LMFDB - Embedded newform 2671.2.a.a.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2671,2,Mod(1,2671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2671, 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("2671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2671.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:	$21.3280423799$
Analytic rank:	$1$
Dimension:	$100$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	2671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48625 q^{2} -0.481659 q^{3} +4.18145 q^{4} -0.210015 q^{5} +1.19752 q^{6} +3.08014 q^{7} -5.42364 q^{8} -2.76800 q^{9} +O(q^{10})$	\(q-2.48625 q^{2} -0.481659 q^{3} +4.18145 q^{4} -0.210015 q^{5} +1.19752 q^{6} +3.08014 q^{7} -5.42364 q^{8} -2.76800 q^{9} +0.522149 q^{10} -1.17334 q^{11} -2.01403 q^{12} -3.17951 q^{13} -7.65800 q^{14} +0.101155 q^{15} +5.12162 q^{16} +2.75248 q^{17} +6.88196 q^{18} +4.86769 q^{19} -0.878165 q^{20} -1.48357 q^{21} +2.91722 q^{22} -0.145993 q^{23} +2.61234 q^{24} -4.95589 q^{25} +7.90507 q^{26} +2.77821 q^{27} +12.8794 q^{28} -0.623959 q^{29} -0.251498 q^{30} -0.696183 q^{31} -1.88638 q^{32} +0.565150 q^{33} -6.84336 q^{34} -0.646873 q^{35} -11.5743 q^{36} +8.34586 q^{37} -12.1023 q^{38} +1.53144 q^{39} +1.13904 q^{40} +0.734608 q^{41} +3.68854 q^{42} -2.78271 q^{43} -4.90627 q^{44} +0.581321 q^{45} +0.362975 q^{46} -8.71132 q^{47} -2.46688 q^{48} +2.48724 q^{49} +12.3216 q^{50} -1.32576 q^{51} -13.2950 q^{52} -14.3090 q^{53} -6.90733 q^{54} +0.246419 q^{55} -16.7055 q^{56} -2.34456 q^{57} +1.55132 q^{58} -8.14207 q^{59} +0.422976 q^{60} +12.8190 q^{61} +1.73089 q^{62} -8.52583 q^{63} -5.55323 q^{64} +0.667744 q^{65} -1.40511 q^{66} -3.35076 q^{67} +11.5094 q^{68} +0.0703187 q^{69} +1.60829 q^{70} -0.886556 q^{71} +15.0126 q^{72} -0.214860 q^{73} -20.7499 q^{74} +2.38705 q^{75} +20.3540 q^{76} -3.61405 q^{77} -3.80755 q^{78} +4.12858 q^{79} -1.07562 q^{80} +6.96587 q^{81} -1.82642 q^{82} +3.58613 q^{83} -6.20349 q^{84} -0.578061 q^{85} +6.91853 q^{86} +0.300535 q^{87} +6.36377 q^{88} +0.885839 q^{89} -1.44531 q^{90} -9.79333 q^{91} -0.610462 q^{92} +0.335323 q^{93} +21.6585 q^{94} -1.02228 q^{95} +0.908592 q^{96} +14.3901 q^{97} -6.18390 q^{98} +3.24781 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) $ 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9 - 18 * q^10 - 47 * q^11 - 27 * q^12 - 29 * q^13 - 51 * q^14 - 36 * q^15 + 71 * q^16 - 99 * q^17 - 27 * q^18 - 45 * q^19 - 75 * q^20 - 79 * q^21 - 2 * q^22 - 25 * q^23 - 66 * q^24 + 67 * q^25 - 73 * q^26 - 42 * q^27 - 31 * q^28 - 78 * q^29 - 29 * q^30 - 41 * q^31 - 95 * q^32 - 83 * q^33 - 44 * q^34 - 45 * q^35 + 23 * q^36 - 16 * q^37 - 29 * q^38 - 42 * q^39 - 37 * q^40 - 235 * q^41 + 16 * q^42 - 6 * q^43 - 122 * q^44 - 79 * q^45 - 17 * q^46 - 67 * q^47 - 25 * q^48 + 30 * q^49 - 68 * q^50 - 18 * q^51 - 41 * q^52 - 69 * q^53 - 63 * q^54 - 32 * q^55 - 120 * q^56 - 63 * q^57 - 7 * q^58 - 118 * q^59 - 49 * q^60 - 60 * q^61 - 23 * q^62 - 43 * q^63 + 43 * q^64 - 181 * q^65 - 4 * q^66 - 18 * q^67 - 130 * q^68 - 80 * q^69 + 12 * q^70 - 77 * q^71 - 40 * q^72 - 64 * q^73 - 48 * q^74 - 18 * q^75 - 134 * q^76 - 87 * q^77 + 65 * q^78 - 48 * q^79 - 95 * q^80 - 20 * q^81 + 45 * q^82 - 108 * q^83 - 97 * q^84 - 21 * q^85 - 73 * q^86 - 3 * q^87 + 23 * q^88 - 325 * q^89 + 6 * q^90 - 17 * q^91 - 19 * q^92 + 2 * q^93 - 5 * q^94 - 54 * q^95 - 105 * q^96 - 81 * q^97 - 61 * q^98 - 76 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.48625	−1.75805	−0.879023	−	0.476780i	$-0.841804\pi$
$2$	−2.48625	−1.75805	−0.879023	+	0.476780i	$0.841804\pi$
$3$	−0.481659	−0.278086	−0.139043	−	0.990286i	$-0.544403\pi$
$3$	−0.481659	−0.278086	−0.139043	+	0.990286i	$0.544403\pi$
$4$	4.18145	2.09073
$5$	−0.210015	−0.0939213	−0.0469607	−	0.998897i	$-0.514954\pi$
$5$	−0.210015	−0.0939213	−0.0469607	+	0.998897i	$0.514954\pi$
$6$	1.19752	0.488888
$7$	3.08014	1.16418	0.582091	−	0.813124i	$-0.302235\pi$
$7$	3.08014	1.16418	0.582091	+	0.813124i	$0.302235\pi$
$8$	−5.42364	−1.91754
$9$	−2.76800	−0.922668
$10$	0.522149	0.165118
$11$	−1.17334	−0.353776	−0.176888	−	0.984231i	$-0.556603\pi$
$11$	−1.17334	−0.353776	−0.176888	+	0.984231i	$0.556603\pi$
$12$	−2.01403	−0.581401
$13$	−3.17951	−0.881838	−0.440919	−	0.897547i	$-0.645347\pi$
$13$	−3.17951	−0.881838	−0.440919	+	0.897547i	$0.645347\pi$
$14$	−7.65800	−2.04669
$15$	0.101155	0.0261182
$16$	5.12162	1.28041
$17$	2.75248	0.667575	0.333787	−	0.942648i	$-0.391673\pi$
$17$	2.75248	0.667575	0.333787	+	0.942648i	$0.391673\pi$
$18$	6.88196	1.62209
$19$	4.86769	1.11672	0.558362	−	0.829597i	$-0.311430\pi$
$19$	4.86769	1.11672	0.558362	+	0.829597i	$0.311430\pi$
$20$	−0.878165	−0.196364
$21$	−1.48357	−0.323742
$22$	2.91722	0.621954
$23$	−0.145993	−0.0304416	−0.0152208	−	0.999884i	$-0.504845\pi$
$23$	−0.145993	−0.0304416	−0.0152208	+	0.999884i	$0.504845\pi$
$24$	2.61234	0.533242
$25$	−4.95589	−0.991179
$26$	7.90507	1.55031
$27$	2.77821	0.534667
$28$	12.8794	2.43398
$29$	−0.623959	−0.115866	−0.0579331	−	0.998320i	$-0.518451\pi$
$29$	−0.623959	−0.115866	−0.0579331	+	0.998320i	$0.518451\pi$
$30$	−0.251498	−0.0459170
$31$	−0.696183	−0.125038	−0.0625191	−	0.998044i	$-0.519913\pi$
$31$	−0.696183	−0.125038	−0.0625191	+	0.998044i	$0.519913\pi$
$32$	−1.88638	−0.333468
$33$	0.565150	0.0983800
$34$	−6.84336	−1.17363
$35$	−0.646873	−0.109342
$36$	−11.5743	−1.92905
$37$	8.34586	1.37205	0.686026	−	0.727577i	$-0.259354\pi$
$37$	8.34586	1.37205	0.686026	+	0.727577i	$0.259354\pi$
$38$	−12.1023	−1.96325
$39$	1.53144	0.245227
$40$	1.13904	0.180098
$41$	0.734608	0.114726	0.0573632	−	0.998353i	$-0.481731\pi$
$41$	0.734608	0.114726	0.0573632	+	0.998353i	$0.481731\pi$
$42$	3.68854	0.569154
$43$	−2.78271	−0.424360	−0.212180	−	0.977231i	$-0.568056\pi$
$43$	−2.78271	−0.424360	−0.212180	+	0.977231i	$0.568056\pi$
$44$	−4.90627	−0.739648
$45$	0.581321	0.0866582
$46$	0.362975	0.0535177
