LMFDB - Embedded newform 8011.2.a.b.1.13

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			1.13
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)

$f(q)$	$=$	$q-2.61876 q^{2} -0.901244 q^{3} +4.85788 q^{4} -1.31265 q^{5} +2.36014 q^{6} -2.24388 q^{7} -7.48409 q^{8} -2.18776 q^{9} +O(q^{10})$	\(q-2.61876 q^{2} -0.901244 q^{3} +4.85788 q^{4} -1.31265 q^{5} +2.36014 q^{6} -2.24388 q^{7} -7.48409 q^{8} -2.18776 q^{9} +3.43751 q^{10} +5.25836 q^{11} -4.37814 q^{12} -1.46998 q^{13} +5.87617 q^{14} +1.18302 q^{15} +9.88325 q^{16} -0.0584840 q^{17} +5.72921 q^{18} +1.09397 q^{19} -6.37669 q^{20} +2.02228 q^{21} -13.7704 q^{22} -6.84838 q^{23} +6.74499 q^{24} -3.27695 q^{25} +3.84952 q^{26} +4.67544 q^{27} -10.9005 q^{28} -4.73669 q^{29} -3.09803 q^{30} +7.80265 q^{31} -10.9136 q^{32} -4.73907 q^{33} +0.153155 q^{34} +2.94542 q^{35} -10.6279 q^{36} -8.81218 q^{37} -2.86484 q^{38} +1.32481 q^{39} +9.82398 q^{40} -5.59712 q^{41} -5.29586 q^{42} -3.28836 q^{43} +25.5445 q^{44} +2.87176 q^{45} +17.9342 q^{46} +2.16311 q^{47} -8.90722 q^{48} -1.96501 q^{49} +8.58154 q^{50} +0.0527083 q^{51} -7.14100 q^{52} +7.06719 q^{53} -12.2438 q^{54} -6.90238 q^{55} +16.7934 q^{56} -0.985934 q^{57} +12.4042 q^{58} +2.06153 q^{59} +5.74695 q^{60} +4.33875 q^{61} -20.4332 q^{62} +4.90907 q^{63} +8.81363 q^{64} +1.92957 q^{65} +12.4105 q^{66} -0.888835 q^{67} -0.284108 q^{68} +6.17206 q^{69} -7.71334 q^{70} +2.46324 q^{71} +16.3734 q^{72} -3.08122 q^{73} +23.0769 q^{74} +2.95334 q^{75} +5.31438 q^{76} -11.7991 q^{77} -3.46936 q^{78} +0.809398 q^{79} -12.9732 q^{80} +2.34957 q^{81} +14.6575 q^{82} +0.294813 q^{83} +9.82401 q^{84} +0.0767689 q^{85} +8.61140 q^{86} +4.26892 q^{87} -39.3541 q^{88} +4.84930 q^{89} -7.52043 q^{90} +3.29846 q^{91} -33.2686 q^{92} -7.03209 q^{93} -5.66465 q^{94} -1.43600 q^{95} +9.83584 q^{96} -8.32931 q^{97} +5.14588 q^{98} -11.5040 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.61876	−1.85174	−0.925870	−	0.377842i	$-0.876666\pi$
$2$	−2.61876	−1.85174	−0.925870	+	0.377842i	$0.876666\pi$
$3$	−0.901244	−0.520333	−0.260167	−	0.965564i	$-0.583778\pi$
$3$	−0.901244	−0.520333	−0.260167	+	0.965564i	$0.583778\pi$
$4$	4.85788	2.42894
$5$	−1.31265	−0.587034	−0.293517	−	0.955954i	$-0.594826\pi$
$5$	−1.31265	−0.587034	−0.293517	+	0.955954i	$0.594826\pi$
$6$	2.36014	0.963522
$7$	−2.24388	−0.848106	−0.424053	−	0.905637i	$-0.639393\pi$
$7$	−2.24388	−0.848106	−0.424053	+	0.905637i	$0.639393\pi$
$8$	−7.48409	−2.64603
$9$	−2.18776	−0.729253
$10$	3.43751	1.08703
$11$	5.25836	1.58546	0.792728	−	0.609576i	$-0.208660\pi$
$11$	5.25836	1.58546	0.792728	+	0.609576i	$0.208660\pi$
$12$	−4.37814	−1.26386
$13$	−1.46998	−0.407700	−0.203850	−	0.979002i	$-0.565345\pi$
$13$	−1.46998	−0.407700	−0.203850	+	0.979002i	$0.565345\pi$
$14$	5.87617	1.57047
$15$	1.18302	0.305454
$16$	9.88325	2.47081
$17$	−0.0584840	−0.0141844	−0.00709222	−	0.999975i	$-0.502258\pi$
$17$	−0.0584840	−0.0141844	−0.00709222	+	0.999975i	$0.502258\pi$
$18$	5.72921	1.35039
$19$	1.09397	0.250974	0.125487	−	0.992095i	$-0.459951\pi$
$19$	1.09397	0.250974	0.125487	+	0.992095i	$0.459951\pi$
$20$	−6.37669	−1.42587
$21$	2.02228	0.441298
$22$	−13.7704	−2.93585
$23$	−6.84838	−1.42799	−0.713993	−	0.700152i	$-0.753115\pi$
$23$	−6.84838	−1.42799	−0.713993	+	0.700152i	$0.753115\pi$
$24$	6.74499	1.37682
$25$	−3.27695	−0.655391
$26$	3.84952	0.754954
$27$	4.67544	0.899788
$28$	−10.9005	−2.06000
$29$	−4.73669	−0.879582	−0.439791	−	0.898100i	$-0.644947\pi$
$29$	−4.73669	−0.879582	−0.439791	+	0.898100i	$0.644947\pi$
$30$	−3.09803	−0.565620
$31$	7.80265	1.40140	0.700699	−	0.713457i	$-0.252872\pi$
$31$	7.80265	1.40140	0.700699	+	0.713457i	$0.252872\pi$
$32$	−10.9136	−1.92928
$33$	−4.73907	−0.824966
$34$	0.153155	0.0262659
$35$	2.94542	0.497867
$36$	−10.6279	−1.77131
$37$	−8.81218	−1.44871	−0.724356	−	0.689426i	$-0.757863\pi$
$37$	−8.81218	−1.44871	−0.724356	+	0.689426i	$0.757863\pi$
$38$	−2.86484	−0.464739
$39$	1.32481	0.212140
$40$	9.82398	1.55331
$41$	−5.59712	−0.874123	−0.437062	−	0.899432i	$-0.643981\pi$
$41$	−5.59712	−0.874123	−0.437062	+	0.899432i	$0.643981\pi$
$42$	−5.29586	−0.817169
$43$	−3.28836	−0.501470	−0.250735	−	0.968056i	$-0.580672\pi$
$43$	−3.28836	−0.501470	−0.250735	+	0.968056i	$0.580672\pi$
$44$	25.5445	3.85098
$45$	2.87176	0.428096
$46$	17.9342	2.64426
$47$	2.16311	0.315521	0.157761	−	0.987477i	$-0.449573\pi$
$47$	2.16311	0.315521	0.157761	+	0.987477i	$0.449573\pi$
$48$	−8.90722	−1.28565
$49$	−1.96501	−0.280715
$50$	8.58154	1.21361
$51$	0.0527083	0.00738064
$52$	−7.14100	−0.990278
$53$	7.06719	0.970753	0.485377	−	0.874305i	$-0.338682\pi$
$53$	7.06719	0.970753	0.485377	+	0.874305i	$0.338682\pi$
$54$	−12.2438	−1.66617
$55$	−6.90238	−0.930717
$56$	16.7934	2.24411
$57$	−0.985934	−0.130590
$58$	12.4042	1.62876
$59$	2.06153	0.268389	0.134194	−	0.990955i	$-0.457155\pi$
$59$	2.06153	0.268389	0.134194	+	0.990955i	$0.457155\pi$
$60$	5.74695	0.741928
$61$	4.33875	0.555521	0.277760	−	0.960650i	$-0.410408\pi$
$61$	4.33875	0.555521	0.277760	+	0.960650i	$0.410408\pi$
$62$	−20.4332	−2.59502
$63$	4.90907	0.618484
$64$	8.81363	1.10170
$65$	1.92957	0.239334
$66$	12.4105	1.52762
$67$	−0.888835	−0.108589	−0.0542943	−	0.998525i	$-0.517291\pi$
$67$	−0.888835	−0.108589	−0.0542943	+	0.998525i	$0.517291\pi$
$68$	−0.284108	−0.0344532
$69$	6.17206	0.743029
$70$	−7.71334	−0.921921
$71$	2.46324	0.292332	0.146166	−	0.989260i	$-0.453307\pi$
$71$	2.46324	0.292332	0.146166	+	0.989260i	$0.453307\pi$
$72$	16.3734	1.92962
$73$	−3.08122	−0.360629	−0.180315	−	0.983609i	$-0.557712\pi$
