LMFDB - Embedded newform 4001.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4001,2,Mod(1,4001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4001, 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("4001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4001.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:	$31.9481458487$
Analytic rank:	$0$
Dimension:	$184$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77961 q^{2} -0.970175 q^{3} +5.72623 q^{4} +0.973772 q^{5} +2.69671 q^{6} +0.392591 q^{7} -10.3575 q^{8} -2.05876 q^{9} +O(q^{10})$	\(q-2.77961 q^{2} -0.970175 q^{3} +5.72623 q^{4} +0.973772 q^{5} +2.69671 q^{6} +0.392591 q^{7} -10.3575 q^{8} -2.05876 q^{9} -2.70671 q^{10} -4.34690 q^{11} -5.55544 q^{12} +2.35614 q^{13} -1.09125 q^{14} -0.944729 q^{15} +17.3373 q^{16} +6.89369 q^{17} +5.72255 q^{18} +6.69926 q^{19} +5.57604 q^{20} -0.380881 q^{21} +12.0827 q^{22} -2.69910 q^{23} +10.0486 q^{24} -4.05177 q^{25} -6.54914 q^{26} +4.90788 q^{27} +2.24806 q^{28} +0.233462 q^{29} +2.62598 q^{30} +9.20330 q^{31} -27.4759 q^{32} +4.21725 q^{33} -19.1618 q^{34} +0.382294 q^{35} -11.7889 q^{36} -6.23130 q^{37} -18.6213 q^{38} -2.28586 q^{39} -10.0858 q^{40} +11.9724 q^{41} +1.05870 q^{42} +5.31449 q^{43} -24.8913 q^{44} -2.00476 q^{45} +7.50244 q^{46} -5.36754 q^{47} -16.8202 q^{48} -6.84587 q^{49} +11.2623 q^{50} -6.68808 q^{51} +13.4918 q^{52} -5.62281 q^{53} -13.6420 q^{54} -4.23289 q^{55} -4.06624 q^{56} -6.49946 q^{57} -0.648933 q^{58} -7.14186 q^{59} -5.40974 q^{60} +9.12946 q^{61} -25.5816 q^{62} -0.808250 q^{63} +41.6977 q^{64} +2.29434 q^{65} -11.7223 q^{66} -2.47276 q^{67} +39.4749 q^{68} +2.61860 q^{69} -1.06263 q^{70} -7.84018 q^{71} +21.3236 q^{72} -12.2002 q^{73} +17.3206 q^{74} +3.93092 q^{75} +38.3615 q^{76} -1.70655 q^{77} +6.35381 q^{78} -9.57153 q^{79} +16.8825 q^{80} +1.41478 q^{81} -33.2787 q^{82} +13.8667 q^{83} -2.18101 q^{84} +6.71288 q^{85} -14.7722 q^{86} -0.226499 q^{87} +45.0229 q^{88} -9.52619 q^{89} +5.57246 q^{90} +0.924997 q^{91} -15.4557 q^{92} -8.92880 q^{93} +14.9197 q^{94} +6.52355 q^{95} +26.6564 q^{96} +15.4817 q^{97} +19.0289 q^{98} +8.94923 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) $ 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18} + 86 q^{19} + 26 q^{20} + 22 q^{21} + 54 q^{22} + 55 q^{23} + 72 q^{24} + 241 q^{25} + 32 q^{26} + 97 q^{27} + 75 q^{28} + 27 q^{29} - 10 q^{30} + 276 q^{31} + 20 q^{33} + 122 q^{34} + 30 q^{35} + 278 q^{36} + 42 q^{37} + 14 q^{38} + 113 q^{39} + 115 q^{40} + 39 q^{41} + 15 q^{42} + 65 q^{43} + 32 q^{44} + 54 q^{45} + 65 q^{46} + 82 q^{47} + 117 q^{48} + 297 q^{49} + 4 q^{50} + 45 q^{51} + 136 q^{52} + 21 q^{53} + 93 q^{54} + 252 q^{55} + 74 q^{56} + 14 q^{57} + 54 q^{58} + 95 q^{59} + 58 q^{60} + 131 q^{61} + 14 q^{62} + 88 q^{63} + 368 q^{64} - 9 q^{65} + 52 q^{66} + 90 q^{67} + 27 q^{68} + 101 q^{69} + 18 q^{70} + 117 q^{71} - 15 q^{72} + 72 q^{73} + 7 q^{74} + 150 q^{75} + 148 q^{76} + 7 q^{77} + 22 q^{78} + 287 q^{79} + 43 q^{80} + 244 q^{81} + 86 q^{82} + 25 q^{83} + 14 q^{84} + 41 q^{85} + 25 q^{86} + 82 q^{87} + 115 q^{88} + 48 q^{89} + 78 q^{90} + 272 q^{91} + 69 q^{92} + 44 q^{93} + 161 q^{94} + 37 q^{95} + 129 q^{96} + 106 q^{97} - 46 q^{98} + 53 q^{99}+O(q^{100}) \) 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9 + 46 * q^10 + 25 * q^11 + 61 * q^12 + 52 * q^13 + 28 * q^14 + 59 * q^15 + 279 * q^16 + 16 * q^17 - 2 * q^18 + 86 * q^19 + 26 * q^20 + 22 * q^21 + 54 * q^22 + 55 * q^23 + 72 * q^24 + 241 * q^25 + 32 * q^26 + 97 * q^27 + 75 * q^28 + 27 * q^29 - 10 * q^30 + 276 * q^31 + 20 * q^33 + 122 * q^34 + 30 * q^35 + 278 * q^36 + 42 * q^37 + 14 * q^38 + 113 * q^39 + 115 * q^40 + 39 * q^41 + 15 * q^42 + 65 * q^43 + 32 * q^44 + 54 * q^45 + 65 * q^46 + 82 * q^47 + 117 * q^48 + 297 * q^49 + 4 * q^50 + 45 * q^51 + 136 * q^52 + 21 * q^53 + 93 * q^54 + 252 * q^55 + 74 * q^56 + 14 * q^57 + 54 * q^58 + 95 * q^59 + 58 * q^60 + 131 * q^61 + 14 * q^62 + 88 * q^63 + 368 * q^64 - 9 * q^65 + 52 * q^66 + 90 * q^67 + 27 * q^68 + 101 * q^69 + 18 * q^70 + 117 * q^71 - 15 * q^72 + 72 * q^73 + 7 * q^74 + 150 * q^75 + 148 * q^76 + 7 * q^77 + 22 * q^78 + 287 * q^79 + 43 * q^80 + 244 * q^81 + 86 * q^82 + 25 * q^83 + 14 * q^84 + 41 * q^85 + 25 * q^86 + 82 * q^87 + 115 * q^88 + 48 * q^89 + 78 * q^90 + 272 * q^91 + 69 * q^92 + 44 * q^93 + 161 * q^94 + 37 * q^95 + 129 * q^96 + 106 * q^97 - 46 * q^98 + 53 * 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 $

$2$	−2.77961	−1.96548	−0.982741	−	0.184989i	$-0.940775\pi$
$2$	−2.77961	−1.96548	−0.982741	+	0.184989i	$0.940775\pi$
$3$	−0.970175	−0.560131	−0.280065	−	0.959981i	$-0.590356\pi$
$3$	−0.970175	−0.560131	−0.280065	+	0.959981i	$0.590356\pi$
$4$	5.72623	2.86312
$5$	0.973772	0.435484	0.217742	−	0.976006i	$-0.430131\pi$
$5$	0.973772	0.435484	0.217742	+	0.976006i	$0.430131\pi$
$6$	2.69671	1.10093
$7$	0.392591	0.148385	0.0741926	−	0.997244i	$-0.476362\pi$
$7$	0.392591	0.148385	0.0741926	+	0.997244i	$0.476362\pi$
$8$	−10.3575	−3.66192
$9$	−2.05876	−0.686254
$10$	−2.70671	−0.855936
$11$	−4.34690	−1.31064	−0.655320	−	0.755352i	$-0.727466\pi$
$11$	−4.34690	−1.31064	−0.655320	+	0.755352i	$0.727466\pi$
$12$	−5.55544	−1.60372
$13$	2.35614	0.653475	0.326737	−	0.945115i	$-0.394051\pi$
$13$	2.35614	0.653475	0.326737	+	0.945115i	$0.394051\pi$
$14$	−1.09125	−0.291648
$15$	−0.944729	−0.243928
$16$	17.3373	4.33432
$17$	6.89369	1.67196	0.835982	−	0.548756i	$-0.184898\pi$
$17$	6.89369	1.67196	0.835982	+	0.548756i	$0.184898\pi$
$18$	5.72255	1.34882
$19$	6.69926	1.53692	0.768458	−	0.639900i	$-0.221024\pi$
$19$	6.69926	1.53692	0.768458	+	0.639900i	$0.221024\pi$
$20$	5.57604	1.24684
$21$	−0.380881	−0.0831151
$22$	12.0827	2.57604
$23$	−2.69910	−0.562801	−0.281400	−	0.959590i	$-0.590799\pi$
$23$	−2.69910	−0.562801	−0.281400	+	0.959590i	$0.590799\pi$
$24$	10.0486	2.05115
$25$	−4.05177	−0.810354
$26$	−6.54914	−1.28439
$27$	4.90788	0.944522
$28$	2.24806	0.424844
$29$	0.233462	0.0433528	0.0216764	−	0.999765i	$-0.493100\pi$
$29$	0.233462	0.0433528	0.0216764	+	0.999765i	$0.493100\pi$
$30$	2.62598	0.479436
