LMFDB - Embedded newform 8011.2.a.a.1.11

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			1.11
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)

$f(q)$	$=$	$q-2.67381 q^{2} -2.54689 q^{3} +5.14927 q^{4} -3.71609 q^{5} +6.80992 q^{6} +3.32085 q^{7} -8.42057 q^{8} +3.48667 q^{9} +O(q^{10})$	\(q-2.67381 q^{2} -2.54689 q^{3} +5.14927 q^{4} -3.71609 q^{5} +6.80992 q^{6} +3.32085 q^{7} -8.42057 q^{8} +3.48667 q^{9} +9.93612 q^{10} -0.879850 q^{11} -13.1147 q^{12} +2.32566 q^{13} -8.87934 q^{14} +9.46448 q^{15} +12.2165 q^{16} +6.68257 q^{17} -9.32271 q^{18} +7.23197 q^{19} -19.1351 q^{20} -8.45786 q^{21} +2.35255 q^{22} +1.22445 q^{23} +21.4463 q^{24} +8.80929 q^{25} -6.21838 q^{26} -1.23950 q^{27} +17.1000 q^{28} -0.845759 q^{29} -25.3062 q^{30} +0.0194370 q^{31} -15.8234 q^{32} +2.24089 q^{33} -17.8679 q^{34} -12.3406 q^{35} +17.9538 q^{36} -5.55169 q^{37} -19.3369 q^{38} -5.92321 q^{39} +31.2915 q^{40} -1.42366 q^{41} +22.6147 q^{42} +6.47502 q^{43} -4.53059 q^{44} -12.9568 q^{45} -3.27394 q^{46} -11.6379 q^{47} -31.1141 q^{48} +4.02807 q^{49} -23.5544 q^{50} -17.0198 q^{51} +11.9755 q^{52} +6.15307 q^{53} +3.31419 q^{54} +3.26960 q^{55} -27.9635 q^{56} -18.4191 q^{57} +2.26140 q^{58} +1.90446 q^{59} +48.7352 q^{60} -7.56466 q^{61} -0.0519710 q^{62} +11.5787 q^{63} +17.8759 q^{64} -8.64235 q^{65} -5.99171 q^{66} -13.2536 q^{67} +34.4104 q^{68} -3.11853 q^{69} +32.9964 q^{70} +14.4597 q^{71} -29.3597 q^{72} +15.1125 q^{73} +14.8442 q^{74} -22.4363 q^{75} +37.2394 q^{76} -2.92185 q^{77} +15.8376 q^{78} -9.65196 q^{79} -45.3974 q^{80} -7.30314 q^{81} +3.80659 q^{82} -8.06679 q^{83} -43.5519 q^{84} -24.8330 q^{85} -17.3130 q^{86} +2.15406 q^{87} +7.40884 q^{88} +3.48116 q^{89} +34.6440 q^{90} +7.72318 q^{91} +6.30501 q^{92} -0.0495041 q^{93} +31.1177 q^{94} -26.8746 q^{95} +40.3006 q^{96} -13.7842 q^{97} -10.7703 q^{98} -3.06775 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.67381	−1.89067	−0.945335	−	0.326099i	$-0.894266\pi$
$2$	−2.67381	−1.89067	−0.945335	+	0.326099i	$0.894266\pi$
$3$	−2.54689	−1.47045	−0.735225	−	0.677823i	$-0.762924\pi$
$3$	−2.54689	−1.47045	−0.735225	+	0.677823i	$0.762924\pi$
$4$	5.14927	2.57464
$5$	−3.71609	−1.66188	−0.830942	−	0.556359i	$-0.812198\pi$
$5$	−3.71609	−1.66188	−0.830942	+	0.556359i	$0.812198\pi$
$6$	6.80992	2.78014
$7$	3.32085	1.25516	0.627582	−	0.778550i	$-0.284045\pi$
$7$	3.32085	1.25516	0.627582	+	0.778550i	$0.284045\pi$
$8$	−8.42057	−2.97712
$9$	3.48667	1.16222
$10$	9.93612	3.14208
$11$	−0.879850	−0.265285	−0.132642	−	0.991164i	$-0.542346\pi$
$11$	−0.879850	−0.265285	−0.132642	+	0.991164i	$0.542346\pi$
$12$	−13.1147	−3.78587
$13$	2.32566	0.645022	0.322511	−	0.946566i	$-0.395473\pi$
$13$	2.32566	0.645022	0.322511	+	0.946566i	$0.395473\pi$
$14$	−8.87934	−2.37310
$15$	9.46448	2.44372
$16$	12.2165	3.05412
$17$	6.68257	1.62076	0.810381	−	0.585903i	$-0.199260\pi$
$17$	6.68257	1.62076	0.810381	+	0.585903i	$0.199260\pi$
$18$	−9.32271	−2.19738
$19$	7.23197	1.65913	0.829564	−	0.558411i	$-0.188589\pi$
$19$	7.23197	1.65913	0.829564	+	0.558411i	$0.188589\pi$
$20$	−19.1351	−4.27875
$21$	−8.45786	−1.84566
$22$	2.35255	0.501566
$23$	1.22445	0.255315	0.127657	−	0.991818i	$-0.459254\pi$
$23$	1.22445	0.255315	0.127657	+	0.991818i	$0.459254\pi$
$24$	21.4463	4.37771
$25$	8.80929	1.76186
$26$	−6.21838	−1.21952
$27$	−1.23950	−0.238542
$28$	17.1000	3.23159
$29$	−0.845759	−0.157054	−0.0785268	−	0.996912i	$-0.525022\pi$
$29$	−0.845759	−0.157054	−0.0785268	+	0.996912i	$0.525022\pi$
$30$	−25.3062	−4.62027
$31$	0.0194370	0.00349100	0.00174550	−	0.999998i	$-0.499444\pi$
$31$	0.0194370	0.00349100	0.00174550	+	0.999998i	$0.499444\pi$
$32$	−15.8234	−2.79721
$33$	2.24089	0.390088
$34$	−17.8679	−3.06433
$35$	−12.3406	−2.08594
$36$	17.9538	2.99230
$37$	−5.55169	−0.912693	−0.456346	−	0.889802i	$-0.650842\pi$
$37$	−5.55169	−0.912693	−0.456346	+	0.889802i	$0.650842\pi$
$38$	−19.3369	−3.13687
$39$	−5.92321	−0.948473
$40$	31.2915	4.94763
$41$	−1.42366	−0.222338	−0.111169	−	0.993802i	$-0.535459\pi$
$41$	−1.42366	−0.222338	−0.111169	+	0.993802i	$0.535459\pi$
$42$	22.6147	3.48953
$43$	6.47502	0.987431	0.493715	−	0.869624i	$-0.335639\pi$
$43$	6.47502	0.987431	0.493715	+	0.869624i	$0.335639\pi$
$44$	−4.53059	−0.683012
$45$	−12.9568	−1.93148
$46$	−3.27394	−0.482716
$47$	−11.6379	−1.69757	−0.848784	−	0.528740i	$-0.822665\pi$
$47$	−11.6379	−1.69757	−0.848784	+	0.528740i	$0.822665\pi$
$48$	−31.1141	−4.49093
$49$	4.02807	0.575438
$50$	−23.5544	−3.33110
$51$	−17.0198	−2.38325
$52$	11.9755	1.66070
$53$	6.15307	0.845189	0.422594	−	0.906319i	$-0.361120\pi$
$53$	6.15307	0.845189	0.422594	+	0.906319i	$0.361120\pi$
$54$	3.31419	0.451005
$55$	3.26960	0.440873
$56$	−27.9635	−3.73678
$57$	−18.4191	−2.43967
$58$	2.26140	0.296937
$59$	1.90446	0.247939	0.123970	−	0.992286i	$-0.460437\pi$
$59$	1.90446	0.247939	0.123970	+	0.992286i	$0.460437\pi$
$60$	48.7352	6.29169
$61$	−7.56466	−0.968555	−0.484278	−	0.874914i	$-0.660918\pi$
$61$	−7.56466	−0.968555	−0.484278	+	0.874914i	$0.660918\pi$
$62$	−0.0519710	−0.00660033
$63$	11.5787	1.45878
$64$	17.8759	2.23449
$65$	−8.64235	−1.07195
$66$	−5.99171	−0.737528
$67$	−13.2536	−1.61918	−0.809590	−	0.586995i	$-0.800311\pi$
$67$	−13.2536	−1.61918	−0.809590	+	0.586995i	$0.800311\pi$
$68$	34.4104	4.17287
$69$	−3.11853	−0.375427
$70$	32.9964	3.94382
$71$	14.4597	1.71605	0.858025	−	0.513608i	$-0.171692\pi$
$71$	14.4597	1.71605	0.858025	+	0.513608i	$0.171692\pi$
$72$	−29.3597	−3.46008
$73$	15.1125	1.76879	0.884395	−	0.466740i	$-0.154572\pi$
