LMFDB - Embedded newform 8017.2.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8017,2,Mod(1,8017)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8017, 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("8017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8017.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:	$64.0160673005$
Analytic rank:	$1$
Dimension:	$327$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8017.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74759 q^{2} -3.21743 q^{3} +5.54926 q^{4} +2.43668 q^{5} +8.84019 q^{6} -3.59070 q^{7} -9.75191 q^{8} +7.35187 q^{9} +O(q^{10})$	\(q-2.74759 q^{2} -3.21743 q^{3} +5.54926 q^{4} +2.43668 q^{5} +8.84019 q^{6} -3.59070 q^{7} -9.75191 q^{8} +7.35187 q^{9} -6.69501 q^{10} +0.00627230 q^{11} -17.8544 q^{12} +1.52653 q^{13} +9.86576 q^{14} -7.83986 q^{15} +15.6957 q^{16} +3.55083 q^{17} -20.1999 q^{18} +2.66893 q^{19} +13.5218 q^{20} +11.5528 q^{21} -0.0172337 q^{22} +0.469460 q^{23} +31.3761 q^{24} +0.937427 q^{25} -4.19429 q^{26} -14.0019 q^{27} -19.9257 q^{28} +1.22055 q^{29} +21.5407 q^{30} -0.631805 q^{31} -23.6217 q^{32} -0.0201807 q^{33} -9.75622 q^{34} -8.74939 q^{35} +40.7974 q^{36} +4.51097 q^{37} -7.33314 q^{38} -4.91152 q^{39} -23.7623 q^{40} -7.66232 q^{41} -31.7424 q^{42} -3.67706 q^{43} +0.0348066 q^{44} +17.9142 q^{45} -1.28989 q^{46} -3.41187 q^{47} -50.5000 q^{48} +5.89309 q^{49} -2.57567 q^{50} -11.4245 q^{51} +8.47113 q^{52} +8.78712 q^{53} +38.4714 q^{54} +0.0152836 q^{55} +35.0161 q^{56} -8.58711 q^{57} -3.35358 q^{58} +6.54754 q^{59} -43.5054 q^{60} +5.26373 q^{61} +1.73594 q^{62} -26.3983 q^{63} +33.5112 q^{64} +3.71968 q^{65} +0.0554483 q^{66} +1.70734 q^{67} +19.7044 q^{68} -1.51046 q^{69} +24.0397 q^{70} +1.77921 q^{71} -71.6948 q^{72} -15.7465 q^{73} -12.3943 q^{74} -3.01611 q^{75} +14.8106 q^{76} -0.0225219 q^{77} +13.4948 q^{78} +7.06939 q^{79} +38.2456 q^{80} +22.9944 q^{81} +21.0529 q^{82} -17.5669 q^{83} +64.1096 q^{84} +8.65224 q^{85} +10.1031 q^{86} -3.92704 q^{87} -0.0611669 q^{88} +7.02628 q^{89} -49.2209 q^{90} -5.48132 q^{91} +2.60516 q^{92} +2.03279 q^{93} +9.37441 q^{94} +6.50335 q^{95} +76.0011 q^{96} +17.8751 q^{97} -16.1918 q^{98} +0.0461131 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) $ 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * 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 $

$2$	−2.74759	−1.94284	−0.971420	−	0.237367i	$-0.923716\pi$
$2$	−2.74759	−1.94284	−0.971420	+	0.237367i	$0.923716\pi$
$3$	−3.21743	−1.85759	−0.928793	−	0.370600i	$-0.879152\pi$
$3$	−3.21743	−1.85759	−0.928793	+	0.370600i	$0.879152\pi$
$4$	5.54926	2.77463
$5$	2.43668	1.08972	0.544859	−	0.838528i	$-0.316583\pi$
$5$	2.43668	1.08972	0.544859	+	0.838528i	$0.316583\pi$
$6$	8.84019	3.60899
$7$	−3.59070	−1.35716	−0.678578	−	0.734529i	$-0.737403\pi$
$7$	−3.59070	−1.35716	−0.678578	+	0.734529i	$0.737403\pi$
$8$	−9.75191	−3.44782
$9$	7.35187	2.45062
$10$	−6.69501	−2.11715
$11$	0.00627230	0.00189117	0.000945584	−	1.00000i	$-0.499699\pi$
$11$	0.00627230	0.00189117	0.000945584		1.00000i	$0.499699\pi$
$12$	−17.8544	−5.15411
$13$	1.52653	0.423384	0.211692	−	0.977336i	$-0.432103\pi$
$13$	1.52653	0.423384	0.211692	+	0.977336i	$0.432103\pi$
$14$	9.86576	2.63674
$15$	−7.83986	−2.02424
$16$	15.6957	3.92394
$17$	3.55083	0.861202	0.430601	−	0.902542i	$-0.358302\pi$
$17$	3.55083	0.861202	0.430601	+	0.902542i	$0.358302\pi$
$18$	−20.1999	−4.76117
$19$	2.66893	0.612295	0.306148	−	0.951984i	$-0.400960\pi$
$19$	2.66893	0.612295	0.306148	+	0.951984i	$0.400960\pi$
$20$	13.5218	3.02356
$21$	11.5528	2.52103
$22$	−0.0172337	−0.00367424
$23$	0.469460	0.0978893	0.0489446	−	0.998801i	$-0.484414\pi$
$23$	0.469460	0.0978893	0.0489446	+	0.998801i	$0.484414\pi$
$24$	31.3761	6.40462
$25$	0.937427	0.187485
$26$	−4.19429	−0.822568
$27$	−14.0019	−2.69466
$28$	−19.9257	−3.76560
$29$	1.22055	0.226651	0.113325	−	0.993558i	$-0.463850\pi$
$29$	1.22055	0.226651	0.113325	+	0.993558i	$0.463850\pi$
$30$	21.5407	3.93278
$31$	−0.631805	−0.113475	−0.0567377	−	0.998389i	$-0.518070\pi$
$31$	−0.631805	−0.113475	−0.0567377	+	0.998389i	$0.518070\pi$
$32$	−23.6217	−4.17576
$33$	−0.0201807	−0.00351301
$34$	−9.75622	−1.67318
$35$	−8.74939	−1.47892
$36$	40.7974	6.79957
$37$	4.51097	0.741599	0.370800	−	0.928713i	$-0.379084\pi$
$37$	4.51097	0.741599	0.370800	+	0.928713i	$0.379084\pi$
$38$	−7.33314	−1.18959
$39$	−4.91152	−0.786473
$40$	−23.7623	−3.75715
$41$	−7.66232	−1.19665	−0.598327	−	0.801252i	$-0.704168\pi$
$41$	−7.66232	−1.19665	−0.598327	+	0.801252i	$0.704168\pi$
$42$	−31.7424	−4.89796
$43$	−3.67706	−0.560747	−0.280373	−	0.959891i	$-0.590458\pi$
$43$	−3.67706	−0.560747	−0.280373	+	0.959891i	$0.590458\pi$
$44$	0.0348066	0.00524729
$45$	17.9142	2.67049
$46$	−1.28989	−0.190183
$47$	−3.41187	−0.497672	−0.248836	−	0.968546i	$-0.580048\pi$
$47$	−3.41187	−0.497672	−0.248836	+	0.968546i	$0.580048\pi$
$48$	−50.5000	−7.28904
$49$	5.89309	0.841870
$50$	−2.57567	−0.364254
$51$	−11.4245	−1.59976
$52$	8.47113	1.17473
$53$	8.78712	1.20700	0.603502	−	0.797362i	$-0.293772\pi$
$53$	8.78712	1.20700	0.603502	+	0.797362i	$0.293772\pi$
$54$	38.4714	5.23529
$55$	0.0152836	0.00206084
$56$	35.0161	4.67923
$57$	−8.58711	−1.13739
$58$	−3.35358	−0.440346
$59$	6.54754	0.852417	0.426208	−	0.904625i	$-0.359849\pi$
$59$	6.54754	0.852417	0.426208	+	0.904625i	$0.359849\pi$
$60$	−43.5054	−5.61653
$61$	5.26373	0.673952	0.336976	−	0.941513i	$-0.390596\pi$
$61$	5.26373	0.673952	0.336976	+	0.941513i	$0.390596\pi$
$62$	1.73594	0.220465
$63$	−26.3983	−3.32588
$64$	33.5112	4.18890
$65$	3.71968	0.461370
