LMFDB - Embedded newform 4019.2.a.b.1.18

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			1.18
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)

$f(q)$	$=$	$q-2.40616 q^{2} -0.556574 q^{3} +3.78961 q^{4} +1.68267 q^{5} +1.33921 q^{6} +2.28423 q^{7} -4.30608 q^{8} -2.69023 q^{9} +O(q^{10})$	\(q-2.40616 q^{2} -0.556574 q^{3} +3.78961 q^{4} +1.68267 q^{5} +1.33921 q^{6} +2.28423 q^{7} -4.30608 q^{8} -2.69023 q^{9} -4.04878 q^{10} +2.91752 q^{11} -2.10920 q^{12} +6.13861 q^{13} -5.49623 q^{14} -0.936532 q^{15} +2.78191 q^{16} -7.57808 q^{17} +6.47311 q^{18} +8.35943 q^{19} +6.37667 q^{20} -1.27134 q^{21} -7.02002 q^{22} -4.30211 q^{23} +2.39665 q^{24} -2.16861 q^{25} -14.7705 q^{26} +3.16703 q^{27} +8.65634 q^{28} -2.31811 q^{29} +2.25345 q^{30} +10.1378 q^{31} +1.91844 q^{32} -1.62382 q^{33} +18.2341 q^{34} +3.84361 q^{35} -10.1949 q^{36} -2.31179 q^{37} -20.1141 q^{38} -3.41659 q^{39} -7.24573 q^{40} -0.874310 q^{41} +3.05906 q^{42} +0.103907 q^{43} +11.0563 q^{44} -4.52677 q^{45} +10.3516 q^{46} +0.979261 q^{47} -1.54834 q^{48} -1.78229 q^{49} +5.21803 q^{50} +4.21776 q^{51} +23.2629 q^{52} +2.46421 q^{53} -7.62039 q^{54} +4.90923 q^{55} -9.83609 q^{56} -4.65264 q^{57} +5.57773 q^{58} +7.94536 q^{59} -3.54909 q^{60} -0.119062 q^{61} -24.3931 q^{62} -6.14509 q^{63} -10.1799 q^{64} +10.3293 q^{65} +3.90716 q^{66} +13.0806 q^{67} -28.7179 q^{68} +2.39444 q^{69} -9.24835 q^{70} -1.52675 q^{71} +11.5843 q^{72} -5.80152 q^{73} +5.56254 q^{74} +1.20699 q^{75} +31.6789 q^{76} +6.66429 q^{77} +8.22087 q^{78} +3.24083 q^{79} +4.68104 q^{80} +6.30799 q^{81} +2.10373 q^{82} +1.20009 q^{83} -4.81789 q^{84} -12.7514 q^{85} -0.250016 q^{86} +1.29020 q^{87} -12.5631 q^{88} +3.53011 q^{89} +10.8921 q^{90} +14.0220 q^{91} -16.3033 q^{92} -5.64241 q^{93} -2.35626 q^{94} +14.0662 q^{95} -1.06776 q^{96} -4.69774 q^{97} +4.28848 q^{98} -7.84879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.40616	−1.70141	−0.850706	−	0.525642i	$-0.823825\pi$
$2$	−2.40616	−1.70141	−0.850706	+	0.525642i	$0.823825\pi$
$3$	−0.556574	−0.321338	−0.160669	−	0.987008i	$-0.551365\pi$
$3$	−0.556574	−0.321338	−0.160669	+	0.987008i	$0.551365\pi$
$4$	3.78961	1.89480
$5$	1.68267	0.752514	0.376257	−	0.926515i	$-0.377211\pi$
$5$	1.68267	0.752514	0.376257	+	0.926515i	$0.377211\pi$
$6$	1.33921	0.546729
$7$	2.28423	0.863358	0.431679	−	0.902027i	$-0.357921\pi$
$7$	2.28423	0.863358	0.431679	+	0.902027i	$0.357921\pi$
$8$	−4.30608	−1.52243
$9$	−2.69023	−0.896742
$10$	−4.04878	−1.28034
$11$	2.91752	0.879666	0.439833	−	0.898080i	$-0.355038\pi$
$11$	2.91752	0.879666	0.439833	+	0.898080i	$0.355038\pi$
$12$	−2.10920	−0.608873
$13$	6.13861	1.70254	0.851272	−	0.524725i	$-0.175832\pi$
$13$	6.13861	1.70254	0.851272	+	0.524725i	$0.175832\pi$
$14$	−5.49623	−1.46893
$15$	−0.936532	−0.241812
$16$	2.78191	0.695478
$17$	−7.57808	−1.83795	−0.918977	−	0.394311i	$-0.870983\pi$
$17$	−7.57808	−1.83795	−0.918977	+	0.394311i	$0.870983\pi$
$18$	6.47311	1.52573
$19$	8.35943	1.91778	0.958892	−	0.283772i	$-0.0915858\pi$
$19$	8.35943	1.91778	0.958892	+	0.283772i	$0.0915858\pi$
$20$	6.37667	1.42587
$21$	−1.27134	−0.277430
$22$	−7.02002	−1.49667
$23$	−4.30211	−0.897052	−0.448526	−	0.893770i	$-0.648051\pi$
$23$	−4.30211	−0.897052	−0.448526	+	0.893770i	$0.648051\pi$
$24$	2.39665	0.489215
$25$	−2.16861	−0.433723
$26$	−14.7705	−2.89673
$27$	3.16703	0.609496
$28$	8.65634	1.63589
$29$	−2.31811	−0.430461	−0.215231	−	0.976563i	$-0.569050\pi$
$29$	−2.31811	−0.430461	−0.215231	+	0.976563i	$0.569050\pi$
$30$	2.25345	0.411421
$31$	10.1378	1.82079	0.910397	−	0.413736i	$-0.135776\pi$
$31$	10.1378	1.82079	0.910397	+	0.413736i	$0.135776\pi$
$32$	1.91844	0.339136
$33$	−1.62382	−0.282670
$34$	18.2341	3.12712
$35$	3.84361	0.649689
$36$	−10.1949	−1.69915
$37$	−2.31179	−0.380056	−0.190028	−	0.981779i	$-0.560858\pi$
$37$	−2.31179	−0.380056	−0.190028	+	0.981779i	$0.560858\pi$
$38$	−20.1141	−3.26294
$39$	−3.41659	−0.547093
$40$	−7.24573	−1.14565
$41$	−0.874310	−0.136544	−0.0682721	−	0.997667i	$-0.521749\pi$
$41$	−0.874310	−0.136544	−0.0682721	+	0.997667i	$0.521749\pi$
$42$	3.05906	0.472023
$43$	0.103907	0.0158456	0.00792282	−	0.999969i	$-0.497478\pi$
$43$	0.103907	0.0158456	0.00792282	+	0.999969i	$0.497478\pi$
$44$	11.0563	1.66679
$45$	−4.52677	−0.674811
$46$	10.3516	1.52625
$47$	0.979261	0.142840	0.0714199	−	0.997446i	$-0.477247\pi$
$47$	0.979261	0.142840	0.0714199	+	0.997446i	$0.477247\pi$
$48$	−1.54834	−0.223484
$49$	−1.78229	−0.254613
$50$	5.21803	0.737941
$51$	4.21776	0.590605
$52$	23.2629	3.22599
$53$	2.46421	0.338485	0.169242	−	0.985574i	$-0.445868\pi$
$53$	2.46421	0.338485	0.169242	+	0.985574i	$0.445868\pi$
$54$	−7.62039	−1.03700
$55$	4.90923	0.661960
$56$	−9.83609	−1.31440
$57$	−4.65264	−0.616257
$58$	5.57773	0.732392
$59$	7.94536	1.03440	0.517199	−	0.855865i	$-0.326975\pi$
$59$	7.94536	1.03440	0.517199	+	0.855865i	$0.326975\pi$
$60$	−3.54909	−0.458185
$61$	−0.119062	−0.0152443	−0.00762216	−	0.999971i	$-0.502426\pi$
$61$	−0.119062	−0.0152443	−0.00762216	+	0.999971i	$0.502426\pi$
$62$	−24.3931	−3.09792
$63$	−6.14509	−0.774209
$64$	−10.1799	−1.27249
$65$	10.3293	1.28119
$66$	3.90716	0.480939
$67$	13.0806	1.59805	0.799026	−	0.601297i	$-0.205349\pi$
$67$	13.0806	1.59805	0.799026	+	0.601297i	$0.205349\pi$
$68$	−28.7179	−3.48256
$69$	2.39444	0.288257
$70$	−9.24835	−1.10539
$71$	−1.52675	−0.181192	−0.0905960	−	0.995888i	$-0.528877\pi$
$71$	−1.52675	−0.181192	−0.0905960	+	0.995888i	$0.528877\pi$
$72$	11.5843	1.36523
$73$	−5.80152	−0.679017	−0.339508	−	0.940603i	$-0.610261\pi$