$47$	−8.71132	−1.27068	−0.635338	−	0.772234i	$-0.719139\pi$
$47$	−8.71132	−1.27068	−0.635338	+	0.772234i	$0.719139\pi$
$48$	−2.46688	−0.356063
$49$	2.48724	0.355320
$50$	12.3216	1.74254
$51$	−1.32576	−0.185643
$52$	−13.2950	−1.84368
$53$	−14.3090	−1.96549	−0.982745	−	0.184964i	$-0.940783\pi$
$53$	−14.3090	−1.96549	−0.982745	+	0.184964i	$0.940783\pi$
$54$	−6.90733	−0.939969
$55$	0.246419	0.0332271
$56$	−16.7055	−2.23237
$57$	−2.34456	−0.310545
$58$	1.55132	0.203698
$59$	−8.14207	−1.06001	−0.530004	−	0.847995i	$-0.677810\pi$
$59$	−8.14207	−1.06001	−0.530004	+	0.847995i	$0.677810\pi$
$60$	0.422976	0.0546060
$61$	12.8190	1.64130	0.820650	−	0.571432i	$-0.193612\pi$
$61$	12.8190	1.64130	0.820650	+	0.571432i	$0.193612\pi$
$62$	1.73089	0.219823
$63$	−8.52583	−1.07415
$64$	−5.55323	−0.694154
$65$	0.667744	0.0828234
$66$	−1.40511	−0.172956
$67$	−3.35076	−0.409361	−0.204680	−	0.978829i	$-0.565616\pi$
$67$	−3.35076	−0.409361	−0.204680	+	0.978829i	$0.565616\pi$
$68$	11.5094	1.39572
$69$	0.0703187	0.00846538
$70$	1.60829	0.192227
$71$	−0.886556	−0.105215	−0.0526074	−	0.998615i	$-0.516753\pi$
$71$	−0.886556	−0.105215	−0.0526074	+	0.998615i	$0.516753\pi$
$72$	15.0126	1.76926
$73$	−0.214860	−0.0251475	−0.0125737	−	0.999921i	$-0.504002\pi$
$73$	−0.214860	−0.0251475	−0.0125737	+	0.999921i	$0.504002\pi$
$74$	−20.7499	−2.41213
$75$	2.38705	0.275633
$76$	20.3540	2.33476
$77$	−3.61405	−0.411859
$78$	−3.80755	−0.431120
$79$	4.12858	0.464501	0.232251	−	0.972656i	$-0.425391\pi$
$79$	4.12858	0.464501	0.232251	+	0.972656i	$0.425391\pi$
$80$	−1.07562	−0.120257
$81$	6.96587	0.773985
$82$	−1.82642	−0.201694
$83$	3.58613	0.393628	0.196814	−	0.980441i	$-0.436940\pi$
$83$	3.58613	0.393628	0.196814	+	0.980441i	$0.436940\pi$
$84$	−6.20349	−0.676856
$85$	−0.578061	−0.0626995
$86$	6.91853	0.746044
$87$	0.300535	0.0322207
$88$	6.36377	0.678381
$89$	0.885839	0.0938987	0.0469494	−	0.998897i	$-0.485050\pi$
$89$	0.885839	0.0938987	0.0469494	+	0.998897i	$0.485050\pi$
$90$	−1.44531	−0.152349
$91$	−9.79333	−1.02662
$92$	−0.610462	−0.0636450
$93$	0.335323	0.0347713
$94$	21.6585	2.23391
$95$	−1.02228	−0.104884
$96$	0.908592	0.0927328
$97$	14.3901	1.46110	0.730549	−	0.682861i	$-0.239264\pi$
$97$	14.3901	1.46110	0.730549	+	0.682861i	$0.239264\pi$
$98$	−6.18390	−0.624669
$99$	3.24781	0.326418
$100$	−20.7228	−2.07228
$101$	1.46556	0.145829	0.0729143	−	0.997338i	$-0.476770\pi$
$101$	1.46556	0.145829	0.0729143	+	0.997338i	$0.476770\pi$
$102$	3.29616	0.326369
$103$	−17.5484	−1.72910	−0.864548	−	0.502550i	$-0.832395\pi$
$103$	−17.5484	−1.72910	−0.864548	+	0.502550i	$0.832395\pi$
$104$	17.2445	1.69096
$105$	0.311572	0.0304063
$106$	35.5758	3.45542
$107$	0.819352	0.0792098	0.0396049	−	0.999215i	$-0.487390\pi$
$107$	0.819352	0.0792098	0.0396049	+	0.999215i	$0.487390\pi$
$108$	11.6169	1.11784
$109$	−2.85534	−0.273492	−0.136746	−	0.990606i	$-0.543664\pi$
$109$	−2.85534	−0.273492	−0.136746	+	0.990606i	$0.543664\pi$
$110$	−0.612659	−0.0584147
$111$	−4.01986	−0.381548
$112$	15.7753	1.49063
$113$	−17.4225	−1.63897	−0.819485	−	0.573100i	$-0.805741\pi$
$113$	−17.4225	−1.63897	−0.819485	+	0.573100i	$0.805741\pi$
$114$	5.82918	0.545952
$115$	0.0306606	0.00285912
$116$	−2.60905	−0.242244
$117$	8.80091	0.813644
$118$	20.2432	1.86354
$119$	8.47802	0.777178
$120$	−0.548629	−0.0500828
$121$	−9.62327	−0.874843
$122$	−31.8712	−2.88548
$123$	−0.353830	−0.0319038
$124$	−2.91106	−0.261421
$125$	2.09088	0.187014
$126$	21.1974	1.88841
$127$	3.23317	0.286897	0.143449	−	0.989658i	$-0.454181\pi$
$127$	3.23317	0.286897	0.143449	+	0.989658i	$0.454181\pi$
$128$	17.5795	1.55382
$129$	1.34032	0.118008
$130$	−1.66018	−0.145607
$131$	−12.5952	−1.10045	−0.550225	−	0.835017i	$-0.685458\pi$
$131$	−12.5952	−1.10045	−0.550225	+	0.835017i	$0.685458\pi$
$132$	2.36315	0.205685
$133$	14.9931	1.30007
$134$	8.33084	0.719675
$135$	−0.583464	−0.0502166
$136$	−14.9285	−1.28010
$137$	21.0298	1.79670	0.898350	−	0.439281i	$-0.144767\pi$
$137$	21.0298	1.79670	0.898350	+	0.439281i	$0.144767\pi$
$138$	−0.174830	−0.0148825
$139$	14.4938	1.22934	0.614672	−	0.788783i	$-0.289288\pi$
$139$	14.4938	1.22934	0.614672	+	0.788783i	$0.289288\pi$
$140$	−2.70487	−0.228603
$141$	4.19588	0.353357
$142$	2.20420	0.184973
$143$	3.73065	0.311973
$144$	−14.1767	−1.18139
$145$	0.131040	0.0108823
$146$	0.534196	0.0442104
$147$	−1.19800	−0.0988094
$148$	34.8978	2.86858
$149$	−22.5050	−1.84368	−0.921840	−	0.387571i	$-0.873314\pi$
$149$	−22.5050	−1.84368	−0.921840	+	0.387571i	$0.873314\pi$
$150$	−5.93481	−0.484575
$151$	8.89161	0.723589	0.361794	−	0.932258i	$-0.382164\pi$
$151$	8.89161	0.723589	0.361794	+	0.932258i	$0.382164\pi$
$152$	−26.4006	−2.14137
$153$	−7.61888	−0.615950
$154$	8.98544	0.724067
$155$	0.146209	0.0117438
$156$	6.40364	0.512702
$157$	18.4795	1.47482	0.737412	−	0.675443i	$-0.236048\pi$
$157$	18.4795	1.47482	0.737412	+	0.675443i	$0.236048\pi$
$158$	−10.2647	−0.816615
$159$	6.89205	0.546575
$160$	0.396167	0.0313198
$161$	−0.449678	−0.0354396
$162$	−17.3189	−1.36070
$163$	−8.18989	−0.641481	−0.320741	−	0.947167i	$-0.603932\pi$
$163$	−8.18989	−0.641481	−0.320741	+	0.947167i	$0.603932\pi$
$164$	3.07173	0.239861
$165$	−0.118690	−0.00923998
$166$	−8.91601	−0.692017
$167$	9.33225	0.722151	0.361076	−	0.932537i	$-0.382410\pi$
$167$	9.33225	0.722151	0.361076	+	0.932537i	$0.382410\pi$
$168$	8.04637	0.620791
$169$	−2.89069	−0.222361
$170$	1.43721	0.110229
$171$	−13.4738	−1.03037
$172$	−11.6358	−0.887220
$173$	4.44662	0.338070	0.169035	−	0.985610i	$-0.445935\pi$
$173$	4.44662	0.338070	0.169035	+	0.985610i	$0.445935\pi$
$174$	−0.747206	−0.0566455
$175$	−15.2648	−1.15391
$176$	−6.00941	−0.452977
$177$	3.92170	0.294773
$178$	−2.20242	−0.165078
$179$	−26.1313	−1.95314	−0.976572	−	0.215190i	$-0.930963\pi$
$179$	−26.1313	−1.95314	−0.976572	+	0.215190i	$0.930963\pi$
$180$	2.43077	0.181179
$181$	−6.70495	−0.498375	−0.249187	−	0.968455i	$-0.580164\pi$
$181$	−6.70495	−0.498375	−0.249187	+	0.968455i	$0.580164\pi$
