LMFDB - Embedded newform 8011.2.a.a.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8011,2,Mod(1,8011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8011, 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("8011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8011.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:	$63.9681570592$
Analytic rank:	$1$
Dimension:	$309$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61660 q^{2} -0.249789 q^{3} +4.84659 q^{4} -1.85842 q^{5} +0.653599 q^{6} -0.258344 q^{7} -7.44839 q^{8} -2.93761 q^{9} +O(q^{10})$	\(q-2.61660 q^{2} -0.249789 q^{3} +4.84659 q^{4} -1.85842 q^{5} +0.653599 q^{6} -0.258344 q^{7} -7.44839 q^{8} -2.93761 q^{9} +4.86274 q^{10} -3.07610 q^{11} -1.21063 q^{12} +5.18331 q^{13} +0.675984 q^{14} +0.464214 q^{15} +9.79626 q^{16} -0.788937 q^{17} +7.68653 q^{18} -2.88591 q^{19} -9.00700 q^{20} +0.0645317 q^{21} +8.04891 q^{22} -0.724357 q^{23} +1.86053 q^{24} -1.54627 q^{25} -13.5626 q^{26} +1.48315 q^{27} -1.25209 q^{28} +0.327314 q^{29} -1.21466 q^{30} +7.89734 q^{31} -10.7361 q^{32} +0.768377 q^{33} +2.06433 q^{34} +0.480113 q^{35} -14.2374 q^{36} -7.91118 q^{37} +7.55128 q^{38} -1.29474 q^{39} +13.8422 q^{40} +9.96442 q^{41} -0.168854 q^{42} +5.69635 q^{43} -14.9086 q^{44} +5.45931 q^{45} +1.89535 q^{46} -6.49140 q^{47} -2.44700 q^{48} -6.93326 q^{49} +4.04598 q^{50} +0.197068 q^{51} +25.1214 q^{52} +2.10659 q^{53} -3.88081 q^{54} +5.71668 q^{55} +1.92425 q^{56} +0.720871 q^{57} -0.856450 q^{58} +0.351934 q^{59} +2.24985 q^{60} -0.996522 q^{61} -20.6642 q^{62} +0.758914 q^{63} +8.49957 q^{64} -9.63277 q^{65} -2.01053 q^{66} -9.34552 q^{67} -3.82366 q^{68} +0.180937 q^{69} -1.25626 q^{70} -4.96038 q^{71} +21.8804 q^{72} +4.72618 q^{73} +20.7004 q^{74} +0.386243 q^{75} -13.9868 q^{76} +0.794693 q^{77} +3.38780 q^{78} +9.62030 q^{79} -18.2056 q^{80} +8.44234 q^{81} -26.0729 q^{82} +2.40998 q^{83} +0.312759 q^{84} +1.46618 q^{85} -14.9051 q^{86} -0.0817597 q^{87} +22.9120 q^{88} -1.09993 q^{89} -14.2848 q^{90} -1.33908 q^{91} -3.51066 q^{92} -1.97267 q^{93} +16.9854 q^{94} +5.36324 q^{95} +2.68177 q^{96} +10.5657 q^{97} +18.1416 q^{98} +9.03636 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) $ 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9} - 23 q^{10} - 72 q^{11} - 42 q^{12} - 57 q^{13} - 77 q^{14} - 44 q^{15} + 205 q^{16} - 86 q^{17} - 82 q^{18} - 58 q^{19} - 134 q^{20} - 123 q^{21} - 31 q^{22} - 94 q^{23} - 84 q^{24} + 225 q^{25} - 92 q^{26} - 48 q^{27} - 36 q^{28} - 345 q^{29} - 85 q^{30} - 36 q^{31} - 199 q^{32} - 56 q^{33} - 28 q^{34} - 168 q^{35} + 65 q^{36} - 79 q^{37} - 66 q^{38} - 145 q^{39} - 54 q^{40} - 176 q^{41} - 48 q^{42} - 58 q^{43} - 194 q^{44} - 192 q^{45} - 44 q^{46} - 82 q^{47} - 81 q^{48} + 186 q^{49} - 206 q^{50} - 145 q^{51} - 86 q^{52} - 223 q^{53} - 117 q^{54} - 58 q^{55} - 216 q^{56} - 124 q^{57} - 151 q^{59} - 91 q^{60} - 184 q^{61} - 124 q^{62} - 78 q^{63} + 101 q^{64} - 194 q^{65} - 112 q^{66} - 53 q^{67} - 182 q^{68} - 243 q^{69} - 193 q^{71} - 208 q^{72} - 69 q^{73} - 236 q^{74} - 62 q^{75} - 142 q^{76} - 324 q^{77} - 20 q^{78} - 91 q^{79} - 223 q^{80} - 27 q^{81} + 2 q^{82} - 117 q^{83} - 157 q^{84} - 171 q^{85} - 203 q^{86} - 69 q^{87} - 36 q^{88} - 172 q^{89} - 10 q^{90} - 84 q^{91} - 226 q^{92} - 220 q^{93} - 96 q^{94} - 166 q^{95} - 118 q^{96} - 12 q^{97} - 116 q^{98} - 154 q^{99}+O(q^{100}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9 - 23 * q^10 - 72 * q^11 - 42 * q^12 - 57 * q^13 - 77 * q^14 - 44 * q^15 + 205 * q^16 - 86 * q^17 - 82 * q^18 - 58 * q^19 - 134 * q^20 - 123 * q^21 - 31 * q^22 - 94 * q^23 - 84 * q^24 + 225 * q^25 - 92 * q^26 - 48 * q^27 - 36 * q^28 - 345 * q^29 - 85 * q^30 - 36 * q^31 - 199 * q^32 - 56 * q^33 - 28 * q^34 - 168 * q^35 + 65 * q^36 - 79 * q^37 - 66 * q^38 - 145 * q^39 - 54 * q^40 - 176 * q^41 - 48 * q^42 - 58 * q^43 - 194 * q^44 - 192 * q^45 - 44 * q^46 - 82 * q^47 - 81 * q^48 + 186 * q^49 - 206 * q^50 - 145 * q^51 - 86 * q^52 - 223 * q^53 - 117 * q^54 - 58 * q^55 - 216 * q^56 - 124 * q^57 - 151 * q^59 - 91 * q^60 - 184 * q^61 - 124 * q^62 - 78 * q^63 + 101 * q^64 - 194 * q^65 - 112 * q^66 - 53 * q^67 - 182 * q^68 - 243 * q^69 - 193 * q^71 - 208 * q^72 - 69 * q^73 - 236 * q^74 - 62 * q^75 - 142 * q^76 - 324 * q^77 - 20 * q^78 - 91 * q^79 - 223 * q^80 - 27 * q^81 + 2 * q^82 - 117 * q^83 - 157 * q^84 - 171 * q^85 - 203 * q^86 - 69 * q^87 - 36 * q^88 - 172 * q^89 - 10 * q^90 - 84 * q^91 - 226 * q^92 - 220 * q^93 - 96 * q^94 - 166 * q^95 - 118 * q^96 - 12 * q^97 - 116 * q^98 - 154 * 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 $

$2$	−2.61660	−1.85021	−0.925107	−	0.379705i	$-0.876025\pi$
$2$	−2.61660	−1.85021	−0.925107	+	0.379705i	$0.876025\pi$
$3$	−0.249789	−0.144216	−0.0721080	−	0.997397i	$-0.522973\pi$
$3$	−0.249789	−0.144216	−0.0721080	+	0.997397i	$0.522973\pi$
$4$	4.84659	2.42330
$5$	−1.85842	−0.831111	−0.415555	−	0.909568i	$-0.636413\pi$
$5$	−1.85842	−0.831111	−0.415555	+	0.909568i	$0.636413\pi$
$6$	0.653599	0.266831
$7$	−0.258344	−0.0976450	−0.0488225	−	0.998807i	$-0.515547\pi$
$7$	−0.258344	−0.0976450	−0.0488225	+	0.998807i	$0.515547\pi$
$8$	−7.44839	−2.63340
$9$	−2.93761	−0.979202
$10$	4.86274	1.53773
$11$	−3.07610	−0.927478	−0.463739	−	0.885972i	$-0.653493\pi$
$11$	−3.07610	−0.927478	−0.463739	+	0.885972i	$0.653493\pi$
$12$	−1.21063	−0.349478
$13$	5.18331	1.43759	0.718796	−	0.695222i	$-0.244694\pi$
$13$	5.18331	1.43759	0.718796	+	0.695222i	$0.244694\pi$
$14$	0.675984	0.180664
$15$	0.464214	0.119859
$16$	9.79626	2.44906
$17$	−0.788937	−0.191345	−0.0956727	−	0.995413i	$-0.530500\pi$
$17$	−0.788937	−0.191345	−0.0956727	+	0.995413i	$0.530500\pi$
$18$	7.68653	1.81173
$19$	−2.88591	−0.662074	−0.331037	−	0.943618i	$-0.607399\pi$
$19$	−2.88591	−0.662074	−0.331037	+	0.943618i	$0.607399\pi$
$20$	−9.00700	−2.01403
$21$	0.0645317	0.0140820
$22$	8.04891	1.71603
$23$	−0.724357	−0.151039	−0.0755194	−	0.997144i	$-0.524061\pi$
$23$	−0.724357	−0.151039	−0.0755194	+	0.997144i	$0.524061\pi$
$24$	1.86053	0.379779
$25$	−1.54627	−0.309255
$26$	−13.5626	−2.65985
$27$	1.48315	0.285433
$28$	−1.25209	−0.236623
$29$	0.327314	0.0607807	0.0303904	−	0.999538i	$-0.490325\pi$
