LMFDB - Embedded newform 8013.2.a.a.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.9841271397$
Analytic rank:	$1$
Dimension:	$94$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.15634 q^{2} +1.00000 q^{3} +2.64980 q^{4} -1.53192 q^{5} -2.15634 q^{6} -0.507117 q^{7} -1.40120 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.15634 q^{2} +1.00000 q^{3} +2.64980 q^{4} -1.53192 q^{5} -2.15634 q^{6} -0.507117 q^{7} -1.40120 q^{8} +1.00000 q^{9} +3.30334 q^{10} +1.74023 q^{11} +2.64980 q^{12} -1.52451 q^{13} +1.09352 q^{14} -1.53192 q^{15} -2.27815 q^{16} +1.16590 q^{17} -2.15634 q^{18} -0.415640 q^{19} -4.05929 q^{20} -0.507117 q^{21} -3.75253 q^{22} -8.97462 q^{23} -1.40120 q^{24} -2.65322 q^{25} +3.28736 q^{26} +1.00000 q^{27} -1.34376 q^{28} -1.07074 q^{29} +3.30334 q^{30} +7.70123 q^{31} +7.71486 q^{32} +1.74023 q^{33} -2.51408 q^{34} +0.776863 q^{35} +2.64980 q^{36} +6.40140 q^{37} +0.896260 q^{38} -1.52451 q^{39} +2.14652 q^{40} +6.40374 q^{41} +1.09352 q^{42} -9.27233 q^{43} +4.61126 q^{44} -1.53192 q^{45} +19.3523 q^{46} +5.09286 q^{47} -2.27815 q^{48} -6.74283 q^{49} +5.72124 q^{50} +1.16590 q^{51} -4.03964 q^{52} +11.4016 q^{53} -2.15634 q^{54} -2.66589 q^{55} +0.710570 q^{56} -0.415640 q^{57} +2.30887 q^{58} +10.2104 q^{59} -4.05929 q^{60} +3.05821 q^{61} -16.6065 q^{62} -0.507117 q^{63} -12.0796 q^{64} +2.33542 q^{65} -3.75253 q^{66} +15.2932 q^{67} +3.08941 q^{68} -8.97462 q^{69} -1.67518 q^{70} -3.39555 q^{71} -1.40120 q^{72} -12.8568 q^{73} -13.8036 q^{74} -2.65322 q^{75} -1.10136 q^{76} -0.882500 q^{77} +3.28736 q^{78} -17.2393 q^{79} +3.48995 q^{80} +1.00000 q^{81} -13.8086 q^{82} +2.99279 q^{83} -1.34376 q^{84} -1.78607 q^{85} +19.9943 q^{86} -1.07074 q^{87} -2.43840 q^{88} +2.71575 q^{89} +3.30334 q^{90} +0.773104 q^{91} -23.7810 q^{92} +7.70123 q^{93} -10.9819 q^{94} +0.636727 q^{95} +7.71486 q^{96} -8.69139 q^{97} +14.5398 q^{98} +1.74023 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 94 q - 13 q^{2} + 94 q^{3} + 73 q^{4} - 14 q^{5} - 13 q^{6} - 55 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) $ 94 * q - 13 * q^2 + 94 * q^3 + 73 * q^4 - 14 * q^5 - 13 * q^6 - 55 * q^7 - 36 * q^8 + 94 * q^9	\( 94 q - 13 q^{2} + 94 q^{3} + 73 q^{4} - 14 q^{5} - 13 q^{6} - 55 q^{7} - 36 q^{8} + 94 q^{9} - 39 q^{10} - 49 q^{11} + 73 q^{12} - 52 q^{13} - 7 q^{14} - 14 q^{15} + 43 q^{16} - 22 q^{17} - 13 q^{18} - 89 q^{19} - 22 q^{20} - 55 q^{21} - 36 q^{22} - 46 q^{23} - 36 q^{24} + 18 q^{25} + q^{26} + 94 q^{27} - 123 q^{28} - 20 q^{29} - 39 q^{30} - 61 q^{31} - 65 q^{32} - 49 q^{33} - 67 q^{34} - 40 q^{35} + 73 q^{36} - 83 q^{37} - 19 q^{38} - 52 q^{39} - 101 q^{40} - 25 q^{41} - 7 q^{42} - 150 q^{43} - 71 q^{44} - 14 q^{45} - 72 q^{46} - 39 q^{47} + 43 q^{48} - q^{49} - 45 q^{50} - 22 q^{51} - 110 q^{52} - 30 q^{53} - 13 q^{54} - 54 q^{55} - 5 q^{56} - 89 q^{57} - 77 q^{58} - 43 q^{59} - 22 q^{60} - 109 q^{61} - 33 q^{62} - 55 q^{63} + 10 q^{64} - 66 q^{65} - 36 q^{66} - 155 q^{67} - 46 q^{68} - 46 q^{69} - 43 q^{70} - 27 q^{71} - 36 q^{72} - 157 q^{73} - 29 q^{74} + 18 q^{75} - 176 q^{76} - 9 q^{77} + q^{78} - 99 q^{79} - 18 q^{80} + 94 q^{81} - 53 q^{82} - 144 q^{83} - 123 q^{84} - 105 q^{85} + 23 q^{86} - 20 q^{87} - 88 q^{88} - 4 q^{89} - 39 q^{90} - 99 q^{91} - 76 q^{92} - 61 q^{93} - 65 q^{94} - 49 q^{95} - 65 q^{96} - 139 q^{97} - 6 q^{98} - 49 q^{99}+O(q^{100}) \) 94 * q - 13 * q^2 + 94 * q^3 + 73 * q^4 - 14 * q^5 - 13 * q^6 - 55 * q^7 - 36 * q^8 + 94 * q^9 - 39 * q^10 - 49 * q^11 + 73 * q^12 - 52 * q^13 - 7 * q^14 - 14 * q^15 + 43 * q^16 - 22 * q^17 - 13 * q^18 - 89 * q^19 - 22 * q^20 - 55 * q^21 - 36 * q^22 - 46 * q^23 - 36 * q^24 + 18 * q^25 + q^26 + 94 * q^27 - 123 * q^28 - 20 * q^29 - 39 * q^30 - 61 * q^31 - 65 * q^32 - 49 * q^33 - 67 * q^34 - 40 * q^35 + 73 * q^36 - 83 * q^37 - 19 * q^38 - 52 * q^39 - 101 * q^40 - 25 * q^41 - 7 * q^42 - 150 * q^43 - 71 * q^44 - 14 * q^45 - 72 * q^46 - 39 * q^47 + 43 * q^48 - q^49 - 45 * q^50 - 22 * q^51 - 110 * q^52 - 30 * q^53 - 13 * q^54 - 54 * q^55 - 5 * q^56 - 89 * q^57 - 77 * q^58 - 43 * q^59 - 22 * q^60 - 109 * q^61 - 33 * q^62 - 55 * q^63 + 10 * q^64 - 66 * q^65 - 36 * q^66 - 155 * q^67 - 46 * q^68 - 46 * q^69 - 43 * q^70 - 27 * q^71 - 36 * q^72 - 157 * q^73 - 29 * q^74 + 18 * q^75 - 176 * q^76 - 9 * q^77 + q^78 - 99 * q^79 - 18 * q^80 + 94 * q^81 - 53 * q^82 - 144 * q^83 - 123 * q^84 - 105 * q^85 + 23 * q^86 - 20 * q^87 - 88 * q^88 - 4 * q^89 - 39 * q^90 - 99 * q^91 - 76 * q^92 - 61 * q^93 - 65 * q^94 - 49 * q^95 - 65 * q^96 - 139 * q^97 - 6 * q^98 - 49 * 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 $

$2$	−2.15634	−1.52476	−0.762381	−	0.647128i	$-0.775970\pi$
$2$	−2.15634	−1.52476	−0.762381	+	0.647128i	$0.775970\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.64980	1.32490
$5$	−1.53192	−0.685096	−0.342548	−	0.939500i	$-0.611290\pi$
$5$	−1.53192	−0.685096	−0.342548	+	0.939500i	$0.611290\pi$
$6$	−2.15634	−0.880322
$7$	−0.507117	−0.191672	−0.0958361	−	0.995397i	$-0.530552\pi$
$7$	−0.507117	−0.191672	−0.0958361	+	0.995397i	$0.530552\pi$
$8$	−1.40120	−0.495397
$9$	1.00000	0.333333
$10$	3.30334	1.04461
$11$	1.74023	0.524699	0.262349	−	0.964973i	$-0.415503\pi$
$11$	1.74023	0.524699	0.262349	+	0.964973i	$0.415503\pi$
$12$	2.64980	0.764932
$13$	−1.52451	−0.422822	−0.211411	−	0.977397i	$-0.567806\pi$
$13$	−1.52451	−0.422822	−0.211411	+	0.977397i	$0.567806\pi$
$14$	1.09352	0.292255
$15$	−1.53192	−0.395540
$16$	−2.27815	−0.569538
$17$	1.16590	0.282773	0.141387	−	0.989954i	$-0.454844\pi$
$17$	1.16590	0.282773	0.141387	+	0.989954i	$0.454844\pi$
$18$	−2.15634	−0.508254
$19$	−0.415640	−0.0953543	−0.0476771	−	0.998863i	$-0.515182\pi$
$19$	−0.415640	−0.0953543	−0.0476771	+	0.998863i	$0.515182\pi$
$20$	−4.05929	−0.907684
$21$	−0.507117	−0.110662
$22$	−3.75253	−0.800041
$23$	−8.97462	−1.87134	−0.935669	−	0.352878i	$-0.885203\pi$
$23$	−8.97462	−1.87134	−0.935669	+	0.352878i	$0.885203\pi$
$24$	−1.40120	−0.286018
$25$	−2.65322	−0.530644
$26$	3.28736	0.644704
$27$	1.00000	0.192450
$28$	−1.34376	−0.253947
$29$	−1.07074	−0.198831	−0.0994154	−	0.995046i	$-0.531697\pi$
$29$	−1.07074	−0.198831	−0.0994154	+	0.995046i	$0.531697\pi$
$30$	3.30334	0.603105
