LMFDB - Embedded newform 4006.2.a.i.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4006,2,Mod(1,4006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4006, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.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:	$31.9880710497$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.676583 q^{3} +1.00000 q^{4} -1.65458 q^{5} -0.676583 q^{6} +3.29858 q^{7} +1.00000 q^{8} -2.54224 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.676583 q^{3} +1.00000 q^{4} -1.65458 q^{5} -0.676583 q^{6} +3.29858 q^{7} +1.00000 q^{8} -2.54224 q^{9} -1.65458 q^{10} +5.58444 q^{11} -0.676583 q^{12} -0.428028 q^{13} +3.29858 q^{14} +1.11946 q^{15} +1.00000 q^{16} +3.61123 q^{17} -2.54224 q^{18} +3.36876 q^{19} -1.65458 q^{20} -2.23176 q^{21} +5.58444 q^{22} +0.496977 q^{23} -0.676583 q^{24} -2.26237 q^{25} -0.428028 q^{26} +3.74978 q^{27} +3.29858 q^{28} -2.59691 q^{29} +1.11946 q^{30} -8.75402 q^{31} +1.00000 q^{32} -3.77833 q^{33} +3.61123 q^{34} -5.45776 q^{35} -2.54224 q^{36} +1.22822 q^{37} +3.36876 q^{38} +0.289596 q^{39} -1.65458 q^{40} +3.45839 q^{41} -2.23176 q^{42} +9.11784 q^{43} +5.58444 q^{44} +4.20633 q^{45} +0.496977 q^{46} -2.38354 q^{47} -0.676583 q^{48} +3.88062 q^{49} -2.26237 q^{50} -2.44330 q^{51} -0.428028 q^{52} +3.55211 q^{53} +3.74978 q^{54} -9.23989 q^{55} +3.29858 q^{56} -2.27924 q^{57} -2.59691 q^{58} +6.55764 q^{59} +1.11946 q^{60} +10.1406 q^{61} -8.75402 q^{62} -8.38576 q^{63} +1.00000 q^{64} +0.708205 q^{65} -3.77833 q^{66} +0.840034 q^{67} +3.61123 q^{68} -0.336246 q^{69} -5.45776 q^{70} -15.5267 q^{71} -2.54224 q^{72} +2.78194 q^{73} +1.22822 q^{74} +1.53068 q^{75} +3.36876 q^{76} +18.4207 q^{77} +0.289596 q^{78} -12.8084 q^{79} -1.65458 q^{80} +5.08967 q^{81} +3.45839 q^{82} -9.96242 q^{83} -2.23176 q^{84} -5.97507 q^{85} +9.11784 q^{86} +1.75702 q^{87} +5.58444 q^{88} +1.84796 q^{89} +4.20633 q^{90} -1.41188 q^{91} +0.496977 q^{92} +5.92282 q^{93} -2.38354 q^{94} -5.57387 q^{95} -0.676583 q^{96} +11.8356 q^{97} +3.88062 q^{98} -14.1970 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) $ 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9} + 23 q^{10} + 39 q^{11} + 21 q^{12} + 8 q^{13} + 26 q^{14} + 14 q^{15} + 46 q^{16} + 36 q^{17} + 59 q^{18} + 37 q^{19} + 23 q^{20} + 20 q^{21} + 39 q^{22} + 38 q^{23} + 21 q^{24} + 57 q^{25} + 8 q^{26} + 63 q^{27} + 26 q^{28} + 23 q^{29} + 14 q^{30} + 44 q^{31} + 46 q^{32} + 25 q^{33} + 36 q^{34} + 26 q^{35} + 59 q^{36} + 9 q^{37} + 37 q^{38} - 2 q^{39} + 23 q^{40} + 50 q^{41} + 20 q^{42} + 46 q^{43} + 39 q^{44} + 30 q^{45} + 38 q^{46} + 57 q^{47} + 21 q^{48} + 62 q^{49} + 57 q^{50} + 5 q^{51} + 8 q^{52} + 21 q^{53} + 63 q^{54} + 40 q^{55} + 26 q^{56} + 3 q^{57} + 23 q^{58} + 68 q^{59} + 14 q^{60} - q^{61} + 44 q^{62} + 40 q^{63} + 46 q^{64} + 18 q^{65} + 25 q^{66} + 42 q^{67} + 36 q^{68} - 7 q^{69} + 26 q^{70} + 67 q^{71} + 59 q^{72} + 48 q^{73} + 9 q^{74} + 71 q^{75} + 37 q^{76} - 5 q^{77} - 2 q^{78} + 40 q^{79} + 23 q^{80} + 82 q^{81} + 50 q^{82} + 48 q^{83} + 20 q^{84} - 68 q^{85} + 46 q^{86} + 18 q^{87} + 39 q^{88} + 90 q^{89} + 30 q^{90} + 9 q^{91} + 38 q^{92} - 42 q^{93} + 57 q^{94} + 6 q^{95} + 21 q^{96} + 46 q^{97} + 62 q^{98} + 61 q^{99}+O(q^{100}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9 + 23 * q^10 + 39 * q^11 + 21 * q^12 + 8 * q^13 + 26 * q^14 + 14 * q^15 + 46 * q^16 + 36 * q^17 + 59 * q^18 + 37 * q^19 + 23 * q^20 + 20 * q^21 + 39 * q^22 + 38 * q^23 + 21 * q^24 + 57 * q^25 + 8 * q^26 + 63 * q^27 + 26 * q^28 + 23 * q^29 + 14 * q^30 + 44 * q^31 + 46 * q^32 + 25 * q^33 + 36 * q^34 + 26 * q^35 + 59 * q^36 + 9 * q^37 + 37 * q^38 - 2 * q^39 + 23 * q^40 + 50 * q^41 + 20 * q^42 + 46 * q^43 + 39 * q^44 + 30 * q^45 + 38 * q^46 + 57 * q^47 + 21 * q^48 + 62 * q^49 + 57 * q^50 + 5 * q^51 + 8 * q^52 + 21 * q^53 + 63 * q^54 + 40 * q^55 + 26 * q^56 + 3 * q^57 + 23 * q^58 + 68 * q^59 + 14 * q^60 - q^61 + 44 * q^62 + 40 * q^63 + 46 * q^64 + 18 * q^65 + 25 * q^66 + 42 * q^67 + 36 * q^68 - 7 * q^69 + 26 * q^70 + 67 * q^71 + 59 * q^72 + 48 * q^73 + 9 * q^74 + 71 * q^75 + 37 * q^76 - 5 * q^77 - 2 * q^78 + 40 * q^79 + 23 * q^80 + 82 * q^81 + 50 * q^82 + 48 * q^83 + 20 * q^84 - 68 * q^85 + 46 * q^86 + 18 * q^87 + 39 * q^88 + 90 * q^89 + 30 * q^90 + 9 * q^91 + 38 * q^92 - 42 * q^93 + 57 * q^94 + 6 * q^95 + 21 * q^96 + 46 * q^97 + 62 * q^98 + 61 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.676583	−0.390625	−0.195313	−	0.980741i	$-0.562572\pi$
$3$	−0.676583	−0.390625	−0.195313	+	0.980741i	$0.562572\pi$
$4$	1.00000	0.500000
$5$	−1.65458	−0.739950	−0.369975	−	0.929042i	$-0.620634\pi$
$5$	−1.65458	−0.739950	−0.369975	+	0.929042i	$0.620634\pi$
$6$	−0.676583	−0.276214
$7$	3.29858	1.24675	0.623373	−	0.781925i	$-0.285762\pi$
$7$	3.29858	1.24675	0.623373	+	0.781925i	$0.285762\pi$
$8$	1.00000	0.353553
$9$	−2.54224	−0.847412
$10$	−1.65458	−0.523224
$11$	5.58444	1.68377	0.841885	−	0.539656i	$-0.181446\pi$
$11$	5.58444	1.68377	0.841885	+	0.539656i	$0.181446\pi$
$12$	−0.676583	−0.195313
$13$	−0.428028	−0.118714	−0.0593568	−	0.998237i	$-0.518905\pi$
$13$	−0.428028	−0.118714	−0.0593568	+	0.998237i	$0.518905\pi$
$14$	3.29858	0.881582
$15$	1.11946	0.289043
$16$	1.00000	0.250000
$17$	3.61123	0.875853	0.437927	−	0.899011i	$-0.355713\pi$
$17$	3.61123	0.875853	0.437927	+	0.899011i	$0.355713\pi$
$18$	−2.54224	−0.599211
$19$	3.36876	0.772845	0.386423	−	0.922322i	$-0.373711\pi$
$19$	3.36876	0.772845	0.386423	+	0.922322i	$0.373711\pi$
$20$	−1.65458	−0.369975
$21$	−2.23176	−0.487010
$22$	5.58444	1.19061
$23$	0.496977	0.103627	0.0518134	−	0.998657i	$-0.483500\pi$
$23$	0.496977	0.103627	0.0518134	+	0.998657i	$0.483500\pi$
$24$	−0.676583	−0.138107
$25$	−2.26237	−0.452474
$26$	−0.428028	−0.0839431
$27$	3.74978	0.721646
$28$	3.29858	0.623373
$29$	−2.59691	−0.482234	−0.241117	−	0.970496i	$-0.577514\pi$
$29$	−2.59691	−0.482234	−0.241117	+	0.970496i	$0.577514\pi$
$30$	1.11946	0.204384
$31$	−8.75402	−1.57227	−0.786135	−	0.618055i	$-0.787921\pi$
$31$	−8.75402	−1.57227	−0.786135	+	0.618055i	$0.787921\pi$
$32$	1.00000	0.176777
$33$	−3.77833	−0.657723
$34$	3.61123	0.619322