$73$	−5.80152	−0.679017	−0.339508	+	0.940603i	$0.610261\pi$
$74$	5.56254	0.646632
$75$	1.20699	0.139372
$76$	31.6789	3.63382
$77$	6.66429	0.759466
$78$	8.22087	0.930830
$79$	3.24083	0.364622	0.182311	−	0.983241i	$-0.441642\pi$
$79$	3.24083	0.364622	0.182311	+	0.983241i	$0.441642\pi$
$80$	4.68104	0.523357
$81$	6.30799	0.700887
$82$	2.10373	0.232318
$83$	1.20009	0.131728	0.0658638	−	0.997829i	$-0.479020\pi$
$83$	1.20009	0.131728	0.0658638	+	0.997829i	$0.479020\pi$
$84$	−4.81789	−0.525675
$85$	−12.7514	−1.38309
$86$	−0.250016	−0.0269600
$87$	1.29020	0.138324
$88$	−12.5631	−1.33923
$89$	3.53011	0.374191	0.187095	−	0.982342i	$-0.440093\pi$
$89$	3.53011	0.374191	0.187095	+	0.982342i	$0.440093\pi$
$90$	10.8921	1.14813
$91$	14.0220	1.46991
$92$	−16.3033	−1.69974
$93$	−5.64241	−0.585091
$94$	−2.35626	−0.243030
$95$	14.0662	1.44316
$96$	−1.06776	−0.108977
$97$	−4.69774	−0.476983	−0.238491	−	0.971145i	$-0.576653\pi$
$97$	−4.69774	−0.476983	−0.238491	+	0.971145i	$0.576653\pi$
$98$	4.28848	0.433202
$99$	−7.84879	−0.788833
$100$	−8.21820	−0.821820
$101$	6.03244	0.600250	0.300125	−	0.953900i	$-0.402972\pi$
$101$	6.03244	0.600250	0.300125	+	0.953900i	$0.402972\pi$
$102$	−10.1486	−1.00486
$103$	12.3773	1.21957	0.609787	−	0.792565i	$-0.291255\pi$
$103$	12.3773	1.21957	0.609787	+	0.792565i	$0.291255\pi$
$104$	−26.4334	−2.59200
$105$	−2.13926	−0.208770
$106$	−5.92927	−0.575902
$107$	7.95681	0.769213	0.384607	−	0.923081i	$-0.374337\pi$
$107$	7.95681	0.769213	0.384607	+	0.923081i	$0.374337\pi$
$108$	12.0018	1.15487
$109$	15.7072	1.50448	0.752240	−	0.658889i	$-0.228973\pi$
$109$	15.7072	1.50448	0.752240	+	0.658889i	$0.228973\pi$
$110$	−11.8124	−1.12627
$111$	1.28668	0.122127
$112$	6.35453	0.600446
$113$	−4.43851	−0.417540	−0.208770	−	0.977965i	$-0.566946\pi$
$113$	−4.43851	−0.417540	−0.208770	+	0.977965i	$0.566946\pi$
$114$	11.1950	1.04851
$115$	−7.23904	−0.675044
$116$	−8.78471	−0.815640
$117$	−16.5142	−1.52674
$118$	−19.1178	−1.75994
$119$	−17.3101	−1.58681
$120$	4.03278	0.368141
$121$	−2.48807	−0.226189
$122$	0.286482	0.0259369
$123$	0.486618	0.0438769
$124$	38.4181	3.45005
$125$	−12.0624	−1.07890
$126$	14.7861	1.31725
$127$	1.16954	0.103780	0.0518902	−	0.998653i	$-0.483475\pi$
$127$	1.16954	0.103780	0.0518902	+	0.998653i	$0.483475\pi$
$128$	20.6576	1.82589
$129$	−0.0578318	−0.00509181
$130$	−24.8539	−2.17983
$131$	11.4104	0.996927	0.498464	−	0.866911i	$-0.333898\pi$
$131$	11.4104	0.996927	0.498464	+	0.866911i	$0.333898\pi$
$132$	−6.15363	−0.535605
$133$	19.0949	1.65573
$134$	−31.4741	−2.71894
$135$	5.32908	0.458654
$136$	32.6318	2.79816
$137$	3.91272	0.334286	0.167143	−	0.985933i	$-0.446546\pi$
$137$	3.91272	0.334286	0.167143	+	0.985933i	$0.446546\pi$
$138$	−5.76141	−0.490444
$139$	−17.6305	−1.49540	−0.747700	−	0.664037i	$-0.768842\pi$
$139$	−17.6305	−1.49540	−0.747700	+	0.664037i	$0.768842\pi$
$140$	14.5658	1.23103
$141$	−0.545031	−0.0458999
$142$	3.67361	0.308282
$143$	17.9095	1.49767
$144$	−7.48397	−0.623664
$145$	−3.90061	−0.323928
$146$	13.9594	1.15529
$147$	0.991977	0.0818169
$148$	−8.76078	−0.720132
$149$	4.06396	0.332932	0.166466	−	0.986047i	$-0.446764\pi$
$149$	4.06396	0.332932	0.166466	+	0.986047i	$0.446764\pi$
$150$	−2.90422	−0.237129
$151$	−0.855728	−0.0696381	−0.0348191	−	0.999394i	$-0.511085\pi$
$151$	−0.855728	−0.0696381	−0.0348191	+	0.999394i	$0.511085\pi$
$152$	−35.9964	−2.91969
$153$	20.3867	1.64817
$154$	−16.0353	−1.29217
$155$	17.0585	1.37017
$156$	−12.9475	−1.03663
$157$	−9.90959	−0.790872	−0.395436	−	0.918494i	$-0.629406\pi$
$157$	−9.90959	−0.790872	−0.395436	+	0.918494i	$0.629406\pi$
$158$	−7.79796	−0.620373
$159$	−1.37151	−0.108768
$160$	3.22811	0.255204
$161$	−9.82701	−0.774477
$162$	−15.1780	−1.19250
$163$	−9.27230	−0.726263	−0.363131	−	0.931738i	$-0.618292\pi$
$163$	−9.27230	−0.726263	−0.363131	+	0.931738i	$0.618292\pi$
$164$	−3.31329	−0.258725
$165$	−2.73235	−0.212713
$166$	−2.88762	−0.224123
$167$	13.8101	1.06866	0.534328	−	0.845277i	$-0.320565\pi$
$167$	13.8101	1.06866	0.534328	+	0.845277i	$0.320565\pi$
$168$	5.47451	0.422368
$169$	24.6825	1.89866
$170$	30.6820	2.35320
$171$	−22.4887	−1.71976
$172$	0.393766	0.0300244
$173$	−4.08808	−0.310811	−0.155405	−	0.987851i	$-0.549668\pi$
$173$	−4.08808	−0.310811	−0.155405	+	0.987851i	$0.549668\pi$
$174$	−3.10442	−0.235346
$175$	−4.95362	−0.374458
$176$	8.11628	0.611788
$177$	−4.42218	−0.332392
$178$	−8.49401	−0.636653
$179$	−9.57235	−0.715471	−0.357736	−	0.933823i	$-0.616451\pi$
$179$	−9.57235	−0.715471	−0.357736	+	0.933823i	$0.616451\pi$
$180$	−17.1547	−1.27863
$181$	−9.28015	−0.689788	−0.344894	−	0.938642i	$-0.612085\pi$
$181$	−9.28015	−0.689788	−0.344894	+	0.938642i	$0.612085\pi$
$182$	−33.7392	−2.50091
$183$	0.0662668	0.00489858
$184$	18.5252	1.36570
$185$	−3.88999	−0.285997
$186$	13.5765	0.995481
$187$	−22.1092	−1.61678
$188$	3.71101	0.270654
$189$	7.23423	0.526213
$190$	−33.8455	−2.45541
$191$	−15.0179	−1.08666	−0.543329	−	0.839520i	$-0.682836\pi$
$191$	−15.0179	−1.08666	−0.543329	+	0.839520i	$0.682836\pi$
$192$	5.66587	0.408899
$193$	−11.0433	−0.794917	−0.397459	−	0.917620i	$-0.630108\pi$
$193$	−11.0433	−0.794917	−0.397459	+	0.917620i	$0.630108\pi$
$194$	11.3035	0.811544
$195$	−5.74901	−0.411695
$196$	−6.75418	−0.482441
$197$	−25.7060	−1.83148	−0.915738	−	0.401777i	$-0.868393\pi$
$197$	−25.7060	−1.83148	−0.915738	+	0.401777i	$0.868393\pi$
$198$	18.8854	1.34213
$199$	8.87747	0.629307	0.314654	−	0.949207i	$-0.398112\pi$
$199$	8.87747	0.629307	0.314654	+	0.949207i	$0.398112\pi$