$29$	0.327314	0.0607807	0.0303904	+	0.999538i	$0.490325\pi$
$30$	−1.21466	−0.221766
$31$	7.89734	1.41840	0.709202	−	0.705006i	$-0.249056\pi$
$31$	7.89734	1.41840	0.709202	+	0.705006i	$0.249056\pi$
$32$	−10.7361	−1.89789
$33$	0.768377	0.133757
$34$	2.06433	0.354030
$35$	0.480113	0.0811538
$36$	−14.2374	−2.37289
$37$	−7.91118	−1.30059	−0.650295	−	0.759682i	$-0.725355\pi$
$37$	−7.91118	−1.30059	−0.650295	+	0.759682i	$0.725355\pi$
$38$	7.55128	1.22498
$39$	−1.29474	−0.207324
$40$	13.8422	2.18865
$41$	9.96442	1.55618	0.778090	−	0.628152i	$-0.216189\pi$
$41$	9.96442	1.55618	0.778090	+	0.628152i	$0.216189\pi$
$42$	−0.168854	−0.0260547
$43$	5.69635	0.868685	0.434343	−	0.900748i	$-0.356981\pi$
$43$	5.69635	0.868685	0.434343	+	0.900748i	$0.356981\pi$
$44$	−14.9086	−2.24755
$45$	5.45931	0.813825
$46$	1.89535	0.279454
$47$	−6.49140	−0.946868	−0.473434	−	0.880829i	$-0.656986\pi$
$47$	−6.49140	−0.946868	−0.473434	+	0.880829i	$0.656986\pi$
$48$	−2.44700	−0.353194
$49$	−6.93326	−0.990465
$50$	4.04598	0.572188
$51$	0.197068	0.0275951
$52$	25.1214	3.48371
$53$	2.10659	0.289362	0.144681	−	0.989478i	$-0.453784\pi$
$53$	2.10659	0.289362	0.144681	+	0.989478i	$0.453784\pi$
$54$	−3.88081	−0.528112
$55$	5.71668	0.770837
$56$	1.92425	0.257139
$57$	0.720871	0.0954817
$58$	−0.856450	−0.112457
$59$	0.351934	0.0458179	0.0229089	−	0.999738i	$-0.492707\pi$
$59$	0.351934	0.0458179	0.0229089	+	0.999738i	$0.492707\pi$
$60$	2.24985	0.290455
$61$	−0.996522	−0.127592	−0.0637958	−	0.997963i	$-0.520321\pi$
$61$	−0.996522	−0.127592	−0.0637958	+	0.997963i	$0.520321\pi$
$62$	−20.6642	−2.62435
$63$	0.758914	0.0956142
$64$	8.49957	1.06245
$65$	−9.63277	−1.19480
$66$	−2.01053	−0.247480
$67$	−9.34552	−1.14174	−0.570869	−	0.821041i	$-0.693393\pi$
$67$	−9.34552	−1.14174	−0.570869	+	0.821041i	$0.693393\pi$
$68$	−3.82366	−0.463686
$69$	0.180937	0.0217822
$70$	−1.25626	−0.150152
$71$	−4.96038	−0.588689	−0.294345	−	0.955699i	$-0.595101\pi$
$71$	−4.96038	−0.588689	−0.294345	+	0.955699i	$0.595101\pi$
$72$	21.8804	2.57863
$73$	4.72618	0.553157	0.276579	−	0.960991i	$-0.410799\pi$
$73$	4.72618	0.553157	0.276579	+	0.960991i	$0.410799\pi$
$74$	20.7004	2.40637
$75$	0.386243	0.0445995
$76$	−13.9868	−1.60440
$77$	0.794693	0.0905636
$78$	3.38780	0.383593
$79$	9.62030	1.08237	0.541184	−	0.840904i	$-0.317976\pi$
$79$	9.62030	1.08237	0.541184	+	0.840904i	$0.317976\pi$
$80$	−18.2056	−2.03544
$81$	8.44234	0.938038
$82$	−26.0729	−2.87927
$83$	2.40998	0.264530	0.132265	−	0.991214i	$-0.457775\pi$
$83$	2.40998	0.264530	0.132265	+	0.991214i	$0.457775\pi$
$84$	0.312759	0.0341248
$85$	1.46618	0.159029
$86$	−14.9051	−1.60725
$87$	−0.0817597	−0.00876556
$88$	22.9120	2.44242
$89$	−1.09993	−0.116593	−0.0582963	−	0.998299i	$-0.518567\pi$
$89$	−1.09993	−0.116593	−0.0582963	+	0.998299i	$0.518567\pi$
$90$	−14.2848	−1.50575
$91$	−1.33908	−0.140374
$92$	−3.51066	−0.366012
$93$	−1.97267	−0.204556
$94$	16.9854	1.75191
$95$	5.36324	0.550257
$96$	2.68177	0.273707
$97$	10.5657	1.07278	0.536390	−	0.843970i	$-0.319788\pi$
$97$	10.5657	1.07278	0.536390	+	0.843970i	$0.319788\pi$
$98$	18.1416	1.83257
$99$	9.03636	0.908188
$100$	−7.49415	−0.749415
$101$	−4.00640	−0.398652	−0.199326	−	0.979933i	$-0.563875\pi$
$101$	−4.00640	−0.398652	−0.199326	+	0.979933i	$0.563875\pi$
$102$	−0.515648	−0.0510568
$103$	13.3766	1.31804	0.659020	−	0.752126i	$-0.270971\pi$
$103$	13.3766	1.31804	0.659020	+	0.752126i	$0.270971\pi$
$104$	−38.6073	−3.78576
$105$	−0.119927	−0.0117037
$106$	−5.51210	−0.535382
$107$	−3.21742	−0.311040	−0.155520	−	0.987833i	$-0.549705\pi$
$107$	−3.21742	−0.311040	−0.155520	+	0.987833i	$0.549705\pi$
$108$	7.18823	0.691687
$109$	13.7123	1.31340	0.656700	−	0.754152i	$-0.271952\pi$
$109$	13.7123	1.31340	0.656700	+	0.754152i	$0.271952\pi$
$110$	−14.9583	−1.42621
$111$	1.97613	0.187566
$112$	−2.53081	−0.239139
$113$	−4.21826	−0.396820	−0.198410	−	0.980119i	$-0.563578\pi$
$113$	−4.21826	−0.396820	−0.198410	+	0.980119i	$0.563578\pi$
$114$	−1.88623	−0.176662
$115$	1.34616	0.125530
$116$	1.58636	0.147290
$117$	−15.2265	−1.40769
$118$	−0.920869	−0.0847729
$119$	0.203818	0.0186839
$120$	−3.45764	−0.315638
$121$	−1.53763	−0.139784
$122$	2.60750	0.236072
$123$	−2.48901	−0.224426
$124$	38.2752	3.43721
$125$	12.1657	1.08814
$126$	−1.98577	−0.176907
$127$	7.43240	0.659519	0.329759	−	0.944065i	$-0.393032\pi$
$127$	7.43240	0.659519	0.329759	+	0.944065i	$0.393032\pi$
$128$	−0.767752	−0.0678603
$129$	−1.42289	−0.125278
$130$	25.2051	2.21063
$131$	−8.72334	−0.762162	−0.381081	−	0.924542i	$-0.624448\pi$
$131$	−8.72334	−0.762162	−0.381081	+	0.924542i	$0.624448\pi$
$132$	3.72401	0.324133
$133$	0.745560	0.0646482
$134$	24.4535	2.11246
$135$	−2.75632	−0.237226
$136$	5.87631	0.503889
$137$	−0.767017	−0.0655307	−0.0327653	−	0.999463i	$-0.510431\pi$
$137$	−0.767017	−0.0655307	−0.0327653	+	0.999463i	$0.510431\pi$
$138$	−0.473439	−0.0403018
$139$	18.6916	1.58540	0.792699	−	0.609613i	$-0.208675\pi$
$139$	18.6916	1.58540	0.792699	+	0.609613i	$0.208675\pi$
$140$	2.32691	0.196660
$141$	1.62148	0.136554
$142$	12.9793	1.08920
$143$	−15.9444	−1.33333
$144$	−28.7775	−2.39813
$145$	−0.608288	−0.0505155
$146$	−12.3665	−1.02346
$147$	1.73185	0.142841
$148$	−38.3423	−3.15171
$149$	23.1756	1.89862	0.949308	−	0.314348i	$-0.101786\pi$
$149$	23.1756	1.89862	0.949308	+	0.314348i	$0.101786\pi$
$150$	−1.01064	−0.0825186
$151$	10.1588	0.826715	0.413358	−	0.910569i	$-0.364356\pi$
$151$	10.1588	0.826715	0.413358	+	0.910569i	$0.364356\pi$
$152$	21.4954	1.74351
$153$	2.31759	0.187366
$154$	−2.07939	−0.167562
$155$	−14.6766	−1.17885
$156$	−6.27505	−0.502406
$157$	−5.97470	−0.476833	−0.238416	−	0.971163i	$-0.576628\pi$
$157$	−5.97470	−0.476833	−0.238416	+	0.971163i	$0.576628\pi$
$158$	−25.1725	−2.00261
$159$	−0.526204	−0.0417307
$160$	19.9522	1.57736
$161$	0.187134	0.0147482
$162$	−22.0902	−1.73557
$163$	5.77108	0.452026	0.226013	−	0.974124i	$-0.427431\pi$
$163$	5.77108	0.452026	0.226013	+	0.974124i	$0.427431\pi$
$164$	48.2935	3.77109
$165$	−1.42797	−0.111167
$166$	−6.30596	−0.489438
$167$	−17.6328	−1.36447	−0.682235	−	0.731133i	$-0.738992\pi$
$167$	−17.6328	−1.36447	−0.682235	+	0.731133i	$0.738992\pi$
$168$	−0.480657	−0.0370835
$169$	13.8667	1.06667