$35$	−5.45776	−0.922529
$36$	−2.54224	−0.423706
$37$	1.22822	0.201918	0.100959	−	0.994891i	$-0.467809\pi$
$37$	1.22822	0.201918	0.100959	+	0.994891i	$0.467809\pi$
$38$	3.36876	0.546484
$39$	0.289596	0.0463725
$40$	−1.65458	−0.261612
$41$	3.45839	0.540110	0.270055	−	0.962845i	$-0.412958\pi$
$41$	3.45839	0.540110	0.270055	+	0.962845i	$0.412958\pi$
$42$	−2.23176	−0.344368
$43$	9.11784	1.39046	0.695229	−	0.718788i	$-0.255303\pi$
$43$	9.11784	1.39046	0.695229	+	0.718788i	$0.255303\pi$
$44$	5.58444	0.841885
$45$	4.20633	0.627043
$46$	0.496977	0.0732752
$47$	−2.38354	−0.347675	−0.173838	−	0.984774i	$-0.555617\pi$
$47$	−2.38354	−0.347675	−0.173838	+	0.984774i	$0.555617\pi$
$48$	−0.676583	−0.0976563
$49$	3.88062	0.554374
$50$	−2.26237	−0.319947
$51$	−2.44330	−0.342130
$52$	−0.428028	−0.0593568
$53$	3.55211	0.487920	0.243960	−	0.969785i	$-0.421553\pi$
$53$	3.55211	0.487920	0.243960	+	0.969785i	$0.421553\pi$
$54$	3.74978	0.510280
$55$	−9.23989	−1.24591
$56$	3.29858	0.440791
$57$	−2.27924	−0.301893
$58$	−2.59691	−0.340991
$59$	6.55764	0.853732	0.426866	−	0.904315i	$-0.359618\pi$
$59$	6.55764	0.853732	0.426866	+	0.904315i	$0.359618\pi$
$60$	1.11946	0.144522
$61$	10.1406	1.29837	0.649183	−	0.760632i	$-0.275111\pi$
$61$	10.1406	1.29837	0.649183	+	0.760632i	$0.275111\pi$
$62$	−8.75402	−1.11176
$63$	−8.38576	−1.05651
$64$	1.00000	0.125000
$65$	0.708205	0.0878421
$66$	−3.77833	−0.465081
$67$	0.840034	0.102627	0.0513133	−	0.998683i	$-0.483659\pi$
$67$	0.840034	0.102627	0.0513133	+	0.998683i	$0.483659\pi$
$68$	3.61123	0.437927
$69$	−0.336246	−0.0404792
$70$	−5.45776	−0.652327
$71$	−15.5267	−1.84268	−0.921338	−	0.388764i	$-0.872902\pi$
$71$	−15.5267	−1.84268	−0.921338	+	0.388764i	$0.872902\pi$
$72$	−2.54224	−0.299605
$73$	2.78194	0.325602	0.162801	−	0.986659i	$-0.447947\pi$
$73$	2.78194	0.325602	0.162801	+	0.986659i	$0.447947\pi$
$74$	1.22822	0.142778
$75$	1.53068	0.176748
$76$	3.36876	0.386423
$77$	18.4207	2.09923
$78$	0.289596	0.0327903
$79$	−12.8084	−1.44106	−0.720531	−	0.693423i	$-0.756102\pi$
$79$	−12.8084	−1.44106	−0.720531	+	0.693423i	$0.756102\pi$
$80$	−1.65458	−0.184988
$81$	5.08967	0.565519
$82$	3.45839	0.381916
$83$	−9.96242	−1.09352	−0.546759	−	0.837290i	$-0.684139\pi$
$83$	−9.96242	−1.09352	−0.546759	+	0.837290i	$0.684139\pi$
$84$	−2.23176	−0.243505
$85$	−5.97507	−0.648088
$86$	9.11784	0.983202
$87$	1.75702	0.188373
$88$	5.58444	0.595303
$89$	1.84796	0.195884	0.0979418	−	0.995192i	$-0.468774\pi$
$89$	1.84796	0.195884	0.0979418	+	0.995192i	$0.468774\pi$
$90$	4.20633	0.443386
$91$	−1.41188	−0.148006
$92$	0.496977	0.0518134
$93$	5.92282	0.614168
$94$	−2.38354	−0.245844
$95$	−5.57387	−0.571867
$96$	−0.676583	−0.0690534
$97$	11.8356	1.20172	0.600860	−	0.799355i	$-0.294825\pi$
$97$	11.8356	1.20172	0.600860	+	0.799355i	$0.294825\pi$
$98$	3.88062	0.392002
$99$	−14.1970	−1.42685
$100$	−2.26237	−0.226237
$101$	−5.50946	−0.548212	−0.274106	−	0.961699i	$-0.588382\pi$
$101$	−5.50946	−0.548212	−0.274106	+	0.961699i	$0.588382\pi$
$102$	−2.44330	−0.241923
$103$	4.57783	0.451067	0.225534	−	0.974235i	$-0.427587\pi$
$103$	4.57783	0.451067	0.225534	+	0.974235i	$0.427587\pi$
$104$	−0.428028	−0.0419716
$105$	3.69262	0.360363
$106$	3.55211	0.345011
$107$	6.11403	0.591066	0.295533	−	0.955333i	$-0.404503\pi$
$107$	6.11403	0.591066	0.295533	+	0.955333i	$0.404503\pi$
$108$	3.74978	0.360823
$109$	4.99257	0.478201	0.239101	−	0.970995i	$-0.423147\pi$
$109$	4.99257	0.478201	0.239101	+	0.970995i	$0.423147\pi$
$110$	−9.23989	−0.880989
$111$	−0.830993	−0.0788743
$112$	3.29858	0.311686
$113$	21.2190	1.99611	0.998056	−	0.0623175i	$-0.0198491\pi$
$113$	21.2190	1.99611	0.998056	+	0.0623175i	$0.0198491\pi$
$114$	−2.27924	−0.213470
$115$	−0.822287	−0.0766786
$116$	−2.59691	−0.241117
$117$	1.08815	0.100599
$118$	6.55764	0.603680
$119$	11.9119	1.09197
$120$	1.11946	0.102192
$121$	20.1859	1.83508
$122$	10.1406	0.918083
$123$	−2.33989	−0.210981
$124$	−8.75402	−0.786135
$125$	12.0162	1.07476
$126$	−8.38576	−0.747063
$127$	2.98084	0.264507	0.132253	−	0.991216i	$-0.457779\pi$
$127$	2.98084	0.264507	0.132253	+	0.991216i	$0.457779\pi$
$128$	1.00000	0.0883883
$129$	−6.16897	−0.543148
$130$	0.708205	0.0621137
$131$	4.13183	0.361000	0.180500	−	0.983575i	$-0.442228\pi$
$131$	4.13183	0.361000	0.180500	+	0.983575i	$0.442228\pi$
$132$	−3.77833	−0.328862
$133$	11.1121	0.963541
$134$	0.840034	0.0725679
$135$	−6.20431	−0.533982
$136$	3.61123	0.309661
$137$	13.7802	1.17732	0.588661	−	0.808380i	$-0.299655\pi$
$137$	13.7802	1.17732	0.588661	+	0.808380i	$0.299655\pi$
$138$	−0.336246	−0.0286231
$139$	12.2974	1.04305	0.521525	−	0.853236i	$-0.325363\pi$
$139$	12.2974	1.04305	0.521525	+	0.853236i	$0.325363\pi$
$140$	−5.45776	−0.461265
$141$	1.61266	0.135811
$142$	−15.5267	−1.30297
$143$	−2.39029	−0.199886
$144$	−2.54224	−0.211853
$145$	4.29679	0.356829
$146$	2.78194	0.230235
$147$	−2.62556	−0.216552
$148$	1.22822	0.100959
$149$	−2.70350	−0.221480	−0.110740	−	0.993849i	$-0.535322\pi$
$149$	−2.70350	−0.221480	−0.110740	+	0.993849i	$0.535322\pi$
$150$	1.53068	0.124980
$151$	−5.04602	−0.410639	−0.205320	−	0.978695i	$-0.565823\pi$
$151$	−5.04602	−0.410639	−0.205320	+	0.978695i	$0.565823\pi$
$152$	3.36876	0.273242
$153$	−9.18061	−0.742208
$154$	18.4207	1.48438
$155$	14.4842	1.16340
$156$	0.289596	0.0231862
$157$	5.67712	0.453084	0.226542	−	0.974001i	$-0.427258\pi$
$157$	5.67712	0.453084	0.226542	+	0.974001i	$0.427258\pi$
$158$	−12.8084	−1.01898
$159$	−2.40330	−0.190594
$160$	−1.65458	−0.130806
$161$	1.63932	0.129196
$162$	5.08967	0.399882
$163$	16.4670	1.28979	0.644896	−	0.764270i	$-0.276901\pi$
$163$	16.4670	1.28979	0.644896	+	0.764270i	$0.276901\pi$
$164$	3.45839	0.270055
$165$	6.25155	0.486682
$166$	−9.96242	−0.773234
$167$	24.8888	1.92595	0.962976	−	0.269586i	$-0.0868867\pi$
$167$	24.8888	1.92595	0.962976	+	0.269586i	$0.0868867\pi$
$168$	−2.23176	−0.172184
$169$	−12.8168	−0.985907
$170$	−5.97507	−0.458267
$171$	−8.56417	−0.654918
$172$	9.11784	0.695229
$173$	−23.9307	−1.81942	−0.909710	−	0.415245i	$-0.863696\pi$
$173$	−23.9307	−1.81942	−0.909710	+	0.415245i	$0.863696\pi$
$174$	1.75702	0.133200
$175$	−7.46260	−0.564120
$176$	5.58444	0.420943
