LMFDB - Embedded newform 8011.2.a.a.1.1

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			1.1
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)

$f(q)$	$=$	$q-2.81833 q^{2} +1.84881 q^{3} +5.94296 q^{4} -3.66460 q^{5} -5.21056 q^{6} -0.909168 q^{7} -11.1126 q^{8} +0.418106 q^{9} +O(q^{10})$	\(q-2.81833 q^{2} +1.84881 q^{3} +5.94296 q^{4} -3.66460 q^{5} -5.21056 q^{6} -0.909168 q^{7} -11.1126 q^{8} +0.418106 q^{9} +10.3280 q^{10} +3.59251 q^{11} +10.9874 q^{12} -5.43991 q^{13} +2.56233 q^{14} -6.77516 q^{15} +19.4329 q^{16} +2.15373 q^{17} -1.17836 q^{18} -2.00061 q^{19} -21.7786 q^{20} -1.68088 q^{21} -10.1249 q^{22} +0.378955 q^{23} -20.5450 q^{24} +8.42931 q^{25} +15.3314 q^{26} -4.77344 q^{27} -5.40315 q^{28} -10.6253 q^{29} +19.0946 q^{30} +6.15474 q^{31} -32.5431 q^{32} +6.64188 q^{33} -6.06992 q^{34} +3.33174 q^{35} +2.48479 q^{36} +9.98019 q^{37} +5.63838 q^{38} -10.0574 q^{39} +40.7231 q^{40} +5.18077 q^{41} +4.73727 q^{42} +11.0588 q^{43} +21.3502 q^{44} -1.53219 q^{45} -1.06802 q^{46} +7.24380 q^{47} +35.9277 q^{48} -6.17341 q^{49} -23.7565 q^{50} +3.98185 q^{51} -32.3292 q^{52} +1.03895 q^{53} +13.4531 q^{54} -13.1651 q^{55} +10.1032 q^{56} -3.69876 q^{57} +29.9456 q^{58} -0.881813 q^{59} -40.2645 q^{60} -15.5037 q^{61} -17.3461 q^{62} -0.380129 q^{63} +52.8512 q^{64} +19.9351 q^{65} -18.7190 q^{66} +2.25281 q^{67} +12.7996 q^{68} +0.700616 q^{69} -9.38993 q^{70} -4.48569 q^{71} -4.64622 q^{72} +13.6558 q^{73} -28.1274 q^{74} +15.5842 q^{75} -11.8896 q^{76} -3.26620 q^{77} +28.3449 q^{78} +9.20837 q^{79} -71.2137 q^{80} -10.0795 q^{81} -14.6011 q^{82} +1.49174 q^{83} -9.98941 q^{84} -7.89258 q^{85} -31.1674 q^{86} -19.6442 q^{87} -39.9220 q^{88} +2.55688 q^{89} +4.31822 q^{90} +4.94579 q^{91} +2.25211 q^{92} +11.3790 q^{93} -20.4154 q^{94} +7.33145 q^{95} -60.1660 q^{96} -8.25333 q^{97} +17.3987 q^{98} +1.50205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.81833	−1.99286	−0.996429	−	0.0844380i	$-0.973091\pi$
$2$	−2.81833	−1.99286	−0.996429	+	0.0844380i	$0.973091\pi$
$3$	1.84881	1.06741	0.533706	−	0.845670i	$-0.320799\pi$
$3$	1.84881	1.06741	0.533706	+	0.845670i	$0.320799\pi$
$4$	5.94296	2.97148
$5$	−3.66460	−1.63886	−0.819430	−	0.573179i	$-0.805710\pi$
$5$	−3.66460	−1.63886	−0.819430	+	0.573179i	$0.805710\pi$
$6$	−5.21056	−2.12720
$7$	−0.909168	−0.343633	−0.171817	−	0.985129i	$-0.554964\pi$
$7$	−0.909168	−0.343633	−0.171817	+	0.985129i	$0.554964\pi$
$8$	−11.1126	−3.92888
$9$	0.418106	0.139369
$10$	10.3280	3.26601
$11$	3.59251	1.08318	0.541592	−	0.840641i	$-0.317822\pi$
$11$	3.59251	1.08318	0.541592	+	0.840641i	$0.317822\pi$
$12$	10.9874	3.17179
$13$	−5.43991	−1.50876	−0.754380	−	0.656438i	$-0.772062\pi$
$13$	−5.43991	−1.50876	−0.754380	+	0.656438i	$0.772062\pi$
$14$	2.56233	0.684812
$15$	−6.77516	−1.74934
$16$	19.4329	4.85822
$17$	2.15373	0.522357	0.261179	−	0.965290i	$-0.415889\pi$
$17$	2.15373	0.522357	0.261179	+	0.965290i	$0.415889\pi$
$18$	−1.17836	−0.277742
$19$	−2.00061	−0.458972	−0.229486	−	0.973312i	$-0.573704\pi$
$19$	−2.00061	−0.458972	−0.229486	+	0.973312i	$0.573704\pi$
$20$	−21.7786	−4.86984
$21$	−1.68088	−0.366798
$22$	−10.1249	−2.15863
$23$	0.378955	0.0790175	0.0395087	−	0.999219i	$-0.487421\pi$
$23$	0.378955	0.0790175	0.0395087	+	0.999219i	$0.487421\pi$
$24$	−20.5450	−4.19373
$25$	8.42931	1.68586
$26$	15.3314	3.00674
$27$	−4.77344	−0.918648
$28$	−5.40315	−1.02110
$29$	−10.6253	−1.97307	−0.986535	−	0.163549i	$-0.947706\pi$
$29$	−10.6253	−1.97307	−0.986535	+	0.163549i	$0.947706\pi$
$30$	19.0946	3.48618
$31$	6.15474	1.10542	0.552712	−	0.833372i	$-0.313593\pi$
$31$	6.15474	1.10542	0.552712	+	0.833372i	$0.313593\pi$
$32$	−32.5431	−5.75286
$33$	6.64188	1.15620
$34$	−6.06992	−1.04098
$35$	3.33174	0.563167
$36$	2.48479	0.414131
$37$	9.98019	1.64073	0.820366	−	0.571838i	$-0.193770\pi$
$37$	9.98019	1.64073	0.820366	+	0.571838i	$0.193770\pi$
$38$	5.63838	0.914665
$39$	−10.0574	−1.61047
$40$	40.7231	6.43888
$41$	5.18077	0.809100	0.404550	−	0.914516i	$-0.367428\pi$
$41$	5.18077	0.809100	0.404550	+	0.914516i	$0.367428\pi$
$42$	4.73727	0.730977
$43$	11.0588	1.68646	0.843228	−	0.537556i	$-0.180652\pi$
$43$	11.0588	1.68646	0.843228	+	0.537556i	$0.180652\pi$
$44$	21.3502	3.21866
$45$	−1.53219	−0.228406
$46$	−1.06802	−0.157471
$47$	7.24380	1.05662	0.528308	−	0.849053i	$-0.322826\pi$
$47$	7.24380	1.05662	0.528308	+	0.849053i	$0.322826\pi$
$48$	35.9277	5.18572
$49$	−6.17341	−0.881916
$50$	−23.7565	−3.35968
$51$	3.98185	0.557570
$52$	−32.3292	−4.48325
$53$	1.03895	0.142711	0.0713554	−	0.997451i	$-0.477268\pi$
$53$	1.03895	0.142711	0.0713554	+	0.997451i	$0.477268\pi$
$54$	13.4531	1.83074
$55$	−13.1651	−1.77519
$56$	10.1032	1.35009
$57$	−3.69876	−0.489912
$58$	29.9456	3.93205
$59$	−0.881813	−0.114802	−0.0574011	−	0.998351i	$-0.518281\pi$
$59$	−0.881813	−0.114802	−0.0574011	+	0.998351i	$0.518281\pi$
$60$	−40.2645	−5.19813
$61$	−15.5037	−1.98504	−0.992520	−	0.122085i	$-0.961042\pi$
$61$	−15.5037	−1.98504	−0.992520	+	0.122085i	$0.961042\pi$
$62$	−17.3461	−2.20295
$63$	−0.380129	−0.0478917
$64$	52.8512	6.60640
$65$	19.9351	2.47265
$66$	−18.7190	−2.30415
$67$	2.25281	0.275225	0.137612	−	0.990486i	$-0.456057\pi$
$67$	2.25281	0.275225	0.137612	+	0.990486i	$0.456057\pi$
$68$	12.7996	1.55217
$69$	0.700616	0.0843442
$70$	−9.38993	−1.12231
$71$	−4.48569	−0.532354	−0.266177	−	0.963924i	$-0.585761\pi$
$71$	−4.48569	−0.532354	−0.266177	+	0.963924i	$0.585761\pi$
$72$	−4.64622	−0.547563
$73$	13.6558	1.59829	0.799146	−	0.601137i	$-0.205285\pi$
