LMFDB - Embedded newform 8011.2.a.a.1.8

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			1.8
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)

$f(q)$	$=$	$q-2.69623 q^{2} -0.432527 q^{3} +5.26965 q^{4} +2.72420 q^{5} +1.16619 q^{6} -0.628855 q^{7} -8.81573 q^{8} -2.81292 q^{9} +O(q^{10})$	\(q-2.69623 q^{2} -0.432527 q^{3} +5.26965 q^{4} +2.72420 q^{5} +1.16619 q^{6} -0.628855 q^{7} -8.81573 q^{8} -2.81292 q^{9} -7.34507 q^{10} +5.20890 q^{11} -2.27927 q^{12} +2.03838 q^{13} +1.69554 q^{14} -1.17829 q^{15} +13.2299 q^{16} +0.386637 q^{17} +7.58428 q^{18} -1.28113 q^{19} +14.3556 q^{20} +0.271997 q^{21} -14.0444 q^{22} +3.31775 q^{23} +3.81304 q^{24} +2.42128 q^{25} -5.49594 q^{26} +2.51425 q^{27} -3.31384 q^{28} +1.62399 q^{29} +3.17694 q^{30} -1.10329 q^{31} -18.0394 q^{32} -2.25299 q^{33} -1.04246 q^{34} -1.71313 q^{35} -14.8231 q^{36} -2.16211 q^{37} +3.45423 q^{38} -0.881654 q^{39} -24.0158 q^{40} -0.638545 q^{41} -0.733365 q^{42} -0.275563 q^{43} +27.4491 q^{44} -7.66297 q^{45} -8.94543 q^{46} -13.2015 q^{47} -5.72230 q^{48} -6.60454 q^{49} -6.52833 q^{50} -0.167231 q^{51} +10.7415 q^{52} -3.71727 q^{53} -6.77898 q^{54} +14.1901 q^{55} +5.54381 q^{56} +0.554126 q^{57} -4.37865 q^{58} -14.0865 q^{59} -6.20919 q^{60} -10.7929 q^{61} +2.97473 q^{62} +1.76892 q^{63} +22.1786 q^{64} +5.55296 q^{65} +6.07458 q^{66} +11.0925 q^{67} +2.03744 q^{68} -1.43502 q^{69} +4.61898 q^{70} -14.9022 q^{71} +24.7979 q^{72} -11.3700 q^{73} +5.82955 q^{74} -1.04727 q^{75} -6.75113 q^{76} -3.27564 q^{77} +2.37714 q^{78} -9.73011 q^{79} +36.0410 q^{80} +7.35128 q^{81} +1.72166 q^{82} +15.1119 q^{83} +1.43333 q^{84} +1.05328 q^{85} +0.742982 q^{86} -0.702420 q^{87} -45.9202 q^{88} +9.67650 q^{89} +20.6611 q^{90} -1.28184 q^{91} +17.4834 q^{92} +0.477204 q^{93} +35.5942 q^{94} -3.49007 q^{95} +7.80255 q^{96} -7.09037 q^{97} +17.8074 q^{98} -14.6522 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.69623	−1.90652	−0.953261	−	0.302148i	$-0.902296\pi$
$2$	−2.69623	−1.90652	−0.953261	+	0.302148i	$0.902296\pi$
$3$	−0.432527	−0.249720	−0.124860	−	0.992174i	$-0.539848\pi$
$3$	−0.432527	−0.249720	−0.124860	+	0.992174i	$0.539848\pi$
$4$	5.26965	2.63483
$5$	2.72420	1.21830	0.609150	−	0.793055i	$-0.291511\pi$
$5$	2.72420	1.21830	0.609150	+	0.793055i	$0.291511\pi$
$6$	1.16619	0.476096
$7$	−0.628855	−0.237685	−0.118842	−	0.992913i	$-0.537918\pi$
$7$	−0.628855	−0.237685	−0.118842	+	0.992913i	$0.537918\pi$
$8$	−8.81573	−3.11683
$9$	−2.81292	−0.937640
$10$	−7.34507	−2.32272
$11$	5.20890	1.57054	0.785271	−	0.619152i	$-0.212524\pi$
$11$	5.20890	1.57054	0.785271	+	0.619152i	$0.212524\pi$
$12$	−2.27927	−0.657968
$13$	2.03838	0.565345	0.282672	−	0.959217i	$-0.408779\pi$
$13$	2.03838	0.565345	0.282672	+	0.959217i	$0.408779\pi$
$14$	1.69554	0.453151
$15$	−1.17829	−0.304234
$16$	13.2299	3.30748
$17$	0.386637	0.0937733	0.0468866	−	0.998900i	$-0.485070\pi$
$17$	0.386637	0.0937733	0.0468866	+	0.998900i	$0.485070\pi$
$18$	7.58428	1.78763
$19$	−1.28113	−0.293912	−0.146956	−	0.989143i	$-0.546948\pi$
$19$	−1.28113	−0.293912	−0.146956	+	0.989143i	$0.546948\pi$
$20$	14.3556	3.21001
$21$	0.271997	0.0593545
$22$	−14.0444	−2.99427
$23$	3.31775	0.691800	0.345900	−	0.938271i	$-0.387574\pi$
$23$	3.31775	0.691800	0.345900	+	0.938271i	$0.387574\pi$
$24$	3.81304	0.778334
$25$	2.42128	0.484256
$26$	−5.49594	−1.07784
$27$	2.51425	0.483867
$28$	−3.31384	−0.626258
$29$	1.62399	0.301568	0.150784	−	0.988567i	$-0.451820\pi$
$29$	1.62399	0.301568	0.150784	+	0.988567i	$0.451820\pi$
$30$	3.17694	0.580028
$31$	−1.10329	−0.198157	−0.0990785	−	0.995080i	$-0.531589\pi$
$31$	−1.10329	−0.198157	−0.0990785	+	0.995080i	$0.531589\pi$
$32$	−18.0394	−3.18895
$33$	−2.25299	−0.392195
$34$	−1.04246	−0.178781
$35$	−1.71313	−0.289571
$36$	−14.8231	−2.47052
$37$	−2.16211	−0.355449	−0.177724	−	0.984080i	$-0.556874\pi$
$37$	−2.16211	−0.355449	−0.177724	+	0.984080i	$0.556874\pi$
$38$	3.45423	0.560351
$39$	−0.881654	−0.141178
$40$	−24.0158	−3.79724
$41$	−0.638545	−0.0997239	−0.0498620	−	0.998756i	$-0.515878\pi$
$41$	−0.638545	−0.0997239	−0.0498620	+	0.998756i	$0.515878\pi$
$42$	−0.733365	−0.113161
$43$	−0.275563	−0.0420230	−0.0210115	−	0.999779i	$-0.506689\pi$
$43$	−0.275563	−0.0420230	−0.0210115	+	0.999779i	$0.506689\pi$
$44$	27.4491	4.13810
$45$	−7.66297	−1.14233
$46$	−8.94543	−1.31893
$47$	−13.2015	−1.92563	−0.962817	−	0.270154i	$-0.912925\pi$
$47$	−13.2015	−1.92563	−0.962817	+	0.270154i	$0.912925\pi$
$48$	−5.72230	−0.825943
$49$	−6.60454	−0.943506
$50$	−6.52833	−0.923245
$51$	−0.167231	−0.0234170
$52$	10.7415	1.48958
$53$	−3.71727	−0.510607	−0.255303	−	0.966861i	$-0.582175\pi$
$53$	−3.71727	−0.510607	−0.255303	+	0.966861i	$0.582175\pi$
$54$	−6.77898	−0.922503
$55$	14.1901	1.91339
$56$	5.54381	0.740823
$57$	0.554126	0.0733957
$58$	−4.37865	−0.574945
$59$	−14.0865	−1.83391	−0.916955	−	0.398991i	$-0.869360\pi$
$59$	−14.0865	−1.83391	−0.916955	+	0.398991i	$0.869360\pi$
$60$	−6.20919	−0.801603
$61$	−10.7929	−1.38189	−0.690944	−	0.722909i	$-0.742805\pi$
$61$	−10.7929	−1.38189	−0.690944	+	0.722909i	$0.742805\pi$
$62$	2.97473	0.377791
$63$	1.76892	0.222863
$64$	22.1786	2.77233
$65$	5.55296	0.688760
$66$	6.07458	0.747729
$67$	11.0925	1.35516	0.677582	−	0.735447i	$-0.263028\pi$
$67$	11.0925	1.35516	0.677582	+	0.735447i	$0.263028\pi$
$68$	2.03744	0.247076
$69$	−1.43502	−0.172756
$70$	4.61898	0.552074
$71$	−14.9022	−1.76857	−0.884286	−	0.466946i	$-0.845354\pi$
$71$	−14.9022	−1.76857	−0.884286	+	0.466946i	$0.845354\pi$
$72$	24.7979	2.92247
