LMFDB - Embedded newform 6011.2.a.e.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6011.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$47.9980766550$
Analytic rank:	$1$
Dimension:	$221$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52486 q^{2} +3.20374 q^{3} +4.37490 q^{4} -3.72596 q^{5} -8.08898 q^{6} -4.85825 q^{7} -5.99630 q^{8} +7.26393 q^{9} +O(q^{10})$	\(q-2.52486 q^{2} +3.20374 q^{3} +4.37490 q^{4} -3.72596 q^{5} -8.08898 q^{6} -4.85825 q^{7} -5.99630 q^{8} +7.26393 q^{9} +9.40752 q^{10} +1.44558 q^{11} +14.0160 q^{12} -0.222930 q^{13} +12.2664 q^{14} -11.9370 q^{15} +6.38998 q^{16} +0.523011 q^{17} -18.3404 q^{18} +0.0421204 q^{19} -16.3007 q^{20} -15.5646 q^{21} -3.64989 q^{22} -1.04369 q^{23} -19.2106 q^{24} +8.88278 q^{25} +0.562867 q^{26} +13.6605 q^{27} -21.2544 q^{28} +1.97327 q^{29} +30.1392 q^{30} -8.62827 q^{31} -4.14120 q^{32} +4.63126 q^{33} -1.32053 q^{34} +18.1016 q^{35} +31.7790 q^{36} +5.82204 q^{37} -0.106348 q^{38} -0.714210 q^{39} +22.3420 q^{40} +5.11644 q^{41} +39.2983 q^{42} +3.02160 q^{43} +6.32428 q^{44} -27.0651 q^{45} +2.63517 q^{46} +4.10292 q^{47} +20.4718 q^{48} +16.6026 q^{49} -22.4278 q^{50} +1.67559 q^{51} -0.975299 q^{52} +2.68171 q^{53} -34.4909 q^{54} -5.38618 q^{55} +29.1315 q^{56} +0.134943 q^{57} -4.98223 q^{58} -5.95418 q^{59} -52.2232 q^{60} -7.38295 q^{61} +21.7852 q^{62} -35.2900 q^{63} -2.32402 q^{64} +0.830630 q^{65} -11.6933 q^{66} +14.5418 q^{67} +2.28812 q^{68} -3.34371 q^{69} -45.7041 q^{70} -7.19340 q^{71} -43.5567 q^{72} -13.2163 q^{73} -14.6998 q^{74} +28.4581 q^{75} +0.184273 q^{76} -7.02300 q^{77} +1.80328 q^{78} -10.0764 q^{79} -23.8088 q^{80} +21.9729 q^{81} -12.9183 q^{82} +7.27007 q^{83} -68.0934 q^{84} -1.94872 q^{85} -7.62912 q^{86} +6.32185 q^{87} -8.66814 q^{88} +9.11072 q^{89} +68.3356 q^{90} +1.08305 q^{91} -4.56605 q^{92} -27.6427 q^{93} -10.3593 q^{94} -0.156939 q^{95} -13.2673 q^{96} -2.34729 q^{97} -41.9192 q^{98} +10.5006 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9}+O(q^{10}) $ 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9} - 61 q^{10} - 50 q^{11} - 43 q^{12} - 87 q^{13} - 41 q^{14} - 62 q^{15} + 129 q^{16} - 29 q^{17} - 61 q^{18} - 107 q^{19} - 59 q^{20} - 163 q^{21} - 70 q^{22} - 31 q^{23} - 98 q^{24} + 119 q^{25} - 23 q^{26} - 41 q^{27} - 112 q^{28} - 152 q^{29} - 66 q^{30} - 117 q^{31} - 93 q^{32} - 60 q^{33} - 80 q^{34} - 21 q^{35} + 92 q^{36} - 231 q^{37} + 2 q^{38} - 81 q^{39} - 143 q^{40} - 81 q^{41} - 6 q^{42} - 126 q^{43} - 115 q^{44} - 156 q^{45} - 205 q^{46} - 4 q^{47} - 55 q^{48} + 103 q^{49} - 61 q^{50} - 106 q^{51} - 164 q^{52} - 87 q^{53} - 110 q^{54} - 62 q^{55} - 73 q^{56} - 136 q^{57} - 128 q^{58} - 76 q^{59} - 148 q^{60} - 345 q^{61} + 5 q^{62} - 74 q^{63} - 25 q^{64} - 110 q^{65} - 34 q^{66} - 104 q^{67} - 48 q^{68} - 133 q^{69} - 92 q^{70} - 39 q^{71} - 177 q^{72} - 175 q^{73} - 44 q^{74} - 23 q^{75} - 268 q^{76} - 81 q^{77} - 19 q^{78} - 272 q^{79} - 60 q^{80} + 77 q^{81} - 13 q^{82} - 40 q^{83} - 221 q^{84} - 376 q^{85} - 82 q^{86} - 3 q^{87} - 234 q^{88} - 92 q^{89} - 91 q^{90} - 205 q^{91} - 11 q^{92} - 125 q^{93} - 126 q^{94} - 56 q^{95} - 148 q^{96} - 133 q^{97} - 4 q^{98} - 195 q^{99}+O(q^{100}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9 - 61 * q^10 - 50 * q^11 - 43 * q^12 - 87 * q^13 - 41 * q^14 - 62 * q^15 + 129 * q^16 - 29 * q^17 - 61 * q^18 - 107 * q^19 - 59 * q^20 - 163 * q^21 - 70 * q^22 - 31 * q^23 - 98 * q^24 + 119 * q^25 - 23 * q^26 - 41 * q^27 - 112 * q^28 - 152 * q^29 - 66 * q^30 - 117 * q^31 - 93 * q^32 - 60 * q^33 - 80 * q^34 - 21 * q^35 + 92 * q^36 - 231 * q^37 + 2 * q^38 - 81 * q^39 - 143 * q^40 - 81 * q^41 - 6 * q^42 - 126 * q^43 - 115 * q^44 - 156 * q^45 - 205 * q^46 - 4 * q^47 - 55 * q^48 + 103 * q^49 - 61 * q^50 - 106 * q^51 - 164 * q^52 - 87 * q^53 - 110 * q^54 - 62 * q^55 - 73 * q^56 - 136 * q^57 - 128 * q^58 - 76 * q^59 - 148 * q^60 - 345 * q^61 + 5 * q^62 - 74 * q^63 - 25 * q^64 - 110 * q^65 - 34 * q^66 - 104 * q^67 - 48 * q^68 - 133 * q^69 - 92 * q^70 - 39 * q^71 - 177 * q^72 - 175 * q^73 - 44 * q^74 - 23 * q^75 - 268 * q^76 - 81 * q^77 - 19 * q^78 - 272 * q^79 - 60 * q^80 + 77 * q^81 - 13 * q^82 - 40 * q^83 - 221 * q^84 - 376 * q^85 - 82 * q^86 - 3 * q^87 - 234 * q^88 - 92 * q^89 - 91 * q^90 - 205 * q^91 - 11 * q^92 - 125 * q^93 - 126 * q^94 - 56 * q^95 - 148 * q^96 - 133 * q^97 - 4 * q^98 - 195 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.52486	−1.78534	−0.892672	−	0.450707i	$-0.851172\pi$
$2$	−2.52486	−1.78534	−0.892672	+	0.450707i	$0.851172\pi$
$3$	3.20374	1.84968	0.924839	−	0.380358i	$-0.124199\pi$
$3$	3.20374	1.84968	0.924839	+	0.380358i	$0.124199\pi$
$4$	4.37490	2.18745
$5$	−3.72596	−1.66630	−0.833150	−	0.553047i	$-0.813465\pi$
$5$	−3.72596	−1.66630	−0.833150	+	0.553047i	$0.813465\pi$
$6$	−8.08898	−3.30231
$7$	−4.85825	−1.83625	−0.918123	−	0.396296i	$-0.870295\pi$
$7$	−4.85825	−1.83625	−0.918123	+	0.396296i	$0.870295\pi$
$8$	−5.99630	−2.12001
$9$	7.26393	2.42131
$10$	9.40752	2.97492
$11$	1.44558	0.435859	0.217930	−	0.975964i	$-0.430070\pi$
$11$	1.44558	0.435859	0.217930	+	0.975964i	$0.430070\pi$
$12$	14.0160	4.04608
$13$	−0.222930	−0.0618298	−0.0309149	−	0.999522i	$-0.509842\pi$
$13$	−0.222930	−0.0618298	−0.0309149	+	0.999522i	$0.509842\pi$
$14$	12.2664	3.27833
$15$	−11.9370	−3.08212
$16$	6.38998	1.59750
$17$	0.523011	0.126849	0.0634244	−	0.997987i	$-0.479798\pi$
$17$	0.523011	0.126849	0.0634244	+	0.997987i	$0.479798\pi$
$18$	−18.3404	−4.32287
$19$	0.0421204	0.00966308	0.00483154	−	0.999988i	$-0.498462\pi$
$19$	0.0421204	0.00966308	0.00483154	+	0.999988i	$0.498462\pi$
$20$	−16.3007	−3.64495
$21$	−15.5646	−3.39646
$22$	−3.64989	−0.778159
$23$	−1.04369	−0.217625	−0.108812	−	0.994062i	$-0.534705\pi$
$23$	−1.04369	−0.217625	−0.108812	+	0.994062i	$0.534705\pi$
$24$	−19.2106	−3.92134
$25$	8.88278	1.77656
$26$	0.562867	0.110387
$27$	13.6605	2.62897
$28$	−21.2544	−4.01670
$29$	1.97327	0.366428	0.183214	−	0.983073i	$-0.441350\pi$
$29$	1.97327	0.366428	0.183214	+	0.983073i	$0.441350\pi$
$30$	30.1392	5.50264
$31$	−8.62827	−1.54968	−0.774842	−	0.632155i	$-0.782171\pi$