$200$	9.33823	0.660313
$201$	−7.28033	−0.513515
$202$	−14.5150	−1.02127
$203$	−5.29509	−0.371642
$204$	15.9837	1.11908
$205$	−1.47118	−0.102751
$206$	−29.7818	−2.07500
$207$	11.5736	0.804424
$208$	17.0771	1.18408
$209$	24.3888	1.68701
$210$	5.14739	0.355204
$211$	−25.8826	−1.78183	−0.890917	−	0.454166i	$-0.849937\pi$
$211$	−25.8826	−1.78183	−0.890917	+	0.454166i	$0.849937\pi$
$212$	9.33837	0.641362
$213$	0.849751	0.0582240
$214$	−19.1453	−1.30875
$215$	0.174841	0.0119241
$216$	−13.6375	−0.927915
$217$	23.1570	1.57200
$218$	−37.7941	−2.55974
$219$	3.22898	0.218194
$220$	18.6041	1.25429
$221$	−46.5189	−3.12920
$222$	−3.09597	−0.207788
$223$	23.0931	1.54643	0.773214	−	0.634145i	$-0.218648\pi$
$223$	23.0931	1.54643	0.773214	+	0.634145i	$0.218648\pi$
$224$	4.38217	0.292796
$225$	5.83406	0.388937
$226$	10.6798	0.710407
$227$	−20.1279	−1.33594	−0.667969	−	0.744189i	$-0.732836\pi$
$227$	−20.1279	−1.33594	−0.667969	+	0.744189i	$0.732836\pi$
$228$	−17.6317	−1.16769
$229$	8.30562	0.548851	0.274425	−	0.961608i	$-0.411512\pi$
$229$	8.30562	0.548851	0.274425	+	0.961608i	$0.411512\pi$
$230$	17.4183	1.14853
$231$	−3.70917	−0.244046
$232$	9.98195	0.655347
$233$	1.42485	0.0933447	0.0466724	−	0.998910i	$-0.485138\pi$
$233$	1.42485	0.0933447	0.0466724	+	0.998910i	$0.485138\pi$
$234$	39.7359	2.59762
$235$	1.64777	0.107489
$236$	30.1098	1.95998
$237$	−1.80376	−0.117167
$238$	41.6508	2.69982
$239$	29.1802	1.88751	0.943755	−	0.330644i	$-0.107266\pi$
$239$	29.1802	1.88751	0.943755	+	0.330644i	$0.107266\pi$
$240$	−2.60535	−0.168175
$241$	−28.4431	−1.83218	−0.916092	−	0.400968i	$-0.868674\pi$
$241$	−28.4431	−1.83218	−0.916092	+	0.400968i	$0.868674\pi$
$242$	5.98671	0.384840
$243$	−13.0120	−0.834718
$244$	−0.451198	−0.0288850
$245$	−2.99901	−0.191600
$246$	−1.17088	−0.0746527
$247$	51.3153	3.26511
$248$	−43.6540	−2.77203
$249$	−0.667942	−0.0423291
$250$	29.0241	1.83565
$251$	6.97150	0.440037	0.220019	−	0.975496i	$-0.429388\pi$
$251$	6.97150	0.440037	0.220019	+	0.975496i	$0.429388\pi$
$252$	−23.2875	−1.46697
$253$	−12.5515	−0.789106
$254$	−2.81411	−0.176573
$255$	7.09711	0.444439
$256$	−29.3457	−1.83410
$257$	5.37505	0.335286	0.167643	−	0.985848i	$-0.446384\pi$
$257$	5.37505	0.335286	0.167643	+	0.985848i	$0.446384\pi$
$258$	0.139153	0.00866327
$259$	−5.28066	−0.328124
$260$	39.1439	2.42760
$261$	6.23623	0.386013
$262$	−27.4551	−1.69618
$263$	−11.7684	−0.725671	−0.362836	−	0.931853i	$-0.618191\pi$
$263$	−11.7684	−0.725671	−0.362836	+	0.931853i	$0.618191\pi$
$264$	6.99229	0.430346
$265$	4.14645	0.254714
$266$	−45.9453	−2.81709
$267$	−1.96477	−0.120242
$268$	49.5704	3.02799
$269$	10.1204	0.617053	0.308527	−	0.951216i	$-0.400164\pi$
$269$	10.1204	0.617053	0.308527	+	0.951216i	$0.400164\pi$
$270$	−12.8226	−0.780360
$271$	−15.4078	−0.935959	−0.467979	−	0.883739i	$-0.655018\pi$
$271$	−15.4078	−0.935959	−0.467979	+	0.883739i	$0.655018\pi$
$272$	−21.0815	−1.27826
$273$	−7.80429	−0.472337
$274$	−9.41464	−0.568759
$275$	−6.32698	−0.381531
$276$	9.07400	0.546191
$277$	−11.1500	−0.669940	−0.334970	−	0.942229i	$-0.608726\pi$
$277$	−11.1500	−0.669940	−0.334970	+	0.942229i	$0.608726\pi$
$278$	42.4218	2.54429
$279$	−27.2728	−1.63278
$280$	−16.5509	−0.989106
$281$	−8.70776	−0.519461	−0.259731	−	0.965681i	$-0.583634\pi$
$281$	−8.70776	−0.519461	−0.259731	+	0.965681i	$0.583634\pi$
$282$	1.31143	0.0780947
$283$	18.9866	1.12864	0.564319	−	0.825557i	$-0.309139\pi$
$283$	18.9866	1.12864	0.564319	+	0.825557i	$0.309139\pi$
$284$	−5.78579	−0.343323
$285$	−7.82887	−0.463742
$286$	−43.0932	−2.54815
$287$	−1.99713	−0.117887
$288$	−5.16104	−0.304117
$289$	40.4273	2.37808
$290$	9.38550	0.551135
$291$	2.61464	0.153273
$292$	−21.9855	−1.28660
$293$	29.4454	1.72022	0.860110	−	0.510108i	$-0.170395\pi$
$293$	29.4454	1.72022	0.860110	+	0.510108i	$0.170395\pi$
$294$	−2.38686	−0.139204
$295$	13.3694	0.778399
$296$	9.95476	0.578609
$297$	9.23988	0.536152
$298$	−9.77854	−0.566455
$299$	−26.4090	−1.52727
$300$	4.57404	0.264082
$301$	0.237347	0.0136805
$302$	2.05902	0.118483
$303$	−3.35750	−0.192883
$304$	23.2552	1.33378
$305$	−0.200342	−0.0114716
$306$	−49.0538	−2.80422
$307$	−3.60190	−0.205571	−0.102786	−	0.994704i	$-0.532776\pi$
$307$	−3.60190	−0.205571	−0.102786	+	0.994704i	$0.532776\pi$
$308$	25.2550	1.43904
$309$	−6.88890	−0.391896
$310$	−41.0455	−2.33123
$311$	21.8332	1.23805	0.619025	−	0.785372i	$-0.287528\pi$
$311$	21.8332	1.23805	0.619025	+	0.785372i	$0.287528\pi$
$312$	14.7121	0.832910
$313$	12.6608	0.715628	0.357814	−	0.933793i	$-0.383522\pi$
$313$	12.6608	0.715628	0.357814	+	0.933793i	$0.383522\pi$
$314$	23.8441	1.34560
$315$	−10.3402	−0.582603
$316$	12.2815	0.690888
$317$	27.2151	1.52855	0.764275	−	0.644891i	$-0.223097\pi$
$317$	27.2151	1.52855	0.764275	+	0.644891i	$0.223097\pi$
$318$	3.30008	0.185059
$319$	−6.76312	−0.378662
$320$	−17.1294	−0.957565
$321$	−4.42855	−0.247178
$322$	23.6454	1.31770
$323$	−63.3484	−3.52480
$324$	23.9048	1.32804
$325$	−13.3123	−0.738432
$326$	22.3106	1.23567
$327$	−8.74224	−0.483447
$328$	3.76485	0.207879
$329$	2.23686	0.123322
$330$	6.57448	0.361913
$331$	20.6735	1.13632	0.568160	−	0.822918i	$-0.307655\pi$
$331$	20.6735	1.13632	0.568160	+	0.822918i	$0.307655\pi$
$332$	4.54789	0.249598
$333$	6.21924	0.340812
$334$	−33.2293	−1.81823
$335$	22.0104	1.20256
$336$	−3.53677	−0.192946
$337$	7.85757	0.428029	0.214015	−	0.976830i	$-0.431346\pi$
$337$	7.85757	0.428029	0.214015	+	0.976830i	$0.431346\pi$
$338$	−59.3901	−3.23040
$339$	2.47036	0.134171
$340$	−48.3229	−2.62068
$341$	29.5771	1.60169