$31$	9.20330	1.65296	0.826480	−	0.562966i	$-0.190340\pi$
$31$	9.20330	1.65296	0.826480	+	0.562966i	$0.190340\pi$
$32$	−27.4759	−4.85710
$33$	4.21725	0.734129
$34$	−19.1618	−3.28622
$35$	0.382294	0.0646194
$36$	−11.7889	−1.96482
$37$	−6.23130	−1.02442	−0.512210	−	0.858860i	$-0.671173\pi$
$37$	−6.23130	−1.02442	−0.512210	+	0.858860i	$0.671173\pi$
$38$	−18.6213	−3.02078
$39$	−2.28586	−0.366031
$40$	−10.0858	−1.59471
$41$	11.9724	1.86978	0.934890	−	0.354937i	$-0.115498\pi$
$41$	11.9724	1.86978	0.934890	+	0.354937i	$0.115498\pi$
$42$	1.05870	0.163361
$43$	5.31449	0.810452	0.405226	−	0.914217i	$-0.367193\pi$
$43$	5.31449	0.810452	0.405226	+	0.914217i	$0.367193\pi$
$44$	−24.8913	−3.75251
$45$	−2.00476	−0.298852
$46$	7.50244	1.10617
$47$	−5.36754	−0.782937	−0.391468	−	0.920192i	$-0.628033\pi$
$47$	−5.36754	−0.782937	−0.391468	+	0.920192i	$0.628033\pi$
$48$	−16.8202	−2.42778
$49$	−6.84587	−0.977982
$50$	11.2623	1.59273
$51$	−6.68808	−0.936519
$52$	13.4918	1.87097
$53$	−5.62281	−0.772352	−0.386176	−	0.922425i	$-0.626204\pi$
$53$	−5.62281	−0.772352	−0.386176	+	0.922425i	$0.626204\pi$
$54$	−13.6420	−1.85644
$55$	−4.23289	−0.570762
$56$	−4.06624	−0.543375
$57$	−6.49946	−0.860874
$58$	−0.648933	−0.0852091
$59$	−7.14186	−0.929791	−0.464896	−	0.885366i	$-0.653908\pi$
$59$	−7.14186	−0.929791	−0.464896	+	0.885366i	$0.653908\pi$
$60$	−5.40974	−0.698394
$61$	9.12946	1.16891	0.584454	−	0.811427i	$-0.301309\pi$
$61$	9.12946	1.16891	0.584454	+	0.811427i	$0.301309\pi$
$62$	−25.5816	−3.24886
$63$	−0.808250	−0.101830
$64$	41.6977	5.21222
$65$	2.29434	0.284578
$66$	−11.7223	−1.44292
$67$	−2.47276	−0.302096	−0.151048	−	0.988526i	$-0.548265\pi$
$67$	−2.47276	−0.302096	−0.151048	+	0.988526i	$0.548265\pi$
$68$	39.4749	4.78703
$69$	2.61860	0.315242
$70$	−1.06263	−0.127008
$71$	−7.84018	−0.930458	−0.465229	−	0.885190i	$-0.654028\pi$
$71$	−7.84018	−0.930458	−0.465229	+	0.885190i	$0.654028\pi$
$72$	21.3236	2.51301
$73$	−12.2002	−1.42792	−0.713962	−	0.700185i	$-0.753101\pi$
$73$	−12.2002	−1.42792	−0.713962	+	0.700185i	$0.753101\pi$
$74$	17.3206	2.01348
$75$	3.93092	0.453904
$76$	38.3615	4.40037
$77$	−1.70655	−0.194480
$78$	6.35381	0.719427
$79$	−9.57153	−1.07688	−0.538441	−	0.842663i	$-0.680986\pi$
$79$	−9.57153	−1.07688	−0.538441	+	0.842663i	$0.680986\pi$
$80$	16.8825	1.88753
$81$	1.41478	0.157198
$82$	−33.2787	−3.67502
$83$	13.8667	1.52207	0.761037	−	0.648709i	$-0.224691\pi$
$83$	13.8667	1.52207	0.761037	+	0.648709i	$0.224691\pi$
$84$	−2.18101	−0.237968
$85$	6.71288	0.728114
$86$	−14.7722	−1.59293
$87$	−0.226499	−0.0242832
$88$	45.0229	4.79945
$89$	−9.52619	−1.00977	−0.504887	−	0.863185i	$-0.668466\pi$
$89$	−9.52619	−1.00977	−0.504887	+	0.863185i	$0.668466\pi$
$90$	5.57246	0.587389
$91$	0.924997	0.0969660
$92$	−15.4557	−1.61136
$93$	−8.92880	−0.925874
$94$	14.9197	1.53885
$95$	6.52355	0.669302
$96$	26.6564	2.72061
$97$	15.4817	1.57193	0.785964	−	0.618273i	$-0.212167\pi$
$97$	15.4817	1.57193	0.785964	+	0.618273i	$0.212167\pi$
$98$	19.0289	1.92220
$99$	8.94923	0.899431
$100$	−23.2014	−2.32014
$101$	2.44716	0.243502	0.121751	−	0.992561i	$-0.461149\pi$
$101$	2.44716	0.243502	0.121751	+	0.992561i	$0.461149\pi$
$102$	18.5903	1.84071
$103$	17.2924	1.70387	0.851934	−	0.523650i	$-0.175430\pi$
$103$	17.2924	1.70387	0.851934	+	0.523650i	$0.175430\pi$
$104$	−24.4036	−2.39297
$105$	−0.370892	−0.0361953
$106$	15.6292	1.51804
$107$	6.25436	0.604632	0.302316	−	0.953208i	$-0.402240\pi$
$107$	6.25436	0.604632	0.302316	+	0.953208i	$0.402240\pi$
$108$	28.1037	2.70428
$109$	−1.22278	−0.117122	−0.0585608	−	0.998284i	$-0.518651\pi$
$109$	−1.22278	−0.117122	−0.0585608	+	0.998284i	$0.518651\pi$
$110$	11.7658	1.12182
$111$	6.04545	0.573809
$112$	6.80645	0.643149
$113$	−2.78485	−0.261977	−0.130988	−	0.991384i	$-0.541815\pi$
$113$	−2.78485	−0.261977	−0.130988	+	0.991384i	$0.541815\pi$
$114$	18.0660	1.69203
$115$	−2.62830	−0.245091
$116$	1.33686	0.124124
$117$	−4.85072	−0.448450
$118$	19.8516	1.82749
$119$	2.70640	0.248095
$120$	9.78500	0.893244
$121$	7.89552	0.717775
$122$	−25.3764	−2.29747
$123$	−11.6154	−1.04732
$124$	52.7002	4.73262
$125$	−8.81436	−0.788380
$126$	2.24662	0.200145
$127$	−7.66055	−0.679764	−0.339882	−	0.940468i	$-0.610387\pi$
$127$	−7.66055	−0.679764	−0.339882	+	0.940468i	$0.610387\pi$
$128$	−60.9517	−5.38742
$129$	−5.15598	−0.453959
$130$	−6.37737	−0.559332
$131$	4.42940	0.386998	0.193499	−	0.981100i	$-0.438016\pi$
$131$	4.42940	0.386998	0.193499	+	0.981100i	$0.438016\pi$
$132$	24.1490	2.10190
$133$	2.63007	0.228056
$134$	6.87331	0.593763
$135$	4.77916	0.411324
$136$	−71.4012	−6.12260
$137$	−21.1506	−1.80701	−0.903507	−	0.428573i	$-0.859016\pi$
$137$	−21.1506	−1.80701	−0.903507	+	0.428573i	$0.859016\pi$
$138$	−7.27867	−0.619602
$139$	10.6865	0.906416	0.453208	−	0.891405i	$-0.350279\pi$
$139$	10.6865	0.906416	0.453208	+	0.891405i	$0.350279\pi$
$140$	2.18910	0.185013
$141$	5.20746	0.438547
$142$	21.7926	1.82880
$143$	−10.2419	−0.856470
$144$	−35.6933	−2.97444
$145$	0.227339	0.0188795
$146$	33.9118	2.80656
$147$	6.64169	0.547798
$148$	−35.6819	−2.93303
$149$	12.4241	1.01782	0.508911	−	0.860819i	$-0.330048\pi$
$149$	12.4241	1.01782	0.508911	+	0.860819i	$0.330048\pi$
$150$	−10.9264	−0.892140
$151$	−0.852439	−0.0693705	−0.0346853	−	0.999398i	$-0.511043\pi$
$151$	−0.852439	−0.0693705	−0.0346853	+	0.999398i	$0.511043\pi$
$152$	−69.3874	−5.62806
$153$	−14.1925	−1.14739
$154$	4.74355	0.382246
$155$	8.96191	0.719838
$156$	−13.0894	−1.04799
$157$	−1.03294	−0.0824377	−0.0412188	−	0.999150i	$-0.513124\pi$
$157$	−1.03294	−0.0824377	−0.0412188	+	0.999150i	$0.513124\pi$
$158$	26.6051	2.11659
$159$	5.45511	0.432618
$160$	−26.7553	−2.11519
$161$	−1.05964	−0.0835113
$162$	−3.93254	−0.308969
$163$	2.54589	0.199410	0.0997048	−	0.995017i	$-0.468210\pi$
$163$	2.54589	0.199410	0.0997048	+	0.995017i	$0.468210\pi$
$164$	68.5569	5.35340
$165$	4.10664	0.319701
$166$	−38.5441	−2.99161
$167$	−5.05576	−0.391227	−0.195613	−	0.980681i	$-0.562670\pi$
$167$	−5.05576	−0.391227	−0.195613	+	0.980681i	$0.562670\pi$
$168$	3.94497	0.304361
$169$	−7.44862	−0.572971
$170$	−18.6592	−1.43109
$171$	−13.7922	−1.05471