$73$	15.1125	1.76879	0.884395	+	0.466740i	$0.154572\pi$
$74$	14.8442	1.72560
$75$	−22.4363	−2.59073
$76$	37.2394	4.27165
$77$	−2.92185	−0.332976
$78$	15.8376	1.79325
$79$	−9.65196	−1.08593	−0.542965	−	0.839755i	$-0.682698\pi$
$79$	−9.65196	−1.08593	−0.542965	+	0.839755i	$0.682698\pi$
$80$	−45.3974	−5.07559
$81$	−7.30314	−0.811460
$82$	3.80659	0.420367
$83$	−8.06679	−0.885446	−0.442723	−	0.896659i	$-0.645987\pi$
$83$	−8.06679	−0.885446	−0.442723	+	0.896659i	$0.645987\pi$
$84$	−43.5519	−4.75190
$85$	−24.8330	−2.69352
$86$	−17.3130	−1.86691
$87$	2.15406	0.230939
$88$	7.40884	0.789784
$89$	3.48116	0.369003	0.184501	−	0.982832i	$-0.440933\pi$
$89$	3.48116	0.369003	0.184501	+	0.982832i	$0.440933\pi$
$90$	34.6440	3.65180
$91$	7.72318	0.809609
$92$	6.30501	0.657342
$93$	−0.0495041	−0.00513334
$94$	31.1177	3.20954
$95$	−26.8746	−2.75728
$96$	40.3006	4.11316
$97$	−13.7842	−1.39957	−0.699786	−	0.714353i	$-0.746721\pi$
$97$	−13.7842	−1.39957	−0.699786	+	0.714353i	$0.746721\pi$
$98$	−10.7703	−1.08796
$99$	−3.06775	−0.308320
$100$	45.3615	4.53615
$101$	−14.0852	−1.40153	−0.700763	−	0.713394i	$-0.747157\pi$
$101$	−14.0852	−1.40153	−0.700763	+	0.713394i	$0.747157\pi$
$102$	45.5078	4.50594
$103$	6.73091	0.663217	0.331608	−	0.943417i	$-0.392409\pi$
$103$	6.73091	0.663217	0.331608	+	0.943417i	$0.392409\pi$
$104$	−19.5834	−1.92031
$105$	31.4301	3.06727
$106$	−16.4521	−1.59797
$107$	−2.80634	−0.271299	−0.135649	−	0.990757i	$-0.543312\pi$
$107$	−2.80634	−0.271299	−0.135649	+	0.990757i	$0.543312\pi$
$108$	−6.38253	−0.614159
$109$	−1.35105	−0.129407	−0.0647033	−	0.997905i	$-0.520610\pi$
$109$	−1.35105	−0.129407	−0.0647033	+	0.997905i	$0.520610\pi$
$110$	−8.74229	−0.833545
$111$	14.1396	1.34207
$112$	40.5691	3.83342
$113$	2.05268	0.193100	0.0965499	−	0.995328i	$-0.469219\pi$
$113$	2.05268	0.193100	0.0965499	+	0.995328i	$0.469219\pi$
$114$	49.2492	4.61261
$115$	−4.55015	−0.424303
$116$	−4.35505	−0.404356
$117$	8.10881	0.749660
$118$	−5.09216	−0.468772
$119$	22.1918	2.03432
$120$	−79.6963	−7.27524
$121$	−10.2259	−0.929624
$122$	20.2265	1.83122
$123$	3.62590	0.326936
$124$	0.100087	0.00898805
$125$	−14.1557	−1.26612
$126$	−30.9593	−2.75808
$127$	7.69995	0.683260	0.341630	−	0.939834i	$-0.389021\pi$
$127$	7.69995	0.683260	0.341630	+	0.939834i	$0.389021\pi$
$128$	−16.1500	−1.42747
$129$	−16.4912	−1.45197
$130$	23.1080	2.02671
$131$	−19.3828	−1.69348	−0.846741	−	0.532005i	$-0.821439\pi$
$131$	−19.3828	−1.69348	−0.846741	+	0.532005i	$0.821439\pi$
$132$	11.5389	1.00433
$133$	24.0163	2.08248
$134$	35.4375	3.06134
$135$	4.60609	0.396429
$136$	−56.2710	−4.82520
$137$	11.8803	1.01500	0.507499	−	0.861652i	$-0.330570\pi$
$137$	11.8803	1.01500	0.507499	+	0.861652i	$0.330570\pi$
$138$	8.33837	0.709810
$139$	−3.41342	−0.289522	−0.144761	−	0.989467i	$-0.546241\pi$
$139$	−3.41342	−0.289522	−0.144761	+	0.989467i	$0.546241\pi$
$140$	−63.5450	−5.37053
$141$	29.6406	2.49619
$142$	−38.6625	−3.24448
$143$	−2.04623	−0.171115
$144$	42.5948	3.54957
$145$	3.14291	0.261005
$146$	−40.4081	−3.34420
$147$	−10.2591	−0.846154
$148$	−28.5872	−2.34985
$149$	−23.5304	−1.92769	−0.963844	−	0.266466i	$-0.914144\pi$
$149$	−23.5304	−1.92769	−0.963844	+	0.266466i	$0.914144\pi$
$150$	59.9906	4.89821
$151$	−16.6627	−1.35599	−0.677994	−	0.735067i	$-0.737151\pi$
$151$	−16.6627	−1.35599	−0.677994	+	0.735067i	$0.737151\pi$
$152$	−60.8973	−4.93942
$153$	23.2999	1.88369
$154$	7.81249	0.629548
$155$	−0.0722297	−0.00580163
$156$	−30.5002	−2.44197
$157$	−19.1924	−1.53172	−0.765862	−	0.643005i	$-0.777687\pi$
$157$	−19.1924	−1.53172	−0.765862	+	0.643005i	$0.777687\pi$
$158$	25.8075	2.05314
$159$	−15.6712	−1.24281
$160$	58.8012	4.64864
$161$	4.06620	0.320462
$162$	19.5272	1.53420
$163$	−1.91776	−0.150211	−0.0751055	−	0.997176i	$-0.523929\pi$
$163$	−1.91776	−0.150211	−0.0751055	+	0.997176i	$0.523929\pi$
$164$	−7.33079	−0.572439
$165$	−8.32732	−0.648281
$166$	21.5691	1.67409
$167$	−16.3864	−1.26802	−0.634008	−	0.773327i	$-0.718591\pi$
$167$	−16.3864	−1.26802	−0.634008	+	0.773327i	$0.718591\pi$
$168$	71.2200	5.49474
$169$	−7.59131	−0.583947
$170$	66.3988	5.09256
$171$	25.2155	1.92828
$172$	33.3416	2.54227
$173$	9.47676	0.720505	0.360252	−	0.932855i	$-0.382691\pi$
$173$	9.47676	0.720505	0.360252	+	0.932855i	$0.382691\pi$
$174$	−5.75955	−0.436631
$175$	29.2544	2.21142
$176$	−10.7487	−0.810211
$177$	−4.85045	−0.364582
$178$	−9.30798	−0.697663
$179$	12.6123	0.942687	0.471343	−	0.881950i	$-0.343769\pi$
$179$	12.6123	0.942687	0.471343	+	0.881950i	$0.343769\pi$
$180$	−66.7180	−4.97286
$181$	−17.2925	−1.28534	−0.642672	−	0.766142i	$-0.722174\pi$
$181$	−17.2925	−1.28534	−0.642672	+	0.766142i	$0.722174\pi$
$182$	−20.6503	−1.53070
$183$	19.2664	1.42421
$184$	−10.3105	−0.760102
$185$	20.6306	1.51679
$186$	0.132365	0.00970545
$187$	−5.87966	−0.429963
$188$	−59.9269	−4.37062
$189$	−4.11620	−0.299410
$190$	71.8577	5.21311
$191$	−3.02625	−0.218972	−0.109486	−	0.993988i	$-0.534920\pi$
$191$	−3.02625	−0.218972	−0.109486	+	0.993988i	$0.534920\pi$
$192$	−45.5280	−3.28570
$193$	7.48726	0.538945	0.269472	−	0.963008i	$-0.413151\pi$
$193$	7.48726	0.538945	0.269472	+	0.963008i	$0.413151\pi$
$194$	36.8563	2.64613
$195$	22.0112	1.57625
$196$	20.7416	1.48154
$197$	14.9532	1.06537	0.532686	−	0.846313i	$-0.321183\pi$
$197$	14.9532	1.06537	0.532686	+	0.846313i	$0.321183\pi$
$198$	8.20258	0.582932
$199$	−24.0887	−1.70760	−0.853800	−	0.520601i	$-0.825708\pi$
$199$	−24.0887	−1.70760	−0.853800	+	0.520601i	$0.825708\pi$
$200$	−74.1792	−5.24526
