LMFDB - Embedded newform 8011.2.a.b.1.7

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			1.7
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)

$f(q)$	$=$	$q-2.69935 q^{2} +1.61559 q^{3} +5.28646 q^{4} +2.80670 q^{5} -4.36103 q^{6} +2.73763 q^{7} -8.87130 q^{8} -0.389878 q^{9} +O(q^{10})$	\(q-2.69935 q^{2} +1.61559 q^{3} +5.28646 q^{4} +2.80670 q^{5} -4.36103 q^{6} +2.73763 q^{7} -8.87130 q^{8} -0.389878 q^{9} -7.57626 q^{10} +3.22381 q^{11} +8.54074 q^{12} +4.46543 q^{13} -7.38981 q^{14} +4.53447 q^{15} +13.3738 q^{16} +5.42508 q^{17} +1.05242 q^{18} -2.28573 q^{19} +14.8375 q^{20} +4.42288 q^{21} -8.70217 q^{22} -6.19782 q^{23} -14.3324 q^{24} +2.87757 q^{25} -12.0537 q^{26} -5.47664 q^{27} +14.4724 q^{28} +0.0185387 q^{29} -12.2401 q^{30} +5.36769 q^{31} -18.3578 q^{32} +5.20834 q^{33} -14.6442 q^{34} +7.68372 q^{35} -2.06108 q^{36} -7.87298 q^{37} +6.16997 q^{38} +7.21429 q^{39} -24.8991 q^{40} +2.29163 q^{41} -11.9389 q^{42} -0.973599 q^{43} +17.0425 q^{44} -1.09427 q^{45} +16.7301 q^{46} +9.69254 q^{47} +21.6065 q^{48} +0.494627 q^{49} -7.76757 q^{50} +8.76469 q^{51} +23.6063 q^{52} -7.73306 q^{53} +14.7834 q^{54} +9.04826 q^{55} -24.2864 q^{56} -3.69279 q^{57} -0.0500423 q^{58} +12.1987 q^{59} +23.9713 q^{60} -10.2477 q^{61} -14.4893 q^{62} -1.06734 q^{63} +22.8066 q^{64} +12.5331 q^{65} -14.0591 q^{66} +6.76491 q^{67} +28.6795 q^{68} -10.0131 q^{69} -20.7410 q^{70} +15.3486 q^{71} +3.45873 q^{72} -5.09820 q^{73} +21.2519 q^{74} +4.64897 q^{75} -12.0834 q^{76} +8.82559 q^{77} -19.4739 q^{78} -5.64660 q^{79} +37.5362 q^{80} -7.67836 q^{81} -6.18591 q^{82} -5.87421 q^{83} +23.3814 q^{84} +15.2266 q^{85} +2.62808 q^{86} +0.0299509 q^{87} -28.5994 q^{88} +0.696095 q^{89} +2.95382 q^{90} +12.2247 q^{91} -32.7646 q^{92} +8.67198 q^{93} -26.1635 q^{94} -6.41536 q^{95} -29.6587 q^{96} +8.33689 q^{97} -1.33517 q^{98} -1.25689 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.69935	−1.90873	−0.954363	−	0.298650i	$-0.903464\pi$
$2$	−2.69935	−1.90873	−0.954363	+	0.298650i	$0.903464\pi$
$3$	1.61559	0.932760	0.466380	−	0.884585i	$-0.345558\pi$
$3$	1.61559	0.932760	0.466380	+	0.884585i	$0.345558\pi$
$4$	5.28646	2.64323
$5$	2.80670	1.25520	0.627598	−	0.778538i	$-0.284038\pi$
$5$	2.80670	1.25520	0.627598	+	0.778538i	$0.284038\pi$
$6$	−4.36103	−1.78038
$7$	2.73763	1.03473	0.517364	−	0.855766i	$-0.326913\pi$
$7$	2.73763	1.03473	0.517364	+	0.855766i	$0.326913\pi$
$8$	−8.87130	−3.13648
$9$	−0.389878	−0.129959
$10$	−7.57626	−2.39582
$11$	3.22381	0.972014	0.486007	−	0.873955i	$-0.338453\pi$
$11$	3.22381	0.972014	0.486007	+	0.873955i	$0.338453\pi$
$12$	8.54074	2.46550
$13$	4.46543	1.23849	0.619244	−	0.785199i	$-0.287439\pi$
$13$	4.46543	1.23849	0.619244	+	0.785199i	$0.287439\pi$
$14$	−7.38981	−1.97501
$15$	4.53447	1.17080
$16$	13.3738	3.34344
$17$	5.42508	1.31578	0.657888	−	0.753116i	$-0.271450\pi$
$17$	5.42508	1.31578	0.657888	+	0.753116i	$0.271450\pi$
$18$	1.05242	0.248057
$19$	−2.28573	−0.524382	−0.262191	−	0.965016i	$-0.584445\pi$
$19$	−2.28573	−0.524382	−0.262191	+	0.965016i	$0.584445\pi$
$20$	14.8375	3.31777
$21$	4.42288	0.965152
$22$	−8.70217	−1.85531
$23$	−6.19782	−1.29234	−0.646168	−	0.763195i	$-0.723629\pi$
$23$	−6.19782	−1.29234	−0.646168	+	0.763195i	$0.723629\pi$
$24$	−14.3324	−2.92558
$25$	2.87757	0.575515
$26$	−12.0537	−2.36393
$27$	−5.47664	−1.05398
$28$	14.4724	2.73503
$29$	0.0185387	0.00344255	0.00172127	−	0.999999i	$-0.499452\pi$
$29$	0.0185387	0.00344255	0.00172127	+	0.999999i	$0.499452\pi$
$30$	−12.2401	−2.23473
$31$	5.36769	0.964066	0.482033	−	0.876153i	$-0.339899\pi$
$31$	5.36769	0.964066	0.482033	+	0.876153i	$0.339899\pi$
$32$	−18.3578	−3.24524
$33$	5.20834	0.906656
$34$	−14.6442	−2.51145
$35$	7.68372	1.29878
$36$	−2.06108	−0.343513
$37$	−7.87298	−1.29431	−0.647155	−	0.762359i	$-0.724041\pi$
$37$	−7.87298	−1.29431	−0.647155	+	0.762359i	$0.724041\pi$
$38$	6.16997	1.00090
$39$	7.21429	1.15521
$40$	−24.8991	−3.93689
$41$	2.29163	0.357893	0.178946	−	0.983859i	$-0.442731\pi$
$41$	2.29163	0.357893	0.178946	+	0.983859i	$0.442731\pi$
$42$	−11.9389	−1.84221
$43$	−0.973599	−0.148472	−0.0742362	−	0.997241i	$-0.523652\pi$
$43$	−0.973599	−0.148472	−0.0742362	+	0.997241i	$0.523652\pi$
$44$	17.0425	2.56926
$45$	−1.09427	−0.163124
$46$	16.7301	2.46671
$47$	9.69254	1.41380	0.706901	−	0.707312i	$-0.250093\pi$
$47$	9.69254	1.41380	0.706901	+	0.707312i	$0.250093\pi$
$48$	21.6065	3.11863
$49$	0.494627	0.0706610
$50$	−7.76757	−1.09850
$51$	8.76469	1.22730
$52$	23.6063	3.27361
$53$	−7.73306	−1.06222	−0.531108	−	0.847304i	$-0.678224\pi$
$53$	−7.73306	−1.06222	−0.531108	+	0.847304i	$0.678224\pi$
$54$	14.7834	2.01176
$55$	9.04826	1.22007
$56$	−24.2864	−3.24540
$57$	−3.69279	−0.489122
$58$	−0.0500423	−0.00657088
$59$	12.1987	1.58813	0.794065	−	0.607832i	$-0.207961\pi$
$59$	12.1987	1.58813	0.794065	+	0.607832i	$0.207961\pi$
$60$	23.9713	3.09468
$61$	−10.2477	−1.31208	−0.656042	−	0.754724i	$-0.727771\pi$
$61$	−10.2477	−1.31208	−0.656042	+	0.754724i	$0.727771\pi$
$62$	−14.4893	−1.84014
$63$	−1.06734	−0.134473
$64$	22.8066	2.85082
$65$	12.5331	1.55454
$66$	−14.0591	−1.73056
$67$	6.76491	0.826465	0.413233	−	0.910625i	$-0.364400\pi$
$67$	6.76491	0.826465	0.413233	+	0.910625i	$0.364400\pi$
$68$	28.6795	3.47790
$69$	−10.0131	−1.20544
$70$	−20.7410	−2.47902
$71$	15.3486	1.82155	0.910774	−	0.412904i	$-0.135486\pi$
$71$	15.3486	1.82155	0.910774	+	0.412904i	$0.135486\pi$
$72$	3.45873	0.407615
$73$	−5.09820	−0.596699	−0.298350	−	0.954457i	$-0.596436\pi$