$31$	7.70123	1.38318	0.691591	−	0.722289i	$-0.256910\pi$
$31$	7.70123	1.38318	0.691591	+	0.722289i	$0.256910\pi$
$32$	7.71486	1.36381
$33$	1.74023	0.302935
$34$	−2.51408	−0.431162
$35$	0.776863	0.131314
$36$	2.64980	0.441634
$37$	6.40140	1.05238	0.526192	−	0.850366i	$-0.323619\pi$
$37$	6.40140	1.05238	0.526192	+	0.850366i	$0.323619\pi$
$38$	0.896260	0.145393
$39$	−1.52451	−0.244117
$40$	2.14652	0.339395
$41$	6.40374	1.00010	0.500048	−	0.865998i	$-0.333316\pi$
$41$	6.40374	1.00010	0.500048	+	0.865998i	$0.333316\pi$
$42$	1.09352	0.168733
$43$	−9.27233	−1.41402	−0.707008	−	0.707205i	$-0.749956\pi$
$43$	−9.27233	−1.41402	−0.707008	+	0.707205i	$0.749956\pi$
$44$	4.61126	0.695174
$45$	−1.53192	−0.228365
$46$	19.3523	2.85335
$47$	5.09286	0.742871	0.371435	−	0.928459i	$-0.378866\pi$
$47$	5.09286	0.742871	0.371435	+	0.928459i	$0.378866\pi$
$48$	−2.27815	−0.328823
$49$	−6.74283	−0.963262
$50$	5.72124	0.809106
$51$	1.16590	0.163259
$52$	−4.03964	−0.560198
$53$	11.4016	1.56613	0.783067	−	0.621937i	$-0.213654\pi$
$53$	11.4016	1.56613	0.783067	+	0.621937i	$0.213654\pi$
$54$	−2.15634	−0.293441
$55$	−2.66589	−0.359469
$56$	0.710570	0.0949539
$57$	−0.415640	−0.0550528
$58$	2.30887	0.303170
$59$	10.2104	1.32929	0.664644	−	0.747161i	$-0.268583\pi$
$59$	10.2104	1.32929	0.664644	+	0.747161i	$0.268583\pi$
$60$	−4.05929	−0.524052
$61$	3.05821	0.391563	0.195782	−	0.980648i	$-0.437276\pi$
$61$	3.05821	0.391563	0.195782	+	0.980648i	$0.437276\pi$
$62$	−16.6065	−2.10902
$63$	−0.507117	−0.0638908
$64$	−12.0796	−1.50994
$65$	2.33542	0.289674
$66$	−3.75253	−0.461904
$67$	15.2932	1.86836	0.934178	−	0.356807i	$-0.116135\pi$
$67$	15.2932	1.86836	0.934178	+	0.356807i	$0.116135\pi$
$68$	3.08941	0.374647
$69$	−8.97462	−1.08042
$70$	−1.67518	−0.200223
$71$	−3.39555	−0.402978	−0.201489	−	0.979491i	$-0.564578\pi$
$71$	−3.39555	−0.402978	−0.201489	+	0.979491i	$0.564578\pi$
$72$	−1.40120	−0.165132
$73$	−12.8568	−1.50478	−0.752388	−	0.658720i	$-0.771098\pi$
$73$	−12.8568	−1.50478	−0.752388	+	0.658720i	$0.771098\pi$
$74$	−13.8036	−1.60464
$75$	−2.65322	−0.306367
$76$	−1.10136	−0.126335
$77$	−0.882500	−0.100570
$78$	3.28736	0.372220
$79$	−17.2393	−1.93957	−0.969784	−	0.243964i	$-0.921552\pi$
$79$	−17.2393	−1.93957	−0.969784	+	0.243964i	$0.921552\pi$
$80$	3.48995	0.390188
$81$	1.00000	0.111111
$82$	−13.8086	−1.52491
$83$	2.99279	0.328502	0.164251	−	0.986419i	$-0.447479\pi$
$83$	2.99279	0.328502	0.164251	+	0.986419i	$0.447479\pi$
$84$	−1.34376	−0.146616
$85$	−1.78607	−0.193727
$86$	19.9943	2.15604
$87$	−1.07074	−0.114795
$88$	−2.43840	−0.259934
$89$	2.71575	0.287869	0.143934	−	0.989587i	$-0.454025\pi$
$89$	2.71575	0.287869	0.143934	+	0.989587i	$0.454025\pi$
$90$	3.30334	0.348203
$91$	0.773104	0.0810433
$92$	−23.7810	−2.47934
$93$	7.70123	0.798580
$94$	−10.9819	−1.13270
$95$	0.636727	0.0653268
$96$	7.71486	0.787395
$97$	−8.69139	−0.882477	−0.441238	−	0.897390i	$-0.645461\pi$
$97$	−8.69139	−0.882477	−0.441238	+	0.897390i	$0.645461\pi$
$98$	14.5398	1.46875
$99$	1.74023	0.174900
$100$	−7.03051	−0.703051
$101$	−9.11757	−0.907232	−0.453616	−	0.891197i	$-0.649866\pi$
$101$	−9.11757	−0.907232	−0.453616	+	0.891197i	$0.649866\pi$
$102$	−2.51408	−0.248931
$103$	−19.0964	−1.88162	−0.940812	−	0.338928i	$-0.889936\pi$
$103$	−19.0964	−1.88162	−0.940812	+	0.338928i	$0.889936\pi$
$104$	2.13613	0.209465
$105$	0.776863	0.0758141
$106$	−24.5858	−2.38798
$107$	−8.05230	−0.778445	−0.389222	−	0.921144i	$-0.627256\pi$
$107$	−8.05230	−0.778445	−0.389222	+	0.921144i	$0.627256\pi$
$108$	2.64980	0.254977
$109$	12.7694	1.22309	0.611544	−	0.791210i	$-0.290549\pi$
$109$	12.7694	1.22309	0.611544	+	0.791210i	$0.290549\pi$
$110$	5.74857	0.548105
$111$	6.40140	0.607594
$112$	1.15529	0.109165
$113$	−11.6613	−1.09700	−0.548499	−	0.836151i	$-0.684801\pi$
$113$	−11.6613	−1.09700	−0.548499	+	0.836151i	$0.684801\pi$
$114$	0.896260	0.0839425
$115$	13.7484	1.28205
$116$	−2.83724	−0.263431
$117$	−1.52451	−0.140941
$118$	−22.0172	−2.02685
$119$	−0.591250	−0.0541998
$120$	2.14652	0.195950
$121$	−7.97160	−0.724691
$122$	−6.59453	−0.597041
$123$	6.40374	0.577406
$124$	20.4067	1.83258
$125$	11.7241	1.04864
$126$	1.09352	0.0974183
$127$	0.147545	0.0130925	0.00654624	−	0.999979i	$-0.497916\pi$
$127$	0.147545	0.0130925	0.00654624	+	0.999979i	$0.497916\pi$
$128$	10.6179	0.938500
$129$	−9.27233	−0.816383
$130$	−5.03597	−0.441684
$131$	12.3665	1.08047	0.540234	−	0.841515i	$-0.318336\pi$
$131$	12.3665	1.08047	0.540234	+	0.841515i	$0.318336\pi$
$132$	4.61126	0.401359
$133$	0.210778	0.0182768
$134$	−32.9772	−2.84880
$135$	−1.53192	−0.131847
$136$	−1.63366	−0.140085
$137$	−12.2274	−1.04466	−0.522331	−	0.852743i	$-0.674937\pi$
$137$	−12.2274	−1.04466	−0.522331	+	0.852743i	$0.674937\pi$
$138$	19.3523	1.64738
$139$	−5.28557	−0.448316	−0.224158	−	0.974553i	$-0.571963\pi$
$139$	−5.28557	−0.448316	−0.224158	+	0.974553i	$0.571963\pi$
$140$	2.05853	0.173978
$141$	5.09286	0.428897
$142$	7.32197	0.614446
$143$	−2.65299	−0.221854
$144$	−2.27815	−0.189846
$145$	1.64028	0.136218
$146$	27.7236	2.29443
$147$	−6.74283	−0.556139
$148$	16.9624	1.39430
$149$	−2.78936	−0.228513	−0.114257	−	0.993451i	$-0.536449\pi$
$149$	−2.78936	−0.228513	−0.114257	+	0.993451i	$0.536449\pi$
$150$	5.72124	0.467137
$151$	5.00962	0.407677	0.203839	−	0.979005i	$-0.434658\pi$
$151$	5.00962	0.407677	0.203839	+	0.979005i	$0.434658\pi$
$152$	0.582392	0.0472382
$153$	1.16590	0.0942577
$154$	1.90297	0.153346
$155$	−11.7977	−0.947612
$156$	−4.03964	−0.323430
$157$	21.3647	1.70509	0.852546	−	0.522652i	$-0.175057\pi$
$157$	21.3647	1.70509	0.852546	+	0.522652i	$0.175057\pi$
$158$	37.1737	2.95738
$159$	11.4016	0.904208
$160$	−11.8186	−0.934339
$161$	4.55119	0.358684
$162$	−2.15634	−0.169418
$163$	1.37421	0.107637	0.0538184	−	0.998551i	$-0.482861\pi$
$163$	1.37421	0.107637	0.0538184	+	0.998551i	$0.482861\pi$
$164$	16.9686	1.32503
$165$	−2.66589	−0.207539
$166$	−6.45348	−0.500887
$167$	−9.06389	−0.701385	−0.350692	−	0.936491i	$-0.614054\pi$
$167$	−9.06389	−0.701385	−0.350692	+	0.936491i	$0.614054\pi$
$168$	0.710570	0.0548217
$169$	−10.6759	−0.821221
$170$	3.85138	0.295387
$171$	−0.415640	−0.0317848
$172$	−24.5698	−1.87343
$173$	−8.39099	−0.637955	−0.318978	−	0.947762i	$-0.603339\pi$