$31$	−8.62827	−1.54968	−0.774842	+	0.632155i	$0.782171\pi$
$32$	−4.14120	−0.732068
$33$	4.63126	0.806200
$34$	−1.32053	−0.226469
$35$	18.1016	3.05974
$36$	31.7790	5.29650
$37$	5.82204	0.957137	0.478568	−	0.878050i	$-0.341156\pi$
$37$	5.82204	0.957137	0.478568	+	0.878050i	$0.341156\pi$
$38$	−0.106348	−0.0172519
$39$	−0.714210	−0.114365
$40$	22.3420	3.53257
$41$	5.11644	0.799053	0.399527	−	0.916722i	$-0.369175\pi$
$41$	5.11644	0.799053	0.399527	+	0.916722i	$0.369175\pi$
$42$	39.2983	6.06386
$43$	3.02160	0.460790	0.230395	−	0.973097i	$-0.425998\pi$
$43$	3.02160	0.460790	0.230395	+	0.973097i	$0.425998\pi$
$44$	6.32428	0.953422
$45$	−27.0651	−4.03463
$46$	2.63517	0.388535
$47$	4.10292	0.598472	0.299236	−	0.954179i	$-0.403268\pi$
$47$	4.10292	0.598472	0.299236	+	0.954179i	$0.403268\pi$
$48$	20.4718	2.95485
$49$	16.6026	2.37180
$50$	−22.4278	−3.17176
$51$	1.67559	0.234629
$52$	−0.975299	−0.135250
$53$	2.68171	0.368361	0.184181	−	0.982892i	$-0.441037\pi$
$53$	2.68171	0.368361	0.184181	+	0.982892i	$0.441037\pi$
$54$	−34.4909	−4.69361
$55$	−5.38618	−0.726273
$56$	29.1315	3.89286
$57$	0.134943	0.0178736
$58$	−4.98223	−0.654199
$59$	−5.95418	−0.775169	−0.387584	−	0.921834i	$-0.626690\pi$
$59$	−5.95418	−0.775169	−0.387584	+	0.921834i	$0.626690\pi$
$60$	−52.2232	−6.74199
$61$	−7.38295	−0.945290	−0.472645	−	0.881253i	$-0.656701\pi$
$61$	−7.38295	−0.945290	−0.472645	+	0.881253i	$0.656701\pi$
$62$	21.7852	2.76672
$63$	−35.2900	−4.44612
$64$	−2.32402	−0.290502
$65$	0.830630	0.103027
$66$	−11.6933	−1.43934
$67$	14.5418	1.77656	0.888281	−	0.459301i	$-0.151900\pi$
$67$	14.5418	1.77656	0.888281	+	0.459301i	$0.151900\pi$
$68$	2.28812	0.277476
$69$	−3.34371	−0.402536
$70$	−45.7041	−5.46268
$71$	−7.19340	−0.853700	−0.426850	−	0.904323i	$-0.640377\pi$
$71$	−7.19340	−0.853700	−0.426850	+	0.904323i	$0.640377\pi$
$72$	−43.5567	−5.13320
$73$	−13.2163	−1.54685	−0.773425	−	0.633887i	$-0.781458\pi$
$73$	−13.2163	−1.54685	−0.773425	+	0.633887i	$0.781458\pi$
$74$	−14.6998	−1.70882
$75$	28.4581	3.28606
$76$	0.184273	0.0211375
$77$	−7.02300	−0.800345
$78$	1.80328	0.204181
$79$	−10.0764	−1.13368	−0.566842	−	0.823826i	$-0.691835\pi$
$79$	−10.0764	−1.13368	−0.566842	+	0.823826i	$0.691835\pi$
$80$	−23.8088	−2.66191
$81$	21.9729	2.44144
$82$	−12.9183	−1.42658
$83$	7.27007	0.797993	0.398997	−	0.916952i	$-0.369359\pi$
$83$	7.27007	0.797993	0.398997	+	0.916952i	$0.369359\pi$
$84$	−68.0934	−7.42960
$85$	−1.94872	−0.211368
$86$	−7.62912	−0.822669
$87$	6.32185	0.677773
$88$	−8.66814	−0.924026
$89$	9.11072	0.965734	0.482867	−	0.875694i	$-0.339595\pi$
$89$	9.11072	0.965734	0.482867	+	0.875694i	$0.339595\pi$
$90$	68.3356	7.20320
$91$	1.08305	0.113535
$92$	−4.56605	−0.476044
$93$	−27.6427	−2.86642
$94$	−10.3593	−1.06848
$95$	−0.156939	−0.0161016
$96$	−13.2673	−1.35409
$97$	−2.34729	−0.238331	−0.119166	−	0.992874i	$-0.538022\pi$
$97$	−2.34729	−0.238331	−0.119166	+	0.992874i	$0.538022\pi$
$98$	−41.9192	−4.23448
$99$	10.5006	1.05535
$100$	38.8613	3.88613
$101$	12.9792	1.29148	0.645741	−	0.763557i	$-0.276549\pi$
$101$	12.9792	1.29148	0.645741	+	0.763557i	$0.276549\pi$
$102$	−4.23062	−0.418894
$103$	−3.07065	−0.302560	−0.151280	−	0.988491i	$-0.548340\pi$
$103$	−3.07065	−0.302560	−0.151280	+	0.988491i	$0.548340\pi$
$104$	1.33676	0.131080
$105$	57.9929	5.65953
$106$	−6.77094	−0.657652
$107$	−18.0410	−1.74409	−0.872047	−	0.489423i	$-0.837208\pi$
$107$	−18.0410	−1.74409	−0.872047	+	0.489423i	$0.837208\pi$
$108$	59.7635	5.75074
$109$	−11.9767	−1.14716	−0.573581	−	0.819149i	$-0.694446\pi$
$109$	−11.9767	−1.14716	−0.573581	+	0.819149i	$0.694446\pi$
$110$	13.5993	1.29665
$111$	18.6523	1.77040
$112$	−31.0441	−2.93339
$113$	16.1056	1.51509	0.757546	−	0.652782i	$-0.226398\pi$
$113$	16.1056	1.51509	0.757546	+	0.652782i	$0.226398\pi$
$114$	−0.340711	−0.0319105
$115$	3.88875	0.362628
$116$	8.63288	0.801543
$117$	−1.61935	−0.149709
$118$	15.0335	1.38394
$119$	−2.54092	−0.232925
$120$	71.5778	6.53413
$121$	−8.91029	−0.810027
$122$	18.6409	1.68767
$123$	16.3917	1.47799
$124$	−37.7479	−3.38986
$125$	−14.4671	−1.29398
$126$	89.1022	7.93786
$127$	−3.61305	−0.320607	−0.160303	−	0.987068i	$-0.551247\pi$
$127$	−3.61305	−0.320607	−0.160303	+	0.987068i	$0.551247\pi$
$128$	14.1502	1.25071
$129$	9.68042	0.852314
$130$	−2.09722	−0.183938
$131$	−5.84216	−0.510432	−0.255216	−	0.966884i	$-0.582147\pi$
$131$	−5.84216	−0.510432	−0.255216	+	0.966884i	$0.582147\pi$
$132$	20.2613	1.76352
$133$	−0.204631	−0.0177438
$134$	−36.7159	−3.17177
$135$	−50.8986	−4.38065
$136$	−3.13613	−0.268921
$137$	−8.47793	−0.724318	−0.362159	−	0.932116i	$-0.617960\pi$
$137$	−8.47793	−0.724318	−0.362159	+	0.932116i	$0.617960\pi$
$138$	8.44240	0.718665
$139$	−7.62245	−0.646527	−0.323264	−	0.946309i	$-0.604780\pi$
$139$	−7.62245	−0.646527	−0.323264	+	0.946309i	$0.604780\pi$
$140$	79.1930	6.69303
$141$	13.1447	1.10698
$142$	18.1623	1.52415
$143$	−0.322264	−0.0269491
$144$	46.4164	3.86803
$145$	−7.35234	−0.610578
$146$	33.3693	2.76166
$147$	53.1903	4.38707
$148$	25.4709	2.09369
$149$	−16.7344	−1.37094	−0.685469	−	0.728102i	$-0.740403\pi$
$149$	−16.7344	−1.37094	−0.685469	+	0.728102i	$0.740403\pi$
$150$	−71.8527	−5.86674
$151$	16.1881	1.31736	0.658682	−	0.752421i	$-0.271114\pi$
$151$	16.1881	1.31736	0.658682	+	0.752421i	$0.271114\pi$
$152$	−0.252566	−0.0204858
$153$	3.79911	0.307140
$154$	17.7321	1.42889
$155$	32.1486	2.58224
$156$	−3.12460	−0.250168
$157$	3.92889	0.313560	0.156780	−	0.987634i	$-0.449889\pi$
$157$	3.92889	0.313560	0.156780	+	0.987634i	$0.449889\pi$
$158$	25.4415	2.02402
$159$	8.59150	0.681350
$160$	15.4300	1.21985
$161$	5.07051	0.399612
$162$	−55.4785	−4.35880
$163$	−17.8769	−1.40023	−0.700115	−	0.714030i	$-0.746868\pi$
$163$	−17.8769	−1.40023	−0.700115	+	0.714030i	$0.746868\pi$
$164$	22.3839	1.74789
$165$	−17.2559	−1.34337
$166$	−18.3559	−1.42469
$167$	2.09491	0.162109	0.0810545	−	0.996710i	$-0.474171\pi$
$167$	2.09491	0.162109	0.0810545	+	0.996710i	$0.474171\pi$
$168$	93.3297	7.20054
$169$	−12.9503	−0.996177
$170$	4.92023	0.377365
$171$	0.305960	0.0233973
$172$	13.2192	1.00796
$173$	−5.34749	−0.406562	−0.203281	−	0.979120i	$-0.565161\pi$