$73$	13.6558	1.59829	0.799146	+	0.601137i	$0.205285\pi$
$74$	−28.1274	−3.26975
$75$	15.5842	1.79951
$76$	−11.8896	−1.36383
$77$	−3.26620	−0.372218
$78$	28.3449	3.20943
$79$	9.20837	1.03602	0.518011	−	0.855374i	$-0.326673\pi$
$79$	9.20837	1.03602	0.518011	+	0.855374i	$0.326673\pi$
$80$	−71.2137	−7.96194
$81$	−10.0795	−1.11995
$82$	−14.6011	−1.61242
$83$	1.49174	0.163739	0.0818696	−	0.996643i	$-0.473911\pi$
$83$	1.49174	0.163739	0.0818696	+	0.996643i	$0.473911\pi$
$84$	−9.98941	−1.08993
$85$	−7.89258	−0.856070
$86$	−31.1674	−3.36087
$87$	−19.6442	−2.10608
$88$	−39.9220	−4.25570
$89$	2.55688	0.271028	0.135514	−	0.990775i	$-0.456731\pi$
$89$	2.55688	0.271028	0.135514	+	0.990775i	$0.456731\pi$
$90$	4.31822	0.455180
$91$	4.94579	0.518460
$92$	2.25211	0.234799
$93$	11.3790	1.17994
$94$	−20.4154	−2.10569
$95$	7.33145	0.752191
$96$	−60.1660	−6.14067
$97$	−8.25333	−0.837999	−0.419000	−	0.907986i	$-0.637619\pi$
$97$	−8.25333	−0.837999	−0.419000	+	0.907986i	$0.637619\pi$
$98$	17.3987	1.75753
$99$	1.50205	0.150962
$100$	50.0951	5.00951
$101$	−9.73742	−0.968909	−0.484455	−	0.874816i	$-0.660982\pi$
$101$	−9.73742	−0.968909	−0.484455	+	0.874816i	$0.660982\pi$
$102$	−11.2221	−1.11116
$103$	−0.139473	−0.0137427	−0.00687133	−	0.999976i	$-0.502187\pi$
$103$	−0.139473	−0.0137427	−0.00687133	+	0.999976i	$0.502187\pi$
$104$	60.4513	5.92774
$105$	6.15976	0.601131
$106$	−2.92810	−0.284402
$107$	6.50241	0.628612	0.314306	−	0.949322i	$-0.398228\pi$
$107$	6.50241	0.628612	0.314306	+	0.949322i	$0.398228\pi$
$108$	−28.3684	−2.72975
$109$	14.6931	1.40735	0.703674	−	0.710523i	$-0.251542\pi$
$109$	14.6931	1.40735	0.703674	+	0.710523i	$0.251542\pi$
$110$	37.1036	3.53769
$111$	18.4515	1.75134
$112$	−17.6678	−1.66945
$113$	−4.20739	−0.395798	−0.197899	−	0.980222i	$-0.563412\pi$
$113$	−4.20739	−0.395798	−0.197899	+	0.980222i	$0.563412\pi$
$114$	10.4243	0.976325
$115$	−1.38872	−0.129499
$116$	−63.1458	−5.86294
$117$	−2.27446	−0.210274
$118$	2.48524	0.228785
$119$	−1.95811	−0.179499
$120$	75.2893	6.87294
$121$	1.90616	0.173288
$122$	43.6943	3.95590
$123$	9.57827	0.863643
$124$	36.5774	3.28475
$125$	−12.5670	−1.12403
$126$	1.07133	0.0954414
$127$	−14.1824	−1.25848	−0.629241	−	0.777210i	$-0.716634\pi$
$127$	−14.1824	−1.25848	−0.629241	+	0.777210i	$0.716634\pi$
$128$	−83.8659	−7.41276
$129$	20.4457	1.80014
$130$	−56.1836	−4.92763
$131$	−16.2217	−1.41730	−0.708649	−	0.705561i	$-0.750695\pi$
$131$	−16.2217	−1.41730	−0.708649	+	0.705561i	$0.750695\pi$
$132$	39.4725	3.43564
$133$	1.81889	0.157718
$134$	−6.34915	−0.548483
$135$	17.4927	1.50554
$136$	−23.9335	−2.05228
$137$	5.58044	0.476769	0.238384	−	0.971171i	$-0.423382\pi$
$137$	5.58044	0.476769	0.238384	+	0.971171i	$0.423382\pi$
$138$	−1.97456	−0.168086
$139$	11.1068	0.942065	0.471033	−	0.882116i	$-0.343881\pi$
$139$	11.1068	0.942065	0.471033	+	0.882116i	$0.343881\pi$
$140$	19.8004	1.67344
$141$	13.3924	1.12785
$142$	12.6421	1.06091
$143$	−19.5430	−1.63426
$144$	8.12500	0.677083
$145$	38.9375	3.23359
$146$	−38.4866	−3.18517
$147$	−11.4135	−0.941368
$148$	59.3119	4.87541
$149$	−13.3150	−1.09081	−0.545405	−	0.838173i	$-0.683624\pi$
$149$	−13.3150	−1.09081	−0.545405	+	0.838173i	$0.683624\pi$
$150$	−43.9214	−3.58617
$151$	5.82609	0.474120	0.237060	−	0.971495i	$-0.423816\pi$
$151$	5.82609	0.474120	0.237060	+	0.971495i	$0.423816\pi$
$152$	22.2319	1.80325
$153$	0.900489	0.0728002
$154$	9.20522	0.741778
$155$	−22.5547	−1.81164
$156$	−59.7706	−4.78548
$157$	4.68496	0.373901	0.186950	−	0.982369i	$-0.440140\pi$
$157$	4.68496	0.373901	0.186950	+	0.982369i	$0.440140\pi$
$158$	−25.9522	−2.06465
$159$	1.92082	0.152331
$160$	119.257	9.42812
$161$	−0.344533	−0.0271530
$162$	28.4073	2.23189
$163$	21.5949	1.69145	0.845723	−	0.533622i	$-0.179170\pi$
$163$	21.5949	1.69145	0.845723	+	0.533622i	$0.179170\pi$
$164$	30.7891	2.40423
$165$	−24.3399	−1.89486
$166$	−4.20420	−0.326309
$167$	−1.10187	−0.0852653	−0.0426327	−	0.999091i	$-0.513575\pi$
$167$	−1.10187	−0.0852653	−0.0426327	+	0.999091i	$0.513575\pi$
$168$	18.6789	1.44111
$169$	16.5926	1.27636
$170$	22.2439	1.70603
$171$	−0.836468	−0.0639663
$172$	65.7222	5.01127
$173$	2.78761	0.211938	0.105969	−	0.994369i	$-0.466206\pi$
$173$	2.78761	0.211938	0.105969	+	0.994369i	$0.466206\pi$
$174$	55.3638	4.19712
$175$	−7.66366	−0.579318
$176$	69.8129	5.26234
$177$	−1.63031	−0.122541
$178$	−7.20611	−0.540121
$179$	11.0247	0.824028	0.412014	−	0.911177i	$-0.364825\pi$
$179$	11.0247	0.824028	0.412014	+	0.911177i	$0.364825\pi$
$180$	−9.10576	−0.678703
$181$	−2.28231	−0.169643	−0.0848213	−	0.996396i	$-0.527032\pi$
$181$	−2.28231	−0.169643	−0.0848213	+	0.996396i	$0.527032\pi$
$182$	−13.9389	−1.03322
$183$	−28.6633	−2.11886
$184$	−4.21115	−0.310450
$185$	−36.5734	−2.68893
$186$	−32.0696	−2.35146
$187$	7.73732	0.565809
$188$	43.0496	3.13972
$189$	4.33986	0.315678
$190$	−20.6624	−1.49901
$191$	−11.0676	−0.800824	−0.400412	−	0.916335i	$-0.631133\pi$
$191$	−11.0676	−0.800824	−0.400412	+	0.916335i	$0.631133\pi$
$192$	97.7120	7.05175
$193$	7.90636	0.569112	0.284556	−	0.958659i	$-0.408154\pi$
$193$	7.90636	0.569112	0.284556	+	0.958659i	$0.408154\pi$
$194$	23.2606	1.67001
$195$	36.8563	2.63933
$196$	−36.6884	−2.62060
$197$	−25.5719	−1.82192	−0.910961	−	0.412492i	$-0.864659\pi$
$197$	−25.5719	−1.82192	−0.910961	+	0.412492i	$0.864659\pi$
$198$	−4.23327	−0.300846
$199$	−6.19851	−0.439401	−0.219700	−	0.975567i	$-0.570508\pi$
$199$	−6.19851	−0.439401	−0.219700	+	0.975567i	$0.570508\pi$
$200$	−93.6711	−6.62355
