LMFDB - Embedded newform 8013.2.a.b.1.20

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:	$0$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q-1.79051 q^{2} -1.00000 q^{3} +1.20593 q^{4} -0.580006 q^{5} +1.79051 q^{6} +0.129222 q^{7} +1.42179 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.79051 q^{2} -1.00000 q^{3} +1.20593 q^{4} -0.580006 q^{5} +1.79051 q^{6} +0.129222 q^{7} +1.42179 q^{8} +1.00000 q^{9} +1.03851 q^{10} -0.673869 q^{11} -1.20593 q^{12} -1.11973 q^{13} -0.231374 q^{14} +0.580006 q^{15} -4.95759 q^{16} -0.433570 q^{17} -1.79051 q^{18} -7.59984 q^{19} -0.699448 q^{20} -0.129222 q^{21} +1.20657 q^{22} -6.17795 q^{23} -1.42179 q^{24} -4.66359 q^{25} +2.00488 q^{26} -1.00000 q^{27} +0.155833 q^{28} -8.90427 q^{29} -1.03851 q^{30} +3.06700 q^{31} +6.03305 q^{32} +0.673869 q^{33} +0.776312 q^{34} -0.0749496 q^{35} +1.20593 q^{36} -9.25311 q^{37} +13.6076 q^{38} +1.11973 q^{39} -0.824645 q^{40} -3.38993 q^{41} +0.231374 q^{42} +8.49201 q^{43} -0.812641 q^{44} -0.580006 q^{45} +11.0617 q^{46} -11.2635 q^{47} +4.95759 q^{48} -6.98330 q^{49} +8.35022 q^{50} +0.433570 q^{51} -1.35031 q^{52} -4.83160 q^{53} +1.79051 q^{54} +0.390848 q^{55} +0.183726 q^{56} +7.59984 q^{57} +15.9432 q^{58} +1.88342 q^{59} +0.699448 q^{60} -6.75702 q^{61} -5.49150 q^{62} +0.129222 q^{63} -0.887069 q^{64} +0.649448 q^{65} -1.20657 q^{66} -4.29714 q^{67} -0.522856 q^{68} +6.17795 q^{69} +0.134198 q^{70} -4.23507 q^{71} +1.42179 q^{72} +11.1598 q^{73} +16.5678 q^{74} +4.66359 q^{75} -9.16490 q^{76} -0.0870788 q^{77} -2.00488 q^{78} -5.63711 q^{79} +2.87543 q^{80} +1.00000 q^{81} +6.06971 q^{82} +2.32685 q^{83} -0.155833 q^{84} +0.251473 q^{85} -15.2051 q^{86} +8.90427 q^{87} -0.958098 q^{88} +10.4931 q^{89} +1.03851 q^{90} -0.144693 q^{91} -7.45019 q^{92} -3.06700 q^{93} +20.1674 q^{94} +4.40795 q^{95} -6.03305 q^{96} -1.69359 q^{97} +12.5037 q^{98} -0.673869 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9}+O(q^{10}) $ 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9	\( 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9} - 3 q^{10} + 55 q^{11} - 109 q^{12} - 8 q^{13} + 27 q^{14} - 16 q^{15} + 111 q^{16} + 28 q^{17} + 15 q^{18} + q^{19} + 54 q^{20} - 35 q^{21} + 20 q^{22} + 62 q^{23} - 48 q^{24} + 102 q^{25} + 21 q^{26} - 106 q^{27} + 79 q^{28} + 36 q^{29} + 3 q^{30} + q^{31} + 111 q^{32} - 55 q^{33} - 27 q^{34} + 72 q^{35} + 109 q^{36} + 31 q^{37} + 43 q^{38} + 8 q^{39} - 13 q^{40} + 35 q^{41} - 27 q^{42} + 98 q^{43} + 121 q^{44} + 16 q^{45} + 8 q^{46} + 75 q^{47} - 111 q^{48} + 49 q^{49} + 83 q^{50} - 28 q^{51} - 18 q^{52} + 60 q^{53} - 15 q^{54} + 14 q^{55} + 85 q^{56} - q^{57} + 65 q^{58} + 77 q^{59} - 54 q^{60} - 55 q^{61} + 83 q^{62} + 35 q^{63} + 122 q^{64} + 86 q^{65} - 20 q^{66} + 121 q^{67} + 80 q^{68} - 62 q^{69} - 11 q^{70} + 79 q^{71} + 48 q^{72} - 29 q^{73} + 91 q^{74} - 102 q^{75} - 10 q^{76} + 87 q^{77} - 21 q^{78} + 15 q^{79} + 108 q^{80} + 106 q^{81} + 21 q^{82} + 196 q^{83} - 79 q^{84} - 5 q^{85} + 65 q^{86} - 36 q^{87} + 84 q^{88} + 34 q^{89} - 3 q^{90} + 17 q^{91} + 162 q^{92} - q^{93} - 35 q^{94} + 113 q^{95} - 111 q^{96} - 63 q^{97} + 112 q^{98} + 55 q^{99}+O(q^{100}) \) 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9 - 3 * q^10 + 55 * q^11 - 109 * q^12 - 8 * q^13 + 27 * q^14 - 16 * q^15 + 111 * q^16 + 28 * q^17 + 15 * q^18 + q^19 + 54 * q^20 - 35 * q^21 + 20 * q^22 + 62 * q^23 - 48 * q^24 + 102 * q^25 + 21 * q^26 - 106 * q^27 + 79 * q^28 + 36 * q^29 + 3 * q^30 + q^31 + 111 * q^32 - 55 * q^33 - 27 * q^34 + 72 * q^35 + 109 * q^36 + 31 * q^37 + 43 * q^38 + 8 * q^39 - 13 * q^40 + 35 * q^41 - 27 * q^42 + 98 * q^43 + 121 * q^44 + 16 * q^45 + 8 * q^46 + 75 * q^47 - 111 * q^48 + 49 * q^49 + 83 * q^50 - 28 * q^51 - 18 * q^52 + 60 * q^53 - 15 * q^54 + 14 * q^55 + 85 * q^56 - q^57 + 65 * q^58 + 77 * q^59 - 54 * q^60 - 55 * q^61 + 83 * q^62 + 35 * q^63 + 122 * q^64 + 86 * q^65 - 20 * q^66 + 121 * q^67 + 80 * q^68 - 62 * q^69 - 11 * q^70 + 79 * q^71 + 48 * q^72 - 29 * q^73 + 91 * q^74 - 102 * q^75 - 10 * q^76 + 87 * q^77 - 21 * q^78 + 15 * q^79 + 108 * q^80 + 106 * q^81 + 21 * q^82 + 196 * q^83 - 79 * q^84 - 5 * q^85 + 65 * q^86 - 36 * q^87 + 84 * q^88 + 34 * q^89 - 3 * q^90 + 17 * q^91 + 162 * q^92 - q^93 - 35 * q^94 + 113 * q^95 - 111 * q^96 - 63 * q^97 + 112 * q^98 + 55 * 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 $

$2$	−1.79051	−1.26608	−0.633042	−	0.774118i	$-0.718194\pi$
$2$	−1.79051	−1.26608	−0.633042	+	0.774118i	$0.718194\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.20593	0.602966
$5$	−0.580006	−0.259386	−0.129693	−	0.991554i	$-0.541399\pi$
$5$	−0.580006	−0.259386	−0.129693	+	0.991554i	$0.541399\pi$
$6$	1.79051	0.730973
$7$	0.129222	0.0488414	0.0244207	−	0.999702i	$-0.492226\pi$
$7$	0.129222	0.0488414	0.0244207	+	0.999702i	$0.492226\pi$
$8$	1.42179	0.502678
$9$	1.00000	0.333333
$10$	1.03851	0.328405
$11$	−0.673869	−0.203179	−0.101590	−	0.994826i	$-0.532393\pi$
$11$	−0.673869	−0.203179	−0.101590	+	0.994826i	$0.532393\pi$
$12$	−1.20593	−0.348123
$13$	−1.11973	−0.310556	−0.155278	−	0.987871i	$-0.549627\pi$
$13$	−1.11973	−0.310556	−0.155278	+	0.987871i	$0.549627\pi$
$14$	−0.231374	−0.0618372
$15$	0.580006	0.149757
$16$	−4.95759	−1.23940
$17$	−0.433570	−0.105156	−0.0525781	−	0.998617i	$-0.516744\pi$
$17$	−0.433570	−0.105156	−0.0525781	+	0.998617i	$0.516744\pi$
$18$	−1.79051	−0.422028
$19$	−7.59984	−1.74352	−0.871762	−	0.489930i	$-0.837022\pi$
$19$	−7.59984	−1.74352	−0.871762	+	0.489930i	$0.837022\pi$
$20$	−0.699448	−0.156401
$21$	−0.129222	−0.0281986
$22$	1.20657	0.257242
$23$	−6.17795	−1.28819	−0.644096	−	0.764945i	$-0.722766\pi$
$23$	−6.17795	−1.28819	−0.644096	+	0.764945i	$0.722766\pi$
$24$	−1.42179	−0.290221
$25$	−4.66359	−0.932719
$26$	2.00488	0.393190
$27$	−1.00000	−0.192450
$28$	0.155833	0.0294497
$29$	−8.90427	−1.65348	−0.826741	−	0.562582i	$-0.809808\pi$
$29$	−8.90427	−1.65348	−0.826741	+	0.562582i	$0.809808\pi$
$30$	−1.03851	−0.189605
$31$	3.06700	0.550849	0.275425	−	0.961323i	$-0.411182\pi$
$31$	3.06700	0.550849	0.275425	+	0.961323i	$0.411182\pi$
$32$	6.03305	1.06650
$33$	0.673869	0.117306
$34$	0.776312	0.133136
$35$	−0.0749496	−0.0126688
