LMFDB - Embedded newform 8011.2.a.a.1.96

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$63.9681570592$
Analytic rank:	$1$
Dimension:	$309$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.96
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)

$f(q)$	$=$	$q-1.34757 q^{2} -0.394313 q^{3} -0.184066 q^{4} -4.35953 q^{5} +0.531362 q^{6} -2.11767 q^{7} +2.94317 q^{8} -2.84452 q^{9} +O(q^{10})$	\(q-1.34757 q^{2} -0.394313 q^{3} -0.184066 q^{4} -4.35953 q^{5} +0.531362 q^{6} -2.11767 q^{7} +2.94317 q^{8} -2.84452 q^{9} +5.87475 q^{10} -5.69964 q^{11} +0.0725797 q^{12} +1.70126 q^{13} +2.85370 q^{14} +1.71902 q^{15} -3.59799 q^{16} -6.00470 q^{17} +3.83317 q^{18} -5.56568 q^{19} +0.802443 q^{20} +0.835024 q^{21} +7.68064 q^{22} +5.50011 q^{23} -1.16053 q^{24} +14.0055 q^{25} -2.29256 q^{26} +2.30457 q^{27} +0.389792 q^{28} -6.50876 q^{29} -2.31649 q^{30} -2.06541 q^{31} -1.03782 q^{32} +2.24744 q^{33} +8.09172 q^{34} +9.23205 q^{35} +0.523580 q^{36} +5.56664 q^{37} +7.50013 q^{38} -0.670829 q^{39} -12.8309 q^{40} -8.90778 q^{41} -1.12525 q^{42} -6.65767 q^{43} +1.04911 q^{44} +12.4008 q^{45} -7.41176 q^{46} -5.92006 q^{47} +1.41873 q^{48} -2.51547 q^{49} -18.8733 q^{50} +2.36773 q^{51} -0.313145 q^{52} -4.29133 q^{53} -3.10555 q^{54} +24.8478 q^{55} -6.23267 q^{56} +2.19462 q^{57} +8.77099 q^{58} +6.45882 q^{59} -0.316413 q^{60} +3.15547 q^{61} +2.78328 q^{62} +6.02375 q^{63} +8.59451 q^{64} -7.41670 q^{65} -3.02857 q^{66} +0.763133 q^{67} +1.10526 q^{68} -2.16876 q^{69} -12.4408 q^{70} -0.322674 q^{71} -8.37191 q^{72} +10.3916 q^{73} -7.50141 q^{74} -5.52255 q^{75} +1.02446 q^{76} +12.0700 q^{77} +0.903986 q^{78} +10.2895 q^{79} +15.6855 q^{80} +7.62483 q^{81} +12.0038 q^{82} +5.74397 q^{83} -0.153700 q^{84} +26.1777 q^{85} +8.97165 q^{86} +2.56649 q^{87} -16.7750 q^{88} +10.2746 q^{89} -16.7108 q^{90} -3.60271 q^{91} -1.01238 q^{92} +0.814417 q^{93} +7.97767 q^{94} +24.2638 q^{95} +0.409226 q^{96} -14.2991 q^{97} +3.38976 q^{98} +16.2127 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) $ 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9} - 23 q^{10} - 72 q^{11} - 42 q^{12} - 57 q^{13} - 77 q^{14} - 44 q^{15} + 205 q^{16} - 86 q^{17} - 82 q^{18} - 58 q^{19} - 134 q^{20} - 123 q^{21} - 31 q^{22} - 94 q^{23} - 84 q^{24} + 225 q^{25} - 92 q^{26} - 48 q^{27} - 36 q^{28} - 345 q^{29} - 85 q^{30} - 36 q^{31} - 199 q^{32} - 56 q^{33} - 28 q^{34} - 168 q^{35} + 65 q^{36} - 79 q^{37} - 66 q^{38} - 145 q^{39} - 54 q^{40} - 176 q^{41} - 48 q^{42} - 58 q^{43} - 194 q^{44} - 192 q^{45} - 44 q^{46} - 82 q^{47} - 81 q^{48} + 186 q^{49} - 206 q^{50} - 145 q^{51} - 86 q^{52} - 223 q^{53} - 117 q^{54} - 58 q^{55} - 216 q^{56} - 124 q^{57} - 151 q^{59} - 91 q^{60} - 184 q^{61} - 124 q^{62} - 78 q^{63} + 101 q^{64} - 194 q^{65} - 112 q^{66} - 53 q^{67} - 182 q^{68} - 243 q^{69} - 193 q^{71} - 208 q^{72} - 69 q^{73} - 236 q^{74} - 62 q^{75} - 142 q^{76} - 324 q^{77} - 20 q^{78} - 91 q^{79} - 223 q^{80} - 27 q^{81} + 2 q^{82} - 117 q^{83} - 157 q^{84} - 171 q^{85} - 203 q^{86} - 69 q^{87} - 36 q^{88} - 172 q^{89} - 10 q^{90} - 84 q^{91} - 226 q^{92} - 220 q^{93} - 96 q^{94} - 166 q^{95} - 118 q^{96} - 12 q^{97} - 116 q^{98} - 154 q^{99}+O(q^{100}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9 - 23 * q^10 - 72 * q^11 - 42 * q^12 - 57 * q^13 - 77 * q^14 - 44 * q^15 + 205 * q^16 - 86 * q^17 - 82 * q^18 - 58 * q^19 - 134 * q^20 - 123 * q^21 - 31 * q^22 - 94 * q^23 - 84 * q^24 + 225 * q^25 - 92 * q^26 - 48 * q^27 - 36 * q^28 - 345 * q^29 - 85 * q^30 - 36 * q^31 - 199 * q^32 - 56 * q^33 - 28 * q^34 - 168 * q^35 + 65 * q^36 - 79 * q^37 - 66 * q^38 - 145 * q^39 - 54 * q^40 - 176 * q^41 - 48 * q^42 - 58 * q^43 - 194 * q^44 - 192 * q^45 - 44 * q^46 - 82 * q^47 - 81 * q^48 + 186 * q^49 - 206 * q^50 - 145 * q^51 - 86 * q^52 - 223 * q^53 - 117 * q^54 - 58 * q^55 - 216 * q^56 - 124 * q^57 - 151 * q^59 - 91 * q^60 - 184 * q^61 - 124 * q^62 - 78 * q^63 + 101 * q^64 - 194 * q^65 - 112 * q^66 - 53 * q^67 - 182 * q^68 - 243 * q^69 - 193 * q^71 - 208 * q^72 - 69 * q^73 - 236 * q^74 - 62 * q^75 - 142 * q^76 - 324 * q^77 - 20 * q^78 - 91 * q^79 - 223 * q^80 - 27 * q^81 + 2 * q^82 - 117 * q^83 - 157 * q^84 - 171 * q^85 - 203 * q^86 - 69 * q^87 - 36 * q^88 - 172 * q^89 - 10 * q^90 - 84 * q^91 - 226 * q^92 - 220 * q^93 - 96 * q^94 - 166 * q^95 - 118 * q^96 - 12 * q^97 - 116 * q^98 - 154 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.34757	−0.952873	−0.476436	−	0.879209i	$-0.658072\pi$
$2$	−1.34757	−0.952873	−0.476436	+	0.879209i	$0.658072\pi$
$3$	−0.394313	−0.227656	−0.113828	−	0.993500i	$-0.536311\pi$
$3$	−0.394313	−0.227656	−0.113828	+	0.993500i	$0.536311\pi$
$4$	−0.184066	−0.0920332
$5$	−4.35953	−1.94964	−0.974821	−	0.222990i	$-0.928418\pi$
$5$	−4.35953	−1.94964	−0.974821	+	0.222990i	$0.928418\pi$
$6$	0.531362	0.216928
$7$	−2.11767	−0.800405	−0.400202	−	0.916427i	$-0.631060\pi$
$7$	−2.11767	−0.800405	−0.400202	+	0.916427i	$0.631060\pi$
$8$	2.94317	1.04057
$9$	−2.84452	−0.948173
$10$	5.87475	1.85776
$11$	−5.69964	−1.71851	−0.859253	−	0.511551i	$-0.829071\pi$
$11$	−5.69964	−1.71851	−0.859253	+	0.511551i	$0.829071\pi$
$12$	0.0725797	0.0209520
$13$	1.70126	0.471845	0.235922	−	0.971772i	$-0.424189\pi$
$13$	1.70126	0.471845	0.235922	+	0.971772i	$0.424189\pi$
$14$	2.85370	0.762684
$15$	1.71902	0.443848
$16$	−3.59799	−0.899497
$17$	−6.00470	−1.45635	−0.728177	−	0.685390i	$-0.759632\pi$
$17$	−6.00470	−1.45635	−0.728177	+	0.685390i	$0.759632\pi$
$18$	3.83317	0.903488
$19$	−5.56568	−1.27686	−0.638428	−	0.769682i	$-0.720415\pi$
$19$	−5.56568	−1.27686	−0.638428	+	0.769682i	$0.720415\pi$
$20$	0.802443	0.179432
$21$	0.835024	0.182217
$22$	7.68064	1.63752
$23$	5.50011	1.14685	0.573426	−	0.819258i	$-0.305614\pi$
$23$	5.50011	1.14685	0.573426	+	0.819258i	$0.305614\pi$
$24$	−1.16053	−0.236892
$25$	14.0055	2.80110
$26$	−2.29256	−0.449608
$27$	2.30457	0.443514
$28$	0.389792	0.0736638
$29$	−6.50876	−1.20865	−0.604324	−	0.796739i	$-0.706557\pi$
$29$	−6.50876	−1.20865	−0.604324	+	0.796739i	$0.706557\pi$
$30$	−2.31649	−0.422931
$31$	−2.06541	−0.370959	−0.185479	−	0.982648i	$-0.559384\pi$
