LMFDB - Embedded newform 5077.2.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5077,2,Mod(1,5077)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5077, 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("5077.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5077 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5077.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:	$40.5400491062$
Analytic rank:	$1$
Dimension:	$205$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	5077.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61107 q^{2} -0.462954 q^{3} +4.81767 q^{4} -1.81913 q^{5} +1.20880 q^{6} +2.59865 q^{7} -7.35711 q^{8} -2.78567 q^{9} +O(q^{10})$	\(q-2.61107 q^{2} -0.462954 q^{3} +4.81767 q^{4} -1.81913 q^{5} +1.20880 q^{6} +2.59865 q^{7} -7.35711 q^{8} -2.78567 q^{9} +4.74986 q^{10} +1.34250 q^{11} -2.23036 q^{12} +4.53166 q^{13} -6.78525 q^{14} +0.842172 q^{15} +9.57458 q^{16} +5.01523 q^{17} +7.27358 q^{18} +3.08832 q^{19} -8.76395 q^{20} -1.20306 q^{21} -3.50536 q^{22} +0.321651 q^{23} +3.40601 q^{24} -1.69078 q^{25} -11.8325 q^{26} +2.67850 q^{27} +12.5194 q^{28} -5.84309 q^{29} -2.19897 q^{30} -6.98902 q^{31} -10.2856 q^{32} -0.621516 q^{33} -13.0951 q^{34} -4.72727 q^{35} -13.4204 q^{36} -7.95507 q^{37} -8.06380 q^{38} -2.09795 q^{39} +13.3835 q^{40} -9.46124 q^{41} +3.14126 q^{42} +11.8768 q^{43} +6.46772 q^{44} +5.06749 q^{45} -0.839851 q^{46} -2.17193 q^{47} -4.43259 q^{48} -0.247022 q^{49} +4.41473 q^{50} -2.32182 q^{51} +21.8320 q^{52} -14.4176 q^{53} -6.99374 q^{54} -2.44218 q^{55} -19.1186 q^{56} -1.42975 q^{57} +15.2567 q^{58} +9.41549 q^{59} +4.05731 q^{60} +6.87100 q^{61} +18.2488 q^{62} -7.23899 q^{63} +7.70730 q^{64} -8.24367 q^{65} +1.62282 q^{66} +8.89890 q^{67} +24.1617 q^{68} -0.148910 q^{69} +12.3432 q^{70} -6.27424 q^{71} +20.4945 q^{72} -9.07975 q^{73} +20.7712 q^{74} +0.782752 q^{75} +14.8785 q^{76} +3.48869 q^{77} +5.47789 q^{78} -1.64199 q^{79} -17.4174 q^{80} +7.11700 q^{81} +24.7039 q^{82} -6.32088 q^{83} -5.79592 q^{84} -9.12335 q^{85} -31.0110 q^{86} +2.70508 q^{87} -9.87693 q^{88} -7.55249 q^{89} -13.2316 q^{90} +11.7762 q^{91} +1.54961 q^{92} +3.23559 q^{93} +5.67106 q^{94} -5.61804 q^{95} +4.76177 q^{96} -9.25972 q^{97} +0.644991 q^{98} -3.73977 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) $ 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * 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 $

$2$	−2.61107	−1.84630	−0.923151	−	0.384437i	$-0.874396\pi$
$2$	−2.61107	−1.84630	−0.923151	+	0.384437i	$0.874396\pi$
$3$	−0.462954	−0.267287	−0.133643	−	0.991029i	$-0.542668\pi$
$3$	−0.462954	−0.267287	−0.133643	+	0.991029i	$0.542668\pi$
$4$	4.81767	2.40883
$5$	−1.81913	−0.813538	−0.406769	−	0.913531i	$-0.633345\pi$
$5$	−1.81913	−0.813538	−0.406769	+	0.913531i	$0.633345\pi$
$6$	1.20880	0.493492
$7$	2.59865	0.982197	0.491099	−	0.871104i	$-0.336595\pi$
$7$	2.59865	0.982197	0.491099	+	0.871104i	$0.336595\pi$
$8$	−7.35711	−2.60113
$9$	−2.78567	−0.928558
$10$	4.74986	1.50204
$11$	1.34250	0.404779	0.202390	−	0.979305i	$-0.435129\pi$
$11$	1.34250	0.404779	0.202390	+	0.979305i	$0.435129\pi$
$12$	−2.23036	−0.643849
$13$	4.53166	1.25686	0.628429	−	0.777867i	$-0.283698\pi$
$13$	4.53166	1.25686	0.628429	+	0.777867i	$0.283698\pi$
$14$	−6.78525	−1.81343
$15$	0.842172	0.217448
$16$	9.57458	2.39364
$17$	5.01523	1.21637	0.608186	−	0.793794i	$-0.291897\pi$
$17$	5.01523	1.21637	0.608186	+	0.793794i	$0.291897\pi$
$18$	7.27358	1.71440
$19$	3.08832	0.708508	0.354254	−	0.935149i	$-0.384735\pi$
$19$	3.08832	0.708508	0.354254	+	0.935149i	$0.384735\pi$
$20$	−8.76395	−1.95968
$21$	−1.20306	−0.262528
$22$	−3.50536	−0.747345
$23$	0.321651	0.0670688	0.0335344	−	0.999438i	$-0.489324\pi$
$23$	0.321651	0.0670688	0.0335344	+	0.999438i	$0.489324\pi$
$24$	3.40601	0.695248
$25$	−1.69078	−0.338155
$26$	−11.8325	−2.32054
$27$	2.67850	0.515478
$28$	12.5194	2.36595
$29$	−5.84309	−1.08504	−0.542518	−	0.840044i	$-0.682529\pi$
$29$	−5.84309	−1.08504	−0.542518	+	0.840044i	$0.682529\pi$
$30$	−2.19897	−0.401475
$31$	−6.98902	−1.25526	−0.627632	−	0.778510i	$-0.715976\pi$
$31$	−6.98902	−1.25526	−0.627632	+	0.778510i	$0.715976\pi$
$32$	−10.2856	−1.81826
$33$	−0.621516	−0.108192
$34$	−13.0951	−2.24579
$35$	−4.72727	−0.799055
$36$	−13.4204	−2.23674
$37$	−7.95507	−1.30780	−0.653902	−	0.756579i	$-0.726869\pi$
$37$	−7.95507	−1.30780	−0.653902	+	0.756579i	$0.726869\pi$
$38$	−8.06380	−1.30812
$39$	−2.09795	−0.335941
$40$	13.3835	2.11612
$41$	−9.46124	−1.47760	−0.738798	−	0.673927i	$-0.764606\pi$
$41$	−9.46124	−1.47760	−0.738798	+	0.673927i	$0.764606\pi$
$42$	3.14126	0.484706
$43$	11.8768	1.81119	0.905595	−	0.424144i	$-0.139425\pi$
$43$	11.8768	1.81119	0.905595	+	0.424144i	$0.139425\pi$
$44$	6.46772	0.975046
$45$	5.06749	0.755417
$46$	−0.839851	−0.123829
$47$	−2.17193	−0.316809	−0.158404	−	0.987374i	$-0.550635\pi$
$47$	−2.17193	−0.316809	−0.158404	+	0.987374i	$0.550635\pi$
$48$	−4.43259	−0.639789
$49$	−0.247022	−0.0352889
$50$	4.41473	0.624337
$51$	−2.32182	−0.325120
$52$	21.8320	3.02756
$53$	−14.4176	−1.98041	−0.990206	−	0.139612i	$-0.955414\pi$
$53$	−14.4176	−1.98041	−0.990206	+	0.139612i	$0.955414\pi$
$54$	−6.99374	−0.951728
$55$	−2.44218	−0.329303
$56$	−19.1186	−2.55482
$57$	−1.42975	−0.189375
$58$	15.2567	2.00330
$59$	9.41549	1.22579	0.612896	−	0.790164i	$-0.290004\pi$
$59$	9.41549	1.22579	0.612896	+	0.790164i	$0.290004\pi$
$60$	4.05731	0.523796
$61$	6.87100	0.879742	0.439871	−	0.898061i	$-0.355024\pi$
$61$	6.87100	0.879742	0.439871	+	0.898061i	$0.355024\pi$
$62$	18.2488	2.31760
$63$	−7.23899	−0.912027
$64$	7.70730	0.963413
