LMFDB - Embedded newform 8011.2.a.a.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:	$1$
Dimension:	$309$
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)

$f(q)$	$=$	$q-2.65734 q^{2} -0.429161 q^{3} +5.06145 q^{4} +2.18236 q^{5} +1.14043 q^{6} +3.77949 q^{7} -8.13530 q^{8} -2.81582 q^{9} +O(q^{10})$	\(q-2.65734 q^{2} -0.429161 q^{3} +5.06145 q^{4} +2.18236 q^{5} +1.14043 q^{6} +3.77949 q^{7} -8.13530 q^{8} -2.81582 q^{9} -5.79927 q^{10} +3.44115 q^{11} -2.17217 q^{12} +1.47106 q^{13} -10.0434 q^{14} -0.936583 q^{15} +11.4954 q^{16} -7.69561 q^{17} +7.48259 q^{18} -1.43776 q^{19} +11.0459 q^{20} -1.62201 q^{21} -9.14430 q^{22} +0.585137 q^{23} +3.49135 q^{24} -0.237311 q^{25} -3.90910 q^{26} +2.49592 q^{27} +19.1297 q^{28} -7.83308 q^{29} +2.48882 q^{30} -2.80548 q^{31} -14.2765 q^{32} -1.47681 q^{33} +20.4498 q^{34} +8.24821 q^{35} -14.2521 q^{36} +4.15204 q^{37} +3.82060 q^{38} -0.631320 q^{39} -17.7541 q^{40} -3.75651 q^{41} +4.31023 q^{42} -10.3114 q^{43} +17.4172 q^{44} -6.14513 q^{45} -1.55491 q^{46} +7.90430 q^{47} -4.93336 q^{48} +7.28456 q^{49} +0.630615 q^{50} +3.30265 q^{51} +7.44568 q^{52} -2.39777 q^{53} -6.63251 q^{54} +7.50982 q^{55} -30.7473 q^{56} +0.617028 q^{57} +20.8151 q^{58} -1.35133 q^{59} -4.74046 q^{60} +5.03491 q^{61} +7.45512 q^{62} -10.6424 q^{63} +14.9466 q^{64} +3.21038 q^{65} +3.92437 q^{66} -10.6036 q^{67} -38.9509 q^{68} -0.251118 q^{69} -21.9183 q^{70} +9.27541 q^{71} +22.9076 q^{72} +14.6635 q^{73} -11.0334 q^{74} +0.101844 q^{75} -7.27712 q^{76} +13.0058 q^{77} +1.67763 q^{78} -1.99138 q^{79} +25.0870 q^{80} +7.37631 q^{81} +9.98232 q^{82} -15.6554 q^{83} -8.20972 q^{84} -16.7946 q^{85} +27.4010 q^{86} +3.36165 q^{87} -27.9948 q^{88} +12.3172 q^{89} +16.3297 q^{90} +5.55985 q^{91} +2.96164 q^{92} +1.20400 q^{93} -21.0044 q^{94} -3.13770 q^{95} +6.12689 q^{96} +14.5278 q^{97} -19.3575 q^{98} -9.68966 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.65734	−1.87902	−0.939511	−	0.342519i	$-0.888720\pi$
$2$	−2.65734	−1.87902	−0.939511	+	0.342519i	$0.888720\pi$
$3$	−0.429161	−0.247776	−0.123888	−	0.992296i	$-0.539536\pi$
$3$	−0.429161	−0.247776	−0.123888	+	0.992296i	$0.539536\pi$
$4$	5.06145	2.53072
$5$	2.18236	0.975980	0.487990	−	0.872849i	$-0.337730\pi$
$5$	2.18236	0.975980	0.487990	+	0.872849i	$0.337730\pi$
$6$	1.14043	0.465577
$7$	3.77949	1.42851	0.714257	−	0.699884i	$-0.246765\pi$
$7$	3.77949	1.42851	0.714257	+	0.699884i	$0.246765\pi$
$8$	−8.13530	−2.87626
$9$	−2.81582	−0.938607
$10$	−5.79927	−1.83389
$11$	3.44115	1.03755	0.518773	−	0.854912i	$-0.326389\pi$
$11$	3.44115	1.03755	0.518773	+	0.854912i	$0.326389\pi$
$12$	−2.17217	−0.627053
$13$	1.47106	0.407998	0.203999	−	0.978971i	$-0.434606\pi$
$13$	1.47106	0.407998	0.203999	+	0.978971i	$0.434606\pi$
$14$	−10.0434	−2.68421
$15$	−0.936583	−0.241825
$16$	11.4954	2.87384
$17$	−7.69561	−1.86646	−0.933229	−	0.359282i	$-0.883022\pi$
$17$	−7.69561	−1.86646	−0.933229	+	0.359282i	$0.883022\pi$
$18$	7.48259	1.76366
$19$	−1.43776	−0.329844	−0.164922	−	0.986307i	$-0.552737\pi$
$19$	−1.43776	−0.329844	−0.164922	+	0.986307i	$0.552737\pi$
$20$	11.0459	2.46994
$21$	−1.62201	−0.353951
$22$	−9.14430	−1.94957
$23$	0.585137	0.122009	0.0610047	−	0.998137i	$-0.480570\pi$
$23$	0.585137	0.122009	0.0610047	+	0.998137i	$0.480570\pi$
$24$	3.49135	0.712669
$25$	−0.237311	−0.0474621
$26$	−3.90910	−0.766637
$27$	2.49592	0.480340
$28$	19.1297	3.61517
$29$	−7.83308	−1.45457	−0.727283	−	0.686338i	$-0.759217\pi$
$29$	−7.83308	−1.45457	−0.727283	+	0.686338i	$0.759217\pi$
$30$	2.48882	0.454394
$31$	−2.80548	−0.503879	−0.251940	−	0.967743i	$-0.581068\pi$
$31$	−2.80548	−0.503879	−0.251940	+	0.967743i	$0.581068\pi$
$32$	−14.2765	−2.52374
$33$	−1.47681	−0.257079
$34$	20.4498	3.50712
$35$	8.24821	1.39420
$36$	−14.2521	−2.37536
$37$	4.15204	0.682591	0.341295	−	0.939956i	$-0.389134\pi$
$37$	4.15204	0.682591	0.341295	+	0.939956i	$0.389134\pi$
$38$	3.82060	0.619784
$39$	−0.631320	−0.101092
$40$	−17.7541	−2.80718
$41$	−3.75651	−0.586669	−0.293334	−	0.956010i	$-0.594765\pi$
$41$	−3.75651	−0.586669	−0.293334	+	0.956010i	$0.594765\pi$
$42$	4.31023	0.665083
$43$	−10.3114	−1.57248	−0.786240	−	0.617921i	$-0.787975\pi$
$43$	−10.3114	−1.57248	−0.786240	+	0.617921i	$0.787975\pi$
$44$	17.4172	2.62574
$45$	−6.14513	−0.916062
$46$	−1.55491	−0.229259
$47$	7.90430	1.15296	0.576480	−	0.817111i	$-0.304426\pi$
$47$	7.90430	1.15296	0.576480	+	0.817111i	$0.304426\pi$
$48$	−4.93336	−0.712069
$49$	7.28456	1.04065
$50$	0.630615	0.0891824
$51$	3.30265	0.462464
$52$	7.44568	1.03253
$53$	−2.39777	−0.329359	−0.164680	−	0.986347i	$-0.552659\pi$
$53$	−2.39777	−0.329359	−0.164680	+	0.986347i	$0.552659\pi$
$54$	−6.63251	−0.902570
$55$	7.50982	1.01262
$56$	−30.7473	−4.10878
$57$	0.617028	0.0817274
$58$	20.8151	2.73316
$59$	−1.35133	−0.175928	−0.0879641	−	0.996124i	$-0.528036\pi$
$59$	−1.35133	−0.175928	−0.0879641	+	0.996124i	$0.528036\pi$
$60$	−4.74046	−0.611991
$61$	5.03491	0.644654	0.322327	−	0.946628i	$-0.395535\pi$
$61$	5.03491	0.644654	0.322327	+	0.946628i	$0.395535\pi$
$62$	7.45512	0.946801
$63$	−10.6424	−1.34081
$64$	14.9466	1.86833
$65$	3.21038	0.398198
$66$	3.92437	0.483057
$67$	−10.6036	−1.29544	−0.647719	−	0.761879i	$-0.724277\pi$
$67$	−10.6036	−1.29544	−0.647719	+	0.761879i	$0.724277\pi$
$68$	−38.9509	−4.72349
$69$	−0.251118	−0.0302310
$70$	−21.9183	−2.61974
$71$	9.27541	1.10079	0.550394	−	0.834905i	$-0.314477\pi$
$71$	9.27541	1.10079	0.550394	+	0.834905i	$0.314477\pi$
$72$	22.9076	2.69968