$31$	−2.06541	−0.370959	−0.185479	+	0.982648i	$0.559384\pi$
$32$	−1.03782	−0.183463
$33$	2.24744	0.391229
$34$	8.09172	1.38772
$35$	9.23205	1.56050
$36$	0.523580	0.0872634
$37$	5.56664	0.915150	0.457575	−	0.889171i	$-0.348718\pi$
$37$	5.56664	0.915150	0.457575	+	0.889171i	$0.348718\pi$
$38$	7.50013	1.21668
$39$	−0.670829	−0.107419
$40$	−12.8309	−2.02874
$41$	−8.90778	−1.39116	−0.695581	−	0.718448i	$-0.744853\pi$
$41$	−8.90778	−1.39116	−0.695581	+	0.718448i	$0.744853\pi$
$42$	−1.12525	−0.173630
$43$	−6.65767	−1.01529	−0.507643	−	0.861568i	$-0.669483\pi$
$43$	−6.65767	−1.01529	−0.507643	+	0.861568i	$0.669483\pi$
$44$	1.04911	0.158160
$45$	12.4008	1.84860
$46$	−7.41176	−1.09280
$47$	−5.92006	−0.863529	−0.431765	−	0.901986i	$-0.642109\pi$
$47$	−5.92006	−0.863529	−0.431765	+	0.901986i	$0.642109\pi$
$48$	1.41873	0.204776
$49$	−2.51547	−0.359353
$50$	−18.8733	−2.66909
$51$	2.36773	0.331548
$52$	−0.313145	−0.0434254
$53$	−4.29133	−0.589460	−0.294730	−	0.955581i	$-0.595230\pi$
$53$	−4.29133	−0.589460	−0.294730	+	0.955581i	$0.595230\pi$
$54$	−3.10555	−0.422613
$55$	24.8478	3.35047
$56$	−6.23267	−0.832876
$57$	2.19462	0.290684
$58$	8.77099	1.15169
$59$	6.45882	0.840867	0.420434	−	0.907323i	$-0.361878\pi$
$59$	6.45882	0.840867	0.420434	+	0.907323i	$0.361878\pi$
$60$	−0.316413	−0.0408488
$61$	3.15547	0.404017	0.202008	−	0.979384i	$-0.435253\pi$
$61$	3.15547	0.404017	0.202008	+	0.979384i	$0.435253\pi$
$62$	2.78328	0.353476
$63$	6.02375	0.758922
$64$	8.59451	1.07431
$65$	−7.41670	−0.919928
$66$	−3.02857	−0.372792
$67$	0.763133	0.0932315	0.0466158	−	0.998913i	$-0.485156\pi$
$67$	0.763133	0.0932315	0.0466158	+	0.998913i	$0.485156\pi$
$68$	1.10526	0.134033
$69$	−2.16876	−0.261088
$70$	−12.4408	−1.48696
$71$	−0.322674	−0.0382943	−0.0191472	−	0.999817i	$-0.506095\pi$
$71$	−0.322674	−0.0382943	−0.0191472	+	0.999817i	$0.506095\pi$
$72$	−8.37191	−0.986639
$73$	10.3916	1.21625	0.608125	−	0.793842i	$-0.291922\pi$
$73$	10.3916	1.21625	0.608125	+	0.793842i	$0.291922\pi$
$74$	−7.50141	−0.872021
$75$	−5.52255	−0.637689
$76$	1.02446	0.117513
$77$	12.0700	1.37550
$78$	0.903986	0.102356
$79$	10.2895	1.15766	0.578829	−	0.815449i	$-0.303510\pi$
$79$	10.2895	1.15766	0.578829	+	0.815449i	$0.303510\pi$
$80$	15.6855	1.75370
$81$	7.62483	0.847204
$82$	12.0038	1.32560
$83$	5.74397	0.630482	0.315241	−	0.949012i	$-0.397915\pi$
$83$	5.74397	0.630482	0.315241	+	0.949012i	$0.397915\pi$
$84$	−0.153700	−0.0167700
$85$	26.1777	2.83937
$86$	8.97165	0.967438
$87$	2.56649	0.275156
$88$	−16.7750	−1.78822
$89$	10.2746	1.08911	0.544555	−	0.838725i	$-0.316698\pi$
$89$	10.2746	1.08911	0.544555	+	0.838725i	$0.316698\pi$
$90$	−16.7108	−1.76148
$91$	−3.60271	−0.377667
$92$	−1.01238	−0.105548
$93$	0.814417	0.0844511
$94$	7.97767	0.822834
$95$	24.2638	2.48941
$96$	0.409226	0.0417665
$97$	−14.2991	−1.45185	−0.725927	−	0.687772i	$-0.758589\pi$
$97$	−14.2991	−1.45185	−0.725927	+	0.687772i	$0.758589\pi$
$98$	3.38976	0.342417
$99$	16.2127	1.62944
$100$	−2.57794	−0.257794
$101$	19.2919	1.91962	0.959809	−	0.280654i	$-0.0905514\pi$
$101$	19.2919	1.91962	0.959809	+	0.280654i	$0.0905514\pi$
$102$	−3.19067	−0.315923
$103$	9.32984	0.919297	0.459648	−	0.888101i	$-0.347975\pi$
$103$	9.32984	0.919297	0.459648	+	0.888101i	$0.347975\pi$
$104$	5.00711	0.490987
$105$	−3.64031	−0.355258
$106$	5.78286	0.561681
$107$	−1.50331	−0.145331	−0.0726654	−	0.997356i	$-0.523151\pi$
$107$	−1.50331	−0.145331	−0.0726654	+	0.997356i	$0.523151\pi$
$108$	−0.424193	−0.0408180
$109$	5.58762	0.535197	0.267599	−	0.963531i	$-0.413770\pi$
$109$	5.58762	0.535197	0.267599	+	0.963531i	$0.413770\pi$
$110$	−33.4840	−3.19257
$111$	−2.19500	−0.208340
$112$	7.61935	0.719961
$113$	−10.0321	−0.943741	−0.471871	−	0.881668i	$-0.656421\pi$
$113$	−10.0321	−0.943741	−0.471871	+	0.881668i	$0.656421\pi$
$114$	−2.95739	−0.276985
$115$	−23.9779	−2.23595
$116$	1.19804	0.111236
$117$	−4.83927	−0.447390
$118$	−8.70369	−0.801240
$119$	12.7160	1.16567
$120$	5.05937	0.461855
$121$	21.4859	1.95326
$122$	−4.25221	−0.384977
$123$	3.51245	0.316707
$124$	0.380173	0.0341405
$125$	−39.2598	−3.51150
$126$	−8.11740	−0.723156
$127$	−17.6502	−1.56620	−0.783101	−	0.621895i	$-0.786363\pi$
$127$	−17.6502	−1.56620	−0.783101	+	0.621895i	$0.786363\pi$
$128$	−9.50602	−0.840221
$129$	2.62520	0.231136
$130$	9.99449	0.876575
$131$	−10.0600	−0.878947	−0.439474	−	0.898256i	$-0.644835\pi$
$131$	−10.0600	−0.878947	−0.439474	+	0.898256i	$0.644835\pi$
$132$	−0.413678	−0.0360061
$133$	11.7863	1.02200
$134$	−1.02837	−0.0888378
$135$	−10.0468	−0.864693
$136$	−17.6729	−1.51544
$137$	−4.84438	−0.413884	−0.206942	−	0.978353i	$-0.566351\pi$
$137$	−4.84438	−0.413884	−0.206942	+	0.978353i	$0.566351\pi$
$138$	2.92255	0.248784
$139$	8.30469	0.704395	0.352197	−	0.935926i	$-0.385435\pi$
$139$	8.30469	0.704395	0.352197	+	0.935926i	$0.385435\pi$
$140$	−1.69931	−0.143618
$141$	2.33435	0.196588
$142$	0.434824	0.0364896
$143$	−9.69658	−0.810869
$144$	10.2345	0.852878
$145$	28.3752	2.35643
$146$	−14.0034	−1.15893
$147$	0.991881	0.0818089
$148$	−1.02463	−0.0842242
$149$	9.48818	0.777302	0.388651	−	0.921385i	$-0.372941\pi$
$149$	9.48818	0.777302	0.388651	+	0.921385i	$0.372941\pi$
$150$	7.44200	0.607636
$151$	3.65333	0.297304	0.148652	−	0.988890i	$-0.452507\pi$
$151$	3.65333	0.297304	0.148652	+	0.988890i	$0.452507\pi$
$152$	−16.3808	−1.32866
$153$	17.0805	1.38087
$154$	−16.2651	−1.31068
$155$	9.00422	0.723236
$156$	0.123477	0.00988607
$157$	14.3674	1.14665	0.573323	−	0.819330i	$-0.305654\pi$
$157$	14.3674	1.14665	0.573323	+	0.819330i	$0.305654\pi$
$158$	−13.8658	−1.10310
$159$	1.69213	0.134194
$160$	4.52442	0.357687
$161$	−11.6474	−0.917945
$162$	−10.2750	−0.807277
$163$	7.09710	0.555888	0.277944	−	0.960597i	$-0.410347\pi$
$163$	7.09710	0.555888	0.277944	+	0.960597i	$0.410347\pi$
$164$	1.63962	0.128033
$165$	−9.79778	−0.762756
$166$	−7.74037	−0.600769
$167$	−8.78876	−0.680094	−0.340047	−	0.940408i	$-0.610443\pi$
$167$	−8.78876	−0.680094	−0.340047	+	0.940408i	$0.610443\pi$
$168$	2.45762	0.189610
$169$	−10.1057	−0.777362
$170$	−35.2761	−2.70556
$171$	15.8317	1.21068
$172$	1.22545	0.0934400
$173$	−16.7381	−1.27257	−0.636285	−	0.771454i	$-0.719530\pi$
