LMFDB - Embedded newform 8017.2.a.b.1.13

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:	$0$
Dimension:	$340$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-2.61837 q^{2} -0.666893 q^{3} +4.85585 q^{4} -0.00270488 q^{5} +1.74617 q^{6} +0.156538 q^{7} -7.47768 q^{8} -2.55525 q^{9} +O(q^{10})$	\(q-2.61837 q^{2} -0.666893 q^{3} +4.85585 q^{4} -0.00270488 q^{5} +1.74617 q^{6} +0.156538 q^{7} -7.47768 q^{8} -2.55525 q^{9} +0.00708236 q^{10} -3.18382 q^{11} -3.23833 q^{12} +0.332975 q^{13} -0.409874 q^{14} +0.00180386 q^{15} +9.86761 q^{16} +2.24762 q^{17} +6.69060 q^{18} -6.62649 q^{19} -0.0131345 q^{20} -0.104394 q^{21} +8.33641 q^{22} -6.53995 q^{23} +4.98681 q^{24} -4.99999 q^{25} -0.871852 q^{26} +3.70476 q^{27} +0.760126 q^{28} +2.95982 q^{29} -0.00472318 q^{30} +1.98406 q^{31} -10.8817 q^{32} +2.12327 q^{33} -5.88509 q^{34} -0.000423416 q^{35} -12.4079 q^{36} -0.895876 q^{37} +17.3506 q^{38} -0.222059 q^{39} +0.0202262 q^{40} +7.29983 q^{41} +0.273342 q^{42} -7.46828 q^{43} -15.4602 q^{44} +0.00691164 q^{45} +17.1240 q^{46} +7.36014 q^{47} -6.58064 q^{48} -6.97550 q^{49} +13.0918 q^{50} -1.49892 q^{51} +1.61688 q^{52} -5.77759 q^{53} -9.70043 q^{54} +0.00861184 q^{55} -1.17054 q^{56} +4.41916 q^{57} -7.74989 q^{58} -8.96379 q^{59} +0.00875929 q^{60} -6.52824 q^{61} -5.19501 q^{62} -0.399994 q^{63} +8.75704 q^{64} -0.000900656 q^{65} -5.55949 q^{66} -11.3308 q^{67} +10.9141 q^{68} +4.36145 q^{69} +0.00110866 q^{70} +9.30763 q^{71} +19.1074 q^{72} -9.28947 q^{73} +2.34573 q^{74} +3.33446 q^{75} -32.1773 q^{76} -0.498389 q^{77} +0.581432 q^{78} +11.0450 q^{79} -0.0266907 q^{80} +5.19508 q^{81} -19.1137 q^{82} -10.3381 q^{83} -0.506922 q^{84} -0.00607952 q^{85} +19.5547 q^{86} -1.97388 q^{87} +23.8076 q^{88} +1.32719 q^{89} -0.0180972 q^{90} +0.0521232 q^{91} -31.7571 q^{92} -1.32316 q^{93} -19.2716 q^{94} +0.0179238 q^{95} +7.25692 q^{96} +3.59622 q^{97} +18.2644 q^{98} +8.13547 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) $ 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9} + 36 q^{10} + 70 q^{11} + 92 q^{12} + 45 q^{13} + 44 q^{14} + 71 q^{15} + 362 q^{16} + 162 q^{17} + 41 q^{18} + 49 q^{19} + 147 q^{20} + 41 q^{21} + 32 q^{22} + 244 q^{23} + 85 q^{24} + 355 q^{25} + 83 q^{26} + 155 q^{27} + 129 q^{28} + 91 q^{29} + 51 q^{30} + 65 q^{31} + 113 q^{32} + 73 q^{33} + 26 q^{34} + 200 q^{35} + 380 q^{36} + 28 q^{37} + 171 q^{38} + 117 q^{39} + 95 q^{40} + 115 q^{41} + 42 q^{42} + 98 q^{43} + 139 q^{44} + 127 q^{45} + 29 q^{46} + 312 q^{47} + 168 q^{48} + 365 q^{49} + 64 q^{50} + 72 q^{51} + 100 q^{52} + 154 q^{53} + 89 q^{54} + 161 q^{55} + 89 q^{56} + 82 q^{57} + 29 q^{58} + 149 q^{59} + 93 q^{60} + 70 q^{61} + 257 q^{62} + 376 q^{63} + 346 q^{64} + 125 q^{65} + 48 q^{66} + 65 q^{67} + 464 q^{68} + 58 q^{69} - 54 q^{70} + 216 q^{71} + 90 q^{72} + 93 q^{73} + 147 q^{74} + 162 q^{75} + 64 q^{76} + 190 q^{77} + 12 q^{78} + 139 q^{79} + 274 q^{80} + 376 q^{81} + 59 q^{82} + 402 q^{83} + 10 q^{84} + 32 q^{85} + 53 q^{86} + 364 q^{87} + 42 q^{88} + 114 q^{89} + 126 q^{90} + 43 q^{91} + 422 q^{92} + 47 q^{93} + 2 q^{94} + 347 q^{95} + 146 q^{96} + 47 q^{97} + 96 q^{98} + 129 q^{99}+O(q^{100}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9 + 36 * q^10 + 70 * q^11 + 92 * q^12 + 45 * q^13 + 44 * q^14 + 71 * q^15 + 362 * q^16 + 162 * q^17 + 41 * q^18 + 49 * q^19 + 147 * q^20 + 41 * q^21 + 32 * q^22 + 244 * q^23 + 85 * q^24 + 355 * q^25 + 83 * q^26 + 155 * q^27 + 129 * q^28 + 91 * q^29 + 51 * q^30 + 65 * q^31 + 113 * q^32 + 73 * q^33 + 26 * q^34 + 200 * q^35 + 380 * q^36 + 28 * q^37 + 171 * q^38 + 117 * q^39 + 95 * q^40 + 115 * q^41 + 42 * q^42 + 98 * q^43 + 139 * q^44 + 127 * q^45 + 29 * q^46 + 312 * q^47 + 168 * q^48 + 365 * q^49 + 64 * q^50 + 72 * q^51 + 100 * q^52 + 154 * q^53 + 89 * q^54 + 161 * q^55 + 89 * q^56 + 82 * q^57 + 29 * q^58 + 149 * q^59 + 93 * q^60 + 70 * q^61 + 257 * q^62 + 376 * q^63 + 346 * q^64 + 125 * q^65 + 48 * q^66 + 65 * q^67 + 464 * q^68 + 58 * q^69 - 54 * q^70 + 216 * q^71 + 90 * q^72 + 93 * q^73 + 147 * q^74 + 162 * q^75 + 64 * q^76 + 190 * q^77 + 12 * q^78 + 139 * q^79 + 274 * q^80 + 376 * q^81 + 59 * q^82 + 402 * q^83 + 10 * q^84 + 32 * q^85 + 53 * q^86 + 364 * q^87 + 42 * q^88 + 114 * q^89 + 126 * q^90 + 43 * q^91 + 422 * q^92 + 47 * q^93 + 2 * q^94 + 347 * q^95 + 146 * q^96 + 47 * q^97 + 96 * q^98 + 129 * 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 $

$2$	−2.61837	−1.85147	−0.925733	−	0.378178i	$-0.876551\pi$
$2$	−2.61837	−1.85147	−0.925733	+	0.378178i	$0.876551\pi$
$3$	−0.666893	−0.385031	−0.192515	−	0.981294i	$-0.561665\pi$
$3$	−0.666893	−0.385031	−0.192515	+	0.981294i	$0.561665\pi$
$4$	4.85585	2.42793
$5$	−0.00270488	−0.00120966	−0.000604829	−	1.00000i	$-0.500193\pi$
$5$	−0.00270488	−0.00120966	−0.000604829		1.00000i	$0.500193\pi$
$6$	1.74617	0.712872
$7$	0.156538	0.0591658	0.0295829	−	0.999562i	$-0.490582\pi$
$7$	0.156538	0.0591658	0.0295829	+	0.999562i	$0.490582\pi$
$8$	−7.47768	−2.64376
$9$	−2.55525	−0.851751
$10$	0.00708236	0.00223964
$11$	−3.18382	−0.959958	−0.479979	−	0.877280i	$-0.659356\pi$
$11$	−3.18382	−0.959958	−0.479979	+	0.877280i	$0.659356\pi$
$12$	−3.23833	−0.934827
$13$	0.332975	0.0923507	0.0461753	−	0.998933i	$-0.485297\pi$
$13$	0.332975	0.0923507	0.0461753	+	0.998933i	$0.485297\pi$
$14$	−0.409874	−0.109543
$15$	0.00180386	0.000465755 0
$16$	9.86761	2.46690
$17$	2.24762	0.545127	0.272563	−	0.962138i	$-0.412129\pi$
$17$	2.24762	0.545127	0.272563	+	0.962138i	$0.412129\pi$
$18$	6.69060	1.57699
$19$	−6.62649	−1.52022	−0.760111	−	0.649794i	$-0.774855\pi$
$19$	−6.62649	−1.52022	−0.760111	+	0.649794i	$0.774855\pi$
$20$	−0.0131345	−0.00293696
$21$	−0.104394	−0.0227807
$22$	8.33641	1.77733
$23$	−6.53995	−1.36367	−0.681837	−	0.731504i	$-0.738819\pi$
$23$	−6.53995	−1.36367	−0.681837	+	0.731504i	$0.738819\pi$
$24$	4.98681	1.01793
$25$	−4.99999	−0.999999
$26$	−0.871852	−0.170984
$27$	3.70476	0.712981
$28$	0.760126	0.143650
$29$	2.95982	0.549624	0.274812	−	0.961498i	$-0.411384\pi$
$29$	2.95982	0.549624	0.274812	+	0.961498i	$0.411384\pi$
$30$	−0.00472318	−0.000862330 0
$31$	1.98406	0.356348	0.178174	−	0.983999i	$-0.442981\pi$
$31$	1.98406	0.356348	0.178174	+	0.983999i	$0.442981\pi$
$32$	−10.8817	−1.92363
$33$	2.12327	0.369613