$173$	−5.34749	−0.406562	−0.203281	+	0.979120i	$0.565161\pi$
$174$	−15.9618	−1.21006
$175$	−43.1548	−3.26219
$176$	9.23724	0.696283
$177$	−19.0756	−1.43381
$178$	−23.0033	−1.72417
$179$	11.0859	0.828596	0.414298	−	0.910141i	$-0.364027\pi$
$179$	11.0859	0.828596	0.414298	+	0.910141i	$0.364027\pi$
$180$	−118.407	−8.82556
$181$	−4.39007	−0.326312	−0.163156	−	0.986600i	$-0.552167\pi$
$181$	−4.39007	−0.326312	−0.163156	+	0.986600i	$0.552167\pi$
$182$	−2.73455	−0.202698
$183$	−23.6530	−1.74848
$184$	6.25828	0.461367
$185$	−21.6927	−1.59488
$186$	69.7939	5.11754
$187$	0.756055	0.0552882
$188$	17.9499	1.30913
$189$	−66.3662	−4.82743
$190$	0.396249	0.0287469
$191$	−9.42725	−0.682132	−0.341066	−	0.940039i	$-0.610788\pi$
$191$	−9.42725	−0.682132	−0.341066	+	0.940039i	$0.610788\pi$
$192$	−7.44555	−0.537336
$193$	−26.4113	−1.90113	−0.950565	−	0.310526i	$-0.899495\pi$
$193$	−26.4113	−1.90113	−0.950565	+	0.310526i	$0.899495\pi$
$194$	5.92658	0.425503
$195$	2.66112	0.190567
$196$	72.6348	5.18820
$197$	25.5168	1.81800	0.908999	−	0.416798i	$-0.136848\pi$
$197$	25.5168	1.81800	0.908999	+	0.416798i	$0.136848\pi$
$198$	−26.5125	−1.88416
$199$	14.1943	1.00621	0.503103	−	0.864227i	$-0.332192\pi$
$199$	14.1943	1.00621	0.503103	+	0.864227i	$0.332192\pi$
$200$	−53.2638	−3.76632
$201$	46.5880	3.28607
$202$	−32.7707	−2.30574
$203$	−9.58665	−0.672851
$204$	7.33054	0.513241
$205$	−19.0636	−1.33146
$206$	7.75296	0.540174
$207$	−7.58130	−0.526937
$208$	−1.42452	−0.0987728
$209$	0.0608885	0.00421175
$210$	−146.424	−10.1042
$211$	−14.2111	−0.978331	−0.489165	−	0.872191i	$-0.662699\pi$
$211$	−14.2111	−0.978331	−0.489165	+	0.872191i	$0.662699\pi$
$212$	11.7322	0.805773
$213$	−23.0458	−1.57907
$214$	45.5511	3.11381
$215$	−11.2584	−0.767815
$216$	−81.9125	−5.57344
$217$	41.9183	2.84560
$218$	30.2395	2.04808
$219$	−42.3415	−2.86118
$220$	−23.5640	−1.58869
$221$	−0.116595	−0.00784302
$222$	−47.0943	−3.16076
$223$	23.3432	1.56318	0.781588	−	0.623795i	$-0.214410\pi$
$223$	23.3432	1.56318	0.781588	+	0.623795i	$0.214410\pi$
$224$	20.1190	1.34426
$225$	64.5239	4.30160
$226$	−40.6645	−2.70496
$227$	−22.7061	−1.50705	−0.753527	−	0.657417i	$-0.771649\pi$
$227$	−22.7061	−1.50705	−0.753527	+	0.657417i	$0.771649\pi$
$228$	0.590362	0.0390976
$229$	−16.2194	−1.07181	−0.535905	−	0.844278i	$-0.680030\pi$
$229$	−16.2194	−1.07181	−0.535905	+	0.844278i	$0.680030\pi$
$230$	−9.81855	−0.647416
$231$	−22.4998	−1.48038
$232$	−11.8323	−0.776830
$233$	−8.23373	−0.539409	−0.269705	−	0.962943i	$-0.586926\pi$
$233$	−8.23373	−0.539409	−0.269705	+	0.962943i	$0.586926\pi$
$234$	4.08863	0.267282
$235$	−15.2873	−0.997234
$236$	−26.0490	−1.69564
$237$	−32.2822	−2.09695
$238$	6.41545	0.415852
$239$	−4.11596	−0.266239	−0.133120	−	0.991100i	$-0.542499\pi$
$239$	−4.11596	−0.266239	−0.133120	+	0.991100i	$0.542499\pi$
$240$	−76.2772	−4.92367
$241$	13.4932	0.869170	0.434585	−	0.900631i	$-0.356895\pi$
$241$	13.4932	0.869170	0.434585	+	0.900631i	$0.356895\pi$
$242$	22.4972	1.44618
$243$	29.4139	1.88690
$244$	−32.2997	−2.06778
$245$	−61.8606	−3.95213
$246$	−41.3867	−2.63872
$247$	−0.00938992	−0.000597466 0
$248$	51.7377	3.28535
$249$	23.2914	1.47603
$250$	36.5274	2.31019
$251$	−19.2858	−1.21731	−0.608655	−	0.793435i	$-0.708291\pi$
$251$	−19.2858	−1.21731	−0.608655	+	0.793435i	$0.708291\pi$
$252$	−154.390	−9.72568
$253$	−1.50874	−0.0948537
$254$	9.12245	0.572393
$255$	−6.24318	−0.390963
$256$	−31.0793	−1.94245
$257$	−24.0102	−1.49772	−0.748858	−	0.662730i	$-0.769398\pi$
$257$	−24.0102	−1.49772	−0.748858	+	0.662730i	$0.769398\pi$
$258$	−24.4417	−1.52167
$259$	−28.2849	−1.75754
$260$	3.63393	0.225367
$261$	14.3337	0.887235
$262$	14.7506	0.911297
$263$	9.58393	0.590971	0.295485	−	0.955347i	$-0.404519\pi$
$263$	9.58393	0.590971	0.295485	+	0.955347i	$0.404519\pi$
$264$	−27.7704	−1.70915
$265$	−9.99195	−0.613801
$266$	0.516665	0.0316788
$267$	29.1883	1.78630
$268$	63.6189	3.88614
$269$	16.7214	1.01952	0.509762	−	0.860316i	$-0.329734\pi$
$269$	16.7214	1.01952	0.509762	+	0.860316i	$0.329734\pi$
$270$	128.512	7.82097
$271$	−2.73408	−0.166084	−0.0830418	−	0.996546i	$-0.526463\pi$
$271$	−2.73408	−0.166084	−0.0830418	+	0.996546i	$0.526463\pi$
$272$	3.34203	0.202640
$273$	3.46981	0.210003
$274$	21.4056	1.29316
$275$	12.8408	0.774329
$276$	−14.6284	−0.880528
$277$	−20.7934	−1.24935	−0.624677	−	0.780883i	$-0.714769\pi$
$277$	−20.7934	−1.24935	−0.624677	+	0.780883i	$0.714769\pi$
$278$	19.2456	1.15427
$279$	−62.6752	−3.75227
$280$	−108.543	−6.48668
$281$	−31.4556	−1.87648	−0.938242	−	0.345981i	$-0.887546\pi$
$281$	−31.4556	−1.87648	−0.938242	+	0.345981i	$0.887546\pi$
$282$	−33.1884	−1.97634
$283$	−8.66474	−0.515065	−0.257533	−	0.966270i	$-0.582910\pi$
$283$	−8.66474	−0.515065	−0.257533	+	0.966270i	$0.582910\pi$
$284$	−31.4704	−1.86743
$285$	−0.502791	−0.0297828
$286$	0.813671	0.0481134
$287$	−24.8569	−1.46726
$288$	−30.0814	−1.77256
$289$	−16.7265	−0.983909
$290$	18.5636	1.09009
$291$	−7.52011	−0.440836
$292$	−57.8200	−3.38366
$293$	28.2728	1.65171	0.825857	−	0.563879i	$-0.190692\pi$
$293$	28.2728	1.65171	0.825857	+	0.563879i	$0.190692\pi$
$294$	−134.298	−7.83242
$295$	22.1851	1.29166
$296$	−34.9107	−2.02914
$297$	19.7474	1.14586
$298$	42.2521	2.44760
$299$	0.232670	0.0134557
$300$	124.502	7.18810
$301$	−14.6797	−0.846124
$302$	−40.8725	−2.35195
$303$	41.5820	2.38883
$304$	0.269149	0.0154367
$305$	27.5086	1.57514
$306$	−9.59222	−0.548351
$307$	9.31195	0.531461	0.265730	−	0.964047i	$-0.414387\pi$
$307$	9.31195	0.531461	0.265730	+	0.964047i	$0.414387\pi$
$308$	−30.7249	−1.75072
$309$	−9.83756	−0.559639
$310$	−81.1707	−4.61018
$311$	26.9361	1.52741	0.763703	−	0.645568i	$-0.223379\pi$
$311$	26.9361	1.52741	0.763703	+	0.645568i	$0.223379\pi$
$312$	4.28262	0.242455
$313$	−20.4179	−1.15409	−0.577045	−	0.816713i	$-0.695794\pi$
$313$	−20.4179	−1.15409	−0.577045	+	0.816713i	$0.695794\pi$
$314$	−9.91989	−0.559812
$315$	131.489	7.40857
$316$	−44.0833	−2.47988
$317$	31.0229	1.74242	0.871209	−	0.490913i	$-0.163337\pi$
$317$	31.0229	1.74242	0.871209	+	0.490913i	$0.163337\pi$
$318$	−21.6923	−1.21644
$319$	2.85253	0.159711
$320$	8.65921	0.484064
$321$	−57.7988	−3.22601