$73$	−3.08122	−0.360629	−0.180315	+	0.983609i	$0.557712\pi$
$74$	23.0769	2.68264
$75$	2.95334	0.341022
$76$	5.31438	0.609601
$77$	−11.7991	−1.34464
$78$	−3.46936	−0.392828
$79$	0.809398	0.0910644	0.0455322	−	0.998963i	$-0.485502\pi$
$79$	0.809398	0.0910644	0.0455322	+	0.998963i	$0.485502\pi$
$80$	−12.9732	−1.45045
$81$	2.34957	0.261063
$82$	14.6575	1.61865
$83$	0.294813	0.0323599	0.0161800	−	0.999869i	$-0.494850\pi$
$83$	0.294813	0.0323599	0.0161800	+	0.999869i	$0.494850\pi$
$84$	9.82401	1.07189
$85$	0.0767689	0.00832675
$86$	8.61140	0.928592
$87$	4.26892	0.457676
$88$	−39.3541	−4.19516
$89$	4.84930	0.514025	0.257013	−	0.966408i	$-0.417262\pi$
$89$	4.84930	0.514025	0.257013	+	0.966408i	$0.417262\pi$
$90$	−7.52043	−0.792723
$91$	3.29846	0.345773
$92$	−33.2686	−3.46850
$93$	−7.03209	−0.729194
$94$	−5.66465	−0.584264
$95$	−1.43600	−0.147330
$96$	9.83584	1.00387
$97$	−8.32931	−0.845714	−0.422857	−	0.906197i	$-0.638973\pi$
$97$	−8.32931	−0.845714	−0.422857	+	0.906197i	$0.638973\pi$
$98$	5.14588	0.519812
$99$	−11.5040	−1.15620
$100$	−15.9191	−1.59191
$101$	−2.58697	−0.257413	−0.128706	−	0.991683i	$-0.541082\pi$
$101$	−2.58697	−0.257413	−0.128706	+	0.991683i	$0.541082\pi$
$102$	−0.138030	−0.0136670
$103$	−0.273875	−0.0269857	−0.0134929	−	0.999909i	$-0.504295\pi$
$103$	−0.273875	−0.0269857	−0.0134929	+	0.999909i	$0.504295\pi$
$104$	11.0015	1.07878
$105$	−2.65455	−0.259057
$106$	−18.5072	−1.79758
$107$	1.33036	0.128611	0.0643056	−	0.997930i	$-0.479517\pi$
$107$	1.33036	0.128611	0.0643056	+	0.997930i	$0.479517\pi$
$108$	22.7127	2.18553
$109$	−15.4832	−1.48302	−0.741512	−	0.670940i	$-0.765891\pi$
$109$	−15.4832	−1.48302	−0.741512	+	0.670940i	$0.765891\pi$
$110$	18.0756	1.72345
$111$	7.94192	0.753814
$112$	−22.1768	−2.09551
$113$	−14.9630	−1.40760	−0.703802	−	0.710396i	$-0.748516\pi$
$113$	−14.9630	−1.40760	−0.703802	+	0.710396i	$0.748516\pi$
$114$	2.58192	0.241819
$115$	8.98952	0.838277
$116$	−23.0103	−2.13645
$117$	3.21597	0.297316
$118$	−5.39865	−0.496986
$119$	0.131231	0.0120299
$120$	−8.85380	−0.808238
$121$	16.6504	1.51367
$122$	−11.3621	−1.02868
$123$	5.04437	0.454836
$124$	37.9044	3.40391
$125$	10.8647	0.971771
$126$	−12.8556	−1.14527
$127$	−0.830429	−0.0736887	−0.0368443	−	0.999321i	$-0.511731\pi$
$127$	−0.830429	−0.0736887	−0.0368443	+	0.999321i	$0.511731\pi$
$128$	−1.25348	−0.110793
$129$	2.96361	0.260932
$130$	−5.05307	−0.443184
$131$	9.17248	0.801404	0.400702	−	0.916209i	$-0.368766\pi$
$131$	9.17248	0.801404	0.400702	+	0.916209i	$0.368766\pi$
$132$	−23.0218	−2.00379
$133$	−2.45474	−0.212853
$134$	2.32764	0.201078
$135$	−6.13720	−0.528206
$136$	0.437699	0.0375324
$137$	−12.5284	−1.07037	−0.535186	−	0.844734i	$-0.679758\pi$
$137$	−12.5284	−1.07037	−0.535186	+	0.844734i	$0.679758\pi$
$138$	−16.1631	−1.37590
$139$	−17.6971	−1.50105	−0.750524	−	0.660843i	$-0.770199\pi$
$139$	−17.6971	−1.50105	−0.750524	+	0.660843i	$0.770199\pi$
$140$	14.3085	1.20929
$141$	−1.94949	−0.164176
$142$	−6.45061	−0.541323
$143$	−7.72970	−0.646390
$144$	−21.6222	−1.80185
$145$	6.21761	0.516345
$146$	8.06895	0.667791
$147$	1.77095	0.146066
$148$	−42.8085	−3.51884
$149$	−16.0671	−1.31627	−0.658133	−	0.752902i	$-0.728653\pi$
$149$	−16.0671	−1.31627	−0.658133	+	0.752902i	$0.728653\pi$
$150$	−7.73406	−0.631484
$151$	8.18383	0.665991	0.332995	−	0.942928i	$-0.391941\pi$
$151$	8.18383	0.665991	0.332995	+	0.942928i	$0.391941\pi$
$152$	−8.18738	−0.664084
$153$	0.127949	0.0103440
$154$	30.8990	2.48991
$155$	−10.2421	−0.822668
$156$	6.43578	0.515275
$157$	1.48627	0.118617	0.0593085	−	0.998240i	$-0.481110\pi$
$157$	1.48627	0.118617	0.0593085	+	0.998240i	$0.481110\pi$
$158$	−2.11962	−0.168628
$159$	−6.36926	−0.505115
$160$	14.3258	1.13255
$161$	15.3669	1.21108
$162$	−6.15295	−0.483421
$163$	−7.00634	−0.548779	−0.274390	−	0.961619i	$-0.588476\pi$
$163$	−7.00634	−0.548779	−0.274390	+	0.961619i	$0.588476\pi$
$164$	−27.1901	−2.12319
$165$	6.22073	0.484283
$166$	−0.772043	−0.0599221
$167$	−5.34483	−0.413595	−0.206798	−	0.978384i	$-0.566304\pi$
$167$	−5.34483	−0.413595	−0.206798	+	0.978384i	$0.566304\pi$
$168$	−15.1349	−1.16769
$169$	−10.8392	−0.833781
$170$	−0.201039	−0.0154190
$171$	−2.39334	−0.183024
$172$	−15.9744	−1.21804
$173$	12.3255	0.937087	0.468543	−	0.883440i	$-0.344779\pi$
$173$	12.3255	0.937087	0.468543	+	0.883440i	$0.344779\pi$
$174$	−11.1793	−0.847497
$175$	7.35309	0.555841
$176$	51.9697	3.91736
$177$	−1.85794	−0.139652
$178$	−12.6991	−0.951841
$179$	18.8803	1.41118	0.705589	−	0.708621i	$-0.250683\pi$
$179$	18.8803	1.41118	0.705589	+	0.708621i	$0.250683\pi$
$180$	13.9507	1.03982
$181$	−8.94589	−0.664943	−0.332472	−	0.943113i	$-0.607883\pi$
$181$	−8.94589	−0.664943	−0.332472	+	0.943113i	$0.607883\pi$
$182$	−8.63787	−0.640281
$183$	−3.91028	−0.289056
$184$	51.2539	3.77849
$185$	11.5673	0.850444
$186$	18.4153	1.35028
$187$	−0.307530	−0.0224888
$188$	10.5081	0.766383
$189$	−10.4911	−0.763116
$190$	3.76053	0.272817
$191$	−2.48542	−0.179839	−0.0899195	−	0.995949i	$-0.528661\pi$
$191$	−2.48542	−0.179839	−0.0899195	+	0.995949i	$0.528661\pi$
$192$	−7.94323	−0.573253
$193$	−5.86390	−0.422093	−0.211046	−	0.977476i	$-0.567687\pi$
$193$	−5.86390	−0.422093	−0.211046	+	0.977476i	$0.567687\pi$
$194$	21.8124	1.56604
$195$	−1.73901	−0.124533
$196$	−9.54578	−0.681841
$197$	−10.2518	−0.730409	−0.365204	−	0.930927i	$-0.619001\pi$
$197$	−10.2518	−0.730409	−0.365204	+	0.930927i	$0.619001\pi$
$198$	30.1262	2.14098
$199$	−22.2605	−1.57800	−0.789001	−	0.614392i	$-0.789401\pi$
$199$	−22.2605	−1.57800	−0.789001	+	0.614392i	$0.789401\pi$
