LMFDB - Embedded newform 4013.2.a.c.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4013,2,Mod(1,4013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4013, 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("4013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4013.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.0439663311$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37116 q^{2} +2.70615 q^{3} +3.62242 q^{4} +4.34995 q^{5} -6.41674 q^{6} +1.61584 q^{7} -3.84703 q^{8} +4.32327 q^{9} +O(q^{10})$	\(q-2.37116 q^{2} +2.70615 q^{3} +3.62242 q^{4} +4.34995 q^{5} -6.41674 q^{6} +1.61584 q^{7} -3.84703 q^{8} +4.32327 q^{9} -10.3145 q^{10} -0.242281 q^{11} +9.80283 q^{12} +1.30886 q^{13} -3.83143 q^{14} +11.7716 q^{15} +1.87710 q^{16} -6.22777 q^{17} -10.2512 q^{18} +5.58380 q^{19} +15.7574 q^{20} +4.37272 q^{21} +0.574488 q^{22} -0.911131 q^{23} -10.4107 q^{24} +13.9221 q^{25} -3.10352 q^{26} +3.58096 q^{27} +5.85327 q^{28} +1.37997 q^{29} -27.9125 q^{30} -8.77018 q^{31} +3.24314 q^{32} -0.655649 q^{33} +14.7671 q^{34} +7.02885 q^{35} +15.6607 q^{36} +0.930161 q^{37} -13.2401 q^{38} +3.54197 q^{39} -16.7344 q^{40} +6.04459 q^{41} -10.3684 q^{42} +1.88733 q^{43} -0.877643 q^{44} +18.8060 q^{45} +2.16044 q^{46} -9.12877 q^{47} +5.07973 q^{48} -4.38905 q^{49} -33.0115 q^{50} -16.8533 q^{51} +4.74124 q^{52} -11.5955 q^{53} -8.49105 q^{54} -1.05391 q^{55} -6.21621 q^{56} +15.1106 q^{57} -3.27213 q^{58} +13.1400 q^{59} +42.6418 q^{60} +9.98765 q^{61} +20.7955 q^{62} +6.98573 q^{63} -11.4442 q^{64} +5.69347 q^{65} +1.55465 q^{66} +8.09269 q^{67} -22.5596 q^{68} -2.46566 q^{69} -16.6666 q^{70} -3.99256 q^{71} -16.6317 q^{72} +12.8000 q^{73} -2.20557 q^{74} +37.6753 q^{75} +20.2269 q^{76} -0.391488 q^{77} -8.39860 q^{78} -14.5838 q^{79} +8.16531 q^{80} -3.27917 q^{81} -14.3327 q^{82} +16.8360 q^{83} +15.8399 q^{84} -27.0905 q^{85} -4.47516 q^{86} +3.73440 q^{87} +0.932062 q^{88} -11.2028 q^{89} -44.5921 q^{90} +2.11491 q^{91} -3.30050 q^{92} -23.7334 q^{93} +21.6458 q^{94} +24.2892 q^{95} +8.77644 q^{96} +13.1433 q^{97} +10.4072 q^{98} -1.04744 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) $ 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9 + 43 * q^10 + 18 * q^11 + 95 * q^12 + 95 * q^13 + 2 * q^14 + 36 * q^15 + 225 * q^16 + 35 * q^17 + 46 * q^18 + 127 * q^19 + 4 * q^20 + 32 * q^21 + 60 * q^22 + 35 * q^23 + 26 * q^24 + 207 * q^25 + 19 * q^26 + 191 * q^27 + 87 * q^28 + 16 * q^29 + 28 * q^30 + 93 * q^31 + 73 * q^32 + 70 * q^33 + 45 * q^34 + 73 * q^35 + 206 * q^36 + 64 * q^37 + 35 * q^38 + 72 * q^39 + 139 * q^40 + 19 * q^41 + 35 * q^42 + 261 * q^43 + 11 * q^44 + 12 * q^45 + 58 * q^46 + 40 * q^47 + 130 * q^48 + 234 * q^49 - 14 * q^50 + 76 * q^51 + 263 * q^52 + 17 * q^53 + 28 * q^54 + 170 * q^55 - 10 * q^56 + 60 * q^57 + 52 * q^58 + 69 * q^59 + 37 * q^60 + 110 * q^61 + 71 * q^62 + 101 * q^63 + 250 * q^64 - q^65 + 43 * q^66 + 190 * q^67 + 48 * q^68 + 45 * q^69 + 14 * q^70 + 9 * q^71 + 98 * q^72 + 182 * q^73 - 23 * q^74 + 219 * q^75 + 197 * q^76 + 25 * q^77 - 26 * q^78 + 105 * q^79 + 20 * q^80 + 236 * q^81 + 107 * q^82 + 130 * q^83 + 38 * q^84 + 73 * q^85 - 24 * q^86 + 171 * q^87 + 165 * q^88 + 40 * q^89 + 45 * q^90 + 182 * q^91 - 4 * q^92 + 23 * q^93 + 98 * q^94 + 30 * q^95 - 2 * q^96 + 168 * q^97 + 82 * q^98 + 50 * 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 $

$2$	−2.37116	−1.67667	−0.838333	−	0.545158i	$-0.816470\pi$
$2$	−2.37116	−1.67667	−0.838333	+	0.545158i	$0.816470\pi$
$3$	2.70615	1.56240	0.781199	−	0.624282i	$-0.214608\pi$
$3$	2.70615	1.56240	0.781199	+	0.624282i	$0.214608\pi$
$4$	3.62242	1.81121
$5$	4.34995	1.94536	0.972679	−	0.232156i	$-0.0745779\pi$
$5$	4.34995	1.94536	0.972679	+	0.232156i	$0.0745779\pi$
$6$	−6.41674	−2.61962
$7$	1.61584	0.610732	0.305366	−	0.952235i	$-0.401221\pi$
$7$	1.61584	0.610732	0.305366	+	0.952235i	$0.401221\pi$
$8$	−3.84703	−1.36013
$9$	4.32327	1.44109
$10$	−10.3145	−3.26172
$11$	−0.242281	−0.0730504	−0.0365252	−	0.999333i	$-0.511629\pi$
$11$	−0.242281	−0.0730504	−0.0365252	+	0.999333i	$0.511629\pi$
$12$	9.80283	2.82983
$13$	1.30886	0.363012	0.181506	−	0.983390i	$-0.441903\pi$
$13$	1.30886	0.363012	0.181506	+	0.983390i	$0.441903\pi$
$14$	−3.83143	−1.02399
$15$	11.7716	3.03942
$16$	1.87710	0.469276
$17$	−6.22777	−1.51046	−0.755228	−	0.655462i	$-0.772474\pi$
$17$	−6.22777	−1.51046	−0.755228	+	0.655462i	$0.772474\pi$
$18$	−10.2512	−2.41623
$19$	5.58380	1.28101	0.640506	−	0.767953i	$-0.278725\pi$
$19$	5.58380	1.28101	0.640506	+	0.767953i	$0.278725\pi$
$20$	15.7574	3.52345
$21$	4.37272	0.954206
$22$	0.574488	0.122481
$23$	−0.911131	−0.189984	−0.0949920	−	0.995478i	$-0.530283\pi$
$23$	−0.911131	−0.189984	−0.0949920	+	0.995478i	$0.530283\pi$
$24$	−10.4107	−2.12507
$25$	13.9221	2.78441
$26$	−3.10352	−0.608650
$27$	3.58096	0.689156
$28$	5.85327	1.10616
$29$	1.37997	0.256253	0.128127	−	0.991758i	$-0.459104\pi$
$29$	1.37997	0.256253	0.128127	+	0.991758i	$0.459104\pi$
$30$	−27.9125	−5.09610
$31$	−8.77018	−1.57517	−0.787585	−	0.616206i	$-0.788669\pi$
$31$	−8.77018	−1.57517	−0.787585	+	0.616206i	$0.788669\pi$
$32$	3.24314	0.573312
$33$	−0.655649	−0.114134
$34$	14.7671	2.53253
$35$	7.02885	1.18809
$36$	15.6607	2.61012
$37$	0.930161	0.152918	0.0764588	−	0.997073i	$-0.475639\pi$
$37$	0.930161	0.152918	0.0764588	+	0.997073i	$0.475639\pi$
$38$	−13.2401	−2.14783
$39$	3.54197	0.567169
$40$	−16.7344	−2.64594
$41$	6.04459	0.944006	0.472003	−	0.881597i	$-0.343531\pi$
$41$	6.04459	0.944006	0.472003	+	0.881597i	$0.343531\pi$
$42$	−10.3684	−1.59989
$43$	1.88733	0.287815	0.143907	−	0.989591i	$-0.454033\pi$
$43$	1.88733	0.287815	0.143907	+	0.989591i	$0.454033\pi$
$44$	−0.877643	−0.132310
$45$	18.8060	2.80343
$46$	2.16044	0.318540
$47$	−9.12877	−1.33157	−0.665784	−	0.746144i	$-0.731903\pi$