$170$	−3.83640	−0.294238
$171$	8.47768	0.648304
$172$	27.6079	2.10508
$173$	−10.6820	−0.812134	−0.406067	−	0.913843i	$-0.633100\pi$
$173$	−10.6820	−0.812134	−0.406067	+	0.913843i	$0.633100\pi$
$174$	0.213932	0.0162182
$175$	0.399471	0.0301972
$176$	−30.1342	−2.27145
$177$	−0.0879093	−0.00660767
$178$	2.87808	0.215721
$179$	−7.19587	−0.537845	−0.268922	−	0.963162i	$-0.586668\pi$
$179$	−7.19587	−0.537845	−0.268922	+	0.963162i	$0.586668\pi$
$180$	26.4590	1.97214
$181$	0.965373	0.0717556	0.0358778	−	0.999356i	$-0.488577\pi$
$181$	0.965373	0.0717556	0.0358778	+	0.999356i	$0.488577\pi$
$182$	3.50383	0.259721
$183$	0.248921	0.0184007
$184$	5.39529	0.397746
$185$	14.7023	1.08093
$186$	5.16169	0.378473
$187$	2.42685	0.177469
$188$	−31.4612	−2.29454
$189$	−0.383164	−0.0278711
$190$	−14.0335	−1.01809
$191$	−6.65825	−0.481774	−0.240887	−	0.970553i	$-0.577438\pi$
$191$	−6.65825	−0.481774	−0.240887	+	0.970553i	$0.577438\pi$
$192$	−2.12310	−0.153222
$193$	5.81502	0.418574	0.209287	−	0.977854i	$-0.432886\pi$
$193$	5.81502	0.418574	0.209287	+	0.977854i	$0.432886\pi$
$194$	−27.6461	−1.98487
$195$	2.40616	0.172309
$196$	−33.6027	−2.40019
$197$	−14.4448	−1.02915	−0.514574	−	0.857446i	$-0.672050\pi$
$197$	−14.4448	−1.02915	−0.514574	+	0.857446i	$0.672050\pi$
$198$	−23.6445	−1.68034
$199$	−16.7160	−1.18496	−0.592482	−	0.805584i	$-0.701852\pi$
$199$	−16.7160	−1.18496	−0.592482	+	0.805584i	$0.701852\pi$
$200$	11.5172	0.814392
$201$	2.33441	0.164657
$202$	10.4831	0.737591
$203$	−0.0845598	−0.00593494
$204$	0.955109	0.0668710
$205$	−18.5181	−1.29336
$206$	−35.0013	−2.43866
$207$	2.12788	0.147898
$208$	50.7770	3.52075
$209$	8.87735	0.614059
$210$	0.313801	0.0216543
$211$	7.44640	0.512631	0.256316	−	0.966593i	$-0.417491\pi$
$211$	7.44640	0.512631	0.256316	+	0.966593i	$0.417491\pi$
$212$	10.2098	0.701210
$213$	1.23905	0.0848984
$214$	8.41871	0.575491
$215$	−10.5862	−0.721974
$216$	−11.0471	−0.751659
$217$	−2.04023	−0.138500
$218$	−35.8796	−2.43007
$219$	−1.18055	−0.0797741
$220$	27.7064	1.86797
$221$	−4.08930	−0.275076
$222$	−5.17074	−0.347037
$223$	5.28107	0.353646	0.176823	−	0.984243i	$-0.443418\pi$
$223$	5.28107	0.353646	0.176823	+	0.984243i	$0.443418\pi$
$224$	2.77361	0.185320
$225$	4.54234	0.302823
$226$	11.0375	0.734203
$227$	−7.52549	−0.499484	−0.249742	−	0.968312i	$-0.580346\pi$
$227$	−7.52549	−0.499484	−0.249742	+	0.968312i	$0.580346\pi$
$228$	3.49377	0.231380
$229$	−26.7767	−1.76945	−0.884727	−	0.466109i	$-0.845656\pi$
$229$	−26.7767	−1.76945	−0.884727	+	0.466109i	$0.845656\pi$
$230$	−3.52236	−0.232258
$231$	−0.198506	−0.0130607
$232$	−2.43796	−0.160060
$233$	−2.78788	−0.182640	−0.0913200	−	0.995822i	$-0.529109\pi$
$233$	−2.78788	−0.182640	−0.0913200	+	0.995822i	$0.529109\pi$
$234$	39.8417	2.60453
$235$	12.0638	0.786953
$236$	1.70568	0.111030
$237$	−2.40305	−0.156095
$238$	−0.533309	−0.0345693
$239$	1.40441	0.0908435	0.0454218	−	0.998968i	$-0.485537\pi$
$239$	1.40441	0.0908435	0.0454218	+	0.998968i	$0.485537\pi$
$240$	4.54756	0.293544
$241$	10.2823	0.662344	0.331172	−	0.943570i	$-0.392556\pi$
$241$	10.2823	0.662344	0.331172	+	0.943570i	$0.392556\pi$
$242$	4.02335	0.258631
$243$	−6.55826	−0.420713
$244$	−4.82973	−0.309192
$245$	12.8849	0.823187
$246$	6.51273	0.415237
$247$	−14.9586	−0.951792
$248$	−58.8224	−3.73523
$249$	−0.601989	−0.0381495
$250$	−31.8328	−2.01329
$251$	−9.49725	−0.599461	−0.299731	−	0.954024i	$-0.596897\pi$
$251$	−9.49725	−0.599461	−0.299731	+	0.954024i	$0.596897\pi$
$252$	3.67814	0.231701
$253$	2.22819	0.140085
$254$	−19.4476	−1.22025
$255$	−0.366236	−0.0229346
$256$	−14.9902	−0.936890
$257$	−4.48212	−0.279587	−0.139793	−	0.990181i	$-0.544644\pi$
$257$	−4.48212	−0.279587	−0.139793	+	0.990181i	$0.544644\pi$
$258$	3.72313	0.231792
$259$	2.04381	0.126996
$260$	−46.6861	−2.89535
$261$	−0.961520	−0.0595166
$262$	22.8255	1.41016
$263$	18.7219	1.15444	0.577222	−	0.816587i	$-0.304137\pi$
$263$	18.7219	1.15444	0.577222	+	0.816587i	$0.304137\pi$
$264$	−5.72317	−0.352237
$265$	−3.91493	−0.240492
$266$	−1.95083	−0.119613
$267$	0.274751	0.0168145
$268$	−45.2939	−2.76677
$269$	−20.6480	−1.25893	−0.629466	−	0.777028i	$-0.716726\pi$
$269$	−20.6480	−1.25893	−0.629466	+	0.777028i	$0.716726\pi$
$270$	7.21218	0.438919
$271$	3.40993	0.207138	0.103569	−	0.994622i	$-0.466974\pi$
$271$	3.40993	0.207138	0.103569	+	0.994622i	$0.466974\pi$
$272$	−7.72863	−0.468617
$273$	0.334488	0.0202441
$274$	2.00698	0.121246
$275$	4.75649	0.286827
$276$	0.876926	0.0527848
$277$	17.7595	1.06707	0.533534	−	0.845779i	$-0.320864\pi$
$277$	17.7595	1.06707	0.533534	+	0.845779i	$0.320864\pi$
$278$	−48.9084	−2.93333
$279$	−23.1993	−1.38890
$280$	−3.57606	−0.213711
$281$	−24.1778	−1.44233	−0.721164	−	0.692765i	$-0.756392\pi$
$281$	−24.1778	−1.44233	−0.721164	+	0.692765i	$0.756392\pi$
$282$	−4.24277	−0.252653
$283$	9.41103	0.559428	0.279714	−	0.960083i	$-0.409760\pi$
$283$	9.41103	0.559428	0.279714	+	0.960083i	$0.409760\pi$
$284$	−24.0409	−1.42657
$285$	−1.33968	−0.0793559
$286$	41.7200	2.46696
$287$	−2.57425	−0.151953
$288$	31.5384	1.85842
$289$	−16.3776	−0.963387
$290$	1.59164	0.0934646
$291$	−2.63919	−0.154712
$292$	22.9058	1.34046
$293$	19.1889	1.12103	0.560514	−	0.828145i	$-0.310604\pi$
$293$	19.1889	1.12103	0.560514	+	0.828145i	$0.310604\pi$
$294$	−4.53157	−0.264287
$295$	−0.654041	−0.0380797
$296$	58.9255	3.42498
$297$	−4.56232	−0.264733
$298$	−60.6411	−3.51285
$299$	−3.75457	−0.217132
$300$	1.87196	0.108078
$301$	−1.47162	−0.0848228
$302$	−26.5816	−1.52960
$303$	1.00076	0.0574920
$304$	−28.2712	−1.62146
$305$	1.85196	0.106043
$306$	−6.06419	−0.346667
$307$	4.73011	0.269961	0.134981	−	0.990848i	$-0.456903\pi$
$307$	4.73011	0.269961	0.134981	+	0.990848i	$0.456903\pi$
$308$	3.85155	0.219462
$309$	−3.34134	−0.190082
$310$	38.4027	2.18113
$311$	8.57564	0.486280	0.243140	−	0.969991i	$-0.421823\pi$
$311$	8.57564	0.486280	0.243140	+	0.969991i	$0.421823\pi$
$312$	9.64369	0.545967
$313$	3.54019	0.200103	0.100052	−	0.994982i	$-0.468099\pi$
$313$	3.54019	0.200103	0.100052	+	0.994982i	$0.468099\pi$
$314$	15.6334	0.882243
$315$	−1.41038	−0.0794660
$316$	46.6256	2.62290
$317$	15.1828	0.852750	0.426375	−	0.904547i	$-0.359790\pi$
$317$	15.1828	0.852750	0.426375	+	0.904547i	$0.359790\pi$