$73$	14.6635	1.71623	0.858115	−	0.513457i	$-0.171635\pi$
$73$	14.6635	1.71623	0.858115	+	0.513457i	$0.171635\pi$
$74$	−11.0334	−1.28260
$75$	0.101844	0.0117600
$76$	−7.27712	−0.834743
$77$	13.0058	1.48215
$78$	1.67763	0.189954
$79$	−1.99138	−0.224048	−0.112024	−	0.993706i	$-0.535733\pi$
$79$	−1.99138	−0.224048	−0.112024	+	0.993706i	$0.535733\pi$
$80$	25.0870	2.80481
$81$	7.37631	0.819590
$82$	9.98232	1.10236
$83$	−15.6554	−1.71840	−0.859200	−	0.511641i	$-0.829038\pi$
$83$	−15.6554	−1.71840	−0.859200	+	0.511641i	$0.829038\pi$
$84$	−8.20972	−0.895753
$85$	−16.7946	−1.82163
$86$	27.4010	2.95473
$87$	3.36165	0.360407
$88$	−27.9948	−2.98425
$89$	12.3172	1.30562	0.652811	−	0.757521i	$-0.273590\pi$
$89$	12.3172	1.30562	0.652811	+	0.757521i	$0.273590\pi$
$90$	16.3297	1.72130
$91$	5.55985	0.582831
$92$	2.96164	0.308772
$93$	1.20400	0.124849
$94$	−21.0044	−2.16644
$95$	−3.13770	−0.321921
$96$	6.12689	0.625323
$97$	14.5278	1.47508	0.737540	−	0.675304i	$-0.235987\pi$
$97$	14.5278	1.47508	0.737540	+	0.675304i	$0.235987\pi$
$98$	−19.3575	−1.95541
$99$	−9.68966	−0.973847
$100$	−1.20114	−0.120114
$101$	−14.4300	−1.43584	−0.717921	−	0.696124i	$-0.754906\pi$
$101$	−14.4300	−1.43584	−0.717921	+	0.696124i	$0.754906\pi$
$102$	−8.77626	−0.868980
$103$	−0.370502	−0.0365067	−0.0182533	−	0.999833i	$-0.505811\pi$
$103$	−0.370502	−0.0365067	−0.0182533	+	0.999833i	$0.505811\pi$
$104$	−11.9675	−1.17351
$105$	−3.53981	−0.345450
$106$	6.37169	0.618873
$107$	−1.37186	−0.132623	−0.0663113	−	0.997799i	$-0.521123\pi$
$107$	−1.37186	−0.132623	−0.0663113	+	0.997799i	$0.521123\pi$
$108$	12.6330	1.21561
$109$	7.07383	0.677550	0.338775	−	0.940867i	$-0.389987\pi$
$109$	7.07383	0.677550	0.338775	+	0.940867i	$0.389987\pi$
$110$	−19.9561	−1.90274
$111$	−1.78189	−0.169130
$112$	43.4466	4.10532
$113$	−6.49070	−0.610594	−0.305297	−	0.952257i	$-0.598756\pi$
$113$	−6.49070	−0.610594	−0.305297	+	0.952257i	$0.598756\pi$
$114$	−1.63965	−0.153568
$115$	1.27698	0.119079
$116$	−39.6467	−3.68111
$117$	−4.14223	−0.382950
$118$	3.59094	0.330573
$119$	−29.0855	−2.66626
$120$	7.61938	0.695551
$121$	0.841506	0.0765006
$122$	−13.3795	−1.21132
$123$	1.61215	0.145362
$124$	−14.1998	−1.27518
$125$	−11.4297	−1.02230
$126$	28.2804	2.51942
$127$	6.80440	0.603793	0.301896	−	0.953341i	$-0.402380\pi$
$127$	6.80440	0.603793	0.301896	+	0.953341i	$0.402380\pi$
$128$	−11.1654	−0.986891
$129$	4.42527	0.389623
$130$	−8.53105	−0.748223
$131$	−6.09926	−0.532895	−0.266448	−	0.963849i	$-0.585850\pi$
$131$	−6.09926	−0.532895	−0.266448	+	0.963849i	$0.585850\pi$
$132$	−7.47478	−0.650596
$133$	−5.43398	−0.471186
$134$	28.1774	2.43416
$135$	5.44700	0.468803
$136$	62.6061	5.36843
$137$	−4.99812	−0.427018	−0.213509	−	0.976941i	$-0.568489\pi$
$137$	−4.99812	−0.427018	−0.213509	+	0.976941i	$0.568489\pi$
$138$	0.667305	0.0568048
$139$	7.27174	0.616781	0.308390	−	0.951260i	$-0.400210\pi$
$139$	7.27174	0.616781	0.308390	+	0.951260i	$0.400210\pi$
$140$	41.7479	3.52834
$141$	−3.39222	−0.285676
$142$	−24.6479	−2.06841
$143$	5.06213	0.423316
$144$	−32.3689	−2.69741
$145$	−17.0946	−1.41963
$146$	−38.9658	−3.22484
$147$	−3.12625	−0.257848
$148$	21.0153	1.72745
$149$	−4.22474	−0.346104	−0.173052	−	0.984913i	$-0.555363\pi$
$149$	−4.22474	−0.346104	−0.173052	+	0.984913i	$0.555363\pi$
$150$	−0.270635	−0.0220973
$151$	−21.0875	−1.71608	−0.858039	−	0.513584i	$-0.828317\pi$
$151$	−21.0875	−1.71608	−0.858039	+	0.513584i	$0.828317\pi$
$152$	11.6966	0.948718
$153$	21.6694	1.75187
$154$	−34.5608	−2.78499
$155$	−6.12257	−0.491777
$156$	−3.19539	−0.255836
$157$	−20.6103	−1.64488	−0.822441	−	0.568851i	$-0.807388\pi$
$157$	−20.6103	−1.64488	−0.822441	+	0.568851i	$0.807388\pi$
$158$	5.29178	0.420991
$159$	1.02903	0.0816073
$160$	−31.1563	−2.46312
$161$	2.21152	0.174292
$162$	−19.6014	−1.54003
$163$	13.1636	1.03105	0.515525	−	0.856874i	$-0.327597\pi$
$163$	13.1636	1.03105	0.515525	+	0.856874i	$0.327597\pi$
$164$	−19.0134	−1.48470
$165$	−3.22292	−0.250904
$166$	41.6016	3.22891
$167$	−14.4011	−1.11439	−0.557197	−	0.830380i	$-0.688123\pi$
$167$	−14.4011	−1.11439	−0.557197	+	0.830380i	$0.688123\pi$
$168$	13.1955	1.01806
$169$	−10.8360	−0.833538
$170$	44.6289	3.42288
$171$	4.04846	0.309594
$172$	−52.1908	−3.97951
$173$	−7.54238	−0.573436	−0.286718	−	0.958015i	$-0.592564\pi$
$173$	−7.54238	−0.573436	−0.286718	+	0.958015i	$0.592564\pi$
$174$	−8.93304	−0.677212
$175$	−0.896913	−0.0678003
$176$	39.5572	2.98174
$177$	0.579938	0.0435908
$178$	−32.7310	−2.45329
$179$	−10.3119	−0.770749	−0.385375	−	0.922760i	$-0.625928\pi$
$179$	−10.3119	−0.770749	−0.385375	+	0.922760i	$0.625928\pi$
$180$	−31.1033	−2.31830
$181$	6.51553	0.484295	0.242148	−	0.970239i	$-0.422148\pi$
$181$	6.51553	0.484295	0.242148	+	0.970239i	$0.422148\pi$
$182$	−14.7744	−1.09515
$183$	−2.16079	−0.159730
$184$	−4.76027	−0.350932
$185$	9.06123	0.666195
$186$	−3.19944	−0.234595
$187$	−26.4817	−1.93654
$188$	40.0072	2.91783
$189$	9.43332	0.686173
$190$	8.33793	0.604897
$191$	−17.3806	−1.25762	−0.628810	−	0.777559i	$-0.716458\pi$
$191$	−17.3806	−1.25762	−0.628810	+	0.777559i	$0.716458\pi$
$192$	−6.41452	−0.462928
$193$	−7.63042	−0.549250	−0.274625	−	0.961551i	$-0.588554\pi$
$193$	−7.63042	−0.549250	−0.274625	+	0.961551i	$0.588554\pi$
$194$	−38.6054	−2.77171
$195$	−1.37777	−0.0986639
$196$	36.8704	2.63360
$197$	−14.7659	−1.05203	−0.526015	−	0.850475i	$-0.676314\pi$
$197$	−14.7659	−1.05203	−0.526015	+	0.850475i	$0.676314\pi$
$198$	25.7487	1.82988
$199$	15.6216	1.10739	0.553695	−	0.832720i	$-0.313218\pi$
$199$	15.6216	1.10739	0.553695	+	0.832720i	$0.313218\pi$