$66$	0.0554483	0.00682521
$67$	1.70734	0.208584	0.104292	−	0.994547i	$-0.466742\pi$
$67$	1.70734	0.208584	0.104292	+	0.994547i	$0.466742\pi$
$68$	19.7044	2.38951
$69$	−1.51046	−0.181838
$70$	24.0397	2.87330
$71$	1.77921	0.211153	0.105577	−	0.994411i	$-0.466331\pi$
$71$	1.77921	0.211153	0.105577	+	0.994411i	$0.466331\pi$
$72$	−71.6948	−8.44931
$73$	−15.7465	−1.84299	−0.921497	−	0.388386i	$-0.873033\pi$
$73$	−15.7465	−1.84299	−0.921497	+	0.388386i	$0.873033\pi$
$74$	−12.3943	−1.44081
$75$	−3.01611	−0.348270
$76$	14.8106	1.69889
$77$	−0.0225219	−0.00256661
$78$	13.4948	1.52799
$79$	7.06939	0.795369	0.397684	−	0.917522i	$-0.369814\pi$
$79$	7.06939	0.795369	0.397684	+	0.917522i	$0.369814\pi$
$80$	38.2456	4.27598
$81$	22.9944	2.55493
$82$	21.0529	2.32491
$83$	−17.5669	−1.92822	−0.964108	−	0.265512i	$-0.914459\pi$
$83$	−17.5669	−1.92822	−0.964108	+	0.265512i	$0.914459\pi$
$84$	64.1096	6.99493
$85$	8.65224	0.938467
$86$	10.1031	1.08944
$87$	−3.92704	−0.421023
$88$	−0.0611669	−0.00652041
$89$	7.02628	0.744784	0.372392	−	0.928076i	$-0.378538\pi$
$89$	7.02628	0.744784	0.372392	+	0.928076i	$0.378538\pi$
$90$	−49.2209	−5.18833
$91$	−5.48132	−0.574598
$92$	2.60516	0.271606
$93$	2.03279	0.210790
$94$	9.37441	0.966897
$95$	6.50335	0.667229
$96$	76.0011	7.75683
$97$	17.8751	1.81495	0.907473	−	0.420110i	$-0.138009\pi$
$97$	17.8751	1.81495	0.907473	+	0.420110i	$0.138009\pi$
$98$	−16.1918	−1.63562
$99$	0.0461131	0.00463454
$100$	5.20202	0.520202
$101$	−9.30268	−0.925652	−0.462826	−	0.886449i	$-0.653164\pi$
$101$	−9.30268	−0.925652	−0.462826	+	0.886449i	$0.653164\pi$
$102$	31.3900	3.10807
$103$	−19.9995	−1.97061	−0.985304	−	0.170810i	$-0.945362\pi$
$103$	−19.9995	−1.97061	−0.985304	+	0.170810i	$0.945362\pi$
$104$	−14.8866	−1.45975
$105$	28.1506	2.74721
$106$	−24.1434	−2.34502
$107$	−9.52555	−0.920870	−0.460435	−	0.887694i	$-0.652306\pi$
$107$	−9.52555	−0.920870	−0.460435	+	0.887694i	$0.652306\pi$
$108$	−77.6999	−7.47667
$109$	−6.88443	−0.659409	−0.329704	−	0.944084i	$-0.606949\pi$
$109$	−6.88443	−0.659409	−0.329704	+	0.944084i	$0.606949\pi$
$110$	−0.0419931	−0.00400388
$111$	−14.5138	−1.37758
$112$	−56.3586	−5.32539
$113$	7.07154	0.665234	0.332617	−	0.943062i	$-0.392068\pi$
$113$	7.07154	0.665234	0.332617	+	0.943062i	$0.392068\pi$
$114$	23.5939	2.20977
$115$	1.14393	0.106672
$116$	6.77316	0.628872
$117$	11.2229	1.03756
$118$	−17.9900	−1.65611
$119$	−12.7499	−1.16878
$120$	76.4536	6.97923
$121$	−11.0000	−0.999996
$122$	−14.4626	−1.30938
$123$	24.6530	2.22289
$124$	−3.50605	−0.314852
$125$	−9.89921	−0.885412
$126$	72.5318	6.46165
$127$	1.14823	0.101889	0.0509445	−	0.998701i	$-0.483777\pi$
$127$	1.14823	0.101889	0.0509445	+	0.998701i	$0.483777\pi$
$128$	−44.8317	−3.96260
$129$	11.8307	1.04164
$130$	−10.2202	−0.896367
$131$	−7.80012	−0.681499	−0.340750	−	0.940154i	$-0.610681\pi$
$131$	−7.80012	−0.681499	−0.340750	+	0.940154i	$0.610681\pi$
$132$	−0.111988	−0.00974729
$133$	−9.58333	−0.830980
$134$	−4.69106	−0.405246
$135$	−34.1181	−2.93642
$136$	−34.6273	−2.96927
$137$	11.5077	0.983170	0.491585	−	0.870830i	$-0.336418\pi$
$137$	11.5077	0.983170	0.491585	+	0.870830i	$0.336418\pi$
$138$	4.15012	0.353282
$139$	−18.3960	−1.56033	−0.780164	−	0.625576i	$-0.784864\pi$
$139$	−18.3960	−1.56033	−0.780164	+	0.625576i	$0.784864\pi$
$140$	−48.5526	−4.10344
$141$	10.9774	0.924468
$142$	−4.88854	−0.410237
$143$	0.00957487	0.000800691 0
$144$	115.393	9.61609
$145$	2.97410	0.246985
$146$	43.2651	3.58064
$147$	−18.9606	−1.56385
$148$	25.0326	2.05766
$149$	−8.22549	−0.673858	−0.336929	−	0.941530i	$-0.609388\pi$
$149$	−8.22549	−0.673858	−0.336929	+	0.941530i	$0.609388\pi$
$150$	8.28703	0.676633
$151$	12.0344	0.979342	0.489671	−	0.871907i	$-0.337117\pi$
$151$	12.0344	0.979342	0.489671	+	0.871907i	$0.337117\pi$
$152$	−26.0272	−2.11108
$153$	26.1052	2.11048
$154$	0.0618810	0.00498651
$155$	−1.53951	−0.123656
$156$	−27.2553	−2.18217
$157$	11.9785	0.955987	0.477993	−	0.878363i	$-0.341364\pi$
$157$	11.9785	0.955987	0.477993	+	0.878363i	$0.341364\pi$
$158$	−19.4238	−1.54527
$159$	−28.2720	−2.24211
$160$	−57.5585	−4.55040
$161$	−1.68569	−0.132851
$162$	−63.1792	−4.96383
$163$	−3.40316	−0.266556	−0.133278	−	0.991079i	$-0.542550\pi$
$163$	−3.40316	−0.266556	−0.133278	+	0.991079i	$0.542550\pi$
$164$	−42.5202	−3.32027
$165$	−0.0491740	−0.00382819
$166$	48.2666	3.74621
$167$	3.17396	0.245608	0.122804	−	0.992431i	$-0.460811\pi$
$167$	3.17396	0.245608	0.122804	+	0.992431i	$0.460811\pi$
$168$	−112.662	−8.69206
$169$	−10.6697	−0.820746
$170$	−23.7728	−1.82329
$171$	19.6217	1.50051
$172$	−20.4050	−1.55586
$173$	−12.6036	−0.958232	−0.479116	−	0.877752i	$-0.659043\pi$
$173$	−12.6036	−0.958232	−0.479116	+	0.877752i	$0.659043\pi$
$174$	10.7899	0.817981
$175$	−3.36601	−0.254447
$176$	0.0984483	0.00742082
$177$	−21.0663	−1.58344
$178$	−19.3053	−1.44700
$179$	17.8740	1.33597	0.667984	−	0.744175i	$-0.267157\pi$
$179$	17.8740	1.33597	0.667984	+	0.744175i	$0.267157\pi$
$180$	99.4104	7.40961
$181$	−12.7178	−0.945303	−0.472652	−	0.881249i	$-0.656703\pi$
$181$	−12.7178	−0.945303	−0.472652	+	0.881249i	$0.656703\pi$
$182$	15.0604	1.11635
$183$	−16.9357	−1.25192
$184$	−4.57813	−0.337505
$185$	10.9918	0.808134
$186$	−5.58527	−0.409532
$187$	0.0222718	0.00162868
$188$	−18.9333	−1.38085
$189$	50.2764	3.65707
$190$	−17.8685	−1.29632
$191$	−20.5726	−1.48858	−0.744290	−	0.667856i	$-0.767212\pi$
$191$	−20.5726	−1.48858	−0.744290	+	0.667856i	$0.767212\pi$
$192$	−107.820	−7.78124
$193$	4.78053	0.344110	0.172055	−	0.985087i	$-0.444959\pi$
$193$	4.78053	0.344110	0.172055	+	0.985087i	$0.444959\pi$
$194$	−49.1136	−3.52615
$195$	−11.9678	−0.857033