$34$	−5.88509	−1.00928
$35$	−0.000423416 0	−7.15703e−5 0
$36$	−12.4079	−2.06799
$37$	−0.895876	−0.147281	−0.0736405	−	0.997285i	$-0.523462\pi$
$37$	−0.895876	−0.147281	−0.0736405	+	0.997285i	$0.523462\pi$
$38$	17.3506	2.81464
$39$	−0.222059	−0.0355579
$40$	0.0202262	0.00319804
$41$	7.29983	1.14004	0.570021	−	0.821630i	$-0.306935\pi$
$41$	7.29983	1.14004	0.570021	+	0.821630i	$0.306935\pi$
$42$	0.273342	0.0421776
$43$	−7.46828	−1.13890	−0.569451	−	0.822025i	$-0.692844\pi$
$43$	−7.46828	−1.13890	−0.569451	+	0.822025i	$0.692844\pi$
$44$	−15.4602	−2.33071
$45$	0.00691164	0.00103033
$46$	17.1240	2.52480
$47$	7.36014	1.07359	0.536793	−	0.843714i	$-0.319636\pi$
$47$	7.36014	1.07359	0.536793	+	0.843714i	$0.319636\pi$
$48$	−6.58064	−0.949834
$49$	−6.97550	−0.996499
$50$	13.0918	1.85146
$51$	−1.49892	−0.209891
$52$	1.61688	0.224221
$53$	−5.77759	−0.793613	−0.396807	−	0.917902i	$-0.629882\pi$
$53$	−5.77759	−0.793613	−0.396807	+	0.917902i	$0.629882\pi$
$54$	−9.70043	−1.32006
$55$	0.00861184	0.00116122
$56$	−1.17054	−0.156420
$57$	4.41916	0.585332
$58$	−7.74989	−1.01761
$59$	−8.96379	−1.16699	−0.583493	−	0.812118i	$-0.698314\pi$
$59$	−8.96379	−1.16699	−0.583493	+	0.812118i	$0.698314\pi$
$60$	0.00875929	0.00113082
$61$	−6.52824	−0.835855	−0.417928	−	0.908480i	$-0.637243\pi$
$61$	−6.52824	−0.835855	−0.417928	+	0.908480i	$0.637243\pi$
$62$	−5.19501	−0.659767
$63$	−0.399994	−0.0503945
$64$	8.75704	1.09463
$65$	−0.000900656 0	−0.000111713 0
$66$	−5.55949	−0.684327
$67$	−11.3308	−1.38427	−0.692136	−	0.721767i	$-0.743330\pi$
$67$	−11.3308	−1.38427	−0.692136	+	0.721767i	$0.743330\pi$
$68$	10.9141	1.32353
$69$	4.36145	0.525057
$70$	0.00110866	0.000132510 0
$71$	9.30763	1.10461	0.552306	−	0.833641i	$-0.313748\pi$
$71$	9.30763	1.10461	0.552306	+	0.833641i	$0.313748\pi$
$72$	19.1074	2.25182
$73$	−9.28947	−1.08725	−0.543625	−	0.839328i	$-0.682949\pi$
$73$	−9.28947	−1.08725	−0.543625	+	0.839328i	$0.682949\pi$
$74$	2.34573	0.272686
$75$	3.33446	0.385030
$76$	−32.1773	−3.69099
$77$	−0.498389	−0.0567967
$78$	0.581432	0.0658342
$79$	11.0450	1.24266	0.621329	−	0.783550i	$-0.286593\pi$
$79$	11.0450	1.24266	0.621329	+	0.783550i	$0.286593\pi$
$80$	−0.0266907	−0.00298411
$81$	5.19508	0.577231
$82$	−19.1137	−2.11075
$83$	−10.3381	−1.13475	−0.567377	−	0.823458i	$-0.692042\pi$
$83$	−10.3381	−1.13475	−0.567377	+	0.823458i	$0.692042\pi$
$84$	−0.506922	−0.0553098
$85$	−0.00607952	−0.000659417 0
$86$	19.5547	2.10864
$87$	−1.97388	−0.211622
$88$	23.8076	2.53790
$89$	1.32719	0.140682	0.0703409	−	0.997523i	$-0.477591\pi$
$89$	1.32719	0.140682	0.0703409	+	0.997523i	$0.477591\pi$
$90$	−0.0180972	−0.00190762
$91$	0.0521232	0.00546400
$92$	−31.7571	−3.31090
$93$	−1.32316	−0.137205
$94$	−19.2716	−1.98771
$95$	0.0179238	0.00183895
$96$	7.25692	0.740656
$97$	3.59622	0.365141	0.182571	−	0.983193i	$-0.441558\pi$
$97$	3.59622	0.365141	0.182571	+	0.983193i	$0.441558\pi$
$98$	18.2644	1.84498
$99$	8.13547	0.817645
$100$	−24.2792	−2.42792
$101$	−4.21975	−0.419880	−0.209940	−	0.977714i	$-0.567327\pi$
$101$	−4.21975	−0.419880	−0.209940	+	0.977714i	$0.567327\pi$
$102$	3.92472	0.388606
$103$	−0.223634	−0.0220353	−0.0110177	−	0.999939i	$-0.503507\pi$
$103$	−0.223634	−0.0220353	−0.0110177	+	0.999939i	$0.503507\pi$
$104$	−2.48988	−0.244153
$105$	0.000282373 0	2.75568e−5 0
$106$	15.1279	1.46935
$107$	−0.184322	−0.0178190	−0.00890952	−	0.999960i	$-0.502836\pi$
$107$	−0.184322	−0.0178190	−0.00890952	+	0.999960i	$0.502836\pi$
$108$	17.9898	1.73107
$109$	−17.3045	−1.65747	−0.828735	−	0.559641i	$-0.810939\pi$
$109$	−17.3045	−1.65747	−0.828735	+	0.559641i	$0.810939\pi$
$110$	−0.0225490	−0.00214996
$111$	0.597453	0.0567078
$112$	1.54466	0.145956
$113$	−14.0268	−1.31953	−0.659765	−	0.751472i	$-0.729344\pi$
$113$	−14.0268	−1.31953	−0.659765	+	0.751472i	$0.729344\pi$
$114$	−11.5710	−1.08372
$115$	0.0176898	0.00164958
$116$	14.3724	1.33445
$117$	−0.850836	−0.0786598
$118$	23.4705	2.16063
$119$	0.351837	0.0322529
$120$	−0.0134887	−0.00123134
$121$	−0.863294	−0.0784812
$122$	17.0933	1.54756
$123$	−4.86821	−0.438952
$124$	9.63432	0.865188
$125$	0.0270487	0.00241931
$126$	1.04733	0.0933038
$127$	−8.58120	−0.761458	−0.380729	−	0.924687i	$-0.624327\pi$
$127$	−8.58120	−0.761458	−0.380729	+	0.924687i	$0.624327\pi$
$128$	−1.16579	−0.103042
$129$	4.98054	0.438512
$130$	0.00235825	0.000206832 0
$131$	8.73494	0.763176	0.381588	−	0.924333i	$-0.375377\pi$
$131$	8.73494	0.763176	0.381588	+	0.924333i	$0.375377\pi$
$132$	10.3103	0.897394
$133$	−1.03730	−0.0899451
$134$	29.6681	2.56293
$135$	−0.0100209	−0.000862463 0
$136$	−16.8070	−1.44118
$137$	10.8074	0.923336	0.461668	−	0.887053i	$-0.347251\pi$
$137$	10.8074	0.923336	0.461668	+	0.887053i	$0.347251\pi$
$138$	−11.4199	−0.972125
$139$	−19.3378	−1.64021	−0.820107	−	0.572211i	$-0.806086\pi$
$139$	−19.3378	−1.64021	−0.820107	+	0.572211i	$0.806086\pi$
$140$	−0.00205605	−0.000173768 0
$141$	−4.90842	−0.413364
$142$	−24.3708	−2.04515
$143$	−1.06013	−0.0886527
$144$	−25.2142	−2.10119
$145$	−0.00800593	−0.000664857 0
$146$	24.3233	2.01301
$147$	4.65191	0.383683
$148$	−4.35024	−0.357588
$149$	−13.8543	−1.13499	−0.567496	−	0.823376i	$-0.692088\pi$
$149$	−13.8543	−1.13499	−0.567496	+	0.823376i	$0.692088\pi$
$150$	−8.73084	−0.712871
$151$	−4.25140	−0.345974	−0.172987	−	0.984924i	$-0.555342\pi$
$151$	−4.25140	−0.345974	−0.172987	+	0.984924i	$0.555342\pi$
$152$	49.5508	4.01910
$153$	−5.74323	−0.464313
$154$	1.30497	0.105157
$155$	−0.00536665	−0.000431059 0
$156$	−1.07828	−0.0863319
$157$	11.3094	0.902587	0.451294	−	0.892375i	$-0.350963\pi$
$157$	11.3094	0.902587	0.451294	+	0.892375i	$0.350963\pi$
$158$	−28.9198	−2.30074
$159$	3.85304	0.305566
$160$	0.0294336	0.00232693
$161$	−1.02375	−0.0806829
$162$	−13.6026	−1.06872
$163$	16.2718	1.27451	0.637253	−	0.770655i	$-0.280071\pi$
$163$	16.2718	1.27451	0.637253	+	0.770655i	$0.280071\pi$
$164$	35.4469	2.76794
$165$	−0.00574317	−0.000447105 0
$166$	27.0690	2.10096
$167$	24.1113	1.86579	0.932895	−	0.360149i	$-0.117274\pi$
$167$	24.1113	1.86579	0.932895	+	0.360149i	$0.117274\pi$
$168$	0.780625	0.0602265
$169$	−12.8891	−0.991471
$170$	0.0159184	0.00122089
$171$	16.9324	1.29485
$172$	−36.2649	−2.76517
$173$	−16.6785	−1.26804	−0.634020	−	0.773317i	$-0.718596\pi$
$173$	−16.6785	−1.26804	−0.634020	+	0.773317i	$0.718596\pi$