$200$	1.93059	0.136514
$201$	4.55066	0.320979
$202$	38.3455	2.69798
$203$	−29.6051	−2.07787
$204$	16.7162	1.17037
$205$	−8.19806	−0.572577
$206$	0.984550	0.0685968
$207$	−1.64764	−0.114519
$208$	16.9103	1.17252
$209$	−4.94753	−0.342228
$210$	9.40646	0.649108
$211$	13.9350	0.959328	0.479664	−	0.877452i	$-0.340759\pi$
$211$	13.9350	0.959328	0.479664	+	0.877452i	$0.340759\pi$
$212$	−12.1362	−0.833517
$213$	−3.98064	−0.272749
$214$	3.64549	0.249201
$215$	−22.5033	−1.53471
$216$	−20.3051	−1.38159
$217$	−10.6033	−0.719799
$218$	−18.7976	−1.27313
$219$	−6.29299	−0.425241
$220$	38.0106	2.56267
$221$	−11.3207	−0.761511
$222$	4.73509	0.317798
$223$	18.8348	1.26127	0.630636	−	0.776079i	$-0.282794\pi$
$223$	18.8348	1.26127	0.630636	+	0.776079i	$0.282794\pi$
$224$	−53.9577	−3.60520
$225$	0.668224	0.0445483
$226$	17.2480	1.14732
$227$	8.60792	0.571327	0.285664	−	0.958330i	$-0.407786\pi$
$227$	8.60792	0.571327	0.285664	+	0.958330i	$0.407786\pi$
$228$	3.12306	0.206829
$229$	−15.2521	−1.00788	−0.503942	−	0.863737i	$-0.668118\pi$
$229$	−15.2521	−1.00788	−0.503942	+	0.863737i	$0.668118\pi$
$230$	−3.39336	−0.223752
$231$	−5.58158	−0.367241
$232$	63.7245	4.18372
$233$	−8.71359	−0.570846	−0.285423	−	0.958402i	$-0.592134\pi$
$233$	−8.71359	−0.570846	−0.285423	+	0.958402i	$0.592134\pi$
$234$	11.0073	0.719571
$235$	17.2500	1.12527
$236$	−6.83969	−0.445226
$237$	0.854623	0.0555137
$238$	77.2900	5.00996
$239$	−3.24719	−0.210043	−0.105022	−	0.994470i	$-0.533491\pi$
$239$	−3.24719	−0.210043	−0.105022	+	0.994470i	$0.533491\pi$
$240$	−10.7664	−0.694965
$241$	−17.6499	−1.13693	−0.568465	−	0.822708i	$-0.692462\pi$
$241$	−17.6499	−1.13693	−0.568465	+	0.822708i	$0.692462\pi$
$242$	−2.23617	−0.143746
$243$	−10.6534	−0.683415
$244$	25.4839	1.63144
$245$	15.8975	1.01566
$246$	−4.28402	−0.273139
$247$	−2.11502	−0.134576
$248$	22.8234	1.44929
$249$	6.71867	0.425778
$250$	30.3726	1.92093
$251$	−23.0003	−1.45176	−0.725882	−	0.687819i	$-0.758568\pi$
$251$	−23.0003	−1.45176	−0.725882	+	0.687819i	$0.758568\pi$
$252$	−53.8658	−3.39323
$253$	2.01354	0.126590
$254$	−18.0816	−1.13454
$255$	7.20757	0.451356
$256$	−0.223047	−0.0139404
$257$	−3.54218	−0.220955	−0.110478	−	0.993879i	$-0.535238\pi$
$257$	−3.54218	−0.220955	−0.110478	+	0.993879i	$0.535238\pi$
$258$	−11.7594	−0.732110
$259$	15.6926	0.975090
$260$	16.2491	1.00773
$261$	22.0565	1.36527
$262$	16.2078	1.00132
$263$	1.81619	0.111991	0.0559955	−	0.998431i	$-0.482167\pi$
$263$	1.81619	0.111991	0.0559955	+	0.998431i	$0.482167\pi$
$264$	12.0143	0.739427
$265$	−5.23280	−0.321448
$266$	14.4399	0.885369
$267$	−5.28607	−0.323502
$268$	−53.6697	−3.27840
$269$	20.2796	1.23647	0.618234	−	0.785994i	$-0.287848\pi$
$269$	20.2796	1.23647	0.618234	+	0.785994i	$0.287848\pi$
$270$	−14.4745	−0.880891
$271$	−22.5368	−1.36901	−0.684507	−	0.729007i	$-0.739982\pi$
$271$	−22.5368	−1.36901	−0.684507	+	0.729007i	$0.739982\pi$
$272$	−88.4637	−5.36390
$273$	−2.38607	−0.144411
$274$	13.2817	0.802376
$275$	−0.816621	−0.0492441
$276$	−1.27102	−0.0765064
$277$	2.24975	0.135174	0.0675872	−	0.997713i	$-0.478470\pi$
$277$	2.24975	0.135174	0.0675872	+	0.997713i	$0.478470\pi$
$278$	−19.3235	−1.15895
$279$	7.89974	0.472945
$280$	−67.1017	−4.01009
$281$	−18.3127	−1.09245	−0.546223	−	0.837640i	$-0.683935\pi$
$281$	−18.3127	−1.09245	−0.546223	+	0.837640i	$0.683935\pi$
$282$	9.01427	0.536792
$283$	−28.9172	−1.71895	−0.859473	−	0.511181i	$-0.829208\pi$
$283$	−28.9172	−1.71895	−0.859473	+	0.511181i	$0.829208\pi$
$284$	46.9470	2.78579
$285$	1.34658	0.0797643
$286$	−13.4518	−0.795421
$287$	−14.1977	−0.838064
$288$	40.1999	2.36880
$289$	42.2223	2.48367
$290$	45.4261	2.66751
$291$	−6.23478	−0.365489
$292$	74.2185	4.34331
$293$	16.5192	0.965061	0.482530	−	0.875879i	$-0.339718\pi$
$293$	16.5192	0.965061	0.482530	+	0.875879i	$0.339718\pi$
$294$	8.30749	0.484503
$295$	−2.94909	−0.171702
$296$	−33.7781	−1.96331
$297$	8.58884	0.498375
$298$	11.2266	0.650338
$299$	0.860770	0.0497796
$300$	0.515480	0.0297613
$301$	−38.9720	−2.24631
$302$	56.0367	3.22455
$303$	6.19281	0.355767
$304$	−16.5275	−0.947918
$305$	10.9880	0.629170
$306$	−57.5831	−3.29180
$307$	−20.0962	−1.14695	−0.573476	−	0.819223i	$-0.694405\pi$
$307$	−20.0962	−1.14695	−0.573476	+	0.819223i	$0.694405\pi$
$308$	65.8281	3.75091
$309$	0.159005	0.00904548
$310$	16.2697	0.924059
$311$	−27.7098	−1.57128	−0.785639	−	0.618685i	$-0.787666\pi$
$311$	−27.7098	−1.57128	−0.785639	+	0.618685i	$0.787666\pi$
$312$	5.13598	0.290768
$313$	−8.57437	−0.484652	−0.242326	−	0.970195i	$-0.577910\pi$
$313$	−8.57437	−0.484652	−0.242326	+	0.970195i	$0.577910\pi$
$314$	54.7686	3.09077
$315$	−23.2255	−1.30861
$316$	−10.0793	−0.567004
$317$	20.3674	1.14395	0.571973	−	0.820272i	$-0.306178\pi$
$317$	20.3674	1.14395	0.571973	+	0.820272i	$0.306178\pi$
$318$	−2.73448	−0.153342
$319$	−26.9548	−1.50918
$320$	32.6189	1.82345
$321$	0.588748	0.0328607
$322$	−5.87676	−0.327499
$323$	11.0644	0.615640
$324$	37.3348	2.07416
$325$	−0.349098	−0.0193644
$326$	−34.9801	−1.93737
$327$	−3.03581	−0.167881
$328$	30.5604	1.68741
$329$	29.8742	1.64702
$330$	8.56439	0.471454
$331$	−21.1315	−1.16149	−0.580745	−	0.814085i	$-0.697239\pi$
$331$	−21.1315	−1.16149	−0.580745	+	0.814085i	$0.697239\pi$
$332$	−79.2388	−4.34879
$333$	−11.6914	−0.640684
$334$	38.2687	2.09397
$335$	−23.1409	−1.26432
$336$	−18.6456	−1.01720
$337$	34.0027	1.85224	0.926122	−	0.377223i	$-0.123121\pi$
$337$	34.0027	1.85224	0.926122	+	0.377223i	$0.123121\pi$
$338$	28.7949	1.56624
$339$	2.78555	0.151291