$322$	−12.8023	−0.713445
$323$	0.0220294	0.00122575
$324$	96.1294	5.34052
$325$	−1.98024	−0.109844
$326$	45.1367	2.49989
$327$	−38.3703	−2.12188
$328$	−30.6797	−1.69400
$329$	−19.9330	−1.09894
$330$	43.5687	2.39838
$331$	29.6728	1.63096	0.815482	−	0.578782i	$-0.196472\pi$
$331$	29.6728	1.63096	0.815482	+	0.578782i	$0.196472\pi$
$332$	31.8058	1.74557
$333$	42.2909	2.31753
$334$	−5.28935	−0.289420
$335$	−54.1821	−2.96028
$336$	−99.4572	−5.42584
$337$	10.5512	0.574762	0.287381	−	0.957816i	$-0.407215\pi$
$337$	10.5512	0.574762	0.287381	+	0.957816i	$0.407215\pi$
$338$	32.6977	1.77852
$339$	51.5983	2.80243
$340$	−8.52545	−0.462358
$341$	−12.4729	−0.675444
$342$	−0.772505	−0.0417723
$343$	−46.6518	−2.51896
$344$	−18.1184	−0.976880
$345$	12.4585	0.670745
$346$	13.5016	0.725853
$347$	18.4188	0.988770	0.494385	−	0.869243i	$-0.335393\pi$
$347$	18.4188	0.988770	0.494385	+	0.869243i	$0.335393\pi$
$348$	27.6575	1.48260
$349$	−21.0862	−1.12872	−0.564360	−	0.825528i	$-0.690877\pi$
$349$	−21.0862	−1.12872	−0.564360	+	0.825528i	$0.690877\pi$
$350$	108.960	5.82414
$351$	−3.04534	−0.162548
$352$	−5.98645	−0.319079
$353$	−4.92494	−0.262128	−0.131064	−	0.991374i	$-0.541839\pi$
$353$	−4.92494	−0.262128	−0.131064	+	0.991374i	$0.541839\pi$
$354$	48.1633	2.55985
$355$	26.8023	1.42252
$356$	39.8585	2.11250
$357$	−8.14043	−0.430837
$358$	−27.9902	−1.47933
$359$	18.2400	0.962668	0.481334	−	0.876537i	$-0.340152\pi$
$359$	18.2400	0.962668	0.481334	+	0.876537i	$0.340152\pi$
$360$	162.291	8.55346
$361$	−18.9982	−0.999907
$362$	11.0843	0.582579
$363$	−28.5462	−1.49829
$364$	4.73825	0.248352
$365$	49.2434	2.57752
$366$	59.7205	3.12164
$367$	−27.3904	−1.42977	−0.714883	−	0.699244i	$-0.753520\pi$
$367$	−27.3904	−1.42977	−0.714883	+	0.699244i	$0.753520\pi$
$368$	−6.66917	−0.347654
$369$	37.1654	1.93476
$370$	54.7709	2.84740
$371$	−13.0284	−0.676402
$372$	−120.934	−6.27015
$373$	−19.2343	−0.995914	−0.497957	−	0.867202i	$-0.665916\pi$
$373$	−19.2343	−0.995914	−0.497957	+	0.867202i	$0.665916\pi$
$374$	−1.90893	−0.0987084
$375$	−46.3488	−2.39344
$376$	−24.6023	−1.26877
$377$	−0.439902	−0.0226561
$378$	167.565	8.61862
$379$	−6.48037	−0.332874	−0.166437	−	0.986052i	$-0.553226\pi$
$379$	−6.48037	−0.332874	−0.166437	+	0.986052i	$0.553226\pi$
$380$	−0.686593	−0.0352215
$381$	−11.5753	−0.593019
$382$	23.8025	1.21784
$383$	−29.0763	−1.48573	−0.742866	−	0.669440i	$-0.766534\pi$
$383$	−29.0763	−1.48573	−0.742866	+	0.669440i	$0.766534\pi$
$384$	45.3336	2.31342
$385$	26.1674	1.33361
$386$	66.6849	3.39417
$387$	21.9487	1.11572
$388$	−10.2692	−0.521339
$389$	−32.0716	−1.62609	−0.813047	−	0.582198i	$-0.802193\pi$
$389$	−32.0716	−1.62609	−0.813047	+	0.582198i	$0.802193\pi$
$390$	−6.71895	−0.340227
$391$	−0.545862	−0.0276054
$392$	−99.5540	−5.02824
$393$	−18.7168	−0.944135
$394$	−64.4263	−3.24575
$395$	37.5443	1.88906
$396$	45.9392	2.30853
$397$	5.47557	0.274811	0.137405	−	0.990515i	$-0.456124\pi$
$397$	5.47557	0.274811	0.137405	+	0.990515i	$0.456124\pi$
$398$	−35.8385	−1.79642
$399$	−0.655585	−0.0328203
$400$	56.7608	2.83804
$401$	−21.2910	−1.06322	−0.531610	−	0.846989i	$-0.678413\pi$
$401$	−21.2910	−1.06322	−0.531610	+	0.846989i	$0.678413\pi$
$402$	−117.628	−5.86676
$403$	1.92350	0.0958166
$404$	56.7829	2.82505
$405$	−81.8702	−4.06816
$406$	24.2049	1.20127
$407$	8.41623	0.417177
$408$	−10.0473	−0.497417
$409$	−10.3480	−0.511674	−0.255837	−	0.966720i	$-0.582351\pi$
$409$	−10.3480	−0.511674	−0.255837	+	0.966720i	$0.582351\pi$
$410$	48.1330	2.37712
$411$	−27.1610	−1.33976
$412$	−13.4338	−0.661836
$413$	28.9269	1.42340
$414$	19.1417	0.940764
$415$	−27.0880	−1.32970
$416$	0.923200	0.0452636
$417$	−24.4203	−1.19587
$418$	−0.153735	−0.00751941
$419$	−4.26172	−0.208199	−0.104099	−	0.994567i	$-0.533196\pi$
$419$	−4.26172	−0.208199	−0.104099	+	0.994567i	$0.533196\pi$
$420$	253.714	12.3800
$421$	−4.55790	−0.222138	−0.111069	−	0.993813i	$-0.535428\pi$
$421$	−4.55790	−0.222138	−0.111069	+	0.993813i	$0.535428\pi$
$422$	35.8809	1.74666
$423$	29.8033	1.44909
$424$	−16.0803	−0.780930
$425$	4.64579	0.225354
$426$	58.1873	2.81918
$427$	35.8682	1.73578
$428$	−78.9278	−3.81512
$429$	−1.03245	−0.0498471
$430$	28.4258	1.37081
$431$	15.9203	0.766852	0.383426	−	0.923572i	$-0.374744\pi$
$431$	15.9203	0.766852	0.383426	+	0.923572i	$0.374744\pi$
$432$	87.2905	4.19976
$433$	28.6181	1.37530	0.687648	−	0.726044i	$-0.258643\pi$
$433$	28.6181	1.37530	0.687648	+	0.726044i	$0.258643\pi$
$434$	−105.838	−5.08037
$435$	−23.5550	−1.12937
$436$	−52.3971	−2.50936
$437$	−0.0439607	−0.00210293
$438$	106.906	5.10818
$439$	−20.9346	−0.999155	−0.499578	−	0.866269i	$-0.666511\pi$
$439$	−20.9346	−0.999155	−0.499578	+	0.866269i	$0.666511\pi$
$440$	32.2971	1.53971
$441$	120.600	5.74286
$442$	0.294386	0.0140025
$443$	0.712901	0.0338710	0.0169355	−	0.999857i	$-0.494609\pi$
$443$	0.712901	0.0338710	0.0169355	+	0.999857i	$0.494609\pi$
$444$	81.6019	3.87266
$445$	−33.9462	−1.60920
$446$	−58.9382	−2.79081
$447$	−53.6127	−2.53579
$448$	11.2907	0.533434
$449$	0.524711	0.0247627	0.0123813	−	0.999923i	$-0.496059\pi$
$449$	0.524711	0.0247627	0.0123813	+	0.999923i	$0.496059\pi$
$450$	−162.914	−7.67983
$451$	7.39623	0.348275
$452$	70.4607	3.31419
$453$	51.8623	2.43670
$454$	57.3295	2.69061
$455$	−4.03541	−0.189183
$456$	−0.809156	−0.0378922
$457$	−31.9501	−1.49456	−0.747282	−	0.664507i	$-0.768642\pi$
$457$	−31.9501	−1.49456	−0.747282	+	0.664507i	$0.768642\pi$
$458$	40.9518	1.91355
$459$	7.14460	0.333481
$460$	17.0129	0.793232
$461$	−14.4887	−0.674804	−0.337402	−	0.941361i	$-0.609548\pi$
$461$	−14.4887	−0.674804	−0.337402	+	0.941361i	$0.609548\pi$
$462$	56.8089	2.64299
$463$	−21.3752	−0.993392	−0.496696	−	0.867925i	$-0.665454\pi$
$463$	−21.3752	−0.993392	−0.496696	+	0.867925i	$0.665454\pi$
$464$	12.6092	0.585366
$465$	102.996	4.77631
$466$	20.7890	0.963031
$467$	−24.7437	−1.14500	−0.572501	−	0.819904i	$-0.694027\pi$
$467$	−24.7437	−1.14500	−0.572501	+	0.819904i	$0.694027\pi$
$468$	−7.08451	−0.327481
$469$	−70.6476	−3.26220
$470$	38.5983	1.78041
$471$	12.5871	0.579985
$472$	35.7030	1.64337
$473$	4.36797	0.200840
$474$	81.5079	3.74378
$475$	0.374146	0.0171670
$476$	−11.1163	−0.509513