$182$	24.3487	1.80485
$183$	−6.17436	−0.456422
$184$	0.791812	0.0583731
$185$	−1.75275	−0.128865
$186$	−0.833697	−0.0611296
$187$	−3.22960	−0.236172
$188$	−36.4260	−2.65664
$189$	8.55726	0.622449
$190$	2.54166	0.184391
$191$	−23.0734	−1.66953	−0.834767	−	0.550603i	$-0.814398\pi$
$191$	−23.0734	−1.66953	−0.834767	+	0.550603i	$0.814398\pi$
$192$	2.67476	0.193034
$193$	0.980013	0.0705429	0.0352715	−	0.999378i	$-0.488770\pi$
$193$	0.980013	0.0705429	0.0352715	+	0.999378i	$0.488770\pi$
$194$	−35.7775	−2.56868
$195$	−0.321625	−0.0230320
$196$	10.4003	0.742876
$197$	−8.08807	−0.576251	−0.288125	−	0.957593i	$-0.593032\pi$
$197$	−8.08807	−0.576251	−0.288125	+	0.957593i	$0.593032\pi$
$198$	−8.07488	−0.573857
$199$	−4.34085	−0.307715	−0.153857	−	0.988093i	$-0.549170\pi$
$199$	−4.34085	−0.307715	−0.153857	+	0.988093i	$0.549170\pi$
$200$	26.8790	1.90063
$201$	1.61392	0.113837
$202$	−3.64375	−0.256374
$203$	−1.92188	−0.134889
$204$	−5.54358	−0.388128
$205$	−0.154278	−0.0107753
$206$	43.6298	3.03983
$207$	0.404109	0.0280875
$208$	−16.2843	−1.12911
$209$	−5.71146	−0.395070
$210$	−0.774647	−0.0534557
$211$	−5.15788	−0.355083	−0.177541	−	0.984113i	$-0.556814\pi$
$211$	−5.15788	−0.355083	−0.177541	+	0.984113i	$0.556814\pi$
$212$	−59.8323	−4.10930
$213$	0.427017	0.0292588
$214$	−2.03712	−0.139254
$215$	0.584410	0.0398564
$216$	−15.0680	−1.02525
$217$	−2.14434	−0.145567
$218$	7.09909	0.480811
$219$	0.103489	0.00699315
$220$	1.03039	0.0694687
$221$	−8.75155	−0.588693
$222$	9.99438	0.670779
$223$	0.529804	0.0354783	0.0177391	−	0.999843i	$-0.494353\pi$
$223$	0.529804	0.0354783	0.0177391	+	0.999843i	$0.494353\pi$
$224$	−5.81031	−0.388218
$225$	13.7179	0.914529
$226$	43.3167	2.88139
$227$	6.99009	0.463949	0.231974	−	0.972722i	$-0.425481\pi$
$227$	6.99009	0.463949	0.231974	+	0.972722i	$0.425481\pi$
$228$	−9.80368	−0.649264
$229$	5.16872	0.341559	0.170779	−	0.985309i	$-0.445371\pi$
$229$	5.16872	0.341559	0.170779	+	0.985309i	$0.445371\pi$
$230$	−0.0762300	−0.00502646
$231$	1.74074	0.114532
$232$	3.38412	0.222179
$233$	12.1214	0.794099	0.397050	−	0.917797i	$-0.370034\pi$
$233$	12.1214	0.794099	0.397050	+	0.917797i	$0.370034\pi$
$234$	−21.8813	−1.43042
$235$	1.82950	0.119344
$236$	−34.0457	−2.21618
$237$	−1.98857	−0.129171
$238$	−21.0785	−1.36632
$239$	−22.1220	−1.43095	−0.715475	−	0.698638i	$-0.753790\pi$
$239$	−22.1220	−1.43095	−0.715475	+	0.698638i	$0.753790\pi$
$240$	0.518080	0.0334419
$241$	−2.43045	−0.156559	−0.0782794	−	0.996931i	$-0.524943\pi$
$241$	−2.43045	−0.156559	−0.0782794	+	0.996931i	$0.524943\pi$
$242$	23.9259	1.53801
$243$	−11.6898	−0.749901
$244$	53.6018	3.43151
$245$	−0.522356	−0.0333721
$246$	0.879711	0.0560883
$247$	−15.4769	−0.984770
$248$	3.77584	0.239766
$249$	−1.72729	−0.109462
$250$	−5.19846	−0.328780
$251$	−25.4566	−1.60681	−0.803404	−	0.595434i	$-0.796980\pi$
$251$	−25.4566	−1.60681	−0.803404	+	0.595434i	$0.796980\pi$
$252$	−35.6503	−2.24576
$253$	0.171299	0.0107695
$254$	−8.03847	−0.504379
$255$	0.278428	0.0174358
$256$	−32.6006	−2.03754
$257$	−11.2203	−0.699904	−0.349952	−	0.936768i	$-0.613802\pi$
$257$	−11.2203	−0.699904	−0.349952	+	0.936768i	$0.613802\pi$
$258$	−3.33237	−0.207464
$259$	25.7064	1.59732
$260$	2.79214	0.173161
$261$	1.72712	0.106906
$262$	31.3149	1.93464
$263$	27.2366	1.67948	0.839740	−	0.542988i	$-0.182707\pi$
$263$	27.2366	1.67948	0.839740	+	0.542988i	$0.182707\pi$
$264$	−3.06517	−0.188648
$265$	3.00509	0.184602
$266$	−37.2767	−2.28558
$267$	−0.426672	−0.0261119
$268$	−14.0111	−0.855861
$269$	−13.4328	−0.819009	−0.409505	−	0.912308i	$-0.634298\pi$
$269$	−13.4328	−0.819009	−0.409505	+	0.912308i	$0.634298\pi$
$270$	1.45064	0.0882831
$271$	−3.95256	−0.240101	−0.120051	−	0.992768i	$-0.538306\pi$
$271$	−3.95256	−0.240101	−0.120051	+	0.992768i	$0.538306\pi$
$272$	14.0972	0.854767
$273$	4.71704	0.285489
$274$	−52.2855	−3.15868
$275$	5.81495	0.350655
$276$	0.294034	0.0176988
$277$	−12.3151	−0.739942	−0.369971	−	0.929043i	$-0.620632\pi$
$277$	−12.3151	−0.739942	−0.369971	+	0.929043i	$0.620632\pi$
$278$	−36.0351	−2.16124
$279$	1.92704	0.115369
$280$	3.50840	0.209667
$281$	−18.1997	−1.08570	−0.542851	−	0.839829i	$-0.682655\pi$
$281$	−18.1997	−1.08570	−0.542851	+	0.839829i	$0.682655\pi$
$282$	−10.4320	−0.621218
$283$	11.0269	0.655478	0.327739	−	0.944768i	$-0.393713\pi$
$283$	11.0269	0.655478	0.327739	+	0.944768i	$0.393713\pi$
$284$	−3.70709	−0.219975
$285$	0.492392	0.0291668
$286$	−9.27535	−0.548463
$287$	2.26269	0.133562
$288$	5.22151	0.307681
$289$	−9.42385	−0.554344
$290$	−0.325799	−0.0191316
$291$	−6.93114	−0.406310
$292$	−0.898427	−0.0525764
$293$	−8.58385	−0.501474	−0.250737	−	0.968055i	$-0.580673\pi$
$293$	−8.58385	−0.501474	−0.250737	+	0.968055i	$0.580673\pi$
$294$	2.97853	0.173711
$295$	1.70995	0.0995573
$296$	−45.2649	−2.63097
$297$	−3.25979	−0.189152
$298$	55.9531	3.24127
$299$	0.464186	0.0268446
$300$	9.98133	0.576272
$301$	−8.57114	−0.494032
$302$	−22.1068	−1.27210
$303$	−0.705900	−0.0405529
$304$	24.9305	1.42986
$305$	−2.69217	−0.154153
$306$	18.9425	1.08287
$307$	−13.4901	−0.769919	−0.384959	−	0.922934i	$-0.625785\pi$
$307$	−13.4901	−0.769919	−0.384959	+	0.922934i	$0.625785\pi$
$308$	−15.1120	−0.861084
$309$	8.45234	0.480837
$310$	−0.363511	−0.0206461
$311$	12.4334	0.705033	0.352517	−	0.935806i	$-0.385326\pi$
$311$	12.4334	0.705033	0.352517	+	0.935806i	$0.385326\pi$
$312$	−8.30597	−0.470233
$313$	−28.4472	−1.60793	−0.803966	−	0.594676i	$-0.797280\pi$
$313$	−28.4472	−1.60793	−0.803966	+	0.594676i	$0.797280\pi$
$314$	−45.9447	−2.59281
$315$	1.79055	0.100886
$316$	17.2634	0.971144
$317$	20.6042	1.15725	0.578624	−	0.815594i	$-0.303590\pi$
$317$	20.6042	1.15725	0.578624	+	0.815594i	$0.303590\pi$
$318$	−17.1354	−0.960904
$319$	0.732116	0.0409906
$320$	1.16626	0.0651959
$321$	−0.394648	−0.0220271
$322$	1.11801	0.0623044
$323$	13.3982	0.745497
$324$	29.1274	1.61819
$325$	15.7573	0.874059