$340$	−85.0048	−4.61003
$341$	−9.65408	−0.522798
$342$	−10.7581	−0.581733
$343$	1.07548	0.0580706
$344$	83.8867	4.52287
$345$	−0.548029	−0.0295049
$346$	20.0427	1.07750
$347$	4.07796	0.218916	0.109458	−	0.993991i	$-0.465088\pi$
$347$	4.07796	0.218916	0.109458	+	0.993991i	$0.465088\pi$
$348$	17.0148	0.912090
$349$	−10.9050	−0.583734	−0.291867	−	0.956459i	$-0.594276\pi$
$349$	−10.9050	−0.583734	−0.291867	+	0.956459i	$0.594276\pi$
$350$	2.38340	0.127398
$351$	3.67164	0.195978
$352$	−49.1274	−2.61850
$353$	31.1923	1.66020	0.830099	−	0.557616i	$-0.188284\pi$
$353$	31.1923	1.66020	0.830099	+	0.557616i	$0.188284\pi$
$354$	−1.54109	−0.0819081
$355$	20.2423	1.07435
$356$	62.3429	3.30417
$357$	12.4823	0.660636
$358$	27.4023	1.44825
$359$	17.8051	0.939717	0.469858	−	0.882742i	$-0.344305\pi$
$359$	17.8051	0.939717	0.469858	+	0.882742i	$0.344305\pi$
$360$	49.9925	2.63484
$361$	−16.9329	−0.891203
$362$	−17.3140	−0.910002
$363$	−0.361141	−0.0189550
$364$	28.1409	1.47498
$365$	32.0010	1.67501
$366$	5.74194	0.300136
$367$	37.7203	1.96898	0.984491	−	0.175433i	$-0.0561326\pi$
$367$	37.7203	1.96898	0.984491	+	0.175433i	$0.0561326\pi$
$368$	6.72636	0.350636
$369$	10.5777	0.550651
$370$	−24.0788	−1.25180
$371$	−9.06236	−0.470494
$372$	6.09400	0.315959
$373$	1.43395	0.0742469	0.0371234	−	0.999311i	$-0.488181\pi$
$373$	1.43395	0.0742469	0.0371234	+	0.999311i	$0.488181\pi$
$374$	70.3709	3.63879
$375$	4.90517	0.253302
$376$	−64.3039	−3.31622
$377$	−11.5229	−0.593460
$378$	−25.0675	−1.28933
$379$	−11.1453	−0.572495	−0.286247	−	0.958156i	$-0.592408\pi$
$379$	−11.1453	−0.572495	−0.286247	+	0.958156i	$0.592408\pi$
$380$	−15.8813	−0.814693
$381$	−2.92018	−0.149605
$382$	46.1863	2.36309
$383$	0.244016	0.0124686	0.00623431	−	0.999981i	$-0.498016\pi$
$383$	0.244016	0.0124686	0.00623431	+	0.999981i	$0.498016\pi$
$384$	4.79175	0.244528
$385$	28.3833	1.44655
$386$	20.2766	1.03205
$387$	29.0352	1.47594
$388$	73.5319	3.73302
$389$	−8.61448	−0.436771	−0.218386	−	0.975863i	$-0.570079\pi$
$389$	−8.61448	−0.436771	−0.218386	+	0.975863i	$0.570079\pi$
$390$	3.66119	0.185392
$391$	−4.50298	−0.227726
$392$	−59.2621	−2.99319
$393$	2.61756	0.132039
$394$	39.2381	1.97679
$395$	−4.34591	−0.218666
$396$	−49.0437	−2.46454
$397$	25.6755	1.28862	0.644308	−	0.764766i	$-0.277145\pi$
$397$	25.6755	1.28862	0.644308	+	0.764766i	$0.277145\pi$
$398$	−41.5120	−2.08081
$399$	2.33205	0.116749
$400$	−2.72797	−0.136399
$401$	−1.83209	−0.0914903	−0.0457452	−	0.998953i	$-0.514566\pi$
$401$	−1.83209	−0.0914903	−0.0457452	+	0.998953i	$0.514566\pi$
$402$	−12.0926	−0.603126
$403$	−4.12703	−0.205582
$404$	−73.0369	−3.63372
$405$	16.0978	0.799904
$406$	78.6707	3.90436
$407$	14.2878	0.708219
$408$	−26.8681	−1.33017
$409$	15.7422	0.778401	0.389201	−	0.921153i	$-0.372751\pi$
$409$	15.7422	0.778401	0.389201	+	0.921153i	$0.372751\pi$
$410$	21.7850	1.07589
$411$	2.14500	0.105805
$412$	−1.87528	−0.0923883
$413$	−5.10734	−0.251316
$414$	4.37834	0.215184
$415$	−34.1656	−1.67712
$416$	−21.0015	−1.02968
$417$	−3.12075	−0.152824
$418$	13.1473	0.643054
$419$	−18.0481	−0.881706	−0.440853	−	0.897579i	$-0.645324\pi$
$419$	−18.0481	−0.881706	−0.440853	+	0.897579i	$0.645324\pi$
$420$	−17.9165	−0.874238
$421$	7.18041	0.349952	0.174976	−	0.984573i	$-0.444015\pi$
$421$	7.18041	0.349952	0.174976	+	0.984573i	$0.444015\pi$
$422$	−37.0301	−1.80260
$423$	−22.2571	−1.08218
$424$	19.5066	0.947324
$425$	1.82625	0.0885861
$426$	10.5779	0.512501
$427$	19.0294	0.920897
$428$	−6.94359	−0.335631
$429$	−2.17247	−0.104888
$430$	59.7988	2.88376
$431$	27.4194	1.32074	0.660372	−	0.750939i	$-0.270399\pi$
$431$	27.4194	1.32074	0.660372	+	0.750939i	$0.270399\pi$
$432$	28.6915	1.38042
$433$	−6.12763	−0.294475	−0.147237	−	0.989101i	$-0.547038\pi$
$433$	−6.12763	−0.294475	−0.147237	+	0.989101i	$0.547038\pi$
$434$	28.1765	1.35252
$435$	7.33633	0.351750
$436$	35.8038	1.71469
$437$	−0.841284	−0.0402441
$438$	16.7226	0.799037
$439$	2.80007	0.133640	0.0668199	−	0.997765i	$-0.478715\pi$
$439$	2.80007	0.133640	0.0668199	+	0.997765i	$0.478715\pi$
$440$	−61.0947	−2.91257
$441$	−20.5120	−0.976762
$442$	30.0829	1.43090
$443$	−4.54948	−0.216152	−0.108076	−	0.994143i	$-0.534469\pi$
$443$	−4.54948	−0.216152	−0.108076	+	0.994143i	$0.534469\pi$
$444$	−9.01895	−0.428020
$445$	26.8806	1.27426
$446$	−50.0505	−2.36996
$447$	1.81309	0.0857564
$448$	56.4907	2.66894
$449$	19.2155	0.906834	0.453417	−	0.891299i	$-0.350205\pi$
$449$	19.2155	0.906834	0.453417	+	0.891299i	$0.350205\pi$
$450$	−1.77570	−0.0837072
$451$	−12.9267	−0.608695
$452$	−32.8523	−1.54524
$453$	9.04994	0.425203
$454$	−22.8741	−1.07354
$455$	12.1336	0.568831
$456$	−5.01971	−0.235070
$457$	6.43794	0.301154	0.150577	−	0.988598i	$-0.451887\pi$
$457$	6.43794	0.301154	0.150577	+	0.988598i	$0.451887\pi$
$458$	40.5299	1.89384
$459$	−19.2076	−0.896535
$460$	6.46336	0.301356
$461$	−30.1864	−1.40592	−0.702960	−	0.711230i	$-0.748139\pi$
$461$	−30.1864	−1.40592	−0.702960	+	0.711230i	$0.748139\pi$
$462$	14.8321	0.690053
$463$	−0.984062	−0.0457332	−0.0228666	−	0.999739i	$-0.507279\pi$
$463$	−0.984062	−0.0457332	−0.0228666	+	0.999739i	$0.507279\pi$
$464$	−90.0440	−4.18019
$465$	2.62757	0.121850
$466$	23.1550	1.07263
$467$	26.0737	1.20655	0.603273	−	0.797535i	$-0.293863\pi$
$467$	26.0737	1.20655	0.603273	+	0.797535i	$0.293863\pi$
$468$	−20.9657	−0.969140
$469$	−40.0763	−1.85055
$470$	−45.8391	−2.11440
$471$	8.84514	0.407562
$472$	10.9935	0.506016
$473$	−35.4832	−1.63152
$474$	−2.27102	−0.104312
$475$	0.341195	0.0156551
$476$	−147.215	−6.74757
