LMFDB - Embedded newform 4019.2.a.b.1.10

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			1.10
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)

$f(q)$	$=$	$q-2.60285 q^{2} -0.581840 q^{3} +4.77483 q^{4} +3.23074 q^{5} +1.51444 q^{6} -2.22687 q^{7} -7.22248 q^{8} -2.66146 q^{9} +O(q^{10})$	\(q-2.60285 q^{2} -0.581840 q^{3} +4.77483 q^{4} +3.23074 q^{5} +1.51444 q^{6} -2.22687 q^{7} -7.22248 q^{8} -2.66146 q^{9} -8.40914 q^{10} +4.03329 q^{11} -2.77819 q^{12} -4.71429 q^{13} +5.79620 q^{14} -1.87978 q^{15} +9.24938 q^{16} -2.68900 q^{17} +6.92739 q^{18} +5.82926 q^{19} +15.4263 q^{20} +1.29568 q^{21} -10.4981 q^{22} -3.12196 q^{23} +4.20233 q^{24} +5.43770 q^{25} +12.2706 q^{26} +3.29407 q^{27} -10.6329 q^{28} +3.30779 q^{29} +4.89278 q^{30} -9.01132 q^{31} -9.62979 q^{32} -2.34673 q^{33} +6.99906 q^{34} -7.19443 q^{35} -12.7080 q^{36} +4.13158 q^{37} -15.1727 q^{38} +2.74296 q^{39} -23.3340 q^{40} +2.52193 q^{41} -3.37246 q^{42} -8.22725 q^{43} +19.2583 q^{44} -8.59850 q^{45} +8.12600 q^{46} +3.83412 q^{47} -5.38166 q^{48} -2.04106 q^{49} -14.1535 q^{50} +1.56457 q^{51} -22.5099 q^{52} -5.42870 q^{53} -8.57396 q^{54} +13.0305 q^{55} +16.0835 q^{56} -3.39170 q^{57} -8.60970 q^{58} +3.04539 q^{59} -8.97562 q^{60} +5.32069 q^{61} +23.4551 q^{62} +5.92672 q^{63} +6.56615 q^{64} -15.2307 q^{65} +6.10819 q^{66} -4.67358 q^{67} -12.8395 q^{68} +1.81648 q^{69} +18.7260 q^{70} +7.47704 q^{71} +19.2224 q^{72} +0.456568 q^{73} -10.7539 q^{74} -3.16387 q^{75} +27.8337 q^{76} -8.98161 q^{77} -7.13952 q^{78} +8.71123 q^{79} +29.8824 q^{80} +6.06777 q^{81} -6.56422 q^{82} +13.8724 q^{83} +6.18666 q^{84} -8.68745 q^{85} +21.4143 q^{86} -1.92461 q^{87} -29.1304 q^{88} -12.9690 q^{89} +22.3806 q^{90} +10.4981 q^{91} -14.9068 q^{92} +5.24315 q^{93} -9.97966 q^{94} +18.8328 q^{95} +5.60300 q^{96} +13.8494 q^{97} +5.31258 q^{98} -10.7345 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.60285	−1.84049	−0.920247	−	0.391338i	$-0.872012\pi$
$2$	−2.60285	−1.84049	−0.920247	+	0.391338i	$0.872012\pi$
$3$	−0.581840	−0.335926	−0.167963	−	0.985793i	$-0.553719\pi$
$3$	−0.581840	−0.335926	−0.167963	+	0.985793i	$0.553719\pi$
$4$	4.77483	2.38742
$5$	3.23074	1.44483	0.722416	−	0.691459i	$-0.243032\pi$
$5$	3.23074	1.44483	0.722416	+	0.691459i	$0.243032\pi$
$6$	1.51444	0.618269
$7$	−2.22687	−0.841677	−0.420838	−	0.907136i	$-0.638264\pi$
$7$	−2.22687	−0.841677	−0.420838	+	0.907136i	$0.638264\pi$
$8$	−7.22248	−2.55353
$9$	−2.66146	−0.887154
$10$	−8.40914	−2.65920
$11$	4.03329	1.21608	0.608042	−	0.793905i	$-0.291955\pi$
$11$	4.03329	1.21608	0.608042	+	0.793905i	$0.291955\pi$
$12$	−2.77819	−0.801995
$13$	−4.71429	−1.30751	−0.653754	−	0.756707i	$-0.726807\pi$
$13$	−4.71429	−1.30751	−0.653754	+	0.756707i	$0.726807\pi$
$14$	5.79620	1.54910
$15$	−1.87978	−0.485356
$16$	9.24938	2.31234
$17$	−2.68900	−0.652177	−0.326089	−	0.945339i	$-0.605731\pi$
$17$	−2.68900	−0.652177	−0.326089	+	0.945339i	$0.605731\pi$
$18$	6.92739	1.63280
$19$	5.82926	1.33732	0.668661	−	0.743567i	$-0.266868\pi$
$19$	5.82926	1.33732	0.668661	+	0.743567i	$0.266868\pi$
$20$	15.4263	3.44942
$21$	1.29568	0.282741
$22$	−10.4981	−2.23819
$23$	−3.12196	−0.650974	−0.325487	−	0.945547i	$-0.605528\pi$
$23$	−3.12196	−0.650974	−0.325487	+	0.945547i	$0.605528\pi$
$24$	4.20233	0.857797
$25$	5.43770	1.08754
$26$	12.2706	2.40646
$27$	3.29407	0.633943
$28$	−10.6329	−2.00943
$29$	3.30779	0.614242	0.307121	−	0.951670i	$-0.400634\pi$
$29$	3.30779	0.614242	0.307121	+	0.951670i	$0.400634\pi$
$30$	4.89278	0.893295
$31$	−9.01132	−1.61848	−0.809241	−	0.587477i	$-0.800121\pi$
$31$	−9.01132	−1.61848	−0.809241	+	0.587477i	$0.800121\pi$
$32$	−9.62979	−1.70232
$33$	−2.34673	−0.408514
$34$	6.99906	1.20033
$35$	−7.19443	−1.21608
$36$	−12.7080	−2.11801
$37$	4.13158	0.679228	0.339614	−	0.940565i	$-0.389704\pi$
$37$	4.13158	0.679228	0.339614	+	0.940565i	$0.389704\pi$
$38$	−15.1727	−2.46133
$39$	2.74296	0.439226
$40$	−23.3340	−3.68943
$41$	2.52193	0.393860	0.196930	−	0.980418i	$-0.436903\pi$
$41$	2.52193	0.393860	0.196930	+	0.980418i	$0.436903\pi$
$42$	−3.37246	−0.520383
$43$	−8.22725	−1.25464	−0.627322	−	0.778760i	$-0.715849\pi$
$43$	−8.22725	−1.25464	−0.627322	+	0.778760i	$0.715849\pi$
$44$	19.2583	2.90330
$45$	−8.59850	−1.28179
$46$	8.12600	1.19811
$47$	3.83412	0.559265	0.279632	−	0.960107i	$-0.409787\pi$
$47$	3.83412	0.559265	0.279632	+	0.960107i	$0.409787\pi$
$48$	−5.38166	−0.776776
$49$	−2.04106	−0.291580
$50$	−14.1535	−2.00161
$51$	1.56457	0.219083
$52$	−22.5099	−3.12157
$53$	−5.42870	−0.745689	−0.372844	−	0.927894i	$-0.621617\pi$
$53$	−5.42870	−0.745689	−0.372844	+	0.927894i	$0.621617\pi$
$54$	−8.57396	−1.16677
$55$	13.0305	1.75704
$56$	16.0835	2.14925
$57$	−3.39170	−0.449241
$58$	−8.60970	−1.13051
$59$	3.04539	0.396477	0.198238	−	0.980154i	$-0.436478\pi$
$59$	3.04539	0.396477	0.198238	+	0.980154i	$0.436478\pi$
$60$	−8.97562	−1.15875
$61$	5.32069	0.681245	0.340622	−	0.940200i	$-0.389362\pi$
$61$	5.32069	0.681245	0.340622	+	0.940200i	$0.389362\pi$
$62$	23.4551	2.97881
$63$	5.92672	0.746697
$64$	6.56615	0.820769
$65$	−15.2307	−1.88913
$66$	6.10819	0.751867
$67$	−4.67358	−0.570968	−0.285484	−	0.958383i	$-0.592154\pi$
$67$	−4.67358	−0.570968	−0.285484	+	0.958383i	$0.592154\pi$
$68$	−12.8395	−1.55702
$69$	1.81648	0.218679
$70$	18.7260	2.23819
$71$	7.47704	0.887361	0.443680	−	0.896185i	$-0.353673\pi$
$71$	7.47704	0.887361	0.443680	+	0.896185i	$0.353673\pi$
$72$	19.2224	2.26538
$73$	0.456568	0.0534372	0.0267186	−	0.999643i	$-0.491494\pi$