$173$	−16.7381	−1.27257	−0.636285	+	0.771454i	$0.719530\pi$
$174$	−3.45851	−0.262189
$175$	−29.6591	−2.24201
$176$	20.5072	1.54579
$177$	−2.54679	−0.191429
$178$	−13.8458	−1.03778
$179$	−8.85543	−0.661886	−0.330943	−	0.943651i	$-0.607367\pi$
$179$	−8.85543	−0.661886	−0.330943	+	0.943651i	$0.607367\pi$
$180$	−2.28256	−0.170132
$181$	−10.1410	−0.753775	−0.376888	−	0.926259i	$-0.623006\pi$
$181$	−10.1410	−0.753775	−0.376888	+	0.926259i	$0.623006\pi$
$182$	4.85489	0.359868
$183$	−1.24424	−0.0919771
$184$	16.1878	1.19338
$185$	−24.2679	−1.78421
$186$	−1.09748	−0.0804712
$187$	34.2246	2.50275
$188$	1.08968	0.0794734
$189$	−4.88031	−0.354991
$190$	−32.6970	−2.37209
$191$	17.7238	1.28245	0.641226	−	0.767352i	$-0.278426\pi$
$191$	17.7238	1.28245	0.641226	+	0.767352i	$0.278426\pi$
$192$	−3.38892	−0.244574
$193$	4.39976	0.316701	0.158351	−	0.987383i	$-0.449382\pi$
$193$	4.39976	0.316701	0.158351	+	0.987383i	$0.449382\pi$
$194$	19.2690	1.38343
$195$	2.92450	0.209428
$196$	0.463013	0.0330724
$197$	26.1264	1.86143	0.930716	−	0.365742i	$-0.119185\pi$
$197$	26.1264	1.86143	0.930716	+	0.365742i	$0.119185\pi$
$198$	−21.8477	−1.55265
$199$	13.9217	0.986880	0.493440	−	0.869780i	$-0.335739\pi$
$199$	13.9217	0.986880	0.493440	+	0.869780i	$0.335739\pi$
$200$	41.2206	2.91474
$201$	−0.300913	−0.0212248
$202$	−25.9971	−1.82915
$203$	13.7834	0.967407
$204$	−0.435819	−0.0305134
$205$	38.8338	2.71227
$206$	−12.5726	−0.875973
$207$	−15.6452	−1.08741
$208$	−6.12112	−0.424423
$209$	31.7224	2.19428
$210$	4.90556	0.338516
$211$	−9.58907	−0.660139	−0.330069	−	0.943957i	$-0.607072\pi$
$211$	−9.58907	−0.660139	−0.330069	+	0.943957i	$0.607072\pi$
$212$	0.789891	0.0542499
$213$	0.127234	0.00871795
$214$	2.02581	0.138482
$215$	29.0243	1.97944
$216$	6.78274	0.461507
$217$	4.37386	0.296917
$218$	−7.52969	−0.509975
$219$	−4.09755	−0.276887
$220$	−4.57364	−0.308355
$221$	−10.2156	−0.687173
$222$	2.95790	0.198521
$223$	−18.1263	−1.21383	−0.606915	−	0.794767i	$-0.707593\pi$
$223$	−18.1263	−1.21383	−0.606915	+	0.794767i	$0.707593\pi$
$224$	2.19777	0.146844
$225$	−39.8389	−2.65593
$226$	13.5189	0.899265
$227$	12.3090	0.816979	0.408490	−	0.912763i	$-0.366056\pi$
$227$	12.3090	0.816979	0.408490	+	0.912763i	$0.366056\pi$
$228$	−0.403956	−0.0267526
$229$	−9.87329	−0.652445	−0.326223	−	0.945293i	$-0.605776\pi$
$229$	−9.87329	−0.652445	−0.326223	+	0.945293i	$0.605776\pi$
$230$	32.3118	2.13058
$231$	−4.75934	−0.313141
$232$	−19.1564	−1.25768
$233$	−9.84432	−0.644923	−0.322461	−	0.946583i	$-0.604510\pi$
$233$	−9.84432	−0.644923	−0.322461	+	0.946583i	$0.604510\pi$
$234$	6.52123	0.426306
$235$	25.8087	1.68357
$236$	−1.18885	−0.0773877
$237$	−4.05728	−0.263548
$238$	−17.1356	−1.11074
$239$	−7.47103	−0.483261	−0.241630	−	0.970368i	$-0.577682\pi$
$239$	−7.47103	−0.483261	−0.241630	+	0.970368i	$0.577682\pi$
$240$	−6.18500	−0.399240
$241$	22.7335	1.46439	0.732197	−	0.681093i	$-0.238495\pi$
$241$	22.7335	1.46439	0.732197	+	0.681093i	$0.238495\pi$
$242$	−28.9537	−1.86121
$243$	−9.92027	−0.636385
$244$	−0.580817	−0.0371830
$245$	10.9663	0.700609
$246$	−4.73326	−0.301782
$247$	−9.46868	−0.602478
$248$	−6.07886	−0.386008
$249$	−2.26492	−0.143533
$250$	52.9052	3.34602
$251$	−21.6770	−1.36824	−0.684120	−	0.729369i	$-0.739814\pi$
$251$	−21.6770	−1.36824	−0.684120	+	0.729369i	$0.739814\pi$
$252$	−1.10877	−0.0698460
$253$	−31.3486	−1.97087
$254$	23.7848	1.49239
$255$	−10.3222	−0.646400
$256$	−4.37903	−0.273689
$257$	−18.7964	−1.17249	−0.586243	−	0.810135i	$-0.699394\pi$
$257$	−18.7964	−1.17249	−0.586243	+	0.810135i	$0.699394\pi$
$258$	−3.53763	−0.220243
$259$	−11.7883	−0.732490
$260$	1.36517	0.0846640
$261$	18.5143	1.14601
$262$	13.5565	0.837525
$263$	−0.0251261	−0.00154934	−0.000774671	−	1.00000i	$-0.500247\pi$
$263$	−0.0251261	−0.00154934	−0.000774671		1.00000i	$0.500247\pi$
$264$	6.61460	0.407101
$265$	18.7082	1.14924
$266$	−15.8828	−0.973837
$267$	−4.05142	−0.247943
$268$	−0.140467	−0.00858039
$269$	16.2129	0.988521	0.494260	−	0.869314i	$-0.335439\pi$
$269$	16.2129	0.988521	0.494260	+	0.869314i	$0.335439\pi$
$270$	13.5388	0.823943
$271$	20.2992	1.23309	0.616544	−	0.787320i	$-0.288532\pi$
$271$	20.2992	1.23309	0.616544	+	0.787320i	$0.288532\pi$
$272$	21.6048	1.30998
$273$	1.42059	0.0859783
$274$	6.52813	0.394379
$275$	−79.8264	−4.81371
$276$	0.399196	0.0240288
$277$	−28.8266	−1.73202	−0.866012	−	0.500023i	$-0.833325\pi$
$277$	−28.8266	−1.73202	−0.866012	+	0.500023i	$0.833325\pi$
$278$	−11.1911	−0.671199
$279$	5.87510	0.351733
$280$	27.1715	1.62381
$281$	−23.3168	−1.39096	−0.695481	−	0.718544i	$-0.744809\pi$
$281$	−23.3168	−1.39096	−0.695481	+	0.718544i	$0.744809\pi$
$282$	−3.14569	−0.187323
$283$	19.2867	1.14647	0.573237	−	0.819389i	$-0.305687\pi$
$283$	19.2867	1.14647	0.573237	+	0.819389i	$0.305687\pi$
$284$	0.0593934	0.00352435
$285$	−9.56751	−0.566730
$286$	13.0668	0.772655
$287$	18.8638	1.11349
$288$	2.95210	0.173954
$289$	19.0564	1.12096
$290$	−38.2374	−2.24538
$291$	5.63831	0.330524
$292$	−1.91275	−0.111935
$293$	18.8673	1.10224	0.551119	−	0.834427i	$-0.314201\pi$
$293$	18.8673	1.10224	0.551119	+	0.834427i	$0.314201\pi$
$294$	−1.33662	−0.0779535
$295$	−28.1574	−1.63939
$296$	16.3836	0.952276
$297$	−13.1352	−0.762182
$298$	−12.7860	−0.740670
$299$	9.35712	0.541136
$300$	1.01652	0.0586885
$301$	14.0988	0.812639
$302$	−4.92311	−0.283293
$303$	−7.60705	−0.437013
$304$	20.0253	1.14853
$305$	−13.7564	−0.787688
$306$	−23.0171	−1.31580
$307$	−8.12288	−0.463597	−0.231799	−	0.972764i	$-0.574461\pi$
$307$	−8.12288	−0.463597	−0.231799	+	0.972764i	$0.574461\pi$
$308$	−2.22168	−0.126592
$309$	−3.67887	−0.209284
$310$	−12.1338	−0.689152
$311$	−20.3114	−1.15176	−0.575878	−	0.817536i	$-0.695340\pi$
$311$	−20.3114	−1.15176	−0.575878	+	0.817536i	$0.695340\pi$
$312$	−1.97436	−0.111776
$313$	−12.5714	−0.710577	−0.355289	−	0.934757i	$-0.615617\pi$
$313$	−12.5714	−0.710577	−0.355289	+	0.934757i	$0.615617\pi$
$314$	−19.3611	−1.09261
$315$	−26.2607	−1.47962
$316$	−1.89395	−0.106543
$317$	28.2675	1.58766	0.793832	−	0.608137i	$-0.208083\pi$
$317$	28.2675	1.58766	0.793832	+	0.608137i	$0.208083\pi$
$318$	−2.28025	−0.127870