$174$	5.16835	0.391811
$175$	−0.782689	−0.0591657
$176$	−31.4167	−2.36812
$177$	5.97789	0.449325
$178$	−3.47507	−0.260468
$179$	1.81750	0.135846	0.0679231	−	0.997691i	$-0.478363\pi$
$179$	1.81750	0.135846	0.0679231	+	0.997691i	$0.478363\pi$
$180$	0.0335619	0.00250156
$181$	−3.82943	−0.284639	−0.142320	−	0.989821i	$-0.545456\pi$
$181$	−3.82943	−0.284639	−0.142320	+	0.989821i	$0.545456\pi$
$182$	−0.136478	−0.0101164
$183$	4.35364	0.321830
$184$	48.9037	3.60523
$185$	0.00242323	0.000178160 0
$186$	3.46452	0.254031
$187$	−7.15600	−0.523299
$188$	35.7398	2.60659
$189$	0.579936	0.0421841
$190$	−0.0469312	−0.00340475
$191$	19.2228	1.39091	0.695455	−	0.718569i	$-0.255203\pi$
$191$	19.2228	1.39091	0.695455	+	0.718569i	$0.255203\pi$
$192$	−5.84001	−0.421466
$193$	7.88857	0.567832	0.283916	−	0.958849i	$-0.408366\pi$
$193$	7.88857	0.567832	0.283916	+	0.958849i	$0.408366\pi$
$194$	−9.41624	−0.676047
$195$	0.000600641 0	4.30128e−5 0
$196$	−33.8720	−2.41943
$197$	−22.7678	−1.62214	−0.811071	−	0.584948i	$-0.801115\pi$
$197$	−22.7678	−1.62214	−0.811071	+	0.584948i	$0.801115\pi$
$198$	−21.3017	−1.51384
$199$	−0.212793	−0.0150845	−0.00754226	−	0.999972i	$-0.502401\pi$
$199$	−0.212793	−0.0150845	−0.00754226	+	0.999972i	$0.502401\pi$
$200$	37.3883	2.64375
$201$	7.55640	0.532987
$202$	11.0488	0.777394
$203$	0.463324	0.0325189
$204$	−7.27853	−0.509599
$205$	−0.0197451	−0.00137906
$206$	0.585557	0.0407977
$207$	16.7112	1.16151
$208$	3.28567	0.227820
$209$	21.0976	1.45935
$210$	−0.000739357 0	−5.10205e−5 0
$211$	22.7472	1.56598	0.782991	−	0.622033i	$-0.213693\pi$
$211$	22.7472	1.56598	0.782991	+	0.622033i	$0.213693\pi$
$212$	−28.0551	−1.92684
$213$	−6.20719	−0.425310
$214$	0.482622	0.0329913
$215$	0.0202008	0.00137768
$216$	−27.7030	−1.88495
$217$	0.310581	0.0210836
$218$	45.3095	3.06875
$219$	6.19508	0.418625
$220$	0.0418178	0.00281936
$221$	0.748400	0.0503428
$222$	−1.56435	−0.104992
$223$	16.7225	1.11982	0.559909	−	0.828554i	$-0.310836\pi$
$223$	16.7225	1.11982	0.559909	+	0.828554i	$0.310836\pi$
$224$	−1.70340	−0.113813
$225$	12.7763	0.851750
$226$	36.7273	2.44307
$227$	25.4547	1.68949	0.844743	−	0.535172i	$-0.179753\pi$
$227$	25.4547	1.68949	0.844743	+	0.535172i	$0.179753\pi$
$228$	21.4588	1.42114
$229$	−27.9815	−1.84907	−0.924534	−	0.381100i	$-0.875545\pi$
$229$	−27.9815	−1.84907	−0.924534	+	0.381100i	$0.875545\pi$
$230$	−0.0463183	−0.00305414
$231$	0.332372	0.0218685
$232$	−22.1325	−1.45307
$233$	−14.0709	−0.921812	−0.460906	−	0.887449i	$-0.652476\pi$
$233$	−14.0709	−0.921812	−0.460906	+	0.887449i	$0.652476\pi$
$234$	2.22780	0.145636
$235$	−0.0199083	−0.00129867
$236$	−43.5268	−2.83336
$237$	−7.36582	−0.478461
$238$	−0.921240	−0.0597151
$239$	24.2197	1.56664	0.783321	−	0.621617i	$-0.213524\pi$
$239$	24.2197	1.56664	0.783321	+	0.621617i	$0.213524\pi$
$240$	0.0177998	0.00114897
$241$	5.65642	0.364362	0.182181	−	0.983265i	$-0.441684\pi$
$241$	5.65642	0.364362	0.182181	+	0.983265i	$0.441684\pi$
$242$	2.26042	0.145305
$243$	−14.5788	−0.935233
$244$	−31.7002	−2.02940
$245$	0.0188679	0.00120542
$246$	12.7468	0.812704
$247$	−2.20646	−0.140393
$248$	−14.8362	−0.942099
$249$	6.89441	0.436916
$250$	−0.0708236	−0.00447928
$251$	3.66534	0.231354	0.115677	−	0.993287i	$-0.463096\pi$
$251$	3.66534	0.231354	0.115677	+	0.993287i	$0.463096\pi$
$252$	−1.94231	−0.122354
$253$	20.8220	1.30907
$254$	22.4687	1.40981
$255$	0.00405439	0.000253896 0
$256$	−14.4616	−0.903851
$257$	15.5684	0.971129	0.485565	−	0.874201i	$-0.338614\pi$
$257$	15.5684	0.971129	0.485565	+	0.874201i	$0.338614\pi$
$258$	−13.0409	−0.811891
$259$	−0.140239	−0.00871400
$260$	−0.00437346	−0.000271230 0
$261$	−7.56308	−0.468143
$262$	−22.8713	−1.41299
$263$	10.0547	0.619998	0.309999	−	0.950737i	$-0.399671\pi$
$263$	10.0547	0.619998	0.309999	+	0.950737i	$0.399671\pi$
$264$	−15.8771	−0.977168
$265$	0.0156277	0.000960000 0
$266$	2.71603	0.166530
$267$	−0.885093	−0.0541668
$268$	−55.0205	−3.36091
$269$	−6.32269	−0.385501	−0.192751	−	0.981248i	$-0.561741\pi$
$269$	−6.32269	−0.385501	−0.192751	+	0.981248i	$0.561741\pi$
$270$	0.0262384	0.00159682
$271$	−13.0175	−0.790759	−0.395380	−	0.918518i	$-0.629387\pi$
$271$	−13.0175	−0.790759	−0.395380	+	0.918518i	$0.629387\pi$
$272$	22.1786	1.34478
$273$	−0.0347606	−0.00210381
$274$	−28.2977	−1.70953
$275$	15.9191	0.959956
$276$	21.1786	1.27480
$277$	10.5446	0.633561	0.316781	−	0.948499i	$-0.397398\pi$
$277$	10.5446	0.633561	0.316781	+	0.948499i	$0.397398\pi$
$278$	50.6336	3.03680
$279$	−5.06979	−0.303520
$280$	0.00316617	0.000189215 0
$281$	−0.263862	−0.0157407	−0.00787035	−	0.999969i	$-0.502505\pi$
$281$	−0.263862	−0.0157407	−0.00787035	+	0.999969i	$0.502505\pi$
$282$	12.8521	0.765329
$283$	2.31003	0.137317	0.0686585	−	0.997640i	$-0.478128\pi$
$283$	2.31003	0.137317	0.0686585	+	0.997640i	$0.478128\pi$
$284$	45.1965	2.68192
$285$	−0.0119533	−0.000708051 0
$286$	2.77582	0.164138
$287$	1.14270	0.0674515
$288$	27.8055	1.63845
$289$	−11.9482	−0.702837
$290$	0.0209625	0.00123096
$291$	−2.39830	−0.140591
$292$	−45.1083	−2.63976
$293$	21.2826	1.24334	0.621670	−	0.783279i	$-0.286455\pi$
$293$	21.2826	1.24334	0.621670	+	0.783279i	$0.286455\pi$
$294$	−12.1804	−0.710376
$295$	0.0242459	0.00141165
$296$	6.69907	0.389376
$297$	−11.7953	−0.684432
$298$	36.2758	2.10140
$299$	−2.17764	−0.125936
$300$	16.1917	0.934825
$301$	−1.16907	−0.0673840
$302$	11.1317	0.640560
$303$	2.81412	0.161667
$304$	−65.3876	−3.75024
$305$	0.0176581	0.00101110
$306$	15.0379	0.859659
$307$	−31.9443	−1.82316	−0.911579	−	0.411125i	$-0.865136\pi$
$307$	−31.9443	−1.82316	−0.911579	+	0.411125i	$0.865136\pi$
$308$	−2.42010	−0.137898
$309$	0.149140	0.00848428
$310$	0.0140519	0.000798092 0
$311$	−23.4728	−1.33102	−0.665509	−	0.746390i	$-0.731786\pi$
$311$	−23.4728	−1.33102	−0.665509	+	0.746390i	$0.731786\pi$
$312$	1.66048	0.0940064
$313$	12.4998	0.706531	0.353265	−	0.935523i	$-0.385071\pi$
$313$	12.4998	0.706531	0.353265	+	0.935523i	$0.385071\pi$
$314$	−29.6121	−1.67111
$315$	0.00108193	6.09601e−5 0
$316$	53.6328	3.01708
$317$	10.6426	0.597750	0.298875	−	0.954292i	$-0.403389\pi$
$317$	10.6426	0.597750	0.298875	+	0.954292i	$0.403389\pi$
$318$	−10.0887	−0.565744
$319$	−9.42352	−0.527616
$320$	−0.0236867	−0.00132413
$321$	0.122923	0.00686088
$322$	2.68056	0.149382