$73$	0.456568	0.0534372	0.0267186	+	0.999643i	$0.491494\pi$
$74$	−10.7539	−1.25011
$75$	−3.16387	−0.365332
$76$	27.8337	3.19275
$77$	−8.98161	−1.02355
$78$	−7.13952	−0.808392
$79$	8.71123	0.980090	0.490045	−	0.871697i	$-0.336980\pi$
$79$	8.71123	0.980090	0.490045	+	0.871697i	$0.336980\pi$
$80$	29.8824	3.34095
$81$	6.06777	0.674196
$82$	−6.56422	−0.724897
$83$	13.8724	1.52269	0.761344	−	0.648348i	$-0.224540\pi$
$83$	13.8724	1.52269	0.761344	+	0.648348i	$0.224540\pi$
$84$	6.18666	0.675020
$85$	−8.68745	−0.942286
$86$	21.4143	2.30916
$87$	−1.92461	−0.206340
$88$	−29.1304	−3.10531
$89$	−12.9690	−1.37471	−0.687355	−	0.726322i	$-0.741228\pi$
$89$	−12.9690	−1.37471	−0.687355	+	0.726322i	$0.741228\pi$
$90$	22.3806	2.35912
$91$	10.4981	1.10050
$92$	−14.9068	−1.55415
$93$	5.24315	0.543689
$94$	−9.97966	−1.02932
$95$	18.8328	1.93221
$96$	5.60300	0.571853
$97$	13.8494	1.40619	0.703095	−	0.711096i	$-0.251801\pi$
$97$	13.8494	1.40619	0.703095	+	0.711096i	$0.251801\pi$
$98$	5.31258	0.536652
$99$	−10.7345	−1.07885
$100$	25.9641	2.59641
$101$	1.37992	0.137307	0.0686537	−	0.997641i	$-0.478130\pi$
$101$	1.37992	0.137307	0.0686537	+	0.997641i	$0.478130\pi$
$102$	−4.07233	−0.403221
$103$	−1.24334	−0.122510	−0.0612552	−	0.998122i	$-0.519510\pi$
$103$	−1.24334	−0.122510	−0.0612552	+	0.998122i	$0.519510\pi$
$104$	34.0489	3.33877
$105$	4.18601	0.408513
$106$	14.1301	1.37244
$107$	18.3026	1.76938	0.884688	−	0.466184i	$-0.154371\pi$
$107$	18.3026	1.76938	0.884688	+	0.466184i	$0.154371\pi$
$108$	15.7286	1.51349
$109$	13.9954	1.34052	0.670259	−	0.742127i	$-0.266183\pi$
$109$	13.9954	1.34052	0.670259	+	0.742127i	$0.266183\pi$
$110$	−33.9165	−3.23381
$111$	−2.40392	−0.228170
$112$	−20.5971	−1.94625
$113$	4.25192	0.399987	0.199994	−	0.979797i	$-0.435908\pi$
$113$	4.25192	0.399987	0.199994	+	0.979797i	$0.435908\pi$
$114$	8.82808	0.826825
$115$	−10.0863	−0.940548
$116$	15.7942	1.46645
$117$	12.5469	1.15996
$118$	−7.92671	−0.729713
$119$	5.98804	0.548922
$120$	13.5766	1.23937
$121$	5.26746	0.478860
$122$	−13.8490	−1.25383
$123$	−1.46736	−0.132308
$124$	−43.0276	−3.86399
$125$	1.41408	0.126479
$126$	−15.4264	−1.37429
$127$	−4.89422	−0.434292	−0.217146	−	0.976139i	$-0.569675\pi$
$127$	−4.89422	−0.434292	−0.217146	+	0.976139i	$0.569675\pi$
$128$	2.16886	0.191702
$129$	4.78695	0.421467
$130$	39.6431	3.47693
$131$	−3.00785	−0.262797	−0.131399	−	0.991330i	$-0.541947\pi$
$131$	−3.00785	−0.262797	−0.131399	+	0.991330i	$0.541947\pi$
$132$	−11.2053	−0.975293
$133$	−12.9810	−1.12559
$134$	12.1646	1.05086
$135$	10.6423	0.915942
$136$	19.4212	1.66536
$137$	−14.1715	−1.21075	−0.605376	−	0.795939i	$-0.706977\pi$
$137$	−14.1715	−1.21075	−0.605376	+	0.795939i	$0.706977\pi$
$138$	−4.72803	−0.402477
$139$	18.1021	1.53540	0.767698	−	0.640812i	$-0.221402\pi$
$139$	18.1021	1.53540	0.767698	+	0.640812i	$0.221402\pi$
$140$	−34.3522	−2.90329
$141$	−2.23085	−0.187871
$142$	−19.4616	−1.63318
$143$	−19.0141	−1.59004
$144$	−24.6169	−2.05141
$145$	10.6866	0.887476
$146$	−1.18838	−0.0983509
$147$	1.18757	0.0979493
$148$	19.7276	1.62160
$149$	−4.87781	−0.399606	−0.199803	−	0.979836i	$-0.564030\pi$
$149$	−4.87781	−0.399606	−0.199803	+	0.979836i	$0.564030\pi$
$150$	8.23508	0.672392
$151$	−6.22854	−0.506871	−0.253436	−	0.967352i	$-0.581561\pi$
$151$	−6.22854	−0.506871	−0.253436	+	0.967352i	$0.581561\pi$
$152$	−42.1017	−3.41490
$153$	7.15666	0.578582
$154$	23.3778	1.88384
$155$	−29.1133	−2.33843
$156$	13.0972	1.04861
$157$	13.4908	1.07668	0.538342	−	0.842727i	$-0.319051\pi$
$157$	13.4908	1.07668	0.538342	+	0.842727i	$0.319051\pi$
$158$	−22.6740	−1.80385
$159$	3.15863	0.250496
$160$	−31.1114	−2.45957
$161$	6.95219	0.547910
$162$	−15.7935	−1.24085
$163$	8.83059	0.691665	0.345833	−	0.938296i	$-0.387596\pi$
$163$	8.83059	0.691665	0.345833	+	0.938296i	$0.387596\pi$
$164$	12.0418	0.940308
$165$	−7.58169	−0.590234
$166$	−36.1077	−2.80250
$167$	−24.2090	−1.87335	−0.936674	−	0.350203i	$-0.886113\pi$
$167$	−24.2090	−1.87335	−0.936674	+	0.350203i	$0.886113\pi$
$168$	−9.35803	−0.721988
$169$	9.22452	0.709578
$170$	22.6121	1.73427
$171$	−15.5143	−1.18641
$172$	−39.2838	−2.99536
$173$	14.8883	1.13193	0.565967	−	0.824428i	$-0.308503\pi$
$173$	14.8883	1.13193	0.565967	+	0.824428i	$0.308503\pi$
$174$	5.00947	0.379767
$175$	−12.1090	−0.915356
$176$	37.3054	2.81200
$177$	−1.77193	−0.133187
$178$	33.7563	2.53014
$179$	−4.44169	−0.331987	−0.165994	−	0.986127i	$-0.553083\pi$
$179$	−4.44169	−0.331987	−0.165994	+	0.986127i	$0.553083\pi$
$180$	−41.0564	−3.06016
$181$	22.8415	1.69779	0.848897	−	0.528558i	$-0.177267\pi$
$181$	22.8415	1.69779	0.848897	+	0.528558i	$0.177267\pi$
$182$	−27.3250	−2.02546
$183$	−3.09579	−0.228848
$184$	22.5483	1.66228
$185$	13.3481	0.981370
$186$	−13.6471	−1.00066
$187$	−10.8455	−0.793102
$188$	18.3073	1.33520
$189$	−7.33545	−0.533575
$190$	−49.0190	−3.55621
$191$	−22.7265	−1.64443	−0.822217	−	0.569174i	$-0.807263\pi$
$191$	−22.7265	−1.64443	−0.822217	+	0.569174i	$0.807263\pi$
$192$	−3.82045	−0.275717
$193$	5.43609	0.391298	0.195649	−	0.980674i	$-0.437319\pi$
$193$	5.43609	0.391298	0.195649	+	0.980674i	$0.437319\pi$
$194$	−36.0478	−2.58808
$195$	8.86181	0.634607
$196$	−9.74574	−0.696124
$197$	8.67401	0.617998	0.308999	−	0.951062i	$-0.400006\pi$
$197$	8.67401	0.617998	0.308999	+	0.951062i	$0.400006\pi$
$198$	27.9402	1.98562
$199$	−0.295069	−0.0209169	−0.0104584	−	0.999945i	$-0.503329\pi$
$199$	−0.295069	−0.0209169	−0.0104584	+	0.999945i	$0.503329\pi$
$200$	−39.2737	−2.77707