$73$	−11.3700	−1.33075	−0.665376	−	0.746508i	$-0.731729\pi$
$73$	−11.3700	−1.33075	−0.665376	+	0.746508i	$0.731729\pi$
$74$	5.82955	0.677671
$75$	−1.04727	−0.120928
$76$	−6.75113	−0.774408
$77$	−3.27564	−0.373294
$78$	2.37714	0.269158
$79$	−9.73011	−1.09472	−0.547361	−	0.836896i	$-0.684368\pi$
$79$	−9.73011	−1.09472	−0.547361	+	0.836896i	$0.684368\pi$
$80$	36.0410	4.02951
$81$	7.35128	0.816809
$82$	1.72166	0.190126
$83$	15.1119	1.65875	0.829374	−	0.558693i	$-0.188697\pi$
$83$	15.1119	1.65875	0.829374	+	0.558693i	$0.188697\pi$
$84$	1.43333	0.156389
$85$	1.05328	0.114244
$86$	0.742982	0.0801178
$87$	−0.702420	−0.0753074
$88$	−45.9202	−4.89511
$89$	9.67650	1.02571	0.512854	−	0.858476i	$-0.328588\pi$
$89$	9.67650	1.02571	0.512854	+	0.858476i	$0.328588\pi$
$90$	20.6611	2.17787
$91$	−1.28184	−0.134374
$92$	17.4834	1.82277
$93$	0.477204	0.0494837
$94$	35.5942	3.67126
$95$	−3.49007	−0.358074
$96$	7.80255	0.796344
$97$	−7.09037	−0.719918	−0.359959	−	0.932968i	$-0.617209\pi$
$97$	−7.09037	−0.719918	−0.359959	+	0.932968i	$0.617209\pi$
$98$	17.8074	1.79881
$99$	−14.6522	−1.47260
$100$	12.7593	1.27593
$101$	−13.0591	−1.29943	−0.649714	−	0.760179i	$-0.725111\pi$
$101$	−13.0591	−1.29943	−0.649714	+	0.760179i	$0.725111\pi$
$102$	0.450893	0.0446451
$103$	6.86189	0.676122	0.338061	−	0.941124i	$-0.390229\pi$
$103$	6.86189	0.676122	0.338061	+	0.941124i	$0.390229\pi$
$104$	−17.9698	−1.76208
$105$	0.740974	0.0723117
$106$	10.0226	0.973483
$107$	−4.19134	−0.405192	−0.202596	−	0.979262i	$-0.564938\pi$
$107$	−4.19134	−0.405192	−0.202596	+	0.979262i	$0.564938\pi$
$108$	13.2492	1.27490
$109$	2.96457	0.283954	0.141977	−	0.989870i	$-0.454654\pi$
$109$	2.96457	0.283954	0.141977	+	0.989870i	$0.454654\pi$
$110$	−38.2597	−3.64792
$111$	0.935172	0.0887626
$112$	−8.31970	−0.786137
$113$	20.7120	1.94842	0.974209	−	0.225646i	$-0.0724492\pi$
$113$	20.7120	1.94842	0.974209	+	0.225646i	$0.0724492\pi$
$114$	−1.49405	−0.139931
$115$	9.03824	0.842820
$116$	8.55787	0.794578
$117$	−5.73380	−0.530090
$118$	37.9805	3.49639
$119$	−0.243139	−0.0222885
$120$	10.3875	0.948245
$121$	16.1326	1.46660
$122$	29.1001	2.63460
$123$	0.276188	0.0249030
$124$	−5.81396	−0.522109
$125$	−7.02495	−0.628331
$126$	−4.76941	−0.424893
$127$	−0.658511	−0.0584334	−0.0292167	−	0.999573i	$-0.509301\pi$
$127$	−0.658511	−0.0584334	−0.0292167	+	0.999573i	$0.509301\pi$
$128$	−23.7198	−2.09655
$129$	0.119189	0.0104940
$130$	−14.9720	−1.31314
$131$	−22.4483	−1.96131	−0.980657	−	0.195732i	$-0.937292\pi$
$131$	−22.4483	−1.96131	−0.980657	+	0.195732i	$0.937292\pi$
$132$	−11.8725	−1.03337
$133$	0.805647	0.0698585
$134$	−29.9079	−2.58365
$135$	6.84932	0.589495
$136$	−3.40849	−0.292275
$137$	−12.7977	−1.09338	−0.546690	−	0.837335i	$-0.684113\pi$
$137$	−12.7977	−1.09338	−0.546690	+	0.837335i	$0.684113\pi$
$138$	3.86914	0.329363
$139$	−16.9793	−1.44017	−0.720085	−	0.693886i	$-0.755897\pi$
$139$	−16.9793	−1.44017	−0.720085	+	0.693886i	$0.755897\pi$
$140$	−9.02758	−0.762970
$141$	5.71000	0.480869
$142$	40.1799	3.37182
$143$	10.6177	0.887897
$144$	−37.2147	−3.10123
$145$	4.42408	0.367400
$146$	30.6560	2.53711
$147$	2.85664	0.235612
$148$	−11.3936	−0.936546
$149$	17.1259	1.40301	0.701505	−	0.712665i	$-0.252512\pi$
$149$	17.1259	1.40301	0.701505	+	0.712665i	$0.252512\pi$
$150$	2.82368	0.230552
$151$	−13.9671	−1.13663	−0.568315	−	0.822811i	$-0.692404\pi$
$151$	−13.9671	−1.13663	−0.568315	+	0.822811i	$0.692404\pi$
$152$	11.2941	0.916075
$153$	−1.08758	−0.0879256
$154$	8.83187	0.711693
$155$	−3.00559	−0.241415
$156$	−4.64601	−0.371979
$157$	1.56758	0.125107	0.0625534	−	0.998042i	$-0.480076\pi$
$157$	1.56758	0.125107	0.0625534	+	0.998042i	$0.480076\pi$
$158$	26.2346	2.08711
$159$	1.60782	0.127509
$160$	−49.1431	−3.88510
$161$	−2.08639	−0.164430
$162$	−19.8207	−1.55726
$163$	8.15699	0.638905	0.319452	−	0.947602i	$-0.396501\pi$
$163$	8.15699	0.638905	0.319452	+	0.947602i	$0.396501\pi$
$164$	−3.36491	−0.262755
$165$	−6.13760	−0.477812
$166$	−40.7452	−3.16244
$167$	−10.1482	−0.785294	−0.392647	−	0.919689i	$-0.628441\pi$
$167$	−10.1482	−0.785294	−0.392647	+	0.919689i	$0.628441\pi$
$168$	−2.39785	−0.184998
$169$	−8.84501	−0.680386
$170$	−2.83988	−0.217809
$171$	3.60373	0.275584
$172$	−1.45212	−0.110723
$173$	−11.8303	−0.899443	−0.449722	−	0.893169i	$-0.648477\pi$
$173$	−11.8303	−0.899443	−0.449722	+	0.893169i	$0.648477\pi$
$174$	1.89389	0.143575
$175$	−1.52263	−0.115100
$176$	68.9133	5.19454
$177$	6.09280	0.457963
$178$	−26.0901	−1.95553
$179$	1.00469	0.0750942	0.0375471	−	0.999295i	$-0.488046\pi$
$179$	1.00469	0.0750942	0.0375471	+	0.999295i	$0.488046\pi$
$180$	−40.3812	−3.00983
$181$	−18.6723	−1.38790	−0.693952	−	0.720021i	$-0.744132\pi$
$181$	−18.6723	−1.38790	−0.693952	+	0.720021i	$0.744132\pi$
$182$	3.45614	0.256186
$183$	4.66822	0.345084
$184$	−29.2484	−2.15622
$185$	−5.89003	−0.433044
$186$	−1.28665	−0.0943418
$187$	2.01395	0.147275
$188$	−69.5672	−5.07371
$189$	−1.58110	−0.115008
$190$	9.41003	0.682675
$191$	−9.03949	−0.654075	−0.327037	−	0.945011i	$-0.606050\pi$
$191$	−9.03949	−0.654075	−0.327037	+	0.945011i	$0.606050\pi$
$192$	−9.59286	−0.692305
$193$	16.1656	1.16363	0.581814	−	0.813322i	$-0.302343\pi$
$193$	16.1656	1.16363	0.581814	+	0.813322i	$0.302343\pi$
$194$	19.1173	1.37254
$195$	−2.40180	−0.171997
$196$	−34.8036	−2.48597
$197$	−12.8343	−0.914406	−0.457203	−	0.889362i	$-0.651149\pi$
$197$	−12.8343	−0.914406	−0.457203	+	0.889362i	$0.651149\pi$
$198$	39.5057	2.80755
$199$	−3.54014	−0.250954	−0.125477	−	0.992097i	$-0.540046\pi$
$199$	−3.54014	−0.250954	−0.125477	+	0.992097i	$0.540046\pi$