$173$	−8.39099	−0.637955	−0.318978	+	0.947762i	$0.603339\pi$
$174$	2.30887	0.175035
$175$	1.34549	0.101710
$176$	−3.96451	−0.298836
$177$	10.2104	0.767464
$178$	−5.85607	−0.438931
$179$	6.04966	0.452173	0.226087	−	0.974107i	$-0.427407\pi$
$179$	6.04966	0.452173	0.226087	+	0.974107i	$0.427407\pi$
$180$	−4.05929	−0.302561
$181$	7.16746	0.532753	0.266376	−	0.963869i	$-0.414174\pi$
$181$	7.16746	0.532753	0.266376	+	0.963869i	$0.414174\pi$
$182$	−1.66708	−0.123572
$183$	3.05821	0.226069
$184$	12.5752	0.927056
$185$	−9.80644	−0.720983
$186$	−16.6065	−1.21765
$187$	2.02894	0.148371
$188$	13.4951	0.984230
$189$	−0.507117	−0.0368874
$190$	−1.37300	−0.0996079
$191$	7.67028	0.555002	0.277501	−	0.960725i	$-0.410494\pi$
$191$	7.67028	0.555002	0.277501	+	0.960725i	$0.410494\pi$
$192$	−12.0796	−0.871767
$193$	25.9572	1.86844	0.934220	−	0.356698i	$-0.116098\pi$
$193$	25.9572	1.86844	0.934220	+	0.356698i	$0.116098\pi$
$194$	18.7416	1.34557
$195$	2.33542	0.167243
$196$	−17.8672	−1.27623
$197$	15.9881	1.13911	0.569554	−	0.821954i	$-0.307116\pi$
$197$	15.9881	1.13911	0.569554	+	0.821954i	$0.307116\pi$
$198$	−3.75253	−0.266680
$199$	−0.983774	−0.0697379	−0.0348690	−	0.999392i	$-0.511101\pi$
$199$	−0.983774	−0.0697379	−0.0348690	+	0.999392i	$0.511101\pi$
$200$	3.71768	0.262880
$201$	15.2932	1.07870
$202$	19.6606	1.38331
$203$	0.542989	0.0381103
$204$	3.08941	0.216302
$205$	−9.81002	−0.685162
$206$	41.1783	2.86903
$207$	−8.97462	−0.623780
$208$	3.47306	0.240813
$209$	−0.723308	−0.0500323
$210$	−1.67518	−0.115599
$211$	3.92310	0.270077	0.135039	−	0.990840i	$-0.456884\pi$
$211$	3.92310	0.270077	0.135039	+	0.990840i	$0.456884\pi$
$212$	30.2121	2.07497
$213$	−3.39555	−0.232659
$214$	17.3635	1.18694
$215$	14.2045	0.968737
$216$	−1.40120	−0.0953393
$217$	−3.90543	−0.265118
$218$	−27.5352	−1.86492
$219$	−12.8568	−0.868783
$220$	−7.06409	−0.476261
$221$	−1.77743	−0.119563
$222$	−13.8036	−0.926437
$223$	−21.9998	−1.47322	−0.736608	−	0.676320i	$-0.763574\pi$
$223$	−21.9998	−1.47322	−0.736608	+	0.676320i	$0.763574\pi$
$224$	−3.91234	−0.261404
$225$	−2.65322	−0.176881
$226$	25.1456	1.67266
$227$	−15.5299	−1.03076	−0.515378	−	0.856963i	$-0.672349\pi$
$227$	−15.5299	−1.03076	−0.515378	+	0.856963i	$0.672349\pi$
$228$	−1.10136	−0.0729395
$229$	−1.11544	−0.0737106	−0.0368553	−	0.999321i	$-0.511734\pi$
$229$	−1.11544	−0.0737106	−0.0368553	+	0.999321i	$0.511734\pi$
$230$	−29.6463	−1.95482
$231$	−0.882500	−0.0580642
$232$	1.50031	0.0985002
$233$	14.4997	0.949907	0.474954	−	0.880011i	$-0.342465\pi$
$233$	14.4997	0.949907	0.474954	+	0.880011i	$0.342465\pi$
$234$	3.28736	0.214901
$235$	−7.80186	−0.508937
$236$	27.0557	1.76117
$237$	−17.2393	−1.11981
$238$	1.27494	0.0826418
$239$	2.52868	0.163567	0.0817833	−	0.996650i	$-0.473938\pi$
$239$	2.52868	0.163567	0.0817833	+	0.996650i	$0.473938\pi$
$240$	3.48995	0.225275
$241$	−6.56067	−0.422610	−0.211305	−	0.977420i	$-0.567771\pi$
$241$	−6.56067	−0.422610	−0.211305	+	0.977420i	$0.567771\pi$
$242$	17.1895	1.10498
$243$	1.00000	0.0641500
$244$	8.10365	0.518783
$245$	10.3295	0.659927
$246$	−13.8086	−0.880407
$247$	0.633646	0.0403179
$248$	−10.7909	−0.685225
$249$	2.99279	0.189660
$250$	−25.2812	−1.59892
$251$	9.21874	0.581882	0.290941	−	0.956741i	$-0.406032\pi$
$251$	9.21874	0.581882	0.290941	+	0.956741i	$0.406032\pi$
$252$	−1.34376	−0.0846490
$253$	−15.6179	−0.981889
$254$	−0.318157	−0.0199629
$255$	−1.78607	−0.111848
$256$	1.26328	0.0789549
$257$	−23.4587	−1.46332	−0.731658	−	0.681672i	$-0.761253\pi$
$257$	−23.4587	−1.46332	−0.731658	+	0.681672i	$0.761253\pi$
$258$	19.9943	1.24479
$259$	−3.24626	−0.201713
$260$	6.18841	0.383789
$261$	−1.07074	−0.0662769
$262$	−26.6664	−1.64746
$263$	8.89703	0.548614	0.274307	−	0.961642i	$-0.411552\pi$
$263$	8.89703	0.548614	0.274307	+	0.961642i	$0.411552\pi$
$264$	−2.43840	−0.150073
$265$	−17.4664	−1.07295
$266$	−0.454509	−0.0278677
$267$	2.71575	0.166201
$268$	40.5238	2.47539
$269$	7.99265	0.487321	0.243660	−	0.969861i	$-0.421652\pi$
$269$	7.99265	0.487321	0.243660	+	0.969861i	$0.421652\pi$
$270$	3.30334	0.201035
$271$	−31.9220	−1.93912	−0.969561	−	0.244851i	$-0.921261\pi$
$271$	−31.9220	−1.93912	−0.969561	+	0.244851i	$0.921261\pi$
$272$	−2.65611	−0.161050
$273$	0.773104	0.0467904
$274$	26.3665	1.59286
$275$	−4.61721	−0.278428
$276$	−23.7810	−1.43145
$277$	−8.99727	−0.540594	−0.270297	−	0.962777i	$-0.587122\pi$
$277$	−8.99727	−0.540594	−0.270297	+	0.962777i	$0.587122\pi$
$278$	11.3975	0.683576
$279$	7.70123	0.461061
$280$	−1.08854	−0.0650525
$281$	9.83739	0.586849	0.293425	−	0.955982i	$-0.405205\pi$
$281$	9.83739	0.586849	0.293425	+	0.955982i	$0.405205\pi$
$282$	−10.9819	−0.653965
$283$	−25.1292	−1.49378	−0.746888	−	0.664950i	$-0.768453\pi$
$283$	−25.1292	−1.49378	−0.746888	+	0.664950i	$0.768453\pi$
$284$	−8.99754	−0.533906
$285$	0.636727	0.0377164
$286$	5.72075	0.338275
$287$	−3.24745	−0.191691
$288$	7.71486	0.454602
$289$	−15.6407	−0.920039
$290$	−3.53701	−0.207700
$291$	−8.69139	−0.509498
$292$	−34.0680	−1.99368
$293$	22.7649	1.32994	0.664971	−	0.746869i	$-0.268444\pi$
$293$	22.7649	1.32994	0.664971	+	0.746869i	$0.268444\pi$
$294$	14.5398	0.847981
$295$	−15.6416	−0.910689
$296$	−8.96961	−0.521348
$297$	1.74023	0.100978
$298$	6.01481	0.348429
$299$	13.6819	0.791244
$300$	−7.03051	−0.405906
$301$	4.70216	0.271028
$302$	−10.8024	−0.621611
$303$	−9.11757	−0.523791
$304$	0.946890	0.0543079
$305$	−4.68493	−0.268258
$306$	−2.51408	−0.143721
$307$	−24.9987	−1.42675	−0.713376	−	0.700782i	$-0.752835\pi$
$307$	−24.9987	−1.42675	−0.713376	+	0.700782i	$0.752835\pi$
$308$	−2.33845	−0.133246
$309$	−19.0964	−1.08636
$310$	25.4398	1.44488
$311$	6.44646	0.365545	0.182773	−	0.983155i	$-0.441493\pi$
$311$	6.44646	0.365545	0.182773	+	0.983155i	$0.441493\pi$
$312$	2.13613	0.120935
$313$	−6.52481	−0.368804	−0.184402	−	0.982851i	$-0.559035\pi$
$313$	−6.52481	−0.368804	−0.184402	+	0.982851i	$0.559035\pi$
$314$	−46.0697	−2.59986
$315$	0.776863	0.0437713
$316$	−45.6806	−2.56974
$317$	10.3024	0.578640	0.289320	−	0.957232i	$-0.406571\pi$
$317$	10.3024	0.578640	0.289320	+	0.957232i	$0.406571\pi$
$318$	−24.5858	−1.37870
$319$	−1.86333	−0.104326
$320$	18.5049	1.03446
$321$	−8.05230	−0.449435
$322$	−9.81391	−0.546908