$177$	−4.43678	−0.333489
$178$	1.84796	0.138511
$179$	9.70481	0.725371	0.362686	−	0.931912i	$-0.381860\pi$
$179$	9.70481	0.725371	0.362686	+	0.931912i	$0.381860\pi$
$180$	4.20633	0.313521
$181$	16.4253	1.22088	0.610440	−	0.792062i	$-0.290992\pi$
$181$	16.4253	1.22088	0.610440	+	0.792062i	$0.290992\pi$
$182$	−1.41188	−0.104656
$183$	−6.86093	−0.507174
$184$	0.496977	0.0366376
$185$	−2.03219	−0.149409
$186$	5.92282	0.434282
$187$	20.1667	1.47474
$188$	−2.38354	−0.173838
$189$	12.3689	0.899708
$190$	−5.57387	−0.404371
$191$	−7.28515	−0.527135	−0.263567	−	0.964641i	$-0.584899\pi$
$191$	−7.28515	−0.527135	−0.263567	+	0.964641i	$0.584899\pi$
$192$	−0.676583	−0.0488281
$193$	−25.4388	−1.83113	−0.915563	−	0.402174i	$-0.868255\pi$
$193$	−25.4388	−1.83113	−0.915563	+	0.402174i	$0.868255\pi$
$194$	11.8356	0.849744
$195$	−0.479159	−0.0343133
$196$	3.88062	0.277187
$197$	−25.7045	−1.83137	−0.915685	−	0.401897i	$-0.868351\pi$
$197$	−25.7045	−1.83137	−0.915685	+	0.401897i	$0.868351\pi$
$198$	−14.1970	−1.00893
$199$	−1.28178	−0.0908629	−0.0454315	−	0.998967i	$-0.514466\pi$
$199$	−1.28178	−0.0908629	−0.0454315	+	0.998967i	$0.514466\pi$
$200$	−2.26237	−0.159974
$201$	−0.568352	−0.0400885
$202$	−5.50946	−0.387645
$203$	−8.56611	−0.601223
$204$	−2.44330	−0.171065
$205$	−5.72218	−0.399655
$206$	4.57783	0.318953
$207$	−1.26343	−0.0878146
$208$	−0.428028	−0.0296784
$209$	18.8126	1.30129
$210$	3.69262	0.254815
$211$	−8.26737	−0.569149	−0.284575	−	0.958654i	$-0.591852\pi$
$211$	−8.26737	−0.569149	−0.284575	+	0.958654i	$0.591852\pi$
$212$	3.55211	0.243960
$213$	10.5051	0.719795
$214$	6.11403	0.417947
$215$	−15.0862	−1.02887
$216$	3.74978	0.255140
$217$	−28.8758	−1.96022
$218$	4.99257	0.338139
$219$	−1.88221	−0.127188
$220$	−9.23989	−0.622953
$221$	−1.54571	−0.103976
$222$	−0.830993	−0.0557726
$223$	9.54293	0.639042	0.319521	−	0.947579i	$-0.396478\pi$
$223$	9.54293	0.639042	0.319521	+	0.947579i	$0.396478\pi$
$224$	3.29858	0.220396
$225$	5.75148	0.383432
$226$	21.2190	1.41146
$227$	13.7467	0.912399	0.456199	−	0.889878i	$-0.349210\pi$
$227$	13.7467	0.912399	0.456199	+	0.889878i	$0.349210\pi$
$228$	−2.27924	−0.150946
$229$	−2.45132	−0.161988	−0.0809939	−	0.996715i	$-0.525809\pi$
$229$	−2.45132	−0.161988	−0.0809939	+	0.996715i	$0.525809\pi$
$230$	−0.822287	−0.0542200
$231$	−12.4631	−0.820013
$232$	−2.59691	−0.170495
$233$	−1.89178	−0.123935	−0.0619673	−	0.998078i	$-0.519737\pi$
$233$	−1.89178	−0.123935	−0.0619673	+	0.998078i	$0.519737\pi$
$234$	1.08815	0.0711344
$235$	3.94376	0.257262
$236$	6.55764	0.426866
$237$	8.66596	0.562915
$238$	11.9119	0.772136
$239$	25.1793	1.62872	0.814358	−	0.580363i	$-0.197090\pi$
$239$	25.1793	1.62872	0.814358	+	0.580363i	$0.197090\pi$
$240$	1.11946	0.0722608
$241$	17.8224	1.14804	0.574022	−	0.818840i	$-0.305382\pi$
$241$	17.8224	1.14804	0.574022	+	0.818840i	$0.305382\pi$
$242$	20.1859	1.29760
$243$	−14.6929	−0.942552
$244$	10.1406	0.649183
$245$	−6.42079	−0.410209
$246$	−2.33989	−0.149186
$247$	−1.44192	−0.0917472
$248$	−8.75402	−0.555881
$249$	6.74040	0.427156
$250$	12.0162	0.759969
$251$	−19.1769	−1.21044	−0.605218	−	0.796060i	$-0.706914\pi$
$251$	−19.1769	−1.21044	−0.605218	+	0.796060i	$0.706914\pi$
$252$	−8.38576	−0.528254
$253$	2.77533	0.174484
$254$	2.98084	0.187034
$255$	4.04263	0.253159
$256$	1.00000	0.0625000
$257$	21.1599	1.31992	0.659958	−	0.751303i	$-0.270574\pi$
$257$	21.1599	1.31992	0.659958	+	0.751303i	$0.270574\pi$
$258$	−6.16897	−0.384064
$259$	4.05138	0.251741
$260$	0.708205	0.0439210
$261$	6.60195	0.408651
$262$	4.13183	0.255265
$263$	−11.4536	−0.706262	−0.353131	−	0.935574i	$-0.614883\pi$
$263$	−11.4536	−0.706262	−0.353131	+	0.935574i	$0.614883\pi$
$264$	−3.77833	−0.232540
$265$	−5.87724	−0.361036
$266$	11.1121	0.681327
$267$	−1.25030	−0.0765171
$268$	0.840034	0.0513133
$269$	−3.19130	−0.194577	−0.0972886	−	0.995256i	$-0.531017\pi$
$269$	−3.19130	−0.194577	−0.0972886	+	0.995256i	$0.531017\pi$
$270$	−6.20431	−0.377582
$271$	−16.8017	−1.02063	−0.510314	−	0.859988i	$-0.670471\pi$
$271$	−16.8017	−1.02063	−0.510314	+	0.859988i	$0.670471\pi$
$272$	3.61123	0.218963
$273$	0.955255	0.0578147
$274$	13.7802	0.832492
$275$	−12.6341	−0.761862
$276$	−0.336246	−0.0202396
$277$	−27.4118	−1.64702	−0.823508	−	0.567305i	$-0.807986\pi$
$277$	−27.4118	−1.64702	−0.823508	+	0.567305i	$0.807986\pi$
$278$	12.2974	0.737547
$279$	22.2548	1.33236
$280$	−5.45776	−0.326163
$281$	1.34077	0.0799836	0.0399918	−	0.999200i	$-0.487267\pi$
$281$	1.34077	0.0799836	0.0399918	+	0.999200i	$0.487267\pi$
$282$	1.61266	0.0960327
$283$	19.7543	1.17427	0.587137	−	0.809488i	$-0.300255\pi$
$283$	19.7543	1.17427	0.587137	+	0.809488i	$0.300255\pi$
$284$	−15.5267	−0.921338
$285$	3.77118	0.223386
$286$	−2.39029	−0.141341
$287$	11.4078	0.673380
$288$	−2.54224	−0.149803
$289$	−3.95898	−0.232881
$290$	4.29679	0.252316
$291$	−8.00774	−0.469422
$292$	2.78194	0.162801
$293$	−32.1468	−1.87804	−0.939019	−	0.343864i	$-0.888264\pi$
$293$	−32.1468	−1.87804	−0.939019	+	0.343864i	$0.888264\pi$
$294$	−2.62556	−0.153126
$295$	−10.8501	−0.631719
$296$	1.22822	0.0713889
$297$	20.9404	1.21509
$298$	−2.70350	−0.156610
$299$	−0.212720	−0.0123019
$300$	1.53068	0.0883739
$301$	30.0759	1.73355
$302$	−5.04602	−0.290366
$303$	3.72761	0.214145
$304$	3.36876	0.193211
$305$	−16.7784	−0.960726
$306$	−9.18061	−0.524821
$307$	−20.2540	−1.15596	−0.577979	−	0.816051i	$-0.696159\pi$
$307$	−20.2540	−1.15596	−0.577979	+	0.816051i	$0.696159\pi$
$308$	18.4207	1.04962
$309$	−3.09728	−0.176198
$310$	14.4842	0.822649
$311$	−16.7206	−0.948136	−0.474068	−	0.880488i	$-0.657215\pi$
$311$	−16.7206	−0.948136	−0.474068	+	0.880488i	$0.657215\pi$
$312$	0.289596	0.0163951
$313$	−1.00965	−0.0570688	−0.0285344	−	0.999593i	$-0.509084\pi$
$313$	−1.00965	−0.0570688	−0.0285344	+	0.999593i	$0.509084\pi$
$314$	5.67712	0.320379
$315$	13.8749	0.781762
$316$	−12.8084	−0.720531
$317$	14.9009	0.836915	0.418458	−	0.908236i	$-0.362571\pi$
$317$	14.9009	0.836915	0.418458	+	0.908236i	$0.362571\pi$
$318$	−2.40330	−0.134770
$319$	−14.5023	−0.811971
$320$	−1.65458	−0.0924938
$321$	−4.13665	−0.230885
$322$	1.63932	0.0913555
$323$	12.1654	0.676899