$200$	−21.3454	−1.50934
$201$	−4.79781	−0.338411
$202$	35.2103	2.47739
$203$	−1.02125	−0.0716780
$204$	−0.881249	−0.0616998
$205$	−1.73953	−0.121494
$206$	−18.5012	−1.28904
$207$	−9.33258	−0.648659
$208$	26.9676	1.86987
$209$	−6.67330	−0.461602
$210$	−1.99784	−0.137864
$211$	3.97835	0.273881	0.136941	−	0.990579i	$-0.456273\pi$
$211$	3.97835	0.273881	0.136941	+	0.990579i	$0.456273\pi$
$212$	−19.5887	−1.34536
$213$	6.44563	0.441647
$214$	11.3008	0.772507
$215$	−0.750690	−0.0511966
$216$	−22.1649	−1.50813
$217$	0.693810	0.0470989
$218$	−7.99315	−0.541364
$219$	4.91781	0.332315
$220$	74.7768	5.04145
$221$	0.788113	0.0530142
$222$	−2.52144	−0.169228
$223$	10.9873	0.735762	0.367881	−	0.929873i	$-0.380083\pi$
$223$	10.9873	0.735762	0.367881	+	0.929873i	$0.380083\pi$
$224$	11.3442	0.757965
$225$	−6.81087	−0.454058
$226$	−55.8442	−3.71470
$227$	−8.45956	−0.561481	−0.280740	−	0.959784i	$-0.590580\pi$
$227$	−8.45956	−0.561481	−0.280740	+	0.959784i	$0.590580\pi$
$228$	2.92005	0.193385
$229$	16.0121	1.05811	0.529053	−	0.848589i	$-0.322547\pi$
$229$	16.0121	1.05811	0.529053	+	0.848589i	$0.322547\pi$
$230$	−24.3692	−1.60685
$231$	1.41680	0.0932188
$232$	−14.3167	−0.939935
$233$	7.70165	0.504552	0.252276	−	0.967655i	$-0.418821\pi$
$233$	7.70165	0.504552	0.252276	+	0.967655i	$0.418821\pi$
$234$	15.4596	1.01063
$235$	−35.9635	−2.34600
$236$	−74.2311	−4.83203
$237$	4.20854	0.273374
$238$	0.655557	0.0424935
$239$	−26.2973	−1.70103	−0.850515	−	0.525950i	$-0.823710\pi$
$239$	−26.2973	−1.70103	−0.850515	+	0.525950i	$0.823710\pi$
$240$	−15.5887	−1.00625
$241$	0.391369	0.0252103	0.0126052	−	0.999921i	$-0.495988\pi$
$241$	0.391369	0.0252103	0.0126052	+	0.999921i	$0.495988\pi$
$242$	−43.4972	−2.79611
$243$	−10.7224	−0.687840
$244$	−56.8747	−3.64103
$245$	−17.9921	−1.14947
$246$	−0.744666	−0.0474782
$247$	−2.61144	−0.166162
$248$	9.72632	0.617622
$249$	−6.53632	−0.414222
$250$	18.9409	1.19793
$251$	18.6578	1.17767	0.588834	−	0.808254i	$-0.299587\pi$
$251$	18.6578	1.17767	0.588834	+	0.808254i	$0.299587\pi$
$252$	9.32158	0.587204
$253$	17.2818	1.08650
$254$	1.77550	0.111405
$255$	−0.455571	−0.0285290
$256$	19.5967	1.22479
$257$	14.6091	0.911292	0.455646	−	0.890161i	$-0.349408\pi$
$257$	14.6091	0.911292	0.455646	+	0.890161i	$0.349408\pi$
$258$	−0.321360	−0.0200070
$259$	1.35965	0.0844848
$260$	29.2621	1.81476
$261$	−4.56816	−0.282762
$262$	60.5257	3.73929
$263$	−14.5202	−0.895356	−0.447678	−	0.894195i	$-0.647749\pi$
$263$	−14.5202	−0.895356	−0.447678	+	0.894195i	$0.647749\pi$
$264$	19.8617	1.22241
$265$	−10.1266	−0.622073
$266$	−2.17221	−0.133187
$267$	−4.18535	−0.256139
$268$	58.4536	3.57062
$269$	25.7216	1.56828	0.784138	−	0.620587i	$-0.213105\pi$
$269$	25.7216	1.56828	0.784138	+	0.620587i	$0.213105\pi$
$270$	−18.4673	−1.12389
$271$	13.7138	0.833056	0.416528	−	0.909123i	$-0.363247\pi$
$271$	13.7138	0.833056	0.416528	+	0.909123i	$0.363247\pi$
$272$	5.11518	0.310153
$273$	0.554432	0.0335558
$274$	34.5055	2.08455
$275$	12.6122	0.760545
$276$	−7.56205	−0.455182
$277$	−13.8489	−0.832097	−0.416049	−	0.909342i	$-0.636585\pi$
$277$	−13.8489	−0.832097	−0.416049	+	0.909342i	$0.636585\pi$
$278$	45.7802	2.74571
$279$	3.10347	0.185800
$280$	15.1025	0.902545
$281$	−0.382163	−0.0227979	−0.0113990	−	0.999935i	$-0.503628\pi$
$281$	−0.382163	−0.0227979	−0.0113990	+	0.999935i	$0.503628\pi$
$282$	−15.3955	−0.916787
$283$	23.2298	1.38087	0.690435	−	0.723395i	$-0.257419\pi$
$283$	23.2298	1.38087	0.690435	+	0.723395i	$0.257419\pi$
$284$	−78.5296	−4.65988
$285$	1.50955	0.0894180
$286$	−28.6278	−1.69280
$287$	0.401552	0.0237028
$288$	50.7435	2.99009
$289$	−16.8505	−0.991207
$290$	−11.9283	−0.700456
$291$	3.06678	0.179778
$292$	−59.9157	−3.50630
$293$	−29.1488	−1.70289	−0.851447	−	0.524441i	$-0.824274\pi$
$293$	−29.1488	−1.70289	−0.851447	+	0.524441i	$0.824274\pi$
$294$	−7.70217	−0.449199
$295$	−38.3745	−2.23425
$296$	19.0606	1.10787
$297$	13.0964	0.759933
$298$	−46.1754	−2.67487
$299$	6.76284	0.391105
$300$	−5.51875	−0.318625
$301$	0.173289	0.00998822
$302$	37.6586	2.16701
$303$	5.64841	0.324493
$304$	−16.9493	−0.972110
$305$	−29.4020	−1.68355
$306$	2.93236	0.167632
$307$	25.6524	1.46406	0.732030	−	0.681272i	$-0.238573\pi$
$307$	25.6524	1.46406	0.732030	+	0.681272i	$0.238573\pi$
$308$	−17.2615	−0.983564
$309$	−2.96796	−0.168841
$310$	8.10376	0.460263
$311$	−15.5761	−0.883242	−0.441621	−	0.897202i	$-0.645596\pi$
$311$	−15.5761	−0.883242	−0.441621	+	0.897202i	$0.645596\pi$
$312$	7.77242	0.440027
$313$	15.8464	0.895692	0.447846	−	0.894111i	$-0.352191\pi$
$313$	15.8464	0.895692	0.447846	+	0.894111i	$0.352191\pi$
$314$	−4.22656	−0.238519
$315$	4.81889	0.271514
$316$	−51.2743	−2.88440
$317$	−4.33703	−0.243592	−0.121796	−	0.992555i	$-0.538865\pi$
$317$	−4.33703	−0.243592	−0.121796	+	0.992555i	$0.538865\pi$
$318$	−4.33506	−0.243098
$319$	8.45920	0.473625
$320$	60.4191	3.37753
$321$	1.81287	0.101184
$322$	5.62537	0.313490
$323$	−0.495334	−0.0275611
$324$	38.7387	2.15215
$325$	4.93549	0.273772
$326$	−21.9931	−1.21809
$327$	−1.28226	−0.0709089
$328$	5.62924	0.310823
$329$	8.30181	0.457694
$330$	16.5484	0.910958
$331$	6.37596	0.350454	0.175227	−	0.984528i	$-0.443934\pi$
$331$	6.37596	0.350454	0.175227	+	0.984528i	$0.443934\pi$
$332$	79.6345	4.37051
$333$	6.08185	0.333283
$334$	27.3620	1.49718
$335$	30.2182	1.65100
$336$	3.59849	0.196314
$337$	22.4298	1.22183	0.610914	−	0.791697i	$-0.290802\pi$
$337$	22.4298	1.22183	0.610914	+	0.791697i	$0.290802\pi$
$338$	23.8482	1.29717
$339$	−8.95849	−0.486558
$340$	5.55041	0.301013