$200$	24.5250	1.73418
$201$	0.801058	0.0565022
$202$	6.77463	0.476661
$203$	10.6286	0.745979
$204$	0.256051	0.0179271
$205$	7.34705	0.513140
$206$	0.717212	0.0499706
$207$	14.9826	1.04136
$208$	−14.5282	−1.00735
$209$	5.75249	0.397908
$210$	6.95161	0.479706
$211$	0.289562	0.0199343	0.00996714	−	0.999950i	$-0.496827\pi$
$211$	0.289562	0.0199343	0.00996714	+	0.999950i	$0.496827\pi$
$212$	34.3316	2.35790
$213$	−2.21998	−0.152110
$214$	−3.48390	−0.238154
$215$	4.31646	0.294380
$216$	−34.9914	−2.38086
$217$	−17.5082	−1.18853
$218$	40.5468	2.74617
$219$	2.77693	0.187647
$220$	−33.5309	−2.26066
$221$	0.0859704	0.00578299
$222$	−20.7979	−1.39587
$223$	22.8791	1.53210	0.766049	−	0.642783i	$-0.222220\pi$
$223$	22.8791	1.53210	0.766049	+	0.642783i	$0.222220\pi$
$224$	24.4889	1.63623
$225$	7.16919	0.477946
$226$	39.1846	2.60652
$227$	25.1983	1.67247	0.836234	−	0.548373i	$-0.184753\pi$
$227$	25.1983	1.67247	0.836234	+	0.548373i	$0.184753\pi$
$228$	−4.78955	−0.317196
$229$	7.13969	0.471804	0.235902	−	0.971777i	$-0.424196\pi$
$229$	7.13969	0.471804	0.235902	+	0.971777i	$0.424196\pi$
$230$	−23.5414	−1.55227
$231$	10.6339	0.699659
$232$	35.4499	2.32740
$233$	−15.3423	−1.00510	−0.502552	−	0.864547i	$-0.667606\pi$
$233$	−15.3423	−1.00510	−0.502552	+	0.864547i	$0.667606\pi$
$234$	−8.42183	−0.550552
$235$	−2.83940	−0.185222
$236$	10.0147	0.651901
$237$	−0.729465	−0.0473838
$238$	−0.343662	−0.0222763
$239$	26.6429	1.72339	0.861693	−	0.507430i	$-0.169404\pi$
$239$	26.6429	1.72339	0.861693	+	0.507430i	$0.169404\pi$
$240$	11.6920	0.754718
$241$	−3.32320	−0.214066	−0.107033	−	0.994255i	$-0.534135\pi$
$241$	−3.32320	−0.214066	−0.107033	+	0.994255i	$0.534135\pi$
$242$	−43.6032	−2.80292
$243$	−16.1438	−1.03563
$244$	21.0772	1.34933
$245$	2.57936	0.164790
$246$	−13.2100	−0.842237
$247$	−1.60812	−0.102322
$248$	−58.3958	−3.70814
$249$	−0.265698	−0.0168379
$250$	−28.4521	−1.79947
$251$	0.495028	0.0312459	0.0156229	−	0.999878i	$-0.495027\pi$
$251$	0.495028	0.0312459	0.0156229	+	0.999878i	$0.495027\pi$
$252$	23.8477	1.50226
$253$	−36.0113	−2.26401
$254$	2.17469	0.136452
$255$	−0.0691875	−0.00433269
$256$	−14.3447	−0.896543
$257$	−0.936392	−0.0584105	−0.0292053	−	0.999573i	$-0.509298\pi$
$257$	−0.936392	−0.0584105	−0.0292053	+	0.999573i	$0.509298\pi$
$258$	−7.76098	−0.483177
$259$	19.7735	1.22866
$260$	9.37362	0.581327
$261$	10.3627	0.641438
$262$	−24.0205	−1.48399
$263$	−7.05732	−0.435173	−0.217586	−	0.976041i	$-0.569818\pi$
$263$	−7.05732	−0.435173	−0.217586	+	0.976041i	$0.569818\pi$
$264$	35.4676	2.18288
$265$	−9.27674	−0.569865
$266$	6.42836	0.394148
$267$	−4.37041	−0.267465
$268$	−4.31786	−0.263755
$269$	−22.9255	−1.39780	−0.698898	−	0.715222i	$-0.746326\pi$
$269$	−22.9255	−1.39780	−0.698898	+	0.715222i	$0.746326\pi$
$270$	16.0718	0.978101
$271$	20.1635	1.22484	0.612422	−	0.790531i	$-0.290195\pi$
$271$	20.1635	1.22484	0.612422	+	0.790531i	$0.290195\pi$
$272$	−0.578011	−0.0350471
$273$	−2.97272	−0.179917
$274$	32.8088	1.98205
$275$	−17.2314	−1.03909
$276$	29.9832	1.80477
$277$	−6.68451	−0.401634	−0.200817	−	0.979629i	$-0.564360\pi$
$277$	−6.68451	−0.401634	−0.200817	+	0.979629i	$0.564360\pi$
$278$	46.3444	2.77955
$279$	−17.0703	−1.02197
$280$	−22.0438	−1.31737
$281$	4.30473	0.256798	0.128399	−	0.991723i	$-0.459016\pi$
$281$	4.30473	0.256798	0.128399	+	0.991723i	$0.459016\pi$
$282$	5.10523	0.304012
$283$	−13.8808	−0.825126	−0.412563	−	0.910929i	$-0.635366\pi$
$283$	−13.8808	−0.825126	−0.412563	+	0.910929i	$0.635366\pi$
$284$	11.9661	0.710058
$285$	1.29419	0.0766609
$286$	20.2422	1.19695
$287$	12.5593	0.741350
$288$	23.8764	1.40693
$289$	−16.9966	−0.999799
$290$	−16.2824	−0.956136
$291$	7.50674	0.440053
$292$	−14.9682	−0.875947
$293$	18.1249	1.05887	0.529434	−	0.848351i	$-0.322404\pi$
$293$	18.1249	1.05887	0.529434	+	0.848351i	$0.322404\pi$
$294$	−4.63769	−0.270476
$295$	−2.70607	−0.157553
$296$	65.9511	3.83333
$297$	24.5851	1.42657
$298$	42.0757	2.43738
$299$	10.0670	0.582190
$300$	14.3470	0.828322
$301$	7.37867	0.425300
$302$	−21.4315	−1.23324
$303$	2.33149	0.133940
$304$	10.8120	0.620110
$305$	−5.69526	−0.326110
$306$	−0.335067	−0.0191545
$307$	−13.9760	−0.797654	−0.398827	−	0.917026i	$-0.630583\pi$
$307$	−13.9760	−0.797654	−0.398827	+	0.917026i	$0.630583\pi$
$308$	−57.3188	−3.26604
$309$	0.246828	0.0140416
$310$	26.8217	1.52337
$311$	1.31078	0.0743274	0.0371637	−	0.999309i	$-0.488168\pi$
$311$	1.31078	0.0743274	0.0371637	+	0.999309i	$0.488168\pi$
$312$	−9.91502	−0.561328
$313$	−20.4467	−1.15572	−0.577858	−	0.816137i	$-0.696111\pi$
$313$	−20.4467	−1.15572	−0.577858	+	0.816137i	$0.696111\pi$
$314$	−3.89217	−0.219648
$315$	−6.44388	−0.363071
$316$	3.93196	0.221190
$317$	−24.4394	−1.37266	−0.686328	−	0.727292i	$-0.740778\pi$
$317$	−24.4394	−1.37266	−0.686328	+	0.727292i	$0.740778\pi$
$318$	16.6795	0.935342
$319$	−24.9072	−1.39454
$320$	−11.5692	−0.646738
$321$	−1.19898	−0.0669207
$322$	−40.2423	−2.24261
$323$	−0.0639797	−0.00355993
$324$	11.4139	0.634107
$325$	4.81706	0.267203
$326$	18.3479	1.01620
$327$	13.9542	0.771667
$328$	41.8894	2.31295
$329$	−4.85375	−0.267596
$330$	−16.2906	−0.896766
$331$	−2.15567	−0.118486	−0.0592431	−	0.998244i	$-0.518869\pi$
$331$	−2.15567	−0.118486	−0.0592431	+	0.998244i	$0.518869\pi$
$332$	1.43217	0.0786003
$333$	19.2789	1.05648
$334$	13.9968	0.765871
$335$	1.16673	0.0637452
$336$	19.9867	1.09036
$337$	−5.23249	−0.285032	−0.142516	−	0.989792i	$-0.545519\pi$
$337$	−5.23249	−0.285032	−0.142516	+	0.989792i	$0.545519\pi$
$338$	28.3851	1.54395