$342$	54.1115	2.92602
$343$	−20.0608	−1.08318
$344$	−0.447431	−0.0241239
$345$	4.02906	0.216917
$346$	9.83657	0.528817
$347$	−9.71597	−0.521581	−0.260790	−	0.965395i	$-0.583983\pi$
$347$	−9.71597	−0.521581	−0.260790	+	0.965395i	$0.583983\pi$
$348$	4.88934	0.262096
$349$	1.76402	0.0944258	0.0472129	−	0.998885i	$-0.484966\pi$
$349$	1.76402	0.0944258	0.0472129	+	0.998885i	$0.484966\pi$
$350$	11.9192	0.637108
$351$	19.4412	1.03769
$352$	5.59710	0.298326
$353$	2.65431	0.141275	0.0706373	−	0.997502i	$-0.477497\pi$
$353$	2.65431	0.141275	0.0706373	+	0.997502i	$0.477497\pi$
$354$	10.6405	0.565535
$355$	−2.56902	−0.136350
$356$	13.3777	0.709018
$357$	9.63435	0.509904
$358$	23.0326	1.21731
$359$	19.5283	1.03066	0.515331	−	0.856991i	$-0.327669\pi$
$359$	19.5283	1.03066	0.515331	+	0.856991i	$0.327669\pi$
$360$	19.4926	1.02735
$361$	50.8800	2.67789
$362$	22.3295	1.17361
$363$	1.38480	0.0726831
$364$	53.1379	2.78518
$365$	−9.76206	−0.510970
$366$	−0.159448	−0.00833451
$367$	20.2910	1.05918	0.529591	−	0.848253i	$-0.322345\pi$
$367$	20.2910	1.05918	0.529591	+	0.848253i	$0.322345\pi$
$368$	−11.9681	−0.623880
$369$	2.35209	0.122445
$370$	9.35993	0.486600
$371$	5.62881	0.292233
$372$	−21.3825	−1.10863
$373$	−17.8583	−0.924669	−0.462335	−	0.886706i	$-0.652988\pi$
$373$	−17.8583	−0.924669	−0.462335	+	0.886706i	$0.652988\pi$
$374$	53.1983	2.75082
$375$	6.71364	0.346691
$376$	−4.21678	−0.217464
$377$	−14.2299	−0.732880
$378$	−17.4067	−0.895305
$379$	38.1531	1.95979	0.979897	−	0.199506i	$-0.0639336\pi$
$379$	38.1531	1.95979	0.979897	+	0.199506i	$0.0639336\pi$
$380$	53.3053	2.73450
$381$	−0.650938	−0.0333486
$382$	36.1355	1.84885
$383$	3.62027	0.184987	0.0924935	−	0.995713i	$-0.470516\pi$
$383$	3.62027	0.184987	0.0924935	+	0.995713i	$0.470516\pi$
$384$	−11.4975	−0.586728
$385$	11.2138	0.571509
$386$	26.5721	1.35248
$387$	−0.279533	−0.0142094
$388$	−17.8026	−0.903789
$389$	−4.81242	−0.243999	−0.122000	−	0.992530i	$-0.538931\pi$
$389$	−4.81242	−0.243999	−0.122000	+	0.992530i	$0.538931\pi$
$390$	13.8330	0.700463
$391$	32.6017	1.64874
$392$	7.67469	0.387630
$393$	−6.35071	−0.320351
$394$	61.8527	3.11609
$395$	5.45326	0.274383
$396$	−29.7438	−1.49468
$397$	−19.1435	−0.960785	−0.480393	−	0.877054i	$-0.659506\pi$
$397$	−19.1435	−0.960785	−0.480393	+	0.877054i	$0.659506\pi$
$398$	−21.3606	−1.07071
$399$	−10.6277	−0.532051
$400$	−6.03289	−0.301645
$401$	33.2623	1.66104	0.830520	−	0.556989i	$-0.188044\pi$
$401$	33.2623	1.66104	0.830520	+	0.556989i	$0.188044\pi$
$402$	17.5177	0.873701
$403$	62.2317	3.09998
$404$	22.8606	1.13736
$405$	10.6143	0.527427
$406$	12.7408	0.632317
$407$	−6.74470	−0.334322
$408$	−18.1620	−0.899155
$409$	23.3100	1.15260	0.576302	−	0.817237i	$-0.304495\pi$
$409$	23.3100	1.15260	0.576302	+	0.817237i	$0.304495\pi$
$410$	3.53989	0.174823
$411$	−2.17772	−0.107419
$412$	46.9052	2.31085
$413$	18.1490	0.893056
$414$	−27.8480	−1.36866
$415$	2.01937	0.0991268
$416$	11.7766	0.577394
$417$	9.81268	0.480529
$418$	−58.6833	−2.87030
$419$	27.0258	1.32030	0.660148	−	0.751136i	$-0.270494\pi$
$419$	27.0258	1.32030	0.660148	+	0.751136i	$0.270494\pi$
$420$	−8.10694	−0.395578
$421$	−7.31578	−0.356549	−0.178275	−	0.983981i	$-0.557052\pi$
$421$	−7.31578	−0.356549	−0.178275	+	0.983981i	$0.557052\pi$
$422$	62.2778	3.03163
$423$	−2.63443	−0.128090
$424$	−10.6111	−0.515319
$425$	16.4339	0.797163
$426$	−2.04464	−0.0990630
$427$	−0.271965	−0.0131613
$428$	30.1532	1.45751
$429$	−9.96798	−0.481259
$430$	−0.420696	−0.0202877
$431$	−2.22051	−0.106958	−0.0534791	−	0.998569i	$-0.517031\pi$
$431$	−2.22051	−0.106958	−0.0534791	+	0.998569i	$0.517031\pi$
$432$	8.81040	0.423891
$433$	−2.88593	−0.138689	−0.0693445	−	0.997593i	$-0.522091\pi$
$433$	−2.88593	−0.138689	−0.0693445	+	0.997593i	$0.522091\pi$
$434$	−55.7194	−2.67461
$435$	2.17098	0.104091
$436$	59.5242	2.85069
$437$	−35.9632	−1.72035
$438$	−7.76944	−0.371238
$439$	4.61864	0.220436	0.110218	−	0.993907i	$-0.464845\pi$
$439$	4.61864	0.220436	0.110218	+	0.993907i	$0.464845\pi$
$440$	−21.1396	−1.00779
$441$	4.79476	0.228322
$442$	111.932	5.32406
$443$	−12.0674	−0.573341	−0.286671	−	0.958029i	$-0.592549\pi$
$443$	−12.0674	−0.573341	−0.286671	+	0.958029i	$0.592549\pi$
$444$	4.87602	0.231406
$445$	5.94002	0.281584
$446$	−55.5657	−2.63111
$447$	−2.26189	−0.106984
$448$	−23.2532	−1.09861
$449$	−30.7493	−1.45115	−0.725574	−	0.688144i	$-0.758426\pi$
$449$	−30.7493	−1.45115	−0.725574	+	0.688144i	$0.758426\pi$
$450$	−14.0377	−0.661743
$451$	−2.55082	−0.120113
$452$	−16.8202	−0.791156
$453$	0.476276	0.0223774
$454$	48.4310	2.27298
$455$	23.5944	1.10612
$456$	20.0347	0.938209
$457$	0.367359	0.0171843	0.00859216	−	0.999963i	$-0.497265\pi$
$457$	0.367359	0.0171843	0.00859216	+	0.999963i	$0.497265\pi$
$458$	−19.9846	−0.933821
$459$	−24.0000	−1.12023
$460$	−27.4331	−1.27908
$461$	−17.8744	−0.832496	−0.416248	−	0.909251i	$-0.636655\pi$
$461$	−17.8744	−0.832496	−0.416248	+	0.909251i	$0.636655\pi$
$462$	8.92486	0.415222
$463$	−19.9222	−0.925863	−0.462932	−	0.886394i	$-0.653202\pi$
$463$	−19.9222	−0.925863	−0.462932	+	0.886394i	$0.653202\pi$
$464$	−6.44876	−0.299376
$465$	−9.49433	−0.440289
$466$	−3.42841	−0.158818
$467$	−16.7977	−0.777305	−0.388653	−	0.921384i	$-0.627059\pi$
$467$	−16.7977	−0.777305	−0.388653	+	0.921384i	$0.627059\pi$
$468$	−62.5825	−2.89288
$469$	29.8791	1.37969
$470$	−3.96481	−0.182883
$471$	5.51542	0.254137
$472$	−34.2134	−1.57480
$473$	0.303150	0.0139389
$474$	4.34015	0.199350
$475$	−18.1284	−0.831787
$476$	−65.5984	−3.00670
$477$	−6.62927	−0.303533