$341$	−5.74693	−0.311214
$342$	−9.71648	−0.525407
$343$	8.55528	0.461942
$344$	2.42929	0.130979
$345$	−3.90928	−0.210469
$346$	31.8973	1.71481
$347$	12.1409	0.651758	0.325879	−	0.945411i	$-0.394340\pi$
$347$	12.1409	0.651758	0.325879	+	0.945411i	$0.394340\pi$
$348$	−3.70151	−0.198422
$349$	3.02703	0.162033	0.0810167	−	0.996713i	$-0.474183\pi$
$349$	3.02703	0.162033	0.0810167	+	0.996713i	$0.474183\pi$
$350$	4.10537	0.219441
$351$	5.12499	0.273551
$352$	−93.9656	−5.00838
$353$	7.62591	0.405886	0.202943	−	0.979191i	$-0.434949\pi$
$353$	7.62591	0.405886	0.202943	+	0.979191i	$0.434949\pi$
$354$	−16.4276	−0.873117
$355$	−40.5967	−2.15465
$356$	50.9918	2.70256
$357$	0.105164	0.00556587
$358$	−2.70888	−0.143169
$359$	−1.10759	−0.0584565	−0.0292282	−	0.999573i	$-0.509305\pi$
$359$	−1.10759	−0.0584565	−0.0292282	+	0.999573i	$0.509305\pi$
$360$	67.5546	3.56044
$361$	−17.3587	−0.913615
$362$	50.3449	2.64607
$363$	−6.97779	−0.366239
$364$	−6.75487	−0.354051
$365$	−30.9741	−1.62126
$366$	−12.5866	−0.657911
$367$	16.0597	0.838311	0.419156	−	0.907914i	$-0.362326\pi$
$367$	16.0597	0.838311	0.419156	+	0.907914i	$0.362326\pi$
$368$	43.8936	2.28811
$369$	1.79618	0.0935051
$370$	15.8809	0.825607
$371$	2.33763	0.121363
$372$	2.51470	0.130381
$373$	−9.93265	−0.514293	−0.257146	−	0.966372i	$-0.582782\pi$
$373$	−9.93265	−0.514293	−0.257146	+	0.966372i	$0.582782\pi$
$374$	−5.43008	−0.280783
$375$	3.03848	0.156907
$376$	116.381	6.00188
$377$	3.31031	0.170490
$378$	4.26299	0.219265
$379$	26.9765	1.38569	0.692844	−	0.721087i	$-0.256357\pi$
$379$	26.9765	1.38569	0.692844	+	0.721087i	$0.256357\pi$
$380$	−18.3915	−0.943462
$381$	0.284824	0.0145920
$382$	24.3725	1.24701
$383$	−35.6661	−1.82245	−0.911226	−	0.411906i	$-0.864863\pi$
$383$	−35.6661	−1.82245	−0.911226	+	0.411906i	$0.864863\pi$
$384$	10.2594	0.523550
$385$	−8.92351	−0.454784
$386$	−43.5862	−2.21848
$387$	0.775137	0.0394025
$388$	−37.3638	−1.89686
$389$	11.1162	0.563613	0.281806	−	0.959471i	$-0.409066\pi$
$389$	11.1162	0.563613	0.281806	+	0.959471i	$0.409066\pi$
$390$	6.47582	0.327916
$391$	1.28277	0.0648723
$392$	58.2238	2.94075
$393$	9.70949	0.489779
$394$	34.6042	1.74333
$395$	−26.5068	−1.33370
$396$	−77.2121	−3.88005
$397$	−31.6964	−1.59080	−0.795399	−	0.606087i	$-0.792738\pi$
$397$	−31.6964	−1.59080	−0.795399	+	0.606087i	$0.792738\pi$
$398$	9.54503	0.478449
$399$	−0.348464	−0.0174450
$400$	32.0334	1.60167
$401$	−26.7222	−1.33444	−0.667221	−	0.744859i	$-0.732517\pi$
$401$	−26.7222	−1.33444	−0.667221	+	0.744859i	$0.732517\pi$
$402$	12.9360	0.645188
$403$	−2.24893	−0.112027
$404$	−68.8168	−3.42376
$405$	20.0264	0.995119
$406$	2.75354	0.136656
$407$	−11.2622	−0.558247
$408$	1.47426	0.0729869
$409$	25.2919	1.25060	0.625302	−	0.780383i	$-0.284976\pi$
$409$	25.2919	1.25060	0.625302	+	0.780383i	$0.284976\pi$
$410$	4.69016	0.231630
$411$	5.53535	0.273039
$412$	36.1598	1.78146
$413$	8.85838	0.435892
$414$	25.1628	1.23668
$415$	41.1679	2.02085
$416$	−36.7712	−1.80286
$417$	7.34403	0.359639
$418$	17.9927	0.880054
$419$	22.3604	1.09238	0.546188	−	0.837662i	$-0.316078\pi$
$419$	22.3604	1.09238	0.546188	+	0.837662i	$0.316078\pi$
$420$	3.90468	0.190529
$421$	27.8125	1.35550	0.677748	−	0.735294i	$-0.262956\pi$
$421$	27.8125	1.35550	0.677748	+	0.735294i	$0.262956\pi$
$422$	−10.7265	−0.522160
$423$	37.1347	1.80555
$424$	32.7705	1.59148
$425$	0.936157	0.0454103
$426$	−17.3789	−0.842010
$427$	6.78715	0.328453
$428$	−22.0869	−1.06761
$429$	−4.59245	−0.221725
$430$	2.02403	0.0976075
$431$	7.95560	0.383208	0.191604	−	0.981472i	$-0.438631\pi$
$431$	7.95560	0.383208	0.191604	+	0.981472i	$0.438631\pi$
$432$	33.2633	1.60038
$433$	25.2236	1.21217	0.606085	−	0.795400i	$-0.292739\pi$
$433$	25.2236	1.21217	0.606085	+	0.795400i	$0.292739\pi$
$434$	−1.87067	−0.0897951
$435$	−1.91354	−0.0917470
$436$	15.6222	0.748169
$437$	−4.25049	−0.203329
$438$	−13.2596	−0.633566
$439$	6.56403	0.313284	0.156642	−	0.987655i	$-0.449933\pi$
$439$	6.56403	0.313284	0.156642	+	0.987655i	$0.449933\pi$
$440$	−125.096	−5.96372
$441$	18.5780	0.884669
$442$	−2.12493	−0.101073
$443$	−23.0788	−1.09651	−0.548253	−	0.836312i	$-0.684707\pi$
$443$	−23.0788	−1.09651	−0.548253	+	0.836312i	$0.684707\pi$
$444$	4.92803	0.233874
$445$	26.3608	1.24962
$446$	−29.6242	−1.40275
$447$	−7.40742	−0.350359
$448$	−13.9471	−0.658940
$449$	−40.9208	−1.93117	−0.965586	−	0.260083i	$-0.916250\pi$
$449$	−40.9208	−1.93117	−0.965586	+	0.260083i	$0.916250\pi$
$450$	18.3637	0.865672
$451$	−3.32611	−0.156621
$452$	109.145	5.13374
$453$	6.04117	0.283839
$454$	22.8089	1.07048
$455$	−3.49200	−0.163708
$456$	−4.88502	−0.228762
$457$	22.5795	1.05623	0.528113	−	0.849174i	$-0.322900\pi$
$457$	22.5795	1.05623	0.528113	+	0.849174i	$0.322900\pi$
$458$	−43.1722	−2.01730
$459$	0.972101	0.0453738
$460$	47.6284	2.22068
$461$	−5.41794	−0.252339	−0.126169	−	0.992009i	$-0.540268\pi$
$461$	−5.41794	−0.252339	−0.126169	+	0.992009i	$0.540268\pi$
$462$	−3.82003	−0.177724
$463$	−8.02398	−0.372906	−0.186453	−	0.982464i	$-0.559699\pi$
$463$	−8.02398	−0.372906	−0.186453	+	0.982464i	$0.559699\pi$
$464$	21.4853	0.997429
$465$	1.30000	0.0602860
$466$	−20.7654	−0.961939
$467$	−16.8690	−0.780604	−0.390302	−	0.920687i	$-0.627629\pi$
$467$	−16.8690	−0.780604	−0.390302	+	0.920687i	$0.627629\pi$
$468$	−30.2151	−1.39669
$469$	−6.97557	−0.322102
$470$	96.9659	4.47270
$471$	−0.678023	−0.0312416
$472$	124.183	5.71598
$473$	−1.43538	−0.0659989
$474$	−11.3472	−0.521193
$475$	−3.10199	−0.142329
$476$	−1.28126	−0.0587262
$477$	10.4564	0.478766
$478$	70.9035	3.24305