$47$	−9.12877	−1.33157	−0.665784	+	0.746144i	$0.731903\pi$
$48$	5.07973	0.733196
$49$	−4.38905	−0.627007
$50$	−33.0115	−4.66854
$51$	−16.8533	−2.35993
$52$	4.74124	0.657491
$53$	−11.5955	−1.59277	−0.796385	−	0.604790i	$-0.793257\pi$
$53$	−11.5955	−1.59277	−0.796385	+	0.604790i	$0.793257\pi$
$54$	−8.49105	−1.15548
$55$	−1.05391	−0.142109
$56$	−6.21621	−0.830676
$57$	15.1106	2.00145
$58$	−3.27213	−0.429651
$59$	13.1400	1.71068	0.855342	−	0.518064i	$-0.173347\pi$
$59$	13.1400	1.71068	0.855342	+	0.518064i	$0.173347\pi$
$60$	42.6418	5.50504
$61$	9.98765	1.27879	0.639394	−	0.768879i	$-0.279185\pi$
$61$	9.98765	1.27879	0.639394	+	0.768879i	$0.279185\pi$
$62$	20.7955	2.64104
$63$	6.98573	0.880119
$64$	−11.4442	−1.43053
$65$	5.69347	0.706188
$66$	1.55465	0.191364
$67$	8.09269	0.988679	0.494340	−	0.869269i	$-0.335410\pi$
$67$	8.09269	0.988679	0.494340	+	0.869269i	$0.335410\pi$
$68$	−22.5596	−2.73576
$69$	−2.46566	−0.296831
$70$	−16.6666	−1.99203
$71$	−3.99256	−0.473829	−0.236915	−	0.971530i	$-0.576136\pi$
$71$	−3.99256	−0.473829	−0.236915	+	0.971530i	$0.576136\pi$
$72$	−16.6317	−1.96007
$73$	12.8000	1.49813	0.749065	−	0.662497i	$-0.230503\pi$
$73$	12.8000	1.49813	0.749065	+	0.662497i	$0.230503\pi$
$74$	−2.20557	−0.256392
$75$	37.6753	4.35037
$76$	20.2269	2.32018
$77$	−0.391488	−0.0446142
$78$	−8.39860	−0.950954
$79$	−14.5838	−1.64081	−0.820403	−	0.571786i	$-0.806251\pi$
$79$	−14.5838	−1.64081	−0.820403	+	0.571786i	$0.806251\pi$
$80$	8.16531	0.912910
$81$	−3.27917	−0.364352
$82$	−14.3327	−1.58278
$83$	16.8360	1.84799	0.923995	−	0.382405i	$-0.124904\pi$
$83$	16.8360	1.84799	0.923995	+	0.382405i	$0.124904\pi$
$84$	15.8399	1.72827
$85$	−27.0905	−2.93838
$86$	−4.47516	−0.482569
$87$	3.73440	0.400370
$88$	0.932062	0.0993582
$89$	−11.2028	−1.18750	−0.593750	−	0.804650i	$-0.702353\pi$
$89$	−11.2028	−1.18750	−0.593750	+	0.804650i	$0.702353\pi$
$90$	−44.5921	−4.70042
$91$	2.11491	0.221703
$92$	−3.30050	−0.344101
$93$	−23.7334	−2.46104
$94$	21.6458	2.23260
$95$	24.2892	2.49202
$96$	8.77644	0.895742
$97$	13.1433	1.33450	0.667248	−	0.744836i	$-0.267472\pi$
$97$	13.1433	1.33450	0.667248	+	0.744836i	$0.267472\pi$
$98$	10.4072	1.05128
$99$	−1.04744	−0.105272
$100$	50.4316	5.04316
$101$	−6.21407	−0.618323	−0.309161	−	0.951010i	$-0.600048\pi$
$101$	−6.21407	−0.618323	−0.309161	+	0.951010i	$0.600048\pi$
$102$	39.9620	3.95682
$103$	−10.3808	−1.02285	−0.511423	−	0.859329i	$-0.670881\pi$
$103$	−10.3808	−1.02285	−0.511423	+	0.859329i	$0.670881\pi$
$104$	−5.03522	−0.493744
$105$	19.0211	1.85627
$106$	27.4949	2.67054
$107$	4.40372	0.425724	0.212862	−	0.977082i	$-0.431722\pi$
$107$	4.40372	0.425724	0.212862	+	0.977082i	$0.431722\pi$
$108$	12.9718	1.24821
$109$	5.98060	0.572838	0.286419	−	0.958104i	$-0.407535\pi$
$109$	5.98060	0.572838	0.286419	+	0.958104i	$0.407535\pi$
$110$	2.49899	0.238270
$111$	2.51716	0.238918
$112$	3.03311	0.286602
$113$	8.95310	0.842237	0.421119	−	0.907006i	$-0.361638\pi$
$113$	8.95310	0.842237	0.421119	+	0.907006i	$0.361638\pi$
$114$	−35.8298	−3.35576
$115$	−3.96338	−0.369587
$116$	4.99882	0.464129
$117$	5.65854	0.523132
$118$	−31.1571	−2.86825
$119$	−10.0631	−0.922484
$120$	−45.2859	−4.13402
$121$	−10.9413	−0.994664
$122$	−23.6824	−2.14410
$123$	16.3576	1.47491
$124$	−31.7693	−2.85297
$125$	38.8106	3.47132
$126$	−16.5643	−1.47567
$127$	19.9707	1.77212	0.886058	−	0.463575i	$-0.153434\pi$
$127$	19.9707	1.77212	0.886058	+	0.463575i	$0.153434\pi$
$128$	20.6499	1.82521
$129$	5.10739	0.449681
$130$	−13.5002	−1.18404
$131$	9.17933	0.802002	0.401001	−	0.916078i	$-0.368662\pi$
$131$	9.17933	0.802002	0.401001	+	0.916078i	$0.368662\pi$
$132$	−2.37504	−0.206721
$133$	9.02255	0.782354
$134$	−19.1891	−1.65769
$135$	15.5770	1.34065
$136$	23.9584	2.05442
$137$	8.74796	0.747388	0.373694	−	0.927552i	$-0.378091\pi$
$137$	8.74796	0.747388	0.373694	+	0.927552i	$0.378091\pi$
$138$	5.84649	0.497686
$139$	21.3077	1.80730	0.903648	−	0.428276i	$-0.140879\pi$
$139$	21.3077	1.80730	0.903648	+	0.428276i	$0.140879\pi$
$140$	25.4615	2.15189
$141$	−24.7039	−2.08044
$142$	9.46701	0.794454
$143$	−0.317111	−0.0265182
$144$	8.11522	0.676269
$145$	6.00278	0.498504
$146$	−30.3510	−2.51186
$147$	−11.8774	−0.979634
$148$	3.36944	0.276966
$149$	−15.6918	−1.28552	−0.642759	−	0.766068i	$-0.722210\pi$
$149$	−15.6918	−1.28552	−0.642759	+	0.766068i	$0.722210\pi$
$150$	−89.3343	−7.29411
$151$	7.41355	0.603306	0.301653	−	0.953418i	$-0.402462\pi$
$151$	7.41355	0.603306	0.301653	+	0.953418i	$0.402462\pi$
$152$	−21.4811	−1.74234
$153$	−26.9243	−2.17670
$154$	0.928283	0.0748032
$155$	−38.1498	−3.06427
$156$	12.8305	1.02726
$157$	−2.35213	−0.187721	−0.0938603	−	0.995585i	$-0.529921\pi$
$157$	−2.35213	−0.187721	−0.0938603	+	0.995585i	$0.529921\pi$
$158$	34.5806	2.75108
$159$	−31.3793	−2.48854
$160$	14.1075	1.11530
$161$	−1.47225	−0.116029
$162$	7.77546	0.610898
$163$	2.48798	0.194874	0.0974370	−	0.995242i	$-0.468936\pi$
$163$	2.48798	0.194874	0.0974370	+	0.995242i	$0.468936\pi$
$164$	21.8961	1.70980
$165$	−2.85204	−0.222031
$166$	−39.9209	−3.09846
$167$	2.17971	0.168671	0.0843354	−	0.996437i	$-0.473123\pi$
$167$	2.17971	0.168671	0.0843354	+	0.996437i	$0.473123\pi$
$168$	−16.8220	−1.29785
$169$	−11.2869	−0.868222
$170$	64.2361	4.92668
$171$	24.1402	1.84605
$172$	6.83670	0.521293
$173$	−17.8704	−1.35866	−0.679332	−	0.733831i	$-0.737731\pi$
$173$	−17.8704	−1.35866	−0.679332	+	0.733831i	$0.737731\pi$
$174$	−8.85487	−0.671286
$175$	22.4959	1.70053
$176$	−0.454786	−0.0342808
$177$	35.5589	2.67277
$178$	26.5638	1.99104
$179$	10.9727	0.820139	0.410069	−	0.912054i	$-0.365504\pi$
$179$	10.9727	0.820139	0.410069	+	0.912054i	$0.365504\pi$
$180$	68.1233	5.07761
$181$	−8.82573	−0.656012	−0.328006	−	0.944676i	$-0.606377\pi$
$181$	−8.82573	−0.656012	−0.328006	+	0.944676i	$0.606377\pi$
$182$	−5.01480	−0.371722
$183$	27.0281	1.99798
$184$	3.50515	0.258403
