{56} + 65 q^{57} + 62 q^{58} + 41 q^{59} + q^{60} + 377 q^{61} + 29 q^{62} + 39 q^{63} + 311 q^{64} + 21 q^{65} + 35 q^{66} + 42 q^{67} + 24 q^{68} + 137 q^{69} + 35 q^{70} + 17 q^{71} - 8 q^{72} + 213 q^{73} - 9 q^{74} + 2 q^{75} + 242 q^{76} + 60 q^{77} + 103 q^{79} + 80 q^{80} + 270 q^{81} + 84 q^{82} + 42 q^{83} + 137 q^{84} + 294 q^{85} - 9 q^{86} + 22 q^{87} - 13 q^{88} + 78 q^{89} + 69 q^{90} + 118 q^{91} + 49 q^{92} + 51 q^{93} + 93 q^{94} + 10 q^{95} + 260 q^{96} + 142 q^{97} - 31 q^{98} + 78 q^{99}+O(q^{100}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9 + 50 * q^10 + 25 * q^11 + 17 * q^12 + 113 * q^13 + 12 * q^14 + 12 * q^15 + 252 * q^16 + 35 * q^17 + 13 * q^18 + 97 * q^19 + 55 * q^20 + 115 * q^21 + 14 * q^22 + 27 * q^23 + 122 * q^24 + 244 * q^25 + 39 * q^26 + 34 * q^27 + 66 * q^28 + 91 * q^29 + 4 * q^30 + 135 * q^31 + 21 * q^32 + 32 * q^33 + 58 * q^34 + 17 * q^35 + 273 * q^36 + 133 * q^37 - 3 * q^38 + 55 * q^39 + 142 * q^40 + 97 * q^41 - 8 * q^42 + 67 * q^43 + 44 * q^44 + 154 * q^45 + 101 * q^46 + 20 * q^47 - 7 * q^48 + 312 * q^49 + 21 * q^50 + 23 * q^51 + 193 * q^52 + 22 * q^53 + 141 * q^54 + 88 * q^55 + 28 * q^56 + 65 * q^57 + 62 * q^58 + 41 * q^59 + q^60 + 377 * q^61 + 29 * q^62 + 39 * q^63 + 311 * q^64 + 21 * q^65 + 35 * q^66 + 42 * q^67 + 24 * q^68 + 137 * q^69 + 35 * q^70 + 17 * q^71 - 8 * q^72 + 213 * q^73 - 9 * q^74 + 2 * q^75 + 242 * q^76 + 60 * q^77 + 103 * q^79 + 80 * q^80 + 270 * q^81 + 84 * q^82 + 42 * q^83 + 137 * q^84 + 294 * q^85 - 9 * q^86 + 22 * q^87 - 13 * q^88 + 78 * q^89 + 69 * q^90 + 118 * q^91 + 49 * q^92 + 51 * q^93 + 93 * q^94 + 10 * q^95 + 260 * q^96 + 142 * q^97 - 31 * q^98 + 78 * q^99

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