$36$	1.20593	0.200989
$37$	−9.25311	−1.52120	−0.760601	−	0.649220i	$-0.775096\pi$
$37$	−9.25311	−1.52120	−0.760601	+	0.649220i	$0.775096\pi$
$38$	13.6076	2.20745
$39$	1.11973	0.179300
$40$	−0.824645	−0.130388
$41$	−3.38993	−0.529418	−0.264709	−	0.964328i	$-0.585276\pi$
$41$	−3.38993	−0.529418	−0.264709	+	0.964328i	$0.585276\pi$
$42$	0.231374	0.0357017
$43$	8.49201	1.29502	0.647510	−	0.762057i	$-0.275810\pi$
$43$	8.49201	1.29502	0.647510	+	0.762057i	$0.275810\pi$
$44$	−0.812641	−0.122510
$45$	−0.580006	−0.0864622
$46$	11.0617	1.63096
$47$	−11.2635	−1.64295	−0.821473	−	0.570248i	$-0.806847\pi$
$47$	−11.2635	−1.64295	−0.821473	+	0.570248i	$0.806847\pi$
$48$	4.95759	0.715567
$49$	−6.98330	−0.997615
$50$	8.35022	1.18090
$51$	0.433570	0.0607119
$52$	−1.35031	−0.187255
$53$	−4.83160	−0.663671	−0.331836	−	0.943337i	$-0.607668\pi$
$53$	−4.83160	−0.663671	−0.331836	+	0.943337i	$0.607668\pi$
$54$	1.79051	0.243658
$55$	0.390848	0.0527019
$56$	0.183726	0.0245515
$57$	7.59984	1.00662
$58$	15.9432	2.09345
$59$	1.88342	0.245200	0.122600	−	0.992456i	$-0.460877\pi$
$59$	1.88342	0.245200	0.122600	+	0.992456i	$0.460877\pi$
$60$	0.699448	0.0902983
$61$	−6.75702	−0.865148	−0.432574	−	0.901598i	$-0.642395\pi$
$61$	−6.75702	−0.865148	−0.432574	+	0.901598i	$0.642395\pi$
$62$	−5.49150	−0.697421
$63$	0.129222	0.0162805
$64$	−0.887069	−0.110884
$65$	0.649448	0.0805541
$66$	−1.20657	−0.148519
$67$	−4.29714	−0.524979	−0.262489	−	0.964935i	$-0.584543\pi$
$67$	−4.29714	−0.524979	−0.262489	+	0.964935i	$0.584543\pi$
$68$	−0.522856	−0.0634056
$69$	6.17795	0.743738
$70$	0.134198	0.0160397
$71$	−4.23507	−0.502610	−0.251305	−	0.967908i	$-0.580860\pi$
$71$	−4.23507	−0.502610	−0.251305	+	0.967908i	$0.580860\pi$
$72$	1.42179	0.167559
$73$	11.1598	1.30616	0.653079	−	0.757290i	$-0.273477\pi$
$73$	11.1598	1.30616	0.653079	+	0.757290i	$0.273477\pi$
$74$	16.5678	1.92597
$75$	4.66359	0.538505
$76$	−9.16490	−1.05129
$77$	−0.0870788	−0.00992355
$78$	−2.00488	−0.227008
$79$	−5.63711	−0.634225	−0.317112	−	0.948388i	$-0.602713\pi$
$79$	−5.63711	−0.634225	−0.317112	+	0.948388i	$0.602713\pi$
$80$	2.87543	0.321483
$81$	1.00000	0.111111
$82$	6.06971	0.670288
$83$	2.32685	0.255405	0.127703	−	0.991813i	$-0.459240\pi$
$83$	2.32685	0.255405	0.127703	+	0.991813i	$0.459240\pi$
$84$	−0.155833	−0.0170028
$85$	0.251473	0.0272761
$86$	−15.2051	−1.63960
$87$	8.90427	0.954638
$88$	−0.958098	−0.102134
$89$	10.4931	1.11226	0.556132	−	0.831094i	$-0.312285\pi$
$89$	10.4931	1.11226	0.556132	+	0.831094i	$0.312285\pi$
$90$	1.03851	0.109468
$91$	−0.144693	−0.0151680
$92$	−7.45019	−0.776736
$93$	−3.06700	−0.318033
$94$	20.1674	2.08011
$95$	4.40795	0.452246
$96$	−6.03305	−0.615746
$97$	−1.69359	−0.171958	−0.0859788	−	0.996297i	$-0.527402\pi$
$97$	−1.69359	−0.171958	−0.0859788	+	0.996297i	$0.527402\pi$
$98$	12.5037	1.26306
$99$	−0.673869	−0.0677264
$100$	−5.62398	−0.562398
$101$	15.2520	1.51763	0.758813	−	0.651308i	$-0.225779\pi$
$101$	15.2520	1.51763	0.758813	+	0.651308i	$0.225779\pi$
$102$	−0.776312	−0.0768663
$103$	−12.0902	−1.19128	−0.595642	−	0.803250i	$-0.703102\pi$
$103$	−12.0902	−1.19128	−0.595642	+	0.803250i	$0.703102\pi$
$104$	−1.59201	−0.156110
$105$	0.0749496	0.00731433
$106$	8.65104	0.840263
$107$	−5.47959	−0.529732	−0.264866	−	0.964285i	$-0.585328\pi$
$107$	−5.47959	−0.529732	−0.264866	+	0.964285i	$0.585328\pi$
$108$	−1.20593	−0.116041
$109$	10.7643	1.03104	0.515519	−	0.856878i	$-0.327599\pi$
$109$	10.7643	1.03104	0.515519	+	0.856878i	$0.327599\pi$
$110$	−0.699818	−0.0667250
$111$	9.25311	0.878266
$112$	−0.640631	−0.0605339
$113$	18.6336	1.75290	0.876451	−	0.481490i	$-0.159904\pi$
$113$	18.6336	1.75290	0.876451	+	0.481490i	$0.159904\pi$
$114$	−13.6076	−1.27447
$115$	3.58325	0.334139
$116$	−10.7380	−0.996994
$117$	−1.11973	−0.103519
$118$	−3.37228	−0.310443
$119$	−0.0560268	−0.00513597
$120$	0.824645	0.0752794
$121$	−10.5459	−0.958718
$122$	12.0985	1.09535
$123$	3.38993	0.305660
$124$	3.69859	0.332144
$125$	5.60494	0.501321
$126$	−0.231374	−0.0206124
$127$	−21.0174	−1.86499	−0.932496	−	0.361180i	$-0.882374\pi$
$127$	−21.0174	−1.86499	−0.932496	+	0.361180i	$0.882374\pi$
$128$	−10.4778	−0.926115
$129$	−8.49201	−0.747680
$130$	−1.16284	−0.101988
$131$	8.21089	0.717389	0.358695	−	0.933455i	$-0.383222\pi$
$131$	8.21089	0.717389	0.358695	+	0.933455i	$0.383222\pi$
$132$	0.812641	0.0707313
$133$	−0.982068	−0.0851561
$134$	7.69407	0.664667
$135$	0.580006	0.0499190
$136$	−0.616444	−0.0528596
$137$	1.64076	0.140180	0.0700899	−	0.997541i	$-0.477671\pi$
$137$	1.64076	0.140180	0.0700899	+	0.997541i	$0.477671\pi$
$138$	−11.0617	−0.941634
$139$	17.3466	1.47132	0.735661	−	0.677350i	$-0.236871\pi$
$139$	17.3466	1.47132	0.735661	+	0.677350i	$0.236871\pi$
$140$	−0.0903842	−0.00763886
$141$	11.2635	0.948555
$142$	7.58294	0.636346
$143$	0.754549	0.0630986
$144$	−4.95759	−0.413133
$145$	5.16453	0.428891
$146$	−19.9818	−1.65370
$147$	6.98330	0.575973
$148$	−11.1586	−0.917233
$149$	−20.4055	−1.67168	−0.835840	−	0.548973i	$-0.815019\pi$
$149$	−20.4055	−1.67168	−0.835840	+	0.548973i	$0.815019\pi$
$150$	−8.35022	−0.681793
$151$	11.5983	0.943860	0.471930	−	0.881636i	$-0.343558\pi$
$151$	11.5983	0.943860	0.471930	+	0.881636i	$0.343558\pi$
$152$	−10.8054	−0.876430
$153$	−0.433570	−0.0350520
$154$	0.155916	0.0125640
$155$	−1.77888	−0.142883
$156$	1.35031	0.108112
$157$	−10.3390	−0.825143	−0.412572	−	0.910925i	$-0.635369\pi$
$157$	−10.3390	−0.825143	−0.412572	+	0.910925i	$0.635369\pi$
$158$	10.0933	0.802981
$159$	4.83160	0.383171
$160$	−3.49921	−0.276636
$161$	−0.798328	−0.0629171
$162$	−1.79051	−0.140676
$163$	−15.8826	−1.24402	−0.622012	−	0.783008i	$-0.713685\pi$
$163$	−15.8826	−1.24402	−0.622012	+	0.783008i	$0.713685\pi$
$164$	−4.08803	−0.319221
$165$	−0.390848	−0.0304275
$166$	−4.16626	−0.323364
$167$	−4.52117	−0.349859	−0.174929	−	0.984581i	$-0.555970\pi$
$167$	−4.52117	−0.349859	−0.174929	+	0.984581i	$0.555970\pi$
$168$	−0.183726	−0.0141748
$169$	−11.7462	−0.903555
$170$	−0.450265	−0.0345338
$171$	−7.59984	−0.581175
$172$	10.2408	0.780853
$173$	−8.76842	−0.666651	−0.333325	−	0.942812i	$-0.608171\pi$
$173$	−8.76842	−0.666651	−0.333325	+	0.942812i	$0.608171\pi$
$174$	−15.9432	−1.20865