$478$	−70.2123	−3.21143
$479$	17.5135	0.800211	0.400105	−	0.916469i	$-0.368974\pi$
$479$	17.5135	0.800211	0.400105	+	0.916469i	$0.368974\pi$
$480$	−1.79668	−0.0820070
$481$	−14.1912	−0.647062
$482$	68.4388	3.11730
$483$	5.46946	0.248869
$484$	−9.42883	−0.428583
$485$	−7.90475	−0.358936
$486$	31.3089	1.42020
$487$	−20.7302	−0.939377	−0.469689	−	0.882832i	$-0.655634\pi$
$487$	−20.7302	−0.939377	−0.469689	+	0.882832i	$0.655634\pi$
$488$	0.512690	0.0232084
$489$	5.16073	0.233376
$490$	7.21610	0.325990
$491$	19.8753	0.896959	0.448480	−	0.893793i	$-0.351966\pi$
$491$	19.8753	0.896959	0.448480	+	0.893793i	$0.351966\pi$
$492$	1.84409	0.0831381
$493$	17.5668	0.791168
$494$	−123.473	−5.55530
$495$	−13.2069	−0.593608
$496$	28.2023	1.26632
$497$	−3.48745	−0.156434
$498$	1.60718	0.0720192
$499$	−8.12700	−0.363815	−0.181907	−	0.983316i	$-0.558227\pi$
$499$	−8.12700	−0.363815	−0.181907	+	0.983316i	$0.558227\pi$
$500$	−45.7119	−2.04430
$501$	−7.68634	−0.343400
$502$	−16.7746	−0.748685
$503$	−30.4466	−1.35755	−0.678773	−	0.734348i	$-0.737488\pi$
$503$	−30.4466	−1.35755	−0.678773	+	0.734348i	$0.737488\pi$
$504$	26.4613	1.17868
$505$	10.1506	0.451696
$506$	30.2009	1.34259
$507$	−13.7377	−0.610111
$508$	4.43212	0.196643
$509$	31.9373	1.41559	0.707797	−	0.706416i	$-0.249689\pi$
$509$	31.9373	1.41559	0.707797	+	0.706416i	$0.249689\pi$
$510$	−17.0768	−0.756173
$511$	−13.2520	−0.586235
$512$	29.2952	1.29468
$513$	26.4746	1.16888
$514$	−12.9332	−0.570460
$515$	20.8270	0.917746
$516$	−0.219160	−0.00964798
$517$	2.85701	0.125651
$518$	12.7061	0.558275
$519$	2.27532	0.0998754
$520$	−44.4787	−1.95052
$521$	1.94539	0.0852292	0.0426146	−	0.999092i	$-0.486431\pi$
$521$	1.94539	0.0852292	0.0426146	+	0.999092i	$0.486431\pi$
$522$	−15.0054	−0.656767
$523$	22.3009	0.975151	0.487576	−	0.873081i	$-0.337881\pi$
$523$	22.3009	0.975151	0.487576	+	0.873081i	$0.337881\pi$
$524$	43.2408	1.88898
$525$	2.75705	0.120328
$526$	28.3167	1.23467
$527$	−76.8247	−3.34654
$528$	−4.51731	−0.196591
$529$	−4.49186	−0.195298
$530$	−9.97702	−0.433374
$531$	−21.3748	−0.927588
$532$	72.3620	3.13729
$533$	−5.36705	−0.232473
$534$	4.72755	0.204581
$535$	13.3887	0.578844
$536$	−56.3262	−2.43292
$537$	5.32773	0.229908
$538$	−24.3514	−1.04986
$539$	−5.19987	−0.223974
$540$	20.1951	0.869059
$541$	34.7892	1.49571	0.747853	−	0.663865i	$-0.231085\pi$
$541$	34.7892	1.49571	0.747853	+	0.663865i	$0.231085\pi$
$542$	37.0737	1.59245
$543$	5.16509	0.221655
$544$	−14.5381	−0.623316
$545$	26.4301	1.13214
$546$	18.7784	0.803640
$547$	38.6167	1.65113	0.825565	−	0.564307i	$-0.190857\pi$
$547$	38.6167	1.65113	0.825565	+	0.564307i	$0.190857\pi$
$548$	14.8277	0.633407
$549$	0.320303	0.0136702
$550$	15.2237	0.649142
$551$	−19.3780	−0.825532
$552$	−10.3107	−0.438851
$553$	7.40281	0.314800
$554$	26.8287	1.13984
$555$	2.16507	0.0919019
$556$	−66.8127	−2.83349
$557$	6.86687	0.290958	0.145479	−	0.989361i	$-0.453528\pi$
$557$	6.86687	0.290958	0.145479	+	0.989361i	$0.453528\pi$
$558$	65.6228	2.77803
$559$	0.637843	0.0269779
$560$	10.6926	0.451844
$561$	12.3054	0.519535
$562$	20.9523	0.883818
$563$	1.08013	0.0455219	0.0227609	−	0.999741i	$-0.492754\pi$
$563$	1.08013	0.0455219	0.0227609	+	0.999741i	$0.492754\pi$
$564$	−2.06545	−0.0869713
$565$	−7.46855	−0.314204
$566$	−45.6849	−1.92028
$567$	14.4089	0.605117
$568$	6.57432	0.275852
$569$	3.84367	0.161135	0.0805676	−	0.996749i	$-0.474327\pi$
$569$	3.84367	0.161135	0.0805676	+	0.996749i	$0.474327\pi$
$570$	18.8375	0.789017
$571$	26.2993	1.10059	0.550295	−	0.834970i	$-0.314515\pi$
$571$	26.2993	1.10059	0.550295	+	0.834970i	$0.314515\pi$
$572$	67.8701	2.83779
$573$	8.35858	0.349185
$574$	4.80540	0.200574
$575$	9.32962	0.389072
$576$	27.3862	1.14109
$577$	−39.9218	−1.66197	−0.830984	−	0.556296i	$-0.812222\pi$
$577$	−39.9218	−1.66197	−0.830984	+	0.556296i	$0.812222\pi$
$578$	−97.2745	−4.04609
$579$	6.14644	0.255437
$580$	−14.7818	−0.613780
$581$	2.74129	0.113728
$582$	−6.29124	−0.260780
$583$	7.18937	0.297753
$584$	24.9818	1.03376
$585$	−27.7881	−1.14889
$586$	−70.8504	−2.92680
$587$	−16.5921	−0.684828	−0.342414	−	0.939549i	$-0.611245\pi$
$587$	−16.5921	−0.684828	−0.342414	+	0.939549i	$0.611245\pi$
$588$	3.75920	0.155027
$589$	84.7458	3.49189
$590$	−32.1690	−1.32438
$591$	14.3073	0.588523
$592$	−6.43120	−0.264320
$593$	16.1580	0.663531	0.331765	−	0.943362i	$-0.392356\pi$
$593$	16.1580	0.663531	0.331765	+	0.943362i	$0.392356\pi$
$594$	−22.2326	−0.912216
$595$	−29.1272	−1.19410
$596$	15.4008	0.630842
$597$	−4.94097	−0.202221
$598$	63.5442	2.59852
$599$	−19.9373	−0.814615	−0.407308	−	0.913291i	$-0.633532\pi$
$599$	−19.9373	−0.814615	−0.407308	+	0.913291i	$0.633532\pi$
$600$	−5.19742	−0.212184
$601$	23.1243	0.943260	0.471630	−	0.881796i	$-0.343666\pi$
$601$	23.1243	0.943260	0.471630	+	0.881796i	$0.343666\pi$
$602$	−0.571095	−0.0232761
$603$	−35.1898	−1.43304
$604$	−3.24287	−0.131951
$605$	−4.18661	−0.170210
$606$	8.07868	0.328174
$607$	−26.8611	−1.09026	−0.545130	−	0.838352i	$-0.683520\pi$
$607$	−26.8611	−1.09026	−0.545130	+	0.838352i	$0.683520\pi$
$608$	16.0371	0.650389
$609$	2.94711	0.119423
$610$	0.482055	0.0195178
$611$	6.01130	0.243191
$612$	77.2577	3.12296
$613$	4.29756	0.173577	0.0867884	−	0.996227i	$-0.472340\pi$
$613$	4.29756	0.173577	0.0867884	+	0.996227i	$0.472340\pi$
$614$	8.66674	0.349761
$615$	0.818819	0.0330180
$616$	−28.6970	−1.15623
$617$	38.2377	1.53939	0.769695	−	0.638411i	$-0.220408\pi$
$617$	38.2377	1.53939	0.769695	+	0.638411i	$0.220408\pi$
$618$	16.5758	0.666776
