LMFDB - Embedded newform 8011.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8011.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$63.9681570592$
Analytic rank:	$0$
Dimension:	$358$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.75246 q^{2} -1.71159 q^{3} +5.57605 q^{4} +1.50064 q^{5} +4.71110 q^{6} +0.944355 q^{7} -9.84296 q^{8} -0.0704466 q^{9} +O(q^{10})$	\(q-2.75246 q^{2} -1.71159 q^{3} +5.57605 q^{4} +1.50064 q^{5} +4.71110 q^{6} +0.944355 q^{7} -9.84296 q^{8} -0.0704466 q^{9} -4.13045 q^{10} +0.611364 q^{11} -9.54394 q^{12} -3.57160 q^{13} -2.59930 q^{14} -2.56848 q^{15} +15.9403 q^{16} -5.12363 q^{17} +0.193902 q^{18} +5.61300 q^{19} +8.36763 q^{20} -1.61635 q^{21} -1.68276 q^{22} +7.81440 q^{23} +16.8471 q^{24} -2.74809 q^{25} +9.83071 q^{26} +5.25536 q^{27} +5.26578 q^{28} +7.35068 q^{29} +7.06965 q^{30} +9.10223 q^{31} -24.1891 q^{32} -1.04641 q^{33} +14.1026 q^{34} +1.41713 q^{35} -0.392814 q^{36} +1.70928 q^{37} -15.4496 q^{38} +6.11313 q^{39} -14.7707 q^{40} +9.74313 q^{41} +4.44895 q^{42} +9.00559 q^{43} +3.40900 q^{44} -0.105715 q^{45} -21.5088 q^{46} +11.4725 q^{47} -27.2833 q^{48} -6.10819 q^{49} +7.56401 q^{50} +8.76957 q^{51} -19.9155 q^{52} +5.09236 q^{53} -14.4652 q^{54} +0.917435 q^{55} -9.29525 q^{56} -9.60717 q^{57} -20.2325 q^{58} -8.13814 q^{59} -14.3220 q^{60} -13.3359 q^{61} -25.0536 q^{62} -0.0665267 q^{63} +34.6990 q^{64} -5.35968 q^{65} +2.88019 q^{66} -7.89789 q^{67} -28.5696 q^{68} -13.3751 q^{69} -3.90061 q^{70} +15.2970 q^{71} +0.693403 q^{72} -5.45219 q^{73} -4.70472 q^{74} +4.70361 q^{75} +31.2984 q^{76} +0.577344 q^{77} -16.8262 q^{78} +1.25624 q^{79} +23.9206 q^{80} -8.78370 q^{81} -26.8176 q^{82} +12.9172 q^{83} -9.01287 q^{84} -7.68870 q^{85} -24.7876 q^{86} -12.5814 q^{87} -6.01763 q^{88} +1.21934 q^{89} +0.290976 q^{90} -3.37286 q^{91} +43.5735 q^{92} -15.5793 q^{93} -31.5777 q^{94} +8.42307 q^{95} +41.4019 q^{96} -2.49661 q^{97} +16.8126 q^{98} -0.0430685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) $ 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9} + 21 q^{10} + 70 q^{11} + 20 q^{12} + 53 q^{13} + 69 q^{14} + 28 q^{15} + 449 q^{16} + 88 q^{17} + 86 q^{18} + 44 q^{19} + 136 q^{20} + 125 q^{21} + 17 q^{22} + 104 q^{23} + 84 q^{24} + 444 q^{25} + 100 q^{26} + 32 q^{27} + 46 q^{28} + 373 q^{29} + 99 q^{30} + 30 q^{31} + 221 q^{32} + 56 q^{33} + 26 q^{34} + 164 q^{35} + 599 q^{36} + 81 q^{37} + 66 q^{38} + 143 q^{39} + 42 q^{40} + 182 q^{41} + 32 q^{42} + 40 q^{43} + 184 q^{44} + 198 q^{45} + 54 q^{46} + 66 q^{47} + 5 q^{48} + 479 q^{49} + 184 q^{50} + 123 q^{51} + 64 q^{52} + 221 q^{53} + 67 q^{54} + 38 q^{55} + 174 q^{56} + 84 q^{57} + 44 q^{58} + 127 q^{59} + 29 q^{60} + 174 q^{61} + 86 q^{62} + 48 q^{63} + 549 q^{64} + 202 q^{65} + 32 q^{66} + 29 q^{67} + 172 q^{68} + 249 q^{69} + 12 q^{70} + 185 q^{71} + 218 q^{72} + 57 q^{73} + 272 q^{74} + 24 q^{75} + 84 q^{76} + 384 q^{77} + 12 q^{78} + 93 q^{79} + 215 q^{80} + 702 q^{81} + 48 q^{82} + 121 q^{83} + 179 q^{84} + 177 q^{85} + 209 q^{86} + 91 q^{87} + 36 q^{88} + 186 q^{89} + 66 q^{90} + 32 q^{91} + 272 q^{92} + 220 q^{93} + 60 q^{94} + 170 q^{95} + 162 q^{96} + 22 q^{97} + 196 q^{98} + 152 q^{99}+O(q^{100}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9 + 21 * q^10 + 70 * q^11 + 20 * q^12 + 53 * q^13 + 69 * q^14 + 28 * q^15 + 449 * q^16 + 88 * q^17 + 86 * q^18 + 44 * q^19 + 136 * q^20 + 125 * q^21 + 17 * q^22 + 104 * q^23 + 84 * q^24 + 444 * q^25 + 100 * q^26 + 32 * q^27 + 46 * q^28 + 373 * q^29 + 99 * q^30 + 30 * q^31 + 221 * q^32 + 56 * q^33 + 26 * q^34 + 164 * q^35 + 599 * q^36 + 81 * q^37 + 66 * q^38 + 143 * q^39 + 42 * q^40 + 182 * q^41 + 32 * q^42 + 40 * q^43 + 184 * q^44 + 198 * q^45 + 54 * q^46 + 66 * q^47 + 5 * q^48 + 479 * q^49 + 184 * q^50 + 123 * q^51 + 64 * q^52 + 221 * q^53 + 67 * q^54 + 38 * q^55 + 174 * q^56 + 84 * q^57 + 44 * q^58 + 127 * q^59 + 29 * q^60 + 174 * q^61 + 86 * q^62 + 48 * q^63 + 549 * q^64 + 202 * q^65 + 32 * q^66 + 29 * q^67 + 172 * q^68 + 249 * q^69 + 12 * q^70 + 185 * q^71 + 218 * q^72 + 57 * q^73 + 272 * q^74 + 24 * q^75 + 84 * q^76 + 384 * q^77 + 12 * q^78 + 93 * q^79 + 215 * q^80 + 702 * q^81 + 48 * q^82 + 121 * q^83 + 179 * q^84 + 177 * q^85 + 209 * q^86 + 91 * q^87 + 36 * q^88 + 186 * q^89 + 66 * q^90 + 32 * q^91 + 272 * q^92 + 220 * q^93 + 60 * q^94 + 170 * q^95 + 162 * q^96 + 22 * q^97 + 196 * q^98 + 152 * 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 $

$2$	−2.75246	−1.94629	−0.973143	−	0.230203i	$-0.926061\pi$
$2$	−2.75246	−1.94629	−0.973143	+	0.230203i	$0.926061\pi$
$3$	−1.71159	−0.988189	−0.494095	−	0.869408i	$-0.664500\pi$
$3$	−1.71159	−0.988189	−0.494095	+	0.869408i	$0.664500\pi$
$4$	5.57605	2.78803
$5$	1.50064	0.671105	0.335553	−	0.942021i	$-0.391077\pi$
$5$	1.50064	0.671105	0.335553	+	0.942021i	$0.391077\pi$
$6$	4.71110	1.92330
$7$	0.944355	0.356933	0.178466	−	0.983946i	$-0.442886\pi$
$7$	0.944355	0.356933	0.178466	+	0.983946i	$0.442886\pi$
$8$	−9.84296	−3.48001
$9$	−0.0704466	−0.0234822
$10$	−4.13045	−1.30616
$11$	0.611364	0.184333	0.0921665	−	0.995744i	$-0.470621\pi$
$11$	0.611364	0.184333	0.0921665	+	0.995744i	$0.470621\pi$
$12$	−9.54394	−2.75510
$13$	−3.57160	−0.990584	−0.495292	−	0.868726i	$-0.664939\pi$
$13$	−3.57160	−0.990584	−0.495292	+	0.868726i	$0.664939\pi$
$14$	−2.59930	−0.694693
$15$	−2.56848	−0.663179
$16$	15.9403	3.98507
$17$	−5.12363	−1.24266	−0.621331	−	0.783548i	$-0.713408\pi$
$17$	−5.12363	−1.24266	−0.621331	+	0.783548i	$0.713408\pi$
$18$	0.193902	0.0457031
$19$	5.61300	1.28771	0.643855	−	0.765148i	$-0.277334\pi$
$19$	5.61300	1.28771	0.643855	+	0.765148i	$0.277334\pi$
$20$	8.36763	1.87106
$21$	−1.61635	−0.352717
$22$	−1.68276	−0.358765
$23$	7.81440	1.62941	0.814707	−	0.579872i	$-0.196898\pi$
$23$	7.81440	1.62941	0.814707	+	0.579872i	$0.196898\pi$
$24$	16.8471	3.43891
$25$	−2.74809	−0.549618
$26$	9.83071	1.92796
$27$	5.25536	1.01139
$28$	5.26578	0.995138
$29$	7.35068	1.36499	0.682494	−	0.730892i	$-0.260895\pi$
$29$	7.35068	1.36499	0.682494	+	0.730892i	$0.260895\pi$
$30$	7.06965	1.29074
$31$	9.10223	1.63481	0.817405	−	0.576064i	$-0.195412\pi$