$201$	33.7554	2.38092
$202$	37.6611	2.64982
$203$	−2.80864	−0.197128
$204$	−87.6396	−6.13600
$205$	5.29043	0.369499
$206$	−17.9972	−1.25392
$207$	4.26924	0.296733
$208$	28.4113	1.96997
$209$	−6.36305	−0.440142
$210$	−84.0383	−5.79920
$211$	−5.25709	−0.361913	−0.180956	−	0.983491i	$-0.557919\pi$
$211$	−5.25709	−0.361913	−0.180956	+	0.983491i	$0.557919\pi$
$212$	31.6838	2.17605
$213$	−36.8273	−2.52337
$214$	7.50361	0.512937
$215$	−24.0617	−1.64100
$216$	10.4373	0.710169
$217$	0.0645476	0.00438178
$218$	3.61244	0.244665
$219$	−38.4901	−2.60092
$220$	16.8361	1.13509
$221$	15.5414	1.04543
$222$	−37.8066	−2.53741
$223$	7.85255	0.525846	0.262923	−	0.964817i	$-0.415314\pi$
$223$	7.85255	0.525846	0.262923	+	0.964817i	$0.415314\pi$
$224$	−52.5472	−3.51096
$225$	30.7151	2.04767
$226$	−5.48848	−0.365088
$227$	10.8870	0.722593	0.361297	−	0.932451i	$-0.382334\pi$
$227$	10.8870	0.722593	0.361297	+	0.932451i	$0.382334\pi$
$228$	−94.8449	−6.28125
$229$	27.8265	1.83882	0.919412	−	0.393295i	$-0.128665\pi$
$229$	27.8265	1.83882	0.919412	+	0.393295i	$0.128665\pi$
$230$	12.1662	0.802218
$231$	7.44165	0.489625
$232$	7.12177	0.467567
$233$	−10.1474	−0.664778	−0.332389	−	0.943142i	$-0.607855\pi$
$233$	−10.1474	−0.664778	−0.332389	+	0.943142i	$0.607855\pi$
$234$	−21.6814	−1.41736
$235$	43.2476	2.82116
$236$	9.80657	0.638353
$237$	24.5825	1.59681
$238$	−59.3368	−3.84624
$239$	10.7897	0.697929	0.348964	−	0.937136i	$-0.386533\pi$
$239$	10.7897	0.697929	0.348964	+	0.937136i	$0.386533\pi$
$240$	115.622	7.46340
$241$	1.63610	0.105390	0.0526952	−	0.998611i	$-0.483219\pi$
$241$	1.63610	0.105390	0.0526952	+	0.998611i	$0.483219\pi$
$242$	27.3420	1.75761
$243$	22.3188	1.43175
$244$	−38.9525	−2.49368
$245$	−14.9687	−0.956312
$246$	−9.69498	−0.618129
$247$	16.8191	1.07017
$248$	−0.163671	−0.0103931
$249$	20.5453	1.30200
$250$	37.8496	2.39382
$251$	−21.4138	−1.35163	−0.675813	−	0.737073i	$-0.736207\pi$
$251$	−21.4138	−1.35163	−0.675813	+	0.737073i	$0.736207\pi$
$252$	59.6220	3.75583
$253$	−1.07733	−0.0677311
$254$	−20.5882	−1.29182
$255$	63.2471	3.96069
$256$	7.43023	0.464389
$257$	−13.5628	−0.846026	−0.423013	−	0.906124i	$-0.639027\pi$
$257$	−13.5628	−0.846026	−0.423013	+	0.906124i	$0.639027\pi$
$258$	44.0943	2.74519
$259$	−18.4364	−1.14558
$260$	−44.5018	−2.75989
$261$	−2.94889	−0.182531
$262$	51.8259	3.20182
$263$	−14.8911	−0.918222	−0.459111	−	0.888379i	$-0.651832\pi$
$263$	−14.8911	−0.918222	−0.459111	+	0.888379i	$0.651832\pi$
$264$	−18.8695	−1.16134
$265$	−22.8653	−1.40461
$266$	−64.2152	−3.93728
$267$	−8.86616	−0.542600
$268$	−68.2462	−4.16880
$269$	29.2620	1.78414	0.892068	−	0.451902i	$-0.149254\pi$
$269$	29.2620	1.78414	0.892068	+	0.451902i	$0.149254\pi$
$270$	−12.3158	−0.749518
$271$	13.1652	0.799729	0.399865	−	0.916574i	$-0.369057\pi$
$271$	13.1652	0.799729	0.399865	+	0.916574i	$0.369057\pi$
$272$	81.6374	4.95000
$273$	−19.6701	−1.19049
$274$	−31.7656	−1.91903
$275$	−7.75086	−0.467394
$276$	−16.0582	−0.966589
$277$	−25.5648	−1.53604	−0.768021	−	0.640425i	$-0.778758\pi$
$277$	−25.5648	−1.53604	−0.768021	+	0.640425i	$0.778758\pi$
$278$	9.12683	0.547391
$279$	0.0677706	0.00405732
$280$	103.915	6.21009
$281$	22.4449	1.33895	0.669474	−	0.742836i	$-0.266520\pi$
$281$	22.4449	1.33895	0.669474	+	0.742836i	$0.266520\pi$
$282$	−79.2534	−4.71947
$283$	15.1330	0.899561	0.449781	−	0.893139i	$-0.351502\pi$
$283$	15.1330	0.899561	0.449781	+	0.893139i	$0.351502\pi$
$284$	74.4569	4.41820
$285$	68.4469	4.05444
$286$	5.47124	0.323521
$287$	−4.72775	−0.279070
$288$	−55.1710	−3.25098
$289$	27.6568	1.62687
$290$	−8.40356	−0.493474
$291$	35.1069	2.05800
$292$	77.8186	4.55399
$293$	22.5276	1.31608	0.658038	−	0.752985i	$-0.271387\pi$
$293$	22.5276	1.31608	0.658038	+	0.752985i	$0.271387\pi$
$294$	27.4308	1.59980
$295$	−7.07713	−0.412046
$296$	46.7484	2.71720
$297$	1.09058	0.0632816
$298$	62.9160	3.64462
$299$	2.84764	0.164684
$300$	−115.531	−6.67018
$301$	21.5026	1.23939
$302$	44.5528	2.56373
$303$	35.8734	2.06087
$304$	88.3492	5.06717
$305$	28.1109	1.60963
$306$	−62.2997	−3.56143
$307$	15.2156	0.868402	0.434201	−	0.900816i	$-0.357031\pi$
$307$	15.2156	0.868402	0.434201	+	0.900816i	$0.357031\pi$
$308$	−15.0454	−0.857292
$309$	−17.1429	−0.975227
$310$	0.193129	0.0109690
$311$	−13.1895	−0.747907	−0.373954	−	0.927447i	$-0.621998\pi$
$311$	−13.1895	−0.747907	−0.373954	+	0.927447i	$0.621998\pi$
$312$	49.8768	2.82372
$313$	7.49776	0.423798	0.211899	−	0.977292i	$-0.432035\pi$
$313$	7.49776	0.423798	0.211899	+	0.977292i	$0.432035\pi$
$314$	51.3170	2.89599
$315$	−43.0275	−2.42433
$316$	−49.7006	−2.79588
$317$	7.34829	0.412721	0.206361	−	0.978476i	$-0.433838\pi$
$317$	7.34829	0.412721	0.206361	+	0.978476i	$0.433838\pi$
$318$	41.9019	2.34974
$319$	0.744141	0.0416639
$320$	−66.4284	−3.71346
$321$	7.14744	0.398931
$322$	−10.8723	−0.605888
$323$	48.3282	2.68905
$324$	−37.6058	−2.08921
$325$	20.4874	1.13644
$326$	5.12774	0.283999
$327$	3.44097	0.190286
$328$	11.9880	0.661926
$329$	−38.6479	−2.13073
$330$	22.2657	1.22569
$331$	−31.0852	−1.70860	−0.854299	−	0.519782i	$-0.826013\pi$
$331$	−31.0852	−1.70860	−0.854299	+	0.519782i	$0.826013\pi$
$332$	−41.5381	−2.27970
$333$	−19.3569	−1.06075
$334$	43.8141	2.39740
$335$	49.2514	2.69089
$336$	−103.325	−5.63685
$337$	−9.52026	−0.518602	−0.259301	−	0.965797i	$-0.583492\pi$
$337$	−9.52026	−0.518602	−0.259301	+	0.965797i	$0.583492\pi$
$338$	20.2977	1.10405
$339$	−5.22796	−0.283944
$340$	−127.872	−6.93483
$341$	−0.0171017	−0.000926108 0
$342$	−67.4216	−3.64574
$343$	−9.86935	−0.532895