$477$	19.4798	0.891918
$478$	10.3922	0.475328
$479$	−22.7210	−1.03815	−0.519075	−	0.854729i	$-0.673723\pi$
$479$	−22.7210	−1.03815	−0.519075	+	0.854729i	$0.673723\pi$
$480$	49.4335	2.25632
$481$	−1.29791	−0.0591795
$482$	−34.0683	−1.55177
$483$	16.2446	0.739154
$484$	−38.9817	−1.77189
$485$	8.74592	0.397132
$486$	−74.2659	−3.36877
$487$	0.111905	0.00507090	0.00253545	−	0.999997i	$-0.499193\pi$
$487$	0.111905	0.00507090	0.00253545	+	0.999997i	$0.499193\pi$
$488$	44.2703	2.00402
$489$	−57.2730	−2.58998
$490$	156.189	7.05591
$491$	43.0390	1.94232	0.971161	−	0.238423i	$-0.0766304\pi$
$491$	43.0390	1.94232	0.971161	+	0.238423i	$0.0766304\pi$
$492$	71.7122	3.23304
$493$	1.03204	0.0464809
$494$	0.0237082	0.00106668
$495$	−39.1249	−1.75853
$496$	−55.1345	−2.47561
$497$	34.9473	1.56760
$498$	−58.8074	−2.63522
$499$	7.09793	0.317747	0.158873	−	0.987299i	$-0.449214\pi$
$499$	7.09793	0.317747	0.158873	+	0.987299i	$0.449214\pi$
$500$	−63.2922	−2.83051
$501$	6.71154	0.299849
$502$	48.6939	2.17332
$503$	31.3397	1.39737	0.698684	−	0.715431i	$-0.253770\pi$
$503$	31.3397	1.39737	0.698684	+	0.715431i	$0.253770\pi$
$504$	211.609	9.42583
$505$	−48.3601	−2.15200
$506$	3.80936	0.169347
$507$	−41.4894	−1.84261
$508$	−15.8068	−0.701312
$509$	−39.2926	−1.74161	−0.870806	−	0.491626i	$-0.836403\pi$
$509$	−39.2926	−1.74161	−0.870806	+	0.491626i	$0.836403\pi$
$510$	15.7631	0.698003
$511$	64.2081	2.84040
$512$	50.1702	2.21723
$513$	0.575387	0.0254039
$514$	60.6224	2.67394
$515$	11.4411	0.504156
$516$	42.3509	1.86440
$517$	5.93110	0.260850
$518$	71.4154	3.13781
$519$	−17.1320	−0.752009
$520$	−4.98070	−0.218418
$521$	2.68226	0.117512	0.0587560	−	0.998272i	$-0.481287\pi$
$521$	2.68226	0.117512	0.0587560	+	0.998272i	$0.481287\pi$
$522$	−36.1906	−1.58402
$523$	38.7446	1.69418	0.847092	−	0.531446i	$-0.178351\pi$
$523$	38.7446	1.69418	0.847092	+	0.531446i	$0.178351\pi$
$524$	−25.5589	−1.11655
$525$	−138.257	−6.03401
$526$	−24.1981	−1.05509
$527$	−4.51268	−0.196575
$528$	29.5937	1.28790
$529$	−21.9107	−0.952640
$530$	25.2283	1.09585
$531$	−43.2508	−1.87692
$532$	−0.895243	−0.0388137
$533$	−1.14061	−0.0494053
$534$	−73.6964	−3.18916
$535$	67.2202	2.90618
$536$	−87.1968	−3.76633
$537$	35.5162	1.53264
$538$	−42.2192	−1.82020
$539$	24.0004	1.03377
$540$	−222.676	−9.58246
$541$	−22.3341	−0.960218	−0.480109	−	0.877209i	$-0.659403\pi$
$541$	−22.3341	−0.960218	−0.480109	+	0.877209i	$0.659403\pi$
$542$	6.90316	0.296516
$543$	−14.0646	−0.603572
$544$	−2.16589	−0.0928619
$545$	44.6248	1.91152
$546$	−8.76078	−0.374927
$547$	−6.47554	−0.276874	−0.138437	−	0.990371i	$-0.544208\pi$
$547$	−6.47554	−0.276874	−0.138437	+	0.990371i	$0.544208\pi$
$548$	−37.0901	−1.58441
$549$	−53.6292	−2.28884
$550$	−32.4212	−1.38244
$551$	0.0831150	0.00354082
$552$	20.0499	0.853380
$553$	48.9537	2.08172
$554$	52.5004	2.23053
$555$	−69.4976	−2.95001
$556$	−33.3475	−1.41425
$557$	−3.28976	−0.139391	−0.0696957	−	0.997568i	$-0.522203\pi$
$557$	−3.28976	−0.139391	−0.0696957	+	0.997568i	$0.522203\pi$
$558$	158.246	6.69908
$559$	−0.673607	−0.0284905
$560$	115.669	4.88792
$561$	2.42220	0.102265
$562$	79.4209	3.35017
$563$	8.40423	0.354196	0.177098	−	0.984193i	$-0.443329\pi$
$563$	8.40423	0.354196	0.177098	+	0.984193i	$0.443329\pi$
$564$	57.5067	2.42147
$565$	−60.0090	−2.52460
$566$	21.8772	0.919569
$567$	−106.750	−4.48307
$568$	43.1338	1.80985
$569$	−33.6387	−1.41021	−0.705104	−	0.709104i	$-0.749100\pi$
$569$	−33.6387	−1.41021	−0.705104	+	0.709104i	$0.749100\pi$
$570$	1.26948	0.0531725
$571$	19.8443	0.830456	0.415228	−	0.909717i	$-0.363702\pi$
$571$	19.8443	0.830456	0.415228	+	0.909717i	$0.363702\pi$
$572$	−1.40987	−0.0589498
$573$	−30.2024	−1.26172
$574$	62.7602	2.61956
$575$	−9.27088	−0.386623
$576$	−16.8815	−0.703397
$577$	35.5566	1.48024	0.740120	−	0.672475i	$-0.234769\pi$
$577$	35.5566	1.48024	0.740120	+	0.672475i	$0.234769\pi$
$578$	42.2319	1.75662
$579$	−84.6150	−3.51648
$580$	−32.1658	−1.33561
$581$	−35.3198	−1.46531
$582$	18.9872	0.787045
$583$	3.87663	0.160554
$584$	79.2488	3.27934
$585$	6.03364	0.249460
$586$	−71.3848	−2.94888
$587$	−6.82683	−0.281773	−0.140887	−	0.990026i	$-0.544995\pi$
$587$	−6.82683	−0.281773	−0.140887	+	0.990026i	$0.544995\pi$
$588$	232.703	9.59650
$589$	−0.363426	−0.0149747
$590$	−56.0141	−2.30606
$591$	81.7492	3.36271
$592$	37.2027	1.52902
$593$	−11.8795	−0.487832	−0.243916	−	0.969796i	$-0.578432\pi$
$593$	−11.8795	−0.487832	−0.243916	+	0.969796i	$0.578432\pi$
$594$	−49.8594	−2.04575
$595$	9.46735	0.388124
$596$	−73.2115	−2.99886
$597$	45.4747	1.86116
$598$	−0.587460	−0.0240230
$599$	18.8226	0.769071	0.384535	−	0.923110i	$-0.374362\pi$
$599$	18.8226	0.769071	0.384535	+	0.923110i	$0.374362\pi$
$600$	−170.643	−6.96648
$601$	8.37568	0.341651	0.170826	−	0.985301i	$-0.445357\pi$
$601$	8.37568	0.341651	0.170826	+	0.985301i	$0.445357\pi$
$602$	37.0642	1.51062
$603$	105.631	4.30161
$604$	70.8212	2.88167
$605$	33.1994	1.34975
$606$	−104.989	−4.26488
$607$	22.0444	0.894755	0.447377	−	0.894345i	$-0.352358\pi$
$607$	22.0444	0.894755	0.447377	+	0.894345i	$0.352358\pi$
$608$	−0.174429	−0.00707403
$609$	−30.7131	−1.24456
$610$	−69.4552	−2.81216
$611$	−0.914664	−0.0370034
$612$	16.6208	0.671854
$613$	−17.2068	−0.694977	−0.347488	−	0.937684i	$-0.612965\pi$
$613$	−17.2068	−0.694977	−0.347488	+	0.937684i	$0.612965\pi$
$614$	−23.5113	−0.948840
$615$	−61.0749	−2.46278
$616$	42.1120	1.69674
$617$	−45.9096	−1.84825	−0.924126	−	0.382087i	$-0.875205\pi$
$617$	−45.9096	−1.84825	−0.924126	+	0.382087i	$0.875205\pi$
$618$	24.8384	0.999148
$619$	−32.2483	−1.29617	−0.648083	−	0.761569i	$-0.724429\pi$
$619$	−32.2483	−1.29617	−0.648083	+	0.761569i	$0.724429\pi$
$620$	140.647	5.64852
$621$	−14.2574	−0.572128
$622$	−68.0098	−2.72694
$623$	−44.2621	−1.77333
$624$	−4.56379	−0.182698
$625$	9.48993	0.379597
$626$	51.5524	2.06045
$627$	0.195071	0.00779037
$628$	17.1885	0.685897
$629$	3.04499	0.121412
$630$	−331.991	−13.2269
$631$	13.7043	0.545560	0.272780	−	0.962076i	$-0.412057\pi$
$631$	13.7043	0.545560	0.272780	+	0.962076i	$0.412057\pi$
$632$	60.4211	2.40342
$633$	−45.5286	−1.80960
$634$	−78.3283	−3.11081
$635$	13.4621	0.534227