$185$	4.04616	0.297479
$186$	56.2759	4.12635
$187$	1.50887	0.110339
$188$	−33.0683	−2.41175
$189$	5.78627	0.420890
$190$	−57.5938	−4.17829
$191$	3.17363	0.229636	0.114818	−	0.993387i	$-0.463372\pi$
$191$	3.17363	0.229636	0.114818	+	0.993387i	$0.463372\pi$
$192$	−30.9699	−2.23506
$193$	−3.16922	−0.228126	−0.114063	−	0.993474i	$-0.536387\pi$
$193$	−3.16922	−0.228126	−0.114063	+	0.993474i	$0.536387\pi$
$194$	−31.1648	−2.23750
$195$	15.4074	1.10335
$196$	−15.8990	−1.13564
$197$	1.66072	0.118321	0.0591605	−	0.998248i	$-0.481158\pi$
$197$	1.66072	0.118321	0.0591605	+	0.998248i	$0.481158\pi$
$198$	2.48366	0.176506
$199$	−9.47067	−0.671358	−0.335679	−	0.941976i	$-0.608966\pi$
$199$	−9.47067	−0.671358	−0.335679	+	0.941976i	$0.608966\pi$
$200$	−53.5587	−3.78717
$201$	21.9001	1.54471
$202$	14.7346	1.03672
$203$	2.22981	0.156502
$204$	−61.0498	−4.27434
$205$	26.2937	1.83643
$206$	24.6145	1.71497
$207$	−3.93906	−0.273784
$208$	2.45686	0.170353
$209$	−1.35285	−0.0935784
$210$	−45.1022	−3.11235
$211$	−15.3781	−1.05867	−0.529336	−	0.848413i	$-0.677559\pi$
$211$	−15.3781	−1.05867	−0.529336	+	0.848413i	$0.677559\pi$
$212$	−42.0040	−2.88484
$213$	−10.8045	−0.740310
$214$	−10.4419	−0.713797
$215$	8.20978	0.559902
$216$	−13.7761	−0.937343
$217$	−14.1712	−0.962007
$218$	−14.1810	−0.960458
$219$	34.6388	2.34067
$220$	−3.81771	−0.257390
$221$	−8.15127	−0.548314
$222$	−5.96860	−0.400586
$223$	−22.6813	−1.51885	−0.759425	−	0.650595i	$-0.774519\pi$
$223$	−22.6813	−1.51885	−0.759425	+	0.650595i	$0.774519\pi$
$224$	5.24041	0.350140
$225$	60.1888	4.01259
$226$	−21.2293	−1.41215
$227$	−16.6903	−1.10777	−0.553887	−	0.832592i	$-0.686856\pi$
$227$	−16.6903	−1.10777	−0.553887	+	0.832592i	$0.686856\pi$
$228$	54.7370	3.62505
$229$	0.428456	0.0283132	0.0141566	−	0.999900i	$-0.495494\pi$
$229$	0.428456	0.0283132	0.0141566	+	0.999900i	$0.495494\pi$
$230$	9.39782	0.619674
$231$	−1.05943	−0.0697052
$232$	−5.30877	−0.348538
$233$	−8.71085	−0.570667	−0.285333	−	0.958428i	$-0.592104\pi$
$233$	−8.71085	−0.570667	−0.285333	+	0.958428i	$0.592104\pi$
$234$	−13.4173	−0.877118
$235$	−39.7097	−2.59038
$236$	47.5987	3.09841
$237$	−39.4660	−2.56359
$238$	23.8613	1.54670
$239$	−18.4583	−1.19397	−0.596985	−	0.802252i	$-0.703635\pi$
$239$	−18.4583	−1.19397	−0.596985	+	0.802252i	$0.703635\pi$
$240$	22.0966	1.42633
$241$	−8.80838	−0.567398	−0.283699	−	0.958913i	$-0.591562\pi$
$241$	−8.80838	−0.567398	−0.283699	+	0.958913i	$0.591562\pi$
$242$	25.9436	1.66772
$243$	−19.6168	−1.25842
$244$	36.1795	2.31616
$245$	−19.0921	−1.21975
$246$	−38.7865	−2.47294
$247$	7.30840	0.465022
$248$	33.7392	2.14244
$249$	45.5608	2.88730
$250$	−92.0263	−5.82025
$251$	−26.2443	−1.65653	−0.828264	−	0.560339i	$-0.810671\pi$
$251$	−26.2443	−1.65653	−0.828264	+	0.560339i	$0.810671\pi$
$252$	25.3053	1.59408
$253$	0.220750	0.0138784
$254$	−47.3539	−2.97125
$255$	−73.3111	−4.59092
$256$	−26.0758	−1.62974
$257$	−20.7961	−1.29722	−0.648612	−	0.761119i	$-0.724650\pi$
$257$	−20.7961	−1.29722	−0.648612	+	0.761119i	$0.724650\pi$
$258$	−12.1105	−0.753965
$259$	1.50300	0.0933916
$260$	20.6242	1.27906
$261$	5.96596	0.369284
$262$	−21.7657	−1.34469
$263$	−15.5427	−0.958405	−0.479203	−	0.877704i	$-0.659074\pi$
$263$	−15.5427	−0.958405	−0.479203	+	0.877704i	$0.659074\pi$
$264$	2.52230	0.155237
$265$	−50.4400	−3.09851
$266$	−21.3940	−1.31175
$267$	−30.3166	−1.85535
$268$	29.3151	1.79071
$269$	24.1824	1.47443	0.737213	−	0.675660i	$-0.236141\pi$
$269$	24.1824	1.47443	0.737213	+	0.675660i	$0.236141\pi$
$270$	−36.9356	−2.24783
$271$	20.0392	1.21729	0.608647	−	0.793441i	$-0.291712\pi$
$271$	20.0392	1.21729	0.608647	+	0.793441i	$0.291712\pi$
$272$	−11.6902	−0.708821
$273$	5.72327	0.346388
$274$	−20.7428	−1.25312
$275$	−3.37305	−0.203403
$276$	−8.93167	−0.537623
$277$	−18.5032	−1.11175	−0.555874	−	0.831267i	$-0.687616\pi$
$277$	−18.5032	−1.11175	−0.555874	+	0.831267i	$0.687616\pi$
$278$	−50.5241	−3.03023
$279$	−37.9158	−2.26996
$280$	−27.0402	−1.61596
$281$	12.6659	0.755584	0.377792	−	0.925890i	$-0.376683\pi$
$281$	12.6659	0.755584	0.377792	+	0.925890i	$0.376683\pi$
$282$	58.5769	3.48820
$283$	−2.67978	−0.159296	−0.0796482	−	0.996823i	$-0.525380\pi$
$283$	−2.67978	−0.159296	−0.0796482	+	0.996823i	$0.525380\pi$
$284$	−14.4627	−0.858205
$285$	65.7304	3.89353
$286$	0.751923	0.0444621
$287$	9.76712	0.576535
$288$	14.0210	0.826193
$289$	21.7851	1.28148
$290$	−14.2336	−0.835825
$291$	35.5677	2.08501
$292$	46.3671	2.71343
$293$	−10.6541	−0.622421	−0.311210	−	0.950341i	$-0.600734\pi$
$293$	−10.6541	−0.622421	−0.311210	+	0.950341i	$0.600734\pi$
$294$	28.1633	1.64252
$295$	57.1584	3.32789
$296$	−3.57836	−0.207988
$297$	−0.867598	−0.0503431
$298$	37.2077	2.15539
$299$	−1.19254	−0.0689665
$300$	136.476	7.87943
$301$	3.04963	0.175778
$302$	−17.5787	−1.01154
$303$	−16.8162	−0.966067
$304$	10.4814	0.601148
$305$	43.4458	2.48770
$306$	63.8420	3.64960
$307$	1.48040	0.0844908	0.0422454	−	0.999107i	$-0.486549\pi$
$307$	1.48040	0.0844908	0.0422454	+	0.999107i	$0.486549\pi$
$308$	−1.41814	−0.0808058
$309$	−28.0919	−1.59809
$310$	90.4595	5.13776
$311$	−5.37779	−0.304947	−0.152473	−	0.988308i	$-0.548724\pi$
$311$	−5.37779	−0.304947	−0.152473	+	0.988308i	$0.548724\pi$
$312$	−13.6261	−0.771425
$313$	−26.4192	−1.49330	−0.746651	−	0.665216i	$-0.768339\pi$
$313$	−26.4192	−1.49330	−0.746651	+	0.665216i	$0.768339\pi$
$314$	5.57729	0.314745
$315$	30.3876	1.71215
$316$	−52.8287	−2.97185
$317$	−3.76122	−0.211251	−0.105626	−	0.994406i	$-0.533685\pi$
$317$	−3.76122	−0.211251	−0.105626	+	0.994406i	$0.533685\pi$
$318$	74.4055	4.17245
$319$	−0.334339	−0.0187194
$320$	−49.7819	−2.78289
$321$	11.9171	0.665150
$322$	3.49094	0.194542
$323$	−34.7746	−1.93491
$324$	−11.8785	−0.659919
$325$	18.2220	1.01078
$326$	−5.89942	−0.326739
$327$	16.1844	0.895001
$328$	−23.2537	−1.28397
$329$	−14.7507	−0.813231