$339$	13.4854	0.732424
$340$	0.372934	0.0202252
$341$	41.0292	2.22185
$342$	6.26758	0.338912
$343$	20.1164	1.08618
$344$	24.6104	1.32690
$345$	−8.10175	−0.436184
$346$	−32.2773	−1.73524
$347$	−1.45563	−0.0781424	−0.0390712	−	0.999236i	$-0.512440\pi$
$347$	−1.45563	−0.0781424	−0.0390712	+	0.999236i	$0.512440\pi$
$348$	20.7379	1.11167
$349$	−0.812222	−0.0434773	−0.0217386	−	0.999764i	$-0.506920\pi$
$349$	−0.812222	−0.0434773	−0.0217386	+	0.999764i	$0.506920\pi$
$350$	−19.2559	−1.02927
$351$	−6.87281	−0.366843
$352$	−57.3878	−3.05878
$353$	10.6193	0.565209	0.282605	−	0.959236i	$-0.408802\pi$
$353$	10.6193	0.565209	0.282605	+	0.959236i	$0.408802\pi$
$354$	4.86550	0.258599
$355$	−3.23336	−0.171609
$356$	23.5573	1.24854
$357$	−0.118271	−0.00625957
$358$	−49.4428	−2.61313
$359$	22.5915	1.19233	0.596166	−	0.802861i	$-0.296690\pi$
$359$	22.5915	1.19233	0.596166	+	0.802861i	$0.296690\pi$
$360$	−21.4925	−1.13275
$361$	−17.8032	−0.937012
$362$	23.4271	1.23130
$363$	−15.0060	−0.787613
$364$	16.0235	0.839861
$365$	4.04455	0.211702
$366$	10.2401	0.535256
$367$	18.7786	0.980237	0.490118	−	0.871656i	$-0.336954\pi$
$367$	18.7786	0.980237	0.490118	+	0.871656i	$0.336954\pi$
$368$	−67.6843	−3.52829
$369$	12.2452	0.637457
$370$	−30.2919	−1.57480
$371$	−15.8579	−0.823302
$372$	−34.1611	−1.77117
$373$	−19.7564	−1.02295	−0.511473	−	0.859300i	$-0.670900\pi$
$373$	−19.7564	−1.02295	−0.511473	+	0.859300i	$0.670900\pi$
$374$	0.805345	0.0416434
$375$	−9.79177	−0.505645
$376$	−16.1889	−0.834878
$377$	6.96286	0.358605
$378$	27.4737	1.41309
$379$	−6.31261	−0.324257	−0.162128	−	0.986770i	$-0.551836\pi$
$379$	−6.31261	−0.324257	−0.162128	+	0.986770i	$0.551836\pi$
$380$	−6.97591	−0.357857
$381$	0.748419	0.0383427
$382$	6.50872	0.333015
$383$	12.9466	0.661538	0.330769	−	0.943712i	$-0.392692\pi$
$383$	12.9466	0.661538	0.330769	+	0.943712i	$0.392692\pi$
$384$	1.12970	0.0576495
$385$	15.4881	0.789347
$386$	15.3561	0.781606
$387$	7.19413	0.365698
$388$	−40.4628	−2.05419
$389$	−7.44001	−0.377224	−0.188612	−	0.982052i	$-0.560399\pi$
$389$	−7.44001	−0.377224	−0.188612	+	0.982052i	$0.560399\pi$
$390$	4.55405	0.230603
$391$	0.400521	0.0202552
$392$	14.7063	0.742781
$393$	−8.26664	−0.416997
$394$	26.8469	1.35253
$395$	−1.06245	−0.0534579
$396$	−55.8852	−2.80834
$397$	−23.5160	−1.18023	−0.590117	−	0.807318i	$-0.700918\pi$
$397$	−23.5160	−1.18023	−0.590117	+	0.807318i	$0.700918\pi$
$398$	58.2947	2.92205
$399$	2.21232	0.110754
$400$	−32.3870	−1.61935
$401$	−14.4370	−0.720950	−0.360475	−	0.932769i	$-0.617385\pi$
$401$	−14.4370	−0.720950	−0.360475	+	0.932769i	$0.617385\pi$
$402$	−2.09777	−0.104627
$403$	−11.4698	−0.571349
$404$	−12.5672	−0.625240
$405$	−3.08416	−0.153253
$406$	−27.8336	−1.38136
$407$	−46.3376	−2.29687
$408$	−0.394474	−0.0195294
$409$	−5.62839	−0.278306	−0.139153	−	0.990271i	$-0.544438\pi$
$409$	−5.62839	−0.278306	−0.139153	+	0.990271i	$0.544438\pi$
$410$	−19.2401	−0.950202
$411$	11.2911	0.556950
$412$	−1.33045	−0.0655467
$413$	−4.62583	−0.227622
$414$	−39.2358	−1.92833
$415$	−0.386985	−0.0189964
$416$	16.0428	0.786565
$417$	15.9494	0.781046
$418$	−15.0644	−0.736823
$419$	−21.2788	−1.03954	−0.519769	−	0.854307i	$-0.673982\pi$
$419$	−21.2788	−1.03954	−0.519769	+	0.854307i	$0.673982\pi$
$420$	−12.8955	−0.629234
$421$	−0.291480	−0.0142059	−0.00710294	−	0.999975i	$-0.502261\pi$
$421$	−0.291480	−0.0142059	−0.00710294	+	0.999975i	$0.502261\pi$
$422$	−0.758292	−0.0369131
$423$	−4.73236	−0.230095
$424$	−52.8915	−2.56864
$425$	0.191649	0.00929635
$426$	5.81357	0.281669
$427$	−9.73564	−0.471141
$428$	6.46275	0.312389
$429$	6.96634	0.336338
$430$	−11.3037	−0.545115
$431$	10.8396	0.522123	0.261062	−	0.965322i	$-0.415927\pi$
$431$	10.8396	0.522123	0.261062	+	0.965322i	$0.415927\pi$
$432$	46.2085	2.22321
$433$	19.2482	0.925010	0.462505	−	0.886617i	$-0.346951\pi$
$433$	19.2482	0.925010	0.462505	+	0.886617i	$0.346951\pi$
$434$	45.8497	2.20086
$435$	−5.60359	−0.268671
$436$	−75.2157	−3.60218
$437$	−7.49193	−0.358388
$438$	−7.27210	−0.347474
$439$	24.1607	1.15313	0.576563	−	0.817053i	$-0.304394\pi$
$439$	24.1607	1.15313	0.576563	+	0.817053i	$0.304394\pi$
$440$	51.6581	2.46270
$441$	4.29896	0.204713
$442$	−0.225135	−0.0107086
$443$	2.85937	0.135853	0.0679264	−	0.997690i	$-0.478362\pi$
$443$	2.85937	0.135853	0.0679264	+	0.997690i	$0.478362\pi$
$444$	38.5809	1.83097
$445$	−6.36543	−0.301750
$446$	−59.9147	−2.83705
$447$	14.4803	0.684897
$448$	−19.7767	−0.934362
$449$	−13.4059	−0.632662	−0.316331	−	0.948649i	$-0.602451\pi$
$449$	−13.4059	−0.632662	−0.316331	+	0.948649i	$0.602451\pi$
$450$	−18.7744	−0.885031
$451$	−29.4317	−1.38588
$452$	−72.6887	−3.41899
$453$	−7.37563	−0.346537
$454$	−65.9881	−3.09698
$455$	−4.32972	−0.202980
$456$	7.37882	0.345545
$457$	18.8094	0.879865	0.439933	−	0.898031i	$-0.355002\pi$
$457$	18.8094	0.879865	0.439933	+	0.898031i	$0.355002\pi$
$458$	−18.6971	−0.873659
$459$	−0.273438	−0.0127630
$460$	43.6700	2.03613
$461$	11.1609	0.519817	0.259908	−	0.965633i	$-0.416308\pi$
$461$	11.1609	0.519817	0.259908	+	0.965633i	$0.416308\pi$
$462$	−27.8476	−1.29559
$463$	−11.9519	−0.555454	−0.277727	−	0.960660i	$-0.589581\pi$
$463$	−11.9519	−0.555454	−0.277727	+	0.960660i	$0.589581\pi$
$464$	−46.8139	−2.17328
$465$	9.23067	0.428062
$466$	40.1776	1.86119
$467$	23.8755	1.10483	0.552414	−	0.833570i	$-0.313707\pi$
$467$	23.8755	1.10483	0.552414	+	0.833570i	$0.313707\pi$
$468$	15.6228	0.722164
$469$	1.99444	0.0920946
$470$	7.43569	0.342983
$471$	−1.33949	−0.0617204
$472$	−15.4287	−0.710164
$473$	−17.2914	−0.795058
$474$	1.91029	0.0877426