$326$	20.3621	1.12775
$327$	1.37530	0.0760542
$328$	−3.98424	−0.219993
$329$	−26.8321	−1.47930
$330$	0.295092	0.0162443
$331$	0.849983	0.0467193	0.0233596	−	0.999727i	$-0.492564\pi$
$331$	0.849983	0.0467193	0.0233596	+	0.999727i	$0.492564\pi$
$332$	14.9952	0.822969
$333$	−23.1014	−1.26595
$334$	−23.2023	−1.26957
$335$	0.703709	0.0384477
$336$	−7.59831	−0.414522
$337$	−15.7643	−0.858738	−0.429369	−	0.903129i	$-0.641264\pi$
$337$	−15.7643	−0.858738	−0.429369	+	0.903129i	$0.641264\pi$
$338$	7.18699	0.390921
$339$	8.39170	0.455774
$340$	−2.41713	−0.131087
$341$	0.816860	0.0442355
$342$	33.4992	1.81143
$343$	−13.8999	−0.750525
$344$	15.0924	0.813729
$345$	−0.0147679	−0.000795079 0
$346$	−11.0554	−0.594343
$347$	8.13344	0.436626	0.218313	−	0.975879i	$-0.429945\pi$
$347$	8.13344	0.436626	0.218313	+	0.975879i	$0.429945\pi$
$348$	1.25667	0.0673647
$349$	−11.0720	−0.592669	−0.296334	−	0.955084i	$-0.595764\pi$
$349$	−11.0720	−0.592669	−0.296334	+	0.955084i	$0.595764\pi$
$350$	37.9522	2.02863
$351$	−8.83335	−0.471490
$352$	2.21337	0.117973
$353$	23.0791	1.22838	0.614188	−	0.789160i	$-0.289484\pi$
$353$	23.0791	1.22838	0.614188	+	0.789160i	$0.289484\pi$
$354$	−9.75033	−0.518224
$355$	0.186190	0.00988192
$356$	3.70409	0.196316
$357$	−4.08351	−0.216122
$358$	64.9690	3.43372
$359$	0.808981	0.0426964	0.0213482	−	0.999772i	$-0.493204\pi$
$359$	0.808981	0.0426964	0.0213482	+	0.999772i	$0.493204\pi$
$360$	−3.15287	−0.166171
$361$	4.69438	0.247072
$362$	16.6702	0.876166
$363$	4.63513	0.243281
$364$	−40.9503	−2.14638
$365$	0.0451237	0.00236188
$366$	15.3510	0.802411
$367$	−15.3248	−0.799950	−0.399975	−	0.916526i	$-0.630981\pi$
$367$	−15.3248	−0.799950	−0.399975	+	0.916526i	$0.630981\pi$
$368$	−0.747720	−0.0389776
$369$	−2.03340	−0.105854
$370$	4.35778	0.226550
$371$	−44.0736	−2.28819
$372$	1.40214	0.0726973
$373$	−24.2272	−1.25444	−0.627219	−	0.778843i	$-0.715807\pi$
$373$	−24.2272	−1.25444	−0.627219	+	0.778843i	$0.715807\pi$
$374$	8.02960	0.415201
$375$	−1.00709	−0.0520060
$376$	47.2470	2.43658
$377$	1.98388	0.102175
$378$	−21.2755	−1.09429
$379$	−17.5814	−0.903097	−0.451549	−	0.892246i	$-0.649128\pi$
$379$	−17.5814	−0.903097	−0.451549	+	0.892246i	$0.649128\pi$
$380$	−4.27463	−0.219284
$381$	−1.55728	−0.0797821
$382$	57.3663	2.93512
$383$	24.3147	1.24242	0.621212	−	0.783642i	$-0.286640\pi$
$383$	24.3147	1.24242	0.621212	+	0.783642i	$0.286640\pi$
$384$	−8.46732	−0.432096
$385$	0.759003	0.0386824
$386$	−2.43656	−0.124018
$387$	7.70256	0.391543
$388$	60.1716	3.05475
$389$	−7.29271	−0.369755	−0.184878	−	0.982762i	$-0.559189\pi$
$389$	−7.29271	−0.369755	−0.184878	+	0.982762i	$0.559189\pi$
$390$	0.799640	0.0404913
$391$	−0.401842	−0.0203220
$392$	−13.4899	−0.681342
$393$	6.06660	0.306019
$394$	20.1090	1.01308
$395$	−0.867061	−0.0436266
$396$	13.5806	0.682449
$397$	−5.81527	−0.291860	−0.145930	−	0.989295i	$-0.546617\pi$
$397$	−5.81527	−0.291860	−0.145930	+	0.989295i	$0.546617\pi$
$398$	10.7924	0.540976
$399$	−7.22158	−0.361531
$400$	−25.3822	−1.26911
$401$	10.8377	0.541208	0.270604	−	0.962691i	$-0.412777\pi$
$401$	10.8377	0.541208	0.270604	+	0.962691i	$0.412777\pi$
$402$	−4.01262	−0.200131
$403$	2.21352	0.110264
$404$	6.12817	0.304888
$405$	−1.46293	−0.0726937
$406$	4.77827	0.237142
$407$	−9.79254	−0.485398
$408$	7.19042	0.355979
$409$	−29.7872	−1.47288	−0.736441	−	0.676502i	$-0.763495\pi$
$409$	−29.7872	−1.47288	−0.736441	+	0.676502i	$0.763495\pi$
$410$	0.383575	0.0189434
$411$	−10.1292	−0.499637
$412$	−73.3778	−3.61506
$413$	−25.0787	−1.23404
$414$	−1.00472	−0.0493791
$415$	−0.753138	−0.0369701
$416$	5.99777	0.294065
$417$	−6.98104	−0.341863
$418$	14.2001	0.694551
$419$	−29.7516	−1.45346	−0.726730	−	0.686923i	$-0.758961\pi$
$419$	−29.7516	−1.45346	−0.726730	+	0.686923i	$0.758961\pi$
$420$	1.30282	0.0635713
$421$	−26.6818	−1.30039	−0.650194	−	0.759768i	$-0.725313\pi$
$421$	−26.6818	−1.30039	−0.650194	+	0.759768i	$0.725313\pi$
$422$	12.8238	0.624252
$423$	24.1130	1.17241
$424$	77.6067	3.76892
$425$	−13.6410	−0.661686
$426$	−1.06167	−0.0514382
$427$	39.4841	1.91077
$428$	3.42608	0.165606
$429$	−1.79690	−0.0867552
$430$	−1.45299	−0.0700695
$431$	−24.2338	−1.16730	−0.583651	−	0.812005i	$-0.698376\pi$
$431$	−24.2338	−1.16730	−0.583651	+	0.812005i	$0.698376\pi$
$432$	14.2289	0.684591
$433$	−12.2602	−0.589188	−0.294594	−	0.955623i	$-0.595184\pi$
$433$	−12.2602	−0.589188	−0.294594	+	0.955623i	$0.595184\pi$
$434$	5.33137	0.255914
$435$	−0.0631167	−0.00302622
$436$	−11.9395	−0.571796
$437$	−0.710647	−0.0339949
$438$	−0.257300	−0.0122943
$439$	−40.4944	−1.93269	−0.966347	−	0.257241i	$-0.917186\pi$
$439$	−40.4944	−1.93269	−0.966347	+	0.257241i	$0.917186\pi$
$440$	−1.33648	−0.0637144
$441$	−6.88469	−0.327842
$442$	21.7586	1.03495
$443$	5.50681	0.261636	0.130818	−	0.991406i	$-0.458240\pi$
$443$	5.50681	0.261636	0.130818	+	0.991406i	$0.458240\pi$
$444$	−16.8088	−0.797712
$445$	−0.186039	−0.00881909
$446$	−1.31723	−0.0623725
$447$	10.8397	0.512701
$448$	−17.1047	−0.808121
$449$	−34.2501	−1.61636	−0.808181	−	0.588935i	$-0.799548\pi$
$449$	−34.2501	−1.61636	−0.808181	+	0.588935i	$0.799548\pi$
$450$	−34.1063	−1.60778
$451$	−0.861945	−0.0405874
$452$	−72.8513	−3.42664
$453$	−4.28272	−0.201220
$454$	−17.3791	−0.815643
$455$	2.05674	0.0964216
$456$	12.7161	0.595484
$457$	22.2074	1.03882	0.519408	−	0.854526i	$-0.326152\pi$
$457$	22.2074	1.03882	0.519408	+	0.854526i	$0.326152\pi$
$458$	−12.8507	−0.600476
$459$	7.64697	0.356930
$460$	0.128206	0.00597763
$461$	35.8566	1.67001	0.835004	−	0.550244i	$-0.185465\pi$
$461$	35.8566	1.67001	0.835004	+	0.550244i	$0.185465\pi$
$462$	−4.32792	−0.201353
$463$	−19.3584	−0.899661	−0.449830	−	0.893114i	$-0.648516\pi$
$463$	−19.3584	−0.899661	−0.449830	+	0.893114i	$0.648516\pi$
$464$	−3.19568	−0.148356
$465$	−0.0704226	−0.00326577
$466$	−30.1369	−1.39606
$467$	0.744230	0.0344389	0.0172194	−	0.999852i	$-0.494519\pi$
$467$	0.744230	0.0344389	0.0172194	+	0.999852i	$0.494519\pi$