$31$	9.10223	1.63481	0.817405	+	0.576064i	$0.195412\pi$
$32$	−24.1891	−4.27607
$33$	−1.04641	−0.182156
$34$	14.1026	2.41857
$35$	1.41713	0.239539
$36$	−0.392814	−0.0654690
$37$	1.70928	0.281003	0.140502	−	0.990080i	$-0.455128\pi$
$37$	1.70928	0.281003	0.140502	+	0.990080i	$0.455128\pi$
$38$	−15.4496	−2.50625
$39$	6.11313	0.978885
$40$	−14.7707	−2.33545
$41$	9.74313	1.52162	0.760810	−	0.648974i	$-0.224802\pi$
$41$	9.74313	1.52162	0.760810	+	0.648974i	$0.224802\pi$
$42$	4.44895	0.686488
$43$	9.00559	1.37334	0.686670	−	0.726970i	$-0.259072\pi$
$43$	9.00559	1.37334	0.686670	+	0.726970i	$0.259072\pi$
$44$	3.40900	0.513926
$45$	−0.105715	−0.0157590
$46$	−21.5088	−3.17131
$47$	11.4725	1.67344	0.836719	−	0.547633i	$-0.184471\pi$
$47$	11.4725	1.67344	0.836719	+	0.547633i	$0.184471\pi$
$48$	−27.2833	−3.93800
$49$	−6.10819	−0.872599
$50$	7.56401	1.06971
$51$	8.76957	1.22798
$52$	−19.9155	−2.76178
$53$	5.09236	0.699490	0.349745	−	0.936845i	$-0.386268\pi$
$53$	5.09236	0.699490	0.349745	+	0.936845i	$0.386268\pi$
$54$	−14.4652	−1.96846
$55$	0.917435	0.123707
$56$	−9.29525	−1.24213
$57$	−9.60717	−1.27250
$58$	−20.2325	−2.65665
$59$	−8.13814	−1.05949	−0.529747	−	0.848155i	$-0.677713\pi$
$59$	−8.13814	−1.05949	−0.529747	+	0.848155i	$0.677713\pi$
$60$	−14.3220	−1.84896
$61$	−13.3359	−1.70749	−0.853744	−	0.520693i	$-0.825674\pi$
$61$	−13.3359	−1.70749	−0.853744	+	0.520693i	$0.825674\pi$
$62$	−25.0536	−3.18181
$63$	−0.0665267	−0.00838157
$64$	34.6990	4.33738
$65$	−5.35968	−0.664787
$66$	2.88019	0.354527
$67$	−7.89789	−0.964881	−0.482440	−	0.875929i	$-0.660250\pi$
$67$	−7.89789	−0.964881	−0.482440	+	0.875929i	$0.660250\pi$
$68$	−28.5696	−3.46457
$69$	−13.3751	−1.61017
$70$	−3.90061	−0.466212
$71$	15.2970	1.81541	0.907707	−	0.419604i	$-0.137831\pi$
$71$	15.2970	1.81541	0.907707	+	0.419604i	$0.137831\pi$
$72$	0.693403	0.0817184
$73$	−5.45219	−0.638131	−0.319065	−	0.947733i	$-0.603369\pi$
$73$	−5.45219	−0.638131	−0.319065	+	0.947733i	$0.603369\pi$
$74$	−4.70472	−0.546913
$75$	4.70361	0.543126
$76$	31.2984	3.59017
$77$	0.577344	0.0657945
$78$	−16.8262	−1.90519
$79$	1.25624	0.141338	0.0706689	−	0.997500i	$-0.477487\pi$
$79$	1.25624	0.141338	0.0706689	+	0.997500i	$0.477487\pi$
$80$	23.9206	2.67440
$81$	−8.78370	−0.975966
$82$	−26.8176	−2.96151
$83$	12.9172	1.41785	0.708925	−	0.705284i	$-0.249180\pi$
$83$	12.9172	1.41785	0.708925	+	0.705284i	$0.249180\pi$
$84$	−9.01287	−0.983385
$85$	−7.68870	−0.833957
$86$	−24.7876	−2.67291
$87$	−12.5814	−1.34887
$88$	−6.01763	−0.641481
$89$	1.21934	0.129250	0.0646250	−	0.997910i	$-0.479415\pi$
$89$	1.21934	0.129250	0.0646250	+	0.997910i	$0.479415\pi$
$90$	0.290976	0.0306716
$91$	−3.37286	−0.353572
$92$	43.5735	4.54285
$93$	−15.5793	−1.61550
$94$	−31.5777	−3.25699
$95$	8.42307	0.864189
$96$	41.4019	4.22556
$97$	−2.49661	−0.253492	−0.126746	−	0.991935i	$-0.540453\pi$
$97$	−2.49661	−0.253492	−0.126746	+	0.991935i	$0.540453\pi$
$98$	16.8126	1.69833
$99$	−0.0430685	−0.00432855
$100$	−15.3235	−1.53235
$101$	17.1416	1.70565	0.852827	−	0.522194i	$-0.174886\pi$
$101$	17.1416	1.70565	0.852827	+	0.522194i	$0.174886\pi$
$102$	−24.1379	−2.39001
$103$	−9.73513	−0.959231	−0.479616	−	0.877479i	$-0.659224\pi$
$103$	−9.73513	−0.959231	−0.479616	+	0.877479i	$0.659224\pi$
$104$	35.1551	3.44724
$105$	−2.42556	−0.236710
$106$	−14.0165	−1.36141
$107$	−14.6618	−1.41741	−0.708704	−	0.705505i	$-0.750720\pi$
$107$	−14.6618	−1.41741	−0.708704	+	0.705505i	$0.750720\pi$
$108$	29.3042	2.81979
$109$	2.06717	0.197999	0.0989995	−	0.995087i	$-0.468436\pi$
$109$	2.06717	0.197999	0.0989995	+	0.995087i	$0.468436\pi$
$110$	−2.52521	−0.240769
$111$	−2.92559	−0.277684
$112$	15.0533	1.42240
$113$	−19.1268	−1.79930	−0.899651	−	0.436610i	$-0.856179\pi$
$113$	−19.1268	−1.79930	−0.899651	+	0.436610i	$0.856179\pi$
$114$	26.4434	2.47665
$115$	11.7266	1.09351
$116$	40.9878	3.80562
$117$	0.251607	0.0232611
$118$	22.3999	2.06208
$119$	−4.83852	−0.443547
$120$	25.2814	2.30787
$121$	−10.6262	−0.966021
$122$	36.7066	3.32326
$123$	−16.6763	−1.50365
$124$	50.7545	4.55789
$125$	−11.6271	−1.03996
$126$	0.183112	0.0163129
$127$	−8.06538	−0.715686	−0.357843	−	0.933782i	$-0.616488\pi$
$127$	−8.06538	−0.715686	−0.357843	+	0.933782i	$0.616488\pi$
$128$	−47.1297	−4.16571
$129$	−15.4139	−1.35712
$130$	14.7523	1.29386
$131$	8.13972	0.711171	0.355585	−	0.934644i	$-0.384282\pi$
$131$	8.13972	0.711171	0.355585	+	0.934644i	$0.384282\pi$
$132$	−5.83482	−0.507856
$133$	5.30066	0.459626
$134$	21.7387	1.87793
$135$	7.88638	0.678752
$136$	50.4316	4.32448
$137$	10.8097	0.923536	0.461768	−	0.887001i	$-0.347215\pi$
$137$	10.8097	0.923536	0.461768	+	0.887001i	$0.347215\pi$
$138$	36.8144	3.13385
$139$	9.26636	0.785962	0.392981	−	0.919547i	$-0.371444\pi$
$139$	9.26636	0.785962	0.392981	+	0.919547i	$0.371444\pi$
$140$	7.90202	0.667842
$141$	−19.6363	−1.65367
$142$	−42.1043	−3.53331
$143$	−2.18355	−0.182597
$144$	−1.12294	−0.0935782
$145$	11.0307	0.916050
$146$	15.0070	1.24198
$147$	10.4547	0.862293
$148$	9.53102	0.783445
$149$	−3.61458	−0.296118	−0.148059	−	0.988979i	$-0.547302\pi$
$149$	−3.61458	−0.296118	−0.148059	+	0.988979i	$0.547302\pi$
$150$	−12.9465	−1.05708
$151$	−3.25708	−0.265058	−0.132529	−	0.991179i	$-0.542310\pi$
$151$	−3.25708	−0.265058	−0.132529	+	0.991179i	$0.542310\pi$
$152$	−55.2485	−4.48124
$153$	0.360942	0.0291805
$154$	−1.58912	−0.128055
$155$	13.6592	1.09713
$156$	34.0872	2.72916
$157$	−7.15675	−0.571170	−0.285585	−	0.958353i	$-0.592188\pi$
$157$	−7.15675	−0.571170	−0.285585	+	0.958353i	$0.592188\pi$
$158$	−3.45775	−0.275084
$159$	−8.71606	−0.691228
$160$	−36.2990	−2.86969
$161$	7.37957	0.581591
$162$	24.1768	1.89951
$163$	−7.95311	−0.622936	−0.311468	−	0.950257i	$-0.600821\pi$
$163$	−7.95311	−0.622936	−0.311468	+	0.950257i	$0.600821\pi$
$164$	54.3282	4.24232
$165$	−1.57028	−0.122246
$166$	−35.5542	−2.75954
$167$	6.79112	0.525513	0.262756	−	0.964862i	$-0.415368\pi$
$167$	6.79112	0.525513	0.262756	+	0.964862i	$0.415368\pi$
$168$	15.9097	1.22746
$169$	−0.243651	−0.0187424
$170$	21.1629	1.62312
$171$	−0.395417	−0.0302383
$172$	50.2156	3.82891
$173$	−2.11215	−0.160584	−0.0802918	−	0.996771i	$-0.525585\pi$