$323$	−0.484596	−0.0269636
$324$	2.64980	0.147211
$325$	4.04485	0.224368
$326$	−2.96327	−0.164121
$327$	12.7694	0.706150
$328$	−8.97289	−0.495445
$329$	−2.58268	−0.142388
$330$	5.74857	0.316448
$331$	18.9992	1.04429	0.522145	−	0.852856i	$-0.325132\pi$
$331$	18.9992	1.04429	0.522145	+	0.852856i	$0.325132\pi$
$332$	7.93031	0.435232
$333$	6.40140	0.350794
$334$	19.5448	1.06945
$335$	−23.4279	−1.28000
$336$	1.15529	0.0630262
$337$	−23.1698	−1.26214	−0.631070	−	0.775726i	$-0.717384\pi$
$337$	−23.1698	−1.26214	−0.631070	+	0.775726i	$0.717384\pi$
$338$	23.0208	1.25217
$339$	−11.6613	−0.633352
$340$	−4.73274	−0.256669
$341$	13.4019	0.725754
$342$	0.896260	0.0484642
$343$	6.96923	0.376303
$344$	12.9923	0.700500
$345$	13.7484	0.740190
$346$	18.0938	0.972730
$347$	22.3559	1.20012	0.600062	−	0.799953i	$-0.295142\pi$
$347$	22.3559	1.20012	0.600062	+	0.799953i	$0.295142\pi$
$348$	−2.83724	−0.152092
$349$	9.79732	0.524438	0.262219	−	0.965008i	$-0.415546\pi$
$349$	9.79732	0.524438	0.262219	+	0.965008i	$0.415546\pi$
$350$	−2.90134	−0.155083
$351$	−1.52451	−0.0813722
$352$	13.4256	0.715588
$353$	−9.96597	−0.530435	−0.265217	−	0.964189i	$-0.585444\pi$
$353$	−9.96597	−0.530435	−0.265217	+	0.964189i	$0.585444\pi$
$354$	−22.0172	−1.17020
$355$	5.20172	0.276079
$356$	7.19619	0.381397
$357$	−0.591250	−0.0312923
$358$	−13.0451	−0.689457
$359$	−25.8677	−1.36525	−0.682624	−	0.730770i	$-0.739161\pi$
$359$	−25.8677	−1.36525	−0.682624	+	0.730770i	$0.739161\pi$
$360$	2.14652	0.113132
$361$	−18.8272	−0.990908
$362$	−15.4555	−0.812322
$363$	−7.97160	−0.418401
$364$	2.04857	0.107374
$365$	19.6956	1.03092
$366$	−6.59453	−0.344702
$367$	2.69401	0.140626	0.0703132	−	0.997525i	$-0.477600\pi$
$367$	2.69401	0.140626	0.0703132	+	0.997525i	$0.477600\pi$
$368$	20.4456	1.06580
$369$	6.40374	0.333365
$370$	21.1460	1.09933
$371$	−5.78197	−0.300185
$372$	20.4067	1.05804
$373$	−11.8768	−0.614959	−0.307480	−	0.951555i	$-0.599486\pi$
$373$	−11.8768	−0.614959	−0.307480	+	0.951555i	$0.599486\pi$
$374$	−4.37508	−0.226230
$375$	11.7241	0.605431
$376$	−7.13610	−0.368016
$377$	1.63235	0.0840701
$378$	1.09352	0.0562445
$379$	14.0258	0.720456	0.360228	−	0.932864i	$-0.382699\pi$
$379$	14.0258	0.720456	0.360228	+	0.932864i	$0.382699\pi$
$380$	1.68720	0.0865516
$381$	0.147545	0.00755894
$382$	−16.5397	−0.846246
$383$	−12.4590	−0.636626	−0.318313	−	0.947986i	$-0.603116\pi$
$383$	−12.4590	−0.636626	−0.318313	+	0.947986i	$0.603116\pi$
$384$	10.6179	0.541843
$385$	1.35192	0.0689002
$386$	−55.9725	−2.84893
$387$	−9.27233	−0.471339
$388$	−23.0305	−1.16919
$389$	−12.2921	−0.623233	−0.311617	−	0.950208i	$-0.600870\pi$
$389$	−12.2921	−0.623233	−0.311617	+	0.950208i	$0.600870\pi$
$390$	−5.03597	−0.255006
$391$	−10.4635	−0.529164
$392$	9.44802	0.477197
$393$	12.3665	0.623808
$394$	−34.4759	−1.73687
$395$	26.4092	1.32879
$396$	4.61126	0.231725
$397$	−28.7482	−1.44283	−0.721416	−	0.692502i	$-0.756508\pi$
$397$	−28.7482	−1.44283	−0.721416	+	0.692502i	$0.756508\pi$
$398$	2.12135	0.106334
$399$	0.210778	0.0105521
$400$	6.04443	0.302222
$401$	−4.96437	−0.247909	−0.123954	−	0.992288i	$-0.539558\pi$
$401$	−4.96437	−0.247909	−0.123954	+	0.992288i	$0.539558\pi$
$402$	−32.9772	−1.64476
$403$	−11.7406	−0.584840
$404$	−24.1598	−1.20199
$405$	−1.53192	−0.0761218
$406$	−1.17087	−0.0581092
$407$	11.1399	0.552184
$408$	−1.63366	−0.0808782
$409$	29.8008	1.47356	0.736778	−	0.676135i	$-0.236346\pi$
$409$	29.8008	1.47356	0.736778	+	0.676135i	$0.236346\pi$
$410$	21.1537	1.04471
$411$	−12.2274	−0.603135
$412$	−50.6017	−2.49297
$413$	−5.17789	−0.254788
$414$	19.3523	0.951116
$415$	−4.58472	−0.225055
$416$	−11.7614	−0.576648
$417$	−5.28557	−0.258836
$418$	1.55970	0.0762873
$419$	−30.9202	−1.51055	−0.755276	−	0.655406i	$-0.772497\pi$
$419$	−30.9202	−1.51055	−0.755276	+	0.655406i	$0.772497\pi$
$420$	2.05853	0.100446
$421$	1.98733	0.0968566	0.0484283	−	0.998827i	$-0.484579\pi$
$421$	1.98733	0.0968566	0.0484283	+	0.998827i	$0.484579\pi$
$422$	−8.45954	−0.411804
$423$	5.09286	0.247624
$424$	−15.9759	−0.775859
$425$	−3.09340	−0.150052
$426$	7.32197	0.354750
$427$	−1.55087	−0.0750518
$428$	−21.3370	−1.03136
$429$	−2.65299	−0.128088
$430$	−30.6297	−1.47709
$431$	−34.8204	−1.67724	−0.838619	−	0.544719i	$-0.816636\pi$
$431$	−34.8204	−1.67724	−0.838619	+	0.544719i	$0.816636\pi$
$432$	−2.27815	−0.109608
$433$	−36.8059	−1.76878	−0.884389	−	0.466751i	$-0.845424\pi$
$433$	−36.8059	−1.76878	−0.884389	+	0.466751i	$0.845424\pi$
$434$	8.42143	0.404242
$435$	1.64028	0.0786456
$436$	33.8364	1.62047
$437$	3.73021	0.178440
$438$	27.7236	1.32469
$439$	−5.35475	−0.255568	−0.127784	−	0.991802i	$-0.540786\pi$
$439$	−5.35475	−0.255568	−0.127784	+	0.991802i	$0.540786\pi$
$440$	3.73544	0.178080
$441$	−6.74283	−0.321087
$442$	3.83274	0.182305
$443$	32.7767	1.55727	0.778634	−	0.627478i	$-0.215913\pi$
$443$	32.7767	1.55727	0.778634	+	0.627478i	$0.215913\pi$
$444$	16.9624	0.805002
$445$	−4.16031	−0.197218
$446$	47.4391	2.24630
$447$	−2.78936	−0.131932
$448$	6.12575	0.289415
$449$	−23.5880	−1.11319	−0.556594	−	0.830784i	$-0.687892\pi$
$449$	−23.5880	−1.11319	−0.556594	+	0.830784i	$0.687892\pi$
$450$	5.72124	0.269702
$451$	11.1440	0.524749
$452$	−30.9000	−1.45341
$453$	5.00962	0.235373
$454$	33.4878	1.57166
$455$	−1.18433	−0.0555224
$456$	0.582392	0.0272730
$457$	15.9542	0.746304	0.373152	−	0.927770i	$-0.378277\pi$
$457$	15.9542	0.746304	0.373152	+	0.927770i	$0.378277\pi$
$458$	2.40527	0.112391
$459$	1.16590	0.0544197
$460$	36.4306	1.69858
$461$	7.97406	0.371389	0.185694	−	0.982608i	$-0.440547\pi$
$461$	7.97406	0.371389	0.185694	+	0.982608i	$0.440547\pi$
$462$	1.90297	0.0885342
$463$	6.27960	0.291838	0.145919	−	0.989297i	$-0.453386\pi$
$463$	6.27960	0.291838	0.145919	+	0.989297i	$0.453386\pi$
$464$	2.43930	0.113242
$465$	−11.7977	−0.547104
$466$	−31.2663	−1.44838
$467$	16.6738	0.771571	0.385786	−	0.922588i	$-0.373930\pi$
$467$	16.6738	0.771571	0.385786	+	0.922588i	$0.373930\pi$
$468$	−4.03964	−0.186733
$469$	−7.75542	−0.358112
$470$	16.8235	0.776009
$471$	21.3647	0.984435
$472$	−14.3068	−0.658525
$473$	−16.1360	−0.741933
$474$	37.1737	1.70745
$475$	1.10278	0.0505991
$476$	−1.56670	−0.0718094
$477$	11.4016	0.522045
$478$	−5.45269	−0.249400