$479$	31.8758	1.45644	0.728222	−	0.685342i	$-0.240347\pi$
$479$	31.8758	1.45644	0.728222	+	0.685342i	$0.240347\pi$
$480$	21.2557	0.970187
$481$	−4.40720	−0.200951
$482$	−1.05522	−0.0480640
$483$	0.902418	0.0410615
$484$	85.0133	3.86424
$485$	−19.3156	−0.877076
$486$	28.9100	1.31138
$487$	12.7465	0.577600	0.288800	−	0.957389i	$-0.406744\pi$
$487$	12.7465	0.577600	0.288800	+	0.957389i	$0.406744\pi$
$488$	95.1471	4.30711
$489$	−3.52812	−0.159547
$490$	48.5109	2.19150
$491$	−5.46747	−0.246743	−0.123372	−	0.992361i	$-0.539371\pi$
$491$	−5.46747	−0.246743	−0.123372	+	0.992361i	$0.539371\pi$
$492$	1.45541	0.0656151
$493$	0.627895	0.0282790
$494$	7.04103	0.316791
$495$	−39.9156	−1.79407
$496$	−14.5965	−0.655400
$497$	9.37135	0.420362
$498$	17.6234	0.789724
$499$	32.4570	1.45297	0.726487	−	0.687180i	$-0.241152\pi$
$499$	32.4570	1.45297	0.726487	+	0.687180i	$0.241152\pi$
$500$	−37.0191	−1.65554
$501$	4.38939	0.196103
$502$	−50.3056	−2.24525
$503$	−6.20748	−0.276778	−0.138389	−	0.990378i	$-0.544192\pi$
$503$	−6.20748	−0.276778	−0.138389	+	0.990378i	$0.544192\pi$
$504$	−15.5943	−0.694625
$505$	−35.5756	−1.58309
$506$	−46.5958	−2.07144
$507$	3.82571	0.169906
$508$	−3.47012	−0.153962
$509$	35.3313	1.56603	0.783015	−	0.622002i	$-0.213681\pi$
$509$	35.3313	1.56603	0.783015	+	0.622002i	$0.213681\pi$
$510$	1.22832	0.0543911
$511$	7.15005	0.316299
$512$	−5.39760	−0.238542
$513$	−3.22109	−0.142214
$514$	−39.3895	−1.73740
$515$	18.6932	0.823720
$516$	0.628082	0.0276498
$517$	−68.7652	−3.02429
$518$	−3.66594	−0.161072
$519$	5.11694	0.224609
$520$	−48.9534	−2.14675
$521$	−24.8443	−1.08845	−0.544224	−	0.838940i	$-0.683176\pi$
$521$	−24.8443	−1.08845	−0.544224	+	0.838940i	$0.683176\pi$
$522$	12.3168	0.539092
$523$	2.52242	0.110298	0.0551489	−	0.998478i	$-0.482437\pi$
$523$	2.52242	0.110298	0.0551489	+	0.998478i	$0.482437\pi$
$524$	−118.295	−5.16772
$525$	0.658581	0.0287428
$526$	39.1499	1.70702
$527$	−0.426573	−0.0185818
$528$	−29.8069	−1.29718
$529$	−11.9925	−0.521413
$530$	27.3037	1.18600
$531$	39.6243	1.71955
$532$	4.24548	0.184065
$533$	−1.30160	−0.0563784
$534$	11.2847	0.488335
$535$	−11.4181	−0.493646
$536$	−97.7884	−4.22382
$537$	−0.434557	−0.0187525
$538$	−69.3514	−2.98995
$539$	−34.4024	−1.48182
$540$	36.0935	1.55322
$541$	−35.9538	−1.54577	−0.772887	−	0.634544i	$-0.781188\pi$
$541$	−35.9538	−1.54577	−0.772887	+	0.634544i	$0.781188\pi$
$542$	−36.9757	−1.58824
$543$	8.07630	0.346587
$544$	−6.97472	−0.299039
$545$	8.07608	0.345941
$546$	−1.49488	−0.0639748
$547$	−0.968989	−0.0414310	−0.0207155	−	0.999785i	$-0.506594\pi$
$547$	−0.968989	−0.0414310	−0.0207155	+	0.999785i	$0.506594\pi$
$548$	−67.4394	−2.88087
$549$	30.3595	1.29571
$550$	−34.0054	−1.45000
$551$	−2.08055	−0.0886345
$552$	12.6507	0.538451
$553$	6.11882	0.260199
$554$	37.3397	1.58641
$555$	2.54760	0.108140
$556$	−89.4752	−3.79460
$557$	−33.7640	−1.43063	−0.715314	−	0.698804i	$-0.753716\pi$
$557$	−33.7640	−1.43063	−0.715314	+	0.698804i	$0.753716\pi$
$558$	−8.36767	−0.354232
$559$	−0.561702	−0.0237575
$560$	−22.6645	−0.957752
$561$	−0.871089	−0.0367774
$562$	1.03040	0.0434648
$563$	31.6121	1.33229	0.666145	−	0.745823i	$-0.267943\pi$
$563$	31.6121	1.33229	0.666145	+	0.745823i	$0.267943\pi$
$564$	30.0897	1.26701
$565$	56.4236	2.37376
$566$	−62.6329	−2.63266
$567$	−4.62289	−0.194143
$568$	131.374	5.51234
$569$	2.27691	0.0954532	0.0477266	−	0.998860i	$-0.484802\pi$
$569$	2.27691	0.0954532	0.0477266	+	0.998860i	$0.484802\pi$
$570$	−4.07009	−0.170477
$571$	−14.8376	−0.620935	−0.310467	−	0.950584i	$-0.600486\pi$
$571$	−14.8376	−0.620935	−0.310467	+	0.950584i	$0.600486\pi$
$572$	55.9516	2.33945
$573$	3.90983	0.163335
$574$	−1.08268	−0.0451900
$575$	8.03322	0.335008
$576$	−62.3867	−2.59945
$577$	−20.3022	−0.845190	−0.422595	−	0.906319i	$-0.638881\pi$
$577$	−20.3022	−0.845190	−0.422595	+	0.906319i	$0.638881\pi$
$578$	45.4328	1.88976
$579$	−6.99207	−0.290581
$580$	23.3134	0.968035
$581$	−9.50320	−0.394259
$582$	−8.26873	−0.342750
$583$	−19.3629	−0.801929
$584$	100.234	4.14773
$585$	−15.6200	−0.645809
$586$	78.5920	3.24660
$587$	29.6013	1.22178	0.610888	−	0.791717i	$-0.290813\pi$
$587$	29.6013	1.22178	0.610888	+	0.791717i	$0.290813\pi$
$588$	15.0535	0.620797
$589$	1.41346	0.0582408
$590$	103.467	4.25965
$591$	5.55118	0.228345
$592$	−28.6046	−1.17564
$593$	−36.3686	−1.49348	−0.746741	−	0.665115i	$-0.768382\pi$
$593$	−36.3686	−1.49348	−0.746741	+	0.665115i	$0.768382\pi$
$594$	−35.3110	−1.44883
$595$	−0.662359	−0.0271541
$596$	90.2476	3.69669
$597$	1.53121	0.0626681
$598$	−18.2342	−0.745651
$599$	1.49659	0.0611490	0.0305745	−	0.999532i	$-0.490266\pi$
$599$	1.49659	0.0611490	0.0305745	+	0.999532i	$0.490266\pi$
$600$	9.23245	0.376913
$601$	−12.2079	−0.497970	−0.248985	−	0.968507i	$-0.580097\pi$
$601$	−12.2079	−0.497970	−0.248985	+	0.968507i	$0.580097\pi$
$602$	−0.467227	−0.0190428
$603$	−31.2023	−1.27066
$604$	−73.6020	−2.99482
$605$	43.9485	1.78676
$606$	−15.2294	−0.618652
$607$	−22.6215	−0.918178	−0.459089	−	0.888390i	$-0.651824\pi$
$607$	−22.6215	−0.918178	−0.459089	+	0.888390i	$0.651824\pi$
$608$	23.1110	0.937273
$609$	0.441720	0.0178994
$610$	79.2745	3.20973
$611$	−26.9096	−1.08865
$612$	−5.73116	−0.231669
$613$	−10.0169	−0.404579	−0.202289	−	0.979326i	$-0.564838\pi$
$613$	−10.0169	−0.404579	−0.202289	+	0.979326i	$0.564838\pi$
$614$	−69.1648	−2.79126
$615$	0.752392	0.0303394
$616$	28.8771	1.16349
$617$	21.0534	0.847577	0.423789	−	0.905761i	$-0.360700\pi$
$617$	21.0534	0.847577	0.423789	+	0.905761i	$0.360700\pi$
$618$	8.00229	0.321899
$619$	35.7928	1.43863	0.719317	−	0.694682i	$-0.244455\pi$