$319$	37.0976	2.07707
$320$	−37.4680	−2.09453
$321$	0.592776	0.0330855
$322$	15.6957	0.874685
$323$	33.4202	1.85955
$324$	−1.40348	−0.0779709
$325$	23.8270	1.32169
$326$	−9.56381	−0.529691
$327$	−2.20327	−0.121841
$328$	−26.2171	−1.44760
$329$	12.5367	0.691173
$330$	13.2032	0.726810
$331$	2.01769	0.110902	0.0554512	−	0.998461i	$-0.482340\pi$
$331$	2.01769	0.110902	0.0554512	+	0.998461i	$0.482340\pi$
$332$	−1.05727	−0.0580253
$333$	−15.8344	−0.867720
$334$	11.8434	0.648043
$335$	−3.32690	−0.181768
$336$	−3.00441	−0.163904
$337$	−4.12084	−0.224477	−0.112238	−	0.993681i	$-0.535802\pi$
$337$	−4.12084	−0.224477	−0.112238	+	0.993681i	$0.535802\pi$
$338$	13.6181	0.740728
$339$	3.95578	0.214849
$340$	−4.81843	−0.261316
$341$	11.7721	0.637495
$342$	−21.3342	−1.15362
$343$	20.1506	1.08803
$344$	−19.5947	−1.05647
$345$	9.45478	0.509028
$346$	22.5556	1.21260
$347$	−1.80545	−0.0969217	−0.0484609	−	0.998825i	$-0.515432\pi$
$347$	−1.80545	−0.0969217	−0.0484609	+	0.998825i	$0.515432\pi$
$348$	−0.472404	−0.0253235
$349$	−13.2059	−0.706895	−0.353448	−	0.935454i	$-0.614991\pi$
$349$	−13.2059	−0.706895	−0.353448	+	0.935454i	$0.614991\pi$
$350$	39.9675	2.13635
$351$	3.92067	0.209270
$352$	5.91522	0.315282
$353$	7.70896	0.410307	0.205153	−	0.978730i	$-0.434231\pi$
$353$	7.70896	0.410307	0.205153	+	0.978730i	$0.434231\pi$
$354$	3.43197	0.182407
$355$	1.40671	0.0746602
$356$	−1.89122	−0.100234
$357$	−5.01407	−0.265373
$358$	11.9333	0.630693
$359$	31.9188	1.68461	0.842304	−	0.539003i	$-0.181199\pi$
$359$	31.9188	1.68461	0.842304	+	0.539003i	$0.181199\pi$
$360$	36.4976	1.92359
$361$	11.9768	0.630360
$362$	13.6657	0.718252
$363$	−8.47216	−0.444673
$364$	0.663138	0.0347579
$365$	−45.3027	−2.37125
$366$	1.67670	0.0876424
$367$	30.1978	1.57631	0.788157	−	0.615474i	$-0.211035\pi$
$367$	30.1978	1.57631	0.788157	+	0.615474i	$0.211035\pi$
$368$	−19.7893	−1.03159
$369$	25.3383	1.31906
$370$	32.7026	1.70013
$371$	9.08764	0.471807
$372$	−0.149907	−0.00777231
$373$	−22.9314	−1.18734	−0.593671	−	0.804707i	$-0.702322\pi$
$373$	−22.9314	−1.18734	−0.593671	+	0.804707i	$0.702322\pi$
$374$	−46.1199	−2.38480
$375$	15.4806	0.799416
$376$	−17.4238	−0.898562
$377$	−11.0731	−0.570294
$378$	6.57654	0.338261
$379$	−7.87174	−0.404344	−0.202172	−	0.979350i	$-0.564800\pi$
$379$	−7.87174	−0.404344	−0.202172	+	0.979350i	$0.564800\pi$
$380$	−4.46615	−0.229108
$381$	6.95969	0.356556
$382$	−23.8840	−1.22201
$383$	−10.4752	−0.535259	−0.267629	−	0.963522i	$-0.586240\pi$
$383$	−10.4752	−0.535259	−0.267629	+	0.963522i	$0.586240\pi$
$384$	3.74834	0.191282
$385$	−52.6194	−2.68173
$386$	−5.92896	−0.301776
$387$	18.9379	0.962666
$388$	2.63198	0.133619
$389$	−25.2547	−1.28046	−0.640231	−	0.768182i	$-0.721161\pi$
$389$	−25.2547	−1.28046	−0.640231	+	0.768182i	$0.721161\pi$
$390$	−3.94095	−0.199558
$391$	−33.0265	−1.67022
$392$	−7.40346	−0.373931
$393$	3.96679	0.200098
$394$	−35.2071	−1.77371
$395$	−44.8574	−2.25702
$396$	−2.98422	−0.149963
$397$	−6.67921	−0.335220	−0.167610	−	0.985853i	$-0.553605\pi$
$397$	−6.67921	−0.335220	−0.167610	+	0.985853i	$0.553605\pi$
$398$	−18.7603	−0.940371
$399$	−4.64748	−0.232665
$400$	−50.3916	−2.51958
$401$	9.86316	0.492543	0.246271	−	0.969201i	$-0.420795\pi$
$401$	9.86316	0.492543	0.246271	+	0.969201i	$0.420795\pi$
$402$	0.405500	0.0202245
$403$	−3.51380	−0.175035
$404$	−3.55099	−0.176669
$405$	−33.2407	−1.65174
$406$	−18.5741	−0.921816
$407$	−31.7278	−1.57269
$408$	6.96863	0.344999
$409$	−7.72372	−0.381913	−0.190957	−	0.981598i	$-0.561159\pi$
$409$	−7.72372	−0.381913	−0.190957	+	0.981598i	$0.561159\pi$
$410$	−52.3310	−2.58445
$411$	1.91020	0.0942233
$412$	−1.71731	−0.0846058
$413$	−13.6777	−0.673034
$414$	21.0829	1.03617
$415$	−25.0410	−1.22921
$416$	−1.76561	−0.0865660
$417$	−3.27464	−0.160360
$418$	−42.7480	−2.09087
$419$	21.5957	1.05502	0.527510	−	0.849549i	$-0.323126\pi$
$419$	21.5957	1.05502	0.527510	+	0.849549i	$0.323126\pi$
$420$	0.670060	0.0326956
$421$	20.2054	0.984749	0.492374	−	0.870383i	$-0.336129\pi$
$421$	20.2054	0.984749	0.492374	+	0.870383i	$0.336129\pi$
$422$	12.9219	0.629028
$423$	16.8397	0.818775
$424$	−12.6301	−0.613374
$425$	−84.0988	−4.07939
$426$	−0.171457	−0.00830709
$427$	−6.68225	−0.323377
$428$	0.276710	0.0133753
$429$	3.82348	0.184599
$430$	−39.1122	−1.88616
$431$	14.2095	0.684446	0.342223	−	0.939619i	$-0.388820\pi$
$431$	14.2095	0.684446	0.342223	+	0.939619i	$0.388820\pi$
$432$	−8.29180	−0.398939
$433$	18.3566	0.882162	0.441081	−	0.897467i	$-0.354595\pi$
$433$	18.3566	0.882162	0.441081	+	0.897467i	$0.354595\pi$
$434$	−5.89406	−0.282924
$435$	−11.1887	−0.536456
$436$	−1.02849	−0.0492559
$437$	−30.6119	−1.46436
$438$	5.52172	0.263838
$439$	27.9328	1.33316	0.666580	−	0.745433i	$-0.267757\pi$
$439$	27.9328	1.33316	0.666580	+	0.745433i	$0.267757\pi$
$440$	73.1313	3.48640
$441$	7.15529	0.340728
$442$	13.7661	0.654788
$443$	−10.1100	−0.480342	−0.240171	−	0.970731i	$-0.577204\pi$
$443$	−10.1100	−0.480342	−0.240171	+	0.970731i	$0.577204\pi$
$444$	0.404025	0.0191742
$445$	−44.7926	−2.12337
$446$	24.4264	1.15663
$447$	−3.74131	−0.176958
$448$	−18.2003	−0.859885
$449$	18.5458	0.875229	0.437615	−	0.899163i	$-0.355823\pi$
$449$	18.5458	0.875229	0.437615	+	0.899163i	$0.355823\pi$
$450$	53.6856	2.53076
$451$	50.7712	2.39072
$452$	1.84657	0.0868555
$453$	−1.44056	−0.0676832
$454$	−16.5872	−0.778477
$455$	15.7061	0.736315
$456$	6.45914	0.302477
$457$	−11.0122	−0.515129	−0.257564	−	0.966261i	$-0.582920\pi$
$457$	−11.0122	−0.515129	−0.257564	+	0.966261i	$0.582920\pi$
$458$	13.3049	0.621697
$459$	−13.8382	−0.645913
$460$	4.41352	0.205782
$461$	−35.8492	−1.66966	−0.834831	−	0.550506i	$-0.814435\pi$
$461$	−35.8492	−1.66966	−0.834831	+	0.550506i	$0.814435\pi$
$462$	6.41352	0.298384
$463$	12.4259	0.577479	0.288739	−	0.957408i	$-0.406764\pi$
$463$	12.4259	0.577479	0.288739	+	0.957408i	$0.406764\pi$
$464$	23.4184	1.08717
$465$	−3.55048	−0.164649
$466$	13.2659	0.614530
$467$	−19.9824	−0.924677	−0.462338	−	0.886704i	$-0.652989\pi$
$467$	−19.9824	−0.924677	−0.462338	+	0.886704i	$0.652989\pi$
$468$	0.890747	0.0411748
$469$	−1.61606	−0.0746229
$470$	−34.7789	−1.60423
$471$	−5.66526	−0.261041