$175$	−0.602640	−0.0455553
$176$	3.34077	0.251820
$177$	−1.88342	−0.141566
$178$	−18.7880	−1.40822
$179$	19.4820	1.45615	0.728075	−	0.685498i	$-0.240415\pi$
$179$	19.4820	1.45615	0.728075	+	0.685498i	$0.240415\pi$
$180$	−0.699448	−0.0521338
$181$	4.12420	0.306549	0.153275	−	0.988184i	$-0.451018\pi$
$181$	4.12420	0.306549	0.153275	+	0.988184i	$0.451018\pi$
$182$	0.259075	0.0192039
$183$	6.75702	0.499494
$184$	−8.78373	−0.647545
$185$	5.36686	0.394579
$186$	5.49150	0.402656
$187$	0.292169	0.0213655
$188$	−13.5830	−0.990641
$189$	−0.129222	−0.00939953
$190$	−7.89249	−0.572582
$191$	12.0639	0.872911	0.436456	−	0.899726i	$-0.356234\pi$
$191$	12.0639	0.872911	0.436456	+	0.899726i	$0.356234\pi$
$192$	0.887069	0.0640187
$193$	9.01217	0.648710	0.324355	−	0.945935i	$-0.394853\pi$
$193$	9.01217	0.648710	0.324355	+	0.945935i	$0.394853\pi$
$194$	3.03239	0.217713
$195$	−0.649448	−0.0465079
$196$	−8.42139	−0.601528
$197$	−6.04644	−0.430791	−0.215396	−	0.976527i	$-0.569104\pi$
$197$	−6.04644	−0.430791	−0.215396	+	0.976527i	$0.569104\pi$
$198$	1.20657	0.0857472
$199$	−8.35314	−0.592138	−0.296069	−	0.955167i	$-0.595676\pi$
$199$	−8.35314	−0.592138	−0.296069	+	0.955167i	$0.595676\pi$
$200$	−6.63064	−0.468857
$201$	4.29714	0.303097
$202$	−27.3088	−1.92144
$203$	−1.15063	−0.0807584
$204$	0.522856	0.0366072
$205$	1.96618	0.137324
$206$	21.6477	1.50827
$207$	−6.17795	−0.429397
$208$	5.55115	0.384903
$209$	5.12130	0.354248
$210$	−0.134198	−0.00926055
$211$	−25.1061	−1.72837	−0.864186	−	0.503172i	$-0.832166\pi$
$211$	−25.1061	−1.72837	−0.864186	+	0.503172i	$0.832166\pi$
$212$	−5.82658	−0.400171
$213$	4.23507	0.290182
$214$	9.81128	0.670685
$215$	−4.92542	−0.335911
$216$	−1.42179	−0.0967404
$217$	0.396324	0.0269042
$218$	−19.2737	−1.30538
$219$	−11.1598	−0.754110
$220$	0.471336	0.0317775
$221$	0.485480	0.0326569
$222$	−16.5678	−1.11196
$223$	−17.9553	−1.20237	−0.601186	−	0.799109i	$-0.705305\pi$
$223$	−17.9553	−1.20237	−0.601186	+	0.799109i	$0.705305\pi$
$224$	0.779604	0.0520895
$225$	−4.66359	−0.310906
$226$	−33.3637	−2.21932
$227$	11.1454	0.739745	0.369873	−	0.929082i	$-0.379401\pi$
$227$	11.1454	0.739745	0.369873	+	0.929082i	$0.379401\pi$
$228$	9.16490	0.606960
$229$	17.0523	1.12685	0.563423	−	0.826168i	$-0.309484\pi$
$229$	17.0523	1.12685	0.563423	+	0.826168i	$0.309484\pi$
$230$	−6.41585	−0.423048
$231$	0.0870788	0.00572937
$232$	−12.6600	−0.831169
$233$	−3.41794	−0.223917	−0.111958	−	0.993713i	$-0.535712\pi$
$233$	−3.41794	−0.223917	−0.111958	+	0.993713i	$0.535712\pi$
$234$	2.00488	0.131063
$235$	6.53287	0.426158
$236$	2.27127	0.147847
$237$	5.63711	0.366170
$238$	0.100317	0.00650257
$239$	18.4912	1.19610	0.598050	−	0.801459i	$-0.295943\pi$
$239$	18.4912	1.19610	0.598050	+	0.801459i	$0.295943\pi$
$240$	−2.87543	−0.185608
$241$	−19.4708	−1.25423	−0.627113	−	0.778928i	$-0.715764\pi$
$241$	−19.4708	−1.25423	−0.627113	+	0.778928i	$0.715764\pi$
$242$	18.8826	1.21382
$243$	−1.00000	−0.0641500
$244$	−8.14852	−0.521655
$245$	4.05036	0.258768
$246$	−6.06971	−0.386991
$247$	8.50975	0.541462
$248$	4.36062	0.276900
$249$	−2.32685	−0.147458
$250$	−10.0357	−0.634714
$251$	17.2095	1.08625	0.543126	−	0.839651i	$-0.317241\pi$
$251$	17.2095	1.08625	0.543126	+	0.839651i	$0.317241\pi$
$252$	0.155833	0.00981657
$253$	4.16313	0.261734
$254$	37.6319	2.36123
$255$	−0.251473	−0.0157479
$256$	20.5348	1.28342
$257$	−1.52962	−0.0954149	−0.0477074	−	0.998861i	$-0.515192\pi$
$257$	−1.52962	−0.0954149	−0.0477074	+	0.998861i	$0.515192\pi$
$258$	15.2051	0.946625
$259$	−1.19571	−0.0742976
$260$	0.783190	0.0485714
$261$	−8.90427	−0.551161
$262$	−14.7017	−0.908274
$263$	20.5459	1.26691	0.633456	−	0.773779i	$-0.281636\pi$
$263$	20.5459	1.26691	0.633456	+	0.773779i	$0.281636\pi$
$264$	0.958098	0.0589669
$265$	2.80236	0.172147
$266$	1.75840	0.107815
$267$	−10.4931	−0.642166
$268$	−5.18206	−0.316544
$269$	17.8682	1.08945	0.544723	−	0.838616i	$-0.316635\pi$
$269$	17.8682	1.08945	0.544723	+	0.838616i	$0.316635\pi$
$270$	−1.03851	−0.0632015
$271$	−23.5389	−1.42989	−0.714943	−	0.699182i	$-0.753548\pi$
$271$	−23.5389	−1.42989	−0.714943	+	0.699182i	$0.753548\pi$
$272$	2.14946	0.130330
$273$	0.144693	0.00875725
$274$	−2.93780	−0.177479
$275$	3.14265	0.189509
$276$	7.45019	0.448449
$277$	−22.6839	−1.36294	−0.681471	−	0.731845i	$-0.738660\pi$
$277$	−22.6839	−1.36294	−0.681471	+	0.731845i	$0.738660\pi$
$278$	−31.0594	−1.86282
$279$	3.06700	0.183616
$280$	−0.106562	−0.00636832
$281$	−25.3514	−1.51234	−0.756169	−	0.654377i	$-0.772931\pi$
$281$	−25.3514	−1.51234	−0.756169	+	0.654377i	$0.772931\pi$
$282$	−20.1674	−1.20095
$283$	−12.8032	−0.761073	−0.380537	−	0.924766i	$-0.624261\pi$
$283$	−12.8032	−0.761073	−0.380537	+	0.924766i	$0.624261\pi$
$284$	−5.10721	−0.303057
$285$	−4.40795	−0.261105
$286$	−1.35103	−0.0798880
$287$	−0.438054	−0.0258575
$288$	6.03305	0.355501
$289$	−16.8120	−0.988942
$290$	−9.24715	−0.543012
$291$	1.69359	0.0992798
$292$	13.4580	0.787569
$293$	3.82739	0.223599	0.111799	−	0.993731i	$-0.464339\pi$
$293$	3.82739	0.223599	0.111799	+	0.993731i	$0.464339\pi$
$294$	−12.5037	−0.729230
$295$	−1.09239	−0.0636015
$296$	−13.1559	−0.764674
$297$	0.673869	0.0391019
$298$	36.5362	2.11649
$299$	6.91761	0.400056
$300$	5.62398	0.324701
$301$	1.09736	0.0632506
$302$	−20.7670	−1.19500
$303$	−15.2520	−0.876202
$304$	37.6769	2.16092
$305$	3.91911	0.224408
$306$	0.776312	0.0443788
$307$	12.0290	0.686534	0.343267	−	0.939238i	$-0.388466\pi$
$307$	12.0290	0.686534	0.343267	+	0.939238i	$0.388466\pi$
$308$	−0.105011	−0.00598357
$309$	12.0902	0.687789
$310$	3.18510	0.180902
$311$	−1.62464	−0.0921251	−0.0460625	−	0.998939i	$-0.514667\pi$
$311$	−1.62464	−0.0921251	−0.0460625	+	0.998939i	$0.514667\pi$
$312$	1.59201	0.0901300
$313$	23.4653	1.32634	0.663169	−	0.748469i	$-0.269211\pi$
$313$	23.4653	1.32634	0.663169	+	0.748469i	$0.269211\pi$
$314$	18.5121	1.04470
$315$	−0.0749496	−0.00422293
$316$	−6.79798	−0.382416
$317$	25.4927	1.43181	0.715907	−	0.698196i	$-0.246013\pi$
$317$	25.4927	1.43181	0.715907	+	0.698196i	$0.246013\pi$
$318$	−8.65104	−0.485126
$319$	6.00032	0.335953
$320$	0.514505	0.0287617
$321$	5.47959	0.305841
$322$	1.42942	0.0796582
$323$	3.29506	0.183342