$619$	35.7928	1.43863	0.719317	+	0.694682i	$0.244455\pi$
$620$	−15.8384	−0.636086
$621$	8.34165	0.334739
$622$	41.9969	1.68392
$623$	−6.08511	−0.243795
$624$	−11.6642	−0.466942
$625$	−31.2438	−1.24975
$626$	−42.7255	−1.70766
$627$	2.88638	0.115271
$628$	8.26062	0.329635
$629$	−0.835953	−0.0333316
$630$	−12.9928	−0.517647
$631$	5.98532	0.238272	0.119136	−	0.992878i	$-0.461988\pi$
$631$	5.98532	0.238272	0.119136	+	0.992878i	$0.461988\pi$
$632$	85.7780	3.41207
$633$	−1.72075	−0.0683935
$634$	11.6936	0.464413
$635$	−1.79392	−0.0711894
$636$	8.47266	0.335963
$637$	−13.4626	−0.533406
$638$	−22.8080	−0.902975
$639$	41.9188	1.65828
$640$	−64.6175	−2.55423
$641$	25.3015	0.999348	0.499674	−	0.866214i	$-0.333453\pi$
$641$	25.3015	0.999348	0.499674	+	0.866214i	$0.333453\pi$
$642$	−4.88791	−0.192910
$643$	12.9856	0.512104	0.256052	−	0.966663i	$-0.417578\pi$
$643$	12.9856	0.512104	0.256052	+	0.966663i	$0.417578\pi$
$644$	−10.9945	−0.433245
$645$	0.324694	0.0127848
$646$	1.33553	0.0525459
$647$	21.1232	0.830439	0.415220	−	0.909721i	$-0.363705\pi$
$647$	21.1232	0.830439	0.415220	+	0.909721i	$0.363705\pi$
$648$	−64.8069	−2.54586
$649$	−73.3753	−2.88023
$650$	−13.3072	−0.521952
$651$	−0.300092	−0.0117615
$652$	42.9845	1.68340
$653$	−35.0568	−1.37188	−0.685940	−	0.727658i	$-0.740609\pi$
$653$	−35.0568	−1.37188	−0.685940	+	0.727658i	$0.740609\pi$
$654$	3.45725	0.135189
$655$	−61.1537	−2.38947
$656$	−8.44789	−0.329835
$657$	31.9828	1.24777
$658$	−22.3836	−0.872603
$659$	−3.74580	−0.145916	−0.0729578	−	0.997335i	$-0.523244\pi$
$659$	−3.74580	−0.145916	−0.0729578	+	0.997335i	$0.523244\pi$
$660$	−32.3430	−1.25895
$661$	13.4859	0.524542	0.262271	−	0.964994i	$-0.415529\pi$
$661$	13.4859	0.524542	0.262271	+	0.964994i	$0.415529\pi$
$662$	−17.1910	−0.668149
$663$	−0.340880	−0.0132387
$664$	−133.223	−5.17004
$665$	2.19475	0.0851086
$666$	−16.3981	−0.635412
$667$	5.38801	0.208624
$668$	−53.4777	−2.06911
$669$	−4.75229	−0.183734
$670$	−81.4752	−3.14766
$671$	−56.2190	−2.17031
$672$	−4.90667	−0.189279
$673$	27.9266	1.07649	0.538246	−	0.842788i	$-0.319087\pi$
$673$	27.9266	1.07649	0.538246	+	0.842788i	$0.319087\pi$
$674$	−60.4759	−2.32944
$675$	6.08770	0.234316
$676$	−46.6101	−1.79270
$677$	−12.0483	−0.463054	−0.231527	−	0.972828i	$-0.574372\pi$
$677$	−12.0483	−0.463054	−0.231527	+	0.972828i	$0.574372\pi$
$678$	24.1541	0.927634
$679$	4.45881	0.171113
$680$	−9.28541	−0.356079
$681$	3.65899	0.140213
$682$	15.4950	0.593336
$683$	−38.9932	−1.49203	−0.746017	−	0.665926i	$-0.768036\pi$
$683$	−38.9932	−1.49203	−0.746017	+	0.665926i	$0.768036\pi$
$684$	18.9904	0.726116
$685$	−34.8635	−1.33207
$686$	−23.0670	−0.880702
$687$	−6.92565	−0.264230
$688$	−3.64568	−0.138990
$689$	−7.57721	−0.288669
$690$	10.5403	0.401263
$691$	29.6570	1.12821	0.564104	−	0.825704i	$-0.309222\pi$
$691$	29.6570	1.12821	0.564104	+	0.825704i	$0.309222\pi$
$692$	−62.3417	−2.36988
$693$	9.21411	0.350015
$694$	−32.7347	−1.24259
$695$	−46.2552	−1.75456
$696$	6.19235	0.234720
$697$	−0.246885	−0.00935144
$698$	−8.16158	−0.308920
$699$	−3.33117	−0.125997
$700$	−8.02375	−0.303269
$701$	5.21982	0.197150	0.0985750	−	0.995130i	$-0.468572\pi$
$701$	5.21982	0.197150	0.0985750	+	0.995130i	$0.468572\pi$
$702$	−13.8181	−0.521532
$703$	2.76996	0.104471
$704$	115.526	4.35406
$705$	15.5552	0.585843
$706$	−20.5612	−0.773831
$707$	8.21227	0.308854
$708$	32.1070	1.20665
$709$	−34.1303	−1.28179	−0.640895	−	0.767629i	$-0.721436\pi$
$709$	−34.1303	−1.28179	−0.640895	+	0.767629i	$0.721436\pi$
$710$	109.458	4.10789
$711$	27.3700	1.02646
$712$	−85.3054	−3.19696
$713$	−3.66045	−0.137085
$714$	−0.283546	−0.0106115
$715$	28.9248	1.08173
$716$	5.29438	0.197860
$717$	11.3743	0.424781
$718$	2.98632	0.111449
$719$	−20.3846	−0.760216	−0.380108	−	0.924942i	$-0.624113\pi$
$719$	−20.3846	−0.760216	−0.380108	+	0.924942i	$0.624113\pi$
$720$	−101.380	−3.77823
$721$	−4.31513	−0.160704
$722$	46.8030	1.74183
$723$	−0.169278	−0.00629551
$724$	−98.3967	−3.65689
$725$	3.93214	0.146036
$726$	18.8137	0.698243
$727$	42.0393	1.55915	0.779576	−	0.626308i	$-0.215435\pi$
$727$	42.0393	1.55915	0.779576	+	0.626308i	$0.215435\pi$
$728$	11.3004	0.418820
$729$	−17.4161	−0.645042
$730$	83.5132	3.09096
$731$	−0.106543	−0.00394063
$732$	24.5999	0.909237
$733$	−5.68087	−0.209828	−0.104914	−	0.994481i	$-0.533457\pi$
$733$	−5.68087	−0.209828	−0.104914	+	0.994481i	$0.533457\pi$
$734$	−43.3007	−1.59826
$735$	7.78208	0.287046
$736$	−59.8504	−2.20612
$737$	57.7797	2.12834
$738$	−4.84290	−0.178270
$739$	20.2680	0.745571	0.372786	−	0.927917i	$-0.378403\pi$
$739$	20.2680	0.745571	0.372786	+	0.927917i	$0.378403\pi$
$740$	−31.0384	−1.14099
$741$	1.12952	0.0414939
$742$	−6.30277	−0.231382
$743$	−33.7272	−1.23733	−0.618666	−	0.785654i	$-0.712326\pi$
$743$	−33.7272	−1.23733	−0.618666	+	0.785654i	$0.712326\pi$
$744$	−4.20690	−0.154232
$745$	46.6545	1.70929
$746$	26.7807	0.980511
$747$	−42.5086	−1.55531
$748$	10.6128	0.388044
$749$	2.63574	0.0963079
$750$	−8.19245	−0.299146
$751$	17.0167	0.620949	0.310474	−	0.950582i	$-0.399512\pi$
$751$	17.0167	0.620949	0.310474	+	0.950582i	$0.399512\pi$
$752$	−174.655	−6.36900
$753$	−8.06999	−0.294087
$754$	−8.92535	−0.325042
$755$	−38.0493	−1.38476
$756$	−8.33182	−0.303025
$757$	24.6136	0.894598	0.447299	−	0.894385i	$-0.352386\pi$
$757$	24.6136	0.894598	0.447299	+	0.894385i	$0.352386\pi$
$758$	−72.7348	−2.64185
$759$	−7.47487	−0.271321
$760$	30.7675	1.11606
$761$	−42.6633	−1.54654	−0.773271	−	0.634075i	$-0.781381\pi$
$761$	−42.6633	−1.54654	−0.773271	+	0.634075i	$0.781381\pi$