$65$	−8.24367	−1.02250
$66$	1.62282	0.199755
$67$	8.89890	1.08717	0.543587	−	0.839353i	$-0.317066\pi$
$67$	8.89890	1.08717	0.543587	+	0.839353i	$0.317066\pi$
$68$	24.1617	2.93004
$69$	−0.148910	−0.0179266
$70$	12.3432	1.47530
$71$	−6.27424	−0.744616	−0.372308	−	0.928109i	$-0.621433\pi$
$71$	−6.27424	−0.744616	−0.372308	+	0.928109i	$0.621433\pi$
$72$	20.4945	2.41530
$73$	−9.07975	−1.06270	−0.531352	−	0.847151i	$-0.678316\pi$
$73$	−9.07975	−1.06270	−0.531352	+	0.847151i	$0.678316\pi$
$74$	20.7712	2.41460
$75$	0.782752	0.0903844
$76$	14.8785	1.70668
$77$	3.48869	0.397573
$78$	5.47789	0.620249
$79$	−1.64199	−0.184738	−0.0923692	−	0.995725i	$-0.529444\pi$
$79$	−1.64199	−0.184738	−0.0923692	+	0.995725i	$0.529444\pi$
$80$	−17.4174	−1.94732
$81$	7.11700	0.790778
$82$	24.7039	2.72809
$83$	−6.32088	−0.693807	−0.346903	−	0.937901i	$-0.612767\pi$
$83$	−6.32088	−0.693807	−0.346903	+	0.937901i	$0.612767\pi$
$84$	−5.79592	−0.632387
$85$	−9.12335	−0.989566
$86$	−31.0110	−3.34400
$87$	2.70508	0.290015
$88$	−9.87693	−1.05288
$89$	−7.55249	−0.800563	−0.400281	−	0.916392i	$-0.631088\pi$
$89$	−7.55249	−0.800563	−0.400281	+	0.916392i	$0.631088\pi$
$90$	−13.2316	−1.39473
$91$	11.7762	1.23448
$92$	1.54961	0.161558
$93$	3.23559	0.335515
$94$	5.67106	0.584925
$95$	−5.61804	−0.576399
$96$	4.76177	0.485996
$97$	−9.25972	−0.940182	−0.470091	−	0.882618i	$-0.655779\pi$
$97$	−9.25972	−0.940182	−0.470091	+	0.882618i	$0.655779\pi$
$98$	0.644991	0.0651539
$99$	−3.73977	−0.375861
$100$	−8.14560	−0.814560
$101$	13.6339	1.35663	0.678313	−	0.734773i	$-0.262711\pi$
$101$	13.6339	1.35663	0.678313	+	0.734773i	$0.262711\pi$
$102$	6.06243	0.600270
$103$	17.8344	1.75728	0.878639	−	0.477486i	$-0.158452\pi$
$103$	17.8344	1.75728	0.878639	+	0.477486i	$0.158452\pi$
$104$	−33.3400	−3.26925
$105$	2.18851	0.213577
$106$	37.6454	3.65644
$107$	−1.54310	−0.149177	−0.0745885	−	0.997214i	$-0.523764\pi$
$107$	−1.54310	−0.149177	−0.0745885	+	0.997214i	$0.523764\pi$
$108$	12.9041	1.24170
$109$	−8.22466	−0.787779	−0.393890	−	0.919158i	$-0.628871\pi$
$109$	−8.22466	−0.787779	−0.393890	+	0.919158i	$0.628871\pi$
$110$	6.37669	0.607994
$111$	3.68283	0.349559
$112$	24.8810	2.35103
$113$	2.48602	0.233865	0.116933	−	0.993140i	$-0.462694\pi$
$113$	2.48602	0.233865	0.116933	+	0.993140i	$0.462694\pi$
$114$	3.73317	0.349643
$115$	−0.585124	−0.0545631
$116$	−28.1501	−2.61367
$117$	−12.6237	−1.16706
$118$	−24.5845	−2.26318
$119$	13.0328	1.19472
$120$	−6.19596	−0.565611
$121$	−9.19769	−0.836154
$122$	−17.9406	−1.62427
$123$	4.38012	0.394942
$124$	−33.6707	−3.02372
$125$	12.1714	1.08864
$126$	18.9015	1.68388
$127$	−18.3662	−1.62974	−0.814870	−	0.579644i	$-0.803192\pi$
$127$	−18.3662	−1.62974	−0.814870	+	0.579644i	$0.803192\pi$
$128$	0.446985	0.0395083
$129$	−5.49839	−0.484107
$130$	21.5248	1.88785
$131$	−10.7824	−0.942065	−0.471032	−	0.882116i	$-0.656119\pi$
$131$	−10.7824	−0.942065	−0.471032	+	0.882116i	$0.656119\pi$
$132$	−2.99426	−0.260617
$133$	8.02545	0.695895
$134$	−23.2356	−2.00725
$135$	−4.87253	−0.419361
$136$	−36.8976	−3.16395
$137$	−6.49586	−0.554979	−0.277490	−	0.960729i	$-0.589502\pi$
$137$	−6.49586	−0.554979	−0.277490	+	0.960729i	$0.589502\pi$
$138$	0.388813	0.0330979
$139$	−4.54081	−0.385146	−0.192573	−	0.981283i	$-0.561683\pi$
$139$	−4.54081	−0.385146	−0.192573	+	0.981283i	$0.561683\pi$
$140$	−22.7744	−1.92479
$141$	1.00550	0.0846788
$142$	16.3825	1.37479
$143$	6.08376	0.508750
$144$	−26.6716	−2.22264
$145$	10.6293	0.882718
$146$	23.7078	1.96207
$147$	0.114360	0.00943224
$148$	−38.3249	−3.15028
$149$	−2.61456	−0.214193	−0.107096	−	0.994249i	$-0.534155\pi$
$149$	−2.61456	−0.214193	−0.107096	+	0.994249i	$0.534155\pi$
$150$	−2.04382	−0.166877
$151$	11.2309	0.913961	0.456980	−	0.889477i	$-0.348931\pi$
$151$	11.2309	0.913961	0.456980	+	0.889477i	$0.348931\pi$
$152$	−22.7211	−1.84292
$153$	−13.9708	−1.12947
$154$	−9.10920	−0.734040
$155$	12.7139	1.02121
$156$	−10.1072	−0.809226
$157$	5.59700	0.446689	0.223345	−	0.974740i	$-0.428302\pi$
$157$	5.59700	0.446689	0.223345	+	0.974740i	$0.428302\pi$
$158$	4.28735	0.341083
$159$	6.67470	0.529338
$160$	18.7109	1.47922
$161$	0.835857	0.0658748
$162$	−18.5830	−1.46001
$163$	1.12352	0.0880010	0.0440005	−	0.999032i	$-0.485990\pi$
$163$	1.12352	0.0880010	0.0440005	+	0.999032i	$0.485990\pi$
$164$	−45.5811	−3.55928
$165$	1.13062	0.0880184
$166$	16.5042	1.28098
$167$	−1.51052	−0.116887	−0.0584436	−	0.998291i	$-0.518614\pi$
$167$	−1.51052	−0.116887	−0.0584436	+	0.998291i	$0.518614\pi$
$168$	8.85101	0.682871
$169$	7.53597	0.579690
$170$	23.8217	1.82704
$171$	−8.60304	−0.657891
$172$	57.2183	4.36285
$173$	−6.85496	−0.521173	−0.260587	−	0.965450i	$-0.583916\pi$
$173$	−6.85496	−0.521173	−0.260587	+	0.965450i	$0.583916\pi$
$174$	−7.06315	−0.535456
$175$	−4.39374	−0.332135
$176$	12.8539	0.968898
$177$	−4.35894	−0.327638
$178$	19.7201	1.47808
$179$	4.21105	0.314748	0.157374	−	0.987539i	$-0.449697\pi$
$179$	4.21105	0.314748	0.157374	+	0.987539i	$0.449697\pi$
$180$	24.4135	1.81967
$181$	18.2514	1.35662	0.678308	−	0.734777i	$-0.262713\pi$
$181$	18.2514	1.35662	0.678308	+	0.734777i	$0.262713\pi$
$182$	−30.7484	−2.27923
$183$	−3.18096	−0.235143
$184$	−2.36642	−0.174455
$185$	14.4713	1.06395
$186$	−8.44835	−0.619463
$187$	6.73295	0.492362
$188$	−10.4636	−0.763140
$189$	6.96048	0.506301
$190$	14.6691	1.06421
$191$	12.4260	0.899114	0.449557	−	0.893252i	$-0.351582\pi$
$191$	12.4260	0.899114	0.449557	+	0.893252i	$0.351582\pi$
$192$	−3.56813	−0.257507
$193$	−0.527182	−0.0379474	−0.0189737	−	0.999820i	$-0.506040\pi$
$193$	−0.527182	−0.0379474	−0.0189737	+	0.999820i	$0.506040\pi$