$73$	−5.09820	−0.596699	−0.298350	+	0.954457i	$0.596436\pi$
$74$	21.2519	2.47048
$75$	4.64897	0.536817
$76$	−12.0834	−1.38606
$77$	8.82559	1.00577
$78$	−19.4739	−2.20498
$79$	−5.64660	−0.635292	−0.317646	−	0.948209i	$-0.602892\pi$
$79$	−5.64660	−0.635292	−0.317646	+	0.948209i	$0.602892\pi$
$80$	37.5362	4.19667
$81$	−7.67836	−0.853151
$82$	−6.18591	−0.683119
$83$	−5.87421	−0.644778	−0.322389	−	0.946607i	$-0.604486\pi$
$83$	−5.87421	−0.644778	−0.322389	+	0.946607i	$0.604486\pi$
$84$	23.3814	2.55112
$85$	15.2266	1.65156
$86$	2.62808	0.283393
$87$	0.0299509	0.00321107
$88$	−28.5994	−3.04870
$89$	0.696095	0.0737860	0.0368930	−	0.999319i	$-0.488254\pi$
$89$	0.696095	0.0737860	0.0368930	+	0.999319i	$0.488254\pi$
$90$	2.95382	0.311360
$91$	12.2247	1.28150
$92$	−32.7646	−3.41594
$93$	8.67198	0.899242
$94$	−26.1635	−2.69856
$95$	−6.41536	−0.658202
$96$	−29.6587	−3.02703
$97$	8.33689	0.846483	0.423241	−	0.906017i	$-0.360892\pi$
$97$	8.33689	0.846483	0.423241	+	0.906017i	$0.360892\pi$
$98$	−1.33517	−0.134872
$99$	−1.25689	−0.126322
$100$	15.2122	1.52122
$101$	13.6484	1.35807	0.679035	−	0.734106i	$-0.262398\pi$
$101$	13.6484	1.35807	0.679035	+	0.734106i	$0.262398\pi$
$102$	−23.6589	−2.34258
$103$	9.86724	0.972248	0.486124	−	0.873890i	$-0.338410\pi$
$103$	9.86724	0.972248	0.486124	+	0.873890i	$0.338410\pi$
$104$	−39.6142	−3.88449
$105$	12.4137	1.21145
$106$	20.8742	2.02748
$107$	4.82711	0.466655	0.233327	−	0.972398i	$-0.425039\pi$
$107$	4.82711	0.466655	0.233327	+	0.972398i	$0.425039\pi$
$108$	−28.9521	−2.78592
$109$	−2.47040	−0.236622	−0.118311	−	0.992977i	$-0.537748\pi$
$109$	−2.47040	−0.236622	−0.118311	+	0.992977i	$0.537748\pi$
$110$	−24.4244	−2.32877
$111$	−12.7195	−1.20728
$112$	36.6125	3.45955
$113$	−8.12829	−0.764645	−0.382323	−	0.924029i	$-0.624876\pi$
$113$	−8.12829	−0.764645	−0.382323	+	0.924029i	$0.624876\pi$
$114$	9.96812	0.933600
$115$	−17.3954	−1.62213
$116$	0.0980042	0.00909946
$117$	−1.74097	−0.160953
$118$	−32.9284	−3.03131
$119$	14.8519	1.36147
$120$	−40.2267	−3.67218
$121$	−0.607074	−0.0551885
$122$	27.6621	2.50441
$123$	3.70233	0.333828
$124$	28.3761	2.54825
$125$	−5.95701	−0.532812
$126$	2.88113	0.256671
$127$	−16.0014	−1.41990	−0.709949	−	0.704253i	$-0.751282\pi$
$127$	−16.0014	−1.41990	−0.709949	+	0.704253i	$0.751282\pi$
$128$	−24.8472	−2.19620
$129$	−1.57293	−0.138489
$130$	−33.8312	−2.96720
$131$	−5.38695	−0.470660	−0.235330	−	0.971915i	$-0.575617\pi$
$131$	−5.38695	−0.470660	−0.235330	+	0.971915i	$0.575617\pi$
$132$	27.5337	2.39650
$133$	−6.25748	−0.542592
$134$	−18.2608	−1.57750
$135$	−15.3713	−1.32295
$136$	−48.1275	−4.12690
$137$	10.0662	0.860014	0.430007	−	0.902826i	$-0.358511\pi$
$137$	10.0662	0.860014	0.430007	+	0.902826i	$0.358511\pi$
$138$	27.0289	2.30085
$139$	−5.65923	−0.480010	−0.240005	−	0.970772i	$-0.577149\pi$
$139$	−5.65923	−0.480010	−0.240005	+	0.970772i	$0.577149\pi$
$140$	40.6197	3.43299
$141$	15.6591	1.31874
$142$	−41.4313	−3.47684
$143$	14.3957	1.20383
$144$	−5.21414	−0.434512
$145$	0.0520326	0.00432107
$146$	13.7618	1.13893
$147$	0.799113	0.0659098
$148$	−41.6202	−3.42116
$149$	6.90427	0.565620	0.282810	−	0.959176i	$-0.408733\pi$
$149$	6.90427	0.565620	0.282810	+	0.959176i	$0.408733\pi$
$150$	−12.5492	−1.02464
$151$	10.1032	0.822185	0.411092	−	0.911594i	$-0.365147\pi$
$151$	10.1032	0.822185	0.411092	+	0.911594i	$0.365147\pi$
$152$	20.2774	1.64471
$153$	−2.11512	−0.170997
$154$	−23.8233	−1.91974
$155$	15.0655	1.21009
$156$	38.1381	3.05349
$157$	12.8612	1.02644	0.513219	−	0.858258i	$-0.328453\pi$
$157$	12.8612	1.02644	0.513219	+	0.858258i	$0.328453\pi$
$158$	15.2421	1.21260
$159$	−12.4934	−0.990793
$160$	−51.5250	−4.07341
$161$	−16.9674	−1.33722
$162$	20.7265	1.62843
$163$	16.9697	1.32917	0.664584	−	0.747214i	$-0.268609\pi$
$163$	16.9697	1.32917	0.664584	+	0.747214i	$0.268609\pi$
$164$	12.1146	0.945994
$165$	14.6183	1.13803
$166$	15.8565	1.23070
$167$	7.98754	0.618094	0.309047	−	0.951047i	$-0.399990\pi$
$167$	7.98754	0.618094	0.309047	+	0.951047i	$0.399990\pi$
$168$	−39.2367	−3.02718
$169$	6.94006	0.533851
$170$	−41.1018	−3.15237
$171$	0.891155	0.0681483
$172$	−5.14690	−0.392447
$173$	−3.21956	−0.244779	−0.122389	−	0.992482i	$-0.539056\pi$
$173$	−3.21956	−0.244779	−0.122389	+	0.992482i	$0.539056\pi$
$174$	−0.0808478	−0.00612905
$175$	7.87774	0.595501
$176$	43.1145	3.24987
$177$	19.7080	1.48134
$178$	−1.87900	−0.140837
$179$	11.6585	0.871397	0.435698	−	0.900093i	$-0.356501\pi$
$179$	11.6585	0.871397	0.435698	+	0.900093i	$0.356501\pi$
$180$	−5.78483	−0.431176
$181$	−4.39941	−0.327005	−0.163503	−	0.986543i	$-0.552279\pi$
$181$	−4.39941	−0.327005	−0.163503	+	0.986543i	$0.552279\pi$
$182$	−32.9987	−2.44603
$183$	−16.5561	−1.22386
$184$	54.9828	4.05338
$185$	−22.0971	−1.62461
$186$	−23.4087	−1.71641
$187$	17.4894	1.27895
$188$	51.2393	3.73701
$189$	−14.9930	−1.09058
$190$	17.3173	1.25633
$191$	10.5877	0.766098	0.383049	−	0.923728i	$-0.374874\pi$
$191$	10.5877	0.766098	0.383049	+	0.923728i	$0.374874\pi$
$192$	36.8460	2.65913
$193$	3.73706	0.268999	0.134500	−	0.990914i	$-0.457057\pi$
$193$	3.73706	0.268999	0.134500	+	0.990914i	$0.457057\pi$
$194$	−22.5041	−1.61570
$195$	20.2484	1.45002
$196$	2.61483	0.186774
$197$	16.4679	1.17329	0.586643	−	0.809845i	$-0.300449\pi$
$197$	16.4679	1.17329	0.586643	+	0.809845i	$0.300449\pi$
$198$	3.39278	0.241115
$199$	−6.85488	−0.485930	−0.242965	−	0.970035i	$-0.578120\pi$
$199$	−6.85488	−0.485930	−0.242965	+	0.970035i	$0.578120\pi$
$200$	−25.5278	−1.80509
$201$	10.9293	0.770894