$173$	−2.11215	−0.160584	−0.0802918	+	0.996771i	$0.525585\pi$
$174$	34.6298	2.62528
$175$	−2.59517	−0.196177
$176$	9.74530	0.734580
$177$	13.9292	1.04698
$178$	−3.35620	−0.251558
$179$	−16.8490	−1.25935	−0.629675	−	0.776858i	$-0.716812\pi$
$179$	−16.8490	−1.25935	−0.629675	+	0.776858i	$0.716812\pi$
$180$	−0.589472	−0.0439366
$181$	−14.6311	−1.08752	−0.543760	−	0.839241i	$-0.683000\pi$
$181$	−14.6311	−1.08752	−0.543760	+	0.839241i	$0.683000\pi$
$182$	9.28368	0.688152
$183$	22.8257	1.68732
$184$	−76.9168	−5.67038
$185$	2.56500	0.188583
$186$	42.8815	3.14423
$187$	−3.13240	−0.229064
$188$	63.9713	4.66559
$189$	4.96292	0.361000
$190$	−23.1842	−1.68196
$191$	−12.5164	−0.905652	−0.452826	−	0.891599i	$-0.649584\pi$
$191$	−12.5164	−0.905652	−0.452826	+	0.891599i	$0.649584\pi$
$192$	−59.3907	−4.28615
$193$	−2.50055	−0.179994	−0.0899968	−	0.995942i	$-0.528686\pi$
$193$	−2.50055	−0.179994	−0.0899968	+	0.995942i	$0.528686\pi$
$194$	6.87182	0.493368
$195$	9.17360	0.656935
$196$	−34.0596	−2.43283
$197$	10.1068	0.720083	0.360042	−	0.932936i	$-0.382762\pi$
$197$	10.1068	0.720083	0.360042	+	0.932936i	$0.382762\pi$
$198$	0.118545	0.00842459
$199$	7.91658	0.561191	0.280596	−	0.959826i	$-0.409468\pi$
$199$	7.91658	0.561191	0.280596	+	0.959826i	$0.409468\pi$
$200$	27.0493	1.91268
$201$	13.5180	0.953485
$202$	−47.1816	−3.31969
$203$	6.94165	0.487209
$204$	48.8996	3.42365
$205$	14.6209	1.02117
$206$	26.7956	1.86694
$207$	−0.550498	−0.0382623
$208$	−56.9323	−3.94755
$209$	3.43158	0.237368
$210$	6.67626	0.460706
$211$	15.9196	1.09595	0.547974	−	0.836496i	$-0.315399\pi$
$211$	15.9196	1.09595	0.547974	+	0.836496i	$0.315399\pi$
$212$	28.3953	1.95020
$213$	−26.1822	−1.79397
$214$	40.3560	2.75868
$215$	13.5141	0.921655
$216$	−51.7283	−3.51966
$217$	8.59574	0.583517
$218$	−5.68981	−0.385363
$219$	9.33194	0.630594
$220$	5.11567	0.344898
$221$	18.2996	1.23096
$222$	8.05257	0.540453
$223$	14.3497	0.960924	0.480462	−	0.877015i	$-0.340469\pi$
$223$	14.3497	0.960924	0.480462	+	0.877015i	$0.340469\pi$
$224$	−22.8431	−1.52627
$225$	0.193594	0.0129062
$226$	52.6459	3.50195
$227$	9.19679	0.610412	0.305206	−	0.952286i	$-0.401275\pi$
$227$	9.19679	0.610412	0.305206	+	0.952286i	$0.401275\pi$
$228$	−53.5701	−3.54777
$229$	17.6167	1.16414	0.582071	−	0.813138i	$-0.302242\pi$
$229$	17.6167	1.16414	0.582071	+	0.813138i	$0.302242\pi$
$230$	−32.2770	−2.12828
$231$	−0.988179	−0.0650174
$232$	−72.3524	−4.75017
$233$	−22.4809	−1.47277	−0.736386	−	0.676562i	$-0.763469\pi$
$233$	−22.4809	−1.47277	−0.736386	+	0.676562i	$0.763469\pi$
$234$	−0.692540	−0.0452728
$235$	17.2161	1.12305
$236$	−45.3787	−2.95390
$237$	−2.15017	−0.139669
$238$	13.3179	0.863268
$239$	5.10039	0.329917	0.164958	−	0.986301i	$-0.447251\pi$
$239$	5.10039	0.329917	0.164958	+	0.986301i	$0.447251\pi$
$240$	−40.9423	−2.64281
$241$	17.4929	1.12681	0.563407	−	0.826179i	$-0.309490\pi$
$241$	17.4929	1.12681	0.563407	+	0.826179i	$0.309490\pi$
$242$	29.2483	1.88015
$243$	−0.731950	−0.0469546
$244$	−74.3617	−4.76052
$245$	−9.16618	−0.585606
$246$	45.9008	2.92653
$247$	−20.0474	−1.27559
$248$	−89.5929	−5.68915
$249$	−22.1091	−1.40110
$250$	32.0031	2.02405
$251$	4.10823	0.259309	0.129655	−	0.991559i	$-0.458613\pi$
$251$	4.10823	0.259309	0.129655	+	0.991559i	$0.458613\pi$
$252$	−0.370956	−0.0233680
$253$	4.77744	0.300355
$254$	22.1997	1.39293
$255$	13.1599	0.824107
$256$	60.3246	3.77028
$257$	−14.8678	−0.927426	−0.463713	−	0.885985i	$-0.653483\pi$
$257$	−14.8678	−0.927426	−0.463713	+	0.885985i	$0.653483\pi$
$258$	42.4262	2.64134
$259$	1.61416	0.100299
$260$	−29.8859	−1.85344
$261$	−0.517831	−0.0320529
$262$	−22.4043	−1.38414
$263$	6.16724	0.380288	0.190144	−	0.981756i	$-0.439104\pi$
$263$	6.16724	0.380288	0.190144	+	0.981756i	$0.439104\pi$
$264$	10.2997	0.633905
$265$	7.64179	0.469431
$266$	−14.5899	−0.894563
$267$	−2.08702	−0.127724
$268$	−44.0391	−2.69011
$269$	−5.56928	−0.339565	−0.169782	−	0.985482i	$-0.554307\pi$
$269$	−5.56928	−0.339565	−0.169782	+	0.985482i	$0.554307\pi$
$270$	−21.7070	−1.32104
$271$	28.6775	1.74203	0.871017	−	0.491252i	$-0.163461\pi$
$271$	28.6775	1.74203	0.871017	+	0.491252i	$0.163461\pi$
$272$	−81.6720	−4.95209
$273$	5.77297	0.349396
$274$	−29.7533	−1.79746
$275$	−1.68008	−0.101313
$276$	−74.5801	−4.48920
$277$	−6.26340	−0.376331	−0.188166	−	0.982137i	$-0.560254\pi$
$277$	−6.26340	−0.376331	−0.188166	+	0.982137i	$0.560254\pi$
$278$	−25.5053	−1.52971
$279$	−0.641222	−0.0383889
$280$	−13.9488	−0.833600
$281$	25.7411	1.53559	0.767793	−	0.640698i	$-0.221355\pi$
$281$	25.7411	1.53559	0.767793	+	0.640698i	$0.221355\pi$
$282$	54.0481	3.21852
$283$	−1.17812	−0.0700321	−0.0350161	−	0.999387i	$-0.511148\pi$
$283$	−1.17812	−0.0700321	−0.0350161	+	0.999387i	$0.511148\pi$
$284$	85.2966	5.06142
$285$	−14.4169	−0.853982
$286$	6.01014	0.355387
$287$	9.20097	0.543116
$288$	1.70404	0.100412
$289$	9.25154	0.544208
$290$	−30.3616	−1.78290
$291$	4.27318	0.250498
$292$	−30.4017	−1.77913
$293$	−28.5715	−1.66917	−0.834584	−	0.550881i	$-0.814292\pi$
$293$	−28.5715	−1.66917	−0.834584	+	0.550881i	$0.814292\pi$
$294$	−28.7763	−1.67827
$295$	−12.2124	−0.711033
$296$	−16.8243	−0.977895
$297$	3.21293	0.186433
$298$	9.94899	0.576329
$299$	−27.9099	−1.61407
$300$	26.2276	1.51425
$301$	8.50447	0.490190
$302$	8.96500	0.515878
$303$	−29.3395	−1.68551
$304$	89.4727	5.13161
$305$	−20.0124	−1.14590
$306$	−0.993480	−0.0567935
$307$	29.7440	1.69758	0.848789	−	0.528732i	$-0.177333\pi$
$307$	29.7440	1.69758	0.848789	+	0.528732i	$0.177333\pi$
$308$	3.21930	0.183437
$309$	16.6626	0.947902
$310$	−37.5963	−2.13533
$311$	−0.164876	−0.00934926	−0.00467463	−	0.999989i	$-0.501488\pi$
$311$	−0.164876	−0.00934926	−0.00467463	+	0.999989i	$0.501488\pi$
$312$	−60.1713	−3.40653
$313$	15.5123	0.876807	0.438403	−	0.898778i	$-0.355544\pi$
$313$	15.5123	0.876807	0.438403	+	0.898778i	$0.355544\pi$
$314$	19.6987	1.11166
$315$	−0.0998324	−0.00562492
$316$	7.00485	0.394054
$317$	−23.3794	−1.31312	−0.656560	−	0.754274i	$-0.727989\pi$
$317$	−23.3794	−1.31312	−0.656560	+	0.754274i	$0.727989\pi$
$318$	23.9906	1.34533
$319$	4.49394	0.251612