$196$	32.7023	2.33588
$197$	−8.68174	−0.618548	−0.309274	−	0.950973i	$-0.600086\pi$
$197$	−8.68174	−0.618548	−0.309274	+	0.950973i	$0.600086\pi$
$198$	−0.126700	−0.00900418
$199$	−2.91472	−0.206619	−0.103309	−	0.994649i	$-0.532943\pi$
$199$	−2.91472	−0.206619	−0.103309	+	0.994649i	$0.532943\pi$
$200$	−9.14170	−0.646416
$201$	−5.49324	−0.387463
$202$	25.5600	1.79839
$203$	−4.38263	−0.307600
$204$	−63.3977	−4.43873
$205$	−18.6706	−1.30401
$206$	54.9504	3.82858
$207$	3.45141	0.239890
$208$	23.9601	1.66133
$209$	0.0167403	0.00115795
$210$	−77.3462	−5.33740
$211$	21.9654	1.51216	0.756081	−	0.654478i	$-0.227111\pi$
$211$	21.9654	1.51216	0.756081	+	0.654478i	$0.227111\pi$
$212$	48.7620	3.34899
$213$	−5.72449	−0.392235
$214$	26.1723	1.78910
$215$	−8.95984	−0.611056
$216$	136.545	9.29069
$217$	2.26862	0.154004
$218$	18.9156	1.28113
$219$	50.6634	3.42352
$220$	0.0848126	0.00571807
$221$	5.42046	0.364619
$222$	39.8779	2.67643
$223$	6.42020	0.429929	0.214964	−	0.976622i	$-0.431036\pi$
$223$	6.42020	0.429929	0.214964	+	0.976622i	$0.431036\pi$
$224$	84.8182	5.66715
$225$	6.89184	0.459456
$226$	−19.4297	−1.29244
$227$	−20.6846	−1.37288	−0.686442	−	0.727185i	$-0.740828\pi$
$227$	−20.6846	−1.37288	−0.686442	+	0.727185i	$0.740828\pi$
$228$	−47.6521	−3.15584
$229$	−0.503337	−0.0332615	−0.0166307	−	0.999862i	$-0.505294\pi$
$229$	−0.503337	−0.0332615	−0.0166307	+	0.999862i	$0.505294\pi$
$230$	−3.14304	−0.207246
$231$	0.0724627	0.00476770
$232$	−11.9027	−0.781451
$233$	7.95571	0.521196	0.260598	−	0.965447i	$-0.416080\pi$
$233$	7.95571	0.521196	0.260598	+	0.965447i	$0.416080\pi$
$234$	−30.8359	−2.01581
$235$	−8.31364	−0.542322
$236$	36.3340	2.36514
$237$	−22.7453	−1.47747
$238$	35.0316	2.27076
$239$	−0.0232496	−0.00150389	−0.000751945	−	1.00000i	$-0.500239\pi$
$239$	−0.0232496	−0.00150389	−0.000751945		1.00000i	$0.500239\pi$
$240$	−123.052	−7.94300
$241$	2.70709	0.174379	0.0871894	−	0.996192i	$-0.472211\pi$
$241$	2.70709	0.174379	0.0871894	+	0.996192i	$0.472211\pi$
$242$	30.2234	1.94283
$243$	−31.9774	−2.05135
$244$	29.2098	1.86997
$245$	14.3596	0.917401
$246$	−67.7364	−4.31871
$247$	4.07422	0.259236
$248$	6.16130	0.391243
$249$	56.5202	3.58182
$250$	27.1990	1.72021
$251$	23.8495	1.50537	0.752683	−	0.658383i	$-0.228759\pi$
$251$	23.8495	1.50537	0.752683	+	0.658383i	$0.228759\pi$
$252$	−146.491	−9.22807
$253$	0.00294459	0.000185125 0
$254$	−3.15487	−0.197954
$255$	−27.8380	−1.74328
$256$	56.1569	3.50980
$257$	−1.10912	−0.0691852	−0.0345926	−	0.999401i	$-0.511013\pi$
$257$	−1.10912	−0.0691852	−0.0345926	+	0.999401i	$0.511013\pi$
$258$	−32.5059	−2.02373
$259$	−16.1975	−1.00647
$260$	20.6415	1.28013
$261$	8.97334	0.555436
$262$	21.4315	1.32404
$263$	−14.5260	−0.895713	−0.447857	−	0.894105i	$-0.647813\pi$
$263$	−14.5260	−0.895713	−0.447857	+	0.894105i	$0.647813\pi$
$264$	0.196800	0.0121122
$265$	21.4114	1.31529
$266$	26.3311	1.61446
$267$	−22.6066	−1.38350
$268$	9.47445	0.578744
$269$	−22.2167	−1.35458	−0.677289	−	0.735717i	$-0.736845\pi$
$269$	−22.2167	−1.35458	−0.677289	+	0.735717i	$0.736845\pi$
$270$	93.7425	5.70499
$271$	1.47015	0.0893055	0.0446528	−	0.999003i	$-0.485782\pi$
$271$	1.47015	0.0893055	0.0446528	+	0.999003i	$0.485782\pi$
$272$	55.7328	3.37930
$273$	17.6358	1.06737
$274$	−31.6185	−1.91014
$275$	0.00587982	0.000354566 0
$276$	−8.38191	−0.504532
$277$	12.5660	0.755015	0.377508	−	0.926006i	$-0.376781\pi$
$277$	12.5660	0.755015	0.377508	+	0.926006i	$0.376781\pi$
$278$	50.5446	3.03147
$279$	−4.64495	−0.278086
$280$	85.3232	5.09904
$281$	−32.5212	−1.94005	−0.970027	−	0.242997i	$-0.921869\pi$
$281$	−32.5212	−1.94005	−0.970027	+	0.242997i	$0.921869\pi$
$282$	−30.1615	−1.79609
$283$	16.4775	0.979486	0.489743	−	0.871867i	$-0.337091\pi$
$283$	16.4775	0.979486	0.489743	+	0.871867i	$0.337091\pi$
$284$	9.87329	0.585872
$285$	−20.9241	−1.23944
$286$	−0.0263078	−0.00155562
$287$	27.5131	1.62404
$288$	−173.663	−10.2332
$289$	−4.39164	−0.258332
$290$	−8.17161	−0.479853
$291$	−57.5121	−3.37142
$292$	−87.3816	−5.11362
$293$	7.77557	0.454254	0.227127	−	0.973865i	$-0.427067\pi$
$293$	7.77557	0.454254	0.227127	+	0.973865i	$0.427067\pi$
$294$	52.0960	3.03830
$295$	15.9543	0.928894
$296$	−43.9906	−2.55690
$297$	−0.0878238	−0.00509605
$298$	22.6003	1.30920
$299$	0.716647	0.0414448
$300$	−16.7372	−0.966320
$301$	13.2032	0.761021
$302$	−33.0655	−1.90271
$303$	29.9308	1.71948
$304$	41.8909	2.40261
$305$	12.8260	0.734417
$306$	−71.7264	−4.10033
$307$	26.3244	1.50241	0.751206	−	0.660068i	$-0.229472\pi$
$307$	26.3244	1.50241	0.751206	+	0.660068i	$0.229472\pi$
$308$	−0.124980	−0.00712139
$309$	64.3470	3.66057
$310$	4.22994	0.240244
$311$	10.7205	0.607902	0.303951	−	0.952688i	$-0.401694\pi$
$311$	10.7205	0.607902	0.303951	+	0.952688i	$0.401694\pi$
$312$	47.8967	2.71162
$313$	15.8036	0.893272	0.446636	−	0.894716i	$-0.352622\pi$
$313$	15.8036	0.893272	0.446636	+	0.894716i	$0.352622\pi$
$314$	−32.9120	−1.85733
$315$	−64.3244	−3.62427
$316$	39.2299	2.20685
$317$	−17.3831	−0.976331	−0.488166	−	0.872751i	$-0.662334\pi$
$317$	−17.3831	−0.976331	−0.488166	+	0.872751i	$0.662334\pi$
$318$	77.6798	4.35607
$319$	0.00765566	0.000428635 0
$320$	81.6562	4.56472
$321$	30.6478	1.71059
$322$	4.63158	0.258108
$323$	9.47692	0.527310
$324$	127.602	7.08899
$325$	1.43101	0.0793784
$326$	9.35049	0.517876
$327$	22.1502	1.22491
$328$	74.7222	4.12585
$329$	12.2510	0.675418
$330$	0.135110	0.00743756
$331$	11.4727	0.630595	0.315297	−	0.948993i	$-0.397896\pi$
$331$	11.4727	0.630595	0.315297	+	0.948993i	$0.397896\pi$
$332$	−97.4831	−5.35008
$333$	33.1641	1.81738
$334$	−8.72074	−0.477178