$324$	1.20593	0.0669963
$325$	5.22195	0.289662
$326$	28.4381	1.57504
$327$	−10.7643	−0.595270
$328$	−4.81976	−0.266127
$329$	−1.45549	−0.0802437
$330$	0.699818	0.0385237
$331$	−17.9605	−0.987200	−0.493600	−	0.869689i	$-0.664319\pi$
$331$	−17.9605	−0.987200	−0.493600	+	0.869689i	$0.664319\pi$
$332$	2.80603	0.154001
$333$	−9.25311	−0.507067
$334$	8.09522	0.442951
$335$	2.49236	0.136172
$336$	0.640631	0.0349493
$337$	18.1119	0.986619	0.493309	−	0.869854i	$-0.335787\pi$
$337$	18.1119	0.986619	0.493309	+	0.869854i	$0.335787\pi$
$338$	21.0317	1.14398
$339$	−18.6336	−1.01204
$340$	0.303260	0.0164466
$341$	−2.06676	−0.111921
$342$	13.6076	0.735815
$343$	−1.80695	−0.0975662
$344$	12.0738	0.650978
$345$	−3.58325	−0.192916
$346$	15.7000	0.844035
$347$	−12.7911	−0.686663	−0.343331	−	0.939214i	$-0.611555\pi$
$347$	−12.7911	−0.686663	−0.343331	+	0.939214i	$0.611555\pi$
$348$	10.7380	0.575615
$349$	−21.9678	−1.17591	−0.587955	−	0.808894i	$-0.700067\pi$
$349$	−21.9678	−1.17591	−0.587955	+	0.808894i	$0.700067\pi$
$350$	1.07903	0.0576768
$351$	1.11973	0.0597666
$352$	−4.06549	−0.216691
$353$	14.5965	0.776896	0.388448	−	0.921471i	$-0.373011\pi$
$353$	14.5965	0.776896	0.388448	+	0.921471i	$0.373011\pi$
$354$	3.37228	0.179235
$355$	2.45637	0.130370
$356$	12.6539	0.670658
$357$	0.0560268	0.00296525
$358$	−34.8827	−1.84361
$359$	−19.2895	−1.01806	−0.509031	−	0.860748i	$-0.669996\pi$
$359$	−19.2895	−1.01806	−0.509031	+	0.860748i	$0.669996\pi$
$360$	−0.824645	−0.0434626
$361$	38.7576	2.03987
$362$	−7.38442	−0.388117
$363$	10.5459	0.553516
$364$	−0.174491	−0.00914579
$365$	−6.47276	−0.338799
$366$	−12.0985	−0.632400
$367$	−37.9141	−1.97910	−0.989550	−	0.144189i	$-0.953943\pi$
$367$	−37.9141	−1.97910	−0.989550	+	0.144189i	$0.953943\pi$
$368$	30.6278	1.59658
$369$	−3.38993	−0.176473
$370$	−9.60942	−0.499570
$371$	−0.624350	−0.0324146
$372$	−3.69859	−0.191763
$373$	−1.03664	−0.0536751	−0.0268376	−	0.999640i	$-0.508544\pi$
$373$	−1.03664	−0.0536751	−0.0268376	+	0.999640i	$0.508544\pi$
$374$	−0.523133	−0.0270505
$375$	−5.60494	−0.289438
$376$	−16.0142	−0.825872
$377$	9.97035	0.513499
$378$	0.231374	0.0119006
$379$	26.3646	1.35426	0.677130	−	0.735864i	$-0.263224\pi$
$379$	26.3646	1.35426	0.677130	+	0.735864i	$0.263224\pi$
$380$	5.31569	0.272689
$381$	21.0174	1.07675
$382$	−21.6005	−1.10518
$383$	32.3407	1.65253	0.826267	−	0.563279i	$-0.190460\pi$
$383$	32.3407	1.65253	0.826267	+	0.563279i	$0.190460\pi$
$384$	10.4778	0.534693
$385$	0.0505062	0.00257404
$386$	−16.1364	−0.821321
$387$	8.49201	0.431673
$388$	−2.04235	−0.103685
$389$	−28.3267	−1.43622	−0.718109	−	0.695930i	$-0.754992\pi$
$389$	−28.3267	−1.43622	−0.718109	+	0.695930i	$0.754992\pi$
$390$	1.16284	0.0588829
$391$	2.67857	0.135461
$392$	−9.92877	−0.501478
$393$	−8.21089	−0.414185
$394$	10.8262	0.545417
$395$	3.26956	0.164509
$396$	−0.812641	−0.0408367
$397$	12.7429	0.639548	0.319774	−	0.947494i	$-0.396393\pi$
$397$	12.7429	0.639548	0.319774	+	0.947494i	$0.396393\pi$
$398$	14.9564	0.749696
$399$	0.982068	0.0491649
$400$	23.1202	1.15601
$401$	−2.42265	−0.120981	−0.0604906	−	0.998169i	$-0.519267\pi$
$401$	−2.42265	−0.120981	−0.0604906	+	0.998169i	$0.519267\pi$
$402$	−7.69407	−0.383745
$403$	−3.43420	−0.171070
$404$	18.3928	0.915078
$405$	−0.580006	−0.0288207
$406$	2.06022	0.102247
$407$	6.23538	0.309077
$408$	0.616444	0.0305185
$409$	−13.5208	−0.668560	−0.334280	−	0.942474i	$-0.608493\pi$
$409$	−13.5208	−0.668560	−0.334280	+	0.942474i	$0.608493\pi$
$410$	−3.52047	−0.173864
$411$	−1.64076	−0.0809328
$412$	−14.5800	−0.718305
$413$	0.243379	0.0119759
$414$	11.0617	0.543653
$415$	−1.34959	−0.0662487
$416$	−6.75537	−0.331209
$417$	−17.3466	−0.849469
$418$	−9.16975	−0.448507
$419$	11.2025	0.547280	0.273640	−	0.961832i	$-0.411772\pi$
$419$	11.2025	0.547280	0.273640	+	0.961832i	$0.411772\pi$
$420$	0.0903842	0.00441030
$421$	−38.9053	−1.89613	−0.948064	−	0.318079i	$-0.896962\pi$
$421$	−38.9053	−1.89613	−0.948064	+	0.318079i	$0.896962\pi$
$422$	44.9527	2.18826
$423$	−11.2635	−0.547648
$424$	−6.86951	−0.333613
$425$	2.02199	0.0980811
$426$	−7.58294	−0.367395
$427$	−0.873157	−0.0422550
$428$	−6.60802	−0.319411
$429$	−0.754549	−0.0364300
$430$	8.81902	0.425291
$431$	−27.9326	−1.34547	−0.672734	−	0.739884i	$-0.734880\pi$
$431$	−27.9326	−1.34547	−0.672734	+	0.739884i	$0.734880\pi$
$432$	4.95759	0.238522
$433$	35.1693	1.69013	0.845064	−	0.534665i	$-0.179562\pi$
$433$	35.1693	1.69013	0.845064	+	0.534665i	$0.179562\pi$
$434$	−0.709623	−0.0340630
$435$	−5.16453	−0.247620
$436$	12.9811	0.621681
$437$	46.9515	2.24599
$438$	19.9818	0.954766
$439$	19.3958	0.925712	0.462856	−	0.886434i	$-0.346825\pi$
$439$	19.3958	0.925712	0.462856	+	0.886434i	$0.346825\pi$
$440$	0.555703	0.0264921
$441$	−6.98330	−0.332538
$442$	−0.869257	−0.0413463
$443$	30.6677	1.45707	0.728534	−	0.685010i	$-0.240202\pi$
$443$	30.6677	1.45707	0.728534	+	0.685010i	$0.240202\pi$
$444$	11.1586	0.529565
$445$	−6.08605	−0.288506
$446$	32.1491	1.52230
$447$	20.4055	0.965145
$448$	−0.114629	−0.00541571
$449$	1.02481	0.0483639	0.0241820	−	0.999708i	$-0.492302\pi$
$449$	1.02481	0.0483639	0.0241820	+	0.999708i	$0.492302\pi$
$450$	8.35022	0.393633
$451$	2.28437	0.107567
$452$	22.4709	1.05694
$453$	−11.5983	−0.544938
$454$	−19.9559	−0.936579
$455$	0.0839230	0.00393437
$456$	10.8054	0.506007
$457$	22.5240	1.05363	0.526813	−	0.849981i	$-0.323387\pi$
$457$	22.5240	1.05363	0.526813	+	0.849981i	$0.323387\pi$
$458$	−30.5323	−1.42668
$459$	0.433570	0.0202373
$460$	4.32115	0.201475
$461$	−33.9521	−1.58131	−0.790653	−	0.612265i	$-0.790259\pi$
$461$	−33.9521	−1.58131	−0.790653	+	0.612265i	$0.790259\pi$
$462$	−0.155916	−0.00725385
$463$	15.3364	0.712742	0.356371	−	0.934345i	$-0.384014\pi$
$463$	15.3364	0.712742	0.356371	+	0.934345i	$0.384014\pi$
$464$	44.1438	2.04932
$465$	1.77888	0.0824934
$466$	6.11986	0.283497
$467$	−5.14899	−0.238267	−0.119134	−	0.992878i	$-0.538012\pi$
$467$	−5.14899	−0.238267	−0.119134	+	0.992878i	$0.538012\pi$
$468$	−1.35031	−0.0624183
$469$	−0.555285	−0.0256407
$470$	−11.6972	−0.539551
$471$	10.3390	0.476397
$472$	2.67782	0.123257
$473$	−5.72251	−0.263121
$474$	−10.0933	−0.463601
$475$	35.4426	1.62622
$476$	−0.0675646	−0.00309682