$344$	−54.5233	−2.93970
$345$	11.5887	0.623917
$346$	−25.3391	−1.36224
$347$	14.9188	0.800885	0.400443	−	0.916322i	$-0.368856\pi$
$347$	14.9188	0.800885	0.400443	+	0.916322i	$0.368856\pi$
$348$	11.0918	0.594585
$349$	−21.5357	−1.15278	−0.576391	−	0.817174i	$-0.695539\pi$
$349$	−21.5357	−1.15278	−0.576391	+	0.817174i	$0.695539\pi$
$350$	−78.2207	−4.18107
$351$	−2.88266	−0.153865
$352$	13.9222	0.742057
$353$	−0.387448	−0.0206218	−0.0103109	−	0.999947i	$-0.503282\pi$
$353$	−0.387448	−0.0206218	−0.0103109	+	0.999947i	$0.503282\pi$
$354$	12.9692	0.689305
$355$	−53.7334	−2.85188
$356$	17.9255	0.950048
$357$	−56.5203	−2.99137
$358$	−33.7229	−1.78231
$359$	−19.1367	−1.01000	−0.504998	−	0.863120i	$-0.668507\pi$
$359$	−19.1367	−1.01000	−0.504998	+	0.863120i	$0.668507\pi$
$360$	109.103	5.75025
$361$	33.3015	1.75271
$362$	46.2370	2.43016
$363$	26.0442	1.36697
$364$	39.7687	2.08445
$365$	−56.1595	−2.93952
$366$	−51.5147	−2.69272
$367$	7.98334	0.416727	0.208364	−	0.978051i	$-0.433186\pi$
$367$	7.98334	0.416727	0.208364	+	0.978051i	$0.433186\pi$
$368$	14.9584	0.779761
$369$	−4.96382	−0.258406
$370$	−55.1623	−2.86775
$371$	20.4334	1.06085
$372$	−0.254910	−0.0132165
$373$	−7.38915	−0.382596	−0.191298	−	0.981532i	$-0.561270\pi$
$373$	−7.38915	−0.382596	−0.191298	+	0.981532i	$0.561270\pi$
$374$	15.7211	0.812919
$375$	36.0530	1.86177
$376$	97.9981	5.05386
$377$	−1.96695	−0.101303
$378$	11.0060	0.566085
$379$	−0.438063	−0.0225018	−0.0112509	−	0.999937i	$-0.503581\pi$
$379$	−0.438063	−0.0225018	−0.0112509	+	0.999937i	$0.503581\pi$
$380$	−138.385	−7.09899
$381$	−19.6110	−1.00470
$382$	8.09162	0.414003
$383$	−6.75847	−0.345342	−0.172671	−	0.984980i	$-0.555240\pi$
$383$	−6.75847	−0.345342	−0.172671	+	0.984980i	$0.555240\pi$
$384$	41.1323	2.09902
$385$	10.8579	0.553368
$386$	−20.0195	−1.01897
$387$	22.5763	1.14762
$388$	−70.9785	−3.60339
$389$	−16.2948	−0.826181	−0.413090	−	0.910690i	$-0.635551\pi$
$389$	−16.2948	−0.826181	−0.413090	+	0.910690i	$0.635551\pi$
$390$	−58.8537	−2.98017
$391$	8.18245	0.413804
$392$	−33.9186	−1.71315
$393$	49.3659	2.49018
$394$	−39.9821	−2.01427
$395$	35.8675	1.80469
$396$	−15.7967	−0.793813
$397$	−32.8091	−1.64664	−0.823320	−	0.567577i	$-0.807881\pi$
$397$	−32.8091	−1.64664	−0.823320	+	0.567577i	$0.807881\pi$
$398$	64.4086	3.22851
$399$	−61.1671	−3.06218
$400$	107.618	5.38092
$401$	−13.2262	−0.660486	−0.330243	−	0.943896i	$-0.607131\pi$
$401$	−13.2262	−0.660486	−0.330243	+	0.943896i	$0.607131\pi$
$402$	−90.2557	−4.50155
$403$	0.0452040	0.00225177
$404$	−72.5284	−3.60842
$405$	27.1391	1.34855
$406$	7.50979	0.372704
$407$	4.88466	0.242124
$408$	143.316	7.09522
$409$	−6.79251	−0.335868	−0.167934	−	0.985798i	$-0.553710\pi$
$409$	−6.79251	−0.335868	−0.167934	+	0.985798i	$0.553710\pi$
$410$	−14.1456	−0.698602
$411$	−30.2578	−1.49251
$412$	34.6593	1.70754
$413$	6.32442	0.311205
$414$	−11.4151	−0.561024
$415$	29.9769	1.47151
$416$	−36.7999	−1.80426
$417$	8.69361	0.425728
$418$	17.0136	0.832163
$419$	−9.09511	−0.444325	−0.222163	−	0.975010i	$-0.571312\pi$
$419$	−9.09511	−0.444325	−0.222163	+	0.975010i	$0.571312\pi$
$420$	161.842	7.89710
$421$	−19.2074	−0.936113	−0.468056	−	0.883699i	$-0.655046\pi$
$421$	−19.2074	−0.936113	−0.468056	+	0.883699i	$0.655046\pi$
$422$	14.0565	0.684258
$423$	−40.5777	−1.97295
$424$	−51.8123	−2.51623
$425$	58.8687	2.85555
$426$	98.4693	4.77085
$427$	−25.1211	−1.21570
$428$	−14.4506	−0.698495
$429$	5.21154	0.251615
$430$	64.3365	3.10258
$431$	13.9950	0.674117	0.337059	−	0.941484i	$-0.390568\pi$
$431$	13.9950	0.674117	0.337059	+	0.941484i	$0.390568\pi$
$432$	−15.1423	−0.728536
$433$	−2.44745	−0.117617	−0.0588085	−	0.998269i	$-0.518730\pi$
$433$	−2.44745	−0.117617	−0.0588085	+	0.998269i	$0.518730\pi$
$434$	−0.172588	−0.00828450
$435$	−8.00467	−0.383795
$436$	−6.95690	−0.333175
$437$	8.85516	0.423600
$438$	102.915	4.91748
$439$	−1.87887	−0.0896737	−0.0448369	−	0.998994i	$-0.514277\pi$
$439$	−1.87887	−0.0896737	−0.0448369	+	0.998994i	$0.514277\pi$
$440$	−27.5319	−1.31253
$441$	14.0446	0.668788
$442$	−41.5548	−1.97656
$443$	−18.4407	−0.876142	−0.438071	−	0.898940i	$-0.644338\pi$
$443$	−18.4407	−0.876142	−0.438071	+	0.898940i	$0.644338\pi$
$444$	72.8086	3.45534
$445$	−12.9363	−0.613240
$446$	−20.9963	−0.994201
$447$	59.9295	2.83457
$448$	59.3633	2.80465
$449$	13.0334	0.615083	0.307541	−	0.951535i	$-0.400494\pi$
$449$	13.0334	0.615083	0.307541	+	0.951535i	$0.400494\pi$
$450$	−82.1265	−3.87148
$451$	1.25260	0.0589828
$452$	10.5698	0.497162
$453$	42.4380	1.99391
$454$	−29.1097	−1.36619
$455$	−28.7000	−1.34548
$456$	155.099	7.26318
$457$	12.3927	0.579705	0.289852	−	0.957071i	$-0.406394\pi$
$457$	12.3927	0.579705	0.289852	+	0.957071i	$0.406394\pi$
$458$	−74.4028	−3.47661
$459$	−8.28306	−0.386620
$460$	−23.4299	−1.09243
$461$	−18.8891	−0.879754	−0.439877	−	0.898058i	$-0.644978\pi$
$461$	−18.8891	−0.879754	−0.439877	+	0.898058i	$0.644978\pi$
$462$	−19.8976	−0.925719
$463$	0.698815	0.0324767	0.0162383	−	0.999868i	$-0.494831\pi$
$463$	0.698815	0.0324767	0.0162383	+	0.999868i	$0.494831\pi$
$464$	−10.3322	−0.479660
$465$	0.183962	0.00853101
$466$	27.1322	1.25688
$467$	−36.5471	−1.69120	−0.845600	−	0.533817i	$-0.820757\pi$
$467$	−36.5471	−1.69120	−0.845600	+	0.533817i	$0.820757\pi$
$468$	41.7545	1.93010
$469$	−44.0132	−2.03234
$470$	−115.636	−5.33389
$471$	48.8811	2.25232
$472$	−16.0366	−0.738145
$473$	−5.69704	−0.261950
$474$	−65.7291	−3.01904
$475$	63.7086	2.92315
$476$	114.272	5.23764
$477$	21.4537	0.982298
$478$	−28.8497	−1.31955