$472$	19.0094	0.874980
$473$	37.9463	1.74477
$474$	5.46745	0.251128
$475$	−77.9502	−3.57660
$476$	−2.34058	−0.107280
$477$	12.2068	0.558910
$478$	10.0677	0.460486
$479$	14.4556	0.660493	0.330246	−	0.943895i	$-0.392868\pi$
$479$	14.4556	0.660493	0.330246	+	0.943895i	$0.392868\pi$
$480$	−1.78404	−0.0814297
$481$	9.47031	0.431809
$482$	−30.6349	−1.39538
$483$	4.59272	0.208976
$484$	−3.95483	−0.179765
$485$	62.3373	2.83059
$486$	13.3682	0.606394
$487$	−24.7109	−1.11976	−0.559879	−	0.828574i	$-0.689152\pi$
$487$	−24.7109	−1.11976	−0.559879	+	0.828574i	$0.689152\pi$
$488$	9.28710	0.420407
$489$	−2.79848	−0.126551
$490$	−14.7778	−0.667591
$491$	−29.3513	−1.32461	−0.662304	−	0.749235i	$-0.730421\pi$
$491$	−29.3513	−1.32461	−0.662304	+	0.749235i	$0.730421\pi$
$492$	−0.646524	−0.0291476
$493$	39.0832	1.76022
$494$	12.7597	0.574085
$495$	−70.6799	−3.17682
$496$	7.43132	0.333676
$497$	0.683317	0.0306509
$498$	3.05213	0.136769
$499$	−20.8026	−0.931254	−0.465627	−	0.884981i	$-0.654171\pi$
$499$	−20.8026	−0.931254	−0.465627	+	0.884981i	$0.654171\pi$
$500$	7.22641	0.323175
$501$	3.46552	0.154828
$502$	29.2112	1.30376
$503$	10.4112	0.464212	0.232106	−	0.972691i	$-0.425438\pi$
$503$	10.4112	0.464212	0.232106	+	0.972691i	$0.425438\pi$
$504$	17.7289	0.789710
$505$	−84.1037	−3.74257
$506$	42.2443	1.87799
$507$	3.98481	0.176972
$508$	3.24881	0.144143
$509$	20.9907	0.930397	0.465198	−	0.885206i	$-0.345983\pi$
$509$	20.9907	0.930397	0.465198	+	0.885206i	$0.345983\pi$
$510$	13.9098	0.615937
$511$	−22.0061	−0.973491
$512$	24.9131	1.10101
$513$	−12.8265	−0.566303
$514$	25.3294	1.11723
$515$	−40.6737	−1.79230
$516$	−0.483212	−0.0212722
$517$	33.7422	1.48398
$518$	15.8855	0.697970
$519$	6.60003	0.289709
$520$	−21.8286	−0.957249
$521$	−0.729671	−0.0319674	−0.0159837	−	0.999872i	$-0.505088\pi$
$521$	−0.729671	−0.0319674	−0.0159837	+	0.999872i	$0.505088\pi$
$522$	−24.9492	−1.09200
$523$	−15.6085	−0.682510	−0.341255	−	0.939971i	$-0.610852\pi$
$523$	−15.6085	−0.682510	−0.341255	+	0.939971i	$0.610852\pi$
$524$	1.85171	0.0808923
$525$	11.6949	0.510409
$526$	0.0338591	0.00147633
$527$	12.4022	0.540247
$528$	−8.08626	−0.351909
$529$	7.25118	0.315269
$530$	−25.2105	−1.09508
$531$	−18.3722	−0.797287
$532$	−2.16946	−0.0940580
$533$	−15.1545	−0.656413
$534$	5.45956	0.236258
$535$	6.55374	0.283343
$536$	2.24603	0.0970138
$537$	3.49181	0.150683
$538$	−21.8480	−0.941935
$539$	14.3373	0.617550
$540$	1.84928	0.0795805
$541$	20.7923	0.893932	0.446966	−	0.894551i	$-0.352504\pi$
$541$	20.7923	0.893932	0.446966	+	0.894551i	$0.352504\pi$
$542$	−27.3545	−1.17498
$543$	3.99873	0.171602
$544$	6.23181	0.267187
$545$	−24.3594	−1.04344
$546$	−1.91434	−0.0819264
$547$	−39.3099	−1.68077	−0.840386	−	0.541989i	$-0.817672\pi$
$547$	−39.3099	−1.68077	−0.840386	+	0.541989i	$0.817672\pi$
$548$	0.891688	0.0380910
$549$	−8.97580	−0.383078
$550$	107.571	4.58686
$551$	36.2257	1.54327
$552$	−6.38304	−0.271680
$553$	−21.7898	−0.926595
$554$	38.8458	1.65040
$555$	9.56915	0.406188
$556$	−1.52861	−0.0648277
$557$	−9.77999	−0.414392	−0.207196	−	0.978299i	$-0.566434\pi$
$557$	−9.77999	−0.414392	−0.207196	+	0.978299i	$0.566434\pi$
$558$	−7.91708	−0.335157
$559$	−11.3264	−0.479057
$560$	−33.2168	−1.40367
$561$	−13.4952	−0.569768
$562$	31.4209	1.32541
$563$	−2.25670	−0.0951084	−0.0475542	−	0.998869i	$-0.515143\pi$
$563$	−2.25670	−0.0951084	−0.0475542	+	0.998869i	$0.515143\pi$
$564$	−0.429676	−0.0180926
$565$	43.7353	1.83996
$566$	−25.9901	−1.09244
$567$	−16.1469	−0.678106
$568$	−0.949684	−0.0398479
$569$	−29.9551	−1.25578	−0.627892	−	0.778301i	$-0.716082\pi$
$569$	−29.9551	−1.25578	−0.627892	+	0.778301i	$0.716082\pi$
$570$	12.8928	0.540022
$571$	−40.3195	−1.68732	−0.843660	−	0.536878i	$-0.819604\pi$
$571$	−40.3195	−1.68732	−0.843660	+	0.536878i	$0.819604\pi$
$572$	1.78481	0.0746268
$573$	−6.98873	−0.291958
$574$	−25.4202	−1.06102
$575$	77.0318	3.21245
$576$	−24.4472	−1.01863
$577$	21.3100	0.887145	0.443573	−	0.896238i	$-0.353711\pi$
$577$	21.3100	0.887145	0.443573	+	0.896238i	$0.353711\pi$
$578$	−25.6797	−1.06814
$579$	−1.73488	−0.0720991
$580$	−5.22291	−0.216870
$581$	−12.1638	−0.504641
$582$	−7.59800	−0.314947
$583$	24.4591	1.01299
$584$	30.5844	1.26559
$585$	21.0969	0.872251
$586$	−25.4249	−1.05029
$587$	−2.24877	−0.0928165	−0.0464082	−	0.998923i	$-0.514778\pi$
$587$	−2.24877	−0.0928165	−0.0464082	+	0.998923i	$0.514778\pi$
$588$	−0.182572	−0.00752914
$589$	11.4954	0.473661
$590$	37.9440	1.56213
$591$	−10.3020	−0.423767
$592$	−20.0287	−0.823174
$593$	−33.0465	−1.35706	−0.678529	−	0.734574i	$-0.737382\pi$
$593$	−33.0465	−1.35706	−0.678529	+	0.734574i	$0.737382\pi$
$594$	17.7005	0.726262
$595$	−55.4357	−2.27264
$596$	−1.74646	−0.0715376
$597$	−5.48948	−0.224670
$598$	−12.6093	−0.515634
$599$	−1.49354	−0.0610245	−0.0305122	−	0.999534i	$-0.509714\pi$
$599$	−1.49354	−0.0610245	−0.0305122	+	0.999534i	$0.509714\pi$
$600$	−16.2538	−0.663559
$601$	−24.3676	−0.993973	−0.496987	−	0.867758i	$-0.665560\pi$
$601$	−24.3676	−0.993973	−0.496987	+	0.867758i	$0.665560\pi$
$602$	−18.9990	−0.774342
$603$	−2.17074	−0.0883996
$604$	−0.672456	−0.0273619
$605$	−93.6685	−3.80816
$606$	10.2510	0.416418
$607$	19.7204	0.800427	0.400213	−	0.916422i	$-0.368936\pi$
$607$	19.7204	0.800427	0.400213	+	0.916422i	$0.368936\pi$
$608$	5.77619	0.234256
$609$	−5.43498	−0.220236
$610$	18.5376	0.750567
$611$	−10.0716	−0.407452
$612$	−3.14394	−0.127086
$613$	9.31927	0.376402	0.188201	−	0.982131i	$-0.439734\pi$
$613$	9.31927	0.376402	0.188201	+	0.982131i	$0.439734\pi$
$614$	10.9461	0.441749
$615$	−15.3126	−0.617465
$616$	35.5240	1.43130
$617$	34.2178	1.37756	0.688778	−	0.724972i	$-0.258147\pi$
$617$	34.2178	1.37756	0.688778	+	0.724972i	$0.258147\pi$
$618$	4.95752	0.199421
$619$	5.90459	0.237326	0.118663	−	0.992935i	$-0.462139\pi$
$619$	5.90459	0.237326	0.118663	+	0.992935i	$0.462139\pi$
$620$	−1.65737	−0.0665618
$621$	12.6754	0.508645
$622$	27.3710	1.09748
$623$	−21.7583	−0.871729
$624$	2.41363	0.0966226
$625$	101.127	4.04507
$626$	16.9408	0.677090
$627$	−12.5085	−0.499543
$628$	−2.64456	−0.105529
$629$	−33.4260	−1.33278
$630$	35.3881	1.40989