$636$	37.5870	1.49042
$637$	−3.70122	−0.146648
$638$	−7.20222	−0.285139
$639$	−52.2524	−2.06707
$640$	−52.7232	−2.08407
$641$	−41.9228	−1.65585	−0.827926	−	0.560837i	$-0.810479\pi$
$641$	−41.9228	−1.65585	−0.827926	+	0.560837i	$0.810479\pi$
$642$	145.934	5.75954
$643$	4.26714	0.168280	0.0841398	−	0.996454i	$-0.473186\pi$
$643$	4.26714	0.168280	0.0841398	+	0.996454i	$0.473186\pi$
$644$	22.1830	0.874133
$645$	−36.0689	−1.42021
$646$	−0.0556211	−0.00218838
$647$	41.7599	1.64175	0.820876	−	0.571106i	$-0.193486\pi$
$647$	41.7599	1.64175	0.820876	+	0.571106i	$0.193486\pi$
$648$	−131.756	−5.17587
$649$	−8.60726	−0.337865
$650$	4.99983	0.196109
$651$	134.295	5.26345
$652$	−78.2099	−3.06294
$653$	46.4701	1.81851	0.909257	−	0.416234i	$-0.136650\pi$
$653$	46.4701	1.81851	0.909257	+	0.416234i	$0.136650\pi$
$654$	96.8795	3.78829
$655$	21.7677	0.850533
$656$	32.6939	1.27648
$657$	−96.0023	−3.74541
$658$	50.3280	1.96199
$659$	−9.36891	−0.364961	−0.182480	−	0.983209i	$-0.558413\pi$
$659$	−9.36891	−0.364961	−0.182480	+	0.983209i	$0.558413\pi$
$660$	−75.4930	−2.93856
$661$	26.1136	1.01570	0.507851	−	0.861445i	$-0.330440\pi$
$661$	26.1136	1.01570	0.507851	+	0.861445i	$0.330440\pi$
$662$	−74.9196	−2.91183
$663$	−0.373540	−0.0145071
$664$	−43.5935	−1.69175
$665$	0.762449	0.0295665
$666$	−106.778	−4.13758
$667$	−2.05949	−0.0797437
$668$	9.16503	0.354606
$669$	74.7854	2.89137
$670$	136.802	5.28513
$671$	−10.6727	−0.412013
$672$	64.4560	2.48644
$673$	−0.413719	−0.0159477	−0.00797385	−	0.999968i	$-0.502538\pi$
$673$	−0.413719	−0.0159477	−0.00797385	+	0.999968i	$0.502538\pi$
$674$	−26.6403	−1.02615
$675$	121.343	4.67051
$676$	−56.6563	−2.17909
$677$	−12.7301	−0.489258	−0.244629	−	0.969617i	$-0.578666\pi$
$677$	−12.7301	−0.489258	−0.244629	+	0.969617i	$0.578666\pi$
$678$	−130.278	−5.00331
$679$	11.4037	0.437635
$680$	11.6851	0.448103
$681$	−72.7442	−2.78756
$682$	31.4922	1.20590
$683$	24.9446	0.954477	0.477239	−	0.878774i	$-0.341638\pi$
$683$	24.9446	0.954477	0.477239	+	0.878774i	$0.341638\pi$
$684$	1.33854	0.0511805
$685$	31.5884	1.20693
$686$	117.789	4.49721
$687$	−51.9628	−1.98251
$688$	19.3080	0.736110
$689$	−0.597835	−0.0227757
$690$	−31.4560	−1.19751
$691$	13.5491	0.515433	0.257716	−	0.966221i	$-0.417030\pi$
$691$	13.5491	0.515433	0.257716	+	0.966221i	$0.417030\pi$
$692$	−23.3948	−0.889335
$693$	−51.0146	−1.93788
$694$	−46.5047	−1.76530
$695$	28.4009	1.07731
$696$	−37.9077	−1.43689
$697$	2.67595	0.101359
$698$	53.2398	2.01515
$699$	−26.3787	−0.997734
$700$	−188.798	−7.13590
$701$	−37.7440	−1.42557	−0.712785	−	0.701383i	$-0.752566\pi$
$701$	−37.7440	−1.42557	−0.712785	+	0.701383i	$0.752566\pi$
$702$	7.68906	0.290205
$703$	0.245227	0.00924889
$704$	−3.35956	−0.126618
$705$	−48.9765	−1.84456
$706$	12.4348	0.467989
$707$	−63.0563	−2.37148
$708$	−83.4541	−3.13640
$709$	11.5906	0.435294	0.217647	−	0.976028i	$-0.430162\pi$
$709$	11.5906	0.435294	0.217647	+	0.976028i	$0.430162\pi$
$710$	−67.6721	−2.53969
$711$	−73.1944	−2.74500
$712$	−54.6306	−2.04737
$713$	9.00525	0.337249
$714$	20.5534	0.769192
$715$	1.20074	0.0449053
$716$	48.4996	1.81251
$717$	−13.1864	−0.492457
$718$	−46.0533	−1.71869
$719$	−35.9893	−1.34217	−0.671087	−	0.741379i	$-0.734172\pi$
$719$	−35.9893	−1.34217	−0.671087	+	0.741379i	$0.734172\pi$
$720$	−172.946	−6.44531
$721$	14.9180	0.555575
$722$	47.9678	1.78518
$723$	43.2285	1.60769
$724$	−19.2062	−0.713791
$725$	17.5282	0.650979
$726$	72.0752	2.67496
$727$	30.3921	1.12718	0.563590	−	0.826055i	$-0.309420\pi$
$727$	30.3921	1.12718	0.563590	+	0.826055i	$0.309420\pi$
$728$	−6.49430	−0.240695
$729$	28.3156	1.04873
$730$	−124.333	−4.60176
$731$	1.58033	0.0584506
$732$	−103.480	−3.82472
$733$	−39.5095	−1.45932	−0.729658	−	0.683812i	$-0.760321\pi$
$733$	−39.5095	−1.45932	−0.729658	+	0.683812i	$0.760321\pi$
$734$	69.1568	2.55262
$735$	−198.185	−7.31017
$736$	4.32214	0.159316
$737$	21.0213	0.774331
$738$	−93.8375	−3.45420
$739$	−19.3589	−0.712128	−0.356064	−	0.934462i	$-0.615881\pi$
$739$	−19.3589	−0.712128	−0.356064	+	0.934462i	$0.615881\pi$
$740$	−94.9034	−3.48872
$741$	−0.0300828	−0.00110512
$742$	32.8949	1.20761
$743$	16.1657	0.593062	0.296531	−	0.955023i	$-0.404170\pi$
$743$	16.1657	0.593062	0.296531	+	0.955023i	$0.404170\pi$
$744$	165.754	6.07683
$745$	62.3518	2.28439
$746$	48.5639	1.77805
$747$	52.8093	1.93219
$748$	3.30767	0.120940
$749$	87.6479	3.20258
$750$	117.024	4.27312
$751$	−50.1837	−1.83123	−0.915614	−	0.402059i	$-0.868295\pi$
$751$	−50.1837	−1.83123	−0.915614	+	0.402059i	$0.868295\pi$
$752$	26.2176	0.956056
$753$	−61.7867	−2.25163
$754$	1.11069	0.0404490
$755$	−60.3160	−2.19513
$756$	−290.346	−10.5598
$757$	36.1148	1.31261	0.656307	−	0.754494i	$-0.272118\pi$
$757$	36.1148	1.31261	0.656307	+	0.754494i	$0.272118\pi$
$758$	16.3620	0.594295
$759$	−4.83361	−0.175449
$760$	0.941053	0.0341356
$761$	−39.0305	−1.41486	−0.707428	−	0.706785i	$-0.750145\pi$
$761$	−39.0305	−1.41486	−0.707428	+	0.706785i	$0.750145\pi$
$762$	29.2259	1.05874
$763$	58.1860	2.10647
$764$	−41.2433	−1.49213
$765$	−14.1554	−0.511788
$766$	73.4136	2.65254
$767$	1.32737	0.0479285
$768$	−99.5698	−3.59291
$769$	8.12995	0.293173	0.146587	−	0.989198i	$-0.453171\pi$
$769$	8.12995	0.293173	0.146587	+	0.989198i	$0.453171\pi$
$770$	−66.0690	−2.38096
$771$	−76.9224	−2.77029
$772$	−115.547	−4.15863
$773$	3.05468	0.109869	0.0549346	−	0.998490i	$-0.482505\pi$
$773$	3.05468	0.109869	0.0549346	+	0.998490i	$0.482505\pi$
$774$	−55.4174	−1.99194
$775$	−76.6431	−2.75310
$776$	14.0751	0.505265
$777$	−90.6174	−3.25088
$778$	80.9762	2.90314
$779$	0.215506	0.00772132
$780$	11.6421	0.416856
$781$	−10.3987	−0.372093
$782$	1.37822	0.0492851
$783$	26.9559	0.963326
$784$	106.090	3.78894
$785$	−14.6389	−0.522485
$786$	47.2571	1.68561
$787$	8.61536	0.307104	0.153552	−	0.988141i	$-0.450929\pi$
$787$	8.61536	0.307104	0.153552	+	0.988141i	$0.450929\pi$
$788$	111.634	3.97678
$789$	30.7044	1.09311
$790$	−94.7940	−3.37262
$791$	−78.2453	−2.78208
$792$	−62.9648	−2.23736
$793$	1.64588	0.0584470
$794$	−13.8250	−0.490632
$795$	−32.0116	−1.13533
$796$	62.0986	2.20103
$797$	11.1484	0.394898	0.197449	−	0.980313i	$-0.436734\pi$