$324$	5.08967	0.282760
$325$	0.968357	0.0537148
$326$	16.4670	0.912021
$327$	−3.37788	−0.186797
$328$	3.45839	0.190958
$329$	−7.86230	−0.433463
$330$	6.25155	0.344136
$331$	−15.7243	−0.864286	−0.432143	−	0.901805i	$-0.642242\pi$
$331$	−15.7243	−0.864286	−0.432143	+	0.901805i	$0.642242\pi$
$332$	−9.96242	−0.546759
$333$	−3.12243	−0.171108
$334$	24.8888	1.36185
$335$	−1.38990	−0.0759385
$336$	−2.23176	−0.121753
$337$	−8.96007	−0.488086	−0.244043	−	0.969764i	$-0.578474\pi$
$337$	−8.96007	−0.488086	−0.244043	+	0.969764i	$0.578474\pi$
$338$	−12.8168	−0.697142
$339$	−14.3564	−0.779732
$340$	−5.97507	−0.324044
$341$	−48.8863	−2.64734
$342$	−8.56417	−0.463097
$343$	−10.2895	−0.555582
$344$	9.11784	0.491601
$345$	0.556345	0.0299526
$346$	−23.9307	−1.28652
$347$	20.0486	1.07626	0.538131	−	0.842861i	$-0.319130\pi$
$347$	20.0486	1.07626	0.538131	+	0.842861i	$0.319130\pi$
$348$	1.75702	0.0941863
$349$	27.8258	1.48948	0.744741	−	0.667353i	$-0.232573\pi$
$349$	27.8258	1.48948	0.744741	+	0.667353i	$0.232573\pi$
$350$	−7.46260	−0.398893
$351$	−1.60501	−0.0856691
$352$	5.58444	0.297651
$353$	8.91375	0.474431	0.237216	−	0.971457i	$-0.423765\pi$
$353$	8.91375	0.474431	0.237216	+	0.971457i	$0.423765\pi$
$354$	−4.43678	−0.235812
$355$	25.6901	1.36349
$356$	1.84796	0.0979418
$357$	−8.05941	−0.426549
$358$	9.70481	0.512915
$359$	36.6570	1.93468	0.967341	−	0.253479i	$-0.0815748\pi$
$359$	36.6570	1.93468	0.967341	+	0.253479i	$0.0815748\pi$
$360$	4.20633	0.221693
$361$	−7.65149	−0.402710
$362$	16.4253	0.863293
$363$	−13.6574	−0.716830
$364$	−1.41188	−0.0740028
$365$	−4.60294	−0.240929
$366$	−6.86093	−0.358626
$367$	−4.60045	−0.240142	−0.120071	−	0.992765i	$-0.538312\pi$
$367$	−4.60045	−0.240142	−0.120071	+	0.992765i	$0.538312\pi$
$368$	0.496977	0.0259067
$369$	−8.79205	−0.457696
$370$	−2.03219	−0.105648
$371$	11.7169	0.608312
$372$	5.92282	0.307084
$373$	−6.35424	−0.329010	−0.164505	−	0.986376i	$-0.552603\pi$
$373$	−6.35424	−0.329010	−0.164505	+	0.986376i	$0.552603\pi$
$374$	20.1667	1.04280
$375$	−8.12993	−0.419828
$376$	−2.38354	−0.122922
$377$	1.11155	0.0572477
$378$	12.3689	0.636190
$379$	−13.0565	−0.670666	−0.335333	−	0.942100i	$-0.608849\pi$
$379$	−13.0565	−0.670666	−0.335333	+	0.942100i	$0.608849\pi$
$380$	−5.57387	−0.285933
$381$	−2.01678	−0.103323
$382$	−7.28515	−0.372740
$383$	25.3105	1.29331	0.646654	−	0.762783i	$-0.276168\pi$
$383$	25.3105	1.29331	0.646654	+	0.762783i	$0.276168\pi$
$384$	−0.676583	−0.0345267
$385$	−30.4785	−1.55333
$386$	−25.4388	−1.29480
$387$	−23.1797	−1.17829
$388$	11.8356	0.600860
$389$	2.10430	0.106692	0.0533462	−	0.998576i	$-0.483011\pi$
$389$	2.10430	0.106692	0.0533462	+	0.998576i	$0.483011\pi$
$390$	−0.479159	−0.0242632
$391$	1.79470	0.0907618
$392$	3.88062	0.196001
$393$	−2.79553	−0.141016
$394$	−25.7045	−1.29497
$395$	21.1926	1.06631
$396$	−14.1970	−0.713424
$397$	−15.4005	−0.772930	−0.386465	−	0.922304i	$-0.626304\pi$
$397$	−15.4005	−0.772930	−0.386465	+	0.922304i	$0.626304\pi$
$398$	−1.28178	−0.0642498
$399$	−7.51826	−0.376384
$400$	−2.26237	−0.113118
$401$	29.1646	1.45641	0.728205	−	0.685359i	$-0.240355\pi$
$401$	29.1646	1.45641	0.728205	+	0.685359i	$0.240355\pi$
$402$	−0.568352	−0.0283468
$403$	3.74696	0.186650
$404$	−5.50946	−0.274106
$405$	−8.42126	−0.418456
$406$	−8.56611	−0.425129
$407$	6.85892	0.339984
$408$	−2.44330	−0.120961
$409$	−16.7066	−0.826089	−0.413045	−	0.910711i	$-0.635535\pi$
$409$	−16.7066	−0.826089	−0.413045	+	0.910711i	$0.635535\pi$
$410$	−5.72218	−0.282598
$411$	−9.32344	−0.459891
$412$	4.57783	0.225534
$413$	21.6309	1.06439
$414$	−1.26343	−0.0620943
$415$	16.4836	0.809149
$416$	−0.428028	−0.0209858
$417$	−8.32019	−0.407441
$418$	18.8126	0.920154
$419$	−23.2769	−1.13715	−0.568575	−	0.822631i	$-0.692505\pi$
$419$	−23.2769	−1.13715	−0.568575	+	0.822631i	$0.692505\pi$
$420$	3.69262	0.180182
$421$	−10.5463	−0.513994	−0.256997	−	0.966412i	$-0.582733\pi$
$421$	−10.5463	−0.513994	−0.256997	+	0.966412i	$0.582733\pi$
$422$	−8.26737	−0.402449
$423$	6.05953	0.294624
$424$	3.55211	0.172506
$425$	−8.16995	−0.396301
$426$	10.5051	0.508972
$427$	33.4494	1.61873
$428$	6.11403	0.295533
$429$	1.61723	0.0780806
$430$	−15.0862	−0.727521
$431$	−2.31258	−0.111393	−0.0556965	−	0.998448i	$-0.517738\pi$
$431$	−2.31258	−0.111393	−0.0556965	+	0.998448i	$0.517738\pi$
$432$	3.74978	0.180411
$433$	16.6026	0.797872	0.398936	−	0.916979i	$-0.369380\pi$
$433$	16.6026	0.797872	0.398936	+	0.916979i	$0.369380\pi$
$434$	−28.8758	−1.38608
$435$	−2.90713	−0.139386
$436$	4.99257	0.239101
$437$	1.67419	0.0800875
$438$	−1.88221	−0.0899356
$439$	−9.60639	−0.458488	−0.229244	−	0.973369i	$-0.573625\pi$
$439$	−9.60639	−0.458488	−0.229244	+	0.973369i	$0.573625\pi$
$440$	−9.23989	−0.440494
$441$	−9.86545	−0.469783
$442$	−1.54571	−0.0735219
$443$	−28.8654	−1.37143	−0.685717	−	0.727868i	$-0.740511\pi$
$443$	−28.8654	−1.37143	−0.685717	+	0.727868i	$0.740511\pi$
$444$	−0.830993	−0.0394372
$445$	−3.05760	−0.144944
$446$	9.54293	0.451871
$447$	1.82914	0.0865155
$448$	3.29858	0.155843
$449$	15.5270	0.732764	0.366382	−	0.930465i	$-0.380596\pi$
$449$	15.5270	0.732764	0.366382	+	0.930465i	$0.380596\pi$
$450$	5.75148	0.271127
$451$	19.3132	0.909422
$452$	21.2190	0.998056
$453$	3.41405	0.160406
$454$	13.7467	0.645163
$455$	2.33607	0.109517
$456$	−2.27924	−0.106735
$457$	−8.28544	−0.387577	−0.193788	−	0.981043i	$-0.562078\pi$
$457$	−8.28544	−0.387577	−0.193788	+	0.981043i	$0.562078\pi$
$458$	−2.45132	−0.114543
$459$	13.5413	0.632056
$460$	−0.822287	−0.0383393
$461$	−22.8531	−1.06437	−0.532187	−	0.846627i	$-0.678629\pi$
$461$	−22.8531	−1.06437	−0.532187	+	0.846627i	$0.678629\pi$
$462$	−12.4631	−0.579837
$463$	−25.2125	−1.17172	−0.585861	−	0.810411i	$-0.699244\pi$
$463$	−25.2125	−1.17172	−0.585861	+	0.810411i	$0.699244\pi$
$464$	−2.59691	−0.120558
$465$	−9.79977	−0.454454
$466$	−1.89178	−0.0876350
$467$	13.2235	0.611912	0.305956	−	0.952046i	$-0.401024\pi$
$467$	13.2235	0.611912	0.305956	+	0.952046i	$0.401024\pi$
$468$	1.08815	0.0502996
$469$	2.77092	0.127949
$470$	3.94376	0.181912
$471$	−3.84104	−0.176986
$472$	6.55764	0.301840
$473$	50.9180	2.34121
$474$	8.66596	0.398041
$475$	−7.62137	−0.349692