$194$	24.1777	1.73586
$195$	3.81644	0.273301
$196$	−1.19007	−0.0850050
$197$	−9.82546	−0.700035	−0.350017	−	0.936743i	$-0.613824\pi$
$197$	−9.82546	−0.700035	−0.350017	+	0.936743i	$0.613824\pi$
$198$	9.76479	0.693953
$199$	17.1454	1.21541	0.607703	−	0.794164i	$-0.292091\pi$
$199$	17.1454	1.21541	0.607703	+	0.794164i	$0.292091\pi$
$200$	12.4392	0.879587
$201$	−4.11978	−0.290587
$202$	−35.5991	−2.50474
$203$	−15.1841	−1.06572
$204$	−11.1858	−0.783160
$205$	17.2112	1.20208
$206$	−46.5669	−3.24447
$207$	−0.896014	−0.0622773
$208$	43.3888	3.00847
$209$	4.14607	0.286790
$210$	−5.71435	−0.394327
$211$	−18.3190	−1.26113	−0.630566	−	0.776136i	$-0.717177\pi$
$211$	−18.3190	−1.26113	−0.630566	+	0.776136i	$0.717177\pi$
$212$	−69.4593	−4.77048
$213$	2.90469	0.199026
$214$	4.02913	0.275426
$215$	−21.6053	−1.47347
$216$	−19.7060	−1.34083
$217$	−18.1620	−1.23292
$218$	21.4751	1.45448
$219$	4.20350	0.284047
$220$	−11.7656	−0.793237
$221$	22.7273	1.52881
$222$	−9.61611	−0.645391
$223$	−4.97438	−0.333109	−0.166554	−	0.986032i	$-0.553264\pi$
$223$	−4.97438	−0.333109	−0.166554	+	0.986032i	$0.553264\pi$
$224$	−26.7287	−1.78589
$225$	4.70995	0.313997
$226$	−6.49117	−0.431786
$227$	1.43549	0.0952770	0.0476385	−	0.998865i	$-0.484830\pi$
$227$	1.43549	0.0952770	0.0476385	+	0.998865i	$0.484830\pi$
$228$	−6.88805	−0.456172
$229$	0.339139	0.0224109	0.0112055	−	0.999937i	$-0.496433\pi$
$229$	0.339139	0.0224109	0.0112055	+	0.999937i	$0.496433\pi$
$230$	1.52780	0.100740
$231$	−1.61510	−0.106266
$232$	42.9883	2.82232
$233$	−3.84444	−0.251858	−0.125929	−	0.992039i	$-0.540191\pi$
$233$	−3.84444	−0.251858	−0.125929	+	0.992039i	$0.540191\pi$
$234$	32.9614	2.15475
$235$	3.95102	0.257736
$236$	45.3607	2.95273
$237$	0.760166	0.0493781
$238$	−34.0296	−2.20581
$239$	1.89137	0.122342	0.0611712	−	0.998127i	$-0.480516\pi$
$239$	1.89137	0.122342	0.0611712	+	0.998127i	$0.480516\pi$
$240$	8.06344	0.520493
$241$	8.18032	0.526940	0.263470	−	0.964668i	$-0.415133\pi$
$241$	8.18032	0.526940	0.263470	+	0.964668i	$0.415133\pi$
$242$	24.0158	1.54379
$243$	−11.3303	−0.726842
$244$	33.1022	2.11915
$245$	0.449364	0.0287088
$246$	−11.4368	−0.729182
$247$	13.9952	0.890494
$248$	51.4190	3.26511
$249$	2.92628	0.185445
$250$	−31.7803	−2.00996
$251$	11.3917	0.719040	0.359520	−	0.933137i	$-0.382940\pi$
$251$	11.3917	0.719040	0.359520	+	0.933137i	$0.382940\pi$
$252$	−34.8750	−2.19692
$253$	0.431816	0.0271481
$254$	47.9555	3.00899
$255$	4.22369	0.264498
$256$	−16.5817	−1.03636
$257$	10.9582	0.683553	0.341777	−	0.939781i	$-0.388971\pi$
$257$	10.9582	0.683553	0.341777	+	0.939781i	$0.388971\pi$
$258$	14.3567	0.893807
$259$	−20.6724	−1.28452
$260$	−39.7153	−2.46304
$261$	16.2769	1.00752
$262$	28.1536	1.73934
$263$	−9.54408	−0.588513	−0.294257	−	0.955726i	$-0.595072\pi$
$263$	−9.54408	−0.588513	−0.294257	+	0.955726i	$0.595072\pi$
$264$	4.57257	0.281422
$265$	26.2275	1.61114
$266$	−20.9550	−1.28483
$267$	3.49646	0.213980
$268$	42.8719	2.61882
$269$	−14.2808	−0.870714	−0.435357	−	0.900258i	$-0.643378\pi$
$269$	−14.2808	−0.870714	−0.435357	+	0.900258i	$0.643378\pi$
$270$	12.7225	0.774267
$271$	4.49065	0.272787	0.136394	−	0.990655i	$-0.456449\pi$
$271$	4.49065	0.272787	0.136394	+	0.990655i	$0.456449\pi$
$272$	48.0187	2.91156
$273$	−5.45184	−0.329960
$274$	16.9611	1.02466
$275$	−2.26987	−0.136878
$276$	−0.717396	−0.0431822
$277$	−3.61564	−0.217243	−0.108621	−	0.994083i	$-0.534644\pi$
$277$	−3.61564	−0.217243	−0.108621	+	0.994083i	$0.534644\pi$
$278$	11.8564	0.711097
$279$	19.4691	1.16559
$280$	34.7791	2.07845
$281$	−25.7170	−1.53415	−0.767073	−	0.641560i	$-0.778288\pi$
$281$	−25.7170	−1.53415	−0.767073	+	0.641560i	$0.778288\pi$
$282$	−2.62544	−0.156343
$283$	9.72281	0.577961	0.288980	−	0.957335i	$-0.406684\pi$
$283$	9.72281	0.577961	0.288980	+	0.957335i	$0.406684\pi$
$284$	−30.2272	−1.79366
$285$	2.60089	0.154064
$286$	−15.8851	−0.939306
$287$	−24.5864	−1.45129
$288$	28.6524	1.68836
$289$	8.15255	0.479562
$290$	−27.7539	−1.62976
$291$	4.28682	0.251298
$292$	−43.7432	−2.55988
$293$	−8.00370	−0.467581	−0.233791	−	0.972287i	$-0.575113\pi$
$293$	−8.00370	−0.467581	−0.233791	+	0.972287i	$0.575113\pi$
$294$	−0.298601	−0.0174148
$295$	−17.1280	−0.997229
$296$	58.5263	3.40177
$297$	3.59589	0.208655
$298$	6.82678	0.395465
$299$	1.45761	0.0842959
$300$	3.77104	0.217721
$301$	30.8635	1.77894
$302$	−29.3247	−1.68745
$303$	−6.31188	−0.362608
$304$	29.5693	1.69592
$305$	−12.4992	−0.715704
$306$	36.4787	2.08535
$307$	6.67062	0.380712	0.190356	−	0.981715i	$-0.439036\pi$
$307$	6.67062	0.380712	0.190356	+	0.981715i	$0.439036\pi$
$308$	16.8073	0.957687
$309$	−8.25652	−0.469697
$310$	−33.1969	−1.88545
$311$	4.50420	0.255410	0.127705	−	0.991812i	$-0.459239\pi$
$311$	4.50420	0.255410	0.127705	+	0.991812i	$0.459239\pi$
$312$	15.4349	0.873827
$313$	−8.25817	−0.466779	−0.233390	−	0.972383i	$-0.574982\pi$
$313$	−8.25817	−0.466779	−0.233390	+	0.972383i	$0.574982\pi$
$314$	−14.6141	−0.824724
$315$	13.1686	0.741969
$316$	−7.91056	−0.445004
$317$	−29.1168	−1.63536	−0.817682	−	0.575670i	$-0.804741\pi$
$317$	−29.1168	−1.63536	−0.817682	+	0.575670i	$0.804741\pi$
$318$	−17.4281	−0.977318
$319$	−7.84436	−0.439200
$320$	−14.0206	−0.783773
$321$	0.714384	0.0398730
$322$	−2.18248	−0.121625
$323$	15.4886	0.861810
$324$	34.2873	1.90485
$325$	−7.66203	−0.425013
$326$	−2.93359	−0.162477
$327$	3.80764	0.210563
$328$	69.6074	3.84342
$329$	−5.64409	−0.311169
$330$	−2.95212	−0.162509
$331$	−16.9603	−0.932220	−0.466110	−	0.884727i	$-0.654345\pi$
$331$	−16.9603	−0.932220	−0.466110	+	0.884727i	$0.654345\pi$
$332$	−30.4519	−1.67126
$333$	22.1602	1.21437