$320$	52.0707	2.91084
$321$	25.0950	1.40067
$322$	−20.3120	−1.13194
$323$	−28.7589	−1.60019
$324$	−48.9784	−2.72102
$325$	9.81508	0.544443
$326$	21.8907	1.21241
$327$	−3.53816	−0.195661
$328$	−95.9012	−5.29526
$329$	10.8341	0.597305
$330$	4.32213	0.237925
$331$	−0.122025	−0.00670709	−0.00335354	−	0.999994i	$-0.501067\pi$
$331$	−0.122025	−0.00670709	−0.00335354	+	0.999994i	$0.501067\pi$
$332$	72.0272	3.95300
$333$	−0.120413	−0.00659858
$334$	−18.6923	−1.02280
$335$	−11.8519	−0.647537
$336$	−25.7651	−1.40560
$337$	−10.9612	−0.597095	−0.298547	−	0.954395i	$-0.596502\pi$
$337$	−10.9612	−0.597095	−0.298547	+	0.954395i	$0.596502\pi$
$338$	0.670641	0.0364780
$339$	32.7374	1.77805
$340$	−42.8726	−2.32509
$341$	5.56478	0.301349
$342$	1.08837	0.0588523
$343$	−12.3788	−0.668392
$344$	−88.6416	−4.77924
$345$	−20.0711	−1.08059
$346$	5.81361	0.312541
$347$	9.45123	0.507369	0.253684	−	0.967287i	$-0.418358\pi$
$347$	9.45123	0.507369	0.253684	+	0.967287i	$0.418358\pi$
$348$	−70.1545	−3.76067
$349$	14.5920	0.781091	0.390545	−	0.920584i	$-0.372286\pi$
$349$	14.5920	0.781091	0.390545	+	0.920584i	$0.372286\pi$
$350$	7.14311	0.381815
$351$	−18.7701	−1.00187
$352$	−14.7883	−0.788221
$353$	13.3253	0.709235	0.354618	−	0.935011i	$-0.384611\pi$
$353$	13.3253	0.709235	0.354618	+	0.935011i	$0.384611\pi$
$354$	−38.3396	−2.03772
$355$	22.9552	1.21833
$356$	6.79912	0.360353
$357$	8.28159	0.438308
$358$	46.3762	2.45106
$359$	−9.88362	−0.521638	−0.260819	−	0.965388i	$-0.583993\pi$
$359$	−9.88362	−0.521638	−0.260819	+	0.965388i	$0.583993\pi$
$360$	1.04055	0.0548416
$361$	12.5057	0.658197
$362$	40.2716	2.11663
$363$	18.1878	0.954612
$364$	−18.8073	−0.985768
$365$	−8.18176	−0.428253
$366$	−62.8268	−3.28401
$367$	−29.7747	−1.55423	−0.777113	−	0.629361i	$-0.783317\pi$
$367$	−29.7747	−1.55423	−0.777113	+	0.629361i	$0.783317\pi$
$368$	124.564	6.49333
$369$	−0.686371	−0.0357310
$370$	−7.06008	−0.367036
$371$	4.80900	0.249671
$372$	−86.8712	−4.50406
$373$	−0.847837	−0.0438993	−0.0219497	−	0.999759i	$-0.506987\pi$
$373$	−0.847837	−0.0438993	−0.0219497	+	0.999759i	$0.506987\pi$
$374$	8.62181	0.445823
$375$	19.9008	1.02767
$376$	−112.923	−5.82358
$377$	−26.2537	−1.35214
$378$	−13.6603	−0.702608
$379$	−33.8622	−1.73938	−0.869691	−	0.493596i	$-0.835682\pi$
$379$	−33.8622	−1.73938	−0.869691	+	0.493596i	$0.835682\pi$
$380$	46.9675	2.40938
$381$	13.8046	0.707234
$382$	34.4508	1.76266
$383$	26.3682	1.34735	0.673676	−	0.739027i	$-0.264714\pi$
$383$	26.3682	1.34735	0.673676	+	0.739027i	$0.264714\pi$
$384$	80.6668	4.11651
$385$	0.866385	0.0441550
$386$	6.88267	0.350319
$387$	−0.634414	−0.0322491
$388$	−13.9212	−0.706743
$389$	35.9335	1.82190	0.910951	−	0.412515i	$-0.135350\pi$
$389$	35.9335	1.82190	0.910951	+	0.412515i	$0.135350\pi$
$390$	−25.2500	−1.27858
$391$	−40.0381	−2.02481
$392$	60.1227	3.03665
$393$	−13.9319	−0.702771
$394$	−27.8187	−1.40149
$395$	1.88516	0.0948526
$396$	−0.240152	−0.0120681
$397$	−3.91474	−0.196475	−0.0982376	−	0.995163i	$-0.531321\pi$
$397$	−3.91474	−0.196475	−0.0982376	+	0.995163i	$0.531321\pi$
$398$	−21.7901	−1.09224
$399$	−9.07258	−0.454197
$400$	−43.8053	−2.19026
$401$	−33.3995	−1.66789	−0.833945	−	0.551848i	$-0.813923\pi$
$401$	−33.3995	−1.66789	−0.833945	+	0.551848i	$0.813923\pi$
$402$	−37.2077	−1.85575
$403$	−32.5096	−1.61942
$404$	95.5825	4.75541
$405$	−13.1811	−0.654976
$406$	−19.1066	−0.948247
$407$	1.04499	0.0517982
$408$	−86.3185	−4.27340
$409$	−5.58478	−0.276150	−0.138075	−	0.990422i	$-0.544091\pi$
$409$	−5.58478	−0.276150	−0.138075	+	0.990422i	$0.544091\pi$
$410$	−40.2435	−1.98748
$411$	−18.5018	−0.912628
$412$	−54.2836	−2.67436
$413$	−7.68529	−0.378168
$414$	1.51523	0.0744693
$415$	19.3841	0.951527
$416$	86.3938	4.23581
$417$	−15.8602	−0.776679
$418$	−9.44530	−0.461985
$419$	−19.2037	−0.938161	−0.469080	−	0.883155i	$-0.655415\pi$
$419$	−19.2037	−0.938161	−0.469080	+	0.883155i	$0.655415\pi$
$420$	−13.5250	−0.659955
$421$	−6.73509	−0.328248	−0.164124	−	0.986440i	$-0.552480\pi$
$421$	−6.73509	−0.328248	−0.164124	+	0.986440i	$0.552480\pi$
$422$	−43.8180	−2.13303
$423$	−0.808200	−0.0392960
$424$	−50.1239	−2.43423
$425$	14.0802	0.682989
$426$	72.0655	3.49158
$427$	−12.5938	−0.609458
$428$	−81.7549	−3.95177
$429$	3.73735	0.180441
$430$	−37.1971	−1.79380
$431$	−5.26670	−0.253688	−0.126844	−	0.991923i	$-0.540485\pi$
$431$	−5.26670	−0.253688	−0.126844	+	0.991923i	$0.540485\pi$
$432$	83.7718	4.03047
$433$	−15.2698	−0.733819	−0.366909	−	0.930257i	$-0.619584\pi$
$433$	−15.2698	−0.733819	−0.366909	+	0.930257i	$0.619584\pi$
$434$	−23.6595	−1.13569
$435$	−18.8801	−0.905231
$436$	11.5267	0.552027
$437$	43.8622	2.09821
$438$	−25.6858	−1.22732
$439$	−1.84481	−0.0880479	−0.0440240	−	0.999030i	$-0.514018\pi$
$439$	−1.84481	−0.0880479	−0.0440240	+	0.999030i	$0.514018\pi$
$440$	−9.03027	−0.430501
$441$	0.430302	0.0204906
$442$	−50.3689	−2.39580
$443$	2.16447	0.102837	0.0514185	−	0.998677i	$-0.483626\pi$
$443$	2.16447	0.102837	0.0514185	+	0.998677i	$0.483626\pi$
$444$	−16.3132	−0.774192
$445$	1.82979	0.0867404
$446$	−39.4969	−1.87023
$447$	6.18668	0.292620
$448$	32.7682	1.54815
$449$	16.8845	0.796829	0.398415	−	0.917205i	$-0.369561\pi$
$449$	16.8845	0.796829	0.398415	+	0.917205i	$0.369561\pi$
$450$	−0.532859	−0.0251192
$451$	5.95659	0.280485
$452$	−106.652	−5.01650
$453$	5.57480	0.261927
$454$	−25.3138	−1.18804
$455$	−5.06144	−0.237284
$456$	94.5630	4.42832
$457$	26.7153	1.24969	0.624843	−	0.780750i	$-0.285163\pi$
$457$	26.7153	1.24969	0.624843	+	0.780750i	$0.285163\pi$
$458$	−48.4893	−2.26575
$459$	−26.9265	−1.25682
$460$	65.3880	3.04873
$461$	4.31675	0.201051	0.100526	−	0.994934i	$-0.467948\pi$
$461$	4.31675	0.201051	0.100526	+	0.994934i	$0.467948\pi$
$462$	2.71993	0.126542
$463$	35.5288	1.65116	0.825581	−	0.564283i	$-0.190847\pi$
$463$	35.5288	1.65116	0.825581	+	0.564283i	$0.190847\pi$
$464$	117.172	5.43957
$465$	−23.3789	−1.08417
$466$	61.8778	2.86643
$467$	30.2358	1.39915	0.699573	−	0.714561i	$-0.253374\pi$
$467$	30.2358	1.39915	0.699573	+	0.714561i	$0.253374\pi$
$468$	1.40298	0.0648526
$469$	−7.45841	−0.344398
$470$	−47.3866	−2.18578
$471$	12.2494	0.564424
$472$	80.1033	3.68705