$172$	30.4320	2.32042
$173$	−10.2984	−0.782974	−0.391487	−	0.920184i	$-0.628039\pi$
$173$	−10.2984	−0.782974	−0.391487	+	0.920184i	$0.628039\pi$
$174$	0.629579	0.0477282
$175$	−1.59069	−0.120245
$176$	−75.3633	−5.68072
$177$	6.92885	0.520804
$178$	26.4791	1.98469
$179$	4.01654	0.300210	0.150105	−	0.988670i	$-0.452039\pi$
$179$	4.01654	0.300210	0.150105	+	0.988670i	$0.452039\pi$
$180$	−11.4797	−0.855649
$181$	−8.51582	−0.632976	−0.316488	−	0.948597i	$-0.602504\pi$
$181$	−8.51582	−0.632976	−0.316488	+	0.948597i	$0.602504\pi$
$182$	−2.57113	−0.190585
$183$	−8.85718	−0.654741
$184$	27.9558	2.06093
$185$	−6.06786	−0.446118
$186$	24.8186	1.81979
$187$	−29.9662	−2.19134
$188$	−30.7358	−2.24164
$189$	1.92679	0.140153
$190$	−18.1329	−1.31550
$191$	25.2990	1.83057	0.915286	−	0.402805i	$-0.131965\pi$
$191$	25.2990	1.83057	0.915286	+	0.402805i	$0.131965\pi$
$192$	−40.4541	−2.91952
$193$	0.181638	0.0130746	0.00653728	−	0.999979i	$-0.497919\pi$
$193$	0.181638	0.0130746	0.00653728	+	0.999979i	$0.497919\pi$
$194$	−43.0331	−3.08959
$195$	−2.22591	−0.159401
$196$	−39.2011	−2.80008
$197$	13.2097	0.941149	0.470575	−	0.882360i	$-0.344047\pi$
$197$	13.2097	0.941149	0.470575	+	0.882360i	$0.344047\pi$
$198$	−24.8754	−1.76781
$199$	10.3487	0.733597	0.366798	−	0.930300i	$-0.380454\pi$
$199$	10.3487	0.733597	0.366798	+	0.930300i	$0.380454\pi$
$200$	41.9661	2.96745
$201$	2.39901	0.169213
$202$	−6.80216	−0.478598
$203$	0.0916550	0.00643292
$204$	−38.2975	−2.68136
$205$	11.6584	0.814259
$206$	−48.0660	−3.34892
$207$	5.55680	0.386224
$208$	40.8490	2.83237
$209$	−29.1210	−2.01434
$210$	1.03093	0.0711412
$211$	7.27640	0.500928	0.250464	−	0.968126i	$-0.419417\pi$
$211$	7.27640	0.500928	0.250464	+	0.968126i	$0.419417\pi$
$212$	−32.1975	−2.21133
$213$	7.60634	0.521178
$214$	−17.3847	−1.18839
$215$	5.17510	0.352939
$216$	−50.8332	−3.45876
$217$	3.61313	0.245275
$218$	3.39886	0.230200
$219$	11.8363	0.799824
$220$	−24.2385	−1.63416
$221$	16.2425	1.09259
$222$	−16.8040	−1.12781
$223$	−10.3405	−0.692450	−0.346225	−	0.938151i	$-0.612537\pi$
$223$	−10.3405	−0.692450	−0.346225	+	0.938151i	$0.612537\pi$
$224$	−10.7868	−0.720722
$225$	8.34162	0.556108
$226$	7.74079	0.514910
$227$	−23.6579	−1.57023	−0.785115	−	0.619349i	$-0.787396\pi$
$227$	−23.6579	−1.57023	−0.785115	+	0.619349i	$0.787396\pi$
$228$	−37.2174	−2.46478
$229$	1.31477	0.0868827	0.0434414	−	0.999056i	$-0.486168\pi$
$229$	1.31477	0.0868827	0.0434414	+	0.999056i	$0.486168\pi$
$230$	7.30566	0.481721
$231$	1.65565	0.108934
$232$	−2.41808	−0.158754
$233$	−10.2122	−0.669026	−0.334513	−	0.942391i	$-0.608572\pi$
$233$	−10.2122	−0.669026	−0.334513	+	0.942391i	$0.608572\pi$
$234$	13.4831	0.881419
$235$	−5.22676	−0.340956
$236$	−40.8960	−2.66210
$237$	9.28606	0.603194
$238$	−7.52273	−0.487626
$239$	28.3329	1.83270	0.916351	−	0.400376i	$-0.131121\pi$
$239$	28.3329	1.83270	0.916351	+	0.400376i	$0.131121\pi$
$240$	−16.3790	−1.05726
$241$	13.5986	0.875961	0.437980	−	0.898985i	$-0.355694\pi$
$241$	13.5986	0.875961	0.437980	+	0.898985i	$0.355694\pi$
$242$	−21.9465	−1.41077
$243$	−16.0962	−1.03257
$244$	52.2774	3.34672
$245$	−6.66632	−0.425895
$246$	32.2861	2.05849
$247$	15.7844	1.00434
$248$	−95.3229	−6.05301
$249$	−13.4532	−0.852560
$250$	24.5005	1.54955
$251$	2.90600	0.183425	0.0917124	−	0.995786i	$-0.470766\pi$
$251$	2.90600	0.183425	0.0917124	+	0.995786i	$0.470766\pi$
$252$	−4.62823	−0.291551
$253$	11.7327	0.737629
$254$	21.2933	1.33606
$255$	−6.51267	−0.407839
$256$	86.0264	5.37665
$257$	26.4072	1.64724	0.823618	−	0.567146i	$-0.191952\pi$
$257$	26.4072	1.64724	0.823618	+	0.567146i	$0.191952\pi$
$258$	14.3316	0.892247
$259$	−2.44635	−0.152009
$260$	13.1379	0.814779
$261$	−0.480643	−0.0297510
$262$	−12.3120	−0.760638
$263$	3.26317	0.201215	0.100608	−	0.994926i	$-0.467921\pi$
$263$	3.26317	0.201215	0.100608	+	0.994926i	$0.467921\pi$
$264$	−43.6800	−2.68832
$265$	−5.47533	−0.336347
$266$	−7.31056	−0.448239
$267$	9.24207	0.565605
$268$	−14.1596	−0.864935
$269$	27.2067	1.65882	0.829410	−	0.558640i	$-0.188677\pi$
$269$	27.2067	1.65882	0.829410	+	0.558640i	$0.188677\pi$
$270$	−13.2842	−0.808450
$271$	32.4618	1.97191	0.985956	−	0.167005i	$-0.0534095\pi$
$271$	32.4618	1.97191	0.985956	+	0.167005i	$0.0534095\pi$
$272$	119.518	7.24683
$273$	−0.897409	−0.0543136
$274$	58.7903	3.55165
$275$	17.6126	1.06208
$276$	14.9947	0.902574
$277$	−30.1935	−1.81415	−0.907076	−	0.420967i	$-0.861691\pi$
$277$	−30.1935	−1.81415	−0.907076	+	0.420967i	$0.861691\pi$
$278$	−29.7043	−1.78154
$279$	−18.9474	−1.13435
$280$	−3.95959	−0.236631
$281$	6.96537	0.415519	0.207760	−	0.978180i	$-0.433383\pi$
$281$	6.96537	0.415519	0.207760	+	0.978180i	$0.433383\pi$
$282$	−14.4747	−0.861956
$283$	10.3628	0.616005	0.308002	−	0.951386i	$-0.400340\pi$
$283$	10.3628	0.616005	0.308002	+	0.951386i	$0.400340\pi$
$284$	−44.8947	−2.66401
$285$	−6.32899	−0.374897
$286$	28.4685	1.68337
$287$	4.70026	0.277448
$288$	56.5663	3.33320
$289$	30.5229	1.79547
$290$	−0.631913	−0.0371072
$291$	−15.0199	−0.880485
$292$	−69.8611	−4.08831
$293$	15.7984	0.922951	0.461476	−	0.887153i	$-0.347320\pi$
$293$	15.7984	0.922951	0.461476	+	0.887153i	$0.347320\pi$
$294$	−18.4613	−1.07669
$295$	−6.95454	−0.404909
$296$	64.5405	3.75134
$297$	−21.3341	−1.23793
$298$	−34.5342	−2.00051
$299$	−6.35944	−0.367776
$300$	22.5094	1.29958
$301$	2.08642	0.120259
$302$	2.36945	0.136346
$303$	−2.37418	−0.136393
$304$	116.147	6.66148
$305$	8.89002	0.509041
$306$	39.4495	2.25518
$307$	−26.7690	−1.52779	−0.763893	−	0.645343i	$-0.776715\pi$
$307$	−26.7690	−1.52779	−0.763893	+	0.645343i	$0.776715\pi$
$308$	−9.77211	−0.556817
$309$	−16.7766	−0.954388
$310$	−24.9106	−1.41483
$311$	−4.80028	−0.272199	−0.136099	−	0.990695i	$-0.543457\pi$
$311$	−4.80028	−0.272199	−0.136099	+	0.990695i	$0.543457\pi$
$312$	23.6758	1.34038
$313$	−12.3026	−0.695382	−0.347691	−	0.937609i	$-0.613034\pi$
$313$	−12.3026	−0.695382	−0.347691	+	0.937609i	$0.613034\pi$
$314$	2.87117	0.162030
$315$	−0.787051	−0.0443453
$316$	−54.8088	−3.08324
$317$	26.2909	1.47664	0.738321	−	0.674450i	$-0.235619\pi$
$317$	26.2909	1.47664	0.738321	+	0.674450i	$0.235619\pi$