$202$	−36.8419	−2.59218
$203$	0.0507521	0.00356210
$204$	46.3342	3.24405
$205$	6.43193	0.449225
$206$	−26.6351	−1.85575
$207$	2.41640	0.167951
$208$	59.7196	4.14081
$209$	−7.36874	−0.509707
$210$	−33.5089	−2.31233
$211$	−11.4328	−0.787067	−0.393534	−	0.919310i	$-0.628748\pi$
$211$	−11.4328	−0.787067	−0.393534	+	0.919310i	$0.628748\pi$
$212$	−40.8805	−2.80769
$213$	24.7971	1.69907
$214$	−13.0300	−0.890715
$215$	−2.73260	−0.186362
$216$	48.5850	3.30579
$217$	14.6948	0.997546
$218$	6.66847	0.451646
$219$	−8.23659	−0.556577
$220$	47.8333	3.22492
$221$	24.2253	1.62957
$222$	34.3343	2.30437
$223$	16.5915	1.11105	0.555525	−	0.831500i	$-0.312517\pi$
$223$	16.5915	1.11105	0.555525	+	0.831500i	$0.312517\pi$
$224$	−50.2570	−3.35794
$225$	−1.12190	−0.0747936
$226$	21.9411	1.45950
$227$	−16.2801	−1.08055	−0.540275	−	0.841489i	$-0.681680\pi$
$227$	−16.2801	−1.08055	−0.540275	+	0.841489i	$0.681680\pi$
$228$	−19.5218	−1.29286
$229$	−27.7587	−1.83435	−0.917173	−	0.398490i	$-0.869534\pi$
$229$	−27.7587	−1.83435	−0.917173	+	0.398490i	$0.869534\pi$
$230$	46.9563	3.09621
$231$	14.2585	0.938141
$232$	−0.164462	−0.0107975
$233$	11.7529	0.769960	0.384980	−	0.922925i	$-0.374208\pi$
$233$	11.7529	0.769960	0.384980	+	0.922925i	$0.374208\pi$
$234$	4.69949	0.307215
$235$	27.2041	1.77460
$236$	64.4878	4.19780
$237$	−9.12257	−0.592575
$238$	−40.0903	−2.59867
$239$	20.9303	1.35387	0.676935	−	0.736043i	$-0.263308\pi$
$239$	20.9303	1.35387	0.676935	+	0.736043i	$0.263308\pi$
$240$	60.6430	3.91449
$241$	12.8154	0.825514	0.412757	−	0.910841i	$-0.364566\pi$
$241$	12.8154	0.825514	0.412757	+	0.910841i	$0.364566\pi$
$242$	1.63870	0.105340
$243$	4.02487	0.258195
$244$	−54.1741	−3.46814
$245$	1.38827	0.0886934
$246$	−9.99387	−0.637186
$247$	−10.2068	−0.649440
$248$	−47.6184	−3.02377
$249$	−9.49029	−0.601423
$250$	16.0800	1.01699
$251$	−0.636455	−0.0401727	−0.0200863	−	0.999798i	$-0.506394\pi$
$251$	−0.636455	−0.0401727	−0.0200863	+	0.999798i	$0.506394\pi$
$252$	−5.64247	−0.355442
$253$	−19.9806	−1.25617
$254$	43.1934	2.71020
$255$	24.5999	1.54050
$256$	21.4579	1.34112
$257$	−20.1060	−1.25418	−0.627088	−	0.778948i	$-0.715753\pi$
$257$	−20.1060	−1.25418	−0.627088	+	0.778948i	$0.715753\pi$
$258$	4.24589	0.264338
$259$	−21.5533	−1.33926
$260$	66.2559	4.10902
$261$	−0.00722783	−0.000447392 0
$262$	14.5412	0.898361
$263$	11.1092	0.685025	0.342512	−	0.939513i	$-0.388722\pi$
$263$	11.1092	0.685025	0.342512	+	0.939513i	$0.388722\pi$
$264$	−46.2048	−2.84371
$265$	−21.7044	−1.33329
$266$	16.8911	1.03566
$267$	1.12460	0.0688246
$268$	35.7625	2.18454
$269$	−4.00083	−0.243935	−0.121968	−	0.992534i	$-0.538920\pi$
$269$	−4.00083	−0.243935	−0.121968	+	0.992534i	$0.538920\pi$
$270$	41.4925	2.52515
$271$	10.1515	0.616659	0.308329	−	0.951280i	$-0.400230\pi$
$271$	10.1515	0.616659	0.308329	+	0.951280i	$0.400230\pi$
$272$	72.5538	4.39922
$273$	19.7501	1.19533
$274$	−27.1722	−1.64153
$275$	9.27674	0.559409
$276$	−52.9340	−3.18625
$277$	−5.71052	−0.343112	−0.171556	−	0.985174i	$-0.554879\pi$
$277$	−5.71052	−0.343112	−0.171556	+	0.985174i	$0.554879\pi$
$278$	15.2762	0.916207
$279$	−2.09275	−0.125289
$280$	−68.1646	−4.07361
$281$	11.8737	0.708326	0.354163	−	0.935184i	$-0.384766\pi$
$281$	11.8737	0.708326	0.354163	+	0.935184i	$0.384766\pi$
$282$	−42.2694	−2.51711
$283$	15.3477	0.912328	0.456164	−	0.889896i	$-0.349223\pi$
$283$	15.3477	0.912328	0.456164	+	0.889896i	$0.349223\pi$
$284$	81.1400	4.81478
$285$	−10.3646	−0.613944
$286$	−38.8589	−2.29778
$287$	6.27364	0.370322
$288$	7.15732	0.421749
$289$	12.4315	0.731266
$290$	−0.140454	−0.00824774
$291$	13.4690	0.789565
$292$	−26.9514	−1.57721
$293$	16.9583	0.990715	0.495357	−	0.868689i	$-0.335037\pi$
$293$	16.9583	0.990715	0.495357	+	0.868689i	$0.335037\pi$
$294$	−2.15708	−0.125804
$295$	34.2380	1.99341
$296$	69.8436	4.05957
$297$	−17.6556	−1.02448
$298$	−18.6370	−1.07961
$299$	−27.6759	−1.60054
$300$	24.5766	1.41893
$301$	−2.66536	−0.153629
$302$	−27.2720	−1.56932
$303$	22.0502	1.26675
$304$	−30.5688	−1.75324
$305$	−28.7623	−1.64692
$306$	5.70944	0.326387
$307$	15.8443	0.904282	0.452141	−	0.891947i	$-0.350660\pi$
$307$	15.8443	0.904282	0.452141	+	0.891947i	$0.350660\pi$
$308$	46.6562	2.65848
$309$	15.9414	0.906874
$310$	−40.6670	−2.30973
$311$	−30.0204	−1.70230	−0.851150	−	0.524922i	$-0.824095\pi$
$311$	−30.0204	−1.70230	−0.851150	+	0.524922i	$0.824095\pi$
$312$	−64.0001	−3.62329
$313$	34.1666	1.93121	0.965606	−	0.260009i	$-0.0837256\pi$
$313$	34.1666	1.93121	0.965606	+	0.260009i	$0.0837256\pi$
$314$	−34.7169	−1.95919
$315$	−2.99571	−0.168789
$316$	−29.8506	−1.67922
$317$	−16.3123	−0.916192	−0.458096	−	0.888903i	$-0.651468\pi$
$317$	−16.3123	−0.916192	−0.458096	+	0.888903i	$0.651468\pi$
$318$	33.7241	1.89115
$319$	0.0597652	0.00334621
$320$	64.0113	3.57834
$321$	7.79862	0.435277
$322$	45.8008	2.55238
$323$	−12.4003	−0.689969
$324$	−40.5914	−2.25508
$325$	12.8496	0.712768
$326$	−45.8070	−2.53702
$327$	−3.99115	−0.220711
$328$	−20.3298	−1.12252
$329$	26.5346	1.46290
$330$	−39.4597	−2.17219
$331$	−12.4746	−0.685666	−0.342833	−	0.939396i	$-0.611387\pi$
$331$	−12.4746	−0.685666	−0.342833	+	0.939396i	$0.611387\pi$
$332$	−31.0538	−1.70430
$333$	3.06950	0.168208
$334$	−21.5611	−1.17977
$335$	18.9871	1.03738
$336$	59.1506	3.22693
$337$	−5.91282	−0.322092	−0.161046	−	0.986947i	$-0.551487\pi$
$337$	−5.91282	−0.322092	−0.161046	+	0.986947i	$0.551487\pi$
$338$	−18.7336	−1.01897
$339$	−13.1320	−0.713230
$340$	80.4948	4.36544
$341$	17.3044	0.937086
$342$	−2.40554	−0.130076