$468$	36.8006	1.70111
$469$	−10.3208	−0.476571
$470$	−4.54861	−0.209812
$471$	−8.90081	−0.410128
$472$	44.1596	2.03261
$473$	3.26507	0.150128
$474$	4.94407	0.227089
$475$	−24.1237	−1.10687
$476$	35.4504	1.62487
$477$	39.6073	1.81350
$478$	55.0008	2.51568
$479$	0.686495	0.0313667	0.0156834	−	0.999877i	$-0.495008\pi$
$479$	0.686495	0.0313667	0.0156834	+	0.999877i	$0.495008\pi$
$480$	−0.190817	−0.00870959
$481$	−26.5358	−1.20993
$482$	6.04270	0.275238
$483$	0.216591	0.00985524
$484$	−40.2392	−1.82906
$485$	−3.02214	−0.137228
$486$	29.0638	1.31836
$487$	5.65658	0.256324	0.128162	−	0.991753i	$-0.459092\pi$
$487$	5.65658	0.256324	0.128162	+	0.991753i	$0.459092\pi$
$488$	−69.5254	−3.14726
$489$	3.94473	0.178387
$490$	1.29871	0.0586697
$491$	32.6030	1.47135	0.735677	−	0.677332i	$-0.236864\pi$
$491$	32.6030	1.47135	0.735677	+	0.677332i	$0.236864\pi$
$492$	−1.47952	−0.0667020
$493$	−1.71743	−0.0773493
$494$	38.4794	1.73127
$495$	−0.682088	−0.0306576
$496$	−3.56559	−0.160100
$497$	−2.73071	−0.122489
$498$	4.29448	0.192440
$499$	−11.6016	−0.519360	−0.259680	−	0.965695i	$-0.583617\pi$
$499$	−11.6016	−0.519360	−0.259680	+	0.965695i	$0.583617\pi$
$500$	8.74292	0.390995
$501$	−4.49496	−0.200820
$502$	63.2916	2.82484
$503$	14.6777	0.654448	0.327224	−	0.944947i	$-0.393887\pi$
$503$	14.6777	0.654448	0.327224	+	0.944947i	$0.393887\pi$
$504$	46.2410	2.05974
$505$	−0.307789	−0.0136964
$506$	−0.425893	−0.0189333
$507$	1.39233	0.0618354
$508$	13.5193	0.599824
$509$	−0.240870	−0.0106764	−0.00533818	−	0.999986i	$-0.501699\pi$
$509$	−0.240870	−0.0106764	−0.00533818	+	0.999986i	$0.501699\pi$
$510$	−0.692242	−0.0306530
$511$	−0.661798	−0.0292762
$512$	45.8943	2.02826
$513$	13.5235	0.597075
$514$	27.8965	1.23046
$515$	3.68542	0.162399
$516$	5.60447	0.246723
$517$	10.2214	0.449534
$518$	−63.9126	−2.80816
$519$	−2.14175	−0.0940125
$520$	−3.62160	−0.158818
$521$	25.5777	1.12058	0.560291	−	0.828296i	$-0.310689\pi$
$521$	25.5777	1.12058	0.560291	+	0.828296i	$0.310689\pi$
$522$	−4.29406	−0.187946
$523$	−1.03517	−0.0452646	−0.0226323	−	0.999744i	$-0.507205\pi$
$523$	−1.03517	−0.0452646	−0.0226323	+	0.999744i	$0.507205\pi$
$524$	−52.6663	−2.30074
$525$	7.35244	0.320887
$526$	−67.7171	−2.95260
$527$	−1.91623	−0.0834723
$528$	2.89449	0.125966
$529$	−22.9787	−0.999073
$530$	−7.47142	−0.324538
$531$	22.5373	0.978035
$532$	62.6931	2.71809
$533$	−2.33569	−0.101170
$534$	1.06081	0.0459059
$535$	−0.172076	−0.00743949
$536$	18.1733	0.784968
$537$	12.5864	0.543142
$538$	33.3972	1.43986
$539$	−2.91838	−0.125704
$540$	−2.43973	−0.104989
$541$	−22.6676	−0.974555	−0.487278	−	0.873247i	$-0.662010\pi$
$541$	−22.6676	−0.974555	−0.487278	+	0.873247i	$0.662010\pi$
$542$	9.82707	0.422109
$543$	3.22950	0.138591
$544$	−5.19223	−0.222615
$545$	0.599663	0.0256867
$546$	−11.7278	−0.501902
$547$	14.1153	0.603527	0.301763	−	0.953383i	$-0.402425\pi$
$547$	14.1153	0.603527	0.301763	+	0.953383i	$0.402425\pi$
$548$	87.9352	3.75641
$549$	−35.4829	−1.51437
$550$	−14.4574	−0.616467
$551$	−3.03724	−0.129391
$552$	−0.381383	−0.0162327
$553$	12.7166	0.540764
$554$	30.6184	1.30085
$555$	0.844228	0.0358355
$556$	60.6049	2.57022
$557$	22.5525	0.955580	0.477790	−	0.878474i	$-0.341438\pi$
$557$	22.5525	0.955580	0.477790	+	0.878474i	$0.341438\pi$
$558$	−4.79110	−0.202824
$559$	8.84767	0.374217
$560$	−3.31304	−0.140002
$561$	1.55556	0.0656760
$562$	45.2490	1.90871
$563$	27.4494	1.15685	0.578427	−	0.815734i	$-0.303667\pi$
$563$	27.4494	1.15685	0.578427	+	0.815734i	$0.303667\pi$
$564$	17.5449	0.738773
$565$	3.65898	0.153934
$566$	−27.4155	−1.15236
$567$	21.4558	0.901060
$568$	4.80836	0.201754
$569$	1.13800	0.0477075	0.0238537	−	0.999715i	$-0.492406\pi$
$569$	1.13800	0.0477075	0.0238537	+	0.999715i	$0.492406\pi$
$570$	−1.22421	−0.0512766
$571$	26.4752	1.10795	0.553977	−	0.832532i	$-0.313110\pi$
$571$	26.4752	1.10795	0.553977	+	0.832532i	$0.313110\pi$
$572$	15.5995	0.652250
$573$	11.1135	0.464274
$574$	−5.62562	−0.234809
$575$	0.723525	0.0301731
$576$	15.3714	0.640474
$577$	−37.4862	−1.56057	−0.780285	−	0.625424i	$-0.784926\pi$
$577$	−37.4862	−1.56057	−0.780285	+	0.625424i	$0.784926\pi$
$578$	23.4301	0.974562
$579$	−0.472032	−0.0196170
$580$	0.547939	0.0227519
$581$	11.0458	0.458255
$582$	17.2325	0.714312
$583$	16.7893	0.695343
$584$	1.16532	0.0482214
$585$	−1.84832	−0.0764186
$586$	21.3416	0.881614
$587$	11.2719	0.465241	0.232621	−	0.972568i	$-0.425270\pi$
$587$	11.2719	0.465241	0.232621	+	0.972568i	$0.425270\pi$
$588$	−5.00938	−0.206583
$589$	−3.38880	−0.139633
$590$	−4.25138	−0.175026
$591$	3.89569	0.160247
$592$	42.7444	1.75678
$593$	2.03484	0.0835609	0.0417805	−	0.999127i	$-0.486697\pi$
$593$	2.03484	0.0835609	0.0417805	+	0.999127i	$0.486697\pi$
$594$	8.10465	0.332538
$595$	−1.78051	−0.0729936
$596$	−94.1034	−3.85463
$597$	2.09081	0.0855710
$598$	−1.15408	−0.0471940
$599$	31.1285	1.27188	0.635938	−	0.771740i	$-0.280613\pi$
$599$	31.1285	1.27188	0.635938	+	0.771740i	$0.280613\pi$
$600$	−12.9465	−0.528538
$601$	35.0498	1.42971	0.714856	−	0.699272i	$-0.246492\pi$
$601$	35.0498	1.42971	0.714856	+	0.699272i	$0.246492\pi$
$602$	21.3100	0.868531
$603$	9.27493	0.377704
$604$	37.1798	1.51283
$605$	2.02103	0.0821664
$606$	1.75504	0.0712938
$607$	10.9766	0.445527	0.222763	−	0.974873i	$-0.428492\pi$
$607$	10.9766	0.445527	0.222763	+	0.974873i	$0.428492\pi$
$608$	−9.18231	−0.372392
$609$	0.925689	0.0375108
$610$	6.69341	0.271008
$611$	27.6978	1.12053
$612$	−31.8580	−1.28778
$613$	−16.3621	−0.660860	−0.330430	−	0.943831i	$-0.607194\pi$
$613$	−16.3621	−0.660860	−0.330430	+	0.943831i	$0.607194\pi$
$614$	33.5397	1.35355
$615$	0.0743095	0.00299645
$616$	19.6013	0.789758
$617$	−19.8851	−0.800545	−0.400273	−	0.916396i	$-0.631085\pi$
$617$	−19.8851	−0.800545	−0.400273	+	0.916396i	$0.631085\pi$
$618$	−21.0147	−0.845333
$619$	25.8349	1.03839	0.519196	−	0.854655i	$-0.326232\pi$
$619$	25.8349	1.03839	0.519196	+	0.854655i	$0.326232\pi$