$479$	23.5075	1.07409	0.537043	−	0.843555i	$-0.319541\pi$
$479$	23.5075	1.07409	0.537043	+	0.843555i	$0.319541\pi$
$480$	−11.8186	−0.539441
$481$	−9.75898	−0.444971
$482$	14.1470	0.644380
$483$	4.55119	0.207086
$484$	−21.1232	−0.960144
$485$	13.3145	0.604581
$486$	−2.15634	−0.0978136
$487$	−34.2215	−1.55073	−0.775363	−	0.631516i	$-0.782433\pi$
$487$	−34.2215	−1.55073	−0.775363	+	0.631516i	$0.782433\pi$
$488$	−4.28515	−0.193979
$489$	1.37421	0.0621441
$490$	−22.2739	−1.00623
$491$	12.7393	0.574916	0.287458	−	0.957793i	$-0.407190\pi$
$491$	12.7393	0.574916	0.287458	+	0.957793i	$0.407190\pi$
$492$	16.9686	0.765006
$493$	−1.24838	−0.0562240
$494$	−1.36636	−0.0614752
$495$	−2.66589	−0.119823
$496$	−17.5446	−0.787775
$497$	1.72194	0.0772397
$498$	−6.45348	−0.289187
$499$	−26.0208	−1.16485	−0.582426	−	0.812884i	$-0.697896\pi$
$499$	−26.0208	−1.16485	−0.582426	+	0.812884i	$0.697896\pi$
$500$	31.0666	1.38934
$501$	−9.06389	−0.404945
$502$	−19.8787	−0.887232
$503$	−12.0559	−0.537546	−0.268773	−	0.963203i	$-0.586618\pi$
$503$	−12.0559	−0.537546	−0.268773	+	0.963203i	$0.586618\pi$
$504$	0.710570	0.0316513
$505$	13.9674	0.621541
$506$	33.6775	1.49715
$507$	−10.6759	−0.474132
$508$	0.390964	0.0173462
$509$	31.8516	1.41180	0.705899	−	0.708313i	$-0.250543\pi$
$509$	31.8516	1.41180	0.705899	+	0.708313i	$0.250543\pi$
$510$	3.85138	0.170542
$511$	6.51991	0.288424
$512$	−23.9599	−1.05889
$513$	−0.415640	−0.0183509
$514$	50.5850	2.23121
$515$	29.2542	1.28909
$516$	−24.5698	−1.08163
$517$	8.86275	0.389783
$518$	7.00004	0.307564
$519$	−8.39099	−0.368324
$520$	−3.27239	−0.143504
$521$	−17.9905	−0.788176	−0.394088	−	0.919073i	$-0.628939\pi$
$521$	−17.9905	−0.788176	−0.394088	+	0.919073i	$0.628939\pi$
$522$	2.30887	0.101057
$523$	−31.1382	−1.36158	−0.680789	−	0.732480i	$-0.738363\pi$
$523$	−31.1382	−1.36158	−0.680789	+	0.732480i	$0.738363\pi$
$524$	32.7688	1.43151
$525$	1.34549	0.0587221
$526$	−19.1850	−0.836507
$527$	8.97889	0.391127
$528$	−3.96451	−0.172533
$529$	57.5439	2.50191
$530$	37.6635	1.63600
$531$	10.2104	0.443096
$532$	0.558520	0.0242149
$533$	−9.76255	−0.422863
$534$	−5.85607	−0.253417
$535$	12.3355	0.533309
$536$	−21.4287	−0.925579
$537$	6.04966	0.261062
$538$	−17.2349	−0.743048
$539$	−11.7341	−0.505422
$540$	−4.05929	−0.174684
$541$	−21.7233	−0.933956	−0.466978	−	0.884269i	$-0.654657\pi$
$541$	−21.7233	−0.933956	−0.466978	+	0.884269i	$0.654657\pi$
$542$	68.8346	2.95670
$543$	7.16746	0.307585
$544$	8.99478	0.385648
$545$	−19.5617	−0.837933
$546$	−1.66708	−0.0713442
$547$	−13.1559	−0.562506	−0.281253	−	0.959634i	$-0.590750\pi$
$547$	−13.1559	−0.562506	−0.281253	+	0.959634i	$0.590750\pi$
$548$	−32.4003	−1.38407
$549$	3.05821	0.130521
$550$	9.95627	0.424537
$551$	0.445040	0.0189594
$552$	12.5752	0.535236
$553$	8.74233	0.371762
$554$	19.4012	0.824277
$555$	−9.80644	−0.416260
$556$	−14.0057	−0.593975
$557$	−41.0885	−1.74097	−0.870487	−	0.492192i	$-0.836196\pi$
$557$	−41.0885	−1.74097	−0.870487	+	0.492192i	$0.836196\pi$
$558$	−16.6065	−0.703008
$559$	14.1357	0.597878
$560$	−1.76981	−0.0747882
$561$	2.02894	0.0856619
$562$	−21.2127	−0.894806
$563$	−10.3282	−0.435281	−0.217641	−	0.976029i	$-0.569836\pi$
$563$	−10.3282	−0.435281	−0.217641	+	0.976029i	$0.569836\pi$
$564$	13.4951	0.568246
$565$	17.8641	0.751549
$566$	54.1871	2.27765
$567$	−0.507117	−0.0212969
$568$	4.75783	0.199634
$569$	5.71841	0.239728	0.119864	−	0.992790i	$-0.461754\pi$
$569$	5.71841	0.239728	0.119864	+	0.992790i	$0.461754\pi$
$570$	−1.37300	−0.0575086
$571$	−19.4582	−0.814300	−0.407150	−	0.913361i	$-0.633477\pi$
$571$	−19.4582	−0.814300	−0.407150	+	0.913361i	$0.633477\pi$
$572$	−7.02991	−0.293935
$573$	7.67028	0.320431
$574$	7.00260	0.292283
$575$	23.8116	0.993014
$576$	−12.0796	−0.503315
$577$	−3.02048	−0.125744	−0.0628722	−	0.998022i	$-0.520026\pi$
$577$	−3.02048	−0.125744	−0.0628722	+	0.998022i	$0.520026\pi$
$578$	33.7266	1.40284
$579$	25.9572	1.07874
$580$	4.34643	0.180476
$581$	−1.51770	−0.0629646
$582$	18.7416	0.776864
$583$	19.8415	0.821749
$584$	18.0149	0.745462
$585$	2.33542	0.0965579
$586$	−49.0890	−2.02785
$587$	36.5876	1.51013	0.755066	−	0.655649i	$-0.227605\pi$
$587$	36.5876	1.51013	0.755066	+	0.655649i	$0.227605\pi$
$588$	−17.8672	−0.736830
$589$	−3.20094	−0.131892
$590$	33.7286	1.38858
$591$	15.9881	0.657664
$592$	−14.5834	−0.599372
$593$	−20.5737	−0.844862	−0.422431	−	0.906395i	$-0.638823\pi$
$593$	−20.5737	−0.844862	−0.422431	+	0.906395i	$0.638823\pi$
$594$	−3.75253	−0.153968
$595$	0.905748	0.0371320
$596$	−7.39125	−0.302758
$597$	−0.983774	−0.0402632
$598$	−29.5028	−1.20646
$599$	−15.5515	−0.635415	−0.317708	−	0.948189i	$-0.602913\pi$
$599$	−15.5515	−0.635415	−0.317708	+	0.948189i	$0.602913\pi$
$600$	3.71768	0.151774
$601$	3.34263	0.136349	0.0681743	−	0.997673i	$-0.478283\pi$
$601$	3.34263	0.136349	0.0681743	+	0.997673i	$0.478283\pi$
$602$	−10.1394	−0.413253
$603$	15.2932	0.622785
$604$	13.2745	0.540132
$605$	12.2119	0.496483
$606$	19.6606	0.798657
$607$	20.9847	0.851741	0.425871	−	0.904784i	$-0.359968\pi$
$607$	20.9847	0.851741	0.425871	+	0.904784i	$0.359968\pi$
$608$	−3.20660	−0.130045
$609$	0.542989	0.0220030
$610$	10.1023	0.409030
$611$	−7.76411	−0.314102
$612$	3.08941	0.124882
$613$	8.42188	0.340156	0.170078	−	0.985431i	$-0.445598\pi$
$613$	8.42188	0.340156	0.170078	+	0.985431i	$0.445598\pi$
$614$	53.9057	2.17546
$615$	−9.81002	−0.395578
$616$	1.23656	0.0498222
$617$	−45.0309	−1.81288	−0.906439	−	0.422337i	$-0.861210\pi$
$617$	−45.0309	−1.81288	−0.906439	+	0.422337i	$0.861210\pi$
$618$	41.1783	1.65644
$619$	6.13810	0.246711	0.123355	−	0.992363i	$-0.460634\pi$
$619$	6.13810	0.246711	0.123355	+	0.992363i	$0.460634\pi$
$620$	−31.2615	−1.25549
$621$	−8.97462	−0.360139
$622$	−13.9008	−0.557370
$623$	−1.37720	−0.0551764
$624$	3.47306	0.139034
$625$	−4.69434	−0.187773
$626$	14.0697	0.562339
$627$	−0.723308	−0.0288861
$628$	56.6124	2.25908
$629$	7.46341	0.297586
$630$	−1.67518	−0.0667408
$631$	13.3837	0.532797	0.266399	−	0.963863i	$-0.414166\pi$
$631$	13.3837	0.532797	0.266399	+	0.963863i	$0.414166\pi$
$632$	24.1556	0.960857
$633$	3.92310	0.155929
$634$	−22.2155	−0.882288
$635$	−0.226027	−0.00896960
$636$	30.2121	1.19799
$637$	10.2795	0.407289
$638$	4.01797	0.159073
$639$	−3.39555	−0.134326