$318$	−15.1631	−0.850303
$319$	−1.01484	−0.0568199
$320$	40.6041	2.26984
$321$	−6.06782	−0.338673
$322$	2.94539	0.164140
$323$	46.1826	2.56967
$324$	8.10136	0.450076
$325$	−9.54652	−0.529546
$326$	−7.07659	−0.391936
$327$	1.18631	0.0656034
$328$	−124.004	−6.84698
$329$	−2.10725	−0.116176
$330$	−11.4149	−0.628367
$331$	32.6548	1.79487	0.897435	−	0.441147i	$-0.145428\pi$
$331$	32.6548	1.79487	0.897435	+	0.441147i	$0.145428\pi$
$332$	79.4042	4.35787
$333$	12.8288	0.703012
$334$	14.0530	0.768949
$335$	−2.40790	−0.131558
$336$	−6.60344	−0.360247
$337$	2.86894	0.156281	0.0781407	−	0.996942i	$-0.475102\pi$
$337$	2.86894	0.156281	0.0781407	+	0.996942i	$0.475102\pi$
$338$	20.7043	1.12616
$339$	2.70179	0.146741
$340$	38.4395	2.08467
$341$	−40.0058	−2.16644
$342$	38.3369	2.07302
$343$	−5.43576	−0.293503
$344$	−55.0446	−2.96781
$345$	2.54991	0.137283
$346$	28.6256	1.53892
$347$	−2.06265	−0.110729	−0.0553644	−	0.998466i	$-0.517632\pi$
$347$	−2.06265	−0.110729	−0.0553644	+	0.998466i	$0.517632\pi$
$348$	−1.29699	−0.0695257
$349$	−8.40748	−0.450042	−0.225021	−	0.974354i	$-0.572245\pi$
$349$	−8.40748	−0.450042	−0.225021	+	0.974354i	$0.572245\pi$
$350$	4.42149	0.236338
$351$	11.5636	0.617222
$352$	119.435	6.36590
$353$	4.46462	0.237628	0.118814	−	0.992917i	$-0.462091\pi$
$353$	4.46462	0.237628	0.118814	+	0.992917i	$0.462091\pi$
$354$	−19.2595	−1.02363
$355$	−7.63454	−0.405200
$356$	−54.5492	−2.89110
$357$	−2.62568	−0.138966
$358$	−11.1644	−0.590057
$359$	0.452733	0.0238943	0.0119472	−	0.999929i	$-0.496197\pi$
$359$	0.452733	0.0238943	0.0119472	+	0.999929i	$0.496197\pi$
$360$	20.7643	1.09437
$361$	25.8801	1.36211
$362$	23.6707	1.24410
$363$	−7.66004	−0.402048
$364$	5.29675	0.277625
$365$	−11.8802	−0.621838
$366$	24.6195	1.28688
$367$	17.8679	0.932697	0.466348	−	0.884601i	$-0.345569\pi$
$367$	17.8679	0.932697	0.466348	+	0.884601i	$0.345569\pi$
$368$	−46.7950	−2.43936
$369$	−24.6484	−1.28314
$370$	16.8663	0.876837
$371$	−2.20746	−0.114606
$372$	−51.1284	−2.65088
$373$	−8.93177	−0.462469	−0.231235	−	0.972898i	$-0.574277\pi$
$373$	−8.93177	−0.462469	−0.231235	+	0.972898i	$0.574277\pi$
$374$	83.2942	4.30704
$375$	8.55147	0.441596
$376$	55.5942	2.86705
$377$	0.550069	0.0283300
$378$	−5.35572	−0.275468
$379$	−13.6225	−0.699741	−0.349870	−	0.936798i	$-0.613774\pi$
$379$	−13.6225	−0.699741	−0.349870	+	0.936798i	$0.613774\pi$
$380$	37.3554	1.91629
$381$	7.43207	0.380757
$382$	−70.3214	−3.59795
$383$	−12.3858	−0.632887	−0.316444	−	0.948611i	$-0.602489\pi$
$383$	−12.3858	−0.632887	−0.316444	+	0.948611i	$0.602489\pi$
$384$	59.1338	3.01766
$385$	−1.66179	−0.0846927
$386$	−0.504882	−0.0256978
$387$	−10.9413	−0.556175
$388$	88.6518	4.50061
$389$	−3.63343	−0.184222	−0.0921111	−	0.995749i	$-0.529362\pi$
$389$	−3.63343	−0.184222	−0.0921111	+	0.995749i	$0.529362\pi$
$390$	6.18716	0.313299
$391$	−18.6067	−0.940983
$392$	70.9059	3.58129
$393$	−4.29729	−0.216770
$394$	−36.7177	−1.84981
$395$	−9.32049	−0.468965
$396$	51.2453	2.57518
$397$	13.9378	0.699517	0.349758	−	0.936840i	$-0.386264\pi$
$397$	13.9378	0.699517	0.349758	+	0.936840i	$0.386264\pi$
$398$	−28.7652	−1.44187
$399$	−2.55162	−0.127741
$400$	−70.2466	−3.51233
$401$	4.09635	0.204562	0.102281	−	0.994756i	$-0.467386\pi$
$401$	4.09635	0.204562	0.102281	+	0.994756i	$0.467386\pi$
$402$	−6.66831	−0.332585
$403$	21.6842	1.08017
$404$	14.0130	0.697174
$405$	1.37767	0.0684572
$406$	−0.254765	−0.0126438
$407$	27.0868	1.34264
$408$	69.2716	3.42946
$409$	39.6504	1.96059	0.980294	−	0.197546i	$-0.0632972\pi$
$409$	39.6504	1.96059	0.980294	+	0.197546i	$0.0632972\pi$
$410$	−32.4059	−1.60041
$411$	20.5197	1.01216
$412$	99.0201	4.87837
$413$	−2.80383	−0.137967
$414$	−15.4457	−0.759116
$415$	13.5030	0.662839
$416$	−64.7370	−3.17399
$417$	−10.3678	−0.507711
$418$	80.9451	3.95915
$419$	27.1912	1.32838	0.664190	−	0.747564i	$-0.268777\pi$
$419$	27.1912	1.32838	0.664190	+	0.747564i	$0.268777\pi$
$420$	−2.12381	−0.103631
$421$	6.93651	0.338065	0.169032	−	0.985611i	$-0.445936\pi$
$421$	6.93651	0.338065	0.169032	+	0.985611i	$0.445936\pi$
$422$	−20.2256	−0.984565
$423$	11.0505	0.537293
$424$	58.2381	2.82829
$425$	−27.9316	−1.35488
$426$	−21.1427	−1.02437
$427$	3.58414	0.173449
$428$	35.8139	1.73113
$429$	9.93642	0.479735
$430$	−14.3847	−0.693694
$431$	14.5160	0.699210	0.349605	−	0.936897i	$-0.386316\pi$
$431$	14.5160	0.699210	0.349605	+	0.936897i	$0.386316\pi$
$432$	85.0893	4.09386
$433$	−14.6779	−0.705373	−0.352686	−	0.935742i	$-0.614732\pi$
$433$	−14.6779	−0.705373	−0.352686	+	0.935742i	$0.614732\pi$
$434$	−10.0431	−0.482083
$435$	−0.220558	−0.0105750
$436$	−7.00195	−0.335333
$437$	−18.0820	−0.864978
$438$	−32.9003	−1.57204
$439$	30.1764	1.44024	0.720121	−	0.693849i	$-0.244086\pi$
$439$	30.1764	1.44024	0.720121	+	0.693849i	$0.244086\pi$
$440$	43.8420	2.09009
$441$	14.0940	0.671144
$442$	−45.1477	−2.14746
$443$	26.7445	1.27067	0.635335	−	0.772237i	$-0.280862\pi$
$443$	26.7445	1.27067	0.635335	+	0.772237i	$0.280862\pi$
$444$	34.6176	1.64288
$445$	−9.27633	−0.439740
$446$	28.7425	1.36100
$447$	−12.0536	−0.570113
$448$	16.3701	0.773416
$449$	−17.2811	−0.815546	−0.407773	−	0.913083i	$-0.633695\pi$
$449$	−17.2811	−0.815546	−0.407773	+	0.913083i	$0.633695\pi$
$450$	−23.1865	−1.09302
$451$	−52.0430	−2.45061
$452$	−15.9467	−0.750069
$453$	0.827015	0.0388565
$454$	65.7598	3.08626
$455$	0.900736	0.0422272
$456$	67.3179	3.15245
$457$	−14.4572	−0.676278	−0.338139	−	0.941096i	$-0.609797\pi$
$457$	−14.4572	−0.676278	−0.338139	+	0.941096i	$0.609797\pi$
$458$	−3.65456	−0.170766
$459$	33.8334	1.57921
$460$	−15.0503	−0.701723
$461$	−38.8363	−1.80879	−0.904394	−	0.426698i	$-0.859677\pi$
$461$	−38.8363	−1.80879	−0.904394	+	0.426698i	$0.859677\pi$
$462$	−4.60207	−0.214108
$463$	6.46308	0.300365	0.150182	−	0.988658i	$-0.452014\pi$
$463$	6.46308	0.300365	0.150182	+	0.988658i	$0.452014\pi$
$464$	4.04759	0.187905
$465$	−8.69462	−0.403203
$466$	28.3860	1.31496
$467$	−17.3404	−0.802420	−0.401210	−	0.915986i	$-0.631410\pi$
$467$	−17.3404	−0.802420	−0.401210	+	0.915986i	$0.631410\pi$
$468$	−27.7764	−1.28396
$469$	−0.970782	−0.0448265
$470$	14.5284	0.670143