$479$	−4.75435	−0.217232	−0.108616	−	0.994084i	$-0.534642\pi$
$479$	−4.75435	−0.217232	−0.108616	+	0.994084i	$0.534642\pi$
$480$	−149.760	−6.83559
$481$	−12.9114	−0.588707
$482$	−4.37462	−0.199259
$483$	−10.3562	−0.471223
$484$	−52.6558	−2.39344
$485$	51.2232	2.32593
$486$	−59.6763	−2.70697
$487$	−0.500697	−0.0226887	−0.0113444	−	0.999936i	$-0.503611\pi$
$487$	−0.500697	−0.0226887	−0.0113444	+	0.999936i	$0.503611\pi$
$488$	63.6987	2.88350
$489$	4.88434	0.220878
$490$	40.0234	1.80807
$491$	−23.1148	−1.04316	−0.521579	−	0.853203i	$-0.674657\pi$
$491$	−23.1148	−1.04316	−0.521579	+	0.853203i	$0.674657\pi$
$492$	18.6708	0.841743
$493$	−5.65185	−0.254546
$494$	−44.9712	−2.02335
$495$	11.4000	0.512393
$496$	0.237452	0.0106619
$497$	48.0185	2.15392
$498$	−54.9342	−2.46166
$499$	14.7206	0.658985	0.329493	−	0.944158i	$-0.393122\pi$
$499$	14.7206	0.658985	0.329493	+	0.944158i	$0.393122\pi$
$500$	−72.8914	−3.25980
$501$	41.7344	1.86455
$502$	57.2565	2.55548
$503$	28.1868	1.25679	0.628394	−	0.777895i	$-0.283713\pi$
$503$	28.1868	1.25679	0.628394	+	0.777895i	$0.283713\pi$
$504$	−97.4994	−4.34297
$505$	52.3417	2.32917
$506$	2.88057	0.128057
$507$	19.3343	0.858665
$508$	39.6492	1.75915
$509$	−31.1484	−1.38063	−0.690313	−	0.723510i	$-0.742527\pi$
$509$	−31.1484	−1.38063	−0.690313	+	0.723510i	$0.742527\pi$
$510$	−169.111	−7.48835
$511$	50.1865	2.22012
$512$	12.4329	0.549463
$513$	−8.96404	−0.395772
$514$	36.2644	1.59956
$515$	−25.0127	−1.10219
$516$	−84.9176	−3.73829
$517$	10.2396	0.450339
$518$	49.2954	2.16591
$519$	−24.1363	−1.05947
$520$	72.7735	3.19133
$521$	−12.8146	−0.561416	−0.280708	−	0.959793i	$-0.590569\pi$
$521$	−12.8146	−0.561416	−0.280708	+	0.959793i	$0.590569\pi$
$522$	7.88477	0.345107
$523$	−17.9140	−0.783326	−0.391663	−	0.920109i	$-0.628100\pi$
$523$	−17.9140	−0.783326	−0.391663	+	0.920109i	$0.628100\pi$
$524$	−99.8073	−4.36010
$525$	−74.5078	−3.25179
$526$	39.8159	1.73606
$527$	0.129890	0.00565808
$528$	27.3757	1.19137
$529$	−21.5007	−0.934814
$530$	61.1376	2.65565
$531$	6.64022	0.288161
$532$	123.667	5.36163
$533$	−3.31094	−0.143413
$534$	23.7064	1.02588
$535$	10.4286	0.450867
$536$	111.603	4.82049
$537$	−32.1222	−1.38617
$538$	−78.2411	−3.37321
$539$	−3.54410	−0.152655
$540$	23.7180	1.02066
$541$	25.5177	1.09709	0.548546	−	0.836120i	$-0.315181\pi$
$541$	25.5177	1.09709	0.548546	+	0.836120i	$0.315181\pi$
$542$	−35.2013	−1.51203
$543$	44.0423	1.89003
$544$	−105.741	−4.53361
$545$	5.02060	0.215059
$546$	52.5942	2.25082
$547$	10.3574	0.442849	0.221425	−	0.975177i	$-0.428929\pi$
$547$	10.3574	0.442849	0.221425	+	0.975177i	$0.428929\pi$
$548$	61.1747	2.61325
$549$	−26.3755	−1.12568
$550$	20.7243	0.883689
$551$	−6.11651	−0.260572
$552$	26.2598	1.11769
$553$	−32.0527	−1.36302
$554$	68.3555	2.90415
$555$	−52.5439	−2.23036
$556$	−17.5766	−0.745414
$557$	13.6697	0.579203	0.289602	−	0.957147i	$-0.406477\pi$
$557$	13.6697	0.579203	0.289602	+	0.957147i	$0.406477\pi$
$558$	−0.181206	−0.00767106
$559$	15.0587	0.636914
$560$	−150.758	−6.37070
$561$	14.9749	0.632240
$562$	−60.0133	−2.53151
$563$	−19.5806	−0.825224	−0.412612	−	0.910907i	$-0.635384\pi$
$563$	−19.5806	−0.825224	−0.412612	+	0.910907i	$0.635384\pi$
$564$	152.628	6.42678
$565$	−7.62793	−0.320909
$566$	−40.4627	−1.70077
$567$	−24.2526	−1.01852
$568$	−121.759	−5.10888
$569$	34.1890	1.43328	0.716639	−	0.697444i	$-0.245680\pi$
$569$	34.1890	1.43328	0.716639	+	0.697444i	$0.245680\pi$
$570$	−183.014	−7.66562
$571$	−23.1638	−0.969374	−0.484687	−	0.874688i	$-0.661066\pi$
$571$	−23.1638	−0.969374	−0.484687	+	0.874688i	$0.661066\pi$
$572$	−10.5366	−0.440558
$573$	7.70754	0.321987
$574$	12.6411	0.527630
$575$	10.7865	0.449828
$576$	62.3274	2.59697
$577$	31.9355	1.32949	0.664746	−	0.747069i	$-0.268540\pi$
$577$	31.9355	1.32949	0.664746	+	0.747069i	$0.268540\pi$
$578$	−73.9491	−3.07588
$579$	−19.0693	−0.792491
$580$	16.1837	0.671993
$581$	−26.7886	−1.11138
$582$	−93.8691	−3.89100
$583$	−5.41378	−0.224216
$584$	−127.256	−5.26590
$585$	−30.1330	−1.24585
$586$	−60.2345	−2.48827
$587$	−38.5765	−1.59222	−0.796112	−	0.605150i	$-0.793113\pi$
$587$	−38.5765	−1.59222	−0.796112	+	0.605150i	$0.793113\pi$
$588$	−52.8267	−2.17854
$589$	0.140568	0.00579201
$590$	18.9229	0.779044
$591$	−38.0843	−1.56658
$592$	−67.8221	−2.78747
$593$	27.0716	1.11170	0.555848	−	0.831284i	$-0.312394\pi$
$593$	27.0716	1.11170	0.555848	+	0.831284i	$0.312394\pi$
$594$	−2.91599	−0.119645
$595$	−82.4668	−3.38081
$596$	−121.165	−4.96310
$597$	61.3513	2.51094
$598$	−7.61407	−0.311362
$599$	26.7828	1.09432	0.547158	−	0.837029i	$-0.315710\pi$
$599$	26.7828	1.09432	0.547158	+	0.837029i	$0.315710\pi$
$600$	188.927	7.71290
$601$	−18.8769	−0.770006	−0.385003	−	0.922915i	$-0.625800\pi$
$601$	−18.8769	−0.770006	−0.385003	+	0.922915i	$0.625800\pi$
$602$	−57.4939	−2.34327
$603$	−46.2108	−1.88185
$604$	−85.8006	−3.49118
$605$	38.0002	1.54493
$606$	−95.9188	−3.89644
$607$	33.6515	1.36587	0.682936	−	0.730478i	$-0.260703\pi$
$607$	33.6515	1.36587	0.682936	+	0.730478i	$0.260703\pi$
$608$	−114.435	−4.64093
$609$	7.15332	0.289867
$610$	−75.1633	−3.04327
$611$	−27.0659	−1.09497
$612$	119.978	4.84981
$613$	−22.7438	−0.918614	−0.459307	−	0.888278i	$-0.651902\pi$
$613$	−22.7438	−0.918614	−0.459307	+	0.888278i	$0.651902\pi$
$614$	−40.6838	−1.64186
$615$	−13.4742	−0.543331
$616$	24.6037	0.991310
$617$	21.7548	0.875817	0.437909	−	0.899020i	$-0.355719\pi$
$617$	21.7548	0.875817	0.437909	+	0.899020i	$0.355719\pi$
$618$	45.8370	1.84383
$619$	41.6671	1.67474	0.837372	−	0.546634i	$-0.184091\pi$
