LMFDB - Embedded newform 6011.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6011,2,Mod(1,6011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6011, 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("6011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6011.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:	$47.9980766550$
Analytic rank:	$1$
Dimension:	$221$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80701 q^{2} -2.40971 q^{3} +5.87930 q^{4} +2.03862 q^{5} +6.76409 q^{6} +2.90054 q^{7} -10.8892 q^{8} +2.80672 q^{9} +O(q^{10})$	\(q-2.80701 q^{2} -2.40971 q^{3} +5.87930 q^{4} +2.03862 q^{5} +6.76409 q^{6} +2.90054 q^{7} -10.8892 q^{8} +2.80672 q^{9} -5.72241 q^{10} +3.14005 q^{11} -14.1674 q^{12} +2.69329 q^{13} -8.14184 q^{14} -4.91248 q^{15} +18.8076 q^{16} -1.79784 q^{17} -7.87850 q^{18} -4.91002 q^{19} +11.9856 q^{20} -6.98947 q^{21} -8.81415 q^{22} +6.45977 q^{23} +26.2400 q^{24} -0.844045 q^{25} -7.56008 q^{26} +0.465738 q^{27} +17.0531 q^{28} -3.33973 q^{29} +13.7894 q^{30} -8.38060 q^{31} -31.0146 q^{32} -7.56662 q^{33} +5.04656 q^{34} +5.91308 q^{35} +16.5016 q^{36} +5.64219 q^{37} +13.7825 q^{38} -6.49005 q^{39} -22.1990 q^{40} +7.77771 q^{41} +19.6195 q^{42} -7.30203 q^{43} +18.4613 q^{44} +5.72183 q^{45} -18.1326 q^{46} +7.29568 q^{47} -45.3210 q^{48} +1.41313 q^{49} +2.36924 q^{50} +4.33229 q^{51} +15.8346 q^{52} +4.22124 q^{53} -1.30733 q^{54} +6.40135 q^{55} -31.5847 q^{56} +11.8317 q^{57} +9.37467 q^{58} -14.4073 q^{59} -28.8820 q^{60} -12.6474 q^{61} +23.5244 q^{62} +8.14101 q^{63} +49.4432 q^{64} +5.49058 q^{65} +21.2396 q^{66} -1.18890 q^{67} -10.5701 q^{68} -15.5662 q^{69} -16.5981 q^{70} +9.54703 q^{71} -30.5631 q^{72} -15.9005 q^{73} -15.8377 q^{74} +2.03391 q^{75} -28.8675 q^{76} +9.10783 q^{77} +18.2176 q^{78} -11.3899 q^{79} +38.3415 q^{80} -9.54247 q^{81} -21.8321 q^{82} +9.21341 q^{83} -41.0932 q^{84} -3.66511 q^{85} +20.4969 q^{86} +8.04781 q^{87} -34.1928 q^{88} -1.69093 q^{89} -16.0612 q^{90} +7.81198 q^{91} +37.9790 q^{92} +20.1948 q^{93} -20.4790 q^{94} -10.0096 q^{95} +74.7364 q^{96} -12.2287 q^{97} -3.96666 q^{98} +8.81325 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9}+O(q^{10}) $ 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9} - 61 q^{10} - 50 q^{11} - 43 q^{12} - 87 q^{13} - 41 q^{14} - 62 q^{15} + 129 q^{16} - 29 q^{17} - 61 q^{18} - 107 q^{19} - 59 q^{20} - 163 q^{21} - 70 q^{22} - 31 q^{23} - 98 q^{24} + 119 q^{25} - 23 q^{26} - 41 q^{27} - 112 q^{28} - 152 q^{29} - 66 q^{30} - 117 q^{31} - 93 q^{32} - 60 q^{33} - 80 q^{34} - 21 q^{35} + 92 q^{36} - 231 q^{37} + 2 q^{38} - 81 q^{39} - 143 q^{40} - 81 q^{41} - 6 q^{42} - 126 q^{43} - 115 q^{44} - 156 q^{45} - 205 q^{46} - 4 q^{47} - 55 q^{48} + 103 q^{49} - 61 q^{50} - 106 q^{51} - 164 q^{52} - 87 q^{53} - 110 q^{54} - 62 q^{55} - 73 q^{56} - 136 q^{57} - 128 q^{58} - 76 q^{59} - 148 q^{60} - 345 q^{61} + 5 q^{62} - 74 q^{63} - 25 q^{64} - 110 q^{65} - 34 q^{66} - 104 q^{67} - 48 q^{68} - 133 q^{69} - 92 q^{70} - 39 q^{71} - 177 q^{72} - 175 q^{73} - 44 q^{74} - 23 q^{75} - 268 q^{76} - 81 q^{77} - 19 q^{78} - 272 q^{79} - 60 q^{80} + 77 q^{81} - 13 q^{82} - 40 q^{83} - 221 q^{84} - 376 q^{85} - 82 q^{86} - 3 q^{87} - 234 q^{88} - 92 q^{89} - 91 q^{90} - 205 q^{91} - 11 q^{92} - 125 q^{93} - 126 q^{94} - 56 q^{95} - 148 q^{96} - 133 q^{97} - 4 q^{98} - 195 q^{99}+O(q^{100}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9 - 61 * q^10 - 50 * q^11 - 43 * q^12 - 87 * q^13 - 41 * q^14 - 62 * q^15 + 129 * q^16 - 29 * q^17 - 61 * q^18 - 107 * q^19 - 59 * q^20 - 163 * q^21 - 70 * q^22 - 31 * q^23 - 98 * q^24 + 119 * q^25 - 23 * q^26 - 41 * q^27 - 112 * q^28 - 152 * q^29 - 66 * q^30 - 117 * q^31 - 93 * q^32 - 60 * q^33 - 80 * q^34 - 21 * q^35 + 92 * q^36 - 231 * q^37 + 2 * q^38 - 81 * q^39 - 143 * q^40 - 81 * q^41 - 6 * q^42 - 126 * q^43 - 115 * q^44 - 156 * q^45 - 205 * q^46 - 4 * q^47 - 55 * q^48 + 103 * q^49 - 61 * q^50 - 106 * q^51 - 164 * q^52 - 87 * q^53 - 110 * q^54 - 62 * q^55 - 73 * q^56 - 136 * q^57 - 128 * q^58 - 76 * q^59 - 148 * q^60 - 345 * q^61 + 5 * q^62 - 74 * q^63 - 25 * q^64 - 110 * q^65 - 34 * q^66 - 104 * q^67 - 48 * q^68 - 133 * q^69 - 92 * q^70 - 39 * q^71 - 177 * q^72 - 175 * q^73 - 44 * q^74 - 23 * q^75 - 268 * q^76 - 81 * q^77 - 19 * q^78 - 272 * q^79 - 60 * q^80 + 77 * q^81 - 13 * q^82 - 40 * q^83 - 221 * q^84 - 376 * q^85 - 82 * q^86 - 3 * q^87 - 234 * q^88 - 92 * q^89 - 91 * q^90 - 205 * q^91 - 11 * q^92 - 125 * q^93 - 126 * q^94 - 56 * q^95 - 148 * q^96 - 133 * q^97 - 4 * q^98 - 195 * 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 $

$2$	−2.80701	−1.98486	−0.992428	−	0.122829i	$-0.960803\pi$
$2$	−2.80701	−1.98486	−0.992428	+	0.122829i	$0.960803\pi$
$3$	−2.40971	−1.39125	−0.695625	−	0.718405i	$-0.744872\pi$
$3$	−2.40971	−1.39125	−0.695625	+	0.718405i	$0.744872\pi$
$4$	5.87930	2.93965
$5$	2.03862	0.911697	0.455848	−	0.890057i	$-0.349336\pi$
$5$	2.03862	0.911697	0.455848	+	0.890057i	$0.349336\pi$
$6$	6.76409	2.76143
$7$	2.90054	1.09630	0.548150	−	0.836380i	$-0.315332\pi$
$7$	2.90054	1.09630	0.548150	+	0.836380i	$0.315332\pi$
$8$	−10.8892	−3.84993
$9$	2.80672	0.935575
$10$	−5.72241	−1.80959
$11$	3.14005	0.946760	0.473380	−	0.880858i	$-0.343034\pi$
$11$	3.14005	0.946760	0.473380	+	0.880858i	$0.343034\pi$
$12$	−14.1674	−4.08979
$13$	2.69329	0.746983	0.373492	−	0.927634i	$-0.378160\pi$
$13$	2.69329	0.746983	0.373492	+	0.927634i	$0.378160\pi$
$14$	−8.14184	−2.17600
$15$	−4.91248	−1.26840
$16$	18.8076	4.70190
$17$	−1.79784	−0.436041	−0.218020	−	0.975944i	$-0.569960\pi$
$17$	−1.79784	−0.436041	−0.218020	+	0.975944i	$0.569960\pi$
$18$	−7.87850	−1.85698
$19$	−4.91002	−1.12643	−0.563217	−	0.826309i	$-0.690437\pi$
$19$	−4.91002	−1.12643	−0.563217	+	0.826309i	$0.690437\pi$
$20$	11.9856	2.68007
$21$	−6.98947	−1.52523
$22$	−8.81415	−1.87918
$23$	6.45977	1.34696	0.673478	−	0.739207i	$-0.264800\pi$
$23$	6.45977	1.34696	0.673478	+	0.739207i	$0.264800\pi$
$24$	26.2400	5.35621
$25$	−0.844045	−0.168809
$26$	−7.56008	−1.48265
$27$	0.465738	0.0896313
$28$	17.0531	3.22274