$471$	1.00213	0.0461759
$472$	73.9716	3.40482
$473$	−23.1015	−1.06221
$474$	−25.8116	−1.18557
$475$	−27.1439	−1.24545
$476$	15.4975	0.710325
$477$	11.5760	0.530029
$478$	−78.7544	−3.60214
$479$	1.84876	0.0844720	0.0422360	−	0.999108i	$-0.486552\pi$
$479$	1.84876	0.0844720	0.0422360	+	0.999108i	$0.486552\pi$
$480$	25.9573	1.18478
$481$	−14.6818	−0.669432
$482$	−37.7987	−1.72168
$483$	1.02804	0.0467772
$484$	45.2116	2.05507
$485$	15.0756	0.684549
$486$	44.7412	2.02950
$487$	−6.00067	−0.271916	−0.135958	−	0.990715i	$-0.543411\pi$
$487$	−6.00067	−0.271916	−0.135958	+	0.990715i	$0.543411\pi$
$488$	−94.5582	−4.28045
$489$	−2.46996	−0.111695
$490$	18.5298	0.837089
$491$	−30.6878	−1.38492	−0.692461	−	0.721456i	$-0.743473\pi$
$491$	−30.6878	−1.38492	−0.692461	+	0.721456i	$0.743473\pi$
$492$	−66.5122	−2.99860
$493$	1.60941	0.0724844
$494$	−43.8744	−1.97400
$495$	8.71450	0.391688
$496$	159.560	7.16446
$497$	−3.07798	−0.138066
$498$	37.3946	1.67569
$499$	−0.291563	−0.0130521	−0.00652607	−	0.999979i	$-0.502077\pi$
$499$	−0.291563	−0.0130521	−0.00652607	+	0.999979i	$0.502077\pi$
$500$	−50.4730	−2.25722
$501$	4.90497	0.219138
$502$	−8.07754	−0.360518
$503$	−9.25364	−0.412599	−0.206300	−	0.978489i	$-0.566142\pi$
$503$	−9.25364	−0.412599	−0.206300	+	0.978489i	$0.566142\pi$
$504$	8.37143	0.372893
$505$	2.38298	0.106041
$506$	−32.6123	−1.44979
$507$	7.22646	0.320938
$508$	−43.8661	−1.94624
$509$	15.4761	0.685966	0.342983	−	0.939342i	$-0.388563\pi$
$509$	15.4761	0.685966	0.342983	+	0.939342i	$0.388563\pi$
$510$	18.1027	0.801600
$511$	−4.78968	−0.211883
$512$	−117.216	−5.18029
$513$	32.8792	1.45165
$514$	−73.4017	−3.23761
$515$	16.8388	0.742007
$516$	−29.5243	−1.29974
$517$	23.3322	1.02615
$518$	6.79990	0.298770
$519$	9.99126	0.438568
$520$	−23.7636	−1.04210
$521$	−6.10225	−0.267344	−0.133672	−	0.991026i	$-0.542677\pi$
$521$	−6.10225	−0.267344	−0.133672	+	0.991026i	$0.542677\pi$
$522$	1.33600	0.0584751
$523$	17.3036	0.756633	0.378317	−	0.925676i	$-0.376503\pi$
$523$	17.3036	0.756633	0.378317	+	0.925676i	$0.376503\pi$
$524$	25.3638	1.10802
$525$	1.54324	0.0673526
$526$	−9.07033	−0.395485
$527$	63.4447	2.76369
$528$	73.1156	3.18195
$529$	−15.7149	−0.683255
$530$	15.2193	0.661084
$531$	14.7034	0.638073
$532$	15.0604	0.652950
$533$	28.2087	1.22185
$534$	−25.6893	−1.11169
$535$	6.09032	0.263308
$536$	25.6115	1.10625
$537$	−3.89674	−0.168157
$538$	−75.6239	−3.26038
$539$	29.7583	1.28178
$540$	27.3666	1.17767
$541$	21.6632	0.931373	0.465687	−	0.884950i	$-0.345807\pi$
$541$	21.6632	0.931373	0.465687	+	0.884950i	$0.345807\pi$
$542$	−90.2311	−3.87576
$543$	8.26183	0.354549
$544$	−189.410	−8.12090
$545$	−1.19071	−0.0510046
$546$	2.49445	0.106752
$547$	14.8153	0.633456	0.316728	−	0.948516i	$-0.397416\pi$
$547$	14.8153	0.633456	0.316728	+	0.948516i	$0.397416\pi$
$548$	−121.113	−5.17369
$549$	−18.7954	−0.802168
$550$	−48.9562	−2.08750
$551$	1.56402	0.0666296
$552$	−27.1220	−1.15439
$553$	−3.75769	−0.159793
$554$	83.9262	3.56568
$555$	5.88689	0.249884
$556$	61.1933	2.59517
$557$	−33.5218	−1.42036	−0.710181	−	0.704019i	$-0.751387\pi$
$557$	−33.5218	−1.42036	−0.710181	+	0.704019i	$0.751387\pi$
$558$	52.6663	2.22954
$559$	12.5217	0.529610
$560$	6.62793	0.280081
$561$	29.0724	1.22744
$562$	−19.3610	−0.816695
$563$	−27.3604	−1.15310	−0.576552	−	0.817061i	$-0.695602\pi$
$563$	−27.3604	−1.15310	−0.576552	+	0.817061i	$0.695602\pi$
$564$	29.8191	1.25561
$565$	−2.71181	−0.114087
$566$	−28.8045	−1.21075
$567$	0.555430	0.0233258
$568$	81.2044	3.40726
$569$	14.8151	0.621081	0.310541	−	0.950560i	$-0.399490\pi$
$569$	14.8151	0.621081	0.310541	+	0.950560i	$0.399490\pi$
$570$	17.5921	0.736853
$571$	0.893242	0.0373810	0.0186905	−	0.999825i	$-0.494050\pi$
$571$	0.893242	0.0373810	0.0186905	+	0.999825i	$0.494050\pi$
$572$	−58.6474	−2.45217
$573$	−24.5445	−1.02536
$574$	−13.0649	−0.545318
$575$	10.9361	0.456068
$576$	−85.8457	−3.57690
$577$	−29.1151	−1.21208	−0.606039	−	0.795435i	$-0.707243\pi$
$577$	−29.1151	−1.21208	−0.606039	+	0.795435i	$0.707243\pi$
$578$	−84.8419	−3.52896
$579$	−0.176220	−0.00732346
$580$	1.30179	0.0540541
$581$	5.44395	0.225853
$582$	41.7496	1.73058
$583$	24.4418	1.01227
$584$	126.363	5.22894
$585$	−4.72350	−0.195293
$586$	−43.9133	−1.81404
$587$	−0.453052	−0.0186995	−0.00934974	−	0.999956i	$-0.502976\pi$
$587$	−0.453052	−0.0186995	−0.00934974	+	0.999956i	$0.502976\pi$
$588$	38.0319	1.56841
$589$	61.6553	2.54046
$590$	19.3309	0.795841
$591$	−12.8157	−0.527166
$592$	−108.034	−4.44016
$593$	36.1971	1.48644	0.743219	−	0.669048i	$-0.233298\pi$
$593$	36.1971	1.48644	0.743219	+	0.669048i	$0.233298\pi$
$594$	59.3004	2.43312
$595$	2.63541	0.108041
$596$	71.1433	2.91414
$597$	−10.0400	−0.410910
$598$	17.6768	0.722857
$599$	41.1469	1.68122	0.840609	−	0.541642i	$-0.182197\pi$
$599$	41.1469	1.68122	0.840609	+	0.541642i	$0.182197\pi$
$600$	−40.7144	−1.66216
$601$	−5.59294	−0.228141	−0.114070	−	0.993473i	$-0.536389\pi$
$601$	−5.59294	−0.228141	−0.114070	+	0.993473i	$0.536389\pi$
$602$	−5.79942	−0.236367
$603$	5.09082	0.207314
$604$	−4.88126	−0.198616
$605$	7.68844	0.312579
$606$	6.59928	0.268078
$607$	22.5401	0.914874	0.457437	−	0.889242i	$-0.348768\pi$
$607$	22.5401	0.914874	0.457437	+	0.889242i	$0.348768\pi$
$608$	−184.068	−7.46495
$609$	−0.0889213	−0.00360327
$610$	−24.7108	−1.00051
$611$	−12.6467	−0.511629
$612$	−81.2693	−3.28512
$613$	1.19664	0.0483320	0.0241660	−	0.999708i	$-0.492307\pi$
$613$	1.19664	0.0483320	0.0241660	+	0.999708i	$0.492307\pi$
$614$	74.4073	3.00283
$615$	−11.3107	−0.456092
$616$	17.6756	0.712168
$617$	−27.6002	−1.11114	−0.555571	−	0.831469i	$-0.687500\pi$
$617$	−27.6002	−1.11114	−0.555571	+	0.831469i	$0.687500\pi$
$618$	46.6324	1.87583
$619$	−16.6919	−0.670905	−0.335453	−	0.942057i	$-0.608889\pi$
$619$	−16.6919	−0.670905	−0.335453	+	0.942057i	$0.608889\pi$
$620$	51.3180	2.06098
$621$	−13.2468	−0.531578
$622$	13.3429	0.535002
$623$	−3.73989	−0.149836
$624$	−39.6306	−1.58650
$625$	11.6757	0.467027
$626$	34.1963	1.36676
$627$	28.2525	1.12830
$628$	−5.91486	−0.236029
$629$	−42.9566	−1.71279
$630$	2.18770	0.0871599