$619$	41.6671	1.67474	0.837372	+	0.546634i	$0.184091\pi$
$620$	−0.371931	−0.0149371
$621$	−1.51770	−0.0609033
$622$	35.2662	1.41405
$623$	11.5604	0.463159
$624$	−72.3607	−2.89675
$625$	8.55719	0.342287
$626$	−20.0476	−0.801263
$627$	16.2060	0.647206
$628$	−98.8272	−3.94363
$629$	−37.0996	−1.47926
$630$	115.048	4.58361
$631$	2.40203	0.0956233	0.0478116	−	0.998856i	$-0.484775\pi$
$631$	2.40203	0.0956233	0.0478116	+	0.998856i	$0.484775\pi$
$632$	81.2750	3.23294
$633$	13.3892	0.532175
$634$	−19.6480	−0.780320
$635$	−28.6137	−1.13550
$636$	−80.6953	−3.19978
$637$	9.36792	0.371170
$638$	−1.98969	−0.0787728
$639$	50.4162	1.99443
$640$	60.0147	2.37229
$641$	−34.6910	−1.37021	−0.685106	−	0.728443i	$-0.740244\pi$
$641$	−34.6910	−1.37021	−0.685106	+	0.728443i	$0.740244\pi$
$642$	−19.1109	−0.754248
$643$	0.822980	0.0324551	0.0162276	−	0.999868i	$-0.494834\pi$
$643$	0.822980	0.0324551	0.0162276	+	0.999868i	$0.494834\pi$
$644$	20.9380	0.825073
$645$	61.2826	2.41300
$646$	−129.221	−5.08411
$647$	18.6329	0.732537	0.366268	−	0.930509i	$-0.380635\pi$
$647$	18.6329	0.732537	0.366268	+	0.930509i	$0.380635\pi$
$648$	61.4965	2.41581
$649$	−1.67564	−0.0657745
$650$	−54.7795	−2.14863
$651$	−0.164396	−0.00644318
$652$	−9.87510	−0.386739
$653$	−0.661912	−0.0259026	−0.0129513	−	0.999916i	$-0.504123\pi$
$653$	−0.661912	−0.0259026	−0.0129513	+	0.999916i	$0.504123\pi$
$654$	−9.20051	−0.359768
$655$	72.0281	2.81437
$656$	−17.3920	−0.679045
$657$	52.6925	2.05573
$658$	103.337	4.02851
$659$	−24.7573	−0.964408	−0.482204	−	0.876059i	$-0.660164\pi$
$659$	−24.7573	−0.964408	−0.482204	+	0.876059i	$0.660164\pi$
$660$	−42.8797	−1.66909
$661$	49.6201	1.93000	0.965000	−	0.262250i	$-0.0844645\pi$
$661$	49.6201	1.93000	0.965000	+	0.262250i	$0.0844645\pi$
$662$	83.1160	3.23040
$663$	−39.5823	−1.53725
$664$	67.9270	2.63608
$665$	−89.2467	−3.46084
$666$	51.7568	2.00554
$667$	−1.03559	−0.0400981
$668$	−84.3779	−3.26468
$669$	−19.9996	−0.773230
$670$	−131.689	−5.08759
$671$	6.65576	0.256943
$672$	133.832	5.16269
$673$	−4.54017	−0.175011	−0.0875053	−	0.996164i	$-0.527889\pi$
$673$	−4.54017	−0.175011	−0.0875053	+	0.996164i	$0.527889\pi$
$674$	25.4554	0.980505
$675$	−10.9191	−0.420278
$676$	−39.0897	−1.50345
$677$	−49.9657	−1.92034	−0.960169	−	0.279418i	$-0.909858\pi$
$677$	−49.9657	−1.92034	−0.960169	+	0.279418i	$0.909858\pi$
$678$	13.9786	0.536844
$679$	−45.7752	−1.75669
$680$	209.108	8.01893
$681$	−27.7279	−1.06254
$682$	0.0457267	0.00175097
$683$	−10.1191	−0.387197	−0.193598	−	0.981081i	$-0.562016\pi$
$683$	−10.1191	−0.387197	−0.193598	+	0.981081i	$0.562016\pi$
$684$	129.842	4.96462
$685$	−44.1481	−1.68681
$686$	26.3888	1.00753
$687$	−70.8711	−2.70390
$688$	79.1018	3.01573
$689$	14.3099	0.545165
$690$	−30.9861	−1.17962
$691$	−38.5561	−1.46674	−0.733372	−	0.679828i	$-0.762055\pi$
$691$	−38.5561	−1.46674	−0.733372	+	0.679828i	$0.762055\pi$
$692$	48.7984	1.85504
$693$	−10.1875	−0.386993
$694$	−39.8902	−1.51421
$695$	12.6845	0.481152
$696$	−18.1384	−0.687534
$697$	−9.51368	−0.360356
$698$	57.5825	2.17953
$699$	25.8443	0.977522
$700$	150.639	5.69361
$701$	−0.516132	−0.0194940	−0.00974701	−	0.999952i	$-0.503103\pi$
$701$	−0.516132	−0.0194940	−0.00974701	+	0.999952i	$0.503103\pi$
$702$	7.70769	0.290908
$703$	−40.1497	−1.51427
$704$	−15.7281	−0.592776
$705$	−110.147	−4.14838
$706$	1.03596	0.0389890
$707$	−46.7748	−1.75915
$708$	−24.9763	−0.938667
$709$	−22.2088	−0.834068	−0.417034	−	0.908891i	$-0.636930\pi$
$709$	−22.2088	−0.834068	−0.417034	+	0.908891i	$0.636930\pi$
$710$	143.673	5.39196
$711$	−33.6532	−1.26209
$712$	−29.3134	−1.09857
$713$	0.0237996	0.000891302 0
$714$	151.125	5.65570
$715$	7.60397	0.284372
$716$	64.9441	2.42708
$717$	−27.4803	−1.02627
$718$	51.1679	1.90957
$719$	28.1080	1.04825	0.524125	−	0.851641i	$-0.324392\pi$
$719$	28.1080	1.04825	0.524125	+	0.851641i	$0.324392\pi$
$720$	−158.286	−5.89897
$721$	22.3524	0.832446
$722$	−89.0419	−3.31379
$723$	−4.16697	−0.154971
$724$	−89.0440	−3.30929
$725$	−7.45054	−0.276706
$726$	−69.6373	−2.58448
$727$	14.1905	0.526296	0.263148	−	0.964756i	$-0.415239\pi$
$727$	14.1905	0.526296	0.263148	+	0.964756i	$0.415239\pi$
$728$	−65.0335	−2.41030
$729$	−34.9343	−1.29386
$730$	150.160	5.55767
$731$	43.2698	1.60039
$732$	99.2079	3.66683
$733$	−16.7802	−0.619792	−0.309896	−	0.950770i	$-0.600294\pi$
$733$	−16.7802	−0.619792	−0.309896	+	0.950770i	$0.600294\pi$
$734$	−21.3460	−0.787894
$735$	38.1236	1.40621
$736$	−19.3749	−0.714169
$737$	11.6611	0.429544
$738$	13.2723	0.488561
$739$	28.0258	1.03095	0.515473	−	0.856906i	$-0.327616\pi$
$739$	28.0258	1.03095	0.515473	+	0.856906i	$0.327616\pi$
$740$	106.232	3.90518
$741$	−42.8365	−1.57364
$742$	−54.6352	−2.00572
$743$	32.3602	1.18718	0.593591	−	0.804767i	$-0.297710\pi$
$743$	32.3602	1.18718	0.593591	+	0.804767i	$0.297710\pi$
$744$	0.416853	0.0152826
$745$	87.4411	3.20360
$746$	19.7572	0.723362
$747$	−28.1263	−1.02909
$748$	−30.2760	−1.10700
$749$	−9.31943	−0.340525
$750$	−96.3989	−3.51999
$751$	9.48669	0.346174	0.173087	−	0.984907i	$-0.444626\pi$
$751$	9.48669	0.346174	0.173087	+	0.984907i	$0.444626\pi$
$752$	−142.175	−5.18457
$753$	54.5387	1.98750
$754$	5.25925	0.191531
$755$	61.9199	2.25350
$756$	−21.1955	−0.770871
$757$	−34.2934	−1.24642	−0.623208	−	0.782056i	$-0.714171\pi$
$757$	−34.2934	−1.24642	−0.623208	+	0.782056i	$0.714171\pi$
$758$	1.17130	0.0425434
$759$	2.74384	0.0995952
$760$	226.300	8.20875
$761$	−13.2899	−0.481760	−0.240880	−	0.970555i	$-0.577436\pi$