$762$	−0.767950	−0.0278199
$763$	−1.86428	−0.0674915
$764$	−47.6350	−1.72337
$765$	−2.96279	−0.107120
$766$	96.1640	3.47455
$767$	−28.7137	−1.03679
$768$	−8.47610	−0.305855
$769$	−33.5656	−1.21041	−0.605204	−	0.796070i	$-0.706908\pi$
$769$	−33.5656	−1.21041	−0.605204	+	0.796070i	$0.706908\pi$
$770$	24.0598	0.867056
$771$	−6.31884	−0.227567
$772$	85.1872	3.06596
$773$	−16.0130	−0.575946	−0.287973	−	0.957639i	$-0.592981\pi$
$773$	−16.0130	−0.575946	−0.287973	+	0.957639i	$0.592981\pi$
$774$	−2.08995	−0.0751216
$775$	−2.67138	−0.0959588
$776$	62.5067	2.24386
$777$	−0.588087	−0.0210975
$778$	−29.9718	−1.07454
$779$	0.818062	0.0293101
$780$	−12.6567	−0.453182
$781$	−77.6243	−2.77761
$782$	−3.45863	−0.123681
$783$	4.08311	0.145919
$784$	−87.3776	−3.12063
$785$	4.27042	0.152418
$786$	−26.1790	−0.933774
$787$	6.59742	0.235173	0.117586	−	0.993063i	$-0.462484\pi$
$787$	6.59742	0.235173	0.117586	+	0.993063i	$0.462484\pi$
$788$	−67.6323	−2.40930
$789$	6.28039	0.223588
$790$	71.4684	2.54273
$791$	−13.0248	−0.463109
$792$	129.170	4.58985
$793$	−22.0000	−0.781242
$794$	85.4608	3.03289
$795$	4.38003	0.155344
$796$	−18.6553	−0.661219
$797$	46.8166	1.65833	0.829164	−	0.559005i	$-0.188817\pi$
$797$	46.8166	1.65833	0.829164	+	0.559005i	$0.188817\pi$
$798$	0.939540	0.0332593
$799$	−5.10418	−0.180573
$800$	−43.6786	−1.54427
$801$	−27.2192	−0.961744
$802$	72.0492	2.54414
$803$	−59.2249	−2.09000
$804$	−25.2828	−0.891654
$805$	−5.68374	−0.200325
$806$	6.06362	0.213582
$807$	−11.1253	−0.391629
$808$	115.125	4.05010
$809$	−47.8278	−1.68153	−0.840767	−	0.541396i	$-0.817896\pi$
$809$	−47.8278	−1.68153	−0.840767	+	0.541396i	$0.817896\pi$
$810$	−53.9957	−1.89722
$811$	−5.53567	−0.194384	−0.0971918	−	0.995266i	$-0.530986\pi$
$811$	−5.53567	−0.194384	−0.0971918	+	0.995266i	$0.530986\pi$
$812$	−5.38165	−0.188859
$813$	−5.93161	−0.208031
$814$	30.3655	1.06431
$815$	22.2213	0.778378
$816$	−2.21245	−0.0774514
$817$	0.353034	0.0123511
$818$	−68.1927	−2.38430
$819$	3.60572	0.125994
$820$	−9.16669	−0.320115
$821$	20.3162	0.709041	0.354521	−	0.935048i	$-0.384644\pi$
$821$	20.3162	0.709041	0.354521	+	0.935048i	$0.384644\pi$
$822$	−14.9246	−0.520554
$823$	−1.97318	−0.0687807	−0.0343904	−	0.999408i	$-0.510949\pi$
$823$	−1.97318	−0.0687807	−0.0343904	+	0.999408i	$0.510949\pi$
$824$	−60.4926	−2.10736
$825$	−5.45512	−0.189923
$826$	−23.8842	−0.831038
$827$	29.2531	1.01723	0.508616	−	0.860994i	$-0.330157\pi$
$827$	29.2531	1.01723	0.508616	+	0.860994i	$0.330157\pi$
$828$	−49.1794	−1.70910
$829$	−27.5082	−0.955399	−0.477700	−	0.878523i	$-0.658529\pi$
$829$	−27.5082	−0.955399	−0.477700	+	0.878523i	$0.658529\pi$
$830$	−110.998	−3.85280
$831$	5.99001	0.207791
$832$	45.2084	1.56732
$833$	−2.55356	−0.0884756
$834$	−19.8012	−0.685659
$835$	−27.6459	−0.956724
$836$	−35.1660	−1.21624
$837$	−2.77395	−0.0958816
$838$	−60.2888	−2.08264
$839$	29.1267	1.00557	0.502783	−	0.864413i	$-0.332310\pi$
$839$	29.1267	1.00557	0.502783	+	0.864413i	$0.332310\pi$
$840$	−6.53223	−0.225383
$841$	−26.3627	−0.909057
$842$	−74.9888	−2.58428
$843$	0.165296	0.00569309
$844$	20.9645	0.721629
$845$	−24.0956	−0.828914
$846$	−100.124	−3.44232
$847$	−10.1451	−0.348589
$848$	−49.1792	−1.68882
$849$	−10.0475	−0.344830
$850$	−2.52409	−0.0865757
$851$	−7.17336	−0.245900
$852$	33.9662	1.16366
$853$	3.70762	0.126946	0.0634732	−	0.997984i	$-0.479782\pi$
$853$	3.70762	0.126946	0.0634732	+	0.997984i	$0.479782\pi$
$854$	−18.2997	−0.626204
$855$	9.81729	0.335744
$856$	36.9497	1.26291
$857$	−21.7988	−0.744633	−0.372317	−	0.928106i	$-0.621436\pi$
$857$	−21.7988	−0.744633	−0.372317	+	0.928106i	$0.621436\pi$
$858$	12.3823	0.422724
$859$	9.15940	0.312515	0.156257	−	0.987716i	$-0.450057\pi$
$859$	9.15940	0.312515	0.156257	+	0.987716i	$0.450057\pi$
$860$	−3.95588	−0.134894
$861$	−0.173682	−0.00591907
$862$	−21.4501	−0.730594
$863$	−45.4574	−1.54739	−0.773694	−	0.633560i	$-0.781593\pi$
$863$	−45.4574	−1.54739	−0.773694	+	0.633560i	$0.781593\pi$
$864$	−45.3556	−1.54303
$865$	−32.2282	−1.09579
$866$	−68.0087	−2.31103
$867$	7.28830	0.247524
$868$	3.65614	0.124097
$869$	−50.6831	−1.71931
$870$	5.15933	0.174918
$871$	22.6107	0.766135
$872$	−26.1348	−0.885036
$873$	19.9446	0.675024
$874$	11.4603	0.387650
$875$	4.41767	0.149345
$876$	25.9152	0.875592
$877$	−28.7246	−0.969959	−0.484980	−	0.874525i	$-0.661173\pi$
$877$	−28.7246	−0.969959	−0.484980	+	0.874525i	$0.661173\pi$
$878$	−17.6981	−0.597283
$879$	12.6077	0.425246
$880$	187.734	6.32851
$881$	−40.2242	−1.35519	−0.677593	−	0.735437i	$-0.736977\pi$
$881$	−40.2242	−1.35519	−0.677593	+	0.735437i	$0.736977\pi$
$882$	−50.0907	−1.68664
$883$	−1.35428	−0.0455751	−0.0227875	−	0.999740i	$-0.507254\pi$
$883$	−1.35428	−0.0455751	−0.0227875	+	0.999740i	$0.507254\pi$
$884$	4.15308	0.139683
$885$	16.5980	0.557937
$886$	62.2257	2.09051
$887$	19.9253	0.669026	0.334513	−	0.942391i	$-0.391428\pi$
$887$	19.9253	0.669026	0.334513	+	0.942391i	$0.391428\pi$
$888$	−8.24422	−0.276658
$889$	0.414107	0.0138887
$890$	−71.0746	−2.38243
$891$	38.2921	1.28283
$892$	57.8990	1.93860
$893$	16.9129	0.565968
$894$	19.9721	0.667967
$895$	2.73698	0.0914873
$896$	14.9163	0.498318
$897$	−2.92511	−0.0976667
$898$	110.332	3.68182
$899$	−1.79174	−0.0597577
$900$	−35.8909	−1.19636
$901$	−1.43724	−0.0478813
$902$	8.96796	0.298601
$903$	−0.0749523	−0.00249426
$904$	−182.591	−6.07289
$905$	−50.8673	−1.69088
$906$	−16.2884	−0.541145
$907$	54.6631	1.81506	0.907530	−	0.419987i	$-0.137966\pi$
$907$	54.6631	1.81506	0.907530	+	0.419987i	$0.137966\pi$
$908$	−44.5789	−1.47940