$620$	0.611364	0.0245530
$621$	−0.405599	−0.0162761
$622$	−30.9125	−1.23948
$623$	2.72850	0.109315
$624$	7.84346	0.313990
$625$	24.3404	0.973614
$626$	70.7269	2.82682
$627$	2.75097	0.109863
$628$	77.2711	3.08345
$629$	22.9718	0.915946
$630$	−4.45176	−0.177362
$631$	5.85647	0.233142	0.116571	−	0.993182i	$-0.462810\pi$
$631$	5.85647	0.233142	0.116571	+	0.993182i	$0.462810\pi$
$632$	−22.3919	−0.890702
$633$	2.48434	0.0987435
$634$	−51.2273	−2.03450
$635$	−0.679012	−0.0269458
$636$	28.8188	1.14274
$637$	−7.90821	−0.313335
$638$	−1.82023	−0.0720634
$639$	2.45399	0.0970784
$640$	−3.69195	−0.145937
$641$	43.8462	1.73182	0.865910	−	0.500200i	$-0.166740\pi$
$641$	43.8462	1.73182	0.865910	+	0.500200i	$0.166740\pi$
$642$	0.981195	0.0387247
$643$	15.5876	0.614714	0.307357	−	0.951594i	$-0.400555\pi$
$643$	15.5876	0.614714	0.307357	+	0.951594i	$0.400555\pi$
$644$	−1.88030	−0.0740944
$645$	−0.281486	−0.0110835
$646$	−33.3113	−1.31062
$647$	−17.4662	−0.686666	−0.343333	−	0.939214i	$-0.611556\pi$
$647$	−17.4662	−0.686666	−0.343333	+	0.939214i	$0.611556\pi$
$648$	−37.7803	−1.48415
$649$	9.55343	0.375005
$650$	−39.1767	−1.53664
$651$	1.03284	0.0404802
$652$	−34.2456	−1.34116
$653$	−24.3936	−0.954594	−0.477297	−	0.878742i	$-0.658383\pi$
$653$	−24.3936	−0.954594	−0.477297	+	0.878742i	$0.658383\pi$
$654$	−3.41934	−0.133707
$655$	2.64518	0.103356
$656$	3.76238	0.146896
$657$	0.594734	0.0232028
$658$	66.7113	2.60068
$659$	−1.14944	−0.0447757	−0.0223878	−	0.999749i	$-0.507127\pi$
$659$	−1.14944	−0.0447757	−0.0223878	+	0.999749i	$0.507127\pi$
$660$	−0.496295	−0.0193183
$661$	5.16888	0.201046	0.100523	−	0.994935i	$-0.467948\pi$
$661$	5.16888	0.201046	0.100523	+	0.994935i	$0.467948\pi$
$662$	−2.11327	−0.0821346
$663$	4.21526	0.163707
$664$	−19.4498	−0.754800
$665$	−3.14878	−0.122104
$666$	57.4359	2.22559
$667$	0.0910935	0.00352715
$668$	39.0223	1.50982
$669$	−0.255185	−0.00986601
$670$	−1.74960	−0.0675929
$671$	−15.0410	−0.580652
$672$	2.79859	0.107958
$673$	−48.7004	−1.87726	−0.938632	−	0.344921i	$-0.887906\pi$
$673$	−48.7004	−1.87726	−0.938632	+	0.344921i	$0.887906\pi$
$674$	39.1941	1.50970
$675$	−13.7685	−0.529950
$676$	−12.0873	−0.464896
$677$	−34.6704	−1.33249	−0.666246	−	0.745732i	$-0.732100\pi$
$677$	−34.6704	−1.33249	−0.666246	+	0.745732i	$0.732100\pi$
$678$	−20.8639	−0.801272
$679$	44.3236	1.70098
$680$	3.13519	0.120229
$681$	−3.36684	−0.129017
$682$	−2.03092	−0.0777680
$683$	4.85190	0.185653	0.0928263	−	0.995682i	$-0.470410\pi$
$683$	4.85190	0.185653	0.0928263	+	0.995682i	$0.470410\pi$
$684$	−56.3399	−2.15421
$685$	−4.41657	−0.168748
$686$	34.5587	1.31946
$687$	−2.48956	−0.0949826
$688$	−14.2520	−0.543353
$689$	45.4956	1.73324
$690$	0.0367168	0.00139779
$691$	5.34513	0.203338	0.101669	−	0.994818i	$-0.467582\pi$
$691$	5.34513	0.203338	0.101669	+	0.994818i	$0.467582\pi$
$692$	18.5933	0.706812
$693$	10.0037	0.380009
$694$	−20.2218	−0.767608
$695$	−3.04390	−0.115462
$696$	−1.62999	−0.0617847
$697$	2.02199	0.0765885
$698$	27.5277	1.04194
$699$	−5.83838	−0.220828
$700$	−63.8291	−2.41251
$701$	−50.7230	−1.91578	−0.957890	−	0.287136i	$-0.907297\pi$
$701$	−50.7230	−1.91578	−0.957890	+	0.287136i	$0.907297\pi$
$702$	21.9619	0.828900
$703$	40.6250	1.53220
$704$	6.51583	0.245575
$705$	−0.881196	−0.0331878
$706$	−57.3804	−2.15954
$707$	4.51413	0.169771
$708$	16.3984	0.616289
$709$	44.8056	1.68271	0.841355	−	0.540483i	$-0.181759\pi$
$709$	44.8056	1.68271	0.841355	+	0.540483i	$0.181759\pi$
$710$	−0.462914	−0.0173729
$711$	−11.4279	−0.428581
$712$	−4.80447	−0.180055
$713$	0.101638	0.00380636
$714$	10.1526	0.379953
$715$	−0.783491	−0.0293009
$716$	−109.267	−4.08349
$717$	10.6552	0.397927
$718$	−2.01133	−0.0750622
$719$	−39.7534	−1.48255	−0.741275	−	0.671201i	$-0.765779\pi$
$719$	−39.7534	−1.48255	−0.741275	+	0.671201i	$0.765779\pi$
$720$	2.97731	0.110958
$721$	−54.0515	−2.01298
$722$	−11.6714	−0.434365
$723$	1.17065	0.0435368
$724$	−28.0364	−1.04196
$725$	3.09227	0.114844
$726$	−11.5241	−0.427700
$727$	−2.79245	−0.103566	−0.0517832	−	0.998658i	$-0.516490\pi$
$727$	−2.79245	−0.103566	−0.0517832	+	0.998658i	$0.516490\pi$
$728$	53.1155	1.96859
$729$	−15.2671	−0.565448
$730$	−0.112189	−0.00415230
$731$	−7.65936	−0.283292
$732$	−25.8178	−0.954253
$733$	38.1334	1.40849	0.704245	−	0.709957i	$-0.251286\pi$
$733$	38.1334	1.40849	0.704245	+	0.709957i	$0.251286\pi$
$734$	38.1014	1.40635
$735$	0.251597	0.00928031
$736$	0.275398	0.0101513
$737$	3.93159	0.144822
$738$	5.05554	0.186097
$739$	41.2948	1.51905	0.759527	−	0.650475i	$-0.225430\pi$
$739$	41.2948	1.51905	0.759527	+	0.650475i	$0.225430\pi$
$740$	−7.32904	−0.269421
$741$	7.45457	0.273851
$742$	109.578	4.02274
$743$	−28.4990	−1.04553	−0.522763	−	0.852478i	$-0.675099\pi$
$743$	−28.4990	−1.04553	−0.522763	+	0.852478i	$0.675099\pi$
$744$	−1.81867	−0.0666756
$745$	4.72637	0.173161
$746$	60.2350	2.20536
$747$	−9.92641	−0.363188
$748$	−13.5044	−0.493770
$749$	2.52372	0.0922146
$750$	2.50388	0.0914289
$751$	−25.2898	−0.922837	−0.461418	−	0.887183i	$-0.652659\pi$
$751$	−25.2898	−0.922837	−0.461418	+	0.887183i	$0.652659\pi$
$752$	−44.6161	−1.62698
$753$	12.2614	0.446831
$754$	−4.93244	−0.179629
$755$	−1.86737	−0.0679604
$756$	35.7818	1.30137
$757$	−27.9228	−1.01487	−0.507436	−	0.861689i	$-0.669407\pi$
$757$	−27.9228	−1.01487	−0.507436	+	0.861689i	$0.669407\pi$
$758$	43.7119	1.58769
$759$	−0.0825078	−0.00299484
$760$	5.54450	0.201120
$761$	−7.55897	−0.274012	−0.137006	−	0.990570i	$-0.543748\pi$
$761$	−7.55897	−0.274012	−0.137006	+	0.990570i	$0.543748\pi$
$762$	3.87180	0.140261
$763$	−8.79483	−0.318394
$764$	−96.4804	−3.49054
$765$	1.60008	0.0578508
$766$	−60.4526	−2.18424
$767$	25.8878	0.934755
$768$	15.7024	0.566610
$769$	17.2353	0.621521	0.310761	−	0.950488i	$-0.399416\pi$
$769$	17.2353	0.621521	0.310761	+	0.950488i	$0.399416\pi$
$770$	−1.88707	−0.0680054
$771$	5.40436	0.194633
$772$	4.09788	0.147486