$201$	2.71927	0.191803
$202$	−3.59173	−0.252713
$203$	−7.36602	−0.516993
$204$	7.47054	0.523043
$205$	8.14772	0.569061
$206$	3.23624	0.225479
$207$	8.30898	0.577514
$208$	−43.6042	−3.02341
$209$	23.5111	1.62630
$210$	−10.8956	−0.751865
$211$	19.1222	1.31643	0.658214	−	0.752831i	$-0.271312\pi$
$211$	19.1222	1.31643	0.658214	+	0.752831i	$0.271312\pi$
$212$	−25.9211	−1.78027
$213$	−4.35044	−0.298087
$214$	−47.6389	−3.25653
$215$	−26.5801	−1.81275
$216$	−23.7913	−1.61880
$217$	20.0670	1.36224
$218$	−36.4280	−2.46722
$219$	−0.265650	−0.0179509
$220$	62.2186	4.19478
$221$	12.6767	0.852727
$222$	6.25705	0.419945
$223$	−23.2979	−1.56014	−0.780072	−	0.625690i	$-0.784818\pi$
$223$	−23.2979	−1.56014	−0.780072	+	0.625690i	$0.784818\pi$
$224$	21.4443	1.43280
$225$	−14.4722	−0.964815
$226$	−11.0671	−0.736174
$227$	−5.74978	−0.381627	−0.190813	−	0.981626i	$-0.561113\pi$
$227$	−5.74978	−0.381627	−0.190813	+	0.981626i	$0.561113\pi$
$228$	−16.1948	−1.07253
$229$	0.0805382	0.00532211	0.00266106	−	0.999996i	$-0.499153\pi$
$229$	0.0805382	0.00532211	0.00266106	+	0.999996i	$0.499153\pi$
$230$	26.2530	1.73107
$231$	5.22586	0.343836
$232$	−23.8905	−1.56849
$233$	1.96070	0.128450	0.0642250	−	0.997935i	$-0.479542\pi$
$233$	1.96070	0.128450	0.0642250	+	0.997935i	$0.479542\pi$
$234$	−32.6577	−2.13490
$235$	12.3871	0.808043
$236$	14.5413	0.946555
$237$	−5.06854	−0.329237
$238$	−15.5860	−1.01029
$239$	30.2860	1.95904	0.979518	−	0.201358i	$-0.0645353\pi$
$239$	30.2860	1.95904	0.979518	+	0.201358i	$0.0645353\pi$
$240$	−17.3868	−1.12231
$241$	1.44120	0.0928356	0.0464178	−	0.998922i	$-0.485219\pi$
$241$	1.44120	0.0928356	0.0464178	+	0.998922i	$0.485219\pi$
$242$	−13.7104	−0.881338
$243$	−13.4127	−0.860423
$244$	25.4054	1.62642
$245$	−6.59415	−0.421285
$246$	3.81933	0.243511
$247$	−27.4808	−1.74856
$248$	65.0841	4.13285
$249$	−8.07149	−0.511510
$250$	−3.68065	−0.232785
$251$	−2.99460	−0.189017	−0.0945087	−	0.995524i	$-0.530128\pi$
$251$	−2.99460	−0.189017	−0.0945087	+	0.995524i	$0.530128\pi$
$252$	28.2991	1.78268
$253$	−12.5918	−0.791639
$254$	12.7389	0.799311
$255$	5.05471	0.316538
$256$	−18.7775	−1.17360
$257$	10.6987	0.667368	0.333684	−	0.942685i	$-0.391708\pi$
$257$	10.6987	0.667368	0.333684	+	0.942685i	$0.391708\pi$
$258$	−12.4597	−0.775707
$259$	−9.20048	−0.571690
$260$	−72.7238	−4.51014
$261$	−8.80357	−0.544927
$262$	7.82899	0.483677
$263$	29.3837	1.81188	0.905939	−	0.423409i	$-0.139167\pi$
$263$	29.3837	1.81188	0.905939	+	0.423409i	$0.139167\pi$
$264$	16.9492	1.04315
$265$	−17.5387	−1.07739
$266$	33.7876	2.07165
$267$	7.54588	0.461800
$268$	−22.3156	−1.36314
$269$	−17.3531	−1.05804	−0.529019	−	0.848610i	$-0.677440\pi$
$269$	−17.3531	−1.05804	−0.529019	+	0.848610i	$0.677440\pi$
$270$	−27.7003	−1.68578
$271$	15.3610	0.933116	0.466558	−	0.884491i	$-0.345494\pi$
$271$	15.3610	0.933116	0.466558	+	0.884491i	$0.345494\pi$
$272$	−24.8715	−1.50806
$273$	−6.10821	−0.369686
$274$	36.8863	2.22838
$275$	21.9318	1.32254
$276$	8.67340	0.522078
$277$	26.8801	1.61507	0.807533	−	0.589822i	$-0.200802\pi$
$277$	26.8801	1.61507	0.807533	+	0.589822i	$0.200802\pi$
$278$	−47.1170	−2.82589
$279$	23.9833	1.43584
$280$	51.9617	3.10530
$281$	−10.1136	−0.603329	−0.301664	−	0.953414i	$-0.597542\pi$
$281$	−10.1136	−0.603329	−0.301664	+	0.953414i	$0.597542\pi$
$282$	5.80657	0.345776
$283$	−11.9043	−0.707637	−0.353819	−	0.935314i	$-0.615117\pi$
$283$	−11.9043	−0.707637	−0.353819	+	0.935314i	$0.615117\pi$
$284$	35.7016	2.11850
$285$	−10.9577	−0.649078
$286$	49.4909	2.92646
$287$	−5.61601	−0.331503
$288$	25.6293	1.51022
$289$	−9.76930	−0.574665
$290$	−27.8157	−1.63339
$291$	−8.05812	−0.472375
$292$	2.18004	0.127577
$293$	−5.53789	−0.323527	−0.161764	−	0.986830i	$-0.551718\pi$
$293$	−5.53789	−0.323527	−0.161764	+	0.986830i	$0.551718\pi$
$294$	−3.09107	−0.180275
$295$	9.83889	0.572842
$296$	−29.8403	−1.73443
$297$	13.2859	0.770928
$298$	12.6962	0.735472
$299$	14.7178	0.851154
$300$	−15.1070	−0.872200
$301$	18.3210	1.05600
$302$	16.2120	0.932894
$303$	−0.802894	−0.0461251
$304$	53.9170	3.09235
$305$	17.1898	0.984284
$306$	−18.6277	−1.06488
$307$	−21.6036	−1.23298	−0.616491	−	0.787362i	$-0.711446\pi$
$307$	−21.6036	−1.23298	−0.616491	+	0.787362i	$0.711446\pi$
$308$	−42.8857	−2.44364
$309$	0.723427	0.0411543
$310$	75.7775	4.30387
$311$	3.07867	0.174575	0.0872877	−	0.996183i	$-0.472180\pi$
$311$	3.07867	0.174575	0.0872877	+	0.996183i	$0.472180\pi$
$312$	−19.8110	−1.12158
$313$	20.8198	1.17680	0.588401	−	0.808569i	$-0.299758\pi$
$313$	20.8198	1.17680	0.588401	+	0.808569i	$0.299758\pi$
$314$	−35.1146	−1.98163
$315$	19.1477	1.07885
$316$	41.5947	2.33988
$317$	−18.8171	−1.05688	−0.528438	−	0.848972i	$-0.677222\pi$
$317$	−18.8171	−1.05688	−0.528438	+	0.848972i	$0.677222\pi$
$318$	−8.22145	−0.461036
$319$	13.3413	0.746970
$320$	21.2135	1.18587
$321$	−10.6492	−0.594379
$322$	−18.0955	−1.00842
$323$	−15.6748	−0.872172
$324$	28.9726	1.60959
$325$	−25.6349	−1.42197
$326$	−22.9847	−1.27301
$327$	−8.14310	−0.450315
$328$	−18.2146	−1.00573
$329$	−8.53809	−0.470720
$330$	19.7340	1.08632
$331$	−23.4155	−1.28703	−0.643515	−	0.765434i	$-0.722525\pi$
$331$	−23.4155	−1.28703	−0.643515	+	0.765434i	$0.722525\pi$
$332$	66.2382	3.63529
$333$	−10.9960	−0.602580
$334$	63.0124	3.44788
$335$	−15.0991	−0.824953
$336$	11.9842	0.653794
$337$	9.52740	0.518991	0.259495	−	0.965744i	$-0.416444\pi$
$337$	9.52740	0.518991	0.259495	+	0.965744i	$0.416444\pi$
$338$	−24.0101	−1.30597
$339$	−2.47394	−0.134366
$340$	−41.4811	−2.24963