$335$	4.16024	0.227298
$336$	181.330	9.89236
$337$	30.7945	1.67748	0.838741	−	0.544531i	$-0.183292\pi$
$337$	30.7945	1.67748	0.838741	+	0.544531i	$0.183292\pi$
$338$	29.3160	1.59458
$339$	−22.7522	−1.23573
$340$	48.0135	2.60390
$341$	−0.00396287	−0.000214601 0
$342$	−53.9123	−2.91524
$343$	3.97457	0.214607
$344$	35.8584	1.93335
$345$	−3.68051	−0.198152
$346$	34.6295	1.86169
$347$	31.9256	1.71386	0.856928	−	0.515436i	$-0.172370\pi$
$347$	31.9256	1.71386	0.856928	+	0.515436i	$0.172370\pi$
$348$	−21.7922	−1.16818
$349$	−11.3632	−0.608258	−0.304129	−	0.952631i	$-0.598365\pi$
$349$	−11.3632	−0.608258	−0.304129	+	0.952631i	$0.598365\pi$
$350$	9.24843	0.494349
$351$	−21.3743	−1.14088
$352$	−0.148162	−0.00789707
$353$	−20.8455	−1.10949	−0.554746	−	0.832019i	$-0.687185\pi$
$353$	−20.8455	−1.10949	−0.554746	+	0.832019i	$0.687185\pi$
$354$	57.8815	3.07636
$355$	4.33537	0.230098
$356$	38.9906	2.06650
$357$	41.0220	2.17112
$358$	−49.1106	−2.59557
$359$	29.1600	1.53900	0.769502	−	0.638644i	$-0.220504\pi$
$359$	29.1600	1.53900	0.769502	+	0.638644i	$0.220504\pi$
$360$	−174.697	−9.20736
$361$	−11.8768	−0.625094
$362$	34.9432	1.83657
$363$	35.3916	1.85758
$364$	−30.4172	−1.59430
$365$	−38.3693	−2.00834
$366$	46.5324	2.43229
$367$	−0.527310	−0.0275254	−0.0137627	−	0.999905i	$-0.504381\pi$
$367$	−0.527310	−0.0275254	−0.0137627	+	0.999905i	$0.504381\pi$
$368$	7.36853	0.384111
$369$	−56.3324	−2.93255
$370$	−30.2010	−1.57008
$371$	−31.5519	−1.63809
$372$	11.2805	0.584865
$373$	−24.2143	−1.25377	−0.626884	−	0.779113i	$-0.715670\pi$
$373$	−24.2143	−1.25377	−0.626884	+	0.779113i	$0.715670\pi$
$374$	−0.0611939	−0.00316426
$375$	31.8500	1.64473
$376$	33.2722	1.71588
$377$	1.86321	0.0959604
$378$	−138.139	−7.10510
$379$	15.9116	0.817322	0.408661	−	0.912686i	$-0.365996\pi$
$379$	15.9116	0.817322	0.408661	+	0.912686i	$0.365996\pi$
$380$	36.0887	1.85131
$381$	−3.69436	−0.189268
$382$	56.5251	2.89207
$383$	33.5373	1.71367	0.856837	−	0.515588i	$-0.172426\pi$
$383$	33.5373	1.71367	0.856837	+	0.515588i	$0.172426\pi$
$384$	144.243	7.36087
$385$	−0.0548788	−0.00279688
$386$	−13.1349	−0.668550
$387$	−27.0333	−1.37418
$388$	99.1938	5.03580
$389$	−17.8116	−0.903082	−0.451541	−	0.892250i	$-0.649126\pi$
$389$	−17.8116	−0.903082	−0.451541	+	0.892250i	$0.649126\pi$
$390$	32.8827	1.66508
$391$	1.66697	0.0843024
$392$	−57.4689	−2.90262
$393$	25.0963	1.26594
$394$	23.8539	1.20174
$395$	17.2259	0.866728
$396$	0.255894	0.0128591
$397$	−0.938654	−0.0471097	−0.0235548	−	0.999723i	$-0.507498\pi$
$397$	−0.938654	−0.0471097	−0.0235548	+	0.999723i	$0.507498\pi$
$398$	8.00846	0.401428
$399$	30.8337	1.54362
$400$	14.7136	0.735680
$401$	1.42194	0.0710082	0.0355041	−	0.999370i	$-0.488696\pi$
$401$	1.42194	0.0710082	0.0355041	+	0.999370i	$0.488696\pi$
$402$	15.0932	0.752780
$403$	−0.964471	−0.0480437
$404$	−51.6230	−2.56834
$405$	56.0301	2.78416
$406$	12.0417	0.597618
$407$	0.0282942	0.00140249
$408$	111.411	5.51567
$409$	28.4455	1.40654	0.703269	−	0.710924i	$-0.251723\pi$
$409$	28.4455	1.40654	0.703269	+	0.710924i	$0.251723\pi$
$410$	51.2993	2.53349
$411$	−37.0253	−1.82632
$412$	−110.982	−5.46771
$413$	−23.5102	−1.15686
$414$	−9.48307	−0.466067
$415$	−42.8049	−2.10121
$416$	−36.0593	−1.76795
$417$	59.1878	2.89844
$418$	−0.0459956	−0.00224972
$419$	−30.5402	−1.49199	−0.745993	−	0.665954i	$-0.768025\pi$
$419$	−30.5402	−1.49199	−0.745993	+	0.665954i	$0.768025\pi$
$420$	156.215	7.62250
$421$	−14.8713	−0.724784	−0.362392	−	0.932026i	$-0.618040\pi$
$421$	−14.8713	−0.724784	−0.362392	+	0.932026i	$0.618040\pi$
$422$	−60.3520	−2.93789
$423$	−25.0836	−1.21961
$424$	−85.6912	−4.16153
$425$	3.32864	0.161463
$426$	15.7286	0.762051
$427$	−18.9004	−0.914657
$428$	−52.8597	−2.55507
$429$	−0.0308065	−0.00148735
$430$	24.6180	1.18718
$431$	24.3583	1.17330	0.586649	−	0.809841i	$-0.300447\pi$
$431$	24.3583	1.17330	0.586649	+	0.809841i	$0.300447\pi$
$432$	−219.769	−10.5737
$433$	25.1413	1.20821	0.604106	−	0.796904i	$-0.293530\pi$
$433$	25.1413	1.20821	0.604106	+	0.796904i	$0.293530\pi$
$434$	−6.23324	−0.299205
$435$	−9.56896	−0.458797
$436$	−38.2035	−1.82961
$437$	1.25296	0.0599371
$438$	−139.202	−6.65135
$439$	−35.6986	−1.70380	−0.851900	−	0.523705i	$-0.824549\pi$
$439$	−35.6986	−1.70380	−0.851900	+	0.523705i	$0.824549\pi$
$440$	−0.149044	−0.00710541
$441$	43.3252	2.06311
$442$	−14.8932	−0.708397
$443$	−28.1097	−1.33553	−0.667767	−	0.744371i	$-0.732750\pi$
$443$	−28.1097	−1.33553	−0.667767	+	0.744371i	$0.732750\pi$
$444$	−80.5405	−3.82228
$445$	17.1208	0.811604
$446$	−17.6401	−0.835283
$447$	26.4649	1.25175
$448$	−120.328	−5.68499
$449$	28.8056	1.35942	0.679709	−	0.733482i	$-0.262106\pi$
$449$	28.8056	1.35942	0.679709	+	0.733482i	$0.262106\pi$
$450$	−18.9360	−0.892650
$451$	−0.0480603	−0.00226307
$452$	39.2418	1.84578
$453$	−38.7197	−1.81921
$454$	56.8327	2.66729
$455$	−13.3562	−0.626150
$456$	83.7407	3.92152
$457$	2.46783	0.115440	0.0577202	−	0.998333i	$-0.481617\pi$
$457$	2.46783	0.115440	0.0577202	+	0.998333i	$0.481617\pi$
$458$	1.38297	0.0646217
$459$	−49.7181	−2.32064
$460$	6.34794	0.295974
$461$	9.82167	0.457441	0.228720	−	0.973492i	$-0.426546\pi$
$461$	9.82167	0.457441	0.228720	+	0.973492i	$0.426546\pi$
$462$	−0.199098	−0.00926287
$463$	19.6523	0.913320	0.456660	−	0.889641i	$-0.349046\pi$
$463$	19.6523	0.913320	0.456660	+	0.889641i	$0.349046\pi$
$464$	19.1575	0.889363
$465$	4.95326	0.229702
$466$	−21.8590	−1.01260
$467$	−18.3094	−0.847256	−0.423628	−	0.905836i	$-0.639244\pi$
$467$	−18.3094	−0.847256	−0.423628	+	0.905836i	$0.639244\pi$
$468$	62.2787	2.87883
$469$	−6.13053	−0.283081
$470$	22.8425	1.05364
$471$	−38.5400	−1.77583