$323$	−14.8938	−0.828714
$324$	25.2266	1.40148
$325$	−1.66487	−0.0923505
$326$	−42.6056	−2.35971
$327$	11.5402	0.638177
$328$	−54.5858	−3.01400
$329$	1.15214	0.0635196
$330$	0.0150377	0.000827801 0
$331$	21.6569	1.19037	0.595186	−	0.803588i	$-0.297078\pi$
$331$	21.6569	1.19037	0.595186	+	0.803588i	$0.297078\pi$
$332$	−50.2003	−2.75510
$333$	2.28919	0.125447
$334$	−63.1323	−3.45445
$335$	0.0306483	0.00167449
$336$	−1.03012	−0.0561977
$337$	34.2780	1.86724	0.933621	−	0.358261i	$-0.116630\pi$
$337$	34.2780	1.86724	0.933621	+	0.358261i	$0.116630\pi$
$338$	33.7485	1.83568
$339$	9.35437	0.508060
$340$	−0.0295213	−0.00160102
$341$	−6.31690	−0.342079
$342$	−44.3352	−2.39737
$343$	−2.18770	−0.118124
$344$	55.8454	3.01098
$345$	−0.0117972	−0.000635139 0
$346$	43.6704	2.34773
$347$	−25.2643	−1.35626	−0.678129	−	0.734943i	$-0.737209\pi$
$347$	−25.2643	−1.35626	−0.678129	+	0.734943i	$0.737209\pi$
$348$	−9.58487	−0.513803
$349$	−10.1680	−0.544280	−0.272140	−	0.962258i	$-0.587731\pi$
$349$	−10.1680	−0.544280	−0.272140	+	0.962258i	$0.587731\pi$
$350$	2.04937	0.109543
$351$	1.23359	0.0658443
$352$	34.6453	1.84660
$353$	14.9362	0.794975	0.397488	−	0.917608i	$-0.369882\pi$
$353$	14.9362	0.794975	0.397488	+	0.917608i	$0.369882\pi$
$354$	−15.6523	−0.831911
$355$	−0.0251760	−0.00133620
$356$	6.44464	0.341565
$357$	−0.234638	−0.0124183
$358$	−4.75888	−0.251515
$359$	−23.6864	−1.25012	−0.625060	−	0.780577i	$-0.714926\pi$
$359$	−23.6864	−1.25012	−0.625060	+	0.780577i	$0.714926\pi$
$360$	−0.0516831	−0.00272394
$361$	24.9104	1.31107
$362$	10.0269	0.527000
$363$	0.575725	0.0302177
$364$	0.253103	0.0132662
$365$	0.0251269	0.00131520
$366$	−11.3994	−0.595857
$367$	−7.64155	−0.398886	−0.199443	−	0.979909i	$-0.563913\pi$
$367$	−7.64155	−0.398886	−0.199443	+	0.979909i	$0.563913\pi$
$368$	−64.5337	−3.36405
$369$	−18.6529	−0.971033
$370$	−0.00634492	−0.000329857 0
$371$	−0.904413	−0.0469548
$372$	−6.42506	−0.333124
$373$	−12.2007	−0.631728	−0.315864	−	0.948804i	$-0.602294\pi$
$373$	−12.2007	−0.631728	−0.315864	+	0.948804i	$0.602294\pi$
$374$	18.7371	0.968870
$375$	−0.0180386	−0.000931510 0
$376$	−55.0367	−2.83830
$377$	0.985545	0.0507581
$378$	−1.51849	−0.0781024
$379$	−23.7501	−1.21996	−0.609980	−	0.792417i	$-0.708822\pi$
$379$	−23.7501	−1.21996	−0.609980	+	0.792417i	$0.708822\pi$
$380$	0.0870355	0.00446483
$381$	5.72274	0.293185
$382$	−50.3323	−2.57522
$383$	−14.6064	−0.746351	−0.373176	−	0.927761i	$-0.621731\pi$
$383$	−14.6064	−0.746351	−0.373176	+	0.927761i	$0.621731\pi$
$384$	0.777454	0.0396743
$385$	0.00134808	6.87045e−5 0
$386$	−20.6552	−1.05132
$387$	19.0833	0.970061
$388$	17.4627	0.886536
$389$	−18.1835	−0.921941	−0.460970	−	0.887416i	$-0.652499\pi$
$389$	−18.1835	−0.921941	−0.460970	+	0.887416i	$0.652499\pi$
$390$	−0.00157270	−7.96368e−5 0
$391$	−14.6993	−0.743376
$392$	52.1605	2.63450
$393$	−5.82527	−0.293846
$394$	59.6146	3.00334
$395$	−0.0298753	−0.00150319
$396$	39.5046	1.98518
$397$	−26.5562	−1.33282	−0.666409	−	0.745587i	$-0.732169\pi$
$397$	−26.5562	−1.33282	−0.666409	+	0.745587i	$0.732169\pi$
$398$	0.557171	0.0279285
$399$	0.691766	0.0346316
$400$	−49.3380	−2.46690
$401$	−16.0102	−0.799510	−0.399755	−	0.916622i	$-0.630905\pi$
$401$	−16.0102	−0.799510	−0.399755	+	0.916622i	$0.630905\pi$
$402$	−19.7854	−0.986808
$403$	0.660644	0.0329090
$404$	−20.4905	−1.01944
$405$	−0.0140521	−0.000698252 0
$406$	−1.21315	−0.0602077
$407$	2.85231	0.141384
$408$	11.2084	0.554900
$409$	2.26321	0.111908	0.0559541	−	0.998433i	$-0.482180\pi$
$409$	2.26321	0.111908	0.0559541	+	0.998433i	$0.482180\pi$
$410$	0.0517001	0.00255328
$411$	−7.20736	−0.355513
$412$	−1.08593	−0.0535002
$413$	−1.40317	−0.0690456
$414$	−43.7562	−2.15050
$415$	0.0279633	0.00137266
$416$	−3.62333	−0.177648
$417$	12.8963	0.631533
$418$	−55.2412	−2.70193
$419$	−2.45307	−0.119840	−0.0599202	−	0.998203i	$-0.519085\pi$
$419$	−2.45307	−0.119840	−0.0599202	+	0.998203i	$0.519085\pi$
$420$	0.00137116	6.69059e−5 0
$421$	−17.6105	−0.858281	−0.429140	−	0.903238i	$-0.641183\pi$
$421$	−17.6105	−0.858281	−0.429140	+	0.903238i	$0.641183\pi$
$422$	−59.5606	−2.89936
$423$	−18.8070	−0.914429
$424$	43.2030	2.09812
$425$	−11.2381	−0.545126
$426$	16.2527	0.787447
$427$	−1.02192	−0.0494540
$428$	−0.895038	−0.0432633
$429$	0.706995	0.0341340
$430$	−0.0528931	−0.00255073
$431$	18.3522	0.883993	0.441996	−	0.897017i	$-0.354270\pi$
$431$	18.3522	0.883993	0.441996	+	0.897017i	$0.354270\pi$
$432$	36.5571	1.75886
$433$	24.4261	1.17384	0.586922	−	0.809643i	$-0.300339\pi$
$433$	24.4261	1.17384	0.586922	+	0.809643i	$0.300339\pi$
$434$	−0.813216	−0.0390356
$435$	0.00533910	0.000255990 0
$436$	−84.0281	−4.02422
$437$	43.3369	2.07309
$438$	−16.2210	−0.775070
$439$	−2.61054	−0.124594	−0.0622970	−	0.998058i	$-0.519843\pi$
$439$	−2.61054	−0.124594	−0.0622970	+	0.998058i	$0.519843\pi$
$440$	−0.0643965	−0.00306998
$441$	17.8242	0.848770
$442$	−1.95959	−0.0932081
$443$	−26.7013	−1.26862	−0.634308	−	0.773081i	$-0.718715\pi$
$443$	−26.7013	−1.26862	−0.634308	+	0.773081i	$0.718715\pi$
$444$	2.90115	0.137682
$445$	−0.00358988	−0.000170177 0
$446$	−43.7855	−2.07331
$447$	9.23936	0.437007
$448$	1.37081	0.0647646
$449$	−29.5584	−1.39495	−0.697473	−	0.716612i	$-0.745692\pi$
$449$	−29.5584	−1.39495	−0.697473	+	0.716612i	$0.745692\pi$
$450$	−33.4529	−1.57699
$451$	−23.2414	−1.09439
$452$	−68.1121	−3.20372
$453$	2.83523	0.133211
$454$	−66.6497	−3.12803
$455$	−0.000140987 0	−6.60957e−6 0
$456$	−33.0451	−1.54748
$457$	−33.4000	−1.56239	−0.781193	−	0.624289i	$-0.785389\pi$
$457$	−33.4000	−1.56239	−0.781193	+	0.624289i	$0.785389\pi$
$458$	73.2658	3.42349
$459$	8.32688	0.388665
$460$	0.0858989	0.00400506
$461$	−32.1557	−1.49764	−0.748821	−	0.662772i	$-0.769380\pi$
$461$	−32.1557	−1.49764	−0.748821	+	0.662772i	$0.769380\pi$
$462$	−0.870272	−0.0404887
$463$	−16.7151	−0.776817	−0.388409	−	0.921487i	$-0.626975\pi$
$463$	−16.7151	−0.776817	−0.388409	+	0.921487i	$0.626975\pi$
$464$	29.2063	1.35587
$465$	0.00357898	0.000165971 0
$466$	36.8427	1.70670
$467$	19.5055	0.902608	0.451304	−	0.892370i	$-0.350959\pi$
$467$	19.5055	0.902608	0.451304	+	0.892370i	$0.350959\pi$
$468$	−4.13153	−0.190980
$469$	−1.77369	−0.0819015
$470$	0.0521272	0.00240445
$471$	−7.54215	−0.347524
$472$	67.0283	3.08523
$473$	23.7777	1.09330