$475$	−3.58489	−0.164486
$476$	0.637504	0.0292200
$477$	−15.4613	−0.707925
$478$	−69.7712	−3.19126
$479$	−10.3133	−0.471228	−0.235614	−	0.971847i	$-0.575710\pi$
$479$	−10.3133	−0.471228	−0.235614	+	0.971847i	$0.575710\pi$
$480$	−12.9110	−0.589304
$481$	12.9537	0.590640
$482$	8.70264	0.396394
$483$	−13.8494	−0.630168
$484$	80.8855	3.67661
$485$	10.9335	0.496463
$486$	42.2768	1.91771
$487$	−22.7203	−1.02955	−0.514777	−	0.857324i	$-0.672125\pi$
$487$	−22.7203	−1.02955	−0.514777	+	0.857324i	$0.672125\pi$
$488$	−32.4716	−1.46992
$489$	6.31443	0.285548
$490$	−6.75473	−0.305147
$491$	−3.37996	−0.152536	−0.0762678	−	0.997087i	$-0.524300\pi$
$491$	−3.37996	−0.152536	−0.0762678	+	0.997087i	$0.524300\pi$
$492$	24.5050	1.10477
$493$	0.277021	0.0124764
$494$	4.21127	0.189474
$495$	15.1007	0.678728
$496$	77.1156	3.46259
$497$	−5.52720	−0.247929
$498$	0.695799	0.0311795
$499$	2.66008	0.119082	0.0595408	−	0.998226i	$-0.481036\pi$
$499$	2.66008	0.119082	0.0595408	+	0.998226i	$0.481036\pi$
$500$	52.7796	2.36037
$501$	4.81699	0.215207
$502$	−1.29636	−0.0578593
$503$	−19.1406	−0.853438	−0.426719	−	0.904384i	$-0.640331\pi$
$503$	−19.1406	−0.853438	−0.426719	+	0.904384i	$0.640331\pi$
$504$	−36.7399	−1.63653
$505$	3.39578	0.151110
$506$	94.3047	4.19236
$507$	9.76872	0.433844
$508$	−4.03413	−0.178985
$509$	22.0754	0.978474	0.489237	−	0.872151i	$-0.337275\pi$
$509$	22.0754	0.978474	0.489237	+	0.872151i	$0.337275\pi$
$510$	0.181185	0.00802301
$511$	6.91388	0.305852
$512$	40.0722	1.77096
$513$	5.11479	0.225823
$514$	2.45218	0.108161
$515$	0.359502	0.0158415
$516$	14.3969	0.633787
$517$	11.3744	0.500245
$518$	−51.7818	−2.27516
$519$	−11.1082	−0.487598
$520$	−14.4411	−0.633283
$521$	−27.1076	−1.18761	−0.593803	−	0.804611i	$-0.702374\pi$
$521$	−27.1076	−1.18761	−0.593803	+	0.804611i	$0.702374\pi$
$522$	−27.1375	−1.18778
$523$	−21.3228	−0.932382	−0.466191	−	0.884684i	$-0.654374\pi$
$523$	−21.3228	−0.932382	−0.466191	+	0.884684i	$0.654374\pi$
$524$	44.5588	1.94656
$525$	−6.62693	−0.289223
$526$	18.4814	0.805827
$527$	−0.456330	−0.0198780
$528$	−46.8374	−2.03834
$529$	23.9004	1.03915
$530$	24.2935	1.05524
$531$	−4.51014	−0.195723
$532$	−11.9248	−0.517007
$533$	8.22767	0.356380
$534$	11.4450	0.495275
$535$	−1.74630	−0.0754991
$536$	6.65213	0.287328
$537$	−17.0157	−0.734283
$538$	60.0364	2.58835
$539$	−10.3327	−0.445062
$540$	−29.8138	−1.28298
$541$	−11.3051	−0.486044	−0.243022	−	0.970021i	$-0.578139\pi$
$541$	−11.3051	−0.486044	−0.243022	+	0.970021i	$0.578139\pi$
$542$	−52.8032	−2.26809
$543$	8.06243	0.345992
$544$	0.638272	0.0273657
$545$	20.3240	0.870586
$546$	7.78482	0.333160
$547$	34.3608	1.46916	0.734580	−	0.678522i	$-0.237379\pi$
$547$	34.3608	1.46916	0.734580	+	0.678522i	$0.237379\pi$
$548$	−60.8614	−2.59987
$549$	−9.49215	−0.405115
$550$	45.1249	1.92413
$551$	−5.18180	−0.220752
$552$	−46.1923	−1.96608
$553$	−1.81619	−0.0772323
$554$	17.5051	0.743721
$555$	−10.4249	−0.442514
$556$	−85.9704	−3.64596
$557$	−32.7272	−1.38670	−0.693349	−	0.720602i	$-0.743865\pi$
$557$	−32.7272	−1.38670	−0.693349	+	0.720602i	$0.743865\pi$
$558$	44.7030	1.89243
$559$	4.83383	0.204449
$560$	29.1104	1.23014
$561$	0.277159	0.0117017
$562$	−11.2730	−0.475524
$563$	−12.0272	−0.506887	−0.253444	−	0.967350i	$-0.581563\pi$
$563$	−12.0272	−0.506887	−0.253444	+	0.967350i	$0.581563\pi$
$564$	−9.47037	−0.398775
$565$	19.6412	0.826312
$566$	36.3503	1.52792
$567$	−5.27215	−0.221409
$568$	−18.4351	−0.773519
$569$	−24.0773	−1.00937	−0.504686	−	0.863303i	$-0.668392\pi$
$569$	−24.0773	−1.00937	−0.504686	+	0.863303i	$0.668392\pi$
$570$	−3.38915	−0.141956
$571$	17.2168	0.720500	0.360250	−	0.932856i	$-0.382691\pi$
$571$	17.2168	0.720500	0.360250	+	0.932856i	$0.382691\pi$
$572$	−37.5500	−1.57004
$573$	2.23997	0.0935762
$574$	−32.8896	−1.37279
$575$	22.4418	0.935890
$576$	−19.2821	−0.803421
$577$	17.9542	0.747444	0.373722	−	0.927541i	$-0.378081\pi$
$577$	17.9542	0.747444	0.373722	+	0.927541i	$0.378081\pi$
$578$	44.5099	1.85137
$579$	5.28481	0.219629
$580$	30.2044	1.25417
$581$	−0.661524	−0.0274446
$582$	−19.6583	−0.814864
$583$	37.1618	1.53909
$584$	23.0601	0.954234
$585$	−4.22143	−0.174535
$586$	−47.4647	−1.96075
$587$	17.0435	0.703460	0.351730	−	0.936102i	$-0.385594\pi$
$587$	17.0435	0.703460	0.351730	+	0.936102i	$0.385594\pi$
$588$	8.60307	0.354785
$589$	8.53587	0.351714
$590$	7.08653	0.291748
$591$	9.23935	0.380056
$592$	−87.0929	−3.57950
$593$	39.0129	1.60207	0.801034	−	0.598619i	$-0.204283\pi$
$593$	39.0129	1.60207	0.801034	+	0.598619i	$0.204283\pi$
$594$	−64.3825	−2.64164
$595$	−0.172260	−0.00706197
$596$	−78.0519	−3.19713
$597$	20.0621	0.821087
$598$	−26.3630	−1.07806
$599$	34.2148	1.39798	0.698990	−	0.715132i	$-0.253633\pi$
$599$	34.2148	1.39798	0.698990	+	0.715132i	$0.253633\pi$
$600$	−22.1030	−0.902353
$601$	8.26767	0.337245	0.168623	−	0.985681i	$-0.446068\pi$
$601$	8.26767	0.337245	0.168623	+	0.985681i	$0.446068\pi$
$602$	−19.3229	−0.787545
$603$	1.94456	0.0791885
$604$	39.7561	1.61765
$605$	−21.8561	−0.888576
$606$	−6.10560	−0.248023
$607$	−44.9054	−1.82265	−0.911326	−	0.411685i	$-0.864940\pi$
$607$	−44.9054	−1.82265	−0.911326	+	0.411685i	$0.864940\pi$
$608$	−11.9392	−0.484198
$609$	−9.57893	−0.388158
$610$	14.9145	0.603870
$611$	−3.17973	−0.128638
$612$	0.621560	0.0251251
$613$	−8.11165	−0.327626	−0.163813	−	0.986491i	$-0.552379\pi$
$613$	−8.11165	−0.327626	−0.163813	+	0.986491i	$0.552379\pi$
$614$	36.5998	1.47705
$615$	−6.62149	−0.267004
$616$	88.3058	3.55794
$617$	22.2908	0.897393	0.448696	−	0.893684i	$-0.351888\pi$