$201$	4.16502	0.293778
$202$	27.4432	1.93090
$203$	9.66020	0.678013
$204$	23.6640	1.65681
$205$	−18.9855	−1.32600
$206$	0.393080	0.0273872
$207$	0.158443	0.0110126
$208$	−105.713	−7.32988
$209$	−7.18723	−0.497151
$210$	−17.3602	−1.19797
$211$	−2.92617	−0.201446	−0.100723	−	0.994915i	$-0.532116\pi$
$211$	−2.92617	−0.201446	−0.100723	+	0.994915i	$0.532116\pi$
$212$	6.17444	0.424062
$213$	−8.29320	−0.568241
$214$	−18.3259	−1.25273
$215$	−40.5262	−2.76387
$216$	53.0451	3.60926
$217$	−5.59570	−0.379861
$218$	−41.4101	−2.80464
$219$	25.2470	1.70604
$220$	−78.2399	−5.27493
$221$	−11.7161	−0.788111
$222$	−52.0023	−3.49017
$223$	19.9003	1.33262	0.666310	−	0.745674i	$-0.267873\pi$
$223$	19.9003	1.33262	0.666310	+	0.745674i	$0.267873\pi$
$224$	29.5871	1.97687
$225$	3.52434	0.234956
$226$	11.8578	0.788769
$227$	−16.6617	−1.10588	−0.552939	−	0.833222i	$-0.686494\pi$
$227$	−16.6617	−1.10588	−0.552939	+	0.833222i	$0.686494\pi$
$228$	−21.9816	−1.45576
$229$	−11.0535	−0.730439	−0.365220	−	0.930921i	$-0.619006\pi$
$229$	−11.0535	−0.730439	−0.365220	+	0.930921i	$0.619006\pi$
$230$	3.91386	0.258072
$231$	−6.03859	−0.397310
$232$	118.074	7.75196
$233$	28.1717	1.84559	0.922795	−	0.385292i	$-0.125899\pi$
$233$	28.1717	1.84559	0.922795	+	0.385292i	$0.125899\pi$
$234$	6.41017	0.419046
$235$	−26.5456	−1.73165
$236$	−5.24058	−0.341133
$237$	17.0245	1.10586
$238$	5.51858	0.357717
$239$	−19.8323	−1.28285	−0.641424	−	0.767187i	$-0.721656\pi$
$239$	−19.8323	−1.28285	−0.641424	+	0.767187i	$0.721656\pi$
$240$	−131.661	−8.49867
$241$	−17.2355	−1.11024	−0.555119	−	0.831771i	$-0.687327\pi$
$241$	−17.2355	−1.11024	−0.555119	+	0.831771i	$0.687327\pi$
$242$	−5.37219	−0.345337
$243$	−4.31480	−0.276795
$244$	−92.1376	−5.89851
$245$	22.6231	1.44534
$246$	−26.9947	−1.72112
$247$	10.8831	0.692478
$248$	−68.3949	−4.34308
$249$	2.75794	0.174777
$250$	35.4180	2.24003
$251$	8.41975	0.531450	0.265725	−	0.964049i	$-0.414389\pi$
$251$	8.41975	0.531450	0.265725	+	0.964049i	$0.414389\pi$
$252$	−2.25909	−0.142309
$253$	1.36140	0.0855905
$254$	39.9705	2.50797
$255$	−14.5919	−0.913780
$256$	130.659	8.16618
$257$	−14.6730	−0.915274	−0.457637	−	0.889139i	$-0.651304\pi$
$257$	−14.6730	−0.915274	−0.457637	+	0.889139i	$0.651304\pi$
$258$	−57.6227	−3.58743
$259$	−9.07367	−0.563810
$260$	118.474	7.34742
$261$	−4.44251	−0.274984
$262$	45.7181	2.82447
$263$	−6.93825	−0.427831	−0.213916	−	0.976852i	$-0.568622\pi$
$263$	−6.93825	−0.427831	−0.213916	+	0.976852i	$0.568622\pi$
$264$	−73.8083	−4.54259
$265$	−3.80734	−0.233883
$266$	−5.12623	−0.314310
$267$	4.72718	0.289299
$268$	13.3884	0.817825
$269$	1.13771	0.0693672	0.0346836	−	0.999398i	$-0.488958\pi$
$269$	1.13771	0.0693672	0.0346836	+	0.999398i	$0.488958\pi$
$270$	−49.3003	−3.00032
$271$	−16.7622	−1.01823	−0.509116	−	0.860698i	$-0.670028\pi$
$271$	−16.7622	−1.01823	−0.509116	+	0.860698i	$0.670028\pi$
$272$	41.8532	2.53772
$273$	9.14384	0.553411
$274$	−15.7275	−0.950133
$275$	30.2824	1.82610
$276$	4.16373	0.250627
$277$	−28.3197	−1.70157	−0.850783	−	0.525517i	$-0.823872\pi$
$277$	−28.3197	−1.70157	−0.850783	+	0.525517i	$0.823872\pi$
$278$	−31.3025	−1.87740
$279$	2.57333	0.154062
$280$	−37.0241	−2.21262
$281$	−3.16322	−0.188702	−0.0943509	−	0.995539i	$-0.530078\pi$
$281$	−3.16322	−0.188702	−0.0943509	+	0.995539i	$0.530078\pi$
$282$	−37.7442	−2.24764
$283$	20.3576	1.21014	0.605068	−	0.796174i	$-0.293146\pi$
$283$	20.3576	1.21014	0.605068	+	0.796174i	$0.293146\pi$
$284$	−26.6583	−1.58188
$285$	13.5545	0.802897
$286$	55.0784	3.25686
$287$	−4.71019	−0.278034
$288$	−13.6065	−0.801768
$289$	−12.3614	−0.727143
$290$	−109.739	−6.44408
$291$	−15.2589	−0.894490
$292$	81.1560	4.74930
$293$	9.07882	0.530390	0.265195	−	0.964195i	$-0.414564\pi$
$293$	9.07882	0.530390	0.265195	+	0.964195i	$0.414564\pi$
$294$	32.1669	1.87601
$295$	3.23149	0.188145
$296$	−110.905	−6.44624
$297$	−17.1486	−0.995065
$298$	37.5261	2.17383
$299$	−2.06148	−0.119218
$300$	92.6163	5.34721
$301$	−10.0543	−0.579523
$302$	−16.4198	−0.944854
$303$	−18.0027	−1.03423
$304$	−38.8776	−2.22979
$305$	56.8147	3.25320
$306$	−2.53787	−0.145080
$307$	−4.10020	−0.234011	−0.117005	−	0.993131i	$-0.537329\pi$
$307$	−4.10020	−0.234011	−0.117005	+	0.993131i	$0.537329\pi$
$308$	−19.4109	−1.10604
$309$	−0.257859	−0.0146691
$310$	63.5664	3.61033
$311$	−15.2846	−0.866712	−0.433356	−	0.901223i	$-0.642671\pi$
$311$	−15.2846	−0.866712	−0.433356	+	0.901223i	$0.642671\pi$
$312$	111.763	6.32734
$313$	−10.0734	−0.569380	−0.284690	−	0.958620i	$-0.591891\pi$
$313$	−10.0734	−0.569380	−0.284690	+	0.958620i	$0.591891\pi$
$314$	−13.2037	−0.745131
$315$	1.39302	0.0784878
$316$	54.7250	3.07852
$317$	−4.06426	−0.228271	−0.114136	−	0.993465i	$-0.536410\pi$
$317$	−4.06426	−0.228271	−0.114136	+	0.993465i	$0.536410\pi$
$318$	−5.41350	−0.303574
$319$	−38.1716	−2.13720
$320$	−193.679	−10.8270
$321$	12.0217	0.670988
$322$	0.971008	0.0541121
$323$	−4.30879	−0.239747
$324$	−59.9021	−3.32790
$325$	−45.8547	−2.54356
$326$	−60.8616	−3.37081
$327$	27.1648	1.50222
$328$	−57.5716	−3.17886
$329$	−6.58583	−0.363089
$330$	68.5977	3.77618
$331$	−16.8661	−0.927043	−0.463522	−	0.886086i	$-0.653414\pi$
$331$	−16.8661	−0.927043	−0.463522	+	0.886086i	$0.653414\pi$
$332$	8.86533	0.486548
$333$	4.17278	0.228667
$334$	3.10543	0.169922
$335$	−8.25565	−0.451055
$336$	−32.6644	−1.78199
$337$	17.8497	0.972333	0.486167	−	0.873866i	$-0.338395\pi$
$337$	17.8497	0.972333	0.486167	+	0.873866i	$0.338395\pi$
$338$	−46.7634	−2.54359
$339$	−7.77868	−0.422480