$797$	11.1484	0.394898	0.197449	+	0.980313i	$0.436734\pi$
$798$	1.65526	0.0585956
$799$	2.14587	0.0759154
$800$	−36.7854	−1.30056
$801$	66.1796	2.33834
$802$	53.7567	1.89821
$803$	−19.1052	−0.674209
$804$	203.818	7.18812
$805$	−18.8925	−0.665874
$806$	−4.85657	−0.171065
$807$	53.5711	1.88579
$808$	−77.8273	−2.73795
$809$	−16.0296	−0.563571	−0.281786	−	0.959477i	$-0.590927\pi$
$809$	−16.0296	−0.563571	−0.281786	+	0.959477i	$0.590927\pi$
$810$	206.711	7.26307
$811$	−10.5959	−0.372072	−0.186036	−	0.982543i	$-0.559564\pi$
$811$	−10.5959	−0.372072	−0.186036	+	0.982543i	$0.559564\pi$
$812$	−41.9407	−1.47183
$813$	−8.75927	−0.307201
$814$	−21.2498	−0.744805
$815$	66.6088	2.33320
$816$	10.7070	0.374819
$817$	0.127271	0.00445265
$818$	26.1271	0.913513
$819$	7.86721	0.274903
$820$	−83.4016	−2.91251
$821$	10.9152	0.380943	0.190471	−	0.981693i	$-0.438998\pi$
$821$	10.9152	0.380943	0.190471	+	0.981693i	$0.438998\pi$
$822$	68.5778	2.39192
$823$	−1.92808	−0.0672088	−0.0336044	−	0.999435i	$-0.510699\pi$
$823$	−1.92808	−0.0672088	−0.0336044	+	0.999435i	$0.510699\pi$
$824$	18.4125	0.641431
$825$	41.1385	1.43226
$826$	−73.0363	−2.54126
$827$	48.4414	1.68447	0.842236	−	0.539109i	$-0.181239\pi$
$827$	48.4414	1.68447	0.842236	+	0.539109i	$0.181239\pi$
$828$	−33.1675	−1.15265
$829$	11.4431	0.397437	0.198718	−	0.980057i	$-0.436322\pi$
$829$	11.4431	0.397437	0.198718	+	0.980057i	$0.436322\pi$
$830$	68.3933	2.37397
$831$	−66.6166	−2.31090
$832$	0.518094	0.0179617
$833$	8.68333	0.300860
$834$	61.6578	2.13504
$835$	−7.80555	−0.270122
$836$	0.266381	0.00921299
$837$	−117.867	−4.07407
$838$	10.7602	0.371706
$839$	−0.469359	−0.0162041	−0.00810204	−	0.999967i	$-0.502579\pi$
$839$	−0.469359	−0.0162041	−0.00810204	+	0.999967i	$0.502579\pi$
$840$	−347.743	−11.9983
$841$	−25.1062	−0.865731
$842$	11.5080	0.396593
$843$	−100.775	−3.47089
$844$	−62.1721	−2.14005
$845$	48.2523	1.65993
$846$	−75.2491	−2.58712
$847$	43.2884	1.48741
$848$	17.1361	0.588456
$849$	−27.7596	−0.952706
$850$	−11.7300	−0.402334
$851$	−6.07641	−0.208297
$852$	−100.823	−3.45414
$853$	11.8333	0.405163	0.202581	−	0.979265i	$-0.435067\pi$
$853$	11.8333	0.405163	0.202581	+	0.979265i	$0.435067\pi$
$854$	−90.5621	−3.09897
$855$	−1.13999	−0.0389870
$856$	108.179	3.69750
$857$	−11.9605	−0.408563	−0.204282	−	0.978912i	$-0.565486\pi$
$857$	−11.9605	−0.408563	−0.204282	+	0.978912i	$0.565486\pi$
$858$	2.60679	0.0889943
$859$	3.54568	0.120977	0.0604884	−	0.998169i	$-0.480734\pi$
$859$	3.54568	0.120977	0.0604884	+	0.998169i	$0.480734\pi$
$860$	−49.2543	−1.67956
$861$	−79.6351	−2.71396
$862$	−40.1964	−1.36909
$863$	11.1442	0.379353	0.189677	−	0.981847i	$-0.439256\pi$
$863$	11.1442	0.379353	0.189677	+	0.981847i	$0.439256\pi$
$864$	−56.5710	−1.92458
$865$	19.9245	0.677455
$866$	−72.2565	−2.45538
$867$	−53.5872	−1.81992
$868$	183.389	6.22461
$869$	−14.5663	−0.494127
$870$	59.4729	2.01632
$871$	−3.24180	−0.109844
$872$	71.8160	2.43200
$873$	−17.0506	−0.577074
$874$	0.110994	0.00375444
$875$	70.2848	2.37606
$876$	−185.240	−6.25869
$877$	−31.0658	−1.04902	−0.524510	−	0.851405i	$-0.675751\pi$
$877$	−31.0658	−1.04902	−0.524510	+	0.851405i	$0.675751\pi$
$878$	52.8570	1.78384
$879$	90.5786	3.05514
$880$	−34.4176	−1.16022
$881$	30.2452	1.01899	0.509493	−	0.860475i	$-0.329833\pi$
$881$	30.2452	1.01899	0.509493	+	0.860475i	$0.329833\pi$
$882$	−304.498	−10.2530
$883$	24.6218	0.828590	0.414295	−	0.910143i	$-0.364028\pi$
$883$	24.6218	0.828590	0.414295	+	0.910143i	$0.364028\pi$
$884$	−0.510092	−0.0171562
$885$	71.0751	2.38916
$886$	−1.79997	−0.0604713
$887$	−6.84619	−0.229873	−0.114936	−	0.993373i	$-0.536666\pi$
$887$	−6.84619	−0.229873	−0.114936	+	0.993373i	$0.536666\pi$
$888$	−111.845	−3.75326
$889$	17.5531	0.588713
$890$	85.7093	2.87298
$891$	31.7636	1.06412
$892$	102.124	3.41937
$893$	0.172816	0.00578308
$894$	135.364	4.52727
$895$	−41.3055	−1.38069
$896$	−68.7453	−2.29662
$897$	0.745415	0.0248887
$898$	−1.32482	−0.0442099
$899$	−17.0259	−0.567847
$900$	282.286	9.40954
$901$	1.40256	0.0467262
$902$	−18.6744	−0.621790
$903$	−47.0299	−1.56506
$904$	−96.5742	−3.21201
$905$	16.3572	0.543733
$906$	−130.945	−4.35035
$907$	−29.1207	−0.966936	−0.483468	−	0.875362i	$-0.660623\pi$
$907$	−29.1207	−0.966936	−0.483468	+	0.875362i	$0.660623\pi$
$908$	−99.3368	−3.29661
$909$	94.2802	3.12708
$910$	10.1888	0.337756
$911$	11.6205	0.385005	0.192502	−	0.981297i	$-0.438340\pi$
$911$	11.6205	0.385005	0.192502	+	0.981297i	$0.438340\pi$
$912$	0.862282	0.0285530
$913$	10.5095	0.347813
$914$	80.6695	2.66831
$915$	88.1302	2.91350
$916$	−70.9585	−2.34454
$917$	28.3827	0.937279
$918$	−18.0391	−0.595379
$919$	46.3660	1.52947	0.764737	−	0.644342i	$-0.222869\pi$
$919$	46.3660	1.52947	0.764737	+	0.644342i	$0.222869\pi$
$920$	−23.3181	−0.768775
$921$	29.8330	0.983032
$922$	36.5818	1.20476
$923$	1.60363	0.0527840
$924$	−98.4347	−3.23826
$925$	51.7159	1.70041
$926$	53.9694	1.77355
$927$	−22.3050	−0.732592
$928$	−8.17172	−0.268250
$929$	34.1156	1.11930	0.559648	−	0.828730i	$-0.310936\pi$
$929$	34.1156	1.11930	0.559648	+	0.828730i	$0.310936\pi$
$930$	−260.049	−8.52736
$931$	0.699308	0.0229189
$932$	−36.0218	−1.17993
$933$	86.2961	2.82521
$934$	62.4743	2.04422
$935$	−2.81703	−0.0921267
$936$	9.71011	0.317385
$937$	23.5277	0.768615	0.384308	−	0.923205i	$-0.374440\pi$
$937$	23.5277	0.768615	0.384308	+	0.923205i	$0.374440\pi$
$938$	178.375	5.82415
$939$	−65.4137	−2.13469
$940$	−66.8805	−2.18140
$941$	4.68732	0.152802	0.0764011	−	0.997077i	$-0.475657\pi$
$941$	4.68732	0.152802	0.0764011	+	0.997077i	$0.475657\pi$
$942$	−31.7807	−1.03547
$943$	−5.33998	−0.173894
$944$	−38.0471	−1.23833
$945$	247.278	8.04395
$946$	−11.0285	−0.358568
$947$	−5.28323	−0.171682	−0.0858409	−	0.996309i	$-0.527358\pi$
$947$	−5.28323	−0.171682	−0.0858409	+	0.996309i	$0.527358\pi$
$948$	−141.231	−4.58698
$949$	2.94631	0.0956414
$950$	−0.944666	−0.0306490
$951$	99.3891	3.22291
$952$	15.2361	0.493804
$953$	13.7301	0.444761	0.222380	−	0.974960i	$-0.428617\pi$
$953$	13.7301	0.444761	0.222380	+	0.974960i	$0.428617\pi$
$954$	−49.1836	−1.59238
$955$	35.1255	1.13664
$956$	−18.0069	−0.582385
$957$	9.13875	0.295414