$330$	6.76266	0.372272
$331$	11.7573	0.646238	0.323119	−	0.946358i	$-0.395269\pi$
$331$	11.7573	0.646238	0.323119	+	0.946358i	$0.395269\pi$
$332$	60.9871	3.34710
$333$	4.02133	0.220368
$334$	−5.16845	−0.282805
$335$	35.2028	1.92333
$336$	8.20806	0.447786
$337$	−10.3386	−0.563179	−0.281590	−	0.959535i	$-0.590862\pi$
$337$	−10.3386	−0.563179	−0.281590	+	0.959535i	$0.590862\pi$
$338$	26.7631	1.45572
$339$	24.2285	1.31591
$340$	−98.1333	−5.32202
$341$	2.12484	0.115067
$342$	−57.2405	−3.09521
$343$	−18.4029	−0.993665
$344$	−7.26061	−0.391466
$345$	−10.7255	−0.577442
$346$	42.3738	2.27803
$347$	−5.43039	−0.291519	−0.145759	−	0.989320i	$-0.546563\pi$
$347$	−5.43039	−0.291519	−0.145759	+	0.989320i	$0.546563\pi$
$348$	13.5276	0.725154
$349$	−6.78700	−0.363300	−0.181650	−	0.983363i	$-0.558144\pi$
$349$	−6.78700	−0.363300	−0.181650	+	0.983363i	$0.558144\pi$
$350$	−53.3415	−2.85122
$351$	4.68697	0.250172
$352$	−0.785751	−0.0418807
$353$	−29.4491	−1.56742	−0.783709	−	0.621128i	$-0.786675\pi$
$353$	−29.4491	−1.56742	−0.783709	+	0.621128i	$0.786675\pi$
$354$	−84.3160	−4.48134
$355$	−17.3674	−0.921767
$356$	−40.5815	−2.15081
$357$	−27.2323	−1.44129
$358$	−26.0181	−1.37510
$359$	−19.5362	−1.03108	−0.515541	−	0.856865i	$-0.672409\pi$
$359$	−19.5362	−1.03108	−0.515541	+	0.856865i	$0.672409\pi$
$360$	−72.3473	−3.81304
$361$	12.1788	0.640990
$362$	20.9273	1.09991
$363$	−29.6088	−1.55406
$364$	7.66110	0.401551
$365$	55.6795	2.91440
$366$	−64.0881	−3.34994
$367$	19.8420	1.03575	0.517873	−	0.855458i	$-0.326724\pi$
$367$	19.8420	1.03575	0.517873	+	0.855458i	$0.326724\pi$
$368$	−1.71029	−0.0891550
$369$	26.1324	1.36040
$370$	−9.59410	−0.498774
$371$	−18.7366	−0.972755
$372$	−85.9726	−4.45747
$373$	−2.48878	−0.128864	−0.0644321	−	0.997922i	$-0.520524\pi$
$373$	−2.48878	−0.128864	−0.0644321	+	0.997922i	$0.520524\pi$
$374$	−3.57778	−0.185002
$375$	105.027	5.42359
$376$	35.1187	1.81111
$377$	1.80618	0.0930229
$378$	−13.7202	−0.705692
$379$	4.17105	0.214252	0.107126	−	0.994245i	$-0.465835\pi$
$379$	4.17105	0.214252	0.107126	+	0.994245i	$0.465835\pi$
$380$	87.9859	4.51358
$381$	54.0438	2.76875
$382$	−7.52520	−0.385023
$383$	−6.05334	−0.309311	−0.154655	−	0.987968i	$-0.549427\pi$
$383$	−6.05334	−0.309311	−0.154655	+	0.987968i	$0.549427\pi$
$384$	55.8818	2.85170
$385$	−1.70295	−0.0867906
$386$	7.51475	0.382491
$387$	8.15941	0.414766
$388$	47.6104	2.41705
$389$	−8.55246	−0.433627	−0.216814	−	0.976213i	$-0.569566\pi$
$389$	−8.55246	−0.433627	−0.216814	+	0.976213i	$0.569566\pi$
$390$	−36.5335	−1.84994
$391$	5.67432	0.286963
$392$	16.8848	0.852812
$393$	24.8407	1.25305
$394$	−3.93783	−0.198385
$395$	−63.4388	−3.19195
$396$	−3.79429	−0.190670
$397$	15.9938	0.802708	0.401354	−	0.915923i	$-0.368540\pi$
$397$	15.9938	0.802708	0.401354	+	0.915923i	$0.368540\pi$
$398$	22.4565	1.12564
$399$	24.4164	1.22235
$400$	26.1332	1.30666
$401$	7.84967	0.391994	0.195997	−	0.980605i	$-0.437206\pi$
$401$	7.84967	0.391994	0.195997	+	0.980605i	$0.437206\pi$
$402$	−51.9286	−2.58996
$403$	−11.4789	−0.571805
$404$	−22.5100	−1.11991
$405$	−14.2642	−0.708796
$406$	−5.28725	−0.262402
$407$	−0.225360	−0.0111707
$408$	64.8352	3.20982
$409$	18.6284	0.921116	0.460558	−	0.887630i	$-0.347649\pi$
$409$	18.6284	0.921116	0.460558	+	0.887630i	$0.347649\pi$
$410$	−62.3466	−3.07908
$411$	23.6733	1.16772
$412$	−37.6035	−1.85259
$413$	21.2322	1.04477
$414$	9.34017	0.459044
$415$	73.2357	3.59500
$416$	4.24481	0.208119
$417$	57.6619	2.82372
$418$	3.20782	0.156900
$419$	−30.6536	−1.49753	−0.748764	−	0.662837i	$-0.769352\pi$
$419$	−30.6536	−1.49753	−0.748764	+	0.662837i	$0.769352\pi$
$420$	68.9026	3.36210
$421$	26.3760	1.28549	0.642745	−	0.766080i	$-0.277796\pi$
$421$	26.3760	1.28549	0.642745	+	0.766080i	$0.277796\pi$
$422$	36.4640	1.77504
$423$	−39.4661	−1.91891
$424$	44.6084	2.16638
$425$	−86.7035	−4.20574
$426$	25.6192	1.24125
$427$	16.1385	0.780997
$428$	15.9521	0.771076
$429$	−0.858151	−0.0414319
$430$	−19.4667	−0.938769
$431$	5.22838	0.251842	0.125921	−	0.992040i	$-0.459811\pi$
$431$	5.22838	0.251842	0.125921	+	0.992040i	$0.459811\pi$
$432$	6.72184	0.323404
$433$	39.0049	1.87446	0.937228	−	0.348716i	$-0.113382\pi$
$433$	39.0049	1.87446	0.937228	+	0.348716i	$0.113382\pi$
$434$	33.6024	1.61296
$435$	16.2445	0.778862
$436$	21.6643	1.03753
$437$	−5.08757	−0.243372
$438$	−82.1344	−3.92453
$439$	−31.4103	−1.49913	−0.749567	−	0.661929i	$-0.769738\pi$
$439$	−31.4103	−1.49913	−0.749567	+	0.661929i	$0.769738\pi$
$440$	4.05443	0.193287
$441$	−18.9750	−0.903572
$442$	19.3280	0.919339
$443$	−5.94728	−0.282564	−0.141282	−	0.989969i	$-0.545122\pi$
$443$	−5.94728	−0.282564	−0.141282	+	0.989969i	$0.545122\pi$
$444$	9.11822	0.432731
$445$	−48.7318	−2.31011
$446$	53.7810	2.54660
$447$	−42.4643	−2.00849
$448$	−18.4921	−0.873670
$449$	10.6867	0.504337	0.252168	−	0.967683i	$-0.418856\pi$
$449$	10.6867	0.504337	0.252168	+	0.967683i	$0.418856\pi$
$450$	−142.718	−6.72777
$451$	−1.46449	−0.0689600
$452$	32.4319	1.52547
$453$	20.0622	0.942604
$454$	39.5755	1.85737
$455$	9.19976	0.431291
$456$	−58.1310	−2.72224
$457$	21.5058	1.00600	0.502999	−	0.864287i	$-0.332230\pi$
$457$	21.5058	1.00600	0.502999	+	0.864287i	$0.332230\pi$
$458$	−1.01594	−0.0474718
$459$	−22.3014	−1.04094
$460$	−14.3570	−0.669400
$461$	−31.6104	−1.47224	−0.736120	−	0.676851i	$-0.763344\pi$
$461$	−31.6104	−1.47224	−0.736120	+	0.676851i	$0.763344\pi$
$462$	2.51208	0.116872
$463$	−7.90320	−0.367293	−0.183646	−	0.982992i	$-0.558790\pi$
$463$	−7.90320	−0.367293	−0.183646	+	0.982992i	$0.558790\pi$
$464$	2.59034	0.120254
$465$	−103.239	−4.78761
$466$	20.6549	0.956818
$467$	1.93562	0.0895699	0.0447849	−	0.998997i	$-0.485740\pi$
$467$	1.93562	0.0895699	0.0447849	+	0.998997i	$0.485740\pi$
$468$	20.4976	0.947503
$469$	13.0765	0.603818
$470$	94.1583	4.34320
$471$	−6.36523	−0.293294