$476$	11.9119	0.545983
$477$	−9.03030	−0.413469
$478$	25.1793	1.15168
$479$	14.4898	0.662055	0.331028	−	0.943621i	$-0.392605\pi$
$479$	14.4898	0.662055	0.331028	+	0.943621i	$0.392605\pi$
$480$	1.11946	0.0510961
$481$	−0.525712	−0.0239704
$482$	17.8224	0.811790
$483$	−1.10913	−0.0504673
$484$	20.1859	0.917542
$485$	−19.5829	−0.889212
$486$	−14.6929	−0.666485
$487$	19.7764	0.896155	0.448078	−	0.893995i	$-0.352109\pi$
$487$	19.7764	0.896155	0.448078	+	0.893995i	$0.352109\pi$
$488$	10.1406	0.459042
$489$	−11.1413	−0.503825
$490$	−6.42079	−0.290062
$491$	−37.1360	−1.67593	−0.837963	−	0.545727i	$-0.816254\pi$
$491$	−37.1360	−1.67593	−0.837963	+	0.545727i	$0.816254\pi$
$492$	−2.33989	−0.105490
$493$	−9.37805	−0.422366
$494$	−1.44192	−0.0648751
$495$	23.4900	1.05580
$496$	−8.75402	−0.393067
$497$	−51.2159	−2.29735
$498$	6.74040	0.302045
$499$	−7.88880	−0.353151	−0.176576	−	0.984287i	$-0.556502\pi$
$499$	−7.88880	−0.353151	−0.176576	+	0.984287i	$0.556502\pi$
$500$	12.0162	0.537379
$501$	−16.8393	−0.752326
$502$	−19.1769	−0.855908
$503$	−2.05731	−0.0917309	−0.0458655	−	0.998948i	$-0.514605\pi$
$503$	−2.05731	−0.0917309	−0.0458655	+	0.998948i	$0.514605\pi$
$504$	−8.38576	−0.373532
$505$	9.11584	0.405650
$506$	2.77533	0.123379
$507$	8.67162	0.385120
$508$	2.98084	0.132253
$509$	16.1044	0.713815	0.356907	−	0.934140i	$-0.383831\pi$
$509$	16.1044	0.713815	0.356907	+	0.934140i	$0.383831\pi$
$510$	4.04263	0.179011
$511$	9.17645	0.405942
$512$	1.00000	0.0441942
$513$	12.6321	0.557720
$514$	21.1599	0.933321
$515$	−7.57438	−0.333767
$516$	−6.16897	−0.271574
$517$	−13.3107	−0.585405
$518$	4.05138	0.178008
$519$	16.1911	0.710711
$520$	0.708205	0.0310569
$521$	32.1266	1.40749	0.703745	−	0.710452i	$-0.251510\pi$
$521$	32.1266	1.40749	0.703745	+	0.710452i	$0.251510\pi$
$522$	6.60195	0.288960
$523$	−28.8986	−1.26365	−0.631824	−	0.775112i	$-0.717693\pi$
$523$	−28.8986	−1.26365	−0.631824	+	0.775112i	$0.717693\pi$
$524$	4.13183	0.180500
$525$	5.04907	0.220359
$526$	−11.4536	−0.499403
$527$	−31.6128	−1.37708
$528$	−3.77833	−0.164431
$529$	−22.7530	−0.989261
$530$	−5.87724	−0.255291
$531$	−16.6711	−0.723463
$532$	11.1121	0.481771
$533$	−1.48029	−0.0641184
$534$	−1.25030	−0.0541058
$535$	−10.1161	−0.437359
$536$	0.840034	0.0362839
$537$	−6.56610	−0.283348
$538$	−3.19130	−0.137587
$539$	21.6711	0.933439
$540$	−6.20431	−0.266991
$541$	−45.6060	−1.96076	−0.980379	−	0.197124i	$-0.936840\pi$
$541$	−45.6060	−1.96076	−0.980379	+	0.197124i	$0.936840\pi$
$542$	−16.8017	−0.721693
$543$	−11.1131	−0.476907
$544$	3.61123	0.154830
$545$	−8.26059	−0.353845
$546$	0.955255	0.0408812
$547$	−26.9939	−1.15418	−0.577088	−	0.816682i	$-0.695811\pi$
$547$	−26.9939	−1.15418	−0.577088	+	0.816682i	$0.695811\pi$
$548$	13.7802	0.588661
$549$	−25.7797	−1.10025
$550$	−12.6341	−0.538718
$551$	−8.74835	−0.372692
$552$	−0.336246	−0.0143116
$553$	−42.2496	−1.79664
$554$	−27.4118	−1.16462
$555$	1.37494	0.0583631
$556$	12.2974	0.521525
$557$	42.1452	1.78575	0.892875	−	0.450304i	$-0.148684\pi$
$557$	42.1452	1.78575	0.892875	+	0.450304i	$0.148684\pi$
$558$	22.2548	0.942121
$559$	−3.90269	−0.165066
$560$	−5.45776	−0.230632
$561$	−13.6444	−0.576069
$562$	1.34077	0.0565569
$563$	14.2210	0.599342	0.299671	−	0.954043i	$-0.403123\pi$
$563$	14.2210	0.599342	0.299671	+	0.954043i	$0.403123\pi$
$564$	1.61266	0.0679054
$565$	−35.1085	−1.47702
$566$	19.7543	0.830336
$567$	16.7887	0.705058
$568$	−15.5267	−0.651484
$569$	−5.41254	−0.226906	−0.113453	−	0.993543i	$-0.536191\pi$
$569$	−5.41254	−0.226906	−0.113453	+	0.993543i	$0.536191\pi$
$570$	3.77118	0.157957
$571$	7.87465	0.329544	0.164772	−	0.986332i	$-0.447311\pi$
$571$	7.87465	0.329544	0.164772	+	0.986332i	$0.447311\pi$
$572$	−2.39029	−0.0999432
$573$	4.92900	0.205912
$574$	11.4078	0.476151
$575$	−1.12434	−0.0468884
$576$	−2.54224	−0.105927
$577$	41.5728	1.73070	0.865350	−	0.501168i	$-0.167096\pi$
$577$	41.5728	1.73070	0.865350	+	0.501168i	$0.167096\pi$
$578$	−3.95898	−0.164672
$579$	17.2115	0.715284
$580$	4.29679	0.178414
$581$	−32.8618	−1.36334
$582$	−8.00774	−0.331931
$583$	19.8365	0.821545
$584$	2.78194	0.115118
$585$	−1.80043	−0.0744384
$586$	−32.1468	−1.32797
$587$	−36.8546	−1.52115	−0.760575	−	0.649250i	$-0.775083\pi$
$587$	−36.8546	−1.52115	−0.760575	+	0.649250i	$0.775083\pi$
$588$	−2.62556	−0.108276
$589$	−29.4902	−1.21512
$590$	−10.8501	−0.446693
$591$	17.3912	0.715379
$592$	1.22822	0.0504796
$593$	38.5493	1.58303	0.791515	−	0.611149i	$-0.209292\pi$
$593$	38.5493	1.58303	0.791515	+	0.611149i	$0.209292\pi$
$594$	20.9404	0.859195
$595$	−19.7092	−0.808000
$596$	−2.70350	−0.110740
$597$	0.867229	0.0354933
$598$	−0.212720	−0.00869876
$599$	4.75172	0.194150	0.0970750	−	0.995277i	$-0.469051\pi$
$599$	4.75172	0.194150	0.0970750	+	0.995277i	$0.469051\pi$
$600$	1.53068	0.0624898
$601$	−25.7773	−1.05148	−0.525739	−	0.850646i	$-0.676211\pi$
$601$	−25.7773	−1.05148	−0.525739	+	0.850646i	$0.676211\pi$
$602$	30.0759	1.22580
$603$	−2.13557	−0.0869669
$604$	−5.04602	−0.205320
$605$	−33.3992	−1.35787
$606$	3.72761	0.151424
$607$	−36.8234	−1.49462	−0.747308	−	0.664478i	$-0.768654\pi$
$607$	−36.8234	−1.49462	−0.747308	+	0.664478i	$0.768654\pi$
$608$	3.36876	0.136621
$609$	5.79568	0.234853
$610$	−16.7784	−0.679336
$611$	1.02022	0.0412738
$612$	−9.18061	−0.371104
$613$	−29.0198	−1.17210	−0.586050	−	0.810275i	$-0.699318\pi$
$613$	−29.0198	−1.17210	−0.586050	+	0.810275i	$0.699318\pi$
$614$	−20.2540	−0.817386
$615$	3.87153	0.156115
$616$	18.4207	0.742191
$617$	−23.9070	−0.962461	−0.481230	−	0.876594i	$-0.659810\pi$
$617$	−23.9070	−0.962461	−0.481230	+	0.876594i	$0.659810\pi$
$618$	−3.09728	−0.124591
$619$	−15.0517	−0.604977	−0.302489	−	0.953153i	$-0.597817\pi$
$619$	−15.0517	−0.604977	−0.302489	+	0.953153i	$0.597817\pi$
$620$	14.4842	0.581700
$621$	1.86355	0.0747818
$622$	−16.7206	−0.670433
$623$	6.09565	0.244217
$624$	0.289596	0.0115931
$625$	−8.56983	−0.342793
$626$	−1.00965	−0.0403537
$627$	−12.7283	−0.508318
$628$	5.67712	0.226542
$629$	4.43539	0.176851
$630$	13.8749	0.552789
$631$	−26.1042	−1.03919	−0.519596	−	0.854412i	$-0.673917\pi$
$631$	−26.1042	−1.03919	−0.519596	+	0.854412i	$0.673917\pi$