$343$	−17.8093	−0.961613
$344$	8.63709	0.465681
$345$	−28.1039	−1.51306
$346$	8.69071	0.467215
$347$	−20.0116	−1.07428	−0.537139	−	0.843494i	$-0.680495\pi$
$347$	−20.0116	−1.07428	−0.537139	+	0.843494i	$0.680495\pi$
$348$	0.158334	0.00848761
$349$	32.4820	1.73872	0.869362	−	0.494176i	$-0.164530\pi$
$349$	32.4820	1.73872	0.869362	+	0.494176i	$0.164530\pi$
$350$	−21.2647	−1.13665
$351$	−24.4556	−1.30534
$352$	−59.1821	−3.15442
$353$	−28.1593	−1.49877	−0.749384	−	0.662135i	$-0.769650\pi$
$353$	−28.1593	−1.49877	−0.749384	+	0.662135i	$0.769650\pi$
$354$	−53.1987	−2.82748
$355$	43.0791	2.28640
$356$	3.67988	0.195033
$357$	23.9945	1.26992
$358$	−31.4703	−1.66326
$359$	−7.12188	−0.375879	−0.187939	−	0.982181i	$-0.560181\pi$
$359$	−7.12188	−0.375879	−0.187939	+	0.982181i	$0.560181\pi$
$360$	9.70761	0.511636
$361$	−13.7754	−0.725024
$362$	11.8755	0.624164
$363$	−0.980780	−0.0514776
$364$	64.6254	3.38729
$365$	−14.3091	−0.748974
$366$	44.6905	2.33601
$367$	−29.3222	−1.53061	−0.765303	−	0.643670i	$-0.777411\pi$
$367$	−29.3222	−1.53061	−0.765303	+	0.643670i	$0.777411\pi$
$368$	−82.8883	−4.32085
$369$	−0.893457	−0.0465115
$370$	59.6477	3.10094
$371$	−21.1703	−1.09911
$372$	45.8441	2.37691
$373$	4.56753	0.236498	0.118249	−	0.992984i	$-0.462272\pi$
$373$	4.56753	0.236498	0.118249	+	0.992984i	$0.462272\pi$
$374$	−47.2100	−2.44117
$375$	−9.62408	−0.496985
$376$	−85.9855	−4.43436
$377$	0.0827832	0.00426355
$378$	40.4714	2.08162
$379$	−24.3399	−1.25026	−0.625129	−	0.780522i	$-0.714954\pi$
$379$	−24.3399	−1.25026	−0.625129	+	0.780522i	$0.714954\pi$
$380$	−33.9145	−1.73978
$381$	−25.8517	−1.32442
$382$	−28.5798	−1.46227
$383$	−26.1459	−1.33599	−0.667996	−	0.744165i	$-0.732847\pi$
$383$	−26.1459	−1.33599	−0.667996	+	0.744165i	$0.732847\pi$
$384$	−40.1428	−2.04853
$385$	24.7708	1.26244
$386$	−10.0876	−0.513446
$387$	0.379585	0.0192954
$388$	44.0726	2.23745
$389$	24.5896	1.24674	0.623372	−	0.781925i	$-0.285762\pi$
$389$	24.5896	1.24674	0.623372	+	0.781925i	$0.285762\pi$
$390$	−54.6573	−2.76768
$391$	−33.6237	−1.70042
$392$	−4.38799	−0.221627
$393$	−8.70309	−0.439013
$394$	−44.4525	−2.23948
$395$	−15.8483	−0.797416
$396$	−6.64451	−0.333899
$397$	−34.5838	−1.73571	−0.867856	−	0.496816i	$-0.834503\pi$
$397$	−34.5838	−1.73571	−0.867856	+	0.496816i	$0.834503\pi$
$398$	18.5037	0.927506
$399$	−10.1095	−0.506108
$400$	38.4840	1.92420
$401$	16.5443	0.826183	0.413092	−	0.910689i	$-0.364449\pi$
$401$	16.5443	0.826183	0.413092	+	0.910689i	$0.364449\pi$
$402$	−29.5020	−1.47142
$403$	23.9691	1.19398
$404$	72.1520	3.58970
$405$	−21.5509	−1.07087
$406$	−0.136997	−0.00679907
$407$	−25.3810	−1.25809
$408$	−77.7542	−3.84941
$409$	−30.7387	−1.51993	−0.759965	−	0.649964i	$-0.774784\pi$
$409$	−30.7387	−1.51993	−0.759965	+	0.649964i	$0.774784\pi$
$410$	−17.3620	−0.857448
$411$	16.2628	0.802186
$412$	52.1628	2.56988
$413$	33.3955	1.64328
$414$	−6.52269	−0.320573
$415$	−16.4871	−0.809322
$416$	−81.9756	−4.01918
$417$	−9.14298	−0.447734
$418$	19.8908	0.972890
$419$	−12.1334	−0.592757	−0.296378	−	0.955071i	$-0.595779\pi$
$419$	−12.1334	−0.592757	−0.296378	+	0.955071i	$0.595779\pi$
$420$	65.6246	3.20215
$421$	−33.6381	−1.63942	−0.819709	−	0.572780i	$-0.805865\pi$
$421$	−33.6381	−1.63942	−0.819709	+	0.572780i	$0.805865\pi$
$422$	30.8611	1.50230
$423$	−3.77891	−0.183737
$424$	68.6023	3.33162
$425$	15.6111	0.757249
$426$	−66.9359	−3.24305
$427$	−28.0544	−1.35765
$428$	25.5184	1.23348
$429$	23.2575	1.12288
$430$	7.37624	0.355714
$431$	32.2483	1.55335	0.776674	−	0.629903i	$-0.216905\pi$
$431$	32.2483	1.55335	0.776674	+	0.629903i	$0.216905\pi$
$432$	−73.2434	−3.52392
$433$	14.7476	0.708727	0.354363	−	0.935108i	$-0.384698\pi$
$433$	14.7476	0.708727	0.354363	+	0.935108i	$0.384698\pi$
$434$	−39.6662	−1.90404
$435$	0.0840632	0.00403052
$436$	−13.0597	−0.625446
$437$	14.1665	0.677677
$438$	22.2334	1.06235
$439$	−10.7878	−0.514875	−0.257437	−	0.966295i	$-0.582878\pi$
$439$	−10.7878	−0.514875	−0.257437	+	0.966295i	$0.582878\pi$
$440$	−80.2699	−3.82672
$441$	−0.192844	−0.00918306
$442$	−65.3925	−3.11040
$443$	−10.8152	−0.513846	−0.256923	−	0.966432i	$-0.582709\pi$
$443$	−10.8152	−0.513846	−0.256923	+	0.966432i	$0.582709\pi$
$444$	−67.2411	−3.19112
$445$	1.95373	0.0926158
$446$	−44.7862	−2.12069
$447$	11.1544	0.527587
$448$	62.4360	2.94982
$449$	−18.9551	−0.894548	−0.447274	−	0.894397i	$-0.647605\pi$
$449$	−18.9551	−0.894548	−0.447274	+	0.894397i	$0.647605\pi$
$450$	3.02840	0.142760
$451$	7.38778	0.347877
$452$	−42.9699	−2.02114
$453$	16.3226	0.766901
$454$	43.9457	2.06247
$455$	34.3111	1.60853
$456$	32.7599	1.53412
$457$	41.8831	1.95921	0.979605	−	0.200931i	$-0.0643967\pi$
$457$	41.8831	1.95921	0.979605	+	0.200931i	$0.0643967\pi$
$458$	74.9303	3.50126
$459$	−29.7112	−1.38680
$460$	−91.9604	−4.28768
$461$	18.8518	0.878016	0.439008	−	0.898483i	$-0.355330\pi$
$461$	18.8518	0.878016	0.439008	+	0.898483i	$0.355330\pi$
$462$	−38.4887	−1.79065
$463$	−17.9107	−0.832380	−0.416190	−	0.909278i	$-0.636635\pi$
$463$	−17.9107	−0.832380	−0.416190	+	0.909278i	$0.636635\pi$
$464$	0.247932	0.0115100
$465$	24.3396	1.12872
$466$	−31.7252	−1.46964
$467$	−8.62539	−0.399136	−0.199568	−	0.979884i	$-0.563954\pi$
$467$	−8.62539	−0.399136	−0.199568	+	0.979884i	$0.563954\pi$
$468$	−9.20359	−0.425436
$469$	18.5198	0.855166
$470$	−73.4332	−3.38722
$471$	20.7784	0.957420
$472$	−108.218	−4.98114
$473$	−3.13869	−0.144317
$474$	24.6250	1.13106
$475$	−6.57735	−0.301790
$476$	78.5139	3.59868
$477$	3.01495	0.138045
$478$	−56.4982	−2.58417