$472$	−50.5501	−2.32676
$473$	−0.457263	−0.0210250
$474$	93.5804	4.29829
$475$	77.7381	3.56687
$476$	−36.4529	−1.67081
$477$	−50.1306	−2.29532
$478$	43.7678	2.00189
$479$	−38.5660	−1.76213	−0.881063	−	0.472999i	$-0.843171\pi$
$479$	−38.5660	−1.76213	−0.881063	+	0.472999i	$0.843171\pi$
$480$	38.1771	1.74254
$481$	1.21745	0.0555109
$482$	20.8861	0.951337
$483$	−3.98413	−0.181284
$484$	−39.6340	−1.80155
$485$	57.1725	2.59607
$486$	46.5147	2.10995
$487$	−24.7796	−1.12287	−0.561436	−	0.827520i	$-0.689751\pi$
$487$	−24.7796	−1.12287	−0.561436	+	0.827520i	$0.689751\pi$
$488$	−38.4228	−1.73932
$489$	6.73287	0.304471
$490$	45.2706	2.04512
$491$	−12.3573	−0.557679	−0.278840	−	0.960338i	$-0.589950\pi$
$491$	−12.3573	−0.557679	−0.278840	+	0.960338i	$0.589950\pi$
$492$	59.2541	2.67138
$493$	−8.59411	−0.387059
$494$	−17.3294	−0.779687
$495$	−4.55633	−0.204792
$496$	−16.4625	−0.739190
$497$	−6.45135	−0.289383
$498$	−108.032	−4.84103
$499$	32.9451	1.47483	0.737413	−	0.675442i	$-0.236047\pi$
$499$	32.9451	1.47483	0.737413	+	0.675442i	$0.236047\pi$
$500$	140.588	6.28730
$501$	5.89862	0.263531
$502$	62.2296	2.77744
$503$	0.676766	0.0301755	0.0150878	−	0.999886i	$-0.495197\pi$
$503$	0.676766	0.0301755	0.0150878	+	0.999886i	$0.495197\pi$
$504$	−26.8743	−1.19708
$505$	−27.0309	−1.20286
$506$	−0.523434	−0.0232695
$507$	−30.5441	−1.35651
$508$	72.3424	3.20968
$509$	−4.41370	−0.195634	−0.0978168	−	0.995204i	$-0.531186\pi$
$509$	−4.41370	−0.195634	−0.0978168	+	0.995204i	$0.531186\pi$
$510$	173.833	7.69744
$511$	20.6828	0.914955
$512$	20.5303	0.907319
$513$	19.9954	0.882817
$514$	49.3110	2.17501
$515$	−45.1558	−1.98980
$516$	18.5011	0.814467
$517$	2.21173	0.0972716
$518$	−3.56385	−0.156587
$519$	−48.3602	−2.12278
$520$	−21.9030	−0.960508
$521$	−2.26029	−0.0990249	−0.0495125	−	0.998774i	$-0.515767\pi$
$521$	−2.26029	−0.0990249	−0.0495125	+	0.998774i	$0.515767\pi$
$522$	−14.1463	−0.619165
$523$	12.1366	0.530694	0.265347	−	0.964153i	$-0.414513\pi$
$523$	12.1366	0.530694	0.265347	+	0.964153i	$0.414513\pi$
$524$	33.2514	1.45260
$525$	60.8774	2.65691
$526$	36.8544	1.60693
$527$	54.6186	2.37923
$528$	−1.23072	−0.0535603
$529$	−22.1698	−0.963906
$530$	119.602	5.19516
$531$	56.8078	2.46525
$532$	32.6835	1.41701
$533$	7.91151	0.342686
$534$	71.8857	3.11080
$535$	19.1560	0.828185
$536$	−31.1328	−1.34473
$537$	29.6938	1.28138
$538$	−57.3405	−2.47212
$539$	1.06338	0.0458031
$540$	56.4265	2.42821
$541$	−30.7293	−1.32116	−0.660578	−	0.750757i	$-0.729689\pi$
$541$	−30.7293	−1.32116	−0.660578	+	0.750757i	$0.729689\pi$
$542$	−47.5162	−2.04100
$543$	−23.8838	−1.02495
$544$	−20.1976	−0.865963
$545$	26.0153	1.11437
$546$	−13.5708	−0.580778
$547$	−0.859237	−0.0367383	−0.0183692	−	0.999831i	$-0.505847\pi$
$547$	−0.859237	−0.0367383	−0.0183692	+	0.999831i	$0.505847\pi$
$548$	31.6888	1.35368
$549$	43.1793	1.84285
$550$	7.99806	0.341038
$551$	7.70545	0.328263
$552$	9.48548	0.403729
$553$	−23.5652	−1.00209
$554$	43.8740	1.86403
$555$	10.9495	0.464781
$556$	77.1855	3.27340
$557$	14.8544	0.629400	0.314700	−	0.949191i	$-0.398096\pi$
$557$	14.8544	0.629400	0.314700	+	0.949191i	$0.398096\pi$
$558$	89.9046	3.80597
$559$	2.47024	0.104480
$560$	13.1939	0.557543
$561$	4.08323	0.172394
$562$	−30.0329	−1.26686
$563$	−17.3425	−0.730897	−0.365449	−	0.930831i	$-0.619084\pi$
$563$	−17.3425	−0.730897	−0.365449	+	0.930831i	$0.619084\pi$
$564$	−89.4878	−3.76812
$565$	38.9456	1.63845
$566$	6.35420	0.267087
$567$	−5.29863	−0.222522
$568$	15.3595	0.644470
$569$	−33.0925	−1.38731	−0.693656	−	0.720307i	$-0.744001\pi$
$569$	−33.0925	−1.38731	−0.693656	+	0.720307i	$0.744001\pi$
$570$	−155.858	−6.52816
$571$	21.7061	0.908371	0.454185	−	0.890907i	$-0.349930\pi$
$571$	21.7061	0.908371	0.454185	+	0.890907i	$0.349930\pi$
$572$	−1.14871	−0.0480300
$573$	8.58833	0.358782
$574$	−23.1595	−0.966657
$575$	−12.6848	−0.528994
$576$	−49.4765	−2.06152
$577$	3.52923	0.146924	0.0734619	−	0.997298i	$-0.476595\pi$
$577$	3.52923	0.146924	0.0734619	+	0.997298i	$0.476595\pi$
$578$	−51.6562	−2.14861
$579$	−8.57640	−0.356423
$580$	21.7446	0.902896
$581$	27.2043	1.12863
$582$	−84.3368	−3.49587
$583$	2.80938	0.116352
$584$	−49.2421	−2.03765
$585$	24.6144	1.01768
$586$	25.2627	1.04359
$587$	20.7574	0.856750	0.428375	−	0.903601i	$-0.359086\pi$
$587$	20.7574	0.856750	0.428375	+	0.903601i	$0.359086\pi$
$588$	−43.0251	−1.77432
$589$	−48.9709	−2.01781
$590$	−135.532	−5.57976
$591$	4.49415	0.184865
$592$	1.74601	0.0717606
$593$	35.3883	1.45322	0.726611	−	0.687049i	$-0.241094\pi$
$593$	35.3883	1.45322	0.726611	+	0.687049i	$0.241094\pi$
$594$	2.05722	0.0844086
$595$	−43.7740	−1.79456
$596$	−56.8422	−2.32835
$597$	−25.6291	−1.04893
$598$	2.82771	0.115634
$599$	−16.0674	−0.656495	−0.328248	−	0.944592i	$-0.606458\pi$
$599$	−16.0674	−0.656495	−0.328248	+	0.944592i	$0.606458\pi$
$600$	−144.938	−5.91707
$601$	27.3105	1.11402	0.557010	−	0.830506i	$-0.311949\pi$
$601$	27.3105	1.11402	0.557010	+	0.830506i	$0.311949\pi$
$602$	−7.23117	−0.294720
$603$	34.9868	1.42477
$604$	26.8550	1.09271
$605$	−47.5941	−1.93498
$606$	39.8740	1.61977
$607$	45.3593	1.84108	0.920538	−	0.390652i	$-0.127751\pi$
$607$	45.3593	1.84108	0.920538	+	0.390652i	$0.127751\pi$
$608$	18.1091	0.734419
$609$	6.03421	0.244518
$610$	−103.017	−4.17104
$611$	−11.9483	−0.483375
$612$	−97.5313	−3.94247
$613$	30.8112	1.24445	0.622226	−	0.782838i	$-0.286229\pi$
$613$	30.8112	1.24445	0.622226	+	0.782838i	$0.286229\pi$
$614$	−3.51027	−0.141663
$615$	71.1547	2.86923
$616$	1.50607	0.0606812
$617$	−36.9843	−1.48893	−0.744466	−	0.667660i	$-0.767296\pi$
$617$	−36.9843	−1.48893	−0.744466	+	0.667660i	$0.767296\pi$
$618$	66.6106	2.67947
$619$	−11.4714	−0.461076	−0.230538	−	0.973063i	$-0.574049\pi$
$619$	−11.4714	−0.461076	−0.230538	+	0.973063i	$0.574049\pi$
$620$	−138.195	−5.55004
$621$	−3.26272	−0.130929
$622$	12.7516	0.511294