$318$	1.37686	0.0772107
$319$	−1.00685	−0.0563728
$320$	−15.7958	−0.883010
$321$	0.803679	0.0448570
$322$	−0.489654	−0.0272873
$323$	2.27680	0.126685
$324$	40.9166	2.27314
$325$	−8.01481	−0.444582
$326$	−15.1006	−0.836345
$327$	−3.42519	−0.189413
$328$	−74.2188	−4.09805
$329$	1.67702	0.0924570
$330$	3.73642	0.205683
$331$	−1.58653	−0.0872034	−0.0436017	−	0.999049i	$-0.513883\pi$
$331$	−1.58653	−0.0872034	−0.0436017	+	0.999049i	$0.513883\pi$
$332$	11.6802	0.641035
$333$	23.2399	1.27354
$334$	46.1380	2.52456
$335$	17.3679	0.948910
$336$	0.632169	0.0344877
$337$	−14.3639	−0.782453	−0.391226	−	0.920294i	$-0.627949\pi$
$337$	−14.3639	−0.782453	−0.391226	+	0.920294i	$0.627949\pi$
$338$	−36.2836	−1.97357
$339$	1.05368	0.0572278
$340$	7.10596	0.385375
$341$	−24.2930	−1.31554
$342$	−22.1827	−1.19950
$343$	3.59958	0.194359
$344$	−42.4286	−2.28760
$345$	−0.336257	−0.0181034
$346$	27.9504	1.50262
$347$	13.4737	0.723304	0.361652	−	0.932313i	$-0.382213\pi$
$347$	13.4737	0.723304	0.361652	+	0.932313i	$0.382213\pi$
$348$	−0.396256	−0.0212415
$349$	10.5202	0.563133	0.281567	−	0.959542i	$-0.409146\pi$
$349$	10.5202	0.563133	0.281567	+	0.959542i	$0.409146\pi$
$350$	−1.04526	−0.0558713
$351$	7.68763	0.410335
$352$	33.0253	1.76025
$353$	14.7063	0.782737	0.391368	−	0.920234i	$-0.372002\pi$
$353$	14.7063	0.782737	0.391368	+	0.920234i	$0.372002\pi$
$354$	0.230023	0.0122256
$355$	9.21848	0.489266
$356$	−5.33092	−0.282538
$357$	−0.0509115	−0.00269452
$358$	18.8287	0.995128
$359$	13.8331	0.730083	0.365042	−	0.930991i	$-0.381055\pi$
$359$	13.8331	0.730083	0.365042	+	0.930991i	$0.381055\pi$
$360$	−40.6630	−2.14313
$361$	−10.6715	−0.561658
$362$	−2.52599	−0.132763
$363$	0.384083	0.0201591
$364$	−6.48997	−0.340167
$365$	−8.78322	−0.459735
$366$	−0.651325	−0.0340453
$367$	20.9508	1.09362	0.546812	−	0.837255i	$-0.315841\pi$
$367$	20.9508	1.09362	0.546812	+	0.837255i	$0.315841\pi$
$368$	−7.09599	−0.369904
$369$	−29.2715	−1.52382
$370$	−38.4700	−1.99996
$371$	−0.544226	−0.0282548
$372$	−9.56073	−0.495701
$373$	1.09760	0.0568315	0.0284158	−	0.999596i	$-0.490954\pi$
$373$	1.09760	0.0568315	0.0284158	+	0.999596i	$0.490954\pi$
$374$	−6.35009	−0.328355
$375$	−3.03887	−0.156927
$376$	48.3505	2.49348
$377$	1.69657	0.0873779
$378$	1.00259	0.0515675
$379$	−28.5511	−1.46657	−0.733286	−	0.679920i	$-0.762014\pi$
$379$	−28.5511	−1.46657	−0.733286	+	0.679920i	$0.762014\pi$
$380$	25.9934	1.33343
$381$	−1.85654	−0.0951132
$382$	17.4220	0.891386
$383$	13.7639	0.703303	0.351652	−	0.936131i	$-0.385620\pi$
$383$	13.7639	0.703303	0.351652	+	0.936131i	$0.385620\pi$
$384$	0.191776	0.00978654
$385$	−1.47687	−0.0752684
$386$	−15.2156	−0.774453
$387$	−16.7336	−0.850618
$388$	51.2074	2.59966
$389$	−3.53253	−0.179107	−0.0895533	−	0.995982i	$-0.528544\pi$
$389$	−3.53253	−0.179107	−0.0895533	+	0.995982i	$0.528544\pi$
$390$	−6.29597	−0.318809
$391$	0.571472	0.0289006
$392$	51.6416	2.60829
$393$	2.17900	0.109916
$394$	37.7962	1.90414
$395$	−17.8786	−0.899568
$396$	43.7955	2.20081
$397$	11.5982	0.582098	0.291049	−	0.956708i	$-0.405996\pi$
$397$	11.5982	0.582098	0.291049	+	0.956708i	$0.405996\pi$
$398$	43.7390	2.19244
$399$	−0.186233	−0.00932331
$400$	−15.1477	−0.757385
$401$	27.6953	1.38303	0.691517	−	0.722360i	$-0.256943\pi$
$401$	27.6953	1.38303	0.691517	+	0.722360i	$0.256943\pi$
$402$	−6.10822	−0.304651
$403$	40.9343	2.03908
$404$	−19.4174	−0.966051
$405$	−15.6894	−0.779613
$406$	0.221259	0.0109809
$407$	24.3356	1.20627
$408$	−1.46784	−0.0726689
$409$	11.6834	0.577705	0.288852	−	0.957374i	$-0.406726\pi$
$409$	11.6834	0.577705	0.288852	+	0.957374i	$0.406726\pi$
$410$	48.4544	2.39299
$411$	0.191593	0.00945057
$412$	64.8311	3.19400
$413$	−0.0909201	−0.00447389
$414$	−5.56780	−0.273642
$415$	−4.47877	−0.219854
$416$	−55.6485	−2.72839
$417$	−4.66896	−0.228640
$418$	−23.2285	−1.13614
$419$	−0.701004	−0.0342463	−0.0171231	−	0.999853i	$-0.505451\pi$
$419$	−0.701004	−0.0342463	−0.0171231	+	0.999853i	$0.505451\pi$
$420$	−0.581237	−0.0283615
$421$	−14.3105	−0.697453	−0.348726	−	0.937225i	$-0.613386\pi$
$421$	−14.3105	−0.697453	−0.348726	+	0.937225i	$0.613386\pi$
$422$	−19.4842	−0.948478
$423$	19.0692	0.927175
$424$	−15.6907	−0.762007
$425$	1.21991	0.0591745
$426$	−3.24210	−0.157080
$427$	0.257446	0.0124587
$428$	−15.5935	−0.753742
$429$	3.98273	0.192288
$430$	27.6999	1.33581
$431$	4.83209	0.232754	0.116377	−	0.993205i	$-0.462872\pi$
$431$	4.83209	0.232754	0.116377	+	0.993205i	$0.462872\pi$
$432$	14.5293	0.699043
$433$	−17.6678	−0.849059	−0.424529	−	0.905414i	$-0.639560\pi$
$433$	−17.6678	−0.849059	−0.424529	+	0.905414i	$0.639560\pi$
$434$	5.33847	0.256255
$435$	0.151944	0.00728515
$436$	66.4579	3.18275
$437$	2.09043	0.0999989
$438$	3.08902	0.147599
$439$	6.03702	0.288131	0.144066	−	0.989568i	$-0.453982\pi$
$439$	6.03702	0.288131	0.144066	+	0.989568i	$0.453982\pi$
$440$	−42.5801	−2.02992
$441$	20.3672	0.969865
$442$	10.7001	0.508950
$443$	−14.8072	−0.703509	−0.351755	−	0.936092i	$-0.614415\pi$
$443$	−14.8072	−0.703509	−0.351755	+	0.936092i	$0.614415\pi$
$444$	9.57749	0.454528
$445$	2.04414	0.0969014
$446$	−13.8184	−0.654322
$447$	−5.78901	−0.273811
$448$	−2.19582	−0.103743
$449$	−17.0534	−0.804801	−0.402401	−	0.915464i	$-0.631824\pi$
$449$	−17.0534	−0.804801	−0.402401	+	0.915464i	$0.631824\pi$
$450$	−11.8855	−0.560287
$451$	−30.6515	−1.44332
$452$	−20.4442	−0.961612
$453$	−2.53757	−0.119226
$454$	19.6912	0.924153
$455$	2.48857	0.116666
$456$	−5.36932	−0.251442
$457$	1.60844	0.0752397	0.0376199	−	0.999292i	$-0.488022\pi$
$457$	1.60844	0.0752397	0.0376199	+	0.999292i	$0.488022\pi$
$458$	70.0639	3.27387
$459$	−1.17011	−0.0546162
$460$	6.52429	0.304196
$461$	18.1695	0.846236	0.423118	−	0.906075i	$-0.360936\pi$
$461$	18.1695	0.846236	0.423118	+	0.906075i	$0.360936\pi$
$462$	0.519410	0.0241651
$463$	−2.96938	−0.137999	−0.0689994	−	0.997617i	$-0.521981\pi$
$463$	−2.96938	−0.137999	−0.0689994	+	0.997617i	$0.521981\pi$
$464$	3.20646	0.148856
$465$	3.66605	0.170009
$466$	7.29476	0.337923
$467$	35.6162	1.64812	0.824060	−	0.566503i	$-0.191704\pi$
$467$	35.6162	1.64812	0.824060	+	0.566503i	$0.191704\pi$
$468$	−73.7967	−3.41125
$469$	2.41436	0.111485
$470$	−31.5660	−1.45603
$471$	1.49242	0.0687669