$632$	−12.8084	−0.509492
$633$	5.59356	0.222324
$634$	14.9009	0.591789
$635$	−4.93203	−0.195722
$636$	−2.40330	−0.0952968
$637$	−1.66101	−0.0658117
$638$	−14.5023	−0.574150
$639$	39.4724	1.56150
$640$	−1.65458	−0.0654030
$641$	−22.6013	−0.892699	−0.446350	−	0.894859i	$-0.647276\pi$
$641$	−22.6013	−0.892699	−0.446350	+	0.894859i	$0.647276\pi$
$642$	−4.13665	−0.163260
$643$	−38.8056	−1.53034	−0.765171	−	0.643827i	$-0.777346\pi$
$643$	−38.8056	−1.53034	−0.765171	+	0.643827i	$0.777346\pi$
$644$	1.63932	0.0645981
$645$	10.2071	0.401902
$646$	12.1654	0.478640
$647$	−4.40075	−0.173012	−0.0865058	−	0.996251i	$-0.527570\pi$
$647$	−4.40075	−0.173012	−0.0865058	+	0.996251i	$0.527570\pi$
$648$	5.08967	0.199941
$649$	36.6207	1.43749
$650$	0.968357	0.0379821
$651$	19.5369	0.765711
$652$	16.4670	0.644896
$653$	4.16728	0.163078	0.0815392	−	0.996670i	$-0.474016\pi$
$653$	4.16728	0.163078	0.0815392	+	0.996670i	$0.474016\pi$
$654$	−3.37788	−0.132086
$655$	−6.83644	−0.267122
$656$	3.45839	0.135028
$657$	−7.07235	−0.275919
$658$	−7.86230	−0.306504
$659$	24.8817	0.969255	0.484627	−	0.874721i	$-0.338955\pi$
$659$	24.8817	0.969255	0.484627	+	0.874721i	$0.338955\pi$
$660$	6.25155	0.243341
$661$	4.97004	0.193312	0.0966562	−	0.995318i	$-0.469185\pi$
$661$	4.97004	0.193312	0.0966562	+	0.995318i	$0.469185\pi$
$662$	−15.7243	−0.611142
$663$	1.04580	0.0406155
$664$	−9.96242	−0.386617
$665$	−18.3858	−0.712973
$666$	−3.12243	−0.120992
$667$	−1.29060	−0.0499723
$668$	24.8888	0.962976
$669$	−6.45658	−0.249626
$670$	−1.38990	−0.0536966
$671$	56.6293	2.18615
$672$	−2.23176	−0.0860920
$673$	−9.23455	−0.355966	−0.177983	−	0.984034i	$-0.556957\pi$
$673$	−9.23455	−0.355966	−0.177983	+	0.984034i	$0.556957\pi$
$674$	−8.96007	−0.345129
$675$	−8.48339	−0.326526
$676$	−12.8168	−0.492954
$677$	37.0683	1.42465	0.712325	−	0.701850i	$-0.247642\pi$
$677$	37.0683	1.42465	0.712325	+	0.701850i	$0.247642\pi$
$678$	−14.3564	−0.551354
$679$	39.0405	1.49824
$680$	−5.97507	−0.229134
$681$	−9.30076	−0.356406
$682$	−48.8863	−1.87195
$683$	32.9255	1.25986	0.629930	−	0.776652i	$-0.283084\pi$
$683$	32.9255	1.25986	0.629930	+	0.776652i	$0.283084\pi$
$684$	−8.56417	−0.327459
$685$	−22.8004	−0.871159
$686$	−10.2895	−0.392856
$687$	1.65852	0.0632765
$688$	9.11784	0.347615
$689$	−1.52040	−0.0579227
$690$	0.556345	0.0211797
$691$	0.607928	0.0231267	0.0115633	−	0.999933i	$-0.496319\pi$
$691$	0.607928	0.0231267	0.0115633	+	0.999933i	$0.496319\pi$
$692$	−23.9307	−0.909710
$693$	−46.8298	−1.77892
$694$	20.0486	0.761033
$695$	−20.3470	−0.771804
$696$	1.75702	0.0665998
$697$	12.4891	0.473057
$698$	27.8258	1.05322
$699$	1.27995	0.0484120
$700$	−7.46260	−0.282060
$701$	−19.5594	−0.738749	−0.369375	−	0.929281i	$-0.620428\pi$
$701$	−19.5594	−0.738749	−0.369375	+	0.929281i	$0.620428\pi$
$702$	−1.60501	−0.0605772
$703$	4.13757	0.156052
$704$	5.58444	0.210471
$705$	−2.66828	−0.100493
$706$	8.91375	0.335473
$707$	−18.1734	−0.683481
$708$	−4.43678	−0.166745
$709$	−4.79382	−0.180036	−0.0900179	−	0.995940i	$-0.528692\pi$
$709$	−4.79382	−0.180036	−0.0900179	+	0.995940i	$0.528692\pi$
$710$	25.6901	0.964131
$711$	32.5621	1.22117
$712$	1.84796	0.0692553
$713$	−4.35055	−0.162929
$714$	−8.05941	−0.301616
$715$	3.95493	0.147906
$716$	9.70481	0.362686
$717$	−17.0359	−0.636217
$718$	36.6570	1.36803
$719$	−11.3823	−0.424488	−0.212244	−	0.977217i	$-0.568077\pi$
$719$	−11.3823	−0.424488	−0.212244	+	0.977217i	$0.568077\pi$
$720$	4.20633	0.156761
$721$	15.1003	0.562366
$722$	−7.65149	−0.284759
$723$	−12.0584	−0.448455
$724$	16.4253	0.610440
$725$	5.87517	0.218198
$726$	−13.6574	−0.506875
$727$	34.7676	1.28946	0.644729	−	0.764411i	$-0.276970\pi$
$727$	34.7676	1.28946	0.644729	+	0.764411i	$0.276970\pi$
$728$	−1.41188	−0.0523279
$729$	−5.32804	−0.197335
$730$	−4.60294	−0.170362
$731$	32.9267	1.21784
$732$	−6.86093	−0.253587
$733$	−21.7239	−0.802390	−0.401195	−	0.915993i	$-0.631405\pi$
$733$	−21.7239	−0.802390	−0.401195	+	0.915993i	$0.631405\pi$
$734$	−4.60045	−0.169806
$735$	4.34419	0.160238
$736$	0.496977	0.0183188
$737$	4.69112	0.172800
$738$	−8.79205	−0.323640
$739$	10.7301	0.394712	0.197356	−	0.980332i	$-0.436765\pi$
$739$	10.7301	0.394712	0.197356	+	0.980332i	$0.436765\pi$
$740$	−2.03219	−0.0747047
$741$	0.975578	0.0358388
$742$	11.7169	0.430141
$743$	34.7023	1.27310	0.636552	−	0.771234i	$-0.280360\pi$
$743$	34.7023	1.27310	0.636552	+	0.771234i	$0.280360\pi$
$744$	5.92282	0.217141
$745$	4.47316	0.163884
$746$	−6.35424	−0.232645
$747$	25.3268	0.926660
$748$	20.1667	0.737368
$749$	20.1676	0.736909
$750$	−8.12993	−0.296863
$751$	−21.9655	−0.801531	−0.400766	−	0.916181i	$-0.631256\pi$
$751$	−21.9655	−0.801531	−0.400766	+	0.916181i	$0.631256\pi$
$752$	−2.38354	−0.0869188
$753$	12.9748	0.472827
$754$	1.11155	0.0404802
$755$	8.34903	0.303852
$756$	12.3689	0.449854
$757$	−43.3822	−1.57675	−0.788377	−	0.615193i	$-0.789078\pi$
$757$	−43.3822	−1.57675	−0.788377	+	0.615193i	$0.789078\pi$
$758$	−13.0565	−0.474232
$759$	−1.87774	−0.0681577
$760$	−5.57387	−0.202186
$761$	−38.4152	−1.39255	−0.696276	−	0.717774i	$-0.745161\pi$
$761$	−38.4152	−1.39255	−0.696276	+	0.717774i	$0.745161\pi$
$762$	−2.01678	−0.0730603
$763$	16.4684	0.596195
$764$	−7.28515	−0.263567
$765$	15.1900	0.549197
$766$	25.3105	0.914507
$767$	−2.80685	−0.101350
$768$	−0.676583	−0.0244141
$769$	33.3246	1.20171	0.600857	−	0.799356i	$-0.294826\pi$
$769$	33.3246	1.20171	0.600857	+	0.799356i	$0.294826\pi$
$770$	−30.4785	−1.09837
$771$	−14.3164	−0.515592
$772$	−25.4388	−0.915563
$773$	2.40299	0.0864295	0.0432148	−	0.999066i	$-0.486240\pi$
$773$	2.40299	0.0864295	0.0432148	+	0.999066i	$0.486240\pi$
$774$	−23.1797	−0.833178
$775$	19.8048	0.711411
$776$	11.8356	0.424872
$777$	−2.74109	−0.0983362
$778$	2.10430	0.0754430
$779$	11.6505	0.417422
$780$	−0.479159	−0.0171567
$781$	−86.7076	−3.10264
$782$	1.79470	0.0641783
$783$	−9.73784	−0.348002
$784$	3.88062	0.138594
$785$	−9.39325	−0.335259
$786$	−2.79553	−0.0997131
$787$	−9.06700	−0.323204	−0.161602	−	0.986856i	$-0.551666\pi$
$787$	−9.06700	−0.323204	−0.161602	+	0.986856i	$0.551666\pi$
$788$	−25.7045	−0.915685
$789$	7.74934	0.275884
$790$	21.1926	0.753997