$472$	−63.8510	−2.93898
$473$	−0.0230636	−0.00106047
$474$	62.4948	2.87048
$475$	2.50193	0.114796
$476$	−70.7526	−3.24294
$477$	64.6018	2.95791
$478$	0.0638803	0.00292182
$479$	−1.99616	−0.0912071	−0.0456035	−	0.998960i	$-0.514521\pi$
$479$	−1.99616	−0.0912071	−0.0456035	+	0.998960i	$0.514521\pi$
$480$	185.191	8.45276
$481$	6.88615	0.313982
$482$	−7.43797	−0.338790
$483$	5.42359	0.246782
$484$	−61.0416	−2.77462
$485$	43.5561	1.97778
$486$	87.8607	3.98544
$487$	7.35487	0.333281	0.166641	−	0.986018i	$-0.446708\pi$
$487$	7.35487	0.333281	0.166641	+	0.986018i	$0.446708\pi$
$488$	−51.3314	−2.32366
$489$	10.9494	0.495151
$490$	−39.4543	−1.78236
$491$	−27.1475	−1.22515	−0.612574	−	0.790413i	$-0.709866\pi$
$491$	−27.1475	−1.22515	−0.612574	+	0.790413i	$0.709866\pi$
$492$	136.806	6.16768
$493$	4.33397	0.195192
$494$	−11.1943	−0.503655
$495$	0.112363	0.00505034
$496$	−9.91664	−0.445270
$497$	−6.38860	−0.286568
$498$	−155.294	−6.95891
$499$	28.2326	1.26387	0.631933	−	0.775023i	$-0.282262\pi$
$499$	28.2326	1.26387	0.631933	+	0.775023i	$0.282262\pi$
$500$	−54.9332	−2.45669
$501$	−10.2120	−0.456239
$502$	−65.5286	−2.92469
$503$	−23.8876	−1.06509	−0.532547	−	0.846400i	$-0.678765\pi$
$503$	−23.8876	−1.06509	−0.532547	+	0.846400i	$0.678765\pi$
$504$	257.434	11.4670
$505$	−22.6677	−1.00870
$506$	−0.00809054	−0.000359669 0
$507$	34.3290	1.52461
$508$	6.37183	0.282704
$509$	−20.4221	−0.905192	−0.452596	−	0.891716i	$-0.649502\pi$
$509$	−20.4221	−0.905192	−0.452596	+	0.891716i	$0.649502\pi$
$510$	76.4874	3.38692
$511$	56.5410	2.50123
$512$	−64.6327	−2.85639
$513$	−37.3700	−1.64993
$514$	3.04742	0.134416
$515$	−48.7324	−2.14741
$516$	65.6516	2.89015
$517$	−0.0214002	−0.000941181 0
$518$	44.5042	1.95540
$519$	40.5511	1.78000
$520$	−36.2740	−1.59072
$521$	−38.0587	−1.66738	−0.833691	−	0.552231i	$-0.813777\pi$
$521$	−38.0587	−1.66738	−0.833691	+	0.552231i	$0.813777\pi$
$522$	−24.6551	−1.07912
$523$	−33.8046	−1.47817	−0.739086	−	0.673611i	$-0.764742\pi$
$523$	−33.8046	−1.47817	−0.739086	+	0.673611i	$0.764742\pi$
$524$	−43.2848	−1.89091
$525$	10.8299	0.472656
$526$	39.9116	1.74023
$527$	−2.24343	−0.0977253
$528$	−0.316751	−0.0137848
$529$	−22.7796	−0.990418
$530$	−58.8298	−2.55541
$531$	48.1366	2.08895
$532$	−53.1803	−2.30566
$533$	−11.6968	−0.506644
$534$	62.1136	2.68792
$535$	−23.2107	−1.00349
$536$	−16.6498	−0.719162
$537$	−57.5085	−2.48168
$538$	61.0425	2.63173
$539$	0.0369632	0.00159212
$540$	−189.330	−8.14747
$541$	36.1880	1.55584	0.777922	−	0.628361i	$-0.216274\pi$
$541$	36.1880	1.55584	0.777922	+	0.628361i	$0.216274\pi$
$542$	−4.03938	−0.173506
$543$	40.9185	1.75598
$544$	−83.8764	−3.59617
$545$	−16.7752	−0.718570
$546$	−48.4559	−2.07372
$547$	−19.3870	−0.828929	−0.414464	−	0.910065i	$-0.636031\pi$
$547$	−19.3870	−0.828929	−0.414464	+	0.910065i	$0.636031\pi$
$548$	63.8592	2.72793
$549$	38.6983	1.65160
$550$	−0.0161553	−0.000688866 0
$551$	3.25757	0.138777
$552$	14.7298	0.626944
$553$	−25.3840	−1.07944
$554$	−34.5261	−1.46687
$555$	−35.3654	−1.50118
$556$	−102.084	−4.32933
$557$	−16.5480	−0.701160	−0.350580	−	0.936533i	$-0.614016\pi$
$557$	−16.5480	−0.701160	−0.350580	+	0.936533i	$0.614016\pi$
$558$	12.7624	0.540276
$559$	−5.61316	−0.237411
$560$	−137.328	−5.80317
$561$	−0.0716581	−0.00302541
$562$	89.3551	3.76922
$563$	−35.1825	−1.48277	−0.741383	−	0.671082i	$-0.765830\pi$
$563$	−35.1825	−1.48277	−0.741383	+	0.671082i	$0.765830\pi$
$564$	60.9167	2.56506
$565$	17.2311	0.724918
$566$	−45.2735	−1.90299
$567$	−82.5659	−3.46744
$568$	−17.3507	−0.728019
$569$	18.0967	0.758653	0.379327	−	0.925263i	$-0.376156\pi$
$569$	18.0967	0.758653	0.379327	+	0.925263i	$0.376156\pi$
$570$	57.4908	2.40802
$571$	29.4132	1.23090	0.615452	−	0.788174i	$-0.288973\pi$
$571$	29.4132	1.23090	0.615452	+	0.788174i	$0.288973\pi$
$572$	0.0531334	0.00222162
$573$	66.1909	2.76517
$574$	−75.5946	−3.15526
$575$	0.440085	0.0183528
$576$	246.370	10.2654
$577$	−3.91576	−0.163015	−0.0815076	−	0.996673i	$-0.525973\pi$
$577$	−3.91576	−0.163015	−0.0815076	+	0.996673i	$0.525973\pi$
$578$	12.0664	0.501897
$579$	−15.3810	−0.639213
$580$	16.5040	0.685293
$581$	63.0773	2.61689
$582$	158.020	6.55013
$583$	0.0551154	0.00228265
$584$	153.559	6.35431
$585$	27.3466	1.13064
$586$	−21.3641	−0.882542
$587$	15.4712	0.638567	0.319283	−	0.947659i	$-0.396558\pi$
$587$	15.4712	0.638567	0.319283	+	0.947659i	$0.396558\pi$
$588$	−105.217	−4.33909
$589$	−1.68624	−0.0694805
$590$	−43.8358	−1.80469
$591$	27.9329	1.14901
$592$	70.8031	2.90999
$593$	39.0076	1.60185	0.800925	−	0.598765i	$-0.204342\pi$
$593$	39.0076	1.60185	0.800925	+	0.598765i	$0.204342\pi$
$594$	0.241304	0.00990081
$595$	−31.0675	−1.27365
$596$	−45.6453	−1.86971
$597$	9.37791	0.383812
$598$	−1.96905	−0.0805206
$599$	−36.6182	−1.49618	−0.748090	−	0.663597i	$-0.769029\pi$
$599$	−36.6182	−1.49618	−0.748090	+	0.663597i	$0.769029\pi$
$600$	29.4128	1.20077
$601$	5.49462	0.224130	0.112065	−	0.993701i	$-0.464253\pi$
$601$	5.49462	0.224130	0.112065	+	0.993701i	$0.464253\pi$
$602$	−36.2770	−1.47854
$603$	12.5521	0.511162
$604$	66.7818	2.71731
$605$	−26.8034	−1.08971
$606$	−82.2375	−3.34067
$607$	30.4775	1.23704	0.618522	−	0.785768i	$-0.287732\pi$
$607$	30.4775	1.23704	0.618522	+	0.785768i	$0.287732\pi$
$608$	−63.0446	−2.55680
$609$	14.1008	0.571394
$610$	−35.2407	−1.42686
$611$	−5.20833	−0.210706
$612$	144.865	5.85580
$613$	26.7971	1.08233	0.541163	−	0.840918i	$-0.317984\pi$
$613$	26.7971	1.08233	0.541163	+	0.840918i	$0.317984\pi$
$614$	−72.3287	−2.91895
$615$	60.0716	2.42232
$616$	0.219632	0.00884921
$617$	−9.42177	−0.379306	−0.189653	−	0.981851i	$-0.560736\pi$