$472$	−2.62134	−0.120657
$473$	−17.5225	−0.805687
$474$	6.28782	0.288809
$475$	4.46241	0.204750
$476$	0.987820	0.0452767
$477$	−6.18833	−0.283344
$478$	−3.67477	−0.168080
$479$	7.40675	0.338423	0.169212	−	0.985580i	$-0.445878\pi$
$479$	7.40675	0.338423	0.169212	+	0.985580i	$0.445878\pi$
$480$	−4.98385	−0.227481
$481$	−41.0061	−1.86972
$482$	−26.9048	−1.22548
$483$	−0.0467440	−0.00212693
$484$	−7.45224	−0.338738
$485$	−19.6354	−0.891600
$486$	17.1603	0.778409
$487$	−5.65158	−0.256098	−0.128049	−	0.991768i	$-0.540871\pi$
$487$	−5.65158	−0.256098	−0.128049	+	0.991768i	$0.540871\pi$
$488$	7.42248	0.336000
$489$	−1.44155	−0.0651894
$490$	−33.7146	−1.52307
$491$	−43.6690	−1.97075	−0.985377	−	0.170388i	$-0.945498\pi$
$491$	−43.6690	−1.97075	−0.985377	+	0.170388i	$0.945498\pi$
$492$	−12.0632	−0.543851
$493$	−0.258230	−0.0116301
$494$	39.1406	1.76102
$495$	−16.7934	−0.754805
$496$	77.3643	3.47376
$497$	1.28149	0.0574826
$498$	1.57516	0.0705848
$499$	−17.5218	−0.784385	−0.392193	−	0.919883i	$-0.628283\pi$
$499$	−17.5218	−0.784385	−0.392193	+	0.919883i	$0.628283\pi$
$500$	58.9623	2.63687
$501$	4.40449	0.196778
$502$	24.8505	1.10913
$503$	−8.54402	−0.380959	−0.190479	−	0.981691i	$-0.561004\pi$
$503$	−8.54402	−0.380959	−0.190479	+	0.981691i	$0.561004\pi$
$504$	−5.65268	−0.251791
$505$	7.44558	0.331324
$506$	−5.83029	−0.259188
$507$	−3.46375	−0.153831
$508$	36.0218	1.59821
$509$	6.00888	0.266339	0.133169	−	0.991093i	$-0.457485\pi$
$509$	6.00888	0.266339	0.133169	+	0.991093i	$0.457485\pi$
$510$	0.958292	0.0424339
$511$	−1.22098	−0.0540130
$512$	40.7589	1.80131
$513$	−4.28025	−0.188978
$514$	11.7279	0.517296
$515$	−24.8594	−1.09544
$516$	−6.89616	−0.303586
$517$	19.9682	0.878200
$518$	−5.34783	−0.234970
$519$	2.66824	0.117123
$520$	71.7486	3.14638
$521$	−32.1965	−1.41055	−0.705277	−	0.708932i	$-0.749177\pi$
$521$	−32.1965	−1.41055	−0.705277	+	0.708932i	$0.749177\pi$
$522$	2.51591	0.110119
$523$	−3.34443	−0.146242	−0.0731208	−	0.997323i	$-0.523296\pi$
$523$	−3.34443	−0.146242	−0.0731208	+	0.997323i	$0.523296\pi$
$524$	−42.2785	−1.84694
$525$	−0.0997837	−0.00435492
$526$	−48.9878	−2.13597
$527$	−6.23050	−0.271405
$528$	7.52722	0.327580
$529$	−22.4753	−0.977187
$530$	10.2438	0.444962
$531$	−1.03384	−0.0448649
$532$	3.61342	0.156662
$533$	51.6487	2.23715
$534$	−0.718914	−0.0311105
$535$	5.97933	0.258509
$536$	69.6091	3.00665
$537$	1.79745	0.0775658
$538$	54.0276	2.32929
$539$	21.3274	0.918635
$540$	−13.3587	−0.574869
$541$	−38.3396	−1.64835	−0.824174	−	0.566337i	$-0.808360\pi$
$541$	−38.3396	−1.64835	−0.824174	+	0.566337i	$0.808360\pi$
$542$	−8.92241	−0.383250
$543$	−0.241140	−0.0103483
$544$	8.47011	0.363153
$545$	−25.4832	−1.09158
$546$	−0.875220	−0.0374560
$547$	−17.0400	−0.728578	−0.364289	−	0.931286i	$-0.618688\pi$
$547$	−17.0400	−0.728578	−0.364289	+	0.931286i	$0.618688\pi$
$548$	−3.71742	−0.158800
$549$	2.92739	0.124938
$550$	−12.4458	−0.530692
$551$	−0.944601	−0.0402414
$552$	−1.34769	−0.0573614
$553$	−2.48535	−0.105688
$554$	−46.4696	−1.97430
$555$	−3.67248	−0.155888
$556$	90.5904	3.84189
$557$	18.6099	0.788527	0.394263	−	0.918997i	$-0.371000\pi$
$557$	18.6099	0.788527	0.394263	+	0.918997i	$0.371000\pi$
$558$	60.7031	2.56977
$559$	29.5259	1.24881
$560$	4.70331	0.198751
$561$	−0.606201	−0.0255938
$562$	63.2636	2.66862
$563$	−5.43630	−0.229113	−0.114556	−	0.993417i	$-0.536545\pi$
$563$	−5.43630	−0.229113	−0.114556	+	0.993417i	$0.536545\pi$
$564$	7.85867	0.330910
$565$	7.83929	0.329802
$566$	−24.6249	−1.03506
$567$	−2.18103	−0.0915947
$568$	36.9468	1.55026
$569$	3.40765	0.142856	0.0714280	−	0.997446i	$-0.477244\pi$
$569$	3.40765	0.142856	0.0714280	+	0.997446i	$0.477244\pi$
$570$	3.50541	0.146825
$571$	−30.4461	−1.27413	−0.637065	−	0.770810i	$-0.719852\pi$
$571$	−30.4461	−1.27413	−0.637065	+	0.770810i	$0.719852\pi$
$572$	−77.2758	−3.23106
$573$	1.66316	0.0694796
$574$	6.73579	0.281146
$575$	1.12005	0.0467095
$576$	−24.9684	−1.04035
$577$	−6.31950	−0.263084	−0.131542	−	0.991311i	$-0.541993\pi$
$577$	−6.31950	−0.263084	−0.131542	+	0.991311i	$0.541993\pi$
$578$	42.8536	1.78247
$579$	−1.45253	−0.0603651
$580$	−2.94812	−0.122414
$581$	−0.622606	−0.0258301
$582$	6.90571	0.286251
$583$	−6.48007	−0.268377
$584$	−35.2024	−1.45669
$585$	28.2973	1.16995
$586$	−50.2097	−2.07414
$587$	−17.7839	−0.734021	−0.367011	−	0.930217i	$-0.619619\pi$
$587$	−17.7839	−0.734021	−0.367011	+	0.930217i	$0.619619\pi$
$588$	8.39359	0.346146
$589$	−22.7910	−0.939088
$590$	1.71136	0.0704557
$591$	3.60815	0.148419
$592$	−77.5000	−3.18523
$593$	5.72998	0.235302	0.117651	−	0.993055i	$-0.462464\pi$
$593$	5.72998	0.235302	0.117651	+	0.993055i	$0.462464\pi$
$594$	11.9378	0.489812
$595$	−0.378779	−0.0155284
$596$	112.322	4.60091
$597$	4.17548	0.170891
$598$	9.82419	0.401741
$599$	−35.9957	−1.47074	−0.735372	−	0.677663i	$-0.762993\pi$
$599$	−35.9957	−1.47074	−0.735372	+	0.677663i	$0.762993\pi$
$600$	−2.87689	−0.117448
$601$	−15.9722	−0.651522	−0.325761	−	0.945452i	$-0.605620\pi$
$601$	−15.9722	−0.651522	−0.325761	+	0.945452i	$0.605620\pi$
$602$	3.85064	0.156940
$603$	27.4535	1.11799
$604$	49.2358	2.00337
$605$	2.85755	0.116176
$606$	−2.61858	−0.106373
$607$	−10.7514	−0.436384	−0.218192	−	0.975906i	$-0.570016\pi$
$607$	−10.7514	−0.436384	−0.218192	+	0.975906i	$0.570016\pi$
$608$	30.9835	1.25655
$609$	0.0211222	0.000855913 0
$610$	−4.84583	−0.196202
$611$	−33.6469	−1.36121
$612$	11.2324	0.454042
$613$	2.06699	0.0834850	0.0417425	−	0.999128i	$-0.486709\pi$
$613$	2.06699	0.0834850	0.0417425	+	0.999128i	$0.486709\pi$
$614$	−12.3768	−0.499487
$615$	4.62562	0.186523
$616$	−5.91918	−0.238490
$617$	29.6394	1.19324	0.596619	−	0.802525i	$-0.296510\pi$
$617$	29.6394	1.19324	0.596619	+	0.802525i	$0.296510\pi$
$618$	8.74296	0.351693
$619$	−3.72750	−0.149821	−0.0749105	−	0.997190i	$-0.523867\pi$
$619$	−3.72750	−0.149821	−0.0749105	+	0.997190i	$0.523867\pi$
$620$	−71.1313	−2.85670
$621$	−1.07433	−0.0431114
$622$	−22.4390	−0.899723
$623$	0.284161	0.0113847
$624$	−12.6836	−0.507749
$625$	−14.8777	−0.595107
$626$	−9.26326	−0.370234
$627$	−2.21747	−0.0885572
$628$	−28.9569	−1.15551
$629$	6.24143	0.248862
$630$	3.69040	0.147029
$631$	−8.17381	−0.325394	−0.162697	−	0.986676i	$-0.552019\pi$