$474$	19.2864	0.885855
$475$	33.1324	1.52022
$476$	1.70847	0.0783076
$477$	14.7632	0.675961
$478$	−63.4161	−2.90058
$479$	0.730758	0.0333892	0.0166946	−	0.999861i	$-0.494686\pi$
$479$	0.730758	0.0333892	0.0166946	+	0.999861i	$0.494686\pi$
$480$	−0.0196291	−0.000895940 0
$481$	−0.298304	−0.0136015
$482$	−14.8106	−0.674604
$483$	0.682732	0.0310654
$484$	−4.19203	−0.190547
$485$	−0.00972734	−0.000441696 0
$486$	38.1728	1.73155
$487$	37.0750	1.68003	0.840015	−	0.542563i	$-0.182546\pi$
$487$	37.0750	1.68003	0.840015	+	0.542563i	$0.182546\pi$
$488$	48.8161	2.20980
$489$	−10.8516	−0.490724
$490$	−0.0494030	−0.00223180
$491$	22.9565	1.03601	0.518006	−	0.855377i	$-0.326674\pi$
$491$	22.9565	1.03601	0.518006	+	0.855377i	$0.326674\pi$
$492$	−23.6393	−1.06574
$493$	6.65253	0.299615
$494$	5.77732	0.259934
$495$	−0.0220054	−0.000989070 0
$496$	19.5780	0.879077
$497$	1.45700	0.0653553
$498$	−18.0521	−0.808934
$499$	15.6686	0.701422	0.350711	−	0.936484i	$-0.385940\pi$
$499$	15.6686	0.701422	0.350711	+	0.936484i	$0.385940\pi$
$500$	0.131345	0.00587391
$501$	−16.0797	−0.718386
$502$	−9.59722	−0.428345
$503$	5.33963	0.238083	0.119041	−	0.992889i	$-0.462018\pi$
$503$	5.33963	0.238083	0.119041	+	0.992889i	$0.462018\pi$
$504$	2.99103	0.133231
$505$	0.0114139	0.000507911 0
$506$	−54.5197	−2.42370
$507$	8.59567	0.381747
$508$	−41.6691	−1.84877
$509$	9.98579	0.442613	0.221306	−	0.975204i	$-0.428968\pi$
$509$	9.98579	0.442613	0.221306	+	0.975204i	$0.428968\pi$
$510$	−0.0106159	−0.000470079 0
$511$	−1.45416	−0.0643280
$512$	40.1974	1.77649
$513$	−24.5496	−1.08389
$514$	−40.7638	−1.79801
$515$	0.000604903 0	2.66552e−5 0
$516$	24.1848	1.06468
$517$	−23.4334	−1.03060
$518$	0.367196	0.0161337
$519$	11.1227	0.488234
$520$	0.00673482	0.000295341 0
$521$	9.61911	0.421421	0.210710	−	0.977549i	$-0.432422\pi$
$521$	9.61911	0.421421	0.210710	+	0.977549i	$0.432422\pi$
$522$	19.8029	0.866751
$523$	42.7182	1.86794	0.933969	−	0.357355i	$-0.116321\pi$
$523$	42.7182	1.86794	0.933969	+	0.357355i	$0.116321\pi$
$524$	42.4156	1.85293
$525$	0.521970	0.0227806
$526$	−26.3269	−1.14791
$527$	4.45941	0.194255
$528$	20.9516	0.911800
$529$	19.7710	0.859608
$530$	−0.0409190	−0.00177741
$531$	22.9048	0.993982
$532$	−5.03697	−0.218380
$533$	2.43066	0.105284
$534$	2.31750	0.100288
$535$	0.000498567 0	2.15549e−5 0
$536$	84.7277	3.65968
$537$	−1.21208	−0.0523050
$538$	16.5551	0.713742
$539$	22.2087	0.956597
$540$	−0.0486601	−0.00209400
$541$	−7.12163	−0.306183	−0.153091	−	0.988212i	$-0.548923\pi$
$541$	−7.12163	−0.306183	−0.153091	+	0.988212i	$0.548923\pi$
$542$	34.0847	1.46406
$543$	2.55382	0.109595
$544$	−24.4578	−1.04862
$545$	0.0468065	0.00200497
$546$	0.0910161	0.00389513
$547$	−0.718950	−0.0307401	−0.0153700	−	0.999882i	$-0.504893\pi$
$547$	−0.718950	−0.0307401	−0.0153700	+	0.999882i	$0.504893\pi$
$548$	52.4790	2.24179
$549$	16.6813	0.711941
$550$	−41.6820	−1.77733
$551$	−19.6132	−0.835550
$552$	−32.6135	−1.38812
$553$	1.72896	0.0735228
$554$	−27.6095	−1.17302
$555$	−0.00161604	−6.85969e−5 0
$556$	−93.9017	−3.98232
$557$	11.9875	0.507927	0.253963	−	0.967214i	$-0.418266\pi$
$557$	11.9875	0.507927	0.253963	+	0.967214i	$0.418266\pi$
$558$	13.2746	0.561957
$559$	−2.48675	−0.105178
$560$	−0.00417810	−0.000176557 0
$561$	4.77229	0.201486
$562$	0.690888	0.0291434
$563$	−24.9922	−1.05330	−0.526649	−	0.850083i	$-0.676552\pi$
$563$	−24.9922	−1.05330	−0.526649	+	0.850083i	$0.676552\pi$
$564$	−23.8346	−1.00362
$565$	0.0379408	0.00159618
$566$	−6.04851	−0.254238
$567$	0.813228	0.0341524
$568$	−69.5995	−2.92033
$569$	−14.7602	−0.618779	−0.309390	−	0.950935i	$-0.600125\pi$
$569$	−14.7602	−0.618779	−0.309390	+	0.950935i	$0.600125\pi$
$570$	0.0312981	0.00131093
$571$	38.1750	1.59757	0.798787	−	0.601615i	$-0.205476\pi$
$571$	38.1750	1.59757	0.798787	+	0.601615i	$0.205476\pi$
$572$	−5.14785	−0.215242
$573$	−12.8195	−0.535544
$574$	−2.99201	−0.124884
$575$	32.6997	1.36367
$576$	−22.3765	−0.932352
$577$	5.51499	0.229592	0.114796	−	0.993389i	$-0.463379\pi$
$577$	5.51499	0.229592	0.114796	+	0.993389i	$0.463379\pi$
$578$	31.2848	1.30128
$579$	−5.26083	−0.218633
$580$	−0.0388756	−0.00161422
$581$	−1.61831	−0.0671387
$582$	6.27963	0.260299
$583$	18.3948	0.761835
$584$	69.4637	2.87443
$585$	0.00230141	9.51514e−5 0
$586$	−55.7256	−2.30200
$587$	3.42192	0.141238	0.0706188	−	0.997503i	$-0.477503\pi$
$587$	3.42192	0.141238	0.0706188	+	0.997503i	$0.477503\pi$
$588$	22.5890	0.931554
$589$	−13.1474	−0.541728
$590$	−0.0634848	−0.00261363
$591$	15.1837	0.624574
$592$	−8.84015	−0.363328
$593$	−13.7956	−0.566516	−0.283258	−	0.959044i	$-0.591415\pi$
$593$	−13.7956	−0.566516	−0.283258	+	0.959044i	$0.591415\pi$
$594$	30.8844	1.26720
$595$	−0.000951676 0	−3.90149e−5 0
$596$	−67.2746	−2.75568
$597$	0.141910	0.00580800
$598$	5.70187	0.233167
$599$	−20.1601	−0.823720	−0.411860	−	0.911247i	$-0.635121\pi$
$599$	−20.1601	−0.823720	−0.411860	+	0.911247i	$0.635121\pi$
$600$	−24.9340	−1.01793
$601$	3.38299	0.137995	0.0689975	−	0.997617i	$-0.478020\pi$
$601$	3.38299	0.137995	0.0689975	+	0.997617i	$0.478020\pi$
$602$	3.06105	0.124759
$603$	28.9529	1.17906
$604$	−20.6442	−0.840000
$605$	0.00233510	9.49354e−5 0
$606$	−7.36840	−0.299321
$607$	31.1244	1.26330	0.631649	−	0.775254i	$-0.282378\pi$
$607$	31.1244	1.26330	0.631649	+	0.775254i	$0.282378\pi$
$608$	72.1074	2.92434
$609$	−0.308987	−0.0125208
$610$	−0.0462353	−0.00187201
$611$	2.45074	0.0991464
$612$	−27.8883	−1.12732
$613$	−6.59234	−0.266262	−0.133131	−	0.991098i	$-0.542503\pi$
$613$	−6.59234	−0.266262	−0.133131	+	0.991098i	$0.542503\pi$
$614$	83.6420	3.37552
$615$	0.0131679	0.000530981 0
$616$	3.72679	0.150157
$617$	7.66631	0.308634	0.154317	−	0.988021i	$-0.450682\pi$
$617$	7.66631	0.308634	0.154317	+	0.988021i	$0.450682\pi$
$618$	−0.390504	−0.0157084
$619$	−0.891134	−0.0358177	−0.0179089	−	0.999840i	$-0.505701\pi$
$619$	−0.891134	−0.0358177	−0.0179089	+	0.999840i	$0.505701\pi$
$620$	−0.0260597	−0.00104658
$621$	−24.2290	−0.972274
$622$	61.4604	2.46434
$623$	0.207755	0.00832355
$624$	−2.19119	−0.0877178
$625$	24.9999	0.999996
$626$	−32.7291	−1.30812
$627$	−14.0698	−0.561894
$628$	54.9167	2.19142
$629$	−2.01359	−0.0802869
$630$	−0.00283290	−0.000112866 0
$631$	12.1359	0.483122	0.241561	−	0.970386i	$-0.422341\pi$
$631$	12.1359	0.483122	0.241561	+	0.970386i	$0.422341\pi$