$340$	−46.9053	−2.54380
$341$	22.1110	1.19738
$342$	2.35744	0.127476
$343$	11.9769	0.646689
$344$	−122.892	−6.62588
$345$	−2.56748	−0.138228
$346$	−7.85639	−0.422362
$347$	−10.7163	−0.575283	−0.287641	−	0.957738i	$-0.592871\pi$
$347$	−10.7163	−0.575283	−0.287641	+	0.957738i	$0.592871\pi$
$348$	−116.745	−6.25817
$349$	−35.6828	−1.91006	−0.955029	−	0.296512i	$-0.904176\pi$
$349$	−35.6828	−1.91006	−0.955029	+	0.296512i	$0.904176\pi$
$350$	21.5987	1.15450
$351$	25.9671	1.38602
$352$	−116.911	−6.23140
$353$	5.51201	0.293375	0.146687	−	0.989183i	$-0.453139\pi$
$353$	5.51201	0.293375	0.146687	+	0.989183i	$0.453139\pi$
$354$	4.59474	0.244207
$355$	16.4383	0.872453
$356$	15.1954	0.805355
$357$	−3.62017	−0.191600
$358$	−31.0713	−1.64217
$359$	−10.7221	−0.565890	−0.282945	−	0.959136i	$-0.591311\pi$
$359$	−10.7221	−0.565890	−0.282945	+	0.959136i	$0.591311\pi$
$360$	17.0266	0.897379
$361$	−14.9976	−0.789345
$362$	6.43229	0.338074
$363$	3.52414	0.184969
$364$	29.3927	1.54059
$365$	−50.0431	−2.61938
$366$	80.7826	4.22258
$367$	6.32436	0.330129	0.165064	−	0.986283i	$-0.447217\pi$
$367$	6.32436	0.330129	0.165064	+	0.986283i	$0.447217\pi$
$368$	7.36418	0.383884
$369$	2.16611	0.112763
$370$	103.076	5.35866
$371$	−0.944580	−0.0490402
$372$	67.6247	3.50618
$373$	−22.6178	−1.17111	−0.585554	−	0.810634i	$-0.699123\pi$
$373$	−22.6178	−1.17111	−0.585554	+	0.810634i	$0.699123\pi$
$374$	−21.8063	−1.12758
$375$	−23.2341	−1.19980
$376$	−80.4971	−4.15132
$377$	57.8007	2.97689
$378$	−12.2311	−0.629102
$379$	−12.3478	−0.634263	−0.317131	−	0.948382i	$-0.602720\pi$
$379$	−12.3478	−0.634263	−0.317131	+	0.948382i	$0.602720\pi$
$380$	43.5705	2.23512
$381$	−26.2205	−1.34332
$382$	31.1921	1.59593
$383$	31.8907	1.62954	0.814770	−	0.579784i	$-0.196863\pi$
$383$	31.8907	1.62954	0.814770	+	0.579784i	$0.196863\pi$
$384$	−155.052	−7.91247
$385$	11.9693	0.610013
$386$	−22.2827	−1.13416
$387$	4.62376	0.235039
$388$	−49.0492	−2.49010
$389$	−21.7608	−1.10332	−0.551659	−	0.834070i	$-0.686005\pi$
$389$	−21.7608	−1.10332	−0.551659	+	0.834070i	$0.686005\pi$
$390$	−103.873	−5.25981
$391$	0.816167	0.0412754
$392$	68.6024	3.46494
$393$	−29.9909	−1.51284
$394$	72.0700	3.63083
$395$	−33.7450	−1.69790
$396$	8.92664	0.448580
$397$	21.9543	1.10186	0.550928	−	0.834553i	$-0.314274\pi$
$397$	21.9543	1.10186	0.550928	+	0.834553i	$0.314274\pi$
$398$	17.4694	0.875664
$399$	3.36279	0.168350
$400$	163.806	8.19028
$401$	−22.1952	−1.10837	−0.554187	−	0.832392i	$-0.686971\pi$
$401$	−22.1952	−1.10837	−0.554187	+	0.832392i	$0.686971\pi$
$402$	−11.7384	−0.585458
$403$	−33.4812	−1.66782
$404$	−57.8691	−2.87910
$405$	36.9374	1.83543
$406$	−27.2256	−1.35118
$407$	35.8540	1.77722
$408$	−44.2485	−2.19063
$409$	37.1009	1.83452	0.917261	−	0.398286i	$-0.130395\pi$
$409$	37.1009	1.83452	0.917261	+	0.398286i	$0.130395\pi$
$410$	53.5072	2.64253
$411$	10.3172	0.508909
$412$	−0.828882	−0.0408361
$413$	0.801716	0.0394499
$414$	−0.446545	−0.0219465
$415$	−5.46662	−0.268346
$416$	177.031	8.67967
$417$	20.5344	1.00557
$418$	20.2560	0.990751
$419$	3.99231	0.195037	0.0975184	−	0.995234i	$-0.468910\pi$
$419$	3.99231	0.195037	0.0975184	+	0.995234i	$0.468910\pi$
$420$	36.6072	1.78625
$421$	22.1871	1.08133	0.540666	−	0.841237i	$-0.318172\pi$
$421$	22.1871	1.08133	0.540666	+	0.841237i	$0.318172\pi$
$422$	8.24690	0.401453
$423$	3.02868	0.147259
$424$	−11.5454	−0.560693
$425$	18.1545	0.880622
$426$	23.3729	1.13242
$427$	14.0954	0.682126
$428$	38.6436	1.86791
$429$	−36.1313	−1.74443
$430$	114.216	5.50799
$431$	2.18094	0.105052	0.0525261	−	0.998620i	$-0.483273\pi$
$431$	2.18094	0.105052	0.0525261	+	0.998620i	$0.483273\pi$
$432$	−92.7616	−4.46299
$433$	−9.84752	−0.473242	−0.236621	−	0.971602i	$-0.576040\pi$
$433$	−9.84752	−0.473242	−0.236621	+	0.971602i	$0.576040\pi$
$434$	15.7705	0.757008
$435$	71.9882	3.45157
$436$	87.3208	4.18191
$437$	−0.758141	−0.0362668
$438$	−71.1544	−3.39989
$439$	−13.8277	−0.659961	−0.329980	−	0.943988i	$-0.607042\pi$
$439$	−13.8277	−0.659961	−0.329980	+	0.943988i	$0.607042\pi$
$440$	146.298	6.97450
$441$	−2.58114	−0.122911
$442$	33.0198	1.57059
$443$	−28.2570	−1.34253	−0.671265	−	0.741218i	$-0.734249\pi$
$443$	−28.2570	−1.34253	−0.671265	+	0.741218i	$0.734249\pi$
$444$	109.656	5.20407
$445$	−9.36993	−0.444177
$446$	−56.0855	−2.65572
$447$	−24.6170	−1.16434
$448$	−48.0507	−2.27018
$449$	1.85290	0.0874440	0.0437220	−	0.999044i	$-0.486078\pi$
$449$	1.85290	0.0874440	0.0437220	+	0.999044i	$0.486078\pi$
$450$	−9.93275	−0.468234
$451$	18.6120	0.876404
$452$	−25.0044	−1.17611
$453$	10.7713	0.506082
$454$	46.9582	2.20386
$455$	−18.1244	−0.849683
$456$	41.1026	1.92481
$457$	−40.4428	−1.89184	−0.945918	−	0.324407i	$-0.894835\pi$
$457$	−40.4428	−1.89184	−0.945918	+	0.324407i	$0.894835\pi$
$458$	31.1525	1.45566
$459$	−10.2807	−0.479863
$460$	−8.25310	−0.384803
$461$	24.7691	1.15361	0.576805	−	0.816882i	$-0.304299\pi$
$461$	24.7691	1.15361	0.576805	+	0.816882i	$0.304299\pi$
$462$	17.0187	0.791783
$463$	−6.89099	−0.320252	−0.160126	−	0.987097i	$-0.551190\pi$
$463$	−6.89099	−0.320252	−0.160126	+	0.987097i	$0.551190\pi$
$464$	−206.480	−9.58561
$465$	−41.6994	−1.93376
$466$	−79.3970	−3.67800
$467$	8.32611	0.385286	0.192643	−	0.981269i	$-0.438294\pi$
$467$	8.32611	0.385286	0.192643	+	0.981269i	$0.438294\pi$
$468$	−13.5170	−0.624825
$469$	−2.04818	−0.0945763
$470$	74.8143	3.45093
$471$	8.66161	0.399106
$472$	9.79919	0.451044
$473$	39.7290	1.82674
$474$	−47.9807	−2.20383
$475$	−16.8638	−0.773763
$476$	−11.6370	−0.533379