$773$	−12.6489	−0.454949	−0.227475	−	0.973784i	$-0.573047\pi$
$773$	−12.6489	−0.454949	−0.227475	+	0.973784i	$0.573047\pi$
$774$	−19.1505	−0.688351
$775$	3.45021	0.123935
$776$	−78.0469	−2.80172
$777$	−12.3817	−0.444191
$778$	18.1315	0.650046
$779$	3.57584	0.128118
$780$	−1.34486	−0.0481536
$781$	1.04023	0.0372225
$782$	0.999081	0.0357271
$783$	−1.73349	−0.0619498
$784$	12.7387	0.454954
$785$	−3.88096	−0.138517
$786$	−15.0831	−0.537996
$787$	−30.0791	−1.07220	−0.536102	−	0.844153i	$-0.680104\pi$
$787$	−30.0791	−1.07220	−0.536102	+	0.844153i	$0.680104\pi$
$788$	−33.8198	−1.20478
$789$	−13.1187	−0.467040
$790$	2.15573	0.0766975
$791$	−53.6637	−1.90806
$792$	−17.6150	−0.625920
$793$	−40.7581	−1.44736
$794$	14.4582	0.513103
$795$	−1.44743	−0.0513351
$796$	−18.1510	−0.643347
$797$	11.2469	0.398386	0.199193	−	0.979960i	$-0.436168\pi$
$797$	11.2469	0.398386	0.199193	+	0.979960i	$0.436168\pi$
$798$	17.9547	0.635588
$799$	−23.9777	−0.848272
$800$	9.34870	0.330527
$801$	−2.45201	−0.0866374
$802$	−26.9452	−0.951468
$803$	0.252104	0.00889656
$804$	6.74854	0.238003
$805$	0.0944388	0.00332853
$806$	−5.50338	−0.193848
$807$	6.47000	0.227755
$808$	−7.94866	−0.279633
$809$	36.5829	1.28619	0.643093	−	0.765788i	$-0.277651\pi$
$809$	36.5829	1.28619	0.643093	+	0.765788i	$0.277651\pi$
$810$	3.63722	0.127799
$811$	16.5684	0.581795	0.290897	−	0.956754i	$-0.406046\pi$
$811$	16.5684	0.581795	0.290897	+	0.956754i	$0.406046\pi$
$812$	−8.03624	−0.282017
$813$	1.90379	0.0667687
$814$	24.3467	0.853352
$815$	1.72000	0.0602488
$816$	−6.79003	−0.237698
$817$	−13.5454	−0.473893
$818$	74.0585	2.58939
$819$	27.1080	0.947230
$820$	−0.645107	−0.0225281
$821$	−1.90936	−0.0666370	−0.0333185	−	0.999445i	$-0.510608\pi$
$821$	−1.90936	−0.0666370	−0.0333185	+	0.999445i	$0.510608\pi$
$822$	25.1837	0.878384
$823$	37.8982	1.32105	0.660524	−	0.750805i	$-0.270334\pi$
$823$	37.8982	1.32105	0.660524	+	0.750805i	$0.270334\pi$
$824$	95.1762	3.31562
$825$	−2.80082	−0.0975121
$826$	62.3520	2.16950
$827$	−17.4725	−0.607578	−0.303789	−	0.952739i	$-0.598252\pi$
$827$	−17.4725	−0.607578	−0.303789	+	0.952739i	$0.598252\pi$
$828$	1.68976	0.0587232
$829$	27.3387	0.949511	0.474755	−	0.880118i	$-0.342537\pi$
$829$	27.3387	0.949511	0.474755	+	0.880118i	$0.342537\pi$
$830$	1.87249	0.0649952
$831$	5.93167	0.205767
$832$	17.6566	0.612132
$833$	6.84608	0.237203
$834$	17.3566	0.601011
$835$	−1.95991	−0.0678254
$836$	−23.8822	−0.825982
$837$	−1.93414	−0.0668538
$838$	73.9699	2.55525
$839$	−9.87364	−0.340876	−0.170438	−	0.985368i	$-0.554518\pi$
$839$	−9.87364	−0.340876	−0.170438	+	0.985368i	$0.554518\pi$
$840$	−1.68985	−0.0583055
$841$	−28.6107	−0.986575
$842$	66.3376	2.28614
$843$	8.76603	0.301918
$844$	−21.5674	−0.742381
$845$	0.607088	0.0208845
$846$	−59.9510	−2.06116
$847$	−29.6410	−1.01848
$848$	−73.2853	−2.51663
$849$	−5.31118	−0.182279
$850$	33.9150	1.16327
$851$	−1.21844	−0.0417674
$852$	1.78555	0.0611720
$853$	37.0343	1.26803	0.634016	−	0.773320i	$-0.281405\pi$
$853$	37.0343	1.26803	0.634016	+	0.773320i	$0.281405\pi$
$854$	−98.1675	−3.35922
$855$	2.82969	0.0967733
$856$	−4.44387	−0.151888
$857$	−42.9147	−1.46594	−0.732970	−	0.680261i	$-0.761866\pi$
$857$	−42.9147	−1.46594	−0.732970	+	0.680261i	$0.761866\pi$
$858$	4.46755	0.152520
$859$	41.1096	1.40264	0.701320	−	0.712847i	$-0.252594\pi$
$859$	41.1096	1.40264	0.701320	+	0.712847i	$0.252594\pi$
$860$	2.44368	0.0833289
$861$	−1.08984	−0.0371418
$862$	60.2514	2.05217
$863$	−5.75640	−0.195950	−0.0979750	−	0.995189i	$-0.531237\pi$
$863$	−5.75640	−0.195950	−0.0979750	+	0.995189i	$0.531237\pi$
$864$	−5.24076	−0.178294
$865$	−0.933855	−0.0317520
$866$	30.4820	1.03582
$867$	4.53908	0.154155
$868$	−8.96645	−0.304341
$869$	−4.84423	−0.164329
$870$	0.156924	0.00532023
$871$	10.6538	0.360990
$872$	15.4863	0.524433
$873$	−39.8320	−1.34811
$874$	1.76685	0.0597645
$875$	6.44020	0.217719
$876$	0.432735	0.0146208
$877$	18.9082	0.638486	0.319243	−	0.947673i	$-0.396571\pi$
$877$	18.9082	0.638486	0.319243	+	0.947673i	$0.396571\pi$
$878$	100.679	3.39777
$879$	4.13448	0.139453
$880$	1.26206	0.0425442
$881$	52.0019	1.75199	0.875994	−	0.482321i	$-0.160206\pi$
$881$	52.0019	1.75199	0.875994	+	0.482321i	$0.160206\pi$
$882$	17.1171	0.576362
$883$	−57.5278	−1.93597	−0.967983	−	0.251017i	$-0.919235\pi$
$883$	−57.5278	−1.93597	−0.967983	+	0.251017i	$0.919235\pi$
$884$	−36.5942	−1.23080
$885$	−0.823614	−0.0276855
$886$	−13.6913	−0.459969
$887$	−27.5992	−0.926689	−0.463345	−	0.886178i	$-0.653351\pi$
$887$	−27.5992	−0.926689	−0.463345	+	0.886178i	$0.653351\pi$
$888$	21.8022	0.731635
$889$	9.95860	0.334001
$890$	0.462540	0.0155044
$891$	−8.17334	−0.273817
$892$	2.21535	0.0741754
$893$	−42.4040	−1.41900
$894$	−26.9503	−0.901352
$895$	5.48795	0.183442
$896$	54.1472	1.80893
$897$	−0.223579	−0.00746509
$898$	85.1544	2.84164
$899$	0.434390	0.0144877
$900$	57.3609	1.91203
$901$	−39.3852	−1.31211
$902$	2.14301	0.0713545
$903$	4.12836	0.137383
$904$	94.4933	3.14280
$905$	1.40814	0.0468080
$906$	10.6479	0.353754
$907$	21.6900	0.720204	0.360102	−	0.932913i	$-0.382742\pi$
$907$	21.6900	0.720204	0.360102	+	0.932913i	$0.382742\pi$
$908$	29.2287	0.969989
$909$	−4.05668	−0.134552
$910$	−5.11358	−0.169514
$911$	−38.2981	−1.26887	−0.634436	−	0.772976i	$-0.718767\pi$
$911$	−38.2981	−1.26887	−0.634436	+	0.772976i	$0.718767\pi$
$912$	−12.0080	−0.397624
$913$	−4.20775	−0.139256
$914$	−55.2131	−1.82629
$915$	1.29671	0.0428678
$916$	21.6128	0.714105
$917$	−38.7950	−1.28112
$918$	−19.0123	−0.627499
$919$	−19.1351	−0.631208	−0.315604	−	0.948891i	$-0.602207\pi$
$919$	−19.1351	−0.631208	−0.315604	+	0.948891i	$0.602207\pi$
$920$	−0.166292	−0.00548248
$921$	6.49761	0.214103
$922$	−89.1485	−2.93595
$923$	2.81882	0.0927825
$924$	7.27881	0.239455
$925$	−41.3612	−1.35995
$926$	48.1298	1.58164
$927$	48.5741	1.59538
$928$	1.17702	0.0386377
$929$	−28.3890	−0.931412	−0.465706	−	0.884939i	$-0.654200\pi$