$473$	5.50569	0.253152
$474$	5.91826	0.271835
$475$	−15.4250	−0.707748
$476$	−26.9799	−1.23662
$477$	−0.358740	−0.0164256
$478$	−14.0386	−0.642112
$479$	−20.6712	−0.944490	−0.472245	−	0.881467i	$-0.656556\pi$
$479$	−20.6712	−0.944490	−0.472245	+	0.881467i	$0.656556\pi$
$480$	62.1292	2.83580
$481$	−6.10486	−0.278358
$482$	−48.1485	−2.19310
$483$	−12.6308	−0.574722
$484$	−59.2525	−2.69329
$485$	−3.74650	−0.170120
$486$	2.01467	0.0913871
$487$	25.2315	1.14335	0.571673	−	0.820481i	$-0.306294\pi$
$487$	25.2315	1.14335	0.571673	+	0.820481i	$0.306294\pi$
$488$	131.265	5.94207
$489$	13.6125	0.615579
$490$	25.2296	1.13976
$491$	23.8124	1.07464	0.537319	−	0.843379i	$-0.319437\pi$
$491$	23.8124	1.07464	0.537319	+	0.843379i	$0.319437\pi$
$492$	−92.9878	−4.19221
$493$	−37.6621	−1.69622
$494$	55.1797	2.48265
$495$	−0.0646302	−0.00290491
$496$	145.092	6.51483
$497$	14.4458	0.647981
$498$	60.8544	2.72695
$499$	−15.5076	−0.694216	−0.347108	−	0.937825i	$-0.612836\pi$
$499$	−15.5076	−0.694216	−0.347108	+	0.937825i	$0.612836\pi$
$500$	−64.8332	−2.89943
$501$	−11.6236	−0.519306
$502$	−11.3078	−0.504690
$503$	20.6707	0.921660	0.460830	−	0.887488i	$-0.347552\pi$
$503$	20.6707	0.921660	0.460830	+	0.887488i	$0.347552\pi$
$504$	0.654819	0.0291680
$505$	25.7233	1.14467
$506$	−13.1497	−0.584577
$507$	0.417032	0.0185210
$508$	−44.9730	−1.99535
$509$	−9.35289	−0.414560	−0.207280	−	0.978282i	$-0.566461\pi$
$509$	−9.35289	−0.414560	−0.207280	+	0.978282i	$0.566461\pi$
$510$	−36.2222	−1.60395
$511$	−5.14881	−0.227770
$512$	−71.7818	−3.17234
$513$	29.4983	1.30238
$514$	40.9230	1.80504
$515$	−14.6089	−0.643745
$516$	−85.9488	−3.78368
$517$	7.01388	0.308470
$518$	−4.44293	−0.195211
$519$	3.61514	0.158687
$520$	52.7551	2.31346
$521$	2.79080	0.122267	0.0611336	−	0.998130i	$-0.480528\pi$
$521$	2.79080	0.122267	0.0611336	+	0.998130i	$0.480528\pi$
$522$	1.42531	0.0623841
$523$	−1.41850	−0.0620268	−0.0310134	−	0.999519i	$-0.509873\pi$
$523$	−1.41850	−0.0620268	−0.0310134	+	0.999519i	$0.509873\pi$
$524$	45.3875	1.98276
$525$	4.44188	0.193860
$526$	−16.9751	−0.740149
$527$	−46.6364	−2.03152
$528$	−16.6800	−0.725904
$529$	38.0648	1.65499
$530$	−21.0337	−0.913647
$531$	0.573304	0.0248793
$532$	29.5568	1.28145
$533$	−34.7986	−1.50729
$534$	5.74444	0.248586
$535$	−22.0020	−0.951231
$536$	77.7386	3.35780
$537$	28.8386	1.24448
$538$	15.3292	0.660890
$539$	−3.73433	−0.160849
$540$	43.9749	1.89238
$541$	−4.58534	−0.197139	−0.0985696	−	0.995130i	$-0.531427\pi$
$541$	−4.58534	−0.197139	−0.0985696	+	0.995130i	$0.531427\pi$
$542$	−78.9338	−3.39050
$543$	25.0425	1.07468
$544$	123.936	5.31371
$545$	3.10207	0.132878
$546$	−15.8899	−0.680024
$547$	22.1477	0.946969	0.473485	−	0.880802i	$-0.342996\pi$
$547$	22.1477	0.946969	0.473485	+	0.880802i	$0.342996\pi$
$548$	60.2755	2.57484
$549$	0.939470	0.0400956
$550$	4.62436	0.197183
$551$	41.2594	1.75771
$552$	131.650	5.60341
$553$	1.18634	0.0504481
$554$	17.2398	0.732448
$555$	−4.39025	−0.186356
$556$	51.6697	2.19128
$557$	11.6154	0.492161	0.246081	−	0.969249i	$-0.420857\pi$
$557$	11.6154	0.492161	0.246081	+	0.969249i	$0.420857\pi$
$558$	1.76494	0.0747159
$559$	−32.1644	−1.36041
$560$	22.5895	0.954581
$561$	5.36139	0.226358
$562$	−70.8515	−2.98869
$563$	24.9084	1.04976	0.524882	−	0.851175i	$-0.324109\pi$
$563$	24.9084	1.04976	0.524882	+	0.851175i	$0.324109\pi$
$564$	−109.493	−4.61048
$565$	−28.7024	−1.20752
$566$	3.24274	0.136302
$567$	−8.29493	−0.348354
$568$	−150.567	−6.31766
$569$	31.5565	1.32292	0.661458	−	0.749982i	$-0.269938\pi$
$569$	31.5565	1.32292	0.661458	+	0.749982i	$0.269938\pi$
$570$	39.6819	1.66209
$571$	27.5027	1.15095	0.575475	−	0.817819i	$-0.304817\pi$
$571$	27.5027	1.15095	0.575475	+	0.817819i	$0.304817\pi$
$572$	−12.1756	−0.509087
$573$	21.4229	0.894956
$574$	−25.3253	−1.05706
$575$	−21.4747	−0.895555
$576$	−2.44443	−0.101851
$577$	−41.8195	−1.74097	−0.870483	−	0.492198i	$-0.836194\pi$
$577$	−41.8195	−1.74097	−0.870483	+	0.492198i	$0.836194\pi$
$578$	−25.4645	−1.05918
$579$	4.27993	0.177868
$580$	61.5078	2.55397
$581$	12.1985	0.506077
$582$	−11.7618	−0.487541
$583$	3.11329	0.128939
$584$	53.6657	2.22070
$585$	0.377571	0.0156107
$586$	78.6421	3.24868
$587$	19.9585	0.823776	0.411888	−	0.911234i	$-0.364869\pi$
$587$	19.9585	0.823776	0.411888	+	0.911234i	$0.364869\pi$
$588$	58.2962	2.40410
$589$	51.0908	2.10516
$590$	33.6141	1.38387
$591$	−17.2988	−0.711578
$592$	27.2463	1.11982
$593$	26.2358	1.07738	0.538688	−	0.842505i	$-0.318920\pi$
$593$	26.2358	1.07738	0.538688	+	0.842505i	$0.318920\pi$
$594$	−8.84348	−0.362853
$595$	−7.26087	−0.297667
$596$	−20.1551	−0.825584
$597$	−13.5500	−0.554563
$598$	76.8211	3.14145
$599$	−24.7231	−1.01016	−0.505080	−	0.863073i	$-0.668537\pi$
$599$	−24.7231	−1.01016	−0.505080	+	0.863073i	$0.668537\pi$
$600$	−46.2974	−1.89008
$601$	13.8333	0.564273	0.282137	−	0.959374i	$-0.408957\pi$
$601$	13.8333	0.564273	0.282137	+	0.959374i	$0.408957\pi$
$602$	−23.4083	−0.954049
$603$	0.556380	0.0226575
$604$	−18.1617	−0.738988
$605$	−15.9461	−0.648302
$606$	80.7558	3.28048
$607$	−30.9280	−1.25533	−0.627664	−	0.778484i	$-0.715989\pi$
$607$	−30.9280	−1.25533	−0.627664	+	0.778484i	$0.715989\pi$
$608$	−135.773	−5.50633
$609$	−11.8813	−0.481454
$610$	55.0833	2.23026
$611$	−40.9753	−1.65768
$612$	2.01263	0.0813559
$613$	35.3420	1.42745	0.713726	−	0.700425i	$-0.247006\pi$
$613$	35.3420	1.42745	0.713726	+	0.700425i	$0.247006\pi$
$614$	−81.8691	−3.30397
$615$	−25.0250	−1.00911
$616$	−5.68278	−0.228966
$617$	34.0593	1.37118	0.685588	−	0.727990i	$-0.259545\pi$
$617$	34.0593	1.37118	0.685588	+	0.727990i	$0.259545\pi$
$618$	−45.8632	−1.84489
$619$	−16.7521	−0.673323	−0.336662	−	0.941626i	$-0.609298\pi$
$619$	−16.7521	−0.673323	−0.336662	+	0.941626i	$0.609298\pi$
$620$	76.1642	3.05883
$621$	41.0675	1.64798
$622$	0.453815	0.0181963
$623$	1.15149	0.0461336
$624$	97.4450	3.90092
$625$	−3.70757	−0.148303
$626$	−42.6970	−1.70652
$627$	−5.87348	−0.234564
$628$	−39.9064	−1.59244
$629$	−8.75770	−0.349192
$630$	0.274785	0.0109477
$631$	−23.0795	−0.918781	−0.459390	−	0.888235i	$-0.651932\pi$
$631$	−23.0795	−0.918781	−0.459390	+	0.888235i	$0.651932\pi$