$632$	−82.5908	−3.28529
$633$	−15.1699	−0.602951
$634$	−27.8663	−1.10671
$635$	0.0232111	0.000921104 0
$636$	18.7098	0.741891
$637$	−2.32267	−0.0920274
$638$	24.6742	0.976863
$639$	−23.7834	−0.940855
$640$	0.00315331	0.000124645 0
$641$	11.0447	0.436241	0.218120	−	0.975922i	$-0.430007\pi$
$641$	11.0447	0.436241	0.218120	+	0.975922i	$0.430007\pi$
$642$	−0.321857	−0.0127027
$643$	6.85067	0.270164	0.135082	−	0.990834i	$-0.456870\pi$
$643$	6.85067	0.270164	0.135082	+	0.990834i	$0.456870\pi$
$644$	−4.97118	−0.195892
$645$	−0.0134717	−0.000530450 0
$646$	38.9975	1.53434
$647$	7.29478	0.286787	0.143394	−	0.989666i	$-0.454198\pi$
$647$	7.29478	0.286787	0.143394	+	0.989666i	$0.454198\pi$
$648$	−38.8472	−1.52606
$649$	28.5391	1.12026
$650$	4.35925	0.170984
$651$	−0.207125	−0.00811785
$652$	79.0135	3.09441
$653$	37.9496	1.48508	0.742540	−	0.669801i	$-0.233621\pi$
$653$	37.9496	1.48508	0.742540	+	0.669801i	$0.233621\pi$
$654$	−30.2166	−1.18156
$655$	−0.0236269	−0.000923181 0
$656$	72.0319	2.81237
$657$	23.7370	0.926067
$658$	−3.01673	−0.117604
$659$	49.8564	1.94213	0.971064	−	0.238819i	$-0.0767603\pi$
$659$	49.8564	1.94213	0.971064	+	0.238819i	$0.0767603\pi$
$660$	−0.0278880	−0.00108554
$661$	42.0820	1.63680	0.818400	−	0.574650i	$-0.194862\pi$
$661$	42.0820	1.63680	0.818400	+	0.574650i	$0.194862\pi$
$662$	−56.7058	−2.20393
$663$	−0.499103	−0.0193835
$664$	77.3050	3.00002
$665$	0.00280576	0.000108803 0
$666$	−5.99394	−0.232261
$667$	−19.3571	−0.749508
$668$	117.081	4.53000
$669$	−11.1521	−0.431165
$670$	−0.0802485	−0.00310027
$671$	20.7847	0.802386
$672$	1.13598	0.0438215
$673$	0.203787	0.00785540	0.00392770	−	0.999992i	$-0.498750\pi$
$673$	0.203787	0.00785540	0.00392770	+	0.999992i	$0.498750\pi$
$674$	−89.7525	−3.45714
$675$	−18.5238	−0.712980
$676$	−62.5877	−2.40722
$677$	−7.33834	−0.282035	−0.141018	−	0.990007i	$-0.545037\pi$
$677$	−7.33834	−0.282035	−0.141018	+	0.990007i	$0.545037\pi$
$678$	−24.4932	−0.940656
$679$	0.562946	0.0216039
$680$	0.0454607	0.00174334
$681$	−16.9755	−0.650504
$682$	16.5400	0.633348
$683$	34.4375	1.31771	0.658857	−	0.752268i	$-0.271040\pi$
$683$	34.4375	1.31771	0.658857	+	0.752268i	$0.271040\pi$
$684$	82.2211	3.14380
$685$	−0.0292326	−0.00111692
$686$	5.72819	0.218703
$687$	18.6606	0.711948
$688$	−73.6941	−2.80956
$689$	−1.92379	−0.0732907
$690$	0.0308894	0.00117594
$691$	−21.9698	−0.835771	−0.417885	−	0.908500i	$-0.637229\pi$
$691$	−21.9698	−0.835771	−0.417885	+	0.908500i	$0.637229\pi$
$692$	−80.9882	−3.07871
$693$	1.27351	0.0483766
$694$	66.1512	2.51107
$695$	0.0523064	0.00198410
$696$	14.7600	0.559478
$697$	16.4072	0.621468
$698$	26.6235	1.00772
$699$	9.38375	0.354926
$700$	−3.80062	−0.143650
$701$	−25.8851	−0.977668	−0.488834	−	0.872377i	$-0.662578\pi$
$701$	−25.8851	−0.977668	−0.488834	+	0.872377i	$0.662578\pi$
$702$	−3.23000	−0.121909
$703$	5.93651	0.223900
$704$	−27.8808	−1.05080
$705$	0.0132767	0.000500029 0
$706$	−39.1085	−1.47187
$707$	−0.660550	−0.0248426
$708$	29.0277	1.09093
$709$	0.930746	0.0349549	0.0174774	−	0.999847i	$-0.494436\pi$
$709$	0.930746	0.0349549	0.0174774	+	0.999847i	$0.494436\pi$
$710$	0.0659200	0.00247393
$711$	−28.2227	−1.05843
$712$	−9.92429	−0.371929
$713$	−12.9757	−0.485943
$714$	0.614368	0.0229922
$715$	0.00286753	0.000107239 0
$716$	8.82551	0.329825
$717$	−16.1519	−0.603205
$718$	62.0197	2.31456
$719$	−33.5940	−1.25285	−0.626423	−	0.779483i	$-0.715482\pi$
$719$	−33.5940	−1.25285	−0.626423	+	0.779483i	$0.715482\pi$
$720$	0.0682014	0.00254172
$721$	−0.0350072	−0.00130374
$722$	−65.2246	−2.42741
$723$	−3.77223	−0.140291
$724$	−18.5952	−0.691083
$725$	−14.7991	−0.549623
$726$	−1.50746	−0.0559470
$727$	43.0657	1.59722	0.798610	−	0.601849i	$-0.205569\pi$
$727$	43.0657	1.59722	0.798610	+	0.601849i	$0.205569\pi$
$728$	−0.389761	−0.0144455
$729$	−5.86272	−0.217138
$730$	−0.0657914	−0.00243505
$731$	−16.7858	−0.620846
$732$	21.1406	0.781380
$733$	40.6030	1.49971	0.749853	−	0.661605i	$-0.230124\pi$
$733$	40.6030	1.49971	0.749853	+	0.661605i	$0.230124\pi$
$734$	20.0084	0.738523
$735$	−0.0125828	−0.000464125 0
$736$	71.1657	2.62320
$737$	36.0751	1.32884
$738$	48.8402	1.79783
$739$	43.4117	1.59693	0.798463	−	0.602044i	$-0.205647\pi$
$739$	43.4117	1.59693	0.798463	+	0.602044i	$0.205647\pi$
$740$	0.0117669	0.000432559 0
$741$	1.47147	0.0540558
$742$	2.36809	0.0869352
$743$	−37.9855	−1.39355	−0.696776	−	0.717289i	$-0.745383\pi$
$743$	−37.9855	−1.39355	−0.696776	+	0.717289i	$0.745383\pi$
$744$	9.89415	0.362737
$745$	0.0374743	0.00137295
$746$	31.9459	1.16962
$747$	26.4165	0.966529
$748$	−34.7485	−1.27053
$749$	−0.0288533	−0.00105428
$750$	0.0472317	0.00172466
$751$	−10.9771	−0.400558	−0.200279	−	0.979739i	$-0.564185\pi$
$751$	−10.9771	−0.400558	−0.200279	+	0.979739i	$0.564185\pi$
$752$	72.6270	2.64843
$753$	−2.44439	−0.0890786
$754$	−2.58052	−0.0939770
$755$	0.0114995	0.000418510 0
$756$	2.81608	0.102420
$757$	−3.23990	−0.117756	−0.0588780	−	0.998265i	$-0.518752\pi$
$757$	−3.23990	−0.117756	−0.0588780	+	0.998265i	$0.518752\pi$
$758$	62.1865	2.25871
$759$	−13.8861	−0.504032
$760$	−0.134029	−0.00486173
$761$	24.7677	0.897830	0.448915	−	0.893574i	$-0.351811\pi$
$761$	24.7677	0.897830	0.448915	+	0.893574i	$0.351811\pi$
$762$	−14.9842	−0.542822
$763$	−2.70881	−0.0980655
$764$	93.3430	3.37703
$765$	0.0155347	0.000561659 0
$766$	38.2449	1.38184
$767$	−2.98472	−0.107772
$768$	9.64435	0.348011
$769$	−31.5021	−1.13600	−0.567998	−	0.823030i	$-0.692282\pi$
$769$	−31.5021	−1.13600	−0.567998	+	0.823030i	$0.692282\pi$
$770$	−0.00352977	−0.000127204 0
$771$	−10.3824	−0.373915
$772$	38.3058	1.37865
$773$	53.7834	1.93445	0.967227	−	0.253911i	$-0.0817172\pi$
$773$	53.7834	1.93445	0.967227	+	0.253911i	$0.0817172\pi$
$774$	−49.9672	−1.79604
$775$	−9.92030	−0.356348
$776$	−26.8914	−0.965345
$777$	0.0935241	0.00335516
$778$	47.6111	1.70694
$779$	−48.3723	−1.73312
$780$	0.00291663	0.000104432 0
$781$	−29.6338	−1.06038
$782$	38.4882	1.37633
$783$	10.9654	0.391872
$784$	−68.8315	−2.45827
$785$	−0.0305905	−0.00109182
$786$	15.2527	0.544046
$787$	−45.5775	−1.62466	−0.812331	−	0.583197i	$-0.801801\pi$
$787$	−45.5775	−1.62466	−0.812331	+	0.583197i	$0.801801\pi$
$788$	−110.557	−3.93844
$789$	−6.70540	−0.238718
$790$	0.0782245	0.00278310
$791$	−2.19573	−0.0780711