$341$	−36.3453	−1.96821
$342$	40.3815	2.18358
$343$	20.1332	1.08709
$344$	59.4212	3.20377
$345$	5.86859	0.315954
$346$	−38.7519	−2.08332
$347$	23.8554	1.28063	0.640313	−	0.768114i	$-0.278805\pi$
$347$	23.8554	1.28063	0.640313	+	0.768114i	$0.278805\pi$
$348$	−9.18968	−0.492619
$349$	6.10555	0.326823	0.163411	−	0.986558i	$-0.447750\pi$
$349$	6.10555	0.326823	0.163411	+	0.986558i	$0.447750\pi$
$350$	31.5180	1.68471
$351$	−15.5292	−0.828886
$352$	−38.8398	−2.07017
$353$	−13.5805	−0.722817	−0.361408	−	0.932408i	$-0.617704\pi$
$353$	−13.5805	−0.722817	−0.361408	+	0.932408i	$0.617704\pi$
$354$	4.61208	0.245129
$355$	24.1564	1.28209
$356$	−61.9248	−3.28201
$357$	−3.48408	−0.184397
$358$	11.5611	0.611021
$359$	−20.4483	−1.07922	−0.539610	−	0.841915i	$-0.681428\pi$
$359$	−20.4483	−1.07922	−0.539610	+	0.841915i	$0.681428\pi$
$360$	62.1025	3.27309
$361$	14.9802	0.788433
$362$	−59.4530	−3.12478
$363$	−3.06482	−0.160861
$364$	50.1267	2.62735
$365$	1.47505	0.0772078
$366$	8.05789	0.421193
$367$	27.7405	1.44804	0.724021	−	0.689778i	$-0.242292\pi$
$367$	27.7405	1.44804	0.724021	+	0.689778i	$0.242292\pi$
$368$	−28.8762	−1.50528
$369$	−6.71203	−0.349414
$370$	−34.7430	−1.80621
$371$	12.0890	0.627629
$372$	25.0352	1.29801
$373$	15.4342	0.799153	0.399577	−	0.916700i	$-0.369157\pi$
$373$	15.4342	0.799153	0.399577	+	0.916700i	$0.369157\pi$
$374$	28.2292	1.45970
$375$	−0.822770	−0.0424877
$376$	−27.6919	−1.42810
$377$	−15.5939	−0.803127
$378$	19.0931	0.982042
$379$	−13.4640	−0.691597	−0.345798	−	0.938309i	$-0.612392\pi$
$379$	−13.4640	−0.691597	−0.345798	+	0.938309i	$0.612392\pi$
$380$	89.9236	4.61298
$381$	2.84765	0.145890
$382$	59.1538	3.02657
$383$	24.5086	1.25233	0.626166	−	0.779690i	$-0.284623\pi$
$383$	24.5086	1.25233	0.626166	+	0.779690i	$0.284623\pi$
$384$	−1.26193	−0.0643976
$385$	−29.0173	−1.47886
$386$	−14.1493	−0.720182
$387$	21.8965	1.11306
$388$	66.1284	3.35716
$389$	27.5094	1.39478	0.697391	−	0.716691i	$-0.254344\pi$
$389$	27.5094	1.39478	0.697391	+	0.716691i	$0.254344\pi$
$390$	−23.0660	−1.16799
$391$	8.39494	0.424550
$392$	14.7415	0.744560
$393$	1.75009	0.0882803
$394$	−22.5772	−1.13742
$395$	28.1437	1.41607
$396$	−51.2553	−2.57567
$397$	12.2939	0.617011	0.308506	−	0.951223i	$-0.400171\pi$
$397$	12.2939	0.617011	0.308506	+	0.951223i	$0.400171\pi$
$398$	0.768020	0.0384974
$399$	7.55285	0.378116
$400$	50.2953	2.51476
$401$	23.5370	1.17538	0.587692	−	0.809085i	$-0.300037\pi$
$401$	23.5370	1.17538	0.587692	+	0.809085i	$0.300037\pi$
$402$	−7.07787	−0.353012
$403$	42.4820	2.11618
$404$	6.58890	0.327810
$405$	19.6034	0.974100
$406$	19.1726	0.951523
$407$	16.6639	0.825998
$408$	−11.3000	−0.559436
$409$	34.6341	1.71255	0.856273	−	0.516523i	$-0.172774\pi$
$409$	34.6341	1.71255	0.856273	+	0.516523i	$0.172774\pi$
$410$	−21.2073	−1.04735
$411$	8.24555	0.406723
$412$	−5.93676	−0.292483
$413$	−6.78169	−0.333705
$414$	−21.6270	−1.06291
$415$	44.8180	2.20003
$416$	45.3976	2.22580
$417$	−10.5325	−0.515779
$418$	−61.1959	−2.99319
$419$	−17.9310	−0.875986	−0.437993	−	0.898978i	$-0.644311\pi$
$419$	−17.9310	−0.875986	−0.437993	+	0.898978i	$0.644311\pi$
$420$	19.9875	0.975291
$421$	33.4713	1.63129	0.815645	−	0.578553i	$-0.196383\pi$
$421$	33.4713	1.63129	0.815645	+	0.578553i	$0.196383\pi$
$422$	−49.7723	−2.42288
$423$	−10.2044	−0.496154
$424$	39.2087	1.90414
$425$	−14.6219	−0.709268
$426$	11.3235	0.548628
$427$	−11.8485	−0.573388
$428$	87.3917	4.22424
$429$	11.0632	0.534135
$430$	69.1841	3.33635
$431$	−19.4577	−0.937246	−0.468623	−	0.883398i	$-0.655250\pi$
$431$	−19.4577	−0.937246	−0.468623	+	0.883398i	$0.655250\pi$
$432$	30.4681	1.46590
$433$	14.3230	0.688318	0.344159	−	0.938911i	$-0.388164\pi$
$433$	14.3230	0.688318	0.344159	+	0.938911i	$0.388164\pi$
$434$	−52.2315	−2.50719
$435$	−6.21791	−0.298126
$436$	66.8259	3.20038
$437$	−18.1987	−0.870562
$438$	0.691446	0.0330386
$439$	13.2270	0.631291	0.315645	−	0.948877i	$-0.397779\pi$
$439$	13.2270	0.631291	0.315645	+	0.948877i	$0.397779\pi$
$440$	−94.1128	−4.48665
$441$	5.43221	0.258677
$442$	−32.9956	−1.56944
$443$	−8.59899	−0.408550	−0.204275	−	0.978914i	$-0.565484\pi$
$443$	−8.59899	−0.408550	−0.204275	+	0.978914i	$0.565484\pi$
$444$	−11.4783	−0.544737
$445$	−41.8995	−1.98622
$446$	60.6410	2.87144
$447$	2.83811	0.134238
$448$	−14.6219	−0.690822
$449$	−28.0592	−1.32419	−0.662097	−	0.749418i	$-0.730333\pi$
$449$	−28.0592	−1.32419	−0.662097	+	0.749418i	$0.730333\pi$
$450$	37.6690	1.77574
$451$	10.1717	0.478967
$452$	20.3022	0.954936
$453$	3.62401	0.170271
$454$	14.9658	0.702381
$455$	33.9166	1.59004
$456$	24.4965	1.14715
$457$	32.9619	1.54189	0.770945	−	0.636901i	$-0.219784\pi$
$457$	32.9619	1.54189	0.770945	+	0.636901i	$0.219784\pi$
$458$	−0.209629	−0.00979531
$459$	−8.85773	−0.413443
$460$	−48.1602	−2.24548
$461$	−17.9855	−0.837667	−0.418834	−	0.908063i	$-0.637561\pi$
$461$	−17.9855	−0.837667	−0.418834	+	0.908063i	$0.637561\pi$
$462$	−13.6021	−0.632829
$463$	33.0169	1.53443	0.767213	−	0.641393i	$-0.221643\pi$
$463$	33.0169	1.53443	0.767213	+	0.641393i	$0.221643\pi$
$464$	30.5950	1.42034
$465$	16.9393	0.785540
$466$	−5.10342	−0.236411
$467$	22.4296	1.03792	0.518958	−	0.854800i	$-0.326320\pi$
$467$	22.4296	1.03792	0.518958	+	0.854800i	$0.326320\pi$
$468$	59.9094	2.76931
$469$	10.4074	0.480571
$470$	−32.2417	−1.48720
$471$	−7.84949	−0.361686
$472$	−21.9953	−1.01242
$473$	−33.1829	−1.52575
$474$	13.1927	0.605959
$475$	31.6977	1.45439
$476$	28.5919	1.31051
$477$	14.4483	0.661541
$478$	−78.8298	−3.60559