$632$	−12.3651	−0.491857
$633$	−27.2478	−1.08300
$634$	64.3510	2.55571
$635$	−12.1032	−0.480301
$636$	−48.6012	−1.92716
$637$	21.8160	0.864383
$638$	−12.3694	−0.489709
$639$	−1.07762	−0.0426299
$640$	−70.7245	−2.79563
$641$	32.0696	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$641$	32.0696	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$642$	−69.0732	−2.72610
$643$	36.4086	1.43582	0.717908	−	0.696138i	$-0.245100\pi$
$643$	36.4086	1.43582	0.717908	+	0.696138i	$0.245100\pi$
$644$	41.1489	1.62149
$645$	−23.1307	−0.910770
$646$	79.1578	3.11442
$647$	31.9188	1.25486	0.627428	−	0.778675i	$-0.284108\pi$
$647$	31.9188	1.25486	0.627428	+	0.778675i	$0.284108\pi$
$648$	86.4575	3.39637
$649$	−4.97536	−0.195300
$650$	−27.0156	−1.05964
$651$	−14.7124	−0.576625
$652$	−44.3470	−1.73676
$653$	−24.6483	−0.964564	−0.482282	−	0.876016i	$-0.660192\pi$
$653$	−24.6483	−0.964564	−0.482282	+	0.876016i	$0.660192\pi$
$654$	9.73865	0.380811
$655$	12.2148	0.477271
$656$	155.308	6.06376
$657$	0.384089	0.0149847
$658$	−29.8205	−1.16253
$659$	47.1202	1.83554	0.917772	−	0.397109i	$-0.129986\pi$
$659$	47.1202	1.83554	0.917772	+	0.397109i	$0.129986\pi$
$660$	−8.75594	−0.340825
$661$	19.8936	0.773772	0.386886	−	0.922128i	$-0.373551\pi$
$661$	19.8936	0.773772	0.386886	+	0.922128i	$0.373551\pi$
$662$	0.335869	0.0130539
$663$	−31.3214	−1.21642
$664$	−127.144	−4.93413
$665$	7.95437	0.308457
$666$	0.331432	0.0128427
$667$	57.4412	2.22413
$668$	37.8677	1.46514
$669$	−24.5608	−0.949575
$670$	32.6218	1.26029
$671$	−8.15309	−0.314746
$672$	39.0981	1.50824
$673$	34.6907	1.33723	0.668615	−	0.743609i	$-0.266888\pi$
$673$	34.6907	1.33723	0.668615	+	0.743609i	$0.266888\pi$
$674$	30.1703	1.16212
$675$	−14.4422	−0.555880
$676$	−1.35861	−0.0522543
$677$	−23.9765	−0.921490	−0.460745	−	0.887532i	$-0.652418\pi$
$677$	−23.9765	−0.921490	−0.460745	+	0.887532i	$0.652418\pi$
$678$	−90.1084	−3.46059
$679$	−2.35768	−0.0904796
$680$	75.6796	2.90218
$681$	−15.7412	−0.603203
$682$	−15.3168	−0.586512
$683$	8.22951	0.314893	0.157447	−	0.987527i	$-0.449674\pi$
$683$	8.22951	0.314893	0.157447	+	0.987527i	$0.449674\pi$
$684$	−2.20487	−0.0843051
$685$	16.2214	0.619790
$686$	34.0722	1.30088
$687$	−30.1526	−1.15039
$688$	143.552	5.47285
$689$	−18.1879	−0.692904
$690$	55.2451	2.10314
$691$	−20.9088	−0.795409	−0.397704	−	0.917514i	$-0.630193\pi$
$691$	−20.9088	−0.795409	−0.397704	+	0.917514i	$0.630193\pi$
$692$	−11.7774	−0.447711
$693$	−0.0406720	−0.00154500
$694$	−26.0142	−0.987484
$695$	13.9054	0.527463
$696$	123.838	4.69407
$697$	−49.9201	−1.89086
$698$	−40.1639	−1.52023
$699$	38.4782	1.45538
$700$	−14.4708	−0.546945
$701$	−23.9326	−0.903922	−0.451961	−	0.892038i	$-0.649275\pi$
$701$	−23.9326	−0.903922	−0.451961	+	0.892038i	$0.649275\pi$
$702$	51.6639	1.94993
$703$	9.59417	0.361851
$704$	21.2137	0.799523
$705$	−29.4669	−1.10979
$706$	−36.6774	−1.38037
$707$	16.1878	0.608803
$708$	77.6699	2.91901
$709$	−31.9484	−1.19985	−0.599923	−	0.800058i	$-0.704802\pi$
$709$	−31.9484	−1.19985	−0.599923	+	0.800058i	$0.704802\pi$
$710$	−63.1833	−2.37123
$711$	−0.0884978	−0.00331893
$712$	−12.0019	−0.449792
$713$	71.1285	2.66378
$714$	−22.7948	−0.853072
$715$	−3.27671	−0.122542
$716$	−93.9507	−3.51110
$717$	−8.72979	−0.326020
$718$	27.2043	1.01526
$719$	14.8505	0.553830	0.276915	−	0.960894i	$-0.410688\pi$
$719$	14.8505	0.553830	0.276915	+	0.960894i	$0.410688\pi$
$720$	−1.68512	−0.0628008
$721$	−9.19342	−0.342381
$722$	−34.4216	−1.28104
$723$	−29.9407	−1.11351
$724$	−81.5838	−3.03204
$725$	−20.2003	−0.750221
$726$	−50.0612	−1.85795
$727$	−26.3571	−0.977529	−0.488764	−	0.872416i	$-0.662552\pi$
$727$	−26.3571	−0.977529	−0.488764	+	0.872416i	$0.662552\pi$
$728$	33.1989	1.23043
$729$	27.6039	1.02237
$730$	22.5200	0.833502
$731$	−46.1413	−1.70660
$732$	127.277	4.70430
$733$	13.5951	0.502147	0.251073	−	0.967968i	$-0.419216\pi$
$733$	13.5951	0.502147	0.251073	+	0.967968i	$0.419216\pi$
$734$	81.9537	3.02497
$735$	15.6888	0.578689
$736$	−189.023	−6.96749
$737$	−4.82848	−0.177859
$738$	1.88921	0.0695428
$739$	3.04740	0.112100	0.0560502	−	0.998428i	$-0.482149\pi$
$739$	3.04740	0.112100	0.0560502	+	0.998428i	$0.482149\pi$
$740$	14.3026	0.525774
$741$	34.3130	1.26052
$742$	−13.2366	−0.485931
$743$	−24.5291	−0.899886	−0.449943	−	0.893057i	$-0.648556\pi$
$743$	−24.5291	−0.899886	−0.449943	+	0.893057i	$0.648556\pi$
$744$	153.347	5.62196
$745$	−5.42417	−0.198726
$746$	2.33364	0.0854407
$747$	−0.909976	−0.0332943
$748$	−17.4664	−0.638636
$749$	−13.8459	−0.505920
$750$	−54.7763	−2.00015
$751$	−3.25735	−0.118862	−0.0594311	−	0.998232i	$-0.518929\pi$
$751$	−3.25735	−0.118862	−0.0594311	+	0.998232i	$0.518929\pi$
$752$	182.875	6.66876
$753$	−7.03162	−0.256247
$754$	72.2624	2.63164
$755$	−4.88770	−0.177882
$756$	27.6735	1.00648
$757$	20.2033	0.734300	0.367150	−	0.930162i	$-0.380334\pi$
$757$	20.2033	0.734300	0.367150	+	0.930162i	$0.380334\pi$
$758$	93.2044	3.38533
$759$	−8.17704	−0.296808
$760$	−82.9079	−3.00739
$761$	−15.4696	−0.560771	−0.280386	−	0.959887i	$-0.590462\pi$
$761$	−15.4696	−0.560771	−0.280386	+	0.959887i	$0.590462\pi$
$762$	−37.9968	−1.37648
$763$	1.95214	0.0706723
$764$	−69.7919	−2.52498
$765$	0.541643	0.0195832
$766$	−72.5775	−2.62233
$767$	29.0662	1.04952
$768$	−103.251	−3.72575
$769$	−33.9822	−1.22543	−0.612714	−	0.790305i	$-0.709922\pi$
$769$	−33.9822	−1.22543	−0.612714	+	0.790305i	$0.709922\pi$
$770$	−2.38469	−0.0859383
$771$	25.4476	0.916472
$772$	−13.9432	−0.501827
$773$	−8.36360	−0.300818	−0.150409	−	0.988624i	$-0.548059\pi$
$773$	−8.36360	−0.300818	−0.150409	+	0.988624i	$0.548059\pi$
$774$	1.74620	0.0627659
$775$	−25.0137	−0.898520
$776$	24.5740	0.882155
$777$	−2.76279	−0.0991147
$778$	−98.9057	−3.54594
$779$	54.6881	1.95941
$780$	51.1525	1.83155
$781$	9.35200	0.334641
$782$	110.203	3.94086
$783$	38.6305	1.38054
$784$	−97.3662	−3.47737
$785$	−10.7397	−0.383316
$786$	38.3470	1.36779
$787$	−34.5988	−1.23332	−0.616658	−	0.787232i	$-0.711514\pi$
$787$	−34.5988	−1.23332	−0.616658	+	0.787232i	$0.711514\pi$
$788$	56.3563	2.00761
$789$	−10.5558	−0.375797
$790$	−5.18883	−0.184610
$791$	−18.0625	−0.642230