$623$	−18.1021	−0.725244
$624$	6.64865	0.266159
$625$	99.2138	3.96855
$626$	62.6443	2.50377
$627$	−3.66101	−0.146207
$628$	−8.52042	−0.340002
$629$	−5.79283	−0.230975
$630$	−72.0539	−2.87070
$631$	21.0790	0.839141	0.419571	−	0.907723i	$-0.362181\pi$
$631$	21.0790	0.839141	0.419571	+	0.907723i	$0.362181\pi$
$632$	56.1044	2.23171
$633$	−41.6155	−1.65407
$634$	8.91847	0.354198
$635$	86.8717	3.44740
$636$	−113.669	−4.50727
$637$	−5.74464	−0.227611
$638$	0.792773	0.0313862
$639$	−17.2609	−0.682830
$640$	89.8260	3.55068
$641$	−12.7854	−0.504994	−0.252497	−	0.967598i	$-0.581252\pi$
$641$	−12.7854	−0.504994	−0.252497	+	0.967598i	$0.581252\pi$
$642$	−28.2575	−1.11524
$643$	5.20665	0.205330	0.102665	−	0.994716i	$-0.467263\pi$
$643$	5.20665	0.205330	0.102665	+	0.994716i	$0.467263\pi$
$644$	−5.33310	−0.210154
$645$	22.2169	0.874790
$646$	82.4564	3.24420
$647$	30.4167	1.19580	0.597902	−	0.801569i	$-0.296001\pi$
$647$	30.4167	1.19580	0.597902	+	0.801569i	$0.296001\pi$
$648$	12.6151	0.495567
$649$	−3.18357	−0.124966
$650$	−43.2074	−1.69473
$651$	−38.3495	−1.50304
$652$	9.01253	0.352958
$653$	−5.44790	−0.213193	−0.106596	−	0.994302i	$-0.533995\pi$
$653$	−5.44790	−0.213193	−0.106596	+	0.994302i	$0.533995\pi$
$654$	−38.3760	−1.50062
$655$	39.9297	1.56018
$656$	11.3463	0.443000
$657$	55.3379	2.15894
$658$	34.9763	1.36352
$659$	−12.0995	−0.471328	−0.235664	−	0.971835i	$-0.575727\pi$
$659$	−12.0995	−0.471328	−0.235664	+	0.971835i	$0.575727\pi$
$660$	−10.3313	−0.402145
$661$	−5.93615	−0.230890	−0.115445	−	0.993314i	$-0.536829\pi$
$661$	−5.93615	−0.230890	−0.115445	+	0.993314i	$0.536829\pi$
$662$	−27.8784	−1.08353
$663$	−22.0586	−0.856684
$664$	−64.7686	−2.51351
$665$	39.2477	1.52196
$666$	−9.53525	−0.369483
$667$	−1.25733	−0.0486840
$668$	7.89583	0.305499
$669$	−61.3789	−2.37305
$670$	−83.4716	−3.22479
$671$	−2.41982	−0.0934160
$672$	14.1814	0.547058
$673$	−7.51832	−0.289810	−0.144905	−	0.989446i	$-0.546288\pi$
$673$	−7.51832	−0.289810	−0.144905	+	0.989446i	$0.546288\pi$
$674$	24.5145	0.944264
$675$	49.8544	1.91890
$676$	−40.8859	−1.57253
$677$	−17.4847	−0.671992	−0.335996	−	0.941863i	$-0.609073\pi$
$677$	−17.4847	−0.671992	−0.335996	+	0.941863i	$0.609073\pi$
$678$	−57.4497	−2.20634
$679$	21.2375	0.815019
$680$	104.218	3.99658
$681$	−45.1665	−1.73079
$682$	−5.03836	−0.192929
$683$	23.9038	0.914655	0.457328	−	0.889298i	$-0.348807\pi$
$683$	23.9038	0.914655	0.457328	+	0.889298i	$0.348807\pi$
$684$	87.4462	3.34359
$685$	38.0532	1.45394
$686$	43.6364	1.66604
$687$	1.15947	0.0442365
$688$	3.54271	0.135065
$689$	−15.1769	−0.578194
$690$	25.4319	0.968178
$691$	−23.3866	−0.889668	−0.444834	−	0.895613i	$-0.646737\pi$
$691$	−23.3866	−0.889668	−0.444834	+	0.895613i	$0.646737\pi$
$692$	−64.7343	−2.46083
$693$	−1.69251	−0.0642930
$694$	12.8764	0.488780
$695$	92.6875	3.51584
$696$	−14.3664	−0.544555
$697$	−37.6443	−1.42588
$698$	16.0931	0.609132
$699$	−23.5729	−0.891609
$700$	81.4897	3.08002
$701$	3.38366	0.127799	0.0638995	−	0.997956i	$-0.479646\pi$
$701$	3.38366	0.127799	0.0638995	+	0.997956i	$0.479646\pi$
$702$	−11.1136	−0.419455
$703$	5.19383	0.195889
$704$	2.77272	0.104501
$705$	−107.461	−4.04720
$706$	69.8287	2.62804
$707$	−10.0410	−0.377630
$708$	128.809	4.84095
$709$	−37.7891	−1.41920	−0.709600	−	0.704604i	$-0.751125\pi$
$709$	−37.7891	−1.41920	−0.709600	+	0.704604i	$0.751125\pi$
$710$	41.1810	1.54550
$711$	−63.0496	−2.36455
$712$	43.0977	1.61516
$713$	7.99078	0.299257
$714$	64.5723	2.41656
$715$	−1.37942	−0.0515873
$716$	39.7478	1.48544
$717$	−49.9511	−1.86546
$718$	46.3236	1.72878
$719$	−6.83982	−0.255082	−0.127541	−	0.991833i	$-0.540708\pi$
$719$	−6.83982	−0.255082	−0.127541	+	0.991833i	$0.540708\pi$
$720$	35.3008	1.31558
$721$	−16.7737	−0.624685
$722$	−28.8780	−1.07473
$723$	−23.8368	−0.886501
$724$	−31.9705	−1.18818
$725$	19.2120	0.713515
$726$	70.2074	2.60564
$727$	37.7610	1.40048	0.700239	−	0.713908i	$-0.253077\pi$
$727$	37.7610	1.40048	0.700239	+	0.713908i	$0.253077\pi$
$728$	−8.13613	−0.301545
$729$	−43.2486	−1.60180
$730$	−132.025	−4.88647
$731$	−11.7538	−0.434731
$732$	97.9073	3.61876
$733$	9.88519	0.365118	0.182559	−	0.983195i	$-0.441562\pi$
$733$	9.88519	0.365118	0.182559	+	0.983195i	$0.441562\pi$
$734$	−47.0487	−1.73660
$735$	−51.6662	−1.90574
$736$	−2.95493	−0.108920
$737$	−1.96070	−0.0722234
$738$	−61.9642	−2.28093
$739$	−26.9707	−0.992132	−0.496066	−	0.868285i	$-0.665223\pi$
$739$	−26.9707	−0.992132	−0.496066	+	0.868285i	$0.665223\pi$
$740$	14.6569	0.538798
$741$	19.7776	0.726550
$742$	44.4275	1.63099
$743$	8.33045	0.305615	0.152807	−	0.988256i	$-0.451169\pi$
$743$	8.33045	0.305615	0.152807	+	0.988256i	$0.451169\pi$
$744$	91.3033	3.34734
$745$	−68.2584	−2.50079
$746$	5.90131	0.216062
$747$	72.7865	2.66312
$748$	5.46576	0.199848
$749$	7.11573	0.260003
$750$	−249.037	−9.09356
$751$	30.0175	1.09535	0.547676	−	0.836690i	$-0.315512\pi$
$751$	30.0175	1.09535	0.547676	+	0.836690i	$0.315512\pi$
$752$	−17.1357	−0.624873
$753$	−71.0212	−2.58816
$754$	−4.28275	−0.155968
$755$	32.2486	1.17365
$756$	20.9603	0.762320
$757$	−43.5538	−1.58299	−0.791494	−	0.611177i	$-0.790696\pi$
$757$	−43.5538	−1.58299	−0.791494	+	0.611177i	$0.790696\pi$
$758$	−9.89025	−0.359230
$759$	0.597382	0.0216836
$760$	−93.4416	−3.38948
$761$	−16.6145	−0.602276	−0.301138	−	0.953581i	$-0.597367\pi$
$761$	−16.6145	−0.602276	−0.301138	+	0.953581i	$0.597367\pi$
$762$	−128.147	−4.64227
$763$	9.66373	0.349850
$764$	11.4962	0.415919
$765$	−117.119	−4.23446
$766$	14.3535	0.518611
$767$	17.1984	0.620998
$768$	−70.5652	−2.54630
$769$	9.04477	0.326163	0.163081	−	0.986613i	$-0.447857\pi$
$769$	9.04477	0.326163	0.163081	+	0.986613i	$0.447857\pi$
$770$	4.03798	0.145519
$771$	−56.2774	−2.02678
$772$	−11.4803	−0.413184
$773$	19.7092	0.708892	0.354446	−	0.935076i	$-0.384669\pi$
$773$	19.7092	0.708892	0.354446	+	0.935076i	$0.384669\pi$