$617$	−9.42177	−0.379306	−0.189653	+	0.981851i	$0.560736\pi$
$618$	−176.799	−7.11191
$619$	31.8463	1.28001	0.640005	−	0.768371i	$-0.278932\pi$
$619$	31.8463	1.28001	0.640005	+	0.768371i	$0.278932\pi$
$620$	−8.54313	−0.343100
$621$	−6.57331	−0.263778
$622$	−29.4555	−1.18106
$623$	−25.2292	−1.01079
$624$	−77.0899	−3.08607
$625$	−28.8084	−1.15233
$626$	−43.4218	−1.73549
$627$	−0.0538609	−0.00215100
$628$	66.4717	2.65251
$629$	16.0177	0.638667
$630$	176.737	7.04137
$631$	6.45383	0.256923	0.128461	−	0.991715i	$-0.458996\pi$
$631$	6.45383	0.256923	0.128461	+	0.991715i	$0.458996\pi$
$632$	−68.9401	−2.74229
$633$	−70.6723	−2.80897
$634$	47.7616	1.89686
$635$	2.79788	0.111030
$636$	−156.888	−6.22103
$637$	8.99601	0.356435
$638$	−0.0210346	−0.000832769 0
$639$	13.0805	0.517457
$640$	−109.241	−4.31812
$641$	−0.599241	−0.0236686	−0.0118343	−	0.999930i	$-0.503767\pi$
$641$	−0.599241	−0.0236686	−0.0118343	+	0.999930i	$0.503767\pi$
$642$	−84.2076	−3.32341
$643$	2.83246	0.111701	0.0558506	−	0.998439i	$-0.482213\pi$
$643$	2.83246	0.111701	0.0558506	+	0.998439i	$0.482213\pi$
$644$	−9.35432	−0.368612
$645$	28.8277	1.13509
$646$	−26.0387	−1.02448
$647$	5.87849	0.231107	0.115554	−	0.993301i	$-0.463136\pi$
$647$	5.87849	0.231107	0.115554	+	0.993301i	$0.463136\pi$
$648$	−224.239	−8.80895
$649$	0.0410681	0.00161206
$650$	−3.93184	−0.154219
$651$	−7.29913	−0.286075
$652$	−18.8850	−0.739594
$653$	3.69020	0.144409	0.0722044	−	0.997390i	$-0.476997\pi$
$653$	3.69020	0.144409	0.0722044	+	0.997390i	$0.476997\pi$
$654$	−60.8597	−2.37980
$655$	−19.0064	−0.742642
$656$	−120.266	−4.69559
$657$	−115.767	−4.51648
$658$	−33.6607	−1.31223
$659$	18.0963	0.704931	0.352466	−	0.935825i	$-0.385343\pi$
$659$	18.0963	0.704931	0.352466	+	0.935825i	$0.385343\pi$
$660$	−0.272879	−0.0106218
$661$	38.3172	1.49036	0.745182	−	0.666861i	$-0.232362\pi$
$661$	38.3172	1.49036	0.745182	+	0.666861i	$0.232362\pi$
$662$	−31.5222	−1.22514
$663$	−17.4399	−0.677312
$664$	171.311	6.64814
$665$	−23.3515	−0.905534
$666$	−91.1214	−3.53088
$667$	0.573001	0.0221867
$668$	17.6131	0.681472
$669$	−20.6566	−0.798629
$670$	−11.4306	−0.441604
$671$	0.0330157	0.00127456
$672$	−272.897	−10.5272
$673$	17.5716	0.677336	0.338668	−	0.940906i	$-0.390024\pi$
$673$	17.5716	0.677336	0.338668	+	0.940906i	$0.390024\pi$
$674$	−84.6106	−3.25908
$675$	−13.1257	−0.505209
$676$	−59.2089	−2.27726
$677$	14.7944	0.568596	0.284298	−	0.958736i	$-0.408240\pi$
$677$	14.7944	0.568596	0.284298	+	0.958736i	$0.408240\pi$
$678$	62.5137	2.40083
$679$	−64.1842	−2.46316
$680$	−84.3758	−3.23566
$681$	66.5512	2.55025
$682$	0.0108883	0.000416936 0
$683$	−33.1043	−1.26670	−0.633350	−	0.773865i	$-0.718321\pi$
$683$	−33.1043	−1.26670	−0.633350	+	0.773865i	$0.718321\pi$
$684$	108.886	4.16335
$685$	28.0407	1.07138
$686$	−10.9205	−0.416946
$687$	1.61945	0.0617860
$688$	−57.7142	−2.20033
$689$	13.4138	0.511026
$690$	10.1125	0.384977
$691$	8.34497	0.317458	0.158729	−	0.987322i	$-0.449260\pi$
$691$	8.34497	0.317458	0.158729	+	0.987322i	$0.449260\pi$
$692$	−69.9405	−2.65874
$693$	−0.165578	−0.00628979
$694$	−87.7185	−3.32975
$695$	−44.8252	−1.70032
$696$	38.2962	1.45161
$697$	−27.2076	−1.03056
$698$	31.2214	1.18175
$699$	−25.5970	−0.968166
$700$	−18.6789	−0.705995
$701$	−34.1124	−1.28841	−0.644203	−	0.764855i	$-0.722811\pi$
$701$	−34.1124	−1.28841	−0.644203	+	0.764855i	$0.722811\pi$
$702$	58.7278	2.21654
$703$	12.0395	0.454078
$704$	0.210192	0.00792191
$705$	26.7486	1.00741
$706$	57.2749	2.15557
$707$	33.4031	1.25625
$708$	−116.902	−4.39345
$709$	−17.9641	−0.674655	−0.337328	−	0.941387i	$-0.609523\pi$
$709$	−17.9641	−0.674655	−0.337328	+	0.941387i	$0.609523\pi$
$710$	−11.9118	−0.447043
$711$	51.9733	1.94915
$712$	−68.5196	−2.56788
$713$	−0.296607	−0.0111080
$714$	−112.712	−4.21813
$715$	0.0233309	0.000872528 0
$716$	99.1877	3.70682
$717$	0.0748039	0.00279360
$718$	−80.1197	−2.99004
$719$	29.4144	1.09697	0.548485	−	0.836160i	$-0.315205\pi$
$719$	29.4144	1.09697	0.548485	+	0.836160i	$0.315205\pi$
$720$	281.176	10.4788
$721$	71.8121	2.67442
$722$	32.6326	1.21446
$723$	−8.70987	−0.323923
$724$	−70.5741	−2.62286
$725$	1.14418	0.0424937
$726$	−97.2417	−3.60898
$727$	−40.3343	−1.49592	−0.747958	−	0.663746i	$-0.768965\pi$
$727$	−40.3343	−1.49592	−0.747958	+	0.663746i	$0.768965\pi$
$728$	53.4533	1.98111
$729$	33.9018	1.25562
$730$	105.423	3.90189
$731$	−13.0566	−0.482916
$732$	−93.9805	−3.47362
$733$	28.8816	1.06677	0.533383	−	0.845874i	$-0.320920\pi$
$733$	28.8816	1.06677	0.533383	+	0.845874i	$0.320920\pi$
$734$	1.44883	0.0534774
$735$	−46.2010	−1.70415
$736$	−11.0894	−0.408762
$737$	0.0107089	0.000394468 0
$738$	154.778	5.69747
$739$	−6.79253	−0.249867	−0.124934	−	0.992165i	$-0.539872\pi$
$739$	−6.79253	−0.249867	−0.124934	+	0.992165i	$0.539872\pi$
$740$	60.9964	2.24227
$741$	−13.1085	−0.481554
$742$	86.6916	3.18255
$743$	8.01089	0.293891	0.146946	−	0.989145i	$-0.453056\pi$
$743$	8.01089	0.293891	0.146946	+	0.989145i	$0.453056\pi$
$744$	−19.8236	−0.726767
$745$	−20.0429	−0.734315
$746$	66.5309	2.43587
$747$	−129.149	−4.72533
$748$	0.123592	0.00451898
$749$	34.2033	1.24976
$750$	−87.5108	−3.19544
$751$	24.5696	0.896557	0.448279	−	0.893894i	$-0.352037\pi$
$751$	24.5696	0.896557	0.448279	+	0.893894i	$0.352037\pi$
$752$	−53.5518	−1.95283
$753$	−76.7341	−2.79635
$754$	−5.11935	−0.186436
$755$	29.3239	1.06721
$756$	278.997	10.1470
$757$	22.4220	0.814943	0.407472	−	0.913218i	$-0.366411\pi$
$757$	22.4220	0.814943	0.407472	+	0.913218i	$0.366411\pi$
$758$	−43.7185	−1.58793
$759$	−0.00947404	−0.000343886 0
$760$	−63.4200	−2.30049
$761$	−44.2086	−1.60256	−0.801280	−	0.598290i	$-0.795847\pi$