$640$	−16.2658	−0.642962
$641$	10.0570	0.397227	0.198614	−	0.980078i	$-0.436356\pi$
$641$	10.0570	0.397227	0.198614	+	0.980078i	$0.436356\pi$
$642$	17.3635	0.685282
$643$	−1.80557	−0.0712047	−0.0356023	−	0.999366i	$-0.511335\pi$
$643$	−1.80557	−0.0712047	−0.0356023	+	0.999366i	$0.511335\pi$
$644$	12.0597	0.475221
$645$	14.2045	0.559300
$646$	1.04495	0.0411131
$647$	14.9686	0.588476	0.294238	−	0.955732i	$-0.404934\pi$
$647$	14.9686	0.588476	0.294238	+	0.955732i	$0.404934\pi$
$648$	−1.40120	−0.0550442
$649$	17.7685	0.697475
$650$	−8.72208	−0.342108
$651$	−3.90543	−0.153066
$652$	3.64140	0.142608
$653$	14.2369	0.557135	0.278567	−	0.960417i	$-0.410140\pi$
$653$	14.2369	0.557135	0.278567	+	0.960417i	$0.410140\pi$
$654$	−27.5352	−1.07671
$655$	−18.9445	−0.740224
$656$	−14.5887	−0.569593
$657$	−12.8568	−0.501592
$658$	5.56913	0.217107
$659$	−17.3667	−0.676512	−0.338256	−	0.941054i	$-0.609837\pi$
$659$	−17.3667	−0.676512	−0.338256	+	0.941054i	$0.609837\pi$
$660$	−7.06409	−0.274969
$661$	48.2953	1.87847	0.939236	−	0.343273i	$-0.111536\pi$
$661$	48.2953	1.87847	0.939236	+	0.343273i	$0.111536\pi$
$662$	−40.9688	−1.59230
$663$	−1.77743	−0.0690296
$664$	−4.19348	−0.162739
$665$	−0.322895	−0.0125213
$666$	−13.8036	−0.534878
$667$	9.60946	0.372080
$668$	−24.0175	−0.929265
$669$	−21.9998	−0.850562
$670$	50.5185	1.95170
$671$	5.32198	0.205453
$672$	−3.91234	−0.150922
$673$	−43.6224	−1.68152	−0.840760	−	0.541408i	$-0.817891\pi$
$673$	−43.6224	−1.68152	−0.840760	+	0.541408i	$0.817891\pi$
$674$	49.9620	1.92446
$675$	−2.65322	−0.102122
$676$	−28.2890	−1.08804
$677$	−38.3952	−1.47565	−0.737824	−	0.674993i	$-0.764147\pi$
$677$	−38.3952	−1.47565	−0.737824	+	0.674993i	$0.764147\pi$
$678$	25.1456	0.965712
$679$	4.40755	0.169146
$680$	2.50264	0.0959717
$681$	−15.5299	−0.595108
$682$	−28.8991	−1.10660
$683$	−16.4368	−0.628936	−0.314468	−	0.949268i	$-0.601826\pi$
$683$	−16.4368	−0.628936	−0.314468	+	0.949268i	$0.601826\pi$
$684$	−1.10136	−0.0421117
$685$	18.7315	0.715693
$686$	−15.0280	−0.573773
$687$	−1.11544	−0.0425568
$688$	21.1238	0.805336
$689$	−17.3819	−0.662197
$690$	−29.6463	−1.12861
$691$	−44.7831	−1.70363	−0.851815	−	0.523843i	$-0.824498\pi$
$691$	−44.7831	−1.70363	−0.851815	+	0.523843i	$0.824498\pi$
$692$	−22.2345	−0.845228
$693$	−0.882500	−0.0335234
$694$	−48.2068	−1.82991
$695$	8.09708	0.307140
$696$	1.50031	0.0568691
$697$	7.46614	0.282800
$698$	−21.1263	−0.799644
$699$	14.4997	0.548429
$700$	3.56529	0.134755
$701$	−1.15105	−0.0434746	−0.0217373	−	0.999764i	$-0.506920\pi$
$701$	−1.15105	−0.0434746	−0.0217373	+	0.999764i	$0.506920\pi$
$702$	3.28736	0.124073
$703$	−2.66067	−0.100349
$704$	−21.0212	−0.792266
$705$	−7.80186	−0.293835
$706$	21.4900	0.808787
$707$	4.62368	0.173891
$708$	27.0557	1.01681
$709$	−26.9139	−1.01077	−0.505386	−	0.862894i	$-0.668650\pi$
$709$	−26.9139	−1.01077	−0.505386	+	0.862894i	$0.668650\pi$
$710$	−11.2167	−0.420954
$711$	−17.2393	−0.646523
$712$	−3.80529	−0.142609
$713$	−69.1157	−2.58840
$714$	1.27494	0.0477133
$715$	4.06417	0.151992
$716$	16.0304	0.599085
$717$	2.52868	0.0944352
$718$	55.7797	2.08168
$719$	11.0050	0.410418	0.205209	−	0.978718i	$-0.434213\pi$
$719$	11.0050	0.410418	0.205209	+	0.978718i	$0.434213\pi$
$720$	3.48995	0.130063
$721$	9.68411	0.360655
$722$	40.5979	1.51090
$723$	−6.56067	−0.243994
$724$	18.9923	0.705845
$725$	2.84090	0.105508
$726$	17.1895	0.637962
$727$	23.4790	0.870787	0.435394	−	0.900240i	$-0.356609\pi$
$727$	23.4790	0.870787	0.435394	+	0.900240i	$0.356609\pi$
$728$	−1.08327	−0.0401487
$729$	1.00000	0.0370370
$730$	−42.4704	−1.57190
$731$	−10.8106	−0.399846
$732$	8.10365	0.299519
$733$	−27.4794	−1.01497	−0.507487	−	0.861659i	$-0.669426\pi$
$733$	−27.4794	−1.01497	−0.507487	+	0.861659i	$0.669426\pi$
$734$	−5.80921	−0.214422
$735$	10.3295	0.381009
$736$	−69.2380	−2.55215
$737$	26.6136	0.980324
$738$	−13.8086	−0.508303
$739$	−38.4639	−1.41492	−0.707458	−	0.706756i	$-0.750158\pi$
$739$	−38.4639	−1.41492	−0.707458	+	0.706756i	$0.750158\pi$
$740$	−25.9851	−0.955232
$741$	0.633646	0.0232776
$742$	12.4679	0.457710
$743$	−45.9341	−1.68516	−0.842579	−	0.538573i	$-0.818964\pi$
$743$	−45.9341	−1.68516	−0.842579	+	0.538573i	$0.818964\pi$
$744$	−10.7909	−0.395615
$745$	4.27308	0.156553
$746$	25.6105	0.937667
$747$	2.99279	0.109501
$748$	5.37629	0.196577
$749$	4.08346	0.149206
$750$	−25.2812	−0.923139
$751$	−3.94521	−0.143963	−0.0719814	−	0.997406i	$-0.522932\pi$
$751$	−3.94521	−0.143963	−0.0719814	+	0.997406i	$0.522932\pi$
$752$	−11.6023	−0.423093
$753$	9.21874	0.335950
$754$	−3.51989	−0.128187
$755$	−7.67434	−0.279298
$756$	−1.34376	−0.0488721
$757$	5.09190	0.185068	0.0925341	−	0.995710i	$-0.470503\pi$
$757$	5.09190	0.185068	0.0925341	+	0.995710i	$0.470503\pi$
$758$	−30.2443	−1.09852
$759$	−15.6179	−0.566894
$760$	−0.892179	−0.0323627
$761$	−22.0936	−0.800893	−0.400447	−	0.916320i	$-0.631145\pi$
$761$	−22.0936	−0.800893	−0.400447	+	0.916320i	$0.631145\pi$
$762$	−0.318157	−0.0115256
$763$	−6.47559	−0.234432
$764$	20.3247	0.735323
$765$	−1.78607	−0.0645756
$766$	26.8659	0.970704
$767$	−15.5659	−0.562052
$768$	1.26328	0.0455846
$769$	6.41770	0.231428	0.115714	−	0.993283i	$-0.463084\pi$
$769$	6.41770	0.231428	0.115714	+	0.993283i	$0.463084\pi$
$770$	−2.91520	−0.105057
$771$	−23.4587	−0.844846
$772$	68.7814	2.47550
$773$	14.7452	0.530347	0.265174	−	0.964201i	$-0.414571\pi$
$773$	14.7452	0.530347	0.265174	+	0.964201i	$0.414571\pi$
$774$	19.9943	0.718680
$775$	−20.4331	−0.733977
$776$	12.1783	0.437177
$777$	−3.24626	−0.116459
$778$	26.5059	0.950283
$779$	−2.66165	−0.0953634
$780$	6.18841	0.221581
$781$	−5.90904	−0.211442
$782$	22.5630	0.806850
$783$	−1.07074	−0.0382650
$784$	15.3612	0.548614
$785$	−32.7291	−1.16815
$786$	−26.6664	−0.951160
$787$	−17.6792	−0.630196	−0.315098	−	0.949059i	$-0.602037\pi$
$787$	−17.6792	−0.630196	−0.315098	+	0.949059i	$0.602037\pi$
$788$	42.3654	1.50921
$789$	8.89703	0.316743
$790$	−56.9472	−2.02609
$791$	5.91362	0.210264
$792$	−2.43840	−0.0866448
$793$	−4.66226	−0.165562
$794$	61.9909	2.19998
$795$	−17.4664	−0.619469
$796$	−2.60681	−0.0923959
$797$	−7.77792	−0.275508	−0.137754	−	0.990466i	$-0.543988\pi$
$797$	−7.77792	−0.275508	−0.137754	+	0.990466i	$0.543988\pi$