$477$	−4.83160	−0.221224
$478$	−33.1088	−1.51436
$479$	−34.1427	−1.56002	−0.780011	−	0.625766i	$-0.784787\pi$
$479$	−34.1427	−1.56002	−0.780011	+	0.625766i	$0.784787\pi$
$480$	3.49921	0.159716
$481$	10.3609	0.472419
$482$	34.8628	1.58796
$483$	0.798328	0.0363252
$484$	−12.7176	−0.578075
$485$	0.982290	0.0446035
$486$	1.79051	0.0812193
$487$	−18.3414	−0.831126	−0.415563	−	0.909564i	$-0.636415\pi$
$487$	−18.3414	−0.831126	−0.415563	+	0.909564i	$0.636415\pi$
$488$	−9.60705	−0.434891
$489$	15.8826	0.718238
$490$	−7.25221	−0.327621
$491$	16.7143	0.754307	0.377154	−	0.926151i	$-0.376903\pi$
$491$	16.7143	0.754307	0.377154	+	0.926151i	$0.376903\pi$
$492$	4.08803	0.184303
$493$	3.86062	0.173874
$494$	−15.2368	−0.685536
$495$	0.390848	0.0175673
$496$	−15.2049	−0.682721
$497$	−0.547265	−0.0245482
$498$	4.16626	0.186694
$499$	7.16782	0.320876	0.160438	−	0.987046i	$-0.448709\pi$
$499$	7.16782	0.320876	0.160438	+	0.987046i	$0.448709\pi$
$500$	6.75918	0.302280
$501$	4.52117	0.201991
$502$	−30.8138	−1.37529
$503$	−33.4252	−1.49036	−0.745178	−	0.666865i	$-0.767636\pi$
$503$	−33.4252	−1.49036	−0.745178	+	0.666865i	$0.767636\pi$
$504$	0.183726	0.00818382
$505$	−8.84623	−0.393652
$506$	−7.45413	−0.331377
$507$	11.7462	0.521668
$508$	−25.3456	−1.12453
$509$	−30.9523	−1.37194	−0.685968	−	0.727632i	$-0.740621\pi$
$509$	−30.9523	−1.37194	−0.685968	+	0.727632i	$0.740621\pi$
$510$	0.450265	0.0199381
$511$	1.44209	0.0637945
$512$	−15.8121	−0.698804
$513$	7.59984	0.335541
$514$	2.73880	0.120803
$515$	7.01240	0.309003
$516$	−10.2408	−0.450826
$517$	7.59010	0.333812
$518$	2.14093	0.0940669
$519$	8.76842	0.384891
$520$	0.923376	0.0404927
$521$	−23.2532	−1.01874	−0.509371	−	0.860547i	$-0.670122\pi$
$521$	−23.2532	−1.01874	−0.509371	+	0.860547i	$0.670122\pi$
$522$	15.9432	0.697815
$523$	2.26600	0.0990851	0.0495425	−	0.998772i	$-0.484224\pi$
$523$	2.26600	0.0990851	0.0495425	+	0.998772i	$0.484224\pi$
$524$	9.90178	0.432561
$525$	0.602640	0.0263013
$526$	−36.7876	−1.60402
$527$	−1.32976	−0.0579252
$528$	−3.34077	−0.145388
$529$	15.1671	0.659438
$530$	−5.01765	−0.217953
$531$	1.88342	0.0817333
$532$	−1.18431	−0.0513463
$533$	3.79580	0.164414
$534$	18.7880	0.813035
$535$	3.17820	0.137405
$536$	−6.10961	−0.263895
$537$	−19.4820	−0.840708
$538$	−31.9933	−1.37933
$539$	4.70583	0.202695
$540$	0.699448	0.0300994
$541$	−3.45069	−0.148357	−0.0741783	−	0.997245i	$-0.523633\pi$
$541$	−3.45069	−0.148357	−0.0741783	+	0.997245i	$0.523633\pi$
$542$	42.1467	1.81036
$543$	−4.12420	−0.176986
$544$	−2.61575	−0.112149
$545$	−6.24338	−0.267437
$546$	−0.259075	−0.0110874
$547$	7.31995	0.312979	0.156489	−	0.987680i	$-0.449982\pi$
$547$	7.31995	0.312979	0.156489	+	0.987680i	$0.449982\pi$
$548$	1.97865	0.0845237
$549$	−6.75702	−0.288383
$550$	−5.62695	−0.239934
$551$	67.6711	2.88289
$552$	8.78373	0.373860
$553$	−0.728440	−0.0309764
$554$	40.6158	1.72560
$555$	−5.36686	−0.227810
$556$	20.9189	0.887158
$557$	16.8864	0.715499	0.357750	−	0.933818i	$-0.383544\pi$
$557$	16.8864	0.715499	0.357750	+	0.933818i	$0.383544\pi$
$558$	−5.49150	−0.232474
$559$	−9.50873	−0.402177
$560$	0.371569	0.0157017
$561$	−0.292169	−0.0123354
$562$	45.3920	1.91474
$563$	13.9328	0.587196	0.293598	−	0.955929i	$-0.405147\pi$
$563$	13.9328	0.587196	0.293598	+	0.955929i	$0.405147\pi$
$564$	13.5830	0.571947
$565$	−10.8076	−0.454679
$566$	22.9243	0.963582
$567$	0.129222	0.00542682
$568$	−6.02137	−0.252651
$569$	−9.58123	−0.401666	−0.200833	−	0.979625i	$-0.564365\pi$
$569$	−9.58123	−0.401666	−0.200833	+	0.979625i	$0.564365\pi$
$570$	7.89249	0.330580
$571$	24.4201	1.02195	0.510974	−	0.859596i	$-0.329285\pi$
$571$	24.4201	1.02195	0.510974	+	0.859596i	$0.329285\pi$
$572$	0.909935	0.0380463
$573$	−12.0639	−0.503976
$574$	0.784341	0.0327378
$575$	28.8114	1.20152
$576$	−0.887069	−0.0369612
$577$	17.2174	0.716768	0.358384	−	0.933574i	$-0.383328\pi$
$577$	17.2174	0.716768	0.358384	+	0.933574i	$0.383328\pi$
$578$	30.1021	1.25208
$579$	−9.01217	−0.374533
$580$	6.22808	0.258607
$581$	0.300681	0.0124743
$582$	−3.03239	−0.125696
$583$	3.25587	0.134844
$584$	15.8669	0.656576
$585$	0.649448	0.0268514
$586$	−6.85299	−0.283095
$587$	23.5925	0.973766	0.486883	−	0.873467i	$-0.338134\pi$
$587$	23.5925	0.973766	0.486883	+	0.873467i	$0.338134\pi$
$588$	8.42139	0.347292
$589$	−23.3087	−0.960419
$590$	1.95594	0.0805248
$591$	6.04644	0.248717
$592$	45.8731	1.88537
$593$	2.40591	0.0987987	0.0493994	−	0.998779i	$-0.484269\pi$
$593$	2.40591	0.0987987	0.0493994	+	0.998779i	$0.484269\pi$
$594$	−1.20657	−0.0495062
$595$	0.0324959	0.00133220
$596$	−24.6076	−1.00797
$597$	8.35314	0.341871
$598$	−12.3861	−0.506504
$599$	−13.5324	−0.552917	−0.276459	−	0.961026i	$-0.589161\pi$
$599$	−13.5324	−0.552917	−0.276459	+	0.961026i	$0.589161\pi$
$600$	6.63064	0.270695
$601$	−35.5973	−1.45204	−0.726021	−	0.687672i	$-0.758633\pi$
$601$	−35.5973	−1.45204	−0.726021	+	0.687672i	$0.758633\pi$
$602$	−1.96483	−0.0800805
$603$	−4.29714	−0.174993
$604$	13.9868	0.569116
$605$	6.11668	0.248679
$606$	27.3088	1.10934
$607$	18.7318	0.760301	0.380150	−	0.924925i	$-0.375872\pi$
$607$	18.7318	0.760301	0.380150	+	0.924925i	$0.375872\pi$
$608$	−45.8503	−1.85947
$609$	1.15063	0.0466259
$610$	−7.01722	−0.284119
$611$	12.6120	0.510227
$612$	−0.522856	−0.0211352
$613$	27.5964	1.11461	0.557303	−	0.830309i	$-0.311836\pi$
$613$	27.5964	1.11461	0.557303	+	0.830309i	$0.311836\pi$
$614$	−21.5382	−0.869209
$615$	−1.96618	−0.0792840
$616$	−0.123808	−0.00498835
$617$	10.6270	0.427826	0.213913	−	0.976853i	$-0.431379\pi$
$617$	10.6270	0.427826	0.213913	+	0.976853i	$0.431379\pi$
$618$	−21.6477	−0.870797
$619$	21.4746	0.863137	0.431569	−	0.902080i	$-0.357960\pi$
$619$	21.4746	0.863137	0.431569	+	0.902080i	$0.357960\pi$
$620$	−2.14521	−0.0861535
$621$	6.17795	0.247913
$622$	2.90894	0.116638
$623$	1.35594	0.0543245
$624$	−5.55115	−0.222224
$625$	20.0671	0.802683
$626$	−42.0149	−1.67925
$627$	−5.12130	−0.204525
$628$	−12.4682	−0.497534
$629$	4.01187	0.159964
$630$	0.134198	0.00534658
$631$	−29.9281	−1.19142	−0.595710	−	0.803200i	$-0.703129\pi$
$631$	−29.9281	−1.19142	−0.595710	+	0.803200i	$0.703129\pi$
$632$	−8.01477	−0.318810
$633$	25.1061	0.997876
$634$	−45.6450	−1.81280