$29$	−3.33973	−0.620173	−0.310087	−	0.950708i	$-0.600358\pi$
$29$	−3.33973	−0.620173	−0.310087	+	0.950708i	$0.600358\pi$
$30$	13.7894	2.51759
$31$	−8.38060	−1.50520	−0.752600	−	0.658478i	$-0.771201\pi$
$31$	−8.38060	−1.50520	−0.752600	+	0.658478i	$0.771201\pi$
$32$	−31.0146	−5.48267
$33$	−7.56662	−1.31718
$34$	5.04656	0.865478
$35$	5.91308	0.999494
$36$	16.5016	2.75026
$37$	5.64219	0.927570	0.463785	−	0.885948i	$-0.346491\pi$
$37$	5.64219	0.927570	0.463785	+	0.885948i	$0.346491\pi$
$38$	13.7825	2.23581
$39$	−6.49005	−1.03924
$40$	−22.1990	−3.50997
$41$	7.77771	1.21467	0.607337	−	0.794444i	$-0.292238\pi$
$41$	7.77771	1.21467	0.607337	+	0.794444i	$0.292238\pi$
$42$	19.6195	3.02736
$43$	−7.30203	−1.11355	−0.556774	−	0.830664i	$-0.687961\pi$
$43$	−7.30203	−1.11355	−0.556774	+	0.830664i	$0.687961\pi$
$44$	18.4613	2.78315
$45$	5.72183	0.852961
$46$	−18.1326	−2.67351
$47$	7.29568	1.06418	0.532092	−	0.846687i	$-0.321406\pi$
$47$	7.29568	1.06418	0.532092	+	0.846687i	$0.321406\pi$
$48$	−45.3210	−6.54152
$49$	1.41313	0.201875
$50$	2.36924	0.335061
$51$	4.33229	0.606642
$52$	15.8346	2.19587
$53$	4.22124	0.579831	0.289916	−	0.957052i	$-0.406373\pi$
$53$	4.22124	0.579831	0.289916	+	0.957052i	$0.406373\pi$
$54$	−1.30733	−0.177905
$55$	6.40135	0.863158
$56$	−31.5847	−4.22068
$57$	11.8317	1.56715
$58$	9.37467	1.23095
$59$	−14.4073	−1.87567	−0.937836	−	0.347080i	$-0.887173\pi$
$59$	−14.4073	−1.87567	−0.937836	+	0.347080i	$0.887173\pi$
$60$	−28.8820	−3.72865
$61$	−12.6474	−1.61934	−0.809668	−	0.586888i	$-0.800353\pi$
$61$	−12.6474	−1.61934	−0.809668	+	0.586888i	$0.800353\pi$
$62$	23.5244	2.98760
$63$	8.14101	1.02567
$64$	49.4432	6.18040
$65$	5.49058	0.681022
$66$	21.2396	2.61441
$67$	−1.18890	−0.145248	−0.0726238	−	0.997359i	$-0.523137\pi$
$67$	−1.18890	−0.145248	−0.0726238	+	0.997359i	$0.523137\pi$
$68$	−10.5701	−1.28181
$69$	−15.5662	−1.87395
$70$	−16.5981	−1.98385
$71$	9.54703	1.13302	0.566512	−	0.824054i	$-0.308293\pi$
$71$	9.54703	1.13302	0.566512	+	0.824054i	$0.308293\pi$
$72$	−30.5631	−3.60190
$73$	−15.9005	−1.86102	−0.930509	−	0.366270i	$-0.880635\pi$
$73$	−15.9005	−1.86102	−0.930509	+	0.366270i	$0.880635\pi$
$74$	−15.8377	−1.84109
$75$	2.03391	0.234855
$76$	−28.8675	−3.31133
$77$	9.10783	1.03793
$78$	18.2176	2.06274
$79$	−11.3899	−1.28146	−0.640731	−	0.767765i	$-0.721369\pi$
$79$	−11.3899	−1.28146	−0.640731	+	0.767765i	$0.721369\pi$
$80$	38.3415	4.28671
$81$	−9.54247	−1.06027
$82$	−21.8321	−2.41095
$83$	9.21341	1.01130	0.505652	−	0.862738i	$-0.331252\pi$
$83$	9.21341	1.01130	0.505652	+	0.862738i	$0.331252\pi$
$84$	−41.0932	−4.48364
$85$	−3.66511	−0.397537
$86$	20.4969	2.21023
$87$	8.04781	0.862816
$88$	−34.1928	−3.64496
$89$	−1.69093	−0.179238	−0.0896189	−	0.995976i	$-0.528565\pi$
$89$	−1.69093	−0.179238	−0.0896189	+	0.995976i	$0.528565\pi$
$90$	−16.0612	−1.69300
$91$	7.81198	0.818918
$92$	37.9790	3.95958
$93$	20.1948	2.09411
$94$	−20.4790	−2.11225
$95$	−10.0096	−1.02697
$96$	74.7364	7.62775
$97$	−12.2287	−1.24163	−0.620816	−	0.783956i	$-0.713199\pi$
$97$	−12.2287	−1.24163	−0.620816	+	0.783956i	$0.713199\pi$
$98$	−3.96666	−0.400693
$99$	8.81325	0.885765
$100$	−4.96240	−0.496240
$101$	−13.3800	−1.33136	−0.665679	−	0.746238i	$-0.731858\pi$
$101$	−13.3800	−1.33136	−0.665679	+	0.746238i	$0.731858\pi$
$102$	−12.1608	−1.20410
$103$	−13.2523	−1.30578	−0.652892	−	0.757451i	$-0.726444\pi$
$103$	−13.2523	−1.30578	−0.652892	+	0.757451i	$0.726444\pi$
$104$	−29.3278	−2.87583
$105$	−14.2488	−1.39055
$106$	−11.8491	−1.15088
$107$	−11.9292	−1.15324	−0.576619	−	0.817013i	$-0.695628\pi$
$107$	−11.9292	−1.15324	−0.576619	+	0.817013i	$0.695628\pi$
$108$	2.73821	0.263485
$109$	−8.41527	−0.806036	−0.403018	−	0.915192i	$-0.632039\pi$
$109$	−8.41527	−0.806036	−0.403018	+	0.915192i	$0.632039\pi$
$110$	−17.9687	−1.71324
$111$	−13.5961	−1.29048
$112$	54.5522	5.15470
$113$	7.00220	0.658711	0.329356	−	0.944206i	$-0.393169\pi$
$113$	7.00220	0.658711	0.329356	+	0.944206i	$0.393169\pi$
$114$	−33.2118	−3.11057
$115$	13.1690	1.22802
$116$	−19.6353	−1.82309
$117$	7.55931	0.698859
$118$	40.4414	3.72294
$119$	−5.21471	−0.478032
$120$	53.4932	4.88324
$121$	−1.14009	−0.103645
$122$	35.5014	3.21415
$123$	−18.7421	−1.68992
$124$	−49.2721	−4.42476
$125$	−11.9138	−1.06560
$126$	−22.8519	−2.03581
$127$	−14.6872	−1.30328	−0.651640	−	0.758529i	$-0.725919\pi$
$127$	−14.6872	−1.30328	−0.651640	+	0.758529i	$0.725919\pi$
$128$	−76.7582	−6.78453
$129$	17.5958	1.54922
$130$	−15.4121	−1.35173
$131$	−5.36410	−0.468663	−0.234332	−	0.972157i	$-0.575290\pi$
$131$	−5.36410	−0.468663	−0.234332	+	0.972157i	$0.575290\pi$
$132$	−44.4865	−3.87205
$133$	−14.2417	−1.23491
$134$	3.33726	0.288296
$135$	0.949460	0.0817165
$136$	19.5771	1.67873
$137$	4.47551	0.382368	0.191184	−	0.981554i	$-0.438767\pi$
$137$	4.47551	0.382368	0.191184	+	0.981554i	$0.438767\pi$
$138$	43.6945	3.71952
$139$	13.6864	1.16087	0.580434	−	0.814307i	$-0.302883\pi$
$139$	13.6864	1.16087	0.580434	+	0.814307i	$0.302883\pi$
$140$	34.7648	2.93816
$141$	−17.5805	−1.48055
$142$	−26.7986	−2.24889
$143$	8.45705	0.707214
$144$	52.7878	4.39898
$145$	−6.80844	−0.565410
$146$	44.6330	3.69385
$147$	−3.40523	−0.280859
$148$	33.1721	2.72673
$149$	−23.2884	−1.90786	−0.953931	−	0.300025i	$-0.903005\pi$
$149$	−23.2884	−1.90786	−0.953931	+	0.300025i	$0.903005\pi$
$150$	−5.70920	−0.466154
$151$	−24.0795	−1.95956	−0.979779	−	0.200082i	$-0.935879\pi$
$151$	−24.0795	−1.95956	−0.979779	+	0.200082i	$0.935879\pi$
$152$	53.4664	4.33669
$153$	−5.04605	−0.407949
$154$	−25.5658	−2.06015
$155$	−17.0848	−1.37229
$156$	−38.1570	−3.05500
$157$	14.8049	1.18156	0.590778	−	0.806834i	$-0.298821\pi$
$157$	14.8049	1.18156	0.590778	+	0.806834i	$0.298821\pi$
$158$	31.9715	2.54352
$159$	−10.1720	−0.806690
$160$	−63.2269	−4.99853
$161$	18.7368	1.47667
$162$	26.7858	2.10449
$163$	7.80147	0.611059	0.305529	−	0.952183i	$-0.401167\pi$
$163$	7.80147	0.611059	0.305529	+	0.952183i	$0.401167\pi$
$164$	45.7275	3.57072
$165$	−15.4254	−1.20087
$166$	−25.8621	−2.00729
$167$	1.61644	0.125084	0.0625420	−	0.998042i	$-0.480079\pi$
$167$	1.61644	0.125084	0.0625420	+	0.998042i	$0.480079\pi$
$168$	76.1100	5.87202