$631$	−8.17381	−0.325394	−0.162697	+	0.986676i	$0.552019\pi$
$632$	−71.6557	−2.85031
$633$	−1.86003	−0.0739296
$634$	−39.7272	−1.57777
$635$	−13.8125	−0.548133
$636$	−2.55029	−0.101126
$637$	−35.9372	−1.42388
$638$	2.63452	0.104302
$639$	14.5716	0.576445
$640$	1.42681	0.0563994
$641$	−36.2961	−1.43361	−0.716805	−	0.697273i	$-0.754396\pi$
$641$	−36.2961	−1.43361	−0.716805	+	0.697273i	$0.754396\pi$
$642$	−2.10290	−0.0829950
$643$	−46.7626	−1.84414	−0.922069	−	0.387025i	$-0.873503\pi$
$643$	−46.7626	−1.84414	−0.922069	+	0.387025i	$0.873503\pi$
$644$	0.906960	0.0357392
$645$	2.64432	0.104120
$646$	−5.95748	−0.234394
$647$	16.7151	0.657138	0.328569	−	0.944480i	$-0.393434\pi$
$647$	16.7151	0.657138	0.328569	+	0.944480i	$0.393434\pi$
$648$	−62.8818	−2.47023
$649$	−1.08258	−0.0424951
$650$	20.9716	0.822572
$651$	0.509629	0.0199739
$652$	27.9701	1.09539
$653$	−27.4429	−1.07392	−0.536962	−	0.843606i	$-0.680428\pi$
$653$	−27.4429	−1.07392	−0.536962	+	0.843606i	$0.680428\pi$
$654$	8.96234	0.350455
$655$	16.2116	0.633441
$656$	97.6140	3.81119
$657$	−13.8836	−0.541653
$658$	−4.38808	−0.171065
$659$	−2.22469	−0.0866616	−0.0433308	−	0.999061i	$-0.513797\pi$
$659$	−2.22469	−0.0866616	−0.0433308	+	0.999061i	$0.513797\pi$
$660$	−6.92077	−0.269391
$661$	−10.4020	−0.404590	−0.202295	−	0.979325i	$-0.564840\pi$
$661$	−10.4020	−0.404590	−0.202295	+	0.979325i	$0.564840\pi$
$662$	4.15130	0.161345
$663$	1.02147	0.0396704
$664$	−17.9505	−0.696614
$665$	−1.38556	−0.0537298
$666$	−60.8096	−2.35632
$667$	−0.237092	−0.00918026
$668$	−85.4591	−3.30651
$669$	−1.31915	−0.0510015
$670$	−45.4449	−1.75569
$671$	3.06540	0.118338
$672$	−0.692819	−0.0267261
$673$	15.4057	0.593845	0.296922	−	0.954902i	$-0.404040\pi$
$673$	15.4057	0.593845	0.296922	+	0.954902i	$0.404040\pi$
$674$	37.5846	1.44771
$675$	−2.29336	−0.0882714
$676$	67.2062	2.58485
$677$	−27.7796	−1.06766	−0.533828	−	0.845593i	$-0.679247\pi$
$677$	−27.7796	−1.06766	−0.533828	+	0.845593i	$0.679247\pi$
$678$	−2.75705	−0.105884
$679$	−2.72958	−0.104752
$680$	−10.9207	−0.418788
$681$	1.87979	0.0720336
$682$	63.5650	2.43403
$683$	44.0353	1.68497	0.842483	−	0.538724i	$-0.181093\pi$
$683$	44.0353	1.68497	0.842483	+	0.538724i	$0.181093\pi$
$684$	41.0878	1.57103
$685$	1.42544	0.0544633
$686$	−9.41866	−0.359606
$687$	6.68854	0.255184
$688$	55.8029	2.12747
$689$	10.9191	0.415985
$690$	0.879849	0.0334953
$691$	−12.9255	−0.491708	−0.245854	−	0.969307i	$-0.579068\pi$
$691$	−12.9255	−0.491708	−0.245854	+	0.969307i	$0.579068\pi$
$692$	−51.7710	−1.96804
$693$	−2.33449	−0.0886801
$694$	−35.2552	−1.33827
$695$	−34.7368	−1.31764
$696$	0.608978	0.0230832
$697$	−7.86130	−0.297768
$698$	−27.5271	−1.04192
$699$	0.696383	0.0263396
$700$	1.93607	0.0731767
$701$	43.0745	1.62690	0.813451	−	0.581634i	$-0.197586\pi$
$701$	43.0745	1.62690	0.813451	+	0.581634i	$0.197586\pi$
$702$	−20.1154	−0.759209
$703$	22.8310	0.861087
$704$	−26.1455	−0.985396
$705$	−3.01340	−0.113491
$706$	−38.4805	−1.44823
$707$	1.03503	0.0389264
$708$	−0.426060	−0.0160123
$709$	1.16876	0.0438936	0.0219468	−	0.999759i	$-0.493014\pi$
$709$	1.16876	0.0438936	0.0219468	+	0.999759i	$0.493014\pi$
$710$	−24.1211	−0.905247
$711$	−28.2606	−1.05986
$712$	8.19272	0.307035
$713$	−5.72049	−0.214234
$714$	0.133215	0.00498544
$715$	29.6313	1.10815
$716$	−34.8754	−1.30336
$717$	−0.350806	−0.0131011
$718$	−36.1957	−1.35081
$719$	22.6717	0.845511	0.422755	−	0.906244i	$-0.361063\pi$
$719$	22.6717	0.845511	0.422755	+	0.906244i	$0.361063\pi$
$720$	53.4808	1.99311
$721$	−3.45578	−0.128700
$722$	27.9230	1.03919
$723$	−2.56842	−0.0955206
$724$	4.67877	0.173885
$725$	−0.506117	−0.0187967
$726$	−1.00499	−0.0372987
$727$	25.7359	0.954490	0.477245	−	0.878770i	$-0.341635\pi$
$727$	25.7359	0.954490	0.477245	+	0.878770i	$0.341635\pi$
$728$	9.97398	0.369660
$729$	−23.6888	−0.877364
$730$	22.9822	0.850609
$731$	−4.49406	−0.166219
$732$	1.20642	0.0445904
$733$	−35.6649	−1.31731	−0.658656	−	0.752444i	$-0.728875\pi$
$733$	−35.6649	−1.31731	−0.658656	+	0.752444i	$0.728875\pi$
$734$	−54.8199	−2.02344
$735$	−3.21851	−0.118717
$736$	7.77677	0.286656
$737$	28.7477	1.05894
$738$	76.5919	2.81939
$739$	8.02712	0.295282	0.147641	−	0.989041i	$-0.452832\pi$
$739$	8.02712	0.295282	0.147641	+	0.989041i	$0.452832\pi$
$740$	71.2560	2.61942
$741$	3.73650	0.137264
$742$	1.42402	0.0522774
$743$	10.2758	0.376982	0.188491	−	0.982075i	$-0.439640\pi$
$743$	10.2758	0.376982	0.188491	+	0.982075i	$0.439640\pi$
$744$	14.6932	0.538679
$745$	−43.0699	−1.57796
$746$	−2.87198	−0.105150
$747$	−7.07958	−0.259028
$748$	11.7619	0.430059
$749$	0.831204	0.0303715
$750$	7.95151	0.290348
$751$	17.4127	0.635397	0.317699	−	0.948192i	$-0.397090\pi$
$751$	17.4127	0.635397	0.317699	+	0.948192i	$0.397090\pi$
$752$	−63.5914	−2.31894
$753$	2.37231	0.0864519
$754$	−4.43925	−0.161668
$755$	−18.8794	−0.687092
$756$	−1.85704	−0.0675398
$757$	−0.646357	−0.0234923	−0.0117461	−	0.999931i	$-0.503739\pi$
$757$	−0.646357	−0.0234923	−0.0117461	+	0.999931i	$0.503739\pi$
$758$	74.7068	2.71347
$759$	−0.556579	−0.0202025
$760$	−39.9475	−1.44905
$761$	21.4923	0.779095	0.389548	−	0.921006i	$-0.372631\pi$
$761$	21.4923	0.779095	0.389548	+	0.921006i	$0.372631\pi$
$762$	4.85781	0.175980
$763$	−3.54249	−0.128247
$764$	−32.2698	−1.16748
$765$	−4.30705	−0.155722
$766$	−36.0146	−1.30126
$767$	1.82418	0.0658673
$768$	3.74440	0.135115
$769$	−31.8582	−1.14884	−0.574419	−	0.818562i	$-0.694772\pi$
$769$	−31.8582	−1.14884	−0.574419	+	0.818562i	$0.694772\pi$
$770$	3.86438	0.139263
$771$	1.11959	0.0403209
$772$	28.1830	1.01433
$773$	17.6929	0.636369	0.318184	−	0.948029i	$-0.396927\pi$
$773$	17.6929	0.636369	0.318184	+	0.948029i	$0.396927\pi$
$774$	43.7852	1.57383
$775$	−12.2114	−0.438648
$776$	−78.6971	−2.82506
$777$	−0.510522	−0.0183149
$778$	9.24323	0.331386
$779$	−28.7565	−1.03031
$780$	11.6617	0.417555
$781$	15.2586	0.545996
$782$	−1.49531	−0.0534723
$783$	0.485457	0.0173488
$784$	−67.9200	−2.42571
$785$	11.1035	0.396301
$786$	−5.70157	−0.203368
$787$	−7.76715	−0.276869	−0.138434	−	0.990372i	$-0.544207\pi$
$787$	−7.76715	−0.276869	−0.138434	+	0.990372i	$0.544207\pi$
$788$	−70.0079	−2.49393
$789$	−4.67654	−0.166489
$790$	46.7810	1.66439
$791$	1.08976	0.0387475