$798$	−0.454509	−0.0160894
$799$	5.93779	0.210064
$800$	−20.4692	−0.723696
$801$	2.71575	0.0959562
$802$	10.7049	0.378002
$803$	−22.3738	−0.789554
$804$	40.5238	1.42917
$805$	−6.97206	−0.245733
$806$	25.3167	0.891743
$807$	7.99265	0.281355
$808$	12.7755	0.449440
$809$	9.98307	0.350986	0.175493	−	0.984481i	$-0.443848\pi$
$809$	9.98307	0.350986	0.175493	+	0.984481i	$0.443848\pi$
$810$	3.30334	0.116068
$811$	51.1291	1.79538	0.897692	−	0.440623i	$-0.145243\pi$
$811$	51.1291	1.79538	0.897692	+	0.440623i	$0.145243\pi$
$812$	1.43881	0.0504924
$813$	−31.9220	−1.11955
$814$	−24.0214	−0.841950
$815$	−2.10519	−0.0737415
$816$	−2.65611	−0.0929823
$817$	3.85395	0.134832
$818$	−64.2607	−2.24682
$819$	0.773104	0.0270144
$820$	−25.9946	−0.907771
$821$	4.66511	0.162813	0.0814067	−	0.996681i	$-0.474059\pi$
$821$	4.66511	0.162813	0.0814067	+	0.996681i	$0.474059\pi$
$822$	26.3665	0.919638
$823$	52.6200	1.83422	0.917108	−	0.398638i	$-0.130517\pi$
$823$	52.6200	1.83422	0.917108	+	0.398638i	$0.130517\pi$
$824$	26.7578	0.932152
$825$	−4.61721	−0.160751
$826$	11.1653	0.388491
$827$	29.8510	1.03802	0.519011	−	0.854768i	$-0.326300\pi$
$827$	29.8510	1.03802	0.519011	+	0.854768i	$0.326300\pi$
$828$	−23.7810	−0.826446
$829$	−33.5978	−1.16690	−0.583449	−	0.812149i	$-0.698297\pi$
$829$	−33.5978	−1.16690	−0.583449	+	0.812149i	$0.698297\pi$
$830$	9.88621	0.343155
$831$	−8.99727	−0.312112
$832$	18.4154	0.638438
$833$	−7.86149	−0.272385
$834$	11.3975	0.394663
$835$	13.8852	0.480516
$836$	−1.91662	−0.0662878
$837$	7.70123	0.266193
$838$	66.6746	2.30323
$839$	−20.4803	−0.707058	−0.353529	−	0.935424i	$-0.615018\pi$
$839$	−20.4803	−0.707058	−0.353529	+	0.935424i	$0.615018\pi$
$840$	−1.08854	−0.0375581
$841$	−27.8535	−0.960466
$842$	−4.28536	−0.147683
$843$	9.83739	0.338818
$844$	10.3954	0.357826
$845$	16.3546	0.562615
$846$	−10.9819	−0.377567
$847$	4.04254	0.138903
$848$	−25.9747	−0.891973
$849$	−25.1292	−0.862431
$850$	6.67042	0.228793
$851$	−57.4502	−1.96937
$852$	−8.99754	−0.308251
$853$	−43.8620	−1.50181	−0.750903	−	0.660412i	$-0.770381\pi$
$853$	−43.8620	−1.50181	−0.750903	+	0.660412i	$0.770381\pi$
$854$	3.34420	0.114436
$855$	0.636727	0.0217756
$856$	11.2828	0.385640
$857$	−16.1381	−0.551269	−0.275634	−	0.961263i	$-0.588888\pi$
$857$	−16.1381	−0.551269	−0.275634	+	0.961263i	$0.588888\pi$
$858$	5.72075	0.195303
$859$	−6.87939	−0.234722	−0.117361	−	0.993089i	$-0.537443\pi$
$859$	−6.87939	−0.234722	−0.117361	+	0.993089i	$0.537443\pi$
$860$	37.6390	1.28348
$861$	−3.24745	−0.110673
$862$	75.0845	2.55739
$863$	−9.62998	−0.327808	−0.163904	−	0.986476i	$-0.552409\pi$
$863$	−9.62998	−0.327808	−0.163904	+	0.986476i	$0.552409\pi$
$864$	7.71486	0.262465
$865$	12.8543	0.437060
$866$	79.3660	2.69697
$867$	−15.6407	−0.531185
$868$	−10.3486	−0.351255
$869$	−30.0003	−1.01769
$870$	−3.53701	−0.119916
$871$	−23.3145	−0.789983
$872$	−17.8925	−0.605915
$873$	−8.69139	−0.294159
$874$	−8.04360	−0.272079
$875$	−5.94551	−0.200995
$876$	−34.0680	−1.15105
$877$	−46.8276	−1.58125	−0.790627	−	0.612297i	$-0.790245\pi$
$877$	−46.8276	−1.58125	−0.790627	+	0.612297i	$0.790245\pi$
$878$	11.5467	0.389681
$879$	22.7649	0.767843
$880$	6.07331	0.204731
$881$	−6.74918	−0.227386	−0.113693	−	0.993516i	$-0.536268\pi$
$881$	−6.74918	−0.227386	−0.113693	+	0.993516i	$0.536268\pi$
$882$	14.5398	0.489582
$883$	−6.94844	−0.233834	−0.116917	−	0.993142i	$-0.537301\pi$
$883$	−6.94844	−0.233834	−0.116917	+	0.993142i	$0.537301\pi$
$884$	−4.70984	−0.158409
$885$	−15.6416	−0.525787
$886$	−70.6777	−2.37447
$887$	27.4833	0.922797	0.461399	−	0.887193i	$-0.347348\pi$
$887$	27.4833	0.922797	0.461399	+	0.887193i	$0.347348\pi$
$888$	−8.96961	−0.301000
$889$	−0.0748225	−0.00250946
$890$	8.97104	0.300710
$891$	1.74023	0.0582999
$892$	−58.2951	−1.95187
$893$	−2.11680	−0.0708359
$894$	6.01481	0.201165
$895$	−9.26760	−0.309782
$896$	−5.38453	−0.179884
$897$	13.6819	0.456825
$898$	50.8638	1.69735
$899$	−8.24599	−0.275019
$900$	−7.03051	−0.234350
$901$	13.2932	0.442861
$902$	−24.0302	−0.800118
$903$	4.70216	0.156478
$904$	16.3397	0.543450
$905$	−10.9800	−0.364987
$906$	−10.8024	−0.358887
$907$	−8.66722	−0.287790	−0.143895	−	0.989593i	$-0.545963\pi$
$907$	−8.66722	−0.287790	−0.143895	+	0.989593i	$0.545963\pi$
$908$	−41.1512	−1.36565
$909$	−9.11757	−0.302411
$910$	2.55383	0.0846586
$911$	−41.5364	−1.37616	−0.688082	−	0.725633i	$-0.741547\pi$
$911$	−41.5364	−1.37616	−0.688082	+	0.725633i	$0.741547\pi$
$912$	0.946890	0.0313547
$913$	5.20814	0.172364
$914$	−34.4026	−1.13794
$915$	−4.68493	−0.154879
$916$	−2.95570	−0.0976592
$917$	−6.27127	−0.207096
$918$	−2.51408	−0.0829772
$919$	−2.61286	−0.0861901	−0.0430951	−	0.999071i	$-0.513722\pi$
$919$	−2.61286	−0.0861901	−0.0430951	+	0.999071i	$0.513722\pi$
$920$	−19.2642	−0.635122
$921$	−24.9987	−0.823735
$922$	−17.1948	−0.566280
$923$	5.17655	0.170388
$924$	−2.33845	−0.0769294
$925$	−16.9843	−0.558441
$926$	−13.5409	−0.444983
$927$	−19.0964	−0.627208
$928$	−8.26058	−0.271167
$929$	−44.9542	−1.47490	−0.737450	−	0.675401i	$-0.763970\pi$
$929$	−44.9542	−1.47490	−0.737450	+	0.675401i	$0.763970\pi$
$930$	25.4398	0.834204
$931$	2.80259	0.0918511
$932$	38.4214	1.25853
$933$	6.44646	0.211048
$934$	−35.9544	−1.17646
$935$	−3.10817	−0.101648
$936$	2.13613	0.0698217
$937$	30.7284	1.00385	0.501927	−	0.864910i	$-0.332625\pi$
$937$	30.7284	1.00385	0.501927	+	0.864910i	$0.332625\pi$
$938$	16.7233	0.546036
$939$	−6.52481	−0.212929
$940$	−20.6734	−0.674292
$941$	2.07613	0.0676800	0.0338400	−	0.999427i	$-0.489226\pi$
$941$	2.07613	0.0676800	0.0338400	+	0.999427i	$0.489226\pi$
$942$	−46.0697	−1.50103
$943$	−57.4712	−1.87152
$944$	−23.2609	−0.757079
$945$	0.776863	0.0252714
$946$	34.7946	1.13127
$947$	−1.87274	−0.0608557	−0.0304279	−	0.999537i	$-0.509687\pi$
$947$	−1.87274	−0.0608557	−0.0304279	+	0.999537i	$0.509687\pi$
$948$	−45.6806	−1.48364
$949$	19.6003	0.636253
$950$	−2.37797	−0.0771517
$951$	10.3024	0.334078
$952$	0.828457	0.0268504
$953$	12.9947	0.420940	0.210470	−	0.977600i	$-0.432501\pi$
$953$	12.9947	0.420940	0.210470	+	0.977600i	$0.432501\pi$
$954$	−24.5858	−0.795995
$955$	−11.7503	−0.380229
$956$	6.70049	0.216709
$957$	−1.86333	−0.0602328
$958$	−50.6902	−1.63773
$959$	6.20075	0.200233