$477$	6.75170	0.309139
$478$	8.62889	0.394676
$479$	−22.1640	−1.01270	−0.506350	−	0.862328i	$-0.669006\pi$
$479$	−22.1640	−1.01270	−0.506350	+	0.862328i	$0.669006\pi$
$480$	13.3711	0.610303
$481$	6.10789	0.278496
$482$	46.9017	2.13632
$483$	−0.949098	−0.0431854
$484$	4.25924	0.193602
$485$	31.7050	1.43965
$486$	28.3097	1.28415
$487$	−18.7234	−0.848437	−0.424218	−	0.905560i	$-0.639451\pi$
$487$	−18.7234	−0.848437	−0.424218	+	0.905560i	$0.639451\pi$
$488$	−40.9605	−1.85420
$489$	−5.64929	−0.255470
$490$	−42.2451	−1.90844
$491$	1.32691	0.0598826	0.0299413	−	0.999552i	$-0.490468\pi$
$491$	1.32691	0.0598826	0.0299413	+	0.999552i	$0.490468\pi$
$492$	8.15980	0.367872
$493$	60.2803	2.71489
$494$	5.62033	0.252870
$495$	−21.1463	−0.950456
$496$	−32.2500	−1.44807
$497$	35.0563	1.57249
$498$	−17.8538	−0.800047
$499$	−5.08872	−0.227802	−0.113901	−	0.993492i	$-0.536335\pi$
$499$	−5.08872	−0.227802	−0.113901	+	0.993492i	$0.536335\pi$
$500$	−57.8508	−2.58717
$501$	6.18041	0.276120
$502$	61.1195	2.72790
$503$	1.41095	0.0629110	0.0314555	−	0.999505i	$-0.489986\pi$
$503$	1.41095	0.0629110	0.0314555	+	0.999505i	$0.489986\pi$
$504$	86.5789	3.85653
$505$	−31.4915	−1.40135
$506$	−5.35067	−0.237866
$507$	4.65038	0.206531
$508$	34.4401	1.52803
$509$	−12.5729	−0.557283	−0.278642	−	0.960395i	$-0.589884\pi$
$509$	−12.5729	−0.557283	−0.278642	+	0.960395i	$0.589884\pi$
$510$	−19.1530	−0.848107
$511$	55.4205	2.45166
$512$	22.9235	1.01309
$513$	−3.58853	−0.158437
$514$	9.41278	0.415180
$515$	−0.808569	−0.0356298
$516$	22.3983	0.986029
$517$	27.1999	1.19625
$518$	−41.7005	−1.83222
$519$	3.23689	0.142084
$520$	−26.1174	−1.14532
$521$	35.3269	1.54770	0.773850	−	0.633368i	$-0.218328\pi$
$521$	35.3269	1.54770	0.773850	+	0.633368i	$0.218328\pi$
$522$	−58.6117	−2.56536
$523$	−35.9092	−1.57020	−0.785101	−	0.619368i	$-0.787389\pi$
$523$	−35.9092	−1.57020	−0.785101	+	0.619368i	$0.787389\pi$
$524$	−30.8711	−1.34861
$525$	0.384920	0.0167993
$526$	−4.82623	−0.210433
$527$	21.5899	0.940470
$528$	−16.9764	−0.738804
$529$	−22.6576	−0.985114
$530$	13.9053	0.604008
$531$	3.80510	0.165127
$532$	−27.5038	−1.19244
$533$	−5.52605	−0.239360
$534$	14.0469	0.607867
$535$	−2.99389	−0.129437
$536$	86.2636	3.72602
$537$	4.42547	0.190973
$538$	−53.8897	−2.32335
$539$	25.0672	1.07972
$540$	27.5697	1.18641
$541$	25.9068	1.11382	0.556910	−	0.830573i	$-0.311987\pi$
$541$	25.9068	1.11382	0.556910	+	0.830573i	$0.311987\pi$
$542$	59.8879	2.57241
$543$	−2.79621	−0.119997
$544$	109.866	4.71046
$545$	15.4376	0.661276
$546$	6.34059	0.271352
$547$	39.2652	1.67886	0.839428	−	0.543470i	$-0.182890\pi$
$547$	39.2652	1.67886	0.839428	+	0.543470i	$0.182890\pi$
$548$	−25.2977	−1.08066
$549$	−14.1774	−0.605077
$550$	2.17004	0.0925308
$551$	11.2621	0.479779
$552$	2.04292	0.0869524
$553$	−7.52641	−0.320056
$554$	−5.97835	−0.253996
$555$	−3.88873	−0.165067
$556$	36.8055	1.56090
$557$	−17.8436	−0.756059	−0.378030	−	0.925793i	$-0.623398\pi$
$557$	−17.8436	−0.756059	−0.378030	+	0.925793i	$0.623398\pi$
$558$	−20.9923	−0.888674
$559$	−15.1687	−0.641569
$560$	94.8161	4.00671
$561$	11.3649	0.479827
$562$	48.6632	2.05273
$563$	−37.6903	−1.58846	−0.794228	−	0.607620i	$-0.792124\pi$
$563$	−37.6903	−1.58846	−0.794228	+	0.607620i	$0.792124\pi$
$564$	−17.1695	−0.722967
$565$	−14.1650	−0.595928
$566$	76.8427	3.22994
$567$	27.8787	1.17080
$568$	−75.4583	−3.16616
$569$	34.1977	1.43364	0.716821	−	0.697258i	$-0.245597\pi$
$569$	34.1977	1.43364	0.716821	+	0.697258i	$0.245597\pi$
$570$	−3.57831	−0.149879
$571$	−46.7319	−1.95567	−0.977834	−	0.209382i	$-0.932855\pi$
$571$	−46.7319	−1.95567	−0.977834	+	0.209382i	$0.932855\pi$
$572$	25.6217	1.07130
$573$	7.45909	0.311608
$574$	37.7281	1.57474
$575$	−0.138859	−0.00579083
$576$	−42.0871	−1.75363
$577$	−15.4558	−0.643431	−0.321716	−	0.946836i	$-0.604260\pi$
$577$	−15.4558	−0.643431	−0.321716	+	0.946836i	$0.604260\pi$
$578$	−112.199	−4.66686
$579$	3.27468	0.136091
$580$	−86.5234	−3.59269
$581$	−59.1693	−2.45476
$582$	16.5679	0.686763
$583$	−8.25109	−0.341725
$584$	−119.292	−4.93633
$585$	−9.03984	−0.373751
$586$	−43.8970	−1.81337
$587$	−40.1485	−1.65711	−0.828553	−	0.559911i	$-0.810835\pi$
$587$	−40.1485	−1.65711	−0.828553	+	0.559911i	$0.810835\pi$
$588$	−15.8233	−0.652543
$589$	4.03360	0.166201
$590$	7.83672	0.322633
$591$	6.33696	0.260668
$592$	47.7292	1.96166
$593$	−27.1224	−1.11378	−0.556892	−	0.830585i	$-0.688006\pi$
$593$	−27.1224	−1.11378	−0.556892	+	0.830585i	$0.688006\pi$
$594$	−22.8235	−0.936458
$595$	−63.4749	−2.60222
$596$	−21.3833	−0.875895
$597$	−6.70420	−0.274385
$598$	−2.28736	−0.0935370
$599$	17.8560	0.729575	0.364787	−	0.931091i	$-0.381142\pi$
$599$	17.8560	0.729575	0.364787	+	0.931091i	$0.381142\pi$
$600$	−0.828535	−0.0338248
$601$	5.28742	0.215678	0.107839	−	0.994168i	$-0.465607\pi$
$601$	5.28742	0.215678	0.107839	+	0.994168i	$0.465607\pi$
$602$	103.562	4.22087
$603$	29.8579	1.21591
$604$	−106.733	−4.34292
$605$	1.83647	0.0746630
$606$	−16.4564	−0.668495
$607$	5.55615	0.225517	0.112759	−	0.993622i	$-0.464031\pi$
$607$	5.55615	0.225517	0.112759	+	0.993622i	$0.464031\pi$
$608$	20.5260	0.832441
$609$	12.7053	0.514846
$610$	−29.1988	−1.18222
$611$	11.6277	0.470406
$612$	109.679	4.43350
$613$	31.3736	1.26717	0.633584	−	0.773674i	$-0.281583\pi$
$613$	31.3736	1.26717	0.633584	+	0.773674i	$0.281583\pi$
$614$	53.4024	2.15515
$615$	3.51828	0.141871
$616$	−105.806	−4.26305
$617$	−41.2963	−1.66253	−0.831264	−	0.555878i	$-0.812382\pi$
$617$	−41.2963	−1.66253	−0.831264	+	0.555878i	$0.812382\pi$