$619$	−36.9349	−1.48454	−0.742270	−	0.670101i	$-0.766251\pi$
$619$	−36.9349	−1.48454	−0.742270	+	0.670101i	$0.766251\pi$
$620$	64.6451	2.59621
$621$	−13.6249	−0.546749
$622$	−52.5343	−2.10643
$623$	8.06358	0.323061
$624$	−9.50466	−0.380491
$625$	−9.45404	−0.378162
$626$	−30.4638	−1.21758
$627$	−13.5742	−0.542100
$628$	−37.5535	−1.49855
$629$	17.5189	0.698526
$630$	24.8801	0.991248
$631$	−20.1757	−0.803181	−0.401590	−	0.915819i	$-0.631542\pi$
$631$	−20.1757	−0.803181	−0.401590	+	0.915819i	$0.631542\pi$
$632$	−13.9553	−0.555112
$633$	14.4056	0.572572
$634$	−65.4838	−2.60069
$635$	1.96796	0.0780961
$636$	−5.19750	−0.206094
$637$	−10.9408	−0.433490
$638$	16.2732	0.644260
$639$	4.10731	0.162483
$640$	34.7600	1.37401
$641$	39.2156	1.54892	0.774462	−	0.632621i	$-0.218021\pi$
$641$	39.2156	1.54892	0.774462	+	0.632621i	$0.218021\pi$
$642$	10.6558	0.420551
$643$	40.4232	1.59414	0.797068	−	0.603889i	$-0.206383\pi$
$643$	40.4232	1.59414	0.797068	+	0.603889i	$0.206383\pi$
$644$	−37.2405	−1.46748
$645$	−0.0973120	−0.00383166
$646$	152.426	5.99714
$647$	−27.6683	−1.08775	−0.543876	−	0.839165i	$-0.683044\pi$
$647$	−27.6683	−1.08775	−0.543876	+	0.839165i	$0.683044\pi$
$648$	−27.1627	−1.06705
$649$	23.1808	0.909924
$650$	32.0315	1.25638
$651$	−12.8886	−0.505143
$652$	−35.1384	−1.37613
$653$	−34.5177	−1.35078	−0.675390	−	0.737460i	$-0.736025\pi$
$653$	−34.5177	−1.35078	−0.675390	+	0.737460i	$0.736025\pi$
$654$	21.0352	0.822543
$655$	19.1999	0.750202
$656$	−2.43225	−0.0949635
$657$	15.6074	0.608903
$658$	−5.38224	−0.209821
$659$	−23.8792	−0.930202	−0.465101	−	0.885258i	$-0.653982\pi$
$659$	−23.8792	−0.930202	−0.465101	+	0.885258i	$0.653982\pi$
$660$	−10.3545	−0.403050
$661$	−8.13565	−0.316440	−0.158220	−	0.987404i	$-0.550576\pi$
$661$	−8.13565	−0.316440	−0.158220	+	0.987404i	$0.550576\pi$
$662$	−49.7438	−1.93335
$663$	25.8912	1.00553
$664$	−5.16771	−0.200546
$665$	32.1304	1.24596
$666$	−14.9645	−0.579862
$667$	9.97274	0.386146
$668$	52.3348	2.02489
$669$	−12.8530	−0.496927
$670$	−52.9605	−2.04604
$671$	−0.347365	−0.0134099
$672$	−2.43900	−0.0940865
$673$	1.53057	0.0589993	0.0294996	−	0.999565i	$-0.490609\pi$
$673$	1.53057	0.0589993	0.0294996	+	0.999565i	$0.490609\pi$
$674$	−18.9066	−0.728254
$675$	−6.86807	−0.264352
$676$	93.5371	3.59758
$677$	9.94538	0.382232	0.191116	−	0.981567i	$-0.438789\pi$
$677$	9.94538	0.382232	0.191116	+	0.981567i	$0.438789\pi$
$678$	−5.94408	−0.228281
$679$	−10.7307	−0.411807
$680$	54.9087	2.10565
$681$	11.2027	0.429288
$682$	−71.1672	−2.72513
$683$	−48.6450	−1.86135	−0.930674	−	0.365849i	$-0.880779\pi$
$683$	−48.6450	−1.86135	−0.930674	+	0.365849i	$0.880779\pi$
$684$	−85.2235	−3.25860
$685$	6.58383	0.251555
$686$	48.2694	1.84294
$687$	−4.62269	−0.176367
$688$	0.289059	0.0110203
$689$	15.1268	0.576285
$690$	−9.69457	−0.369066
$691$	36.2774	1.38006	0.690028	−	0.723783i	$-0.257598\pi$
$691$	36.2774	1.38006	0.690028	+	0.723783i	$0.257598\pi$
$692$	−15.4922	−0.588926
$693$	−17.9284	−0.681045
$694$	23.3782	0.887424
$695$	−29.6663	−1.12531
$696$	−5.55570	−0.210588
$697$	6.62559	0.250962
$698$	−4.24452	−0.160657
$699$	−0.793032	−0.0299952
$700$	−18.7723	−0.709525
$701$	−17.2324	−0.650857	−0.325429	−	0.945567i	$-0.605509\pi$
$701$	−17.2324	−0.650857	−0.325429	+	0.945567i	$0.605509\pi$
$702$	−46.7786	−1.76554
$703$	−19.3252	−0.728865
$704$	−29.7001	−1.11936
$705$	−0.917109	−0.0345403
$706$	−6.38670	−0.240366
$707$	13.7795	0.518230
$708$	−16.7583	−0.629817
$709$	33.8268	1.27039	0.635196	−	0.772351i	$-0.280920\pi$
$709$	33.8268	1.27039	0.635196	+	0.772351i	$0.280920\pi$
$710$	6.18148	0.231987
$711$	−8.71857	−0.326972
$712$	−15.2009	−0.569679
$713$	−43.6137	−1.63335
$714$	−23.1818	−0.867556
$715$	30.1359	1.12702
$716$	−36.2755	−1.35568
$717$	−16.2410	−0.606530
$718$	−46.9882	−1.75358
$719$	−12.0771	−0.450398	−0.225199	−	0.974313i	$-0.572303\pi$
$719$	−12.0771	−0.450398	−0.225199	+	0.974313i	$0.572303\pi$
$720$	−12.5931	−0.469316
$721$	28.2727	1.05293
$722$	−122.425	−4.55620
$723$	15.8307	0.588751
$724$	−35.1681	−1.30701
$725$	5.02708	0.186701
$726$	−3.33205	−0.123664
$727$	−20.6823	−0.767065	−0.383533	−	0.923527i	$-0.625293\pi$
$727$	−20.6823	−0.767065	−0.383533	+	0.923527i	$0.625293\pi$
$728$	−60.3799	−2.23783
$729$	−11.6818	−0.432661
$730$	23.4891	0.869370
$731$	−0.787414	−0.0291236
$732$	0.251125	0.00928185
$733$	−8.93399	−0.329985	−0.164992	−	0.986295i	$-0.552760\pi$
$733$	−8.93399	−0.329985	−0.164992	+	0.986295i	$0.552760\pi$
$734$	−48.8234	−1.80211
$735$	1.66917	0.0615683
$736$	−8.25335	−0.304222
$737$	38.1630	1.40575
$738$	−5.65951	−0.208329
$739$	44.9249	1.65259	0.826295	−	0.563237i	$-0.190444\pi$
$739$	44.9249	1.65259	0.826295	+	0.563237i	$0.190444\pi$
$740$	−14.7415	−0.541909
$741$	−28.5607	−1.04921
$742$	−13.5438	−0.497210
$743$	52.5320	1.92721	0.963606	−	0.267327i	$-0.0861404\pi$
$743$	52.5320	1.92721	0.963606	+	0.267327i	$0.0861404\pi$
$744$	24.2967	0.890760
$745$	6.83831	0.250536
$746$	42.9700	1.57324
$747$	−3.22852	−0.118126
$748$	−83.7852	−3.06349
$749$	18.1752	0.664107
$750$	−16.1541	−0.589864
$751$	50.4441	1.84073	0.920365	−	0.391059i	$-0.127891\pi$
$751$	50.4441	1.84073	0.920365	+	0.391059i	$0.127891\pi$
$752$	2.72422	0.0993419
$753$	−3.88016	−0.141401
$754$	34.2395	1.24693
$755$	−1.43991	−0.0524037
$756$	27.4149	0.997071
$757$	−28.4695	−1.03474	−0.517371	−	0.855761i	$-0.673089\pi$
$757$	−28.4695	−1.03474	−0.517371	+	0.855761i	$0.673089\pi$
$758$	−91.8025	−3.33442
$759$	6.98584	0.253570
$760$	−60.5701	−2.19711
$761$	−28.2130	−1.02272	−0.511361	−	0.859366i	$-0.670858\pi$