$631$	36.7274	1.46210	0.731048	−	0.682326i	$-0.239032\pi$
$631$	36.7274	1.46210	0.731048	+	0.682326i	$0.239032\pi$
$632$	30.2838	1.20462
$633$	3.78109	0.150285
$634$	−38.0924	−1.51284
$635$	76.9466	3.05353
$636$	−0.311464	−0.0123503
$637$	−4.27947	−0.169559
$638$	−49.9915	−1.97918
$639$	0.917851	0.0363096
$640$	41.4418	1.63813
$641$	−39.3052	−1.55246	−0.776231	−	0.630449i	$-0.782871\pi$
$641$	−39.3052	−1.55246	−0.776231	+	0.630449i	$0.782871\pi$
$642$	−0.798804	−0.0315263
$643$	−11.1173	−0.438423	−0.219211	−	0.975677i	$-0.570348\pi$
$643$	−11.1173	−0.438423	−0.219211	+	0.975677i	$0.570348\pi$
$644$	2.14390	0.0844814
$645$	−11.4447	−0.450633
$646$	−45.0360	−1.77192
$647$	25.4596	1.00092	0.500460	−	0.865760i	$-0.333164\pi$
$647$	25.4596	1.00092	0.500460	+	0.865760i	$0.333164\pi$
$648$	22.4412	0.881574
$649$	−36.8130	−1.44504
$650$	−32.1085	−1.25940
$651$	−1.72467	−0.0675951
$652$	−1.30634	−0.0511602
$653$	−38.9028	−1.52239	−0.761193	−	0.648525i	$-0.775386\pi$
$653$	−38.9028	−1.52239	−0.761193	+	0.648525i	$0.775386\pi$
$654$	2.96905	0.116099
$655$	43.8569	1.71363
$656$	32.0501	1.25135
$657$	−29.5592	−1.15321
$658$	−16.8941	−0.658600
$659$	−38.5620	−1.50216	−0.751081	−	0.660210i	$-0.770467\pi$
$659$	−38.5620	−1.50216	−0.751081	+	0.660210i	$0.770467\pi$
$660$	1.80344	0.0701989
$661$	8.98194	0.349357	0.174679	−	0.984626i	$-0.444111\pi$
$661$	8.98194	0.349357	0.174679	+	0.984626i	$0.444111\pi$
$662$	−2.71897	−0.105676
$663$	4.02812	0.156439
$664$	16.9055	0.656060
$665$	−51.3827	−1.99254
$666$	21.3379	0.826827
$667$	−35.7989	−1.38614
$668$	1.61771	0.0625913
$669$	7.14744	0.276336
$670$	4.48322	0.173202
$671$	−17.9851	−0.694306
$672$	−0.866607	−0.0334301
$673$	12.0472	0.464386	0.232193	−	0.972670i	$-0.425410\pi$
$673$	12.0472	0.464386	0.232193	+	0.972670i	$0.425410\pi$
$674$	5.55311	0.213898
$675$	32.2766	1.24233
$676$	1.86012	0.0715431
$677$	37.6514	1.44706	0.723531	−	0.690292i	$-0.242518\pi$
$677$	37.6514	1.44706	0.723531	+	0.690292i	$0.242518\pi$
$678$	−5.33068	−0.204724
$679$	30.2808	1.16207
$680$	77.0454	2.95456
$681$	−4.85361	−0.185991
$682$	−15.8637	−0.607452
$683$	19.3553	0.740611	0.370305	−	0.928910i	$-0.379253\pi$
$683$	19.3553	0.740611	0.370305	+	0.928910i	$0.379253\pi$
$684$	−2.91408	−0.111423
$685$	21.1192	0.806925
$686$	−27.1543	−1.03676
$687$	3.89316	0.148533
$688$	23.9542	0.913246
$689$	−7.30068	−0.278134
$690$	−12.7409	−0.485039
$691$	−48.3913	−1.84089	−0.920447	−	0.390868i	$-0.872175\pi$
$691$	−48.3913	−1.84089	−0.920447	+	0.390868i	$0.872175\pi$
$692$	3.08091	0.117119
$693$	−34.3332	−1.30421
$694$	2.43296	0.0923541
$695$	−36.2046	−1.37332
$696$	7.55362	0.286319
$697$	53.4885	2.02602
$698$	17.7958	0.673581
$699$	3.88174	0.146821
$700$	5.45924	0.206340
$701$	−51.1405	−1.93155	−0.965776	−	0.259378i	$-0.916482\pi$
$701$	−51.1405	−1.93155	−0.965776	+	0.259378i	$0.916482\pi$
$702$	−5.28336	−0.199408
$703$	−30.9822	−1.16851
$704$	−48.9856	−1.84621
$705$	−10.1767	−0.383276
$706$	−10.3883	−0.390970
$707$	−40.8539	−1.53647
$708$	0.468779	0.0176178
$709$	26.7546	1.00479	0.502395	−	0.864638i	$-0.332452\pi$
$709$	26.7546	1.00479	0.502395	+	0.864638i	$0.332452\pi$
$710$	−1.89563	−0.0711417
$711$	−29.2687	−1.09766
$712$	30.2401	1.13329
$713$	−11.3600	−0.425435
$714$	6.75679	0.252866
$715$	42.2725	1.58090
$716$	1.62999	0.0609155
$717$	2.94592	0.110017
$718$	−43.0126	−1.60522
$719$	2.88074	0.107433	0.0537167	−	0.998556i	$-0.482893\pi$
$719$	2.88074	0.107433	0.0537167	+	0.998556i	$0.482893\pi$
$720$	−44.6178	−1.66281
$721$	−19.7575	−0.735809
$722$	−16.1396	−0.600653
$723$	−8.96410	−0.333379
$724$	1.86662	0.0693723
$725$	−91.1585	−3.38554
$726$	11.4168	0.423717
$727$	31.4637	1.16692	0.583461	−	0.812141i	$-0.301698\pi$
$727$	31.4637	1.16692	0.583461	+	0.812141i	$0.301698\pi$
$728$	−10.6034	−0.392988
$729$	−18.9628	−0.702326
$730$	61.0483	2.25950
$731$	39.9773	1.47861
$732$	0.229023	0.00846494
$733$	22.5829	0.834119	0.417060	−	0.908879i	$-0.363061\pi$
$733$	22.5829	0.834119	0.417060	+	0.908879i	$0.363061\pi$
$734$	−40.6936	−1.50203
$735$	−4.32413	−0.159498
$736$	−5.70813	−0.210405
$737$	−4.34958	−0.160219
$738$	−34.1451	−1.25690
$739$	40.1338	1.47634	0.738172	−	0.674613i	$-0.235689\pi$
$739$	40.1338	1.47634	0.738172	+	0.674613i	$0.235689\pi$
$740$	4.46691	0.164207
$741$	3.73362	0.137158
$742$	−12.2462	−0.449572
$743$	21.2021	0.777830	0.388915	−	0.921274i	$-0.372850\pi$
$743$	21.2021	0.777830	0.388915	+	0.921274i	$0.372850\pi$
$744$	2.39697	0.0878772
$745$	−41.3640	−1.51546
$746$	30.9016	1.13139
$747$	−16.3388	−0.597806
$748$	−6.29960	−0.230336
$749$	3.18353	0.116323
$750$	−20.8612	−0.761742
$751$	30.7551	1.12227	0.561135	−	0.827724i	$-0.310365\pi$
$751$	30.7551	1.12227	0.561135	+	0.827724i	$0.310365\pi$
$752$	21.3003	0.776742
$753$	8.54751	0.311489
$754$	14.9217	0.543418
$755$	−15.9268	−0.579636
$756$	0.898302	0.0326709
$757$	−2.86490	−0.104127	−0.0520633	−	0.998644i	$-0.516580\pi$
$757$	−2.86490	−0.104127	−0.0520633	+	0.998644i	$0.516580\pi$
$758$	10.6077	0.385288
$759$	12.3612	0.448682
$760$	71.4125	2.59040
$761$	5.80786	0.210535	0.105267	−	0.994444i	$-0.466430\pi$
$761$	5.80786	0.210535	0.105267	+	0.994444i	$0.466430\pi$
$762$	−9.37864	−0.339752
$763$	−11.8327	−0.428374
$764$	−3.26236	−0.118028
$765$	−74.4628	−2.69221
$766$	14.1161	0.510034
$767$	10.9881	0.396759
$768$	1.72671	0.0623071
$769$	34.4410	1.24198	0.620988	−	0.783820i	$-0.286732\pi$
$769$	34.4410	1.24198	0.620988	+	0.783820i	$0.286732\pi$
$770$	70.9081	2.55535
$771$	7.41165	0.266924
$772$	−0.809847	−0.0291470
$773$	−22.4901	−0.808912	−0.404456	−	0.914557i	$-0.632539\pi$
$773$	−22.4901	−0.808912	−0.404456	+	0.914557i	$0.632539\pi$
$774$	−25.5200	−0.917298
$775$	−28.9271	−1.03909
$776$	−42.0847	−1.51075
$777$	4.64828	0.166756
$778$	34.0323	1.22012
$779$	49.5779	1.77631
$780$	−0.538302	−0.0192743
$781$	1.83912	0.0658090
$782$	44.5054	1.59151
$783$	−14.9999	−0.536052
$784$	9.05062	0.323236
$785$	−62.6352	−2.23555
$786$	−5.34551	−0.190668
$787$	−9.18312	−0.327343	−0.163671	−	0.986515i	$-0.552334\pi$
$787$	−9.18312	−0.327343	−0.163671	+	0.986515i	$0.552334\pi$
$788$	−4.80900	−0.171314
$789$	0.00990754	0.000352718 0