$631$	−1.49618	−0.0595620	−0.0297810	−	0.999556i	$-0.509481\pi$
$631$	−1.49618	−0.0595620	−0.0297810	+	0.999556i	$0.509481\pi$
$632$	99.1369	3.94345
$633$	−7.05938	−0.280585
$634$	−73.0783	−2.90231
$635$	−7.45963	−0.296026
$636$	31.2372	1.23864
$637$	−16.1298	−0.639086
$638$	2.82085	0.111678
$639$	16.1411	0.638530
$640$	−59.3530	−2.34613
$641$	18.1503	0.716893	0.358447	−	0.933550i	$-0.383306\pi$
$641$	18.1503	0.716893	0.358447	+	0.933550i	$0.383306\pi$
$642$	16.8662	0.665655
$643$	49.5946	1.95582	0.977909	−	0.209030i	$-0.0670305\pi$
$643$	49.5946	1.95582	0.977909	+	0.209030i	$0.0670305\pi$
$644$	−6.06774	−0.239103
$645$	−5.02075	−0.197692
$646$	−128.370	−5.05064
$647$	34.1541	1.34274	0.671368	−	0.741124i	$-0.265707\pi$
$647$	34.1541	1.34274	0.671368	+	0.741124i	$0.265707\pi$
$648$	−14.6536	−0.575646
$649$	31.0449	1.21862
$650$	26.5356	1.04081
$651$	−3.50536	−0.137386
$652$	14.5784	0.570933
$653$	−35.1164	−1.37421	−0.687105	−	0.726558i	$-0.741119\pi$
$653$	−35.1164	−1.37421	−0.687105	+	0.726558i	$0.741119\pi$
$654$	−3.29749	−0.128942
$655$	4.31322	0.168532
$656$	207.569	8.10422
$657$	25.1173	0.979918
$658$	5.85732	0.228342
$659$	11.6728	0.454707	0.227354	−	0.973812i	$-0.426993\pi$
$659$	11.6728	0.454707	0.227354	+	0.973812i	$0.426993\pi$
$660$	23.5156	0.915342
$661$	−11.0462	−0.429645	−0.214823	−	0.976653i	$-0.568917\pi$
$661$	−11.0462	−0.429645	−0.214823	+	0.976653i	$0.568917\pi$
$662$	−90.7676	−3.52778
$663$	−15.7580	−0.611991
$664$	−143.624	−5.57371
$665$	2.56109	0.0993146
$666$	−35.6589	−1.38176
$667$	−0.630137	−0.0243990
$668$	−28.9505	−1.12013
$669$	10.0321	0.387863
$670$	6.69303	0.258574
$671$	−39.6849	−1.53202
$672$	10.4651	0.403698
$673$	45.7913	1.76512	0.882562	−	0.470196i	$-0.155817\pi$
$673$	45.7913	1.76512	0.882562	+	0.470196i	$0.155817\pi$
$674$	−7.97455	−0.307168
$675$	−19.8856	−0.765397
$676$	−42.6525	−1.64048
$677$	−26.8492	−1.03190	−0.515949	−	0.856619i	$-0.672561\pi$
$677$	−26.8492	−1.03190	−0.515949	+	0.856619i	$0.672561\pi$
$678$	−7.50992	−0.288417
$679$	6.07797	0.233251
$680$	−69.5284	−2.66629
$681$	22.9523	0.879534
$682$	111.200	4.25809
$683$	38.5149	1.47373	0.736867	−	0.676038i	$-0.236304\pi$
$683$	38.5149	1.47373	0.736867	+	0.676038i	$0.236304\pi$
$684$	−78.9772	−3.01977
$685$	−20.5958	−0.786926
$686$	15.1093	0.576875
$687$	−1.27556	−0.0486657
$688$	92.1387	3.51275
$689$	−13.2481	−0.504713
$690$	−7.08777	−0.269827
$691$	37.1327	1.41259	0.706297	−	0.707916i	$-0.250364\pi$
$691$	37.1327	1.41259	0.706297	+	0.707916i	$0.250364\pi$
$692$	−58.9711	−2.24175
$693$	3.51338	0.133462
$694$	5.73336	0.217636
$695$	10.4062	0.394730
$696$	2.34596	0.0889232
$697$	82.5342	3.12621
$698$	23.3695	0.884550
$699$	9.90765	0.374742
$700$	−9.10864	−0.344274
$701$	−1.35551	−0.0511969	−0.0255984	−	0.999672i	$-0.508149\pi$
$701$	−1.35551	−0.0511969	−0.0255984	+	0.999672i	$0.508149\pi$
$702$	−32.1424	−1.21314
$703$	−41.7451	−1.57445
$704$	−181.256	−6.83134
$705$	5.07087	0.190980
$706$	−12.4099	−0.467053
$707$	0.960733	0.0361321
$708$	39.6762	1.49112
$709$	−47.2669	−1.77515	−0.887573	−	0.460667i	$-0.847610\pi$
$709$	−47.2669	−1.77515	−0.887573	+	0.460667i	$0.847610\pi$
$710$	21.2211	0.796412
$711$	19.7055	0.739014
$712$	98.6672	3.69771
$713$	−24.8406	−0.930287
$714$	7.29836	0.273134
$715$	−9.97326	−0.372979
$716$	22.9996	0.859536
$717$	−27.4878	−1.02655
$718$	−1.25842	−0.0469638
$719$	17.9037	0.667695	0.333847	−	0.942627i	$-0.391653\pi$
$719$	17.9037	0.667695	0.333847	+	0.942627i	$0.391653\pi$
$720$	−34.7571	−1.29532
$721$	6.78882	0.252829
$722$	−71.9367	−2.67721
$723$	−13.1930	−0.490652
$724$	−48.7636	−1.81228
$725$	−0.945934	−0.0351311
$726$	21.2919	0.790217
$727$	−22.0310	−0.817085	−0.408542	−	0.912739i	$-0.633963\pi$
$727$	−22.0310	−0.817085	−0.408542	+	0.912739i	$0.633963\pi$
$728$	−9.58063	−0.355082
$729$	11.3718	0.421178
$730$	33.0223	1.22221
$731$	36.6364	1.35505
$732$	−50.7182	−1.87460
$733$	40.7096	1.50364	0.751821	−	0.659367i	$-0.229176\pi$
$733$	40.7096	1.50364	0.751821	+	0.659367i	$0.229176\pi$
$734$	−49.6658	−1.83320
$735$	6.46749	0.238557
$736$	74.1601	2.73358
$737$	10.7488	0.395938
$738$	68.5129	2.52199
$739$	−0.0849355	−0.00312440	−0.00156220	−	0.999999i	$-0.500497\pi$
$739$	−0.0849355	−0.00312440	−0.00156220	+	0.999999i	$0.500497\pi$
$740$	−34.7460	−1.27729
$741$	−15.3136	−0.562559
$742$	6.13588	0.225255
$743$	16.1883	0.593891	0.296946	−	0.954894i	$-0.404032\pi$
$743$	16.1883	0.593891	0.296946	+	0.954894i	$0.404032\pi$
$744$	92.4798	3.39048
$745$	12.0982	0.443245
$746$	24.8268	0.908975
$747$	−28.5483	−1.04453
$748$	−171.593	−6.27407
$749$	2.45540	0.0897185
$750$	−23.7697	−0.867948
$751$	7.48195	0.273020	0.136510	−	0.990639i	$-0.456411\pi$
$751$	7.48195	0.273020	0.136510	+	0.990639i	$0.456411\pi$
$752$	−93.0585	−3.39350
$753$	−2.81932	−0.102742
$754$	−1.52898	−0.0556820
$755$	−0.830081	−0.0302097
$756$	11.0332	0.401275
$757$	25.0984	0.912216	0.456108	−	0.889924i	$-0.349243\pi$
$757$	25.0984	0.912216	0.456108	+	0.889924i	$0.349243\pi$
$758$	37.8652	1.37533
$759$	−11.3828	−0.413168
$760$	−67.5675	−2.45093
$761$	12.8860	0.467117	0.233558	−	0.972343i	$-0.424963\pi$
$761$	12.8860	0.467117	0.233558	+	0.972343i	$0.424963\pi$
$762$	−20.6583	−0.748370
$763$	−0.480054	−0.0173791
$764$	144.868	5.24114
$765$	−13.8202	−0.499671
$766$	34.4278	1.24393
$767$	−16.8272	−0.607595
$768$	−83.4606	−3.01163
$769$	−7.68380	−0.277085	−0.138542	−	0.990357i	$-0.544242\pi$
$769$	−7.68380	−0.277085	−0.138542	+	0.990357i	$0.544242\pi$
$770$	4.61913	0.166462
$771$	−25.6196	−0.922667
$772$	1.04010	0.0374340
$773$	9.86788	0.354923	0.177461	−	0.984128i	$-0.443211\pi$
$773$	9.86788	0.354923	0.177461	+	0.984128i	$0.443211\pi$
$774$	30.4124	1.09315
$775$	−37.2896	−1.33948
$776$	−160.351	−5.75627
$777$	2.37339	0.0851447
$778$	10.0995	0.362085
$779$	80.2065	2.87370
$780$	−12.7461	−0.456383
$781$	34.0805	1.21949
$782$	51.7195	1.84948
$783$	1.14580	0.0409477
$784$	−118.689	−4.23888
$785$	−1.00585	−0.0359003
$786$	11.9448	0.426057
$787$	52.9736	1.88830	0.944152	−	0.329510i	$-0.106884\pi$
$787$	52.9736	1.88830	0.944152	+	0.329510i	$0.106884\pi$
$788$	75.6416	2.69462