$635$	12.1902	0.483754
$636$	5.82658	0.231039
$637$	7.81939	0.309815
$638$	−10.7436	−0.425345
$639$	−4.23507	−0.167537
$640$	6.07718	0.240222
$641$	−17.2757	−0.682349	−0.341174	−	0.940000i	$-0.610825\pi$
$641$	−17.2757	−0.682349	−0.341174	+	0.940000i	$0.610825\pi$
$642$	−9.81128	−0.387220
$643$	−25.9934	−1.02508	−0.512539	−	0.858664i	$-0.671295\pi$
$643$	−25.9934	−1.02508	−0.512539	+	0.858664i	$0.671295\pi$
$644$	−0.962730	−0.0379369
$645$	4.92542	0.193938
$646$	−5.89985	−0.232126
$647$	31.9097	1.25450	0.627250	−	0.778818i	$-0.284180\pi$
$647$	31.9097	1.25450	0.627250	+	0.778818i	$0.284180\pi$
$648$	1.42179	0.0558531
$649$	−1.26918	−0.0498195
$650$	−9.34996	−0.366736
$651$	−0.396324	−0.0155332
$652$	−19.1534	−0.750105
$653$	−37.2042	−1.45591	−0.727956	−	0.685624i	$-0.759530\pi$
$653$	−37.2042	−1.45591	−0.727956	+	0.685624i	$0.759530\pi$
$654$	19.2737	0.753661
$655$	−4.76237	−0.186081
$656$	16.8059	0.656160
$657$	11.1598	0.435386
$658$	2.60607	0.101595
$659$	25.4140	0.989988	0.494994	−	0.868896i	$-0.335170\pi$
$659$	25.4140	0.989988	0.494994	+	0.868896i	$0.335170\pi$
$660$	−0.471336	−0.0183467
$661$	−38.9865	−1.51640	−0.758199	−	0.652023i	$-0.773920\pi$
$661$	−38.9865	−1.51640	−0.758199	+	0.652023i	$0.773920\pi$
$662$	32.1585	1.24988
$663$	−0.485480	−0.0188545
$664$	3.30829	0.128386
$665$	0.569605	0.0220883
$666$	16.5678	0.641989
$667$	55.0102	2.13000
$668$	−5.45223	−0.210953
$669$	17.9553	0.694190
$670$	−4.46261	−0.172406
$671$	4.55335	0.175780
$672$	−0.779604	−0.0300739
$673$	−34.7593	−1.33987	−0.669937	−	0.742418i	$-0.733679\pi$
$673$	−34.7593	−1.33987	−0.669937	+	0.742418i	$0.733679\pi$
$674$	−32.4296	−1.24914
$675$	4.66359	0.179502
$676$	−14.1651	−0.544813
$677$	33.8164	1.29967	0.649834	−	0.760076i	$-0.274838\pi$
$677$	33.8164	1.29967	0.649834	+	0.760076i	$0.274838\pi$
$678$	33.3637	1.28133
$679$	−0.218849	−0.00839865
$680$	0.357541	0.0137111
$681$	−11.1454	−0.427092
$682$	3.70055	0.141701
$683$	−5.22081	−0.199769	−0.0998844	−	0.994999i	$-0.531847\pi$
$683$	−5.22081	−0.199769	−0.0998844	+	0.994999i	$0.531847\pi$
$684$	−9.16490	−0.350429
$685$	−0.951652	−0.0363607
$686$	3.23537	0.123527
$687$	−17.0523	−0.650585
$688$	−42.0999	−1.60505
$689$	5.41007	0.206107
$690$	6.41585	0.244247
$691$	47.1464	1.79353	0.896766	−	0.442504i	$-0.145910\pi$
$691$	47.1464	1.79353	0.896766	+	0.442504i	$0.145910\pi$
$692$	−10.5741	−0.401968
$693$	−0.0870788	−0.00330785
$694$	22.9026	0.869372
$695$	−10.0612	−0.381641
$696$	12.6600	0.479875
$697$	1.46977	0.0556716
$698$	39.3336	1.48880
$699$	3.41794	0.129278
$700$	−0.726743	−0.0274683
$701$	−19.4010	−0.732764	−0.366382	−	0.930464i	$-0.619404\pi$
$701$	−19.4010	−0.732764	−0.366382	+	0.930464i	$0.619404\pi$
$702$	−2.00488	−0.0756694
$703$	70.3222	2.65225
$704$	0.597768	0.0225292
$705$	−6.53287	−0.246042
$706$	−26.1353	−0.983614
$707$	1.97089	0.0741230
$708$	−2.27127	−0.0853597
$709$	3.44527	0.129390	0.0646949	−	0.997905i	$-0.479393\pi$
$709$	3.44527	0.129390	0.0646949	+	0.997905i	$0.479393\pi$
$710$	−4.39815	−0.165060
$711$	−5.63711	−0.211408
$712$	14.9189	0.559110
$713$	−18.9478	−0.709599
$714$	−0.100317	−0.00375426
$715$	−0.437643	−0.0163669
$716$	23.4939	0.878009
$717$	−18.4912	−0.690568
$718$	34.5381	1.28895
$719$	44.8701	1.67337	0.836685	−	0.547684i	$-0.184490\pi$
$719$	44.8701	1.67337	0.836685	+	0.547684i	$0.184490\pi$
$720$	2.87543	0.107161
$721$	−1.56232	−0.0581840
$722$	−69.3960	−2.58265
$723$	19.4708	0.724128
$724$	4.97350	0.184839
$725$	41.5259	1.54223
$726$	−18.8826	−0.700798
$727$	−33.4829	−1.24181	−0.620907	−	0.783884i	$-0.713235\pi$
$727$	−33.4829	−1.24181	−0.620907	+	0.783884i	$0.713235\pi$
$728$	−0.205723	−0.00762461
$729$	1.00000	0.0370370
$730$	11.5895	0.428948
$731$	−3.68188	−0.136179
$732$	8.14852	0.301178
$733$	36.4588	1.34664	0.673318	−	0.739353i	$-0.264869\pi$
$733$	36.4588	1.34664	0.673318	+	0.739353i	$0.264869\pi$
$734$	67.8857	2.50571
$735$	−4.05036	−0.149400
$736$	−37.2719	−1.37386
$737$	2.89571	0.106665
$738$	6.06971	0.223429
$739$	−14.1189	−0.519373	−0.259686	−	0.965693i	$-0.583619\pi$
$739$	−14.1189	−0.519373	−0.259686	+	0.965693i	$0.583619\pi$
$740$	6.47207	0.237918
$741$	−8.50975	−0.312613
$742$	1.11791	0.0410396
$743$	−4.40778	−0.161706	−0.0808529	−	0.996726i	$-0.525764\pi$
$743$	−4.40778	−0.161706	−0.0808529	+	0.996726i	$0.525764\pi$
$744$	−4.36062	−0.159868
$745$	11.8353	0.433611
$746$	1.85611	0.0679571
$747$	2.32685	0.0851351
$748$	0.352337	0.0128827
$749$	−0.708085	−0.0258729
$750$	10.0357	0.366452
$751$	15.8855	0.579669	0.289834	−	0.957077i	$-0.406400\pi$
$751$	15.8855	0.579669	0.289834	+	0.957077i	$0.406400\pi$
$752$	55.8397	2.03626
$753$	−17.2095	−0.627148
$754$	−17.8520	−0.650133
$755$	−6.72711	−0.244824
$756$	−0.155833	−0.00566760
$757$	21.3100	0.774527	0.387263	−	0.921969i	$-0.373420\pi$
$757$	21.3100	0.774527	0.387263	+	0.921969i	$0.373420\pi$
$758$	−47.2062	−1.71460
$759$	−4.16313	−0.151112
$760$	6.26717	0.227334
$761$	19.3813	0.702570	0.351285	−	0.936269i	$-0.385745\pi$
$761$	19.3813	0.702570	0.351285	+	0.936269i	$0.385745\pi$
$762$	−37.6319	−1.36326
$763$	1.39099	0.0503573
$764$	14.5482	0.526336
$765$	0.251473	0.00909203
$766$	−57.9064	−2.09224
$767$	−2.10891	−0.0761484
$768$	−20.5348	−0.740984
$769$	−49.8269	−1.79680	−0.898402	−	0.439175i	$-0.855271\pi$
$769$	−49.8269	−1.79680	−0.898402	+	0.439175i	$0.855271\pi$
$770$	−0.0904320	−0.00325894
$771$	1.52962	0.0550878
$772$	10.8681	0.391150
$773$	−12.0774	−0.434393	−0.217197	−	0.976128i	$-0.569691\pi$
$773$	−12.0774	−0.434393	−0.217197	+	0.976128i	$0.569691\pi$
$774$	−15.2051	−0.546534
$775$	−14.3032	−0.513787
$776$	−2.40792	−0.0864393
$777$	1.19571	0.0428957
$778$	50.7192	1.81837
$779$	25.7630	0.923054
$780$	−0.783190	−0.0280427
$781$	2.85388	0.102120
$782$	−4.79602	−0.171505
$783$	8.90427	0.318213
$784$	34.6204	1.23644
$785$	5.99669	0.214031
$786$	14.7017	0.524392
$787$	26.1610	0.932538	0.466269	−	0.884643i	$-0.345598\pi$
$787$	26.1610	0.932538	0.466269	+	0.884643i	$0.345598\pi$
$788$	−7.29160	−0.259753
$789$	−20.5459	−0.731452
$790$	−5.85418	−0.208282
$791$	2.40788	0.0856142
$792$	−0.958098	−0.0340445
$793$	7.56602	0.268677
$794$	−22.8163	−0.809721
$795$	−2.80236	−0.0993893