$792$	0.423922	0.0150634
$793$	47.6306	1.69141
$794$	10.7752	0.382397
$795$	−13.0796	−0.463887
$796$	44.1433	1.56462
$797$	−26.2878	−0.931163	−0.465581	−	0.885005i	$-0.654155\pi$
$797$	−26.2878	−0.931163	−0.465581	+	0.885005i	$0.654155\pi$
$798$	24.9719	0.883997
$799$	−58.7808	−2.07952
$800$	66.4737	2.35020
$801$	−0.0858986	−0.00303508
$802$	91.9308	3.24619
$803$	−3.33327	−0.117629
$804$	75.3770	2.65834
$805$	11.0741	0.390309
$806$	89.4814	3.15185
$807$	9.53234	0.335554
$808$	−168.724	−5.93569
$809$	43.0017	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$809$	43.0017	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$810$	36.2806	1.27477
$811$	7.09563	0.249161	0.124581	−	0.992209i	$-0.460241\pi$
$811$	7.09563	0.249161	0.124581	+	0.992209i	$0.460241\pi$
$812$	38.7070	1.35835
$813$	−49.0843	−1.72146
$814$	−2.87630	−0.100814
$815$	−11.9347	−0.418056
$816$	139.789	4.89360
$817$	50.5483	1.76846
$818$	15.3719	0.537466
$819$	0.237607	0.00830265
$820$	81.5269	2.84704
$821$	17.1138	0.597277	0.298639	−	0.954366i	$-0.403467\pi$
$821$	17.1138	0.597277	0.298639	+	0.954366i	$0.403467\pi$
$822$	50.9256	1.77623
$823$	−28.2620	−0.985151	−0.492576	−	0.870270i	$-0.663944\pi$
$823$	−28.2620	−0.985151	−0.492576	+	0.870270i	$0.663944\pi$
$824$	95.8225	3.33813
$825$	2.87562	0.100116
$826$	21.1535	0.736024
$827$	31.2483	1.08661	0.543306	−	0.839535i	$-0.317173\pi$
$827$	31.2483	1.08661	0.543306	+	0.839535i	$0.317173\pi$
$828$	−3.06961	−0.106676
$829$	−52.4772	−1.82261	−0.911304	−	0.411734i	$-0.864923\pi$
$829$	−52.4772	−1.82261	−0.911304	+	0.411734i	$0.864923\pi$
$830$	−53.3540	−1.85194
$831$	10.7204	0.371887
$832$	−123.931	−4.29654
$833$	31.2961	1.08435
$834$	43.6547	1.51164
$835$	10.1910	0.352674
$836$	19.1347	0.661787
$837$	47.8355	1.65344
$838$	52.8574	1.82593
$839$	2.93793	0.101429	0.0507144	−	0.998713i	$-0.483850\pi$
$839$	2.93793	0.101429	0.0507144	+	0.998713i	$0.483850\pi$
$840$	23.8747	0.823754
$841$	25.0325	0.863190
$842$	18.5381	0.638864
$843$	−44.0583	−1.51745
$844$	88.7683	3.05553
$845$	−0.365632	−0.0125781
$846$	2.22454	0.0764813
$847$	−10.0349	−0.344805
$848$	81.1736	2.78751
$849$	2.01647	0.0692050
$850$	−38.7552	−1.32929
$851$	13.3570	0.457871
$852$	−145.993	−5.00164
$853$	−18.3308	−0.627633	−0.313817	−	0.949484i	$-0.601608\pi$
$853$	−18.3308	−0.627633	−0.313817	+	0.949484i	$0.601608\pi$
$854$	34.6641	1.18618
$855$	−0.593377	−0.0202931
$856$	144.315	4.93260
$857$	−40.2916	−1.37633	−0.688167	−	0.725553i	$-0.741584\pi$
$857$	−40.2916	−1.37633	−0.688167	+	0.725553i	$0.741584\pi$
$858$	−10.2869	−0.351189
$859$	26.6612	0.909668	0.454834	−	0.890576i	$-0.349699\pi$
$859$	26.6612	0.909668	0.454834	+	0.890576i	$0.349699\pi$
$860$	75.3555	2.56960
$861$	−15.7483	−0.536702
$862$	14.4964	0.493749
$863$	32.7476	1.11474	0.557371	−	0.830263i	$-0.311810\pi$
$863$	32.7476	1.11474	0.557371	+	0.830263i	$0.311810\pi$
$864$	−127.122	−4.32479
$865$	−3.16957	−0.107768
$866$	42.0295	1.42822
$867$	−15.8349	−0.537781
$868$	47.9303	1.62686
$869$	0.768018	0.0260532
$870$	51.9667	1.76184
$871$	28.2081	0.955796
$872$	−20.3471	−0.689039
$873$	0.175878	0.00595256
$874$	−120.729	−4.08372
$875$	−10.9801	−0.371195
$876$	52.0354	1.75811
$877$	20.9037	0.705869	0.352934	−	0.935648i	$-0.385184\pi$
$877$	20.9037	0.705869	0.352934	+	0.935648i	$0.385184\pi$
$878$	5.07777	0.171366
$879$	48.9029	1.64945
$880$	14.6242	0.492980
$881$	−35.4510	−1.19437	−0.597187	−	0.802102i	$-0.703715\pi$
$881$	−35.4510	−1.19437	−0.597187	+	0.802102i	$0.703715\pi$
$882$	−1.18439	−0.0398805
$883$	41.6814	1.40269	0.701346	−	0.712821i	$-0.252583\pi$
$883$	41.6814	1.40269	0.701346	+	0.712821i	$0.252583\pi$
$884$	102.039	3.43195
$885$	20.9026	0.702635
$886$	−5.95762	−0.200150
$887$	−1.92146	−0.0645164	−0.0322582	−	0.999480i	$-0.510270\pi$
$887$	−1.92146	−0.0645164	−0.0322582	+	0.999480i	$0.510270\pi$
$888$	28.7964	0.966345
$889$	−7.61658	−0.255452
$890$	−5.03643	−0.168822
$891$	−5.37003	−0.179903
$892$	80.0145	2.67908
$893$	64.3952	2.15490
$894$	−17.0286	−0.569522
$895$	−25.2842	−0.845157
$896$	−44.5071	−1.48688
$897$	47.7705	1.59501
$898$	−46.4740	−1.55086
$899$	66.9076	2.23149
$900$	1.07949	0.0359829
$901$	−26.0914	−0.869229
$902$	−16.3953	−0.545904
$903$	−14.5562	−0.484400
$904$	188.265	6.26159
$905$	−21.9560	−0.729841
$906$	−15.3444	−0.509785
$907$	−54.8672	−1.82184	−0.910918	−	0.412587i	$-0.864625\pi$
$907$	−54.8672	−1.82184	−0.910918	+	0.412587i	$0.864625\pi$
$908$	51.2818	1.70185
$909$	−1.20757	−0.0400525
$910$	13.9314	0.461822
$911$	−36.1490	−1.19767	−0.598835	−	0.800873i	$-0.704369\pi$
$911$	−36.1490	−1.19767	−0.598835	+	0.800873i	$0.704369\pi$
$912$	−153.141	−5.07100
$913$	7.89713	0.261357
$914$	−73.5328	−2.43225
$915$	34.2530	1.13237
$916$	98.2316	3.24566
$917$	7.68679	0.253840
$918$	74.1142	2.44613
$919$	−28.7768	−0.949260	−0.474630	−	0.880185i	$-0.657418\pi$
$919$	−28.7768	−0.949260	−0.474630	+	0.880185i	$0.657418\pi$
$920$	−115.424	−3.80542
$921$	−50.9096	−1.67753
$922$	−11.8817	−0.391303
$923$	−54.6346	−1.79832
$924$	−5.51014	−0.181270
$925$	−4.69724	−0.154444
$926$	−97.7917	−3.21363
$927$	0.685807	0.0225249
$928$	−177.806	−5.83678
$929$	19.3341	0.634332	0.317166	−	0.948370i	$-0.397269\pi$
$929$	19.3341	0.634332	0.317166	+	0.948370i	$0.397269\pi$
$930$	64.3496	2.11011
$931$	−34.2853	−1.12365
$932$	−125.355	−4.10613
$933$	0.282201	0.00923884
$934$	−83.2229	−2.72314
$935$	−4.70059	−0.153726
$936$	−2.47656	−0.0809489
$937$	16.6280	0.543215	0.271607	−	0.962408i	$-0.412445\pi$
$937$	16.6280	0.543215	0.271607	+	0.962408i	$0.412445\pi$
$938$	20.5290	0.670296
$939$	−26.5507	−0.866451
$940$	95.9978	3.13110
$941$	−24.0769	−0.784884	−0.392442	−	0.919777i	$-0.628370\pi$
$941$	−24.0769	−0.784884	−0.392442	+	0.919777i	$0.628370\pi$
$942$	−33.7161	−1.09853
$943$	76.1367	2.47935
$944$	−129.724	−4.22216
$945$	7.44755	0.242269
$946$	−15.1542	−0.492706
$947$	41.0617	1.33433	0.667164	−	0.744911i	$-0.267508\pi$
$947$	41.0617	1.33433	0.667164	+	0.744911i	$0.267508\pi$
$948$	−11.9895	−0.389400
$949$	19.4731	0.632122
$950$	42.4568	1.37748
$951$	40.0161	1.29761
$952$	47.6254	1.54355
$953$	−36.1456	−1.17087	−0.585436	−	0.810719i	$-0.699076\pi$