$774$	−19.3473	−0.695425
$775$	−122.099	−4.38593
$776$	−50.5626	−1.81509
$777$	4.06734	0.145915
$778$	20.2793	0.727048
$779$	33.7518	1.20928
$780$	55.8121	1.99839
$781$	0.967320	0.0346134
$782$	−13.4547	−0.481141
$783$	4.94160	0.176598
$784$	−8.23870	−0.294239
$785$	−10.2317	−0.365184
$786$	−58.9014	−2.10094
$787$	38.7918	1.38278	0.691390	−	0.722482i	$-0.256999\pi$
$787$	38.7918	1.38278	0.691390	+	0.722482i	$0.256999\pi$
$788$	6.01582	0.214305
$789$	−42.0610	−1.49741
$790$	150.424	5.35184
$791$	14.4668	0.514381
$792$	4.02955	0.143184
$793$	13.0724	0.464215
$794$	−37.9240	−1.34587
$795$	−136.498	−4.84110
$796$	−34.3068	−1.21597
$797$	−42.1936	−1.49457	−0.747287	−	0.664502i	$-0.768644\pi$
$797$	−42.1936	−1.49457	−0.747287	+	0.664502i	$0.768644\pi$
$798$	−57.8953	−2.04947
$799$	56.8519	2.01128
$800$	45.1513	1.59634
$801$	−48.4329	−1.71129
$802$	−18.6129	−0.657243
$803$	−3.10120	−0.109439
$804$	79.3313	2.79780
$805$	−6.40420	−0.225718
$806$	27.2184	0.958727
$807$	65.4413	2.30364
$808$	23.9057	0.841001
$809$	13.3921	0.470842	0.235421	−	0.971893i	$-0.424353\pi$
$809$	13.3921	0.470842	0.235421	+	0.971893i	$0.424353\pi$
$810$	33.8229	1.18841
$811$	1.48549	0.0521627	0.0260814	−	0.999660i	$-0.491697\pi$
$811$	1.48549	0.0521627	0.0260814	+	0.999660i	$0.491697\pi$
$812$	8.07732	0.283458
$813$	54.2291	1.90190
$814$	0.534366	0.0187295
$815$	10.8226	0.379099
$816$	−31.6354	−1.10746
$817$	10.5384	0.368694
$818$	−44.1710	−1.54440
$819$	9.14332	0.319494
$820$	95.2468	3.32616
$821$	13.5289	0.472160	0.236080	−	0.971734i	$-0.424137\pi$
$821$	13.5289	0.472160	0.236080	+	0.971734i	$0.424137\pi$
$822$	−56.1333	−1.95787
$823$	36.9620	1.28841	0.644207	−	0.764852i	$-0.277188\pi$
$823$	36.9620	1.28841	0.644207	+	0.764852i	$0.277188\pi$
$824$	39.9351	1.39121
$825$	−9.12799	−0.317796
$826$	−50.3451	−1.75173
$827$	−0.501176	−0.0174276	−0.00871381	−	0.999962i	$-0.502774\pi$
$827$	−0.501176	−0.0174276	−0.00871381	+	0.999962i	$0.502774\pi$
$828$	−14.2690	−0.495880
$829$	0.0860715	0.00298939	0.00149469	−	0.999999i	$-0.499524\pi$
$829$	0.0860715	0.00298939	0.00149469	+	0.999999i	$0.499524\pi$
$830$	−173.654	−6.02762
$831$	−50.0724	−1.73699
$832$	−14.9789	−0.519299
$833$	27.3340	0.947066
$834$	−136.726	−4.73443
$835$	9.48162	0.328125
$836$	−4.90058	−0.169490
$837$	−31.4056	−1.08554
$838$	72.6848	2.51085
$839$	36.4694	1.25906	0.629531	−	0.776975i	$-0.283247\pi$
$839$	36.4694	1.25906	0.629531	+	0.776975i	$0.283247\pi$
$840$	−73.1749	−2.52478
$841$	−27.0957	−0.934334
$842$	−62.5419	−2.15534
$843$	34.2759	1.18052
$844$	−55.7059	−1.91748
$845$	−49.0974	−1.68900
$846$	93.5806	3.21737
$847$	−17.6794	−0.607473
$848$	−21.7660	−0.747449
$849$	−7.25189	−0.248884
$850$	205.588	7.05162
$851$	−0.847499	−0.0290519
$852$	−39.1384	−1.34086
$853$	−27.6523	−0.946796	−0.473398	−	0.880849i	$-0.656973\pi$
$853$	−27.6523	−0.946796	−0.473398	+	0.880849i	$0.656973\pi$
$854$	−38.2670	−1.30947
$855$	105.009	3.59123
$856$	−16.9413	−0.579040
$857$	−55.0032	−1.87887	−0.939437	−	0.342722i	$-0.888651\pi$
$857$	−55.0032	−1.87887	−0.939437	+	0.342722i	$0.888651\pi$
$858$	2.03482	0.0694675
$859$	−26.5865	−0.907121	−0.453561	−	0.891225i	$-0.649846\pi$
$859$	−26.5865	−0.907121	−0.453561	+	0.891225i	$0.649846\pi$
$860$	29.7393	1.01410
$861$	26.4313	0.900777
$862$	−12.3973	−0.422255
$863$	−22.6674	−0.771606	−0.385803	−	0.922581i	$-0.626076\pi$
$863$	−22.6674	−0.771606	−0.385803	+	0.922581i	$0.626076\pi$
$864$	11.6136	0.395101
$865$	−77.7356	−2.64309
$866$	−92.4871	−3.14284
$867$	58.9539	2.00218
$868$	−51.3342	−1.74240
$869$	3.53337	0.119862
$870$	−38.5183	−1.30589
$871$	10.5922	0.358902
$872$	−23.0076	−0.779135
$873$	56.8218	1.92313
$874$	12.0635	0.408053
$875$	62.7119	2.12005
$876$	125.476	4.23946
$877$	−36.1300	−1.22002	−0.610011	−	0.792393i	$-0.708835\pi$
$877$	−36.1300	−1.22002	−0.610011	+	0.792393i	$0.708835\pi$
$878$	74.4791	2.51355
$879$	−28.8317	−0.972469
$880$	−1.97830	−0.0666884
$881$	−55.5029	−1.86994	−0.934970	−	0.354728i	$-0.884574\pi$
$881$	−55.5029	−1.86994	−0.934970	+	0.354728i	$0.884574\pi$
$882$	44.9929	1.51499
$883$	−15.4425	−0.519683	−0.259841	−	0.965651i	$-0.583670\pi$
$883$	−15.4425	−0.519683	−0.259841	+	0.965651i	$0.583670\pi$
$884$	−29.5273	−0.993112
$885$	154.679	5.19949
$886$	14.1020	0.473765
$887$	33.9481	1.13987	0.569933	−	0.821691i	$-0.306969\pi$
$887$	33.9481	1.13987	0.569933	+	0.821691i	$0.306969\pi$
$888$	−9.68360	−0.324960
$889$	32.2696	1.08229
$890$	115.551	3.87329
$891$	0.794480	0.0266161
$892$	−82.1611	−2.75096
$893$	−50.9732	−1.70575
$894$	100.690	3.36757
$895$	47.7307	1.59546
$896$	33.3670	1.11471
$897$	−3.22720	−0.107753
$898$	−25.3399	−0.845604
$899$	−12.1025	−0.403642
$900$	218.029	7.26765
$901$	72.2144	2.40581
$902$	3.47254	0.115623
$903$	8.25276	0.274635
$904$	−34.4429	−1.14555
$905$	−38.3915	−1.27618
$906$	−47.5708	−1.58043
$907$	32.2502	1.07085	0.535425	−	0.844583i	$-0.320151\pi$
$907$	32.2502	1.07085	0.535425	+	0.844583i	$0.320151\pi$
$908$	−60.4594	−2.00641
$909$	−26.8651	−0.891058
$910$	−21.8141	−0.723132
$911$	−38.3377	−1.27018	−0.635092	−	0.772437i	$-0.719038\pi$
$911$	−38.3377	−1.27018	−0.635092	+	0.772437i	$0.719038\pi$
$912$	28.3642	0.939233
$913$	−4.07904	−0.134996
$914$	−50.9938	−1.68672
$915$	117.571	3.88678
$916$	1.55205	0.0512812
$917$	14.8324	0.489808
$918$	52.8803	1.74531
$919$	−10.8181	−0.356855	−0.178427	−	0.983953i	$-0.557101\pi$
$919$	−10.8181	−0.356855	−0.178427	+	0.983953i	$0.557101\pi$
$920$	15.2472	0.502687
$921$	4.00619	0.132008
$922$	74.9534	2.46846
$923$	−5.22569	−0.172006
$924$	−3.83769	−0.126251
$925$	12.9498	0.425786
$926$	18.7398	0.615828
$927$	−44.8788	−1.47401
$928$	4.47542	0.146913
$929$	8.22786	0.269947	0.134974	−	0.990849i	$-0.456905\pi$
$929$	8.22786	0.269947	0.134974	+	0.990849i	$0.456905\pi$
$930$	244.797	8.02722