$929$	−28.3890	−0.931412	−0.465706	+	0.884939i	$0.654200\pi$
$930$	0.175088	0.00574138
$931$	12.1071	0.396794
$932$	50.6850	1.66024
$933$	−5.98865	−0.196060
$934$	−1.85034	−0.0605451
$935$	0.678263	0.0221816
$936$	−47.7329	−1.56020
$937$	−21.9471	−0.716982	−0.358491	−	0.933533i	$-0.616709\pi$
$937$	−21.9471	−0.716982	−0.358491	+	0.933533i	$0.616709\pi$
$938$	25.6601	0.837833
$939$	13.7018	0.447143
$940$	7.64998	0.249515
$941$	1.51164	0.0492780	0.0246390	−	0.999696i	$-0.492156\pi$
$941$	1.51164	0.0492780	0.0246390	+	0.999696i	$0.492156\pi$
$942$	22.1297	0.721023
$943$	−0.107247	−0.00349246
$944$	−41.7006	−1.35724
$945$	−1.79715	−0.0584613
$946$	−8.11779	−0.263932
$947$	−23.3277	−0.758048	−0.379024	−	0.925387i	$-0.623740\pi$
$947$	−23.3277	−0.758048	−0.379024	+	0.925387i	$0.623740\pi$
$948$	−8.31509	−0.270061
$949$	0.683150	0.0221760
$950$	59.9777	1.94593
$951$	−9.92420	−0.321814
$952$	−45.9817	−1.49027
$953$	53.4787	1.73234	0.866172	−	0.499745i	$-0.166573\pi$
$953$	53.4787	1.73234	0.866172	+	0.499745i	$0.166573\pi$
$954$	−98.4739	−3.18821
$955$	4.84575	0.156805
$956$	−92.5019	−2.99172
$957$	−0.352630	−0.0113989
$958$	−1.70680	−0.0551442
$959$	64.7747	2.09169
$960$	−0.561739	−0.0181300
$961$	−30.5153	−0.984365
$962$	65.9746	2.12711
$963$	−2.26797	−0.0730843
$964$	−10.1628	−0.327321
$965$	−0.205817	−0.00662548
$966$	−0.538500	−0.0173260
$967$	47.1733	1.51699	0.758495	−	0.651679i	$-0.225935\pi$
$967$	47.1733	1.51699	0.758495	+	0.651679i	$0.225935\pi$
$968$	52.1931	1.67755
$969$	−6.45337	−0.207312
$970$	7.51380	0.241253
$971$	−25.7148	−0.825229	−0.412614	−	0.910906i	$-0.635384\pi$
$971$	−25.7148	−0.825229	−0.412614	+	0.910906i	$0.635384\pi$
$972$	−48.8803	−1.56784
$973$	44.6427	1.43118
$974$	−14.0637	−0.450630
$975$	−7.58966	−0.243063
$976$	65.6539	2.10153
$977$	29.5825	0.946428	0.473214	−	0.880947i	$-0.343094\pi$
$977$	29.5825	0.946428	0.473214	+	0.880947i	$0.343094\pi$
$978$	−9.80759	−0.313612
$979$	−1.03939	−0.0332191
$980$	−2.18421	−0.0697719
$981$	7.90359	0.252342
$982$	−81.0594	−2.58671
$983$	−12.3288	−0.393226	−0.196613	−	0.980481i	$-0.562994\pi$
$983$	−12.3288	−0.393226	−0.196613	+	0.980481i	$0.562994\pi$
$984$	1.91905	0.0611769
$985$	1.69861	0.0541223
$986$	4.26997	0.135984
$987$	12.9239	0.411372
$988$	−64.7158	−2.05888
$989$	0.406256	0.0129182
$990$	1.69584	0.0538974
$991$	−14.5248	−0.461395	−0.230698	−	0.973026i	$-0.574101\pi$
$991$	−14.5248	−0.461395	−0.230698	+	0.973026i	$0.574101\pi$
$992$	1.31327	0.0416963
$993$	−0.409402	−0.0129920
$994$	6.78924	0.215342
$995$	0.911641	0.0289010
$996$	−7.22257	−0.228856
$997$	19.8727	0.629373	0.314687	−	0.949196i	$-0.398101\pi$
$997$	19.8727	0.629373	0.314687	+	0.949196i	$0.398101\pi$
$998$	28.8446	0.913059
$999$	23.1866	0.733590

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.a.1.10	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.a.1.10	✓	100	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:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48625 q^{2} -0.481659 q^{3} +4.18145 q^{4} -0.210015 q^{5} +1.19752 q^{6} +3.08014 q^{7} -5.42364 q^{8} -2.76800 q^{9} +O(q^{10})\)	\(q-2.48625 q^{2} -0.481659 q^{3} +4.18145 q^{4} -0.210015 q^{5} +1.19752 q^{6} +3.08014 q^{7} -5.42364 q^{8} -2.76800 q^{9} +0.522149 q^{10} -1.17334 q^{11} -2.01403 q^{12} -3.17951 q^{13} -7.65800 q^{14} +0.101155 q^{15} +5.12162 q^{16} +2.75248 q^{17} +6.88196 q^{18} +4.86769 q^{19} -0.878165 q^{20} -1.48357 q^{21} +2.91722 q^{22} -0.145993 q^{23} +2.61234 q^{24} -4.95589 q^{25} +7.90507 q^{26} +2.77821 q^{27} +12.8794 q^{28} -0.623959 q^{29} -0.251498 q^{30} -0.696183 q^{31} -1.88638 q^{32} +0.565150 q^{33} -6.84336 q^{34} -0.646873 q^{35} -11.5743 q^{36} +8.34586 q^{37} -12.1023 q^{38} +1.53144 q^{39} +1.13904 q^{40} +0.734608 q^{41} +3.68854 q^{42} -2.78271 q^{43} -4.90627 q^{44} +0.581321 q^{45} +0.362975 q^{46} -8.71132 q^{47} -2.46688 q^{48} +2.48724 q^{49} +12.3216 q^{50} -1.32576 q^{51} -13.2950 q^{52} -14.3090 q^{53} -6.90733 q^{54} +0.246419 q^{55} -16.7055 q^{56} -2.34456 q^{57} +1.55132 q^{58} -8.14207 q^{59} +0.422976 q^{60} +12.8190 q^{61} +1.73089 q^{62} -8.52583 q^{63} -5.55323 q^{64} +0.667744 q^{65} -1.40511 q^{66} -3.35076 q^{67} +11.5094 q^{68} +0.0703187 q^{69} +1.60829 q^{70} -0.886556 q^{71} +15.0126 q^{72} -0.214860 q^{73} -20.7499 q^{74} +2.38705 q^{75} +20.3540 q^{76} -3.61405 q^{77} -3.80755 q^{78} +4.12858 q^{79} -1.07562 q^{80} +6.96587 q^{81} -1.82642 q^{82} +3.58613 q^{83} -6.20349 q^{84} -0.578061 q^{85} +6.91853 q^{86} +0.300535 q^{87} +6.36377 q^{88} +0.885839 q^{89} -1.44531 q^{90} -9.79333 q^{91} -0.610462 q^{92} +0.335323 q^{93} +21.6585 q^{94} -1.02228 q^{95} +0.908592 q^{96} +14.3901 q^{97} -6.18390 q^{98} +3.24781 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9 - 18 * q^10 - 47 * q^11 - 27 * q^12 - 29 * q^13 - 51 * q^14 - 36 * q^15 + 71 * q^16 - 99 * q^17 - 27 * q^18 - 45 * q^19 - 75 * q^20 - 79 * q^21 - 2 * q^22 - 25 * q^23 - 66 * q^24 + 67 * q^25 - 73 * q^26 - 42 * q^27 - 31 * q^28 - 78 * q^29 - 29 * q^30 - 41 * q^31 - 95 * q^32 - 83 * q^33 - 44 * q^34 - 45 * q^35 + 23 * q^36 - 16 * q^37 - 29 * q^38 - 42 * q^39 - 37 * q^40 - 235 * q^41 + 16 * q^42 - 6 * q^43 - 122 * q^44 - 79 * q^45 - 17 * q^46 - 67 * q^47 - 25 * q^48 + 30 * q^49 - 68 * q^50 - 18 * q^51 - 41 * q^52 - 69 * q^53 - 63 * q^54 - 32 * q^55 - 120 * q^56 - 63 * q^57 - 7 * q^58 - 118 * q^59 - 49 * q^60 - 60 * q^61 - 23 * q^62 - 43 * q^63 + 43 * q^64 - 181 * q^65 - 4 * q^66 - 18 * q^67 - 130 * q^68 - 80 * q^69 + 12 * q^70 - 77 * q^71 - 40 * q^72 - 64 * q^73 - 48 * q^74 - 18 * q^75 - 134 * q^76 - 87 * q^77 + 65 * q^78 - 48 * q^79 - 95 * q^80 - 20 * q^81 + 45 * q^82 - 108 * q^83 - 97 * q^84 - 21 * q^85 - 73 * q^86 - 3 * q^87 + 23 * q^88 - 325 * q^89 + 6 * q^90 - 17 * q^91 - 19 * q^92 + 2 * q^93 - 5 * q^94 - 54 * q^95 - 105 * q^96 - 81 * q^97 - 61 * q^98 - 76 * q^99

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