$761$	−44.2086	−1.60256	−0.801280	+	0.598290i	$0.795847\pi$
$762$	10.1506	0.367717
$763$	24.7199	0.894920
$764$	−114.163	−4.13026
$765$	63.6101	2.29983
$766$	−92.1467	−3.32939
$767$	9.99504	0.360900
$768$	−180.681	−6.51976
$769$	−14.6645	−0.528815	−0.264407	−	0.964411i	$-0.585176\pi$
$769$	−14.6645	−0.528815	−0.264407	+	0.964411i	$0.585176\pi$
$770$	0.150784	0.00543389
$771$	3.56853	0.128517
$772$	26.5284	0.954777
$773$	−52.9871	−1.90581	−0.952906	−	0.303266i	$-0.901923\pi$
$773$	−52.9871	−1.90581	−0.952906	+	0.303266i	$0.901923\pi$
$774$	74.2764	2.66981
$775$	−0.592271	−0.0212750
$776$	−174.317	−6.25761
$777$	52.1145	1.86960
$778$	48.9389	1.75454
$779$	−20.4502	−0.732705
$780$	−66.4125	−2.37795
$781$	0.0111597	0.000399327 0
$782$	−4.58016	−0.163786
$783$	−17.0900	−0.610746
$784$	92.4964	3.30344
$785$	29.1878	1.04176
$786$	−68.9545	−2.45953
$787$	−23.5878	−0.840814	−0.420407	−	0.907336i	$-0.638113\pi$
$787$	−23.5878	−0.840814	−0.420407	+	0.907336i	$0.638113\pi$
$788$	−48.1772	−1.71624
$789$	46.7365	1.66386
$790$	−47.3297	−1.68391
$791$	−25.3917	−0.902826
$792$	−0.449691	−0.0159791
$793$	8.03526	0.285341
$794$	2.57904	0.0915266
$795$	−68.8898	−2.44327
$796$	−16.1745	−0.573291
$797$	45.9796	1.62868	0.814341	−	0.580386i	$-0.197098\pi$
$797$	45.9796	1.62868	0.814341	+	0.580386i	$0.197098\pi$
$798$	−84.7184	−2.99900
$799$	−12.1149	−0.428596
$800$	−22.1436	−0.782894
$801$	51.6563	1.82519
$802$	−3.90691	−0.137958
$803$	−0.0987670	−0.00348541
$804$	−30.4834	−1.07507
$805$	−4.10749	−0.144770
$806$	2.64997	0.0933413
$807$	71.4808	2.51624
$808$	90.7189	3.19148
$809$	−6.09235	−0.214196	−0.107098	−	0.994248i	$-0.534156\pi$
$809$	−6.09235	−0.214196	−0.107098	+	0.994248i	$0.534156\pi$
$810$	−153.948	−5.40917
$811$	3.67873	0.129178	0.0645889	−	0.997912i	$-0.479426\pi$
$811$	3.67873	0.129178	0.0645889	+	0.997912i	$0.479426\pi$
$812$	−24.3203	−0.853476
$813$	−4.73012	−0.165893
$814$	−0.0777408	−0.00272481
$815$	−8.29242	−0.290471
$816$	−179.317	−6.27734
$817$	−9.81384	−0.343343
$818$	−78.1565	−2.73268
$819$	−40.2979	−1.40812
$820$	−103.608	−3.61816
$821$	−13.5094	−0.471481	−0.235740	−	0.971816i	$-0.575752\pi$
$821$	−13.5094	−0.471481	−0.235740	+	0.971816i	$0.575752\pi$
$822$	101.730	3.54825
$823$	−38.4535	−1.34041	−0.670203	−	0.742178i	$-0.733793\pi$
$823$	−38.4535	−1.34041	−0.670203	+	0.742178i	$0.733793\pi$
$824$	195.033	6.79430
$825$	−0.0189179	−0.000658637 0
$826$	64.5964	2.24760
$827$	−18.1663	−0.631703	−0.315851	−	0.948809i	$-0.602290\pi$
$827$	−18.1663	−0.631703	−0.315851	+	0.948809i	$0.602290\pi$
$828$	19.1528	0.665605
$829$	12.5580	0.436157	0.218079	−	0.975931i	$-0.430021\pi$
$829$	12.5580	0.436157	0.218079	+	0.975931i	$0.430021\pi$
$830$	117.610	4.08232
$831$	−40.4301	−1.40251
$832$	51.1560	1.77351
$833$	20.9253	0.725020
$834$	−162.624	−5.63121
$835$	7.73394	0.267644
$836$	0.0928965	0.00321289
$837$	8.84644	0.305778
$838$	83.9119	2.89869
$839$	4.62519	0.159679	0.0798396	−	0.996808i	$-0.474559\pi$
$839$	4.62519	0.159679	0.0798396	+	0.996808i	$0.474559\pi$
$840$	−274.522	−9.47190
$841$	−27.5103	−0.948629
$842$	40.8603	1.40814
$843$	104.635	3.60382
$844$	121.892	4.19569
$845$	−25.9987	−0.894381
$846$	68.9195	2.36950
$847$	39.4975	1.35715
$848$	137.920	4.73620
$849$	−53.0153	−1.81948
$850$	−9.14574	−0.313696
$851$	2.11772	0.0725946
$852$	−31.7667	−1.08831
$853$	−28.8462	−0.987677	−0.493838	−	0.869554i	$-0.664407\pi$
$853$	−28.8462	−0.987677	−0.493838	+	0.869554i	$0.664407\pi$
$854$	51.9307	1.77703
$855$	47.8118	1.63513
$856$	92.8923	3.17499
$857$	7.21454	0.246444	0.123222	−	0.992379i	$-0.460677\pi$
$857$	7.21454	0.246444	0.123222	+	0.992379i	$0.460677\pi$
$858$	0.0846437	0.00288969
$859$	−48.8349	−1.66623	−0.833113	−	0.553102i	$-0.813444\pi$
$859$	−48.8349	−1.66623	−0.833113	+	0.553102i	$0.813444\pi$
$860$	−49.7205	−1.69545
$861$	−88.5214	−3.01680
$862$	−66.9267	−2.27953
$863$	15.6511	0.532769	0.266384	−	0.963867i	$-0.414171\pi$
$863$	15.6511	0.532769	0.266384	+	0.963867i	$0.414171\pi$
$864$	330.747	11.2522
$865$	−30.7109	−1.04420
$866$	−69.0779	−2.34736
$867$	14.1298	0.479873
$868$	12.5891	0.427303
$869$	0.0443413	0.00150418
$870$	26.2916	0.891368
$871$	2.60631	0.0883114
$872$	67.1363	2.27352
$873$	131.416	4.44775
$874$	−3.44262	−0.116448
$875$	35.5450	1.20164
$876$	281.144	9.49899
$877$	−29.2191	−0.986658	−0.493329	−	0.869843i	$-0.664220\pi$
$877$	−29.2191	−0.986658	−0.493329	+	0.869843i	$0.664220\pi$
$878$	98.0851	3.31021
$879$	−25.0174	−0.843815
$880$	0.239887	0.00808660
$881$	−9.50457	−0.320217	−0.160109	−	0.987099i	$-0.551184\pi$
$881$	−9.50457	−0.320217	−0.160109	+	0.987099i	$0.551184\pi$
$882$	−119.040	−4.00829
$883$	−3.53496	−0.118961	−0.0594804	−	0.998229i	$-0.518944\pi$
$883$	−3.53496	−0.118961	−0.0594804	+	0.998229i	$0.518944\pi$
$884$	30.0795	1.01168
$885$	−51.3318	−1.72550
$886$	77.2340	2.59473
$887$	3.16422	0.106244	0.0531220	−	0.998588i	$-0.483083\pi$
$887$	3.16422	0.106244	0.0531220	+	0.998588i	$0.483083\pi$
$888$	141.537	4.74966
$889$	−4.12295	−0.138279
$890$	−47.0410	−1.57682
$891$	0.144228	0.00483181
$892$	35.6274	1.19289
$893$	−9.10604	−0.304722
$894$	−72.7148	−2.43195
$895$	43.5534	1.45583
$896$	160.977	5.37787
$897$	−2.30576	−0.0769872
$898$	−79.1459	−2.64113
$899$	−0.771150	−0.0257193
$900$	38.2446	1.27482
$901$	31.2015	1.03947
$902$	0.132050	0.00439679
$903$	−42.4804	−1.41366
$904$	−68.9610	−2.29361
$905$	−30.9891	−1.03011
$906$	106.386	3.53444
$907$	41.5872	1.38088	0.690440	−	0.723390i	$-0.257417\pi$
$907$	41.5872	1.38088	0.690440	+	0.723390i	$0.257417\pi$
$908$	−114.784	−3.80924
$909$	−68.3921	−2.26842