$761$	−28.2130	−1.02272	−0.511361	+	0.859366i	$0.670858\pi$
$762$	1.56626	0.0567397
$763$	35.8789	1.29890
$764$	−56.9120	−2.05900
$765$	34.3042	1.24027
$766$	−8.71094	−0.314739
$767$	48.7735	1.76111
$768$	16.3330	0.589368
$769$	18.4467	0.665205	0.332602	−	0.943067i	$-0.392073\pi$
$769$	18.4467	0.665205	0.332602	+	0.943067i	$0.392073\pi$
$770$	−26.9822	−0.972372
$771$	−2.99161	−0.107740
$772$	−41.8499	−1.50621
$773$	−32.3116	−1.16217	−0.581083	−	0.813844i	$-0.697371\pi$
$773$	−32.3116	−1.16217	−0.581083	+	0.813844i	$0.697371\pi$
$774$	0.672600	0.0241761
$775$	−21.9849	−0.789720
$776$	20.2288	0.726173
$777$	2.93908	0.105439
$778$	11.5794	0.415143
$779$	−7.30873	−0.261862
$780$	−21.7865	−0.780081
$781$	−4.45433	−0.159388
$782$	−78.4450	−2.80519
$783$	−7.34152	−0.262364
$784$	−4.95817	−0.177078
$785$	−16.6746	−0.595142
$786$	15.2808	0.545049
$787$	35.5540	1.26736	0.633682	−	0.773593i	$-0.281543\pi$
$787$	35.5540	1.26736	0.633682	+	0.773593i	$0.281543\pi$
$788$	−97.4156	−3.47029
$789$	6.54999	0.233186
$790$	−13.1214	−0.466839
$791$	−10.1386	−0.360486
$792$	33.7975	1.20094
$793$	−0.730875	−0.0259541
$794$	46.0624	1.63469
$795$	−2.30781	−0.0818495
$796$	33.6421	1.19241
$797$	−16.7698	−0.594017	−0.297009	−	0.954875i	$-0.595989\pi$
$797$	−16.7698	−0.594017	−0.297009	+	0.954875i	$0.595989\pi$
$798$	25.5720	0.905238
$799$	−7.42092	−0.262533
$800$	−4.16036	−0.147091
$801$	−9.49679	−0.335552
$802$	−80.0344	−2.82611
$803$	−16.9261	−0.597308
$804$	−27.5896	−0.973010
$805$	−16.5356	−0.582805
$806$	−149.739	−5.27435
$807$	−5.63277	−0.198283
$808$	−25.9762	−0.913838
$809$	50.1650	1.76371	0.881855	−	0.471521i	$-0.156295\pi$
$809$	50.1650	1.76371	0.881855	+	0.471521i	$0.156295\pi$
$810$	−25.5396	−0.897372
$811$	−33.2954	−1.16916	−0.584579	−	0.811337i	$-0.698740\pi$
$811$	−33.2954	−1.16916	−0.584579	+	0.811337i	$0.698740\pi$
$812$	−20.0663	−0.704189
$813$	8.57560	0.300759
$814$	16.2288	0.568820
$815$	−15.6022	−0.546523
$816$	11.7334	0.410753
$817$	0.868601	0.0303885
$818$	−56.0875	−1.96106
$819$	−37.7223	−1.31813
$820$	−5.57518	−0.194694
$821$	−27.9620	−0.975881	−0.487940	−	0.872877i	$-0.662252\pi$
$821$	−27.9620	−0.975881	−0.487940	+	0.872877i	$0.662252\pi$
$822$	5.23994	0.182764
$823$	19.1976	0.669186	0.334593	−	0.942363i	$-0.391401\pi$
$823$	19.1976	0.669186	0.334593	+	0.942363i	$0.391401\pi$
$824$	−53.2978	−1.85672
$825$	3.52143	0.122601
$826$	−43.6695	−1.51946
$827$	5.55876	0.193297	0.0966484	−	0.995319i	$-0.469188\pi$
$827$	5.55876	0.193297	0.0966484	+	0.995319i	$0.469188\pi$
$828$	43.8596	1.52423
$829$	10.1057	0.350986	0.175493	−	0.984481i	$-0.443848\pi$
$829$	10.1057	0.350986	0.175493	+	0.984481i	$0.443848\pi$
$830$	−4.85892	−0.168656
$831$	6.20581	0.215277
$832$	−62.4905	−2.16647
$833$	13.5063	0.467967
$834$	−23.6109	−0.817578
$835$	23.2378	0.804179
$836$	92.4240	3.19655
$837$	32.1066	1.10977
$838$	−65.0284	−2.24637
$839$	−24.7698	−0.855148	−0.427574	−	0.903980i	$-0.640632\pi$
$839$	−24.7698	−0.855148	−0.427574	+	0.903980i	$0.640632\pi$
$840$	9.21181	0.317838
$841$	−23.6264	−0.814703
$842$	17.6029	0.606637
$843$	4.84651	0.166923
$844$	−98.0850	−3.37623
$845$	41.5326	1.42877
$846$	6.33887	0.217935
$847$	−5.68334	−0.195282
$848$	6.85520	0.235409
$849$	−10.5675	−0.362675
$850$	−39.5427	−1.35630
$851$	9.94558	0.340930
$852$	3.22022	0.110323
$853$	−30.9842	−1.06088	−0.530439	−	0.847723i	$-0.677973\pi$
$853$	−30.9842	−1.06088	−0.530439	+	0.847723i	$0.677973\pi$
$854$	0.654391	0.0223928
$855$	−37.8412	−1.29414
$856$	−34.2627	−1.17107
$857$	−47.2147	−1.61282	−0.806412	−	0.591354i	$-0.798594\pi$
$857$	−47.2147	−1.61282	−0.806412	+	0.591354i	$0.798594\pi$
$858$	23.9846	0.818819
$859$	20.1118	0.686206	0.343103	−	0.939298i	$-0.388522\pi$
$859$	20.1118	0.686206	0.343103	+	0.939298i	$0.388522\pi$
$860$	0.662579	0.0225938
$861$	1.11155	0.0378815
$862$	5.34290	0.181980
$863$	7.46998	0.254281	0.127141	−	0.991885i	$-0.459420\pi$
$863$	7.46998	0.254281	0.127141	+	0.991885i	$0.459420\pi$
$864$	6.07577	0.206702
$865$	−6.87890	−0.233889
$866$	6.94401	0.235967
$867$	−22.5008	−0.764167
$868$	87.7558	2.97863
$869$	9.45520	0.320746
$870$	−5.22373	−0.177101
$871$	80.2968	2.72075
$872$	−67.6366	−2.29047
$873$	12.6380	0.427730
$874$	86.5331	2.92703
$875$	−27.5534	−0.931474
$876$	12.2366	0.413435
$877$	16.7380	0.565201	0.282600	−	0.959238i	$-0.408803\pi$
$877$	16.7380	0.565201	0.282600	+	0.959238i	$0.408803\pi$
$878$	−11.1132	−0.375052
$879$	−16.3886	−0.552773
$880$	13.6570	0.460379
$881$	−53.0385	−1.78691	−0.893455	−	0.449152i	$-0.851726\pi$
$881$	−53.0385	−1.78691	−0.893455	+	0.449152i	$0.851726\pi$
$882$	−11.5370	−0.388470
$883$	11.5588	0.388983	0.194492	−	0.980904i	$-0.437694\pi$
$883$	11.5588	0.388983	0.194492	+	0.980904i	$0.437694\pi$
$884$	−176.288	−5.92922
$885$	−7.44109	−0.250129
$886$	29.0362	0.975490
$887$	45.4621	1.52647	0.763235	−	0.646121i	$-0.223610\pi$
$887$	45.4621	1.52647	0.763235	+	0.646121i	$0.223610\pi$
$888$	−5.54056	−0.185929
$889$	2.67151	0.0895996
$890$	−14.2926	−0.479090
$891$	18.4037	0.616546
$892$	87.5138	2.93018
$893$	8.18606	0.273936
$894$	5.44248	0.182024
$895$	−16.1071	−0.538402
$896$	47.1867	1.57640
$897$	14.6986	0.490770
$898$	73.9877	2.46900
$899$	−23.5004	−0.783781
$900$	22.1088	0.736960
$901$	−18.6739	−0.622119
$902$	6.13767	0.204362
$903$	−0.132101	−0.00439605
$904$	19.1126	0.635675
$905$	−15.6155	−0.519075
$906$	−1.14600	−0.0380732
$907$	16.5695	0.550182	0.275091	−	0.961418i	$-0.411292\pi$
$907$	16.5695	0.550182	0.275091	+	0.961418i	$0.411292\pi$