$791$	69.9924	2.48864
$792$	−14.1970	−0.504467
$793$	−4.34044	−0.154134
$794$	−15.4005	−0.546544
$795$	3.97644	0.141030
$796$	−1.28178	−0.0454315
$797$	3.00313	0.106376	0.0531882	−	0.998585i	$-0.483062\pi$
$797$	3.00313	0.106376	0.0531882	+	0.998585i	$0.483062\pi$
$798$	−7.51826	−0.266143
$799$	−8.60753	−0.304512
$800$	−2.26237	−0.0799869
$801$	−4.69796	−0.165994
$802$	29.1646	1.02984
$803$	15.5356	0.548239
$804$	−0.568352	−0.0200442
$805$	−2.71238	−0.0955987
$806$	3.74696	0.131981
$807$	2.15918	0.0760068
$808$	−5.50946	−0.193822
$809$	26.9351	0.946988	0.473494	−	0.880797i	$-0.342993\pi$
$809$	26.9351	0.946988	0.473494	+	0.880797i	$0.342993\pi$
$810$	−8.42126	−0.295893
$811$	−42.6785	−1.49865	−0.749323	−	0.662205i	$-0.769621\pi$
$811$	−42.6785	−1.49865	−0.749323	+	0.662205i	$0.769621\pi$
$812$	−8.56611	−0.300611
$813$	11.3677	0.398683
$814$	6.85892	0.240405
$815$	−27.2459	−0.954382
$816$	−2.44330	−0.0855326
$817$	30.7158	1.07461
$818$	−16.7066	−0.584133
$819$	3.58934	0.125422
$820$	−5.72218	−0.199827
$821$	47.0251	1.64119	0.820594	−	0.571511i	$-0.193643\pi$
$821$	47.0251	1.64119	0.820594	+	0.571511i	$0.193643\pi$
$822$	−9.32344	−0.325192
$823$	−49.4901	−1.72512	−0.862559	−	0.505957i	$-0.831140\pi$
$823$	−49.4901	−1.72512	−0.862559	+	0.505957i	$0.831140\pi$
$824$	4.57783	0.159476
$825$	8.54798	0.297603
$826$	21.6309	0.752635
$827$	−45.5275	−1.58315	−0.791574	−	0.611074i	$-0.790738\pi$
$827$	−45.5275	−1.58315	−0.791574	+	0.611074i	$0.790738\pi$
$828$	−1.26343	−0.0439073
$829$	52.9210	1.83802	0.919010	−	0.394233i	$-0.128990\pi$
$829$	52.9210	1.83802	0.919010	+	0.394233i	$0.128990\pi$
$830$	16.4836	0.572154
$831$	18.5464	0.643366
$832$	−0.428028	−0.0148392
$833$	14.0138	0.485550
$834$	−8.32019	−0.288104
$835$	−41.1805	−1.42511
$836$	18.8126	0.650647
$837$	−32.8257	−1.13462
$838$	−23.2769	−0.804087
$839$	−9.73087	−0.335947	−0.167973	−	0.985792i	$-0.553722\pi$
$839$	−9.73087	−0.335947	−0.167973	+	0.985792i	$0.553722\pi$
$840$	3.69262	0.127408
$841$	−22.2561	−0.767451
$842$	−10.5463	−0.363449
$843$	−0.907141	−0.0312436
$844$	−8.26737	−0.284575
$845$	21.2064	0.729522
$846$	6.05953	0.208331
$847$	66.5848	2.28788
$848$	3.55211	0.121980
$849$	−13.3654	−0.458701
$850$	−8.16995	−0.280227
$851$	0.610397	0.0209241
$852$	10.5051	0.359898
$853$	−44.6045	−1.52723	−0.763614	−	0.645673i	$-0.776577\pi$
$853$	−44.6045	−1.52723	−0.763614	+	0.645673i	$0.776577\pi$
$854$	33.4494	1.14462
$855$	14.1701	0.484607
$856$	6.11403	0.208973
$857$	7.18410	0.245404	0.122702	−	0.992444i	$-0.460844\pi$
$857$	7.18410	0.245404	0.122702	+	0.992444i	$0.460844\pi$
$858$	1.61723	0.0552113
$859$	12.0629	0.411582	0.205791	−	0.978596i	$-0.434023\pi$
$859$	12.0629	0.411582	0.205791	+	0.978596i	$0.434023\pi$
$860$	−15.0862	−0.514435
$861$	−7.71830	−0.263039
$862$	−2.31258	−0.0787667
$863$	3.49297	0.118902	0.0594510	−	0.998231i	$-0.481065\pi$
$863$	3.49297	0.118902	0.0594510	+	0.998231i	$0.481065\pi$
$864$	3.74978	0.127570
$865$	39.5953	1.34628
$866$	16.6026	0.564181
$867$	2.67858	0.0909693
$868$	−28.8758	−0.980110
$869$	−71.5279	−2.42642
$870$	−2.90713	−0.0985610
$871$	−0.359558	−0.0121832
$872$	4.99257	0.169070
$873$	−30.0888	−1.01835
$874$	1.67419	0.0566304
$875$	39.6362	1.33995
$876$	−1.88221	−0.0635941
$877$	−2.56841	−0.0867289	−0.0433645	−	0.999059i	$-0.513808\pi$
$877$	−2.56841	−0.0867289	−0.0433645	+	0.999059i	$0.513808\pi$
$878$	−9.60639	−0.324200
$879$	21.7500	0.733609
$880$	−9.23989	−0.311477
$881$	−39.2166	−1.32124	−0.660620	−	0.750720i	$-0.729707\pi$
$881$	−39.2166	−1.32124	−0.660620	+	0.750720i	$0.729707\pi$
$882$	−9.86545	−0.332187
$883$	−26.9574	−0.907189	−0.453594	−	0.891208i	$-0.649858\pi$
$883$	−26.9574	−0.907189	−0.453594	+	0.891208i	$0.649858\pi$
$884$	−1.54571	−0.0519878
$885$	7.34101	0.246765
$886$	−28.8654	−0.969751
$887$	6.02815	0.202405	0.101203	−	0.994866i	$-0.467731\pi$
$887$	6.02815	0.202405	0.101203	+	0.994866i	$0.467731\pi$
$888$	−0.830993	−0.0278863
$889$	9.83253	0.329772
$890$	−3.05760	−0.102491
$891$	28.4229	0.952205
$892$	9.54293	0.319521
$893$	−8.02957	−0.268699
$894$	1.82914	0.0611757
$895$	−16.0574	−0.536739
$896$	3.29858	0.110198
$897$	0.143922	0.00480543
$898$	15.5270	0.518142
$899$	22.7334	0.758201
$900$	5.75148	0.191716
$901$	12.8275	0.427346
$902$	19.3132	0.643058
$903$	−20.3488	−0.677167
$904$	21.2190	0.705732
$905$	−27.1769	−0.903391
$906$	3.41405	0.113424
$907$	−13.5729	−0.450680	−0.225340	−	0.974280i	$-0.572349\pi$
$907$	−13.5729	−0.450680	−0.225340	+	0.974280i	$0.572349\pi$
$908$	13.7467	0.456199
$909$	14.0064	0.464562
$910$	2.33607	0.0774400
$911$	−15.8920	−0.526526	−0.263263	−	0.964724i	$-0.584799\pi$
$911$	−15.8920	−0.526526	−0.263263	+	0.964724i	$0.584799\pi$
$912$	−2.27924	−0.0754732
$913$	−55.6345	−1.84123
$914$	−8.28544	−0.274058
$915$	11.3519	0.375284
$916$	−2.45132	−0.0809939
$917$	13.6292	0.450075
$918$	13.5413	0.446931
$919$	4.65380	0.153515	0.0767573	−	0.997050i	$-0.475543\pi$
$919$	4.65380	0.153515	0.0767573	+	0.997050i	$0.475543\pi$
$920$	−0.822287	−0.0271100
$921$	13.7035	0.451546
$922$	−22.8531	−0.752625
$923$	6.64584	0.218750
$924$	−12.4631	−0.410007
$925$	−2.77869	−0.0913627
$926$	−25.2125	−0.828533
$927$	−11.6379	−0.382240
$928$	−2.59691	−0.0852477
$929$	−30.2545	−0.992618	−0.496309	−	0.868146i	$-0.665312\pi$
$929$	−30.2545	−0.992618	−0.496309	+	0.868146i	$0.665312\pi$
$930$	−9.79977	−0.321347
$931$	13.0729	0.428446
$932$	−1.89178	−0.0619673
$933$	11.3128	0.370366
$934$	13.2235	0.432687
$935$	−33.3674	−1.09123
$936$	1.08815	0.0355672
$937$	−12.3315	−0.402853	−0.201426	−	0.979504i	$-0.564558\pi$
$937$	−12.3315	−0.402853	−0.201426	+	0.979504i	$0.564558\pi$
$938$	2.77092	0.0904737
$939$	0.683112	0.0222925
$940$	3.94376	0.128631
$941$	29.5876	0.964527	0.482264	−	0.876026i	$-0.339815\pi$
$941$	29.5876	0.964527	0.482264	+	0.876026i	$0.339815\pi$
$942$	−3.84104	−0.125148
$943$	1.71874	0.0559699
$944$	6.55764	0.213433
$945$	−20.4654	−0.665739
$946$	50.9180	1.65549
$947$	−19.4261	−0.631263	−0.315631	−	0.948882i	$-0.602216\pi$
$947$	−19.4261	−0.631263	−0.315631	+	0.948882i	$0.602216\pi$
$948$	8.66596	0.281457
$949$	−1.19075	−0.0386533
$950$	−7.62137	−0.247270