$790$	60.4483	2.15065
$791$	21.2447	0.755375
$792$	47.7169	1.69555
$793$	5.36828	0.190633
$794$	9.00067	0.319422
$795$	−7.37688	−0.261631
$796$	−2.56251	−0.0908257
$797$	5.30130	0.187782	0.0938909	−	0.995582i	$-0.470070\pi$
$797$	5.30130	0.187782	0.0938909	+	0.995582i	$0.470070\pi$
$798$	6.26279	0.221700
$799$	35.5482	1.25760
$800$	−14.5352	−0.513898
$801$	−29.2264	−1.03266
$802$	−13.2913	−0.469330
$803$	−59.2286	−2.09013
$804$	0.0553879	0.00195338
$805$	50.7773	1.78966
$806$	4.73508	0.166786
$807$	−6.39297	−0.225043
$808$	56.7795	1.99749
$809$	34.6554	1.21842	0.609209	−	0.793009i	$-0.291487\pi$
$809$	34.6554	1.21842	0.609209	+	0.793009i	$0.291487\pi$
$810$	44.7940	1.57390
$811$	−24.1629	−0.848475	−0.424238	−	0.905551i	$-0.639458\pi$
$811$	−24.1629	−0.848475	−0.424238	+	0.905551i	$0.639458\pi$
$812$	−2.53706	−0.0890335
$813$	−8.00423	−0.280721
$814$	42.7554	1.49857
$815$	−30.9400	−1.08378
$816$	−8.51905	−0.298226
$817$	37.0545	1.29637
$818$	10.4082	0.363915
$819$	10.2480	0.358093
$820$	−7.14799	−0.249619
$821$	6.64177	0.231799	0.115900	−	0.993261i	$-0.463025\pi$
$821$	6.64177	0.231799	0.115900	+	0.993261i	$0.463025\pi$
$822$	−2.57412	−0.0897828
$823$	4.56886	0.159261	0.0796303	−	0.996824i	$-0.474626\pi$
$823$	4.56886	0.159261	0.0796303	+	0.996824i	$0.474626\pi$
$824$	27.4593	0.956591
$825$	31.4765	1.09587
$826$	18.4316	0.641316
$827$	36.7224	1.27696	0.638482	−	0.769637i	$-0.279563\pi$
$827$	36.7224	1.27696	0.638482	+	0.769637i	$0.279563\pi$
$828$	2.87975	0.100078
$829$	−49.2419	−1.71024	−0.855120	−	0.518430i	$-0.826517\pi$
$829$	−49.2419	−1.71024	−0.855120	+	0.518430i	$0.826517\pi$
$830$	33.7444	1.17128
$831$	11.3667	0.394307
$832$	14.6215	0.506909
$833$	15.1046	0.523344
$834$	4.41280	0.152803
$835$	38.3148	1.32594
$836$	−5.83903	−0.201947
$837$	−4.75988	−0.164525
$838$	−29.1016	−1.00530
$839$	−17.9494	−0.619683	−0.309841	−	0.950788i	$-0.600276\pi$
$839$	−17.9494	−0.619683	−0.309841	+	0.950788i	$0.600276\pi$
$840$	−10.7141	−0.369671
$841$	13.3640	0.460828
$842$	−27.2280	−0.938341
$843$	9.19410	0.316661
$844$	1.76503	0.0607547
$845$	44.0562	1.51558
$846$	−22.6926	−0.780188
$847$	−45.5001	−1.56340
$848$	15.4402	0.530217
$849$	−7.60498	−0.261002
$850$	113.329	3.88714
$851$	30.6171	1.04954
$852$	−0.0234195	−0.000802341 0
$853$	36.1452	1.23759	0.618794	−	0.785553i	$-0.287622\pi$
$853$	36.1452	1.23759	0.618794	+	0.785553i	$0.287622\pi$
$854$	9.00478	0.308137
$855$	−69.0187	−2.36039
$856$	−4.42451	−0.151227
$857$	9.83518	0.335963	0.167982	−	0.985790i	$-0.446275\pi$
$857$	9.83518	0.335963	0.167982	+	0.985790i	$0.446275\pi$
$858$	−5.15239	−0.175900
$859$	−26.3332	−0.898477	−0.449239	−	0.893412i	$-0.648305\pi$
$859$	−26.3332	−0.898477	−0.449239	+	0.893412i	$0.648305\pi$
$860$	−5.34240	−0.182174
$861$	−7.43822	−0.253494
$862$	−19.1482	−0.652190
$863$	−25.0614	−0.853099	−0.426550	−	0.904464i	$-0.640271\pi$
$863$	−25.0614	−0.853099	−0.426550	+	0.904464i	$0.640271\pi$
$864$	−2.39173	−0.0813683
$865$	72.9701	2.48106
$866$	−24.7367	−0.840588
$867$	−7.51417	−0.255195
$868$	−0.805081	−0.0273262
$869$	−58.6464	−1.98944
$870$	15.0775	0.511174
$871$	1.29829	0.0439908
$872$	16.4453	0.556909
$873$	40.6740	1.37661
$874$	41.2515	1.39535
$875$	83.1393	2.81062
$876$	0.754222	0.0254828
$877$	10.6112	0.358314	0.179157	−	0.983821i	$-0.442663\pi$
$877$	10.6112	0.358314	0.179157	+	0.983821i	$0.442663\pi$
$878$	−37.6413	−1.27033
$879$	−7.43960	−0.250932
$880$	−89.4019	−3.01374
$881$	−21.3165	−0.718173	−0.359086	−	0.933304i	$-0.616912\pi$
$881$	−21.3165	−0.718173	−0.359086	+	0.933304i	$0.616912\pi$
$882$	−9.64223	−0.324671
$883$	53.1827	1.78974	0.894870	−	0.446326i	$-0.147268\pi$
$883$	53.1827	1.78974	0.894870	+	0.446326i	$0.147268\pi$
$884$	1.88034	0.0632427
$885$	11.1028	0.373218
$886$	13.6239	0.457705
$887$	10.7221	0.360012	0.180006	−	0.983665i	$-0.442388\pi$
$887$	10.7221	0.360012	0.180006	+	0.983665i	$0.442388\pi$
$888$	−6.46025	−0.216792
$889$	37.3773	1.25359
$890$	60.3610	2.02331
$891$	−43.4588	−1.45592
$892$	3.33645	0.111713
$893$	32.9492	1.10260
$894$	5.04166	0.168618
$895$	38.6055	1.29044
$896$	20.1306	0.672517
$897$	−3.68963	−0.123193
$898$	−24.9916	−0.833982
$899$	13.4433	0.448358
$900$	7.33301	0.244434
$901$	25.7682	0.858462
$902$	−68.4175	−2.27805
$903$	−5.55932	−0.185003
$904$	−29.5262	−0.982028
$905$	44.2100	1.46959
$906$	1.94124	0.0644935
$907$	−36.6452	−1.21678	−0.608391	−	0.793637i	$-0.708185\pi$
$907$	−36.6452	−1.21678	−0.608391	+	0.793637i	$0.708185\pi$
$908$	−2.26568	−0.0751892
$909$	−54.8762	−1.82013
$910$	−21.1650	−0.701615
$911$	40.1080	1.32884	0.664418	−	0.747361i	$-0.268679\pi$
$911$	40.1080	1.32884	0.664418	+	0.747361i	$0.268679\pi$
$912$	−7.89621	−0.261470
$913$	−32.7385	−1.08349
$914$	14.8397	0.490852
$915$	5.42431	0.179322
$916$	1.81734	0.0600466
$917$	21.3038	0.703513
$918$	18.6479	0.615473
$919$	−27.5860	−0.909980	−0.454990	−	0.890497i	$-0.650357\pi$
$919$	−27.5860	−0.909980	−0.454990	+	0.890497i	$0.650357\pi$
$920$	−70.5711	−2.32666
$921$	3.20295	0.105541
$922$	48.3091	1.59098
$923$	−0.548952	−0.0180690
$924$	0.876034	0.0288194
$925$	77.9636	2.56343
$926$	−16.7447	−0.550264
$927$	−26.5389	−0.871652
$928$	6.75494	0.221742
$929$	5.75530	0.188825	0.0944126	−	0.995533i	$-0.469903\pi$
$929$	5.75530	0.188825	0.0944126	+	0.995533i	$0.469903\pi$
$930$	4.78450	0.156890
$931$	14.0003	0.458841
$932$	1.81201	0.0593543
$933$	8.00906	0.262205
$934$	26.9276	0.881099
$935$	−149.203	−4.87947
$936$	−14.2428	−0.465541
$937$	13.9395	0.455383	0.227692	−	0.973733i	$-0.426882\pi$
$937$	13.9395	0.455383	0.227692	+	0.973733i	$0.426882\pi$
$938$	2.17775	0.0711062
$939$	4.95706	0.161768
$940$	−4.75051	−0.154945
$941$	51.3982	1.67553	0.837767	−	0.546027i	$-0.183860\pi$
$941$	51.3982	1.67553	0.837767	+	0.546027i	$0.183860\pi$
$942$	7.63431	0.248739
$943$	−48.9938	−1.59546
$944$	−23.2388	−0.756357
$945$	21.2759	0.692104
$946$	−51.1352	−1.66255
$947$	−28.2772	−0.918887	−0.459443	−	0.888207i	$-0.651951\pi$
$947$	−28.2772	−0.918887	−0.459443	+	0.888207i	$0.651951\pi$
$948$	0.746808	0.0242552
$949$	17.6789	0.573881
$950$	105.043	3.40805
$951$	−11.1462	−0.361442
$952$	37.4253	1.21296