$908$	−76.2769	−2.53134
$909$	−16.2286	−0.538269
$910$	−56.7720	−1.88197
$911$	23.4779	0.777857	0.388928	−	0.921268i	$-0.372845\pi$
$911$	23.4779	0.777857	0.388928	+	0.921268i	$0.372845\pi$
$912$	−12.9432	−0.428593
$913$	3.50130	0.115876
$914$	−0.883924	−0.0292376
$915$	0.111505	0.00368625
$916$	31.4750	1.03996
$917$	26.0639	0.860705
$918$	57.7479	1.90597
$919$	53.7691	1.77368	0.886839	−	0.462079i	$-0.152896\pi$
$919$	53.7691	1.77368	0.886839	+	0.462079i	$0.152896\pi$
$920$	31.1719	1.02771
$921$	2.00472	0.0660578
$922$	43.0088	1.41642
$923$	−9.37213	−0.308488
$924$	−14.0563	−0.462419
$925$	5.01338	0.164839
$926$	47.9360	1.57528
$927$	−33.2978	−1.09364
$928$	−4.44715	−0.145985
$929$	32.5623	1.06833	0.534167	−	0.845379i	$-0.320625\pi$
$929$	32.5623	1.06833	0.534167	+	0.845379i	$0.320625\pi$
$930$	22.8449	0.749113
$931$	−14.8989	−0.488292
$932$	5.39960	0.176870
$933$	−12.1518	−0.397833
$934$	40.4180	1.32252
$935$	−37.2025	−1.21665
$936$	71.1117	2.32436
$937$	−46.1034	−1.50613	−0.753066	−	0.657945i	$-0.771426\pi$
$937$	−46.1034	−1.50613	−0.753066	+	0.657945i	$0.771426\pi$
$938$	−71.8940	−2.34742
$939$	−7.04665	−0.229959
$940$	6.24442	0.203671
$941$	6.64359	0.216575	0.108287	−	0.994120i	$-0.465463\pi$
$941$	6.64359	0.216575	0.108287	+	0.994120i	$0.465463\pi$
$942$	−13.2710	−0.432392
$943$	3.76138	0.122487
$944$	22.1033	0.719401
$945$	12.1728	0.395983
$946$	−0.729428	−0.0237157
$947$	8.65510	0.281253	0.140627	−	0.990063i	$-0.455088\pi$
$947$	8.65510	0.281253	0.140627	+	0.990063i	$0.455088\pi$
$948$	−6.83556	−0.222009
$949$	−35.6133	−1.15606
$950$	43.6198	1.41521
$951$	−15.1472	−0.491182
$952$	74.5386	2.41581
$953$	30.0422	0.973161	0.486581	−	0.873636i	$-0.338244\pi$
$953$	30.0422	0.973161	0.486581	+	0.873636i	$0.338244\pi$
$954$	15.9511	0.516435
$955$	−25.2702	−0.817725
$956$	110.582	3.57646
$957$	3.76418	0.121679
$958$	−42.1402	−1.36149
$959$	8.93756	0.288609
$960$	9.53380	0.307702
$961$	71.7740	2.31529
$962$	34.1463	1.10092
$963$	−21.4056	−0.689786
$964$	−107.788	−3.47163
$965$	−18.5823	−0.598186
$966$	−13.1604	−0.423429
$967$	−49.5192	−1.59243	−0.796215	−	0.605014i	$-0.793167\pi$
$967$	−49.5192	−1.59243	−0.796215	+	0.605014i	$0.793167\pi$
$968$	10.7139	0.344356
$969$	35.2581	1.13265
$970$	19.0201	0.610698
$971$	−41.5437	−1.33320	−0.666601	−	0.745415i	$-0.732251\pi$
$971$	−41.5437	−1.33320	−0.666601	+	0.745415i	$0.732251\pi$
$972$	−49.3102	−1.58163
$973$	−40.2721	−1.29106
$974$	49.8803	1.59827
$975$	7.40927	0.237287
$976$	−0.331220	−0.0106021
$977$	37.0902	1.18662	0.593310	−	0.804974i	$-0.297821\pi$
$977$	37.0902	1.18662	0.593310	+	0.804974i	$0.297821\pi$
$978$	−12.4175	−0.397069
$979$	10.2992	0.329163
$980$	−11.3651	−0.363044
$981$	−42.2560	−1.34913
$982$	−47.8231	−1.52610
$983$	−38.8827	−1.24016	−0.620082	−	0.784537i	$-0.712901\pi$
$983$	−38.8827	−1.24016	−0.620082	+	0.784537i	$0.712901\pi$
$984$	−2.09542	−0.0667995
$985$	−43.2547	−1.37821
$986$	−42.2685	−1.34610
$987$	−1.24498	−0.0396281
$988$	194.465	6.18675
$989$	−0.447018	−0.0142144
$990$	31.7780	1.00997
$991$	−55.1144	−1.75077	−0.875383	−	0.483430i	$-0.839391\pi$
$991$	−55.1144	−1.75077	−0.875383	+	0.483430i	$0.839391\pi$
$992$	19.4487	0.617497
$993$	−11.5064	−0.365143
$994$	8.39137	0.266158
$995$	14.9379	0.473563
$996$	−2.53124	−0.0802053
$997$	−5.89602	−0.186729	−0.0933644	−	0.995632i	$-0.529762\pi$
$997$	−5.89602	−0.186729	−0.0933644	+	0.995632i	$0.529762\pi$
$998$	19.5549	0.618999
$999$	−7.32152	−0.231643

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.b.1.18	✓	186

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.b.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-2.40616 q^{2} -0.556574 q^{3} +3.78961 q^{4} +1.68267 q^{5} +1.33921 q^{6} +2.28423 q^{7} -4.30608 q^{8} -2.69023 q^{9} +O(q^{10})\)	\(q-2.40616 q^{2} -0.556574 q^{3} +3.78961 q^{4} +1.68267 q^{5} +1.33921 q^{6} +2.28423 q^{7} -4.30608 q^{8} -2.69023 q^{9} -4.04878 q^{10} +2.91752 q^{11} -2.10920 q^{12} +6.13861 q^{13} -5.49623 q^{14} -0.936532 q^{15} +2.78191 q^{16} -7.57808 q^{17} +6.47311 q^{18} +8.35943 q^{19} +6.37667 q^{20} -1.27134 q^{21} -7.02002 q^{22} -4.30211 q^{23} +2.39665 q^{24} -2.16861 q^{25} -14.7705 q^{26} +3.16703 q^{27} +8.65634 q^{28} -2.31811 q^{29} +2.25345 q^{30} +10.1378 q^{31} +1.91844 q^{32} -1.62382 q^{33} +18.2341 q^{34} +3.84361 q^{35} -10.1949 q^{36} -2.31179 q^{37} -20.1141 q^{38} -3.41659 q^{39} -7.24573 q^{40} -0.874310 q^{41} +3.05906 q^{42} +0.103907 q^{43} +11.0563 q^{44} -4.52677 q^{45} +10.3516 q^{46} +0.979261 q^{47} -1.54834 q^{48} -1.78229 q^{49} +5.21803 q^{50} +4.21776 q^{51} +23.2629 q^{52} +2.46421 q^{53} -7.62039 q^{54} +4.90923 q^{55} -9.83609 q^{56} -4.65264 q^{57} +5.57773 q^{58} +7.94536 q^{59} -3.54909 q^{60} -0.119062 q^{61} -24.3931 q^{62} -6.14509 q^{63} -10.1799 q^{64} +10.3293 q^{65} +3.90716 q^{66} +13.0806 q^{67} -28.7179 q^{68} +2.39444 q^{69} -9.24835 q^{70} -1.52675 q^{71} +11.5843 q^{72} -5.80152 q^{73} +5.56254 q^{74} +1.20699 q^{75} +31.6789 q^{76} +6.66429 q^{77} +8.22087 q^{78} +3.24083 q^{79} +4.68104 q^{80} +6.30799 q^{81} +2.10373 q^{82} +1.20009 q^{83} -4.81789 q^{84} -12.7514 q^{85} -0.250016 q^{86} +1.29020 q^{87} -12.5631 q^{88} +3.53011 q^{89} +10.8921 q^{90} +14.0220 q^{91} -16.3033 q^{92} -5.64241 q^{93} -2.35626 q^{94} +14.0662 q^{95} -1.06776 q^{96} -4.69774 q^{97} +4.28848 q^{98} -7.84879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) \) 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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