$953$	−36.1456	−1.17087	−0.585436	+	0.810719i	$0.699076\pi$
$954$	0.987418	0.0319688
$955$	−18.7825	−0.607788
$956$	28.4400	0.919816
$957$	−7.69180	−0.248641
$958$	56.8966	1.83825
$959$	10.2082	0.329640
$960$	−89.1238	−2.87646
$961$	51.8507	1.67260
$962$	16.8034	0.541763
$963$	1.03287	0.0332839
$964$	97.5412	3.14159
$965$	−3.75242	−0.120795
$966$	34.7659	1.11857
$967$	53.5904	1.72335	0.861675	−	0.507461i	$-0.169416\pi$
$967$	53.5904	1.72335	0.861675	+	0.507461i	$0.169416\pi$
$968$	104.594	3.36176
$969$	49.2236	1.58129
$970$	10.3121	0.331102
$971$	−24.7388	−0.793905	−0.396953	−	0.917839i	$-0.629932\pi$
$971$	−24.7388	−0.793905	−0.396953	+	0.917839i	$0.629932\pi$
$972$	−4.08139	−0.130911
$973$	8.75073	0.280536
$974$	−69.4487	−2.22528
$975$	−16.7994	−0.538012
$976$	−212.578	−6.80445
$977$	17.7151	0.566756	0.283378	−	0.959008i	$-0.408545\pi$
$977$	17.7151	0.566756	0.283378	+	0.959008i	$0.408545\pi$
$978$	−37.4679	−1.19809
$979$	0.745462	0.0238251
$980$	−51.1111	−1.63268
$981$	−0.145625	−0.00464946
$982$	−65.5428	−2.09155
$983$	9.64708	0.307694	0.153847	−	0.988095i	$-0.450834\pi$
$983$	9.64708	0.307694	0.153847	+	0.988095i	$0.450834\pi$
$984$	164.144	5.23272
$985$	15.1667	0.483252
$986$	103.664	3.30132
$987$	−18.5436	−0.590250
$988$	−111.785	−3.55637
$989$	70.3733	2.23774
$990$	0.177892	0.00565379
$991$	23.6945	0.752682	0.376341	−	0.926481i	$-0.377182\pi$
$991$	23.6945	0.752682	0.376341	+	0.926481i	$0.377182\pi$
$992$	−220.175	−6.99056
$993$	0.208857	0.00662787
$994$	−39.7614	−1.26116
$995$	11.8799	0.376618
$996$	−123.281	−3.90632
$997$	37.4332	1.18552	0.592761	−	0.805379i	$-0.298038\pi$
$997$	37.4332	1.18552	0.592761	+	0.805379i	$0.298038\pi$
$998$	42.6841	1.35114
$999$	8.98286	0.284205

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.b.1.4	✓	358

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.b.1.4	✓	358	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.75246 q^{2} -1.71159 q^{3} +5.57605 q^{4} +1.50064 q^{5} +4.71110 q^{6} +0.944355 q^{7} -9.84296 q^{8} -0.0704466 q^{9} +O(q^{10})\)	\(q-2.75246 q^{2} -1.71159 q^{3} +5.57605 q^{4} +1.50064 q^{5} +4.71110 q^{6} +0.944355 q^{7} -9.84296 q^{8} -0.0704466 q^{9} -4.13045 q^{10} +0.611364 q^{11} -9.54394 q^{12} -3.57160 q^{13} -2.59930 q^{14} -2.56848 q^{15} +15.9403 q^{16} -5.12363 q^{17} +0.193902 q^{18} +5.61300 q^{19} +8.36763 q^{20} -1.61635 q^{21} -1.68276 q^{22} +7.81440 q^{23} +16.8471 q^{24} -2.74809 q^{25} +9.83071 q^{26} +5.25536 q^{27} +5.26578 q^{28} +7.35068 q^{29} +7.06965 q^{30} +9.10223 q^{31} -24.1891 q^{32} -1.04641 q^{33} +14.1026 q^{34} +1.41713 q^{35} -0.392814 q^{36} +1.70928 q^{37} -15.4496 q^{38} +6.11313 q^{39} -14.7707 q^{40} +9.74313 q^{41} +4.44895 q^{42} +9.00559 q^{43} +3.40900 q^{44} -0.105715 q^{45} -21.5088 q^{46} +11.4725 q^{47} -27.2833 q^{48} -6.10819 q^{49} +7.56401 q^{50} +8.76957 q^{51} -19.9155 q^{52} +5.09236 q^{53} -14.4652 q^{54} +0.917435 q^{55} -9.29525 q^{56} -9.60717 q^{57} -20.2325 q^{58} -8.13814 q^{59} -14.3220 q^{60} -13.3359 q^{61} -25.0536 q^{62} -0.0665267 q^{63} +34.6990 q^{64} -5.35968 q^{65} +2.88019 q^{66} -7.89789 q^{67} -28.5696 q^{68} -13.3751 q^{69} -3.90061 q^{70} +15.2970 q^{71} +0.693403 q^{72} -5.45219 q^{73} -4.70472 q^{74} +4.70361 q^{75} +31.2984 q^{76} +0.577344 q^{77} -16.8262 q^{78} +1.25624 q^{79} +23.9206 q^{80} -8.78370 q^{81} -26.8176 q^{82} +12.9172 q^{83} -9.01287 q^{84} -7.68870 q^{85} -24.7876 q^{86} -12.5814 q^{87} -6.01763 q^{88} +1.21934 q^{89} +0.290976 q^{90} -3.37286 q^{91} +43.5735 q^{92} -15.5793 q^{93} -31.5777 q^{94} +8.42307 q^{95} +41.4019 q^{96} -2.49661 q^{97} +16.8126 q^{98} -0.0430685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9} + 21 q^{10} + 70 q^{11} + 20 q^{12} + 53 q^{13} + 69 q^{14} + 28 q^{15} + 449 q^{16} + 88 q^{17} + 86 q^{18} + 44 q^{19} + 136 q^{20} + 125 q^{21} + 17 q^{22} + 104 q^{23} + 84 q^{24} + 444 q^{25} + 100 q^{26} + 32 q^{27} + 46 q^{28} + 373 q^{29} + 99 q^{30} + 30 q^{31} + 221 q^{32} + 56 q^{33} + 26 q^{34} + 164 q^{35} + 599 q^{36} + 81 q^{37} + 66 q^{38} + 143 q^{39} + 42 q^{40} + 182 q^{41} + 32 q^{42} + 40 q^{43} + 184 q^{44} + 198 q^{45} + 54 q^{46} + 66 q^{47} + 5 q^{48} + 479 q^{49} + 184 q^{50} + 123 q^{51} + 64 q^{52} + 221 q^{53} + 67 q^{54} + 38 q^{55} + 174 q^{56} + 84 q^{57} + 44 q^{58} + 127 q^{59} + 29 q^{60} + 174 q^{61} + 86 q^{62} + 48 q^{63} + 549 q^{64} + 202 q^{65} + 32 q^{66} + 29 q^{67} + 172 q^{68} + 249 q^{69} + 12 q^{70} + 185 q^{71} + 218 q^{72} + 57 q^{73} + 272 q^{74} + 24 q^{75} + 84 q^{76} + 384 q^{77} + 12 q^{78} + 93 q^{79} + 215 q^{80} + 702 q^{81} + 48 q^{82} + 121 q^{83} + 179 q^{84} + 177 q^{85} + 209 q^{86} + 91 q^{87} + 36 q^{88} + 186 q^{89} + 66 q^{90} + 32 q^{91} + 272 q^{92} + 220 q^{93} + 60 q^{94} + 170 q^{95} + 162 q^{96} + 22 q^{97} + 196 q^{98} + 152 q^{99}+O(q^{100}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9 + 21 * q^10 + 70 * q^11 + 20 * q^12 + 53 * q^13 + 69 * q^14 + 28 * q^15 + 449 * q^16 + 88 * q^17 + 86 * q^18 + 44 * q^19 + 136 * q^20 + 125 * q^21 + 17 * q^22 + 104 * q^23 + 84 * q^24 + 444 * q^25 + 100 * q^26 + 32 * q^27 + 46 * q^28 + 373 * q^29 + 99 * q^30 + 30 * q^31 + 221 * q^32 + 56 * q^33 + 26 * q^34 + 164 * q^35 + 599 * q^36 + 81 * q^37 + 66 * q^38 + 143 * q^39 + 42 * q^40 + 182 * q^41 + 32 * q^42 + 40 * q^43 + 184 * q^44 + 198 * q^45 + 54 * q^46 + 66 * q^47 + 5 * q^48 + 479 * q^49 + 184 * q^50 + 123 * q^51 + 64 * q^52 + 221 * q^53 + 67 * q^54 + 38 * q^55 + 174 * q^56 + 84 * q^57 + 44 * q^58 + 127 * q^59 + 29 * q^60 + 174 * q^61 + 86 * q^62 + 48 * q^63 + 549 * q^64 + 202 * q^65 + 32 * q^66 + 29 * q^67 + 172 * q^68 + 249 * q^69 + 12 * q^70 + 185 * q^71 + 218 * q^72 + 57 * q^73 + 272 * q^74 + 24 * q^75 + 84 * q^76 + 384 * q^77 + 12 * q^78 + 93 * q^79 + 215 * q^80 + 702 * q^81 + 48 * q^82 + 121 * q^83 + 179 * q^84 + 177 * q^85 + 209 * q^86 + 91 * q^87 + 36 * q^88 + 186 * q^89 + 66 * q^90 + 32 * q^91 + 272 * q^92 + 220 * q^93 + 60 * q^94 + 170 * q^95 + 162 * q^96 + 22 * q^97 + 196 * q^98 + 152 * q^99

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