$169$	−5.74621	−0.442016
$170$	10.2880	0.789054
$171$	−13.7811	−1.05386
$172$	−42.9308	−3.27345
$173$	−19.4374	−1.47780	−0.738900	−	0.673815i	$-0.764654\pi$
$173$	−19.4374	−1.47780	−0.738900	+	0.673815i	$0.764654\pi$
$174$	−22.5903	−1.71256
$175$	−2.44819	−0.185065
$176$	59.0568	4.45157
$177$	34.7175	2.60953
$178$	4.74645	0.355761
$179$	0.586484	0.0438358	0.0219179	−	0.999760i	$-0.493023\pi$
$179$	0.586484	0.0438358	0.0219179	+	0.999760i	$0.493023\pi$
$180$	33.6404	2.50741
$181$	−9.00599	−0.669410	−0.334705	−	0.942323i	$-0.608637\pi$
$181$	−9.00599	−0.669410	−0.334705	+	0.942323i	$0.608637\pi$
$182$	−21.9283	−1.62543
$183$	30.4767	2.25290
$184$	−70.3420	−5.18568
$185$	11.5023	0.845663
$186$	−56.6871	−4.15650
$187$	−5.64531	−0.412826
$188$	42.8935	3.12833
$189$	1.35089	0.0982628
$190$	28.0971	2.03838
$191$	−14.6848	−1.06255	−0.531277	−	0.847198i	$-0.678288\pi$
$191$	−14.6848	−1.06255	−0.531277	+	0.847198i	$0.678288\pi$
$192$	−119.144	−8.59848
$193$	−15.9202	−1.14596	−0.572981	−	0.819569i	$-0.694213\pi$
$193$	−15.9202	−1.14596	−0.572981	+	0.819569i	$0.694213\pi$
$194$	34.3260	2.46446
$195$	−13.2307	−0.947472
$196$	8.30820	0.593443
$197$	−5.69376	−0.405664	−0.202832	−	0.979214i	$-0.565014\pi$
$197$	−5.69376	−0.405664	−0.202832	+	0.979214i	$0.565014\pi$
$198$	−24.7389	−1.75812
$199$	14.3304	1.01585	0.507927	−	0.861400i	$-0.330412\pi$
$199$	14.3304	1.01585	0.507927	+	0.861400i	$0.330412\pi$
$200$	9.19101	0.649903
$201$	2.86492	0.202076
$202$	37.5577	2.64255
$203$	−9.68703	−0.679896
$204$	25.4708	1.78331
$205$	15.8558	1.10742
$206$	37.1992	2.59179
$207$	18.1308	1.26018
$208$	50.6543	3.51224
$209$	−15.4177	−1.06646
$210$	39.9967	2.76003
$211$	2.35983	0.162457	0.0812286	−	0.996695i	$-0.474116\pi$
$211$	2.35983	0.162457	0.0812286	+	0.996695i	$0.474116\pi$
$212$	24.8179	1.70450
$213$	−23.0056	−1.57632
$214$	33.4853	2.28901
$215$	−14.8860	−1.01522
$216$	−5.07153	−0.345074
$217$	−24.3082	−1.65015
$218$	23.6217	1.59987
$219$	38.3158	2.58914
$220$	37.6355	2.53739
$221$	−4.84210	−0.325715
$222$	38.1643	2.56142
$223$	22.8067	1.52725	0.763624	−	0.645661i	$-0.223418\pi$
$223$	22.8067	1.52725	0.763624	+	0.645661i	$0.223418\pi$
$224$	−89.9592	−6.01065
$225$	−2.36900	−0.157933
$226$	−19.6552	−1.30745
$227$	4.41891	0.293293	0.146647	−	0.989189i	$-0.453152\pi$
$227$	4.41891	0.293293	0.146647	+	0.989189i	$0.453152\pi$
$228$	69.5624	4.60688
$229$	21.4665	1.41855	0.709273	−	0.704934i	$-0.249023\pi$
$229$	21.4665	1.41855	0.709273	+	0.704934i	$0.249023\pi$
$230$	−36.9655	−2.43743
$231$	−21.9473	−1.44403
$232$	36.3672	2.38762
$233$	17.8027	1.16629	0.583147	−	0.812366i	$-0.301821\pi$
$233$	17.8027	1.16629	0.583147	+	0.812366i	$0.301821\pi$
$234$	−21.2191	−1.38713
$235$	14.8731	0.970213
$236$	−84.7049	−5.51382
$237$	27.4464	1.78283
$238$	14.6377	0.948824
$239$	26.2287	1.69659	0.848295	−	0.529523i	$-0.177629\pi$
$239$	26.2287	1.69659	0.848295	+	0.529523i	$0.177629\pi$
$240$	−92.3920	−5.96388
$241$	22.5137	1.45023	0.725117	−	0.688625i	$-0.241785\pi$
$241$	22.5137	1.45023	0.725117	+	0.688625i	$0.241785\pi$
$242$	3.20025	0.205720
$243$	21.5974	1.38547
$244$	−74.3581	−4.76029
$245$	2.88082	0.184049
$246$	52.6092	3.35424
$247$	−13.2241	−0.841428
$248$	91.2584	5.79491
$249$	−22.2017	−1.40697
$250$	33.4420	2.11506
$251$	−17.5525	−1.10790	−0.553952	−	0.832549i	$-0.686881\pi$
$251$	−17.5525	−1.10790	−0.553952	+	0.832549i	$0.686881\pi$
$252$	47.8635	3.01512
$253$	20.2840	1.27524
$254$	41.2271	2.58682
$255$	8.83187	0.553073
$256$	116.575	7.28592
$257$	−12.7630	−0.796134	−0.398067	−	0.917356i	$-0.630319\pi$
$257$	−12.7630	−0.796134	−0.398067	+	0.917356i	$0.630319\pi$
$258$	−49.3916	−3.07499
$259$	16.3654	1.01690
$260$	32.2808	2.00197
$261$	−9.37372	−0.580218
$262$	15.0571	0.930229
$263$	−20.4341	−1.26002	−0.630011	−	0.776586i	$-0.716950\pi$
$263$	−20.4341	−1.26002	−0.630011	+	0.776586i	$0.716950\pi$
$264$	82.3948	5.07105
$265$	8.60548	0.528631
$266$	39.9766	2.45112
$267$	4.07465	0.249365
$268$	−6.98992	−0.426978
$269$	3.85934	0.235308	0.117654	−	0.993055i	$-0.462463\pi$
$269$	3.85934	0.235308	0.117654	+	0.993055i	$0.462463\pi$
$270$	−2.66514	−0.162196
$271$	15.0700	0.915438	0.457719	−	0.889097i	$-0.348667\pi$
$271$	15.0700	0.915438	0.457719	+	0.889097i	$0.348667\pi$
$272$	−33.8131	−2.05022
$273$	−18.8246	−1.13932
$274$	−12.5628	−0.758946
$275$	−2.65034	−0.159822
$276$	−91.5185	−5.50877
$277$	3.90012	0.234335	0.117168	−	0.993112i	$-0.462619\pi$
$277$	3.90012	0.234335	0.117168	+	0.993112i	$0.462619\pi$
$278$	−38.4180	−2.30416
$279$	−23.5220	−1.40823
$280$	−64.3890	−3.84798
$281$	−20.4043	−1.21722	−0.608609	−	0.793470i	$-0.708272\pi$
$281$	−20.4043	−1.21722	−0.608609	+	0.793470i	$0.708272\pi$
$282$	49.3486	2.93867
$283$	−1.68327	−0.100060	−0.0500299	−	0.998748i	$-0.515932\pi$
$283$	−1.68327	−0.100060	−0.0500299	+	0.998748i	$0.515932\pi$
$284$	56.1299	3.33070
$285$	24.1204	1.42877
$286$	−23.7390	−1.40372
$287$	22.5596	1.33165
$288$	−87.0496	−5.12944
$289$	−13.7678	−0.809868
$290$	19.1113	1.12226
$291$	29.4676	1.72742
$292$	−93.4841	−5.47074
$293$	−7.63000	−0.445750	−0.222875	−	0.974847i	$-0.571544\pi$
$293$	−7.63000	−0.445750	−0.222875	+	0.974847i	$0.571544\pi$
$294$	9.55851	0.557464
$295$	−29.3710	−1.71004
$296$	−61.4392	−3.57108
$297$	1.46244	0.0848593
$298$	65.3709	3.78683
$299$	17.3980	1.00615
$300$	11.9580	0.690393
$301$	−21.1798	−1.22078
$302$	67.5913	3.88944
$303$	32.2419	1.85225
$304$	−92.3456	−5.29639
$305$	−25.7832	−1.47634
$306$	14.1643	0.809720
$307$	14.1650	0.808439	0.404219	−	0.914662i	$-0.367543\pi$
$307$	14.1650	0.808439	0.404219	+	0.914662i	$0.367543\pi$
$308$	53.5477	3.05116
$309$	31.9342	1.81667
$310$	47.9573	2.72379
$311$	2.13602	0.121123	0.0605614	−	0.998164i	$-0.480711\pi$
$311$	2.13602	0.121123	0.0605614	+	0.998164i	$0.480711\pi$
$312$	70.6717	4.00100
$313$	12.6973	0.717693	0.358846	−	0.933397i	$-0.383170\pi$
$313$	12.6973	0.717693	0.358846	+	0.933397i	$0.383170\pi$
$314$	−41.5574	−2.34522
$315$	16.5964	0.935101
$316$	−66.9646	−3.76705
$317$	18.9841	1.06626	0.533128	−	0.846035i	$-0.321016\pi$
$317$	18.9841	1.06626	0.533128	+	0.846035i	$0.321016\pi$