$792$	−67.3063	−2.39162
$793$	−5.16528	−0.183424
$794$	−30.3479	−1.07701
$795$	0.977908	0.0346828
$796$	−81.0155	−2.87152
$797$	22.3858	0.792946	0.396473	−	0.918046i	$-0.370234\pi$
$797$	22.3858	0.792946	0.396473	+	0.918046i	$0.370234\pi$
$798$	0.487297	0.0172501
$799$	5.12131	0.181179
$800$	16.6010	0.586932
$801$	3.23117	0.114168
$802$	−72.4674	−2.55891
$803$	−14.5382	−0.513041
$804$	11.3139	0.399012
$805$	−0.347773	−0.0122574
$806$	−107.109	−3.77274
$807$	5.15766	0.181558
$808$	29.8412	1.04981
$809$	20.5675	0.723115	0.361557	−	0.932350i	$-0.382245\pi$
$809$	20.5675	0.723115	0.361557	+	0.932350i	$0.382245\pi$
$810$	41.0529	1.44245
$811$	−34.4629	−1.21016	−0.605079	−	0.796166i	$-0.706858\pi$
$811$	−34.4629	−1.21016	−0.605079	+	0.796166i	$0.706858\pi$
$812$	−0.409827	−0.0143821
$813$	−0.851764	−0.0298727
$814$	−63.6764	−2.23186
$815$	−10.7251	−0.375684
$816$	1.93053	0.0675821
$817$	−16.4392	−0.575134
$818$	−30.5706	−1.06888
$819$	3.93369	0.137454
$820$	−89.7495	−3.13419
$821$	−44.4198	−1.55026	−0.775131	−	0.631801i	$-0.782316\pi$
$821$	−44.4198	−1.55026	−0.775131	+	0.631801i	$0.782316\pi$
$822$	−0.501321	−0.0174856
$823$	−4.73934	−0.165203	−0.0826015	−	0.996583i	$-0.526323\pi$
$823$	−4.73934	−0.165203	−0.0826015	+	0.996583i	$0.526323\pi$
$824$	−99.6344	−3.47093
$825$	−1.18812	−0.0413650
$826$	0.237901	0.00827765
$827$	32.5114	1.13053	0.565265	−	0.824909i	$-0.308774\pi$
$827$	32.5114	1.13053	0.565265	+	0.824909i	$0.308774\pi$
$828$	10.3129	0.358399
$829$	1.54696	0.0537283	0.0268641	−	0.999639i	$-0.491448\pi$
$829$	1.54696	0.0537283	0.0268641	+	0.999639i	$0.491448\pi$
$830$	11.7191	0.406777
$831$	−4.43615	−0.153888
$832$	44.0559	1.52736
$833$	5.46991	0.189521
$834$	12.2168	0.423033
$835$	32.7692	1.13403
$836$	43.0249	1.48805
$837$	11.7129	0.404859
$838$	1.83425	0.0633629
$839$	−12.4560	−0.430028	−0.215014	−	0.976611i	$-0.568980\pi$
$839$	−12.4560	−0.430028	−0.215014	+	0.976611i	$0.568980\pi$
$840$	0.893263	0.0308205
$841$	−28.8929	−0.996306
$842$	37.4449	1.29044
$843$	6.03936	0.208007
$844$	36.0896	1.24226
$845$	−25.7701	−0.886520
$846$	−49.8964	−1.71547
$847$	0.397237	0.0136492
$848$	20.6367	0.708667
$849$	−2.35078	−0.0806784
$850$	−3.19202	−0.109485
$851$	5.73052	0.196440
$852$	6.00517	0.205734
$853$	37.5207	1.28469	0.642343	−	0.766417i	$-0.277963\pi$
$853$	37.5207	1.28469	0.642343	+	0.766417i	$0.277963\pi$
$854$	−0.673633	−0.0230512
$855$	−15.7551	−0.538813
$856$	23.9646	0.819094
$857$	−39.7815	−1.35891	−0.679455	−	0.733717i	$-0.737784\pi$
$857$	−39.7815	−1.35891	−0.679455	+	0.733717i	$0.737784\pi$
$858$	−10.4212	−0.355774
$859$	−52.3428	−1.78591	−0.892956	−	0.450144i	$-0.851373\pi$
$859$	−52.3428	−1.78591	−0.892956	+	0.450144i	$0.851373\pi$
$860$	−51.3070	−1.74956
$861$	0.643021	0.0219141
$862$	−12.6436	−0.430644
$863$	−39.4114	−1.34158	−0.670789	−	0.741648i	$-0.734045\pi$
$863$	−39.4114	−1.34158	−0.670789	+	0.741648i	$0.734045\pi$
$864$	−15.9233	−0.541721
$865$	19.8516	0.674973
$866$	46.2295	1.57094
$867$	4.09095	0.138936
$868$	−9.88817	−0.335626
$869$	−29.5930	−1.00387
$870$	−0.397576	−0.0134791
$871$	−48.4407	−1.64135
$872$	−102.134	−3.45871
$873$	−31.0377	−1.05047
$874$	−5.46982	−0.185020
$875$	−3.14295	−0.106251
$876$	−5.72164	−0.193316
$877$	−14.9376	−0.504405	−0.252203	−	0.967674i	$-0.581155\pi$
$877$	−14.9376	−0.504405	−0.252203	+	0.967674i	$0.581155\pi$
$878$	−15.7965	−0.533105
$879$	−4.79319	−0.161670
$880$	56.0021	1.88783
$881$	−19.1465	−0.645063	−0.322531	−	0.946559i	$-0.604534\pi$
$881$	−19.1465	−0.645063	−0.322531	+	0.946559i	$0.604534\pi$
$882$	−53.2927	−1.79446
$883$	53.1198	1.78762	0.893811	−	0.448443i	$-0.148021\pi$
$883$	53.1198	1.78762	0.893811	+	0.448443i	$0.148021\pi$
$884$	−19.8192	−0.666591
$885$	0.163372	0.00549171
$886$	38.7444	1.30164
$887$	−19.8129	−0.665253	−0.332626	−	0.943059i	$-0.607935\pi$
$887$	−19.8129	−0.665253	−0.332626	+	0.943059i	$0.607935\pi$
$888$	−14.7190	−0.493937
$889$	−1.92012	−0.0643987
$890$	−5.34869	−0.179288
$891$	−25.9695	−0.870010
$892$	25.5952	0.856989
$893$	18.7336	0.626897
$894$	15.1475	0.506609
$895$	13.3730	0.447009
$896$	0.198344	0.00662622
$897$	0.937851	0.0313139
$898$	44.6220	1.48906
$899$	2.58491	0.0862116
$900$	22.0149	0.733829
$901$	−1.66197	−0.0553681
$902$	80.2027	2.67046
$903$	0.367595	0.0122328
$904$	31.4192	1.04499
$905$	−1.79407	−0.0596368
$906$	6.63981	0.220593
$907$	−32.5030	−1.07925	−0.539623	−	0.841907i	$-0.681433\pi$
$907$	−32.5030	−1.07925	−0.539623	+	0.841907i	$0.681433\pi$
$908$	−36.4730	−1.21040
$909$	11.7692	0.390361
$910$	−6.51159	−0.215857
$911$	−8.75619	−0.290106	−0.145053	−	0.989424i	$-0.546335\pi$
$911$	−8.75619	−0.290106	−0.145053	+	0.989424i	$0.546335\pi$
$912$	7.06184	0.233841
$913$	−7.41335	−0.245346
$914$	−4.20865	−0.139210
$915$	−0.462599	−0.0152931
$916$	−129.776	−4.28791
$917$	2.25363	0.0744213
$918$	3.06172	0.101052
$919$	23.7203	0.782459	0.391230	−	0.920293i	$-0.372050\pi$
$919$	23.7203	0.782459	0.391230	+	0.920293i	$0.372050\pi$
$920$	−10.0267	−0.330571
$921$	−1.18153	−0.0389328
$922$	−47.5422	−1.56572
$923$	−25.7112	−0.846294
$924$	−0.962076	−0.0316500
$925$	12.2329	0.402214
$926$	7.76968	0.255328
$927$	−39.2953	−1.29063
$928$	−3.51408	−0.115355
$929$	−16.6959	−0.547775	−0.273887	−	0.961762i	$-0.588310\pi$
$929$	−16.6959	−0.547775	−0.273887	+	0.961762i	$0.588310\pi$
$930$	−9.59259	−0.314553
$931$	20.0088	0.655761
$932$	−13.5117	−0.442591
$933$	−2.14211	−0.0701294
$934$	−93.1932	−3.04937
$935$	−4.51010	−0.147496
$936$	113.413	3.70702
$937$	−15.9829	−0.522140	−0.261070	−	0.965320i	$-0.584075\pi$
$937$	−15.9829	−0.522140	−0.261070	+	0.965320i	$0.584075\pi$
$938$	−6.31742	−0.206271
$939$	−0.884302	−0.0288581
$940$	58.4681	1.90702
$941$	−55.5241	−1.81003	−0.905017	−	0.425376i	$-0.860142\pi$
$941$	−55.5241	−1.81003	−0.905017	+	0.425376i	$0.860142\pi$
$942$	−3.90505	−0.127234
$943$	−7.21780	−0.235044
$944$	3.44763	0.112211
$945$	0.712080	0.0231639
$946$	45.8494	1.49069
$947$	−12.5338	−0.407295	−0.203647	−	0.979044i	$-0.565280\pi$
$947$	−12.5338	−0.407295	−0.203647	+	0.979044i	$0.565280\pi$
$948$	−11.6466	−0.378264
$949$	24.4972	0.795214
$950$	−11.6763	−0.378831
$951$	−3.79250	−0.122980
$952$	−1.51811	−0.0492023