$477$	0.434391	0.0198894
$478$	55.8940	2.55653
$479$	7.19407	0.328705	0.164353	−	0.986402i	$-0.447447\pi$
$479$	7.19407	0.328705	0.164353	+	0.986402i	$0.447447\pi$
$480$	220.484	10.0637
$481$	−54.2913	−2.47547
$482$	48.5753	2.21255
$483$	−0.636978	−0.0289835
$484$	11.3283	0.514921
$485$	30.2452	1.37336
$486$	12.1605	0.551612
$487$	26.4225	1.19732	0.598660	−	0.801003i	$-0.295700\pi$
$487$	26.4225	1.19732	0.598660	+	0.801003i	$0.295700\pi$
$488$	172.285	7.79898
$489$	39.9250	1.80547
$490$	−63.7593	−2.88035
$491$	−0.503736	−0.0227333	−0.0113667	−	0.999935i	$-0.503618\pi$
$491$	−0.503736	−0.0227333	−0.0113667	+	0.999935i	$0.503618\pi$
$492$	56.9233	2.56630
$493$	−22.8841	−1.03065
$494$	−30.6723	−1.38001
$495$	−5.50442	−0.247405
$496$	119.604	5.37039
$497$	4.07825	0.182934
$498$	−7.77277	−0.348306
$499$	−7.30778	−0.327141	−0.163571	−	0.986532i	$-0.552301\pi$
$499$	−7.30778	−0.327141	−0.163571	+	0.986532i	$0.552301\pi$
$500$	−74.6855	−3.34004
$501$	−2.03715	−0.0910132
$502$	−23.7296	−1.05910
$503$	39.0054	1.73916	0.869582	−	0.493789i	$-0.164389\pi$
$503$	39.0054	1.73916	0.869582	+	0.493789i	$0.164389\pi$
$504$	4.22420	0.188161
$505$	35.6838	1.58791
$506$	−3.83687	−0.170570
$507$	30.6766	1.36240
$508$	−84.2853	−3.73955
$509$	30.1021	1.33425	0.667126	−	0.744945i	$-0.267524\pi$
$509$	30.1021	1.33425	0.667126	+	0.744945i	$0.267524\pi$
$510$	41.1247	1.82103
$511$	−12.4154	−0.549227
$512$	−200.508	−8.86127
$513$	9.54979	0.421634
$514$	41.3532	1.82401
$515$	0.511112	0.0225223
$516$	121.508	5.34909
$517$	26.0235	1.14451
$518$	25.5726	1.12359
$519$	5.15376	0.226225
$520$	−221.530	−9.71473
$521$	−4.19938	−0.183978	−0.0919891	−	0.995760i	$-0.529322\pi$
$521$	−4.19938	−0.183978	−0.0919891	+	0.995760i	$0.529322\pi$
$522$	12.5204	0.548004
$523$	−36.7607	−1.60744	−0.803718	−	0.595011i	$-0.797148\pi$
$523$	−36.7607	−1.60744	−0.803718	+	0.595011i	$0.797148\pi$
$524$	−96.4050	−4.21147
$525$	−14.1687	−0.618371
$526$	19.5543	0.852606
$527$	13.2557	0.577426
$528$	129.071	5.61709
$529$	−22.8564	−0.993756
$530$	10.7303	0.466095
$531$	−0.368691	−0.0159998
$532$	10.8096	0.468656
$533$	−28.1829	−1.22074
$534$	−13.3227	−0.576531
$535$	−23.8287	−1.03021
$536$	−25.0345	−1.08132
$537$	20.3827	0.879578
$538$	−3.20643	−0.138239
$539$	−22.1781	−0.955277
$540$	103.959	4.47367
$541$	27.1042	1.16530	0.582649	−	0.812724i	$-0.302016\pi$
$541$	27.1042	1.16530	0.582649	+	0.812724i	$0.302016\pi$
$542$	47.2414	2.02919
$543$	−4.21956	−0.181079
$544$	−70.0891	−3.00505
$545$	−53.8445	−2.30644
$546$	−25.7703	−1.10287
$547$	−42.0540	−1.79810	−0.899050	−	0.437847i	$-0.855741\pi$
$547$	−42.0540	−1.79810	−0.899050	+	0.437847i	$0.855741\pi$
$548$	33.1643	1.41671
$549$	−6.48217	−0.276652
$550$	−85.3457	−3.63915
$551$	21.2571	0.905584
$552$	−7.78563	−0.331378
$553$	−8.37196	−0.356012
$554$	79.8142	3.39098
$555$	−67.6174	−2.87020
$556$	66.0072	2.79933
$557$	−1.30221	−0.0551765	−0.0275882	−	0.999619i	$-0.508783\pi$
$557$	−1.30221	−0.0551765	−0.0275882	+	0.999619i	$0.508783\pi$
$558$	−7.25250	−0.307023
$559$	−60.1590	−2.54446
$560$	64.7453	2.73599
$561$	14.3049	0.603951
$562$	8.91498	0.376056
$563$	28.9580	1.22043	0.610217	−	0.792234i	$-0.291082\pi$
$563$	28.9580	1.22043	0.610217	+	0.792234i	$0.291082\pi$
$564$	79.5907	3.35137
$565$	15.4184	0.648658
$566$	−57.3745	−2.41163
$567$	9.16397	0.384850
$568$	49.8475	2.09155
$569$	−2.68857	−0.112711	−0.0563553	−	0.998411i	$-0.517948\pi$
$569$	−2.68857	−0.112711	−0.0563553	+	0.998411i	$0.517948\pi$
$570$	−38.2009	−1.60006
$571$	−36.1276	−1.51189	−0.755946	−	0.654634i	$-0.772823\pi$
$571$	−36.1276	−1.51189	−0.755946	+	0.654634i	$0.772823\pi$
$572$	−116.143	−4.85618
$573$	−20.4619	−0.854809
$574$	13.2749	0.554082
$575$	3.19432	0.133213
$576$	22.0974	0.920726
$577$	5.57159	0.231948	0.115974	−	0.993252i	$-0.463001\pi$
$577$	5.57159	0.231948	0.115974	+	0.993252i	$0.463001\pi$
$578$	34.8385	1.44909
$579$	14.6174	0.607477
$580$	231.404	9.60854
$581$	−1.35624	−0.0562663
$582$	43.0044	1.78259
$583$	3.73244	0.154582
$584$	−151.751	−6.27950
$585$	8.33499	0.344609
$586$	−25.5871	−1.05699
$587$	5.51661	0.227695	0.113847	−	0.993498i	$-0.463682\pi$
$587$	5.51661	0.227695	0.113847	+	0.993498i	$0.463682\pi$
$588$	−67.8299	−2.79726
$589$	−12.3133	−0.507359
$590$	−9.10740	−0.374946
$591$	−47.2776	−1.94474
$592$	193.944	7.97104
$593$	0.647362	0.0265840	0.0132920	−	0.999912i	$-0.495769\pi$
$593$	0.647362	0.0265840	0.0132920	+	0.999912i	$0.495769\pi$
$594$	48.3305	1.98302
$595$	7.17568	0.294174
$596$	−79.1308	−3.24132
$597$	−11.4599	−0.469022
$598$	5.80992	0.237585
$599$	21.7252	0.887666	0.443833	−	0.896109i	$-0.353618\pi$
$599$	21.7252	0.887666	0.443833	+	0.896109i	$0.353618\pi$
$600$	−173.180	−7.07006
$601$	16.1073	0.657031	0.328516	−	0.944499i	$-0.393452\pi$
$601$	16.1073	0.657031	0.328516	+	0.944499i	$0.393452\pi$
$602$	28.3364	1.15491
$603$	0.941914	0.0383577
$604$	34.6242	1.40884
$605$	−6.98533	−0.283994
$606$	50.7374	2.06106
$607$	28.4722	1.15565	0.577826	−	0.816160i	$-0.303901\pi$
$607$	28.4722	1.15565	0.577826	+	0.816160i	$0.303901\pi$
$608$	65.1060	2.64040
$609$	17.8599	0.723719
$610$	−160.122	−6.48317
$611$	−39.4056	−1.59418
$612$	5.35157	0.216324
$613$	7.46930	0.301682	0.150841	−	0.988558i	$-0.451802\pi$
$613$	7.46930	0.301682	0.150841	+	0.988558i	$0.451802\pi$
$614$	11.5557	0.466350
$615$	−35.1005	−1.41539
$616$	36.2958	1.46240
$617$	−41.5874	−1.67425	−0.837123	−	0.547015i	$-0.815764\pi$
$617$	−41.5874	−1.67425	−0.837123	+	0.547015i	$0.815764\pi$
$618$	0.726731	0.0292334