$334$	3.94406	0.215809
$335$	−16.1882	−0.884458
$336$	−11.5187	−0.628399
$337$	−28.7784	−1.56766	−0.783830	−	0.620976i	$-0.786737\pi$
$337$	−28.7784	−1.56766	−0.783830	+	0.620976i	$0.786737\pi$
$338$	−19.6769	−1.07028
$339$	−1.15091	−0.0625091
$340$	−43.9532	−2.38370
$341$	−9.38276	−0.508105
$342$	22.4631	1.21467
$343$	−18.8325	−1.01686
$344$	−87.3787	−4.71114
$345$	0.270885	0.0145840
$346$	17.8988	0.962243
$347$	19.7216	1.05871	0.529354	−	0.848401i	$-0.322434\pi$
$347$	19.7216	1.05871	0.529354	+	0.848401i	$0.322434\pi$
$348$	13.0322	0.698599
$349$	−32.0564	−1.71594	−0.857970	−	0.513700i	$-0.828274\pi$
$349$	−32.0564	−1.71594	−0.857970	+	0.513700i	$0.828274\pi$
$350$	11.4723	0.613222
$351$	12.1381	0.647882
$352$	−13.8085	−0.735994
$353$	−11.7238	−0.623994	−0.311997	−	0.950083i	$-0.600998\pi$
$353$	−11.7238	−0.623994	−0.311997	+	0.950083i	$0.600998\pi$
$354$	11.3815	0.604918
$355$	11.4136	0.605774
$356$	−36.3854	−1.92842
$357$	−6.03360	−0.319332
$358$	−10.9953	−0.581121
$359$	32.4253	1.71134	0.855671	−	0.517521i	$-0.173145\pi$
$359$	32.4253	1.71134	0.855671	+	0.517521i	$0.173145\pi$
$360$	−37.2821	−1.96494
$361$	−9.46230	−0.498016
$362$	−47.6556	−2.50472
$363$	4.25811	0.223493
$364$	56.7338	2.97366
$365$	16.5172	0.864550
$366$	8.30569	0.434145
$367$	17.4673	0.911787	0.455894	−	0.890034i	$-0.349320\pi$
$367$	17.4673	0.911787	0.455894	+	0.890034i	$0.349320\pi$
$368$	3.07967	0.160539
$369$	26.3559	1.37203
$370$	−37.7855	−1.96437
$371$	−37.4663	−1.94516
$372$	15.5880	0.808201
$373$	2.28957	0.118549	0.0592747	−	0.998242i	$-0.481121\pi$
$373$	2.28957	0.118549	0.0592747	+	0.998242i	$0.481121\pi$
$374$	−17.5802	−0.909050
$375$	−5.63479	−0.290979
$376$	15.9792	0.824062
$377$	−26.4789	−1.36373
$378$	−18.1743	−0.934784
$379$	27.8648	1.43132	0.715659	−	0.698450i	$-0.246127\pi$
$379$	27.8648	1.43132	0.715659	+	0.698450i	$0.246127\pi$
$380$	−27.0658	−1.38845
$381$	8.50272	0.435608
$382$	−32.4451	−1.66004
$383$	−0.652068	−0.0333191	−0.0166596	−	0.999861i	$-0.505303\pi$
$383$	−0.652068	−0.0333191	−0.0166596	+	0.999861i	$0.505303\pi$
$384$	−0.206934	−0.0105600
$385$	−6.34637	−0.323441
$386$	1.37651	0.0700624
$387$	−33.0848	−1.68179
$388$	−44.6102	−2.26474
$389$	−32.8277	−1.66443	−0.832216	−	0.554452i	$-0.812928\pi$
$389$	−32.8277	−1.66443	−0.832216	+	0.554452i	$0.812928\pi$
$390$	−9.96498	−0.504596
$391$	1.61315	0.0815807
$392$	1.81737	0.0917910
$393$	4.99177	0.251801
$394$	25.6549	1.29248
$395$	2.98699	0.150292
$396$	−18.0170	−0.905386
$397$	25.3253	1.27104	0.635520	−	0.772085i	$-0.280786\pi$
$397$	25.3253	1.27104	0.635520	+	0.772085i	$0.280786\pi$
$398$	−44.7678	−2.24401
$399$	−3.71542	−0.186003
$400$	−16.1885	−0.809424
$401$	−14.7395	−0.736057	−0.368028	−	0.929815i	$-0.619967\pi$
$401$	−14.7395	−0.736057	−0.368028	+	0.929815i	$0.619967\pi$
$402$	10.7570	0.536512
$403$	−31.6719	−1.57769
$404$	65.6837	3.26788
$405$	−12.9467	−0.643328
$406$	39.6468	1.96764
$407$	−10.6797	−0.529372
$408$	17.0819	0.845681
$409$	23.1449	1.14444	0.572222	−	0.820099i	$-0.306082\pi$
$409$	23.1449	1.14444	0.572222	+	0.820099i	$0.306082\pi$
$410$	−44.9396	−2.21941
$411$	3.00729	0.148338
$412$	85.9203	4.23299
$413$	24.4675	1.20397
$414$	2.33955	0.114983
$415$	11.4985	0.564438
$416$	−46.6110	−2.28529
$417$	2.10219	0.102944
$418$	−10.8257	−0.529500
$419$	29.7269	1.45226	0.726128	−	0.687560i	$-0.241318\pi$
$419$	29.7269	1.45226	0.726128	+	0.687560i	$0.241318\pi$
$420$	10.5435	0.514471
$421$	11.7210	0.571245	0.285623	−	0.958342i	$-0.407800\pi$
$421$	11.7210	0.571245	0.285623	+	0.958342i	$0.407800\pi$
$422$	47.8321	2.32843
$423$	6.05029	0.294175
$424$	106.072	5.15132
$425$	−8.47964	−0.411323
$426$	−7.58433	−0.367462
$427$	17.8553	0.864080
$428$	−7.43413	−0.359342
$429$	−2.81650	−0.135982
$430$	56.4130	2.72048
$431$	6.56430	0.316191	0.158096	−	0.987424i	$-0.449465\pi$
$431$	6.56430	0.316191	0.158096	+	0.987424i	$0.449465\pi$
$432$	25.6455	1.23387
$433$	−33.5307	−1.61138	−0.805690	−	0.592337i	$-0.798205\pi$
$433$	−33.5307	−1.61138	−0.805690	+	0.592337i	$0.798205\pi$
$434$	47.4222	2.27634
$435$	−4.92089	−0.235939
$436$	−39.6236	−1.89763
$437$	0.993359	0.0475188
$438$	−10.9756	−0.524436
$439$	−0.636767	−0.0303912	−0.0151956	−	0.999885i	$-0.504837\pi$
$439$	−0.636767	−0.0303912	−0.0151956	+	0.999885i	$0.504837\pi$
$440$	17.9674	0.856562
$441$	0.688123	0.0327677
$442$	−59.3426	−2.82264
$443$	6.09615	0.289637	0.144818	−	0.989458i	$-0.453740\pi$
$443$	6.09615	0.289637	0.144818	+	0.989458i	$0.453740\pi$
$444$	17.7426	0.842029
$445$	13.7389	0.651288
$446$	12.9884	0.615020
$447$	1.21042	0.0572509
$448$	20.0286	0.946261
$449$	−36.5003	−1.72256	−0.861279	−	0.508133i	$-0.830336\pi$
$449$	−36.5003	−1.72256	−0.861279	+	0.508133i	$0.830336\pi$
$450$	−12.2980	−0.579733
$451$	−12.7017	−0.598101
$452$	11.9768	0.563342
$453$	−5.19941	−0.244290
$454$	−3.74817	−0.175910
$455$	−21.4224	−1.00430
$456$	10.5188	0.492589
$457$	24.8660	1.16318	0.581590	−	0.813482i	$-0.302431\pi$
$457$	24.8660	1.16318	0.581590	+	0.813482i	$0.302431\pi$
$458$	−0.885514	−0.0413774
$459$	13.4333	0.627013
$460$	−2.81893	−0.131433
$461$	11.2405	0.523521	0.261760	−	0.965133i	$-0.415697\pi$
$461$	11.2405	0.523521	0.261760	+	0.965133i	$0.415697\pi$
$462$	4.21714	0.196199
$463$	−18.4913	−0.859364	−0.429682	−	0.902980i	$-0.641374\pi$
$463$	−18.4913	−0.859364	−0.429682	+	0.902980i	$0.641374\pi$
$464$	−55.9451	−2.59719
$465$	−5.88596	−0.272955
$466$	10.0381	0.465006
$467$	−31.8365	−1.47322	−0.736610	−	0.676318i	$-0.763575\pi$
$467$	−31.8365	−1.47322	−0.736610	+	0.676318i	$0.763575\pi$
$468$	−60.8169	−2.81126
$469$	23.1251	1.06782
$470$	−10.3164	−0.475859