$909$	36.7342	1.21840
$910$	9.41524	0.312112
$911$	1.09615	0.0363170	0.0181585	−	0.999835i	$-0.494220\pi$
$911$	1.09615	0.0363170	0.0181585	+	0.999835i	$0.494220\pi$
$912$	7.33104	0.242755
$913$	78.7164	2.60513
$914$	−60.8796	−2.01372
$915$	12.7172	0.420417
$916$	84.3780	2.78793
$917$	14.1167	0.466175
$918$	−2.62101	−0.0865061
$919$	−32.7505	−1.08034	−0.540170	−	0.841556i	$-0.681640\pi$
$919$	−32.7505	−1.08034	−0.540170	+	0.841556i	$0.681640\pi$
$920$	−79.6786	−2.62693
$921$	−11.0954	−0.365605
$922$	14.6080	0.481089
$923$	−30.3764	−0.999852
$924$	7.46606	0.245615
$925$	−5.23508	−0.172128
$926$	21.6345	0.710953
$927$	−19.3020	−0.633959
$928$	−29.2959	−0.961685
$929$	52.7109	1.72939	0.864695	−	0.502297i	$-0.167512\pi$
$929$	52.7109	1.72939	0.864695	+	0.502297i	$0.167512\pi$
$930$	−3.50510	−0.114937
$931$	8.46131	0.277308
$932$	40.5850	1.32941
$933$	6.73711	0.220563
$934$	45.4827	1.48824
$935$	5.48642	0.179425
$936$	50.5476	1.65220
$937$	33.0160	1.07858	0.539292	−	0.842119i	$-0.318692\pi$
$937$	33.0160	1.07858	0.539292	+	0.842119i	$0.318692\pi$
$938$	18.8077	0.614094
$939$	−6.85400	−0.223672
$940$	−189.515	−6.18130
$941$	53.7467	1.75209	0.876047	−	0.482226i	$-0.160172\pi$
$941$	53.7467	1.75209	0.876047	+	0.482226i	$0.160172\pi$
$942$	1.82810	0.0595628
$943$	−2.11853	−0.0689890
$944$	−186.364	−6.06562
$945$	−4.30722	−0.140114
$946$	3.87012	0.125828
$947$	−26.5456	−0.862618	−0.431309	−	0.902204i	$-0.641948\pi$
$947$	−26.5456	−0.862618	−0.431309	+	0.902204i	$0.641948\pi$
$948$	22.1775	0.720292
$949$	−23.1763	−0.752334
$950$	8.36367	0.271353
$951$	1.87588	0.0608297
$952$	2.14344	0.0694694
$953$	2.63578	0.0853813	0.0426907	−	0.999088i	$-0.486407\pi$
$953$	2.63578	0.0853813	0.0426907	+	0.999088i	$0.486407\pi$
$954$	−28.1928	−0.912777
$955$	−24.6254	−0.796860
$956$	−138.578	−4.48192
$957$	−3.65884	−0.118273
$958$	−85.9445	−2.77674
$959$	8.04789	0.259880
$960$	−26.1329	−0.843435
$961$	−29.7827	−0.960734
$962$	11.8828	0.383118
$963$	11.7899	0.379924
$964$	2.06238	0.0664248
$965$	44.0385	1.41765
$966$	−2.43313	−0.0782846
$967$	11.4406	0.367905	0.183953	−	0.982935i	$-0.441111\pi$
$967$	11.4406	0.367905	0.183953	+	0.982935i	$0.441111\pi$
$968$	−142.221	−4.57115
$969$	0.214245	0.00688256
$970$	52.0793	1.67216
$971$	5.51851	0.177097	0.0885487	−	0.996072i	$-0.471777\pi$
$971$	5.51851	0.177097	0.0885487	+	0.996072i	$0.471777\pi$
$972$	−56.5031	−1.81234
$973$	10.6775	0.342306
$974$	−34.3676	−1.10121
$975$	−2.13473	−0.0683662
$976$	−142.789	−4.57056
$977$	0.931357	0.0297968	0.0148984	−	0.999889i	$-0.495258\pi$
$977$	0.931357	0.0297968	0.0148984	+	0.999889i	$0.495258\pi$
$978$	9.51262	0.304180
$979$	50.4039	1.61092
$980$	−94.8122	−3.02866
$981$	−8.33909	−0.266247
$982$	14.7415	0.470422
$983$	−16.1985	−0.516651	−0.258325	−	0.966058i	$-0.583171\pi$
$983$	−16.1985	−0.516651	−0.258325	+	0.966058i	$0.583171\pi$
$984$	−2.43480	−0.0776185
$985$	−34.9632	−1.11402
$986$	−1.69295	−0.0539145
$987$	−3.59076	−0.114295
$988$	−13.7614	−0.437807
$989$	−0.914251	−0.0290715
$990$	107.622	3.42044
$991$	−52.4931	−1.66750	−0.833750	−	0.552143i	$-0.813810\pi$
$991$	−52.4931	−1.66750	−0.833750	+	0.552143i	$0.813810\pi$
$992$	19.9028	0.631913
$993$	−2.75777	−0.0875153
$994$	−25.2673	−0.801430
$995$	−9.64406	−0.305737
$996$	−34.4441	−1.09140
$997$	−45.9958	−1.45670	−0.728351	−	0.685205i	$-0.759713\pi$
$997$	−45.9958	−1.45670	−0.728351	+	0.685205i	$0.759713\pi$
$998$	−87.5115	−2.77013
$999$	−5.43608	−0.171990

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.a.1.8	✓	309

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.a.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-2.69623 q^{2} -0.432527 q^{3} +5.26965 q^{4} +2.72420 q^{5} +1.16619 q^{6} -0.628855 q^{7} -8.81573 q^{8} -2.81292 q^{9} +O(q^{10})\)	\(q-2.69623 q^{2} -0.432527 q^{3} +5.26965 q^{4} +2.72420 q^{5} +1.16619 q^{6} -0.628855 q^{7} -8.81573 q^{8} -2.81292 q^{9} -7.34507 q^{10} +5.20890 q^{11} -2.27927 q^{12} +2.03838 q^{13} +1.69554 q^{14} -1.17829 q^{15} +13.2299 q^{16} +0.386637 q^{17} +7.58428 q^{18} -1.28113 q^{19} +14.3556 q^{20} +0.271997 q^{21} -14.0444 q^{22} +3.31775 q^{23} +3.81304 q^{24} +2.42128 q^{25} -5.49594 q^{26} +2.51425 q^{27} -3.31384 q^{28} +1.62399 q^{29} +3.17694 q^{30} -1.10329 q^{31} -18.0394 q^{32} -2.25299 q^{33} -1.04246 q^{34} -1.71313 q^{35} -14.8231 q^{36} -2.16211 q^{37} +3.45423 q^{38} -0.881654 q^{39} -24.0158 q^{40} -0.638545 q^{41} -0.733365 q^{42} -0.275563 q^{43} +27.4491 q^{44} -7.66297 q^{45} -8.94543 q^{46} -13.2015 q^{47} -5.72230 q^{48} -6.60454 q^{49} -6.52833 q^{50} -0.167231 q^{51} +10.7415 q^{52} -3.71727 q^{53} -6.77898 q^{54} +14.1901 q^{55} +5.54381 q^{56} +0.554126 q^{57} -4.37865 q^{58} -14.0865 q^{59} -6.20919 q^{60} -10.7929 q^{61} +2.97473 q^{62} +1.76892 q^{63} +22.1786 q^{64} +5.55296 q^{65} +6.07458 q^{66} +11.0925 q^{67} +2.03744 q^{68} -1.43502 q^{69} +4.61898 q^{70} -14.9022 q^{71} +24.7979 q^{72} -11.3700 q^{73} +5.82955 q^{74} -1.04727 q^{75} -6.75113 q^{76} -3.27564 q^{77} +2.37714 q^{78} -9.73011 q^{79} +36.0410 q^{80} +7.35128 q^{81} +1.72166 q^{82} +15.1119 q^{83} +1.43333 q^{84} +1.05328 q^{85} +0.742982 q^{86} -0.702420 q^{87} -45.9202 q^{88} +9.67650 q^{89} +20.6611 q^{90} -1.28184 q^{91} +17.4834 q^{92} +0.477204 q^{93} +35.5942 q^{94} -3.49007 q^{95} +7.80255 q^{96} -7.09037 q^{97} +17.8074 q^{98} -14.6522 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) \) 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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