$479$	−7.67865	−0.350846	−0.175423	−	0.984493i	$-0.556129\pi$
$479$	−7.67865	−0.350846	−0.175423	+	0.984493i	$0.556129\pi$
$480$	−83.2431	−3.79951
$481$	−35.1562	−1.60299
$482$	−34.5932	−1.57568
$483$	−27.4122	−1.24730
$484$	−3.20927	−0.145876
$485$	23.3992	1.06250
$486$	−10.8645	−0.492824
$487$	−38.6373	−1.75082	−0.875411	−	0.483380i	$-0.839409\pi$
$487$	−38.6373	−1.75082	−0.875411	+	0.483380i	$0.839409\pi$
$488$	90.9105	4.11532
$489$	27.4160	1.23979
$490$	−3.74742	−0.169291
$491$	0.300054	0.0135413	0.00677063	−	0.999977i	$-0.497845\pi$
$491$	0.300054	0.0135413	0.00677063	+	0.999977i	$0.497845\pi$
$492$	19.5722	0.882385
$493$	0.100574	0.00452962
$494$	27.5516	1.23960
$495$	−3.52772	−0.158559
$496$	71.7863	3.22330
$497$	42.0189	1.88481
$498$	25.6176	1.14795
$499$	17.7761	0.795766	0.397883	−	0.917436i	$-0.369745\pi$
$499$	17.7761	0.795766	0.397883	+	0.917436i	$0.369745\pi$
$500$	−31.4915	−1.40834
$501$	12.9046	0.576533
$502$	1.71801	0.0766786
$503$	−12.1693	−0.542603	−0.271301	−	0.962494i	$-0.587454\pi$
$503$	−12.1693	−0.542603	−0.271301	+	0.962494i	$0.587454\pi$
$504$	9.46872	0.421770
$505$	38.3071	1.70464
$506$	53.9345	2.39768
$507$	11.2123	0.497954
$508$	−84.5911	−3.75312
$509$	−19.0334	−0.843638	−0.421819	−	0.906680i	$-0.638608\pi$
$509$	−19.0334	−0.843638	−0.421819	+	0.906680i	$0.638608\pi$
$510$	−66.4036	−2.94040
$511$	−13.9570	−0.617421
$512$	−8.22797	−0.363628
$513$	12.5181	0.552688
$514$	54.2730	2.39388
$515$	27.6944	1.22036
$516$	−8.31526	−0.366059
$517$	31.2469	1.37424
$518$	58.1798	2.55627
$519$	−5.20148	−0.228320
$520$	−111.185	−4.87579
$521$	7.78162	0.340919	0.170460	−	0.985365i	$-0.445475\pi$
$521$	7.78162	0.340919	0.170460	+	0.985365i	$0.445475\pi$
$522$	0.0195104	0.000853948 0
$523$	−12.4006	−0.542241	−0.271120	−	0.962545i	$-0.587394\pi$
$523$	−12.4006	−0.542241	−0.271120	+	0.962545i	$0.587394\pi$
$524$	−28.4779	−1.24406
$525$	12.7272	0.555459
$526$	−29.9876	−1.30752
$527$	29.1202	1.26849
$528$	69.6552	3.03135
$529$	15.4130	0.670132
$530$	58.5876	2.54488
$531$	−4.75599	−0.206392
$532$	−33.0799	−1.43420
$533$	10.2331	0.443246
$534$	−3.03569	−0.131367
$535$	13.5483	0.585743
$536$	−60.0136	−2.59219
$537$	18.8353	0.812804
$538$	10.7996	0.465605
$539$	1.59458	0.0686835
$540$	−81.2599	−3.49687
$541$	43.8931	1.88711	0.943555	−	0.331215i	$-0.107459\pi$
$541$	43.8931	1.88711	0.943555	+	0.331215i	$0.107459\pi$
$542$	−27.4023	−1.17703
$543$	−7.10763	−0.305018
$544$	−99.5928	−4.27000
$545$	−6.93368	−0.297006
$546$	−53.3123	−2.28155
$547$	−34.1980	−1.46220	−0.731101	−	0.682269i	$-0.760993\pi$
$547$	−34.1980	−1.46220	−0.731101	+	0.682269i	$0.760993\pi$
$548$	53.2146	2.27322
$549$	3.99536	0.170518
$550$	−25.0411	−1.06776
$551$	−0.0423744	−0.00180521
$552$	88.8295	3.78083
$553$	−15.4583	−0.657354
$554$	15.4147	0.654906
$555$	−35.6998	−1.51537
$556$	−29.9173	−1.26878
$557$	29.3786	1.24481	0.622406	−	0.782694i	$-0.286155\pi$
$557$	29.3786	1.24481	0.622406	+	0.782694i	$0.286155\pi$
$558$	5.64904	0.239143
$559$	−4.34754	−0.183881
$560$	102.760	4.34241
$561$	28.2557	1.19296
$562$	−32.0512	−1.35200
$563$	46.1162	1.94356	0.971782	−	0.235880i	$-0.0757973\pi$
$563$	46.1162	1.94356	0.971782	+	0.235880i	$0.0757973\pi$
$564$	82.7815	3.48573
$565$	−22.8137	−0.959779
$566$	−41.4288	−1.74138
$567$	−21.0205	−0.882779
$568$	−136.162	−5.71325
$569$	−31.4702	−1.31930	−0.659651	−	0.751572i	$-0.729296\pi$
$569$	−31.4702	−1.31930	−0.659651	+	0.751572i	$0.729296\pi$
$570$	27.9775	1.17185
$571$	20.8366	0.871983	0.435991	−	0.899951i	$-0.356398\pi$
$571$	20.8366	0.871983	0.435991	+	0.899951i	$0.356398\pi$
$572$	76.1022	3.18199
$573$	17.1053	0.714586
$574$	−16.9347	−0.706842
$575$	−17.8347	−0.743759
$576$	−8.89179	−0.370491
$577$	−5.56596	−0.231714	−0.115857	−	0.993266i	$-0.536961\pi$
$577$	−5.56596	−0.231714	−0.115857	+	0.993266i	$0.536961\pi$
$578$	−33.5570	−1.39579
$579$	6.03754	0.250912
$580$	0.275068	0.0114216
$581$	−16.0814	−0.667170
$582$	−36.3574	−1.50706
$583$	−24.9299	−1.03249
$584$	45.2277	1.87153
$585$	−4.88639	−0.202027
$586$	−45.7763	−1.89100
$587$	−34.0176	−1.40406	−0.702028	−	0.712149i	$-0.747722\pi$
$587$	−34.0176	−1.40406	−0.702028	+	0.712149i	$0.747722\pi$
$588$	4.22448	0.174215
$589$	−12.2691	−0.505539
$590$	−92.4202	−3.80488
$591$	26.6053	1.09439
$592$	−105.291	−4.32745
$593$	−15.4788	−0.635638	−0.317819	−	0.948151i	$-0.602950\pi$
$593$	−15.4788	−0.635638	−0.317819	+	0.948151i	$0.602950\pi$
$594$	47.6587	1.95546
$595$	41.6848	1.70891
$596$	36.4992	1.49506
$597$	−11.0747	−0.453256
$598$	74.7069	3.05499
$599$	−2.06024	−0.0841790	−0.0420895	−	0.999114i	$-0.513401\pi$
$599$	−2.06024	−0.0841790	−0.0420895	+	0.999114i	$0.513401\pi$
$600$	−41.2424	−1.68372
$601$	−5.82283	−0.237518	−0.118759	−	0.992923i	$-0.537892\pi$
$601$	−5.82283	−0.237518	−0.118759	+	0.992923i	$0.537892\pi$
$602$	7.19471	0.293235
$603$	−2.63749	−0.107407
$604$	53.4101	2.17322
$605$	−1.70387	−0.0692724
$606$	−59.5212	−2.41788
$607$	−11.0835	−0.449866	−0.224933	−	0.974374i	$-0.572216\pi$
$607$	−11.0835	−0.449866	−0.224933	+	0.974374i	$0.572216\pi$
$608$	41.9610	1.70174
$609$	0.0819945	0.00332258
$610$	77.6393	3.14352
$611$	43.2814	1.75098
$612$	−11.1815	−0.451986
$613$	−3.81036	−0.153899	−0.0769494	−	0.997035i	$-0.524518\pi$
$613$	−3.81036	−0.153899	−0.0769494	+	0.997035i	$0.524518\pi$
$614$	−42.7692	−1.72603
$615$	10.3913	0.419019
$616$	−78.2945	−3.15458
$617$	−4.92207	−0.198155	−0.0990776	−	0.995080i	$-0.531589\pi$
$617$	−4.92207	−0.198155	−0.0990776	+	0.995080i	$0.531589\pi$