$617$	22.2908	0.897393	0.448696	+	0.893684i	$0.351888\pi$
$618$	−0.646383	−0.0260014
$619$	2.00944	0.0807661	0.0403831	−	0.999184i	$-0.487142\pi$
$619$	2.00944	0.0807661	0.0403831	+	0.999184i	$0.487142\pi$
$620$	−49.7551	−1.99821
$621$	−32.0192	−1.28489
$622$	−3.43261	−0.137635
$623$	−10.8813	−0.435948
$624$	13.0935	0.524158
$625$	2.12320	0.0849281
$626$	53.5449	2.14009
$627$	−5.18440	−0.207045
$628$	7.22011	0.288114
$629$	0.515371	0.0205492
$630$	16.8749	0.672314
$631$	−7.57409	−0.301520	−0.150760	−	0.988570i	$-0.548172\pi$
$631$	−7.57409	−0.301520	−0.150760	+	0.988570i	$0.548172\pi$
$632$	−6.05761	−0.240959
$633$	−0.260966	−0.0103725
$634$	64.0009	2.54180
$635$	1.09006	0.0432578
$636$	−30.9411	−1.22690
$637$	2.88853	0.114448
$638$	65.2260	2.58232
$639$	−5.38897	−0.213184
$640$	1.64538	0.0650395
$641$	45.6521	1.80315	0.901575	−	0.432624i	$-0.142412\pi$
$641$	45.6521	1.80315	0.901575	+	0.432624i	$0.142412\pi$
$642$	3.13984	0.123920
$643$	2.39068	0.0942793	0.0471397	−	0.998888i	$-0.484989\pi$
$643$	2.39068	0.0942793	0.0471397	+	0.998888i	$0.484989\pi$
$644$	74.6508	2.94165
$645$	−3.89018	−0.153176
$646$	0.167547	0.00659206
$647$	12.3138	0.484107	0.242053	−	0.970263i	$-0.422179\pi$
$647$	12.3138	0.484107	0.242053	+	0.970263i	$0.422179\pi$
$648$	−17.5844	−0.690780
$649$	10.8403	0.425519
$650$	−12.6147	−0.494790
$651$	15.7792	0.618434
$652$	−34.0360	−1.33295
$653$	45.4456	1.77842	0.889212	−	0.457495i	$-0.151253\pi$
$653$	45.4456	1.77842	0.889212	+	0.457495i	$0.151253\pi$
$654$	−36.5425	−1.42893
$655$	−12.0402	−0.470451
$656$	−55.3177	−2.15979
$657$	6.74096	0.262990
$658$	12.7108	0.495518
$659$	7.72380	0.300876	0.150438	−	0.988619i	$-0.451932\pi$
$659$	7.72380	0.300876	0.150438	+	0.988619i	$0.451932\pi$
$660$	30.2196	1.17629
$661$	29.9995	1.16685	0.583423	−	0.812169i	$-0.301713\pi$
$661$	29.9995	1.16685	0.583423	+	0.812169i	$0.301713\pi$
$662$	5.64517	0.219406
$663$	−0.0774803	−0.00300908
$664$	−2.20641	−0.0856252
$665$	3.22221	0.124952
$666$	−50.4868	−1.95632
$667$	32.4387	1.25603
$668$	−25.9645	−1.00460
$669$	−20.6196	−0.797201
$670$	−3.05538	−0.118039
$671$	22.8147	0.880753
$672$	−22.0704	−0.851386
$673$	−14.6450	−0.564524	−0.282262	−	0.959337i	$-0.591085\pi$
$673$	−14.6450	−0.564524	−0.282262	+	0.959337i	$0.591085\pi$
$674$	13.7026	0.527805
$675$	−15.3212	−0.589713
$676$	−52.6553	−2.02520
$677$	35.0577	1.34738	0.673688	−	0.739016i	$-0.264709\pi$
$677$	35.0577	1.34738	0.673688	+	0.739016i	$0.264709\pi$
$678$	−35.3148	−1.35626
$679$	18.6900	0.717255
$680$	−0.574545	−0.0220328
$681$	−22.7098	−0.870241
$682$	−107.445	−4.11430
$683$	36.1070	1.38160	0.690798	−	0.723047i	$-0.257259\pi$
$683$	36.1070	1.38160	0.690798	+	0.723047i	$0.257259\pi$
$684$	−11.6266	−0.444553
$685$	16.4454	0.628345
$686$	−52.6799	−2.01133
$687$	−6.43461	−0.245496
$688$	−32.4997	−1.23904
$689$	−10.3886	−0.395776
$690$	21.2165	0.807699
$691$	−30.8427	−1.17331	−0.586657	−	0.809836i	$-0.699556\pi$
$691$	−30.8427	−1.17331	−0.586657	+	0.809836i	$0.699556\pi$
$692$	59.8756	2.27613
$693$	25.8136	0.980579
$694$	3.81194	0.144699
$695$	23.2301	0.881167
$696$	−31.9490	−1.21102
$697$	0.327342	0.0123990
$698$	2.12701	0.0805086
$699$	13.8271	0.522989
$700$	35.7204	1.35011
$701$	−14.1942	−0.536106	−0.268053	−	0.963404i	$-0.586380\pi$
$701$	−14.1942	−0.536106	−0.268053	+	0.963404i	$0.586380\pi$
$702$	17.9982	0.679299
$703$	−9.64026	−0.363589
$704$	46.3453	1.74670
$705$	2.55899	0.0963771
$706$	−27.8094	−1.04662
$707$	5.80484	0.218313
$708$	−9.02568	−0.339206
$709$	−25.7519	−0.967135	−0.483567	−	0.875307i	$-0.660659\pi$
$709$	−25.7519	−0.967135	−0.483567	+	0.875307i	$0.660659\pi$
$710$	8.46738	0.317775
$711$	−1.77077	−0.0664090
$712$	−36.2927	−1.36012
$713$	−53.4356	−2.00118
$714$	0.309723	0.0115911
$715$	10.1464	0.379453
$716$	91.7181	3.42767
$717$	−24.0118	−0.896735
$718$	−59.1616	−2.20789
$719$	−9.25780	−0.345258	−0.172629	−	0.984987i	$-0.555226\pi$
$719$	−9.25780	−0.345258	−0.172629	+	0.984987i	$0.555226\pi$
$720$	28.3823	1.05775
$721$	0.614543	0.0228868
$722$	46.6223	1.73510
$723$	2.99501	0.111386
$724$	−43.4581	−1.61511
$725$	15.5219	0.576470
$726$	39.2972	1.45845
$727$	2.91949	0.108278	0.0541389	−	0.998533i	$-0.482759\pi$
$727$	2.91949	0.108278	0.0541389	+	0.998533i	$0.482759\pi$
$728$	−24.6860	−0.914924
$729$	7.50084	0.277809
$730$	−10.5917	−0.392016
$731$	0.192316	0.00711307
$732$	−18.9957	−0.702100
$733$	25.0044	0.923558	0.461779	−	0.886995i	$-0.347211\pi$
$733$	25.0044	0.923558	0.461779	+	0.886995i	$0.347211\pi$
$734$	−49.1766	−1.81514
$735$	−2.32464	−0.0857455
$736$	74.7407	2.75498
$737$	−4.67382	−0.172162
$738$	−32.0671	−1.18040
$739$	24.1406	0.888028	0.444014	−	0.896020i	$-0.353554\pi$
$739$	24.1406	0.888028	0.444014	+	0.896020i	$0.353554\pi$
$740$	56.1925	2.06568
$741$	1.44931	0.0532416
$742$	41.5280	1.52454
$743$	41.7345	1.53109	0.765544	−	0.643383i	$-0.222470\pi$
$743$	41.7345	1.53109	0.765544	+	0.643383i	$0.222470\pi$
$744$	52.6288	1.92947
$745$	21.0904	0.772693
$746$	51.7371	1.89423
$747$	−0.644979	−0.0235986
$748$	−1.49394	−0.0546240
$749$	−2.98518	−0.109076
$750$	25.6423	0.936323
$751$	38.2762	1.39672	0.698359	−	0.715748i	$-0.253914\pi$
$751$	38.2762	1.39672	0.698359	+	0.715748i	$0.253914\pi$
$752$	21.3785	0.779594
$753$	−0.446141	−0.0162583
$754$	−18.2340	−0.664044
$755$	−10.7425	−0.390959
$756$	−50.9646	−1.85356
$757$	44.6475	1.62274	0.811371	−	0.584532i	$-0.198722\pi$
$757$	44.6475	1.62274	0.811371	+	0.584532i	$0.198722\pi$
$758$	16.5312	0.600439
$759$	32.4549	1.17804
$760$	10.7471	0.389840