$479$	7.54402	0.344695	0.172347	−	0.985036i	$-0.444865\pi$
$479$	7.54402	0.344695	0.172347	+	0.985036i	$0.444865\pi$
$480$	18.1018	0.826232
$481$	−19.4775	−0.888096
$482$	−3.75122	−0.170863
$483$	−4.04507	−0.184057
$484$	25.1512	1.14324
$485$	44.7437	2.03171
$486$	34.9112	1.58360
$487$	−41.5037	−1.88071	−0.940355	−	0.340193i	$-0.889507\pi$
$487$	−41.5037	−1.88071	−0.940355	+	0.340193i	$0.889507\pi$
$488$	−38.4286	−1.73958
$489$	−5.13799	−0.232348
$490$	17.1636	0.775372
$491$	−2.05169	−0.0925913	−0.0462957	−	0.998928i	$-0.514742\pi$
$491$	−2.05169	−0.0925913	−0.0462957	+	0.998928i	$0.514742\pi$
$492$	−7.00641	−0.315874
$493$	−8.89464	−0.400595
$494$	71.5284	3.21822
$495$	−34.6803	−1.55876
$496$	−83.3491	−3.74249
$497$	−16.6504	−0.746871
$498$	21.0089	0.941431
$499$	−17.7304	−0.793721	−0.396861	−	0.917879i	$-0.629900\pi$
$499$	−17.7304	−0.793721	−0.396861	+	0.917879i	$0.629900\pi$
$500$	6.75201	0.301959
$501$	14.0858	0.629305
$502$	7.79450	0.347885
$503$	16.2304	0.723678	0.361839	−	0.932241i	$-0.382149\pi$
$503$	16.2304	0.723678	0.361839	+	0.932241i	$0.382149\pi$
$504$	−42.8056	−1.90671
$505$	4.45817	0.198386
$506$	32.7745	1.45701
$507$	−5.36720	−0.238366
$508$	−23.3691	−1.03684
$509$	−16.6480	−0.737909	−0.368955	−	0.929447i	$-0.620284\pi$
$509$	−16.6480	−0.737909	−0.368955	+	0.929447i	$0.620284\pi$
$510$	−13.1567	−0.582586
$511$	−1.01672	−0.0449769
$512$	44.5374	1.96829
$513$	19.2020	0.847787
$514$	−27.8472	−1.22829
$515$	−4.01692	−0.177007
$516$	22.8569	1.00622
$517$	15.4642	0.680113
$518$	23.9475	1.05219
$519$	−8.66259	−0.380246
$520$	110.003	4.82396
$521$	14.9806	0.656311	0.328156	−	0.944624i	$-0.393573\pi$
$521$	14.9806	0.656311	0.328156	+	0.944624i	$0.393573\pi$
$522$	22.9144	1.00294
$523$	−27.7237	−1.21227	−0.606137	−	0.795360i	$-0.707282\pi$
$523$	−27.7237	−1.21227	−0.606137	+	0.795360i	$0.707282\pi$
$524$	−14.3620	−0.627407
$525$	7.04552	0.307492
$526$	−76.4814	−3.33475
$527$	24.2314	1.05554
$528$	−21.7058	−0.944624
$529$	−13.2534	−0.576233
$530$	45.6507	1.98294
$531$	−8.10520	−0.351736
$532$	−61.9820	−2.68726
$533$	−11.8891	−0.514975
$534$	−19.6408	−0.849940
$535$	59.1309	2.55645
$536$	33.7548	1.45799
$537$	2.58435	0.111523
$538$	45.1676	1.94731
$539$	−8.23220	−0.354586
$540$	50.8151	2.18673
$541$	23.0589	0.991379	0.495689	−	0.868500i	$-0.334915\pi$
$541$	23.0589	0.991379	0.495689	+	0.868500i	$0.334915\pi$
$542$	−39.9825	−1.71739
$543$	−13.2901	−0.570333
$544$	25.8945	1.11022
$545$	45.2156	1.93682
$546$	15.8988	0.680405
$547$	−25.6204	−1.09545	−0.547725	−	0.836658i	$-0.684506\pi$
$547$	−25.6204	−1.09545	−0.547725	+	0.836658i	$0.684506\pi$
$548$	−67.6666	−2.89057
$549$	−14.1608	−0.604369
$550$	−57.0853	−2.43412
$551$	19.2820	0.821440
$552$	−13.1195	−0.558404
$553$	−19.3988	−0.824919
$554$	−69.9648	−2.97252
$555$	−7.76645	−0.329667
$556$	86.4343	3.66563
$557$	27.1151	1.14890	0.574452	−	0.818538i	$-0.305215\pi$
$557$	27.1151	1.14890	0.574452	+	0.818538i	$0.305215\pi$
$558$	−62.4250	−2.64266
$559$	38.7856	1.64046
$560$	−66.5440	−2.81200
$561$	6.31035	0.266423
$562$	26.3243	1.11042
$563$	−40.4603	−1.70520	−0.852599	−	0.522566i	$-0.824975\pi$
$563$	−40.4603	−1.70520	−0.852599	+	0.522566i	$0.824975\pi$
$564$	−10.6519	−0.448527
$565$	13.7369	0.577914
$566$	30.9851	1.30240
$567$	−13.5121	−0.567455
$568$	−54.0028	−2.26591
$569$	20.1464	0.844583	0.422291	−	0.906460i	$-0.361226\pi$
$569$	20.1464	0.844583	0.422291	+	0.906460i	$0.361226\pi$
$570$	28.5212	1.19462
$571$	−27.3543	−1.14474	−0.572372	−	0.819994i	$-0.693977\pi$
$571$	−27.3543	−1.14474	−0.572372	+	0.819994i	$0.693977\pi$
$572$	−90.7892	−3.79609
$573$	13.2232	0.552407
$574$	14.6176	0.610129
$575$	−16.9763	−0.707960
$576$	−17.4756	−0.728148
$577$	34.8432	1.45054	0.725270	−	0.688464i	$-0.241715\pi$
$577$	34.8432	1.45054	0.725270	+	0.688464i	$0.241715\pi$
$578$	25.4280	1.05767
$579$	−3.16293	−0.131447
$580$	51.0269	2.11878
$581$	−30.8919	−1.28161
$582$	20.9741	0.869404
$583$	−21.8955	−0.906820
$584$	−3.29755	−0.136454
$585$	40.5358	1.67595
$586$	14.4143	0.595450
$587$	−17.0271	−0.702783	−0.351392	−	0.936229i	$-0.614291\pi$
$587$	−17.0271	−0.702783	−0.351392	+	0.936229i	$0.614291\pi$
$588$	5.67046	0.233846
$589$	−52.5293	−2.16443
$590$	−25.6092	−1.05431
$591$	−5.04689	−0.207601
$592$	38.2145	1.57061
$593$	−22.8666	−0.939018	−0.469509	−	0.882928i	$-0.655569\pi$
$593$	−22.8666	−0.939018	−0.469509	+	0.882928i	$0.655569\pi$
$594$	−34.5813	−1.41889
$595$	19.3458	0.793100
$596$	−23.2907	−0.954026
$597$	0.171683	0.00702651
$598$	−38.3083	−1.56654
$599$	20.6924	0.845471	0.422735	−	0.906253i	$-0.361070\pi$
$599$	20.6924	0.845471	0.422735	+	0.906253i	$0.361070\pi$
$600$	22.8510	0.932888
$601$	−22.5292	−0.918984	−0.459492	−	0.888182i	$-0.651969\pi$
$601$	−22.5292	−0.918984	−0.459492	+	0.888182i	$0.651969\pi$
$602$	−47.6868	−1.94357
$603$	12.4385	0.506537
$604$	−29.7402	−1.21011
$605$	17.0178	0.691872
$606$	2.08981	0.0848929
$607$	−44.0656	−1.78857	−0.894284	−	0.447500i	$-0.852314\pi$
$607$	−44.0656	−1.78857	−0.894284	+	0.447500i	$0.852314\pi$
$608$	−56.1345	−2.27655
$609$	4.28585	0.173671
$610$	−44.7425	−1.81157
$611$	−18.0752	−0.731243
$612$	34.1719	1.38132
$613$	17.2550	0.696922	0.348461	−	0.937323i	$-0.386704\pi$
$613$	17.2550	0.696922	0.348461	+	0.937323i	$0.386704\pi$
$614$	56.2309	2.26930
$615$	−4.74067	−0.191162
$616$	64.8695	2.61367
$617$	30.1514	1.21385	0.606925	−	0.794759i	$-0.292403\pi$
$617$	30.1514	1.21385	0.606925	+	0.794759i	$0.292403\pi$
$618$	−1.88297	−0.0757443