$618$	−43.0313	−1.73097
$619$	4.37056	0.175668	0.0878338	−	0.996135i	$-0.472006\pi$
$619$	4.37056	0.175668	0.0878338	+	0.996135i	$0.472006\pi$
$620$	79.6433	3.19855
$621$	33.9433	1.36210
$622$	81.0354	3.24922
$623$	1.90565	0.0763484
$624$	96.4823	3.86238
$625$	−31.1074	−1.24430
$626$	−92.2275	−3.68615
$627$	−11.9048	−0.475434
$628$	67.9904	2.71311
$629$	−42.7115	−1.70302
$630$	8.08646	0.322172
$631$	7.85577	0.312733	0.156367	−	0.987699i	$-0.450022\pi$
$631$	7.85577	0.312733	0.156367	+	0.987699i	$0.450022\pi$
$632$	50.0927	1.99258
$633$	−18.4707	−0.734145
$634$	44.0326	1.74876
$635$	−44.9113	−1.78225
$636$	−66.0461	−2.61890
$637$	2.20872	0.0875128
$638$	−0.161327	−0.00638699
$639$	−5.98410	−0.236727
$640$	−69.7386	−2.75666
$641$	−10.2451	−0.404659	−0.202329	−	0.979318i	$-0.564851\pi$
$641$	−10.2451	−0.404659	−0.202329	+	0.979318i	$0.564851\pi$
$642$	−21.0512	−0.830823
$643$	−37.7100	−1.48714	−0.743568	−	0.668661i	$-0.766868\pi$
$643$	−37.7100	−1.48714	−0.743568	+	0.668661i	$0.766868\pi$
$644$	−89.6973	−3.53457
$645$	−4.41476	−0.173831
$646$	33.4726	1.31696
$647$	−5.74231	−0.225753	−0.112877	−	0.993609i	$-0.536007\pi$
$647$	−5.74231	−0.225753	−0.112877	+	0.993609i	$0.536007\pi$
$648$	68.1171	2.67589
$649$	39.3261	1.54369
$650$	−34.6855	−1.36048
$651$	23.7407	0.930470
$652$	89.7096	3.51330
$653$	38.1894	1.49447	0.747233	−	0.664562i	$-0.231382\pi$
$653$	38.1894	1.49447	0.747233	+	0.664562i	$0.231382\pi$
$654$	10.7735	0.421277
$655$	−15.1196	−0.590771
$656$	30.6478	1.19659
$657$	1.98768	0.0775466
$658$	−71.6261	−2.79227
$659$	−39.1887	−1.52658	−0.763288	−	0.646058i	$-0.776416\pi$
$659$	−39.1887	−1.52658	−0.763288	+	0.646058i	$0.776416\pi$
$660$	77.2789	3.00808
$661$	−36.2542	−1.41012	−0.705062	−	0.709146i	$-0.749081\pi$
$661$	−36.2542	−1.41012	−0.705062	+	0.709146i	$0.749081\pi$
$662$	33.6733	1.30875
$663$	39.1381	1.52000
$664$	52.1119	2.02233
$665$	−17.5629	−0.681059
$666$	−8.28564	−0.321062
$667$	−0.114900	−0.00444893
$668$	42.2258	1.63377
$669$	26.8050	1.03634
$670$	−51.2527	−1.98006
$671$	−33.0366	−1.27536
$672$	−81.1945	−3.13215
$673$	−36.9331	−1.42367	−0.711833	−	0.702349i	$-0.752135\pi$
$673$	−36.9331	−1.42367	−0.711833	+	0.702349i	$0.752135\pi$
$674$	15.9608	0.614785
$675$	−15.7595	−0.606582
$676$	36.6884	1.41109
$677$	−42.4817	−1.63270	−0.816351	−	0.577556i	$-0.804007\pi$
$677$	−42.4817	−1.63270	−0.816351	+	0.577556i	$0.804007\pi$
$678$	35.4477	1.36136
$679$	22.8233	0.875879
$680$	−135.080	−5.18007
$681$	−26.3020	−1.00789
$682$	−46.7106	−1.78864
$683$	2.12189	0.0811919	0.0405959	−	0.999176i	$-0.487074\pi$
$683$	2.12189	0.0811919	0.0405959	+	0.999176i	$0.487074\pi$
$684$	4.71106	0.180132
$685$	28.2528	1.07949
$686$	48.0735	1.83545
$687$	−44.8466	−1.71100
$688$	−13.0207	−0.496409
$689$	−34.5314	−1.31554
$690$	75.8620	2.88802
$691$	5.18365	0.197195	0.0985976	−	0.995127i	$-0.468564\pi$
$691$	5.18365	0.197195	0.0985976	+	0.995127i	$0.468564\pi$
$692$	−17.0201	−0.647007
$693$	−3.44091	−0.130709
$694$	54.0182	2.05050
$695$	−15.8838	−0.602506
$696$	−0.265703	−0.0100715
$697$	12.4323	0.470907
$698$	−87.6803	−3.31875
$699$	18.9879	0.718187
$700$	41.6454	1.57405
$701$	9.51629	0.359425	0.179713	−	0.983719i	$-0.442483\pi$
$701$	9.51629	0.359425	0.179713	+	0.983719i	$0.442483\pi$
$702$	66.0140	2.49154
$703$	17.9955	0.678712
$704$	73.5240	2.77104
$705$	43.9506	1.65527
$706$	76.0117	2.86074
$707$	37.3644	1.40523
$708$	104.186	3.91554
$709$	2.57052	0.0965379	0.0482689	−	0.998834i	$-0.484630\pi$
$709$	2.57052	0.0965379	0.0482689	+	0.998834i	$0.484630\pi$
$710$	−116.285	−4.36411
$711$	2.20149	0.0825622
$712$	−6.17527	−0.231428
$713$	−33.2680	−1.24590
$714$	−64.7694	−2.42394
$715$	40.4044	1.51104
$716$	61.6322	2.30330
$717$	33.8148	1.26284
$718$	19.2244	0.717449
$719$	14.7960	0.551799	0.275900	−	0.961186i	$-0.411024\pi$
$719$	14.7960	0.551799	0.275900	+	0.961186i	$0.411024\pi$
$720$	−14.6345	−0.545397
$721$	27.0129	1.00601
$722$	37.1847	1.38387
$723$	20.7044	0.770006
$724$	−23.2573	−0.864351
$725$	0.0533465	0.00198124
$726$	2.64746	0.0982566
$727$	8.98077	0.333078	0.166539	−	0.986035i	$-0.446741\pi$
$727$	8.98077	0.333078	0.166539	+	0.986035i	$0.446741\pi$
$728$	−108.449	−4.01939
$729$	29.5376	1.09399
$730$	38.6253	1.42959
$731$	−5.28186	−0.195356
$732$	−87.5230	−3.23494
$733$	−32.0349	−1.18324	−0.591618	−	0.806218i	$-0.701511\pi$
$733$	−32.0349	−1.18324	−0.591618	+	0.806218i	$0.701511\pi$
$734$	79.1508	2.92151
$735$	2.24287	0.0827296
$736$	113.779	4.19394
$737$	21.8088	0.803336
$738$	2.41175	0.0887777
$739$	28.8906	1.06276	0.531378	−	0.847135i	$-0.321674\pi$
$739$	28.8906	1.06276	0.531378	+	0.847135i	$0.321674\pi$
$740$	−116.816	−4.29422
$741$	−16.4899	−0.605772
$742$	57.1458	2.09789
$743$	−13.2257	−0.485205	−0.242603	−	0.970126i	$-0.578001\pi$
$743$	−13.2257	−0.485205	−0.242603	+	0.970126i	$0.578001\pi$
$744$	−76.9317	−2.82045
$745$	19.3782	0.709963
$746$	−12.3293	−0.451409
$747$	2.29022	0.0837949
$748$	92.4572	3.38057
$749$	13.2149	0.482860
$750$	25.9787	0.948608
$751$	−37.8946	−1.38279	−0.691397	−	0.722475i	$-0.743005\pi$
$751$	−37.8946	−1.38279	−0.691397	+	0.722475i	$0.743005\pi$
$752$	129.626	4.72697
$753$	−1.02825	−0.0374715
$754$	−0.223461	−0.00813795
$755$	28.3566	1.03200
$756$	−79.2601	−2.88266
$757$	9.04277	0.328665	0.164333	−	0.986405i	$-0.447453\pi$
$757$	9.04277	0.328665	0.164333	+	0.986405i	$0.447453\pi$
$758$	65.7018	2.38640
$759$	−32.2804	−1.17170
$760$	56.9126	2.06444
$761$	13.1822	0.477853	0.238927	−	0.971038i	$-0.423204\pi$