$960$	18.5049	0.597244
$961$	28.3090	0.913192
$962$	21.0437	0.678476
$963$	−8.05230	−0.259482
$964$	−17.3845	−0.559917
$965$	−39.7644	−1.28006
$966$	−9.81391	−0.315757
$967$	43.3601	1.39437	0.697184	−	0.716893i	$-0.254436\pi$
$967$	43.3601	1.39437	0.697184	+	0.716893i	$0.254436\pi$
$968$	11.1698	0.359010
$969$	−0.484596	−0.0155675
$970$	−28.7106	−0.921843
$971$	−59.2183	−1.90040	−0.950202	−	0.311634i	$-0.899124\pi$
$971$	−59.2183	−1.90040	−0.950202	+	0.311634i	$0.899124\pi$
$972$	2.64980	0.0849925
$973$	2.68041	0.0859298
$974$	73.7933	2.36449
$975$	4.04485	0.129539
$976$	−6.96706	−0.223010
$977$	25.8656	0.827514	0.413757	−	0.910387i	$-0.364216\pi$
$977$	25.8656	0.827514	0.413757	+	0.910387i	$0.364216\pi$
$978$	−2.96327	−0.0947550
$979$	4.72602	0.151044
$980$	27.3711	0.874338
$981$	12.7694	0.407696
$982$	−27.4702	−0.876611
$983$	21.7274	0.692997	0.346499	−	0.938050i	$-0.387371\pi$
$983$	21.7274	0.692997	0.346499	+	0.938050i	$0.387371\pi$
$984$	−8.97289	−0.286045
$985$	−24.4926	−0.780398
$986$	2.69192	0.0857283
$987$	−2.58268	−0.0822076
$988$	1.67904	0.0534173
$989$	83.2156	2.64610
$990$	5.74857	0.182702
$991$	24.3384	0.773134	0.386567	−	0.922261i	$-0.373661\pi$
$991$	24.3384	0.773134	0.386567	+	0.922261i	$0.373661\pi$
$992$	59.4139	1.88639
$993$	18.9992	0.602922
$994$	−3.71310	−0.117772
$995$	1.50706	0.0477772
$996$	7.93031	0.251281
$997$	32.8068	1.03900	0.519500	−	0.854470i	$-0.326118\pi$
$997$	32.8068	1.03900	0.519500	+	0.854470i	$0.326118\pi$
$998$	56.1097	1.77612
$999$	6.40140	0.202531

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.a.1.14	✓	94

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.a.1.14	✓	94	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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.15634 q^{2} +1.00000 q^{3} +2.64980 q^{4} -1.53192 q^{5} -2.15634 q^{6} -0.507117 q^{7} -1.40120 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.15634 q^{2} +1.00000 q^{3} +2.64980 q^{4} -1.53192 q^{5} -2.15634 q^{6} -0.507117 q^{7} -1.40120 q^{8} +1.00000 q^{9} +3.30334 q^{10} +1.74023 q^{11} +2.64980 q^{12} -1.52451 q^{13} +1.09352 q^{14} -1.53192 q^{15} -2.27815 q^{16} +1.16590 q^{17} -2.15634 q^{18} -0.415640 q^{19} -4.05929 q^{20} -0.507117 q^{21} -3.75253 q^{22} -8.97462 q^{23} -1.40120 q^{24} -2.65322 q^{25} +3.28736 q^{26} +1.00000 q^{27} -1.34376 q^{28} -1.07074 q^{29} +3.30334 q^{30} +7.70123 q^{31} +7.71486 q^{32} +1.74023 q^{33} -2.51408 q^{34} +0.776863 q^{35} +2.64980 q^{36} +6.40140 q^{37} +0.896260 q^{38} -1.52451 q^{39} +2.14652 q^{40} +6.40374 q^{41} +1.09352 q^{42} -9.27233 q^{43} +4.61126 q^{44} -1.53192 q^{45} +19.3523 q^{46} +5.09286 q^{47} -2.27815 q^{48} -6.74283 q^{49} +5.72124 q^{50} +1.16590 q^{51} -4.03964 q^{52} +11.4016 q^{53} -2.15634 q^{54} -2.66589 q^{55} +0.710570 q^{56} -0.415640 q^{57} +2.30887 q^{58} +10.2104 q^{59} -4.05929 q^{60} +3.05821 q^{61} -16.6065 q^{62} -0.507117 q^{63} -12.0796 q^{64} +2.33542 q^{65} -3.75253 q^{66} +15.2932 q^{67} +3.08941 q^{68} -8.97462 q^{69} -1.67518 q^{70} -3.39555 q^{71} -1.40120 q^{72} -12.8568 q^{73} -13.8036 q^{74} -2.65322 q^{75} -1.10136 q^{76} -0.882500 q^{77} +3.28736 q^{78} -17.2393 q^{79} +3.48995 q^{80} +1.00000 q^{81} -13.8086 q^{82} +2.99279 q^{83} -1.34376 q^{84} -1.78607 q^{85} +19.9943 q^{86} -1.07074 q^{87} -2.43840 q^{88} +2.71575 q^{89} +3.30334 q^{90} +0.773104 q^{91} -23.7810 q^{92} +7.70123 q^{93} -10.9819 q^{94} +0.636727 q^{95} +7.71486 q^{96} -8.69139 q^{97} +14.5398 q^{98} +1.74023 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 94 q - 13 q^{2} + 94 q^{3} + 73 q^{4} - 14 q^{5} - 13 q^{6} - 55 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) \) 94 * q - 13 * q^2 + 94 * q^3 + 73 * q^4 - 14 * q^5 - 13 * q^6 - 55 * q^7 - 36 * q^8 + 94 * q^9	\( 94 q - 13 q^{2} + 94 q^{3} + 73 q^{4} - 14 q^{5} - 13 q^{6} - 55 q^{7} - 36 q^{8} + 94 q^{9} - 39 q^{10} - 49 q^{11} + 73 q^{12} - 52 q^{13} - 7 q^{14} - 14 q^{15} + 43 q^{16} - 22 q^{17} - 13 q^{18} - 89 q^{19} - 22 q^{20} - 55 q^{21} - 36 q^{22} - 46 q^{23} - 36 q^{24} + 18 q^{25} + q^{26} + 94 q^{27} - 123 q^{28} - 20 q^{29} - 39 q^{30} - 61 q^{31} - 65 q^{32} - 49 q^{33} - 67 q^{34} - 40 q^{35} + 73 q^{36} - 83 q^{37} - 19 q^{38} - 52 q^{39} - 101 q^{40} - 25 q^{41} - 7 q^{42} - 150 q^{43} - 71 q^{44} - 14 q^{45} - 72 q^{46} - 39 q^{47} + 43 q^{48} - q^{49} - 45 q^{50} - 22 q^{51} - 110 q^{52} - 30 q^{53} - 13 q^{54} - 54 q^{55} - 5 q^{56} - 89 q^{57} - 77 q^{58} - 43 q^{59} - 22 q^{60} - 109 q^{61} - 33 q^{62} - 55 q^{63} + 10 q^{64} - 66 q^{65} - 36 q^{66} - 155 q^{67} - 46 q^{68} - 46 q^{69} - 43 q^{70} - 27 q^{71} - 36 q^{72} - 157 q^{73} - 29 q^{74} + 18 q^{75} - 176 q^{76} - 9 q^{77} + q^{78} - 99 q^{79} - 18 q^{80} + 94 q^{81} - 53 q^{82} - 144 q^{83} - 123 q^{84} - 105 q^{85} + 23 q^{86} - 20 q^{87} - 88 q^{88} - 4 q^{89} - 39 q^{90} - 99 q^{91} - 76 q^{92} - 61 q^{93} - 65 q^{94} - 49 q^{95} - 65 q^{96} - 139 q^{97} - 6 q^{98} - 49 q^{99}+O(q^{100}) \) 94 * q - 13 * q^2 + 94 * q^3 + 73 * q^4 - 14 * q^5 - 13 * q^6 - 55 * q^7 - 36 * q^8 + 94 * q^9 - 39 * q^10 - 49 * q^11 + 73 * q^12 - 52 * q^13 - 7 * q^14 - 14 * q^15 + 43 * q^16 - 22 * q^17 - 13 * q^18 - 89 * q^19 - 22 * q^20 - 55 * q^21 - 36 * q^22 - 46 * q^23 - 36 * q^24 + 18 * q^25 + q^26 + 94 * q^27 - 123 * q^28 - 20 * q^29 - 39 * q^30 - 61 * q^31 - 65 * q^32 - 49 * q^33 - 67 * q^34 - 40 * q^35 + 73 * q^36 - 83 * q^37 - 19 * q^38 - 52 * q^39 - 101 * q^40 - 25 * q^41 - 7 * q^42 - 150 * q^43 - 71 * q^44 - 14 * q^45 - 72 * q^46 - 39 * q^47 + 43 * q^48 - q^49 - 45 * q^50 - 22 * q^51 - 110 * q^52 - 30 * q^53 - 13 * q^54 - 54 * q^55 - 5 * q^56 - 89 * q^57 - 77 * q^58 - 43 * q^59 - 22 * q^60 - 109 * q^61 - 33 * q^62 - 55 * q^63 + 10 * q^64 - 66 * q^65 - 36 * q^66 - 155 * q^67 - 46 * q^68 - 46 * q^69 - 43 * q^70 - 27 * q^71 - 36 * q^72 - 157 * q^73 - 29 * q^74 + 18 * q^75 - 176 * q^76 - 9 * q^77 + q^78 - 99 * q^79 - 18 * q^80 + 94 * q^81 - 53 * q^82 - 144 * q^83 - 123 * q^84 - 105 * q^85 + 23 * q^86 - 20 * q^87 - 88 * q^88 - 4 * q^89 - 39 * q^90 - 99 * q^91 - 76 * q^92 - 61 * q^93 - 65 * q^94 - 49 * q^95 - 65 * q^96 - 139 * q^97 - 6 * q^98 - 49 * q^99

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