$318$	28.5528	1.60116
$319$	−10.4869	−0.587155
$320$	100.796	5.63465
$321$	28.7459	1.60444
$322$	−52.5944	−2.93097
$323$	8.82744	0.491172
$324$	−56.1031	−3.11684
$325$	−2.27325	−0.126097
$326$	−21.8988	−1.21286
$327$	20.2784	1.12140
$328$	−84.6934	−4.67641
$329$	21.1614	1.16667
$330$	43.2994	2.38355
$331$	−3.52956	−0.194002	−0.0970011	−	0.995284i	$-0.530925\pi$
$331$	−3.52956	−0.194002	−0.0970011	+	0.995284i	$0.530925\pi$
$332$	54.1684	2.97288
$333$	15.8361	0.867811
$334$	−4.53737	−0.248274
$335$	−2.42372	−0.132422
$336$	−131.455	−7.17147
$337$	2.24160	0.122108	0.0610538	−	0.998134i	$-0.480554\pi$
$337$	2.24160	0.122108	0.0610538	+	0.998134i	$0.480554\pi$
$338$	16.1297	0.877338
$339$	−16.8733	−0.916431
$340$	−21.5483	−1.16862
$341$	−26.3155	−1.42506
$342$	38.6836	2.09177
$343$	−16.2049	−0.874985
$344$	79.5136	4.28708
$345$	−31.7335	−1.70848
$346$	54.5610	2.93322
$347$	−1.52977	−0.0821222	−0.0410611	−	0.999157i	$-0.513074\pi$
$347$	−1.52977	−0.0821222	−0.0410611	+	0.999157i	$0.513074\pi$
$348$	47.3155	2.53638
$349$	14.6465	0.784010	0.392005	−	0.919963i	$-0.371782\pi$
$349$	14.6465	0.784010	0.392005	+	0.919963i	$0.371782\pi$
$350$	6.87208	0.367328
$351$	1.25436	0.0669530
$352$	−97.3875	−5.19077
$353$	4.42469	0.235502	0.117751	−	0.993043i	$-0.462431\pi$
$353$	4.42469	0.235502	0.117751	+	0.993043i	$0.462431\pi$
$354$	−97.4523	−5.17953
$355$	19.4627	1.03297
$356$	−9.94147	−0.526897
$357$	12.5660	0.665062
$358$	−1.64626	−0.0870078
$359$	17.4973	0.923471	0.461735	−	0.887018i	$-0.347227\pi$
$359$	17.4973	0.923471	0.461735	+	0.887018i	$0.347227\pi$
$360$	−62.3064	−3.28384
$361$	5.10826	0.268856
$362$	25.2799	1.32868
$363$	2.74730	0.144196
$364$	45.9290	2.40733
$365$	−32.4151	−1.69668
$366$	−85.5484	−4.47168
$367$	12.3112	0.642642	0.321321	−	0.946970i	$-0.395873\pi$
$367$	12.3112	0.642642	0.321321	+	0.946970i	$0.395873\pi$
$368$	121.493	6.33325
$369$	21.8299	1.13642
$370$	−32.2869	−1.67852
$371$	12.2439	0.635670
$372$	118.732	6.15595
$373$	−10.8775	−0.563215	−0.281607	−	0.959530i	$-0.590868\pi$
$373$	−10.8775	−0.563215	−0.281607	+	0.959530i	$0.590868\pi$
$374$	15.8464	0.819400
$375$	28.7088	1.48251
$376$	−79.4444	−4.09703
$377$	−8.99486	−0.463259
$378$	−3.79196	−0.195037
$379$	−10.8404	−0.556833	−0.278416	−	0.960460i	$-0.589810\pi$
$379$	−10.8404	−0.556833	−0.278416	+	0.960460i	$0.589810\pi$
$380$	−58.8497	−3.01893
$381$	35.3920	1.81319
$382$	41.2204	2.10902
$383$	−21.6398	−1.10574	−0.552870	−	0.833267i	$-0.686468\pi$
$383$	−21.6398	−1.10574	−0.552870	+	0.833267i	$0.686468\pi$
$384$	184.965	9.43898
$385$	18.5674	0.946281
$386$	44.6882	2.27457
$387$	−20.4948	−1.04181
$388$	−71.8960	−3.64997
$389$	7.55024	0.382813	0.191406	−	0.981511i	$-0.438695\pi$
$389$	7.55024	0.382813	0.191406	+	0.981511i	$0.438695\pi$
$390$	37.1388	1.88059
$391$	−11.6137	−0.587328
$392$	−15.3879	−0.777205
$393$	12.9259	0.652028
$394$	15.9824	0.805184
$395$	−23.2196	−1.16831
$396$	51.8158	2.60384
$397$	−18.9553	−0.951340	−0.475670	−	0.879624i	$-0.657794\pi$
$397$	−18.9553	−0.951340	−0.475670	+	0.879624i	$0.657794\pi$
$398$	−40.2256	−2.01632
$399$	34.3184	1.71807
$400$	−15.8745	−0.793723
$401$	11.4586	0.572218	0.286109	−	0.958197i	$-0.407638\pi$
$401$	11.4586	0.572218	0.286109	+	0.958197i	$0.407638\pi$
$402$	−8.04185	−0.401091
$403$	−22.5713	−1.12436
$404$	−78.6649	−3.91373
$405$	−19.4534	−0.966649
$406$	27.1916	1.34950
$407$	17.7168	0.878187
$408$	−47.1753	−2.33553
$409$	−9.98169	−0.493563	−0.246781	−	0.969071i	$-0.579373\pi$
$409$	−9.98169	−0.493563	−0.246781	+	0.969071i	$0.579373\pi$
$410$	−44.5073	−2.19806
$411$	−10.7847	−0.531970
$412$	−77.9140	−3.83855
$413$	−41.7889	−2.05630
$414$	−50.8934	−2.50127
$415$	18.7826	0.922002
$416$	−83.5313	−4.09546
$417$	−32.9804	−1.61506
$418$	43.2776	2.11678
$419$	11.6072	0.567050	0.283525	−	0.958965i	$-0.408496\pi$
$419$	11.6072	0.567050	0.283525	+	0.958965i	$0.408496\pi$
$420$	−83.7733	−4.08772
$421$	−23.7773	−1.15884	−0.579418	−	0.815031i	$-0.696720\pi$
$421$	−23.7773	−1.15884	−0.579418	+	0.815031i	$0.696720\pi$
$422$	−6.62406	−0.322454
$423$	20.4770	0.995624
$424$	−45.9661	−2.23231
$425$	1.51746	0.0736076
$426$	64.5770	3.12877
$427$	−36.6843	−1.77528
$428$	−70.1353	−3.39012
$429$	−20.3791	−0.983911
$430$	41.7852	2.01506
$431$	11.9699	0.576570	0.288285	−	0.957545i	$-0.406915\pi$
$431$	11.9699	0.576570	0.288285	+	0.957545i	$0.406915\pi$
$432$	8.75941	0.421437
$433$	4.56041	0.219159	0.109580	−	0.993978i	$-0.465050\pi$
$433$	4.56041	0.219159	0.109580	+	0.993978i	$0.465050\pi$
$434$	68.2335	3.27531
$435$	16.4064	0.786626
$436$	−49.4759	−2.36947
$437$	−31.7176	−1.51726
$438$	−107.553	−5.13907
$439$	12.2664	0.585445	0.292723	−	0.956197i	$-0.405439\pi$
$439$	12.2664	0.585445	0.292723	+	0.956197i	$0.405439\pi$
$440$	−69.7059	−3.32310
$441$	3.96626	0.188869
$442$	13.5918	0.646498
$443$	−32.9377	−1.56492	−0.782460	−	0.622701i	$-0.786035\pi$
$443$	−32.9377	−1.56492	−0.782460	+	0.622701i	$0.786035\pi$
$444$	−79.9354	−3.79357
$445$	−3.44715	−0.163411
$446$	−64.0186	−3.03137
$447$	56.1185	2.65431
$448$	143.412	6.77557
$449$	−8.36889	−0.394952	−0.197476	−	0.980308i	$-0.563274\pi$
$449$	−8.36889	−0.394952	−0.197476	+	0.980308i	$0.563274\pi$
$450$	6.64981	0.313475
$451$	24.4224	1.15001
$452$	41.1680	1.93638
$453$	58.0246	2.72623
$454$	−12.4039	−0.582145
$455$	15.9256	0.746605
$456$	−128.839	−6.03342
$457$	40.4475	1.89206	0.946028	−	0.324084i	$-0.105056\pi$
$457$	40.4475	1.89206	0.946028	+	0.324084i	$0.105056\pi$
$458$	−60.2567	−2.81561
$459$	−0.837323	−0.0390829
$460$	77.4245	3.60994
$461$	15.3109	0.713098	0.356549	−	0.934277i	$-0.383953\pi$
$461$	15.3109	0.713098	0.356549	+	0.934277i	$0.383953\pi$
$462$	61.6062	2.86618
$463$	10.4392	0.485150	0.242575	−	0.970133i	$-0.422008\pi$
$463$	10.4392	0.485150	0.242575	+	0.970133i	$0.422008\pi$
$464$	−62.8124	−2.91599
$465$	41.1695	1.90919
$466$	−49.9724	−2.31493
$467$	25.5021	1.18010	0.590048	−	0.807368i	$-0.299109\pi$
$467$	25.5021	1.18010	0.590048	+	0.807368i	$0.299109\pi$
$468$	44.4435	2.05440
$469$	−3.44846	−0.159235
$470$	−41.7489	−1.92573
$471$	−35.6755	−1.64384
$472$	156.885	7.22120