$761$	13.1822	0.477853	0.238927	+	0.971038i	$0.423204\pi$
$762$	69.7827	2.52796
$763$	−6.76305	−0.244839
$764$	55.9714	2.02498
$765$	−5.93651	−0.214635
$766$	70.5767	2.55004
$767$	54.4723	1.96688
$768$	34.6671	1.25094
$769$	18.1294	0.653764	0.326882	−	0.945065i	$-0.394002\pi$
$769$	18.1294	0.653764	0.326882	+	0.945065i	$0.394002\pi$
$770$	−66.8650	−2.40965
$771$	−32.4830	−1.16984
$772$	19.7558	0.711027
$773$	50.4186	1.81343	0.906715	−	0.421745i	$-0.138582\pi$
$773$	50.4186	1.81343	0.906715	+	0.421745i	$0.138582\pi$
$774$	−1.02463	−0.0368296
$775$	15.4459	0.554834
$776$	−73.9590	−2.65497
$777$	−34.8213	−1.24921
$778$	−66.3759	−2.37969
$779$	−5.23805	−0.187673
$780$	107.042	3.83273
$781$	49.4810	1.77057
$782$	90.7620	3.24564
$783$	−0.101530	−0.00362838
$784$	6.61503	0.236251
$785$	36.0976	1.28838
$786$	23.4927	0.837955
$787$	−32.9223	−1.17355	−0.586776	−	0.809749i	$-0.699603\pi$
$787$	−32.9223	−1.17355	−0.586776	+	0.809749i	$0.699603\pi$
$788$	87.0568	3.10127
$789$	17.9479	0.638963
$790$	42.7801	1.52205
$791$	−22.2523	−0.791200
$792$	11.1503	0.396207
$793$	−45.7604	−1.62500
$794$	93.3537	3.31300
$795$	−35.0653	−1.24364
$796$	−36.2381	−1.28442
$797$	7.58142	0.268548	0.134274	−	0.990944i	$-0.457130\pi$
$797$	7.58142	0.268548	0.134274	+	0.990944i	$0.457130\pi$
$798$	27.2890	0.966022
$799$	52.5828	1.86025
$800$	−52.8260	−1.86768
$801$	−0.271392	−0.00958918
$802$	−44.6588	−1.57696
$803$	−16.4356	−0.580000
$804$	57.7774	2.03765
$805$	−47.6223	−1.67847
$806$	−64.7007	−2.27899
$807$	−6.46370	−0.227533
$808$	−121.079	−4.25956
$809$	−13.4190	−0.471786	−0.235893	−	0.971779i	$-0.575801\pi$
$809$	−13.4190	−0.471786	−0.235893	+	0.971779i	$0.575801\pi$
$810$	58.1732	2.04400
$811$	41.3274	1.45120	0.725600	−	0.688117i	$-0.241562\pi$
$811$	41.3274	1.45120	0.725600	+	0.688117i	$0.241562\pi$
$812$	0.268299	0.00941546
$813$	16.4006	0.575194
$814$	68.5119	2.40134
$815$	47.6288	1.66836
$816$	117.217	4.10342
$817$	2.22538	0.0778563
$818$	82.9744	2.90113
$819$	−4.76614	−0.166543
$820$	34.0022	1.18741
$821$	−5.55948	−0.194027	−0.0970136	−	0.995283i	$-0.530929\pi$
$821$	−5.55948	−0.194027	−0.0970136	+	0.995283i	$0.530929\pi$
$822$	−43.8990	−1.53115
$823$	−45.2400	−1.57697	−0.788484	−	0.615055i	$-0.789134\pi$
$823$	−45.2400	−1.57697	−0.788484	+	0.615055i	$0.789134\pi$
$824$	−87.5353	−3.04944
$825$	14.9874	0.521794
$826$	−90.1458	−3.13658
$827$	−6.93929	−0.241303	−0.120651	−	0.992695i	$-0.538498\pi$
$827$	−6.93929	−0.241303	−0.120651	+	0.992695i	$0.538498\pi$
$828$	12.7742	0.443934
$829$	14.8485	0.515709	0.257855	−	0.966184i	$-0.416984\pi$
$829$	14.8485	0.515709	0.257855	+	0.966184i	$0.416984\pi$
$830$	44.5045	1.54477
$831$	−9.22584	−0.320041
$832$	101.841	3.53071
$833$	2.68339	0.0929741
$834$	24.6801	0.854601
$835$	22.4186	0.775829
$836$	−38.9546	−1.34727
$837$	−29.3969	−1.01611
$838$	32.7523	1.13141
$839$	−29.8208	−1.02953	−0.514765	−	0.857331i	$-0.672121\pi$
$839$	−29.8208	−1.02953	−0.514765	+	0.857331i	$0.672121\pi$
$840$	−110.126	−3.79970
$841$	−28.9997	−0.999988
$842$	90.8007	3.12920
$843$	19.1830	0.660698
$844$	−60.4392	−2.08040
$845$	19.4787	0.670087
$846$	10.2006	0.350703
$847$	−1.66194	−0.0571051
$848$	−103.420	−3.55146
$849$	24.7956	0.850983
$850$	−42.1397	−1.44538
$851$	48.7953	1.67268
$852$	131.089	4.49103
$853$	19.1923	0.657132	0.328566	−	0.944481i	$-0.393435\pi$
$853$	19.1923	0.657132	0.328566	+	0.944481i	$0.393435\pi$
$854$	75.7286	2.59138
$855$	2.50121	0.0855395
$856$	−42.8228	−1.46365
$857$	0.848419	0.0289814	0.0144907	−	0.999895i	$-0.495387\pi$
$857$	0.848419	0.0289814	0.0144907	+	0.999895i	$0.495387\pi$
$858$	−62.7799	−2.14327
$859$	30.4113	1.03762	0.518810	−	0.854889i	$-0.326375\pi$
$859$	30.4113	1.03762	0.518810	+	0.854889i	$0.326375\pi$
$860$	−14.4458	−0.492598
$861$	10.1356	0.345421
$862$	−87.0494	−2.96491
$863$	−39.6186	−1.34863	−0.674317	−	0.738442i	$-0.735562\pi$
$863$	−39.6186	−1.34863	−0.674317	+	0.738442i	$0.735562\pi$
$864$	100.539	3.42042
$865$	−9.03635	−0.307245
$866$	−39.8090	−1.35276
$867$	20.0842	0.682095
$868$	77.6834	2.63674
$869$	−18.2035	−0.617513
$870$	−0.226916	−0.00769316
$871$	30.2082	1.02357
$872$	21.9157	0.742159
$873$	−3.25037	−0.110008
$874$	−38.2404	−1.29350
$875$	−16.3081	−0.551315
$876$	−43.5424	−1.47116
$877$	−9.66034	−0.326207	−0.163103	−	0.986609i	$-0.552150\pi$
$877$	−9.66034	−0.326207	−0.163103	+	0.986609i	$0.552150\pi$
$878$	29.1201	0.982755
$879$	27.3976	0.924099
$880$	121.009	4.07923
$881$	6.52132	0.219709	0.109854	−	0.993948i	$-0.464962\pi$
$881$	6.52132	0.219709	0.109854	+	0.993948i	$0.464962\pi$
$882$	0.520553	0.0175279
$883$	−53.2641	−1.79248	−0.896240	−	0.443570i	$-0.853712\pi$
$883$	−53.2641	−1.79248	−0.896240	+	0.443570i	$0.853712\pi$
$884$	128.066	4.30734
$885$	55.3145	1.85938
$886$	29.1940	0.980791
$887$	13.9897	0.469727	0.234863	−	0.972028i	$-0.424536\pi$
$887$	13.9897	0.469727	0.234863	+	0.972028i	$0.424536\pi$
$888$	112.838	3.78661
$889$	−43.8061	−1.46921
$890$	−5.27380	−0.176778
$891$	−24.7535	−0.829275
$892$	87.7105	2.93676
$893$	−22.1545	−0.741372
$894$	−30.1097	−1.00702
$895$	32.7219	1.09377
$896$	−68.0224	−2.27247
$897$	−44.7129	−1.49292
$898$	51.1665	1.70745
$899$	0.0995100	0.00331885
$900$	−5.93090	−0.197697
$901$	−41.9525	−1.39764
$902$	−19.9422	−0.664001
$903$	−4.30611	−0.143299
$904$	72.1085	2.39829
$905$	−12.3478	−0.410456
$906$	−44.0602	−1.46380
$907$	1.50238	0.0498858	0.0249429	−	0.999689i	$-0.492060\pi$
$907$	1.50238	0.0498858	0.0249429	+	0.999689i	$0.492060\pi$
$908$	−86.0643	−2.85614
$909$	−5.32123	−0.176494