$953$	16.6151	0.538216	0.269108	−	0.963110i	$-0.413271\pi$
$953$	16.6151	0.538216	0.269108	+	0.963110i	$0.413271\pi$
$954$	16.1924	0.524247
$955$	12.3738	0.400408
$956$	6.80658	0.220141
$957$	0.251501	0.00812986
$958$	−19.3805	−0.626155
$959$	0.198155	0.00639874
$960$	3.94562	0.127344
$961$	31.3679	1.01187
$962$	107.297	3.45938
$963$	9.45152	0.304571
$964$	49.8343	1.60505
$965$	−10.8068	−0.347882
$966$	0.122310	0.00393527
$967$	18.0476	0.580371	0.290186	−	0.956970i	$-0.406283\pi$
$967$	18.0476	0.580371	0.290186	+	0.956970i	$0.406283\pi$
$968$	11.4528	0.368108
$969$	−0.568722	−0.0182700
$970$	51.3781	1.64965
$971$	1.06174	0.0340727	0.0170364	−	0.999855i	$-0.494577\pi$
$971$	1.06174	0.0340727	0.0170364	+	0.999855i	$0.494577\pi$
$972$	−31.7852	−1.01951
$973$	−4.82886	−0.154806
$974$	14.7879	0.473836
$975$	2.00202	0.0641158
$976$	−9.76218	−0.312480
$977$	10.3087	0.329804	0.164902	−	0.986310i	$-0.447269\pi$
$977$	10.3087	0.329804	0.164902	+	0.986310i	$0.447269\pi$
$978$	3.77197	0.120614
$979$	3.38350	0.108137
$980$	62.4479	1.99482
$981$	−40.2813	−1.28608
$982$	114.264	3.64632
$983$	−41.6046	−1.32698	−0.663491	−	0.748184i	$-0.730926\pi$
$983$	−41.6046	−1.32698	−0.663491	+	0.748184i	$0.730926\pi$
$984$	18.5391	0.591004
$985$	26.8445	0.855335
$986$	0.675685	0.0215182
$987$	−0.418901	−0.0133338
$988$	−72.4981	−2.30647
$989$	−4.12619	−0.131205
$990$	43.9415	1.39655
$991$	0.180336	0.00572856	0.00286428	−	0.999996i	$-0.499088\pi$
$991$	0.180336	0.00572856	0.00286428	+	0.999996i	$0.499088\pi$
$992$	−84.7866	−2.69198
$993$	0.396298	0.0125761
$994$	−3.35314	−0.106355
$995$	31.0653	0.984837
$996$	−2.91759	−0.0924475
$997$	10.2025	0.323116	0.161558	−	0.986863i	$-0.448348\pi$
$997$	10.2025	0.323116	0.161558	+	0.986863i	$0.448348\pi$
$998$	45.8476	1.45128
$999$	−11.7335	−0.371231

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.a.1.16	✓	309

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.a.1.16	✓	309	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:	\( N \)	\(=\)	\( 8011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61660 q^{2} -0.249789 q^{3} +4.84659 q^{4} -1.85842 q^{5} +0.653599 q^{6} -0.258344 q^{7} -7.44839 q^{8} -2.93761 q^{9} +O(q^{10})\)	\(q-2.61660 q^{2} -0.249789 q^{3} +4.84659 q^{4} -1.85842 q^{5} +0.653599 q^{6} -0.258344 q^{7} -7.44839 q^{8} -2.93761 q^{9} +4.86274 q^{10} -3.07610 q^{11} -1.21063 q^{12} +5.18331 q^{13} +0.675984 q^{14} +0.464214 q^{15} +9.79626 q^{16} -0.788937 q^{17} +7.68653 q^{18} -2.88591 q^{19} -9.00700 q^{20} +0.0645317 q^{21} +8.04891 q^{22} -0.724357 q^{23} +1.86053 q^{24} -1.54627 q^{25} -13.5626 q^{26} +1.48315 q^{27} -1.25209 q^{28} +0.327314 q^{29} -1.21466 q^{30} +7.89734 q^{31} -10.7361 q^{32} +0.768377 q^{33} +2.06433 q^{34} +0.480113 q^{35} -14.2374 q^{36} -7.91118 q^{37} +7.55128 q^{38} -1.29474 q^{39} +13.8422 q^{40} +9.96442 q^{41} -0.168854 q^{42} +5.69635 q^{43} -14.9086 q^{44} +5.45931 q^{45} +1.89535 q^{46} -6.49140 q^{47} -2.44700 q^{48} -6.93326 q^{49} +4.04598 q^{50} +0.197068 q^{51} +25.1214 q^{52} +2.10659 q^{53} -3.88081 q^{54} +5.71668 q^{55} +1.92425 q^{56} +0.720871 q^{57} -0.856450 q^{58} +0.351934 q^{59} +2.24985 q^{60} -0.996522 q^{61} -20.6642 q^{62} +0.758914 q^{63} +8.49957 q^{64} -9.63277 q^{65} -2.01053 q^{66} -9.34552 q^{67} -3.82366 q^{68} +0.180937 q^{69} -1.25626 q^{70} -4.96038 q^{71} +21.8804 q^{72} +4.72618 q^{73} +20.7004 q^{74} +0.386243 q^{75} -13.9868 q^{76} +0.794693 q^{77} +3.38780 q^{78} +9.62030 q^{79} -18.2056 q^{80} +8.44234 q^{81} -26.0729 q^{82} +2.40998 q^{83} +0.312759 q^{84} +1.46618 q^{85} -14.9051 q^{86} -0.0817597 q^{87} +22.9120 q^{88} -1.09993 q^{89} -14.2848 q^{90} -1.33908 q^{91} -3.51066 q^{92} -1.97267 q^{93} +16.9854 q^{94} +5.36324 q^{95} +2.68177 q^{96} +10.5657 q^{97} +18.1416 q^{98} +9.03636 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9} - 23 q^{10} - 72 q^{11} - 42 q^{12} - 57 q^{13} - 77 q^{14} - 44 q^{15} + 205 q^{16} - 86 q^{17} - 82 q^{18} - 58 q^{19} - 134 q^{20} - 123 q^{21} - 31 q^{22} - 94 q^{23} - 84 q^{24} + 225 q^{25} - 92 q^{26} - 48 q^{27} - 36 q^{28} - 345 q^{29} - 85 q^{30} - 36 q^{31} - 199 q^{32} - 56 q^{33} - 28 q^{34} - 168 q^{35} + 65 q^{36} - 79 q^{37} - 66 q^{38} - 145 q^{39} - 54 q^{40} - 176 q^{41} - 48 q^{42} - 58 q^{43} - 194 q^{44} - 192 q^{45} - 44 q^{46} - 82 q^{47} - 81 q^{48} + 186 q^{49} - 206 q^{50} - 145 q^{51} - 86 q^{52} - 223 q^{53} - 117 q^{54} - 58 q^{55} - 216 q^{56} - 124 q^{57} - 151 q^{59} - 91 q^{60} - 184 q^{61} - 124 q^{62} - 78 q^{63} + 101 q^{64} - 194 q^{65} - 112 q^{66} - 53 q^{67} - 182 q^{68} - 243 q^{69} - 193 q^{71} - 208 q^{72} - 69 q^{73} - 236 q^{74} - 62 q^{75} - 142 q^{76} - 324 q^{77} - 20 q^{78} - 91 q^{79} - 223 q^{80} - 27 q^{81} + 2 q^{82} - 117 q^{83} - 157 q^{84} - 171 q^{85} - 203 q^{86} - 69 q^{87} - 36 q^{88} - 172 q^{89} - 10 q^{90} - 84 q^{91} - 226 q^{92} - 220 q^{93} - 96 q^{94} - 166 q^{95} - 118 q^{96} - 12 q^{97} - 116 q^{98} - 154 q^{99}+O(q^{100}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9 - 23 * q^10 - 72 * q^11 - 42 * q^12 - 57 * q^13 - 77 * q^14 - 44 * q^15 + 205 * q^16 - 86 * q^17 - 82 * q^18 - 58 * q^19 - 134 * q^20 - 123 * q^21 - 31 * q^22 - 94 * q^23 - 84 * q^24 + 225 * q^25 - 92 * q^26 - 48 * q^27 - 36 * q^28 - 345 * q^29 - 85 * q^30 - 36 * q^31 - 199 * q^32 - 56 * q^33 - 28 * q^34 - 168 * q^35 + 65 * q^36 - 79 * q^37 - 66 * q^38 - 145 * q^39 - 54 * q^40 - 176 * q^41 - 48 * q^42 - 58 * q^43 - 194 * q^44 - 192 * q^45 - 44 * q^46 - 82 * q^47 - 81 * q^48 + 186 * q^49 - 206 * q^50 - 145 * q^51 - 86 * q^52 - 223 * q^53 - 117 * q^54 - 58 * q^55 - 216 * q^56 - 124 * q^57 - 151 * q^59 - 91 * q^60 - 184 * q^61 - 124 * q^62 - 78 * q^63 + 101 * q^64 - 194 * q^65 - 112 * q^66 - 53 * q^67 - 182 * q^68 - 243 * q^69 - 193 * q^71 - 208 * q^72 - 69 * q^73 - 236 * q^74 - 62 * q^75 - 142 * q^76 - 324 * q^77 - 20 * q^78 - 91 * q^79 - 223 * q^80 - 27 * q^81 + 2 * q^82 - 117 * q^83 - 157 * q^84 - 171 * q^85 - 203 * q^86 - 69 * q^87 - 36 * q^88 - 172 * q^89 - 10 * q^90 - 84 * q^91 - 226 * q^92 - 220 * q^93 - 96 * q^94 - 166 * q^95 - 118 * q^96 - 12 * q^97 - 116 * q^98 - 154 * q^99

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