$473$	−22.9287	−1.05426
$474$	−77.0423	−3.53867
$475$	4.14427	0.190152
$476$	−30.6589	−1.40525
$477$	11.8479	0.542476
$478$	−73.6241	−3.36749
$479$	20.0656	0.916819	0.458410	−	0.888741i	$-0.348419\pi$
$479$	20.0656	0.916819	0.458410	+	0.888741i	$0.348419\pi$
$480$	152.359	6.95420
$481$	15.1960	0.692879
$482$	−63.1962	−2.87851
$483$	−45.1504	−2.05441
$484$	−6.70295	−0.304680
$485$	−24.9296	−1.13199
$486$	−60.6242	−2.74997
$487$	3.55264	0.160985	0.0804927	−	0.996755i	$-0.474351\pi$
$487$	3.55264	0.160985	0.0804927	+	0.996755i	$0.474351\pi$
$488$	137.721	6.23433
$489$	−18.7993	−0.850135
$490$	−8.08649	−0.365310
$491$	−39.2019	−1.76916	−0.884579	−	0.466391i	$-0.845554\pi$
$491$	−39.2019	−1.76916	−0.884579	+	0.466391i	$0.845554\pi$
$492$	−110.190	−4.96776
$493$	6.00432	0.270421
$494$	37.1201	1.67011
$495$	17.9668	0.807549
$496$	−157.619	−7.07730
$497$	27.6915	1.24213
$498$	62.3204	2.79264
$499$	−26.1163	−1.16912	−0.584562	−	0.811349i	$-0.698734\pi$
$499$	−26.1163	−1.16912	−0.584562	+	0.811349i	$0.698734\pi$
$500$	−70.0446	−3.13249
$501$	−3.89516	−0.174023
$502$	49.2700	2.19903
$503$	14.0366	0.625861	0.312930	−	0.949776i	$-0.398689\pi$
$503$	14.0366	0.625861	0.312930	+	0.949776i	$0.398689\pi$
$504$	−88.6495	−3.94876
$505$	−27.2766	−1.21379
$506$	−56.9374	−2.53118
$507$	13.8467	0.614955
$508$	−86.3506	−3.83119
$509$	24.2306	1.07400	0.537000	−	0.843582i	$-0.319557\pi$
$509$	24.2306	1.07400	0.537000	+	0.843582i	$0.319557\pi$
$510$	−24.7911	−1.09777
$511$	−46.1201	−2.04023
$512$	−173.710	−7.67696
$513$	−2.28678	−0.100964
$514$	35.8258	1.58021
$515$	−27.0163	−1.19048
$516$	103.451	4.55418
$517$	22.9088	1.00753
$518$	−45.9378	−2.01839
$519$	46.8386	2.05599
$520$	−59.7882	−2.62189
$521$	−22.4482	−0.983474	−0.491737	−	0.870744i	$-0.663638\pi$
$521$	−22.4482	−0.983474	−0.491737	+	0.870744i	$0.663638\pi$
$522$	26.3121	1.15165
$523$	25.6291	1.12068	0.560342	−	0.828262i	$-0.310670\pi$
$523$	25.6291	1.12068	0.560342	+	0.828262i	$0.310670\pi$
$524$	−31.5372	−1.37771
$525$	5.89943	0.257472
$526$	57.3588	2.50096
$527$	15.0670	0.656329
$528$	−142.310	−6.19325
$529$	18.7287	0.814290
$530$	−24.1557	−1.04926
$531$	−40.4373	−1.75483
$532$	−83.7312	−3.63021
$533$	20.9476	0.907342
$534$	−11.4376	−0.494953
$535$	−24.3190	−1.05140
$536$	12.9463	0.559193
$537$	−1.41326	−0.0609866
$538$	−10.8332	−0.467052
$539$	4.43728	0.191127
$540$	5.58217	0.240218
$541$	−27.5292	−1.18357	−0.591787	−	0.806094i	$-0.701577\pi$
$541$	−27.5292	−1.18357	−0.591787	+	0.806094i	$0.701577\pi$
$542$	−42.3017	−1.81701
$543$	21.7019	0.931316
$544$	55.7594	2.39067
$545$	−17.1555	−0.734861
$546$	52.8410	2.26138
$547$	−1.03009	−0.0440436	−0.0220218	−	0.999757i	$-0.507010\pi$
$547$	−1.03009	−0.0440436	−0.0220218	+	0.999757i	$0.507010\pi$
$548$	26.3129	1.12403
$549$	−35.4978	−1.51501
$550$	7.43954	0.317223
$551$	16.3982	0.698585
$552$	169.504	7.21458
$553$	−33.0368	−1.40487
$554$	−10.9477	−0.465122
$555$	−27.7172	−1.17653
$556$	80.4667	3.41255
$557$	−38.8195	−1.64484	−0.822418	−	0.568884i	$-0.807375\pi$
$557$	−38.8195	−1.64484	−0.822418	+	0.568884i	$0.807375\pi$
$558$	66.0266	2.79513
$559$	−19.6665	−0.831802
$560$	111.211	4.69952
$561$	13.6036	0.574344
$562$	57.2750	2.41600
$563$	−5.70168	−0.240297	−0.120149	−	0.992756i	$-0.538337\pi$
$563$	−5.70168	−0.240297	−0.120149	+	0.992756i	$0.538337\pi$
$564$	−103.361	−4.35229
$565$	14.2748	0.600545
$566$	4.72495	0.198604
$567$	−27.6783	−1.16238
$568$	−103.960	−4.36206
$569$	29.7048	1.24529	0.622645	−	0.782504i	$-0.286058\pi$
$569$	29.7048	1.24529	0.622645	+	0.782504i	$0.286058\pi$
$570$	−67.7061	−2.83590
$571$	31.7320	1.32794	0.663972	−	0.747758i	$-0.268870\pi$
$571$	31.7320	1.32794	0.663972	+	0.747758i	$0.268870\pi$
$572$	49.7216	2.07896
$573$	35.3862	1.47828
$574$	−63.3249	−2.64313
$575$	−5.45234	−0.227378
$576$	138.773	5.78223
$577$	−24.9222	−1.03753	−0.518763	−	0.854918i	$-0.673607\pi$
$577$	−24.9222	−1.03753	−0.518763	+	0.854918i	$0.673607\pi$
$578$	38.6462	1.60747
$579$	38.3631	1.59432
$580$	−40.0289	−1.66211
$581$	26.7239	1.10869
$582$	−82.7158	−3.42868
$583$	13.2549	0.548961
$584$	173.145	7.16478
$585$	15.4105	0.637147
$586$	21.4175	0.884748
$587$	10.4129	0.429787	0.214893	−	0.976638i	$-0.431060\pi$
$587$	10.4129	0.429787	0.214893	+	0.976638i	$0.431060\pi$
$588$	−20.0204	−0.825627
$589$	41.1489	1.69551
$590$	82.4446	3.39419
$591$	13.7203	0.564379
$592$	106.116	4.36134
$593$	−28.4219	−1.16715	−0.583574	−	0.812060i	$-0.698346\pi$
$593$	−28.4219	−1.16715	−0.583574	+	0.812060i	$0.698346\pi$
$594$	−4.10508	−0.168434
$595$	−10.6308	−0.435820
$596$	−136.920	−5.60845
$597$	−34.5322	−1.41331
$598$	−48.8364	−1.99707
$599$	2.62236	0.107147	0.0535734	−	0.998564i	$-0.482939\pi$
$599$	2.62236	0.107147	0.0535734	+	0.998564i	$0.482939\pi$
$600$	−22.1477	−0.904177
$601$	36.2788	1.47984	0.739922	−	0.672693i	$-0.234863\pi$
$601$	36.2788	1.47984	0.739922	+	0.672693i	$0.234863\pi$
$602$	59.4520	2.42308
$603$	−3.33692	−0.135890
$604$	−141.570	−5.76042
$605$	−2.32421	−0.0944926
$606$	−90.5034	−3.67645
$607$	16.5378	0.671247	0.335624	−	0.941996i	$-0.391053\pi$
$607$	16.5378	0.671247	0.335624	+	0.941996i	$0.391053\pi$
$608$	152.282	6.17587
$609$	23.3430	0.945905
$610$	72.3738	2.93033
$611$	19.6493	0.794927
$612$	−29.6673	−1.19923
$613$	−2.42228	−0.0978349	−0.0489174	−	0.998803i	$-0.515577\pi$
$613$	−2.42228	−0.0978349	−0.0489174	+	0.998803i	$0.515577\pi$
$614$	−39.7613	−1.60463
$615$	−38.2079	−1.54069
$616$	−99.1774	−3.99597
$617$	2.15760	0.0868619	0.0434309	−	0.999056i	$-0.486171\pi$
$617$	2.15760	0.0868619	0.0434309	+	0.999056i	$0.486171\pi$
$618$	−89.6395	−3.60583
$619$	−10.6565	−0.428321	−0.214160	−	0.976799i	$-0.568702\pi$
$619$	−10.6565	−0.428321	−0.214160	+	0.976799i	$0.568702\pi$
$620$	−100.447	−4.03404
$621$	3.00856	0.120729
$622$	−5.99584	−0.240411
$623$	−4.90460	−0.196499
$624$	−122.062	−4.88640
$625$	−20.0674	−0.802695
$626$	−35.6414	−1.42452
$627$	37.1522	1.48372
$628$	87.0422	3.47336
$629$	−10.1438	−0.404458
$630$	−46.5863	−1.85604
$631$	−44.4304	−1.76875	−0.884374	−	0.466779i	$-0.845414\pi$
$631$	−44.4304	−1.76875	−0.884374	+	0.466779i	$0.845414\pi$