$910$	−92.6175	−3.07024
$911$	−59.1264	−1.95894	−0.979472	−	0.201581i	$-0.935392\pi$
$911$	−59.1264	−1.95894	−0.979472	+	0.201581i	$0.935392\pi$
$912$	−49.3866	−1.63535
$913$	−18.9373	−0.626733
$914$	−113.057	−3.73960
$915$	−46.4679	−1.53618
$916$	−146.745	−4.84860
$917$	−14.7475	−0.487005
$918$	80.2009	2.64702
$919$	−36.0789	−1.19013	−0.595066	−	0.803677i	$-0.702874\pi$
$919$	−36.0789	−1.19013	−0.595066	+	0.803677i	$0.702874\pi$
$920$	154.320	5.08779
$921$	25.5978	0.843477
$922$	−50.8875	−1.67589
$923$	68.5383	2.25596
$924$	75.3771	2.47973
$925$	−22.6551	−0.744894
$926$	48.3471	1.58878
$927$	−3.84702	−0.126353
$928$	−0.340330	−0.0111719
$929$	−8.87876	−0.291303	−0.145651	−	0.989336i	$-0.546528\pi$
$929$	−8.87876	−0.291303	−0.145651	+	0.989336i	$0.546528\pi$
$930$	−65.7011	−2.15442
$931$	−1.13058	−0.0370534
$932$	62.1314	2.03518
$933$	−48.5006	−1.58784
$934$	23.2829	0.761840
$935$	49.0876	1.60534
$936$	15.4447	0.504826
$937$	−6.86339	−0.224217	−0.112109	−	0.993696i	$-0.535760\pi$
$937$	−6.86339	−0.224217	−0.112109	+	0.993696i	$0.535760\pi$
$938$	−49.9914	−1.63228
$939$	55.1992	1.80136
$940$	143.813	4.69067
$941$	25.6964	0.837680	0.418840	−	0.908060i	$-0.362437\pi$
$941$	25.6964	0.837680	0.418840	+	0.908060i	$0.362437\pi$
$942$	−56.0882	−1.82745
$943$	−14.2031	−0.462518
$944$	163.142	5.30983
$945$	−42.0810	−1.36889
$946$	8.47242	0.275462
$947$	46.0583	1.49669	0.748347	−	0.663308i	$-0.230848\pi$
$947$	46.0583	1.49669	0.748347	+	0.663308i	$0.230848\pi$
$948$	−48.2262	−1.56631
$949$	−22.7656	−0.739004
$950$	17.7545	0.576033
$951$	−26.3540	−0.854587
$952$	−131.755	−4.27022
$953$	5.48758	0.177760	0.0888800	−	0.996042i	$-0.471671\pi$
$953$	5.48758	0.177760	0.0888800	+	0.996042i	$0.471671\pi$
$954$	−8.13839	−0.263490
$955$	29.7165	0.961603
$956$	110.647	3.57859
$957$	0.0965558	0.00312121
$958$	20.7273	0.669669
$959$	27.5576	0.889880
$960$	103.416	3.33773
$961$	−2.18787	−0.0705765
$962$	94.8988	3.05966
$963$	−1.88199	−0.0606461
$964$	67.7483	2.18203
$965$	10.4888	0.337646
$966$	73.9951	2.38075
$967$	−16.3524	−0.525857	−0.262928	−	0.964815i	$-0.584688\pi$
$967$	−16.3524	−0.525857	−0.262928	+	0.964815i	$0.584688\pi$
$968$	5.38553	0.173098
$969$	−20.0337	−0.643575
$970$	−63.1624	−2.02802
$971$	−7.74233	−0.248463	−0.124232	−	0.992253i	$-0.539647\pi$
$971$	−7.74233	−0.248463	−0.124232	+	0.992253i	$0.539647\pi$
$972$	21.2773	0.682471
$973$	−15.4929	−0.496679
$974$	104.295	3.34184
$975$	20.7597	0.664841
$976$	−137.051	−4.38688
$977$	−3.92299	−0.125507	−0.0627537	−	0.998029i	$-0.519988\pi$
$977$	−3.92299	−0.125507	−0.0627537	+	0.998029i	$0.519988\pi$
$978$	−74.0052	−2.36643
$979$	2.24408	0.0717210
$980$	7.33905	0.234437
$981$	0.963156	0.0307512
$982$	−0.809950	−0.0258465
$983$	−38.0284	−1.21292	−0.606458	−	0.795115i	$-0.707410\pi$
$983$	−38.0284	−1.21292	−0.606458	+	0.795115i	$0.707410\pi$
$984$	−32.8445	−1.04704
$985$	46.2204	1.47270
$986$	−0.271484	−0.00864581
$987$	42.8690	1.36453
$988$	−53.9576	−1.71662
$989$	6.03420	0.191876
$990$	9.52253	0.302646
$991$	44.7232	1.42068	0.710339	−	0.703860i	$-0.248542\pi$
$991$	44.7232	1.42068	0.710339	+	0.703860i	$0.248542\pi$
$992$	−98.5392	−3.12862
$993$	−20.1538	−0.639562
$994$	−113.424	−3.59758
$995$	−19.2396	−0.609937
$996$	−50.1701	−1.58970
$997$	11.7821	0.373142	0.186571	−	0.982441i	$-0.440263\pi$
$997$	11.7821	0.373142	0.186571	+	0.982441i	$0.440263\pi$
$998$	−47.9838	−1.51890
$999$	43.1175	1.36418

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.b.1.7	✓	358

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.b.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-2.69935 q^{2} +1.61559 q^{3} +5.28646 q^{4} +2.80670 q^{5} -4.36103 q^{6} +2.73763 q^{7} -8.87130 q^{8} -0.389878 q^{9} +O(q^{10})\)	\(q-2.69935 q^{2} +1.61559 q^{3} +5.28646 q^{4} +2.80670 q^{5} -4.36103 q^{6} +2.73763 q^{7} -8.87130 q^{8} -0.389878 q^{9} -7.57626 q^{10} +3.22381 q^{11} +8.54074 q^{12} +4.46543 q^{13} -7.38981 q^{14} +4.53447 q^{15} +13.3738 q^{16} +5.42508 q^{17} +1.05242 q^{18} -2.28573 q^{19} +14.8375 q^{20} +4.42288 q^{21} -8.70217 q^{22} -6.19782 q^{23} -14.3324 q^{24} +2.87757 q^{25} -12.0537 q^{26} -5.47664 q^{27} +14.4724 q^{28} +0.0185387 q^{29} -12.2401 q^{30} +5.36769 q^{31} -18.3578 q^{32} +5.20834 q^{33} -14.6442 q^{34} +7.68372 q^{35} -2.06108 q^{36} -7.87298 q^{37} +6.16997 q^{38} +7.21429 q^{39} -24.8991 q^{40} +2.29163 q^{41} -11.9389 q^{42} -0.973599 q^{43} +17.0425 q^{44} -1.09427 q^{45} +16.7301 q^{46} +9.69254 q^{47} +21.6065 q^{48} +0.494627 q^{49} -7.76757 q^{50} +8.76469 q^{51} +23.6063 q^{52} -7.73306 q^{53} +14.7834 q^{54} +9.04826 q^{55} -24.2864 q^{56} -3.69279 q^{57} -0.0500423 q^{58} +12.1987 q^{59} +23.9713 q^{60} -10.2477 q^{61} -14.4893 q^{62} -1.06734 q^{63} +22.8066 q^{64} +12.5331 q^{65} -14.0591 q^{66} +6.76491 q^{67} +28.6795 q^{68} -10.0131 q^{69} -20.7410 q^{70} +15.3486 q^{71} +3.45873 q^{72} -5.09820 q^{73} +21.2519 q^{74} +4.64897 q^{75} -12.0834 q^{76} +8.82559 q^{77} -19.4739 q^{78} -5.64660 q^{79} +37.5362 q^{80} -7.67836 q^{81} -6.18591 q^{82} -5.87421 q^{83} +23.3814 q^{84} +15.2266 q^{85} +2.62808 q^{86} +0.0299509 q^{87} -28.5994 q^{88} +0.696095 q^{89} +2.95382 q^{90} +12.2247 q^{91} -32.7646 q^{92} +8.67198 q^{93} -26.1635 q^{94} -6.41536 q^{95} -29.6587 q^{96} +8.33689 q^{97} -1.33517 q^{98} -1.25689 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) \) 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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