$789$	−3.16584	−0.112707
$790$	25.9073	0.921741
$791$	−1.09331	−0.0388735
$792$	−92.6913	−3.29364
$793$	21.5103	0.763852
$794$	−38.7416	−1.37489
$795$	5.31203	0.188398
$796$	59.2588	2.10037
$797$	37.0332	1.31178	0.655891	−	0.754856i	$-0.272293\pi$
$797$	37.0332	1.31178	0.655891	+	0.754856i	$0.272293\pi$
$798$	7.09252	0.251073
$799$	−37.0022	−1.30904
$800$	111.326	3.93597
$801$	19.6121	0.692961
$802$	−11.3862	−0.402062
$803$	53.0330	1.87149
$804$	13.7373	0.484477
$805$	−1.03185	−0.0363678
$806$	−60.2737	−2.12305
$807$	−26.3952	−0.929156
$808$	−25.3464	−0.891684
$809$	2.80512	0.0986228	0.0493114	−	0.998783i	$-0.484297\pi$
$809$	2.80512	0.0986228	0.0493114	+	0.998783i	$0.484297\pi$
$810$	−3.82940	−0.134551
$811$	6.48967	0.227883	0.113942	−	0.993487i	$-0.463652\pi$
$811$	6.48967	0.227883	0.113942	+	0.993487i	$0.463652\pi$
$812$	0.524838	0.0184182
$813$	−31.4936	−1.10453
$814$	−75.2908	−2.63894
$815$	2.47912	0.0868397
$816$	−115.953	−4.05917
$817$	35.6031	1.24560
$818$	−110.213	−3.85350
$819$	−1.90435	−0.0665433
$820$	66.7588	2.33132
$821$	−6.85515	−0.239246	−0.119623	−	0.992819i	$-0.538169\pi$
$821$	−6.85515	−0.239246	−0.119623	+	0.992819i	$0.538169\pi$
$822$	−57.0369	−1.98939
$823$	−11.3055	−0.394084	−0.197042	−	0.980395i	$-0.563133\pi$
$823$	−11.3055	−0.394084	−0.197042	+	0.980395i	$0.563133\pi$
$824$	−179.105	−6.23942
$825$	−17.0873	−0.594904
$826$	7.79355	0.271172
$827$	30.4961	1.06045	0.530226	−	0.847856i	$-0.322107\pi$
$827$	30.4961	1.06045	0.530226	+	0.847856i	$0.322107\pi$
$828$	31.8195	1.10580
$829$	46.5293	1.61603	0.808015	−	0.589162i	$-0.200542\pi$
$829$	46.5293	1.61603	0.808015	+	0.589162i	$0.200542\pi$
$830$	−37.5332	−1.30280
$831$	29.2930	1.01616
$832$	98.2456	3.40605
$833$	−47.1933	−1.63515
$834$	28.8183	0.997897
$835$	−4.92316	−0.170373
$836$	−166.754	−5.76730
$837$	45.1687	1.56126
$838$	−75.5811	−2.61090
$839$	−33.6644	−1.16222	−0.581112	−	0.813824i	$-0.697382\pi$
$839$	−33.6644	−1.16222	−0.581112	+	0.813824i	$0.697382\pi$
$840$	3.84150	0.132544
$841$	−28.9455	−0.998121
$842$	−19.2808	−0.664460
$843$	−6.75763	−0.232745
$844$	41.6664	1.43422
$845$	−7.25326	−0.249520
$846$	−30.7161	−1.05604
$847$	3.09971	0.106507
$848$	−97.4841	−3.34762
$849$	−10.0537	−0.345043
$850$	77.6390	2.66300
$851$	16.8189	0.576544
$852$	43.5557	1.49219
$853$	−24.3110	−0.832393	−0.416197	−	0.909275i	$-0.636637\pi$
$853$	−24.3110	−0.832393	−0.416197	+	0.909275i	$0.636637\pi$
$854$	−9.96251	−0.340910
$855$	−13.4304	−0.459311
$856$	−64.7794	−2.21411
$857$	−6.58629	−0.224983	−0.112492	−	0.993653i	$-0.535883\pi$
$857$	−6.58629	−0.224983	−0.112492	+	0.993653i	$0.535883\pi$
$858$	−27.6194	−0.942910
$859$	−16.8816	−0.575994	−0.287997	−	0.957631i	$-0.592989\pi$
$859$	−16.8816	−0.575994	−0.287997	+	0.957631i	$0.592989\pi$
$860$	29.6338	1.01050
$861$	−4.56008	−0.155407
$862$	−40.3487	−1.37428
$863$	51.6720	1.75894	0.879468	−	0.475957i	$-0.157898\pi$
$863$	51.6720	1.75894	0.879468	+	0.475957i	$0.157898\pi$
$864$	−134.848	−4.58764
$865$	−10.0283	−0.340973
$866$	40.7987	1.38640
$867$	−29.6126	−1.00570
$868$	20.6896	0.702251
$869$	41.6065	1.41140
$870$	0.613066	0.0207849
$871$	−5.82616	−0.197412
$872$	12.6650	0.428890
$873$	−31.8731	−1.07874
$874$	50.2608	1.70010
$875$	−3.46043	−0.116984
$876$	67.7775	2.28999
$877$	−3.24977	−0.109737	−0.0548685	−	0.998494i	$-0.517474\pi$
$877$	−3.24977	−0.109737	−0.0548685	+	0.998494i	$0.517474\pi$
$878$	−83.8786	−2.83077
$879$	−15.3272	−0.516973
$880$	−73.3867	−2.47386
$881$	36.0616	1.21495	0.607473	−	0.794341i	$-0.292183\pi$
$881$	36.0616	1.21495	0.607473	+	0.794341i	$0.292183\pi$
$882$	−39.1759	−1.31912
$883$	−49.1387	−1.65365	−0.826825	−	0.562459i	$-0.809855\pi$
$883$	−49.1387	−1.65365	−0.826825	+	0.562459i	$0.809855\pi$
$884$	93.0082	3.12820
$885$	6.74712	0.226802
$886$	−74.3393	−2.49748
$887$	40.7917	1.36965	0.684825	−	0.728707i	$-0.259878\pi$
$887$	40.7917	1.36965	0.684825	+	0.728707i	$0.259878\pi$
$888$	−62.6156	−2.10124
$889$	−3.00746	−0.100867
$890$	25.7846	0.864301
$891$	−6.14991	−0.206030
$892$	−59.2120	−1.98257
$893$	−35.9586	−1.20331
$894$	33.5042	1.12055
$895$	3.91119	0.130737
$896$	−23.9290	−0.799413
$897$	6.16977	0.206003
$898$	48.0347	1.60294
$899$	2.14862	0.0716605
$900$	47.7661	1.59220
$901$	−38.7619	−1.29135
$902$	144.659	4.81662
$903$	−2.02419	−0.0673608
$904$	28.8440	0.959337
$905$	−8.29246	−0.275651
$906$	−2.29878	−0.0763718
$907$	−11.2754	−0.374393	−0.187196	−	0.982323i	$-0.559940\pi$
$907$	−11.2754	−0.374393	−0.187196	+	0.982323i	$0.559940\pi$
$908$	−135.471	−4.49575
$909$	−5.03813	−0.167104
$910$	−2.50369	−0.0829967
$911$	16.8216	0.557324	0.278662	−	0.960389i	$-0.410109\pi$
$911$	16.8216	0.557324	0.278662	+	0.960389i	$0.410109\pi$
$912$	−112.683	−3.73130
$913$	−60.2773	−1.99489
$914$	40.1853	1.32921
$915$	−8.62487	−0.285129
$916$	7.52870	0.248755
$917$	1.73894	0.0574248
$918$	−94.0437	−3.10390
$919$	10.9219	0.360281	0.180141	−	0.983641i	$-0.442345\pi$
$919$	10.9219	0.360281	0.180141	+	0.983641i	$0.442345\pi$
$920$	27.2226	0.897502
$921$	25.9706	0.855760
$922$	107.950	3.55514
$923$	−18.4725	−0.608031
$924$	9.48065	0.311890
$925$	25.2478	0.830142
$926$	−17.9649	−0.590362
$927$	−35.6008	−1.16929
$928$	−6.41458	−0.210569
$929$	2.42455	0.0795468	0.0397734	−	0.999209i	$-0.487336\pi$
$929$	2.42455	0.0795468	0.0397734	+	0.999209i	$0.487336\pi$
$930$	24.1676	0.792488
$931$	−45.8623	−1.50308
$932$	−58.4776	−1.91550
$933$	4.65711	0.152467
$934$	48.1996	1.57714
$935$	−29.1802	−0.954295
$936$	50.2412	1.64219
$937$	−20.3532	−0.664910	−0.332455	−	0.943119i	$-0.607877\pi$
$937$	−20.3532	−0.664910	−0.332455	+	0.943119i	$0.607877\pi$
$938$	2.69840	0.0881057
$939$	11.9356	0.389505
$940$	−29.9297	−0.976198
$941$	−43.4342	−1.41592	−0.707958	−	0.706255i	$-0.750383\pi$
$941$	−43.4342	−1.41592	−0.707958	+	0.706255i	$0.750383\pi$
$942$	−2.78554	−0.0907578
$943$	−32.3148	−1.05231
$944$	−123.820	−4.03001
$945$	1.87625	0.0610345
$946$	64.2132	2.08775
$947$	−44.1484	−1.43463	−0.717315	−	0.696749i	$-0.754629\pi$
$947$	−44.1484	−1.43463	−0.717315	+	0.696749i	$0.754629\pi$
$948$	53.1741	1.72701
$949$	−28.7453	−0.933112
$950$	75.4494	2.44790