$632$	124.027	4.93354
$633$	−5.68651	−0.226019
$634$	−53.2887	−2.11636
$635$	−29.9416	−1.18820
$636$	−59.8041	−2.37139
$637$	3.80595	0.150797
$638$	29.4369	1.16542
$639$	26.7959	1.06003
$640$	−156.481	−6.18544
$641$	0.270416	0.0106808	0.00534039	−	0.999986i	$-0.498300\pi$
$641$	0.270416	0.0106808	0.00534039	+	0.999986i	$0.498300\pi$
$642$	−80.6901	−3.18458
$643$	−42.0256	−1.65733	−0.828663	−	0.559748i	$-0.810898\pi$
$643$	−42.0256	−1.65733	−0.828663	+	0.559748i	$0.810898\pi$
$644$	110.159	4.34089
$645$	35.8711	1.41242
$646$	−24.7787	−0.974905
$647$	−12.4770	−0.490521	−0.245261	−	0.969457i	$-0.578874\pi$
$647$	−12.4770	−0.490521	−0.245261	+	0.969457i	$0.578874\pi$
$648$	103.910	4.08198
$649$	−45.2396	−1.77581
$650$	6.38105	0.250285
$651$	58.5759	2.29577
$652$	45.8672	1.79630
$653$	43.4796	1.70149	0.850744	−	0.525581i	$-0.176152\pi$
$653$	43.4796	1.70149	0.850744	+	0.525581i	$0.176152\pi$
$654$	−56.9217	−2.22581
$655$	−10.9353	−0.427279
$656$	146.280	5.71128
$657$	−44.6284	−1.74112
$658$	−59.4002	−2.31566
$659$	−4.73733	−0.184540	−0.0922702	−	0.995734i	$-0.529412\pi$
$659$	−4.73733	−0.184540	−0.0922702	+	0.995734i	$0.529412\pi$
$660$	−90.6908	−3.53014
$661$	−7.43295	−0.289108	−0.144554	−	0.989497i	$-0.546175\pi$
$661$	−7.43295	−0.289108	−0.144554	+	0.989497i	$0.546175\pi$
$662$	9.90751	0.385066
$663$	11.6681	0.453151
$664$	−100.327	−3.89344
$665$	−29.0333	−1.12586
$666$	−44.4520	−1.72248
$667$	−21.5739	−0.835346
$668$	9.50355	0.367703
$669$	−54.9576	−2.12478
$670$	6.80340	0.262838
$671$	−39.7135	−1.53312
$672$	216.776	8.36231
$673$	3.73540	0.143989	0.0719945	−	0.997405i	$-0.477064\pi$
$673$	3.73540	0.143989	0.0719945	+	0.997405i	$0.477064\pi$
$674$	−6.29218	−0.242366
$675$	−0.393104	−0.0151306
$676$	−33.7837	−1.29937
$677$	7.38185	0.283708	0.141854	−	0.989888i	$-0.454694\pi$
$677$	7.38185	0.283708	0.141854	+	0.989888i	$0.454694\pi$
$678$	47.3635	1.81898
$679$	−35.4697	−1.36120
$680$	39.9103	1.53049
$681$	−10.6483	−0.408044
$682$	73.8678	2.82855
$683$	11.1239	0.425643	0.212822	−	0.977091i	$-0.431735\pi$
$683$	11.1239	0.425643	0.212822	+	0.977091i	$0.431735\pi$
$684$	−81.0231	−3.09799
$685$	9.12384	0.348604
$686$	45.4874	1.73672
$687$	−51.7281	−1.97355
$688$	−137.334	−5.23580
$689$	11.3690	0.433124
$690$	89.0763	3.39108
$691$	39.1151	1.48801	0.744003	−	0.668176i	$-0.232925\pi$
$691$	39.1151	1.48801	0.744003	+	0.668176i	$0.232925\pi$
$692$	−114.278	−4.34422
$693$	25.5632	0.971065
$694$	4.29407	0.163001
$695$	27.9014	1.05836
$696$	−87.6345	−3.32178
$697$	−13.9831	−0.529648
$698$	−41.1129	−1.55615
$699$	−42.8995	−1.62261
$700$	−14.3936	−0.544028
$701$	−11.1580	−0.421431	−0.210716	−	0.977547i	$-0.567579\pi$
$701$	−11.1580	−0.421431	−0.210716	+	0.977547i	$0.567579\pi$
$702$	−3.52101	−0.132892
$703$	−27.7032	−1.04485
$704$	155.254	5.85136
$705$	−35.8399	−1.34981
$706$	−12.4201	−0.467438
$707$	−38.8091	−1.45957
$708$	204.115	7.67110
$709$	−36.1427	−1.35737	−0.678683	−	0.734431i	$-0.737449\pi$
$709$	−36.1427	−1.35737	−0.678683	+	0.734431i	$0.737449\pi$
$710$	−54.6321	−2.05030
$711$	−31.9683	−1.19890
$712$	18.4129	0.690053
$713$	−54.1368	−2.02744
$714$	−35.2728	−1.32005
$715$	17.2407	0.644765
$716$	3.44811	0.128862
$717$	−63.2036	−2.36038
$718$	−49.1150	−1.83296
$719$	−19.4559	−0.725582	−0.362791	−	0.931870i	$-0.618176\pi$
$719$	−19.4559	−0.725582	−0.362791	+	0.931870i	$0.618176\pi$
$720$	107.614	4.01054
$721$	−38.4387	−1.43153
$722$	−14.3389	−0.533640
$723$	−54.2516	−2.01764
$724$	−52.9489	−1.96783
$725$	2.81889	0.104691
$726$	−7.71169	−0.286208
$727$	34.5099	1.27990	0.639950	−	0.768416i	$-0.278955\pi$
$727$	34.5099	1.27990	0.639950	+	0.768416i	$0.278955\pi$
$728$	−85.0666	−3.15278
$729$	−23.4162	−0.867267
$730$	90.9895	3.36767
$731$	13.1279	0.485553
$732$	179.182	6.62275
$733$	−13.1059	−0.484076	−0.242038	−	0.970267i	$-0.577816\pi$
$733$	−13.1059	−0.484076	−0.242038	+	0.970267i	$0.577816\pi$
$734$	−34.5578	−1.27555
$735$	−6.94196	−0.256058
$736$	−200.348	−7.38491
$737$	−3.73321	−0.137515
$738$	−61.2768	−2.25563
$739$	17.2000	0.632711	0.316355	−	0.948641i	$-0.397541\pi$
$739$	17.2000	0.632711	0.316355	+	0.948641i	$0.397541\pi$
$740$	67.6253	2.48595
$741$	31.8663	1.17064
$742$	−34.3686	−1.26171
$743$	−26.3465	−0.966558	−0.483279	−	0.875466i	$-0.660554\pi$
$743$	−26.3465	−0.966558	−0.483279	+	0.875466i	$0.660554\pi$
$744$	−219.907	−8.06217
$745$	−47.4762	−1.73939
$746$	30.5332	1.11790
$747$	25.8595	0.946150
$748$	−33.1905	−1.21357
$749$	−34.6010	−1.26429
$750$	−80.5858	−2.94258
$751$	37.6788	1.37492	0.687459	−	0.726224i	$-0.258726\pi$
$751$	37.6788	1.37492	0.687459	+	0.726224i	$0.258726\pi$
$752$	137.214	5.00369
$753$	42.2965	1.54137
$754$	25.2487	0.919502
$755$	−49.0888	−1.78652
$756$	7.94229	0.288858
$757$	−10.2812	−0.373677	−0.186839	−	0.982391i	$-0.559824\pi$
$757$	−10.2812	−0.373677	−0.186839	+	0.982391i	$0.559824\pi$
$758$	30.4290	1.10523
$759$	−48.8787	−1.77418
$760$	108.997	3.95375
$761$	35.6859	1.29361	0.646807	−	0.762654i	$-0.276104\pi$
$761$	35.6859	1.29361	0.646807	+	0.762654i	$0.276104\pi$
$762$	−99.3456	−3.59891
$763$	−24.4088	−0.883658
$764$	−86.3364	−3.12354
$765$	−10.2870	−0.371926
$766$	60.7431	2.19474
$767$	−38.8030	−1.40109
$768$	−280.912	−10.1365
$769$	14.8278	0.534705	0.267352	−	0.963599i	$-0.413851\pi$
$769$	14.8278	0.534705	0.267352	+	0.963599i	$0.413851\pi$
$770$	−52.1188	−1.87823
$771$	30.7552	1.10762
$772$	−93.5997	−3.36873
$773$	28.3114	1.01829	0.509145	−	0.860681i	$-0.329962\pi$
$773$	28.3114	1.01829	0.509145	+	0.860681i	$0.329962\pi$
$774$	57.5291	2.06784
$775$	7.07360	0.254091
$776$	133.161	4.78020
$777$	−39.4359	−1.41476
$778$	−21.1936	−0.759828
$779$	−38.1887	−1.36825
$780$	−77.7874	−2.78524
$781$	29.9781	1.07270
$782$	32.5996	1.16576
$783$	−1.55544	−0.0555869
$784$	26.5775	0.949197
$785$	30.1814	1.07722
$786$	−36.2832	−1.29418
$787$	45.8998	1.63615	0.818075	−	0.575111i	$-0.195041\pi$
$787$	45.8998	1.63615	0.818075	+	0.575111i	$0.195041\pi$
$788$	−33.4753	−1.19251
$789$	49.2404	1.75300
$790$	65.1777	2.31892
$791$	20.3101	0.722145
$792$	−95.9697	−3.41013
$793$	−34.0631	−1.20962
$794$	53.2078	1.88827