$618$	−0.422530	−0.0169967
$619$	24.4700	0.983533	0.491767	−	0.870727i	$-0.336351\pi$
$619$	24.4700	0.983533	0.491767	+	0.870727i	$0.336351\pi$
$620$	−30.9891	−1.24455
$621$	1.46046	0.0586061
$622$	73.6343	2.95247
$623$	46.5528	1.86510
$624$	−7.25725	−0.290523
$625$	−23.7571	−0.950285
$626$	22.7850	0.910672
$627$	2.12329	0.0847959
$628$	−104.318	−4.16274
$629$	−31.9524	−1.27403
$630$	61.7179	2.45890
$631$	−20.7714	−0.826897	−0.413448	−	0.910528i	$-0.635676\pi$
$631$	−20.7714	−0.826897	−0.413448	+	0.910528i	$0.635676\pi$
$632$	16.2005	0.644421
$633$	−5.98037	−0.237698
$634$	−54.1231	−2.14950
$635$	14.8496	0.589290
$636$	5.20838	0.206526
$637$	10.7160	0.424583
$638$	71.6280	2.83578
$639$	−26.1179	−1.03321
$640$	−24.3669	−0.963187
$641$	−33.4802	−1.32239	−0.661194	−	0.750215i	$-0.729950\pi$
$641$	−33.4802	−1.32239	−0.661194	+	0.750215i	$0.729950\pi$
$642$	−1.56450	−0.0617460
$643$	−11.3416	−0.447268	−0.223634	−	0.974673i	$-0.571792\pi$
$643$	−11.3416	−0.447268	−0.223634	+	0.974673i	$0.571792\pi$
$644$	11.1935	0.441086
$645$	9.65752	0.380265
$646$	−29.4018	−1.15680
$647$	7.97320	0.313459	0.156729	−	0.987642i	$-0.449905\pi$
$647$	7.97320	0.313459	0.156729	+	0.987642i	$0.449905\pi$
$648$	−60.0085	−2.35736
$649$	−4.65013	−0.182534
$650$	0.927670	0.0363862
$651$	4.55052	0.178349
$652$	66.6267	2.60930
$653$	38.0636	1.48954	0.744772	−	0.667319i	$-0.232558\pi$
$653$	38.0636	1.48954	0.744772	+	0.667319i	$0.232558\pi$
$654$	8.06718	0.315452
$655$	−13.3108	−0.520095
$656$	−43.1825	−1.68599
$657$	−41.2897	−1.61087
$658$	−79.3860	−3.09479
$659$	2.76718	0.107794	0.0538971	−	0.998546i	$-0.482836\pi$
$659$	2.76718	0.107794	0.0538971	+	0.998546i	$0.482836\pi$
$660$	−16.3126	−0.634969
$661$	−40.2516	−1.56561	−0.782803	−	0.622269i	$-0.786211\pi$
$661$	−40.2516	−1.56561	−0.782803	+	0.622269i	$0.786211\pi$
$662$	56.1535	2.18247
$663$	4.85839	0.188684
$664$	127.361	4.94257
$665$	−11.8589	−0.459869
$666$	31.0680	1.20386
$667$	−4.58342	−0.177471
$668$	−72.8906	−2.82022
$669$	−8.08316	−0.312513
$670$	61.4932	2.37569
$671$	17.3259	0.668858
$672$	23.1565	0.893283
$673$	23.4295	0.903141	0.451570	−	0.892236i	$-0.350864\pi$
$673$	23.4295	0.903141	0.451570	+	0.892236i	$0.350864\pi$
$674$	−90.3567	−3.48041
$675$	−0.592309	−0.0227980
$676$	−54.8458	−2.10945
$677$	19.6900	0.756747	0.378373	−	0.925653i	$-0.376484\pi$
$677$	19.6900	0.756747	0.378373	+	0.925653i	$0.376484\pi$
$678$	−7.40216	−0.284278
$679$	54.9079	2.10717
$680$	136.629	5.23948
$681$	−3.69418	−0.141561
$682$	25.6542	0.982349
$683$	25.2641	0.966704	0.483352	−	0.875426i	$-0.339419\pi$
$683$	25.2641	0.966704	0.483352	+	0.875426i	$0.339419\pi$
$684$	20.4911	0.783496
$685$	−10.9077	−0.416761
$686$	−2.85792	−0.109116
$687$	6.54559	0.249730
$688$	−118.534	−4.51906
$689$	−3.52726	−0.134378
$690$	1.45630	0.0554404
$691$	−32.7818	−1.24708	−0.623540	−	0.781792i	$-0.714306\pi$
$691$	−32.7818	−1.24708	−0.623540	+	0.781792i	$0.714306\pi$
$692$	−38.1754	−1.45121
$693$	−36.6220	−1.39115
$694$	−10.8365	−0.411348
$695$	15.8695	0.601966
$696$	−27.3480	−1.03662
$697$	28.9086	1.09499
$698$	28.9784	1.09685
$699$	3.73953	0.141442
$700$	−4.53968	−0.171584
$701$	−6.21125	−0.234596	−0.117298	−	0.993097i	$-0.537423\pi$
$701$	−6.21125	−0.234596	−0.117298	+	0.993097i	$0.537423\pi$
$702$	−9.75680	−0.368247
$703$	−5.96961	−0.225148
$704$	51.4336	1.93848
$705$	−7.40303	−0.278814
$706$	−82.8885	−3.11955
$707$	−54.5382	−2.05112
$708$	2.93533	0.110316
$709$	6.08052	0.228359	0.114179	−	0.993460i	$-0.463576\pi$
$709$	6.08052	0.228359	0.114179	+	0.993460i	$0.463576\pi$
$710$	−53.7906	−2.01872
$711$	5.60737	0.210293
$712$	−100.204	−3.75531
$713$	−1.64159	−0.0614781
$714$	−33.1698	−1.24135
$715$	11.0474	0.413149
$716$	−52.1932	−1.95055
$717$	1.39357	0.0520437
$718$	−47.3141	−1.76575
$719$	−20.6543	−0.770277	−0.385139	−	0.922859i	$-0.625846\pi$
$719$	−20.6543	−0.770277	−0.385139	+	0.922859i	$0.625846\pi$
$720$	−70.6405	−2.63262
$721$	−1.40031	−0.0521503
$722$	44.9963	1.67459
$723$	7.57464	0.281704
$724$	32.9780	1.22562
$725$	1.85887	0.0690368
$726$	0.959675	0.0356169
$727$	28.1315	1.04334	0.521670	−	0.853148i	$-0.325309\pi$
$727$	28.1315	1.04334	0.521670	+	0.853148i	$0.325309\pi$
$728$	−45.2311	−1.67637
$729$	−17.5569	−0.650256
$730$	−85.0374	−3.14738
$731$	79.3528	2.93497
$732$	−10.9367	−0.404232
$733$	−51.9599	−1.91918	−0.959592	−	0.281394i	$-0.909203\pi$
$733$	−51.9599	−1.91918	−0.959592	+	0.281394i	$0.909203\pi$
$734$	−100.236	−3.69976
$735$	−6.82259	−0.251655
$736$	−8.35368	−0.307921
$737$	−36.4886	−1.34408
$738$	−28.1084	−1.03469
$739$	23.2249	0.854344	0.427172	−	0.904170i	$-0.359510\pi$
$739$	23.2249	0.854344	0.427172	+	0.904170i	$0.359510\pi$
$740$	45.8630	1.68596
$741$	0.907684	0.0333446
$742$	24.0818	0.884069
$743$	−20.7796	−0.762331	−0.381166	−	0.924507i	$-0.624477\pi$
$743$	−20.7796	−0.762331	−0.381166	+	0.924507i	$0.624477\pi$
$744$	−9.79493	−0.359099
$745$	−9.21991	−0.337791
$746$	−3.81048	−0.139512
$747$	44.0827	1.61290
$748$	−134.036	−4.90084
$749$	−5.18493	−0.189453
$750$	−13.0347	−0.475960
$751$	−43.9076	−1.60221	−0.801106	−	0.598523i	$-0.795755\pi$
$751$	−43.9076	−1.60221	−0.801106	+	0.598523i	$0.795755\pi$
$752$	90.8628	3.31342
$753$	9.87081	0.359712
$754$	30.6203	1.11512
$755$	−46.0205	−1.67486
$756$	47.7462	1.73651
$757$	9.59074	0.348581	0.174291	−	0.984694i	$-0.444237\pi$
$757$	9.59074	0.348581	0.174291	+	0.984694i	$0.444237\pi$
$758$	29.6168	1.07573
$759$	−0.864134	−0.0313661
$760$	25.5261	0.925930
$761$	16.9363	0.613939	0.306969	−	0.951719i	$-0.400685\pi$