$792$	−60.8344	−2.16166
$793$	−2.17374	−0.0771918
$794$	69.5339	2.46767
$795$	−0.0104220	−0.000369630 0
$796$	−1.03329	−0.0366241
$797$	37.3108	1.32162	0.660808	−	0.750555i	$-0.270214\pi$
$797$	37.3108	1.32162	0.660808	+	0.750555i	$0.270214\pi$
$798$	−1.81130	−0.0641193
$799$	16.5428	0.585241
$800$	54.4083	1.92363
$801$	−3.39130	−0.119826
$802$	41.9205	1.48027
$803$	29.5760	1.04371
$804$	36.6928	1.29405
$805$	0.00276912	9.75986e−5 0
$806$	−1.72981	−0.0609299
$807$	4.21656	0.148430
$808$	31.5539	1.11006
$809$	29.3923	1.03338	0.516689	−	0.856173i	$-0.327164\pi$
$809$	29.3923	1.03338	0.516689	+	0.856173i	$0.327164\pi$
$810$	0.0367935	0.00129279
$811$	12.3688	0.434328	0.217164	−	0.976135i	$-0.430319\pi$
$811$	12.3688	0.434328	0.217164	+	0.976135i	$0.430319\pi$
$812$	2.24983	0.0789536
$813$	8.68130	0.304467
$814$	−7.46839	−0.261767
$815$	−0.0440132	−0.00154172
$816$	−14.7908	−0.517780
$817$	49.4885	1.73138
$818$	−5.92591	−0.207194
$819$	−0.133188	−0.00465397
$820$	−0.0958795	−0.00334826
$821$	−52.4306	−1.82984	−0.914921	−	0.403633i	$-0.867747\pi$
$821$	−52.4306	−1.82984	−0.914921	+	0.403633i	$0.867747\pi$
$822$	18.8715	0.658220
$823$	−21.5650	−0.751708	−0.375854	−	0.926679i	$-0.622651\pi$
$823$	−21.5650	−0.751708	−0.375854	+	0.926679i	$0.622651\pi$
$824$	1.67226	0.0582561
$825$	−10.6163	−0.369613
$826$	3.67402	0.127836
$827$	−2.57559	−0.0895620	−0.0447810	−	0.998997i	$-0.514259\pi$
$827$	−2.57559	−0.0895620	−0.0447810	+	0.998997i	$0.514259\pi$
$828$	81.1473	2.82006
$829$	−16.5727	−0.575594	−0.287797	−	0.957691i	$-0.592923\pi$
$829$	−16.5727	−0.575594	−0.287797	+	0.957691i	$0.592923\pi$
$830$	−0.0732182	−0.00254144
$831$	−7.03209	−0.243941
$832$	2.91588	0.101090
$833$	−15.6782	−0.543219
$834$	−33.7672	−1.16926
$835$	−0.0652181	−0.00225697
$836$	102.447	3.54319
$837$	7.35048	0.254070
$838$	6.42305	0.221881
$839$	−24.5325	−0.846957	−0.423479	−	0.905906i	$-0.639191\pi$
$839$	−24.5325	−0.846957	−0.423479	+	0.905906i	$0.639191\pi$
$840$	−0.00211149	−7.28535e−5 0
$841$	−20.2395	−0.697914
$842$	46.1107	1.58908
$843$	0.175968	0.00606065
$844$	110.457	3.80209
$845$	0.0348635	0.00119934
$846$	49.2437	1.69303
$847$	−0.135138	−0.00464341
$848$	−57.0110	−1.95777
$849$	−1.54054	−0.0528713
$850$	29.4254	1.00928
$851$	5.85899	0.200843
$852$	−30.1412	−1.03262
$853$	23.2086	0.794647	0.397324	−	0.917679i	$-0.369939\pi$
$853$	23.2086	0.794647	0.397324	+	0.917679i	$0.369939\pi$
$854$	2.67576	0.0915625
$855$	−0.0458000	−0.00156633
$856$	1.37830	0.0471092
$857$	17.3185	0.591588	0.295794	−	0.955252i	$-0.404416\pi$
$857$	17.3185	0.591588	0.295794	+	0.955252i	$0.404416\pi$
$858$	−1.85117	−0.0631980
$859$	−24.3299	−0.830126	−0.415063	−	0.909793i	$-0.636240\pi$
$859$	−24.3299	−0.830126	−0.415063	+	0.909793i	$0.636240\pi$
$860$	0.0980920	0.00334491
$861$	−0.762059	−0.0259709
$862$	−48.0527	−1.63668
$863$	43.5170	1.48134	0.740668	−	0.671871i	$-0.234509\pi$
$863$	43.5170	1.48134	0.740668	+	0.671871i	$0.234509\pi$
$864$	−40.3140	−1.37151
$865$	0.0451132	0.00153389
$866$	−63.9566	−2.17333
$867$	7.96818	0.270614
$868$	1.50814	0.0511895
$869$	−35.1652	−1.19290
$870$	−0.0139797	−0.000473957 0
$871$	−3.77286	−0.127838
$872$	129.397	4.38195
$873$	−9.18927	−0.311010
$874$	−113.472	−3.83825
$875$	0.00423415	0.000143141 0
$876$	30.0824	1.01639
$877$	35.1463	1.18681	0.593403	−	0.804906i	$-0.297784\pi$
$877$	35.1463	1.18681	0.593403	+	0.804906i	$0.297784\pi$
$878$	6.83534	0.230682
$879$	−14.1932	−0.478724
$880$	0.0849782	0.00286462
$881$	51.4219	1.73245	0.866223	−	0.499657i	$-0.166541\pi$
$881$	51.4219	1.73245	0.866223	+	0.499657i	$0.166541\pi$
$882$	−46.6702	−1.57147
$883$	52.4774	1.76601	0.883003	−	0.469368i	$-0.155518\pi$
$883$	52.4774	1.76601	0.883003	+	0.469368i	$0.155518\pi$
$884$	3.63412	0.122229
$885$	−0.0161694	−0.000543530 0
$886$	69.9137	2.34880
$887$	−23.1280	−0.776562	−0.388281	−	0.921541i	$-0.626931\pi$
$887$	−23.1280	−0.776562	−0.388281	+	0.921541i	$0.626931\pi$
$888$	−4.46756	−0.149922
$889$	−1.34328	−0.0450523
$890$	0.00939963	0.000315076 0
$891$	−16.5402	−0.554118
$892$	81.2018	2.71884
$893$	−48.7719	−1.63209
$894$	−24.1920	−0.809103
$895$	−0.00491611	−0.000164327 0
$896$	−0.182490	−0.00609655
$897$	1.45225	0.0484893
$898$	77.3947	2.58269
$899$	5.87246	0.195858
$900$	62.0396	2.06799
$901$	−12.9858	−0.432620
$902$	60.8544	2.02623
$903$	0.779644	0.0259449
$904$	104.888	3.48852
$905$	0.0103581	0.000344316 0
$906$	−7.42368	−0.246635
$907$	20.2740	0.673188	0.336594	−	0.941650i	$-0.390725\pi$
$907$	20.2740	0.673188	0.336594	+	0.941650i	$0.390725\pi$
$908$	123.604	4.10195
$909$	10.7825	0.357634
$910$	0.000369156 0	1.22374e−5 0
$911$	39.9323	1.32302	0.661508	−	0.749938i	$-0.269917\pi$
$911$	39.9323	1.32302	0.661508	+	0.749938i	$0.269917\pi$
$912$	43.6065	1.44396
$913$	32.9147	1.08932
$914$	87.4535	2.89271
$915$	−0.0117760	−0.000389304 0
$916$	−135.874	−4.48940
$917$	1.36735	0.0451539
$918$	−21.8028	−0.719601
$919$	25.9960	0.857529	0.428765	−	0.903416i	$-0.358949\pi$
$919$	25.9960	0.857529	0.428765	+	0.903416i	$0.358949\pi$
$920$	−0.132278	−0.00436109
$921$	21.3034	0.701972
$922$	84.1956	2.77283
$923$	3.09921	0.102012
$924$	1.61395	0.0530950
$925$	4.47937	0.147281
$926$	43.7663	1.43825
$927$	0.571442	0.0187686
$928$	−32.2078	−1.05727
$929$	−4.37183	−0.143435	−0.0717175	−	0.997425i	$-0.522848\pi$
$929$	−4.37183	−0.143435	−0.0717175	+	0.997425i	$0.522848\pi$
$930$	−0.00937109	−0.000307290 0
$931$	46.2231	1.51490
$932$	−68.3260	−2.23809
$933$	15.6538	0.512483
$934$	−51.0727	−1.67115
$935$	0.0193561	0.000633012 0
$936$	6.36228	0.207958
$937$	−24.5444	−0.801831	−0.400916	−	0.916115i	$-0.631308\pi$
$937$	−24.5444	−0.801831	−0.400916	+	0.916115i	$0.631308\pi$
$938$	4.64418	0.151638
$939$	−8.33603	−0.272036
$940$	−0.0966716	−0.00315308
$941$	−16.5199	−0.538534	−0.269267	−	0.963066i	$-0.586781\pi$
$941$	−16.5199	−0.538534	−0.269267	+	0.963066i	$0.586781\pi$
$942$	19.7481	0.643429
$943$	−47.7406	−1.55465
$944$	−88.4512	−2.87884
$945$	−0.00156865	−5.10283e−5 0
$946$	−62.2587	−2.02420
$947$	−37.1946	−1.20866	−0.604331	−	0.796734i	$-0.706559\pi$
$947$	−37.1946	−1.20866	−0.604331	+	0.796734i	$0.706559\pi$
$948$	−35.7673	−1.16167
$949$	−3.09316	−0.100408
$950$	−86.7529	−2.81463
$951$	−7.09749	−0.230152
$952$	−2.63093	−0.0852688