$619$	−14.4811	−0.582044	−0.291022	−	0.956716i	$-0.593995\pi$
$619$	−14.4811	−0.582044	−0.291022	+	0.956716i	$0.593995\pi$
$620$	−139.011	−5.58282
$621$	−10.2839	−0.412681
$622$	−8.01333	−0.321305
$623$	28.8802	1.15706
$624$	25.3707	1.01564
$625$	−22.6199	−0.904798
$626$	−54.1907	−2.16590
$627$	−13.6797	−0.546315
$628$	64.4164	2.57049
$629$	−11.1098	−0.442977
$630$	−49.8386	−1.98562
$631$	19.6561	0.782498	0.391249	−	0.920285i	$-0.372043\pi$
$631$	19.6561	0.782498	0.391249	+	0.920285i	$0.372043\pi$
$632$	−62.9167	−2.50269
$633$	−11.1261	−0.442222
$634$	48.9782	1.94517
$635$	−15.8120	−0.627479
$636$	15.0819	0.598038
$637$	9.62216	0.381244
$638$	−34.7254	−1.37479
$639$	−19.8998	−0.787226
$640$	7.00703	0.276977
$641$	1.05505	0.0416721	0.0208361	−	0.999783i	$-0.493367\pi$
$641$	1.05505	0.0416721	0.0208361	+	0.999783i	$0.493367\pi$
$642$	27.7182	1.09395
$643$	31.2750	1.23336	0.616682	−	0.787212i	$-0.288476\pi$
$643$	31.2750	1.23336	0.616682	+	0.787212i	$0.288476\pi$
$644$	33.1956	1.30809
$645$	15.4654	0.608949
$646$	40.7993	1.60523
$647$	26.8238	1.05455	0.527275	−	0.849694i	$-0.323214\pi$
$647$	26.8238	1.05455	0.527275	+	0.849694i	$0.323214\pi$
$648$	−43.8243	−1.72158
$649$	12.2830	0.482149
$650$	66.7238	2.61712
$651$	−11.6758	−0.457611
$652$	42.1646	1.65129
$653$	−5.67564	−0.222105	−0.111053	−	0.993815i	$-0.535422\pi$
$653$	−5.67564	−0.222105	−0.111053	+	0.993815i	$0.535422\pi$
$654$	21.1953	0.828801
$655$	−9.71759	−0.379698
$656$	23.3263	0.910740
$657$	−1.21514	−0.0474070
$658$	22.2234	0.866357
$659$	−9.04844	−0.352477	−0.176239	−	0.984347i	$-0.556393\pi$
$659$	−9.04844	−0.352477	−0.176239	+	0.984347i	$0.556393\pi$
$660$	−36.2013	−1.40913
$661$	−3.69108	−0.143566	−0.0717831	−	0.997420i	$-0.522869\pi$
$661$	−3.69108	−0.143566	−0.0717831	+	0.997420i	$0.522869\pi$
$662$	60.9470	2.36877
$663$	−7.37581	−0.286453
$664$	−100.193	−3.88824
$665$	−41.9382	−1.62629
$666$	28.6211	1.10904
$667$	−10.3268	−0.399855
$668$	−115.594	−4.47246
$669$	13.5557	0.524092
$670$	39.3008	1.51832
$671$	21.4599	0.828451
$672$	−12.4771	−0.481316
$673$	0.0110551	0.000426142 0	0.000213071	−	1.00000i	$-0.499932\pi$
$673$	0.0110551	0.000426142 0	0.000213071		1.00000i	$0.499932\pi$
$674$	−24.7984	−0.955199
$675$	17.9121	0.689438
$676$	44.0456	1.69406
$677$	−8.81460	−0.338773	−0.169386	−	0.985550i	$-0.554179\pi$
$677$	−8.81460	−0.338773	−0.169386	+	0.985550i	$0.554179\pi$
$678$	6.43929	0.247300
$679$	−30.8407	−1.18356
$680$	62.7450	2.40616
$681$	3.34546	0.128198
$682$	94.6014	3.62248
$683$	−22.2786	−0.852467	−0.426233	−	0.904613i	$-0.640160\pi$
$683$	−22.2786	−0.852467	−0.426233	+	0.904613i	$0.640160\pi$
$684$	−74.0784	−2.83246
$685$	−45.7845	−1.74933
$686$	−52.4038	−2.00079
$687$	−0.0468603	−0.00178783
$688$	−76.0969	−2.90117
$689$	25.5924	0.974994
$690$	−15.2751	−0.581512
$691$	38.5630	1.46700	0.733502	−	0.679687i	$-0.237885\pi$
$691$	38.5630	1.46700	0.733502	+	0.679687i	$0.237885\pi$
$692$	71.0890	2.70240
$693$	23.9042	0.908046
$694$	−62.0921	−2.35698
$695$	58.4831	2.21839
$696$	13.9004	0.526895
$697$	−6.78147	−0.256867
$698$	−15.8918	−0.601515
$699$	−1.14082	−0.0431497
$700$	−57.8186	−2.18534
$701$	17.1364	0.647231	0.323616	−	0.946189i	$-0.395102\pi$
$701$	17.1364	0.647231	0.323616	+	0.946189i	$0.395102\pi$
$702$	40.4201	1.52556
$703$	24.0840	0.908347
$704$	26.4832	0.998124
$705$	−7.20729	−0.271442
$706$	35.3480	1.33034
$707$	−3.07290	−0.115568
$708$	−8.46069	−0.317972
$709$	22.3435	0.839128	0.419564	−	0.907726i	$-0.362183\pi$
$709$	22.3435	0.839128	0.419564	+	0.907726i	$0.362183\pi$
$710$	−62.8754	−2.35967
$711$	−23.1846	−0.869491
$712$	93.6683	3.51037
$713$	28.1330	1.05359
$714$	9.06854	0.339382
$715$	−61.4297	−2.29734
$716$	−21.2083	−0.792592
$717$	−17.6216	−0.658090
$718$	53.2239	1.98630
$719$	10.0020	0.373011	0.186505	−	0.982454i	$-0.440284\pi$
$719$	10.0020	0.373011	0.186505	+	0.982454i	$0.440284\pi$
$720$	−79.5307	−2.96394
$721$	2.76876	0.103114
$722$	−38.9913	−1.45111
$723$	−0.838546	−0.0311859
$724$	109.064	4.05334
$725$	17.9868	0.668012
$726$	7.97726	0.296064
$727$	38.9666	1.44519	0.722595	−	0.691271i	$-0.242949\pi$
$727$	38.9666	1.44519	0.722595	+	0.691271i	$0.242949\pi$
$728$	−75.8223	−2.81016
$729$	−10.3993	−0.385158
$730$	−3.83934	−0.142100
$731$	22.1230	0.818250
$732$	−14.7819	−0.546355
$733$	26.4891	0.978399	0.489199	−	0.872172i	$-0.337289\pi$
$733$	26.4891	0.978399	0.489199	+	0.872172i	$0.337289\pi$
$734$	−72.2044	−2.66511
$735$	3.83674	0.141520
$736$	30.0638	1.10817
$737$	−18.8499	−0.694345
$738$	17.4704	0.643095
$739$	9.04353	0.332672	0.166336	−	0.986069i	$-0.446806\pi$
$739$	9.04353	0.332672	0.166336	+	0.986069i	$0.446806\pi$
$740$	63.7348	2.34294
$741$	15.9894	0.587386
$742$	−31.4658	−1.15515
$743$	8.83323	0.324060	0.162030	−	0.986786i	$-0.448196\pi$
$743$	8.83323	0.324060	0.162030	+	0.986786i	$0.448196\pi$
$744$	−37.8686	−1.38833
$745$	−15.7590	−0.577363
$746$	−40.1730	−1.47084
$747$	−36.9207	−1.35086
$748$	−51.7855	−1.89347
$749$	−40.7574	−1.48924
$750$	2.14155	0.0781983
$751$	−8.64589	−0.315493	−0.157747	−	0.987480i	$-0.550423\pi$
$751$	−8.64589	−0.315493	−0.157747	+	0.987480i	$0.550423\pi$
$752$	35.4633	1.29321
$753$	1.74238	0.0634958
$754$	40.5886	1.47815
$755$	−20.1228	−0.732344
$756$	−35.0255	−1.27387
$757$	12.6187	0.458634	0.229317	−	0.973352i	$-0.426351\pi$
$757$	12.6187	0.458634	0.229317	+	0.973352i	$0.426351\pi$
$758$	35.0447	1.27288
$759$	7.32641	0.265932
$760$	−136.020	−4.93395
$761$	19.4618	0.705488	0.352744	−	0.935720i	$-0.385249\pi$