$471$	−2.59116	−0.119394
$472$	−69.2708	−3.18845
$473$	15.9446	0.733132
$474$	−1.98484	−0.0911669
$475$	−5.22165	−0.239586
$476$	62.7878	2.87788
$477$	40.1628	1.83893
$478$	−4.93848	−0.225881
$479$	35.9241	1.64141	0.820707	−	0.571349i	$-0.193580\pi$
$479$	35.9241	1.64141	0.820707	+	0.571349i	$0.193580\pi$
$480$	−8.66227	−0.395377
$481$	−36.0497	−1.64372
$482$	−21.3593	−0.972891
$483$	−0.386964	−0.0176075
$484$	−44.3114	−2.01415
$485$	16.8446	0.764874
$486$	29.5843	1.34197
$487$	−35.4665	−1.60714	−0.803571	−	0.595209i	$-0.797069\pi$
$487$	−35.4665	−1.60714	−0.803571	+	0.595209i	$0.797069\pi$
$488$	−50.5507	−2.28832
$489$	−0.520139	−0.0235215
$490$	−1.17332	−0.0530052
$491$	−0.282401	−0.0127446	−0.00637228	−	0.999980i	$-0.502028\pi$
$491$	−0.282401	−0.0127446	−0.00637228	+	0.999980i	$0.502028\pi$
$492$	21.1019	0.951349
$493$	−29.3045	−1.31981
$494$	−36.5424	−1.64412
$495$	6.80312	0.305777
$496$	−66.9169	−3.00466
$497$	−16.3046	−0.731360
$498$	−7.64070	−0.342388
$499$	2.58689	0.115805	0.0579025	−	0.998322i	$-0.481559\pi$
$499$	2.58689	0.115805	0.0579025	+	0.998322i	$0.481559\pi$
$500$	58.6376	2.62235
$501$	0.699300	0.0312424
$502$	−29.7446	−1.32756
$503$	−4.49377	−0.200367	−0.100184	−	0.994969i	$-0.531943\pi$
$503$	−4.49377	−0.200367	−0.100184	+	0.994969i	$0.531943\pi$
$504$	53.2581	2.37230
$505$	−24.8018	−1.10367
$506$	−1.12750	−0.0501235
$507$	−3.48881	−0.154943
$508$	−88.4824	−3.92577
$509$	42.8807	1.90065	0.950327	−	0.311252i	$-0.100748\pi$
$509$	42.8807	1.90065	0.950327	+	0.311252i	$0.100748\pi$
$510$	−11.0283	−0.488343
$511$	−23.5951	−1.04378
$512$	42.4020	1.87392
$513$	8.27206	0.365220
$514$	−28.6126	−1.26205
$515$	−32.4431	−1.42961
$516$	−26.4894	−1.16613
$517$	−2.91582	−0.128238
$518$	53.9771	2.37162
$519$	3.17353	0.139303
$520$	60.6496	2.65966
$521$	8.09294	0.354558	0.177279	−	0.984161i	$-0.443271\pi$
$521$	8.09294	0.354558	0.177279	+	0.984161i	$0.443271\pi$
$522$	−42.5002	−1.86018
$523$	−31.8558	−1.39296	−0.696479	−	0.717577i	$-0.745251\pi$
$523$	−31.8558	−1.39296	−0.696479	+	0.717577i	$0.745251\pi$
$524$	−51.9461	−2.26928
$525$	2.03410	0.0887753
$526$	24.9202	1.08657
$527$	−35.0515	−1.52687
$528$	−5.95076	−0.258973
$529$	−22.8965	−0.995502
$530$	−68.4817	−2.97465
$531$	−26.2285	−1.13822
$532$	38.6639	1.67629
$533$	−42.8751	−1.85713
$534$	−9.12948	−0.395071
$535$	2.80709	0.121361
$536$	−65.4702	−2.82788
$537$	−1.94952	−0.0841280
$538$	37.2880	1.60760
$539$	−0.331627	−0.0142842
$540$	−23.4742	−1.01017
$541$	4.06257	0.174664	0.0873318	−	0.996179i	$-0.472166\pi$
$541$	4.06257	0.174664	0.0873318	+	0.996179i	$0.472166\pi$
$542$	−11.7254	−0.503648
$543$	−8.44956	−0.362605
$544$	−51.5848	−2.21168
$545$	14.9617	0.640889
$546$	14.2351	0.609207
$547$	−12.8215	−0.548209	−0.274104	−	0.961700i	$-0.588381\pi$
$547$	−12.8215	−0.548209	−0.274104	+	0.961700i	$0.588381\pi$
$548$	−31.2949	−1.33685
$549$	−19.1404	−0.816891
$550$	5.92678	0.252719
$551$	−18.0453	−0.768756
$552$	1.09554	0.0466295
$553$	−4.26696	−0.181449
$554$	9.44067	0.401096
$555$	−6.69954	−0.284379
$556$	−21.8761	−0.927753
$557$	−10.6187	−0.449927	−0.224964	−	0.974367i	$-0.572226\pi$
$557$	−10.6187	−0.449927	−0.224964	+	0.974367i	$0.572226\pi$
$558$	−50.8351	−2.15202
$559$	53.8215	2.27641
$560$	−45.2616	−1.91265
$561$	−3.11705	−0.131602
$562$	67.1487	2.83250
$563$	6.98260	0.294281	0.147141	−	0.989116i	$-0.452993\pi$
$563$	6.98260	0.294281	0.147141	+	0.989116i	$0.452993\pi$
$564$	4.84419	0.203977
$565$	−4.52239	−0.190258
$566$	−25.3869	−1.06709
$567$	18.4946	0.776699
$568$	46.1603	1.93684
$569$	−23.9125	−1.00246	−0.501232	−	0.865313i	$-0.667120\pi$
$569$	−23.9125	−1.00246	−0.501232	+	0.865313i	$0.667120\pi$
$570$	−6.79111	−0.284448
$571$	−31.7826	−1.33006	−0.665030	−	0.746817i	$-0.731581\pi$
$571$	−31.7826	−1.33006	−0.665030	+	0.746817i	$0.731581\pi$
$572$	29.3095	1.22549
$573$	−5.75267	−0.240321
$574$	64.1968	2.67952
$575$	−0.543840	−0.0226797
$576$	−21.4700	−0.894584
$577$	−7.46597	−0.310813	−0.155406	−	0.987851i	$-0.549669\pi$
$577$	−7.46597	−0.310813	−0.155406	+	0.987851i	$0.549669\pi$
$578$	−21.2869	−0.885417
$579$	0.244061	0.0101428
$580$	51.2086	2.12632
$581$	−16.4257	−0.681455
$582$	−11.1932	−0.463972
$583$	−19.3557	−0.801630
$584$	66.8007	2.76423
$585$	22.9642	0.949452
$586$	20.8982	0.863297
$587$	−23.0760	−0.952450	−0.476225	−	0.879323i	$-0.657995\pi$
$587$	−23.0760	−0.952450	−0.476225	+	0.879323i	$0.657995\pi$
$588$	0.550947	0.0227207
$589$	−21.5843	−0.889365
$590$	44.7223	1.84119
$591$	4.54874	0.187110
$592$	−76.1664	−3.13042
$593$	34.0183	1.39697	0.698483	−	0.715627i	$-0.253859\pi$
$593$	34.0183	1.39697	0.698483	+	0.715627i	$0.253859\pi$
$594$	−9.38911	−0.385240
$595$	−23.7084	−0.971949
$596$	−12.5961	−0.515955
$597$	−7.93754	−0.324862
$598$	−3.80592	−0.155636
$599$	−14.2917	−0.583944	−0.291972	−	0.956427i	$-0.594311\pi$
$599$	−14.2917	−0.583944	−0.291972	+	0.956427i	$0.594311\pi$
$600$	−5.75879	−0.235102
$601$	−43.0217	−1.75489	−0.877445	−	0.479677i	$-0.840754\pi$
$601$	−43.0217	−1.75489	−0.877445	+	0.479677i	$0.840754\pi$
$602$	−80.5867	−3.28447
$603$	−24.7894	−1.00950
$604$	54.1069	2.20158
$605$	16.7318	0.680243
$606$	16.4807	0.669484
$607$	19.7066	0.799864	0.399932	−	0.916545i	$-0.369034\pi$
$607$	19.7066	0.799864	0.399932	+	0.916545i	$0.369034\pi$
$608$	−31.7653	−1.28825
$609$	7.02956	0.284852
$610$	32.6363	1.32141
$611$	−9.84247	−0.398184
$612$	−67.3067	−2.72071
$613$	−31.3027	−1.26430	−0.632152	−	0.774845i	$-0.717828\pi$
$613$	−31.3027	−1.26430	−0.632152	+	0.774845i	$0.717828\pi$
$614$	−17.4174	−0.702910
$615$	−7.96799	−0.321300
$616$	−25.6667	−1.03414