$619$	3.64438	0.146480	0.0732399	−	0.997314i	$-0.476666\pi$
$619$	3.64438	0.146480	0.0732399	+	0.997314i	$0.476666\pi$
$620$	−134.042	−5.38324
$621$	−1.80892	−0.0725893
$622$	43.0771	1.72723
$623$	−2.32463	−0.0931343
$624$	−195.444	−7.82401
$625$	3.90669	0.156268
$626$	28.3900	1.13469
$627$	−13.2878	−0.530665
$628$	27.8425	1.11104
$629$	21.4947	0.857048
$630$	−3.92599	−0.156415
$631$	−44.0064	−1.75187	−0.875934	−	0.482431i	$-0.839754\pi$
$631$	−44.0064	−1.75187	−0.875934	+	0.482431i	$0.839754\pi$
$632$	−102.328	−4.07041
$633$	−5.40994	−0.215026
$634$	11.4544	0.454912
$635$	51.9727	2.06248
$636$	11.4154	0.452649
$637$	33.5828	1.33060
$638$	107.580	4.25913
$639$	−1.87549	−0.0741934
$640$	307.335	12.1485
$641$	−29.5965	−1.16899	−0.584495	−	0.811397i	$-0.698707\pi$
$641$	−29.5965	−1.16899	−0.584495	+	0.811397i	$0.698707\pi$
$642$	−33.8812	−1.33718
$643$	−11.6457	−0.459263	−0.229632	−	0.973278i	$-0.573752\pi$
$643$	−11.6457	−0.459263	−0.229632	+	0.973278i	$0.573752\pi$
$644$	−2.04755	−0.0806848
$645$	−74.9254	−2.95018
$646$	12.1436	0.477782
$647$	19.0448	0.748728	0.374364	−	0.927282i	$-0.377861\pi$
$647$	19.0448	0.748728	0.374364	+	0.927282i	$0.377861\pi$
$648$	112.009	4.40013
$649$	−3.16793	−0.124352
$650$	129.233	5.06895
$651$	−10.3454	−0.405468
$652$	128.338	5.02610
$653$	12.5477	0.491029	0.245514	−	0.969393i	$-0.421043\pi$
$653$	12.5477	0.491029	0.245514	+	0.969393i	$0.421043\pi$
$654$	−76.5594	−2.99371
$655$	59.4461	2.32275
$656$	100.677	3.93078
$657$	5.70958	0.222752
$658$	18.5610	0.723584
$659$	19.1004	0.744045	0.372023	−	0.928224i	$-0.378664\pi$
$659$	19.1004	0.744045	0.372023	+	0.928224i	$0.378664\pi$
$660$	−144.651	−5.63053
$661$	−13.2527	−0.515471	−0.257735	−	0.966216i	$-0.582976\pi$
$661$	−13.2527	−0.515471	−0.257735	+	0.966216i	$0.582976\pi$
$662$	47.5341	1.84747
$663$	−21.6609	−0.841240
$664$	−16.5770	−0.643312
$665$	−6.66552	−0.258478
$666$	−11.7602	−0.455700
$667$	−4.02651	−0.155907
$668$	−6.54838	−0.253364
$669$	36.7919	1.42246
$670$	23.2671	0.898887
$671$	−55.6971	−2.15016
$672$	54.7010	2.11014
$673$	−8.19204	−0.315780	−0.157890	−	0.987457i	$-0.550469\pi$
$673$	−8.19204	−0.315780	−0.157890	+	0.987457i	$0.550469\pi$
$674$	−50.3062	−1.93772
$675$	−40.2368	−1.54871
$676$	98.6093	3.79266
$677$	−25.0632	−0.963257	−0.481629	−	0.876375i	$-0.659955\pi$
$677$	−25.0632	−0.963257	−0.481629	+	0.876375i	$0.659955\pi$
$678$	21.9228	0.841942
$679$	7.50367	0.287964
$680$	87.7067	3.36340
$681$	−30.8044	−1.18043
$682$	−62.3160	−2.38620
$683$	−41.6108	−1.59219	−0.796097	−	0.605170i	$-0.793105\pi$
$683$	−41.6108	−1.59219	−0.796097	+	0.605170i	$0.793105\pi$
$684$	−4.97110	−0.190075
$685$	−20.4501	−0.781357
$686$	−33.7547	−1.28876
$687$	−20.4359	−0.779680
$688$	214.905	8.19317
$689$	−5.65179	−0.215316
$690$	7.23599	0.275469
$691$	40.5385	1.54216	0.771078	−	0.636740i	$-0.219718\pi$
$691$	40.5385	1.54216	0.771078	+	0.636740i	$0.219718\pi$
$692$	16.5667	0.629770
$693$	−1.36562	−0.0518755
$694$	30.2021	1.14646
$695$	−40.7019	−1.54391
$696$	218.297	8.27453
$697$	11.1580	0.422639
$698$	100.566	3.80647
$699$	52.0842	1.97000
$700$	−45.5448	−1.72143
$701$	−27.5627	−1.04103	−0.520514	−	0.853853i	$-0.674260\pi$
$701$	−27.5627	−1.04103	−0.520514	+	0.853853i	$0.674260\pi$
$702$	−73.1837	−2.76214
$703$	−19.9665	−0.753050
$704$	189.869	7.15595
$705$	−49.0779	−1.84838
$706$	−15.5347	−0.584654
$707$	8.85295	0.332950
$708$	−9.68885	−0.364129
$709$	−26.8149	−1.00705	−0.503527	−	0.863979i	$-0.667965\pi$
$709$	−26.8149	−1.00705	−0.503527	+	0.863979i	$0.667965\pi$
$710$	−46.3284	−1.73867
$711$	3.85008	0.144389
$712$	−28.4134	−1.06484
$713$	2.33237	0.0873479
$714$	10.2028	0.381831
$715$	71.6172	2.67833
$716$	65.5197	2.44858
$717$	−36.6663	−1.36933
$718$	30.2183	1.12774
$719$	−15.8393	−0.590705	−0.295353	−	0.955388i	$-0.595437\pi$
$719$	−15.8393	−0.590705	−0.295353	+	0.955388i	$0.595437\pi$
$720$	−29.7749	−1.10964
$721$	0.126804	0.00472244
$722$	42.2680	1.57305
$723$	−31.8653	−1.18508
$724$	−13.5637	−0.504090
$725$	−89.5640	−3.32632
$726$	−9.93217	−0.368617
$727$	−27.8058	−1.03126	−0.515631	−	0.856811i	$-0.672442\pi$
$727$	−27.8058	−1.03126	−0.515631	+	0.856811i	$0.672442\pi$
$728$	−54.9604	−2.03697
$729$	22.2613	0.824491
$730$	141.038	5.22005
$731$	23.8178	0.880932
$732$	−170.345	−6.29614
$733$	15.5563	0.574584	0.287292	−	0.957843i	$-0.407245\pi$
$733$	15.5563	0.574584	0.287292	+	0.957843i	$0.407245\pi$
$734$	−17.8241	−0.657900
$735$	41.8259	1.54277
$736$	−12.3323	−0.454576
$737$	8.09325	0.298119
$738$	−6.10481	−0.224721
$739$	−18.9778	−0.698108	−0.349054	−	0.937103i	$-0.613497\pi$
$739$	−18.9778	−0.698108	−0.349054	+	0.937103i	$0.613497\pi$
$740$	−217.354	−7.99011
$741$	20.1209	0.739160
$742$	2.66213	0.0977300
$743$	−47.5368	−1.74396	−0.871978	−	0.489546i	$-0.837163\pi$
$743$	−47.5368	−1.74396	−0.871978	+	0.489546i	$0.837163\pi$
$744$	−126.449	−4.63586
$745$	48.7943	1.78769
$746$	63.7444	2.33385
$747$	0.623704	0.0228201
$748$	45.9826	1.68129
$749$	−5.91178	−0.216012
$750$	65.4813	2.39104
$751$	−19.0387	−0.694731	−0.347365	−	0.937730i	$-0.612924\pi$
$751$	−19.0387	−0.694731	−0.347365	+	0.937730i	$0.612924\pi$
$752$	140.768	5.13327
$753$	15.5665	0.567276
$754$	−162.901	−5.93252
$755$	−21.3503	−0.777017
$756$	25.7916	0.938032
$757$	47.4204	1.72352	0.861762	−	0.507313i	$-0.169361\pi$
$757$	47.4204	1.72352	0.861762	+	0.507313i	$0.169361\pi$
$758$	34.8001	1.26400
$759$	2.51697	0.0913603
$760$	−81.4711	−2.95527
$761$	18.8439	0.683089	0.341545	−	0.939866i	$-0.389050\pi$