$953$	56.1317	1.81828	0.909142	−	0.416486i	$-0.136739\pi$
$953$	56.1317	1.81828	0.909142	+	0.416486i	$0.136739\pi$
$954$	−38.6555	−1.25152
$955$	−0.0519952	−0.00168253
$956$	117.607	3.80369
$957$	6.28448	0.203148
$958$	−1.91339	−0.0618189
$959$	1.69176	0.0546299
$960$	0.0157965	0.000509830 0
$961$	−27.0635	−0.873016
$962$	0.781071	0.0251827
$963$	0.470988	0.0151774
$964$	27.4668	0.884645
$965$	−0.0213376	−0.000686882 0
$966$	−1.78764	−0.0575165
$967$	38.3151	1.23213	0.616065	−	0.787695i	$-0.288726\pi$
$967$	38.3151	1.23213	0.616065	+	0.787695i	$0.288726\pi$
$968$	6.45543	0.207485
$969$	9.93258	0.319080
$970$	0.0254698	0.000817785 0
$971$	11.2164	0.359952	0.179976	−	0.983671i	$-0.442398\pi$
$971$	11.2164	0.359952	0.179976	+	0.983671i	$0.442398\pi$
$972$	−70.7927	−2.27068
$973$	−3.02710	−0.0970445
$974$	−97.0761	−3.11052
$975$	1.11029	0.0355578
$976$	−64.4181	−2.06197
$977$	29.1466	0.932482	0.466241	−	0.884658i	$-0.345608\pi$
$977$	29.1466	0.932482	0.466241	+	0.884658i	$0.345608\pi$
$978$	28.4134	0.908559
$979$	−4.22553	−0.135049
$980$	0.0916195	0.00292668
$981$	44.2174	1.41175
$982$	−60.1086	−1.91814
$983$	−51.1486	−1.63139	−0.815693	−	0.578485i	$-0.803644\pi$
$983$	−51.1486	−1.63139	−0.815693	+	0.578485i	$0.803644\pi$
$984$	36.4029	1.16048
$985$	0.0615842	0.00196224
$986$	−17.4188	−0.554727
$987$	−0.768355	−0.0244570
$988$	−10.7142	−0.340865
$989$	48.8422	1.55309
$990$	0.0576183	0.00183123
$991$	7.39632	0.234952	0.117476	−	0.993076i	$-0.462520\pi$
$991$	7.39632	0.234952	0.117476	+	0.993076i	$0.462520\pi$
$992$	−21.5900	−0.685482
$993$	−14.4428	−0.458330
$994$	−3.81496	−0.121003
$995$	0.000575579 0	1.82471e−5 0
$996$	33.4783	1.06080
$997$	−45.7307	−1.44831	−0.724153	−	0.689640i	$-0.757769\pi$
$997$	−45.7307	−1.44831	−0.724153	+	0.689640i	$0.757769\pi$
$998$	−41.0261	−1.29866
$999$	−3.31900	−0.105009

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.b.1.13	✓	340

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.b.1.13	✓	340	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)

\(f(q)\)	\(=\)	\(q-2.61837 q^{2} -0.666893 q^{3} +4.85585 q^{4} -0.00270488 q^{5} +1.74617 q^{6} +0.156538 q^{7} -7.47768 q^{8} -2.55525 q^{9} +O(q^{10})\)	\(q-2.61837 q^{2} -0.666893 q^{3} +4.85585 q^{4} -0.00270488 q^{5} +1.74617 q^{6} +0.156538 q^{7} -7.47768 q^{8} -2.55525 q^{9} +0.00708236 q^{10} -3.18382 q^{11} -3.23833 q^{12} +0.332975 q^{13} -0.409874 q^{14} +0.00180386 q^{15} +9.86761 q^{16} +2.24762 q^{17} +6.69060 q^{18} -6.62649 q^{19} -0.0131345 q^{20} -0.104394 q^{21} +8.33641 q^{22} -6.53995 q^{23} +4.98681 q^{24} -4.99999 q^{25} -0.871852 q^{26} +3.70476 q^{27} +0.760126 q^{28} +2.95982 q^{29} -0.00472318 q^{30} +1.98406 q^{31} -10.8817 q^{32} +2.12327 q^{33} -5.88509 q^{34} -0.000423416 q^{35} -12.4079 q^{36} -0.895876 q^{37} +17.3506 q^{38} -0.222059 q^{39} +0.0202262 q^{40} +7.29983 q^{41} +0.273342 q^{42} -7.46828 q^{43} -15.4602 q^{44} +0.00691164 q^{45} +17.1240 q^{46} +7.36014 q^{47} -6.58064 q^{48} -6.97550 q^{49} +13.0918 q^{50} -1.49892 q^{51} +1.61688 q^{52} -5.77759 q^{53} -9.70043 q^{54} +0.00861184 q^{55} -1.17054 q^{56} +4.41916 q^{57} -7.74989 q^{58} -8.96379 q^{59} +0.00875929 q^{60} -6.52824 q^{61} -5.19501 q^{62} -0.399994 q^{63} +8.75704 q^{64} -0.000900656 q^{65} -5.55949 q^{66} -11.3308 q^{67} +10.9141 q^{68} +4.36145 q^{69} +0.00110866 q^{70} +9.30763 q^{71} +19.1074 q^{72} -9.28947 q^{73} +2.34573 q^{74} +3.33446 q^{75} -32.1773 q^{76} -0.498389 q^{77} +0.581432 q^{78} +11.0450 q^{79} -0.0266907 q^{80} +5.19508 q^{81} -19.1137 q^{82} -10.3381 q^{83} -0.506922 q^{84} -0.00607952 q^{85} +19.5547 q^{86} -1.97388 q^{87} +23.8076 q^{88} +1.32719 q^{89} -0.0180972 q^{90} +0.0521232 q^{91} -31.7571 q^{92} -1.32316 q^{93} -19.2716 q^{94} +0.0179238 q^{95} +7.25692 q^{96} +3.59622 q^{97} +18.2644 q^{98} +8.13547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9} + 36 q^{10} + 70 q^{11} + 92 q^{12} + 45 q^{13} + 44 q^{14} + 71 q^{15} + 362 q^{16} + 162 q^{17} + 41 q^{18} + 49 q^{19} + 147 q^{20} + 41 q^{21} + 32 q^{22} + 244 q^{23} + 85 q^{24} + 355 q^{25} + 83 q^{26} + 155 q^{27} + 129 q^{28} + 91 q^{29} + 51 q^{30} + 65 q^{31} + 113 q^{32} + 73 q^{33} + 26 q^{34} + 200 q^{35} + 380 q^{36} + 28 q^{37} + 171 q^{38} + 117 q^{39} + 95 q^{40} + 115 q^{41} + 42 q^{42} + 98 q^{43} + 139 q^{44} + 127 q^{45} + 29 q^{46} + 312 q^{47} + 168 q^{48} + 365 q^{49} + 64 q^{50} + 72 q^{51} + 100 q^{52} + 154 q^{53} + 89 q^{54} + 161 q^{55} + 89 q^{56} + 82 q^{57} + 29 q^{58} + 149 q^{59} + 93 q^{60} + 70 q^{61} + 257 q^{62} + 376 q^{63} + 346 q^{64} + 125 q^{65} + 48 q^{66} + 65 q^{67} + 464 q^{68} + 58 q^{69} - 54 q^{70} + 216 q^{71} + 90 q^{72} + 93 q^{73} + 147 q^{74} + 162 q^{75} + 64 q^{76} + 190 q^{77} + 12 q^{78} + 139 q^{79} + 274 q^{80} + 376 q^{81} + 59 q^{82} + 402 q^{83} + 10 q^{84} + 32 q^{85} + 53 q^{86} + 364 q^{87} + 42 q^{88} + 114 q^{89} + 126 q^{90} + 43 q^{91} + 422 q^{92} + 47 q^{93} + 2 q^{94} + 347 q^{95} + 146 q^{96} + 47 q^{97} + 96 q^{98} + 129 q^{99}+O(q^{100}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9 + 36 * q^10 + 70 * q^11 + 92 * q^12 + 45 * q^13 + 44 * q^14 + 71 * q^15 + 362 * q^16 + 162 * q^17 + 41 * q^18 + 49 * q^19 + 147 * q^20 + 41 * q^21 + 32 * q^22 + 244 * q^23 + 85 * q^24 + 355 * q^25 + 83 * q^26 + 155 * q^27 + 129 * q^28 + 91 * q^29 + 51 * q^30 + 65 * q^31 + 113 * q^32 + 73 * q^33 + 26 * q^34 + 200 * q^35 + 380 * q^36 + 28 * q^37 + 171 * q^38 + 117 * q^39 + 95 * q^40 + 115 * q^41 + 42 * q^42 + 98 * q^43 + 139 * q^44 + 127 * q^45 + 29 * q^46 + 312 * q^47 + 168 * q^48 + 365 * q^49 + 64 * q^50 + 72 * q^51 + 100 * q^52 + 154 * q^53 + 89 * q^54 + 161 * q^55 + 89 * q^56 + 82 * q^57 + 29 * q^58 + 149 * q^59 + 93 * q^60 + 70 * q^61 + 257 * q^62 + 376 * q^63 + 346 * q^64 + 125 * q^65 + 48 * q^66 + 65 * q^67 + 464 * q^68 + 58 * q^69 - 54 * q^70 + 216 * q^71 + 90 * q^72 + 93 * q^73 + 147 * q^74 + 162 * q^75 + 64 * q^76 + 190 * q^77 + 12 * q^78 + 139 * q^79 + 274 * q^80 + 376 * q^81 + 59 * q^82 + 402 * q^83 + 10 * q^84 + 32 * q^85 + 53 * q^86 + 364 * q^87 + 42 * q^88 + 114 * q^89 + 126 * q^90 + 43 * q^91 + 422 * q^92 + 47 * q^93 + 2 * q^94 + 347 * q^95 + 146 * q^96 + 47 * q^97 + 96 * q^98 + 129 * q^99

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