$617$	8.97028	0.361130	0.180565	−	0.983563i	$-0.442207\pi$
$617$	8.97028	0.361130	0.180565	+	0.983563i	$0.442207\pi$
$618$	21.5583	0.867203
$619$	−13.4288	−0.539748	−0.269874	−	0.962896i	$-0.586982\pi$
$619$	−13.4288	−0.539748	−0.269874	+	0.962896i	$0.586982\pi$
$620$	61.2514	2.45991
$621$	0.861542	0.0345725
$622$	−11.7608	−0.471564
$623$	−19.6263	−0.786310
$624$	−20.0870	−0.804124
$625$	−13.6874	−0.547496
$626$	21.5626	0.861816
$627$	−1.91944	−0.0766550
$628$	26.9645	1.07600
$629$	−39.8965	−1.59078
$630$	−34.3842	−1.36990
$631$	20.7636	0.826585	0.413293	−	0.910598i	$-0.364379\pi$
$631$	20.7636	0.826585	0.413293	+	0.910598i	$0.364379\pi$
$632$	12.0803	0.480529
$633$	8.48085	0.337084
$634$	76.0260	3.01938
$635$	33.4105	1.32586
$636$	32.1565	1.27509
$637$	−1.11942	−0.0443530
$638$	20.4821	0.810896
$639$	17.4780	0.691419
$640$	−0.813123	−0.0321415
$641$	−32.0263	−1.26496	−0.632482	−	0.774575i	$-0.717964\pi$
$641$	−32.0263	−1.26496	−0.632482	+	0.774575i	$0.717964\pi$
$642$	−1.86530	−0.0736176
$643$	12.4877	0.492467	0.246233	−	0.969211i	$-0.420807\pi$
$643$	12.4877	0.492467	0.246233	+	0.969211i	$0.420807\pi$
$644$	4.02688	0.158681
$645$	10.0023	0.393839
$646$	−40.4418	−1.59116
$647$	14.2616	0.560682	0.280341	−	0.959900i	$-0.409552\pi$
$647$	14.2616	0.560682	0.280341	+	0.959900i	$0.409552\pi$
$648$	−52.3606	−2.05692
$649$	12.6403	0.496175
$650$	20.0061	0.784702
$651$	8.40817	0.329542
$652$	5.41275	0.211980
$653$	19.4500	0.761138	0.380569	−	0.924752i	$-0.375728\pi$
$653$	19.4500	0.761138	0.380569	+	0.924752i	$0.375728\pi$
$654$	−9.94199	−0.388763
$655$	19.6146	0.766406
$656$	−90.5873	−3.53684
$657$	25.2932	0.986782
$658$	14.7371	0.574512
$659$	15.2562	0.594299	0.297150	−	0.954831i	$-0.403964\pi$
$659$	15.2562	0.594299	0.297150	+	0.954831i	$0.403964\pi$
$660$	5.44694	0.212022
$661$	−23.3643	−0.908764	−0.454382	−	0.890807i	$-0.650140\pi$
$661$	−23.3643	−0.908764	−0.454382	+	0.890807i	$0.650140\pi$
$662$	44.2844	1.72116
$663$	−10.5217	−0.408630
$664$	46.5034	1.80468
$665$	−14.5993	−0.566137
$666$	−57.8618	−2.24210
$667$	−1.87944	−0.0727720
$668$	−7.27717	−0.281562
$669$	2.30291	0.0890356
$670$	42.2686	1.63298
$671$	9.22433	0.356101
$672$	12.3742	0.477344
$673$	−37.7185	−1.45394	−0.726971	−	0.686668i	$-0.759072\pi$
$673$	−37.7185	−1.45394	−0.726971	+	0.686668i	$0.759072\pi$
$674$	75.1423	2.89437
$675$	−4.52875	−0.174312
$676$	36.3058	1.39638
$677$	−27.6224	−1.06161	−0.530807	−	0.847493i	$-0.678111\pi$
$677$	−27.6224	−1.06161	−0.530807	+	0.847493i	$0.678111\pi$
$678$	3.00511	0.115411
$679$	−24.0628	−0.923444
$680$	67.1215	2.57399
$681$	−0.664567	−0.0254663
$682$	24.4990	0.938115
$683$	−14.3043	−0.547340	−0.273670	−	0.961824i	$-0.588238\pi$
$683$	−14.3043	−0.547340	−0.273670	+	0.961824i	$0.588238\pi$
$684$	−41.4466	−1.58475
$685$	11.8168	0.451497
$686$	49.1728	1.87743
$687$	−0.157006	−0.00599014
$688$	113.715	4.33534
$689$	−65.3358	−2.48910
$690$	−0.707300	−0.0269264
$691$	−21.4783	−0.817073	−0.408537	−	0.912742i	$-0.633961\pi$
$691$	−21.4783	−0.817073	−0.408537	+	0.912742i	$0.633961\pi$
$692$	−33.0249	−1.25542
$693$	−9.71835	−0.369170
$694$	−51.4943	−1.95470
$695$	8.26031	0.313331
$696$	−19.9016	−0.754368
$697$	−47.4503	−1.79731
$698$	83.7014	3.16814
$699$	1.77980	0.0673183
$700$	−21.1676	−0.800058
$701$	−11.7490	−0.443755	−0.221877	−	0.975075i	$-0.571218\pi$
$701$	−11.7490	−0.443755	−0.221877	+	0.975075i	$0.571218\pi$
$702$	−31.6933	−1.19619
$703$	−24.5678	−0.926591
$704$	10.3471	0.389969
$705$	−1.82914	−0.0688894
$706$	30.6116	1.15208
$707$	35.4298	1.33247
$708$	−20.9999	−0.789225
$709$	51.7713	1.94431	0.972157	−	0.234332i	$-0.0752903\pi$
$709$	51.7713	1.94431	0.972157	+	0.234332i	$0.0752903\pi$
$710$	−29.8018	−1.11844
$711$	4.57405	0.171540
$712$	55.5646	2.08237
$713$	−2.24802	−0.0841891
$714$	15.7541	0.589584
$715$	−11.0671	−0.413887
$716$	20.2874	0.758176
$717$	−0.875616	−0.0327005
$718$	−84.6646	−3.15965
$719$	−38.1766	−1.42375	−0.711873	−	0.702308i	$-0.752153\pi$
$719$	−38.1766	−1.42375	−0.711873	+	0.702308i	$0.752153\pi$
$720$	48.5191	1.80820
$721$	46.3454	1.72599
$722$	24.7067	0.919488
$723$	−3.78711	−0.140844
$724$	87.9292	3.26786
$725$	9.87936	0.366910
$726$	−11.1182	−0.412635
$727$	−12.2396	−0.453941	−0.226970	−	0.973902i	$-0.572882\pi$
$727$	−12.2396	−0.453941	−0.226970	+	0.973902i	$0.572882\pi$
$728$	−86.6389	−3.21105
$729$	−16.1056	−0.596502
$730$	−43.1275	−1.59622
$731$	59.5647	2.20308
$732$	−15.3248	−0.566421
$733$	−37.2249	−1.37493	−0.687466	−	0.726216i	$-0.741277\pi$
$733$	−37.2249	−1.37493	−0.687466	+	0.726216i	$0.741277\pi$
$734$	−45.6083	−1.68343
$735$	−0.208035	−0.00767349
$736$	−3.30838	−0.121948
$737$	11.9468	0.440066
$738$	−68.8170	−2.53319
$739$	−12.3171	−0.453093	−0.226546	−	0.974000i	$-0.572744\pi$
$739$	−12.3171	−0.453093	−0.226546	+	0.974000i	$0.572744\pi$
$740$	69.7178	2.56288
$741$	−6.47914	−0.238017
$742$	97.8271	3.59135
$743$	−6.37525	−0.233885	−0.116943	−	0.993139i	$-0.537309\pi$
$743$	−6.37525	−0.233885	−0.116943	+	0.993139i	$0.537309\pi$
$744$	−23.8046	−0.872720
$745$	4.75621	0.174254
$746$	−5.97822	−0.218878
$747$	17.6079	0.644240
$748$	32.4371	1.18602
$749$	−4.00997	−0.146521
$750$	14.7128	0.537236
$751$	29.0513	1.06010	0.530048	−	0.847968i	$-0.322174\pi$
$751$	29.0513	1.06010	0.530048	+	0.847968i	$0.322174\pi$
$752$	−20.7953	−0.758328
$753$	−5.27385	−0.192190
$754$	69.1382	2.51787
$755$	−20.4305	−0.743542
$756$	33.5333	1.21959
$757$	−50.6066	−1.83933	−0.919665	−	0.392704i	$-0.871540\pi$
$757$	−50.6066	−1.83933	−0.919665	+	0.392704i	$0.871540\pi$
$758$	−72.7568	−2.64265
$759$	−0.199911	−0.00725632
$760$	41.3326	1.49929