$761$	19.4618	0.705488	0.352744	+	0.935720i	$0.385249\pi$
$762$	−7.41202	−0.268509
$763$	−31.1660	−1.12828
$764$	−108.515	−3.92595
$765$	23.1213	0.835953
$766$	−63.7923	−2.30491
$767$	−14.3569	−0.518397
$768$	10.9255	0.394241
$769$	6.06539	0.218723	0.109362	−	0.994002i	$-0.465119\pi$
$769$	6.06539	0.218723	0.109362	+	0.994002i	$0.465119\pi$
$770$	75.5276	2.72183
$771$	−6.22495	−0.224186
$772$	25.9564	0.934192
$773$	−14.7377	−0.530079	−0.265040	−	0.964238i	$-0.585385\pi$
$773$	−14.7377	−0.530079	−0.265040	+	0.964238i	$0.585385\pi$
$774$	−56.9934	−2.04858
$775$	−49.0008	−1.76016
$776$	−100.027	−3.59075
$777$	5.35321	0.192045
$778$	−71.6028	−2.56709
$779$	14.7010	0.526718
$780$	42.3137	1.51507
$781$	30.1571	1.07911
$782$	−21.8508	−0.781382
$783$	10.8961	0.389395
$784$	−18.8786	−0.674234
$785$	43.5853	1.55563
$786$	−4.55522	−0.162479
$787$	−39.3387	−1.40227	−0.701136	−	0.713027i	$-0.747324\pi$
$787$	−39.3387	−1.40227	−0.701136	+	0.713027i	$0.747324\pi$
$788$	41.4170	1.47542
$789$	−17.0966	−0.608656
$790$	−73.2540	−2.60626
$791$	−9.46846	−0.336660
$792$	77.5294	2.75489
$793$	−25.0833	−0.890734
$794$	−31.9991	−1.13561
$795$	10.2047	0.361924
$796$	−1.40890	−0.0499373
$797$	−12.2574	−0.434178	−0.217089	−	0.976152i	$-0.569656\pi$
$797$	−12.2574	−0.434178	−0.217089	+	0.976152i	$0.569656\pi$
$798$	−19.6590	−0.695919
$799$	−10.3099	−0.364740
$800$	−52.3639	−1.85134
$801$	34.5165	1.21958
$802$	−61.2634	−2.16329
$803$	1.84147	0.0649841
$804$	12.9841	0.457913
$805$	22.4607	0.791637
$806$	−110.574	−3.89481
$807$	10.0967	0.355422
$808$	−9.96647	−0.350619
$809$	14.4996	0.509780	0.254890	−	0.966970i	$-0.417961\pi$
$809$	14.4996	0.509780	0.254890	+	0.966970i	$0.417961\pi$
$810$	−51.0247	−1.79283
$811$	34.0733	1.19647	0.598237	−	0.801319i	$-0.295868\pi$
$811$	34.0733	1.19647	0.598237	+	0.801319i	$0.295868\pi$
$812$	−35.1715	−1.23428
$813$	−8.93766	−0.313458
$814$	−43.3736	−1.52024
$815$	28.5294	0.999340
$816$	14.4713	0.506595
$817$	−47.9587	−1.67786
$818$	−90.1475	−3.15193
$819$	−27.9403	−0.976312
$820$	38.9040	1.35859
$821$	−42.4020	−1.47984	−0.739920	−	0.672695i	$-0.765137\pi$
$821$	−42.4020	−1.47984	−0.739920	+	0.672695i	$0.765137\pi$
$822$	−21.4619	−0.748571
$823$	28.5204	0.994160	0.497080	−	0.867705i	$-0.334406\pi$
$823$	28.5204	0.994160	0.497080	+	0.867705i	$0.334406\pi$
$824$	8.98003	0.312834
$825$	−12.7608	−0.444275
$826$	17.6517	0.614182
$827$	−51.4704	−1.78980	−0.894901	−	0.446266i	$-0.852754\pi$
$827$	−51.4704	−1.78980	−0.894901	+	0.446266i	$0.852754\pi$
$828$	39.6740	1.37877
$829$	51.5474	1.79032	0.895158	−	0.445748i	$-0.147062\pi$
$829$	51.5474	1.79032	0.895158	+	0.445748i	$0.147062\pi$
$830$	−116.655	−4.04914
$831$	−15.6399	−0.542542
$832$	−30.9547	−1.07316
$833$	5.48841	0.190162
$834$	27.4145	0.949288
$835$	−78.2130	−2.70667
$836$	112.262	3.88265
$837$	−29.6839	−1.02603
$838$	46.6717	1.61225
$839$	21.7819	0.751995	0.375998	−	0.926621i	$-0.377300\pi$
$839$	21.7819	0.751995	0.375998	+	0.926621i	$0.377300\pi$
$840$	−30.2334	−1.04315
$841$	−18.0585	−0.622707
$842$	−87.1207	−3.00238
$843$	5.88452	0.202674
$844$	91.3054	3.14286
$845$	29.8020	1.02522
$846$	26.5605	0.913168
$847$	−11.7299	−0.403045
$848$	−50.2120	−1.72429
$849$	6.92640	0.237713
$850$	38.0587	1.30540
$851$	−12.8986	−0.442160
$852$	−20.7726	−0.711659
$853$	11.5969	0.397071	0.198535	−	0.980094i	$-0.436381\pi$
$853$	11.5969	0.397071	0.198535	+	0.980094i	$0.436381\pi$
$854$	30.8398	1.05532
$855$	−50.1228	−1.71416
$856$	−132.190	−4.51816
$857$	33.3487	1.13917	0.569584	−	0.821933i	$-0.307104\pi$
$857$	33.3487	1.13917	0.569584	+	0.821933i	$0.307104\pi$
$858$	−28.7958	−0.983072
$859$	1.56628	0.0534409	0.0267205	−	0.999643i	$-0.491494\pi$
$859$	1.56628	0.0534409	0.0267205	+	0.999643i	$0.491494\pi$
$860$	−126.916	−4.32779
$861$	3.26762	0.111360
$862$	50.6456	1.72500
$863$	44.0570	1.49972	0.749859	−	0.661598i	$-0.230122\pi$
$863$	44.0570	1.49972	0.749859	+	0.661598i	$0.230122\pi$
$864$	−31.7212	−1.07918
$865$	48.1001	1.63545
$866$	−37.2805	−1.26684
$867$	5.68417	0.193045
$868$	95.8167	3.25223
$869$	35.1350	1.19187
$870$	16.1843	0.548699
$871$	22.0326	0.746546
$872$	−101.082	−3.42306
$873$	−36.8596	−1.24751
$874$	47.3685	1.60226
$875$	−3.14897	−0.106455
$876$	−1.26843	−0.0428564
$877$	14.5725	0.492077	0.246039	−	0.969260i	$-0.420871\pi$
$877$	14.5725	0.492077	0.246039	+	0.969260i	$0.420871\pi$
$878$	−34.4279	−1.16189
$879$	3.22217	0.108681
$880$	120.524	4.06287
$881$	−29.2885	−0.986755	−0.493378	−	0.869815i	$-0.664238\pi$
$881$	−29.2885	−0.986755	−0.493378	+	0.869815i	$0.664238\pi$
$882$	−14.1392	−0.476093
$883$	−37.8388	−1.27338	−0.636688	−	0.771121i	$-0.719696\pi$
$883$	−37.8388	−1.27338	−0.636688	+	0.771121i	$0.719696\pi$
$884$	60.5292	2.03582
$885$	−5.72466	−0.192432
$886$	22.3819	0.751934
$887$	−6.93190	−0.232751	−0.116375	−	0.993205i	$-0.537128\pi$
$887$	−6.93190	−0.232751	−0.116375	+	0.993205i	$0.537128\pi$
$888$	17.3623	0.582640
$889$	10.8988	0.365533
$890$	109.058	3.65563
$891$	24.4731	0.819879
$892$	−111.244	−3.72472
$893$	22.3501	0.747917
$894$	−7.38717	−0.247064
$895$	−14.3500	−0.479666
$896$	−4.82976	−0.161351
$897$	−8.56342	−0.285924
$898$	73.0338	2.43717
$899$	−29.8076	−0.994139
$900$	−69.1025	−2.30342
$901$	14.5977	0.486321
$902$	−26.4754	−0.881535
$903$	−10.6599	−0.354739
$904$	−30.7094	−1.02138
$905$	73.7950	2.45303
$906$	−9.43277	−0.313383
$907$	33.2360	1.10358	0.551792	−	0.833982i	$-0.313944\pi$
$907$	33.2360	1.10358	0.551792	+	0.833982i	$0.313944\pi$