$795$	−20.7368	−0.735457
$796$	84.2527	2.98626
$797$	31.6335	1.12051	0.560257	−	0.828319i	$-0.310702\pi$
$797$	31.6335	1.12051	0.560257	+	0.828319i	$0.310702\pi$
$798$	−96.3321	−3.41012
$799$	−13.1165	−0.464028
$800$	26.1777	0.925523
$801$	−4.74596	−0.167690
$802$	−32.1645	−1.13577
$803$	−49.9285	−1.76194
$804$	16.8437	0.594032
$805$	38.1972	1.34627
$806$	63.3580	2.23169
$807$	−9.29990	−0.327372
$808$	145.698	5.12563
$809$	7.73992	0.272121	0.136061	−	0.990701i	$-0.456556\pi$
$809$	7.73992	0.272121	0.136061	+	0.990701i	$0.456556\pi$
$810$	54.6060	1.91866
$811$	38.7074	1.35920	0.679600	−	0.733583i	$-0.262153\pi$
$811$	38.7074	1.35920	0.679600	+	0.733583i	$0.262153\pi$
$812$	−56.9530	−1.99866
$813$	−36.3144	−1.27360
$814$	−49.7311	−1.74307
$815$	15.9042	0.557100
$816$	81.4799	2.85237
$817$	35.8531	1.25434
$818$	28.0187	0.979651
$819$	21.9261	0.766159
$820$	93.2209	3.25541
$821$	−6.38459	−0.222824	−0.111412	−	0.993774i	$-0.535537\pi$
$821$	−6.38459	−0.222824	−0.111412	+	0.993774i	$0.535537\pi$
$822$	30.2727	1.05588
$823$	−8.50946	−0.296621	−0.148311	−	0.988941i	$-0.547384\pi$
$823$	−8.50946	−0.296621	−0.148311	+	0.988941i	$0.547384\pi$
$824$	144.307	5.02717
$825$	6.38657	0.222352
$826$	117.302	4.08146
$827$	32.8047	1.14073	0.570366	−	0.821391i	$-0.306802\pi$
$827$	32.8047	1.14073	0.570366	+	0.821391i	$0.306802\pi$
$828$	106.597	3.70449
$829$	−31.3225	−1.08788	−0.543938	−	0.839125i	$-0.683067\pi$
$829$	−31.3225	−1.08788	−0.543938	+	0.839125i	$0.683067\pi$
$830$	−52.7229	−1.83004
$831$	−9.39817	−0.326019
$832$	133.165	4.61665
$833$	−2.54058	−0.0880258
$834$	92.5763	3.20566
$835$	3.29530	0.114039
$836$	−90.6453	−3.13503
$837$	−3.90316	−0.134913
$838$	−32.5816	−1.12551
$839$	45.6442	1.57581	0.787907	−	0.615794i	$-0.211165\pi$
$839$	45.6442	1.57581	0.787907	+	0.615794i	$0.211165\pi$
$840$	155.159	5.35350
$841$	−17.8462	−0.615385
$842$	66.7432	2.30012
$843$	49.1685	1.69345
$844$	13.8741	0.477568
$845$	−11.7143	−0.402985
$846$	−57.4790	−1.97617
$847$	−3.30688	−0.113626
$848$	79.3913	2.72631
$849$	4.05619	0.139208
$850$	−4.25952	−0.146100
$851$	36.4473	1.24940
$852$	−135.257	−4.63383
$853$	−9.75538	−0.334018	−0.167009	−	0.985955i	$-0.553411\pi$
$853$	−9.75538	−0.334018	−0.167009	+	0.985955i	$0.553411\pi$
$854$	102.973	3.52367
$855$	−28.0943	−0.960805
$856$	129.900	4.43988
$857$	10.3431	0.353313	0.176656	−	0.984273i	$-0.443472\pi$
$857$	10.3431	0.353313	0.176656	+	0.984273i	$0.443472\pi$
$858$	57.2043	1.95292
$859$	24.1864	0.825229	0.412615	−	0.910906i	$-0.364616\pi$
$859$	24.1864	0.825229	0.412615	+	0.910906i	$0.364616\pi$
$860$	−87.5195	−2.98439
$861$	−54.3621	−1.85266
$862$	−33.5996	−1.14441
$863$	4.79192	0.163119	0.0815595	−	0.996668i	$-0.474010\pi$
$863$	4.79192	0.163119	0.0815595	+	0.996668i	$0.474010\pi$
$864$	−14.4447	−0.491418
$865$	−39.6254	−1.34731
$866$	−12.8011	−0.435000
$867$	33.1764	1.12673
$868$	−142.916	−4.85087
$869$	−35.7648	−1.21324
$870$	−46.0529	−1.56134
$871$	−3.20206	−0.108498
$872$	91.6359	3.10318
$873$	−34.3225	−1.16164
$874$	89.0316	3.01154
$875$	−34.5563	−1.16822
$876$	225.270	7.61117
$877$	5.07084	0.171230	0.0856150	−	0.996328i	$-0.472714\pi$
$877$	5.07084	0.171230	0.0856150	+	0.996328i	$0.472714\pi$
$878$	−34.4320	−1.16202
$879$	18.3861	0.620149
$880$	120.394	4.05848
$881$	9.23543	0.311149	0.155575	−	0.987824i	$-0.450277\pi$
$881$	9.23543	0.311149	0.155575	+	0.987824i	$0.450277\pi$
$882$	−11.1333	−0.374878
$883$	11.2785	0.379551	0.189775	−	0.981828i	$-0.439224\pi$
$883$	11.2785	0.379551	0.189775	+	0.981828i	$0.439224\pi$
$884$	−28.4682	−0.957489
$885$	70.7756	2.37910
$886$	92.4566	3.10614
$887$	5.49509	0.184507	0.0922536	−	0.995736i	$-0.470593\pi$
$887$	5.49509	0.184507	0.0922536	+	0.995736i	$0.470593\pi$
$888$	148.051	4.96826
$889$	−42.6008	−1.42879
$890$	9.67618	0.324346
$891$	−29.9638	−1.00383
$892$	134.087	4.48958
$893$	−35.8219	−1.19873
$894$	−157.525	−5.26843
$895$	1.19561	0.0399650
$896$	−222.640	−7.43789
$897$	−41.9243	−1.39981
$898$	23.4915	0.783923
$899$	27.9890	0.933484
$900$	−13.9281	−0.464269
$901$	−7.58912	−0.252830
$902$	−68.5539	−2.28260
$903$	51.0373	1.69842
$904$	−76.2486	−2.53599
$905$	−18.3598	−0.610299
$906$	−162.876	−5.41118
$907$	−31.0743	−1.03180	−0.515902	−	0.856648i	$-0.672543\pi$
$907$	−31.0743	−1.03180	−0.515902	+	0.856648i	$0.672543\pi$
$908$	25.9801	0.862180
$909$	−37.5539	−1.24558
$910$	−44.7034	−1.48190
$911$	−36.8474	−1.22081	−0.610404	−	0.792090i	$-0.708993\pi$
$911$	−36.8474	−1.22081	−0.610404	+	0.792090i	$0.708993\pi$
$912$	222.527	7.36859
$913$	28.9306	0.957462
$914$	−113.537	−3.75546
$915$	62.1303	2.05396
$916$	126.208	4.17003
$917$	−15.5588	−0.513796
$918$	2.35037	0.0775739
$919$	32.4185	1.06939	0.534694	−	0.845046i	$-0.320427\pi$
$919$	32.4185	1.06939	0.534694	+	0.845046i	$0.320427\pi$
$920$	−143.400	−4.72777
$921$	−34.1336	−1.12474
$922$	−42.9777	−1.41540
$923$	25.7129	0.846350
$924$	−129.035	−4.24493
$925$	−4.76226	−0.156582
$926$	−29.3029	−0.962953
$927$	−37.1954	−1.22166
$928$	103.581	3.40020
$929$	−44.6355	−1.46444	−0.732221	−	0.681067i	$-0.761516\pi$
$929$	−44.6355	−1.46444	−0.732221	+	0.681067i	$0.761516\pi$
$930$	−115.563	−3.78947
$931$	−6.93847	−0.227399
$932$	104.668	3.42850
$933$	−5.14721	−0.168512
$934$	−71.5847	−2.34232
$935$	−11.5086	−0.376372
$936$	−82.3152	−2.69056
$937$	−24.0655	−0.786186	−0.393093	−	0.919499i	$-0.628595\pi$
$937$	−24.0655	−0.786186	−0.393093	+	0.919499i	$0.628595\pi$
$938$	9.67986	0.316059
$939$	−30.5968	−0.998490
$940$	87.4434	2.85209
$941$	12.8510	0.418930	0.209465	−	0.977816i	$-0.432828\pi$
$941$	12.8510	0.418930	0.209465	+	0.977816i	$0.432828\pi$
$942$	100.141	3.26278
$943$	50.2423	1.63611
$944$	−270.967	−8.81922
$945$	2.75395	0.0895859
$946$	64.3612	2.09256
$947$	37.4384	1.21658	0.608292	−	0.793713i	$-0.291855\pi$
$947$	37.4384	1.21658	0.608292	+	0.793713i	$0.291855\pi$
$948$	161.366	5.24091
$949$	−42.8247	−1.39015
$950$	−11.6330	−0.377425
$951$	−45.7464	−1.48343
$952$	56.7843	1.84039
$953$	−15.4033	−0.498963	−0.249482	−	0.968380i	$-0.580260\pi$
$953$	−15.4033	−0.498963	−0.249482	+	0.968380i	$0.580260\pi$
$954$	−33.2570	−1.07674