$953$	32.7665	1.06141	0.530706	−	0.847556i	$-0.321927\pi$
$953$	32.7665	1.06141	0.530706	+	0.847556i	$0.321927\pi$
$954$	−16.4494	−0.532570
$955$	−77.2676	−2.50032
$956$	1.37517	0.0444760
$957$	−14.6281	−0.472858
$958$	−19.4799	−0.629366
$959$	10.2588	0.331274
$960$	14.7741	0.476832
$961$	−26.7341	−0.862390
$962$	−12.7619	−0.411459
$963$	4.27620	0.137799
$964$	−4.18447	−0.134773
$965$	−19.1809	−0.617454
$966$	−6.18900	−0.199128
$967$	−15.5934	−0.501451	−0.250726	−	0.968058i	$-0.580669\pi$
$967$	−15.5934	−0.501451	−0.250726	+	0.968058i	$0.580669\pi$
$968$	63.2367	2.03251
$969$	−13.1780	−0.423339
$970$	−84.0037	−2.69720
$971$	−34.9153	−1.12048	−0.560242	−	0.828329i	$-0.689292\pi$
$971$	−34.9153	−1.12048	−0.560242	+	0.828329i	$0.689292\pi$
$972$	1.82599	0.0585686
$973$	−17.5866	−0.563801
$974$	33.2996	1.06699
$975$	−9.39530	−0.300890
$976$	−11.3534	−0.363412
$977$	3.93544	0.125906	0.0629530	−	0.998016i	$-0.479948\pi$
$977$	3.93544	0.125906	0.0629530	+	0.998016i	$0.479948\pi$
$978$	3.77113	0.120587
$979$	−58.5618	−1.87164
$980$	−2.01852	−0.0644793
$981$	−15.8941	−0.507459
$982$	39.5529	1.26218
$983$	−22.2227	−0.708794	−0.354397	−	0.935095i	$-0.615314\pi$
$983$	−22.2227	−0.708794	−0.354397	+	0.935095i	$0.615314\pi$
$984$	10.3378	0.329555
$985$	−113.899	−3.62913
$986$	−52.6671	−1.67726
$987$	−4.94339	−0.157350
$988$	1.74287	0.0554480
$989$	−36.6179	−1.16438
$990$	95.2458	3.02711
$991$	61.3343	1.94835	0.974174	−	0.225800i	$-0.0724997\pi$
$991$	61.3343	1.94835	0.974174	+	0.225800i	$0.0724997\pi$
$992$	2.14353	0.0680571
$993$	−0.795601	−0.0252476
$994$	−0.920814	−0.0292064
$995$	−60.6919	−1.92406
$996$	0.416895	0.0132098
$997$	0.348639	0.0110415	0.00552076	−	0.999985i	$-0.498243\pi$
$997$	0.348639	0.0110415	0.00552076	+	0.999985i	$0.498243\pi$
$998$	28.0329	0.887367
$999$	12.8287	0.405882

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.a.1.96	✓	309

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.a.1.96	✓	309	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.34757 q^{2} -0.394313 q^{3} -0.184066 q^{4} -4.35953 q^{5} +0.531362 q^{6} -2.11767 q^{7} +2.94317 q^{8} -2.84452 q^{9} +O(q^{10})\)	\(q-1.34757 q^{2} -0.394313 q^{3} -0.184066 q^{4} -4.35953 q^{5} +0.531362 q^{6} -2.11767 q^{7} +2.94317 q^{8} -2.84452 q^{9} +5.87475 q^{10} -5.69964 q^{11} +0.0725797 q^{12} +1.70126 q^{13} +2.85370 q^{14} +1.71902 q^{15} -3.59799 q^{16} -6.00470 q^{17} +3.83317 q^{18} -5.56568 q^{19} +0.802443 q^{20} +0.835024 q^{21} +7.68064 q^{22} +5.50011 q^{23} -1.16053 q^{24} +14.0055 q^{25} -2.29256 q^{26} +2.30457 q^{27} +0.389792 q^{28} -6.50876 q^{29} -2.31649 q^{30} -2.06541 q^{31} -1.03782 q^{32} +2.24744 q^{33} +8.09172 q^{34} +9.23205 q^{35} +0.523580 q^{36} +5.56664 q^{37} +7.50013 q^{38} -0.670829 q^{39} -12.8309 q^{40} -8.90778 q^{41} -1.12525 q^{42} -6.65767 q^{43} +1.04911 q^{44} +12.4008 q^{45} -7.41176 q^{46} -5.92006 q^{47} +1.41873 q^{48} -2.51547 q^{49} -18.8733 q^{50} +2.36773 q^{51} -0.313145 q^{52} -4.29133 q^{53} -3.10555 q^{54} +24.8478 q^{55} -6.23267 q^{56} +2.19462 q^{57} +8.77099 q^{58} +6.45882 q^{59} -0.316413 q^{60} +3.15547 q^{61} +2.78328 q^{62} +6.02375 q^{63} +8.59451 q^{64} -7.41670 q^{65} -3.02857 q^{66} +0.763133 q^{67} +1.10526 q^{68} -2.16876 q^{69} -12.4408 q^{70} -0.322674 q^{71} -8.37191 q^{72} +10.3916 q^{73} -7.50141 q^{74} -5.52255 q^{75} +1.02446 q^{76} +12.0700 q^{77} +0.903986 q^{78} +10.2895 q^{79} +15.6855 q^{80} +7.62483 q^{81} +12.0038 q^{82} +5.74397 q^{83} -0.153700 q^{84} +26.1777 q^{85} +8.97165 q^{86} +2.56649 q^{87} -16.7750 q^{88} +10.2746 q^{89} -16.7108 q^{90} -3.60271 q^{91} -1.01238 q^{92} +0.814417 q^{93} +7.97767 q^{94} +24.2638 q^{95} +0.409226 q^{96} -14.2991 q^{97} +3.38976 q^{98} +16.2127 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9} - 23 q^{10} - 72 q^{11} - 42 q^{12} - 57 q^{13} - 77 q^{14} - 44 q^{15} + 205 q^{16} - 86 q^{17} - 82 q^{18} - 58 q^{19} - 134 q^{20} - 123 q^{21} - 31 q^{22} - 94 q^{23} - 84 q^{24} + 225 q^{25} - 92 q^{26} - 48 q^{27} - 36 q^{28} - 345 q^{29} - 85 q^{30} - 36 q^{31} - 199 q^{32} - 56 q^{33} - 28 q^{34} - 168 q^{35} + 65 q^{36} - 79 q^{37} - 66 q^{38} - 145 q^{39} - 54 q^{40} - 176 q^{41} - 48 q^{42} - 58 q^{43} - 194 q^{44} - 192 q^{45} - 44 q^{46} - 82 q^{47} - 81 q^{48} + 186 q^{49} - 206 q^{50} - 145 q^{51} - 86 q^{52} - 223 q^{53} - 117 q^{54} - 58 q^{55} - 216 q^{56} - 124 q^{57} - 151 q^{59} - 91 q^{60} - 184 q^{61} - 124 q^{62} - 78 q^{63} + 101 q^{64} - 194 q^{65} - 112 q^{66} - 53 q^{67} - 182 q^{68} - 243 q^{69} - 193 q^{71} - 208 q^{72} - 69 q^{73} - 236 q^{74} - 62 q^{75} - 142 q^{76} - 324 q^{77} - 20 q^{78} - 91 q^{79} - 223 q^{80} - 27 q^{81} + 2 q^{82} - 117 q^{83} - 157 q^{84} - 171 q^{85} - 203 q^{86} - 69 q^{87} - 36 q^{88} - 172 q^{89} - 10 q^{90} - 84 q^{91} - 226 q^{92} - 220 q^{93} - 96 q^{94} - 166 q^{95} - 118 q^{96} - 12 q^{97} - 116 q^{98} - 154 q^{99}+O(q^{100}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9 - 23 * q^10 - 72 * q^11 - 42 * q^12 - 57 * q^13 - 77 * q^14 - 44 * q^15 + 205 * q^16 - 86 * q^17 - 82 * q^18 - 58 * q^19 - 134 * q^20 - 123 * q^21 - 31 * q^22 - 94 * q^23 - 84 * q^24 + 225 * q^25 - 92 * q^26 - 48 * q^27 - 36 * q^28 - 345 * q^29 - 85 * q^30 - 36 * q^31 - 199 * q^32 - 56 * q^33 - 28 * q^34 - 168 * q^35 + 65 * q^36 - 79 * q^37 - 66 * q^38 - 145 * q^39 - 54 * q^40 - 176 * q^41 - 48 * q^42 - 58 * q^43 - 194 * q^44 - 192 * q^45 - 44 * q^46 - 82 * q^47 - 81 * q^48 + 186 * q^49 - 206 * q^50 - 145 * q^51 - 86 * q^52 - 223 * q^53 - 117 * q^54 - 58 * q^55 - 216 * q^56 - 124 * q^57 - 151 * q^59 - 91 * q^60 - 184 * q^61 - 124 * q^62 - 78 * q^63 + 101 * q^64 - 194 * q^65 - 112 * q^66 - 53 * q^67 - 182 * q^68 - 243 * q^69 - 193 * q^71 - 208 * q^72 - 69 * q^73 - 236 * q^74 - 62 * q^75 - 142 * q^76 - 324 * q^77 - 20 * q^78 - 91 * q^79 - 223 * q^80 - 27 * q^81 + 2 * q^82 - 117 * q^83 - 157 * q^84 - 171 * q^85 - 203 * q^86 - 69 * q^87 - 36 * q^88 - 172 * q^89 - 10 * q^90 - 84 * q^91 - 226 * q^92 - 220 * q^93 - 96 * q^94 - 166 * q^95 - 118 * q^96 - 12 * q^97 - 116 * q^98 - 154 * q^99

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