$761$	16.9363	0.613939	0.306969	+	0.951719i	$0.400685\pi$
$762$	7.75991	0.281112
$763$	26.7355	0.967890
$764$	−87.9712	−3.18269
$765$	47.2905	1.70979
$766$	−0.648432	−0.0234288
$767$	−1.98788	−0.0717783
$768$	0.0957230	0.00345411
$769$	45.1294	1.62741	0.813704	−	0.581279i	$-0.197448\pi$
$769$	45.1294	1.62741	0.813704	+	0.581279i	$0.197448\pi$
$770$	−75.4241	−2.71809
$771$	1.52017	0.0547474
$772$	−38.6210	−1.39000
$773$	22.5774	0.812053	0.406027	−	0.913861i	$-0.366914\pi$
$773$	22.5774	0.812053	0.406027	+	0.913861i	$0.366914\pi$
$774$	−77.1563	−2.77333
$775$	0.665771	0.0239152
$776$	−118.188	−4.24272
$777$	−6.73464	−0.241604
$778$	22.8916	0.820703
$779$	5.40095	0.193509
$780$	−6.97350	−0.249691
$781$	31.9181	1.14212
$782$	11.9660	0.427902
$783$	−19.5508	−0.698687
$784$	83.7386	2.99066
$785$	−44.9791	−1.60537
$786$	−6.95576	−0.248104
$787$	−31.2274	−1.11313	−0.556567	−	0.830802i	$-0.687882\pi$
$787$	−31.2274	−1.11313	−0.556567	+	0.830802i	$0.687882\pi$
$788$	−74.7370	−2.66240
$789$	−0.779436	−0.0277487
$790$	11.5486	0.410879
$791$	−24.5316	−0.872242
$792$	78.8283	2.80104
$793$	7.40664	0.263018
$794$	−68.2285	−2.42134
$795$	2.24571	0.0796472
$796$	79.0681	2.80250
$797$	1.47034	0.0520820	0.0260410	−	0.999661i	$-0.491710\pi$
$797$	1.47034	0.0520820	0.0260410	+	0.999661i	$0.491710\pi$
$798$	−6.19705	−0.219373
$799$	−60.8284	−2.15195
$800$	3.38795	0.119782
$801$	−34.6831	−1.22547
$802$	4.86849	0.171912
$803$	50.4592	1.78067
$804$	23.0329	0.812308
$805$	4.82633	0.170106
$806$	10.9669	0.386293
$807$	−8.70320	−0.306367
$808$	117.393	4.12986
$809$	−16.4166	−0.577176	−0.288588	−	0.957453i	$-0.593186\pi$
$809$	−16.4166	−0.577176	−0.288588	+	0.957453i	$0.593186\pi$
$810$	−42.7772	−1.50304
$811$	21.4925	0.754705	0.377353	−	0.926070i	$-0.376835\pi$
$811$	21.4925	0.754705	0.377353	+	0.926070i	$0.376835\pi$
$812$	−149.844	−5.25851
$813$	9.67191	0.339209
$814$	−37.9675	−1.33076
$815$	28.7276	1.00628
$816$	37.9652	1.32905
$817$	14.8253	0.518673
$818$	−41.8323	−1.46263
$819$	−15.6555	−0.547049
$820$	−41.4940	−1.44903
$821$	−19.2734	−0.672647	−0.336324	−	0.941746i	$-0.609184\pi$
$821$	−19.2734	−0.672647	−0.336324	+	0.941746i	$0.609184\pi$
$822$	−5.69998	−0.198810
$823$	12.5761	0.438377	0.219188	−	0.975683i	$-0.429659\pi$
$823$	12.5761	0.438377	0.219188	+	0.975683i	$0.429659\pi$
$824$	3.01415	0.105003
$825$	0.350462	0.0122015
$826$	13.5719	0.472228
$827$	−16.8524	−0.586017	−0.293008	−	0.956110i	$-0.594656\pi$
$827$	−16.8524	−0.586017	−0.293008	+	0.956110i	$0.594656\pi$
$828$	−8.33945	−0.289816
$829$	−40.7833	−1.41646	−0.708231	−	0.705981i	$-0.750507\pi$
$829$	−40.7833	−1.41646	−0.708231	+	0.705981i	$0.750507\pi$
$830$	90.7896	3.15135
$831$	−0.965504	−0.0334930
$832$	21.9874	0.762275
$833$	−56.0591	−1.94233
$834$	8.29288	0.287159
$835$	−31.4285	−1.08763
$836$	−25.0417	−0.866084
$837$	−7.00227	−0.242034
$838$	47.9598	1.65675
$839$	−8.83865	−0.305144	−0.152572	−	0.988292i	$-0.548756\pi$
$839$	−8.83865	−0.305144	−0.152572	+	0.988292i	$0.548756\pi$
$840$	28.7974	0.993605
$841$	32.3571	1.11576
$842$	−19.0808	−0.657567
$843$	7.85911	0.270682
$844$	70.5315	2.42779
$845$	−23.6480	−0.813516
$846$	59.1446	2.03343
$847$	3.18047	0.109282
$848$	−27.5632	−0.946526
$849$	12.4101	0.425914
$850$	−4.85296	−0.166455
$851$	2.42951	0.0832826
$852$	−20.1478	−0.690253
$853$	−39.8595	−1.36476	−0.682382	−	0.730995i	$-0.739056\pi$
$853$	−39.8595	−1.36476	−0.682382	+	0.730995i	$0.739056\pi$
$854$	−50.5675	−1.73039
$855$	8.83520	0.302157
$856$	11.1605	0.381457
$857$	−50.0094	−1.70829	−0.854144	−	0.520037i	$-0.825918\pi$
$857$	−50.0094	−1.70829	−0.854144	+	0.520037i	$0.825918\pi$
$858$	5.77298	0.197086
$859$	19.9154	0.679506	0.339753	−	0.940515i	$-0.389657\pi$
$859$	19.9154	0.679506	0.339753	+	0.940515i	$0.389657\pi$
$860$	−113.899	−3.88393
$861$	6.09310	0.207652
$862$	−72.8625	−2.48171
$863$	32.5698	1.10869	0.554344	−	0.832288i	$-0.312969\pi$
$863$	32.5698	1.10869	0.554344	+	0.832288i	$0.312969\pi$
$864$	−35.6329	−1.21226
$865$	−16.4602	−0.559663
$866$	16.2832	0.553325
$867$	−18.1202	−0.615393
$868$	−53.6680	−1.82161
$869$	−6.85264	−0.232460
$870$	−19.4951	−0.660946
$871$	−15.5985	−0.528536
$872$	−57.5478	−1.94881
$873$	−40.9078	−1.38452
$874$	2.23558	0.0756195
$875$	−43.1984	−1.46037
$876$	−31.8516	−1.07617
$877$	27.1156	0.915630	0.457815	−	0.889048i	$-0.348632\pi$
$877$	27.1156	0.915630	0.457815	+	0.889048i	$0.348632\pi$
$878$	−7.44072	−0.251112
$879$	−7.08938	−0.239119
$880$	86.3281	2.91012
$881$	−55.0255	−1.85386	−0.926928	−	0.375239i	$-0.877561\pi$
$881$	−55.0255	−1.85386	−0.926928	+	0.375239i	$0.877561\pi$
$882$	54.5074	1.83536
$883$	21.6560	0.728783	0.364391	−	0.931246i	$-0.381277\pi$
$883$	21.6560	0.728783	0.364391	+	0.931246i	$0.381277\pi$
$884$	−57.2990	−1.92717
$885$	1.26563	0.0425438
$886$	12.0895	0.406155
$887$	28.6557	0.962165	0.481082	−	0.876675i	$-0.340244\pi$
$887$	28.6557	0.962165	0.481082	+	0.876675i	$0.340244\pi$
$888$	14.4962	0.486462
$889$	25.7172	0.862526
$890$	−71.4308	−2.39437
$891$	25.3830	0.850362
$892$	95.3314	3.19193
$893$	−11.3645	−0.380297
$894$	−4.81800	−0.161138
$895$	−22.5043	−0.752236
$896$	−42.1995	−1.40979
$897$	−0.369409	−0.0123342
$898$	−51.0620	−1.70396
$899$	21.9756	0.732926
$900$	3.38218	0.112739
$901$	18.4523	0.614735
$902$	34.3507	1.14375
$903$	16.7253	0.556582
$904$	52.8038	1.75623
$905$	14.2192	0.472663
$906$	−24.0487	−0.798966
$907$	39.3347	1.30609	0.653044	−	0.757320i	$-0.273492\pi$
$907$	39.3347	1.30609	0.653044	+	0.757320i	$0.273492\pi$