$761$	18.8439	0.683089	0.341545	+	0.939866i	$0.389050\pi$
$762$	73.8980	2.67704
$763$	−13.3585	−0.483611
$764$	−65.7743	−2.37963
$765$	−3.29993	−0.119309
$766$	−89.8785	−3.24744
$767$	4.79698	0.173209
$768$	241.564	8.71668
$769$	29.2685	1.05545	0.527724	−	0.849416i	$-0.323046\pi$
$769$	29.2685	1.05545	0.527724	+	0.849416i	$0.323046\pi$
$770$	−33.7335	−1.21567
$771$	−27.1275	−0.976974
$772$	46.9872	1.69111
$773$	−20.6768	−0.743693	−0.371847	−	0.928294i	$-0.621275\pi$
$773$	−20.6768	−0.743693	−0.371847	+	0.928294i	$0.621275\pi$
$774$	−13.0313	−0.468400
$775$	51.8802	1.86359
$776$	91.7156	3.29240
$777$	−16.7755	−0.601818
$778$	61.3291	2.19875
$779$	−10.3647	−0.371354
$780$	219.035	7.84272
$781$	−16.1149	−0.576637
$782$	−2.30023	−0.0822559
$783$	50.7192	1.81256
$784$	−119.967	−4.28454
$785$	−17.1685	−0.612771
$786$	84.5241	3.01488
$787$	−36.1812	−1.28972	−0.644860	−	0.764301i	$-0.723084\pi$
$787$	−36.1812	−1.28972	−0.644860	+	0.764301i	$0.723084\pi$
$788$	−151.973	−5.41381
$789$	−12.8275	−0.456672
$790$	95.1045	3.38366
$791$	3.82523	0.136009
$792$	−16.6916	−0.593111
$793$	84.3385	2.99495
$794$	−61.8745	−2.19584
$795$	−7.03905	−0.249649
$796$	−36.8375	−1.30567
$797$	30.0370	1.06396	0.531982	−	0.846756i	$-0.321447\pi$
$797$	30.0370	1.06396	0.531982	+	0.846756i	$0.321447\pi$
$798$	−9.47744	−0.335498
$799$	15.6012	0.551931
$800$	−274.316	−9.69852
$801$	1.06904	0.0377728
$802$	62.5533	2.20883
$803$	49.0587	1.73125
$804$	24.7526	0.872956
$805$	1.26258	0.0445000
$806$	94.3611	3.32373
$807$	2.10341	0.0740434
$808$	108.208	3.80673
$809$	−6.20168	−0.218039	−0.109020	−	0.994040i	$-0.534771\pi$
$809$	−6.20168	−0.218039	−0.109020	+	0.994040i	$0.534771\pi$
$810$	−104.102	−3.65776
$811$	−49.5236	−1.73901	−0.869505	−	0.493924i	$-0.835562\pi$
$811$	−49.5236	−1.73901	−0.869505	+	0.493924i	$0.835562\pi$
$812$	57.4102	2.01470
$813$	−30.9902	−1.08687
$814$	−101.048	−3.54174
$815$	−79.1368	−2.77204
$816$	77.3788	2.70880
$817$	−22.1244	−0.774036
$818$	−104.562	−3.65594
$819$	2.06787	0.0722571
$820$	−112.830	−3.94019
$821$	−36.0432	−1.25792	−0.628959	−	0.777439i	$-0.716519\pi$
$821$	−36.0432	−1.25792	−0.628959	+	0.777439i	$0.716519\pi$
$822$	−29.0772	−1.01418
$823$	−33.1171	−1.15439	−0.577195	−	0.816606i	$-0.695853\pi$
$823$	−33.1171	−1.15439	−0.577195	+	0.816606i	$0.695853\pi$
$824$	1.54990	0.0539933
$825$	55.9865	1.94920
$826$	−2.25950	−0.0786180
$827$	−36.7555	−1.27811	−0.639057	−	0.769159i	$-0.720675\pi$
$827$	−36.7555	−1.27811	−0.639057	+	0.769159i	$0.720675\pi$
$828$	0.941622	0.0327236
$829$	44.0032	1.52829	0.764147	−	0.645043i	$-0.223160\pi$
$829$	44.0032	1.52829	0.764147	+	0.645043i	$0.223160\pi$
$830$	15.4067	0.534775
$831$	−52.3578	−1.81627
$832$	−287.506	−9.96747
$833$	−13.2959	−0.460675
$834$	−57.8725	−2.00396
$835$	4.03792	0.139738
$836$	−42.7134	−1.47727
$837$	−29.3793	−1.01550
$838$	−11.2516	−0.388681
$839$	0.252696	0.00872403	0.00436201	−	0.999990i	$-0.498612\pi$
$839$	0.252696	0.00872403	0.00436201	+	0.999990i	$0.498612\pi$
$840$	−68.4507	−2.36177
$841$	83.8972	2.89301
$842$	−62.5305	−2.15494
$843$	−5.84820	−0.201423
$844$	−17.3901	−0.598592
$845$	−60.8053	−2.09177
$846$	−8.53580	−0.293467
$847$	−1.73302	−0.0595474
$848$	20.1898	0.693320
$849$	37.6375	1.29171
$850$	−51.1653	−1.75495
$851$	3.78204	0.129647
$852$	−49.2862	−1.68852
$853$	0.390043	0.0133548	0.00667741	−	0.999978i	$-0.497874\pi$
$853$	0.390043	0.0133548	0.00667741	+	0.999978i	$0.497874\pi$
$854$	−39.7255	−1.35938
$855$	3.06532	0.104832
$856$	−72.2584	−2.46974
$857$	−14.9562	−0.510893	−0.255447	−	0.966823i	$-0.582223\pi$
$857$	−14.9562	−0.510893	−0.255447	+	0.966823i	$0.582223\pi$
$858$	101.830	3.47641
$859$	−16.6607	−0.568456	−0.284228	−	0.958757i	$-0.591737\pi$
$859$	−16.6607	−0.568456	−0.284228	+	0.958757i	$0.591737\pi$
$860$	−240.846	−8.21277
$861$	−8.70826	−0.296777
$862$	−6.14660	−0.209354
$863$	14.3550	0.488649	0.244324	−	0.969694i	$-0.421434\pi$
$863$	14.3550	0.488649	0.244324	+	0.969694i	$0.421434\pi$
$864$	155.342	5.28485
$865$	−10.2155	−0.347337
$866$	27.7535	0.943103
$867$	−22.8540	−0.776161
$868$	−33.2550	−1.12875
$869$	33.0812	1.12220
$870$	−202.886	−6.87849
$871$	−12.2551	−0.415248
$872$	−163.278	−5.52930
$873$	−3.45077	−0.116791
$874$	2.13669	0.0722746
$875$	11.4256	0.386255
$876$	150.042	5.06946
$877$	8.27648	0.279477	0.139738	−	0.990188i	$-0.455374\pi$
$877$	8.27648	0.279477	0.139738	+	0.990188i	$0.455374\pi$
$878$	38.9710	1.31521
$879$	16.7850	0.566145
$880$	−255.836	−8.62424
$881$	48.2985	1.62722	0.813609	−	0.581412i	$-0.197500\pi$
$881$	48.2985	1.62722	0.813609	+	0.581412i	$0.197500\pi$
$882$	7.27450	0.244945
$883$	−26.6316	−0.896225	−0.448113	−	0.893977i	$-0.647904\pi$
$883$	−26.6316	−0.896225	−0.448113	+	0.893977i	$0.647904\pi$
$884$	−69.6284	−2.34186
$885$	5.97442	0.200828
$886$	79.6374	2.67547
$887$	30.3526	1.01914	0.509570	−	0.860429i	$-0.329805\pi$
$887$	30.3526	1.01914	0.509570	+	0.860429i	$0.329805\pi$
$888$	−205.043	−6.88080
$889$	12.8942	0.432456
$890$	26.4075	0.885182
$891$	−36.2108	−1.21311
$892$	118.267	3.95986
$893$	−14.4920	−0.484957
$894$	69.3787	2.32037
$895$	−40.4013	−1.35047
$896$	76.2482	2.54727
$897$	−3.81129	−0.127255
$898$	−5.22209	−0.174263
$899$	−65.3960	−2.18108
$900$	20.9450	0.698168
$901$	2.23762	0.0745460
$902$	−52.4546	−1.74655
$903$	−18.5886	−0.618589
$904$	46.7549	1.55504
$905$	8.36375	0.278021
$906$	−30.3572	−1.00855
$907$	−39.3363	−1.30614	−0.653070	−	0.757297i	$-0.726519\pi$
$907$	−39.3363	−1.30614	−0.653070	+	0.757297i	$0.726519\pi$