$931$	−24.5075	−0.803202
$932$	−31.5544	−1.03360
$933$	−14.5531	−0.476448
$934$	−4.58968	−0.150179
$935$	6.56351	0.214650
$936$	−21.7686	−0.711529
$937$	−16.8131	−0.549261	−0.274631	−	0.961550i	$-0.588556\pi$
$937$	−16.8131	−0.549261	−0.274631	+	0.961550i	$0.588556\pi$
$938$	−31.0066	−1.01240
$939$	−71.4944	−2.33313
$940$	−143.845	−4.69172
$941$	4.91071	0.160085	0.0800423	−	0.996791i	$-0.474494\pi$
$941$	4.91071	0.160085	0.0800423	+	0.996791i	$0.474494\pi$
$942$	15.0930	0.491757
$943$	−5.50742	−0.179346
$944$	24.6652	0.802783
$945$	25.1700	0.818780
$946$	1.08425	0.0352519
$947$	−3.69207	−0.119976	−0.0599881	−	0.998199i	$-0.519106\pi$
$947$	−3.69207	−0.119976	−0.0599881	+	0.998199i	$0.519106\pi$
$948$	−142.963	−4.64321
$949$	16.7534	0.543839
$950$	−184.330	−5.98045
$951$	−10.1784	−0.330058
$952$	38.7131	1.25470
$953$	4.75588	0.154058	0.0770290	−	0.997029i	$-0.475457\pi$
$953$	4.75588	0.154058	0.0770290	+	0.997029i	$0.475457\pi$
$954$	118.868	3.84849
$955$	13.8051	0.446723
$956$	−66.8639	−2.16253
$957$	−0.904773	−0.0292472
$958$	91.4464	2.95450
$959$	14.1353	0.456454
$960$	−134.717	−4.34798
$961$	45.9160	1.48116
$962$	−2.88677	−0.0930733
$963$	19.0385	0.613506
$964$	−31.9077	−1.02768
$965$	−13.7860	−0.443786
$966$	9.44702	0.303953
$967$	16.4810	0.529994	0.264997	−	0.964249i	$-0.414629\pi$
$967$	16.4810	0.529994	0.264997	+	0.964249i	$0.414629\pi$
$968$	42.0916	1.35287
$969$	−94.1055	−3.02310
$970$	−135.566	−4.35275
$971$	−26.2495	−0.842386	−0.421193	−	0.906971i	$-0.638389\pi$
$971$	−26.2495	−0.842386	−0.421193	+	0.906971i	$0.638389\pi$
$972$	−71.0604	−2.27926
$973$	34.4299	1.10377
$974$	58.7566	1.88268
$975$	49.3116	1.57923
$976$	18.7479	0.600105
$977$	35.7513	1.14379	0.571893	−	0.820328i	$-0.306209\pi$
$977$	35.7513	1.14379	0.571893	+	0.820328i	$0.306209\pi$
$978$	−15.9647	−0.510496
$979$	2.71423	0.0867473
$980$	−69.1598	−2.20923
$981$	25.8557	0.825510
$982$	29.3013	0.935042
$983$	−18.4659	−0.588970	−0.294485	−	0.955656i	$-0.595148\pi$
$983$	−18.4659	−0.588970	−0.294485	+	0.955656i	$0.595148\pi$
$984$	−62.9282	−2.00608
$985$	7.22403	0.230177
$986$	20.3781	0.648969
$987$	−39.9176	−1.27059
$988$	26.4741	0.842254
$989$	−1.71960	−0.0546802
$990$	10.8038	0.343368
$991$	28.6531	0.910197	0.455099	−	0.890441i	$-0.349604\pi$
$991$	28.6531	0.910197	0.455099	+	0.890441i	$0.349604\pi$
$992$	−28.4429	−0.903064
$993$	31.8170	1.00968
$994$	15.2972	0.485198
$995$	−41.1969	−1.30603
$996$	165.040	5.22950
$997$	58.9988	1.86851	0.934255	−	0.356606i	$-0.116066\pi$
$997$	58.9988	1.86851	0.934255	+	0.356606i	$0.116066\pi$
$998$	−78.1183	−2.47279
$999$	3.33087	0.105384

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4013.2.a.c.1.18	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4013.2.a.c.1.18	✓	176	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:	\( N \)	\(=\)	\( 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37116 q^{2} +2.70615 q^{3} +3.62242 q^{4} +4.34995 q^{5} -6.41674 q^{6} +1.61584 q^{7} -3.84703 q^{8} +4.32327 q^{9} +O(q^{10})\)	\(q-2.37116 q^{2} +2.70615 q^{3} +3.62242 q^{4} +4.34995 q^{5} -6.41674 q^{6} +1.61584 q^{7} -3.84703 q^{8} +4.32327 q^{9} -10.3145 q^{10} -0.242281 q^{11} +9.80283 q^{12} +1.30886 q^{13} -3.83143 q^{14} +11.7716 q^{15} +1.87710 q^{16} -6.22777 q^{17} -10.2512 q^{18} +5.58380 q^{19} +15.7574 q^{20} +4.37272 q^{21} +0.574488 q^{22} -0.911131 q^{23} -10.4107 q^{24} +13.9221 q^{25} -3.10352 q^{26} +3.58096 q^{27} +5.85327 q^{28} +1.37997 q^{29} -27.9125 q^{30} -8.77018 q^{31} +3.24314 q^{32} -0.655649 q^{33} +14.7671 q^{34} +7.02885 q^{35} +15.6607 q^{36} +0.930161 q^{37} -13.2401 q^{38} +3.54197 q^{39} -16.7344 q^{40} +6.04459 q^{41} -10.3684 q^{42} +1.88733 q^{43} -0.877643 q^{44} +18.8060 q^{45} +2.16044 q^{46} -9.12877 q^{47} +5.07973 q^{48} -4.38905 q^{49} -33.0115 q^{50} -16.8533 q^{51} +4.74124 q^{52} -11.5955 q^{53} -8.49105 q^{54} -1.05391 q^{55} -6.21621 q^{56} +15.1106 q^{57} -3.27213 q^{58} +13.1400 q^{59} +42.6418 q^{60} +9.98765 q^{61} +20.7955 q^{62} +6.98573 q^{63} -11.4442 q^{64} +5.69347 q^{65} +1.55465 q^{66} +8.09269 q^{67} -22.5596 q^{68} -2.46566 q^{69} -16.6666 q^{70} -3.99256 q^{71} -16.6317 q^{72} +12.8000 q^{73} -2.20557 q^{74} +37.6753 q^{75} +20.2269 q^{76} -0.391488 q^{77} -8.39860 q^{78} -14.5838 q^{79} +8.16531 q^{80} -3.27917 q^{81} -14.3327 q^{82} +16.8360 q^{83} +15.8399 q^{84} -27.0905 q^{85} -4.47516 q^{86} +3.73440 q^{87} +0.932062 q^{88} -11.2028 q^{89} -44.5921 q^{90} +2.11491 q^{91} -3.30050 q^{92} -23.7334 q^{93} +21.6458 q^{94} +24.2892 q^{95} +8.77644 q^{96} +13.1433 q^{97} +10.4072 q^{98} -1.04744 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9 + 43 * q^10 + 18 * q^11 + 95 * q^12 + 95 * q^13 + 2 * q^14 + 36 * q^15 + 225 * q^16 + 35 * q^17 + 46 * q^18 + 127 * q^19 + 4 * q^20 + 32 * q^21 + 60 * q^22 + 35 * q^23 + 26 * q^24 + 207 * q^25 + 19 * q^26 + 191 * q^27 + 87 * q^28 + 16 * q^29 + 28 * q^30 + 93 * q^31 + 73 * q^32 + 70 * q^33 + 45 * q^34 + 73 * q^35 + 206 * q^36 + 64 * q^37 + 35 * q^38 + 72 * q^39 + 139 * q^40 + 19 * q^41 + 35 * q^42 + 261 * q^43 + 11 * q^44 + 12 * q^45 + 58 * q^46 + 40 * q^47 + 130 * q^48 + 234 * q^49 - 14 * q^50 + 76 * q^51 + 263 * q^52 + 17 * q^53 + 28 * q^54 + 170 * q^55 - 10 * q^56 + 60 * q^57 + 52 * q^58 + 69 * q^59 + 37 * q^60 + 110 * q^61 + 71 * q^62 + 101 * q^63 + 250 * q^64 - q^65 + 43 * q^66 + 190 * q^67 + 48 * q^68 + 45 * q^69 + 14 * q^70 + 9 * q^71 + 98 * q^72 + 182 * q^73 - 23 * q^74 + 219 * q^75 + 197 * q^76 + 25 * q^77 - 26 * q^78 + 105 * q^79 + 20 * q^80 + 236 * q^81 + 107 * q^82 + 130 * q^83 + 38 * q^84 + 73 * q^85 - 24 * q^86 + 171 * q^87 + 165 * q^88 + 40 * q^89 + 45 * q^90 + 182 * q^91 - 4 * q^92 + 23 * q^93 + 98 * q^94 + 30 * q^95 - 2 * q^96 + 168 * q^97 + 82 * q^98 + 50 * q^99

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