$908$	43.5685	1.44587
$909$	40.6324	1.34769
$910$	−32.2430	−1.06885
$911$	−28.8575	−0.956093	−0.478046	−	0.878335i	$-0.658655\pi$
$911$	−28.8575	−0.956093	−0.478046	+	0.878335i	$0.658655\pi$
$912$	7.09296	0.234871
$913$	−53.8724	−1.78292
$914$	−17.1078	−0.565875
$915$	−4.71561	−0.155893
$916$	−77.1975	−2.55068
$917$	−23.0521	−0.761248
$918$	51.0412	1.68461
$919$	−17.7542	−0.585656	−0.292828	−	0.956165i	$-0.594596\pi$
$919$	−17.7542	−0.585656	−0.292828	+	0.956165i	$0.594596\pi$
$920$	−10.3886	−0.342502
$921$	8.62450	0.284187
$922$	80.2154	2.64175
$923$	13.6447	0.449119
$924$	−28.2509	−0.929385
$925$	−0.985322	−0.0323972
$926$	2.61499	0.0859338
$927$	1.04327	0.0342654
$928$	111.829	3.67095
$929$	49.8725	1.63626	0.818132	−	0.575031i	$-0.195010\pi$
$929$	49.8725	1.63626	0.818132	+	0.575031i	$0.195010\pi$
$930$	−6.98233	−0.228960
$931$	−10.4734	−0.343252
$932$	−44.1034	−1.44465
$933$	11.8920	0.389325
$934$	−69.2866	−2.26713
$935$	−57.7926	−1.89002
$936$	33.6983	1.10146
$937$	−43.5376	−1.42231	−0.711155	−	0.703035i	$-0.751828\pi$
$937$	−43.5376	−1.42231	−0.711155	+	0.703035i	$0.751828\pi$
$938$	106.496	3.47723
$939$	3.67978	0.120085
$940$	87.3101	2.84774
$941$	−49.3079	−1.60739	−0.803696	−	0.595041i	$-0.797136\pi$
$941$	−49.3079	−1.60739	−0.803696	+	0.595041i	$0.797136\pi$
$942$	−23.5045	−0.765819
$943$	−2.19807	−0.0715791
$944$	−15.5340	−0.505589
$945$	20.5869	0.669691
$946$	94.2909	3.06566
$947$	−57.2850	−1.86151	−0.930757	−	0.365639i	$-0.880850\pi$
$947$	−57.2850	−1.86151	−0.930757	+	0.365639i	$0.880850\pi$
$948$	4.32563	0.140490
$949$	21.5708	0.700219
$950$	−0.906669	−0.0294162
$951$	−8.74089	−0.283443
$952$	236.619	7.66887
$953$	30.5374	0.989203	0.494601	−	0.869120i	$-0.335314\pi$
$953$	30.5374	0.989203	0.494601	+	0.869120i	$0.335314\pi$
$954$	−17.9415	−0.580879
$955$	−37.9308	−1.22741
$956$	−16.4355	−0.531562
$957$	11.5679	0.373938
$958$	58.8974	1.90289
$959$	−18.8903	−0.610001
$960$	−13.9988	−0.451808
$961$	−23.1293	−0.746105
$962$	−16.2307	−0.523299
$963$	3.86291	0.124480
$964$	−89.3340	−2.87725
$965$	−16.6523	−0.536057
$966$	2.52207	0.0811464
$967$	21.8319	0.702065	0.351033	−	0.936363i	$-0.385831\pi$
$967$	21.8319	0.702065	0.351033	+	0.936363i	$0.385831\pi$
$968$	−6.84591	−0.220036
$969$	−4.74841	−0.152541
$970$	−84.2508	−2.70513
$971$	−49.7417	−1.59629	−0.798143	−	0.602468i	$-0.794184\pi$
$971$	−49.7417	−1.59629	−0.798143	+	0.602468i	$0.794184\pi$
$972$	−53.9216	−1.72954
$973$	27.4835	0.881080
$974$	49.7543	1.59423
$975$	0.149819	0.00479805
$976$	57.8781	1.85263
$977$	−29.2594	−0.936090	−0.468045	−	0.883705i	$-0.655042\pi$
$977$	−29.2594	−0.936090	−0.468045	+	0.883705i	$0.655042\pi$
$978$	15.0121	0.480033
$979$	42.3854	1.35464
$980$	80.4645	2.57034
$981$	−19.9186	−0.635953
$982$	−3.52605	−0.112521
$983$	24.1718	0.770960	0.385480	−	0.922716i	$-0.374036\pi$
$983$	24.1718	0.770960	0.385480	+	0.922716i	$0.374036\pi$
$984$	−13.1153	−0.418101
$985$	−32.2246	−1.02676
$986$	−160.185	−5.10133
$987$	−12.8209	−0.408092
$988$	−10.7051	−0.340574
$989$	−6.03361	−0.191858
$990$	56.1929	1.78593
$991$	−24.4644	−0.777137	−0.388568	−	0.921420i	$-0.627030\pi$
$991$	−24.4644	−0.777137	−0.388568	+	0.921420i	$0.627030\pi$
$992$	40.0523	1.27166
$993$	9.06880	0.287790
$994$	−93.1565	−2.95475
$995$	34.0920	1.08079
$996$	34.0062	1.07753
$997$	50.7766	1.60811	0.804055	−	0.594555i	$-0.202672\pi$
$997$	50.7766	1.60811	0.804055	+	0.594555i	$0.202672\pi$
$998$	13.5224	0.428046
$999$	10.3632	0.327876

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.a.1.13	✓	309

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

\(f(q)\)	\(=\)	\(q-2.65734 q^{2} -0.429161 q^{3} +5.06145 q^{4} +2.18236 q^{5} +1.14043 q^{6} +3.77949 q^{7} -8.13530 q^{8} -2.81582 q^{9} +O(q^{10})\)	\(q-2.65734 q^{2} -0.429161 q^{3} +5.06145 q^{4} +2.18236 q^{5} +1.14043 q^{6} +3.77949 q^{7} -8.13530 q^{8} -2.81582 q^{9} -5.79927 q^{10} +3.44115 q^{11} -2.17217 q^{12} +1.47106 q^{13} -10.0434 q^{14} -0.936583 q^{15} +11.4954 q^{16} -7.69561 q^{17} +7.48259 q^{18} -1.43776 q^{19} +11.0459 q^{20} -1.62201 q^{21} -9.14430 q^{22} +0.585137 q^{23} +3.49135 q^{24} -0.237311 q^{25} -3.90910 q^{26} +2.49592 q^{27} +19.1297 q^{28} -7.83308 q^{29} +2.48882 q^{30} -2.80548 q^{31} -14.2765 q^{32} -1.47681 q^{33} +20.4498 q^{34} +8.24821 q^{35} -14.2521 q^{36} +4.15204 q^{37} +3.82060 q^{38} -0.631320 q^{39} -17.7541 q^{40} -3.75651 q^{41} +4.31023 q^{42} -10.3114 q^{43} +17.4172 q^{44} -6.14513 q^{45} -1.55491 q^{46} +7.90430 q^{47} -4.93336 q^{48} +7.28456 q^{49} +0.630615 q^{50} +3.30265 q^{51} +7.44568 q^{52} -2.39777 q^{53} -6.63251 q^{54} +7.50982 q^{55} -30.7473 q^{56} +0.617028 q^{57} +20.8151 q^{58} -1.35133 q^{59} -4.74046 q^{60} +5.03491 q^{61} +7.45512 q^{62} -10.6424 q^{63} +14.9466 q^{64} +3.21038 q^{65} +3.92437 q^{66} -10.6036 q^{67} -38.9509 q^{68} -0.251118 q^{69} -21.9183 q^{70} +9.27541 q^{71} +22.9076 q^{72} +14.6635 q^{73} -11.0334 q^{74} +0.101844 q^{75} -7.27712 q^{76} +13.0058 q^{77} +1.67763 q^{78} -1.99138 q^{79} +25.0870 q^{80} +7.37631 q^{81} +9.98232 q^{82} -15.6554 q^{83} -8.20972 q^{84} -16.7946 q^{85} +27.4010 q^{86} +3.36165 q^{87} -27.9948 q^{88} +12.3172 q^{89} +16.3297 q^{90} +5.55985 q^{91} +2.96164 q^{92} +1.20400 q^{93} -21.0044 q^{94} -3.13770 q^{95} +6.12689 q^{96} +14.5278 q^{97} -19.3575 q^{98} -9.68966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) \) 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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