$761$	54.9865	1.99326	0.996629	−	0.0820385i	$-0.0261431\pi$
$761$	54.9865	1.99326	0.996629	+	0.0820385i	$0.0261431\pi$
$762$	−1.95993	−0.0710007
$763$	34.7425	1.25776
$764$	−12.0739	−0.436818
$765$	−0.167952	−0.00607231
$766$	−33.9039	−1.22500
$767$	−3.03042	−0.109422
$768$	12.9281	0.466501
$769$	43.8665	1.58187	0.790933	−	0.611902i	$-0.209596\pi$
$769$	43.8665	1.58187	0.790933	+	0.611902i	$0.209596\pi$
$770$	−40.5596	−1.46166
$771$	0.843917	0.0303929
$772$	−28.4861	−1.02524
$773$	41.9860	1.51013	0.755066	−	0.655649i	$-0.227605\pi$
$773$	41.9860	1.51013	0.755066	+	0.655649i	$0.227605\pi$
$774$	−18.8397	−0.677178
$775$	−25.5689	−0.918463
$776$	62.3374	2.23778
$777$	−17.8207	−0.639314
$778$	19.4836	0.698520
$779$	−6.12308	−0.219382
$780$	−8.44792	−0.302484
$781$	12.9526	0.463480
$782$	−1.04887	−0.0375074
$783$	−22.1461	−0.791438
$784$	−19.4207	−0.693595
$785$	−1.95095	−0.0696323
$786$	21.6483	0.772170
$787$	17.4984	0.623749	0.311875	−	0.950123i	$-0.399043\pi$
$787$	17.4984	0.623749	0.311875	+	0.950123i	$0.399043\pi$
$788$	−49.8019	−1.77412
$789$	6.36037	0.226435
$790$	2.78231	0.0989901
$791$	33.5753	1.19380
$792$	86.0972	3.05933
$793$	−6.37789	−0.226486
$794$	61.5826	2.18549
$795$	8.36060	0.296520
$796$	−108.139	−3.83287
$797$	−26.2150	−0.928584	−0.464292	−	0.885682i	$-0.653691\pi$
$797$	−26.2150	−0.928584	−0.464292	+	0.885682i	$0.653691\pi$
$798$	−5.79352	−0.205088
$799$	−0.126507	−0.00447550
$800$	35.7635	1.26443
$801$	−10.6091	−0.374855
$802$	37.8070	1.33501
$803$	−16.2022	−0.571762
$804$	3.89144	0.137241
$805$	−20.1714	−0.710948
$806$	30.0365	1.05799
$807$	20.6615	0.727320
$808$	19.3611	0.681121
$809$	45.1262	1.58655	0.793276	−	0.608862i	$-0.208374\pi$
$809$	45.1262	1.58655	0.793276	+	0.608862i	$0.208374\pi$
$810$	8.07665	0.283785
$811$	−40.2914	−1.41482	−0.707411	−	0.706803i	$-0.750137\pi$
$811$	−40.2914	−1.41482	−0.707411	+	0.706803i	$0.750137\pi$
$812$	51.6323	1.81194
$813$	−18.1722	−0.637327
$814$	121.347	4.25321
$815$	9.19687	0.322152
$816$	0.520929	0.0182362
$817$	−3.59737	−0.125856
$818$	14.7394	0.515350
$819$	−7.21624	−0.252156
$820$	35.6911	1.24639
$821$	−18.0485	−0.629896	−0.314948	−	0.949109i	$-0.601987\pi$
$821$	−18.0485	−0.629896	−0.314948	+	0.949109i	$0.601987\pi$
$822$	−29.5687	−1.03133
$823$	43.8574	1.52877	0.764387	−	0.644758i	$-0.223042\pi$
$823$	43.8574	1.52877	0.764387	+	0.644758i	$0.223042\pi$
$824$	2.04971	0.0714050
$825$	15.5297	0.540675
$826$	12.1139	0.421497
$827$	−3.22810	−0.112252	−0.0561261	−	0.998424i	$-0.517875\pi$
$827$	−3.22810	−0.112252	−0.0561261	+	0.998424i	$0.517875\pi$
$828$	72.7838	2.52941
$829$	−33.7011	−1.17049	−0.585243	−	0.810858i	$-0.699001\pi$
$829$	−33.7011	−1.17049	−0.585243	+	0.810858i	$0.699001\pi$
$830$	1.01342	0.0351763
$831$	6.02438	0.208983
$832$	−12.9559	−0.449164
$833$	0.114921	0.00398179
$834$	−41.7676	−1.44629
$835$	7.01588	0.242794
$836$	27.9449	0.966496
$837$	36.4808	1.26096
$838$	55.7240	1.92495
$839$	−53.8946	−1.86065	−0.930324	−	0.366738i	$-0.880475\pi$
$839$	−53.8946	−1.86065	−0.930324	+	0.366738i	$0.880475\pi$
$840$	19.8669	0.685472
$841$	−6.56373	−0.226336
$842$	0.763316	0.0263056
$843$	−3.87961	−0.133621
$844$	1.40666	0.0484192
$845$	14.2280	0.489458
$846$	12.3929	0.426076
$847$	−37.3614	−1.28375
$848$	69.8468	2.39855
$849$	12.5100	0.429341
$850$	−0.501883	−0.0172144
$851$	60.3492	2.06874
$852$	−10.7844	−0.369467
$853$	−9.47927	−0.324564	−0.162282	−	0.986744i	$-0.551885\pi$
$853$	−9.47927	−0.324564	−0.162282	+	0.986744i	$0.551885\pi$
$854$	25.4953	0.872430
$855$	3.14162	0.107441
$856$	−9.95657	−0.340309
$857$	7.70389	0.263160	0.131580	−	0.991306i	$-0.457995\pi$
$857$	7.70389	0.263160	0.131580	+	0.991306i	$0.457995\pi$
$858$	−18.2432	−0.622811
$859$	33.6201	1.14710	0.573552	−	0.819169i	$-0.305565\pi$
$859$	33.6201	1.14710	0.573552	+	0.819169i	$0.305565\pi$
$860$	20.9688	0.715031
$861$	−11.3190	−0.385749
$862$	−28.3862	−0.966837
$863$	24.1626	0.822505	0.411253	−	0.911521i	$-0.365091\pi$
$863$	24.1626	0.822505	0.411253	+	0.911521i	$0.365091\pi$
$864$	−51.0260	−1.73594
$865$	−16.1790	−0.550102
$866$	−50.4064	−1.71288
$867$	15.3181	0.520229
$868$	−85.0528	−2.88688
$869$	4.25611	0.144379
$870$	14.6744	0.497510
$871$	1.30657	0.0442715
$872$	115.878	3.92412
$873$	18.2225	0.616739
$874$	19.6195	0.663641
$875$	−24.3791	−0.824165
$876$	13.4900	0.455784
$877$	−43.9049	−1.48256	−0.741282	−	0.671194i	$-0.765782\pi$
$877$	−43.9049	−1.48256	−0.741282	+	0.671194i	$0.765782\pi$
$878$	−63.2709	−2.13529
$879$	−16.3350	−0.550965
$880$	−68.2179	−2.29963
$881$	48.8546	1.64595	0.822976	−	0.568076i	$-0.192312\pi$
$881$	48.8546	1.64595	0.822976	+	0.568076i	$0.192312\pi$
$882$	−11.2579	−0.379074
$883$	−28.7852	−0.968700	−0.484350	−	0.874874i	$-0.660944\pi$
$883$	−28.7852	−0.968700	−0.484350	+	0.874874i	$0.660944\pi$
$884$	0.417634	0.0140465
$885$	2.43883	0.0819803
$886$	−7.48799	−0.251564
$887$	−1.30317	−0.0437562	−0.0218781	−	0.999761i	$-0.506965\pi$
$887$	−1.30317	−0.0437562	−0.0218781	+	0.999761i	$0.506965\pi$
$888$	−59.4381	−1.99461
$889$	1.86338	0.0624958
$890$	16.6695	0.558763
$891$	12.3549	0.413904
$892$	111.144	3.72137
$893$	2.36637	0.0791877
$894$	−37.9205	−1.26825
$895$	−24.7832	−0.828410
$896$	2.81267	0.0939646
$897$	−9.07283	−0.302933
$898$	35.1067	1.17153
$899$	−36.9588	−1.23264
$900$	34.8271	1.16090
$901$	−0.413317	−0.0137696
$902$	77.0744	2.56630
$903$	−6.64999	−0.221298
$904$	111.985	3.72456
$905$	11.7428	0.390344
$906$	19.3150	0.641697
$907$	24.6075	0.817077	0.408539	−	0.912741i	$-0.366039\pi$
$907$	24.6075	0.817077	0.408539	+	0.912741i	$0.366039\pi$