$951$	−25.5067	−0.827112
$952$	−28.0314	−0.908504
$953$	21.3291	0.690917	0.345458	−	0.938434i	$-0.387723\pi$
$953$	21.3291	0.690917	0.345458	+	0.938434i	$0.387723\pi$
$954$	−32.1768	−1.04176
$955$	24.6355	0.797185
$956$	162.241	5.24724
$957$	0.984568	0.0318266
$958$	−5.13883	−0.166028
$959$	−8.30351	−0.268134
$960$	−39.3931	−1.27141
$961$	53.7007	1.73228
$962$	40.8097	1.31576
$963$	−12.8762	−0.414931
$964$	77.8685	2.50798
$965$	0.176874	0.00569376
$966$	−2.85754	−0.0919398
$967$	−38.9584	−1.25282	−0.626409	−	0.779495i	$-0.715476\pi$
$967$	−38.9584	−1.25282	−0.626409	+	0.779495i	$0.715476\pi$
$968$	−81.7777	−2.62843
$969$	−44.8052	−1.43935
$970$	−41.9044	−1.34547
$971$	−45.1226	−1.44805	−0.724027	−	0.689771i	$-0.757711\pi$
$971$	−45.1226	−1.44805	−0.724027	+	0.689771i	$0.757711\pi$
$972$	−92.1707	−2.95638
$973$	4.19541	0.134499
$974$	16.6795	0.534446
$975$	9.26179	0.296615
$976$	158.280	5.06642
$977$	−49.0844	−1.57035	−0.785174	−	0.619275i	$-0.787426\pi$
$977$	−49.0844	−1.57035	−0.785174	+	0.619275i	$0.787426\pi$
$978$	6.86552	0.219535
$979$	41.4094	1.32345
$980$	−38.1729	−1.21939
$981$	2.51742	0.0803751
$982$	85.3001	2.72204
$983$	11.7156	0.373669	0.186834	−	0.982391i	$-0.440177\pi$
$983$	11.7156	0.373669	0.186834	+	0.982391i	$0.440177\pi$
$984$	120.306	3.83520
$985$	12.8632	0.409855
$986$	−4.47354	−0.142467
$987$	2.04440	0.0650739
$988$	90.3850	2.87553
$989$	−14.3443	−0.456123
$990$	−24.2229	−0.769855
$991$	−13.7963	−0.438253	−0.219127	−	0.975696i	$-0.570321\pi$
$991$	−13.7963	−0.438253	−0.219127	+	0.975696i	$0.570321\pi$
$992$	−252.869	−8.02859
$993$	−31.6809	−1.00536
$994$	8.55558	0.271367
$995$	10.0772	0.319470
$996$	−77.0360	−2.44098
$997$	−14.6007	−0.462409	−0.231204	−	0.972905i	$-0.574267\pi$
$997$	−14.6007	−0.462409	−0.231204	+	0.972905i	$0.574267\pi$
$998$	0.810431	0.0256537
$999$	−30.5825	−0.967587

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.3	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.3	✓	184	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:	\( N \)	\(=\)	\( 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77961 q^{2} -0.970175 q^{3} +5.72623 q^{4} +0.973772 q^{5} +2.69671 q^{6} +0.392591 q^{7} -10.3575 q^{8} -2.05876 q^{9} +O(q^{10})\)	\(q-2.77961 q^{2} -0.970175 q^{3} +5.72623 q^{4} +0.973772 q^{5} +2.69671 q^{6} +0.392591 q^{7} -10.3575 q^{8} -2.05876 q^{9} -2.70671 q^{10} -4.34690 q^{11} -5.55544 q^{12} +2.35614 q^{13} -1.09125 q^{14} -0.944729 q^{15} +17.3373 q^{16} +6.89369 q^{17} +5.72255 q^{18} +6.69926 q^{19} +5.57604 q^{20} -0.380881 q^{21} +12.0827 q^{22} -2.69910 q^{23} +10.0486 q^{24} -4.05177 q^{25} -6.54914 q^{26} +4.90788 q^{27} +2.24806 q^{28} +0.233462 q^{29} +2.62598 q^{30} +9.20330 q^{31} -27.4759 q^{32} +4.21725 q^{33} -19.1618 q^{34} +0.382294 q^{35} -11.7889 q^{36} -6.23130 q^{37} -18.6213 q^{38} -2.28586 q^{39} -10.0858 q^{40} +11.9724 q^{41} +1.05870 q^{42} +5.31449 q^{43} -24.8913 q^{44} -2.00476 q^{45} +7.50244 q^{46} -5.36754 q^{47} -16.8202 q^{48} -6.84587 q^{49} +11.2623 q^{50} -6.68808 q^{51} +13.4918 q^{52} -5.62281 q^{53} -13.6420 q^{54} -4.23289 q^{55} -4.06624 q^{56} -6.49946 q^{57} -0.648933 q^{58} -7.14186 q^{59} -5.40974 q^{60} +9.12946 q^{61} -25.5816 q^{62} -0.808250 q^{63} +41.6977 q^{64} +2.29434 q^{65} -11.7223 q^{66} -2.47276 q^{67} +39.4749 q^{68} +2.61860 q^{69} -1.06263 q^{70} -7.84018 q^{71} +21.3236 q^{72} -12.2002 q^{73} +17.3206 q^{74} +3.93092 q^{75} +38.3615 q^{76} -1.70655 q^{77} +6.35381 q^{78} -9.57153 q^{79} +16.8825 q^{80} +1.41478 q^{81} -33.2787 q^{82} +13.8667 q^{83} -2.18101 q^{84} +6.71288 q^{85} -14.7722 q^{86} -0.226499 q^{87} +45.0229 q^{88} -9.52619 q^{89} +5.57246 q^{90} +0.924997 q^{91} -15.4557 q^{92} -8.92880 q^{93} +14.9197 q^{94} +6.52355 q^{95} +26.6564 q^{96} +15.4817 q^{97} +19.0289 q^{98} +8.94923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18} + 86 q^{19} + 26 q^{20} + 22 q^{21} + 54 q^{22} + 55 q^{23} + 72 q^{24} + 241 q^{25} + 32 q^{26} + 97 q^{27} + 75 q^{28} + 27 q^{29} - 10 q^{30} + 276 q^{31} + 20 q^{33} + 122 q^{34} + 30 q^{35} + 278 q^{36} + 42 q^{37} + 14 q^{38} + 113 q^{39} + 115 q^{40} + 39 q^{41} + 15 q^{42} + 65 q^{43} + 32 q^{44} + 54 q^{45} + 65 q^{46} + 82 q^{47} + 117 q^{48} + 297 q^{49} + 4 q^{50} + 45 q^{51} + 136 q^{52} + 21 q^{53} + 93 q^{54} + 252 q^{55} + 74 q^{56} + 14 q^{57} + 54 q^{58} + 95 q^{59} + 58 q^{60} + 131 q^{61} + 14 q^{62} + 88 q^{63} + 368 q^{64} - 9 q^{65} + 52 q^{66} + 90 q^{67} + 27 q^{68} + 101 q^{69} + 18 q^{70} + 117 q^{71} - 15 q^{72} + 72 q^{73} + 7 q^{74} + 150 q^{75} + 148 q^{76} + 7 q^{77} + 22 q^{78} + 287 q^{79} + 43 q^{80} + 244 q^{81} + 86 q^{82} + 25 q^{83} + 14 q^{84} + 41 q^{85} + 25 q^{86} + 82 q^{87} + 115 q^{88} + 48 q^{89} + 78 q^{90} + 272 q^{91} + 69 q^{92} + 44 q^{93} + 161 q^{94} + 37 q^{95} + 129 q^{96} + 106 q^{97} - 46 q^{98} + 53 q^{99}+O(q^{100}) \) 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9 + 46 * q^10 + 25 * q^11 + 61 * q^12 + 52 * q^13 + 28 * q^14 + 59 * q^15 + 279 * q^16 + 16 * q^17 - 2 * q^18 + 86 * q^19 + 26 * q^20 + 22 * q^21 + 54 * q^22 + 55 * q^23 + 72 * q^24 + 241 * q^25 + 32 * q^26 + 97 * q^27 + 75 * q^28 + 27 * q^29 - 10 * q^30 + 276 * q^31 + 20 * q^33 + 122 * q^34 + 30 * q^35 + 278 * q^36 + 42 * q^37 + 14 * q^38 + 113 * q^39 + 115 * q^40 + 39 * q^41 + 15 * q^42 + 65 * q^43 + 32 * q^44 + 54 * q^45 + 65 * q^46 + 82 * q^47 + 117 * q^48 + 297 * q^49 + 4 * q^50 + 45 * q^51 + 136 * q^52 + 21 * q^53 + 93 * q^54 + 252 * q^55 + 74 * q^56 + 14 * q^57 + 54 * q^58 + 95 * q^59 + 58 * q^60 + 131 * q^61 + 14 * q^62 + 88 * q^63 + 368 * q^64 - 9 * q^65 + 52 * q^66 + 90 * q^67 + 27 * q^68 + 101 * q^69 + 18 * q^70 + 117 * q^71 - 15 * q^72 + 72 * q^73 + 7 * q^74 + 150 * q^75 + 148 * q^76 + 7 * q^77 + 22 * q^78 + 287 * q^79 + 43 * q^80 + 244 * q^81 + 86 * q^82 + 25 * q^83 + 14 * q^84 + 41 * q^85 + 25 * q^86 + 82 * q^87 + 115 * q^88 + 48 * q^89 + 78 * q^90 + 272 * q^91 + 69 * q^92 + 44 * q^93 + 161 * q^94 + 37 * q^95 + 129 * q^96 + 106 * q^97 - 46 * q^98 + 53 * q^99

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