$796$	−10.0733	−0.357039
$797$	33.2555	1.17797	0.588985	−	0.808144i	$-0.299528\pi$
$797$	33.2555	1.17797	0.588985	+	0.808144i	$0.299528\pi$
$798$	−1.75840	−0.0622468
$799$	4.88350	0.172766
$800$	−28.1357	−0.994747
$801$	10.4931	0.370755
$802$	4.33778	0.153172
$803$	−7.52025	−0.265384
$804$	5.18206	0.182757
$805$	0.463035	0.0163198
$806$	6.14897	0.216588
$807$	−17.8682	−0.628992
$808$	21.6850	0.762877
$809$	20.4583	0.719274	0.359637	−	0.933092i	$-0.382900\pi$
$809$	20.4583	0.719274	0.359637	+	0.933092i	$0.382900\pi$
$810$	1.03851	0.0364894
$811$	−7.77429	−0.272992	−0.136496	−	0.990641i	$-0.543584\pi$
$811$	−7.77429	−0.272992	−0.136496	+	0.990641i	$0.543584\pi$
$812$	−1.38758	−0.0486946
$813$	23.5389	0.825545
$814$	−11.1645	−0.391317
$815$	9.21202	0.322683
$816$	−2.14946	−0.0752462
$817$	−64.5380	−2.25790
$818$	24.2091	0.846453
$819$	−0.144693	−0.00505600
$820$	2.37108	0.0828017
$821$	−15.5425	−0.542438	−0.271219	−	0.962518i	$-0.587427\pi$
$821$	−15.5425	−0.542438	−0.271219	+	0.962518i	$0.587427\pi$
$822$	2.93780	0.102468
$823$	−24.9921	−0.871171	−0.435586	−	0.900147i	$-0.643459\pi$
$823$	−24.9921	−0.871171	−0.435586	+	0.900147i	$0.643459\pi$
$824$	−17.1897	−0.598832
$825$	−3.14265	−0.109413
$826$	−0.435773	−0.0151625
$827$	33.1048	1.15117	0.575583	−	0.817743i	$-0.304775\pi$
$827$	33.1048	1.15117	0.575583	+	0.817743i	$0.304775\pi$
$828$	−7.45019	−0.258912
$829$	−34.0514	−1.18265	−0.591326	−	0.806432i	$-0.701395\pi$
$829$	−34.0514	−1.18265	−0.591326	+	0.806432i	$0.701395\pi$
$830$	2.41645	0.0838763
$831$	22.6839	0.786895
$832$	0.993274	0.0344356
$833$	3.02775	0.104905
$834$	31.0594	1.07550
$835$	2.62231	0.0907487
$836$	6.17594	0.213599
$837$	−3.06700	−0.106011
$838$	−20.0583	−0.692901
$839$	−1.64709	−0.0568640	−0.0284320	−	0.999596i	$-0.509051\pi$
$839$	−1.64709	−0.0568640	−0.0284320	+	0.999596i	$0.509051\pi$
$840$	0.106562	0.00367675
$841$	50.2861	1.73400
$842$	69.6604	2.40066
$843$	25.3514	0.873148
$844$	−30.2762	−1.04215
$845$	6.81287	0.234370
$846$	20.1674	0.693368
$847$	−1.36276	−0.0468251
$848$	23.9531	0.822553
$849$	12.8032	0.439406
$850$	−3.62040	−0.124179
$851$	57.1652	1.95960
$852$	5.10721	0.174970
$853$	−27.4035	−0.938278	−0.469139	−	0.883124i	$-0.655436\pi$
$853$	−27.4035	−0.938278	−0.469139	+	0.883124i	$0.655436\pi$
$854$	1.56340	0.0534984
$855$	4.40795	0.150749
$856$	−7.79081	−0.266285
$857$	−51.7936	−1.76924	−0.884618	−	0.466317i	$-0.845581\pi$
$857$	−51.7936	−1.76924	−0.884618	+	0.466317i	$0.845581\pi$
$858$	1.35103	0.0461234
$859$	38.9406	1.32864	0.664318	−	0.747450i	$-0.268722\pi$
$859$	38.9406	1.32864	0.664318	+	0.747450i	$0.268722\pi$
$860$	−5.93972	−0.202543
$861$	0.438054	0.0149288
$862$	50.0137	1.70347
$863$	−35.6222	−1.21259	−0.606297	−	0.795238i	$-0.707346\pi$
$863$	−35.6222	−1.21259	−0.606297	+	0.795238i	$0.707346\pi$
$864$	−6.03305	−0.205249
$865$	5.08574	0.172920
$866$	−62.9710	−2.13984
$867$	16.8120	0.570966
$868$	0.477940	0.0162223
$869$	3.79867	0.128861
$870$	9.24715	0.313508
$871$	4.81162	0.163035
$872$	15.3046	0.518279
$873$	−1.69359	−0.0573192
$874$	−84.0671	−2.84361
$875$	0.724282	0.0244852
$876$	−13.4580	−0.454703
$877$	−31.4997	−1.06367	−0.531834	−	0.846848i	$-0.678497\pi$
$877$	−31.4997	−1.06367	−0.531834	+	0.846848i	$0.678497\pi$
$878$	−34.7284	−1.17203
$879$	−3.82739	−0.129095
$880$	−1.93766	−0.0653187
$881$	16.2214	0.546513	0.273256	−	0.961941i	$-0.411899\pi$
$881$	16.2214	0.546513	0.273256	+	0.961941i	$0.411899\pi$
$882$	12.5037	0.421021
$883$	−17.7420	−0.597066	−0.298533	−	0.954399i	$-0.596497\pi$
$883$	−17.7420	−0.597066	−0.298533	+	0.954399i	$0.596497\pi$
$884$	0.585456	0.0196910
$885$	1.09239	0.0367204
$886$	−54.9109	−1.84477
$887$	−21.9512	−0.737050	−0.368525	−	0.929618i	$-0.620137\pi$
$887$	−21.9512	−0.737050	−0.368525	+	0.929618i	$0.620137\pi$
$888$	13.1559	0.441485
$889$	−2.71591	−0.0910888
$890$	10.8971	0.365273
$891$	−0.673869	−0.0225755
$892$	−21.6528	−0.724990
$893$	85.6006	2.86451
$894$	−36.5362	−1.22195
$895$	−11.2996	−0.377706
$896$	−1.35396	−0.0452327
$897$	−6.91761	−0.230972
$898$	−1.83494	−0.0612328
$899$	−27.3094	−0.910819
$900$	−5.62398	−0.187466
$901$	2.09484	0.0697891
$902$	−4.09019	−0.136189
$903$	−1.09736	−0.0365177
$904$	26.4930	0.881145
$905$	−2.39206	−0.0795147
$906$	20.7670	0.689936
$907$	21.1769	0.703168	0.351584	−	0.936156i	$-0.385643\pi$
$907$	21.1769	0.703168	0.351584	+	0.936156i	$0.385643\pi$
$908$	13.4406	0.446041
$909$	15.2520	0.505876
$910$	−0.150265	−0.00498124
$911$	20.7918	0.688862	0.344431	−	0.938812i	$-0.388072\pi$
$911$	20.7918	0.688862	0.344431	+	0.938812i	$0.388072\pi$
$912$	−37.6769	−1.24761
$913$	−1.56799	−0.0518930
$914$	−40.3294	−1.33398
$915$	−3.91911	−0.129562
$916$	20.5639	0.679450
$917$	1.06103	0.0350383
$918$	−0.776312	−0.0256221
$919$	44.4763	1.46714	0.733568	−	0.679616i	$-0.237853\pi$
$919$	44.4763	1.46714	0.733568	+	0.679616i	$0.237853\pi$
$920$	5.09461	0.167964
$921$	−12.0290	−0.396371
$922$	60.7916	2.00206
$923$	4.74212	0.156089
$924$	0.105011	0.00345461
$925$	43.1527	1.41885
$926$	−27.4600	−0.902390
$927$	−12.0902	−0.397095
$928$	−53.7200	−1.76344
$929$	−19.2583	−0.631844	−0.315922	−	0.948785i	$-0.602314\pi$
$929$	−19.2583	−0.631844	−0.315922	+	0.948785i	$0.602314\pi$
$930$	−3.18510	−0.104444
$931$	53.0720	1.73936
$932$	−4.12180	−0.135014
$933$	1.62464	0.0531884
$934$	9.21933	0.301666
$935$	−0.169460	−0.00554193
$936$	−1.59201	−0.0520366
$937$	−25.7938	−0.842648	−0.421324	−	0.906910i	$-0.638435\pi$
$937$	−25.7938	−0.842648	−0.421324	+	0.906910i	$0.638435\pi$
$938$	0.994245	0.0324632
$939$	−23.4653	−0.765762
$940$	7.87821	0.256959
$941$	−10.7942	−0.351882	−0.175941	−	0.984401i	$-0.556297\pi$
$941$	−10.7942	−0.351882	−0.175941	+	0.984401i	$0.556297\pi$
$942$	−18.5121	−0.603158
$943$	20.9428	0.681992
$944$	−9.33721	−0.303900
$945$	0.0749496	0.00243811
$946$	10.2462	0.333133
$947$	−20.5076	−0.666406	−0.333203	−	0.942855i	$-0.608129\pi$
$947$	−20.5076	−0.666406	−0.333203	+	0.942855i	$0.608129\pi$
$948$	6.79798	0.220788
$949$	−12.4959	−0.405635
$950$	−63.4604	−2.05893
$951$	−25.4927	−0.826658
$952$	−0.0796582	−0.00258174
$953$	−56.8250	−1.84074	−0.920371	−	0.391047i	$-0.872113\pi$
$953$	−56.8250	−1.84074	−0.920371	+	0.391047i	$0.872113\pi$