$910$	36.6975	1.21651
$911$	−0.731179	−0.0242251	−0.0121125	−	0.999927i	$-0.503856\pi$
$911$	−0.731179	−0.0242251	−0.0121125	+	0.999927i	$0.503856\pi$
$912$	−134.781	−4.46305
$913$	−0.110185	−0.00364658
$914$	−6.78060	−0.224282
$915$	−41.2669	−1.36424
$916$	−2.79315	−0.0922882
$917$	28.0078	0.924900
$918$	136.605	4.50864
$919$	−18.9494	−0.625083	−0.312542	−	0.949904i	$-0.601180\pi$
$919$	−18.9494	−0.625083	−0.312542	+	0.949904i	$0.601180\pi$
$920$	−11.1555	−0.367785
$921$	−84.6969	−2.79086
$922$	−26.9859	−0.888734
$923$	2.71602	0.0893990
$924$	0.402114	0.0132286
$925$	4.22871	0.139039
$926$	−53.9965	−1.77443
$927$	−147.034	−4.82922
$928$	−28.8315	−0.946439
$929$	−26.9373	−0.883783	−0.441891	−	0.897069i	$-0.645692\pi$
$929$	−26.9373	−0.883783	−0.441891	+	0.897069i	$0.645692\pi$
$930$	−13.6095	−0.446274
$931$	15.7283	0.515473
$932$	44.1483	1.44612
$933$	−34.4924	−1.12923
$934$	50.3066	1.64608
$935$	0.0542694	0.00177480
$936$	−109.445	−3.57731
$937$	32.0504	1.04704	0.523520	−	0.852013i	$-0.324619\pi$
$937$	32.0504	1.04704	0.523520	+	0.852013i	$0.324619\pi$
$938$	16.8442	0.549982
$939$	−50.8470	−1.65933
$940$	−46.1345	−1.50474
$941$	−3.03937	−0.0990805	−0.0495402	−	0.998772i	$-0.515776\pi$
$941$	−3.03937	−0.0990805	−0.0495402	+	0.998772i	$0.515776\pi$
$942$	105.892	3.45015
$943$	−3.59716	−0.117140
$944$	102.768	3.34483
$945$	122.508	3.98517
$946$	0.0633694	0.00206032
$947$	20.5256	0.666993	0.333497	−	0.942751i	$-0.391771\pi$
$947$	20.5256	0.666993	0.333497	+	0.942751i	$0.391771\pi$
$948$	−126.219	−4.09942
$949$	−24.0376	−0.780295
$950$	−6.87428	−0.223031
$951$	55.9289	1.81362
$952$	124.336	4.02976
$953$	−17.0511	−0.552338	−0.276169	−	0.961109i	$-0.589065\pi$
$953$	−17.0511	−0.552338	−0.276169	+	0.961109i	$0.589065\pi$
$954$	−177.499	−5.74675
$955$	−50.1289	−1.62213
$956$	−0.129018	−0.00417273
$957$	−0.0246316	−0.000796226 0
$958$	5.48464	0.177201
$959$	−41.3207	−1.33431
$960$	−262.723	−8.47935
$961$	−30.6008	−0.987123
$962$	−18.9203	−0.610016
$963$	−70.0306	−2.25670
$964$	15.0223	0.483836
$965$	11.6486	0.374983
$966$	−14.9018	−0.479458
$967$	−46.6201	−1.49920	−0.749600	−	0.661891i	$-0.769754\pi$
$967$	−46.6201	−1.49920	−0.749600	+	0.661891i	$0.769754\pi$
$968$	107.271	3.44781
$969$	−30.4913	−0.979523
$970$	−119.674	−3.84251
$971$	14.9229	0.478898	0.239449	−	0.970909i	$-0.423033\pi$
$971$	14.9229	0.478898	0.239449	+	0.970909i	$0.423033\pi$
$972$	−177.451	−5.69173
$973$	66.0544	2.11761
$974$	−20.2082	−0.647512
$975$	−4.60419	−0.147452
$976$	82.6181	2.64454
$977$	−33.3134	−1.06579	−0.532896	−	0.846181i	$-0.678896\pi$
$977$	−33.3134	−1.06579	−0.532896	+	0.846181i	$0.678896\pi$
$978$	−30.0846	−0.961998
$979$	0.0440709	0.00140851
$980$	79.6851	2.54545
$981$	−50.6134	−1.61596
$982$	74.5902	2.38027
$983$	−46.5660	−1.48523	−0.742613	−	0.669721i	$-0.766414\pi$
$983$	−46.5660	−1.48523	−0.742613	+	0.669721i	$0.766414\pi$
$984$	−240.414	−7.66411
$985$	−21.1546	−0.674043
$986$	−11.9080	−0.379227
$987$	−39.4167	−1.25465
$988$	22.6089	0.719284
$989$	−1.72624	−0.0548911
$990$	−0.308728	−0.00981201
$991$	−6.94040	−0.220469	−0.110234	−	0.993906i	$-0.535160\pi$
$991$	−6.94040	−0.220469	−0.110234	+	0.993906i	$0.535160\pi$
$992$	14.9243	0.473846
$993$	−36.9125	−1.17138
$994$	17.5533	0.556756
$995$	−7.10225	−0.225156
$996$	313.645	9.93823
$997$	−2.95079	−0.0934525	−0.0467262	−	0.998908i	$-0.514879\pi$
$997$	−2.95079	−0.0934525	−0.0467262	+	0.998908i	$0.514879\pi$
$998$	−77.5717	−2.45549
$999$	−63.1620	−1.99836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.a.1.7	✓	327

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.a.1.7	✓	327	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:	\( N \)	\(=\)	\( 8017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74759 q^{2} -3.21743 q^{3} +5.54926 q^{4} +2.43668 q^{5} +8.84019 q^{6} -3.59070 q^{7} -9.75191 q^{8} +7.35187 q^{9} +O(q^{10})\)	\(q-2.74759 q^{2} -3.21743 q^{3} +5.54926 q^{4} +2.43668 q^{5} +8.84019 q^{6} -3.59070 q^{7} -9.75191 q^{8} +7.35187 q^{9} -6.69501 q^{10} +0.00627230 q^{11} -17.8544 q^{12} +1.52653 q^{13} +9.86576 q^{14} -7.83986 q^{15} +15.6957 q^{16} +3.55083 q^{17} -20.1999 q^{18} +2.66893 q^{19} +13.5218 q^{20} +11.5528 q^{21} -0.0172337 q^{22} +0.469460 q^{23} +31.3761 q^{24} +0.937427 q^{25} -4.19429 q^{26} -14.0019 q^{27} -19.9257 q^{28} +1.22055 q^{29} +21.5407 q^{30} -0.631805 q^{31} -23.6217 q^{32} -0.0201807 q^{33} -9.75622 q^{34} -8.74939 q^{35} +40.7974 q^{36} +4.51097 q^{37} -7.33314 q^{38} -4.91152 q^{39} -23.7623 q^{40} -7.66232 q^{41} -31.7424 q^{42} -3.67706 q^{43} +0.0348066 q^{44} +17.9142 q^{45} -1.28989 q^{46} -3.41187 q^{47} -50.5000 q^{48} +5.89309 q^{49} -2.57567 q^{50} -11.4245 q^{51} +8.47113 q^{52} +8.78712 q^{53} +38.4714 q^{54} +0.0152836 q^{55} +35.0161 q^{56} -8.58711 q^{57} -3.35358 q^{58} +6.54754 q^{59} -43.5054 q^{60} +5.26373 q^{61} +1.73594 q^{62} -26.3983 q^{63} +33.5112 q^{64} +3.71968 q^{65} +0.0554483 q^{66} +1.70734 q^{67} +19.7044 q^{68} -1.51046 q^{69} +24.0397 q^{70} +1.77921 q^{71} -71.6948 q^{72} -15.7465 q^{73} -12.3943 q^{74} -3.01611 q^{75} +14.8106 q^{76} -0.0225219 q^{77} +13.4948 q^{78} +7.06939 q^{79} +38.2456 q^{80} +22.9944 q^{81} +21.0529 q^{82} -17.5669 q^{83} +64.1096 q^{84} +8.65224 q^{85} +10.1031 q^{86} -3.92704 q^{87} -0.0611669 q^{88} +7.02628 q^{89} -49.2209 q^{90} -5.48132 q^{91} +2.60516 q^{92} +2.03279 q^{93} +9.37441 q^{94} +6.50335 q^{95} +76.0011 q^{96} +17.8751 q^{97} -16.1918 q^{98} +0.0461131 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * q^99

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