$908$	−99.0200	−3.28609
$909$	−4.07127	−0.135036
$910$	51.0804	1.69330
$911$	−3.75599	−0.124441	−0.0622207	−	0.998062i	$-0.519818\pi$
$911$	−3.75599	−0.124441	−0.0622207	+	0.998062i	$0.519818\pi$
$912$	−71.8774	−2.38010
$913$	5.35908	0.177360
$914$	113.981	3.77016
$915$	105.040	3.47251
$916$	−65.6908	−2.17049
$917$	14.7483	0.487031
$918$	28.9744	0.956298
$919$	−34.7793	−1.14726	−0.573631	−	0.819114i	$-0.694466\pi$
$919$	−34.7793	−1.14726	−0.573631	+	0.819114i	$0.694466\pi$
$920$	15.4322	0.508784
$921$	−7.58049	−0.249786
$922$	−69.8073	−2.29898
$923$	24.4018	0.803194
$924$	−35.8871	−1.18060
$925$	84.1261	2.76605
$926$	19.4211	0.638216
$927$	−0.0583144	−0.00191530
$928$	345.780	11.3508
$929$	29.4448	0.966054	0.483027	−	0.875605i	$-0.339537\pi$
$929$	29.4448	0.966054	0.483027	+	0.875605i	$0.339537\pi$
$930$	117.522	3.85371
$931$	12.3506	0.404775
$932$	167.423	5.48413
$933$	−28.2584	−0.925139
$934$	−23.4657	−0.767821
$935$	−28.3542	−0.927282
$936$	25.2750	0.826141
$937$	−21.1881	−0.692184	−0.346092	−	0.938201i	$-0.612492\pi$
$937$	−21.1881	−0.692184	−0.346092	+	0.938201i	$0.612492\pi$
$938$	5.77245	0.188477
$939$	−18.6237	−0.607763
$940$	−157.760	−5.14556
$941$	42.4648	1.38431	0.692157	−	0.721747i	$-0.256661\pi$
$941$	42.4648	1.38431	0.692157	+	0.721747i	$0.256661\pi$
$942$	−24.4112	−0.795361
$943$	1.96328	0.0639331
$944$	−17.1362	−0.557734
$945$	−15.9039	−0.517352
$946$	−111.969	−3.64044
$947$	−5.59342	−0.181762	−0.0908809	−	0.995862i	$-0.528968\pi$
$947$	−5.59342	−0.181762	−0.0908809	+	0.995862i	$0.528968\pi$
$948$	101.176	3.28605
$949$	−74.2864	−2.41144
$950$	47.5276	1.54200
$951$	−7.51405	−0.243660
$952$	21.7596	0.705231
$953$	25.1314	0.814084	0.407042	−	0.913409i	$-0.366560\pi$
$953$	25.1314	0.814084	0.407042	+	0.913409i	$0.366560\pi$
$954$	−1.22426	−0.0396367
$955$	40.5584	1.31244
$956$	−117.863	−3.81196
$957$	−70.5721	−2.28127
$958$	−20.2752	−0.655063
$959$	−5.07356	−0.163834
$960$	−358.076	−11.5568
$961$	6.88085	0.221963
$962$	153.011	4.93326
$963$	2.71870	0.0876088
$964$	−102.430	−3.29905
$965$	−28.9737	−0.932695
$966$	1.79521	0.0577600
$967$	25.1088	0.807446	0.403723	−	0.914881i	$-0.367716\pi$
$967$	25.1088	0.807446	0.403723	+	0.914881i	$0.367716\pi$
$968$	−21.1823	−0.680826
$969$	−7.96613	−0.255909
$970$	−85.2408	−2.73692
$971$	2.73313	0.0877102	0.0438551	−	0.999038i	$-0.486036\pi$
$971$	2.73313	0.0877102	0.0438551	+	0.999038i	$0.486036\pi$
$972$	−25.6427	−0.822490
$973$	−10.0979	−0.323725
$974$	−74.4673	−2.38609
$975$	−84.7767	−2.71503
$976$	−301.281	−9.64375
$977$	−22.0824	−0.706480	−0.353240	−	0.935533i	$-0.614920\pi$
$977$	−22.0824	−0.706480	−0.353240	+	0.935533i	$0.614920\pi$
$978$	−112.522	−3.59804
$979$	9.18561	0.293573
$980$	134.448	4.29479
$981$	6.14329	0.196140
$982$	1.41969	0.0453042
$983$	−13.8123	−0.440545	−0.220272	−	0.975438i	$-0.570695\pi$
$983$	−13.8123	−0.440545	−0.220272	+	0.975438i	$0.570695\pi$
$984$	−106.439	−3.39315
$985$	93.7109	2.98588
$986$	64.4948	2.05393
$987$	−12.1760	−0.387565
$988$	64.6781	2.05769
$989$	4.19079	0.133260
$990$	15.5133	0.493044
$991$	16.6223	0.528025	0.264013	−	0.964519i	$-0.414954\pi$
$991$	16.6223	0.528025	0.264013	+	0.964519i	$0.414954\pi$
$992$	−200.294	−6.35935
$993$	−31.1822	−0.989537
$994$	−11.4938	−0.364562
$995$	22.7151	0.720117
$996$	16.3903	0.519347
$997$	−6.40048	−0.202705	−0.101353	−	0.994851i	$-0.532317\pi$
$997$	−6.40048	−0.202705	−0.101353	+	0.994851i	$0.532317\pi$
$998$	20.5957	0.651945
$999$	−47.6398	−1.50726

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.a.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-2.81833 q^{2} +1.84881 q^{3} +5.94296 q^{4} -3.66460 q^{5} -5.21056 q^{6} -0.909168 q^{7} -11.1126 q^{8} +0.418106 q^{9} +O(q^{10})\)	\(q-2.81833 q^{2} +1.84881 q^{3} +5.94296 q^{4} -3.66460 q^{5} -5.21056 q^{6} -0.909168 q^{7} -11.1126 q^{8} +0.418106 q^{9} +10.3280 q^{10} +3.59251 q^{11} +10.9874 q^{12} -5.43991 q^{13} +2.56233 q^{14} -6.77516 q^{15} +19.4329 q^{16} +2.15373 q^{17} -1.17836 q^{18} -2.00061 q^{19} -21.7786 q^{20} -1.68088 q^{21} -10.1249 q^{22} +0.378955 q^{23} -20.5450 q^{24} +8.42931 q^{25} +15.3314 q^{26} -4.77344 q^{27} -5.40315 q^{28} -10.6253 q^{29} +19.0946 q^{30} +6.15474 q^{31} -32.5431 q^{32} +6.64188 q^{33} -6.06992 q^{34} +3.33174 q^{35} +2.48479 q^{36} +9.98019 q^{37} +5.63838 q^{38} -10.0574 q^{39} +40.7231 q^{40} +5.18077 q^{41} +4.73727 q^{42} +11.0588 q^{43} +21.3502 q^{44} -1.53219 q^{45} -1.06802 q^{46} +7.24380 q^{47} +35.9277 q^{48} -6.17341 q^{49} -23.7565 q^{50} +3.98185 q^{51} -32.3292 q^{52} +1.03895 q^{53} +13.4531 q^{54} -13.1651 q^{55} +10.1032 q^{56} -3.69876 q^{57} +29.9456 q^{58} -0.881813 q^{59} -40.2645 q^{60} -15.5037 q^{61} -17.3461 q^{62} -0.380129 q^{63} +52.8512 q^{64} +19.9351 q^{65} -18.7190 q^{66} +2.25281 q^{67} +12.7996 q^{68} +0.700616 q^{69} -9.38993 q^{70} -4.48569 q^{71} -4.64622 q^{72} +13.6558 q^{73} -28.1274 q^{74} +15.5842 q^{75} -11.8896 q^{76} -3.26620 q^{77} +28.3449 q^{78} +9.20837 q^{79} -71.2137 q^{80} -10.0795 q^{81} -14.6011 q^{82} +1.49174 q^{83} -9.98941 q^{84} -7.89258 q^{85} -31.1674 q^{86} -19.6442 q^{87} -39.9220 q^{88} +2.55688 q^{89} +4.31822 q^{90} +4.94579 q^{91} +2.25211 q^{92} +11.3790 q^{93} -20.4154 q^{94} +7.33145 q^{95} -60.1660 q^{96} -8.25333 q^{97} +17.3987 q^{98} +1.50205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) \) 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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