$955$	−29.9367	−0.968728
$956$	154.206	4.98739
$957$	25.2705	0.816880
$958$	−56.3243	−1.81975
$959$	12.9814	0.419191
$960$	−242.889	−7.83920
$961$	39.2344	1.26563
$962$	−42.6554	−1.37527
$963$	−33.4819	−1.07894
$964$	132.365	4.26319
$965$	−32.4552	−1.04477
$966$	126.738	4.07772
$967$	31.7341	1.02050	0.510249	−	0.860027i	$-0.329553\pi$
$967$	31.7341	1.02050	0.510249	+	0.860027i	$0.329553\pi$
$968$	12.4147	0.399025
$969$	−21.2716	−0.683342
$970$	69.9775	2.24684
$971$	−2.38864	−0.0766550	−0.0383275	−	0.999265i	$-0.512203\pi$
$971$	−2.38864	−0.0766550	−0.0383275	+	0.999265i	$0.512203\pi$
$972$	126.978	4.07281
$973$	39.6980	1.27266
$974$	−9.97229	−0.319533
$975$	5.47790	0.175433
$976$	−237.868	−7.61396
$977$	37.1203	1.18758	0.593792	−	0.804618i	$-0.297630\pi$
$977$	37.1203	1.18758	0.593792	+	0.804618i	$0.297630\pi$
$978$	52.7699	1.68739
$979$	−5.30959	−0.169695
$980$	16.9372	0.541040
$981$	−23.6193	−0.754108
$982$	110.040	3.51152
$983$	36.0330	1.14927	0.574637	−	0.818408i	$-0.305143\pi$
$983$	36.0330	1.14927	0.574637	+	0.818408i	$0.305143\pi$
$984$	204.087	6.50605
$985$	−11.6074	−0.369842
$986$	−16.8542	−0.536746
$987$	−50.9929	−1.62312
$988$	−77.7484	−2.47351
$989$	−47.1695	−1.49990
$990$	−50.4331	−1.60287
$991$	−13.4028	−0.425753	−0.212877	−	0.977079i	$-0.568283\pi$
$991$	−13.4028	−0.425753	−0.212877	+	0.977079i	$0.568283\pi$
$992$	259.921	8.25251
$993$	8.50523	0.269905
$994$	−77.7304	−2.46546
$995$	29.2142	0.926151
$996$	−130.530	−4.13602
$997$	−2.65503	−0.0840858	−0.0420429	−	0.999116i	$-0.513387\pi$
$997$	−2.65503	−0.0840858	−0.0420429	+	0.999116i	$0.513387\pi$
$998$	73.3086	2.32054
$999$	2.62778	0.0831393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.e.1.1	✓	221

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.e.1.1	✓	221	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:	\( N \)	\(=\)	\( 6011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.80701 q^{2} -2.40971 q^{3} +5.87930 q^{4} +2.03862 q^{5} +6.76409 q^{6} +2.90054 q^{7} -10.8892 q^{8} +2.80672 q^{9} +O(q^{10})\)	\(q-2.80701 q^{2} -2.40971 q^{3} +5.87930 q^{4} +2.03862 q^{5} +6.76409 q^{6} +2.90054 q^{7} -10.8892 q^{8} +2.80672 q^{9} -5.72241 q^{10} +3.14005 q^{11} -14.1674 q^{12} +2.69329 q^{13} -8.14184 q^{14} -4.91248 q^{15} +18.8076 q^{16} -1.79784 q^{17} -7.87850 q^{18} -4.91002 q^{19} +11.9856 q^{20} -6.98947 q^{21} -8.81415 q^{22} +6.45977 q^{23} +26.2400 q^{24} -0.844045 q^{25} -7.56008 q^{26} +0.465738 q^{27} +17.0531 q^{28} -3.33973 q^{29} +13.7894 q^{30} -8.38060 q^{31} -31.0146 q^{32} -7.56662 q^{33} +5.04656 q^{34} +5.91308 q^{35} +16.5016 q^{36} +5.64219 q^{37} +13.7825 q^{38} -6.49005 q^{39} -22.1990 q^{40} +7.77771 q^{41} +19.6195 q^{42} -7.30203 q^{43} +18.4613 q^{44} +5.72183 q^{45} -18.1326 q^{46} +7.29568 q^{47} -45.3210 q^{48} +1.41313 q^{49} +2.36924 q^{50} +4.33229 q^{51} +15.8346 q^{52} +4.22124 q^{53} -1.30733 q^{54} +6.40135 q^{55} -31.5847 q^{56} +11.8317 q^{57} +9.37467 q^{58} -14.4073 q^{59} -28.8820 q^{60} -12.6474 q^{61} +23.5244 q^{62} +8.14101 q^{63} +49.4432 q^{64} +5.49058 q^{65} +21.2396 q^{66} -1.18890 q^{67} -10.5701 q^{68} -15.5662 q^{69} -16.5981 q^{70} +9.54703 q^{71} -30.5631 q^{72} -15.9005 q^{73} -15.8377 q^{74} +2.03391 q^{75} -28.8675 q^{76} +9.10783 q^{77} +18.2176 q^{78} -11.3899 q^{79} +38.3415 q^{80} -9.54247 q^{81} -21.8321 q^{82} +9.21341 q^{83} -41.0932 q^{84} -3.66511 q^{85} +20.4969 q^{86} +8.04781 q^{87} -34.1928 q^{88} -1.69093 q^{89} -16.0612 q^{90} +7.81198 q^{91} +37.9790 q^{92} +20.1948 q^{93} -20.4790 q^{94} -10.0096 q^{95} +74.7364 q^{96} -12.2287 q^{97} -3.96666 q^{98} +8.81325 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9}+O(q^{10}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9} - 61 q^{10} - 50 q^{11} - 43 q^{12} - 87 q^{13} - 41 q^{14} - 62 q^{15} + 129 q^{16} - 29 q^{17} - 61 q^{18} - 107 q^{19} - 59 q^{20} - 163 q^{21} - 70 q^{22} - 31 q^{23} - 98 q^{24} + 119 q^{25} - 23 q^{26} - 41 q^{27} - 112 q^{28} - 152 q^{29} - 66 q^{30} - 117 q^{31} - 93 q^{32} - 60 q^{33} - 80 q^{34} - 21 q^{35} + 92 q^{36} - 231 q^{37} + 2 q^{38} - 81 q^{39} - 143 q^{40} - 81 q^{41} - 6 q^{42} - 126 q^{43} - 115 q^{44} - 156 q^{45} - 205 q^{46} - 4 q^{47} - 55 q^{48} + 103 q^{49} - 61 q^{50} - 106 q^{51} - 164 q^{52} - 87 q^{53} - 110 q^{54} - 62 q^{55} - 73 q^{56} - 136 q^{57} - 128 q^{58} - 76 q^{59} - 148 q^{60} - 345 q^{61} + 5 q^{62} - 74 q^{63} - 25 q^{64} - 110 q^{65} - 34 q^{66} - 104 q^{67} - 48 q^{68} - 133 q^{69} - 92 q^{70} - 39 q^{71} - 177 q^{72} - 175 q^{73} - 44 q^{74} - 23 q^{75} - 268 q^{76} - 81 q^{77} - 19 q^{78} - 272 q^{79} - 60 q^{80} + 77 q^{81} - 13 q^{82} - 40 q^{83} - 221 q^{84} - 376 q^{85} - 82 q^{86} - 3 q^{87} - 234 q^{88} - 92 q^{89} - 91 q^{90} - 205 q^{91} - 11 q^{92} - 125 q^{93} - 126 q^{94} - 56 q^{95} - 148 q^{96} - 133 q^{97} - 4 q^{98} - 195 q^{99}+O(q^{100}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9 - 61 * q^10 - 50 * q^11 - 43 * q^12 - 87 * q^13 - 41 * q^14 - 62 * q^15 + 129 * q^16 - 29 * q^17 - 61 * q^18 - 107 * q^19 - 59 * q^20 - 163 * q^21 - 70 * q^22 - 31 * q^23 - 98 * q^24 + 119 * q^25 - 23 * q^26 - 41 * q^27 - 112 * q^28 - 152 * q^29 - 66 * q^30 - 117 * q^31 - 93 * q^32 - 60 * q^33 - 80 * q^34 - 21 * q^35 + 92 * q^36 - 231 * q^37 + 2 * q^38 - 81 * q^39 - 143 * q^40 - 81 * q^41 - 6 * q^42 - 126 * q^43 - 115 * q^44 - 156 * q^45 - 205 * q^46 - 4 * q^47 - 55 * q^48 + 103 * q^49 - 61 * q^50 - 106 * q^51 - 164 * q^52 - 87 * q^53 - 110 * q^54 - 62 * q^55 - 73 * q^56 - 136 * q^57 - 128 * q^58 - 76 * q^59 - 148 * q^60 - 345 * q^61 + 5 * q^62 - 74 * q^63 - 25 * q^64 - 110 * q^65 - 34 * q^66 - 104 * q^67 - 48 * q^68 - 133 * q^69 - 92 * q^70 - 39 * q^71 - 177 * q^72 - 175 * q^73 - 44 * q^74 - 23 * q^75 - 268 * q^76 - 81 * q^77 - 19 * q^78 - 272 * q^79 - 60 * q^80 + 77 * q^81 - 13 * q^82 - 40 * q^83 - 221 * q^84 - 376 * q^85 - 82 * q^86 - 3 * q^87 - 234 * q^88 - 92 * q^89 - 91 * q^90 - 205 * q^91 - 11 * q^92 - 125 * q^93 - 126 * q^94 - 56 * q^95 - 148 * q^96 - 133 * q^97 - 4 * q^98 - 195 * q^99

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