$761$	−13.2899	−0.481760	−0.240880	+	0.970555i	$0.577436\pi$
$762$	52.4361	1.89956
$763$	−4.48662	−0.162427
$764$	−15.5830	−0.563773
$765$	−86.5846	−3.13047
$766$	18.0709	0.652927
$767$	4.42912	0.159926
$768$	−18.9240	−0.682861
$769$	−29.9966	−1.08171	−0.540853	−	0.841117i	$-0.681899\pi$
$769$	−29.9966	−1.08171	−0.540853	+	0.841117i	$0.681899\pi$
$770$	−29.0319	−1.04624
$771$	34.5431	1.24404
$772$	38.5539	1.38759
$773$	−36.2091	−1.30235	−0.651176	−	0.758927i	$-0.725724\pi$
$773$	−36.2091	−1.30235	−0.651176	+	0.758927i	$0.725724\pi$
$774$	−60.3647	−2.16976
$775$	0.171227	0.00615064
$776$	116.071	4.16669
$777$	46.9555	1.68452
$778$	43.5693	1.56204
$779$	−10.2958	−0.368887
$780$	113.341	4.05828
$781$	−12.7224	−0.455242
$782$	−21.8783	−0.782367
$783$	1.04832	0.0374639
$784$	49.2088	1.75746
$785$	71.3208	2.54555
$786$	−131.995	−4.70811
$787$	−16.3071	−0.581285	−0.290643	−	0.956832i	$-0.593869\pi$
$787$	−16.3071	−0.581285	−0.290643	+	0.956832i	$0.593869\pi$
$788$	76.9982	2.74295
$789$	37.9260	1.35020
$790$	−95.9030	−3.41208
$791$	6.81665	0.242372
$792$	25.8322	0.917906
$793$	−17.5928	−0.624739
$794$	87.7253	3.11325
$795$	58.2356	2.06540
$796$	−124.039	−4.39645
$797$	1.92850	0.0683109	0.0341554	−	0.999417i	$-0.489126\pi$
$797$	1.92850	0.0683109	0.0341554	+	0.999417i	$0.489126\pi$
$798$	163.549	5.78958
$799$	−77.7714	−2.75135
$800$	−139.393	−4.92829
$801$	12.1377	0.428864
$802$	35.3644	1.24876
$803$	−13.2968	−0.469233
$804$	173.816	6.13002
$805$	−15.1104	−0.532570
$806$	−0.120867	−0.00425736
$807$	−74.5272	−2.62348
$808$	118.605	4.17251
$809$	−28.2978	−0.994899	−0.497450	−	0.867493i	$-0.665730\pi$
$809$	−28.2978	−0.994899	−0.497450	+	0.867493i	$0.665730\pi$
$810$	−72.5648	−2.54967
$811$	46.2353	1.62354	0.811770	−	0.583977i	$-0.198504\pi$
$811$	46.2353	1.62354	0.811770	+	0.583977i	$0.198504\pi$
$812$	−14.4625	−0.507533
$813$	−33.5304	−1.17596
$814$	−13.0607	−0.457776
$815$	7.12658	0.249633
$816$	−207.922	−7.27872
$817$	46.8271	1.63827
$818$	18.1619	0.635016
$819$	26.9282	0.940947
$820$	27.2419	0.951327
$821$	−0.905589	−0.0316053	−0.0158026	−	0.999875i	$-0.505030\pi$
$821$	−0.905589	−0.0316053	−0.0158026	+	0.999875i	$0.505030\pi$
$822$	80.9036	2.82184
$823$	−17.9616	−0.626100	−0.313050	−	0.949737i	$-0.601351\pi$
$823$	−17.9616	−0.626100	−0.313050	+	0.949737i	$0.601351\pi$
$824$	−56.6781	−1.97448
$825$	19.7406	0.687280
$826$	−16.9103	−0.588385
$827$	−1.49155	−0.0518664	−0.0259332	−	0.999664i	$-0.508256\pi$
$827$	−1.49155	−0.0518664	−0.0259332	+	0.999664i	$0.508256\pi$
$828$	21.9835	0.763979
$829$	−32.7731	−1.13826	−0.569129	−	0.822249i	$-0.692719\pi$
$829$	−32.7731	−1.13826	−0.569129	+	0.822249i	$0.692719\pi$
$830$	−80.1526	−2.78214
$831$	65.1109	2.25867
$832$	41.5733	1.44129
$833$	26.9179	0.932649
$834$	−23.2451	−0.804911
$835$	60.8932	2.10730
$836$	−32.7651	−1.13320
$837$	−0.0240923	−0.000832750 0
$838$	24.3186	0.840072
$839$	−56.2084	−1.94053	−0.970265	−	0.242044i	$-0.922182\pi$
$839$	−56.2084	−1.94053	−0.970265	+	0.242044i	$0.922182\pi$
$840$	−264.660	−9.13163
$841$	−28.2847	−0.975334
$842$	51.3571	1.76988
$843$	−57.1647	−1.96886
$844$	−27.0702	−0.931794
$845$	28.2099	0.970452
$846$	108.497	3.73021
$847$	−33.9586	−1.16683
$848$	75.1687	2.58130
$849$	−38.5421	−1.32276
$850$	−157.404	−5.39891
$851$	−6.79775	−0.233024
$852$	−189.634	−6.49675
$853$	33.4792	1.14631	0.573154	−	0.819448i	$-0.305720\pi$
$853$	33.4792	1.14631	0.573154	+	0.819448i	$0.305720\pi$
$854$	67.1692	2.29848
$855$	−93.7030	−3.20458
$856$	23.6309	0.807689
$857$	36.2240	1.23739	0.618695	−	0.785631i	$-0.287662\pi$
$857$	36.2240	1.23739	0.618695	+	0.785631i	$0.287662\pi$
$858$	−13.9347	−0.475722
$859$	13.8388	0.472175	0.236088	−	0.971732i	$-0.424135\pi$
$859$	13.8388	0.472175	0.236088	+	0.971732i	$0.424135\pi$
$860$	−123.900	−4.22497
$861$	12.0411	0.410359
$862$	−37.4201	−1.27453
$863$	−14.5678	−0.495895	−0.247948	−	0.968773i	$-0.579756\pi$
$863$	−14.5678	−0.495895	−0.247948	+	0.968773i	$0.579756\pi$
$864$	19.6131	0.667253
$865$	−35.2165	−1.19740
$866$	6.54402	0.222375
$867$	−70.4389	−2.39223
$868$	0.332373	0.0112815
$869$	8.49228	0.288081
$870$	21.4030	0.725629
$871$	−30.8233	−1.04441
$872$	11.3766	0.385259
$873$	−48.0609	−1.62662
$874$	−23.6770	−0.800888
$875$	−47.0089	−1.58919
$876$	−198.196	−6.69642
$877$	7.39785	0.249808	0.124904	−	0.992169i	$-0.460138\pi$
$877$	7.39785	0.249808	0.124904	+	0.992169i	$0.460138\pi$
$878$	5.02375	0.169543
$879$	−57.3754	−1.93522
$880$	39.9429	1.34648
$881$	−16.5774	−0.558505	−0.279253	−	0.960218i	$-0.590087\pi$
$881$	−16.5774	−0.558505	−0.279253	+	0.960218i	$0.590087\pi$
$882$	−37.5525	−1.26446
$883$	−47.7452	−1.60676	−0.803378	−	0.595470i	$-0.796966\pi$
$883$	−47.7452	−1.60676	−0.803378	+	0.595470i	$0.796966\pi$
$884$	80.0269	2.69159
$885$	18.0247	0.605894
$886$	49.3069	1.65650
$887$	−34.3245	−1.15250	−0.576252	−	0.817272i	$-0.695485\pi$
$887$	−34.3245	−1.15250	−0.576252	+	0.817272i	$0.695485\pi$
$888$	−119.063	−3.99550
$889$	25.5704	0.857604
$890$	34.5893	1.15943
$891$	6.42566	0.215268
$892$	40.4349	1.35386
$893$	−84.1653	−2.81648
$894$	−160.240	−5.35924
$895$	−46.8683	−1.56664
$896$	−53.6317	−1.79171
$897$	−7.25265	−0.242159
$898$	−34.8488	−1.16292
$899$	−0.0164391	−0.000548274 0
$900$	158.161	5.27202
$901$	41.1183	1.36985
$902$	−3.34923	−0.111517
$903$	−54.7648	−1.82246
$904$	−17.2847	−0.574881
$905$	64.2605	2.13609
$906$	−113.471	−3.76983
$907$	23.2325	0.771424	0.385712	−	0.922619i	$-0.373956\pi$
$907$	23.2325	0.771424	0.385712	+	0.922619i	$0.373956\pi$
$908$	56.0600	1.86041