$951$	−10.0817	−0.326920
$952$	11.9119	0.386068
$953$	12.7091	0.411687	0.205843	−	0.978585i	$-0.434006\pi$
$953$	12.7091	0.411687	0.205843	+	0.978585i	$0.434006\pi$
$954$	−9.03030	−0.292367
$955$	12.0538	0.390053
$956$	25.1793	0.814358
$957$	9.81198	0.317176
$958$	14.4898	0.468144
$959$	45.4551	1.46782
$960$	1.11946	0.0361304
$961$	45.6330	1.47203
$962$	−0.525712	−0.0169496
$963$	−15.5433	−0.500876
$964$	17.8224	0.574022
$965$	42.0905	1.35494
$966$	−1.10913	−0.0356858
$967$	21.9106	0.704597	0.352298	−	0.935888i	$-0.385400\pi$
$967$	21.9106	0.704597	0.352298	+	0.935888i	$0.385400\pi$
$968$	20.1859	0.648800
$969$	−8.23087	−0.264414
$970$	−19.5829	−0.628768
$971$	17.0965	0.548653	0.274326	−	0.961637i	$-0.411545\pi$
$971$	17.0965	0.548653	0.274326	+	0.961637i	$0.411545\pi$
$972$	−14.6929	−0.471276
$973$	40.5638	1.30042
$974$	19.7764	0.633677
$975$	−0.655173	−0.0209823
$976$	10.1406	0.324592
$977$	19.3030	0.617559	0.308780	−	0.951134i	$-0.400079\pi$
$977$	19.3030	0.617559	0.308780	+	0.951134i	$0.400079\pi$
$978$	−11.1413	−0.356258
$979$	10.3198	0.329823
$980$	−6.42079	−0.205105
$981$	−12.6923	−0.405233
$982$	−37.1360	−1.18506
$983$	−50.2033	−1.60124	−0.800619	−	0.599174i	$-0.795496\pi$
$983$	−50.2033	−1.60124	−0.800619	+	0.599174i	$0.795496\pi$
$984$	−2.33989	−0.0745929
$985$	42.5301	1.35512
$986$	−9.37805	−0.298658
$987$	5.31949	0.169321
$988$	−1.44192	−0.0458736
$989$	4.53136	0.144089
$990$	23.4900	0.746560
$991$	−27.8925	−0.886035	−0.443017	−	0.896513i	$-0.646092\pi$
$991$	−27.8925	−0.886035	−0.443017	+	0.896513i	$0.646092\pi$
$992$	−8.75402	−0.277941
$993$	10.6388	0.337612
$994$	−51.2159	−1.62447
$995$	2.12080	0.0672340
$996$	6.74040	0.213578
$997$	26.3790	0.835430	0.417715	−	0.908578i	$-0.362831\pi$
$997$	26.3790	0.835430	0.417715	+	0.908578i	$0.362831\pi$
$998$	−7.88880	−0.249716
$999$	4.60556	0.145713

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.i.1.15	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.i.1.15	✓	46	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:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.676583 q^{3} +1.00000 q^{4} -1.65458 q^{5} -0.676583 q^{6} +3.29858 q^{7} +1.00000 q^{8} -2.54224 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.676583 q^{3} +1.00000 q^{4} -1.65458 q^{5} -0.676583 q^{6} +3.29858 q^{7} +1.00000 q^{8} -2.54224 q^{9} -1.65458 q^{10} +5.58444 q^{11} -0.676583 q^{12} -0.428028 q^{13} +3.29858 q^{14} +1.11946 q^{15} +1.00000 q^{16} +3.61123 q^{17} -2.54224 q^{18} +3.36876 q^{19} -1.65458 q^{20} -2.23176 q^{21} +5.58444 q^{22} +0.496977 q^{23} -0.676583 q^{24} -2.26237 q^{25} -0.428028 q^{26} +3.74978 q^{27} +3.29858 q^{28} -2.59691 q^{29} +1.11946 q^{30} -8.75402 q^{31} +1.00000 q^{32} -3.77833 q^{33} +3.61123 q^{34} -5.45776 q^{35} -2.54224 q^{36} +1.22822 q^{37} +3.36876 q^{38} +0.289596 q^{39} -1.65458 q^{40} +3.45839 q^{41} -2.23176 q^{42} +9.11784 q^{43} +5.58444 q^{44} +4.20633 q^{45} +0.496977 q^{46} -2.38354 q^{47} -0.676583 q^{48} +3.88062 q^{49} -2.26237 q^{50} -2.44330 q^{51} -0.428028 q^{52} +3.55211 q^{53} +3.74978 q^{54} -9.23989 q^{55} +3.29858 q^{56} -2.27924 q^{57} -2.59691 q^{58} +6.55764 q^{59} +1.11946 q^{60} +10.1406 q^{61} -8.75402 q^{62} -8.38576 q^{63} +1.00000 q^{64} +0.708205 q^{65} -3.77833 q^{66} +0.840034 q^{67} +3.61123 q^{68} -0.336246 q^{69} -5.45776 q^{70} -15.5267 q^{71} -2.54224 q^{72} +2.78194 q^{73} +1.22822 q^{74} +1.53068 q^{75} +3.36876 q^{76} +18.4207 q^{77} +0.289596 q^{78} -12.8084 q^{79} -1.65458 q^{80} +5.08967 q^{81} +3.45839 q^{82} -9.96242 q^{83} -2.23176 q^{84} -5.97507 q^{85} +9.11784 q^{86} +1.75702 q^{87} +5.58444 q^{88} +1.84796 q^{89} +4.20633 q^{90} -1.41188 q^{91} +0.496977 q^{92} +5.92282 q^{93} -2.38354 q^{94} -5.57387 q^{95} -0.676583 q^{96} +11.8356 q^{97} +3.88062 q^{98} -14.1970 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9} + 23 q^{10} + 39 q^{11} + 21 q^{12} + 8 q^{13} + 26 q^{14} + 14 q^{15} + 46 q^{16} + 36 q^{17} + 59 q^{18} + 37 q^{19} + 23 q^{20} + 20 q^{21} + 39 q^{22} + 38 q^{23} + 21 q^{24} + 57 q^{25} + 8 q^{26} + 63 q^{27} + 26 q^{28} + 23 q^{29} + 14 q^{30} + 44 q^{31} + 46 q^{32} + 25 q^{33} + 36 q^{34} + 26 q^{35} + 59 q^{36} + 9 q^{37} + 37 q^{38} - 2 q^{39} + 23 q^{40} + 50 q^{41} + 20 q^{42} + 46 q^{43} + 39 q^{44} + 30 q^{45} + 38 q^{46} + 57 q^{47} + 21 q^{48} + 62 q^{49} + 57 q^{50} + 5 q^{51} + 8 q^{52} + 21 q^{53} + 63 q^{54} + 40 q^{55} + 26 q^{56} + 3 q^{57} + 23 q^{58} + 68 q^{59} + 14 q^{60} - q^{61} + 44 q^{62} + 40 q^{63} + 46 q^{64} + 18 q^{65} + 25 q^{66} + 42 q^{67} + 36 q^{68} - 7 q^{69} + 26 q^{70} + 67 q^{71} + 59 q^{72} + 48 q^{73} + 9 q^{74} + 71 q^{75} + 37 q^{76} - 5 q^{77} - 2 q^{78} + 40 q^{79} + 23 q^{80} + 82 q^{81} + 50 q^{82} + 48 q^{83} + 20 q^{84} - 68 q^{85} + 46 q^{86} + 18 q^{87} + 39 q^{88} + 90 q^{89} + 30 q^{90} + 9 q^{91} + 38 q^{92} - 42 q^{93} + 57 q^{94} + 6 q^{95} + 21 q^{96} + 46 q^{97} + 62 q^{98} + 61 q^{99}+O(q^{100}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9 + 23 * q^10 + 39 * q^11 + 21 * q^12 + 8 * q^13 + 26 * q^14 + 14 * q^15 + 46 * q^16 + 36 * q^17 + 59 * q^18 + 37 * q^19 + 23 * q^20 + 20 * q^21 + 39 * q^22 + 38 * q^23 + 21 * q^24 + 57 * q^25 + 8 * q^26 + 63 * q^27 + 26 * q^28 + 23 * q^29 + 14 * q^30 + 44 * q^31 + 46 * q^32 + 25 * q^33 + 36 * q^34 + 26 * q^35 + 59 * q^36 + 9 * q^37 + 37 * q^38 - 2 * q^39 + 23 * q^40 + 50 * q^41 + 20 * q^42 + 46 * q^43 + 39 * q^44 + 30 * q^45 + 38 * q^46 + 57 * q^47 + 21 * q^48 + 62 * q^49 + 57 * q^50 + 5 * q^51 + 8 * q^52 + 21 * q^53 + 63 * q^54 + 40 * q^55 + 26 * q^56 + 3 * q^57 + 23 * q^58 + 68 * q^59 + 14 * q^60 - q^61 + 44 * q^62 + 40 * q^63 + 46 * q^64 + 18 * q^65 + 25 * q^66 + 42 * q^67 + 36 * q^68 - 7 * q^69 + 26 * q^70 + 67 * q^71 + 59 * q^72 + 48 * q^73 + 9 * q^74 + 71 * q^75 + 37 * q^76 - 5 * q^77 - 2 * q^78 + 40 * q^79 + 23 * q^80 + 82 * q^81 + 50 * q^82 + 48 * q^83 + 20 * q^84 - 68 * q^85 + 46 * q^86 + 18 * q^87 + 39 * q^88 + 90 * q^89 + 30 * q^90 + 9 * q^91 + 38 * q^92 - 42 * q^93 + 57 * q^94 + 6 * q^95 + 21 * q^96 + 46 * q^97 + 62 * q^98 + 61 * q^99

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