$954$	8.65104	0.280088
$955$	−6.99712	−0.226421
$956$	22.2992	0.721207
$957$	−6.00032	−0.193963
$958$	61.1330	1.97512
$959$	0.212023	0.00684657
$960$	−0.514505	−0.0166056
$961$	−21.5935	−0.696565
$962$	−18.5514	−0.598121
$963$	−5.47959	−0.176577
$964$	−23.4805	−0.756257
$965$	−5.22711	−0.168267
$966$	−1.42942	−0.0459907
$967$	57.3360	1.84380	0.921901	−	0.387427i	$-0.126636\pi$
$967$	57.3360	1.84380	0.921901	+	0.387427i	$0.126636\pi$
$968$	−14.9940	−0.481926
$969$	−3.29506	−0.105853
$970$	−1.75880	−0.0564717
$971$	−43.2660	−1.38847	−0.694235	−	0.719748i	$-0.744257\pi$
$971$	−43.2660	−1.38847	−0.694235	+	0.719748i	$0.744257\pi$
$972$	−1.20593	−0.0386803
$973$	2.24157	0.0718614
$974$	32.8404	1.05227
$975$	−5.22195	−0.167236
$976$	33.4986	1.07226
$977$	20.5904	0.658745	0.329372	−	0.944200i	$-0.393163\pi$
$977$	20.5904	0.658745	0.329372	+	0.944200i	$0.393163\pi$
$978$	−28.4381	−0.909349
$979$	−7.07096	−0.225989
$980$	4.88446	0.156028
$981$	10.7643	0.343679
$982$	−29.9272	−0.955016
$983$	39.6010	1.26308	0.631538	−	0.775345i	$-0.282424\pi$
$983$	39.6010	1.26308	0.631538	+	0.775345i	$0.282424\pi$
$984$	4.81976	0.153648
$985$	3.50697	0.111741
$986$	−6.91249	−0.220139
$987$	1.45549	0.0463287
$988$	10.2622	0.326483
$989$	−52.4632	−1.66823
$990$	−0.699818	−0.0222417
$991$	24.3937	0.774892	0.387446	−	0.921892i	$-0.373357\pi$
$991$	24.3937	0.774892	0.387446	+	0.921892i	$0.373357\pi$
$992$	18.5034	0.587482
$993$	17.9605	0.569960
$994$	0.979884	0.0310800
$995$	4.84487	0.153593
$996$	−2.80603	−0.0889124
$997$	−1.03191	−0.0326808	−0.0163404	−	0.999866i	$-0.505202\pi$
$997$	−1.03191	−0.0326808	−0.0163404	+	0.999866i	$0.505202\pi$
$998$	−12.8341	−0.406255
$999$	9.25311	0.292755

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.b.1.20	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.b.1.20	✓	106	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)

\(f(q)\)	\(=\)	\(q-1.79051 q^{2} -1.00000 q^{3} +1.20593 q^{4} -0.580006 q^{5} +1.79051 q^{6} +0.129222 q^{7} +1.42179 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.79051 q^{2} -1.00000 q^{3} +1.20593 q^{4} -0.580006 q^{5} +1.79051 q^{6} +0.129222 q^{7} +1.42179 q^{8} +1.00000 q^{9} +1.03851 q^{10} -0.673869 q^{11} -1.20593 q^{12} -1.11973 q^{13} -0.231374 q^{14} +0.580006 q^{15} -4.95759 q^{16} -0.433570 q^{17} -1.79051 q^{18} -7.59984 q^{19} -0.699448 q^{20} -0.129222 q^{21} +1.20657 q^{22} -6.17795 q^{23} -1.42179 q^{24} -4.66359 q^{25} +2.00488 q^{26} -1.00000 q^{27} +0.155833 q^{28} -8.90427 q^{29} -1.03851 q^{30} +3.06700 q^{31} +6.03305 q^{32} +0.673869 q^{33} +0.776312 q^{34} -0.0749496 q^{35} +1.20593 q^{36} -9.25311 q^{37} +13.6076 q^{38} +1.11973 q^{39} -0.824645 q^{40} -3.38993 q^{41} +0.231374 q^{42} +8.49201 q^{43} -0.812641 q^{44} -0.580006 q^{45} +11.0617 q^{46} -11.2635 q^{47} +4.95759 q^{48} -6.98330 q^{49} +8.35022 q^{50} +0.433570 q^{51} -1.35031 q^{52} -4.83160 q^{53} +1.79051 q^{54} +0.390848 q^{55} +0.183726 q^{56} +7.59984 q^{57} +15.9432 q^{58} +1.88342 q^{59} +0.699448 q^{60} -6.75702 q^{61} -5.49150 q^{62} +0.129222 q^{63} -0.887069 q^{64} +0.649448 q^{65} -1.20657 q^{66} -4.29714 q^{67} -0.522856 q^{68} +6.17795 q^{69} +0.134198 q^{70} -4.23507 q^{71} +1.42179 q^{72} +11.1598 q^{73} +16.5678 q^{74} +4.66359 q^{75} -9.16490 q^{76} -0.0870788 q^{77} -2.00488 q^{78} -5.63711 q^{79} +2.87543 q^{80} +1.00000 q^{81} +6.06971 q^{82} +2.32685 q^{83} -0.155833 q^{84} +0.251473 q^{85} -15.2051 q^{86} +8.90427 q^{87} -0.958098 q^{88} +10.4931 q^{89} +1.03851 q^{90} -0.144693 q^{91} -7.45019 q^{92} -3.06700 q^{93} +20.1674 q^{94} +4.40795 q^{95} -6.03305 q^{96} -1.69359 q^{97} +12.5037 q^{98} -0.673869 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9}+O(q^{10}) \) 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9	\( 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9} - 3 q^{10} + 55 q^{11} - 109 q^{12} - 8 q^{13} + 27 q^{14} - 16 q^{15} + 111 q^{16} + 28 q^{17} + 15 q^{18} + q^{19} + 54 q^{20} - 35 q^{21} + 20 q^{22} + 62 q^{23} - 48 q^{24} + 102 q^{25} + 21 q^{26} - 106 q^{27} + 79 q^{28} + 36 q^{29} + 3 q^{30} + q^{31} + 111 q^{32} - 55 q^{33} - 27 q^{34} + 72 q^{35} + 109 q^{36} + 31 q^{37} + 43 q^{38} + 8 q^{39} - 13 q^{40} + 35 q^{41} - 27 q^{42} + 98 q^{43} + 121 q^{44} + 16 q^{45} + 8 q^{46} + 75 q^{47} - 111 q^{48} + 49 q^{49} + 83 q^{50} - 28 q^{51} - 18 q^{52} + 60 q^{53} - 15 q^{54} + 14 q^{55} + 85 q^{56} - q^{57} + 65 q^{58} + 77 q^{59} - 54 q^{60} - 55 q^{61} + 83 q^{62} + 35 q^{63} + 122 q^{64} + 86 q^{65} - 20 q^{66} + 121 q^{67} + 80 q^{68} - 62 q^{69} - 11 q^{70} + 79 q^{71} + 48 q^{72} - 29 q^{73} + 91 q^{74} - 102 q^{75} - 10 q^{76} + 87 q^{77} - 21 q^{78} + 15 q^{79} + 108 q^{80} + 106 q^{81} + 21 q^{82} + 196 q^{83} - 79 q^{84} - 5 q^{85} + 65 q^{86} - 36 q^{87} + 84 q^{88} + 34 q^{89} - 3 q^{90} + 17 q^{91} + 162 q^{92} - q^{93} - 35 q^{94} + 113 q^{95} - 111 q^{96} - 63 q^{97} + 112 q^{98} + 55 q^{99}+O(q^{100}) \) 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9 - 3 * q^10 + 55 * q^11 - 109 * q^12 - 8 * q^13 + 27 * q^14 - 16 * q^15 + 111 * q^16 + 28 * q^17 + 15 * q^18 + q^19 + 54 * q^20 - 35 * q^21 + 20 * q^22 + 62 * q^23 - 48 * q^24 + 102 * q^25 + 21 * q^26 - 106 * q^27 + 79 * q^28 + 36 * q^29 + 3 * q^30 + q^31 + 111 * q^32 - 55 * q^33 - 27 * q^34 + 72 * q^35 + 109 * q^36 + 31 * q^37 + 43 * q^38 + 8 * q^39 - 13 * q^40 + 35 * q^41 - 27 * q^42 + 98 * q^43 + 121 * q^44 + 16 * q^45 + 8 * q^46 + 75 * q^47 - 111 * q^48 + 49 * q^49 + 83 * q^50 - 28 * q^51 - 18 * q^52 + 60 * q^53 - 15 * q^54 + 14 * q^55 + 85 * q^56 - q^57 + 65 * q^58 + 77 * q^59 - 54 * q^60 - 55 * q^61 + 83 * q^62 + 35 * q^63 + 122 * q^64 + 86 * q^65 - 20 * q^66 + 121 * q^67 + 80 * q^68 - 62 * q^69 - 11 * q^70 + 79 * q^71 + 48 * q^72 - 29 * q^73 + 91 * q^74 - 102 * q^75 - 10 * q^76 + 87 * q^77 - 21 * q^78 + 15 * q^79 + 108 * q^80 + 106 * q^81 + 21 * q^82 + 196 * q^83 - 79 * q^84 - 5 * q^85 + 65 * q^86 - 36 * q^87 + 84 * q^88 + 34 * q^89 - 3 * q^90 + 17 * q^91 + 162 * q^92 - q^93 - 35 * q^94 + 113 * q^95 - 111 * q^96 - 63 * q^97 + 112 * q^98 + 55 * q^99

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