$761$	−21.4298	−0.776830	−0.388415	−	0.921485i	$-0.626977\pi$
$761$	−21.4298	−0.776830	−0.388415	+	0.921485i	$0.626977\pi$
$762$	−22.2012	−0.804264
$763$	−21.3730	−0.773754
$764$	59.8644	2.16582
$765$	25.4147	0.918869
$766$	1.70259	0.0615172
$767$	42.6678	1.54065
$768$	7.67657	0.277004
$769$	−17.2084	−0.620551	−0.310276	−	0.950647i	$-0.600421\pi$
$769$	−17.2084	−0.620551	−0.310276	+	0.950647i	$0.600421\pi$
$770$	16.5708	0.597170
$771$	−5.07314	−0.182705
$772$	−2.53979	−0.0914090
$773$	38.4251	1.38205	0.691027	−	0.722829i	$-0.257159\pi$
$773$	38.4251	1.38205	0.691027	+	0.722829i	$0.257159\pi$
$774$	86.3866	3.10510
$775$	11.8169	0.424474
$776$	68.1248	2.44554
$777$	9.57038	0.343336
$778$	85.7154	3.07304
$779$	−29.2193	−1.04689
$780$	18.3863	0.658337
$781$	−8.42318	−0.301405
$782$	−4.21205	−0.150623
$783$	−15.6507	−0.559311
$784$	−2.36513	−0.0844690
$785$	−10.1817	−0.363399
$786$	−13.0338	−0.464901
$787$	−30.2685	−1.07896	−0.539478	−	0.842000i	$-0.681378\pi$
$787$	−30.2685	−1.07896	−0.539478	+	0.842000i	$0.681378\pi$
$788$	−47.3358	−1.68627
$789$	4.41847	0.157302
$790$	−7.79923	−0.277484
$791$	6.46030	0.229702
$792$	27.5139	0.977664
$793$	31.1371	1.10571
$794$	−66.1260	−2.34672
$795$	−12.1421	−0.430637
$796$	82.6009	2.92771
$797$	−37.0943	−1.31395	−0.656974	−	0.753913i	$-0.728164\pi$
$797$	−37.0943	−1.31395	−0.656974	+	0.753913i	$0.728164\pi$
$798$	9.70119	0.343419
$799$	−10.8927	−0.385358
$800$	17.3907	0.614854
$801$	21.0388	0.743369
$802$	38.4859	1.35898
$803$	−12.1896	−0.430160
$804$	−19.8477	−0.699976
$805$	−1.52053	−0.0535917
$806$	82.6973	2.91289
$807$	6.61134	0.232730
$808$	−100.306	−3.52876
$809$	25.1769	0.885172	0.442586	−	0.896726i	$-0.354061\pi$
$809$	25.1769	0.885172	0.442586	+	0.896726i	$0.354061\pi$
$810$	33.8048	1.18778
$811$	−53.7159	−1.88622	−0.943110	−	0.332482i	$-0.892114\pi$
$811$	−53.7159	−1.88622	−0.943110	+	0.332482i	$0.892114\pi$
$812$	−73.1522	−2.56714
$813$	−2.07896	−0.0729124
$814$	27.8854	0.977381
$815$	−2.04383	−0.0715922
$816$	−22.2305	−0.778222
$817$	36.6792	1.28324
$818$	−60.4329	−2.11299
$819$	−32.8047	−1.14629
$820$	82.9178	2.89561
$821$	13.8552	0.483549	0.241775	−	0.970332i	$-0.422270\pi$
$821$	13.8552	0.483549	0.241775	+	0.970332i	$0.422270\pi$
$822$	−7.85222	−0.273878
$823$	−53.8873	−1.87839	−0.939197	−	0.343379i	$-0.888428\pi$
$823$	−53.8873	−1.87839	−0.939197	+	0.343379i	$0.888428\pi$
$824$	−131.210	−4.57091
$825$	1.05085	0.0365857
$826$	−63.8864	−2.22289
$827$	3.21856	0.111920	0.0559601	−	0.998433i	$-0.482178\pi$
$827$	3.21856	0.111920	0.0559601	+	0.998433i	$0.482178\pi$
$828$	−4.31670	−0.150016
$829$	9.37173	0.325494	0.162747	−	0.986668i	$-0.447965\pi$
$829$	9.37173	0.325494	0.162747	+	0.986668i	$0.447965\pi$
$830$	−30.0233	−1.04212
$831$	1.67387	0.0580661
$832$	34.9269	1.21087
$833$	−1.23887	−0.0429244
$834$	−5.48895	−0.190067
$835$	2.74782	0.0950923
$836$	19.9744	0.690828
$837$	−18.7201	−0.647061
$838$	−77.6190	−2.68130
$839$	20.7695	0.717043	0.358522	−	0.933521i	$-0.383281\pi$
$839$	20.7695	0.717043	0.358522	+	0.933521i	$0.383281\pi$
$840$	−16.1011	−0.555541
$841$	5.14173	0.177301
$842$	−30.6042	−1.05469
$843$	11.9058	0.410057
$844$	−88.2548	−3.03785
$845$	−13.7089	−0.471600
$846$	−15.7977	−0.543137
$847$	−23.9016	−0.821268
$848$	−138.043	−4.74040
$849$	−4.50121	−0.154481
$850$	22.1409	0.759426
$851$	−2.55875	−0.0877129
$852$	13.9938	0.479420
$853$	26.6516	0.912533	0.456266	−	0.889843i	$-0.349186\pi$
$853$	26.6516	0.912533	0.456266	+	0.889843i	$0.349186\pi$
$854$	−46.6214	−1.59535
$855$	15.6500	0.535220
$856$	11.3527	0.388029
$857$	24.0944	0.823049	0.411524	−	0.911399i	$-0.364997\pi$
$857$	24.0944	0.823049	0.411524	+	0.911399i	$0.364997\pi$
$858$	7.35407	0.251064
$859$	51.8706	1.76980	0.884901	−	0.465779i	$-0.154226\pi$
$859$	51.8706	1.76980	0.884901	+	0.465779i	$0.154226\pi$
$860$	−104.087	−3.54935
$861$	11.3824	0.387911
$862$	−17.1398	−0.583785
$863$	56.3248	1.91732	0.958659	−	0.284556i	$-0.0918461\pi$
$863$	56.3248	1.91732	0.958659	+	0.284556i	$0.0918461\pi$
$864$	−27.5501	−0.937272
$865$	12.4700	0.423994
$866$	87.5507	2.97510
$867$	−3.77426	−0.128181
$868$	−87.4985	−2.96989
$869$	−2.20437	−0.0747782
$870$	12.8488	0.435614
$871$	40.3268	1.36642
$872$	60.5097	2.04912
$873$	25.7946	0.873013
$874$	−2.59373	−0.0877341
$875$	31.6291	1.06926
$876$	20.2511	0.684221
$877$	−49.5380	−1.67278	−0.836390	−	0.548134i	$-0.815338\pi$
$877$	−49.5380	−1.67278	−0.836390	+	0.548134i	$0.815338\pi$
$878$	1.66264	0.0561114
$879$	3.70535	0.124978
$880$	−23.3828	−0.788235
$881$	20.7213	0.698119	0.349059	−	0.937101i	$-0.386501\pi$
$881$	20.7213	0.698119	0.349059	+	0.937101i	$0.386501\pi$
$882$	−1.79673	−0.0604992
$883$	−0.980615	−0.0330003	−0.0165002	−	0.999864i	$-0.505252\pi$
$883$	−0.980615	−0.0330003	−0.0165002	+	0.999864i	$0.505252\pi$
$884$	109.493	3.68264
$885$	7.92946	0.266546
$886$	−15.9174	−0.534757
$887$	−17.1029	−0.574260	−0.287130	−	0.957892i	$-0.592701\pi$
$887$	−17.1029	−0.574260	−0.287130	+	0.957892i	$0.592701\pi$
$888$	−27.0950	−0.909249
$889$	−47.7274	−1.60073
$890$	−35.8733	−1.20248
$891$	9.55458	0.320090
$892$	−23.9649	−0.802404
$893$	−6.70761	−0.224462
$894$	−3.16049	−0.105702
$895$	−7.66043	−0.256060
$896$	1.16156	0.0388049
$897$	−0.674808	−0.0225312
$898$	95.3048	3.18036
$899$	40.8375	1.36201
$900$	22.6910	0.756366
$901$	−72.3077	−2.40892
$902$	33.1650	1.10427
$903$	−14.2884	−0.475488
$904$	−18.2899	−0.608314
$905$	−33.2016	−1.10366
$906$	13.5760	0.451032
$907$	39.3973	1.30816	0.654082	−	0.756423i	$-0.273055\pi$
$907$	39.3973	1.30816	0.654082	+	0.756423i	$0.273055\pi$
$908$	6.91573	0.229507