$908$	−27.4543	−0.911102
$909$	−3.67261	−0.121813
$910$	−88.2800	−2.92645
$911$	−52.6522	−1.74445	−0.872223	−	0.489108i	$-0.837322\pi$
$911$	−52.6522	−1.74445	−0.872223	+	0.489108i	$0.837322\pi$
$912$	−31.3711	−1.03880
$913$	55.9513	1.85172
$914$	−85.7948	−2.83784
$915$	−10.0017	−0.330646
$916$	0.384556	0.0127061
$917$	6.69808	0.221190
$918$	23.0554	0.760940
$919$	53.9502	1.77965	0.889826	−	0.456299i	$-0.150825\pi$
$919$	53.9502	1.77965	0.889826	+	0.456299i	$0.150825\pi$
$920$	72.8478	2.40172
$921$	12.5698	0.414190
$922$	46.8135	1.54172
$923$	−35.2489	−1.16023
$924$	24.9526	0.820881
$925$	22.4663	0.738687
$926$	−85.9381	−2.82410
$927$	3.30911	0.108686
$928$	−31.8534	−1.04564
$929$	37.6109	1.23397	0.616987	−	0.786974i	$-0.288353\pi$
$929$	37.6109	1.23397	0.616987	+	0.786974i	$0.288353\pi$
$930$	−44.0904	−1.44578
$931$	−11.8979	−0.389937
$932$	9.36204	0.306664
$933$	−1.79130	−0.0586444
$934$	−58.3808	−1.91028
$935$	−35.0390	−1.14590
$936$	−90.6198	−2.96200
$937$	52.6193	1.71900	0.859498	−	0.511139i	$-0.170776\pi$
$937$	52.6193	1.71900	0.859498	+	0.511139i	$0.170776\pi$
$938$	−27.0890	−0.884487
$939$	−12.1138	−0.395318
$940$	59.1462	1.92914
$941$	11.0840	0.361327	0.180663	−	0.983545i	$-0.442176\pi$
$941$	11.0840	0.361327	0.180663	+	0.983545i	$0.442176\pi$
$942$	20.4311	0.665680
$943$	−7.87338	−0.256393
$944$	28.1680	0.916790
$945$	−23.6989	−0.770927
$946$	86.3702	2.80814
$947$	−29.9174	−0.972184	−0.486092	−	0.873908i	$-0.661578\pi$
$947$	−29.9174	−0.972184	−0.486092	+	0.873908i	$0.661578\pi$
$948$	−24.2015	−0.786027
$949$	−2.15239	−0.0698696
$950$	−82.5044	−2.67680
$951$	10.9486	0.355031
$952$	−43.2485	−1.40169
$953$	16.0720	0.520622	0.260311	−	0.965525i	$-0.416175\pi$
$953$	16.0720	0.520622	0.260311	+	0.965525i	$0.416175\pi$
$954$	−37.6067	−1.21756
$955$	−73.4236	−2.37593
$956$	144.610	4.67704
$957$	−7.76251	−0.250926
$958$	−19.6360	−0.634409
$959$	31.5580	1.01906
$960$	−12.3429	−0.398365
$961$	50.2040	1.61948
$962$	50.6969	1.63454
$963$	−48.7116	−1.56971
$964$	6.88147	0.221637
$965$	17.5626	0.565360
$966$	10.5287	0.338755
$967$	23.9050	0.768731	0.384366	−	0.923181i	$-0.374420\pi$
$967$	23.9050	0.768731	0.384366	+	0.923181i	$0.374420\pi$
$968$	−38.0441	−1.22278
$969$	9.12025	0.292985
$970$	−116.461	−3.73935
$971$	−42.8623	−1.37552	−0.687758	−	0.725940i	$-0.741405\pi$
$971$	−42.8623	−1.37552	−0.687758	+	0.725940i	$0.741405\pi$
$972$	−64.0433	−2.05419
$973$	−40.3109	−1.29231
$974$	108.028	3.46144
$975$	14.9154	0.477675
$976$	49.2131	1.57527
$977$	23.5289	0.752757	0.376379	−	0.926466i	$-0.377169\pi$
$977$	23.5289	0.752757	0.376379	+	0.926466i	$0.377169\pi$
$978$	13.3734	0.427635
$979$	−52.3077	−1.67176
$980$	−31.4860	−1.00578
$981$	−37.2483	−1.18925
$982$	5.34024	0.170414
$983$	15.2508	0.486423	0.243212	−	0.969973i	$-0.421799\pi$
$983$	15.2508	0.486423	0.243212	+	0.969973i	$0.421799\pi$
$984$	10.5980	0.337852
$985$	28.0235	0.892903
$986$	23.1514	0.737292
$987$	4.96780	0.158127
$988$	−131.216	−4.17454
$989$	25.6852	0.816741
$990$	90.2676	2.86889
$991$	−14.9054	−0.473485	−0.236743	−	0.971572i	$-0.576080\pi$
$991$	−14.9054	−0.473485	−0.236743	+	0.971572i	$0.576080\pi$
$992$	86.7771	2.75518
$993$	13.6241	0.432346
$994$	43.3384	1.37461
$995$	−0.953291	−0.0302214
$996$	−38.5400	−1.22119
$997$	9.82443	0.311143	0.155571	−	0.987825i	$-0.450278\pi$
$997$	9.82443	0.311143	0.155571	+	0.987825i	$0.450278\pi$
$998$	46.1496	1.46084
$999$	13.6097	0.430592

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.b.1.10	✓	186

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.b.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-2.60285 q^{2} -0.581840 q^{3} +4.77483 q^{4} +3.23074 q^{5} +1.51444 q^{6} -2.22687 q^{7} -7.22248 q^{8} -2.66146 q^{9} +O(q^{10})\)	\(q-2.60285 q^{2} -0.581840 q^{3} +4.77483 q^{4} +3.23074 q^{5} +1.51444 q^{6} -2.22687 q^{7} -7.22248 q^{8} -2.66146 q^{9} -8.40914 q^{10} +4.03329 q^{11} -2.77819 q^{12} -4.71429 q^{13} +5.79620 q^{14} -1.87978 q^{15} +9.24938 q^{16} -2.68900 q^{17} +6.92739 q^{18} +5.82926 q^{19} +15.4263 q^{20} +1.29568 q^{21} -10.4981 q^{22} -3.12196 q^{23} +4.20233 q^{24} +5.43770 q^{25} +12.2706 q^{26} +3.29407 q^{27} -10.6329 q^{28} +3.30779 q^{29} +4.89278 q^{30} -9.01132 q^{31} -9.62979 q^{32} -2.34673 q^{33} +6.99906 q^{34} -7.19443 q^{35} -12.7080 q^{36} +4.13158 q^{37} -15.1727 q^{38} +2.74296 q^{39} -23.3340 q^{40} +2.52193 q^{41} -3.37246 q^{42} -8.22725 q^{43} +19.2583 q^{44} -8.59850 q^{45} +8.12600 q^{46} +3.83412 q^{47} -5.38166 q^{48} -2.04106 q^{49} -14.1535 q^{50} +1.56457 q^{51} -22.5099 q^{52} -5.42870 q^{53} -8.57396 q^{54} +13.0305 q^{55} +16.0835 q^{56} -3.39170 q^{57} -8.60970 q^{58} +3.04539 q^{59} -8.97562 q^{60} +5.32069 q^{61} +23.4551 q^{62} +5.92672 q^{63} +6.56615 q^{64} -15.2307 q^{65} +6.10819 q^{66} -4.67358 q^{67} -12.8395 q^{68} +1.81648 q^{69} +18.7260 q^{70} +7.47704 q^{71} +19.2224 q^{72} +0.456568 q^{73} -10.7539 q^{74} -3.16387 q^{75} +27.8337 q^{76} -8.98161 q^{77} -7.13952 q^{78} +8.71123 q^{79} +29.8824 q^{80} +6.06777 q^{81} -6.56422 q^{82} +13.8724 q^{83} +6.18666 q^{84} -8.68745 q^{85} +21.4143 q^{86} -1.92461 q^{87} -29.1304 q^{88} -12.9690 q^{89} +22.3806 q^{90} +10.4981 q^{91} -14.9068 q^{92} +5.24315 q^{93} -9.97966 q^{94} +18.8328 q^{95} +5.60300 q^{96} +13.8494 q^{97} +5.31258 q^{98} -10.7345 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) \) 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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