$909$	−49.1103	−1.62889
$910$	76.7384	2.54385
$911$	−22.3361	−0.740029	−0.370014	−	0.929026i	$-0.620647\pi$
$911$	−22.3361	−0.740029	−0.370014	+	0.929026i	$0.620647\pi$
$912$	−225.016	−7.45103
$913$	7.09757	0.234895
$914$	−33.1357	−1.09603
$915$	−71.5955	−2.36688
$916$	143.286	4.73431
$917$	−64.3674	−2.12560
$918$	22.1473	0.730971
$919$	−38.6109	−1.27366	−0.636829	−	0.771005i	$-0.719754\pi$
$919$	−38.6109	−1.27366	−0.636829	+	0.771005i	$0.719754\pi$
$920$	38.3148	1.26320
$921$	−38.7526	−1.27694
$922$	50.5060	1.66333
$923$	33.6283	1.10689
$924$	38.3191	1.26061
$925$	−48.9065	−1.60804
$926$	−1.86850	−0.0614027
$927$	23.4685	0.770806
$928$	13.3828	0.439312
$929$	3.25287	0.106723	0.0533615	−	0.998575i	$-0.483006\pi$
$929$	3.25287	0.106723	0.0533615	+	0.998575i	$0.483006\pi$
$930$	−0.491879	−0.0161293
$931$	29.1309	0.954727
$932$	−52.2517	−1.71156
$933$	33.5922	1.09976
$934$	97.7202	3.19750
$935$	21.8493	0.714549
$936$	−68.2808	−2.23183
$937$	15.0156	0.490538	0.245269	−	0.969455i	$-0.421124\pi$
$937$	15.0156	0.490538	0.245269	+	0.969455i	$0.421124\pi$
$938$	117.683	3.84248
$939$	−19.0960	−0.623174
$940$	222.694	7.26347
$941$	50.7815	1.65543	0.827714	−	0.561150i	$-0.189641\pi$
$941$	50.7815	1.65543	0.827714	+	0.561150i	$0.189641\pi$
$942$	−130.699	−4.25840
$943$	−1.74319	−0.0567660
$944$	23.2657	0.757235
$945$	15.2962	0.497584
$946$	15.2328	0.495262
$947$	−10.1768	−0.330701	−0.165351	−	0.986235i	$-0.552876\pi$
$947$	−10.1768	−0.330701	−0.165351	+	0.986235i	$0.552876\pi$
$948$	126.582	4.11120
$949$	35.1466	1.14091
$950$	−170.345	−5.52672
$951$	−18.7153	−0.606886
$952$	−186.868	−6.05642
$953$	−29.5438	−0.957017	−0.478508	−	0.878083i	$-0.658822\pi$
$953$	−29.5438	−0.957017	−0.478508	+	0.878083i	$0.658822\pi$
$954$	−57.3632	−1.85720
$955$	11.2458	0.363906
$956$	55.5592	1.79691
$957$	−1.89525	−0.0612647
$958$	12.7122	0.410714
$959$	39.4526	1.27399
$960$	169.186	5.46046
$961$	−30.9996	−0.999988
$962$	34.5225	1.11305
$963$	−9.78477	−0.315310
$964$	8.42472	0.271342
$965$	−27.8233	−0.895663
$966$	27.6905	0.890928
$967$	−47.5446	−1.52893	−0.764465	−	0.644665i	$-0.776997\pi$
$967$	−47.5446	−1.52893	−0.764465	+	0.644665i	$0.776997\pi$
$968$	86.1076	2.76760
$969$	−123.087	−3.95412
$970$	−136.961	−4.39756
$971$	−19.9728	−0.640957	−0.320479	−	0.947256i	$-0.603844\pi$
$971$	−19.9728	−0.640957	−0.320479	+	0.947256i	$0.603844\pi$
$972$	114.926	3.68624
$973$	−11.3355	−0.363398
$974$	1.33877	0.0428970
$975$	−52.1793	−1.67107
$976$	−92.4134	−2.95808
$977$	50.1335	1.60391	0.801956	−	0.597383i	$-0.203793\pi$
$977$	50.1335	1.60391	0.801956	+	0.597383i	$0.203793\pi$
$978$	−13.0598	−0.417607
$979$	−3.06290	−0.0978908
$980$	−77.0777	−2.46216
$981$	−4.71065	−0.150400
$982$	61.8048	1.97227
$983$	−33.4836	−1.06796	−0.533980	−	0.845497i	$-0.679304\pi$
$983$	−33.4836	−1.06796	−0.533980	+	0.845497i	$0.679304\pi$
$984$	−30.5321	−0.973329
$985$	−55.5674	−1.77053
$986$	15.1120	0.481264
$987$	98.4321	3.13313
$988$	86.6062	2.75531
$989$	7.92830	0.252105
$990$	−30.4815	−0.968766
$991$	−16.1771	−0.513883	−0.256942	−	0.966427i	$-0.582715\pi$
$991$	−16.1771	−0.513883	−0.256942	+	0.966427i	$0.582715\pi$
$992$	−0.307560	−0.00976505
$993$	79.1708	2.51241
$994$	−128.392	−4.07236
$995$	89.5155	2.83783
$996$	105.793	3.35219
$997$	−13.5234	−0.428292	−0.214146	−	0.976802i	$-0.568697\pi$
$997$	−13.5234	−0.428292	−0.214146	+	0.976802i	$0.568697\pi$
$998$	−39.3602	−1.24592
$999$	6.88133	0.217716

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.a.1.11	✓	309

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.a.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-2.67381 q^{2} -2.54689 q^{3} +5.14927 q^{4} -3.71609 q^{5} +6.80992 q^{6} +3.32085 q^{7} -8.42057 q^{8} +3.48667 q^{9} +O(q^{10})\)	\(q-2.67381 q^{2} -2.54689 q^{3} +5.14927 q^{4} -3.71609 q^{5} +6.80992 q^{6} +3.32085 q^{7} -8.42057 q^{8} +3.48667 q^{9} +9.93612 q^{10} -0.879850 q^{11} -13.1147 q^{12} +2.32566 q^{13} -8.87934 q^{14} +9.46448 q^{15} +12.2165 q^{16} +6.68257 q^{17} -9.32271 q^{18} +7.23197 q^{19} -19.1351 q^{20} -8.45786 q^{21} +2.35255 q^{22} +1.22445 q^{23} +21.4463 q^{24} +8.80929 q^{25} -6.21838 q^{26} -1.23950 q^{27} +17.1000 q^{28} -0.845759 q^{29} -25.3062 q^{30} +0.0194370 q^{31} -15.8234 q^{32} +2.24089 q^{33} -17.8679 q^{34} -12.3406 q^{35} +17.9538 q^{36} -5.55169 q^{37} -19.3369 q^{38} -5.92321 q^{39} +31.2915 q^{40} -1.42366 q^{41} +22.6147 q^{42} +6.47502 q^{43} -4.53059 q^{44} -12.9568 q^{45} -3.27394 q^{46} -11.6379 q^{47} -31.1141 q^{48} +4.02807 q^{49} -23.5544 q^{50} -17.0198 q^{51} +11.9755 q^{52} +6.15307 q^{53} +3.31419 q^{54} +3.26960 q^{55} -27.9635 q^{56} -18.4191 q^{57} +2.26140 q^{58} +1.90446 q^{59} +48.7352 q^{60} -7.56466 q^{61} -0.0519710 q^{62} +11.5787 q^{63} +17.8759 q^{64} -8.64235 q^{65} -5.99171 q^{66} -13.2536 q^{67} +34.4104 q^{68} -3.11853 q^{69} +32.9964 q^{70} +14.4597 q^{71} -29.3597 q^{72} +15.1125 q^{73} +14.8442 q^{74} -22.4363 q^{75} +37.2394 q^{76} -2.92185 q^{77} +15.8376 q^{78} -9.65196 q^{79} -45.3974 q^{80} -7.30314 q^{81} +3.80659 q^{82} -8.06679 q^{83} -43.5519 q^{84} -24.8330 q^{85} -17.3130 q^{86} +2.15406 q^{87} +7.40884 q^{88} +3.48116 q^{89} +34.6440 q^{90} +7.72318 q^{91} +6.30501 q^{92} -0.0495041 q^{93} +31.1177 q^{94} -26.8746 q^{95} +40.3006 q^{96} -13.7842 q^{97} -10.7703 q^{98} -3.06775 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) \) 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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