$909$	−37.9796	−1.25971
$910$	55.9353	1.85424
$911$	27.9353	0.925538	0.462769	−	0.886479i	$-0.346856\pi$
$911$	27.9353	0.925538	0.462769	+	0.886479i	$0.346856\pi$
$912$	−13.6892	−0.453296
$913$	−8.48579	−0.280839
$914$	−64.9267	−2.14758
$915$	5.78657	0.191298
$916$	1.63386	0.0539842
$917$	−28.0197	−0.925293
$918$	−35.0752	−1.15766
$919$	−24.4102	−0.805218	−0.402609	−	0.915372i	$-0.631897\pi$
$919$	−24.4102	−0.805218	−0.402609	+	0.915372i	$0.631897\pi$
$920$	4.30482	0.141926
$921$	−3.08819	−0.101759
$922$	−29.3496	−0.966578
$923$	−28.4328	−0.935876
$924$	−7.78103	−0.255977
$925$	13.4502	0.442241
$926$	48.2820	1.58665
$927$	−49.6809	−1.63173
$928$	60.0999	1.97288
$929$	−22.0381	−0.723048	−0.361524	−	0.932363i	$-0.617743\pi$
$929$	−22.0381	−0.723048	−0.361524	+	0.932363i	$0.617743\pi$
$930$	15.3686	0.503957
$931$	−0.762882	−0.0250024
$932$	−18.5213	−0.606684
$933$	−2.08524	−0.0682676
$934$	83.1273	2.72001
$935$	−12.2481	−0.400556
$936$	92.8742	3.03569
$937$	38.8250	1.26836	0.634178	−	0.773187i	$-0.281339\pi$
$937$	38.8250	1.26836	0.634178	+	0.773187i	$0.281339\pi$
$938$	−60.3812	−1.97152
$939$	3.82315	0.124764
$940$	19.0347	0.620844
$941$	−17.1915	−0.560428	−0.280214	−	0.959938i	$-0.590405\pi$
$941$	−17.1915	−0.560428	−0.280214	+	0.959938i	$0.590405\pi$
$942$	6.76568	0.220438
$943$	−3.04321	−0.0991007
$944$	90.1493	2.93411
$945$	−12.6620	−0.411895
$946$	−41.6323	−1.35358
$947$	−8.36168	−0.271718	−0.135859	−	0.990728i	$-0.543379\pi$
$947$	−8.36168	−0.271718	−0.135859	+	0.990728i	$0.543379\pi$
$948$	3.66223	0.118944
$949$	−41.1463	−1.33567
$950$	13.6341	0.442348
$951$	13.4798	0.437111
$952$	−95.8840	−3.10762
$953$	57.1395	1.85093	0.925465	−	0.378833i	$-0.123675\pi$
$953$	57.1395	1.85093	0.925465	+	0.378833i	$0.123675\pi$
$954$	−104.868	−3.39522
$955$	−22.6045	−0.731464
$956$	9.11198	0.294702
$957$	3.63158	0.117392
$958$	−93.8002	−3.03055
$959$	−16.8805	−0.545099
$960$	6.49087	0.209492
$961$	17.8463	0.575688
$962$	94.1281	3.03481
$963$	4.29857	0.138519
$964$	39.4100	1.26931
$965$	0.959011	0.0308717
$966$	1.01039	0.0325087
$967$	−9.73072	−0.312919	−0.156459	−	0.987684i	$-0.550008\pi$
$967$	−9.73072	−0.312919	−0.156459	+	0.987684i	$0.550008\pi$
$968$	67.6685	2.17495
$969$	−7.17052	−0.230350
$970$	−43.9824	−1.41219
$971$	21.4134	0.687187	0.343594	−	0.939118i	$-0.388356\pi$
$971$	21.4134	0.687187	0.343594	+	0.939118i	$0.388356\pi$
$972$	−54.5858	−1.75084
$973$	−11.8000	−0.378290
$974$	92.6054	2.96727
$975$	3.54717	0.113600
$976$	65.7869	2.10579
$977$	−21.3185	−0.682039	−0.341019	−	0.940056i	$-0.610772\pi$
$977$	−21.3185	−0.682039	−0.341019	+	0.940056i	$0.610772\pi$
$978$	1.35812	0.0434278
$979$	−10.1392	−0.324051
$980$	2.16489	0.0691548
$981$	22.9112	0.731498
$982$	0.737367	0.0235303
$983$	28.6450	0.913633	0.456817	−	0.889561i	$-0.348990\pi$
$983$	28.6450	0.913633	0.456817	+	0.889561i	$0.348990\pi$
$984$	−32.2250	−1.02730
$985$	17.8738	0.569505
$986$	76.5159	2.43676
$987$	2.61295	0.0831713
$988$	67.4242	2.14505
$989$	3.82017	0.121474
$990$	−17.7634	−0.564557
$991$	50.5488	1.60574	0.802869	−	0.596156i	$-0.203306\pi$
$991$	50.5488	1.60574	0.802869	+	0.596156i	$0.203306\pi$
$992$	71.8864	2.28240
$993$	7.85182	0.249170
$994$	42.5723	1.35031
$995$	−31.1897	−0.988779
$996$	14.0978	0.446707
$997$	−28.2657	−0.895184	−0.447592	−	0.894238i	$-0.647718\pi$
$997$	−28.2657	−0.895184	−0.447592	+	0.894238i	$0.647718\pi$
$998$	−6.75453	−0.213811
$999$	−21.3077	−0.674144

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.b.1.13	✓	205

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.b.1.13	✓	205	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:	\( N \)	\(=\)	\( 5077 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5077.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61107 q^{2} -0.462954 q^{3} +4.81767 q^{4} -1.81913 q^{5} +1.20880 q^{6} +2.59865 q^{7} -7.35711 q^{8} -2.78567 q^{9} +O(q^{10})\)	\(q-2.61107 q^{2} -0.462954 q^{3} +4.81767 q^{4} -1.81913 q^{5} +1.20880 q^{6} +2.59865 q^{7} -7.35711 q^{8} -2.78567 q^{9} +4.74986 q^{10} +1.34250 q^{11} -2.23036 q^{12} +4.53166 q^{13} -6.78525 q^{14} +0.842172 q^{15} +9.57458 q^{16} +5.01523 q^{17} +7.27358 q^{18} +3.08832 q^{19} -8.76395 q^{20} -1.20306 q^{21} -3.50536 q^{22} +0.321651 q^{23} +3.40601 q^{24} -1.69078 q^{25} -11.8325 q^{26} +2.67850 q^{27} +12.5194 q^{28} -5.84309 q^{29} -2.19897 q^{30} -6.98902 q^{31} -10.2856 q^{32} -0.621516 q^{33} -13.0951 q^{34} -4.72727 q^{35} -13.4204 q^{36} -7.95507 q^{37} -8.06380 q^{38} -2.09795 q^{39} +13.3835 q^{40} -9.46124 q^{41} +3.14126 q^{42} +11.8768 q^{43} +6.46772 q^{44} +5.06749 q^{45} -0.839851 q^{46} -2.17193 q^{47} -4.43259 q^{48} -0.247022 q^{49} +4.41473 q^{50} -2.32182 q^{51} +21.8320 q^{52} -14.4176 q^{53} -6.99374 q^{54} -2.44218 q^{55} -19.1186 q^{56} -1.42975 q^{57} +15.2567 q^{58} +9.41549 q^{59} +4.05731 q^{60} +6.87100 q^{61} +18.2488 q^{62} -7.23899 q^{63} +7.70730 q^{64} -8.24367 q^{65} +1.62282 q^{66} +8.89890 q^{67} +24.1617 q^{68} -0.148910 q^{69} +12.3432 q^{70} -6.27424 q^{71} +20.4945 q^{72} -9.07975 q^{73} +20.7712 q^{74} +0.782752 q^{75} +14.8785 q^{76} +3.48869 q^{77} +5.47789 q^{78} -1.64199 q^{79} -17.4174 q^{80} +7.11700 q^{81} +24.7039 q^{82} -6.32088 q^{83} -5.79592 q^{84} -9.12335 q^{85} -31.0110 q^{86} +2.70508 q^{87} -9.87693 q^{88} -7.55249 q^{89} -13.2316 q^{90} +11.7762 q^{91} +1.54961 q^{92} +3.23559 q^{93} +5.67106 q^{94} -5.61804 q^{95} +4.76177 q^{96} -9.25972 q^{97} +0.644991 q^{98} -3.73977 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * q^99

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