$908$	122.410	4.06233
$909$	5.65966	0.187719
$910$	11.3385	0.375867
$911$	10.0081	0.331585	0.165792	−	0.986161i	$-0.446982\pi$
$911$	10.0081	0.331585	0.165792	+	0.986161i	$0.446982\pi$
$912$	−9.74424	−0.322664
$913$	1.55023	0.0513052
$914$	−49.2572	−1.62928
$915$	5.13282	0.169686
$916$	34.6838	1.14598
$917$	−20.5819	−0.679676
$918$	0.716067	0.0236337
$919$	53.6454	1.76960	0.884800	−	0.465972i	$-0.154295\pi$
$919$	53.6454	1.76960	0.884800	+	0.465972i	$0.154295\pi$
$920$	−67.2784	−2.21810
$921$	12.5958	0.415046
$922$	−29.2278	−0.962566
$923$	−3.62091	−0.119184
$924$	51.6582	1.69943
$925$	28.8771	0.949473
$926$	31.2992	1.02856
$927$	0.599173	0.0196794
$928$	51.6945	1.69696
$929$	11.9246	0.391234	0.195617	−	0.980680i	$-0.437329\pi$
$929$	11.9246	0.391234	0.195617	+	0.980680i	$0.437329\pi$
$930$	−24.1729	−0.792659
$931$	−2.14966	−0.0704523
$932$	−74.5308	−2.44134
$933$	−1.18133	−0.0386750
$934$	−62.5242	−2.04585
$935$	0.403678	0.0132017
$936$	−24.0686	−0.786707
$937$	57.5435	1.87986	0.939932	−	0.341362i	$-0.110888\pi$
$937$	57.5435	1.87986	0.939932	+	0.341362i	$0.110888\pi$
$938$	−5.22295	−0.170535
$939$	18.4275	0.601358
$940$	−13.7935	−0.449893
$941$	35.6327	1.16159	0.580796	−	0.814049i	$-0.302741\pi$
$941$	35.6327	1.16159	0.580796	+	0.814049i	$0.302741\pi$
$942$	3.50780	0.114290
$943$	38.3312	1.24824
$944$	20.3747	0.663138
$945$	13.7711	0.447975
$946$	45.2819	1.47224
$947$	−13.4996	−0.438678	−0.219339	−	0.975649i	$-0.570390\pi$
$947$	−13.4996	−0.438678	−0.219339	+	0.975649i	$0.570390\pi$
$948$	−3.54365	−0.115093
$949$	4.52933	0.147028
$950$	9.38796	0.304585
$951$	22.0259	0.714239
$952$	−0.982144	−0.0318315
$953$	9.77739	0.316721	0.158360	−	0.987381i	$-0.449379\pi$
$953$	9.77739	0.316721	0.158360	+	0.987381i	$0.449379\pi$
$954$	40.4894	1.31089
$955$	3.26249	0.105572
$956$	129.428	4.18600
$957$	22.4475	0.725625
$958$	27.0081	0.872591
$959$	28.1122	0.907789
$960$	10.4267	0.336519
$961$	29.8814	0.963915
$962$	−33.9227	−1.09371
$963$	−2.91052	−0.0937901
$964$	−16.1437	−0.519953
$965$	7.69724	0.247783
$966$	36.2681	1.16691
$967$	6.63701	0.213432	0.106716	−	0.994290i	$-0.465966\pi$
$967$	6.63701	0.213432	0.106716	+	0.994290i	$0.465966\pi$
$968$	−124.613	−4.00521
$969$	0.0576613	0.00185235
$970$	−28.6321	−0.919320
$971$	−34.7681	−1.11576	−0.557881	−	0.829921i	$-0.688385\pi$
$971$	−34.7681	−1.11576	−0.557881	+	0.829921i	$0.688385\pi$
$972$	−78.4249	−2.51548
$973$	39.7102	1.27305
$974$	59.4989	1.90647
$975$	−4.34135	−0.139034
$976$	42.8810	1.37259
$977$	−55.2328	−1.76705	−0.883527	−	0.468380i	$-0.844838\pi$
$977$	−55.2328	−1.76705	−0.883527	+	0.468380i	$0.844838\pi$
$978$	−16.5359	−0.528761
$979$	25.4994	0.814964
$980$	12.5302	0.400264
$981$	33.8736	1.08150
$982$	8.85129	0.282456
$983$	34.8213	1.11063	0.555313	−	0.831641i	$-0.312598\pi$
$983$	34.8213	1.11063	0.555313	+	0.831641i	$0.312598\pi$
$984$	−37.7525	−1.20351
$985$	13.4570	0.428775
$986$	−0.725449	−0.0231030
$987$	4.37441	0.139239
$988$	−7.81204	−0.248534
$989$	22.5199	0.716092
$990$	−39.5452	−1.25683
$991$	9.66400	0.306987	0.153493	−	0.988150i	$-0.450948\pi$
$991$	9.66400	0.306987	0.153493	+	0.988150i	$0.450948\pi$
$992$	−85.1553	−2.70368
$993$	1.94278	0.0616524
$994$	14.4744	0.459100
$995$	29.2201	0.926341
$996$	−1.29073	−0.0408984
$997$	−35.9193	−1.13758	−0.568788	−	0.822484i	$-0.692588\pi$
$997$	−35.9193	−1.13758	−0.568788	+	0.822484i	$0.692588\pi$
$998$	−6.96611	−0.220508
$999$	−41.2008	−1.30353

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.b.1.13	✓	358

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.b.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-2.61876 q^{2} -0.901244 q^{3} +4.85788 q^{4} -1.31265 q^{5} +2.36014 q^{6} -2.24388 q^{7} -7.48409 q^{8} -2.18776 q^{9} +O(q^{10})\)	\(q-2.61876 q^{2} -0.901244 q^{3} +4.85788 q^{4} -1.31265 q^{5} +2.36014 q^{6} -2.24388 q^{7} -7.48409 q^{8} -2.18776 q^{9} +3.43751 q^{10} +5.25836 q^{11} -4.37814 q^{12} -1.46998 q^{13} +5.87617 q^{14} +1.18302 q^{15} +9.88325 q^{16} -0.0584840 q^{17} +5.72921 q^{18} +1.09397 q^{19} -6.37669 q^{20} +2.02228 q^{21} -13.7704 q^{22} -6.84838 q^{23} +6.74499 q^{24} -3.27695 q^{25} +3.84952 q^{26} +4.67544 q^{27} -10.9005 q^{28} -4.73669 q^{29} -3.09803 q^{30} +7.80265 q^{31} -10.9136 q^{32} -4.73907 q^{33} +0.153155 q^{34} +2.94542 q^{35} -10.6279 q^{36} -8.81218 q^{37} -2.86484 q^{38} +1.32481 q^{39} +9.82398 q^{40} -5.59712 q^{41} -5.29586 q^{42} -3.28836 q^{43} +25.5445 q^{44} +2.87176 q^{45} +17.9342 q^{46} +2.16311 q^{47} -8.90722 q^{48} -1.96501 q^{49} +8.58154 q^{50} +0.0527083 q^{51} -7.14100 q^{52} +7.06719 q^{53} -12.2438 q^{54} -6.90238 q^{55} +16.7934 q^{56} -0.985934 q^{57} +12.4042 q^{58} +2.06153 q^{59} +5.74695 q^{60} +4.33875 q^{61} -20.4332 q^{62} +4.90907 q^{63} +8.81363 q^{64} +1.92957 q^{65} +12.4105 q^{66} -0.888835 q^{67} -0.284108 q^{68} +6.17206 q^{69} -7.71334 q^{70} +2.46324 q^{71} +16.3734 q^{72} -3.08122 q^{73} +23.0769 q^{74} +2.95334 q^{75} +5.31438 q^{76} -11.7991 q^{77} -3.46936 q^{78} +0.809398 q^{79} -12.9732 q^{80} +2.34957 q^{81} +14.6575 q^{82} +0.294813 q^{83} +9.82401 q^{84} +0.0767689 q^{85} +8.61140 q^{86} +4.26892 q^{87} -39.3541 q^{88} +4.84930 q^{89} -7.52043 q^{90} +3.29846 q^{91} -33.2686 q^{92} -7.03209 q^{93} -5.66465 q^{94} -1.43600 q^{95} +9.83584 q^{96} -8.32931 q^{97} +5.14588 q^{98} -11.5040 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) \) 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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