$958$	57.3673	1.85345
$959$	41.1879	1.33003
$960$	27.7418	0.895363
$961$	43.4471	1.40152
$962$	3.27703	0.105656
$963$	−131.049	−4.22299
$964$	59.0313	1.90127
$965$	98.4076	3.16785
$966$	−41.0153	−1.31964
$967$	−26.1021	−0.839386	−0.419693	−	0.907666i	$-0.637862\pi$
$967$	−26.1021	−0.839386	−0.419693	+	0.907666i	$0.637862\pi$
$968$	53.4288	1.71727
$969$	0.0705765	0.00226724
$970$	−22.0822	−0.709017
$971$	35.4027	1.13613	0.568063	−	0.822985i	$-0.307693\pi$
$971$	35.4027	1.13613	0.568063	+	0.822985i	$0.307693\pi$
$972$	128.683	4.12751
$973$	37.0317	1.18718
$974$	−0.282544	−0.00905329
$975$	−6.34418	−0.203176
$976$	−47.1769	−1.51010
$977$	−0.813572	−0.0260285	−0.0130142	−	0.999915i	$-0.504143\pi$
$977$	−0.813572	−0.0260285	−0.0130142	+	0.999915i	$0.504143\pi$
$978$	144.606	4.62400
$979$	13.1703	0.420924
$980$	−270.634	−8.64509
$981$	−86.9982	−2.77764
$982$	−108.667	−3.46771
$983$	24.5798	0.783973	0.391987	−	0.919971i	$-0.371788\pi$
$983$	24.5798	0.783973	0.391987	+	0.919971i	$0.371788\pi$
$984$	−98.2896	−3.13336
$985$	−95.0747	−3.02933
$986$	−2.60576	−0.0829843
$987$	−63.8601	−2.03269
$988$	−0.0410800	−0.00130693
$989$	−3.15362	−0.100279
$990$	98.7847	3.13958
$991$	1.28527	0.0408280	0.0204140	−	0.999792i	$-0.493502\pi$
$991$	1.28527	0.0408280	0.0204140	+	0.999792i	$0.493502\pi$
$992$	35.7314	1.13447
$993$	95.0639	3.01676
$994$	−88.2371	−2.79871
$995$	−52.8873	−1.67664
$996$	101.898	3.22875
$997$	−28.2220	−0.893800	−0.446900	−	0.894584i	$-0.647472\pi$
$997$	−28.2220	−0.893800	−0.446900	+	0.894584i	$0.647472\pi$
$998$	−17.9213	−0.567287
$999$	79.5320	2.51628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.e.1.14	✓	221

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.e.1.14	✓	221	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.52486 q^{2} +3.20374 q^{3} +4.37490 q^{4} -3.72596 q^{5} -8.08898 q^{6} -4.85825 q^{7} -5.99630 q^{8} +7.26393 q^{9} +O(q^{10})\)	\(q-2.52486 q^{2} +3.20374 q^{3} +4.37490 q^{4} -3.72596 q^{5} -8.08898 q^{6} -4.85825 q^{7} -5.99630 q^{8} +7.26393 q^{9} +9.40752 q^{10} +1.44558 q^{11} +14.0160 q^{12} -0.222930 q^{13} +12.2664 q^{14} -11.9370 q^{15} +6.38998 q^{16} +0.523011 q^{17} -18.3404 q^{18} +0.0421204 q^{19} -16.3007 q^{20} -15.5646 q^{21} -3.64989 q^{22} -1.04369 q^{23} -19.2106 q^{24} +8.88278 q^{25} +0.562867 q^{26} +13.6605 q^{27} -21.2544 q^{28} +1.97327 q^{29} +30.1392 q^{30} -8.62827 q^{31} -4.14120 q^{32} +4.63126 q^{33} -1.32053 q^{34} +18.1016 q^{35} +31.7790 q^{36} +5.82204 q^{37} -0.106348 q^{38} -0.714210 q^{39} +22.3420 q^{40} +5.11644 q^{41} +39.2983 q^{42} +3.02160 q^{43} +6.32428 q^{44} -27.0651 q^{45} +2.63517 q^{46} +4.10292 q^{47} +20.4718 q^{48} +16.6026 q^{49} -22.4278 q^{50} +1.67559 q^{51} -0.975299 q^{52} +2.68171 q^{53} -34.4909 q^{54} -5.38618 q^{55} +29.1315 q^{56} +0.134943 q^{57} -4.98223 q^{58} -5.95418 q^{59} -52.2232 q^{60} -7.38295 q^{61} +21.7852 q^{62} -35.2900 q^{63} -2.32402 q^{64} +0.830630 q^{65} -11.6933 q^{66} +14.5418 q^{67} +2.28812 q^{68} -3.34371 q^{69} -45.7041 q^{70} -7.19340 q^{71} -43.5567 q^{72} -13.2163 q^{73} -14.6998 q^{74} +28.4581 q^{75} +0.184273 q^{76} -7.02300 q^{77} +1.80328 q^{78} -10.0764 q^{79} -23.8088 q^{80} +21.9729 q^{81} -12.9183 q^{82} +7.27007 q^{83} -68.0934 q^{84} -1.94872 q^{85} -7.62912 q^{86} +6.32185 q^{87} -8.66814 q^{88} +9.11072 q^{89} +68.3356 q^{90} +1.08305 q^{91} -4.56605 q^{92} -27.6427 q^{93} -10.3593 q^{94} -0.156939 q^{95} -13.2673 q^{96} -2.34729 q^{97} -41.9192 q^{98} +10.5006 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9}+O(q^{10}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9	\( 221 q - 15 q^{2} - 17 q^{3} + 189 q^{4} - 32 q^{5} - 33 q^{6} - 40 q^{7} - 39 q^{8} + 176 q^{9} - 61 q^{10} - 50 q^{11} - 43 q^{12} - 87 q^{13} - 41 q^{14} - 62 q^{15} + 129 q^{16} - 29 q^{17} - 61 q^{18} - 107 q^{19} - 59 q^{20} - 163 q^{21} - 70 q^{22} - 31 q^{23} - 98 q^{24} + 119 q^{25} - 23 q^{26} - 41 q^{27} - 112 q^{28} - 152 q^{29} - 66 q^{30} - 117 q^{31} - 93 q^{32} - 60 q^{33} - 80 q^{34} - 21 q^{35} + 92 q^{36} - 231 q^{37} + 2 q^{38} - 81 q^{39} - 143 q^{40} - 81 q^{41} - 6 q^{42} - 126 q^{43} - 115 q^{44} - 156 q^{45} - 205 q^{46} - 4 q^{47} - 55 q^{48} + 103 q^{49} - 61 q^{50} - 106 q^{51} - 164 q^{52} - 87 q^{53} - 110 q^{54} - 62 q^{55} - 73 q^{56} - 136 q^{57} - 128 q^{58} - 76 q^{59} - 148 q^{60} - 345 q^{61} + 5 q^{62} - 74 q^{63} - 25 q^{64} - 110 q^{65} - 34 q^{66} - 104 q^{67} - 48 q^{68} - 133 q^{69} - 92 q^{70} - 39 q^{71} - 177 q^{72} - 175 q^{73} - 44 q^{74} - 23 q^{75} - 268 q^{76} - 81 q^{77} - 19 q^{78} - 272 q^{79} - 60 q^{80} + 77 q^{81} - 13 q^{82} - 40 q^{83} - 221 q^{84} - 376 q^{85} - 82 q^{86} - 3 q^{87} - 234 q^{88} - 92 q^{89} - 91 q^{90} - 205 q^{91} - 11 q^{92} - 125 q^{93} - 126 q^{94} - 56 q^{95} - 148 q^{96} - 133 q^{97} - 4 q^{98} - 195 q^{99}+O(q^{100}) \) 221 * q - 15 * q^2 - 17 * q^3 + 189 * q^4 - 32 * q^5 - 33 * q^6 - 40 * q^7 - 39 * q^8 + 176 * q^9 - 61 * q^10 - 50 * q^11 - 43 * q^12 - 87 * q^13 - 41 * q^14 - 62 * q^15 + 129 * q^16 - 29 * q^17 - 61 * q^18 - 107 * q^19 - 59 * q^20 - 163 * q^21 - 70 * q^22 - 31 * q^23 - 98 * q^24 + 119 * q^25 - 23 * q^26 - 41 * q^27 - 112 * q^28 - 152 * q^29 - 66 * q^30 - 117 * q^31 - 93 * q^32 - 60 * q^33 - 80 * q^34 - 21 * q^35 + 92 * q^36 - 231 * q^37 + 2 * q^38 - 81 * q^39 - 143 * q^40 - 81 * q^41 - 6 * q^42 - 126 * q^43 - 115 * q^44 - 156 * q^45 - 205 * q^46 - 4 * q^47 - 55 * q^48 + 103 * q^49 - 61 * q^50 - 106 * q^51 - 164 * q^52 - 87 * q^53 - 110 * q^54 - 62 * q^55 - 73 * q^56 - 136 * q^57 - 128 * q^58 - 76 * q^59 - 148 * q^60 - 345 * q^61 + 5 * q^62 - 74 * q^63 - 25 * q^64 - 110 * q^65 - 34 * q^66 - 104 * q^67 - 48 * q^68 - 133 * q^69 - 92 * q^70 - 39 * q^71 - 177 * q^72 - 175 * q^73 - 44 * q^74 - 23 * q^75 - 268 * q^76 - 81 * q^77 - 19 * q^78 - 272 * q^79 - 60 * q^80 + 77 * q^81 - 13 * q^82 - 40 * q^83 - 221 * q^84 - 376 * q^85 - 82 * q^86 - 3 * q^87 - 234 * q^88 - 92 * q^89 - 91 * q^90 - 205 * q^91 - 11 * q^92 - 125 * q^93 - 126 * q^94 - 56 * q^95 - 148 * q^96 - 133 * q^97 - 4 * q^98 - 195 * q^99

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